File is Postscript, 3868994 bytes long (194972 lines, 543325 words). Produces 273 pages of text, including 14 figures. Good luck! BODY %! PS-Adobe-2.0 %%Creator: dvips 5.47 Copyright 1986-91 Radical Eye Software %%Title: renorm_v12.dvi %%Pages: 273 1 %%BoundingBox: 0 0 612 792 %%EndComments %%BeginProcSet: tex.pro /TeXDict 200 dict def TeXDict begin /N /def load def /B{bind def}N /S /exch load def /X{S N}B /TR /translate load N /isls false N /vsize 10 N /@rigin{ isls{[0 1 -1 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale Resolution VResolution vsize neg mul TR matrix currentmatrix dup dup 4 get round 4 exch put dup dup 5 get round 5 exch put setmatrix}N /@letter{/vsize 10 N}B /@landscape{/isls true N /vsize -1 N}B /@a4{/vsize 10.6929133858 N}B /@a3{ /vsize 15.5531 N}B /@ledger{/vsize 16 N}B /@legal{/vsize 13 N}B /@manualfeed{ statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{/nn 8 dict N nn begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N string /base X array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{/sf 1 N /fntrx FMat N df-tail} B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0]N df-tail}B /E{pop nn dup definefont setfont}B /ch-width{ch-data dup length 5 sub get}B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{128 ch-data dup length 3 sub get sub}B /ch-yoff{ ch-data dup length 2 sub get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup type /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N /rc 0 N /gp 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 add]{ch-image} imagemask restore}B /D{/cc X dup type /stringtype ne{]}if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1 sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{cc 1 add D}B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin 0 0 moveto}N /eop{clear SI restore showpage userdict /eop-hook known{eop-hook}if}N /@start{userdict /start-hook known{start-hook}if /VResolution X /Resolution X 1000 div /DVImag X /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for}N /p /show load N /RMat[1 0 0 -1 0 0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V statusdict begin /product where{pop product dup length 7 ge{0 7 getinterval(Display)eq}{pop false}ifelse}{false}ifelse end{{gsave TR -.1 -.1 TR 1 1 scale rulex ruley false RMat{BDot}imagemask grestore}}{{gsave TR -.1 -.1 TR rulex ruley scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /a{ moveto}B /delta 0 N /tail{dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{ S p tail}B /c{-4 M}B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{3 M}B /k{4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p -1 w }B /q{p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{3 2 roll p a}B /bos{/SS save N}B /eos{clear SS restore}B end %%EndProcSet %%BeginProcSet: special.pro TeXDict begin /SDict 200 dict N SDict begin /@SpecialDefaults{/hs 612 N /vs 792 N /ho 0 N /vo 0 N /hsc 1 N /vsc 1 N /ang 0 N /CLIP false N /BBcalc false N /p 3 def}B /@scaleunit 100 N /@hscale{@scaleunit div /hsc X}B /@vscale{ @scaleunit div /vsc X}B /@hsize{/hs X /CLIP true N}B /@vsize{/vs X /CLIP true N}B /@hoffset{/ho X}B /@voffset{/vo X}B /@angle{/ang X}B /@rwi{10 div /rwi X} B /@llx{/llx X}B /@lly{/lly X}B /@urx{/urx X}B /@ury{/ury X /BBcalc true N}B /magscale true def end /@MacSetUp{userdict /md known{userdict /md get type /dicttype eq{md begin /letter{}N /note{}N /legal{}N /od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{ itransform moveto}}{transform{itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{closepath}}pathforall newpath counttomark array astore /gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{ PaintBlack}if}N /txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if} ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N /cp{pop pop showpage pm restore}N end}if} if}N /normalscale{Resolution 72 div VResolution 72 div neg scale magscale{ DVImag dup scale}if}N /psfts{S 65536 div N}N /startTexFig{/psf$SavedState save N userdict maxlength dict begin /magscale false def normalscale currentpoint TR /psf$ury psfts /psf$urx psfts /psf$lly psfts /psf$llx psfts /psf$y psfts /psf$x psfts currentpoint /psf$cy X /psf$cx X /psf$sx psf$x psf$urx psf$llx sub div N /psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR /showpage{}N /erasepage{}N /copypage{}N /p 3 def @MacSetUp}N /doclip{psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N /endTexFig{end psf$SavedState restore}N /@beginspecial{SDict begin /SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults}N /@setspecial{CLIP{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate BBcalc{rwi urx llx sub div dup scale llx neg lly neg TR}if /showpage{}N /erasepage{}N /copypage{}N newpath}N /@endspecial{grestore clear SpecialSave restore end}N /@defspecial{SDict begin}N /@fedspecial{end}B /li{lineto}B /rl{rlineto}B /rc{rcurveto}B /np{/SaveX currentpoint /SaveY X N 1 setlinecap newpath}N /st{stroke SaveX SaveY moveto}N /fil{fill SaveX SaveY moveto}N /ellipse{/endangle X /startangle X /yrad X /xrad X /savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet TeXDict begin 1000 300 300 @start /Fa 1 25 df<0000000000700000000007F000000000 7F800000000FF800000000FF800000000FF000000000FF000000000FF000000001FF000000001F F000000000FE0000000000E000000000002C0C818A00>24 D E /Fb 1 22 df21 D E /Fc 1 101 df<000000F000001FF000001FF0000001 F0000001E0000001E0000001E0000001E0000003C0000003C0000003C0000003C0000007800000 07800000078000000780001F0F000070CF0001C02F0003802F0007801E000F001E001E001E001E 001E003E003C003C003C007C003C007C003C00F8007800F8007800F8007800F8007800F000F000 F000F040F000F040F000F040F001E0807003E0807804E0803808E1001C30710007C01E001C2A7E A91F>100 D E /Fd 37 122 df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e 1 49 df<181818303030606060C0C0050B7E8B09>48 D E /Ff 1 66 df<01C00003E00003E0000360000360000770000770000770000770000630000E38000E38 000E38000E38000E38001FFC001FFC001C1C001C1C003C1E00380E00FE3F80FE3F8011177F9614 >65 D E /Fg 1 103 df<007F0001E38003C7C00787C00F87C00F83800F80000F80000F80000F 80000F8000FFF800FFF8000F80000F80000F80000F80000F80000F80000F80000F80000F80000F 80000F80000F80000F80000F80007FF8007FF800121D809C0F>102 D E /Fh 3 71 df<001C0000003E0000003E0000002E0000006700000067000000E7800000C7800000 C3800001C3C0000183C0000181C0000381E0000381E0000700F0000700F0000600F0000E007800 0FFFF8000FFFF8001C003C001C003C0018003C0038001E0038001E0070001F0070000F0070000F 00E0000780191D7F9C1C>65 DI70 D E /Fi 2 71 df<001F0000001F0000003F8000003F8000003B8000007BC00000 73C0000071C00000F1E00000F1E00000E0E00001E0F00001E0F00001C0F00003C0780003C07800 0380780007803C0007803C0007003C000F001E000F001E000FFFFE001FFFFF001FFFFF001C000F 003C0007803C00078038000780780003C0780003C0700003C0F00001E0F00001E0E00001E01C23 7EA220>65 D 70 D E /Fj 4 111 df<00030000000780000007800000078000000FC000000FC000001BE00000 1BE000001BE0000031F0000031F0000060F8000060F80000E0FC0000C07C0000C07C0001803E00 01FFFE0003FFFF0003001F0003001F0006000F8006000F800E000FC0FFC07FFCFFC07FFC1E1A7F 9921>65 D89 D<00FE0003C700078F800F0F800F0F800F07000F00000F00000F0000FFF000FFF0000F00000F00 000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00007FE0007FE0 00111A80990E>102 D110 D E /Fk 8 117 df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l 3 91 df<01FE0007FF801F03C03E00E036006076 0000660000E60000C60000C60000C60000C60000E600006600007600003600603E00E01F03C007 FF8001FE0013147E9319>67 D82 D90 D E /Fm 1 23 df22 D E /Fn 4 111 df<0F8030C060804000C000C000C04061803E000A097E880D>99 D<0808000000007098B0303060646870070F7D8E0B>105 D<7800180018001800300030C03360 344078007E0063006320C340C1800B0E7E8D10>107 D<73809C40986030C030C030C031886190 60E00E097D8812>110 D E /Fo 13 111 df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p 29 122 df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q 5 91 df<0007F800C0003FFF01C000FC0FC38001E001E7000780007E000F00003C000C 00003C001C00007E00380000E700300001C3007000038380600007018060000E0180E0001C01C0 C0003800C0C0007000C0C000E000C0C001C000C0C0038000C0C0070000C0E00E0001C0601C0001 806038000180707000038030E000030039C00007001F80000E000F00000C000F00003C001F8000 780039E001E00070FC0FC000E03FFF0000C007F8000022227DA129>63 D<001FF000007FFF0001 F01FC003C001E0070000700E0000381E0000183E00000036000000760000006600000066000000 E6000000C6000000C6000000C6000000C6000000C6000000C6000000C6000000C6000000E60000 00660000006600000076000000360000003E0000001E0000180E0000380700007003C001E001F0 1FC0007FFF00001FF0001D227DA124>67 D78 D82 D90 D E /Fr 29 121 df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s 26 121 df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t 6 104 df0 D<0C000C008C40EDC07F800C007F80EDC08C 400C000C000A0B7D8B10>3 D<081C1C3838383070706060C0C0060D7E8D09>48 D<1F00F833818440C202806401803801801801801C018026014043022181CC1F00F8180B7D8A1E >I<01C006000C000C000C000C000C000C000C000C000C001800E00018000C000C000C000C000C 000C000C000C000C00060001C00A197D9210>102 D I E /Fu 28 111 df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v 57 123 df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w 31 123 df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x 52 114 df12 DI<0006000C001800300070006000 C001C0018003800300070006000E000C001C001C00180038003800380030007000700070007000 70007000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E0 00700070007000700070007000300038003800380018001C001C000C000E000600070003000380 018001C000C00060007000300018000C00060F4A788119>16 DI<0000300000600000C00001800003 00000700000E00000C0000180000380000300000700000E00000C00001C0000180000380000380 000300000700000600000E00000E00000C00001C00001C00001C00001800003800003800003800 00380000700000700000700000700000700000700000700000E00000E00000E00000E00000E000 00E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E000 00E00000E00000E000007000007000007000007000007000007000007000003800003800003800 003800001800001C00001C00001C00000C00000E00000E00000600000700000300000380000380 0001800001C00000C00000E000007000003000003800001800000C00000E000007000003000001 800000C0000060000030146377811F>IIII<0000700001F00003C000 0780000E00001C0000380000700000700000F00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00001C00001C00001 C0000380000700000600000E0000380000700000C000007000003800000E000006000007000003 800001C00001C00001C00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000F000007000007000003800001C0000 0E000007800003C00001F000007014637B811F>26 DI<0000180000300000600000E00000C000018000038000070000 0600000E00000C00001C0000380000380000700000700000E00000E00001E00001C00001C00003 80000380000380000780000700000700000F00000E00000E00001E00001E00001E00001C00001C 00003C00003C00003C00003C000038000078000078000078000078000078000078000078000078 0000700000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F0 0000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F0 0000F000007000007800007800007800007800007800007800007800007800003800003C00003C 00003C00003C00001C00001C00001E00001E00001E00000E00000E00000F000007000007000007 800003800003800003800001C00001C00001E00000E00000E00000700000700000380000380000 1C00000C00000E000006000007000003800001800000C00000E0000060000030000018157C7681 21>32 DIIII<000E000E000E000E000E000E000E000E000E000E000E 000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00 0E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E 000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00 0E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E 000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00 0E000E000E000E000E000E000E000E000E000E000E000E000EFFFEFFFEFFFE0F7C80811B>I<00 001C00003C0000F80001E00003C0000780000F00000E00001E00003C00003C00003C0000780000 780000780000780000780000780000780000780000780000780000780000780000780000780000 780000780000780000780000780000780000780000780000780000780000780000780000780000 780000780000780000780000780000780000780000780000780000780000780000F00000F00000 F00001E00001E00003C0000380000700000E00001C0000780000E00000E000007800001C00000E 000007000003800003C00001E00001E00000F00000F00000F00000780000780000780000780000 780000780000780000780000780000780000780000780000780000780000780000780000780000 780000780000780000780000780000780000780000780000780000780000780000780000780000 7800007800007800007800007800007800007800007800003C00003C00003C00001E00000E0000 0F000007800003C00001E00000F800003C00001C167C7B8121>40 DI<00000C0000180000380000300000600000E00000C000 01C0000380000380000700000700000E00000E00001C00001C0000380000380000780000700000 F00000F00000E00001E00001E00003C00003C00003C00003C0000780000780000780000F80000F 00000F00000F00001F00001F00001E00001E00001E00003E00003E00003E00003E00003C00003C 00003C00007C00007C00007C00007C00007C00007C00007C00007C0000780000780000F80000F8 0000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F8 0000F80000F80000164B748024>48 DIIII<001C001C001C001C001C001C001C001C001C001C001C001C001C001C 001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C 001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001CFFFCFF FCFFFC0E4A80811C>III<00 18007800F001E003C007800F001F001E003E003C007C007C007800F800F800F800F800F800F800 F800F800F800F800F800F800F800F800F800F800F800F800F800F800F800F800F8000D25707E25 >I58 D<007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C00 7C007C007C007C007C007C007C007C00F800F800F800F001F001E003E003C0078007000E001C00 3800F000C000F00038001C000E000700078003C003E001E001F000F000F800F800F8007C007C00 7C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C 007C007C0E4D798025>60 D62 D64 D<00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C0000 7C00007C00007C00007C00007C0000780000780000F80000F80000F80000F80000F80000F80000 F80000F80000F00000F00000F00001F00001F00001F00001F00001E00001E00001E00003E00003 E00003C00003C00003C00007C0000780000780000780000F00000F00000F00000F00001E00001E 00001C00003C00003C0000380000780000700000700000E00000E00001C00001C0000380000380 000700000700000E00000C00001C0000180000300000700000600000C00000164B7F8224>III80 DI<0000F80001 8400030600060E000604000E00000E00000E00000C00001C00001C00001C00001C00001C00001C 00001C00001C00001C000038000038000038000038000038000038000038000038000038000038 0000700000700000700000700000700000700000700000700000700000600000E00000E00000E0 0040C000E0C000C180004300003E0000172E7E7F14>II<001FE000007FF80001FFFE0007E01F800F8007C01E0001E01C0000E03800007038000070 7000003870000038E000001CE000001CE000001CE000001CE000001CE000001CE000001CE00000 1CE000001CE000001CE000001CE000001CE000001CE000001CE000001CE000001CE000001CE000 001CE000001CE000001CE000001CE000001CE000001CE000001CE000001CE000001CE000001CE0 00001CE000001CE000001CE000001C1E2A7E7F23>I88 DI<000000038000000006600000000C700000000CF00000000CF0000000 1C6000000018000000003800000000380000000038000000007000000000700000000070000000 007000000000F000000000E000000000E000000000E000000001E000000001E000000001C00000 0001C000000003C000000003C000000003C000000003C000000007800000000780000000078000 000007800000000F800000000F800000000F000000000F000000001F000000001F000000001F00 0000001F000000001E000000003E000000003E000000003E000000003E000000003C000000007C 000000007C000000007C000000007C000000007800000000F800000000F800000000F800000000 F800000000F000000001F000000001F000000001F000000001F000000001E000000001E0000000 03E000000003E000000003C000000003C000000003C000000003C0000000078000000007800000 0007800000000780000000070000000007000000000F000000000F000000000E000000000E0000 00000E000000001E000000001C000000001C000000001C00000000180000000038000000003800 0000003000000000700000006060000000F060000000F0C0000000E18000000063000000001E00 000000245C7E7F17>II<0000FF8000000007FFF00000001FFFFC0000007F007F000000 F8000F800003E00003E00007C00001F0000700000070000E00000038001E0000003C001C000000 1C00380000000E00380000000E00700000000700700000000700700000000700E00000000380E0 0000000380E00000000380E00000000380E00000000380E00000000380E00000000380E0000000 0380E00000000380E00000000380E00000000380E00000000380E00000000380E00000000380E0 0000000380E00000000380E00000000380E00000000380E00000000380E00000000380E0000000 0380E00000000380E00000000380E00000000380E00000000380E00000000380E00000000380E0 0000000380E00000000380E00000000380E00000000380E00000000380E00000000380E0000000 0380E00000000380E00000000380E00000000380E00000000380E00000000380E00000000380E0 0000000380E00000000380293A7E7F2E>I<00300000FC0001CE000703801C00E0300030C0000C 1607809E17>98 D<07C0041FE018307830601FE0800F801605809D17>101 D<007F8000008003FFF80007001E007F003C0070000FFFE000800000FF00002905809E2A>I104 DI<0000E00003E0000F80001E00003C0000700000700000E00000E00000E00000E0 0000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E0 0000E00000E00000E00000E00000E00000E00001C00001C0000380000700000E00003C0000F000 00F000003C00000E000007000003800001C00001C00000E00000E00000E00000E00000E00000E0 0000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E0 0000E00000E00000E00000E000007000007000003C00001E00000F800003E00000E0134A7C811C >110 DI<00 000000060000000006000000000E000000000C000000000C000000001C00000000180000000018 00000000380000000030000000003000000000700000000060000000006000000000E000000000 C000000000C000000001C000000001800000000180000000038000000003000000000300000000 0700000000060000000006000000000E000000000C000000000C000000001C0000000018000000 00180000000038000000003000000000300000000070000000006000000000600008000060001C 0000E0003C0000C0007C0000C000DC0001C0008E000180000E000180000E000380000700030000 070003000007000700000380060000038006000003800E000003800C000001C00C000001C01C00 0001C018000000E018000000E038000000E030000000E030000000707000000070600000007060 00000038E000000038C000000038C00000001DC00000001D800000001D800000001F800000000F 000000000F000000000F00000000060000000006000000274B7C812A>113 D E /Fy 38 111 df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z 90 128 df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df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df<0001FF0000001FFFC000007F80F00000FE00F80003FC01FC0003F803FC00 07F003FC0007F003FC0007F003FC0007F001F80007F000F00007F000000007F000000007F00000 0007F0000000FFFFFFFC00FFFFFFFC00FFFFFFFC0007F001FC0007F001FC0007F001FC0007F001 FC0007F001FC0007F001FC0007F001FC0007F001FC0007F001FC0007F001FC0007F001FC0007F0 01FC0007F001FC0007F001FC0007F001FC0007F001FC0007F001FC0007F001FC0007F001FC0007 F001FC0007F001FC007FFF1FFFC07FFF1FFFC07FFF1FFFC0222A7FA926>12 D<0001FF803FE000001FFFE3FFF800007F80FFF01E0000FE007FC01F0003FC01FF803F8003F801 FF007F8007F001FE007F8007F001FE007F8007F001FE007F8007F001FE003F0007F000FE001E00 07F000FE00000007F000FE00000007F000FE00000007F000FE000000FFFFFFFFFFFF80FFFFFFFF FFFF80FFFFFFFFFFFF8007F000FE003F8007F000FE003F8007F000FE003F8007F000FE003F8007 F000FE003F8007F000FE003F8007F000FE003F8007F000FE003F8007F000FE003F8007F000FE00 3F8007F000FE003F8007F000FE003F8007F000FE003F8007F000FE003F8007F000FE003F8007F0 00FE003F8007F000FE003F8007F000FE003F8007F000FE003F8007F000FE003F8007F000FE003F 807FFF0FFFE3FFF87FFF0FFFE3FFF87FFF0FFFE3FFF8352A7FA939>14 D<1C007F00FF80FF80FF C0FFC0FFC07FC01CC000C000C001C0018001800380070006000E001C00380030000A157BA913> 39 D<00030007001E003C007800F800F001E003E007C007C00F800F801F801F003F003F003E00 3E007E007E007E007C00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC007C 007E007E007E003E003E003F003F001F001F800F800F8007C007C003E001E000F000F80078003C 001E00070003103C7AAC1B>II<1C007F00FF80FF80FFC0FFC0FFC07FC0 1CC000C000C001C0018001800380070006000E001C00380030000A157B8813>44 DI<1C007F00FF80FF80FF80FF80FF 807F001C0009097B8813>I<000E00001E00007E0007FE00FFFE00FFFE00F8FE0000FE0000FE00 00FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE00 00FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE00 00FE007FFFFE7FFFFE7FFFFE17277BA622>49 D<00FF800003FFF0000FFFFC003F03FF007C00FF 807C007FC0FE007FC0FF003FE0FF003FE0FF003FE0FF001FE07E001FE03C003FE000003FE00000 3FC000003FC000007F8000007F800000FF000001FE000001FC000003F0000007E000000FC00000 1F0000003E0000007C00E0007800E000F000E001E001C0038001C0070001C00FFFFFC01FFFFFC0 3FFFFFC07FFFFFC0FFFFFF80FFFFFF80FFFFFF801B277DA622>I<007F800003FFF00007FFFC00 1F81FE001F00FF003F80FF003F807F803FC07F803F807F803F807F801F007F800000FF800000FF 000000FF000001FE000003F8000007F00000FFC00000FFF0000001FC000000FF0000007F800000 7FC000003FC000003FE000003FE000003FE03C003FE07E003FE0FF003FE0FF003FE0FF003FC0FF 007FC0FE007F807C00FF803F01FF001FFFFC0007FFF00000FF80001B277DA622>I<00000E0000 001E0000003E0000007E000000FE000000FE000001FE000003FE0000077E00000E7E00000E7E00 001C7E0000387E0000707E0000E07E0000E07E0001C07E0003807E0007007E000E007E000E007E 001C007E0038007E0070007E00E0007E00FFFFFFF8FFFFFFF8FFFFFFF80000FE000000FE000000 FE000000FE000000FE000000FE000000FE000000FE00007FFFF8007FFFF8007FFFF81D277EA622 >I<0C0003000F803F000FFFFE000FFFFE000FFFFC000FFFF8000FFFE0000FFFC0000FFE00000E 0000000E0000000E0000000E0000000E0000000E0000000E7FC0000FFFF8000F80FE000E007F00 0C003F8000003F8000001FC000001FC000001FE000001FE018001FE07E001FE0FE001FE0FE001F E0FE001FE0FE001FE0FE001FC078003FC078003F803C007F001F01FE000FFFFC0003FFF00000FF 80001B277DA622>I<0007F000003FFC0000FFFF0001FC0F0007F01F800FE03F800FC03F801FC0 3F803F803F803F801F007F8000007F0000007F0000007F000000FF000000FF0FC000FF3FF800FF 70FE00FFE03F00FFC03F80FF801FC0FF801FC0FF801FC0FF001FE0FF001FE0FF001FE0FF001FE0 7F001FE07F001FE07F001FE07F001FE03F801FC03F801FC01F803F800FC03F8007E0FF0003FFFC 0000FFF000003FC0001B277DA622>I<1C007F00FF80FF80FF80FF80FF807F001C000000000000 000000000000000000000000001C007F00FF80FF80FF80FF80FF807F001C00091B7B9A13>58 D<000003800000000007C00000000007C0000000000FE0000000000FE0000000000FE000000000 1FF0000000001FF0000000003FF8000000003FF8000000003FF80000000073FC0000000073FC00 000000F3FE00000000E1FE00000000E1FE00000001C0FF00000001C0FF00000003C0FF80000003 807F80000007807FC0000007003FC0000007003FC000000E003FE000000E001FE000001E001FF0 00001C000FF000001FFFFFF000003FFFFFF800003FFFFFF80000780007FC0000700003FC000070 0003FC0000E00001FE0000E00001FE0001E00001FF0001C00000FF0001C00000FF00FFFE001FFF FEFFFE001FFFFEFFFE001FFFFE2F297EA834>65 D I<00003FF001800003FFFE0780000FFFFF8F80003FF007FF8000FF8001FF8001FE00007F8007FC 00003F8007F800001F800FF000000F801FE000000F803FE0000007803FC0000007807FC0000003 807FC0000003807FC000000380FF8000000000FF8000000000FF8000000000FF8000000000FF80 00000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF80000000 007FC0000000007FC0000003807FC0000003803FC0000003803FE0000003801FE0000007800FF0 0000070007F800000F0007FC00001E0001FE00003C0000FF8000F800003FF007F000000FFFFFC0 000003FFFF000000003FF8000029297CA832>II< FFFFFFFFE0FFFFFFFFE0FFFFFFFFE003FC001FE003FC0007F003FC0001F003FC0001F003FC0000 F003FC00007003FC00007003FC00007003FC01C07803FC01C03803FC01C03803FC01C03803FC03 C00003FC03C00003FC0FC00003FFFFC00003FFFFC00003FFFFC00003FC0FC00003FC03C00003FC 03C00003FC01C00E03FC01C00E03FC01C00E03FC01C01C03FC00001C03FC00001C03FC00001C03 FC00003C03FC00003803FC00007803FC0000F803FC0001F803FC0003F803FC001FF8FFFFFFFFF0 FFFFFFFFF0FFFFFFFFF027297DA82D>II<00007FE003 000003FFFC0F00001FFFFF1F00007FF00FFF0000FF8001FF0003FE0000FF0007FC00007F000FF8 00003F000FF000001F001FE000001F003FE000000F003FC000000F007FC0000007007FC0000007 007FC000000700FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF80 00000000FF8000000000FF8000000000FF8000000000FF8001FFFFF8FF8001FFFFF87FC001FFFF F87FC00000FF007FC00000FF003FC00000FF003FE00000FF001FE00000FF000FF00000FF000FF8 0000FF0007FC0000FF0003FE0001FF0000FF8001FF00007FF007FF00001FFFFFBF000003FFFE0F 0000007FF003002D297CA836>III76 DII<0000FFE000000007FFFC00 00003FC07F8000007F001FC00001FC0007F00003F80003F80007F00001FC000FF00001FE001FE0 0000FF001FE00000FF003FC000007F803FC000007F807FC000007FC07F8000003FC07F8000003F C07F8000003FC0FF8000003FE0FF8000003FE0FF8000003FE0FF8000003FE0FF8000003FE0FF80 00003FE0FF8000003FE0FF8000003FE0FF8000003FE0FF8000003FE07F8000003FC07FC000007F C07FC000007FC03FC000007F803FC000007F801FE00000FF001FE00000FF000FF00001FE0007F0 0001FC0003F80003F80001FC0007F00000FF001FE000003FC07F8000000FFFFE00000000FFE000 002B297CA834>II<0000FFE000000007FFFC0000003F C07F8000007F001FC00001FC0007F00003F80003F80007F00001FC000FF00001FE001FE00000FF 001FE00000FF003FC000007F803FC000007F807FC000007FC07FC000007FC07F8000003FC07F80 00003FC0FF8000003FE0FF8000003FE0FF8000003FE0FF8000003FE0FF8000003FE0FF8000003F E0FF8000003FE0FF8000003FE0FF8000003FE0FF8000003FE07F8000003FC07F8000003FC07FC0 00007FC03FC000007F803FC000007F801FE00000FF001FE01F00FF000FF07FC1FE0007F0E0E1FC 0003F8C073F80001FCC077F00000FFC03FE000003FE07F8000000FFFFE00000000FFFE00600000 001F00600000001F00E00000001FC1E00000000FFFE00000000FFFE00000000FFFC00000000FFF C000000007FFC000000007FF8000000003FF0000000001FE000000000078002B357CA834>II<007F806003FFF0E00FFFFFE01F807FE03F001FE07E 0007E07E0003E07C0003E0FC0001E0FC0001E0FC0000E0FE0000E0FE0000E0FF000000FFC00000 7FFE00007FFFE0003FFFFC003FFFFF001FFFFF8007FFFFC003FFFFE000FFFFF00007FFF000007F F000000FF8000007F8000003F8E00003F8E00001F8E00001F8E00001F8F00001F8F00001F0F800 03F0FC0003E0FF0007E0FFE01FC0FFFFFF00E0FFFE00C01FF0001D297CA826>I<7FFFFFFFFFC0 7FFFFFFFFFC07FFFFFFFFFC07F803FC03FC07E003FC007C078003FC003C078003FC003C070003F C001C0F0003FC001E0F0003FC001E0E0003FC000E0E0003FC000E0E0003FC000E0E0003FC000E0 E0003FC000E000003FC0000000003FC0000000003FC0000000003FC0000000003FC0000000003F C0000000003FC0000000003FC0000000003FC0000000003FC0000000003FC0000000003FC00000 00003FC0000000003FC0000000003FC0000000003FC0000000003FC0000000003FC0000000003F C0000000003FC0000000003FC0000000003FC00000007FFFFFE000007FFFFFE000007FFFFFE000 2B287EA730>IIII<3FFFFFFF803F FFFFFF803FFFFFFF803FF001FF003F8001FF003F0003FE003E0007FC003C0007FC007C000FF800 78001FF00078001FF00070003FE00070007FC00070007FC0007000FF80000001FF00000001FF00 000003FE00000007FC00000007FC0000000FF80000001FF00000001FF00000003FE00000007FC0 01C0007FC001C000FF8001C001FF0001C001FF0001C003FE0003C007FC0003C007FC0003C00FF8 0007801FF00007801FF0000F803FE0001F807FC0007F807FC001FF80FFFFFFFF80FFFFFFFF80FF FFFFFF8022297CA82A>90 D<01FF800007FFF0000F81FC001FC0FE001FC07F001FC07F001FC03F 800F803F8000003F8000003F8000003F80000FFF8000FFFF8007FC3F801FE03F803F803F807F80 3F807F003F80FE003F80FE003F80FE003F80FE007F80FF007F807F00FFC03F83DFFC0FFF0FFC01 FC03FC1E1B7E9A21>97 DI<001FF80000FF FE0003F01F000FE03F801FC03F803F803F803F803F807F801F007F000000FF000000FF000000FF 000000FF000000FF000000FF000000FF000000FF000000FF0000007F0000007F8000003F8001C0 3FC001C01FC003C00FE0078003F01F0000FFFC00001FE0001A1B7E9A1F>I<00003FF80000003F F80000003FF800000003F800000003F800000003F800000003F800000003F800000003F8000000 03F800000003F800000003F800000003F800000003F800000003F800001FE3F80000FFFBF80003 F03FF8000FE00FF8001FC007F8003F8003F8003F8003F8007F8003F8007F0003F800FF0003F800 FF0003F800FF0003F800FF0003F800FF0003F800FF0003F800FF0003F800FF0003F800FF0003F8 007F0003F8007F0003F8003F8003F8003F8007F8001FC00FF8000FE01FF80003F03FFF8000FFF3 FF80003FC3FF80212A7EA926>I<003FE00001FFF80003F07E000FE03F001FC01F803F800FC03F 800FC07F000FC07F0007E0FF0007E0FF0007E0FF0007E0FFFFFFE0FFFFFFE0FF000000FF000000 FF000000FF0000007F0000007F8000003F8000E03F8001E01FC001C00FE003C003F81F8000FFFE 00001FF0001B1B7E9A20>I<0007F0003FFC00FE3E01FC7F03F87F03F87F07F07F07F03E07F000 07F00007F00007F00007F00007F00007F000FFFFC0FFFFC0FFFFC007F00007F00007F00007F000 07F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007F000 07F00007F00007F00007F0007FFF807FFF807FFF80182A7EA915>I<00FF81F003FFE7FC0FC1FE 7C1F80FC7C3F80FE7C3F007E107F007F007F007F007F007F007F007F007F007F007F007F003F00 7E003F80FE001F80FC000FC1F8001FFFE00018FF8000380000003C0000003C0000003E0000003F FFF8003FFFFF001FFFFFC00FFFFFE007FFFFF01FFFFFF07E0007F87C0001F8F80001F8F80000F8 F80000F8F80000F8FC0001F87E0003F03F0007E00FC01F8003FFFE00007FF0001E287E9A22>I< FFE0000000FFE0000000FFE00000000FE00000000FE00000000FE00000000FE00000000FE00000 000FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE07F 00000FE1FFC0000FE787E0000FEE07F0000FFC03F8000FF803F8000FF003F8000FF003F8000FF0 03F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000F E003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F800 FFFE3FFF80FFFE3FFF80FFFE3FFF80212A7DA926>I<07001FC01FE03FE03FE03FE01FE01FC007 000000000000000000000000000000FFE0FFE0FFE00FE00FE00FE00FE00FE00FE00FE00FE00FE0 0FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE0FFFEFFFEFFFE0F2B7DAA14>I107 DIII<003FE00001FFFC0003F07E000FC01F801F800FC0 3F800FE03F0007E07F0007F07F0007F07F0007F0FF0007F8FF0007F8FF0007F8FF0007F8FF0007 F8FF0007F8FF0007F8FF0007F87F0007F07F0007F03F800FE03F800FE01F800FC00FC01F8007F0 7F0001FFFC00003FE0001D1B7E9A22>II114 D<03FE300FFFF03E03F07800F07000F0F00070F00070F80070FC0000FFE000FFFE007FFFC03FFF E01FFFF007FFF800FFFC0003FC0000FCE0007CE0003CF0003CF0003CF80078FC0078FF01F0F7FF C0C1FF00161B7E9A1B>I<00700000700000700000700000F00000F00000F00001F00003F00003 F00007F0001FFFF0FFFFF0FFFFF007F00007F00007F00007F00007F00007F00007F00007F00007 F00007F00007F00007F00007F00007F03807F03807F03807F03807F03807F03807F03803F87001 F8F000FFE0001F8015267FA51B>I II120 DI<3FFFFF803FFFFF803F00FF803C00FF003801 FE007803FC007807FC007007F800700FF000701FE000001FE000003FC000007F800000FF800000 FF000001FE038003FC038003FC038007F803800FF007801FF007801FE007003FC00F007F801F00 FF807F00FFFFFF00FFFFFF00191B7E9A1F>I E /FC 2 42 df<04081030206040C0C0C0C0C0C0 C0C04060203010080406167D8F0B>40 D<804020301018080C0C0C0C0C0C0C0C08181030204080 06167E8F0B>I E /FD 70 123 df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df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df<003F000000E180000380C02007006040 0E0070401C0070403C0070803C003880780039007800390078003A00F0003A00F0003C00F00038 00F000380070003800700078003000B800380338401C1C188007E00F001B157E941F>11 D<00007C00000183000002018000040180000801C0001001C0002001C0002001C0004001C00040 038000800380008003000080070001000E000107FC0001083800010FDC0002000E0002000E0002 000F0002000F0004000F0004000F0004000F0004000F0008001E0008001E0008001C0008003C00 14003800140070001400E0001201C00021838000207C0000200000002000000040000000400000 004000000040000000800000008000000080000000800000001A2D7EA21C>I<01F00107F8010F FC021FFC02380E046002044003088001088001080000900000900000A00000A00000A00000C000 00C00000C000008000008000008000018000018000018000030000030000030000030000060000 060000060000040000040018207F9419>I<000F8000186000602000401000C000018000018000 01800001800001C00001E00001F00000F800003C00003E0000EF000387000703800E03801C0180 3C01803C0180780180780180780180F00100F00100F00300F00200700600700400300C00380800 1C300007C00014237EA216>I<007E038007000E001C00380078007000FFF8F000F000E000E000 E000E000E0007000700038061C1807E00F157D9414>I<3C0F804610C047606087807087807087 00708700700E00E00E00E00E00E00E00E01C01C01C01C01C01C01C01C038038038038038038038 0380700700300700000700000700000E00000E00000E00000E00001C00001C00001C00001C0000 180015207E9418>17 D<000F000031800060C000E0C001C0E00180E00380E00700E00700E00F00 E00E00E01E00E01E00E01C01E03C01E03C01E03C01E07FFFC07803C07803C07803C0700780F007 80F00700F00F00F00E00F00E00E01C00601C0060380070300070600030C0001180000F00001323 7EA217>I<0300700701F80702780E04700E08000E30000E40001C80001F00001FF0001C3C0038 0E00380E00380700380704700E08700E08700E08700610E003206001C016157D941C>20 D<03800000E00000F000007000007000007800003800003800003C00001C00001C00001C00001E 00000E00000E00000F00000700000700000780000780000F80001B800031C00021C00041C000C1 E00180E00300E00600F00C00701C0070380078700038E00038C0001C16237DA21C>I<00C00C01 C01C01C01C0380380380380380380380380700700700700700700700700E00E00E00E00E00E00E 00E11E01C21E01C21E03C21E04C43F08C439F038380000380000700000700000700000700000E0 0000E00000E00000E00000C0000018207E941D>I<0F00187F00380F00380E00700E00700E0070 0E00E01C00E01C01C01C01801C0380380700380600380C0038180070300070600070C000730000 FC0000F0000015157D9418>I<000400000800000800000800000FE0003C200073E000E00001C0 0003C00007800007800007800007000007000007000007800003BF0001C100037E000600000C00 00180000100000300000200000600000600000600000E00000E000006000007000007C00003F00 001FE00007F80001FE00003F00000F00000700000300020600018400007800132D7FA215>I<07 FFFF1FFFFF3FFFFF30410040410080410080C30000820000820001820001820001060003060003 07000707000607000E07000E07001C03801C038018030018157E941C>I<000F800018E0007070 00E07000C0380180380380780380780700780700780700780E00F00E00F00E00F00E01E01C01C0 1C01C01E03801E0700390C0038F000380000380000700000700000700000700000E00000E00000 E00000E00000C0000015207E9419>I<007FFF8001FFFF8003FFFF800783C0000E01C0001C00E0 003800E0003800E0007000E0007000E0007000E000E001C000E001C000E001C000E0038000E003 000060070000600E0000301800001870000007C0000019157E941C>I<07FFF81FFFF83FFFF830 200040200080200080600000600000600000C00000C00000C00000C00001C00001800001800003 800003800003800007000003000015157E9415>I<000020000040000040000040000040000080 000080000080000080000100000100000100000100000200001FC000F27001821807040C0E0406 1C0406180407380807700807700807700807E0100EE0100EE0100C60101C6020387020303020E0 1821C00E470003F800004000004000008000008000008000008000010000010000010000010000 182D7DA21D>30 D<1F0000402380008021C0010001C0010001E0020000E0040000F00800007010 0000702000007820000038400000388000003D0000001E0000001C0000001E0000000E0000001E 0000002E0000004F000000870000010700000207800002038000040380000803C0001001C00020 01E0004000E1008000720080003C001A1F7E941F>I<0000080000000800000010000000100000 001000000010000000200000002000000020000000200000004000000040000000400000004000 1E0080C0230081E0438081F0438080F0838100708381003087010030070100200E0200200E0200 200E0200201C0200401C0400401C0400801C0401001C0402001C0804000E080800060810000388 E000007F0000001000000010000000100000002000000020000000200000002000000040000000 400000004000001D2D7EA220>I<04000060080000F0080000F810000078100000382000001820 0000184003001040030010400600104006001040060020C0040020C00C0040C00C00C0C01E0180 E07607807FE7FF007FE7FE003F83FC001F01F0001D1580941E>I<003F0001FFC00381E0040040 0800001000001000001000001060000B98000FF800100000200000400000400000400000800000 C00080400080600100380E001FFC0007E00013177F9517>I<08001F0010003F8010007FC02000 E0E04001806040030020400200208004002080040020800800208008006080000040801000C080 100080C01003006020060038201C003F20F8000FFFF00007FFC00000FF000000C0000000C00000 00C0000001C0000001C000000180000001800000038000000380000003800000030000001B207E 9420>39 D<70F8F8F87005057C840E>58 D<70F8FCFC7404040404080810102040060F7C840E> I<0000001800000078000001E00000078000001E00000078000003E000000F8000003C000000F0 000003C000000F0000003C000000F0000000F00000003C0000000F00000003C0000000F0000000 3C0000000F80000003E0000000780000001E0000000780000001E000000078000000181D1C7C99 26>I<000180000180000380000300000300000700000600000600000E00000C00000C00001C00 00180000180000180000380000300000300000700000600000600000E00000C00000C00001C000 0180000180000380000300000300000700000600000600000E00000C00000C00000C00001C0000 180000180000380000300000300000700000600000600000E00000C00000C0000011317DA418> II<000FC000003030000040180000800C000100060001C0070003C0070003C0030001800380 00000380000003800000038000000380001F87800070478001C0278003801780070017800E001F 001E001F001C001F003C001F0038001E0078001E0078001E0078003C00F0003C00F0003800F000 7800F00070007000E0007000E0007001C00038038000180700000C1C000003F0000019257EA31A >64 D<00000080000000018000000001C000000003C000000003C000000007C00000000BC00000 000BC000000013C000000033C000000023C000000043C000000043E000000081E000000181E000 000101E000000201E000000201E000000401E000000C01E000000801E000001001E000001FFFF0 00002000F000006000F000004000F000008000F000008000F000010000F000030000F000020000 F000040000F8000C0000F8001E0000F800FF800FFF8021237EA225>I<007FFFF8000007800F00 000780078000078003C0000F0001C0000F0001C0000F0001E0000F0001E0001E0001C0001E0003 C0001E0003C0001E000780003C000F00003C001E00003C003C00003C01F000007FFFE000007800 78000078003C000078001E0000F0001E0000F0000E0000F0000F0000F0000F0001E0001E0001E0 001E0001E0001E0001E0003C0003C0003C0003C000780003C000F00003C001C00007C00F8000FF FFFC000023227EA125>I<00007F00800003808100000E00630000380027000070001F0000E000 0E0001C0000E000380000E000700000E000F000004000E000004001E000004003C000004003C00 000800780000000078000000007800000000F000000000F000000000F000000000F000000000F0 00000000E000000000E000002000E000002000E000004000E000004000F0000080007000008000 7000010000380002000018000400001C0008000006003000000381C0000000FE00000021247DA2 23>I<007FFFF8000007801E0000078007000007800380000F0001C0000F0001C0000F0000E000 0F0000E0001E0000E0001E0000F0001E0000F0001E0000F0003C0000F0003C0000F0003C0000F0 003C0000F000780001E000780001E000780001E000780001E000F00003C000F00003C000F00003 8000F000078001E000070001E0000E0001E0001E0001E0001C0003C000380003C000700003C000 E00003C003800007C00E0000FFFFF8000024227EA128>I<007FFFFFC000078003C000078000C0 00078000C0000F0000C0000F0000C0000F000080000F000080001E000080001E000080001E0080 80001E008000003C010000003C010000003C030000003C070000007FFE00000078060000007806 0000007806000000F004000000F004000000F004010000F000020001E000020001E000020001E0 00040001E0000C0003C000080003C000180003C000300003C000700007C003F000FFFFFFE00022 227EA124>I<007FFFFFC000078003C000078000C000078000C0000F0000C0000F0000C0000F00 0080000F000080001E000080001E000080001E008080001E008000003C010000003C010000003C 030000003C070000007FFE000000780600000078060000007806000000F004000000F004000000 F004000000F000000001E000000001E000000001E000000001E000000003C000000003C0000000 03C000000003C000000007C0000000FFFE00000022227EA120>I<00007F00400003C0C080000E 002180001C0013800070000F8000E000070001C0000700038000070007000007000F000002000E 000002001E000002003C000002003C00000400780000000078000000007800000000F000000000 F000000000F000000000F000000000F0003FFF00E00000F000E00000F000E00000F000E00001E0 00F00001E000F00001E000700001E000700003C000380003C000180007C0000C0009C000060011 80000380E08000007F00000022247DA226>I<007FFC1FFF00078001E000078001E000078001E0 000F0003C0000F0003C0000F0003C0000F0003C0001E000780001E000780001E000780001E0007 80003C000F00003C000F00003C000F00003C000F00007FFFFE000078001E000078001E00007800 1E0000F0003C0000F0003C0000F0003C0000F0003C0001E000780001E000780001E000780001E0 00780003C000F00003C000F00003C000F00003C000F00007C001F000FFFC3FFF0028227EA128> I<00FFFC0007C0000780000780000F00000F00000F00000F00001E00001E00001E00001E00003C 00003C00003C00003C0000780000780000780000780000F00000F00000F00000F00001E00001E0 0001E00001E00003C00003C00003C00003C00007C000FFFC0016227EA116>I<0007FFE000001E 0000001E0000001E0000003C0000003C0000003C0000003C000000780000007800000078000000 78000000F0000000F0000000F0000000F0000001E0000001E0000001E0000001E0000003C00000 03C0000003C0000003C00000078000000780003807800078078000F80F0000F80F0000F01E0000 401C00004038000030E000000F8000001B237DA11B>I<007FFC01FF0007800078000780006000 078000C0000F000180000F000200000F000400000F000800001E001000001E004000001E008000 001E010000003C020000003C040000003C1E0000003C3E000000785F000000788F0000007A0F00 00007C07800000F807800000F007C00000F003C00000F003C00001E001E00001E001E00001E001 E00001E000F00003C000F00003C000F80003C000780003C000780007C000FC00FFFC07FF802822 7EA129>I<007FFE000007C0000007800000078000000F0000000F0000000F0000000F0000001E 0000001E0000001E0000001E0000003C0000003C0000003C0000003C0000007800000078000000 7800000078000000F0000000F0000000F0001000F0001001E0002001E0002001E0004001E00040 03C000C003C0008003C0018003C0078007C01F00FFFFFF001C227EA121>I<007FC00001FF0007 C00003E00007C00005E00007C00005E00009E0000BC00009E0000BC00009E00013C00009E00023 C00011E00027800011E00047800011E00047800011E00087800021E0010F000020F0010F000020 F0020F000020F0040F000040F0041E000040F0081E000040F0081E000040F0101E000080F0203C 00008078203C00008078403C00008078803C000100788078000100790078000100790078000100 7A00780002007C00F00002007C00F00002003800F00006003800F0000F003001F000FFE0203FFF 0030227EA12F>I<007FC003FF0007C000780007C000600005E000200009E000400009E0004000 08F000400008F000400010F800800010780080001078008000103C008000203C010000203E0100 00201E010000201E010000400F020000400F020000400F020000400782000080078400008007C4 00008003C400008003C400010001E800010001E800010001F800010000F800020000F000020000 7000020000700006000070000F00002000FFE000200028227EA127>I<00007F00000381C0000E 0060003800380070003800E0001C01C0001E0380000E0700000E0F00000F0E00000F1C00000F3C 00000F3C00000F7800000F7800000F7800000FF000001EF000001EF000001EF000003CF000003C F000003CE0000078E0000078E00000F0F00000E0F00001E0F00003C0700007807800070038000E 001C0038000E0070000783C00000FE000020247DA225>I<007FFFF0000007801C000007800F00 0007800700000F000380000F000380000F000380000F000380001E000780001E000780001E0007 80001E000F00003C000F00003C001E00003C003C00003C007000007801E000007FFF0000007800 0000007800000000F000000000F000000000F000000000F000000001E000000001E000000001E0 00000001E000000003C000000003C000000003C000000003C000000007C0000000FFFC00000021 227EA11F>I<00007F00000381C0000E0060003800380070003800E0001C01C0001E0380000E07 00000E0F00000F0E00000F1E00000F3C00000F3C00000F7800000F7800000F7800000FF000001E F000001EF000001EF000001CF000003CE000003CE0000078E0000078E00000F0E00000E0F00001 E0F01E03C0702103807840870038408E001C40B8000E40F00007C1C02000FE8020000080200001 8040000180C00001C0800001C3800001FF000000FF000000FE0000007800202D7DA227>I<007F FFE0000007803C000007800E000007800700000F000780000F000380000F0003C0000F0003C000 1E000780001E000780001E000780001E000F00003C001E00003C003C00003C007000003C01C000 007FFE00000078078000007801C000007801E00000F000F00000F000F00000F000F00000F000F0 0001E001E00001E001E00001E001E00001E001E00003C003C00003C003C04003C003C04003C001 C08007C001C080FFFC00E3000000003C0022237EA125>I<0003F010000E0C2000180260002001 E0004000E000C000C0008000C0018000C0018000C00380008003800080038000000380000003C0 000001F0000001FE000000FFE000007FF000001FF8000001FC0000003C0000001C0000000E0000 000E0000000E0020000C0020000C0020000C002000080060001800600010007000200070004000 C8008000C603000081FC00001C247DA21E>I<1FFFFFFE1E01E00E1801E0063001E0062003C006 2003C0064003C0044003C00440078004800780048007800400078000000F0000000F0000000F00 00000F0000001E0000001E0000001E0000001E0000003C0000003C0000003C0000003C00000078 000000780000007800000078000000F0000000F0000000F0000000F0000001F00000FFFFC0001F 227EA11D>I<3FFE01FF8003C0003C0003C000300003C000100007800020000780002000078000 200007800020000F000040000F000040000F000040000F000040001E000080001E000080001E00 0080001E000080003C000100003C000100003C000100003C000100007800020000780002000078 0002000078000200007000040000F000040000F000080000700008000070001000007000200000 380040000038008000001C01000000060600000001F800000021237DA121>III<007FFC03FF0007E000F80007C000E00003C000800003E001000001E002000001F006000001 F00C000000F018000000F81000000078200000007C400000007C800000003D000000003E000000 001E000000001F000000001F000000002F000000006F80000000C78000000187C000000103C000 000203C000000403E000000801E000001001F000002000F000004000F800008000F80001800078 000300007C000F8000FC00FFE007FFC028227FA128>II<007FFFFE007E001E0070003C00E0007800C000F0008001E0018003E0010003C00100 078002000F0002001E0000003C0000007C00000078000000F0000001E0000003C0000007800000 0F8000000F0000001E0000003C00200078002000F0004001F0004001E0004003C0008007800080 0F0001801E0003001E0007003C000F0078007E00FFFFFE001F227DA121>I<000380000640000C 2000182000182000304000304000604000604000E08000C08001C10001C1000182000382000384 000384000708000710000720000720000640000E80000F00000E00000E00000E00001E00002600 00460000860080060100030200010C0000F000132380A214>96 D<00786001C4E00302E00601C0 0E01C01C01C03C01C0380380780380780380780380F00700F00700F00700F00708F00E10700E10 701E1030262018C6200F01C015157E941A>I<03C0003F80000380000380000380000700000700 000700000700000E00000E00000E00000E00001C00001C78001D8E001E07003C07003803803803 80380780700780700780700780700780E00F00E00F00E00F00E01E00E01C00601C006038003070 0030C0000F000011237DA215>I<003F0000E0800380C00701C00E03C01C03C03C00003C000078 0000780000780000F00000F00000F00000F000007000407000403001803802001C1C0007E00012 157E9415>I<00001E0001FC00001C00001C00001C000038000038000038000038000070000070 0000700000700000E00078E001C4E00302E00601C00E01C01C01C03C01C0380380780380780380 780380F00700F00700F00700F00708F00E10700E10701E1030262018C6200F01C017237EA219> I<007C000382000701000E01001C0100380100780200700400FFF800F00000F00000E00000E000 00E00000E00000E00080E000807003003004001838000FC00011157D9417>I<00001E00000063 800000C7800001C7800001C3000001800000038000000380000003800000038000000700000007 0000000700000007000000FFF800000E0000000E0000000E0000000E0000000E0000000E000000 1C0000001C0000001C0000001C0000001C00000038000000380000003800000038000000380000 007000000070000000700000007000000060000000E0000000E0000000E0000000C0000070C000 00F1800000F1000000620000003C000000192D7EA218>I<000F0C00389C00605C00C03801C038 0380380780380700700F00700F00700F00701E00E01E00E01E00E01E00E01E01C00E01C00E03C0 0605C0031B8001E380000380000380000700000700000700700E00F00C00F018006070003FC000 161F809417>I<00F0000FE00000E00000E00000E00001C00001C00001C00001C0000380000380 00038000038000070000071F0007218007C0C00F00E00F00E00E00E00E00E01C01C01C01C01C01 C01C01C0380380380380380700380704700708700E08700E08700610E006206003C016237DA21C >I<00E000E001E000C00000000000000000000000000000000000001E00230043804380838083 80870007000E000E000E001C001C0038003820384070407040308031001E000C227EA111>I<00 00E00001E00001E00000C000000000000000000000000000000000000000000000000000000000 1E00002300004380008380010380010380010380000700000700000700000700000E00000E0000 0E00000E00001C00001C00001C00001C0000380000380000380000380000700000700000700070 E000F0C000F180006300003E0000132C81A114>I<00F0000FE00000E00000E00000E00001C000 01C00001C00001C0000380000380000380000380000700000700F00703080704380E08780E1078 0E20300E40001C80001F00001FC0001C7000383800383800381C00381C10703820703820703820 701840E00C8060070015237DA219>I<01E01FC001C001C001C003800380038003800700070007 0007000E000E000E000E001C001C001C001C0038003800380038007000700070007100E200E200 E200620064001C000B237DA20F>I<3C07E01F00461830618047201880C087401D00E087801E00 E087801C00E087001C00E00E003801C00E003801C00E003801C00E003801C01C007003801C0070 03801C007007001C007007043800E007083800E00E083800E00E083800E006107001C006203000 C003C027157E942B>I<3C07C0004618600047203000874038008780380087003800870038000E 0070000E0070000E0070000E0070001C00E0001C00E0001C01C0001C01C1003801C20038038200 3803820038018400700188003000F00019157E941D>I<003E0000C1800380C00700E00E00E01C 00F03C00F03C00F07800F07800F07800F0F001E0F001E0F001C0F003C070038070070070060038 1C001C380007E00014157E9417>I<03C0F004631C04740E08780E08700708700708700F00E00F 00E00F00E00F00E00F01C01E01C01E01C01E01C03C03803803803803C07003C0E0072180071E00 0700000700000E00000E00000E00000E00001C00001C00001C0000FFC000181F819418>I<0078 2001C4600302E00601C00E01C01C01C03C01C0380380780380780380780380F00700F00700F007 00F00700F00E00700E00701E00302E0018DC000F1C00001C00001C000038000038000038000038 0000700000700000700007FF00131F7E9416>I<3C0F004630C04741C08783C08783C087018087 00000E00000E00000E00000E00001C00001C00001C00001C000038000038000038000038000070 000030000013157E9416>I<007E0000810003008002018006038006030006000007000007F800 03FE0001FF00003F00000780000380700380F00300F00300E002004004003018000FE00011157E 9417>I<006000E000E000E000E001C001C001C001C00380FFFC0380038007000700070007000E 000E000E000E001C001C001C001C08381038103820182018C007000E1F7F9E12>I<1E00182300 384380384380708380708380708700700700E00E00E00E00E00E00E01C01C01C01C01C01C01C01 C21C03841C03841C07840C09880E118803E07018157E941C>I<1E0018182300383C4380383E43 80701E8380700E83807006870070060700E0040E00E0040E00E0040E00E0041C01C0081C01C008 1C01C0081C01C0101C01C0101C01C0201C03C0400C04C0C00708E10001F03E0020157E9423> 119 D<01E0F006310C081A1C101A3C201C3C201C18201C00003800003800003800003800007000 00700000700000700860E010F0E010F0E020E170404230803C1F0016157E941C>I<1E00302300 704380704380E08380E08380E08700E00701C00E01C00E01C00E01C01C03801C03801C03801C03 801C07001C07001C07001C0F000C3E0003CE00000E00000E00001C00601C00F03800F03000E060 0080C0004180003E0000151F7E9418>I<00E01003F02007F860060FC008008008010000020000 040000080000100000200000C0000100000200000400400800801001803F830061FE0040FC0080 780014157E9417>I E /FG 52 123 df<00001FFC00000001FFFF00000007FFFFC000001FF807 E000007FC007F00000FF000FF00001FF000FF00001FE000FF00003FC001FF80003FC000FF00003 FC000FF00003FC0007E00003FC0001800003FC0000000003FC0000000003FC0000000003FC0000 000003FC00FFF800FFFFFFFFF800FFFFFFFFF800FFFFFFFFF80003FC0007F80003FC0007F80003 FC0007F80003FC0007F80003FC0007F80003FC0007F80003FC0007F80003FC0007F80003FC0007 F80003FC0007F80003FC0007F80003FC0007F80003FC0007F80003FC0007F80003FC0007F80003 FC0007F80003FC0007F80003FC0007F80003FC0007F80003FC0007F80003FC0007F80003FC0007 F80003FC0007F80003FC0007F80003FC0007F80003FC0007F8007FFFE0FFFFC07FFFE0FFFFC07F FFE0FFFFC02A327FB12E>12 D<0000700000F00003E00007C0000F80001F00003E00007E00007C 0000F80001F80001F00003F00007E00007E0000FC0000FC0000FC0001F80001F80003F80003F80 003F00003F00007F00007F00007F00007E00007E0000FE0000FE0000FE0000FE0000FE0000FE00 00FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE00007E00007E00007F00007F00 007F00003F00003F00003F80003F80001F80001F80000FC0000FC0000FC00007E00007E00003F0 0001F00001F80000F800007C00007E00003E00001F00000F800007C00003E00000F00000701449 7AB520>40 DI45 D<1F003F807FC0FFE0FFE0FFE0 FFE0FFE07FC03F801F000B0B7A8A17>I<0001E0000003E000000FE000007FE0001FFFE000FFFF E000FFBFE000E03FE000003FE000003FE000003FE000003FE000003FE000003FE000003FE00000 3FE000003FE000003FE000003FE000003FE000003FE000003FE000003FE000003FE000003FE000 003FE000003FE000003FE000003FE000003FE000003FE000003FE000003FE000003FE000003FE0 00003FE000003FE000003FE000003FE000003FE000003FE000003FE000003FE0007FFFFFF07FFF FFF07FFFFFF01C2E7AAD29>49 D<003FF00001FFFE0007FFFF801FC07FE03F003FF07C001FF87F 000FFCFF8007FEFFC007FEFFC003FFFFC003FFFFC003FFFFC003FF7F8003FF3F0003FF000003FF 000003FF000007FE000007FE000007FC00000FF800001FF800001FF000003FE000007F8000007F 000000FE000001FC000003F0000007E000000FC007001F8007003E0007007C000F00F8000E01F0 000E01E0001E03FFFFFE07FFFFFE0FFFFFFE1FFFFFFE3FFFFFFE7FFFFFFCFFFFFFFCFFFFFFFCFF FFFFFC202E7CAD29>I<000FFC0000007FFF800001F01FE00003C00FF00007800FF8000FE007FC 001FF007FE001FF807FE001FF807FE001FF807FE001FF807FE001FF807FE000FF007FE0007E007 FC0001800FFC0000000FF80000000FF80000001FF00000003FE00000007F8000001FFE0000001F FC0000001FFF800000001FF00000000FF800000007FE00000003FF00000003FF00000001FF8000 0001FF800E0001FFC03F8001FFC07FC001FFC0FFE001FFC0FFE001FFC0FFE001FFC0FFE001FFC0 FFE001FF80FFE003FF807FC003FF007F0007FE003F000FFC001FE01FF80007FFFFE00001FFFF80 00001FFC0000222E7DAD29>I<0000007800000000F800000001F800000003F800000007F80000 0007F80000000FF80000001FF80000003FF80000007FF800000077F8000000F7F8000001E7F800 0003C7F800000787F800000707F800000F07F800001E07F800003C07F800007807F800007007F8 0000F007F80001E007F80003C007F800078007F8000F0007F8000F0007F8001E0007F8003C0007 F800780007F800F00007F800FFFFFFFFF0FFFFFFFFF0FFFFFFFFF000000FF80000000FF8000000 0FF80000000FF80000000FF80000000FF80000000FF80000000FF80000000FF800000FFFFFF000 0FFFFFF0000FFFFFF0242E7EAD29>I<0C0000380FC003F80FFFFFF80FFFFFF00FFFFFE00FFFFF C00FFFFF800FFFFF000FFFFC000FFFF0000FFF00000F0000000F0000000F0000000F0000000F00 00000F0000000F0000000F0FF8000F7FFF000FFFFFC00FF01FE00F800FF00F0007F80E0007FC00 0003FE000003FE000003FE000003FF000003FF1E0003FF7F8003FFFF8003FFFFC003FFFFC003FF FFC003FFFF8003FEFF8003FE7F0007FC7C0007FC3C000FF81E001FF00FC07FE007FFFF8001FFFE 00003FE000202E7CAD29>I<00007F80000007FFF000001FC07800007F001C0000FE001E0001FC 007E0003F800FF0007F001FF000FF001FF001FE001FF001FE001FF003FE000FE003FE0007C007F C00000007FC00000007FC00000007FC0000000FFC3FF8000FFC7FFE000FFCFBFF000FFDC03FC00 FFF803FE00FFF001FF00FFF000FF00FFE000FF80FFE000FF80FFE000FFC0FFC000FFC0FFC000FF C0FFC000FFC0FFC000FFC07FC000FFC07FC000FFC07FC000FFC07FC000FFC03FC000FFC03FC000 FF801FE000FF801FE000FF000FE001FF000FF001FE0007F803FC0001FC0FF80000FFFFE000003F FF80000007FC0000222E7DAD29>I<1F003F807FC0FFE0FFE0FFE0FFE0FFE07FC03F801F000000 0000000000000000000000000000000000001F003F807FC0FFE0FFE0FFE0FFE0FFE07FC03F801F 000B207A9F17>58 D<0000007C0000000000007C000000000000FE000000000000FE0000000000 00FE000000000001FF000000000001FF000000000003FF800000000003FF800000000007FFC000 00000007FFC00000000007FFC0000000000FFFE0000000000F7FE0000000001F7FF0000000001E 3FF0000000001E3FF0000000003E3FF8000000003C1FF8000000007C1FFC00000000780FFC0000 0000780FFC00000000F80FFE00000000F007FE00000001F007FF00000001E003FF00000001E003 FF00000003E003FF80000003C001FF80000007C001FFC00000078000FFC00000078000FFC00000 0FFFFFFFE000000FFFFFFFE000001FFFFFFFF000001E00003FF000001E00003FF000003C00003F F800003C00001FF800007C00001FFC00007800000FFC00007800000FFC0000F0000007FE0000F0 000007FE0001F0000007FF0003F8000003FF00FFFFC001FFFFFEFFFFC001FFFFFEFFFFC001FFFF FE37317DB03E>65 DI<000003FF80038000003FFFF007800001FFFFFC0F800007FF007F1F80001FF8 000FFF80007FE00003FF8000FFC00001FF8001FF000000FF8003FE0000007F8007FE0000003F80 0FFC0000001F801FF80000001F801FF80000000F803FF80000000F803FF00000000F803FF00000 0007807FF000000007807FF000000007807FE00000000000FFE00000000000FFE00000000000FF E00000000000FFE00000000000FFE00000000000FFE00000000000FFE00000000000FFE0000000 0000FFE00000000000FFE00000000000FFE000000000007FE000000000007FF000000000007FF0 00000003803FF000000003803FF000000003803FF800000003801FF800000007801FF800000007 000FFC0000000F0007FE0000000E0003FF0000001E0001FF0000003C0000FFC000007800007FE0 0001F000001FF80003E0000007FF003F80000001FFFFFE000000003FFFF80000000003FF800000 31317BB03C>IIII<000003FF8003 8000003FFFF007800001FFFFFC0F800007FF007F1F80001FF8000FFF80007FE00003FF8000FFC0 0001FF8001FF000000FF8003FE0000007F8007FE0000003F800FFC0000001F801FF80000001F80 1FF80000000F803FF80000000F803FF00000000F803FF000000007807FF000000007807FF00000 0007807FE00000000000FFE00000000000FFE00000000000FFE00000000000FFE00000000000FF E00000000000FFE00000000000FFE00000000000FFE00000000000FFE00000000000FFE00007FF FFFEFFE00007FFFFFE7FE00007FFFFFE7FF0000001FF807FF0000001FF803FF0000001FF803FF0 000001FF803FF8000001FF801FF8000001FF801FFC000001FF800FFC000001FF8007FE000001FF 8003FF000001FF8001FF800001FF8000FFC00003FF80007FE00003FF80001FF80007FF800007FF 803FFF800001FFFFFE1F8000003FFFF80780000003FFC0018037317BB041>I 73 D76 D<00000FFE0000000000FFFFE000000007FFFFFC0000001FFC07FF0000003FE000FF800000FF80 003FE00001FF00001FF00003FE00000FF80007FC000007FC0007FC000007FC000FF8000003FE00 1FF8000003FF001FF0000001FF003FF0000001FF803FF0000001FF803FF0000001FF807FE00000 00FFC07FE0000000FFC07FE0000000FFC0FFE0000000FFE0FFE0000000FFE0FFE0000000FFE0FF E0000000FFE0FFE0000000FFE0FFE0000000FFE0FFE0000000FFE0FFE0000000FFE0FFE0000000 FFE0FFE0000000FFE0FFE0000000FFE07FE0000000FFC07FE0000000FFC07FF0000001FFC07FF0 000001FFC03FF0000001FF803FF0000001FF801FF8000003FF001FF8000003FF000FFC000007FE 000FFC000007FE0007FE00000FFC0003FF00001FF80001FF80003FF00000FFC0007FE000003FE0 00FF8000001FFC07FF00000007FFFFFC00000000FFFFE0000000000FFE00000033317BB03E>79 DI<00000FFE0000000000FF FFE000000007FFFFFC0000001FFC07FF0000003FE000FF800000FFC0007FE00001FF00001FF000 03FE00000FF80007FE00000FFC0007FC000007FC000FF8000003FE001FF8000003FF001FF80000 03FF003FF0000001FF803FF0000001FF803FF0000001FF807FF0000001FFC07FE0000000FFC07F E0000000FFC0FFE0000000FFE0FFE0000000FFE0FFE0000000FFE0FFE0000000FFE0FFE0000000 FFE0FFE0000000FFE0FFE0000000FFE0FFE0000000FFE0FFE0000000FFE0FFE0000000FFE0FFE0 000000FFE07FE0000000FFC07FE0000000FFC07FF0000001FFC07FF0000001FFC03FF0000001FF 803FF0000001FF801FF8000003FF001FF8000003FF000FF803F003FE000FFC0FFC07FE0007FE1F FE0FFC0003FE1C0F0FF80001FF38079FF00000FFF803FFE000003FF803FF8000001FFC07FF0000 0007FFFFFC00000000FFFFF0004000000FFEF800E000000000FC00E000000000FC01E000000000 FF03E000000000FFFFE0000000007FFFE0000000007FFFC0000000007FFFC0000000003FFFC000 0000003FFF80000000003FFF80000000001FFF00000000000FFE000000000007FC000000000001 F000333F7BB03E>II<001FF0038000FFFF078003FFFFCF8007F00FFF801F C001FF801F80007F803F00003F807F00001F807E00000F807E00000F80FE00000780FE00000780 FF00000380FF00000380FF80000380FFC0000000FFE0000000FFFC0000007FFFE000007FFFFE00 003FFFFFC0003FFFFFF0001FFFFFFC000FFFFFFE0007FFFFFF0001FFFFFF00007FFFFF80001FFF FFC00000FFFFC0000007FFC0000000FFE00000007FE00000003FE00000001FE0E000001FE0E000 000FE0E000000FE0E000000FE0F000000FE0F000000FC0F800000FC0F800001F80FC00001F80FF 00003F00FFC0007E00FFFC01FC00F9FFFFF800F03FFFE000E007FF000023317BB02E>I<3FFFFF FFFFFF003FFFFFFFFFFF003FFFFFFFFFFF003FE00FFC01FF007F000FFC003F807E000FFC001F80 7C000FFC000F8078000FFC00078078000FFC00078070000FFC00038070000FFC00038070000FFC 00038070000FFC000380E0000FFC0001C0E0000FFC0001C0E0000FFC0001C0E0000FFC0001C000 000FFC00000000000FFC00000000000FFC00000000000FFC00000000000FFC00000000000FFC00 000000000FFC00000000000FFC00000000000FFC00000000000FFC00000000000FFC0000000000 0FFC00000000000FFC00000000000FFC00000000000FFC00000000000FFC00000000000FFC0000 0000000FFC00000000000FFC00000000000FFC00000000000FFC00000000000FFC00000000000F FC00000000000FFC00000000000FFC00000000000FFC00000000000FFC00000000000FFC000000 007FFFFFFF8000007FFFFFFF8000007FFFFFFF800032307DAF39>I86 D<007FF8000003FFFF00000FFFFFC0001FE01FF0001FF007F8001FF007FC001FF003FC001FF001 FE000FE001FE0007C001FE00010001FE00000001FE00000001FE000001FFFE00003FFFFE0001FF F1FE0007FE01FE001FF001FE003FE001FE007FC001FE007F8001FE00FF8001FE00FF0001FE00FF 0001FE00FF0001FE00FF8003FE00FF8007FE007FC00FFE003FF03EFF001FFFF87FF807FFF03FF8 00FF800FF825207E9F28>97 D<01F8000000FFF8000000FFF8000000FFF80000000FF800000007 F800000007F800000007F800000007F800000007F800000007F800000007F800000007F8000000 07F800000007F800000007F800000007F800000007F800000007F80FF00007F87FFE0007F9FFFF 8007FFE03FE007FF000FF007FE0007F807FC0007F807F80003FC07F80003FE07F80003FE07F800 01FE07F80001FF07F80001FF07F80001FF07F80001FF07F80001FF07F80001FF07F80001FF07F8 0001FF07F80001FF07F80001FF07F80001FE07F80003FE07F80003FC07FC0003FC07FC0007F807 FE000FF007FF801FE007E7E07FC007C1FFFF8007807FFE0007001FE00028327EB12E>I<0007FF 00007FFFE001FFFFF803FC03FC07F807FC0FF007FC1FE007FC3FC007FC3FC003F87FC001F07F80 0040FF800000FF800000FF800000FF800000FF800000FF800000FF800000FF800000FF800000FF 8000007FC000007FC000003FC0000E3FE0000E1FE0001E0FF0003C07F8007803FF01F001FFFFE0 007FFF800007FC001F207D9F25>I<00000007E0000003FFE0000003FFE0000003FFE00000003F E00000001FE00000001FE00000001FE00000001FE00000001FE00000001FE00000001FE0000000 1FE00000001FE00000001FE00000001FE00000001FE00000001FE0000FF81FE0007FFF1FE001FF FFDFE003FE03FFE00FF800FFE01FF0007FE01FE0003FE03FC0001FE03FC0001FE07FC0001FE07F 80001FE0FF80001FE0FF80001FE0FF80001FE0FF80001FE0FF80001FE0FF80001FE0FF80001FE0 FF80001FE0FF80001FE0FF80001FE07F80001FE07FC0001FE07FC0001FE03FC0003FE01FE0007F E01FE000FFE00FF001FFE007FC07DFF001FFFF9FFF007FFE1FFF000FF01FFF28327DB12E>I<00 07FC0000003FFF800000FFFFE00003FC07F00007F801F8000FE000FC001FE0007E003FC0007E00 3FC0003F007FC0003F007F80003F007F80003F80FF80003F80FF80003F80FFFFFFFF80FFFFFFFF 80FFFFFFFF80FF80000000FF80000000FF800000007F800000007F800000003FC00000003FC000 03801FC00003801FE00007800FF0000F0007F8001E0003FE00FC0000FFFFF800003FFFE0000003 FF000021207E9F26>I<0000FF000007FFC0001FFFF0007FC7F000FF0FF801FF0FF801FE0FF803 FE0FF803FC0FF803FC07F003FC01C003FC000003FC000003FC000003FC000003FC000003FC0000 03FC0000FFFFF800FFFFF800FFFFF80003FC000003FC000003FC000003FC000003FC000003FC00 0003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC 000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003 FC00007FFFF0007FFFF0007FFFF0001D327EB119>I<001FF007E000FFFE3FF003FFFFFFF807F8 3FF1F80FE00FE1F81FE00FF1F81FC007F0603FC007F8003FC007F8003FC007F8003FC007F8003F C007F8003FC007F8003FC007F8001FC007F0001FE00FF0000FE00FE00007F83FC00007FFFF8000 0EFFFE00000E1FF000000E000000001E000000001E000000001F000000001F800000001FFFFFC0 000FFFFFF8000FFFFFFE0007FFFFFF8007FFFFFFC007FFFFFFE01FFFFFFFE03F00007FE07E0000 0FF0FE000007F0FC000003F0FC000003F0FC000003F0FE000007F07E000007E07F00000FE03FC0 003FC01FF801FF8007FFFFFE0000FFFFF000001FFF8000252F7E9F29>I<01F800000000FFF800 000000FFF800000000FFF8000000000FF80000000007F80000000007F80000000007F800000000 07F80000000007F80000000007F80000000007F80000000007F80000000007F80000000007F800 00000007F80000000007F80000000007F80000000007F807F8000007F83FFF000007F87FFF8000 07F9F03FC00007FBC01FE00007FF801FE00007FF000FF00007FE000FF00007FC000FF00007FC00 0FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF000 07F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F800 0FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF000 FFFFC1FFFF80FFFFC1FFFF80FFFFC1FFFF8029327DB12E>I<03C0000FF0000FF0001FF8001FF8 001FFC001FF8001FF8000FF0000FF00003C0000000000000000000000000000000000000000000 0000000001F800FFF800FFF800FFF8000FF80007F80007F80007F80007F80007F80007F80007F8 0007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F8 0007F80007F80007F80007F800FFFF80FFFF80FFFF8011337DB217>I<01F8000000FFF8000000 FFF8000000FFF80000000FF800000007F800000007F800000007F800000007F800000007F80000 0007F800000007F800000007F800000007F800000007F800000007F800000007F800000007F800 000007F8007FFC07F8007FFC07F8007FFC07F8001FC007F8001F0007F8003E0007F800780007F8 01F00007F803E00007F807800007F81F000007F83E000007F87C000007F9FE000007FBFF000007 FFFF800007FF7FC00007FE3FE00007F81FE00007F01FF00007F00FF80007F007FC0007F003FE00 07F001FF0007F000FF0007F000FF8007F0007FC007F0003FE007F0003FF0FFFF80FFFFFFFF80FF FFFFFF80FFFF28327EB12C>107 D<01F800FFF800FFF800FFF8000FF80007F80007F80007F800 07F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F800 07F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F800 07F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F800 FFFFC0FFFFC0FFFFC012327DB117>I<03F007F8000FF000FFF03FFF007FFE00FFF07FFF80FFFF 00FFF1F03FC3E07F800FF3C01FE7803FC007F7801FEF003FC007F7000FFE001FE007FE000FFC00 1FE007FC000FF8001FE007FC000FF8001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0 001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000F F0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F800 0FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8 000FF0001FE007F8000FF0001FE0FFFFC1FFFF83FFFFFFFFC1FFFF83FFFFFFFFC1FFFF83FFFF40 207D9F47>I<03F007F80000FFF03FFF0000FFF07FFF8000FFF1F03FC0000FF3C01FE00007F780 1FE00007F7000FF00007FE000FF00007FC000FF00007FC000FF00007F8000FF00007F8000FF000 07F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F800 0FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF000 07F8000FF00007F8000FF00007F8000FF00007F8000FF000FFFFC1FFFF80FFFFC1FFFF80FFFFC1 FFFF8029207D9F2E>I<0007FE0000003FFFC00000FFFFF00003FC03FC0007F000FE000FE0007F 001FC0003F803FC0003FC03FC0003FC07F80001FE07F80001FE07F80001FE0FF80001FF0FF8000 1FF0FF80001FF0FF80001FF0FF80001FF0FF80001FF0FF80001FF0FF80001FF07F80001FE07F80 001FE07F80001FE03FC0003FC03FC0003FC01FE0007F800FE0007F0007F801FE0003FE07FC0001 FFFFF800003FFFC0000007FE000024207E9F29>I<01F80FF000FFF87FFE00FFF9FFFF80FFFFE0 7FE00FFF001FF007FE000FF807FC0007F807F80007FC07F80003FE07F80003FE07F80003FE07F8 0001FF07F80001FF07F80001FF07F80001FF07F80001FF07F80001FF07F80001FF07F80001FF07 F80001FF07F80003FF07F80003FE07F80003FE07F80003FC07FC0007FC07FC000FF807FE000FF0 07FF801FE007FFE07FC007F9FFFF8007F87FFE0007F81FE00007F800000007F800000007F80000 0007F800000007F800000007F800000007F800000007F800000007F800000007F800000007F800 0000FFFFC00000FFFFC00000FFFFC00000282E7E9F2E>I<0007F800E0007FFE01E001FFFF83E0 03FE07C3E007F801E7E00FF000FFE01FF0007FE03FE0003FE03FC0003FE07FC0001FE07FC0001F E0FFC0001FE0FF80001FE0FF80001FE0FF80001FE0FF80001FE0FF80001FE0FF80001FE0FF8000 1FE0FF80001FE0FF80001FE07FC0001FE07FC0001FE07FC0001FE03FE0003FE01FE0007FE01FF0 00FFE00FF801FFE007FE07DFE001FFFF9FE0007FFE1FE0000FF01FE00000001FE00000001FE000 00001FE00000001FE00000001FE00000001FE00000001FE00000001FE00000001FE00000001FE0 0000001FE0000003FFFF000003FFFF000003FFFF282E7D9F2C>I<03F03F00FFF0FFC0FFF1FFF0 FFF3C7F00FF78FF807F70FF807FE0FF807FE0FF807FC07F007FC03E007FC008007FC000007F800 0007F8000007F8000007F8000007F8000007F8000007F8000007F8000007F8000007F8000007F8 000007F8000007F8000007F8000007F8000007F8000007F80000FFFFE000FFFFE000FFFFE0001D 207E9F22>I<00FF870007FFEF001FFFFF003F007F007C001F007C000F00F8000F00F8000700FC 000700FC000700FF000000FFF800007FFFC0007FFFF0003FFFFC001FFFFE0007FFFF0001FFFF80 001FFF800000FFC000001FC0E0000FC0E0000FC0F00007C0F00007C0F80007C0FC000F80FE001F 80FF803F00FFFFFE00F3FFF800E07FC0001A207D9F21>I<003800003800003800003800003800 00780000780000780000F80000F80001F80003F80007F8001FF800FFFFFEFFFFFEFFFFFE07F800 07F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F800 07F80007F80007F80707F80707F80707F80707F80707F80707F80707FC0F03FC0E03FE1E01FFFC 007FF8000FE0182E7EAD20>I<01F80003F000FFF801FFF000FFF801FFF000FFF801FFF0000FF8 001FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF0 0007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8 000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8001FF0 0007F8001FF00007F8003FF00007F8007FF00003FC00FFF00003FE03EFF80001FFFFCFFF80007F FF0FFF80000FFC0FFF8029207D9F2E>III121 D<3FFFFFFC3FFFFFFC3F FFFFFC3FC00FF83E001FF03C003FF038003FE078007FC07800FF807001FF807001FF007003FE00 7007FC00000FF800000FF800001FF000003FE000007FC00E007FC00E00FF800E01FF000E03FE00 0E07FE001E07FC001E0FF8001C1FF0003C3FF0007C3FE000FC7FC007FCFFFFFFFCFFFFFFFCFFFF FFFC1F207E9F25>I E /FH 48 123 df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df21 D<000F0038006000E001C001C001C001C001C001C001C001C001C001C001C001C001C0 01C001C0038007001E00F8001E000700038001C001C001C001C001C001C001C001C001C001C001 C001C001C001C001C000E000600038000F102D7DA117>102 DI106 D E /FJ 7 105 df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df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df<0000E000000000E000000001F000000001F000000001F000 000003F800000003F800000006FC00000006FC0000000EFE0000000C7E0000000C7E000000183F 000000183F000000303F800000301F800000701FC00000600FC00000600FC00000C007E00000FF FFE00001FFFFF000018003F000018003F000030001F800030001F800060001FC00060000FC000E 0000FE00FFE00FFFE0FFE00FFFE0231F7E9E28>65 D<07FC001FFF003F0F803F07C03F03E03F03 E00C03E00003E0007FE007FBE01F03E03C03E07C03E0F803E0F803E0F803E0FC05E07E0DE03FF9 FE0FE07E17147F9319>97 DI<01FE 0007FF801F0FC03E0FC03E0FC07C0FC07C0300FC0000FC0000FC0000FC0000FC0000FC00007C00 007E00003E00603F00C01F81C007FF0001FC0013147E9317>I114 D<0FE63FFE701E600EE006E006F800FFC07FF83FFC1FFE 03FE001FC007C007E007F006F81EFFFCC7F010147E9315>I<0180018001800380038003800780 0F803F80FFFCFFFC0F800F800F800F800F800F800F800F800F800F800F860F860F860F860F8607 CC03F801F00F1D7F9C14>I E /FM 81 124 df<000FF83F00007FFDFFC001F81FE3E003E03F87 E007C03F87E00F803F07E00F803F03C00F801F00000F801F00000F801F00000F801F00000F801F 00000F801F0000FFFFFFFC00FFFFFFFC000F801F00000F801F00000F801F00000F801F00000F80 1F00000F801F00000F801F00000F801F00000F801F00000F801F00000F801F00000F801F00000F 801F00000F801F00000F801F00000F801F00000F801F00000F801F00007FF0FFF0007FF0FFF000 23237FA221>11 D<000FF000007FFC0001F80E0003E01F0007C03F000F803F000F803F000F801E 000F800C000F8000000F8000000F8000000F800000FFFFFF00FFFFFF000F801F000F801F000F80 1F000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F 801F000F801F000F801F000F801F000F801F000F801F007FF0FFE07FF0FFE01B237FA21F>I<00 0FFF00007FFF0001F83F0003E03F0007C03F000F803F000F801F000F801F000F801F000F801F00 0F801F000F801F000F801F00FFFFFF00FFFFFF000F801F000F801F000F801F000F801F000F801F 000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F80 1F000F801F000F801F000F801F007FF0FFE07FF0FFE01B237FA21F>I<0007F80FF000007FFE7F FC0001F80FF80E0003E00FE01F0007C01FC03F000F801F803F000F801F803F000F800F801E000F 800F800C000F800F8000000F800F8000000F800F8000000F800F800000FFFFFFFFFF00FFFFFFFF FF000F800F801F000F800F801F000F800F801F000F800F801F000F800F801F000F800F801F000F 800F801F000F800F801F000F800F801F000F800F801F000F800F801F000F800F801F000F800F80 1F000F800F801F000F800F801F000F800F801F000F800F801F000F800F801F007FF07FF0FFE07F F07FF0FFE02B237FA22F>I16 D18 D<03C007C00FC00FC01F803E007C00F00060000A0975A21C>I<3803 807C07C0FE0FE0FF0FF0FF0FF07F07F03B03B00300300300300700700600600600600C00C01C01 C018018070070020020014117EA21D>34 D<387CFEFFFF7F3B03030706060C1C18702008117CA2 10>39 D<00180030006000C001C00380070007000E001E001C003C003C003C0078007800780078 00F800F000F000F000F000F000F000F000F000F000F000F000F80078007800780078003C003C00 3C001C001E000E0007000700038001C000C00060003000180D317BA416>II<387CFEFFFF7F3B03030706060C1C18702008117C 8610>44 DI<387CFEFEFE7C3807077C8610>I<00FE0007FFC0 0F83E01F01F03E00F83E00F87C007C7C007C7C007CFC007CFC007EFC007EFC007EFC007EFC007E FC007EFC007EFC007EFC007EFC007EFC007EFC007EFC007E7C007C7C007C7C007C3E00F83E00F8 1F01F00F83E007FFC000FE0017207E9F1C>48 D<00180000780001F800FFF800FFF80001F80001 F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001 F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F8007FFFE07FFFE013 207C9F1C>I<03FC000FFF003C1FC07007E07C07F0FE03F0FE03F8FE03F8FE01F87C01F83803F8 0003F80003F00003F00007E00007C0000F80001F00003E0000380000700000E01801C018038018 0700180E00380FFFF01FFFF03FFFF07FFFF0FFFFF0FFFFF015207D9F1C>I<00FE0007FFC00F07 E01E03F03F03F03F81F83F81F83F81F81F03F81F03F00003F00003E00007C0001F8001FE0001FF 000007C00001F00001F80000FC0000FC3C00FE7E00FEFF00FEFF00FEFF00FEFF00FC7E01FC7801 F81E07F00FFFC001FE0017207E9F1C>I<0000E00001E00003E00003E00007E0000FE0001FE000 1FE00037E00077E000E7E001C7E00187E00307E00707E00E07E00C07E01807E03807E07007E0E0 07E0FFFFFEFFFFFE0007E00007E00007E00007E00007E00007E00007E000FFFE00FFFE17207E9F 1C>I<1000201E01E01FFFC01FFF801FFF001FFE001FF8001BC000180000180000180000180000 19FC001FFF001E0FC01807E01803E00003F00003F00003F80003F83803F87C03F8FE03F8FE03F8 FC03F0FC03F07007E03007C01C1F800FFF0003F80015207D9F1C>I<001F8000FFE003F07007C0 F00F01F81F01F83E01F83E01F87E00F07C00007C0000FC0800FC7FC0FCFFE0FD80F0FF00F8FE00 7CFE007CFC007EFC007EFC007EFC007E7C007E7C007E7C007E3C007C3E007C1E00F80F00F00783 E003FFC000FF0017207E9F1C>I<6000007800007FFFFE7FFFFE7FFFFC7FFFF87FFFF87FFFF0E0 0060E000C0C00180C00300C00300000600000C00001C0000180000380000780000780000F00000 F00000F00001F00001F00001F00003F00003F00003F00003F00003F00003F00003F00001E00017 227DA11C>I<00FE0003FFC00601E00C00701800701800383800383C00383F00383F80783FE070 1FF8E01FFFC00FFF8007FFC003FFE007FFF01E7FF83C1FFC7807FC7801FEF000FEF0003EF0001E F0001EF0001CF8001C7800383C00381F01F00FFFC001FF0017207E9F1C>I<01FE0007FF800F83 E01E01F03E00F07C00F87C0078FC007CFC007CFC007CFC007EFC007EFC007EFC007E7C00FE7C00 FE3E01FE1E037E0FFE7E07FC7E00207E00007C00007C1E007C3F00F83F00F83F00F03F01E01E03 C01C0F800FFE0003F80017207E9F1C>I<387CFEFEFE7C380000000000000000387CFEFEFE7C38 07167C9510>I<7FFFFFFFF0FFFFFFFFF8FFFFFFFFF80000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000FFFFFFFFF8FFFFFFFFF87F FFFFFFF0250F7D932C>61 D<07FC001FFF00380F807007C0F807E0FC07E0FC07E0FC07E07807E0 000FC0001F80001F00003C0000780000700000E00000E00000C00000C00000C00000C00000C000 00C00000000000000000000000000000000001C00003E00007F00007F00007F00003E00001C000 13237DA21A>63 D<000070000000007000000000F800000000F800000000F800000001FC000000 01FC00000003FE00000003FE00000003FE00000006FF000000067F0000000E7F8000000C3F8000 000C3F800000183FC00000181FC00000381FE00000300FE00000300FE00000600FF000006007F0 0000E007F80000FFFFF80000FFFFF800018001FC00018001FC00038001FE00030000FE00030000 FE000600007F000600007F00FFE00FFFF8FFE00FFFF825227EA12A>65 DI<0003FE0080001FFF818000FF01E38001F8003F8003E0001F8007C0 000F800F800007801F800007803F000003803F000003807F000001807E000001807E00000180FE 00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000 7E000000007E000001807F000001803F000001803F000003801F800003000F8000030007C00006 0003F0000C0001F800380000FF00F000001FFFC0000003FE000021227DA128>IIII<0003FE0040001FFFC0C000 7F00F1C001F8003FC003F0000FC007C00007C00FC00003C01F800003C03F000001C03F000001C0 7F000000C07E000000C07E000000C0FE00000000FE00000000FE00000000FE00000000FE000000 00FE00000000FE00000000FE000FFFFC7E000FFFFC7F00001FC07F00001FC03F00001FC03F0000 1FC01F80001FC00FC0001FC007E0001FC003F0001FC001FC003FC0007F80E7C0001FFFC3C00003 FF00C026227DA12C>III75 DIII<0007FC0000003FFF80 0000FC07E00003F001F80007E000FC000FC0007E001F80003F001F80003F003F00001F803F0000 1F807F00001FC07E00000FC07E00000FC0FE00000FE0FE00000FE0FE00000FE0FE00000FE0FE00 000FE0FE00000FE0FE00000FE0FE00000FE0FE00000FE07E00000FC07F00001FC07F00001FC03F 00001F803F80003F801F80003F000FC0007E0007E000FC0003F001F80000FC07E000003FFF8000 0007FC000023227DA12A>II<00 07FC0000003FFF800000FC07E00003F001F80007E000FC000FC0007E001F80003F001F80003F00 3F00001F803F00001F807F00001FC07E00000FC07E00000FC0FE00000FE0FE00000FE0FE00000F E0FE00000FE0FE00000FE0FE00000FE0FE00000FE0FE00000FE0FE00000FE07E00000FC07F0000 1FC07F00001FC03F00001F803F81F03F801F83F83F000FC70C7E0007E606FC0003F607F80000FF 07E000003FFF80000007FF80200000038020000001C020000001E0E0000001FFE0000001FFC000 0000FFC0000000FFC00000007F800000007F000000001E00232C7DA12A>II<01FC0407FF8C1F03FC3C007C7C003C78001C78001CF8000CF800 0CFC000CFC0000FF0000FFE0007FFF007FFFC03FFFF01FFFF80FFFFC03FFFE003FFE0003FF0000 7F00003F00003FC0001FC0001FC0001FE0001EE0001EF0003CFC003CFF00F8C7FFE080FF801822 7DA11F>I<7FFFFFFF807FFFFFFF807E03F80F807803F807807003F803806003F80180E003F801 C0E003F801C0C003F800C0C003F800C0C003F800C0C003F800C00003F800000003F800000003F8 00000003F800000003F800000003F800000003F800000003F800000003F800000003F800000003 F800000003F800000003F800000003F800000003F800000003F800000003F800000003F8000000 03F800000003F8000003FFFFF80003FFFFF80022227EA127>III I89 D<3FFFFFE03FFFFFE03F801FC03E003FC0 3C003F8038007F007000FF007000FE007001FE006003FC006003F8006007F8000007F000000FE0 00001FE000001FC000003FC000007F8000007F000000FF000000FE006001FC006003FC006003F8 006007F800E00FF000E00FE000E01FE001C01FC001C03F8003C07F8007C07F003FC0FFFFFFC0FF FFFFC01B227DA122>II<0400 400E00E0180180380380300300600600600600E00E00C00C00C00C00DC0DC0FE0FE0FF0FF0FF0F F07F07F03E03E01C01C014117AA21D>II<07FC001FFF803F07C03F03E03F01E03F01F01E01F00001F00001F0003FF003FDF01F C1F03F01F07E01F0FC01F0FC01F0FC01F0FC01F07E02F07E0CF81FF87F07E03F18167E951B>97 DI<00FF8007FFE00F83 F01F03F03E03F07E03F07C01E07C0000FC0000FC0000FC0000FC0000FC0000FC00007C00007E00 007E00003E00301F00600FC0E007FF8000FE0014167E9519>I<0001FE000001FE0000003E0000 003E0000003E0000003E0000003E0000003E0000003E0000003E0000003E0000003E0000003E00 01FC3E0007FFBE000F81FE001F007E003E003E007E003E007C003E00FC003E00FC003E00FC003E 00FC003E00FC003E00FC003E00FC003E00FC003E007C003E007C003E003E007E001E00FE000F83 BE0007FF3FC001FC3FC01A237EA21F>I<00FE0007FF800F87C01E01E03E01F07C00F07C00F8FC 00F8FC00F8FFFFF8FFFFF8FC0000FC0000FC00007C00007C00007E00003E00181F00300FC07003 FFC000FF0015167E951A>I<003F8000FFC001E3E003C7E007C7E00F87E00F83C00F80000F8000 0F80000F80000F80000F8000FFFC00FFFC000F80000F80000F80000F80000F80000F80000F8000 0F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80007FF8007FF800 13237FA211>I<03FC1E0FFF7F1F0F8F3E07CF3C03C07C03E07C03E07C03E07C03E07C03E03C03 C03E07C01F0F801FFF0013FC003000003000003800003FFF801FFFF00FFFF81FFFFC3800FC7000 3EF0001EF0001EF0001EF0001E78003C7C007C3F01F80FFFE001FF0018217E951C>II<1C003F007F007F007F003F001C 000000000000000000000000000000FF00FF001F001F001F001F001F001F001F001F001F001F00 1F001F001F001F001F001F001F001F00FFE0FFE00B247EA310>I<0038007C00FE00FE00FE007C 0038000000000000000000000000000003FE03FE003E003E003E003E003E003E003E003E003E00 3E003E003E003E003E003E003E003E003E003E003E003E003E003E783EFC3EFC3CFC7C78F87FE0 1F800F2E83A311>II< FF00FF001F001F001F001F001F001F001F001F001F001F001F001F001F001F001F001F001F001F 001F001F001F001F001F001F001F001F001F001F001F001F001F00FFE0FFE00B237EA210>III<00 FE0007FFC00F83E01E00F03E00F87C007C7C007C7C007CFC007EFC007EFC007EFC007EFC007EFC 007EFC007E7C007C7C007C3E00F81F01F00F83E007FFC000FE0017167E951C>II<00FE030007FF87000FC1C7001F006F003F003F007E003F007E001F 007C001F00FC001F00FC001F00FC001F00FC001F00FC001F00FC001F00FC001F007E001F007E00 1F003E003F001F007F000FC1DF0007FF9F0001FC1F0000001F0000001F0000001F0000001F0000 001F0000001F0000001F0000001F000000FFE00000FFE01B207E951E>II<0FF3003FFF00781F00600700E003 00E00300F00300FC00007FE0007FF8003FFE000FFF0001FF00000F80C00780C00380E00380E003 80F00700FC0E00EFFC00C7F00011167E9516>I<01800001800001800001800003800003800007 80000780000F80003F8000FFFF00FFFF000F80000F80000F80000F80000F80000F80000F80000F 80000F80000F80000F80000F81800F81800F81800F81800F81800F830007C30003FE0000F80011 207F9F16>II I III<7FFFF0 7FFFF07C03E07007C0600FC0E01F80C01F00C03E00C07E0000FC0000F80001F00003F03007E030 07C0300F80701F80703F00603E00E07C03E0FFFFE0FFFFE014167E9519>II E /FN 13 117 df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df<3078FCFC7830060676851A>46 D<01FC0007FF001FFF801E03C03C01 C03C00E03C00E00000E00000E00001C00003C000078001FF0001FF0001FFC00003E00000F00000 70000078000038000038600038F00038F00078E000707000F07E03E03FFFC00FFF0001FC00151E 7E9D1A>51 D<000F80001F80003B80003B8000738000F38000E38001C38003C380038380078380 0F03800E03801E03803C0380380380780380F00380FFFFFEFFFFFEFFFFFE000380000380000380 000380000380000380003FF8007FFC003FF8171E7F9D1A>I<003E0001FF8003FFC007C1E00F00 E01E0F703C3FF0387FF07070F870E07870E078E1C038E1C038E1C038E1C038E1C038E1C038E1C0 38E1C03870E07070E0707070E0387FE03C3FC01E0F000F003807C0F803FFF001FFE0003F00151E 7E9D1A>64 D<003800007C00007C00006C0000EE0000EE0000EE0000C60000C60001C70001C700 01C70001C7000383800383800383800383800701C00701C007FFC007FFC00FFFE00E00E00E00E0 0E00E00E00E01C00707F01FCFF83FE7F01FC171E7F9D1A>I<007C3801FF3807FFF80F83F81E00 F81C0078380078380038700038700038700000E00000E00000E00000E00000E00000E00000E000 00E000007000007000387000383800383800381C00701E00F00F83E007FFC001FF80007C00151E 7E9D1A>67 D<7FFE00FFFF007FFF801C07C01C01E01C00F01C00701C00781C00381C00381C003C 1C001C1C001C1C001C1C001C1C001C1C001C1C001C1C001C1C003C1C00381C00381C00781C0070 1C00F01C01E01C07C07FFFC0FFFF007FFE00161E7F9D1A>II<7FFFFCFFFFFC7FFFFC0E001C0E001C0E001C0E001C0E00000E00000E00000E03800E 03800E03800FFF800FFF800FFF800E03800E03800E03800E00000E00000E00000E00000E00000E 00000E00000E00007FE000FFE0007FE000161E7F9D1A>I<00F8E003FEE007FFE00F07E01E03E0 3C01E03800E07000E07000E07000E0E00000E00000E00000E00000E00000E00000E00FF8E00FF8 E00FF8E000E07000E07000E07001E03801E03C03E01E03E00F07E007FFE003FEE000F8E0151E7E 9D1A>II<7F03F8FF87FC7F03F81C01E01C03C01C 03801C07001C0F001C1E001C1C001C38001C78001CF0001CF8001DF8001FDC001F9C001F0E001E 0F001E07001C07801C03801C01C01C01C01C00E01C00E01C00707F00FCFF81FE7F00FC171E7F9D 1A>75 D<7FE000FFF0007FE0000E00000E00000E00000E00000E00000E00000E00000E00000E00 000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E001C0E001C0E00 1C0E001C0E001C7FFFFCFFFFFC7FFFFC161E7F9D1A>I78 D<0FFE003FFF807FFFC07C07C07001C0F001E0E000E0E000E0E000E0E000E0E000E0E000 E0E000E0E000E0E000E0E000E0E000E0E000E0E000E0E000E0E000E0E000E0E000E0F001E0F001 E07001C07C07C07FFFC03FFF800FFE00131E7D9D1A>II82 D<03F1C00FFDC03FFFC07C0FC07003C0E0 03C0E001C0E001C0E001C0E000007000007800003F00001FF00007FE0000FF00000F800003C000 01C00000E00000E06000E0E000E0E000E0E001C0F001C0FC0780FFFF80EFFE00E3F800131E7D9D 1A>I<7FFFFEFFFFFEFFFFFEE0380EE0380EE0380EE0380E003800003800003800003800003800 003800003800003800003800003800003800003800003800003800003800003800003800003800 00380000380003FF8003FF8003FF80171E7F9D1A>II89 D E /FP 86 128 df<00000FC0F800003071 8E0000E0F31E0000C0F71E0001C0660C0001800E000003800E000003800E000003800E00000700 1C000007001C000007001C000007001C000007001C0000FFFFFFC0000E003800000E003800000E 003800000E003800001C007000001C007000001C007000001C007000001C007000001C00E00000 3800E000003800E000003800E000003800E000003801C000007001C000007001C000007001C000 007001C000006003800000E003800000E003800000E003000000C003000001C0070000718E0600 00F19E0C0000F31E180000620C3000003C07C00000272D82A21E>11 D<00000FE0000030180000 E01C0001C03C0001803C0003803800038000000380000007000000070000000700000007000000 070000000E000000FFFFE0000E00E0000E00E0000E01C0001C01C0001C01C0001C01C0001C0380 001C038000380380003803800038070000380700003807000070070800700E1000700E1000700E 1000700E2000E0062000E003C000E0000000E0000000C0000001C0000001C0000071800000F180 0000F3000000620000003C0000001E2D82A21B>I<00000FF3800000303F000000607F000000C0 7F000001C037000001800E000003800E000003800E000003800E000003801C000007001C000007 001C000007001C00000700380000FFFFF800000E003800000E003800000E007000000E00700000 0E007000001C007000001C00E000001C00E000001C00E000001C00E000003801C000003801C000 003801C000003801C20000380384000070038400007003840000700388000070018800007000F0 0000E000000000E000000000E000000000C000000000C00000007180000000F180000000F10000 000062000000003C00000000212D82A21D>I<00000FF01FE000003838601800006079C01C0000 C07B803C0001C033003C0001C00700380003800700000003800700000003800E00000003800E00 000007000E00000007000E00000007000E00000007001C000000FFFFFFFFE0000E001C00E0000E 001C00E0000E001C01C0000E003801C0000E003801C0001C003801C0001C00380380001C003803 80001C00700380001C00700380001C00700700003800700700003800700700003800E007080038 00E00E10003800E00E10007000E00E10007000E00E20007001C00620007001C003C0006001C000 0000E00180000000E00380000000C00380000000C00300000071C703000000F18F06000000F10F 0C0000006206180000003C03E00000002E2D82A22B>I<60F070703818180C04060972A219>18 D<0180038007800E000C00180030006000C0000A096FA219>I<00000200000400000400000800 0010001FA00070E000C0600180B00300B00701380E02380E04381C04381C08381C103838207038 20703840603880E01900C01901801A03000C0600061C0009F00010000020000020000040000080 0000171F7D9919>28 D<007000F001F001F001F001E001E001E003C003C003C003800380038007 00070007000600060006000C000C000C00080008000800000000000000000000007000F800F800 F000E0000C247AA30F>33 D<0C06001E0F003F1F803F1F801D0E80020100020100020100040200 040200080400100800201000402000804000110F78A219>I<0C1E3F3F1D020202040408102040 80080F75A20F>39 D<00008000010000020000040000080000100000300000600000C00000C000 0180000300000300000600000600000E00000C00001C0000180000180000380000300000300000 700000700000600000600000E00000E00000E00000C00000C00000C00000C00000C00000C00000 C00000C00000C00000C00000C00000C00000C00000400000600000600000200000300000100000 080000113278A414>I<0008000004000006000002000003000003000001000001800001800001 800001800001800001800001800001800001800001800001800001800001800003800003800003 80000300000300000700000700000600000600000E00000C00000C00001C000018000038000030 0000300000600000600000C0000180000180000300000600000400000800001000002000004000 00800000113280A414>I<000070000000600000006000000060000000E0000000C0000000C000 0000C0000001C0000001800000018000000180000003800000030000FFFFFFFCFFFFFFFC000700 00000600000006000000060000000E0000000C0000000C0000000C0000001C0000001800000018 00000018000000380000003000001E1E7A9A25>43 D<0E1E1E1E1E02020404080810204080070F 7D840F>II<70F8F8F0E005057A840F>I<000F800030C000E06001 C0700380700300700700700F00700E00701E00701E00701C00F03C00F03C00F03C00F07801E078 01E07801E07801E0F003C0F003C0F003C0F00380E00780E00780E00700E00F00E00E00E01C00E0 1C00E0380060700030E0001F000014227AA019>48 D<0001000300030006001E002E03CE001C00 1C001C001C0038003800380038007000700070007000E000E000E000E001C001C001C001C00380 0380038003800780FFFC10217AA019>I<000FC000106000603800801800801C01001C02201E02 101E04101E04101E04101E08203C08203C0840380840780880F00700E00001C000030000060000 180000200000C0000100000200000400100800301000202000605F80C063FFC040FF80807F0080 1E0017227CA019>I<000FC000307000C01801001C02001C04000C04401C08201C08201C08201C 08403808C0380700700000600001C000070000FC000007000003800003800001C00001C00001C0 0003C06003C0F003C0F00380E00780800700800E00801C0040380020F0001F800016227BA019> I<0000180000380000380000700000700000700000E00000E00000E00000C00001C00001800003 80000300000300000600000600000C00000C000018000010000031800061C00043800083800183 800303800207000407000807003FC700403E00800FF0000E00000E00001C00001C00001C00001C 00003800003800003800003000152B7EA019>I<00400400703800FFF000FFE000BF8000800001 0000010000010000010000020000020000023E0002C3000501800601C00401C00001E00001E000 01E00001E00001E00001E07003C0F003C0F003C0E00780800700800F00800E00401C0040380030 E0000F800016227BA019>I<0003E0000C1000380800603800C07801C078038030070000070000 0E00001E00001E00001C7C003C86003D03007A03807C03807801C07803C0F803C0F003C0F003C0 F003C0E00780E00780E00780E00700E00F00E00E00E01C0060180060300030E0000F800015227A A019>I<02780204FC0407FC040FFC080F0C181E04701803A03000602000406000C04000808001 80000380000300000700000600000E00000E00001C00001C00003C0000380000780000780000F0 0000F00000F00001E00001E00001E00003E00003C00003C000018000172279A019>I<000FC000 306000401000801801000803000C03000C06001807001807001007003007C06007E0C003F18001 FE0000FC0000FE00033F00061F800C07C01803C03001C06001C06000C0C000C0C000C0C00080C0 0180C00100C00200C006006008003030000FC00016227BA019>I<000FC000386000703000E030 01C0380380380780380700380F00380F00380F00381E00781E00781E00781E00F81E00F01C00F0 0E01F00E02F00605E00309E001F1E00003C00003C0000380000700000700600E00F00C00F01800 E0300080600041C0003F000015227BA019>I<07000F800F800F000E0000000000000000000000 0000000000000000000000007000F800F800F000E00009157A940F>I<00E001F001F001E001C0 000000000000000000000000000000000000000000000E001E001E001E001E0002000200040004 000800080010002000400080000C1F7D940F>I<0000030000000300000007000000070000000F 0000000F0000001F0000002F0000002F0000004F0000004F800000878000008780000107800002 07800002078000040780000407800008078000080780001007800030078000200780007FFF8000 4007C0008007C0008003C0010003C0030003C0020003C0040003C0040003C00C0003C03C0007C0 FF003FFC1E237DA224>65 D<00FFFFE0000F0038000F001C000F001E001E000E001E000F001E00 0F001E000F003C000E003C001E003C001E003C003C00780078007800F0007801E00078078000FF FF8000F001E000F000F000F0007801E0007801E0003801E0003C01E0003C03C0007803C0007803 C0007803C000F0078000F0078001E0078003C0078007000F801E00FFFFF00020227DA122>I<00 007F00800003808100000E00630000380027000070001F0000E0000E0001C0000E000380000E00 0700000E000F000004000E000004001E000004003C000004003C00000800780000000078000000 007800000000F000000000F000000000F000000000F000000000F000000000E000000000E00000 2000E000002000E000004000E000004000F0000080007000008000700001000038000200001800 0400001C0008000006003000000381C0000000FE000000212479A223>I<00FFFFF000000F003C 00000F000E00000F000700001E000380001E000380001E0001C0001E0001C0003C0001C0003C00 01E0003C0001E0003C0001E000780001E000780001E000780001E000780001E000F00003C000F0 0003C000F00003C000F00003C001E000078001E000078001E000070001E0000F0003C0000E0003 C0001C0003C0003C0003C00038000780007000078000E000078001C00007800700000F801C0000 FFFFF0000023227DA125>I<00FFFFFF80000F000780000F000180000F000180001E000180001E 000180001E000100001E000100003C000100003C000100003C010100003C010000007802000000 78020000007806000000780E000000FFFC000000F00C000000F00C000000F00C000001E0080000 01E008000001E008040001E000080003C000080003C000080003C000100003C000100007800020 000780006000078000C000078001C0000F8007C000FFFFFF800021227DA121>I<00FFFFFF000F 000F000F0003000F0003001E0003001E0003001E0002001E0002003C0002003C0002003C010200 3C010000780200007802000078060000780E0000FFFC0000F00C0000F00C0000F00C0001E00800 01E0080001E0080001E0000003C0000003C0000003C0000003C000000780000007800000078000 00078000000F800000FFFC000020227DA120>I<00007F00800003808100000E00630000380027 000070001F0000E0000E0001C0000E000380000E000700000E000F000004000E000004001E0000 04003C000004003C00000800780000000078000000007800000000F000000000F000000000F000 000000F000000000F0003FFC00E00001E000E00001E000E00001E000E00003C000E00003C000F0 0003C000700003C0007000078000380007800018000F80001C0013800006002300000381C10000 00FE000000212479A226>I<00FFF87FFC000F000780000F000780000F000780001E000F00001E 000F00001E000F00001E000F00003C001E00003C001E00003C001E00003C001E000078003C0000 78003C000078003C000078003C0000FFFFF80000F000780000F000780000F000780001E000F000 01E000F00001E000F00001E000F00003C001E00003C001E00003C001E00003C001E000078003C0 00078003C000078003C000078003C0000F8007C000FFF87FFC0026227DA124>I<00FFF8000F00 000F00000F00001E00001E00001E00001E00003C00003C00003C00003C00007800007800007800 00780000F00000F00000F00000F00001E00001E00001E00001E00003C00003C00003C00003C000 0780000780000780000780000F8000FFF80015227DA113>I<0007FFC000003C0000003C000000 3C00000078000000780000007800000078000000F0000000F0000000F0000000F0000001E00000 01E0000001E0000001E0000003C0000003C0000003C0000003C000000780000007800000078000 00078000000F0000000F0000380F0000780F0000F81E0000F81E0000F03C000040380000407000 0021E000001F8000001A237CA11A>I<00FFF807FC000F0001E0000F0001C0000F000100001E00 0200001E000400001E001000001E002000003C004000003C008000003C010000003C0400000078 0800000078180000007838000000787C000000F0BC000000F23C000000F41E000000F81E000001 F01F000001E00F000001E00F000001E00F800003C007800003C007800003C003C00003C003C000 078003C000078001E000078001E000078001E0000F8001F000FFF80FFE0026227DA125>I<00FF FC00000F8000000F0000000F0000001E0000001E0000001E0000001E0000003C0000003C000000 3C0000003C00000078000000780000007800000078000000F0000000F0000000F0000000F00000 01E0000001E0000001E0002001E0002003C0004003C0004003C0008003C0008007800180078001 000780030007800F000F803E00FFFFFE001B227DA11F>I<00FF800007FC000F80000F80000F80 001780000F80001780001780002F000013C0002F000013C0004F000013C0008F000023C0009E00 0023C0011E000023C0011E000023C0021E000043C0043C000043C0043C000043C0083C000041E0 083C000081E01078000081E02078000081E02078000081E04078000101E040F0000101E080F000 0101E100F0000101E100F0000200F201E0000200F201E0000200F401E0000200F801E0000400F8 03C0000400F003C0000400F003C0000C00E003C0001E00C007C000FFC0C07FFC002E227DA12C> I<00FF000FFC000F8001E0000F800180000FC000800013C001000013C001000011E001000011E0 01000021E002000020F002000020F002000020F002000040780400004078040000407804000040 3C040000803C080000803E080000801E080000801E080001001F100001000F100001000F100001 00079000020007A000020007A000020003E000020003E000040003C000040001C000040001C000 0C0001C0001E00008000FFC000800026227DA124>I<0000FE0000078380000C00E00038007000 70003800E0003801C0001C0380001C0700001C0F00001E1E00001E1C00001E3C00001E3C00001E 7800001E7800001E7800001EF000003CF000003CF000003CF0000078F0000078E0000078E00000 F0E00000F0E00001E0E00001C0F00003C0F00007807000070078000E0038001C001C0038000E00 E0000703800001FC00001F2479A225>I<00FFFFE0000F0038000F001E000F000E001E0007001E 0007001E0007001E0007003C000F003C000F003C000F003C001E0078001E0078003C0078007800 7800E000F003C000FFFE0000F0000000F0000001E0000001E0000001E0000001E0000003C00000 03C0000003C0000003C00000078000000780000007800000078000000F800000FFF8000020227D A121>I<0000FE0000078380000C00E0003800700070003800E0003801C0003C0380001C070000 1C0F00001E1E00001E1E00001E3C00001E3C00001E7800001E7800001E7800001EF000003CF000 003CF000003CF0000038F0000078E0000078E00000F0E00000F0E00001E0E00001C0E00003C0F0 1E03807061070070810E0038811C001C8138000E81E0000783804001FD00400001004000018080 0001818000018100000387000001FE000001FE000001FC000000F0001F2D79A225>I<00FFFFC0 000F0070000F003C000F001C001E000E001E000E001E000F001E000F003C001E003C001E003C00 1E003C003C0078003800780070007801E00078078000FFFC0000F00E0000F0070000F0038001E0 03C001E003C001E003C001E003C003C0078003C0078003C0078003C0078007800F0007800F0107 800F01078007020F800702FFF8038C000000F020237DA124>I<0001F020000E0C40001802C000 3001C0006001C000E0018000C0018001C0018001C0018003C0010003C0010003C0000003C00000 03E0000001F8000001FF000000FFE000007FF000001FF8000003FC0000007C0000003C0000001E 0000001E0000001E0020001C0020001C0020001C00200018006000380060003000700060007000 C000C8018000C607000081FC00001B247DA21B>I<1FFFFFF81E03C0381803C0183003C0182007 8018200780184007801040078010400F0010800F0010800F0010000F0000001E0000001E000000 1E0000001E0000003C0000003C0000003C0000003C000000780000007800000078000000780000 00F0000000F0000000F0000000F0000001E0000001E0000001E0000001E0000003E00000FFFF00 001D2277A123>I<3FFE03FF03C0007803C0006003C00020078000400780004007800040078000 400F0000800F0000800F0000800F0000801E0001001E0001001E0001001E0001003C0002003C00 02003C0002003C0002007800040078000400780004007800040070000800F0000800F000100070 00100070002000700040003000400038018000180200000E0C000003F00000202377A124>III<007FF81FF8000FC007C000078003000007C002000003C004000003 C008000003E010000001E030000001E020000001F040000000F080000000F100000000FA000000 007C000000007C000000007C000000003C000000003C000000007E000000009E000000011E0000 00031F000000060F000000040F000000080F80000010078000002007C000004007C00000C003C0 00018003E000010001E000070001E0001F0003F000FFC01FFE0025227EA124>II<007FFFFE007E001E0078003C0060007800C000 F000C001E0008003E0008003C00100078001000F0001001E0000003C0000007C00000078000000 F0000001E0000003C00000078000000F8000000F0000001E0000003C00400078004000F0008001 F0008001E0008003C00100078001000F0003001E0006001E0006003C001E0078007C00FFFFFC00 1F227DA11E>I<000FF0000FF0000C000018000018000018000018000030000030000030000030 0000600000600000600000600000C00000C00000C00000C0000180000180000180000180000300 000300000300000300000600000600000600000600000C00000C00000C00000C00001800001800 00180000180000300000300000300000300000600000600000600000600000FF0000FF00001431 7EA40F>I<010080020100040200080400100800201000201000402000402000804000B85C00FC 7E00FC7E00F87C00703800110F73A219>I<000FF0000FF0000030000060000060000060000060 0000C00000C00000C00000C0000180000180000180000180000300000300000300000300000600 000600000600000600000C00000C00000C00000C00001800001800001800001800003000003000 00300000300000600000600000600000600000C00000C00000C00000C000018000018000018000 018000FF0000FF0000143182A40F>I<00F8C00185C00705C00E03800E03801C03803C03803807 00780700780700780700F00E00F00E00F00E00F00E10F01C20701C20703C20305C40308C400F07 8014157B9419>97 D<03C03F8003800380038007000700070007000E000E000E000E001C001CF8 1D0C1E0E3C0638073807380F700F700F700F700FE01EE01EE01EE03CE038E038607060E031C01F 0010237BA216>I<007E0001C1000301800703800E07801C07803C000038000078000078000078 0000F00000F00000F00000F00000F00100700100700200300C001830000FC00011157B9416>I< 00003C0003F80000380000380000380000700000700000700000700000E00000E00000E00000E0 0001C000F9C00185C00705C00E03800E03801C03803C0380380700780700780700780700F00E00 F00E00F00E00F00E10F01C20701C20703C20305C40308C400F078016237BA219>I<00F803840E 021C023C0238027804F018FFE0F000F000E000E000E000E000E002E0026004701830600F800F15 7A9416>I<00003E0000470000CF00018F00018600038000038000038000070000070000070000 0700000700000E0000FFF0000E00000E00000E00001C00001C00001C00001C00001C0000380000 380000380000380000380000700000700000700000700000700000E00000E00000E00000E00000 C00001C00001C000718000F18000F300006200003C0000182D82A20F>I<001F180030B800E0B8 01C07001C0700380700780700700E00F00E00F00E00F00E01E01C01E01C01E01C01E01C01E0380 0E03800E0780060B8006170001E700000700000700000E00000E00000E00701C00F01800F03000 60E0003F8000151F7E9416>I<00F0000FE00000E00000E00000E00001C00001C00001C00001C0 00038000038000038000038000070000071F0007218007C0C00F00E00F00E00E00E00E00E01C01 C01C01C01C01C01C01C0380380380380380380380704700708700E08700E10700610E006206003 C016237DA219>I<00C001E001C001C0000000000000000000000000000000001C002300430043 008700870087000E000E001C001C001C00380038003840708070807080710032001C000C217BA0 0F>I<0000E00001E00001E00000C0000000000000000000000000000000000000000000000000 001E00002300004380008380008380010380010380000700000700000700000700000E00000E00 000E00000E00001C00001C00001C00001C00003800003800003800003800007000007000007000 70E000F0C000F180006300003C0000132B82A00F>I<00F0000FE00000E00000E00000E00001C0 0001C00001C00001C0000380000380000380000380000700000701E0070210070C700E10F00E10 F00E20600E40001D80001E00001FC0001C7000383800383800381C00381C207038407038407038 40701880E01880600F0014237DA216>I<01E01FC001C001C001C0038003800380038007000700 070007000E000E000E000E001C001C001C001C0038003800380038007000700070007100E200E2 00E200E200640038000B237CA20C>I<1C0F80F8002610C10C0047606606008780780700878078 0700870070070087007007000E00E00E000E00E00E000E00E00E000E00E00E001C01C01C001C01 C01C001C01C01C001C01C038203803803840380380704038038070803803803080700700310030 03001E0024157B9428>I<1C0F002631C04740C08780E08780E08700E08700E00E01C00E01C00E 01C00E01C01C03801C03801C03801C0704380708380E08380E103806107006203003C017157B94 1B>I<007E0001C3000381800701C00E01C01C01E03C01E03801E07801E07801E07801E0F003C0 F003C0F00380F00780700700700E00700C0030180018700007C00013157B9419>I<01C1F00262 1804741C08780C08700E08700E08701E00E01E00E01E00E01E00E01E01C03C01C03C01C03C01C0 7803807003807003C0E003C1C0072380071E000700000700000E00000E00000E00000E00001C00 001C00001C0000FFC000171F7F9419>I<00F8400184C00705C00E03800E03801C03803C038038 0700780700780700780700F00E00F00E00F00E00F00E00F01C00701C00703C00305C0030B8000F 380000380000380000700000700000700000700000E00000E00000E0000FFE00121F7B9416>I< 1C1F002620804741C08783C08703C08701808700000E00000E00000E00000E00001C00001C0000 1C00001C000038000038000038000038000070000030000013157B9415>I<00FC000183000200 800401800C03800C03000C00000F00000FF00007FC0003FE00003E00000F00000700700700F006 00F00600E004004008002030001FC00011157D9414>I<00C001C001C001C001C0038003800380 03800700FFF8070007000E000E000E000E001C001C001C001C0038003800380038107020702070 40708031001E000D1F7C9E10>I<1E00602300E04380E04381C08381C08701C08701C00703800E 03800E03800E03801C07001C07001C07001C07081C0E10180E101C0E101C1E200C262007C3C016 157B941A>I<1E03802307C04387C04383C08381C08700C08700C00700800E00800E00800E0080 1C01001C01001C01001C02001C02001C04001C08001C08000C300003C00013157B9416>I<1E00 60E02300E1F04380E1F04381C0F08381C0708701C0308701C030070380200E0380200E0380200E 0380201C0700401C0700401C0700401C0700801C0700801C0701001C0F01000C0F020006138C00 03E0F0001D157B9420>I<03C1E0046210083470103CF02038F020386020380000700000700000 700000700000E00000E00000E00000E02061C040F1C040F1C080E2C100446200383C0014157D94 16>I<1E00302300704380704380E08380E08700E08700E00701C00E01C00E01C00E01C01C0380 1C03801C03801C03801C07001C07001C07001C0F000C3E0003CE00000E00000E00001C00601C00 F03800F03000E0600080C0004380003E0000151F7B9418>I<01E02003F06007F8C0041F800801 000802000004000008000010000020000040000080000100000200000400800801001003003F06 0061FC0040F80080700013157D9414>III< 3038787CF87CF87870700E0573A119>127 D E /FQ 105 128 df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df45 D<000000FFC0006000000007FFF800E00000003FFFFE00E0000000FFC01F01E0000003FE0007C3 E0000007F80001E7E000001FE00000F7E000003FC000003FE000007F8000001FE00000FF000000 1FE00001FE0000000FE00003FC00000007E00003F800000003E00007F800000003E0000FF00000 0001E0000FF000000001E0001FE000000001E0001FE000000000E0003FE000000000E0003FC000 000000E0003FC00000000060007FC00000000060007FC00000000060007FC0000000006000FF80 000000000000FF80000000000000FF80000000000000FF80000000000000FF80000000000000FF 80000000000000FF80000000000000FF80000000000000FF80000000000000FF80000000000000 FF80000000000000FF80000000000000FF800000FFFFFF807FC00000FFFFFF807FC00000FFFFFF 807FC00000007FF0003FC00000001FE0003FC00000001FE0003FE00000001FE0001FE00000001F E0001FE00000001FE0000FF00000001FE0000FF00000001FE00007F80000001FE00003FC000000 1FE00003FC0000001FE00001FE0000001FE00000FF0000001FE000007F8000003FE000003FC000 003FE000001FE000007FE0000007F80000E7E0000003FE0003C3E0000000FFC01F81E00000003F FFFE00E000000007FFF8006000000000FFC0000000393D7BBB44>71 D80 D 82 D<000FF80060003FFF00E000FFFFC0E003F807E1E007E000FBE00FC0003FE01F80001FE03F 00000FE03E000007E07E000003E07E000003E07C000001E0FC000001E0FC000000E0FC000000E0 FC000000E0FE00000060FE00000060FE00000060FF00000060FF800000007FC00000007FE00000 007FF80000003FFF8000001FFFF800001FFFFF80000FFFFFF00007FFFFF80003FFFFFE0000FFFF FF00003FFFFF800007FFFFC000007FFFC0000007FFE00000007FE00000003FF00000001FF00000 000FF000000007F800000003F8C0000003F8C0000003F8C0000001F8C0000001F8C0000001F8E0 000001F8E0000001F8E0000001F0F0000001F0F0000003F0F8000003E0FC000007E0FE000007C0 FF00000FC0FFC0001F80FBF0003F00F0FE00FE00E03FFFF800E00FFFE000C001FF8000253D7BBB 30>I<3FFFFFFFFFFFF83FFFFFFFFFFFF83FFFFFFFFFFFF83FE001FF8007F83F0000FF0001F87C 0000FF00007C780000FF00003C780000FF00003C700000FF00001C700000FF00001C600000FF00 000C600000FF00000C600000FF00000C600000FF00000C600000FF00000CE00000FF00000EC000 00FF000006C00000FF000006C00000FF000006C00000FF000006000000FF000000000000FF0000 00000000FF000000000000FF000000000000FF000000000000FF000000000000FF000000000000 FF000000000000FF000000000000FF000000000000FF000000000000FF000000000000FF000000 000000FF000000000000FF000000000000FF000000000000FF000000000000FF000000000000FF 000000000000FF000000000000FF000000000000FF000000000000FF000000000000FF00000000 0000FF000000000000FF000000000000FF000000000000FF000000000000FF000000000000FF00 0000000000FF000000000000FF000000000000FF000000000000FF000000000000FF0000000000 03FFC00000001FFFFFFFF800001FFFFFFFF800001FFFFFFFF800373B7DBA3E>I<003FC0000001 FFF8000007C07E00000E001F80001E000FC0003F8007E0003FC007E0003FC003F0003FC003F000 3FC001F8001F8001F8000F0001F800000001F800000001F800000001F800000001F80000001FF8 000007FFF800003FF9F80000FF01F80003F801F80007F001F8001FE001F8001FC001F8003F8001 F8007F0001F8007F0001F800FF0001F80CFE0001F80CFE0001F80CFE0001F80CFE0003F80CFE00 03F80CFF0007F80C7F000EF80C3F800C7C181FC03C7E380FE0703FF003FFE01FE0007F800F8026 287CA62B>97 D<0003FE00001FFFC0007E01F000F8003801F0003C03E000FE07E001FE0FC001FE 1F8001FE1F8001FE3F8000FC3F0000787F0000007F0000007E000000FE000000FE000000FE0000 00FE000000FE000000FE000000FE000000FE000000FE000000FE0000007E0000007F0000007F00 00007F0000033F0000033F8000071F8000060FC0000E0FC0000C07E0001C03F0003800F800F000 7E03C0001FFF000003FC0020287DA626>99 D<00000007E000000003FFE000000003FFE0000000 03FFE0000000001FE00000000007E00000000007E00000000007E00000000007E00000000007E0 0000000007E00000000007E00000000007E00000000007E00000000007E00000000007E0000000 0007E00000000007E00000000007E00000000007E00000000007E00000000007E0000001FC07E0 00000FFF87E000003F03C7E00000FC00F7E00001F0003FE00003E0001FE00007E0001FE0000FC0 000FE0001F800007E0001F800007E0003F000007E0003F000007E0007F000007E0007F000007E0 007E000007E000FE000007E000FE000007E000FE000007E000FE000007E000FE000007E000FE00 0007E000FE000007E000FE000007E000FE000007E0007E000007E0007E000007E0007F000007E0 007F000007E0003F000007E0003F800007E0001F80000FE0000FC0000FE0000FC0001FE00007E0 003FE00003F00077F80000F800E7FFC0007E03C7FFC0001FFF07FFC00003FC07E0002A3D7DBB30 >I<0003FC0000001FFF0000007E07C00000F803F00003F001F80007E000FC0007C0007C000FC0 007E001F80003E003F80003F003F00001F003F00001F007F00001F807F00001F807E00001F80FE 00001F80FE00001F80FFFFFFFF80FFFFFFFF80FE00000000FE00000000FE00000000FE00000000 FE00000000FE000000007E000000007F000000007F000000003F000001803F000001801F800003 801F800003000FC000070007E0000E0003E0000C0001F0003C0000FC007000003F01E000000FFF 80000001FE000021287EA626>I<00003F000001FFC00003E0F0000FC3F0001F87F8003F07F800 3F07F8007E07F8007E07F800FE03F000FC000000FC000000FC000000FC000000FC000000FC0000 00FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC0000FFFFFC00FFFFFC 00FFFFFC0000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC 000000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC000000 FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC0000 00FC000000FC000001FE00007FFFFC007FFFFC007FFFFC001D3D7FBC1A>I<0007F001F8003FFE 0FFC00FC1FBE3E01F007F03E03E003E03E07E003F01C07C001F0000FC001F8000F8000F8001F80 00FC001F8000FC001F8000FC001F8000FC001F8000FC001F8000FC001F8000FC000F8000F8000F C001F80007C001F00007E003F00003E003E00003F007C00003FC1F8000073FFE00000607F00000 0E000000000E000000000E000000000F000000000F000000000F8000000007C000000007FFFFC0 0003FFFFFC0003FFFFFF0000FFFFFFC003FFFFFFE00F80003FF01F000007F03E000003F87C0000 01F87C000000FCFC000000FCF80000007CF80000007CF80000007CF80000007CFC000000FC7C00 0000F87E000001F83E000001F01F000003E00FC0000FC003E0001F0001FC00FE00003FFFF00000 07FF800027397EA52B>I<01F800000000FFF800000000FFF800000000FFF80000000007F80000 000001F80000000001F80000000001F80000000001F80000000001F80000000001F80000000001 F80000000001F80000000001F80000000001F80000000001F80000000001F80000000001F80000 000001F80000000001F80000000001F80000000001F80000000001F807F8000001F81FFE000001 F8781F800001F8E00FC00001F9C007E00001FB8007E00001FF0007E00001FE0003F00001FE0003 F00001FC0003F00001FC0003F00001FC0003F00001F80003F00001F80003F00001F80003F00001 F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001F80003 F00001F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001 F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001F80003F00003FC0007 F800FFFFF1FFFFE0FFFFF1FFFFE0FFFFF1FFFFE02B3C7EBB30>I<01C00007F0000FF8000FF800 0FF8000FF8000FF80007F00001C000000000000000000000000000000000000000000000000000 00000000000000000001F8007FF8007FF8007FF80007F80001F80001F80001F80001F80001F800 01F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F800 01F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80003FC00FFFFE0 FFFFE0FFFFE0133A7FB917>I<01F800FFF800FFF800FFF80007F80001F80001F80001F80001F8 0001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F8 0001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F8 0001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F8 0001F80001F80001F80001F80001F80001F80001F80001F80003FC00FFFFF0FFFFF0FFFFF0143C 7FBB17>108 D<01F803F80003F80000FFF81FFF001FFF0000FFF87C0FC07C0FC000FFF8E007E0 E007E00007F9C003E1C003E00001FB8003F38003F00001FF0003F70003F00001FE0001FE0001F8 0001FE0001FE0001F80001FC0001FC0001F80001FC0001FC0001F80001FC0001FC0001F80001F8 0001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F8 0001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F8 0001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F8 0001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F8 0001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F8 0003FC0003FC0003FC00FFFFF0FFFFF0FFFFF0FFFFF0FFFFF0FFFFF0FFFFF0FFFFF0FFFFF04426 7EA549>I<01F807F80000FFF81FFE0000FFF8781F8000FFF8E00FC00007F9C007E00001FB8007 E00001FF0007E00001FE0003F00001FE0003F00001FC0003F00001FC0003F00001FC0003F00001 F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001F80003 F00001F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001 F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001F80003 F00001F80003F00001F80003F00003FC0007F800FFFFF1FFFFE0FFFFF1FFFFE0FFFFF1FFFFE02B 267EA530>I<0001FE0000000FFFC000003F03F00000F8007C0001F0003E0003E0001F0007C000 0F800F800007C00F800007C01F000003E03F000003F03F000003F03F000003F07E000001F87E00 0001F87E000001F8FE000001FCFE000001FCFE000001FCFE000001FCFE000001FCFE000001FCFE 000001FCFE000001FCFE000001FC7E000001F87E000001F87F000003F83F000003F03F000003F0 1F000003E01F800007E00F800007C007C0000F8003E0001F0001F0003E0000F8007C00003F03F0 00000FFFC0000001FE000026287EA62B>I<01F80FF00000FFF83FFE0000FFF8F01F8000FFF9C0 0FC00003FB8007F00001FF0003F80001FE0001FC0001FC0000FC0001F80000FE0001F800007F00 01F800007F0001F800003F8001F800003F8001F800003F8001F800003F8001F800001FC001F800 001FC001F800001FC001F800001FC001F800001FC001F800001FC001F800001FC001F800001FC0 01F800001FC001F800003F8001F800003F8001F800003F8001F800003F0001F800007F0001F800 007E0001FC0000FE0001FC0000FC0001FE0001F80001FF0003F00001FB8007E00001F9C00FC000 01F8F03F000001F87FFC000001F80FE0000001F80000000001F80000000001F80000000001F800 00000001F80000000001F80000000001F80000000001F80000000001F80000000001F800000000 01F80000000001F80000000003FC00000000FFFFF0000000FFFFF0000000FFFFF00000002A377E A530>I<03F00F80FFF03FE0FFF0F1F0FFF1C3F807F383F801F303F801F703F801F601F001FE00 4001FC000001FC000001FC000001FC000001F8000001F8000001F8000001F8000001F8000001F8 000001F8000001F8000001F8000001F8000001F8000001F8000001F8000001F8000001F8000001 F8000001F8000001F8000001F8000001F8000001F8000003FC0000FFFFF800FFFFF800FFFFF800 1D267EA522>114 D<007F818003FFE3800F807F801E001F803C000F807800078070000380F000 0380F0000380F0000180F8000180F8000180FC000180FE0000007F8000007FFC00003FFFC0001F FFF0000FFFFC0007FFFE0001FFFF00001FFF800000FFC000001FC0C0000FE0C00007E0C00003E0 E00003E0E00001E0E00001E0F00001E0F00001E0F80001C0F80003C0FC000380FE000780FF000F 00F3C03E00E0FFF800C03FC0001B287DA622>I<00180000001800000018000000180000001800 0000380000003800000038000000380000007800000078000000F8000000F8000001F8000003F8 000007F800001FFFFF00FFFFFF00FFFFFF0001F8000001F8000001F8000001F8000001F8000001 F8000001F8000001F8000001F8000001F8000001F8000001F8000001F8000001F8000001F80000 01F8000001F8000001F8000001F8018001F8018001F8018001F8018001F8018001F8018001F801 8001F8018001F8018001F8018000FC038000FC0300007C0300007E0700003F0E00000FFC000003 F00019367EB421>I<01F80003F000FFF801FFF000FFF801FFF000FFF801FFF00007F8000FF000 01F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001F800 03F00001F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001F80003F000 01F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001F80003F00001F800 03F00001F80003F00001F80003F00001F80003F00001F80007F00001F80007F00001F80007F000 01F8000FF00000F8000FF00000FC001FF000007C003BFC00007E0073FFE0001F81E3FFE0000FFF 83FFE00001FE03F0002B277EA530>I121 D<1FFFFFFE1FFFFFFE1FC001FE 1F0001FC1E0003F81C0007F0180007F038000FE038001FC030003FC030003F8030007F003000FE 003000FE000001FC000003F8000007F8000007F000000FE000001FC000003FC000003F8006007F 000600FE000600FE000601FC000603F8000E07F8000E07F0000E0FE0000C1FC0001C1FC0001C3F 80003C7F00007CFF0003FCFFFFFFFCFFFFFFFC1F257EA426>I E end %%EndProlog %%BeginSetup %%Feature: *Resolution 300 TeXDict begin %%EndSetup %%Page: 1 1 bop 257 45 a FR(Regularit)n(y)32 b(Prop)r(erties)e(and)e(P)n(athologies)193 148 y(of)h(P)n(osition-Space)h(Renormalization-Group)668 252 y(T)-7 b(ransformations)709 475 y FQ(Aernout)16 b(C.)g(D.)g(v)m(an)h(En)o (ter)633 538 y FP(Institute)i(for)e(The)n(or)n(etic)n(al)g(Physics)682 595 y(R)o(ijksuniversiteit)i(Gr)n(oningen)829 652 y(P.O.)f(Box)g(800)760 709 y(9747)f(A)o(G)g(Gr)n(oningen)726 766 y(THE)h(NETHERLANDS)680 829 y FO(AENTER@RUGT)o(H4)o(.TH)o(.RU)o(G.N)o(L)772 984 y FQ(Rob)q(erto)f(F)l (ern\023)-24 b(andez)647 1047 y FP(Institut)18 b(de)g(Physique)g(Th)o(\023) -24 b(eorique)524 1104 y(Ec)n(ole)19 b(Polyte)n(chnique)g(F)o(\023)-24 b(ed)o(\023)g(er)n(ale)18 b(de)f(L)n(ausanne)800 1161 y(PHB)h({)g(Ecublens) 768 1218 y(CH{1015)f(L)n(ausanne)791 1275 y(SWITZERLAND)706 1338 y FO(FERNANDE@E)o(LD)o(P.E)o(PFL)o(.CH)826 1494 y FQ(Alan)f(D.)g(Sok)m (al)734 1557 y FP(Dep)n(artment)h(of)h(Physics)753 1614 y(New)g(Y)l(ork)g (University)763 1671 y(4)f(Washington)h(Plac)n(e)747 1728 y(New)h(Y)l(ork,)e (NY)h(10003)925 1785 y(USA)744 1848 y FO(SOKAL@ACF3.)o(NYU)o(.E)o(DU)752 2027 y FN(Octob)r(er)i(16,)f(1992)60 2262 y FP(Short)e(title:)26 b FQ(Renormalization-Group)16 b(P)o(athologies)60 2369 y FM(KEY)24 b(W)n(ORDS:)e FQ(Renormalization)d(group;)24 b(p)q(osition-space)e (renormalization;)g(real-space)60 2430 y(renormalization;)g(decimation)e (transformation;)k(ma)s(jorit)o(y-rule)19 b(transformation;)24 b(Kadano\013)60 2490 y(transformation;)14 b(blo)q(c)o(k-spin)f (transformation;)h(relativ)o(e)e(en)o(trop)o(y;)h(large)g(deviations;)h (Gri\016ths-)60 2550 y(P)o(earce)d(pathologies;)i(Gibbs)f(measure;)g (non-Gibbsian)h(measure;)e(quasilo)q(calit)o(y;)h(Pirogo)o(v-Sinai)60 2610 y(theory;)k(F)l(ermat's)e(last)j(theorem.)p eop %%Page: 2 2 bop 875 91 a FL(Abstract)250 176 y FK(W)l(e)13 b(reconsider)i(the)e (conceptual)h(foundations)g(of)f(the)g(renormalization-group)h(\(R)o(G\))182 232 y(formalism,)19 b(and)f(pro)o(v)o(e)g(some)g(rigorous)g(theorems)g(on)g (the)g(regularit)o(y)h(prop)q(erties)g(and)182 289 y(p)q(ossible)j (pathologies)f(of)f(the)h(R)o(G)f(map.)36 b(Regarding)21 b(regularit)o(y)l(,) h(w)o(e)e(sho)o(w)g(that)g(the)182 345 y(R)o(G)14 b(map,)g(de\014ned)i(on)e (a)h(suitable)g(space)g(of)f(in)o(teractions)h(\(=)f(formal)g (Hamiltonians\),)i(is)182 401 y(alw)o(a)o(ys)f(single-v)m(alued)20 b(and)c(Lipsc)o(hitz)i(con)o(tin)o(uous)f(on)f(its)h(domain)g(of)e (de\014nition.)25 b(This)182 458 y(rules)14 b(out)f(a)g(recen)o(tly)h(prop)q (osed)g(scenario)g(for)f(the)g(R)o(G)h(description)h(of)e(\014rst-order)g (phase)182 514 y(transitions.)20 b(On)14 b(the)g(pathological)h(side,)g(w)o (e)f(mak)o(e)f(rigorous)h(some)f(argumen)o(ts)g(of)h(Grif-)182 571 y(\014ths,)e(P)o(earce)g(and)h(Israel,)g(and)f(pro)o(v)o(e)g(in)h(sev)o (eral)g(cases)f(that)f(the)i(renormalized)g(measure)182 627 y(is)j(not)f(a)f(Gibbs)i(measure)g(for)e(an)o(y)h(reasonable)h(in)o (teraction.)k(This)c(means)f(that)g(the)g(R)o(G)182 684 y(map)g(is)g (ill-de\014ned)q(,)i(and)e(that)g(the)g(con)o(v)o(en)o(tional)g(R)o(G)g (description)i(of)d(\014rst-order)h(phase)182 740 y(transitions)g(is)h(not)f (univ)o(ersally)i(v)m(alid.)k(F)l(or)15 b(decimation)h(or)f(Kadano\013)f (transformations)182 797 y(applied)23 b(to)e(the)g(Ising)h(mo)q(del)g(in)g (dimension)h FJ(d)f FI(\025)h FK(3,)f(these)f(pathologies)h(o)q(ccur)f(in)h (a)182 853 y(full)17 b(neigh)o(b)q(orho)q(o)q(d)g FI(f)p FJ(\014)f(>)e(\014) 688 860 y FH(0)708 853 y FJ(;)g FI(j)p FJ(h)p FI(j)g FJ(<)g(\017)p FK(\()p FJ(\014)r FK(\))p FI(g)h FK(of)h(the)g(lo)o(w-temp)q(erature)f(part)h (of)f(the)h(\014rst-)182 910 y(order)i(phase-transition)i(surface.)29 b(F)l(or)18 b(blo)q(c)o(k-a)o(v)o(eraging)h(transformations)e(applied)k(to) 182 966 y(the)c(Ising)g(mo)q(del)h(in)f(dimension)i FJ(d)c FI(\025)g FK(2,)i(the)f(pathologies)h(o)q(ccur)h(at)e(lo)o(w)g(temp)q (eratures)182 1022 y(for)f(arbitrary)h(magnetic-\014eld)i(strength.)k(P)o (athologies)16 b(ma)o(y)f(also)h(o)q(ccur)g(in)h(the)g(critical)182 1079 y(region)j(for)f(Ising)h(mo)q(dels)g(in)h(dimension)g FJ(d)e FI(\025)h FK(4.)33 b(W)l(e)19 b(discuss)i(in)f(detail)h(the)e (distinc-)182 1135 y(tion)e(b)q(et)o(w)o(een)f(Gibbsian)i(and)f(non-Gibbsian) h(measures)e(and)h(the)g(p)q(ossible)h(o)q(ccurrence)182 1192 y(of)i(the)h(latter)g(in)h(other)e(situations,)i(and)f(giv)o(e)g(a)g(rather)f (complete)i(catalogue)f(of)f(the)182 1248 y(kno)o(wn)f(examples.)34 b(Finally)l(,)23 b(w)o(e)c(discuss)i(the)e(heuristic)j(and)e(n)o(umerical)h (evidence)g(on)182 1305 y(R)o(G)15 b(pathologies)h(in)g(the)f(ligh)o(t)h(of)e (our)h(rigorous)g(theorems.)60 1875 y FG(Con)n(ten)n(ts)60 1985 y FM(1)45 b(In)n(tro)r(duction)18 b(and)h(Summary)d(of)j(Results)795 b(7)133 2045 y FQ(1.1)50 b(General)16 b(In)o(tro)q(duction)32 b FF(:)25 b(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h (:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)88 b FQ(7)133 2105 y(1.2)50 b(Plan)17 b(of)f(This)h(P)o(ap)q(er)f(\(Or,)g(What)h(to)f(Read)h (and)g(What)f(to)h(Skip\))34 b FF(:)24 b(:)h(:)f(:)h(:)f(:)g(:)88 b FQ(9)133 2165 y(1.3)50 b(Summary)14 b(of)j(First)f(and)g(Second)h(F)l (undamen)o(tal)d(Theorems)f FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(10)133 2226 y(1.4)50 b(Summary)14 b(of)j(Gri\016ths-P)o(earce-Israel)e (P)o(athologies)k FF(:)24 b(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g (:)63 b FQ(14)60 2334 y FM(2)45 b(In\014nite-V)-5 b(olume)16 b(Lattice)i(Systems:)k(General)c(F)-5 b(ormalism)404 b(15)133 2395 y FQ(2.1)50 b(Con\014gurations,)18 b(Ev)o(en)o(ts,)d(F)l(unctions,)h (Measures)32 b FF(:)25 b(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g (:)63 b FQ(17)245 2455 y(2.1.1)56 b(Con\014gurations)19 b(and)d(Ev)o(en)o(ts) 27 b FF(:)e(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f (:)h(:)f(:)g(:)63 b FQ(18)245 2515 y(2.1.2)56 b(F)l(unctions)17 b(\(=)f(Observ)m(ables\))24 b FF(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f (:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(19)245 2575 y(2.1.3)56 b(Measures)51 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(20)133 2635 y(2.2)50 b(In)o(teractions)16 b(and)h(Hamiltonians)24 b FF(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)h(:)f(:)g(:)63 b FQ(22)963 2784 y(2)p eop %%Page: 3 3 bop 133 91 a FQ(2.3)50 b(Sp)q(eci\014cations)16 b(and)h(Gibbs)g(Measures)50 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)g(:)63 b FQ(25)245 152 y(2.3.1)56 b(Sp)q(eci\014cations)36 b FF(:)25 b(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h (:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(26)245 212 y(2.3.2)56 b(Gibbsian)17 b(Sp)q(eci\014cations)f(and)h(Gibbs)f(Measures)34 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(28)245 272 y(2.3.3)56 b(Quasilo)q(calit)o(y)46 b FF(:)25 b(:)f(:)h(:)f(:)g(:)h(:)f (:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f (:)g(:)63 b FQ(30)245 332 y(2.3.4)56 b(F)l(eller)15 b(Prop)q(ert)o(y)41 b FF(:)24 b(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f (:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(33)245 392 y(2.3.5)56 b(Ph)o(ysical)16 b(Equiv)m(alence)f(in)h(the)g(DLR)g(Sense)24 b FF(:)g(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(34)245 452 y(2.3.6)56 b(Structure)16 b(of)h(the)f(Space)g FE(G)s FQ(\(\005\))30 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(36)245 513 y(2.3.7)56 b(Conditioning)17 b(on)g(an)g(Arbitrary)e(Subset)h(of)h(Spins)42 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(41)133 573 y(2.4)50 b(T)l(ranslation)17 b(In)o(v)m(ariance)42 b FF(:)24 b(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h (:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(42)245 633 y(2.4.1)56 b(V)l(an)17 b(Ho)o(v)o(e)e(Con)o(v)o(ergence)26 b FF(:)f(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(42)245 693 y(2.4.2)56 b(T)l(ranslation-In)o(v)m(arian)o(t)17 b(Measures)45 b FF(:)24 b(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f (:)h(:)f(:)g(:)63 b FQ(43)245 753 y(2.4.3)56 b(Dividing)16 b(Out)g(T)l(ranslation)h(In)o(v)m(ariance)48 b FF(:)25 b(:)f(:)g(:)h(:)f(:)h (:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(46)245 814 y(2.4.4)56 b(Spaces)17 b(of)f(T)l(ranslation-In)o(v)m(arian)o(t)h(In)o(teractions)45 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(47)245 874 y(2.4.5)56 b(The)17 b(Observ)m(able)f FF(f)777 881 y FH(\010)820 874 y FQ(Corresp)q(onding)i(to)f(an)g(In)o(teraction)e(\010)e FF(:)25 b(:)f(:)h(:)f(:)g(:)63 b FQ(48)245 934 y(2.4.6)56 b(Ph)o(ysical)16 b(Equiv)m(alence)f(in)h(the)g(Ruelle)e(Sense)32 b FF(:)24 b(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(49)245 994 y(2.4.7)56 b(Estimates)16 b(on)g(Hamiltonians:)k(Bulk)15 b(v)o(ersus)h(Surface)g (E\013ects)i FF(:)24 b(:)h(:)f(:)g(:)63 b FQ(50)245 1054 y(2.4.8)56 b(Ho)o(w)17 b(to)f(Obtain)g(an)h(In)o(teraction)e(from)h(a)g(Gibbs)h(Measure) 42 b FF(:)25 b(:)f(:)h(:)f(:)g(:)63 b FQ(52)245 1115 y(2.4.9)56 b(T)l(ranslation-In)o(v)m(arian)o(t)17 b(Sp)q(eci\014cations)f(and)h(Gibbs)g (Measures)41 b FF(:)25 b(:)f(:)g(:)63 b FQ(52)133 1175 y(2.5)50 b(En)o(trop)o(y)l(,)14 b(Large)h(Deviations)e(and)h(the)g(V)l(ariational)g (Principle:)k(Finite-V)l(olume)245 1235 y(Case)35 b FF(:)25 b(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(55)245 1295 y(2.5.1)56 b(F)l(ree)16 b(Energy)29 b FF(:)24 b(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h (:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(55)245 1355 y(2.5.2)56 b(Relativ)o(e)15 b(En)o(trop)o(y)38 b FF(:)25 b(:)f(:)g(:)h(:)f(:)h(:)f(:)h (:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(56)245 1416 y(2.5.3)56 b(Large)18 b(Deviations)39 b FF(:)25 b(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)g(:)63 b FQ(58)245 1476 y(2.5.4)56 b(V)l(ariational)16 b(Principle)35 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:) f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(60)133 1536 y(2.6)50 b(En)o(trop)o(y)l(,)11 b(Large)h(Deviations)f(and)g(the)g(V)l (ariational)f(Principle:)17 b(In\014nite-V)l(olume)245 1596 y(Case)35 b FF(:)25 b(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h (:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)g(:)63 b FQ(61)245 1656 y(2.6.1)56 b(F)l(ree)16 b(Energy)g(Densit)o(y) g(\(\\Pressure"\))29 b FF(:)c(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f (:)h(:)f(:)g(:)63 b FQ(61)245 1716 y(2.6.2)56 b(Relativ)o(e)15 b(En)o(trop)o(y)h(Densit)o(y)d FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g (:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(64)245 1777 y(2.6.3)56 b(Large)18 b(Deviations)39 b FF(:)25 b(:)f(:)g(:)h(:)f(:)h(:) f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:) 63 b FQ(66)245 1837 y(2.6.4)56 b(V)l(ariational)16 b(Principle)35 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h (:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(68)245 1897 y(2.6.5)56 b(What)17 b(is)f(a)h(Phase)g(T)l(ransition?)23 b FF(:)h(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h (:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(70)245 1957 y(2.6.6)56 b(When)17 b(is)f(the)g(Relativ)o(e)e(En)o(trop)o(y)i(Densit)o(y)f (Zero?)28 b FF(:)c(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(73)245 2017 y(2.6.7)56 b(P)o(athologies)17 b(in)f(V)l(arious)g(In)o (teraction)g(Spaces)g FE(B)1334 2024 y FD(h)1380 2017 y FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(74)60 2126 y FM(3)45 b(P)n(osition-Space)24 b(Renormalization)e(T)-5 b(ransformations:) 35 b(Regularit)n(y)23 b(Prop-)133 2187 y(erties)1566 b(76)133 2247 y FQ(3.1)50 b(Basic)16 b(Set-Up)49 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)g(:)63 b FQ(76)245 2307 y(3.1.1)56 b(Renormalization)15 b(T)l(ransformation)h(Acting)g(on)h(Measures)36 b FF(:)25 b(:)f(:)h(:)f(:)g (:)63 b FQ(76)245 2367 y(3.1.2)56 b(Examples)41 b FF(:)25 b(:)f(:)h(:)f(:)h (:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)g(:)63 b FQ(78)245 2427 y(3.1.3)56 b(Renormalization)15 b(T)l(ransformation)h(Acting)g(on)h(In)o(teractions)i FF(:)24 b(:)h(:)f(:)g(:)63 b FQ(83)245 2488 y(3.1.4)56 b(A)16 b(Remark)f(on)i (Systems)d(of)j(Un)o(b)q(ounded)f(Spins)g FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)h(:)f(:)g(:)63 b FQ(84)133 2548 y(3.2)50 b(First)16 b(F)l(undamen)o(tal)f(Theorem:)20 b(Single-V)l(aluedness)15 b(of)i(the)f(R)l(T)g(Map)f FF(:)24 b(:)h(:)f(:)g(:)63 b FQ(85)133 2608 y(3.3)50 b(Second)17 b(F)l(undamen)o(tal)d(Theorem:)20 b(Con)o(tin)o(uit)o(y)15 b(Prop)q(erties)h(of)h(the)f(R)l(T)g(Map)36 b FF(:)63 b FQ(88)963 2784 y(3)p eop %%Page: 4 4 bop 60 91 a FM(4)45 b(Pro)n(v)m(ably)18 b(P)n(athological)h(Renormalization)d (T)-5 b(ransformations)325 b(91)133 152 y FQ(4.1)50 b(Gri\016ths-P)o (earce-Israel)15 b(P)o(athologies)i(I:)f(Israel's)f(Example)32 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)63 b FQ(91)245 212 y(4.1.1)56 b(In)o(tro)q(duction)20 b FF(:)k(:)h(:)f(:)h(:)f(:)g(:)h(:)f (:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f (:)g(:)63 b FQ(91)245 272 y(4.1.2)56 b(Israel's)16 b(Example:)j(Decimation)c (in)h FF(d)e FQ(=)g(2)46 b FF(:)24 b(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)g(:)63 b FQ(92)133 332 y(4.2)50 b(Gri\016ths-P)o(earce-Israel)15 b(P)o(athologies)i(I)q(I:)f(General)f(Metho)q(d)k FF(:)25 b(:)f(:)h(:)f(:)h (:)f(:)h(:)f(:)g(:)39 b FQ(101)133 392 y(4.3)50 b(Gri\016ths-P)o (earce-Israel)15 b(P)o(athologies)i(I)q(I)q(I:)f(Some)f(F)l(urther)g (Examples)26 b FF(:)e(:)h(:)f(:)g(:)39 b FQ(106)245 452 y(4.3.1)56 b(Israel's)16 b(Example)e(in)i(Dimension)f FF(d)f FE(\025)g FQ(3)44 b FF(:)25 b(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(107)245 513 y(4.3.2)56 b(Decimation)15 b(with)h(Spacing)h FF(b)c FE(\025)h FQ(3)46 b FF(:)24 b(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h (:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(112)245 573 y(4.3.3)56 b(Kadano\013)18 b(T)l(ransformation)f(with)f FF(p)h FQ(Finite)29 b FF(:)24 b(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(113)245 633 y(4.3.4)56 b(Ma)s(jorit)o(y-Rule)15 b(T)l(ransformation)25 b FF(:)g(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g (:)39 b FQ(115)245 693 y(4.3.5)56 b(Blo)q(c)o(k-Av)o(eraging)15 b(T)l(ransformations)33 b FF(:)25 b(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)g(:)39 b FQ(119)245 753 y(4.3.6)56 b(Generalization)16 b(to)h(Nonzero)f(Magnetic)f(Field)42 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)h(:)f (:)h(:)f(:)g(:)39 b FQ(122)133 814 y(4.4)50 b(Large-Cell)17 b(Renormalization)d(Maps)j(in)f(Dimension)f FF(d)1311 817 y FC(\()28 b(\))1317 805 y FE(\025)1369 814 y FQ(4)d FF(:)g(:)f(:)h(:)f(:)h(:)f (:)h(:)f(:)g(:)39 b FQ(127)245 874 y(4.4.1)56 b(Non-Gibbsianness)18 b(of)e(the)g(Sign)g(Field)f(of)i(an)g(\(An\)harmonic)d(Crystal)51 b(128)245 934 y(4.4.2)56 b(Non-Gibbsianness)12 b(of)f(Lo)q(cal)h(Nonlinear)e (F)l(unctions)h(of)g(an)g(\(An\)harmonic)401 994 y(Crystal)k FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(136)245 1054 y(4.4.3)56 b(Ph)o(ysical)16 b(In)o(terpretation)24 b FF(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)h(:)f(:)g(:)39 b FQ(137)245 1115 y(4.4.4)56 b(Application)16 b(to)g(the)g(Renormalization)f(Group)30 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)h(:)f(:)g(:)39 b FQ(138)133 1175 y(4.5)50 b(Other)16 b(Results)g(on)h(Non-Gibbsianness)g(and)g(Non-Quasilo)q(calit)o(y)32 b FF(:)24 b(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(139)245 1235 y(4.5.1)56 b(T)l(rivial)22 b(Example:)33 b(Con)o(v)o(ex)22 b(Com)o(bination)f(of)j (Gibbs)f(Measures)f(for)401 1295 y(Di\013eren)o(t)16 b(In)o(teractions)23 b FF(:)h(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)g(:)39 b FQ(139)245 1355 y(4.5.2)56 b(Restriction)16 b(of)g(the)g(Tw)o(o-Dimensional)g(Ising)g(Mo)q(del)g(to)g(an)h(Axis)h FF(:)24 b(:)g(:)39 b FQ(141)245 1416 y(4.5.3)56 b(F)l(ortuin-Kasteleyn)16 b(Random-Cluster)g(Mo)q(del)39 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:) f(:)g(:)39 b FQ(144)245 1476 y(4.5.4)56 b(Stationary)17 b(Measures)f(in)g (Nonequilibrium)d(Statistical)j(Mec)o(hanics)g FF(:)24 b(:)39 b FQ(147)245 1536 y(4.5.5)56 b(Comparison)17 b(of)f(Metho)q(ds)h(for)g(Pro)o (ving)f(Non-Gibbsianness)44 b FF(:)24 b(:)h(:)f(:)g(:)39 b FQ(149)245 1596 y(4.5.6)56 b(Are)16 b(\\Most")h(Measures)f(Non-Gibbsian?)29 b FF(:)c(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(151)60 1705 y FM(5)45 b(Discussion)1417 b(153)133 1765 y FQ(5.1)50 b(Numerically)13 b(Observ)o(ed)i(Discon)o(tin)o(uities)g(of)h (the)g(R)o(G)g(Map)30 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(153)245 1825 y(5.1.1)56 b(Statemen)o(t)15 b(of)h(the)g(Problem)39 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f (:)h(:)f(:)g(:)39 b FQ(153)245 1886 y(5.1.2)56 b(An)16 b(Idealized)f(Mo)q (del)h(of)g(P)o(arameter)f(Estimation)i FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)g(:)39 b FQ(154)245 1946 y(5.1.3)56 b(Application)16 b(to)g(the)g(Renormalization)f(Group)30 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)h(:)f(:)g(:)39 b FQ(159)133 2006 y(5.2)50 b(A)16 b(Remark)f(on)h (Dangerous)i(Irrelev)m(an)o(t)d(V)l(ariables)k FF(:)25 b(:)f(:)g(:)h(:)f(:)h (:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(162)60 2115 y FM(6)45 b(Conclusions)19 b(and)g(Op)r(en)f(Questions)866 b(166)133 2175 y FQ(6.1)50 b(Conclusions)37 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f (:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)h(:)f(:)g(:)39 b FQ(166)245 2235 y(6.1.1)56 b(Ho)o(w)17 b(Muc)o(h)e(of)i(the)f(Standard)h(Picture)e(of)i(the)f(R)o(G)g(Map)g(is)g(T)l (rue?)44 b FF(:)24 b(:)39 b FQ(166)245 2296 y(6.1.2)56 b(Resp)q(onses)18 b(to)e(Some)f(Ob)s(jections)j FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h (:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(167)245 2356 y(6.1.3)56 b(Where)16 b(Do)q(es)h(All)e(This)i(Lea)o(v)o(e)e(R)o(G)h(Theory?)32 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(169)245 2416 y(6.1.4)56 b(T)l(o)o(w)o(ards)17 b(a)g(Non-Gibbsian)g(P)o (oin)o(t)f(of)g(View)24 b FF(:)g(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f (:)g(:)39 b FQ(171)133 2476 y(6.2)50 b(Some)15 b(Op)q(en)i(Questions)49 b FF(:)24 b(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f (:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(172)963 2784 y(4)p eop %%Page: 5 5 bop 60 91 a FM(A)31 b(Pro)r(ofs)19 b(of)g(Some)e(Theorems)f(from)i(Section)g (2)664 b(174)133 152 y FQ(A.1)37 b(Pro)q(ofs)18 b(and)f(References)e(for)h (Section)g(2.1)31 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)g(:)39 b FQ(174)133 212 y(A.2)e(Pro)q(ofs)18 b(and)f(References)e(for)h(Section)g(2.3)31 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f (:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(175)133 272 y(A.3)e(Pro)q(ofs)18 b(and)f(References)e(for)h(Section)g(2.4)31 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f (:)g(:)39 b FQ(176)245 332 y(A.3.1)k(V)l(an)17 b(Ho)o(v)o(e)e(Con)o(v)o (ergence)26 b FF(:)f(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(176)245 392 y(A.3.2)k(T)l (ranslation-In)o(v)m(arian)o(t)17 b(Measures)45 b FF(:)24 b(:)h(:)f(:)h(:)f (:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(177)245 452 y(A.3.3)k(A)16 b(Digression)h(on)g(Subadditivit)o(y)24 b FF(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g (:)39 b FQ(177)245 513 y(A.3.4)k(A)16 b(Lemma)e(on)j(Sums)e(of)i(T)l (ranslates)49 b FF(:)25 b(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)g(:)39 b FQ(180)245 573 y(A.3.5)k(The)17 b(Quotien)o(t)e(Seminorm)34 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)h(:)f(:)g(:)39 b FQ(181)245 633 y(A.3.6)k(Closed)17 b(and)g(Compact)e(Sets)i(in)e FE(B)1057 615 y FH(0)1111 633 y FF(:)24 b(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g (:)39 b FQ(185)245 693 y(A.3.7)k(Ph)o(ysical)16 b(Equiv)m(alence)31 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h (:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(188)245 753 y(A.3.8)k(Estimates)16 b(on)g(Hamiltonians)f(and)i(Gibbs)f(Measures)29 b FF(:)24 b(:)h(:)f(:)h(:)f (:)h(:)f(:)g(:)39 b FQ(189)133 814 y(A.4)e(Pro)q(ofs)18 b(and)f(References)e (for)h(Section)g(2.5)31 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(193)133 874 y(A.5)e(Pro)q(ofs)18 b(and)f(References)e(for)h(Section)g(2.6)31 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f (:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(194)245 934 y(A.5.1)k(The)17 b(In\014nite-V)l(olume)c(Limit:)20 b(Pro)q(ofs)14 b FF(:)25 b(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(194)245 994 y(A.5.2)k(The)17 b(In\014nite-V)l(olume)c(Limit:)20 b(Coun)o(terexamples)12 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(196)60 1103 y FM(B)33 b(Lo)n(w-T)-5 b(emp)r(erature)16 b(Phase)j(Diagrams)f(and)h(Pirogo)n(v-Sinai)f(Theory)172 b(198)133 1163 y FQ(B.1)39 b(Generalities)15 b(on)i(Phase)g(Diagrams)30 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)h(:)f(:)g(:)39 b FQ(198)133 1224 y(B.2)g(Zero-T)l(emp)q(erature)15 b(Lattice)h(Systems.)k(General)c(F)l(ormalism)29 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(199)245 1284 y(B.2.1)45 b(Zero-T)l(emp)q(erature)15 b(Gibbs)i(Measures)47 b FF(:)24 b(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(200)245 1344 y(B.2.2)45 b(Ground-State)13 b(Con\014gurations.)21 b(Supp)q(ort)12 b(Prop)q(erties)f(of)g(Zero-T)l(emp)q(erature)401 1404 y(Gibbs)17 b(Measures)25 b FF(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:) h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(200)245 1464 y(B.2.3)45 b(Rigid)16 b(Ground-State)i(Con\014gurations)39 b FF(:)24 b(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(202)245 1524 y(B.2.4)45 b(Con)o(vivial)16 b(Con\014gurations.)23 b(Zero-T)l(emp)q(erature)15 b(En)o(trop)o(y)31 b FF(:)25 b(:)f(:)h(:)f(:)g(:) 39 b FQ(203)245 1585 y(B.2.5)45 b(Sup)q(er\015uous)18 b(Ground-State)f (Con\014gurations)k FF(:)j(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(206)245 1645 y(B.2.6)45 b(Non)o(uniqueness)16 b(of)g(Sp)q (eci\014cations)h(and)f(In)o(teractions)f FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f (:)g(:)39 b FQ(207)245 1705 y(B.2.7)45 b(Stabilit)o(y)15 b(and)i(w-Stabilit)o (y)29 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)g(:)39 b FQ(208)245 1765 y(B.2.8)45 b(V)l (ariational-Principle)15 b(Approac)o(h)45 b FF(:)24 b(:)h(:)f(:)h(:)f(:)g(:)h (:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(210)245 1825 y(B.2.9)45 b(In\014nite)16 b(Range)g(and)h(Lac)o(k)f(of)h(Quasilo)q (calit)o(y)36 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(212)133 1886 y(B.3)g(Phase)17 b(Diagrams)k FF(:)j(:)h(:)f(:)h(:)f(:)h(:) f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)h(:)f(:)g(:)39 b FQ(213)245 1946 y(B.3.1)45 b(Regular)17 b(Phase)f(Diagrams)29 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f (:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(213)245 2006 y(B.3.2)45 b(Zero-T)l(emp)q(erature)15 b(Regular)i(Phase)g(Diagrams)50 b FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(214)245 2066 y(B.3.3)45 b(Lo)o(w-T)l(emp)q(erature)14 b(Phase)h(Diagrams.)20 b(Scop)q(e)15 b(of)f(Pirogo)o(v-Sinai)g(Theory)r(216)133 2126 y(B.4)39 b(Pirogo)o(v-Sinai)17 b(Theory)26 b FF(:)f(:)f(:)h(:)f(:)g(:)h(:)f (:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f (:)g(:)39 b FQ(218)245 2187 y(B.4.1)45 b(Boundary)17 b(of)g(a)f (Con\014guration.)23 b(The)16 b(P)o(eierls)f(Condition)g FF(:)24 b(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(218)245 2247 y(B.4.2)45 b(Con)o(tours.)23 b(The)16 b(Generalized)f(P)o(eierls)g(Condition)g FF(:)24 b(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)g(:)39 b FQ(223)245 2307 y(B.4.3)45 b(Results)16 b(of)h(the)f(Theory)e FF(:)24 b(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g (:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(227)245 2367 y(B.4.4)45 b(Extensions)17 b(of)f(the)g(Theory)l(.)22 b(The)16 b(Random)g(Case)50 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(233)133 2427 y(B.5)g(Application)16 b(to)g(the)g(Examples)f(of)h (Section)g(4)24 b FF(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h (:)f(:)g(:)39 b FQ(234)245 2488 y(B.5.1)45 b(General)16 b(Strategies)50 b FF(:)24 b(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(234)245 2548 y(B.5.2)45 b(In)o(ternal-Spin)16 b(Systems)f(with)h(Unique)f(Ground-State)i (Con\014gurations)36 b(236)245 2608 y(B.5.3)45 b(In)o(ternal)16 b(Spins)g(under)g(Decimation)c FF(:)24 b(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f (:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(236)963 2784 y(5)p eop %%Page: 6 6 bop 245 91 a FQ(B.5.4)45 b(In)o(ternal)16 b(Spins)g(under)g(the)g(Kadano\013) i(T)l(ransformation.)k(Uniformit)o(y)16 b FF(:)39 b FQ(241)245 152 y(B.5.5)45 b(In)o(ternal)16 b(Spins)g(under)g(Ma)s(jorit)o(y)f(Rule)32 b FF(:)24 b(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(243)245 212 y(B.5.6)45 b(In)o(ternal)16 b(Spins)g(under)g(Blo)q(c)o (k-Av)o(eraging)f(T)l(ransformations)42 b FF(:)24 b(:)h(:)f(:)g(:)39 b FQ(243)245 272 y(B.5.7)45 b(In)o(ternal)16 b(Spins)g(when)g FF(h)e FE(6)p FQ(=)g(0.)22 b(Random)15 b(Field)40 b FF(:)25 b(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)h(:)f(:)g(:)39 b FQ(243)60 381 y FM(C)33 b(Solution)18 b(of)h(the)f(Diophan)n(tine)h(Equation)f (\(4.34\))588 b(244)60 490 y(References)1482 b(248)963 2784 y FQ(6)p eop %%Page: 7 7 bop 60 100 a FG(1)83 b(In)n(tro)r(duction)27 b(and)g(Summ)n(ary)e(of)i (Results)60 224 y FB(1.1)70 b(General)22 b(In)n(tro)r(duction)60 316 y FQ(A)17 b(principal)f(tenet)g(of)h(the)g(renormalization-group)g(\(R)o (G\))f(theory)h(of)h(phase)f(transitions)h([365,)60 376 y(277)q(,)j(254)q(,)g (118)r(])g(is)g(that)h(the)f(R)o(G)g(map,)h(de\014ned)f(on)h(a)g(suitable)f (space)h(of)f(Hamiltonians,)g(is)60 436 y FP(smo)n(oth)f FQ(\(i.e.)15 b(analytic)i(or)g(at)h(least)f(sev)o(eral-times)d(di\013eren)o(tiable\),)h (ev)o(en)h(on)i(phase-transition)60 497 y(surfaces.)j(The)15 b(singularities)f(asso)q(ciated)h(with)g(critical)e(p)q(oin)o(ts)i([365)q(,)f (277)q(,)g(254)q(,)h(118)q(])f(and)h(\014rst-)60 557 y(order)j(phase)g (transitions)g([280)q(,)f(217)r(,)g(119)q(])h(are)f(then)h(explained)f(in)g (terms)f(of)i(the)g(b)q(eha)o(vior)g(of)60 617 y(the)e(R)o(G)g(map)f(under)i (in\014nite)e(iteration.)133 677 y(This)k(picture)f(of)h(a)h(smo)q(oth)f(R)o (G)f(map)g(has,)i(ho)o(w)o(ev)o(er,)e(b)q(een)h(questioned,)g(particularly)e (as)60 737 y(regards)i(the)g(b)q(eha)o(vior)f(at)h(or)g(near)g(a)g FP(\014rst-or)n(der)k FQ(phase)c(transition.)29 b(On)19 b(the)f(one)h(hand,)g (the)60 798 y(existence)11 b(of)i(sev)o(eral)f(phases)i(raises)e(the)h(p)q (ossibilit)o(y)f(that)h(the)g(R)o(G)f(map)g(ma)o(y)f(b)q(e)i FP(disc)n(ontinuous)60 858 y FQ(or)20 b FP(multi-value)n(d)26 b FQ([173)q(,)19 b(197)q(,)g(305)q(])g(on)g(the)h(\014rst-order)g(transition) f(surface,)h(as)g(the)f(n)o(umerical)60 918 y(evidence)c(rep)q(orted)i(b)o(y) g(sev)o(eral)e(groups)j([33)q(,)e(233)q(,)h(72)q(,)f(163)q(])h(seems)e(to)i (suggest.)24 b(On)17 b(the)g(other)60 978 y(hand,)f(Gri\016ths)e(and)i(P)o (earce)f([172,)g(173)q(,)g(171)q(])g(ha)o(v)o(e)f(p)q(oin)o(ted)h(out)h(some) e(\\p)q(eculiarities")g(of)h(the)60 1038 y(commonly)c(used)i(discrete-spin)f (p)q(osition-space)j(R)o(G)e(transformations)h(\(decimation,)d(ma)s(jorit)o (y)60 1099 y(rule,)i(etc.\);)h(in)g(particular)f(they)h(suggested)h(that)g (the)f(R)o(G)g(map)f(for)i(the)f(t)o(w)o(o-dimensional)e(Ising)60 1159 y(mo)q(del)21 b(m)o(ust)g(ha)o(v)o(e)g(singularities)h(\(or)g(other)g (strange)h(b)q(eha)o(vior\))f(in)g(a)h(rather)f(large)g(part)h(of)60 1219 y(\()p FF(\014)s(;)8 b(h)p FQ(\)-plane)17 b(\(see)g(also)i([54,)e(334)q (]\).)738 1201 y FH(1)783 1219 y FQ(In)h(an)g(imp)q(ortan)o(t)f(but)h (apparen)o(tly)f(little-kno)o(wn)g(pap)q(er,)60 1279 y(Israel)j([207)q(])g (clari\014ed)g(the)h(nature)g(of)g(the)g(Gri\016ths-P)o(earce)f(p)q (eculiarities:)29 b(he)21 b(sho)o(w)o(ed)g(that)60 1339 y(in)g(at)i(least)e (one)h(case)g(the)g(renormalized)d(system)h(cannot)j(b)q(e)f(describ)q(ed)f (b)o(y)g(a)h(Boltzmann-)60 1399 y(Gibbs)f(prescription)f(for)h(an)o(y)f (reasonable)i(Hamiltonian,)d(i.e.)g(the)h(renormalized)f(measure)g(is)60 1460 y FP(non-Gibbsian)t FQ(.)133 1520 y(In)d(this)h(pap)q(er)410 1502 y FH(2)446 1520 y FQ(w)o(e)f(reconsider)g(the)g(conceptual)g (foundations)i(of)f(the)f(R)o(G)g(formalism,)d(and)60 1580 y(pro)o(v)o(e)20 b(some)f(rigorous)i(theorems)f(on)g(the)h(nature)f(of)h(the) f(R)o(G)h(map.)32 b(On)21 b(the)f(one)h(hand,)g(w)o(e)60 1640 y(pro)o(v)o(e)c(t)o(w)o(o)h(F)l(undamen)o(tal)f(Theorems)g(on)i(the)f (single-v)m(aluedness)g(and)h(con)o(tin)o(uit)o(y)d(of)i(the)g(R)o(G)60 1700 y(map;)i(these)g(theorems)f FP(rule)i(out)k FQ(the)19 b(discon)o(tin)o(uous-\015o)o(w)i(scenario)f(prop)q(osed)h(in)e(references)60 1761 y([33,)f(233)q(,)g(72)q(,)g(163)q(,)f(197)r(,)g(305)r(].)26 b(On)18 b(the)g(other)h(hand,)g(w)o(e)e(pro)o(v)o(e,)h(completing)e(and)j (extending)60 1821 y(Israel's)13 b(argumen)o(t,)f(that)i(in)f(sev)o(eral)g (cases)h(the)f(R)o(G)g(map)g(is)g(ill-de\014ned)g(for)g(a)h(m)o(uc)o(h)e (more)g(basic)60 1881 y(reason:)27 b FP(the)20 b(r)n(enormalize)n(d)g (Hamiltonian)g(may)g(fail)g(to)g(exist)g(alto)n(gether)5 b FQ(.)30 b(This)19 b(implies)e(that)60 1941 y(the)h(con)o(v)o(en)o(tional)f(R) o(G)h(description)f(of)h(\014rst-order)h(phase)g(transitions)f([280)q(,)g (217)q(,)g(119)q(])g(is)g(not)60 2001 y(v)m(alid)12 b(either)g(\(at)h(least)f (in)h(these)f(mo)q(dels)f(and)j(for)f(these)f(R)o(G)g(transformations\).)20 b(Moreo)o(v)o(er,)12 b(this)60 2062 y(pathology)g(can)f(o)q(ccur)g(in)g(the)g FP(vicinity)16 b FQ(of)c(|)e(not)i(only)f FP(at)k FQ(|)c(a)h(\014rst-order)f (phase)h(transition:)19 b(for)60 2122 y(the)11 b(Ising)g(mo)q(del)g(in)g (dimension)e FF(d)15 b FE(\025)e FQ(3)f(it)f(o)q(ccurs)h(in)f(a)h(full)e (neigh)o(b)q(orho)q(o)q(d)k FE(f)p FF(\014)i(>)d(\014)1606 2129 y FH(0)1626 2122 y FF(;)j FE(j)p FF(h)p FE(j)d FF(<)h(\017)p FQ(\()p FF(\014)s FQ(\))p FE(g)60 2182 y FQ(of)23 b(the)g(lo)o(w-temp)q (erature)e(part)i(of)g(the)g(\014rst-order)g(phase-transition)h(surface.)41 b(Indeed,)23 b(for)60 2242 y(certain)14 b(blo)q(c)o(k-a)o(v)o(eraging)g (transformations)h(w)o(e)f(are)h(able)f(to)h(sho)o(w)g(that)h(the)e (pathology)i(o)q(ccurs)60 2302 y(at)h(lo)o(w)f(temp)q(erature)e(and)j FP(al)r(l)23 b FQ(magnetic)15 b(\014elds)h FF(h)p FQ(.)133 2363 y(Our)g(p)q(oin)o(t)f(of)h(view)f(is)g(the)g(follo)o(wing:)21 b(An)15 b(R)o(G)g(map)g(is)g(de\014ned)g(initially)f(as)i(a)g(rule)f(\(whic)o (h)p 60 2409 732 2 v 116 2463 a FA(1)135 2478 y Fz(Similar)9 b(p)q(eculiarities,)j(and)g(also)f(di\013eren)o(t)i(ones,)f(ha)o(v)o(e)g(b)q (een)h(found)f(b)o(y)f(Hasenfratz)i(and)f(Hasenfratz)h([189)o(].)60 2528 y(The)k(phenomena)f(found)g(in)h(Section)g(4)f(of)g(their)h(pap)q(er)h (are)f(v)o(ery)g(closely)g(related)g(to)f(those)i(of)e(Gri\016ths)g(and)60 2578 y(P)o(earce,)f(while)e(those)i(in)e(Sections)i(2)f(and)f(3)h(seem)g(to)f (b)q(e)i(quite)f(di\013eren)o(t.)116 2636 y FA(2)135 2651 y Fz(Brief)g(summaries)e(of)h(our)h(results)h(ha)o(v)o(e)f(app)q(eared)g (previously)g([352)o(,)f(353,)g(354)o(,)h(355)o(].)963 2784 y FQ(7)p eop %%Page: 8 8 bop 60 91 a FQ(ma)o(y)16 b(b)q(e)j(either)e(deterministic)d(or)19 b(sto)q(c)o(hastic\))f(for)g(generating)g(a)h(con\014guration)g FF(!)1666 73 y Fy(0)1696 91 y FQ(of)f(\\blo)q(c)o(k)60 152 y(spins")k(giv)o(en)f(a)h(con\014guration)h FF(!)h FQ(of)e(\\original)g (spins".)38 b(Mathematically)20 b(this)h(is)h(giv)o(en)f(b)o(y)60 212 y(a)h(probabilit)o(y)g(k)o(ernel)e FF(T)7 b FQ(\()p FF(!)25 b FE(!)f FF(!)727 194 y Fy(0)739 212 y FQ(\).)38 b(Using)22 b(suc)o(h)g(a)h(map,)f(one)g(can)g(immedi)o(ately)d(de\014ne)j(a)60 272 y(probabilit)o(y)d(distribution)g FF(\026)611 254 y Fy(0)623 272 y FQ(\()p FF(!)674 254 y Fy(0)686 272 y FQ(\))h(of)g(blo)q(c)o(k)f(spins) h(from)f(an)o(y)h(giv)o(en)f(probabilit)o(y)f(distribution)60 332 y FF(\026)p FQ(\()p FF(!)r FQ(\))f(of)f(original)g(spins,)g(namely)513 433 y FF(\026)542 412 y Fy(0)554 433 y FQ(\()p FF(!)605 412 y Fy(0)616 433 y FQ(\))28 b(=)g(\()p FF(\026T)7 b FQ(\)\()p FF(!)883 412 y Fy(0)894 433 y FQ(\))28 b FE(\021)1007 391 y Fx(X)1026 478 y FD(!)1075 433 y FF(\026)p FQ(\()p FF(!)r FQ(\))8 b FF(T)f FQ(\()p FF(!)17 b FE(!)c FF(!)1379 412 y Fy(0)1391 433 y FQ(\))h FF(:)352 b FQ(\(1)p FF(:)p FQ(1\))60 561 y(In)14 b(other)g(w)o(ords,)h(the)f(R)o(G)g(map)f(is)h(easily)f(de\014ned)h(as)h(a)f (map)g FP(fr)n(om)g(me)n(asur)n(es)h(to)g(me)n(asur)n(es)t FQ(.)20 b(On)60 621 y(the)g(other)g(hand,)h(most)e(applications)h(of)h(the)e (renormalization)g(group)i(assume)e(\(and)h(in)g(fact)60 682 y(need\))14 b(that)h(the)g(R)o(G)f(map)g(is)h(de\014ned)f(as)i(a)f(map)f FP(fr)n(om)g(Hamiltonians)j(to)f(Hamiltonians)t FQ(.)22 b(That)60 742 y(is,)i(if)f FF(\026)h FQ(is)f(the)g(Gibbs)h(measure)e(for)i(a)f (statistical-mec)o(hanical)e(system)h(with)h(Hamiltonian)60 802 y FF(H)t FQ(,)g(then)e(one)g(usually)h(assumes)f(that)g FF(\026)856 784 y Fy(0)890 802 y FQ(is)g(the)g(Gibbs)h(measure)e(for)i(a)g (system)e(with)h(some)60 862 y(Hamiltonian)h FF(H)392 844 y Fy(0)404 862 y FQ(;)28 b(this)c(is)g(tak)o(en)f(to)i(de\014ne)e(an)i(R)o(G)f (map)f FE(R)h FQ(on)h(some)e(suitable)h(space)g(of)60 922 y(Hamiltonians,)14 b(b)o(y)i(the)g(diagram)793 1030 y FF(\026)898 1003 y FD(T)871 1030 y FE(\000)-9 b(!)42 b FF(\026)1022 1012 y Fy(0)1048 1030 y FE(\021)13 b FF(\026T)795 1090 y FE(")173 b(#)785 1162 y FF(H)896 1135 y Fy(R)871 1162 y FE(\000)-9 b(!)42 b FF(H)1037 1144 y Fy(0)1790 1091 y FQ(\(1)p FF(:)p FQ(2\))60 1259 y FP(F)l(ormal)r(ly)22 b FQ(the)16 b(relation)h(b)q(et)o(w)o(een)f(a)h(Hamiltonian)e(and)j(its)e (corresp)q(onding)i(Gibbs)g(measure)d(is)60 1319 y(giv)o(en)k(b)o(y)h FF(\026)h FQ(=)g(const)14 b FE(\002)f FF(e)572 1301 y Fy(\000)p FD(H)633 1319 y FQ(,)21 b(and)g(hence)e(the)h(R)o(G)g(map)g(on)h(the)f(space) g(of)h(Hamiltonians)d(is)60 1379 y(de\014ned)e FP(formal)r(ly)21 b FQ(b)o(y)300 1508 y FF(H)344 1487 y Fy(0)356 1508 y FQ(\()p FF(!)407 1487 y Fy(0)419 1508 y FQ(\))27 b(=)h(\()p FE(R)p FF(H)t FQ(\)\()p FF(!)706 1487 y Fy(0)718 1508 y FQ(\))g(=)f FE(\000)8 b FQ(log)949 1435 y Fx(")973 1466 y(X)991 1553 y FD(!)1041 1508 y FF(e)1064 1487 y Fy(\000)p FD(H)s FH(\()p FD(!)q FH(\))1184 1508 y FF(T)f FQ(\()p FF(!)15 b FE(!)f FF(!)1380 1487 y Fy(0)1391 1508 y FQ(\))1410 1435 y Fx(#)1454 1508 y FQ(+)19 b(const)c FF(:)139 b FQ(\(1)p FF(:)p FQ(3\))60 1637 y(Ho)o(w)o(ev)o(er,)11 b FP(this)i(formula)h(is)f(valid)h(only)g(in)g (\014nite)h(volume)t FQ(;)f(in)e(in\014nite)f(v)o(olume,)f(the)i(Hamiltonian) 60 1697 y FF(H)t FQ(\()p FF(!)r FQ(\))g(is)g(ill-de\014ned)e(\(its)h(v)m (alue)h(is)f(almost)g(surely)g FE(\0061)p FQ(\),)h(and)g(the)g(connection)f (b)q(et)o(w)o(een)g(a)h(formal)60 1757 y(Hamiltonian)k(\(more)h(precisely)l (,)e(an)k FP(inter)n(action)t FQ(\))f(and)h(its)e(corresp)q(onding)i(Gibbs)f (measure\(s\))60 1817 y(is)d(m)o(uc)o(h)d(more)i(complicated.)k(W)l(e)d (emphasize)e(that)i(this)g(is)f(not)h(a)h(mere)c(mathematical)g(nicet)o(y)l (,)60 1877 y(but)22 b(con)o(tains)f(the)g(fundamen)o(tal)f FP(physics)25 b FQ(of)d(phase)g(transitions.)37 b(In)22 b(\014nite)e(v)o (olume,)g(where)60 1938 y(the)15 b(form)o(ula)f FF(\026)g FQ(=)g(const)9 b FE(\002)f FF(e)606 1919 y Fy(\000)p FD(H)682 1938 y FQ(mak)o(es)14 b(sense,)h(all)f(thermo)q(dynamic)f(functions)i(are)g(manifestly)60 1998 y(analytic)j(functions)g(of)h(the)f(parameters)g(in)g(the)g (Hamiltonian,)f(so)i(a)g(phase)g(transition)f(is)h(im-)60 2058 y(p)q(ossible.)i(Phase)14 b(transitions)h(o)q(ccur)f FP(only)19 b FQ(for)14 b(in\014nite-v)o(olume)d(systems.)19 b(No)o(w,)14 b(one)g(feature)g(of)60 2118 y(the)h(in\014nite-v)o(olume)d(limit)h(is)i(the) f(p)q(ossibilit)o(y)h(that)g(the)g(Gibbs)h(measure)d(ma)o(y)h(b)q(e)h (non-unique:)60 2178 y(corresp)q(onding)20 b(to)f(a)h(giv)o(en)e(formal)g (Hamiltonian)f(\(=)i(in)o(teraction\))e(there)i(ma)o(y)e(exist)h FP(sever)n(al)60 2238 y(distinct)j FQ(Gibbs)16 b(measures,)e(eac)o(h)h(one)h (corresp)q(onding)h(to)e(a)h(distinct)f(thermo)q(dynamically)d(sta-)60 2299 y(ble)18 b(\\pure)h(phase")h(of)f(the)f(system.)28 b(Indeed,)18 b(suc)o(h)g(a)h(m)o(ultiple-phase)e(co)q(existence)g(can)i(serv)o(e)60 2359 y(as)e(one)f(de\014nition)g(of)g(a)h(\014rst-order)f(phase)h (transition.)22 b(Therefore,)15 b(for)h(Hamiltonians)f FF(H)20 b FQ(with)60 2419 y(a)g(non-unique)g(Gibbs)f(measure)g(\(=)g(Hamiltonians)f (lying)h(on)h(a)g(\014rst-order)g(phase-transition)60 2479 y(surface\),)c(the)h(up)o(w)o(ard)g(v)o(ertical)e(arro)o(w)j(in)e(\(1.2\))h (ma)o(y)e(w)o(ell)h(b)q(e)h(a)g(m)o(ulti-v)m(alued)e(map;)g(and)j(one)60 2539 y(migh)o(t)f(fear)j(that)f(this)g(could)g(cause)g(the)g(putativ)o(e)g(R) o(G)g(map)f FE(R)h FQ(to)h(b)q(ecome)e(m)o(ulti-v)m(alued)e(as)60 2600 y(w)o(ell.)k(\(W)l(e)15 b(shall)h(see)g(later,)f(ho)o(w)o(ev)o(er,)f (that)i(this)g(pathology)h FP(c)n(annot)k FQ(o)q(ccur.\))g(Ev)o(en)16 b(more)e(sub-)60 2660 y(tle)i(problems)g(arise)h(from)f(the)h(do)o(wn)o(w)o (ard)h(v)o(ertical)d(arro)o(w)j(in)e(\(1.2\):)24 b(though)18 b(at)f(most)g(one)g FF(H)1878 2642 y Fy(0)963 2784 y FQ(8)p eop %%Page: 9 9 bop 60 91 a FQ(can)16 b(corresp)q(ond)h(to)f(a)h(giv)o(en)e FF(\026)653 73 y Fy(0)681 91 y FQ([174)q(],)g(it)g(can)h(happ)q(en)h(that)f FP(no)k FF(H)1341 73 y Fy(0)1369 91 y FQ(corresp)q(onds)d(to)f(the)g(giv)o (en)60 152 y FF(\026)89 133 y Fy(0)120 152 y FQ(|)j(that)g(is,)g FP(it)h(c)n(an)g(o)n(c)n(cur)f(that)h(the)g(image)h(me)n(asur)n(e)e FF(\026)1186 133 y Fy(0)1218 152 y FP(is)g(not)i(a)e(Gibbs)i(me)n(asur)n(e)e (for)g(any)60 212 y(r)n(e)n(asonable)e(Hamiltonian)t FQ(.)22 b(In)15 b(Section)g(3)h(w)o(e)f(shall)h(sho)o(w)g(that)g(suc)o(h)f (non-Gibbsianness)i(is)e(the)60 272 y FP(only)23 b FQ(w)o(a)o(y)17 b(that)h(the)g(R)o(G)g(map)f(can)h(b)q(ecome)e(grossly)i(\\pathological".)28 b(In)17 b(Section)h(4)g(w)o(e)f(shall)60 332 y(sho)o(w)g(that)g(this)f (pathology)h(do)q(es)g(in)f(fact)g(o)q(ccur)g(in)g(a)h(rather)f(wide)g(v)m (ariet)o(y)f(of)i(examples.)133 392 y(\(Of)11 b(course,)h(w)o(e)e(m)o(ust)g (mak)o(e)f(precise)h(what)h(w)o(e)g(mean)f(b)o(y)g(a)h(\\reasonable")i (Hamiltonian,)c(and)60 452 y(con)o(vince)g(the)i(reader)g(that)g(our)h(class) f(is)f(su\016cien)o(tly)f(wide)i(to)g(capture)g(fully)e(the)i(in)o(tuitiv)o (e)e(notion)60 513 y(of)17 b(\\ph)o(ysical)f(reasonableness".)25 b(This)17 b(will)f(b)q(e)h(discussed)f(in)h(detail)f(in)h(Sections)f(2)i (\(esp)q(ecially)60 573 y(2.3.3,)25 b(2.4.4)g(and)f(2.6.7\))g(and)g(6.1.2.)44 b(Su\016ce)23 b(it)h(to)g(sa)o(y)g(no)o(w)g(that)g(w)o(e)f(allo)o(w)h(in)o (teractions)60 633 y(of)g(arbitrarily)f(long)h(range)g(and)g(in)o(v)o(olving) e(arbitrarily)h(man)o(y)f(spins,)k(sub)s(ject)d(only)g(to)h(the)60 693 y(condition)16 b(of)h(absolute)f(summabilit)o(y)-5 b(.\))133 753 y(These)22 b(results)f(lea)o(v)o(e)f(R)o(G)h(theory)h(in)f(roughly)h(the) f(follo)o(wing)h(situation:)32 b(The)21 b(R)o(G)h(map)60 814 y(has)e(b)q(een)f(pro)o(v)o(en)g(to)g(b)q(e)h(w)o(ell-de\014ned)d(and)j (analytic)f(at)g(high)h(temp)q(erature)d([207)q(,)i(212)q(])g(and,)60 874 y(in)f(some)g(cases,)h(at)g(large)g(magnetic)e(\014eld)h([173)q(])g(|)h (regions)g(in)f(whic)o(h)h(phase)g(transitions)g(are)60 934 y(absen)o(t,)h(and)f(R)o(G)g(theory)h(is)f(unnecessary)l(.)30 b(The)19 b(R)o(G)g(map)f(has)i(b)q(een)f(pro)o(v)o(en)g(in)g(some)f(cases)60 994 y(to)g(b)q(e)f(ill-de\014ned)f(at)h(lo)o(w)g(temp)q(erature)f(\(Section)h (4\).)24 b(Near)17 b(the)g(critical)e(p)q(oin)o(t)i(|)g(where)g(R)o(G)60 1054 y(theory)c(is)g(of)g(the)g(most)f(in)o(terest)g(|)g(v)o(ery)g(little)g (is)g(kno)o(wn)i(ab)q(out)g(the)f(b)q(eha)o(vior)f(of)i(the)f(R)o(G)f(map,)60 1115 y(but)19 b(there)g(are)g(some)f(indications)g(of)i(p)q(ossible)f (pathologies)h(in)e(dimensions)g FF(d)1590 1118 y FC(\()29 b(\))1597 1106 y FE(\025)1654 1115 y FQ(4)19 b(\(Sections)60 1175 y(4.4)i(and)g(5.2\).)33 b(Nev)o(ertheless,)19 b(R)o(G)h FP(ide)n(as)k FQ(ha)o(v)o(e)c(b)q(een)g(of)h(great)f(v)m(alue)g(ev)o(en)g(in) g(situations)g(in)60 1235 y(whic)o(h)c(the)g(strict)g(Wilson)g(prescription)g (\(1.2\))h(has)g(not)g(b)q(een)g(|)f(and)h(ma)o(yb)q(e)e(ev)o(en)h(cannot)h (b)q(e)60 1295 y(|)j(implem)o(e)o(n)o(ted)d([147,)j(148)q(,)f(150)q(,)h(149)q (,)f(151)q(,)h(181)q(,)f(188)q(,)h(53)q(,)f(134)q(,)g(135)r(,)g(137)q(,)g(4)q (,)g(3,)h(112)q(,)f(145)q(,)60 1355 y(146)q(,)d(44)q(,)g(52,)g(183)q(,)g(184) q(,)g(185)q(,)g(187)q(,)g(186)q(].)21 b(W)l(e)16 b(discuss)g(these)g(issues)h (further)e(in)h(Section)g(6.1.)60 1500 y FB(1.2)70 b(Plan)31 b(of)h(This)f(P)n(ap)r(er)h(\(Or,)h(What)f(to)g(Read)f(and)i(What)f(to)217 1574 y(Skip\))60 1667 y FQ(W)l(e)16 b(hop)q(e)h(that)g(this)f(pap)q(er)h (will)f(b)q(e)g(read)h(\(and)g(readable\))f(b)q(oth)h(b)o(y)f(theoretical)g (ph)o(ysicists)f(|)60 1727 y(particularly)k(those)h(doing)h(real-space)f(R)o (G)g(and)g(Mon)o(te)g(Carlo)h(R)o(G)e(calculations)h(|)g(and)h(b)o(y)60 1787 y(mathematical)14 b(ph)o(ysicists)i(in)o(terested)f(in)i(the)g (statistical)f(mec)o(hanics)f(of)i(lattice)f(systems.)22 b(F)l(or)60 1847 y(this)13 b(reason)h(w)o(e)e(ha)o(v)o(e)h(giv)o(en)f(in)h(Section)f(2)i (a)f(rather)g(detailed)f(\(and,)i(w)o(e)f(hop)q(e,)h(comprehensible\))60 1908 y(summary)c(of)i(the)f(general)h(theory)g(of)g(in\014nite-v)o(olume)d (lattice)i(systems,)g(in)g(whic)o(h)h(w)o(e)f(mak)o(e)f(pre-)60 1968 y(cise)16 b(the)h(concepts)g(of)g(\\in)o(teraction",)g(\\Hamiltonian",)f (\\Gibbs)h(measure")f(and)i(\\equilibrium)60 2028 y(measure")e(and)h(the)f (connections)g(b)q(et)o(w)o(een)g(them.)k(As)c(w)o(e)g(ha)o(v)o(e)g(argued,)g (a)h(careful)f(treatmen)o(t)60 2088 y(of)e(the)f(in\014nite-v)o(olume)d (problem)i(is)h(essen)o(tial)f(for)i(a)f(correct)g FP(physic)n(al)18 b FQ(understanding)c(of)g(phase)60 2148 y(transitions)19 b(in)g(general,)f (and)i(of)f(the)f(renormalization)f(group)j(in)e(particular.)29 b(W)l(e)18 b(hop)q(e)i(that)60 2209 y(Section)c(2)h(will)f(b)q(e)h(useful)f (to)h(ph)o(ysicists)f(who)h(ma)o(y)e(not)i(b)q(e)g(familiar)e(with)h(these)h (ideas.)22 b(Some)60 2269 y(abstract)16 b(mathematics)c(is)i(of)h(necessit)o (y)f(in)o(v)o(olv)o(ed;)e(w)o(e)j(ha)o(v)o(e)f(tried)g(hard)h(to)g(minimi)o (ze)d(\\mathe-)60 2329 y(matics)g(for)i(the)f(sak)o(e)g(of)h(mathematics",)d (and)j(to)g(in)o(tro)q(duce)f(only)g(those)h(mathematical)c(ob)s(jects)60 2389 y(whic)o(h)18 b(corresp)q(ond)i(to)f(clear)f FP(physic)n(al)24 b FQ(concepts.)29 b(The)19 b(reader)g(can)g(judge)g(whether)f(w)o(e)h(ha)o(v) o(e)60 2449 y(succeeded.)284 2431 y FH(3)p 60 2483 732 2 v 116 2537 a FA(3)135 2552 y Fz(The)h(\\exp)q(erts")h(will)e(notice)h(a)g(few)g (inno)o(v)n(ations)e(and)i(new)g(results)h(in)f(Section)g(2)g(and)g(the)g (asso)q(ciated)60 2602 y(App)q(endix)13 b(A:)k(the)c(extensiv)o(e)g (discussion)g(of)e(ph)o(ysical)h(equiv)n(alence)g(\(Sections)h(2.3.5,)e (2.4.3,)f(2.4.5,)g(2.4.6,)h(A.3.4,)60 2652 y(A.3.5)i(and)h(A.3.7\);)f(some)h (precise)h(estimates)g(on)f(bulk)f(vs.)i(surface)g(e\013ects)h(\(Sections)g (2.4.7,)c(2.4.8)g(and)j(A.3.8\);)963 2784 y FQ(9)p eop %%Page: 10 10 bop 133 91 a FQ(In)13 b(Section)g(3)h(w)o(e)g(de\014ne)f(our)h(general)f (framew)o(ork)f(for)i(studying)g(renormalization)e(transfor-)60 152 y(mations,)g(and)g(pro)o(v)o(e)f(the)h(t)o(w)o(o)f(F)l(undamen)o(tal)g (Theorems)f(on)j(single-v)m(aluedness)e(and)i(con)o(tin)o(uit)o(y)60 212 y(of)19 b(the)f(R)o(G)g(map.)26 b(These)18 b(theorems)f(sho)o(w)i(that)g (the)f(R)o(G)g(map)f FE(R)i FQ(can)f(nev)o(er)f(b)q(ecome)g(m)o(ulti-)60 272 y(v)m(alued)23 b(or)g(discon)o(tin)o(uous;)j(but)e(it)e(can)h(b)q(ecome)f FP(non)t FQ(-v)m(alued,)j(whic)o(h)d(o)q(ccurs)i(if)e(the)h(image)60 332 y(measure)14 b FF(\026)278 314 y Fy(0)306 332 y FQ(is)h(non-Gibbsian.)22 b(This)16 b(fo)q(cus)g(on)g(non-Gibbsianness)h(|)e(whic)o(h)g(is)g(the)g (real)g(mes-)60 392 y(sage)g(of)g(our)g(pap)q(er)g(|)f(is)h(a)g(profound)g (insigh)o(t)f(due)h(to)f(Israel)g([207)q(].)20 b(In)14 b(Section)g(4)h(w)o(e) f(complete)60 452 y(and)g(extend)e(Israel's)h(argumen)o(t,)f(and)i(sho)o(w)g (that)g(in)e(a)i(large)f(class)h(of)f(examples)f(\(alw)o(a)o(ys)h(at)g(lo)o (w)60 513 y(temp)q(erature,)f(but)i(not)g(only)f(on)h(phase-transition)h (surfaces\))e(the)h(image)e(measure)g FF(\026)1680 495 y Fy(0)1705 513 y FQ(is)i(indeed)60 573 y(non-Gibbsian.)30 b(W)l(e)19 b(also)h(discuss)f (some)e(other)i(op)q(erations)i(that)e(can)g(lead)g(to)g(non-Gibbsian)60 633 y(measures,)f(including)g(one)h(whic)o(h)f(is)h(relev)m(an)o(t)f(to)h (\\large-cell")f(ma)s(jorit)o(y-rule)f(maps;)i(and)g(w)o(e)60 693 y(giv)o(e)d(a)h(rather)f(complete)f(catalogue)i(of)g(the)f(kno)o(wn)h (examples)d(of)j(non-Gibbsianness.)24 b(In)16 b(Sec-)60 753 y(tion)h(5)g(w)o(e)f(discuss)h(the)g(heuristic)f(and)h(n)o(umerical)d (evidence)h(on)j(R)o(G)e(pathologies)i(in)e(the)h(ligh)o(t)60 814 y(of)j(our)g(rigorous)g(theorems.)29 b(W)l(e)19 b(also)h(discuss)g(some)e (heuristic)g(argumen)o(ts)h(for)h(the)f(p)q(ossible)60 874 y(existence)13 b(of)i(R)o(G)g(pathologies)g FP(in)h(the)h(critic)n(al)f(r)n (e)n(gion)i FQ(for)d(Ising-to-Ising)h(R)o(G)e(maps)g(in)h(dimen-)60 934 y(sion)i FF(d)195 937 y FC(\()29 b(\))201 926 y FE(\025)255 934 y FQ(4.)24 b(In)16 b(Section)g(6)i(w)o(e)e(summarize)e(our)j(results)g (and)g(discuss)g(their)f(implications.)21 b(W)l(e)60 994 y(conclude)16 b(with)g(a)g(list)g(of)g(op)q(en)h(questions.)133 1054 y(In)22 b(App)q(endix)f(A)h(w)o(e)g(supply)f(the)h(pro)q(ofs)i(of)e(some)f(theorems)g (that)h(are)g(stated)h(without)60 1115 y(pro)q(of)15 b(in)e(Section)g(2.)21 b(In)13 b(App)q(endix)g(B)g(w)o(e)h(pro)o(vide)f(a)h(brief)e(summary)g(of)i (Pirogo)o(v-Sinai)g(theory)l(,)60 1175 y(whic)o(h)e(is)g(needed)f(as)i(a)g (tec)o(hnical)d(to)q(ol)j(in)f(Section)g(4.)1045 1157 y FH(4)1085 1175 y FQ(In)g(App)q(endix)g(C)g(w)o(e)g(solv)o(e)g(a)g(Diophan)o(tine)60 1235 y(equation)k(arising)h(in)f(our)g(study)h(of)f(the)g(ma)s(jorit)o (y-rule)e(map.)133 1295 y(Let)j(us)f(again)h(express)f(our)h(hop)q(e)g(that)g (the)f(reader)g(will)f(at)i(least)f(p)q(eruse)h(Section)f(2.)22 b(\(Hey)l(,)60 1355 y(w)o(e)d(sp)q(en)o(t)h(a)g(long)g(time)e(on)i(it,)f(and) h(w)o(e)g(think)f(it)g(is)g(rather)h(go)q(o)q(d)i(p)q(edagogy)l(.\))33 b(Ho)o(w)o(ev)o(er,)18 b(for)60 1416 y(the)d(reader)g(who)h(is)f(truly)f (allergic)g(to)i(abstract)g(mathematics,)c(w)o(e)j(o\013er)g(the)g(follo)o (wing)g(advice:)60 1476 y(read)i(the)h(remainder)d(of)j(this)f(In)o(tro)q (duction,)g(follo)o(w)o(ed)f(b)o(y)h(Sections)g(3)h(\(skipping)f(the)g(pro)q (ofs\),)60 1536 y(4.1.1,)c(4.4)h(\(skipping)e(the)h(pro)q(ofs\),)h(5.2)g(and) f(6.)21 b(Finally)l(,)11 b(for)j(the)e(reader)h(who)g(is)g(allergic)f(b)q (oth)i(to)60 1596 y(abstract)j(mathematics)c(and)j(to)h(250-page)h(pap)q (ers,)e(w)o(e)f(o\013er)i(\\R)o(G)f(lite":)k(read)c(the)g(remainder)60 1656 y(of)h(this)f(In)o(tro)q(duction,)f(and)i(then)f(skip)g(to)h(the)f (Conclusion)g(\(Section)g(6.1\).)60 1801 y FB(1.3)70 b(Summ)n(ary)20 b(of)k(First)e(and)i(Second)f(F)-6 b(undamen)n(tal)21 b(Theorems)60 1893 y FQ(W)l(e)13 b(w)o(ould)f(lik)o(e)f(next)h(to)i(summarize)9 b(the)k(t)o(w)o(o)f(F)l(undamen)o(tal)g(Theorems)f(and)j(giv)o(e)d(the)i(ph)o (ysical)60 1953 y(in)o(tuition)h(b)q(ehind)g(their)g(pro)q(ofs.)22 b(Consider,)15 b(for)g(concreteness,)f(the)g(Ising)h(mo)q(del)e(in)i (dimension)60 2013 y FF(d)20 b FE(\025)g FQ(2)g(at)g(lo)o(w)g(temp)q(erature) e(\()p FF(\014)k FE(\035)e FF(\014)811 2020 y FD(c)828 2013 y FQ(\))g(and)g(zero)f(magnetic)g(\014eld.)31 b(A)o(t)19 b(suc)o(h)h(a)g(p)q (oin)o(t)g(there)60 2074 y(are)g(precisely)f(t)o(w)o(o)h([141])g(pure)g (phases)h(\(extremal)d(translation-in)o(v)m(arian)o(t)i(Gibbs)h(measures\):) 60 2134 y(the)15 b(p)q(ositiv)o(ely)f(magnetized)g(\(or)i(\\+"\))g(phase)g FF(\026)982 2141 y FH(+)1012 2134 y FQ(,)f(and)h(the)f(negativ)o(ely)f (magnetized)g(\(or)i(\\)p FE(\000)p FQ("\))60 2194 y(phase)24 b FF(\026)232 2201 y Fy(\000)262 2194 y FQ(.)43 b(These)23 b(pure)g(phases)i(can)e(b)q(e)h(obtained)f(b)o(y)g(taking)h(the)f (in\014nite-v)o(olume)e(limit)p 60 2239 732 2 v 60 2308 a Fz(a)12 b(consisten)o(t)i(use)f(of)f(v)n(an)g(Ho)o(v)o(e)g(con)o(v)o(ergence)i(and)e Fw(c)n(omplete)k Fz(subadditivit)o(y)11 b(\(Sections)j(2.4.1,)c(A.3.3,)h (A.3.4)g(and)60 2358 y(A.3.5\);)g(and)i(some)f(in)o(teresting)h(coun)o (terexamples)g(concerning)g(the)g(pressure)i(and)e(en)o(trop)o(y)f(\(App)q (endix)i(A.5.2\).)60 2408 y(The)e(\014rst)h(t)o(w)o(o)e(of)h(these)h(inno)o (v)n(ations)d(pla)o(y)h(a)h(crucial)g(role)f(in)h(our)g(pro)q(of)f(of)h(the)g (Second)h(F)m(undamen)o(tal)c(Theorem)60 2457 y(\(Section)14 b(3.3\).)116 2515 y FA(4)135 2530 y Fz(The)19 b(\\exp)q(erts")i(will)c (notice)j(some)e(small)f(inno)o(v)n(ations)g(in)i(our)g(presen)o(tation)h(of) e(Pirogo)o(v-Sinai)f(theory)m(,)60 2580 y(notably)c(our)i(emphasis)e(on)h (questions)h(of)f Fw(uniformity)t Fz(.)k(This)c(pla)o(ys)g(an)g(imp)q(ortan)o (t)f(role)h(in)g(our)g(application)f(to)60 2630 y(the)h(Kadano\013)g (transformation:)i(see)f(Section)g(4.3.3)d(and)i(App)q(endix)g(B.5.4.)951 2784 y FQ(10)p eop %%Page: 11 11 bop 60 91 a FQ(using)15 b(\\+")g(or)f(\\)p FE(\000)p FQ(")h(b)q(oundary)h (conditions,)e(resp)q(ectiv)o(ely)l(.)k(Both)c(of)h(these)f(phases)h(ha)o(v)o (e)e(a)i(large)60 152 y(magnetization)j FE(\006)p FF(M)466 159 y FH(0)505 152 y FQ(and)i(a)g(small)e(correlation)h(length)g FF(\030)r FQ(.)31 b(No)o(w)19 b(let)g(us)h(apply)f(some)f(blo)q(c)o(k-)60 212 y(spin)g(transformation)g FF(T)7 b FQ(,)18 b(suc)o(h)g(as)h(the)f(ma)s (jorit)o(y-rule)e(transformation)i(on)h(blo)q(c)o(ks)f(of)g(size)g(2)1856 194 y FD(d)1876 212 y FQ(.)60 272 y(Then)f(the)f(image)g(measures)f FF(\026)652 254 y Fy(0)652 284 y(\006)697 272 y FQ(=)g FF(\026)779 279 y Fy(\006)809 272 y FF(T)23 b FQ(will)15 b(ha)o(v)o(e)h(a)h(y)o(et)f (larger)h(magnetization)e FE(\006)p FF(M)1736 254 y Fy(0)1731 284 y FH(0)1768 272 y FQ(\(since)60 332 y(minorities)g(tend)j(to)g(get)g (\\outv)o(oted"\))h(and)f(a)g(y)o(et)f(smaller)f(correlation)i(length)f FF(\030)1629 314 y Fy(0)1659 332 y FQ(\(w)o(e)h(exp)q(ect)60 392 y(roughly)c FF(\030)258 374 y Fy(0)284 392 y FE(\031)g FF(\030)r(=)p FQ(2,)h(since)e(distances)h(are)g(b)q(eing)f(scaled)h(b)o(y)f (a)h(factor)g(of)g(2\).)21 b(W)l(e)14 b(no)o(w)g(ask:)20 b(These)60 452 y(image)15 b(measures)g FF(\026)439 434 y Fy(0)439 465 y(\006)485 452 y FQ(are)i(t)o(ypical)d(of)j(what)g(kind)f(of)g(Hamiltonian)f (\(if)g(an)o(y\)?)133 513 y(One)e(p)q(ossibilit)o(y)g(|)g(and)h(the)g(one)f (con)o(v)o(en)o(tionally)f(assumed)g([280)q(,)h(217)q(,)g(119)r(])g(|)g(is)g (that)h(the)60 573 y(R)o(G)j(\015o)o(w)g(is)f(to)o(w)o(ard)i(lo)o(w)o(er)d (temp)q(eratures)h FP(along)j(the)g FF(h)14 b FQ(=)h(0)j FP(line)t FQ(.)1333 555 y FH(5)1377 573 y FQ(This)f(picture)f(is)g(certainly)60 633 y(consisten)o(t)h(with)h(the)f(in)o(tuitiv)o(e)e(idea)i(that)h (magnetization)f(increases)g(and)h(correlation)f(length)60 693 y(decreases)h(under)g(the)g(R)o(G)g(map.)26 b(In)18 b(this)g(scenario)g ([Figure)f(1\(a\)],)h(the)g(t)o(w)o(o)g(image)f(measures)60 753 y FF(\026)89 735 y Fy(0)89 766 y(\006)137 753 y FQ(w)o(ould)h(b)q(e)g (Gibbsian)h(for)f(the)g FP(same)k FQ(Hamiltonian)17 b FF(H)1176 735 y Fy(0)1187 753 y FQ(,)i(and)f(this)g(Hamiltonian)f(w)o(ould)h(b)q(e)60 814 y(in)o(v)m(arian)o(t)e(under)g(the)g FF(\033)f FE(!)f(\000)p FF(\033)j FQ(symmetry)l(.)133 874 y(A)j(di\013eren)o(t)f(p)q(ossibilit)o(y)g (w)o(as)i(adv)o(o)q(cated)f(b)o(y)g(Dec)o(k)o(er,)f(Hasenfratz)h(and)h (Hasenfratz)f([72].)60 934 y(In)i(this)f(scenario)h([Figure)f(1\(b\)],)i(the) f(R)o(G)f(\015o)o(w)i(is)e FP(disc)n(ontinuous)27 b FQ(at)22 b(the)g(phase-transition)60 994 y(line)d FF(h)g FQ(=)h(0:)28 b(Hamiltonians)18 b FF(H)24 b FQ(with)c(an)g(in\014nitesimal)d(p)q(ositiv)o (e)i(\(resp.)g(negativ)o(e\))g(magnetic)60 1054 y(\014eld)i FF(h)h FQ(get)f(mapp)q(ed)g(b)o(y)g(a)h(single)f(R)o(G)g(step)h(to)g (renormalized)d(Hamiltonians)h FF(H)1670 1036 y Fy(0)1703 1054 y FQ(ha)o(ving)i(a)60 1115 y(strictly)16 b(p)q(ositiv)o(e)h(\(resp.)g (strictly)f(negativ)o(e\))g(magnetic)g(\014eld)h FF(h)1272 1096 y Fy(0)1284 1115 y FQ(.)24 b(F)l(urthermore,)16 b FP(at)22 b FF(h)16 b FQ(=)f(0)j(the)60 1175 y(renormalized)13 b(Hamiltonian)h FF(H)673 1157 y Fy(0)700 1175 y FQ(dep)q(ends)i(on)g(whic)o(h)f(pure)g (phase,)h FF(\026)1382 1182 y FH(+)1428 1175 y FQ(or)f FF(\026)1515 1182 y Fy(\000)1545 1175 y FQ(,)h(one)f(uses)h(in)f(the)60 1235 y(top)e(left)f(corner)g(of)h(\(1.2\):)20 b(the)12 b(image)g(measure)f FF(\026)989 1217 y Fy(0)989 1247 y FH(+)1032 1235 y FQ(w)o(ould)h(b)q(e)h (Gibbsian)g(for)g(some)f(Hamiltonian)60 1295 y FF(H)104 1277 y Fy(0)100 1307 y FH(+)146 1295 y FQ(ha)o(ving)k(\(among)g(other)g (couplings\))g(a)h(strictly)d(p)q(ositiv)o(e)i(magnetic)e(\014eld,)h(while)h (the)f(image)60 1355 y(measure)k FF(\026)283 1337 y Fy(0)283 1368 y(\000)333 1355 y FQ(w)o(ould)h(b)q(e)g(Gibbsian)g(for)h(some)e (Hamiltonian)f FF(H)1292 1337 y Fy(0)1288 1368 y(\000)1338 1355 y FQ(ha)o(ving)i(a)g(strictly)f(negativ)o(e)60 1416 y(magnetic)e (\014eld.)29 b(\(Ob)o(viously)18 b FF(H)699 1397 y Fy(0)695 1428 y FH(+)743 1416 y FQ(and)i FF(H)885 1397 y Fy(0)881 1428 y(\000)930 1416 y FQ(w)o(ould)f(b)q(e)g(related)f(b)o(y)g(the)h FF(\033)h FE(!)e(\000)p FF(\033)i FQ(symmetry)-5 b(,)60 1476 y(i.e.)19 b(b)o(y)h(rev)o(ersing)g(the)g(signs)h(of)g(all)f FP(o)n(dd)25 b FQ(couplings.\))35 b(In)20 b(this)h(scenario,)g(therefore,)g (the)f(R)o(G)60 1536 y(map)c FE(R)h FQ(is)f FP(disc)n(ontinuous)22 b FQ(as)17 b(one)g(approac)o(hes)g(the)g(phase-transition)h(line,)d(and)i FP(multi-value)n(d)60 1596 y FQ(on)e(that)g(line.)321 1578 y FH(6)360 1596 y FQ(This)f(picture)g(is)g(also)h(consisten)o(t)f(with)g(the) g(in)o(tuitiv)o(e)e(idea)i(that)h(magnetization)60 1656 y(increases)h(and)h (correlation)e(length)i(decreases)e(under)i(the)f(R)o(G)g(map.)133 1716 y(Ho)o(w)h(can)g(w)o(e)g(distinguish)g(b)q(et)o(w)o(een)f(these)h(t)o(w) o(o)g(scenarios?)24 b(Otherwise)16 b(put:)23 b(Supp)q(ose)18 b(w)o(e)60 1777 y(are)f(giv)o(en)f(a)h(measure)f FF(\026)531 1759 y Fy(0)560 1777 y FQ(with)h(a)g(large)g(p)q(ositiv)o(e)f(magnetization)g (and)h(a)g(small)f(\(but)h(nonzero\))60 1837 y(correlation)g(length.)26 b(Do)q(es)19 b(this)f(measure)e(come)h(from)g(a)h(Hamiltonian)e FF(H)1500 1819 y Fy(0)1530 1837 y FQ(with)h FF(\014)k FQ(large)c(and)60 1897 y FF(h)g FQ(=)f(0,)j(or)f(do)q(es)h(it)e(come)g(from)f(a)j(Hamiltonian)d (with)i FF(\014)i FQ(not)e(so)h(large)f(\(p)q(ossibly)g(ev)o(en)f(small\))60 1957 y(and)k FF(h)f FQ(large)g(and)h(p)q(ositiv)o(e?)33 b FP(Both)24 b FQ(of)d(these)f(regions)g(in)g(the)g(\()p FF(\014)s(;)8 b(h)p FQ(\)-plane)20 b(corresp)q(ond)h(to)g(a)60 2017 y(large)e(p)q(ositiv)o(e)f (magnetization)g(and)h(a)h(small)d(correlation)i(length.)29 b(Ho)o(w)19 b(can)g(w)o(e)f(distinguish)60 2078 y(b)q(et)o(w)o(een)d(the)h(t) o(w)o(o?)133 2138 y(The)k(answ)o(er)f(has)i(to)f(do)g(with)f(the)g FP(lar)n(ge-deviation)25 b FQ(prop)q(erties)20 b(of)f(the)h(measure)e FF(\026)1762 2120 y Fy(0)1774 2138 y FQ(.)31 b(Let)60 2198 y(\003)22 b(b)q(e)f(a)h(large)g(cubical)f(b)q(o)o(x)h(of)g(side)f FF(L)p FQ(,)h(and)h(let)e FE(M)1098 2205 y FH(\003)1147 2198 y FE(\021)1209 2165 y Fx(P)1253 2208 y FD(x)p Fy(2)p FH(\003)1331 2198 y FF(\033)1359 2205 y FD(x)1402 2198 y FQ(b)q(e)h(the)f(total)h(spin)g (in)f(\003)p 60 2245 732 2 v 116 2298 a FA(5)135 2313 y Fz(More)13 b(precisely)m(,)g(the)g(\015o)o(w)g(w)o(ould)e(tak)o(e)i(place)g(in)f(an)h (in\014nite-dimensional)d(space)k(of)e(couplings,)g(but)h(w)o(ould)60 2363 y(resp)q(ect)k(the)e Fv(\033)f Fu(!)e(\000)p Fv(\033)k Fz(symmetry)m(.)i(That)c(is,)h(second-nearest-neigh)o(b)q(or)h(and)f (longer-distance)g(pair)f(couplings,)60 2413 y(four-spin)c(couplings,)h (six-spin)f(couplings)h(and)f(so)h(forth)g(w)o(ould)f(certainly)h(b)q(e)g (induced;)h(but)f Fw(no)j Fz(magnetic)c(\014elds,)60 2463 y(three-spin)15 b(couplings)e(or)h(other)h Fw(o)n(dd)j Fz(in)o(teractions)d(w)o(ould)e (arise.)116 2521 y FA(6)135 2536 y Fz(This)c(p)q(ossibilit)o(y)f(w)o(as)i (suggested)h(earlier,)f(in)f(the)h(con)o(text)h(of)e(the)h(3-state)g(P)o (otts)g(mo)q(del)e(in)h(three)i(dimensions,)60 2586 y(b)o(y)k(Bl\177)-21 b(ote)16 b(and)f(Sw)o(endsen)h([33)o(])f(and)g(with)g(esp)q(ecial)h(clarit)o (y)f(b)o(y)g(Rebbi)g(and)g(Sw)o(endsen)h([305)o(,)f(p.)g(4099].)21 b(It)15 b(w)o(as)60 2636 y(also)e(suggested,)i(in)e(the)i(con)o(text)g(of)e (a)g(mean-\014eld)g(computation,)f(b)o(y)h(Hud\023)-21 b(ak)14 b([197)o(].)951 2784 y FQ(11)p eop %%Page: 12 12 bop 243 1058 a @beginspecial 24 @llx 33.500000 @lly 424 @urx 259.500000 @ury 3513 @rwi @setspecial %%BeginDocument: fig1a.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n []/_Symbol/Symbol Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Italic/Times-Italic Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 0.5 w 4 M []0 d 386 60.5 m 386 242.5 L 96 242.5 L 96 60.5 L 386 60.5 L s 1 w 241 151.5 m S 95.75 151 m 386 151.75 l S u 0 g 96 237.6917 m 98.8117 237.6917 101.0911 239.8445 101.0911 242.5 c 101.0911 245.1555 98.8117 247.3083 96 247.3083 c 93.1883 247.3083 90.9089 245.1555 90.9089 242.5 c 90.9089 239.8445 93.1883 237.6917 96 237.6917 c f 96 242.5 m F U u 96 237.6917 m 98.8117 237.6917 101.0911 239.8445 101.0911 242.5 c 101.0911 245.1555 98.8117 247.3083 96 247.3083 c 93.1883 247.3083 90.9089 245.1555 90.9089 242.5 c 90.9089 239.8445 93.1883 237.6917 96 237.6917 c f 96 242.5 m F U u 96 55.6917 m 98.8117 55.6917 101.0911 57.8445 101.0911 60.5 c 101.0911 63.1555 98.8117 65.3083 96 65.3083 c 93.1883 65.3083 90.9089 63.1555 90.9089 60.5 c 90.9089 57.8445 93.1883 55.6917 96 55.6917 c f 96 60.5 m F U u 96 55.6917 m 98.8117 55.6917 101.0911 57.8445 101.0911 60.5 c 101.0911 63.1555 98.8117 65.3083 96 65.3083 c 93.1883 65.3083 90.9089 63.1555 90.9089 60.5 c 90.9089 57.8445 93.1883 55.6917 96 55.6917 c f 96 60.5 m F U u 95.75 146.1917 m 98.5617 146.1917 100.8411 148.3445 100.8411 151 c 100.8411 153.6555 98.5617 155.8083 95.75 155.8083 c 92.9383 155.8083 90.6589 153.6555 90.6589 151 c 90.6589 148.3445 92.9383 146.1917 95.75 146.1917 c f 95.75 151 m F U u 95.75 146.1917 m 98.5617 146.1917 100.8411 148.3445 100.8411 151 c 100.8411 153.6555 98.5617 155.8083 95.75 155.8083 c 92.9383 155.8083 90.6589 153.6555 90.6589 151 c F U u 241 146.6917 m 243.8117 146.6917 246.0911 148.8445 246.0911 151.5 c 246.0911 154.1555 243.8117 156.3083 241 156.3083 c 238.1883 156.3083 235.9089 154.1555 235.9089 151.5 c 235.9089 148.8445 238.1883 146.6917 241 146.6917 c f 241 151.5 m F U u 241 146.6917 m 243.8117 146.6917 246.0911 148.8445 246.0911 151.5 c 246.0911 154.1555 243.8117 156.3083 241 156.3083 c 238.1883 156.3083 235.9089 154.1555 235.9089 151.5 c 235.9089 148.8445 238.1883 146.6917 241 146.6917 c f 241 151.5 m F U u 386 146.9417 m 388.8117 146.9417 391.0911 149.0945 391.0911 151.75 c 391.0911 154.4055 388.8117 156.5583 386 156.5583 c 383.1883 156.5583 380.9089 154.4055 380.9089 151.75 c 380.9089 149.0945 383.1883 146.9417 386 146.9417 c f 386 151.75 m F U u 386 146.9417 m 388.8117 146.9417 391.0911 149.0945 391.0911 151.75 c 391.0911 154.4055 388.8117 156.5583 386 156.5583 c 383.1883 156.5583 380.9089 154.4055 380.9089 151.75 c 380.9089 149.0945 383.1883 146.9417 386 146.9417 c f U u 0 G 241 151.5 m S 250.0995 151.5 m 250.0995 154.4679 248.0625 156.8739 245.5498 156.8739 c S 245.5498 156.8739 m 243.037 156.8739 241 154.4679 241 151.5 c S 245.5498 151.5 m S U u 250.0775 151.6 m 250.0775 148.6321 252.1145 146.2261 254.6272 146.2261 c 257.1399 146.2261 259.177 148.6321 259.177 151.6 c S 254.6272 156.9739 m S 250.0775 151.6 m S 254.6272 151.6 m S U u 263.7212 145.9261 m S 268.271 151.3 m 268.271 154.2679 266.2339 156.6739 263.7212 156.6739 c 261.2085 156.6739 259.1715 154.2679 259.1715 151.3 c S 263.7212 151.3 m S U u 268.2489 151.4 m 268.2489 148.4321 270.2859 146.0261 272.7987 146.0261 c 275.3114 146.0261 277.3484 148.4321 277.3484 151.4 c S 272.7987 156.7739 m S 272.7987 151.4 m S U u 277.3484 151.4 m S 286.448 151.4 m 286.448 154.3679 284.4109 156.7739 281.8982 156.7739 c S 281.8982 156.7739 m 279.3855 156.7739 277.3484 154.3679 277.3484 151.4 c S 281.8982 151.4 m S U u 286.4259 151.5 m 286.4259 148.5321 288.4629 146.126 290.9757 146.126 c 293.4884 146.126 295.5254 148.5321 295.5254 151.5 c S 290.9757 156.8739 m S 286.4259 151.5 m S 290.9757 151.5 m S U u 300.0697 145.8261 m S 304.6194 151.2 m 304.6194 154.1679 302.5824 156.5739 300.0697 156.5739 c 297.5569 156.5739 295.5199 154.1679 295.5199 151.2 c S 300.0697 151.2 m S U u 304.5974 151.3 m 304.5974 148.3321 306.6344 145.9261 309.1471 145.9261 c 311.6598 145.9261 313.6969 148.3321 313.6969 151.3 c S 309.1471 156.6739 m S 309.1471 151.3 m S U u 313.6969 151.3 m S 322.7964 151.3 m 322.7964 154.2679 320.7594 156.6739 318.2467 156.6739 c S 318.2467 156.6739 m 315.7339 156.6739 313.6969 154.2679 313.6969 151.3 c S 318.2467 151.3 m S U u 322.7743 151.4 m 322.7743 148.4321 324.8114 146.0261 327.3241 146.0261 c 329.8368 146.0261 331.8739 148.4321 331.8739 151.4 c S 327.3241 156.7739 m S 322.7743 151.4 m S 327.3241 151.4 m S U u 336.4181 145.7261 m S 340.9679 151.1 m 340.9679 154.0679 338.9308 156.4739 336.4181 156.4739 c 333.9054 156.4739 331.8684 154.0679 331.8684 151.1 c S 336.4181 151.1 m S U u 340.9458 151.2 m 340.9458 148.2321 342.9828 145.8261 345.4956 145.8261 c 348.0083 145.8261 350.0453 148.2321 350.0453 151.2 c S 345.4956 156.5739 m S 345.4956 151.2 m S U u 350.0453 151.2 m S 359.1448 151.2 m 359.1448 154.1679 357.1078 156.5739 354.5951 156.5739 c S 354.5951 156.5739 m 352.0824 156.5739 350.0453 154.1679 350.0453 151.2 c S 354.5951 151.2 m S U u 359.1228 151.3 m 359.1228 148.3321 361.1598 145.9261 363.6726 145.9261 c 366.1853 145.9261 368.2223 148.3321 368.2223 151.3 c S 363.6726 156.6739 m S 359.1228 151.3 m S 363.6726 151.3 m S U u 372.7666 145.6261 m S 377.3163 151 m 377.3163 153.9679 375.2793 156.3739 372.7666 156.3739 c 370.2538 156.3739 368.2168 153.9679 368.2168 151 c S 372.7666 151 m S U u 377.2942 151.1 m 377.2942 148.1321 379.3313 145.7261 381.844 145.7261 c 384.3567 145.7261 386.3938 148.1321 386.3938 151.1 c S 381.844 156.4739 m S 381.844 151.1 m S U u u 0 g /_Times-Italic 12 14.5 0 0 z [1 0 0 1 37 243]e (h)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 43 243]e ( = +)t T U U u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 36.5 151.25]e (h)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 42.5 151.25]e ( = 0)t T U U u u /_Symbol 12 14.5 0 0 z [1 0 0 1 77.25 135]e ( b = 0)t T U U u u /_Symbol 12 14.5 0 0 z [1 0 0 1 372.5 135]e (b = )t T U U 0 G 394.7417 138.658 m S 401.2583 138.8421 m S u 0 g 309.0412 145.9161 m 310.9973 151.5 L 309.0412 157.0839 L 319.9588 151.5 L 309.0412 145.9161 L f U u 181.4588 145.9161 m 179.5027 151.5 L 181.4588 157.0839 L 170.5412 151.5 L 181.4588 145.9161 L f U u 0 G 267.5 162.3518 m 287.628 162.3518 305.8304 166.3128 318.9139 172.7007 c S 318.9139 172.7007 m 331.7225 178.9543 339.6249 187.5339 339.6249 197 c S 267.5 231.6482 m S 195.3751 197 m S 267.5 197 m S U u 0 g 204.72 226.5968 m 203.3639 232.3558 L 205.898 237.702 L 194.4527 233.3011 L 204.72 226.5968 L f U u 0 G 98.0065 238.1846 m 98.0065 228.6697 166.222 220.9561 250.3672 220.9561 c 252.1035 220.8967 l 286.6831 220.8967 314.7164 208.7911 314.7164 193.8585 c 314.7164 178.9259 286.6831 166.8202 252.1035 166.8202 c S 189.4905 193.8585 m S 252.1035 193.8585 m S U u 0 g 169.103 219.4548 m 167.9257 223.9489 L 170.1257 228.1209 L 160.1898 224.6865 L 169.103 219.4548 L f U u 0 G 166.2313 200.7501 m 166.2313 199.5929 199.3566 198.6548 240.2173 198.6548 c 241.1035 198.6226 l 258.7528 198.6226 273.0609 192.0629 273.0609 183.9714 c 273.0609 175.8799 258.7528 169.3202 241.1035 169.3202 c S 209.146 183.9714 m S 241.1035 183.9714 m S U 0 g 367.3374 210.334 m F 0 G 0.3 w 10 M 240.2173 202.8456 m S 0 g 1 w 4 M 240.2173 210.334 m F u 0 G 96 242.5 m 96 219.4425 127.4442 200.75 166.2313 200.75 c S 236.4626 242.5 m S 164.7583 235.1085 m S 164.7583 218.7945 m S U u 0 g 171.9453 195.1669 m 170.768 199.661 L 172.9679 203.833 L 163.032 200.3987 L 171.9453 195.1669 L f U u 0 G 120.9999 167.5004 m 120.9999 162.7812 170.4734 158.9553 231.5 158.9553 c S 342.0001 167.5004 m S 231.5 176.0454 m S 218.6488 168.6216 m S U u 96.5001 240.5 m 96.5001 200.184 107.4693 167.5004 121 167.5004 c S 145.4999 240.5 m S 122 209.6954 m S 122 190.25 m S U u 0 g 121.449 160.2305 m 122.356 166.077 L 126.7131 170.0796 L 114.4527 170.3011 L 121.449 160.2305 L f U 0 G 256.2807 198.75 m S 267.5001 163.8516 m S 97.9996 242.0003 m 97.9996 236.3251 172.9935 231.7243 265.5 231.7243 c 267.5001 231.6484 l 307.247 231.6484 339.4693 216.4713 339.4693 197.75 c S 298 198.75 m S u 268.2693 139.059 m 288.3972 138.9546 306.5792 134.8992 319.6295 128.4434 c S 319.6295 128.4434 m 332.4056 122.1233 340.2635 113.5027 340.2144 104.0366 c S 267.9098 69.7626 m S 195.9646 104.785 m S 268.0895 104.4108 m S U 0.3 w 10 M 265.8027 49.1449 m S u 0 g 1 w 4 M 205.156 75.1397 m 203.77 69.3878 L 206.2764 64.0284 L 194.8539 68.4887 L 205.156 75.1397 L f U u 0 G 98.3823 64.1055 m 98.4317 73.6204 166.6872 80.9801 250.8325 80.5435 c 252.569 80.5939 l 287.1486 80.4145 315.2447 92.3748 315.3222 107.3074 c 315.3997 122.24 287.4292 134.4911 252.8495 134.6705 c S 190.0963 107.957 m S 252.7093 107.6322 m S U 0.3 w 10 M 250.6537 46.0866 m S u 0 g 1 w 4 M 169.576 82.4665 m 168.3754 77.9785 L 170.5537 73.7951 L 160.6356 77.281 L 169.576 82.4665 L f U u 0 G 241.8366 132.2276 m 259.4859 132.136 273.76 125.5021 273.718 117.4105 c 273.6761 109.319 259.3339 102.8336 241.6846 102.9252 c S 209.8031 117.7421 m S 241.7606 117.5764 m S U 0 g 367.8577 90.5589 m F 0 G 0.3 w 10 M 240.7765 98.7068 m S 1 w 166.8014 101.186 m 166.8074 102.3433 199.9375 103.1096 240.7982 102.8976 c 242.5 103 l S 0 g 4 M 240.7376 91.2184 m F u 0 G 96.3535 59.8005 m 96.4731 82.8581 128.0143 101.3874 166.8014 101.1862 c S 236.8161 59.0718 m S 165.1501 66.8353 m S 165.2347 83.1493 m S U u 0 g 172.5443 106.7396 m 171.3437 102.2516 L 173.522 98.0682 L 163.6039 101.5541 L 172.5443 106.7396 L f U u 0 G 121.7425 134.6705 m 121.767 139.3897 171.2603 142.9589 232.2869 142.6423 c S 342.7426 133.5239 m S 232.1982 125.5521 m S 219.3855 133.0426 m S U u 96.864 61.798 m 97.0731 102.114 108.2119 134.7407 121.7426 134.6705 c S 145.8637 61.5438 m S 122.5236 92.4702 m S 122.6245 111.9157 m S U u 0 g 122.2293 141.938 m 123.1059 136.0868 L 127.4423 132.0616 L 115.1807 131.9038 L 122.2293 141.938 L f U u 0 G 256.8611 102.719 m S 268.2615 137.5592 m S 98.3557 60.2898 m 98.3851 65.965 173.4028 70.1768 265.9094 69.6968 c 267.9098 69.7624 l 307.6567 69.5562 339.9578 84.5661 340.0549 103.2874 c S 298.5804 102.5026 m S U 96 237.6917 m 96 65.3083 l S u u 0 g /_Times-Roman 12 14.5 0 0 z [1 0 0 1 239.5 36.5]e (\(a\))t T U U u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 36.5 60]e (h)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 42.5 60]e (=)t T U U 0 G 52.25 63.25 m 57.75 63.25 l S u u 0 g /_Symbol 12 14.5 0 0 z [1 0 0 1 236 135.5]e (b)t T U u /_Times-Roman 10 14.5 0 0 z [1 0 0 1 242.5859 135.5]e (c)t T U U u u /_Symbol 18 21.5 0 0 z [1 0 0 1 391.084 134.1094]e (\245)t T U U u u /_Symbol 18 21.5 0 0 z [1 0 0 1 60.584 58.1094]e (\245)t T U U u u /_Symbol 18 21.5 0 0 z [1 0 0 1 63.584 241.1094]e (\245)t T U U showpage _E end %%EndDocument @endspecial 1071 x @beginspecial 24 @llx 32.500000 @lly 424 @urx 259.500000 @ury 3513 @rwi @setspecial %%BeginDocument: fig1b.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n []/_Symbol/Symbol Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Italic/Times-Italic Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z u 0 G 0 i 0 J 0 j 0.5 w 4 M []0 d 385.6454 59.9042 m 385.6454 241.9042 L 95.6454 241.9042 L 95.6454 59.9042 L 385.6454 59.9042 L s 240.6454 150.9042 m S U 1 w 95.3954 150.4042 m 385.6454 151.1542 l S u 0 g 95.6454 237.0959 m 98.457 237.0959 100.7364 239.2487 100.7364 241.9042 c 100.7364 244.5596 98.457 246.7124 95.6454 246.7124 c 92.8336 246.7124 90.5542 244.5596 90.5542 241.9042 c 90.5542 239.2487 92.8336 237.0959 95.6454 237.0959 c f 95.6454 241.9042 m F U u 95.6454 237.0959 m 98.457 237.0959 100.7364 239.2487 100.7364 241.9042 c 100.7364 244.5596 98.457 246.7124 95.6454 246.7124 c 92.8336 246.7124 90.5542 244.5596 90.5542 241.9042 c 90.5542 239.2487 92.8336 237.0959 95.6454 237.0959 c f 95.6454 241.9042 m F U u 95.6454 55.0959 m 98.457 55.0959 100.7364 57.2487 100.7364 59.9042 c 100.7364 62.5596 98.457 64.7124 95.6454 64.7124 c 92.8336 64.7124 90.5542 62.5596 90.5542 59.9042 c 90.5542 57.2487 92.8336 55.0959 95.6454 55.0959 c f 95.6454 59.9042 m F U u 95.6454 55.0959 m 98.457 55.0959 100.7364 57.2487 100.7364 59.9042 c 100.7364 62.5596 98.457 64.7124 95.6454 64.7124 c 92.8336 64.7124 90.5542 62.5596 90.5542 59.9042 c 90.5542 57.2487 92.8336 55.0959 95.6454 55.0959 c f 95.6454 59.9042 m F U u 95.3954 145.5959 m 98.207 145.5959 100.4864 147.7487 100.4864 150.4042 c 100.4864 153.0596 98.207 155.2124 95.3954 155.2124 c 92.5836 155.2124 90.3042 153.0596 90.3042 150.4042 c 90.3042 147.7487 92.5836 145.5959 95.3954 145.5959 c f 95.3954 150.4042 m F U u 95.3954 145.5959 m 98.207 145.5959 100.4864 147.7487 100.4864 150.4042 c 100.4864 153.0596 98.207 155.2124 95.3954 155.2124 c 92.5836 155.2124 90.3042 153.0596 90.3042 150.4042 c F U u 240.6454 146.0959 m 243.457 146.0959 245.7364 148.2487 245.7364 150.9042 c 245.7364 153.5596 243.457 155.7124 240.6454 155.7124 c 237.8336 155.7124 235.5542 153.5596 235.5542 150.9042 c 235.5542 148.2487 237.8336 146.0959 240.6454 146.0959 c f 240.6454 150.9042 m F U u 240.6454 146.0959 m 243.457 146.0959 245.7364 148.2487 245.7364 150.9042 c 245.7364 153.5596 243.457 155.7124 240.6454 155.7124 c 237.8336 155.7124 235.5542 153.5596 235.5542 150.9042 c 235.5542 148.2487 237.8336 146.0959 240.6454 146.0959 c f 240.6454 150.9042 m F U u 385.6454 146.3459 m 388.457 146.3459 390.7364 148.4987 390.7364 151.1542 c 390.7364 153.8096 388.457 155.9624 385.6454 155.9624 c 382.8336 155.9624 380.5542 153.8096 380.5542 151.1542 c 380.5542 148.4987 382.8336 146.3459 385.6454 146.3459 c f 385.6454 151.1542 m F U u 385.6454 146.3459 m 388.457 146.3459 390.7364 148.4987 390.7364 151.1542 c 390.7364 153.8096 388.457 155.9624 385.6454 155.9624 c 382.8336 155.9624 380.5542 153.8096 380.5542 151.1542 c 380.5542 148.4987 382.8336 146.3459 385.6454 146.3459 c f U u 0 G 240.6454 150.9042 m S 249.7448 150.9042 m 249.7448 153.8721 247.7079 156.278 245.1951 156.278 c S 245.1951 156.278 m 242.6823 156.278 240.6454 153.8721 240.6454 150.9042 c S 245.1951 150.9042 m S U u 249.7229 151.0041 m 249.7229 148.0363 251.7598 145.6302 254.2725 145.6302 c 256.7852 145.6302 258.8223 148.0363 258.8223 151.0041 c S 254.2725 156.378 m S 249.7229 151.0041 m S 254.2725 151.0041 m S U u 263.3665 145.3302 m S 267.9163 150.7041 m 267.9163 153.6721 265.8792 156.078 263.3665 156.078 c 260.8538 156.078 258.8168 153.6721 258.8168 150.7041 c S 263.3665 150.7041 m S U u 267.8942 150.8041 m 267.8942 147.8363 269.9312 145.4302 272.444 145.4302 c 274.9567 145.4302 276.9937 147.8363 276.9937 150.8041 c S 272.444 156.1781 m S 272.444 150.8041 m S U u 276.9937 150.8041 m S 286.0933 150.8041 m 286.0933 153.772 284.0562 156.1781 281.5435 156.1781 c S 281.5435 156.1781 m 279.0308 156.1781 276.9937 153.772 276.9937 150.8041 c S 281.5435 150.8041 m S U u 286.0712 150.9042 m 286.0712 147.9362 288.1082 145.5301 290.621 145.5301 c 293.1337 145.5301 295.1707 147.9362 295.1707 150.9042 c S 290.621 156.278 m S 286.0712 150.9042 m S 290.621 150.9042 m S U u 299.715 145.2303 m S 304.2647 150.6042 m 304.2647 153.572 302.2277 155.9781 299.715 155.9781 c 297.2022 155.9781 295.1652 153.572 295.1652 150.6042 c S 299.715 150.6042 m S U u 304.2427 150.7041 m 304.2427 147.7362 306.2798 145.3302 308.7924 145.3302 c 311.3051 145.3302 313.3423 147.7362 313.3423 150.7041 c S 308.7924 156.078 m S 308.7924 150.7041 m S U u 313.3423 150.7041 m S 322.4417 150.7041 m 322.4417 153.6721 320.4048 156.078 317.892 156.078 c S 317.892 156.078 m 315.3792 156.078 313.3423 153.6721 313.3423 150.7041 c S 317.892 150.7041 m S U u 322.4196 150.8041 m 322.4196 147.8363 324.4567 145.4302 326.9694 145.4302 c 329.4821 145.4302 331.5192 147.8363 331.5192 150.8041 c S 326.9694 156.1781 m S 322.4196 150.8041 m S 326.9694 150.8041 m S U u 336.0634 145.1302 m S 340.6132 150.5041 m 340.6132 153.472 338.5761 155.878 336.0634 155.878 c 333.5507 155.878 331.5137 153.472 331.5137 150.5041 c S 336.0634 150.5041 m S U u 340.5911 150.6042 m 340.5911 147.6362 342.6281 145.2303 345.1409 145.2303 c 347.6536 145.2303 349.6906 147.6362 349.6906 150.6042 c S 345.1409 155.9781 m S 345.1409 150.6042 m S U u 349.6906 150.6042 m S 358.7901 150.6042 m 358.7901 153.572 356.7531 155.9781 354.2404 155.9781 c S 354.2404 155.9781 m 351.7277 155.9781 349.6906 153.572 349.6906 150.6042 c S 354.2404 150.6042 m S U u 358.7681 150.7041 m 358.7681 147.7362 360.8051 145.3302 363.3179 145.3302 c 365.8306 145.3302 367.8676 147.7362 367.8676 150.7041 c S 363.3179 156.078 m S 358.7681 150.7041 m S 363.3179 150.7041 m S U u 372.4119 145.0303 m S 376.9617 150.4042 m 376.9617 153.3721 374.9246 155.778 372.4119 155.778 c 369.8992 155.778 367.8621 153.3721 367.8621 150.4042 c S 372.4119 150.4042 m S U u 376.9395 150.5041 m 376.9395 147.5363 378.9766 145.1302 381.4893 145.1302 c 384.002 145.1302 386.0391 147.5363 386.0391 150.5041 c S 381.4893 155.878 m S 381.4893 150.5041 m S U u u 0 g /_Times-Italic 12 14.5 0 0 z [1 0 0 1 36.6454 242.4042]e (h)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 42.6454 242.4042]e ( = +)t T U U u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 36.1454 150.6542]e (h)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 42.1454 150.6542]e ( = 0)t T U U u u /_Symbol 12 14.5 0 0 z [1 0 0 1 76.8954 134.4042]e ( b = 0)t T U U u u /_Symbol 12 14.5 0 0 z [1 0 0 1 372.1454 134.4042]e (b = )t T U U 0 G 297 159 m 316.5 182.5 l S 297 143 m S u 0 g 310.9875 184.6486 m 316.5 182.5 L 319.4666 177.3811 L 322.3318 189.304 L 310.9875 184.6486 L f U 0 G 297 143 m 318.1564 120.9793 l S u 0 g 312.8146 118.4356 m 318.1564 120.9793 L 320.7431 126.3003 L 324.4673 114.6171 L 312.8146 118.4356 L f U 0 G 95.6454 237.0959 m 95.6454 64.7124 l S u u 0 g /_Times-Roman 12 14.5 0 0 z [1 0 0 1 240 36]e (\(b\))t T U U u u /_Symbol 12 14.5 0 0 z [1 0 0 1 234.9878 134.9062]e (b)t T U u /_Times-Roman 10 14.5 0 0 z [1 0 0 1 241.5737 134.9062]e (c)t T U U u 297 156.041 m 298.8075 156.041 300.2728 157.3658 300.2728 159 c 300.2728 160.6341 298.8075 161.9589 297 161.9589 c 295.1925 161.9589 293.7272 160.6341 293.7272 159 c 293.7272 157.3658 295.1925 156.041 297 156.041 c f 297 159 m F U u 297 140.041 m 298.8075 140.041 300.2728 141.3658 300.2728 143 c 300.2728 144.6341 298.8075 145.9589 297 145.9589 c 295.1925 145.9589 293.7272 144.6341 293.7272 143 c 293.7272 141.3658 295.1925 140.041 297 140.041 c f 297 143 m F U u u /_Symbol 18 21.5 0 0 z [1 0 0 1 390.9453 132.8125]e (\245)t T U U u u /_Symbol 18 21.5 0 0 z [1 0 0 1 63.084 240.6094]e (\245)t T U U u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 36.0889 58.5]e (h)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 42.0889 58.5]e (=)t T U U 0 G 51.8389 61.75 m 57.3389 61.75 l S u u 0 g /_Symbol 18 21.5 0 0 z [1 0 0 1 60.1728 56.6094]e (\245)t T U U showpage _E end %%EndDocument @endspecial 60 2403 a FQ(Figure)12 b(1:)19 b(Tw)o(o)13 b(p)q(ossible)f (scenarios)h(for)f(the)g(R)o(G)g(\015o)o(w)h(in)f(the)f(Ising)i(mo)q(del)d (at)j(lo)o(w)f(temp)q(erature.)60 2463 y(\(a\))k(R)o(G)g(map)e(is)i(con)o (tin)o(uous)g(and)g(single-v)m(alued)f(on)h(the)g(phase-transition)h(line.)j (\(b\))15 b(R)o(G)h(map)60 2523 y(is)g(discon)o(tin)o(uous)g(and)h(m)o (ulti-v)m(alued)d(on)i(the)g(phase-transition)i(line.)951 2784 y(12)p eop %%Page: 13 13 bop 60 91 a FQ(\(a)20 b(random)g(v)m(ariable\).)32 b(Clearly)19 b(there)h(is)f(an)i(o)o(v)o(erwhelming)c(probabilit)o(y)i(that)i FE(M)1698 98 y FH(\003)1744 91 y FQ(will)e(b)q(e)60 152 y(p)q(ositiv)o(e)d (\(and)h(in)g(fact)g(v)o(ery)e(close)i(to)g(its)g(mean)e(v)m(alue)i FF(L)1154 133 y FD(d)1174 152 y FF(M)1226 133 y Fy(0)1221 164 y FH(0)1256 152 y FQ(=)e FF(L)1342 133 y FD(d)1362 152 y FE(h)p FF(\033)r FE(i)1430 159 y FD(\026)1451 150 y Ft(0)1465 152 y FQ(\);)i(but)g(ho)o(w)g(rare)g(is)f(it)60 212 y(to)f(ha)o(v)o(e)f FE(M)289 219 y FH(\003)330 212 y FP(ne)n(gative)t FQ(?)23 b(If)14 b FF(\026)625 194 y Fy(0)651 212 y FQ(is)h(a)g(Gibbs)g(measure)e(for)i(some)f (Hamiltonian)f(with)i FF(h)e(>)h FQ(0,)h(then)60 272 y(the)h(ev)o(en)o(t)f FE(M)333 279 y FH(\003)373 272 y FF(<)f FQ(0)i(is)g(suppressed)h(b)o(y)f(the) g FP(bulk)23 b FQ(magnetic)15 b(\014eld:)677 382 y(Prob)781 389 y FD(\026)802 380 y Ft(0)815 382 y FQ(\()p FE(M)894 389 y FH(\003)934 382 y FF(<)f FQ(0\))g FE(\030)g FF(e)1119 361 y Fy(\000)p FD(O)q FH(\()p FD(L)1212 350 y Fs(d)1230 361 y FH(\))1259 382 y FF(:)517 b FQ(\(1)p FF(:)p FQ(4\))60 492 y(On)20 b(the)h(other)f(hand,)i(if)e FF(\026)584 474 y Fy(0)616 492 y FQ(is)g(a)h(Gibbs)g(measure)e(for)i(some)e(Hamiltonian)g(with)h FF(h)h FQ(=)g(0)f(and)60 552 y FF(\014)c(>)e(\014)184 559 y FD(c)201 552 y FQ(,)i(then)g(the)g(ev)o(en)o(t)e FE(M)614 559 y FH(\003)655 552 y FF(<)f FQ(0)k(is)f(suppressed)h(only)f(b)o(y)g(a)g FP(surfac)n(e)k FQ(energy:)658 662 y(Prob)761 669 y FD(\026)782 660 y Ft(0)796 662 y FQ(\()p FE(M)875 669 y FH(\003)915 662 y FF(<)14 b FQ(0\))g FE(\030)f FF(e)1099 642 y Fy(\000)p FD(O)q FH(\()p FD(L)1192 630 y Fs(d)p Ft(\000)p Fr(1)1249 642 y FH(\))1279 662 y FF(:)497 b FQ(\(1)p FF(:)p FQ(5\))133 772 y(It)15 b(is)g(no)o(w)h(easy) g(to)g(decide)e(b)q(et)o(w)o(een)g(the)i(t)o(w)o(o)f(scenarios)h(for)f(the)g (R)o(G)h(\015o)o(w.)21 b(In)15 b(the)g(starting)60 832 y(measure)d FF(\026)276 839 y FH(+)306 832 y FQ(,)h(the)g(o)q(ccurrence)f(of)h(a)h(large) f(region)g(with)g(negativ)o(e)f(total)h(spin)g(is)g(suppressed)g(only)60 892 y(lik)o(e)18 b FF(e)176 874 y Fy(\000)p FD(O)q FH(\()p FD(L)269 863 y Fs(d)p Ft(\000)p Fr(1)326 874 y FH(\))341 892 y FQ(;)j(roughly)f(sp)q(eaking,)h(the)e(measure)g FF(\026)1086 899 y FH(+)1135 892 y FQ(\\kno)o(ws")i(that)f(it)f(is)h(degenerate)f(with)60 953 y(the)d(measure)g FF(\026)364 960 y Fy(\000)394 953 y FQ(.)22 b(But)17 b(then)f(in)g(the)h(blo)q(c)o(k-spin)f(measure)g FF(\026)1233 935 y Fy(0)1233 965 y FH(+)1277 953 y FQ(=)f FF(\026)1359 960 y FH(+)1388 953 y FF(T)7 b FQ(,)16 b(there)g(m)o(ust)g(also)h(b)q(e)g(a)60 1020 y(probabilit)o(y)308 1032 y FE(\030)308 1011 y FF(>)360 1020 y(e)383 1002 y Fy(\000)p FD(O)q FH(\()p FD(L)476 990 y Fs(d)p Ft(\000)p Fr(1)532 1002 y FH(\))563 1020 y FQ(of)e(observing)g(a)g (negativ)o(e)f(total)h(spin)g(\(since)f(a)h(net)f(negativ)o(e)g(original)60 1080 y(spin)k(implies,)d(with)j(high)g(probabilit)o(y)l(,)f(a)i(net)e (negativ)o(e)h(blo)q(c)o(k)f(spin\).)26 b(Since)17 b(this)h(con)o(tradicts)60 1140 y(\(1.4\),)c(w)o(e)f(conclude)g(that)h FF(\026)587 1122 y Fy(0)587 1152 y FH(+)631 1140 y FP(c)n(annot)19 b FQ(b)q(e)14 b(the)f(Gibbs)h(measure)f(of)h(a)g(Hamiltonian)e(with)h(strictly)60 1200 y(p)q(ositiv)o(e)e(magnetic)f(\014eld.)19 b(Picturesquely)l(,)10 b(the)i(image)e(measure)g FF(\026)1303 1182 y Fy(0)1303 1213 y FH(+)1345 1200 y FQ(\\remem)o(b)q(ers")f(that)j(it)f(arose)60 1260 y(from)k(an)h(original)f(Hamiltonian)f FF(H)20 b FQ(with)c(co)q (existing)f(phases.)22 b(Therefore,)15 b(the)g(discon)o(tin)o(uous-)60 1321 y(\015o)o(w)i(scenario)f(is)g(imp)q(ossible;)e(the)i(R)o(G)g(map)g FP(c)n(annot)21 b FQ(b)q(e)c(m)o(ulti-v)m(alued)c(or)k(discon)o(tin)o(uous.) 133 1381 y(It)d(is)g(a)g(relativ)o(ely)e(short)i(step)g(from)f(these)h(in)o (tuitiv)o(e)d(ideas)j(to)h(a)f(rigorous)h(pro)q(of.)22 b(In)14 b(Section)60 1441 y(3)j(w)o(e)e(pro)o(v)o(e,)g(in)h(great)h(generalit)o(y)l (,)d(the)i(follo)o(wing)g(t)o(w)o(o)g(theorems:)182 1543 y FM(First)24 b(fundamen)n(tal)g(theorem.)46 b FQ(If)21 b FF(\026)h FQ(and)g FF(\027)j FQ(are)c(Gibbs)h(measures)f(for)g(the)182 1603 y(same)f(in)o(teraction,)g(then)h(either)f FF(\026T)28 b FQ(and)21 b FF(\027)s(T)28 b FQ(are)21 b(b)q(oth)h(non-Gibbsian,)h(or)e (else)182 1663 y(there)16 b(exists)f(an)i(in)o(teraction)e(for)i(whic)o(h)f (b)q(oth)h FF(\026T)23 b FQ(and)17 b FF(\027)s(T)23 b FQ(are)16 b(Gibbs)h(measures.)182 1723 y(In)f(the)h(latter)f(case,)g(this)g(is)h(the)f FP(only)21 b FQ(in)o(teraction)16 b(for)h(whic)o(h)e(either)h FF(\026T)23 b FQ(or)17 b FF(\027)s(T)23 b FQ(is)182 1783 y(a)18 b(Gibbs)f(measure.)23 b(Therefore,)17 b(the)g(renormalization-group)g(map)f FE(R)i FQ(cannot)g(b)q(e)182 1844 y(m)o(ulti-v)m(alued.)182 1937 y FM(Second)k(fundamen)n(tal)f(theorem.)46 b FQ(The)20 b(renormalization-group)e(map)h FE(R)g FQ(is)182 1997 y(con)o(tin)o(uous)12 b(\(in)g(fact,)g(Lipsc)o(hitz)f(con)o(tin)o(uous\))h(on)h(the)f(domain)f (where)h(it)g(is)g(de\014ned.)60 2099 y(Of)20 b(course,)g(these)g(summaries)d (of)j(the)g(theorems)f(are)h(not)g(quite)f(precise:)28 b(w)o(e)19 b(need)h(to)g(mak)o(e)60 2159 y(clear,)14 b(for)i(example,)c(in)j(what)h (space)f(of)h(in)o(teractions)e(w)o(e)h(are)g(w)o(orking,)g(and)h(in)e(what)i (norm)e(w)o(e)60 2219 y(are)j(de\014ning)g(con)o(tin)o(uit)o(y)l(.)k(The)c (detailed)f(statemen)o(t)g(of)h(the)f(F)l(undamen)o(tal)g(Theorems)g(can)h(b) q(e)60 2280 y(found)h(in)e(Sections)h(3.2)g(and)h(3.3,)f(resp)q(ectiv)o(ely)l (.)j(The)d(pro)q(ofs)i(of)e(the)g(F)l(undamen)o(tal)e(Theorems)60 2340 y(are)g(based)g(on)h(the)e(general)h(theory)g(of)g(in\014nite-v)o(olume) d(lattice)h(systems)h(dev)o(elop)q(ed)g(in)h(Section)60 2400 y(2.)21 b(These)13 b(t)o(w)o(o)h(theorems)e(mak)o(e)g(clear)h(that)h(the)g FP(only)k FQ(w)o(a)o(y)13 b(in)h(whic)o(h)f(the)g(R)o(G)h(map)f(can)g(b)q (ecome)60 2460 y(grossly)18 b(pathological)f(is)g(for)h(it)e(to)i(b)q(e)f FP(unde\014ne)n(d)5 b FQ(,)19 b(i.e.)c(for)j(the)f(image)e(measure)h FF(\026)1638 2442 y Fy(0)1667 2460 y FQ(to)i(b)q(e)f(non-)60 2520 y(Gibbsian.)951 2784 y(13)p eop %%Page: 14 14 bop 60 91 a FB(1.4)70 b(Summ)n(ary)20 b(of)k(Gri\016ths-P)n(earce-Israel)d(P) n(athologies)60 184 y FQ(This)14 b(is)g(not,)g(ho)o(w)o(ev)o(er,)f(the)h(end) f(of)i(the)e(story:)21 b(although)15 b(the)e(discon)o(tin)o(uous-\015o)o(w)i (scenario)f(for)60 244 y(the)g(R)o(G)f(map)h(in)f(the)h(lo)o(w-temp)q (erature)e(Ising)i(mo)q(del)f(is)h(not)g(correct,)f(the)h(traditional)g (scenario)60 304 y(is)j(in)g(man)o(y)f(cases)i(not)g(correct)e(either!)24 b(The)17 b(First)g(F)l(undamen)o(tal)f(Theorem)g(lea)o(v)o(es)g(op)q(en)i (the)60 364 y(p)q(ossibilit)o(y)f(that)i(the)g(image)e(measure)g FF(\026)853 346 y Fy(0)883 364 y FQ(=)g FF(\026T)25 b FQ(ma)o(y)17 b(b)q(e)i FP(non-Gibbsian)t FQ(,)h(in)e(whic)o(h)g(case)g(the)60 424 y(R)o(G)f(map)f FE(R)h FQ(w)o(ould)f(b)q(e)h FP(unde\014ne)n(d)5 b FQ(.)25 b(It)16 b(turns)i(out)f(that)g FP(this)h(p)n(atholo)n(gy)f(do)n(es) h(in)g(fact)h(o)n(c)n(cur)i FQ(in)60 485 y(a)d(rather)f(wide)g(v)m(ariet)o(y) f(of)h(examples.)22 b(The)17 b(o)q(ccurrence)g(of)g(non-Gibbsianness)i(for)e (the)g(image)60 545 y(measure)11 b FF(\026)275 527 y Fy(0)299 545 y FQ(w)o(as)i(\014rst)g(p)q(oin)o(ted)f(out)h(b)o(y)e(Israel)h([207)q(])g (in)g(one)g(of)h(the)f(cases)g(suggested)h(b)o(y)f(Gri\016ths)60 605 y(and)21 b(P)o(earce)e([173)q(,)h(171)q(].)33 b(In)20 b(Section)g(4)h(w)o (e)f(complete)e(and)j(extend)e(Israel's)h(argumen)o(t,)f(and)60 665 y(sho)o(w)i(that)f(in)g(a)g(large)g(class)g(of)h(examples)d(\(alw)o(a)o (ys)i(at)g(lo)o(w)g(temp)q(erature,)f(but)h(not)h(only)f(on)60 725 y(phase-transition)d(surfaces\))g(the)f(image)f(measure)f FF(\026)1064 707 y Fy(0)1093 725 y FQ(is)i(non-Gibbsian.)133 786 y(The)e(non-Gibbsianness)h(arises)f(from)f(the)g(fact)h(|)g(already)f (noted)h(b)o(y)g(Gri\016ths)f(and)i(P)o(earce)60 846 y(|)k(that)h(the)f(\\in) o(ternal)f(spins")i(\(the)f(v)m(ariables)g(b)q(eing)g(in)o(tegrated)g(o)o(v)o (er)f(in)h(the)g(R)o(G)g(transfor-)60 906 y(mation\))d(ma)o(y)g(undergo)i(a)g (\014rst-order)g(phase)g(transition)f(for)h(some)e(\014xed)h(blo)q(c)o (k-spin)g(con\014gu-)60 966 y(ration)f FF(!)235 948 y Fy(0)233 978 y FH(sp)q(ecial)338 966 y FQ(.)21 b(Moreo)o(v)o(er,)14 b(in)h(some)f(cases)i(the)f(di\013eren)o(t)f(phases)j(\(=)e(Gibbs)g (measures\))g(of)g(the)60 1026 y(in)o(ternal-spin)i(system)g(can)h(b)q(e)g (selected)e(b)o(y)i(an)g(appropriate)h(c)o(hoice)d(of)i FP(blo)n(ck-spin)24 b FQ(b)q(oundary)60 1087 y(conditions.)c(In)14 b(this)f(w)o(a)o(y)l(,)h (information)f(can)g(b)q(e)h(transmitted)f(from)f(distan)o(t)i(blo)q(c)o(k)f (spins)h(to)g(the)60 1147 y(blo)q(c)o(k)f(spin)g(at)h(the)g(origin)f(via)g (the)h(in)o(ternal)e(spins)i(in)f(the)g(in)o(termediate)e(region,)i(ev)o(en)g (when)g(the)60 1207 y(blo)q(c)o(k)18 b(spins)h(in)f(the)g(in)o(termediate)e (region)i(are)h FP(\014xe)n(d)5 b FQ(.)29 b(As)18 b(a)h(consequence,)f(the)g (renormalized)60 1267 y(measure)h FF(\026)283 1249 y Fy(0)315 1267 y FQ(violates)g(a)h(v)o(ery)f(w)o(eak)h(lo)q(calit)o(y)e(condition)i(|)g FP(quasilo)n(c)n(ality)t FQ(,)h(see)e(Section)h(2.3.3)60 1327 y(|)d(whic)o(h)g(is)h(ob)q(ey)o(ed)f(b)o(y)g(ev)o(ery)g(Gibbs)g(measure)g (coming)f(from)h(a)h(reasonable)g(in)o(teraction.)24 b(It)60 1388 y(follo)o(ws)16 b(immedi)o(ately)d(that)k(the)f(renormalized)e(measure)g FF(\026)1196 1369 y Fy(0)1225 1388 y FQ(m)o(ust)h(b)q(e)h(non-Gibbsian.)133 1448 y(It)23 b(is)g(at)h(\014rst)f(surprising)h(that)f(the)g(existence)f(of)i (pathologies)g(for)f(a)h FP(single)k FQ(blo)q(c)o(k-spin)60 1508 y(con\014guration)15 b FF(!)385 1490 y Fy(0)383 1520 y FH(sp)q(ecial)501 1508 y FQ(|)f(whic)o(h)e(has,)j(of)e(course,)h(probabilit)o (y)e(zero)h(|)h(can)f(nev)o(ertheless)f(cause)60 1568 y(the)18 b(non-Gibbsianness)h(of)f(the)g(renormalized)d(measure;)i(and)i(indeed,)e (this)g(fact)h FP(alone)23 b FQ(is)18 b FP(not)60 1628 y FQ(su\016cien)o(t)13 b(for)i(concluding)f(non-Gibbsianness.)22 b(Rather,)15 b(what)g(happ)q(ens)g (in)f(these)h(examples)d(is)60 1688 y(that)18 b(for)f(blo)q(c)o(k-spin)g (con\014gurations)h(whic)o(h)f(are)g FP(ne)n(ar)22 b FQ(\(in)17 b(the)g(pro)q(duct)h(top)q(ology\))g(to)f FF(!)1786 1670 y Fy(0)1784 1701 y FH(sp)q(ecial)60 1749 y FQ(|)f(namely)l(,)d(those)k(whic)o (h)e(agree)h(with)g FF(!)840 1731 y Fy(0)838 1761 y FH(sp)q(ecial)959 1749 y FQ(in)g(a)g(large)g(cub)q(e)g(and)g(di\013er)g(from)f(it)g(outside)h (|)60 1809 y(the)f(in)o(ternal-spin)f(phase)i(dep)q(ends)g(sensitiv)o(ely)c (on)k(the)f(blo)q(c)o(k)g(spins)g FP(outside)k FQ(the)c(cub)q(e.)21 b(These)60 1869 y(con\014gurations)16 b(ha)o(v)o(e)e(a)i(small)d(but)i FP(nonzer)n(o)j FQ(probabilit)o(y)l(,)c(and)h(this)g(turns)h(out)f(to)g(b)q (e)g(su\016cien)o(t)60 1929 y(for)i(pro)o(ving)f(non-Gibbsianness.)22 b(The)17 b(details)e(of)i(the)f(pro)q(of)h(are)f(giv)o(en)g(in)g(Sections)g (4.1{4.3.)133 1989 y(W)l(e)h(pro)o(v)o(e)e(non-Gibbsianness)k(at)e(lo)o(w)f (temp)q(erature)f(and)j(zero)e(magnetic)f(\014eld)h(in)g(the)h(fol-)60 2050 y(lo)o(wing)f(examples:)133 2151 y FE(\017)24 b FQ(Decimation)14 b(with)i(an)o(y)g(spacing)h FF(b)d FE(\025)f FQ(2,)j(for)h(the)f(Ising)g(mo)q (del)f(in)h(an)o(y)g(dimension)e FF(d)g FE(\025)g FQ(2.)133 2253 y FE(\017)24 b FQ(The)15 b(Kadano\013)h(transformation)f(with)f (\014nite)h FF(p)g FQ(and)g(arbitrary)g(blo)q(c)o(k)f(size)g FF(b)g FE(\025)f FQ(1,)i(for)g(the)182 2313 y(Ising)h(mo)q(del)f(in)h (dimension)f FF(d)f FE(\025)f FQ(2.)862 2295 y FH(7)133 2415 y FE(\017)24 b FQ(The)17 b(ma)s(jorit)o(y-rule)d(transformation)i(with)h(7)12 b FE(\002)f FQ(7)17 b(\(or)g(41)12 b FE(\002)f FQ(41,)17 b(239)c FE(\002)e FQ(239,)17 b FF(:)8 b(:)g(:)g FQ(\))16 b(blo)q(c)o(ks)182 2475 y(for)g(the)g(t)o(w)o(o-dimensional)f(Ising)h(mo)q(del.)p 60 2519 732 2 v 116 2573 a FA(7)135 2588 y Fz(In)f(earlier)g(v)o(ersions)h (of)e(this)i(w)o(ork)e([352)o(,)h(353)o(],)g(w)o(e)g(claimed)e(this)j(result) f(only)g(for)g Fw(smal)r(l)j Fv(p)p Fz(.)k(Subsequen)o(tly)60 2638 y(w)o(e)14 b(found)g(a)f(pro)q(of)h(v)n(alid)e(for)i Fw(al)r(l)j Fz(0)11 b Fv(<)h(p)g(<)g Fu(1)p Fz(,)g(whic)o(h)i(w)o(e)g(presen)o(t)i(here.) 951 2784 y FQ(14)p eop %%Page: 15 15 bop 133 91 a FE(\017)24 b FQ(Av)o(eraging)16 b(transformation)g(with)g(an)o (y)g FP(even)22 b FQ(blo)q(c)o(k)16 b(size)g FF(b)d FE(\025)h FQ(2,)i(for)h(the)f(Ising)g(mo)q(del)f(in)182 152 y(an)o(y)h(dimension)f FF(d)f FE(\025)f FQ(2.)60 231 y(Moreo)o(v)o(er,)23 b(in)g(sev)o(eral)f(cases) i(w)o(e)f(can)g(pro)o(v)o(e)f(that)i(these)f(pathologies)h(are)f(presen)o(t)g (also)h(at)60 291 y FP(nonzer)n(o)d FQ(magnetic)16 b(\014eld.)24 b(F)l(or)18 b(the)f(\014rst)h(t)o(w)o(o)g(examples,)d(w)o(e)i(pro)o(v)o(e)g (non-Gibbsianness)i(in)e(di-)60 351 y(mension)12 b FF(d)j FE(\025)e FQ(3)h(in)g(a)g(full)f(neigh)o(b)q(orho)q(o)q(d)j FE(f)p FF(\014)g(>)d(\014) 1005 358 y FH(0)1025 351 y FF(;)j FE(j)p FF(h)p FE(j)d FF(<)h(\017)p FQ(\()p FF(\014)s FQ(\))p FE(g)f FQ(of)h(the)f(lo)o(w-temp)q(erature)g(part) 60 411 y(of)k(the)f(\014rst-order)h(phase-transition)g(surface.)k(In)16 b(the)g(last)h(example,)c(the)j(pathologies)h(can)g(b)q(e)60 472 y(pro)o(v)o(en)i(in)g(an)o(y)h(dimension)e FF(d)i FE(\025)f FQ(2)h(and)g(for)g FP(arbitr)n(ary)j FQ(v)m(alues)c(of)h(the)g(magnetic)e (\014eld,)h(again)60 532 y(at)i(lo)o(w)g(temp)q(erature.)35 b(These)21 b(latter)f(results)h(mak)o(e)e(clear)i(that)g(the)g(Gri\016ths-P)o (earce-Israel)60 592 y(pathologies)h(are)g FP(not)27 b FQ(asso)q(ciated)22 b(with)g(the)f(fact)h(that)g(the)f(original)h(mo)q(del)e(is)i FP(sitting)h(on)j FQ(a)60 652 y(phase-transition)19 b(surface.)27 b(Rather,)18 b(it)g(su\016ces)g(that)g(a)h(\014rst-order)g(phase)f (transition)h(can)f(b)q(e)60 712 y(induced)g(in)g(the)g(in)o(ternal-spin)g (system)f(b)o(y)h(c)o(ho)q(osing)h(an)g(appropriate)g(blo)q(c)o(k-spin)g (con\014gura-)60 773 y(tion.)34 b(F)l(or)21 b(this)g(w)o(e)f(need)g(to)h(w)o (ork)g(at)g(lo)o(w)f(temp)q(erature)g(but)g(not)i(necessarily)d(close)h(to)h (the)60 833 y(phase-transition)c(surface.)133 893 y(Though)12 b(w)o(e)f(ha)o(v)o(e)f(not)h(y)o(et)f(b)q(een)h(able)f(to)h(demonstrate)f (non-Gibbsianness)j(for)e(the)f(ma)s(jorit)o(y-)60 953 y(rule)15 b(transformation)h(on)h(2)11 b FE(\002)f FQ(2)17 b(or)f(3)11 b FE(\002)f FQ(3)17 b(blo)q(c)o(ks,)e(or)h(for)h(an)o(y)f(blo)q(c)o(k)f(size) g(in)h(dimension)e FF(d)g FE(\025)g FQ(3,)60 1013 y(w)o(e)k(feel)f(that)i (the)g(obstacles)f(are)h(tec)o(hnical)e(rather)h(than)h(fundamen)o(tal.)27 b(Indeed,)18 b(the)g(results)60 1073 y(in)d(Section)g(4)h(suggest)g(that)g (non-Gibbsianness)h(ma)o(y)d(b)q(e)i(the)f FP(normal)21 b FQ(situation)16 b(for)f(R)o(G)h(maps)60 1134 y(at)h(lo)o(w)f(temp)q(erature)e(and/or)k(near)e (a)h(\014rst-order)g(phase)g(transition.)133 1194 y(The)j(reader)h(will)e (probably)h(not)h(b)q(e)g(surprised)f(that)h(the)f(decimation)e (transformation)i(is)60 1254 y(\\pathological":)39 b(this)24 b(transformation,)i(unlik)o(e)d(other)h(R)o(G)g(transformations,)i(do)q(es)g (not)e(in)60 1314 y(an)o(y)18 b(sense)h(in)o(tegrate)e(out)i(the)g (\\high-momen)o(tum)c(mo)q(des")j(and)h(lea)o(v)o(e)e(the)h(\\lo)o(w-momen)o (tum)60 1374 y(mo)q(des";)j(it)e(merely)e(in)o(tegrates)i(out)i(one)e (sublattice)g(and)i(lea)o(v)o(es)d(another.)32 b(In)20 b(particular,)g(if)60 1435 y(the)h(sublattice)g(of)i(in)o(ternal)d(\(in)o(tegrated-out\))i(spins)g (is)g FP(c)n(onne)n(cte)n(d)5 b FQ(,)23 b(it)f(is)f(hardly)h(surprising)60 1495 y(that)f(the)g(in)o(ternal-spin)f(system)f(can)i(exhibit)f(a)h(phase)g (transition,)h(and)f(that)g(this)g(can)g(giv)o(e)60 1555 y(rise)c(to)h(R)o(G) f(pathologies.)25 b(W)l(e)17 b(therefore)g(w)o(an)o(t)h(to)f(stress)h(that)g (the)f(same)g(pathology)h(|)f(non-)60 1615 y(Gibbsianness)c(after)g(one)g (renormalization)e(step)h(|)h(is)f(also)i(presen)o(t)e(at)h(lo)o(w)f(temp)q (erature)g(for)h(at)60 1675 y(least)j(some)g(Kadano\013,)i(ma)s(jorit)o (y-rule)c(and)j(blo)q(c)o(k-a)o(v)o(eraging)f(transformations.)23 b(These)16 b(latter)60 1736 y(transformations)22 b FP(do)j FQ(\(at)d(least)g(seemingly\))d(in)o(tegrate)j(out)g(the)g(\\high-momen)o (tum)c(mo)q(des")60 1796 y(and)j(lea)o(v)o(e)f(the)g(\\lo)o(w-momen)o(tum)d (mo)q(des",)22 b(and)f(they)g(ha)o(v)o(e)f(b)q(een)g(generally)g(considered)h (to)60 1856 y(b)q(e)f(w)o(ell-b)q(eha)o(v)o(ed.)29 b(Indeed,)19 b(nearly)g(all)g(real-space)g(R)o(G)g(studies)h(of)f(Ising)h(mo)q(dels)e(ha)o (v)o(e)h(used)60 1916 y(some)f(v)m(arian)o(t)h(of)h(these)f(transformations.) 30 b(It)19 b(is)g(th)o(us)g(a)g(highly)g(non-trivial)g(fact)g(that)g(these)60 1976 y(R)o(G)d(maps)g(can)g(b)q(e)h(ill-de\014ned)d(at)j(lo)o(w)f(temp)q (erature.)60 2139 y FG(2)83 b(In\014nite-V)-7 b(olume)31 b(Lattice)h(Systems) o(:)45 b(General)32 b(F)-7 b(or-)184 2230 y(malism)60 2340 y FQ(Consider)18 b(a)h(classical)e(statistical-mec)o(hanical)e(system)i(with) h(con\014guration)h(space)f(\012,)g(Hamil-)60 2400 y(tonian)i FF(H)25 b FQ(and)20 b FP(a)h(priori)j FQ(measure)18 b FF(\026)792 2407 y FH(0)812 2400 y FQ(.)33 b(The)20 b(Boltzmann-Gibbs)e(distribution)i FF(\026)1655 2407 y FD(B)r(G)1733 2400 y FQ(for)g(this)60 2460 y(system)g(in)i(the)f(canonical)h(ensem)o(ble)d(at)j(in)o(v)o(erse)f(temp)q (erature)f FF(\014)k FQ(can)e(b)q(e)g(c)o(haracterized)e(in)60 2520 y(either)15 b(of)i(t)o(w)o(o)f(w)o(a)o(ys:)95 2600 y(\(a\))25 b FP(Explicit)19 b(formula.)684 2660 y FF(d\026)738 2667 y FD(B)r(G)796 2660 y FQ(\()p FF(!)r FQ(\))28 b(=)g FF(Z)997 2639 y Fy(\000)p FH(1)1052 2660 y FF(e)1075 2639 y Fy(\000)p FD(\014)r(H)s FH(\()p FD(!)q FH(\))1216 2660 y FF(d\026)1270 2667 y FH(0)1291 2660 y FQ(\()p FF(!)r FQ(\))14 b FF(;)401 b FQ(\(2)p FF(:)p FQ(1\))951 2784 y(15)p eop %%Page: 16 16 bop 182 91 a FQ(where)16 b(of)g(course)778 152 y FF(Z)32 b FQ(=)908 93 y Fx(Z)958 152 y FF(e)981 131 y Fy(\000)p FD(\014)r(H)s FH(\()p FD(!)q FH(\))1122 152 y FF(d\026)1176 159 y FH(0)1196 152 y FQ(\()p FF(!)r FQ(\))14 b FF(:)496 b FQ(\(2)p FF(:)p FQ(2\))93 274 y(\(b\))24 b FP(V)l(ariational)17 b(principle.)23 b FF(\026)688 281 y FD(B)r(G)762 274 y FQ(is)15 b(that)h(probabilit)o(y)f (measure)f(whic)o(h)h(maximiz)o(es)e(en)o(trop)o(y)182 335 y(min)o(us)h FF(\014)19 b FQ(times)14 b(mean)h(energy:)640 445 y FF(\026)669 452 y FD(B)r(G)743 445 y FQ(maximize)o(s)f FF(S)s FQ(\()p FF(\026)p FE(j)p FF(\026)1105 452 y FH(0)1125 445 y FQ(\))d FE(\000)g FF(\014)s(E)s FQ(\()p FF(H)q(;)d(\026)p FQ(\))13 b FF(;)358 b FQ(\(2)p FF(:)p FQ(3\))182 555 y(where)643 683 y FF(S)s FQ(\()p FF(\026)p FE(j)p FF(\026)767 690 y FH(0)787 683 y FQ(\))42 b(=)f FE(\000)974 625 y Fx(Z)1024 610 y( )1057 683 y FQ(log)1143 650 y FF(d\026)p 1133 672 75 2 v 1133 717 a(d\026)1187 724 y FH(0)1212 610 y Fx(!)1262 683 y FF(d\026)848 824 y FQ(=)g FE(\000)974 766 y Fx(Z)1024 751 y( )1072 791 y FF(d\026)p 1062 813 V 1062 859 a(d\026)1116 866 y FH(0)1149 824 y FQ(log)1236 791 y FF(d\026)p 1226 813 V 1226 859 a(d\026)1280 866 y FH(0)1305 751 y Fx(!)1355 824 y FF(d\026)1409 831 y FH(0)1790 824 y FQ(\(2.4\))182 963 y(and)642 1023 y FF(E)s FQ(\()p FF(H)q(;)8 b(\026)p FQ(\))28 b(=)g FE(h)p FF(H)t FE(i)987 1030 y FD(\026)1039 1023 y FE(\021)1105 964 y Fx(Z)1155 1023 y FF(H)t FQ(\()p FF(!)r FQ(\))8 b FF(d\026)p FQ(\()p FF(!)r FQ(\))15 b FF(:)360 b FQ(\(2)p FF(:)p FQ(5\))60 1143 y(The)15 b(equiv)m(alence)f(of)h(these)g(t)o(w)o(o)h(c) o(haracterizations)e(is)h(a)h(simple)d(computation)i(in)g(the)g(calculus)60 1203 y(of)i(v)m(ariations.)133 1264 y(Unfortunately)l(,)k(this)f(elemen)o (tary)d(theory)k FP(do)n(es)g(not)h(apply)i FQ(to)d(in\014nite-v)o(olume)d (systems,)60 1324 y(b)q(ecause)g(the)g(Hamiltonian)f FF(H)t FQ(\()p FF(!)r FQ(\))h(is)g(ill-de\014ned:)24 b(for)19 b(almost)e(an)o(y)h (con\014guration)i FF(!)g FQ(w)o(e)e(ha)o(v)o(e)60 1384 y FF(H)t FQ(\()p FF(!)r FQ(\))i(=)g FE(\0061)p FQ(.)31 b(Nev)o(ertheless,)18 b(non-trivial)h FP(analo)n(gues)25 b FQ(of)20 b(these)f(t)o(w)o(o)h(c)o (haracterizations)f(can)60 1444 y(b)q(e)24 b(dev)o(elop)q(ed)f(for)i (in\014nite-v)o(olume)c(systems.)44 b(The)24 b(analogue)h(of)g(the)e (explicit)f(form)o(ula)h(is)60 1504 y(the)17 b(theory)h(of)f(sp)q (eci\014cations)h(and)g FP(Gibbs)h(me)n(asur)n(es)t FQ(:)k(an)18 b(in\014nite-v)o(olume)c(Gibbs)k(measure)e(is)60 1565 y(one)h(whose)g (conditional)f(probabilities)g(for)g(\014nite)g(subsystems)g(are)h(giv)o(en)e (b)o(y)h(the)g(Boltzmann-)60 1625 y(Gibbs)i(form)o(ula.)24 b(The)17 b(analogue)i(of)f(the)f(v)m(ariational)h(approac)o(h)g(is)g(the)f (theory)g(of)h FP(e)n(quilibrium)60 1685 y(me)n(asur)n(es)t FQ(:)26 b(an)19 b(equilibrium)c(measure)j(is)g(a)h(translation-in)o(v)m (arian)o(t)g(measure)f(that)h(maximi)o(zes)60 1745 y(en)o(trop)o(y)f FP(density)23 b FQ(min)o(us)17 b FF(\014)k FQ(times)c(mean)g(energy)h FP(density)t FQ(.)29 b(These)19 b(approac)o(hes)g(are)g(review)o(ed)60 1805 y(in)f(Sections)h(2.3)g(and)h(2.5{2.6,)g(resp)q(ectiv)o(ely)l(.)26 b(The)19 b(fundamen)o(tal)e(feature)i(of)g(in\014nite-v)o(olume)60 1865 y(systems,)12 b(whic)o(h)g(distinguishes)g(them)f(from)h(\014nite-v)o (olume)e(systems,)h(is)i(that)g(the)f(map)g(b)q(et)o(w)o(een)60 1926 y(\\Hamiltonians")f(\(more)g(precisely)l(,)f(in)o(teractions\))h(and)i (Gibbs)f(measures)f(\(or)i(equilibrium)8 b(mea-)60 1986 y(sures\))19 b(is)g(neither)g(single-v)m(alued)f(nor)i(on)o(to:)28 b(some)18 b(in)o(teractions)g(ha)o(v)o(e)h(m)o(ultiple)d(Gibbs)j(mea-)60 2046 y(sures,)h(while)f(some)f(measures)g(are)i(not)g(Gibbsian)f(for)h(an)o (y)f(in)o(teraction.)30 b(These)20 b(facts)f(are)h(at)60 2106 y(the)c(heart)g(of)h(the)f(theory)g(of)h(phase)f(transitions,)h(and)f(of)h (the)f(renormalization)f(group.)133 2166 y(The)20 b(standard)h(references)e (for)h(the)g(material)e(in)h(this)h(section)g(are)g(the)f(b)q(o)q(oks)j(of)e (Georgii)60 2227 y([157)q(],)h(Preston)h([299)q(])f(and)h(Israel)e([206)q(].) 36 b(Georgii)21 b(and)h(Preston)g(deal)f(principally)e(with)i(the)60 2287 y(theory)15 b(of)g(Gibbs)h(measures,)e(while)g(Israel)h(deals)g (principally)e(with)i(the)g(theory)g(of)g(equilibrium)60 2347 y(measures.)133 2407 y(W)l(e)f(assume)f(in)h(this)g(section)g(that)h(the)e (reader)h(has)h(some)e(kno)o(wledge)h(of)g(metric)e(spaces)i(and)60 2467 y(Banac)o(h)19 b(spaces,)g(ideally)f(at)h(the)g(lev)o(el)e(of)i(Ro)o (yden)g([309)q(])f(or)i(Reed)e(and)i(Simon)e([306],)h(and)h(of)60 2528 y(measure)14 b(theory)h(and)h(probabilit)o(y)f(theory)l(,)g(ideally)f (at)h(the)h(lev)o(el)d(of)j(Bauer)f([25])g(or)h(Kric)o(k)o(eb)q(erg)60 2588 y([224)q(].)23 b(Ho)o(w)o(ev)o(er,)15 b(w)o(e)i(realize)f(that)h(for)h (man)o(y)d(readers)i(these)g(theories)g(b)q(elong)h(to)f(only)g(fain)o(tly)60 2648 y(remem)n(b)q(ered)g(mathematics)f(courses)k(and)g(are)g(rather)f (distan)o(t)h(from)e(their)h(da)o(y-to-da)o(y)h(w)o(ork)951 2784 y(16)p eop %%Page: 17 17 bop 60 91 a FQ(in)14 b(theoretical)f(ph)o(ysics.)20 b(Nev)o(ertheless,)12 b(w)o(e)i(urge)h(suc)o(h)f(readers)g(not)h(to)g(b)q(e)f(discouraged)h(b)o(y)f (the)60 152 y(abstract)j(jargon,)f(and)h(to)f(use)g(the)g(examples)e(w)o(e)i (pro)o(vide)f(as)h(a)h(means)e(to)h(grasp)h(the)f(essen)o(tial)60 212 y FP(physic)n(al)21 b FQ(ideas)16 b(underlying)g(the)g(mathematics.)133 272 y(In)k(this)g(section)f(the)h(emphasis)f(is)g(on)i(concepts)e(and)i (ideas)f(\(b)q(oth)h(ph)o(ysical)d(and)j(mathe-)60 332 y(matical\),)12 b(not)j(on)f(tec)o(hniques)f(of)h(pro)q(of.)21 b(Therefore,)14 b(all)g(de\014nitions)f(and)i(theorems)e(are)h(stated)60 392 y(precisely)l(,)g(but)i(pro)q(ofs)h(are)f(omitted.)k(In)c(App)q(endix)f(A)h (w)o(e)f(pro)o(vide,)g(for)h(eac)o(h)g(theorem,)e(either)60 452 y(a)j(published)e(reference)g(\(if)h(the)g(result)f(is)h(kno)o(wn\))h(or) g(a)f(pro)q(of)i(\(if)d(it)h(is)g(new\).)133 513 y(Henceforth)c(w)o(e)g (absorb)i FF(\014)g FQ(in)o(to)f(the)f(Hamiltonian)f FF(H)t FQ(;)i(this)g(simpli\014es)d(the)i(notation.)21 b(Let)13 b(us)60 573 y(also)18 b(remark)f(that)h(although)h(our)f(exp)q(osition)g(is)f(couc)o (hed)h(in)f(the)h(language)g(of)h(the)e(canonical)60 633 y(ensem)o(ble,)23 b(the)h(formalism)d(is)j(equally)f(applicable)g(to)h(the)g(grand)h(canonical) f(ensem)o(ble:)34 b(it)60 693 y(su\016ces)22 b(to)i(in)o(terpret)d(our)j FF(H)j FQ(to)c(mean)f(\\)p FF(\014)s(H)d FE(\000)c FF(\014)s(\026N)5 b FQ(".)42 b(In)22 b(fact,)j(this)d(formalism)e(applies)60 753 y(to)f(an)h(arbitrary)f(\\generalized)g(\(grand\))h(canonical)f(ensem)o (ble")d(with)j(parameters)f FF(\014)1710 760 y FH(1)1730 753 y FF(;)8 b(:)g(:)g(:)f(;)h(\014)1867 760 y FD(n)60 814 y FQ(conjugate)17 b(to)f(observ)m(ables)h FF(H)637 821 y FH(1)657 814 y FF(;)8 b(:)g(:)g(:)g(;)g(H)807 821 y FD(n)830 814 y FQ(.)60 956 y FB(2.1)70 b(Con\014gurations,)24 b(Ev)n(en)n(ts,)f(F)-6 b(unctions,)23 b(Measures)60 1031 y FH(8)133 1109 y FQ(Classical)c(statistical)f(mec)o (hanics)e(is)j(a)g(branc)o(h)g(of)g(probabilit)o(y)f(theory)l(.)28 b(The)19 b(basic)g(struc-)60 1169 y(tures)d(of)h(probabilit)o(y)e(theory)h (are:)133 1261 y FE(\017)24 b FQ(A)15 b(con\014guration)i(space)e(\012)h(|)f (this)g(is)h(the)f(set)g(of)h(all)f(p)q(ossible)g(\(microscopic\))f (con\014gura-)182 1321 y(tions)i(of)h(the)f(system)f(under)h(study)l(.)133 1419 y FE(\017)24 b FQ(A)12 b FF(\033)r FQ(-\014eld)g FE(F)17 b FQ(of)12 b(subsets)h(of)g(\012)g(|)f(this)g(is)g(the)g(set)h(of)f(all)g(ev) o(en)o(ts)f(\(=)i(y)o(es-no)f(questions\))h(that)182 1480 y(are)19 b(measurable)f(b)o(y)h(some)f(conceiv)m(able)g(\(p)q(ossibly)i(extremely)c (idealized\))h(exp)q(erimen)o(t.)182 1540 y(V)l(arious)g(sub-)p FF(\033)r FQ(-\014elds)g FE(A)e(\032)g(F)22 b FQ(ma)o(y)16 b(corresp)q(ond)i(to)f(restricted)f(classes)h(of)h(exp)q(erimen)o(ts)182 1600 y(\(e.g.)d(exp)q(erimen)o(ts)f(p)q(erformed)h(within)h(a)g(sp)q (eci\014ed)g(region)g(of)h(space\).)133 1698 y FE(\017)24 b FQ(Observ)m(ables)13 b(\(=)h(random)f(v)m(ariables)g(=)h(real-v)m(alued)f FE(F)5 b FQ(-measurable)12 b(functions)i(on)g(\012\))f(|)182 1758 y(these)h(corresp)q(ond)i(to)f(exp)q(erimen)o(ts)d(whic)o(h)i(giv)o(e)f (a)i(real)g(n)o(um)o(b)q(er)e(as)i(an)g(answ)o(er.)21 b(V)l(arious)182 1819 y(sub)q(classes)d(of)f(observ)m(ables)h(\(e.g.)e(those)i(measurable)e (with)h(resp)q(ect)g(to)g(a)h(sp)q(eci\014ed)e(sub-)182 1879 y FF(\033)r FQ(-\014eld)g FE(A)p FQ(\))g(ma)o(y)f(corresp)q(ond)i(to)g (restricted)f(classes)g(of)h(exp)q(erimen)o(ts)d(\(e.g.)i(exp)q(erimen)o(ts) 182 1939 y(p)q(erformed)f(within)h(a)g(sp)q(eci\014ed)g(region)g(of)h (space\).)133 2037 y FE(\017)24 b FQ(A)15 b(probabilit)o(y)g(measure)f(\(=)h (probabilit)o(y)g(distribution\))g FF(\026)h FQ(on)g(\(\012)p FF(;)8 b FE(F)d FQ(\))15 b(|)g(this)g(describ)q(es)182 2098 y(either)c(our)h(state)g(of)g(partial)g(kno)o(wledge)g(of)g(the)f(system)g (\(if)g(w)o(e)h(tak)o(e)f(a)h(\\sub)s(jectiv)o(e")f(in)o(ter-)182 2158 y(pretation)j(of)h(probabilit)o(y)e(theory\))h(or)g(an)h(ensem)o(ble)c (of)k(\\iden)o(tically)d(prepared")i(random)182 2218 y(systems)21 b(\(if)h(w)o(e)f(tak)o(e)h(an)h(\\ob)s(jectiv)o(e")e(in)o(terpretation)g(of)i (probabilit)o(y)e(theory\).)39 b(The)182 2278 y(mathematics)11 b(of)j(statistical)g(mec)o(hanics)d(do)q(es)k(not)f(dep)q(end)g(on)h(an)o(y)f (particular)f(in)o(terpre-)182 2338 y(tation)20 b(of)f(its)h(mathematical)c (ob)s(jects,)k(so)g(the)f(reader)g(is)g(urged)h(to)g(emplo)o(y)d(whic)o(hev)o (er)182 2399 y(in)o(terpretation)e(he/she)i(prefers.)60 2490 y(In)f(this)h(section)f(w)o(e)g(describ)q(e)f(the)i(particular)f(case)g(of)h (this)f(structure)h(that)f(is)h(appropriate)g(for)60 2551 y(the)f (equilibrium)d(statistical)j(mec)o(hanics)d(of)k(an)g FP(in\014nite-volume)23 b FQ(classical)16 b FP(lattic)n(e)21 b FQ(system.)p 60 2591 732 2 v 116 2645 a FA(8)135 2660 y Fz(A)14 b(reference)i(for)e(this)g (section)g(is)g(Georgii)f([157)n(,)h(In)o(tro)q(duction)g(and)g(Sections)g (1.1)f(and)h(2.2].)951 2784 y FQ(17)p eop %%Page: 18 18 bop 60 91 a FM(2.1.1)55 b(Con\014gurations)20 b(and)f(Ev)n(en)n(ts)60 184 y FQ(The)12 b(con\014guration)h(space)f(of)h(an)f(in\014nite-v)o(olume)d (lattice)i(system)g(is)g(sp)q(eci\014ed)h(b)o(y)g(the)f(follo)o(wing)60 244 y(ingredien)o(ts:)133 346 y FE(\017)24 b FQ(The)f FP(single-spin)j(sp)n (ac)n(e)g FQ(\012)708 353 y FH(0)728 346 y FQ(.)42 b(This)23 b(is)g(the)g(space)g(of)g(p)q(ossible)g(con\014gurations)i(of)e(the)182 406 y(ph)o(ysical)15 b(v)m(ariable\(s\))h(at)h(a)g(single)f(lattice)f(site.) 21 b(\(F)l(or)16 b(brevit)o(y)f(w)o(e)h(call)f(these)h(v)m(ariables)h(a)182 466 y(\\spin".\))24 b FM(Examples:)c FQ(Ising)c(mo)q(del,)f(\012)959 473 y FH(0)994 466 y FQ(=)g FE(f\000)p FQ(1)p FF(;)8 b FQ(1)p FE(g)p FQ(;)17 b FF(N)5 b FQ(-v)o(ector)16 b(mo)q(del,)f(\012)1638 473 y FH(0)1673 466 y FQ(=)g FF(S)1759 448 y FD(N)t Fy(\000)p FH(1)1852 466 y FQ(=)182 526 y(unit)h(sphere)g(in)g Fq(R)527 505 y FD(N)561 526 y FQ(;)f FF(N)5 b FQ(-comp)q(onen)o(t)16 b(Gaussian)h(or)f FF(')1200 508 y FH(4)1235 526 y FQ(mo)q(del,)e(\012)1428 533 y FH(0)1462 526 y FQ(=)g Fq(R)1547 505 y FD(N)1581 526 y FQ(;)h(solid-on-solid)182 586 y(\(SOS\))h(or)h(discrete)e(Gaussian)j(mo)q (del,)c(\012)970 593 y FH(0)1004 586 y FQ(=)g Fq(Z)p FQ(.)231 667 y(Since)i(statistical)h(mec)o(hanics)e(is)i(based)g(on)h(probabilit)o(y)e (theory)l(,)h(w)o(e)g(shall)g(alw)o(a)o(ys)g(as-)182 727 y(sume)e(\012)342 734 y FH(0)379 727 y FQ(to)i(b)q(e)f(equipp)q(ed)g(with)h(a)g FF(\033)r FQ(-\014eld)f FE(F)1055 734 y FH(0)1091 727 y FQ(of)g(\\measurable) g(sets".)23 b(Usually)16 b(\012)1778 734 y FH(0)1814 727 y FQ(will)182 788 y(also)k(come)e(equipp)q(ed)h(with)h(a)g(ph)o(ysically)d (natural)k(top)q(ology;)h(in)d(fact,)h(\012)1614 795 y FH(0)1653 788 y FQ(will)f(almost)182 848 y(alw)o(a)o(ys)d(b)q(e)g(a)h(complete)d (separable)i(metric)e(space,)i(and)h FE(F)1292 855 y FH(0)1327 848 y FQ(will)f(b)q(e)g(the)g FF(\033)r FQ(-\014eld)f(of)i(Borel)182 908 y(sets.)k(If)15 b(\012)379 915 y FH(0)415 908 y FQ(is)g(a)h FP(c)n(omp)n(act)21 b FQ(metric)13 b(space,)i(w)o(e)g(sa)o(y)h(that)g(the)g (system)e(has)i FP(b)n(ounde)n(d)h(spins)t FQ(;)182 968 y(otherwise)i(w)o(e)f (sa)o(y)h(that)g(the)g(system)e(has)j FP(unb)n(ounde)n(d)h(spins)t FQ(.)29 b FM(Examples:)24 b FQ(The)19 b(Ising)182 1028 y(and)h FF(N)5 b FQ(-v)o(ector)19 b(mo)q(dels)g(ha)o(v)o(e)g(b)q(ounded)h(spins;)h (the)e(Gaussian,)j FF(')1464 1010 y FH(4)1483 1028 y FQ(,)e(SOS)g(and)g (discrete)182 1089 y(Gaussian)d(mo)q(dels)f(ha)o(v)o(e)f(un)o(b)q(ounded)i (spins.)133 1190 y FE(\017)24 b FQ(The)16 b FP(lattic)n(e)k FE(L)c FQ(|)f(a)h(coun)o(tably)f(in\014nite)g(set)g(of)h(\\sites".)22 b(F)l(or)15 b(the)h(momen)o(t)c(w)o(e)j(need)h(not)182 1251 y(giv)o(e)e FE(L)h FQ(an)o(y)f(geometric)f(structure,)h(but)g(for)h (concreteness)f(the)h(reader)f(can)h(imagine)e FE(L)i FQ(to)182 1311 y(b)q(e)h(some)g FF(d)p FQ(-dimensional)f(lattice.)60 1412 y(The)h(in\014nite-v)o(olume)d(con\014guration)k(space)e(\012)i(is)e (then)h(de\014ned)f(to)i(b)q(e)e(the)h(Cartesian)g(pro)q(duct)60 1473 y(\(\012)114 1480 y FH(0)134 1473 y FQ(\))153 1455 y Fy(L)179 1473 y FQ(;)g(that)g(is,)f(it)g(is)g(the)g(set)h(of)f(all)h(con\014gurations) g FF(!)g FQ(=)e(\()p FF(!)1213 1480 y FD(x)1235 1473 y FQ(\))1254 1480 y FD(x)p Fy(2L)1340 1473 y FQ(with)h FF(!)1480 1480 y FD(x)1516 1473 y FE(2)f FQ(\012)1598 1480 y FH(0)1634 1473 y FQ(for)i(eac)o(h)f(site)60 1533 y FF(x)p FQ(.)21 b(The)16 b(space)g(\012)h(is)f(equipp)q(ed)f(with)h(the)g(pro)q(duct)h FF(\033)r FQ(-\014eld)e FE(F)k FQ(=)14 b(\()p FE(F)1353 1540 y FH(0)1372 1533 y FQ(\))1391 1515 y Fy(L)1434 1533 y FQ(and)i(with)g(the)g (pro)q(duct)60 1593 y(top)q(ology)l(.)253 1575 y FH(9)294 1593 y FQ(The)e(pro)q(duct)g(top)q(ology)g(means)f(that)h(a)g(sequence)e(\(or)i (net\))f(of)h(con\014gurations)g(\()p FF(!)1847 1575 y FD(n)1871 1593 y FQ(\))60 1653 y(con)o(v)o(erges)g(to)i(a)f(con\014guration)i FF(!)g FQ(if)d(and)i(only)f(if)g FF(!)1036 1635 y FD(n)1034 1665 y(x)1073 1653 y FE(!)f FF(!)1167 1660 y FD(x)1204 1653 y FQ(for)i(all)e FF(x)g FE(2)g(L)p FQ(.)21 b(If)15 b(\012)1585 1660 y FH(0)1620 1653 y FQ(is)g(metrizable)60 1713 y(\(resp.)h(separable,)g (complete)e(metric,)f(compact\),)h(then)j(so)f(is)h(\012.)133 1774 y(It)11 b(is)h(imp)q(ortan)o(t)f(to)h(understand)g FP(physic)n(al)r(ly)k FQ(what)d(the)e(pro)q(duct)h(top)q(ology)h(means.)19 b(Supp)q(ose)60 1834 y(for)e(simplicit)o(y)c(that)18 b(\012)500 1841 y FH(0)537 1834 y FQ(is)e(a)i(metric)c(space.)24 b(Then)17 b(a)g(t)o(ypical)f(neigh)o(b) q(orho)q(o)q(d)j(of)e FF(!)g FE(2)e FQ(\012)j(is)e(the)60 1894 y(set)483 1954 y FE(N)524 1961 y FD(!)q(;\017;)p FH(\003)635 1954 y FQ(=)28 b FE(f)p FF(!)758 1934 y Fy(0)769 1954 y FQ(:)22 b(dist\()p FF(!)933 1961 y FD(x)955 1954 y FF(;)8 b(!)1009 1934 y Fy(0)1007 1966 y FD(x)1029 1954 y FQ(\))14 b FF(<)g(\017)i FQ(for)g(all)g FF(x)e FE(2)g FQ(\003)p FE(g)f FF(;)323 b FQ(\(2)p FF(:)p FQ(6\))60 2041 y(where)14 b FF(\017)g(>)f FQ(0)i(and)g(\003)f(is)h(a)f FP(\014nite)20 b FQ(subset)15 b(of)f FE(L)p FQ(.)926 2023 y FH(10)985 2041 y FQ(That)h(is,)f(a)h(t)o(ypical)e(neigh)o(b)q(orho)q(o)q(d)j (of)f FF(!)h FQ(in)e(the)60 2101 y(pro)q(duct)k(top)q(ology)h(is)f(the)f(set) g(of)h(con\014gurations)h(that)f(are)g(close)f(to)h FF(!)i FQ(on)e(some)f FP(\014nite)22 b FQ(set)c(of)60 2162 y(sites)d(\003,)h(but)g (are)g FP(arbitr)n(ary)f(outside)i FQ(\003.)k(In)16 b(particular,)f(if)g (\012)1218 2169 y FH(0)1254 2162 y FQ(is)g(discrete)g(\(as)h(e.g.)f(in)h(the) f(Ising)60 2222 y(mo)q(del\),)d(then)h(a)g(neigh)o(b)q(orho)q(o)q(d)i(of)f FF(!)h FQ(is)e(the)g(set)g(of)g(con\014gurations)h(that)g FP(agr)n(e)n(e)g (with)j FF(!)e FQ(on)f(some)60 2282 y(\014nite)19 b(set)g(of)g(sites)g(\003,) g(but)g(are)g(arbitrary)h(outside)f(\003.)29 b(These)19 b(facts)h(will)e(pla) o(y)g(an)i(imp)q(ortan)o(t)60 2342 y(role)c(in)g(our)g(discussion)h(of)f (non-Gibbsianness)i(for)f(R)o(G)f(image)f(measures)g(\(Sections)h(4.1{4.3\).) p 60 2389 732 2 v 116 2443 a FA(9)135 2458 y Fz(If)11 b(\012)204 2464 y FA(0)233 2458 y Fz(is)h(a)f(separable)h(metric)e(space,)j(then)f(the)f (pro)q(duct)i Fv(\033)q Fz(-\014eld)e(of)g(the)h(individual)d(Borel)j Fv(\033)q Fz(-\014elds)f(coincides)60 2507 y(with)j(the)g(Borel)g Fv(\033)q Fz(-\014eld)g(for)g(the)g(pro)q(duct)h(top)q(ology)m(.)100 2565 y FA(10)135 2581 y Fz(More)20 b(precisely)m(,)i(the)f(sets)g Fu(N)633 2587 y Fp(!)q(;\017;)p FA(\003)733 2581 y Fz(form)e(a)h Fw(neighb)n(orho)n(o)n(d)h(b)n(asis)i Fz(of)d Fv(!)q Fz(,)h(i.e.)e(ev)o(ery)i (neigh)o(b)q(orho)q(o)q(d)f(of)g Fv(!)60 2630 y Fz(con)o(tains)14 b(one)g(of)f(the)i(sets)g Fu(N)533 2636 y Fp(!)q(;\017;)p FA(\003)613 2630 y Fz(.)951 2784 y FQ(18)p eop %%Page: 19 19 bop 133 91 a FQ(F)l(or)18 b(eac)o(h)f(subset)g(\003)f FE(\032)f(L)p FQ(,)j(w)o(e)f(let)f FE(F)833 98 y FH(\003)876 91 y FE(\032)f(F)22 b FQ(b)q(e)c(the)f(sub-)p FF(\033)r FQ(-\014eld)g(corresp)q(onding)i(to)e(ev) o(en)o(ts)60 152 y(dep)q(ending)12 b(only)f(on)h(the)f(spins)h FF(!)682 159 y FH(\003)722 152 y FQ(=)i(\()p FF(!)823 159 y FD(x)845 152 y FQ(\))864 159 y FD(x)p Fy(2)p FH(\003)934 152 y FQ(;)f(that)f(is,)g FE(F)1157 159 y FH(\003)1194 152 y FQ(is)g(the)f FF(\033)r FQ(-\014eld)f(of)i FP(events)j(me)n(asur)n(able)60 212 y(within)j(the)f(subset)h FQ(\003.)i(W)l(e)c(denote)f(b)o(y)g FE(S)20 b FQ(the)15 b(class)h(of)f(all)g(nonempt)o(y)f FP(\014nite)21 b FQ(subsets)16 b(of)g FE(L)p FQ(.)21 b(W)l(e)60 272 y(denote)16 b(b)o(y)g(\003)319 254 y FD(c)352 272 y FQ(the)g(complemen)n(t)e(of)i(\003)g (in)g FE(L)p FQ(.)133 332 y FM(Remark.)i FQ(The)12 b(Cartesian)h(pro)q(duct)f (\(\012)907 339 y FH(0)927 332 y FQ(\))946 314 y Fy(L)985 332 y FQ(is)g(not)g(the)g(most)f(general)h(con\014guration)h(space.)60 392 y(Often)j(one)g(wishes)h(to)f(study)h(a)g(lattice)e(mo)q(del)g(with)h FP(lo)n(c)n(al)i(c)n(onstr)n(aints)i FQ(\(e.g.)15 b(hard-core)i(exclu-)60 452 y(sions\).)31 b(One)19 b(w)o(a)o(y)g(\(not)g(the)g(only)g(one\))h(to)f (treat)g(these)g(constrain)o(ts)h(is)f(to)g(cut)g(the)g(excluded)60 513 y(con\014gurations)i(out)e(of)h(the)f(con\014guration)i(space:)27 b(that)20 b(is,)f(w)o(e)g(let)f(the)i(con\014guration)g(space)60 573 y(\012)g(b)q(e)f(an)h(appropriate)g FP(subset)25 b FQ(of)20 b(the)f(pro)q(duct)h(space)f(\(\012)1191 580 y FH(0)1211 573 y FQ(\))1230 555 y Fy(L)1257 573 y FQ(.)30 b(W)l(e)19 b(do)h(not)g(allo)o(w)f (this)g(m)o(uc)o(h)60 633 y(generalit)o(y)13 b(here,)h(but)g(m)o(uc)o(h)e(of) j(the)f(presen)o(t)g(theory)g(go)q(es)h(through)g(\(with)g(some)e(mo)q (di\014cation\))60 693 y(in)j(this)g(situation)h([313,)f(269)q(,)g(15)q(].)60 821 y FM(2.1.2)55 b(F)-5 b(unctions)19 b(\(=)f(Observ)m(ables\))60 913 y FQ(An)f FP(observable)23 b FQ(is)17 b(simply)d(a)k(real-v)m(alued)f (measurable)f(function)h(on)g(\012.)25 b(W)l(e)16 b(consider)h(v)m(arious)60 973 y(spaces)g(of)f(suc)o(h)g(functions:)133 1062 y FE(\017)24 b FQ(The)14 b(space)h FF(B)s FQ(\(\012\))e(=)h FF(B)s FQ(\(\012)p FF(;)8 b FE(F)d FQ(\))14 b(of)h(b)q(ounded)g(measurable)e(functions.)21 b(This)14 b(is)h(the)f(largest)182 1122 y(space)i(of)h(functions)f(w)o(e)g (shall)g(consider.)133 1220 y FE(\017)24 b FQ(The)c(space)g FF(B)457 1227 y FD(loc)502 1220 y FQ(\(\012\))g(=)653 1187 y Fx(S)688 1230 y FH(\003)p Fy(2S)770 1220 y FF(B)s FQ(\(\012)p FF(;)8 b FE(F)922 1227 y FH(\003)948 1220 y FQ(\))20 b(of)g(b)q(ounded)h FP(lo)n(c)n(al)k FQ(functions.)32 b(A)20 b(function)f(is)182 1280 y FP(lo)n(c)n(al)j FQ(if)15 b(it)h(dep)q(ends)h(on)f(only)g(\014nitely)f (man)o(y)g(spins.)133 1377 y FE(\017)24 b FQ(The)g(space)h FF(B)466 1384 y FD(q)q(l)496 1377 y FQ(\(\012\))j(=)p 662 1335 156 2 v 27 w FF(B)699 1384 y FD(loc)745 1377 y FQ(\(\012\))c(of)h(b)q(ounded) g FP(quasilo)n(c)n(al)30 b FQ(functions.)46 b(A)24 b(function)g(is)182 1438 y FP(quasilo)n(c)n(al)f FQ(if)18 b(it)f(is)g(the)h(uniformly)e(con)o(v)o (ergen)o(t)g(limit)f(of)j(some)f(sequence)f(of)i(lo)q(cal)g(func-)182 1498 y(tions.)41 b(Equiv)m(alen)o(tly)l(,)23 b(a)g(function)g(is)f(quasilo)q (cal)h(if)g(it)f(\\dep)q(ends)i(w)o(eakly)e(on)h(distan)o(t)182 1558 y(spins")17 b(in)f(the)g(sense)g(that)684 1540 y FH(11)680 1653 y FQ(lim)681 1683 y FH(\003)p Fy("L)811 1653 y FQ(sup)777 1699 y FD(!)q(;)6 b(!)839 1687 y Ft(0)860 1699 y Fy(2)j FH(\012)780 1741 y FD(!)802 1747 y Fr(\003)834 1741 y FH(=)h FD(!)894 1730 y Ft(0)893 1753 y Fr(\003)956 1653 y FE(j)p FF(f)5 b FQ(\()p FF(!)r FQ(\))11 b FE(\000)g FF(f)5 b FQ(\()p FF(!)1210 1632 y Fy(0)1222 1653 y FQ(\))p FE(j)28 b FQ(=)f(0)15 b FF(:)389 b FQ(\(2)p FF(:)p FQ(7\))133 1853 y FE(\017)24 b FQ(The)16 b(space)h FF(C)t FQ(\(\012\))e(of)i(b)q(ounded)g FP(c)n(ontinuous)k FQ(functions.)133 1950 y FE(\017)j FQ(The)16 b(space)h FF(C)448 1957 y FD(loc)493 1950 y FQ(\(\012\))d FE(\021)f FF(B)669 1957 y FD(loc)715 1950 y FQ(\(\012\))e FE(\\)g FF(C)t FQ(\(\012\))16 b(of)h(b)q(ounded)g FP(c)n(ontinuous)h(lo)n(c)n(al)k FQ(functions.)133 2048 y FE(\017)i FQ(The)16 b(space)h FF(C)448 2055 y FD(q)q(l)477 2048 y FQ(\(\012\))d FE(\021)g FF(B)654 2055 y FD(q)q(l)684 2048 y FQ(\(\012\))d FE(\\)g FF(C)t FQ(\(\012\))16 b(of)h(b)q(ounded)g FP(c)n(ontinuous)h(quasilo)n(c)n(al)k FQ(functions.)133 2137 y FM(Examples.)33 b FQ(1.)i(F)l(or)21 b(\012)619 2144 y FH(0)660 2137 y FQ(=)h Fq(R)p FQ(,)g(the)e(function)h FF(f)5 b FQ(\()p FF(')p FQ(\))22 b(=)f(sgn)q(\()p FF(')1375 2144 y FH(0)1395 2137 y FQ(\))f(is)h(b)q(ounded)h(and)f(lo)q(cal)60 2197 y(\(hence)h(quasilo)q (cal\))i(but)f(not)h(con)o(tin)o(uous.)42 b(Analogous)24 b(functions)f(can)h (ob)o(viously)e(b)q(e)i(con-)60 2257 y(structed)f(for)h(\012)374 2264 y FH(0)421 2257 y FQ(=)i FF(S)518 2239 y FD(N)t Fy(\000)p FH(1)620 2257 y FQ(or)e Fq(R)721 2236 y FD(N)754 2257 y FQ(,)h(and)f(indeed)f (on)h(an)o(y)g(single-spin)f(space)h(whic)o(h)f(is)h(not)60 2317 y(discrete.)p 60 2347 732 2 v 100 2401 a FA(11)135 2416 y Fz(The)14 b(statemen)o(t)i(lim)413 2443 y FA(\003)p Fo("L)483 2416 y Fv(F)6 b Fz(\(\003\))11 b(=)h Fv(\013)h Fz(\(where)i Fv(\013)d Fu(2)f Fq(R)j Fz(or)g Fq(C)p Fz(\))g(means)f(that)h(for)f(eac)o(h)i Fv(\017)c(>)h Fz(0,)h(there)i(exists)g(a)f(\014nite)60 2488 y(subset)i Fv(K)223 2494 y Fp(\017)253 2488 y Fu(\032)d(L)h Fz(suc)o(h)i(that)f Fu(j)p Fv(F)6 b Fz(\(\003\))j Fu(\000)h Fv(\013)p Fu(j)i Fv(<)i(\017)g Fz(whenev)o(er)j(\003)c Fu(\033)g Fv(K)1118 2494 y Fp(\017)1134 2488 y Fz(.)21 b(Statemen)o(ts)c(lim)1384 2515 y FA(\003)p Fo("L)1453 2488 y Fv(F)6 b Fz(\(\003\))13 b(=)h(+)p Fu(1)g Fz(or)h Fu(\0001)g Fz(are)60 2560 y(to)f(b)q(e)h(in)o (terpreted)h(analogously)m(.)i(\(Mathematicians)13 b(call)g(this)i(\\con)o(v) o(ergence)h(along)d(the)i(net)g(of)f(\014nite)g(subsets)60 2610 y(of)g Fu(L)p Fz(,)h(directed)h(b)o(y)f(inclusion".\))20 b(Please)15 b Fw(do)i(not)i Fz(confuse)d(this)f(notion)f(of)g(con)o(v)o (ergence)j(with)d(the)i(limit)c(in)i(the)60 2660 y(sense)i(of)d(v)n(an)g(Ho)o (v)o(e,)g(to)h(b)q(e)h(de\014ned)g(in)e(Section)h(2.4.1.)951 2784 y FQ(19)p eop %%Page: 20 20 bop 133 91 a FQ(2.)23 b(If)16 b(\012)278 98 y FH(0)313 91 y FQ(=)f FE(L)g FQ(=)f Fq(Z)q FQ(,)i(an)o(y)h(\(b)q(ounded\))g(function)g(of)g FF(\033)1134 98 y FD(\033)1154 103 y Fr(0)1190 91 y FQ(is)f(\(b)q(ounded)i (and\))f(con)o(tin)o(uous)g(but)60 152 y(not)k(quasilo)q(cal.)34 b(\(This)21 b(example,)e(whic)o(h)h(w)o(as)h(suggested)h(to)f(us)g(b)o(y)f (Hans-Otto)h(Georgii,)g(is)60 212 y(further)16 b(discussed)g(in)g(App)q (endix)g(A.1.\))133 322 y(W)l(e)d(equip)f(eac)o(h)g(of)h(the)g(ab)q(o)o(v)o (e)f(spaces)i(with)e(the)h(\\suprem)o(um)d(norm")j(\(or)g(\\uniform)f (norm"\))665 432 y FE(k)p FF(f)5 b FE(k)28 b FQ(=)g FE(k)p FF(f)5 b FE(k)917 439 y Fy(1)982 432 y FE(\021)27 b FQ(sup)1049 471 y FD(!)q Fy(2)p FH(\012)1130 432 y FE(j)p FF(f)5 b FQ(\()p FF(!)r FQ(\))p FE(j)14 b FF(:)505 b FQ(\(2)p FF(:)p FQ(8\))60 569 y(So)21 b(equipp)q(ed,)e(the)h(spaces)h FF(B)s FQ(\(\012\),)f FF(B)784 576 y FD(q)q(l)814 569 y FQ(\(\012\),)g FF(C)t FQ(\(\012\))g(and)h FF(C)1187 576 y FD(q)q(l)1217 569 y FQ(\(\012\))f(are)g(Banac)o(h)g(spaces.) 33 b(Let)20 b(us)60 629 y(notice)c(that:)95 730 y(\(a\))25 b(If)e(the)g(single-spin)h(space)f(\012)748 737 y FH(0)792 730 y FQ(is)g(a)h FP(c)n(omp)n(act)k FQ(metric)22 b(space,)j(then)e(ev)o(ery) f(con)o(tin)o(uous)182 791 y(function)16 b(is)g(b)q(ounded)h(and)g(quasilo)q (cal.)k(Hence)15 b FF(C)t FQ(\(\012\))f(=)f FF(C)1317 798 y FD(q)q(l)1347 791 y FQ(\(\012\))h FE(\032)g FF(B)1524 798 y FD(q)q(l)1554 791 y FQ(\(\012\).)93 892 y(\(b\))24 b(If)11 b(the)g(single-spin)h(space)f(\012)700 899 y FH(0)732 892 y FQ(is)g FP(discr)n(ete)t FQ(,)h(then)f(ev)o(ery)f(quasilo)q(cal)i(function)f (is)h(con)o(tin)o(uous.)182 953 y(In)k(particular,)f FF(B)518 960 y FD(q)q(l)548 953 y FQ(\(\012\))f(=)g FF(C)722 960 y FD(q)q(l)752 953 y FQ(\(\012\))g FE(\032)g FF(C)t FQ(\(\012\).)98 1054 y(\(c\))24 b(If)15 b(the)g(single-spin)h(space)f(\012)716 1061 y FH(0)752 1054 y FQ(is)g FP(\014nite)t FQ(,)i(then)e(quasilo)q(calit)o(y)g(and)h(con)o (tin)o(uit)o(y)e(are)h(equiv)m(a-)182 1114 y(len)o(t)g(\(and)i(imply)d(b)q (oundedness\).)22 b(Hence)15 b FF(C)t FQ(\(\012\))f(=)f FF(C)1210 1121 y FD(q)q(l)1240 1114 y FQ(\(\012\))h(=)g FF(B)1416 1121 y FD(q)q(l)1446 1114 y FQ(\(\012\).)60 1244 y FM(2.1.3)55 b(Measures)60 1337 y FQ(Next)12 b(w)o(e)h(study)h(measures)e(on)i(\012.)20 b(Let)14 b FF(M)5 b FQ(\(\012\))14 b(=)g FF(M)5 b FQ(\(\012)p FF(;)j FE(F)d FQ(\))13 b(b)q(e)h(the)f(space)g(of)h(\014nite)f(signed)g(mea-) 60 1397 y(sures)k(on)h(\012,)f(and)h FF(M)461 1404 y FH(+1)509 1397 y FQ(\(\012\))d(=)h FF(M)698 1404 y FH(+1)745 1397 y FQ(\(\012)p FF(;)8 b FE(F)d FQ(\))15 b FE(\032)g FF(M)5 b FQ(\(\012\))18 b(b)q(e)f(the)g(space)h(of)f(probabilit)o(y)g(measures.)60 1457 y(There)e(is)f(a)i(natural)f(dualit)o(y)f(b)q(et)o(w)o(een)g(spaces)i (of)f(functions)g(and)h(spaces)f(of)g(measures,)f(namely)692 1579 y FE(h)p FF(\026;)8 b(f)d FE(i)29 b(\021)f FF(\026)p FQ(\()p FF(f)5 b FQ(\))28 b FE(\021)1096 1521 y Fx(Z)1138 1579 y FF(f)14 b(d\026)g(:)532 b FQ(\(2)p FF(:)p FQ(9\))60 1704 y(If)15 b(\012)g(is)h (compact,)d(then)j FP(every)k FQ(b)q(ounded)c(linear)f(functional)g(on)h FF(C)t FQ(\(\012\))f(arises)g(in)g(this)g(w)o(a)o(y)g(from)60 1765 y(a)f(\014nite)g(signed)g(measure)e(\(Riesz-Mark)o(o)o(v)h(theorem\);)f (otherwise)i(put,)g(the)g(Banac)o(h-space)g(dual)60 1825 y(of)j FF(C)t FQ(\(\012\))e(is)h(exactly)f FF(M)5 b FQ(\(\012\).)133 1885 y(Let)19 b FF(\026)f FQ(b)q(e)h(a)f(probabilit)o(y)f(measure)g(on)i (\012;)g(then)f(the)g FP(supp)n(ort)h(of)g FF(\026)f FQ(\(denoted)g(supp)q FF(\026)p FQ(\))h(is)f(a)60 1945 y(closed)e(subset)g(of)h(\012)f(that)h(can)g (b)q(e)f(de\014ned)g(in)g(an)o(y)g(of)h(three)e(equiv)m(alen)o(t)g(w)o(a)o (ys:)95 2047 y(\(a\))25 b(The)16 b(set)g(of)h(all)f FF(!)g FE(2)e FQ(\012)i(suc)o(h)g(that)h(ev)o(ery)e(neigh)o(b)q(orho)q(o)q(d)j(of)e FF(!)j FQ(has)e(nonzero)f(measure.)93 2148 y(\(b\))24 b(The)16 b(in)o(tersection)f(of)i(all)e(closed)h(sets)h(of)f(measure)f(1.)98 2250 y(\(c\))24 b(The)16 b(complemen)n(t)e(of)i(the)g(union)h(of)f(all)g(op)q (en)h(sets)f(of)h(measure)e(zero.)60 2352 y(The)f(k)o(ey)f(theorem)f(is:)20 b(if)14 b(\012)g(is)g(a)g FP(sep)n(ar)n(able)k FQ(metric)12 b(space,)i(then)g FF(\026)p FQ(\(supp)q FF(\026)p FQ(\))g(=)g(1,)g(so)h(that) f(supp)q FF(\026)60 2412 y FQ(is)i(the)g(smallest)f(closed)g(set)i(ha)o(ving) f(measure)f(1.)133 2472 y(W)l(e)e(need)f(to)h(discuss)g(what)g(it)g(means)e (for)i(a)h(sequence)d(\(or)i(net\))g(of)g(measures)e FF(\026)1617 2479 y FD(n)1654 2472 y FQ(to)i FP(c)n(onver)n(ge)60 2532 y FQ(to)g(a)g(limiting)e(measure)g FF(\026)p FQ(;)j(in)e(other)h(w)o(ords,)h(w) o(e)e(need)h(to)g(equip)f(the)h(spaces)g FF(M)5 b FQ(\(\012\))13 b(and)g FF(M)1769 2539 y FH(+1)1817 2532 y FQ(\(\012\))60 2593 y(with)g(a)g FP(top)n(olo)n(gy)t FQ(.)20 b(In)13 b(fact,)g(there)g(are)g FP(sever)n(al)19 b FQ(mathematicall)o(y)10 b(natural)j(top)q(ologies,)i(eac)o (h)d(with)951 2784 y(20)p eop %%Page: 21 21 bop 60 91 a FQ(a)20 b(distinct)e FP(physic)n(al)24 b FQ(meaning.)k(The)20 b(simplest)d(top)q(ology)j(is)f(the)g(norm)f(top)q(ology)j(de\014ned)e(b)o(y) 60 152 y(the)d FP(total)i(variation)g(norm)572 257 y FE(k)p FF(\026)11 b FE(\000)g FF(\027)s FE(k)41 b FQ(=)120 b(sup)881 303 y FD(f)13 b Fy(2)c FD(B)r FH(\(\012)p FD(;)c Fy(F)s FH(\))899 345 y Fy(k)p FD(f)t Fy(k)956 349 y Ft(1)997 345 y Fy(\024)10 b FH(1)1099 257 y FE(j)p FF(\026)p FQ(\()p FF(f)5 b FQ(\))11 b FE(\000)g FF(\027)s FQ(\()p FF(f)5 b FQ(\))p FE(j)780 416 y FQ(=)102 b(sup)885 462 y FD(f)13 b Fy(2)d FD(C)r FH(\(\012\))881 504 y Fy(k)p FD(f)t Fy(k)938 508 y Ft(1)979 504 y Fy(\024)g FH(1)1063 416 y FE(j)p FF(\026)p FQ(\()p FF(f)5 b FQ(\))11 b FE(\000)g FF(\027)s FQ(\()p FF(f)5 b FQ(\))p FE(j)780 575 y FQ(=)42 b(2)11 b(sup)892 614 y FD(A)p Fy(2F)979 575 y FE(j)p FF(\026)p FQ(\()p FF(A)p FQ(\))g FE(\000)g FF(\027)s FQ(\()p FF(A)p FQ(\))p FE(j)i FF(:)440 b FQ(\(2.10a\))60 707 y(A)16 b(sequence)g(\(or)h(net\))g FF(\026)528 714 y FD(n)568 707 y FQ(con)o(v)o(erges)f(in)h(v)m(ariation)g(norm)f(to)h FF(\026)g FQ(if)g FE(k)p FF(\026)1384 714 y FD(n)1419 707 y FE(\000)11 b FF(\026)p FE(k)k(!)g FQ(0.)23 b(Ph)o(ysically)l(,)60 767 y(norm)18 b(con)o(v)o(ergence)g(of)i FF(\026)551 774 y FD(n)594 767 y FQ(to)g FF(\026)g FQ(means)e(that)i(exp)q(ectation)f(v)m(alues)g(in)g FF(\026)1470 774 y FD(n)1514 767 y FQ(con)o(v)o(erge)f(to)i(those)60 827 y(in)e FF(\026)p FQ(,)h FP(uniformly)j FQ(for)d(all)e(b)q(ounded)i (observ)m(ables)g FF(f)5 b FQ(.)28 b(This)18 b(is)g(an)h(extremely)c(strong)k (notion)g(of)60 887 y(con)o(v)o(ergence,)11 b(whic)o(h)h(o)q(ccurs)i(only)e (rarely)g(in)h(ph)o(ysical)e(applications.)21 b(Therefore,)12 b(w)o(e)g(in)o(tro)q(duce)60 948 y(also)17 b(the)g FP(we)n(ak)h(top)n(olo)n (gies)j FQ(induced)16 b(b)o(y)h(the)f(v)m(arious)i(classes)f(of)g(functions)g (de\014ned)f(in)h(Section)60 1008 y(2.1.2:)133 1105 y FE(\017)24 b FQ(The)17 b FP(b)n(ounde)n(d)h(me)n(asur)n(able)g(top)n(olo)n(gy)t FQ(:)k FF(\026)957 1112 y FD(n)996 1105 y FE(!)15 b FF(\026)i FQ(if)f FF(\026)1181 1112 y FD(n)1205 1105 y FQ(\()p FF(f)5 b FQ(\))15 b FE(!)g FF(\026)p FQ(\()p FF(f)5 b FQ(\))17 b(for)g(all)g FF(f)j FE(2)15 b FF(B)s FQ(\(\012)p FF(;)8 b FE(F)d FQ(\).)182 1165 y([If)13 b(the)i FF(\026)354 1172 y FD(n)392 1165 y FQ(are)f(probabilit) o(y)g(measures,)f(it)h(su\016ces)g(to)h(c)o(hec)o(k)e(that)i FF(\026)1472 1172 y FD(n)1495 1165 y FQ(\()p FF(A)p FQ(\))f FE(!)f FF(\026)p FQ(\()p FF(A)p FQ(\))i(for)g(all)182 1226 y FF(A)e FE(2)h(F)5 b FQ(.])133 1326 y FE(\017)24 b FQ(The)17 b FP(b)n(ounde)n(d)h(quasilo)n(c)n(al)h(top)n(olo)n(gy)t FQ(:)j FF(\026)927 1333 y FD(n)966 1326 y FE(!)15 b FF(\026)j FQ(if)e FF(\026)1152 1333 y FD(n)1176 1326 y FQ(\()p FF(f)5 b FQ(\))15 b FE(!)g FF(\026)p FQ(\()p FF(f)5 b FQ(\))18 b(for)f(all)g FF(f)j FE(2)c FF(B)1711 1333 y FD(q)q(l)1741 1326 y FQ(\(\012)p FF(;)8 b FE(F)d FQ(\).)182 1386 y([If)23 b(the)h FF(\026)373 1393 y FD(n)422 1386 y FQ(are)g(probabilit)o(y)f(measures,)i(it)f(su\016ces)g (to)h(c)o(hec)o(k)d(con)o(v)o(ergence)h(for)i FF(f)33 b FE(2)182 1446 y FF(B)219 1453 y FD(loc)264 1446 y FQ(\(\012)p FF(;)8 b FE(F)d FQ(\),)16 b(or)h(alternativ)o(ely)d(for)i(all)g FF(A)d FE(2)1031 1413 y Fx(S)1012 1484 y FH(\003)p Fy(2S)1092 1446 y FE(F)1128 1453 y FH(\003)1155 1446 y FQ(.])133 1572 y FE(\017)24 b FQ(The)16 b(\(ordinary\))h FP(we)n(ak)h(top)n(olo)n(gy)t FQ(:)j FF(\026)872 1579 y FD(n)909 1572 y FE(!)14 b FF(\026)j FQ(if)e FF(\026)1092 1579 y FD(n)1116 1572 y FQ(\()p FF(f)5 b FQ(\))14 b FE(!)g FF(\026)p FQ(\()p FF(f)5 b FQ(\))17 b(for)f(all)g FF(f)j FE(2)14 b FF(C)t FQ(\(\012\).)133 1672 y FE(\017)24 b FQ(The)c FP(we)n(ak)i(quasilo)n(c)n(al)g(top)n(olo)n(gy)t FQ(:)30 b FF(\026)876 1679 y FD(n)921 1672 y FE(!)21 b FF(\026)g FQ(if)f FF(\026)1120 1679 y FD(n)1144 1672 y FQ(\()p FF(f)5 b FQ(\))21 b FE(!)g FF(\026)p FQ(\()p FF(f)5 b FQ(\))21 b(for)g(all)f FF(f)26 b FE(2)c FF(C)1711 1679 y FD(q)q(l)1741 1672 y FQ(\(\012)p FF(;)8 b FE(F)d FQ(\).)182 1733 y([If)23 b(the)h FF(\026)373 1740 y FD(n)422 1733 y FQ(are)g(probabilit)o(y)f(measures,)i(it)f(su\016ces)g (to)h(c)o(hec)o(k)d(con)o(v)o(ergence)h(for)i FF(f)33 b FE(2)182 1793 y FF(C)217 1800 y FD(loc)262 1793 y FQ(\(\012)p FF(;)8 b FE(F)d FQ(\).])60 1890 y(W)l(e)18 b(emphasize)f(that)h(the)h(con)o(v)o (ergence)d(is)j(required)e(to)i(o)q(ccur)f(for)h(eac)o(h)f(observ)m(able)g FF(f)24 b FQ(in)18 b(the)60 1951 y(designated)23 b(class,)i(but)e(the)g(con)o (v)o(ergence)f(is)h FP(not)29 b FQ(required)22 b(to)h(b)q(e)h(uniform)d(in)i FF(f)5 b FQ(.)43 b(This)23 b(is)60 2011 y(imp)q(ortan)o(t,)17 b(since)g FF(f)23 b FQ(could)17 b(equally)g(w)o(ell)f(b)q(e)i(the)g(lo)q(cal) f(energy)g(densit)o(y)g(in)h(New)f(Y)l(ork)g(or)h(the)60 2071 y(lo)q(cal)c(energy)f(densit)o(y)g(on)i(Andromeda;)e(and)h(one)g(should)h (not)f(exp)q(ect,)f(in)h(most)f(situations,)h(the)60 2131 y(con)o(v)o (ergence)i(to)j(b)q(e)f(uniform)e(on)j(all)e(suc)o(h)h(observ)m(ables.)27 b(This)18 b(reasoning)h(also)f(suggests)i(that)60 2191 y(the)c(t)o(w)o(o)g (quasilo)q(cal)g(top)q(ologies)i(are)e(lik)o(ely)e(to)i(b)q(e)h(the)f(ones)g (of)h(greatest)f(ph)o(ysical)g(relev)m(ance.)60 2299 y FM(Examples.)24 b FQ(1.)j(Let)18 b(\012)526 2306 y FH(0)563 2299 y FQ(=)f Fq(R)p FQ(,)h(and)h(let)e FF(\026)881 2306 y FD(n)923 2299 y FQ(\(resp.)h FF(\026)p FQ(\))g(b)q(e)g(the)g(Dirac)g(delta)f(measure)g(concen-)60 2359 y(trated)h(on)h(the)e(con\014guration)j(in)d(whic)o(h)h(all)f(the)h (spins)g(tak)o(e)g(the)g(v)m(alue)f(1)p FF(=n)i FQ(\(resp.)f(0\).)27 b(Then)60 2419 y FF(\026)89 2426 y FD(n)127 2419 y FE(!)13 b FF(\026)g FQ(in)f(the)g(w)o(eak)h(and)g(w)o(eak)f(quasilo)q(cal)g(top)q (ologies,)i(but)f(not)g(in)f(the)g(b)q(ounded)h(measurable)60 2479 y(or)k(b)q(ounded)g(quasilo)q(cal)f(top)q(ologies.)133 2539 y(2.)29 b(Let)19 b(\012)325 2546 y FH(0)363 2539 y FQ(=)g FE(f\000)p FQ(1)p FF(;)8 b FQ(1)p FE(g)p FQ(,)19 b(and)g(let)f FF(\026)811 2546 y FD(n)854 2539 y FQ(b)q(e)h(the)f(Dirac)h(delta)f(measure)g (concen)o(trated)g(on)h(the)60 2600 y(con\014guration)h(whic)o(h)e(is)h(+1)g (for)g(all)f(spins)h(at)g(a)g(distance)g FE(\024)f FF(n)h FQ(from)e(the)i (origin)f(and)i FE(\000)p FQ(1)f(for)60 2660 y(all)g(other)g(spins.)31 b(Let)20 b FF(\026)f FQ(b)q(e)h(the)f(Dirac)g(delta)g(measure)f(concen)o (trated)h(on)h(the)f(con\014guration)951 2784 y(21)p eop %%Page: 22 22 bop 60 91 a FQ(whic)o(h)18 b(is)h(all)f(+1.)29 b(Then)19 b FF(\026)588 98 y FD(n)630 91 y FE(!)e FF(\026)j FQ(in)e(the)g(b)q(ounded)i (quasilo)q(cal,)f(w)o(eak)f(and)i(w)o(eak)e(quasilo)q(cal)60 152 y(top)q(ologies,)f(but)f(not)h(in)f(the)g(b)q(ounded)h(measurable)e(top)q (ology)l(.)133 257 y(Georgii)21 b(bases)g(his)f(theory)h(on)g(the)f(b)q (ounded)i(quasilo)q(cal)e(top)q(ology)i(\(whic)o(h)e(he)g(calls)g(the)60 318 y(\\top)q(ology)e(of)f(lo)q(cal)f(con)o(v)o(ergence")f(or)i(the)f(\\)p FE(L)p FQ(-top)q(ology"\))j([157,)d(Chapter)h(4];)f(Israel)g(restricts)60 378 y(atten)o(tion)21 b(to)i(compact)d(metric)f(single-spin)j(spaces,)h(and)f (uses)g(mainly)e(the)h(w)o(eak)h(\(=)f(w)o(eak)60 438 y(quasilo)q(cal\))16 b(top)q(ology)i([206,)e(Chapters)h(I)q(I)f(and)h(IV].)133 498 y(Finally)l(,)c(let)g(us)h(remark)f(that)h(with)g(resp)q(ect)g(to)g(the)g (\(ordinary\))g(w)o(eak)g(top)q(ology)l(,)h FF(M)1723 505 y FH(+1)1770 498 y FQ(\(\012\))f(is)60 558 y(separable)j(and)g(metrizable)d (\(resp.)j(complete)d(metrizable,)g(compact)i(metrizable\))e(if)i(and)h(only) 60 619 y(if)f(\012)g(is.)21 b(Let)16 b(us)h(also)f(remark)f(that)h(if)g(\012) 823 626 y FH(0)859 619 y FQ(is)g(separable)g(and)h(metrizable)c(\(resp.)j (coun)o(table)f(and)60 679 y(discrete\),)j(then)h(the)g(b)q(ounded)h(quasilo) q(cal)f(top)q(ology)h(is)f(stronger)h(than)g(\(resp.)e(equal)h(to\))g(the)60 739 y(\(ordinary\))c(w)o(eak)f(top)q(ology;)i(this)e(is)h(true)f(ev)o(en)g (though)h(these)g(h)o(yp)q(otheses)f(do)i FP(not)j FQ(imply)13 b(that)60 799 y FF(C)t FQ(\(\012\))g FE(\032)h FF(B)275 806 y FD(q)q(l)305 799 y FQ(\(\012\).)60 942 y FB(2.2)70 b(In)n(teractions)22 b(and)i(Hami)o(l)o(tonians)60 1017 y FH(12)133 1095 y FQ(As)g(discussed)g(in) g(the)g(In)o(tro)q(duction)g(to)g(this)g(section,)h(the)f(Hamiltonian)f FF(H)t FQ(\()p FF(!)r FQ(\))h(for)h(an)60 1155 y(in\014nite-v)o(olume)15 b(system)h(is)i(an)g(ill-de\014ned)f(ob)s(ject.)26 b(Therefore)17 b(w)o(e)h(m)o(ust)e(pro)q(ceed)i(more)f(cau-)60 1215 y(tiously)l(.)j(W)l(e)13 b(de\014ne)h(\014rst)g(the)f(concept)h(of)g(an)g FP(inter)n(action)t FQ(,)g(whic)o(h)f(corresp)q(onds)i(roughly)f(to)g(the)60 1276 y(idea)k(of)g(a)h(\\formal)e(Hamiltonian")g(or)h(a)h(\\set)f(of)h(coupling)f (constan)o(ts".)28 b(Then)18 b(w)o(e)f(de\014ne)h(the)60 1336 y FP(\014nite-volume)23 b(Hamiltonians)h FQ(corresp)q(onding)19 b(to)h(a)f(giv)o(en)f(in)o(teraction)f(and)j(giv)o(en)e(b)q(oundary)60 1396 y(conditions.)133 1456 y(The)e(\(meaningless\))e(Hamiltonian)g(of)i(an)h (in\014nite-v)o(olume)12 b(system)j(is)g(written)g(formally)f(as)60 1516 y(a)j(sum)f(of)h(terms)f(corresp)q(onding)h(to)h(v)m(arious)f(\014nite)f (subsets)i(of)f(the)f(lattice:)22 b(one-b)q(o)q(dy)c(terms,)60 1577 y(t)o(w)o(o-b)q(o)q(dy)23 b(terms,)f(three-b)q(o)q(dy)h(terms)d(and)j (so)f(forth.)39 b(Mathematically)20 b(this)i(idea)f(is)h(made)60 1637 y(precise)15 b(as)i(follo)o(ws:)60 1732 y FM(De\014nition)h(2.1)24 b FP(A)o(n)16 b FQ(in)o(teraction)g FP(\(or)g FQ(in)o(teraction)e(p)q(oten)o (tial)j FP(or)f FQ(p)q(oten)o(tial)p FP(\))g(is)g(a)h(family)f FQ(\010)e(=)60 1792 y(\(\010)114 1799 y FD(A)143 1792 y FQ(\))162 1799 y FD(A)p Fy(2S)261 1792 y FP(of)24 b(functions)h FQ(\010)578 1799 y FD(A)607 1792 y FQ(:)33 b(\012)26 b FE(!)f Fq(R)q FP(,)g(such)f(that)g (for)f(e)n(ach)h FF(A)h FE(2)h(S)t FP(,)f(the)g(function)g FQ(\010)1803 1799 y FD(A)1855 1792 y FP(is)60 1853 y FE(F)96 1860 y FD(A)124 1853 y FP(-me)n(asur)n(able)18 b(\(i.e.)g(dep)n(ends)g(only)f (on)h(the)g(spins)g(in)f(the)h(\014nite)h(subset)g FF(A)p FP(\).)133 1948 y FM(Remark.)31 b FQ(Note)19 b(that)i(w)o(e)f(do)g FP(not)25 b FQ(allo)o(w)20 b(the)g(in)o(teraction)f(\010)1349 1955 y FD(A)1398 1948 y FQ(to)i(tak)o(e)e(the)h(v)m(alue)g(+)p FE(1)p FQ(.)60 2008 y(Therefore,)15 b(a)i(\\hard-core)g(in)o(teraction")f(is)g FP(not)21 b FQ(included)15 b(in)h(our)h(form)o(ulation.)133 2091 y FM(Example.)22 b FQ(Consider)17 b(the)g(Ising)g(mo)q(del)f(whose)i (formal)e(\(i.e.)f(meaningless\))h(Hamiltonian)60 2151 y(is)570 2212 y FF(H)t FQ(\()p FF(!)r FQ(\))e(\\=")26 b FE(\000)862 2170 y Fx(X)860 2264 y Fy(h)p FD(xy)q Fy(i)934 2212 y FF(J)961 2219 y FD(xy)1001 2212 y FF(!)1031 2219 y FD(x)1054 2212 y FF(!)1084 2219 y FD(y)1124 2212 y FE(\000)1182 2170 y Fx(X)1202 2257 y FD(x)1250 2212 y FF(h)1278 2219 y FD(x)1300 2212 y FF(!)1330 2219 y FD(x)1367 2212 y FF(:)384 b FQ(\(2)p FF(:)p FQ(11\))60 2342 y(This)16 b(mo)q(del)f(is)h(de\014ned)g(\(meaningfully!\))j(b)o(y)d(the) g(in)o(teraction)559 2493 y(\010)594 2500 y FD(A)623 2493 y FQ(\()p FF(!)r FQ(\))27 b(=)786 2405 y Fx(8)786 2443 y(<)786 2517 y(:)831 2439 y FE(\000)p FF(h)898 2446 y FD(x)920 2439 y FF(!)950 2446 y FD(x)1090 2439 y FQ(if)15 b FF(A)f FQ(=)g FE(f)p FF(x)p FE(g)831 2499 y(\000)p FF(J)897 2506 y FD(xy)938 2499 y FF(!)968 2506 y FD(x)990 2499 y FF(!)1020 2506 y FD(y)1090 2499 y FQ(if)h FF(A)f FQ(=)g FE(f)p FF(x;)8 b(y)r FE(g)831 2559 y FQ(0)235 b(otherwise)1765 2493 y(\(2)p FF(:)p FQ(12\))p 60 2591 732 2 v 100 2645 a FA(12)135 2660 y Fz(References)16 b(for)d(this)h(section)h(are)f(Georgii)f([157)o(,)g(Section)h(2.1])f(and)g (Israel)i([206)n(,)f(Sections)g(I.1)g(and)f(I.2].)951 2784 y FQ(22)p eop %%Page: 23 23 bop 133 91 a FQ(The)18 b(next)f(step)h(is)g(to)g(de\014ne)f(the)h (Hamiltonian)e FF(H)1117 73 y FH(\010)1113 104 y(\003)1163 91 y FQ(corresp)q(onding)i(to)h(an)f(in)o(teraction)f(\010)60 152 y(acting)f(in)f(a)i(\014nite)e(v)o(olume)e(\003.)21 b(This)16 b(dep)q(ends,)g(ho)o(w)o(ev)o(er,)e(on)i(what)h(b)q(oundary)g(conditions)f (one)60 212 y(c)o(ho)q(oses.)22 b(The)16 b(simplest)e(case)j(is)f FP(fr)n(e)n(e)g(b)n(oundary)h(c)n(onditions)t FQ(:)60 308 y FM(De\014nition)h(2.2)24 b FP(L)n(et)f FQ(\010)h FP(b)n(e)g(an)g(inter)n (action.)43 b(Then,)26 b(for)d(e)n(ach)h FQ(\003)h FE(2)h(S)t FP(,)g(the)e(Hamiltonian)60 369 y FF(H)104 350 y FH(\010)100 381 y(\003)p FD(;f)t(r)q(ee)224 369 y FP(for)17 b(volume)i FQ(\003)e FP(with)h(fr)n(e)n(e)f(b)n(oundary)g(c)n(onditions)h(is)f(the)h (function)735 481 y FF(H)779 460 y FH(\010)775 493 y(\003)p FD(;f)t(r)q(ee)910 481 y FQ(=)1015 440 y Fx(X)999 538 y FD(A)10 b Fy(2)f(S)996 580 y FD(A)i Fy(\032)f FH(\003)1123 481 y FQ(\010)1158 488 y FD(A)1201 481 y FF(:)550 b FQ(\(2)p FF(:)p FQ(13\))60 680 y(Note)12 b(that)g(this)g(is)g(alw)o(a)o(ys)f(a)i FP(\014nite)k FQ(sum,)11 b(so)i(the)f(free-b.c.)e(Hamiltonian)g(is)i(alw)o(a)o(ys)g(w)o (ell-de\014ned.)60 740 y(Note)k(also)h(that)f FF(H)425 722 y FH(\010)421 752 y(\003)p FD(;f)t(r)q(ee)545 740 y FQ(dep)q(ends)g(only)g (on)h(the)f(spins)g FP(inside)21 b FQ(\003.)133 800 y(F)l(ree)c(b)q(oundary)h (conditions)f(are)h(not,)f(ho)o(w)o(ev)o(er,)f(su\016cien)o(t:)22 b(for)17 b(man)o(y)f(purp)q(oses)j(w)o(e)d(need)60 860 y(Hamiltonians)k(in)i (whic)o(h)f(the)h(in)o(terior)e(of)j(the)e(v)o(olume)f(\003)i(is)f(allo)o(w)o (ed)g(to)i(in)o(teract)e(with)g(the)60 921 y(exterior.)26 b(T)l(o)19 b(do)g(this,)f(w)o(e)g(m)o(ust)f(consider)h(the)g(b)q(onds)h(that)g(couple)f (a)h(giv)o(en)e(v)o(olume)f(\003)i(with)60 981 y(its)e(exterior;)f(these)h (giv)o(e)f(a)i(con)o(tribution)e(of)i(the)f(form)700 1085 y FF(W)753 1064 y FH(\010)746 1097 y(\003)p FD(;)p FH(\003)804 1088 y Fs(c)850 1085 y FQ(=)1003 1043 y Fx(X)987 1142 y FD(A)10 b Fy(2)f(S)944 1189 y FD(A)g Fy(\\)e FH(\003)j Fy(6)p FH(=)h Fq(?)936 1235 y FD(A)e Fy(\\)e FH(\003)1026 1224 y Fs(c)1052 1235 y Fy(6)p FH(=)k Fq(?)1159 1085 y FQ(\010)1194 1092 y FD(A)1237 1085 y FF(:)514 b FQ(\(2)p FF(:)p FQ(14\))60 1335 y(Note)14 b(that)h(no)o(w)f(w)o(e)g(are)h(dealing)f(with)g(an)h FP(in\014nite)20 b FQ(sum;)13 b(therefore)h(w)o(e)g(m)o(ust)f(b)q(e)h(careful)g(ab)q(out)60 1395 y(its)23 b(con)o(v)o(ergence.)41 b(In)23 b(an)o(y)g(case,)h(the)f (Hamiltonian)f(for)h(v)o(olume)e(\003)i(with)g FP(gener)n(al)i(external)60 1455 y(b)n(oundary)17 b(c)n(onditions)k FQ(corresp)q(onds)c(to)g(adding)g (the)f(con)o(tributions)g(\(2.13\))g(and)h(\(2.14\):)60 1552 y FM(De\014nition)h(2.3)24 b FP(L)n(et)17 b FQ(\010)i FP(b)n(e)g(an)f(inter)n (action.)26 b(Then,)19 b(for)e(e)n(ach)i FQ(\003)c FE(2)h(S)t FP(,)i(the)h(Hamiltonian)g FF(H)1862 1534 y FH(\010)1858 1564 y(\003)60 1612 y FP(for)e(volume)h FQ(\003)g FP(with)g(gener)n(al)g(external) h(b)n(oundary)e(c)n(onditions)h(is)f(the)h(function)586 1716 y FF(H)630 1696 y FH(\010)626 1728 y(\003)658 1716 y FQ(\()p FF(!)r FQ(\))42 b(=)929 1675 y Fx(X)913 1773 y FD(A)10 b Fy(2)f(S)871 1820 y FD(A)f Fy(\\)f FH(\003)j Fy(6)p FH(=)h Fq(?)1077 1716 y FQ(\010)1112 1723 y FD(A)1141 1716 y FQ(\()p FF(!)r FQ(\))530 b(\(2.15a\))770 1897 y FE(\021)41 b FF(H)894 1876 y FH(\010)890 1909 y(\003)p FD(;f)t(r)q(ee)997 1897 y FQ(\()p FF(!)r FQ(\))19 b(+)h FF(W)1197 1876 y FH(\010)1190 1909 y(\003)p FD(;)p FH(\003)1248 1899 y Fs(c)1266 1897 y FQ(\()p FF(!)r FQ(\))14 b FF(;)374 b FQ(\(2.15b\))60 2001 y FP(pr)n(ovide)n(d)18 b(that)h(this)g(sum)f(c)n (onver)n(ges)i(to)f(a)g(\014nite)h(limit)f(for)f(al)r(l)i FF(!)f FE(2)d FQ(\012)p FP(,)k(in)f(which)g(c)n(ase)g(we)h(c)n(al)r(l)60 2061 y(the)e(inter)n(action)g FQ(\010)g(con)o(v)o(ergen)o(t)p FP(.)685 2043 y FH(13)60 2157 y FQ(Here)f(the)i(con)o(v)o(ergence)d(is)j(not) g(required)e(to)i(b)q(e)f(absolute,)h(nor)g(is)g(it)f(required)f(to)i(b)q(e)f (uniform)60 2218 y(in)d FF(!)r FQ(;)g(w)o(e)g(insist)g(only)g(that)h(the)f (\014nite-v)o(olume)e(Hamiltonian)g FF(H)1284 2200 y FH(\010)1280 2230 y(\003)1312 2218 y FQ(\()p FF(!)r FQ(\))h FE(\021)g FF(H)1493 2200 y FH(\010)1489 2230 y(\003)1521 2218 y FQ(\()p FF(!)1570 2225 y FH(\003)1597 2218 y FF(;)8 b(!)1649 2225 y FH(\003)1673 2216 y Fs(c)1691 2218 y FQ(\))16 b(b)q(e)f(w)o(ell-)60 2278 y(de\014ned)21 b(for)h(all)f(con\014gurations)i FF(!)h FQ(\(i.e.)c(all)h (pairs)h(consisting)f(of)h(an)g(in)o(ternal)f(con\014guration)p 60 2323 732 2 v 100 2466 a FA(13)135 2481 y Fz(More)16 b(precisely)m(,)g (what)g(this)f(means)g(is)h(that)g(the)g(net)1023 2335 y Fx(0)1023 2408 y(B)1023 2433 y(B)1023 2458 y(B)1023 2483 y(B)1023 2508 y(B)1023 2534 y(@)1143 2450 y(P)1121 2523 y Fp(A)9 b Fo(2)h(S)1080 2567 y Fp(A)e Fo(\\)g FA(\003)h Fo(6)p FA(=)h Fq(?)1117 2602 y Fp(A)f Fo(\032)h FA(\001)1278 2481 y Fz(\010)1308 2487 y Fp(A)1335 2481 y Fz(\()p Fv(!)q Fz(\))1394 2335 y Fx(1)1394 2408 y(C)1394 2433 y(C)1394 2458 y(C)1394 2483 y(C)1394 2508 y(C)1394 2534 y(A)1431 2619 y FA(\001)p Fo(2S)1521 2481 y Fz(con)o(v)o(erges) 17 b(to)e(a)h(\014nite)60 2660 y(limit)11 b(\(for)j(eac)o(h)g Fv(!)f Fu(2)e Fz(\012\))j(as)g(\001)d Fu(")h(L)p Fz(.)951 2784 y FQ(23)p eop %%Page: 24 24 bop 60 91 a FF(!)90 98 y FH(\003)137 91 y FQ(and)20 b(an)h(external)e (con\014guration)i FF(!)828 98 y FH(\003)852 89 y Fs(c)871 91 y FQ(\).)32 b(This)20 b(is)g(a)g(v)o(ery)f(mo)q(dest)g(requiremen)o(t.)29 b(It)19 b(rules)60 152 y(out,)c(ho)o(w)o(ev)o(er,)e(the)h(use)h(of)g(this)f (formalism)e(for)i(a)h(Coulom)o(b)f(system,)f(in)h(whic)o(h)g(the)g(in)o (teraction)60 212 y(deca)o(ys)i(to)q(o)h(slo)o(wly)f(to)g(b)q(e)h(summable)c (in)j(an)o(y)g(reasonable)h(sense.)1314 194 y FH(14)133 272 y FQ(F)l(or)f(man)o(y)e(purp)q(oses)j(it)e(is)h(con)o(v)o(enien)o(t)d(to)j (think)g(of)g(the)f(con\014guration)i(outside)f(\003)f(as)h(\014xed)60 332 y(\(the)h(\\b)q(oundary)h(condition"\))f(and)h(the)e(con\014guration)i (inside)e(\003)h(as)h(v)m(ariable.)23 b(Therefore,)16 b(for)60 392 y(an)o(y)22 b(\014xed)f FF(\034)29 b FE(2)23 b FQ(\012,)g(w)o(e)f (de\014ne)f(the)g(Hamiltonian)f FF(H)1102 374 y FH(\010)1098 405 y(\003)p FD(;\034)1176 392 y FQ(whic)o(h)h(uses)h FP(b)n(oundary)g(c)n (ondition)h FF(\034)60 452 y FP(outside)18 b(the)g(volume)g FQ(\003)f(to)f(b)q(e)686 562 y FF(H)730 542 y FH(\010)726 575 y(\003)p FD(;\034)782 562 y FQ(\()p FF(!)r FQ(\))28 b(=)f FF(H)989 542 y FH(\010)985 575 y(\003)1017 562 y FQ(\()p FF(!)1066 569 y FH(\003)1104 562 y FE(\002)11 b FF(\034)1175 569 y FH(\003)1199 560 y Fs(c)1218 562 y FQ(\))j FF(:)500 b FQ(\(2)p FF(:)p FQ(16\))60 672 y(Here)16 b FF(!)206 679 y FH(\003)245 672 y FE(\002)11 b FF(\034)316 679 y FH(\003)340 670 y Fs(c)376 672 y FQ(is)18 b(the)f(con\014guration)h(whic)o(h)f(agrees)g(with)g FF(!)j FQ(on)e(\003)f(and)h(with)f FF(\034)23 b FQ(on)18 b(\003)1733 654 y FD(c)1750 672 y FQ(.)24 b(Note)60 733 y(that)17 b FF(H)210 715 y FH(\010)206 745 y(\003)p FD(;\034)262 733 y FQ(\()p FF(!)r FQ(\))f(dep)q(ends)h(only)f(on)h(the)f(b)q(eha)o(vior)g(of)g FF(!)j FP(inside)h FQ(\003.)133 793 y(It)e(is)g(also)h(p)q(ossible)g(to)f (de\014ne)g(the)h(Hamiltonian)d(with)i(other)h(b)q(oundary)g(conditions)g (\(e.g.)60 853 y(p)q(erio)q(dic\),)c(but)i(w)o(e)f(shall)g(ha)o(v)o(e)f(no)i (need)f(for)g(these.)133 938 y(The)c(summabilit)o(y)c(prop)q(erties)k(of)h (the)f(Hamiltonian)e(\(2.15a\))j(ha)o(v)o(e)e(imp)q(ortan)o(t)g(implications) 60 998 y(for)i(the)f(c)o(haracteristics)f(of)i(the)f(measures)g(constructed)g (with)g(them.)19 b(In)12 b(addition)g(to)h(the)g(notion)60 1059 y(of)j FP(c)n(onver)n(genc)n(e)21 b FQ(in)o(tro)q(duced)15 b(in)g(De\014nition)g(2.3)h(ab)q(o)o(v)o(e,)f(w)o(e)g(wish)h(to)g (distinguish)f(t)o(w)o(o)g(stronger)60 1119 y(notions)i(of)g(summabili)o(t)o (y:)60 1220 y FM(De\014nition)h(2.4)24 b FP(We)17 b(c)n(al)r(l)i(the)f(inter) n(action)g FQ(\010)133 1322 y FE(\017)24 b FQ(uniformly)17 b(con)o(v)o(ergen)o(t)h FP(if,)i(for)f(every)h FQ(\003)e FE(2)g(S)t FP(,)j(the)f(sum)f(\(2.15a\))h(c)n(onver)n(ges)g(uniformly)182 1382 y(in)e FF(!)r FP(;)133 1484 y FE(\017)24 b FQ(absolutely)d(summable)e FP(if,)k(for)e(every)i FQ(\003)e FE(2)i(S)t FP(,)g(the)f(sum)g(\(2.15a\))f(c) n(onver)n(ges)i(in)f FF(B)s FQ(\(\012\))182 1544 y FP(norm.)41 b(This)24 b(is)g(e)n(quivalent)i(to)e(the)g(c)n(ondition)h(that)1285 1511 y Fx(P)1260 1589 y FD(A)11 b Fy(2)e(S)1266 1631 y FD(A)i Fy(3)e FD(i)1383 1544 y FE(k)p FQ(\010)1443 1551 y FD(A)1471 1544 y FE(k)1496 1551 y Fy(1)1568 1544 y FF(<)34 b FE(1)24 b FP(for)f(e)n(ach)182 1686 y FF(i)13 b FE(2)h(L)p FP(.)60 1788 y FQ(Ob)o(viously)l(,)19 b(absolutely)g(summable)d(implies)h(uniformly)g (con)o(v)o(ergen)o(t,)i(whic)o(h)f(in)h(turn)h(implies)60 1848 y(the)c(con)o(v)o(ergence)f(of)h(\(2.15a\).)22 b(Some)15 b(commen)o(ts)f(and) j(examples)d(are)i(in)g(order:)133 1908 y(1\))c(The)g(ph)o(ysical)e(in)o (terpretation)h(of)g(absolute)h(summabilit)o(y)c(is)j(roughly)h(that)g(the)f FP(maximum)60 1968 y FQ(in)o(teraction)h(energy)h(b)q(et)o(w)o(een)f(one)i (spin)f(and)h(the)f(rest)g(of)h(the)f(univ)o(erse)f(is)h(\014nite.)19 b(Alternativ)o(ely)l(,)60 2029 y(the)d(\015ipping)g(of)h(one)f(spin)g(pro)q (duces)h(alw)o(a)o(ys)f(a)h(b)q(ounded)g(c)o(hange)f(in)g(energy)l(.)p 60 2072 732 2 v 100 2126 a FA(14)135 2141 y Fz(Lattice)d(Coulom)o(b)e (systems)i(admit)e(a)h(partial)g(thermo)q(dynamic)f(treatmen)o(t)i(based)g (on)g(free)h(b)q(oundary)f(con-)60 2191 y(ditions)e(and)g(a)g(carefully)g (tak)o(en)h(in\014nite-v)o(olume)d(limit)f(\(ensuring)k(o)o(v)o(erall)f (neutralit)o(y)g(of)f(the)i(plasma\))e([136)o(,)h(and)60 2241 y(references)j(therein].)j(It)11 b Fw(may)k Fz(b)q(e)d(p)q(ossible)f(to)g (cast)h(that)f(theory)g(in)o(to)g(a)f Fw(gener)n(alize)n(d)15 b Fz(v)o(ersion)c(of)g(the)g(Gibbs{DLR)60 2291 y(framew)o(ork)g(in)h(whic)o (h)h(the)g(\\bad")f(external)h(con\014gurations)f(|)g(here)i(the)f (non-neutral)g(ones)g(|)f(are)h(made)e(inac-)60 2340 y(cessible)j(to)f(all)f (Gibbs)h(measures)h([299)o(,)e(pp.)h(16{18)f(and)h(Chapter)h(6].)j(If)c(so,)g (man)o(y)e(\(but)j(not)f(all\))f(of)h(the)h(results)60 2390 y(discussed)k(in)e(this)h(section)g(w)o(ould)e(b)q(e)i(v)n(alid)e(also)h(for) g(suc)o(h)h(systems.)26 b(The)17 b(case)h(of)d(gra)o(vitational)f(systems)j (is)60 2440 y(ev)o(en)12 b(w)o(orse,)h(b)q(ecause)g(there)g(is)f(no)f (condition)h(analogous)e(to)i(neutralit)o(y)f(that)h(can)g(b)q(e)g(enforced.) 19 b(These)13 b(systems)60 2490 y(are)h(not)g(ev)o(en)h(thermo)q(dynamicall)o (y)c(stable.)951 2784 y FQ(24)p eop %%Page: 25 25 bop 133 91 a FQ(2\))11 b(An)g(example)d(of)k(a)f(uniformly)e(con)o(v)o(ergen) o(t)g(in)o(teraction)h(whic)o(h)g(is)h(not)g(absolutely)f(summable)60 152 y(is)16 b(the)g(follo)o(wing)g(one-dimensional)f(Ising)h(mo)q(del)f([336) q(]:)181 338 y(\010)216 345 y FD(A)245 338 y FQ(\()p FF(!)r FQ(\))28 b(=)408 226 y Fx(8)408 263 y(>)408 276 y(>)408 288 y(<)408 363 y(>)408 376 y(>)408 388 y(:)466 260 y FQ(\()p FE(\000)p FQ(1\))567 242 y FD(n)591 260 y FF(c)612 267 y FD(n)677 260 y FQ(if)15 b FF(A)h FQ(is)g(a)h(non-empt)o(y)e(set)h(of)g FF(n)h FQ(adjacen)o(t)f(p)q(oin)o(ts)725 320 y(and)h FF(!)850 327 y FD(x)886 320 y FQ(=)d(+1)j(for)f(all)g FF(x)d FE(2)h FF(A)466 416 y FQ(0)187 b(otherwise)1765 338 y(\(2)p FF(:)p FQ(17\))60 525 y(for)17 b(a)f(suitable)g(sequence)g(of)h(non-negativ)o(e)f(n)o(um)o(b)q (ers)f(\()p FF(c)1140 532 y FD(n)1163 525 y FQ(\))1182 532 y FD(n)p Fy(\025)p FH(1)1251 525 y FQ(.)21 b(If)16 b FF(nc)1385 532 y FD(n)1423 525 y FE(#)e FQ(0,)j(this)f(in)o(teraction)f(is)60 585 y(uniformly)i(con)o(v)o(ergen)o(t;)i(but)h(it)f(is)g(not)h(absolutely)f (summable)d(unless)1450 552 y Fx(P)1493 595 y FD(n)1525 585 y FF(nc)1575 592 y FD(n)1618 585 y FF(<)j FE(1)p FQ(.)30 b(Th)o(us,)60 645 y FF(c)81 652 y FD(n)118 645 y FQ(=)14 b FF(n)199 627 y Fy(\000)p FD(\013)268 645 y FQ(with)i(1)f FF(<)e(\013)i FE(\024)f FQ(2)i(pro)o(vides)g(the)g(desired)g(coun)o(terexample.)j(\(In)d(fact,)f(if) 1654 612 y Fx(P)1698 656 y FD(n)1730 645 y FF(c)1751 652 y FD(n)1788 645 y FQ(=)f FE(1)60 705 y FQ(|)20 b(for)h(example,)e FF(c)439 712 y FD(n)484 705 y FQ(=)i(1)p FF(=n)8 b FQ(log)r(\()p FF(n)14 b FQ(+)g(1\))21 b(|)g(the)f(in)o(teraction)f(do)q(es)j(not)f(ev)o(en) e(b)q(elong)i(to)g(the)60 766 y(largest)14 b(space)f(of)h(in)o(teractions)e (considered)h(in)g(the)h(usual)f(thermo)q(dynamic)e(formalism,)g(namely)60 826 y(the)16 b(space)g FE(B)309 808 y FH(0)345 826 y FQ(in)o(tro)q(duced)f (in)h(Section)g(2.4.4)h(b)q(elo)o(w.\))133 886 y(3\))k(In)o(teractions)f(can) h(also)h(b)q(e)e(classi\014ed)h(according)g(to)g(the)f(maxim)o(um)c(spatial) 21 b(distance)60 946 y(o)o(v)o(er)13 b(whic)o(h)g(they)g(extend:)20 b(the)13 b FP(r)n(ange)18 b FQ(of)c(\010)g(is)g(de\014ned)f(to)i(b)q(e)f(the) f(suprem)o(um)e(of)j(the)g(diameters)60 1006 y(of)20 b(the)f(sets)h FF(A)g FQ(with)f(\010)511 1013 y FD(A)560 1006 y FE(6\021)g FQ(0.)32 b(Th)o(us,)20 b(an)h(in)o(teraction)d(\010)i(is)g FP(of)g(\014nite)i(r)n(ange)f FF(R)f FQ(\()p FF(R)g(<)g FE(1)p FQ(\))g(if)60 1067 y(\010)95 1074 y FD(A)142 1067 y FE(\021)f FQ(0)g(whenev)o(er)f(diam)o(\()p FF(A)p FQ(\))g FF(>)g(R)p FQ(.)31 b(F)l(or)19 b(a)g(\014nite-range)g(in)o(teraction,)g(the)g(sum)f (\(2.15a\))i(is)f(a)60 1127 y(\014nite)e(sum,)f(so)i(\010)f(is)g (\(trivially\))f(a)h(uniformly)e(con)o(v)o(ergen)o(t)h(in)o(teraction.)24 b(If,)16 b(in)h(addition,)h(eac)o(h)60 1187 y(\010)95 1194 y FD(A)140 1187 y FQ(is)e(a)h(b)q(ounded)g(function,)e(then)i(\010)f(is)g (absolutely)g(summable.)133 1247 y(4\))i(Let)g(us)g(no)o(w)g(in)o(tro)q(duce) f(t)o(w)o(o)h(natural)g(pieces)e(of)i(terminology:)23 b(First,)17 b(w)o(e)g(shall)h(call)f(an)60 1307 y(in)o(teraction)i(\010)h FP(b)n(ounde)n(d)25 b FQ(if)19 b(eac)o(h)g(\010)753 1314 y FD(A)801 1307 y FQ(is)h(a)g(b)q(ounded)h(function.)31 b(Note)19 b(that)h(if)g(\010)g(is)f(b)q(ounded)60 1367 y(\(resp.)e(absolutely)h (summable\),)d(then)j(eac)o(h)g(Hamiltonian)e FF(H)1247 1349 y FH(\010)1243 1380 y(\003)p FD(;f)t(r)q(ee)1368 1367 y FQ(\(resp.)h FF(H)1549 1349 y FH(\010)1545 1380 y(\003)1577 1367 y FQ(\))h(is)g(a)g(b)q (ounded)60 1428 y(lo)q(cal)c(\(resp.)g(b)q(ounded)i(quasilo)q(cal\))e (function.)21 b(A)14 b(b)q(ounded)h(in)o(teraction,)f(ho)o(w)o(ev)o(er,)f(ma) o(y)g(fail)h(to)60 1488 y(b)q(e)i(absolutely)g(summable)e(if)i(the)g(b)q (ounds)h FE(k)p FQ(\010)947 1495 y FD(A)976 1488 y FE(k)1001 1495 y Fy(1)1054 1488 y FQ(do)g(not)g(deca)o(y)e(fast)i(enough.)133 1548 y(5\))24 b(Second:)34 b(if,)24 b(as)g(is)e(usual,)j(the)e(space)g(\012) 999 1555 y FH(0)1042 1548 y FQ(\(and)g(hence)g(\012\))g(comes)e(equipp)q(ed)i (with)g(a)60 1608 y(top)q(ology)l(,)16 b(then)e(w)o(e)h(call)e(an)j(in)o (teraction)d(\010)i FP(c)n(ontinuous)20 b FQ(if)14 b(eac)o(h)g(\010)1329 1615 y FD(A)1373 1608 y FQ(is)g(a)h(con)o(tin)o(uous)g(function.)60 1668 y(Note)k(that)h(if)f(\010)h(is)f(con)o(tin)o(uous)g(\(resp.)g(con)o(tin) o(uous)g(and)h(uniformly)e(con)o(v)o(ergen)o(t\),)g(then)i(eac)o(h)60 1729 y(Hamiltonian)c FF(H)386 1711 y FH(\010)382 1741 y(\003)p FD(;f)t(r)q(ee)507 1729 y FQ(\(resp.)i FF(H)689 1711 y FH(\010)685 1741 y(\003)716 1729 y FQ(\))g(is)g(a)g(con)o(tin)o(uous)g(function.)26 b(All)17 b(the)h(in)o(teractions)f(consid-)60 1789 y(ered)i(in)h(this)f(w)o (ork)h(\(and)g(an)g(o)o(v)o(erwhelming)d(ma)s(jorit)o(y)h(of)i(those)g (considered)f(elsewhere\))g(are)60 1849 y(con)o(tin)o(uous.)133 1909 y(6\))12 b(If)e(\012)266 1916 y FH(0)297 1909 y FQ(\(and)i(hence)e (\012\))h(is)g FP(c)n(omp)n(act)5 b FQ(,)11 b(then)g(ev)o(ery)f(con)o(tin)o (uous)h(in)o(teraction)f(is)h(automatically)60 1969 y(b)q(ounded.)33 b(This)20 b(is)g(one)g(reason)g(wh)o(y)g(systems)f(of)h(b)q(ounded)h(spins)f (are)g(easier)f(to)h(w)o(ork)g(with)60 2030 y(than)d(systems)e(of)h(un)o(b)q (ounded)h(spins.)133 2090 y(7\))i(Nev)o(ertheless,)e(as)j(w)o(e)e(discuss)h (later)g(\(Section)f(2.3.5\),)h(all)g(the)f(prop)q(erties)h(of)g(an)h(in)o (ter-)60 2150 y(action)d(m)o(ust)f(b)q(e)i(in)o(terpreted)d(mo)q(dulo)i(ph)o (ysical)f(equiv)m(alence.)23 b(In)17 b(this)g(regard,)h(the)f(apparen)o(t)60 2210 y(summabilit)n(y)i(prop)q(erties)i(ma)o(y)g(turn)g(out)h(to)g(b)q(e)g (misleading,)f(as)h(they)f(ma)o(y)g(c)o(hange)g(widely)60 2270 y(from)15 b(one)i(ph)o(ysically)d(equiv)m(alen)o(t)h(in)o(teraction)g(to)i (another)f([351)q(].)60 2415 y FB(2.3)70 b(Sp)r(eci\014cations)21 b(and)i(Gibbs)g(Measures)60 2489 y FH(15)p 60 2541 732 2 v 100 2595 a FA(15)135 2610 y Fz(References)18 b(for)d(this)h(section)g(are)g (Georgii)f([157)o(,)g(Chapters)i(1{4])e(and)g(Preston)i([299)o(,)f(Chapters)g (1,)g(2)f(and)60 2660 y(5].)951 2784 y FQ(25)p eop %%Page: 26 26 bop 133 91 a FQ(W)l(e)15 b(no)o(w)g(come)e(to)i(the)f(heart)h(of)g(the)f (theory)h(of)g(in\014nite-v)o(olume)c(lattice)j(systems,)f(whic)o(h)h(is)60 152 y(to)j(mak)o(e)e(precise)g(what)j(w)o(e)e(mean)g(b)o(y)g(an)h FP(in\014nite-volume)k(Gibbs)d(me)n(asur)n(e)i FQ(for)d(a)g(giv)o(en)f(in)o (ter-)60 212 y(action)f(\010.)21 b(W)l(e)14 b(cannot)h(simply)e(use)i(the)f (explicit)f(form)o(ula)g(\(2.1\),)i(b)q(ecause)g(the)f(in\014nite-v)o(olume) 60 272 y(Hamiltonian)j FF(H)23 b FQ(is)c(ill-de\014ned.)28 b(The)19 b(traditional)g(solution)h(is)e(to)i(de\014ne)e(an)i(in\014nite-v)o (olume)60 332 y(Gibbs)g(measure)e(to)h(b)q(e)h(an)o(y)f(measure)f(whic)o(h)h (is)g(a)h(limit)c(\(in)j(a)h(suitable)f(top)q(ology\))i(of)e(\014nite-)60 392 y(v)o(olume)d(Gibbs)i(measures)f(with)h(some)f(c)o(hosen)g(b)q(oundary)i (conditions.)27 b(The)18 b(disadv)m(an)o(tage)h(of)60 452 y(this)h (de\014nition)f(is)g(that)i(it)e(is)g(cum)o(b)q(ersome)e(to)j(c)o(hec)o(k:)27 b(giv)o(en)18 b(a)j(measure)d FF(\026)i FQ(on)g(the)g(in\014nite-)60 513 y(v)o(olume)14 b(con\014guration)j(space,)f(ho)o(w)g(do)h(w)o(e)e (determine)f(whether)i(there)f FP(exists)21 b FQ(some)15 b(sequence)60 573 y(of)i(\014nite-v)o(olume)c(Gibbs)k(measures)e(con)o(v)o(erging)h(to)h FF(\026)p FQ(?)22 b(W)l(e)16 b(w)o(ould)h(prefer,)e(therefore,)g(to)i(ha)o(v) o(e)60 633 y(a)h(more)f(direct)g(condition)h(on)g(the)g(in\014nite-v)o(olume) d(measure)h FF(\026)p FQ(.)27 b(Suc)o(h)17 b(a)i(condition)e(w)o(as)i (\014rst)60 693 y(prop)q(osed)i(b)o(y)d(Dobrushin)i([83)q(])f(and)g(Lanford)i (and)f(Ruelle)e([232]:)27 b(their)19 b(idea)g(is)g(to)h(de\014ne)f(an)60 753 y(in\014nite-v)o(olume)13 b(Gibbs)i(measure)f(to)i(b)q(e)g(one)g(whose)g FP(c)n(onditional)h(pr)n(ob)n(abilities)j FQ(for)c FP(\014nite)k FQ(sub-)60 814 y(systems)e(\003,)h(conditioned)f(on)i(the)f(con\014guration)h (outside)f(\003,)g(are)g(giv)o(en)f(b)o(y)h(the)f(Boltzmann-)60 874 y(Gibbs)f(form)o(ula)e(based)i(on)h(the)e(Hamiltonian)f FF(H)995 856 y FH(\010)991 886 y(\003)1023 874 y FQ(.)22 b(This)17 b(is)g(the)f(approac)o(h)i(w)o(e)e(shall)g(tak)o(e;)g(the)60 934 y(traditional)g(approac)o(h)h(can)g(then)f(b)q(e)g(justi\014ed)g FP(a)h(p)n(osteriori)j FQ(\(Prop)q(ositions)e(2.22)f(and)g(2.23\).)133 994 y(Let)h(us)h(note)f(that,)g(in)g(general,)f(w)o(e)h(m)o(ust)e(condition)i (on)h(the)e(con\014guration)i(in)f(the)g FP(entir)n(e)60 1054 y FQ(exterior)c(of)i(\003)f(|)h(that)f(is,)g(w)o(e)g(m)o(ust)f(sp)q(ecify)h (a)h(complete)d(\\external)i(condition".)21 b(Ho)o(w)o(ev)o(er,)13 b(in)60 1115 y(the)18 b(sp)q(ecial)h(case)f(of)h(a)g(nearest-neigh)o(b)q(or)g (in)o(teraction)f(\(resp.)g(an)h(in)o(teraction)f(of)g(\014nite)g(range)60 1175 y FF(R)p FQ(\),)24 b(it)e(su\016ces)g(to)g(sp)q(ecify)g(the)g(spins)h (imm)o(ediatel)o(y)c(adjacen)o(t)k(to)f(\003)g(\(resp.)g(the)g(spins)h(at)g (a)60 1235 y(distance)f FE(\024)i FF(R)g FQ(from)d(\003\))h(|)h(hence)e(the)i (term)d(\\b)q(oundary)25 b(condition".)40 b(W)l(e)22 b(shall)g(usually)60 1295 y(b)q(o)o(w)e(to)f(tradition)g(and)g(call)f(our)i(external)e (con\014gurations)i(\\b)q(oundary)h(conditions",)e(but)g(w)o(e)60 1355 y(emphasize)h(that)j(in)f(the)g(general)f(case)i(of)f(an)h (in\014nite-range)f(in)o(teraction)f(it)g(is)h(essen)o(tial)g(to)60 1416 y(sp)q(ecify)15 b(the)h(con\014guration)i(in)e(the)g(en)o(tire)f (exterior)g(region.)133 1476 y(Let)j(us)g(also)g(remind)e(the)h(reader)h(of)g (the)f(ph)o(ysical)g(role)g(pla)o(y)o(ed)f(b)o(y)i(b)q(oundary)g(conditions:) 60 1536 y(in)f(in\014nite)g(v)o(olume)e(the)i(Gibbs)h(measure)f(\(to)g(b)q(e) h(de\014ned)f(shortly\))h(ma)o(y)e(not)i(b)q(e)g(unique,)e(and)60 1596 y(the)j(b)q(oundary)h(conditions)f(serv)o(e)f(to)i(select)e(a)h (particular)g(Gibbs)h(measure)d(\(i.e.)h(a)h(particular)60 1656 y(\\phase"\).)j(All)15 b(this)h(will)g(b)q(e)g(describ)q(ed)g(in)g (greater)g(detail)f(in)h(what)h(follo)o(ws.)60 1786 y FM(2.3.1)55 b(Sp)r(eci\014cations)60 1879 y FQ(W)l(e)22 b(b)q(egin)g(b)o(y)f(formalizing) f(the)i(idea)g(of)g(\\conditioning)g(on)g(the)g(exterior)f(of)h(a)h(v)o (olume)c(\003",)60 1939 y(irresp)q(ectiv)o(e)g(of)i(an)o(y)g(particular)g (form)o(ula)f(for)h(these)g(conditional)g(probabilities.)35 b(The)21 b(p)q(oin)o(t)60 1999 y(is)h(that)h(for)g(a)g(giv)o(en)f(external)g (con\014guration)i FF(!)1016 2006 y FH(\003)1040 1997 y Fs(c)1058 1999 y FQ(,)g(w)o(e)e(wish)h(to)g(sp)q(ecify)f(the)g(\(conditional\))60 2059 y(probabilit)o(y)17 b(distribution)h(of)g(the)g(spins)h(inside)e(the)h (v)o(olume)e(\003:)25 b(that)18 b(is,)g(w)o(e)g(w)o(an)o(t)g(to)h(sp)q(ecify) 60 2119 y(Prob)164 2126 y FD(!)186 2132 y Fr(\003)207 2125 y Fs(c)226 2119 y FQ(\()p FF(d!)300 2126 y FH(\003)328 2119 y FQ(\).)i(Suc)o(h)15 b(an)g(ob)s(ject)g(is)g(called)g(a)g FP(pr)n(ob)n(ability)h(kernel)1302 2101 y FH(16)1341 2119 y FQ(.)21 b(In)15 b(general,)g(a)h(probabilit)o(y)60 2180 y(k)o(ernel)h FF(\031)j FQ(from)d(a)i(space)f(\(\012)p FF(;)8 b FE(F)d FQ(\))19 b(to)f(another)h(space)g(\(\012)1130 2161 y Fy(0)1142 2180 y FF(;)8 b FE(F)1205 2161 y Fy(0)1216 2180 y FQ(\))18 b(is)h(an)g(ob)s(ject)e FF(\031)r FQ(\()p FF(!)r(;)8 b(A)p FQ(\))18 b(with)g(t)o(w)o(o)60 2240 y(\\slots":)26 b(an)18 b(\\input")h(slot)f(that)g(accepts)g(an)h(input)e (con\014guration)i FF(!)g FE(2)e FQ(\012,)i(and)f(an)h(\\output")60 2300 y(slot)c(that)g(accepts)f(a)i(set)e FF(A)f FE(2)i(F)677 2282 y Fy(0)703 2300 y FQ(and)g(returns)g(its)f(probabilit)o(y)l(.)20 b(More)14 b(formally)l(,)f(a)i(probabilit)o(y)60 2360 y(k)o(ernel)g(from)g (\(\012)p FF(;)8 b FE(F)d FQ(\))16 b(to)g(\(\012)584 2342 y Fy(0)596 2360 y FF(;)8 b FE(F)659 2342 y Fy(0)670 2360 y FQ(\))17 b(is)f(a)g(map)g FF(\031)r FQ(:)f(\012)d FE(\002)f(F)1101 2342 y Fy(0)1126 2360 y FE(!)i FQ([0)p FF(;)8 b FQ(1])16 b(satisfying:)95 2462 y(\(a\))25 b(F)l(or)16 b(eac)o(h)g(\014xed)g FF(!)g FE(2)e FQ(\012,)i FF(\031)r FQ(\()p FF(!)r(;)g FE(\001)8 b FQ(\))16 b(is)g(a)h(probabilit)o(y)e(measure)g(on)i(\(\012)1474 2444 y Fy(0)1486 2462 y FF(;)8 b FE(F)1549 2444 y Fy(0)1560 2462 y FQ(\).)p 60 2508 732 2 v 100 2562 a FA(16)135 2577 y Fz(F)m(or)13 b(a)g(more)f(extensiv)o(e)j(in)o(tro)q(duction)e(to)g(probabilit)o(y)f(k)o (ernels)i(and)f(their)h(prop)q(erties,)h(see)f([25)o(,)f(Section)h(56])60 2627 y(or)g([272)o(,)f(Section)h(I)q(I)q(I{2].)951 2784 y FQ(26)p eop %%Page: 27 27 bop 93 91 a FQ(\(b\))24 b(F)l(or)16 b(eac)o(h)g(\014xed)g FF(A)d FE(2)h(F)635 73 y Fy(0)647 91 y FQ(,)i FF(\031)r FQ(\()8 b FE(\001)g FF(;)g(A)p FQ(\))15 b(is)h(a)h FE(F)5 b FQ(-measurable)15 b(function)h(on)h(\012.)60 193 y(W)l(e)i(shall)h(write)e(suc)o(h)i(a)g (probabilit)o(y)e(k)o(ernel)g(equiv)m(alen)o(tly)f(as)j FF(\031)r FQ(\()p FF(!)r(;)8 b(A)p FQ(\))19 b FE(\021)g FF(\031)r FQ(\()p FF(A)p FE(j)p FF(!)r FQ(\))f FE(\021)h FF(\031)1777 200 y FD(!)1802 193 y FQ(\()p FF(A)p FQ(\).)60 253 y(The)h(\014rst)g(notation)h(emphasizes)d (that)i FF(\031)i FQ(is)d(a)i(kind)e(of)h(\\transition)h(probabilit)o(y")e (\(as)i(in)e(the)60 313 y(theory)f(of)h(Mark)o(o)o(v)f(pro)q(cesses\);)i(the) e(second)h(notation)g(emphasizes)e(that)i FF(\031)h FQ(will)d(later)h(b)q(e)h (in-)60 374 y(terpreted)e(as)i(a)g(conditional)f(probabilit)o(y;)g(and)h(the) f(third)g(notation)h(emphasizes)d(that)j FF(!)i FQ(is)d(a)60 434 y(parameter)d(\(\\b)q(oundary)j(condition"\))e(indexing)g(the)g (probabilit)o(y)f(measure)g(on)i(\012)1636 416 y Fy(0)1648 434 y FQ(.)133 494 y(Th)o(us,)23 b(in)d(our)i(case)f(w)o(e)g(need)g(to)h(sp)q (ecify)e(a)i(probabilit)o(y)e(k)o(ernel)g FF(\031)1442 501 y FH(\003)1489 494 y FQ(from)g(\(\012)1663 501 y FH(\003)1687 492 y Fs(c)1706 494 y FF(;)8 b FE(F)1764 501 y FH(\003)1788 492 y Fs(c)1806 494 y FQ(\))22 b(to)60 554 y(\(\012)114 561 y FH(\003)141 554 y FF(;)8 b FE(F)199 561 y FH(\003)225 554 y FQ(\).)35 b(F)l(or)21 b(tec)o(hnical)e(reasons,)k(ho)o(w)o(ev)o(er,)d(it)g (is)h(con)o(v)o(enien)o(t)e(to)i(de\014ne)f FF(\031)1581 561 y FH(\003)1628 554 y FQ(instead)h(as)h(a)60 614 y(probabilit)o(y)c(k)o(ernel) g(from)g(the)h FP(ful)r(l)26 b FQ(space)20 b(\(\012)p FF(;)8 b FE(F)d FQ(\))19 b(to)g(itself:)27 b(w)o(e)18 b(then)i(imp)q(ose)e (explicitly)e(the)60 675 y(condition)k(that)g FF(\031)r FQ(\()p FF(!)r(;)c FE(\001)8 b FQ(\))19 b(dep)q(end)h(on)h FF(!)h FQ(only)d(through)i (its)f(comp)q(onen)o(ts)f FF(!)1527 682 y FH(\003)1551 673 y Fs(c)1589 675 y FQ(\(i.e.)f(it)i(is)f FE(F)1831 682 y FH(\003)1855 673 y Fs(c)1874 675 y FQ(-)60 735 y(measurable\),)e(and)i(that)f(it)g(repro)q (duce)g(the)g(\\b)q(oundary)i(condition")f FF(!)1436 742 y FH(\003)1460 733 y Fs(c)1497 735 y FQ(when)f(the)g(question)60 795 y(fed)c(in)o(to)h(its)f(second)h(slot)f(concerns)h(only)f(spins)h (outside)g(\003)f(\(i.e.)f(when)i FF(A)e FE(2)h(F)1541 802 y FH(\003)1565 793 y Fs(c)1583 795 y FQ(\).)21 b(W)l(e)14 b(are)h(th)o(us)60 855 y(led)h(to)g(the)g(follo)o(wing)g(de\014nition)689 837 y FH(17)726 855 y FQ(:)60 969 y FM(De\014nition)i(2.5)24 b FP(A)19 b FQ(sp)q(eci\014cation)735 951 y FH(18)791 969 y FP(is)g(a)f(family) h FQ(\005)d(=)h(\()p FF(\031)1193 976 y FH(\003)1219 969 y FQ(\))1238 976 y FH(\003)p Fy(2S)1331 969 y FP(of)h(pr)n(ob)n(ability)h (kernels)h(fr)n(om)60 1029 y FQ(\(\012)p FF(;)8 b FE(F)d FQ(\))17 b FP(to)h(itself,)g(satisfying)g(the)g(fol)r(lowing)h(c)n(onditions:)93 1131 y(\(a\))24 b(F)l(or)17 b(e)n(ach)g FF(A)d FE(2)g(F)5 b FP(,)17 b(the)h(function)h FF(\031)854 1138 y FH(\003)880 1131 y FQ(\()8 b FE(\001)g FF(;)g(A)p FQ(\))17 b FP(is)h FE(F)1113 1138 y FH(\003)1137 1129 y Fs(c)1155 1131 y FP(-me)n(asur)n(able.)95 1233 y(\(b\))25 b FF(\031)210 1240 y FH(\003)254 1233 y FP(is)17 b FE(F)342 1240 y FH(\003)366 1231 y Fs(c)384 1233 y FP(-pr)n(op)n(er,)f (i.e.)i(for)f(e)n(ach)g FF(B)g FE(2)d(F)976 1240 y FH(\003)1000 1231 y Fs(c)1018 1233 y FP(,)k FF(\031)1079 1240 y FH(\003)1105 1233 y FQ(\()p FF(!)r(;)8 b(B)s FQ(\))13 b(=)h FF(\037)1333 1240 y FD(B)1363 1233 y FQ(\()p FF(!)r FQ(\))p FP(.)95 1335 y(\(c\))25 b(If)17 b FQ(\003)d FE(\032)f FQ(\003)367 1317 y Fy(0)379 1335 y FP(,)k(then)i FF(\031)548 1342 y FH(\003)572 1333 y Ft(0)585 1335 y FF(\031)613 1342 y FH(\003)653 1335 y FQ(=)14 b FF(\031)733 1342 y FH(\003)757 1333 y Ft(0)770 1335 y FP(.)785 1317 y FH(19)133 1449 y FQ(Ph)o(ysically)l(,)i(the)h(idea)h (is)f(that)h FF(\031)752 1456 y FH(\003)778 1449 y FQ(\()p FF(!)r(;)e FE(\001)8 b FQ(\))18 b(is)g(the)f(equilibrium)d(probabilit)o(y)j (distribution)g(for)60 1509 y(v)o(olume)g(\003)i(sub)s(ject)g(to)g(the)g(b)q (oundary)i(condition)e FF(!)i FQ(outside)f(\003.)30 b(Condition)19 b(\(a\))h(states)g(that)60 1569 y(this)h(measure)f(dep)q(ends,)j(in)e(fact,)h (only)f(on)g(the)g(b)q(eha)o(vior)h(of)f FF(!)j FP(outside)h FQ(\003.)36 b(Condition)22 b(\(b\))60 1629 y(states)d(that)g(for)g(observ)m (ations)h FP(outside)i FQ(\003,)d(this)g(measure)e(equals)h(the)h(delta)f (measure)f FF(\016)1770 1636 y FD(!)1795 1629 y FQ(,)i(i.e.)p 60 1673 732 2 v 100 1727 a FA(17)135 1742 y Fz(See)c([299)n(,)f(Section)g(1]) f(for)h(a)f(more)g(leisurely)h(discussion)g(of)g(these)h(p)q(oin)o(ts.)100 1800 y FA(18)135 1815 y Fz(In)i(some)f(mathematical-ph)o(ysics)f(literature)j (\(e.g.)f([123)n(]\))g(the)h(term)f(\\lo)q(cal)f(sp)q(eci\014cation")i(is)f (used.)29 b(W)m(e)60 1865 y(emphasize)19 b(that)h(this)f(adjectiv)o(e)h(\\lo) q(cal")e(is)h(sup)q(er\015uous;)24 b(the)c(concepts)h(discussed)g(here)g(and) e(in)g([123)o(])g(are)60 1915 y(iden)o(tical.)g(In)c(particular,)f(the)h (reader)h(should)f Fw(not)j Fz(confuse)e(this)e(\(redundan)o(t\))i(use)f(of)f (the)i(w)o(ord)e(\\lo)q(cal")f(with)60 1964 y(our)h(concept)h(of)e(\\quasilo) q(cal)g(sp)q(eci\014cation")h(to)g(b)q(e)g(in)o(tro)q(duced)h(in)e(Section)i (2.3.3.)100 2022 y FA(19)135 2037 y Fz(The)f(pro)q(duct)h(of)e(t)o(w)o(o)h (probabilit)o(y)e(k)o(ernels)j(is)e(a)h(probabilit)o(y)e(k)o(ernel:)612 2148 y(\()p Fv(\031)652 2154 y FA(1)670 2148 y Fv(\031)694 2154 y FA(2)712 2148 y Fz(\)\()p Fv(!)q(;)7 b(A)p Fz(\))24 b Fu(\021)916 2091 y Fx(Z)964 2148 y Fv(\031)988 2154 y FA(1)1007 2148 y Fz(\()p Fv(!)q(;)7 b(d!)1118 2131 y Fo(0)1129 2148 y Fz(\))g Fv(\031)1176 2154 y FA(2)1195 2148 y Fz(\()p Fv(!)1238 2131 y Fo(0)1250 2148 y Fv(;)g(A)p Fz(\))k Fv(:)60 2258 y Fz(F)m(or)i(future) i(reference)h(w)o(e)e(also)g(de\014ne)h(t)o(w)o(o)e(w)o(a)o(ys)h(of)f(m)o (ultiplying)d(a)k(measure)g(b)o(y)f(a)h(probabilit)o(y)e(k)o(ernel:)606 2368 y(\()p Fv(\026\031)q Fz(\)\()p Fv(A)p Fz(\))43 b Fu(\021)868 2312 y Fx(Z)916 2368 y Fv(\026)p Fz(\()p Fv(d!)q Fz(\))7 b Fv(\031)q Fz(\()p Fv(!)q(;)g(A)p Fz(\))553 2477 y(\()p Fv(\026)j Fu(\002)f Fv(\031)q Fz(\)\()p Fv(B)r Fz(\))43 b Fu(\021)868 2421 y Fx(Z)916 2477 y Fv(\026)p Fz(\()p Fv(d!)q Fz(\))7 b Fv(\031)q Fz(\()p Fv(!)q(;)g(d!)1165 2460 y Fo(0)1177 2477 y Fz(\))p Fv(\037)1219 2483 y Fp(B)1247 2477 y Fz(\()p Fv(!)k Fu(\002)f Fv(!)1369 2460 y Fo(0)1381 2477 y Fz(\))60 2590 y(where)j Fv(A)f Fu(2)f(F)16 b Fz(and)11 b Fv(B)j Fu(2)e(F)d(\002)c(F)579 2575 y Fo(0)591 2590 y Fz(.)17 b(Th)o(us,)12 b Fv(\026)5 b Fu(\002)g Fv(\031)14 b Fz(is)d(a)h(probabilit)o(y)e(measure)i(on)g(the)g(pro) q(duct)h(space)g(\(\012)5 b Fu(\002)g Fz(\012)1788 2575 y Fo(0)1800 2590 y Fv(;)i Fu(F)i(\002)60 2639 y(F)94 2624 y Fo(0)106 2639 y Fz(\),)k(while)h Fv(\026\031)h Fz(is)e(its)h(marginal)d(on)j(the)g(second)h (space)g(\(\012)1012 2624 y Fo(0)1024 2639 y Fv(;)7 b Fu(F)1077 2624 y Fo(0)1088 2639 y Fz(\).)951 2784 y FQ(27)p eop %%Page: 28 28 bop 60 91 a FQ(it)19 b(repro)q(duces)g(the)f(b)q(oundary)j(condition.)29 b(Condition)19 b(\(c\))g(is)g(a)g(compatibilit)o(y)d(condition)j(for)60 152 y(pairs)14 b(of)g(v)o(olumes)d(\003)j FE(\032)f FQ(\003)548 133 y Fy(0)560 152 y FQ(:)20 b(it)13 b(states)h(that)f(if)g(a)h(v)o(olume)e (\003)1158 133 y Fy(0)1183 152 y FQ(is)h(in)g(equilibrium)d(with)j(its)h (exterior,)60 212 y(then)i(all)g(subsets)h(of)f(\003)497 194 y Fy(0)525 212 y FQ(are)g(in)g(equilibrium)d(with)j FP(their)22 b FQ(exteriors.)60 317 y FM(De\014nition)c(2.6)24 b FP(A)19 b(pr)n(ob)n(ability)g(me)n(asur)n(e)f FF(\026)i FP(on)f FQ(\012)h FP(is)f(said)g(to)g(b)n(e)h FQ(consisten)o(t)e(with)g(the)g(sp)q(ec-)60 377 y(i\014cation)g(\005)d(=)h(\()p FF(\031)402 384 y FH(\003)428 377 y FQ(\))447 384 y FH(\003)p Fy(2S)539 377 y FP(if)j(its)f(c)n(onditional) h(pr)n(ob)n(abilities)g(for)f(\014nite)h(subsystems)g(ar)n(e)f(given)i(by)60 438 y(the)e FQ(\()p FF(\031)188 445 y FH(\003)214 438 y FQ(\))233 445 y FH(\003)p Fy(2S)307 438 y FP(:)k(that)c(is,)340 540 y(F)l(or)f(e)n(ach) g FQ(\003)d FE(2)g(S)21 b FP(and)d FF(A)c FE(2)g(F)5 b FF(;)35 b(E)1005 547 y FD(\026)1028 540 y FQ(\()p FF(\037)1078 547 y FD(A)1106 540 y FE(jF)1156 547 y FH(\003)1180 538 y Fs(c)1198 540 y FQ(\))14 b(=)g FF(\031)1311 547 y FH(\003)1337 540 y FQ(\()8 b FE(\001)g FF(;)g(A)p FQ(\))22 b FF(\026)p FP(-a.e.)156 b FQ(\(2)p FF(:)p FQ(18\))60 642 y FP(We)18 b(denote)g(by)g FE(G)s FQ(\(\005\))e FP(the)i(set)g(of)f(al)r(l)i(me)n(asur)n(es)e(c)n (onsistent)h(with)g FQ(\005)p FP(.)133 748 y FQ(The)f(follo)o(wing)f(prop)q (osition)h(giv)o(es)f(t)o(w)o(o)g(apparen)o(tly)g(w)o(eak)o(er,)f(but)i(in)f (fact)g(equiv)m(alen)o(t,)e(for-)60 808 y(m)o(ulations)h(of)h(the)g (condition)g(\(2.18\):)60 913 y FM(Prop)r(osition)i(2.7)24 b FP(L)n(et)15 b FQ(\005)e(=)h(\()p FF(\031)690 920 y FH(\003)716 913 y FQ(\))735 920 y FH(\003)p Fy(2S)825 913 y FP(b)n(e)h(a)h(sp)n(e)n (ci\014c)n(ation,)g(let)g FF(\026)g FP(b)n(e)g(a)f(pr)n(ob)n(ability)g(me)n (asur)n(e)g(on)60 974 y FQ(\012)p FP(,)j(and)f(let)i FQ(\003)13 b FE(2)h(S)t FP(.)23 b(Then)18 b(the)g(fol)r(lowing)h(ar)n(e)e(e)n (quivalent:)93 1069 y(\(a\))24 b(F)l(or)17 b(e)n(ach)g FF(A)d FE(2)g(F)5 b FP(,)31 b FF(E)603 1076 y FD(\026)626 1069 y FQ(\()p FF(\037)676 1076 y FD(A)704 1069 y FE(jF)754 1076 y FH(\003)778 1067 y Fs(c)797 1069 y FQ(\))13 b(=)h FF(\031)909 1076 y FH(\003)935 1069 y FQ(\()8 b FE(\001)g FF(;)g(A)p FQ(\))31 b FF(\026)p FP(-a.e.)95 1168 y(\(b\))25 b(Ther)n(e)17 b(exists)h(a)g(me)n(asur)n(e)e FF(\027)710 1175 y FH(\003)754 1168 y FP(such)i(that)g FF(\026)c FQ(=)g FF(\027)1084 1175 y FH(\003)1110 1168 y FF(\031)1138 1175 y FH(\003)1165 1168 y FP(.)95 1268 y(\(c\))25 b FF(\026)14 b FQ(=)g FF(\026\031)334 1275 y FH(\003)360 1268 y FP(.)60 1373 y FQ(Ph)o(ysically)l(,)j(\(b\))j(states)f(that)g FF(\026)h FQ(is)e(the)h(equilibrium)d(probabilit)o(y)i(distribution)g(for)h(v)o(olume)e (\003)60 1433 y(with)k(some)g(\(p)q(ossibly)h(sto)q(c)o(hastic\))g(b)q (oundary)g(condition)g FF(\027)1234 1440 y FH(\003)1260 1433 y FQ(,)h(while)e(\(c\))g(states)h(that)g FF(\026)g FQ(can)60 1494 y(itself)15 b(pla)o(y)h(the)g(role)g(of)g FF(\027)542 1501 y FH(\003)569 1494 y FQ(.)133 1599 y(Let)g(us)f(note)h(that)f FE(G)s FQ(\(\005\),)f(the)h(set)g(of)h(all)f(measures)f(consisten)o(t)h(with) g(\005,)f(is)i(a)f FP(c)n(onvex)23 b FQ(set:)e(if)60 1659 y FF(\026)89 1666 y FH(1)109 1659 y FF(;)8 b(:)g(:)g(:)f(;)h(\026)247 1666 y FD(n)285 1659 y FQ(b)q(elong)14 b(to)g FE(G)s FQ(\(\005\),)f(then)h (so)g(do)q(es)g(an)o(y)g(con)o(v)o(ex)e(com)o(bination)h(of)h(them.)k(The)c (ph)o(ysical)60 1720 y(in)o(terpretation)k(of)h(suc)o(h)g(con)o(v)o(ex)e(com) o(binations,)h(and)h(of)h(the)e(extremal)f(p)q(oin)o(ts)i(of)g FE(G)s FQ(\(\005\),)f(will)60 1780 y(b)q(e)e(discussed)h(in)e(Section)h (2.3.6.)133 1840 y(W)l(e)e(also)g(mak)o(e)e(the)i(\(trivial\))e(remark)g (that)j(if)e(the)g(lattice)g FE(L)h FQ(w)o(ere)f FP(\014nite)t FQ(,)i(then)f(there)f(w)o(ould)60 1900 y(b)q(e)18 b(a)g FP(unique)24 b FQ(measure)16 b(consisten)o(t)i(with)g(\005,)f(namely)f(the)i(measure)f FF(\031)1410 1907 y Fy(L)1436 1900 y FQ(\()p FF(!)r(;)f FE(\001)8 b FQ(\))18 b(whic)o(h)f(m)o(ust)g(b)q(e)60 1960 y(indep)q(enden)o(t)d(of)h FF(!)r FQ(.)21 b(This)15 b(is)f(one)h(asp)q(ect)h(of)f(the)f(fact)h(that)g (phase)h(transitions)f(cannot)g(o)q(ccur)g(in)60 2021 y(\014nite)h(systems.) 60 2149 y FM(2.3.2)55 b(Gibbsian)19 b(Sp)r(eci\014cations)e(and)i(Gibbs)g (Measures)60 2242 y FQ(An)g(imp)q(ortan)o(t)g(example)f(of)i(a)g(sp)q (eci\014cation)f(is)g(the)h FP(Gibbsian)h(sp)n(e)n(ci\014c)n(ation)j FQ(\005)1617 2224 y FH(\010)1664 2242 y FQ(=)19 b(\()p FF(\031)1770 2224 y FH(\010)1768 2254 y(\003)1797 2242 y FQ(\))1816 2249 y FH(\003)p Fy(2S)60 2302 y FQ(corresp)q(onding)i(to)e(a)h(giv)o(en)f(in)o (teraction)f(\010.)32 b(More)19 b(precisely)l(,)f(let)h(\010)g(b)q(e)h(a)g FP(c)n(onver)n(gent)26 b FQ(in)o(ter-)60 2362 y(action,)c(so)g(that)f(w)o(e)g (can)g(de\014ne)g(the)g(Hamiltonians)f FF(H)1156 2344 y FH(\010)1152 2374 y(\003)1205 2362 y FQ(with)h(general)g(external)f(b)q(oundary)60 2422 y(conditions.)h(Let)15 b FF(\026)427 2404 y FH(0)461 2422 y FQ(=)527 2389 y Fx(Q)513 2460 y FD(x)p Fy(2L)589 2422 y FF(\026)618 2404 y FH(0)618 2435 y FD(x)655 2422 y FQ(b)q(e)h(a)f(probabilit)o(y)g (measure,)e(called)h(the)h FP(a)i(priori)i FQ(measure.)g(W)l(e)60 2505 y(then)d(de\014ne)g(the)g(conditional)g(partition)g(function)531 2620 y FF(Z)568 2599 y FH(\010)564 2632 y(\003)596 2620 y FQ(\()p FF(!)645 2627 y FH(\003)669 2618 y Fs(c)688 2620 y FQ(\))27 b(=)800 2561 y Fx(Z)850 2620 y FQ(exp)o([)p FE(\000)p FF(H)1021 2599 y FH(\010)1017 2632 y(\003)1048 2620 y FQ(\()p FF(!)r FQ(\)])1156 2578 y Fx(Y)1148 2670 y FD(x)p Fy(2)p FH(\003)1225 2620 y FF(d\026)1279 2599 y FH(0)1279 2632 y FD(x)1301 2620 y FQ(\()p FF(!)1350 2627 y FD(x)1373 2620 y FQ(\))13 b FF(:)346 b FQ(\(2)p FF(:)p FQ(19\))951 2784 y(28)p eop %%Page: 29 29 bop 60 91 a FQ([Note)16 b(that)h(the)f(Hamiltonian)f FF(H)707 73 y FH(\010)703 104 y(\003)735 91 y FQ(\()p FF(!)r FQ(\))i(dep)q(ends)g(on)g FP(b)n(oth)j FQ(the)c(spins)h FF(!)1422 98 y FH(\003)1466 91 y FQ(inside)f(\003)g FP(and)22 b FQ(on)17 b(the)60 152 y(\\b)q(oundary)e (conditions")g FF(!)587 159 y FH(\003)611 150 y Fs(c)630 152 y FQ(.)20 b(After)13 b(in)o(tegrating)g(out)i(the)e(spins)h FF(!)1350 159 y FH(\003)1377 152 y FQ(,)g(w)o(e)g(obtain)g(a)g(function)g(of) 60 212 y FF(!)90 219 y FH(\003)114 210 y Fs(c)133 212 y FQ(.])21 b(Since)16 b FF(H)354 194 y FH(\010)350 224 y(\003)398 212 y FQ(is)g(ev)o(erywhere)f(\014nite,)g(it)h(follo)o(ws)g(that)h FF(Z)1191 194 y FH(\010)1187 224 y(\003)1219 212 y FQ(\()p FF(!)1268 219 y FH(\003)1292 210 y Fs(c)1311 212 y FQ(\))d FF(>)g FQ(0)j(for)f(all)g FF(!)r FQ(.)22 b(If)16 b(moreo)o(v)o(er)60 272 y FF(Z)97 254 y FH(\010)93 284 y(\003)125 272 y FQ(\()p FF(!)174 279 y FH(\003)198 270 y Fs(c)216 272 y FQ(\))23 b FF(<)f FQ(+)p FE(1)e FQ(for)i(all)e(\003)i FE(2)h(S)i FQ(and)d(all)e FF(!)k FE(2)f FQ(\012,)f(w)o(e)f(sa)o(y)g(that)g(the)g(in)o(teraction)f(\010) i(is)f FF(\026)1853 254 y FH(0)1873 272 y FP(-)60 332 y(admissible)t FQ(.)32 b(Note)19 b(in)g(particular)g(that)h(if)f(eac)o(h)g FF(H)1049 314 y FH(\010)1045 344 y(\003)1097 332 y FQ(is)g(b)q(ounded)i(b)q (elo)o(w)e(|)h(whic)o(h)e(certainly)60 392 y(o)q(ccurs)23 b(if)f(\010)g(is)h (absolutely)f(summable,)f(since)g(this)i(mak)o(es)e(eac)o(h)h FF(H)1411 374 y FH(\010)1407 405 y(\003)1461 392 y FQ(b)q(ounded)h(|)f(then)h (\010)60 452 y(is)c(automatically)f FF(\026)452 434 y FH(0)472 452 y FQ(-admissible.)30 b(Also,)20 b(if)f(the)g(single-spin)h(space)g(\012) 1429 459 y FH(0)1468 452 y FQ(is)g(\014nite,)f(then)h(ev)o(ery)60 513 y(con)o(v)o(ergen)o(t)h(in)o(teraction)g(is)h(automatically)e FF(\026)958 495 y FH(0)979 513 y FQ(-admissible)g([b)q(ecause)i(the)g(in)o (tegral)f(\(2.19\))i(is)60 573 y(then)16 b(a)h(\014nite)e(sum)h(of)g (\014nite)g(terms].)60 687 y FM(De\014nition)i(2.8)24 b FP(L)n(et)19 b FF(\026)533 669 y FH(0)571 687 y FQ(=)641 654 y Fx(Q)626 725 y FD(x)p Fy(2L)702 687 y FF(\026)731 669 y FH(0)731 699 y FD(x)773 687 y FP(b)n(e)h(a)g(pr)n(ob)n(ability)f(me)n(asur)n(e,)g(and)h (let)g FQ(\010)g FP(b)n(e)g(a)g(c)n(onver)n(gent,)60 776 y FF(\026)89 758 y FH(0)109 776 y FP(-admissible)f(inter)n(action.)k(Then)18 b(the)g(pr)n(ob)n(ability)e(me)n(asur)n(e)h FF(\031)1289 758 y FH(\010)1287 788 y(\003)1316 776 y FQ(\()p FF(!)r(;)f FE(\001)8 b FQ(\))18 b FP(on)g FE(F)k FP(de\014ne)n(d)c(by)351 901 y FF(\031)381 881 y FH(\010)379 913 y(\003)408 901 y FQ(\()p FF(!)r(;)8 b(A)p FQ(\))28 b(=)f FF(Z)667 881 y FH(\010)663 913 y(\003)695 901 y FQ(\()p FF(!)744 908 y FH(\003)768 899 y Fs(c)787 901 y FQ(\))806 881 y Fy(\000)p FH(1)861 843 y Fx(Z)911 901 y FF(\037)942 908 y FD(A)970 901 y FQ(\()p FF(!)r FQ(\))17 b(exp)o([)p FE(\000)p FF(H)1228 881 y FH(\010)1224 913 y(\003)1255 901 y FQ(\()p FF(!)r FQ(\)])1363 860 y Fx(Y)1356 951 y FD(x)p Fy(2)p FH(\003)1432 901 y FF(d\026)1486 881 y FH(0)1486 913 y FD(x)1508 901 y FQ(\()p FF(!)1557 908 y FD(x)1580 901 y FQ(\))166 b(\(2)p FF(:)p FQ(20\))60 1046 y FP(is)14 b(c)n(al)r(le)n(d)h(the)f FQ(Gibbs)f(distribution)f(in)g(v)o(olume)e(\003)i(with)g(b)q(oundary)i (condition)e FF(!)1543 1053 y FH(\003)1567 1044 y Fs(c)1600 1046 y FP(c)n(orr)n(esp)n(onding)60 1106 y(to)18 b(the)f(inter)n(action)i FQ(\010)e FP(and)h(the)g(a)f(priori)g(me)n(asur)n(e)f FF(\026)1073 1088 y FH(0)1093 1106 y FP(.)60 1221 y FQ(It)h(is)g(straigh)o(tforw)o(ard)h (to)g(v)o(erify)e(that)h(the)g(family)f(\005)1085 1203 y FH(\010)1127 1221 y FQ(=)g(\()p FF(\031)1230 1203 y FH(\010)1228 1233 y(\003)1257 1221 y FQ(\))1276 1228 y FH(\003)p Fy(2S)1367 1221 y FQ(is)h(indeed)g(a)h(sp) q(eci\014cation;)60 1281 y(it)h(is)f(called)g(the)h FP(Gibbsian)i(sp)n(e)n (ci\014c)n(ation)i FQ(for)c(\010)h(\(and)f FF(\026)1151 1263 y FH(0)1171 1281 y FQ(\).)30 b(A)19 b(measure)e(consisten)o(t)i(with)g(\005) 1863 1263 y FH(\010)60 1341 y FQ(is)e(called)e(a)j FP(Gibbs)g(me)n(asur)n(e)i FQ(for)d(\010)g(\(and)g FF(\026)887 1323 y FH(0)907 1341 y FQ(\).)23 b(By)16 b(Prop)q(osition)i(2.7,)f(a)g(measure)f FF(\026)h FQ(is)g(a)g(Gibbs)60 1401 y(measure)e(for)h(\005)361 1383 y FH(\010)405 1401 y FQ(if)g(and)g(only)g(if)g FF(\026\031)755 1383 y FH(\010)753 1413 y(\003)796 1401 y FQ(=)e FF(\026)j FQ(for)f(all)g(\003,)g(i.e.)101 1467 y Fx(Z)150 1526 y FF(d\026)p FQ(\()p FF(\034)6 b FQ(\))i FF(Z)314 1505 y FH(\010)310 1538 y(\003)343 1526 y FQ(\()p FF(\034)383 1533 y FH(\003)407 1524 y Fs(c)425 1526 y FQ(\))444 1505 y Fy(\000)p FH(1)500 1467 y Fx(Z)550 1526 y FF(\037)581 1533 y FD(A)609 1526 y FQ(\()p FF(!)658 1533 y FH(\003)696 1526 y FE(\002)i FF(\034)766 1533 y FH(\003)790 1524 y Fs(c)809 1526 y FQ(\))17 b(exp)o([)p FE(\000)p FF(H)1016 1505 y FH(\010)1012 1538 y(\003)1043 1526 y FQ(\()p FF(!)1092 1533 y FH(\003)1130 1526 y FE(\002)11 b FF(\034)1201 1533 y FH(\003)1225 1524 y Fs(c)1244 1526 y FQ(\)])1300 1485 y Fx(Y)1293 1576 y FD(x)p Fy(2)p FH(\003)1369 1526 y FF(d\026)1423 1505 y FH(0)1423 1538 y FD(x)1446 1526 y FQ(\()p FF(!)1495 1533 y FD(x)1517 1526 y FQ(\))28 b(=)f FF(\026)p FQ(\()p FF(A)p FQ(\))32 b(\(2)p FF(:)p FQ(21\))60 1674 y(for)20 b(all)f FF(A)h FE(2)g(F)k FQ(and)d(all)e(\003)h FE(2)g(S)t FQ(.)32 b(The)19 b(equation)h(\(2.21\))h(is)e(called)g(the)g(Dobrushin-Lanford-)60 1734 y(Ruelle)g(\(DLR\))j(equation.)34 b(A)21 b(sligh)o(tly)e(simpler)g (equation)h(is)h(obtained)g(b)o(y)f(restricting)g FF(A)h FQ(to)60 1794 y FE(F)96 1801 y FH(\003)122 1794 y FQ(:)213 1890 y FF(d\026)267 1897 y FH(\003)p 213 1912 82 2 v 213 1958 a FF(d\026)267 1941 y FH(0)267 1970 y(\003)299 1924 y FQ(\()p FF(!)348 1931 y FH(\003)375 1924 y FQ(\))27 b(=)487 1866 y Fx(Z)537 1924 y FF(d\026)p FQ(\()p FF(\034)6 b FQ(\))i FF(Z)701 1904 y FH(\010)697 1936 y(\003)729 1924 y FQ(\()p FF(\034)769 1931 y FH(\003)793 1922 y Fs(c)812 1924 y FQ(\))831 1904 y Fy(\000)p FH(1)894 1924 y FQ(exp[)p FE(\000)p FF(H)1066 1904 y FH(\010)1062 1936 y(\003)1093 1924 y FQ(\()p FF(!)1142 1931 y FH(\003)1180 1924 y FE(\002)j FF(\034)1251 1931 y FH(\003)1275 1922 y Fs(c)1294 1924 y FQ(\)])145 b FF(\026)1501 1904 y FH(0)1501 1936 y(\003)1528 1924 y FQ(-a.e.)i(\(2)p FF(:)p FQ(22\))60 2062 y(In)21 b(general)g(\(2.22\))h(is)f(w)o(eak)o(er)f(than)h (\(2.21\);)j(the)d(former)f(is)h(a)h(necessary)e(but)i(not)f(su\016cien)o(t) 60 2122 y(condition)11 b(for)h FF(\026)g FQ(to)g(b)q(e)g(a)g(Gibbs)g(measure) e(for)i(\005)962 2104 y FH(\010)989 2122 y FQ(.)20 b(Ho)o(w)o(ev)o(er,)10 b(in)h(nearly)h(all)f(practical)g(situations)60 2182 y(the)16 b(t)o(w)o(o)g(conditions)g(are)h(equiv)m(alen)o(t:)i(see)d(Remark)f(3)h(at)h (the)f(end)g(of)h(Section)e(2.3.3)i(b)q(elo)o(w.)133 2292 y(A)o(t)12 b(this)h(p)q(oin)o(t)g(the)g(reader)f(ma)o(y)g(b)q(e)h(w)o(ondering:)19 b(Wh)o(y)13 b(ha)o(v)o(e)f(w)o(e)g(b)q(othered)i(to)f(in)o(tro)q(duce)f(the) 60 2352 y(v)o(ery)g(general)g(\(and)i(abstract\))f(concept)g(of)g(a)g(sp)q (eci\014cation,)g(when)g(virtually)f(all)g(of)h(the)g(concrete)60 2413 y(mo)q(dels)e(studied)i(in)f(statistical)g(mec)o(hanics)e(corresp)q(ond) j(to)g FP(Gibbsian)k FQ(sp)q(eci\014cations?)k(W)l(e)12 b(ha)o(v)o(e)60 2473 y(t)o(w)o(o)i(reasons:)20 b(Firstly)l(,)13 b(non-Gibbsian)i(sp)q (eci\014cations)e(m)o(ust)g(b)q(e)g(emplo)o(y)o(ed)e(in)j(some)e(in)o (teresting)60 2533 y(statistical-mec)o(hanical)18 b(problems,)i(notably)h (those)g(in)o(v)o(olving)e(hard-core)i(exclusions)f(\(whic)o(h)60 2593 y(w)o(e)15 b(do)i(not)f(consider)g(in)f(this)h(pap)q(er\))g(or)g(zero)g (temp)q(erature)e(\(App)q(endix)h(B.2.1\).)21 b(But)15 b(p)q(erhaps)60 2653 y(more)f(imp)q(ortan)o(tly)l(,)g(w)o(e)h(w)o(an)o(t)h(to)g(b)q(e)g (consisten)o(t)f(with)h(the)f(underlying)g(message)g(of)h(this)f(w)o(ork,)951 2784 y(29)p eop %%Page: 30 30 bop 60 91 a FQ(whic)o(h)18 b(is)h(that)g FP(not)h(everything)h(in)g(the)f (world)g(is)g(Gibbsian)t FQ(.)29 b(Therefore,)19 b(w)o(e)f(m)o(ust)f(in)o (tro)q(duce)60 152 y(concepts)d(whic)o(h)f(are)h(general)f(enough)i(so)g (that)f(the)f(problems)g(w)o(e)g(wish)h(to)h(study)f(will)e(not)j(ha)o(v)o(e) 60 212 y(b)q(een)e(excluded)e(simply)f FP(by)15 b(de\014nition)t FQ(.)21 b(Ha)o(ving)12 b(done)h(so,)g(w)o(e)g(will)e(then)i(b)q(e)g(able)f (to)h(in)o(v)o(estigate,)60 272 y(without)20 b FP(a)h(priori)i FQ(preconceptions,)d(whic)o(h)f(problems)g(giv)o(e)f(rise)i(to)g FP(Gibbsian)k FQ(sp)q(eci\014cations)60 332 y(and)17 b(whic)o(h)e(ones)i(do)g (not.)60 462 y FM(2.3.3)55 b(Quasilo)r(calit)n(y)60 554 y FQ(In)17 b(all)g(theoretical)g(ph)o(ysics,)f(a)i(fundamen)o(tal)e(role)h(is)g(pla)o(y) o(ed)g(b)o(y)g(the)g(concept)g(of)h(an)g(\\isolated)60 615 y(system".)36 b(A)21 b(completely)e(isolated)i(system)g(is)g(of)h(course)g (an)g(idealization,)f(but)h(one)g(can)f(in)60 675 y(general)e(render)g(a)g (system)f FP(as)i(close)h(to)f(isolate)n(d)g(as)g(desir)n(e)n(d)k FQ(b)o(y)18 b(mo)o(ving)g(it)h(a)g(large)g(distance)60 735 y(a)o(w)o(a)o(y)14 b(from)g(all)g(other)h(ob)s(jects.)20 b(\(Here)14 b(w)o(e)g(neglect)f(cosmological)h(e\013ects,)g(as)h(w)o(ell)f(as)h (couplings)60 795 y(to)e(\014elds)g(that)h(could)f(carry)g(o\013)h (radiation.\))20 b(This)13 b(asymptotic)f(isolation)i(is)e(p)q(ossible,)i(of) f(course,)60 855 y(b)q(ecause)24 b(the)f(in)o(teraction)f(p)q(oten)o(tials)i (deca)o(y)e(to)i(zero)f(as)h(the)f(spatial)h(separation)g(tends)g(to)60 915 y(in\014nit)o(y)l(.)19 b(One)14 b(can)h(ev)o(en)e(argue)i(that)g(this)g (deca)o(y)e(of)i(in)o(teractions)f(is)g(an)h(essen)o(tial)e(precondition)60 976 y(for)21 b(the)g(p)q(ossibilit)o(y)f(of)h(doing)h(science:)29 b(without)21 b(it,)h(the)e(results)h(of)h(exp)q(erimen)o(ts)c(on)j(Earth)60 1036 y(w)o(ould)e(dep)q(end)h(sensitiv)o(ely)d(on)i(conditions)h(on)f (Andromeda,)g(and)h(the)f(rep)q(eatabilit)o(y)f(that)h(is)60 1096 y(fundamen)o(tal)c(to)h(the)g(scien)o(ti\014c)f(metho)q(d)g(w)o(ould)i (b)q(e)f(absen)o(t.)133 1156 y(These)i(remarks)f(justify)h(the)g(in)o(tro)q (duction)g(of)g(a)h(class)f(of)g(sp)q(eci\014cations)g(that)h(will)e(pla)o(y) h(a)60 1216 y(cen)o(tral)d(role)h(in)g(the)g(remainder)e(of)j(this)f(pap)q (er:)60 1318 y FM(De\014nition)i(2.9)24 b FP(A)14 b(sp)n(e)n(ci\014c)n(ation) h FQ(\005)e(=)h(\()p FF(\031)887 1325 y FH(\003)913 1318 y FQ(\))932 1325 y FH(\003)p Fy(2S)1021 1318 y FP(is)g(said)g(to)h(b)n(e)g FQ(quasilo)q(cal)f FP(if,)h(for)f(e)n(ach)g FQ(\003)g FE(2)g(S)t FP(,)60 1378 y FF(f)19 b FE(2)14 b FF(B)187 1385 y FD(q)q(l)217 1378 y FQ(\(\012\))k FP(implies)g FF(\031)503 1385 y FH(\003)529 1378 y FF(f)h FE(2)14 b FF(B)656 1385 y FD(q)q(l)686 1378 y FQ(\(\012\))p FP(.)23 b([Equivalently:)h FF(f)c FE(2)14 b FF(B)1235 1385 y FD(loc)1280 1378 y FQ(\(\012\))k FP(implies)g FF(\031)1566 1385 y FH(\003)1592 1378 y FF(f)h FE(2)14 b FF(B)1719 1385 y FD(q)q(l)1749 1378 y FQ(\(\012\))p FP(.])60 1480 y FQ(Note)22 b(that)h(\()p FF(\031)343 1487 y FH(\003)369 1480 y FF(f)5 b FQ(\)\()p FF(!)r FQ(\))25 b FE(\021)574 1445 y Fx(R)610 1480 y FF(\031)638 1487 y FH(\003)665 1480 y FQ(\()p FF(!)r(;)8 b(d!)795 1462 y Fy(0)807 1480 y FQ(\))g FF(f)d FQ(\()p FF(!)914 1462 y Fy(0)926 1480 y FQ(\))23 b(is)f(the)g(mean)f(v)m(alue)h(of)h FF(f)k FQ(in)22 b(the)g(equilibrium)60 1540 y(probabilit)o(y)13 b(distribution)g(for)h(v)o(olume)d(\003)j(with)f(b)q(oundary)i(condition)f FF(!)1422 1547 y FH(\003)1446 1538 y Fs(c)1464 1540 y FQ(.)21 b(Therefore,)13 b(a)h(sp)q(eci-)60 1600 y(\014cation)h(is)f(quasilo)q(cal)h (if)f(the)h(mean)e(v)m(alues)i(of)g(\(quasi\)lo)q(cal)g(observ)m(ables)g(dep) q(end)g(v)o(ery)e(w)o(eakly)60 1661 y(on)h(the)g(external)f(spins)h(far)g (from)f(\003)g(\(e.g.)g(outside)h(a)g(v)o(ery)f(large)g(v)o(olume)f(\003)1476 1643 y Fy(0)1488 1661 y FQ(\))h FP(when)k(the)e(external)60 1721 y(spins)j(in)f(the)h(interme)n(diate)g(r)n(e)n(gion)f FQ(\003)786 1703 y Fy(0)809 1721 y FE(n)11 b FQ(\003)17 b FP(ar)n(e)g(\014xe) n(d)5 b FQ(,)17 b(i.e.)475 1831 y(lim)470 1861 y FH(\003)494 1852 y Ft(0)506 1861 y Fy("L)664 1831 y FQ(sup)620 1877 y FD(!)642 1882 y Fr(1)659 1877 y FD(;)6 b(!)697 1882 y Fr(2)724 1877 y Fy(2)j FH(\012)577 1919 y(\()p FD(!)613 1924 y Fr(1)630 1919 y FH(\))644 1929 y Fr(\003)665 1922 y Ft(0)687 1919 y FH(=)i(\()p FD(!)761 1924 y Fr(2)778 1919 y FH(\))792 1929 y Fr(\003)813 1922 y Ft(0)863 1831 y FE(j)p FQ(\()p FF(\031)924 1838 y FH(\003)950 1831 y FF(f)5 b FQ(\)\()p FF(!)1047 1838 y FH(1)1067 1831 y FQ(\))11 b FE(\000)g FQ(\()p FF(\031)1194 1838 y FH(\003)1220 1831 y FF(f)5 b FQ(\)\()p FF(!)1317 1838 y FH(2)1337 1831 y FQ(\))p FE(j)28 b FQ(=)g(0)277 b(\(2)p FF(:)p FQ(23\))60 2029 y(for)18 b(all)f FF(f)22 b FE(2)16 b FF(B)337 2036 y FD(q)q(l)367 2029 y FQ(\(\012\))i([or)f FF(B)569 2036 y FD(loc)615 2029 y FQ(\(\012\)].)716 2011 y FH(20)778 2029 y FQ(W)l(e)g(emphasize)f(that)i (\(2.23\))h(constrains)f(only)f(the)h FP(dir)n(e)n(ct)60 2089 y FQ(in\015uence)d(of)h(the)g(spins)h(outside)f(\003)727 2071 y Fy(0)754 2089 y FQ(\(since)g(the)f(spins)i(in)e(the)h(\\ann)o(ulus")h(\003) 1502 2071 y Fy(0)1525 2089 y FE(n)10 b FQ(\003)16 b(are)g FP(\014xe)n(d)5 b FQ(\).)22 b(In)60 2150 y(particular,)e(\(2.23\))g(is)f(p)q(erfectly)f (compatible)g(with)h(the)g(o)q(ccurrence)g(of)h(long-range)h(order:)27 b(it)60 2210 y(sa)o(ys)15 b(merely)d(that)j(an)o(y)f(in\015uence)g(on)h(\003) f(from)g(the)g(spins)h(outside)f(\003)1346 2192 y Fy(0)1372 2210 y FQ(has)i(to)f(b)q(e)f FP(tr)n(ansmitte)n(d)20 b FQ(b)o(y)60 2270 y(the)c(in)o(termedi)o(ate)d(region.)22 b(W)l(e)15 b(emphasize)f(also)j (that)f(this)g(condition)f(of)h(\\w)o(eak)g(dep)q(endence")60 2330 y(is)g(form)o(ulated)f(in)h(the)g(suprem)o(um)d(norm,)i(i.e.)f(it)i(is)g (a)h(\\w)o(orst-case")h(condition.)p 60 2374 732 2 v 100 2428 a FA(20)135 2443 y Fz(If)11 b(the)h(state)h(space)f(\012)481 2449 y FA(0)511 2443 y Fz(is)g(\014nite,)g(it)f(su\016ces)i(to)e(c)o(hec)o(k) i(\(2.23\))d(for)h Fv(f)17 b Fu(2)11 b Fv(B)r Fz(\(\012)p Fv(;)c Fu(F)1385 2449 y FA(\003)1410 2443 y Fz(\),)k(b)q(ecause)j(an)o(y)d Fv(f)16 b Fu(2)11 b Fv(B)1783 2449 y Fp(loc)1828 2443 y Fz(\(\012\))60 2498 y([sa)o(y)m(,)g Fv(f)16 b Fu(2)11 b Fv(B)r Fz(\(\012)p Fv(;)c Fu(F)353 2514 y Fx(e)353 2516 y FA(\003)378 2498 y Fz(\))12 b(for)g(some)573 2487 y Fx(e)570 2498 y Fz(\003)f Fu(\033)h Fz(\003])f(corresp)q(onds)j(to)e(\014nitely)f(man)o(y)f(di\013eren)o(t)j (functions)f(in)g Fv(B)r Fz(\(\012)p Fv(;)7 b Fu(F)1743 2504 y FA(\003)1767 2498 y Fz(\))12 b(when)60 2548 y(one)h(\014xes)h(the)f (con\014guration)g Fv(!)575 2563 y Fx(e)575 2565 y FA(\003)p Fo(n)p FA(\003)639 2548 y Fz(.)18 b(If)13 b(the)g(state)h(space)g(\012)1021 2554 y FA(0)1052 2548 y Fz(is)f(in\014nite,)g(w)o(e)g(do)g(not)f(kno)o(w)h (whether)h(or)f(not)g(this)60 2612 y(w)o(eak)o(er)h(condition)g(is)f(equiv)n (alen)o(t)g(to)h(\(2.23\).)951 2784 y FQ(30)p eop %%Page: 31 31 bop 60 91 a FM(Examples.)19 b FQ(1.)j(If)16 b(all)g(the)g(Hamiltonians)e FF(H)936 73 y FH(\010)932 104 y(\003)981 91 y FQ(are)i FP(lo)n(c)n(al)22 b FQ(functions,)16 b(then)g(\005)1548 73 y FH(\010)1591 91 y FQ(is)g(a)h(quasilo)q(cal)60 152 y(sp)q(eci\014cation.)43 b(This)23 b(o)q(ccurs,)i(in)e(particular,)i(if)e(\010)g(is)h(a)g FP(\014nite-r)n(ange)29 b FQ(\(and)24 b FF(\026)1615 133 y FH(0)1635 152 y FQ(-admissible\))60 212 y(in)o(teraction.)133 272 y(2.)d(If)13 b(all)h(the)f(Hamiltonians)f FF(H)726 254 y FH(\010)722 284 y(\003)768 272 y FQ(are)i FP(quasilo)n(c)n(al)20 b FQ(functions,)13 b(then)h(\005)1434 254 y FH(\010)1475 272 y FQ(is)g(a)g(quasilo)q(cal)g(sp)q(ec-)60 332 y(i\014cation.)20 b(This)15 b(o)q(ccurs,)g(in)f(particular,)g(if)h(\010)f(is)h(a)g FP(uniformly)h(c)n(onver)n(gent)21 b FQ(\(and)15 b FF(\026)1615 314 y FH(0)1635 332 y FQ(-admissible\))60 392 y(in)o(teraction.)133 452 y(3.)21 b(Although)13 b(w)o(e)f(ha)o(v)o(e)g(not)h(sho)o(wn)h(explicitly) c(here)i(ho)o(w)h(to)g(treat)g(mo)q(dels)f(with)h(constrain)o(ts)60 513 y(\(e.g.)e(hard-core)i(exclusions\),)f(it)g(is)g(easy)g(to)h(see)e(that)i FP(lo)n(c)n(al)18 b FQ(constrain)o(ts)12 b(do)h(not)g(disrupt)f(quasilo-)60 573 y(calit)o(y)l(.)133 657 y(Examples)18 b(1)i(and)g(3)g(co)o(v)o(er)e(all)h (reasonable)h(systems)e(\(of)i(either)e(b)q(ounded)i(or)g(un)o(b)q(ounded)60 718 y(spins\))15 b(with)g(\014nite-range)g(in)o(teractions.)20 b(Examples)14 b(2)h(and)h(3)f(co)o(v)o(er)f(all)g(reasonable)i(systems)e(of) 60 778 y(b)q(ounded)j(spins.)k(Therefore,)15 b(w)o(e)h(argue)g(that)h FP(al)r(l)h(systems)f(of)g(physic)n(al)g(inter)n(est)h(ar)n(e)f(quasilo)n(c)n (al)60 838 y FQ(with)11 b(the)h(exception)e(of)i(mo)q(dels)f(of)h FP(unb)n(ounde)n(d)h(spins)j FQ(with)c FP(in\014nite-r)n(ange)17 b FQ(in)o(teractions.)i(These)60 898 y(latter)d(systems)f(are,)h (unfortunately)l(,)f(usually)h FP(not)22 b FQ(quasilo)q(cal:)133 983 y(4.)34 b(Consider)20 b(a)h(mo)q(del)e(of)h(real-v)m(alued)g(spins)h FE(f)p FF(')1101 990 y FD(i)1114 983 y FE(g)g FQ(|)f(for)g(example,)f(a)h (Gaussian)i(or)e FF(')1870 964 y FH(4)60 1043 y FQ(mo)q(del)15 b(|)h(with)g(formal)f(Hamiltonian)772 1151 y FF(H)32 b FQ(=)27 b FE(\000)956 1109 y Fx(X)967 1200 y FD(i;j)1025 1151 y FF(J)1052 1158 y FD(ij)1082 1151 y FF(')1114 1158 y FD(i)1128 1151 y FF(')1160 1158 y FD(j)1765 1151 y FQ(\(2)p FF(:)p FQ(24\))60 1297 y(where)16 b FF(J)22 b FQ(has)17 b(in\014nite)f(range.)23 b(Then)16 b(the)h(resulting)f(sp)q(eci\014cation)g(is)h FP(not)22 b FQ(quasilo)q(cal,)16 b(b)q(ecause)60 1357 y(an)f(external)e(spin)i (arbitrarily)e(far)i(a)o(w)o(a)o(y)f(from)f(the)h(v)o(olume)e(\003)i(can,)h (b)o(y)f(taking)g(extremely)d(large)60 1418 y(v)m(alues,)22 b(ha)o(v)o(e)e(large)h(e\013ects)g(inside)f(\003.)35 b(The)21 b(trouble)g(here)f(is)h(that)h(quasilo)q(calit)o(y)d(is)i(de\014ned)60 1478 y(in)d(the)h(suprem)o(um)c(norm,)j(whic)o(h)g(is)g(to)q(o)i(strong)f(a)g (condition)g(for)g(systems)e(with)h(un)o(b)q(ounded)60 1538 y(Hamiltonians.)35 b(\(There)21 b(is)g(in)g(fact)g(a)h(more)e(serious)h (di\016cult)o(y)e(in)i(this)g(example:)29 b(for)22 b(some)60 1598 y(external)13 b(conditions)g(the)g(Hamiltonian)f FF(H)879 1580 y FH(\010)875 1610 y(\003)920 1598 y FQ(is)i(div)o(ergen)o(t.)19 b(Therefore,)13 b(to)h(treat)f(these)g(systems)60 1658 y(it)19 b(is)g(necessary)h(to)f(enlarge)h(sligh)o(tly)e(the)h(concept)g(of)h(sp)q (eci\014cation)f(in)g(order)h(to)g(allo)o(w)f(some)60 1719 y(external)c(conditions)h(to)g(b)q(e)g(\\forbidden")g([299)q(,)g(pp.)f(16{18) j(and)e(89])g([245)q(,)f(60)q(],)g(or)h(else)f(to)i(pla)o(y)60 1779 y(some)e(minor)g(tric)o(k)o(ery)f([157)q(,)h(pp.)h(261,)h(264{265)i(and) e(424{425].\))133 1887 y(W)l(e)f(summarize)d(the)j(main)f(conclusion)h(from)f (this)i(discussion:)60 1999 y FM(Theorem)g(2.10)24 b FP(L)n(et)d FQ(\010)g FP(b)n(e)h(a)f(uniformly)g(c)n(onver)n(gent)i(and)f FF(\026)1275 1981 y FH(0)1295 1999 y FP(-admissible)g(inter)n(action.)35 b([In)60 2059 y(p)n(articular)22 b(this)h(happ)n(ens)g(if)g FQ(\010)g FP(is)g(absolutely)i(summable,)g(or)d(if)h FQ(\010)g FP(is)g(\014nite-r)n(ange)i(and)f FF(\026)1853 2041 y FH(0)1873 2059 y FP(-)60 2119 y(admissible.])f(Then)18 b(the)g(sp)n(e)n(ci\014c)n (ation)g FQ(\005)847 2101 y FH(\010)891 2119 y FP(is)g(quasilo)n(c)n(al.)133 2280 y FQ(The)d(Gibbsian)f(sp)q(eci\014cation)g(arising)h(from)e(a)i(mo)q (del)e(with)h(\014nite)g(\(resp.)g(b)q(ounded\))h(Hamil-)60 2340 y(tonians)i(has)g(an)g(additional)f(c)o(haracteristic)f(prop)q(ert)o(y:) 60 2440 y FM(De\014nition)j(2.11)24 b FP(A)17 b(sp)n(e)n(ci\014c)n(ation)h FQ(\005)13 b(=)h(\()p FF(\031)921 2447 y FH(\003)947 2440 y FQ(\))966 2447 y FH(\003)p Fy(2S)1058 2440 y FP(is)j(said)g(to)h(b)n(e)133 2540 y FE(\017)24 b FQ(nonn)o(ull)16 b(\(with)g(resp)q(ect)g(to)g FF(\026)742 2521 y FH(0)762 2540 y FQ(\))i FP(if,)f(for)g(e)n(ach)g FQ(\003)d FE(2)g(S)22 b FP(and)17 b(e)n(ach)h FF(A)13 b FE(2)h(F)1532 2547 y FH(\003)1559 2540 y FP(,)551 2647 y FF(\026)580 2627 y FH(0)600 2647 y FQ(\()p FF(A)p FQ(\))g FF(>)f FQ(0)42 b(=)-8 b FE(\))41 b FF(\031)955 2654 y FH(\003)982 2647 y FQ(\()p FF(!)r(;)8 b(A)p FQ(\))13 b FF(>)h FQ(0)j FP(for)g(al)r(l)i FF(!)d FE(2)e FQ(\012)g FF(:)244 b FQ(\(2)p FF(:)p FQ(25\))951 2784 y(31)p eop %%Page: 32 32 bop 133 91 a FE(\017)24 b FQ(uniformly)16 b(nonn)o(ull)h(\(with)h(resp)q(ect) g(to)g FF(\026)973 73 y FH(0)993 91 y FQ(\))h FP(if,)h(for)e(e)n(ach)h FQ(\003)e FE(2)g(S)t FP(,)i(ther)n(e)g(exist)h(c)n(onstants)182 152 y FQ(0)14 b FF(<)g(\013)303 159 y FH(\003)343 152 y FE(\024)g FF(\014)424 159 y FH(\003)464 152 y FF(<)g FE(1)j FP(such)h(that)663 254 y FF(\013)694 261 y FH(\003)729 254 y FF(\026)758 234 y FH(0)778 254 y FQ(\()p FF(A)p FQ(\))27 b FE(\024)g FF(\031)974 261 y FH(\003)1001 254 y FQ(\()p FF(!)r(;)8 b(A)p FQ(\))27 b FE(\024)g FF(\014)1251 261 y FH(\003)1286 254 y FF(\026)1315 234 y FH(0)1335 254 y FQ(\()p FF(A)p FQ(\))355 b(\(2)p FF(:)p FQ(26\))182 357 y FP(for)17 b(al)r(l)i FF(!)d FE(2)e FQ(\012)j FP(and)h(al)r(l)h FF(A)13 b FE(2)h(F)773 364 y FH(\003)799 357 y FP(.)60 453 y FQ(Roughly)g(sp)q(eaking,)g(\\nonn)o(ull")g(means)f(that) h(there)f(are)h(no)g(hard-core)h(exclusions,)e(while)g(\\uni-)60 513 y(formly)h(nonn)o(ull")h(means)g(that)g(moreo)o(v)o(er)f(the)h (\014nite-v)o(olume)e(Hamiltonians)h(are)h(b)q(ounded)h(\(as)60 573 y(a)h(function)f(of)g(b)q(oth)h(the)f(in)o(terior)f(spins)i FF(!)871 580 y FH(\003)914 573 y FQ(and)g(the)f(exterior)f(spins)i FF(!)1426 580 y FH(\003)1450 571 y Fs(c)1469 573 y FQ(\).)133 633 y(It)22 b(turns)h(out)g(that)f(the)h(t)o(win)e(prop)q(erties)i(of)f(b)q (eing)h(quasilo)q(cal)f(and)h(uniformly)d(nonn)o(ull)60 694 y(exactly)15 b(c)o(haracterize)g(the)h(Gibbsian)g(sp)q(eci\014cations)g(for)h (absolutely)f(summable)d(in)o(teractions:)60 800 y FM(Theorem)k(2.12)h (\(Gibbs)g(represen)n(tation\))23 b FP(L)n(et)g FQ(\005)f FP(b)n(e)i(a)e(sp)n (e)n(ci\014c)n(ation,)j(and)e(let)h FF(\026)1757 782 y FH(0)1800 800 y FP(b)n(e)f(a)60 860 y(pr)n(o)n(duct)16 b(me)n(asur)n(e.)22 b(Then)c(the)g(fol)r(lowing)i(ar)n(e)d(e)n(quivalent:)93 955 y(\(a\))24 b(Ther)n(e)c(exists)h(an)g(absolutely)g(summable)h(inter)n(action) f FQ(\010)f FP(such)h(that)f FQ(\005)g FP(is)h(the)f(Gibbsian)182 1016 y(sp)n(e)n(ci\014c)n(ation)e(for)f FQ(\010)g FP(and)h FF(\026)709 998 y FH(0)729 1016 y FP(.)95 1115 y(\(b\))25 b FQ(\005)17 b FP(is)g(quasilo)n(c)n(al)h(and)g(is)f(uniformly)g(nonnul)r(l)k (with)c(r)n(esp)n(e)n(ct)g(to)h FF(\026)1406 1097 y FH(0)1426 1115 y FP(.)60 1211 y(Mor)n(e)n(over,)e(if)i(the)g(single-spin)h(sp)n(ac)n(e) e FQ(\012)821 1218 y FH(0)859 1211 y FP(is)g(\014nite,)i(then)f(these)g(ar)n (e)f(also)h(e)n(quivalent)h(to)95 1307 y(\(c\))25 b FQ(\005)17 b FP(is)g(quasilo)n(c)n(al)h(and)g(is)f(nonnul)r(l)j(with)e(r)n(esp)n(e)n(ct) f(to)g FF(\026)1183 1288 y FH(0)1203 1307 y FP(.)133 1413 y FQ(The)g(pro)q(of)i(that)f(\(a\))f(=)-8 b FE(\))17 b FQ(\(b\))g(is)h(easy;)f (the)g(non)o(trivial)f(pro)q(of)j(that)f(\(b\))f(=)-8 b FE(\))17 b FQ(\(a\))g(is)g(due)h(to)60 1473 y(Kozlo)o(v)g([222)q(].)28 b(The)19 b(observ)m(ation)h(that)f(\(c\))f(=)-8 b FE(\))18 b FQ(\(b\))h(for)g(\014nite)f(single-spin)h(space)g(w)o(as)g(made)60 1533 y(b)o(y)d(b)q(oth)h(Sulliv)m(an)f([336])g(and)h(Kozlo)o(v)e([222)q(].)60 1639 y FM(De\014nition)j(2.13)24 b FP(A)16 b(me)n(asur)n(e)g FF(\026)h FP(on)g FQ(\012)g FP(is)g(said)f(to)h(b)n(e)g FQ(quasilo)q(cal)f FP(if)h(ther)n(e)f(exists)i(a)f(quasilo)n(c)n(al)60 1699 y(sp)n(e)n(ci\014c)n (ation)h(with)g(which)g FF(\026)g FP(is)f(c)n(onsistent.)24 b(\(Sul)r(livan)c([336])d(uses)h(the)g(term)f(\\almost)h(Marko-)60 1759 y(vian)-5 b(")18 b(in)g(plac)n(e)g(of)f(\\quasilo)n(c)n(al".\))133 1865 y FQ(Theorem)i(2.12)i(implies)c(that)j(quasilo)q(calit)o(y)f(is)h(only)g (sligh)o(tly)f(more)f(general)i(than)h(Gibb-)60 1926 y(sianness)13 b(for)g(an)g(absolutely)g(summable)d(in)o(teraction:)18 b(roughly)13 b(sp)q(eaking,)h(quasilo)q(calit)o(y)d(allo)o(ws)60 1986 y(for)17 b(lo)q(cal)f(constrain)o(ts)g(\(e.g.)g(hard-core)g(exclusions\))g(while)f (Gibbsianness)i(do)q(es)g(not.)133 2092 y FM(Remarks.)42 b FQ(1.)j(F)l(or)24 b(further)f(discussion)h(on)h(the)e(Gibbs)h(represen)o (tation)g(theorem,)f(in)60 2152 y(connection)16 b(with)g(translation)h(in)o (v)m(ariance,)e(see)h(the)g(Remark)e(at)j(the)f(end)g(of)g(Section)g(2.4.9.) 133 2212 y(2.)37 b(Sulliv)m(an)21 b([336)q(])g(and)g(Gross)i([178)q(,)f(pp.)f (194{195])j(ha)o(v)o(e)c(in)o(tro)q(duced)h(a)h(sligh)o(tly)e(larger)60 2272 y(class)j(of)f(in)o(teractions)g(than)h(those)g(considered)f(here,)h (based)g(on)g(the)f(observ)m(ation)h(that)g(the)60 2333 y(only)15 b(energies)f(whic)o(h)h(pla)o(y)f(a)i(role)e(in)h(the)g(de\014nition)g(of)g (the)g(sp)q(eci\014cation)g(\005)1531 2314 y FH(\010)1573 2333 y FQ(are)g(the)g FP(r)n(elative)60 2393 y FQ(energies)h(of)i(pairs)f(of)g (con\014gurations)i FP(that)f(di\013er)g(at)g(only)h(\014nitely)g(many)f (sites)t FQ(.)24 b(Therefore,)16 b(it)60 2453 y(is)g(not)h(necessary)f(for)g (the)g(Hamiltonians)691 2556 y FF(H)735 2535 y FH(\010)731 2568 y(\003)762 2556 y FQ(\()p FF(!)r FQ(\))e(=)978 2514 y Fx(X)961 2613 y FD(A)c Fy(2)g(S)919 2660 y FD(A)e Fy(\\)f FH(\003)k Fy(6)p FH(=)f Fq(?)1126 2556 y FQ(\010)1161 2563 y FD(A)1189 2556 y FQ(\()p FF(!)r FQ(\))506 b(\(2)p FF(:)p FQ(27\))951 2784 y(32)p eop %%Page: 33 33 bop 60 91 a FQ(to)17 b(b)q(e)f(w)o(ell-de\014ned,)e(but)j(only)f(the)g FP(r)n(elative)i(Hamiltonians)521 201 y FF(H)565 181 y FH(\010)561 214 y FD(r)q(el;)p FH(\003)641 201 y FQ(\()p FF(!)r(;)8 b(!)746 181 y Fy(0)758 201 y FQ(\))14 b(=)923 160 y Fx(X)906 258 y FD(A)c Fy(2)f(S)864 305 y FD(A)f Fy(\\)f FH(\003)k Fy(6)p FH(=)f Fq(?)1062 201 y FQ([\010)1111 208 y FD(A)1139 201 y FQ(\()p FF(!)r FQ(\))i FE(\000)e FQ(\010)1305 208 y FD(A)1334 201 y FQ(\()p FF(!)1385 181 y Fy(0)1397 201 y FQ(\)])335 b(\(2)p FF(:)p FQ(28\))60 413 y(for)21 b(con\014gurations)h FF(!)r(;)8 b(!)544 395 y Fy(0)577 413 y FQ(that)22 b FP(agr)n(e)n(e)f(outside)h FQ(\003.)35 b(It)21 b(turns)g(out)g([336)q(,)h(Prop)q(osition)g(3])f(that)60 473 y(for)f(in)o(teractions)f(whose)h FP(r)n(elative)k FQ(Hamiltonians)18 b(are)h(uniformly)f(con)o(v)o(ergen)o(t)g(\(Sulliv)m(an)h(calls)60 534 y(these)d(in)o(teractions)g(\\)p FE(L)p FQ(-con)o(v)o(ergen)o(t"\),)g (the)g(corresp)q(onding)h(sp)q(eci\014cation)g(is)f(again)h(quasilo)q(cal)60 594 y(and)24 b(nonn)o(ull)g(\(at)g(least)g(for)g(\014nite)f(single-spin)h (space\).)44 b(So)24 b(this)g(generalization)f(do)q(es)i(not)60 654 y(pro)o(vide)c(examples)f(of)j(ph)o(ysically)d(in)o(teresting)h (non-quasilo)q(cal)i(sp)q(eci\014cations.)39 b(Indeed,)22 b(w)o(e)60 714 y(can)c(com)o(bine)e(this)i(result)g(with)g(\(c\))f(=)-8 b FE(\))18 b FQ(\(a\))g(of)h(Theorem)d(2.12,)j(and)g(conclude)e(that)i(for)f (an)o(y)60 774 y(\\relativ)o(ely)d(uniformly)g(con)o(v)o(ergen)o(t")h(in)o (teraction)g(\010)h(\(at)g(least)g(on)g(a)h(\014nite)e(single-spin)h(space\)) 60 835 y(there)e(is)h(an)g FP(absolutely)i(summable)j FQ(in)o(teraction)14 b(\010)1029 817 y Fy(0)1057 835 y FQ(suc)o(h)h(that)i(\005)1309 817 y FH(\010)1349 835 y FQ(=)d(\005)1438 817 y FH(\010)1463 805 y Ft(0)1477 835 y FQ(.)21 b(Roughly)15 b(sp)q(eaking)60 895 y(this)h(means)f(that)i(\010)g(and)f(\010)591 877 y Fy(0)620 895 y FQ(are)g(\\ph)o(ysically)f(equiv)m(alen)o(t")g(\(see)h(Section)f (2.3.5\).)133 955 y(3.)21 b(If)15 b(\005)f(is)h(a)g(quasilo)q(cal)g(sp)q (eci\014cation,)f(then)h(the)f(criterion)g(for)h FF(\026)g FQ(to)g(b)q(e)g(consisten)o(t)g(with)f(\005)60 1015 y(can)i(b)q(e)h(w)o(eak)o (ened)e(sligh)o(tly:)20 b(instead)c(of)h(requiring)e FF(\026)g FQ(=)e FF(\026\031)1207 1022 y FH(\003)1250 1015 y FQ([Prop)q(osition)k (2.7\(c\)],)f(it)f(su\016ces)60 1075 y(to)22 b(ha)o(v)o(e)f FF(\026)j FQ(=)g FF(\026\031)415 1082 y FH(\003)463 1075 y FP(on)f(the)h FF(\033)r FP(-\014eld)f FE(F)817 1082 y FH(\003)866 1075 y FQ([157,)g(Remark)e(4.21].)38 b(Th)o(us,)23 b(if)f(\010)g(is)g(a)g (uniformly)60 1136 y(con)o(v)o(ergen)o(t)15 b(\(and)i FF(\026)447 1118 y FH(0)467 1136 y FQ(-admissible\))d(in)o(teraction,)h(then)h(the)g (alternate)g(DLR)g(equation)g(\(2.22\))h(is)60 1196 y FP(e)n(quivalent)23 b FQ(to)17 b(the)f(standard)h(DLR)g(equation)f(\(2.21\).)133 1256 y(4.)22 b(In)16 b(rather)g(great)g(generalit)o(y)f(it)h(can)g(b)q(e)g (pro)o(v)o(en)f([161)q(,)h(300)q(,)g(330)q(])f(that)i FP(every)k FQ(measure)15 b FF(\026)60 1316 y FQ(is)f(consisten)o(t)h(with)f FP(some)19 b FQ(sp)q(eci\014cation.)h(Ho)o(w)o(ev)o(er,)13 b(this)h(sp)q(eci\014cation)h(will)e(in)h(general)h(not)g(b)q(e)60 1376 y(quasilo)q(cal.)21 b(Indeed,)14 b(in)i(Section)f(4)h(w)o(e)f(shall)h (giv)o(e)e(n)o(umerous)h(examples)e(of)j(measures)f(that)h(are)60 1437 y(not)h(consisten)o(t)f(with)g(an)o(y)g(quasilo)q(cal)g(sp)q (eci\014cation.)60 1566 y FM(2.3.4)55 b(F)-5 b(eller)18 b(Prop)r(ert)n(y)60 1659 y FQ(It)23 b(is)g(useful)g(to)h(single)f(out)h(a)f(class)h(of)g(sp)q (eci\014cations)f(in)g(whic)o(h)g(the)g(\014nite-v)o(olume)e(Gibbs)60 1719 y(measure)11 b FF(\031)274 1726 y FH(\003)300 1719 y FQ(\()p FF(!)r(;)16 b FE(\001)8 b FQ(\))13 b(dep)q(ends)f(in)g(a)h(\\su\016cien)o (tly)e(con)o(tin)o(uous")h(w)o(a)o(y)g(on)h(the)f(b)q(oundary)h(condition)60 1779 y FF(!)r FQ(:)60 1881 y FM(De\014nition)18 b(2.14)24 b FP(A)19 b(sp)n(e)n(ci\014c)n(ation)g FQ(\005)e(=)g(\()p FF(\031)931 1888 y FH(\003)957 1881 y FQ(\))976 1888 y FH(\003)p Fy(2S)1069 1881 y FP(is)i(said)g(to)g(b)n(e)h FQ(F)l(eller)d FP(if,)i(for)g(e)n(ach)g FQ(\003)e FE(2)g(S)t FP(,)60 1941 y FF(f)i FE(2)14 b FF(C)t FQ(\(\012\))j FP(implies)h FF(\031)474 1948 y FH(\003)500 1941 y FF(f)i FE(2)14 b FF(C)t FQ(\(\012\))p FP(.)133 2043 y FM(Example.)29 b FQ(If)19 b(the)h(in)o(teraction)e(\010)i(is)g(con)o(tin)o(uous)f(and)i (uniformly)c(con)o(v)o(ergen)o(t)h(\(and)j FF(\026)1854 2025 y FH(0)1874 2043 y FQ(-)60 2103 y(admissible\),)13 b(then)i(the)g(sp)q (eci\014cation)f(\005)834 2085 y FH(\010)877 2103 y FQ(is)g(F)l(eller.)19 b(Th)o(us,)d(nearly)e(all)h(sp)q(eci\014cations)g(of)g(ph)o(ys-)60 2163 y(ical)g(in)o(terest)g(are)i(F)l(eller.)133 2223 y(It)g(is)g(w)o(orth)g (remarking)f(that)h(the)g(de\014nition)g(of)g(the)g(F)l(eller)e(prop)q(ert)o (y)i(formally)f(resem)o(bles)60 2284 y(that)g(of)g(quasilo)q(calit)o(y:)k (indeed,)15 b(De\014nition)g(2.14)h(is)g(iden)o(tical)e(to)i(De\014nition)g (2.9,)f(with)h FF(B)1787 2291 y FD(q)q(l)1817 2284 y FQ(\(\012\))60 2344 y(replaced)g(ev)o(erywhere)g(b)o(y)g FF(C)t FQ(\(\012\).)24 b(In)17 b(particular,)g(if)g(the)g(single-spin)g(space)g(\012)1565 2351 y FH(0)1602 2344 y FQ(is)g FP(\014nite)t FQ(,)h(then)60 2404 y FF(B)97 2411 y FD(q)q(l)127 2404 y FQ(\(\012\))c(=)g FF(C)t FQ(\(\012\),)h(so)h(the)f(concepts)h(of)g(\\quasilo)q(cal)g(sp)q (eci\014cation")f(and)i(\\F)l(eller)d(sp)q(eci\014cation")60 2464 y(coincide.)133 2524 y(W)l(e)i(can)h(no)o(w)f(state)h(a)f(v)o(ery)f(imp) q(ortan)o(t)h(uniqueness)f(theorem:)951 2784 y(33)p eop %%Page: 34 34 bop 60 91 a FM(Theorem)17 b(2.15)24 b FP(L)n(et)d FF(\026)i FP(b)n(e)f(a)g(pr)n(ob)n(ability)g(me)n(asur)n(e)f(that)i(gives)g(nonzer)n(o) f(me)n(asur)n(e)f(to)i(every)60 152 y(op)n(en)h(set)g FF(U)30 b FE(\032)25 b FQ(\012)p FP(.)440 133 y FH(21)518 152 y FP(Then)f(ther)n(e)g (is)f(at)h(most)f(one)h(F)l(el)r(ler)i(sp)n(e)n(ci\014c)n(ation)d(with)h (which)g FF(\026)g FP(is)60 212 y(c)n(onsistent.)f(In)17 b(p)n(articular,)f (if)g(the)h(single-spin)i(sp)n(ac)n(e)d FQ(\012)1134 219 y FH(0)1170 212 y FP(is)g(\014nite,)i(then)g(ther)n(e)e(is)g(at)h(most)f(one)60 272 y(quasilo)n(c)n(al)i(sp)n(e)n(ci\014c)n(ation)g(with)g(which)g FF(\026)f FP(is)h(c)n(onsistent.)133 367 y FQ(This)12 b(theorem)f(has)i(an)g (imp)q(ortan)o(t)e(consequence)g(for)i(the)f(renormalization)e(group:)20 b(it)12 b(sho)o(ws)60 427 y(that)i(the)f(do)o(wn)o(w)o(ard)h(v)o(ertical)e (arro)o(w)i(in)f(\(1.2\))h(cannot)g(b)q(e)f(a)h(m)o(ulti-v)m(alued)d(map,)i (pro)o(vided)g(that)60 487 y(w)o(e)j(in)o(terpret)f FF(H)378 469 y Fy(0)406 487 y FQ(as)i(standing)g(for)f(a)h(sp)q(eci\014cation.)133 567 y FM(Remark.)h FQ(Suc)o(h)10 b(uniqueness)h(do)q(es)h(not)g(hold)g(in)f (general)g(for)g(non-F)l(eller)f(sp)q(eci\014cations.)20 b(In-)60 627 y(deed,)13 b(if)g FF(\026)256 634 y FH(1)276 627 y FF(;)8 b(\026)327 634 y FH(2)347 627 y FF(;)g(:)g(:)g(:)13 b FQ(is)g FP(any)18 b FQ(\014nite)13 b(or)g(coun)o(tably)h(in\014nite)e(set)h(of)h (probabilit)o(y)f(measures)f(that)i(are)60 688 y(distinguishable)g(at)g (in\014nit)o(y)602 669 y FH(22)638 688 y FQ(,)h(there)e(exists)h(a)g(sp)q (eci\014cation)g(\(in)g(general)g(non-F)l(eller)f(and)i(non-)60 748 y(quasilo)q(cal\))i(with)f(whic)o(h)g(all)h(these)f(measures)g(are)h (consisten)o(t.)1267 730 y FH(23)1327 748 y FQ(F)l(or)g(example,)d(let)i FF(\026)1720 755 y FH(1)1740 748 y FF(;)8 b(\026)1791 755 y FH(2)1811 748 y FF(;)g(:)g(:)g(:)60 808 y FQ(b)q(e)23 b(Gibbs)f(measures)f (of)i(the)f(t)o(w)o(o-dimensional)f(Ising)h(mo)q(del)f(at)i(an)g(arbitrary)f (sequence)g(of)60 868 y(temp)q(eratures)17 b FF(\014)387 875 y FH(1)407 868 y FF(;)8 b(\014)457 875 y FH(2)476 868 y FF(;)g(:)g(:)g(:)16 b FE(2)i FQ([)p FE(\0001)p FF(;)8 b FQ(+)p FE(1)p FQ(];)18 b(then)g(there)g(exists)g(a)h(sp)q(eci\014cation)f(with)h(whic)o(h)f FP(al)r(l)60 928 y FQ(these)g(measures)f(are)i(consisten)o(t!)27 b(\(By)17 b(Theorem)h(2.15,)h(suc)o(h)f(a)h(sp)q(eci\014cation)f(is)g(of)g (necessit)o(y)60 989 y(non-F)l(eller)g(and)h(non-quasilo)q(cal.\))29 b(This)19 b(remark)e(sho)o(ws)i(that)h(non-quasilo)q(cal)f(sp)q (eci\014cations)60 1049 y(can)f(b)q(e)g(extremely)d(pathological)j(and)h (\\unph)o(ysical";)f(it)f(is)h(an)g(additional)g(argumen)o(t)f(for)h(the)60 1109 y(imp)q(ortance)d(of)i(quasilo)q(calit)o(y)l(.)60 1276 y FM(2.3.5)55 b(Ph)n(ysical)19 b(Equiv)m(alence)d(in)i(the)g(DLR)h(Sense)60 1369 y FQ(The)h(same)e(ph)o(ysical)h(situation)g(can)h(b)q(e)g(describ)q(ed)f (b)o(y)g(man)o(y)f(di\013eren)o(t)h(in)o(teractions)f(\010.)32 b(F)l(or)60 1429 y(example,)14 b(the)i(in)o(teractions)534 1567 y(\010)569 1574 y FD(A)597 1567 y FQ(\()p FF(!)r FQ(\))28 b(=)761 1480 y Fx(8)761 1517 y(<)761 1592 y(:)806 1513 y FE(\000)p FF(h!)903 1520 y FD(i)1059 1513 y FQ(if)16 b FF(A)d FQ(=)h FE(f)p FF(i)p FE(g)806 1573 y(\000)p FF(J)5 b(!)907 1580 y FD(i)921 1573 y FF(!)951 1580 y FD(i)p FH(+1)1059 1573 y FQ(if)16 b FF(A)d FQ(=)h FE(f)p FF(i;)8 b(i)i FQ(+)h(1)p FE(g)806 1633 y FQ(0)229 b(otherwise)1765 1567 y(\(2)p FF(:)p FQ(29\))60 1705 y(and)469 1773 y(\010)504 1752 y Fy(0)504 1785 y FD(A)532 1773 y FQ(\()p FF(!)r FQ(\))28 b(=)696 1712 y Fx(\032)735 1752 y FE(\000)779 1732 y FD(h)p 779 1740 21 2 v 780 1769 a FH(2)804 1752 y FF(!)834 1759 y FD(i)860 1752 y FE(\000)11 b FF(J)5 b(!)972 1759 y FD(i)986 1752 y FF(!)1016 1759 y FD(i)p FH(+1)1124 1752 y FQ(if)16 b FF(A)d FQ(=)h FE(f)p FF(i;)8 b(i)i FQ(+)h(1)p FE(g)735 1812 y FQ(0)365 b(otherwise)1765 1773 y(\(2)p FF(:)p FQ(30\))60 1870 y(b)q(oth)24 b(describ)q(e)f(the)g(one-dimensional)f(Ising)i (mo)q(del)e(with)h(nearest-neigh)o(b)q(or)h(in)o(teraction)e FF(J)60 1930 y FQ(and)h(magnetic)e(\014eld)h FF(h)p FQ(;)j(they)d(are)h(ob)o (viously)f(\\ph)o(ysically)f(equiv)m(alen)o(t".)39 b(The)22 b(reason)i(they)60 1991 y(are)18 b(\\ph)o(ysically)f(equiv)m(alen)o(t")h(is)g (that)h(they)e FP(de\014ne)k(the)f(same)g(sp)n(e)n(ci\014c)n(ation)i FQ(|)c(and)h(it)f(is)g(the)60 2051 y(sp)q(eci\014cation)e(that)h(determines)d (the)i(ph)o(ysics.)133 2111 y(Re\015ecting)22 b(a)h(little)e(bit)i(on)g(this) g(and)g(similar)e(examples,)h(one)h(comes)f(to)h(the)f(follo)o(wing)60 2171 y(de\014nition)16 b([157,)g(Section)g(2.4]:)p 60 2213 732 2 v 100 2267 a FA(21)135 2282 y Fz(This)c(means,)f(roughly)h(sp)q (eaking,)g(that)g(ev)o(ery)h(con\014guration)f(in)g(\012)g(is)g(\\p)q (ossible",)g(i.e.)f(there)j(are)e(no)g(\\hard-)60 2332 y(core)j(exclusions".) 100 2390 y FA(22)135 2405 y Fz(This)h(means)g(that)g(there)i(exist)e Fw(disjoint)k Fz(sets)e Fv(F)929 2411 y FA(1)947 2405 y Fv(;)7 b(F)993 2411 y FA(2)1011 2405 y Fv(;)g(:)g(:)g(:)13 b Fu(2)1147 2394 y Fx(b)1137 2405 y Fu(F)1167 2411 y Fo(1)1217 2405 y Fu(\021)1282 2373 y Fx(T)1265 2442 y FA(\003)p Fo(2S)1340 2405 y Fu(F)1370 2411 y FA(\003)1393 2403 y Fn(c)1426 2405 y Fz(suc)o(h)k(that)g Fv(\026)1640 2411 y Fp(k)1660 2405 y Fz(\()p Fv(F)1703 2411 y Fp(k)1724 2405 y Fz(\))e(=)h(1)g(for)60 2487 y(eac)o(h)e Fv(k)q Fz(.)100 2545 y FA(23)135 2560 y Fw(Pr)n(o)n(of:)27 b Fz(F)m(orm)15 b(the)j(measure)f Fv(\026)g Fz(=)716 2529 y Fx(P)759 2573 y Fp(k)787 2560 y Fv(c)805 2566 y Fp(k)825 2560 y Fv(\026)850 2566 y Fp(k)871 2560 y Fz(,)g(where)i Fv(c)1042 2566 y FA(1)1060 2560 y Fv(;)7 b(c)1097 2566 y FA(2)1115 2560 y Fv(;)g(:)g(:)g(:)15 b(>)j Fz(0)e(is)i(an)o(y)e(sequence)k(with)d(sum)f(1.) 28 b(By)60 2610 y([161)o(,)15 b(300)o(,)h(330)o(])f(there)i(exists)g(a)e(sp)q (eci\014cation)i(\005)f(with)f(whic)o(h)h Fv(\026)g Fz(is)f(consisten)o(t.)25 b(But)17 b(then)f Fv(\026)1609 2616 y Fp(k)1645 2610 y Fz(=)f Fv(c)1710 2592 y Fo(\000)p FA(1)1710 2623 y Fp(k)1754 2610 y Fv(\037)1780 2616 y Fp(F)1801 2620 y Fn(k)1821 2610 y Fv(\026)h Fz(is)60 2660 y(also)d(consisten)o(t)i(with)f(\005)g([299)o(,)f(Lemma)e (2.4].)951 2784 y FQ(34)p eop %%Page: 35 35 bop 60 91 a FM(De\014nition)18 b(2.16)24 b FP(L)n(et)17 b FQ(\010)i FP(and)f FQ(\010)714 73 y Fy(0)744 91 y FP(b)n(e)g(c)n(onver)n(gent)i(inter)n (actions.)25 b(We)18 b(say)g(that)g FQ(\010)g FP(and)h FQ(\010)1795 73 y Fy(0)1825 91 y FP(ar)n(e)60 152 y FQ(ph)o(ysically)g(equiv)m(alen)o(t)g (in)h(the)g(DLR)h(sense)g FP(if,)h(for)f(al)r(l)h FQ(\003)f FE(2)g(S)t FP(,)h(the)g(function)h FF(H)1657 133 y FH(\010)1653 164 y(\003)1698 152 y FE(\000)14 b FF(H)1795 133 y FH(\010)1820 122 y Ft(0)1791 164 y FH(\003)1855 152 y FP(is)60 212 y FE(F)96 219 y FH(\003)120 210 y Fs(c)138 212 y FP(-me)n(asur)n(able)k(\(i.e.)g(dep)n (ends)g(only)g(on)f(the)h(spins)g FQ(outside)f(\003)p FP(\).)60 313 y FQ(One)f(can)g(then)g(pro)o(v)o(e)g(the)g(follo)o(wing)g(theorem:)60 428 y FM(Theorem)h(2.17)24 b FP(L)n(et)18 b FQ(\010)h FP(and)g FQ(\010)692 409 y Fy(0)722 428 y FP(b)n(e)g(c)n(onver)n(gent)h FF(\026)1054 409 y FH(0)1074 428 y FP(-admissible)g(inter)n(actions.)27 b(Consider)18 b(the)60 488 y(fol)r(lowing)i(statements:)93 589 y(\(a\))k FQ(\010)18 b FP(and)f FQ(\010)364 571 y Fy(0)394 589 y FP(ar)n(e)f(physic)n(al)r(ly)i(e)n(quivalent)i(in)d(the)h(DLR)f(sense.) 95 691 y(\(b\))25 b FQ(\005)219 673 y FH(\010)260 691 y FQ(=)14 b(\005)349 673 y FH(\010)374 661 y Ft(0)387 691 y FP(,)j(i.e.)h(the)g(sp)n(e) n(ci\014c)n(ations)g(for)e FQ(\010)i FP(and)g FQ(\010)1138 673 y Fy(0)1167 691 y FP(c)n(oincide.)60 793 y(Then)25 b(\(a\))e FQ(=)-8 b FE(\))24 b FP(\(b\).)42 b(Mor)n(e)n(over,)24 b(if)g FF(\026)825 775 y FH(0)845 793 y FQ(\()p FF(U)5 b FQ(\))27 b FF(>)e FQ(0)g FP(for)e(every)i(op)n(en)f(set)g FF(U)31 b FE(\032)26 b FQ(\012)p FP(,)1662 775 y FH(24)1725 793 y FP(and)e(the)60 853 y(inter)n(actions)18 b FQ(\010)g FP(and)f FQ(\010)509 835 y Fy(0)539 853 y FP(ar)n(e)g(c)n(ontinuous,)h(then)g(\(b\))g FQ(=)-8 b FE(\))17 b FP(\(a\).)60 967 y FM(Corollary)h(2.18)g (\(Gri\016ths{Ruelle\))k FP(L)n(et)17 b FQ(\010)g FP(and)h FQ(\010)1149 949 y Fy(0)1178 967 y FP(b)n(e)g(uniformly)f(c)n(onver)n(gent,)i (c)n(ontinu-)60 1027 y(ous,)e FF(\026)192 1009 y FH(0)212 1027 y FP(-admissible)h(inter)n(actions;)g(and)f(assume)g(that)g FF(\026)1137 1009 y FH(0)1157 1027 y FQ(\()p FF(U)5 b FQ(\))14 b FF(>)g FQ(0)j FP(for)f(every)i(op)n(en)f(set)g FF(U)i FE(\032)14 b FQ(\012)p FP(.)60 1088 y(If)23 b(ther)n(e)f(exists)i(a)f(me)n(asur)n(e)f FF(\026)h FP(that)g(is)g(Gibbsian)h(for)e(b)n(oth)h FQ(\010)g FP(and)g FQ(\010)1432 1070 y Fy(0)1444 1088 y FP(,)h(then)g FQ(\010)f FP(and)g FQ(\010)1790 1070 y Fy(0)1825 1088 y FP(ar)n(e)60 1148 y(physic)n(al)r(ly)d(e)n(quivalent)i(in)e(the)h(DLR)e(sense,)i(and)f FQ(\005)1063 1130 y FH(\010)1109 1148 y FQ(=)e(\005)1202 1130 y FH(\010)1227 1118 y Ft(0)1260 1148 y FP([henc)n(e)j FQ(\010)f FP(and)g FQ(\010)1599 1130 y Fy(0)1631 1148 y FP(have)h(exactly)60 1208 y(the)d(same)f(Gibbs)h(me)n(asur)n(es].)133 1322 y FQ(There)e(are)h(sev) o(eral)e(w)o(a)o(ys)i(to)f(deal)h(with)f(the)g(am)o(biguit)o(y)e(caused)j(b)o (y)f(ph)o(ysical)f(equiv)m(alence.)60 1382 y(One)k(w)o(a)o(y)f(is)h(to)g (select)f(a)i(single)e(\\preferred")h(represen)o(tativ)o(e)e(from)h(eac)o(h)g (class)h(of)h(ph)o(ysically)60 1443 y(equiv)m(alen)o(t)h(in)o(teractions:)34 b(in)23 b(the)g(Ising)f(mo)q(del)g(this)h(is)g(exempli\014e)o(d)e(b)o(y)h (the)h(p)q(ossibilit)o(y)f(of)60 1503 y(using)e(\\spin")g(in)o(teractions)f (\010)649 1510 y FD(A)697 1503 y FQ(=)h FE(\000)p FF(J)821 1510 y FD(A)849 1503 y FF(\033)879 1485 y FD(A)927 1503 y FQ(or)g (\\lattice-gas")g(in)o(teractions)f(\010)1578 1510 y FD(A)1626 1503 y FQ(=)h FE(\000)p FF(J)1750 1510 y FD(A)1778 1503 y FF(\032)1803 1485 y FD(A)1851 1503 y FE(\021)60 1576 y(\000)p FF(J)126 1583 y FD(A)163 1528 y Fx(\020)192 1556 y FH(1+)p FD(\033)p 192 1564 67 2 v 217 1593 a FH(2)264 1528 y Fx(\021)288 1539 y FD(A)338 1576 y FQ([206)q(,)h(351)q(];)i(and)f(more)e(generally)g(it)h(is)g (exempli\014ed)d(b)o(y)j(the)g(concepts)g(of)h(\\)p FF(\013)p FQ(-)60 1642 y(normalized")16 b(in)o(teractions)h(and)h(\\gas")h(in)o (teractions)e([157,)h(Sections)f(2.3)h(and)g(2.4].)24 b(Ho)o(w)o(ev)o(er,)60 1703 y(for)18 b(in)o(teractions)e(whic)o(h)h(are)h(not)g(\014nite-range,)f (this)h(approac)o(h)g(can)f(giv)o(e)g(rise)g(to)h(con)o(v)o(ergence)60 1763 y(problems)d([351)q(].)133 1823 y(The)22 b(other)h(approac)o(h)g(is)f (to)h(accept)f(the)g(am)o(biguit)o(y)e(as)j(inevitable,)e(and)i(to)g(w)o(ork) f(with)60 1883 y FP(e)n(quivalenc)n(e)j(classes)j FQ(of)23 b(in)o(teractions)e(mo)q(dulo)h(ph)o(ysical)g(equiv)m(alence.)38 b(W)l(e)22 b(shall)g(tak)o(e)g(this)60 1943 y(latter)h(approac)o(h.)44 b(The)24 b(k)o(ey)e(result)i(here)f(is)g(Corollary)h(2.18,)i(due)d (originally)g(\(alb)q(eit)g(in)h(a)60 2003 y(v)o(ery)16 b(sligh)o(tly)f(w)o (eak)o(er)h(form\))g(to)h(Gri\016ths)f(and)i(Ruelle)d([174)q(].)22 b(This)17 b(result)f(has)i(an)f(imp)q(ortan)o(t)60 2064 y(consequence)d(for)h (the)g(renormalization)e(group:)21 b(it)15 b(sho)o(ws)g(that)h(the)e(do)o(wn) o(w)o(ard)h(v)o(ertical)e(arro)o(w)60 2124 y(in)k(\(1.2\))h(cannot)g(b)q(e)g (a)g(m)o(ulti-v)m(alued)d(map,)h(pro)o(vided)h(that)h(w)o(e)f(in)o(terpret)f FF(H)1542 2106 y Fy(0)1571 2124 y FQ(as)i(standing)h(for)60 2184 y(an)e(equiv)m(alence)d(class)j(of)f(in)o(teractions)g(mo)q(dulo)f(ph)o (ysical)h(equiv)m(alence.)133 2244 y(T)l(o)c(a)o(v)o(oid)f(trivialities,)f FP(we)k(assume)f(henc)n(eforth)h(that)f FF(\026)1156 2226 y FH(0)1176 2244 y FQ(\()p FF(U)5 b FQ(\))14 b FF(>)g FQ(0)f FP(for)g(every)g(op)n(en)g(set)h FF(U)19 b FE(\032)14 b FQ(\012)p FP(.)p 60 2291 732 2 v 100 2345 a FA(24)135 2360 y Fz(This)f(means,)f (roughly)h(sp)q(eaking,)g(that)h(ev)o(ery)g(con\014guration)f(in)g(\012)g(is) h(\\p)q(ossible".)j(If)c(it)g(w)o(ere)i(not)e(so,)g(then)60 2409 y(the)18 b Fw(true)j Fz(con\014guration)c(space)i(w)o(ould)e(b)q(e)h(a)g (prop)q(er)g(closed)h(subset)g Fv(F)k Fz(=)1318 2378 y Fx(Q)1357 2422 y Fp(x)p Fo(2L)1430 2409 y Fz(supp)q Fv(\026)1541 2415 y FA(0)p Fp(x)1596 2409 y Fu(\032)18 b Fz(\012.)30 b(W)m(e)17 b(could)60 2459 y(then)d(mak)o(e)d(the)j(condition)e(hold)h(simply)e(b)o(y)h (rede\014ning)i(the)g(con\014guration)e(space)j(to)d(b)q(e)i Fv(F)19 b Fz(rather)13 b(than)h(\012.)j(So)60 2509 y(the)c(condition)g(means) f(simply)f(that)h(the)i(con\014guration)e(space)i(do)q(es)g(not)f(con)o(tain) f(an)o(y)h(\\useless)h(p)q(oin)o(ts".)j(Some)60 2559 y(suc)o(h)d(condition)g (is)f(needed)i(for)f(\(b\))g(=)-7 b Fu(\))13 b Fz(\(a\))h(to)g(hold,)e(b)q (ecause)k(the)e(in)o(teraction)g(\010)f(is)h(completely)e(arbitrary)i(at)60 2609 y(the)g(\\useless)i(p)q(oin)o(ts")d Fv(!)g Fu(2)e Fz(\012)e Fu(n)g Fv(F)d Fz(.)951 2784 y FQ(35)p eop %%Page: 36 36 bop 60 91 a FM(2.3.6)55 b(Structure)18 b(of)h(the)f(Space)h FE(G)s FQ(\(\005\))60 184 y(Ph)o(ysical)f(systems)f(exhibit)h(in)g(general)h (one)g(or)g(more)e(p)q(ossible)i(\\macrostates")1601 166 y FH(25)1639 184 y FQ(,)g(dep)q(ending)60 244 y(on)k(the)g(v)m(alues)g(of)g (some)f(con)o(trol)g(parameters.)41 b(F)l(or)23 b(instance,)g(w)o(ater)g(can) g(b)q(e)g(in)g(a)g(liquid,)60 304 y(solid)18 b(or)g(gaseous)h(\\macrostate")f (dep)q(ending)g(on)g(temp)q(erature)f(and)h(pressure;)g(and)h(there)e(are)60 364 y(p)q(oin)o(ts)e(on)g(the)f(temp)q(erature-pressure)g(phase)h(diagram)f (where)g(t)o(w)o(o)g(or)h(ev)o(en)e(all)i(three)e(of)i(these)60 424 y(\\macrostates")i(are)f(p)q(ossible.)133 485 y(The)i(ph)o(ysical)f (relev)m(ance)f(of)i(the)f(theory)h(dev)o(elop)q(ed)f(in)g(the)g(preceding)g (subsections)h(relies)60 545 y(on)j(the)f(assumption)g(that)g(for)h(eac)o(h)e (ph)o(ysical)h(system)e(there)i(exists)g(a)g(sp)q(eci\014cation)g(\005)g (from)60 605 y(whic)o(h)i(all)g(the)g(statistical-mec)o(hanical)e (information)h(ab)q(out)j(the)e(system)f(can)i(b)q(e)f(obtained:)60 665 y(that)i(is,)i(suc)o(h)d(that)i(the)e(space)h FE(G)s FQ(\(\005\))f(of)i (measures)e(consisten)o(t)g(with)h(\005)f(describ)q(es)h(all)f(the)60 725 y(\\macrostates")18 b(of)g(the)g(ph)o(ysical)e(system)h(that)h(are)g(p)q (ossible)f(for)h(the)g(giv)o(en)f(c)o(hoice)f(of)i(con)o(trol)60 786 y(parameters.)h(Therefore,)13 b(w)o(e)g(m)o(ust)g(b)q(e)g(able)g(to)h (transcrib)q(e)g(all)e(the)i(exp)q(ected)e(prop)q(erties)i(of)f(the)60 846 y(set)i(of)g(these)g(\\macrostates")h(in)e(terms)g(of)h(prop)q(erties)g (of)h(the)f(space)g FE(G)s FQ(\(\005\).)20 b(W)l(e)15 b(brie\015y)f(discuss) 60 906 y(here)j(this)h(transcription.)26 b(In)18 b(consistency)f(with)g(our)i (main)d(message)h(that)i(not)f(ev)o(erything)e(in)60 966 y(the)22 b(w)o(orld)f(is)h(Gibbsian,)h FP(everything)h(in)f(this)g(subse)n(ction)h (holds)e(for)g(gener)n(al)i(sp)n(e)n(ci\014c)n(ations)t FQ(,)60 1026 y(whic)o(h)f(need)h(not)g(b)q(e)g(Gibbsian.)45 b(\(This)24 b(generalit)o(y)e(will)h(also)h(b)q(e)g(useful)g(when)g(discussing)60 1087 y(statistical)15 b(mec)o(hanics)e(at)i(zero)g(temp)q(erature:)20 b(see)15 b(App)q(endix)f(B.2.1.\))20 b(Ho)o(w)o(ev)o(er,)14 b(for)h(the)g(sak)o(e)60 1147 y(of)k(brevit)o(y)d(and)j(familiarit)o(y)l(,)c (w)o(e)j(will)f(sometimes)e(refer)j(to)g(the)g(measures)g(consisten)o(t)f (with)h(\005)60 1207 y(as)h(the)f(\\Gibbs)i(measures")e(for)g(\005)h(|)f (whic)o(h)g(is)g(a)h(sligh)o(t)f(abuse)h(of)g(language)g(when)g(\005)f(is)h (not)60 1267 y(Gibbsian.)133 1327 y(There)d(are)h(t)o(w)o(o)f(imp)q(ortan)o (t)f(prop)q(erties)i(that)f(c)o(haracterize)f(the)h(macroscopic)f(systems)g (ob-)60 1388 y(serv)o(ed)h(in)h(nature.)24 b(Firstly)l(,)16 b(these)h(systems)f(in)o(v)o(olv)o(e)f(a)j(h)o(uge)f(n)o(um)o(b)q(er)e(of)j (degrees)f(of)g(freedom,)60 1448 y(so)d(large)e(that)i(only)e(a)i (statistical)e(description)g(is)h(p)q(ossible.)20 b(Ho)o(w)o(ev)o(er,)11 b(these)i(statistical)f(asp)q(ects)60 1508 y(do)j(not)h(manifest)d(themselv)o (es)f(at)k(a)f(macroscopic)f(lev)o(el:)k(that)d(is,)g FP(macr)n(osc)n(opic)g (observables)j(do)60 1568 y(not)g(\015uctuate)t FQ(;)g(the)e(system)g(b)q (eha)o(v)o(es)g(deterministicall)o(y)e(with)i(resp)q(ect)h(to)g(them.)k(The)c (second)60 1628 y(prop)q(ert)o(y)k(refers)f(to)h(the)f(microscopic)f(observ)m (ables:)30 b(they)20 b(do)h(\015uctuate,)h(but)e(their)g(\015uctua-)60 1688 y(tions)e(are)f(only)g(lo)q(cal,)g(not)h(a\013ecting)g(large)f(regions.) 25 b(Equiv)m(alen)o(tly)l(,)15 b FP(lo)n(c)n(al)k(observations)g(made)60 1749 y(far)e(away)g(one)h(fr)n(om)e(the)i(other)g(ar)n(e)f(almost)g(indep)n (endent)5 b FQ(.)133 1809 y(T)l(o)14 b(translate)h(these)e(prop)q(erties)h (in)o(to)f(precise)g(mathematical)e(statemen)o(ts,)h(w)o(e)h(need)h(\014rst)g (to)60 1869 y(sp)q(ecify)g(what)h(a)g(macroscopic)f(observ)m(able)g(is.)21 b(As)14 b(is)h(usual)g(with)f(long-used)i(concepts,)e(there)g(is)60 1929 y(more)f(than)h(one)g(p)q(ossible)g(meaning.)19 b(Some)13 b(p)q(eople)g(consider)h(a)g(macroscopic)f(observ)m(able)h(to)g(b)q(e)60 1989 y(an)o(y)k(translation-in)o(v)m(arian)o(t)h(measurable)e(function.)28 b(A)o(t)17 b(this)i(p)q(oin)o(t,)f(ho)o(w)o(ev)o(er,)f(w)o(e)h(w)o(ould)h (lik)o(e)60 2050 y(to)d(remain)f(at)h(a)h(general)e(lev)o(el,)f(lea)o(ving)h (the)h(asp)q(ects)g(related)g(to)g(translation-in)o(v)m(ariance)g(un)o(til)60 2110 y(the)k(next)h(section.)33 b(So)22 b(w)o(e)e(adopt)h(an)g(alternativ)o (e)f(de\014nition,)h(whic)o(h)e(corresp)q(onds)j(to)f(what)60 2170 y(could)16 b(b)q(e)h(called)f(\\global")h(observ)m(ables,)g(namely)e (observ)m(ables)h(that)h(do)h(not)f(dep)q(end)f(on)h(what)60 2230 y(happ)q(ens)i(to)f(\014nitely)f(man)o(y)g(spins.)27 b(Recall)16 b(that)j(if)e(\003)h(is)g(a)g(\014nite)g(subset)g(of)h(the)e(lattice,)g(then) 60 2290 y FE(F)96 2297 y FH(\003)120 2288 y Fs(c)159 2290 y FQ(is)j(the)g FF(\033)r FQ(-\014eld)f(consisting)i(of)f(all)g(ev)o(en)o(ts)f (that)i(are)f(measurable)f(b)o(y)h(observ)m(ations)h(made)p 60 2334 732 2 v 100 2388 a FA(25)135 2403 y Fz(These)g(\\macrostates")e(are)h (also)f(referred)i(to)e(as)h(\\phases")g(in)f(the)h(c)o(hemical)e(and)i(ph)o (ysical)f(literature.)60 2453 y(Here,)e(follo)o(wing)c(an)i(established)i (mathematical)o(-ph)o(ysics)c(nomenclature,)i(w)o(e)h(reserv)o(e)i(the)e(w)o (ord)g(\\phase")f(for)60 2503 y(the)d(notion)f(of)g(\\pure)h(phase",)g(to)f (b)q(e)h(de\014ned)g(in)f(Section)h(2.4.9)e(b)q(elo)o(w.)17 b(F)m(or)11 b(this)h(informal)c(discussion)k(w)o(e)g(prefer)60 2552 y(to)j(use)h(the)g(w)o(ord)f(\\macrostate",)f(but)h(k)o(eeping)g(the)h (quotation)e(marks)g(to)h(emphasize)g(the)h(informalit)o(y)c(of)i(the)60 2602 y(concept.)25 b(W)m(e)16 b(do)f(not)h(w)o(an)o(t)g(to)f(get)i(en)o (tangled)f(with)f(the)i(man)o(y)d(di\013eren)o(t)i(senses)i(adopted)f(in)e (the)h(literature)60 2652 y(for)e(the)g(w)o(ord)g(\\state".)951 2784 y FQ(36)p eop %%Page: 37 37 bop 60 91 a FQ(solely)13 b FP(outside)19 b FQ(\003;)14 b(that)h(is,)f(they)g (are)g(the)g(ev)o(en)o(ts)f(that)i(do)g(not)f(dep)q(end)h(on)f(the)g(b)q(eha) o(vior)h(of)f(the)60 152 y(spins)k(inside)f(\003.)25 b(No)o(w)17 b(consider)g(the)h(ev)o(en)o(ts)e(that)i(b)q(elong)g(to)g FE(F)1296 159 y FH(\003)1320 150 y Fs(c)1356 152 y FQ(for)g FP(every)h(\014nite)k FQ(subset)18 b(\003:)60 212 y(these)e(ev)o(en)o(ts)f(constitute)h(a)g FF(\033)r FQ(-\014eld)813 306 y Fx(b)798 322 y FE(F)834 329 y Fy(1)899 322 y FE(\021)979 280 y Fx(\\)966 372 y FH(\003)p Fy(2S)1046 322 y FE(F)1082 329 y FH(\003)1106 320 y Fs(c)1138 322 y FF(;)613 b FQ(\(2)p FF(:)p FQ(31\))60 467 y(whic)o(h)19 b(consists)g(of)h(all)f(those)h(ev)o(en)o(ts)e(whose)i(de\014nition)f(is)g (not)h(a\013ected)f(b)o(y)g(c)o(hanges)g(on)h(an)o(y)60 527 y(\014nite)e(n)o(um)o(b)q(er)g(of)h(spins.)30 b(This)19 b(\014eld)f(is)h (usually)g(called)f(in)g(mathematics)f(the)h FP(tail)j(\014eld)5 b FQ(,)20 b(and)60 587 y(could)13 b(b)q(e)g(though)o(t)g(as)h FP(the)h(\014eld)g(of)f(glob)n(al)i(events)t FQ(.)22 b(The)13 b(functions)g(measurable)e(with)i(resp)q(ect)g(to)60 647 y(this)i(\014eld)f (are)h(called)f FP(observables)k(at)e(in\014nity)g FQ(and)f(can)g(b)q(e)h(in) o(terpreted)d(as)i FP(glob)n(al)j(observables)t FQ(.)133 757 y FM(Examples)i(of)i(global)g(observ)m(ables.)30 b FQ(1.)g(All)18 b(\\macroscopic)h(a)o(v)o(erages",)h(for)f(instance)60 818 y(observ)m(ables)e(of)f(the)g(form)p 441 923 30 2 v 441 962 a FF(f)33 b FE(\021)564 875 y Fx(8)564 912 y(<)564 987 y(:)622 911 y FQ(lim)609 936 y FD(n)p Fy(!1)710 911 y FE(j)p FQ(\003)758 918 y FD(n)781 911 y FE(j)795 893 y Fy(\000)p FH(1)873 878 y Fx(P)850 949 y FD(x)p Fy(2)p FH(\003)918 953 y Fs(n)948 911 y FF(f)5 b FQ(\()p FF(!)1026 918 y FD(x)1048 911 y FQ(\))49 b(if)16 b(the)g(limit)d(exists)609 1015 y(0)k(\(or)g(whatev)o(er\))175 b(otherwise)1765 962 y(\(2)p FF(:)p FQ(32\))60 1119 y(where)11 b(\(\003)249 1126 y FD(n)272 1119 y FQ(\))g(is)f(a)i(suitable)e(increasing)h (sequence)e(of)i(\014nite)g(subsets)g(of)g FE(L)h FQ(whic)o(h)e(together)h (exhaust)60 1179 y FE(L)h FQ(\(w)o(e)f(will)g(discuss)g(this)h(further)f(in)h (Section)f(2.4.1\),)h(and)g FF(f)5 b FQ(:)j(\012)1228 1186 y FH(0)1262 1179 y FE(!)14 b Fq(R)e FQ(is)f(a)h(measurable)f(function.)60 1240 y(A)20 b(macroscopic)e(a)o(v)o(erage)i(as)g(in)g(\(2.32\))h(is)e(ob)o (viously)h(una\013ected)g(b)o(y)f(altering)h(\014nitely)e(man)o(y)60 1300 y(spins,)e(so)p 256 1260 V 17 w FF(f)22 b FQ(is)16 b(indeed)f(an)i (observ)m(able)f(at)h(in\014nit)o(y)l(.)133 1360 y(2.)22 b(In)16 b(an)g(Ising)h(mo)q(del,)d(consider)358 1523 y FF(g)r FQ(\()p FF(!)r FQ(\))28 b(=)547 1424 y Fx(8)547 1461 y(>)547 1473 y(<)547 1548 y(>)547 1561 y(:)592 1460 y FQ(1)49 b(if)16 b(there)f(exists)h(an)h (in\014nite)e(connected)h(cluster)714 1520 y(of)g(+)g(spins)592 1597 y(0)49 b(otherwise)1765 1523 y(\(2)p FF(:)p FQ(33\))60 1687 y(The)20 b(existence)f(of)i(an)g(in\014nite)e(cluster)h(is)g(ob)o (viously)g(una\013ected)g(b)o(y)g(altering)g(\014nitely)f(man)o(y)60 1747 y(spins,)d(so)h FF(g)i FQ(is)d(indeed)f(an)i(observ)m(able)g(at)g (in\014nit)o(y)l(.)j(\(This)c(observ)m(able)h(is)f(of)h(particular)f(imp)q (or-)60 1807 y(tance)g(in)g(p)q(ercolation)g(theory)l(.\))133 1867 y(3.)33 b(In)20 b(an)h(Ising)f(mo)q(del,)f(consider)h(the)f FP(di\013er)n(enc)n(e)25 b FQ(in)19 b(magnetization)g(b)q(et)o(w)o(een)g(the) h(ev)o(en)60 1927 y(and)d(o)q(dd)g(sublattices:)p 349 2029 60 2 v 349 2068 a FE(M)409 2075 y FD(stag)q(g)522 2068 y FE(\021)589 1981 y Fx(8)589 2019 y(<)589 2093 y(:)646 2027 y FQ(lim)634 2052 y FD(n)p Fy(!1)734 2027 y FE(j)p FQ(\003)782 2034 y FD(n)806 2027 y FE(j)820 2009 y Fy(\000)p FH(1)898 1993 y Fx(P)875 2065 y FD(x)p Fy(2)p FH(\003)943 2069 y Fs(n)964 2027 y FQ(\()p FE(\000)p FQ(1\))1065 2009 y Fy(j)p FD(x)p Fy(j)1115 2027 y FF(!)1145 2034 y FD(x)1216 2027 y FQ(if)f(the)g(limit)d(exists)634 2128 y(0)558 b(otherwise)1765 2068 y(\(2)p FF(:)p FQ(34\))60 2222 y(where)16 b(\(\003)254 2229 y FD(n)277 2222 y FQ(\))g(is)g(as)h(b)q (efore.)22 b(This)16 b(also)h(is)f(ob)o(viously)g(an)g(observ)m(able)h(at)f (in\014nit)o(y)l(.)133 2332 y(Th)o(us,)i(the)f(usual)g(macroscopic)f (measuremen)o(ts)e(p)q(erformed)i(on)i(real)f(systems)f(corresp)q(ond)60 2392 y(to)h(global)h(observ)m(ables,)f(but)g(the)g(con)o(v)o(erse)f(is)h(not) h(true:)k(as)c(Example)d(3)j(illustrates,)e(our)i(con-)60 2452 y(cept)d(of)g(\\global)i(observ)m(ables")f(includes)e(some)g(quan)o(tities)h (that)g(are)h(exp)q(erimen)o(tall)o(y)c(not)k(v)o(ery)60 2513 y(accessible.)j(F)l(or)13 b(example,)e(in)i(the)g(an)o(tiferromagnetic)e (Ising)i(mo)q(del,)f(the)h(sign)h(of)f(the)g(staggered)60 2573 y(magnetization)k(is)g(an)i(observ)m(able)f(at)g(in\014nit)o(y)l(,)e(whic)o (h)i(detects)f(whic)o(h)g(of)h(the)g(t)o(w)o(o)g(sublattices)60 2633 y(is)h(p)q(ositiv)o(ely)f(magnetized)g(and)i(whic)o(h)e(is)h(negativ)o (ely)f(magnetized.)29 b(But)19 b(it)g(is)g(v)o(ery)f(unlik)o(ely)951 2784 y(37)p eop %%Page: 38 38 bop 60 91 a FQ(that)16 b(an)g(exp)q(erimen)o(ter)d(could)i(succeed)g(in)g (reliably)f(lab)q(elling)h(the)h(t)o(w)o(o)f(sublattices,)g(m)o(uc)o(h)e (less)60 152 y(in)j(measuring)f(separately)h(their)g(magnetizations.)133 262 y(After)h(the)g(previous)g(discussion,)g(w)o(e)g(can)g(no)o(w)h(state)f (more)f(precisely)g(whic)o(h)g(prop)q(erties)i(a)60 322 y(measure)h FF(\026)i FQ(represen)o(ting)e(a)i(\\macrostate")f(of)h(a)g(ph)o(ysical)e (system)g(m)o(ust)g(ha)o(v)o(e:)29 b(\(i\))19 b(It)h(m)o(ust)60 382 y(b)q(e)i(deterministic)d(on)j(global)g(ev)o(en)o(ts,)g(that)g(is)g FF(\026)p FQ(\()p FF(A)p FQ(\))g(can)g(only)g(tak)o(e)f(the)h(v)m(alues)g(0)g (or)g(1)h(for)60 442 y(an)c(ev)o(en)o(t)f FF(A)g FE(2)383 426 y Fx(b)368 442 y FE(F)404 449 y Fy(1)441 442 y FQ(;)i(and)g(\(ii\))e(its)g (exp)q(ectation)h(for)g(spatially)f(distan)o(t)h(ev)o(en)o(ts)f(m)o(ust,)f (in)i(some)60 502 y(sense,)j(asymptotically)d(factorize)h(\(=)h(short-range)h (correlations)f(=)g(\(some)f(t)o(yp)q(e)g(of)s(\))i(cluster)60 562 y(prop)q(ert)o(y\).)f(It)16 b(turns)h(out)f(that)h(these)f(t)o(w)o(o)g (prop)q(erties)g(are)h(equiv)m(alen)o(t:)60 664 y FM(Prop)r(osition)h(2.19)24 b FP(L)n(et)17 b FF(\026)d FE(2)g FF(M)708 671 y FH(+1)755 664 y FQ(\(\012\))p FP(.)23 b(Then)18 b(the)g(fol)r(lowing)i(pr)n(op)n (erties)c(ar)n(e)h(e)n(quivalent:)93 766 y(\(a\))24 b FF(\026)18 b FP(has)f(trivial)h(tail)g(\014eld,)g(that)g(is,)f(if)g FF(A)d FE(2)991 750 y Fx(b)977 766 y FE(F)1013 773 y Fy(1)1067 766 y FP(then)19 b FF(\026)p FQ(\()p FF(A)p FQ(\))e FP(e)n(quals)h(either)g(0)f (or)g(1.)95 868 y(\(b\))25 b FF(\026)18 b FP(has)f(short-r)n(ange)g(c)n(orr)n (elations,)g(that)h(is,)f(for)g(e)n(ach)h FF(A)13 b FE(2)h(F)22 b FP(we)d(have)619 978 y FQ(lim)609 1014 y FH(\003)11 b Fy(")e(L)607 1056 y FH(\003)h Fy(2)f(S)748 978 y FQ(sup)727 1017 y FD(B)r Fy(2F)805 1023 y Fr(\003)826 1016 y Fs(c)851 978 y FE(j)p FF(\026)p FQ(\()p FF(A)i FE(\\)g FF(B)s FQ(\))g FE(\000)g FF(\026)p FQ(\()p FF(A)p FQ(\))p FF(\026)p FQ(\()p FF(B)s FQ(\))p FE(j)27 b FQ(=)h(0)14 b FF(:)270 b FQ(\(2)p FF(:)p FQ(35\))60 1185 y(Prop)q(ert)o(y)21 b(\(a\))g(states,)i(roughly)e(sp)q(eaking,)h(that)g(all)e(the)h(observ)m (ables)g(at)h(in\014nit)o(y)e(\(=)h(global)60 1245 y(observ)m(ables\))j(tak)o (e)g(a)g(constan)o(t)h(v)m(alue)f(from)f(the)h(p)q(oin)o(t)g(of)g(view)g(of)g (the)g(measure)f FF(\026)p FQ(.)45 b(F)l(or)60 1305 y(instance,)15 b(the)h(fact)g(that)h(all)e(the)h(sets)h(of)f(the)g(form)f FE(f)p FF(!)h FE(2)e FQ(\012:)p 1225 1266 30 2 v 8 w FF(f)5 b FQ(\()p FF(!)r FQ(\))14 b FE(2)g FF(B)s FE(g)i FQ(ha)o(v)o(e)f(measure)g (either)60 1366 y(0)22 b(or)h(1)f(means)f(that)i(there)e(is)h(a)g(precise)f (v)m(alue)h FF(f)1038 1373 y FD(\026)1083 1366 y FQ(suc)o(h)g(that)p 1311 1326 V 23 w FF(f)29 b FQ(=)23 b FF(f)1449 1373 y FD(\026)1495 1366 y FQ(with)e FF(\026)p FQ(-probabilit)o(y)60 1426 y(1.)35 b(Prop)q(ert)o(y)20 b(\(b\))h(is)f(a)h(strong)h(\\cluster)e(prop)q(ert)o(y":) 31 b(it)20 b(states)h(that)g(distan)o(t)f(regions)h(of)g(the)60 1486 y(lattice)f(are)h(asymptotically)e(indep)q(enden)o(t)i(\(ev)o(en)f(if)g (one)i(of)f(the)g(regions)h(in)o(v)o(olv)o(es)d(in\014nitely)60 1546 y(man)o(y)c(spins\),)h FP(uniformly)k FQ(in)c(the)g(observ)m(able)h (measured)e(in)g(the)h(second)h(region.)133 1606 y(No)o(w)i(\014x)h(a)g(sp)q (eci\014cation)f(\005,)g(and)h(let)f(us)h(consider)f(the)g(structure)g(of)h (the)f(set)g FE(G)s FQ(\(\005\).)30 b(W)l(e)60 1667 y(kno)o(w)18 b(that)f FE(G)s FQ(\(\005\))g(is)g(a)h FP(c)n(onvex)25 b FQ(set,)17 b(so)h(it)f(is)h(natural)f(to)h(ask)g(what)g(are)g(its)f(extreme)e(p)q(oin)o (ts.)1853 1648 y FH(26)60 1727 y FQ(The)h(answ)o(er)h(is:)60 1828 y FM(Prop)r(osition)h(2.20)24 b FP(L)n(et)17 b FF(\026)d FE(2)g(G)s FQ(\(\005\))p FP(.)22 b(Then)c(the)g(fol)r(lowing)h(pr)n(op)n (erties)d(ar)n(e)h(e)n(quivalent:)93 1930 y(\(a\))24 b FF(\026)18 b FP(is)f(an)h(extr)n(eme)g(p)n(oint)f(of)h FE(G)s FQ(\(\005\))p FP(.)95 2032 y(\(b\))25 b FF(\026)18 b FP(has)f(trivial)h(tail)g(\014eld.)95 2134 y(\(c\))25 b FF(\026)18 b FP(has)f(short-r)n(ange)g(c)n(orr)n(elations.) 133 2235 y FQ(The)24 b(upshot)g(of)f(the)h(preceding)e(discussion)i(is)f (that)h(the)f(\\macrostates")h(of)f(a)h(ph)o(ysical)60 2295 y(system)14 b(describ)q(ed)h(b)o(y)f(a)i(certain)f(sp)q(eci\014cation)g (corresp)q(ond)h(to)g(the)f FP(extr)n(emal)i(Gibbs)g(me)n(asur)n(es)60 2356 y FQ(for)12 b(this)g(sp)q(eci\014cation.)20 b(What)12 b(is)g(the)g(in)o(terpretation)f(of)h(the)g(non-extremal)f(measures)g(of)h FE(G)s FQ(\(\005\)?)60 2416 y(F)l(or)17 b(\\nice")g(con)o(v)o(ex)f(sets,)h (ev)o(ery)e(p)q(oin)o(t)i(in)g(the)g(set)g(can)g(b)q(e)g(represen)o(ted)f(as) i(the)f(barycen)o(ter)f(of)60 2476 y(a)h(probabilit)o(y)e(measure)g(concen)o (trated)g(on)i(the)f(extreme)d(p)q(oin)o(ts)k(\(this)e(is)h(a)h(kind)f(of)g (\\in)o(tegral")p 60 2522 732 2 v 100 2576 a FA(26)135 2591 y Fz(W)m(e)11 b(recall)h(that)g(the)g(extreme)h(p)q(oin)o(ts)e(of)h(a)f(con)o (v)o(ex)h(set)h(are)f(those)h(that)f(cannot)g(b)q(e)h(written)f(as)g(a)g (non-trivial)60 2641 y(con)o(v)o(ex)i(com)o(bination)d(of)j(other)g(p)q(oin)o (ts)g(in)f(the)i(set.)951 2784 y FQ(38)p eop %%Page: 39 39 bop 60 91 a FQ(con)o(v)o(ex)15 b(com)o(bination\).)21 b(It)c(turns)g(out)g (that)g FE(G)s FQ(\(\005\))f FP(is)21 b FQ(nice)15 b(in)i(this)f(sense.)1468 73 y FH(27)1528 91 y FQ(Th)o(us,)h(ev)o(ery)e(non-)60 152 y(extremal)10 b(measure)g(in)i FE(G)s FQ(\(\005\))f(is)h(an)h(\(in)o(tegral\))e(con)o(v)o (ex)g(com)o(bination)f(of)j(extremal)c(ones.)21 b(In)12 b(fact,)60 212 y(a)g(deep)f(result)g(\([299)q(,)h(Theorem)e(2.2],)i([157,)g(Theorem)f (7.26]\))g(states)h(that)g(this)g(decomp)q(osition)e(is)60 272 y FP(unique)t FQ(,)k(that)e(is,)g(that)g FE(G)s FQ(\(\005\))f(is)h(a)g FP(simplex)6 b FQ(.)21 b(These)12 b(results)f(mean,)g(in)h(exp)q(erimen)o (tal)d(terms,)i(that)60 332 y(a)20 b(non-extremal)d(Gibbs)j(measure)e (corresp)q(onds)i(simply)d(to)j(the)f(preparation)h(of)f(a)h(randomly)60 392 y(c)o(hosen)i(extremal)e(Gibbs)i(measure.)38 b(The)22 b(probabilities)g (for)g(this)g(c)o(hoice)f(are)h(giv)o(en)g(b)o(y)f(the)60 452 y(\\co)q(e\016cien)o(ts")14 b(of)h(the)g(con)o(v)o(ex)e(com)o(bination.)19 b(This)c(extra)g(randomness)f(can)h(b)q(e)g(in)o(terpreted)e(as)60 513 y(represen)o(ting)d(ignorance)i(on)f(the)g(part)h(of)f(the)g(exp)q (erimen)o(ter)d(ab)q(out)13 b(the)d(system's)g(\\macrostate")60 573 y(\(i.e.)18 b(o)o(v)o(er)h(and)h(ab)q(o)o(v)o(e)g(his/her)g(una)o(v)o (oidable)f(ignorance)h(ab)q(out)i(its)d(microstate\).)31 b(F)l(rom)18 b(this)60 633 y(p)q(oin)o(t)23 b(of)g(view,)g(the)f(ph)o(ysical)f(system)h (itself)f(can)i(alw)o(a)o(ys)f(b)q(e)h(considered)f(to)h(b)q(e)g(in)f(a)h(w)o (ell-)60 693 y(de\014ned)e(\\macrostate")f(describ)q(ed)h(b)o(y)f(an)h FP(extr)n(emal)27 b FQ(Gibbs)21 b(measure.)33 b(Th)o(us,)22 b(the)e(extremal)60 753 y(Gibbs)d(measures)e(are)h(the)g(\\pure")h(ph)o (ysical)e(ob)s(jects.)133 862 y(As)j(a)h(consequence)e(of)h(the)g(preceding)f (discussion,)i(w)o(e)e(conclude)h(that)g(the)g(cardinalit)o(y)f(of)60 922 y(the)e(set)g(of)h(extremal)d(measures)h(of)i FE(G)s FQ(\(\005\))e (represen)o(ts)h(the)g(n)o(um)o(b)q(er)f(of)h(ph)o(ysical)g(\\macrostates")60 982 y(a)o(v)m(ailable)g(to)h(the)f(system.)20 b(A)15 b(c)o(hange)h(in)f(this) g(n)o(um)o(b)q(er)f(as)i(the)g(con)o(trol)f(parameters)g(are)g(v)m(aried)60 1043 y(corresp)q(onds)f(to)g(a)g FP(phase)g(tr)n(ansition)j FQ(\(more)12 b(precisely)l(,)g(to)h FP(one)18 b FQ(of)13 b(the)g(notions)h (of)g(phase)g(transi-)60 1103 y(tion,)h(see)g(Section)g(2.6.5\);)g(and)h(the) f(v)m(ariation)h(of)f(this)g(n)o(um)o(b)q(er)f(as)i(a)g(function)f(of)g (these)g(con)o(trol)60 1163 y(parameters)i(\(temp)q(erature,)f(magnetic)g (\014eld,)h(c)o(hemical)e(p)q(oten)o(tial,)i(etc.\))f(can)i(b)q(e)g(recorded) f(in)60 1223 y(the)j(form)g(of)h(a)g FP(phase)h(diagr)n(am)t FQ(.)33 b(Therefore,)21 b(the)g(study)g(of)g(the)f(set)h(of)g(extremal)d (measures)60 1283 y(of)j FE(G)s FQ(\(\005\))e(is)i(a)g(cen)o(tral)e(problem)g (in)h(statistical)g(mec)o(hanics.)32 b(As)21 b(a)g(\014rst)f(step,)i(it)e(is) g(essen)o(tial)60 1344 y(to)c(determine)d(conditions)j(under)g(whic)o(h)f (the)g(set)h FE(G)s FQ(\(\005\))f(is)g FP(nonempty)t FQ(,)i(i.e.)d(under)i (whic)o(h)f(there)60 1404 y(exists)e(at)g(least)g(one)h(in\014nite-v)o(olume) c(Gibbs)j(measure.)19 b(Con)o(trary)14 b(to)f(what)h(one)g(migh)o(t)d (initially)60 1464 y(think,)i(this)g(is)g(a)g(non-trivial)g(problem,)f(since) g(there)h(exist)f(ph)o(ysically)f(quite)h(reasonable)i(mo)q(dels)60 1524 y(for)k(whic)o(h)e(there)h(are)h FP(no)i FQ(in\014nite-v)o(olume)15 b(Gibbs)i(measures.)24 b(The)17 b(t)o(ypical)f(examples)g(are)h(the)60 1584 y(short-range)f(massless)d(Gaussian)i(mo)q(dels)e(\(harmonic)g (crystals\))h(in)g(dimension)e FF(d)i FE(\024)g FQ(2,)h(and)f(the)60 1644 y(solid-on-solid)21 b(or)g(the)f(discrete)f(Gaussian)i(mo)q(dels)e(in)h FF(d)h FQ(=)g(1.)34 b(The)20 b(essen)o(tial)f(p)q(oin)o(t)i(here)e(is)60 1705 y(that)f(the)f(existence)f(of)i(Gibbs)g(measures)e(in)h(these)g(mo)q (dels)g(is)g(equiv)m(alen)o(t)f(to)i(the)f(breaking)h(of)60 1765 y(a)f(non-compact)f(symmetry)d(of)j(the)h(single-spin)f(space)g(\(the)g (shift)g(of)h(all)f(the)g(spin)g(v)m(alues)h(b)o(y)f(a)60 1825 y(constan)o(t\);)f(and,)g(as)h(is)e(w)o(ell)g(kno)o(wn,)g(it)g(is)h(imp)q (ossible)e(to)i(break)g(discrete)e(symmetrie)o(s)f(in)j FF(d)f FQ(=)g(1)60 1885 y(or)21 b(con)o(tin)o(uous)g(symmetries)d(in)j FF(d)h FE(\024)g FQ(2.)36 b(W)l(e)21 b(refer)f(to)i([157)q(,)g(Chapter)f(9])g (for)g(precise)g(state-)60 1945 y(men)o(ts,)13 b(references)h(and)i(further)f (examples.)k(In)14 b(an)o(y)i(case,)e(the)h(follo)o(wing)g(theorem)f (su\016ces)h(for)60 2006 y(virtually)g(all)h(applications)g(to)g(mo)q(dels)g (of)g FP(b)n(ounde)n(d)22 b FQ(spins:)60 2105 y FM(Prop)r(osition)c(2.21)24 b FP(L)n(et)17 b FQ(\012)h FP(b)n(e)f(a)h FQ(compact)e FP(metric)i(sp)n(ac)n (e,)f(and)h(let)g FQ(\005)c(=)f(\()p FF(\031)1530 2112 y FH(\003)1557 2105 y FQ(\))1576 2112 y FH(\003)p Fy(2S)1667 2105 y FP(b)n(e)18 b(a)f(F)l(el)r(ler)60 2165 y(sp)n(e)n(ci\014c)n(ation.)23 b(Then)18 b FE(G)s FQ(\(\005\))e FP(is)i(nonempty.)60 2265 y FQ(This)24 b(result)g(is,)h(in)f(fact,)h(an)f(immediate)d(consequence)i(of)h(Prop)q (osition)h(2.22)g(b)q(elo)o(w:)37 b(tak)o(e)60 2325 y(an)o(y)18 b(sequence)g(whatso)q(ev)o(er)h(of)g(b)q(oundary)h(conditions)e(\()p FF(\027)1173 2332 y FD(n)1197 2325 y FQ(\);)h(b)o(y)f(compactness,)g(the)g (sequence)60 2385 y(\()p FF(\027)103 2392 y FD(n)127 2385 y FF(\031)155 2392 y FH(\003)179 2396 y Fs(n)202 2385 y FQ(\))i(m)o(ust)f(ha)o (v)o(e)h(at)h(least)f(one)h(limit)c(p)q(oin)o(t)k FF(\026)p FQ(,)g(and)g(Prop)q(osition)h(2.22)f(then)f(guaran)o(tees)60 2446 y(that)d FF(\026)d FE(2)g(G)s FQ(\(\005\).)p 60 2491 732 2 v 100 2545 a FA(27)135 2560 y Fz(F)m(or)e(systems)g(of)g(b)q(ounded)h (spins)f(this)h(can)f(b)q(e)h(pro)o(v)o(en)g(b)o(y)f(app)q(ealing)f(to)h(the) h(Cho)q(quet)g(theorem)f([293)o(,)g(206)o(].)60 2610 y(F)m(or)17 b(general)h(systems)f(it)g(can)h(b)q(e)g(pro)o(v)o(en)f(through)g(direct)i (probabilistic)d(argumen)o(ts)h([299)n(,)h(pp.)f(24{32])f([157)n(,)60 2660 y(Section)e(7.3)f(and)h(the)g(asso)q(ciated)h(notes])f([107)o(].)951 2784 y FQ(39)p eop %%Page: 40 40 bop 133 91 a FQ(If)22 b(there)f(are)h(sev)o(eral)f(\\macrostates")h(a)o(v)m (ailable)g(to)g(the)g(system,)f(and)i(an)f(exp)q(erimen)o(ter)60 152 y(w)o(an)o(ts)f(to)h(select)e(a)h(particular)g(one)g(with)g(absolute)h (certain)o(t)o(y)l(,)e(ho)o(w)h(m)o(ust)f(he/she)h(pro)q(ceed?)60 212 y(There)16 b(are)h(basically)f(t)o(w)o(o)h(w)o(a)o(ys:)22 b(One)17 b(approac)o(h)g(is)g(to)g(add)g(to)g(the)g(Hamiltonian)e(some)h (addi-)60 272 y(tional)i(\014elds,)g(suc)o(h)f(that)i(an)f(in\014nitesimal)e (v)m(alue)h(of)i(these)e(\014elds)h(|)g(more)e(precisely)l(,)g(a)j(limit)60 332 y(pro)q(cess)14 b(consisting)g(in)f(turning)g(them)f(on)i(and)g(then)f (slo)o(wly)g(o\013)h(in)f(some)f(appropriate)i(sequence)60 392 y(|)19 b(selects)f(one)i(or)g(the)f(other)g(of)h(the)f(\\macrostates".)31 b(F)l(or)19 b(example,)f(in)h(an)g(Ising)h(mo)q(del)e(at)60 452 y(lo)o(w)e(temp)q(erature,)e(one)j(ma)o(y)d(add)j(to)f(the)g(Hamiltonian) f(a)h(magnetic)f(\014eld)h FF(h)p FQ(;)f(the)h(limits)e FF(h)g FE(#)g FQ(0)60 513 y(and)19 b FF(h)e FE(")g FQ(0)i(then)f(select)f(the)h (extremal)e(Gibbs)j(measures)e FF(\026)1209 520 y FH(+)1257 513 y FQ(and)i FF(\026)1383 520 y Fy(\000)1431 513 y FQ(of)g(the)f FP(zer)n(o-\014eld)24 b FQ(Ising)60 573 y(mo)q(del.)30 b(An)19 b(alternativ)o(e)f(approac)o(h)i(is)f(to)h(immerse)c(the)j(\(\014nite\))g (sample)f(in)h(a)h(con\014guration)60 633 y(t)o(ypical)d(of)i(the)g(in)o (tended)e(\\macrostate")i(\(selection)f(via)g(b)q(oundary)i(conditions\).)28 b(F)l(or)19 b(exam-)60 693 y(ple,)c(in)h(the)g(Ising)g(case)g(w)o(e)f(could)h (use)g(b)q(oundary)i(conditions)e(in)g(whic)o(h)f(the)h(spins)g(outside)g (the)60 753 y(v)o(olume)g(\003)i(are)g(\014xed)g(to)h(b)q(e)f(all)g(+)g(or)h (all)f FE(\000)p FQ(;)g(taking)g(the)g(limit)e(\003)h FE(")g(L)i FQ(with)f(these)g(b)q(oundary)60 814 y(conditions)h(again)h(selects)e FF(\026)613 821 y FH(+)661 814 y FQ(or)i FF(\026)753 821 y Fy(\000)782 814 y FQ(,)g(resp)q(ectiv)o(ely)l(.)26 b(In)19 b(relation)f(with)h(this)g(second)g(p)q(oin)o(t)g(of)60 874 y(view)13 b(w)o(e)f(presen)o(t)h(t)o(w)o(o)g(prop)q(ositions,)i(the)e (\014rst)h(of)g(whic)o(h)e(justi\014es)h FP(a)i(p)n(osteriori)i FQ(the)c(traditional)60 934 y(approac)o(h)k(to)g(in\014nite-v)o(olume)c (lattice)i(systems)g(based)i(on)f(in\014nite-v)o(olume)e(limits:)60 1048 y FM(Prop)r(osition)k(2.22)24 b FP(L)n(et)c FQ(\005)f(=)g(\()p FF(\031)734 1055 y FH(\003)760 1048 y FQ(\))779 1055 y FH(\003)p Fy(2S)873 1048 y FP(b)n(e)i(a)f(F)l(el)r(ler)i(sp)n(e)n(ci\014c)n(ation.)32 b(L)n(et)20 b FQ(\(\003)1564 1055 y FD(n)1587 1048 y FQ(\))1606 1055 y FD(n)p Fy(\025)p FH(1)1695 1048 y FP(b)n(e)h(an)f(in-)60 1108 y(cr)n(e)n(asing)f(se)n(quenc)n(e)i(of)e(\014nite)i(volumes)f(whose)g (union)g(is)f FE(L)p FP(,)h(and)g(let)g FQ(\()p FF(\027)1440 1115 y FD(n)1464 1108 y FQ(\))1483 1115 y FD(n)p Fy(\025)p FH(1)1571 1108 y FP(b)n(e)f(an)h(arbitr)n(ary)60 1169 y(se)n(quenc)n(e)d(of)d (pr)n(ob)n(ability)h(me)n(asur)n(es)f(on)h FQ(\012)h FP(\(i.e.)f(arbitr)n (ary)e(deterministic)j(or)f(r)n(andom)f(b)n(oundary)60 1229 y(c)n(onditions\).)22 b(L)n(et)15 b FF(\026)g FP(b)n(e)h(any)f(limit)g(p)n (oint)g(\(in)h(the)f(we)n(ak)h(top)n(olo)n(gy\))e(of)h(the)h(se)n(quenc)n(e)h FQ(\()p FF(\027)1689 1236 y FD(n)1712 1229 y FF(\031)1740 1236 y FH(\003)1764 1240 y Fs(n)1788 1229 y FQ(\))1807 1236 y FD(n)p Fy(\025)p FH(1)1875 1229 y FP(.)60 1289 y(Then)h FF(\026)g FP(is)f(c)n(onsistent)i(with)f FQ(\005)p FP(.)k(In)17 b(p)n(articular,)g FE(G)s FQ(\(\005\))g FP(is)g(a)g(close)n(d)h(subset)h(of)e FF(M)1604 1296 y FH(+1)1651 1289 y FQ(\(\012\))p FP(.)60 1403 y FM(Prop)r(osition)h(2.23)24 b FP(L)n(et)f FQ(\012)h FP(b)n(e)g(a)g FQ(compact)f FP(metric)h(sp)n(ac)n(e,)h(let)g FQ(\005)g(=)g(\()p FF(\031)1511 1410 y FH(\003)1538 1403 y FQ(\))1557 1410 y FH(\003)p Fy(2S)1654 1403 y FP(b)n(e)f(a)g(F)l(el)r(ler)60 1463 y(sp)n(e)n(ci\014c)n (ation,)18 b(and)f(let)i FF(\026)f FP(b)n(e)f(an)h FQ(extreme)d FP(p)n(oint)i(of)g FE(G)s FQ(\(\005\))p FP(.)22 b(Then,)c(for)f FF(\026)p FP(-a.e.)h FF(!)r FP(,)829 1573 y FQ(lim)820 1610 y FH(\003)10 b Fy(")g(L)817 1652 y FH(\003)h Fy(2)e(S)938 1573 y FF(\016)960 1580 y FD(!)985 1573 y FF(\031)1013 1580 y FH(\003)1067 1573 y FQ(=)27 b FF(\026)604 b FQ(\(2)p FF(:)p FQ(36\))60 1757 y FP(in)18 b(the)g(we)n(ak)g(top)n(olo)n(gy.)60 1871 y FQ(Prop)q(osition)25 b(2.22)f(states)g(that)g(an)o(y)g(w)o(eak)f(limit)e(of)i(\014nite-v)o(olume)e (Gibbs)j(measures,)g(with)60 1932 y(arbitrary)e(deterministic)c(or)k(random)f (b)q(oundary)i(conditions,)g(is)e(an)h(in\014nite-v)o(olume)d(Gibbs)60 1992 y(measure.)34 b(This)21 b(is)f(the)h(link)f(b)q(et)o(w)o(een)g(the)g (DLR)i(approac)o(h)f(and)h(the)e(traditional)h(approac)o(h)60 2052 y(via)g(limits)e(of)j(correlations.)36 b(Prop)q(osition)23 b(2.23)f(is)f(a)h(v)o(ery)e(strong)i(con)o(v)o(erse)e(statemen)o(t,)h(for)60 2112 y(the)c(sp)q(ecial)g(case)h(of)f FP(extr)n(emal)24 b FQ(Gibbs)17 b(measures:)23 b(it)17 b(states)g(that)h(if)f(one)h(tak)o(es)f FP(any)22 b FQ(\\t)o(ypical")60 2172 y(con\014guration)17 b(from)e(the)h (measure)f FF(\026)i FQ(and)f(uses)h(it)f(as)g(a)h(b)q(oundary)g(condition,)f (in)g(the)g(in\014nite-)60 2232 y(v)o(olume)j(limit)g(one)i(reco)o(v)o(ers)f FF(\026)p FQ(.)37 b(This)22 b(is)f(the)g(mathematical)d(transcription)k(of)f (the)g(pro)q(cess)60 2293 y(of)h(selecting)e(a)i(\\macrostate")g(b)o(y)f (preparing)h(the)f(sample)f(with)i(an)g(appropriate)g(b)q(oundary)60 2353 y(condition.)31 b(In)19 b(fact,)h(there)f(is)g(a)h(rev)o(ealing)e (generalization)h(of)h(this,)g(that)f(states)h(that)g(if)f FF(\026)h FQ(is)60 2413 y FP(any)25 b FQ(Gibbs)20 b(measure,)g(then)g(if)g (one)h(tak)o(es)f(a)h(\\t)o(ypical")f(con\014guration)h(from)e(the)i(measure) e FF(\026)60 2473 y FQ(and)h(uses)f(it)g(as)g(a)h(b)q(oundary)g(condition,)f (in)g(the)g(in\014nite-v)o(olume)d(limit)g(one)k(reco)o(v)o(ers)d(one)j(of)60 2533 y(the)g(extremal)d(Gibbs)j(measures)f(in)g(the)h(decomp)q(osition)f(of)h FF(\026)g FQ([156)q(].)32 b(This)20 b(theorem)e(can)i(b)q(e)60 2594 y(in)o(terpreted)f(as)i(sa)o(ying)f(that)h(the)f(result)g(of)h(a)f (measuremen)o(t)e(on)i(a)h(large)f(\(strictly)f(sp)q(eaking)60 2654 y(in\014nite\))f(system)g(will)h(alw)o(a)o(ys)g(yield)f(a)i(v)m(alue)f (c)o(haracteristic)f(of)i(one)f(of)h(the)f FP(extr)n(emal)26 b FQ(Gibbs)951 2784 y(40)p eop %%Page: 41 41 bop 60 91 a FQ(measures:)18 b(for)13 b(example,)e(a)i(measuremen)o(t)d(of)j (the)f(magnetization)f(in)i(a)g(lo)o(w-temp)q(erature)e(Ising)60 152 y(mo)q(del)k(at)i(zero)f(magnetic)e(\014eld)i(will)f(alw)o(a)o(ys)h (yield)f FE(\006)p FF(M)1134 159 y FH(0)1154 152 y FQ(,)g(not)i(an)g(in)o (termediate)c(v)m(alue.)133 212 y(Finally)l(,)g(the)h(consistency)f(b)q(et)o (w)o(een)g(the)h(ph)o(ysical)f(picture)g(and)h(the)g(mathematical)d(formal-) 60 272 y(ism)k(requires)g(some)g(discussion)h(of)h(the)f(issue)g(of)g (distinguishabilit)o(y)f(of)h(\\macrostates".)22 b(Ph)o(ys-)60 332 y(ically)l(,)c(t)o(w)o(o)h(\\macrostates")g(should)h(b)q(e)f(considered)f (di\013eren)o(t)h(only)g(if)f(there)h(is)f(some)g FP(macr)n(o-)60 392 y(sc)n(opic)f FQ(measuremen)n(t)11 b(that)j(can)g(tell)e(the)i (di\013erence.)19 b(In)13 b(terms)f(of)i(the)g(formalism)d(discussed)i(so)60 452 y(far,)j(this)h(corresp)q(onds)h(to)f(the)f(requiremen)o(t)d(that)k FP(glob)n(al)23 b FQ(observ)m(ables)17 b(b)q(e)g(able)f(to)h(distinguish)60 513 y(among)i(the)f(di\013eren)o(t)g(extremal)e(measures)i(for)h(a)g(giv)o (en)e(sp)q(eci\014cation.)29 b(The)18 b(follo)o(wing)h(theo-)60 573 y(rem)e(sho)o(ws)j(that)g(ev)o(en)e(more)g(is)h(true:)26 b(the)19 b(global)h(observ)m(ables)f(uniquely)f(c)o(haracterize)g(eac)o(h)60 633 y(measure)d(|)h(extremal)e(or)i(not)h(|)f(consisten)o(t)g(with)g(a)h(giv) o(en)e(sp)q(eci\014cation.)60 730 y FM(Theorem)i(2.24)24 b FP(L)n(et)17 b FQ(\005)g FP(b)n(e)g(an)h(sp)n(e)n(ci\014c)n(ation.)23 b(Then:)93 826 y(\(a\))h(The)18 b(extr)n(emal)h(me)n(asur)n(es)e(of)g FE(G)s FQ(\(\005\))g FP(ar)n(e)h(mutual)r(ly)h(singular)g(when)g(r)n (estricte)n(d)e(to)h(the)h(tail)182 887 y(\014eld.)28 b(That)19 b(is,)g(if)g FF(\026)g FP(and)g FF(\027)j FP(ar)n(e)d(distinct)h(extr)n(emal) f(me)n(asur)n(es)f(of)h FE(G)s FQ(\(\005\))p FP(,)f(ther)n(e)h(exists)h(a)182 947 y(set)e FF(A)13 b FE(2)370 931 y Fx(b)355 947 y FE(F)391 954 y Fy(1)446 947 y FP(such)18 b(that)f FF(\026)p FQ(\()p FF(A)p FQ(\))d(=)g(1)k FP(and)f FF(\027)s FQ(\()p FF(A)p FQ(\))d(=)g(0)p FP(.)95 1047 y(\(b\))25 b(Each)16 b(me)n(asur)n(e)f FF(\026)f FE(2)g(G)s FQ(\(\005\))h FP(is)h(uniquely)h(determine)n(d)f([among)g(the)h (me)n(asur)n(es)e(of)g FE(G)s FQ(\(\005\))p FP(])g(by)182 1107 y(the)20 b(events)h(in)f(the)g(tail)g(\014eld.)30 b(That)19 b(is,)h(if)g FF(\026)f FP(and)h FF(\027)j FP(ar)n(e)c(me)n(asur)n(es)f(in)i FE(G)s FQ(\(\005\))f FP(such)h(that)182 1167 y FF(\026)p FQ(\()p FF(A)p FQ(\))14 b(=)f FF(\027)s FQ(\()p FF(A)p FQ(\))18 b FP(for)e(e)n(ach)i FF(A)13 b FE(2)770 1151 y Fx(b)755 1167 y FE(F)791 1174 y Fy(1)829 1167 y FP(,)k(then)h FF(\026)d FQ(=)e FF(\027)s FP(.)60 1264 y FQ(F)l(or)j(the)g(pro)q(of,)h(see)f([157)q(,)g(Theorem)f(7.7].)60 1393 y FM(2.3.7)55 b(Conditioning)18 b(on)h(an)g(Arbitrary)f(Subset)h(of)g (Spins)60 1485 y FQ(The)c(DLR)g(equations)g(tell)f(us)h(ho)o(w)g(to)h (condition)e(on)i(the)e(spins)h(in)g(the)f(complemen)n(t)e(of)j(a)h FP(\014nite)60 1545 y FQ(set.)30 b(Ho)o(w)o(ev)o(er,)17 b(in)i(Section)g(4)g (w)o(e)g(shall)g(need)g(to)g(condition)g(on)h(sets)f(of)h(spins)f(whic)o(h)f (are)i FP(not)60 1606 y FQ(compleme)o(n)o(ts)e(of)j(\014nite)f(sets.)34 b(Therefore,)21 b(w)o(e)f(need)g(the)g(follo)o(wing)g(tec)o(hnical)f (construction,)60 1666 y(whic)o(h)d(can)g(b)q(e)g(skipp)q(ed)g(on)h(a)g (\014rst)f(reading.)133 1726 y(Let)k(\005)e(=)h(\()p FF(\031)383 1733 y FH(\003)410 1726 y FQ(\))429 1733 y FH(\003)p Fy(2S)522 1726 y FQ(b)q(e)g(a)h(sp)q(eci\014cation.)30 b(Let)20 b(\001)f(b)q(e)g(a)h (subset)g(of)f FE(L)h FQ(\()p FP(not)25 b FQ(necessarily)18 b(co-)60 1786 y(\014nite!\).)i(Let)15 b FF(!)h FE(2)e FQ(\012)i(b)q(e)g(a)f (con\014guration)i(\(but)e(only)h(its)f(comp)q(onen)o(ts)f FF(!)1444 1793 y FH(\001)1492 1786 y FQ(will)g(pla)o(y)h(an)o(y)g(role\).)60 1846 y(W)l(e)21 b(then)f(de\014ne)h(the)f FP(system)i(r)n(estricte)n(d)f(to)h (the)g(volume)h FE(L)14 b(n)g FQ(\001,)21 b(with)g(con\014guration)h(space)60 1907 y(\(\012)114 1914 y FH(0)134 1907 y FQ(\))153 1889 y Fy(Ln)p FH(\001)226 1907 y FQ(:)f(the)16 b FP(sp)n(e)n(ci\014c)n(ation)h(for)g (volume)h FE(L)11 b(n)f FQ(\001)17 b FP(with)g(external)i(spins)e(set)h(to)f FF(!)1577 1914 y FH(\001)1625 1907 y FQ(is)f(the)f(family)60 1967 y(\005)97 1949 y FD(!)136 1967 y FQ(=)e(\()p FF(\031)236 1949 y FD(!)234 1979 y FH(\003)261 1967 y FQ(\))280 1975 y FH(\003)p Fy(2S)r FD(;)6 b FH(\003)p Fy(\032Ln)p FH(\001)509 1967 y FQ(de\014ned)16 b(b)o(y)672 2071 y FF(\031)702 2050 y FD(!)700 2083 y FH(\003)727 2071 y FQ(\()p FF(!)778 2050 y Fy(0)790 2071 y FF(;)8 b(A)p FQ(\))27 b(=)g FF(\031)988 2078 y FH(\003)1015 2071 y FQ(\()p FF(!)1064 2078 y FH(\001)1107 2071 y FE(\002)10 b FF(!)1188 2050 y Fy(0)1200 2071 y FF(;)e(A)p FQ(\))487 b(\(2)p FF(:)p FQ(37\))60 2175 y(where)23 b FF(!)240 2157 y Fy(0)278 2175 y FE(2)j FQ(\(\012)391 2182 y FH(0)411 2175 y FQ(\))430 2157 y Fy(Ln)p FH(\001)527 2175 y FQ(and)e FF(A)h FE(2)i(F)787 2183 y Fy(Ln)p FH(\001)860 2175 y FQ(.)43 b(Clearly)22 b(the)h(functions)h FF(\031)1432 2157 y FD(!)1430 2187 y FH(\003)1456 2175 y FQ(\()8 b FE(\001)g FF(;)g(A)p FQ(\))24 b(are)f FE(F)1731 2183 y FH(\()p Fy(Ln)p FH(\001\))p Fy(n)p FH(\003)1874 2175 y FQ(-)60 2235 y(measurable.)g(It)16 b(is)h(easy)h(to)f (see)g(that)h(the)e(family)f(\005)1067 2217 y FD(!)1109 2235 y FQ(de\014nes)i(a)h(sp)q(eci\014cation)f(on)h(the)e(system)60 2296 y(with)g(lattice)f FE(L)d(n)f FQ(\001.)133 2356 y(Let)16 b(no)o(w)g FF(\026)h FQ(b)q(e)f(a)g(measure)f(consisten)o(t)g(with)h(\005.)k (Let)c FF(\026)1187 2338 y FD(!)1229 2356 y FQ(b)q(e)g(a)g(regular)g (conditional)g(proba-)60 2416 y(bilit)o(y)f(for)h FF(\026)h FQ(giv)o(en)f FE(F)472 2423 y FH(\001)503 2416 y FQ(.)22 b(\(Suc)o(h)17 b(regular)f(conditional)h(probabilities)e(alw)o(a)o(ys)i(exist)e(if)h(\(\012) p FF(;)8 b FE(F)d FQ(\))17 b(is,)60 2476 y(for)h(example,)d(a)j(standard)g (Borel)f(space.)25 b(This)18 b(includes)e(all)h(examples)e(of)j(ph)o(ysical)f (in)o(terest.\))60 2536 y(W)l(e)f(then)g(ha)o(v)o(e)g(the)g(follo)o(wing)f (in)o(tuitiv)o(ely)f(ob)o(vious)i(result:)60 2644 y FM(Prop)r(osition)i(2.25) 24 b FP(F)l(or)17 b FF(\026)p FP(-a.e.)h FF(!)r FP(,)g(the)g(me)n(asur)n(e)e FF(\026)1082 2626 y FD(!)1108 2644 y Fm(\026)p FE(F)1169 2652 y Fy(Ln)p FH(\001)1259 2644 y FP(is)i(c)n(onsistent)g(with)g FQ(\005)1681 2626 y FD(!)1706 2644 y FP(.)951 2784 y FQ(41)p eop %%Page: 42 42 bop 60 91 a FB(2.4)70 b(T)-6 b(ranslation)23 b(In)n(v)l(ariance)60 166 y FH(28)133 244 y FQ(Un)o(til)15 b(no)o(w)j(the)e(lattice)g FE(L)h FQ(has)h(b)q(een)f(simply)e(a)i(coun)o(tably)f(in\014nite)g(set)h(of)g (sites,)g(dev)o(oid)f(of)60 304 y(an)o(y)i(geometric)e(structure.)26 b(In)17 b(most)g(applications,)h(ho)o(w)o(ev)o(er,)f FE(L)h FQ(is)g(a)g(regular)g FF(d)p FQ(-dimensional)60 364 y(lattice;)13 b(this)g(additional)h(structure)f(allo)o(ws)h(us)g(to)f(de\014ne)h(the)f (notion)h(of)g FP(tr)n(anslation)h(invarianc)n(e)60 424 y FQ(for)f(measures,) e(in)o(teractions,)h(sp)q(eci\014cations)h(and)g(so)g(forth.)21 b(F)l(or)13 b(simplicit)o(y)d(w)o(e)j(shall)h(tak)o(e)f FE(L)h FQ(to)60 485 y(b)q(e)j(the)g(simple)d(\(h)o(yp)q(er\)cubic)i(lattice)f Fq(Z)831 464 y FD(d)851 485 y FQ(.)23 b(This)17 b(is)g(no)g(real)f(loss)i(of) f(generalit)o(y)l(,)e(b)q(ecause)i(other)60 545 y(regular)f(lattices)g(can)g (b)q(e)g(mapp)q(ed)g(to)h Fq(Z)825 524 y FD(d)862 545 y FQ(b)o(y)e(an)i (appropriate)g(lab)q(elling)e(of)i(sites.)1619 527 y FH(29)60 675 y FM(2.4.1)55 b(V)-5 b(an)20 b(Ho)n(v)n(e)e(Con)n(v)n(ergence)60 767 y FQ(An)12 b(imp)q(ortan)o(t)f(role)h(in)g(the)g(statistical)f(mec)o (hanics)f(of)j(translation-in)o(v)m(arian)o(t)f(systems)f(is)h(pla)o(y)o(ed) 60 827 y(b)o(y)g(sequences)f(of)h(v)o(olumes)e(\(\003)628 834 y FD(n)651 827 y FQ(\))i(whic)o(h)g(gro)o(w)g(in)g(suc)o(h)g(a)g(w)o(a)o(y)g (that)g(the)g(surface-to-v)o(olume)f(ratio)60 887 y(tends)16 b(to)h(zero.)k(W)l(e)16 b(therefore)f(mak)o(e)g(the)h(follo)o(wing)g (de\014nitions:)60 989 y FM(De\014nition)i(2.26)24 b FP(L)n(et)17 b FF(r)e(>)f FQ(0)p FP(,)j(and)h(let)h FQ(\003)13 b FE(\032)h Fq(Z)969 968 y FD(d)989 989 y FP(.)23 b(We)17 b(then)i(de\014ne)133 1091 y FE(\017)24 b FP(the)18 b FQ(inner)e FF(r)q FQ(-b)q(oundary)j FF(@)677 1073 y Fy(\000)674 1103 y FD(r)706 1091 y FQ(\003)j(=)h FE(f)p FF(x)13 b FE(2)h FQ(\003:)22 b(dist)o(\()p FF(x;)8 b FQ(\003)1187 1073 y FD(c)1204 1091 y FQ(\))14 b FE(\024)g FF(r)q FE(g)133 1193 y(\017)24 b FP(the)18 b FQ(outer)e FF(r)q FQ(-b)q(oundary)k FF(@)680 1174 y FH(+)677 1205 y FD(r)709 1193 y FQ(\003)i(=)g FE(f)p FF(x)14 b FE(2)g FQ(\003)973 1174 y FD(c)990 1193 y FQ(:)22 b(dist)o(\()p FF(x;)8 b FQ(\003\))14 b FE(\024)f FF(r)q FE(g)133 1294 y(\017)24 b FP(the)18 b FF(r)q FQ(-b)q(oundary)i FF(@)550 1301 y FD(r)569 1294 y FQ(\003)i(=)g FF(@)714 1276 y Fy(\000)711 1307 y FD(r)743 1294 y FQ(\003)11 b FE([)g FF(@)861 1276 y FH(+)858 1307 y FD(r)890 1294 y FQ(\003)60 1396 y(W)l(e)16 b(can)g(then)h(state)f(the)g(desired)g(condition)g(in)g(a)g(n)o(um)o(b)q(er)f (of)h(equiv)m(alen)o(t)f(w)o(a)o(ys:)60 1498 y FM(Prop)r(osition)j(2.27)24 b FP(L)n(et)18 b FQ(\(\003)625 1505 y FD(n)648 1498 y FQ(\))667 1505 y FD(n)p Fy(\025)p FH(1)754 1498 y FP(b)n(e)h(a)f(se)n(quenc)n(e)i(of)e (nonempty)h(\014nite)g(subsets)h(of)e Fq(Z)1720 1477 y FD(d)1740 1498 y FP(.)25 b(Then)60 1558 y(the)18 b(fol)r(lowing)i(ar)n(e)c(e)n (quivalent:)93 1660 y(\(a\))36 b FQ(lim)182 1684 y FD(n)p Fy(!1)282 1660 y FE(j)p FF(@)325 1639 y Fy(\000)322 1670 y FH(1)354 1660 y FQ(\003)388 1667 y FD(n)411 1660 y FE(j)p FF(=)p FE(j)p FQ(\003)497 1667 y FD(n)521 1660 y FE(j)13 b FQ(=)h(0)p FP(.)95 1775 y(\(b\))37 b FQ(lim)182 1800 y FD(n)p Fy(!1)282 1775 y FE(j)p FF(@)325 1754 y FH(+)322 1786 y(1)354 1775 y FQ(\003)388 1782 y FD(n)411 1775 y FE(j)p FF(=)p FE(j)p FQ(\003)497 1782 y FD(n)521 1775 y FE(j)13 b FQ(=)h(0)p FP(.)95 1887 y(\(c\))25 b(F)l(or)17 b(e)n(ach)g FF(r)f(>)d FQ(0)p FP(,)30 b FQ(lim)528 1912 y FD(n)p Fy(!1)628 1887 y FE(j)p FF(@)668 1894 y FD(r)687 1887 y FQ(\003)721 1894 y FD(n)744 1887 y FE(j)p FF(=)p FE(j)p FQ(\003)830 1894 y FD(n)854 1887 y FE(j)13 b FQ(=)h(0)p FP(.)93 2006 y(\(d\))24 b(F)l(or)17 b(e)n(ach)g FF(a)d FE(2)g Fq(Z)499 1985 y FD(d)520 2006 y FP(,)29 b FQ(lim)552 2031 y FD(n)p Fy(!1)652 2006 y FE(j)p FQ(\003)700 2013 y FD(n)735 2006 y FE(n)11 b FQ(\(\003)824 2013 y FD(n)858 2006 y FQ(+)g FF(a)p FQ(\))p FE(j)p FF(=)p FE(j)p FQ(\003)1038 2013 y FD(n)1061 2006 y FE(j)j FQ(=)f(0)p FP(.)95 2124 y(\(e\))25 b(F)l(or)17 b(e)n(ach)g FF(a)d FE(2)g Fq(Z)499 2104 y FD(d)520 2124 y FP(,)29 b FQ(lim)552 2149 y FD(n)p Fy(!1)652 2124 y FE(j)p FQ(\(\003)719 2131 y FD(n)754 2124 y FQ(+)11 b FF(a)p FQ(\))f FE(n)h FQ(\003)928 2131 y FD(n)951 2124 y FE(j)p FF(=)p FE(j)p FQ(\003)1037 2131 y FD(n)1061 2124 y FE(j)j FQ(=)f(0)p FP(.)98 2243 y(\(f)5 b(\))24 b(F)l(or)17 b(e)n(ach)g(\014nite)i(subset)g FF(A)13 b FE(\032)h Fq(Z)786 2222 y FD(d)806 2243 y FP(,)30 b FQ(lim)839 2268 y FD(n)p Fy(!1)939 2243 y FE(j)p FQ(\003)987 2250 y FD(n)1010 2243 y FE(4)p FQ(\(\003)1108 2250 y FD(n)1142 2243 y FQ(+)11 b FF(A)p FQ(\))p FE(j)p FF(=)p FE(j)p FQ(\003)1333 2250 y FD(n)1356 2243 y FE(j)i FQ(=)h(0)p FP(.)p 60 2306 732 2 v 100 2360 a FA(28)135 2375 y Fz(References)j(for)e (this)g(section)h(are)f(Georgii)f([157)o(,)h(Chapter)h(14],)e(Israel)h([206)o (,)g(Chapter)h(IV],)e(Preston)j([299)n(,)60 2425 y(Chapter)e(4])e(and)g (Ruelle)h([313)o(,)f(Chapter)i(3].)100 2483 y FA(29)135 2498 y Fz(What)10 b(is)h(really)f(relev)n(an)o(t)h(here)h(is)f(not)g(that)g Fu(L)g Fw(e)n(quals)j Fq(Z)1027 2474 y Fp(d)1047 2498 y Fz(,)d(but)g(merely)f (that)h(the)h(additiv)o(e)e(group)h Fq(Z)1732 2474 y Fp(d)1762 2498 y Fw(acts)h(on)60 2554 y Fu(L)p Fz(:)19 b(that)c(is,)f(there)i(should)e (exist)h(bijections)g Fv(t)805 2560 y Fp(a)825 2554 y Fz(:)k Fu(L)13 b(!)f(L)i Fz(\()p Fv(a)f Fu(2)f Fq(Z)1117 2530 y Fp(d)1136 2554 y Fz(\))j(suc)o(h)g(that)g Fv(t)1367 2560 y Fp(a)1387 2554 y Fv(t)1402 2560 y Fp(b)1431 2554 y Fz(=)e Fv(t)1491 2560 y Fp(a)p FA(+)p Fp(b)1566 2554 y Fz(and)i Fv(t)1663 2560 y FA(0)1694 2554 y Fz(=)e(iden)o(tit)o(y)o(.)60 2604 y(The)j(form)o(ulae)d(b)q (elo)o(w)i(can)h(easily)f(b)q(e)h(generalized)g(to)f(this)h(case,)g(b)o(y)f (replacing)g(eac)o(h)h(o)q(ccurrence)j(of)14 b Fv(x)c Fu(\000)h Fv(a)k Fz(b)o(y)60 2654 y Fv(t)75 2660 y Fp(a)95 2654 y Fz(\()p Fv(x)p Fz(\).)951 2784 y FQ(42)p eop %%Page: 43 43 bop 60 91 a FP(Mor)n(e)n(over,)16 b(al)r(l)j(of)e(these)i(c)n(onditions)e (imply)h(that:)86 187 y(\()p FF(\013)p FP(\))37 b FQ(lim)182 212 y FD(n)p Fy(!1)282 187 y FE(j)p FQ(\003)330 194 y FD(n)353 187 y FE(j)14 b FQ(=)g FE(1)p FP(.)87 304 y(\()p FF(\014)s FP(\))24 b(Ther)n(e)d(exist)h(ve)n(ctors)f FF(a)636 311 y FD(n)680 304 y FE(2)g Fq(Z)765 283 y FD(d)806 304 y FP(such)h(that)f(the)h(tr)n (anslates)g FQ(\003)1367 311 y FD(n)1404 304 y FE(\000)13 b FF(a)1482 311 y FD(n)1527 304 y FP(\014l)r(l)23 b(out)e Fq(Z)1722 283 y FD(d)1763 304 y FP(in)g(the)182 364 y(fol)r(lowing)f(sense:)k(for)17 b(e)n(ach)h(\014nite)h(subset)f FF(A)c FE(\032)g Fq(Z)1132 343 y FD(d)1152 364 y FP(,)j(ther)n(e)h(exists)h FF(n)1469 371 y FH(0)1488 364 y FQ(\()p FF(A)p FQ(\))14 b FF(<)g FE(1)k FP(such)g(that)182 424 y FF(A)13 b FE(\032)h FQ(\003)319 431 y FD(n)353 424 y FE(\000)d FF(a)429 431 y FD(n)470 424 y FP(for)16 b(al)r(l)j FF(n)14 b FE(\025)g FF(n)742 431 y FH(0)762 424 y FQ(\()p FF(A)p FQ(\))p FP(.)60 531 y FM(De\014nition)k(2.28)24 b FP(A)18 b(se)n(quenc)n(e)i FQ(\(\003)752 538 y FD(n)776 531 y FQ(\))795 538 y FD(n)p Fy(\025)p FH(1)882 531 y FP(of)e(nonempty)h (\014nite)h(subsets)f(of)f Fq(Z)1546 510 y FD(d)1585 531 y FP(is)g(said)g(to)h FQ(con-)60 591 y(v)o(erge)g(to)i(in\014nit)o(y)e(in)h (the)g(sense)g(of)h(v)m(an)g(Ho)o(v)o(e)f FP(\(denote)n(d)h FQ(\003)1222 598 y FD(n)1267 591 y FE(\045)f(1)p FP(\))h(if)g(it)g (satis\014es)h(any)f(one)60 651 y(\(henc)n(e)d(al)r(l\))h(of)e(the)h(e)n (quivalent)i(c)n(onditions)e(of)f(Pr)n(op)n(osition)f(2.27.)60 758 y FM(De\014nition)i(2.29)24 b FP(L)n(et)c FF(F)27 b FP(b)n(e)21 b(a)g(function)h(fr)n(om)d FE(S)25 b FP(\(the)c(nonempty)g(\014nite)h (subsets)g(of)f Fq(Z)1788 737 y FD(d)1808 758 y FP(\))g(to)60 818 y(some)e(metric)g(sp)n(ac)n(e)f FF(W)7 b FP(,)18 b(and)h(let)h FF(w)f FP(b)n(e)g(some)g(element)h(of)f FF(W)7 b FP(.)25 b(We)19 b(write)32 b FQ(lim)1510 848 y FH(\003)p Fy(\0451)1613 818 y FF(F)7 b FQ(\(\003\))15 b(=)h FF(w)k FP(in)60 900 y(c)n(ase)29 b FQ(lim)164 925 y FD(n)p Fy(!1)265 900 y FF(F)7 b FQ(\(\003)357 907 y FD(n)379 900 y FQ(\))14 b(=)g FF(w)k FP(for)f(every)h(se)n(quenc)n(e)g FQ(\(\003)974 907 y FD(n)998 900 y FQ(\))f FP(that)g(tends)h(to)g(in\014nity) g(in)f(the)h(sense)g(of)f(van)60 967 y(Hove.)60 1096 y FM(2.4.2)55 b(T)-5 b(ranslation-In)n(v)m(arian)n(t)19 b(Measures)60 1188 y FQ(With)d(these)g(preparations,)g(w)o(e)g(no)o(w)h(fo)q(cus)g(atten)o(tion) f(sp)q(eci\014cally)e(on)j(translation)g(in)o(v)m(ariance)60 1249 y(in)i(lattice)f(spin)i(systems.)30 b(With)19 b FE(L)h FQ(=)f Fq(Z)859 1228 y FD(d)880 1249 y FQ(,)h(the)f(translation)h(group)g Fq(Z)1423 1228 y FD(d)1463 1249 y FQ(acts)f(on)h(the)g(in\014nite-)60 1322 y(v)o(olume)14 b(con\014guration)j(space)g(\012)d(=)g(\(\012)809 1329 y FH(0)828 1322 y FQ(\))847 1304 y Fq(Z)878 1280 y Fs(d)914 1322 y FQ(b)o(y)627 1425 y(\()p FF(T)675 1432 y FD(a)695 1425 y FF(!)r FQ(\))746 1432 y FD(x)796 1425 y FQ(=)28 b FF(!)892 1432 y FD(x)p Fy(\000)p FD(a)1058 1425 y FQ(for)16 b(all)g FF(x)e FE(2)g(L)442 b FQ(\(2)p FF(:)p FQ(38\))60 1528 y(where)16 b FF(a)e FE(2)h Fq(Z)319 1507 y FD(d)339 1528 y FQ(.)22 b(\(The)17 b(min)o(us)d(sign)j(here)f(means)g(that)h FF(T)1129 1535 y FD(a)1149 1528 y FF(!)i FQ(is)d(the)g(con\014guration)i FF(!)h FQ(translated)60 1588 y FP(forwar)n(d)24 b FQ(b)o(y)19 b FF(a)p FQ(.\))33 b(This)20 b(action)g(on)g(the)g(con\014guration)h(space)f(induces)g (in)g(turn)g(an)g(action)h(on)60 1649 y(functions)576 1709 y(\()p FF(T)624 1716 y FD(a)644 1709 y FF(f)5 b FQ(\)\()p FF(!)r FQ(\))29 b FE(\021)e FF(f)5 b FQ(\()p FF(T)934 1716 y FD(a)955 1709 y FF(!)r FQ(\))97 b(for)17 b(all)f FF(!)g FE(2)e FQ(\012)391 b(\(2)p FF(:)p FQ(39\))60 1793 y(and)17 b(on)g(measures)523 1853 y(\()p FF(T)571 1860 y FD(a)591 1853 y FF(\026)p FQ(\)\()p FF(A)p FQ(\))28 b FE(\021)f FF(\026)p FQ(\()p FF(T)892 1833 y Fy(\000)p FH(1)885 1866 y FD(a)939 1853 y FQ([)p FF(A)p FQ(]\))96 b(for)17 b(all)e FF(A)f FE(2)g(F)19 b FF(:)337 b FQ(\(2)p FF(:)p FQ(40\))60 1938 y(A)18 b(function)g FF(f)k FE(2)17 b FF(B)s FQ(\(\012\))h(is)g(said)g(to)g(b)q(e)h FP(tr)n(anslation-invariant)24 b FQ(if)17 b FF(T)1354 1945 y FD(a)1375 1938 y FF(f)22 b FQ(=)17 b FF(f)23 b FQ(for)c(all)e FF(a)g FE(2)g Fq(Z)1792 1917 y FD(d)1813 1938 y FQ(.)26 b(A)60 1998 y(measure)16 b FF(\026)h FQ(is)g(said)g(to)h(b)q (e)f FP(tr)n(anslation-invariant)23 b FQ(if)16 b FF(T)1110 2005 y FD(a)1131 1998 y FF(\026)f FQ(=)g FF(\026)j FQ(for)f(all)g FF(a)d FE(2)i Fq(Z)1538 1977 y FD(d)1558 1998 y FQ(.)24 b(W)l(e)17 b(denote)g(b)o(y)60 2058 y FF(M)107 2065 y FD(inv)161 2058 y FQ(\(\012\))e(and)h FF(M)390 2065 y FH(+1)p FD(;inv)499 2058 y FQ(\(\012\))f(the)g(spaces)g(of)g(translation-in)o(v)m(arian)o(t)g (measures.)20 b(All)14 b(this)h(is)f(just)i(a)60 2118 y(precise)f (mathematical)e(statemen)o(t)i(of)h(the)g(ob)o(vious)h(notions)g(that)f(ev)o (eryb)q(o)q(dy)g(has)h(in)f(mind.)133 2178 y(A)o(t)h(this)g(p)q(oin)o(t)g(w)o (e)g(can)g(rep)q(eat)g(the)g(considerations)h(done)f(in)g(Section)g(2.3.6,)g (this)g(time)e(re-)60 2238 y(garding)k(the)f(relationship)g(b)q(et)o(w)o(een) f(ph)o(ysical)h(\\macrostates")g(and)h(elemen)o(ts)d(of)i FF(M)1694 2245 y FH(+1)p FD(;inv)1803 2238 y FQ(\(\012\).)60 2299 y(If)h(w)o(e)h(tak)o (e)f(the)g(p)q(oin)o(t)h(of)g(view)f(that)h(the)g(\\macroscopic")f(observ)m (ables)h(are)g(the)f FP(tr)n(anslation-)60 2359 y(invariant)g FQ(b)q(ounded)c(measurable)e(functions,)h(then)g(the)g(requiremen)o(ts)d(for) k(a)f(measure)f FF(\026)h FQ(repre-)60 2419 y(sen)o(ting)i(a)h(ph)o(ysical)f (\\macrostate")h(are:)22 b(\(i\))16 b(T)l(ranslation-in)o(v)m(arian)o(t)h (functions)g(in)f FF(B)s FQ(\(\012\))g(m)o(ust)60 2479 y(not)h(ha)o(v)o(e)f (\015uctuations)h(with)g(resp)q(ect)f(to)h FF(\026)p FQ(,)g(i.e.)e(they)h(m)o (ust)g(b)q(e)h(constan)o(t)g(with)f FF(\026)p FQ(-probabilit)o(y)60 2539 y(one;)d(and)e(\(ii\))f(the)h(probabilit)o(y)f(of)i(far-a)o(w)o(a)o(y)f (ev)o(en)o(ts)f(m)o(ust)g(factorize)g(in)h(some)f(sense.)19 b(Once)11 b(more,)60 2600 y(the)k(extremal)e(measures)i(are)g(the)g(ob)s (jects)h(with)f(the)g(righ)o(t)g(prop)q(erties.)21 b(Indeed,)15 b FF(M)1660 2607 y FH(+1)p FD(;inv)1769 2600 y FQ(\(\012\))g(is)60 2660 y(a)i(con)o(v)o(ex)e(set,)g(and)i(its)f(extreme)e(p)q(oin)o(ts)i(are)h (c)o(haracterized)d(b)o(y)i(the)g(follo)o(wing)g(theorem:)951 2784 y(43)p eop %%Page: 44 44 bop 60 91 a FM(Prop)r(osition)18 b(2.30)24 b FP(L)n(et)17 b FF(\026)d FE(2)g FF(M)708 98 y FH(+1)p FD(;inv)817 91 y FQ(\(\012\))p FP(.)23 b(Then)18 b(the)g(fol)r(lowing)h(pr)n(op)n(erties)d(ar)n(e)h(e)n (quivalent:)93 193 y(\(a\))24 b FF(\026)18 b FP(is)f(an)h(extr)n(eme)g(p)n (oint)f(of)h FF(M)760 200 y FH(+1)p FD(;inv)868 193 y FQ(\(\012\))p FP(.)95 295 y(\(b\))25 b(Every)17 b(tr)n(anslation-invariant)i(function)g FF(f)g FE(2)14 b FF(B)s FQ(\(\012\))j FP(is)h FF(\026)p FP(-a.e.)g(c)n (onstant.)95 396 y(\(c\))25 b FQ(lim)250 403 y FD(n)p Fy(!1)352 396 y FF(n)381 378 y Fy(\000)p FD(d)437 363 y Fx(P)481 407 y FD(a)p Fy(2)p FD(C)549 411 y Fs(n)580 396 y FF(\026)p FQ(\()p FF(f)14 b(T)695 403 y FD(a)715 396 y FF(g)r FQ(\))58 b(=)f FF(\026)p FQ(\()p FF(f)5 b FQ(\))p FF(\026)p FQ(\()p FF(g)r FQ(\))27 b FP(for)e(al)r(l)i FF(f)s(;)8 b(g)30 b FE(2)f FF(B)s FQ(\(\012\))c FP([or)g FF(B)1716 403 y FD(q)q(l)1746 396 y FQ(\(\012\))h FP(or)182 457 y FF(B)219 464 y FD(loc)264 457 y FQ(\(\012\))18 b FP(or)f FF(C)t FQ(\(\012\))p FP(],)g(wher)n(e)g FF(C)749 464 y FD(n)790 457 y FP(is)h(a)f(cub)n(e)h(of)f(side)h FF(n)p FP(.)93 558 y(\(d\))24 b FQ(lim)250 565 y FH(\003)p Fy(\0451)355 558 y FE(j)p FQ(\003)p FE(j)417 540 y Fy(\000)p FH(1)472 525 y Fx(P)516 569 y FD(a)p Fy(2)p FH(\003)593 558 y FF(\026)p FQ(\()p FF(f)14 b(T)708 565 y FD(a)728 558 y FF(g)r FQ(\))55 b(=)g FF(\026)p FQ(\()p FF(f)5 b FQ(\))p FF(\026)p FQ(\()p FF(g)r FQ(\))25 b FP(for)g(al)r(l)h FF(f)s(;)8 b(g)29 b FE(2)e FF(B)s FQ(\(\012\))e FP([or)f FF(B)1717 565 y FD(q)q(l)1747 558 y FQ(\(\012\))h FP(or)182 619 y FF(B)219 626 y FD(loc)264 619 y FQ(\(\012\))18 b FP(or)f FF(C)t FQ(\(\012\))p FP(].)60 720 y FQ(W)l(e)22 b(notice)f(that)i(the)e(\\cluster)h(prop)q(ert)o(y")g(em)o (b)q(o)q(died)f(b)o(y)g(prop)q(erties)h(\(c\))g(and)g(\(d\))g(is)g(m)o(uc)o (h)60 780 y(w)o(eak)o(er)h(than)h(the)g(one)g(presen)o(ted)f(in)g(Section)g (2.3.6)h([part)g(\(b\))g(of)g(Prop)q(osition)h(2.19]:)36 b(\(c\))60 841 y(and)20 b(\(d\))f(state)h(that)g(distan)o(t)f(regions)h(of)f(the)g (lattice)f(are)i(asymptotically)d(indep)q(enden)o(t,)i(but)60 901 y(only)f(in)g(an)g(a)o(v)o(eraged)g(sense.)27 b(A)17 b(measure)g FF(\026)h FE(2)f FF(M)1041 908 y FH(+1)p FD(;inv)1150 901 y FQ(\(\012\))h(ha)o(ving)g(the)g(prop)q(erties)g(listed)f(in)60 961 y(Prop)q(osition)g(2.30)g(is)f(said)h(to)g(b)q(e)f FP(er)n(go)n(dic)s FQ(.)133 1021 y(Therefore,)f(b)o(y)g(considerations)h(analogous)i(to)e(those) g(of)g(Section)g(2.3.6,)f(if)h(w)o(e)f(consider)g(the)60 1081 y(translation-in)o(v)m(arian)o(t)i(functions)g(to)g(b)q(e)g(the)g(only)f (\\macroscopic")h(observ)m(ables,)g(then)f(the)h(er-)60 1142 y(go)q(dic)c(measures)e(are)i(asso)q(ciated)g(to)g(ph)o(ysical)f (\\macrostates")g(and)h(their)f(con)o(v)o(ex)f(com)o(binations)60 1202 y(to)19 b(\\mixtures")e(represen)o(ting)h(ignorance)h(on)g(the)f(part)h (of)g(the)g(exp)q(erimen)o(ter.)25 b(Note)18 b(that,)h(as)60 1262 y(in)h(the)h(\014rst)f(part)i(of)e(Section)h(2.3.6)f(\(through)i(Prop)q (osition)g(2.19\),)g(w)o(e)e(ha)o(v)o(e)g(not)h(made)e(an)o(y)60 1322 y(reference)g(to)i(in)o(teractions,)g(sp)q(eci\014cations)g(or)g (Gibbsianness;)i(the)e(presen)o(t)f(commen)o(ts)e(ha)o(v)o(e)60 1382 y(general)e(v)m(alidit)o(y)l(.)133 1443 y(W)l(e)21 b(ha)o(v)o(e)f(no)o (w)h(in)o(tro)q(duced)g(t)o(w)o(o)g(distinct)f(classes)h(of)g(observ)m(ables) h(that)f(could)g(plausibly)60 1503 y(b)q(e)g(called)g(\\macroscopic":)31 b(the)21 b FP(glob)n(al)27 b FQ(observ)m(ables)22 b(\(Section)f(2.3.6\))g (and)h(the)f FP(tr)n(anslation-)60 1563 y(invariant)g FQ(observ)m(ables)c (\(presen)o(t)e(section\).)21 b(Whic)o(h)15 b(class)h(truly)g(corresp)q(onds) h(to)f(the)g(\\exp)q(eri-)60 1623 y(men)o(tally)f(accessible")h(observ)m (ables?)26 b(This)18 b(question)f(do)q(es)i(not)f(ha)o(v)o(e)e(a)i(canonical) f(answ)o(er:)24 b(it)60 1683 y(all)12 b(dep)q(ends)h(on)f(the)g(system)f(and) i(the)f(exp)q(erimen)o(ts.)18 b(It)11 b(is)i(kno)o(wn)f([157)q(,)g(Prop)q (osition)i(14.9])f(that)60 1743 y(for)19 b(a)h(translation-in)o(v)m(arian)o (t)f(measure)f FF(\026)p FQ(,)h(ev)o(ery)f(translation-in)o(v)m(arian)o(t)h (function)g(is)g(measur-)60 1804 y(able)c(at)h(in\014nit)o(y)l(,)e(mo)q(dulo) h(a)g(set)h(of)f FF(\026)p FQ(-measure)g(zero.)21 b(The)15 b(con)o(v)o(erse)f(is)i FP(not)k FQ(true.)h(By)15 b(limiting)60 1864 y(ourselv)o(es)21 b(to)h(translation-in)o(v)m(arian)o(t)g(observ)m (ables,)h(w)o(e)e(eliminate)e(some)h(not-v)o(ery-accessible)60 1924 y(global)d(observ)m(ables,)f(lik)o(e)e(the)i(staggered)h(magnetization)e (men)o(tioned)f(in)i(Section)g(2.3.6.)133 1984 y(Analogous)e(questions)e (could)h(b)q(e)g(p)q(osed)g(in)f(relation)g(to)h(whether)g(the)f(extremal)e (measures)i(of)60 2044 y FE(G)s FQ(\(\005\))i(or)h(the)f(extremal)e(measures) i(of)h FF(M)831 2051 y FH(+1)p FD(;inv)940 2044 y FQ(\(\012\))g(should)g (represen)o(t)e(ph)o(ysical)h(\\macrostates".)60 2105 y(W)l(e)d(shall)f (commen)o(t)e(brie\015y)i(on)i(this)e(p)q(oin)o(t)i(once)e(w)o(e)h(de\014ne)f (the)h(notion)h(of)f(translation-in)o(v)m(arian)o(t)60 2165 y(sp)q(eci\014cations)j(\(Section)g(2.4.9\).)21 b(F)l(or)14 b(no)o(w,)h(let)f(us)g(commen)o(t)d(that)k(the)f(ergo)q(dic)h(measures)e(ha)o (v)o(e)60 2225 y(the)g(additional)g(app)q(eal)h(of)f(b)q(eing)h(precisely)d (those)j(for)f(whic)o(h)f(\\space)i(a)o(v)o(erages)f(equal)g(ensem)o(ble)60 2285 y(a)o(v)o(erages":)60 2399 y FM(Prop)r(osition)18 b(2.31)g(\(Ergo)r(dic) f(theorem\))22 b FP(L)n(et)12 b FF(\026)h FP(b)n(e)g(an)g(er)n(go)n(dic)f(tr) n(anslation-invariant)i(pr)n(ob-)60 2460 y(ability)k(me)n(asur)n(e)f(on)g FQ(\012)p FP(,)h(and)g(let)g FF(f)h FE(2)14 b FF(L)819 2441 y FH(1)839 2460 y FQ(\()p FF(\026)p FQ(\))p FP(.)23 b(Then:)93 2561 y(\(a\))38 b FQ(lim)182 2591 y FH(\003)p Fy(\0451)285 2561 y FE(j)p FQ(\003)p FE(j)347 2543 y Fy(\000)p FH(1)422 2528 y Fx(P)411 2599 y FD(a)p Fy(2)p FH(\003)486 2561 y FF(T)515 2568 y FD(a)535 2561 y FF(f)33 b FQ(=)658 2526 y Fx(R)685 2561 y FF(f)14 b(d\026)k FP(in)g FF(L)888 2543 y FH(1)908 2561 y FQ(\()p FF(\026)p FQ(\))g FP(norm.)951 2784 y FQ(44)p eop %%Page: 45 45 bop 95 91 a FP(\(b\))37 b FQ(lim)182 116 y FD(n)p Fy(!1)282 91 y FF(n)311 73 y Fy(\000)p FD(d)398 58 y Fx(P)376 129 y FD(a)p Fy(2)p FD(C)444 133 y Fs(n)473 91 y FF(T)502 98 y FD(a)522 91 y FF(f)c FQ(=)645 56 y Fx(R)672 91 y FF(f)14 b(d\026)k FP(p)n(ointwise)g FF(\026)p FP(-a.e.)60 235 y FQ(P)o(art)c(\(a\))g(is)g(called)f(the)h FF(L)542 217 y FH(1)575 235 y FQ(\(or)h(mean\))d(ergo)q(dic)i(theorem;)f(it)h (is)f(easily)g(generalized)g(to)h FF(L)1732 217 y FD(p)1766 235 y FQ(for)h(all)60 295 y FF(p)h(<)g FE(1)p FQ(.)24 b(P)o(art)18 b(\(b\),)f(whic)o(h)g(is)g(m)o(uc)o(h)e(deep)q(er,)i(is)g(called)g(the)g (Birkho\013)g(\(or)h(individual\))e(ergo)q(dic)60 356 y(theorem.)133 466 y(The)f(simplex)e FF(M)456 473 y FH(+1)p FD(;inv)565 466 y FQ(\(\012\))i(of)h(translation-in)o(v)m(arian)o(t)f(measures)g(has)g(the)g (prop)q(ert)o(y)h(that)f(its)60 526 y(extremal)h(elemen)o(ts)f(|)j(namely)l (,)f(the)h(ergo)q(dic)g(measures)f(|)i(are)f FP(dense)23 b FQ(in)18 b(the)g(whole)g(set,)g(in)60 586 y(the)f(b)q(ounded)i(quasilo)q(cal) f(or)g(w)o(eak)f(quasilo)q(cal)h(top)q(ology)l(.)26 b(In)18 b(other)f(w)o(ords,)i(an)o(y)e(translation-)60 646 y(in)o(v)m(arian)o(t)f (measure)f FF(\026)i FQ(can)f(b)q(e)h(appro)o(ximated)e(arbitrarily)h (closely)l(,)e(with)j(regard)g(to)f(an)o(y)h FP(\014nite)60 706 y FQ(set)11 b(of)h FP(\(quasi\)lo)n(c)n(al)17 b FQ(observ)m(ables,)12 b(b)o(y)f(ergo)q(dic)g(measures.)19 b(Ph)o(ysically)10 b(this)h(means)f(that) i(through)60 766 y(observ)m(ations)i(in)e(an)o(y)g FP(\014nite)18 b FQ(v)o(olume,)10 b(no)j(matter)f(ho)o(w)h(large,)f(one)h(cannot)g(learn)g (the)f(long-range)60 827 y(correlation)17 b(prop)q(erties)h(of)g(the)f (measure)f FF(\026)i FQ(\(ergo)q(dicit)o(y)f(or)h(the)f(lac)o(k)g(thereof)s (\).)25 b(The)18 b(pro)q(of)h(of)60 887 y(this)h(fact)f(is)h(really)e(quite)h (simple:)26 b(P)o(a)o(v)o(e)19 b Fq(Z)904 866 y FD(d)944 887 y FQ(b)o(y)g(cub)q(es)h(of)g(side)g FF(n)p FQ(;)h(let)e FF(\026)1481 894 y FD(n)1524 887 y FQ(b)q(e)h(equal)f(to)h FF(\026)h FQ(on)60 947 y(eac)o(h)d(cub)q(e,)h(but)g FP(indep)n(endent)25 b FQ(b)q(et)o(w)o(een) 18 b(cub)q(es)h(\(i.e.)e(cut)i(the)f(correlations)h(b)q(et)o(w)o(een)f (distinct)60 1007 y(cub)q(es\);)25 b(and)d(\014nally)l(,)h(let)582 1003 y Fx(e)577 1007 y FF(\026)606 1014 y FD(n)652 1007 y FQ(b)q(e)f FF(\026)753 1014 y FD(n)799 1007 y FQ(a)o(v)o(eraged)g(o)o(v)o(er)f(the)h FF(n)1236 989 y FD(d)1278 1007 y FQ(p)q(ossible)h(translates)f(\(so)h(as)g (to)60 1067 y(mak)o(e)e(it)h(translation-in)o(v)m(arian)o(t\).)40 b(Then)23 b(it)f(is)g(easy)h(to)g(see)f(that)1382 1063 y Fx(e)1378 1067 y FF(\026)1407 1074 y FD(n)1453 1067 y FQ(is)h(ergo)q(dic,)g(and)h(that) 60 1128 y(lim)128 1135 y FD(n)p Fy(!1)235 1124 y Fx(e)230 1128 y FF(\026)259 1135 y FD(n)300 1128 y FQ(=)17 b FF(\026)h FQ(in)g(the)g(b)q (ounded)h(quasilo)q(cal)f(top)q(ology)l(.)28 b(W)l(e)18 b(ha)o(v)o(e)f(just)h (sk)o(etc)o(hed)f(the)h(pro)q(of)60 1188 y(of:)60 1302 y FM(Prop)r(osition)g (2.32)24 b FP(The)i(er)n(go)n(dic)f(me)n(asur)n(es)g(ar)n(e)g(a)g FQ(dense)h FP(subset)g(of)g FF(M)1534 1309 y FH(+1)p FD(;inv)1643 1302 y FQ(\(\012\))p FP(,)i(in)d(the)60 1362 y(b)n(ounde)n(d)18 b(quasilo)n(c)n(al)f(top)n(olo)n(gy)g([and)h(henc)n(e)g(also)g(in)g(the)g(we) n(ak)g(quasilo)n(c)n(al)g(top)n(olo)n(gy].)133 1476 y FQ(The)23 b(densit)o(y)f(of)i(the)f(ergo)q(dic)g(measures)f(is)h(th)o(us)g(an)g(in)o (trinsic)f(and)h(natural)h(feature)f(of)60 1537 y(in\014nite-v)o(olume)14 b(ph)o(ysics.)22 b(Geometrically)l(,)14 b(ho)o(w)o(ev)o(er,)h(a)j(simplex)c (with)j(dense)f(extreme)f(p)q(oin)o(ts)60 1597 y(\(a)f(so-called)f FP(Poulsen)k(simplex)6 b FQ(\))14 b(is)f(highly)g(unin)o(tuitiv)o(e.)18 b(Indeed,)13 b(our)h(usual)g(in)o(tuition,)f(deriv)o(ed)60 1657 y(from)d(\014nite-dimensional)f(geometry)l(,)h(is)h(that)g(the)g (extreme)e(p)q(oin)o(ts)i(should)g(form)f(a)i FP(close)n(d)17 b FQ(subset)60 1717 y(\(as)22 b(e.g.)f(the)g(v)o(ertices)f(of)i(a)g (triangle,)g(of)g(a)g(tetrahedron,)h(etc.\).)36 b(The)21 b(un)o(usual)h(b)q (eha)o(vior)g(of)60 1777 y FF(M)107 1784 y FH(+1)p FD(;inv)216 1777 y FQ(\(\012\))c(is)g(p)q(ossible)h(only)f(in)g(in\014nite)f(dimensions.) 26 b(It)17 b(will)g(b)q(e)i(at)f(the)g(origin)g(of)h(man)o(y)e(of)60 1837 y(the)f(\\pathologies")i(to)e(b)q(e)h(discussed)f(in)g(Section)g(2.6.7.) 133 1898 y FM(Remark.)32 b FQ(It)20 b(is)g(an)h(amazing)e(mathematical)f (fact)i(that)h(a)g(\(compact)e(metrizable\))e(sim-)60 1958 y(plex)e(with)h(dense)g(extreme)e(p)q(oin)o(ts)i(is)g(essen)o(tially)f (unique:)20 b(all)c(P)o(oulsen)g(simplices)e(are)i(a\016nely)60 2018 y(homeomorphic)e(to)i(eac)o(h)g(other)h([252,)f(284)q(].)133 2128 y(If)g(w)o(e)g(think)g(of)g(the)g(ergo)q(dic)h(measures)e(as)i(represen) o(ting)e(all)h(the)g(\\macrostates")h(a)o(v)m(ailable)60 2188 y(to)k(the)f(system,)g(it)g(is)g(natural)h(to)g(inquire)e(whether)i(the)f FP(tr)n(anslation-invariant)27 b FQ(observ)m(ables)60 2248 y(distinguish)19 b(b)q(et)o(w)o(een)g(di\013eren)o(t)f(suc)o(h)i(measures,)e (as)i(is)g(desirable)e(on)i(ph)o(ysical)f(grounds)h(\(see)60 2309 y(the)c(analogous)i(discussion)f(at)f(the)g(end)g(of)h(Section)f (2.3.6\).)21 b(The)16 b(answ)o(er)h(is)f(y)o(es:)60 2471 y FM(Theorem)h(2.33)56 b FP(\(a\))24 b(The)15 b(extr)n(emal)g(me)n(asur)n(es)f (of)g FF(M)1140 2478 y FH(+1)p FD(;inv)1249 2471 y FQ(\(\012\))h FP(\(i.e.)g(the)g(er)n(go)n(dic)f(me)n(asur)n(es\))182 2531 y(ar)n(e)j(mutual)r(ly)j(singular)e(when)i(r)n(estricte)n(d)d(to)h(the)h FF(\033)r FP(-\014eld)g FE(F)1322 2538 y FD(inv)1394 2531 y FP(of)f(tr)n(anslation-invariant)182 2591 y(events.)46 b(That)24 b(is,)j(if)d FF(\026)h FP(and)g FF(\027)j FP(ar)n(e)c(distinct)i(er)n(go)n (dic)e(me)n(asur)n(es,)i(ther)n(e)e(exists)i(a)e(set)182 2651 y FF(A)13 b FE(2)h(F)315 2658 y FD(inv)386 2651 y FP(such)k(that)g FF(\026)p FQ(\()p FF(A)p FQ(\))c(=)f(1)18 b FP(and)g FF(\027)s FQ(\()p FF(A)p FQ(\))13 b(=)h(0)p FP(.)951 2784 y FQ(45)p eop %%Page: 46 46 bop 95 91 a FP(\(b\))25 b(Each)e(me)n(asur)n(e)e FF(\026)i FE(2)h FF(M)659 98 y FH(+1)p FD(;inv)768 91 y FQ(\(\012\))e FP(is)g(uniquely)i(determine)n(d)f([among)g(the)g(me)n(asur)n(es)e(of)182 152 y FF(M)229 159 y FH(+1)p FD(;inv)338 152 y FQ(\(\012\))p FP(])f(by)g(the)g(tr)n(anslation-invariant)i(events.)31 b(That)20 b(is,)g FF(\026)g FP(and)g FF(\027)k FP(ar)n(e)19 b(me)n(asur)n(es)182 212 y(in)f FF(M)289 219 y FH(+1)p FD(;inv)398 212 y FQ(\(\012\))f FP(such)h(that)g FF(\026)p FQ(\()p FF(A)p FQ(\))13 b(=)h FF(\027)s FQ(\()p FF(A)p FQ(\))j FP(for)g(e)n(ach)h FF(A)13 b FE(2)h(F)1308 219 y FD(inv)1362 212 y FP(,)j(then)i FF(\026)14 b FQ(=)g FF(\027)s FP(.)60 289 y FQ(F)l(or)22 b(the)f(pro)q(of,)j(see)d([157)q(,)i(Theorem)d (14.5].)38 b(In)21 b(fact,)i(this)e(theorem)g(is)g(also)h(true)g(with)f(the) 60 349 y(in)o(v)m(arian)o(t)e(\014eld)h FE(F)414 356 y FD(inv)487 349 y FQ(replaced)f(ev)o(erywhere)g(b)o(y)g(the)h(tail)f(\014eld)1314 333 y Fx(b)1300 349 y FE(F)1336 356 y Fy(1)1373 349 y FQ(;)i(this)f(follo)o (ws)g(from)f([157,)60 409 y(Prop)q(osition)e(14.9].)60 535 y FM(2.4.3)55 b(Dividing)17 b(Out)i(T)-5 b(ranslation)19 b(In)n(v)m(ariance) 60 628 y FQ(T)l(ranslation)k(in)o(v)m(ariance)f(brings)h(along)g(some)f (natural)g(notions)i(of)f(\\equiv)m(alence".)38 b(F)l(or)23 b(in-)60 688 y(stance,)14 b(di\013eren)o(t)g(observ)m(ables)h(cannot)g(alw)o (a)o(ys)f(b)q(e)h(distinguished)f(when)g(lo)q(ok)o(ed)g(at)h(in)f(a)h FP(tr)n(ans-)60 748 y(lation-invariant)26 b FQ(measure.)j(\()p FM(Example:)24 b FF(\033)936 755 y FH(0)975 748 y FQ(v)o(ersus)19 b FF(\033)1153 755 y FH(17)1190 748 y FQ(.\))30 b(In)19 b(this)g(section)g(w) o(e)g(discuss)g(the)60 808 y(cen)o(tral)12 b(ob)s(ject)h(generating)g(all)g (these)g(notions)h(of)g(\\equiv)m(alence",)e(namely)f(the)i(set)g(of)h (functions)60 868 y(that)j(ha)o(v)o(e)e(zero)h(a)o(v)o(erage)g(with)g(resp)q (ect)g(to)h(all)e(translation-in)o(v)m(arian)o(t)i(measures.)133 928 y(F)l(rom)e(no)o(w)i(on)g(un)o(til)e(the)h(end)g(of)h(Section)e(2,)i(w)o (e)e(shall)i(generally)e(assume)g(that)i(the)f(single-)60 989 y(spin)e(space)g(\012)324 996 y FH(0)358 989 y FQ(is)g(a)h(compact)e(metric)e (space,)k(i.e.)d(w)o(e)i(restrict)f(atten)o(tion)h(to)g(mo)q(dels)f(of)i FP(b)n(ounde)n(d)60 1049 y(spins)t FQ(.)45 b(The)24 b(con\014guration)i (space)e(\012)g(is)g(then)g(also)h(compact.)44 b(This)24 b(restriction)f(is)h (made)60 1109 y(primarily)9 b(to)j(simplify)e(the)h(exp)q(osition;)i(in)f (App)q(endix)f(A)g(w)o(e)g(partially)g(remo)o(v)o(e)f(this)h(restriction.)133 1169 y(The)16 b(functions)h(of)f(in)o(terest)f(here)h(are)g(c)o(haracterized) f(b)o(y)h(the)g(follo)o(wing)g(prop)q(osition:)60 1247 y FM(Prop)r(osition)i (2.34)24 b FP(L)n(et)d FQ(\012)610 1254 y FH(0)651 1247 y FP(b)n(e)h(a)f(c)n (omp)n(act)g(metric)h(sp)n(ac)n(e,)g(and)g(let)g FF(f)27 b FE(2)21 b FF(C)t FQ(\(\012\))p FP(.)34 b(Then)22 b(the)60 1307 y(fol)r(lowing)e(pr)n(op)n(erties)c(ar)n(e)h(e)n(quivalent:)93 1384 y(\(a\))24 b FF(f)g FP(has)19 b(zer)n(o)f(me)n(an)g(with)i(r)n(esp)n(e)n (ct)e(to)g(every)i(tr)n(anslation-invariant)g(pr)n(ob)n(ability)e(me)n(asur)n (e,)182 1444 y(i.e.)267 1409 y Fx(R)294 1444 y FF(f)c(d\026)g FQ(=)g(0)k FP(for)f(al)r(l)i FF(\026)14 b FE(2)g FF(M)779 1451 y FH(+1)p FD(;inv)888 1444 y FQ(\(\012\))p FP(.)95 1538 y(\(b\))25 b FF(f)20 b FP(has)15 b(zer)n(o)g(me)n(an)g(with)h(r)n(esp)n(e)n(ct)e(to)h (every)h(tr)n(anslation-invariant)h(\014nite)f(signe)n(d)g(me)n(asur)n(e,)182 1598 y(i.e.)267 1563 y Fx(R)294 1598 y FF(f)e(d\026)g FQ(=)g(0)k FP(for)f(al)r(l)i FF(\026)14 b FE(2)g FF(M)779 1605 y FD(inv)833 1598 y FQ(\(\012\))p FP(.)95 1692 y(\(c\))25 b FF(f)c FP(lies)16 b(in)f(the)h(close)n(d)g(line)n(ar)f(sp)n(an)g(of)g(the)h(family)f(of)g (functions)i FE(f)p FF(g)8 b FE(\000)e FF(T)1508 1699 y FD(a)1529 1692 y FF(g)r FQ(:)22 b FF(g)16 b FE(2)e FF(C)t FQ(\(\012\))p FF(;)h(a)f FE(2)182 1752 y Fq(Z)212 1731 y FD(d)233 1752 y FE(g)p FP(.)93 1852 y(\(d\))36 b FQ(lim)182 1877 y FD(n)p Fy(!1)282 1852 y FF(n)311 1834 y Fy(\000)p FD(d)359 1802 y Fx(\015)359 1827 y(\015)359 1852 y(\015)404 1819 y(P)382 1890 y FD(a)p Fy(2)p FD(C)450 1894 y Fs(n)479 1852 y FF(T)508 1859 y FD(a)528 1852 y FF(f)557 1802 y Fx(\015)557 1827 y(\015)557 1852 y(\015)581 1879 y Fy(1)640 1852 y FQ(=)22 b(0)p FP(.)95 1985 y(\(e\))39 b FQ(lim)182 2015 y FH(\003)p Fy(\0451)285 1985 y FE(j)p FQ(\003)p FE(j)347 1967 y Fy(\000)p FH(1)402 1936 y Fx(\015)402 1960 y(\015)402 1985 y(\015)437 1952 y(P)425 2023 y FD(a)p Fy(2)p FH(\003)500 1985 y FF(T)529 1992 y FD(a)550 1985 y FF(f)579 1936 y Fx(\015)579 1960 y(\015)579 1985 y(\015)602 2012 y Fy(1)662 1985 y FQ(=)22 b(0)p FP(.)60 2085 y FQ(W)l(e)17 b(denote)f(b)o(y)h FE(I)j FQ(the)d(class)g(of)g(functions)g(ha)o(ving)f(the)h(prop)q(erties)g (sp)q(eci\014ed)f(in)h(the)f(foregoing)60 2146 y(prop)q(osition;)23 b(it)c(is)h(a)h(closed)f(linear)f(subspace)h(of)h FF(C)t FQ(\(\012\),)f(and)h (is)f(exactly)f(the)h(annihilator)g(of)60 2206 y FF(M)107 2213 y FD(inv)161 2206 y FQ(\(\012\).)36 b(The)21 b(space)g FE(I)k FQ(will)19 b(pla)o(y)i(a)g(v)o(ery)f(imp)q(ortan)o(t)g(role)h(in)f(the)h (theory)g(of)g(translation-)60 2266 y(in)o(v)m(arian)o(t)16 b(equilibrium)c(measures,)j(and)i(in)f(particular)g(in)g(the)g(discussion)h (of)f(\\ph)o(ysical)g(equiv-)60 2326 y(alence".)21 b(W)l(e)16 b(de\014ne)g(the)g(quotien)o(t)f(\(semi\)norms:)473 2408 y FE(k)p FF(f)5 b FE(k)552 2416 y FD(C)r FH(\(\012\))p FD(=const)777 2408 y FE(\021)43 b FQ(inf)857 2435 y FD(c)p Fy(2)p Fl(R)927 2408 y FE(k)p FF(f)17 b FE(\000)11 b FF(c)p FE(k)1089 2415 y Fy(1)1153 2408 y FQ(=)1224 2388 y FH(1)p 1224 2396 18 2 v 1224 2425 a(2)1247 2408 y FQ(\(sup)d FF(f)17 b FE(\000)11 b FQ(inf)g FF(f)5 b FQ(\))212 b(\(2.41\))534 2518 y FE(k)p FF(f)5 b FE(k)613 2526 y FD(C)r FH(\(\012\))p FD(=)p Fy(I)777 2518 y FE(\021)43 b FQ(inf)857 2548 y FD(g)q Fy(2I)929 2518 y FE(k)p FF(f)16 b FE(\000)11 b FF(g)r FE(k)1094 2525 y Fy(1)1765 2518 y FQ(\(2.42\))397 2636 y FE(k)p FF(f)5 b FE(k)476 2644 y FD(C)r FH(\(\012\))p FD(=)p FH(\()p Fy(I)r FH(+)p FD(const)p FH(\))777 2636 y FE(\021)98 b FQ(inf)857 2666 y FD(g)q Fy(2I)r FH(+)p FD(const)1039 2636 y FE(k)p FF(f)16 b FE(\000)11 b FF(g)r FE(k)1204 2643 y Fy(1)1765 2636 y FQ(\(2.43\))951 2784 y(46)p eop %%Page: 47 47 bop 60 91 a FQ(The)13 b(quotien)o(t)e(\(semi\)norms)f(in)i FF(C)t FQ(\(\012\))p FF(=)p FE(I)17 b FQ(and)c FF(C)t FQ(\(\012\))p FF(=)p FQ(\()p FE(I)7 b FQ(+)s FF(const)p FQ(\))13 b(are)f(giv)o(en)g(b)o(y)g (simple)e(explicit)60 152 y(form)o(ulae:)60 253 y FM(Prop)r(osition)18 b(2.35)24 b FP(L)n(et)17 b FF(f)i FE(2)14 b FF(C)t FQ(\(\012\))p FP(.)22 b(Then:)93 360 y(\(a\))38 b FQ(lim)182 390 y FH(\003)p Fy(\0451)285 360 y FE(j)p FQ(\003)p FE(j)347 342 y Fy(\000)p FH(1)402 311 y Fx(\015)402 335 y(\015)402 360 y(\015)437 327 y(P)425 398 y FD(a)p Fy(2)p FH(\003)500 360 y FF(T)529 367 y FD(a)550 360 y FF(f)579 311 y Fx(\015)579 335 y(\015)579 360 y(\015)602 387 y Fy(1)657 360 y FP(exists)18 b(and)g(e)n(quals)g FE(k)p FF(f)5 b FE(k)1107 368 y FD(C)r FH(\(\012\))p FD(=)p Fy(I)1229 360 y FP(.)95 500 y(\(b\))39 b FQ(lim)182 530 y FH(\003)p Fy(\0451)285 500 y FE(j)p FQ(\003)p FE(j)347 482 y Fy(\000)p FH(1)402 450 y Fx(\015)402 475 y(\015)402 500 y(\015)437 467 y(P)425 538 y FD(a)p Fy(2)p FH(\003)500 500 y FF(T)529 507 y FD(a)550 500 y FF(f)579 450 y Fx(\015)579 475 y(\015)579 500 y(\015)602 527 y FD(C)r FH(\(\012\))p FD(=const)803 500 y FP(exists)18 b(and)f(e)n(quals)i FE(k)p FF(f)5 b FE(k)1253 508 y FD(C)r FH(\(\012\))p FD(=)p FH(\()p Fy(I)r FH(+)p FD(const)p FH(\))1512 500 y FP(.)60 652 y FM(2.4.4)55 b(Spaces)19 b(of)g(T)-5 b(ranslation-In)n(v)m(arian)n(t)18 b(In)n(teractions)60 745 y FQ(With)e FE(L)e FQ(=)g Fq(Z)316 724 y FD(d)337 745 y FQ(,)h(it)h(also)h (mak)o(es)e(sense)h(to)g(discuss)h(translation-in)o(v)m(ariance)f(of)h(in)o (teractions:)60 846 y FM(De\014nition)h(2.36)24 b FP(A)o(n)17 b(inter)n(action)i FQ(\010)14 b(=)f(\(\010)927 853 y FD(A)956 846 y FQ(\))k FP(is)h(said)f(to)g(b)n(e)h FQ(translation-in)o(v)m(arian)o(t)g FP(if)525 956 y FQ(\010)560 963 y FD(A)p FH(+)p FD(x)664 956 y FQ(=)28 b FF(T)759 963 y FD(x)780 956 y FQ(\010)815 963 y FD(A)943 956 y FP(for)17 b(al)r(l)i FF(A)13 b FE(2)h(S)t FF(;)22 b(x)14 b FE(2)g Fq(Z)1377 935 y FD(d)1411 956 y FF(:)340 b FQ(\(2)p FF(:)p FQ(44\))133 1065 y(F)l(or)17 b(example,)c(the)j(Ising)h(in)o (teraction)e(\(2.12\))i(is)f(translation-in)o(v)m(arian)o(t)g(i\013)h FF(J)1600 1072 y FD(xy)1654 1065 y FQ(=)d FF(J)5 b FQ(\()p FF(x)11 b FE(\000)f FF(y)r FQ(\))60 1125 y(and)17 b FF(h)183 1132 y FD(x)219 1125 y FQ(=)c FF(h)h FQ(=)j(constan)o(t.)133 1235 y(W)l(e)f(no)o(w)h(in)o(tro)q(duce)f(some)f(imp)q(ortan)o(t)g(Banac)o(h) h(spaces)h(of)f(in)o(teractions:)60 1336 y FM(De\014nition)i(2.37)24 b FP(F)l(or)18 b(e)n(ach)h FF(\013)d FE(\025)g FQ(0)p FP(,)k(we)f(denote)h (by)f FE(B)1140 1318 y FD(\013)1183 1336 y FP(the)g(sp)n(ac)n(e)f(of)h(tr)n (anslation-invariant)60 1397 y(c)n(ontinuous)f(inter)n(actions)g(with)g(norm) 582 1506 y FE(k)p FQ(\010)p FE(k)667 1513 y Fy(B)691 1504 y Fs(\013)743 1506 y FE(\021)816 1465 y Fx(X)810 1557 y FD(X)s Fy(3)p FH(0)891 1506 y FE(j)p FF(X)t FE(j)963 1486 y FD(\013)p Fy(\000)p FH(1)1041 1506 y FE(k)p FQ(\010)1101 1513 y FD(X)1135 1506 y FE(k)1160 1513 y Fy(1)1225 1506 y FF(<)27 b FE(1)14 b FF(:)397 b FQ(\(2)p FF(:)p FQ(45\))60 1654 y FP(Mor)n(e)16 b(gener)n(al)r(ly,)i(for)e(any)h(tr)n(anslation-invariant)g(function)h FF(h)p FQ(:)k FE(S)c(!)c FQ([1)p FF(;)8 b FE(1)p FQ(\))p FP(,)16 b(we)h(let)h FE(B)1729 1661 y FD(h)1768 1654 y FP(b)n(e)e(the)60 1714 y(sp)n(ac)n(e)h(of)g(tr)n(anslation-invariant)i(c)n(ontinuous)f(inter)n (actions)h(with)e(norm)595 1848 y FE(k)p FQ(\010)p FE(k)680 1855 y Fy(B)703 1861 y Fs(h)753 1848 y FE(\021)825 1807 y Fx(X)819 1898 y FD(X)s Fy(3)p FH(0)905 1814 y FF(h)p FQ(\()p FF(X)t FQ(\))p 905 1836 111 2 v 924 1882 a FE(j)p FF(X)t FE(j)1029 1848 y(k)p FQ(\010)1089 1855 y FD(X)1123 1848 y FE(k)1148 1855 y Fy(1)1213 1848 y FF(<)27 b FE(1)14 b FF(:)409 b FQ(\(2)p FF(:)p FQ(46\))60 1998 y(The)16 b(most)g(imp)q(ortan)o(t)f(of)i(these)f (spaces)g(are)g FE(B)956 1980 y FH(0)992 1998 y FQ(\(\\Israel's)f(big)i (Banac)o(h)f(space"\))h(and)f FE(B)1758 1980 y FH(1)1794 1998 y FQ(\(\\Is-)60 2058 y(rael's)h(small)f(Banac)o(h)h(space"\).)26 b(Indeed,)16 b FE(B)898 2040 y FH(0)935 2058 y FQ(is)h(naturally)g(related)g (to)h FF(C)t FQ(\(\012\))f([see)g(Prop)q(osition)60 2118 y(2.40)e(b)q(elo)o (w],)f(and)h(so)g(will)e(b)q(e)h(the)g(natural)h(space)f(on)h(whic)o(h)f(to)g (dev)o(elop)g(the)g(theory)g(of)g(equilib-)60 2178 y(rium)i(measures)h (\(Section)h(2.6\);)g(while)f FE(B)858 2160 y FH(1)895 2178 y FQ(is)h(the)g(space)g(of)g(translation-in)o(v)m(arian)o(t)g(absolutely)60 2238 y(summable)11 b(con)o(tin)o(uous)j(in)o(teractions)f(\(see)g (De\014nition)g(2.3\),)h(and)g(so)h(is)e(a)h(natural)h(space)e(for)h(the)60 2299 y(theory)d(of)h(Gibbs)g(measures.)19 b(Note)11 b(that)h(our)g (assumption)f FF(h)j FE(\025)g FQ(1)e(implies)d(that)j FE(k)p FQ(\010)p FE(k)1650 2306 y Fy(B)1673 2312 y Fs(h)1709 2299 y FE(\025)i(k)p FQ(\010)p FE(k)1847 2307 y Fy(B)1871 2298 y Fr(0)60 2359 y FQ(and)j(hence)e FE(B)323 2366 y FD(h)359 2359 y FE(\032)f(B)447 2341 y FH(0)466 2359 y FQ(;)i(so)h FE(B)591 2341 y FH(0)626 2359 y FQ(is)f(the)g(largest)g(space)h(of)f(in)o(teractions)g (that)g(w)o(e)g(shall)g(consider.)133 2419 y(Let)25 b(us)g(also)g(in)o(tro)q (duce)f(the)g(space)h FE(B)895 2426 y Fk(\014nite)1000 2419 y FQ(consisting)g(of)g(all)f FP(\014nite-r)n(ange)30 b FQ(translation-)60 2479 y(in)o(v)m(arian)o(t)11 b(con)o(tin)o(uous)g(in)o(teractions.)19 b FE(B)814 2486 y Fk(\014nite)907 2479 y FQ(is)11 b(a)h(dense)g(linear)f (subspace)h(of)g(eac)o(h)f(of)h(the)f(Banac)o(h)60 2539 y(spaces)18 b FE(B)244 2546 y FD(h)267 2539 y FQ(.)26 b(It)18 b(will)f(sometimes)e(b)q(e) j(con)o(v)o(enien)o(t)e(to)j(carry)f(out)g(pro)q(ofs)i(\014rst)e(for)g(some)g (class)g(of)60 2600 y(\\nice")e(in)o(teractions)g(|)g(e.g.)f(\014nite-range)i (ones)g(|)f(and)h(then)f(extend)g(to)h(more)e(general)h(in)o(ter-)60 2660 y(actions)h(b)o(y)e(a)i(densit)o(y)e(argumen)o(t.)951 2784 y(47)p eop %%Page: 48 48 bop 133 91 a FM(Remark.)19 b FQ(The)d(h)o(yp)q(othesis)h(of)f FP(c)n(ontinuity)22 b FQ(of)16 b(the)g(in)o(teraction)f(pla)o(ys)h(a)h(role)f (in)g(some)f(but)60 152 y(not)j(all)f(of)h(the)g(theorems)e(b)q(elo)o(w)i (\(the)g(mathematical)o(ly)c(inclined)j(reader)g(is)h(in)o(vited)e(to)i (\014gure)60 212 y(out)g(whic)o(h)g(ones\).)26 b(T)l(o)19 b(a)o(v)o(oid)e (complicating)f(the)h(notation,)i(w)o(e)f(ha)o(v)o(e)f(included)f(con)o(tin)o (uit)o(y)g(as)60 272 y(part)h(of)f(the)g(de\014nition)g(of)h(the)f(spaces)g FE(B)846 254 y FD(\013)870 272 y FQ(,)g FE(B)933 279 y FD(h)971 272 y FQ(and)h FE(B)1099 279 y Fk(\014nite)1180 272 y FQ(.)133 332 y(W)l(e)f(emphasize)f(that)i(all)f(the)h(spaces)g FE(B)895 314 y FD(\013)935 332 y FQ(p)q(ermit)e(t)o(w)o(o-b)q(o)q(dy)j(\(or)f(more)e (generally)h FF(n)p FQ(-b)q(o)q(dy\))60 392 y(in)o(teractions)c(of)h FP(arbitr)n(arily)f(long)k(r)n(ange)t FQ(,)d(pro)o(vided)e(only)i(that)g (they)f(are)h(absolutely)f(summable.)60 452 y(Indeed,)i(for)i(a)g(pure)g FF(n)p FQ(-b)q(o)q(dy)h(in)o(teraction)d(\010,)i(the)f(norms)g FE(k)i(\001)h(k)1261 459 y Fy(B)1285 450 y Fs(\013)1325 452 y FQ(are)d(all)g(equiv)m(alen)o(t:)20 b(w)o(e)15 b(ha)o(v)o(e)60 513 y FE(k)p FQ(\010)p FE(k)145 520 y Fy(B)169 511 y Fs(\013)215 513 y FQ(=)22 b FF(n)304 495 y FD(\013)329 513 y FE(k)p FQ(\010)p FE(k)414 521 y Fy(B)438 512 y Fr(0)457 513 y FQ(.)36 b(The)21 b(di\013erence)f(b)q(et)o(w)o(een)g(the)h(spaces)h FE(B)1307 495 y FD(\013)1352 513 y FQ(is)f(that)g(lo)o(w)o(er)f(v)m(alues)h(of)h FF(\013)60 573 y FQ(p)q(ermit)d(in)o(teractions)i(whic)o(h)f(con)o(tain)h (hea)o(vier)f(con)o(tributions)g(from)g(large)h FF(n)p FQ(,)h(i.e.)e(whic)o (h)g(are)60 633 y(\\more)15 b(strongly)i(man)o(y-b)q(o)q(dy".)k(If)16 b(w)o(e)g(w)o(an)o(t)g(to)g(force)g(\010)g(to)h(b)q(e)f(\\short-range",)i(w)o (e)e(m)o(ust)f(tak)o(e)60 693 y FF(h)p FQ(\()p FF(X)t FQ(\))22 b(to)h(gro)o(w)g(to)f(+)p FE(1)g FQ(as)g(the)g FP(diameter)28 b FQ(of)22 b FF(X)27 b FQ(\(and)22 b(not)h(just)f(its)g(cardinalit)o(y\))f (tends)h(to)60 753 y(in\014nit)o(y)15 b([199)q(,)h(294)q(]:)60 852 y FM(De\014nition)i(2.38)24 b FP(We)19 b(write)h FF(h)708 864 y FE(\030)708 843 y(\035)775 852 y FQ(1)g FP(if,)f(for)g(e)n(ach)h FF(K)h(<)d FE(1)p FP(,)i(ther)n(e)f(exists)h FF(R)e FQ(=)g FF(R)p FQ(\()p FF(K)t FQ(\))g FF(<)f FE(1)60 912 y FP(such)j(that)g FF(h)p FQ(\()p FF(X)t FQ(\))e FE(\025)g FF(K)23 b FP(whenever)f FQ(diam)n(\()p FF(X)t FQ(\))c FE(\025)g FF(R)p FP(.)29 b([Equivalently,)23 b(for)c(e)n(ach)h FF(K)h(<)d FE(1)p FP(,)i(ther)n(e)60 972 y(ar)n(e)e(only)i(\014nitely)h(many)e FF(X)k FP(\(mo)n(dulo)c(tr)n (anslation\))g(such)h(that)f FF(h)p FQ(\()p FF(X)t FQ(\))e FF(<)g(K)t FP(.])28 b(In)19 b(this)g(c)n(ase)g(we)60 1032 y(say)e(that)h FE(B)279 1039 y FD(h)318 1032 y FP(is)f(a)h(sp)n(ac)n(e)f(of)g FQ(short-range)h(in)o(teractions)p FP(.)133 1131 y FQ(The)e(follo)o(wing)g (prop)q(osition)i(will)d(b)q(e)h(useful)g(in)g(Sections)g(3.3)g(and)h(5.1.2:) 60 1229 y FM(Prop)r(osition)h(2.39)24 b FP(Fix)17 b(a)f(tr)n (anslation-invariant)j(weight)f(function)g FF(h)p FQ(:)j FE(S)d(!)c FQ([1)p FF(;)8 b FE(1)p FQ(\))p FP(,)16 b(and)h(\014x)60 1289 y FF(M)i(<)14 b FE(1)p FP(.)22 b(Then:)93 1379 y(\(a\))i(The)18 b(b)n(al)r(l)g FE(f)p FQ(\010:)k FE(k)p FQ(\010)p FE(k)552 1386 y Fy(B)575 1392 y Fs(h)611 1379 y FE(\024)14 b FF(M)5 b FE(g)18 b FP(is)f(a)g FQ(closed)g FP(subset)i(of)e FE(B)1235 1361 y FH(0)1254 1379 y FP(.)95 1477 y(\(b\))25 b(If)17 b FF(h)275 1489 y FE(\030)275 1469 y(\035)339 1477 y FQ(1)g FP(and)h(the)g(single-spin)h (sp)n(ac)n(e)e FQ(\012)959 1484 y FH(0)996 1477 y FP(is)h(\014nite,)g(then)h (the)e(b)n(al)r(l)i FE(f)p FQ(\010:)j FE(k)p FQ(\010)p FE(k)1649 1484 y Fy(B)1672 1490 y Fs(h)1708 1477 y FE(\024)13 b FF(M)5 b FE(g)18 b FP(is)182 1537 y(a)f FQ(compact)g FP(subset)h(of)f FE(B)657 1519 y FH(0)676 1537 y FP(.)133 1677 y FM(Remark.)i FQ(Since)13 b(w)o(e)i(are)f(here)g(using)h(the)g(sup)g(norm)e FE(k)p FQ(\010)1225 1684 y FD(A)1254 1677 y FE(k)1279 1684 y Fy(1)1331 1677 y FQ(to)i(measure)e(the)i(strength)g(of)60 1737 y(an)e(in)o(teraction,)e(all)h(of)h(the)f(ab)q(o)o(v)o(e)g(spaces)h (consist)g(solely)e(of)i FP(b)n(ounde)n(d)k FQ(in)o(teractions.)j(This)12 b(is)g(\014ne)60 1798 y(for)j(systems)e(of)h(b)q(ounded)i(spins,)e(but)h (these)f(spaces)g(are)h(not)f(adequate)h(for)f(treating)h(ph)o(ysically)60 1858 y(in)o(teresting)g(systems)g(of)h FP(unb)n(ounde)n(d)22 b FQ(spins)17 b(\(Gaussian)g(mo)q(del,)e FF(')1321 1840 y FH(4)1356 1858 y FQ(mo)q(del,)g(SOS)h(mo)q(del,)f(etc.\).)60 1918 y(It)g(is)g(an)h(op)q (en)h(problem)d(to)i(devise)e(a)i(ph)o(ysically)e(reasonable)i(and)g (adequately)f(comprehensiv)o(e)60 1978 y(space)j(of)h(in)o(teractions)e(for)i (un)o(b)q(ounded-spin)g(systems.)26 b(W)l(e)18 b(remark)f(that)i(an)o(y)f (suc)o(h)g(space)g(is)60 2038 y(unlik)o(ely)g(to)i(b)q(e)g(a)g(linear)f (space,)i(b)q(ecause)f(it)f(is)h(p)q(erfectly)e(p)q(ossible)i(for)g(an)h(in)o (teraction)e(\010)h(to)60 2099 y(b)q(e)e(reasonable)g(while)f FE(\000)p FQ(\010)h(is)g(unstable.)26 b(Nor)18 b(can)g(it)g(b)q(e)g(a)g(con)o (v)o(ex)f(cone,)g(b)q(ecause)h(\010)h(ma)o(y)d(b)q(e)60 2159 y(reasonable)h(while)e FF(\025)p FQ(\010)i(is)g(unstable)f(for)h FF(\025)g FQ(large)f(and)h(p)q(ositiv)o(e.)k(Ho)o(w)o(ev)o(er,)14 b(suc)o(h)i(a)h(space)f(could)60 2219 y(conceiv)m(ably)f(b)q(e)i(a)f(con)o(v) o(ex)f(subset)i(of)f(an)h(appropriate)g(linear)e(space.)60 2347 y FM(2.4.5)55 b(The)19 b(Observ)m(able)e FF(f)658 2354 y FH(\010)704 2347 y FM(Corresp)r(onding)i(to)f(an)h(In)n(teraction)f FQ(\010)60 2439 y(Let)g(\010)g(b)q(e)g(an)g(in)o(teraction)f(in)h FE(B)680 2421 y FH(0)698 2439 y FQ(.)26 b(Then)18 b(it)g(is)f(useful)h(to)g (de\014ne)f(an)i(observ)m(able)f(\(=)f(function\))60 2499 y FF(f)84 2506 y FH(\010)126 2499 y FQ(that)e(corresp)q(onds)g(roughly)g(to)g (\\the)f(con)o(tribution)g(to)h(the)f(energy)g(from)f(the)h(neigh)o(b)q(orho) q(o)q(d)60 2560 y(of)j(the)f(origin":)750 2620 y FF(f)774 2627 y FH(\010)829 2620 y FE(\021)902 2578 y Fx(X)895 2670 y FD(X)s Fy(3)p FH(0)976 2620 y FE(j)p FF(X)t FE(j)1048 2599 y Fy(\000)p FH(1)1104 2620 y FQ(\010)1139 2627 y FD(X)1187 2620 y FF(:)564 b FQ(\(2)p FF(:)p FQ(47\))951 2784 y(48)p eop %%Page: 49 49 bop 60 91 a FQ(It)15 b(is)g(ob)o(vious)g(from)g(the)g(de\014nition)f(of)i FE(B)838 73 y FH(0)872 91 y FQ(that)g(this)f(sum)f(is)h(con)o(v)o(ergen)o(t)f (in)h FE(k)j(\001)f(k)1619 98 y Fy(1)1671 91 y FQ(norm,)d(and)60 152 y(that)j FE(k)p FF(f)215 159 y FH(\010)242 152 y FE(k)267 159 y Fy(1)318 152 y FE(\024)d(k)p FQ(\010)p FE(k)456 160 y Fy(B)480 150 y Fr(0)499 152 y FQ(.)21 b(Note)16 b(also)h(that)g FF(f)880 159 y FH(\010)924 152 y FQ(is)f(a)g FP(quasilo)n(c)n(al)22 b FQ(function,)16 b(i.e.)e FF(f)20 b FE(2)14 b FF(C)1644 159 y FD(q)q(l)1674 152 y FQ(\(\012\).)133 212 y(This)j(de\014nition)e(of)i FF(f)541 219 y FH(\010)585 212 y FQ(is)f(not)g(unique:)21 b(one)16 b(could)g(equally)f(w)o(ell)g(use)i(instead)797 314 y FF(f)826 294 y Fy(0)821 327 y FH(\010)877 314 y FE(\021)979 273 y Fx(X)943 365 y FD(X)s Fy(3)999 370 y Fs(min)1058 365 y FH(0)1084 314 y FQ(\010)1119 321 y FD(X)1765 314 y FQ(\(2)p FF(:)p FQ(48\))60 455 y(where)j FF(X)k FE(3)302 462 y FD(min)389 455 y FQ(0)d(denotes)f(that)g (0)h(is)e(the)h(smallest)e(elemen)o(t)f(of)k FF(X)j FQ(in)c(lexicographic)e (order,)60 515 y(or)23 b(man)o(y)f(other)h(de\014nitions)f([313)q(,)i (Section)f(3.2].)41 b(The)23 b(imp)q(ortan)o(t)f(p)q(oin)o(t)h(is)f(that)i (all)e(suc)o(h)60 576 y(de\014nitions)f(giv)o(e)g(the)g(same)f(v)m(alue)i (for)f(the)g(mean)g(of)g FF(f)1143 583 y FH(\010)1193 576 y FQ(with)g(resp)q(ect)g(to)h(an)o(y)f(translation-)60 636 y(in)o(v)m(arian)o (t)13 b(measure)g(\(that)h(is,)g(they)f(giv)o(e)g(the)h(same)f(\\mean)g (energy)g(p)q(er)h(site"\);)g(in)g(other)g(w)o(ords,)60 696 y(an)o(y)f(t)o(w)o(o)g(suc)o(h)f(de\014nitions)h(of)g FF(f)653 703 y FH(\010)694 696 y FQ(di\013er)f(b)o(y)h(an)g(elemen)o(t)d(of)j(the)g (space)g FE(I)k FQ(de\014ned)12 b(in)h(Prop)q(osition)60 756 y(2.34.)21 b(Therefore,)14 b(what)i(is)e(de\014ned)g(naturally)h(is)f(not)h (the)f(map)g(\010)g FE(7!)g FF(f)1415 763 y FH(\010)1457 756 y FQ(of)h FE(B)1546 738 y FH(0)1580 756 y FQ(in)o(to)f FF(C)t FQ(\(\012\),)g(but)60 816 y(rather)k(the)h(map)e(\010)h FE(7!)f FQ([)p FF(f)563 823 y FH(\010)590 816 y FQ(])h(of)h FE(B)715 798 y FH(0)752 816 y FQ(in)o(to)f(the)g(quotien)o(t)g(space)g FF(C)t FQ(\(\012\))p FF(=)p FE(I)t FQ(.)28 b(W)l(e)18 b(can)g(then)g (de\014ne)60 877 y(the)e(follo)o(wing)g(subspaces)h(of)f FE(B)663 859 y FH(0)685 979 y FP(Const)42 b FQ(=)g FE(f)p FQ(\010:)21 b FF(f)1049 986 y FH(\010)1091 979 y FQ(=)14 b FF(constant)p FE(g)410 b FQ(\(2.49\))766 1052 y FE(J)50 b FQ(=)42 b FE(f)p FQ(\010:)21 b FF(f)1049 1059 y FH(\010)1091 1052 y FE(2)14 b(I)t(g)571 b FQ(\(2.50\))582 1125 y FE(J)20 b FQ(+)11 b FP(Const)42 b FQ(=)g FE(f)p FQ(\010:)21 b FF(f)1049 1132 y FH(\010)1091 1125 y FE(2)14 b(I)h FQ(+)c FF(const)p FE(g)397 b FQ(\(2.51\))60 1227 y(and)17 b(the)f(corresp)q(onding)h(quotien)o(t)e(\(semi\)norms)622 1330 y FE(k)p FQ(\010)p FE(k)707 1338 y Fy(B)731 1329 y Fr(0)748 1338 y FD(=)p Fk(Const)900 1330 y FQ(=)82 b(inf)979 1360 y FH(\011)p Fy(2)p Fk(Const)1128 1330 y FE(k)p FQ(\010)12 b FE(\000)e FQ(\011)p FE(k)1312 1338 y Fy(B)1336 1329 y Fr(0)1765 1330 y FQ(\(2.52\))682 1420 y FE(k)p FQ(\010)p FE(k)767 1428 y Fy(B)791 1419 y Fr(0)808 1428 y FD(=)p Fy(J)900 1420 y FQ(=)52 b(inf)979 1449 y FH(\011)p Fy(2J)1068 1420 y FE(k)p FQ(\010)12 b FE(\000)e FQ(\011)p FE(k)1252 1428 y Fy(B)1276 1419 y Fr(0)1765 1420 y FQ(\(2.53\))537 1511 y FE(k)p FQ(\010)p FE(k)622 1519 y Fy(B)646 1510 y Fr(0)663 1519 y FD(=)p FH(\()p Fy(J)c FH(+)p Fk(Const)o FH(\))900 1511 y FQ(=)111 b(inf)979 1540 y FH(\011)p Fy(2J)6 b FH(+)p Fk(Const)1186 1511 y FE(k)p FQ(\010)11 b FE(\000)g FQ(\011)p FE(k)1370 1519 y Fy(B)1394 1510 y Fr(0)1765 1511 y FQ(\(2.54\))60 1629 y(It)16 b(is)g(then)g(not)h(di\016cult)e(to)h(v)o (erify)f(that:)60 1725 y FM(Prop)r(osition)j(2.40)24 b FP(L)n(et)17 b FQ(\012)606 1732 y FH(0)643 1725 y FP(b)n(e)h(a)f(c)n(omp)n(act)g(metric)h (sp)n(ac)n(e.)k(Then)c(the)g(map)f FQ([\010])d FE(7!)f FQ([)p FF(f)1727 1732 y FH(\010)1754 1725 y FQ(])k FP(is)h(an)60 1785 y FQ(isometry)e FP(of)i FE(B)354 1767 y FH(0)373 1785 y FF(=)p FE(J)26 b FP(onto)18 b FF(C)t FQ(\(\012\))p FF(=)p FE(I)t FP(,)f(and)h(of)f FE(B)954 1767 y FH(0)973 1785 y FF(=)p FQ(\()p FE(J)k FQ(+)11 b FP(Const)p FQ(\))17 b FP(onto)h FF(C)t FQ(\(\012\))p FF(=)p FQ(\()p FE(I)d FQ(+)c FF(const)p FQ(\))p FP(.)60 1914 y FM(2.4.6)55 b(Ph)n(ysical)19 b(Equiv)m(alence)d(in)i(the)g(Ruelle)f(Sense)60 2006 y FQ(The)f(discussion)h(in)f(the)g(preceding)f(section)h(motiv)m(ates)f (the)h(follo)o(wing)g(de\014nition:)60 2112 y FM(De\014nition)i(2.41)24 b FP(L)n(et)19 b FQ(\010)p FF(;)8 b FQ(\010)624 2094 y Fy(0)654 2112 y FE(2)18 b(B)740 2094 y FH(0)759 2112 y FP(.)29 b(We)19 b(say)g(that)h FQ(\010)g FP(and)g FQ(\010)1270 2094 y Fy(0)1301 2112 y FP(ar)n(e)f FQ(ph)o(ysically)e(equiv)m(alen)o(t)g(in)60 2172 y(the)f(Ruelle)f(sense)i FP(if)g FQ(\010)12 b FE(\000)f FQ(\010)599 2154 y Fy(0)624 2172 y FE(2)j(J)20 b FQ(+)11 b FF(C)t(onst)p FP(,)17 b(i.e.)h(if)f FF(f)1094 2179 y FH(\010)1133 2172 y FE(\000)11 b FF(f)1207 2179 y FH(\010)1232 2170 y Ft(0)1259 2172 y FE(2)j(I)h FQ(+)c FF(const)p FP(.)60 2278 y FQ(Ruelle)j([313])h(w)o (as)h(the)e(\014rst,)i(to)f(our)h(kno)o(wledge,)e(to)i(highligh)o(t)e(the)h (cen)o(tral)f(role)h(pla)o(y)o(ed)f(b)o(y)g(the)60 2338 y(subspace)j FE(I)j FQ(in)c(the)g(v)m(ariational)g(theory)g(\(see)g(also)h([199)q(,)f(209) q(]\).)133 2444 y(W)l(e)d(ha)o(v)o(e)f(no)o(w)i(de\014ned)f(t)o(w)o(o)g (distinct)f(notions)i(of)g(\\ph)o(ysical)e(equiv)m(alence")g(for)h(in)o (teractions:)133 2539 y FE(\017)24 b FQ(The)13 b(DLR)h(sense)f(\(Section)f (2.3.5\),)i(whic)o(h)e(is)h(de\014ned)g(for)g(arbitrary)h(con)o(v)o(ergen)o (t)d(\(but)j(not)182 2600 y(necessarily)f(translation-in)o(v)m(arian)o(t\))h (in)o(teractions,)g(and)g(whic)o(h)g(guaran)o(tees)h(the)f(equalit)o(y)182 2660 y(of)i(the)g(sp)q(eci\014cations)h(\(Theorem)e(2.17\).)951 2784 y(49)p eop %%Page: 50 50 bop 133 91 a FE(\017)24 b FQ(The)11 b(Ruelle)f(sense,)i(whic)o(h)f(is)g (de\014ned)g(for)h(arbitrary)f(translation-in)o(v)m(arian)o(t)h(\(but)f(not)h (nec-)182 152 y(essarily)17 b(absolutely)h(summable)d(or)j(ev)o(en)f(con)o(v) o(ergen)o(t\))f(in)o(teractions)h(in)h FE(B)1620 133 y FH(0)1639 152 y FQ(,)f(and)i(whic)o(h)182 212 y(guaran)o(tees)f(the)g(equalit)o(y)e(of) i(the)g(family)d(of)j(equilibrium)d(measures)h(\(Prop)q(osition)j(2.65)182 272 y(b)q(elo)o(w\).)60 374 y(It)11 b(is)f(natural)i(to)f(ask,)h(therefore,)f (whether)g(these)g(t)o(w)o(o)g(notions)h(are)f(equiv)m(alen)o(t)e(on)j(their) e(common)60 434 y(domain)15 b(of)i(de\014nition.)k(The)16 b(answ)o(er,)g (fortunately)l(,)g(is)g(y)o(es:)60 548 y FM(Theorem)h(2.42)24 b FP(L)n(et)15 b(the)h(single-spin)h(sp)n(ac)n(e)f FQ(\012)983 555 y FH(0)1018 548 y FP(b)n(e)g(a)f(c)n(omplete)i(sep)n(ar)n(able)e(metric)h (sp)n(ac)n(e,)g(and)60 608 y(let)21 b FQ(\010)p FF(;)8 b FQ(\010)223 590 y Fy(0)256 608 y FP(b)n(e)20 b(inter)n(actions)h(in)g FE(B)686 590 y FH(1)705 608 y FP(.)31 b(Then)21 b FQ(\010)f FP(and)h FQ(\010)1069 590 y Fy(0)1101 608 y FP(ar)n(e)f(physic)n(al)r(ly)g(e)n (quivalent)j(in)d(the)h(DLR)60 668 y(sense)e(if)e(and)g(only)h(if)g(they)f (ar)n(e)g(physic)n(al)r(ly)h(e)n(quivalent)h(in)f(the)g(R)o(uel)r(le)h (sense.)133 832 y FQ(In)12 b(Sections)g(3.3)g(and)h(5.1.2)f(w)o(e)g(will)e (need)i(a)g(v)o(ersion)g(of)g(Prop)q(osition)h(2.39)g(\\mo)q(dulo)f(ph)o (ysical)60 892 y(equiv)m(alence".)25 b(Unfortunately)l(,)18 b(w)o(e)g(ha)o(v)o(e)f(not)h(b)q(een)h(able)e(to)i(pro)o(v)o(e)e(suc)o(h)h(a) h(result)e(for)i FE(B)1791 874 y FH(1)1828 892 y FQ(\(or)60 953 y(an)o(y)13 b(space)h FE(B)312 935 y FD(\013)336 953 y FQ(\),)f(and)h(w)o(e)f(do)h(not)g(kno)o(w)f(whether)g(it)g(it)g(true.)20 b(All)12 b(w)o(e)h(ha)o(v)o(e)f(is)h(a)h(result)f(for)h(spaces)60 1013 y FE(B)93 1020 y FD(h)131 1013 y FQ(of)j FP(short-r)n(ange)j FQ(in)o(teractions:)60 1127 y FM(Prop)r(osition)e(2.43)24 b FP(If)17 b FF(h)579 1139 y FE(\030)579 1119 y(\035)643 1127 y FQ(1)g FP(and)h(the)f(single-spin)i(sp)n(ac)n(e)e FQ(\012)1262 1134 y FH(0)1299 1127 y FP(is)g(\014nite,)h(then)g(for)f(e)n(ach)g FF(M)i(<)60 1187 y FE(1)g FP(the)h(sets)g FE(f)p FQ(\010:)25 b FE(k)p FQ(\010)p FE(k)494 1195 y Fy(B)517 1201 y Fs(h)538 1195 y FD(=)p Fy(J)605 1187 y FE(\024)17 b FF(M)5 b FE(g)20 b FP(and)f FE(f)p FQ(\010:)26 b FE(k)p FQ(\010)p FE(k)1039 1195 y Fy(B)1062 1201 y Fs(h)1082 1195 y FD(=)p FH(\()p Fy(J)5 b FH(+)p FD(C)r(onst)p FH(\))1299 1187 y FE(\024)17 b FF(M)5 b FE(g)20 b FP(ar)n(e)f FQ(closed)g FP(subsets)h(of)60 1247 y FE(B)95 1229 y FH(0)114 1247 y FP(.)60 1377 y FM(2.4.7)55 b(Estimates)17 b(on)h(Hamiltonians:)23 b(Bulk)18 b(v)n(ersus)g(Surface)h (E\013ects)60 1470 y FQ(W)l(e)e(can)g(no)o(w)g(pro)o(v)o(e)f(some)g (estimates)f(on)j(the)e(\014nite-v)o(olume)f(Hamiltonians,)g(whic)o(h)h(will) g(pla)o(y)60 1530 y(a)j(k)o(ey)e(role)h(b)q(oth)h(in)f(the)g(v)m(ariational)g (theory)g(\(Section)g(2.6\))h(and)g(in)f(our)g(applications)h(to)f(the)60 1590 y(renormalization)10 b(group)j(\(Sections)f(3.2)g(and)g(3.3\).)20 b(The)12 b(main)f(ph)o(ysical)g(idea)h(in)f(these)h(estimates)60 1650 y(is)23 b(to)g(distinguish)f(b)q(et)o(w)o(een)g(\\bulk")h(e\013ects)f ([namely)l(,)g(those)h(whic)o(h)f(are)h(of)g(order)g FE(j)p FQ(\003)p FE(j)p FQ(])e(and)60 1710 y(\\surface")15 b(e\013ects)g([those)f (whic)o(h)g(are)h FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\)].)20 b(The)14 b(upshot)i(is)e(that,)h(pro)o(vided)f(one)h(can)f(con)o(trol)60 1771 y(the)19 b(surface)f(con)o(tributions,)h(man)o(y)f(natural)h(quan)o (tities)f(are)h(equiv)m(alen)o(t)e(\\in)i(the)g(bulk":)26 b(this)60 1831 y(includes)16 b(the)g(Hamiltonians)f FF(H)676 1813 y FH(\010)672 1843 y(\003)p FD(;f)t(r)q(ee)795 1831 y FQ(and)i FF(H)934 1813 y FH(\010)930 1843 y(\003)p FD(;\034)987 1831 y FQ(,)f(as)h(w)o(ell)e(as)i (the)f(\\Hamiltonian-lik)o(e)e(ob)s(jects")60 1858 y Fx(P)104 1901 y FD(x)p Fy(2)p FH(\003)182 1891 y FF(T)211 1898 y FD(x)233 1891 y FF(f)257 1898 y FH(\010)300 1891 y FQ(and)j FE(\000)8 b FQ(log)i FF(d\026)568 1898 y FH(\003)595 1891 y FF(=d\026)673 1873 y FH(0)673 1903 y(\003)700 1891 y FQ(.)133 1951 y(F)l(or)17 b FP(fr)n(e)n(e)i FQ(b)q(oundary)e(conditions,)f(it)g(su\016ces)g(to)g(tak)o (e)g(\010)h(in)f(the)g(\\big")h(Banac)o(h)f(space)g FE(B)1824 1933 y FH(0)1843 1951 y FQ(:)60 2053 y FM(Prop)r(osition)i(2.44)24 b FP(L)n(et)17 b FQ(\010)d FE(2)g(B)702 2035 y FH(0)721 2053 y FP(.)22 b(Then)133 2113 y(\(a\))698 2173 y FE(k)p FF(H)767 2153 y FH(\010)763 2186 y(\003)p FD(;f)t(r)q(ee)870 2173 y FE(k)895 2180 y Fy(1)960 2173 y FE(\024)27 b(j)p FQ(\003)p FE(j)8 b(k)p FQ(\010)p FE(k)1181 2182 y Fy(B)1205 2172 y Fr(0)1238 2173 y FF(:)513 b FQ(\(2)p FF(:)p FQ(55\))133 2260 y FP(\(b\))551 2370 y FE(k)p FF(H)620 2350 y FH(\010)616 2383 y(\003)p FD(;f)t(r)q(ee)723 2370 y FE(k)748 2377 y Fy(1)827 2370 y FQ(=)41 b FE(j)p FQ(\003)p FE(j)8 b(k)p FQ(\010)p FE(k)1061 2379 y Fy(B)1085 2369 y Fr(0)1102 2379 y FD(=)p Fy(J)1172 2370 y FQ(+)19 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))827 2443 y(=)41 b FE(j)p FQ(\003)p FE(j)8 b(k)p FF(f)1025 2450 y FH(\010)1053 2443 y FE(k)1078 2451 y FD(C)r FH(\(\012\))p FD(=)p Fy(I)1219 2443 y FQ(+)19 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))366 b(\(2.56\))60 2553 y FP(as)17 b FQ(\003)d FE(\045)g(1)j FP(\(van)h(Hove\).)951 2784 y FQ(50)p eop %%Page: 51 51 bop 133 91 a FP(\(c\))409 183 y FE(k)p FF(H)478 162 y FH(\010)474 195 y(\003)p FD(;f)t(r)q(ee)581 183 y FE(k)606 190 y FD(C)r FH(\(\012\))p FD(=const)831 183 y FQ(=)41 b FE(j)p FQ(\003)p FE(j)8 b(k)p FQ(\010)p FE(k)1065 191 y Fy(B)1089 182 y Fr(0)1106 191 y FD(=)p FH(\()p Fy(J)e FH(+)p FD(C)r(onst)p FH(\))1325 183 y FQ(+)20 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))831 255 y(=)41 b FE(j)p FQ(\003)p FE(j)8 b(k)p FF(f)1029 262 y FH(\010)1057 255 y FE(k)1082 263 y FD(C)r FH(\(\012\))p FD(=)p FH(\()p Fy(I)r FH(+)p FD(const)p FH(\))1360 255 y FQ(+)20 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))224 b(\(2.57\))60 347 y FP(as)17 b FQ(\003)d FE(\045)g(1)j FP(\(van)h(Hove\).)133 407 y(\(d\))632 423 y Fx(\015)632 448 y(\015)632 473 y(\015)p FF(H)699 453 y FH(\010)695 486 y(\003)p FD(;f)t(r)q(ee)813 473 y FE(\000)867 432 y Fx(X)863 524 y FD(x)p Fy(2)p FH(\003)939 473 y FF(T)968 480 y FD(x)989 473 y FF(f)1013 480 y FH(\010)1041 423 y Fx(\015)1041 448 y(\015)1041 473 y(\015)1064 500 y Fy(1)1129 473 y FE(\024)27 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))447 b(\(2)p FF(:)p FQ(58\))60 590 y FP(as)17 b FQ(\003)d FE(\045)g(1)j FP(\(van)h(Hove\).)60 676 y FQ(Note,)13 b(in)h(particular,)f(part)h(\(d\))g (of)g(this)f(prop)q(osition:)21 b(since)13 b FF(f)1222 683 y FH(\010)1263 676 y FQ(is)h(\(roughly\))g(\\the)g(con)o(tribution)60 736 y(to)19 b(the)g(energy)f(from)g(the)g(neigh)o(b)q(orho)q(o)q(d)j(of)e (the)g(origin",)g(it)f(follo)o(ws)h(that)1526 703 y Fx(P)1570 747 y FD(x)p Fy(2)p FH(\003)1648 736 y FF(T)1677 743 y FD(x)1699 736 y FF(f)1723 743 y FH(\010)1769 736 y FQ(ough)o(t)60 796 y(to)d(b)q(e)f(\(roughly\))g(\\the)h(con)o(tribution)f(to)g(the)g(energy)g (from)f(the)h(v)o(olume)e(\003".)21 b(And)15 b(indeed)g(it)g(is:)60 857 y(while)c(this)h(sum)f(do)q(es)i(not)g(exactly)d(equal)i FF(H)894 839 y FH(\010)890 869 y(\003)p FD(;f)t(r)q(ee)997 857 y FQ(,)g(it)g(di\013ers)g(from)f(it)h(only)f(b)o(y)h(a)g(\\surface")h (term.)60 917 y(In)k(this)f(sense,)357 884 y Fx(P)401 927 y FD(x)p Fy(2)p FH(\003)479 917 y FF(T)508 924 y FD(x)530 917 y FF(f)554 924 y FH(\010)598 917 y FQ(can)h(b)q(e)g(though)o(t)h(of)f(as)h(y) o(et)e(another)i(Hamiltonian)d(for)i(v)o(olume)e(\003,)60 977 y(corresp)q(onding)i(to)g(some)e(new)h(t)o(yp)q(e)g(of)h(\\b)q(oundary)g (condition".)133 1057 y(In)f(order)g(to)g(con)o(trol)f(the)h(Hamiltonians)e (with)i(general)f(external)g(b)q(oundary)i(conditions,)e(it)60 1117 y(is)h(necessary)g(to)h(tak)o(e)e(\010)i(to)f(lie)f(in)h(the)g(\\small") g(Banac)o(h)g(space)g FE(B)1323 1099 y FH(1)1342 1117 y FQ(:)60 1203 y FM(Prop)r(osition)i(2.45)24 b FP(L)n(et)17 b FQ(\010)d FE(2)g(B)702 1185 y FH(1)721 1203 y FP(.)22 b(Then:)133 1263 y(\(a\))17 b FQ(\010)h FP(is)f(absolutely)i(summable,)g(and)736 1354 y FE(k)p FF(H)805 1334 y FH(\010)801 1366 y(\003)832 1354 y FE(k)857 1361 y Fy(1)922 1354 y FE(\024)28 b(j)p FQ(\003)p FE(j)8 b(k)p FQ(\010)p FE(k)1144 1363 y Fy(B)1168 1353 y Fr(1)1201 1354 y FF(:)550 b FQ(\(2)p FF(:)p FQ(59\))133 1446 y FP(\(b\))589 1537 y FE(k)p FF(H)658 1516 y FH(\010)654 1549 y(\003)685 1537 y FE(k)710 1544 y Fy(1)789 1537 y FQ(=)42 b FE(j)p FQ(\003)p FE(j)8 b(k)p FQ(\010)p FE(k)1024 1545 y Fy(B)1048 1536 y Fr(0)1065 1545 y FD(=)p Fy(J)1134 1537 y FQ(+)19 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))789 1609 y(=)42 b FE(j)p FQ(\003)p FE(j)8 b(k)p FF(f)988 1616 y FH(\010)1015 1609 y FE(k)1040 1617 y FD(C)r FH(\(\012\))p FD(=)p Fy(I)1181 1609 y FQ(+)19 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))404 b(\(2.60\))60 1701 y FP(as)17 b FQ(\003)d FE(\045)g(1)j FP(\(van)h(Hove\).)133 1761 y(\(c\))447 1852 y FE(k)p FF(H)516 1832 y FH(\010)512 1865 y(\003)544 1852 y FE(k)569 1860 y FD(C)r FH(\(\012\))p FD(=const)793 1852 y FQ(=)42 b FE(j)p FQ(\003)p FE(j)8 b(k)p FQ(\010)p FE(k)1028 1861 y Fy(B)1052 1851 y Fr(0)1069 1861 y FD(=)p FH(\()p Fy(J)d FH(+)p FD(C)r(onst)p FH(\))1288 1852 y FQ(+)19 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))793 1925 y(=)42 b FE(j)p FQ(\003)p FE(j)8 b(k)p FF(f)992 1932 y FH(\010)1019 1925 y FE(k)1044 1933 y FD(C)r FH(\(\012\))p FD(=)p FH(\()p Fy(I)r FH(+)p FD(const)p FH(\))1323 1925 y FQ(+)19 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))262 b(\(2.61\))60 2016 y FP(as)17 b FQ(\003)d FE(\045)g(1)j FP(\(van)h(Hove\).)133 2076 y(\(d\))234 2168 y FE(k)p FF(W)312 2147 y FH(\010)305 2180 y(\003)p FD(;)p FH(\003)363 2171 y Fs(c)382 2168 y FE(k)407 2175 y Fy(1)472 2168 y FE(\021)27 b(k)p FF(H)607 2147 y FH(\010)603 2180 y(\003)646 2168 y FE(\000)11 b FF(H)740 2147 y FH(\010)736 2180 y(\003)p FD(;f)t(r)q(ee)843 2168 y FE(k)868 2175 y Fy(1)933 2168 y FQ(=)27 b(sup)1001 2207 y FD(\034)t Fy(2)p FH(\012)1080 2168 y FE(k)p FF(H)1149 2147 y FH(\010)1145 2180 y(\003)p FD(;\034)1212 2168 y FE(\000)11 b FF(H)1306 2147 y FH(\010)1302 2180 y(\003)p FD(;f)t(r)q(ee)1409 2168 y FE(k)1434 2175 y Fy(1)1513 2168 y FE(\024)41 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))25 b(\(2.62a\))475 2276 y FE(k)p FF(H)544 2255 y FH(\010)540 2288 y(\003)583 2276 y FE(\000)636 2234 y Fx(X)632 2326 y FD(x)p Fy(2)p FH(\003)709 2276 y FF(T)738 2283 y FD(x)759 2276 y FF(f)783 2283 y FH(\010)811 2276 y FE(k)836 2283 y Fy(1)901 2276 y FE(\024)i FQ(sup)969 2315 y FD(\034)t Fy(2)p FH(\012)1049 2276 y FE(k)p FF(H)1118 2255 y FH(\010)1114 2288 y(\003)p FD(;\034)1181 2276 y FE(\000)1235 2234 y Fx(X)1231 2326 y FD(x)p Fy(2)p FH(\003)1307 2276 y FF(T)1336 2283 y FD(x)1357 2276 y FF(f)1381 2283 y FH(\010)1409 2276 y FE(k)1434 2283 y Fy(1)1513 2276 y FE(\024)41 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))22 b(\(2.62b\))60 2405 y FP(as)17 b FQ(\003)d FE(\045)g(1)j FP(\(van)h(Hove\).)133 2491 y FQ(In)e(summary)l(,)d(\010)h FE(2)g(B)547 2473 y FH(0)582 2491 y FQ(su\016ces)i(to)g(con)o(trol)g(the)g(Hamiltonian)e(with)i FP(fr)n(e)n(e)j FQ(b)q(oundary)e(condi-)60 2551 y(tions,)c(but)g(\010)h FE(2)g(B)407 2533 y FH(1)438 2551 y FQ(is)f(needed)f(in)g(order)h(to)g(con)o (trol)f(the)g(Hamiltonian)f(with)h FP(external)20 b FQ(b)q(oundary)60 2611 y(conditions)c(and)h(hence)f(to)g(apply)g(the)g(theory)g(of)h(sp)q (eci\014cations)f(and)h(Gibbs)g(measures.)951 2784 y(51)p eop %%Page: 52 52 bop 60 91 a FM(2.4.8)55 b(Ho)n(w)20 b(to)e(Obtain)h(an)g(In)n(teraction)f (from)f(a)i(Gibbs)g(Measure)60 184 y FQ(If)d FF(\026)h FQ(is)g(a)g(Gibbs)g (measure)e(for)i(an)h(in)o(teraction)d(\010)g FE(2)g(B)1100 166 y FH(1)1119 184 y FQ(,)h(then)h(the)f(DLR)i(equations)f(p)q(ermit)e(us)60 244 y(to)i(read)f(o\013)h(the)f(in)o(teraction)f(\010,)h(mo)q(dulo)g(ph)o (ysical)f(equiv)m(alence,)f(from)i(the)g(measure)e FF(\026)p FQ(:)60 358 y FM(Prop)r(osition)k(2.46)93 460 y FP(\(a\))24 b(L)n(et)12 b FF(\026)i FP(b)n(e)f(a)f(Gibbs)i(me)n(asur)n(e)e(\(not)h(ne)n (c)n(essarily)g(tr)n(anslation-invariant\))h(for)e(an)h(inter)n(action)182 520 y FQ(\010)h FE(2)g(B)313 502 y FH(1)332 520 y FP(.)22 b(Then)580 545 y Fx(\015)580 569 y(\015)580 594 y(\015)p FE(\000)8 b FQ(log)727 561 y FF(d\026)781 568 y FH(\003)p 727 583 82 2 v 727 628 a FF(d\026)781 611 y FH(0)781 641 y(\003)832 594 y FE(\000)894 553 y Fx(X)890 645 y FD(x)p Fy(2)p FH(\003)967 594 y FF(T)996 601 y FD(x)1017 594 y FF(f)1041 601 y FH(\010)1069 545 y Fx(\015)1069 569 y(\015)1069 594 y(\015)1092 621 y FD(C)r FH(\(\012\))p FD(=const)1302 594 y FE(\024)28 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))273 b(\(2)p FF(:)p FQ(63\))182 723 y FP(as)17 b FQ(\003)d FE(\045)g(1)j FP(\(van)h(Hove\).)23 b(In)18 b(fact,)g(this)f(b)n (ound)h(is)f(uniform)g(for)g FF(\026)d FE(2)g(G)s FQ(\(\005)1602 705 y FH(\010)1629 723 y FQ(\))p FP(.)95 825 y(\(b\))25 b(L)n(et)19 b FF(\026)297 832 y FH(1)317 825 y FF(;)8 b(\026)368 832 y FH(2)407 825 y FP(b)n(e)20 b(Gibbs)f(me)n(asur)n(es)g(\(not)h(ne)n(c)n (essarily)f(tr)n(anslation-invariant\))i(for)d(inter)n(ac-)182 885 y(tions)g FQ(\010)338 892 y FH(1)358 885 y FF(;)8 b FQ(\010)415 892 y FH(2)448 885 y FE(2)14 b(B)530 867 y FH(1)549 885 y FP(,)k(r)n(esp)n(e) n(ctively.)k(Then)535 967 y Fx(\015)535 992 y(\015)535 1017 y(\015)p FQ(log)635 983 y FF(d\026)689 990 y FH(1\003)p 635 1005 99 2 v 635 1051 a FF(d\026)689 1058 y FH(2\003)738 967 y Fx(\015)738 992 y(\015)738 1017 y(\015)762 1044 y Fy(1)840 1017 y FE(\024)42 b FQ(2)p FE(j)p FQ(\003)p FE(j)8 b(k)p FQ(\010)1075 1024 y FH(1)1106 1017 y FE(\000)j FQ(\010)1191 1024 y FH(2)1211 1017 y FE(k)1236 1025 y Fy(B)1260 1016 y Fr(0)1277 1025 y FD(=)p FH(\()p Fy(J)5 b FH(+)p Fk(Const)p FH(\))1496 1017 y FQ(+)25 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))1765 1114 y(\(2.64\))390 1162 y Fx(\015)390 1187 y(\015)390 1212 y(\015)p FQ(log)489 1178 y FF(d\026)543 1185 y FH(1\003)p 489 1200 V 489 1246 a FF(d\026)543 1253 y FH(2\003)593 1162 y Fx(\015)593 1187 y(\015)593 1212 y(\015)616 1239 y FD(C)r FH(\(\012\))p FD(=const)841 1212 y FQ(=)42 b FE(j)p FQ(\003)p FE(j)8 b(k)p FQ(\010)1051 1219 y FH(1)1081 1212 y FE(\000)j FQ(\010)1166 1219 y FH(2)1186 1212 y FE(k)1211 1220 y Fy(B)1235 1211 y Fr(0)1252 1220 y FD(=)p FH(\()p Fy(J)6 b FH(+)p Fk(Const)o FH(\))1472 1212 y FQ(+)25 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))1765 1310 y(\(2.65\))182 1420 y FP(as)d FQ(\003)h FE(\045)h(1)e FP(\(van)h(Hove\).)39 b(In)22 b(fact,)j(this)d(b)n(ound)h(is)f(uniform)h(for)e FF(\026)1538 1427 y FH(1)1582 1420 y FE(2)i(G)s FQ(\(\005)1727 1402 y FH(\010)1752 1407 y Fr(1)1771 1420 y FQ(\))g FP(and)182 1480 y FF(\026)211 1487 y FH(2)245 1480 y FE(2)14 b(G)s FQ(\(\005)381 1462 y FH(\010)406 1467 y Fr(2)425 1480 y FQ(\))p FP(.)133 1594 y FQ(P)o(art)20 b(\(a\))h(of)f(this)g(prop)q(osition)h(tells)e(us)h(that)h(the)f(in)o (teraction)f(can)h(b)q(e)g(reconstructed)g(b)o(y)60 1654 y(taking)e(the)f (logarithm)f(of)i(the)f(\014nite-v)o(olume)e(densities.)23 b(This)18 b(corresp)q(onds)g(to)g(the)f(fact)h(that)60 1714 y(Boltzmann)h(factors)j(are)f(exp)q(onen)o(tials)g(of)g(Hamiltonians.)34 b(An)21 b(immedi)o(ate)e(consequence)h(of)60 1775 y(this)g(is)g(part)g (\(b\).)32 b(One)20 b(implication)d(of)k(part)f(\(b\))g(is)g(that)g(the)g (reconstructed)f(in)o(teraction)g(is)60 1835 y(unique)f(mo)q(dulo)h(ph)o (ysical)f(equiv)m(alence)g(\(Gri\016ths-Ruelle)g(theorem\):)25 b(just)20 b(tak)o(e)e FF(\026)1685 1842 y FH(1)1724 1835 y FQ(=)h FF(\026)1810 1842 y FH(2)1849 1835 y FQ(in)60 1895 y(\(2.65\))j(to)f (conclude)g(that)h FE(k)p FQ(\010)647 1902 y FH(1)681 1895 y FE(\000)14 b FQ(\010)769 1902 y FH(2)789 1895 y FE(k)814 1903 y Fy(B)838 1894 y Fr(0)855 1903 y FD(=)p FH(\()p Fy(J)6 b FH(+)p Fk(Const)o FH(\))1072 1895 y FQ(=)23 b(0.)36 b(In)21 b(other)g(w)o(ords,)i(if)e FF(\026)g FQ(is)g(a)h(Gibbs)60 1955 y(measure)14 b(for)i(in)o(teractions)e(\010)621 1962 y FH(1)641 1955 y FF(;)8 b FQ(\010)698 1962 y FH(2)732 1955 y FE(2)14 b(B)814 1937 y FH(1)833 1955 y FQ(,)h(then)g(\010)1007 1962 y FH(1)1043 1955 y FQ(and)h(\010)1172 1962 y FH(2)1207 1955 y FQ(m)o(ust)e(b)q(e)i(ph)o(ysically)e(equiv)m(alen)o(t)f(in)60 2015 y(the)i(Ruelle)f(sense.)21 b(Of)15 b(course,)g(w)o(e)g(already)g(knew)g (this)h(\(Corollary)f(2.18)h(plus)g(Theorem)e(2.42\).)133 2076 y(It)d(is)h(curious)f(that)h(although)h(\010)724 2083 y FH(1)744 2076 y FF(;)8 b FQ(\010)801 2083 y FH(2)832 2076 y FQ(are)j(required)g(to)h (b)q(elong)g(to)g(the)f(\\small")g(Banac)o(h)g(space)60 2136 y FE(B)95 2118 y FH(1)114 2136 y FQ(,)k(the)g(\014nal)h(estimate)d(is)j(in)f (terms)f(of)h(the)g FE(B)940 2118 y FH(0)959 2136 y FF(=)p FE(J)25 b FQ(norm,)14 b(hence)h(m)o(uc)o(h)e(stronger.)22 b(The)15 b(reason)60 2196 y(is)e(that)h(\010)244 2203 y FH(1)264 2196 y FF(;)8 b FQ(\010)321 2203 y FH(2)355 2196 y FE(2)14 b(B)437 2178 y FH(1)470 2196 y FQ(is)f(needed)g(in)g(order)h(to)g(ensure)f(that)h (the)g FP(b)n(oundary)j FQ(energy)c(con)o(tributions)60 2256 y(are)f(indeed)g FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\);)h(but)f(once)g (this)g(is)g(done,)h(then)f(the)g FP(bulk)19 b FQ(energy)12 b(con)o(tribution)g(is)g(determined)60 2316 y(b)o(y)k(the)g FE(B)247 2298 y FH(0)266 2316 y FF(=)p FE(J)25 b FQ(norm,)15 b(as)i(in)f(Prop)q(osition)h(2.44\(b\).)60 2446 y FM(2.4.9)55 b(T)-5 b(ranslation-In)n(v)m(arian)n(t)19 b(Sp)r(eci\014cations)e(and)i (Gibbs)g(Measures)60 2539 y FQ(W)l(e)g(can)g(no)o(w)h(examine)d(the)i(theory) g(of)g(sp)q(eci\014cations)h(and)f(Gibbs)h(measures)e(under)h(the)g(h)o(y-)60 2599 y(p)q(othesis)e(of)f(translation)h(in)o(v)m(ariance.)951 2784 y(52)p eop %%Page: 53 53 bop 60 91 a FM(De\014nition)18 b(2.47)24 b FP(A)17 b(sp)n(e)n(ci\014c)n (ation)h FQ(\005)13 b(=)h(\()p FF(\031)921 98 y FH(\003)947 91 y FQ(\))966 98 y FH(\003)p Fy(2S)1058 91 y FP(is)j(said)g(to)h(b)n(e)f FQ(translation-in)o(v)m(arian)o(t)h FP(if)673 188 y FF(\031)701 195 y FH(\003)727 188 y FQ(\()p FF(!)r(;)8 b(A)p FQ(\))28 b(=)f FF(\031)977 195 y FH(\003+)p FD(a)1050 188 y FQ(\()p FF(T)1098 195 y FD(a)1118 188 y FF(!)r(;)8 b(T)1201 195 y FD(a)1221 188 y FF(A)p FQ(\))488 b(\(2)p FF(:)p FQ(66\))60 286 y FP(for)17 b(al)r(l)i FQ(\003)13 b FE(2)h(S)t FP(,)k FF(!)e FE(2)e FQ(\012)p FP(,)j FF(A)d FE(2)g(F)22 b FP(and)c FF(a)13 b FE(2)h Fq(Z)896 265 y FD(d)917 286 y FP(.)60 385 y FQ(In)e(particular,)g(if)f(\010)h(is)g(a)g (translation-in)o(v)m(arian)o(t)h(\(and)f(con)o(v)o(ergen)o(t,)f FF(\026)1360 367 y FH(0)1380 385 y FQ(-admissible\))f(in)o(teraction,)60 445 y(then)16 b(\005)208 427 y FH(\010)251 445 y FQ(is)h(ob)o(viously)e(a)i (translation-in)o(v)m(arian)o(t)f(sp)q(eci\014cation.)133 506 y(Fix)26 b(a)g(translation-in)o(v)m(arian)o(t)h(sp)q(eci\014cation)f(\005.)51 b(W)l(e)27 b(denote)f(b)o(y)g FE(G)1503 513 y FD(inv)1556 506 y FQ(\(\005\))31 b FE(\021)g(G)s FQ(\(\005\))17 b FE(\\)60 566 y FF(M)107 573 y FH(+1)p FD(;inv)216 566 y FQ(\(\012\))22 b(the)h(set)f(of)g(all)g(translation-in)o(v)m(arian)o(t)h(measures)e (consisten)o(t)h(with)g(\005.)39 b FE(G)1762 573 y FD(inv)1816 566 y FQ(\(\005\))60 626 y(is)16 b(a)h(con)o(v)o(ex)e(set,)g(and)i(its)f (extreme)e(p)q(oin)o(ts)i(are)h(c)o(haracterized)d(b)o(y)i(the)g(follo)o (wing)g(theorem:)60 717 y FM(Prop)r(osition)i(2.48)24 b FP(L)n(et)17 b FQ(\005)g FP(b)n(e)h(a)f(tr)n(anslation-invariant)i(sp)n(e)n(ci\014c)n (ation.)j(Then:)133 777 y(\(a\))e(A)g(me)n(asur)n(e)f FF(\026)g FE(2)g(G)595 784 y FD(inv)649 777 y FQ(\(\005\))g FP(is)h(extr)n(emal)h(in)f FE(G)1089 784 y FD(inv)1143 777 y FQ(\(\005\))f FP(if)h(and)g(only)h(if)f(it) g(is)g(extr)n(emal)h(in)60 837 y FF(M)107 844 y FH(+1)p FD(;inv)216 837 y FQ(\(\012\))p FP(,)c(i.e.)h(if)f(and)h(only)g(if)f(it)h(is)f(er)n(go)n (dic.)133 897 y(\(b\))h FE(G)243 904 y FD(inv)296 897 y FQ(\(\005\))f FP(is)g(a)g(fac)n(e)h(of)f FF(M)686 904 y FH(+1)p FD(;inv)795 897 y FQ(\(\012\))p FP(:)22 b(that)c(is,)f(if)g FF(\026;)8 b(\027)17 b FE(2)d FF(M)1305 904 y FH(+1)p FD(;inv)1414 897 y FQ(\(\012\))j FP(and)h FQ(0)c FF(<)g(\025)g(<)g FQ(1)k FP(ar)n(e)60 957 y(such)g(that)f FF(\025\026)12 b FQ(+)f(\(1)h FE(\000)f FF(\025)p FQ(\))p FF(\027)17 b FE(2)d(G)658 964 y FD(inv)712 957 y FQ(\(\005\))p FP(,)i(then)j(in)f(fact)g FF(\026;)8 b(\027)17 b FE(2)d(G)1252 964 y FD(inv)1305 957 y FQ(\(\005\))p FP(.)133 1048 y FQ(It)h(is)g(no)o(w)g(the)g(righ)o(t)g(momen)o(t)d(to)j(mak)o(e)e (some)h(remarks)g(that)h(ma)o(y)f(at)h(\014rst)h(seem)d(p)q(edan)o(tic,)60 1108 y(but)24 b(could)g(actually)f(b)q(e)h(helpful)e(to)j(p)q(eople)e(haun)o (ted)h(b)o(y)f(an)i(\(unfortunately)e(established\))60 1168 y(terminology)e(that)j(is)f(confusing)h(or)f(at)h(least)f(b)q(othersomely)e (subtle.)42 b(The)23 b(situation)g(is)g(as)60 1229 y(follo)o(ws.)38 b(If)22 b(the)f(sp)q(eci\014cation)h(\005)f(is)h(translation-in)o(v)m(arian)o (t,)h(w)o(e)f(ha)o(v)o(e)f(at)h(our)g(disp)q(osal)h(t)o(w)o(o)60 1289 y(di\013eren)o(t)15 b(spaces)i(of)g(measures)e(of)h(ph)o(ysical)f(in)o (terest:)133 1379 y FE(\017)24 b(G)s FQ(\(\005\),)h(the)f(space)g(of)g FP(al)r(l)31 b FQ(measures)23 b(consisten)o(t)g(with)h(\005,)i(whether)d(or)i (not)f(they)g(are)182 1440 y(translation-in)o(v)m(arian)o(t;)16 b(and)133 1538 y FE(\017)24 b(G)212 1545 y FD(inv)265 1538 y FQ(\(\005\),)16 b(the)g(space)g(of)h(all)e FP(tr)n(anslation-invariant)23 b FQ(measures)15 b(consisten)o(t)h(with)g(\005.)60 1628 y(Ph)o(ysical)g (\\macrostates")g(are)h(in)o(terpreted)e(as)i(extremal)d(measures,)h(but)i (the)f(question)h(is:)k(ex-)60 1689 y(tremal)14 b(in)i(whic)o(h)g(space?)22 b(It)16 b(is)g(imp)q(ortan)o(t)f(to)i(observ)o(e)e(that)i(w)o(e)f(ha)o(v)o(e) f FP(thr)n(e)n(e)20 b FQ(p)q(ossibilities:)106 1779 y(\(i\))k(The)c(extremal) d(p)q(oin)o(ts)k(of)f FE(G)s FQ(\(\005\).)31 b(These)20 b(measures)e(are)i(c) o(haracterized)f(b)o(y)g(v)o(ery)g(strict)182 1839 y(prop)q(erties)13 b(\(Prop)q(osition)i(2.19\):)21 b(they)13 b(sho)o(w)h(no)g(\015uctuations)g (for)g(the)f(observ)m(ables)h(mea-)182 1900 y(surable)g(at)g(in\014nit)o(y)e (\(\\global)j(observ)m(ables"\))f(|)g(whic)o(h,)f(for)h(translation-in)o(v)m (arian)o(t)g(mea-)182 1960 y(sures,)22 b(is)f(larger)g(than)h(the)f(set)g(of) h(translation-in)o(v)m(arian)o(t)f(observ)m(ables)h(\(\\macroscopic)182 2020 y(observ)m(ables"\))14 b(|)g(and)g(they)f(exhibit)f(v)o(ery)h(strong)h (cluster)f(prop)q(erties)h(\(short-range)h(cor-)182 2080 y(relations\).)93 2178 y(\(ii\))23 b(The)15 b(translation-in)o(v)m(arian)o(t)h(extremal)d(p)q (oin)o(ts)i(of)h FE(G)s FQ(\(\005\).)k(This)c(is)f(often)g(a)h(small)d(set,)i (and)182 2238 y(in)j(man)o(y)e(cases)i(it)g(is)g(empt)o(y)l(.)24 b(F)l(or)18 b(example,)e(in)h(the)h(t)o(w)o(o-dimensional)e(Ising)i(an)o (tiferro-)182 2299 y(magnet)h(at)h(lo)o(w)g(temp)q(erature,)f(there)h(are)g (only)f(t)o(w)o(o)h(extremal)e(Gibbs)i(measures:)28 b(one)182 2359 y(has)14 b(+)f(magnetization)f(on)i(the)f(ev)o(en)f(sublattice)g(and)i FE(\000)f FQ(magnetization)f(on)h(the)g(o)q(dd)h(sub-)182 2419 y(lattice)g(\(let)g(us)h(call)f(this)h(measure)f FF(\026)879 2426 y Fy(\006)909 2419 y FQ(\),)h(and)g(the)g(other)g(has)h(the)f(rev)o (erse)e(magnetization)182 2479 y(\(call)h(this)h(measure)f FF(\026)601 2486 y Fy(\007)631 2479 y FQ(\).)20 b(Neither)14 b(of)h(these)g(t)o(w)o(o)g(measures)f(is)g(translation-in)o(v)m(arian)o(t,)h (so)182 2539 y(the)i(set)h(in)f(question)h(is)g(empt)o(y)l(.)23 b(More)17 b(dramatically)l(,)f(there)h(are)h(examples)e(due)h(to)h(v)m(an)182 2600 y(En)o(ter)c(and)i(Mi\030)-22 b(ekisz)13 b([356)q(])h(in)g(whic)o(h)h (there)f(are)h(not)g(ev)o(en)f(an)o(y)h FP(p)n(erio)n(dic)h FQ(extremal)d(Gibbs)182 2660 y(measures.)951 2784 y(53)p eop %%Page: 54 54 bop 79 91 a FQ(\(iii\))23 b(The)g(extremal)d(p)q(oin)o(ts)j(of)g FE(G)742 98 y FD(inv)795 91 y FQ(\(\005\).)40 b(This)23 b(is)f(a)h(m)o(uc)o (h)e(larger)h(set)h(than)g(the)f(one)h(dis-)182 152 y(cussed)c(in)f(\(ii\).) 27 b(In)18 b(particular)g(it)g(is)h(nev)o(er)e(empt)o(y)g(for)h(compact-spin) g(mo)q(dels)f(\(see)i(b)q(e-)182 212 y(lo)o(w\).)35 b(F)l(or)21 b(instance,)h(in)e(the)h(example)e(of)i(the)g(Ising)g(an)o(tiferromagnet,)f (there)g(is)h(only)182 272 y(one)h(translation-in)o(v)m(arian)o(t)g(Gibbs)g (measure)f(|)1152 252 y FH(1)p 1152 260 18 2 v 1152 289 a(2)1175 272 y FQ(\()p FF(\026)1223 279 y Fy(\006)1268 272 y FQ(+)14 b FF(\026)1349 279 y Fy(\007)1379 272 y FQ(\))22 b(|)g(whic)o(h)f(is)h(ob)o (viously)182 332 y(extremal)15 b(in)i FE(G)473 339 y FD(inv)526 332 y FQ(\(\005\))g(but)h(not)f(in)g FE(G)s FQ(\(\005\).)24 b(These)17 b(measures)f(satisfy)i(the)f(comparativ)o(ely)182 392 y(w)o(eak)o(er)f(prop)q(erties)h(of)g(Prop)q(osition)h(2.30:)23 b(they)16 b(are)h(deterministic)d(for)j(the)f(smaller)f(set)182 452 y(of)20 b(translation-in)o(v)m(arian)o(t)g(observ)m(ables,)g(and)g(they)f (exhibit)g(the)g(cluster)g(prop)q(ert)o(y)g(only)182 513 y(in)d(the)g(w)o (eak)o(est)g(\(Cesaro-a)o(v)o(eraged\))h(sense,)f(namely)f(ergo)q(dicit)o(y)l (.)21 b(In)16 b(the)g(mathematical)182 573 y(statistical-mec)o(hanics)10 b(literature,)i(these)g(measures)f(|)h(the)h(extremal)d(p)q(oin)o(ts)j(of)f FE(G)1748 580 y FD(inv)1802 573 y FQ(\(\005\),)182 633 y(or)17 b(equiv)m(alen)o(tly)d(the)i(ergo)q(dic)g(elemen)o(ts)e(of)j FE(G)1052 640 y FD(inv)1105 633 y FQ(\(\005\))f(|)g(are)h(called)e FP(pur)n(e)i(phases)k FQ(for)16 b(the)182 693 y(sp)q(eci\014cation)i(\005.)27 b(\(Unfortunately)l(,)18 b(the)g(term)f(\\pure)i(phase")g(is)f(sometimes)e (used)i(with)182 753 y(di\013eren)o(t)d(but)i(closely)e(related)g(meanings:) 21 b(see)16 b(e.g.)f(App)q(endix)h(B.3.1.\))133 851 y(Whic)o(h)i(set)g(is)g (in)o(terpreted)f(as)i(represen)o(ting)e(the)h(ph)o(ysical)g(\\macrostates")g (is)h(a)f(problem-)60 912 y(dep)q(enden)o(t)i(issue.)34 b(In)20 b(problems)f(where)h(non-translation-in)o(v)m(arian)o(t)i(measures)d(are)i (relev)m(an)o(t)60 972 y(\(in)o(terfaces,)d(surface)i(tension,)f(crystal)g (shap)q(e,)i(w)o(etting,)e(systems)f(with)h(disorder,)h(quasicrys-)60 1032 y(tals\),)26 b(it)e(is)g(mandatory)g(to)h(consider)f(the)g(set)h FE(G)s FQ(\(\005\))e(of)i FP(al)r(l)31 b FQ(Gibbs)24 b(measures.)45 b(Then)24 b(the)60 1092 y(\\macrostates")17 b(should)g(corresp)q(ond)g(to)g (the)f(measures)f(in)h(\(i\),)g(and)h(the)f FP(tr)n(anslation-invariant)60 1152 y FQ(\\macrostates")d(should)g(corresp)q(ond)h(to)f(the)f(measures)g(in) g(\(ii\).)19 b(On)13 b(the)g(other)f(hand,)i(if)e(one)h(lim-)60 1213 y(its)i(oneself)g(to)g(measuring)f FP(bulk)22 b FQ(observ)m(ables)16 b(\(i.e.)d(macroscopic)h(a)o(v)o(erages\),)h(then)g(it)g(is)g(natural)60 1273 y(to)k(consider)f(only)g(the)g FP(tr)n(anslation-invariant)24 b FQ(Gibbs)19 b(measures)e FE(G)1355 1280 y FD(inv)1408 1273 y FQ(\(\005\))h(and)h FP(their)24 b FQ(extreme)60 1333 y(p)q(oin)o(ts:)k (that)20 b(is,)g(\(iii\))e(is)h(the)h(natural)g(c)o(hoice)e([\(ii\))g(b)q (eing)i(often)f(to)q(o)i(small,)d(e.g.)h(empt)o(y].)28 b(In)60 1393 y(this)14 b(regard,)h(the)g(use)f(of)h(the)g(catc)o(h)o(y)e(lab)q(el)h (\\pure)h(phases")h(for)f(the)f(measures)f(in)i(\(iii\))e(is)h(on)h(the)60 1453 y(one)f(hand)g(natural,)g(giv)o(en)f(the)g(traditional)h(in)o(terest)e (in)h(\\macrostates")h(with)g(symmetry)c(under)60 1514 y(translations,)k(but) f(on)h(the)f(other)g(hand)h(unfortunate)f(for)h(the)f(curren)o(t)f(in)o (terest)g(in)g(more)g(general)60 1574 y(phenomena.)29 b(A)19 b(nomenclature)e(more)h(consisten)o(t)h(with)g(our)g(purp)q(oses)i(could)e(b) q(e)g(to)g(call)g FP(ex-)60 1634 y(tr)n(emal)13 b(Gibbs)h(me)n(asur)n(es)h FQ(those)d(in)f(\(i\),)h FP(tr)n(anslation-invariant)i(extr)n(emal)g(Gibbs)g (me)n(asur)n(es)h FQ(those)60 1694 y(in)g(\(ii\),)f(and)i(just)g FP(er)n(go)n(dic)g(Gibbs)h(me)n(asur)n(es)i FQ(those)c(of)h(\(iii\))e([or)h FP(extr)n(emal)j(tr)n(anslation-invariant)60 1754 y(Gibbs)e(me)n(asur)n(es)t FQ(,)e(pro)o(vided)g(that)h(w)o(e)g(pa)o(y)f(atten)o(tion)h(to)g(the)f (subtleties)g(of)h(w)o(ord-ordering].)21 b(In)60 1815 y(an)o(y)14 b(case,)g(in)g(the)g(remainder)e(of)j(this)f(pap)q(er)h(w)o(e)f(shall)g(use)g (the)g(term)f(\\phase")i(or)g(\\pure)f(phase")60 1875 y(to)19 b(denote)f(the)g(measures)f(in)h(\(iii\),)e FP(with)k(one)g(exc)n(eption)t FQ(:)26 b(in)18 b(App)q(endix)g(B)f(\(and)i(only)f(there!\))60 1935 y(w)o(e)j(shall)g(succum)o(b)f(to)i(the)f(customary)g(terminology)e(of)j (Pirogo)o(v-Sinai)g(theory)f(\(as)h(w)o(ell)e(as)60 1995 y(brevit)o(y\))15 b(and)h(use)g(the)g(term)f(\\pure)h(phase")h(to)g(denote)f(the)g(measures)f (in)g(\(ii\))h([in)f(fact)h(a)h(sligh)o(t)60 2055 y(generalization)f(of)g (them].)133 2163 y(Regarding)k(the)e(conditions)h(under)g(whic)o(h)g(the)f (set)h FE(G)1171 2170 y FD(inv)1225 2163 y FQ(\(\005\))f(is)h(non-empt)o(y)l (,)f(it)g(su\016ces)h(to)60 2223 y(men)o(tion)14 b(a)j(result)f(analogous)i (to)f(Prop)q(osition)g(2.21)g(\(Section)f(2.3.6\):)60 2321 y FM(Prop)r(osition)i(2.49)24 b FP(L)n(et)i FQ(\012)h FP(b)n(e)g(a)g FQ(compact)e FP(metric)i(sp)n(ac)n(e,)i(and)e(let)h FQ(\005)i(=)h(\()p FF(\031)1650 2328 y FH(\003)1676 2321 y FQ(\))1695 2328 y FH(\003)p Fy(2S)1796 2321 y FP(b)n(e)c(a)60 2381 y(tr)n(anslation-invariant)19 b(F)l(el)r(ler)g(sp)n(e)n(ci\014c)n(ation.)k(Then)18 b FE(G)1104 2388 y FD(inv)1157 2381 y FQ(\(\005\))f FP(is)g(nonempty.)60 2479 y FQ(Because)22 b(the)g(translations)h(form)e(an)i(Ab)q(elian)e(group,)k (this)d(is)g(an)g(immediate)d(consequence)60 2539 y(of)h(Prop)q(osition)i (2.21)f(and)f(the)g(Mark)o(o)o(v-Kakutani)g(theorem)e([104)q(,)i(306)q(].)32 b(The)20 b(idea)g(is)g(that,)60 2600 y(giv)o(en)14 b(a)i(measure)e FF(\026)h FE(2)f(G)s FQ(\(\005\),)g(w)o(e)h(can)g(construct)h(a)g(measure)e (in)h FE(G)1330 2607 y FD(inv)1383 2600 y FQ(\(\005\))g(b)o(y)g(a)o(v)o (eraging)g FF(\026)h FQ(o)o(v)o(er)60 2660 y(translations)h(\(and)g (extracting,)e(if)h(necessary)l(,)f(a)i(con)o(v)o(ergen)o(t)e(subsequence\).) 951 2784 y(54)p eop %%Page: 55 55 bop 133 91 a FM(Remark.)19 b FQ(One)14 b(w)o(ould)g(lik)o(e)f(to)i(ha)o(v)o (e)e(a)i(translation-in)o(v)m(arian)o(t)g(v)o(ersion)e(of)i(the)f(Gibbs)h (Rep-)60 152 y(resen)o(tation)i(Theorem)f(\(Theorem)g(2.12\).)25 b(That)18 b(is,)f(if)g(\005)g(is)g(a)h(quasilo)q(cal,)f(uniformly)e(nonn)o (ull)60 212 y(and)22 b FP(tr)n(anslation-invariant)27 b FQ(sp)q (eci\014cation,)22 b(one)f(w)o(ould)g(lik)o(e)f(to)h(pro)o(v)o(e)g(that)g (there)g(exists)g(an)60 272 y(absolutely)16 b(summable)e FP(tr)n (anslation-invariant)22 b FQ(in)o(teraction)15 b(\010)i(suc)o(h)f(that)h (\005)c(=)h(\005)1634 254 y FH(\010)1661 272 y FQ(.)21 b(Ho)o(w)o(ev)o(er,)60 332 y(it)d(seems)f(to)h(b)q(e)h(an)g(op)q(en)g(question)f(whether)g(this)g (is)g(true)g(or)h(not.)28 b(Sulliv)m(an)18 b([336,)h(Corollary)60 392 y(to)k(Theorem)e(2])i(constructed)g(a)g(translation-in)o(v)m(arian)o(t)g (\010)f(whic)o(h)g(is)h(\\)p FP(r)n(elatively)28 b FQ(absolutely)60 452 y(summable")17 b(\(see)j(Remark)e(2)i(at)g(the)f(end)h(of)f(Section)h (2.3.3\),)g(while)f(Kozlo)o(v)g([222,)h(Theorem)60 513 y(3])d(constructed)g (a)h(translation-in)o(v)m(arian)o(t)f(absolutely)g(summable)d(\010)j(under)g (a)h(condition)f(on)g(\005)60 573 y FP(str)n(onger)k FQ(than)c(quasilo)q (calit)o(y)l(.)644 555 y FH(30)60 715 y FB(2.5)70 b(En)n(trop)n(y)-6 b(,)19 b(Large)f(Deviations)d(and)j(the)e(V)-6 b(ariational)16 b(Principle:)217 790 y(Finite-V)-6 b(olum)n(e)19 b(Case)60 864 y FH(31)133 943 y FQ(W)l(e)e(no)o(w)h(b)q(egin)g(the)f(study)h(of)g(the)f (second)h(approac)o(h)g(to)g(classical)f(statistical)g(mec)o(hanics,)60 1003 y(namely)f(the)h(one)h(based)h(on)f(the)g FP(variational)h(principle)t FQ(,)f(whic)o(h)f(states)i(that)f(the)f(Boltzmann-)60 1063 y(Gibbs)22 b(measure)e(is)i(the)f(one)h(that)g(maximi)o(zes)d(en)o(trop)o(y)h (min)o(us)g(mean)h(energy)l(.)37 b(The)21 b(theory)60 1123 y(dev)o(elop)q(ed)e(in)g(this)g(section)h(is)f(applicable)g(to)h(an)g (arbitrary)f(classical-statistical-mec)o(hanical)60 1183 y(system)g(for)h (whic)o(h)f(the)h(Hamiltonian)e FF(H)25 b FQ(mak)o(es)18 b(sense.)33 b(In)20 b(practice)f(this)h(usually)f(means)h(a)60 1244 y(\014nite-v)o(olume) 10 b(system.)18 b(First)12 b(w)o(e)g(in)o(tro)q(duce)g(the)g FP(fr)n(e)n(e)h(ener)n(gy)t FQ(;)h(next)e(w)o(e)g(in)o(tro)q(duce)f(the)h (concept)60 1304 y(of)17 b FP(r)n(elative)h(entr)n(opy)j FQ(and)c(its)f(in)o (terpretation)g(in)g(terms)f(of)i FP(lar)n(ge)h(deviations)t FQ(;)g(\014nally)e(w)o(e)g(pro)o(v)o(e)60 1364 y(the)21 b FP(variational)i (principle)j FQ(that)c(connects)f(these)g(t)o(w)o(o)h(quan)o(tities.)35 b(In)21 b(Section)g(2.6)h(w)o(e)f(will)60 1424 y(dev)o(elop)15 b(the)h(analogous)i(theory)e(for)h(translation-in)o(v)m(arian)o(t)f (in\014nite-v)o(olume)e(lattice)h(systems.)133 1484 y(In)c(this)f(section)h (w)o(e)f(are)h(w)o(orking)g(in)f(a)i(completely)7 b(general)k (classical-statistical-mec)o(hanical)60 1544 y(\(=)16 b(probabilistic\))g (con)o(text:)k(\(\012)p FF(;)8 b FQ(\006\))16 b(is)g(an)h(arbitrary)f (measurable)f(space.)60 1672 y FM(2.5.1)55 b(F)-5 b(ree)18 b(Energy)60 1765 y(De\014nition)g(2.50)24 b FP(L)n(et)f FF(\027)j FP(b)n(e)e(a)f(pr)n(ob)n(ability)f(me)n(asur)n(e)h(on)h FQ(\(\012)p FF(;)8 b FQ(\006\))p FP(,)25 b(and)e(let)h FF(f)29 b FP(b)n(e)24 b(a)f(b)n(ounde)n(d)60 1825 y(me)n(asur)n(able)17 b(function)i(on)f FQ(\012)p FP(.)23 b(We)17 b(then)h(de\014ne)732 1934 y FF(P)7 b FQ(\()p FF(f)e FE(j)p FF(\027)s FQ(\))28 b(=)g(log)1043 1875 y Fx(Z)1085 1934 y FF(e)1108 1913 y FD(f)1138 1934 y FF(d\027)18 b(:)546 b FQ(\(2)p FF(:)p FQ(67\))60 2047 y(Ph)o(ysically)l(,)18 b FF(P)7 b FQ(\()p FF(f)e FE(j)p FF(\027)s FQ(\))21 b(is)e(min)o(us)f(the)i (free)e(energy)i(for)g(a)g(system)e(with)h(Hamiltonian)f FF(H)24 b FQ(=)c FE(\000)p FF(f)60 2108 y FQ(and)h FP(a)h(priori)i FQ(measure)c FF(\027)s FQ(.)35 b(Our)21 b(c)o(hoice)e(of)i(sign)g(con)o(v)o (en)o(tion)f(mak)o(es)f(the)h(form)o(ulae)f(sligh)o(tly)60 2168 y(more)c(elegan)o(t.)133 2228 y(It)h(is)g(easy)g(to)h(pro)o(v)o(e)e(the) h(follo)o(wing)g(prop)q(erties)h(of)f(the)g(free)g(energy:)60 2318 y FM(Prop)r(osition)i(2.51)24 b FP(L)n(et)e FF(\027)k FP(b)n(e)d(a)g(pr)n(ob)n(ability)f(me)n(asur)n(e)g(on)h FQ(\(\012)p FF(;)8 b FQ(\006\))p FP(.)38 b(Then)24 b FF(P)7 b FQ(\()h FE(\001)g(j)p FF(\027)s FQ(\))23 b FP(has)f(the)60 2378 y(fol)r(lowing)e(pr)n(op)n(erties:) p 60 2418 732 2 v 100 2472 a FA(30)135 2487 y Fz(Kozlo)o(v's)10 b(Theorem)h(3)g(uses)i(\(at)e(least)g(in)g(the)h(English)f(translation\))g (the)h(w)o(ords)f(\\necessary)i(and)e(su\016cien)o(t",)60 2537 y(but)j(in)g(fact)f(he)i(pro)o(v)o(es)f(only)f(the)i(su\016ciency)m(.)100 2595 y FA(31)135 2610 y Fz(References)e(for)d(this)i(section)f(are)h(Georgii) d([157)o(,)i(Section)h(15.1],)d(Israel)i([206)o(,)g(Section)h(I.2)e(and)h(I)q (I.2],)f(Preston)60 2660 y([299)o(,)j(Chapter)i(7])e(and)h(Ellis)f([110)n(,)h (Chapters)h(I,)e(I)q(I,)h(VI)q(I)g(and)f(VI)q(I)q(I].)951 2784 y FQ(55)p eop %%Page: 56 56 bop 93 91 a FP(\(a\))24 b FF(P)7 b FQ(\()p FM(0)p FE(j)p FF(\027)s FQ(\))22 b(=)g(0)p FP(.)95 193 y(\(b\))j FF(f)19 b FE(\024)14 b FF(g)43 b FQ(=)-8 b FE(\))41 b FF(P)7 b FQ(\()p FF(f)e FE(j)p FF(\027)s FQ(\))15 b FE(\024)e FF(P)7 b FQ(\()p FF(g)r FE(j)p FF(\027)s FQ(\))p FP(.)95 295 y(\(c\))25 b FF(P)7 b FQ(\()p FF(f)17 b FQ(+)11 b FF(c)p FE(j)p FF(\027)s FQ(\))22 b(=)g FF(P)7 b FQ(\()p FF(f)e FE(j)p FF(\027)s FQ(\))11 b(+)g FF(c)18 b FP(for)f(any)g(r)n(e)n(al)g(numb)n(er)h FF(c)p FP(.)93 403 y(\(d\))182 353 y Fx(\014)182 378 y(\014)182 403 y(\014)p FF(P)7 b FQ(\()p FF(f)e FE(j)p FF(\027)s FQ(\))14 b FE(\000)g FF(P)7 b FQ(\()p FF(g)r FE(j)p FF(\027)s FQ(\))551 353 y Fx(\014)551 378 y(\014)551 403 y(\014)30 b FE(\024)g(k)p FF(f)19 b FE(\000)14 b FF(g)r FE(k)835 410 y Fy(1)872 403 y FP(.)35 b(That)21 b(is,)h FF(P)7 b FQ(\()h FE(\001)g(j)p FF(\027)s FQ(\))23 b FP(is)e(Lipschitz)g(c)n (ontinuous)i(with)182 463 y(Lipschitz)17 b(c)n(onstant)h(1.)95 565 y(\(e\))25 b FF(P)7 b FQ(\()h FE(\001)g(j)p FF(\027)s FQ(\))18 b FP(is)f(c)n(onvex.)98 666 y(\(f)5 b(\))24 b FF(P)7 b FQ(\()h FE(\001)g(j)p FF(\027)s FQ(\))20 b FP(is)g(strictly)f(c)n(onvex)i(in)f(dir)n (e)n(ctions)f(c)n(orr)n(esp)n(onding)g(to)h(functions)h(which)f(ar)n(e)f(not) 182 726 y FF(\027)s FP(-a.e.)f(c)n(onstant.)60 856 y FM(2.5.2)55 b(Relativ)n(e)17 b(En)n(trop)n(y)60 949 y(De\014nition)h(2.52)24 b FP(L)n(et)d FF(\026)h FP(and)g FF(\027)j FP(b)n(e)d(any)f(two)h(pr)n(ob)n (ability)f(me)n(asur)n(es)g(on)h FQ(\(\012)p FF(;)8 b FQ(\006\))p FP(.)35 b(Then)22 b(the)60 1009 y FQ(relativ)o(e)13 b(en)o(trop)o(y)k FP(\(or)f FQ(information)e(gain)j FP(or)f FQ(Kullbac)o(k-Leibler)d (information)p FP(\))i(of)i FF(\026)g FP(r)n(elative)g(to)60 1069 y FF(\027)k FP(is)c(de\014ne)n(d)h(as)343 1225 y FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))28 b(=)570 1138 y Fx(8)570 1175 y(<)570 1250 y(:)615 1133 y(Z)665 1143 y(\020)690 1191 y FQ(log)766 1170 y FD(d\026)p 766 1180 40 2 v 767 1208 a(d\027)811 1143 y Fx(\021)852 1191 y FF(d\026)23 b FQ(=)989 1133 y Fx(Z)1039 1143 y(\020)1069 1170 y FD(d\026)p 1069 1180 V 1070 1208 a(d\027)1121 1191 y FQ(log)1198 1170 y FD(d\026)p 1198 1180 V 1199 1208 a(d\027)1242 1143 y Fx(\021)1283 1191 y FF(d\027)54 b FP(if)17 b FF(\026)d FE(\034)g FF(\027)615 1289 y FQ(+)p FE(1)683 b FP(otherwise)1765 1225 y FQ(\(2)p FF(:)p FQ(68\))60 1381 y FP(Mor)n(e)16 b(gener)n(al)r(ly,)k(if)d FE(A)g FP(is)g(any)h(sub-)p FF(\033)r FP(-\014eld)h(of)f FQ(\006)p FP(,)f(then)h(we)h(de\014ne)689 1491 y FF(I)711 1498 y Fy(A)741 1491 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))28 b(=)f FF(I)968 1443 y Fx(\020)993 1491 y FF(\026)p Fm(\026)p FE(A)1095 1441 y Fx(\014)1095 1466 y(\014)1095 1491 y(\014)8 b FF(\027)s Fm(\026)p FE(A)1209 1443 y Fx(\021)1248 1491 y FF(:)503 b FQ(\(2)p FF(:)p FQ(69\))60 1611 y(Actually)l(,)13 b(our)j FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))e(is)h(the)g FP(ne)n(gative)20 b FQ(of)15 b(the)g(usual)g(relativ)o(e)e(en)o(trop)o(y)h FF(S)s FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\);)h(but)g(it)g(is)f(more)60 1672 y(con)o(v)o(enien)o(t)i(to)i(w)o(ork)g(with)f FF(I)k FQ(than)e(with)e FF(S)s FQ(,)h(and)g(it)f(is)h(to)q(o)h(cum)o(b)q(ersome)c(to)j(k)o(eep)e(sa)o (ying)i(the)60 1732 y(w)o(ords)d(\\negativ)o(e)g(of)s(".)22 b(So)15 b(w)o(e)g(shall)f(just)i(call)e FF(I)k FQ(the)d(\\relativ)o(e)e(en)o (trop)o(y")i FP(tout)h(c)n(ourt)5 b FQ(.)21 b(But)14 b(this)60 1792 y(sign)21 b(di\013erence)f(should)i(b)q(e)f(b)q(orne)h(in)f(mind)e(when) i(in)o(terpreting)f(the)h(v)m(ariational)g(principle!)60 1852 y(\(See)d(also)i(the)e(Remarks)f(at)i(the)g(end)g(of)g(this)f(subsection)h (for)g(a)g(comparison)g(with)f(the)h(usual)60 1912 y(ph)o(ysicists')c(en)o (trop)o(y)l(.\))133 2022 y(It)h(is)g(not)h(hard)g(to)f(pro)o(v)o(e)g(the)g (follo)o(wing)g(prop)q(erties)g(of)g(the)g(relativ)o(e)f(en)o(trop)o(y:)60 2124 y FM(Prop)r(osition)j(2.53)24 b FP(L)n(et)17 b FF(\026;)8 b(\027)21 b FP(b)n(e)d(pr)n(ob)n(ability)e(me)n(asur)n(es)h(on)h FQ(\(\012)p FF(;)8 b FQ(\006\))p FP(.)22 b(Then:)93 2226 y(\(a\))i FQ(0)g FE(\024)f FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))g FE(\024)g FF(I)533 2233 y FD(max)619 2226 y FE(\021)15 b(\000)8 b FQ(log)i FF(\027)816 2233 y FD(min)882 2226 y FP(,)19 b(wher)n(e)f FF(\027)1078 2233 y FD(min)1160 2226 y FQ(=)57 b(inf)1213 2267 y Fq(?)o Fy(6)p FH(=)p FD(A)p Fy(2)p FH(\006)1365 2226 y FF(\027)s FQ(\()p FF(A)p FQ(\))p FP(.)24 b([F)l(or)17 b(example,)j(if)e FF(\027)182 2319 y FP(is)g(normalize)n(d)g(c)n(ounting)h (me)n(asur)n(e)f(on)g(a)g(\014nite)i(sp)n(ac)n(e)d FQ(\012)p FP(,)i(then)g FF(I)1437 2326 y FD(max)1523 2319 y FQ(=)c(log)10 b FE(j)p FQ(\012)p FE(j)p FP(.)24 b(If)18 b FQ(\012)g FP(is)182 2379 y(an)g(in\014nite)h(sp)n(ac)n(e,)e(then)h FF(I)692 2386 y FD(max)777 2379 y FQ(=)c(+)p FE(1)p FP(.])95 2481 y(\(b\))25 b FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))d(=)g(0)c FP(if)f(and)h(only)g(if)f FF(\026)d FQ(=)g FF(\027)s FP(.)95 2582 y(\(c\))25 b FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))17 b FP(is)g(a)h(c)n(onvex)h(function)g(of)e(the)h(p)n(air)e FQ(\()p FF(\026;)8 b(\027)s FQ(\))p FP(.)951 2784 y FQ(56)p eop %%Page: 57 57 bop 93 91 a FP(\(d\))24 b(F)l(or)17 b(\014xe)n(d)h FF(\027)s FP(,)g FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))f FP(is)g(\\almost")h (a)f(c)n(onc)n(ave)h(function)h(of)e FF(\026)p FP(,)h(in)g(the)g(sense)g (that)542 229 y FF(I)568 181 y Fx(\020)611 175 y FD(n)592 187 y Fx(X)594 278 y FD(i)p FH(=1)660 229 y FF(\025)688 236 y FD(i)703 229 y FF(\026)732 236 y FD(i)755 229 y FE(j)8 b FF(\027)804 181 y Fx(\021)870 229 y FE(\025)970 175 y FD(n)951 187 y Fx(X)952 278 y FD(i)p FH(=1)1019 229 y FF(\025)1047 236 y FD(i)1061 229 y FF(I)t FQ(\()p FF(\026)1135 236 y FD(i)1149 229 y FE(j)p FF(\027)s FQ(\))25 b(+)1316 175 y FD(n)1297 187 y Fx(X)1298 278 y FD(i)p FH(=1)1365 229 y FF(\025)1393 236 y FD(i)1416 229 y FQ(log)9 b FF(\025)1515 236 y FD(i)1741 229 y FQ(\(2.70a\))870 371 y FE(\025)970 317 y FD(n)951 330 y Fx(X)952 421 y FD(i)p FH(=1)1019 371 y FF(\025)1047 378 y FD(i)1061 371 y FF(I)t FQ(\()p FF(\026)1135 378 y FD(i)1149 371 y FE(j)p FF(\027)s FQ(\))25 b FE(\000)g FQ(log)9 b FF(n)340 b FQ(\(2.70b\))182 512 y FP(for)12 b(any)g(pr)n(ob)n(ability)g(me)n(asur)n(es)g FF(\026)806 519 y FH(1)826 512 y FF(;)c(:)g(:)g(:)f(;)h(\026)964 519 y FD(n)1000 512 y FP(and)13 b(numb)n(ers)g FF(\025)1307 519 y FH(1)1327 512 y FF(;)8 b(:)g(:)g(:)f(;)h(\025)1464 519 y FD(n)1502 512 y FE(\025)13 b FQ(0)g FP(with)1692 479 y Fx(P)1736 492 y FD(n)1736 525 y(i)p FH(=1)1803 512 y FF(\025)1831 519 y FD(i)1860 512 y FQ(=)182 573 y(1)p FP(.)95 674 y(\(e\))25 b(F)l(or)17 b(\014xe)n(d)h FF(\027)s FP(,)g FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))g FP(is)f(a)h(lower)g(semic)n(ontinuous)h (function)g(of)e FF(\026)h FP(in)g(the)g(b)n(ounde)n(d)g(me)n(a-)182 734 y(sur)n(able)i(top)n(olo)n(gy)518 716 y FH(32)554 734 y FP(,)g(and)g(in)g(the)g(we)n(ak)g(top)n(olo)n(gy)f(if)g FQ(\012)h FP(is)f(a)h(c)n(omplete)g(sep)n(ar)n(able)g(metric)182 794 y(sp)n(ac)n(e.)98 895 y(\(f)5 b(\))24 b(F)l(or)16 b(\014xe)n(d)i FF(\027)i FP(and)d(\014xe)n(d)h FF(c)c(<)f FE(1)p FP(,)k(the)h(set)f FE(f)p FF(\026)p FQ(:)22 b FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))14 b FE(\024)f FF(c)p FE(g)k FP(is)g(c)n(omp)n(act)g(and)g (se)n(quential)r(ly)182 956 y(c)n(omp)n(act)c(in)g(the)h(b)n(ounde)n(d)f(me)n (asur)n(able)g(top)n(olo)n(gy)f(\(and)i(henc)n(e)g(also)f(in)g(the)h(we)n(ak) g(top)n(olo)n(gy\).)95 1057 y(\(g\))25 b FF(I)204 1064 y Fy(A)234 1057 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))18 b FP(is)f(an)h(incr)n(e)n (asing)f(function)i(of)e FE(A)p FP(.)93 1158 y(\(h\))24 b(If)c FE(A)276 1165 y FH(1)314 1158 y FE(\032)f(A)412 1165 y FH(2)450 1158 y FE(\032)g FQ(\006)p FP(,)i(and)f FF(\026)705 1140 y FD(!)705 1170 y Fy(A)733 1175 y Fr(1)773 1158 y FP(\(r)n(esp.)f FF(\027)940 1140 y FD(!)937 1170 y Fy(A)965 1175 y Fr(1)985 1158 y FP(\))h(is)g(a)g(r)n(e)n(gular)g(c)n(onditional)h(pr)n(ob)n(ability)e (for)h FF(\026)182 1218 y FP(\(r)n(esp.)d FF(\027)s FP(\))g(given)i FE(A)551 1225 y FH(1)571 1218 y FP(,)e(then)538 1342 y FF(I)560 1349 y Fy(A)588 1354 y Fr(2)607 1342 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))28 b(=)g FF(I)831 1349 y Fy(A)859 1354 y Fr(1)878 1342 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))19 b(+)1063 1283 y Fx(Z)1104 1342 y FF(d\026)p FQ(\()p FF(!)r FQ(\))8 b FF(I)1258 1349 y Fy(A)1286 1354 y Fr(2)1306 1342 y FQ(\()p FF(\026)1354 1321 y FD(!)1354 1354 y Fy(A)1382 1359 y Fr(1)1402 1342 y FE(j)p FF(\027)1443 1321 y FD(!)1440 1354 y Fy(A)1468 1359 y Fr(1)1488 1342 y FQ(\))14 b FF(:)230 b FQ(\(2)p FF(:)p FQ(71\))182 1465 y FP([This)17 b(obviously)h(r)n(e\014nes)g(\(g\).])103 1567 y(\(i\))24 b(\(Str)n(ong)14 b(sup)n(er)n(additivity\))e(L)n(et)h FE(A)812 1574 y FH(1)831 1567 y FF(;)8 b FE(A)893 1574 y FH(2)913 1567 y FF(;)g FE(A)975 1574 y FH(3)1007 1567 y FP(b)n(e)14 b(sub-)p FF(\033)r FP(-\014elds)h(of)f FQ(\006)f FP(which)h(ar)n(e)f FQ(indep)q(enden)o(t)182 1627 y FP(with)18 b(r)n(esp)n(e)n(ct)f(to)g FF(\027)s FP(.)23 b(Then)360 1735 y FF(I)382 1742 y Fy(A)410 1747 y Fr(1)427 1742 y Fy([A)479 1747 y Fr(2)496 1742 y Fy([A)548 1747 y Fr(3)567 1735 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))11 b(+)g FF(I)757 1742 y Fy(A)785 1747 y Fr(2)805 1735 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))28 b FE(\025)f FF(I)1029 1742 y Fy(A)1057 1747 y Fr(1)1074 1742 y Fy([A)1126 1747 y Fr(2)1145 1735 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))12 b(+)f FF(I)1336 1742 y Fy(A)1364 1747 y Fr(2)1381 1742 y Fy([A)1433 1747 y Fr(3)1452 1735 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))j FF(:)177 b FQ(\(2)p FF(:)p FQ(72\))133 1913 y FM(Remarks.)19 b FQ(1.)i(The)15 b(standard)h(statistical-mec)o(hanics)c(textb)q(o)q(oks)j (\(e.g.)f([213)q(,)h(Chapters)g(2,)60 1974 y(4)i(and)h(5],)e([307)q(,)h (Section)f(9.B],)g([20,)h(Chapter)g(3]\))g(in)o(tro)q(duce)g(a)g(quan)o(tit)o (y)f(whic)o(h)g(is)h FP(app)n(ar)n(ently)60 2034 y FQ(the)f(en)o(trop)o(y)f (of)i(a)g FP(single)k FQ(measure)15 b FF(\026)p FQ(,)h FP(without)22 b FQ(reference)15 b(to)h(a)h(base)f(measure)f FF(\027)s FQ(:)364 2175 y FF(S)394 2182 y FD(book)q(s)481 2175 y FQ(\()p FF(\026)p FQ(\))f(\\=")671 2102 y Fx(\()712 2131 y FE(\000)759 2097 y Fx(P)770 2164 y FD(!)812 2131 y FF(\026)841 2138 y FD(!)883 2131 y FQ(log)9 b FF(\026)983 2138 y FD(!)1183 2131 y FQ(if)16 b(\012)h(is)f(discrete)712 2218 y FE(\000)759 2182 y Fx(R)795 2218 y FF(\026)p FQ(\()p FF(x)p FQ(\))h(log)9 b FF(\026)p FQ(\()p FF(x)p FQ(\))f FF(dx)49 b FQ(if)16 b(\012)h(is)f(con)o(tin)o(uous)1765 2175 y(\(2)p FF(:)p FQ(73\))60 2317 y(Ho)o(w)o(ev)o(er,)11 b(closer)i(examination)f(rev)o(eals)g(that)h(a)h(base)f(measure)f FF(\027)k FQ(has)e(b)q(een)f(in)o(tro)q(duced)g FP(surr)n(ep-)60 2377 y(titiously)22 b FQ(in)16 b(these)h(form)o(ulae,)e(namely)g(coun)o(ting) i(measure)e(in)i(the)f(discrete)g(case)h(or)g(Leb)q(esgue)60 2438 y(measure)i(in)g(the)h(con)o(tin)o(uous)g(case.)32 b(This)20 b(base)h(measure)e FP(do)n(es)k FQ(pla)o(y)d(a)g(ph)o(ysical)f(role)h(in)f (the)60 2498 y(theory:)k(the)17 b(ph)o(ysics)f(w)o(ould)h(b)q(e)h(di\013eren) o(t)e(if)g(coun)o(ting)h(or)h(Leb)q(esgue)g(measure)e(w)o(ere)g(replaced)p 60 2541 732 2 v 100 2595 a FA(32)135 2610 y Fz(Recall)f(that)h(a)g(net)h Fu(f)p Fv(\026)511 2616 y Fp(\013)534 2610 y Fu(g)f Fz(con)o(v)o(erges)h(to)f Fv(\026)g Fz(in)g(the)h(b)q(ounded)g(measurable)e(top)q(ology)g(if)1582 2577 y Fx(R)1610 2610 y Fv(f)d(d\026)1689 2616 y Fp(\013)1727 2610 y Fu(!)1784 2577 y Fx(R)1812 2610 y Fv(f)f(d\026)60 2660 y Fz(for)j(all)e Fv(f)17 b Fu(2)11 b Fv(B)r Fz(\(\012)p Fv(;)c Fz(\006\).)951 2784 y FQ(57)p eop %%Page: 58 58 bop 60 91 a FQ(b)o(y)18 b(some)f(other)i(measure.)573 73 y FH(33)636 91 y FQ(Th)o(us,)g(the)f(form)o(ulae)f(\(2.73\),)i(in)f(whic)o(h)g (the)g(base)h(measure)e FF(\027)k FQ(is)60 152 y(hidden,)g(are)f(quite)g (misleading.)32 b(\(They)20 b(are)g(also)h(inelegan)o(t,)f(as)h(can)g(b)q(e)f (seen)h(from)e(the)h(in-)60 212 y(compatible)e(treatmen)o(t)f(giv)o(en)i(to)h (the)g(discrete)e(and)i(con)o(tin)o(uous)g(cases.\))32 b(What)20 b(is)f(in)o(v)o(olv)o(ed)60 272 y(here)k(is)h(the)f(common)f(sin)h(of)h (failing)g(to)g(distinguish)f(b)q(et)o(w)o(een)g(a)h FP(me)n(asur)n(e)j FQ(and)d(a)h FP(density)60 332 y FQ(\(=)18 b(Radon-Nik)o(o)q(d)q(\023)-25 b(ym)17 b(deriv)m(ativ)o(e\):)24 b(the)18 b(latter)g(is)g(de\014ned)g(only)g (relativ)o(e)e(to)j(a)g(sp)q(eci\014ed)f(base)60 392 y(measure.)32 b(In)20 b(man)o(y)f(situations,)i(this)g(sin)f(is)g(harmless,)g(b)q(ecause)g (there)g(is)g(a)h(\\natural")g(and)60 452 y(univ)o(ersally-agreed)e(c)o (hoice)f(of)i(base)h(measure.)31 b(But)19 b(not)h(here.)32 b(W)l(e)20 b(therefore)f(feel)g(strongly)60 513 y(that)e(in)f(statistical)f (mec)o(hanics)f(the)i(base)h(measure)e FF(\027)k FQ(should)e(b)q(e)f(in)o (tro)q(duced)g FP(explicitly)t FQ(.)133 573 y(Note)11 b(also)g(that)h(the)e (de\014nition)h(\(2.73\))h(uses)f FP(unnormalize)n(d)16 b FQ(coun)o(ting)11 b(or)h(Leb)q(esgue)f(measure)60 633 y(as)24 b(the)e(base)i(measure,)f(while)f (w)o(e)g(alw)o(a)o(ys)h(tak)o(e)g(the)f(base)i(measure)e FF(\027)k FQ(to)d(b)q(e)g(a)h FP(pr)n(ob)n(ability)60 693 y FQ(measure.)c(This)c (causes)h(an)g(\(irrelev)m(an)o(t\))d(additiv)o(e)h(shift)h(in)g(the)g(en)o (trop)o(y:)21 b(e.g.)15 b(for)i(\012)f(\014nite,)645 803 y FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))27 b(=)h FE(\000)p FF(S)941 810 y FD(book)q(s)1027 803 y FQ(\()p FF(\026)p FQ(\))20 b(+)f(log)10 b FE(j)p FQ(\012)p FE(j)459 b FQ(\(2)p FF(:)p FQ(74\))60 913 y(when)17 b FF(\027)k FQ(is)c(normalized)e(coun)o(ting)i (measure)f([)p FF(\027)s FQ(\()p FE(f)p FF(!)r FE(g)p FQ(\))g(=)f(1)p FF(=)p FE(j)p FQ(\012)p FE(j)j FQ(for)g(eac)o(h)e FF(!)i FE(2)e FQ(\012].)24 b(Th)o(us,)17 b(b)q(oth)60 973 y FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))i(and)g FF(S)340 980 y FD(book)q(s)427 973 y FQ(\()p FF(\026)p FQ(\))g(tak)o(e)g(v)m(alues)g(in)f(the)h(in)o(terv)m (al)f([0)p FF(;)8 b FQ(log)h FE(j)p FQ(\012)p FE(j)p FQ(],)19 b(but)g(large)g(v)m(alues)g(of)g FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))60 1034 y(corresp)q(ond)e(to)g(small)d(v)m(alues)j(of)f FF(S)726 1041 y FD(book)q(s)813 1034 y FQ(\()p FF(\026)p FQ(\),)g(and)h(vice) e(v)o(ersa.)133 1094 y(The)g(reader)f(is)h(urged)f(to)h(remem)o(b)q(er)c(the) k(t)o(w)o(o)f(notational)i(di\013erences)d(|)i(the)f(sign)h(and)g(the)60 1154 y(additiv)o(e)g(constan)o(t)i(|)f(when)g(in)o(terpreting)f(our)i (results.)133 1214 y(2.)27 b(The)18 b(relativ)o(e)f(en)o(trop)o(y)g FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))h(pla)o(ys)f(an)i(imp)q (ortan)o(t)e(role)h(in)f(information)h(theory)f(and)60 1274 y(in)h(mathematical)e(statistics)j(\(large-sample)e(asymptotic)h(theory)h(of) g(h)o(yp)q(othesis)g(testing)f(and)60 1335 y(maxim)o(um)n(-lik)n(el)o(iho)q (o)q(d)h(estimation\);)i(this)f(follo)o(ws)g(from)g(the)g(large-deviations)h (theory)f(to)h(b)q(e)60 1395 y(discussed)f(in)f(the)g(next)h(subsection.)31 b(See)20 b(e.g.)e([30)q(,)i(pp.)f(119{125])j(and)f([226,)f(225)q(,)f(16)q(].) 31 b(The)60 1455 y(relationship)15 b(with)h(maxim)o(um)n(-lik)n(el)o(iho)q(o) q(d)e(estimation)g(is)i(discussed)g(also)g(in)f(Section)h(5.1.2)g(b)q(e-)60 1515 y(lo)o(w.)60 1645 y FM(2.5.3)55 b(Large)18 b(Deviations)60 1737 y FQ(The)f(ph)o(ysical)e(in)o(terpretation)h(of)h(relativ)o(e)d(en)o (trop)o(y)i(is)h(asso)q(ciated)g(with)g(the)f(problem)f(of)i FP(lar)n(ge)60 1798 y(deviations)t FQ(,)f(whic)o(h)f(concerns,)g(roughly)h (sp)q(eaking,)f(the)g(estimation)f(of)i(the)f(\(v)o(ery)f(small\))g(prob-)60 1858 y(abilities)h(of)h(large)g(sim)o(ultaneous)f(\015uctuations)i(in)f(a)g (system)f(consisting)h(of)h(a)f(large)g(n)o(um)o(b)q(er)f(of)60 1918 y(random)h(v)m(ariables.)22 b(In)17 b(this)f(section)g(w)o(e)g(will)g (consider)g(the)h(case)f(of)h(indep)q(enden)o(t,)f(iden)o(tically)60 1978 y(distributed)i(\(i.i.d.\))e(random)j(v)m(ariables.)28 b(So)19 b(let)f FF(X)1056 1985 y FH(1)1076 1978 y FF(;)8 b(X)1138 1985 y FH(2)1158 1978 y FF(;)g(:)g(:)g(:)18 b FQ(b)q(e)g(a)h(sequence)f(of)h (indep)q(enden)o(t)60 2038 y(samples)12 b(from)f(the)i(probabilit)o(y)f (distribution)g FF(\027)s FQ(;)i(and)g(let)e FF(f)18 b FQ(b)q(e)13 b(an)o(y)g(b)q(ounded)g(real-v)m(alued)g(mea-)60 2099 y(surable)h(function)g (on)g(\012.)21 b(Then)14 b FF(f)5 b FQ(\()p FF(X)763 2106 y FH(1)783 2099 y FQ(\))p FF(;)j(f)d FQ(\()p FF(X)912 2106 y FH(2)933 2099 y FQ(\))p FF(;)j(:)g(:)g(:)k FQ(is)i(a)g(sequence)f(of)h(indep) q(enden)o(t,)g(iden)o(tically)60 2159 y(distributed)20 b(real-v)m(alued)h (random)f(v)m(ariables.)35 b(In)21 b(suc)o(h)g(a)g(situation)g(the)g(w)o(eak) f(la)o(w)h(of)g(large)60 2219 y(n)o(um)o(b)q(ers)c(states)i(that)g(the)f (sample)f(mean)h FF(S)925 2201 y FD(f)922 2231 y(n)965 2219 y FE(\021)g FF(n)1051 2201 y Fy(\000)p FH(1)1106 2186 y Fx(P)1150 2199 y FD(n)1150 2231 y(i)p FH(=1)1218 2219 y FF(f)5 b FQ(\()p FF(X)1306 2226 y FD(i)1320 2219 y FQ(\))19 b(is,)f(with)h(high)f(probabilit)o (y)l(,)60 2279 y(v)o(ery)d(close)h(to)h(the)g(theoretical)e(mean)h(v)m(alue)g FF(m)e FE(\021)1037 2244 y Fx(R)1065 2279 y FF(f)f(d\027)s FQ(:)23 b(more)15 b(precisely)l(,)f(if)i FF(A)h FQ(is)f(an)o(y)g(closed)p 60 2324 732 2 v 100 2378 a FA(33)135 2393 y Fz(In)f Fw(some)j Fz(cases,)e(coun)o(ting)e(or)h(Leb)q(esgue)h(measure)f(ma)o(y)e(pla)o(y)h(a)g (privileged)h(role)f(b)o(y)h(virtue)g(of)f(some)g(sym-)60 2442 y(metry:)j(e.g.)12 b(spin-\015ip)h(symmetry)f(in)g(the)i(Ising)f(mo)q(del,)e (or)j(symplectic)e(symmetry)g(in)g(a)h(classical)g(Hamiltonian)60 2492 y(system.)32 b(In)19 b(other)g(cases,)i(ho)o(w)o(ev)o(er,)e(the)h (privileged)e(measure)g(could)h(b)q(e)g(some)f(other)h(measure:)27 b(e.g.)18 b(Haar)60 2542 y(measure)c(on)g(a)g(Lie)g(group)g(is)h(not)f(Leb)q (esgue)i(measure)e(except)i(in)d(some)h(v)o(ery)g(sp)q(ecial)h (parametrizations.)j(This)60 2592 y(is)f(y)o(et)g(another)g(reason)h(for)e (making)f(the)i(base)h(measure)f Fv(\027)i Fz(explicit:)k(it)17 b(clari\014es)g(whether)i(or)d(not)h(there)h(is)f(a)60 2642 y(symmetry)12 b(argumen)o(t)h(that)h(privileges)f(one)i(c)o(hoice)f(of)f Fv(\027)j Fz(o)o(v)o(er)e(another.)951 2784 y FQ(58)p eop %%Page: 59 59 bop 60 91 a FQ(subset)18 b(of)h(the)e(real)h(line)f FP(not)23 b FQ(con)o(taining)18 b FF(m)p FQ(,)g(then)g(Prob\()p FF(S)1218 73 y FD(f)1215 104 y(n)1258 91 y FE(2)f FF(A)p FQ(\))f FE(!)h FQ(0)h(as)h FF(n)e FE(!)f(1)p FQ(.)27 b(Large-)60 152 y(deviation)13 b(theorems)f([360)q(,)h(110)r(,)g(75])h(are)f(a)h(strengthening)g(of)g(the)g (w)o(eak)f(la)o(w)g(of)h(large)g(n)o(um)o(b)q(ers,)60 212 y(in)i(that)g(they) f(giv)o(e)g(the)h(precise)f(rate)h(of)g(con)o(v)o(ergence)e(of)j(this)e (probabilit)o(y)g(to)i(zero)e(as)i FF(n)d FE(!)g(1)p FQ(.)60 272 y(It)i(turns)g(out)h(that)g(this)f(probabilit)o(y)f(is)h FP(exp)n(onential)r(ly)23 b FQ(small)15 b(in)h FF(n)p FQ(,)g(that)h(is,)635 360 y(Prob)q(\()p FF(S)791 340 y FD(f)788 373 y(n)827 360 y FE(2)d FF(A)p FQ(\))27 b FE(\030)h FF(e)1047 340 y Fy(\000)p FD(n)p Fy(\002)p FH(const)o(\()p FD(f)r(;\027;A)p FH(\))1765 360 y FQ(\(2)p FF(:)p FQ(75\))60 448 y(where)16 b(const)q(\()p FF(f)s(;)8 b(\027;)g(A)p FQ(\))13 b FF(>)i FQ(0)i(whenev)o(er)e FF(A)h FQ(is)g(a)h(closed)f(set)h(not)g(con)o(taining)f FF(m)p FQ(.)22 b(More)16 b(precisely)l(,)60 509 y(it)g(can)g(b)q(e)h(sho)o(wn)g (that)190 650 y(lim)178 675 y FD(n)p Fy(!1)294 616 y FQ(1)p 292 638 30 2 v 292 684 a FF(n)334 650 y FQ(log)9 b(Prob)q(\()p FF(S)561 629 y FD(f)558 662 y(n)597 650 y FE(2)14 b FF(A)p FQ(\))722 550 y Fx(8)722 588 y(>)722 600 y(<)722 675 y(>)722 687 y(:)767 578 y FE(\024)g(\000)71 b FQ(inf)867 617 y FD(\026)p FH(:)908 585 y Fx(R)935 617 y FD(f)10 b(d\026)p Fy(2)p FD(A)1060 578 y FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))48 b(if)16 b FF(A)g FQ(is)g(a)g(closed)g(set)767 677 y FE(\025)e(\000)71 b FQ(inf)867 715 y FD(\026)p FH(:)908 684 y Fx(R)935 715 y FD(f)10 b(d\026)p Fy(2)p FD(A)1060 677 y FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))48 b(if)16 b FF(A)g FQ(is)g(an)h(op)q(en)f(set)1765 650 y(\(2)p FF(:)p FQ(76\))60 804 y(where)g FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))g(is)g(the)g(relativ)o(e)e(en)o(trop)o(y)l (.)133 864 y(In)h(the)h(preceding)e(though)o(t-exp)q(erimen)o(t,)g(w)o(e)h (lo)q(ok)o(ed)g(at)h(only)f(one)h(real-v)m(alued)f(observ)m(able)60 924 y FF(f)5 b FQ(.)30 b(More)18 b(generally)l(,)g(w)o(e)h(could)g(lo)q(ok)g (at)g(a)h(v)o(ector-v)m(alued)e(observ)m(able)h FM(f)24 b FQ(=)18 b(\()p FF(f)1585 931 y FH(1)1605 924 y FF(;)8 b(:)g(:)g(:)f(;)h(f)1738 931 y FD(k)1759 924 y FQ(\),)19 b(and)60 984 y(ask)e(for)f(the)g(probabilit)o (y)f(that)i FF(S)692 966 y Fj(f)689 997 y FD(n)729 984 y FQ(lies)e(in)h(some) f(subset)i FM(A)d FE(\032)g Fq(R)1284 964 y FD(k)1305 984 y FQ(.)21 b(Not)16 b(surprisingly)g(w)o(e)g(ha)o(v)o(e)184 1138 y(lim)171 1163 y FD(n)p Fy(!1)287 1104 y FQ(1)p 285 1126 V 285 1172 a FF(n)327 1138 y FQ(log)10 b(Prob\()p FF(S)554 1117 y Fj(f)551 1150 y FD(n)589 1138 y FE(2)k FM(A)p FQ(\))719 1038 y Fx(8)719 1076 y(>)719 1088 y(<)719 1163 y(>)719 1175 y(:)764 1066 y FE(\024)g(\000)73 b FQ(inf)864 1105 y FD(\026)p FH(:)905 1073 y Fx(R)932 1105 y Fj(f)10 b FD(d\026)p Fy(2)p Fj(A)1061 1066 y FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))48 b(if)16 b FM(A)g FQ(is)g(a)h(closed)f(set)764 1165 y FE(\025)e(\000)73 b FQ(inf)864 1203 y FD(\026)p FH(:)905 1172 y Fx(R)932 1203 y Fj(f)10 b FD(d\026)p Fy(2)p Fj(A)1061 1165 y FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))48 b(if)16 b FM(A)g FQ(is)g(an)h(op)q(en)g (set)1765 1138 y(\(2)p FF(:)p FQ(77\))133 1289 y(These)f(results)g(can)h(b)q (e)f(written)g(in)g(a)g(more)f(succinct)h(w)o(a)o(y)f(b)o(y)h(noting)h(the)f (trivial)f(iden)o(tit)o(y)660 1372 y(1)p 657 1394 V 657 1440 a FF(n)719 1352 y FD(n)700 1364 y Fx(X)701 1455 y FD(i)p FH(=1)768 1406 y FF(f)5 b FQ(\()p FF(X)856 1413 y FD(i)871 1406 y FQ(\))28 b(=)983 1333 y Fx( )1023 1372 y FQ(1)p 1021 1394 V 1021 1440 a FF(n)1083 1352 y FD(n)1063 1364 y Fx(X)1065 1455 y FD(i)p FH(=1)1132 1406 y FF(\016)1154 1413 y FD(X)1183 1418 y Fs(i)1198 1333 y Fx(!)1230 1406 y FQ(\()p FF(f)5 b FQ(\))468 b(\(2)p FF(:)p FQ(78\))60 1529 y(\(here)16 b FF(\016)207 1536 y FD(x)244 1529 y FQ(is)g(the)g(delta)g(measure)f(at)i FF(x)p FQ(\),)e(whic)o(h)h(can)g (b)q(e)h(written)f(as)711 1632 y FF(S)744 1612 y FD(f)741 1645 y(n)794 1632 y FQ(=)28 b FF(L)893 1639 y FD(n)916 1632 y FQ(\()p FF(f)5 b FQ(\))28 b FE(\021)1078 1574 y Fx(Z)1119 1632 y FF(f)14 b(dL)1215 1639 y FD(n)1765 1632 y FQ(\(2)p FF(:)p FQ(79\))60 1733 y(where)790 1810 y FF(L)823 1817 y FD(n)875 1810 y FE(\021)27 b FF(n)970 1789 y Fy(\000)p FH(1)1045 1756 y FD(n)1026 1768 y Fx(X)1027 1859 y FD(i)p FH(=1)1094 1810 y FF(\016)1116 1817 y FD(X)1145 1822 y Fs(i)1765 1810 y FQ(\(2)p FF(:)p FQ(80\))60 1920 y(is)11 b(called)g(the)g FP(empiric)n(al)i(me)n(asur)n(e)t FQ(.)19 b(W)l(e)11 b(emphasize)f(that)i FF(L)1176 1927 y FD(n)1211 1920 y FQ(is)g(a)g FP(r)n(andom)i FQ(measure:)k(it)11 b(dep)q(ends)60 1980 y(on)20 b(the)f(random)g(sample)e FF(X)605 1987 y FH(1)626 1980 y FF(;)8 b(:)g(:)g(:)f(;)h(X)775 1987 y FD(n)799 1980 y FQ(.)30 b(In)19 b(this)g(language,)i(the)e(w)o(eak)g(la)o(w)g(of)g(large)h (n)o(um)o(b)q(ers)60 2040 y(can)c(b)q(e)f(reform)o(ulated)f(as)i(sa)o(ying)f (that)h(the)f(empirical)e(measure)h FF(L)1329 2047 y FD(n)1368 2040 y FQ(is,)h(with)g(high)g(probabilit)o(y)l(,)60 2100 y(v)o(ery)d(close)i (to)g(the)f(theoretical)f(measure)h FF(\027)s FQ(,)h(when)f(\\closeness")i (is)e(understo)q(o)q(d)i(in)f(the)f(b)q(ounded)60 2160 y(measurable)f(top)q (ology)j(\(that)f(is,)f(the)g(w)o(eak)g(top)q(ology)i(generated)e(b)o(y)g (the)g(b)q(ounded)h(measurable)60 2221 y(functions\).)21 b(More)16 b(precisely)l(,)f(if)g Fi(A)i FQ(is)f(an)o(y)g(closed)g(subset)h(of)f FF(M)1274 2228 y FH(+1)1322 2221 y FQ(\(\012\))g FP(not)22 b FQ(con)o(taining)16 b FF(\027)s FQ(,)g(then)60 2281 y(Prob)q(\()p FF(L)216 2288 y FD(n)253 2281 y FE(2)f Fi(A)p FQ(\))f FE(!)g FQ(0)i(as)h FF(n)e FE(!)e(1)p FQ(.)701 2263 y FH(34)760 2281 y FQ(The)j(large-deviation)h(theorem)d([176)q(,)i(69)q(,)g(34])g(then)h (states)60 2341 y(that)g(this)f(probabilit)o(y)f(is)h(in)g(fact)g(exp)q(onen) o(tially)f(small)g(in)h FF(n)p FQ(,)f(namely)650 2429 y(Prob)q(\()p FF(L)806 2436 y FD(n)843 2429 y FE(2)f Fi(A)p FQ(\))28 b FE(\030)g FF(e)1059 2409 y Fy(\000)p FD(n)p Fy(\002)p FH(const)o(\()p FD(\027;)p Fh(A)p FH(\))1765 2429 y FQ(\(2)p FF(:)p FQ(81\))p 60 2470 732 2 v 100 2523 a FA(34)135 2539 y Fz(In)14 b(this)g(particular)f (top)q(ology)m(,)f(a)i(basis)f(for)h(the)g(neigh)o(b)q(orho)q(o)q(ds)h(of)e Fv(\027)j Fz(is)e(giv)o(en)f(b)o(y)h(the)g(sets)439 2637 y Fh(B)467 2652 y Fp(\027;)p Fg(f)s Fp(;\017)561 2637 y Fu(\021)616 2578 y Fx(\032)647 2637 y Fv(\026)p Fz(:)702 2577 y Fx(\014)702 2602 y(\014)702 2627 y(\014)702 2652 y(\014)716 2580 y(Z)758 2637 y Fv(f)778 2643 y Fp(i)799 2637 y Fv(d\026)9 b Fu(\000)896 2580 y Fx(Z)938 2637 y Fv(f)958 2643 y Fp(i)979 2637 y Fv(d\027)1025 2577 y Fx(\014)1025 2602 y(\014)1025 2627 y(\014)1025 2652 y(\014)1049 2637 y Fv(<)j(\017)h Fz(for)h(all)f Fv(i)e Fz(=)h(1)p Fv(;)7 b(:)g(:)g(:)e(;)i(k)1451 2578 y Fx(\033)1500 2637 y Fv(;)951 2784 y FQ(59)p eop %%Page: 60 60 bop 60 91 a FQ(where)17 b(const\()p FF(\027;)8 b Fi(A)p FQ(\))17 b FF(>)f FQ(0)i(whenev)o(er)e Fi(A)h FQ(is)h(a)g(closed)f(set)g(of)h (measures)e(not)i(con)o(taining)f FF(\027)s FQ(.)25 b(More)60 152 y(precisely)l(,)230 309 y(lim)217 334 y FD(n)p Fy(!1)333 275 y FQ(1)p 331 297 30 2 v 331 343 a FF(n)373 309 y FQ(log)10 b(Prob\()p FF(L)600 316 y FD(n)638 309 y FE(2)k Fi(A)p FQ(\))758 209 y Fx(8)758 247 y(>)758 259 y(<)758 334 y(>)758 346 y(:)803 248 y FE(\024)g(\000)35 b FQ(inf)903 284 y FD(\026)p FH(:)10 b FD(\026)p Fy(2)p Fh(A)1025 248 y FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))48 b(if)16 b Fi(A)g FQ(is)g(a)h(closed)f(set)803 336 y FE(\025)e(\000)35 b FQ(inf)903 372 y FD(\026)p FH(:)10 b FD(\026)p Fy(2)p Fh(A)1025 336 y FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))48 b(if)16 b Fi(A)g FQ(is)g(an)h(op)q(en)g(set)1765 309 y(\(2)p FF(:)p FQ(82\))60 469 y(In)h(fact,)h(this)g(result)f(is)h(merely) d(a)j(sophisticated)g(restatemen)o(t)d(of)k(\(2.77\),)f(since)f(ev)o(ery)f (closed)60 530 y(\(resp.)10 b(op)q(en\))i(set)e(of)i(measures)d Fi(A)i FQ(is)g(con)o(tained)f(in)h(\(resp.)f(con)o(tains\))h(one)g(of)g(the)g (form)f FE(f)p FF(\026)p FQ(:)1742 494 y Fx(R)1778 530 y FM(f)k FF(d\026)g FE(2)60 590 y FM(A)p FE(g)i FQ(for)h(some)e FM(f)k FQ(=)14 b(\()p FF(f)471 597 y FH(1)491 590 y FF(;)8 b(:)g(:)g(:)f(;)h(f)624 597 y FD(k)645 590 y FQ(\))17 b(and)f(some)g FM(A)g FQ(closed)g(\(resp.)g(op) q(en\))h FE(\032)c Fq(R)1459 569 y FD(k)1480 590 y FQ(.)133 650 y(F)l(orm)o(ulas)22 b(\(2.81\)/\(2.82\))j(pro)o(vide)d(a)h(ph)o(ysical)f (in)o(terpretation)g(of)h(the)g(relativ)o(e)e(en)o(trop)o(y)l(.)60 710 y(Indeed,)15 b(w)o(e)h(can)h(sa)o(y)f(\(roughly)g(sp)q(eaking\))h(that)g (the)f(probabilit)o(y)g(that)g(a)h(sample)e FF(X)1683 717 y FH(1)1703 710 y FF(;)8 b(:)g(:)g(:)g(;)g(X)1853 717 y FD(n)1876 710 y FQ(,)60 770 y(tak)o(en)16 b(from)f(the)h(probabilit)o(y)f(distribution) h FF(\027)s FQ(,)g(\\lo)q(oks)i(lik)o(e)c(a)j(t)o(ypical)d(sample)h(from)h FF(\026)p FQ(")h(deca)o(ys)60 831 y(exp)q(onen)o(tially)e(with)h(rate)g FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\):)467 935 y(Prob)570 942 y FD(\027)592 935 y FQ(\()p FF(X)651 942 y FH(1)671 935 y FF(;)8 b(:)g(:)g(:)g(;)g(X)821 942 y FD(n)861 935 y FQ(is)16 b(t)o(ypical)f(for)h FF(\026)p FQ(\))28 b FE(\030)f FF(e)1309 914 y Fy(\000)p FD(nI)s FH(\()p FD(\026)p Fy(j)p FD(\027)r FH(\))1470 935 y FF(:)281 b FQ(\(2)p FF(:)p FQ(83\))133 1039 y(In)20 b(the)g(probabilistic)g(literature,)f(\(2.76\)/\(2.77\))j(are)f (called)e(lev)o(el-1)g(large-deviation)g(for-)60 1099 y(m)o(ulae,)14 b(and)j(\(2.82\))g(is)f(called)f(a)h(lev)o(el-2)f(large-deviation)h(form)o (ula.)60 1229 y FM(2.5.4)55 b(V)-5 b(ariational)19 b(Principle)60 1321 y FQ(The)d(free)f(energy)h(and)h(the)f(relativ)o(e)e(en)o(trop)o(y)h (are)h(related)g(b)o(y)f(the)h(follo)o(wing)g FP(variational)i(prin-)60 1381 y(ciple)t FQ(:)60 1489 y FM(Theorem)f(2.54)h(\(V)-5 b(ariational)18 b(principle\))23 b FP(Fix)12 b(a)h(pr)n(ob)n(ability)f(me)n(asur)n(e)f FF(\027)16 b FP(on)d FQ(\(\012)p FF(;)8 b FQ(\006\))p FP(.)21 b(Then)60 1549 y FF(P)7 b FQ(\()h FE(\001)g(j)p FF(\027)s FQ(\))18 b FP(and)g FF(I)t FQ(\()8 b FE(\001)g(j)p FF(\027)s FQ(\))17 b FP(ar)n(e)g(c)n(onjugate)i(c)n(onvex)f(functions,)h(in)f(the)g(sense)g (that)529 1672 y FF(P)7 b FQ(\()p FF(f)e FE(j)p FF(\027)s FQ(\))42 b(=)109 b(sup)797 1713 y FD(\026)p Fy(2)p FD(M)876 1718 y Fr(+1)916 1713 y FH(\(\012)p FD(;)p FH(\006\))1012 1611 y Fx(\024)1034 1613 y(Z)1076 1672 y FF(f)14 b(d\026)25 b FE(\000)g FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))1391 1611 y Fx(\025)1741 1672 y FQ(\(2.84a\))542 1828 y FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))41 b(=)85 b(sup)797 1870 y FD(f)t Fy(2)p FD(B)r FH(\(\012)p FD(;)p FH(\006\))966 1768 y Fx(\024)988 1770 y(Z)1029 1828 y FF(f)14 b(d\026)25 b FE(\000)g FF(P)7 b FQ(\()p FF(f)e FE(j)p FF(\027)s FQ(\))1356 1768 y Fx(\025)1738 1828 y FQ(\(2.84b\))60 1965 y FP(Mor)n(e)n(over,)16 b(the)h(supr)n(emum)f(is)g(achieve)n(d)i(if)f (and)g(only)g(if)f FF(\026)h FP(e)n(quals)h(the)f(Boltzmann-Gibbs)i(me)n(a-) 60 2025 y(sur)n(e)e(for)g(Hamiltonian)h FF(H)g FQ(=)c FE(\000)p FF(f)23 b FP(\(and)17 b FQ(a)g(priori)g FP(me)n(asur)n(e)g FF(\027)s FP(\),)g(namely)766 2161 y FF(\026)795 2168 y FD(B)r(G;f)r(;\027) 938 2161 y FE(\021)1028 2127 y FF(e)1051 2109 y FD(f)1081 2127 y FF(d\027)p 1010 2149 143 2 v 1010 2160 a Fx(R)1046 2195 y FF(e)1069 2181 y FD(f)1099 2195 y FF(d\027)1171 2161 y(:)580 b FQ(\(2)p FF(:)p FQ(85\))p 60 2238 732 2 v 60 2307 a Fz(where)16 b Fg(f)h Fz(=)c(\()p Fv(f)294 2313 y FA(1)313 2307 y Fv(;)7 b(:)g(:)g(:)e(;)i(f)426 2313 y Fp(k)446 2307 y Fz(\))15 b(runs)g(o)o(v)o(er)g (all)e Fw(\014nite)19 b Fz(famili)o(es)13 b(of)h(b)q(ounded)h(measurable)f (functions,)g(and)h Fv(\017)g Fz(runs)g(o)o(v)o(er)60 2357 y(all)e(strictly)h(p)q(ositiv)o(e)f(n)o(um)o(b)q(ers.)18 b(By)c(the)h(usual)e (w)o(eak)h(la)o(w)f(of)g(large)h(n)o(um)o(b)q(ers)g(w)o(e)g(ha)o(v)o(e)499 2483 y(Prob)q(\()p Fv(L)632 2489 y Fp(n)671 2483 y Fv(=)-26 b Fu(2)11 b Fh(B)733 2497 y Fp(\027;)p Fg(f)t Fp(;\017)805 2483 y Fz(\))23 b Fu(\024)920 2431 y Fp(k)899 2443 y Fx(X)902 2532 y Fp(i)p FA(=1)966 2483 y Fz(Prob\()p Fu(j)p Fv(S)1109 2466 y Fp(f)1125 2470 y Fn(i)1107 2493 y Fp(n)1151 2483 y Fu(\000)9 b Fv(m)1228 2489 y Fp(i)1242 2483 y Fu(j)i(\025)h Fv(\017)p Fz(\))23 b Fu(!)g Fz(0)60 2606 y(as)16 b Fv(n)e Fu(!)g(1)p Fz(,)h(since)i Fv(k)f Fz(is)g(\014nite.)23 b(Since)16 b(an)o(y)f(closed)i (set)f Fh(A)e Fu(63)g Fv(\027)k Fz(is)e(con)o(tained)f(in)g(the)i(complemen)o (t)c(of)i(some)g(set)60 2656 y Fh(B)88 2671 y Fp(\027;)p Fg(f)s Fp(;\017)159 2656 y Fz(,)f(the)g(claim)e(Prob\()p Fv(L)499 2662 y Fp(n)534 2656 y Fu(2)f Fh(A)p Fz(\))g Fu(!)g Fz(0)j(is)g(pro)o(v)o (en.)951 2784 y FQ(60)p eop %%Page: 61 61 bop 60 91 a FQ(This)18 b(complemen)n(tary)e(pair)i(of)h(v)m(ariational)f (principles)f(establishes)h(the)g(equiv)m(alence)e(of)j(\(2.1\))60 152 y(and)f(\(2.3\))f(for)g FP(\014nite-volume)24 b FQ(statistical-mec)o (hanical)14 b(systems.)22 b(Indeed,)1492 116 y Fx(R)1520 152 y FF(f)13 b(d\026)18 b FQ(is)f(min)o(us)e(the)60 212 y(mean)e(energy)h(for)g (a)g(system)f(with)h(Hamiltonian)e FF(H)18 b FQ(=)c FE(\000)p FF(f)5 b FQ(,)14 b(and)h FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))f(is)g(min)o(us)e(the)i(en)o(trop)o(y;)60 272 y(therefore,)h(\(2.84a\)) i(states)g(that)f(the)g(Boltzmann-Gibbs)f(measure)g(is)h(the)g(one)g(that)g (minimi)o(zes)60 332 y(energy)k(min)o(us)f(en)o(trop)o(y)l(,)h(and)i(that)f (the)f(minim)n(um)c(v)m(alue)21 b(of)g(energy)f(min)o(us)e(en)o(trop)o(y)i (equals)60 392 y(the)d(free)g(energy)l(.)23 b(\(In)17 b(thermo)q(dynamic)e (notation,)j FF(F)k FQ(=)15 b FF(E)g FE(\000)c FF(T)c(S)s FQ(;)17 b(recall)f(that)i(w)o(e)f(are)g(taking)60 452 y FF(\014)f FQ(=)e(1.\))60 597 y FB(2.6)70 b(En)n(trop)n(y)-6 b(,)19 b(Large)f(Deviations)d(and)j(the)e (V)-6 b(ariational)16 b(Principle:)217 672 y(In\014nite-V)-6 b(olum)o(e)19 b(Case)60 746 y FH(35)133 824 y FQ(The)d(v)m(ariational)h (approac)o(h)g(dev)o(elop)q(ed)e(in)h(the)g(preceding)f(section)h(is)g (adequate)g(for)g(\014nite-)60 884 y(v)o(olume)c(statistical-mec)o(hanical)f (systems,)i(in)g(whic)o(h)h(the)f(Hamiltonian)g FF(H)18 b FQ(is)c(w)o (ell-de\014ned)e(and)60 945 y(\014nite.)21 b(But)16 b(it)f(is)h(\(not)h (surprisingly\))f(insu\016cien)o(t)e(for)j(the)f(in\014nite-v)o(olume)d (case,)j(in)g(whic)o(h)g(all)60 1005 y(the)g(relev)m(an)o(t)g(quan)o(tities)f (|)i(Hamiltonian,)d(free)i(energy)l(,)f(mean)h(energy)g(and)h(relativ)o(e)e (en)o(trop)o(y)60 1065 y(|)22 b(are)f(almost)g(certainly)g(in\014nite.)37 b(Nev)o(ertheless,)20 b(one)i(migh)o(t)f(hop)q(e)h(that)g(for)g FP(tr)n(anslation-)60 1125 y(invariant)g FQ(in\014nite-v)o(olume)14 b(systems)i(there)h(w)o(ould)g(exist)f(an)h(analogous)i(theory)e(in)g(whic)o (h)f(the)60 1185 y(concepts)h(of)h(free)e(energy)l(,)h(mean)f(energy)h(and)h (relativ)o(e)d(en)o(trop)o(y)i(are)g(replaced)f(b)o(y)h(these)g(same)60 1246 y(quan)o(tities)23 b FP(p)n(er)h(unit)i(volume)t FQ(;)i(one)d(could)f (then)g(de\014ne)f(an)i FP(e)n(quilibrium)h(me)n(asur)n(e)h FQ(to)d(b)q(e)h(a)60 1306 y(translation-in)o(v)m(arian)o(t)17 b(measure)e(that)i(maximiz)o(es)d(the)i(en)o(trop)o(y)g(densit)o(y)g(min)o (us)f(mean)g(energy)60 1366 y(densit)o(y)l(.)20 b(In)14 b(this)h(section)g(w) o(e)f(shall)h(dev)o(elop)f(suc)o(h)h(a)g(theory)l(.)21 b(But)14 b(this)h(in\014nite-v)o(olume)d(theory)60 1426 y(is)g(considerably)h(more)e (subtle)h(than)h(its)g(\014nite-v)o(olume)d(coun)o(terpart:)19 b(this)13 b(subtlet)o(y)e(arises)i(from)60 1486 y(the)18 b(ph)o(ysical)g(p)q (ossibilit)o(y)f(of)i(phase)g(transitions,)g(as)h(w)o(ell)d(as)i(from)e (additional)i(mathematical)60 1546 y(pathologies)e(to)g(b)q(e)f(explained)f (in)h(Section)g(2.6.7)g(b)q(elo)o(w.)133 1607 y(The)g(v)m(ariational)g (approac)o(h)g(to)g(in\014nite-v)o(olume)c(lattice)j(systems)f(is)i(less)f (general)g(than)h(the)60 1667 y(one)23 b(based)f(on)h(the)f(DLR)i(equations,) f(b)q(ecause)g(of)f(its)h(restriction)e(to)i(translation-in)o(v)m(arian)o(t) 60 1727 y(measures)254 1709 y FH(36)290 1727 y FQ(,)c(but)g(within)g(its)f (restricted)g(domain)g(it)h(is)f(equiv)m(alen)o(t)g(to)h(the)f(DLR)i(theory:) 26 b(the)60 1787 y(k)o(ey)16 b(theorem)g(\(Corollary)i(2.68\))g(states)g (that,)g(for)g(an)o(y)g(in)o(teraction)e(\010)g FE(2)h(B)1512 1769 y FH(1)1531 1787 y FQ(,)g(the)g(equilibrium)60 1847 y(measures)e (coincide)g(with)h(the)g(translation-in)o(v)m(arian)o(t)h(Gibbs)f(measures.) 60 1977 y FM(2.6.1)55 b(F)-5 b(ree)18 b(Energy)g(Densit)n(y)g (\(\\Pressure"\))60 2070 y FQ(W)l(e)e(lo)q(ok)h(\014rst)f(at)h(the)f(free)f (energy)h(densit)o(y)l(,)f(or)h(what)h(is)f(equiv)m(alen)o(t,)f(the)h (\\pressure":)60 2184 y FM(De\014nition)i(2.55)24 b FP(L)n(et)18 b FF(\027)k FP(b)n(e)d(a)f(tr)n(anslation-invariant)i(pr)n(ob)n(ability)e(me) n(asur)n(e)g(on)h FQ(\012)e(=)f(\(\012)1795 2191 y FH(0)1815 2184 y FQ(\))1834 2166 y Fl(Z)1855 2154 y Fs(d)1875 2184 y FP(,)60 2244 y(and)21 b(let)h FF(f)k FP(b)n(e)21 b(a)f(b)n(ounde)n(d)h(me)n (asur)n(able)g(function.)33 b(Then)22 b(the)f FQ(pressure)f(of)g FF(f)25 b FQ(relativ)o(e)18 b(to)i FF(\027)k FP(is)p 60 2288 732 2 v 100 2342 a FA(35)135 2357 y Fz(References)17 b(for)e(this)g(section)g (are)h(Georgii)e([157)n(,)h(Chapters)h(15)f(and)g(16],)f(Israel)h([206)o(,)f (Chapters)j(I,)d(I)q(I)h(and)60 2406 y(V],)f(Preston)i([299)o(,)e(Chapters)i (7)e(and)h(8],)e(Ruelle)h([313)o(,)h(Chapters)g(3)g(and)f(4])g(and)h(Ellis)e ([110)o(,)i(Chapters)g(IV)g(and)60 2456 y(V)f(and)g(App)q(endix)g(C].)100 2514 y FA(36)135 2529 y Fz(Ev)o(en)j(if)f(the)h(in)o(teraction)g(is)f (translation-in)o(v)n(arian)o(t,)f(there)j(ma)o(y)c(exist)j (non-translation-in)o(v)n(arian)o(t)d(Gibbs)60 2579 y(measures)e(\(e.g.)f (for)h(the)h(Ising)e(mo)q(del)g(in)g(dimension)f Fv(d)h Fu(\025)h Fz(3)g([85)o(,)f(348]\),)g(and)h(these)h(are)g(of)e(in)o(terest)i(in)e (describing)60 2629 y(in)o(terfaces.)951 2784 y FQ(61)p eop %%Page: 62 62 bop 60 91 a FP(de\014ne)n(d)18 b(as)521 192 y FF(p)p FQ(\()p FF(f)5 b FE(j)p FF(\027)s FQ(\))28 b(=)40 b(lim)747 217 y FD(n)p Fy(!1)873 159 y FQ(1)p 860 181 50 2 v 860 227 a FF(n)889 212 y FD(d)923 192 y FQ(log)994 134 y Fx(Z)1044 192 y FQ(exp)1127 107 y Fx(2)1127 182 y(4)1169 151 y(X)1155 243 y FD(x)p Fy(2)p FD(C)1224 247 y Fs(n)1253 192 y FF(T)1282 199 y FD(x)1303 192 y FF(f)1332 107 y Fx(3)1332 182 y(5)1377 192 y FF(d\027)339 b FQ(\(2)p FF(:)p FQ(86\))60 325 y(if)22 b(this)g(limit)e(exists)p FP(.)39 b(Similarly,)25 b(if)e FQ(\010)g FP(is)g(an)h(inter)n(action)g(in)f FE(B)1337 307 y FH(0)1356 325 y FP(,)i(then)f(the)g FQ(pressure)e(of)h(\010) 60 385 y(relativ)o(e)14 b(to)j FF(\027)k FP(is)c(de\014ne)n(d)h(as)511 515 y FF(p)p FQ(\(\010)p FE(j)p FF(\027)s FQ(\))28 b(=)40 b(lim)743 540 y FD(n)p Fy(!1)869 481 y FQ(1)p 856 503 V 856 549 a FF(n)885 535 y FD(d)919 515 y FQ(log)990 456 y Fx(Z)1040 515 y FQ(exp)1123 467 y Fx(h)1143 515 y FE(\000)p FF(H)1226 494 y FH(\010)1222 527 y FD(C)1247 531 y Fs(n)1268 527 y FD(;f)t(r)q(ee)1350 467 y Fx(i)1387 515 y FF(d\027)329 b FQ(\(2)p FF(:)p FQ(87\))60 638 y(if)16 b(this)g(limit)d(exists)p FP(.)60 752 y FQ(This)h(quan)o(tit)o(y) f(should)i(really)e(b)q(e)h(called)f(\\min)o(us)g(the)h(free)f(energy)h (densit)o(y".)20 b(The)14 b(term)e(\\pres-)60 812 y(sure")h(arises)g(from)e (the)i(in)o(terpretation)e(of)i(the)f(canonical-ensem)o(ble)e(Ising)j(mo)q (del)e(as)j(equiv)m(alen)o(t)60 872 y(to)20 b(a)f(grand-canonical-ensem)o (ble)f(lattice)g(gas;)k(in)d(the)g(general)g(case)g(the)h(term)d(\\pressure") j(is)60 932 y(not)c(really)e(appropriate,)i(but)f(it)g(has)h(b)q(ecome)e (standard)i(among)f(mathematical)d(ph)o(ysicists.)20 b(It)60 993 y(has,)d(at)f(least,)g(the)g(virtue)f(of)i(brevit)o(y)l(.)133 1053 y(W)l(e)f(emphasize)d(that)j(the)g(existence)e(of)i(the)f(limit)e (\(2.86\))k([or)e(\(2.87\)])h(is)f(a)i(non)o(trivial)d(prob-)60 1113 y(lem;)d(in)h(fact,)g(there)g(exist)f(examples)f(of)j(translation-in)o (v)m(arian)o(t)f(measures)f FF(\027)16 b FQ(for)c(whic)o(h)g(the)g(limit)60 1173 y(do)q(es)18 b FP(not)k FQ(exist,)17 b(ev)o(en)f(for)h(simple)e(lo)q (cal)i(functions)g FF(f)23 b FQ(\(see)17 b(App)q(endix)f(A.5.2\).)24 b(Therefore,)16 b(w)o(e)60 1233 y(shall)f(restrict)e(atten)o(tion)i(to)g(t)o (w)o(o)g(cases:)20 b(when)15 b FF(\027)j FQ(is)d(a)g(pro)q(duct)g(measure,)f (and)h(more)e(generally)l(,)60 1293 y(when)j FF(\027)k FQ(is)c(a)h(Gibbs)f (measure)f(for)i(a)f(translation-in)o(v)m(arian)o(t)h(in)o(teraction.)60 1408 y FM(Prop)r(osition)h(2.56)24 b FP(L)n(et)15 b FF(\027)k FP(b)n(e)d(a)g(pr)n(o)n(duct)e(me)n(asur)n(e.)21 b(Then)c(the)f(pr)n(essur)n (e)f FF(p)p FQ(\()p FF(f)5 b FE(j)p FF(\027)s FQ(\))16 b FP(exists)h(for)e (al)r(l)60 1468 y(b)n(ounde)n(d)h(quasilo)n(c)n(al)h(functions)g FF(f)5 b FP(;)17 b(in)g(fact,)f(the)h(limit)f(exists)h(also)g(in)f(van)h (Hove)g(sense,)g(namely)514 1606 y FF(p)p FQ(\()p FF(f)5 b FE(j)p FF(\027)s FQ(\))28 b(=)42 b(lim)740 1636 y FH(\003)p Fy(\0451)875 1572 y FQ(1)p 856 1595 62 2 v 856 1640 a FE(j)p FQ(\003)p FE(j)931 1606 y FQ(log)1003 1548 y Fx(Z)1052 1606 y FQ(exp)1135 1533 y Fx(")1163 1565 y(X)1159 1657 y FD(x)p Fy(2)p FH(\003)1236 1606 y FF(T)1265 1613 y FD(x)1286 1606 y FF(f)1315 1533 y Fx(#)1356 1606 y FF(d\027)18 b(:)328 b FQ(\(2)p FF(:)p FQ(88\))60 1754 y FP(Mor)n(e)n(over,)16 b FF(p)p FQ(\()8 b FE(\001)g(j)p FF(\027)s FQ(\))19 b FP(has)e(the)h(fol)r(lowing)h(pr)n(op)n (erties:)93 1856 y(\(a\))24 b FF(p)p FQ(\()p FM(0)p FE(j)p FF(\027)s FQ(\))f(=)f(0)p FP(.)95 1958 y(\(b\))j FF(f)19 b FE(\024)14 b FF(g)43 b FQ(=)-8 b FE(\))41 b FF(p)p FQ(\()p FF(f)5 b FE(j)p FF(\027)s FQ(\))15 b FE(\024)f FF(p)p FQ(\()p FF(g)r FE(j)p FF(\027)s FQ(\))p FP(.)95 2059 y(\(c\))25 b FF(p)p FQ(\()p FF(f)17 b FQ(+)11 b FF(c)p FE(j)p FF(\027)s FQ(\))22 b(=)g FF(p)p FQ(\()p FF(f)5 b FE(j)p FF(\027)s FQ(\))12 b(+)f FF(c)17 b FP(for)g(any)h(r)n(e)n(al)e(numb)n(er)i FF(c)p FP(.)93 2167 y(\(d\))182 2117 y Fx(\014)182 2142 y(\014)182 2167 y(\014)p FF(p)p FQ(\()p FF(f)5 b FE(j)p FF(\027)s FQ(\))17 b FE(\000)e FF(p)p FQ(\()p FF(g)r FE(j)p FF(\027)s FQ(\))527 2117 y Fx(\014)527 2142 y(\014)527 2167 y(\014)35 b FE(\024)g(k)p FF(f)21 b FE(\000)16 b FF(g)r FE(k)825 2174 y Fy(1)862 2167 y FP(.)42 b(That)24 b(is,)i FF(p)p FQ(\()8 b FE(\001)g(j)p FF(\027)s FQ(\))25 b FP(is)f(Lipschitz)g(c)n(ontinuous)h(with)182 2227 y(Lipschitz)17 b(c)n(onstant)h(1.)95 2329 y(\(e\))25 b FF(p)p FQ(\()p FF(f)17 b FQ(+)11 b FF(h)p FE(j)p FF(\027)s FQ(\))22 b(=)g FF(p)p FQ(\()p FF(f)5 b FE(j)p FF(\027)s FQ(\))18 b FP(for)f(any)h FF(h)c FE(2)g(I)t FP(.)98 2431 y(\(f)5 b(\))24 b FF(p)p FQ(\()8 b FE(\001)g(j)p FF(\027)s FQ(\))18 b FP(is)g(c)n(onvex.)60 2545 y FQ(W)l(e)h(emphasize,)f(in)i(particular,)f(part)h(\(e\):)28 b(the)19 b(pressure)h(is)f(constan)o(t)h(within)f(\\subspaces)i(of)60 2605 y(ph)o(ysical)15 b(equiv)m(alence".)951 2784 y(62)p eop %%Page: 63 63 bop 60 91 a FM(Prop)r(osition)18 b(2.57)24 b FP(L)n(et)19 b FF(\027)j FP(b)n(e)e(a)f(tr)n(anslation-invariant)h(Gibbs)g(me)n(asur)n(e)e (for)h(an)g(inter)n(action)60 152 y FQ(\010)j FE(2)g(B)207 133 y FH(1)248 152 y FP(\(and)g FQ(a)f(priori)h FP(me)n(asur)n(e)f FF(\026)773 133 y FH(0)793 152 y FP(\).)35 b(Then)22 b(the)h(pr)n(essur)n(e)d FF(p)p FQ(\()p FF(f)5 b FE(j)p FF(\027)s FQ(\))23 b FP(exists)g(for)e(al)r(l) i(b)n(ounde)n(d)60 212 y(quasilo)n(c)n(al)18 b(functions)h FF(f)5 b FP(;)17 b(in)h(fact,)g(the)g(limit)g(exists)g(also)g(in)f(van)i (Hove)f(sense,)g(namely)514 350 y FF(p)p FQ(\()p FF(f)5 b FE(j)p FF(\027)s FQ(\))28 b(=)42 b(lim)740 380 y FH(\003)p Fy(\0451)875 316 y FQ(1)p 856 338 62 2 v 856 384 a FE(j)p FQ(\003)p FE(j)931 350 y FQ(log)1003 291 y Fx(Z)1052 350 y FQ(exp)1135 277 y Fx(")1163 309 y(X)1159 400 y FD(x)p Fy(2)p FH(\003)1236 350 y FF(T)1265 357 y FD(x)1286 350 y FF(f)1315 277 y Fx(#)1356 350 y FF(d\027)18 b(:)328 b FQ(\(2)p FF(:)p FQ(89\))60 495 y FP(Mor)n(e)n(over,)16 b(the)i(limit)g(is)f(given)i(by)568 605 y FF(p)p FQ(\()p FF(f)5 b FE(j)p FF(\027)s FQ(\))29 b(=)e FF(p)p FQ(\()p FF(f)17 b FE(\000)11 b FF(f)952 612 y FH(\010)980 605 y FE(j)p FF(\026)1023 585 y FH(0)1042 605 y FQ(\))20 b FE(\000)f FF(p)p FQ(\()p FE(\000)p FF(f)1245 612 y FH(\010)1273 605 y FE(j)p FF(\026)1316 585 y FH(0)1336 605 y FQ(\))13 b FF(:)383 b FQ(\(2)p FF(:)p FQ(90\))60 715 y FP(In)18 b(p)n(articular,)e FF(p)p FQ(\()8 b FE(\001)g(j)p FF(\027)s FQ(\))19 b FP(has)e(al)r(l)i(the)f(pr)n(op)n(erties)e(\(a\){\(f)5 b(\))17 b(of)g(Pr)n(op)n(osition)f(2.56.)133 879 y FQ(The)j(pressure)f(of)h (a)g FP(function)k FF(f)h FQ(is)18 b(the)g(simplest)f(ob)s(ject)h(from)f(a)i (mathematical)c(p)q(oin)o(t)k(of)60 939 y(view,)f(but)h(the)f(pressure)h(of)f (an)i FP(inter)n(action)j FQ(\010)18 b(is)h(p)q(erhaps)g(more)f(familiar)e (to)j(ph)o(ysicists.)27 b(In)60 1000 y(fact)16 b(these)g(t)o(w)o(o)g(ob)s (jects)g(are)g(essen)o(tially)f(iden)o(tical:)60 1114 y FM(Prop)r(osition)j (2.58)24 b FP(L)n(et)15 b FQ(\010)f FE(2)g(B)700 1096 y FH(0)719 1114 y FP(,)i(and)g(let)g FF(\027)j FP(b)n(e)d(a)f(tr)n(anslation-invariant)i (me)n(asur)n(e)e(satisfying)60 1174 y(the)j(c)n(onditions)g(of)f(Pr)n(op)n (osition)f(2.56)h(or)g(2.57.)22 b(Then:)93 1276 y(\(a\))i FF(p)p FQ(\(\010)p FE(j)p FF(\027)s FQ(\))g FP(exists)g(and)f(e)n(quals)h FF(p)p FQ(\()p FE(\000)p FF(f)838 1283 y FH(\010)866 1276 y FE(j)p FF(\027)s FQ(\))p FP(.)40 b(In)23 b(fact,)i(the)f(limit)f(exists)h (also)g(in)f(van)h(Hove)182 1336 y(sense,)18 b(i.e.)562 1415 y FF(p)p FQ(\(\010)p FE(j)p FF(\027)s FQ(\))28 b(=)41 b(lim)794 1445 y FH(\003)p Fy(\0451)929 1382 y FQ(1)p 910 1404 V 910 1450 a FE(j)p FQ(\003)p FE(j)985 1415 y FQ(log)1056 1357 y Fx(Z)1106 1415 y FQ(exp)1189 1367 y Fx(h)1208 1415 y FE(\000)p FF(H)1291 1395 y FH(\010)1287 1428 y(\003)p FD(;f)t(r)q(ee)1394 1367 y Fx(i)1430 1415 y FF(d\027)18 b(:)254 b FQ(\(2)p FF(:)p FQ(91\))95 1573 y FP(\(b\))25 b(If)20 b(in)h(addition)f FQ(\010)g FE(2)g(B)635 1554 y FH(1)654 1573 y FP(,)h(then)g(for)f(any)g FF(\034)26 b FE(2)19 b FQ(\012)p FP(,)35 b FQ(lim)1149 1603 y FH(\003)p Fy(\0451)1284 1553 y FQ(1)p 1265 1561 V 1265 1600 a FE(j)p FQ(\003)p FE(j)1340 1573 y FQ(log)1411 1514 y Fx(Z)1461 1573 y FQ(exp)1544 1524 y Fx(h)1564 1573 y FE(\000)p FF(H)1647 1554 y FH(\010)1643 1585 y(\003)p FD(;\034)1699 1524 y Fx(i)1735 1573 y FF(d\027)24 b FP(also)182 1655 y(exists)18 b(and)g(e)n(quals)g FF(p)p FQ(\()p FE(\000)p FF(f)659 1662 y FH(\010)687 1655 y FE(j)p FF(\027)s FQ(\))p FP(.)60 1769 y FQ(P)o(art)f(\(b\))f(states)h(that,)f (for)h(in)o(teractions)f(\010)e FE(2)h(B)982 1751 y FH(1)1001 1769 y FQ(,)h(the)g(pressure)g(is)g(indep)q(enden)o(t)g(of)h(b)q(oundary)60 1829 y(conditions.)133 1939 y(The)d(reader)g(will)e(note)i(that)g(w)o(e)g(ha) o(v)o(e)f(not)h(asserted)g(the)f FP(strict)19 b FQ(con)o(v)o(exit)o(y)11 b(of)j FF(p)p FQ(\()8 b FE(\001)g(j)p FF(\027)s FQ(\);)16 b(this)d(is)60 1999 y(b)q(ecause,)i(in)f(sharp)h(con)o(trast)g(to)g(the)f(\014nite-v)o (olume)e(case,)i(the)g(in\014nite-v)o(olume)e(pressure)i(is)h FP(not)60 2059 y FQ(strictly)j(con)o(v)o(ex)h(\(not)h(ev)o(en)e(mo)q(dulo)h (ph)o(ysical)g(equiv)m(alence\).)29 b(Indeed,)19 b(this)h(failure)f(of)h (strict)60 2120 y(con)o(v)o(exit)o(y)c(is)h(at)i(the)f(origin)f(of)i(some)e (rather)h(surprising)g(pathologies)h(of)f(the)g(in\014nite-v)o(olume)60 2180 y(v)m(ariational)k(theory)g(in)f(the)g(\\large")i(space)f(of)g(in)o (teractions)e FE(B)1293 2162 y FH(0)1334 2180 y FQ(\(see)h(Section)h(2.6.7)g (b)q(elo)o(w\).)60 2240 y(Ho)o(w)o(ev)o(er,)14 b(in)i(the)g(smaller)e(space)j FE(B)745 2222 y FH(1)780 2240 y FQ(these)f(pathologies)h(do)f(not)h(arise:)60 2354 y FM(Prop)r(osition)h(2.59)g(\(Gri\016ths{Ruelle)e([174]\))23 b FP(L)n(et)h FF(\027)i FP(b)n(e)e(a)g(tr)n(anslation-invariant)h(me)n(a-)60 2414 y(sur)n(e)20 b(satisfying)g(the)g(c)n(onditions)h(of)f(Pr)n(op)n (osition)e(2.56)i(or)f(2.57.)30 b(Then)21 b(the)f(pr)n(essur)n(e)f FF(p)p FQ(\()8 b FE(\001)g(j)p FF(\027)s FQ(\))p FP(,)60 2475 y FQ(restricted)14 b(to)i(the)g(space)g(of)f(in)o(teractions)g FE(B)902 2456 y FH(1)921 2475 y FP(,)i(is)g(strictly)g(c)n(onvex)h(in)g(dir)n (e)n(ctions)k FF(=)-30 b FE(2)14 b(J)19 b FQ(+)10 b FP(Const.)951 2784 y FQ(63)p eop %%Page: 64 64 bop 133 91 a FQ(Note,)18 b(in)f(particular,)g(the)h(con)o(trap)q(ositiv)o(e)f (of)h(this)g(prop)q(osition:)26 b(if)17 b FF(p)p FQ(\()8 b FE(\001)g(j)p FF(\027)s FQ(\))19 b(is)e FP(not)23 b FQ(strictly)60 152 y(con)o(v)o(ex)d(on)i FE(B)333 133 y FH(1)374 152 y FQ(in)f(directions)26 b FF(=)-30 b FE(2)23 b(J)h FQ(+)14 b FP(Const)q FQ(,)22 b(then)f FF(\027)k FQ(is)c FP(not)27 b FQ(the)21 b(Gibbs)h(measure)e(for)i(an)o(y)60 212 y(in)o(teraction)d(in)h FE(B)405 194 y FH(1)424 212 y FQ(.)33 b(This)20 b(giv)o(es)f(a)i(metho)q(d)e(for)h(pro)o(ving)g(non-Gibbsianness,)i (whic)o(h)e(will)f(b)q(e)60 272 y(exploited)c(in)h(Section)g(4.4.)133 381 y FM(Remark.)37 b FQ(The)23 b(failure)e(of)i(strict)e(con)o(v)o(exit)o(y) f(in)i FE(B)1161 362 y FH(0)1202 381 y FQ(w)o(as)h(\014rst)g(p)q(oin)o(ted)f (out)h(b)o(y)f(Fisher)60 441 y([116)q(],)15 b(who)i(pro)o(vided)f(a)g(family) e(of)j(exactly)e(soluble)h(one-dimensional)f(Ising)h(mo)q(dels)f(in)h(whic)o (h)60 501 y(the)f(pressure)g(can)g(b)q(e)g(explicitly)d(seen)i(to)i(ha)o(v)o (e)e(straigh)o(t)h(segmen)o(ts.)k(These)c(mo)q(dels)f(are)h(lattice)60 561 y(v)o(ersions)e(of)g(the)g(Fisher-F)l(elderhof)e([120)q(,)i(121)q(,)f (114)r(,)g(113)q(])h(cluster)f(mo)q(dels.)19 b(The)13 b(failure)f(of)i (strict)60 621 y(con)o(v)o(exit)o(y)j(can)j(here)g(b)q(e)g(giv)o(en)f(a)h(ph) o(ysical)f(in)o(terpretation)g(in)g(terms)g(of)h(the)f(formation)g(of)i(a)60 682 y(p)q(erfectly)c(rigid)i(crystal.)28 b(This)19 b(indicates)f(that)h FE(B)1029 663 y FH(0)1061 682 y FE(n)13 b(B)1134 663 y FH(1)1172 682 y FQ(do)q(es)19 b(con)o(tain)g(some)f(in)o(teractions)g(of)60 742 y(ph)o(ysical)d(in)o(terest,)g(if)h(only)g(for)g(their)g(rather)g (strange)h(thermo)q(dynamic)c(prop)q(erties.)60 871 y FM(2.6.2)55 b(Relativ)n(e)17 b(En)n(trop)n(y)i(Densit)n(y)60 964 y FQ(F)l(or)c(brevit)o (y)e(w)o(e)h(henceforth)g(write)g(the)g(relativ)o(e)f(en)o(trop)o(y)g(in)i(v) o(olume)d(\003)i(as)h FF(I)1521 971 y FH(\003)1547 964 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\),)g(instead)g(of)60 1024 y(the)h(more)f(p)q (edan)o(tic)h FF(I)486 1031 y Fy(F)511 1037 y Fr(\003)535 1024 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\).)22 b(W)l(e)16 b(no)o(w)g (de\014ne)g(the)g(relativ)o(e)f(en)o(trop)o(y)g(densit)o(y:)60 1140 y FM(De\014nition)j(2.60)24 b FP(L)n(et)13 b FF(\026;)8 b(\027)18 b FP(b)n(e)c(tr)n(anslation-invariant)i(pr)n(ob)n(ability)d(me)n (asur)n(es)g(on)i FQ(\012)f(=)g(\(\012)1786 1147 y FH(0)1805 1140 y FQ(\))1824 1122 y Fq(Z)1855 1098 y Fs(d)1875 1140 y FP(.)60 1200 y(The)j FQ(relativ)o(e)c(en)o(trop)o(y)h(densit)o(y)j FP(\(or)e FQ(relativ)o(e)f(en)o(trop)o(y)g(p)q(er)h(unit)g(v)o(olume)p FP(\))g FQ(of)g FF(\026)h FQ(relativ)o(e)d(to)i FF(\027)20 b FP(is)60 1260 y(de\014ne)n(d)e(as)693 1340 y FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))27 b(=)40 b(lim)911 1365 y FD(n)p Fy(!1)1037 1306 y FQ(1)p 1025 1328 50 2 v 1025 1374 a FF(n)1054 1359 y FD(d)1079 1340 y FF(I)1101 1347 y FD(C)1126 1351 y Fs(n)1149 1340 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))508 b(\(2)p FF(:)p FQ(92\))60 1439 y(if)16 b(this)g(limit)d(exists)p FP(.)60 1538 y FQ(W)l(e)20 b(emphasize)e(that)i(the)g(existence)e(of)i(the)g (limit)d(\(2.92\))j(is)g(a)g(non)o(trivial)f(problem;)h(in)g(fact,)60 1598 y(there)h(exist)g(examples)f(of)i(translation-in)o(v)m(arian)o(t)g (measures)e FF(\026;)8 b(\027)26 b FQ(for)c(whic)o(h)f(the)g(limit)e(do)q(es) 60 1659 y FP(not)24 b FQ(exist)19 b(\(see)g(App)q(endix)f(A.5.2\).)30 b(Therefore,)19 b(just)g(as)h(for)g(the)f(pressure,)g(w)o(e)g(shall)g (restrict)60 1719 y(atten)o(tion)d(to)h(t)o(w)o(o)f(cases:)22 b(when)16 b FF(\027)k FQ(is)c(a)h(pro)q(duct)g(measure,)d(and)j(more)e (generally)l(,)g(when)i FF(\027)i FQ(is)e(a)60 1779 y(Gibbs)g(measure)d(for)j (a)g(translation-in)o(v)m(arian)o(t)f(in)o(teraction.)60 1890 y FM(Prop)r(osition)i(2.61)24 b FP(L)n(et)g FF(\027)k FP(b)n(e)d(a)g(pr)n(o)n (duct)f(me)n(asur)n(e.)43 b(Then)26 b(the)f(r)n(elative)g(entr)n(opy)g (density)60 1951 y FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))14 b FP(exists)h(for)f(al)r(l)h(tr)n(anslation-invariant)h(pr)n(ob)n (ability)d(me)n(asur)n(es)h FF(\026)p FP(;)h(in)g(fact,)g(the)g(limit)f (exists)60 2011 y(in)k(van)g(Hove)g(sense)h(and)e(also)h(as)f(a)h(supr)n (emum:)679 2138 y FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))42 b(=)55 b(lim)925 2168 y FH(\003)p Fy(\0451)1061 2104 y FQ(1)p 1042 2126 62 2 v 1042 2172 a FE(j)p FQ(\003)p FE(j)1108 2138 y FF(I)1130 2145 y FH(\003)1157 2138 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))476 b(\(2.93a\))846 2267 y(=)41 b(sup)926 2306 y FH(\003)p Fy(2S)1039 2233 y FQ(1)p 1020 2255 V 1020 2301 a FE(j)p FQ(\003)p FE(j)1087 2267 y FF(I)1109 2274 y FH(\003)1135 2267 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))14 b FF(:)467 b FQ(\(2.93b\))60 2403 y FP(Mor)n(e)n(over,)16 b FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))i FP(has)f(the)h(fol)r(lowing)i(pr)n(op)n (erties:)93 2502 y(\(a\))k FQ(0)g FE(\024)f FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))h FE(\024)f FF(i)520 2509 y FD(max)607 2502 y FE(\021)15 b(\000)8 b FQ(log)i FF(\027)804 2509 y FD(min;)p FH(0)898 2502 y FP(,)18 b(wher)n(e)h FF(\027)1094 2509 y FD(min;)p FH(0)1203 2502 y FQ(=)82 b(inf)1257 2543 y Fq(?)o Fy(6)p FH(=)p FD(A)p Fy(2F)1399 2550 y Ft(f)p Fr(0)p Ft(g)1457 2502 y FF(\027)s FQ(\()p FF(A)p FQ(\))p FP(.)25 b([F)l(or)18 b(example,)182 2600 y(if)i FF(\027)j FP(is)c(the)i(pr)n(o)n(duct)e(of)g (normalize)n(d)h(c)n(ounting)h(me)n(asur)n(e)e(on)h(a)g(\014nite)h (single-spin)h(sp)n(ac)n(e)182 2660 y FQ(\012)217 2667 y FH(0)237 2660 y FP(,)16 b(then)g FF(i)391 2667 y FD(max)476 2660 y FQ(=)e(log)9 b FE(j)p FQ(\012)648 2667 y FH(0)668 2660 y FE(j)p FP(.)21 b(If)15 b(the)h(single-spin)i(sp)n(ac)n(e)c FQ(\012)1245 2667 y FH(0)1281 2660 y FP(is)h(in\014nite,)i(then)f FF(i)1635 2667 y FD(max)1721 2660 y FQ(=)d(+)p FE(1)p FP(.])951 2784 y FQ(64)p eop %%Page: 65 65 bop 95 91 a FP(\(b\))25 b FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))17 b FP(is)h(an)f FQ(a\016ne)h FP(function)g(of)g FF(\026)p FP(,)f(i.e.)721 230 y FF(i)738 182 y Fx(\020)782 176 y FD(n)763 189 y Fx(X)764 280 y FD(i)p FH(=1)831 230 y FF(\025)859 237 y FD(i)873 230 y FF(\026)902 237 y FD(i)925 230 y FE(j)8 b FF(\027)974 182 y Fx(\021)1027 230 y FQ(=)1112 176 y FD(n)1093 189 y Fx(X)1094 280 y FD(i)p FH(=1)1161 230 y FF(\025)1189 237 y FD(i)1212 230 y FF(i)p FQ(\()p FF(\026)1277 237 y FD(i)1291 230 y FE(j)p FF(\027)s FQ(\))414 b(\(2)p FF(:)p FQ(94\))182 375 y FP(for)25 b(any)g(me)n(asur)n(es)g FF(\026)615 382 y FH(1)635 375 y FF(;)8 b(:)g(:)g(:)f(;)h(\026)773 382 y FD(n)826 375 y FE(2)28 b FF(M)934 382 y FH(+1)p FD(;inv)1043 375 y FQ(\(\012\))e FP(and)g(numb)n(ers)f FF(\025)1474 382 y FH(1)1494 375 y FF(;)8 b(:)g(:)g(:)g(;)g(\025)1632 382 y FD(n)1684 375 y FE(\025)29 b FQ(0)d FP(with)182 402 y Fx(P)226 415 y FD(n)226 448 y(i)p FH(=1)293 435 y FF(\025)321 442 y FD(i)350 435 y FQ(=)13 b(1)p FP(.)95 537 y(\(c\))25 b(F)l(or)13 b(\014xe)n(d)i FF(\027)s FP(,)g FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))e FP(is)h(a)g(lower)g (semic)n(ontinuous)h(function)g(of)f FF(\026)g FP(in)h(the)f(b)n(ounde)n(d)g (quasilo-)182 597 y(c)n(al)j(top)n(olo)n(gy)426 579 y FH(37)463 597 y FP(,)g(and)g(in)h(the)f(we)n(ak)h(quasilo)n(c)n(al)f(top)n(olo)n(gy) 1233 579 y FH(38)1287 597 y FP(if)g FQ(\012)1369 604 y FH(0)1406 597 y FP(is)g(a)g(c)n(omplete)h(sep)n(ar)n(able)182 658 y(metric)g(sp)n(ac)n (e.)93 759 y(\(d\))24 b(F)l(or)e(any)h FF(\026)p FP(,)i(ther)n(e)e(exists)h (a)f(se)n(quenc)n(e)h FQ(\()p FF(\026)1011 766 y FD(n)1035 759 y FQ(\))1054 766 y FD(n)p Fy(\025)p FH(1)1145 759 y FP(such)g(that)f FF(\026)1396 766 y FD(n)1444 759 y FE(!)h FF(\026)f FP(in)g(the)h(b)n(ounde)n (d)182 819 y(quasilo)n(c)n(al)h(top)n(olo)n(gy,)g(and)g FF(i)p FQ(\()p FF(\026)784 826 y FD(n)808 819 y FE(j)p FF(\027)s FQ(\))h(=)h FF(i)976 826 y FD(max)1072 819 y FP(for)d(al)r(l)i FF(n)p FP(.)43 b(It)25 b(fol)r(lows)h(that)e FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))h FP(is)f(a)182 880 y FQ(discon)o(tin)o(uous)16 b FP(function)h(of)f FF(\026)h FP(in)f(the)h(b)n(ounde)n(d)f(quasilo)n(c)n (al)h(top)n(olo)n(gy)f(\(and)g(henc)n(e)h(also)g(in)182 940 y(the)h(we)n(ak)g(quasilo)n(c)n(al)g(top)n(olo)n(gy\))f(at)g(e)n(ach)h FF(\026)g FP(satisfying)f FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))d FF(<)g(i)1444 947 y FD(max)1515 940 y FP(.)95 1042 y(\(e\))25 b(F)l(or)19 b(any)g FF(\026)p FP(,)h(ther)n(e)f(exists)h(a)f(se)n (quenc)n(e)i FQ(\()p FF(\026)984 1049 y FD(n)1008 1042 y FQ(\))1027 1049 y FD(n)p Fy(\025)p FH(1)1114 1042 y FP(of)f FQ(ergo)q(dic)f FP(me)n(asur)n(es)f(such)i(that)f FF(\026)1799 1049 y FD(n)1840 1042 y FE(!)182 1102 y FF(\026)24 b FP(in)g(the)g(b)n(ounde)n(d)g(quasilo)n (c)n(al)g(top)n(olo)n(gy,)h(and)e FF(i)p FQ(\()p FF(\026)1179 1109 y FD(n)1203 1102 y FE(j)p FF(\027)s FQ(\))i FE(")h FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))p FP(.)41 b([This)23 b(str)n(engthens)182 1162 y(Pr)n(op)n(osition)16 b(2.32.])98 1264 y(\(f)5 b(\))24 b(F)l(or)17 b(\014xe)n(d)h FF(\027)j FP(and)d(\014xe)n (d)g FF(c)c(<)g FE(1)p FP(,)k(the)g(set)g FE(f)p FF(\026)p FQ(:)k FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))14 b FE(\024)g FF(c)p FE(g)j FP(is)h(c)n(omp)n(act)f(and)h(se)n(quential)r(ly)182 1324 y(c)n(omp)n(act)d(in)i(the)f(b)n(ounde)n(d)g(quasilo)n(c)n(al)h(top)n (olo)n(gy)e(\(and)h(henc)n(e)h(also)f(in)g(the)h(we)n(ak)g(quasilo)n(c)n(al) 182 1384 y(top)n(olo)n(gy\),)g(at)g(le)n(ast)h(if)f FQ(\012)655 1391 y FH(0)693 1384 y FP(is)g(a)g(c)n(omplete)i(sep)n(ar)n(able)e(metric)h (sp)n(ac)n(e.)60 1498 y FQ(It)i(is)h(quite)f(remark)m(able)f(that)j(the)e (relativ)o(e)f(en)o(trop)o(y)h(densit)o(y)g FF(i)p FQ(\()8 b FE(\001)g(j)p FF(\027)s FQ(\))21 b(is)g(an)g FP(a\016ne)26 b FQ(function.)60 1558 y(This)16 b(comes)f(from)h(the)g(fact)g(that)g(the)h (relativ)o(e)d(en)o(trop)o(y)h FF(I)t FQ(\()8 b FE(\001)g(j)p FF(\027)s FQ(\))17 b(is)f(not)g(only)h(con)o(v)o(ex,)d(but)i(also)60 1619 y(conca)o(v)o(e)f(within)g(a)h(\003-indep)q(enden)o(t)f(additiv)o(e)g (constan)o(t;)h(and)g(this)g(constan)o(t)g(disapp)q(ears)h(when)60 1679 y(considering)d(the)h(en)o(trop)o(y)f FP(p)n(er)h(unit)i(volume)j FQ(in)14 b(the)g(in\014nite-v)o(olume)e(limit.)18 b(This)d(a\016neness)g(of) 60 1739 y FF(i)p FQ(\()8 b FE(\001)g(j)p FF(\027)s FQ(\))k(mak)o(es)e(the)h (in\014nite-v)o(olume)d(v)m(ariational)k(theory)g(quite)e(di\013eren)o(t)h (from)f(its)i(\014nite-v)o(olume)60 1799 y(coun)o(terpart.)60 1913 y FM(Prop)r(osition)18 b(2.62)24 b FP(L)n(et)19 b FF(\027)j FP(b)n(e)e(a)f(tr)n(anslation-invariant)h(Gibbs)g(me)n(asur)n(e)e(for)h(an)g (inter)n(action)60 1973 y FQ(\010)d FE(2)g(B)195 1955 y FH(1)233 1973 y FP(\(and)i FQ(a)g(priori)g FP(me)n(asur)n(e)g FF(\026)744 1955 y FH(0)764 1973 y FP(\).)26 b(Then)19 b(the)g(r)n(elative)h(entr)n(opy)e (density)h FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))f FP(exists)i(for)60 2034 y(al)r(l)k(tr)n(anslation-invariant)g(pr)n(ob)n (ability)d(me)n(asur)n(es)h FF(\026)p FP(;)j(in)e(fact,)i(the)e(limit)f (exists)i(also)e(in)h(van)60 2094 y(Hove)18 b(sense,)h(namely)682 2173 y FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))28 b(=)41 b(lim)901 2203 y FH(\003)p Fy(\0451)1036 2140 y FQ(1)p 1017 2162 62 2 v 1017 2208 a FE(j)p FQ(\003)p FE(j)1084 2173 y FF(I)1106 2180 y FH(\003)1132 2173 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))14 b FF(:)497 b FQ(\(2)p FF(:)p FQ(95\))p 60 2254 732 2 v 100 2308 a FA(37)135 2323 y Fz(Recall)13 b(that)h(a)g(net)g Fu(f)p Fv(\026)502 2329 y Fp(\013)525 2323 y Fu(g)g Fz(con)o(v)o(erges)h(to)f Fv(\026)g Fz(in)f(the)i(b)q(ounded)f(quasilo)q(cal)f(top)q(ology)g(if)1526 2290 y Fx(R)1554 2323 y Fv(f)e(d\026)1632 2329 y Fp(\013)1667 2323 y Fu(!)1720 2290 y Fx(R)1748 2323 y Fv(f)h(d\026)h Fz(for)60 2373 y(all)i Fv(f)21 b Fu(2)16 b Fv(B)236 2379 y Fp(q)q(l)266 2373 y Fz(\(\012\).)27 b(In)16 b(Georgii)g([157)o(],)g(this)h(top)q(ology)e (is)i(called)f(the)h(\\top)q(ology)f(of)g(lo)q(cal)g(con)o(v)o(ergence")i(or) e(the)60 2423 y(\\)p Fu(L)p Fz(-top)q(ology".)g(See)f([157)n(,)f(Chapter)g (4])f(for)h(prop)q(erties)h(of)f(this)g(top)q(ology)m(.)100 2481 y FA(38)135 2496 y Fz(Recall)i(that)i(a)f(net)h Fu(f)p Fv(\026)516 2502 y Fp(\013)540 2496 y Fu(g)f Fz(con)o(v)o(erges)i(to)e Fv(\026)h Fz(in)f(the)h(w)o(eak)f(quasilo)q(cal)f(top)q(ology)h(if)1510 2462 y Fx(R)1538 2496 y Fv(f)12 b(d\026)1617 2502 y Fp(\013)1658 2496 y Fu(!)1717 2462 y Fx(R)1744 2496 y Fv(f)g(d\026)17 b Fz(for)60 2546 y(all)f Fv(f)21 b Fu(2)16 b Fv(C)236 2552 y Fp(q)q(l)265 2546 y Fz(\(\012\).)27 b(If)16 b(\012)440 2552 y FA(0)476 2546 y Fz(is)h(a)f(compact)g(metric)g(space,)j(then)e Fv(C)1113 2552 y Fp(q)q(l)1142 2546 y Fz(\(\012\))g(=)f Fv(C)s Fz(\(\012\),)h(and)g(so)g(the)g(w)o(eak)g(quasilo)q(cal)60 2595 y(top)q(ology)c(coincides)h(with)g(the)g(usual)g(w)o(eak)g(top)q(ology)m (.)951 2784 y FQ(65)p eop %%Page: 66 66 bop 60 91 a FP(Mor)n(e)n(over,)16 b(this)i(limit)f(is)h(given)h(by)516 214 y FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))28 b(=)f FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\026)842 193 y FH(0)862 214 y FQ(\))20 b(+)f FF(p)p FQ(\()p FE(\000)p FF(f)1064 221 y FH(\010)1092 214 y FE(j)p FF(\026)1135 193 y FH(0)1155 214 y FQ(\))g(+)1250 155 y Fx(Z)1292 214 y FF(f)1316 221 y FH(\010)1352 214 y FF(d\026)14 b(:)331 b FQ(\(2)p FF(:)p FQ(96\))60 339 y FP(Mor)n(e)n(over,)16 b FF(i)p FQ(\()8 b FE(\001)g(j)p FF(\027)s FQ(\))18 b FP(has)f(pr)n(op)n(erties)f(\(b\))i(and)f(\(c\))h(of)f(Pr)n(op)n (osition)g(2.61.)133 453 y FQ(Note)f(that,)g(b)o(y)f(\(2.96\),)i(the)f (relativ)o(e)e(en)o(trop)o(y)h(densit)o(y)g FF(i)p FQ(\()8 b FE(\001)g(j)p FF(\027)s FQ(\))16 b(dep)q(ends)h(on)f FF(\027)k FQ(only)c(via)f(the)60 513 y(in)o(teraction)k(\010:)30 b(that)21 b(is,)g(if)f FF(\027)639 520 y FH(1)680 513 y FQ(and)h FF(\027)803 520 y FH(2)843 513 y FQ(are)g(translation-in)o(v)m(arian)o(t)f(Gibbs)h (measures)e(for)i(the)60 573 y(same)15 b(in)o(teraction)g(\010)f FE(2)h(B)559 555 y FH(1)577 573 y FQ(,)h(w)o(e)g(ha)o(v)o(e)g FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)895 580 y FH(1)914 573 y FQ(\))e(=)g FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)1102 580 y FH(2)1121 573 y FQ(\))j(for)f(all)g FF(\026)p FQ(.)133 633 y(The)f(reader)f(will)g(note)h(that)g(w)o(e)f(ha)o(v)o(e)g FP(not)20 b FQ(asserted)15 b(that)g FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))f(=)f(0)i(if)f(and)i(only)e(if)g FF(\026)g FQ(=)g FF(\027)s FQ(.)60 693 y(Indeed,)23 b(this)g(naiv)o(e)f(conjecture)g (is)h FP(false)t FQ(:)34 b(as)24 b(w)o(e)e(ha)o(v)o(e)g(just)h(seen,)h FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))h(=)g(0)e(also)h(holds)60 754 y(whenev)o(er)17 b FF(\026)i FQ(and)g FF(\027)j FQ(are)d(translation-in)o (v)m(arian)o(t)g(Gibbs)f(measures)g(for)h(the)f(same)f(in)o(teraction.)60 814 y(In)h(Section)f(2.6.6)h(w)o(e)f(shall)h(sho)o(w)h(that,)f(roughly)g(sp)q (eaking,)g FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))f(=)f(0)j FP(only)j FQ(when)c FF(\026)g FQ(and)h FF(\027)60 874 y FQ(are)f(Gibbs)g (measures)f(for)i(the)e(same)g(in)o(teraction.)26 b(This)18 b(fact)g(will)f(pla)o(y)h(a)g(crucial)f(role)h(in)f(the)60 934 y(pro)q(of)g(of)g(the)f(First)g(F)l(undamen)o(tal)e(Theorem)h(\(see)h (Section)g(3.2\).)133 1044 y FM(Remark.)38 b FQ(W)l(e)22 b(ha)o(v)o(e)g(pro)o (v)o(en)f(the)i(existence)d(of)j FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))g(when)f FF(\027)k FQ(is)c(a)h(Gibbs)g(measure,)60 1104 y(but)f(this)h(do)q(es)g FP(not)k FQ(exhaust)c(the)f(cases)g(for)h(whic) o(h)e FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))i(exists.)38 b(Indeed,)23 b(b)o(y)f(com)o(bining)60 1165 y(Theorem)17 b(3.4)j(with)e(our)h (construction)g(in)g(Section)f(4.1,)h(w)o(e)f(pro)o(vide)g(an)i(explicit)c (example)h(of)60 1225 y(non-Gibbsian)22 b(translation-in)o(v)m(arian)o(t)e (measures)g FF(\026)h FQ(and)g FF(\027)j FQ(for)d(whic)o(h)f FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))g(exists)g(\(and)h(is)60 1285 y(in)e(fact)h(zero\):)28 b(namely)l(,)19 b FF(\026)h FQ(\(resp.)f FF(\027)s FQ(\))h(is)g(the)f(image)g(of)h(the)f(+)h(\(resp.)f FE(\000)p FQ(\))h(phase)g(of)g(the)g(t)o(w)o(o-)60 1345 y(dimensional)h (Ising)h(mo)q(del)g(\(at)h(lo)o(w)f(enough)h(temp)q(erature\))e(under)i(the)f FF(b)i FQ(=)h(2)e(decimation)60 1405 y(transformation.)i(It)17 b(is)g(an)h(in)o(teresting)e(\(and)i(probably)g(di\016cult\))d(mathematical)g (problem)h(to)60 1466 y(c)o(haracterize)f(the)h(pairs)g(\()p FF(\026;)8 b(\027)s FQ(\))17 b(for)f(whic)o(h)g FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))g(exists.)60 1595 y FM(2.6.3)55 b(Large)18 b(Deviations)60 1688 y FQ(In)13 b(Section)f(2.5.3)i(w)o(e)e(dev)o (elop)q(ed)h(the)f(theory)h(of)h(large)f(deviations)g(for)g(indep)q(enden)o (t)f(rep)q(etitions)60 1748 y(of)17 b(an)h(arbitrary)f(probabilistic)f(exp)q (erimen)o(t.)21 b(This)c(theory)g(pro)o(vided)f(a)i(ph)o(ysical)e(\(and)h (statis-)60 1808 y(tical\))h(in)o(terpretation)h(for)g(the)g(concept)g(of)h (relativ)o(e)d(en)o(trop)o(y)l(.)29 b(It)19 b(is)g(natural)h(to)g(ask)f (whether)60 1868 y(there)14 b(is)g(an)g(analogue,)h(for)g(translation-in)o(v) m(arian)o(t)f(measures)f(on)i(a)f(classical)g(lattice)f(system,)f(in)60 1929 y(whic)o(h)g(\\time)e(a)o(v)o(erages")j(are)f(replaced)f(b)o(y)h (\\space)h(a)o(v)o(erages".)20 b(That)13 b(is,)f(instead)h(of)f(considering) 60 1989 y(large)18 b(deviations)f(for)h(the)g(sample)e(mean)g(in)i(a)g(large) g(n)o(um)o(b)q(er)e(of)i(indep)q(enden)o(t)e(rep)q(etitions)i(of)60 2049 y(the)f(same)g(exp)q(erimen)o(t,)d(one)j(migh)o(t)f(instead)i(consider)f (large)g(deviations)g(from)g FP(sp)n(atial)22 b FQ(means)60 2109 y(\(ph)o(ysically)l(,)f(large)h(\015uctuations)g(of)g(extensiv)o(e)e (quan)o(tities\))g(in)i(a)g(single)f(in\014nite-v)o(olume)e(re-)60 2169 y(alization.)33 b(Suc)o(h)21 b(a)f(large-deviation)h(theory)f(w)o(ould)g (then,)h(it)f(is)h(hop)q(ed,)g(pro)o(vide)f(a)h(ph)o(ysical)60 2230 y(in)o(terpretation)15 b(of)i(the)f(relativ)o(e)e(en)o(trop)o(y)i FP(density)t FQ(.)133 2290 y(In)24 b(this)f(section)h(w)o(e)f(describ)q(e)g (\(without)i(pro)q(of)s(!\))g(the)e(basic)h(features)g(of)g(suc)o(h)g(a)g (large-)60 2350 y(deviation)16 b(theory)l(.)21 b(W)l(e)15 b(emphasize)g(that) h(this)g(theory)g(is)g(m)o(uc)o(h)e(more)h(subtle)h(than)g(the)g(theory)60 2410 y(for)e(the)f(indep)q(enden)o(t-rep)q(etitions)g(case,)g(b)q(ecause)h (the)g(spins)g(in)f(disjoin)o(t)g(regions)h(of)g(space)f(need)60 2470 y(not)f(b)q(e)g(probabilistically)d(indep)q(enden)o(t.)19 b(Indeed,)11 b(for)h(general)f(translation-in)o(v)m(arian)o(t)h(measures)60 2530 y(on)23 b(\012,)i(no)e(satisfactory)g(large-deviation)g(theory)f(is)h (kno)o(wn.)41 b(Therefore,)24 b(w)o(e)e(shall)h(restrict)60 2591 y(atten)o(tion)16 b(to)i(the)e(case)h(in)f(whic)o(h)g FF(\027)k FQ(is)c(an)i(ergo)q(dic)e(translation-in)o(v)m(arian)o(t)h(Gibbs)g (measure)f(for)60 2651 y(an)e(in)o(teraction)e(\010)i FE(2)g(B)498 2633 y FH(1)517 2651 y FQ(.)21 b(Our)13 b(exp)q(osition)g(is)h(based)g(on)f (the)h(recen)o(t)e(w)o(ork)h(of)h(F\177)-24 b(ollmer)11 b(and)j(Orey)951 2784 y(66)p eop %%Page: 67 67 bop 60 91 a FQ([124)q(],)19 b(Olla)g([282)q(,)g(283)q(],)h(Comets)e([65)q(])h (and)h(Georgii)f([155)q(])g(\(see)g(also)i([51]\),)e(whic)o(h)g(in)h(turn)f (is)60 152 y(inspired)d(b)o(y)g(the)h(pioneering)f(w)o(ork)h(of)g(Donsk)o(er) g(and)h(V)l(aradhan)f([99)q(,)f(100)q(,)h(101)q(,)f(102)q(,)h(360)q(].)22 b(In)60 212 y(the)17 b(ph)o(ysics)f(literature,)f(the)i(relation)f(b)q(et)o (w)o(een)g(thermo)q(dynamics)f(and)i(large)g(deviations)g(w)o(as)60 272 y(p)q(oin)o(ted)f(out)h(long)g(ago)g(b)o(y)f(Lanford)h([230)q(].)133 332 y(If)e FF(f)21 b FQ(is)15 b(a)h(b)q(ounded)g(measurable)e(function)h(on)h (\012,)g(then)f(the)g(mean)f(ergo)q(dic)i(theorem)e(states)60 392 y(that)h(the)g(spatial)f(a)o(v)o(erages)h FF(S)628 369 y FD(f)625 404 y FH(\003)665 392 y FE(\021)f(j)p FQ(\003)p FE(j)780 374 y Fy(\000)p FH(1)835 359 y Fx(P)879 403 y FD(a)p Fy(2)p FH(\003)956 392 y FF(T)985 399 y FD(a)1005 392 y FF(f)20 b FQ(con)o(v)o(erge)14 b(in)g FF(L)1335 374 y FH(1)1355 392 y FQ(\()p FF(\026)p FQ(\))h(norm)f(to)h(the)f(exp)q(ected)60 452 y(v)m(alue)22 b FF(m)i FE(\021)322 417 y Fx(R)349 452 y FF(f)14 b(d\027)s FQ(,)24 b(as)f(\003)h FE(\045)g(1)p FQ(.)39 b(In)22 b(particular,)h(if)f FF(A)g FQ(is)g(an)o(y)g(closed)g(subset)h(of)f (the)g(real)60 513 y(line)h FP(not)29 b FQ(con)o(taining)24 b FF(m)p FQ(,)h(then)f(Prob)q(\()p FF(S)859 489 y FD(f)856 525 y FH(\003)909 513 y FE(2)j FF(A)p FQ(\))g FE(!)g FQ(0)d(as)h(\003)i FE(\045)g(1)p FQ(.)44 b(The)24 b(mean)f(ergo)q(dic)60 573 y(theorem)15 b(is,)i(therefore,)f(a)i(natural)f(generalization)g(of)g(the)g(w)o(eak)g(la)o (w)f(of)i(large)f(n)o(um)o(b)q(ers.)22 b(The)60 633 y(large-deviation)f (theorems)e(strengthen)i(the)g(ergo)q(dic)g(theorem)e(b)o(y)i(giving)g(a)g (precise)f(rate)h(of)60 693 y(con)o(v)o(ergence)15 b(of)h(Prob)q(\()p FF(S)541 670 y FD(f)538 705 y FH(\003)578 693 y FE(2)e FF(A)p FQ(\))i(to)h(zero)f(as)g(\003)e FE(\045)g(1)p FQ(.)133 753 y(If)19 b(w)o(e)g(\014rst)h(restrict)e(atten)o(tion)i(to)f FP(single-site)26 b FQ(observ)m(ables)20 b FF(f)25 b FQ(\(i.e.)17 b(functions)j(of)g(a)g(single)60 814 y(spin\),)13 b(then)f(the)h (large-deviation)f(theorems)f(for)i(spatial)g(a)o(v)o(erages)f(\(lev)o(el)f (1\))i(and)g(for)g(the)f(single-)60 874 y(site)k(empirical)d(measure)i(\(lev) o(el)f(2\))j(are)f(direct)f(analogues)j(of)e(\(2.76\))h(and)g(\(2.82\):)1612 856 y FH(39)137 1036 y FQ(lim)123 1066 y FH(\003)p Fy(\0451)258 1002 y FQ(1)p 240 1024 62 2 v 240 1070 a FE(j)p FQ(\003)p FE(j)315 1036 y FQ(log)9 b(Prob\()p FF(S)541 1012 y FD(f)538 1048 y FH(\003)579 1036 y FE(2)14 b FF(A)p FQ(\))704 936 y Fx(8)704 973 y(>)704 986 y(<)704 1061 y(>)704 1073 y(:)749 964 y FE(\024)f(\000)175 b FQ(inf)848 1002 y FD(\026)p Fy(2)p FD(M)927 1007 y Fr(+1)p Fs(;inv)1024 1002 y FH(\(\012\):)1096 971 y Fx(R)1124 1002 y FD(f)9 b(d\026)p Fy(2)p FD(A)1248 964 y FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))49 b(if)16 b FF(A)f FQ(is)h(a)h(closed)f(set)749 1063 y FE(\025)d(\000)175 b FQ(inf)848 1101 y FD(\026)p Fy(2)p FD(M)927 1106 y Fr(+1)p Fs(;inv)1024 1101 y FH(\(\012\):)1096 1070 y Fx(R)1124 1101 y FD(f)9 b(d\026)p Fy(2)p FD(A)1248 1063 y FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))49 b(if)16 b FF(A)f FQ(is)h(an)h(op)q(en)g(set)1765 1161 y(\(2)p FF(:)p FQ(97\))60 1222 y(and)125 1374 y(lim)112 1404 y FH(\003)p Fy(\0451)247 1340 y FQ(1)p 228 1362 V 228 1408 a FE(j)p FQ(\003)p FE(j)303 1374 y FQ(log)10 b(Prob\()p FF(L)530 1381 y FH(\003)571 1374 y FE(2)k Fi(A)p FQ(\))691 1262 y Fx(8)691 1299 y(>)691 1312 y(>)691 1324 y(<)691 1399 y(>)691 1411 y(>)691 1424 y(:)736 1300 y FE(\024)g(\000)188 b FQ(inf)836 1342 y FD(\026)p Fy(2)p FD(M)915 1347 y Fr(+1)p Fs(;inv)1011 1342 y FH(\(\012\):)10 b FD(\026)p Fm(\026)p Fy(F)1155 1349 y Ft(f)p Fr(0)p Ft(g)1204 1342 y Fy(2)p Fh(A)1264 1300 y FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))49 b(if)15 b Fi(A)i FQ(is)f(a)g(closed)g(set)736 1401 y FE(\025)e(\000)188 b FQ(inf)836 1442 y FD(\026)p Fy(2)p FD(M)915 1447 y Fr(+1)p Fs(;inv)1011 1442 y FH(\(\012\):)10 b FD(\026)p Fm(\026)p Fy(F)1155 1449 y Ft(f)p Fr(0)p Ft(g)1204 1442 y Fy(2)p Fh(A)1264 1401 y FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))49 b(if)15 b Fi(A)i FQ(is)f(an)h(op)q(en)f(set)1765 1503 y(\(2)p FF(:)p FQ(98\))60 1563 y(where)e FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))f(is)h(the)g(relativ)o(e)e(en)o(trop)o(y)h (densit)o(y)l(,)g(and)h(for)h(eac)o(h)e(con\014guration)i FF(!)h FQ(the)e(single-site)60 1623 y(empirical)f(measure)i(in)h(v)o(olume)e(\003)i (is)g(de\014ned)g(to)h(b)q(e)f FF(L)1112 1630 y FH(\003)1153 1623 y FE(\021)e(j)p FQ(\003)p FE(j)1268 1605 y Fy(\000)p FH(1)1323 1590 y Fx(P)1366 1633 y FD(i)p Fy(2)p FH(\003)1437 1623 y FF(\016)1459 1630 y FD(!)1481 1635 y Fs(i)1496 1623 y FQ(.)133 1683 y(The)19 b(empirical)e(measure)h FF(L)677 1690 y FH(\003)723 1683 y FQ(is)h(a)h(to)q(ol)g(for)f(studying)h(ev)o(en)o(ts)e(o)q(ccurring)h(at)h(a)g FP(single)i(site)60 1743 y FQ(only)l(.)37 b(These)21 b(ev)o(en)o(ts)g(w)o (ould)g(completely)e(c)o(haracterize)h(the)h(measure)f(if)h(it)h(w)o(ere)e(a) i(pro)q(duct)60 1804 y(measure)e(\(as)j(in)e(the)h(i.i.d.)d(case)j(studied)f (in)h(Section)f(2.5.3\),)i(but)f(in)f(the)h(general)f(case)h(one)60 1864 y(clearly)14 b(needs)g(m)o(ulti-site)e(observ)m(ables)k(\(i.e.)d (functions)i(of)g(sev)o(eral)f(spins\))i(in)e(order)h(to)h(describ)q(e)60 1924 y(correlations.)26 b(The)18 b(study)g(of)g(suc)o(h)g(observ)m(ables)h (giv)o(es)e(rise)g(to)h(the)g(\\lev)o(el-3")f(large-deviation)60 1984 y(theory)l(.)k(It)16 b(is)g(based)h(on)f(the)g(trivial)f(iden)o(tit)o(y) 585 2075 y(1)p 566 2097 V 566 2143 a FE(j)p FQ(\003)p FE(j)644 2067 y Fx(X)641 2159 y FD(a)p Fy(2)p FH(\003)707 2109 y FQ(\()p FF(T)755 2116 y FD(a)776 2109 y FF(f)5 b FQ(\)\()p FF(!)r FQ(\))28 b(=)988 2036 y Fx( )1044 2075 y FQ(1)p 1025 2097 V 1025 2143 a FE(j)p FQ(\003)p FE(j)1104 2067 y Fx(X)1100 2159 y FD(a)p Fy(2)p FH(\003)1175 2109 y FF(\016)1197 2116 y FD(T)1218 2120 y Fs(a)1236 2116 y FD(!)1261 2036 y Fx(!)1294 2109 y FQ(\()p FF(f)5 b FQ(\))14 b FF(;)376 b FQ(\(2)p FF(:)p FQ(99\))60 2240 y(whic)o(h)16 b(can)g(b)q(e)g(written)g(as)703 2301 y FF(S)736 2277 y FD(f)733 2313 y FH(\003)788 2301 y FQ(=)27 b FF(R)890 2308 y FH(\003)917 2301 y FQ(\()p FF(f)5 b FQ(\))28 b FE(\021)1078 2242 y Fx(Z)1120 2301 y FF(f)14 b(dR)1220 2308 y FH(\003)1741 2301 y FQ(\(2)p FF(:)p FQ(100\))60 2394 y(where)757 2454 y FF(R)794 2461 y FH(\003)848 2454 y FE(\021)28 b(j)p FQ(\003)p FE(j)977 2434 y Fy(\000)p FH(1)1035 2413 y Fx(X)1032 2505 y FD(a)p Fy(2)p FH(\003)1107 2454 y FF(\016)1129 2461 y FD(T)1150 2465 y Fs(a)1168 2461 y FD(!)1741 2454 y FQ(\(2)p FF(:)p FQ(101\))p 60 2541 732 2 v 100 2595 a FA(39)135 2610 y Fz(In)16 b(the)g(mathematical)d (literature)j(the)h(large-deviation)e(theorems)h(are)g(usually)f(pro)o(v)o (en)h(for)g(sequences)j(of)60 2660 y(cub)q(es,)c(but)f(the)h(same)e(argumen)o (ts)g(ough)o(t)g(to)h(w)o(ork)f(for)h(general)g(v)n(an)f(Ho)o(v)o(e)h (sequences.)951 2784 y FQ(67)p eop %%Page: 68 68 bop 60 91 a FQ(is)22 b(called)g(the)g FP(empiric)n(al)i(\014eld)5 b FQ(.)41 b(W)l(e)23 b(emphasize)d(that)k FF(R)1195 98 y FH(\003)1244 91 y FQ(is)e(a)h FP(r)n(andom)j FQ(measure)21 b(\(on)i(the)60 152 y(in\014nite-v)o(olume)15 b(con\014guration)20 b(space)e(\012\),)g(since) g(it)g(dep)q(ends)g(on)h(the)f(random)g(con\014guration)60 212 y FF(!)r FQ(.)j(In)14 b(this)g(language,)h(the)f(ergo)q(dic)g(theorem)f (can)h(b)q(e)h(reform)o(ulated)d(as)j(implying)d(that)i(the)g(em-)60 272 y(pirical)g(\014eld)h FF(R)350 279 y FH(\003)392 272 y FQ(is,)g(with)g(high)g(probabilit)o(y)l(,)f(v)o(ery)h(close)f(to)i(the)f (theoretical)g(measure)f FF(\027)s FQ(,)h(when)60 332 y(\\closeness")k(is)e (understo)q(o)q(d)j(in)e(the)g(b)q(ounded)h(quasilo)q(cal)f(top)q(ology)h (\(i.e.)d(the)i(w)o(eak)g(top)q(ology)60 392 y(generated)12 b(b)o(y)f(the)g(b)q(ounded)i(quasilo)q(cal)e(functions\).)20 b(More)11 b(precisely)l(,)f(if)h FO(A)h FQ(is)f(an)o(y)g(closed)h(subset)60 452 y(of)17 b FF(M)163 459 y FH(+1)211 452 y FQ(\(\012\))g FP(not)22 b FQ(con)o(taining)16 b FF(\027)s FQ(,)h(then)g(Prob)q(\()p FF(R)958 459 y FH(\003)999 452 y FE(2)e FO(A)p FQ(\))g FE(!)f FQ(0)k(as)f(\003)e FE(\045)g(1)p FQ(.)22 b(The)17 b(large-deviation)60 513 y(theorem)i([155)q(])i(then)f(states)i(that)f(this)g(probabilit)o(y)f(is) h(in)g(fact)f(exp)q(onen)o(tially)g(small)f(in)i FE(j)p FQ(\003)p FE(j)p FQ(,)60 573 y(namely)656 633 y(Prob)q(\()p FF(R)816 640 y FH(\003)857 633 y FE(2)14 b FO(A)p FQ(\))27 b FE(\030)g FF(e)1065 612 y Fy(\000j)p FH(\003)p Fy(j)p FH(const)o(\()p FD(\027;)p Ff(A)p FH(\))1741 633 y FQ(\(2)p FF(:)p FQ(102\))60 720 y(where)19 b(const\()p FF(\027;)8 b FO(A)p FQ(\))19 b FF(>)f FQ(0)i(whenev)o(er)e FO(A)g FQ(is)h(a)h(closed)e(subset)i(of)f FF(M)1305 727 y FH(+1)1353 720 y FQ(\(\012\))g(not)g(con)o(taining)g FF(\027)s FQ(.)30 b(In)60 780 y(detail,)109 944 y(lim)96 974 y FH(\003)p Fy(\0451)231 910 y FQ(1)p 212 932 62 2 v 212 978 a FE(j)p FQ(\003)p FE(j)287 944 y FQ(log)9 b(Prob)q(\()p FF(R)518 951 y FH(\003)558 944 y FE(2)14 b FO(A)p FQ(\))672 844 y Fx(8)672 881 y(>)672 894 y(<)672 969 y(>)672 981 y(:)717 883 y FE(\024)g(\000)135 b FQ(inf)817 915 y FD(\026)p FH(:)10 b FD(\026)p Fy(2)p Ff(A)p Fy(\\)p FD(M)981 920 y Fr(+1)p Fs(;inv)1076 915 y FH(\(\012\))1138 883 y FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))48 b(if)16 b FO(A)g FQ(is)g(a)h(closed)f(set)717 971 y FE(\025)e(\000)135 b FQ(inf)817 1002 y FD(\026)p FH(:)10 b FD(\026)p Fy(2)p Ff(A)p Fy(\\)p FD(M)981 1007 y Fr(+1)p Fs(;inv)1076 1002 y FH(\(\012\))1138 971 y FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))48 b(if)16 b FO(A)g FQ(is)g(an)h(op)q(en)g(set)1741 944 y(\(2)p FF(:)p FQ(103\))133 1107 y(These)i(form)o(ulae)e(pro)o(vide)h(a)i(ph)o(ysical)e(in)o (terpretation)g(for)h(the)f(relativ)o(e)f(en)o(trop)o(y)i FP(density)t FQ(.)60 1167 y(Roughly)f(sp)q(eaking,)h(the)e(probabilit)o(y)g(that)i(a)f (con\014guration)h FF(!)r FQ(,)f(tak)o(en)f(from)g(the)h(probabilit)o(y)60 1227 y(distribution)d FF(\027)s FQ(,)g(\\lo)q(oks)h(in)e(\003)h(lik)o(e)e(a)j (t)o(ypical)e(con\014guration)i(from)e FF(\026)p FQ(")h(deca)o(ys)g(exp)q (onen)o(tially)e(in)60 1288 y(the)j(v)o(olume)e(of)j(\003)f(with)g(rate)g FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\):)547 1398 y(Prob)650 1405 y FD(\027)672 1398 y FQ(\()p FF(!)721 1405 y FH(\003)764 1398 y FQ(is)g(t)o(ypical)f(for)h FF(\026)p FQ(\))28 b FE(\030)g FF(e)1213 1377 y Fy(\000j)p FH(\003)p Fy(j)p FD(i)p FH(\()p FD(\026)p Fy(j)p FD(\027)r FH(\))1390 1398 y FF(:)337 b FQ(\(2)p FF(:)p FQ(104\))60 1508 y(This)20 b(in)o(terpretation)e(of)i(the)f(relativ)o (e)f(en)o(trop)o(y)h(densit)o(y)f(will)h(pla)o(y)g(a)g(k)o(ey)g(role)g(in)g (motiv)m(ating)60 1568 y(the)d(First)g(F)l(undamen)o(tal)e(Theorem)h (\(Section)h(3.2\).)133 1678 y FM(Remarks.)j FQ(1.)h(Some)13 b(of)i(the)f(large-deviation)f(theorems)g(use)h(a)h FP(p)n(erio)n(dize)n(d)i FQ(empirical)12 b(\014eld)60 1738 y FF(R)97 1712 y FH(\()p FD(per)q FH(\))97 1750 y(\003)178 1738 y FQ(,)19 b(whic)o(h)f(is)g(a)h FP(tr)n(anslation-invariant)25 b FQ(measure)17 b(on)i(\012.)29 b(One)18 b(exp)q(ects)g FF(R)1567 1745 y FH(\003)1613 1738 y FQ(and)h FF(R)1747 1712 y FH(\()p FD(per)q FH(\))1747 1750 y(\003)1847 1738 y FQ(to)60 1798 y(b)q(eha)o(v)o(e)d(in)f(the)h(same)g(w)o(a) o(y)l(.)133 1858 y(2.)k(Our)11 b(results)g(in)g(Section)g(4)h(giv)o(e)e (examples)f(of)j(some)e FP(non-Gibbsian)17 b FQ(measures)10 b FF(\027)k FQ(for)e(whic)o(h)60 1919 y(a)18 b(large-deviations)f(theory)g (can)g(b)q(e)g(dev)o(elop)q(ed,)f(e.g.)g FF(\027)j FQ(=)c FF(\032T)24 b FQ(where)17 b FF(\032)g FQ(is)g(a)h(t)o(w)o(o-dimensional)60 1979 y(Ising-mo)q(del)h(Gibbs)i(measure)e(at)h(lo)o(w)g(temp)q(erature,)g (and)h FF(T)26 b FQ(is)20 b(a)h(suitable)f(renormalization)60 2039 y(map.)g(Of)15 b(course,)h(one)f(is)h(able)f(to)h(con)o(trol)f(the)g (large)h(deviations)f(for)h FF(\027)i FQ(only)e(b)o(y)f(reducing)g(it)g(to)60 2099 y(the)h(same)f(problem)g(for)h(the)g(b)q(etter-b)q(eha)o(v)o(ed)g (measure)f FF(\032)p FQ(.)60 2229 y FM(2.6.4)55 b(V)-5 b(ariational)19 b(Principle)60 2321 y FQ(The)e(pressure)g(and)h(the)f(relativ)o(e)f(en)o (trop)o(y)g(densit)o(y)g(are)h(related)g(b)o(y)g(the)g(follo)o(wing)f FP(variational)60 2382 y(principle)t FQ(:)60 2496 y FM(Theorem)h(2.63)h(\(V) -5 b(ariational)18 b(principle\))23 b FP(Fix)c(a)g(tr)n(anslation-invariant)h (me)n(asur)n(e)e FF(\027)23 b FP(sat-)60 2556 y(isfying)13 b(the)h(c)n(onditions)g(of)f(Pr)n(op)n(osition)f(2.56)h(or)g(2.57.)20 b(Then)14 b FF(p)p FQ(\()8 b FE(\001)g(j)p FF(\027)s FQ(\))14 b FP(and)g FF(i)p FQ(\()8 b FE(\001)g(j)p FF(\027)s FQ(\))13 b FP(ar)n(e)g(c)n(onjugate)951 2784 y FQ(68)p eop %%Page: 69 69 bop 60 91 a FP(c)n(onvex)19 b(functions,)g(in)e(the)h(sense)h(that)511 214 y FF(p)p FQ(\()p FF(f)5 b FE(j)p FF(\027)s FQ(\))42 b(=)138 b(sup)765 256 y FD(\026)p Fy(2)p FD(M)844 261 y Fr(+1)p Fs(;inv)940 256 y FH(\(\012)p FD(;)p Fy(F)s FH(\))1040 154 y Fx(\024)1062 156 y(Z)1103 214 y FF(f)14 b(d\026)25 b FE(\000)g FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))1409 154 y Fx(\025)1717 214 y FQ(\(2.105a\))519 372 y FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))41 b(=)100 b(sup)765 414 y FD(f)t Fy(2)p FD(B)837 420 y Fs(q)q(l)863 414 y FH(\(\012)p FD(;)p Fy(F)s FH(\))962 312 y Fx(\024)984 314 y(Z)1026 372 y FF(f)13 b(d\026)26 b FE(\000)e FF(p)p FQ(\()p FF(f)5 b FE(j)p FF(\027)s FQ(\))1338 312 y Fx(\025)1714 372 y FQ(\(2.105b\))60 515 y FP(Written)18 b(in)g(terms)f(of)g(inter)n (actions,)h(this)g(r)n(e)n(ads)473 638 y FF(p)p FQ(\(\010)p FE(j)p FF(\027)s FQ(\))43 b(=)138 b(sup)733 679 y FD(\026)p Fy(2)p FD(M)812 684 y Fr(+1)p Fs(;inv)908 679 y FH(\(\012)p FD(;)p Fy(F)s FH(\))1008 577 y Fx(\024)1030 638 y FE(\000)1077 579 y Fx(Z)1118 638 y FF(f)1142 645 y FH(\010)1178 638 y FF(d\026)26 b FE(\000)f FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))1447 577 y Fx(\025)1717 638 y FQ(\(2.106a\))487 796 y FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))42 b(=)49 b(sup)733 838 y FH(\010)p Fy(2B)806 828 y Fr(0)832 735 y Fx(\024)853 796 y FE(\000)900 737 y Fx(Z)942 796 y FF(f)966 803 y FH(\010)1002 796 y FF(d\026)25 b FE(\000)g FF(p)p FQ(\(\010)p FE(j)p FF(\027)s FQ(\))1283 735 y Fx(\025)1714 796 y FQ(\(2.106b\))133 936 y(This)16 b(v)m(ariational)g(principle)d(giv)o(es)i(us)h(another)g(w)o(a)o(y)f(to)h (asso)q(ciate)h(\(in\014nite-v)o(olume\))12 b(prob-)60 996 y(abilit)o(y)j(measures)g(to)i(a)f(giv)o(en)g(in)o(teraction:)60 1096 y FM(De\014nition)i(2.64)24 b FP(L)n(et)c FQ(\010)g FE(2)g(B)676 1078 y FH(0)715 1096 y FP(and)h FF(\026)f FE(2)g FF(M)962 1103 y FH(+1)p FD(;inv)1071 1096 y FQ(\(\012\))p FP(.)32 b(We)21 b(say)f(that)h FF(\026)f FQ(is)f(an)h(equilibrium)60 1156 y(measure)g(for)h (\010)h FP(\(and)g FQ(a)f(priori)h FP(me)n(asur)n(e)f FF(\026)916 1138 y FH(0)936 1156 y FP(\))h(if)f(the)i(p)n(air)d FQ(\(\010)p FF(;)8 b(\026)p FQ(\))23 b FP(satur)n(ates)e(the)h(variational)60 1216 y(principle)c(\(2.106\))f(with)h FF(\027)f FQ(=)d FF(\026)662 1198 y FH(0)682 1216 y FP(,)j(i.e.)h(if)621 1338 y FF(p)p FQ(\(\010)p FE(j)p FF(\026)742 1318 y FH(0)763 1338 y FQ(\))h(+)g FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\026)966 1318 y FH(0)986 1338 y FQ(\))28 b(=)f FE(\000)1145 1280 y Fx(Z)1187 1338 y FF(f)1211 1345 y FH(\010)1247 1338 y FF(d\026)14 b(:)412 b FQ(\(2)p FF(:)p FQ(107\))133 1458 y(W)l(e)16 b(ha)o(v)o(e)g(no)o(w)g(laid)g(out)h FP(two)h(distinct)k FQ(approac)o(hes)17 b(to)f(in\014nite-v)o(olume)d(ph)o (ysics:)114 1557 y(1\))25 b(The)16 b FP(DLR)f(appr)n(o)n(ach)t FQ(,)f(whic)o(h)h(sa)o(ys)h(what)g(it)f(means)g(for)h(a)g(\(not)g (necessarily)e(translation-)182 1617 y(in)o(v)m(arian)o(t\))j(measure)f FF(\026)i FQ(to)g(b)q(e)g(a)g FP(Gibbs)h(me)n(asur)n(e)i FQ(for)d(a)g(con)o (v)o(ergen)o(t)e(and)j FF(\026)1634 1599 y FH(0)1654 1617 y FQ(-admissible)182 1677 y(\(but)k(not)h(necessarily)d(translation-in)o(v)m (arian)o(t\))i(in)o(teraction)f(\010.)42 b(This)23 b(is)g(the)g(in\014nite-) 182 1737 y(v)o(olume)f(analogue)j(of)f(the)g(explicit)e(form)o(ula)g (\(2.1\).)45 b(This)24 b(approac)o(h)h(is)f(constructed)182 1798 y(purely)11 b(on)i(the)f(basis)h(of)f(probabilit)o(y)f(theory)l(,)i(and) f(hence)g(it)f(can)i(b)q(e)f(called)f(the)h FP(statistic)n(al-)182 1858 y(me)n(chanic)n(al)18 b(appr)n(o)n(ach)t FQ(.)114 1959 y(2\))25 b(The)19 b FP(variational)h(appr)n(o)n(ach)t FQ(,)e(whic)o(h)g(sa)o (ys)h(what)h(it)e(means)g(for)h(a)h(translation-in)o(v)m(arian)o(t)182 2019 y(measure)14 b FF(\026)h FQ(to)h(b)q(e)f(an)h FP(e)n(quilibrium)h(me)n (asur)n(e)h FQ(for)d(a)h(translation-in)o(v)m(arian)o(t)f(\(but)h(not)f(nec-) 182 2079 y(essarily)20 b(con)o(v)o(ergen)o(t\))f(in)o(teraction)h(\010.)34 b(This)21 b(is)g(the)f(in\014nite-v)o(olume)e(analogue)j(of)g(the)182 2139 y(v)m(ariational)f(principle)f(\(2.3\).)33 b(This)21 b(approac)o(h)g(is) f(based)g(on)h(optimization)d(of)j(thermo-)182 2199 y(dynamic)g(p)q(oten)o (tials,)j(and)g(hence)e(it)h(can)g(b)q(e)g(called)f(the)h FP(thermo)n (dynamic)g(appr)n(o)n(ach)t FQ(.)182 2260 y(Ho)o(w)o(ev)o(er,)17 b(as)i(remark)o(ed)d(b)o(y)i(Wigh)o(tman)g([363],)g(con)o(v)o(en)o(tional)g (thermo)q(dynamics)e(refers)182 2320 y(to)g(the)f(optimization)f(of)i(p)q (oten)o(tials)g(with)f(resp)q(ect)h(to)g(a)g(rather)f(reduced)g(n)o(um)o(b)q (er)f(of)i(pa-)182 2380 y(rameters)i(\(temp)q(erature,)g(c)o(hemical)e(p)q (oten)o(tial,)j(etc.\).)30 b(In)19 b(con)o(trast,)h(the)f(optimization)182 2440 y(of)j(the)f(previous)h(prop)q(osition)h(is)e(with)h(resp)q(ect)f(to)h (an)h(in\014nite-dimensional)c(space)j(of)182 2500 y(p)q(ossible)16 b(in)o(teractions.)60 2600 y(F)l(or)26 b(translation-in)o(v)m(arian)o(t)h(in) o(teractions)e(\010)h(and)h(translation-in)o(v)m(arian)o(t)g(measures)e FF(\026)p FQ(,)j(this)60 2660 y(means)11 b(in)h(practice)f(the)h(follo)o (wing:)19 b(The)12 b(DLR)h(approac)o(h)g(applies)f(to)g(a)h(more)d (restricted)h(class)i(of)951 2784 y(69)p eop %%Page: 70 70 bop 60 91 a FQ(in)o(teractions,)15 b(but)h(in)g(return)g(pro)o(vides)g(m)o (uc)o(h)e(more)h(information)g(on)i(the)f(measures.)k(That)d(is,)60 152 y(it)e(requires)g(\010)f FE(2)g(B)422 133 y FH(1)441 152 y FQ(,)h(but)h(giv)o(es)f(strong)i(con)o(trol)e(on)i FF(\026)f FQ(via)f(the)h(DLR)g(equations)g(\(2.21\)/\(2.22\).)60 212 y(On)j(the)h(other)f(hand,)h(the)f(v)m(ariational)h(approac)o(h)g(needs)f (only)h(\010)f FE(2)g(B)1435 194 y FH(0)1454 212 y FQ(,)h(but)f(pro)o(vides)g (m)o(uc)o(h)60 272 y(w)o(eak)o(er)14 b(con)o(trol)h(o)o(v)o(er)f FF(\026)p FQ(.)21 b(In)15 b(an)o(y)g(case,)f FP(the)j(two)g(appr)n(o)n(aches) e(ar)n(e)h(e)n(quivalent)i(in)f(their)f(c)n(ommon)60 332 y(domain)23 b(of)f(applic)n(ability)t FQ(:)33 b(if)22 b(\010)g(is)g(a)g(translation-in)o (v)m(arian)o(t)g(in)o(teraction)f(in)g FE(B)1618 314 y FH(1)1659 332 y FQ(and)i FF(\026)f FQ(is)g(a)60 392 y(translation-in)o(v)m(arian)o(t)c (measure,)f(then)h FF(\026)h FQ(is)f(a)g(Gibbs)g(measure)f(for)i(\010)f(if)g (and)g(only)g(if)g(it)g(is)g(an)60 452 y(equilibrium)13 b(measure)i(for)h (\010.)22 b(W)l(e)16 b(will)f(pro)o(v)o(e)g(this)h(in)g(Corollary)h(2.68)g(b) q(elo)o(w.)133 513 y(A)o(t)c(this)g(p)q(oin)o(t,)h(the)g(reader)f(ma)o(y)f(b) q(e)i(w)o(ondering:)20 b(If)13 b(the)g(DLR)h(and)g(v)m(ariational)g(approac)o (hes)60 573 y(are)22 b(equiv)m(alen)o(t)e(\(for)i(in)o(teractions)f(in)g FE(B)850 555 y FH(1)869 573 y FQ(\),)i(then)e(wh)o(y)h(b)q(other)g(in)o(tro)q (ducing)g(b)q(oth)h(of)f(them?)60 633 y(Wh)o(y)e(not)h(stic)o(k)e(with)h(one) h(or)g(the)f(other,)h(and)g(shorten)g(this)f(article)f(b)o(y)h(at)h(least)f (30)h(pages?)60 693 y(The)f(answ)o(er)g(is)f(that)h(man)o(y)f(deep)g(results) g(are)h(based)g(on)g(the)g FP(interplay)k FQ(b)q(et)o(w)o(een)19 b(DLR)h(and)60 753 y(v)m(ariational)e(ideas.)26 b(This)18 b(is)f(the)h(case)f (for)h(Theorem)f(2.67)h(b)q(elo)o(w,)g(and)g(it)g(is)f(also)h(the)g(case)g (for)60 814 y(man)o(y)d(of)h(our)h(R)o(G)f(results)g(\(notably)h(those)f(in)g (Sections)g(3.2,)g(3.3)h(and)g(4.4\).)133 924 y(Before)12 b(lea)o(ving)h(the) g(sub)s(ject)f(of)h(the)g(v)m(ariational)h(principle,)d(let)i(us)g(note)g(a)h (simple)d(corollary)l(.)60 984 y(Let)22 b FF(F)7 b FQ(\()p FF(\026;)h FQ(\010\))22 b(b)q(e)g(the)f(amoun)o(t)h(b)o(y)f(whic)o(h)g(the)h (pair)g(\()p FF(\026;)8 b FQ(\010\))22 b(fails)g(to)g(satisfy)g(the)g(v)m (ariational)60 1044 y(principle,)14 b(i.e.)465 1116 y FF(F)7 b FQ(\()p FF(\026;)h FQ(\010\))28 b FE(\021)f FF(p)p FQ(\(\010)p FE(j)p FF(\026)843 1096 y FH(0)864 1116 y FQ(\))19 b(+)g FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\026)1067 1096 y FH(0)1087 1116 y FQ(\))g(+)1183 1058 y Fx(Z)1224 1116 y FF(f)1248 1123 y FH(\010)1284 1116 y FF(d\026)29 b FE(\025)e FQ(0)14 b FF(:)256 b FQ(\(2)p FF(:)p FQ(108\))60 1216 y(Then)16 b(it)g(is)g(easy)g(to)h(see)f(that)471 1326 y FE(j)p FF(F)7 b FQ(\()p FF(\026;)h FQ(\010\))i FE(\000)h FF(F)c FQ(\()p FF(\026;)h FQ(\010)852 1305 y Fy(0)863 1326 y FQ(\))p FE(j)28 b(\024)f FQ(2)p FE(k)p FQ(\010)12 b FE(\000)f FQ(\010)1171 1305 y Fy(0)1183 1326 y FE(k)1208 1334 y Fy(B)1232 1325 y Fr(0)1249 1334 y FD(=)p FH(\()p Fy(J)5 b FH(+)p Fk(Const)p FH(\))1458 1326 y FQ(;)269 b(\(2)p FF(:)p FQ(109\))60 1436 y(indeed,)18 b(this)g(is)g(an)h(immedi)o(ate)d(consequence)h(of)i(Prop)q (ositions)h(2.56\(c\){\(e\))f(and)g(2.58\(a\).)28 b(In)60 1496 y(particular,)17 b(if)h FF(\026)g FQ(is)f(an)i(equilibrium)14 b(measure)i(for)j(\010,)e(then)h(the)g(amoun)o(t)f(b)o(y)g(whic)o(h)g FF(\026)h FQ(fails)g(to)60 1556 y(satisfy)e(the)f(v)m(ariational)h(principle) e(for)i(\010)846 1538 y Fy(0)874 1556 y FQ(is)f(at)h(most)f(2)p FE(k)p FQ(\010)10 b FE(\000)g FQ(\010)1278 1538 y Fy(0)1290 1556 y FE(k)1315 1565 y Fy(B)1339 1555 y Fr(0)1356 1565 y FD(=)p FH(\()p Fy(J)c FH(+)p Fk(Const)o FH(\))1551 1556 y FQ(.)21 b(Note)15 b(also)i(that)60 1616 y(if)f(\010)e FE(2)g(B)236 1598 y FH(1)255 1616 y FQ(,)i(then)g FF(F)7 b FQ(\()p FF(\026;)h FQ(\010\))16 b(can)g(b)q(e)g(in)o(terpreted)f(as)i(a)g(relativ)o(e)d(en)o (trop)o(y:)518 1726 y FF(F)7 b FQ(\()p FF(\026;)h FQ(\010\))28 b(=)f FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))65 b(for)17 b(an)o(y)f FF(\027)h FE(2)d(G)1249 1733 y FD(inv)1302 1726 y FQ(\(\005)1358 1706 y FH(\010)1386 1726 y FQ(\))f FF(:)309 b FQ(\(2)p FF(:)p FQ(110\))60 1836 y(This)16 b(is)g(the)g(con)o(ten)o(t)g(of) g(equation)h(\(2.96\).)133 1897 y(A)f(sp)q(ecial)g(case)g(of)h(\(2.109\))g ([whic)o(h)e(is)h(also)h(easy)f(to)h(see)f(directly])e(is)i(the)g(follo)o (wing:)60 2011 y FM(Prop)r(osition)i(2.65)24 b FP(L)n(et)f FQ(\010)p FF(;)8 b FQ(\010)26 b FE(2)f(B)788 1993 y FH(0)831 2011 y FP(b)n(e)f(physic)n(al)r(ly)g(e)n(quivalent)i(in)e(the)g(R)o(uel)r(le) h(sense)g(\(i.e.)60 2071 y FQ(\010)11 b FE(\000)g FQ(\010)191 2053 y Fy(0)217 2071 y FE(2)j(J)20 b FQ(+)11 b FF(C)t(onst)p FP(\).)22 b(Then)c FQ(\010)f FP(and)h FQ(\010)865 2053 y Fy(0)894 2071 y FP(have)h(exactly)f(the)g(same)g(e)n(quilibrium)g(me)n(asur)n(es.)60 2201 y FM(2.6.5)55 b(What)19 b(is)f(a)h(Phase)g(T)-5 b(ransition?)60 2293 y FQ(Informally)l(,)13 b(the)i(o)q(ccurrence)g(of)h(a)g(phase)g (transition)f(is)h(asso)q(ciated)g(to)g(one)g(or)f(b)q(oth)i(of)f(the)f(fol-) 60 2353 y(lo)o(wing)g(phenomena:)20 b(a)c(singularit)o(y)f(of)h(some)f (thermo)q(dynamic)e(p)q(oten)o(tial)i(and/or)i(the)e(c)o(hange)60 2414 y(in)k(the)h(n)o(um)o(b)q(er)e(of)h(\\macrostates")h(a)o(v)m(ailable)f (to)h(the)g(system.)30 b(Historically)l(,)18 b(the)h(\014rst)h(p)q(oin)o(t)60 2474 y(of)f(view)g(w)o(as)g(primarily)e(asso)q(ciated)j(with)f(Ehrenfest,)g (while)f(the)h(second)h(p)q(oin)o(t)f(of)g(view)g(w)o(as)60 2534 y(primarily)11 b(asso)q(ciated)k(with)f(Gibbs.)21 b(Ho)o(w)o(ev)o(er,)12 b(the)h(full)g(formalization)g(of)h(the)g(second)g(p)q(oin)o(t)g(of)60 2594 y(view)f(|)g(in)g(particular,)h(giving)f(a)h(precise)e(meaning)g(to)i (\\macrostate")g(|)f(and)h(the)g(clari\014cation)60 2654 y(of)e(the)f (relation)g(b)q(et)o(w)o(een)f(these)h FP(thermo)n(dynamic)j FQ(concepts)d(and)h(the)f(underlying)f(\(microscopic\))951 2784 y(70)p eop %%Page: 71 71 bop 60 91 a FP(statistic)n(al-me)n(chanic)n(al)22 b FQ(concepts)14 b(had)i(to)f(a)o(w)o(ait)f(the)h(dev)o(elopmen)o(t)d(of)j(the)f(DLR)i(and)f (rigorous)60 152 y(v)m(ariational)i(approac)o(hes.)133 212 y(The)f(general)f(in)o(terpretation)g(of)h(phase)g(transitions)g(as)g (singularities)f(of)h(the)f(\(what)h(turned)60 272 y(out)i(to)g(b)q(e)f (in\014nite-v)o(olume\))e(free)i(energy)g(\(=)g(pressure\))h(ga)o(v)o(e)f (rise)g(to)g(the)h(Ehrenfest)f(classi\014-)60 332 y(cation:)k(a)c(system)d (is)i(said)g(to)h(exhibit)e(an)h FF(n)896 314 y FD(th)931 332 y FP(-or)n(der)h(phase)g(tr)n(ansition)j FQ(if)15 b(some)g FF(n)1631 314 y FD(th)1683 332 y FQ(deriv)m(ativ)o(e)60 392 y(of)k(the)g(free)g(energy)f(is)h(discon)o(tin)o(uous)g(\(and)h(all)f(the)g (deriv)m(ativ)o(es)e(of)j(lo)o(w)o(er)e(order)h(are)g(con)o(tin-)60 452 y(uous\).)27 b(F)l(or)18 b(example,)e(the)h(t)o(w)o(o-dimensional)g (Ising)h(mo)q(del)e(at)j(lo)o(w)e(temp)q(eratures)g(undergo)q(es)60 513 y(a)k(\014rst-order)g(phase)f(transition)h(as)g(the)f(magnetic)e(\014eld) i(passes)h(through)g(zero,)g(b)q(ecause)f(the)60 573 y(magnetization)g(\(=)h (\014rst)h(deriv)m(ativ)o(e)d(of)j(the)f(free)f(energy)h(with)g(resp)q(ect)g (to)g(the)g(\014eld\))g(has)h(a)60 633 y(discon)o(tin)o(uit)o(y)l(.)c(On)d (the)f(other)g(hand,)h(if)f(the)g(\014eld)g(is)g(k)o(ept)g(equal)g(to)g(zero) g(and)h(the)g(temp)q(erature)60 693 y(is)21 b(lo)o(w)o(ered)f(\(starting)i (from)e(a)i(high)f(v)m(alue\),)h(the)f(system)f(undergo)q(es)i(a)g (second-order)g(phase)60 753 y(transition)c(at)h(the)f(critical)e(temp)q (erature,)h(b)q(ecause)h(the)g(magnetization)e(and)j(energy)f(\(=)g(\014rst) 60 814 y(deriv)m(ativ)o(es)i(of)h(the)g(free)g(energy\))g(remain)e(con)o(tin) o(uous)i(but)h(the)f(susceptibilit)o(y)e(and)j(sp)q(eci\014c)60 874 y(heat)g(\(=)f(second)h(deriv)m(ativ)o(es)e(of)i(the)f(free)g(energy\))g (blo)o(w)g(up.)37 b(F)l(rom)20 b(the)i(p)q(oin)o(t)f(of)h(view)f(of)60 934 y(mathematical)c(ph)o(ysics,)j(ho)o(w)o(ev)o(er,)f(the)h(Ehrenfest)g (classi\014cation)g(is)g(b)q(oth)h(to)q(o)g(detailed)e(and)60 994 y(to)q(o)k(crude)f(for)g(our)h(curren)o(t)e(lev)o(el)f(of)i (understanding.)40 b(It)21 b(is)h(to)q(o)h(detailed)e(b)q(ecause,)j(as)e(w)o (e)60 1054 y(discuss)17 b(b)q(elo)o(w,)f(only)h(the)f(distinction)g(b)q(et)o (w)o(een)g(\014rst-order)i(and)f(the)g(rest)f(has)i(b)q(een)f(put)g(on)o(to) 60 1115 y(a)i(\014rm)f(basis.)30 b(Consequen)o(tly)l(,)19 b(authors)h (usually)e(group)i(all)f(the)g(transitions)g(of)h(order)f(t)o(w)o(o)g(or)60 1175 y(higher)d(in)o(to)h(a)g(single)f(class)g(and)i(call)d(all)i(of)f(them)f FP(c)n(ontinuous)k(phase)f(tr)n(ansitions)i FQ(|)d(b)q(ecause)60 1235 y(the)g(order)h(parameter,)f(e.g.)f(the)i(magnetization)e(\(see)h(b)q (elo)o(w\),)h(remains)e(con)o(tin)o(uous.)26 b(On)17 b(the)60 1295 y(other)f(hand,)g(the)g(Ehrenfest)f(classi\014cation)h(is)f(to)q(o)i (crude,)e(b)q(ecause)h(the)g(p)q(ossible)g(singularities)60 1355 y(of)22 b(the)f(free)g(energy)h(are)f(m)o(uc)o(h)f(to)q(o)i(v)m(aried)g (to)g(b)q(e)g(captured)f(in)h(a)g(single)f(in)o(teger)g FF(n)p FQ(.)37 b(Some)60 1416 y(examples)14 b(are:)133 1515 y FE(\017)24 b FQ(The)c(one-dimensional)f(Ising)h(mo)q(del)e(with)i(1)p FF(=r)1104 1497 y FH(2)1145 1515 y FQ(in)o(teraction,)g(in)f(whic)o(h)h(it)f (is)h(b)q(eliev)o(ed)182 1575 y([12,)15 b(11)q(,)f(57)q(])g(that)i(the)e (free)g(energy)h FF(f)5 b FQ(\()p FF(\014)s(;)j(h)13 b FQ(=)h(0\))h(is)g FF(C)1200 1557 y Fy(1)1252 1575 y FQ(but)g(nonanalytic)g(at)g(the)g(critical) 182 1636 y(p)q(oin)o(t)21 b FF(\014)342 1643 y FD(c)359 1636 y FQ(,)i(at)e(the)g(same)g(time)e(as)j(the)f(sp)q(on)o(taneous)i (magnetization)d FF(M)5 b FQ(\()p FF(\014)s(;)j(h)23 b FQ(=)f(0\))h(=)182 1696 y FE(\000)p FF(@)s(f)5 b(=@)s(h)p FE(j)374 1703 y FD(h)p FH(=0)457 1696 y FQ(is)16 b FP(disc)n(ontinuous)21 b FQ(at)c FF(\014)902 1703 y FD(c)935 1696 y FQ(\(Thouless)g(e\013ect\))e([5].)133 1797 y FE(\017)24 b FQ(The)19 b(t)o(w)o(o-dimensional)e FF(X)t(Y)30 b FQ(mo)q(del)17 b(\(Kosterlitz-Thouless)h(transition\),)h(in)f(whic)o(h)g (it)g(is)182 1857 y(b)q(eliev)o(ed)c([220])i(that)g(the)f(free)g(energy)g FF(f)5 b FQ(\()p FF(\014)s(;)j(h)13 b FQ(=)h(0\))i(is)g FF(C)1263 1839 y Fy(1)1315 1857 y FQ(but)g(nonanalytic)f(at)h FF(\014)1754 1864 y FD(c)1771 1857 y FQ(;)g(here)182 1917 y(the)h(sp)q(on)o(taneous)h (magnetization)e FF(M)5 b FQ(\()p FF(\014)s(;)j(h)15 b FQ(=)g(0\))g(=)g FE(\000)p FF(@)s(f)5 b(=@)s(h)p FE(j)1385 1924 y FD(h)p FH(=0)1469 1917 y FQ(v)m(anishes)17 b(iden)o(tically)l(,)182 1977 y(while)12 b(the)i(zero-\014eld)e(susceptibilit)o(y)g FF(\037)p FQ(\()p FF(\014)s(;)c(h)k FQ(=)i(0\))g(=)g FE(\000)p FF(@)1259 1959 y FH(2)1278 1977 y FF(f)5 b(=@)s(h)1388 1959 y FH(2)1408 1977 y FE(j)1422 1984 y FD(h)p FH(=0)1503 1977 y FQ(is)13 b(b)q(eliev)o(ed)e(to)j (blo)o(w)182 2038 y(up)i(at)h FF(\014)340 2045 y FD(c)373 2038 y FQ(and)g(remain)e(in\014nite)g(for)h(all)g FF(\014)g FE(\025)e FF(\014)1063 2045 y FD(c)1080 2038 y FQ(.)133 2139 y FE(\017)24 b FQ(Systems)13 b(with)g(disorder,)h(in)g(whic)o(h)f(it)h(is)g(exp)q(ected)f (in)g(general)h(\(and)h(sometimes)c(pro)o(v)o(en\))182 2199 y(that)j(at)f(high)h(temp)q(erature)e(the)h(free)g(energy)g(is)g(ev)o (erywhere)e FF(C)1382 2181 y Fy(1)1432 2199 y FQ(but)j(no)o(where)f (analytic,)182 2259 y(as)k(a)g(function)f(of)h(temp)q(erature)e(and/or)j (magnetic)d(\014eld.)22 b(This)17 b(phenomenon)e(is)i(kno)o(wn)182 2319 y(as)g(a)f(Gri\016ths)g(singularit)o(y)g([131)q(].)133 2419 y(The)f(description)f(of)i(transitions)f(where)f(the)h(n)o(um)o(b)q(er)e (of)i(\\macrostates")h(c)o(hanges)f(is)g(based)60 2479 y(on)i(the)g(use)g(of) g FP(or)n(der)g(p)n(ar)n(ameters)t FQ(.)22 b(These)17 b(are)g(observ)m(ables) g(acquiring)f(di\013eren)o(t)g(exp)q(ectation)60 2539 y(v)m(alues)k(for)h (the)e(di\013eren)o(t)h(\\macrostates".)33 b(Eac)o(h)20 b(\\macrostate")g (can)g(b)q(e)h(selected)d(either)i(b)o(y)60 2600 y(in)o(tro)q(ducing)k(some)g (extra)g(\014eld)f(that)i(is)f(turned)h(o\013)g(in)f(the)g(limit,)f(or)i(b)o (y)f(using)g(the)g(righ)o(t)60 2660 y(b)q(oundary)18 b(conditions.)24 b(The)16 b(connection)h(b)q(et)o(w)o(een)f(this)h(p)q(oin)o(t)g(of)g(view)f (and)i(the)e(existence)g(of)951 2784 y(71)p eop %%Page: 72 72 bop 60 91 a FQ(singularities)15 b(in)g(the)h(pressure)f(\(free)g(energy\))g (w)o(as)h(informally)e(kno)o(wn)i(since)e(the)i(b)q(eginning)g(of)60 152 y(the)e(\014eld:)20 b(The)14 b(pressure)g(has)h(to)g(b)q(e)f(con)o(v)o (ex)f(|)h(for)h(the)f(sytem)e(to)j(b)q(e)f(stable)h(|)f(hence)f(its)h(only)60 212 y(p)q(ossible)f(discon)o(tin)o(uities)d(are)j(the)f(existence)e(of)j (\\sharp)h(corners")f(where)f(the)g(v)m(arious)h(one-sided)60 272 y(deriv)m(ativ)o(es)f(of)j(the)e(pressure)h(tak)o(e)g(di\013eren)o(t)f(v) m(alues.)20 b(Eac)o(h)14 b(of)g(these)g(v)m(alues)g(de\014nes)g(a)g (di\013eren)o(t)60 332 y(\\macrostate".)20 b(F)l(or)13 b(example,)d(in)i(the) h(case)f(of)h(the)f(Ising)h(mo)q(del,)e(the)i(righ)o(t)f(and)h(left)e(deriv)m (ativ)o(es)60 392 y(with)j(resp)q(ect)f(to)h(the)g(magnetic)e(\014eld)h(giv)o (e)g(the)h(t)o(w)o(o)f(p)q(ossible)h(magnetizations.)20 b(One)13 b(can)h(select)60 452 y(one)20 b(of)g(the)f(magnetizations)f(b)o(y)h(turning) h(o\013)g(a)g(p)q(ositiv)o(e)f(magnetic)f(\014eld)h(\(i.e.)30 b(coming)18 b(from)60 513 y(the)c(righ)o(t\))f(or)i(a)f(negativ)o(e)g(one)g (\(left)f(limit\),)e(or,)k(alternativ)o(ely)l(,)c(b)o(y)j(surrounding)h(the)f (sample)f(b)o(y)60 573 y(spins)k(p)q(olarized)g(in)g(the)g(desired)f(form.)23 b(It)16 b(turns)i(out)f(that)h(this)f(in)o(tuition)f(can)h(b)q(e)g (formalized)60 633 y(in)i(the)f(framew)o(ork)g(of)h(the)g(v)m (ariational-principle)f(approac)o(h.)30 b(Using)19 b(the)g(abstract)g(notion) h(of)60 693 y(tangen)o(t)g(to)h(a)f(con)o(v)o(ex)f(functional)g(in)h(a)g (Banac)o(h)g(space,)h(Galla)o(v)o(otti)e(and)h(Miracle-Sol)o(\023)-23 b(e)19 b([139])60 753 y(and)f(Lanford)h(and)f(Robinson)h([231])f(sho)o(w)o (ed)f(in)g(the)h(mid-1960's)f(ho)o(w)h(the)g(existence)d(of)j(more)60 814 y(than)g(one)f(pure)g(phase)g(\(ergo)q(dic)g(equilibrium)d(measure\))i (is)g(equiv)m(alen)o(t)g(to)h(lac)o(k)f(of)i(\(G^)-24 b(ateaux\))60 874 y(di\013eren)o(tiabilit)o(y)21 b(of)i(the)h(pressure)f(\(see)g(e.g.)g ([206])g(or)h([157)q(,)h(Chapter)f(16]\).)43 b(Moreo)o(v)o(er,)23 b(in)60 934 y(complete)13 b(agreemen)o(t)f(with)j(the)g(ab)q(o)o(v)o(e)f (example)f(of)i(the)g(Ising)f(mo)q(del,)g(the)g(direction)g(in)h(whic)o(h)60 994 y(the)g(di\013eren)o(tiabilit)o(y)e(fails)i(is)g(precisely)f(the)h (direction)f(of)i(the)f(\014eld)g(conjugate)h(to)g(the)f(relev)m(an)o(t)60 1054 y(order)h(parameter,)f(and)i(the)f(di\013eren)o(t)f(directional)g(deriv) m(ativ)o(es)g(giv)o(e)g(the)h(exp)q(ectations)h(of)f(this)60 1115 y(observ)m(able)g(in)g(the)g(di\013eren)o(t)g(pure)g(phases.)133 1175 y(Therefore,)j(if)f(w)o(e)h(restrict)f(ourselv)o(es)g(to)h (translation-in)o(v)m(arian)o(t)h(sp)q(eci\014cations)e(and)i(mea-)60 1235 y(sures,)d(w)o(e)g(ha)o(v)o(e)g(the)g(imp)q(ortan)o(t)f(distinction)h (that)g(\014rst-order)h(phase)g(transitions)g(corresp)q(ond)60 1295 y(to)c(a)g(c)o(hange)f(in)g(the)h(n)o(um)o(b)q(er)d(of)j(ergo)q(dic)g (equilibrium)c(measures)i(\(pure)h(phases\),)i(while)d(con)o(tin-)60 1355 y(uous)17 b(transitions)h(do)f(not)g(necessarily)e(c)o(hange)i(this)f(n) o(um)o(b)q(er)f(and)i(corresp)q(ond)h(to)f(m)o(uc)o(h)d(more)60 1416 y(subtle)24 b(phenomena)f(\(e.g.)h(slo)o(w)g(deca)o(y)f(of)i (correlations)f(=)g(\015uctuations)h(propagating)h(o)o(v)o(er)60 1476 y(macroscopic)14 b(scales)h(=)g(critical)e(opalescence\).)20 b(The)15 b(p)q(oin)o(ts)h(in)f(parameter)f(space)h(where)g(there)60 1536 y(is)j(a)h(second-)g(\(or)g(higher-\))g(order)f(phase)h(transition)g (are)g(customarily)d(called)i FP(critic)n(al)i(p)n(oints)t FQ(,)60 1596 y(in)h(analogy)i(to)e(the)h(critical)e(p)q(oin)o(t)h(of)h (liquid-gas)f(systems,)g(whic)o(h)g(w)o(as)h(the)g(earliest-kno)o(wn)60 1656 y(example)14 b(of)j(this)f(phenomenon.)133 1716 y(F)l(or)c(phenomena)e (in)h(whic)o(h)g(one)h(has)g(to)g(go)g(b)q(ey)o(ond)f(translation)h(in)o(v)m (ariance,)f(the)g(connection)60 1777 y(b)q(et)o(w)o(een)j(free-energy)h (singularities)f(and)i(prop)q(erties)f(of)h(the)f(set)g(of)h(extremal)d (Gibbs)i(measures)60 1837 y(is)k(less)h(clear.)31 b(Nev)o(ertheless,)18 b(transitions)i(in)o(v)o(olving)e(a)i(c)o(hange)g(in)f(the)g(n)o(um)o(b)q(er) f(of)i(extremal)60 1897 y(Gibbs)e(measures)f(are)g(usually)h(called)f(\(b)o (y)g(analogy)h(rather)g(than)h(logic\))e(\\\014rst-order")i(also)f(in)60 1957 y(this)e(general)g(case.)133 2017 y(Corresp)q(onding)i(to)f(the)g(t)o(w) o(o)f(di\013eren)o(t)g(notions)h(of)g(\\phase)h(transition")f(men)o(tioned)d (at)j(the)60 2078 y(b)q(eginning)c(of)g(this)f(subsection,)h(there)f(are)h(t) o(w)o(o)f(di\013eren)o(t)g(t)o(yp)q(es)g(of)h(result)f(on)h(\\absence)g(of)g (phase)60 2138 y(transitions":)25 b(On)18 b(the)g(one)g(hand,)g(there)g(are)g (results)f(pro)o(ving)h(the)g(uniqueness)f(of)h(the)g(Gibbs)60 2198 y(measure)i(\()p FE(jG)s FQ(\(\005\))p FE(j)g FQ(=)i(1\))f([84)q(,)f(90) q(,)g(91)q(,)h(94])g(or)g(of)g(the)g(translation-in)o(v)m(arian)o(t)g(Gibbs)g (measure)60 2258 y(\()p FE(jG)123 2265 y FD(inv)176 2258 y FQ(\(\005\))p FE(j)e FQ(=)h(1\))g([41,)f(262)r(].)31 b(On)19 b(the)h(other)f(hand,)i(there)e(are)h(results)f(on)h(analyticit)o(y)e(of)i (the)60 2318 y(free)h(energy)h(and)h(correlations)f([140)q(,)f(205)r(,)g(286) r(,)g(88)q(,)h(93)q(,)f(96)q(].)39 b(In)22 b(the)f(last)i(t)o(w)o(o)f (references,)60 2379 y(Dobrushin)e(and)f(Shlosman)g(in)o(tro)q(duced)f(an)i (extremely)c(strong)k(notion)f(of)g(absence)g(of)h(phase)60 2439 y(transitions,)c(whic)o(h)f(they)g(call)g(the)g FP(c)n(omplete)j (analyticity)j FQ(condition.)g(It)15 b(corresp)q(onds)i(roughly)60 2499 y(to)g(the)f(analyticit)o(y)e(of)j(all)f(the)g(\014nite-v)o(olume)d (free)j(energies)f FP(uniformly)j(in)f(the)h(volume)h(and)f(in)60 2559 y(the)g(b)n(oundary)f(c)n(onditions)t FQ(.)133 2619 y(It)h(is)f(kno)o (wn)h(that)h(in)e(general)h(the)f(di\013eren)o(t)g(notions)i(of)f(presence)f (and)i(absence)e(of)i(phase)951 2784 y(72)p eop %%Page: 73 73 bop 60 91 a FQ(transitions)13 b(are)f(not)h(equiv)m(alen)o(t.)18 b(This)12 b(non-equiv)m(alence)g(is)g(probably)g(due)g(to)h(ph)o(ysical)e (reasons)60 152 y(in)j(most)f(of)h(the)g(cases,)g(but)g(sometimes)d(it)j (seems)e(an)j(artifact)f(of)g(the)g(mathematical)d(formalism)60 212 y([89,)16 b(351)q(].)60 340 y FM(2.6.6)55 b(When)19 b(is)f(the)g(Relativ) n(e)f(En)n(trop)n(y)i(Densit)n(y)f(Zero?)60 432 y FQ(W)l(e)j(no)o(w)h(come)e (to)i(a)h(k)o(ey)d(question)h(\(whic)o(h)g(will)g(pla)o(y)g(a)h(crucial)f (role)g(in)g(our)h(R)o(G)g(theory\):)60 492 y(Under)15 b(what)h(conditions)f (do)q(es)h FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))e(=)g(0?)21 b(That)16 b(is,)f(under)g(what)h(conditions)g(is)f(the)g(relativ)o(e)60 553 y(en)o(trop)o(y)j(in)g(v)o(olume)f(\003)h(a)h(quan)o(tit)o(y)f FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\),)h(i.e.)e(a)i(\\surface)g (e\013ect"?)29 b(The)18 b(answ)o(er)h(is)g(simple:)60 613 y(if)f FF(\027)j FQ(is)d(a)h(Gibbs)f(measure)f(for)i(some)e(in)o(teraction,)g(then)h FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))f(=)h(0)g(when)g(and)h(only)f (when)h FF(\026)60 673 y FQ(is)g(a)h(Gibbs)f(measure)f(for)i(the)f FP(same)k FQ(in)o(teraction.)29 b(The)20 b(follo)o(wing)f(t)o(w)o(o)g (theorems)f(mak)o(e)f(this)60 733 y(precise,)e(in)h(a)g(rather)h(strong)g (form:)60 834 y FM(Theorem)g(2.66)24 b FP(L)n(et)e FF(\026)540 841 y FH(1)560 834 y FF(;)8 b(\026)611 841 y FH(2)653 834 y FP(b)n(e)23 b(Gibbs)g(me)n(asur)n(es)f(\(not)h(ne)n(c)n(essarily)g(tr)n (anslation-invariant\))60 894 y(for)17 b(inter)n(actions)h FQ(\010)440 901 y FH(1)460 894 y FF(;)8 b FQ(\010)517 901 y FH(2)551 894 y FE(2)14 b(B)633 876 y FH(1)652 894 y FP(,)j(r)n(esp)n(e)n (ctively.)23 b(Then)464 1012 y FQ(lim)8 b(sup)491 1051 y FH(\003)p Fy(\0451)646 978 y FQ(1)p 627 1000 62 2 v 627 1046 a FE(j)p FQ(\003)p FE(j)694 1012 y FF(I)716 1019 y FH(\003)742 1012 y FQ(\()p FF(\026)790 1019 y FH(1)810 1012 y FE(j)p FF(\026)853 1019 y FH(2)873 1012 y FQ(\))27 b FE(\024)h FQ(2)p FE(k)p FQ(\010)1070 1019 y FH(1)1101 1012 y FE(\000)11 b FQ(\010)1186 1019 y FH(2)1206 1012 y FE(k)1231 1020 y Fy(B)1255 1010 y Fr(0)1272 1020 y FD(=)p FH(\()p Fy(J)5 b FH(+)p Fk(Const)p FH(\))1481 1012 y FF(:)246 b FQ(\(2)p FF(:)p FQ(111\))60 1139 y FP(If)17 b FF(\026)140 1146 y FH(1)178 1139 y FP(and)g FF(\026)301 1146 y FH(2)339 1139 y FP(ar)n(e)g(tr)n(anslation-invariant,)h(this)g(me)n(ans)f(that)590 1237 y FF(i)p FQ(\()p FF(\026)655 1244 y FH(1)675 1237 y FE(j)p FF(\026)718 1244 y FH(2)738 1237 y FQ(\))28 b FE(\024)f FQ(2)p FE(k)p FQ(\010)935 1244 y FH(1)966 1237 y FE(\000)11 b FQ(\010)1051 1244 y FH(2)1071 1237 y FE(k)1096 1245 y Fy(B)1120 1236 y Fr(0)1137 1245 y FD(=)p FH(\()p Fy(J)6 b FH(+)p Fk(Const)o FH(\))1346 1237 y FF(:)381 b FQ(\(2)p FF(:)p FQ(112\))60 1335 y FP(In)20 b(p)n(articular,)f(if)h FF(\026)445 1342 y FH(1)485 1335 y FP(and)g FF(\026)611 1342 y FH(2)650 1335 y FP(ar)n(e)f(tr)n (anslation-invariant)i(Gibbs)g(me)n(asur)n(es)d(for)h(the)i FQ(same)d FP(in-)60 1395 y(ter)n(action)g FQ(\010)c FE(2)g(B)396 1377 y FH(1)415 1395 y FP(,)j(then)i FF(i)p FQ(\()p FF(\026)621 1402 y FH(1)640 1395 y FE(j)p FF(\026)683 1402 y FH(2)703 1395 y FQ(\))14 b(=)g(0)p FP(.)60 1496 y FM(Theorem)j(2.67)24 b FP(L)n(et)h FQ(\005)h FP(b)n(e)g(a)g(quasilo)n(c)n(al)g(sp)n(e)n(ci\014c)n (ation,)i(let)f FF(\027)33 b FE(2)d(G)1447 1503 y FD(inv)1500 1496 y FQ(\(\005\))p FP(,)e(and)e(let)h FF(\026)j FE(2)60 1556 y FF(M)107 1563 y FH(+1)p FD(;inv)216 1556 y FQ(\(\012\))p FP(.)22 b(Supp)n(ose)c(that)g(ther)n(e)f(exists)h(a)g(van)g(Hove)g(se)n (quenc)n(e)h FQ(\(\003)1375 1563 y FD(n)1399 1556 y FQ(\))1418 1563 y FD(n)p Fy(\025)p FH(1)1503 1556 y FP(such)f(that)732 1678 y FQ(lim)720 1703 y FD(n)p Fy(!1)856 1644 y FQ(1)p 825 1666 86 2 v 825 1712 a FE(j)p FQ(\003)873 1719 y FD(n)897 1712 y FE(j)915 1678 y FF(I)937 1685 y FH(\003)961 1689 y Fs(n)985 1678 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))28 b(=)f(0)15 b FF(:)502 b FQ(\(2)p FF(:)p FQ(113\))60 1804 y FP(Then)18 b FF(\026)c FE(2)g(G)307 1811 y FD(inv)361 1804 y FQ(\(\005\))p FP(.)133 1905 y FQ(Theorem)c(2.66)h(is)g(an)g(immediate)c(consequence)j(of)i (estimate)d(\(2.64\))i(in)g(Prop)q(osition)h(2.46\(b\).)60 1965 y(Note,)k(again,)g(that)h(although)h(\010)680 1972 y FH(1)700 1965 y FF(;)8 b FQ(\010)757 1972 y FH(2)793 1965 y FQ(are)16 b(required)f(to)i(b)q(elong)g(to)g(the)f(\\small")g(Banac)o(h)g(space)60 2025 y FE(B)95 2007 y FH(1)114 2025 y FQ(,)g(the)g(\014nal)g(estimate)f(is)h (in)f(terms)g(of)i(the)f FE(B)948 2007 y FH(0)967 2025 y FF(=)p FQ(\()p FE(J)k FQ(+)11 b FP(Const)p FQ(\))17 b(norm,)e(hence)g(m)o(uc)o(h)f (stronger.)133 2085 y(Theorem)j(2.67)i(is,)f(on)g(the)g(other)h(hand,)f(a)h (deep)f(and)g(surprising)h(\(at)f(least)g(to)h(us\))f(result:)60 2145 y(from)i(a)i(h)o(yp)q(othesis)f(on)h(the)f(b)q(eha)o(vior)g FP(p)n(er)g(unit)i(volume)g(in)f(the)h(in\014nite-volume)i(limit)30 b FQ(one)60 2205 y(obtains)17 b(a)g(conclusion)f(v)m(alid)g FP(for)g(every)i(volume)j FQ(\(namely)15 b FF(\026\031)1246 2212 y FH(\003)1286 2205 y FQ(=)f FF(\026)p FQ(\).)133 2266 y(The)h(com)o(bination)f(of)i(Theorems)e(2.66)i(and)g(2.67)g(will)e(pla)o(y)h (a)g(k)o(ey)f(role)h(in)g(the)g(pro)q(of)i(of)e(the)60 2326 y(First)h(F)l(undamen)o(tal)e(Theorem)h(\(see)h(Section)g(3.2\).)133 2429 y(Com)o(bining)c(Theorems)h(2.66)h(and)g(2.67,)h(w)o(e)e(deduce)g(the)g (k)o(ey)g(result)g(relating)g(the)g(DLR)h(and)60 2489 y(v)m(ariational)j (approac)o(hes)f(to)h(classical)f(lattice)f(systems:)60 2590 y FM(Corollary)j(2.68)24 b FP(L)n(et)19 b FQ(\010)e FE(2)g(B)656 2572 y FH(1)694 2590 y FP(and)i(let)h FF(\026)d FE(2)h FF(M)1004 2597 y FH(+1)p FD(;inv)1112 2590 y FQ(\(\012\))p FP(.)28 b(Then)20 b FF(\026)f FP(is)g(a)g(Gibbs)g(me)n(asur)n(e)g(for)60 2650 y FQ(\010)f FP(if)f(and)h(only)f(if)h(it)f(is)h(an)f(e)n(quilibrium)i(me)n (asur)n(e)d(for)h FQ(\010)p FP(.)951 2784 y FQ(73)p eop %%Page: 74 74 bop 60 91 a FM(2.6.7)55 b(P)n(athologies)19 b(in)f(V)-5 b(arious)19 b(In)n(teraction)f(Spaces)h FE(B)1300 98 y FD(h)60 184 y FQ(In)k(Section)f (2.4.4)h(w)o(e)f(in)o(tro)q(duced)h(a)g(large)g(class)g(of)g(in)o(teraction)f (spaces)h FE(B)1554 191 y FD(h)1576 184 y FQ(,)h(of)f(whic)o(h)f(the)60 244 y(most)16 b(imp)q(ortan)o(t)h(are)g FE(B)529 226 y FH(0)565 244 y FQ(and)h FE(B)696 226 y FH(1)715 244 y FQ(.)24 b(No)o(w)17 b(w)o(e)g(w)o(ould)g(lik)o(e)e(to)j(discuss)f(the)g FP(physic)n(al)22 b FQ(di\013erences)60 304 y(b)q(et)o(w)o(een)15 b(these)h(spaces.)22 b(This)16 b(is)g(an)h(imp)q(ortan)o(t)e(issue,)h(b)q(ecause)g(w)o(e)g(need)g (to)g(justify)g(our)h(view)60 364 y(that)e(\(roughly)h(sp)q(eaking\))f FE(B)613 346 y FH(1)647 364 y FQ(is)g(the)f(largest)i(\\ph)o(ysically)d (reasonable")j(space)f(of)g(in)o(teractions.)133 424 y(Our)22 b(p)q(oin)o(t)g(of)h(view)e(is)h(that)g(the)g FP(fundamental)i(physic)n(al)f (principles)k FQ(of)22 b(in\014nite-v)o(olume)60 485 y(equilibrium)16 b(statistical)i(mec)o(hanics)f(are)i(giv)o(en)f(b)o(y)g(the)h(theory)g(of)g (sp)q(eci\014cations)g(and)h(Gibbs)60 545 y(measures.)f(\(W)l(e)11 b(consider)g(the)g(v)m(ariational)h(theory)f(of)h(translation-in)o(v)m(arian) o(t)g(equilibrium)c(mea-)60 605 y(sures)15 b(to)h(b)q(e)f(only)f(a)i(useful)e FP(te)n(chnic)n(al)k(to)n(ol)5 b FQ(.\))21 b(F)l(urthermore,)13 b(w)o(e)h(argued)i(in)e(Section)h(2.3.3)g(that,)60 665 y(at)20 b(least)f(for)h(systems)e(of)i FP(b)n(ounde)n(d)k FQ(spins)c(\(including,)f (in)g(particular,)g(all)g(mo)q(dels)f(with)i(\014nite)60 725 y(single-spin)c(space\),)g(a)h(ph)o(ysically)d(reasonable)j(sp)q (eci\014cation)f(m)o(ust)f(b)q(e)h FP(quasilo)n(c)n(al)5 b FQ(.)22 b(If)16 b(then)g(w)o(e)60 786 y(put)j(aside)h(hard-core)f(in)o (teractions,)g(it)g(follo)o(ws)g(from)f(Theorem)g(2.12)i(that)g(a)f(ph)o (ysically)f(rea-)60 846 y(sonable)e(sp)q(eci\014cation)g(m)o(ust)e(b)q(e)i (the)f(Gibbsian)h(sp)q(eci\014cation)g(for)g(some)f FP(absolutely)j(summable) 60 906 y FQ(in)o(teraction.)h(Since)11 b FE(B)481 888 y FH(1)512 906 y FQ(is)h(the)g(space)g(of)h(translation-in)o(v)m(arian)o(t)f(absolutely) g(summable)e(con)o(tin)o(u-)60 966 y(ous)j(in)o(teractions,)f(this)g (justi\014es)f(our)i(con)o(ten)o(tion)e(that)i FE(B)1136 948 y FH(1)1167 966 y FQ(is)f(the)g(largest)g(ph)o(ysically)f(reasonable)60 1026 y(space)16 b(of)h(in)o(teractions.)133 1087 y(F)l(rom)12 b(a)i FP(mathematic)n(al)19 b FQ(p)q(oin)o(t)14 b(of)f(view,)g FE(B)932 1068 y FH(0)965 1087 y FQ(is)g(the)g(natural)h(space)f(of)h(in)o (teractions)f(on)h(whic)o(h)60 1147 y(to)i(dev)o(elop)f(the)h(v)m(ariational) g(theory)g(of)g(equilibrium)d(measures.)20 b(W)l(e)c(nev)o(ertheless)e(claim) g(that)60 1207 y FE(B)95 1189 y FH(0)134 1207 y FQ(is,)20 b(from)e(a)i FP(physic)n(al)25 b FQ(p)q(oin)o(t)20 b(of)g(view,)f(m)o(uc)o(h)e(to)q(o)k (large;)g(ev)o(en)e(the)g(v)m(ariational)h(theory)g(on)60 1267 y FE(B)95 1249 y FH(0)132 1267 y FQ(is)d(\\pathological".)26 b(\(This)18 b(is)f(connected)g(with)g(the)h(fact)f(that)h(in)o(teractions)f (in)g FE(B)1699 1249 y FH(0)1730 1267 y FE(n)12 b(B)1802 1249 y FH(1)1839 1267 y FQ(do)60 1327 y(not)20 b(in)e(general)h(de\014ne)g(sp)q (eci\014cations,)g(so)h(there)f(are)g(no)h(DLR)f(equations.)30 b(F)l(or)20 b(this)f(reason,)60 1388 y(Corollary)g(2.18)h(and)g(Prop)q (ositions)g(2.46)g(and)g(2.59)g(do)f(not)h(hold)f(in)g(general)g(in)f FE(B)1672 1369 y FH(0)1691 1388 y FQ(,)i(and)f(the)60 1448 y(large-deviation)i(theory)g(do)q(es)h(not)f(apply)g(to)h(equilibrium)17 b(measures)k(whic)o(h)f(are)h(not)h(Gibbs)60 1508 y(measures.\))e(T)l(o)15 b(emphasize)e(that)j FE(B)749 1490 y FH(0)782 1508 y FQ(is)f(an)h(unph)o (ysically)d(large)i(space)g(of)g(in)o(teractions,)f(w)o(e)h(list)60 1568 y(here)f(some)f(of)i(the)f(strange)h(phenomena)f(that)h(can)g(b)q(e)f (pro)o(v)o(en)g(for)h(in)o(teractions)e(in)h(this)h(space:)133 1653 y(1\))24 b(There)g(is)f(a)h FP(dense)29 b FQ(set)24 b(of)g(in)o (teractions)f(in)g FE(B)1116 1635 y FH(0)1159 1653 y FQ(with)g(uncoun)o (tably)h(man)o(y)e(extremal)60 1713 y(equilibrium)9 b(measures)j([206)q(,)h (Theorem)e(V.2.2\(c\)].)19 b(\(It)13 b(is)f(p)q(erhaps)i(not)f(surprising)g (that)h(highly)60 1774 y(frustrated)20 b(in)o(teractions)e(could)i(pro)q (duce)f(uncoun)o(tably)h(man)o(y)e(pure)h(phases;)i(but)f(in)f FE(B)1773 1755 y FH(0)1811 1774 y FQ(this)60 1834 y(happ)q(ens)d FP(arbitr)n(arily)f(close)i(to)f(zer)n(o)g(inter)n(action)t FQ(,)f(i.e.)e(at)i(what)h(ough)o(t)f(to)g(corresp)q(ond)h(to)f(\\high)60 1894 y(temp)q(erature".\))133 1979 y(2\))f(F)l(or)f(an)o(y)g(\014nite)g (family)e FF(\026)660 1986 y FH(1)680 1979 y FF(;)d(:)g(:)g(:)g(;)g(\026)819 1986 y FD(n)855 1979 y FQ(of)14 b(ergo)q(dic)f(translation-in)o(v)m(arian)o (t)h(measures)e(of)i(\014nite)60 2039 y(en)o(trop)o(y)g(densit)o(y)g (\(relativ)o(e)g(to)h FF(\026)682 2021 y FH(0)702 2039 y FQ(\),)g(there)g (exists)f(an)i(in)o(teraction)e(in)h FE(B)1409 2021 y FH(0)1443 2039 y FQ(for)g(whic)o(h)f FP(al)r(l)22 b FQ(of)15 b(these)60 2099 y(measures)22 b(are)i FP(simultane)n(ously)k FQ(equilibrium)20 b(measures)i([206)q(,)i(Theorem)e(V.2.2\(a\)].)1724 2081 y FH(40)1803 2099 y FQ(\(W)l(e)60 2160 y(\014nd)h(this)f(result)g(absolutely)h (\015abb)q(ergasting:)35 b(it)22 b(implies,)f(for)i(example,)f(that)h(there)f (exists)60 2220 y(an)h(in)o(teraction)f(in)h FE(B)485 2202 y FH(0)527 2220 y FQ(for)g(whic)o(h)f(the)h(Gibbs)g(measures)f(of)h(the)g (in\014nite-temp)q(erature)d(and)60 2280 y(zero-temp)q(erature)e(Ising)h(mo)q (dels)f(are)h(co)q(existing)g(pure)g(phases!\))30 b(It)19 b(follo)o(ws)g (that)g(in)g FE(B)1784 2262 y FH(0)1822 2280 y FQ(the)60 2340 y(in)o(teraction)g FP(c)n(annot)25 b FQ(b)q(e)20 b(reconstructed)f(uniquely)f (from)h(the)g(equilibrium)d(measure:)27 b(for)20 b(an)o(y)60 2400 y(giv)o(en)12 b(measure)g FF(\026)p FQ(,)h(there)g(are)f FP(many)18 b FQ(di\013eren)o(t)12 b(in)o(teractions)g(in)g FE(B)1298 2382 y FH(0)1330 2400 y FQ(ha)o(ving)h FF(\026)g FQ(as)h(an)f(equilibrium)60 2461 y(measure.)27 b(This)18 b(is)h(in)f(sharp)h (con)o(trast)g(to)g(Prop)q(osition)h(2.46,)f(whic)o(h)f(asserts)h(the)f (uniqueness)p 60 2504 732 2 v 100 2558 a FA(40)135 2573 y Fz(This)d(result)g (is)g(reminiscen)o(t)g(of)f(the)i(corresp)q(onding)g(result)f(in)g(the)g (theory)h(of)e(\(non-quasilo)q(cal\))g(sp)q(eci\014ca-)60 2623 y(tions:)k(see)d(the)f(remark)g(at)f(the)i(end)f(of)f(Section)i(2.3.4.)951 2784 y FQ(74)p eop %%Page: 75 75 bop 60 91 a FQ(\(mo)q(dulo)16 b(ph)o(ysical)f(equiv)m(alence\))f(of)j(the)f (in)o(teraction)f(\(if)h(one)g(exists)g(at)h(all\))e(within)h FE(B)1723 73 y FH(1)1742 91 y FQ(.)133 176 y(3\))h(The)f(pressure)f(is)h(no)o (where)g(F)l(r)o(\023)-23 b(ec)o(het-di\013eren)o(tiable)13 b(in)j FE(B)1279 158 y FH(0)1314 176 y FQ([70].)21 b(By)15 b(con)o(trast,)h(the)g(pres-)60 236 y(sure)f(is)g(F)l(r)o(\023)-23 b(ec)o(het)14 b(di\013eren)o(tiable)f(of)j(order)f FF(n)g FQ(in)g(a)g(neigh)o (b)q(orho)q(o)q(d)i(of)f(the)f(origin)g(\(\\high)g(temp)q(er-)60 296 y(ature"\))i(in)f FE(B)323 278 y FD(n)362 296 y FQ(\()p FF(n)e FE(\025)f FQ(2\))k([177,)f(228)q(,)g(298)q(].)856 278 y FH(41)133 405 y FQ(Ev)o(en)11 b(the)f(space)h FE(B)489 387 y FH(1)519 405 y FQ(is)g(incredibly)e(large,)j(in)e(that)i(it)e(allo)o(ws)h (in)o(teractions)f(whic)o(h)h(are)g(strongly)60 466 y(man)o(y-b)q(o)q(dy)16 b(\(though)h(not)f(quite)f(so)i(strongly)f(as)h(in)e FE(B)1108 447 y FH(0)1127 466 y FQ(\))h(and)h(of)f(arbitrarily)f(long)i(range)f(\(pro-) 60 526 y(vided)21 b(only)h(that)g(they)f(are)h(absolutely)g(summable\).)35 b(This)22 b(means)f(that)h(ev)o(en)f(in)g FE(B)1743 508 y FH(1)1784 526 y FQ(some)60 586 y(rather)16 b(strange)h(phenomena)f(o)q(ccur:)133 671 y(4\))21 b(A)o(t)f(lo)o(w)h(temp)q(erature,)f(the)g(Gibbs)h(phase)g(rule) f(is)h(generically)e(violated)h(in)g(all)g(of)h(the)60 731 y(spaces)c FE(B)245 713 y FD(n)268 731 y FQ(.)23 b(This)17 b(is)g(b)q(ecause)g(a)g(\014rst-order)g(phase)h(transition)f(can)g(b)q(e)g (destro)o(y)o(ed)f(b)o(y)g(an)i(arbi-)60 791 y(trarily)d(w)o(eak)h(\(in)g FF(`)428 773 y FH(1)464 791 y FQ(norm\))f(but)i(v)o(ery)d(long-range)k FP(two-b)n(o)n(dy)i FQ(in)o(teraction)15 b([70,)h(349)q(,)g(332)q(,)g(208)q (].)60 851 y(The)i(Gibbs)g(phase)h(rule)e(can)h(hold)g(only)g(in)g(spaces)g FE(B)1095 858 y FD(h)1135 851 y FQ(where)g(the)f(w)o(eigh)o(t)h FF(h)p FQ(\()p FF(X)t FQ(\))g(gro)o(ws)h(su\016-)60 911 y(cien)o(tly)14 b(fast)j(with)f(the)g FP(diameter)22 b FQ(of)16 b FF(X)21 b FQ(\(and)c(not)g(merely)c(its)j(cardinalit)o(y\).)133 996 y(5\))22 b(The)f(pressure)g(is)f(not)i(analytic)e(in)h(an)o(y)g(op)q(en)h(set)f(in)f (an)o(y)h(of)h(the)e(spaces)i FE(B)1693 978 y FD(n)1736 996 y FQ([89)q(];)g(in)60 1056 y(particular,)e(it)f(is)h(not)g(analytic)g(ev)o (en)e(at)j(\\high)f(temp)q(erature")f(\(i.e.)f(a)i(neigh)o(b)q(orho)q(o)q(d)i (of)e(the)60 1116 y(origin\).)h(In)14 b(fact,)g(for)h(spaces)g FE(B)657 1123 y FD(h)694 1116 y FQ(in)f(whic)o(h)g FF(h)p FQ(\()p FF(X)t FQ(\))h(dep)q(ends)g(only)g(on)g(the)f(cardinalit)o(y)f(of)i FF(X)t FQ(,)g(the)60 1176 y(pressure)g(is)g(analytic)f(in)h(a)g(neigh)o(b)q (orho)q(o)q(d)i(of)f(the)f(origin)g FP(if)h(and)g(only)h(if)26 b FF(h)p FQ(\()p FF(X)t FQ(\))14 b FE(\025)f FQ(const)c FE(\002)g FF(e)1823 1158 y FD(\017)p Fy(j)p FD(X)s Fy(j)60 1237 y FQ(for)17 b(some)e FF(\017)e(>)h FQ(0)j([205,)f(89)q(].)576 1219 y FH(42)133 1321 y FM(Remark.)26 b FQ(In)18 b(the)g(Ising)g(mo)q(del,)f(analyticit)o(y)g (do)q(es)i(hold)f(in)g FE(B)1362 1303 y FH(1)1400 1321 y FQ(norm)f(for)i(the) f FP(subsp)n(ac)n(es)60 1381 y FQ(of)i FE(B)154 1363 y FH(1)193 1381 y FQ(corresp)q(onding)h(to)g(in)o(teractions)e(written)h(in)f (lattice-gas)i(or)f(spin)g(form)f(\(\010)1658 1388 y FD(X)1712 1381 y FQ(=)i FF(J)1798 1388 y FD(X)1831 1381 y FF(\032)1856 1363 y FD(X)60 1442 y FQ(or)d(\010)156 1449 y FD(X)207 1442 y FQ(=)e FF(J)288 1449 y FD(X)322 1442 y FF(\033)352 1424 y FD(X)385 1442 y FQ(,)i(resp)q(ectiv)o(ely\))d([205)q(].)25 b(This)18 b(is)g(a)g(v)o(ery)e(surprising)j(result,)e(whic)o(h)g(w)o(e)g(do)i (not)60 1502 y(completely)f(understand)k(from)e(a)i(ph)o(ysical)e(p)q(oin)o (t)h(of)h(view.)35 b(It)21 b(is)g(related)f(to)i(the)e(fact)i(that)p 60 1545 732 2 v 100 1599 a FA(41)135 1614 y Fz(It)16 b(seems)h(to)g(b)q(e)g (an)f(op)q(en)h(question)g(whether)h(the)f(pressure)i(is)d(once)h(F)m(r)o (\023)-20 b(ec)o(het)18 b(di\013eren)o(tiable)f(in)f(a)g(neigh-)60 1664 y(b)q(orho)q(o)q(d)i(of)f(the)h(origin)e(in)i Fu(B)557 1649 y FA(1)576 1664 y Fz(.)29 b(The)18 b(pro)q(ofs)f(of)g(higher-order)i (di\013eren)o(tiabilit)o(y)d(in)h([177)o(,)g(228)o(,)h(298)o(])f(use)h(the)60 1714 y(Dobrushin)c(uniqueness)h(theorem,)e(whic)o(h)h(applies)g(only)f(in)h Fu(B)1071 1699 y FA(2)1104 1714 y Fz(or)g(higher.)k(See)d(also)f([157)o(,)f (Chapter)i(8)e(and)h(the)60 1763 y(corresp)q(onding)h(notes].)100 1821 y FA(42)135 1837 y Fz(This)9 b(statemen)o(t)h(is)f(a)h(sligh)o(t)e(lie.) 16 b(What)10 b(Dobrushin)f(and)h(Martirosy)o(an)f([89)o(])g(actually)g(pro)o (v)o(e)g(is)h(the)g(follo)o(wing:)60 1886 y(Let)15 b(the)g(single-spin)f (space)h(\012)552 1892 y FA(0)585 1886 y Fz(b)q(e)h(\014nite;)e(let)h Fv(h)p Fz(\()p Fv(X)s Fz(\))g(dep)q(end)h(only)d(on)h(the)h(cardinalit)o(y)f (of)g Fv(X)s Fz(,)g(and)h Fw(not)j Fz(satisfy)60 1936 y Fv(h)p Fz(\()p Fv(X)s Fz(\))d Fu(\025)f Fz(const)d Fu(\002)g Fv(e)381 1921 y Fp(\017)p Fo(j)p Fp(X)r Fo(j)462 1936 y Fz(for)k(an)o(y)g Fv(\017)f(>)g Fz(0;)i(and)f(let)h Fu(B)905 1921 y Fl(C)904 1948 y Fp(h)948 1936 y Fz(b)q(e)g(the)g(complexi\014cation)d(of)i Fu(B)1464 1942 y Fp(h)1486 1936 y Fz(.)22 b(Then,)16 b(in)f(ev)o(ery)i(op)q (en)60 1986 y(set)d Fv(U)i Fu(\032)c(B)240 1971 y Fl(C)239 1998 y Fp(h)280 1986 y Fz(con)o(taining)g(a)g(real)h(p)q(oin)o(t,)f(there)i (exists)f(a)f(complex)g(in)o(teraction)g(\010)g Fu(2)f Fv(U)18 b Fz(and)12 b(a)h(sequence)h(of)e(cub)q(es)60 2050 y(\003)89 2056 y Fp(n)128 2050 y Fu(\045)k(1)g Fz(suc)o(h)i(that)f(the)h(\014nite-v)o (olume)d(partition)h(functions)h Fv(Z)1147 2056 y FA(\003)1170 2060 y Fn(n)1192 2050 y Fz(\(\010\))g Fu(\021)1320 2016 y Fx(R)1355 2050 y Fz(exp)1425 2004 y Fx(h)1445 2050 y Fu(\000)p Fv(H)1515 2035 y FA(\010)1512 2061 y(\003)1535 2065 y Fn(n)1554 2061 y Fp(;f)s(r)q(ee)1634 2004 y Fx(i)1670 2050 y Fz(are)g(all)f Fw(zer)n(o)s Fz(.)60 2112 y(Th)o(us,)c(the)g(\014nite-v)o(olume)d(free)j (energies)h(ha)o(v)o(e)e(\(complex\))f(singularities)h(arbitrarily)f(close)i (to)f(ev)o(ery)h(\(real\))f(p)q(oin)o(t)60 2162 y(in)g Fu(B)133 2168 y Fp(h)154 2162 y Fz(.)17 b(This)11 b(result)h(mak)o(es)e(it)h(v)o(ery)g (unlik)o(ely)f(that)h(the)h(in\014nite-v)o(olume)d(pressure)k(could)e(b)q(e)h (analytic)e(in)h(an)g(op)q(en)60 2211 y(set)16 b(of)f Fu(B)202 2217 y Fp(h)224 2211 y Fz(;)h(but)g(strictly)f(sp)q(eaking)h(it)f(do)q(es)h (not)g(rule)g(it)f(out,)g(b)q(ecause)i(conceiv)n(ably)e(the)i(singularities)d (presen)o(t)60 2261 y(in)j(\014nite)h(v)o(olume)e(could)h(miraculously)f (disapp)q(ear)i(in)f(the)h(passage)h(to)e(the)h(in\014nite-v)o(olume)e (limit.)27 b([Here)18 b(is)60 2311 y(a)e(simple)g(example)f(in)h(one)h (complex)e(v)n(ariable:)23 b(Let)17 b Fv(Z)973 2317 y Fp(n)996 2311 y Fz(\()p Fv(z)r Fz(\))f(=)h Fv(z)c Fu(\000)e Fv(z)1208 2317 y FA(0)1244 2311 y Fz(for)16 b(all)g Fv(n)p Fz(,)g(where)i Fv(z)1566 2317 y FA(0)1601 2311 y Fu(2)e Fq(C)11 b Fu(n)g Fq(R)p Fz(.)26 b(Then)60 2361 y(lim)118 2367 y Fp(n)p Fo(!1)213 2361 y Fv(n)238 2346 y Fo(\000)p FA(1)290 2361 y Fz(log)6 b Fv(Z)378 2367 y Fp(n)401 2361 y Fz(\()p Fv(z)r Fz(\))12 b(=)g(0)f(for)g(all)f Fv(z)k Fu(2)d Fq(R)h Fz(\(pro)o(vided)f(that)h(the)g(branc)o(h)f(cut)h(is)g (c)o(hosen)g(to)f(a)o(v)o(oid)f(the)i(real)g(axis\).)60 2411 y(And)g(the)g(function)g(0)f(certainly)h Fw(do)n(es)k Fz(ha)o(v)o(e)11 b(an)h(analytic)f(con)o(tin)o(uation)f(from)g Fq(R)i Fz(to)g Fq(C)p Fz(!])17 b(W)m(e)11 b(prop)q(ose)i(as)f(an)f Fw(op)n(en)60 2461 y(pr)n(oblem)19 b Fz(to)c(mathematical)e(statistical)j(mec)o(hanicians:) 21 b(pro)o(v)o(e)16 b(that)g(the)g(in\014nite-v)o(olume)e(pressure,)k(whic)o (h)e(is)60 2510 y(w)o(ell-de\014ned)c(on)g(the)g(space)h Fu(B)546 2516 y Fp(h)579 2510 y Fz(of)e Fw(r)n(e)n(al)16 b Fz(in)o(teractions,)c(has)f (no)h(analytic)f(con)o(tin)o(uation)g(to)g(an)o(y)g(op)q(en)i(set)f Fv(U)17 b Fu(\032)11 b(B)1862 2495 y Fl(C)1861 2522 y Fp(h)60 2560 y Fz(con)o(taining)16 b(a)h(real)g(p)q(oin)o(t.)28 b(In)17 b(an)o(y)g(case,)i(the)f(result)g(of)f(Dobrushin)g(and)g(Martirosy)o(an)g(do) q(es)h(sho)o(w)f(that)g(the)60 2610 y(Dobrushin-Shlosman)10 b([93)o(,)i(96])g(complete)f(analyticit)o(y)g(condition)h(do)q(es)h(not)g (hold)e(for)h(an)o(y)g(op)q(en)h(neigh)o(b)q(orho)q(o)q(d)60 2660 y(in)g Fu(B)135 2666 y Fp(h)157 2660 y Fz(,)h(for)f(the)i(sp)q (eci\014ed)g(class)f(of)g Fv(h)p Fz(.)951 2784 y FQ(75)p eop %%Page: 76 76 bop 60 91 a FQ(ph)o(ysically)17 b(equiv)m(alen)o(t)g(in)o(teractions)g(can)i (ha)o(v)o(e)f(widely)f(di\013ering)h(norms)g(in)g(an)o(y)g(giv)o(en)g(space) 60 152 y FE(B)93 159 y FD(h)115 152 y FQ(;)h(in)e(particular,)h(for)g (lattice-gas)g(or)h(spin)f(in)o(teractions,)f(one)h(can)h(ha)o(v)o(e)e FE(k)p FQ(\010)p FE(k)1587 160 y Fy(B)1611 150 y Fr(1)1647 152 y FE(\035)g(k)p FQ(\010)p FE(k)1799 160 y Fy(B)1823 150 y Fr(1)1840 160 y FD(=)p Fy(J)60 212 y FQ([351)q(].)133 297 y(In)d(Section)f(4)h(w)o(e)f(shall)h(pro)o(v)o(e)f(that)h(certain)f (renormalized)e(measures)i(are)h(not)g(Gibbsian)g(for)60 357 y(an)o(y)g(in)o(teraction)g(in)g FE(B)484 339 y FH(1)503 357 y FQ(.)21 b(The)14 b(fact)h(that)g(not)g(ev)o(en)e(in)i FE(B)1120 339 y FH(1)1153 357 y FQ(|)f(a)h(space)g(large)g(enough)g(to)g(supp)q(ort)60 417 y(m)o(uc)o(h)e(p)q(eculiar)h(b)q(eha)o(vior)h(|)g(do)q(es)g(an)h(in)o (teraction)e(exist)g(is)h(an)g(indication)g(of)g(ho)o(w)g(strong)h(this)60 477 y(result)g(is.)60 644 y FG(3)83 b(P)n(osition-Space)18 b(Renormalization)d(T)-7 b(ransformations:)184 735 y(Regularit)n(y)26 b(Prop)r(erties)60 845 y FQ(In)16 b(this)g(section)f(w)o(e)h(de\014ne)f(our)i (general)f(framew)o(ork)e(for)i(studying)h(renormalization)d(transfor-)60 905 y(mations)20 b(\(R)l(Ts\),)i(and)f(pro)o(v)o(e)f(the)h(t)o(w)o(o)f(F)l (undamen)o(tal)g(Theorems)f(on)j(single-v)m(aluedness)e(and)60 965 y(con)o(tin)o(uit)o(y)14 b(of)j(the)f(R)l(T)g(map.)133 1025 y(W)l(e)k(consider)g(only)g(a)h FP(single)26 b FQ(application)20 b(of)g(the)g(R)l(T)h(map.)32 b(Therefore,)21 b(the)f(semigroup)60 1085 y(prop)q(ert)o(y)e(of)g(the)g(\\renormalization)e(\(semi\)group")h(pla)o (ys)h(no)g(role)g(for)g(us.)26 b(In)18 b(particular,)f(w)o(e)60 1146 y(need)j(not)i(assume)e(that)h(the)g(image)e(system)h(is)g(of)h(the)g (same)f(t)o(yp)q(e)g(as)i(the)e(original)h(system.)60 1206 y(Nev)o(ertheless,)12 b(w)o(e)i(shall)g(o)q(ccasionally)g(\(b)o(y)g(abuse)h (of)f(language\))i(use)e(the)g(term)e(\\R)o(G)j(map",)f(for)60 1266 y(reasons)j(of)g(familiarit)o(y)c(and)k(brevit)o(y)l(.)60 1410 y FB(3.1)70 b(Basic)22 b(Set-Up)60 1503 y FM(3.1.1)55 b(Renormalization)16 b(T)-5 b(ransformation)18 b(Acting)g(on)h(Measures)60 1595 y FQ(W)l(e)j(consider)g(a)h(\\renormalization)e(map")h FF(T)28 b FQ(from)21 b(an)i FP(original)28 b FQ(\(or)23 b FP(obje)n(ct)5 b FQ(\))23 b FP(system)j FQ(\(\012)e(=)60 1666 y(\012)95 1648 y Fl(Z)116 1636 y Fs(d)95 1678 y FH(0)137 1666 y FF(;)8 b FE(F)d FF(;)j(\026)251 1648 y FH(0)270 1666 y FQ(\))16 b(to)h(an)f FP(image)21 b FQ(\(or)16 b FP(r)n(enormalize)n(d)5 b FQ(\))16 b FP(system)j FQ(\(\012)1181 1648 y Fy(0)1207 1666 y FQ(=)14 b(\012)1294 1648 y Fy(0)p Fl(Z)1325 1636 y Fs(d)1341 1626 y Ft(0)1294 1678 y FH(0)1356 1666 y FF(;)8 b FE(F)1419 1648 y Fy(0)1430 1666 y FF(;)g(\026)1481 1648 y FH(0)1501 1639 y Fy(0)1513 1666 y FQ(\).)21 b(The)16 b(single-spin)60 1726 y(spaces)f(\012)243 1733 y FH(0)278 1726 y FQ(and)h(\012)407 1708 y Fy(0)407 1738 y FH(0)442 1726 y FQ(need)e(not)i(b)q(e)f(the)g(same;)f(indeed,)g(w)o(e)g (will)g(presen)o(t)h(an)g(imp)q(ortan)o(t)f(example)60 1786 y(in)k(whic)o(h)g(they)g(are)h(not)g(the)f(same)g(\(see)g(Example)f(5)i(b)q (elo)o(w,)f(and)h(Section)f(4.3.5\).)29 b(Although)60 1846 y(our)22 b(theory)e(in)h(this)g(section)g(w)o(orks)g(only)g(when)g(the)g (spatial)g(dimensions)f FF(d)h FQ(and)h FF(d)1703 1828 y Fy(0)1736 1846 y FQ(are)f(the)60 1907 y(same)f(|)h(see)f(the)h(discussion)g(of)g (Example)f(7)h(b)q(elo)o(w,)h(as)f(w)o(ell)f(as)i(Section)e(4.5.2)h(|)g(w)o (e)g(\014nd)60 1967 y(it)g(notationally)g(con)o(v)o(enien)o(t)e(to)i(k)o(eep) f(the)h(prime)e(on)j(all)e(image-system)f(quan)o(tities,)h(as)i(this)60 2027 y(mak)o(es)16 b(it)g(easy)i(to)f(see)g(whic)o(h)g(quan)o(tit)o(y)f (refers)h(to)g(whic)o(h)g(system.)23 b(W)l(e)17 b(assume)f(the)h(follo)o (wing)60 2087 y(prop)q(erties)f(for)h FF(T)7 b FQ(:)79 2189 y(T1\))25 b FF(T)e FQ(is)16 b(a)g(probabilit)o(y)g(k)o(ernel)e(from)h(\(\012) p FF(;)8 b FE(F)d FQ(\))16 b(to)h(\(\012)1097 2171 y Fy(0)1109 2189 y FF(;)8 b FE(F)1172 2171 y Fy(0)1183 2189 y FQ(\).)79 2291 y(T2\))25 b FF(T)20 b FQ(carries)13 b(translation-in)o(v)m(arian)o(t)h (measures)e(on)i(\012)g(in)o(to)f(translation-in)o(v)m(arian)o(t)h(measures) 182 2351 y(on)j(\012)285 2333 y Fy(0)297 2351 y FQ(.)k([That)16 b(is,)g(if)g FF(\026)e FE(2)g(M)725 2358 y FD(inv)778 2351 y FQ(\(\012\),)i(then)h FF(\026T)j FE(2)14 b(M)1178 2358 y FD(inv)1232 2351 y FQ(\(\012)1286 2333 y Fy(0)1298 2351 y FQ(\).])79 2452 y(T3\))25 b FF(T)f FQ(is)17 b FP(strictly)j(lo)n(c)n(al)j FQ(in)17 b(p)q(osition)h(space,)g(with)f(asymptotic)g(v)o(olume)e (compression)i(factor)182 2513 y FF(K)h(<)c FE(1)p FQ(.)19 b(More)11 b(precisely)l(,)f(there)h(exist)g(v)m(an)h(Ho)o(v)o(e)e(sequences)h (\(\003)1406 2520 y FD(n)1429 2513 y FQ(\))j FE(\032)f Fq(Z)1545 2492 y FD(d)1576 2513 y FQ(and)f(\(\003)1719 2495 y Fy(0)1719 2525 y FD(n)1743 2513 y FQ(\))i FE(\032)f Fq(Z)1859 2492 y FD(d)1877 2480 y Ft(0)182 2573 y FQ(suc)o(h)j(that:)951 2784 y(76)p eop %%Page: 77 77 bop 203 91 a FQ(\(a\))24 b(The)15 b(b)q(eha)o(vior)g(of)g(the)g(image)e (spins)j(in)e(\003)1073 73 y Fy(0)1073 104 y FD(n)1111 91 y FQ(dep)q(ends)i(only)e(on)i(the)e(original)h(spins)g(in)289 152 y(\003)323 159 y FD(n)347 152 y FQ(,)g(i.e.)404 241 y(F)l(or)h(eac)o(h)g FF(A)e FE(2)g(F)740 220 y Fy(0)735 253 y FH(\003)759 244 y Ft(0)759 262 y Fs(n)782 241 y FF(;)24 b FQ(the)16 b(function)g FF(T)7 b FQ(\()h FE(\001)g FF(;)g(A)p FQ(\))16 b(is)g FE(F)1359 248 y FH(\003)1383 252 y Fs(n)1406 241 y FQ(-measurable.)114 b(\(3)p FF(:)p FQ(1\))200 367 y(\(b\))24 b(lim)8 b(sup)318 402 y FD(n)p Fy(!1)452 340 y FE(j)p FQ(\003)500 347 y FD(n)523 340 y FE(j)p 452 356 86 2 v 452 396 a(j)p FQ(\003)500 376 y Fy(0)500 409 y FD(n)523 396 y FE(j)556 367 y(\024)13 b FF(K)t FQ(.)133 486 y(\(T1\))21 b(allo)o(ws)f(the)g(renormalization)e(map)h(to)i(b)q (e)f(either)f(deterministic)e(or)j(sto)q(c)o(hastic.)33 b(In)60 546 y(the)21 b(deterministic)d(case,)k(the)f(con\014guration)h FF(!)991 528 y Fy(0)1025 546 y FQ(of)f(the)g(image)f(system)g(is)h(a)h FP(function)k FF(!)1818 528 y Fy(0)1852 546 y FQ(=)60 606 y FF(t)p FQ(\()p FF(!)r FQ(\))21 b(of)g(the)g(original)g(con\014guration.)37 b(The)21 b(most)f(conspicuous)i(examples)d(of)i(these)g(t)o(yp)q(e)g(of)60 666 y(transformations)f(are)f(decimation,)f(linear)g(blo)q(c)o(k-spin)i (transformations,)f(and)h(ma)s(jorit)o(y)e(rule)60 727 y(for)23 b(blo)q(c)o(ks)g(with)f(an)i(o)q(dd)f(n)o(um)o(b)q(er)f(of)h(spins)g(\(see)f (Examples)g(1,2)h(and)g(5)g(b)q(elo)o(w\).)41 b(F)l(or)23 b(the)60 787 y(general)18 b(case)g(of)g(a)g(sto)q(c)o(hastic)g(transformation,)g(giv)o (en)f(an)i(original-system)d(con\014guration)j FF(!)r FQ(,)60 847 y(w)o(e)d(c)o(ho)q(ose)g(an)h(image-system)c(con\014guration)k FF(!)983 829 y Fy(0)1011 847 y FQ(with)f(a)h(certain)e(probabilit)o(y)g FF(T)7 b FQ(\()p FF(!)r(;)h(d!)1740 829 y Fy(0)1752 847 y FQ(\).)21 b(The)60 907 y(sp)q(ecial)g(case)g(of)g(a)h(deterministic)c(map)i FF(t)p FQ(:)c(\012)22 b FE(!)g FQ(\012)1061 889 y Fy(0)1094 907 y FQ(corresp)q(onds)h(to)e(setting)g FF(T)7 b FQ(\()p FF(!)r(;)16 b FE(\001)8 b FQ(\))21 b(to)h(b)q(e)60 967 y(the)h(delta-measure)f FF(\016)492 975 y FD(t)p FH(\()p FD(!)q FH(\))581 967 y FQ([i.e.)f(the)i (con\014guration)i FF(!)1106 949 y Fy(0)1144 967 y FQ(=)h FF(t)p FQ(\()p FF(!)r FQ(\))d(is)g(c)o(hosen)h(with)f(probabilit)o(y)60 1028 y(1].)35 b(Examples)19 b(of)i(sto)q(c)o(hastic)g(transformations)g(are)g (the)g(ma)s(jorit)o(y-rule)d(transformation)j(for)60 1088 y(blo)q(c)o(ks)g (with)g(ev)o(en)f(n)o(um)o(b)q(er)g(of)h(spins,)i(and)f(more)e(generally)g (the)h(Kadano\013)i(transformation)60 1148 y(\(see)13 b(Examples)g(2,)h(3)g (and)h(4)f(b)q(elo)o(w\).)20 b(The)14 b(main)f(p)q(oin)o(t)h(of)g(\(T1\))h (is)e(to)h(exclude)f(transformations)60 1208 y(with)j(negativ)o(e)f(w)o(eigh) o(ts,)h(whic)o(h)f(ha)o(v)o(e)h(no)g(sensible)g(probabilistic)f(in)o (terpretation.)1638 1190 y FH(43)133 1268 y FQ(\(T2\))j(is)f (self-explanatory)l(.)23 b(T)o(ypically)15 b(translations)j(of)f(the)g(image) f(system)g(corresp)q(ond)i(to)60 1328 y(some)f FP(sub)n(gr)n(oup)j FQ(of)e(translations)g(of)g(the)f(original)h(system.)24 b(That)18 b(is,)f(there)g(t)o(ypically)f(exists)h(a)60 1389 y(homomorphism)c FF(R)p FQ(:)k Fq(Z)503 1368 y FD(d)521 1356 y Ft(0)548 1389 y FE(!)c Fq(Z)642 1368 y FD(d)678 1389 y FQ(suc)o(h)j(that)689 1478 y FF(T)7 b FQ(\()p FF(T)773 1486 y FD(R)p FH(\()p FD(x)p FH(\))848 1478 y FF(!)r(;)16 b FE(\001)8 b FQ(\))28 b(=)g FF(T)1074 1485 y FD(x)1103 1478 y FF(T)7 b FQ(\()p FF(!)r(;)16 b FE(\001)8 b FQ(\))529 b(\(3)p FF(:)p FQ(2\))60 1574 y(for)19 b(all)f FF(x)f FE(2)h Fq(Z)333 1553 y FD(d)351 1541 y Ft(0)383 1574 y FQ(and)h(all)f FF(!)i FE(2)e FQ(\012.)700 1556 y FH(44)765 1574 y FQ(F)l(or)h(example,)d(a)j(R)l(T)f(emplo)o(ying)f FF(b)12 b FE(\002)g FF(b)18 b FQ(blo)q(c)o(ks)g(will)g(ha)o(v)o(e)60 1634 y FF(R)p FQ(\()p FF(x)p FQ(\))j(=)f FF(bx)p FQ(.)33 b(Th)o(us)21 b(the)f(translation)h(group)g Fq(Z)977 1613 y FD(d)995 1602 y Ft(0)1029 1634 y FQ(of)f(the)g(image)f(system)g(corresp)q(onds)j(to)e(the) 60 1694 y(subgroup)h FF(R)p FQ([)p Fq(Z)357 1674 y FD(d)375 1662 y Ft(0)388 1694 y FQ(])e FE(\032)h Fq(Z)510 1674 y FD(d)550 1694 y FQ(of)g(translations)h(of)f(the)f(original)h(system.)30 b(Prop)q(ert)o(y)20 b(\(T2\))g(trivially)60 1755 y(follo)o(ws)c(from)f(this.) 21 b(Some)15 b(examples)g(are)h(giv)o(en)f(b)q(elo)o(w.)133 1815 y(Prop)q(erties)20 b(\(T1\))g(and)g(\(T2\))g(mak)o(e)d(rigorous)k(the)e (equation)g(\(1.1\):)28 b(the)20 b(map)e FF(\026)i FE(7!)f FF(\026T)26 b FQ(is)60 1875 y(a)19 b(w)o(ell-de\014ned)f(map)g(from)g FE(M)662 1882 y FH(+1)p FD(;inv)771 1875 y FQ(\(\012\))h(in)o(to)g FE(M)1025 1882 y FH(+1)p FD(;inv)1133 1875 y FQ(\(\012)1187 1857 y Fy(0)1199 1875 y FQ(\).)30 b(This)19 b(justi\014es)g(the)f(claim)f (made)60 1935 y(in)g(the)g(In)o(tro)q(duction,)g(that)g(it)g(is)g(easy)g(to)h (de\014ne)f(the)g(R)l(T)g(map)f FP(fr)n(om)h(me)n(asur)n(es)h(to)g(me)n(asur) n(es)t FQ(.)60 1995 y(The)j(more)f(di\016cult)f(and)j(subtle)f(problem)e(of)j (de\014ning)f(the)f(R)l(T)i(map)e FP(fr)n(om)g(inter)n(actions)j(to)60 2056 y(inter)n(actions)e FQ(will)15 b(b)q(e)i(discussed)f(in)g(Section)f (3.1.3.)133 2116 y(Prop)q(ert)o(y)f(\(T3\))h(|)f(the)g FP(strict)19 b FQ(lo)q(calit)o(y)13 b(of)i(the)f(renormalization)e(map)i(|)g(is)g(crucial) f(for)i(our)60 2176 y(pro)q(ofs)h(of)g(the)f(First)g(and)g(Second)g(F)l (undamen)o(tal)f(Theorems.)20 b(Most)15 b(often)g(\(although)h(w)o(e)f(shall) 60 2236 y(not)i(require)e(this\))h(the)g(probabilit)o(y)f(measure)g FF(T)7 b FQ(\()p FF(!)r(;)16 b FE(\001)8 b FQ(\))16 b(has)h(a)g(pro)q(duct)g (structure)640 2326 y FF(T)7 b FQ(\()p FF(!)r(;)h(d!)806 2305 y Fy(0)817 2326 y FQ(\))28 b(=)950 2284 y Fx(Y)929 2384 y FD(x)p Fy(2)p Fl(Z)994 2374 y Fs(d)1010 2367 y Ft(0)1041 2313 y FQ(\024)1032 2326 y FF(T)6 b FQ(\()p FF(!)1116 2333 y FD(B)1143 2337 y Fs(x)1164 2326 y FF(;)i(d!)1243 2305 y Fy(0)1241 2338 y FD(x)1264 2326 y FQ(\))14 b FF(;)479 b FQ(\(3)p FF(:)p FQ(3\))p 60 2418 732 2 v 100 2472 a FA(43)135 2487 y Fz(T)m(ransformations)12 b(with)h(negativ)o (e)h(w)o(eigh)o(ts)g(ha)o(v)o(e)g(o)q(ccasionally)f(b)q(een)j(used)f(in)e (the)i(ph)o(ysics)g(literature,)f(not)60 2537 y(necessarily)g(in)o(ten)o (tionally:)h(see)f(e.g.)e([335)n(].)18 b(See)13 b(also)f(the)h(commen)o(ts)e (in)h([277)o(,)g(fo)q(otnote)g(on)h(p.)f(453)g(and)g(text)h(on)60 2587 y(p.)g(496].)100 2645 y FA(44)135 2660 y Fz(In)h(more)f(detail,)f Fv(T)6 b Fz(\()p Fv(T)487 2667 y Fp(R)p FA(\()p Fp(x)p FA(\))560 2660 y Fv(!)q(;)h(A)p Fz(\))k(=)h Fv(T)6 b Fz(\()p Fv(!)q(;)h(T)830 2645 y Fo(\000)p FA(1)824 2670 y Fp(x)875 2660 y Fz([)p Fv(A)p Fz(]\))13 b(for)g(all)g Fv(x)e Fu(2)h Fq(Z)1185 2636 y Fp(d)1202 2624 y Fe(0)1216 2660 y Fz(,)h Fv(!)g Fu(2)e Fz(\012)j(and)g Fv(A)d Fu(2)g(F)1559 2645 y Fo(0)1571 2660 y Fz(.)951 2784 y FQ(77)p eop %%Page: 78 78 bop 60 91 a FQ(where)20 b FF(B)242 98 y FD(x)284 91 y FQ(is)g(the)g(\014nite) f(set)h(of)h(original)f(spins)g(whic)o(h)g(together)g(determine)d(the)j (image)f(spin)60 152 y FF(!)92 133 y Fy(0)90 164 y FD(x)112 152 y FQ(.)39 b(No)o(w)23 b(let)e(us)i(supp)q(ose)g(that)g FF(B)766 159 y FD(x)812 152 y FQ(=)h FF(B)911 159 y FH(0)945 152 y FQ(+)16 b FF(R)p FQ(\()p FF(x)p FQ(\))22 b([i.e.)e FF(B)1259 159 y FH(0)1301 152 y FQ(translated)j(b)o(y)e FF(R)p FQ(\()p FF(x)p FQ(\)],)i(where)60 212 y FF(R)p FQ(:)17 b Fq(Z)158 191 y FD(d)176 179 y Ft(0)209 212 y FE(!)i Fq(Z)308 191 y FD(d)348 212 y FQ(is)g(a)h(homomorphism)d(satisfying)i(det)8 b FF(R)20 b FE(6)p FQ(=)f(0)h(\(ob)o(viously)f(this)g(needs)h FF(d)1744 194 y Fy(0)1775 212 y FQ(=)f FF(d)p FQ(\).)60 272 y(W)l(e)f(then)g(claim)f (that)i(\(T3\))g(holds)f(with)h FF(K)i FQ(=)d FE(j)8 b FQ(det)g FF(R)p FE(j)p FQ(.)28 b FP(Pr)n(o)n(of:)f FQ(Let)19 b(\(\003)1468 254 y Fy(0)1468 284 y FD(n)1491 272 y FQ(\))g(b)q(e)f(an)o(y)g(v)m(an)h(Ho)o (v)o(e)60 332 y(sequence)h(in)g Fq(Z)358 311 y FD(d)376 299 y Ft(0)390 332 y FQ(.)34 b(What)21 b(sets)g(\(\003)732 339 y FD(n)755 332 y FQ(\))h FE(\032)f Fq(Z)886 311 y FD(d)927 332 y FQ(should)g(w)o(e)f(tak)o(e)g(to)h(satisfy)g(\(T3\)?)36 b(Clearly)19 b(the)60 392 y(image)c(spins)h(in)g(\003)414 399 y FD(n)454 392 y FQ(dep)q(end)g(only)g(on)h(the)f(original)g(spins)g(in)g (the)g(set)g(\003)1431 374 y Fy(\003)1431 405 y FD(n)1468 392 y FE(\021)e FF(R)p FQ([\003)1606 374 y Fy(0)1606 405 y FD(n)1629 392 y FQ(])d(+)g FF(B)1740 399 y FH(0)1773 392 y FE(\032)j Fq(Z)1856 371 y FD(d)1876 392 y FQ(.)60 452 y(So)f(at)h(\014rst)f(one)g(migh) o(t)e(think)i(to)g(tak)o(e)f(\003)818 459 y FD(n)855 452 y FQ(=)i(\003)941 434 y Fy(\003)941 465 y FD(n)965 452 y FQ(.)20 b(The)13 b(trouble)f(is)h(that)g(the)g(\(\003)1542 434 y Fy(\003)1542 465 y FD(n)1565 452 y FQ(\))g(need)g(not)g(form)60 513 y(a)k(v)m(an)g(Ho)o(v) o(e)e(sequence,)g(b)q(ecause)h(they)g(ma)o(y)f(ha)o(v)o(e)h(a)g(nonzero)h (densit)o(y)f(of)g(\\holes".)23 b([Consider,)60 573 y(for)c(example,)e (decimation)g(with)i(spacing)h FF(b)e(>)h FQ(1:)27 b(here)18 b FF(B)1194 580 y FH(0)1233 573 y FQ(=)g FE(f)p FQ(0)p FE(g)h FQ(and)h FF(R)p FQ(\()p FF(x)p FQ(\))f(=)f FF(bx)p FQ(.])29 b(So)19 b(w)o(e)60 633 y(tak)o(e)d(instead)640 693 y(\003)674 700 y FD(n)725 693 y FQ(=)28 b Fq(Z)821 672 y FD(d)861 693 y FE(\\)19 b FQ(con)o(v)o(ex)c(h)o(ull)h(of)g(\003)1259 673 y Fy(\003)1259 706 y FD(n)1296 693 y FF(:)480 b FQ(\(3)p FF(:)p FQ(4\))60 773 y(Then,)18 b(using)h(the)f(fact)g(that)g(det)8 b FF(R)18 b FE(6)p FQ(=)f(0,)h(it)g(is)g(not)g(hard)h(to)f(con)o(vince)f (oneself)h(that)g(\(\003)1754 780 y FD(n)1778 773 y FQ(\))g(is)g(a)60 833 y(v)m(an)f(Ho)o(v)o(e)e(sequence,)f(and)j(that)759 951 y(lim)746 976 y FD(n)p Fy(!1)852 918 y FE(j)p FQ(\003)900 925 y FD(n)923 918 y FE(j)p 852 940 86 2 v 852 986 a(j)p FQ(\003)900 971 y Fy(0)900 998 y FD(n)923 986 y FE(j)969 951 y FQ(=)28 b FE(j)8 b FQ(det)g FF(R)p FE(j)14 b FF(:)578 b FQ(\(3)p FF(:)p FQ(5\))60 1073 y(Tw)o(o)20 b(p)q(oin)o(ts)g(are)g(relev)m(an)o(t)e(here:)28 b(Firstly)l(,)19 b(w)o(e)g(need)g(det)8 b FF(R)20 b FE(6)p FQ(=)g(0)g(\(and)g(in)f(particular)h FF(d)1757 1054 y Fy(0)1788 1073 y FQ(=)g FF(d)p FQ(\))60 1133 y(in)j(order)g(to)h(guaran)o(tee)g(that)f (the)g(sets)h(\(\003)915 1140 y FD(n)938 1133 y FQ(\))f(are)h(su\016cien)o (tly)d(\\fat")j(to)g(form)e(a)i(v)m(an)f(Ho)o(v)o(e)60 1193 y(sequence)f(\(see)g(the)g(discussion)h(of)g(Example)e(7)i(b)q(elo)o(w)f(for) h(what)g(can)g(happ)q(en)h(if)e(this)g(do)q(es)60 1253 y(not)h(hold\).)278 1235 y FH(45)355 1253 y FQ(Secondly)l(,)g(the)f(quan)o(tit)o(y)g FF(K)28 b FE(\021)c FQ(lim)8 b(sup)1151 1265 y FD(n)p Fy(!1)1253 1253 y FE(j)p FQ(\003)1301 1260 y FD(n)1324 1253 y FE(j)p FF(=)p FE(j)p FQ(\003)1410 1235 y Fy(0)1410 1265 y FD(n)1434 1253 y FE(j)22 b FQ(is)g(b)o(y)g(de\014nition)g(the)60 1313 y FP(asymptotic)f FQ(v)o(olume)c(compression)g(factor:)26 b(as)20 b(suc)o(h,)e(it)g(is)h (determined)d(solely)h(b)o(y)h FF(R)p FQ(;)i(it)e(do)q(es)60 1374 y(not)f(dep)q(end)f(on)h(the)f(size)f(of)i FF(B)653 1381 y FH(0)689 1374 y FQ(as)g(long)f(as)h FF(B)951 1381 y FH(0)987 1374 y FQ(is)f(\014nite.)133 1434 y(W)l(e)h FP(c)n(onje)n(ctur)n(e)k FQ(that)d(the)e(t)o(w)o(o)h(F)l(undamen)o(tal)f(Theorems)g(hold)h(also)h(for) f FP(quasilo)n(c)n(al)23 b FQ(renor-)60 1494 y(malization)14 b(maps)i(|)g(i.e.)f(maps)g(in)h(whic)o(h)g FF(!)926 1476 y Fy(0)924 1506 y FD(x)963 1494 y FQ(dep)q(ends)g(su\016cien)o(tly)e FP(we)n(akly)22 b FQ(on)17 b(distan)o(t)f(spins)60 1554 y FF(!)90 1561 y FD(y)129 1554 y FQ(|)i(but)g(w)o(e)f(are)h FP(not)23 b FQ(able)18 b(to)g(pro)o(v)o(e)g(this)f(with)h(our)h(presen)o(t)e(metho)q (ds.)26 b(Quasilo)q(cal)18 b(renor-)60 1614 y(malization)11 b(maps)i(are)g(of)h(great)f(practical)g(imp)q(ortance:)19 b(for)13 b(example,)e(in)i(\\momen)o(tum)o(-space")60 1674 y(renormalization)i(one)h (often)g(uses)h(a)f(deterministic)d(transformation)733 1768 y FF(!)765 1747 y Fy(0)763 1780 y FD(x)813 1768 y FQ(=)878 1726 y Fx(X)899 1813 y FD(y)947 1768 y FF(F)7 b FQ(\()p FF(bx)i FE(\000)i FF(y)r FQ(\))d FF(!)1196 1775 y FD(y)1790 1768 y FQ(\(3)p FF(:)p FQ(6\))60 1896 y(with)15 b(some)f(length)h(rescaling)g (factor)g FF(b)f(>)g FQ(1)h(and)h(some)e(k)o(ernel)g FF(F)7 b FQ(.)20 b(In)15 b(particular,)f(if)h(one)g(uses)h(a)60 1956 y(\\soft")i(cuto\013)g(in)f(momen)o(tum)c(space)18 b([365,)f(31)q(],)f(then)h (the)g(k)o(ernel)f FF(F)24 b FQ(is)17 b FP(r)n(apid)r(ly)g(de)n(cr)n(e)n (asing)22 b FQ(at)60 2016 y(in\014nit)o(y)17 b(in)g FF(x)p FQ(-space)h(\(e.g.)g(decreasing)f(faster)h(than)h(an)o(y)f(in)o(v)o(erse)e(p) q(o)o(w)o(er)i(of)g(its)g(argumen)o(t\).)25 b(It)60 2076 y(is)16 b(an)h(imp)q(ortan)o(t)e FP(op)n(en)j(pr)n(oblem)i FQ(to)c(extend)g(our)h (results)f(to)g(suc)o(h)g(maps.)60 2204 y FM(3.1.2)55 b(Examples)60 2296 y FQ(1\))22 b FP(De)n(cimation)g(tr)n(ansformation)i FQ([210)q(,)d(364)q (].)36 b(Let)22 b(\012)1116 2278 y Fy(0)1150 2296 y FQ(=)h(\012)f(and)g FF(d)1393 2278 y Fy(0)1427 2296 y FQ(=)h FF(d)p FQ(,)f(and)g(let)f FF(b)g FQ(b)q(e)h(an)60 2356 y(in)o(teger)15 b FE(\025)f FQ(2.)21 b(De\014ne)16 b(the)g(deterministic)d(R)l(T)k(map)855 2450 y FF(!)887 2429 y Fy(0)885 2462 y FD(x)935 2450 y FQ(=)27 b FF(!)1030 2457 y FD(bx)1082 2450 y FF(:)694 b FQ(\(3)p FF(:)p FQ(7\))p 60 2491 732 2 v 100 2545 a FA(45)135 2560 y Fz(Actually)m(,)12 b(all)g(w)o(e)h(really)g(need)h(is)f(that)h Fv(R)p Fz(,)e(considered)j(as)e (a)g Fv(d)8 b Fu(\002)g Fv(d)1204 2545 y Fo(0)1229 2560 y Fz(matrix,)j(ha)o (v)o(e)i(rank)g Fv(d)p Fz(.)k(Th)o(us,)d(w)o(e)f(could)60 2610 y(allo)o(w)g(some)g(cases)j(with)e Fv(d)494 2595 y Fo(0)518 2610 y Fv(>)f(d)p Fz(.)19 b(But)c(these)h(are)f(of)f(little)g(in)o(terest.)21 b(The)15 b(in)o(teresting)g(cases)g(with)g Fv(d)1704 2595 y Fo(0)1727 2610 y Fu(6)p Fz(=)e Fv(d)h Fz(ha)o(v)o(e)60 2660 y Fv(d)82 2645 y Fo(0)105 2660 y Fv(<)e(d)h Fz(\(Example)g(7)g(b)q(elo)o (w\),)g(and)h(these)h(do)f Fw(not)k Fz(satisfy)c(\(T3\).)951 2784 y FQ(78)p eop %%Page: 79 79 bop 60 91 a FQ(This)18 b(map)e(is)h(strictly)g(lo)q(cal)g([in)g(fact,)g(of)h (the)f(pro)q(duct)h(form)e(\(3.3\)])i(with)f(asymptotic)f(v)o(olume)60 152 y(compression)f(factor)i FF(K)h FQ(=)13 b FF(b)605 133 y FD(d)625 152 y FQ(.)22 b(It)15 b(is)i(of)f(the)g(form)f(\(3.2\))i(with)f FF(R)p FQ(\()p FF(x)p FQ(\))e(=)g FF(bx)p FQ(.)133 212 y(More)h(generally)l (,)f(let)g(\012)578 194 y Fy(0)603 212 y FQ(=)g(\012)h(and)h FF(d)824 194 y Fy(0)850 212 y FQ(=)e FF(d)h FQ(and)g(let)f FF(R)i FQ(b)q(e)f(an)o(y)g(homomorphism)d(from)i Fq(Z)1800 191 y FD(d)1818 179 y Ft(0)1847 212 y FQ(to)60 272 y Fq(Z)90 251 y FD(d)127 272 y FQ(satisfying)i(det)8 b FF(R)15 b FE(6)p FQ(=)e(0.)22 b(De\014ne)16 b(the)g(deterministic)d(R)l(T)j(map)835 382 y FF(!)867 361 y Fy(0)865 394 y FD(x)915 382 y FQ(=)28 b FF(!)1011 390 y FD(R)p FH(\()p FD(x)p FH(\))1101 382 y FF(:)675 b FQ(\(3)p FF(:)p FQ(8\))60 492 y(This)18 b(map)e(is)h(strictly)g(lo)q(cal)g ([in)g(fact,)g(of)h(the)f(pro)q(duct)h(form)e(\(3.3\)])i(with)f(asymptotic)f (v)o(olume)60 552 y(compression)f(factor)i FF(K)h FQ(=)13 b FE(j)8 b FQ(det)h FF(R)p FE(j)p FQ(.)21 b(Some)15 b(examples)g(are)h(sho)o (wn)h(in)f(Figure)f(2\(a\){\(b\).)133 637 y(2\))21 b FP(Majority-rule)g(tr)n (ansformation)f(for)g(the)i(Ising)f(mo)n(del)26 b FQ([276,)20 b(278)q(,)g(277)q(].)33 b(Let)20 b FF(b)g FQ(b)q(e)h(an)60 697 y(in)o(teger)14 b FE(\025)g FQ(1,)i(let)e FF(B)433 704 y FH(0)469 697 y FQ(b)q(e)h(a)h(\014xed)f(\014nite)g(subset)h(of)g Fq(Z)1049 676 y FD(d)1085 697 y FQ(\(the)f FP(blo)n(ck)5 b FQ(\),)17 b(and)f(let)e FF(B)1543 704 y FD(x)1579 697 y FQ(=)g FF(B)1668 704 y FH(0)1697 697 y FQ(+)c FF(bx)15 b FQ(\(i.e.)60 758 y FF(B)97 765 y FH(0)133 758 y FQ(translated)i(b)o(y)e FF(bx)p FQ(\).)21 b(De\014ne)16 b(the)g(map)652 924 y FF(\033)682 903 y Fy(0)680 936 y FD(x)729 924 y FQ(=)795 824 y Fx(8)795 861 y(>)795 874 y(<)795 949 y(>)795 961 y(:)840 860 y FQ(+1)50 b(if)996 827 y Fx(P)1040 870 y FD(y)q Fy(2)p FD(B)1109 874 y Fs(x)1139 860 y FF(\033)1167 867 y FD(y)1201 860 y FF(>)14 b FQ(0)840 920 y FE(\000)p FQ(1)49 b(if)996 887 y Fx(P)1040 930 y FD(y)q Fy(2)p FD(B)1109 934 y Fs(x)1139 920 y FF(\033)1167 927 y FD(y)1201 920 y FF(<)14 b FQ(0)840 980 y FE(\006)p FQ(1)49 b(if)996 947 y Fx(P)1040 991 y FD(y)q Fy(2)p FD(B)1109 995 y Fs(x)1139 980 y FF(\033)1167 987 y FD(y)1201 980 y FQ(=)14 b(0)1790 924 y(\(3)p FF(:)p FQ(9\))60 1090 y(where)i(\\)p FE(\006)p FQ(1")g(denotes)h(a)f(random)f(c)o(hoice)g(with)h(probabilities)f(of)h(1)p FF(=)p FQ(2)h(eac)o(h.)k(This)16 b(transforma-)60 1150 y(tion)g(is)g (deterministic)d(if)j FF(b)g FQ(is)g(o)q(dd,)h(sto)q(c)o(hastic)f(if)g FF(b)g FQ(is)g(ev)o(en.)133 1235 y(3\))21 b FP(Kadano\013)g(tr)n (ansformation)f(for)h(the)h(Ising)f(mo)n(del)26 b FQ([210].)33 b(A)20 b(large)g(class)h(of)f(nonlinear)60 1295 y(R)l(T)d(maps)g(for)h(the)f (Ising)g(mo)q(del)g(\012)f(=)f(\012)839 1277 y Fy(0)867 1295 y FQ(=)h FE(f\000)p FQ(1)p FF(;)8 b FQ(1)p FE(g)1080 1277 y Fl(Z)1101 1265 y Fs(d)1139 1295 y FQ(can)17 b(b)q(e)h(represen)o(ted)e(in)h (the)g(follo)o(wing)60 1355 y(form:)k(Consider)d(the)e(same)g(blo)q(c)o(ks)h FF(B)793 1362 y FD(x)832 1355 y FQ(as)g(in)g(the)f(previous)h(example,)e(and) i(let)f FF(p)g(>)f FQ(0.)23 b(De\014ne)60 1416 y(the)16 b(sto)q(c)o(hastic)g (R)l(T)h(map)582 1622 y FF(T)7 b FQ(\()p FF(\033)o(;)h(\033)716 1601 y Fy(0)726 1622 y FQ(\))27 b(=)858 1580 y Fx(Y)838 1680 y FD(x)p Fy(2)p Fl(Z)903 1671 y Fs(d)919 1664 y Ft(0)946 1554 y FQ(exp)1029 1481 y Fx( )1061 1554 y FF(p\033)1115 1536 y Fy(0)1113 1566 y FD(x)1166 1521 y Fx(P)1144 1592 y FD(y)q Fy(2)p FD(B)1213 1596 y Fs(x)1240 1554 y FF(\033)1268 1561 y FD(y)1289 1481 y Fx(!)p 945 1610 377 2 v 945 1690 a FQ(2)8 b(cosh)1079 1617 y Fx( )1111 1690 y FF(p)1166 1657 y Fx(P)1144 1728 y FD(y)q Fy(2)p FD(B)1213 1732 y Fs(x)1241 1690 y FF(\033)1269 1697 y FD(y)1289 1617 y Fx(!)1355 1622 y FF(:)396 b FQ(\(3)p FF(:)p FQ(10\))60 1831 y(This)12 b(map)e(is)i(strictly)e(lo)q(cal)h([and)h(clearly)e (of)i(the)f(pro)q(duct)h(form)e(\(3.3\)])i(with)f(asymptotic)f(v)o(olume)60 1891 y(compression)k(factor)h FF(K)i FQ(=)d FF(b)602 1873 y FD(d)622 1891 y FQ(,)h(and)g(is)f(of)h(the)g(form)e(\(3.2\))i(with)g FF(R)p FQ(\()p FF(x)p FQ(\))f(=)g FF(bx)p FQ(.)20 b(Man)o(y)14 b(w)o(ell-kno)o(wn)60 1952 y(R)l(T)i(maps)g(are)g(sp)q(ecial)g(cases)h(of)f (\(3.10\):)95 2053 y(\(a\))25 b(With)18 b FF(B)347 2060 y FH(0)385 2053 y FQ(=)g FE(f)p FQ(0)p FE(g)h FQ(and)g FF(b)f FQ(=)g(1,)h(\(3.10\))g(is) g(mo)q(del)e(I)h(of)h(Gri\016ths)g(and)g(P)o(earce)f([172)q(,)g(173)q(],)182 2113 y(a)h(kind)g(of)g(\\cop)o(ying)g(with)g(noise".)29 b(\(This)19 b(map)f(also)i(arises)f(in)f(applications)h(to)g(image)182 2174 y(pro)q(cessing)e([129)q(,)e(152)r(].\))20 b(As)c FF(p)f FE(!)e(1)j FQ(it)g(tends)h(to)f(the)g(iden)o(tit)o(y)e(transformation.)93 2275 y(\(b\))24 b(With)15 b FF(B)344 2282 y FH(0)378 2275 y FQ(=)e FE(f)p FQ(0)p FE(g)j FQ(and)g FF(b)e FE(\025)f FQ(2,)j(\(3.10\))g(is)f (mo)q(del)f(I)q(I)h(of)g(Gri\016ths)h(and)g(P)o(earce)e([172)q(,)h(173)q(],)g (a)182 2336 y(kind)h(of)g(\\decimation)f(with)h(noise".)22 b(As)16 b FF(p)e FE(!)g(1)i FQ(it)g(tends)g(to)g(the)h(ordinary)f(decimation) 182 2396 y(transformation)g(\(3.7\).)98 2497 y(\(c\))24 b(With)d FF(B)350 2504 y FH(0)391 2497 y FQ(=)g FE(f)p FQ(0)p FF(;)8 b FQ(1)p FF(;)g(:)g(:)g(:)g(;)g(b)14 b FE(\000)g FQ(1)p FE(g)792 2479 y FD(d)833 2497 y FQ(\(a)22 b(h)o(yp)q(ercub)q(e)e(of)h(side)g FF(b)p FQ(\))f(and)h FF(b)h FE(\025)f FQ(2,)h(\(3.10\))g(is)e(the)182 2558 y(Kadano\013)e(transformation)e([210].)21 b(In)16 b(the)g(limit)d FF(p)h FE(!)g(1)i FQ(it)f(tends)h(to)h(the)f(ma)s(jorit)o(y-rule)182 2618 y(transformation)g(\(3.9\).)951 2784 y(79)p eop %%Page: 80 80 bop 574 380 a @beginspecial 33 @llx 42.500000 @lly 119 @urx 147.500000 @ury 658 @rwi @setspecial %%BeginDocument: fig2a.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 64.4493 138.9931 m S 64.4493 116.7645 m S 41.6392 116.7645 m S 41.6392 138.9931 m S 53.0442 127.8788 m S u 110.0696 94.5358 m S 110.0696 72.3072 m S 87.2595 72.3072 m S 87.2595 94.5358 m S 98.6645 83.4215 m S U u 87.2595 116.7645 m S 87.2595 94.5358 m S 64.4493 94.5358 m S 64.4493 116.7645 m S 75.8544 105.6502 m S U 87.2595 138.9931 m S 87.2595 116.7645 m S 64.4493 116.7645 m S 64.4493 138.9931 m S 75.8544 127.8788 m S 110.0696 138.9931 m S 110.0696 116.7645 m S 87.2595 116.7645 m S 87.2595 138.9931 m S 98.6645 127.8788 m S u 110.0696 116.7645 m S 110.0696 94.5358 m S 87.2595 94.5358 m S 87.2595 116.7645 m S 98.6645 105.6502 m S U u 87.2595 94.5358 m S 87.2595 72.3072 m S 64.4493 72.3072 m S 64.4493 94.5358 m S 75.8544 83.4215 m S U u 64.4493 94.5358 m S 64.4493 72.3072 m S 41.6392 72.3072 m S 41.6392 94.5358 m S 53.0442 83.4215 m S U u 64.4493 116.7645 m S 64.4493 94.5358 m S 41.6392 94.5358 m S 41.6392 116.7645 m S 53.0442 105.6502 m S U 0 g 1 w 4 M 53.0442 127.8788 m F 98.6645 127.8788 m F 53.0442 83.4215 m F 98.6645 83.4215 m F 0 G 0.3 w 10 M 110.0696 116.7645 m S 110.0696 138.9931 m S 110.0696 72.3072 m S 110.0696 94.5358 m S 110.0696 94.5358 m S 110.0696 116.7645 m S 64.4493 72.3072 m S 41.6392 72.3072 m S 53.0442 61.1929 m S 87.2595 72.3072 m S 64.4493 72.3072 m S 75.8544 61.1929 m S 110.0696 72.3072 m S 87.2595 72.3072 m S 98.6645 61.1929 m S 0 g 1 w 4 M 53.0442 61.1929 m F 98.6645 61.1929 m F 0 G 0.3 w 10 M 110.0696 72.3072 m S 41.6392 138.9931 m S 1 g 1 w 4 M 41.6392 134.1848 m 44.4509 134.1848 46.7303 136.3376 46.7303 138.9931 c 46.7303 141.6486 44.4509 143.8014 41.6392 143.8014 c 38.8275 143.8014 36.5481 141.6486 36.5481 138.9931 c 36.5481 136.3376 38.8275 134.1848 41.6392 134.1848 c b 0 g 41.6392 138.9931 m F 0 G 0.3 w 10 M 64.4493 138.9931 m S 1 g 1 w 4 M 64.4493 134.1848 m 67.261 134.1848 69.5404 136.3376 69.5404 138.9931 c 69.5404 141.6486 67.261 143.8014 64.4493 143.8014 c 61.6376 143.8014 59.3582 141.6486 59.3582 138.9931 c 59.3582 136.3376 61.6376 134.1848 64.4493 134.1848 c b 0 g 64.4493 138.9931 m F 0 G 0.3 w 10 M 87.2595 138.9931 m S 1 g 1 w 4 M 87.2595 134.1848 m 90.0712 134.1848 92.3506 136.3376 92.3506 138.9931 c 92.3506 141.6486 90.0712 143.8014 87.2595 143.8014 c 84.4478 143.8014 82.1684 141.6486 82.1684 138.9931 c 82.1684 136.3376 84.4478 134.1848 87.2595 134.1848 c b 0 g 87.2595 138.9931 m F 0 G 0.3 w 10 M 110.0696 138.9931 m S 1 g 1 w 4 M 110.0696 134.1848 m 112.8813 134.1848 115.1607 136.3376 115.1607 138.9931 c 115.1607 141.6486 112.8813 143.8014 110.0696 143.8014 c 107.2579 143.8014 104.9785 141.6486 104.9785 138.9931 c 104.9785 136.3376 107.2579 134.1848 110.0696 134.1848 c b 0 g 110.0696 138.9931 m F 0 G 0.3 w 10 M 64.4493 116.7645 m S 41.6392 116.7645 m S 87.2595 116.7645 m S 64.4493 116.7645 m S 110.0696 116.7645 m S 87.2595 116.7645 m S 110.0696 116.7645 m S 41.6392 116.7645 m S 0 g 1 w 4 M 41.6392 111.9562 m 44.4509 111.9562 46.7303 114.109 46.7303 116.7645 c 46.7303 119.42 44.4509 121.5728 41.6392 121.5728 c 38.8275 121.5728 36.5481 119.42 36.5481 116.7645 c 36.5481 114.109 38.8275 111.9562 41.6392 111.9562 c b 41.6392 116.7645 m F 0 G 0.3 w 10 M 64.4493 116.7645 m S 1 g 1 w 4 M 64.4493 111.9562 m 67.261 111.9562 69.5404 114.109 69.5404 116.7645 c 69.5404 119.42 67.261 121.5728 64.4493 121.5728 c 61.6376 121.5728 59.3582 119.42 59.3582 116.7645 c 59.3582 114.109 61.6376 111.9562 64.4493 111.9562 c b 0 g 64.4493 116.7645 m F 0 G 0.3 w 10 M 87.2595 116.7645 m S 0 g 1 w 4 M 87.2595 111.9562 m 90.0712 111.9562 92.3506 114.109 92.3506 116.7645 c 92.3506 119.42 90.0712 121.5728 87.2595 121.5728 c 84.4478 121.5728 82.1684 119.42 82.1684 116.7645 c 82.1684 114.109 84.4478 111.9562 87.2595 111.9562 c b 87.2595 116.7645 m F 0 G 0.3 w 10 M 110.0696 116.7645 m S 1 g 1 w 4 M 110.0696 111.9562 m 112.8813 111.9562 115.1607 114.109 115.1607 116.7645 c 115.1607 119.42 112.8813 121.5728 110.0696 121.5728 c 107.2579 121.5728 104.9785 119.42 104.9785 116.7645 c 104.9785 114.109 107.2579 111.9562 110.0696 111.9562 c b 0 g 110.0696 116.7645 m F 0 G 0.3 w 10 M 64.4493 94.5358 m S 41.6392 94.5358 m S 87.2595 94.5358 m S 64.4493 94.5358 m S 110.0696 94.5358 m S 87.2595 94.5358 m S 110.0696 94.5358 m S 41.6392 94.5358 m S 1 g 1 w 4 M 41.6392 89.7275 m 44.4509 89.7275 46.7303 91.8803 46.7303 94.5358 c 46.7303 97.1913 44.4509 99.3441 41.6392 99.3441 c 38.8275 99.3441 36.5481 97.1913 36.5481 94.5358 c 36.5481 91.8803 38.8275 89.7275 41.6392 89.7275 c b 0 g 41.6392 94.5358 m F 0 G 0.3 w 10 M 64.4493 94.5358 m S 1 g 1 w 4 M 64.4493 89.7275 m 67.261 89.7275 69.5404 91.8803 69.5404 94.5358 c 69.5404 97.1913 67.261 99.3441 64.4493 99.3441 c 61.6376 99.3441 59.3582 97.1913 59.3582 94.5358 c 59.3582 91.8803 61.6376 89.7275 64.4493 89.7275 c b 0 g 64.4493 94.5358 m F 0 G 0.3 w 10 M 87.2595 94.5358 m S 1 g 1 w 4 M 87.2595 89.7275 m 90.0712 89.7275 92.3506 91.8803 92.3506 94.5358 c 92.3506 97.1913 90.0712 99.3441 87.2595 99.3441 c 84.4478 99.3441 82.1684 97.1913 82.1684 94.5358 c 82.1684 91.8803 84.4478 89.7275 87.2595 89.7275 c b 0 g 87.2595 94.5358 m F 0 G 0.3 w 10 M 110.0696 94.5358 m S 1 g 1 w 4 M 110.0696 89.7275 m 112.8813 89.7275 115.1607 91.8803 115.1607 94.5358 c 115.1607 97.1913 112.8813 99.3441 110.0696 99.3441 c 107.2579 99.3441 104.9785 97.1913 104.9785 94.5358 c 104.9785 91.8803 107.2579 89.7275 110.0696 89.7275 c b 0 g 110.0696 94.5358 m F 0 G 0.3 w 10 M 64.4493 72.3072 m S 41.6392 72.3072 m S 87.2595 72.3072 m S 64.4493 72.3072 m S 110.0696 72.3072 m S 87.2595 72.3072 m S 110.0696 72.3072 m S 41.6392 72.3072 m S 0 g 1 w 4 M 41.6392 67.4989 m 44.4509 67.4989 46.7303 69.6517 46.7303 72.3072 c 46.7303 74.9627 44.4509 77.1155 41.6392 77.1155 c 38.8275 77.1155 36.5481 74.9627 36.5481 72.3072 c 36.5481 69.6517 38.8275 67.4989 41.6392 67.4989 c b 41.6392 72.3072 m F 0 G 0.3 w 10 M 64.4493 72.3072 m S 1 g 1 w 4 M 64.4493 67.4989 m 67.261 67.4989 69.5404 69.6517 69.5404 72.3072 c 69.5404 74.9627 67.261 77.1155 64.4493 77.1155 c 61.6376 77.1155 59.3582 74.9627 59.3582 72.3072 c 59.3582 69.6517 61.6376 67.4989 64.4493 67.4989 c b 0 g 64.4493 72.3072 m F 0 G 0.3 w 10 M 87.2595 72.3072 m S 0 g 1 w 4 M 87.2595 67.4989 m 90.0712 67.4989 92.3506 69.6517 92.3506 72.3072 c 92.3506 74.9627 90.0712 77.1155 87.2595 77.1155 c 84.4478 77.1155 82.1684 74.9627 82.1684 72.3072 c 82.1684 69.6517 84.4478 67.4989 87.2595 67.4989 c b 87.2595 72.3072 m F 0 G 0.3 w 10 M 110.0696 72.3072 m S 1 g 1 w 4 M 110.0696 67.4989 m 112.8813 67.4989 115.1607 69.6517 115.1607 72.3072 c 115.1607 74.9627 112.8813 77.1155 110.0696 77.1155 c 107.2579 77.1155 104.9785 74.9627 104.9785 72.3072 c 104.9785 69.6517 107.2579 67.4989 110.0696 67.4989 c b 0 g 110.0696 72.3072 m F u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 70 46]e (\(a\))t T U U showpage _E end %%EndDocument @endspecial 527 w @beginspecial 31 @llx 32.500000 @lly 117 @urx 137.500000 @ury 658 @rwi @setspecial %%BeginDocument: fig2b.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 39.5 128.9931 m S 62.3101 128.9931 m S 39.5 128.9931 m S 85.1203 128.9931 m S 62.3101 128.9931 m S 107.9304 128.9931 m S 85.1203 128.9931 m S 107.9304 128.9931 m S 62.3101 128.9931 m S 62.3101 106.7645 m S 39.5 106.7645 m S 39.5 128.9931 m S 50.905 117.8788 m S 107.9304 84.5358 m S 107.9304 62.3072 m S 85.1203 62.3072 m S 85.1203 84.5358 m S 96.5253 73.4215 m S u 85.1203 106.7645 m S 85.1203 84.5358 m S 62.3101 84.5358 m S 62.3101 106.7645 m S 73.7152 95.6502 m S U 85.1203 128.9931 m S 85.1203 106.7645 m S 62.3101 106.7645 m S 62.3101 128.9931 m S 73.7152 117.8788 m S 107.9304 128.9931 m S 107.9304 106.7645 m S 85.1203 106.7645 m S 85.1203 128.9931 m S 96.5253 117.8788 m S u 107.9304 106.7645 m S 107.9304 84.5358 m S 85.1203 84.5358 m S 85.1203 106.7645 m S 96.5253 95.6502 m S U 85.1203 84.5358 m S 85.1203 62.3072 m S 62.3101 62.3072 m S 62.3101 84.5358 m S 73.7152 73.4215 m S u 62.3101 84.5358 m S 62.3101 62.3072 m S 39.5 62.3072 m S 39.5 84.5358 m S 50.905 73.4215 m S U u 62.3101 106.7645 m S 62.3101 84.5358 m S 39.5 84.5358 m S 39.5 106.7645 m S 50.905 95.6502 m S U 0 g 1 w 4 M 50.905 117.8788 m F 96.5253 117.8788 m F 50.905 73.4215 m F 96.5253 73.4215 m F 0 G 0.3 w 10 M 107.9304 106.7645 m S 107.9304 128.9931 m S u 62.3101 62.3072 m S 62.3101 40.0785 m S 39.5 40.0785 m S 39.5 62.3072 m S 50.905 51.1929 m S U 85.1203 62.3072 m S 85.1203 40.0785 m S 62.3101 40.0785 m S 62.3101 62.3072 m S 73.7152 51.1929 m S 107.9304 62.3072 m S 107.9304 40.0785 m S 85.1203 40.0785 m S 85.1203 62.3072 m S 96.5253 51.1929 m S 39.5 128.9931 m S 1 g 1 w 4 M 39.5 124.1848 m 42.3117 124.1848 44.5911 126.3376 44.5911 128.9931 c 44.5911 131.6486 42.3117 133.8014 39.5 133.8014 c 36.6883 133.8014 34.4089 131.6486 34.4089 128.9931 c 34.4089 126.3376 36.6883 124.1848 39.5 124.1848 c b 0 g 39.5 128.9931 m F 0 G 0.3 w 10 M 62.3101 128.9931 m S 0 g 1 w 4 M 62.3101 124.1848 m 65.1218 124.1848 67.4012 126.3376 67.4012 128.9931 c 67.4012 131.6486 65.1218 133.8014 62.3101 133.8014 c 59.4984 133.8014 57.219 131.6486 57.219 128.9931 c 57.219 126.3376 59.4984 124.1848 62.3101 124.1848 c b 62.3101 128.9931 m F 0 G 0.3 w 10 M 85.1203 128.9931 m S 1 g 1 w 4 M 85.1203 124.1848 m 87.932 124.1848 90.2114 126.3376 90.2114 128.9931 c 90.2114 131.6486 87.932 133.8014 85.1203 133.8014 c 82.3086 133.8014 80.0292 131.6486 80.0292 128.9931 c 80.0292 126.3376 82.3086 124.1848 85.1203 124.1848 c b 0 g 85.1203 128.9931 m F 0 G 0.3 w 10 M 107.9304 128.9931 m S 0 g 1 w 4 M 107.9304 124.1848 m 110.7421 124.1848 113.0215 126.3376 113.0215 128.9931 c 113.0215 131.6486 110.7421 133.8014 107.9304 133.8014 c 105.1187 133.8014 102.8393 131.6486 102.8393 128.9931 c 102.8393 126.3376 105.1187 124.1848 107.9304 124.1848 c b 107.9304 128.9931 m F 0 G 0.3 w 10 M 62.3101 106.7645 m S 39.5 106.7645 m S 85.1203 106.7645 m S 62.3101 106.7645 m S 107.9304 106.7645 m S 85.1203 106.7645 m S 107.9304 106.7645 m S 39.5 106.7645 m S 0 g 1 w 4 M 39.5 101.9562 m 42.3117 101.9562 44.5911 104.109 44.5911 106.7645 c 44.5911 109.42 42.3117 111.5728 39.5 111.5728 c 36.6883 111.5728 34.4089 109.42 34.4089 106.7645 c 34.4089 104.109 36.6883 101.9562 39.5 101.9562 c b 39.5 106.7645 m F 0 G 0.3 w 10 M 62.3101 106.7645 m S 1 g 1 w 4 M 62.3101 101.9562 m 65.1218 101.9562 67.4012 104.109 67.4012 106.7645 c 67.4012 109.42 65.1218 111.5728 62.3101 111.5728 c 59.4984 111.5728 57.219 109.42 57.219 106.7645 c 57.219 104.109 59.4984 101.9562 62.3101 101.9562 c b 0 g 62.3101 106.7645 m F 0 G 0.3 w 10 M 85.1203 106.7645 m S 0 g 1 w 4 M 85.1203 101.9562 m 87.932 101.9562 90.2114 104.109 90.2114 106.7645 c 90.2114 109.42 87.932 111.5728 85.1203 111.5728 c 82.3086 111.5728 80.0292 109.42 80.0292 106.7645 c 80.0292 104.109 82.3086 101.9562 85.1203 101.9562 c b 85.1203 106.7645 m F 0 G 0.3 w 10 M 107.9304 106.7645 m S 1 g 1 w 4 M 107.9304 101.9562 m 110.7421 101.9562 113.0215 104.109 113.0215 106.7645 c 113.0215 109.42 110.7421 111.5728 107.9304 111.5728 c 105.1187 111.5728 102.8393 109.42 102.8393 106.7645 c 102.8393 104.109 105.1187 101.9562 107.9304 101.9562 c b 0 g 107.9304 106.7645 m F 0 G 0.3 w 10 M 62.3101 84.5358 m S 39.5 84.5358 m S 85.1203 84.5358 m S 62.3101 84.5358 m S 107.9304 84.5358 m S 85.1203 84.5358 m S 107.9304 84.5358 m S 39.5 84.5358 m S 1 g 1 w 4 M 39.5 79.7275 m 42.3117 79.7275 44.5911 81.8803 44.5911 84.5358 c 44.5911 87.1913 42.3117 89.3441 39.5 89.3441 c 36.6883 89.3441 34.4089 87.1913 34.4089 84.5358 c 34.4089 81.8803 36.6883 79.7275 39.5 79.7275 c b 0 g 39.5 84.5358 m F 0 G 0.3 w 10 M 62.3101 84.5358 m S 0 g 1 w 4 M 62.3101 79.7275 m 65.1218 79.7275 67.4012 81.8803 67.4012 84.5358 c 67.4012 87.1913 65.1218 89.3441 62.3101 89.3441 c 59.4984 89.3441 57.219 87.1913 57.219 84.5358 c 57.219 81.8803 59.4984 79.7275 62.3101 79.7275 c b 62.3101 84.5358 m F 0 G 0.3 w 10 M 85.1203 84.5358 m S 1 g 1 w 4 M 85.1203 79.7275 m 87.932 79.7275 90.2114 81.8803 90.2114 84.5358 c 90.2114 87.1913 87.932 89.3441 85.1203 89.3441 c 82.3086 89.3441 80.0292 87.1913 80.0292 84.5358 c 80.0292 81.8803 82.3086 79.7275 85.1203 79.7275 c b 0 g 85.1203 84.5358 m F 0 G 0.3 w 10 M 107.9304 84.5358 m S 0 g 1 w 4 M 107.9304 79.7275 m 110.7421 79.7275 113.0215 81.8803 113.0215 84.5358 c 113.0215 87.1913 110.7421 89.3441 107.9304 89.3441 c 105.1187 89.3441 102.8393 87.1913 102.8393 84.5358 c 102.8393 81.8803 105.1187 79.7275 107.9304 79.7275 c b 107.9304 84.5358 m F 0 G 0.3 w 10 M 62.3101 62.3072 m S 39.5 62.3072 m S 85.1203 62.3072 m S 62.3101 62.3072 m S 107.9304 62.3072 m S 85.1203 62.3072 m S 107.9304 62.3072 m S 39.5 62.3072 m S 0 g 1 w 4 M 39.5 57.4989 m 42.3117 57.4989 44.5911 59.6517 44.5911 62.3072 c 44.5911 64.9627 42.3117 67.1155 39.5 67.1155 c 36.6883 67.1155 34.4089 64.9627 34.4089 62.3072 c 34.4089 59.6517 36.6883 57.4989 39.5 57.4989 c b 39.5 62.3072 m F 0 G 0.3 w 10 M 62.3101 62.3072 m S 1 g 1 w 4 M 62.3101 57.4989 m 65.1218 57.4989 67.4012 59.6517 67.4012 62.3072 c 67.4012 64.9627 65.1218 67.1155 62.3101 67.1155 c 59.4984 67.1155 57.219 64.9627 57.219 62.3072 c 57.219 59.6517 59.4984 57.4989 62.3101 57.4989 c b 0 g 62.3101 62.3072 m F 0 G 0.3 w 10 M 85.1203 62.3072 m S 0 g 1 w 4 M 85.1203 57.4989 m 87.932 57.4989 90.2114 59.6517 90.2114 62.3072 c 90.2114 64.9627 87.932 67.1155 85.1203 67.1155 c 82.3086 67.1155 80.0292 64.9627 80.0292 62.3072 c 80.0292 59.6517 82.3086 57.4989 85.1203 57.4989 c b 85.1203 62.3072 m F 0 G 0.3 w 10 M 107.9304 62.3072 m S 1 g 1 w 4 M 107.9304 57.4989 m 110.7421 57.4989 113.0215 59.6517 113.0215 62.3072 c 113.0215 64.9627 110.7421 67.1155 107.9304 67.1155 c 105.1187 67.1155 102.8393 64.9627 102.8393 62.3072 c 102.8393 59.6517 105.1187 57.4989 107.9304 57.4989 c b 0 g 107.9304 62.3072 m F u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 67.5 35.5]e (\(b\))t T U U showpage _E end %%EndDocument @endspecial 609 836 a @beginspecial 30 @llx 32.500000 @lly 241 @urx 135.500000 @ury 1756 @rwi @setspecial %%BeginDocument: fig2c.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n []/_Symbol/Symbol Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 38.6392 127.6213 m S 0 g 1 w 4 M 50.0442 116.507 m F 0 G 0.3 w 10 M 61.4493 127.6213 m S 61.4493 105.3927 m S 38.6392 105.3927 m S 38.6392 127.6213 m S 50.0442 116.507 m S 107.0696 83.164 m S 107.0696 60.9354 m S 84.2595 60.9354 m S 84.2595 83.164 m S 95.6645 72.0497 m S 84.2595 83.164 m S 61.4493 83.164 m S 61.4493 105.3927 m S 72.8544 94.2784 m S 61.4493 105.3927 m S 61.4493 127.6213 m S 107.0696 83.164 m S 84.2595 83.164 m S 95.6645 94.2784 m S 84.2595 83.164 m S 84.2595 60.9354 m S 61.4493 60.9354 m S 61.4493 83.164 m S 72.8544 72.0497 m S 61.4493 83.164 m S 61.4493 60.9354 m S 38.6392 60.9354 m S 38.6392 83.164 m S 50.0442 72.0497 m S 61.4493 105.3927 m S 61.4493 83.164 m S 38.6392 83.164 m S 38.6392 105.3927 m S 50.0442 94.2784 m S 0 g 1 w 4 M 50.0442 116.507 m F 50.0442 72.0497 m F 95.6645 72.0497 m F 0 G 0.3 w 10 M 129.8797 127.6213 m S 129.8797 105.3927 m S 118.4746 116.507 m S 198.3101 83.164 m S 198.3101 60.9354 m S 175.5 60.9354 m S 175.5 83.164 m S 186.905 72.0497 m S u 152.6899 105.3927 m S 152.6899 83.164 m S 129.8797 83.164 m S 129.8797 105.3927 m S 141.2848 94.2784 m S U u 152.6899 127.6213 m S 152.6899 105.3927 m S 129.8797 105.3927 m S 129.8797 127.6213 m S 141.2848 116.507 m S U u 198.3101 127.6213 m S 198.3101 105.3927 m S 175.5 105.3927 m S 175.5 127.6213 m S 186.905 116.507 m S U u 198.3101 105.3927 m S 198.3101 83.164 m S 175.5 83.164 m S 175.5 105.3927 m S 186.905 94.2784 m S U u 152.6899 83.164 m S 152.6899 60.9354 m S 129.8797 60.9354 m S 129.8797 83.164 m S 141.2848 72.0497 m S U 129.8797 83.164 m S 129.8797 60.9354 m S 107.0696 60.9354 m S 107.0696 83.164 m S 118.4746 72.0497 m S 129.8797 105.3927 m S 129.8797 83.164 m S 107.0696 83.164 m S 118.4746 94.2784 m S 0 g 1 w 4 M 118.4746 116.507 m F 186.905 116.507 m F 118.4746 72.0497 m F 186.905 72.0497 m F u 0 G 0.3 w 10 M 221.1202 127.6213 m S 221.1202 105.3927 m S 198.3101 105.3927 m S 198.3101 127.6213 m S 209.7151 116.507 m S U 221.1202 83.164 m S 221.1202 105.3927 m S 232.5253 94.2784 m S 221.1202 105.3927 m S 221.1202 127.6213 m S 232.5253 116.507 m S 221.1202 60.9354 m S 221.1202 83.164 m S 232.5253 72.0497 m S u 221.1202 83.164 m S 221.1202 60.9354 m S 198.3101 60.9354 m S 198.3101 83.164 m S 209.7151 72.0497 m S U u 221.1202 105.3927 m S 221.1202 83.164 m S 198.3101 83.164 m S 198.3101 105.3927 m S 209.7151 94.2784 m S U 0 g 1 w 4 M 209.7151 116.507 m F 209.7151 72.0497 m F 0 G 0.3 w 10 M 61.4493 60.9354 m S 61.4493 38.7067 m S 38.6392 38.7067 m S 38.6392 60.9354 m S 50.0442 49.8211 m S 84.2595 60.9354 m S 84.2595 38.7067 m S 61.4493 38.7067 m S 61.4493 60.9354 m S 72.8544 49.8211 m S 107.0696 60.9354 m S 107.0696 38.7067 m S 84.2595 38.7067 m S 84.2595 60.9354 m S 95.6645 49.8211 m S 0 g 1 w 4 M 50.0442 49.8211 m F 95.6645 49.8211 m F 0 G 0.3 w 10 M 129.8797 60.9354 m S 129.8797 38.7067 m S 107.0696 38.7067 m S 107.0696 60.9354 m S 118.4746 49.8211 m S 152.6899 60.9354 m S 152.6899 38.7067 m S 129.8797 38.7067 m S 129.8797 60.9354 m S 141.2848 49.8211 m S u 175.5 60.9354 m S 175.5 38.7067 m S 152.6899 38.7067 m S 152.6899 60.9354 m S 164.0949 49.8211 m S U 0 g 1 w 4 M 118.4746 49.8211 m F 164.0949 49.8211 m F u 0 G 0.3 w 10 M 198.3101 60.9354 m S 198.3101 38.7067 m S 175.5 38.7067 m S 175.5 60.9354 m S 186.905 49.8211 m S U u 221.1203 60.9354 m S 221.1203 38.7067 m S 198.3101 38.7067 m S 198.3101 60.9354 m S 209.7152 49.8211 m S U 0 g 1 w 4 M 186.905 49.8211 m F 0 G 0.3 w 10 M 38.6392 127.6213 m S 0 g 1 w 4 M 38.6392 127.6213 m F 0 G 0.3 w 10 M 61.4493 127.6213 m S 0 g 1 w 4 M 61.4493 127.6213 m F 0 G 0.3 w 10 M 61.4493 105.3927 m S 38.6392 105.3927 m S 61.4493 105.3927 m S 38.6392 105.3927 m S 0 g 1 w 4 M 38.6392 105.3927 m F 0 G 0.3 w 10 M 61.4493 105.3927 m S 0 g 1 w 4 M 61.4493 105.3927 m F 0 G 0.3 w 10 M 61.4493 83.164 m S 38.6392 83.164 m S 84.2595 83.164 m S 61.4493 83.164 m S 107.0696 83.164 m S 84.2595 83.164 m S 107.0696 83.164 m S 38.6392 83.164 m S 0 g 1 w 4 M 38.6392 83.164 m F 0 G 0.3 w 10 M 61.4493 83.164 m S 0 g 1 w 4 M 61.4493 83.164 m F 0 G 0.3 w 10 M 84.2595 83.164 m S 0 g 1 w 4 M 84.2595 83.164 m F 0 G 0.3 w 10 M 107.0696 83.164 m S 0 g 1 w 4 M 107.0696 83.164 m F 0 G 0.3 w 10 M 61.4493 60.9354 m S 38.6392 60.9354 m S 84.2595 60.9354 m S 61.4493 60.9354 m S 107.0696 60.9354 m S 84.2595 60.9354 m S 107.0696 60.9354 m S 38.6392 60.9354 m S 0 g 1 w 4 M 38.6392 60.9354 m F 0 G 0.3 w 10 M 61.4493 60.9354 m S 0 g 1 w 4 M 61.4493 60.9354 m F 0 G 0.3 w 10 M 84.2595 60.9354 m S 0 g 1 w 4 M 84.2595 60.9354 m F 0 G 0.3 w 10 M 107.0696 60.9354 m S 0 g 1 w 4 M 107.0696 60.9354 m F 0.7 g 38.6392 127.6213 m 61.4493 127.6213 l 61.4493 105.3927 l 38.6392 105.3927 l 38.6392 127.6213 l f 0 G 0.3 w 10 M 61.4493 127.6213 m S 61.4493 105.3927 m S 61.4493 127.6213 m S 61.4493 127.6213 m S 61.4493 105.3927 m S 38.6392 105.3927 m S 38.6392 127.6213 m S 50.0442 116.507 m S 61.4493 127.6213 m S 38.6392 127.6213 m S 0 g 1 w 4 M 50.0442 116.507 m F 0 G 0.3 w 10 M 61.4493 105.3927 m S 38.6392 105.3927 m S 61.4493 105.3927 m S 61.4493 127.6213 m S 38.6392 127.6213 m S 61.4493 127.6213 m S 38.6392 127.6213 m S 1 g 1 w 4 M 38.6392 122.813 m 41.4509 122.813 43.7303 124.9658 43.7303 127.6213 c 43.7303 130.2768 41.4509 132.4296 38.6392 132.4296 c 35.8275 132.4296 33.5481 130.2768 33.5481 127.6213 c 33.5481 124.9658 35.8275 122.813 38.6392 122.813 c b 0 g 38.6392 127.6213 m F 0 G 0.3 w 10 M 61.4493 127.6213 m S 1 g 1 w 4 M 61.4493 122.813 m 64.261 122.813 66.5404 124.9658 66.5404 127.6213 c 66.5404 130.2768 64.261 132.4296 61.4493 132.4296 c 58.6376 132.4296 56.3582 130.2768 56.3582 127.6213 c 56.3582 124.9658 58.6376 122.813 61.4493 122.813 c b 0 g 61.4493 127.6213 m F 0 G 0.3 w 10 M 61.4493 105.3927 m S 38.6392 105.3927 m S 61.4493 105.3927 m S 38.6392 105.3927 m S 1 g 1 w 4 M 38.6392 100.5844 m 41.4509 100.5844 43.7303 102.7372 43.7303 105.3927 c 43.7303 108.0482 41.4509 110.201 38.6392 110.201 c 35.8275 110.201 33.5481 108.0482 33.5481 105.3927 c 33.5481 102.7372 35.8275 100.5844 38.6392 100.5844 c b 0 g 38.6392 105.3927 m F 0 G 0.3 w 10 M 61.4493 105.3927 m S 1 g 1 w 4 M 61.4493 100.5844 m 64.261 100.5844 66.5404 102.7372 66.5404 105.3927 c 66.5404 108.0482 64.261 110.201 61.4493 110.201 c 58.6376 110.201 56.3582 108.0482 56.3582 105.3927 c 56.3582 102.7372 58.6376 100.5844 61.4493 100.5844 c b 0 g 61.4493 105.3927 m F 0 G 0.3 w 10 M 61.4493 83.164 m S 61.4493 60.9354 m S 38.6392 60.9354 m S 38.6392 83.164 m S 50.0442 72.0497 m S 61.4493 60.9354 m S 61.4493 60.9354 m S 61.4493 83.164 m S 61.4493 60.9354 m S 38.6392 60.9354 m S 0 g 1 w 4 M 50.0442 72.0497 m F 0 G 0.3 w 10 M 38.6392 83.164 m S 0 g 1 w 4 M 38.6392 83.164 m F 0 G 0.3 w 10 M 61.4493 83.164 m S 0 g 1 w 4 M 61.4493 83.164 m F 0 G 0.3 w 10 M 61.4493 60.9354 m S 38.6392 60.9354 m S 61.4493 60.9354 m S 38.6392 60.9354 m S 0 g 1 w 4 M 38.6392 60.9354 m F 0 G 0.3 w 10 M 61.4493 60.9354 m S 0 g 1 w 4 M 61.4493 60.9354 m F 0 G 0.3 w 10 M 107.0696 83.164 m S 107.0696 60.9354 m S 84.2595 60.9354 m S 84.2595 83.164 m S 95.6645 72.0497 m S 107.0696 60.9354 m S 107.0696 60.9354 m S 107.0696 83.164 m S 107.0696 60.9354 m S 84.2595 60.9354 m S 0 g 1 w 4 M 95.6645 72.0497 m F 0 G 0.3 w 10 M 84.2595 83.164 m S 0 g 1 w 4 M 84.2595 83.164 m F 0 G 0.3 w 10 M 107.0696 83.164 m S 0 g 1 w 4 M 107.0696 83.164 m F 0 G 0.3 w 10 M 107.0696 60.9354 m S 84.2595 60.9354 m S 107.0696 60.9354 m S 84.2595 60.9354 m S 0 g 1 w 4 M 84.2595 60.9354 m F 0 G 0.3 w 10 M 107.0696 60.9354 m S 0 g 1 w 4 M 107.0696 60.9354 m F 0 G 0.3 w 10 M 61.4493 83.164 m S 61.4493 60.9354 m S 38.6392 60.9354 m S 38.6392 83.164 m S 50.0442 72.0497 m S 61.4493 60.9354 m S 61.4493 60.9354 m S 61.4493 83.164 m S 61.4493 60.9354 m S 38.6392 60.9354 m S 0 g 1 w 4 M 50.0442 72.0497 m F 0 G 0.3 w 10 M 38.6392 83.164 m S 0 g 1 w 4 M 38.6392 83.164 m F 0 G 0.3 w 10 M 61.4493 83.164 m S 0 g 1 w 4 M 61.4493 83.164 m F 0 G 0.3 w 10 M 61.4493 60.9354 m S 38.6392 60.9354 m S 61.4493 60.9354 m S 38.6392 60.9354 m S 0 g 1 w 4 M 38.6392 60.9354 m F 0 G 0.3 w 10 M 61.4493 60.9354 m S 0 g 1 w 4 M 61.4493 60.9354 m F 0.7 g 38.6392 83.164 m 61.4493 83.164 l 61.4493 60.9354 l 38.6392 60.9354 l 38.6392 83.164 l f 0 G 0.3 w 10 M 61.4493 83.164 m S 61.4493 60.9354 m S 61.4493 83.164 m S 61.4493 83.164 m S 61.4493 60.9354 m S 38.6392 60.9354 m S 38.6392 83.164 m S 50.0442 72.0497 m S 61.4493 83.164 m S 38.6392 83.164 m S 0 g 1 w 4 M 50.0442 72.0497 m F 0 G 0.3 w 10 M 61.4493 60.9354 m S 38.6392 60.9354 m S 61.4493 60.9354 m S 61.4493 83.164 m S 38.6392 83.164 m S 61.4493 83.164 m S 38.6392 83.164 m S 1 g 1 w 4 M 38.6392 78.3557 m 41.4509 78.3557 43.7303 80.5085 43.7303 83.164 c 43.7303 85.8195 41.4509 87.9723 38.6392 87.9723 c 35.8275 87.9723 33.5481 85.8195 33.5481 83.164 c 33.5481 80.5085 35.8275 78.3557 38.6392 78.3557 c b 0 g 38.6392 83.164 m F 0 G 0.3 w 10 M 61.4493 83.164 m S 1 g 1 w 4 M 61.4493 78.3557 m 64.261 78.3557 66.5404 80.5085 66.5404 83.164 c 66.5404 85.8195 64.261 87.9723 61.4493 87.9723 c 58.6376 87.9723 56.3582 85.8195 56.3582 83.164 c 56.3582 80.5085 58.6376 78.3557 61.4493 78.3557 c b 0 g 61.4493 83.164 m F 0 G 0.3 w 10 M 61.4493 60.9354 m S 38.6392 60.9354 m S 61.4493 60.9354 m S 38.6392 60.9354 m S 1 g 1 w 4 M 38.6392 56.1271 m 41.4509 56.1271 43.7303 58.2799 43.7303 60.9354 c 43.7303 63.5909 41.4509 65.7437 38.6392 65.7437 c 35.8275 65.7437 33.5481 63.5909 33.5481 60.9354 c 33.5481 58.2799 35.8275 56.1271 38.6392 56.1271 c b 0 g 38.6392 60.9354 m F 0 G 0.3 w 10 M 61.4493 60.9354 m S 1 g 1 w 4 M 61.4493 56.1271 m 64.261 56.1271 66.5404 58.2799 66.5404 60.9354 c 66.5404 63.5909 64.261 65.7437 61.4493 65.7437 c 58.6376 65.7437 56.3582 63.5909 56.3582 60.9354 c 56.3582 58.2799 58.6376 56.1271 61.4493 56.1271 c b 0 g 61.4493 60.9354 m F 0 G 0.3 w 10 M 107.0696 83.164 m S 107.0696 60.9354 m S 84.2595 60.9354 m S 84.2595 83.164 m S 95.6645 72.0497 m S 107.0696 60.9354 m S 107.0696 60.9354 m S 107.0696 83.164 m S 107.0696 60.9354 m S 84.2595 60.9354 m S 0 g 1 w 4 M 95.6645 72.0497 m F 0 G 0.3 w 10 M 84.2595 83.164 m S 0 g 1 w 4 M 84.2595 83.164 m F 0 G 0.3 w 10 M 107.0696 83.164 m S 0 g 1 w 4 M 107.0696 83.164 m F 0 G 0.3 w 10 M 107.0696 60.9354 m S 84.2595 60.9354 m S 107.0696 60.9354 m S 84.2595 60.9354 m S 0 g 1 w 4 M 84.2595 60.9354 m F 0 G 0.3 w 10 M 107.0696 60.9354 m S 0 g 1 w 4 M 107.0696 60.9354 m F 0.7 g 84.2595 83.164 m 107.0696 83.164 l 107.0696 60.9354 l 84.2595 60.9354 l 84.2595 83.164 l f 0 G 0.3 w 10 M 107.0696 83.164 m S 107.0696 60.9354 m S 107.0696 83.164 m S 107.0696 83.164 m S 107.0696 60.9354 m S 84.2595 60.9354 m S 84.2595 83.164 m S 95.6645 72.0497 m S 107.0696 83.164 m S 84.2595 83.164 m S 0 g 1 w 4 M 95.6645 72.0497 m F 0 G 0.3 w 10 M 107.0696 60.9354 m S 84.2595 60.9354 m S 107.0696 60.9354 m S 107.0696 83.164 m S 84.2595 83.164 m S 107.0696 83.164 m S 84.2595 83.164 m S 1 g 1 w 4 M 84.2595 78.3557 m 87.0712 78.3557 89.3506 80.5085 89.3506 83.164 c 89.3506 85.8195 87.0712 87.9723 84.2595 87.9723 c 81.4478 87.9723 79.1684 85.8195 79.1684 83.164 c 79.1684 80.5085 81.4478 78.3557 84.2595 78.3557 c b 0 g 84.2595 83.164 m F 0 G 0.3 w 10 M 107.0696 83.164 m S 1 g 1 w 4 M 107.0696 78.3557 m 109.8813 78.3557 112.1607 80.5085 112.1607 83.164 c 112.1607 85.8195 109.8813 87.9723 107.0696 87.9723 c 104.2579 87.9723 101.9785 85.8195 101.9785 83.164 c 101.9785 80.5085 104.2579 78.3557 107.0696 78.3557 c b 0 g 107.0696 83.164 m F 0 G 0.3 w 10 M 107.0696 60.9354 m S 84.2595 60.9354 m S 107.0696 60.9354 m S 84.2595 60.9354 m S 1 g 1 w 4 M 84.2595 56.1271 m 87.0712 56.1271 89.3506 58.2799 89.3506 60.9354 c 89.3506 63.5909 87.0712 65.7437 84.2595 65.7437 c 81.4478 65.7437 79.1684 63.5909 79.1684 60.9354 c 79.1684 58.2799 81.4478 56.1271 84.2595 56.1271 c b 0 g 84.2595 60.9354 m F 0 G 0.3 w 10 M 107.0696 60.9354 m S 1 g 1 w 4 M 107.0696 56.1271 m 109.8813 56.1271 112.1607 58.2799 112.1607 60.9354 c 112.1607 63.5909 109.8813 65.7437 107.0696 65.7437 c 104.2579 65.7437 101.9785 63.5909 101.9785 60.9354 c 101.9785 58.2799 104.2579 56.1271 107.0696 56.1271 c b 0 g 107.0696 60.9354 m F 0 G 0.3 w 10 M 107.0696 127.6213 m S 107.0696 105.3927 m S 84.2595 105.3927 m S 84.2595 127.6213 m S 95.6645 116.507 m S 84.2595 127.6213 m S 107.0696 127.6213 m S 84.2595 127.6213 m S 87.8303 114.6675 m S 84.2595 127.6213 m S 84.2595 105.3927 m S 0 g 1 w 4 M 95.6645 116.507 m F 0 G 0.3 w 10 M 107.0696 105.3927 m S 107.0696 127.6213 m S 107.0696 127.6213 m S 84.2595 105.3927 m S 107.0696 105.3927 m S 84.2595 105.3927 m S 95.6645 94.2784 m S 0 g 1 w 4 M 95.6645 94.2784 m F 0 G 0.3 w 10 M 107.0696 105.3927 m S 84.2595 127.6213 m S 107.0696 127.6213 m S 84.2595 127.6213 m S 107.0696 127.6213 m S 84.2595 127.6213 m S 0 g 1 w 4 M 84.2595 127.6213 m F 0 G 0.3 w 10 M 107.0696 127.6213 m S 0 g 1 w 4 M 107.0696 127.6213 m F 0 G 0.3 w 10 M 84.2595 105.3927 m S 107.0696 105.3927 m S 84.2595 105.3927 m S 107.0696 105.3927 m S 84.2595 105.3927 m S 0 g 1 w 4 M 84.2595 105.3927 m F 0 G 0.3 w 10 M 107.0696 105.3927 m S 0 g 1 w 4 M 107.0696 105.3927 m F 0 G 0.3 w 10 M 107.0696 127.6213 m S 107.0696 105.3927 m S 84.2595 105.3927 m S 84.2595 127.6213 m S 95.6645 116.507 m S 107.0696 105.3927 m S 107.0696 105.3927 m S 107.0696 127.6213 m S 107.0696 105.3927 m S 84.2595 105.3927 m S 0 g 1 w 4 M 95.6645 116.507 m F 0 G 0.3 w 10 M 84.2595 127.6213 m S 0 g 1 w 4 M 84.2595 127.6213 m F 0 G 0.3 w 10 M 107.0696 127.6213 m S 0 g 1 w 4 M 107.0696 127.6213 m F 0 G 0.3 w 10 M 107.0696 105.3927 m S 84.2595 105.3927 m S 107.0696 105.3927 m S 84.2595 105.3927 m S 0 g 1 w 4 M 84.2595 105.3927 m F 0 G 0.3 w 10 M 107.0696 105.3927 m S 0 g 1 w 4 M 107.0696 105.3927 m F 0 G 0.3 w 10 M 107.0696 127.6213 m S 107.0696 105.3927 m S 84.2595 105.3927 m S 84.2595 127.6213 m S 95.6645 116.507 m S 107.0696 105.3927 m S 107.0696 105.3927 m S 107.0696 127.6213 m S 107.0696 105.3927 m S 84.2595 105.3927 m S 0 g 1 w 4 M 95.6645 116.507 m F 0 G 0.3 w 10 M 84.2595 127.6213 m S 0 g 1 w 4 M 84.2595 127.6213 m F 0 G 0.3 w 10 M 107.0696 127.6213 m S 0 g 1 w 4 M 107.0696 127.6213 m F 0 G 0.3 w 10 M 107.0696 105.3927 m S 84.2595 105.3927 m S 107.0696 105.3927 m S 84.2595 105.3927 m S 0 g 1 w 4 M 84.2595 105.3927 m F 0 G 0.3 w 10 M 107.0696 105.3927 m S 0 g 1 w 4 M 107.0696 105.3927 m F 0.7 g 84.2595 127.6213 m 107.0696 127.6213 l 107.0696 105.3927 l 84.2595 105.3927 l 84.2595 127.6213 l f 0 G 0.3 w 10 M 107.0696 127.6213 m S 107.0696 105.3927 m S 107.0696 127.6213 m S 107.0696 127.6213 m S 107.0696 105.3927 m S 84.2595 105.3927 m S 84.2595 127.6213 m S 95.6645 116.507 m S 107.0696 127.6213 m S 84.2595 127.6213 m S 0 g 1 w 4 M 95.6645 116.507 m F 0 G 0.3 w 10 M 107.0696 105.3927 m S 84.2595 105.3927 m S 107.0696 105.3927 m S 107.0696 127.6213 m S 84.2595 127.6213 m S 107.0696 127.6213 m S 84.2595 127.6213 m S 1 g 1 w 4 M 84.2595 122.813 m 87.0712 122.813 89.3506 124.9658 89.3506 127.6213 c 89.3506 130.2768 87.0712 132.4296 84.2595 132.4296 c 81.4478 132.4296 79.1684 130.2768 79.1684 127.6213 c 79.1684 124.9658 81.4478 122.813 84.2595 122.813 c b 0 g 84.2595 127.6213 m F 0 G 0.3 w 10 M 107.0696 127.6213 m S 1 g 1 w 4 M 107.0696 122.813 m 109.8813 122.813 112.1607 124.9658 112.1607 127.6213 c 112.1607 130.2768 109.8813 132.4296 107.0696 132.4296 c 104.2579 132.4296 101.9785 130.2768 101.9785 127.6213 c 101.9785 124.9658 104.2579 122.813 107.0696 122.813 c b 0 g 107.0696 127.6213 m F 0 G 0.3 w 10 M 107.0696 105.3927 m S 84.2595 105.3927 m S 107.0696 105.3927 m S 84.2595 105.3927 m S 1 g 1 w 4 M 84.2595 100.5844 m 87.0712 100.5844 89.3506 102.7372 89.3506 105.3927 c 89.3506 108.0482 87.0712 110.201 84.2595 110.201 c 81.4478 110.201 79.1684 108.0482 79.1684 105.3927 c 79.1684 102.7372 81.4478 100.5844 84.2595 100.5844 c b 0 g 84.2595 105.3927 m F 0 G 0.3 w 10 M 107.0696 105.3927 m S 1 g 1 w 4 M 107.0696 100.5844 m 109.8813 100.5844 112.1607 102.7372 112.1607 105.3927 c 112.1607 108.0482 109.8813 110.201 107.0696 110.201 c 104.2579 110.201 101.9785 108.0482 101.9785 105.3927 c 101.9785 102.7372 104.2579 100.5844 107.0696 100.5844 c b 0 g 107.0696 105.3927 m F 0 G 0.3 w 10 M 186.905 116.507 m S 186.905 116.507 m S 186.905 116.507 m S 186.905 116.507 m S 186.905 116.507 m S 186.905 116.507 m S 186.905 116.507 m S 0 g 1 w 4 M 186.905 111.6987 m 189.7167 111.6987 191.9961 113.8515 191.9961 116.507 c 191.9961 119.1625 189.7167 121.3153 186.905 121.3153 c 184.0933 121.3153 181.8139 119.1625 181.8139 116.507 c 181.8139 113.8515 184.0933 111.6987 186.905 111.6987 c b 186.905 116.507 m F 0 G 0.3 w 10 M 232.5253 116.507 m S 232.5253 116.507 m S 232.5253 116.507 m S 232.5253 116.507 m S 232.5253 116.507 m S 232.5253 116.507 m S 232.5253 116.507 m S 0 g 1 w 4 M 232.5253 111.6987 m 235.337 111.6987 237.6164 113.8515 237.6164 116.507 c 237.6164 119.1625 235.337 121.3153 232.5253 121.3153 c 229.7136 121.3153 227.4342 119.1625 227.4342 116.507 c 227.4342 113.8515 229.7136 111.6987 232.5253 111.6987 c b 232.5253 116.507 m F 0 G 0.3 w 10 M 186.905 72.0497 m S 186.905 72.0497 m S 186.905 72.0497 m S 186.905 72.0497 m S 186.905 72.0497 m S 186.905 72.0497 m S 186.905 72.0497 m S 0 g 1 w 4 M 186.905 67.2414 m 189.7167 67.2414 191.9961 69.3942 191.9961 72.0497 c 191.9961 74.7052 189.7167 76.858 186.905 76.858 c 184.0933 76.858 181.8139 74.7052 181.8139 72.0497 c 181.8139 69.3942 184.0933 67.2414 186.905 67.2414 c b 186.905 72.0497 m F 0 G 0.3 w 10 M 232.5253 72.0497 m S 232.5253 72.0497 m S 232.5253 72.0497 m S 232.5253 72.0497 m S 232.5253 72.0497 m S 232.5253 72.0497 m S 232.5253 72.0497 m S 0 g 1 w 4 M 232.5253 67.2414 m 235.337 67.2414 237.6164 69.3942 237.6164 72.0497 c 237.6164 74.7052 235.337 76.858 232.5253 76.858 c 229.7136 76.858 227.4342 74.7052 227.4342 72.0497 c 227.4342 69.3942 229.7136 67.2414 232.5253 67.2414 c b 232.5253 72.0497 m F u u /_Symbol 24 29 0 0 z [1 0 0 1 132.6582 86.8125]e (\256)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 137.5 35.5]e (\(c\))t T U U u 0 G 0.3 w 10 M 94.3797 40.3293 m S 94.3797 62.5579 m S 117.1899 62.5579 m S 117.1899 40.3293 m S 105.7848 51.4436 m S U 117.1899 40.3293 m S 140 40.3293 m S 117.1899 40.3293 m S 140 40.3293 m S 94.3797 40.3293 m S 117.1899 40.3293 m S 94.3797 40.3293 m S 140 40.3293 m S 0 g 1 w 4 M 140 40.3293 m F 0 G 0.3 w 10 M 117.1899 40.3293 m S 0 g 1 w 4 M 117.1899 40.3293 m F 0 G 0.3 w 10 M 94.3797 40.3293 m S 0 g 1 w 4 M 94.3797 40.3293 m F 0 G 0.3 w 10 M 94.3797 40.3293 m S 94.3797 40.3293 m S 94.3797 40.3293 m S 0 g 1 w 4 M 94.3797 40.3293 m F 0 G 0.3 w 10 M 140 40.3293 m S 140 40.3293 m S 140 40.3293 m S 0 g 1 w 4 M 140 40.3293 m F showpage _E end %%EndDocument @endspecial 517 1317 a @beginspecial 30 @llx 32.500000 @lly 453 @urx 209.500000 @ury 2196 @rwi @setspecial %%BeginDocument: fig2d.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n []/_Symbol/Symbol Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 392.4224 102.1031 m S 369.6123 102.1031 m S 376.5173 83.7174 m S u 61.7594 200.8718 m S 61.7594 178.6432 m S 38.9493 178.6432 m S 38.9493 200.8718 m S 50.3543 189.7575 m S U u 107.3797 156.4145 m S 107.3797 134.1859 m S 84.5696 134.1859 m S 84.5696 156.4145 m S 95.9746 145.3002 m S U u 84.5696 178.6432 m S 84.5696 156.4145 m S 61.7594 156.4145 m S 61.7594 178.6432 m S 73.1645 167.5289 m S U u 84.5696 200.8718 m S 84.5696 178.6432 m S 61.7594 178.6432 m S 61.7594 200.8718 m S 73.1645 189.7575 m S U u 107.3797 200.8718 m S 107.3797 178.6432 m S 84.5696 178.6432 m S 84.5696 200.8718 m S 95.9746 189.7575 m S U u 107.3797 178.6432 m S 107.3797 156.4145 m S 84.5696 156.4145 m S 84.5696 178.6432 m S 95.9746 167.5289 m S U u 84.5696 156.4145 m S 84.5696 134.1859 m S 61.7594 134.1859 m S 61.7594 156.4145 m S 73.1645 145.3002 m S U u 61.7594 156.4145 m S 61.7594 134.1859 m S 38.9493 134.1859 m S 38.9493 156.4145 m S 50.3543 145.3002 m S U u 61.7594 178.6432 m S 61.7594 156.4145 m S 38.9493 156.4145 m S 38.9493 178.6432 m S 50.3543 167.5289 m S U 0 g 1 w 4 M 50.3543 189.7575 m F 95.9746 189.7575 m F 50.3543 145.3002 m F 95.9746 145.3002 m F u 0 G 0.3 w 10 M 130.1898 200.8718 m S 130.1898 178.6432 m S 107.3797 178.6432 m S 107.3797 200.8718 m S 118.7847 189.7575 m S U u 175.8101 156.4145 m S 175.8101 134.1859 m S 153 134.1859 m S 153 156.4145 m S 164.405 145.3002 m S U u 153 178.6432 m S 153 156.4145 m S 130.1898 156.4145 m S 130.1898 178.6432 m S 141.5949 167.5289 m S U u 153 200.8718 m S 153 178.6432 m S 130.1898 178.6432 m S 130.1898 200.8718 m S 141.5949 189.7575 m S U u 175.8101 200.8718 m S 175.8101 178.6432 m S 153 178.6432 m S 153 200.8718 m S 164.405 189.7575 m S U u 175.8101 178.6432 m S 175.8101 156.4145 m S 153 156.4145 m S 153 178.6432 m S 164.405 167.5289 m S U u 153 156.4145 m S 153 134.1859 m S 130.1898 134.1859 m S 130.1898 156.4145 m S 141.5949 145.3002 m S U u 130.1898 156.4145 m S 130.1898 134.1859 m S 107.3797 134.1859 m S 107.3797 156.4145 m S 118.7847 145.3002 m S U u 130.1898 178.6432 m S 130.1898 156.4145 m S 107.3797 156.4145 m S 107.3797 178.6432 m S 118.7847 167.5289 m S U 0 g 1 w 4 M 118.7847 189.7575 m F 164.405 189.7575 m F 118.7847 145.3002 m F 164.405 145.3002 m F u 0 G 0.3 w 10 M 198.6202 200.8718 m S 198.6202 178.6432 m S 175.8101 178.6432 m S 175.8101 200.8718 m S 187.2151 189.7575 m S U u 244.2405 156.4145 m S 244.2405 134.1859 m S 221.4304 134.1859 m S 221.4304 156.4145 m S 232.8354 145.3002 m S U u 221.4304 178.6432 m S 221.4304 156.4145 m S 198.6202 156.4145 m S 198.6202 178.6432 m S 210.0253 167.5289 m S U u 221.4304 200.8718 m S 221.4304 178.6432 m S 198.6202 178.6432 m S 198.6202 200.8718 m S 210.0253 189.7575 m S U u 244.2405 200.8718 m S 244.2405 178.6432 m S 221.4304 178.6432 m S 221.4304 200.8718 m S 232.8354 189.7575 m S U u 244.2405 178.6432 m S 244.2405 156.4145 m S 221.4304 156.4145 m S 221.4304 178.6432 m S 232.8354 167.5289 m S U u 221.4304 156.4145 m S 221.4304 134.1859 m S 198.6202 134.1859 m S 198.6202 156.4145 m S 210.0253 145.3002 m S U u 198.6202 156.4145 m S 198.6202 134.1859 m S 175.8101 134.1859 m S 175.8101 156.4145 m S 187.2151 145.3002 m S U u 198.6202 178.6432 m S 198.6202 156.4145 m S 175.8101 156.4145 m S 175.8101 178.6432 m S 187.2151 167.5289 m S U 0 g 1 w 4 M 187.2151 189.7575 m F 232.8354 189.7575 m F 187.2151 145.3002 m F 232.8354 145.3002 m F u 0 G 0.3 w 10 M 267.0506 200.8718 m S 267.0506 178.6432 m S 244.2405 178.6432 m S 244.2405 200.8718 m S 255.6455 189.7575 m S U u 312.6709 156.4145 m S 312.6709 134.1859 m S 289.8608 134.1859 m S 289.8608 156.4145 m S 301.2658 145.3002 m S U u 289.8608 178.6432 m S 289.8608 156.4145 m S 267.0506 156.4145 m S 267.0506 178.6432 m S 278.4557 167.5289 m S U u 289.8608 200.8718 m S 289.8608 178.6432 m S 267.0506 178.6432 m S 267.0506 200.8718 m S 278.4557 189.7575 m S U 312.6709 200.8718 m S 312.6709 178.6432 m S 289.8608 178.6432 m S 289.8608 200.8718 m S 301.2658 189.7575 m S u 312.6709 178.6432 m S 312.6709 156.4145 m S 289.8608 156.4145 m S 289.8608 178.6432 m S 301.2658 167.5289 m S U u 289.8608 156.4145 m S 289.8608 134.1859 m S 267.0506 134.1859 m S 267.0506 156.4145 m S 278.4557 145.3002 m S U u 267.0506 156.4145 m S 267.0506 134.1859 m S 244.2405 134.1859 m S 244.2405 156.4145 m S 255.6455 145.3002 m S U u 267.0506 178.6432 m S 267.0506 156.4145 m S 244.2405 156.4145 m S 244.2405 178.6432 m S 255.6455 167.5289 m S U 0 g 1 w 4 M 255.6455 189.7575 m F 301.2658 189.7575 m F 255.6455 145.3002 m F 301.2658 145.3002 m F u 0 G 0.3 w 10 M 61.7594 134.1859 m S 61.7594 111.9572 m S 38.9493 111.9572 m S 38.9493 134.1859 m S 50.3543 123.0716 m S U u 107.3797 89.7286 m S 107.3797 67.5 m S 84.5696 67.5 m S 84.5696 89.7286 m S 95.9746 78.6143 m S U u 84.5696 111.9572 m S 84.5696 89.7286 m S 61.7594 89.7286 m S 61.7594 111.9572 m S 73.1645 100.843 m S U u 84.5696 134.1859 m S 84.5696 111.9572 m S 61.7594 111.9572 m S 61.7594 134.1859 m S 73.1645 123.0716 m S U u 107.3797 134.1859 m S 107.3797 111.9572 m S 84.5696 111.9572 m S 84.5696 134.1859 m S 95.9746 123.0716 m S U u 107.3797 111.9572 m S 107.3797 89.7286 m S 84.5696 89.7286 m S 84.5696 111.9572 m S 95.9746 100.843 m S U u 84.5696 89.7286 m S 84.5696 67.5 m S 61.7594 67.5 m S 61.7594 89.7286 m S 73.1645 78.6143 m S U u 61.7594 89.7286 m S 61.7594 67.5 m S 38.9493 67.5 m S 38.9493 89.7286 m S 50.3543 78.6143 m S U u 61.7594 111.9572 m S 61.7594 89.7286 m S 38.9493 89.7286 m S 38.9493 111.9572 m S 50.3543 100.843 m S U 0 g 1 w 4 M 50.3543 123.0716 m F 95.9746 123.0716 m F 50.3543 78.6143 m F 95.9746 78.6143 m F u 0 G 0.3 w 10 M 130.1898 134.1859 m S 130.1898 111.9572 m S 107.3797 111.9572 m S 107.3797 134.1859 m S 118.7847 123.0716 m S U u 175.8101 89.7286 m S 175.8101 67.5 m S 153 67.5 m S 153 89.7286 m S 164.405 78.6143 m S U u 153 111.9572 m S 153 89.7286 m S 130.1898 89.7286 m S 130.1898 111.9572 m S 141.5949 100.843 m S U u 153 134.1859 m S 153 111.9572 m S 130.1898 111.9572 m S 130.1898 134.1859 m S 141.5949 123.0716 m S U u 175.8101 134.1859 m S 175.8101 111.9572 m S 153 111.9572 m S 153 134.1859 m S 164.405 123.0716 m S U u 175.8101 111.9572 m S 175.8101 89.7286 m S 153 89.7286 m S 153 111.9572 m S 164.405 100.843 m S U u 153 89.7286 m S 153 67.5 m S 130.1898 67.5 m S 130.1898 89.7286 m S 141.5949 78.6143 m S U u 130.1898 89.7286 m S 130.1898 67.5 m S 107.3797 67.5 m S 107.3797 89.7286 m S 118.7847 78.6143 m S U u 130.1898 111.9572 m S 130.1898 89.7286 m S 107.3797 89.7286 m S 107.3797 111.9572 m S 118.7847 100.843 m S U 0 g 1 w 4 M 118.7847 123.0716 m F 164.405 123.0716 m F 118.7847 78.6143 m F 164.405 78.6143 m F u 0 G 0.3 w 10 M 198.6202 134.1859 m S 198.6202 111.9572 m S 175.8101 111.9572 m S 175.8101 134.1859 m S 187.2151 123.0716 m S U u 244.2405 89.7286 m S 244.2405 67.5 m S 221.4304 67.5 m S 221.4304 89.7286 m S 232.8354 78.6143 m S U u 221.4304 111.9572 m S 221.4304 89.7286 m S 198.6202 89.7286 m S 198.6202 111.9572 m S 210.0253 100.843 m S U u 221.4304 134.1859 m S 221.4304 111.9572 m S 198.6202 111.9572 m S 198.6202 134.1859 m S 210.0253 123.0716 m S U u 244.2405 134.1859 m S 244.2405 111.9572 m S 221.4304 111.9572 m S 221.4304 134.1859 m S 232.8354 123.0716 m S U u 244.2405 111.9572 m S 244.2405 89.7286 m S 221.4304 89.7286 m S 221.4304 111.9572 m S 232.8354 100.843 m S U u 221.4304 89.7286 m S 221.4304 67.5 m S 198.6202 67.5 m S 198.6202 89.7286 m S 210.0253 78.6143 m S U u 198.6202 89.7286 m S 198.6202 67.5 m S 175.8101 67.5 m S 175.8101 89.7286 m S 187.2151 78.6143 m S U u 198.6202 111.9572 m S 198.6202 89.7286 m S 175.8101 89.7286 m S 175.8101 111.9572 m S 187.2151 100.843 m S U 0 g 1 w 4 M 187.2151 123.0716 m F 232.8354 123.0716 m F 187.2151 78.6143 m F 232.8354 78.6143 m F u 0 G 0.3 w 10 M 267.0506 134.1859 m S 267.0506 111.9572 m S 244.2405 111.9572 m S 244.2405 134.1859 m S 255.6455 123.0716 m S U u 312.6709 89.7286 m S 312.6709 67.5 m S 289.8608 67.5 m S 289.8608 89.7286 m S 301.2658 78.6143 m S U u 289.8608 111.9572 m S 289.8608 89.7286 m S 267.0506 89.7286 m S 267.0506 111.9572 m S 278.4557 100.843 m S U u 289.8608 134.1859 m S 289.8608 111.9572 m S 267.0506 111.9572 m S 267.0506 134.1859 m S 278.4557 123.0716 m S U u 312.6709 134.1859 m S 312.6709 111.9572 m S 289.8608 111.9572 m S 289.8608 134.1859 m S 301.2658 123.0716 m S U u 312.6709 111.9572 m S 312.6709 89.7286 m S 289.8608 89.7286 m S 289.8608 111.9572 m S 301.2658 100.843 m S U u 289.8608 89.7286 m S 289.8608 67.5 m S 267.0506 67.5 m S 267.0506 89.7286 m S 278.4557 78.6143 m S U u 267.0506 89.7286 m S 267.0506 67.5 m S 244.2405 67.5 m S 244.2405 89.7286 m S 255.6455 78.6143 m S U u 267.0506 111.9572 m S 267.0506 89.7286 m S 244.2405 89.7286 m S 244.2405 111.9572 m S 255.6455 100.843 m S U 0 g 1 w 4 M 255.6455 123.0716 m F 301.2658 123.0716 m F 255.6455 78.6143 m F 301.2658 78.6143 m F 50.3543 56.3857 m F 95.9746 56.3857 m F 118.7847 56.3857 m F 164.405 56.3857 m F 187.2151 56.3857 m F 232.8354 56.3857 m F 255.6455 56.3857 m F 301.2658 56.3857 m F u 0 G 0.3 w 10 M 61.7594 67.5 m S 61.7594 45.2713 m S 38.9493 45.2713 m S 38.9493 67.5 m S 50.3543 56.3857 m S U u 381.1015 178.6429 m S 381.1015 156.4143 m S 358.2914 156.4143 m S 358.2914 178.6429 m S 369.6964 167.5286 m S U u 358.2914 200.8715 m S 358.2914 178.6429 m S 335.4812 178.6429 m S 335.4812 200.8715 m S 346.8863 189.7572 m S U u 84.5696 67.5 m S 84.5696 45.2713 m S 61.7594 45.2713 m S 61.7594 67.5 m S 73.1645 56.3857 m S U u 107.3797 67.5 m S 107.3797 45.2713 m S 84.5696 45.2713 m S 84.5696 67.5 m S 95.9746 56.3857 m S U u 381.1015 200.8715 m S 381.1015 178.6429 m S 358.2914 178.6429 m S 358.2914 200.8715 m S 369.6964 189.7572 m S U u 358.2914 178.6429 m S 358.2914 156.4143 m S 335.4812 156.4143 m S 335.4812 178.6429 m S 346.8863 167.5286 m S U u 335.4812 178.6429 m S 335.4812 156.4143 m S 312.6711 156.4143 m S 312.6711 178.6429 m S 324.0761 167.5286 m S U 335.4812 200.8715 m S 335.4812 178.6429 m S 312.6711 178.6429 m S 312.6711 200.8715 m S 324.0761 189.7572 m S 0 g 1 w 4 M 50.3543 56.3857 m F 95.9746 56.3857 m F 324.0761 167.5286 m F 369.6964 167.5286 m F u 0 G 0.3 w 10 M 130.1898 67.5 m S 130.1898 45.2713 m S 107.3797 45.2713 m S 107.3797 67.5 m S 118.7847 56.3857 m S U u 449.5319 178.6429 m S 449.5319 156.4143 m S 426.7218 156.4143 m S 426.7218 178.6429 m S 438.1268 167.5286 m S U u 426.7218 200.8715 m S 426.7218 178.6429 m S 403.9116 178.6429 m S 403.9116 200.8715 m S 415.3167 189.7572 m S U u 153 67.5 m S 153 45.2713 m S 130.1898 45.2713 m S 130.1898 67.5 m S 141.5949 56.3857 m S U u 175.8101 67.5 m S 175.8101 45.2713 m S 153 45.2713 m S 153 67.5 m S 164.405 56.3857 m S U u 449.5319 200.8715 m S 449.5319 178.6429 m S 426.7218 178.6429 m S 426.7218 200.8715 m S 438.1268 189.7572 m S U u 426.7218 178.6429 m S 426.7218 156.4143 m S 403.9116 156.4143 m S 403.9116 178.6429 m S 415.3167 167.5286 m S U u 403.9116 178.6429 m S 403.9116 156.4143 m S 381.1015 156.4143 m S 381.1015 178.6429 m S 392.5065 167.5286 m S U u 403.9116 200.8715 m S 403.9116 178.6429 m S 381.1015 178.6429 m S 381.1015 200.8715 m S 392.5065 189.7572 m S U 0 g 1 w 4 M 118.7847 56.3857 m F 164.405 56.3857 m F 392.5065 167.5286 m F 438.1268 167.5286 m F u 0 G 0.3 w 10 M 198.6202 67.5 m S 198.6202 45.2713 m S 175.8101 45.2713 m S 175.8101 67.5 m S 187.2151 56.3857 m S U u 221.4304 67.5 m S 221.4304 45.2713 m S 198.6202 45.2713 m S 198.6202 67.5 m S 210.0253 56.3857 m S U u 244.2405 67.5 m S 244.2405 45.2713 m S 221.4304 45.2713 m S 221.4304 67.5 m S 232.8354 56.3857 m S U 0 g 1 w 4 M 187.2151 56.3857 m F 232.8354 56.3857 m F u 0 G 0.3 w 10 M 267.0506 67.5 m S 267.0506 45.2713 m S 244.2405 45.2713 m S 244.2405 67.5 m S 255.6455 56.3857 m S U u 289.8608 67.5 m S 289.8608 45.2713 m S 267.0506 45.2713 m S 267.0506 67.5 m S 278.4557 56.3857 m S U u 312.6709 67.5 m S 312.6709 45.2713 m S 289.8608 45.2713 m S 289.8608 67.5 m S 301.2658 56.3857 m S U 0 g 1 w 4 M 255.6455 56.3857 m F 301.2658 56.3857 m F u 0 G 0.3 w 10 M 335.4812 156.4143 m S 335.4812 134.1856 m S 312.6711 134.1856 m S 312.6711 156.4143 m S 324.0761 145.3 m S U 381.1015 111.957 m S 381.1015 89.7284 m S 358.2914 89.7284 m S 358.2914 111.957 m S 369.6964 100.8427 m S u 358.2914 134.1856 m S 358.2914 111.957 m S 335.4812 111.957 m S 335.4812 134.1856 m S 346.8863 123.0713 m S U u 358.2914 156.4143 m S 358.2914 134.1856 m S 335.4812 134.1856 m S 335.4812 156.4143 m S 346.8863 145.3 m S U u 381.1015 156.4143 m S 381.1015 134.1856 m S 358.2914 134.1856 m S 358.2914 156.4143 m S 369.6964 145.3 m S U u 381.1015 134.1856 m S 381.1015 111.957 m S 358.2914 111.957 m S 358.2914 134.1856 m S 369.6964 123.0713 m S U u 358.2914 111.957 m S 358.2914 89.7284 m S 335.4812 89.7284 m S 335.4812 111.957 m S 346.8863 100.8427 m S U u 335.4812 111.957 m S 335.4812 89.7284 m S 312.6711 89.7284 m S 312.6711 111.957 m S 324.0761 100.8427 m S U u 335.4812 134.1856 m S 335.4812 111.957 m S 312.6711 111.957 m S 312.6711 134.1856 m S 324.0761 123.0713 m S U 0 g 1 w 4 M 324.0761 145.3 m F 369.6964 145.3 m F 324.0761 100.8427 m F 369.6964 100.8427 m F u 0 G 0.3 w 10 M 403.9116 156.4143 m S 403.9116 134.1856 m S 381.1015 134.1856 m S 381.1015 156.4143 m S 392.5065 145.3 m S U u 449.5319 111.957 m S 449.5319 89.7284 m S 426.7218 89.7284 m S 426.7218 111.957 m S 438.1268 100.8427 m S U u 426.7218 134.1856 m S 426.7218 111.957 m S 403.9116 111.957 m S 403.9116 134.1856 m S 415.3167 123.0713 m S U u 426.7218 156.4143 m S 426.7218 134.1856 m S 403.9116 134.1856 m S 403.9116 156.4143 m S 415.3167 145.3 m S U u 449.5319 156.4143 m S 449.5319 134.1856 m S 426.7218 134.1856 m S 426.7218 156.4143 m S 438.1268 145.3 m S U u 449.5319 134.1856 m S 449.5319 111.957 m S 426.7218 111.957 m S 426.7218 134.1856 m S 438.1268 123.0713 m S U u 426.7218 111.957 m S 426.7218 89.7284 m S 403.9116 89.7284 m S 403.9116 111.957 m S 415.3167 100.8427 m S U 403.9116 111.957 m S 403.9116 89.7284 m S 381.1015 89.7284 m S 381.1015 111.957 m S 392.5065 100.8427 m S u 403.9116 134.1856 m S 403.9116 111.957 m S 381.1015 111.957 m S 381.1015 134.1856 m S 392.5065 123.0713 m S U 0 g 1 w 4 M 392.5065 145.3 m F 438.1268 145.3 m F 392.5065 100.8427 m F 438.1268 100.8427 m F 0 G 0.3 w 10 M 381.1015 67.4998 m S 381.1015 45.2712 m S 358.2914 45.2712 m S 358.2914 67.4998 m S 369.6964 56.3855 m S 358.2914 89.7284 m S 358.2914 67.4998 m S 335.4812 67.4998 m S 335.4812 89.7284 m S 346.8863 78.6141 m S 381.1015 89.7284 m S 381.1015 67.4998 m S 358.2914 67.4998 m S 358.2914 89.7284 m S 369.6964 78.6141 m S 358.2914 67.4998 m S 358.2914 45.2712 m S 335.4812 45.2712 m S 335.4812 67.4998 m S 346.8863 56.3855 m S u 335.4812 67.4998 m S 335.4812 45.2712 m S 312.6711 45.2712 m S 312.6711 67.4998 m S 324.0761 56.3855 m S U u 335.4812 89.7284 m S 335.4812 67.4998 m S 312.6711 67.4998 m S 312.6711 89.7284 m S 324.0761 78.6141 m S U 0 g 1 w 4 M 369.6964 56.3855 m F 0 G 0.3 w 10 M 449.5319 67.4998 m S 449.5319 45.2712 m S 426.7218 45.2712 m S 426.7218 67.4998 m S 438.1268 56.3855 m S 426.7218 89.7284 m S 426.7218 67.4998 m S 403.9116 67.4998 m S 403.9116 89.7284 m S 415.3167 78.6141 m S 449.5319 89.7284 m S 449.5319 67.4998 m S 426.7218 67.4998 m S 426.7218 89.7284 m S 438.1268 78.6141 m S 426.7218 67.4998 m S 426.7218 45.2712 m S 403.9116 45.2712 m S 403.9116 67.4998 m S 415.3167 56.3855 m S 403.9116 67.4998 m S 403.9116 45.2712 m S 381.1015 45.2712 m S 381.1015 67.4998 m S 392.5065 56.3855 m S 403.9116 89.7284 m S 403.9116 67.4998 m S 381.1015 67.4998 m S 381.1015 89.7284 m S 392.5065 78.6141 m S 0 g 1 w 4 M 392.5065 56.3855 m F 438.1268 56.3855 m F 0 G 0.3 w 10 M 335.4812 45.2712 m S 312.6711 45.2712 m S 358.2914 45.2712 m S 335.4812 45.2712 m S 381.1015 45.2712 m S 358.2914 45.2712 m S 403.9116 45.2712 m S 381.1015 45.2712 m S 426.7218 45.2712 m S 403.9116 45.2712 m S 449.5319 45.2712 m S 426.7218 45.2712 m S 61.7594 200.8718 m S 61.7594 178.6432 m S 38.9493 178.6432 m S 38.9493 200.8718 m S 50.3543 189.7575 m S u 107.3797 156.4145 m S 107.3797 134.1859 m S 84.5696 134.1859 m S 84.5696 156.4145 m S 95.9746 145.3002 m S U u 84.5696 178.6432 m S 84.5696 156.4145 m S 61.7594 156.4145 m S 61.7594 178.6432 m S 73.1645 167.5289 m S U 84.5696 200.8718 m S 84.5696 178.6432 m S 61.7594 178.6432 m S 61.7594 200.8718 m S 73.1645 189.7575 m S 84.5696 178.6432 m S 84.5696 200.8718 m S u 107.3797 178.6432 m S 107.3797 156.4145 m S 84.5696 156.4145 m S 84.5696 178.6432 m S 95.9746 167.5289 m S U u 84.5696 156.4145 m S 84.5696 134.1859 m S 61.7594 134.1859 m S 61.7594 156.4145 m S 73.1645 145.3002 m S U 61.7594 156.4145 m S 38.9493 156.4145 m S u 61.7594 178.6432 m S 61.7594 156.4145 m S 38.9493 156.4145 m S 38.9493 178.6432 m S 50.3543 167.5289 m S U 0 g 1 w 4 M 50.3543 189.7575 m F 0 G 0.3 w 10 M 38.9493 200.8718 m S 0 g 1 w 4 M 38.9493 200.8718 m F 0 G 0.3 w 10 M 61.7594 200.8718 m S 0 g 1 w 4 M 61.7594 200.8718 m F 0 G 0.3 w 10 M 84.5696 200.8718 m S 0 g 1 w 4 M 84.5696 200.8718 m F 0 G 0.3 w 10 M 61.7594 178.6432 m S 38.9493 178.6432 m S 84.5696 178.6432 m S 61.7594 178.6432 m S 84.5696 178.6432 m S 38.9493 178.6432 m S 0 g 1 w 4 M 38.9493 178.6432 m F 0 G 0.3 w 10 M 61.7594 178.6432 m S 0 g 1 w 4 M 61.7594 178.6432 m F 0 G 0.3 w 10 M 84.5696 178.6432 m S 0 g 1 w 4 M 84.5696 178.6432 m F 0 G 0.3 w 10 M 61.7594 156.4145 m S 38.9493 156.4145 m S 84.5696 156.4145 m S 61.7594 156.4145 m S 84.5696 156.4145 m S 38.9493 156.4145 m S 0 g 1 w 4 M 38.9493 156.4145 m F 0 G 0.3 w 10 M 61.7594 156.4145 m S 0 g 1 w 4 M 61.7594 156.4145 m F 0 G 0.3 w 10 M 84.5696 156.4145 m S 0 g 1 w 4 M 84.5696 156.4145 m F 0.7 g 38.9493 200.8718 m F 61.7594 178.6432 m F 42.7138 204.0473 m F 65.5239 181.8187 m F 35.4638 197.2973 m F 58.2739 175.0687 m F 66.2138 181.0473 m F 89.0239 158.8187 m F 58.2739 175.0687 m F 81.084 152.8401 m F 42.7138 204.0473 m F 65.5239 181.8187 m F 65.5239 181.8187 m F 88.334 159.5901 m F 84.5696 200.8718 m F 61.7594 178.6432 m F 80.524 203.7973 m F 57.7138 181.5687 m F 88.774 198.2973 m F 65.9638 176.0687 m F 57.7138 181.5687 m F 34.9036 159.3401 m F 65.524 175.5473 m F 42.7138 153.3187 m F 0 G 0.3 w 10 M 54.3689 178.433 m S 61.8689 185.183 m S 68.6189 178.683 m S 61.8689 171.433 m S 0.7 g 1 w 4 M 35.4638 197.2973 m 34.8689 197.183 42.7138 204.0473 y 61.8689 185.183 l 80.524 203.7973 l 88.774 198.2973 l 68.6189 178.683 l 88.8689 159.433 l 81.084 152.8401 l 61.8689 171.433 l 42.7138 153.3187 l 34.9036 159.3401 l 54.3689 178.433 l 35.4638 197.2973 l f 0 G 0.3 w 10 M 38.9493 200.8718 m S 38.9493 200.8718 m S 38.9493 200.8718 m S 1 g 1 w 4 M 38.9493 196.0635 m 41.761 196.0635 44.0404 198.2163 44.0404 200.8718 c 44.0404 203.5273 41.761 205.6801 38.9493 205.6801 c 36.1376 205.6801 33.8582 203.5273 33.8582 200.8718 c 33.8582 198.2163 36.1376 196.0635 38.9493 196.0635 c b 0 g 38.9493 200.8718 m F 0 G 0.3 w 10 M 84.5696 200.8718 m S 84.5696 200.8718 m S 84.5696 200.8718 m S 1 g 1 w 4 M 84.5696 196.0635 m 87.3813 196.0635 89.6607 198.2163 89.6607 200.8718 c 89.6607 203.5273 87.3813 205.6801 84.5696 205.6801 c 81.7579 205.6801 79.4785 203.5273 79.4785 200.8718 c 79.4785 198.2163 81.7579 196.0635 84.5696 196.0635 c b 0 g 84.5696 200.8718 m F 0 G 0.3 w 10 M 84.5696 156.4145 m S 84.5696 156.4145 m S 84.5696 156.4145 m S 1 g 1 w 4 M 84.5696 151.6062 m 87.3813 151.6062 89.6607 153.759 89.6607 156.4145 c 89.6607 159.07 87.3813 161.2228 84.5696 161.2228 c 81.7579 161.2228 79.4785 159.07 79.4785 156.4145 c 79.4785 153.759 81.7579 151.6062 84.5696 151.6062 c b 0 g 84.5696 156.4145 m F 0 G 0.3 w 10 M 38.9493 156.4145 m S 38.9493 156.4145 m S 38.9493 156.4145 m S 1 g 1 w 4 M 38.9493 151.6062 m 41.761 151.6062 44.0404 153.759 44.0404 156.4145 c 44.0404 159.07 41.761 161.2228 38.9493 161.2228 c 36.1376 161.2228 33.8582 159.07 33.8582 156.4145 c 33.8582 153.759 36.1376 151.6062 38.9493 151.6062 c b 0 g 38.9493 156.4145 m F 0 G 0.3 w 10 M 61.7594 178.6432 m S 61.7594 178.6432 m S 61.7594 178.6432 m S 1 g 1 w 4 M 61.7594 173.8349 m 64.5711 173.8349 66.8505 175.9877 66.8505 178.6432 c 66.8505 181.2987 64.5711 183.4515 61.7594 183.4515 c 58.9477 183.4515 56.6683 181.2987 56.6683 178.6432 c 56.6683 175.9877 58.9477 173.8349 61.7594 173.8349 c b 0 g 61.7594 178.6432 m F 0 G 0.3 w 10 M 107.3797 200.8719 m S 84.5696 200.8719 m S u 153 178.6432 m S 153 156.4146 m S 130.1899 156.4146 m S 130.1899 178.6432 m S 141.5949 167.5289 m S U u 130.1899 200.8719 m S 130.1899 178.6432 m S 107.3797 178.6432 m S 107.3797 200.8719 m S 118.7848 189.7576 m S U 130.1899 200.8719 m S 107.3797 200.8719 m S 130.1899 200.8719 m S u 153 200.8719 m S 153 178.6432 m S 130.1899 178.6432 m S 130.1899 200.8719 m S 141.5949 189.7576 m S U u 130.1899 178.6432 m S 130.1899 156.4146 m S 107.3797 156.4146 m S 107.3797 178.6432 m S 118.7848 167.5289 m S U 107.3797 178.6432 m S 84.5696 178.6432 m S u 107.3797 200.8719 m S 107.3797 178.6432 m S 84.5696 178.6432 m S 84.5696 200.8719 m S 95.9746 189.7576 m S U 107.3797 200.8719 m S 84.5696 200.8719 m S 130.1899 200.8719 m S 107.3797 200.8719 m S 130.1899 200.8719 m S 84.5696 200.8719 m S 0 g 1 w 4 M 84.5696 200.8719 m F 0 G 0.3 w 10 M 107.3797 200.8719 m S 0 g 1 w 4 M 107.3797 200.8719 m F 0 G 0.3 w 10 M 130.1899 200.8719 m S 0 g 1 w 4 M 130.1899 200.8719 m F 0 G 0.3 w 10 M 107.3797 178.6432 m S 84.5696 178.6432 m S 130.1899 178.6432 m S 107.3797 178.6432 m S 130.1899 178.6432 m S 84.5696 178.6432 m S 0 g 1 w 4 M 84.5696 178.6432 m F 0 G 0.3 w 10 M 107.3797 178.6432 m S 0 g 1 w 4 M 107.3797 178.6432 m F 0 G 0.3 w 10 M 130.1899 178.6432 m S 0 g 1 w 4 M 130.1899 178.6432 m F 0.7 g 107.3797 200.8719 m F 111.1442 204.0474 m F 103.8942 197.2974 m F 111.8341 203.276 m F 134.6442 181.0474 m F 103.8942 197.2974 m F 126.7043 175.0688 m F 111.1442 204.0474 m F 111.1442 204.0474 m F 133.9543 181.8188 m F 107.3797 200.8719 m F 103.3341 203.7974 m F 111.5841 198.2974 m F 103.3341 203.7974 m F 80.5239 181.5688 m F 111.1443 197.776 m F 88.3341 175.5474 m F 0 G 0.3 w 10 M 99.9892 200.6617 m S 114.2392 200.9117 m S 107.4892 193.6617 m S 130.1899 178.6432 m S 130.1899 178.6432 m S 130.1899 178.6432 m S 0 g 1 w 4 M 130.1899 178.6432 m F 0 G 0.3 w 10 M 84.5696 178.6432 m S 84.5696 178.6432 m S 84.5696 178.6432 m S 0 g 1 w 4 M 84.5696 178.6432 m F 0 G 0.3 w 10 M 107.3797 200.8719 m S 107.3797 200.8719 m S 107.3797 200.8719 m S 0 g 1 w 4 M 107.3797 200.8719 m F 0 G 0.3 w 10 M 130.1898 178.6432 m S 130.1898 156.4146 m S 107.3797 156.4146 m S 107.3797 178.6432 m S 118.7847 167.5289 m S u 175.8101 134.1859 m S 175.8101 111.9573 m S 153 111.9573 m S 153 134.1859 m S 164.405 123.0716 m S U u 153 156.4146 m S 153 134.1859 m S 130.1898 134.1859 m S 130.1898 156.4146 m S 141.5949 145.3003 m S U 153 178.6432 m S 153 156.4146 m S 130.1898 156.4146 m S 130.1898 178.6432 m S 141.5949 167.5289 m S 153 156.4146 m S 153 178.6432 m S u 175.8101 156.4146 m S 175.8101 134.1859 m S 153 134.1859 m S 153 156.4146 m S 164.405 145.3003 m S U u 153 134.1859 m S 153 111.9573 m S 130.1898 111.9573 m S 130.1898 134.1859 m S 141.5949 123.0716 m S U 130.1898 134.1859 m S 107.3797 134.1859 m S u 130.1898 156.4146 m S 130.1898 134.1859 m S 107.3797 134.1859 m S 107.3797 156.4146 m S 118.7847 145.3003 m S U 0 g 1 w 4 M 118.7847 167.5289 m F 0 G 0.3 w 10 M 107.3797 178.6432 m S 0 g 1 w 4 M 107.3797 178.6432 m F 0 G 0.3 w 10 M 130.1898 178.6432 m S 0 g 1 w 4 M 130.1898 178.6432 m F 0 G 0.3 w 10 M 153 178.6432 m S 0 g 1 w 4 M 153 178.6432 m F 0 G 0.3 w 10 M 130.1898 156.4146 m S 107.3797 156.4146 m S 153 156.4146 m S 130.1898 156.4146 m S 153 156.4146 m S 107.3797 156.4146 m S 0 g 1 w 4 M 107.3797 156.4146 m F 0 G 0.3 w 10 M 130.1898 156.4146 m S 0 g 1 w 4 M 130.1898 156.4146 m F 0 G 0.3 w 10 M 153 156.4146 m S 0 g 1 w 4 M 153 156.4146 m F 0 G 0.3 w 10 M 130.1898 134.1859 m S 107.3797 134.1859 m S 153 134.1859 m S 130.1898 134.1859 m S 153 134.1859 m S 107.3797 134.1859 m S 0 g 1 w 4 M 107.3797 134.1859 m F 0 G 0.3 w 10 M 130.1898 134.1859 m S 0 g 1 w 4 M 130.1898 134.1859 m F 0 G 0.3 w 10 M 153 134.1859 m S 0 g 1 w 4 M 153 134.1859 m F 0.7 g 107.3797 178.6432 m F 130.1898 156.4146 m F 111.1442 181.8187 m F 133.9543 159.5901 m F 103.8942 175.0687 m F 126.7043 152.8401 m F 134.6442 158.8187 m F 157.4543 136.5901 m F 126.7043 152.8401 m F 149.5144 130.6115 m F 111.1442 181.8187 m F 133.9543 159.5901 m F 133.9543 159.5901 m F 156.7644 137.3615 m F 153 178.6432 m F 130.1898 156.4146 m F 148.9544 181.5687 m F 126.1442 159.3401 m F 157.2044 176.0687 m F 134.3942 153.8401 m F 126.1442 159.3401 m F 103.334 137.1115 m F 133.9544 153.3187 m F 111.1442 131.0901 m F 0 G 0.3 w 10 M 122.7993 156.2044 m S 130.2993 162.9544 m S 137.0493 156.4544 m S 130.2993 149.2044 m S 0.7 g 1 w 4 M 103.8942 175.0687 m 103.2993 174.9544 111.1442 181.8187 y 130.2993 162.9544 l 148.9544 181.5687 l 157.2044 176.0687 l 137.0493 156.4544 l 157.2993 137.2044 l 149.5144 130.6115 l 130.2993 149.2044 l 111.1442 131.0901 l 103.334 137.1115 l 122.7993 156.2044 l 103.8942 175.0687 l f 0 G 0.3 w 10 M 107.3797 178.6432 m S 107.3797 178.6432 m S 107.3797 178.6432 m S 1 g 1 w 4 M 107.3797 173.8349 m 110.1914 173.8349 112.4708 175.9877 112.4708 178.6432 c 112.4708 181.2987 110.1914 183.4515 107.3797 183.4515 c 104.568 183.4515 102.2886 181.2987 102.2886 178.6432 c 102.2886 175.9877 104.568 173.8349 107.3797 173.8349 c b 0 g 107.3797 178.6432 m F 0 G 0.3 w 10 M 153 178.6432 m S 153 178.6432 m S 153 178.6432 m S 1 g 1 w 4 M 153 173.8349 m 155.8117 173.8349 158.0911 175.9877 158.0911 178.6432 c 158.0911 181.2987 155.8117 183.4515 153 183.4515 c 150.1883 183.4515 147.9089 181.2987 147.9089 178.6432 c 147.9089 175.9877 150.1883 173.8349 153 173.8349 c b 0 g 153 178.6432 m F 0 G 0.3 w 10 M 153 134.1859 m S 153 134.1859 m S 153 134.1859 m S 1 g 1 w 4 M 153 129.3776 m 155.8117 129.3776 158.0911 131.5304 158.0911 134.1859 c 158.0911 136.8414 155.8117 138.9942 153 138.9942 c 150.1883 138.9942 147.9089 136.8414 147.9089 134.1859 c 147.9089 131.5304 150.1883 129.3776 153 129.3776 c b 0 g 153 134.1859 m F 0 G 0.3 w 10 M 107.3797 134.1859 m S 107.3797 134.1859 m S 107.3797 134.1859 m S 1 g 1 w 4 M 107.3797 129.3776 m 110.1914 129.3776 112.4708 131.5304 112.4708 134.1859 c 112.4708 136.8414 110.1914 138.9942 107.3797 138.9942 c 104.568 138.9942 102.2886 136.8414 102.2886 134.1859 c 102.2886 131.5304 104.568 129.3776 107.3797 129.3776 c b 0 g 107.3797 134.1859 m F 0 G 0.3 w 10 M 130.1898 156.4146 m S 130.1898 156.4146 m S 130.1898 156.4146 m S 1 g 1 w 4 M 130.1898 151.6063 m 133.0015 151.6063 135.2809 153.7591 135.2809 156.4146 c 135.2809 159.0701 133.0015 161.2229 130.1898 161.2229 c 127.3781 161.2229 125.0987 159.0701 125.0987 156.4146 c 125.0987 153.7591 127.3781 151.6063 130.1898 151.6063 c b 0 g 130.1898 156.4146 m F 0 G 0.3 w 10 M 175.8101 200.8719 m S 175.8101 178.6433 m S 153 178.6433 m S 153 200.8719 m S 164.405 189.7576 m S u 221.4304 156.4146 m S 221.4304 134.186 m S 198.6203 134.186 m S 198.6203 156.4146 m S 210.0253 145.3003 m S U u 198.6203 178.6433 m S 198.6203 156.4146 m S 175.8101 156.4146 m S 175.8101 178.6433 m S 187.2152 167.529 m S U 198.6203 200.8719 m S 198.6203 178.6433 m S 175.8101 178.6433 m S 175.8101 200.8719 m S 187.2152 189.7576 m S 198.6203 178.6433 m S 198.6203 200.8719 m S u 221.4304 178.6433 m S 221.4304 156.4146 m S 198.6203 156.4146 m S 198.6203 178.6433 m S 210.0253 167.529 m S U u 198.6203 156.4146 m S 198.6203 134.186 m S 175.8101 134.186 m S 175.8101 156.4146 m S 187.2152 145.3003 m S U 175.8101 156.4146 m S 153 156.4146 m S u 175.8101 178.6433 m S 175.8101 156.4146 m S 153 156.4146 m S 153 178.6433 m S 164.405 167.529 m S U 0 g 1 w 4 M 164.405 189.7576 m F 0 G 0.3 w 10 M 153 200.8719 m S 0 g 1 w 4 M 153 200.8719 m F 0 G 0.3 w 10 M 175.8101 200.8719 m S 0 g 1 w 4 M 175.8101 200.8719 m F 0 G 0.3 w 10 M 198.6203 200.8719 m S 0 g 1 w 4 M 198.6203 200.8719 m F 0 G 0.3 w 10 M 175.8101 178.6433 m S 153 178.6433 m S 198.6203 178.6433 m S 175.8101 178.6433 m S 198.6203 178.6433 m S 153 178.6433 m S 0 g 1 w 4 M 153 178.6433 m F 0 G 0.3 w 10 M 175.8101 178.6433 m S 0 g 1 w 4 M 175.8101 178.6433 m F 0 G 0.3 w 10 M 198.6203 178.6433 m S 0 g 1 w 4 M 198.6203 178.6433 m F 0 G 0.3 w 10 M 175.8101 156.4146 m S 153 156.4146 m S 198.6203 156.4146 m S 175.8101 156.4146 m S 198.6203 156.4146 m S 153 156.4146 m S 0 g 1 w 4 M 153 156.4146 m F 0 G 0.3 w 10 M 175.8101 156.4146 m S 0 g 1 w 4 M 175.8101 156.4146 m F 0 G 0.3 w 10 M 198.6203 156.4146 m S 0 g 1 w 4 M 198.6203 156.4146 m F 0.7 g 153 200.8719 m F 175.8101 178.6433 m F 156.7645 204.0474 m F 179.5746 181.8188 m F 149.5145 197.2974 m F 172.3246 175.0688 m F 180.2645 181.0474 m F 203.0746 158.8188 m F 172.3246 175.0688 m F 195.1347 152.8402 m F 156.7645 204.0474 m F 179.5746 181.8188 m F 179.5746 181.8188 m F 202.3847 159.5902 m F 198.6203 200.8719 m F 175.8101 178.6433 m F 194.5747 203.7974 m F 171.7645 181.5688 m F 202.8247 198.2974 m F 180.0145 176.0688 m F 171.7645 181.5688 m F 148.9543 159.3402 m F 179.5747 175.5474 m F 156.7645 153.3188 m F 0 G 0.3 w 10 M 168.4196 178.4331 m S 175.9196 185.1831 m S 182.6696 178.6831 m S 175.9196 171.4331 m S 153 200.8719 m S 153 200.8719 m S 153 200.8719 m S 0 g 1 w 4 M 153 200.8719 m F 0 G 0.3 w 10 M 198.6203 200.8719 m S 198.6203 200.8719 m S 198.6203 200.8719 m S 0 g 1 w 4 M 198.6203 200.8719 m F 0 G 0.3 w 10 M 198.6203 156.4146 m S 198.6203 156.4146 m S 198.6203 156.4146 m S 0 g 1 w 4 M 198.6203 156.4146 m F 0 G 0.3 w 10 M 153 156.4146 m S 153 156.4146 m S 153 156.4146 m S 0 g 1 w 4 M 153 156.4146 m F 0 G 0.3 w 10 M 175.8101 178.6433 m S 175.8101 178.6433 m S 175.8101 178.6433 m S 0 g 1 w 4 M 175.8101 178.6433 m F 0 G 0.3 w 10 M 84.5695 156.4146 m S 84.5695 134.186 m S 61.7594 134.186 m S 61.7594 156.4146 m S 73.1644 145.3003 m S u 130.1898 111.9573 m S 130.1898 89.7287 m S 107.3797 89.7287 m S 107.3797 111.9573 m S 118.7847 100.843 m S U u 107.3797 134.186 m S 107.3797 111.9573 m S 84.5695 111.9573 m S 84.5695 134.186 m S 95.9746 123.0717 m S U 107.3797 156.4146 m S 107.3797 134.186 m S 84.5695 134.186 m S 84.5695 156.4146 m S 95.9746 145.3003 m S 107.3797 134.186 m S 107.3797 156.4146 m S u 130.1898 134.186 m S 130.1898 111.9573 m S 107.3797 111.9573 m S 107.3797 134.186 m S 118.7847 123.0717 m S U u 107.3797 111.9573 m S 107.3797 89.7287 m S 84.5695 89.7287 m S 84.5695 111.9573 m S 95.9746 100.843 m S U 84.5695 111.9573 m S 61.7594 111.9573 m S u 84.5695 134.186 m S 84.5695 111.9573 m S 61.7594 111.9573 m S 61.7594 134.186 m S 73.1644 123.0717 m S U 0 g 1 w 4 M 73.1644 145.3003 m F 0 G 0.3 w 10 M 61.7594 156.4146 m S 0 g 1 w 4 M 61.7594 156.4146 m F 0 G 0.3 w 10 M 84.5695 156.4146 m S 0 g 1 w 4 M 84.5695 156.4146 m F 0 G 0.3 w 10 M 107.3797 156.4146 m S 0 g 1 w 4 M 107.3797 156.4146 m F 0 G 0.3 w 10 M 84.5695 134.186 m S 61.7594 134.186 m S 107.3797 134.186 m S 84.5695 134.186 m S 107.3797 134.186 m S 61.7594 134.186 m S 0 g 1 w 4 M 61.7594 134.186 m F 0 G 0.3 w 10 M 84.5695 134.186 m S 0 g 1 w 4 M 84.5695 134.186 m F 0 G 0.3 w 10 M 107.3797 134.186 m S 0 g 1 w 4 M 107.3797 134.186 m F 0 G 0.3 w 10 M 84.5695 111.9573 m S 61.7594 111.9573 m S 107.3797 111.9573 m S 84.5695 111.9573 m S 107.3797 111.9573 m S 61.7594 111.9573 m S 0 g 1 w 4 M 61.7594 111.9573 m F 0 G 0.3 w 10 M 84.5695 111.9573 m S 0 g 1 w 4 M 84.5695 111.9573 m F 0 G 0.3 w 10 M 107.3797 111.9573 m S 0 g 1 w 4 M 107.3797 111.9573 m F 0.7 g 61.7594 156.4146 m F 84.5695 134.186 m F 65.5239 159.5901 m F 88.334 137.3615 m F 58.2739 152.8401 m F 81.084 130.6115 m F 89.0239 136.5901 m F 111.834 114.3615 m F 81.084 130.6115 m F 103.8941 108.3829 m F 65.5239 159.5901 m F 88.334 137.3615 m F 88.334 137.3615 m F 111.1441 115.1329 m F 107.3797 156.4146 m F 84.5695 134.186 m F 103.3341 159.3401 m F 80.5239 137.1115 m F 111.5841 153.8401 m F 88.7739 131.6115 m F 80.5239 137.1115 m F 57.7137 114.8829 m F 88.3341 131.0901 m F 65.5239 108.8615 m F 0 G 0.3 w 10 M 77.179 133.9758 m S 84.679 140.7258 m S 91.429 134.2258 m S 84.679 126.9758 m S 0.7 g 1 w 4 M 58.2739 152.8401 m 57.679 152.7258 65.5239 159.5901 y 84.679 140.7258 l 103.3341 159.3401 l 111.5841 153.8401 l 91.429 134.2258 l 111.679 114.9758 l 103.8941 108.3829 l 84.679 126.9758 l 65.5239 108.8615 l 57.7137 114.8829 l 77.179 133.9758 l 58.2739 152.8401 l f 0 G 0.3 w 10 M 61.7594 156.4146 m S 61.7594 156.4146 m S 61.7594 156.4146 m S 1 g 1 w 4 M 61.7594 151.6063 m 64.5711 151.6063 66.8505 153.7591 66.8505 156.4146 c 66.8505 159.0701 64.5711 161.2229 61.7594 161.2229 c 58.9477 161.2229 56.6683 159.0701 56.6683 156.4146 c 56.6683 153.7591 58.9477 151.6063 61.7594 151.6063 c b 0 g 61.7594 156.4146 m F 0 G 0.3 w 10 M 107.3797 156.4146 m S 107.3797 156.4146 m S 107.3797 156.4146 m S 1 g 1 w 4 M 107.3797 151.6063 m 110.1914 151.6063 112.4708 153.7591 112.4708 156.4146 c 112.4708 159.0701 110.1914 161.2229 107.3797 161.2229 c 104.568 161.2229 102.2886 159.0701 102.2886 156.4146 c 102.2886 153.7591 104.568 151.6063 107.3797 151.6063 c b 0 g 107.3797 156.4146 m F 0 G 0.3 w 10 M 107.3797 111.9573 m S 107.3797 111.9573 m S 107.3797 111.9573 m S 1 g 1 w 4 M 107.3797 107.149 m 110.1914 107.149 112.4708 109.3018 112.4708 111.9573 c 112.4708 114.6128 110.1914 116.7656 107.3797 116.7656 c 104.568 116.7656 102.2886 114.6128 102.2886 111.9573 c 102.2886 109.3018 104.568 107.149 107.3797 107.149 c b 0 g 107.3797 111.9573 m F 0 G 0.3 w 10 M 61.7594 111.9573 m S 61.7594 111.9573 m S 61.7594 111.9573 m S 1 g 1 w 4 M 61.7594 107.149 m 64.5711 107.149 66.8505 109.3018 66.8505 111.9573 c 66.8505 114.6128 64.5711 116.7656 61.7594 116.7656 c 58.9477 116.7656 56.6683 114.6128 56.6683 111.9573 c 56.6683 109.3018 58.9477 107.149 61.7594 107.149 c b 0 g 61.7594 111.9573 m F 0 G 0.3 w 10 M 84.5695 134.186 m S 84.5695 134.186 m S 84.5695 134.186 m S 1 g 1 w 4 M 84.5695 129.3777 m 87.3812 129.3777 89.6606 131.5305 89.6606 134.186 c 89.6606 136.8415 87.3812 138.9943 84.5695 138.9943 c 81.7578 138.9943 79.4784 136.8415 79.4784 134.186 c 79.4784 131.5305 81.7578 129.3777 84.5695 129.3777 c b 0 g 84.5695 134.186 m F 0 G 0.3 w 10 M 38.9492 134.186 m S 38.9492 111.9574 m S u 84.5695 89.7287 m S 84.5695 67.5001 m S 61.7594 67.5001 m S 61.7594 89.7287 m S 73.1644 78.6144 m S U u 61.7594 111.9574 m S 61.7594 89.7287 m S 38.9492 89.7287 m S 38.9492 111.9574 m S 50.3543 100.8431 m S U 61.7594 134.186 m S 61.7594 111.9574 m S 38.9492 111.9574 m S 38.9492 134.186 m S 50.3543 123.0717 m S 61.7594 111.9574 m S 61.7594 134.186 m S u 84.5695 111.9574 m S 84.5695 89.7287 m S 61.7594 89.7287 m S 61.7594 111.9574 m S 73.1644 100.8431 m S U u 61.7594 89.7287 m S 61.7594 67.5001 m S 38.9492 67.5001 m S 38.9492 89.7287 m S 50.3543 78.6144 m S U 38.9492 89.7287 m S 38.9492 134.186 m S 0 g 1 w 4 M 38.9492 134.186 m F 0 G 0.3 w 10 M 61.7594 134.186 m S 0 g 1 w 4 M 61.7594 134.186 m F 0 G 0.3 w 10 M 38.9492 111.9574 m S 61.7594 111.9574 m S 38.9492 111.9574 m S 61.7594 111.9574 m S 38.9492 111.9574 m S 0 g 1 w 4 M 38.9492 111.9574 m F 0 G 0.3 w 10 M 61.7594 111.9574 m S 0 g 1 w 4 M 61.7594 111.9574 m F 0 G 0.3 w 10 M 38.9492 89.7287 m S 61.7594 89.7287 m S 38.9492 89.7287 m S 61.7594 89.7287 m S 38.9492 89.7287 m S 0 g 1 w 4 M 38.9492 89.7287 m F 0 G 0.3 w 10 M 61.7594 89.7287 m S 0 g 1 w 4 M 61.7594 89.7287 m F 0.7 g 38.9492 111.9574 m F 66.2137 92.1329 m F 58.2738 86.1543 m F 65.5238 92.9043 m F 61.7594 134.186 m F 38.9492 111.9574 m F 57.7138 137.1115 m F 65.9638 131.6115 m F 0 G 0.3 w 10 M 39.0587 118.4972 m S 39.0587 104.7472 m S 61.7594 134.186 m S 61.7594 134.186 m S 61.7594 134.186 m S 0 g 1 w 4 M 61.7594 134.186 m F 0 G 0.3 w 10 M 61.7594 89.7287 m S 61.7594 89.7287 m S 61.7594 89.7287 m S 0 g 1 w 4 M 61.7594 89.7287 m F 0 G 0.3 w 10 M 38.9492 111.9574 m S 38.9492 111.9574 m S 38.9492 111.9574 m S 0 g 1 w 4 M 38.9492 111.9574 m F 0 G 0.3 w 10 M 152.9998 134.186 m S 152.9998 111.9574 m S 130.1898 111.9574 m S 130.1898 134.186 m S 141.5948 123.0717 m S u 198.6201 89.7287 m S 198.6201 67.5001 m S 175.8101 67.5001 m S 175.8101 89.7287 m S 187.2151 78.6144 m S U u 175.8101 111.9574 m S 175.8101 89.7287 m S 152.9998 89.7287 m S 152.9998 111.9574 m S 164.4049 100.8431 m S U 175.8101 134.186 m S 175.8101 111.9574 m S 152.9998 111.9574 m S 152.9998 134.186 m S 164.4049 123.0717 m S 175.8101 111.9574 m S 175.8101 134.186 m S u 198.6201 111.9574 m S 198.6201 89.7287 m S 175.8101 89.7287 m S 175.8101 111.9574 m S 187.2151 100.8431 m S U u 175.8101 89.7287 m S 175.8101 67.5001 m S 152.9998 67.5001 m S 152.9998 89.7287 m S 164.4049 78.6144 m S U 152.9998 89.7287 m S 130.1898 89.7287 m S u 152.9998 111.9574 m S 152.9998 89.7287 m S 130.1898 89.7287 m S 130.1898 111.9574 m S 141.5948 100.8431 m S U 0 g 1 w 4 M 141.5948 123.0717 m F 0 G 0.3 w 10 M 130.1898 134.186 m S 0 g 1 w 4 M 130.1898 134.186 m F 0 G 0.3 w 10 M 152.9998 134.186 m S 0 g 1 w 4 M 152.9998 134.186 m F 0 G 0.3 w 10 M 175.8101 134.186 m S 0 g 1 w 4 M 175.8101 134.186 m F 0 G 0.3 w 10 M 152.9998 111.9574 m S 130.1898 111.9574 m S 175.8101 111.9574 m S 152.9998 111.9574 m S 175.8101 111.9574 m S 130.1898 111.9574 m S 0 g 1 w 4 M 130.1898 111.9574 m F 0 G 0.3 w 10 M 152.9998 111.9574 m S 0 g 1 w 4 M 152.9998 111.9574 m F 0 G 0.3 w 10 M 175.8101 111.9574 m S 0 g 1 w 4 M 175.8101 111.9574 m F 0 G 0.3 w 10 M 152.9998 89.7287 m S 130.1898 89.7287 m S 175.8101 89.7287 m S 152.9998 89.7287 m S 175.8101 89.7287 m S 130.1898 89.7287 m S 0 g 1 w 4 M 130.1898 89.7287 m F 0 G 0.3 w 10 M 152.9998 89.7287 m S 0 g 1 w 4 M 152.9998 89.7287 m F 0 G 0.3 w 10 M 175.8101 89.7287 m S 0 g 1 w 4 M 175.8101 89.7287 m F 0.7 g 130.1898 134.186 m F 152.9998 111.9574 m F 133.9542 137.3615 m F 156.7644 115.1329 m F 126.7042 130.6115 m F 149.5144 108.3829 m F 157.4542 114.3615 m F 180.2644 92.1329 m F 149.5144 108.3829 m F 172.3244 86.1543 m F 133.9542 137.3615 m F 156.7644 115.1329 m F 156.7644 115.1329 m F 179.5744 92.9043 m F 175.8101 134.186 m F 152.9998 111.9574 m F 171.7644 137.1115 m F 148.9542 114.8829 m F 180.0144 131.6115 m F 157.2042 109.3829 m F 148.9542 114.8829 m F 126.1441 92.6543 m F 156.7644 108.8615 m F 133.9542 86.6329 m F 0 G 0.3 w 10 M 145.6094 111.7472 m S 153.1094 118.4972 m S 159.8594 111.9972 m S 153.1094 104.7472 m S 0.7 g 1 w 4 M 126.7042 130.6115 m 126.1094 130.4972 133.9542 137.3615 y 153.1094 118.4972 l 171.7644 137.1115 l 180.0144 131.6115 l 159.8594 111.9972 l 180.1094 92.7472 l 172.3244 86.1543 l 153.1094 104.7472 l 133.9542 86.6329 l 126.1441 92.6543 l 145.6094 111.7472 l 126.7042 130.6115 l f 0 G 0.3 w 10 M 130.1898 134.186 m S 130.1898 134.186 m S 130.1898 134.186 m S 1 g 1 w 4 M 130.1898 129.3777 m 133.0014 129.3777 135.2808 131.5305 135.2808 134.186 c 135.2808 136.8415 133.0014 138.9943 130.1898 138.9943 c 127.378 138.9943 125.0986 136.8415 125.0986 134.186 c 125.0986 131.5305 127.378 129.3777 130.1898 129.3777 c b 0 g 130.1898 134.186 m F 0 G 0.3 w 10 M 175.8101 134.186 m S 175.8101 134.186 m S 175.8101 134.186 m S 1 g 1 w 4 M 175.8101 129.3777 m 178.6217 129.3777 180.9011 131.5305 180.9011 134.186 c 180.9011 136.8415 178.6217 138.9943 175.8101 138.9943 c 172.9983 138.9943 170.7189 136.8415 170.7189 134.186 c 170.7189 131.5305 172.9983 129.3777 175.8101 129.3777 c b 0 g 175.8101 134.186 m F 0 G 0.3 w 10 M 175.8101 89.7287 m S 175.8101 89.7287 m S 175.8101 89.7287 m S 1 g 1 w 4 M 175.8101 84.9204 m 178.6217 84.9204 180.9011 87.0732 180.9011 89.7287 c 180.9011 92.3842 178.6217 94.537 175.8101 94.537 c 172.9983 94.537 170.7189 92.3842 170.7189 89.7287 c 170.7189 87.0732 172.9983 84.9204 175.8101 84.9204 c b 0 g 175.8101 89.7287 m F 0 G 0.3 w 10 M 130.1898 89.7287 m S 130.1898 89.7287 m S 130.1898 89.7287 m S 1 g 1 w 4 M 130.1898 84.9204 m 133.0014 84.9204 135.2808 87.0732 135.2808 89.7287 c 135.2808 92.3842 133.0014 94.537 130.1898 94.537 c 127.378 94.537 125.0986 92.3842 125.0986 89.7287 c 125.0986 87.0732 127.378 84.9204 130.1898 84.9204 c b 0 g 130.1898 89.7287 m F 0 G 0.3 w 10 M 152.9998 111.9574 m S 152.9998 111.9574 m S 152.9998 111.9574 m S 1 g 1 w 4 M 152.9998 107.1491 m 155.8115 107.1491 158.091 109.3019 158.091 111.9574 c 158.091 114.6129 155.8115 116.7657 152.9998 116.7657 c 150.1882 116.7657 147.9087 114.6129 147.9087 111.9574 c 147.9087 109.3019 150.1882 107.1491 152.9998 107.1491 c b 0 g 152.9998 111.9574 m F 0 G 0.3 w 10 M 107.3795 111.9574 m S 107.3795 89.7288 m S 84.5695 89.7288 m S 84.5695 111.9574 m S 95.9745 100.8431 m S u 152.9998 67.5001 m S 152.9998 45.2715 m S 130.1898 45.2715 m S 130.1898 67.5001 m S 141.5948 56.3858 m S U u 130.1898 89.7288 m S 130.1898 67.5001 m S 107.3795 67.5001 m S 107.3795 89.7288 m S 118.7846 78.6145 m S U 130.1898 111.9574 m S 130.1898 89.7288 m S 107.3795 89.7288 m S 107.3795 111.9574 m S 118.7846 100.8431 m S 130.1898 89.7288 m S 130.1898 111.9574 m S u 152.9998 89.7288 m S 152.9998 67.5001 m S 130.1898 67.5001 m S 130.1898 89.7288 m S 141.5948 78.6145 m S U u 130.1898 67.5001 m S 130.1898 45.2715 m S 107.3795 45.2715 m S 107.3795 67.5001 m S 118.7846 56.3858 m S U 107.3795 67.5001 m S 84.5695 67.5001 m S u 107.3795 89.7288 m S 107.3795 67.5001 m S 84.5695 67.5001 m S 84.5695 89.7288 m S 95.9745 78.6145 m S U 0 g 1 w 4 M 95.9745 100.8431 m F 0 G 0.3 w 10 M 84.5695 111.9574 m S 0 g 1 w 4 M 84.5695 111.9574 m F 0 G 0.3 w 10 M 107.3795 111.9574 m S 0 g 1 w 4 M 107.3795 111.9574 m F 0 G 0.3 w 10 M 130.1898 111.9574 m S 0 g 1 w 4 M 130.1898 111.9574 m F 0 G 0.3 w 10 M 107.3795 89.7288 m S 84.5695 89.7288 m S 130.1898 89.7288 m S 107.3795 89.7288 m S 130.1898 89.7288 m S 84.5695 89.7288 m S 0 g 1 w 4 M 84.5695 89.7288 m F 0 G 0.3 w 10 M 107.3795 89.7288 m S 0 g 1 w 4 M 107.3795 89.7288 m F 0 G 0.3 w 10 M 130.1898 89.7288 m S 0 g 1 w 4 M 130.1898 89.7288 m F 0 G 0.3 w 10 M 107.3795 67.5001 m S 84.5695 67.5001 m S 130.1898 67.5001 m S 107.3795 67.5001 m S 130.1898 67.5001 m S 84.5695 67.5001 m S 0 g 1 w 4 M 84.5695 67.5001 m F 0 G 0.3 w 10 M 107.3795 67.5001 m S 0 g 1 w 4 M 107.3795 67.5001 m F 0 G 0.3 w 10 M 130.1898 67.5001 m S 0 g 1 w 4 M 130.1898 67.5001 m F 0.7 g 84.5695 111.9574 m F 107.3795 89.7288 m F 88.3339 115.1329 m F 111.1441 92.9043 m F 81.0839 108.3829 m F 103.8941 86.1543 m F 111.8339 92.1329 m F 134.6441 69.9043 m F 103.8941 86.1543 m F 126.7041 63.9257 m F 88.3339 115.1329 m F 111.1441 92.9043 m F 111.1441 92.9043 m F 133.9541 70.6757 m F 130.1898 111.9574 m F 107.3795 89.7288 m F 126.1441 114.8829 m F 103.3339 92.6543 m F 134.3941 109.3829 m F 111.5839 87.1543 m F 103.3339 92.6543 m F 80.5238 70.4257 m F 111.1441 86.6329 m F 88.3339 64.4043 m F 0 G 0.3 w 10 M 99.9891 89.5186 m S 107.4891 96.2686 m S 114.2391 89.7686 m S 107.4891 82.5186 m S 0.7 g 1 w 4 M 81.0839 108.3829 m 80.4891 108.2686 88.3339 115.1329 y 107.4891 96.2686 l 126.1441 114.8829 l 134.3941 109.3829 l 114.2391 89.7686 l 134.4891 70.5186 l 126.7041 63.9257 l 107.4891 82.5186 l 88.3339 64.4043 l 80.5238 70.4257 l 99.9891 89.5186 l 81.0839 108.3829 l f 0 G 0.3 w 10 M 84.5695 111.9574 m S 84.5695 111.9574 m S 84.5695 111.9574 m S 1 g 1 w 4 M 84.5695 107.1491 m 87.3811 107.1491 89.6605 109.3019 89.6605 111.9574 c 89.6605 114.6129 87.3811 116.7657 84.5695 116.7657 c 81.7577 116.7657 79.4783 114.6129 79.4783 111.9574 c 79.4783 109.3019 81.7577 107.1491 84.5695 107.1491 c b 0 g 84.5695 111.9574 m F 0 G 0.3 w 10 M 130.1898 111.9574 m S 130.1898 111.9574 m S 130.1898 111.9574 m S 1 g 1 w 4 M 130.1898 107.1491 m 133.0014 107.1491 135.2808 109.3019 135.2808 111.9574 c 135.2808 114.6129 133.0014 116.7657 130.1898 116.7657 c 127.378 116.7657 125.0986 114.6129 125.0986 111.9574 c 125.0986 109.3019 127.378 107.1491 130.1898 107.1491 c b 0 g 130.1898 111.9574 m F 0 G 0.3 w 10 M 130.1898 67.5001 m S 130.1898 67.5001 m S 130.1898 67.5001 m S 1 g 1 w 4 M 130.1898 62.6918 m 133.0014 62.6918 135.2808 64.8446 135.2808 67.5001 c 135.2808 70.1556 133.0014 72.3084 130.1898 72.3084 c 127.378 72.3084 125.0986 70.1556 125.0986 67.5001 c 125.0986 64.8446 127.378 62.6918 130.1898 62.6918 c b 0 g 130.1898 67.5001 m F 0 G 0.3 w 10 M 84.5695 67.5001 m S 84.5695 67.5001 m S 84.5695 67.5001 m S 1 g 1 w 4 M 84.5695 62.6918 m 87.3811 62.6918 89.6605 64.8446 89.6605 67.5001 c 89.6605 70.1556 87.3811 72.3084 84.5695 72.3084 c 81.7577 72.3084 79.4783 70.1556 79.4783 67.5001 c 79.4783 64.8446 81.7577 62.6918 84.5695 62.6918 c b 0 g 84.5695 67.5001 m F 0 G 0.3 w 10 M 107.3795 89.7288 m S 107.3795 89.7288 m S 107.3795 89.7288 m S 1 g 1 w 4 M 107.3795 84.9205 m 110.1912 84.9205 112.4707 87.0733 112.4707 89.7288 c 112.4707 92.3843 110.1912 94.5371 107.3795 94.5371 c 104.5679 94.5371 102.2884 92.3843 102.2884 89.7288 c 102.2884 87.0733 104.5679 84.9205 107.3795 84.9205 c b 0 g 107.3795 89.7288 m F 0 G 0.3 w 10 M 61.7592 89.7288 m S 61.7592 67.5002 m S 38.9492 67.5002 m S 38.9492 89.7288 m S 50.3542 78.6145 m S u 381.1014 200.8717 m S 381.1014 178.6431 m S 358.2913 178.6431 m S 358.2913 200.8717 m S 369.6963 189.7574 m S U u 84.5695 67.5002 m S 84.5695 45.2715 m S 61.7592 45.2715 m S 61.7592 67.5002 m S 73.1643 56.3859 m S U 84.5695 89.7288 m S 84.5695 67.5002 m S 61.7592 67.5002 m S 61.7592 89.7288 m S 73.1643 78.6145 m S 84.5695 67.5002 m S 84.5695 89.7288 m S u 107.3795 67.5002 m S 107.3795 45.2715 m S 84.5695 45.2715 m S 84.5695 67.5002 m S 95.9745 56.3859 m S U u 358.2913 200.8717 m S 358.2913 178.6431 m S 335.4811 178.6431 m S 335.4811 200.8717 m S 346.8862 189.7574 m S U 61.7592 45.2715 m S 38.9492 45.2715 m S u 61.7592 67.5002 m S 61.7592 45.2715 m S 38.9492 45.2715 m S 38.9492 67.5002 m S 50.3542 56.3859 m S U 0 g 1 w 4 M 50.3542 78.6145 m F 0 G 0.3 w 10 M 38.9492 89.7288 m S 0 g 1 w 4 M 38.9492 89.7288 m F 0 G 0.3 w 10 M 61.7592 89.7288 m S 0 g 1 w 4 M 61.7592 89.7288 m F 0 G 0.3 w 10 M 84.5695 89.7288 m S 0 g 1 w 4 M 84.5695 89.7288 m F 0 G 0.3 w 10 M 61.7592 67.5002 m S 38.9492 67.5002 m S 84.5695 67.5002 m S 61.7592 67.5002 m S 84.5695 67.5002 m S 38.9492 67.5002 m S 0 g 1 w 4 M 38.9492 67.5002 m F 0 G 0.3 w 10 M 61.7592 67.5002 m S 0 g 1 w 4 M 61.7592 67.5002 m F 0 G 0.3 w 10 M 84.5695 67.5002 m S 0 g 1 w 4 M 84.5695 67.5002 m F 0 G 0.3 w 10 M 61.7592 45.2715 m S 38.9492 45.2715 m S 84.5695 45.2715 m S 61.7592 45.2715 m S 84.5695 45.2715 m S 38.9492 45.2715 m S 0 g 1 w 4 M 38.9492 45.2715 m F 0 G 0.3 w 10 M 61.7592 45.2715 m S 0 g 1 w 4 M 61.7592 45.2715 m F 0 G 0.3 w 10 M 84.5695 45.2715 m S 0 g 1 w 4 M 84.5695 45.2715 m F 0.7 g 38.9492 89.7288 m F 61.7592 67.5002 m F 42.7136 92.9043 m F 65.5238 70.6757 m F 35.4636 86.1543 m F 58.2738 63.9257 m F 66.2136 69.9043 m F 89.0238 47.6757 m F 58.2738 63.9257 m F 81.0838 41.6971 m F 42.7136 92.9043 m F 65.5238 70.6757 m F 65.5238 70.6757 m F 88.3338 48.4471 m F 84.5695 89.7288 m F 61.7592 67.5002 m F 80.5238 92.6543 m F 57.7136 70.4257 m F 88.7738 87.1543 m F 65.9636 64.9257 m F 57.7136 70.4257 m F 34.9035 48.1971 m F 65.5238 64.4043 m F 42.7136 42.1757 m F 0 G 0.3 w 10 M 54.3688 67.29 m S 61.8688 74.04 m S 68.6188 67.54 m S 61.8688 60.29 m S 0.7 g 1 w 4 M 88.8688 48.29 m F 81.0838 41.6971 m F 61.8688 60.29 m F 42.7136 42.1757 m F 34.9035 48.1971 m F 0 G 0.3 w 10 M 38.9492 89.7288 m S 38.9492 89.7288 m S 38.9492 89.7288 m S 0 g 1 w 4 M 38.9492 89.7288 m F 0 G 0.3 w 10 M 84.5695 89.7288 m S 84.5695 89.7288 m S 84.5695 89.7288 m S 0 g 1 w 4 M 84.5695 89.7288 m F 0 G 0.3 w 10 M 84.5695 45.2715 m S 84.5695 45.2715 m S 84.5695 45.2715 m S 0 g 1 w 4 M 84.5695 45.2715 m F 0 G 0.3 w 10 M 38.9492 45.2715 m S 38.9492 45.2715 m S 38.9492 45.2715 m S 0 g 1 w 4 M 38.9492 45.2715 m F 0 G 0.3 w 10 M 61.7592 67.5002 m S 61.7592 67.5002 m S 61.7592 67.5002 m S 0 g 1 w 4 M 61.7592 67.5002 m F 0 G 0.3 w 10 M 61.7592 89.7288 m S 61.7592 67.5002 m S 38.9492 67.5002 m S 38.9492 89.7288 m S 50.3542 78.6145 m S u 84.5695 67.5002 m S 84.5695 45.2715 m S 61.7592 45.2715 m S 61.7592 67.5002 m S 73.1643 56.3859 m S U 84.5695 89.7288 m S 84.5695 67.5002 m S 61.7592 67.5002 m S 61.7592 89.7288 m S 73.1643 78.6145 m S 84.5695 67.5002 m S 84.5695 89.7288 m S u 107.3795 67.5002 m S 107.3795 45.2715 m S 84.5695 45.2715 m S 84.5695 67.5002 m S 95.9745 56.3859 m S U u 61.7592 67.5002 m S 61.7592 45.2715 m S 38.9492 45.2715 m S 38.9492 67.5002 m S 50.3542 56.3859 m S U 0 g 1 w 4 M 50.3542 78.6145 m F 0 G 0.3 w 10 M 38.9492 89.7288 m S 0 g 1 w 4 M 38.9492 89.7288 m F 0 G 0.3 w 10 M 61.7592 89.7288 m S 0 g 1 w 4 M 61.7592 89.7288 m F 0 G 0.3 w 10 M 84.5695 89.7288 m S 0 g 1 w 4 M 84.5695 89.7288 m F 0 G 0.3 w 10 M 61.7592 67.5002 m S 38.9492 67.5002 m S 84.5695 67.5002 m S 61.7592 67.5002 m S 84.5695 67.5002 m S 38.9492 67.5002 m S 0 g 1 w 4 M 38.9492 67.5002 m F 0 G 0.3 w 10 M 61.7592 67.5002 m S 0 g 1 w 4 M 61.7592 67.5002 m F 0 G 0.3 w 10 M 84.5695 67.5002 m S 0 g 1 w 4 M 84.5695 67.5002 m F 0.7 g 38.9492 89.7288 m F 61.7592 67.5002 m F 42.7136 92.9043 m F 65.5238 70.6757 m F 35.4636 86.1543 m F 58.2738 63.9257 m F 66.2136 69.9043 m F 58.2738 63.9257 m F 42.7136 92.9043 m F 65.5238 70.6757 m F 65.5238 70.6757 m F 84.5695 89.7288 m F 61.7592 67.5002 m F 80.5238 92.6543 m F 57.7136 70.4257 m F 88.7738 87.1543 m F 65.9636 64.9257 m F 57.7136 70.4257 m F 65.5238 64.4043 m F 0 G 0.3 w 10 M 54.3688 67.29 m S 61.8688 74.04 m S 68.6188 67.54 m S 61.8688 60.29 m S 0.7 g 1 w 4 M 61.8688 60.29 m F 0 G 0.3 w 10 M 38.9492 89.7288 m S 38.9492 89.7288 m S 38.9492 89.7288 m S 0 g 1 w 4 M 38.9492 89.7288 m F 0 G 0.3 w 10 M 84.5695 89.7288 m S 84.5695 89.7288 m S 84.5695 89.7288 m S 0 g 1 w 4 M 84.5695 89.7288 m F 0 G 0.3 w 10 M 61.7592 67.5002 m S 61.7592 67.5002 m S 61.7592 67.5002 m S 0 g 1 w 4 M 61.7592 67.5002 m F 0.7 g 73.3688 62.79 m 50.1188 62.79 l 54.3688 67.29 l 35.4636 86.1543 l 34.8688 86.04 42.7136 92.9043 y 61.8688 74.04 l 80.5238 92.6543 l 88.7738 87.1543 l 68.6188 67.54 l 73.3688 62.79 l f 0 G 0.3 w 10 M 38.9492 89.7288 m S 1 g 1 w 4 M 38.9492 84.9205 m 41.7608 84.9205 44.0402 87.0733 44.0402 89.7288 c 44.0402 92.3843 41.7608 94.5371 38.9492 94.5371 c 36.1374 94.5371 33.8581 92.3843 33.8581 89.7288 c 33.8581 87.0733 36.1374 84.9205 38.9492 84.9205 c b 38.9492 89.7288 m S 0.3 w 10 M 84.5695 89.7288 m S 1 g 1 w 4 M 84.5695 84.9205 m 87.3811 84.9205 89.6605 87.0733 89.6605 89.7288 c 89.6605 92.3843 87.3811 94.5371 84.5695 94.5371 c 81.7577 94.5371 79.4784 92.3843 79.4784 89.7288 c 79.4784 87.0733 81.7577 84.9205 84.5695 84.9205 c b 84.5695 89.7288 m S 0.3 w 10 M 61.7592 67.5002 m S 1 g 1 w 4 M 61.7592 62.6919 m 64.5709 62.6919 66.8503 64.8447 66.8503 67.5002 c 66.8503 70.1557 64.5709 72.3085 61.7592 72.3085 c 58.9475 72.3085 56.6681 70.1557 56.6681 67.5002 c 56.6681 64.8447 58.9475 62.6919 61.7592 62.6919 c b 61.7592 67.5002 m S u 0.3 w 10 M 127.905 178.6077 m S 127.905 200.8364 m S 150.7151 200.8364 m S 150.7151 178.6077 m S 139.3101 189.722 m S U 104.7753 158.4934 m S 104.7753 180.722 m S 127.5854 180.722 m S 127.5854 158.4934 m S 116.1804 169.6077 m S u 81.9651 180.722 m S 81.9651 202.9507 m S 104.7753 202.9507 m S 104.7753 180.722 m S 93.3702 191.8363 m S U 81.9651 158.4934 m S 81.9651 180.722 m S 104.7753 180.722 m S 104.7753 158.4934 m S 93.3702 169.6077 m S 81.9651 180.722 m S 81.9651 158.4934 m S 59.155 180.722 m S 81.9651 202.9507 m S 81.9651 180.722 m S 70.5601 191.8363 m S u 104.7753 180.722 m S 104.7753 202.9507 m S 127.5854 202.9507 m S 127.5854 180.722 m S 116.1804 191.8363 m S U 0 g 1 w 4 M 116.1804 169.6077 m F 0 G 0.3 w 10 M 127.5854 158.4934 m S 0 g 1 w 4 M 127.5854 158.4934 m F 0 G 0.3 w 10 M 104.7753 158.4934 m S 0 g 1 w 4 M 104.7753 158.4934 m F 0 G 0.3 w 10 M 81.9651 158.4934 m S 0 g 1 w 4 M 81.9651 158.4934 m F 0 G 0.3 w 10 M 104.7753 180.722 m S 127.5854 180.722 m S 81.9651 180.722 m S 104.7753 180.722 m S 81.9651 180.722 m S 127.5854 180.722 m S 0 g 1 w 4 M 127.5854 180.722 m F 0 G 0.3 w 10 M 104.7753 180.722 m S 0 g 1 w 4 M 104.7753 180.722 m F 0 G 0.3 w 10 M 81.9651 180.722 m S 0 g 1 w 4 M 81.9651 180.722 m F 0.7 g 127.5854 158.4934 m F 104.7753 180.722 m F 123.8209 155.3179 m F 101.0108 177.5465 m F 131.0709 162.0679 m F 108.2608 184.2965 m F 100.3209 178.3179 m F 108.2608 184.2965 m F 123.8209 155.3179 m F 101.0108 177.5465 m F 101.0108 177.5465 m F 81.9651 158.4934 m F 104.7753 180.722 m F 86.0107 155.5679 m F 108.8209 177.7965 m F 77.7607 161.0679 m F 108.8209 177.7965 m F 0 G 0.3 w 10 M 112.1658 180.9322 m S 104.6658 174.1822 m S 97.9158 180.6822 m S 104.6658 187.9322 m S 0.7 g 1 w 4 M 104.6658 187.9322 m F 0 G 0.3 w 10 M 127.5854 158.4934 m S 127.5854 158.4934 m S 127.5854 158.4934 m S 0 g 1 w 4 M 127.5854 158.4934 m F 0 G 0.3 w 10 M 81.9651 158.4934 m S 81.9651 158.4934 m S 81.9651 158.4934 m S 0 g 1 w 4 M 81.9651 158.4934 m F 0 G 0.3 w 10 M 104.7753 180.722 m S 104.7753 180.722 m S 104.7753 180.722 m S 0 g 1 w 4 M 104.7753 180.722 m F 0 G 0.3 w 10 M 127.5854 158.4934 m S 1 w 4 M 127.5854 158.4934 m S 0.3 w 10 M 81.9651 158.4934 m S 1 w 4 M 81.9651 158.4934 m S 0.3 w 10 M 104.7753 180.722 m S 1 w 4 M 104.7753 180.722 m S 0.3 w 10 M 107.3797 178.6433 m S 107.3797 200.8719 m S 130.1898 200.8719 m S 130.1898 178.6433 m S 118.7848 189.7576 m S 84.5695 178.6433 m S 84.5695 200.8719 m S 107.3797 200.8719 m S 107.3797 178.6433 m S 95.9746 189.7576 m S 84.5695 200.8719 m S 84.5695 178.6433 m S 0 g 1 w 4 M 118.7848 189.7576 m F 0 G 0.3 w 10 M 130.1898 178.6433 m S 0 g 1 w 4 M 130.1898 178.6433 m F 0 G 0.3 w 10 M 107.3797 178.6433 m S 0 g 1 w 4 M 107.3797 178.6433 m F 0 G 0.3 w 10 M 84.5695 178.6433 m S 0 g 1 w 4 M 84.5695 178.6433 m F 0 G 0.3 w 10 M 107.3797 200.8719 m S 130.1898 200.8719 m S 84.5695 200.8719 m S 107.3797 200.8719 m S 84.5695 200.8719 m S 130.1898 200.8719 m S 0 g 1 w 4 M 130.1898 200.8719 m F 0 G 0.3 w 10 M 107.3797 200.8719 m S 0 g 1 w 4 M 107.3797 200.8719 m F 0 G 0.3 w 10 M 84.5695 200.8719 m S 0 g 1 w 4 M 84.5695 200.8719 m F 0.7 g 130.1898 178.6433 m F 107.3797 200.8719 m F 126.4253 175.4678 m F 103.6152 197.6964 m F 133.6753 182.2178 m F 110.8652 204.4464 m F 102.9253 198.4678 m F 110.8652 204.4464 m F 126.4253 175.4678 m F 103.6152 197.6964 m F 103.6152 197.6964 m F 84.5695 178.6433 m F 107.3797 200.8719 m F 88.6151 175.7178 m F 111.4253 197.9464 m F 80.3651 181.2178 m F 103.1753 203.4464 m F 111.4253 197.9464 m F 103.6151 203.9678 m F 0 G 0.3 w 10 M 114.7702 201.0821 m S 107.2702 194.3321 m S 100.5202 200.8321 m S 130.1898 178.6433 m S 130.1898 178.6433 m S 130.1898 178.6433 m S 0 g 1 w 4 M 130.1898 178.6433 m F 0 G 0.3 w 10 M 84.5695 178.6433 m S 84.5695 178.6433 m S 84.5695 178.6433 m S 0 g 1 w 4 M 84.5695 178.6433 m F 0 G 0.3 w 10 M 107.3797 200.8719 m S 107.3797 200.8719 m S 107.3797 200.8719 m S 0 g 1 w 4 M 107.3797 200.8719 m F 0.7 g 95.7701 205.5821 m 119.0201 205.5821 l 114.7702 201.0821 l 133.6753 182.2178 l 134.2702 182.3321 126.4253 175.4678 y 107.2702 194.3321 l 88.6151 175.7178 l 80.3651 181.2178 l 100.5202 200.8321 l 95.7701 205.5821 l f 0 G 0.3 w 10 M 130.1898 178.6433 m S 1 g 1 w 4 M 130.1898 183.4516 m 127.3781 183.4516 125.0987 181.2988 125.0987 178.6433 c 125.0987 175.9878 127.3781 173.835 130.1898 173.835 c 133.0015 173.835 135.2808 175.9878 135.2808 178.6433 c 135.2808 181.2988 133.0015 183.4516 130.1898 183.4516 c b 130.1898 178.6433 m S 0.3 w 10 M 84.5695 178.6433 m S 1 g 1 w 4 M 84.5695 183.4516 m 81.7578 183.4516 79.4784 181.2988 79.4784 178.6433 c 79.4784 175.9878 81.7578 173.835 84.5695 173.835 c 87.3812 173.835 89.6605 175.9878 89.6605 178.6433 c 89.6605 181.2988 87.3812 183.4516 84.5695 183.4516 c b 84.5695 178.6433 m S 0.3 w 10 M 107.3797 200.8719 m S 1 g 1 w 4 M 107.3797 205.6802 m 104.568 205.6802 102.2886 203.5274 102.2886 200.8719 c 102.2886 198.2164 104.568 196.0636 107.3797 196.0636 c 110.1914 196.0636 112.4708 198.2164 112.4708 200.8719 c 112.4708 203.5274 110.1914 205.6802 107.3797 205.6802 c b 107.3797 200.8719 m S 0.3 w 10 M 175.8101 156.4147 m S 175.8101 178.6433 m S u 152.9998 178.6433 m S 152.9998 200.872 m S 175.8101 200.872 m S 175.8101 178.6433 m S 164.4049 189.7576 m S U 152.9998 156.4147 m S 152.9998 178.6433 m S 175.8101 178.6433 m S 175.8101 156.4147 m S 164.4049 167.529 m S 152.9998 178.6433 m S 152.9998 156.4147 m S u 130.1898 178.6433 m S 130.1898 200.872 m S 152.9998 200.872 m S 152.9998 178.6433 m S 141.5948 189.7576 m S U 175.8101 200.872 m S u 175.8101 178.6433 m S 175.8101 200.872 m S 198.6201 200.872 m S 198.6201 178.6433 m S 187.2151 189.7576 m S U 175.8101 156.4147 m S 0 g 1 w 4 M 175.8101 156.4147 m F 0 G 0.3 w 10 M 152.9998 156.4147 m S 0 g 1 w 4 M 152.9998 156.4147 m F 0 G 0.3 w 10 M 175.8101 178.6433 m S 152.9998 178.6433 m S 175.8101 178.6433 m S 152.9998 178.6433 m S 175.8101 178.6433 m S 0 g 1 w 4 M 175.8101 178.6433 m F 0 G 0.3 w 10 M 152.9998 178.6433 m S 0 g 1 w 4 M 152.9998 178.6433 m F 0 G 0.3 w 10 M 175.8101 200.872 m S 152.9998 200.872 m S 175.8101 200.872 m S 152.9998 200.872 m S 175.8101 200.872 m S 0 g 1 w 4 M 175.8101 200.872 m F 0 G 0.3 w 10 M 152.9998 200.872 m S 0 g 1 w 4 M 152.9998 200.872 m F 0.7 g 175.8101 178.6433 m F 172.0455 175.4678 m F 179.2955 182.2178 m F 171.3556 176.2392 m F 148.5455 198.4678 m F 179.2955 182.2178 m F 156.4855 204.4464 m F 172.0455 175.4678 m F 172.0455 175.4678 m F 149.2355 197.6964 m F 152.9998 156.4147 m F 175.8101 178.6433 m F 157.0455 153.4892 m F 179.8556 175.7178 m F 148.7955 158.9892 m F 171.6056 181.2178 m F 179.8556 175.7178 m F 172.0455 181.7392 m F 0 G 0.3 w 10 M 183.2005 178.8535 m S 175.7005 172.1035 m S 168.9505 178.6035 m S 175.7005 185.8535 m S 0.7 g 1 w 4 M 183.2005 178.8535 m F 0 G 0.3 w 10 M 152.9998 156.4147 m S 152.9998 156.4147 m S 152.9998 156.4147 m S 0 g 1 w 4 M 152.9998 156.4147 m F 0 G 0.3 w 10 M 152.9998 200.872 m S 152.9998 200.872 m S 152.9998 200.872 m S 0 g 1 w 4 M 152.9998 200.872 m F 0 G 0.3 w 10 M 175.8101 178.6433 m S 175.8101 178.6433 m S 175.8101 178.6433 m S 0 g 1 w 4 M 175.8101 178.6433 m F 0.7 g 175.7005 185.8535 m 156.4855 204.4464 l 148.7005 197.8535 l 168.9505 178.6035 l 148.7955 158.9892 l 157.0455 153.4892 l 175.7005 172.1035 l 180.9505 167.6035 l 180.9505 190.6035 l 175.7005 185.8535 l f 1 g 0 G 0.3 w 10 M 175.8101 178.6433 m B 1 w 4 M 175.8101 183.4516 m 172.9984 183.4516 170.719 181.2988 170.719 178.6433 c 170.719 175.9878 172.9984 173.835 175.8101 173.835 c 178.6218 173.835 180.9011 175.9878 180.9011 178.6433 c 180.9011 181.2988 178.6218 183.4516 175.8101 183.4516 c b 175.8101 178.6433 m B 0.3 w 10 M 152.9998 156.4147 m B 1 w 4 M 152.9998 161.223 m 150.1882 161.223 147.9087 159.0702 147.9087 156.4147 c 147.9087 153.7592 150.1882 151.6064 152.9998 151.6064 c 155.8115 151.6064 158.0909 153.7592 158.0909 156.4147 c 158.0909 159.0702 155.8115 161.223 152.9998 161.223 c b 152.9998 156.4147 m B 0.3 w 10 M 152.9998 200.872 m B 1 w 4 M 152.9998 205.6803 m 150.1882 205.6803 147.9087 203.5275 147.9087 200.872 c 147.9087 198.2165 150.1882 196.0637 152.9998 196.0637 c 155.8115 196.0637 158.0909 198.2165 158.0909 200.872 c 158.0909 203.5275 155.8115 205.6803 152.9998 205.6803 c b 152.9998 200.872 m B 0.3 w 10 M 44.3402 158.8138 m S 44.3402 136.5852 m S 32.9351 147.6995 m S 44.3402 136.5852 m S 44.3402 158.8138 m S 44.3402 158.8138 m S 0 g 1 w 4 M 44.3402 158.8138 m F 0 G 0.3 w 10 M 44.3402 136.5852 m S 44.3402 136.5852 m S 44.3402 136.5852 m S 0 g 1 w 4 M 44.3402 136.5852 m F 0.7 g 48.7945 116.7607 m F 48.1046 117.5321 m F 44.3402 158.8138 m F 40.2946 161.7393 m F 48.5446 156.2393 m F 0 G 0.3 w 10 M 44.3402 158.8138 m S 44.3402 158.8138 m S 44.3402 158.8138 m S 0 g 1 w 4 M 44.3402 158.8138 m F 1 g 0 G 0.3 w 10 M 44.3402 158.8138 m B 1 w 4 M 44.3402 158.8138 m B 0.3 w 10 M 38.949 134.1861 m S 38.949 111.9575 m S u 84.5693 89.7288 m S 84.5693 67.5002 m S 61.7592 67.5002 m S 61.7592 89.7288 m S 73.1642 78.6145 m S U u 61.7592 111.9575 m S 61.7592 89.7288 m S 38.949 89.7288 m S 38.949 111.9575 m S 50.3541 100.8432 m S U 61.7592 134.1861 m S 61.7592 111.9575 m S 38.949 111.9575 m S 38.949 134.1861 m S 50.3541 123.0718 m S 61.7592 111.9575 m S 61.7592 134.1861 m S u 84.5693 111.9575 m S 84.5693 89.7288 m S 61.7592 89.7288 m S 61.7592 111.9575 m S 73.1642 100.8432 m S U u 61.7592 89.7288 m S 61.7592 67.5002 m S 38.949 67.5002 m S 38.949 89.7288 m S 50.3541 78.6145 m S U 38.949 89.7288 m S 38.949 134.1861 m S 0 g 1 w 4 M 38.949 134.1861 m F 0 G 0.3 w 10 M 61.7592 134.1861 m S 0 g 1 w 4 M 61.7592 134.1861 m F 0 G 0.3 w 10 M 38.949 111.9575 m S 61.7592 111.9575 m S 38.949 111.9575 m S 61.7592 111.9575 m S 38.949 111.9575 m S 0 g 1 w 4 M 38.949 111.9575 m F 0 G 0.3 w 10 M 61.7592 111.9575 m S 0 g 1 w 4 M 61.7592 111.9575 m F 0 G 0.3 w 10 M 38.949 89.7288 m S 61.7592 89.7288 m S 38.949 89.7288 m S 61.7592 89.7288 m S 38.949 89.7288 m S 0 g 1 w 4 M 38.949 89.7288 m F 0 G 0.3 w 10 M 61.7592 89.7288 m S 0 g 1 w 4 M 61.7592 89.7288 m F 0.7 g 38.949 111.9575 m F 42.7135 115.133 m F 35.4635 108.383 m F 43.4034 114.3616 m F 66.2135 92.133 m F 35.4635 108.383 m F 58.2736 86.1544 m F 42.7135 115.133 m F 42.7135 115.133 m F 65.5236 92.9044 m F 61.7592 134.1861 m F 38.949 111.9575 m F 57.7136 137.1116 m F 34.9034 114.883 m F 65.9636 131.6116 m F 43.1534 109.383 m F 34.9034 114.883 m F 42.7136 108.8616 m F 0 G 0.3 w 10 M 39.0585 118.4973 m S 45.8085 111.9973 m S 39.0585 104.7473 m S 61.7592 134.1861 m S 61.7592 134.1861 m S 61.7592 134.1861 m S 0 g 1 w 4 M 61.7592 134.1861 m F 0 G 0.3 w 10 M 61.7592 89.7288 m S 61.7592 89.7288 m S 61.7592 89.7288 m S 0 g 1 w 4 M 61.7592 89.7288 m F 0 G 0.3 w 10 M 38.949 111.9575 m S 38.949 111.9575 m S 38.949 111.9575 m S 0 g 1 w 4 M 38.949 111.9575 m F 0.7 g 39.0585 104.7473 m 58.2736 86.1544 l 66.0585 92.7473 l 45.8085 111.9973 l 65.9636 131.6116 l 57.7136 137.1116 l 39.0585 118.4973 l 33.8086 122.9973 l 33.8086 99.9973 l 39.0585 104.7473 l f 1 g 0 G 0.3 w 10 M 38.949 111.9575 m B 1 w 4 M 38.949 107.1492 m 41.7607 107.1492 44.0401 109.302 44.0401 111.9575 c 44.0401 114.613 41.7607 116.7658 38.949 116.7658 c 36.1373 116.7658 33.8579 114.613 33.8579 111.9575 c 33.8579 109.302 36.1373 107.1492 38.949 107.1492 c b 38.949 111.9575 m B 0.3 w 10 M 61.7592 134.1861 m B 1 w 4 M 61.7592 129.3778 m 64.5709 129.3778 66.8503 131.5306 66.8503 134.1861 c 66.8503 136.8416 64.5709 138.9944 61.7592 138.9944 c 58.9475 138.9944 56.6681 136.8416 56.6681 134.1861 c 56.6681 131.5306 58.9475 129.3778 61.7592 129.3778 c b 61.7592 134.1861 m B 0.3 w 10 M 61.7592 89.7288 m B 1 w 4 M 61.7592 84.9205 m 64.5709 84.9205 66.8503 87.0733 66.8503 89.7288 c 66.8503 92.3843 64.5709 94.5371 61.7592 94.5371 c 58.9475 94.5371 56.6681 92.3843 56.6681 89.7288 c 56.6681 87.0733 58.9475 84.9205 61.7592 84.9205 c b 61.7592 89.7288 m B 0.3 w 10 M 130.1896 67.5001 m S 130.1896 45.2715 m S 107.3795 45.2715 m S 107.3795 67.5001 m S 118.7845 56.3858 m S u 426.7217 200.8717 m S 426.7217 178.643 m S 403.9115 178.643 m S 403.9115 200.8717 m S 415.3166 189.7574 m S U 152.9998 67.5001 m S 152.9998 45.2715 m S 130.1896 45.2715 m S 130.1896 67.5001 m S 141.5947 56.3858 m S 152.9998 45.2715 m S 152.9998 67.5001 m S u 426.7217 178.643 m S 426.7217 156.4144 m S 403.9115 156.4144 m S 403.9115 178.643 m S 415.3166 167.5287 m S U 403.9115 178.643 m S 381.1014 178.643 m S u 403.9115 200.8717 m S 403.9115 178.643 m S 381.1014 178.643 m S 381.1014 200.8717 m S 392.5064 189.7574 m S U 0 g 1 w 4 M 118.7845 56.3858 m F 0 G 0.3 w 10 M 107.3795 67.5001 m S 0 g 1 w 4 M 107.3795 67.5001 m F 0 G 0.3 w 10 M 130.1896 67.5001 m S 0 g 1 w 4 M 130.1896 67.5001 m F 0 G 0.3 w 10 M 152.9998 67.5001 m S 0 g 1 w 4 M 152.9998 67.5001 m F 0 G 0.3 w 10 M 130.1896 45.2715 m S 107.3795 45.2715 m S 152.9998 45.2715 m S 130.1896 45.2715 m S 152.9998 45.2715 m S 107.3795 45.2715 m S 0 g 1 w 4 M 107.3795 45.2715 m F 0 G 0.3 w 10 M 130.1896 45.2715 m S 0 g 1 w 4 M 130.1896 45.2715 m F 0 G 0.3 w 10 M 152.9998 45.2715 m S 0 g 1 w 4 M 152.9998 45.2715 m F 0 G 0.3 w 10 M 403.9115 178.643 m S 381.1014 178.643 m S 426.7217 178.643 m S 403.9115 178.643 m S 426.7217 178.643 m S 381.1014 178.643 m S 0 g 1 w 4 M 381.1014 178.643 m F 0 G 0.3 w 10 M 403.9115 178.643 m S 0 g 1 w 4 M 403.9115 178.643 m F 0 G 0.3 w 10 M 426.7217 178.643 m S 0 g 1 w 4 M 426.7217 178.643 m F 0.7 g 107.3795 67.5001 m F 130.1896 45.2715 m F 111.144 70.6756 m F 133.9541 48.447 m F 103.894 63.9256 m F 126.7041 41.697 m F 134.644 47.6756 m F 126.7041 41.697 m F 111.144 70.6756 m F 133.9541 48.447 m F 133.9541 48.447 m F 152.9998 67.5001 m F 130.1896 45.2715 m F 148.9542 70.4256 m F 126.144 48.197 m F 157.2042 64.9256 m F 134.394 42.697 m F 126.144 48.197 m F 133.9542 42.1756 m F 0 G 0.3 w 10 M 122.7991 45.0613 m S 130.2991 51.8113 m S 137.0491 45.3113 m S 130.2991 38.0613 m S 0.7 g 1 w 4 M 130.2991 38.0613 m F 0 G 0.3 w 10 M 107.3795 67.5001 m S 107.3795 67.5001 m S 107.3795 67.5001 m S 0 g 1 w 4 M 107.3795 67.5001 m F 0 G 0.3 w 10 M 152.9998 67.5001 m S 152.9998 67.5001 m S 152.9998 67.5001 m S 0 g 1 w 4 M 152.9998 67.5001 m F 0 G 0.3 w 10 M 426.7217 178.643 m S 426.7217 178.643 m S 426.7217 178.643 m S 0 g 1 w 4 M 426.7217 178.643 m F 0 G 0.3 w 10 M 381.1014 178.643 m S 381.1014 178.643 m S 381.1014 178.643 m S 0 g 1 w 4 M 381.1014 178.643 m F 0 G 0.3 w 10 M 130.1896 45.2715 m S 130.1896 45.2715 m S 130.1896 45.2715 m S 0 g 1 w 4 M 130.1896 45.2715 m F 0.7 g 103.3713 64.2714 m 105.1213 62.5214 l 118.8713 62.7714 l 110.8713 70.5214 111.144 70.6756 v 103.2991 63.8113 103.894 63.9256 v F 130.2991 51.8113 m F 154.8713 62.7714 m 141.1213 62.7714 l 148.6213 70.5214 148.9542 70.4256 v 157.2042 64.9256 l 154.8713 63.2714 154.8713 62.7714 v f 0 G 0.3 w 10 M 107.3795 67.5001 m S 1 g 1 w 4 M 107.3795 62.6918 m 110.1912 62.6918 112.4706 64.8446 112.4706 67.5001 c 112.4706 70.1556 110.1912 72.3084 107.3795 72.3084 c 104.5678 72.3084 102.2884 70.1556 102.2884 67.5001 c 102.2884 64.8446 104.5678 62.6918 107.3795 62.6918 c b 107.3795 67.5001 m S 0.3 w 10 M 152.9998 67.5001 m S 1 g 1 w 4 M 152.9998 62.6918 m 155.8115 62.6918 158.0909 64.8446 158.0909 67.5001 c 158.0909 70.1556 155.8115 72.3084 152.9998 72.3084 c 150.1881 72.3084 147.9087 70.1556 147.9087 67.5001 c 147.9087 64.8446 150.1881 62.6918 152.9998 62.6918 c b 152.9998 67.5001 m S 0.3 w 10 M 130.1896 45.2715 m S 1 w 4 M 130.1896 45.2715 m S 0.3 w 10 M 38.949 45.2716 m S 312.6709 178.6431 m S 38.949 67.5002 m S 38.949 45.2716 m S 38.949 45.2716 m S 38.949 67.5002 m S 312.6709 178.6431 m S 312.6709 156.4145 m S 38.949 67.5002 m S 0 g 1 w 4 M 38.949 67.5002 m F 0 G 0.3 w 10 M 38.949 45.2716 m S 38.949 45.2716 m S 38.949 45.2716 m S 0 g 1 w 4 M 312.6709 200.8718 m F 0 G 0.3 w 10 M 312.6709 178.6431 m S 312.6709 178.6431 m S 312.6709 178.6431 m S 0 g 1 w 4 M 312.6709 178.6431 m F 0.7 g 38.949 67.5002 m F 34.9034 70.4257 m F 43.1534 64.9257 m F 0 G 0.3 w 10 M 38.949 67.5002 m S 38.949 67.5002 m S 38.949 67.5002 m S 0 g 1 w 4 M 38.949 67.5002 m F 0 G 0.3 w 10 M 312.6709 178.6431 m S 312.6709 178.6431 m S 312.6709 178.6431 m S 0 g 1 w 4 M 312.6709 178.6431 m F 0.7 g 40.8204 62.7715 m 40.8204 63.2715 43.1534 64.9257 y 34.9034 70.4257 l 33.8579 67.5002 l F 0 G 0.3 w 10 M 38.949 67.5002 m S 1 w 4 M 38.949 67.5002 m S 1 g 40.8204 62.7715 m B 0.3 w 10 M 153 200.872 m S 175.8101 200.872 m S 130.1898 200.872 m S 153 200.872 m S 130.1898 200.872 m S 175.8101 200.872 m S 0 g 1 w 4 M 175.8101 200.872 m F 0 G 0.3 w 10 M 153 200.872 m S 0 g 1 w 4 M 153 200.872 m F 0 G 0.3 w 10 M 130.1898 200.872 m S 0 g 1 w 4 M 130.1898 200.872 m F 0.7 g 175.8101 200.872 m F 172.0456 197.6965 m F 179.2956 204.4465 m F 172.0456 197.6965 m F 130.1898 200.872 m F 134.2354 197.9465 m F 125.9854 203.4465 m F 0 G 0.3 w 10 M 175.8101 200.872 m S 175.8101 200.872 m S 175.8101 200.872 m S 0 g 1 w 4 M 175.8101 200.872 m F 0 G 0.3 w 10 M 130.1898 200.872 m S 130.1898 200.872 m S 130.1898 200.872 m S 0 g 1 w 4 M 130.1898 200.872 m F 0.7 g 179.8183 204.1006 m 178.0683 205.8506 l 164.3183 205.6006 l 172.3183 197.8506 172.0456 197.6965 v 179.8905 204.5608 179.2956 204.4465 v F 128.3183 205.6006 m 142.0683 205.6006 l 134.5683 197.8506 134.2354 197.9465 v 125.9854 203.4465 l 128.3183 205.1006 128.3183 205.6006 v f 0 G 0.3 w 10 M 175.8101 200.872 m S 1 g 1 w 4 M 175.8101 205.6803 m 172.9984 205.6803 170.719 203.5275 170.719 200.872 c 170.719 198.2165 172.9984 196.0637 175.8101 196.0637 c 178.6218 196.0637 180.9012 198.2165 180.9012 200.872 c 180.9012 203.5275 178.6218 205.6803 175.8101 205.6803 c b 175.8101 200.872 m S 0.3 w 10 M 130.1898 200.872 m S 1 g 1 w 4 M 130.1898 205.6803 m 127.3781 205.6803 125.0987 203.5275 125.0987 200.872 c 125.0987 198.2165 127.3781 196.0637 130.1898 196.0637 c 133.0015 196.0637 135.2809 198.2165 135.2809 200.872 c 135.2809 203.5275 133.0015 205.6803 130.1898 205.6803 c b 130.1898 200.872 m S 0.3 w 10 M 38.9493 200.8719 m S 61.7594 200.8719 m S 38.9493 200.8719 m S 61.7594 200.8719 m S 0 g 1 w 4 M 61.7594 200.8719 m F 0 G 0.3 w 10 M 38.9493 200.8719 m S 0 g 1 w 4 M 38.9493 200.8719 m F 0.7 g 61.7594 200.8719 m F 57.9949 197.6964 m F 65.2449 204.4464 m F 57.9949 197.6964 m F 0 G 0.3 w 10 M 61.7594 200.8719 m S 61.7594 200.8719 m S 61.7594 200.8719 m S 0 g 1 w 4 M 61.7594 200.8719 m F 0.7 g 65.7677 204.1006 m 64.0177 205.8506 l 50.2677 205.6006 l 58.2677 197.8506 57.9949 197.6964 v 65.8398 204.5607 65.2449 204.4464 v F 0 G 0.3 w 10 M 61.7594 200.8719 m S 1 g 1 w 4 M 61.7594 205.6802 m 58.9477 205.6802 56.6683 203.5274 56.6683 200.8719 c 56.6683 198.2164 58.9477 196.0636 61.7594 196.0636 c 64.5711 196.0636 66.8505 198.2164 66.8505 200.8719 c 66.8505 203.5274 64.5711 205.6802 61.7594 205.6802 c b 61.7594 200.8719 m S u 0.3 w 10 M 61.7594 134.1859 m S 61.7594 111.9573 m S 38.9493 111.9573 m S 38.9493 134.1859 m S 50.3543 123.0716 m S U 38.9493 178.6432 m S 38.9493 156.4146 m S 38.9493 156.4146 m S 38.9493 178.6432 m S u 61.7594 156.4146 m S 61.7594 134.1859 m S 38.9493 134.1859 m S 38.9493 156.4146 m S 50.3543 145.3003 m S U 38.9493 178.6432 m S 0 g 1 w 4 M 38.9493 178.6432 m F 0 G 0.3 w 10 M 38.9493 156.4146 m S 38.9493 156.4146 m S 38.9493 156.4146 m S 0 g 1 w 4 M 38.9493 156.4146 m F 0 G 0.3 w 10 M 38.9493 134.1859 m S 38.9493 134.1859 m S 38.9493 134.1859 m S 0 g 1 w 4 M 38.9493 134.1859 m F 0.7 g 43.4036 136.5901 m F 35.4637 130.6115 m F 42.7137 137.3615 m F 38.9493 178.6432 m F 34.9037 181.5687 m F 43.1537 176.0687 m F 0 G 0.3 w 10 M 38.9493 178.6432 m S 38.9493 178.6432 m S 38.9493 178.6432 m S 0 g 1 w 4 M 38.9493 178.6432 m F 0 G 0.3 w 10 M 38.9493 134.1859 m S 38.9493 134.1859 m S 38.9493 134.1859 m S 0 g 1 w 4 M 38.9493 134.1859 m F 0.7 g 35.4637 130.6115 m 43.2486 137.2044 l 43.0707 137.4145 33.5707 146.1645 y 33.8207 132.6645 l 35.0707 130.9145 35.4637 130.6115 v f 1 g 0 G 0.3 w 10 M 38.9493 178.6432 m B 1 w 4 M 38.9493 178.6432 m B 0.3 w 10 M 38.9493 134.1859 m B 1 w 4 M 38.9493 129.3776 m 41.761 129.3776 44.0404 131.5304 44.0404 134.1859 c 44.0404 136.8414 41.761 138.9942 38.9493 138.9942 c 36.1376 138.9942 33.8582 136.8414 33.8582 134.1859 c 33.8582 131.5304 36.1376 129.3776 38.9493 129.3776 c b 38.9493 134.1859 m B 0.7 g 43.1537 176.0687 m 34.0707 167.1645 l 33.8207 180.4145 l 34.9866 181.7228 34.9037 181.5687 v 43.1537 176.0687 l f 1 g 0 G 0.3 w 10 M 38.9493 178.6432 m B 1 w 4 M 38.9493 173.8349 m 41.761 173.8349 44.0404 175.9877 44.0404 178.6432 c 44.0404 181.2987 41.761 183.4515 38.9493 183.4515 c 36.1376 183.4515 33.8582 181.2987 33.8582 178.6432 c 33.8582 175.9877 36.1376 173.8349 38.9493 173.8349 c b 38.9493 178.6432 m B 0.3 w 10 M 198.6203 111.9574 m S 198.6203 134.186 m S 221.4304 134.186 m S 221.4304 111.9574 m S 210.0254 123.0717 m S u 153 156.4147 m S 153 178.6433 m S 175.8101 178.6433 m S 175.8101 156.4147 m S 164.4051 167.529 m S U u 175.8101 134.186 m S 175.8101 156.4147 m S 198.6203 156.4147 m S 198.6203 134.186 m S 187.2152 145.3003 m S U 175.8101 111.9574 m S 175.8101 134.186 m S 198.6203 134.186 m S 198.6203 111.9574 m S 187.2152 123.0717 m S 175.8101 134.186 m S 175.8101 111.9574 m S u 153 134.186 m S 153 156.4147 m S 175.8101 156.4147 m S 175.8101 134.186 m S 164.4051 145.3003 m S U u 175.8101 156.4147 m S 175.8101 178.6433 m S 198.6203 178.6433 m S 198.6203 156.4147 m S 187.2152 167.529 m S U 198.6203 156.4147 m S 221.4304 156.4147 m S u 198.6203 134.186 m S 198.6203 156.4147 m S 221.4304 156.4147 m S 221.4304 134.186 m S 210.0254 145.3003 m S U 0 g 1 w 4 M 210.0254 123.0717 m F 0 G 0.3 w 10 M 221.4304 111.9574 m S 0 g 1 w 4 M 221.4304 111.9574 m F 0 G 0.3 w 10 M 198.6203 111.9574 m S 0 g 1 w 4 M 198.6203 111.9574 m F 0 G 0.3 w 10 M 175.8101 111.9574 m S 0 g 1 w 4 M 175.8101 111.9574 m F 0 G 0.3 w 10 M 198.6203 134.186 m S 221.4304 134.186 m S 175.8101 134.186 m S 198.6203 134.186 m S 175.8101 134.186 m S 221.4304 134.186 m S 0 g 1 w 4 M 221.4304 134.186 m F 0 G 0.3 w 10 M 198.6203 134.186 m S 0 g 1 w 4 M 198.6203 134.186 m F 0 G 0.3 w 10 M 175.8101 134.186 m S 0 g 1 w 4 M 175.8101 134.186 m F 0 G 0.3 w 10 M 198.6203 156.4147 m S 221.4304 156.4147 m S 175.8101 156.4147 m S 198.6203 156.4147 m S 175.8101 156.4147 m S 221.4304 156.4147 m S 0 g 1 w 4 M 221.4304 156.4147 m F 0 G 0.3 w 10 M 198.6203 156.4147 m S 0 g 1 w 4 M 198.6203 156.4147 m F 0 G 0.3 w 10 M 175.8101 156.4147 m S 0 g 1 w 4 M 175.8101 156.4147 m F 0.7 g 221.4304 111.9574 m F 198.6203 134.186 m F 217.6659 108.7819 m F 194.8558 131.0105 m F 202.1058 137.7605 m F 194.1659 131.7819 m F 171.3558 154.0105 m F 202.1058 137.7605 m F 179.2957 159.9891 m F 217.6659 108.7819 m F 194.8558 131.0105 m F 194.8558 131.0105 m F 172.0457 153.2391 m F 175.8101 111.9574 m F 198.6203 134.186 m F 179.8557 109.0319 m F 202.6659 131.2605 m F 171.6057 114.5319 m F 194.4159 136.7605 m F 202.6659 131.2605 m F 194.8557 137.2819 m F 217.6659 159.5105 m F 0 G 0.3 w 10 M 206.0108 134.3962 m S 198.5108 127.6462 m S 191.7608 134.1462 m S 198.5108 141.3962 m S 0.7 g 1 w 4 M 217.6659 159.5105 m F 206.0108 134.3962 m F 0 G 0.3 w 10 M 221.4304 111.9574 m S 221.4304 111.9574 m S 221.4304 111.9574 m S 0 g 1 w 4 M 221.4304 111.9574 m F 0 G 0.3 w 10 M 175.8101 111.9574 m S 175.8101 111.9574 m S 175.8101 111.9574 m S 0 g 1 w 4 M 175.8101 111.9574 m F 0 G 0.3 w 10 M 175.8101 156.4147 m S 175.8101 156.4147 m S 175.8101 156.4147 m S 0 g 1 w 4 M 175.8101 156.4147 m F 0 G 0.3 w 10 M 221.4304 156.4147 m S 221.4304 156.4147 m S 221.4304 156.4147 m S 0 g 1 w 4 M 221.4304 156.4147 m F 0 G 0.3 w 10 M 198.6203 134.186 m S 198.6203 134.186 m S 198.6203 134.186 m S 0 g 1 w 4 M 198.6203 134.186 m F 0.7 g 179.2957 159.9891 m 171.5108 153.3962 l 171.6886 153.186 181.1886 144.436 y 180.9386 157.936 l 179.6886 159.686 179.2957 159.9891 v f 191.7608 134.1462 m F 1 g 0 G 0.3 w 10 M 198.6203 134.186 m B 1 w 4 M 198.6203 134.186 m B 0.3 w 10 M 175.8101 111.9574 m B 1 w 4 M 175.8101 111.9574 m B 0.3 w 10 M 175.8101 156.4147 m B 1 w 4 M 175.8101 161.223 m 172.9984 161.223 170.719 159.0702 170.719 156.4147 c 170.719 153.7592 172.9984 151.6064 175.8101 151.6064 c 178.6218 151.6064 180.9012 153.7592 180.9012 156.4147 c 180.9012 159.0702 178.6218 161.223 175.8101 161.223 c b 175.8101 156.4147 m B 0.7 g 171.6057 114.5319 m 180.6886 123.436 l 180.9386 110.186 l 179.7727 108.8777 179.8557 109.0319 v 171.6057 114.5319 l f 1 g 0 G 0.3 w 10 M 175.8101 111.9574 m B 1 w 4 M 175.8101 116.7657 m 172.9984 116.7657 170.719 114.6129 170.719 111.9574 c 170.719 109.3019 172.9984 107.1491 175.8101 107.1491 c 178.6218 107.1491 180.9011 109.3019 180.9011 111.9574 c 180.9011 114.6129 178.6218 116.7657 175.8101 116.7657 c b 175.8101 111.9574 m B 0.3 w 10 M 175.81 45.2714 m S 175.81 67.5001 m S u 130.1897 89.7288 m S 130.1897 111.9573 m S 152.9998 111.9573 m S 152.9998 89.7288 m S 141.5948 100.8431 m S U u 152.9998 67.5001 m S 152.9998 89.7288 m S 175.81 89.7288 m S 175.81 67.5001 m S 164.4049 78.6144 m S U 152.9998 45.2714 m S 152.9998 67.5001 m S 175.81 67.5001 m S 175.81 45.2714 m S 164.4049 56.3858 m S 152.9998 67.5001 m S 152.9998 45.2714 m S u 130.1897 67.5001 m S 130.1897 89.7288 m S 152.9998 89.7288 m S 152.9998 67.5001 m S 141.5948 78.6144 m S U u 152.9998 89.7288 m S 152.9998 111.9573 m S 175.81 111.9573 m S 175.81 89.7288 m S 164.4049 100.8431 m S U 175.81 89.7288 m S u 175.81 67.5001 m S 175.81 89.7288 m S 198.6201 89.7288 m S 198.6201 67.5001 m S 187.2151 78.6144 m S U 175.81 45.2714 m S 0 g 1 w 4 M 175.81 45.2714 m F 0 G 0.3 w 10 M 152.9998 45.2714 m S 0 g 1 w 4 M 152.9998 45.2714 m F 0 G 0.3 w 10 M 175.81 67.5001 m S 152.9998 67.5001 m S 175.81 67.5001 m S 152.9998 67.5001 m S 175.81 67.5001 m S 0 g 1 w 4 M 175.81 67.5001 m F 0 G 0.3 w 10 M 152.9998 67.5001 m S 0 g 1 w 4 M 152.9998 67.5001 m F 0 G 0.3 w 10 M 175.81 89.7288 m S 152.9998 89.7288 m S 175.81 89.7288 m S 152.9998 89.7288 m S 175.81 89.7288 m S 0 g 1 w 4 M 175.81 89.7288 m F 0 G 0.3 w 10 M 152.9998 89.7288 m S 0 g 1 w 4 M 152.9998 89.7288 m F 0.7 g 175.81 67.5001 m F 172.0455 64.3245 m F 179.2955 71.0745 m F 171.3556 65.096 m F 148.5455 87.3245 m F 179.2955 71.0745 m F 156.4854 93.3032 m F 172.0455 64.3245 m F 172.0455 64.3245 m F 149.2354 86.5532 m F 152.9998 45.2714 m F 175.81 67.5001 m F 179.8556 64.5745 m F 148.7954 47.846 m F 171.6056 70.0745 m F 179.8556 64.5745 m F 172.0454 70.596 m F 0 G 0.3 w 10 M 183.2005 67.7102 m S 175.7005 60.9602 m S 168.9505 67.4602 m S 175.7005 74.7102 m S 0.7 g 1 w 4 M 183.2005 67.7102 m F 0 G 0.3 w 10 M 152.9998 45.2714 m S 152.9998 45.2714 m S 152.9998 45.2714 m S 0 g 1 w 4 M 152.9998 45.2714 m F 0 G 0.3 w 10 M 152.9998 89.7288 m S 152.9998 89.7288 m S 152.9998 89.7288 m S 0 g 1 w 4 M 152.9998 89.7288 m F 0 G 0.3 w 10 M 175.81 67.5001 m S 175.81 67.5001 m S 175.81 67.5001 m S 0 g 1 w 4 M 175.81 67.5001 m F 0.7 g 175.7005 60.9602 m F 180.9505 56.4602 m F 1 g 0 G 0.3 w 10 M 175.81 67.5001 m B 1 w 4 M 175.81 67.5001 m B 0.3 w 10 M 152.9998 45.2714 m B 1 w 4 M 152.9998 45.2714 m B 0.3 w 10 M 152.9998 89.7288 m B 1 w 4 M 152.9998 89.7288 m B 0.7 g 163.9049 62.4601 m 180.9049 62.7101 l 180.9505 79.4602 l 175.7005 74.7102 l 156.4854 93.3032 l 148.7005 86.7102 l 168.9505 67.4602 l 163.9049 62.4601 l f 0 G 0.3 w 10 M 175.81 67.5001 m S 1 g 1 w 4 M 175.81 62.6918 m 178.6217 62.6918 180.9011 64.8446 180.9011 67.5001 c 180.9011 70.1556 178.6217 72.3084 175.81 72.3084 c 172.9983 72.3084 170.7189 70.1556 170.7189 67.5001 c 170.7189 64.8446 172.9983 62.6918 175.81 62.6918 c b 175.81 67.5001 m S 1 g 0.3 w 10 M 152.9998 89.7288 m B 1 w 4 M 152.9998 84.9205 m 155.8115 84.9205 158.0909 87.0733 158.0909 89.7288 c 158.0909 92.3843 155.8115 94.5371 152.9998 94.5371 c 150.1881 94.5371 147.9087 92.3843 147.9087 89.7288 c 147.9087 87.0733 150.1881 84.9205 152.9998 84.9205 c b 152.9998 89.7288 m B 0.7 g 33.8579 67.5002 m F 33.8579 67.5002 m 33.8101 62.5 l 40.3101 62.25 l F 0 G 0.3 w 10 M 38.949 67.5002 m S 0 g 1 w 4 M 38.949 67.5002 m F 0 G 0.3 w 10 M 38.949 67.5002 m S 38.949 67.5002 m S 38.949 67.5002 m S 38.949 67.5002 m S 38.949 67.5002 m S 38.949 67.5002 m S 38.949 67.5002 m S 1 g 1 w 4 M 38.949 62.6919 m 41.7607 62.6919 44.0401 64.8447 44.0401 67.5002 c 44.0401 70.1557 41.7607 72.3085 38.949 72.3085 c 36.1373 72.3085 33.8579 70.1557 33.8579 67.5002 c 33.8579 64.8447 36.1373 62.6919 38.949 62.6919 c b 0 g 38.949 67.5002 m F 0 G 0.3 w 10 M 335.4811 178.6431 m S 335.4811 178.6431 m S 335.4811 178.6431 m S 335.4811 178.6431 m S 335.4811 178.6431 m S 335.4811 178.6431 m S 335.4811 178.6431 m S 335.4811 178.6431 m S 0 g 1 w 4 M 335.4811 173.8348 m 338.2928 173.8348 340.5722 175.9876 340.5722 178.6431 c 340.5722 181.2986 338.2928 183.4514 335.4811 183.4514 c 332.6694 183.4514 330.39 181.2986 330.39 178.6431 c 330.39 175.9876 332.6694 173.8348 335.4811 173.8348 c b 335.4811 178.6431 m F 0 G 0.3 w 10 M 358.2914 134.1856 m S 358.2914 134.1856 m S 358.2914 134.1856 m S 358.2914 134.1856 m S 358.2914 134.1856 m S 358.2914 134.1856 m S 358.2914 134.1856 m S 358.2914 134.1856 m S 0 g 1 w 4 M 358.2914 129.3773 m 361.1031 129.3773 363.3825 131.5301 363.3825 134.1856 c 363.3825 136.8411 361.1031 138.9939 358.2914 138.9939 c 355.4797 138.9939 353.2003 136.8411 353.2003 134.1856 c 353.2003 131.5301 355.4797 129.3773 358.2914 129.3773 c b 358.2914 134.1856 m F 0 G 0.3 w 10 M 403.9115 156.4144 m S 403.9115 156.4144 m S 403.9115 156.4144 m S 403.9115 156.4144 m S 403.9115 156.4144 m S 403.9115 156.4144 m S 403.9115 156.4144 m S 403.9115 156.4144 m S 0 g 1 w 4 M 403.9115 151.6061 m 406.7232 151.6061 409.0026 153.7589 409.0026 156.4144 c 409.0026 159.0699 406.7232 161.2227 403.9115 161.2227 c 401.0998 161.2227 398.8204 159.0699 398.8204 156.4144 c 398.8204 153.7589 401.0998 151.6061 403.9115 151.6061 c b 403.9115 156.4144 m F 0 G 0.3 w 10 M 381.1015 89.7284 m S 381.1015 89.7284 m S 381.1015 89.7284 m S 381.1015 89.7284 m S 381.1015 89.7284 m S 381.1015 89.7284 m S 381.1015 89.7284 m S 381.1015 89.7284 m S 0 g 1 w 4 M 381.1015 84.9201 m 383.9132 84.9201 386.1926 87.0729 386.1926 89.7284 c 386.1926 92.3839 383.9132 94.5367 381.1015 94.5367 c 378.2898 94.5367 376.0104 92.3839 376.0104 89.7284 c 376.0104 87.0729 378.2898 84.9201 381.1015 84.9201 c b 381.1015 89.7284 m F 0 G 0.3 w 10 M 426.7218 111.957 m S 426.7218 111.957 m S 426.7218 111.957 m S 426.7218 111.957 m S 426.7218 111.957 m S 426.7218 111.957 m S 426.7218 111.957 m S 426.7218 111.957 m S 0 g 1 w 4 M 426.7218 107.1487 m 429.5335 107.1487 431.8129 109.3015 431.8129 111.957 c 431.8129 114.6125 429.5335 116.7653 426.7218 116.7653 c 423.9101 116.7653 421.6307 114.6125 421.6307 111.957 c 421.6307 109.3015 423.9101 107.1487 426.7218 107.1487 c b 426.7218 111.957 m F 0 G 0.3 w 10 M 449.5319 178.6429 m S 449.5319 178.6429 m S 449.5319 178.6429 m S 449.5319 178.6429 m S 449.5319 178.6429 m S 449.5319 178.6429 m S 449.5319 178.6429 m S 449.5319 178.6429 m S 0 g 1 w 4 M 449.5319 183.4512 m 446.7202 183.4512 444.4408 181.2984 444.4408 178.6429 c 444.4408 175.9874 446.7202 173.8346 449.5319 173.8346 c B 449.5319 178.6429 m F 0 G 0.3 w 10 M 381.1014 200.8717 m S 381.1014 200.8717 m S 381.1014 200.8717 m S 381.1014 200.8717 m S 381.1014 200.8717 m S 381.1014 200.8717 m S 381.1014 200.8717 m S 381.1014 200.8717 m S 0 g 1 w 4 M 381.1014 205.68 m B 376.0103 200.8717 m 376.0103 198.2162 378.2897 196.0634 381.1014 196.0634 c 383.9131 196.0634 386.1925 198.2162 386.1925 200.8717 c B 381.1014 200.8717 m F 0 G 0.3 w 10 M 312.6711 111.957 m S 312.6711 111.957 m S 312.6711 111.957 m S 312.6711 111.957 m S 312.6711 111.957 m S 312.6711 111.957 m S 312.6711 111.957 m S 312.6711 111.957 m S 0 g 1 w 4 M 307.58 111.957 m B 312.6711 107.1487 m 315.4828 107.1487 317.7622 109.3015 317.7622 111.957 c 317.7622 114.6125 315.4828 116.7653 312.6711 116.7653 c B 312.6711 111.957 m F 0 G 0.3 w 10 M 335.4812 67.4998 m S 335.4812 67.4998 m S 335.4812 67.4998 m S 335.4812 67.4998 m S 335.4812 67.4998 m S 335.4812 67.4998 m S 335.4812 67.4998 m S 335.4812 67.4998 m S 0 g 1 w 4 M 335.4812 62.6915 m B 340.5723 67.4998 m 340.5723 70.1553 338.2929 72.3081 335.4812 72.3081 c 332.6695 72.3081 330.3901 70.1553 330.3901 67.4998 c B 335.4812 67.4998 m F 0 G 0.3 w 10 M 426.7218 67.4998 m S 426.7218 67.4998 m S 426.7218 67.4998 m S 426.7218 67.4998 m S 426.7218 67.4998 m S 426.7218 67.4998 m S 426.7218 67.4998 m S 426.7218 67.4998 m S 0 g 1 w 4 M 431.8129 67.4998 m B 426.7218 67.4998 m F 0 G 0.3 w 10 M 449.5319 67.4998 m S 449.5319 67.4998 m S 449.5319 67.4998 m S 449.5319 67.4998 m S 449.5319 67.4998 m S 449.5319 67.4998 m S 449.5319 67.4998 m S 449.5319 67.4998 m S 0 g 1 w 4 M 449.5319 62.6915 m B 444.4408 67.4998 m 444.4408 70.1553 446.7202 72.3081 449.5319 72.3081 c 449.5319 67.4998 l 444.4408 67.4998 l b 449.5319 67.4998 m F u u /_Symbol 24 29 0 0 z [1 0 0 1 230.9683 128.3125]e (\256)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 235.8101 35.5]e (\(d\))t T U U showpage _E end %%EndDocument @endspecial 475 x @beginspecial 31 @llx 33.500000 @lly 413 @urx 190.500000 @ury 2196 @rwi @setspecial %%BeginDocument: fig2e.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n []/_Symbol/Symbol Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z u 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 62.7594 181.8718 m S 62.7594 159.6432 m S 39.9493 159.6432 m S 39.9493 181.8718 m S 51.3543 170.7575 m S U 108.3797 137.4145 m S 108.3797 115.1859 m S 85.5696 115.1859 m S 85.5696 137.4145 m S 96.9746 126.3002 m S 85.5696 159.6432 m S 85.5696 137.4145 m S 62.7594 137.4145 m S 62.7594 159.6432 m S 74.1645 148.5289 m S u 85.5696 181.8718 m S 85.5696 159.6432 m S 62.7594 159.6432 m S 62.7594 181.8718 m S 74.1645 170.7575 m S U u 108.3797 181.8718 m S 108.3797 159.6432 m S 85.5696 159.6432 m S 85.5696 181.8718 m S 96.9746 170.7575 m S U 108.3797 159.6432 m S 108.3797 137.4145 m S 85.5696 137.4145 m S 85.5696 159.6432 m S 96.9746 148.5289 m S 85.5696 137.4145 m S 85.5696 115.1859 m S 62.7594 115.1859 m S 62.7594 137.4145 m S 74.1645 126.3002 m S 62.7594 137.4145 m S 62.7594 115.1859 m S 39.9493 115.1859 m S 39.9493 137.4145 m S 51.3543 126.3002 m S 62.7594 159.6432 m S 62.7594 137.4145 m S 39.9493 137.4145 m S 39.9493 159.6432 m S 51.3543 148.5289 m S 0 g 1 w 4 M 51.3543 170.7575 m F 96.9746 170.7575 m F 51.3543 126.3002 m F 96.9746 126.3002 m F u 0 G 0.3 w 10 M 131.1898 181.8718 m S 131.1898 159.6432 m S 108.3797 159.6432 m S 108.3797 181.8718 m S 119.7847 170.7575 m S U 176.8101 137.4145 m S 176.8101 115.1859 m S 154 115.1859 m S 154 137.4145 m S 165.405 126.3002 m S 154 159.6432 m S 154 137.4145 m S 131.1898 137.4145 m S 131.1898 159.6432 m S 142.5949 148.5289 m S u 154 181.8718 m S 154 159.6432 m S 131.1898 159.6432 m S 131.1898 181.8718 m S 142.5949 170.7575 m S U 176.8101 181.8718 m S 176.8101 159.6432 m S 154 159.6432 m S 154 181.8718 m S 165.405 170.7575 m S 176.8101 159.6432 m S 176.8101 137.4145 m S 154 137.4145 m S 154 159.6432 m S 165.405 148.5289 m S 154 137.4145 m S 154 115.1859 m S 131.1898 115.1859 m S 131.1898 137.4145 m S 142.5949 126.3002 m S 131.1898 137.4145 m S 131.1898 115.1859 m S 108.3797 115.1859 m S 108.3797 137.4145 m S 119.7847 126.3002 m S 131.1898 159.6432 m S 131.1898 137.4145 m S 108.3797 137.4145 m S 108.3797 159.6432 m S 119.7847 148.5289 m S 0 g 1 w 4 M 119.7847 170.7575 m F 165.405 170.7575 m F 119.7847 126.3002 m F 165.405 126.3002 m F 0 G 0.3 w 10 M 199.6202 181.8718 m S 199.6202 159.6432 m S 176.8101 159.6432 m S 176.8101 181.8718 m S 188.2151 170.7575 m S u 245.2405 137.4145 m S 245.2405 115.1859 m S 222.4304 115.1859 m S 222.4304 137.4145 m S 233.8354 126.3002 m S U 222.4304 159.6432 m S 222.4304 137.4145 m S 199.6202 137.4145 m S 199.6202 159.6432 m S 211.0253 148.5289 m S 222.4304 181.8718 m S 222.4304 159.6432 m S 199.6202 159.6432 m S 199.6202 181.8718 m S 211.0253 170.7575 m S u 245.2405 181.8718 m S 245.2405 159.6432 m S 222.4304 159.6432 m S 222.4304 181.8718 m S 233.8354 170.7575 m S U u 245.2405 159.6432 m S 245.2405 137.4145 m S 222.4304 137.4145 m S 222.4304 159.6432 m S 233.8354 148.5289 m S U 222.4304 137.4145 m S 222.4304 115.1859 m S 199.6202 115.1859 m S 199.6202 137.4145 m S 211.0253 126.3002 m S 199.6202 137.4145 m S 199.6202 115.1859 m S 176.8101 115.1859 m S 176.8101 137.4145 m S 188.2151 126.3002 m S 199.6202 159.6432 m S 199.6202 137.4145 m S 176.8101 137.4145 m S 176.8101 159.6432 m S 188.2151 148.5289 m S 0 g 1 w 4 M 188.2151 170.7575 m F 233.8354 170.7575 m F 188.2151 126.3002 m F 233.8354 126.3002 m F u 0 G 0.3 w 10 M 268.0506 181.8718 m S 268.0506 159.6432 m S 245.2405 159.6432 m S 245.2405 181.8718 m S 256.6455 170.7575 m S U u 313.6709 137.4145 m S 313.6709 115.1859 m S 290.8608 115.1859 m S 290.8608 137.4145 m S 302.2658 126.3002 m S U u 290.8608 159.6432 m S 290.8608 137.4145 m S 268.0506 137.4145 m S 268.0506 159.6432 m S 279.4557 148.5289 m S U u 290.8608 181.8718 m S 290.8608 159.6432 m S 268.0506 159.6432 m S 268.0506 181.8718 m S 279.4557 170.7575 m S U 313.6709 181.8718 m S 313.6709 159.6432 m S 290.8608 159.6432 m S 290.8608 181.8718 m S 302.2658 170.7575 m S u 313.6709 159.6432 m S 313.6709 137.4145 m S 290.8608 137.4145 m S 290.8608 159.6432 m S 302.2658 148.5289 m S U u 290.8608 137.4145 m S 290.8608 115.1859 m S 268.0506 115.1859 m S 268.0506 137.4145 m S 279.4557 126.3002 m S U u 268.0506 137.4145 m S 268.0506 115.1859 m S 245.2405 115.1859 m S 245.2405 137.4145 m S 256.6455 126.3002 m S U u 268.0506 159.6432 m S 268.0506 137.4145 m S 245.2405 137.4145 m S 245.2405 159.6432 m S 256.6455 148.5289 m S U 0 g 1 w 4 M 256.6455 170.7575 m F 302.2658 170.7575 m F 256.6455 126.3002 m F 302.2658 126.3002 m F 0 G 0.3 w 10 M 62.7594 115.1859 m S 62.7594 92.9572 m S 39.9493 92.9572 m S 39.9493 115.1859 m S 51.3543 104.0716 m S u 85.5696 92.9572 m S 85.5696 70.7286 m S 62.7594 70.7286 m S 62.7594 92.9572 m S 74.1645 81.843 m S U 85.5696 115.1859 m S 85.5696 92.9572 m S 62.7594 92.9572 m S 62.7594 115.1859 m S 74.1645 104.0716 m S 108.3797 115.1859 m S 108.3797 92.9572 m S 85.5696 92.9572 m S 85.5696 115.1859 m S 96.9746 104.0716 m S u 108.3797 92.9572 m S 108.3797 70.7286 m S 85.5696 70.7286 m S 85.5696 92.9572 m S 96.9746 81.843 m S U u 62.7594 92.9572 m S 62.7594 70.7286 m S 39.9493 70.7286 m S 39.9493 92.9572 m S 51.3543 81.843 m S U 0 g 1 w 4 M 51.3543 104.0716 m F 96.9746 104.0716 m F 51.3543 59.6143 m F 96.9746 59.6143 m F 0 G 0.3 w 10 M 131.1898 115.1859 m S 131.1898 92.9572 m S 108.3797 92.9572 m S 108.3797 115.1859 m S 119.7847 104.0716 m S u 154 92.9572 m S 154 70.7286 m S 131.1898 70.7286 m S 131.1898 92.9572 m S 142.5949 81.843 m S U 154 115.1859 m S 154 92.9572 m S 131.1898 92.9572 m S 131.1898 115.1859 m S 142.5949 104.0716 m S 176.8101 115.1859 m S 176.8101 92.9572 m S 154 92.9572 m S 154 115.1859 m S 165.405 104.0716 m S u 176.8101 92.9572 m S 176.8101 70.7286 m S 154 70.7286 m S 154 92.9572 m S 165.405 81.843 m S U u 131.1898 92.9572 m S 131.1898 70.7286 m S 108.3797 70.7286 m S 108.3797 92.9572 m S 119.7847 81.843 m S U 0 g 1 w 4 M 119.7847 104.0716 m F 165.405 104.0716 m F 119.7847 59.6143 m F 165.405 59.6143 m F 0 G 0.3 w 10 M 199.6202 115.1859 m S 199.6202 92.9572 m S 176.8101 92.9572 m S 176.8101 115.1859 m S 188.2151 104.0716 m S u 222.4304 92.9572 m S 222.4304 70.7286 m S 199.6202 70.7286 m S 199.6202 92.9572 m S 211.0253 81.843 m S U 222.4304 115.1859 m S 222.4304 92.9572 m S 199.6202 92.9572 m S 199.6202 115.1859 m S 211.0253 104.0716 m S u 245.2405 115.1859 m S 245.2405 92.9572 m S 222.4304 92.9572 m S 222.4304 115.1859 m S 233.8354 104.0716 m S U u 245.2405 92.9572 m S 245.2405 70.7286 m S 222.4304 70.7286 m S 222.4304 92.9572 m S 233.8354 81.843 m S U u 199.6202 92.9572 m S 199.6202 70.7286 m S 176.8101 70.7286 m S 176.8101 92.9572 m S 188.2151 81.843 m S U 0 g 1 w 4 M 188.2151 104.0716 m F 233.8354 104.0716 m F 188.2151 59.6143 m F 233.8354 59.6143 m F u 0 G 0.3 w 10 M 268.0506 115.1859 m S 268.0506 92.9572 m S 245.2405 92.9572 m S 245.2405 115.1859 m S 256.6455 104.0716 m S U u 290.8608 92.9572 m S 290.8608 70.7286 m S 268.0506 70.7286 m S 268.0506 92.9572 m S 279.4557 81.843 m S U u 290.8608 115.1859 m S 290.8608 92.9572 m S 268.0506 92.9572 m S 268.0506 115.1859 m S 279.4557 104.0716 m S U u 313.6709 115.1859 m S 313.6709 92.9572 m S 290.8608 92.9572 m S 290.8608 115.1859 m S 302.2658 104.0716 m S U u 313.6709 92.9572 m S 313.6709 70.7286 m S 290.8608 70.7286 m S 290.8608 92.9572 m S 302.2658 81.843 m S U u 268.0506 92.9572 m S 268.0506 70.7286 m S 245.2405 70.7286 m S 245.2405 92.9572 m S 256.6455 81.843 m S U 0 g 1 w 4 M 256.6455 104.0716 m F 302.2658 104.0716 m F 256.6455 59.6143 m F 302.2658 59.6143 m F 0.7 g 39.9493 181.8718 m 85.5696 181.8718 l 62.7594 159.6432 l 39.9493 181.8718 l f 131.1898 181.8718 m 108.3797 159.6432 l 154 159.6432 l 131.1898 181.8718 l f 85.5696 137.4145 m 62.7594 115.1859 l 108.3797 115.1859 l 85.5696 137.4145 l f 131.1898 137.4145 m 176.8101 137.4145 l 154 115.1859 l 131.1898 137.4145 l f 39.9493 92.9572 m 85.5696 92.9572 l 62.7594 70.7286 l 39.9493 92.9572 l f 131.1898 92.9572 m 108.3797 70.7286 l 154 70.7286 l 131.1898 92.9572 l f 0 G 0.3 w 10 M 176.8101 92.9572 m S 176.8101 70.7286 m S 176.8101 70.7286 m S 199.6202 92.9572 m S 199.6202 70.7286 m S 176.8101 70.7286 m S 176.8101 92.9572 m S 188.2151 81.8429 m S 199.6202 70.7286 m S 199.6202 70.7286 m S 199.6202 92.9572 m S 199.6202 70.7286 m S 176.8101 70.7286 m S 0 g 1 w 4 M 188.2151 81.8429 m F 0 G 0.3 w 10 M 39.9493 114.1629 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 114.1629 m S 39.9493 137.4145 m S 0.7 g 1 w 4 M 39.9493 114.1629 m F 0 G 0.3 w 10 M 39.9493 70.7286 m S 39.9493 70.7286 m S 108.3797 70.7286 m S 382.1013 181.8718 m S 359.2912 181.8718 m S 85.5696 70.7286 m S 96.9746 59.6143 m S 85.5696 70.7286 m S 359.2912 181.8718 m S 336.481 181.8718 m S 62.7594 70.7286 m S 74.1645 59.6143 m S 62.7594 70.7286 m S 336.481 181.8718 m S 313.6709 181.8718 m S 39.9493 70.7286 m S 51.3543 59.6143 m S 176.8101 70.7286 m S 154 70.7286 m S 165.405 59.6143 m S 154 70.7286 m S 404.9114 181.8718 m S 131.1898 70.7286 m S 142.5949 59.6143 m S 131.1898 70.7286 m S 404.9114 181.8718 m S 382.1013 181.8718 m S 108.3797 70.7286 m S 119.7847 59.6143 m S 245.2405 70.7286 m S 222.4304 70.7286 m S 233.8354 59.6143 m S 222.4304 70.7286 m S 199.6202 70.7286 m S 211.0253 59.6143 m S 199.6202 70.7286 m S 176.8101 70.7286 m S 188.2151 59.6143 m S 313.6709 70.7286 m S 290.8608 70.7286 m S 302.2658 59.6143 m S 290.8608 70.7286 m S 268.0506 70.7286 m S 279.4557 59.6143 m S 268.0506 70.7286 m S 245.2405 70.7286 m S 256.6455 59.6143 m S 0 g 1 w 4 M 325.0759 170.7575 m F 370.6962 170.7575 m F 393.5063 170.7575 m F 0 G 0.3 w 10 M 336.481 181.8718 m S 336.481 159.6431 m S 313.6709 159.6431 m S 313.6709 181.8718 m S 325.0759 170.7575 m S 382.1013 137.4145 m S 382.1013 115.1859 m S 359.2912 115.1859 m S 359.2912 137.4145 m S 370.6962 126.3002 m S 359.2912 159.6431 m S 359.2912 137.4145 m S 336.481 137.4145 m S 336.481 159.6431 m S 347.8861 148.5288 m S 359.2912 181.8718 m S 359.2912 159.6431 m S 336.481 159.6431 m S 336.481 181.8718 m S 347.8861 170.7575 m S 382.1013 181.8718 m S 382.1013 159.6431 m S 359.2912 159.6431 m S 359.2912 181.8718 m S 370.6962 170.7575 m S 382.1013 159.6431 m S 382.1013 137.4145 m S 359.2912 137.4145 m S 359.2912 159.6431 m S 370.6962 148.5288 m S 359.2912 137.4145 m S 359.2912 115.1859 m S 336.481 115.1859 m S 336.481 137.4145 m S 347.8861 126.3002 m S 336.481 137.4145 m S 336.481 115.1859 m S 313.6709 115.1859 m S 313.6709 137.4145 m S 325.0759 126.3002 m S 336.481 159.6431 m S 336.481 137.4145 m S 313.6709 137.4145 m S 313.6709 159.6431 m S 325.0759 148.5288 m S 0 g 1 w 4 M 325.0759 170.7575 m F 370.6962 170.7575 m F 325.0759 126.3002 m F 370.6962 126.3002 m F 0 G 0.3 w 10 M 404.9114 181.8718 m S 404.9114 159.6431 m S 382.1013 159.6431 m S 382.1013 181.8718 m S 393.5063 170.7575 m S 404.9114 137.4145 m S 404.9114 159.6431 m S 404.9114 159.6431 m S 404.9114 181.8718 m S 404.9114 115.1859 m S 404.9114 137.4145 m S 404.9114 137.4145 m S 404.9114 115.1859 m S 382.1013 115.1859 m S 382.1013 137.4145 m S 393.5063 126.3002 m S 404.9114 159.6431 m S 404.9114 137.4145 m S 382.1013 137.4145 m S 382.1013 159.6431 m S 393.5063 148.5288 m S 0 g 1 w 4 M 393.5063 170.7575 m F 393.5063 126.3002 m F 0 G 0.3 w 10 M 336.481 115.1859 m S 336.481 92.9572 m S 313.6709 92.9572 m S 313.6709 115.1859 m S 325.0759 104.0716 m S 382.1013 70.7286 m S 359.2912 70.7286 m S 370.6962 59.6143 m S 359.2912 92.9572 m S 359.2912 70.7286 m S 336.481 70.7286 m S 336.481 92.9572 m S 347.8861 81.8429 m S 359.2912 115.1859 m S 359.2912 92.9572 m S 336.481 92.9572 m S 336.481 115.1859 m S 347.8861 104.0716 m S 382.1013 115.1859 m S 382.1013 92.9572 m S 359.2912 92.9572 m S 359.2912 115.1859 m S 370.6962 104.0716 m S 382.1013 92.9572 m S 382.1013 70.7286 m S 359.2912 70.7286 m S 359.2912 92.9572 m S 370.6962 81.8429 m S 359.2912 70.7286 m S 336.481 70.7286 m S 347.8861 59.6143 m S 336.481 70.7286 m S 313.6709 70.7286 m S 325.0759 59.6143 m S 336.481 92.9572 m S 336.481 70.7286 m S 313.6709 70.7286 m S 313.6709 92.9572 m S 325.0759 81.8429 m S 0 g 1 w 4 M 325.0759 104.0716 m F 370.6962 104.0716 m F 325.0759 59.6143 m F 370.6962 59.6143 m F 0 G 0.3 w 10 M 404.9114 115.1859 m S 404.9114 92.9572 m S 382.1013 92.9572 m S 382.1013 115.1859 m S 393.5063 104.0716 m S 404.9114 70.7286 m S 404.9114 92.9572 m S 404.9114 92.9572 m S 404.9114 115.1859 m S 404.9114 70.7286 m S 404.9114 70.7286 m S 382.1013 70.7286 m S 393.5063 59.6143 m S 404.9114 92.9572 m S 404.9114 70.7286 m S 382.1013 70.7286 m S 382.1013 92.9572 m S 393.5063 81.8429 m S 0 g 1 w 4 M 393.5063 104.0716 m F 393.5063 59.6143 m F 0 G 0.3 w 10 M 313.6709 181.8718 m S 313.6709 181.8718 m S 313.6709 181.8718 m S 313.6709 181.8718 m S 0.7 g 1 w 4 M 313.6709 181.8718 m F 39.9493 70.7286 m F 0 G 0.3 w 10 M 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 0 g 1 w 4 M 176.8101 181.8718 m F 0 G 0.3 w 10 M 176.8101 137.4145 m S 176.8101 137.4145 m S 176.8101 137.4145 m S 176.8101 137.4145 m S 176.8101 137.4145 m S 176.8101 137.4145 m S 176.8101 137.4145 m S 176.8101 137.4145 m S 176.8101 137.4145 m S 176.8101 137.4145 m S 176.8101 137.4145 m S 176.8101 137.4145 m S 1 g 1 w 4 M 176.8101 132.6062 m 179.6218 132.6062 181.9012 134.759 181.9012 137.4145 c 181.9012 140.07 179.6218 142.2228 176.8101 142.2228 c 173.9984 142.2228 171.719 140.07 171.719 137.4145 c 171.719 134.759 173.9984 132.6062 176.8101 132.6062 c b 0 g 176.8101 137.4145 m F 0 G 0.3 w 10 M 154 159.6432 m S 154 159.6432 m S 154 159.6432 m S 154 159.6432 m S 154 159.6432 m S 154 159.6432 m S 154 159.6432 m S 154 159.6432 m S 154 159.6432 m S 154 159.6432 m S 154 159.6432 m S 154 159.6432 m S 1 g 1 w 4 M 154 154.8349 m 156.8117 154.8349 159.0911 156.9877 159.0911 159.6432 c 159.0911 162.2987 156.8117 164.4515 154 164.4515 c 151.1883 164.4515 148.9089 162.2987 148.9089 159.6432 c 148.9089 156.9877 151.1883 154.8349 154 154.8349 c b 0 g 154 159.6432 m F 0 G 0.3 w 10 M 154 115.1859 m S 154 115.1859 m S 154 115.1859 m S 154 115.1859 m S 154 115.1859 m S 154 115.1859 m S 154 115.1859 m S 154 115.1859 m S 154 115.1859 m S 154 115.1859 m S 154 115.1859 m S 154 115.1859 m S 1 g 1 w 4 M 154 110.3776 m 156.8117 110.3776 159.0911 112.5304 159.0911 115.1859 c 159.0911 117.8414 156.8117 119.9942 154 119.9942 c 151.1883 119.9942 148.9089 117.8414 148.9089 115.1859 c 148.9089 112.5304 151.1883 110.3776 154 110.3776 c b 0 g 154 115.1859 m F 0 G 0.3 w 10 M 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 0 g 1 w 4 M 176.8101 92.9572 m F 0 G 0.3 w 10 M 154 70.7286 m S 154 70.7286 m S 154 70.7286 m S 154 70.7286 m S 154 70.7286 m S 154 70.7286 m S 154 70.7286 m S 154 70.7286 m S 154 70.7286 m S 154 70.7286 m S 154 70.7286 m S 154 70.7286 m S 1 g 1 w 4 M 154 65.9203 m 156.8117 65.9203 159.0911 68.0731 159.0911 70.7286 c 159.0911 73.3841 156.8117 75.5369 154 75.5369 c 151.1883 75.5369 148.9089 73.3841 148.9089 70.7286 c 148.9089 68.0731 151.1883 65.9203 154 65.9203 c b 0 g 154 70.7286 m F 0 G 0.3 w 10 M 108.3797 159.6432 m S 108.3797 159.6432 m S 108.3797 159.6432 m S 108.3797 159.6432 m S 108.3797 159.6432 m S 108.3797 159.6432 m S 108.3797 159.6432 m S 108.3797 159.6432 m S 108.3797 159.6432 m S 108.3797 159.6432 m S 108.3797 159.6432 m S 108.3797 159.6432 m S 1 g 1 w 4 M 108.3797 154.8349 m 111.1914 154.8349 113.4708 156.9877 113.4708 159.6432 c 113.4708 162.2987 111.1914 164.4515 108.3797 164.4515 c 105.568 164.4515 103.2886 162.2987 103.2886 159.6432 c 103.2886 156.9877 105.568 154.8349 108.3797 154.8349 c b 0 g 108.3797 159.6432 m F 0 G 0.3 w 10 M 131.1898 181.8718 m S 131.1898 181.8718 m S 131.1898 181.8718 m S 131.1898 181.8718 m S 131.1898 181.8718 m S 131.1898 181.8718 m S 131.1898 181.8718 m S 131.1898 181.8718 m S 131.1898 181.8718 m S 131.1898 181.8718 m S 131.1898 181.8718 m S 131.1898 181.8718 m S 1 g 1 w 4 M 131.1898 177.0635 m 134.0015 177.0635 136.2809 179.2163 136.2809 181.8718 c 136.2809 184.5273 134.0015 186.6801 131.1898 186.6801 c 128.3781 186.6801 126.0987 184.5273 126.0987 181.8718 c 126.0987 179.2163 128.3781 177.0635 131.1898 177.0635 c b 0 g 131.1898 181.8718 m F 0 G 0.3 w 10 M 62.7594 159.6432 m S 62.7594 159.6432 m S 62.7594 159.6432 m S 62.7594 159.6432 m S 62.7594 159.6432 m S 62.7594 159.6432 m S 62.7594 159.6432 m S 62.7594 159.6432 m S 62.7594 159.6432 m S 62.7594 159.6432 m S 62.7594 159.6432 m S 62.7594 159.6432 m S 1 g 1 w 4 M 62.7594 154.8349 m 65.5711 154.8349 67.8505 156.9877 67.8505 159.6432 c 67.8505 162.2987 65.5711 164.4515 62.7594 164.4515 c 59.9477 164.4515 57.6683 162.2987 57.6683 159.6432 c 57.6683 156.9877 59.9477 154.8349 62.7594 154.8349 c b 0 g 62.7594 159.6432 m F 0 G 0.3 w 10 M 85.5696 181.8718 m S 85.5696 181.8718 m S 85.5696 181.8718 m S 85.5696 181.8718 m S 85.5696 181.8718 m S 85.5696 181.8718 m S 85.5696 181.8718 m S 85.5696 181.8718 m S 85.5696 181.8718 m S 85.5696 181.8718 m S 85.5696 181.8718 m S 85.5696 181.8718 m S 1 g 1 w 4 M 85.5696 177.0635 m 88.3813 177.0635 90.6607 179.2163 90.6607 181.8718 c 90.6607 184.5273 88.3813 186.6801 85.5696 186.6801 c 82.7579 186.6801 80.4785 184.5273 80.4785 181.8718 c 80.4785 179.2163 82.7579 177.0635 85.5696 177.0635 c b 0 g 85.5696 181.8718 m F 0 G 0.3 w 10 M 39.9493 181.8718 m S 39.9493 181.8718 m S 39.9493 181.8718 m S 39.9493 181.8718 m S 39.9493 181.8718 m S 39.9493 181.8718 m S 39.9493 181.8718 m S 39.9493 181.8718 m S 39.9493 181.8718 m S 39.9493 181.8718 m S 39.9493 181.8718 m S 39.9493 181.8718 m S 1 g 1 w 4 M 39.9493 177.0635 m 42.761 177.0635 45.0404 179.2163 45.0404 181.8718 c 45.0404 184.5273 42.761 186.6801 39.9493 186.6801 c 37.1376 186.6801 34.8582 184.5273 34.8582 181.8718 c 34.8582 179.2163 37.1376 177.0635 39.9493 177.0635 c b 0 g 39.9493 181.8718 m F 0 G 0.3 w 10 M 131.1898 137.4145 m S 131.1898 137.4145 m S 131.1898 137.4145 m S 131.1898 137.4145 m S 131.1898 137.4145 m S 131.1898 137.4145 m S 131.1898 137.4145 m S 131.1898 137.4145 m S 131.1898 137.4145 m S 131.1898 137.4145 m S 131.1898 137.4145 m S 131.1898 137.4145 m S 1 g 1 w 4 M 131.1898 132.6062 m 134.0015 132.6062 136.2809 134.759 136.2809 137.4145 c 136.2809 140.07 134.0015 142.2228 131.1898 142.2228 c 128.3781 142.2228 126.0987 140.07 126.0987 137.4145 c 126.0987 134.759 128.3781 132.6062 131.1898 132.6062 c b 0 g 131.1898 137.4145 m F 0 G 0.3 w 10 M 85.5696 137.4145 m S 85.5696 137.4145 m S 85.5696 137.4145 m S 85.5696 137.4145 m S 85.5696 137.4145 m S 85.5696 137.4145 m S 85.5696 137.4145 m S 85.5696 137.4145 m S 85.5696 137.4145 m S 85.5696 137.4145 m S 85.5696 137.4145 m S 85.5696 137.4145 m S 1 g 1 w 4 M 85.5696 132.6062 m 88.3813 132.6062 90.6607 134.759 90.6607 137.4145 c 90.6607 140.07 88.3813 142.2228 85.5696 142.2228 c 82.7579 142.2228 80.4785 140.07 80.4785 137.4145 c 80.4785 134.759 82.7579 132.6062 85.5696 132.6062 c b 0 g 85.5696 137.4145 m F 0 G 0.3 w 10 M 108.3797 115.1859 m S 108.3797 115.1859 m S 108.3797 115.1859 m S 108.3797 115.1859 m S 108.3797 115.1859 m S 108.3797 115.1859 m S 108.3797 115.1859 m S 108.3797 115.1859 m S 108.3797 115.1859 m S 108.3797 115.1859 m S 108.3797 115.1859 m S 108.3797 115.1859 m S 1 g 1 w 4 M 108.3797 110.3776 m 111.1914 110.3776 113.4708 112.5304 113.4708 115.1859 c 113.4708 117.8414 111.1914 119.9942 108.3797 119.9942 c 105.568 119.9942 103.2886 117.8414 103.2886 115.1859 c 103.2886 112.5304 105.568 110.3776 108.3797 110.3776 c b 0 g 108.3797 115.1859 m F 0 G 0.3 w 10 M 62.7594 115.1859 m S 62.7594 115.1859 m S 62.7594 115.1859 m S 62.7594 115.1859 m S 62.7594 115.1859 m S 62.7594 115.1859 m S 62.7594 115.1859 m S 62.7594 115.1859 m S 62.7594 115.1859 m S 62.7594 115.1859 m S 62.7594 115.1859 m S 62.7594 115.1859 m S 1 g 1 w 4 M 62.7594 110.3776 m 65.5711 110.3776 67.8505 112.5304 67.8505 115.1859 c 67.8505 117.8414 65.5711 119.9942 62.7594 119.9942 c 59.9477 119.9942 57.6683 117.8414 57.6683 115.1859 c 57.6683 112.5304 59.9477 110.3776 62.7594 110.3776 c b 0 g 62.7594 115.1859 m F 0 G 0.3 w 10 M 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 0 g 1 w 4 M 39.9493 137.4145 m F 0 G 0.3 w 10 M 131.1898 92.9572 m S 131.1898 92.9572 m S 131.1898 92.9572 m S 131.1898 92.9572 m S 131.1898 92.9572 m S 131.1898 92.9572 m S 131.1898 92.9572 m S 131.1898 92.9572 m S 131.1898 92.9572 m S 131.1898 92.9572 m S 131.1898 92.9572 m S 131.1898 92.9572 m S 1 g 1 w 4 M 131.1898 88.1489 m 134.0015 88.1489 136.2809 90.3017 136.2809 92.9572 c 136.2809 95.6127 134.0015 97.7655 131.1898 97.7655 c 128.3781 97.7655 126.0987 95.6127 126.0987 92.9572 c 126.0987 90.3017 128.3781 88.1489 131.1898 88.1489 c b 0 g 131.1898 92.9572 m F 0 G 0.3 w 10 M 108.3797 70.7286 m S 108.3797 70.7286 m S 108.3797 70.7286 m S 108.3797 70.7286 m S 108.3797 70.7286 m S 108.3797 70.7286 m S 108.3797 70.7286 m S 108.3797 70.7286 m S 108.3797 70.7286 m S 108.3797 70.7286 m S 108.3797 70.7286 m S 108.3797 70.7286 m S 1 g 1 w 4 M 108.3797 65.9203 m 111.1914 65.9203 113.4708 68.0731 113.4708 70.7286 c 113.4708 73.3841 111.1914 75.5369 108.3797 75.5369 c 105.568 75.5369 103.2886 73.3841 103.2886 70.7286 c 103.2886 68.0731 105.568 65.9203 108.3797 65.9203 c b 0 g 108.3797 70.7286 m F 0 G 0.3 w 10 M 85.5696 92.9572 m S 85.5696 92.9572 m S 85.5696 92.9572 m S 85.5696 92.9572 m S 85.5696 92.9572 m S 85.5696 92.9572 m S 85.5696 92.9572 m S 85.5696 92.9572 m S 85.5696 92.9572 m S 85.5696 92.9572 m S 85.5696 92.9572 m S 85.5696 92.9572 m S 1 g 1 w 4 M 85.5696 88.1489 m 88.3813 88.1489 90.6607 90.3017 90.6607 92.9572 c 90.6607 95.6127 88.3813 97.7655 85.5696 97.7655 c 82.7579 97.7655 80.4785 95.6127 80.4785 92.9572 c 80.4785 90.3017 82.7579 88.1489 85.5696 88.1489 c b 0 g 85.5696 92.9572 m F 0 G 0.3 w 10 M 39.9493 92.9572 m S 39.9493 92.9572 m S 39.9493 92.9572 m S 39.9493 92.9572 m S 39.9493 92.9572 m S 39.9493 92.9572 m S 39.9493 92.9572 m S 39.9493 92.9572 m S 39.9493 92.9572 m S 39.9493 92.9572 m S 39.9493 92.9572 m S 39.9493 92.9572 m S 1 g 1 w 4 M 39.9493 88.1489 m 42.761 88.1489 45.0404 90.3017 45.0404 92.9572 c 45.0404 95.6127 42.761 97.7655 39.9493 97.7655 c 37.1376 97.7655 34.8582 95.6127 34.8582 92.9572 c 34.8582 90.3017 37.1376 88.1489 39.9493 88.1489 c b 0 g 39.9493 92.9572 m F 0 G 0.3 w 10 M 62.7594 70.7286 m S 62.7594 70.7286 m S 62.7594 70.7286 m S 62.7594 70.7286 m S 62.7594 70.7286 m S 62.7594 70.7286 m S 62.7594 70.7286 m S 62.7594 70.7286 m S 62.7594 70.7286 m S 62.7594 70.7286 m S 62.7594 70.7286 m S 62.7594 70.7286 m S 1 g 1 w 4 M 62.7594 65.9203 m 65.5711 65.9203 67.8505 68.0731 67.8505 70.7286 c 67.8505 73.3841 65.5711 75.5369 62.7594 75.5369 c 59.9477 75.5369 57.6683 73.3841 57.6683 70.7286 c 57.6683 68.0731 59.9477 65.9203 62.7594 65.9203 c b 0 g 62.7594 70.7286 m F 0.7 g 34.5601 132 m 34.8582 137.4145 l 39.9493 137.4145 l 34.5601 132 l f 36.8101 133.75 m F 181.8101 177 m 181.9012 181.8718 l 176.8101 181.8718 l 181.8101 177 l f 0 G 0.3 w 10 M 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 0 g 1 w 4 M 176.8101 92.9572 m F 0.7 g 181.8101 88.0854 m 181.9012 92.9572 l 176.8101 92.9572 l 181.8101 88.0854 l f 0 G 0.3 w 10 M 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 176.8101 181.8718 m S 1 g 1 w 4 M 176.8101 177.0635 m 179.6218 177.0635 181.9012 179.2163 181.9012 181.8718 c 181.9012 184.5273 179.6218 186.1801 176.8101 186.1801 c 173.9984 186.1801 171.719 184.5273 171.719 181.8718 c 171.719 179.2163 173.9984 177.0635 176.8101 177.0635 c b 0 g 176.8101 181.8718 m F 0 G 0.3 w 10 M 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 176.8101 92.9572 m S 1 g 1 w 4 M 176.8101 88.1489 m 179.6218 88.1489 181.9012 90.3017 181.9012 92.9572 c 181.9012 95.6127 179.6218 97.2655 176.8101 97.2655 c 173.9984 97.2655 171.719 95.6127 171.719 92.9572 c 171.719 90.3017 173.9984 88.1489 176.8101 88.1489 c b 0 g 176.8101 92.9572 m F 0 G 0.3 w 10 M 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 39.9493 137.4145 m S 1 g 1 w 4 M 39.9493 132.6062 m 42.761 132.6062 45.0404 134.759 45.0404 137.4145 c 45.0404 140.07 42.761 141.7228 39.9493 141.7228 c 37.1376 141.7228 34.8582 140.07 34.8582 137.4145 c 34.8582 134.759 37.1376 132.6062 39.9493 132.6062 c b 0 g 39.9493 137.4145 m F 0 G 0.3 w 10 M 313.5601 170.75 m S 313.5601 170.75 m S 313.5601 170.75 m S 313.5601 170.75 m S 313.5601 170.75 m S 313.5601 170.75 m S 313.5601 170.75 m S 313.5601 170.75 m S 313.5601 170.75 m S 313.5601 170.75 m S 313.5601 170.75 m S 313.5601 170.75 m S 0 g 1 w 4 M 313.5601 165.9417 m 316.3718 165.9417 318.6512 168.0945 318.6512 170.75 c 318.6512 173.4055 316.3718 175.0583 313.5601 175.0583 c 310.7484 175.0583 308.469 173.4055 308.469 170.75 c 308.469 168.0945 310.7484 165.9417 313.5601 165.9417 c b 313.5601 170.75 m F 0 G 0.3 w 10 M 370.6962 170.7575 m S 0 g 1 w 4 M 370.6962 170.7575 m F 393.5063 170.7575 m F 0 G 0.3 w 10 M 393.5063 170.7575 m S 0 g 1 w 4 M 393.5063 170.7575 m F 0 G 0.3 w 10 M 381.9905 170.75 m S 381.9905 170.75 m S 381.9905 170.75 m S 381.9905 170.75 m S 381.9905 170.75 m S 381.9905 170.75 m S 381.9905 170.75 m S 381.9905 170.75 m S 381.9905 170.75 m S 381.9905 170.75 m S 381.9905 170.75 m S 381.9905 170.75 m S 0 g 1 w 4 M 381.9905 165.9417 m 384.8022 165.9417 387.0816 168.0945 387.0816 170.75 c 387.0816 173.4055 384.8022 175.0583 381.9905 175.0583 c 379.1788 175.0583 376.8994 173.4055 376.8994 170.75 c 376.8994 168.0945 379.1788 165.9417 381.9905 165.9417 c b 381.9905 170.75 m F 0 G 0.3 w 10 M 325.0759 126.3002 m S 0 g 1 w 4 M 325.0759 126.3002 m F 347.886 126.3002 m F 0 G 0.3 w 10 M 347.886 126.3002 m S 0 g 1 w 4 M 347.886 126.3002 m F 0 G 0.3 w 10 M 336.3702 126.2927 m S 336.3702 126.2927 m S 336.3702 126.2927 m S 336.3702 126.2927 m S 336.3702 126.2927 m S 336.3702 126.2927 m S 336.3702 126.2927 m S 336.3702 126.2927 m S 336.3702 126.2927 m S 336.3702 126.2927 m S 336.3702 126.2927 m S 336.3702 126.2927 m S 0 g 1 w 4 M 336.3702 121.4844 m 339.1819 121.4844 341.4613 123.6372 341.4613 126.2927 c 341.4613 128.9482 339.1819 130.601 336.3702 130.601 c 333.5585 130.601 331.2791 128.9482 331.2791 126.2927 c 331.2791 123.6372 333.5585 121.4844 336.3702 121.4844 c b 336.3702 126.2927 m F 0 G 0.3 w 10 M 393.5063 126.3002 m S 0 g 1 w 4 M 393.5063 126.3002 m F 0 G 0.3 w 10 M 404.8006 126.2927 m S 404.8006 126.2927 m S 404.8006 126.2927 m S 404.8006 126.2927 m S 404.8006 126.2927 m S 404.8006 126.2927 m S 404.8006 126.2927 m S 404.8006 126.2927 m S 404.8006 126.2927 m S 404.8006 126.2927 m S 404.8006 126.2927 m S 404.8006 126.2927 m S 0 g 1 w 4 M 404.8006 121.4844 m 407.6123 121.4844 409.8917 123.6372 409.8917 126.2927 c 409.8917 128.9482 407.6123 130.601 404.8006 130.601 c 401.9889 130.601 399.7095 128.9482 399.7095 126.2927 c 399.7095 123.6372 401.9889 121.4844 404.8006 121.4844 c b 404.8006 126.2927 m F 0 G 0.3 w 10 M 302.2658 81.843 m S 0 g 1 w 4 M 302.2658 81.843 m F 325.0759 81.843 m F 0 G 0.3 w 10 M 325.0759 81.843 m S 0 g 1 w 4 M 325.0759 81.843 m F 0 G 0.3 w 10 M 313.5601 81.8355 m S 313.5601 81.8355 m S 313.5601 81.8355 m S 313.5601 81.8355 m S 313.5601 81.8355 m S 313.5601 81.8355 m S 313.5601 81.8355 m S 313.5601 81.8355 m S 313.5601 81.8355 m S 313.5601 81.8355 m S 313.5601 81.8355 m S 313.5601 81.8355 m S 0 g 1 w 4 M 313.5601 77.0272 m 316.3718 77.0272 318.6512 79.18 318.6512 81.8355 c 318.6512 84.491 316.3718 86.1438 313.5601 86.1438 c 310.7484 86.1438 308.469 84.491 308.469 81.8355 c 308.469 79.18 310.7484 77.0272 313.5601 77.0272 c b 313.5601 81.8355 m F 0 G 0.3 w 10 M 370.6962 81.8429 m S 0 g 1 w 4 M 370.6962 81.8429 m F 393.5063 81.8429 m F 0 G 0.3 w 10 M 393.5063 81.8429 m S 0 g 1 w 4 M 393.5063 81.8429 m F 0 G 0.3 w 10 M 381.9905 81.8354 m S 381.9905 81.8354 m S 381.9905 81.8354 m S 381.9905 81.8354 m S 381.9905 81.8354 m S 381.9905 81.8354 m S 381.9905 81.8354 m S 381.9905 81.8354 m S 381.9905 81.8354 m S 381.9905 81.8354 m S 381.9905 81.8354 m S 381.9905 81.8354 m S 0 g 1 w 4 M 381.9905 77.0271 m 384.8022 77.0271 387.0816 79.1799 387.0816 81.8354 c 387.0816 84.4909 384.8022 86.1437 381.9905 86.1437 c 379.1788 86.1437 376.8994 84.4909 376.8994 81.8354 c 376.8994 79.1799 379.1788 77.0271 381.9905 77.0271 c b 381.9905 81.8354 m F u u /_Symbol 24 29 0 0 z [1 0 0 1 222.1582 118.3125]e (\256)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 221 36.5]e (\(e\))t T U U showpage _E end %%EndDocument @endspecial 346 1948 a FQ(Figure)16 b(2:)21 b(Some)15 b(examples)g(of)h(R)l (T)g(maps)g(in)g(dimension)f FF(d)f FQ(=)g(2.)95 2062 y(\(a\))25 b(Decimation)14 b(with)i FF(b)e FQ(=)g(2)i(and)h FF(K)h FQ(=)c(4.)93 2164 y(\(b\))24 b(Decimation)15 b(with)i FF(R)p FQ(\()p FF(x)638 2171 y FH(1)658 2164 y FF(;)8 b(x)708 2171 y FH(2)727 2164 y FQ(\))15 b(=)f(\()p FF(x)860 2171 y FH(1)891 2164 y FQ(+)e FF(x)969 2171 y FH(2)988 2164 y FF(;)c(x)1038 2171 y FH(1)1069 2164 y FE(\000)j FF(x)1147 2171 y FH(2)1167 2164 y FQ(\))16 b(and)i FF(K)h FQ(=)c(2)i(\(\\c)o(hec)o(k)o(erb)q(oard)f(deci-)182 2224 y(mation"\).)98 2325 y(\(c\))24 b(Blo)q(c)o(k)15 b(transformation)h (with)g FF(b)e FQ(=)g(2,)i FF(B)939 2332 y FH(0)973 2325 y FQ(=)d FE(f)p FQ(\(0)p FF(;)8 b FQ(0\))p FF(;)17 b FQ(\(1)p FF(;)8 b FQ(0\))p FF(;)17 b FQ(\(0)p FF(;)8 b FQ(1\))p FF(;)16 b FQ(\(1)p FF(;)8 b FQ(1\))p FE(g)17 b FQ(and)g FF(K)h FQ(=)c(4.)93 2427 y(\(d\))24 b(Blo)q(c)o(k)41 b(transformation)h(with)g FF(R)p FQ(\()p FF(x)923 2434 y FH(1)943 2427 y FF(;)8 b(x)993 2434 y FH(2)1012 2427 y FQ(\))58 b(=)g(\(2)p FF(x)1256 2434 y FH(1)1305 2427 y FE(\000)28 b FF(x)1400 2434 y FH(2)1420 2427 y FF(;)8 b(x)1470 2434 y FH(1)1518 2427 y FQ(+)28 b(2)p FF(x)1636 2434 y FH(2)1656 2427 y FQ(\),)48 b FF(B)1774 2434 y FH(0)1852 2427 y FQ(=)182 2487 y FE(f)p FQ(\(0)p FF(;)8 b FQ(0\))p FF(;)17 b FQ(\()p FE(\006)p FQ(1)p FF(;)8 b FE(\006)p FQ(1\))p FE(g)16 b FQ(and)h FF(K)h FQ(=)13 b(5)k([357)q(].)98 2589 y(\(e\))24 b(Blo)q(c)o(k)41 b(transformation)h(with)g FF(R)p FQ(\()p FF(x)923 2596 y FH(1)943 2589 y FF(;)8 b(x)993 2596 y FH(2)1013 2589 y FQ(\))58 b(=)g(\(2)p FF(x)1257 2596 y FH(1)1305 2589 y FQ(+)29 b FF(x)1400 2596 y FH(2)1419 2589 y FF(;)8 b(x)1469 2596 y FH(1)1517 2589 y FQ(+)29 b(2)p FF(x)1636 2596 y FH(2)1656 2589 y FQ(\),)48 b FF(B)1774 2596 y FH(0)1852 2589 y FQ(=)182 2649 y FE(f)p FQ(\(0)p FF(;)8 b FQ(0\))p FF(;)17 b FQ(\(1)p FF(;)8 b FQ(0\))p FF(;)16 b FQ(\(1)p FF(;)8 b FQ(1\))p FE(g)17 b FQ(and)g FF(K)h FQ(=)c(3)i([276)q(,)g(278)q(].)951 2784 y(80)p eop %%Page: 81 81 bop 133 91 a FQ(As)17 b(in)f(the)g(decimation)f(transformation,)h(w)o(e)g (can)h(replace)f FF(bx)g FQ(b)o(y)g(a)h(more)e(general)h(nonsin-)60 152 y(gular)j(homomorphism)c FF(R)p FQ(\()p FF(x)p FQ(\).)28 b(Then)18 b FF(K)k FQ(=)17 b FE(j)8 b FQ(det)g FF(R)p FE(j)p FQ(.)28 b(Some)17 b(examples)f(are)j(sho)o(wn)g(in)e(Figure)60 212 y(2\(c\){\(e\).)133 297 y(4\))k FP(Kadano\013)g(tr)n(ansformation)f(for)g (the)i FF(N)5 b FP(-ve)n(ctor)22 b(mo)n(del)5 b FQ(.)32 b(F)l(or)21 b(the)e FF(N)5 b FQ(-v)o(ector)20 b(mo)q(del,)f(in)60 357 y(whic)o(h)c(the)h (spins)g(are)g(unit)f(v)o(ectors)g(in)h Fq(R)843 336 y FD(N)876 357 y FQ(,)g(the)f(natural)i(generalization)e(of)h(the)g(ma)s(jorit)o(y-rule) 60 417 y(transformation)g(is)g(the)g(\\rescaled)g(blo)q(c)o(k-spin)g (transformation")h([321])799 584 y FF(\033)829 563 y Fy(0)827 596 y FD(x)876 584 y FQ(=)983 484 y Fx(P)960 555 y FD(y)q Fy(2)p FD(B)1029 559 y Fs(x)1057 517 y FF(\033)1085 524 y FD(y)p 946 572 173 2 v 946 577 a Fx(\014)946 602 y(\014)946 627 y(\014)946 652 y(\014)946 677 y(\014)983 618 y(P)960 690 y FD(y)q Fy(2)p FD(B)1029 694 y Fs(x)1057 652 y FF(\033)1085 659 y FD(y)1105 577 y Fx(\014)1105 602 y(\014)1105 627 y(\014)1105 652 y(\014)1105 677 y(\014)1138 584 y FF(;)613 b FQ(\(3)p FF(:)p FQ(11\))60 793 y(whic)o(h)12 b(is)g(deterministic.)k(\(In)d(principle)d(one)j(should)g (sp)q(ecify)e(what)i(happ)q(ens)h(when)1647 760 y Fx(P)1691 803 y FD(y)q Fy(2)p FD(B)1760 807 y Fs(x)1790 793 y FF(\033)1818 800 y FD(y)1852 793 y FQ(=)60 853 y(0:)27 b(for)19 b(example,)d(one)j(could)g (c)o(ho)q(ose)g(some)f(particular)g(v)m(alue)g(of)h FF(\033)1359 835 y Fy(0)1357 865 y FD(x)1379 853 y FQ(,)g(or)g(one)g(could)g(let)e FF(\033)1801 835 y Fy(0)1799 865 y FD(x)1840 853 y FQ(b)q(e)60 913 y(uniformly)g(distributed)i(on)h(the)g(unit)f(sphere.)30 b(But)20 b(this)f(situation)h(o)q(ccurs)g(with)f(probabilit)o(y)60 973 y(zero,)13 b(so)i(it)e(is)g(irrelev)m(an)o(t)f(what)j(c)o(hoice)d(one)i (mak)o(es.\))19 b(Similarly)l(,)10 b(the)k(Kadano\013)h(transformation)60 1034 y(has)i(a)g(natural)f(generalization)g([190)q(]:)482 1243 y FF(T)7 b FQ(\()p FF(\033)o(;)h(d\033)641 1222 y Fy(0)651 1243 y FQ(\))28 b(=)784 1201 y Fx(Y)763 1301 y FD(x)p Fy(2)p Fl(Z)828 1291 y Fs(d)844 1284 y Ft(0)870 1175 y FQ(exp)953 1102 y Fx( )986 1175 y FF(p\033)1040 1157 y Fy(0)1038 1187 y FD(x)1071 1175 y FE(\001)1118 1142 y Fx(P)1096 1213 y FD(y)q Fy(2)p FD(B)1165 1217 y Fs(x)1193 1175 y FF(\033)1221 1182 y FD(y)1241 1102 y Fx(!)p 870 1231 404 2 v 916 1311 a FE(Z)952 1318 y FD(N)985 1238 y Fx( )1018 1311 y FF(p)1073 1278 y Fx(P)1051 1349 y FD(y)q Fy(2)p FD(B)1120 1353 y Fs(x)1148 1311 y FF(\033)1176 1318 y FD(y)1196 1238 y Fx(!)1293 1243 y FF(d)p FQ(\012\()p FF(\033)1402 1222 y Fy(0)1400 1255 y FD(x)1422 1243 y FQ(\))14 b FF(;)296 b FQ(\(3)p FF(:)p FQ(12\))60 1449 y(where)359 1546 y FE(Z)395 1553 y FD(N)429 1546 y FQ(\()p FF(h)p FQ(\))28 b FE(\021)614 1487 y Fx(Z)580 1613 y FD(S)603 1603 y Fs(N)s Ft(\000)p Fr(1)689 1546 y FF(e)712 1525 y FD(h)p Fy(\001)p FD(\033)773 1546 y FF(d)p FQ(\012\()p FF(\033)r FQ(\))g(=)g(\000)1033 1485 y Fx(\022)1069 1512 y FF(N)p 1069 1534 45 2 v 1079 1580 a FQ(2)1118 1485 y Fx(\023)1165 1473 y( )1219 1512 y FQ(2)p 1203 1534 56 2 v 1203 1580 a FE(j)p FF(h)p FE(j)1264 1473 y Fx(!)1296 1470 y Fs(N)p 1296 1476 27 2 v 1302 1497 a Fr(2)1328 1484 y Fy(\000)p FH(1)1391 1546 y FF(I)5 b Fs(N)p 1418 1552 V 1424 1572 a Fr(2)1450 1559 y Fy(\000)p FH(1)1497 1546 y FQ(\()p FE(j)p FF(h)p FE(j)p FQ(\))174 b(\(3)p FF(:)p FQ(13\))60 1692 y(and)19 b FF(d)p FQ(\012)f(denotes)g(uniform)f(measure)f(on)j(the)f(unit)f(sphere)h(in)f Fq(R)1295 1671 y FD(N)1328 1692 y FQ(.)27 b(As)17 b FF(p)h FE(!)e(1)i FQ(this)g(tends)g(to)60 1752 y(the)e(deterministic)d(map)i (\(3.11\).)133 1812 y(Analogous)23 b(form)o(ulae)e(can)h(b)q(e)g(used)g(to)h (de\014ne)f(a)g(Kadano\013)i(transformation)e(for)g(the)g FF(q)r FQ(-)60 1872 y(state)i(P)o(otts)h(mo)q(del,)f(using)g(the)g(represen)o (tation)f(of)h(P)o(otts)g(spins)h(as)f(unit)g(v)o(ectors)f(in)h Fq(R)1826 1851 y FD(q)q Fy(\000)p FH(1)60 1932 y FQ(p)q(oin)o(ting)f(from)f (the)h(cen)o(ter)f(of)i(a)f(\\h)o(yp)q(ertetrahedron")h(to)g(its)f(v)o (ertices.)40 b(As)23 b FF(p)j FE(!)f(1)e FQ(this)60 1992 y(transformation)16 b(tends)g(to)g(the)g(\\pluralit)o(y-rule")f(transformation)g(with)h(random)g (tie-break)o(ers.)60 2053 y(The)j(P)o(otts)g(mo)q(del)e(with)h(v)m(acancies)h ([279,)f(305)r(])g(can)g(also)i(b)q(e)e(treated)h(in)f(this)g(framew)o(ork,)g (b)o(y)60 2113 y(represen)o(ting)d(the)h(\\v)m(acancy")h(state)g(as)g(the)f (origin)g(in)g Fq(R)1144 2092 y FD(q)q Fy(\000)p FH(1)1208 2113 y FQ(.)133 2198 y(5\))22 b FP(Line)n(ar)g(blo)n(ck-spin)j(tr)n (ansformations)t FQ(.)37 b(A)21 b(natural)h(c)o(hoice)f(of)h(a)g (deterministic)d(linear)60 2258 y(transformation)d(is)g(the)g FP(aver)n(aging)22 b FQ(transformation)803 2368 y FF(\033)833 2348 y Fy(0)831 2380 y FD(x)880 2368 y FQ(=)28 b FF(c)989 2327 y Fx(X)975 2418 y FD(y)q Fy(2)p FD(B)1044 2422 y Fs(x)1071 2368 y FF(\033)1099 2375 y FD(y)1134 2368 y FF(;)617 b FQ(\(3)p FF(:)p FQ(14\))60 2523 y(for)11 b(a)g(suitably)g(c)o(hosen)g FP(r)n(esc)n(aling)h(factor)17 b FF(c)p FQ(.)i(T)o(ypically)9 b(w)o(e)h(c)o(ho)q(ose)i FE(j)p FF(B)1362 2530 y FH(0)1381 2523 y FE(j)1395 2504 y Fy(\000)p FH(1)1456 2523 y FE(\024)i FF(c)g FE(\024)f FQ(1.)20 b(W)l(e)11 b(observ)o(e)60 2583 y(that)20 b(if)f FF(c)g(>)g FE(j)p FF(B)365 2590 y FH(0)384 2583 y FE(j)398 2565 y Fy(\000)p FH(1)445 2583 y FQ(,)h(this)f(transformation)g(do)q(es)h (not)g(map)f(an)o(y)g(mo)q(del)f(of)h FP(b)n(ounde)n(d)25 b FQ(spins)20 b(to)60 2643 y(itself:)k(if)17 b(\012)282 2650 y FH(0)319 2643 y FQ(=)g([)p FE(\000)p FF(M)r(;)8 b(M)d FQ(],)18 b(w)o(e)g(m)o(ust)f(tak)o(e)g(\012)935 2625 y Fy(0)935 2655 y FH(0)972 2643 y FQ(=)g([)p FE(\000)p FF(M)1132 2625 y Fy(0)1144 2643 y FF(;)8 b(M)1218 2625 y Fy(0)1230 2643 y FQ(])17 b(with)h FF(M)1426 2625 y Fy(0)1455 2643 y FE(\025)f(j)p FF(B)1562 2650 y FH(0)1582 2643 y FE(j)p FF(cM)22 b(>)17 b(M)5 b FQ(.)27 b(As)951 2784 y(81)p eop %%Page: 82 82 bop 60 91 a FQ(a)19 b(consequence,)f(the)g(\014xed)g(p)q(oin)o(t\(s\))h(\(if) f(an)o(y\))h(for)g(suc)o(h)f(a)h(transformation)g(m)o(ust)e(corresp)q(ond)60 152 y(to)23 b(mo)q(del\(s\))e(of)h(un)o(b)q(ounded)i(spins)e(\(i.e.)f(\012) 921 159 y FH(0)965 152 y FQ(=)j Fq(R)p FQ(\).)39 b(F)l(or)23 b(this)f(reason,)i(it)e(is)g(most)g(natural)60 212 y(to)i(consider)f (\(3.14\))h(as)g(acting,)h(righ)o(t)e(from)g(the)g(start,)i(on)f(suc)o(h)g(a) g(system)e(of)h(real-v)m(alued)60 272 y(spins.)e(Ho)o(w)o(ev)o(er,)13 b(in)i(this)f(pap)q(er)i(w)o(e)e(are)h(not)h(concerned)e(with)h(\014xed)f(p)q (oin)o(ts;)i(our)f(in)o(terest)f(is)g(in)60 332 y(whether)j(the)f FP(\014rst)22 b FQ(application)16 b(of)h(the)g(R)l(T)g(map)f(is)g(w)o (ell-de\014ned.)22 b(F)l(or)17 b(this)f(purp)q(ose)i(w)o(e)f(ma)o(y)60 392 y(w)o(ork)k(en)o(tirely)d(with)i(mo)q(dels)g(of)h(b)q(ounded)g(spins,)h (pro)o(vided)d(that)i(w)o(e)g(are)f(willing)g(to)h(accept)60 452 y(\012)95 434 y Fy(0)95 465 y FH(0)136 452 y FE(6)p FQ(=)h(\012)231 459 y FH(0)251 452 y FQ(.)34 b(F)l(or)21 b(example,)e(in)i(the)f(t)o(w)o (o-dimensional)f(Ising)i(mo)q(del)e(with)i(2)14 b FE(\002)g FQ(2)21 b(blo)q(c)o(ks)f(\(and)60 513 y FF(c)14 b FQ(=)g(1\),)i(w)o(e)g(ha)o (v)o(e)f(\012)439 520 y FH(0)473 513 y FQ(=)f FE(f\000)p FQ(1)p FF(;)8 b FQ(1)p FE(g)16 b FQ(but)g(\012)824 495 y Fy(0)824 525 y FH(0)858 513 y FQ(=)e FE(f\000)p FQ(4)p FF(;)8 b FE(\000)p FQ(2)p FF(;)g FQ(0)p FF(;)g FQ(2)p FF(;)g FQ(4)p FE(g)p FQ(.)133 573 y(F)l(or)19 b FP(unb)n(ounde)n(d)24 b FQ(spins)18 b(with)g(v)m(alues)g (in)g Fq(R)h FQ(\(or)f Fq(R)1077 552 y FD(N)1110 573 y FQ(\),)g(one)h(can)f (use)h(either)e(a)h(deterministic)60 633 y FP(line)n(ar)k FQ(blo)q(c)o (k-spin)16 b(transformation)g([147)q(])812 732 y FF(')844 711 y Fy(0)844 744 y FD(x)894 732 y FQ(=)27 b FF(c)1003 690 y Fx(X)989 782 y FD(y)q Fy(2)p FD(B)1058 786 y Fs(x)1085 732 y FF(')1117 739 y FD(y)1765 732 y FQ(\(3)p FF(:)p FQ(15\))60 873 y(or)17 b(the)f(sto)q(c)o(hastic)g(linear)g(blo)q(c)o(k-spin)g(transformation)g([27,) g(18)q(])236 1028 y FF(T)7 b FQ(\()p FF(';)h(d')402 1007 y Fy(0)413 1028 y FQ(\))28 b(=)546 986 y Fx(Y)525 1086 y FD(x)p Fy(2)p Fl(Z)590 1076 y Fs(d)606 1069 y Ft(0)627 1028 y FQ(const)12 b FE(\002)f FQ(exp)882 930 y Fx(2)882 1003 y(6)882 1029 y(4)910 1028 y FE(\000)973 994 y FQ(1)p 954 1016 64 2 v 954 1062 a(2)p FF(\017)998 1048 y FH(2)1031 942 y Fx(0)1031 1017 y(@)1067 1028 y FF(')1099 1007 y Fy(0)1099 1040 y FD(x)1140 1028 y FE(\000)20 b FF(c)1242 986 y Fx(X)1228 1078 y FD(y)q Fy(2)p FD(B)1297 1082 y Fs(x)1324 1028 y FF(')1356 1035 y FD(y)1377 942 y Fx(1)1377 1017 y(A)1413 954 y FH(2)1433 930 y Fx(3)1433 1003 y(7)1433 1029 y(5)1483 1028 y FF(d')1540 1007 y Fy(0)1540 1040 y FD(x)1576 1028 y FF(;)175 b FQ(\(3)p FF(:)p FQ(16\))60 1185 y(whic)o(h)17 b(corresp)q(onds)i(to)f(adding)g(Gaussian)h(white)e(noise)h(of)g(v)m(ariance) f FF(\017)1430 1167 y FH(2)1467 1185 y FQ(to)h(the)f(deterministic)60 1245 y(blo)q(c)o(k)g(spins)g(\(3.15\).)25 b(In)17 b(b)q(oth)i(cases,)e(the)g (rescaling)g(factor)g FF(c)h FQ(m)o(ust)e(b)q(e)h(c)o(hosen)g(appropriately) 60 1305 y(if)g(the)g(transformation)g(is)h(to)f(ha)o(v)o(e)g(a)h(\014xed)f(p) q(oin)o(t:)24 b(e.g.)16 b(for)i(h)o(yp)q(ercubic)e(blo)q(c)o(ks)h(of)h(side)f FF(b)g FQ(one)60 1365 y(tak)o(es)335 1469 y FF(c)28 b FQ(=)449 1369 y Fx(8)449 1407 y(>)449 1419 y(<)449 1494 y(>)449 1506 y(:)495 1413 y FF(b)516 1395 y Fy(\000)p FD(d=)p FH(2)766 1413 y FQ(to)16 b(ha)o(v)o(e)g(a)h(high-temp)q(erature)e(\014xed)h(p)q(oin)o(t)495 1473 y FF(b)516 1455 y Fy(\000)p FD(d)766 1473 y FQ(to)g(ha)o(v)o(e)g(a)h(lo) o(w-temp)q(erature)d(\014xed)i(p)q(oin)o(t)495 1533 y FF(b)516 1515 y Fy(\000)p FH(\()p FD(d)p FH(+2)p Fy(\000)p FD(\021)q FH(\))p FD(=)p FH(2)766 1533 y FQ(to)g(ha)o(v)o(e)g(a)h(critical)d(\014xed)i (p)q(oin)o(t)1765 1469 y(\(3)p FF(:)p FQ(17\))60 1605 y(This)d(need)f(to)g (\014x)h(a)f(parameter)g(is)g(c)o(haracteristic)f(of)i FP(line)n(ar)18 b FQ(renormalization)10 b(transformations.)133 1665 y(Linear)24 b(blo)q(c)o(k-spin)f(transformations)h(ha)o(v)o(e)e(attracted)i(the)f(atten)o (tion)g(of)h(mathematical)60 1725 y(ph)o(ysicists)c(b)q(ecause)h(of)g(their)f (connections)g(with)h(cen)o(tral-limi)o(t)d(theorems:)29 b(see)20 b(for)h(example)60 1785 y([200)q(,)16 b(32,)g(147)q(,)g(71)q(,)g(58].)133 1867 y(6\))k FP(Line)n(ar)g(blo)n(ck-spin)i(tr)n(ansformation)e(with)g(lar)n (ge-\014eld)j(cuto\013)11 b FQ(.)31 b(Ev)o(en)19 b(when)g(the)h(linear)60 1927 y(blo)q(c)o(k-spin)14 b(transformation)g(\(3.14\))h(do)q(es)g(not)f(map) g(mo)q(dels)f(of)h(b)q(ounded)h(spins)g(to)f(themselv)o(es,)60 1988 y(one)21 b(exp)q(ects)f(the)h(corresp)q(onding)h(\014xed-p)q(oin)o(t)f (measure\(s\))e(to)i(ha)o(v)o(e)g(rapidly)f(deca)o(ying)g(\(e.g.)60 2048 y(Gaussian)c(or)g(faster\))f(densities)g(at)g(large)g FF(')p FQ(.)21 b(Therefore,)15 b(it)g(ma)o(y)e(b)q(e)j(a)f(reasonable)h (appro)o(xima-)60 2108 y(tion)h(to)g(mo)q(dify)f(\(3.14\))h(b)o(y)f(cutting)h (o\013)h(the)e(\014elds)h(explicitly)d(at)j FE(j)p FF(\033)r FE(j)d FQ(=)h FF(M)5 b FQ(,)17 b(where)f FF(M)22 b FQ(is)17 b(some)60 2168 y(\014xed)g(large)h(n)o(um)o(b)q(er.)24 b(That)19 b(is,)e(on)i(the)e(space)h(\012)f(=)f(\012)1117 2150 y Fy(0)1145 2168 y FQ(=)h([)p FE(\000)p FF(M)r(;)8 b(M)d FQ(])1390 2150 y Fl(Z)1411 2138 y Fs(d)1449 2168 y FQ(one)18 b(can)g(consider)f(the)60 2228 y(deterministic)c(R)l(T)j(map)452 2383 y FF(')484 2362 y Fy(0)484 2395 y FD(x)534 2383 y FQ(=)599 2283 y Fx(8)599 2320 y(>)599 2333 y(<)599 2407 y(>)599 2420 y(:)645 2331 y FF(c)674 2297 y Fx(P)718 2341 y FD(y)q Fy(2)p FD(B)787 2345 y Fs(x)816 2331 y FF(')848 2338 y FD(y)1069 2331 y FQ(if)g FF(c)1135 2281 y Fx(\014)1135 2306 y(\014)1135 2331 y(\014)1149 2297 y(P)1193 2341 y FD(y)q Fy(2)p FD(B)1262 2345 y Fs(x)1291 2331 y FF(')1323 2338 y FD(y)1344 2281 y Fx(\014)1344 2306 y(\014)1344 2331 y(\014)e FE(\024)f FF(M)645 2434 y(M)g FQ(sgn)776 2386 y Fx(\020)801 2401 y(P)845 2445 y FD(y)q Fy(2)p FD(B)914 2449 y Fs(x)943 2434 y FF(')975 2441 y FD(y)996 2386 y Fx(\021)1069 2434 y FQ(if)j FF(c)1135 2385 y Fx(\014)1135 2409 y(\014)1135 2434 y(\014)1149 2401 y(P)1193 2445 y FD(y)q Fy(2)p FD(B)1262 2449 y Fs(x)1291 2434 y FF(')1323 2441 y FD(y)1344 2385 y Fx(\014)1344 2409 y(\014)1344 2434 y(\014)e FF(>)f(M)1765 2383 y FQ(\(3)p FF(:)p FQ(18\))60 2539 y([This)21 b(w)o(orks)g(also)h(for)f FF(N)5 b FQ(-comp)q(onen)o(t)21 b(spins,)h(if)e(one)h(in)o(terprets)f(sgn)q (\()p FF(')p FQ(\))i(=)g FF('=)p FE(j)p FF(')p FE(j)p FQ(.])35 b(T)l(o)22 b(our)60 2600 y(kno)o(wledge,)g(this)g(transformation)f(has)i(not) f(b)q(een)f(considered)g(previously)l(.)37 b(\(But)21 b(see)g(Cam-)60 2660 y(marota)16 b([56])g(for)h(a)f(related)g(idea.\))951 2784 y(82)p eop %%Page: 83 83 bop 133 91 a FQ(7\))17 b FP(R)n(estriction)g(to)h(a)f(hyp)n(erplane)j FQ([318)q(].)h(Let)16 b(\012)1048 73 y Fy(0)1048 104 y FH(0)1082 91 y FQ(=)d(\012)1168 98 y FH(0)1205 91 y FQ(but)j(tak)o(e)g FF(d)1425 73 y Fy(0)1451 91 y FF(<)d(d)p FQ(,)j(and)h(de\014ne)849 200 y FF(!)881 179 y Fy(0)879 212 y FD(x)929 200 y FQ(=)27 b FF(!)1024 207 y FH(\()p FD(x;)p FH(0\))1765 200 y FQ(\(3)p FF(:)p FQ(19\))60 315 y(where)14 b(0)h(denotes)g(the)g(origin)f(in)h Fq(Z)718 294 y FD(d)p Fy(\000)p FD(d)781 282 y Ft(0)795 315 y FQ(.)21 b(This)14 b(is)h(an)g(un)o(usual)g(t)o(yp)q(e)f(of)h(decimation)e (transforma-)60 375 y(tion)18 b(in)g(whic)o(h)f(the)h(original)g(mo)q(del)f (is)g(restricted)g(to)i(a)f(h)o(yp)q(erplane;)g(it)f(has)i(recen)o(tly)d (elicited)60 435 y(some)j(in)o(terest)g(\(see)g(Section)h(4.5.2\).)33 b(Ho)o(w)o(ev)o(er,)18 b(this)i(transformation)g(do)q(es)h FP(not)k FQ(satisfy)c(our)60 495 y(condition)16 b(\(T3\):)23 b(although)18 b(the)e(image)f(spins)i(in)f(a)h(v)o(olume)e(\003)1261 477 y Fy(0)1261 507 y FD(n)1301 495 y FQ(dep)q(end)h(only)h(on)g(the)f (original)60 555 y(spins)d(in)g(\003)267 537 y Fy(0)267 568 y FD(n)295 555 y FE(\002)5 b(f)p FQ(0)p FE(g)13 b FQ(|)g(so)g(that)h(naiv)o (ely)d(one)j(w)o(ould)f(ha)o(v)o(e)f(a)i(v)o(olume)c(compression)j(factor)g FF(K)18 b FQ(=)c(1)60 616 y(|)19 b(the)h(trouble)f(is)h(that)g(the)f(sets)h (\003)769 597 y Fy(0)769 628 y FD(n)805 616 y FE(\002)14 b(f)p FQ(0)p FE(g)19 b FQ(do)h(not)h(tend)e(to)h(in\014nit)o(y)e(\(in)i Fq(Z)1571 595 y FD(d)1591 616 y FQ(\))g(in)f(v)m(an)h(Ho)o(v)o(e)60 676 y(sense)c(when)g(the)g(\003)430 658 y Fy(0)430 688 y FD(n)469 676 y FQ(do)g(so)h(in)e Fq(Z)683 655 y FD(d)701 643 y Ft(0)714 676 y FQ(.)21 b(T)l(o)c(mak)o(e)d(them)g(tend)i(to)g(in\014nit)o(y)f(in)g(v)m (an)i(Ho)o(v)o(e)d(sense,)i(one)60 736 y(w)o(ould)h(ha)o(v)o(e)g(to)g (\\fatten)h(them)e(out",)i(e.g.)e(b)o(y)h(taking)g(\003)1141 743 y FD(n)1180 736 y FQ(=)f(\003)1268 718 y Fy(0)1268 748 y FD(n)1303 736 y FE(\002)11 b FF(C)1388 743 y FD(R)1415 747 y Fs(n)1455 736 y FQ(where)17 b FF(C)1632 743 y FD(R)1659 747 y Fs(n)1699 736 y FQ(is)g(a)h(cub)q(e)60 796 y(of)e(side)g FF(R)250 803 y FD(n)290 796 y FQ(in)f Fq(Z)377 775 y FD(d)p Fy(\000)p FD(d)440 763 y Ft(0)454 796 y FQ(,)h(and)g FF(R)615 803 y FD(n)653 796 y FE(!)d(1)j FQ(as)h FF(n)d FE(!)f(1)p FQ(.)21 b(But)16 b(then)g(the)g(v)o(olume)e(compression)h(factor)60 856 y FF(K)23 b FQ(w)o(ould)18 b(b)q(e)h(in\014nite.)27 b(This)19 b(example)d(mak)o(es)h(clear)h(wh)o(y)g(w)o(e)h(need)f FF(d)1424 838 y Fy(0)1454 856 y FQ(=)f FF(d)p FQ(.)29 b(Indeed,)18 b(in)g(this)60 916 y(example)d(w)o(e)h(ha)o(v)o(e)g FF(i)p FQ(\()p FF(\026)502 923 y Fy(\000)532 916 y FF(T)7 b FE(j)p FF(\026)611 923 y FH(+)640 916 y FF(T)g FQ(\))14 b FF(>)h FQ(0)j([see)e(Section)g(4.5.2],)h(con)o(trary) f(to)i(what)f(w)o(ould)g(happ)q(en)60 977 y(if)f(\(T3\))h(w)o(ere)e(to)i (hold)f([cf.)f(\(3.30\)].)60 1106 y FM(3.1.3)55 b(Renormalization)16 b(T)-5 b(ransformation)18 b(Acting)g(on)h(In)n(teractions)60 1199 y FQ(W)l(e)e(can)h(no)o(w)f(de\014ne)g(precisely)f(the)h (renormalization)e(map)i FE(R)g FQ(acting)h(on)g(the)f(space)g(of)h(in)o (ter-)60 1259 y(actions,)k(making)e(rigorous)i(the)e(diagram)h(\(1.2\).)35 b(As)21 b(argued)g(in)g(Section)f(2.6.7,)i(the)f(largest)60 1319 y(\\ph)o(ysically)d(reasonable")h(space)g(of)h(in)o(teractions)e(is)h FE(B)1125 1301 y FH(1)1144 1319 y FQ(,)g(the)g(space)g(of)g(translation-in)o (v)m(arian)o(t)60 1379 y(con)o(tin)o(uous)11 b(absolutely)g(summable)d(in)o (teractions.)19 b(Therefore,)11 b(in)g(de\014ning)g FE(R)p FQ(,)h FP(we)h(shal)r(l)h(r)n(estrict)60 1439 y(attention)21 b(to)e(inter)n(actions)g FQ(\010)e FE(2)g(B)735 1421 y FH(1)773 1439 y FP(such)i(that)g(ther)n(e)g(exists)h(an)f(image)h(inter)n(action)g FQ(\010)1743 1421 y Fy(0)1771 1439 y FE(2)d(B)1856 1421 y FH(1)1875 1439 y FP(.)60 1500 y FQ(Since)h FP(a)h(priori)j FQ(w)o(e)c(wish)h(to)g (adopt)g(a)g(completely)d(op)q(en-minded)h(de\014nition)h(|)g(allo)o(wing)h (for)60 1560 y(the)i(p)q(ossibilit)o(y)f(of)h(m)o(ulti-v)m(aluedness)e(|)i(w) o(e)g(m)o(ust)f(de\014ne)g FE(R)i FQ(as)g(a)f(relation)g(rather)g(than)h(a)60 1620 y(function.)60 1720 y FM(De\014nition)c(3.1)24 b FP(L)n(et)c FF(T)27 b FP(b)n(e)21 b(an)g(R)l(T)f(map)h(satisfying)g(pr)n(op)n(erties)e (\(T1\))i(and)f(\(T2\).)32 b(We)21 b(then)60 1781 y(de\014ne)e(the)f(c)n(orr) n(esp)n(onding)f(map)g FE(R)d FQ(=)f FE(R)847 1788 y FD(T)893 1781 y FP(to)k(b)n(e)h(the)g(r)n(elation)125 1889 y FE(R)28 b FQ(=)f FE(f)p FQ(\(\010)p FF(;)8 b FQ(\010)396 1868 y Fy(0)408 1889 y FQ(\))14 b FE(2)g(B)523 1868 y FH(1)553 1889 y FE(\002)d(B)638 1868 y FH(1)657 1889 y FQ(:)21 b FP(ther)n(e)d(exists)g FF(\026)c FE(2)g(G)1067 1896 y FD(inv)1121 1889 y FQ(\(\005)1177 1868 y FH(\010)1204 1889 y FQ(\))j FP(such)h(that)g FF(\026T)i FE(2)14 b(G)1606 1896 y FD(inv)1660 1889 y FQ(\(\005)1716 1868 y FH(\010)1741 1857 y Ft(0)1754 1889 y FQ(\))p FE(g)g FF(:)1765 1949 y FQ(\(3)p FF(:)p FQ(20\))60 2009 y FP(We)j(c)n(an)g(also)g(think)h(of)f FE(R)g FP(as)g(a)f(multi-value)n(d)j(function:)24 b(we)17 b(write)h FQ(\010)1395 1991 y Fy(0)1420 2009 y FE(2)c(R)p FQ(\(\010\))k FP(as)e(a)h(synonym)60 2069 y(for)g FQ(\(\010)p FF(;)8 b FQ(\010)249 2051 y Fy(0)261 2069 y FQ(\))14 b FE(2)g(R)p FP(.)22 b(We)c(de\014ne)h(the)f FQ(domain)d(of)i FE(R)g FP(to)h(b)n(e)g(the)f(set)448 2178 y FQ(dom)7 b FE(R)42 b FQ(=)g FE(f)p FQ(\010:)21 b FP(ther)n(e)d(exists)g FQ(\010)1097 2157 y Fy(0)1126 2178 y FP(with)g FQ(\(\010)p FF(;)8 b FQ(\010)1343 2157 y Fy(0)1355 2178 y FQ(\))14 b FE(2)g(Rg)632 2250 y FQ(=)42 b FE(f)p FQ(\010:)21 b FE(R)p FQ(\(\010\))15 b FE(6)p FQ(=)e Fq(?)p FE(g)h FF(:)683 b FQ(\(3.21\))133 2359 y FP(A)21 b(priori)j FQ(the)c(map)f FE(R)h FQ(could)g(b)q(e)g(m)o(ulti-v)m (alued.)30 b(Indeed,)19 b(the)h(w)o(a)o(y)g(w)o(e)f(ha)o(v)o(e)g(de\014ned)h (it,)60 2419 y(it)i(surely)g FP(is)27 b FQ(m)o(ulti-v)m(alued,)22 b(b)q(ecause)h(of)g(ph)o(ysical)e(equiv)m(alence:)33 b(if)22 b(\010)1448 2401 y Fy(0)1485 2419 y FE(2)j(R)p FQ(\(\010\))e(and)g(\011)1820 2401 y Fy(0)1857 2419 y FE(2)60 2479 y(B)95 2461 y FH(1)122 2479 y FE(\\)8 b FQ(\()p FE(J)16 b FQ(+)8 b FF(C)t(onst)p FQ(\),)13 b(then)i(also)g(\010)697 2461 y Fy(0)716 2479 y FQ(+)8 b(\011)800 2461 y Fy(0)825 2479 y FE(2)14 b(R)p FQ(\(\010\).)21 b(The)15 b(more)e(in)o(teresting)h(question)g(is)g(whether)60 2539 y FE(R)21 b FQ(can)f(b)q(e)h(m)o(ulti-v)m(alued)d FP(ap)n(art)j(fr)n(om)i FQ(the)d(\\trivial")g(m)o(ulti-v)m(aluedness)e(caused)j(b)o(y)f(ph)o(ysical) 60 2600 y(equiv)m(alence.)f(The)c(scenario)h(prop)q(osed)g(in)f([72])g(is)g (precisely)e(the)i(claim)e(that)j(this)f(can)h(happ)q(en;)60 2660 y(w)o(e)e(shall)h(pro)o(v)o(e)f(in)g(our)h(First)g(F)l(undamen)o(tal)e (Theorem)g(\(Theorem)h(3.4\))h(that)g(in)f(fact)h(it)f FP(c)n(annot)951 2784 y FQ(83)p eop %%Page: 84 84 bop 60 91 a FQ(happ)q(en.)44 b(That)25 b(is,)g(w)o(e)e(shall)h(pro)o(v)o(e)e (that)j(the)e(map)g FE(R)h FQ(is)f FP(single-value)o(d)j(mo)n(dulo)e(physic)n (al)60 152 y(e)n(quivalenc)n(e)t FQ(.)f(W)l(e)14 b(shall)h(moreo)o(v)o(er)e (pro)o(v)o(e)h(that)h(the)f(phrase)i(\\there)e(exists)g FF(\026)p FQ(")i(in)e(\(3.20\))i(can)f(b)q(e)60 212 y(replaced)g(equiv)m(alen)o(tly)f (b)o(y)i(\\for)h(all)f FF(\026)p FQ(".)133 321 y(F)l(or)22 b(R)l(T)f(maps)g(satisfying)g(a)h(v)o(ery)e(mild)f(con)o(tin)o(uit)o(y)g (condition,)j(w)o(e)f(can)h(sa)o(y)f(something)60 381 y(ab)q(out)f(the)e (closure)g(prop)q(erties)h(of)g(the)f(m)o(ulti-v)m(alued)e(map)i FE(R)p FQ(.)28 b(T)l(o)19 b(a)o(v)o(oid)f(b)q(othersome)h(top)q(o-)60 441 y(logical)d(complexitie)o(s,)d(w)o(e)j(restrict)f(atten)o(tion)h(to)h (compact)e(metric)f(single-spin)i(spaces)g(\012)1783 448 y FH(0)1803 441 y FQ(.)60 554 y FM(Theorem)h(3.2)24 b FP(L)n(et)d FQ(\012)517 561 y FH(0)559 554 y FP(b)n(e)h(a)g(c)n(omp)n(act)f(metric)h(sp)n (ac)n(e,)h(and)f(assume)g(that)g FF(T)28 b FP(satis\014es)22 b(\(T1\))60 614 y(and)e(\(T2\))g(and)g(is)g(F)l(el)r(ler)i(\(i.e.)e FF(T)7 b(f)25 b FP(is)20 b(c)n(ontinuous)h(if)f FF(f)25 b FP(is\).)30 b(Then)20 b FE(R)h FP(is)f(a)f FQ(closed)h FP(subset)h(of)60 675 y FE(B)95 656 y FH(1)125 675 y FE(\002)11 b(B)210 656 y FH(1)246 675 y FP(with)18 b(r)n(esp)n(e)n(ct)f(to)g(the)h FE(B)685 656 y FH(0)704 675 y FF(=)p FQ(\()p FE(J)j FQ(+)11 b FF(C)t(onst)p FQ(\))f FE(\002)h(B)1097 656 y FH(0)1116 675 y FF(=)p FQ(\()p FE(J)20 b FQ(+)11 b FF(C)t(onst)p FQ(\))18 b FP(seminorm.)60 836 y Fd(Pr)o(oof.)48 b FQ(Assume)14 b(that)j(\(\010)621 843 y FD(n)645 836 y FF(;)8 b FQ(\010)702 818 y Fy(0)702 849 y FD(n)725 836 y FQ(\))14 b FE(2)g(R)i FQ(and)h(\(\010)1012 843 y Fy(1)1050 836 y FF(;)8 b FQ(\010)1107 818 y Fy(0)1107 849 y(1)1144 836 y FQ(\))14 b FE(2)g(B)1259 818 y FH(1)1289 836 y FE(\002)d(B)1374 818 y FH(1)1393 836 y FQ(,)16 b(with)227 945 y(lim)214 970 y FD(n)p Fy(!1)315 945 y FE(k)p FQ(\010)375 952 y FD(n)409 945 y FE(\000)11 b FQ(\010)494 952 y Fy(1)532 945 y FE(k)557 954 y Fy(B)581 944 y Fr(0)598 954 y FD(=)p FH(\()p Fy(J)5 b FH(+)p FD(C)r(onst)p FH(\))825 945 y FQ(=)40 b(lim)891 970 y FD(n)p Fy(!1)991 945 y FE(k)p FQ(\010)1051 925 y Fy(0)1051 958 y FD(n)1086 945 y FE(\000)11 b FQ(\010)1171 925 y Fy(0)1171 958 y(1)1208 945 y FE(k)1233 954 y Fy(B)1257 944 y Fr(0)1274 954 y FD(=)p FH(\()p Fy(J)6 b FH(+)p FD(C)r(onst)p FH(\))1502 945 y FQ(=)27 b(0)15 b FF(:)145 b FQ(\(3)p FF(:)p FQ(22\))60 1064 y(W)l(e)16 b(need)g(to)g(pro)o(v)o(e)g(that)h(\(\010)609 1071 y Fy(1)646 1064 y FF(;)8 b FQ(\010)703 1046 y Fy(0)703 1077 y(1)740 1064 y FQ(\))14 b FE(2)g(R)p FQ(.)133 1125 y(Cho)q(ose,)i(for)f (eac)o(h)e FF(n)p FQ(,)i(a)g(translation-in)o(v)m(arian)o(t)f(Gibbs)h (measure)e FF(\026)1398 1132 y FD(n)1436 1125 y FQ(for)i(\010)1544 1132 y FD(n)1568 1125 y FQ(.)20 b(By)14 b(passing)i(to)60 1185 y(a)i(subsequence,)f(w)o(e)g(can)h(assume)f(without)h(loss)g(of)g(generalit)o (y)e(that)i FF(\026)1423 1192 y FD(n)1464 1185 y FQ(con)o(v)o(erges)f(w)o (eakly)g(to)60 1245 y(some)e(measure)f FF(\026)400 1252 y Fy(1)438 1245 y FQ(;)i(and)g(since)f(\010)716 1252 y FD(n)754 1245 y FE(!)f FQ(\010)853 1252 y Fy(1)906 1245 y FQ(in)i FE(B)998 1227 y FH(0)1017 1245 y FF(=)p FQ(\()p FE(J)j FQ(+)11 b FF(C)t(onst)p FQ(\))k(seminorm,)e(it)i(is)h(easy)g(to)g(see)60 1305 y(that)j FF(\026)197 1312 y Fy(1)253 1305 y FQ(is)g(a)g(translation-in)o(v)m(arian)o (t)g(Gibbs)g(measure)e(for)i(\010)1250 1312 y Fy(1)1288 1305 y FQ(.)28 b(No)o(w)19 b(the)f(F)l(eller)f(h)o(yp)q(othesis)60 1365 y(on)g FF(T)23 b FQ(guaran)o(tees)17 b(that)g FF(\026)558 1372 y FD(n)582 1365 y FF(T)j FE(!)14 b FF(\026)724 1372 y Fy(1)762 1365 y FF(T)23 b FQ(w)o(eakly)l(.)e(Since)15 b FF(\026)1147 1372 y FD(n)1171 1365 y FF(T)23 b FQ(is)16 b(a)h(translation-in)o(v)m(arian)o (t)g(Gibbs)60 1426 y(measure)g(for)h(\010)363 1407 y Fy(0)363 1438 y FD(n)387 1426 y FQ(,)g(and)h(\010)551 1407 y Fy(0)551 1438 y FD(n)591 1426 y FE(!)e FQ(\010)693 1407 y Fy(0)693 1438 y(1)749 1426 y FQ(in)g FE(B)842 1407 y FH(0)861 1426 y FF(=)p FQ(\()p FE(J)22 b FQ(+)12 b FF(C)t(onst)p FQ(\))18 b(seminorm,)d(it)j(follo)o (ws)g(that)g FF(\026)1766 1433 y Fy(1)1804 1426 y FF(T)24 b FQ(is)60 1486 y(a)19 b(translation-in)o(v)m(arian)o(t)g(Gibbs)g(measure)f (for)h(\010)1006 1468 y Fy(0)1006 1498 y(1)1043 1486 y FQ(.)29 b(But)19 b(this)f(implies)e(that)k(\(\010)1614 1493 y Fy(1)1651 1486 y FF(;)8 b FQ(\010)1708 1468 y Fy(0)1708 1498 y(1)1746 1486 y FQ(\))18 b FE(2)g(R)p FQ(.)p 178 1550 25 34 v 60 1725 a FM(3.1.4)55 b(A)19 b(Remark)e(on)i(Systems)d(of)j(Un)n(b)r(ounded)g(Spins) 60 1817 y FQ(The)d(results)g(to)g(b)q(e)h(pro)o(v)o(en)e(in)h(Sections)g(3.2) g(and)h(3.3)f(are)g(in)g(principle)f(applicable)g(to)h(systems)60 1877 y(of)g(either)e(b)q(ounded)i(or)g(un)o(b)q(ounded)g(spins.)22 b(But)15 b(for)g(un)o(b)q(ounded)i(spins)e(our)h(results)f(are)h(not)g(of)60 1938 y(m)o(uc)o(h)g(in)o(terest,)h(b)q(ecause)h(w)o(e)f(restrict)g(atten)o (tion)h(to)h FP(b)n(ounde)n(d)g(Hamiltonians)k FQ(\(i.e.)16 b(absolutely)60 1998 y(summable)i(in)o(teractions\).)35 b(The)21 b(trouble,)g(as)h(discussed)f(at)g(the)g(end)f(Section)h(2.4.4,)h(is)f(that) 60 2058 y(w)o(e)h(lac)o(k)f(at)i(presen)o(t)f(an)g(adequate)h(general)f (theory)g(of)h(un)o(b)q(ounded)g(spin)f(systems:)32 b(w)o(e)22 b(are)60 2118 y(unable)d(to)h(sp)q(ecify)l(,)f(for)h(example,)e(a)h(space)h (of)g(in)o(teractions)e(that)i(includes)f(all)g(\\reasonable")60 2178 y(in)o(teractions.)h(The)c(dev)o(elopmen)o(t)c(of)k(suc)o(h)f(a)h (general)f(theory)h(is)f(an)h(imp)q(ortan)o(t)f FP(op)n(en)i(pr)n(oblem)t FQ(;)60 2238 y(it)f(w)o(ould)g(b)q(e)g(a)g(\014rst)h(step)f(to)o(w)o(ards)g (putting)g(the)g(standard)h(Wilson-st)o(yle)e(R)o(G)h(theory)g([365)q(])g(on) 60 2299 y(a)f(rigorous)g(fo)q(oting.)22 b(In)14 b(particular,)f(in)h(suc)o(h) h(a)f(framew)o(ork)f(one)i(could)f(try)g(to)g(pro)o(v)o(e)g(analogues)60 2359 y(of)j(our)f(First)g(and)h(Second)f(F)l(undamen)o(tal)f(Theorems.)133 2419 y(In)21 b(this)h(regard)g(it)f(should)h(b)q(e)g(remark)o(ed)d(that)j (the)f(imp)q(ortan)o(t)g(w)o(ork)h(of)g(Ga)o(w\030)-22 b(edzki)20 b(and)60 2479 y(Kupiainen)c([147,)g(148)q(,)g(150)q(,)g(151)q(])g(on)h (rigorous)g(R)o(G)f(theory)g(do)q(es)h(not)g(implem)o(e)o(n)o(t)c(exactly)i (the)60 2539 y(standard)k(Wilson)f(prescription,)g(at)g(least)g(for)g(b)q (osonic)h(theories:)25 b(while)17 b(the)g(small-\014eld)g(part)60 2600 y(of)e(the)f(Gibbs)h(measure)f(is)g(represen)o(ted)g(b)o(y)g(a)h (Hamiltonian)e(of)i(the)g(usual)g(kind,)f(the)g(large-\014eld)60 2660 y(part)21 b(is)f(represen)o(ted)f(instead)h(b)o(y)g(a)h(p)q(olymer)e (expansion)i([148].)33 b(\(In)20 b(recen)o(t)f(w)o(ork,)i(Brydges)951 2784 y(84)p eop %%Page: 85 85 bop 60 91 a FQ(and)15 b(Y)l(au)f([53)q(])f(systematize)f(this)j(idea,)f(and)g (form)o(ulate)f(the)h(R)o(G)g FP(pur)n(ely)19 b FQ(in)13 b(terms)g(of)i(a)g (p)q(olymer)60 152 y(expansion.\))33 b(F)l(or)20 b(fermionic)e(theories,)i (where)g(there)f(is)h(no)h(\\large-\014eld)f(region",)h(Ga)o(w\030)-22 b(edzki)60 212 y(and)23 b(Kupiainen)e([149)q(])h(do)g(implem)o(en)o(t)d(the)j (full)f(Wilson)h(prescription;)i(ho)o(w)o(ev)o(er,)e(fermionic)60 272 y(theories)11 b(ha)o(v)o(e)g(no)h(direct)f(probabilistic)f(in)o (terpretation.)19 b(Also,)12 b(for)g(b)q(osons,)h(Ko)q(c)o(h)f(and)g(Witt)o (w)o(er)60 332 y([218)q(,)h(219)q(])g(implem)o(en)o(t)d(the)j(Wilson)h (prescription,)f(but)g(so)h(far)g(only)g(in)f(the)g(hierarc)o(hical)f(mo)q (del.)60 477 y FB(3.2)70 b(First)29 b(F)-6 b(undamen)n(tal)28 b(Theorem:)42 b(Single-V)-6 b(aluedness)28 b(of)j(the)217 551 y(R)-6 b(T)22 b(Map)60 644 y FQ(Among)d(the)h(p)q(ossible)h(pathologies)g(of) f(the)h(R)l(T)f(applied)g(at)g(the)g(lev)o(el)e(of)j(Hamiltonians,)e(the)60 704 y(follo)o(wing)13 b(scenario)g(has)i(b)q(een)e(prop)q(osed)i([72])925 686 y FH(46)962 704 y FQ(:)20 b(Consider)13 b(a)h(Hamiltonian)d FF(H)18 b FQ(lying)13 b(on)h(a)f(\014rst-)60 764 y(order)18 b(phase-transition)i(surface,)e(that)h(is,)f(one)h(for)g(whic)o(h)e(there)h (exist)g(at)g(least)h(t)o(w)o(o)f(distinct)60 824 y(pure)23 b(phases)h(\(extremal)d(translation-in)o(v)m(arian)o(t)i(Gibbs)h(measures\),) f(call)g(them)e FF(\026)1682 831 y FH(1)1726 824 y FQ(and)i FF(\026)1856 831 y FH(2)1876 824 y FQ(.)60 884 y(No)o(w)17 b(p)q(erform)f(a)i(renormalization)d(transformation)i FF(T)24 b FQ(as)18 b(indicated)e(in)h(\(1.1\).)24 b(The)17 b(resulting)60 945 y(renormalized)10 b(measures)h FF(\026)580 926 y Fy(0)580 957 y FH(1)614 945 y FE(\021)i FF(\026)695 952 y FH(1)715 945 y FF(T)19 b FQ(and)13 b FF(\026)883 926 y Fy(0)883 957 y FH(2)916 945 y FE(\021)h FF(\026)998 952 y FH(2)1018 945 y FF(T)19 b FQ(ma)o(y)10 b(then,)i(it)g(is)g(claimed,)e(b)q(e)i(Gibbsian)h(for)60 1005 y(t)o(w)o(o)g FP(di\013er)n(ent)k FQ(renormalized)11 b(Hamiltonians)g FF(H)969 987 y Fy(0)965 1017 y FH(1)999 1005 y FE(6)p FQ(=)i FF(H)1094 987 y Fy(0)1090 1017 y FH(2)1111 1005 y FQ(.)20 b(In)12 b(other)h(w)o(ords,)g(the)g(renormalization)60 1065 y(map)i FE(R)i FQ(from)e(Hamiltonians)g(to)h(Hamiltonians,)f(de\014ned)h(b)o(y)f (\(1.2\),)h(ma)o(y)f(b)q(e)h FP(multi-value)n(d)5 b FQ(.)133 1125 y(Here)22 b(w)o(e)g(dispro)o(v)o(e)g(suc)o(h)h(a)g(scenario.)41 b(W)l(e)23 b(sho)o(w)g(that)g(if)g(t)o(w)o(o)f(initial)g(Gibbs)h(measures)60 1185 y(corresp)q(ond)17 b(to)f(the)f(same)g(in)o(teraction)f(\010,)i(then)f (the)h(renormalized)d(measures)i(are)g(either)g(b)q(oth)60 1246 y(Gibbsian)g(for)g(the)g FP(same)j FQ(renormalized)13 b(in)o(teraction)h(\010)1114 1227 y Fy(0)1125 1246 y FQ(,)h(or)g(else)f(they) g(are)h(b)q(oth)h(non-Gibbsian)60 1306 y(\(in)g(whic)o(h)f(case)i(there)e(is) h FP(no)k FQ(renormalized)14 b(in)o(teraction)h(at)i(all\).)133 1366 y(This)24 b(theorem)e(follo)o(ws)h(from)f(comparing)h(the)g (large-deviation)h(prop)q(erties)f(of)h(di\013eren)o(t)60 1426 y(Gibbs)14 b(measures)e(according)i(to)g(whether)f(they)h(b)q(elong)g(to)g (the)f(same)g(or)h(di\013eren)o(t)e(in)o(teractions.)60 1486 y(Heuristically)l(,)e(if)i FF(\026)h FQ(and)g FF(\027)j FQ(are)d(t)o(w)o(o)f (Gibbs)h(measures)e(corresp)q(onding)j(to)f(di\013eren)o(t)e(in)o (teractions,)60 1546 y(then)16 b(the)g(probabilit)o(y)f(of)i(\014nding)f(in)g FF(\027)k FQ(a)c(large)g(droplet)g(lo)q(oking)h(lik)o(e)d(a)j(t)o(ypical)e (con\014guration)60 1607 y(for)i(the)f(measure)e FF(\026)j FQ(is)f(exp)q(onen)o(tially)f(small)g(in)g(the)h(v)o(olume)e(of)j(the)f (droplet:)581 1717 y(Prob)684 1724 y FD(\027)706 1717 y FQ(\()p FF(!)755 1724 y FH(\003)798 1717 y FQ(is)g(t)o(ypical)f(for)h FF(\026)p FQ(\))f FE(\030)e FF(e)1219 1696 y Fy(\000)p FD(O)q FH(\()p Fy(j)p FH(\003)p Fy(j)p FH(\))1356 1717 y FF(:)395 b FQ(\(3)p FF(:)p FQ(23\))60 1827 y(On)18 b(the)f(other)h(hand,)g(if)g FF(\026)g FQ(and)g FF(\027)j FQ(corresp)q(ond)e(to)f(the)f(same)g(in)o (teraction,)g(this)g(probabilit)o(y)g(is)60 1887 y(sub-exp)q(onen)o(tial:)586 1947 y(Prob)690 1954 y FD(\027)711 1947 y FQ(\()p FF(!)760 1954 y FH(\003)803 1947 y FQ(is)f(t)o(ypical)f(for)i FF(\026)p FQ(\))d FE(\030)f FF(e)1224 1926 y Fy(\000)p FD(o)p FH(\()p Fy(j)p FH(\003)p Fy(j)p FH(\))1350 1947 y FF(:)401 b FQ(\(3)p FF(:)p FQ(24\))60 2034 y(Mathematically)l(,)16 b(as)k(seen)f(in)f(Section)g (2.6,)i(this)f(is)f(expressed)h(in)f(the)h(fact)g(that)g(the)g(relativ)o(e)60 2094 y(en)o(trop)o(y)c(densit)o(y)h(satis\014es)151 2233 y FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))293 2160 y Fx(\()347 2202 y FF(>)e FQ(0)42 b(if)15 b FF(\026)i FQ(and)g FF(\027)i FQ(are)d(Gibbs)h(measures)e(for)i(di\013eren)o(t)e(in)o(teractions) 347 2262 y(=)f(0)42 b(if)15 b FF(\026)i FQ(and)g FF(\027)i FQ(are)d(Gibbs)h(measures)e(for)i(the)f(same)f(in)o(teraction)1765 2233 y(\(3)p FF(:)p FQ(25\))p 60 2317 732 2 v 100 2370 a FA(46)135 2386 y Fz(This)10 b(scenario)i(is)e(stated)i(v)o(ery)f(clearly)g(in)f(the)h (Mon)o(te)g(Carlo)f(pap)q(er)i(of)e(Dec)o(k)o(er,)i(Hasenfratz)f(and)g (Hasenfratz)60 2435 y([72)o(,)g(p.)g(23,)f(lines)h(2{5].)16 b(On)11 b(the)h(other)f(hand,)g(the)h(analytic)e(argumen)o(ts)g(in)g(the)i (companion)d(pap)q(er)j(of)e(Hasenfratz)60 2485 y(and)17 b(Hasenfratz)g([189) o(])g(concern)h(\\singularities")d(whose)j(precise)g(nature)g(is)e(unsp)q (eci\014ed.)29 b(W)m(e)16 b(are)h(unable)g(to)60 2535 y(mak)o(e)12 b(a)i(connection)h(b)q(et)o(w)o(een)g(the)f(t)o(w)o(o)g(lines)g(of)f (reasoning.)951 2784 y FQ(85)p eop %%Page: 86 86 bop 60 91 a FQ(No)o(w,)19 b(under)h(renormalization)d(one)j(lo)q(oks)g(only)f (at)h(the)f(blo)q(c)o(k)f(spins)i(and)g(forgets)g(ab)q(out)g(the)60 152 y(in)o(ternal)15 b(spins,)h(hence)482 252 y(Prob)585 259 y FD(\027)607 252 y FQ(\(blo)q(c)o(k)g(spins)g(in)g FF(!)964 259 y FH(\003)1007 252 y FQ(are)g(t)o(ypical)f(for)i FF(\026)p FQ(\))565 324 y FE(\025)c FQ(Prob)721 331 y FD(\027)742 324 y FQ(\()p FP(al)r(l)18 b FQ(spins)e(in)g FF(!)1039 331 y FH(\003)1083 324 y FQ(are)g(t)o(ypical)f(for)h FF(\026)p FQ(\))8 b FF(:)297 b FQ(\(3.26\))60 424 y(Therefore,)12 b(if)f(initially)e(the)j(probabilit)o(y) e(w)o(as)i(sub)q(exp)q(onen)o(tial)g(\(same)f(in)o(teraction\),)g(then)g (under)60 485 y(renormalization)18 b(it)i(remains)f(so)i(and)f(w)o(e)g(can)g (nev)o(er)f(obtain)i(the)f(exp)q(onen)o(tial)f(deca)o(y)g(\(3.23\))60 545 y(c)o(haracteristic)f(of)j(di\013eren)o(t)e(in)o(teractions.)31 b(Mathematically)l(,)18 b(this)i(is)g(expressed)f(b)o(y)g(the)h(fact)60 605 y(that)d(the)f(relativ)o(e)f(en)o(trop)o(y)h(decreases)g(under)h(the)f (application)h(of)g(arbitrary)f(deterministic)e(or)60 665 y(sto)q(c)o(hastic) i(transformations,)g(in)g(particular)g(under)g(the)g(R)l(T:)60 768 y FM(Lemma)g(3.3)24 b FP(L)n(et)19 b FQ(\(\012)p FF(;)8 b FQ(\006\))21 b FP(and)f FQ(\(\012)743 750 y Fy(0)755 768 y FF(;)8 b FQ(\006)812 750 y Fy(0)824 768 y FQ(\))20 b FP(b)n(e)g(me)n(asur)n (able)g(sp)n(ac)n(es,)g(and)h(let)g FF(T)26 b FP(b)n(e)21 b(a)f(pr)n(ob)n (ability)60 828 y(kernel)f(fr)n(om)d FQ(\(\012)p FF(;)8 b FQ(\006\))18 b FP(to)f FQ(\(\012)580 810 y Fy(0)592 828 y FF(;)8 b FQ(\006)649 810 y Fy(0)661 828 y FQ(\))p FP(.)22 b(Then,)c(if)g FF(\026)f FP(and)h FF(\027)j FP(ar)n(e)c(pr)n(ob)n(ability)f(me)n(asur)n(es)h(on)h FQ(\012)p FP(,)753 928 y FF(I)t FQ(\()p FF(\026T)7 b FE(j)p FF(\027)s(T)g FQ(\))21 b FE(\024)h FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))8 b FF(:)60 1076 y Fd(Pr)o(oof.)48 b FQ(This)15 b(is)h(a)g(w)o(ell-kno)o(wn)e(result,)h(although)i(it)e(is)g (rather)h(di\016cult)e(to)i(\014nd)g(a)g(complete)60 1136 y(pro)q(of)j(in)f (the)g(literature.)27 b(\(Most)18 b(of)h(the)f(published)g(pro)q(ofs)h (concern)f(one)h(or)g(another)f(sp)q(ecial)60 1196 y(case:)25 b FF(T)f FQ(deterministic,)14 b FF(\027)s(T)24 b FQ(=)16 b FF(\027)s FQ(,)i(discrete)f(state)h(space,)g(etc.\))26 b(The)18 b(\014rst)g(complete)e(pro)q(of)j(of)60 1256 y(whic)o(h)d(w)o(e)h(are)g(a)o (w)o(are)g(is)g(due)g(to)g(Csisz\023)-24 b(ar)17 b(\(1963\))i([67];)d(ho)o(w) o(ev)o(er,)g(w)o(e)g(w)o(ould)h(not)h(b)q(e)f(surprised)60 1316 y(to)g(learn)f(that)h(this)f(result)g(w)o(as)h(kno)o(wn)f(m)o(uc)o(h)e (earlier.)21 b(See)16 b(also,)g(for)h(instance,)f([361])g(and)h([61,)60 1376 y(Theorem)12 b(8.1];)i(and)h(see)e([64)q(])g(for)h(some)f(stronger)h (results.)20 b(F)l(or)14 b(the)g(con)o(v)o(enience)d(of)j(the)g(reader,)60 1437 y(let)h(us)i(giv)o(e)e(a)i(one-line)f(pro)q(of:)535 1537 y FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))28 b(=)f FF(I)t FQ(\()p FF(\026)11 b FE(\002)g FF(T)c FE(j)p FF(\027)14 b FE(\002)c FF(T)d FQ(\))27 b FE(\025)h FF(I)t FQ(\()p FF(\026T)7 b FE(j)p FF(\027)s(T)g FQ(\))12 b FF(:)350 b FQ(\(3)p FF(:)p FQ(27\))60 1637 y(Here)15 b(the)h(\014rst)g(equalit)o(y)f(is)g(Prop)q (osition)j(2.53\(h\):)k(the)15 b(measures)g FF(\026)d FE(\002)e FF(T)22 b FQ(and)17 b FF(\027)d FE(\002)d FF(T)22 b FQ(ha)o(v)o(e)15 b(the)60 1697 y(same)e(regular)i(conditional)f(probabilit)o(y)f(giv)o(en)g (\006,)i(namely)d FF(T)7 b FQ(.)20 b([The)14 b(in)o(tuitiv)o(e)e(idea)i(is)g (that)g(the)60 1757 y(pair)j(\()p FF(\026)12 b FE(\002)f FF(T)t(;)d(\027)14 b FE(\002)e FF(T)7 b FQ(\))16 b(con)o(tains)h(at)g(least)g(as)g(m)o(uc)o(h)e (information)h(as)h(the)g(pair)g(\()p FF(\026;)8 b(\027)s FQ(\),)17 b(since)f(the)60 1818 y(latter)j(is)h(the)f(restriction)g(of)h(the)f(former)g (to)h(the)f(sub-)p FF(\033)r FQ(-\014eld)h(\006)g FE(\032)f FQ(\006)14 b FE(\002)f FQ(\006)1523 1799 y Fy(0)1535 1818 y FQ(;)21 b(but)f(it)f(con)o(tains)60 1878 y(no)g(more)e(information,)g(b)q (ecause)i(the)f FP(same)k FQ(probabilit)o(y)c(k)o(ernel)e(has)k(b)q(een)e (used)g(to)h(generate)60 1938 y(b)q(oth)e FF(\026)11 b FE(\002)f FF(T)23 b FQ(and)17 b FF(\027)c FE(\002)e FF(T)22 b FQ(from)15 b FF(\026)i FQ(and)f FF(\027)s FQ(.])21 b(And)16 b(the)g(inequalit)o(y)e(is)i (Prop)q(osition)h(2.53\(g\),)g(since)60 1998 y FF(\026T)23 b FQ(\(resp.)16 b FF(\027)s(T)7 b FQ(\))16 b(is)g(the)g(restriction)g(of)g FF(\026)c FE(\002)f FF(T)23 b FQ(\(resp.)15 b FF(\027)g FE(\002)c FF(T)c FQ(\))15 b(to)i(the)f(sub-)p FF(\033)r FQ(-\014eld)h(\006)1655 1980 y Fy(0)1680 1998 y FE(\032)d FQ(\006)e FE(\002)f FQ(\006)1865 1980 y Fy(0)1876 1998 y FQ(.)p 178 2062 25 34 v 60 2205 a FM(Theorem)17 b(3.4)h(\(First)g(fundamen)n(tal)g(theorem\))k FP(L)n(et)c FF(\026)h FP(and)f FF(\027)k FP(b)n(e)d(tr)n(anslation-invariant)60 2266 y(Gibbs)f(me)n(asur)n(es)f(with)i(r)n(esp)n(e)n(ct)e(to)h(the)g(same)g (inter)n(action)h FQ(\010)c FE(2)g(B)1316 2248 y FH(1)1335 2266 y FP(,)j(and)g(let)h FF(T)24 b FP(b)n(e)19 b(an)f(R)l(T)f(map)60 2326 y(satisfying)h(pr)n(op)n(erties)e(\(T1\){\(T3\).)21 b(Then:)93 2419 y(\(a\))j(Either)16 b FF(\026T)23 b FP(and)16 b FF(\027)s(T)23 b FP(ar)n(e)15 b(b)n(oth)h(non-quasilo)n(c)n(al)i(\(i.e.)e(not)h(c)n (onsistent)g(with)f(any)h(quasilo)n(c)n(al)182 2479 y(sp)n(e)n(ci\014c)n (ation\),)e(or)f(else)i(ther)n(e)e(exists)i(a)e(quasilo)n(c)n(al)h(sp)n(e)n (ci\014c)n(ation)g FQ(\005)1449 2461 y Fy(0)1475 2479 y FP(with)g(which)g FQ(b)q(oth)g FF(\026T)182 2539 y FP(and)k FF(\027)s(T)26 b FP(ar)n(e)19 b(c)n(onsistent.)29 b(In)19 b(the)h(latter)f(c)n(ase,)h(if)f (the)h(single-spin)h(sp)n(ac)n(e)e(is)g(\014nite,)i(then)182 2600 y FQ(\005)219 2582 y Fy(0)246 2600 y FP(is)15 b(the)h FQ(unique)f FP(quasilo)n(c)n(al)h(sp)n(e)n(ci\014c)n(ation)g(with)g(which)g (either)g FF(\026T)22 b FP(or)15 b FF(\027)s(T)22 b FP(is)16 b(c)n(onsistent,)182 2660 y(and)i(it)f(is)g(tr)n(anslation-invariant.)951 2784 y FQ(86)p eop %%Page: 87 87 bop 95 91 a FP(\(b\))25 b(Either)16 b FF(\026T)23 b FP(and)16 b FF(\027)s(T)23 b FP(ar)n(e)15 b(b)n(oth)h(non-Gibbsian)i(\(for)d (absolutely)i(summable)g(inter)n(actions\),)182 152 y(or)e(else)i(ther)n(e)e (exists)i(an)f(absolutely)h(summable)f(inter)n(action)g FQ(\010)1379 133 y Fy(0)1407 152 y FP(for)f(which)h FQ(b)q(oth)h FF(\026T)22 b FP(and)182 212 y FF(\027)s(T)g FP(ar)n(e)15 b(Gibbs)h(me)n(asur)n(es.)21 b(In)15 b(the)h(latter)g(c)n(ase,)g(if)g FQ(\010)1169 194 y Fy(0)1196 212 y FP(is)f(c)n(ontinuous)h([as)g(it)f(always)h(is)f(e.g.)182 272 y(for)g(a)g(discr)n(ete)g(single-spin)j(sp)n(ac)n(e],)d FQ(\010)904 254 y Fy(0)931 272 y FP(is)h(the)f FQ(unique)g FP(c)n(ontinuous)h(absolutely)h(summable)182 332 y(inter)n(action)i(\(mo)n (dulo)f(physic)n(al)f(e)n(quivalenc)n(e)k(in)e(the)f(DLR)f(sense\))i(for)f (which)h(either)f FF(\026T)182 392 y FP(or)f FF(\027)s(T)24 b FP(is)17 b(a)h(Gibbs)f(me)n(asur)n(e.)60 555 y Fd(Pr)o(oof.)48 b FQ(Let)16 b(\(\003)421 562 y FD(n)444 555 y FQ(\))f FE(\032)f Fq(Z)561 534 y FD(d)598 555 y FQ(and)j(\(\003)746 537 y Fy(0)746 567 y FD(n)769 555 y FQ(\))e FE(\032)f Fq(Z)886 534 y FD(d)904 522 y Ft(0)934 555 y FQ(b)q(e)j(v)m(an)g(Ho)o(v)o(e)e(sequences)g(ha)o(ving)i (the)f(prop)q(erties)60 615 y(\(T3\))h(assumed)f(in)g(Section)g(3.1.)22 b(No)o(w,)16 b(b)o(y)g(Theorem)f(2.66,)i(the)f(fact)h(that)g FF(\026)f FQ(and)i FF(\027)h FQ(are)e(Gibbs)60 675 y(measures)e(for)i(the)f (same)f(in)o(teraction)g(implies)f(that)749 804 y(lim)737 829 y FD(n)p Fy(!1)872 770 y FQ(1)p 842 792 86 2 v 842 838 a FE(j)p FQ(\003)890 845 y FD(n)913 838 y FE(j)932 804 y FF(I)954 811 y FH(\003)978 815 y Fs(n)1001 804 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))h(=)e(0)8 b FF(:)544 b FQ(\(3)p FF(:)p FQ(28\))60 940 y(On)14 b(the)f(other)h(hand,)g(the)g(image)e(spins)i(in)f(\003)906 922 y Fy(0)906 952 y FD(n)944 940 y FQ(dep)q(end)g(only)h(on)g(the)f (original)h(spins)g(in)f(\003)1743 947 y FD(n)1767 940 y FQ(:)20 b(that)60 1000 y(is,)14 b(\()p FF(\026T)7 b FQ(\))p Fm(\026)p FE(F)290 982 y Fy(0)285 1012 y FH(\003)309 1003 y Ft(0)309 1021 y Fs(n)347 1000 y FQ(is)15 b(the)g(image)e(under)i FF(T)21 b FQ(of)15 b FF(\026)p Fm(\026)q FE(F)949 1007 y FH(\003)973 1011 y Fs(n)996 1000 y FQ(,)g(and)g(lik)o(ewise)e(for)i FF(\027)s FQ(.)21 b(Hence,)14 b(b)o(y)g(Lemma)f(3.3)60 1060 y(w)o(e)j(ha)o(v)o(e)701 1121 y FF(I)723 1128 y FH(\003)747 1119 y Ft(0)747 1136 y Fs(n)771 1121 y FQ(\()p FF(\026T)7 b FE(j)p FF(\027)s(T)g FQ(\))26 b FE(\024)i FF(I)1066 1128 y FH(\003)1090 1132 y Fs(n)1113 1121 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))14 b FF(:)516 b FQ(\(3)p FF(:)p FQ(29\))60 1207 y(It)16 b(follo)o(ws)g(that)418 1328 y(0)28 b FE(\024)f FQ(lim)8 b(sup)565 1363 y FD(n)p Fy(!1)729 1295 y FQ(1)p 699 1317 V 699 1362 a FE(j)p FQ(\003)747 1348 y Fy(0)747 1375 y FD(n)770 1362 y FE(j)789 1328 y FF(I)811 1335 y FH(\003)835 1326 y Ft(0)835 1344 y Fs(n)858 1328 y FQ(\()p FF(\026T)f FE(j)p FF(\027)s(T)g FQ(\))41 b FE(\024)53 b FQ(lim)1159 1353 y FD(n)p Fy(!1)1284 1295 y FF(K)p 1264 1317 V 1264 1362 a FE(j)p FQ(\003)1312 1369 y FD(n)1336 1362 y FE(j)1354 1328 y FF(I)1376 1335 y FH(\003)1400 1339 y Fs(n)1424 1328 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))1079 1429 y(=)42 b(0)14 b FF(:)554 b FQ(\(3.30\))60 1538 y(Therefore,)14 b(b)o(y)g(Theorem)f(2.67,)i (if)f FF(\027)s(T)21 b FQ(is)15 b(consisten)o(t)f(with)g(a)h(quasilo)q(cal)f (sp)q(eci\014cation)h(\005)1756 1520 y Fy(0)1767 1538 y FQ(,)f(then)60 1598 y FF(\026T)25 b FQ(m)o(ust)17 b(also)h(b)q(e)h(consisten)o(t)e(with)h (this)g FP(same)k FQ(sp)q(eci\014cation)c(\005)1318 1580 y Fy(0)1330 1598 y FQ(.)27 b(The)18 b(same)f(argumen)o(t)g(can)60 1658 y(b)q(e)i(made)f(in)o(terc)o(hanging)h(the)f(roles)h(of)h FF(\026)f FQ(and)h FF(\027)s FQ(.)30 b(Th)o(us,)20 b(either)e FF(\026T)26 b FQ(and)19 b FF(\027)s(T)26 b FQ(are)19 b(b)q(oth)h(non-)60 1718 y(quasilo)q(cal,)h(or)g(else)e(there)h(exists)g(a)h(quasilo)q(cal)f(sp)q (eci\014cation)g(\005)1325 1700 y Fy(0)1357 1718 y FQ(with)g(whic)o(h)g FP(b)n(oth)k FF(\026T)j FQ(and)60 1779 y FF(\027)s(T)f FQ(are)19 b(consisten)o(t.)31 b(In)19 b(the)g(latter)g(case,)g(if)g(the)g(single-spin)g (space)h(is)f(\014nite,)g(Theorem)f(2.15)60 1839 y(guaran)o(tees)i(the)f (uniqueness)h(of)f(\005)738 1821 y Fy(0)750 1839 y FQ(.)31 b(In)19 b(particular,)h(since)f FF(\026T)26 b FQ(and)20 b FF(\027)s(T)26 b FQ(\(b)q(eing)20 b(translation-)60 1899 y(in)o(v)m(arian)o(t\))h(are)g(ob)o (viously)g(consisten)o(t)g(with)g(an)o(y)g(translate)h(of)f(\005)1347 1881 y Fy(0)1358 1899 y FQ(,)h(w)o(e)f(conclude)g(that)h(\005)1825 1881 y Fy(0)1857 1899 y FQ(is)60 1959 y(translation-in)o(v)m(arian)o(t.)133 2019 y(A)17 b(sp)q(ecial)g(case)h(of)f(the)h(foregoing)g(is:)23 b(if)17 b FF(\027)s(T)24 b FQ(\(resp.)17 b FF(\026T)7 b FQ(\))17 b(is)h(Gibbsian)f(with)h(resp)q(ect)f(to)h(an)60 2080 y(absolutely)h (summable)d(in)o(teraction)i(\010)811 2062 y Fy(0)823 2080 y FQ(,)h(then)g FF(\026T)26 b FQ(\(resp.)18 b FF(\027)s(T)7 b FQ(\))19 b(m)o(ust)e(also)j(b)q(e)f(Gibbsian)g(with)60 2140 y(resp)q(ect)c(to)g(this)g FP(same)k FQ(in)o(teraction)14 b(\010)783 2122 y Fy(0)795 2140 y FQ(.)20 b(The)c(uniqueness)e(mo)q(dulo)h(ph)o(ysical)f (equiv)m(alence)f(of)i(\010)1878 2122 y Fy(0)60 2200 y FQ(is)h(then)g(guaran) o(teed)h(b)o(y)f(Corollary)g(2.18.)p 994 2204 25 34 v 133 2310 a(The)e(First)g(F)l(undamen)o(tal)e(Theorem)h(sho)o(ws)h(that)h(the)e(R)l(T)h (map)f FE(R)i FQ(is)e FP(single-value)o(d)k(mo)n(dulo)60 2370 y(physic)n(al)j(e)n(quivalenc)n(e)t FQ(.)32 b(It)18 b(also)i(sho)o(ws)g(that) f(the)g(phrase)h(\\there)f(exists)f FF(\026)p FQ(")i(in)f(the)f(de\014nition) 60 2430 y(\(3.20\))f(can)f(b)q(e)h(replaced)e(equiv)m(alen)o(tly)f(b)o(y)i (\\for)h(all)e FF(\026)p FQ(".)133 2539 y FM(Remarks.)k FQ(1.)j(The)16 b(\014rst)g(step)g(of)h(this)f(pro)q(of)h(\(using)f(Theorem)f(2.66\))i(do)q (es)f(not)h(require)e FF(\026)60 2600 y FQ(and)f FF(\027)j FQ(to)d(b)q(e)f(translation-in)o(v)m(arian)o(t.)21 b(But)13 b(the)g(second)h(step)f(\(using)h(Theorem)e(2.67\))j(do)q(es)f(seem)60 2660 y(to)i(require)e(at)i(least)f FF(\026T)23 b FQ(and)16 b FF(\027)s(T)22 b FQ(to)16 b(b)q(e)f(translation-in)o(v)m(arian)o(t.)22 b(So)16 b(w)o(e)f(do)h(not)g(kno)o(w)f(whether)951 2784 y(87)p eop %%Page: 88 88 bop 60 91 a FQ(the)20 b(h)o(yp)q(othesis)h(of)g(translation-in)o(v)m(ariance) g(of)g FF(\026)g FQ(and)g FF(\027)j FQ(can)d(b)q(e)f(omitted)f(in)i(this)f (theorem.)60 152 y(\(Note:)h(W)l(e)16 b(alw)o(a)o(ys)g(assume)f(that)i(the)f FP(inter)n(action)21 b FQ(\010)16 b(is)g(translation-in)o(v)m(arian)o(t.\)) 133 212 y(2.)26 b(In)18 b(part)g(\(b\),)g(the)f(in)o(teraction)g(\010)831 194 y Fy(0)843 212 y FQ(,)g(if)h(it)f(exists,)g(ough)o(t)h(to)g(b)q(e)g(ph)o (ysically)e(equiv)m(alen)o(t)g(in)60 272 y(the)i(DLR)h(sense)f(to)g(a)h FP(tr)n(anslation-invariant)24 b FQ(in)o(teraction.)i(Unfortunately)l(,)18 b(w)o(e)f(are)i(not)f(able)60 332 y(to)g(pro)o(v)o(e)f(this.)26 b(F)l(rom)16 b(the)i(uniqueness)f(w)o(e)g(kno)o(w)h(that)g(\010)1179 314 y Fy(0)1209 332 y FQ(is)f(ph)o(ysically)f(equiv)m(alen)o(t)g(to)i(all)g (of)60 392 y(its)j(translates;)i(but)e(it)f(seems)f(to)i(b)q(e)g(an)g(op)q (en)h(question)e(whether)h(this)g(guaran)o(tees)g(that)g(\010)1878 374 y Fy(0)60 452 y FQ(is)f(ph)o(ysically)f(equiv)m(alen)o(t)g(in)i(the)f (DLR)h(sense)g(to)g(a)g(translation-in)o(v)m(arian)o(t)g(in)o(teraction.)33 b(An)60 513 y(a\016rmativ)o(e)16 b(answ)o(er)i(w)o(ould)h(also)g(allo)o(w)f (Kozlo)o(v's)f([222)q(])h(Gibbs)g(Represen)o(tation)g(Theorem)f(to)60 573 y(b)q(e)23 b(giv)o(en)f(a)h(satisfactory)g(translation-in)o(v)m(arian)o (t)g(v)o(ersion)f(\(see)g(the)h(Remark)e(at)i(the)f(end)h(of)60 633 y(Section)16 b(2.4.9\).)60 827 y FB(3.3)70 b(Second)16 b(F)-6 b(undamen)n(tal)15 b(Theorem:)24 b(Con)n(tin)n(uit)n(y)16 b(Prop)r(erties)g(of)217 902 y(the)22 b(R)-6 b(T)22 b(Map)60 994 y FQ(A)d(second)g(asp)q(ect)g(of)h(the)e(scenario)h(prop)q(osed)i(b)o(y)d (Dec)o(k)o(er,)g(Hasenfratz)h(and)g(Hasenfratz)g([72])60 1054 y(is)g(that)h(the)f(R)l(T)g(map)g(ma)o(y)f(b)q(e)h FP(disc)n(ontinuous)24 b FQ(at)c(an)g(original)f(Hamiltonian)f FF(H)1632 1061 y FH(0)1671 1054 y FQ(lying)h(on)h(a)60 1114 y(\014rst-order)j(phase-transition)g (surface:)32 b(namely)l(,)21 b(for)h(original)g(Hamiltonians)f FF(H)26 b FQ(arbitrarily)60 1174 y(close)21 b(to)h FF(H)287 1181 y FH(0)328 1174 y FQ(on)g(opp)q(osite)g(sides)f(of)h(the)f (phase-transition)h(surface,)g(it)f(is)h(claimed)c(that)k(the)60 1235 y(corresp)q(onding)17 b(renormalized)d(Hamiltonians)h FF(H)1007 1217 y Fy(0)1035 1235 y FQ(ma)o(y)g(b)q(e)h(a)h(\014nite)e (distance)h(apart.)133 1295 y(Here)d(w)o(e)h(dispro)o(v)o(e)f(this)h (scenario)g(to)q(o.)22 b(W)l(e)14 b(sho)o(w)h(that)f FP(the)j(R)l(T)e(map)g (is)g(always)h(c)n(ontinuous)60 1355 y FQ(\(in)e(a)h(suitable)g(norm\))e FP(on)k(the)f(set)h(of)e(Hamiltonians)i(wher)n(e)f(it)h(is)e(wel)r(l-de\014)q (ne)o(d)5 b FQ(,)17 b(that)e(is,)f(on)h(the)60 1415 y(set)h(of)h (Hamiltonians)d(for)j(whic)o(h)e(the)h(image)f(measures)h(are)g(Gibbsian.)133 1475 y(The)i(k)o(ey)e(idea)h(underlying)g(our)h(pro)q(of)h(is)e(the)h(fact)f (that,)h(if)f FF(\026)h FQ(is)g(a)g(Gibbs)f(measure)g(for)h(an)60 1536 y(in)o(teraction)13 b(\010)h FE(2)g(B)434 1518 y FH(1)453 1536 y FQ(,)g(then)f(the)h(DLR)g(equations)g(allo)o(w)f(the)h(reconstruction) f(of)i(the)e(in)o(teraction)60 1596 y(\010)j(\(mo)q(dulo)g(ph)o(ysical)f (equiv)m(alence\))g(from)g(the)h(measure)f FF(\026)p FQ(:)508 1730 y(log)584 1696 y FF(d\026)638 1703 y FH(\003)p 584 1718 82 2 v 584 1764 a FF(d\026)638 1747 y FH(0)638 1776 y(\003)698 1730 y FQ(=)28 b FE(\000)815 1688 y Fx(X)811 1780 y FD(x)p Fy(2)p FH(\003)887 1730 y FF(T)916 1737 y FD(x)938 1730 y FF(f)962 1737 y FH(\010)1009 1730 y FQ(+)19 b(const\(\010\))h(+)f FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))315 b(\(3)p FF(:)p FQ(31\))60 1877 y(\(see)12 b(Section)g(2.4.8\).)20 b(Therefore,)12 b(if)g FF(\026)775 1884 y FH(1)807 1877 y FQ(and)h FF(\026)927 1884 y FH(2)960 1877 y FQ(are)f(Gibbs)h(measures)e(for)i(in)o(teractions)e(\010) 1746 1884 y FH(1)1766 1877 y FF(;)d FQ(\010)1823 1884 y FH(2)1857 1877 y FE(2)60 1937 y(B)95 1919 y FH(1)114 1937 y FQ(,)16 b(w)o(e)g(ha)o(v)o (e)243 2069 y(log)319 2035 y FF(d\026)373 2042 y FH(1\003)p 319 2057 99 2 v 319 2103 a FF(d\026)373 2110 y FH(2\003)450 2069 y FQ(=)28 b FE(\000)567 2027 y Fx(X)563 2119 y FD(x)p Fy(2)p FH(\003)639 2069 y FF(T)668 2076 y FD(x)690 2069 y FF(f)714 2076 y FH(\010)739 2081 y Fr(1)757 2076 y Fy(\000)p FH(\010)809 2081 y Fr(2)848 2069 y FQ(+)20 b(const\(\010)1071 2076 y FH(1)1091 2069 y FQ(\))f FE(\000)g FQ(const)q(\(\010)1353 2076 y FH(2)1373 2069 y FQ(\))g(+)g FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))174 b(\(3)p FF(:)p FQ(32\))60 2213 y(and)17 b(in)f(particular)347 2295 y Fx(\015)347 2320 y(\015)347 2345 y(\015)p FQ(log)446 2311 y FF(d\026)500 2318 y FH(1\003)p 446 2333 V 446 2379 a FF(d\026)500 2386 y FH(2\003)550 2295 y Fx(\015)550 2320 y(\015)550 2345 y(\015)573 2372 y FD(B)r FH(\(\012\))p FD(=const)784 2345 y FQ(=)28 b FE(j)p FQ(\003)p FE(j)8 b(k)p FQ(\010)980 2352 y FH(1)1011 2345 y FE(\000)i FQ(\010)1095 2352 y FH(2)1115 2345 y FE(k)1140 2353 y Fy(B)1164 2344 y Fr(0)1182 2353 y FD(=)p FH(\()p Fy(J)5 b FH(+)p Fk(Const)p FH(\))1396 2345 y FQ(+)19 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))14 b FF(:)161 b FQ(\(3)p FF(:)p FQ(33\))60 2479 y(No)o(w)18 b(the)g(probabilit)o(y)f (densities)h(of)g(renormalized)e(measures)i(are)g(\(particular\))g(w)o(eigh)o (ted)f(a)o(v-)60 2539 y(erages)i(of)h(the)e(original)h(densities,)f(so)i(the) f(suprem)o(um)d(of)j(the)g(renormalized)d(densit)o(y)i(cannot)60 2600 y(exceed)13 b(that)i(of)f(the)g(original)g(densit)o(y)l(.)20 b(That)15 b(is,)f FE(k)8 b FQ(log)q(\()p FF(d\026)1160 2607 y FH(1)1180 2600 y FF(=d\026)1258 2607 y FH(2)1279 2600 y FQ(\))p FE(k)1323 2607 y FD(B)r FH(\(\012\))p FD(=const)1521 2600 y FQ(can)15 b(only)f(decrease)60 2660 y(under)i(the)g(R)l(T:)951 2784 y(88)p eop %%Page: 89 89 bop 60 91 a FM(Lemma)16 b(3.5)24 b FP(L)n(et)19 b FQ(\(\012)p FF(;)8 b FQ(\006\))21 b FP(and)f FQ(\(\012)743 73 y Fy(0)755 91 y FF(;)8 b FQ(\006)812 73 y Fy(0)824 91 y FQ(\))20 b FP(b)n(e)g(me)n(asur) n(able)g(sp)n(ac)n(es,)g(and)h(let)g FF(T)26 b FP(b)n(e)21 b(a)f(pr)n(ob)n(ability)60 152 y(kernel)f(fr)n(om)e FQ(\(\012)p FF(;)8 b FQ(\006\))18 b FP(to)g FQ(\(\012)582 133 y Fy(0)594 152 y FF(;)8 b FQ(\006)651 133 y Fy(0)662 152 y FQ(\))p FP(.)24 b(L)n(et)17 b FF(\026)h FP(and)g FF(\027)j FP(b)n(e)d(pr)n(ob)n(ability)g(me) n(asur)n(es)e(on)j FQ(\012)p FP(,)f(with)g FF(\026)d FE(\034)f FF(\027)s FP(.)60 212 y(Then)k FF(\026T)j FE(\034)13 b FF(\027)s(T)24 b FP(and)18 b(in)g(fact)577 288 y Fx(\015)577 312 y(\015)577 337 y(\015)p FQ(log)676 304 y FF(d)p FQ(\()p FF(\026T)7 b FQ(\))p 676 326 128 2 v 677 371 a FF(d)p FQ(\()p FF(\027)s(T)g FQ(\))809 288 y Fx(\015)809 312 y(\015)809 337 y(\015)832 364 y FD(L)856 355 y Ft(1)889 364 y FH(\()p FD(\027)r(T)e FH(\))1005 337 y FE(\024)1085 288 y Fx(\015)1085 312 y(\015)1085 337 y(\015)p FQ(log)1185 304 y FF(d\026)p 1185 326 55 2 v 1186 371 a(d\027)1244 288 y Fx(\015)1244 312 y(\015)1244 337 y(\015)1267 364 y FD(L)1291 355 y Ft(1)1324 364 y FH(\()p FD(\027)r FH(\))1765 337 y FQ(\(3.34\))477 434 y Fx(\015)477 459 y(\015)477 483 y(\015)p FQ(log)576 450 y FF(d)p FQ(\()p FF(\026T)i FQ(\))p 576 472 128 2 v 577 518 a FF(d)p FQ(\()p FF(\027)s(T)g FQ(\))709 434 y Fx(\015)709 459 y(\015)709 483 y(\015)732 510 y FD(L)756 501 y Ft(1)789 510 y FH(\()p FD(\027)r(T)e FH(\))p FD(=const)1005 483 y FE(\024)1085 434 y Fx(\015)1085 459 y(\015)1085 483 y(\015)p FQ(log)1185 450 y FF(d\026)p 1185 472 55 2 v 1186 518 a(d\027)1244 434 y Fx(\015)1244 459 y(\015)1244 483 y(\015)1267 510 y FD(L)1291 501 y Ft(1)1324 510 y FH(\()p FD(\027)r FH(\))p FD(=const)1765 483 y FQ(\(3.35\))60 660 y Fd(Pr)o(oof.)48 b FQ(Supp)q(ose)17 b(that)g(the)f(Radon-Nik)o(o)q(d)q(\022)-25 b(ym)15 b(deriv)m(ativ)o(e)f(\(=) i(densit)o(y\))g FF(d\026=d\027)k FQ(satis\014es)590 785 y(0)j FE(\024)f FF(a)f FE(\024)811 752 y FF(d\026)p 811 774 V 812 820 a(d\027)893 785 y FE(\024)h FF(b)g FE(\024)g FQ(+)p FE(1)97 b FF(\027)s FQ(-a.e.)405 b(\(3)p FF(:)p FQ(36\))60 902 y(Then)24 b FF(a\027)30 b FE(\024)c FF(\026)h FE(\024)g FF(b\027)g FQ(\(in)c(the)h (sense)g(of)g(the)f(usual)i(ordering)f(on)g(p)q(ositiv)o(e)f(measures\),)h (so)60 962 y(ob)o(viously)16 b FF(a)p FQ(\()p FF(\027)s(T)7 b FQ(\))13 b FE(\024)g FF(\026T)21 b FE(\024)13 b FF(b)p FQ(\()p FF(\027)s(T)7 b FQ(\).)21 b(It)16 b(follo)o(ws)g(that)656 1090 y FF(a)22 b FE(\024)770 1057 y FF(d)p FQ(\()p FF(\026T)7 b FQ(\))p 770 1079 128 2 v 771 1125 a FF(d)p FQ(\()p FF(\027)s(T)g FQ(\))925 1090 y FE(\024)22 b FF(b)97 b FQ(\()p FF(\027)s(T)7 b FQ(\)-a.e.)470 b(\(3)p FF(:)p FQ(37\))60 1216 y(Since)628 1279 y Fx(\015)628 1304 y(\015)628 1329 y(\015)p FQ(log)727 1295 y FF(d\026)p 727 1317 55 2 v 728 1363 a(d\027)787 1279 y Fx(\015)787 1304 y(\015)787 1329 y(\015)810 1356 y FD(L)834 1347 y Ft(1)866 1356 y FH(\()p FD(\027)r FH(\))957 1329 y FQ(=)41 b(max)o(\(log)9 b FF(b;)f FE(\000)g FQ(log)h FF(a)p FQ(\))342 b(\(3.38\))527 1411 y Fx(\015)527 1436 y(\015)527 1461 y(\015)p FQ(log)627 1427 y FF(d\026)p 627 1449 V 628 1495 a(d\027)686 1411 y Fx(\015)686 1436 y(\015)686 1461 y(\015)709 1488 y FD(L)733 1479 y Ft(1)766 1488 y FH(\()p FD(\027)r FH(\))p FD(=const)957 1461 y FQ(=)1041 1441 y FH(1)p 1041 1449 18 2 v 1041 1478 a(2)1064 1461 y FQ(\(log)9 b FF(b)i FE(\000)g FQ(log)e FF(a)p FQ(\))413 b(\(3.39\))60 1579 y([where)15 b FF(a)f FQ(and)i FF(b)f FQ(are)h(the)f(sharp) q(est)h(v)m(alues)g(making)e(\(3.36\))i(true],)e(with)h(an)h(analogous)h (form)o(ula)60 1639 y(for)g FF(d)p FQ(\()p FF(\026T)7 b FQ(\))p FF(=d)p FQ(\()p FF(\027)s(T)g FQ(\),)16 b(the)g(lemm)o(a)e(is)i(pro)o(v)o (en.)p 1028 1643 25 34 v 60 1787 a FM(Theorem)h(3.6)h(\(Second)g(fundamen)n (tal)g(theorem\))k FP(L)n(et)12 b FF(T)19 b FP(b)n(e)13 b(an)f(R)l(T)h(map)f (satisfying)g(pr)n(op-)60 1847 y(erties)k(\(T1\){\(T3\),)f(and)h(let)h FQ(\010)642 1854 y FH(1)662 1847 y FF(;)8 b FQ(\010)719 1854 y FH(2)753 1847 y FE(2)14 b FQ(dom)7 b FE(R)p FP(.)22 b(Then,)17 b(for)e(al)r(l)i FQ(\010)1299 1829 y Fy(0)1299 1860 y FH(1)1333 1847 y FE(2)d(R)p FQ(\(\010)1476 1854 y FH(1)1496 1847 y FQ(\))i FP(and)g FQ(\010)1659 1829 y Fy(0)1659 1860 y FH(2)1693 1847 y FE(2)e(R)p FQ(\(\010)1836 1854 y FH(2)1856 1847 y FQ(\))p FP(,)435 1948 y FE(k)p FQ(\010)495 1928 y Fy(0)495 1961 y FH(1)526 1948 y FE(\000)d FQ(\010)611 1928 y Fy(0)611 1961 y FH(2)631 1948 y FE(k)656 1957 y Fy(B)680 1947 y Fr(0)697 1957 y FD(=)p FH(\()p Fy(J)5 b FH(+)p Fk(Const)p FH(\))919 1948 y FE(\024)28 b FF(K)t FE(k)p FQ(\010)1091 1955 y FH(1)1122 1948 y FE(\000)11 b FQ(\010)1207 1955 y FH(2)1227 1948 y FE(k)1252 1957 y Fy(B)1276 1947 y Fr(0)1293 1957 y FD(=)p FH(\()p Fy(J)5 b FH(+)p Fk(Const)p FH(\))1501 1948 y FF(:)250 b FQ(\(3)p FF(:)p FQ(40\))60 2049 y FP(That)23 b(is,)h(on)f(its)g(domain)g(the)g(map)f FE(R)h FP(is)g(Lipschitz)g(c)n(ontinuous)g(\(with)h(Lipschitz)e(c)n(onstant)60 2109 y FE(\024)14 b FF(K)t FP(\))j(in)h(the)g FE(B)371 2091 y FH(0)390 2109 y FF(=)p FQ(\()p FE(J)i FQ(+)11 b FP(Const)p FQ(\))18 b FP(norm.)60 2258 y Fd(Pr)o(oof.)48 b FQ(Let)16 b(\(\003)421 2265 y FD(n)444 2258 y FQ(\))f FE(\032)f Fq(Z)561 2237 y FD(d)598 2258 y FQ(and)j(\(\003)746 2240 y Fy(0)746 2270 y FD(n)769 2258 y FQ(\))e FE(\032)f Fq(Z)886 2237 y FD(d)904 2225 y Ft(0)934 2258 y FQ(b)q(e)j(v)m(an)g(Ho)o(v)o(e)e(sequences)g(ha)o(ving)i(the)f(prop)q (erties)60 2318 y(\(T3\))k(assumed)f(in)g(Section)g(3.1.)32 b(Let)20 b FF(\026)838 2325 y FH(1)877 2318 y FE(2)g(G)960 2325 y FD(inv)1014 2318 y FQ(\(\005)1070 2300 y FH(\010)1095 2305 y Fr(1)1114 2318 y FQ(\))g(and)g FF(\026)1280 2325 y FH(2)1319 2318 y FE(2)g(G)1402 2325 y FD(inv)1456 2318 y FQ(\(\005)1512 2300 y FH(\010)1537 2305 y Fr(2)1556 2318 y FQ(\).)31 b(By)19 b(the)g(First)60 2378 y(F)l(undamen)o(tal)c(Theorem)g(\(Theorem)g(3.4\))i(w)o (e)e(ha)o(v)o(e)h FF(\026)1097 2385 y FH(1)1117 2378 y FF(T)k FE(2)15 b(G)1244 2385 y FD(inv)1297 2378 y FQ(\(\005)1353 2360 y FH(\010)1378 2348 y Ft(0)1378 2371 y Fr(1)1398 2378 y FQ(\))h(and)h FF(\026)1557 2385 y FH(2)1577 2378 y FF(T)j FE(2)15 b(G)1704 2385 y FD(inv)1757 2378 y FQ(\(\005)1813 2360 y FH(\010)1838 2348 y Ft(0)1838 2371 y Fr(2)1857 2378 y FQ(\).)60 2438 y(No)o(w)f(the)g (image)e(spins)i(in)g(\003)598 2420 y Fy(0)598 2451 y FD(n)636 2438 y FQ(dep)q(end)g(only)f(on)i(the)f(original)g(spins)g(in)f(\003)1437 2445 y FD(n)1461 2438 y FQ(:)20 b(that)14 b(is,)g(\()p FF(\026)1707 2445 y FH(1)1727 2438 y FF(T)7 b FQ(\))p Fm(\026)o FE(F)1847 2420 y Fy(0)1842 2451 y FH(\003)1866 2441 y Ft(0)1866 2459 y Fs(n)60 2499 y FQ(is)14 b(the)g(image)e(under)j FF(T)20 b FQ(of)14 b FF(\026)595 2506 y FH(1)615 2499 y Fm(\026)p FE(F)676 2506 y FH(\003)700 2510 y Fs(n)724 2499 y FQ(,)g(and)h(lik)o(ewise)d(for)i FF(\026)1123 2506 y FH(2)1143 2499 y FQ(.)21 b(Therefore,)13 b(b)o(y)h(Lemma)e(3.5)i(w)o(e)g(ha)o(v)o(e)420 2577 y Fx(\015)420 2602 y(\015)420 2626 y(\015)p FQ(log)519 2592 y FF(d)p FQ(\()p FF(\026)592 2599 y FH(1)612 2592 y FF(T)7 b FQ(\))667 2599 y FH(\003)691 2590 y Ft(0)691 2608 y Fs(n)p 519 2615 196 2 v 519 2661 a FF(d)p FQ(\()p FF(\026)592 2668 y FH(2)612 2661 y FF(T)g FQ(\))667 2668 y FH(\003)691 2659 y Ft(0)691 2676 y Fs(n)720 2577 y Fx(\015)720 2602 y(\015)720 2626 y(\015)743 2653 y FD(B)r FH(\(\012)811 2644 y Ft(0)821 2653 y FH(\))p FD(=const)965 2626 y FE(\024)1032 2577 y Fx(\015)1032 2602 y(\015)1032 2626 y(\015)p FQ(log)1131 2593 y FF(d)p FQ(\()p FF(\026)1204 2600 y FH(1)1224 2593 y FQ(\))1243 2600 y FH(\003)1267 2604 y Fs(n)p 1131 2615 161 2 v 1131 2661 a FF(d)p FQ(\()p FF(\026)1204 2668 y FH(2)1224 2661 y FQ(\))1243 2668 y FH(\003)1267 2672 y Fs(n)1296 2577 y Fx(\015)1296 2602 y(\015)1296 2626 y(\015)1319 2653 y FD(B)r FH(\(\012\))p FD(=const)1517 2626 y FF(:)234 b FQ(\(3)p FF(:)p FQ(41\))951 2784 y(89)p eop %%Page: 90 90 bop 60 91 a FQ(\(Since)12 b(the)h(measures)g FF(\026)520 98 y FH(2)553 91 y FQ(and)h FF(\026)674 98 y FH(2)694 91 y FF(T)20 b FQ(are)13 b(b)q(oth)h(Gibbsian,)g(they)f(giv)o(e)f(nonzero)i(measure)e(to)i (ev)o(ery)60 152 y(op)q(en)f(set;)f(and)h(moreo)o(v)o(er)d(the)h(in)o (teractions)g(\010)931 159 y FH(1)951 152 y FQ(,)i(\010)1013 159 y FH(2)1033 152 y FQ(,)f(\010)1094 133 y Fy(0)1094 164 y FH(1)1126 152 y FQ(and)g(\010)1251 133 y Fy(0)1251 164 y FH(2)1283 152 y FQ(are)g(all)g(con)o(tin)o(uous.)19 b(Therefore)60 212 y(w)o(e)d(can)g(replace)g(the)g(essen)o(tial)f(sup)h(norms)g(b)o(y)g(the) g(true)g(sup)h(norms.\))j(Then)325 336 y FE(k)p FQ(\010)385 316 y Fy(0)385 348 y FH(1)416 336 y FE(\000)11 b FQ(\010)501 316 y Fy(0)501 348 y FH(2)521 336 y FE(k)546 344 y Fy(B)570 335 y Fr(0)587 344 y FD(=)p FH(\()p Fy(J)5 b FH(+)p Fk(Const)p FH(\))824 336 y FQ(=)54 b(lim)904 361 y FD(n)p Fy(!1)1039 302 y FQ(1)p 1009 325 86 2 v 1009 370 a FE(j)p FQ(\003)1057 356 y Fy(0)1057 383 y FD(n)1080 370 y FE(j)1107 286 y Fx(\015)1107 311 y(\015)1107 336 y(\015)p FQ(log)1206 302 y FF(d)p FQ(\()p FF(\026)1279 309 y FH(1)1300 302 y FF(T)7 b FQ(\))1355 309 y FH(\003)1379 300 y Ft(0)1379 318 y Fs(n)p 1206 325 196 2 v 1206 370 a FF(d)p FQ(\()p FF(\026)1279 377 y FH(2)1300 370 y FF(T)g FQ(\))1355 377 y FH(\003)1379 368 y Ft(0)1379 386 y Fs(n)1407 286 y Fx(\015)1407 311 y(\015)1407 336 y(\015)1430 363 y FD(B)r FH(\(\012)1498 354 y Ft(0)1509 363 y FH(\))p FD(=const)823 474 y FE(\024)54 b FQ(lim)904 499 y FD(n)p Fy(!1)1029 440 y FF(K)p 1009 462 86 2 v 1009 508 a FE(j)p FQ(\003)1057 515 y FD(n)1080 508 y FE(j)1107 424 y Fx(\015)1107 449 y(\015)1107 474 y(\015)p FQ(log)1206 440 y FF(d)p FQ(\()p FF(\026)1279 447 y FH(1)1300 440 y FQ(\))1319 447 y FH(\003)1343 451 y Fs(n)p 1206 462 161 2 v 1206 508 a FF(d)p FQ(\()p FF(\026)1279 515 y FH(2)1300 508 y FQ(\))1319 515 y FH(\003)1343 519 y Fs(n)1372 424 y Fx(\015)1372 449 y(\015)1372 474 y(\015)1395 501 y FD(B)r FH(\(\012\))p FD(=const)824 574 y FQ(=)42 b FF(K)t FE(k)p FQ(\010)1009 581 y FH(1)1040 574 y FE(\000)10 b FQ(\010)1124 581 y FH(2)1144 574 y FE(k)1169 583 y Fy(B)1193 573 y Fr(0)1210 583 y FD(=)p FH(\()p Fy(J)c FH(+)p Fk(Const)p FH(\))1419 574 y FF(;)332 b FQ(\(3.42\))60 671 y(where)16 b(w)o(e)g(ha)o(v)o(e)f(t)o(wice)g(used)i (Prop)q(osition)g(2.46\(b\).)p 1190 675 25 34 v 133 773 a(It)f(is)f(curious)h (that)g(although)h(all)e(the)h(in)o(teractions)f(\010)1160 780 y FH(1)1180 773 y FQ(,)g(\010)1244 780 y FH(2)1264 773 y FQ(,)g(\010)1328 755 y Fy(0)1328 786 y FH(1)1364 773 y FQ(and)h(\010)1493 755 y Fy(0)1493 786 y FH(2)1529 773 y FQ(are)g(here)f(required)60 833 y(to)g(b)q(elong)h(to)f FE(B)366 815 y FH(1)385 833 y FQ(,)f(the)h(Lipsc) o(hitz)f(estimate)f(\(3.40\))i(is)g(stated)g(in)g FE(B)1320 815 y FH(0)1354 833 y FQ(norm.)k(This)c(is)g(b)q(ecause)g FE(B)1871 815 y FH(0)60 894 y FQ(\(or)h(more)e(precisely)g(its)i(quotien)o(t)f(b)o(y)g FE(J)25 b FQ(or)16 b FE(J)j FQ(+)10 b FF(C)t(onst)p FQ(\))15 b(is)g(the)h(natural)g(norm)f(for)h(measuring)60 954 y FP(bulk)k FQ(energy)13 b(con)o(tributions,)g(as)h(discussed)f(in)g(Section)g(2.4.8.)21 b(The)13 b(restriction)g(to)g FE(B)1665 936 y FH(1)1698 954 y FQ(is)g(needed)60 1014 y(solely)k(to)h(ensure)f(that)h(the)f FP(b)n(oundary)22 b FQ(energy)17 b(con)o(tributions)g(are)h FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\),)f(so)h(as)g(to)g(a)o(v)o(oid)f (the)60 1074 y(pathologies)j(discussed)f(in)g(Section)f(2.6.7.)30 b(In)19 b(an)o(y)g(case,)h(w)o(e)e(w)o(ould)i(lik)o(e)d(to)i(emphasize)f (that)60 1134 y(all)j(the)g FE(B)257 1116 y FD(\013)302 1134 y FQ(norms)f(are)i(equiv)m(alen)o(t)d(\(up)j(to)f(a)h(b)q(ounded)g(factor\))g (for)f(in)o(teractions)g(in)o(v)o(olving)60 1195 y(b)q(oundedly)g(man)o(y)e (spins)h(at)h(a)g(time)d(\(e.g.)i(t)o(w)o(o-spin)g(in)o(teractions\),)g(ev)o (en)g(when)g(they)g(are)h(of)60 1255 y(arbitrarily)16 b(long)i(range.)25 b(The)17 b(di\013erence)f(b)q(et)o(w)o(een)g(the)h FE(B)1186 1237 y FD(\013)1227 1255 y FQ(norms)g(concerns)g(ho)o(w)g(they)g(treat)60 1315 y(in)o(teractions)e(that)i(are)f FP(very)i(str)n(ongly)f(multi-b)n(o)n (dy)t FQ(.)133 1417 y(Theorem)12 b(3.6)h(constrains)h(v)o(ery)e(strongly)h (the)g(w)o(a)o(ys)g(in)g(whic)o(h)f(the)h(R)l(T)h(map)e(can)h(blo)o(w)g(up)g (as)60 1478 y(\010)j(approac)o(hes)g(the)f(b)q(oundary)i(of)e(its)g(domain.) 21 b(Indeed,)14 b(supp)q(ose)j(that)e(\(\010)1489 1485 y FD(n)1513 1478 y FQ(\))1532 1485 y FD(n)p Fy(\025)p FH(1)1616 1478 y FQ(is)g(a)h(sequence)60 1538 y(in)21 b(dom)8 b FE(R)23 b(\032)g(B)385 1520 y FH(1)426 1538 y FQ(that)f(con)o(v)o(erges)f FP(in)h FE(B)860 1520 y FH(0)902 1538 y FP(norm)j FQ([or)c(more)g(generally)l(,)g(in) h FE(B)1567 1520 y FH(0)1586 1538 y FF(=)p FQ(\()p FE(J)i FQ(+)14 b FF(C)t(onst)p FQ(\))60 1598 y(seminorm])i(to)j(\010)396 1605 y Fy(1)452 1598 y FE(2)g(B)539 1580 y FH(0)558 1598 y FQ(.)29 b(\(W)l(e)19 b(need)f(not)i(require)d(con)o(v)o(ergence)h(in)g FE(B)1446 1580 y FH(1)1484 1598 y FQ(norm,)h(nor)g(need)f(w)o(e)60 1658 y(require)12 b(that)j(\010)360 1665 y Fy(1)411 1658 y FQ(b)q(elong)f(to)g FE(B)656 1640 y FH(1)675 1658 y FQ(.\))21 b(Next)12 b(let)h(\(\010)967 1640 y Fy(0)967 1670 y FD(n)991 1658 y FQ(\))1010 1665 y FD(n)p Fy(\025)p FH(1)1092 1658 y FQ(b)q(e)h(an)o(y)g(c)o(hoice)e(of)i(renormalized)e(in)o(terac-)60 1718 y(tions)17 b([i.e.)e(\010)308 1700 y Fy(0)308 1731 y FD(n)346 1718 y FE(2)g(R)p FQ(\(\010)490 1725 y FD(n)514 1718 y FQ(\))g FE(\032)f(B)636 1700 y FH(1)655 1718 y FQ(];)j(here)f(the)g(c)o(hoice)g (concerns)g(the)h(selection)f(of)h(represen)o(tativ)o(es)60 1778 y(mo)q(dulo)g(ph)o(ysical)f(equiv)m(alence.)22 b(Then)17 b(\(3.40\))h(guaran)o(tees)g(that)f(\(\010)1377 1760 y Fy(0)1377 1791 y FD(n)1401 1778 y FQ(\))g(is)g(a)g(Cauc)o(h)o(y)g(sequence)60 1839 y(in)i(the)h FE(B)243 1821 y FH(0)262 1839 y FF(=)p FQ(\()p FE(J)j FQ(+)13 b FF(C)t(onst)p FQ(\))19 b(seminorm,)f(hence)h(con)o(v)o (erges)g(in)g FE(B)1280 1821 y FH(0)1299 1839 y FF(=)p FQ(\()p FE(J)k FQ(+)13 b FF(C)t(onst)p FQ(\))20 b(seminorm)d(to)60 1899 y(some)c(\010)215 1881 y Fy(0)215 1911 y(1)266 1899 y FE(2)h(B)348 1881 y FH(0)367 1899 y FQ(;)g(moreo)o(v)o(er,)d(this)j(limit)d (is)i(unique)g(mo)q(dulo)g(ph)o(ysical)g(equiv)m(alence)f(\(i.e.)f(mo)q(dulo) 60 1959 y FE(J)23 b FQ(+)14 b FF(C)t(onst)p FQ(\).)33 b(No)o(w,)21 b(if)f(\010)581 1966 y Fy(1)639 1959 y FQ(and)i(\010)774 1941 y Fy(0)774 1971 y(1)832 1959 y FQ(\(or)f(an)o(y)f(in)o(teractions)g(in)g (their)g(ph)o(ysical-equiv)m(alence)60 2019 y(classes\))f(are)g FP(b)n(oth)j FQ(in)d FE(B)524 2001 y FH(1)543 2019 y FQ(,)g(then)g(it)f (follo)o(ws)h(from)f(Theorem)g(3.2)h(that)g(\(\010)1474 2026 y Fy(1)1512 2019 y FF(;)8 b FQ(\010)1569 2001 y Fy(0)1569 2032 y(1)1606 2019 y FQ(\))19 b FE(2)f(R)p FQ(,)i(hence)60 2079 y(\010)95 2086 y Fy(1)151 2079 y FE(2)e FQ(dom)8 b FE(R)p FQ(.)29 b(Therefore,)19 b(if)f(\010)708 2086 y Fy(1)764 2079 y FE(2)g(B)850 2061 y FH(1)882 2079 y FE(n)13 b FQ(dom)7 b FE(R)p FQ(,)19 b(it)g(m)o(ust)e(b)q(e)i(that)g(\010)1482 2061 y Fy(0)1482 2092 y(1)1539 2079 y FQ(is)f(not)i(ph)o(ysically)60 2140 y(equiv)m(alen)o(t) 15 b(to)h(an)o(y)g(in)o(teraction)g(in)g FE(B)781 2122 y FH(1)800 2140 y FQ(.)133 2200 y(One)11 b(w)o(ould)h(lik)o(e)d(to)j(conclude)f(from)f (this)h(that)h(the)f FE(B)1119 2182 y FH(1)1150 2200 y FQ(\(semi\)norms)e FE(k)p FQ(\010)1485 2182 y Fy(0)1485 2212 y FD(n)1508 2200 y FE(k)1533 2208 y Fy(B)1557 2199 y Fr(1)1574 2208 y FD(=)p FH(\()p Fy(J)d FH(+)p FD(C)r(onst)p FH(\))1785 2200 y FQ(m)o(ust)60 2260 y(div)o(erge)13 b(as)h FF(n)g FE(!)g(1)p FQ(.)20 b(Unfortunately)l(,)14 b(w)o(e)f(are)h(not)h(quite)e(able)h(to)g(pro)o(v)o(e)f(this,)h(b)q(ecause)g (w)o(e)g(ha)o(v)o(e)60 2320 y(not)20 b(b)q(een)g(able)f(to)h(pro)o(v)o(e)f(a) h(v)o(ersion)f(of)h(Prop)q(osition)h(2.39\(a\))g(mo)q(dulo)e(ph)o(ysical)g (equiv)m(alence)60 2380 y(\(cf.)c(Prop)q(osition)j(2.43\).)k(The)16 b(b)q(est)h(w)o(e)e(ha)o(v)o(e)h(b)q(een)g(able)g(to)h(pro)o(v)o(e)e(is)h (the)g(follo)o(wing:)60 2479 y FM(Corollary)i(3.7)24 b FP(L)n(et)18 b FQ(\012)525 2486 y FH(0)564 2479 y FP(b)n(e)h(a)g(c)n(omp)n(act)g(metric)g (sp)n(ac)n(e,)g(and)g(assume)g(that)g FF(T)25 b FP(satis\014es)19 b(\(T1\){)60 2539 y(\(T3\))13 b(and)g(is)g(F)l(el)r(ler.)23 b(L)n(et)13 b FQ(\(\010)602 2546 y FD(n)626 2539 y FQ(\))645 2546 y FD(n)p Fy(\025)p FH(1)727 2539 y FP(b)n(e)g(a)g(se)n(quenc)n(e)i(in)f FQ(dom)7 b FE(R)14 b(\032)g(B)1314 2521 y FH(1)1346 2539 y FP(that)f(c)n(onver)n(ges)h(in)g FE(B)1745 2521 y FH(0)1764 2539 y FF(=)p FQ(\()p FE(J)d FQ(+)60 2600 y FF(C)t(onst)p FQ(\))23 b FP(seminorm)g(to)g FQ(\010)566 2607 y Fy(1)628 2600 y FE(2)i(B)721 2582 y FH(1)755 2600 y FE(n)16 b FQ(dom)7 b FE(R)p FP(.)40 b(F)l(or)23 b(e)n(ach)g FF(n)p FP(,)i(let)f FQ(\010)1383 2582 y Fy(0)1383 2612 y FD(n)1430 2600 y FP(b)n(e)g(any)f(inter)n(action)h(in)60 2660 y FE(R)p FQ(\(\010)156 2667 y FD(n)180 2660 y FQ(\))14 b FE(\032)f(B)300 2642 y FH(1)319 2660 y FP(.)23 b(Then:)951 2784 y FQ(90)p eop %%Page: 91 91 bop 93 91 a FP(\(a\))24 b(Either)17 b FQ(\(\010)385 73 y Fy(0)385 104 y FD(n)409 91 y FQ(\))428 98 y FD(n)p Fy(\025)p FH(1)514 91 y FP(fails)h(to)f(c)n(onver)n(ge)i(in)e FE(B)969 73 y FH(0)988 91 y FP(,)h(or)f(else)h FE(k)p FQ(\010)1238 73 y Fy(0)1238 104 y FD(n)1262 91 y FE(k)1287 100 y Fy(B)1311 90 y Fr(1)1344 91 y FE(!)c(1)p FP(.)60 189 y(If)j(the)h(single-spin)i(sp)n(ac)n(e)d FQ(\012)596 171 y Fy(0)596 202 y FH(0)633 189 y FP(is)g(\014nite,)i(then)f (we)h(also)e(have:)95 287 y(\(b\))25 b(F)l(or)17 b(any)g FF(h)408 300 y FE(\030)408 279 y(\035)472 287 y FQ(1)p FP(,)h FE(k)p FQ(\010)589 269 y Fy(0)589 300 y FD(n)612 287 y FE(k)637 295 y Fy(B)660 301 y Fs(h)680 295 y FD(=)p FH(\()p Fy(J)6 b FH(+)p FD(C)r(onst)p FH(\))894 287 y FE(!)14 b(1)p FP(.)60 444 y Fd(Pr)o(oof.)48 b FQ(\(a\))19 b(Supp)q(ose)g(that)g(\010)698 426 y Fy(0)698 456 y FD(n)740 444 y FE(!)f FQ(\010)843 426 y Fy(0)843 456 y(1)899 444 y FQ(in)h FE(B)994 426 y FH(0)1013 444 y FQ(,)f(but)h FE(k)p FQ(\010)1197 426 y Fy(0)1197 456 y FD(n)1221 444 y FE(k)1246 452 y Fy(B)1270 443 y Fr(1)1307 444 y FE(6!)f(1)p FQ(.)28 b(So)20 b(there)e(is)g(a)h(subse-)60 504 y(quence)d(of)h(\(\010)332 486 y Fy(0)332 516 y FD(n)356 504 y FQ(\))f(on)i(whic)o(h)e(the)g FE(B)719 486 y FH(1)755 504 y FQ(norm)g(is)h(b)q(ounded,)g(sa)o(y)g(b)o(y)f FF(M)5 b FQ(;)18 b(and)f(Prop)q(osition)h(2.39\(a\))60 564 y(then)d(implies)e(that)j(\010)475 546 y Fy(0)475 576 y(1)527 564 y FE(2)e(B)609 546 y FH(1)643 564 y FQ(\(with)i FE(k)p FQ(\010)833 546 y Fy(0)833 576 y(1)870 564 y FE(k)895 572 y Fy(B)919 563 y Fr(1)952 564 y FE(\024)e FF(M)5 b FQ(\).)21 b(But)15 b(b)o(y)g(Theorem)g(3.2)h(this)f(means)g(that)60 624 y(\(\010)114 631 y Fy(1)152 624 y FF(;)8 b FQ(\010)209 606 y Fy(0)209 637 y(1)246 624 y FQ(\))14 b FE(2)g(R)p FQ(,)i(con)o(trary)g(to)h (the)f(h)o(yp)q(othesis)g(that)h(\010)1118 631 y Fy(1)1175 624 y FF(=)-30 b FE(2)14 b FQ(dom)8 b FE(R)p FQ(.)133 684 y(\(b\))19 b(As)f(argued)h(ab)q(o)o(v)o(e,)f(the)h(equiv)m(alence)d(classes)j([\010)1160 666 y Fy(0)1160 697 y FD(n)1183 684 y FQ(])e FE(\021)g FQ(\010)1305 666 y Fy(0)1305 697 y FD(n)1341 684 y FQ(+)c FE(J)21 b FQ(+)13 b FF(C)t(onst)18 b FQ(con)o(v)o(erge)f(in)60 745 y FE(B)95 727 y FH(0)114 745 y FF(=)p FQ(\()p FE(J)22 b FQ(+)13 b FF(C)t(onst)p FQ(\))18 b(to)h(some)f(equiv)m(alence)f(class)i([\010)1046 727 y Fy(0)1046 757 y(1)1083 745 y FQ(].)28 b(It)18 b(follo)o(ws)h(that)g (one)g(can)g(c)o(ho)q(ose)g(new)60 805 y(represen)o(tativ)o(es)401 792 y(^)395 805 y(\010)430 787 y Fy(0)430 817 y FD(n)473 805 y FE(2)g FQ([\010)574 787 y Fy(0)574 817 y FD(n)598 805 y FQ(])f(and)734 792 y(^)728 805 y(\010)763 787 y Fy(0)763 817 y(1)820 805 y FE(2)h FQ([\010)921 787 y Fy(0)921 817 y(1)958 805 y FQ(])g(suc)o(h)g(that) 1218 792 y(^)1212 805 y(\010)1247 787 y Fy(0)1247 817 y FD(n)1290 805 y FE(!)1364 792 y FQ(^)1359 805 y(\010)1394 787 y Fy(0)1394 817 y(1)1451 805 y FQ(in)g FE(B)1546 787 y FH(0)1565 805 y FQ(.)30 b(No)o(w)19 b(supp)q(ose)60 865 y(that)f FE(k)197 852 y FQ(^)192 865 y(\010)227 847 y Fy(0)227 877 y FD(n)251 865 y FE(k)276 873 y Fy(B)299 879 y Fs(h)319 873 y FD(=)p FH(\()p Fy(J)5 b FH(+)p FD(C)r(onst)p FH(\))535 865 y FE(\021)16 b(k)p FQ(\010)650 847 y Fy(0)650 877 y FD(n)673 865 y FE(k)698 873 y Fy(B)721 879 y Fs(h)741 873 y FD(=)p FH(\()p Fy(J)6 b FH(+)p FD(C)r(onst)p FH(\))957 865 y FE(6!)16 b(1)p FQ(.)25 b(Then)18 b(there)f(is)g(a)h(subsequence)f(of)h(\()1817 852 y(^)1812 865 y(\010)1847 847 y Fy(0)1847 877 y FD(n)1871 865 y FQ(\))60 925 y(on)f(whic)o(h)f(the)h FE(B)386 932 y FD(h)408 925 y FF(=)p FQ(\()p FE(J)k FQ(+)11 b FF(C)t(onst)p FQ(\))17 b(seminorm)d(is)i(b)q (ounded,)i(sa)o(y)f(b)o(y)f FF(M)5 b FQ(;)17 b(and)g(Prop)q(osition)h(2.43)60 985 y(then)13 b(implies)e(that)439 973 y(^)434 985 y(\010)469 967 y Fy(0)469 998 y(1)520 985 y FE(2)j(B)600 992 y FD(h)627 985 y FQ(+)5 b FE(J)14 b FQ(+)5 b FF(C)t(onst)13 b FQ(\(with)g FE(k)1063 973 y FQ(^)1058 985 y(\010)1093 967 y Fy(0)1093 998 y(1)1131 985 y FE(k)1156 993 y Fy(B)1179 999 y Fs(h)1199 993 y FD(=)p FH(\()p Fy(J)6 b FH(+)p FD(C)r(onst)p FH(\))1413 985 y FE(\024)13 b FF(M)5 b FQ(\).)21 b(But)13 b(this)g(means)60 1066 y(that)18 b(there)e(exists)439 1040 y(^)433 1053 y(^)428 1066 y(\010)463 1052 y Fy(0)475 1073 y(1)528 1066 y FE(2)g(B)610 1073 y FD(h)647 1066 y FE(\032)g(B)737 1048 y FH(1)773 1066 y FQ(\(with)h FE(k)940 1040 y FQ(^)934 1053 y(^)929 1066 y(\010)964 1052 y Fy(0)976 1073 y(1)1013 1066 y FE(k)1038 1073 y Fy(B)1061 1079 y Fs(h)1099 1066 y FE(\024)e FF(M)5 b FQ(\))18 b(suc)o(h)f(that)1471 1040 y(^)1465 1053 y(^)1459 1066 y(\010)1494 1052 y Fy(0)1506 1073 y(1)1559 1066 y FE(2)f FQ([)1627 1053 y(^)1622 1066 y(\010)1657 1048 y Fy(0)1657 1078 y(1)1694 1066 y FQ(])f(=)h([\010)1826 1048 y Fy(0)1826 1078 y(1)1863 1066 y FQ(].)60 1144 y(And)g(b)o(y)g(Theorem)f (3.2)i(this)f(means)g(that)h(\(\010)925 1151 y Fy(1)962 1144 y FF(;)995 1118 y FQ(^)989 1131 y(^)984 1144 y(\010)1019 1129 y Fy(0)1031 1151 y(1)1068 1144 y FQ(\))d FE(2)h(R)p FQ(,)h(con)o(trary)g(to)h (the)f(h)o(yp)q(othesis)h(that)60 1204 y(\010)95 1211 y Fy(1)152 1204 y FF(=)-30 b FE(2)14 b FQ(dom)8 b FE(R)p FQ(.)p 489 1208 25 34 v 133 1311 a(Our)14 b(inabilit)o(y)e(to)j(pro)o(v)o(e)e(the)h(div)o (ergence)e(of)i(the)g FE(B)1096 1293 y FH(1)1129 1311 y FQ(seminorm)d(is)j (not)h(as)f(serious)g(as)h(it)f(ma)o(y)60 1372 y(seem:)24 b(as)19 b(will)f(b)q(e)h(discussed)f(in)g(Section)g(6.1.2,)h(one)g(probably)g(w)o(an) o(ts)g(an)o(yw)o(a)o(y)f(to)h(form)o(ulate)60 1432 y(R)o(G)g(theory)f(in)h(a) g(space)g FE(B)576 1439 y FD(h)617 1432 y FQ(of)g FP(short-r)n(ange)k FQ(in)o(teractions,)18 b(and)h(for)g(suc)o(h)g(a)g(space)g(our)h(result)60 1492 y(\(b\))c(is)g(su\016cien)o(t)f(\(when)i(\012)577 1474 y Fy(0)577 1504 y FH(0)613 1492 y FQ(is)f(\014nite\).)60 1658 y FG(4)83 b(Pro)n(v)-5 b(ably)39 b(P)n(athological)h(Renormalization)e(T)-7 b(rans-)184 1749 y(formations)60 1873 y FB(4.1)70 b(Gri\016ths-P)n (earce-Israel)21 b(P)n(athologies)h(I:)h(Israel's)g(Example)60 1966 y FM(4.1.1)55 b(In)n(tro)r(duction)60 2058 y FQ(Gri\016ths)18 b(and)i(P)o(earce)e([172,)g(173)r(,)g(171)q(])g(w)o(ere)g(the)h(\014rst)f(to) i(p)q(oin)o(t)e(out)h(the)g(p)q(ossible)g(existence)60 2118 y(of)j(what)h(they)e(called)g(\\p)q(eculiarities")g(of)h(the)g(R)l(T.)f (These)h(p)q(eculiarities)e(w)o(ere)h(exhibited)f(in)60 2178 y(mo)q(dels)13 b(in)g(whic)o(h)g(the)g(in)o(ternal)g(spins)h(undergo)g(a)g (phase)h(transition)e(for)h(some)f(\014xed)g(blo)q(c)o(k-spin)60 2238 y(con\014guration.)25 b(They)16 b(observ)o(ed)h(that)g(in)g(suc)o(h)g(a) g(situation)h(the)e(correlation)h(functions)g(of)g(the)60 2299 y(in)o(ternal-spin)i(system)g(could)g(b)q(ecome)g(discon)o(tin)o(uous)h (functions)g(of)g(the)g(blo)q(c)o(k)f(spins,)i(whic)o(h)60 2359 y(implies)f(that)j(eac)o(h)f(of)h(the)f(terms)f(of)i(the)g(\(formal\))e (expansion)i(yielding)e(the)h(renormalized)60 2419 y(Hamiltonian)d(\(1.3\))i (could)g(b)q(e)g(discon)o(tin)o(uous.)36 b(This)21 b(casts)g(doubts)h(on)g (the)e(con)o(v)o(ergence)g(of)60 2479 y(suc)o(h)f(an)h(expansion,)g(and)g (hence)f(on)h(either)e(the)h(existence)f(or)i(the)f(con)o(tin)o(uit)o(y)e (prop)q(erties)j(of)60 2539 y(the)c(renormalized)e(Hamiltonian.)133 2600 y(This)24 b(situation)f(w)o(as)h(further)f(clari\014ed)f(b)o(y)h(Israel) g([207)q(])f(in)h(the)g(particular)g(case)h(of)f(the)60 2660 y FF(b)h FQ(=)h(2)e(decimation)e(transformation.)40 b(He)22 b(argued)h(that)g(when)f(suc)o(h)h(p)q(eculiarities)e(exist,)i(a)951 2784 y(91)p eop %%Page: 92 92 bop 60 91 a FQ(v)o(ery)16 b(w)o(eak)h(lo)q(calit)o(y)f(condition)g(is)h (violated)g(b)o(y)f(the)h(renormalized)e(measure:)21 b(the)c(conditional)60 152 y(exp)q(ectation)i(for)h(a)f(single)g(site)g(is)g(a)h(discon)o(tin)o (uous)f(function)g(\(in)g(the)g(pro)q(duct)h(top)q(ology\))h(of)60 212 y(the)h(b)q(oundary)h(conditions.)39 b(That)23 b(is,)g(it)f(is)g(p)q (ossible)g(to)h(\014x)f(the)g(blo)q(c)o(k-spin)g(con\014guration)60 272 y(in)g(an)h(arbitrarily)f(large)g(v)o(olume)e(around)k(the)e(origin)h(in) f(suc)o(h)g(a)h(w)o(a)o(y)f(that)h(what)g(happ)q(ens)60 332 y(at)f(the)f(origin)g(dep)q(ends)h(strongly)g(on)g(the)f(blo)q(c)o(k)g(spins) h(whic)o(h)f(are)g FP(outside)26 b FQ(of)21 b(the)h(v)o(olume.)60 392 y(The)f(set)g(of)h(con\014gurations)g(for)f(whic)o(h)g(this)g(pathology)h (o)q(ccurs)g(is)e(improbable,)h(but)g(not)h(of)60 452 y(zero)15 b(measure.)k(In)c(our)h(terminology)l(,)d(the)h(renormalized)f(measure)h(is)h FP(non-quasilo)n(c)n(al)5 b FQ(:)22 b(that)16 b(is,)60 513 y(it)j(is)f(not)i(consisten)o(t)e(with)h(an)o(y)g(quasilo)q(cal)g(sp)q (eci\014cation.)29 b(In)19 b(particular,)g(the)f(renormalized)60 573 y(measure)d(is)h(not)h(the)f(Gibbs)g(measure)f(for)i(an)o(y)f(uniformly)e (con)o(v)o(ergen)o(t)h(in)o(teraction.)133 633 y(In)d(this)g(section)g(w)o(e) f(\014ll)h(in)f(the)h(tec)o(hnical)f(details)g(of)i(Israel's)e(argumen)o(t,)g (thereb)o(y)g(con)o(v)o(erting)60 693 y(it)16 b(in)o(to)f(a)i(rigorous)g(pro) q(of.)22 b(In)16 b(the)g(follo)o(wing)g(sections)g(w)o(e)f(shall)h (generalize)f(Israel's)g(argumen)o(t)60 753 y(to)e(other)f(mo)q(dels)g(and)h (other)f(renormalization)f(transformations.)20 b(In)13 b(all)f(cases,)h(the)f (underlying)60 814 y(ph)o(ysical)k(mec)o(hanism)e(causing)k(the)f (non-Gibbsianness)h(of)g(the)f(renormalized)d(measure)i(is)h(the)60 874 y(same:)i(the)14 b(in\015uence)g(from)f(the)h(blo)q(c)o(k)g(spins)g (outside)h(the)f(sp)q(eci\014ed)g(v)o(olume)e(is)i(transmitted)f(to)60 934 y(the)j(origin)g(via)g(the)g(in)o(ternal)f(spins)h(in)g(the)g(in)o (termediate)d(region,)j(b)o(y-passing)h(the)f(blo)q(c)o(k)g(spins)60 994 y(in)h(the)h(\014nite)f(en)o(vironmen)o(t)d(of)k(the)g(origin.)25 b(This)17 b(o)q(ccurs)h(b)q(ecause)g(the)f(in)o(ternal)g(spins)h(ha)o(v)o(e)f (a)60 1054 y(phase)h(transition,)g(and)g(the)f(blo)q(c)o(k-spin)h(b)q (oundary)h(conditions)e(can)h(pic)o(k)f(di\013eren)o(t)f(phases)j(of)60 1115 y(these)d(in)o(ternal)f(spins.)60 1333 y FM(4.1.2)55 b(Israel's)18 b(Example:)k(Decimation)16 b(in)i FF(d)d FQ(=)e(2)60 1425 y(Let)h(us)g (presen)o(t)f(no)o(w)h(Israel's)f(example)e(|)j(the)f(t)o(w)o(o-dimensional)f (Ising)i(mo)q(del)e(at)i(lo)o(w)f(temp)q(er-)60 1485 y(ature)k(and)h(zero)f (magnetic)f(\014eld,)h(using)g(the)g FF(b)f FQ(=)f(2)j(decimation)d (transformation)j(|)f(together)60 1545 y(with)22 b(the)h(pro)q(of)h(that)f FP(after)g(one)h(r)n(enormalization)f(step)j FQ(the)c(renormalized)f(measure) g(is)i(no)60 1606 y(longer)15 b(Gibbsian.)409 1588 y FH(47)467 1606 y FQ(The)g(strategy)g(of)g(the)g(pro)q(of)h(is)e(to)i(sho)o(w)f(that)g (the)g(renormalized)d(measure)60 1666 y(exhibits)g(grossly)h(non-lo)q(cal)h (correlations,)f(in)g(the)g(sense)g(that)g(the)g(conditional)g(probabilit)o (y)f(dis-)60 1726 y(tribution)i(of)g(the)f(spin)h(at)g(the)g(origin,)g(as)g (a)h(function)e(of)h(all)g(the)f(other)h(spins,)g(dep)q(ends)h(strongly)60 1786 y(on)h(the)g(spins)g(arbitrarily)f(far)h(a)o(w)o(a)o(y)f(from)g(the)g (origin.)21 b(More)16 b(precisely)l(,)d(w)o(e)i(shall)h(sho)o(w)g(that)h(if) 60 1846 y(w)o(e)g(tak)o(e)h(an)g(arbitrarily)f(large)h(cub)q(e)g(and)g(\014x) g(all)f(the)h(blo)q(c)o(k)f(spins)h(inside,)f(except)g(the)h(origin,)60 1907 y(in)d(a)i(fully)d(alternating)i(con\014guration,)h(then)f(the)f (renormalized)f(magnetization)g(at)i(the)g(origin)60 1967 y(dep)q(ends)h (strongly)f(on)h(the)f(blo)q(c)o(k-spin)g(con\014guration)h(outside)g(of)f (the)g(cub)q(e.)133 2027 y(The)24 b(ferromagnetic)f(nearest-neigh)o(b)q(or)i (Ising)f(mo)q(del)f(in)h Fq(Z)1308 2006 y FH(2)1352 2027 y FQ(is)g(de\014ned)g(b)o(y)g(the)g(formal)60 2087 y(Hamiltonian)775 2147 y FF(H)32 b FQ(=)c FE(\000)p FF(J)991 2106 y Fx(X)994 2200 y Fy(h)p FD(ij)r Fy(i)1060 2147 y FF(\033)1088 2154 y FD(i)1101 2147 y FF(\033)1129 2154 y FD(j)1161 2147 y FF(;)615 b FQ(\(4)p FF(:)p FQ(1\))60 2277 y(where)16 b FE(h)p FF(ij)s FE(i)i FQ(denotes)f(nearest-neigh)o(b)q(or)g(pairs)g(and)h FF(J)j FQ(pla)o(ys)16 b(the)h(role)f(of)i(an)f(in)o(v)o(erse)e(temp)q(era-)60 2337 y(ture.)24 b(W)l(e)17 b(shall)h(use)f(the)g(decimation)f(transformation) h(with)g(scale)g(factor)h FF(b)d FQ(=)h(2.)25 b(The)17 b FP(image)60 2397 y FQ(\(or)g FP(blo)n(ck)5 b FQ(\))17 b(spins)g(are)f(those)h(spins)f (with)g(b)q(oth)h(co)q(ordinates)g(ev)o(en,)e(while)g(the)h(remaining)f (spins)p 60 2441 732 2 v 100 2495 a FA(47)135 2510 y Fz(It)i(is)h(w)o(ell)e (kno)o(wn)h(that)h(the)g(decimation)e(transformation)f(is)j(badly)e(b)q(eha)o (v)o(ed)i Fw(in)h(the)f(limit)f(of)h(in\014nitely)60 2560 y(many)c(de)n (cimations)i Fz([210)o(,)c(364)o(]:)17 b(for)12 b(example,)f(an)o(y)h (\014xed)h(p)q(oin)o(t)f(m)o(ust)g(ha)o(v)o(e)g(a)g(t)o(w)o(o-p)q(oin)o(t)g (correlation)g(function)60 2610 y Fu(h)p Fv(\033)100 2616 y FA(0)118 2610 y Fz(;)7 b Fv(\033)161 2616 y Fp(x)182 2610 y Fu(i)18 b Fz(whic)o(h)h(is)f(indep)q(enden)o(t)i(of)e Fv(x)h Fz(\(so)f(in)h(particular)f(do)q(esn't)h(deca)o(y)g(as)g Fu(j)p Fv(x)p Fu(j)f(!)h(1)p Fz(\).)32 b(But)19 b(the)g(presen)o(t)60 2660 y(example)13 b(is)g(m)o(uc)o(h)g(more)g(drastic,)h(as)g(the)g(problems)f (app)q(ear)i(after)f(a)f(single)h(step.)951 2784 y FQ(92)p eop %%Page: 93 93 bop 60 92 a FQ(are)14 b(the)g FP(internal)20 b FQ(spins.)h(W)l(e)14 b(denote)f(b)o(y)h(\()p Fq(Z)898 71 y FH(2)918 92 y FQ(\))937 74 y FD(imag)q(e)1049 92 y FQ(\(resp.)g(\()p Fq(Z)1232 71 y FH(2)1252 92 y FQ(\))1271 74 y FD(int)1319 92 y FQ(\))g(the)g(set)g(of)g (image)f(\(resp.)g(in-)60 152 y(ternal\))g(spins.)20 b(More)13 b(generally)l(,)f(if)g(\003)h(is)g(a)h(subset)f(of)g Fq(Z)1095 131 y FH(2)1114 152 y FQ(,)h(w)o(e)e(denote)h(b)o(y)g(\003)1463 134 y FD(imag)q(e)1575 152 y FE(\021)g FQ(\003)t FE(\\)t FQ(\()p Fq(Z)1753 131 y FH(2)1773 152 y FQ(\))1792 134 y FD(imag)q(e)60 212 y FQ(\(resp.)j(\003)230 194 y FD(int)292 212 y FE(\021)d FQ(\003)e FE(\\)g FQ(\()p Fq(Z)483 192 y FH(2)503 212 y FQ(\))522 194 y FD(int)570 212 y FQ(\))16 b(the)g(set)g(of)h(image)e(\(resp.)g(in)o (ternal\))h(spins)g(in)g(\003.)133 273 y(The)g(pro)q(of)i(of)e(non-quasilo)q (calit)o(y)g(of)h(the)f(renormalized)e(measure)h(go)q(es)i(in)f(four)h (steps:)133 333 y FP(Step)k(0.)28 b(Computation)20 b(of)f(the)i(c)n (onditional)f(pr)n(ob)n(abilities)f(for)g(the)h(image)h(system.)28 b FQ(These)60 393 y(conditional)20 b(probabilities)f(turn)h(out)g(to)h(b)q(e) f(related)f(to)i(exp)q(ectation)e(v)m(alues)h(in)g(a)g(system)f(of)60 453 y(in)o(ternal)c(spins,)h(with)g FP(\014xe)n(d)22 b FQ(image)15 b(spins)i FF(!)899 435 y Fy(0)911 453 y FQ(.)133 513 y FP(Step)23 b(1.)35 b(Sele)n(ction)23 b(of)f(an)g(image-spin)h(c)n(on\014gur)n(ation)f FF(!)1245 495 y Fy(0)1243 526 y FH(sp)q(ecial)1349 513 y FP(.)35 b FQ(W)l(e)21 b(\014nd)g(an)g(image-spin)60 574 y(con\014guration)f FF(!)390 556 y Fy(0)388 586 y FH(sp)q(ecial)512 574 y FQ(suc)o(h)e(that)h (the)f(corresp)q(onding)i(system)d(of)i(in)o(ternal)e(spins)i(has)g(a)g(non-) 60 634 y(unique)d(Gibbs)g(measure)f(\(i.e.)g(a)h(\014rst-order)h(phase)g (transition\).)133 694 y FP(Step)j(2.)27 b(Study)19 b(of)g(a)g(neighb)n(orho) n(o)n(d)f(of)h FF(!)932 676 y Fy(0)930 706 y FH(sp)q(ecial)1035 694 y FQ(.)27 b(W)l(e)17 b(study)h(the)g(in)o(ternal-spin)f(system)g(for)60 754 y(image-spin)e(con\014gurations)j FF(!)651 736 y Fy(0)679 754 y FQ(in)e(a)h(neigh)o(b)q(orho)q(o)q(d)h(of)f FF(!)1171 736 y Fy(0)1169 767 y FH(sp)q(ecial)1274 754 y FQ(,)f(and)h(sho)o(w)g(that)g (the)f(in)o(ternal-)60 814 y(spin)i(order)f(parameter)g(is)g(a)h(discon)o (tin)o(uous)g(function)f(of)h FF(!)1207 796 y Fy(0)1219 814 y FQ(.)25 b(In)18 b(ph)o(ysical)e(terms,)g(this)i(means)60 875 y(that)13 b(the)g(in)o(ternal-spin)f(order)h(parameter)e(dep)q(ends)j (sensitiv)o(ely)c(on)j(the)g(image-spin)f(con\014gura-)60 935 y(tion)k(arbitrarily)f(far)h(from)e(the)i(origin,)f(if)g(the)h(image-spin)e (con\014guration)j(in)f(the)f(in)o(termediate)60 995 y(region)h(is)g(set)h (to)f FF(!)423 977 y Fy(0)421 1007 y FH(sp)q(ecial)527 995 y FQ(.)133 1055 y FP(Step)21 b(3.)28 b(\\Un\014xing")22 b(of)d(the)h(spin)g (at)f(the)h(origin.)29 b FQ(This)19 b(is)f(a)h(tec)o(hnical)e(step)h (relating)g(the)60 1115 y(image)11 b(spin)h(at)h(the)f(origin)g(to)h(the)f (in)o(ternal)f(spins)i(nearb)o(y)l(.)19 b(\(After)12 b(all,)g(w)o(e)g(w)o(an) o(t)g(the)g(conditional)60 1176 y(probabilities)j(for)i(image)e(spins,)h(not) h(in)o(ternal)e(spins.\))133 1236 y(Let)i(us)f(no)o(w)h(discuss)f(these)g (steps)h(in)e(detail:)133 1321 y FP(Step)21 b(0.)30 b(Computation)20 b(of)g(the)g(c)n(onditional)h(pr)n(ob)n(abilities)f(for)f(the)h(image)h (system.)30 b FQ(Let)19 b FF(\026)60 1381 y FQ(b)q(e)f FP(any)k FQ(Gibbs)c(measure)f(for)h(the)g(ferromagnetic)e(Ising)i(mo)q(del)e(in)i Fq(Z)1387 1360 y FH(2)1425 1381 y FQ(with)f(nearest-neigh)o(b)q(or)60 1441 y(coupling)h FF(J)5 b FQ(.)28 b(Our)18 b(goal)i(is)e(to)h(sho)o(w)g (that,)g(for)g FF(J)k FQ(su\016cien)o(tly)16 b(large,)j(the)f(image)f (\(decimated\))60 1501 y(measure)f FF(\026T)24 b FQ(has)18 b(non-quasilo)q(cal)g(conditional)f(probabilities.)24 b(Therefore,)17 b(our)h(\014rst)f(order)h(of)60 1562 y(business)i(m)o(ust)e(b)q(e)h(to)h (compute)e(these)h(conditional)g(probabilities.)30 b(T)l(o)20 b(do)f(this,)h(w)o(e)f(use)g(the)60 1622 y(only)14 b(fact)g(w)o(e)g(kno)o(w)h (ab)q(out)g(the)f(measure)f FF(\026)p FQ(,)i(namely)d(that)j(it)f (satis\014es)g(the)g(DLR)h(equations)g(for)60 1682 y(the)h(ferromagnetic)f (nearest-neigh)o(b)q(or)h(Ising)g(mo)q(del.)133 1742 y(The)i(presen)o(t)f (case)g(is)h(relativ)o(ely)d(simple,)g(b)q(ecause)i(the)h(image)e(spins)i (are)f(simply)f(a)i(subset)60 1802 y(of)h(the)g(original)g(spins.)29 b(Let,)19 b(therefore,)g(\003)893 1784 y Fy(0)923 1802 y FQ(b)q(e)g(a)h (\014nite)e(subset)h(of)h Fq(Z)1404 1781 y FH(2)1424 1802 y FQ(;)g(w)o(e)e(wish)h(to)g(compute)60 1863 y(the)13 b(conditional)g (probabilities)g FF(E)703 1870 y FD(\026T)752 1863 y FQ(\()p FF(f)5 b FE(jf)p FF(\033)869 1844 y Fy(0)867 1875 y FD(j)885 1863 y FE(g)910 1870 y FD(j)r Fy(2)p FH(\003)974 1861 y Ft(0)985 1857 y Fs(c)1003 1863 y FQ(\))13 b(for)h(functions)f FF(f)19 b FQ(of)14 b(the)f(spins)g FE(f)p FF(\033)1665 1844 y Fy(0)1663 1875 y FD(i)1677 1863 y FE(g)1702 1870 y FD(i)p Fy(2)p FH(\003)1762 1861 y Ft(0)1775 1863 y FQ(.)20 b(But)60 1923 y(these)12 b(are)h(just)f(the)h (conditional)f(probabilities)g FF(E)992 1930 y FD(\026)1015 1923 y FQ(\()p FF(f)5 b FE(jf)p FF(\033)1130 1930 y FD(l)1143 1923 y FE(g)1168 1930 y FD(l)p Fy(2)p FH(2\(\003)1259 1921 y Ft(0)1269 1917 y Fs(c)1285 1930 y FH(\))1301 1923 y FQ(\))13 b(for)f(functions)h FF(f)18 b FQ(of)13 b(the)f(spins)60 1983 y FE(f)p FF(\033)113 1990 y FD(k)134 1983 y FE(g)159 1990 y FD(k)q Fy(2)p FH(2\003)244 1981 y Ft(0)257 1983 y FQ(.)21 b(There)14 b(is)h(a)g(sligh)o(t)g(complication)d(no)o(w,)j(b)q(ecause)g(the)g(set)g (2\(\003)1462 1965 y Fy(0)1474 1960 y FD(c)1491 1983 y FQ(\))22 b(=)g(\()p Fq(Z)1642 1962 y FH(2)1661 1983 y FQ(\))1680 1965 y FD(imag)q(e)1787 1983 y FE(n)8 b FQ(2\003)1878 1965 y Fy(0)60 2043 y FQ(is)20 b(not)h(the)f(compleme)o(n)o(t)e(of)i(a)h(\014nite)f(set;)i (its)e(complem)o(en)o(t)d(consists)k(of)g(the)f(image)f(spins)h(in)60 2103 y(2\003)118 2085 y Fy(0)149 2103 y FP(plus)g(al)r(l)i(the)e(internal)i (spins)t FQ(.)30 b(Therefore,)18 b(the)h(DLR)h(equations)f(for)h(the)e (original)h(mo)q(del)60 2164 y(do)e(not)f(immediatel)o(y)d(tell)i(us)i(ho)o (w)f(to)h(condition)f(on)h FE(f)p FF(\033)1135 2171 y FD(l)1148 2164 y FE(g)1173 2171 y FD(l)p Fy(2)p FH(2\(\003)1264 2162 y Ft(0)1274 2158 y Fs(c)1290 2171 y FH(\))1306 2164 y FQ(.)k(Ho)o(w)o(ev)o (er,)14 b(w)o(e)i(ha)o(v)o(e)f(studied)60 2224 y(this)g(problem)f(in)h (Section)g(2.3.7;)g(the)g(conclusion)h(\(Prop)q(osition)g(2.25\))g(is)f(that) h(the)f(conditional)60 2284 y(probabilit)o(y)c(measure)f FF(\026)p FQ(\()e FE(\001)g(jf)p FF(\033)635 2291 y FD(l)648 2284 y FE(g)673 2292 y FD(l)p Fy(2)p FH(2\(\003)764 2282 y Ft(0)775 2279 y Fs(c)791 2292 y FH(\))807 2284 y FQ(\))j(is,)h(for)g FF(\026)p FQ(-almost-ev)o(ery)e FE(f)p FF(\033)1346 2291 y FD(l)1359 2284 y FE(g)1384 2292 y FD(l)p Fy(2)p FH(2\(\003)1475 2282 y Ft(0)1485 2279 y Fs(c)1501 2292 y FH(\))1517 2284 y FQ(,)i(a)g(Gibbs)g (measure)60 2344 y(for)24 b(the)g(Ising)h(mo)q(del)e(restricted)g(to)h(v)o (olume)e(\(2\003)1059 2326 y Fy(0)1071 2344 y FQ(\))16 b FE([)h FQ(\()p Fq(Z)1206 2323 y FH(2)1225 2344 y FQ(\))1244 2326 y FD(int)1317 2344 y FQ(with)24 b(external)f(spins)i(set)f(to)60 2404 y FE(f)p FF(\033)113 2411 y FD(l)126 2404 y FE(g)151 2412 y FD(l)p Fy(2)p FH(2\(\003)242 2403 y Ft(0)252 2399 y Fs(c)268 2412 y FH(\))284 2404 y FQ(.)c(This)15 b(latter)f(system)f(is)h(sp)q (eci\014ed)g(b)o(y)g(the)g(same)f(formal)g(Hamiltonian)g(\(and)i(hence)60 2464 y(the)k(same)g(in)o(teraction\))g(as)h(the)f(original)h(Ising)f(mo)q (del,)g(except)g(that)h(no)o(w)g(only)f(the)g(spins)h(in)60 2525 y(\(2\003)137 2507 y Fy(0)149 2525 y FQ(\))15 b FE([)f FQ(\()p Fq(Z)280 2504 y FH(2)300 2525 y FQ(\))319 2507 y FD(int)388 2525 y FQ(are)22 b(considered)f(to)h(b)q(e)g(random)f(v)m(ariables,)h(and)g (the)g(spins)g FE(f)p FF(\033)1633 2532 y FD(l)1645 2525 y FE(g)1670 2532 y FD(l)p Fy(2)p FH(2\(\003)1761 2523 y Ft(0)1772 2519 y Fs(c)1788 2532 y FH(\))1825 2525 y FQ(are)60 2585 y(considered)16 b(to)g(b)q(e)h(\014xed.)133 2645 y(Note)j(that)g(w)o(e)f(kno)o(w)h(only)g (that)g FF(\026)p FQ(\()8 b FE(\001)g(jf)p FF(\033)935 2652 y FD(l)948 2645 y FE(g)973 2653 y FD(l)p Fy(2)p FH(2\(\003)1064 2643 y Ft(0)1075 2640 y Fs(c)1091 2653 y FH(\))1107 2645 y FQ(\))19 b(is)h FP(some)k FQ(Gibbs)c(measure)e(for)i(the)g(re-)951 2784 y(93)p eop %%Page: 94 94 bop 60 91 a FQ(stricted)14 b(in)o(teraction:)20 b(if)14 b(the)h(restricted)e (in)o(teraction)h(happ)q(ens)i(to)f(ha)o(v)o(e)g(more)e(than)j(one)f(Gibbs)60 152 y(measure,)k(then)g(w)o(e)h(ha)o(v)o(e)f(no)h(w)o(a)o(y)f(of)h(kno)o (wing)g(whic)o(h)f(one)h(is)g FF(\026)p FQ(\()8 b FE(\001)g(jf)p FF(\033)1436 159 y FD(l)1449 152 y FE(g)1474 159 y FD(l)p Fy(2)p FH(2\(\003)1565 150 y Ft(0)1575 146 y Fs(c)1591 159 y FH(\))1607 152 y FQ(\).)32 b(Therefore,)60 212 y(w)o(e)15 b(shall)g(ha)o(v)o(e)g(to)h (pro)o(v)o(e)e(b)q(ounds)j(whic)o(h)e(are)g(v)m(alid)g(uniformly)f(for)i FP(al)r(l)21 b FQ(Gibbs)16 b(measures)f(of)g(the)60 272 y(restricted)g(in)o (teraction.)20 b(This)d(is)f(what)h(w)o(e)e(shall)h(do)h(in)f(Steps)g(2)h (and)g(3)g(b)q(elo)o(w.)133 332 y(Note)i(also)h(that)g(this)g(computation)e (of)i(the)f(conditional)g(probabilities)g(is)g(asserted)h(to)g(b)q(e)60 392 y(v)m(alid)j(only)h(for)g FF(\026)p FP(-almost-every)30 b FE(f)p FF(\033)777 399 y FD(l)790 392 y FE(g)815 400 y FD(l)p Fy(2)p FH(2\(\003)906 391 y Ft(0)916 387 y Fs(c)932 400 y FH(\))948 392 y FQ(;)d(indeed,)d(conditional)g(probabilities)f(are)h FP(only)60 452 y FQ(de\014ned)14 b(up)h(to)g(mo)q(di\014cations)f(on)h(a)g (set)f(of)h(measure)e(zero.)21 b(Therefore,)14 b(in)g(order)h(to)f(pro)o(v)o (e)g(non-)60 513 y(quasilo)q(calit)o(y)20 b(w)o(e)h(m)o(ust)f(pro)o(v)o(e)h (not)g(only)h(that)f(this)h FP(p)n(articular)k FQ(v)o(ersion)20 b(of)i(the)f(conditional)60 573 y(probabilities)16 b(is)h(a)h(discon)o(tin)o (uous)f(function,)f(but)i(that)f FP(no)k FQ(function)16 b(obtained)i(from)e (this)h(one)60 633 y(b)o(y)e(mo)q(di\014cation)g(on)h(a)g(set)g(of)g FF(\026)p FQ(-measure)f(zero)g(can)h(b)q(e)g(con)o(tin)o(uous.)21 b(That)16 b(is,)f(w)o(e)h(m)o(ust)e(pro)o(v)o(e)60 693 y(that)22 b(the)e(conditional)h(probabilities)f(are)i FP(essential)r(ly)i(disc)n (ontinuous)t FQ(.)36 b(W)l(e)21 b(shall)g(do)g(this)g(in)60 753 y(Steps)16 b(2)h(and)g(3)f(b)q(elo)o(w.)133 814 y(It)21 b(is)f(con)o(v)o(enien)o(t)f(to)i(study)g(\014rst)h(the)e(system)g(of)h(in)o (ternal)f(spins)h(alone,)h(i.e.)d(the)h(system)60 874 y(in)g(\()p Fq(Z)170 853 y FH(2)190 874 y FQ(\))209 856 y FD(int)277 874 y FQ(with)g FP(al)r(l)26 b FQ(image)19 b(spins)h FE(f)p FF(\033)795 856 y Fy(0)793 886 y FD(j)811 874 y FE(g)836 882 y FD(j)r Fy(2)p Fl(Z)897 873 y Fr(2)936 874 y FQ(set)g(to)h(\014xed)e(v)m(alues.)33 b(W)l(e)20 b(call)f(this)h(system)e(the)60 934 y FP(mo)n(di\014e)n(d)g(obje)n (ct)h(system)f(for)f(image-spin)j(c)n(on\014gur)n(ation)h FE(f)p FF(\033)1228 916 y Fy(0)1226 946 y FD(j)1244 934 y FE(g)1269 942 y FD(j)r Fy(2)p Fl(Z)1330 933 y Fr(2)1349 934 y FQ(.)j(In)17 b(Step)g(3)g(b)q(elo)o(w)g(w)o(e)g(will)60 994 y(\\un\014x")24 b(the)f(image)e(spins)i(in)g(the)g(v)o(olume)e(\003)970 976 y Fy(0)981 994 y FQ(.)42 b(In)22 b(fact,)i(it)f(su\016ces)g(to)g(consider)g (just)g(one)60 1054 y(particular)16 b(v)o(olume)e(\003)487 1036 y Fy(0)498 1054 y FQ(,)i(whic)o(h)g(w)o(e)g(shall)g(tak)o(e)f(to)i(b)q (e)f FE(f)p FQ(0)p FE(g)p FQ(.)133 1136 y FP(Step)k(1.)25 b(Sele)n(ction)c (of)e(an)f(image-spin)i(c)n(on\014gur)n(ation)f FF(!)1217 1118 y Fy(0)1215 1148 y FH(sp)q(ecial)1321 1136 y FP(.)25 b FQ(Our)18 b(goal)g(is)g(to)f(sho)o(w)i(that)60 1196 y(the)c(conditional)h (probabilities)e FF(\026)p FQ(\()8 b FE(\001)g(jf)p FF(\033)818 1203 y FD(l)832 1196 y FE(g)857 1204 y FD(l)p Fy(2)p FH(2\(\003)948 1194 y Ft(0)958 1191 y Fs(c)974 1204 y FH(\))990 1196 y FQ(\))15 b(are)h(essen)o(tially)e(discon)o(tin)o(uous)h(functions)h(of)60 1256 y FE(f)p FF(\033)113 1263 y FD(l)126 1256 y FE(g)151 1264 y FD(l)p Fy(2)p FH(2\(\003)242 1254 y Ft(0)252 1251 y Fs(c)268 1264 y FH(\))284 1256 y FQ(.)21 b(Therefore,)14 b(w)o(e)g(m)o(ust)f(\014nd)i (a)g(p)q(oin)o(t)g FF(!)1034 1238 y Fy(0)1060 1256 y FQ(=)e FE(f)p FF(\033)1166 1238 y Fy(0)1164 1268 y FD(j)1182 1256 y FE(g)1207 1265 y FD(j)r Fy(2)p Fl(Z)1268 1255 y Fr(2)1302 1256 y FQ(of)i(essen)o(tial)f(discon)o(tin)o(uit)o(y)l(.)k(A)60 1316 y(go)q(o)q(d)e(candidate)e(w)o(ould)f(b)q(e)h(an)h(image-spin)d (con\014guration)j FF(!)1232 1298 y Fy(0)1230 1329 y FH(sp)q(ecial)1349 1316 y FQ(suc)o(h)f(that)g(the)g(corresp)q(ond-)60 1376 y(ing)i(system)f(of)i (in)o(ternal)e(spins)i(has)g(a)f(non-unique)h(Gibbs)f(measure.)21 b(Indeed,)15 b(non-uniqueness)60 1437 y(of)j(the)f(Gibbs)h(measure)f(means)f (that)i(the)g(in)o(ternal)e(spins)i(in)g(v)o(olume)d(2\003)1471 1419 y Fy(0)1501 1437 y FQ(dep)q(end)i(sensitiv)o(ely)60 1497 y(on)f(the)f FP(internal)j(spins)h FQ(arbitrarily)14 b(far)i(from)e(the)h(v)o (olume)e(2\003)1248 1479 y Fy(0)1275 1497 y FQ(\(alb)q(eit)i(with)g(the)g(in) o(termediate)60 1557 y(in)o(ternal)20 b(spins)h(free)f(to)i(\015uctuate\);)h (so)e(it)g(is)f(a)i(reasonable)f(guess)h(that)f(the)g(Gibbs)g(measure)60 1617 y(migh)o(t)d(dep)q(end)j(sensitiv)o(ely)c(also)k(on)f(the)g FP(image)i(spins)i FQ(arbitrarily)19 b(far)h(a)o(w)o(a)o(y)g(\(but)g(with)g (the)60 1677 y(in)o(termediate)15 b(image)i(spins)i(held)f(\014xed)g(at)g FF(!)934 1659 y Fy(0)932 1690 y FH(sp)q(ecial)1038 1677 y FQ(\),)g(and)h (this)f(is)g(precisely)f(the)h(statemen)o(t)f(of)60 1738 y(essen)o(tial)e (discon)o(tin)o(uit)o(y)f(\(see)i(Step)g(2)h(b)q(elo)o(w\).)133 1798 y(F)l(or)e(the)f FF(b)g FQ(=)g(2)h(decimation)e(transformation,)h(suc)o (h)h(a)g(con\014guration)h FF(!)1493 1780 y Fy(0)1491 1810 y FH(sp)q(ecial)1611 1798 y FQ(w)o(as)f(found)h(b)o(y)60 1858 y(Gri\016ths)g(and)h(P)o(earce)e([173)q(,)h(171)q(]:)k(it)c(is)g(the)g(fully) f(alternating)h(con\014guration)i FF(!)1612 1840 y Fy(0)1610 1870 y FD(alt)1671 1858 y FQ(de\014ned)e(b)o(y)671 1955 y FF(\033)701 1934 y Fy(0)699 1967 y FD(i)711 1972 y Fr(1)728 1967 y FD(;i)750 1972 y Fr(2)797 1955 y FE(\021)27 b FF(\033)891 1962 y FH(2)p FD(i)921 1967 y Fr(1)938 1962 y FD(;)p FH(2)p FD(i)978 1967 y Fr(2)1024 1955 y FQ(=)h(\()p FE(\000)p FQ(1\))1191 1934 y FD(i)1203 1939 y Fr(1)1220 1934 y FH(+)p FD(i)1259 1939 y Fr(2)1790 1955 y FQ(\(4)p FF(:)p FQ(2\))60 2052 y([see)13 b(Figure)f(3\(a\)].)21 b(Notice)12 b(that)i(eac)o(h)f(in)o(ternal)f(spin)i(is)f(adjacen)o(t)g (either)f(to)i(t)o(w)o(o)f(image)g(spins)g FP(of)60 2112 y(opp)n(osite)h (sign)k FQ(|)13 b(in)g(whic)o(h)f(case)h(the)g(e\013ectiv)o(e)f(magnetic)f (\014elds)i(cancel)f(|)h(or)h(else)e(to)i(no)f(image)60 2172 y(spin.)26 b(Therefore,)18 b(the)f(mo)q(di\014ed)g(ob)s(ject)h(system)e(is)i (simply)d(a)k(ferromagnetic)d(Ising)i(mo)q(del)e(in)60 2232 y(zero)h(\014eld)f(on)i(a)f FP(de)n(c)n(or)n(ate)n(d)g(lattic)n(e)22 b FQ([342)q(],)16 b(as)i(sho)o(wn)g(in)e(Figure)h(3\(b\).)24 b(No)o(w)17 b(w)o(e)g(can)g(explicitly)60 2293 y(in)o(tegrate)11 b(out)h(the)g(spins)g(in)f(the)g(decorated)h(lattice)f(that)h(ha)o(v)o(e)f (exactly)f(t)o(w)o(o)i(neigh)o(b)q(ors,)g(yielding)60 2353 y(an)17 b(e\013ectiv)o(e)e(coupling)h FF(J)544 2335 y Fy(0)570 2353 y FQ(=)628 2333 y FH(1)p 628 2341 18 2 v 628 2370 a(2)658 2353 y FQ(log)10 b(cosh)e(2)p FF(J)22 b FQ(b)q(et)o(w)o(een)16 b(those)h(t)o(w)o(o)f(neigh)o(b)q(ors.)23 b(The)17 b(result)f(is)h(an)60 2413 y(ordinary)f(ferromagnetic)f(Ising)h(mo)q(del)f(on)h Fq(Z)925 2392 y FH(2)945 2413 y FQ(,)f(with)h(nearest-neigh)o(b)q(or)h(coupling)f FF(J)1681 2395 y Fy(0)1709 2413 y FQ(and)g(zero)60 2473 y(magnetic)22 b(\014eld)h([Figure)g(3\(c\)].)43 b(If)23 b FF(J)807 2455 y Fy(0)845 2473 y FF(>)k(J)937 2480 y FD(c)980 2473 y FQ(=)1050 2454 y FH(1)p 1050 2461 V 1050 2490 a(2)1081 2473 y FQ(log)q(\(1)16 b(+)1257 2432 y FE(p)p 1299 2432 25 2 v 41 x FQ(2\))27 b(=)f(0)p FF(:)p FQ(440686)8 b FF(:)g(:)g(:)i FQ(,)26 b(that)e(is,)60 2539 y FF(J)h(>)174 2520 y FH(1)p 174 2528 18 2 v 174 2557 a(2)205 2539 y FQ(cosh)298 2518 y Fy(\000)p FH(1)345 2539 y FQ(\(1)14 b(+)453 2498 y FE(p)p 495 2498 25 2 v 41 x FQ(2\))20 b(=)g(0)p FF(:)p FQ(764285)8 b FF(:)g(:)g(:)22 b FE(\031)e FQ(1)p FF(:)p FQ(73)p FF(J)1058 2546 y FD(c)1076 2539 y FQ(,)g(then)g(the)f (mo)q(di\014ed)g(ob)s(ject)g(system)g(for)60 2600 y(image-spin)e (con\014guration)i FF(!)635 2582 y Fy(0)633 2612 y FD(alt)697 2600 y FQ(has)f(t)o(w)o(o)h(distinct)e(Gibbs)h(measures,)g(a)g(\\+")h(phase)g (and)g(a)f FE(\000)60 2660 y FQ(phase)f(\(obtainable)f(b)o(y)g(using)h(\\+")g (or)f FE(\000)g FQ(b)q(oundary)i(conditions,)d(resp)q(ectiv)o(ely\).)951 2784 y(94)p eop %%Page: 95 95 bop 655 799 a @beginspecial 31 @llx 31.500000 @lly 211 @urx 224.500000 @ury 1537 @rwi @setspecial %%BeginDocument: fig3a.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z u u 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 63.2618 211.5217 m 63.2618 192.7663 L 44.0158 192.7663 L 44.0158 211.5217 L 63.2618 211.5217 L s 53.6388 202.144 m S U u 101.754 174.0108 m 101.754 155.2555 L 82.5079 155.2555 L 82.5079 174.0108 L 101.754 174.0108 L s 92.131 164.6332 m S U u 82.5079 192.7663 m 82.5079 174.0108 L 63.2618 174.0108 L 63.2618 192.7663 L 82.5079 192.7663 L s 72.8849 183.3886 m S U u 82.5079 211.5217 m 82.5079 192.7663 L 63.2618 192.7663 L 63.2618 211.5217 L 82.5079 211.5217 L s 72.8849 202.144 m S U u 101.754 211.5217 m 101.754 192.7663 L 82.5079 192.7663 L 82.5079 211.5217 L 101.754 211.5217 L s 92.131 202.144 m S U u 101.754 192.7663 m 101.754 174.0108 L 82.5079 174.0108 L 82.5079 192.7663 L 101.754 192.7663 L s 92.131 183.3886 m S U u 82.5079 174.0108 m 82.5079 155.2555 L 63.2618 155.2555 L 63.2618 174.0108 L 82.5079 174.0108 L s 72.8849 164.6332 m S U u 63.2618 174.0108 m 63.2618 155.2555 L 44.0158 155.2555 L 44.0158 174.0108 L 63.2618 174.0108 L s 53.6388 164.6332 m S U u 63.2618 192.7663 m 63.2618 174.0108 L 44.0158 174.0108 L 44.0158 192.7663 L 63.2618 192.7663 L s 53.6388 183.3886 m S U U u 121 211.5217 m 121 192.7663 L 101.754 192.7663 L 101.754 211.5217 L 121 211.5217 L s 111.377 202.144 m S U u 121 174.0108 m 121 155.2555 L 101.754 155.2555 L 101.754 174.0108 L 121 174.0108 L s 111.377 164.6332 m S U u 121 192.7663 m 121 174.0108 L 101.754 174.0108 L 101.754 192.7663 L 121 192.7663 L s 111.377 183.3886 m S U u 63.2618 155.2555 m 63.2618 136.5 L 44.0158 136.5 L 44.0158 155.2555 L 63.2618 155.2555 L s 53.6388 145.8777 m S U u 82.5079 155.2555 m 82.5079 136.5 L 63.2618 136.5 L 63.2618 155.2555 L 82.5079 155.2555 L s 72.8849 145.8777 m S U u 101.754 155.2555 m 101.754 136.5 L 82.5079 136.5 L 82.5079 155.2555 L 101.754 155.2555 L s 92.131 145.8777 m S U u 121 155.2555 m 121 136.5 L 101.754 136.5 L 101.754 155.2555 L 121 155.2555 L s 111.377 145.8777 m S U 101.754 136.5 m 121 136.5 L S 63.2618 155.2555 m S 63.2618 155.2555 m S 101.754 192.7663 m S 101.754 192.7663 m S 63.2618 192.7663 m S 63.2618 192.7663 m S 101.754 155.2555 m S 101.754 155.2555 m S u u 140.246 211.5217 m 140.246 192.7663 L 121 192.7663 L 121 211.5217 L 140.246 211.5217 L s 130.623 202.144 m S U u 178.7381 174.0108 m 178.7381 155.2555 L 159.4921 155.2555 L 159.4921 174.0108 L 178.7381 174.0108 L s 169.1151 164.6332 m S U u 159.4921 192.7663 m 159.4921 174.0108 L 140.246 174.0108 L 140.246 192.7663 L 159.4921 192.7663 L s 149.8691 183.3886 m S U u 159.4921 211.5217 m 159.4921 192.7663 L 140.246 192.7663 L 140.246 211.5217 L 159.4921 211.5217 L s 149.8691 202.144 m S U u 178.7381 211.5217 m 178.7381 192.7663 L 159.4921 192.7663 L 159.4921 211.5217 L 178.7381 211.5217 L s 169.1151 202.144 m S U u 178.7381 192.7663 m 178.7381 174.0108 L 159.4921 174.0108 L 159.4921 192.7663 L 178.7381 192.7663 L s 169.1151 183.3886 m S U u 159.4921 174.0108 m 159.4921 155.2555 L 140.246 155.2555 L 140.246 174.0108 L 159.4921 174.0108 L s 149.8691 164.6332 m S U u 140.246 174.0108 m 140.246 155.2555 L 121 155.2555 L 121 174.0108 L 140.246 174.0108 L s 130.623 164.6332 m S U u 140.246 192.7663 m 140.246 174.0108 L 121 174.0108 L 121 192.7663 L 140.246 192.7663 L s 130.623 183.3886 m S U U u 197.9842 211.5217 m 197.9842 192.7663 L 178.7381 192.7663 L 178.7381 211.5217 L 197.9842 211.5217 L s 188.3611 202.144 m S U u 197.9842 174.0108 m 197.9842 155.2555 L 178.7381 155.2555 L 178.7381 174.0108 L 197.9842 174.0108 L s 188.3611 164.6332 m S U u 197.9842 192.7663 m 197.9842 174.0108 L 178.7381 174.0108 L 178.7381 192.7663 L 197.9842 192.7663 L s 188.3611 183.3886 m S U u 140.246 155.2555 m 140.246 136.5 L 121 136.5 L 121 155.2555 L 140.246 155.2555 L s 130.623 145.8777 m S U u 159.4921 155.2555 m 159.4921 136.5 L 140.246 136.5 L 140.246 155.2555 L 159.4921 155.2555 L s 149.8691 145.8777 m S U u 178.7381 155.2555 m 178.7381 136.5 L 159.4921 136.5 L 159.4921 155.2555 L 178.7381 155.2555 L s 169.1151 145.8777 m S U u 197.9842 155.2555 m 197.9842 136.5 L 178.7381 136.5 L 178.7381 155.2555 L 197.9842 155.2555 L s 188.3611 145.8777 m S U 178.7381 136.5 m 197.9842 136.5 L S 140.246 155.2555 m S 140.246 155.2555 m S 178.7381 192.7663 m S 178.7381 192.7663 m S 140.246 192.7663 m S 140.246 192.7663 m S 178.7381 155.2555 m S 178.7381 155.2555 m S u u 63.2618 136.5 m 63.2618 117.7445 L 44.0158 117.7445 L 44.0158 136.5 L 63.2618 136.5 L s 53.6388 127.1223 m S U u 101.754 98.9891 m 101.754 80.2337 L 82.5079 80.2337 L 82.5079 98.9891 L 101.754 98.9891 L s 92.131 89.6114 m S U u 82.5079 117.7445 m 82.5079 98.9891 L 63.2618 98.9891 L 63.2618 117.7445 L 82.5079 117.7445 L s 72.8849 108.3668 m S U u 82.5079 136.5 m 82.5079 117.7445 L 63.2618 117.7445 L 63.2618 136.5 L 82.5079 136.5 L s 72.8849 127.1223 m S U u 101.754 136.5 m 101.754 117.7445 L 82.5079 117.7445 L 82.5079 136.5 L 101.754 136.5 L s 92.131 127.1223 m S U u 101.754 117.7445 m 101.754 98.9891 L 82.5079 98.9891 L 82.5079 117.7445 L 101.754 117.7445 L s 92.131 108.3668 m S U u 82.5079 98.9891 m 82.5079 80.2337 L 63.2618 80.2337 L 63.2618 98.9891 L 82.5079 98.9891 L s 72.8849 89.6114 m S U u 63.2618 98.9891 m 63.2618 80.2337 L 44.0158 80.2337 L 44.0158 98.9891 L 63.2618 98.9891 L s 53.6388 89.6114 m S U u 63.2618 117.7445 m 63.2618 98.9891 L 44.0158 98.9891 L 44.0158 117.7445 L 63.2618 117.7445 L s 53.6388 108.3668 m S U U u 121 136.5 m 121 117.7445 L 101.754 117.7445 L 101.754 136.5 L 121 136.5 L s 111.377 127.1223 m S U u 121 98.9891 m 121 80.2337 L 101.754 80.2337 L 101.754 98.9891 L 121 98.9891 L s 111.377 89.6114 m S U u 121 117.7445 m 121 98.9891 L 101.754 98.9891 L 101.754 117.7445 L 121 117.7445 L s 111.377 108.3668 m S U u 63.2618 80.2337 m 63.2618 61.4783 L 44.0158 61.4783 L 44.0158 80.2337 L 63.2618 80.2337 L s 53.6388 70.856 m S U u 82.5079 80.2337 m 82.5079 61.4783 L 63.2618 61.4783 L 63.2618 80.2337 L 82.5079 80.2337 L s 72.8849 70.856 m S U u 101.754 80.2337 m 101.754 61.4783 L 82.5079 61.4783 L 82.5079 80.2337 L 101.754 80.2337 L s 92.131 70.856 m S U u 121 80.2337 m 121 61.4783 L 101.754 61.4783 L 101.754 80.2337 L 121 80.2337 L s 111.377 70.856 m S U 101.754 61.4783 m 121 61.4783 L S 63.2618 80.2337 m S 63.2618 80.2337 m S 101.754 117.7445 m S 101.754 117.7445 m S 63.2618 117.7445 m S 63.2618 117.7445 m S 101.754 80.2337 m S 101.754 80.2337 m S u u 140.246 136.5 m 140.246 117.7445 L 121 117.7445 L 121 136.5 L 140.246 136.5 L s 130.623 127.1223 m S U u 178.7381 98.9891 m 178.7381 80.2337 L 159.4921 80.2337 L 159.4921 98.9891 L 178.7381 98.9891 L s 169.1151 89.6114 m S U u 159.4921 117.7445 m 159.4921 98.9891 L 140.246 98.9891 L 140.246 117.7445 L 159.4921 117.7445 L s 149.8691 108.3668 m S U u 159.4921 136.5 m 159.4921 117.7445 L 140.246 117.7445 L 140.246 136.5 L 159.4921 136.5 L s 149.8691 127.1223 m S U u 178.7381 136.5 m 178.7381 117.7445 L 159.4921 117.7445 L 159.4921 136.5 L 178.7381 136.5 L s 169.1151 127.1223 m S U u 178.7381 117.7445 m 178.7381 98.9891 L 159.4921 98.9891 L 159.4921 117.7445 L 178.7381 117.7445 L s 169.1151 108.3668 m S U u 159.4921 98.9891 m 159.4921 80.2337 L 140.246 80.2337 L 140.246 98.9891 L 159.4921 98.9891 L s 149.8691 89.6114 m S U u 140.246 98.9891 m 140.246 80.2337 L 121 80.2337 L 121 98.9891 L 140.246 98.9891 L s 130.623 89.6114 m S U u 140.246 117.7445 m 140.246 98.9891 L 121 98.9891 L 121 117.7445 L 140.246 117.7445 L s 130.623 108.3668 m S U U u 197.9842 136.5 m 197.9842 117.7445 L 178.7381 117.7445 L 178.7381 136.5 L 197.9842 136.5 L s 188.3611 127.1223 m S U u 197.9842 98.9891 m 197.9842 80.2337 L 178.7381 80.2337 L 178.7381 98.9891 L 197.9842 98.9891 L s 188.3611 89.6114 m S U u 197.9842 117.7445 m 197.9842 98.9891 L 178.7381 98.9891 L 178.7381 117.7445 L 197.9842 117.7445 L s 188.3611 108.3668 m S U u 140.246 80.2337 m 140.246 61.4783 L 121 61.4783 L 121 80.2337 L 140.246 80.2337 L s 130.623 70.856 m S U u 159.4921 80.2337 m 159.4921 61.4783 L 140.246 61.4783 L 140.246 80.2337 L 159.4921 80.2337 L s 149.8691 70.856 m S U u 178.7381 80.2337 m 178.7381 61.4783 L 159.4921 61.4783 L 159.4921 80.2337 L 178.7381 80.2337 L s 169.1151 70.856 m S U u 197.9842 80.2337 m 197.9842 61.4783 L 178.7381 61.4783 L 178.7381 80.2337 L 197.9842 80.2337 L s 188.3611 70.856 m S U 178.7381 61.4783 m 197.9842 61.4783 L S 140.246 80.2337 m S 140.246 80.2337 m S 178.7381 117.7445 m S 178.7381 117.7445 m S 140.246 117.7445 m S 140.246 117.7445 m S 178.7381 80.2337 m S 178.7381 80.2337 m S 34.0157 192.7663 m 39.0157 192.7663 L S 39.0157 192.7663 m 44.0158 192.7663 L S 34.0157 211.5217 m 39.0157 211.5217 L S 39.0157 211.5217 m 44.0158 211.5217 L S 34.0157 174.0108 m 39.0157 174.0108 L S 39.0157 174.0108 m 44.0158 174.0108 L S 34.0157 155.2555 m 39.0157 155.2555 L S 39.0157 155.2555 m 44.0158 155.2555 L S 34.0157 136.5 m 39.0157 136.5 L S 39.0157 136.5 m 44.0158 136.5 L S 34.0157 117.7445 m 39.0157 117.7445 L S 39.0157 117.7445 m 44.0158 117.7445 L S 34.0157 98.9891 m 39.0157 98.9891 L S 39.0157 98.9891 m 44.0158 98.9891 L S 34.0157 61.4783 m 39.0157 61.4783 L S 39.0157 61.4783 m 44.0158 61.4783 L S 34.0157 80.2337 m 39.0157 80.2337 L S 39.0157 80.2337 m 44.0158 80.2337 L S 197.9842 211.5217 m 202.9842 211.5217 L S 202.9842 211.5217 m 207.9843 211.5217 L S 197.9842 192.7663 m 202.9842 192.7663 L S 202.9842 192.7663 m 207.9843 192.7663 L S 197.9842 174.0108 m 202.9842 174.0108 L S 202.9842 174.0108 m 207.9843 174.0108 L S 197.9842 155.2555 m 202.9842 155.2555 L S 202.9842 155.2555 m 207.9843 155.2555 L S 197.9842 136.5 m 202.9842 136.5 L S 202.9842 136.5 m 207.9843 136.5 L S 197.9842 117.7445 m 202.9842 117.7445 L S 202.9842 117.7445 m 207.9843 117.7445 L S 197.9842 98.9891 m 202.9842 98.9891 L S 202.9842 98.9891 m 207.9843 98.9891 L S 197.9842 80.2337 m 202.9842 80.2337 L S 202.9842 80.2337 m 207.9843 80.2337 L S 197.9842 61.4783 m 202.9842 61.4783 L S 202.9842 61.4783 m 207.9843 61.4783 L S 197.9842 211.5217 m 197.9765 216.5217 L S 197.9765 216.5217 m 197.9688 221.5218 L S 178.7381 211.5217 m 178.7304 216.5217 L S 178.7304 216.5217 m 178.7227 221.5218 L S 159.4921 211.5217 m 159.4844 216.5217 L S 159.4844 216.5217 m 159.4767 221.5218 L S 140.246 211.5217 m 140.2383 216.5217 L S 140.2383 216.5217 m 140.2306 221.5218 L S 121 211.5217 m 120.9923 216.5217 L S 120.9923 216.5217 m 120.9846 221.5218 L S 101.754 211.5217 m 101.7463 216.5217 L S 101.7463 216.5217 m 101.7386 221.5218 L S 82.5079 211.5217 m 82.5002 216.5217 L S 82.5002 216.5217 m 82.4925 221.5218 L S 63.2618 211.5217 m 63.2541 216.5217 L S 63.2541 216.5217 m 63.2464 221.5218 L S 44.0158 211.5217 m 44.0081 216.5217 L S 44.0081 216.5217 m 44.0004 221.5218 L S 44.0312 51.4782 m 44.0235 56.4782 L S 44.0235 56.4782 m 44.0158 61.4783 L S 63.2772 51.4782 m 63.2695 56.4782 L S 63.2695 56.4782 m 63.2618 61.4783 L S 82.5233 51.4782 m 82.5156 56.4782 L S 82.5156 56.4782 m 82.5079 61.4783 L S 101.7694 51.4782 m 101.7617 56.4782 L S 101.7617 56.4782 m 101.754 61.4783 L S 121.0154 51.4782 m 121.0077 56.4782 L S 121.0077 56.4782 m 121 61.4783 L S 140.2614 51.4782 m 140.2537 56.4782 L S 140.2537 56.4782 m 140.246 61.4783 L S 159.5075 51.4782 m 159.4998 56.4782 L S 159.4998 56.4782 m 159.4921 61.4783 L S 178.7535 51.4782 m 178.7458 56.4782 L S 178.7458 56.4782 m 178.7381 61.4783 L S 197.9996 51.4782 m 197.9919 56.4782 L S 197.9919 56.4782 m 197.9842 61.4783 L S 63.2618 192.7663 m S 0 g 1 w 4 M 63.2618 192.7663 m F 0 G 0.3 w 10 M 63.2618 192.7663 m S 63.2618 192.7663 m S 101.754 155.2555 m S 0 g 1 w 4 M 101.754 155.2555 m F 0 G 0.3 w 10 M 101.754 155.2555 m S 101.754 155.2555 m S 63.2618 117.7445 m S 0 g 1 w 4 M 63.2618 117.7445 m F 0 G 0.3 w 10 M 63.2618 117.7445 m S 63.2618 117.7445 m S 140.246 192.7663 m S 0 g 1 w 4 M 140.246 192.7663 m F 0 G 0.3 w 10 M 140.246 192.7663 m S 140.246 192.7663 m S 178.7381 155.2555 m S 0 g 1 w 4 M 178.7381 155.2555 m F 0 G 0.3 w 10 M 178.7381 155.2555 m S 178.7381 155.2555 m S 140.246 117.7445 m S 0 g 1 w 4 M 140.246 117.7445 m F 0 G 0.3 w 10 M 140.246 117.7445 m S 140.246 117.7445 m S 101.754 80.2337 m S 0 g 1 w 4 M 101.754 80.2337 m F 0 G 0.3 w 10 M 101.754 80.2337 m S 101.754 80.2337 m S 178.7381 80.2337 m S 0 g 1 w 4 M 178.7381 80.2337 m F 0 G 0.3 w 10 M 178.7381 80.2337 m S 178.7381 80.2337 m S 101.754 192.7663 m S 0 g 1 w 4 M 101.754 192.7663 m F 0 G 0.3 w 10 M 101.754 192.7663 m S 0 g 1 w 4 M 101.754 192.7663 m F 0 G 0.3 w 10 M 178.7381 192.7663 m S 0 g 1 w 4 M 178.7381 192.7663 m F 0 G 0.3 w 10 M 178.7381 192.7663 m S 0 g 1 w 4 M 178.7381 192.7663 m F 0 G 0.3 w 10 M 66.125 154.875 m S 0 g 1 w 4 M 66.125 154.875 m F 0 G 0.3 w 10 M 63.2618 155.2555 m S 0 g 1 w 4 M 63.2618 155.2555 m F 0 G 0.3 w 10 M 63.2618 155.2555 m S 0 g 1 w 4 M 63.2618 155.2555 m F 0 G 0.3 w 10 M 140.246 155.2555 m S 0 g 1 w 4 M 140.246 155.2555 m F 0 G 0.3 w 10 M 140.246 155.2555 m S 0 g 1 w 4 M 140.246 155.2555 m F 0 G 0.3 w 10 M 101.754 117.7445 m S 0 g 1 w 4 M 101.754 117.7445 m F 0 G 0.3 w 10 M 101.754 117.7445 m S 0 g 1 w 4 M 101.754 117.7445 m F 0 G 0.3 w 10 M 178.7381 117.7445 m S 0 g 1 w 4 M 178.7381 117.7445 m F 0 G 0.3 w 10 M 178.7381 117.7445 m S 0 g 1 w 4 M 178.7381 117.7445 m F 0 G 0.3 w 10 M 63.2618 80.2337 m S 0 g 1 w 4 M 63.2618 80.2337 m F 0 G 0.3 w 10 M 63.2618 80.2337 m S 0 g 1 w 4 M 63.2618 80.2337 m F 0 G 0.3 w 10 M 140.246 80.2337 m S 0 g 1 w 4 M 140.246 80.2337 m F 0 G 0.3 w 10 M 140.246 80.2337 m S 0 g 1 w 4 M 140.246 80.2337 m F 0 G 0.3 w 10 M 63.2618 192.7663 m S 0 g 1 w 4 M 63.2618 192.7663 m F 0 G 0.3 w 10 M 63.2618 192.7663 m S 63.2618 192.7663 m S 140.246 192.7663 m S 0 g 1 w 4 M 140.246 192.7663 m F 0 G 0.3 w 10 M 140.246 192.7663 m S 140.246 192.7663 m S 82.5079 155.2555 m S 0 g 1 w 4 M 82.5079 155.2555 m F 0 G 0.3 w 10 M 82.5079 155.2555 m S 82.5079 155.2555 m S 178.7381 155.2555 m S 0 g 1 w 4 M 178.7381 155.2555 m F 0 G 0.3 w 10 M 178.7381 155.2555 m S 178.7381 155.2555 m S 101.754 155.2555 m S 0 g 1 w 4 M 101.754 155.2555 m F 0 G 0.3 w 10 M 101.754 155.2555 m S 101.754 155.2555 m S 63.2618 117.7445 m S 0 g 1 w 4 M 63.2618 117.7445 m F 0 G 0.3 w 10 M 63.2618 117.7445 m S 63.2618 117.7445 m S 140.246 117.7445 m S 0 g 1 w 4 M 140.246 117.7445 m F 0 G 0.3 w 10 M 140.246 117.7445 m S 140.246 117.7445 m S 101.754 80.2337 m S 0 g 1 w 4 M 101.754 80.2337 m F 0 G 0.3 w 10 M 101.754 80.2337 m S 101.754 80.2337 m S 178.7381 80.2337 m S 0 g 1 w 4 M 178.7381 80.2337 m F 0 G 0.3 w 10 M 178.7381 80.2337 m S 178.7381 80.2337 m S 101.754 192.7663 m S 0 g 1 w 4 M 101.754 192.7663 m F 0 G 0.3 w 10 M 101.754 192.7663 m S 0 g 1 w 4 M 101.754 192.7663 m F 0 G 0.3 w 10 M 178.7381 192.7663 m S 0 g 1 w 4 M 178.7381 192.7663 m F 0 G 0.3 w 10 M 178.7381 192.7663 m S 0 g 1 w 4 M 178.7381 192.7663 m F 0 G 0.3 w 10 M 63.2618 155.2555 m S 0 g 1 w 4 M 63.2618 155.2555 m F 0 G 0.3 w 10 M 63.2618 155.2555 m S 0 g 1 w 4 M 63.2618 155.2555 m F 0 G 0.3 w 10 M 140.246 155.2555 m S 0 g 1 w 4 M 140.246 155.2555 m F 0 G 0.3 w 10 M 140.246 155.2555 m S 0 g 1 w 4 M 140.246 155.2555 m F 0 G 0.3 w 10 M 101.754 117.7445 m S 0 g 1 w 4 M 101.754 117.7445 m F 0 G 0.3 w 10 M 101.754 117.7445 m S 0 g 1 w 4 M 101.754 117.7445 m F 0 G 0.3 w 10 M 178.7381 117.7445 m S 0 g 1 w 4 M 178.7381 117.7445 m F 0 G 0.3 w 10 M 178.7381 117.7445 m S 0 g 1 w 4 M 178.7381 117.7445 m F 0 G 0.3 w 10 M 63.2618 80.2337 m S 0 g 1 w 4 M 63.2618 80.2337 m F 0 G 0.3 w 10 M 63.2618 80.2337 m S 0 g 1 w 4 M 63.2618 80.2337 m F 0 G 0.3 w 10 M 140.246 80.2337 m S 0 g 1 w 4 M 140.246 80.2337 m F 0 G 0.3 w 10 M 140.246 80.2337 m S 0 g 1 w 4 M 140.246 80.2337 m F 0 G 0.3 w 10 M 101.754 192.7663 m S 0 g 1 w 4 M 101.754 192.7663 m F 0 G 0.3 w 10 M 101.754 192.7663 m S 0 g 1 w 4 M 101.754 192.7663 m F u 1 g 95.7436 192.7663 m 95.7436 189.5445 98.4346 186.9327 101.754 186.9327 c 105.0734 186.9327 107.7644 189.5445 107.7644 192.7663 c F 107.7644 192.7663 m 107.7644 195.9881 105.0734 198.5999 101.754 198.5999 c 98.4346 198.5999 95.7436 195.9881 95.7436 192.7663 c F 101.754 192.7663 m F U 0 G 0.3 w 10 M 101.754 192.7663 m S 0 g 1 w 4 M 101.754 192.7663 m F 0 G 0.3 w 10 M 101.754 192.7663 m S 0 g 1 w 4 M 101.754 192.7663 m F 100.6689 193.8345 m 97.0833 193.8456 L 97.0833 191.6872 L 100.6689 191.6983 L F 102.8391 191.6983 m 106.4247 191.6872 L 106.4247 193.8456 L 102.8391 193.8345 L F 97.0833 193.8456 m 106.4247 193.8456 l 106.4247 191.6872 l 97.0833 191.6872 l 97.0833 193.8456 l f 0 G 0.3 w 10 M 178.7381 192.7663 m S 0 g 1 w 4 M 178.7381 192.7663 m F 0 G 0.3 w 10 M 178.7381 192.7663 m S 0 g 1 w 4 M 178.7381 192.7663 m F u 1 g 172.7277 192.7663 m 172.7277 189.5445 175.4187 186.9327 178.7381 186.9327 c 182.0575 186.9327 184.7485 189.5445 184.7485 192.7663 c F 184.7485 192.7663 m 184.7485 195.9881 182.0575 198.5999 178.7381 198.5999 c 175.4187 198.5999 172.7277 195.9881 172.7277 192.7663 c F 178.7381 192.7663 m F U 0 G 0.3 w 10 M 178.7381 192.7663 m S 0 g 1 w 4 M 178.7381 192.7663 m F 0 G 0.3 w 10 M 178.7381 192.7663 m S 0 g 1 w 4 M 178.7381 192.7663 m F 177.653 193.8345 m 174.0674 193.8456 L 174.0674 191.6872 L 177.653 191.6983 L F 179.8232 191.6983 m 183.4088 191.6872 L 183.4088 193.8456 L 179.8232 193.8345 L F 174.0674 193.8456 m 183.4088 193.8456 l 183.4088 191.6872 l 174.0674 191.6872 l 174.0674 193.8456 l f 0 G 0.3 w 10 M 63.2618 155.2555 m S 0 g 1 w 4 M 63.2618 155.2555 m F 0 G 0.3 w 10 M 63.2618 155.2555 m S 0 g 1 w 4 M 63.2618 155.2555 m F u 1 g 57.2514 155.2555 m 57.2514 152.0337 59.9424 149.4219 63.2618 149.4219 c 66.5812 149.4219 69.2722 152.0337 69.2722 155.2555 c F 69.2722 155.2555 m 69.2722 158.4773 66.5812 161.0891 63.2618 161.0891 c 59.9424 161.0891 57.2514 158.4773 57.2514 155.2555 c F 63.2618 155.2555 m F U 0 G 0.3 w 10 M 63.2618 155.2555 m S 0 g 1 w 4 M 63.2618 155.2555 m F 0 G 0.3 w 10 M 63.2618 155.2555 m S 0 g 1 w 4 M 63.2618 155.2555 m F 62.1767 156.3237 m 58.5911 156.3348 L 58.5911 154.1764 L 62.1767 154.1875 L F 64.3469 154.1875 m 67.9325 154.1764 L 67.9325 156.3348 L 64.3469 156.3237 L F 58.5911 156.3348 m 67.9325 156.3348 l 67.9325 154.1764 l 58.5911 154.1764 l 58.5911 156.3348 l f 0 G 0.3 w 10 M 140.246 155.2555 m S 0 g 1 w 4 M 140.246 155.2555 m F 0 G 0.3 w 10 M 140.246 155.2555 m S 0 g 1 w 4 M 140.246 155.2555 m F u 1 g 134.2356 155.2555 m 134.2356 152.0337 136.9266 149.4219 140.246 149.4219 c 143.5654 149.4219 146.2564 152.0337 146.2564 155.2555 c F 146.2564 155.2555 m 146.2564 158.4773 143.5654 161.0891 140.246 161.0891 c 136.9266 161.0891 134.2356 158.4773 134.2356 155.2555 c F 140.246 155.2555 m F U 0 G 0.3 w 10 M 140.246 155.2555 m S 0 g 1 w 4 M 140.246 155.2555 m F 0 G 0.3 w 10 M 140.246 155.2555 m S 0 g 1 w 4 M 140.246 155.2555 m F 139.1609 156.3237 m 135.5753 156.3348 L 135.5753 154.1764 L 139.1609 154.1875 L F 141.3311 154.1875 m 144.9167 154.1764 L 144.9167 156.3348 L 141.3311 156.3237 L F 135.5753 156.3348 m 144.9167 156.3348 l 144.9167 154.1764 l 135.5753 154.1764 l 135.5753 156.3348 l f 0 G 0.3 w 10 M 82.5079 117.7445 m S 0 g 1 w 4 M 82.5079 117.7445 m F 0 G 0.3 w 10 M 82.5079 117.7445 m S 0 g 1 w 4 M 82.5079 117.7445 m F 0 G 0.3 w 10 M 82.5079 117.7445 m S 0 g 1 w 4 M 82.5079 117.7445 m F 0 G 0.3 w 10 M 82.5079 117.7445 m S 0 g 1 w 4 M 82.5079 117.7445 m F 0 G 0.3 w 10 M 101.754 117.7445 m S 0 g 1 w 4 M 101.754 117.7445 m F 0 G 0.3 w 10 M 101.754 117.7445 m S 0 g 1 w 4 M 101.754 117.7445 m F u 1 g 95.7436 117.7445 m 95.7436 114.5227 98.4346 111.9109 101.754 111.9109 c 105.0734 111.9109 107.7644 114.5227 107.7644 117.7445 c F 107.7644 117.7445 m 107.7644 120.9663 105.0734 123.5781 101.754 123.5781 c 98.4346 123.5781 95.7436 120.9663 95.7436 117.7445 c F 101.754 117.7445 m F U 0 G 0.3 w 10 M 101.754 117.7445 m S 0 g 1 w 4 M 101.754 117.7445 m F 0 G 0.3 w 10 M 101.754 117.7445 m S 0 g 1 w 4 M 101.754 117.7445 m F 100.6689 118.8127 m 97.0833 118.8238 L 97.0833 116.6654 L 100.6689 116.6765 L F 102.8391 116.6765 m 106.4247 116.6654 L 106.4247 118.8238 L 102.8391 118.8127 L F 97.0833 118.8238 m 106.4247 118.8238 l 106.4247 116.6654 l 97.0833 116.6654 l 97.0833 118.8238 l f 0 G 0.3 w 10 M 178.7381 117.7445 m S 0 g 1 w 4 M 178.7381 117.7445 m F 0 G 0.3 w 10 M 178.7381 117.7445 m S 0 g 1 w 4 M 178.7381 117.7445 m F u 1 g 172.7277 117.7445 m 172.7277 114.5227 175.4187 111.9109 178.7381 111.9109 c 182.0575 111.9109 184.7485 114.5227 184.7485 117.7445 c F 184.7485 117.7445 m 184.7485 120.9663 182.0575 123.5781 178.7381 123.5781 c 175.4187 123.5781 172.7277 120.9663 172.7277 117.7445 c F 178.7381 117.7445 m F U 0 G 0.3 w 10 M 178.7381 117.7445 m S 0 g 1 w 4 M 178.7381 117.7445 m F 0 G 0.3 w 10 M 178.7381 117.7445 m S 0 g 1 w 4 M 178.7381 117.7445 m F 177.653 118.8127 m 174.0674 118.8238 L 174.0674 116.6654 L 177.653 116.6765 L F 179.8232 116.6765 m 183.4088 116.6654 L 183.4088 118.8238 L 179.8232 118.8127 L F 174.0674 118.8238 m 183.4088 118.8238 l 183.4088 116.6654 l 174.0674 116.6654 l 174.0674 118.8238 l f 0 G 0.3 w 10 M 63.2618 80.2337 m S 0 g 1 w 4 M 63.2618 80.2337 m F 0 G 0.3 w 10 M 63.2618 80.2337 m S 0 g 1 w 4 M 63.2618 80.2337 m F u 1 g 57.2514 80.2337 m 57.2514 77.0119 59.9424 74.4001 63.2618 74.4001 c 66.5812 74.4001 69.2722 77.0119 69.2722 80.2337 c F 69.2722 80.2337 m 69.2722 83.4555 66.5812 86.0673 63.2618 86.0673 c 59.9424 86.0673 57.2514 83.4555 57.2514 80.2337 c F 63.2618 80.2337 m F U 0 G 0.3 w 10 M 63.2618 80.2337 m S 0 g 1 w 4 M 63.2618 80.2337 m F 0 G 0.3 w 10 M 63.2618 80.2337 m S 0 g 1 w 4 M 63.2618 80.2337 m F 62.1767 81.3019 m 58.5911 81.313 L 58.5911 79.1546 L 62.1767 79.1657 L F 64.3469 79.1657 m 67.9325 79.1546 L 67.9325 81.313 L 64.3469 81.3019 L F 58.5911 81.313 m 67.9325 81.313 l 67.9325 79.1546 l 58.5911 79.1546 l 58.5911 81.313 l f 0 G 0.3 w 10 M 140.246 80.2337 m S 0 g 1 w 4 M 140.246 80.2337 m F 0 G 0.3 w 10 M 140.246 80.2337 m S 0 g 1 w 4 M 140.246 80.2337 m F u 1 g 134.2356 80.2337 m 134.2356 77.0119 136.9266 74.4001 140.246 74.4001 c 143.5654 74.4001 146.2564 77.0119 146.2564 80.2337 c F 146.2564 80.2337 m 146.2564 83.4555 143.5654 86.0673 140.246 86.0673 c 136.9266 86.0673 134.2356 83.4555 134.2356 80.2337 c F 140.246 80.2337 m F U 0 G 0.3 w 10 M 140.246 80.2337 m S 0 g 1 w 4 M 140.246 80.2337 m F 0 G 0.3 w 10 M 140.246 80.2337 m S 0 g 1 w 4 M 140.246 80.2337 m F 139.1609 81.3019 m 135.5753 81.313 L 135.5753 79.1546 L 139.1609 79.1657 L F 141.3311 79.1657 m 144.9167 79.1546 L 144.9167 81.313 L 141.3311 81.3019 L F 135.5753 81.313 m 144.9167 81.313 l 144.9167 79.1546 l 135.5753 79.1546 l 135.5753 81.313 l f 0 G 0.3 w 10 M 62.625 193 m S 0 g 1 w 4 M 62.625 193 m F 0 G 0.3 w 10 M 62.625 193 m S 62.625 193 m S 62.625 193 m S 0 g 1 w 4 M 62.625 193 m F 0 G 0.3 w 10 M 62.625 193 m S 62.625 193 m S 62.625 193 m S 0 g 1 w 4 M 62.625 193 m F 0 G 0.3 w 10 M 62.625 193 m S 62.625 193 m S 140.246 192.7663 m S 0 g 1 w 4 M 140.246 192.7663 m F 0 G 0.3 w 10 M 140.246 192.7663 m S 140.246 192.7663 m S 140.246 192.7663 m S 0 g 1 w 4 M 140.246 192.7663 m F 0 G 0.3 w 10 M 140.246 192.7663 m S 140.246 192.7663 m S u 1 g 1 w 4 M 134.2356 192.7663 m 134.2356 189.5445 136.9266 186.9327 140.246 186.9327 c 143.5654 186.9327 146.2564 189.5445 146.2564 192.7663 c F 146.2564 192.7663 m 146.2564 195.9881 143.5654 198.5999 140.246 198.5999 c 136.9266 198.5999 134.2356 195.9881 134.2356 192.7663 c F 140.246 192.7663 m F U 0 G 0.3 w 10 M 140.246 192.7663 m S 0 g 1 w 4 M 140.246 192.7663 m F 0 G 0.3 w 10 M 140.246 192.7663 m S 140.246 192.7663 m S 0 g 1 w 4 M 139.1609 191.6984 m 139.1609 188.1213 L 141.3311 188.1213 L 141.3311 191.6984 L 144.9167 191.6872 L 144.9167 193.8456 L 141.3311 193.8345 L 141.3311 197.4116 L 139.1609 197.4116 L 139.1609 193.8345 L 135.5753 193.8456 L 135.5753 191.6872 L 139.1609 191.6984 L f 0 G 0.3 w 10 M 63.2618 192.7663 m S 0 g 1 w 4 M 63.2618 192.7663 m F 0 G 0.3 w 10 M 63.2618 192.7663 m S 63.2618 192.7663 m S 63.2618 192.7663 m S 0 g 1 w 4 M 63.2618 192.7663 m F 0 G 0.3 w 10 M 63.2618 192.7663 m S 63.2618 192.7663 m S u 1 g 1 w 4 M 57.2514 192.7663 m 57.2514 189.5445 59.9424 186.9327 63.2618 186.9327 c 66.5812 186.9327 69.2722 189.5445 69.2722 192.7663 c F 69.2722 192.7663 m 69.2722 195.9881 66.5812 198.5999 63.2618 198.5999 c 59.9424 198.5999 57.2514 195.9881 57.2514 192.7663 c F 63.2618 192.7663 m F U 0 G 0.3 w 10 M 63.2618 192.7663 m S 0 g 1 w 4 M 63.2618 192.7663 m F 0 G 0.3 w 10 M 63.2618 192.7663 m S 63.2618 192.7663 m S 0 g 1 w 4 M 62.1767 191.6984 m 62.1767 188.1213 L 64.3469 188.1213 L 64.3469 191.6984 L 67.9325 191.6872 L 67.9325 193.8456 L 64.3469 193.8345 L 64.3469 197.4116 L 62.1767 197.4116 L 62.1767 193.8345 L 58.5911 193.8456 L 58.5911 191.6872 L 62.1767 191.6984 L f 0 G 0.3 w 10 M 63.2618 117.7445 m S 0 g 1 w 4 M 63.2618 117.7445 m F 0 G 0.3 w 10 M 63.2618 117.7445 m S 63.2618 117.7445 m S 63.2618 117.7445 m S 0 g 1 w 4 M 63.2618 117.7445 m F 0 G 0.3 w 10 M 63.2618 117.7445 m S 63.2618 117.7445 m S u 1 g 1 w 4 M 57.2514 117.7445 m 57.2514 114.5227 59.9424 111.9109 63.2618 111.9109 c 66.5812 111.9109 69.2722 114.5227 69.2722 117.7445 c F 69.2722 117.7445 m 69.2722 120.9663 66.5812 123.5781 63.2618 123.5781 c 59.9424 123.5781 57.2514 120.9663 57.2514 117.7445 c F 63.2618 117.7445 m F U 0 G 0.3 w 10 M 63.2618 117.7445 m S 0 g 1 w 4 M 63.2618 117.7445 m F 0 G 0.3 w 10 M 63.2618 117.7445 m S 63.2618 117.7445 m S 0 g 1 w 4 M 62.1767 116.6766 m 62.1767 113.0995 L 64.3469 113.0995 L 64.3469 116.6766 L 67.9325 116.6654 L 67.9325 118.8238 L 64.3469 118.8127 L 64.3469 122.3898 L 62.1767 122.3898 L 62.1767 118.8127 L 58.5911 118.8238 L 58.5911 116.6654 L 62.1767 116.6766 L f 0 G 0.3 w 10 M 140.246 117.7445 m S 0 g 1 w 4 M 140.246 117.7445 m F 0 G 0.3 w 10 M 140.246 117.7445 m S 140.246 117.7445 m S 140.246 117.7445 m S 0 g 1 w 4 M 140.246 117.7445 m F 0 G 0.3 w 10 M 140.246 117.7445 m S 140.246 117.7445 m S u 1 g 1 w 4 M 134.2356 117.7445 m 134.2356 114.5227 136.9266 111.9109 140.246 111.9109 c 143.5654 111.9109 146.2564 114.5227 146.2564 117.7445 c F 146.2564 117.7445 m 146.2564 120.9663 143.5654 123.5781 140.246 123.5781 c 136.9266 123.5781 134.2356 120.9663 134.2356 117.7445 c F 140.246 117.7445 m F U 0 G 0.3 w 10 M 140.246 117.7445 m S 0 g 1 w 4 M 140.246 117.7445 m F 0 G 0.3 w 10 M 140.246 117.7445 m S 140.246 117.7445 m S 0 g 1 w 4 M 139.1609 116.6766 m 139.1609 113.0995 L 141.3311 113.0995 L 141.3311 116.6766 L 144.9167 116.6654 L 144.9167 118.8238 L 141.3311 118.8127 L 141.3311 122.3898 L 139.1609 122.3898 L 139.1609 118.8127 L 135.5753 118.8238 L 135.5753 116.6654 L 139.1609 116.6766 L f 0 G 0.3 w 10 M 101.754 155.2555 m S 0 g 1 w 4 M 101.754 155.2555 m F 0 G 0.3 w 10 M 101.754 155.2555 m S 101.754 155.2555 m S 101.754 155.2555 m S 0 g 1 w 4 M 101.754 155.2555 m F 0 G 0.3 w 10 M 101.754 155.2555 m S 101.754 155.2555 m S u 1 g 1 w 4 M 95.7436 155.2555 m 95.7436 152.0337 98.4346 149.4219 101.754 149.4219 c 105.0734 149.4219 107.7644 152.0337 107.7644 155.2555 c F 107.7644 155.2555 m 107.7644 158.4773 105.0734 161.0891 101.754 161.0891 c 98.4346 161.0891 95.7436 158.4773 95.7436 155.2555 c F 101.754 155.2555 m F U 0 G 0.3 w 10 M 101.754 155.2555 m S 0 g 1 w 4 M 101.754 155.2555 m F 0 G 0.3 w 10 M 101.754 155.2555 m S 101.754 155.2555 m S 0 g 1 w 4 M 100.6689 154.1876 m 100.6689 150.6105 L 102.8391 150.6105 L 102.8391 154.1876 L 106.4247 154.1764 L 106.4247 156.3348 L 102.8391 156.3237 L 102.8391 159.9008 L 100.6689 159.9008 L 100.6689 156.3237 L 97.0833 156.3348 L 97.0833 154.1764 L 100.6689 154.1876 L f 0 G 0.3 w 10 M 101.754 80.2337 m S 0 g 1 w 4 M 101.754 80.2337 m F 0 G 0.3 w 10 M 101.754 80.2337 m S 101.754 80.2337 m S 101.754 80.2337 m S 0 g 1 w 4 M 101.754 80.2337 m F 0 G 0.3 w 10 M 101.754 80.2337 m S 101.754 80.2337 m S u 1 g 1 w 4 M 95.7436 80.2337 m 95.7436 77.0119 98.4346 74.4001 101.754 74.4001 c 105.0734 74.4001 107.7644 77.0119 107.7644 80.2337 c F 107.7644 80.2337 m 107.7644 83.4555 105.0734 86.0673 101.754 86.0673 c 98.4346 86.0673 95.7436 83.4555 95.7436 80.2337 c F 101.754 80.2337 m F U 0 G 0.3 w 10 M 101.754 80.2337 m S 0 g 1 w 4 M 101.754 80.2337 m F 0 G 0.3 w 10 M 101.754 80.2337 m S 101.754 80.2337 m S 0 g 1 w 4 M 100.6689 79.1658 m 100.6689 75.5887 L 102.8391 75.5887 L 102.8391 79.1658 L 106.4247 79.1546 L 106.4247 81.313 L 102.8391 81.3019 L 102.8391 84.879 L 100.6689 84.879 L 100.6689 81.3019 L 97.0833 81.313 L 97.0833 79.1546 L 100.6689 79.1658 L f 0 G 0.3 w 10 M 178.7381 80.2337 m S 0 g 1 w 4 M 178.7381 80.2337 m F 0 G 0.3 w 10 M 178.7381 80.2337 m S 178.7381 80.2337 m S 178.7381 80.2337 m S 0 g 1 w 4 M 178.7381 80.2337 m F 0 G 0.3 w 10 M 178.7381 80.2337 m S 178.7381 80.2337 m S u 1 g 1 w 4 M 172.7277 80.2337 m 172.7277 77.0119 175.4187 74.4001 178.7381 74.4001 c 182.0575 74.4001 184.7485 77.0119 184.7485 80.2337 c F 184.7485 80.2337 m 184.7485 83.4555 182.0575 86.0673 178.7381 86.0673 c 175.4187 86.0673 172.7277 83.4555 172.7277 80.2337 c F 178.7381 80.2337 m F U 0 G 0.3 w 10 M 178.7381 80.2337 m S 0 g 1 w 4 M 178.7381 80.2337 m F 0 G 0.3 w 10 M 178.7381 80.2337 m S 178.7381 80.2337 m S 0 g 1 w 4 M 177.653 79.1658 m 177.653 75.5887 L 179.8232 75.5887 L 179.8232 79.1658 L 183.4088 79.1546 L 183.4088 81.313 L 179.8232 81.3019 L 179.8232 84.879 L 177.653 84.879 L 177.653 81.3019 L 174.0674 81.313 L 174.0674 79.1546 L 177.653 79.1658 L f 0 G 0.3 w 10 M 178.7381 155.2555 m S 0 g 1 w 4 M 178.7381 155.2555 m F 0 G 0.3 w 10 M 178.7381 155.2555 m S 178.7381 155.2555 m S 178.7381 155.2555 m S 0 g 1 w 4 M 178.7381 155.2555 m F 0 G 0.3 w 10 M 178.7381 155.2555 m S 178.7381 155.2555 m S u 1 g 1 w 4 M 172.7277 155.2555 m 172.7277 152.0337 175.4187 149.4219 178.7381 149.4219 c 182.0575 149.4219 184.7485 152.0337 184.7485 155.2555 c F 184.7485 155.2555 m 184.7485 158.4773 182.0575 161.0891 178.7381 161.0891 c 175.4187 161.0891 172.7277 158.4773 172.7277 155.2555 c F 178.7381 155.2555 m F U 0 G 0.3 w 10 M 178.7381 155.2555 m S 0 g 1 w 4 M 178.7381 155.2555 m F 0 G 0.3 w 10 M 178.7381 155.2555 m S 178.7381 155.2555 m S 0 g 1 w 4 M 177.653 154.1876 m 177.653 150.6105 L 179.8232 150.6105 L 179.8232 154.1876 L 183.4088 154.1764 L 183.4088 156.3348 L 179.8232 156.3237 L 179.8232 159.9008 L 177.653 159.9008 L 177.653 156.3237 L 174.0674 156.3348 L 174.0674 154.1764 L 177.653 154.1876 L f u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 114 34.5]e (\(a\))t T U U showpage _E end %%EndDocument @endspecial 777 x @beginspecial 21 @llx 32.500000 @lly 211 @urx 226.500000 @ury 1537 @rwi @setspecial %%BeginDocument: fig3b.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Italic/Times-Italic Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 44.0158 191.7663 m 44.0158 210.5217 L 63.2618 210.5217 L S 53.6388 201.144 m S 82.5079 154.2555 m 82.5079 173.0108 L 101.754 173.0108 L S 92.131 163.6332 m S 82.5079 191.7663 m 82.5079 173.0108 L 63.2618 173.0108 L S 72.8849 182.3886 m S 63.2618 210.5217 m 82.5079 210.5217 L 82.5079 191.7663 L S 72.8849 201.144 m S 82.5079 191.7663 m 82.5079 210.5217 L 101.754 210.5217 L S 92.131 201.144 m S 63.2618 173.0108 m 82.5079 173.0108 L 82.5079 154.2555 L S 72.8849 163.6332 m S 44.0158 154.2555 m 44.0158 173.0108 L 63.2618 173.0108 L S 53.6388 163.6332 m S 63.2618 173.0108 m 44.0158 173.0108 L 44.0158 191.7663 L S 53.6388 182.3886 m S 101.754 210.5217 m 121 210.5217 L 121 191.7663 L S 111.377 201.144 m S 101.754 173.0108 m 121 173.0108 L 121 154.2555 L S 111.377 163.6332 m S 63.2618 135.5 m 44.0158 135.5 L 44.0158 154.2555 L S 53.6388 144.8777 m S 82.5079 154.2555 m 82.5079 135.5 L 63.2618 135.5 L S 72.8849 144.8777 m S 101.754 135.5 m 82.5079 135.5 L 82.5079 154.2555 L S 92.131 144.8777 m S 121 154.2555 m 121 135.5 L 101.754 135.5 L S 111.377 144.8777 m S 101.754 135.5 m 121 135.5 L S 121 191.7663 m 121 210.5217 L 140.246 210.5217 L S 130.623 201.144 m S 159.4921 154.2555 m 159.4921 173.0108 L 178.7381 173.0108 L S 169.1151 163.6332 m S 159.4921 191.7663 m 159.4921 173.0108 L 140.246 173.0108 L S 149.8691 182.3886 m S 140.246 210.5217 m 159.4921 210.5217 L 159.4921 191.7663 L S 149.8691 201.144 m S 159.4921 191.7663 m 159.4921 210.5217 L 178.7381 210.5217 L S 169.1151 201.144 m S 178.7381 173.0108 m 159.4921 173.0108 L 159.4921 191.7663 L S 169.1151 182.3886 m S 140.246 173.0108 m 159.4921 173.0108 L 159.4921 154.2555 L S 149.8691 163.6332 m S 121 154.2555 m 121 173.0108 L 140.246 173.0108 L S 130.623 163.6332 m S 140.246 173.0108 m 121 173.0108 L 121 191.7663 L S 130.623 182.3886 m S 178.7381 210.5217 m 197.9842 210.5217 L 197.9842 191.7663 L S 188.3611 201.144 m S 178.7381 173.0108 m 197.9842 173.0108 L 197.9842 154.2555 L S 188.3611 163.6332 m S 197.9842 191.7663 m 197.9842 173.0108 L 178.7381 173.0108 L S 188.3611 182.3886 m S 140.246 135.5 m 121 135.5 L 121 154.2555 L S 130.623 144.8777 m S 159.4921 154.2555 m 159.4921 135.5 L 140.246 135.5 L S 149.8691 144.8777 m S 178.7381 135.5 m 159.4921 135.5 L 159.4921 154.2555 L S 169.1151 144.8777 m S 197.9842 154.2555 m 197.9842 135.5 L 178.7381 135.5 L S 188.3611 144.8777 m S 178.7381 135.5 m 197.9842 135.5 L S 44.0158 116.7445 m 44.0158 135.5 L 63.2618 135.5 L S 53.6388 126.1223 m S 82.5079 79.2337 m 82.5079 97.9891 L 101.754 97.9891 L S 92.131 88.6114 m S 82.5079 116.7445 m 82.5079 97.9891 L 63.2618 97.9891 L S 72.8849 107.3668 m S 63.2618 135.5 m 82.5079 135.5 L 82.5079 116.7445 L S 72.8849 126.1223 m S 82.5079 116.7445 m 82.5079 135.5 L 101.754 135.5 L S 92.131 126.1223 m S 101.754 97.9891 m 82.5079 97.9891 L 82.5079 116.7445 L S 92.131 107.3668 m S 63.2618 97.9891 m 82.5079 97.9891 L 82.5079 79.2337 L S 72.8849 88.6114 m S 44.0158 79.2337 m 44.0158 97.9891 L 63.2618 97.9891 L S 53.6388 88.6114 m S 63.2618 97.9891 m 44.0158 97.9891 L 44.0158 116.7445 L S 53.6388 107.3668 m S 101.754 135.5 m 121 135.5 L 121 116.7445 L S 111.377 126.1223 m S 101.754 97.9891 m 121 97.9891 L 121 79.2337 L S 111.377 88.6114 m S 121 116.7445 m 121 97.9891 L 101.754 97.9891 L S 111.377 107.3668 m S 63.2618 60.4783 m 44.0158 60.4783 L 44.0158 79.2337 L S 53.6388 69.856 m S 82.5079 79.2337 m 82.5079 60.4783 L 63.2618 60.4783 L S 72.8849 69.856 m S 101.754 60.4783 m 82.5079 60.4783 L 82.5079 79.2337 L S 92.131 69.856 m S 121 79.2337 m 121 60.4783 L 101.754 60.4783 L S 111.377 69.856 m S 101.754 60.4783 m 121 60.4783 L S 121 116.7445 m 121 135.5 L 140.246 135.5 L S 130.623 126.1223 m S 159.4921 79.2337 m 159.4921 97.9891 L 178.7381 97.9891 L S 169.1151 88.6114 m S 159.4921 116.7445 m 159.4921 97.9891 L 140.246 97.9891 L S 149.8691 107.3668 m S 140.246 135.5 m 159.4921 135.5 L 159.4921 116.7445 L S 149.8691 126.1223 m S 159.4921 116.7445 m 159.4921 135.5 L 178.7381 135.5 L S 169.1151 126.1223 m S 178.7381 97.9891 m 159.4921 97.9891 L 159.4921 116.7445 L S 169.1151 107.3668 m S 140.246 97.9891 m 159.4921 97.9891 L 159.4921 79.2337 L S 149.8691 88.6114 m S 121 79.2337 m 121 97.9891 L 140.246 97.9891 L S 130.623 88.6114 m S 140.246 97.9891 m 121 97.9891 L 121 116.7445 L S 130.623 107.3668 m S 178.7381 135.5 m 197.9842 135.5 L 197.9842 116.7445 L S 188.3611 126.1223 m S 178.7381 97.9891 m 197.9842 97.9891 L 197.9842 79.2337 L S 188.3611 88.6114 m S 197.9842 116.7445 m 197.9842 97.9891 L 178.7381 97.9891 L S 188.3611 107.3668 m S 140.246 60.4783 m 121 60.4783 L 121 79.2337 L S 130.623 69.856 m S 159.4921 79.2337 m 159.4921 60.4783 L 140.246 60.4783 L S 149.8691 69.856 m S 178.7381 60.4783 m 159.4921 60.4783 L 159.4921 79.2337 L S 169.1151 69.856 m S 197.9842 79.2337 m 197.9842 60.4783 L 178.7381 60.4783 L S 188.3611 69.856 m S 178.7381 60.4783 m 197.9842 60.4783 L S 43.875 191.5 m 48.875 191.5 L S 77.5079 191.7663 m 82.5079 191.7663 L S 82.5079 191.7663 m 87.508 191.7663 L S 115.9999 191.7663 m 121 191.7663 L S 121 191.7663 m 126 191.7663 L S 154.4921 191.7663 m 159.4921 191.7663 L S 159.4921 191.7663 m 164.4922 191.7663 L S 192.9841 191.7663 m 197.9842 191.7663 L S 192.9841 154.2555 m 197.9842 154.2555 L S 154.4921 154.2555 m 159.4921 154.2555 L S 159.4921 154.2555 m 164.4922 154.2555 L S 116.3749 154.25 m 121.375 154.25 L S 121.375 154.25 m 126.375 154.25 L S 77.5079 154.2555 m 82.5079 154.2555 L S 82.5079 154.2555 m 87.508 154.2555 L S 44.0158 154.2555 m 49.0159 154.2555 L S 44.0158 116.7445 m 49.0159 116.7445 L S 77.5079 116.7445 m 82.5079 116.7445 L S 82.5079 116.7445 m 87.508 116.7445 L S 115.9999 116.7445 m 121 116.7445 L S 121 116.7445 m 126 116.7445 L S 154.4921 116.7445 m 159.4921 116.7445 L S 159.4921 116.7445 m 164.4922 116.7445 L S 192.9841 116.7445 m 197.9842 116.7445 L S 192.9841 79.2337 m 197.9842 79.2337 L S 154.4921 79.2337 m 159.4921 79.2337 L S 159.4921 79.2337 m 164.4922 79.2337 L S 115.9999 79.2337 m 121 79.2337 L S 121 79.2337 m 126 79.2337 L S 77.5079 79.2337 m 82.5079 79.2337 L S 82.5079 79.2337 m 87.508 79.2337 L S 44.0158 79.2337 m 49.0159 79.2337 L S 63.2618 60.4783 m 63.2618 65.4783 L S 63.2618 92.9891 m 63.2618 97.9891 L S 63.2618 97.9891 m 63.2618 102.9892 L S 101.754 60.4783 m 101.754 65.4783 L S 101.754 92.9891 m 101.754 97.9891 L S 101.754 97.9891 m 101.754 102.9892 L S 140.246 60.4783 m 140.246 65.4783 L S 140.246 92.9891 m 140.246 97.9891 L S 140.246 97.9891 m 140.246 102.9892 L S 178.7381 60.4783 m 178.7381 65.4783 L S 178.7381 92.9891 m 178.7381 97.9891 L S 178.7381 97.9891 m 178.7381 102.9892 L S 178.7381 130.5 m 178.7381 135.5 L S 178.7381 135.5 m 178.7381 140.5001 L S 140.246 130.5 m 140.246 135.5 L S 140.246 135.5 m 140.246 140.5001 L S 178.7381 168.0108 m 178.7381 173.0108 L S 178.7381 173.0108 m 178.7381 178.0109 L S 140.246 168.0108 m 140.246 173.0108 L S 140.246 173.0108 m 140.246 178.0109 L S 101.754 130.5 m 101.754 135.5 L S 101.754 135.5 m 101.754 140.5001 L S 63.2618 130.5 m 63.2618 135.5 L S 63.2618 135.5 m 63.2618 140.5001 L S 63.2618 168.0108 m 63.2618 173.0108 L S 63.2618 173.0108 m 63.2618 178.0109 L S 101.754 168.0108 m 101.754 173.0108 L S 101.754 173.0108 m 101.754 178.0109 L S 63.2618 205.5217 m 63.2618 210.5217 L S 101.75 205.25 m 101.75 210.25 L S 140.246 205.5217 m 140.246 210.5217 L S 178.7381 205.5217 m 178.7381 210.5217 L S 38.875 191.5 m 43.875 191.5 L S 43.875 191.5 m 48.8751 191.5 L S 34.0157 210.5217 m 39.0157 210.5217 L S 39.0157 210.5217 m 44.0158 210.5217 L S 34.0157 173.0108 m 39.0157 173.0108 L S 39.0157 173.0108 m 44.0158 173.0108 L S 39.0158 154.2555 m 44.0158 154.2555 L S 44.0158 154.2555 m 49.0159 154.2555 L S 34.0157 135.5 m 39.0157 135.5 L S 39.0157 135.5 m 44.0158 135.5 L S 39.0158 116.7445 m 44.0158 116.7445 L S 44.0158 116.7445 m 49.0159 116.7445 L S 39.0158 79.2337 m 44.0158 79.2337 L S 44.0158 79.2337 m 49.0159 79.2337 L S 34.0157 97.9891 m 39.0157 97.9891 L S 39.0157 97.9891 m 44.0158 97.9891 L S 34.0157 60.4783 m 39.0157 60.4783 L S 39.0157 60.4783 m 44.0158 60.4783 L S 197.9842 210.5217 m 202.9842 210.5217 L S 202.9842 210.5217 m 207.9843 210.5217 L S 192.9842 191.7663 m 197.9842 191.7663 L S 197.9842 191.7663 m 202.9843 191.7663 L S 197.9842 173.0108 m 202.9842 173.0108 L S 202.9842 173.0108 m 207.9843 173.0108 L S 192.9842 154.2555 m 197.9842 154.2555 L S 197.9842 154.2555 m 202.9843 154.2555 L S 197.9842 135.5 m 202.9842 135.5 L S 202.9842 135.5 m 207.9843 135.5 L S 192.9842 116.7445 m 197.9842 116.7445 L S 197.9842 116.7445 m 202.9843 116.7445 L S 192.9842 79.2337 m 197.9842 79.2337 L S 197.9842 79.2337 m 202.9843 79.2337 L S 197.9842 97.9891 m 202.9842 97.9891 L S 202.9842 97.9891 m 207.9843 97.9891 L S 197.9842 60.4783 m 202.9842 60.4783 L S 202.9842 60.4783 m 207.9843 60.4783 L S 44.0158 210.5217 m 44.0081 215.5217 L S 44.0081 215.5217 m 44.0004 220.5218 L S 63.2695 205.5217 m 63.2618 210.5217 L S 63.2618 210.5217 m 63.2541 215.5218 L S 121 210.5217 m 120.9923 215.5217 L S 120.9923 215.5217 m 120.9846 220.5218 L S 82.5079 210.5217 m 82.5002 215.5217 L S 82.5002 215.5217 m 82.4925 220.5218 L S 101.7577 205.25 m 101.75 210.25 L S 101.75 210.25 m 101.7423 215.2501 L S 140.2537 205.5217 m 140.246 210.5217 L S 140.246 210.5217 m 140.2383 215.5218 L S 178.7458 205.5217 m 178.7381 210.5217 L S 178.7381 210.5217 m 178.7304 215.5218 L S 159.4921 210.5217 m 159.4844 215.5217 L S 159.4844 215.5217 m 159.4767 220.5218 L S 197.9842 210.5217 m 197.9765 215.5217 L S 197.9765 215.5217 m 197.9688 220.5218 L S 197.9996 50.4782 m 197.9919 55.4782 L S 197.9919 55.4782 m 197.9842 60.4783 L S 159.5075 50.4782 m 159.4998 55.4782 L S 159.4998 55.4782 m 159.4921 60.4783 L S 178.7458 55.4783 m 178.7381 60.4783 L S 178.7381 60.4783 m 178.7304 65.4784 L S 140.2537 55.4783 m 140.246 60.4783 L S 140.246 60.4783 m 140.2383 65.4784 L S 121.0154 50.4782 m 121.0077 55.4782 L S 121.0077 55.4782 m 121 60.4783 L S 101.7617 55.4783 m 101.754 60.4783 L S 101.754 60.4783 m 101.7463 65.4784 L S 82.5233 50.4782 m 82.5156 55.4782 L S 82.5156 55.4782 m 82.5079 60.4783 L S 63.2695 55.4783 m 63.2618 60.4783 L S 63.2618 60.4783 m 63.2541 65.4784 L S 44.0312 50.4782 m 44.0235 55.4782 L S 44.0235 55.4782 m 44.0158 60.4783 L S u u 0 g 1 w 4 M /_Times-Italic 12 14.5 0 0 z [1 0 0 1 51.5 215]e (J)t T U U u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 71 214.5]e (J)t T U U u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 33 198]e (J)t T U U u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 33.5 180.5]e (J)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 114.5 35.5]e (\(b\))t T U U showpage _E end %%EndDocument @endspecial 788 x @beginspecial 27 @llx 34.500000 @lly 229 @urx 244.500000 @ury 1537 @rwi @setspecial %%BeginDocument: fig3c.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Italic/Times-Italic Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 53.0158 203.7663 m 53.0158 222.5217 L 72.2618 222.5217 L S 62.6388 213.144 m S 91.5079 166.2555 m 91.5079 185.0108 L 110.754 185.0108 L S 101.131 175.6332 m S 91.5079 203.7663 m 91.5079 185.0108 L 72.2618 185.0108 L S 81.8849 194.3886 m S 72.2618 222.5217 m 91.5079 222.5217 L 91.5079 203.7663 L S 81.8849 213.144 m S 91.5079 203.7663 m 91.5079 222.5217 L 110.754 222.5217 L S 101.131 213.144 m S 110.754 185.0108 m 91.5079 185.0108 L 91.5079 203.7663 L S 101.131 194.3886 m S 72.2618 185.0108 m 91.5079 185.0108 L 91.5079 166.2555 L S 81.8849 175.6332 m S 53.0158 166.2555 m 53.0158 185.0108 L 72.2618 185.0108 L S 62.6388 175.6332 m S 72.2618 185.0108 m 53.0158 185.0108 L 53.0158 203.7663 L S 62.6388 194.3886 m S 110.754 222.5217 m 130 222.5217 L 130 203.7663 L S 120.377 213.144 m S 110.754 185.0108 m 130 185.0108 L 130 166.2555 L S 120.377 175.6332 m S 130 203.7663 m 130 185.0108 L 110.754 185.0108 L S 120.377 194.3886 m S 72.2618 147.5 m 53.0158 147.5 L 53.0158 166.2555 L S 62.6388 156.8777 m S 91.5079 166.2555 m 91.5079 147.5 L 72.2618 147.5 L S 81.8849 156.8777 m S 110.754 147.5 m 91.5079 147.5 L 91.5079 166.2555 L S 101.131 156.8777 m S 130 166.2555 m 130 147.5 L 110.754 147.5 L S 120.377 156.8777 m S 110.754 147.5 m 130 147.5 L S 130 203.7663 m 130 222.5217 L 149.246 222.5217 L S 139.623 213.144 m S 168.4921 166.2555 m 168.4921 185.0108 L 187.7381 185.0108 L S 178.1151 175.6332 m S 168.4921 203.7663 m 168.4921 185.0108 L 149.246 185.0108 L S 158.8691 194.3886 m S 149.246 222.5217 m 168.4921 222.5217 L 168.4921 203.7663 L S 158.8691 213.144 m S 168.4921 203.7663 m 168.4921 222.5217 L 187.7381 222.5217 L S 178.1151 213.144 m S 187.7381 185.0108 m 168.4921 185.0108 L 168.4921 203.7663 L S 178.1151 194.3886 m S 149.246 185.0108 m 168.4921 185.0108 L 168.4921 166.2555 L S 158.8691 175.6332 m S 130 166.2555 m 130 185.0108 L 149.246 185.0108 L S 139.623 175.6332 m S 149.246 185.0108 m 130 185.0108 L 130 203.7663 L S 139.623 194.3886 m S 187.7381 222.5217 m 206.9842 222.5217 L 206.9842 203.7663 L S 197.3611 213.144 m S 187.7381 185.0108 m 206.9842 185.0108 L 206.9842 166.2555 L S 197.3611 175.6332 m S 206.9842 203.7663 m 206.9842 185.0108 L 187.7381 185.0108 L S 197.3611 194.3886 m S 149.246 147.5 m 130 147.5 L 130 166.2555 L S 139.623 156.8777 m S 168.4921 166.2555 m 168.4921 147.5 L 149.246 147.5 L S 158.8691 156.8777 m S 187.7381 147.5 m 168.4921 147.5 L 168.4921 166.2555 L S 178.1151 156.8777 m S 206.9842 166.2555 m 206.9842 147.5 L 187.7381 147.5 L S 197.3611 156.8777 m S 187.7381 147.5 m 206.9842 147.5 L S 53.0158 128.7445 m 53.0158 147.5 L 72.2618 147.5 L S 62.6388 138.1223 m S 91.5079 91.2337 m 91.5079 109.9891 L 110.754 109.9891 L S 101.131 100.6114 m S 91.5079 128.7445 m 91.5079 109.9891 L 72.2618 109.9891 L S 81.8849 119.3668 m S 72.2618 147.5 m 91.5079 147.5 L 91.5079 128.7445 L S 81.8849 138.1223 m S 91.5079 128.7445 m 91.5079 147.5 L 110.754 147.5 L S 101.131 138.1223 m S 110.754 109.9891 m 91.5079 109.9891 L 91.5079 128.7445 L S 101.131 119.3668 m S 72.2618 109.9891 m 91.5079 109.9891 L 91.5079 91.2337 L S 81.8849 100.6114 m S 53.0158 91.2337 m 53.0158 109.9891 L 72.2618 109.9891 L S 62.6388 100.6114 m S 72.2618 109.9891 m 53.0158 109.9891 L 53.0158 128.7445 L S 62.6388 119.3668 m S 110.754 147.5 m 130 147.5 L 130 128.7445 L S 120.377 138.1223 m S 110.754 109.9891 m 130 109.9891 L 130 91.2337 L S 120.377 100.6114 m S 130 128.7445 m 130 109.9891 L 110.754 109.9891 L S 120.377 119.3668 m S 72.2618 72.4783 m 53.0158 72.4783 L 53.0158 91.2337 L S 62.6388 81.856 m S 91.5079 91.2337 m 91.5079 72.4783 L 72.2618 72.4783 L S 81.8849 81.856 m S 110.754 72.4783 m 91.5079 72.4783 L 91.5079 91.2337 L S 101.131 81.856 m S 130 91.2337 m 130 72.4783 L 110.754 72.4783 L S 120.377 81.856 m S 110.754 72.4783 m 130 72.4783 L S 130 128.7445 m 130 147.5 L 149.246 147.5 L S 139.623 138.1223 m S 168.4921 91.2337 m 168.4921 109.9891 L 187.7381 109.9891 L S 178.1151 100.6114 m S 168.4921 128.7445 m 168.4921 109.9891 L 149.246 109.9891 L S 158.8691 119.3668 m S 149.246 147.5 m 168.4921 147.5 L 168.4921 128.7445 L S 158.8691 138.1223 m S 168.4921 128.7445 m 168.4921 147.5 L 187.7381 147.5 L S 178.1151 138.1223 m S 187.7381 109.9891 m 168.4921 109.9891 L 168.4921 128.7445 L S 178.1151 119.3668 m S 149.246 109.9891 m 168.4921 109.9891 L 168.4921 91.2337 L S 158.8691 100.6114 m S 130 91.2337 m 130 109.9891 L 149.246 109.9891 L S 139.623 100.6114 m S 149.246 109.9891 m 130 109.9891 L 130 128.7445 L S 139.623 119.3668 m S 187.7381 147.5 m 206.9842 147.5 L 206.9842 128.7445 L S 197.3611 138.1223 m S 187.7381 109.9891 m 206.9842 109.9891 L 206.9842 91.2337 L S 197.3611 100.6114 m S 206.9842 128.7445 m 206.9842 109.9891 L 187.7381 109.9891 L S 197.3611 119.3668 m S 149.246 72.4783 m 130 72.4783 L 130 91.2337 L S 139.623 81.856 m S 168.4921 91.2337 m 168.4921 72.4783 L 149.246 72.4783 L S 158.8691 81.856 m S 187.7381 72.4783 m 168.4921 72.4783 L 168.4921 91.2337 L S 178.1151 81.856 m S 206.9842 91.2337 m 206.9842 72.4783 L 187.7381 72.4783 L S 197.3611 81.856 m S 187.7381 72.4783 m 206.9842 72.4783 L S 33.7698 222.5217 m 53.0158 222.5217 L S 33.7698 185.0108 m 53.0158 185.0108 L S 33.7698 147.5 m 53.0158 147.5 L S 33.7698 109.9891 m 53.0158 109.9891 L S 33.7698 72.4783 m 53.0158 72.4783 L S 206.9842 222.5217 m 226.2302 222.5217 L S 206.9842 185.0108 m 226.2302 185.0108 L S 206.9842 147.5 m 226.2302 147.5 L S 206.9842 109.9891 m 226.2302 109.9891 L S 206.9842 72.4783 m 226.2302 72.4783 L S 206.9842 72.4783 m 206.9818 53.2323 L S 168.4921 72.4783 m 168.4897 53.2323 L S 130 72.4783 m 129.9976 53.2323 L S 91.5079 72.4783 m 91.5055 53.2323 L S 53.0158 72.4783 m 53.0134 53.2323 L S 53.0181 241.7677 m 53.0158 222.5217 L S 91.5102 241.7677 m 91.5079 222.5217 L S 130.0023 241.7677 m 130 222.5217 L S 168.4944 241.7677 m 168.4921 222.5217 L S 206.9865 241.7677 m 206.9842 222.5217 L S u u 0 g 1 w 4 M /_Times-Italic 12 14.5 0 0 z [1 0 0 1 68.5 228.5]e (J')t T U U u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 39 203]e (J')t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 124.5 37.5]e (\(c\))t T U U showpage _E end %%EndDocument @endspecial 60 2578 a FQ(Figure)19 b(3:)27 b(\(a\))19 b(The)h(fully)e (alternating)h(image-spin)f(con\014guration)i FF(!)1410 2560 y Fy(0)1408 2591 y FD(alt)1453 2578 y FQ(.)30 b(\(b\))19 b(The)g(decorated)60 2639 y(system)c(of)h(in)o(ternal)g(spins.)21 b(\(c\))16 b(The)g(equiv)m(alen) o(t)f(nearest-neigh)o(b)q(or)i(in)o(teraction)e(on)i(\(2)p Fq(Z)p FQ(\))1781 2621 y FH(2)1801 2639 y FQ(.)951 2784 y(95)p eop %%Page: 96 96 bop 133 91 a FP(Step)18 b(2.)k(Study)17 b(of)g(a)g(neighb)n(orho)n(o)n(d)f (of)h FF(!)915 73 y Fy(0)913 104 y FH(sp)q(ecial)1033 91 y FQ(=)c FF(!)1116 73 y Fy(0)1114 104 y FD(alt)1159 91 y FP(.)22 b FQ(The)15 b(next)h(step)f(is)h(to)g(study)g(image-)60 152 y(spin)g(con\014gurations)i(in)d(a)i(neigh)o(b)q(orho)q(o)q(d)h(\(in)e(the)g (pro)q(duct)g(top)q(ology\))i(of)e FF(!)1530 133 y Fy(0)1528 164 y FD(alt)1573 152 y FQ(.)21 b(T)l(o)c(sho)o(w)g(that)60 212 y(the)j(order)g(parameter)e FE(h)p FF(\033)562 219 y FD(i)576 212 y FE(i)595 219 y FD(!)618 210 y Ft(0)652 212 y FQ(is)i(an)g(essen)o (tially)e(discon)o(tin)o(uous)i(function)f(of)i(the)e(image-spin)60 272 y(con\014guration)c FF(!)385 254 y Fy(0)397 272 y FQ(,)f(it)g(su\016ces)f (to)i(sho)o(w)f(that)h(there)e(exists)h(a)g(constan)o(t)h FF(\016)g(>)f FQ(0)g(suc)o(h)g(that)h(in)f(eac)o(h)60 332 y(neigh)o(b)q(orho)q(o)q(d)20 b(of)f FF(!)458 314 y Fy(0)456 344 y FD(alt)519 332 y FQ(the)e(essen)o(tial)h (oscillation)f(of)h FE(h)p FF(\033)1137 339 y FD(i)1152 332 y FE(i)1171 339 y FD(!)1194 330 y Ft(0)1226 332 y FQ(is)g(at)g(least)g FF(\016)r FQ(.)26 b(More)18 b(precisely)l(,)e(it)60 392 y(su\016ces)f(to)h (sho)o(w)g(that)g(there)f(exists)h FF(\016)f(>)f FQ(0)i(suc)o(h)f(that)h(in)f (eac)o(h)g(neigh)o(b)q(orho)q(o)q(d)j FE(N)j(3)14 b FF(!)1723 374 y Fy(0)1721 405 y FD(alt)1782 392 y FQ(there)60 452 y(exist)i(nonempt)o (y)f(op)q(en)j(sets)f FE(N)660 459 y FH(+)689 452 y FF(;)8 b FE(N)752 459 y Fy(\000)796 452 y FE(\032)15 b(N)24 b FQ(and)18 b(constan)o(ts)f FF(c)1248 459 y FH(+)1293 452 y FF(>)d(c)1366 459 y Fy(\000)1413 452 y FQ(with)j FF(c)1546 459 y FH(+)1587 452 y FE(\000)11 b FF(c)1658 459 y Fy(\000)1702 452 y FE(\025)k FF(\016)j FQ(suc)o(h)60 513 y(that)587 619 y FE(h)p FF(\033)634 626 y FD(i)648 619 y FE(i)667 626 y FD(!)690 617 y Ft(0)745 619 y FE(\025)42 b FF(c)847 626 y FH(+)974 619 y FQ(whenev)o(er)15 b FF(!)1220 599 y Fy(0)1246 619 y FE(2)f(N)1334 626 y FH(+)1765 619 y FQ(\(4.3a\))587 692 y FE(h)p FF(\033)634 699 y FD(i)648 692 y FE(i)667 699 y FD(!)690 690 y Ft(0)745 692 y FE(\024)42 b FF(c)847 699 y Fy(\000)974 692 y FQ(whenev)o(er)15 b FF(!)1220 671 y Fy(0)1246 692 y FE(2)f(N)1334 699 y Fy(\000)1763 692 y FQ(\(4.3b\))60 798 y(No)o(w)i(a)h(basis)f(for)h(the)f(neigh)o(b)q(orho)q(o) q(ds)i FE(N)j(3)15 b FF(!)957 780 y Fy(0)955 811 y FD(alt)1016 798 y FQ(is)h(giv)o(en)f(b)o(y)h(sets)g(of)h(the)f(form)350 905 y FE(N)391 912 y FD(R)447 905 y FQ(=)28 b FE(f)p FF(!)570 884 y Fy(0)582 905 y FQ(:)21 b FF(!)649 884 y Fy(0)675 905 y FQ(=)14 b FF(!)759 884 y Fy(0)757 917 y FD(alt)818 905 y FQ(on)j(\003)920 912 y FD(R)948 905 y FF(;)22 b(!)1016 884 y Fy(0)1042 905 y FQ(=)30 b(arbitrary)16 b(outside)g(\003)1519 912 y FD(R)1548 905 y FE(g)e FF(;)189 b FQ(\(4)p FF(:)p FQ(4\))60 1011 y(where)21 b(\003)240 1018 y FD(R)289 1011 y FQ(is)g(a)g(square)g(of)h (side)e(2)p FF(R)15 b FQ(+)g(1)21 b(cen)o(tered)e(at)j(the)e(origin)h(\(here) g FF(R)g FQ(is)g(an)g FP(unprime)n(d)60 1072 y FQ(distance\).)g(W)l(e)16 b(shall)g(tak)o(e)g FE(N)633 1079 y FH(+)662 1072 y FF(;)8 b FE(N)725 1079 y Fy(\000)771 1072 y FQ(to)16 b(b)q(e)h(sets)f(of)g(the)g (form)64 1178 y FE(N)105 1185 y FD(R;R)169 1176 y Ft(0)179 1185 y FD(;)p FH(+)260 1178 y FQ(=)41 b FE(f)p FF(!)396 1158 y Fy(0)408 1178 y FQ(:)22 b FF(!)476 1158 y Fy(0)501 1178 y FQ(=)14 b FF(!)585 1158 y Fy(0)583 1190 y FD(alt)644 1178 y FQ(on)j(\003)746 1185 y FD(R)775 1178 y FF(;)k(!)842 1158 y Fy(0)868 1178 y FQ(=)14 b(+1)i(on)h(\003)1100 1185 y FD(R)1127 1176 y Ft(0)1151 1178 y FE(n)11 b FQ(\003)1221 1185 y FD(R)1250 1178 y FF(;)21 b(!)1317 1158 y Fy(0)1343 1178 y FQ(=)30 b(arbitrary)16 b(outside)h(\003)1821 1185 y FD(R)1848 1176 y Ft(0)1861 1178 y FE(g)1765 1251 y FQ(\(4.5a\))64 1323 y FE(N)105 1330 y FD(R;R)169 1321 y Ft(0)179 1330 y FD(;)p Fy(\000)260 1323 y FQ(=)41 b FE(f)p FF(!)396 1303 y Fy(0)408 1323 y FQ(:)22 b FF(!)476 1303 y Fy(0)501 1323 y FQ(=)14 b FF(!)585 1303 y Fy(0)583 1336 y FD(alt)644 1323 y FQ(on)j(\003)746 1330 y FD(R)775 1323 y FF(;)k(!)842 1303 y Fy(0)868 1323 y FQ(=)14 b FE(\000)p FQ(1)i(on)h(\003)1101 1330 y FD(R)1128 1321 y Ft(0)1152 1323 y FE(n)11 b FQ(\003)1222 1330 y FD(R)1251 1323 y FF(;)21 b(!)1318 1303 y Fy(0)1344 1323 y FQ(=)30 b(arbitrary)16 b(outside)h(\003)1822 1330 y FD(R)1849 1321 y Ft(0)1861 1323 y FE(g)1763 1396 y FQ(\(4.5b\))60 1503 y(with)22 b FF(R)214 1485 y Fy(0)249 1503 y FQ(c)o(hosen)g(appropriately)h (as)g(a)g(function)f(of)h FF(R)g FQ(\()p FF(R)i(<)g(R)1333 1485 y Fy(0)1369 1503 y FF(<)g FE(1)p FQ(\).)40 b(The)22 b(motiv)m(ation)60 1563 y(b)q(ehind)16 b(this)g(c)o(hoice)f(is)h(that)h(setting)f(the)g(image)f (spins)i(in)f(\003)1215 1570 y FD(R)1242 1561 y Ft(0)1266 1563 y FE(n)11 b FQ(\003)1336 1570 y FD(R)1381 1563 y FQ(to)16 b(b)q(e)h(all)f(+)g (\(resp.)g(all)f FE(\000)p FQ(\))60 1623 y(is)h(exp)q(ected)f(to)i(push)g (the)e(system)g(in)o(to)h(its)g(+)g(\(resp.)g FE(\000)p FQ(\))g(phase.)22 b(The)16 b(remainder)e(of)j(Step)f(2)g(is)60 1683 y(dev)o(oted)g(to)g(pro)o (ving)g(that)h(this)f(is)g(in)g(fact)g(the)g(case.)133 1743 y(Since)g(w)o(e)g(kno)o(w)g(only)h(that)f(the)h(conditional)f(distribution)g FE(h)8 b(\001)g(i)1344 1750 y FD(!)1367 1741 y Ft(0)1398 1743 y FQ(is)16 b FP(some)21 b FQ(Gibbs)16 b(measure)60 1804 y(for)k(the)g(mo)q (di\014ed)e(ob)s(ject)h(system,)g(w)o(e)h(need)f(to)h(pro)o(v)o(e)f(the)g(b)q (ounds)j(\(4.3\))e FP(uniformly)k FQ(for)c FP(al)r(l)60 1864 y FQ(Gibbs)h(measures)e(for)i(this)g(system.)33 b(It)20 b(su\016ces)g(to)h (sho)o(w)g(that)g(there)f(exists)h FF(R)1624 1846 y Fy(00)1667 1864 y FF(<)g FE(1)f FQ(suc)o(h)60 1924 y(that)c(the)g(Gibbs)h(measure)d(for) j(the)e(mo)q(di\014ed)g(ob)s(ject)h(system)e(in)i(the)g FP(\014nite)21 b FQ(v)o(olume)14 b(\003)1717 1906 y FD(int)1717 1936 y(R)1744 1927 y Ft(00)1766 1924 y FQ(,)h(with)60 1984 y(image)i(spins)i FF(!)360 1966 y Fy(0)390 1984 y FE(2)g(N)483 1991 y FD(R;R)547 1982 y Ft(0)557 1991 y FD(;)p FH(+)615 1984 y FQ(\(or)g FE(N)737 1991 y FD(R;R)801 1982 y Ft(0)812 1991 y FD(;)p Fy(\000)851 1984 y FQ(\))g FP(and)h(arbitr)n(ary)e(internal-spin)j(b)n(oundary)e(c)n (ondition)60 2044 y FE(f)p 85 2018 30 2 v FF(\033)114 2051 y FD(l)127 2044 y FE(g)152 2055 y FD(l)p Fy(2)p FH(\()p Fl(Z)222 2046 y Fr(2)239 2055 y FH(\))253 2046 y Fs(int)297 2055 y Fy(n)p FH(\003)339 2044 y Fs(int)339 2071 y(R)362 2064 y Ft(00)387 2044 y FQ(,)25 b(satis\014es)f(the)f(b)q(ounds)i(\(4.3\).)44 b(F)l(or)24 b(simplicit)n(y)d(w)o(e)i(shall)g(tak)o(e)h FF(R)1715 2026 y Fy(00)1763 2044 y FQ(=)i FF(R)1864 2026 y Fy(0)1876 2044 y FQ(.)60 2113 y(In)18 b(fact,)h(in)g(this)f(t)o(w)o(o-dimensional)f (example)g(\(but)h FP(not)24 b FQ(in)19 b(higher)f(dimensions\))f(w)o(e)i (can)g(tak)o(e)60 2173 y FF(R)97 2155 y Fy(0)123 2173 y FQ(=)14 b FF(R)d FQ(+)g(2.)22 b(Therefore,)15 b(w)o(e)h(are)h(led)e(to)i(the)f(follo) o(wing)g(situation:)133 2233 y(Let)f(\003)253 2240 y FD(R)297 2233 y FQ(b)q(e)g(the)g(square)g(of)g(side)g(2)p FF(R)10 b FQ(+)e(1)15 b(cen)o(tered)f(at)h(the)g(origin,)g(and)g(let)g(\000)1582 2240 y FD(R)1625 2233 y FE(\021)e FQ(\003)1711 2240 y FD(R)1749 2233 y FE(n)8 b FQ(\003)1816 2240 y FD(R)p Fy(\000)p FH(1)60 2293 y FQ(b)q(e)18 b(the)g FF(R)251 2275 y FD(th)305 2293 y FQ(la)o(y)o(er.)25 b(No)o(w)18 b(c)o(ho)q(ose)g(an)h(ev)o(en)e(n)o(um)o(b)q (er)f FF(R)p FQ(,)j(and)g(consider)e(all)h(the)g(con\014gurations)60 2354 y(with)d(the)f(image)g(spins)h(in)g(\003)603 2361 y FD(R)646 2354 y FQ(\014xed)g(in)g(the)f(alternating)h(con\014guration)h FF(!)1475 2335 y Fy(0)1473 2366 y FD(alt)1518 2354 y FQ(,)f(and)g(those)h(in) e(the)60 2414 y(second)k(la)o(y)o(er)f(outside)i(\003)544 2421 y FD(R)591 2414 y FQ(\(that)f(is,)g(in)g(\000)871 2390 y FD(imag)q(e)871 2426 y(R)p FH(+2)970 2414 y FQ(\))g(\014xed)g(to)h(b)q(e)f(\\+".)28 b(The)18 b(spins)h(outside)f(\003)1816 2421 y FD(R)p FH(+2)60 2474 y FQ(\()p FP(b)n(oth)h(image)h(and)g(internal)5 b FQ(\))19 b(are)g(\014xed)e(in)h(some)g(arbitrary)g(con\014guration.)28 b(The)19 b(situation)f(is)60 2534 y(depicted)13 b(in)g(Figure)g(4\(a\),)i (where)e(a)h(circle)e(represen)o(ts)h(an)h(in)o(ternal)f(spin)h(whic)o(h)f (\015uctuates)h(o)o(v)o(er)60 2594 y(all)c(p)q(ossible)i(v)m(alues.)19 b(No)o(w)11 b(consider)g(all)f(the)h(resulting)f(systems)g(of)h(in)o(ternal)f (spins)h(in)g(\003)1694 2576 y FD(int)1694 2607 y(R)p FH(+2)1779 2594 y FQ(giv)o(en)60 2660 y(the)18 b(ab)q(o)o(v)o(e)g(con\014guration)h(of)f (image)f(spins)h(in)g(\003)1000 2636 y FD(imag)q(e)1000 2672 y(R)p FH(+2)1116 2660 y FQ(and)h(an)f(arbitrary)g(\014xed)g(con\014guration) 951 2784 y(96)p eop %%Page: 97 97 bop 60 91 a FQ(\(of)16 b(b)q(oth)g(image)e(and)i(in)o(ternal)e(spins\))i (outside)f(\003)1003 98 y FD(R)p FH(+2)1077 91 y FQ(.)21 b(W)l(e)15 b(w)o(an)o(t)h(to)f(con)o(vince)f(the)h(reader)h(that)60 152 y(all)e(the)f(measures)g(so)i(obtained)g(ha)o(v)o(e)e(lo)q(cal)h (magnetizations)f FE(h)p FF(\033)1275 159 y FD(i)1287 164 y Fr(1)1304 159 y FD(;i)1326 164 y Fr(2)1346 152 y FE(i)h FQ(for)g(\()p FF(i)1487 159 y FH(1)1507 152 y FF(;)8 b(i)1546 159 y FH(2)1565 152 y FQ(\))14 b FE(2)g FQ(\003)1679 133 y FD(int)1679 164 y(R)p FH(+1)1767 152 y FQ(whic)o(h)60 212 y(are)19 b(b)q(ounded)g(b)q(elo)o (w)f(b)o(y)g(a)h(strictly)e(p)q(ositiv)o(e)h(constan)o(t,)h(uniformly)e(in)h FF(R)h FQ(\(su\016cien)o(tly)d(large\))60 272 y(and)h(uniformly)e(in)h(the)g (b)q(oundary)i(condition)e(outside)h(\003)1156 279 y FD(R)p FH(+2)1230 272 y FQ(.)22 b(The)17 b(sequence)e(of)i(b)q(ounds)h(used)60 332 y(in)e(our)h(pro)q(of)g(is)f(summarized)d(in)j(Figure)g(4.)133 392 y(Eac)o(h)h(in)o(ternal)f(spin)h(in)f(\003)631 374 y FD(int)631 405 y(R)p FH(+2)722 392 y FQ(feels)g(an)h(\\e\013ectiv)o(e)f(magnetic)f (\014eld")i FE(\006)p FF(J)k FQ(from)16 b(eac)o(h)g(image)60 452 y(spin)d(adjacen)o(t)g(to)g(it;)g(but)h(b)q(ecause)f(the)g(image-spin)f (con\014guration)i(in)e(\003)1433 459 y FD(R)1475 452 y FQ(is)h(alternating,) g(these)60 513 y(\\e\013ectiv)o(e)i(magnetic)f(\014elds")j(are)f FP(al)r(l)j(zer)n(o)f FQ(except)d(at)i(some)e(sites)h(in)g(la)o(y)o(ers)f (\000)1554 520 y FD(R)p FH(+1)1645 513 y FQ(and)i(\000)1770 520 y FD(R)p FH(+2)1844 513 y FQ(:)106 614 y(\(i\))24 b(An)16 b(in)o(ternal)f(spin)h(in)f(la)o(y)o(er)g(\000)749 621 y FD(R)p FH(+1)840 614 y FQ(feels)g(an)h(e\013ectiv)o(e)e(\014eld)i(+2)p FF(J)21 b FQ(if)15 b(it)h(is)g(adjacen)o(t)g(to)g(t)o(w)o(o)182 675 y(\\+")h(image)e(spins.)93 776 y(\(ii\))23 b(An)c(in)o(ternal)f(spin)h (in)f(la)o(y)o(er)g(\000)764 783 y FD(R)p FH(+2)857 776 y FQ(feels)g(an)i (e\013ectiv)o(e)d(\014eld)i(+3)p FF(J)k FQ(or)d(+)p FF(J)j FQ(dep)q(ending)d(on)182 836 y(whether)11 b(the)g(adjacen)o(t)g(spin)g(in)g (la)o(y)o(er)f(\000)926 843 y FD(R)p FH(+3)1011 836 y FQ(\(whic)o(h)h(is)g (alw)o(a)o(ys)g(an)h(in)o(ternal)e(spin\))h(happ)q(ens)182 897 y(to)17 b(b)q(e)f(\\+")h(or)g(\\)p FE(\000)p FQ(".)60 998 y(W)l(e)j(therefore)g(consider)g(the)g(system)f(of)i(in)o(ternal)e(spins)i (in)f(\003)1271 980 y FD(int)1271 1011 y(R)p FH(+2)1365 998 y FQ(with)g(the)h(magnetic)d(\014elds)60 1059 y(describ)q(ed)e(in)g(\(i\))f (and)i(\(ii\))e(ab)q(o)o(v)o(e)i([Figure)e(4\(b\)].)133 1119 y(Next)i(w)o(e)h(notice)f(that)i(b)o(y)e(the)h(FK)o(G)g(inequalit)o(y)e([126) q(])h(\(or)i(alternativ)o(ely)d(the)i(Gri\016ths)f(I)q(I)60 1179 y(inequalit)o(y)11 b([341)q(]\),)i(the)g(lo)q(cal)g(magnetizations)g FE(h)p FF(\033)1004 1186 y FD(i)1016 1191 y Fr(1)1033 1186 y FD(;i)1055 1191 y Fr(2)1074 1179 y FE(i)h FQ(for)g(\()p FF(i)1215 1186 y FH(1)1234 1179 y FF(;)8 b(i)1273 1186 y FH(2)1292 1179 y FQ(\))14 b FE(2)g FQ(\003)1406 1161 y FD(int)1406 1191 y(R)p FH(+2)1493 1179 y FQ(are)g(b)q(ounded)g(b)q(elo)o(w)60 1239 y(b)o(y)k(the)f(v)m(alues)h(that)h(they)e(w)o(ould)h(tak)o(e)g(if)f(the)h (magnetic)e(\014elds)i(+2)p FF(J)23 b FQ(in)18 b(\(i\))f(w)o(ere)h(c)o (hanged)g(to)60 1299 y(zero,)g(and)i(the)e(\014elds)g(+3)p FF(J)24 b FQ(in)18 b(\(ii\))g(c)o(hanged)h(to)g(+)p FF(J)5 b FQ(.)27 b(W)l(e)19 b(no)o(w)g(ha)o(v)o(e)f(a)h(system)e(consisting)i(of)60 1359 y(the)d(spins)g(in)g(\003)357 1341 y FD(int)357 1372 y(R)p FH(+2)431 1359 y FQ(,)g(with)g(a)h(magnetic)d(\014eld)i(+)p FF(J)21 b FQ(on)c(eac)o(h)e(spin)i(in)e(la)o(y)o(er)g(\000)1498 1341 y FD(int)1498 1372 y(R)p FH(+2)1589 1359 y FQ([Figure)g(4\(c\)].)133 1420 y(This)f(latter)f(system)e(liv)o(es)h(on)i(a)g(\014nite)f(subset)g(of)h (the)f(decorated)g(lattice.)19 b(W)l(e)13 b(can)h(explicitly)60 1480 y(in)o(tegrate)21 b(out)g(the)g(spins)g(in)g(\003)673 1462 y FD(int)673 1492 y(R)p FH(+1)768 1480 y FQ(that)h(ha)o(v)o(e)e(exactly) g(t)o(w)o(o)h(neigh)o(b)q(ors)h(\(namely)l(,)e(the)h(spins)60 1540 y(that)c(ha)o(v)o(e)e(one)i(co)q(ordinate)g(ev)o(en)e(and)i(one)f(co)q (ordinate)h(o)q(dd\),)g(yielding)e(an)i(e\013ectiv)o(e)d(coupling)60 1600 y FF(J)92 1582 y Fy(0)123 1600 y FQ(=)186 1581 y FH(1)p 186 1589 18 2 v 186 1617 a(2)217 1600 y FQ(log)9 b(cosh)g(2)p FF(J)25 b FQ(b)q(et)o(w)o(een)19 b(those)h(t)o(w)o(o)g(neigh)o(b)q(ors.)33 b(Similarly)l(,)17 b(w)o(e)j(can)g(in)o(tegrate)f(out)h(the)60 1660 y(spins)k(in)f(\000)284 1642 y FD(int)284 1673 y(R)p FH(+2)359 1660 y FQ(,)i(yielding)d(an)i(e\013ectiv)o(e)e(magnetic)g(\014eld)h FF(h)1216 1642 y Fy(0)1254 1660 y FQ(=)1324 1641 y FH(1)p 1324 1649 V 1324 1678 a(2)1355 1660 y FQ(log)9 b(cosh)g(2)p FF(J)31 b(>)26 b FQ(0)e(on)h(eac)o(h)60 1721 y(remaining)10 b(spin)j(in)e(\000)465 1703 y FD(int)465 1733 y(R)p FH(+1)540 1721 y FQ(,)h(except)f(that)i(the)e (\014eld)h(is)g(2)p FF(h)1095 1703 y Fy(0)1119 1721 y FQ(at)h(the)e(corners)h ([Figure)g(4\(d\)].)19 b(But)12 b(this)60 1781 y(last)g(system)e(is)h(equiv)m (alen)o(t)f(to)i(a)f(square)h(lattice)e(of)i(size)f(\()p FF(R)r FQ(+)q(2\))q FE(\002)q FQ(\()p FF(R)r FQ(+)q(2\))h(with)f(nearest-neigh)o(b)q (or)60 1841 y(coupling)k FF(J)286 1823 y Fy(0)313 1841 y FQ(and)h(+)f(b)q (oundary)i(conditions)e([Figure)g(4\(e\)].)20 b(As)c FF(R)e FE(!)g(1)h FQ(this)g(system)f(tends)i(to)60 1901 y(the)i(\\+")h(phase)g(for)g (an)g(Ising)f(mo)q(del)f(with)i(coupling)f FF(J)1146 1883 y Fy(0)1157 1901 y FQ(.)28 b(In)18 b(particular,)g(the)g(magnetization)60 1961 y FE(h)p FF(\033)107 1968 y FD(i)119 1973 y Fr(1)136 1968 y FD(;i)158 1973 y Fr(2)178 1961 y FE(i)i FQ(of)h(an)o(y)f(spin)h(remaining)d (in)j(this)f(system)f(\(i.e.)f(an)o(y)j(spin)f(with)g FF(i)1476 1968 y FH(1)1516 1961 y FQ(and)h FF(i)1632 1968 y FH(2)1672 1961 y FQ(b)q(oth)g(o)q(dd\))60 2022 y(tends)c(to)g(the)g(sp)q(on)o(taneous)h (magnetization)e FF(M)978 2029 y FH(0)998 2022 y FQ(\()p FF(J)1049 2004 y Fy(0)1060 2022 y FQ(\),)g(whic)o(h)g(is)h FF(>)e FQ(0)i(if)f FF(J)1470 2004 y Fy(0)1496 2022 y FF(>)f(J)1576 2029 y FD(c)1593 2022 y FQ(.)23 b(W)l(e)17 b(can)g(no)o(w)60 2082 y(return)h(to)h(the)f (decorated)g(lattice,)f(to)i(compute)e(the)h(magnetization)f FE(h)p FF(\033)1462 2089 y FD(i)1474 2094 y Fr(1)1491 2089 y FD(;i)1513 2094 y Fr(2)1533 2082 y FE(i)h FQ(on)h(the)f(in)o(ternal)60 2142 y(spins)e(that)h(got)g(in)o(tegrated)f(out)h(\(i.e.)d(the)i(ones)h(with) f FF(i)1109 2149 y FH(1)1144 2142 y FQ(ev)o(en)g(and)g FF(i)1367 2149 y FH(2)1403 2142 y FQ(o)q(dd)h(or)g(vice)e(v)o(ersa\):)507 2252 y FE(h)p FF(\033)554 2259 y FD(i)566 2264 y Fr(1)583 2259 y FD(;i)605 2264 y Fr(2)624 2252 y FE(i)643 2263 y FH(\003)667 2251 y Fs(int)667 2275 y(R)p Fr(+2)796 2252 y FQ(=)63 b FE(h)p FQ(tanh)q(\()p FF(J)5 b FQ(\()p FF(\033)1114 2231 y Fy(0)1136 2252 y FQ(+)11 b FF(\033)1215 2231 y Fy(00)1235 2252 y FQ(\)\))p FE(i)1292 2259 y FD(R)p FH(+2)796 2336 y FQ(=)63 b FE(h)p FQ(\()940 2316 y FH(1)p 940 2324 V 940 2353 a(2)971 2336 y FQ(tanh)9 b(2)p FF(J)c FQ(\))j(\()p FF(\033)1209 2315 y Fy(0)1231 2336 y FQ(+)j FF(\033)1310 2315 y Fy(00)1331 2336 y FQ(\))p FE(i)1369 2343 y FD(R)p FH(+2)775 2409 y FE(\000)-8 b(!)41 b FQ(\(tanh)9 b(2)p FF(J)c FQ(\))j FF(M)1152 2416 y FH(0)1172 2409 y FQ(\()p FF(J)1223 2388 y Fy(0)1234 2409 y FQ(\))28 b FF(>)f FQ(0)420 b(\(4.6\))60 2519 y(where)14 b FF(\033)229 2501 y Fy(0)255 2519 y FQ(and)i FF(\033)379 2501 y Fy(00)414 2519 y FQ(are)f(the)f(t)o(w)o(o) h(in)o(ternal)f(spins)h(adjacen)o(t)f(to)h FF(\033)1246 2526 y FD(i)1258 2531 y Fr(1)1275 2526 y FD(;i)1297 2531 y Fr(2)1317 2519 y FQ(.)20 b(W)l(e)15 b(ha)o(v)o(e)f(therefore)g(pro)o(v)o(en)60 2579 y(our)19 b(claim)d(that)j(the)f(magnetizations)f FE(h)p FF(\033)860 2586 y FD(i)872 2591 y Fr(1)889 2586 y FD(;i)911 2591 y Fr(2)930 2579 y FE(i)i FQ(for)g(\()p FF(i)1081 2586 y FH(1)1100 2579 y FF(;)8 b(i)1139 2586 y FH(2)1158 2579 y FQ(\))17 b FE(2)h FQ(\003)1279 2561 y FD(int)1279 2591 y(R)p FH(+1)1371 2579 y FQ(are)g(b)q(ounded)i(b)q(elo)o(w)e(b)o(y)g(a)60 2639 y(strictly)d(p)q(ositiv)o(e)h(constan)o(t)h([namely)d(\(1)e FE(\000)f FF(\017)p FQ(\)\(tanh)e(2)p FF(J)c FQ(\))j FF(M)1187 2646 y FH(0)1207 2639 y FQ(\()p FF(J)1258 2621 y Fy(0)1269 2639 y FQ(\))17 b(for)g(an)o(y)f FF(\017)e(>)h FQ(0],)h(uniformly)e(in)951 2784 y(97)p eop %%Page: 98 98 bop 60 2331 a @beginspecial 5 @llx 39.500000 @lly 556 @urx 714.500000 @ury 4392 @rwi @setspecial %%BeginDocument: fig4.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n []/_Symbol/Symbol Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Italic/Times-Italic Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 258.4291 605.4428 m S 387.6862 682.3458 m S 0 g 1 w 4 M 387.6862 682.3458 m F 0 G 0.3 w 10 M 387.6862 682.3458 m S 387.6862 682.3458 m S 387.6862 682.3458 m S 0 g 1 w 4 M 387.6862 682.3458 m F 0 G 0.3 w 10 M 387.6862 682.3458 m S 387.6862 682.3458 m S 1 g 1 w 4 M 387.6862 682.3458 m F 0 G 0.3 w 10 M 387.6862 682.3458 m S 0 g 1 w 4 M 387.6862 682.3458 m F 0 G 0.3 w 10 M 387.6862 682.3458 m S 387.6862 682.3458 m S 400.992 682.3458 m S 0.3 g 1 w 4 M 400.992 677.5375 m 403.8037 677.5375 406.0831 679.6903 406.0831 682.3458 c 406.0831 685.0013 403.8037 687.1541 400.992 687.1541 c 398.1803 687.1541 395.9009 685.0013 395.9009 682.3458 c 395.9009 679.6903 398.1803 677.5375 400.992 677.5375 c b 0 g 400.992 682.3458 m F 0 G 0.3 w 10 M 427.6036 682.3458 m S 0.3 g 1 w 4 M 427.6036 677.5375 m 430.4153 677.5375 432.6947 679.6903 432.6947 682.3458 c 432.6947 685.0013 430.4153 687.1541 427.6036 687.1541 c 424.7919 687.1541 422.5125 685.0013 422.5125 682.3458 c 422.5125 679.6903 424.7919 677.5375 427.6036 677.5375 c b 0 g 427.6036 682.3458 m F 0 G 0.3 w 10 M 387.6862 669.3792 m S 1 g 1 w 4 M 387.6862 664.5709 m 390.4979 664.5709 392.7773 666.7237 392.7773 669.3792 c 392.7773 672.0347 390.4979 674.1875 387.6862 674.1875 c 384.8745 674.1875 382.5951 672.0347 382.5951 669.3792 c 382.5951 666.7237 384.8745 664.5709 387.6862 664.5709 c b 0 g 387.6862 669.3792 m F 0 G 0.3 w 10 M 480.8268 682.3458 m S 0.3 g 1 w 4 M 480.8268 677.5375 m 483.6385 677.5375 485.9179 679.6903 485.9179 682.3458 c 485.9179 685.0013 483.6385 687.1541 480.8268 687.1541 c 477.3485 687.1541 475.7357 685.0012 475.7357 682.3458 c 475.7357 679.6903 478.0151 677.5375 480.8268 677.5375 c b 0 g 480.8268 682.3458 m F 0 G 0.3 w 10 M 507.4385 682.3458 m S 0.3 g 1 w 4 M 507.4385 677.5375 m 510.2501 677.5375 512.5295 679.6903 512.5295 682.3458 c 512.5295 685.0013 510.2501 687.1541 507.4385 687.1541 c 504.6267 687.1541 502.3473 685.0013 502.3473 682.3458 c 502.3473 679.6903 504.6267 677.5375 507.4385 677.5375 c b 0 g 507.4385 682.3458 m F 0 G 0.3 w 10 M 427.6036 656.4126 m S 1 g 1 w 4 M 427.6036 651.6043 m 430.4153 651.6043 432.6947 653.7571 432.6947 656.4126 c 432.6947 659.0681 430.4153 661.2209 427.6036 661.2209 c 424.7919 661.2209 422.5125 659.0681 422.5125 656.4126 c 422.5125 653.7571 424.7919 651.6043 427.6036 651.6043 c b 0 g 427.6036 656.4126 m F 0 G 0.3 w 10 M 454.2152 656.4126 m S 1 g 1 w 4 M 454.2152 651.6043 m 457.0269 651.6043 459.3063 653.7571 459.3063 656.4126 c 459.3063 659.0681 457.0269 661.2209 454.2152 661.2209 c 451.4035 661.2209 449.1241 659.0681 449.1241 656.4126 c 449.1241 653.7571 451.4035 651.6043 454.2152 651.6043 c b 0 g 454.2152 656.4126 m F 0 G 0.3 w 10 M 480.8268 656.4126 m S 1 g 1 w 4 M 480.8268 651.6043 m 483.6385 651.6043 485.9179 653.7571 485.9179 656.4126 c 485.9179 659.0681 483.6385 661.2209 480.8268 661.2209 c 478.0151 661.2209 475.7357 659.0681 475.7357 656.4126 c 475.7357 653.7571 478.0151 651.6043 480.8268 651.6043 c b 0 g 480.8268 656.4126 m F 0 G 0.3 w 10 M 507.4385 656.4126 m S 1 g 1 w 4 M 507.4385 651.6043 m 510.2501 651.6043 512.5295 653.7571 512.5295 656.4126 c 512.5295 659.0681 510.2501 661.2209 507.4385 661.2209 c 504.6267 661.2209 502.3473 659.0681 502.3473 656.4126 c 502.3473 653.7571 504.6267 651.6043 507.4385 651.6043 c b 0 g 507.4385 656.4126 m F 0 G 0.3 w 10 M 454.2152 682.3458 m S 0.3 g 1 w 4 M 454.2152 677.5375 m 457.0269 677.5375 459.3063 679.6903 459.3063 682.3458 c 459.3063 685.0013 457.0269 687.1541 454.2152 687.1541 c 451.4035 687.1541 449.1241 685.0013 449.1241 682.3458 c 449.1241 679.6903 451.4035 677.5375 454.2152 677.5375 c b 0 g 454.2152 682.3458 m F 0 G 0.3 w 10 M 400.992 643.4461 m S 387.6862 643.4461 m S 414.2978 643.4461 m S 400.992 643.4461 m S 414.2978 643.4461 m S 400.992 643.4461 m S 427.6036 643.4461 m S 414.2978 643.4461 m S 427.6036 643.4461 m S 414.2978 643.4461 m S 400.992 643.4461 m S 387.6862 643.4461 m S 440.9094 643.4461 m S 427.6036 643.4461 m S 454.2152 643.4461 m S 440.9094 643.4461 m S 454.2152 643.4461 m S 440.9094 643.4461 m S 467.521 643.4461 m S 454.2152 643.4461 m S 467.521 643.4461 m S 454.2152 643.4461 m S 440.9094 643.4461 m S 427.6036 643.4461 m S 480.8268 643.4461 m S 467.521 643.4461 m S 494.1326 643.4461 m S 480.8268 643.4461 m S 494.1326 643.4461 m S 480.8268 643.4461 m S 507.4385 643.4461 m S 494.1326 643.4461 m S 507.4385 643.4461 m S 494.1326 643.4461 m S 480.8268 643.4461 m S 467.521 643.4461 m S 520.7441 643.4461 m S 507.4385 643.4461 m S 520.7441 643.4461 m S 520.7441 643.4461 m S 520.7441 643.4461 m S 507.4385 643.4461 m S 400.992 643.4461 m S 1 g 1 w 4 M 400.992 638.6378 m 403.8037 638.6378 406.0831 640.7906 406.0831 643.4461 c 406.0831 646.1016 403.8037 648.2544 400.992 648.2544 c 398.1803 648.2544 395.9009 646.1016 395.9009 643.4461 c 395.9009 640.7906 398.1803 638.6378 400.992 638.6378 c b 0 g 400.992 643.4461 m F 0 G 0.3 w 10 M 414.2978 643.4461 m S 1 g 1 w 4 M 414.2978 638.6378 m 417.1095 638.6378 419.389 640.7906 419.389 643.4461 c 419.389 646.1016 417.1095 648.2544 414.2978 648.2544 c 411.4861 648.2544 409.2067 646.1016 409.2067 643.4461 c 409.2067 640.7906 411.4861 638.6378 414.2978 638.6378 c b 0 g 414.2978 643.4461 m F 0 G 0.3 w 10 M 427.6036 643.4461 m S 1 g 1 w 4 M 427.6036 638.6378 m 430.4153 638.6378 432.6947 640.7906 432.6947 643.4461 c 432.6947 646.1016 430.4153 648.2544 427.6036 648.2544 c 424.792 648.2544 422.5125 646.1016 422.5125 643.4461 c 422.5125 640.7906 424.792 638.6378 427.6036 638.6378 c b 0 g 427.6036 643.4461 m F 0 G 0.3 w 10 M 440.9094 643.4461 m S 1 g 1 w 4 M 440.9094 638.6378 m 443.7212 638.6378 446.0005 640.7906 446.0005 643.4461 c 446.0005 646.1016 443.7212 648.2544 440.9094 648.2544 c 438.0978 648.2544 435.8183 646.1016 435.8183 643.4461 c 435.8183 640.7906 438.0978 638.6378 440.9094 638.6378 c b 0 g 440.9094 643.4461 m F 0 G 0.3 w 10 M 454.2152 643.4461 m S 1 g 1 w 4 M 454.2152 638.6378 m 457.027 638.6378 459.3063 640.7906 459.3063 643.4461 c 459.3063 646.1016 457.027 648.2544 454.2152 648.2544 c 451.4035 648.2544 449.1241 646.1016 449.1241 643.4461 c 449.1241 640.7906 451.4035 638.6378 454.2152 638.6378 c b 0 g 454.2152 643.4461 m F 0 G 0.3 w 10 M 467.521 643.4461 m S 1 g 1 w 4 M 467.521 638.6378 m 470.3327 638.6378 472.6121 640.7906 472.6121 643.4461 c 472.6121 646.1016 470.3327 648.2544 467.521 648.2544 c 464.7093 648.2544 462.43 646.1016 462.43 643.4461 c 462.43 640.7906 464.7093 638.6378 467.521 638.6378 c b 0 g 467.521 643.4461 m F 0 G 0.3 w 10 M 480.8268 643.4461 m S 1 g 1 w 4 M 480.8268 638.6378 m 483.6385 638.6378 485.9179 640.7906 485.9179 643.4461 c 485.9179 646.1016 483.6385 648.2544 480.8268 648.2544 c 478.0151 648.2544 475.7357 646.1016 475.7357 643.4461 c 475.7357 640.7906 478.0151 638.6378 480.8268 638.6378 c b 0 g 480.8268 643.4461 m F 0 G 0.3 w 10 M 494.1326 643.4461 m S 1 g 1 w 4 M 494.1326 638.6378 m 496.9443 638.6378 499.2237 640.7906 499.2237 643.4461 c 499.2237 646.1016 496.9443 648.2544 494.1326 648.2544 c 491.3209 648.2544 489.0415 646.1016 489.0415 643.4461 c 489.0415 640.7906 491.3209 638.6378 494.1326 638.6378 c b 0 g 494.1326 643.4461 m F 0 G 0.3 w 10 M 520.7441 643.4461 m S 0.3 g 1 w 4 M 520.7441 638.6378 m 523.5559 638.6378 525.8353 640.7906 525.8353 643.4461 c 525.8353 646.1016 523.5559 648.2544 520.7441 648.2544 c 517.9325 648.2544 515.6531 646.1016 515.6531 643.4461 c 515.6531 640.7906 517.9325 638.6378 520.7441 638.6378 c b 0 g 520.7441 643.4461 m F 0 G 0.3 w 10 M 507.4385 643.4461 m S 1 g 1 w 4 M 507.4385 638.6378 m 510.2501 638.6378 512.5295 640.7906 512.5295 643.4461 c 512.5295 646.1016 510.2501 648.2544 507.4385 648.2544 c 504.6267 648.2544 502.3473 646.1016 502.3473 643.4461 c 502.3473 640.7906 504.6267 638.6378 507.4385 638.6378 c b 0 g 507.4385 643.4461 m F 0 G 0.3 w 10 M 387.6862 643.4461 m S 0.3 g 1 w 4 M 387.6862 638.6378 m 390.4979 638.6378 392.7773 640.7906 392.7773 643.4461 c 392.7773 646.1016 390.4979 648.2544 387.6862 648.2544 c 384.8745 648.2544 382.5951 646.1016 382.5951 643.4461 c 382.5951 640.7906 384.8745 638.6378 387.6862 638.6378 c b 0 g 387.6862 643.4461 m F 0 G 0.3 w 10 M 400.992 617.5129 m S 387.6862 617.5129 m S 414.2978 617.5129 m S 400.992 617.5129 m S 414.2978 617.5129 m S 400.992 617.5129 m S 427.6036 617.5129 m S 414.2978 617.5129 m S 427.6036 617.5129 m S 414.2978 617.5129 m S 400.992 617.5129 m S 387.6862 617.5129 m S 440.9094 617.5129 m S 427.6036 617.5129 m S 454.2152 617.5129 m S 440.9094 617.5129 m S 454.2152 617.5129 m S 440.9094 617.5129 m S 467.521 617.5129 m S 454.2152 617.5129 m S 467.521 617.5129 m S 454.2152 617.5129 m S 440.9094 617.5129 m S 427.6036 617.5129 m S 480.8268 617.5129 m S 467.521 617.5129 m S 494.1326 617.5129 m S 480.8268 617.5129 m S 494.1326 617.5129 m S 480.8268 617.5129 m S 507.4385 617.5129 m S 494.1326 617.5129 m S 507.4385 617.5129 m S 494.1326 617.5129 m S 480.8268 617.5129 m S 467.521 617.5129 m S 520.7441 617.5129 m S 507.4385 617.5129 m S 520.7441 617.5129 m S 520.7441 617.5129 m S 520.7441 617.5129 m S 507.4385 617.5129 m S 400.992 617.5129 m S 0 g 1 w 4 M 400.992 617.5129 m F 0 G 0.3 w 10 M 414.2978 617.5129 m S 0 g 1 w 4 M 414.2978 617.5129 m F 0 G 0.3 w 10 M 427.6036 617.5129 m S 0 g 1 w 4 M 427.6036 617.5129 m F 0 G 0.3 w 10 M 440.9094 617.5129 m S 0 g 1 w 4 M 440.9094 617.5129 m F 0 G 0.3 w 10 M 454.2152 617.5129 m S 0 g 1 w 4 M 454.2152 617.5129 m F 0 G 0.3 w 10 M 467.521 617.5129 m S 0 g 1 w 4 M 467.521 617.5129 m F 0 G 0.3 w 10 M 480.8268 617.5129 m S 0 g 1 w 4 M 480.8268 617.5129 m F 0 G 0.3 w 10 M 494.1326 617.5129 m S 0 g 1 w 4 M 494.1326 617.5129 m F 0 G 0.3 w 10 M 520.7441 617.5129 m S 0 g 1 w 4 M 520.7441 617.5129 m F 0 G 0.3 w 10 M 507.4385 617.5129 m S 0 g 1 w 4 M 507.4385 617.5129 m F 0 G 0.3 w 10 M 387.6862 617.5129 m S 1 g 1 w 4 M 387.6862 612.7046 m 390.4979 612.7046 392.7773 614.8574 392.7773 617.5129 c 392.7773 620.1684 390.4979 622.3212 387.6862 622.3212 c 384.8745 622.3212 382.5951 620.1684 382.5951 617.5129 c 382.5951 614.8574 384.8745 612.7046 387.6862 612.7046 c b 0 g 387.6862 617.5129 m F 0 G 0.3 w 10 M 400.992 617.5129 m S 387.6862 617.5129 m S 414.2978 617.5129 m S 400.992 617.5129 m S 414.2978 617.5129 m S 400.992 617.5129 m S 427.6036 617.5129 m S 414.2978 617.5129 m S 427.6036 617.5129 m S 414.2978 617.5129 m S 400.992 617.5129 m S 387.6862 617.5129 m S 440.9094 617.5129 m S 427.6036 617.5129 m S 454.2152 617.5129 m S 440.9094 617.5129 m S 454.2152 617.5129 m S 440.9094 617.5129 m S 467.521 617.5129 m S 454.2152 617.5129 m S 467.521 617.5129 m S 454.2152 617.5129 m S 440.9094 617.5129 m S 427.6036 617.5129 m S 480.8268 617.5129 m S 467.521 617.5129 m S 494.1326 617.5129 m S 480.8268 617.5129 m S 494.1326 617.5129 m S 480.8268 617.5129 m S 507.4385 617.5129 m S 494.1326 617.5129 m S 507.4385 617.5129 m S 494.1326 617.5129 m S 480.8268 617.5129 m S 467.521 617.5129 m S 520.7441 617.5129 m S 507.4385 617.5129 m S 520.7441 617.5129 m S 520.7441 617.5129 m S 520.7441 617.5129 m S 507.4385 617.5129 m S 400.992 617.5129 m S 1 g 1 w 4 M 400.992 612.7046 m 403.8037 612.7046 406.0831 614.8574 406.0831 617.5129 c 406.0831 620.1684 403.8037 622.3212 400.992 622.3212 c 398.1803 622.3212 395.9009 620.1684 395.9009 617.5129 c 395.9009 614.8574 398.1803 612.7046 400.992 612.7046 c b 0 g 400.992 617.5129 m F 0 G 0.3 w 10 M 414.2978 617.5129 m S 1 g 1 w 4 M 414.2978 612.7046 m 417.1095 612.7046 419.389 614.8574 419.389 617.5129 c 419.389 620.1684 417.1095 622.3212 414.2978 622.3212 c 411.4861 622.3212 409.2067 620.1684 409.2067 617.5129 c 409.2067 614.8574 411.4861 612.7046 414.2978 612.7046 c b 0 g 414.2978 617.5129 m F 0 G 0.3 w 10 M 427.6036 617.5129 m S 1 g 1 w 4 M 427.6036 612.7046 m 430.4153 612.7046 432.6947 614.8574 432.6947 617.5129 c 432.6947 620.1684 430.4153 622.3212 427.6036 622.3212 c 424.792 622.3212 422.5125 620.1684 422.5125 617.5129 c 422.5125 614.8574 424.792 612.7046 427.6036 612.7046 c b 0 g 427.6036 617.5129 m F 0 G 0.3 w 10 M 440.9094 617.5129 m S 1 g 1 w 4 M 440.9094 612.7046 m 443.7212 612.7046 446.0005 614.8574 446.0005 617.5129 c 446.0005 620.1684 443.7212 622.3212 440.9094 622.3212 c 438.0978 622.3212 435.8183 620.1684 435.8183 617.5129 c 435.8183 614.8574 438.0978 612.7046 440.9094 612.7046 c b 0 g 440.9094 617.5129 m F 0 G 0.3 w 10 M 454.2152 617.5129 m S 1 g 1 w 4 M 454.2152 612.7046 m 457.027 612.7046 459.3063 614.8574 459.3063 617.5129 c 459.3063 620.1684 457.027 622.3212 454.2152 622.3212 c 451.4035 622.3212 449.1241 620.1684 449.1241 617.5129 c 449.1241 614.8574 451.4035 612.7046 454.2152 612.7046 c b 0 g 454.2152 617.5129 m F 0 G 0.3 w 10 M 467.521 617.5129 m S 1 g 1 w 4 M 467.521 612.7046 m 470.3327 612.7046 472.6121 614.8574 472.6121 617.5129 c 472.6121 620.1684 470.3327 622.3212 467.521 622.3212 c 464.7093 622.3212 462.43 620.1684 462.43 617.5129 c 462.43 614.8574 464.7093 612.7046 467.521 612.7046 c b 0 g 467.521 617.5129 m F 0 G 0.3 w 10 M 480.8268 617.5129 m S 1 g 1 w 4 M 480.8268 612.7046 m 483.6385 612.7046 485.9179 614.8574 485.9179 617.5129 c 485.9179 620.1684 483.6385 622.3212 480.8268 622.3212 c 478.0151 622.3212 475.7357 620.1684 475.7357 617.5129 c 475.7357 614.8574 478.0151 612.7046 480.8268 612.7046 c b 0 g 480.8268 617.5129 m F 0 G 0.3 w 10 M 494.1326 617.5129 m S 1 g 1 w 4 M 494.1326 612.7046 m 496.9443 612.7046 499.2237 614.8574 499.2237 617.5129 c 499.2237 620.1684 496.9443 622.3212 494.1326 622.3212 c 491.3209 622.3212 489.0415 620.1684 489.0415 617.5129 c 489.0415 614.8574 491.3209 612.7046 494.1326 612.7046 c b 0 g 494.1326 617.5129 m F 0 G 0.3 w 10 M 520.7441 617.5129 m S 0.3 g 1 w 4 M 520.7441 612.7046 m 523.5559 612.7046 525.8353 614.8574 525.8353 617.5129 c 525.8353 620.1684 523.5559 622.3212 520.7441 622.3212 c 517.9325 622.3212 515.6531 620.1684 515.6531 617.5129 c 515.6531 614.8574 517.9325 612.7046 520.7441 612.7046 c b 0 g 520.7441 617.5129 m F 0 G 0.3 w 10 M 507.4385 617.5129 m S 1 g 1 w 4 M 507.4385 612.7046 m 510.2501 612.7046 512.5295 614.8574 512.5295 617.5129 c 512.5295 620.1684 510.2501 622.3212 507.4385 622.3212 c 504.6267 622.3212 502.3473 620.1684 502.3473 617.5129 c 502.3473 614.8574 504.6267 612.7046 507.4385 612.7046 c b 0 g 507.4385 617.5129 m F 0 G 0.3 w 10 M 387.6862 617.5129 m S 0.3 g 1 w 4 M 387.6862 612.7046 m 390.4979 612.7046 392.7773 614.8574 392.7773 617.5129 c 392.7773 620.1684 390.4979 622.3212 387.6862 622.3212 c 385.5412 622.3212 382.5951 620.835 382.5951 617.5129 c 382.5951 614.8574 384.8745 612.7046 387.6862 612.7046 c b 0 g 387.6862 617.5129 m F 0 G 0.3 w 10 M 400.992 591.5797 m S 387.6862 591.5797 m S 414.2978 591.5797 m S 400.992 591.5797 m S 414.2978 591.5797 m S 400.992 591.5797 m S 427.6036 591.5797 m S 414.2978 591.5797 m S 427.6036 591.5797 m S 414.2978 591.5797 m S 400.992 591.5797 m S 387.6862 591.5797 m S 440.9094 591.5797 m S 427.6036 591.5797 m S 454.2152 591.5797 m S 440.9094 591.5797 m S 454.2152 591.5797 m S 440.9094 591.5797 m S 467.521 591.5797 m S 454.2152 591.5797 m S 467.521 591.5797 m S 454.2152 591.5797 m S 440.9094 591.5797 m S 427.6036 591.5797 m S 480.8268 591.5797 m S 467.521 591.5797 m S 494.1326 591.5797 m S 480.8268 591.5797 m S 494.1326 591.5797 m S 480.8268 591.5797 m S 507.4385 591.5797 m S 494.1326 591.5797 m S 507.4385 591.5797 m S 494.1326 591.5797 m S 480.8268 591.5797 m S 467.521 591.5797 m S 520.7441 591.5797 m S 507.4385 591.5797 m S 520.7441 591.5797 m S 520.7441 591.5797 m S 520.7441 591.5797 m S 507.4385 591.5797 m S 400.992 591.5797 m S 1 g 1 w 4 M 400.992 586.7714 m 403.8037 586.7714 406.0831 588.9242 406.0831 591.5797 c 406.0831 594.2352 403.8037 596.388 400.992 596.388 c 398.1803 596.388 395.9009 594.2352 395.9009 591.5797 c 395.9009 588.9242 398.1803 586.7714 400.992 586.7714 c b 0 g 400.992 591.5797 m F 0 G 0.3 w 10 M 414.2978 591.5797 m S 1 g 1 w 4 M 414.2978 586.7714 m 417.1095 586.7714 419.389 588.9242 419.389 591.5797 c 419.389 594.2352 417.1095 596.388 414.2978 596.388 c 411.4861 596.388 409.2067 594.2352 409.2067 591.5797 c 409.2067 588.9242 411.4861 586.7714 414.2978 586.7714 c b 0 g 414.2978 591.5797 m F 0 G 0.3 w 10 M 427.6036 591.5797 m S 1 g 1 w 4 M 427.6036 586.7714 m 430.4153 586.7714 432.6947 588.9242 432.6947 591.5797 c 432.6947 594.2352 430.4153 596.388 427.6036 596.388 c 424.792 596.388 422.5125 594.2352 422.5125 591.5797 c 422.5125 588.9242 424.792 586.7714 427.6036 586.7714 c b 0 g 427.6036 591.5797 m F 0 G 0.3 w 10 M 440.9094 591.5797 m S 1 g 1 w 4 M 440.9094 586.7714 m 443.7212 586.7714 446.0005 588.9242 446.0005 591.5797 c 446.0005 594.2352 443.7212 596.388 440.9094 596.388 c 438.0978 596.388 435.8183 594.2352 435.8183 591.5797 c 435.8183 588.9242 438.0978 586.7714 440.9094 586.7714 c b 0 g 440.9094 591.5797 m F 0 G 0.3 w 10 M 454.2152 591.5797 m S 1 g 1 w 4 M 454.2152 586.7714 m 457.027 586.7714 459.3063 588.9242 459.3063 591.5797 c 459.3063 594.2352 457.027 596.388 454.2152 596.388 c 451.4035 596.388 449.1241 594.2352 449.1241 591.5797 c 449.1241 588.9242 451.4035 586.7714 454.2152 586.7714 c b 0 g 454.2152 591.5797 m F 0 G 0.3 w 10 M 467.521 591.5797 m S 1 g 1 w 4 M 467.521 586.7714 m 470.3327 586.7714 472.6121 588.9242 472.6121 591.5797 c 472.6121 594.2352 470.3327 596.388 467.521 596.388 c 464.7093 596.388 462.43 594.2352 462.43 591.5797 c 462.43 588.9242 464.7093 586.7714 467.521 586.7714 c b 0 g 467.521 591.5797 m F 0 G 0.3 w 10 M 480.8268 591.5797 m S 1 g 1 w 4 M 480.8268 586.7714 m 483.6385 586.7714 485.9179 588.9242 485.9179 591.5797 c 485.9179 594.2352 483.6385 596.388 480.8268 596.388 c 478.0151 596.388 475.7357 594.2352 475.7357 591.5797 c 475.7357 588.9242 478.0151 586.7714 480.8268 586.7714 c b 0 g 480.8268 591.5797 m F 0 G 0.3 w 10 M 494.1326 591.5797 m S 1 g 1 w 4 M 494.1326 586.7714 m 496.9443 586.7714 499.2237 588.9242 499.2237 591.5797 c 499.2237 594.2352 496.9443 596.388 494.1326 596.388 c 491.3209 596.388 489.0415 594.2352 489.0415 591.5797 c 489.0415 588.9242 491.3209 586.7714 494.1326 586.7714 c b 0 g 494.1326 591.5797 m F 0 G 0.3 w 10 M 520.7441 591.5797 m S 0.3 g 1 w 4 M 520.7441 586.7714 m 523.5559 586.7714 525.8353 588.9242 525.8353 591.5797 c 525.8353 594.2352 523.5559 596.388 520.7441 596.388 c 517.9325 596.388 515.6531 594.2352 515.6531 591.5797 c 515.6531 588.9242 517.9325 586.7714 520.7441 586.7714 c b 0 g 520.7441 591.5797 m F 0 G 0.3 w 10 M 507.4385 591.5797 m S 1 g 1 w 4 M 507.4385 586.7714 m 510.2501 586.7714 512.5295 588.9242 512.5295 591.5797 c 512.5295 594.2352 510.2501 596.388 507.4385 596.388 c 504.6267 596.388 502.3473 594.2352 502.3473 591.5797 c 502.3473 588.9242 504.6267 586.7714 507.4385 586.7714 c b 0 g 507.4385 591.5797 m F 0 G 0.3 w 10 M 387.6862 591.5797 m S 0.3 g 1 w 4 M 387.6862 586.7714 m 390.4979 586.7714 392.7773 588.9242 392.7773 591.5797 c 392.7773 594.2352 390.4979 596.388 387.6862 596.388 c 384.8745 596.388 382.5951 594.2352 382.5951 591.5797 c 382.5951 588.9242 384.8745 586.7714 387.6862 586.7714 c b 0 g 387.6862 591.5797 m F 0 G 0.3 w 10 M 507.4385 630.4795 m S 0.7 g 1 w 4 M 507.4385 625.6712 m 510.2501 625.6712 512.5295 627.824 512.5295 630.4795 c 512.5295 633.135 510.2501 635.2878 507.4385 635.2878 c 504.6267 635.2878 502.3473 633.135 502.3473 630.4795 c 502.3473 627.824 504.6267 625.6712 507.4385 625.6712 c b 0 g 507.4385 630.4795 m F 0 G 0.3 w 10 M 480.8268 630.4795 m S 1 g 1 w 4 M 480.8268 625.6712 m 483.6385 625.6712 485.9179 627.824 485.9179 630.4795 c 485.9179 633.135 483.6385 635.2878 480.8268 635.2878 c 478.0151 635.2878 475.7357 633.135 475.7357 630.4795 c 475.7357 627.824 478.0151 625.6712 480.8268 625.6712 c b 0 g 480.8268 630.4795 m F 0 G 0.3 w 10 M 507.4385 604.5463 m S 1 g 1 w 4 M 507.4385 599.738 m 510.2501 599.738 512.5295 601.8908 512.5295 604.5463 c 512.5295 607.2018 510.2501 609.3546 507.4385 609.3546 c 504.6267 609.3546 502.3473 607.2018 502.3473 604.5463 c 502.3473 601.8908 504.6267 599.738 507.4385 599.738 c b 0 g 507.4385 604.5463 m F 0 G 0.3 w 10 M 480.8268 604.5463 m S 1 g 1 w 4 M 480.8268 599.738 m 483.6385 599.738 485.9179 601.8908 485.9179 604.5463 c 485.9179 607.2018 483.6385 609.3546 480.8268 609.3546 c 478.0151 609.3546 475.7357 607.2018 475.7357 604.5463 c 475.7357 601.8908 478.0151 599.738 480.8268 599.738 c b 0 g 480.8268 604.5463 m F 0 G 0.3 w 10 M 427.6036 630.4795 m S 1 g 1 w 4 M 427.6036 625.6712 m 430.4153 625.6712 432.6947 627.824 432.6947 630.4795 c 432.6947 633.135 430.4153 635.2878 427.6036 635.2878 c 424.7919 635.2878 422.5125 633.135 422.5125 630.4795 c 422.5125 627.824 424.7919 625.6712 427.6036 625.6712 c b 0 g 427.6036 630.4795 m F 0 G 0.3 w 10 M 400.992 630.4795 m S 1 g 1 w 4 M 400.992 625.6712 m 403.8037 625.6712 406.0831 627.824 406.0831 630.4795 c 406.0831 633.135 403.8037 635.2878 400.992 635.2878 c 398.1803 635.2878 395.9009 633.135 395.9009 630.4795 c 395.9009 627.824 398.1803 625.6712 400.992 625.6712 c b 0 g 400.992 630.4795 m F 0 G 0.3 w 10 M 400.992 604.5463 m S 0.7 g 1 w 4 M 400.992 599.738 m 403.8037 599.738 406.0831 601.8908 406.0831 604.5463 c 406.0831 607.2018 403.8037 609.3546 400.992 609.3546 c 398.1803 609.3546 395.9009 607.2018 395.9009 604.5463 c 395.9009 601.8908 398.1803 599.738 400.992 599.738 c b 0 g 400.992 604.5463 m F 0 G 0.3 w 10 M 427.6036 604.5463 m S 1 g 1 w 4 M 427.6036 599.738 m 430.4153 599.738 432.6947 601.8908 432.6947 604.5463 c 432.6947 607.2018 430.4153 609.3546 427.6036 609.3546 c 424.7919 609.3546 422.5125 607.2018 422.5125 604.5463 c 422.5125 601.8908 424.7919 599.738 427.6036 599.738 c b 0 g 427.6036 604.5463 m F 0 G 0.3 w 10 M 454.2152 604.5463 m S 1 g 1 w 4 M 454.2152 599.738 m 457.0269 599.738 459.3063 601.8908 459.3063 604.5463 c 459.3063 607.2018 457.0269 609.3546 454.2152 609.3546 c 451.4035 609.3546 449.1241 607.2018 449.1241 604.5463 c 449.1241 601.8908 451.4035 599.738 454.2152 599.738 c b 0 g 454.2152 604.5463 m F 0 G 0.3 w 10 M 454.2152 630.4795 m S 1 g 1 w 4 M 454.2152 625.6712 m 457.0269 625.6712 459.3063 627.824 459.3063 630.4795 c 459.3063 633.135 457.0269 635.2878 454.2152 635.2878 c 451.4035 635.2878 449.1241 633.135 449.1241 630.4795 c 449.1241 627.824 451.4035 625.6712 454.2152 625.6712 c b 0 g 454.2152 630.4795 m F 0 G 0.3 w 10 M 400.992 565.6465 m S 387.6862 565.6465 m S 414.2978 565.6465 m S 400.992 565.6465 m S 414.2978 565.6465 m S 400.992 565.6465 m S 427.6036 565.6465 m S 414.2978 565.6465 m S 427.6036 565.6465 m S 414.2978 565.6465 m S 400.992 565.6465 m S 387.6862 565.6465 m S 440.9094 565.6465 m S 427.6036 565.6465 m S 454.2152 565.6465 m S 440.9094 565.6465 m S 454.2152 565.6465 m S 440.9094 565.6465 m S 467.521 565.6465 m S 454.2152 565.6465 m S 467.521 565.6465 m S 454.2152 565.6465 m S 440.9094 565.6465 m S 427.6036 565.6465 m S 480.8268 565.6465 m S 467.521 565.6465 m S 494.1326 565.6465 m S 480.8268 565.6465 m S 494.1326 565.6465 m S 480.8268 565.6465 m S 507.4385 565.6465 m S 494.1326 565.6465 m S 507.4385 565.6465 m S 494.1326 565.6465 m S 480.8268 565.6465 m S 467.521 565.6465 m S 520.7441 565.6465 m S 507.4385 565.6465 m S 520.7441 565.6465 m S 520.7441 565.6465 m S 520.7441 565.6465 m S 507.4385 565.6465 m S 400.992 565.6465 m S 387.6862 565.6465 m S 414.2978 565.6465 m S 400.992 565.6465 m S 414.2978 565.6465 m S 400.992 565.6465 m S 427.6036 565.6465 m S 414.2978 565.6465 m S 427.6036 565.6465 m S 414.2978 565.6465 m S 400.992 565.6465 m S 387.6862 565.6465 m S 440.9094 565.6465 m S 427.6036 565.6465 m S 454.2152 565.6465 m S 440.9094 565.6465 m S 454.2152 565.6465 m S 440.9094 565.6465 m S 467.521 565.6465 m S 454.2152 565.6465 m S 467.521 565.6465 m S 454.2152 565.6465 m S 440.9094 565.6465 m S 427.6036 565.6465 m S 480.8268 565.6465 m S 467.521 565.6465 m S 494.1326 565.6465 m S 480.8268 565.6465 m S 494.1326 565.6465 m S 480.8268 565.6465 m S 507.4385 565.6465 m S 494.1326 565.6465 m S 507.4385 565.6465 m S 494.1326 565.6465 m S 480.8268 565.6465 m S 467.521 565.6465 m S 520.7441 565.6465 m S 507.4385 565.6465 m S 520.7441 565.6465 m S 520.7441 565.6465 m S 520.7441 565.6465 m S 507.4385 565.6465 m S 400.992 565.6465 m S 1 g 1 w 4 M 400.992 560.8382 m 403.8037 560.8382 406.0831 562.991 406.0831 565.6465 c 406.0831 568.302 403.8037 570.4548 400.992 570.4548 c 398.1803 570.4548 395.9009 568.302 395.9009 565.6465 c 395.9009 562.991 398.1803 560.8382 400.992 560.8382 c b 0 g 400.992 565.6465 m F 0 G 0.3 w 10 M 414.2978 565.6465 m S 1 g 1 w 4 M 414.2978 560.8382 m 417.1095 560.8382 419.389 562.991 419.389 565.6465 c 419.389 568.302 417.1095 570.4548 414.2978 570.4548 c 411.4861 570.4548 409.2067 568.302 409.2067 565.6465 c 409.2067 562.991 411.4861 560.8382 414.2978 560.8382 c b 0 g 414.2978 565.6465 m F 0 G 0.3 w 10 M 427.6036 565.6465 m S 1 g 1 w 4 M 427.6036 560.8382 m 430.4153 560.8382 432.6947 562.991 432.6947 565.6465 c 432.6947 568.302 430.4153 570.4548 427.6036 570.4548 c 424.792 570.4548 422.5125 568.302 422.5125 565.6465 c 422.5125 562.991 424.792 560.8382 427.6036 560.8382 c b 0 g 427.6036 565.6465 m F 0 G 0.3 w 10 M 440.9094 565.6465 m S 0.7 g 1 w 4 M 440.9094 560.8382 m 443.7212 560.8382 446.0005 562.991 446.0005 565.6465 c 446.0005 568.302 443.7212 570.4548 440.9094 570.4548 c 438.0978 570.4548 435.8183 568.302 435.8183 565.6465 c 435.8183 562.991 438.0978 560.8382 440.9094 560.8382 c b 0 g 440.9094 565.6465 m F 0 G 0.3 w 10 M 454.2152 565.6465 m S 1 g 1 w 4 M 454.2152 560.8382 m 457.027 560.8382 459.3063 562.991 459.3063 565.6465 c 459.3063 568.302 457.027 570.4548 454.2152 570.4548 c 451.4035 570.4548 449.1241 568.302 449.1241 565.6465 c 449.1241 562.991 451.4035 560.8382 454.2152 560.8382 c b 0 g 454.2152 565.6465 m F 0 G 0.3 w 10 M 467.521 565.6465 m S 1 g 1 w 4 M 467.521 560.8382 m 470.3327 560.8382 472.6121 562.991 472.6121 565.6465 c 472.6121 568.302 470.3327 570.4548 467.521 570.4548 c 464.7093 570.4548 462.43 568.302 462.43 565.6465 c 462.43 562.991 464.7093 560.8382 467.521 560.8382 c b 0 g 467.521 565.6465 m F 0 G 0.3 w 10 M 480.8268 565.6465 m S 1 g 1 w 4 M 480.8268 560.8382 m 483.6385 560.8382 485.9179 562.991 485.9179 565.6465 c 485.9179 568.302 483.6385 570.4548 480.8268 570.4548 c 478.0151 570.4548 475.7357 568.302 475.7357 565.6465 c 475.7357 562.991 478.0151 560.8382 480.8268 560.8382 c b 0 g 480.8268 565.6465 m F 0 G 0.3 w 10 M 494.1326 565.6465 m S 0.7 g 1 w 4 M 494.1326 560.8382 m 496.9443 560.8382 499.2237 562.991 499.2237 565.6465 c 499.2237 568.302 496.9443 570.4548 494.1326 570.4548 c 491.3209 570.4548 489.0415 568.302 489.0415 565.6465 c 489.0415 562.991 491.3209 560.8382 494.1326 560.8382 c b 0 g 494.1326 565.6465 m F 0 G 0.3 w 10 M 520.7441 565.6465 m S 0.3 g 1 w 4 M 520.7441 560.8382 m 523.5559 560.8382 525.8353 562.991 525.8353 565.6465 c 525.8353 568.302 523.5559 570.4548 520.7441 570.4548 c 517.9325 570.4548 515.6531 568.302 515.6531 565.6465 c 515.6531 562.991 517.9325 560.8382 520.7441 560.8382 c b 0 g 520.7441 565.6465 m F 0 G 0.3 w 10 M 507.4385 565.6465 m S 1 g 1 w 4 M 507.4385 560.8382 m 510.2501 560.8382 512.5295 562.991 512.5295 565.6465 c 512.5295 568.302 510.2501 570.4548 507.4385 570.4548 c 504.6267 570.4548 502.3473 568.302 502.3473 565.6465 c 502.3473 562.991 504.6267 560.8382 507.4385 560.8382 c b 0 g 507.4385 565.6465 m F 0 G 0.3 w 10 M 387.6862 565.6465 m S 0.3 g 1 w 4 M 387.6862 560.8382 m 390.4979 560.8382 392.7773 562.991 392.7773 565.6465 c 392.7773 568.302 390.4979 570.4548 387.6862 570.4548 c 384.8745 570.4548 382.5951 568.302 382.5951 565.6465 c 382.5951 562.991 384.8745 560.8382 387.6862 560.8382 c b 0 g 387.6862 565.6465 m F 0 G 0.3 w 10 M 400.992 578.6131 m S 400.992 578.6131 m S 400.992 578.6131 m S 427.6036 578.6131 m S 427.6036 578.6131 m S 400.992 578.6131 m S 427.6036 578.6131 m S 454.2152 578.6131 m S 454.2152 578.6131 m S 454.2152 578.6131 m S 454.2152 578.6131 m S 427.6036 578.6131 m S 480.8268 578.6131 m S 480.8268 578.6131 m S 480.8268 578.6131 m S 507.4385 578.6131 m S 507.4385 578.6131 m S 480.8268 578.6131 m S 507.4385 578.6131 m S 507.4385 578.6131 m S 507.4385 578.6131 m S 0.7 g 1 w 4 M 507.4385 573.8048 m 510.2501 573.8048 512.5295 575.9576 512.5295 578.6131 c 512.5295 581.2686 510.2501 583.4214 507.4385 583.4214 c 504.6267 583.4214 502.3473 581.2686 502.3473 578.6131 c 502.3473 575.9576 504.6267 573.8048 507.4385 573.8048 c b 0 g 507.4385 578.6131 m F 0 G 0.3 w 10 M 480.8268 578.6131 m S 1 g 1 w 4 M 480.8268 573.8048 m 483.6385 573.8048 485.9179 575.9576 485.9179 578.6131 c 485.9179 581.2686 483.6385 583.4214 480.8268 583.4214 c 478.0151 583.4214 475.7357 581.2686 475.7357 578.6131 c 475.7357 575.9576 478.0151 573.8048 480.8268 573.8048 c b 0 g 480.8268 578.6131 m F 0 G 0.3 w 10 M 427.6036 578.6131 m S 1 g 1 w 4 M 427.6036 573.8048 m 430.4153 573.8048 432.6947 575.9576 432.6947 578.6131 c 432.6947 581.2686 430.4153 583.4214 427.6036 583.4214 c 424.7919 583.4214 422.5125 581.2686 422.5125 578.6131 c 422.5125 575.9576 424.7919 573.8048 427.6036 573.8048 c b 0 g 427.6036 578.6131 m F 0 G 0.3 w 10 M 400.992 578.6131 m S 1 g 1 w 4 M 400.992 573.8048 m 403.8037 573.8048 406.0831 575.9576 406.0831 578.6131 c 406.0831 581.2686 403.8037 583.4214 400.992 583.4214 c 398.1803 583.4214 395.9009 581.2686 395.9009 578.6131 c 395.9009 575.9576 398.1803 573.8048 400.992 573.8048 c b 0 g 400.992 578.6131 m F 0 G 0.3 w 10 M 454.2152 578.6131 m S 1 g 1 w 4 M 454.2152 573.8048 m 457.0269 573.8048 459.3063 575.9576 459.3063 578.6131 c 459.3063 581.2686 457.0269 583.4214 454.2152 583.4214 c 451.4035 583.4214 449.1241 581.2686 449.1241 578.6131 c 449.1241 575.9576 451.4035 573.8048 454.2152 573.8048 c b 0 g 454.2152 578.6131 m F 0 G 0.3 w 10 M 400.992 552.6799 m S 394.3391 546.1966 m S 400.992 552.6799 m S 407.6449 546.1966 m S 427.6036 552.6799 m S 420.9507 546.1966 m S 0 g 1 w 4 M 394.3391 546.1966 m F 420.9507 546.1966 m F 0 G 0.3 w 10 M 427.6036 552.6799 m S 434.2566 546.1966 m S 454.2152 552.6799 m S 447.5624 546.1966 m S 454.2152 552.6799 m S 460.8681 546.1966 m S 0 g 1 w 4 M 434.2566 546.1966 m F 460.8681 546.1966 m F 0 G 0.3 w 10 M 480.8268 552.6799 m S 474.1739 546.1966 m S 480.8268 552.6799 m S 487.4797 546.1966 m S 507.4385 552.6799 m S 500.7855 546.1966 m S 0 g 1 w 4 M 474.1739 546.1966 m F 500.7855 546.1966 m F 0 G 0.3 w 10 M 507.4385 552.6799 m S 514.0913 546.1966 m S 527.3971 546.1966 m S 0 g 1 w 4 M 514.0913 546.1966 m F 0 G 0.3 w 10 M 394.3391 546.1966 m S 0 g 1 w 4 M 394.3391 546.1966 m F 0 G 0.3 w 10 M 400.992 552.6799 m S 400.992 552.6799 m S 400.992 552.6799 m S 0.3 g 1 w 4 M 400.992 547.8716 m 403.8037 547.8716 406.0831 550.0244 406.0831 552.6799 c 406.0831 555.3354 403.8037 557.4882 400.992 557.4882 c 398.1803 557.4882 395.9009 555.3354 395.9009 552.6799 c 395.9009 550.0244 398.1803 547.8716 400.992 547.8716 c b 0 g 400.992 552.6799 m F 0 G 0.3 w 10 M 427.6036 552.6799 m S 0.3 g 1 w 4 M 427.6036 547.8716 m 430.4153 547.8716 432.6947 550.0244 432.6947 552.6799 c 432.6947 555.3354 430.4153 557.4882 427.6036 557.4882 c 424.7919 557.4882 422.5125 555.3354 422.5125 552.6799 c 422.5125 550.0244 424.7919 547.8716 427.6036 547.8716 c b 0 g 427.6036 552.6799 m F 0 G 0.3 w 10 M 480.8268 552.6799 m S 0.3 g 1 w 4 M 480.8268 547.8716 m 483.6385 547.8716 485.9179 550.0244 485.9179 552.6799 c 485.9179 555.3354 483.6385 557.4882 480.8268 557.4882 c 478.0151 557.4882 475.7357 555.3354 475.7357 552.6799 c 475.7357 550.0244 478.0151 547.8716 480.8268 547.8716 c b 0 g 480.8268 552.6799 m F 0 G 0.3 w 10 M 507.4385 552.6799 m S 0.3 g 1 w 4 M 507.4385 547.8716 m 510.2501 547.8716 512.5295 550.0244 512.5295 552.6799 c 512.5295 555.3354 510.2501 557.4882 507.4385 557.4882 c 504.6267 557.4882 502.3473 555.3354 502.3473 552.6799 c 502.3473 550.0244 504.6267 547.8716 507.4385 547.8716 c b 0 g 507.4385 552.6799 m F 0 G 0.3 w 10 M 454.2152 552.6799 m S 0.3 g 1 w 4 M 454.2152 547.8716 m 457.0269 547.8716 459.3063 550.0244 459.3063 552.6799 c 459.3063 555.3354 457.0269 557.4882 454.2152 557.4882 c 451.4035 557.4882 449.1241 555.3354 449.1241 552.6799 c 449.1241 550.0244 451.4035 547.8716 454.2152 547.8716 c b 0 g 454.2152 552.6799 m F 0 G 0.3 w 10 M 361.0746 669.3791 m S 361.0746 682.3457 m S 367.7275 675.8624 m S 400.992 656.4125 m S 400.992 643.446 m S 387.6862 643.446 m S 387.6862 656.4125 m S 394.3391 649.9293 m S 387.6862 669.3791 m S 387.6862 656.4125 m S 381.0333 662.8959 m S 387.6862 682.3457 m S 387.6862 669.3791 m S 381.0333 675.8624 m S u 400.992 682.3457 m S 400.992 669.3791 m S 387.6862 669.3791 m S 387.6862 682.3457 m S 394.3391 675.8624 m S U u 400.992 669.3791 m S 400.992 656.4125 m S 387.6862 656.4125 m S 387.6862 669.3791 m S 394.3391 662.8959 m S U 387.6862 656.4125 m S 387.6862 643.446 m S 381.0333 649.9293 m S 361.0746 643.446 m S 361.0746 656.4125 m S 367.7275 649.9293 m S 361.0746 656.4125 m S 361.0746 669.3791 m S 367.7275 662.8959 m S 0 g 1 w 4 M 367.7275 675.8624 m F 367.7275 649.9293 m F 0 G 0.3 w 10 M 361.0746 630.4794 m S 361.0746 643.446 m S 367.7275 636.9627 m S 400.992 617.5128 m S 400.992 604.5462 m S 387.6862 617.5128 m S 394.3391 611.0295 m S 387.6862 617.5128 m S 381.0333 623.9961 m S 387.6862 643.446 m S 381.0333 636.9627 m S 400.992 643.446 m S 400.992 630.4794 m S 387.6862 643.446 m S 394.3391 636.9627 m S 387.6862 617.5128 m S 381.0333 611.0295 m S 361.0746 604.5462 m S 361.0746 617.5128 m S 367.7275 611.0295 m S 361.0746 617.5128 m S 361.0746 630.4794 m S 367.7275 623.9961 m S 0 g 1 w 4 M 367.7275 636.9627 m F 367.7275 611.0295 m F 367.7275 598.0629 m F 0 G 0.3 w 10 M 361.0746 591.5796 m S 361.0746 604.5462 m S 367.7275 598.0629 m S 387.6862 565.6464 m S 387.6862 591.5796 m S 381.0333 585.0963 m S 387.6862 591.5796 m S 381.0333 598.0629 m S 387.6862 591.5796 m S 387.6862 591.5796 m S 387.6862 565.6464 m S 381.0333 572.1297 m S 361.0746 565.6464 m S 361.0746 578.613 m S 367.7275 572.1297 m S 361.0746 578.613 m S 361.0746 591.5796 m S 367.7275 585.0963 m S 0 g 1 w 4 M 367.7275 598.0629 m F 367.7275 572.1297 m F 0 G 0.3 w 10 M 361.0746 552.6798 m S 361.0746 565.6464 m S 367.7275 559.1631 m S 387.6862 526.7467 m S 381.0333 546.1965 m S 387.6862 565.6464 m S 381.0333 559.1631 m S 387.6862 565.6464 m S 387.6862 526.7467 m S 374.3804 526.7467 m S 381.0333 533.2299 m S 374.3804 526.7467 m S 361.0746 526.7467 m S 361.0746 539.7132 m S 367.7275 533.2299 m S 361.0746 539.7132 m S 361.0746 552.6798 m S 367.7275 546.1965 m S 0 g 1 w 4 M 367.7275 559.1631 m F 367.7275 533.2299 m F 0 G 0.3 w 10 M 400.992 682.3457 m S 387.6862 682.3457 m S 394.3391 688.829 m S 374.3804 695.3122 m S 387.6862 682.3457 m S 374.3804 695.3122 m S 381.0333 688.829 m S 374.3804 695.3122 m S 361.0746 682.3457 m S 361.0746 695.3122 m S 367.7275 688.829 m S 374.3804 695.3122 m S 361.0746 695.3122 m S 367.7275 701.7956 m S 440.9094 682.3457 m S 427.6036 682.3457 m S 434.2565 688.829 m S 427.6036 682.3457 m S 414.2978 682.3457 m S 420.9507 688.829 m S 414.2978 682.3457 m S 400.992 682.3457 m S 407.6449 688.829 m S 454.2152 682.3457 m S 460.8681 688.829 m S 454.2152 682.3457 m S 440.9094 682.3457 m S 447.5623 688.829 m S 527.3971 688.8291 m S 547.3559 695.3123 m S 540.703 701.7956 m S 547.3559 695.3123 m S 547.3559 682.3457 m S 540.703 688.8291 m S 0 g 1 w 4 M 540.703 701.7956 m F 0 G 0.3 w 10 M 361.1996 617.6502 m S 361.1996 630.6168 m S 367.8525 624.1335 m S 387.8112 617.6502 m S 381.1583 611.167 m S 387.8112 617.6502 m S 381.1583 624.1335 m S 387.8112 591.7171 m S 381.1583 598.2004 m S 361.1996 591.7171 m S 361.1996 604.6836 m S 367.8525 598.2004 m S 361.1996 604.6836 m S 361.1996 617.6502 m S 367.8525 611.167 m S 361.1996 578.7505 m S 361.1996 591.7171 m S 367.8525 585.2338 m S 387.8112 591.7171 m S 381.1583 585.2338 m S 361.1996 630.6168 m S 361.1996 643.5833 m S 367.8525 637.1001 m S 361.1996 565.7838 m S 361.1996 578.7504 m S 367.8525 572.2671 m S 387.8112 565.7838 m S 381.1583 559.3006 m S 387.8112 565.7838 m S 381.1583 572.2671 m S 381.1583 546.334 m S 361.1996 539.8507 m S 361.1996 552.8172 m S 367.8525 546.334 m S 361.1996 552.8172 m S 361.1996 565.7838 m S 367.8525 559.3006 m S 374.5054 526.8841 m S 361.1996 526.8841 m S 361.1996 539.8507 m S 367.8525 533.3674 m S 387.8112 526.8841 m S 374.5054 526.8841 m S 381.1583 533.3674 m S 361.1996 578.7504 m S 361.1996 591.7169 m S 367.8525 585.2337 m S 520.8692 591.6923 m S 527.5221 598.1756 m S 520.7442 643.4337 m S 527.3971 636.9504 m S 520.7442 617.5005 m S 527.3971 611.0173 m S 520.7442 591.5674 m S 527.3971 598.0507 m S 520.7442 643.4337 m S 527.3971 649.917 m S 527.4596 688.8668 m S 547.4183 695.3501 m S 547.4183 682.3835 m S 540.7654 688.8668 m S 520.8067 643.4838 m S 527.4596 649.9671 m S 1 w 4 M 363.7573 669.3613 m 366.2043 690.7908 370.1355 704.6869 374.5679 704.6869 c S 388.0029 617.7127 m S 374.5679 530.7386 m 367.1481 530.7386 361.1329 569.679 361.1329 617.7127 c 361.1329 637.0524 362.108 654.9179 363.7573 669.3613 c S 533.9208 704.4747 m 541.3407 704.4747 547.3558 665.5343 547.3558 617.5005 c 547.3558 569.4667 541.3407 530.5264 533.9208 530.5264 c S 520.4858 617.5005 m S u u 0 g /_Times-Italic 36 43 0 0 z [1 0 0 1 321.1603 611.604]e (m)t T U U 0 G 0.3 w 10 M 400.992 669.3792 m S 387.6862 669.3792 m S 414.2978 669.3792 m S 400.992 669.3792 m S 414.2978 669.3792 m S 400.992 669.3792 m S 427.6036 669.3792 m S 414.2978 669.3792 m S 427.6036 669.3792 m S 414.2978 669.3792 m S 400.992 669.3792 m S 387.6862 669.3792 m S 440.9094 669.3792 m S 427.6036 669.3792 m S 454.2152 669.3792 m S 440.9094 669.3792 m S 454.2152 669.3792 m S 440.9094 669.3792 m S 467.521 669.3792 m S 454.2152 669.3792 m S 467.521 669.3792 m S 454.2152 669.3792 m S 440.9094 669.3792 m S 427.6036 669.3792 m S 480.8268 669.3792 m S 467.521 669.3792 m S 494.1326 669.3792 m S 480.8268 669.3792 m S 494.1326 669.3792 m S 480.8268 669.3792 m S 507.4385 669.3792 m S 494.1326 669.3792 m S 507.4385 669.3792 m S 494.1326 669.3792 m S 480.8268 669.3792 m S 467.521 669.3792 m S 520.7441 669.3792 m S 507.4385 669.3792 m S 520.7441 669.3792 m S 520.7441 669.3792 m S 520.7441 669.3792 m S 507.4385 669.3792 m S 400.992 669.3792 m S 1 g 1 w 4 M 400.992 664.5709 m 403.8037 664.5709 406.0831 666.7237 406.0831 669.3792 c 406.0831 672.0347 403.8037 674.1875 400.992 674.1875 c 398.1803 674.1875 395.9009 672.0347 395.9009 669.3792 c 395.9009 666.7237 398.1803 664.5709 400.992 664.5709 c b 0 g 400.992 669.3792 m F 0 G 0.3 w 10 M 414.2978 669.3792 m S 0.7 g 1 w 4 M 414.2978 664.5709 m 417.1095 664.5709 419.389 666.7237 419.389 669.3792 c 419.389 672.0347 417.1095 674.1875 414.2978 674.1875 c 411.4861 674.1875 409.2067 672.0347 409.2067 669.3792 c 409.2067 666.7237 411.4861 664.5709 414.2978 664.5709 c b 0 g 414.2978 669.3792 m F 0 G 0.3 w 10 M 427.6036 669.3792 m S 1 g 1 w 4 M 427.6036 664.5709 m 430.4153 664.5709 432.6947 666.7237 432.6947 669.3792 c 432.6947 672.0347 430.4153 674.1875 427.6036 674.1875 c 424.792 674.1875 422.5125 672.0347 422.5125 669.3792 c 422.5125 666.7237 424.792 664.5709 427.6036 664.5709 c b 0 g 427.6036 669.3792 m F 0 G 0.3 w 10 M 440.9094 669.3792 m S 1 g 1 w 4 M 440.9094 664.5709 m 443.7212 664.5709 446.0005 666.7237 446.0005 669.3792 c 446.0005 672.0347 443.7212 674.1875 440.9094 674.1875 c 438.0978 674.1875 435.8183 672.0347 435.8183 669.3792 c 435.8183 666.7237 438.0978 664.5709 440.9094 664.5709 c b 0 g 440.9094 669.3792 m F 0 G 0.3 w 10 M 454.2152 669.3792 m S 1 g 1 w 4 M 454.2152 664.5709 m 457.027 664.5709 459.3063 666.7237 459.3063 669.3792 c 459.3063 672.0347 457.027 674.1875 454.2152 674.1875 c 451.4035 674.1875 449.1241 672.0347 449.1241 669.3792 c 449.1241 666.7237 451.4035 664.5709 454.2152 664.5709 c b 0 g 454.2152 669.3792 m F 0 G 0.3 w 10 M 467.521 669.3792 m S 0.7 g 1 w 4 M 467.521 664.5709 m 470.3327 664.5709 472.6121 666.7237 472.6121 669.3792 c 472.6121 672.0347 470.3327 674.1875 467.521 674.1875 c 464.7093 674.1875 462.43 672.0347 462.43 669.3792 c 462.43 666.7237 464.7093 664.5709 467.521 664.5709 c b 0 g 467.521 669.3792 m F 0 G 0.3 w 10 M 480.8268 669.3792 m S 1 g 1 w 4 M 480.8268 664.5709 m 483.6385 664.5709 485.9179 666.7237 485.9179 669.3792 c 485.9179 672.0347 483.6385 674.1875 480.8268 674.1875 c 478.0151 674.1875 475.7357 672.0347 475.7357 669.3792 c 475.7357 666.7237 478.0151 664.5709 480.8268 664.5709 c b 0 g 480.8268 669.3792 m F 0 G 0.3 w 10 M 494.1326 669.3792 m S 1 g 1 w 4 M 494.1326 664.5709 m 496.9443 664.5709 499.2237 666.7237 499.2237 669.3792 c 499.2237 672.0347 496.9443 674.1875 494.1326 674.1875 c 491.3209 674.1875 489.0415 672.0347 489.0415 669.3792 c 489.0415 666.7237 491.3209 664.5709 494.1326 664.5709 c b 0 g 494.1326 669.3792 m F 0 G 0.3 w 10 M 520.7441 669.3792 m S 0.3 g 1 w 4 M 520.7441 664.5709 m 523.5559 664.5709 525.8353 666.7237 525.8353 669.3792 c 525.8353 672.0347 523.5559 674.1875 520.7441 674.1875 c 517.2659 674.1875 515.6531 672.0346 515.6531 669.3792 c 515.6531 666.7237 517.9325 664.5709 520.7441 664.5709 c b 0 g 520.7441 669.3792 m F 0 G 0.3 w 10 M 507.4385 669.3792 m S 1 g 1 w 4 M 507.4385 664.5709 m 510.2501 664.5709 512.5295 666.7237 512.5295 669.3792 c 512.5295 672.0347 510.2501 674.1875 507.4385 674.1875 c 504.6267 674.1875 502.3473 672.0347 502.3473 669.3792 c 502.3473 666.7237 504.6267 664.5709 507.4385 664.5709 c b 0 g 507.4385 669.3792 m F 0 G 0.3 w 10 M 387.6862 669.3792 m S 0.3 g 1 w 4 M 387.6862 664.5709 m 390.4979 664.5709 392.7773 666.7237 392.7773 669.3792 c 392.7773 672.0347 390.4979 674.1875 387.6862 674.1875 c 384.8745 674.1875 382.5951 672.0347 382.5951 669.3792 c 382.5951 666.7237 384.8745 664.5709 387.6862 664.5709 c b 0 g 387.6862 669.3792 m F 0 G 0.3 w 10 M 400.992 669.3791 m S 387.6862 669.3791 m S 387.6862 669.3791 m S 387.6862 669.3791 m S 400.992 669.3791 m S 387.6862 669.3791 m S 520.7442 669.3668 m S 520.7442 669.3668 m S 520.8067 669.4169 m S 440.9094 682.3457 m S 0 g 1 w 4 M 440.9094 682.3457 m F 0 G 0.3 w 10 M 440.9094 682.3457 m S 440.9094 682.3457 m S 440.9094 682.3457 m S 0 g 1 w 4 M 440.9094 682.3457 m F 0 G 0.3 w 10 M 440.9094 682.3457 m S 440.9094 682.3457 m S 440.9094 682.3457 m S 0 g 1 w 4 M 440.9094 682.3457 m F 0 G 0.3 w 10 M 440.9094 682.3457 m S 440.9094 682.3457 m S 414.2978 682.3457 m S 0 g 1 w 4 M 414.2978 682.3457 m F 0 G 0.3 w 10 M 414.2978 682.3457 m S 414.2978 682.3457 m S 414.2978 682.3457 m S 0 g 1 w 4 M 414.2978 682.3457 m F 0 G 0.3 w 10 M 414.2978 682.3457 m S 414.2978 682.3457 m S 414.2978 682.3457 m S 0 g 1 w 4 M 414.2978 682.3457 m F 0 G 0.3 w 10 M 414.2978 682.3457 m S 414.2978 682.3457 m S 387.5612 656.2752 m S 0 g 1 w 4 M 387.5612 656.2752 m F 0 G 0.3 w 10 M 387.5612 656.2752 m S 387.5612 656.2752 m S 387.5612 656.2752 m S 0 g 1 w 4 M 387.5612 656.2752 m F 0 G 0.3 w 10 M 387.5612 656.2752 m S 387.5612 656.2752 m S 1 g 1 w 4 M 387.5612 656.2752 m F 0 G 0.3 w 10 M 387.5612 656.2752 m S 0 g 1 w 4 M 387.5612 656.2752 m F 0 G 0.3 w 10 M 387.5612 656.2752 m S 387.5612 656.2752 m S 414.1728 656.2752 m S 0 g 1 w 4 M 414.1728 656.2752 m F 0 G 0.3 w 10 M 414.1728 656.2752 m S 414.1728 656.2752 m S 414.1728 656.2752 m S 0 g 1 w 4 M 414.1728 656.2752 m F 0 G 0.3 w 10 M 414.1728 656.2752 m S 414.1728 656.2752 m S 1 g 1 w 4 M 414.1728 656.2752 m F 0 G 0.3 w 10 M 414.1728 656.2752 m S 0 g 1 w 4 M 414.1728 656.2752 m F 0 G 0.3 w 10 M 414.1728 656.2752 m S 414.1728 656.2752 m S 507.3135 656.2752 m S 1 g 1 w 4 M 507.3135 651.4669 m 510.1251 651.4669 512.4045 653.6197 512.4045 656.2752 c 512.4045 658.9307 510.1251 661.0835 507.3135 661.0835 c 504.5017 661.0835 502.2223 658.9307 502.2223 656.2752 c 502.2223 653.6197 504.5017 651.4669 507.3135 651.4669 c b 0 g 507.3135 656.2752 m F 0 G 0.3 w 10 M 480.7018 656.2752 m S 1 g 1 w 4 M 480.7018 651.4669 m 483.5135 651.4669 485.7929 653.6197 485.7929 656.2752 c 485.7929 658.9307 483.5135 661.0835 480.7018 661.0835 c 477.8901 661.0835 475.6107 658.9307 475.6107 656.2752 c 475.6107 653.6197 477.8901 651.4669 480.7018 651.4669 c b 0 g 480.7018 656.2752 m F 0 G 0.3 w 10 M 400.867 656.2752 m S 0.7 g 1 w 4 M 400.867 651.4669 m 403.6787 651.4669 405.9581 653.6197 405.9581 656.2752 c 405.9581 658.9307 403.6787 661.0835 400.867 661.0835 c 398.0553 661.0835 395.7759 658.9307 395.7759 656.2752 c 395.7759 653.6197 398.0553 651.4669 400.867 651.4669 c b 0 g 400.867 656.2752 m F 0 G 0.3 w 10 M 427.4786 656.2752 m S 1 g 1 w 4 M 427.4786 651.4669 m 430.2903 651.4669 432.5697 653.6197 432.5697 656.2752 c 432.5697 658.9307 430.2903 661.0835 427.4786 661.0835 c 424.6669 661.0835 422.3875 658.9307 422.3875 656.2752 c 422.3875 653.6197 424.6669 651.4669 427.4786 651.4669 c b 0 g 427.4786 656.2752 m F 0 G 0.3 w 10 M 454.0902 656.2752 m S 1 g 1 w 4 M 454.0902 651.4669 m 456.9019 651.4669 459.1813 653.6197 459.1813 656.2752 c 459.1813 658.9307 456.9019 661.0835 454.0902 661.0835 c 451.2785 661.0835 448.9991 658.9307 448.9991 656.2752 c 448.9991 653.6197 451.2785 651.4669 454.0902 651.4669 c b 0 g 454.0902 656.2752 m F 0 G 0.3 w 10 M 400.867 656.2751 m S 387.5612 656.2751 m S 387.5612 656.2751 m S 387.5612 656.2751 m S 387.5612 656.2751 m S 387.6862 656.4125 m S 387.6862 656.4125 m S 381.0333 649.9293 m S 527.3971 649.9045 m S 527.2721 649.7796 m S 255.55 654.4126 m S 0 g 1 w 4 M 255.55 654.4126 m F 0 G 0.3 w 10 M 255.55 654.4126 m S 255.55 654.4126 m S 255.55 628.4795 m S 0 g 1 w 4 M 255.55 628.4795 m F 0 G 0.3 w 10 M 255.55 628.4795 m S 255.55 628.4795 m S 255.55 628.4795 m S 0 g 1 w 4 M 255.55 628.4795 m F 0 G 0.3 w 10 M 255.55 628.4795 m S 255.55 628.4795 m S 255.55 628.4795 m S 0 g 1 w 4 M 255.55 628.4795 m F 0 G 0.3 w 10 M 255.55 628.4795 m S 255.55 628.4795 m S 215.6326 628.4795 m S 0 g 1 w 4 M 215.6326 628.4795 m F 0 G 0.3 w 10 M 215.6326 628.4795 m S 215.6326 628.4795 m S 215.6326 628.4795 m S 0 g 1 w 4 M 215.6326 628.4795 m F 0 G 0.3 w 10 M 215.6326 628.4795 m S 215.6326 628.4795 m S 1 g 1 w 4 M 209.6222 628.4795 m 209.6222 625.2577 212.3132 622.6459 215.6326 622.6459 c 218.9521 622.6459 221.6431 625.2577 221.6431 628.4795 c F 221.6431 628.4795 m 221.6431 631.7013 218.9521 634.3132 215.6326 634.3132 c 212.3132 634.3132 209.6222 631.7013 209.6222 628.4795 c F 215.6326 628.4795 m F 0 G 0.3 w 10 M 215.6326 628.4795 m S 0 g 1 w 4 M 215.6326 628.4795 m F 0 G 0.3 w 10 M 215.6326 628.4795 m S 215.6326 628.4795 m S 0 g 1 w 4 M 214.5476 627.4116 m 214.5476 623.8345 L 216.7177 623.8345 L 216.7177 627.4116 L 220.3033 627.4004 L 220.3033 629.5588 L 216.7177 629.5477 L 216.7177 633.1248 L 214.5476 633.1248 L 214.5476 629.5477 L 210.9619 629.5588 L 210.9619 627.4004 L 214.5476 627.4116 L f 0 G 0.3 w 10 M 242.2441 654.4126 m S 0 g 1 w 4 M 242.2441 654.4126 m F 0 G 0.3 w 10 M 242.2441 654.4126 m S 242.2441 654.4126 m S 242.2441 654.4126 m S 0 g 1 w 4 M 242.2441 654.4126 m F 0 G 0.3 w 10 M 242.2441 654.4126 m S 242.2441 654.4126 m S u 1 g 1 w 4 M 236.2337 654.4126 m 236.2337 651.1909 238.9247 648.579 242.2441 648.579 c 245.5636 648.579 248.2546 651.1909 248.2546 654.4126 c F 248.2546 654.4126 m 248.2546 657.6344 245.5636 660.2463 242.2441 660.2463 c 238.9247 660.2463 236.2337 657.6344 236.2337 654.4126 c F 242.2441 654.4126 m F U 0 G 0.3 w 10 M 242.2441 654.4126 m S 0 g 1 w 4 M 242.2441 654.4126 m F 0 G 0.3 w 10 M 242.2441 654.4126 m S 242.2441 654.4126 m S 0 g 1 w 4 M 241.159 653.3447 m 241.159 649.7676 L 243.3292 649.7676 L 243.3292 653.3447 L 246.9148 653.3335 L 246.9148 655.4919 L 243.3292 655.4808 L 243.3292 659.0579 L 241.159 659.0579 L 241.159 655.4808 L 237.5734 655.4919 L 237.5734 653.3335 L 241.159 653.3447 L f 0 G 0.3 w 10 M 242.2441 628.4795 m S 0 g 1 w 4 M 242.2441 628.4795 m F 0 G 0.3 w 10 M 242.2441 628.4795 m S 242.2441 628.4795 m S 242.2441 628.4795 m S 0 g 1 w 4 M 242.2441 628.4795 m F 0 G 0.3 w 10 M 242.2441 628.4795 m S 242.2441 628.4795 m S 1 g 1 w 4 M 236.2337 628.4795 m 236.2337 625.2577 238.9247 622.6459 242.2441 622.6459 c 245.5636 622.6459 248.2546 625.2577 248.2546 628.4795 c F 248.2546 628.4795 m 248.2546 631.7013 245.5636 634.3132 242.2441 634.3132 c 238.9247 634.3132 236.2337 631.7013 236.2337 628.4795 c F 242.2441 628.4795 m F 0 G 0.3 w 10 M 242.2441 628.4795 m S 0 g 1 w 4 M 242.2441 628.4795 m F 0 G 0.3 w 10 M 242.2441 628.4795 m S 242.2441 628.4795 m S 0 g 1 w 4 M 241.159 627.4116 m 241.159 623.8345 L 243.3292 623.8345 L 243.3292 627.4116 L 246.9148 627.4004 L 246.9148 629.5588 L 243.3292 629.5477 L 243.3292 633.1248 L 241.159 633.1248 L 241.159 629.5477 L 237.5734 629.5588 L 237.5734 627.4004 L 241.159 627.4116 L f 0 G 0.3 w 10 M 162.4094 628.4795 m S 0 g 1 w 4 M 162.4094 628.4795 m F 0 G 0.3 w 10 M 162.4094 628.4795 m S 162.4094 628.4795 m S 162.4094 628.4795 m S 0 g 1 w 4 M 162.4094 628.4795 m F 0 G 0.3 w 10 M 162.4094 628.4795 m S 162.4094 628.4795 m S 1 g 1 w 4 M 156.399 628.4795 m 156.399 625.2577 159.09 622.6459 162.4094 622.6459 c 165.7289 622.6459 168.4198 625.2577 168.4198 628.4795 c F 168.4198 628.4795 m 168.4198 631.7013 165.7289 634.3132 162.4094 634.3132 c 159.09 634.3132 156.399 631.7013 156.399 628.4795 c F 162.4094 628.4795 m F 0 G 0.3 w 10 M 162.4094 628.4795 m S 0 g 1 w 4 M 162.4094 628.4795 m F 0 G 0.3 w 10 M 162.4094 628.4795 m S 162.4094 628.4795 m S 0 g 1 w 4 M 161.3243 627.4116 m 161.3243 623.8345 L 163.4945 623.8345 L 163.4945 627.4116 L 167.0801 627.4004 L 167.0801 629.5588 L 163.4945 629.5477 L 163.4945 633.1248 L 161.3243 633.1248 L 161.3243 629.5477 L 157.7387 629.5588 L 157.7387 627.4004 L 161.3243 627.4116 L f 0 G 0.3 w 10 M 109.1862 628.4795 m S 0 g 1 w 4 M 109.1862 628.4795 m F 0 G 0.3 w 10 M 109.1862 628.4795 m S 109.1862 628.4795 m S 109.1862 628.4795 m S 0 g 1 w 4 M 109.1862 628.4795 m F 0 G 0.3 w 10 M 109.1862 628.4795 m S 109.1862 628.4795 m S 1 g 1 w 4 M 103.1758 628.4795 m 103.1758 625.2577 105.8668 622.6459 109.1862 622.6459 c 112.5057 622.6459 115.1966 625.2577 115.1966 628.4795 c F 115.1966 628.4795 m 115.1966 631.7013 112.5057 634.3132 109.1862 634.3132 c 105.8668 634.3132 103.1758 631.7013 103.1758 628.4795 c F 109.1862 628.4795 m F 0 G 0.3 w 10 M 109.1862 628.4795 m S 0 g 1 w 4 M 109.1862 628.4795 m F 0 G 0.3 w 10 M 109.1862 628.4795 m S 109.1862 628.4795 m S 0 g 1 w 4 M 108.1011 627.4116 m 108.1011 623.8345 L 110.2713 623.8345 L 110.2713 627.4116 L 113.8569 627.4004 L 113.8569 629.5588 L 110.2713 629.5477 L 110.2713 633.1248 L 108.1011 633.1248 L 108.1011 629.5477 L 104.5155 629.5588 L 104.5155 627.4004 L 108.1011 627.4116 L f 0 G 0.3 w 10 M 109.1862 602.5463 m S 0 g 1 w 4 M 109.1862 602.5463 m F 0 G 0.3 w 10 M 109.1862 602.5463 m S 109.1862 602.5463 m S 109.1862 602.5463 m S 0 g 1 w 4 M 109.1862 602.5463 m F 0 G 0.3 w 10 M 109.1862 602.5463 m S 109.1862 602.5463 m S 1 g 1 w 4 M 103.1758 602.5463 m 103.1758 599.3245 105.8668 596.7127 109.1862 596.7127 c 112.5057 596.7127 115.1966 599.3245 115.1966 602.5463 c F 115.1966 602.5463 m 115.1966 605.7681 112.5057 608.38 109.1862 608.38 c 105.8668 608.38 103.1758 605.7681 103.1758 602.5463 c F 109.1862 602.5463 m F 0 G 0.3 w 10 M 109.1862 602.5463 m S 0 g 1 w 4 M 109.1862 602.5463 m F 0 G 0.3 w 10 M 109.1862 602.5463 m S 109.1862 602.5463 m S 0 g 1 w 4 M 108.1011 601.4784 m 108.1011 597.9013 L 110.2713 597.9013 L 110.2713 601.4784 L 113.8569 601.4672 L 113.8569 603.6256 L 110.2713 603.6145 L 110.2713 607.1916 L 108.1011 607.1916 L 108.1011 603.6145 L 104.5155 603.6256 L 104.5155 601.4672 L 108.1011 601.4784 L f 0 G 0.3 w 10 M 135.7978 602.5463 m S 0 g 1 w 4 M 135.7978 602.5463 m F 0 G 0.3 w 10 M 135.7978 602.5463 m S 135.7978 602.5463 m S 135.7978 602.5463 m S 0 g 1 w 4 M 135.7978 602.5463 m F 0 G 0.3 w 10 M 135.7978 602.5463 m S 135.7978 602.5463 m S 1 g 1 w 4 M 129.7874 602.5463 m 129.7874 599.3245 132.4784 596.7127 135.7978 596.7127 c 139.1173 596.7127 141.8082 599.3245 141.8082 602.5463 c F 141.8082 602.5463 m 141.8082 605.7681 139.1173 608.38 135.7978 608.38 c 132.4784 608.38 129.7874 605.7681 129.7874 602.5463 c F 135.7978 602.5463 m F 0 G 0.3 w 10 M 135.7978 602.5463 m S 0 g 1 w 4 M 135.7978 602.5463 m F 0 G 0.3 w 10 M 135.7978 602.5463 m S 135.7978 602.5463 m S 0 g 1 w 4 M 134.7127 601.4784 m 134.7127 597.9013 L 136.8829 597.9013 L 136.8829 601.4784 L 140.4685 601.4672 L 140.4685 603.6256 L 136.8829 603.6145 L 136.8829 607.1916 L 134.7127 607.1916 L 134.7127 603.6145 L 131.1271 603.6256 L 131.1271 601.4672 L 134.7127 601.4784 L f 0 G 0.3 w 10 M 189.021 602.5463 m S 0 g 1 w 4 M 189.021 602.5463 m F 0 G 0.3 w 10 M 189.021 602.5463 m S 189.021 602.5463 m S 189.021 602.5463 m S 0 g 1 w 4 M 189.021 602.5463 m F 0 G 0.3 w 10 M 189.021 602.5463 m S 189.021 602.5463 m S 1 g 1 w 4 M 183.0106 602.5463 m 183.0106 599.3245 185.7016 596.7127 189.021 596.7127 c 192.3405 596.7127 195.0315 599.3245 195.0315 602.5463 c F 195.0315 602.5463 m 195.0315 605.7681 192.3405 608.38 189.021 608.38 c 185.7016 608.38 183.0106 605.7681 183.0106 602.5463 c F 189.021 602.5463 m F 0 G 0.3 w 10 M 189.021 602.5463 m S 0 g 1 w 4 M 189.021 602.5463 m F 0 G 0.3 w 10 M 189.021 602.5463 m S 189.021 602.5463 m S 0 g 1 w 4 M 187.9359 601.4784 m 187.9359 597.9013 L 190.1061 597.9013 L 190.1061 601.4784 L 193.6917 601.4672 L 193.6917 603.6256 L 190.1061 603.6145 L 190.1061 607.1916 L 187.9359 607.1916 L 187.9359 603.6145 L 184.3503 603.6256 L 184.3503 601.4672 L 187.9359 601.4784 L f 0 G 0.3 w 10 M 242.2441 602.5463 m S 0 g 1 w 4 M 242.2441 602.5463 m F 0 G 0.3 w 10 M 242.2441 602.5463 m S 242.2441 602.5463 m S 242.2441 602.5463 m S 0 g 1 w 4 M 242.2441 602.5463 m F 0 G 0.3 w 10 M 242.2441 602.5463 m S 242.2441 602.5463 m S 1 g 1 w 4 M 236.2337 602.5463 m 236.2337 599.3245 238.9247 596.7127 242.2441 596.7127 c 245.5636 596.7127 248.2546 599.3245 248.2546 602.5463 c F 248.2546 602.5463 m 248.2546 605.7681 245.5636 608.38 242.2441 608.38 c 238.9247 608.38 236.2337 605.7681 236.2337 602.5463 c F 242.2441 602.5463 m F 0 G 0.3 w 10 M 242.2441 602.5463 m S 0 g 1 w 4 M 242.2441 602.5463 m F 0 G 0.3 w 10 M 242.2441 602.5463 m S 242.2441 602.5463 m S 0 g 1 w 4 M 241.159 601.4784 m 241.159 597.9013 L 243.3292 597.9013 L 243.3292 601.4784 L 246.9148 601.4672 L 246.9148 603.6256 L 243.3292 603.6145 L 243.3292 607.1916 L 241.159 607.1916 L 241.159 603.6145 L 237.5734 603.6256 L 237.5734 601.4672 L 241.159 601.4784 L f 0 G 0.3 w 10 M 162.4094 654.4126 m S 0 g 1 w 4 M 162.4094 654.4126 m F 0 G 0.3 w 10 M 162.4094 654.4126 m S 0 g 1 w 4 M 162.4094 654.4126 m F u 1 g 156.399 654.4126 m 156.399 651.1909 159.09 648.579 162.4094 648.579 c 165.7289 648.579 168.4198 651.1909 168.4198 654.4126 c F 168.4198 654.4126 m 168.4198 657.6344 165.7289 660.2463 162.4094 660.2463 c 159.09 660.2463 156.399 657.6344 156.399 654.4126 c F 162.4094 654.4126 m F U 0 G 0.3 w 10 M 162.4094 654.4126 m S 0 g 1 w 4 M 162.4094 654.4126 m F 0 G 0.3 w 10 M 162.4094 654.4126 m S 0 g 1 w 4 M 162.4094 654.4126 m F 161.3243 655.4808 m 157.7387 655.4919 L 157.7387 653.3335 L 161.3243 653.3446 L F 163.4945 653.3446 m 167.0801 653.3335 L 167.0801 655.4919 L 163.4945 655.4808 L F 157.7387 655.4919 m 167.0801 655.4919 l 167.0801 653.3335 l 157.7387 653.3335 l 157.7387 655.4919 l f 0 G 0.3 w 10 M 215.6326 654.4126 m S 0 g 1 w 4 M 215.6326 654.4126 m F 0 G 0.3 w 10 M 215.6326 654.4126 m S 0 g 1 w 4 M 215.6326 654.4126 m F u 1 g 209.6222 654.4126 m 209.6222 651.1909 212.3132 648.579 215.6326 648.579 c 218.9521 648.579 221.6431 651.1909 221.6431 654.4126 c F 221.6431 654.4126 m 221.6431 657.6344 218.9521 660.2463 215.6326 660.2463 c 212.3132 660.2463 209.6222 657.6344 209.6222 654.4126 c F 215.6326 654.4126 m F U 0 G 0.3 w 10 M 215.6326 654.4126 m S 0 g 1 w 4 M 215.6326 654.4126 m F 0 G 0.3 w 10 M 215.6326 654.4126 m S 0 g 1 w 4 M 215.6326 654.4126 m F 214.5475 655.4808 m 210.9619 655.4919 L 210.9619 653.3335 L 214.5475 653.3446 L F 216.7177 653.3446 m 220.3033 653.3335 L 220.3033 655.4919 L 216.7177 655.4808 L F 210.9619 655.4919 m 220.3033 655.4919 l 220.3033 653.3335 l 210.9619 653.3335 l 210.9619 655.4919 l f 0 G 0.3 w 10 M 135.7978 628.4795 m S 0 g 1 w 4 M 135.7978 628.4795 m F 0 G 0.3 w 10 M 135.7978 628.4795 m S 0 g 1 w 4 M 135.7978 628.4795 m F 1 g 129.7874 628.4795 m 129.7874 625.2577 132.4784 622.6459 135.7978 622.6459 c 139.1173 622.6459 141.8082 625.2577 141.8082 628.4795 c F 141.8082 628.4795 m 141.8082 631.7013 139.1173 634.3132 135.7978 634.3132 c 132.4784 634.3132 129.7874 631.7013 129.7874 628.4795 c F 135.7978 628.4795 m F 0 G 0.3 w 10 M 135.7978 628.4795 m S 0 g 1 w 4 M 135.7978 628.4795 m F 0 G 0.3 w 10 M 135.7978 628.4795 m S 0 g 1 w 4 M 135.7978 628.4795 m F 134.7127 629.5477 m 131.1271 629.5588 L 131.1271 627.4004 L 134.7127 627.4115 L F 136.8829 627.4115 m 140.4685 627.4004 L 140.4685 629.5588 L 136.8829 629.5477 L F 131.1271 629.5588 m 140.4685 629.5588 l 140.4685 627.4004 l 131.1271 627.4004 l 131.1271 629.5588 l f 0 G 0.3 w 10 M 189.021 628.4795 m S 0 g 1 w 4 M 189.021 628.4795 m F 0 G 0.3 w 10 M 189.021 628.4795 m S 0 g 1 w 4 M 189.021 628.4795 m F 1 g 183.0106 628.4795 m 183.0106 625.2577 185.7016 622.6459 189.021 622.6459 c 192.3405 622.6459 195.0315 625.2577 195.0315 628.4795 c F 195.0315 628.4795 m 195.0315 631.7013 192.3405 634.3132 189.021 634.3132 c 185.7016 634.3132 183.0106 631.7013 183.0106 628.4795 c F 189.021 628.4795 m F 0 G 0.3 w 10 M 189.021 628.4795 m S 0 g 1 w 4 M 189.021 628.4795 m F 0 G 0.3 w 10 M 189.021 628.4795 m S 0 g 1 w 4 M 189.021 628.4795 m F 187.9359 629.5477 m 184.3503 629.5588 L 184.3503 627.4004 L 187.9359 627.4115 L F 190.1061 627.4115 m 193.6917 627.4004 L 193.6917 629.5588 L 190.1061 629.5477 L F 184.3503 629.5588 m 193.6917 629.5588 l 193.6917 627.4004 l 184.3503 627.4004 l 184.3503 629.5588 l f 0 G 0.3 w 10 M 162.4094 602.5463 m S 0 g 1 w 4 M 162.4094 602.5463 m F 0 G 0.3 w 10 M 162.4094 602.5463 m S 0 g 1 w 4 M 162.4094 602.5463 m F 1 g 156.399 602.5463 m 156.399 599.3245 159.09 596.7127 162.4094 596.7127 c 165.7289 596.7127 168.4198 599.3245 168.4198 602.5463 c F 168.4198 602.5463 m 168.4198 605.7681 165.7289 608.38 162.4094 608.38 c 159.09 608.38 156.399 605.7681 156.399 602.5463 c F 162.4094 602.5463 m F 0 G 0.3 w 10 M 162.4094 602.5463 m S 0 g 1 w 4 M 162.4094 602.5463 m F 0 G 0.3 w 10 M 162.4094 602.5463 m S 0 g 1 w 4 M 162.4094 602.5463 m F 161.3243 603.6145 m 157.7387 603.6256 L 157.7387 601.4672 L 161.3243 601.4783 L F 163.4945 601.4783 m 167.0801 601.4672 L 167.0801 603.6256 L 163.4945 603.6145 L F 157.7387 603.6256 m 167.0801 603.6256 l 167.0801 601.4672 l 157.7387 601.4672 l 157.7387 603.6256 l f 0 G 0.3 w 10 M 215.6326 602.5463 m S 0 g 1 w 4 M 215.6326 602.5463 m F 0 G 0.3 w 10 M 215.6326 602.5463 m S 0 g 1 w 4 M 215.6326 602.5463 m F 1 g 209.6222 602.5463 m 209.6222 599.3245 212.3132 596.7127 215.6326 596.7127 c 218.9521 596.7127 221.6431 599.3245 221.6431 602.5463 c F 221.6431 602.5463 m 221.6431 605.7681 218.9521 608.38 215.6326 608.38 c 212.3132 608.38 209.6222 605.7681 209.6222 602.5463 c F 215.6326 602.5463 m F 0 G 0.3 w 10 M 215.6326 602.5463 m S 0 g 1 w 4 M 215.6326 602.5463 m F 0 G 0.3 w 10 M 215.6326 602.5463 m S 0 g 1 w 4 M 215.6326 602.5463 m F 214.5475 603.6145 m 210.9619 603.6256 L 210.9619 601.4672 L 214.5475 601.4783 L F 216.7177 601.4783 m 220.3033 601.4672 L 220.3033 603.6256 L 216.7177 603.6145 L F 210.9619 603.6256 m 220.3033 603.6256 l 220.3033 601.4672 l 210.9619 601.4672 l 210.9619 603.6256 l f 0 G 0.3 w 10 M 242.2441 680.3458 m S 0 g 1 w 4 M 242.2441 680.3458 m F 0 G 0.3 w 10 M 242.2441 680.3458 m S 242.2441 680.3458 m S 242.2441 680.3458 m S 0 g 1 w 4 M 242.2441 680.3458 m F 0 G 0.3 w 10 M 242.2441 680.3458 m S 242.2441 680.3458 m S 1 g 1 w 4 M 236.2337 680.3458 m 236.2337 677.124 238.9247 674.5122 242.2441 674.5122 c 245.5636 674.5122 248.2546 677.124 248.2546 680.3458 c F 248.2546 680.3458 m 248.2546 683.5676 245.5636 686.1795 242.2441 686.1795 c 238.9247 686.1795 236.2337 683.5676 236.2337 680.3458 c F 242.2441 680.3458 m F 0 G 0.3 w 10 M 242.2441 680.3458 m S 0 g 1 w 4 M 242.2441 680.3458 m F 0 G 0.3 w 10 M 242.2441 680.3458 m S 242.2441 680.3458 m S 0 g 1 w 4 M 241.159 679.2779 m 241.159 675.7008 L 243.3292 675.7008 L 243.3292 679.2779 L 246.9148 679.2667 L 246.9148 681.4251 L 243.3292 681.414 L 243.3292 684.9911 L 241.159 684.9911 L 241.159 681.414 L 237.5734 681.4251 L 237.5734 679.2667 L 241.159 679.2779 L f 0 G 0.3 w 10 M 109.1862 680.3458 m S 0 g 1 w 4 M 109.1862 680.3458 m F 0 G 0.3 w 10 M 109.1862 680.3458 m S 109.1862 680.3458 m S 109.1862 680.3458 m S 0 g 1 w 4 M 109.1862 680.3458 m F 0 G 0.3 w 10 M 109.1862 680.3458 m S 109.1862 680.3458 m S 1 g 1 w 4 M 103.1758 680.3458 m 103.1758 677.124 105.8668 674.5122 109.1862 674.5122 c 112.5057 674.5122 115.1966 677.124 115.1966 680.3458 c F 115.1966 680.3458 m 115.1966 683.5676 112.5057 686.1795 109.1862 686.1795 c 105.8668 686.1795 103.1758 683.5676 103.1758 680.3458 c F 109.1862 680.3458 m F 0 G 0.3 w 10 M 109.1862 680.3458 m S 0 g 1 w 4 M 109.1862 680.3458 m F 0 G 0.3 w 10 M 109.1862 680.3458 m S 109.1862 680.3458 m S 0 g 1 w 4 M 108.1011 679.2779 m 108.1011 675.7008 L 110.2713 675.7008 L 110.2713 679.2779 L 113.8569 679.2667 L 113.8569 681.4251 L 110.2713 681.414 L 110.2713 684.9911 L 108.1011 684.9911 L 108.1011 681.414 L 104.5155 681.4251 L 104.5155 679.2667 L 108.1011 679.2779 L f 0 G 0.3 w 10 M 122.492 680.3458 m S 1 g 1 w 4 M 122.492 675.5375 m 125.3037 675.5375 127.5831 677.6903 127.5831 680.3458 c 127.5831 683.0013 125.3037 685.1541 122.492 685.1541 c 119.6803 685.1541 117.4009 683.0013 117.4009 680.3458 c 117.4009 677.6903 119.6803 675.5375 122.492 675.5375 c b 0 g 122.492 680.3458 m F 0 G 0.3 w 10 M 149.1036 680.3458 m S 1 g 1 w 4 M 149.1036 675.5375 m 151.9153 675.5375 154.1947 677.6903 154.1947 680.3458 c 154.1947 683.0013 151.9153 685.1541 149.1036 685.1541 c 146.2919 685.1541 144.0125 683.0013 144.0125 680.3458 c 144.0125 677.6903 146.2919 675.5375 149.1036 675.5375 c b 0 g 149.1036 680.3458 m F 0 G 0.3 w 10 M 109.1862 667.3792 m S 1 g 1 w 4 M 109.1862 662.5709 m 111.9979 662.5709 114.2773 664.7237 114.2773 667.3792 c 114.2773 670.0347 111.9979 672.1875 109.1862 672.1875 c 106.3745 672.1875 104.0951 670.0347 104.0951 667.3792 c 104.0951 664.7237 106.3745 662.5709 109.1862 662.5709 c b 0 g 109.1862 667.3792 m F 0 G 0.3 w 10 M 202.3268 680.3458 m S 1 g 1 w 4 M 202.3268 675.5375 m 205.1385 675.5375 207.4179 677.6903 207.4179 680.3458 c 207.4179 683.0013 205.1385 685.1541 202.3268 685.1541 c 199.5151 685.1541 197.2357 683.0013 197.2357 680.3458 c 197.2357 677.6903 199.5151 675.5375 202.3268 675.5375 c b 0 g 202.3268 680.3458 m F 0 G 0.3 w 10 M 228.9385 680.3458 m S 1 g 1 w 4 M 228.9385 675.5375 m 231.7501 675.5375 234.0295 677.6903 234.0295 680.3458 c 234.0295 683.0013 231.7501 685.1541 228.9385 685.1541 c 226.1267 685.1541 223.8473 683.0013 223.8473 680.3458 c 223.8473 677.6903 226.1267 675.5375 228.9385 675.5375 c b 0 g 228.9385 680.3458 m F 0 G 0.3 w 10 M 149.1036 654.4126 m S 1 g 1 w 4 M 149.1036 649.6043 m 151.9153 649.6043 154.1947 651.7571 154.1947 654.4126 c 154.1947 657.0681 151.9153 659.2209 149.1036 659.2209 c 146.2919 659.2209 144.0125 657.0681 144.0125 654.4126 c 144.0125 651.7571 146.2919 649.6043 149.1036 649.6043 c b 0 g 149.1036 654.4126 m F 0 G 0.3 w 10 M 175.7152 654.4126 m S 1 g 1 w 4 M 175.7152 649.6043 m 178.5269 649.6043 180.8063 651.7571 180.8063 654.4126 c 180.8063 657.0681 178.5269 659.2209 175.7152 659.2209 c 172.9035 659.2209 170.6241 657.0681 170.6241 654.4126 c 170.6241 651.7571 172.9035 649.6043 175.7152 649.6043 c b 0 g 175.7152 654.4126 m F 0 G 0.3 w 10 M 202.3268 654.4126 m S 1 g 1 w 4 M 202.3268 649.6043 m 205.1385 649.6043 207.4179 651.7571 207.4179 654.4126 c 207.4179 657.0681 205.1385 659.2209 202.3268 659.2209 c 199.5151 659.2209 197.2357 657.0681 197.2357 654.4126 c 197.2357 651.7571 199.5151 649.6043 202.3268 649.6043 c b 0 g 202.3268 654.4126 m F 0 G 0.3 w 10 M 228.9385 654.4126 m S 1 g 1 w 4 M 228.9385 649.6043 m 231.7501 649.6043 234.0295 651.7571 234.0295 654.4126 c 234.0295 657.0681 231.7501 659.2209 228.9385 659.2209 c 226.1267 659.2209 223.8473 657.0681 223.8473 654.4126 c 223.8473 651.7571 226.1267 649.6043 228.9385 649.6043 c b 0 g 228.9385 654.4126 m F 0 G 0.3 w 10 M 175.7152 680.3458 m S 1 g 1 w 4 M 175.7152 675.5375 m 178.5269 675.5375 180.8063 677.6903 180.8063 680.3458 c 180.8063 683.0013 178.5269 685.1541 175.7152 685.1541 c 172.9035 685.1541 170.6241 683.0013 170.6241 680.3458 c 170.6241 677.6903 172.9035 675.5375 175.7152 675.5375 c b 0 g 175.7152 680.3458 m F 0 G 0.3 w 10 M 122.492 641.4461 m S 109.1862 641.4461 m S 135.7978 641.4461 m S 122.492 641.4461 m S 135.7978 641.4461 m S 122.492 641.4461 m S 149.1036 641.4461 m S 135.7978 641.4461 m S 149.1036 641.4461 m S 135.7978 641.4461 m S 122.492 641.4461 m S 109.1862 641.4461 m S 162.4094 641.4461 m S 149.1036 641.4461 m S 175.7152 641.4461 m S 162.4094 641.4461 m S 175.7152 641.4461 m S 162.4094 641.4461 m S 189.021 641.4461 m S 175.7152 641.4461 m S 189.021 641.4461 m S 175.7152 641.4461 m S 162.4094 641.4461 m S 149.1036 641.4461 m S 202.3268 641.4461 m S 189.021 641.4461 m S 215.6326 641.4461 m S 202.3268 641.4461 m S 215.6326 641.4461 m S 202.3268 641.4461 m S 228.9385 641.4461 m S 215.6326 641.4461 m S 228.9385 641.4461 m S 215.6326 641.4461 m S 202.3268 641.4461 m S 189.021 641.4461 m S 242.2441 641.4461 m S 228.9385 641.4461 m S 242.2441 641.4461 m S 242.2441 641.4461 m S 242.2441 641.4461 m S 228.9385 641.4461 m S 122.492 641.4461 m S 1 g 1 w 4 M 122.492 636.6378 m 125.3037 636.6378 127.5831 638.7906 127.5831 641.4461 c 127.5831 644.1016 125.3037 646.2544 122.492 646.2544 c 119.6803 646.2544 117.4009 644.1016 117.4009 641.4461 c 117.4009 638.7906 119.6803 636.6378 122.492 636.6378 c b 0 g 122.492 641.4461 m F 0 G 0.3 w 10 M 135.7978 641.4461 m S 1 g 1 w 4 M 135.7978 636.6378 m 138.6095 636.6378 140.889 638.7906 140.889 641.4461 c 140.889 644.1016 138.6095 646.2544 135.7978 646.2544 c 132.9861 646.2544 130.7067 644.1016 130.7067 641.4461 c 130.7067 638.7906 132.9861 636.6378 135.7978 636.6378 c b 0 g 135.7978 641.4461 m F 0 G 0.3 w 10 M 149.1036 641.4461 m S 1 g 1 w 4 M 149.1036 636.6378 m 151.9153 636.6378 154.1947 638.7906 154.1947 641.4461 c 154.1947 644.1016 151.9153 646.2544 149.1036 646.2544 c 146.292 646.2544 144.0125 644.1016 144.0125 641.4461 c 144.0125 638.7906 146.292 636.6378 149.1036 636.6378 c b 0 g 149.1036 641.4461 m F 0 G 0.3 w 10 M 162.4094 641.4461 m S 1 g 1 w 4 M 162.4094 636.6378 m 165.2212 636.6378 167.5005 638.7906 167.5005 641.4461 c 167.5005 644.1016 165.2212 646.2544 162.4094 646.2544 c 159.5978 646.2544 157.3183 644.1016 157.3183 641.4461 c 157.3183 638.7906 159.5978 636.6378 162.4094 636.6378 c b 0 g 162.4094 641.4461 m F 0 G 0.3 w 10 M 175.7152 641.4461 m S 1 g 1 w 4 M 175.7152 636.6378 m 178.527 636.6378 180.8063 638.7906 180.8063 641.4461 c 180.8063 644.1016 178.527 646.2544 175.7152 646.2544 c 172.9035 646.2544 170.6241 644.1016 170.6241 641.4461 c 170.6241 638.7906 172.9035 636.6378 175.7152 636.6378 c b 0 g 175.7152 641.4461 m F 0 G 0.3 w 10 M 189.021 641.4461 m S 1 g 1 w 4 M 189.021 636.6378 m 191.8327 636.6378 194.1121 638.7906 194.1121 641.4461 c 194.1121 644.1016 191.8327 646.2544 189.021 646.2544 c 186.2093 646.2544 183.93 644.1016 183.93 641.4461 c 183.93 638.7906 186.2093 636.6378 189.021 636.6378 c b 0 g 189.021 641.4461 m F 0 G 0.3 w 10 M 202.3268 641.4461 m S 1 g 1 w 4 M 202.3268 636.6378 m 205.1385 636.6378 207.4179 638.7906 207.4179 641.4461 c 207.4179 644.1016 205.1385 646.2544 202.3268 646.2544 c 199.5151 646.2544 197.2357 644.1016 197.2357 641.4461 c 197.2357 638.7906 199.5151 636.6378 202.3268 636.6378 c b 0 g 202.3268 641.4461 m F 0 G 0.3 w 10 M 215.6326 641.4461 m S 1 g 1 w 4 M 215.6326 636.6378 m 218.4443 636.6378 220.7237 638.7906 220.7237 641.4461 c 220.7237 644.1016 218.4443 646.2544 215.6326 646.2544 c 212.8209 646.2544 210.5415 644.1016 210.5415 641.4461 c 210.5415 638.7906 212.8209 636.6378 215.6326 636.6378 c b 0 g 215.6326 641.4461 m F 0 G 0.3 w 10 M 242.2441 641.4461 m S 1 g 1 w 4 M 242.2441 636.6378 m 245.0559 636.6378 247.3353 638.7906 247.3353 641.4461 c 247.3353 644.1016 245.0559 646.2544 242.2441 646.2544 c 239.4325 646.2544 237.1531 644.1016 237.1531 641.4461 c 237.1531 638.7906 239.4325 636.6378 242.2441 636.6378 c b 0 g 242.2441 641.4461 m F 0 G 0.3 w 10 M 228.9385 641.4461 m S 1 g 1 w 4 M 228.9385 636.6378 m 231.7501 636.6378 234.0295 638.7906 234.0295 641.4461 c 234.0295 644.1016 231.7501 646.2544 228.9385 646.2544 c 226.1267 646.2544 223.8473 644.1016 223.8473 641.4461 c 223.8473 638.7906 226.1267 636.6378 228.9385 636.6378 c b 0 g 228.9385 641.4461 m F 0 G 0.3 w 10 M 109.1862 641.4461 m S 1 g 1 w 4 M 109.1862 636.6378 m 111.9979 636.6378 114.2773 638.7906 114.2773 641.4461 c 114.2773 644.1016 111.9979 646.2544 109.1862 646.2544 c 106.3745 646.2544 104.0951 644.1016 104.0951 641.4461 c 104.0951 638.7906 106.3745 636.6378 109.1862 636.6378 c b 0 g 109.1862 641.4461 m F 0 G 0.3 w 10 M 122.492 615.5129 m S 109.1862 615.5129 m S 135.7978 615.5129 m S 122.492 615.5129 m S 135.7978 615.5129 m S 122.492 615.5129 m S 149.1036 615.5129 m S 135.7978 615.5129 m S 149.1036 615.5129 m S 135.7978 615.5129 m S 122.492 615.5129 m S 109.1862 615.5129 m S 162.4094 615.5129 m S 149.1036 615.5129 m S 175.7152 615.5129 m S 162.4094 615.5129 m S 175.7152 615.5129 m S 162.4094 615.5129 m S 189.021 615.5129 m S 175.7152 615.5129 m S 189.021 615.5129 m S 175.7152 615.5129 m S 162.4094 615.5129 m S 149.1036 615.5129 m S 202.3268 615.5129 m S 189.021 615.5129 m S 215.6326 615.5129 m S 202.3268 615.5129 m S 215.6326 615.5129 m S 202.3268 615.5129 m S 228.9385 615.5129 m S 215.6326 615.5129 m S 228.9385 615.5129 m S 215.6326 615.5129 m S 202.3268 615.5129 m S 189.021 615.5129 m S 242.2441 615.5129 m S 228.9385 615.5129 m S 242.2441 615.5129 m S 242.2441 615.5129 m S 242.2441 615.5129 m S 228.9385 615.5129 m S 122.492 615.5129 m S 0 g 1 w 4 M 122.492 615.5129 m F 0 G 0.3 w 10 M 135.7978 615.5129 m S 0 g 1 w 4 M 135.7978 615.5129 m F 0 G 0.3 w 10 M 149.1036 615.5129 m S 0 g 1 w 4 M 149.1036 615.5129 m F 0 G 0.3 w 10 M 162.4094 615.5129 m S 0 g 1 w 4 M 162.4094 615.5129 m F 0 G 0.3 w 10 M 175.7152 615.5129 m S 0 g 1 w 4 M 175.7152 615.5129 m F 0 G 0.3 w 10 M 189.021 615.5129 m S 0 g 1 w 4 M 189.021 615.5129 m F 0 G 0.3 w 10 M 202.3268 615.5129 m S 0 g 1 w 4 M 202.3268 615.5129 m F 0 G 0.3 w 10 M 215.6326 615.5129 m S 0 g 1 w 4 M 215.6326 615.5129 m F 0 G 0.3 w 10 M 242.2441 615.5129 m S 0 g 1 w 4 M 242.2441 615.5129 m F 0 G 0.3 w 10 M 228.9385 615.5129 m S 0 g 1 w 4 M 228.9385 615.5129 m F 0 G 0.3 w 10 M 109.1862 615.5129 m S 1 g 1 w 4 M 109.1862 610.7046 m 111.9979 610.7046 114.2773 612.8574 114.2773 615.5129 c 114.2773 618.1684 111.9979 620.3212 109.1862 620.3212 c 106.3745 620.3212 104.0951 618.1684 104.0951 615.5129 c 104.0951 612.8574 106.3745 610.7046 109.1862 610.7046 c b 0 g 109.1862 615.5129 m F 0 G 0.3 w 10 M 122.492 615.5129 m S 109.1862 615.5129 m S 135.7978 615.5129 m S 122.492 615.5129 m S 135.7978 615.5129 m S 122.492 615.5129 m S 149.1036 615.5129 m S 135.7978 615.5129 m S 149.1036 615.5129 m S 135.7978 615.5129 m S 122.492 615.5129 m S 109.1862 615.5129 m S 162.4094 615.5129 m S 149.1036 615.5129 m S 175.7152 615.5129 m S 162.4094 615.5129 m S 175.7152 615.5129 m S 162.4094 615.5129 m S 189.021 615.5129 m S 175.7152 615.5129 m S 189.021 615.5129 m S 175.7152 615.5129 m S 162.4094 615.5129 m S 149.1036 615.5129 m S 202.3268 615.5129 m S 189.021 615.5129 m S 215.6326 615.5129 m S 202.3268 615.5129 m S 215.6326 615.5129 m S 202.3268 615.5129 m S 228.9385 615.5129 m S 215.6326 615.5129 m S 228.9385 615.5129 m S 215.6326 615.5129 m S 202.3268 615.5129 m S 189.021 615.5129 m S 242.2441 615.5129 m S 228.9385 615.5129 m S 242.2441 615.5129 m S 242.2441 615.5129 m S 242.2441 615.5129 m S 228.9385 615.5129 m S 122.492 615.5129 m S 1 g 1 w 4 M 122.492 610.7046 m 125.3037 610.7046 127.5831 612.8574 127.5831 615.5129 c 127.5831 618.1684 125.3037 620.3212 122.492 620.3212 c 119.6803 620.3212 117.4009 618.1684 117.4009 615.5129 c 117.4009 612.8574 119.6803 610.7046 122.492 610.7046 c b 0 g 122.492 615.5129 m F 0 G 0.3 w 10 M 135.7978 615.5129 m S 1 g 1 w 4 M 135.7978 610.7046 m 138.6095 610.7046 140.889 612.8574 140.889 615.5129 c 140.889 618.1684 138.6095 620.3212 135.7978 620.3212 c 132.9861 620.3212 130.7067 618.1684 130.7067 615.5129 c 130.7067 612.8574 132.9861 610.7046 135.7978 610.7046 c b 0 g 135.7978 615.5129 m F 0 G 0.3 w 10 M 149.1036 615.5129 m S 1 g 1 w 4 M 149.1036 610.7046 m 151.9153 610.7046 154.1947 612.8574 154.1947 615.5129 c 154.1947 618.1684 151.9153 620.3212 149.1036 620.3212 c 146.292 620.3212 144.0125 618.1684 144.0125 615.5129 c 144.0125 612.8574 146.292 610.7046 149.1036 610.7046 c b 0 g 149.1036 615.5129 m F 0 G 0.3 w 10 M 162.4094 615.5129 m S 1 g 1 w 4 M 162.4094 610.7046 m 165.2212 610.7046 167.5005 612.8574 167.5005 615.5129 c 167.5005 618.1684 165.2212 620.3212 162.4094 620.3212 c 159.5978 620.3212 157.3183 618.1684 157.3183 615.5129 c 157.3183 612.8574 159.5978 610.7046 162.4094 610.7046 c b 0 g 162.4094 615.5129 m F 0 G 0.3 w 10 M 175.7152 615.5129 m S 1 g 1 w 4 M 175.7152 610.7046 m 178.527 610.7046 180.8063 612.8574 180.8063 615.5129 c 180.8063 618.1684 178.527 620.3212 175.7152 620.3212 c 172.9035 620.3212 170.6241 618.1684 170.6241 615.5129 c 170.6241 612.8574 172.9035 610.7046 175.7152 610.7046 c b 0 g 175.7152 615.5129 m F 0 G 0.3 w 10 M 189.021 615.5129 m S 1 g 1 w 4 M 189.021 610.7046 m 191.8327 610.7046 194.1121 612.8574 194.1121 615.5129 c 194.1121 618.1684 191.8327 620.3212 189.021 620.3212 c 186.2093 620.3212 183.93 618.1684 183.93 615.5129 c 183.93 612.8574 186.2093 610.7046 189.021 610.7046 c b 0 g 189.021 615.5129 m F 0 G 0.3 w 10 M 202.3268 615.5129 m S 1 g 1 w 4 M 202.3268 610.7046 m 205.1385 610.7046 207.4179 612.8574 207.4179 615.5129 c 207.4179 618.1684 205.1385 620.3212 202.3268 620.3212 c 199.5151 620.3212 197.2357 618.1684 197.2357 615.5129 c 197.2357 612.8574 199.5151 610.7046 202.3268 610.7046 c b 0 g 202.3268 615.5129 m F 0 G 0.3 w 10 M 215.6326 615.5129 m S 1 g 1 w 4 M 215.6326 610.7046 m 218.4443 610.7046 220.7237 612.8574 220.7237 615.5129 c 220.7237 618.1684 218.4443 620.3212 215.6326 620.3212 c 212.8209 620.3212 210.5415 618.1684 210.5415 615.5129 c 210.5415 612.8574 212.8209 610.7046 215.6326 610.7046 c b 0 g 215.6326 615.5129 m F 0 G 0.3 w 10 M 242.2441 615.5129 m S 1 g 1 w 4 M 242.2441 610.7046 m 245.0559 610.7046 247.3353 612.8574 247.3353 615.5129 c 247.3353 618.1684 245.0559 620.3212 242.2441 620.3212 c 239.4325 620.3212 237.1531 618.1684 237.1531 615.5129 c 237.1531 612.8574 239.4325 610.7046 242.2441 610.7046 c b 0 g 242.2441 615.5129 m F 0 G 0.3 w 10 M 228.9385 615.5129 m S 1 g 1 w 4 M 228.9385 610.7046 m 231.7501 610.7046 234.0295 612.8574 234.0295 615.5129 c 234.0295 618.1684 231.7501 620.3212 228.9385 620.3212 c 226.1267 620.3212 223.8473 618.1684 223.8473 615.5129 c 223.8473 612.8574 226.1267 610.7046 228.9385 610.7046 c b 0 g 228.9385 615.5129 m F 0 G 0.3 w 10 M 109.1862 615.5129 m S 1 g 1 w 4 M 109.1862 610.7046 m 111.9979 610.7046 114.2773 612.8574 114.2773 615.5129 c 114.2773 618.1684 111.9979 620.3212 109.1862 620.3212 c 106.3745 620.3212 104.0951 618.1684 104.0951 615.5129 c 104.0951 612.8574 106.3745 610.7046 109.1862 610.7046 c b 0 g 109.1862 615.5129 m F 0 G 0.3 w 10 M 122.492 589.5797 m S 109.1862 589.5797 m S 135.7978 589.5797 m S 122.492 589.5797 m S 135.7978 589.5797 m S 122.492 589.5797 m S 149.1036 589.5797 m S 135.7978 589.5797 m S 149.1036 589.5797 m S 135.7978 589.5797 m S 122.492 589.5797 m S 109.1862 589.5797 m S 162.4094 589.5797 m S 149.1036 589.5797 m S 175.7152 589.5797 m S 162.4094 589.5797 m S 175.7152 589.5797 m S 162.4094 589.5797 m S 189.021 589.5797 m S 175.7152 589.5797 m S 189.021 589.5797 m S 175.7152 589.5797 m S 162.4094 589.5797 m S 149.1036 589.5797 m S 202.3268 589.5797 m S 189.021 589.5797 m S 215.6326 589.5797 m S 202.3268 589.5797 m S 215.6326 589.5797 m S 202.3268 589.5797 m S 228.9385 589.5797 m S 215.6326 589.5797 m S 228.9385 589.5797 m S 215.6326 589.5797 m S 202.3268 589.5797 m S 189.021 589.5797 m S 242.2441 589.5797 m S 228.9385 589.5797 m S 242.2441 589.5797 m S 242.2441 589.5797 m S 242.2441 589.5797 m S 228.9385 589.5797 m S 122.492 589.5797 m S 1 g 1 w 4 M 122.492 584.7714 m 125.3037 584.7714 127.5831 586.9242 127.5831 589.5797 c 127.5831 592.2352 125.3037 594.388 122.492 594.388 c 119.6803 594.388 117.4009 592.2352 117.4009 589.5797 c 117.4009 586.9242 119.6803 584.7714 122.492 584.7714 c b 0 g 122.492 589.5797 m F 0 G 0.3 w 10 M 135.7978 589.5797 m S 1 g 1 w 4 M 135.7978 584.7714 m 138.6095 584.7714 140.889 586.9242 140.889 589.5797 c 140.889 592.2352 138.6095 594.388 135.7978 594.388 c 132.9861 594.388 130.7067 592.2352 130.7067 589.5797 c 130.7067 586.9242 132.9861 584.7714 135.7978 584.7714 c b 0 g 135.7978 589.5797 m F 0 G 0.3 w 10 M 149.1036 589.5797 m S 1 g 1 w 4 M 149.1036 584.7714 m 151.9153 584.7714 154.1947 586.9242 154.1947 589.5797 c 154.1947 592.2352 151.9153 594.388 149.1036 594.388 c 146.292 594.388 144.0125 592.2352 144.0125 589.5797 c 144.0125 586.9242 146.292 584.7714 149.1036 584.7714 c b 0 g 149.1036 589.5797 m F 0 G 0.3 w 10 M 162.4094 589.5797 m S 1 g 1 w 4 M 162.4094 584.7714 m 165.2212 584.7714 167.5005 586.9242 167.5005 589.5797 c 167.5005 592.2352 165.2212 594.388 162.4094 594.388 c 159.5978 594.388 157.3183 592.2352 157.3183 589.5797 c 157.3183 586.9242 159.5978 584.7714 162.4094 584.7714 c b 0 g 162.4094 589.5797 m F 0 G 0.3 w 10 M 175.7152 589.5797 m S 1 g 1 w 4 M 175.7152 584.7714 m 178.527 584.7714 180.8063 586.9242 180.8063 589.5797 c 180.8063 592.2352 178.527 594.388 175.7152 594.388 c 172.9035 594.388 170.6241 592.2352 170.6241 589.5797 c 170.6241 586.9242 172.9035 584.7714 175.7152 584.7714 c b 0 g 175.7152 589.5797 m F 0 G 0.3 w 10 M 189.021 589.5797 m S 1 g 1 w 4 M 189.021 584.7714 m 191.8327 584.7714 194.1121 586.9242 194.1121 589.5797 c 194.1121 592.2352 191.8327 594.388 189.021 594.388 c 186.2093 594.388 183.93 592.2352 183.93 589.5797 c 183.93 586.9242 186.2093 584.7714 189.021 584.7714 c b 0 g 189.021 589.5797 m F 0 G 0.3 w 10 M 202.3268 589.5797 m S 1 g 1 w 4 M 202.3268 584.7714 m 205.1385 584.7714 207.4179 586.9242 207.4179 589.5797 c 207.4179 592.2352 205.1385 594.388 202.3268 594.388 c 199.5151 594.388 197.2357 592.2352 197.2357 589.5797 c 197.2357 586.9242 199.5151 584.7714 202.3268 584.7714 c b 0 g 202.3268 589.5797 m F 0 G 0.3 w 10 M 215.6326 589.5797 m S 1 g 1 w 4 M 215.6326 584.7714 m 218.4443 584.7714 220.7237 586.9242 220.7237 589.5797 c 220.7237 592.2352 218.4443 594.388 215.6326 594.388 c 212.8209 594.388 210.5415 592.2352 210.5415 589.5797 c 210.5415 586.9242 212.8209 584.7714 215.6326 584.7714 c b 0 g 215.6326 589.5797 m F 0 G 0.3 w 10 M 242.2441 589.5797 m S 1 g 1 w 4 M 242.2441 584.7714 m 245.0559 584.7714 247.3353 586.9242 247.3353 589.5797 c 247.3353 592.2352 245.0559 594.388 242.2441 594.388 c 239.4325 594.388 237.1531 592.2352 237.1531 589.5797 c 237.1531 586.9242 239.4325 584.7714 242.2441 584.7714 c b 0 g 242.2441 589.5797 m F 0 G 0.3 w 10 M 228.9385 589.5797 m S 1 g 1 w 4 M 228.9385 584.7714 m 231.7501 584.7714 234.0295 586.9242 234.0295 589.5797 c 234.0295 592.2352 231.7501 594.388 228.9385 594.388 c 226.1267 594.388 223.8473 592.2352 223.8473 589.5797 c 223.8473 586.9242 226.1267 584.7714 228.9385 584.7714 c b 0 g 228.9385 589.5797 m F 0 G 0.3 w 10 M 109.1862 589.5797 m S 1 g 1 w 4 M 109.1862 584.7714 m 111.9979 584.7714 114.2773 586.9242 114.2773 589.5797 c 114.2773 592.2352 111.9979 594.388 109.1862 594.388 c 106.3745 594.388 104.0951 592.2352 104.0951 589.5797 c 104.0951 586.9242 106.3745 584.7714 109.1862 584.7714 c b 0 g 109.1862 589.5797 m F 0 G 0.3 w 10 M 228.9385 628.4795 m S 1 g 1 w 4 M 228.9385 623.6712 m 231.7501 623.6712 234.0295 625.824 234.0295 628.4795 c 234.0295 631.135 231.7501 633.2878 228.9385 633.2878 c 226.1267 633.2878 223.8473 631.135 223.8473 628.4795 c 223.8473 625.824 226.1267 623.6712 228.9385 623.6712 c b 0 g 228.9385 628.4795 m F 0 G 0.3 w 10 M 202.3268 628.4795 m S 1 g 1 w 4 M 202.3268 623.6712 m 205.1385 623.6712 207.4179 625.824 207.4179 628.4795 c 207.4179 631.135 205.1385 633.2878 202.3268 633.2878 c 199.5151 633.2878 197.2357 631.135 197.2357 628.4795 c 197.2357 625.824 199.5151 623.6712 202.3268 623.6712 c b 0 g 202.3268 628.4795 m F 0 G 0.3 w 10 M 228.9385 602.5463 m S 1 g 1 w 4 M 228.9385 597.738 m 231.7501 597.738 234.0295 599.8908 234.0295 602.5463 c 234.0295 605.2018 231.7501 607.3546 228.9385 607.3546 c 226.1267 607.3546 223.8473 605.2018 223.8473 602.5463 c 223.8473 599.8908 226.1267 597.738 228.9385 597.738 c b 0 g 228.9385 602.5463 m F 0 G 0.3 w 10 M 202.3268 602.5463 m S 1 g 1 w 4 M 202.3268 597.738 m 205.1385 597.738 207.4179 599.8908 207.4179 602.5463 c 207.4179 605.2018 205.1385 607.3546 202.3268 607.3546 c 199.5151 607.3546 197.2357 605.2018 197.2357 602.5463 c 197.2357 599.8908 199.5151 597.738 202.3268 597.738 c b 0 g 202.3268 602.5463 m F 0 G 0.3 w 10 M 149.1036 628.4795 m S 1 g 1 w 4 M 149.1036 623.6712 m 151.9153 623.6712 154.1947 625.824 154.1947 628.4795 c 154.1947 631.135 151.9153 633.2878 149.1036 633.2878 c 146.2919 633.2878 144.0125 631.135 144.0125 628.4795 c 144.0125 625.824 146.2919 623.6712 149.1036 623.6712 c b 0 g 149.1036 628.4795 m F 0 G 0.3 w 10 M 122.492 628.4795 m S 1 g 1 w 4 M 122.492 623.6712 m 125.3037 623.6712 127.5831 625.824 127.5831 628.4795 c 127.5831 631.135 125.3037 633.2878 122.492 633.2878 c 119.6803 633.2878 117.4009 631.135 117.4009 628.4795 c 117.4009 625.824 119.6803 623.6712 122.492 623.6712 c b 0 g 122.492 628.4795 m F 0 G 0.3 w 10 M 122.492 602.5463 m S 1 g 1 w 4 M 122.492 597.738 m 125.3037 597.738 127.5831 599.8908 127.5831 602.5463 c 127.5831 605.2018 125.3037 607.3546 122.492 607.3546 c 119.6803 607.3546 117.4009 605.2018 117.4009 602.5463 c 117.4009 599.8908 119.6803 597.738 122.492 597.738 c b 0 g 122.492 602.5463 m F 0 G 0.3 w 10 M 149.1036 602.5463 m S 1 g 1 w 4 M 149.1036 597.738 m 151.9153 597.738 154.1947 599.8908 154.1947 602.5463 c 154.1947 605.2018 151.9153 607.3546 149.1036 607.3546 c 146.2919 607.3546 144.0125 605.2018 144.0125 602.5463 c 144.0125 599.8908 146.2919 597.738 149.1036 597.738 c b 0 g 149.1036 602.5463 m F 0 G 0.3 w 10 M 175.7152 602.5463 m S 1 g 1 w 4 M 175.7152 597.738 m 178.5269 597.738 180.8063 599.8908 180.8063 602.5463 c 180.8063 605.2018 178.5269 607.3546 175.7152 607.3546 c 172.9035 607.3546 170.6241 605.2018 170.6241 602.5463 c 170.6241 599.8908 172.9035 597.738 175.7152 597.738 c b 0 g 175.7152 602.5463 m F 0 G 0.3 w 10 M 175.7152 628.4795 m S 1 g 1 w 4 M 175.7152 623.6712 m 178.5269 623.6712 180.8063 625.824 180.8063 628.4795 c 180.8063 631.135 178.5269 633.2878 175.7152 633.2878 c 172.9035 633.2878 170.6241 631.135 170.6241 628.4795 c 170.6241 625.824 172.9035 623.6712 175.7152 623.6712 c b 0 g 175.7152 628.4795 m F 0 G 0.3 w 10 M 122.492 563.6465 m S 109.1862 563.6465 m S 135.7978 563.6465 m S 122.492 563.6465 m S 135.7978 563.6465 m S 122.492 563.6465 m S 149.1036 563.6465 m S 135.7978 563.6465 m S 149.1036 563.6465 m S 135.7978 563.6465 m S 122.492 563.6465 m S 109.1862 563.6465 m S 162.4094 563.6465 m S 149.1036 563.6465 m S 175.7152 563.6465 m S 162.4094 563.6465 m S 175.7152 563.6465 m S 162.4094 563.6465 m S 189.021 563.6465 m S 175.7152 563.6465 m S 189.021 563.6465 m S 175.7152 563.6465 m S 162.4094 563.6465 m S 149.1036 563.6465 m S 202.3268 563.6465 m S 189.021 563.6465 m S 215.6326 563.6465 m S 202.3268 563.6465 m S 215.6326 563.6465 m S 202.3268 563.6465 m S 228.9385 563.6465 m S 215.6326 563.6465 m S 228.9385 563.6465 m S 215.6326 563.6465 m S 202.3268 563.6465 m S 189.021 563.6465 m S 242.2441 563.6465 m S 228.9385 563.6465 m S 242.2441 563.6465 m S 242.2441 563.6465 m S 242.2441 563.6465 m S 228.9385 563.6465 m S 122.492 563.6465 m S 109.1862 563.6465 m S 135.7978 563.6465 m S 122.492 563.6465 m S 135.7978 563.6465 m S 122.492 563.6465 m S 149.1036 563.6465 m S 135.7978 563.6465 m S 149.1036 563.6465 m S 135.7978 563.6465 m S 122.492 563.6465 m S 109.1862 563.6465 m S 162.4094 563.6465 m S 149.1036 563.6465 m S 175.7152 563.6465 m S 162.4094 563.6465 m S 175.7152 563.6465 m S 162.4094 563.6465 m S 189.021 563.6465 m S 175.7152 563.6465 m S 189.021 563.6465 m S 175.7152 563.6465 m S 162.4094 563.6465 m S 149.1036 563.6465 m S 202.3268 563.6465 m S 189.021 563.6465 m S 215.6326 563.6465 m S 202.3268 563.6465 m S 215.6326 563.6465 m S 202.3268 563.6465 m S 228.9385 563.6465 m S 215.6326 563.6465 m S 228.9385 563.6465 m S 215.6326 563.6465 m S 202.3268 563.6465 m S 189.021 563.6465 m S 242.2441 563.6465 m S 228.9385 563.6465 m S 242.2441 563.6465 m S 242.2441 563.6465 m S 242.2441 563.6465 m S 228.9385 563.6465 m S 122.492 563.6465 m S 1 g 1 w 4 M 122.492 558.8382 m 125.3037 558.8382 127.5831 560.991 127.5831 563.6465 c 127.5831 566.302 125.3037 568.4548 122.492 568.4548 c 119.6803 568.4548 117.4009 566.302 117.4009 563.6465 c 117.4009 560.991 119.6803 558.8382 122.492 558.8382 c b 0 g 122.492 563.6465 m F 0 G 0.3 w 10 M 135.7978 563.6465 m S 1 g 1 w 4 M 135.7978 558.8382 m 138.6095 558.8382 140.889 560.991 140.889 563.6465 c 140.889 566.302 138.6095 568.4548 135.7978 568.4548 c 132.9861 568.4548 130.7067 566.302 130.7067 563.6465 c 130.7067 560.991 132.9861 558.8382 135.7978 558.8382 c b 0 g 135.7978 563.6465 m F 0 G 0.3 w 10 M 149.1036 563.6465 m S 1 g 1 w 4 M 149.1036 558.8382 m 151.9153 558.8382 154.1947 560.991 154.1947 563.6465 c 154.1947 566.302 151.9153 568.4548 149.1036 568.4548 c 146.292 568.4548 144.0125 566.302 144.0125 563.6465 c 144.0125 560.991 146.292 558.8382 149.1036 558.8382 c b 0 g 149.1036 563.6465 m F 0 G 0.3 w 10 M 162.4094 563.6465 m S 1 g 1 w 4 M 162.4094 558.8382 m 165.2212 558.8382 167.5005 560.991 167.5005 563.6465 c 167.5005 566.302 165.2212 568.4548 162.4094 568.4548 c 159.5978 568.4548 157.3183 566.302 157.3183 563.6465 c 157.3183 560.991 159.5978 558.8382 162.4094 558.8382 c b 0 g 162.4094 563.6465 m F 0 G 0.3 w 10 M 175.7152 563.6465 m S 1 g 1 w 4 M 175.7152 558.8382 m 178.527 558.8382 180.8063 560.991 180.8063 563.6465 c 180.8063 566.302 178.527 568.4548 175.7152 568.4548 c 172.9035 568.4548 170.6241 566.302 170.6241 563.6465 c 170.6241 560.991 172.9035 558.8382 175.7152 558.8382 c b 0 g 175.7152 563.6465 m F 0 G 0.3 w 10 M 189.021 563.6465 m S 1 g 1 w 4 M 189.021 558.8382 m 191.8327 558.8382 194.1121 560.991 194.1121 563.6465 c 194.1121 566.302 191.8327 568.4548 189.021 568.4548 c 186.2093 568.4548 183.93 566.302 183.93 563.6465 c 183.93 560.991 186.2093 558.8382 189.021 558.8382 c b 0 g 189.021 563.6465 m F 0 G 0.3 w 10 M 202.3268 563.6465 m S 1 g 1 w 4 M 202.3268 558.8382 m 205.1385 558.8382 207.4179 560.991 207.4179 563.6465 c 207.4179 566.302 205.1385 568.4548 202.3268 568.4548 c 199.5151 568.4548 197.2357 566.302 197.2357 563.6465 c 197.2357 560.991 199.5151 558.8382 202.3268 558.8382 c b 0 g 202.3268 563.6465 m F 0 G 0.3 w 10 M 215.6326 563.6465 m S 1 g 1 w 4 M 215.6326 558.8382 m 218.4443 558.8382 220.7237 560.991 220.7237 563.6465 c 220.7237 566.302 218.4443 568.4548 215.6326 568.4548 c 212.8209 568.4548 210.5415 566.302 210.5415 563.6465 c 210.5415 560.991 212.8209 558.8382 215.6326 558.8382 c b 0 g 215.6326 563.6465 m F 0 G 0.3 w 10 M 242.2441 563.6465 m S 1 g 1 w 4 M 242.2441 558.8382 m 245.0559 558.8382 247.3353 560.991 247.3353 563.6465 c 247.3353 566.302 245.0559 568.4548 242.2441 568.4548 c 239.4325 568.4548 237.1531 566.302 237.1531 563.6465 c 237.1531 560.991 239.4325 558.8382 242.2441 558.8382 c b 0 g 242.2441 563.6465 m F 0 G 0.3 w 10 M 228.9385 563.6465 m S 1 g 1 w 4 M 228.9385 558.8382 m 231.7501 558.8382 234.0295 560.991 234.0295 563.6465 c 234.0295 566.302 231.7501 568.4548 228.9385 568.4548 c 226.1267 568.4548 223.8473 566.302 223.8473 563.6465 c 223.8473 560.991 226.1267 558.8382 228.9385 558.8382 c b 0 g 228.9385 563.6465 m F 0 G 0.3 w 10 M 109.1862 563.6465 m S 1 g 1 w 4 M 109.1862 558.8382 m 111.9979 558.8382 114.2773 560.991 114.2773 563.6465 c 114.2773 566.302 111.9979 568.4548 109.1862 568.4548 c 106.3745 568.4548 104.0951 566.302 104.0951 563.6465 c 104.0951 560.991 106.3745 558.8382 109.1862 558.8382 c b 0 g 109.1862 563.6465 m F 0 G 0.3 w 10 M 122.492 576.6131 m S 109.1862 576.6131 m S 135.7978 576.6131 m S 122.492 576.6131 m S 135.7978 576.6131 m S 122.492 576.6131 m S 149.1036 576.6131 m S 135.7978 576.6131 m S 149.1036 576.6131 m S 135.7978 576.6131 m S 122.492 576.6131 m S 109.1862 576.6131 m S 162.4094 576.6131 m S 149.1036 576.6131 m S 175.7152 576.6131 m S 162.4094 576.6131 m S 175.7152 576.6131 m S 162.4094 576.6131 m S 189.021 576.6131 m S 175.7152 576.6131 m S 189.021 576.6131 m S 175.7152 576.6131 m S 162.4094 576.6131 m S 149.1036 576.6131 m S 202.3268 576.6131 m S 189.021 576.6131 m S 215.6326 576.6131 m S 202.3268 576.6131 m S 215.6326 576.6131 m S 202.3268 576.6131 m S 228.9385 576.6131 m S 215.6326 576.6131 m S 228.9385 576.6131 m S 215.6326 576.6131 m S 202.3268 576.6131 m S 189.021 576.6131 m S 242.2441 576.6131 m S 228.9385 576.6131 m S 242.2441 576.6131 m S 242.2441 576.6131 m S 242.2441 576.6131 m S 228.9385 576.6131 m S 215.6326 576.6131 m S 0 g 1 w 4 M 215.6326 576.6131 m F 0 G 0.3 w 10 M 215.6326 576.6131 m S 215.6326 576.6131 m S 215.6326 576.6131 m S 0 g 1 w 4 M 215.6326 576.6131 m F 0 G 0.3 w 10 M 215.6326 576.6131 m S 215.6326 576.6131 m S 1 g 1 w 4 M 209.6222 576.6131 m 209.6222 573.3914 212.3132 570.7795 215.6326 570.7795 c 218.9521 570.7795 221.6431 573.3914 221.6431 576.6131 c F 221.6431 576.6131 m 221.6431 579.8349 218.9521 582.4468 215.6326 582.4468 c 212.3132 582.4468 209.6222 579.8349 209.6222 576.6131 c F 215.6326 576.6131 m F 0 G 0.3 w 10 M 215.6326 576.6131 m S 0 g 1 w 4 M 215.6326 576.6131 m F 0 G 0.3 w 10 M 215.6326 576.6131 m S 215.6326 576.6131 m S 0 g 1 w 4 M 214.5476 575.5452 m 214.5476 571.9681 L 216.7177 571.9681 L 216.7177 575.5452 L 220.3033 575.534 L 220.3033 577.6924 L 216.7177 577.6813 L 216.7177 581.2584 L 214.5476 581.2584 L 214.5476 577.6813 L 210.9619 577.6924 L 210.9619 575.534 L 214.5476 575.5452 L f 0 G 0.3 w 10 M 242.2441 576.6131 m S 0 g 1 w 4 M 242.2441 576.6131 m F 0 G 0.3 w 10 M 242.2441 576.6131 m S 242.2441 576.6131 m S 242.2441 576.6131 m S 0 g 1 w 4 M 242.2441 576.6131 m F 0 G 0.3 w 10 M 242.2441 576.6131 m S 242.2441 576.6131 m S 1 g 1 w 4 M 236.2337 576.6131 m 236.2337 573.3914 238.9247 570.7795 242.2441 570.7795 c 245.5636 570.7795 248.2546 573.3914 248.2546 576.6131 c F 248.2546 576.6131 m 248.2546 579.8349 245.5636 582.4468 242.2441 582.4468 c 238.9247 582.4468 236.2337 579.8349 236.2337 576.6131 c F 242.2441 576.6131 m F 0 G 0.3 w 10 M 242.2441 576.6131 m S 0 g 1 w 4 M 242.2441 576.6131 m F 0 G 0.3 w 10 M 242.2441 576.6131 m S 242.2441 576.6131 m S 0 g 1 w 4 M 241.159 575.5452 m 241.159 571.9681 L 243.3292 571.9681 L 243.3292 575.5452 L 246.9148 575.534 L 246.9148 577.6924 L 243.3292 577.6813 L 243.3292 581.2584 L 241.159 581.2584 L 241.159 577.6813 L 237.5734 577.6924 L 237.5734 575.534 L 241.159 575.5452 L f 0 G 0.3 w 10 M 162.4094 576.6131 m S 0 g 1 w 4 M 162.4094 576.6131 m F 0 G 0.3 w 10 M 162.4094 576.6131 m S 162.4094 576.6131 m S 162.4094 576.6131 m S 0 g 1 w 4 M 162.4094 576.6131 m F 0 G 0.3 w 10 M 162.4094 576.6131 m S 162.4094 576.6131 m S 1 g 1 w 4 M 156.399 576.6131 m 156.399 573.3914 159.09 570.7795 162.4094 570.7795 c 165.7289 570.7795 168.4198 573.3914 168.4198 576.6131 c F 168.4198 576.6131 m 168.4198 579.8349 165.7289 582.4468 162.4094 582.4468 c 159.09 582.4468 156.399 579.8349 156.399 576.6131 c F 162.4094 576.6131 m F 0 G 0.3 w 10 M 162.4094 576.6131 m S 0 g 1 w 4 M 162.4094 576.6131 m F 0 G 0.3 w 10 M 162.4094 576.6131 m S 162.4094 576.6131 m S 0 g 1 w 4 M 161.3243 575.5452 m 161.3243 571.9681 L 163.4945 571.9681 L 163.4945 575.5452 L 167.0801 575.534 L 167.0801 577.6924 L 163.4945 577.6813 L 163.4945 581.2584 L 161.3243 581.2584 L 161.3243 577.6813 L 157.7387 577.6924 L 157.7387 575.534 L 161.3243 575.5452 L f 0 G 0.3 w 10 M 109.1862 576.6131 m S 0 g 1 w 4 M 109.1862 576.6131 m F 0 G 0.3 w 10 M 109.1862 576.6131 m S 109.1862 576.6131 m S 109.1862 576.6131 m S 0 g 1 w 4 M 109.1862 576.6131 m F 0 G 0.3 w 10 M 109.1862 576.6131 m S 109.1862 576.6131 m S 1 g 1 w 4 M 103.1758 576.6131 m 103.1758 573.3914 105.8668 570.7795 109.1862 570.7795 c 112.5057 570.7795 115.1966 573.3914 115.1966 576.6131 c F 115.1966 576.6131 m 115.1966 579.8349 112.5057 582.4468 109.1862 582.4468 c 105.8668 582.4468 103.1758 579.8349 103.1758 576.6131 c F 109.1862 576.6131 m F 0 G 0.3 w 10 M 109.1862 576.6131 m S 0 g 1 w 4 M 109.1862 576.6131 m F 0 G 0.3 w 10 M 109.1862 576.6131 m S 109.1862 576.6131 m S 0 g 1 w 4 M 108.1011 575.5452 m 108.1011 571.9681 L 110.2713 571.9681 L 110.2713 575.5452 L 113.8569 575.534 L 113.8569 577.6924 L 110.2713 577.6813 L 110.2713 581.2584 L 108.1011 581.2584 L 108.1011 577.6813 L 104.5155 577.6924 L 104.5155 575.534 L 108.1011 575.5452 L f 0 G 0.3 w 10 M 135.7978 576.6131 m S 0 g 1 w 4 M 135.7978 576.6131 m F 0 G 0.3 w 10 M 135.7978 576.6131 m S 0 g 1 w 4 M 135.7978 576.6131 m F 1 g 129.7874 576.6131 m 129.7874 573.3914 132.4784 570.7795 135.7978 570.7795 c 139.1173 570.7795 141.8082 573.3914 141.8082 576.6131 c F 141.8082 576.6131 m 141.8082 579.8349 139.1173 582.4468 135.7978 582.4468 c 132.4784 582.4468 129.7874 579.8349 129.7874 576.6131 c F 135.7978 576.6131 m F 0 G 0.3 w 10 M 135.7978 576.6131 m S 0 g 1 w 4 M 135.7978 576.6131 m F 0 G 0.3 w 10 M 135.7978 576.6131 m S 0 g 1 w 4 M 135.7978 576.6131 m F 134.7127 577.6813 m 131.1271 577.6924 L 131.1271 575.534 L 134.7127 575.5451 L F 136.8829 575.5451 m 140.4685 575.534 L 140.4685 577.6924 L 136.8829 577.6813 L F 131.1271 577.6924 m 140.4685 577.6924 l 140.4685 575.534 l 131.1271 575.534 l 131.1271 577.6924 l f 0 G 0.3 w 10 M 189.021 576.6131 m S 0 g 1 w 4 M 189.021 576.6131 m F 0 G 0.3 w 10 M 189.021 576.6131 m S 0 g 1 w 4 M 189.021 576.6131 m F 1 g 183.0106 576.6131 m 183.0106 573.3914 185.7016 570.7795 189.021 570.7795 c 192.3405 570.7795 195.0315 573.3914 195.0315 576.6131 c F 195.0315 576.6131 m 195.0315 579.8349 192.3405 582.4468 189.021 582.4468 c 185.7016 582.4468 183.0106 579.8349 183.0106 576.6131 c F 189.021 576.6131 m F 0 G 0.3 w 10 M 189.021 576.6131 m S 0 g 1 w 4 M 189.021 576.6131 m F 0 G 0.3 w 10 M 189.021 576.6131 m S 0 g 1 w 4 M 189.021 576.6131 m F 187.9359 577.6813 m 184.3503 577.6924 L 184.3503 575.534 L 187.9359 575.5451 L F 190.1061 575.5451 m 193.6917 575.534 L 193.6917 577.6924 L 190.1061 577.6813 L F 184.3503 577.6924 m 193.6917 577.6924 l 193.6917 575.534 l 184.3503 575.534 l 184.3503 577.6924 l f 0 G 0.3 w 10 M 228.9385 576.6131 m S 1 g 1 w 4 M 228.9385 571.8048 m 231.7501 571.8048 234.0295 573.9576 234.0295 576.6131 c 234.0295 579.2686 231.7501 581.4214 228.9385 581.4214 c 226.1267 581.4214 223.8473 579.2686 223.8473 576.6131 c 223.8473 573.9576 226.1267 571.8048 228.9385 571.8048 c b 0 g 228.9385 576.6131 m F 0 G 0.3 w 10 M 202.3268 576.6131 m S 1 g 1 w 4 M 202.3268 571.8048 m 205.1385 571.8048 207.4179 573.9576 207.4179 576.6131 c 207.4179 579.2686 205.1385 581.4214 202.3268 581.4214 c 199.5151 581.4214 197.2357 579.2686 197.2357 576.6131 c 197.2357 573.9576 199.5151 571.8048 202.3268 571.8048 c b 0 g 202.3268 576.6131 m F 0 G 0.3 w 10 M 149.1036 576.6131 m S 1 g 1 w 4 M 149.1036 571.8048 m 151.9153 571.8048 154.1947 573.9576 154.1947 576.6131 c 154.1947 579.2686 151.9153 581.4214 149.1036 581.4214 c 146.2919 581.4214 144.0125 579.2686 144.0125 576.6131 c 144.0125 573.9576 146.2919 571.8048 149.1036 571.8048 c b 0 g 149.1036 576.6131 m F 0 G 0.3 w 10 M 122.492 576.6131 m S 1 g 1 w 4 M 122.492 571.8048 m 125.3037 571.8048 127.5831 573.9576 127.5831 576.6131 c 127.5831 579.2686 125.3037 581.4214 122.492 581.4214 c 119.6803 581.4214 117.4009 579.2686 117.4009 576.6131 c 117.4009 573.9576 119.6803 571.8048 122.492 571.8048 c b 0 g 122.492 576.6131 m F 0 G 0.3 w 10 M 175.7152 576.6131 m S 1 g 1 w 4 M 175.7152 571.8048 m 178.5269 571.8048 180.8063 573.9576 180.8063 576.6131 c 180.8063 579.2686 178.5269 581.4214 175.7152 581.4214 c 172.9035 581.4214 170.6241 579.2686 170.6241 576.6131 c 170.6241 573.9576 172.9035 571.8048 175.7152 571.8048 c b 0 g 175.7152 576.6131 m F 0 G 0.3 w 10 M 122.492 550.6799 m S 109.1862 550.6799 m S 115.8391 544.1966 m S 135.7978 550.6799 m S 122.492 550.6799 m S 129.1449 544.1966 m S 149.1036 550.6799 m S 135.7978 550.6799 m S 142.4507 544.1966 m S 0 g 1 w 4 M 115.8391 544.1966 m F 142.4507 544.1966 m F 0 G 0.3 w 10 M 162.4094 550.6799 m S 149.1036 550.6799 m S 155.7566 544.1966 m S 175.7152 550.6799 m S 162.4094 550.6799 m S 169.0624 544.1966 m S 189.021 550.6799 m S 175.7152 550.6799 m S 182.3681 544.1966 m S 0 g 1 w 4 M 155.7566 544.1966 m F 182.3681 544.1966 m F 0 G 0.3 w 10 M 202.3268 550.6799 m S 189.021 550.6799 m S 195.6739 544.1966 m S 215.6326 550.6799 m S 202.3268 550.6799 m S 208.9797 544.1966 m S 228.9385 550.6799 m S 215.6326 550.6799 m S 222.2855 544.1966 m S 0 g 1 w 4 M 195.6739 544.1966 m F 222.2855 544.1966 m F 0 G 0.3 w 10 M 242.2441 550.6799 m S 228.9385 550.6799 m S 235.5913 544.1966 m S 242.2441 550.6799 m S 248.8971 544.1966 m S 0 g 1 w 4 M 235.5913 544.1966 m F 0 G 0.3 w 10 M 115.8391 544.1966 m S 0 g 1 w 4 M 115.8391 544.1966 m F 0 G 0.3 w 10 M 122.492 550.6799 m S 122.492 550.6799 m S 135.7978 550.6799 m S 0 g 1 w 4 M 135.7978 550.6799 m F 0 G 0.3 w 10 M 135.7978 550.6799 m S 135.7978 550.6799 m S 135.7978 550.6799 m S 0 g 1 w 4 M 135.7978 550.6799 m F 0 G 0.3 w 10 M 135.7978 550.6799 m S 135.7978 550.6799 m S 1 g 1 w 4 M 129.7874 550.6799 m 129.7874 547.4582 132.4784 544.8463 135.7978 544.8463 c 139.1173 544.8463 141.8082 547.4582 141.8082 550.6799 c F 141.8082 550.6799 m 141.8082 553.9017 139.1173 556.5136 135.7978 556.5136 c 132.4784 556.5136 129.7874 553.9017 129.7874 550.6799 c F 135.7978 550.6799 m F 0 G 0.3 w 10 M 135.7978 550.6799 m S 0 g 1 w 4 M 135.7978 550.6799 m F 0 G 0.3 w 10 M 135.7978 550.6799 m S 135.7978 550.6799 m S 0 g 1 w 4 M 134.7127 549.612 m 134.7127 546.0349 L 136.8829 546.0349 L 136.8829 549.612 L 140.4685 549.6008 L 140.4685 551.7592 L 136.8829 551.7481 L 136.8829 555.3252 L 134.7127 555.3252 L 134.7127 551.7481 L 131.1271 551.7592 L 131.1271 549.6008 L 134.7127 549.612 L f 0 G 0.3 w 10 M 162.4094 550.6799 m S 0 g 1 w 4 M 162.4094 550.6799 m F 0 G 0.3 w 10 M 162.4094 550.6799 m S 162.4094 550.6799 m S 162.4094 550.6799 m S 0 g 1 w 4 M 162.4094 550.6799 m F 0 G 0.3 w 10 M 162.4094 550.6799 m S 162.4094 550.6799 m S 1 g 1 w 4 M 156.399 550.6799 m 156.399 547.4582 159.09 544.8463 162.4094 544.8463 c 165.7289 544.8463 168.4198 547.4582 168.4198 550.6799 c F 168.4198 550.6799 m 168.4198 553.9017 165.7289 556.5136 162.4094 556.5136 c 159.09 556.5136 156.399 553.9017 156.399 550.6799 c F 162.4094 550.6799 m F 0 G 0.3 w 10 M 162.4094 550.6799 m S 0 g 1 w 4 M 162.4094 550.6799 m F 0 G 0.3 w 10 M 162.4094 550.6799 m S 162.4094 550.6799 m S 0 g 1 w 4 M 161.3243 549.612 m 161.3243 546.0349 L 163.4945 546.0349 L 163.4945 549.612 L 167.0801 549.6008 L 167.0801 551.7592 L 163.4945 551.7481 L 163.4945 555.3252 L 161.3243 555.3252 L 161.3243 551.7481 L 157.7387 551.7592 L 157.7387 549.6008 L 161.3243 549.612 L f 0 G 0.3 w 10 M 189.021 550.6799 m S 0 g 1 w 4 M 189.021 550.6799 m F 0 G 0.3 w 10 M 189.021 550.6799 m S 189.021 550.6799 m S 189.021 550.6799 m S 0 g 1 w 4 M 189.021 550.6799 m F 0 G 0.3 w 10 M 189.021 550.6799 m S 189.021 550.6799 m S 1 g 1 w 4 M 183.0106 550.6799 m 183.0106 547.4582 185.7016 544.8463 189.021 544.8463 c 192.3405 544.8463 195.0315 547.4582 195.0315 550.6799 c F 195.0315 550.6799 m 195.0315 553.9017 192.3405 556.5136 189.021 556.5136 c 185.7016 556.5136 183.0106 553.9017 183.0106 550.6799 c F 189.021 550.6799 m F 0 G 0.3 w 10 M 189.021 550.6799 m S 0 g 1 w 4 M 189.021 550.6799 m F 0 G 0.3 w 10 M 189.021 550.6799 m S 189.021 550.6799 m S 0 g 1 w 4 M 187.9359 549.612 m 187.9359 546.0349 L 190.1061 546.0349 L 190.1061 549.612 L 193.6917 549.6008 L 193.6917 551.7592 L 190.1061 551.7481 L 190.1061 555.3252 L 187.9359 555.3252 L 187.9359 551.7481 L 184.3503 551.7592 L 184.3503 549.6008 L 187.9359 549.612 L f 0 G 0.3 w 10 M 215.6326 550.6799 m S 0 g 1 w 4 M 215.6326 550.6799 m F 0 G 0.3 w 10 M 215.6326 550.6799 m S 215.6326 550.6799 m S 215.6326 550.6799 m S 0 g 1 w 4 M 215.6326 550.6799 m F 0 G 0.3 w 10 M 215.6326 550.6799 m S 215.6326 550.6799 m S 1 g 1 w 4 M 209.6222 550.6799 m 209.6222 547.4582 212.3132 544.8463 215.6326 544.8463 c 218.9521 544.8463 221.6431 547.4582 221.6431 550.6799 c F 221.6431 550.6799 m 221.6431 553.9017 218.9521 556.5136 215.6326 556.5136 c 212.3132 556.5136 209.6222 553.9017 209.6222 550.6799 c F 215.6326 550.6799 m F 0 G 0.3 w 10 M 215.6326 550.6799 m S 0 g 1 w 4 M 215.6326 550.6799 m F 0 G 0.3 w 10 M 215.6326 550.6799 m S 215.6326 550.6799 m S 0 g 1 w 4 M 214.5476 549.612 m 214.5476 546.0349 L 216.7177 546.0349 L 216.7177 549.612 L 220.3033 549.6008 L 220.3033 551.7592 L 216.7177 551.7481 L 216.7177 555.3252 L 214.5476 555.3252 L 214.5476 551.7481 L 210.9619 551.7592 L 210.9619 549.6008 L 214.5476 549.612 L f 0 G 0.3 w 10 M 242.2441 550.6799 m S 0 g 1 w 4 M 242.2441 550.6799 m F 0 G 0.3 w 10 M 242.2441 550.6799 m S 242.2441 550.6799 m S 242.2441 550.6799 m S 0 g 1 w 4 M 242.2441 550.6799 m F 0 G 0.3 w 10 M 242.2441 550.6799 m S 242.2441 550.6799 m S 1 g 1 w 4 M 236.2337 550.6799 m 236.2337 547.4582 238.9247 544.8463 242.2441 544.8463 c 245.5636 544.8463 248.2546 547.4582 248.2546 550.6799 c F 248.2546 550.6799 m 248.2546 553.9017 245.5636 556.5136 242.2441 556.5136 c 238.9247 556.5136 236.2337 553.9017 236.2337 550.6799 c F 242.2441 550.6799 m F 0 G 0.3 w 10 M 242.2441 550.6799 m S 0 g 1 w 4 M 242.2441 550.6799 m F 0 G 0.3 w 10 M 242.2441 550.6799 m S 242.2441 550.6799 m S 0 g 1 w 4 M 241.159 549.612 m 241.159 546.0349 L 243.3292 546.0349 L 243.3292 549.612 L 246.9148 549.6008 L 246.9148 551.7592 L 243.3292 551.7481 L 243.3292 555.3252 L 241.159 555.3252 L 241.159 551.7481 L 237.5734 551.7592 L 237.5734 549.6008 L 241.159 549.612 L f 0 G 0.3 w 10 M 109.1862 550.6799 m S 0 g 1 w 4 M 109.1862 550.6799 m F 0 G 0.3 w 10 M 109.1862 550.6799 m S 109.1862 550.6799 m S 109.1862 550.6799 m S 0 g 1 w 4 M 109.1862 550.6799 m F 0 G 0.3 w 10 M 109.1862 550.6799 m S 109.1862 550.6799 m S 1 g 1 w 4 M 103.1758 550.6799 m 103.1758 547.4582 105.8668 544.8463 109.1862 544.8463 c 112.5057 544.8463 115.1966 547.4582 115.1966 550.6799 c F 115.1966 550.6799 m 115.1966 553.9017 112.5057 556.5136 109.1862 556.5136 c 105.8668 556.5136 103.1758 553.9017 103.1758 550.6799 c F 109.1862 550.6799 m F 0 G 0.3 w 10 M 109.1862 550.6799 m S 0 g 1 w 4 M 109.1862 550.6799 m F 0 G 0.3 w 10 M 109.1862 550.6799 m S 109.1862 550.6799 m S 0 g 1 w 4 M 108.1011 549.612 m 108.1011 546.0349 L 110.2713 546.0349 L 110.2713 549.612 L 113.8569 549.6008 L 113.8569 551.7592 L 110.2713 551.7481 L 110.2713 555.3252 L 108.1011 555.3252 L 108.1011 551.7481 L 104.5155 551.7592 L 104.5155 549.6008 L 108.1011 549.612 L f 0 G 0.3 w 10 M 122.492 550.6799 m S 1 g 1 w 4 M 122.492 545.8716 m 125.3037 545.8716 127.5831 548.0244 127.5831 550.6799 c 127.5831 553.3354 125.3037 555.4882 122.492 555.4882 c 119.6803 555.4882 117.4009 553.3354 117.4009 550.6799 c 117.4009 548.0244 119.6803 545.8716 122.492 545.8716 c b 0 g 122.492 550.6799 m F 0 G 0.3 w 10 M 149.1036 550.6799 m S 1 g 1 w 4 M 149.1036 545.8716 m 151.9153 545.8716 154.1947 548.0244 154.1947 550.6799 c 154.1947 553.3354 151.9153 555.4882 149.1036 555.4882 c 146.2919 555.4882 144.0125 553.3354 144.0125 550.6799 c 144.0125 548.0244 146.2919 545.8716 149.1036 545.8716 c b 0 g 149.1036 550.6799 m F 0 G 0.3 w 10 M 202.3268 550.6799 m S 1 g 1 w 4 M 202.3268 545.8716 m 205.1385 545.8716 207.4179 548.0244 207.4179 550.6799 c 207.4179 553.3354 205.1385 555.4882 202.3268 555.4882 c 199.5151 555.4882 197.2357 553.3354 197.2357 550.6799 c 197.2357 548.0244 199.5151 545.8716 202.3268 545.8716 c b 0 g 202.3268 550.6799 m F 0 G 0.3 w 10 M 228.9385 550.6799 m S 1 g 1 w 4 M 228.9385 545.8716 m 231.7501 545.8716 234.0295 548.0244 234.0295 550.6799 c 234.0295 553.3354 231.7501 555.4882 228.9385 555.4882 c 226.1267 555.4882 223.8473 553.3354 223.8473 550.6799 c 223.8473 548.0244 226.1267 545.8716 228.9385 545.8716 c b 0 g 228.9385 550.6799 m F 0 G 0.3 w 10 M 175.7152 550.6799 m S 1 g 1 w 4 M 175.7152 545.8716 m 178.5269 545.8716 180.8063 548.0244 180.8063 550.6799 c 180.8063 553.3354 178.5269 555.4882 175.7152 555.4882 c 172.9035 555.4882 170.6241 553.3354 170.6241 550.6799 c 170.6241 548.0244 172.9035 545.8716 175.7152 545.8716 c b 0 g 175.7152 550.6799 m F u 0 G 0.3 w 10 M 95.8804 680.3457 m S 95.8804 667.3791 m S 82.5746 667.3791 m S 82.5746 680.3457 m S 89.2275 673.8624 m S U 122.492 654.4125 m S 122.492 641.446 m S 109.1862 641.446 m S 109.1862 654.4125 m S 115.8391 647.9293 m S u 109.1862 667.3791 m S 109.1862 654.4125 m S 95.8804 654.4125 m S 95.8804 667.3791 m S 102.5333 660.8959 m S U u 109.1862 680.3457 m S 109.1862 667.3791 m S 95.8804 667.3791 m S 95.8804 680.3457 m S 102.5333 673.8624 m S U u 122.492 680.3457 m S 122.492 667.3791 m S 109.1862 667.3791 m S 109.1862 680.3457 m S 115.8391 673.8624 m S U u 122.492 667.3791 m S 122.492 654.4125 m S 109.1862 654.4125 m S 109.1862 667.3791 m S 115.8391 660.8959 m S U 109.1862 654.4125 m S 109.1862 641.446 m S 95.8804 641.446 m S 95.8804 654.4125 m S 102.5333 647.9293 m S u 95.8804 654.4125 m S 95.8804 641.446 m S 82.5746 641.446 m S 82.5746 654.4125 m S 89.2275 647.9293 m S U u 95.8804 667.3791 m S 95.8804 654.4125 m S 82.5746 654.4125 m S 82.5746 667.3791 m S 89.2275 660.8959 m S U 0 g 1 w 4 M 89.2275 673.8624 m F 89.2275 647.9293 m F u 0 G 0.3 w 10 M 95.8804 641.446 m S 95.8804 628.4794 m S 82.5746 628.4794 m S 82.5746 641.446 m S 89.2275 634.9627 m S U 122.492 615.5128 m S 122.492 602.5462 m S 109.1862 602.5462 m S 109.1862 615.5128 m S 115.8391 609.0295 m S u 109.1862 628.4794 m S 109.1862 615.5128 m S 95.8804 615.5128 m S 95.8804 628.4794 m S 102.5333 621.9961 m S U 109.1862 641.446 m S 109.1862 628.4794 m S 95.8804 628.4794 m S 95.8804 641.446 m S 102.5333 634.9627 m S 122.492 641.446 m S 122.492 628.4794 m S 109.1862 628.4794 m S 109.1862 641.446 m S 115.8391 634.9627 m S u 122.492 628.4794 m S 122.492 615.5128 m S 109.1862 615.5128 m S 109.1862 628.4794 m S 115.8391 621.9961 m S U 109.1862 615.5128 m S 109.1862 602.5462 m S 95.8804 602.5462 m S 95.8804 615.5128 m S 102.5333 609.0295 m S u 95.8804 615.5128 m S 95.8804 602.5462 m S 82.5746 602.5462 m S 82.5746 615.5128 m S 89.2275 609.0295 m S U u 95.8804 628.4794 m S 95.8804 615.5128 m S 82.5746 615.5128 m S 82.5746 628.4794 m S 89.2275 621.9961 m S U 0 g 1 w 4 M 89.2275 634.9627 m F 89.2275 609.0295 m F 89.2275 596.0629 m F 0 G 0.3 w 10 M 95.8804 602.5462 m S 95.8804 589.5796 m S 82.5746 589.5796 m S 82.5746 602.5462 m S 89.2275 596.0629 m S 109.1862 563.6464 m S 109.1862 576.613 m S 109.1862 589.5796 m S 109.1862 576.613 m S 95.8804 576.613 m S 95.8804 589.5796 m S 102.5333 583.0963 m S 109.1862 602.5462 m S 109.1862 589.5796 m S 95.8804 589.5796 m S 95.8804 602.5462 m S 102.5333 596.0629 m S 109.1862 589.5796 m S 109.1862 602.5462 m S 109.1862 576.613 m S 109.1862 589.5796 m S 109.1862 576.613 m S 109.1862 563.6464 m S 95.8804 563.6464 m S 95.8804 576.613 m S 102.5333 570.1297 m S 95.8804 576.613 m S 95.8804 563.6464 m S 82.5746 563.6464 m S 82.5746 576.613 m S 89.2275 570.1297 m S 95.8804 589.5796 m S 95.8804 576.613 m S 82.5746 576.613 m S 82.5746 589.5796 m S 89.2275 583.0963 m S 0 g 1 w 4 M 89.2275 596.0629 m F 89.2275 570.1297 m F 0 G 0.3 w 10 M 95.8804 563.6464 m S 95.8804 550.6798 m S 82.5746 550.6798 m S 82.5746 563.6464 m S 89.2275 557.1631 m S 109.1862 524.7467 m S 109.1862 537.7132 m S 109.1862 550.6798 m S 109.1862 537.7132 m S 95.8804 550.6798 m S 102.5333 544.1965 m S 109.1862 563.6464 m S 109.1862 550.6798 m S 95.8804 550.6798 m S 95.8804 563.6464 m S 102.5333 557.1631 m S 109.1862 550.6798 m S 109.1862 563.6464 m S 109.1862 537.7132 m S 109.1862 550.6798 m S 109.1862 537.7132 m S 109.1862 524.7467 m S 95.8804 524.7467 m S 102.5333 531.2299 m S 95.8804 524.7467 m S 82.5746 524.7467 m S 82.5746 537.7132 m S 89.2275 531.2299 m S 95.8804 550.6798 m S 82.5746 537.7132 m S 82.5746 550.6798 m S 89.2275 544.1965 m S 0 g 1 w 4 M 89.2275 557.1631 m F 89.2275 531.2299 m F 0 G 0.3 w 10 M 122.492 693.3122 m S 122.492 680.3457 m S 109.1862 680.3457 m S 109.1862 693.3122 m S 115.8391 686.829 m S 109.1862 693.3122 m S 95.8804 693.3122 m S 102.5333 699.7956 m S 122.492 693.3122 m S 109.1862 693.3122 m S 115.8391 699.7956 m S 109.1862 693.3122 m S 109.1862 680.3457 m S 95.8804 680.3457 m S 95.8804 693.3122 m S 102.5333 686.829 m S u 95.8804 693.3122 m S 95.8804 680.3457 m S 82.5746 680.3457 m S 82.5746 693.3122 m S 89.2275 686.829 m S U 95.8804 693.3122 m S 82.5746 693.3122 m S 89.2275 699.7956 m S 162.4094 693.3122 m S 162.4094 680.3457 m S 149.1036 680.3457 m S 149.1036 693.3122 m S 155.7565 686.829 m S 149.1036 693.3122 m S 135.7978 693.3122 m S 142.4507 699.7956 m S 162.4094 693.3122 m S 149.1036 693.3122 m S 155.7565 699.7956 m S 149.1036 693.3122 m S 149.1036 680.3457 m S 135.7978 680.3457 m S 135.7978 693.3122 m S 142.4507 686.829 m S 135.7978 693.3122 m S 135.7978 680.3457 m S 122.492 680.3457 m S 122.492 693.3122 m S 129.1449 686.829 m S 135.7978 693.3122 m S 122.492 693.3122 m S 129.1449 699.7956 m S u 202.3268 693.3122 m S 202.3268 680.3457 m S 189.021 680.3457 m S 189.021 693.3122 m S 195.6739 686.829 m S U 189.021 693.3122 m S 175.7152 693.3122 m S 182.3681 699.7956 m S u 202.3268 706.2788 m S 202.3268 693.3122 m S 189.021 693.3122 m S 189.021 706.2788 m S 195.6739 699.7956 m S U 189.021 693.3122 m S 189.021 680.3457 m S 175.7152 680.3457 m S 175.7152 693.3122 m S 182.3681 686.829 m S 175.7152 693.3122 m S 175.7152 680.3457 m S 162.4094 680.3457 m S 162.4094 693.3122 m S 169.0623 686.829 m S 175.7152 693.3122 m S 162.4094 693.3122 m S 169.0623 699.7956 m S u 242.2442 693.3122 m S 242.2442 680.3457 m S 228.9384 680.3457 m S 228.9384 693.3122 m S 235.5913 686.829 m S U u 228.9384 706.2788 m S 228.9384 693.3122 m S 215.6325 693.3122 m S 215.6325 706.2788 m S 222.2854 699.7956 m S U u 242.2442 706.2788 m S 242.2442 693.3122 m S 228.9384 693.3122 m S 228.9384 706.2788 m S 235.5913 699.7956 m S U u 228.9384 693.3122 m S 228.9384 680.3457 m S 215.6325 680.3457 m S 215.6325 693.3122 m S 222.2854 686.829 m S U u 215.6325 693.3122 m S 215.6325 680.3457 m S 202.3268 680.3457 m S 202.3268 693.3122 m S 208.9796 686.829 m S U u 215.6325 706.2788 m S 215.6325 693.3122 m S 202.3268 693.3122 m S 202.3268 706.2788 m S 208.9796 699.7956 m S U u 242.2442 706.279 m S 242.2442 693.3123 m S 228.9385 693.3123 m S 228.9385 706.279 m S 235.5913 699.7956 m S U u 268.8559 680.3457 m S 268.8559 667.3793 m S 255.5501 667.3793 m S 255.5501 680.3457 m S 262.203 673.8625 m S U 255.5501 680.3457 m S 242.2442 680.3457 m S 242.2442 693.3123 m S 248.8971 686.8291 m S 242.2442 693.3123 m S 248.8971 699.7956 m S 268.8559 693.3123 m S 262.203 699.7956 m S 268.8559 693.3123 m S 268.8559 680.3457 m S 255.5501 680.3457 m S 262.203 686.8291 m S u 255.5501 680.3457 m S 255.5501 667.3793 m S 242.2442 667.3793 m S 242.2442 680.3457 m S 248.8971 673.8625 m S U u 242.2442 680.3457 m S 242.2442 667.3793 m S 228.9385 667.3793 m S 228.9385 680.3457 m S 235.5913 673.8625 m S U u 242.2442 693.3123 m S 242.2442 680.3457 m S 228.9385 680.3457 m S 228.9385 693.3123 m S 235.5913 686.8291 m S U 0 g 1 w 4 M 262.203 699.7956 m F 0 G 0.3 w 10 M 106.0603 696.5783 m S 106.0603 690.2962 m S 112.5622 690.2962 m S 106.0603 690.2962 m S 112.5622 696.5783 m S 112.5622 690.2962 m S 106.0603 690.2962 m S 106.0603 696.5783 m S 109.3112 693.4372 m S 112.5622 690.2962 m S 112.5622 696.5783 m S 112.5622 690.2962 m S 106.0603 690.2962 m S 1 g 0.7 G 1 w 4 M 106.0603 696.5783 m 112.5622 690.2962 l B 112.5622 696.5783 m 106.0603 690.2962 l B 0 G 0.3 w 10 M 119.3036 696.5158 m S 119.3036 690.2337 m S 125.8055 690.2337 m S 119.3036 690.2337 m S 125.8055 696.5158 m S 125.8055 690.2337 m S 119.3036 690.2337 m S 119.3036 696.5158 m S 122.5545 693.3747 m S 125.8055 690.2337 m S 125.8055 696.5158 m S 125.8055 690.2337 m S 119.3036 690.2337 m S 1 g 0.7 G 1 w 4 M 119.3036 696.5158 m 125.8055 690.2337 l B 125.8055 696.5158 m 119.3036 690.2337 l B 0 G 0.3 w 10 M 132.5469 696.4533 m S 132.5469 690.1712 m S 139.0488 690.1712 m S 132.5469 690.1712 m S 139.0488 696.4533 m S 139.0488 690.1712 m S 132.5469 690.1712 m S 132.5469 696.4533 m S 135.7978 693.3122 m S 139.0488 690.1712 m S 139.0488 696.4533 m S 139.0488 690.1712 m S 132.5469 690.1712 m S 1 g 0.7 G 1 w 4 M 132.5469 696.4533 m 139.0488 690.1712 l B 139.0488 696.4533 m 132.5469 690.1712 l B 0 G 0.3 w 10 M 162.4161 693.3122 m S 149.1103 693.3122 m S 149.1103 693.3122 m S 162.4161 693.3122 m S 149.1103 693.3122 m S 149.1103 693.3122 m S 175.7219 693.3122 m S 175.7219 693.3122 m S 175.7219 693.3122 m S 162.4161 693.3122 m S 175.7219 693.3122 m S 162.4161 693.3122 m S 145.9844 696.5783 m S 145.9844 690.2962 m S 152.4863 690.2962 m S 145.9844 690.2962 m S 152.4863 696.5783 m S 152.4863 690.2962 m S 145.9844 690.2962 m S 145.9844 696.5783 m S 149.2353 693.4372 m S 152.4863 690.2962 m S 152.4863 696.5783 m S 152.4863 690.2962 m S 145.9844 690.2962 m S 1 g 0.7 G 1 w 4 M 145.9844 696.5783 m 152.4863 690.2962 l B 152.4863 696.5783 m 145.9844 690.2962 l B 0 G 0.3 w 10 M 159.2277 696.5158 m S 159.2277 690.2337 m S 165.7296 690.2337 m S 159.2277 690.2337 m S 165.7296 696.5158 m S 165.7296 690.2337 m S 159.2277 690.2337 m S 159.2277 696.5158 m S 162.4786 693.3747 m S 165.7296 690.2337 m S 165.7296 696.5158 m S 165.7296 690.2337 m S 159.2277 690.2337 m S 1 g 0.7 G 1 w 4 M 159.2277 696.5158 m 165.7296 690.2337 l B 165.7296 696.5158 m 159.2277 690.2337 l B 0 G 0.3 w 10 M 172.471 696.4533 m S 172.471 690.1712 m S 178.9729 690.1712 m S 172.471 690.1712 m S 178.9729 696.4533 m S 178.9729 690.1712 m S 172.471 690.1712 m S 172.471 696.4533 m S 175.7219 693.3122 m S 178.9729 690.1712 m S 178.9729 696.4533 m S 178.9729 690.1712 m S 172.471 690.1712 m S 1 g 0.7 G 1 w 4 M 172.471 696.4533 m 178.9729 690.1712 l B 178.9729 696.4533 m 172.471 690.1712 l B 0 G 0.3 w 10 M 202.309 693.3122 m S 189.0032 693.3122 m S 189.0032 693.3122 m S 202.309 693.3122 m S 189.0032 693.3122 m S 189.0032 693.3122 m S 242.2264 693.3122 m S 228.9206 693.3122 m S 228.9206 693.3122 m S 215.6148 693.3122 m S 242.2264 693.3122 m S 228.9206 693.3122 m S 228.9206 693.3122 m S 215.6148 693.3122 m S 215.6148 693.3122 m S 202.309 693.3122 m S 215.6148 693.3122 m S 202.309 693.3122 m S 242.2264 693.3122 m S 242.2264 693.3122 m S 185.8772 696.5783 m S 185.8772 690.2962 m S 192.3791 690.2962 m S 185.8772 690.2962 m S 192.3791 696.5783 m S 192.3791 690.2962 m S 185.8772 690.2962 m S 185.8772 696.5783 m S 189.1282 693.4372 m S 192.3791 690.2962 m S 192.3791 696.5783 m S 192.3791 690.2962 m S 185.8772 690.2962 m S 1 g 0.7 G 1 w 4 M 185.8772 696.5783 m 192.3791 690.2962 l B 192.3791 696.5783 m 185.8772 690.2962 l B 0 G 0.3 w 10 M 199.1205 696.5158 m S 199.1205 690.2337 m S 205.6224 690.2337 m S 199.1205 690.2337 m S 205.6224 696.5158 m S 205.6224 690.2337 m S 199.1205 690.2337 m S 199.1205 696.5158 m S 202.3715 693.3747 m S 205.6224 690.2337 m S 205.6224 696.5158 m S 205.6224 690.2337 m S 199.1205 690.2337 m S 1 g 0.7 G 1 w 4 M 199.1205 696.5158 m 205.6224 690.2337 l B 205.6224 696.5158 m 199.1205 690.2337 l B 0 G 0.3 w 10 M 212.3639 696.4533 m S 212.3639 690.1712 m S 218.8657 690.1712 m S 212.3639 690.1712 m S 218.8657 696.4533 m S 218.8657 690.1712 m S 212.3639 690.1712 m S 212.3639 696.4533 m S 215.6148 693.3122 m S 218.8657 690.1712 m S 218.8657 696.4533 m S 218.8657 690.1712 m S 212.3639 690.1712 m S 1 g 0.7 G 1 w 4 M 212.3639 696.4533 m 218.8657 690.1712 l B 218.8657 696.4533 m 212.3639 690.1712 l B 0 G 0.3 w 10 M 242.2331 693.3122 m S 228.9273 693.3122 m S 228.9273 693.3122 m S 242.2331 693.3122 m S 228.9273 693.3122 m S 228.9273 693.3122 m S 242.2331 693.3122 m S 242.2331 693.3122 m S 225.8014 696.5783 m S 225.8014 690.2962 m S 232.3032 690.2962 m S 225.8014 690.2962 m S 232.3032 696.5783 m S 232.3032 690.2962 m S 225.8014 690.2962 m S 225.8014 696.5783 m S 229.0523 693.4372 m S 232.3032 690.2962 m S 232.3032 696.5783 m S 232.3032 690.2962 m S 225.8014 690.2962 m S 1 g 0.7 G 1 w 4 M 225.8014 696.5783 m 232.3032 690.2962 l B 232.3032 696.5783 m 225.8014 690.2962 l B 0 G 0.3 w 10 M 239.0447 696.5158 m S 239.0447 690.2337 m S 245.5465 690.2337 m S 239.0447 690.2337 m S 245.5465 696.5158 m S 245.5465 690.2337 m S 239.0447 690.2337 m S 239.0447 696.5158 m S 242.2956 693.3747 m S 245.5465 690.2337 m S 245.5465 696.5158 m S 245.5465 690.2337 m S 239.0447 690.2337 m S 1 g 0.7 G 1 w 4 M 239.0447 696.5158 m 245.5465 690.2337 l B 245.5465 696.5158 m 239.0447 690.2337 l B 0 G 0.3 w 10 M 122.4999 537.7131 m S 109.1941 537.7131 m S 109.1941 537.7131 m S 122.4999 537.7131 m S 109.1941 537.7131 m S 109.1941 537.7131 m S 162.4173 537.7131 m S 149.1115 537.7131 m S 149.1115 537.7131 m S 135.8057 537.7131 m S 162.4173 537.7131 m S 149.1115 537.7131 m S 149.1115 537.7131 m S 135.8057 537.7131 m S 135.8057 537.7131 m S 122.4999 537.7131 m S 135.8057 537.7131 m S 122.4999 537.7131 m S u 202.3347 537.7131 m S 202.3347 524.7466 m S 189.0289 524.7466 m S 189.0289 537.7131 m S 195.6818 531.2299 m S U 189.0289 537.7131 m S 175.7231 537.7131 m S u 202.3347 550.6797 m S 202.3347 537.7131 m S 189.0289 537.7131 m S 189.0289 550.6797 m S 195.6818 544.1965 m S U 189.0289 537.7131 m S 175.7231 537.7131 m S 175.7231 537.7131 m S 162.4173 537.7131 m S 175.7231 537.7131 m S 162.4173 537.7131 m S u 242.2521 537.7131 m S 242.2521 524.7466 m S 228.9463 524.7466 m S 228.9463 537.7131 m S 235.5992 531.2299 m S U u 228.9463 550.6797 m S 228.9463 537.7131 m S 215.6404 537.7131 m S 215.6404 550.6797 m S 222.2933 544.1965 m S U u 242.2521 550.6797 m S 242.2521 537.7131 m S 228.9463 537.7131 m S 228.9463 550.6797 m S 235.5992 544.1965 m S U u 228.9463 537.7131 m S 228.9463 524.7466 m S 215.6404 524.7466 m S 215.6404 537.7131 m S 222.2933 531.2299 m S U u 215.6404 537.7131 m S 215.6404 524.7466 m S 202.3347 524.7466 m S 202.3347 537.7131 m S 208.9875 531.2299 m S U u 215.6404 550.6797 m S 215.6404 537.7131 m S 202.3347 537.7131 m S 202.3347 550.6797 m S 208.9875 544.1965 m S U u 242.2521 550.6798 m S 242.2521 537.7132 m S 228.9464 537.7132 m S 228.9464 550.6798 m S 235.5992 544.1965 m S U 242.2521 537.7132 m S 242.2521 537.7132 m S u 242.2521 537.7132 m S 242.2521 524.7466 m S 228.9464 524.7466 m S 228.9464 537.7132 m S 235.5992 531.23 m S U 106.0681 540.9792 m S 106.0681 534.6971 m S 112.57 534.6971 m S 106.0681 534.6971 m S 112.57 540.9792 m S 112.57 534.6971 m S 106.0681 534.6971 m S 106.0681 540.9792 m S 109.3191 537.8381 m S 112.57 534.6971 m S 112.57 540.9792 m S 112.57 534.6971 m S 106.0681 534.6971 m S 1 g 0.7 G 1 w 4 M 106.0681 540.9792 m 112.57 534.6971 l B 112.57 540.9792 m 106.0681 534.6971 l B 0 G 0.3 w 10 M 119.3114 540.9167 m S 119.3114 534.6346 m S 125.8133 534.6346 m S 119.3114 534.6346 m S 125.8133 540.9167 m S 125.8133 534.6346 m S 119.3114 534.6346 m S 119.3114 540.9167 m S 122.5624 537.7756 m S 125.8133 534.6346 m S 125.8133 540.9167 m S 125.8133 534.6346 m S 119.3114 534.6346 m S 1 g 0.7 G 1 w 4 M 119.3114 540.9167 m 125.8133 534.6346 l B 125.8133 540.9167 m 119.3114 534.6346 l B 0 G 0.3 w 10 M 132.5547 540.8542 m S 132.5547 534.5721 m S 139.0566 534.5721 m S 132.5547 534.5721 m S 139.0566 540.8542 m S 139.0566 534.5721 m S 132.5547 534.5721 m S 132.5547 540.8542 m S 135.8057 537.7131 m S 139.0566 534.5721 m S 139.0566 540.8542 m S 139.0566 534.5721 m S 132.5547 534.5721 m S 1 g 0.7 G 1 w 4 M 132.5547 540.8542 m 139.0566 534.5721 l B 139.0566 540.8542 m 132.5547 534.5721 l B 0 G 0.3 w 10 M 162.424 537.7131 m S 149.1182 537.7131 m S 149.1182 537.7131 m S 162.424 537.7131 m S 149.1182 537.7131 m S 149.1182 537.7131 m S 175.7298 537.7131 m S 175.7298 537.7131 m S 175.7298 537.7131 m S 162.424 537.7131 m S 175.7298 537.7131 m S 162.424 537.7131 m S 145.9922 540.9792 m S 145.9922 534.6971 m S 152.4941 534.6971 m S 145.9922 534.6971 m S 152.4941 540.9792 m S 152.4941 534.6971 m S 145.9922 534.6971 m S 145.9922 540.9792 m S 149.2432 537.8381 m S 152.4941 534.6971 m S 152.4941 540.9792 m S 152.4941 534.6971 m S 145.9922 534.6971 m S 1 g 0.7 G 1 w 4 M 145.9922 540.9792 m 152.4941 534.6971 l B 152.4941 540.9792 m 145.9922 534.6971 l B 0 G 0.3 w 10 M 159.2355 540.9167 m S 159.2355 534.6346 m S 165.7374 534.6346 m S 159.2355 534.6346 m S 165.7374 540.9167 m S 165.7374 534.6346 m S 159.2355 534.6346 m S 159.2355 540.9167 m S 162.4865 537.7756 m S 165.7374 534.6346 m S 165.7374 540.9167 m S 165.7374 534.6346 m S 159.2355 534.6346 m S 1 g 0.7 G 1 w 4 M 159.2355 540.9167 m 165.7374 534.6346 l B 165.7374 540.9167 m 159.2355 534.6346 l B 0 G 0.3 w 10 M 172.4788 540.8542 m S 172.4788 534.5721 m S 178.9807 534.5721 m S 172.4788 534.5721 m S 178.9807 540.8542 m S 178.9807 534.5721 m S 172.4788 534.5721 m S 172.4788 540.8542 m S 175.7298 537.7131 m S 178.9807 534.5721 m S 178.9807 540.8542 m S 178.9807 534.5721 m S 172.4788 534.5721 m S 1 g 0.7 G 1 w 4 M 172.4788 540.8542 m 178.9807 534.5721 l B 178.9807 540.8542 m 172.4788 534.5721 l B 0 G 0.3 w 10 M 202.3168 537.7131 m S 189.011 537.7131 m S 189.011 537.7131 m S 202.3168 537.7131 m S 189.011 537.7131 m S 189.011 537.7131 m S 242.2342 537.7131 m S 228.9284 537.7131 m S 228.9284 537.7131 m S 215.6226 537.7131 m S 242.2342 537.7131 m S 228.9284 537.7131 m S 228.9284 537.7131 m S 215.6226 537.7131 m S 215.6226 537.7131 m S 202.3168 537.7131 m S 215.6226 537.7131 m S 202.3168 537.7131 m S 242.2342 537.7131 m S 242.2342 537.7131 m S 185.8851 540.9792 m S 185.8851 534.6971 m S 192.3869 534.6971 m S 185.8851 534.6971 m S 192.3869 540.9792 m S 192.3869 534.6971 m S 185.8851 534.6971 m S 185.8851 540.9792 m S 189.136 537.8381 m S 192.3869 534.6971 m S 192.3869 540.9792 m S 192.3869 534.6971 m S 185.8851 534.6971 m S 1 g 0.7 G 1 w 4 M 185.8851 540.9792 m 192.3869 534.6971 l B 192.3869 540.9792 m 185.8851 534.6971 l B 0 G 0.3 w 10 M 199.1284 540.9167 m S 199.1284 534.6346 m S 205.6302 534.6346 m S 199.1284 534.6346 m S 205.6302 540.9167 m S 205.6302 534.6346 m S 199.1284 534.6346 m S 199.1284 540.9167 m S 202.3793 537.7756 m S 205.6302 534.6346 m S 205.6302 540.9167 m S 205.6302 534.6346 m S 199.1284 534.6346 m S 1 g 0.7 G 1 w 4 M 199.1284 540.9167 m 205.6302 534.6346 l B 205.6302 540.9167 m 199.1284 534.6346 l B 0 G 0.3 w 10 M 212.3717 540.8542 m S 212.3717 534.5721 m S 218.8735 534.5721 m S 212.3717 534.5721 m S 218.8735 540.8542 m S 218.8735 534.5721 m S 212.3717 534.5721 m S 212.3717 540.8542 m S 215.6226 537.7131 m S 218.8735 534.5721 m S 218.8735 540.8542 m S 218.8735 534.5721 m S 212.3717 534.5721 m S 1 g 0.7 G 1 w 4 M 212.3717 540.8542 m 218.8735 534.5721 l B 218.8735 540.8542 m 212.3717 534.5721 l B 0 G 0.3 w 10 M 242.2409 537.7131 m S 228.9351 537.7131 m S 228.9351 537.7131 m S 242.2409 537.7131 m S 228.9351 537.7131 m S 228.9351 537.7131 m S 242.2409 537.7131 m S 242.2409 537.7131 m S 225.8092 540.9792 m S 225.8092 534.6971 m S 232.311 534.6971 m S 225.8092 534.6971 m S 232.311 540.9792 m S 232.311 534.6971 m S 225.8092 534.6971 m S 225.8092 540.9792 m S 229.0601 537.8381 m S 232.311 534.6971 m S 232.311 540.9792 m S 232.311 534.6971 m S 225.8092 534.6971 m S 1 g 0.7 G 1 w 4 M 225.8092 540.9792 m 232.311 534.6971 l B 232.311 540.9792 m 225.8092 534.6971 l B 0 G 0.3 w 10 M 239.0525 540.9167 m S 239.0525 534.6346 m S 245.5543 534.6346 m S 239.0525 534.6346 m S 245.5543 540.9167 m S 245.5543 534.6346 m S 239.0525 534.6346 m S 239.0525 540.9167 m S 242.3034 537.7756 m S 245.5543 534.6346 m S 245.5543 540.9167 m S 245.5543 534.6346 m S 239.0525 534.6346 m S 1 g 0.7 G 1 w 4 M 239.0525 540.9167 m 245.5543 534.6346 l B 245.5543 540.9167 m 239.0525 534.6346 l B 0 G 0.3 w 10 M 92.6295 683.4868 m S 92.6295 677.2047 m S 99.1314 677.2047 m S 92.6295 677.2047 m S 99.1314 683.4868 m S 99.1314 677.2047 m S 92.6295 677.2047 m S 92.6295 683.4868 m S 95.8804 680.3458 m S 99.1314 677.2047 m S 99.1314 683.4868 m S 99.1314 677.2047 m S 92.6295 677.2047 m S 1 g 0.7 G 1 w 4 M 92.6295 683.4868 m 99.1314 677.2047 l B 99.1314 683.4868 m 92.6295 677.2047 l B 0 G 0.3 w 10 M 92.692 670.5827 m S 92.692 664.3006 m S 99.1939 664.3006 m S 92.692 664.3006 m S 99.1939 670.5827 m S 99.1939 664.3006 m S 92.692 664.3006 m S 92.692 670.5827 m S 95.9429 667.4416 m S 99.1939 664.3006 m S 99.1939 670.5827 m S 99.1939 664.3006 m S 92.692 664.3006 m S 1 g 0.7 G 1 w 4 M 92.692 670.5827 m 99.1939 664.3006 l B 99.1939 670.5827 m 92.692 664.3006 l B 0 G 0.3 w 10 M 92.692 657.6161 m S 92.692 651.334 m S 99.1939 651.334 m S 92.692 651.334 m S 99.1939 657.6161 m S 99.1939 651.334 m S 92.692 651.334 m S 92.692 657.6161 m S 95.9429 654.475 m S 99.1939 651.334 m S 99.1939 657.6161 m S 99.1939 651.334 m S 92.692 651.334 m S 1 g 0.7 G 1 w 4 M 92.692 657.6161 m 99.1939 651.334 l B 99.1939 657.6161 m 92.692 651.334 l B 0 G 0.3 w 10 M 92.692 644.6496 m S 92.692 638.3675 m S 99.1939 638.3675 m S 92.692 638.3675 m S 99.1939 644.6496 m S 99.1939 638.3675 m S 92.692 638.3675 m S 92.692 644.6496 m S 95.9429 641.5086 m S 99.1939 638.3675 m S 99.1939 644.6496 m S 99.1939 638.3675 m S 92.692 638.3675 m S 1 g 0.7 G 1 w 4 M 92.692 644.6496 m 99.1939 638.3675 l B 99.1939 644.6496 m 92.692 638.3675 l B u 0 G 0.3 w 10 M 96.0054 628.6168 m S 96.0054 615.6502 m S 82.6996 615.6502 m S 82.6996 628.6168 m S 89.3525 622.1335 m S U 109.3112 615.6502 m S 109.3112 602.6836 m S 96.0054 602.6836 m S 96.0054 615.6502 m S 102.6583 609.167 m S u 109.3112 628.6168 m S 109.3112 615.6502 m S 96.0054 615.6502 m S 96.0054 628.6168 m S 102.6583 622.1335 m S U 109.3112 602.6836 m S 109.3112 589.7171 m S 96.0054 589.7171 m S 96.0054 602.6836 m S 102.6583 596.2004 m S u 96.0054 602.6836 m S 96.0054 589.7171 m S 82.6996 589.7171 m S 82.6996 602.6836 m S 89.3525 596.2004 m S U u 96.0054 615.6502 m S 96.0054 602.6836 m S 82.6996 602.6836 m S 82.6996 615.6502 m S 89.3525 609.167 m S U u 96.0054 589.7171 m S 96.0054 576.7505 m S 82.6996 576.7505 m S 82.6996 589.7171 m S 89.3525 583.2338 m S U u 109.3112 589.7171 m S 109.3112 576.7505 m S 96.0054 576.7505 m S 96.0054 589.7171 m S 102.6583 583.2338 m S U 96.0054 628.6168 m S u 96.0054 641.5833 m S 96.0054 628.6168 m S 82.6996 628.6168 m S 82.6996 641.5833 m S 89.3525 635.1001 m S U 92.7545 631.7579 m S 92.7545 625.4758 m S 99.2564 625.4758 m S 92.7545 625.4758 m S 99.2564 631.7579 m S 99.2564 625.4758 m S 92.7545 625.4758 m S 92.7545 631.7579 m S 96.0054 628.6169 m S 99.2564 625.4758 m S 99.2564 631.7579 m S 99.2564 625.4758 m S 92.7545 625.4758 m S 1 g 0.7 G 1 w 4 M 92.7545 631.7579 m 99.2564 625.4758 l B 99.2564 631.7579 m 92.7545 625.4758 l B 0 G 0.3 w 10 M 92.817 618.8538 m S 92.817 612.5717 m S 99.3189 612.5717 m S 92.817 612.5717 m S 99.3189 618.8538 m S 99.3189 612.5717 m S 92.817 612.5717 m S 92.817 618.8538 m S 96.0679 615.7127 m S 99.3189 612.5717 m S 99.3189 618.8538 m S 99.3189 612.5717 m S 92.817 612.5717 m S 1 g 0.7 G 1 w 4 M 92.817 618.8538 m 99.3189 612.5717 l B 99.3189 618.8538 m 92.817 612.5717 l B 0 G 0.3 w 10 M 92.817 605.8872 m S 92.817 599.6051 m S 99.3189 599.6051 m S 92.817 599.6051 m S 99.3189 605.8872 m S 99.3189 599.6051 m S 92.817 599.6051 m S 92.817 605.8872 m S 96.0679 602.7461 m S 99.3189 599.6051 m S 99.3189 605.8872 m S 99.3189 599.6051 m S 92.817 599.6051 m S 1 g 0.7 G 1 w 4 M 92.817 605.8872 m 99.3189 599.6051 l B 99.3189 605.8872 m 92.817 599.6051 l B 0 G 0.3 w 10 M 92.817 592.9207 m S 92.817 586.6386 m S 99.3189 586.6386 m S 92.817 586.6386 m S 99.3189 592.9207 m S 99.3189 586.6386 m S 92.817 586.6386 m S 92.817 592.9207 m S 96.0679 589.7797 m S 99.3189 586.6386 m S 99.3189 592.9207 m S 99.3189 586.6386 m S 92.817 586.6386 m S 1 g 0.7 G 1 w 4 M 92.817 592.9207 m 99.3189 586.6386 l B 99.3189 592.9207 m 92.817 586.6386 l B u 0 G 0.3 w 10 M 96.0054 576.7504 m S 96.0054 563.7838 m S 82.6996 563.7838 m S 82.6996 576.7504 m S 89.3525 570.2671 m S U u 109.3112 563.7838 m S 109.3112 550.8172 m S 96.0054 550.8172 m S 96.0054 563.7838 m S 102.6583 557.3006 m S U u 109.3112 576.7504 m S 109.3112 563.7838 m S 96.0054 563.7838 m S 96.0054 576.7504 m S 102.6583 570.2671 m S U 109.3112 550.8172 m S 109.3112 537.8507 m S 96.0054 550.8172 m S 102.6583 544.334 m S 96.0054 550.8172 m S 82.6996 537.8507 m S 82.6996 550.8172 m S 89.3525 544.334 m S u 96.0054 563.7838 m S 96.0054 550.8172 m S 82.6996 550.8172 m S 82.6996 563.7838 m S 89.3525 557.3006 m S U 96.0054 524.8841 m S 82.6996 524.8841 m S 82.6996 537.8507 m S 89.3525 531.3674 m S 109.3112 537.8507 m S 109.3112 524.8841 m S 96.0054 524.8841 m S 102.6583 531.3674 m S 96.0054 576.7504 m S u 96.0054 589.7169 m S 96.0054 576.7504 m S 82.6996 576.7504 m S 82.6996 589.7169 m S 89.3525 583.2337 m S U 92.7545 579.8915 m S 92.7545 573.6094 m S 99.2564 573.6094 m S 92.7545 573.6094 m S 99.2564 579.8915 m S 99.2564 573.6094 m S 92.7545 573.6094 m S 92.7545 579.8915 m S 96.0054 576.7505 m S 99.2564 573.6094 m S 99.2564 579.8915 m S 99.2564 573.6094 m S 92.7545 573.6094 m S 1 g 0.7 G 1 w 4 M 92.7545 579.8915 m 99.2564 573.6094 l B 99.2564 579.8915 m 92.7545 573.6094 l B 0 G 0.3 w 10 M 92.817 566.9874 m S 92.817 560.7053 m S 99.3189 560.7053 m S 92.817 560.7053 m S 99.3189 566.9874 m S 99.3189 560.7053 m S 92.817 560.7053 m S 92.817 566.9874 m S 96.0679 563.8463 m S 99.3189 560.7053 m S 99.3189 566.9874 m S 99.3189 560.7053 m S 92.817 560.7053 m S 1 g 0.7 G 1 w 4 M 92.817 566.9874 m 99.3189 560.7053 l B 99.3189 566.9874 m 92.817 560.7053 l B 0 G 0.3 w 10 M 92.817 554.0208 m S 92.817 547.7387 m S 99.3189 547.7387 m S 92.817 547.7387 m S 99.3189 554.0208 m S 99.3189 547.7387 m S 92.817 547.7387 m S 92.817 554.0208 m S 96.0679 550.8797 m S 99.3189 547.7387 m S 99.3189 554.0208 m S 99.3189 547.7387 m S 92.817 547.7387 m S 1 g 0.7 G 1 w 4 M 92.817 554.0208 m 99.3189 547.7387 l B 99.3189 554.0208 m 92.817 547.7387 l B u 0 G 0.3 w 10 M 255.675 589.6923 m S 255.675 576.7257 m S 242.3692 576.7257 m S 242.3692 589.6923 m S 249.0221 583.209 m S U u 268.9808 576.7257 m S 268.9808 563.7591 m S 255.675 563.7591 m S 255.675 576.7257 m S 262.3279 570.2425 m S U u 268.9808 589.6923 m S 268.9808 576.7257 m S 255.675 576.7257 m S 255.675 589.6923 m S 262.3279 583.209 m S U u 268.9808 563.7591 m S 268.9808 550.7926 m S 255.675 550.7926 m S 255.675 563.7591 m S 262.3279 557.2759 m S U u 255.675 563.7591 m S 255.675 550.7926 m S 242.3692 550.7926 m S 242.3692 563.7591 m S 249.0221 557.2759 m S U u 255.675 576.7257 m S 255.675 563.7591 m S 242.3692 563.7591 m S 242.3692 576.7257 m S 249.0221 570.2425 m S U u 255.675 550.7926 m S 255.675 537.826 m S 242.3692 537.826 m S 242.3692 550.7926 m S 249.0221 544.3093 m S U u 268.9808 550.7926 m S 268.9808 537.826 m S 255.675 537.826 m S 255.675 550.7926 m S 262.3279 544.3093 m S U 255.675 589.6923 m S 255.675 602.6588 m S 255.675 589.6923 m S 242.3692 589.6923 m S 242.3692 602.6588 m S 249.0221 596.1756 m S 252.4241 592.8334 m S 252.4241 586.5513 m S 258.926 586.5513 m S 252.4241 586.5513 m S 258.926 592.8334 m S 258.926 586.5513 m S 252.4241 586.5513 m S 252.4241 592.8334 m S 255.675 589.6924 m S 258.926 586.5513 m S 258.926 592.8334 m S 258.926 586.5513 m S 252.4241 586.5513 m S 1 g 0.7 G 1 w 4 M 252.4241 592.8334 m 258.926 586.5513 l B 258.926 592.8334 m 252.4241 586.5513 l B 0 G 0.3 w 10 M 252.4866 579.9293 m S 252.4866 573.6472 m S 258.9885 573.6472 m S 252.4866 573.6472 m S 258.9885 579.9293 m S 258.9885 573.6472 m S 252.4866 573.6472 m S 252.4866 579.9293 m S 255.7375 576.7882 m S 258.9885 573.6472 m S 258.9885 579.9293 m S 258.9885 573.6472 m S 252.4866 573.6472 m S 1 g 0.7 G 1 w 4 M 252.4866 579.9293 m 258.9885 573.6472 l B 258.9885 579.9293 m 252.4866 573.6472 l B 0 G 0.3 w 10 M 252.4866 566.9627 m S 252.4866 560.6806 m S 258.9885 560.6806 m S 252.4866 560.6806 m S 258.9885 566.9627 m S 258.9885 560.6806 m S 252.4866 560.6806 m S 252.4866 566.9627 m S 255.7375 563.8216 m S 258.9885 560.6806 m S 258.9885 566.9627 m S 258.9885 560.6806 m S 252.4866 560.6806 m S 1 g 0.7 G 1 w 4 M 252.4866 566.9627 m 258.9885 560.6806 l B 258.9885 566.9627 m 252.4866 560.6806 l B 0 G 0.3 w 10 M 252.4866 553.9962 m S 252.4866 547.7141 m S 258.9885 547.7141 m S 252.4866 547.7141 m S 258.9885 553.9962 m S 258.9885 547.7141 m S 252.4866 547.7141 m S 252.4866 553.9962 m S 255.7375 550.8552 m S 258.9885 547.7141 m S 258.9885 553.9962 m S 258.9885 547.7141 m S 252.4866 547.7141 m S 1 g 0.7 G 1 w 4 M 252.4866 553.9962 m 258.9885 547.7141 l B 258.9885 553.9962 m 252.4866 547.7141 l B 0 G 0.3 w 10 M 255.55 641.4337 m S 255.55 628.4671 m S 242.2442 628.4671 m S 242.2442 641.4337 m S 248.8971 634.9504 m S u 268.8558 628.4671 m S 268.8558 615.5005 m S 255.55 615.5005 m S 255.55 628.4671 m S 262.2029 621.9839 m S U u 268.8558 641.4337 m S 268.8558 628.4671 m S 255.55 628.4671 m S 255.55 641.4337 m S 262.2029 634.9504 m S U u 268.8558 615.5005 m S 268.8558 602.534 m S 255.55 602.534 m S 255.55 615.5005 m S 262.2029 609.0173 m S U 255.55 615.5005 m S 255.55 602.534 m S 242.2442 602.534 m S 242.2442 615.5005 m S 248.8971 609.0173 m S u 255.55 628.4671 m S 255.55 615.5005 m S 242.2442 615.5005 m S 242.2442 628.4671 m S 248.8971 621.9839 m S U 255.55 602.534 m S 255.55 589.5674 m S 242.2442 589.5674 m S 242.2442 602.534 m S 248.8971 596.0507 m S u 268.8558 602.534 m S 268.8558 589.5674 m S 255.55 589.5674 m S 255.55 602.534 m S 262.2029 596.0507 m S U 255.55 641.4337 m S 255.55 654.4002 m S 255.55 641.4337 m S 242.2442 641.4337 m S 242.2442 654.4002 m S 248.8971 647.917 m S 252.2991 644.5748 m S 252.2991 638.2927 m S 258.801 638.2927 m S 252.2991 638.2927 m S 258.801 644.5748 m S 258.801 638.2927 m S 252.2991 638.2927 m S 252.2991 644.5748 m S 255.55 641.4338 m S 258.801 638.2927 m S 258.801 644.5748 m S 258.801 638.2927 m S 252.2991 638.2927 m S 1 g 0.7 G 1 w 4 M 252.2991 644.5748 m 258.801 638.2927 l B 258.801 644.5748 m 252.2991 638.2927 l B 0 G 0.3 w 10 M 252.3616 631.6707 m S 252.3616 625.3886 m S 258.8635 625.3886 m S 252.3616 625.3886 m S 258.8635 631.6707 m S 258.8635 625.3886 m S 252.3616 625.3886 m S 252.3616 631.6707 m S 255.6125 628.5296 m S 258.8635 625.3886 m S 258.8635 631.6707 m S 258.8635 625.3886 m S 252.3616 625.3886 m S 1 g 0.7 G 1 w 4 M 252.3616 631.6707 m 258.8635 625.3886 l B 258.8635 631.6707 m 252.3616 625.3886 l B 0 G 0.3 w 10 M 252.3616 618.7041 m S 252.3616 612.422 m S 258.8635 612.422 m S 252.3616 612.422 m S 258.8635 618.7041 m S 258.8635 612.422 m S 252.3616 612.422 m S 252.3616 618.7041 m S 255.6125 615.563 m S 258.8635 612.422 m S 258.8635 618.7041 m S 258.8635 612.422 m S 252.3616 612.422 m S 1 g 0.7 G 1 w 4 M 252.3616 618.7041 m 258.8635 612.422 l B 258.8635 618.7041 m 252.3616 612.422 l B 0 G 0.3 w 10 M 252.3616 605.7376 m S 252.3616 599.4555 m S 258.8635 599.4555 m S 252.3616 599.4555 m S 258.8635 605.7376 m S 258.8635 599.4555 m S 252.3616 599.4555 m S 252.3616 605.7376 m S 255.6125 602.5966 m S 258.8635 599.4555 m S 258.8635 605.7376 m S 258.8635 599.4555 m S 252.3616 599.4555 m S 1 g 0.7 G 1 w 4 M 252.3616 605.7376 m 258.8635 599.4555 l B 258.8635 605.7376 m 252.3616 599.4555 l B 0 G 0.3 w 10 M 255.6125 680.3835 m S 242.3067 680.3835 m S 242.3067 693.3501 m S 248.9596 686.8668 m S u 268.9183 680.3835 m S 268.9183 667.4169 m S 255.6125 667.4169 m S 255.6125 680.3835 m S 262.2654 673.9003 m S U 268.9183 693.3501 m S 268.9183 680.3835 m S 255.6125 680.3835 m S 262.2654 686.8668 m S u 268.9183 667.4169 m S 268.9183 654.4504 m S 255.6125 654.4504 m S 255.6125 667.4169 m S 262.2654 660.9337 m S U u 255.6125 667.4169 m S 255.6125 654.4504 m S 242.3067 654.4504 m S 242.3067 667.4169 m S 248.9596 660.9337 m S U u 255.6125 680.3835 m S 255.6125 667.4169 m S 242.3067 667.4169 m S 242.3067 680.3835 m S 248.9596 673.9003 m S U 255.6125 654.4504 m S 255.6125 641.4838 m S 242.3067 641.4838 m S 242.3067 654.4504 m S 248.9596 647.9671 m S u 268.9183 654.4504 m S 268.9183 641.4838 m S 255.6125 641.4838 m S 255.6125 654.4504 m S 262.2654 647.9671 m S U 242.3067 693.3501 m S 248.9596 699.8334 m S 252.4241 683.5871 m S 252.4241 677.305 m S 258.926 677.305 m S 252.4241 677.305 m S 258.926 683.5871 m S 258.926 677.305 m S 252.4241 677.305 m S 252.4241 683.5871 m S 255.675 680.446 m S 258.926 677.305 m S 258.926 683.5871 m S 258.926 677.305 m S 252.4241 677.305 m S 1 g 0.7 G 1 w 4 M 252.4241 683.5871 m 258.926 677.305 l B 258.926 683.5871 m 252.4241 677.305 l B 0 G 0.3 w 10 M 252.4241 670.6205 m S 252.4241 664.3384 m S 258.926 664.3384 m S 252.4241 664.3384 m S 258.926 670.6205 m S 258.926 664.3384 m S 252.4241 664.3384 m S 252.4241 670.6205 m S 255.675 667.4794 m S 258.926 664.3384 m S 258.926 670.6205 m S 258.926 664.3384 m S 252.4241 664.3384 m S 1 g 0.7 G 1 w 4 M 252.4241 670.6205 m 258.926 664.3384 l B 258.926 670.6205 m 252.4241 664.3384 l B 0 G 0.3 w 10 M 252.4241 657.654 m S 252.4241 651.3719 m S 258.926 651.3719 m S 252.4241 651.3719 m S 258.926 657.654 m S 258.926 651.3719 m S 252.4241 651.3719 m S 252.4241 657.654 m S 255.675 654.5129 m S 258.926 651.3719 m S 258.926 657.654 m S 258.926 651.3719 m S 252.4241 651.3719 m S 1 g 0.7 G 1 w 4 M 252.4241 657.654 m 258.926 651.3719 l B 258.926 657.654 m 252.4241 651.3719 l B u 0 G 85.2573 667.3613 m 87.7043 688.7908 91.6355 702.6869 96.0679 702.6869 c S 109.5029 615.7127 m S 96.0679 528.7386 m 88.6481 528.7386 82.6329 567.679 82.6329 615.7127 c 82.6329 635.0524 83.608 652.9179 85.2573 667.3613 c S 1 g 0.7 G 96.0679 615.7127 m B U u 0 G 255.4208 702.4747 m 262.8407 702.4747 268.8558 663.5343 268.8558 615.5005 c 268.8558 567.4667 262.8407 528.5264 255.4208 528.5264 c S 241.9858 615.5005 m S 255.4208 615.5005 m S U u u 0 g /_Times-Italic 36 43 0 0 z [1 0 0 1 42.6603 609.604]e (m)t T U U 0 G 0.3 w 10 M 122.492 667.3792 m S 109.1862 667.3792 m S 135.7978 667.3792 m S 122.492 667.3792 m S 135.7978 667.3792 m S 122.492 667.3792 m S 149.1036 667.3792 m S 135.7978 667.3792 m S 149.1036 667.3792 m S 135.7978 667.3792 m S 122.492 667.3792 m S 109.1862 667.3792 m S 162.4094 667.3792 m S 149.1036 667.3792 m S 175.7152 667.3792 m S 162.4094 667.3792 m S 175.7152 667.3792 m S 162.4094 667.3792 m S 189.021 667.3792 m S 175.7152 667.3792 m S 189.021 667.3792 m S 175.7152 667.3792 m S 162.4094 667.3792 m S 149.1036 667.3792 m S 202.3268 667.3792 m S 189.021 667.3792 m S 215.6326 667.3792 m S 202.3268 667.3792 m S 215.6326 667.3792 m S 202.3268 667.3792 m S 228.9385 667.3792 m S 215.6326 667.3792 m S 228.9385 667.3792 m S 215.6326 667.3792 m S 202.3268 667.3792 m S 189.021 667.3792 m S 242.2441 667.3792 m S 228.9385 667.3792 m S 242.2441 667.3792 m S 242.2441 667.3792 m S 242.2441 667.3792 m S 228.9385 667.3792 m S 122.492 667.3792 m S 1 g 1 w 4 M 122.492 662.5709 m 125.3037 662.5709 127.5831 664.7237 127.5831 667.3792 c 127.5831 670.0347 125.3037 672.1875 122.492 672.1875 c 119.6803 672.1875 117.4009 670.0347 117.4009 667.3792 c 117.4009 664.7237 119.6803 662.5709 122.492 662.5709 c b 0 g 122.492 667.3792 m F 0 G 0.3 w 10 M 135.7978 667.3792 m S 1 g 1 w 4 M 135.7978 662.5709 m 138.6095 662.5709 140.889 664.7237 140.889 667.3792 c 140.889 670.0347 138.6095 672.1875 135.7978 672.1875 c 132.9861 672.1875 130.7067 670.0347 130.7067 667.3792 c 130.7067 664.7237 132.9861 662.5709 135.7978 662.5709 c b 0 g 135.7978 667.3792 m F 0 G 0.3 w 10 M 149.1036 667.3792 m S 1 g 1 w 4 M 149.1036 662.5709 m 151.9153 662.5709 154.1947 664.7237 154.1947 667.3792 c 154.1947 670.0347 151.9153 672.1875 149.1036 672.1875 c 146.292 672.1875 144.0125 670.0347 144.0125 667.3792 c 144.0125 664.7237 146.292 662.5709 149.1036 662.5709 c b 0 g 149.1036 667.3792 m F 0 G 0.3 w 10 M 162.4094 667.3792 m S 1 g 1 w 4 M 162.4094 662.5709 m 165.2212 662.5709 167.5005 664.7237 167.5005 667.3792 c 167.5005 670.0347 165.2212 672.1875 162.4094 672.1875 c 159.5978 672.1875 157.3183 670.0347 157.3183 667.3792 c 157.3183 664.7237 159.5978 662.5709 162.4094 662.5709 c b 0 g 162.4094 667.3792 m F 0 G 0.3 w 10 M 175.7152 667.3792 m S 1 g 1 w 4 M 175.7152 662.5709 m 178.527 662.5709 180.8063 664.7237 180.8063 667.3792 c 180.8063 670.0347 178.527 672.1875 175.7152 672.1875 c 172.9035 672.1875 170.6241 670.0347 170.6241 667.3792 c 170.6241 664.7237 172.9035 662.5709 175.7152 662.5709 c b 0 g 175.7152 667.3792 m F 0 G 0.3 w 10 M 189.021 667.3792 m S 1 g 1 w 4 M 189.021 662.5709 m 191.8327 662.5709 194.1121 664.7237 194.1121 667.3792 c 194.1121 670.0347 191.8327 672.1875 189.021 672.1875 c 186.2093 672.1875 183.93 670.0347 183.93 667.3792 c 183.93 664.7237 186.2093 662.5709 189.021 662.5709 c b 0 g 189.021 667.3792 m F 0 G 0.3 w 10 M 202.3268 667.3792 m S 1 g 1 w 4 M 202.3268 662.5709 m 205.1385 662.5709 207.4179 664.7237 207.4179 667.3792 c 207.4179 670.0347 205.1385 672.1875 202.3268 672.1875 c 199.5151 672.1875 197.2357 670.0347 197.2357 667.3792 c 197.2357 664.7237 199.5151 662.5709 202.3268 662.5709 c b 0 g 202.3268 667.3792 m F 0 G 0.3 w 10 M 215.6326 667.3792 m S 1 g 1 w 4 M 215.6326 662.5709 m 218.4443 662.5709 220.7237 664.7237 220.7237 667.3792 c 220.7237 670.0347 218.4443 672.1875 215.6326 672.1875 c 212.8209 672.1875 210.5415 670.0347 210.5415 667.3792 c 210.5415 664.7237 212.8209 662.5709 215.6326 662.5709 c b 0 g 215.6326 667.3792 m F 0 G 0.3 w 10 M 242.2441 667.3792 m S 1 g 1 w 4 M 242.2441 662.5709 m 245.0559 662.5709 247.3353 664.7237 247.3353 667.3792 c 247.3353 670.0347 245.0559 672.1875 242.2441 672.1875 c 239.4325 672.1875 237.1531 670.0347 237.1531 667.3792 c 237.1531 664.7237 239.4325 662.5709 242.2441 662.5709 c b 0 g 242.2441 667.3792 m F 0 G 0.3 w 10 M 228.9385 667.3792 m S 1 g 1 w 4 M 228.9385 662.5709 m 231.7501 662.5709 234.0295 664.7237 234.0295 667.3792 c 234.0295 670.0347 231.7501 672.1875 228.9385 672.1875 c 226.1267 672.1875 223.8473 670.0347 223.8473 667.3792 c 223.8473 664.7237 226.1267 662.5709 228.9385 662.5709 c b 0 g 228.9385 667.3792 m F 0 G 0.3 w 10 M 109.1862 667.3792 m S 1 g 1 w 4 M 109.1862 662.5709 m 111.9979 662.5709 114.2773 664.7237 114.2773 667.3792 c 114.2773 670.0347 111.9979 672.1875 109.1862 672.1875 c 106.3745 672.1875 104.0951 670.0347 104.0951 667.3792 c 104.0951 664.7237 106.3745 662.5709 109.1862 662.5709 c b 0 g 109.1862 667.3792 m F 0 G 0.3 w 10 M 122.492 667.3791 m S 109.1862 667.3791 m S 109.1862 667.3791 m S 109.1862 667.3791 m S 122.492 667.3791 m S 109.1862 667.3791 m S 242.2442 667.3668 m S 242.2442 667.3668 m S 242.3067 667.4169 m S 215.6325 680.3457 m S 0 g 1 w 4 M 215.6325 680.3457 m F 0 G 0.3 w 10 M 215.6325 680.3457 m S 215.6325 680.3457 m S 215.6325 680.3457 m S 0 g 1 w 4 M 215.6325 680.3457 m F 0 G 0.3 w 10 M 215.6325 680.3457 m S 215.6325 680.3457 m S u 1 g 1 w 4 M 209.6221 680.3457 m 209.6221 677.1239 212.3131 674.5121 215.6325 674.5121 c 218.9519 674.5121 221.6429 677.1239 221.6429 680.3457 c F 221.6429 680.3457 m 221.6429 683.5675 218.9519 686.1793 215.6325 686.1793 c 212.3131 686.1793 209.6221 683.5675 209.6221 680.3457 c F 215.6325 680.3457 m F U 0 G 0.3 w 10 M 215.6325 680.3457 m S 0 g 1 w 4 M 215.6325 680.3457 m F 0 G 0.3 w 10 M 215.6325 680.3457 m S 215.6325 680.3457 m S 0 g 1 w 4 M 214.5474 679.2778 m 214.5474 675.7007 L 216.7176 675.7007 L 216.7176 679.2778 L 220.3032 679.2666 L 220.3032 681.425 L 216.7176 681.4139 L 216.7176 684.991 L 214.5474 684.991 L 214.5474 681.4139 L 210.9618 681.425 L 210.9618 679.2666 L 214.5474 679.2778 L f 0 G 0.3 w 10 M 189.021 680.3457 m S 0 g 1 w 4 M 189.021 680.3457 m F 0 G 0.3 w 10 M 189.021 680.3457 m S 189.021 680.3457 m S 189.021 680.3457 m S 0 g 1 w 4 M 189.021 680.3457 m F 0 G 0.3 w 10 M 189.021 680.3457 m S 189.021 680.3457 m S u 1 g 1 w 4 M 183.0106 680.3457 m 183.0106 677.1239 185.7016 674.5121 189.021 674.5121 c 192.3404 674.5121 195.0314 677.1239 195.0314 680.3457 c F 195.0314 680.3457 m 195.0314 683.5675 192.3404 686.1793 189.021 686.1793 c 185.7016 686.1793 183.0106 683.5675 183.0106 680.3457 c F 189.021 680.3457 m F U 0 G 0.3 w 10 M 189.021 680.3457 m S 0 g 1 w 4 M 189.021 680.3457 m F 0 G 0.3 w 10 M 189.021 680.3457 m S 189.021 680.3457 m S 0 g 1 w 4 M 187.9359 679.2778 m 187.9359 675.7007 L 190.1061 675.7007 L 190.1061 679.2778 L 193.6917 679.2666 L 193.6917 681.425 L 190.1061 681.4139 L 190.1061 684.991 L 187.9359 684.991 L 187.9359 681.4139 L 184.3503 681.425 L 184.3503 679.2666 L 187.9359 679.2778 L f 0 G 0.3 w 10 M 162.4094 680.3457 m S 0 g 1 w 4 M 162.4094 680.3457 m F 0 G 0.3 w 10 M 162.4094 680.3457 m S 162.4094 680.3457 m S 162.4094 680.3457 m S 0 g 1 w 4 M 162.4094 680.3457 m F 0 G 0.3 w 10 M 162.4094 680.3457 m S 162.4094 680.3457 m S u 1 g 1 w 4 M 156.399 680.3457 m 156.399 677.1239 159.09 674.5121 162.4094 674.5121 c 165.7288 674.5121 168.4198 677.1239 168.4198 680.3457 c F 168.4198 680.3457 m 168.4198 683.5675 165.7288 686.1793 162.4094 686.1793 c 159.09 686.1793 156.399 683.5675 156.399 680.3457 c F 162.4094 680.3457 m F U 0 G 0.3 w 10 M 162.4094 680.3457 m S 0 g 1 w 4 M 162.4094 680.3457 m F 0 G 0.3 w 10 M 162.4094 680.3457 m S 162.4094 680.3457 m S 0 g 1 w 4 M 161.3243 679.2778 m 161.3243 675.7007 L 163.4945 675.7007 L 163.4945 679.2778 L 167.0801 679.2666 L 167.0801 681.425 L 163.4945 681.4139 L 163.4945 684.991 L 161.3243 684.991 L 161.3243 681.4139 L 157.7387 681.425 L 157.7387 679.2666 L 161.3243 679.2778 L f 0 G 0.3 w 10 M 135.7978 680.3457 m S 0 g 1 w 4 M 135.7978 680.3457 m F 0 G 0.3 w 10 M 135.7978 680.3457 m S 135.7978 680.3457 m S 135.7978 680.3457 m S 0 g 1 w 4 M 135.7978 680.3457 m F 0 G 0.3 w 10 M 135.7978 680.3457 m S 135.7978 680.3457 m S u 1 g 1 w 4 M 129.7874 680.3457 m 129.7874 677.1239 132.4784 674.5121 135.7978 674.5121 c 139.1172 674.5121 141.8082 677.1239 141.8082 680.3457 c F 141.8082 680.3457 m 141.8082 683.5675 139.1172 686.1793 135.7978 686.1793 c 132.4784 686.1793 129.7874 683.5675 129.7874 680.3457 c F 135.7978 680.3457 m F U 0 G 0.3 w 10 M 135.7978 680.3457 m S 0 g 1 w 4 M 135.7978 680.3457 m F 0 G 0.3 w 10 M 135.7978 680.3457 m S 135.7978 680.3457 m S 0 g 1 w 4 M 134.7127 679.2778 m 134.7127 675.7007 L 136.8829 675.7007 L 136.8829 679.2778 L 140.4685 679.2666 L 140.4685 681.425 L 136.8829 681.4139 L 136.8829 684.991 L 134.7127 684.991 L 134.7127 681.4139 L 131.1271 681.425 L 131.1271 679.2666 L 134.7127 679.2778 L f 0 G 0.3 w 10 M 109.0612 654.2752 m S 0 g 1 w 4 M 109.0612 654.2752 m F 0 G 0.3 w 10 M 109.0612 654.2752 m S 109.0612 654.2752 m S 109.0612 654.2752 m S 0 g 1 w 4 M 109.0612 654.2752 m F 0 G 0.3 w 10 M 109.0612 654.2752 m S 109.0612 654.2752 m S 1 g 1 w 4 M 103.0508 654.2752 m 103.0508 651.0534 105.7418 648.4416 109.0612 648.4416 c 112.3807 648.4416 115.0716 651.0534 115.0716 654.2752 c F 115.0716 654.2752 m 115.0716 657.497 112.3807 660.1089 109.0612 660.1089 c 105.7418 660.1089 103.0508 657.497 103.0508 654.2752 c F 109.0612 654.2752 m F 0 G 0.3 w 10 M 109.0612 654.2752 m S 0 g 1 w 4 M 109.0612 654.2752 m F 0 G 0.3 w 10 M 109.0612 654.2752 m S 109.0612 654.2752 m S 0 g 1 w 4 M 107.9761 653.2073 m 107.9761 649.6302 L 110.1463 649.6302 L 110.1463 653.2073 L 113.7319 653.1961 L 113.7319 655.3545 L 110.1463 655.3434 L 110.1463 658.9205 L 107.9761 658.9205 L 107.9761 655.3434 L 104.3905 655.3545 L 104.3905 653.1961 L 107.9761 653.2073 L f 0 G 0.3 w 10 M 135.6728 654.2752 m S 0 g 1 w 4 M 135.6728 654.2752 m F 0 G 0.3 w 10 M 135.6728 654.2752 m S 135.6728 654.2752 m S 135.6728 654.2752 m S 0 g 1 w 4 M 135.6728 654.2752 m F 0 G 0.3 w 10 M 135.6728 654.2752 m S 135.6728 654.2752 m S 1 g 1 w 4 M 129.6624 654.2752 m 129.6624 651.0534 132.3534 648.4416 135.6728 648.4416 c 138.9923 648.4416 141.6832 651.0534 141.6832 654.2752 c F 141.6832 654.2752 m 141.6832 657.497 138.9923 660.1089 135.6728 660.1089 c 132.3534 660.1089 129.6624 657.497 129.6624 654.2752 c F 135.6728 654.2752 m F 0 G 0.3 w 10 M 135.6728 654.2752 m S 0 g 1 w 4 M 135.6728 654.2752 m F 0 G 0.3 w 10 M 135.6728 654.2752 m S 135.6728 654.2752 m S 0 g 1 w 4 M 134.5877 653.2073 m 134.5877 649.6302 L 136.7579 649.6302 L 136.7579 653.2073 L 140.3435 653.1961 L 140.3435 655.3545 L 136.7579 655.3434 L 136.7579 658.9205 L 134.5877 658.9205 L 134.5877 655.3434 L 131.0021 655.3545 L 131.0021 653.1961 L 134.5877 653.2073 L f 0 G 0.3 w 10 M 188.896 654.2752 m S 0 g 1 w 4 M 188.896 654.2752 m F 0 G 0.3 w 10 M 188.896 654.2752 m S 188.896 654.2752 m S 188.896 654.2752 m S 0 g 1 w 4 M 188.896 654.2752 m F 0 G 0.3 w 10 M 188.896 654.2752 m S 188.896 654.2752 m S 1 g 1 w 4 M 182.8856 654.2752 m 182.8856 651.0534 185.5766 648.4416 188.896 648.4416 c 192.2155 648.4416 194.9065 651.0534 194.9065 654.2752 c F 194.9065 654.2752 m 194.9065 657.497 192.2155 660.1089 188.896 660.1089 c 185.5766 660.1089 182.8856 657.497 182.8856 654.2752 c F 188.896 654.2752 m F 0 G 0.3 w 10 M 188.896 654.2752 m S 0 g 1 w 4 M 188.896 654.2752 m F 0 G 0.3 w 10 M 188.896 654.2752 m S 188.896 654.2752 m S 0 g 1 w 4 M 187.8109 653.2073 m 187.8109 649.6302 L 189.9811 649.6302 L 189.9811 653.2073 L 193.5667 653.1961 L 193.5667 655.3545 L 189.9811 655.3434 L 189.9811 658.9205 L 187.8109 658.9205 L 187.8109 655.3434 L 184.2253 655.3545 L 184.2253 653.1961 L 187.8109 653.2073 L f 0 G 0.3 w 10 M 242.1191 654.2752 m S 0 g 1 w 4 M 242.1191 654.2752 m F 0 G 0.3 w 10 M 242.1191 654.2752 m S 242.1191 654.2752 m S 242.1191 654.2752 m S 0 g 1 w 4 M 242.1191 654.2752 m F 0 G 0.3 w 10 M 242.1191 654.2752 m S 242.1191 654.2752 m S 1 g 1 w 4 M 236.1087 654.2752 m 236.1087 651.0534 238.7997 648.4416 242.1191 648.4416 c 245.4386 648.4416 248.1296 651.0534 248.1296 654.2752 c F 248.1296 654.2752 m 248.1296 657.497 245.4386 660.1089 242.1191 660.1089 c 238.7997 660.1089 236.1087 657.497 236.1087 654.2752 c F 242.1191 654.2752 m F 0 G 0.3 w 10 M 242.1191 654.2752 m S 0 g 1 w 4 M 242.1191 654.2752 m F 0 G 0.3 w 10 M 242.1191 654.2752 m S 242.1191 654.2752 m S 0 g 1 w 4 M 241.034 653.2073 m 241.034 649.6302 L 243.2042 649.6302 L 243.2042 653.2073 L 246.7898 653.1961 L 246.7898 655.3545 L 243.2042 655.3434 L 243.2042 658.9205 L 241.034 658.9205 L 241.034 655.3434 L 237.4484 655.3545 L 237.4484 653.1961 L 241.034 653.2073 L f 0 G 0.3 w 10 M 162.2844 654.2752 m S 0 g 1 w 4 M 162.2844 654.2752 m F 0 G 0.3 w 10 M 162.2844 654.2752 m S 0 g 1 w 4 M 162.2844 654.2752 m F 1 g 156.274 654.2752 m 156.274 651.0534 158.965 648.4416 162.2844 648.4416 c 165.6039 648.4416 168.2948 651.0534 168.2948 654.2752 c F 168.2948 654.2752 m 168.2948 657.497 165.6039 660.1089 162.2844 660.1089 c 158.965 660.1089 156.274 657.497 156.274 654.2752 c F 162.2844 654.2752 m F 0 G 0.3 w 10 M 162.2844 654.2752 m S 0 g 1 w 4 M 162.2844 654.2752 m F 0 G 0.3 w 10 M 162.2844 654.2752 m S 0 g 1 w 4 M 162.2844 654.2752 m F 161.1993 655.3434 m 157.6137 655.3545 L 157.6137 653.1961 L 161.1993 653.2072 L F 163.3695 653.2072 m 166.9551 653.1961 L 166.9551 655.3545 L 163.3695 655.3434 L F 157.6137 655.3545 m 166.9551 655.3545 l 166.9551 653.1961 l 157.6137 653.1961 l 157.6137 655.3545 l f 0 G 0.3 w 10 M 215.5076 654.2752 m S 0 g 1 w 4 M 215.5076 654.2752 m F 0 G 0.3 w 10 M 215.5076 654.2752 m S 0 g 1 w 4 M 215.5076 654.2752 m F 1 g 209.4972 654.2752 m 209.4972 651.0534 212.1882 648.4416 215.5076 648.4416 c 218.8271 648.4416 221.5181 651.0534 221.5181 654.2752 c F 221.5181 654.2752 m 221.5181 657.497 218.8271 660.1089 215.5076 660.1089 c 212.1882 660.1089 209.4972 657.497 209.4972 654.2752 c F 215.5076 654.2752 m F 0 G 0.3 w 10 M 215.5076 654.2752 m S 0 g 1 w 4 M 215.5076 654.2752 m F 0 G 0.3 w 10 M 215.5076 654.2752 m S 0 g 1 w 4 M 215.5076 654.2752 m F 214.4225 655.3434 m 210.8369 655.3545 L 210.8369 653.1961 L 214.4225 653.2072 L F 216.5927 653.2072 m 220.1783 653.1961 L 220.1783 655.3545 L 216.5927 655.3434 L F 210.8369 655.3545 m 220.1783 655.3545 l 220.1783 653.1961 l 210.8369 653.1961 l 210.8369 655.3545 l f 0 G 0.3 w 10 M 228.8135 654.2752 m S 1 g 1 w 4 M 228.8135 649.4669 m 231.6251 649.4669 233.9045 651.6197 233.9045 654.2752 c 233.9045 656.9307 231.6251 659.0835 228.8135 659.0835 c 226.0017 659.0835 223.7223 656.9307 223.7223 654.2752 c 223.7223 651.6197 226.0017 649.4669 228.8135 649.4669 c b 0 g 228.8135 654.2752 m F 0 G 0.3 w 10 M 202.2018 654.2752 m S 1 g 1 w 4 M 202.2018 649.4669 m 205.0135 649.4669 207.2929 651.6197 207.2929 654.2752 c 207.2929 656.9307 205.0135 659.0835 202.2018 659.0835 c 199.3901 659.0835 197.1107 656.9307 197.1107 654.2752 c 197.1107 651.6197 199.3901 649.4669 202.2018 649.4669 c b 0 g 202.2018 654.2752 m F 0 G 0.3 w 10 M 122.367 654.2752 m S 1 g 1 w 4 M 122.367 649.4669 m 125.1787 649.4669 127.4581 651.6197 127.4581 654.2752 c 127.4581 656.9307 125.1787 659.0835 122.367 659.0835 c 119.5553 659.0835 117.2759 656.9307 117.2759 654.2752 c 117.2759 651.6197 119.5553 649.4669 122.367 649.4669 c b 0 g 122.367 654.2752 m F 0 G 0.3 w 10 M 148.9786 654.2752 m S 1 g 1 w 4 M 148.9786 649.4669 m 151.7903 649.4669 154.0697 651.6197 154.0697 654.2752 c 154.0697 656.9307 151.7903 659.0835 148.9786 659.0835 c 146.1669 659.0835 143.8875 656.9307 143.8875 654.2752 c 143.8875 651.6197 146.1669 649.4669 148.9786 649.4669 c b 0 g 148.9786 654.2752 m F 0 G 0.3 w 10 M 175.5902 654.2752 m S 1 g 1 w 4 M 175.5902 649.4669 m 178.4019 649.4669 180.6813 651.6197 180.6813 654.2752 c 180.6813 656.9307 178.4019 659.0835 175.5902 659.0835 c 172.7785 659.0835 170.4991 656.9307 170.4991 654.2752 c 170.4991 651.6197 172.7785 649.4669 175.5902 649.4669 c b 0 g 175.5902 654.2752 m F 0 G 0.3 w 10 M 122.367 654.2751 m S 109.0612 654.2751 m S 109.0612 654.2751 m S 109.0612 654.2751 m S 109.0612 654.2751 m S 109.1862 654.4125 m S 109.1862 654.4125 m S 102.5333 647.9293 m S 242.2442 654.3877 m S 248.8971 647.9045 m S 242.1192 654.2629 m S 242.1192 654.2629 m S 248.7721 647.7796 m S u u 0 g 1 w 4 M /_Symbol 36 43 0 0 z [1 0 0 1 98.1211 376.7187]e (\263)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 148.0393 499.7628]e (\(a\))t T U U u u /_Times-Roman 36 43 0 0 z [1 0 0 1 288.0393 611.5128]e (=)t T U U 102.6583 557.3006 m F 102.6583 544.334 m F 102.6583 531.3674 m F 0 G 0.5 w 129.1449 534.5128 m 129.1449 528.9798 l S 0.4 G 1 w 128.8949 513.763 m S 0 G 0.5 w 128.8949 528.9798 m 222.2855 528.9798 l S 0.4 G 1 w 222.2855 513.763 m S u 1 g 0 G 0.5 w 141.4177 532.395 m 129.1449 528.9798 L 141.5049 525.8943 L 141.4177 532.395 L b U u 209.968 525.7295 m 222.2855 528.9798 L 209.968 532.2308 L 209.968 525.7295 L b U u u 0 g 1 w /_Times-Roman 12 14.5 0 0 z [1 0 0 1 161.7893 518.0128]e (\62)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 167.7893 518.0128]e (R+)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 183.217 518.0128]e (\61)t T U U 0 G 0.5 w 129.1449 528.9798 m 129.1449 523.4468 l S 222.2855 528.9798 m 222.2855 523.4468 l S 222.2855 534.5128 m 222.2855 528.9798 l S u 0.3 w 10 M 480.8347 549.3969 m S 480.8347 536.4304 m S 467.5289 536.4304 m S 467.5289 549.3969 m S 474.1818 542.9137 m S U u 520.7521 549.3969 m S 520.7521 536.4304 m S 507.4463 536.4304 m S 507.4463 549.3969 m S 514.0992 542.9137 m S U u 507.4463 549.3969 m S 507.4463 536.4304 m S 494.1404 536.4304 m S 494.1404 549.3969 m S 500.7933 542.9137 m S U u 494.1404 549.3969 m S 494.1404 536.4304 m S 480.8347 536.4304 m S 480.8347 549.3969 m S 487.4875 542.9137 m S U u 520.7521 549.397 m S 520.7521 536.4304 m S 507.4464 536.4304 m S 507.4464 549.397 m S 514.0992 542.9138 m S U 0.5 w 4 M 407.6449 546.1966 m 407.6449 540.6636 l S 0.4 G 1 w 407.3949 525.4468 m S 0 G 0.5 w 407.3949 540.6636 m 500.7855 540.6636 l S 0.4 G 1 w 500.7855 525.4468 m S u 1 g 0 G 0.5 w 419.9177 544.0789 m 407.6449 540.6636 L 420.0049 537.5781 L 419.9177 544.0789 L b U u 488.468 537.4133 m 500.7855 540.6636 L 488.468 543.9146 L 488.468 537.4133 L b U u u 0 g 1 w /_Times-Roman 12 14.5 0 0 z [1 0 0 1 440.2893 529.6966]e (\62)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 446.2893 529.6966]e (R+)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 461.717 529.6966]e (\61)t T U U 0 G 0.5 w 407.6449 540.6636 m 407.6449 535.1306 l S 500.7855 540.6636 m 500.7855 535.1306 l S 500.7663 545.1103 m 500.7663 539.5773 l S u u 0 g 1 w /_Times-Roman 12 14.5 0 0 z [1 0 0 1 448.5393 500.0128]e (\(b\))t T U U 0 G 400.992 687.1541 m S 427.6509 701.0128 m S 467.521 674.1875 m 467.5393 692.0128 l S u 0 g 0.3 w 1 M 465.7362 679.9788 m 467.521 674.1875 L 469.0608 680.0488 L 465.7362 679.9788 L b U 425.8188 692.9454 m 427.6036 687.1541 L 429.1434 693.0154 L 425.8188 692.9454 L b u u 1 w 4 M /_Times-Italic 12 14.5 0 0 z [1 0 0 1 454.7893 694.2628]e (h)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 460.7893 694.2628]e (=2)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 473.5569 694.2628]e (J)t T U U u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 402.9009 703.2628]e (h)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 408.9009 703.2628]e (=)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 415.6685 703.2628]e (J)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 420.9946 703.2628]e ( or 3)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 442.9878 703.2628]e (J)t T U U 0 G 0.3 w 10 M 243.1469 447.2705 m S 0 g 1 w 4 M 243.1469 447.2705 m F 0 G 0.3 w 10 M 243.1469 447.2705 m S 243.1469 447.2705 m S 243.1469 447.2705 m S 0 g 1 w 4 M 243.1469 447.2705 m F 0 G 0.3 w 10 M 243.1469 447.2705 m S 243.1469 447.2705 m S 1 g 1 w 4 M 243.1469 447.2705 m F 0 G 0.3 w 10 M 243.1469 447.2705 m S 0 g 1 w 4 M 243.1469 447.2705 m F 0 G 0.3 w 10 M 243.1469 447.2705 m S 243.1469 447.2705 m S 256.4527 447.2705 m S 0.3 g 1 w 4 M 256.4527 442.4622 m 259.2644 442.4622 261.5438 444.615 261.5438 447.2705 c 261.5438 449.926 259.2644 452.0788 256.4527 452.0788 c 253.641 452.0788 251.3616 449.926 251.3616 447.2705 c 251.3616 444.615 253.641 442.4622 256.4527 442.4622 c b 0 g 256.4527 447.2705 m F 0 G 0.3 w 10 M 283.0643 447.2705 m S 0.3 g 1 w 4 M 283.0643 442.4622 m 285.876 442.4622 288.1554 444.615 288.1554 447.2705 c 288.1554 449.926 285.876 452.0788 283.0643 452.0788 c 280.2526 452.0788 277.9732 449.926 277.9732 447.2705 c 277.9732 444.615 280.2526 442.4622 283.0643 442.4622 c b 0 g 283.0643 447.2705 m F 0 G 0.3 w 10 M 243.1469 434.3039 m S 1 g 1 w 4 M 243.1469 429.4956 m 245.9586 429.4956 248.238 431.6484 248.238 434.3039 c 248.238 436.9594 245.9586 439.1122 243.1469 439.1122 c 240.3352 439.1122 238.0558 436.9594 238.0558 434.3039 c 238.0558 431.6484 240.3352 429.4956 243.1469 429.4956 c b 0 g 243.1469 434.3039 m F 0 G 0.3 w 10 M 336.2875 447.2705 m S 0.3 g 1 w 4 M 336.2875 442.4622 m 339.0992 442.4622 341.3786 444.615 341.3786 447.2705 c 341.3786 449.926 339.0992 452.0788 336.2875 452.0788 c 332.8092 452.0788 331.1964 449.9259 331.1964 447.2705 c 331.1964 444.615 333.4758 442.4622 336.2875 442.4622 c b 0 g 336.2875 447.2705 m F 0 G 0.3 w 10 M 362.8992 447.2705 m S 0.3 g 1 w 4 M 362.8992 442.4622 m 365.7108 442.4622 367.9902 444.615 367.9902 447.2705 c 367.9902 449.926 365.7108 452.0788 362.8992 452.0788 c 360.0874 452.0788 357.808 449.926 357.808 447.2705 c 357.808 444.615 360.0874 442.4622 362.8992 442.4622 c b 0 g 362.8992 447.2705 m F 0 G 0.3 w 10 M 283.0643 421.3373 m S 1 g 1 w 4 M 283.0643 416.529 m 285.876 416.529 288.1554 418.6818 288.1554 421.3373 c 288.1554 423.9928 285.876 426.1456 283.0643 426.1456 c 280.2526 426.1456 277.9732 423.9928 277.9732 421.3373 c 277.9732 418.6818 280.2526 416.529 283.0643 416.529 c b 0 g 283.0643 421.3373 m F 0 G 0.3 w 10 M 309.6759 421.3373 m S 1 g 1 w 4 M 309.6759 416.529 m 312.4876 416.529 314.767 418.6818 314.767 421.3373 c 314.767 423.9928 312.4876 426.1456 309.6759 426.1456 c 306.8642 426.1456 304.5848 423.9928 304.5848 421.3373 c 304.5848 418.6818 306.8642 416.529 309.6759 416.529 c b 0 g 309.6759 421.3373 m F 0 G 0.3 w 10 M 336.2875 421.3373 m S 1 g 1 w 4 M 336.2875 416.529 m 339.0992 416.529 341.3786 418.6818 341.3786 421.3373 c 341.3786 423.9928 339.0992 426.1456 336.2875 426.1456 c 333.4758 426.1456 331.1964 423.9928 331.1964 421.3373 c 331.1964 418.6818 333.4758 416.529 336.2875 416.529 c b 0 g 336.2875 421.3373 m F 0 G 0.3 w 10 M 362.8992 421.3373 m S 1 g 1 w 4 M 362.8992 416.529 m 365.7108 416.529 367.9902 418.6818 367.9902 421.3373 c 367.9902 423.9928 365.7108 426.1456 362.8992 426.1456 c 360.0874 426.1456 357.808 423.9928 357.808 421.3373 c 357.808 418.6818 360.0874 416.529 362.8992 416.529 c b 0 g 362.8992 421.3373 m F 0 G 0.3 w 10 M 309.6759 447.2705 m S 0.3 g 1 w 4 M 309.6759 442.4622 m 312.4876 442.4622 314.767 444.615 314.767 447.2705 c 314.767 449.926 312.4876 452.0788 309.6759 452.0788 c 306.8642 452.0788 304.5848 449.926 304.5848 447.2705 c 304.5848 444.615 306.8642 442.4622 309.6759 442.4622 c b 0 g 309.6759 447.2705 m F 0 G 0.3 w 10 M 256.4527 408.3708 m S 243.1469 408.3708 m S 269.7585 408.3708 m S 256.4527 408.3708 m S 269.7585 408.3708 m S 256.4527 408.3708 m S 283.0643 408.3708 m S 269.7585 408.3708 m S 283.0643 408.3708 m S 269.7585 408.3708 m S 256.4527 408.3708 m S 243.1469 408.3708 m S 296.3701 408.3708 m S 283.0643 408.3708 m S 309.6759 408.3708 m S 296.3701 408.3708 m S 309.6759 408.3708 m S 296.3701 408.3708 m S 322.9817 408.3708 m S 309.6759 408.3708 m S 322.9817 408.3708 m S 309.6759 408.3708 m S 296.3701 408.3708 m S 283.0643 408.3708 m S 336.2875 408.3708 m S 322.9817 408.3708 m S 349.5933 408.3708 m S 336.2875 408.3708 m S 349.5933 408.3708 m S 336.2875 408.3708 m S 362.8992 408.3708 m S 349.5933 408.3708 m S 362.8992 408.3708 m S 349.5933 408.3708 m S 336.2875 408.3708 m S 322.9817 408.3708 m S 376.2048 408.3708 m S 362.8992 408.3708 m S 376.2048 408.3708 m S 376.2048 408.3708 m S 376.2048 408.3708 m S 362.8992 408.3708 m S 256.4527 408.3708 m S 1 g 1 w 4 M 256.4527 403.5625 m 259.2644 403.5625 261.5438 405.7153 261.5438 408.3708 c 261.5438 411.0263 259.2644 413.1791 256.4527 413.1791 c 253.641 413.1791 251.3616 411.0263 251.3616 408.3708 c 251.3616 405.7153 253.641 403.5625 256.4527 403.5625 c b 0 g 256.4527 408.3708 m F 0 G 0.3 w 10 M 269.7585 408.3708 m S 1 g 1 w 4 M 269.7585 403.5625 m 272.5702 403.5625 274.8497 405.7153 274.8497 408.3708 c 274.8497 411.0263 272.5702 413.1791 269.7585 413.1791 c 266.9468 413.1791 264.6674 411.0263 264.6674 408.3708 c 264.6674 405.7153 266.9468 403.5625 269.7585 403.5625 c b 0 g 269.7585 408.3708 m F 0 G 0.3 w 10 M 283.0643 408.3708 m S 1 g 1 w 4 M 283.0643 403.5625 m 285.876 403.5625 288.1554 405.7153 288.1554 408.3708 c 288.1554 411.0263 285.876 413.1791 283.0643 413.1791 c 280.2527 413.1791 277.9732 411.0263 277.9732 408.3708 c 277.9732 405.7153 280.2527 403.5625 283.0643 403.5625 c b 0 g 283.0643 408.3708 m F 0 G 0.3 w 10 M 296.3701 408.3708 m S 1 g 1 w 4 M 296.3701 403.5625 m 299.1819 403.5625 301.4612 405.7153 301.4612 408.3708 c 301.4612 411.0263 299.1819 413.1791 296.3701 413.1791 c 293.5585 413.1791 291.279 411.0263 291.279 408.3708 c 291.279 405.7153 293.5585 403.5625 296.3701 403.5625 c b 0 g 296.3701 408.3708 m F 0 G 0.3 w 10 M 309.6759 408.3708 m S 1 g 1 w 4 M 309.6759 403.5625 m 312.4877 403.5625 314.767 405.7153 314.767 408.3708 c 314.767 411.0263 312.4877 413.1791 309.6759 413.1791 c 306.8642 413.1791 304.5848 411.0263 304.5848 408.3708 c 304.5848 405.7153 306.8642 403.5625 309.6759 403.5625 c b 0 g 309.6759 408.3708 m F 0 G 0.3 w 10 M 322.9817 408.3708 m S 1 g 1 w 4 M 322.9817 403.5625 m 325.7934 403.5625 328.0728 405.7153 328.0728 408.3708 c 328.0728 411.0263 325.7934 413.1791 322.9817 413.1791 c 320.17 413.1791 317.8907 411.0263 317.8907 408.3708 c 317.8907 405.7153 320.17 403.5625 322.9817 403.5625 c b 0 g 322.9817 408.3708 m F 0 G 0.3 w 10 M 336.2875 408.3708 m S 1 g 1 w 4 M 336.2875 403.5625 m 339.0992 403.5625 341.3786 405.7153 341.3786 408.3708 c 341.3786 411.0263 339.0992 413.1791 336.2875 413.1791 c 333.4758 413.1791 331.1964 411.0263 331.1964 408.3708 c 331.1964 405.7153 333.4758 403.5625 336.2875 403.5625 c b 0 g 336.2875 408.3708 m F 0 G 0.3 w 10 M 349.5933 408.3708 m S 1 g 1 w 4 M 349.5933 403.5625 m 352.405 403.5625 354.6844 405.7153 354.6844 408.3708 c 354.6844 411.0263 352.405 413.1791 349.5933 413.1791 c 346.7816 413.1791 344.5022 411.0263 344.5022 408.3708 c 344.5022 405.7153 346.7816 403.5625 349.5933 403.5625 c b 0 g 349.5933 408.3708 m F 0 G 0.3 w 10 M 376.2048 408.3708 m S 0.3 g 1 w 4 M 376.2048 403.5625 m 379.0166 403.5625 381.296 405.7153 381.296 408.3708 c 381.296 411.0263 379.0166 413.1791 376.2048 413.1791 c 373.3932 413.1791 371.1138 411.0263 371.1138 408.3708 c 371.1138 405.7153 373.3932 403.5625 376.2048 403.5625 c b 0 g 376.2048 408.3708 m F 0 G 0.3 w 10 M 362.8992 408.3708 m S 1 g 1 w 4 M 362.8992 403.5625 m 365.7108 403.5625 367.9902 405.7153 367.9902 408.3708 c 367.9902 411.0263 365.7108 413.1791 362.8992 413.1791 c 360.0874 413.1791 357.808 411.0263 357.808 408.3708 c 357.808 405.7153 360.0874 403.5625 362.8992 403.5625 c b 0 g 362.8992 408.3708 m F 0 G 0.3 w 10 M 243.1469 408.3708 m S 0.3 g 1 w 4 M 243.1469 403.5625 m 245.9586 403.5625 248.238 405.7153 248.238 408.3708 c 248.238 411.0263 245.9586 413.1791 243.1469 413.1791 c 240.3352 413.1791 238.0558 411.0263 238.0558 408.3708 c 238.0558 405.7153 240.3352 403.5625 243.1469 403.5625 c b 0 g 243.1469 408.3708 m F 0 G 0.3 w 10 M 256.4527 382.4376 m S 243.1469 382.4376 m S 269.7585 382.4376 m S 256.4527 382.4376 m S 269.7585 382.4376 m S 256.4527 382.4376 m S 283.0643 382.4376 m S 269.7585 382.4376 m S 283.0643 382.4376 m S 269.7585 382.4376 m S 256.4527 382.4376 m S 243.1469 382.4376 m S 296.3701 382.4376 m S 283.0643 382.4376 m S 309.6759 382.4376 m S 296.3701 382.4376 m S 309.6759 382.4376 m S 296.3701 382.4376 m S 322.9817 382.4376 m S 309.6759 382.4376 m S 322.9817 382.4376 m S 309.6759 382.4376 m S 296.3701 382.4376 m S 283.0643 382.4376 m S 336.2875 382.4376 m S 322.9817 382.4376 m S 349.5933 382.4376 m S 336.2875 382.4376 m S 349.5933 382.4376 m S 336.2875 382.4376 m S 362.8992 382.4376 m S 349.5933 382.4376 m S 362.8992 382.4376 m S 349.5933 382.4376 m S 336.2875 382.4376 m S 322.9817 382.4376 m S 376.2048 382.4376 m S 362.8992 382.4376 m S 376.2048 382.4376 m S 376.2048 382.4376 m S 376.2048 382.4376 m S 362.8992 382.4376 m S 256.4527 382.4376 m S 0 g 1 w 4 M 256.4527 382.4376 m F 0 G 0.3 w 10 M 269.7585 382.4376 m S 0 g 1 w 4 M 269.7585 382.4376 m F 0 G 0.3 w 10 M 283.0643 382.4376 m S 0 g 1 w 4 M 283.0643 382.4376 m F 0 G 0.3 w 10 M 296.3701 382.4376 m S 0 g 1 w 4 M 296.3701 382.4376 m F 0 G 0.3 w 10 M 309.6759 382.4376 m S 0 g 1 w 4 M 309.6759 382.4376 m F 0 G 0.3 w 10 M 322.9817 382.4376 m S 0 g 1 w 4 M 322.9817 382.4376 m F 0 G 0.3 w 10 M 336.2875 382.4376 m S 0 g 1 w 4 M 336.2875 382.4376 m F 0 G 0.3 w 10 M 349.5933 382.4376 m S 0 g 1 w 4 M 349.5933 382.4376 m F 0 G 0.3 w 10 M 376.2048 382.4376 m S 0 g 1 w 4 M 376.2048 382.4376 m F 0 G 0.3 w 10 M 362.8992 382.4376 m S 0 g 1 w 4 M 362.8992 382.4376 m F 0 G 0.3 w 10 M 243.1469 382.4376 m S 1 g 1 w 4 M 243.1469 377.6293 m 245.9586 377.6293 248.238 379.7821 248.238 382.4376 c 248.238 385.0931 245.9586 387.2459 243.1469 387.2459 c 240.3352 387.2459 238.0558 385.0931 238.0558 382.4376 c 238.0558 379.7821 240.3352 377.6293 243.1469 377.6293 c b 0 g 243.1469 382.4376 m F 0 G 0.3 w 10 M 256.4527 382.4376 m S 243.1469 382.4376 m S 269.7585 382.4376 m S 256.4527 382.4376 m S 269.7585 382.4376 m S 256.4527 382.4376 m S 283.0643 382.4376 m S 269.7585 382.4376 m S 283.0643 382.4376 m S 269.7585 382.4376 m S 256.4527 382.4376 m S 243.1469 382.4376 m S 296.3701 382.4376 m S 283.0643 382.4376 m S 309.6759 382.4376 m S 296.3701 382.4376 m S 309.6759 382.4376 m S 296.3701 382.4376 m S 322.9817 382.4376 m S 309.6759 382.4376 m S 322.9817 382.4376 m S 309.6759 382.4376 m S 296.3701 382.4376 m S 283.0643 382.4376 m S 336.2875 382.4376 m S 322.9817 382.4376 m S 349.5933 382.4376 m S 336.2875 382.4376 m S 349.5933 382.4376 m S 336.2875 382.4376 m S 362.8992 382.4376 m S 349.5933 382.4376 m S 362.8992 382.4376 m S 349.5933 382.4376 m S 336.2875 382.4376 m S 322.9817 382.4376 m S 376.2048 382.4376 m S 362.8992 382.4376 m S 376.2048 382.4376 m S 376.2048 382.4376 m S 376.2048 382.4376 m S 362.8992 382.4376 m S 256.4527 382.4376 m S 1 g 1 w 4 M 256.4527 377.6293 m 259.2644 377.6293 261.5438 379.7821 261.5438 382.4376 c 261.5438 385.0931 259.2644 387.2459 256.4527 387.2459 c 253.641 387.2459 251.3616 385.0931 251.3616 382.4376 c 251.3616 379.7821 253.641 377.6293 256.4527 377.6293 c b 0 g 256.4527 382.4376 m F 0 G 0.3 w 10 M 269.7585 382.4376 m S 1 g 1 w 4 M 269.7585 377.6293 m 272.5702 377.6293 274.8497 379.7821 274.8497 382.4376 c 274.8497 385.0931 272.5702 387.2459 269.7585 387.2459 c 266.9468 387.2459 264.6674 385.0931 264.6674 382.4376 c 264.6674 379.7821 266.9468 377.6293 269.7585 377.6293 c b 0 g 269.7585 382.4376 m F 0 G 0.3 w 10 M 283.0643 382.4376 m S 1 g 1 w 4 M 283.0643 377.6293 m 285.876 377.6293 288.1554 379.7821 288.1554 382.4376 c 288.1554 385.0931 285.876 387.2459 283.0643 387.2459 c 280.2527 387.2459 277.9732 385.0931 277.9732 382.4376 c 277.9732 379.7821 280.2527 377.6293 283.0643 377.6293 c b 0 g 283.0643 382.4376 m F 0 G 0.3 w 10 M 296.3701 382.4376 m S 1 g 1 w 4 M 296.3701 377.6293 m 299.1819 377.6293 301.4612 379.7821 301.4612 382.4376 c 301.4612 385.0931 299.1819 387.2459 296.3701 387.2459 c 293.5585 387.2459 291.279 385.0931 291.279 382.4376 c 291.279 379.7821 293.5585 377.6293 296.3701 377.6293 c b 0 g 296.3701 382.4376 m F 0 G 0.3 w 10 M 309.6759 382.4376 m S 1 g 1 w 4 M 309.6759 377.6293 m 312.4877 377.6293 314.767 379.7821 314.767 382.4376 c 314.767 385.0931 312.4877 387.2459 309.6759 387.2459 c 306.8642 387.2459 304.5848 385.0931 304.5848 382.4376 c 304.5848 379.7821 306.8642 377.6293 309.6759 377.6293 c b 0 g 309.6759 382.4376 m F 0 G 0.3 w 10 M 322.9817 382.4376 m S 1 g 1 w 4 M 322.9817 377.6293 m 325.7934 377.6293 328.0728 379.7821 328.0728 382.4376 c 328.0728 385.0931 325.7934 387.2459 322.9817 387.2459 c 320.17 387.2459 317.8907 385.0931 317.8907 382.4376 c 317.8907 379.7821 320.17 377.6293 322.9817 377.6293 c b 0 g 322.9817 382.4376 m F 0 G 0.3 w 10 M 336.2875 382.4376 m S 1 g 1 w 4 M 336.2875 377.6293 m 339.0992 377.6293 341.3786 379.7821 341.3786 382.4376 c 341.3786 385.0931 339.0992 387.2459 336.2875 387.2459 c 333.4758 387.2459 331.1964 385.0931 331.1964 382.4376 c 331.1964 379.7821 333.4758 377.6293 336.2875 377.6293 c b 0 g 336.2875 382.4376 m F 0 G 0.3 w 10 M 349.5933 382.4376 m S 1 g 1 w 4 M 349.5933 377.6293 m 352.405 377.6293 354.6844 379.7821 354.6844 382.4376 c 354.6844 385.0931 352.405 387.2459 349.5933 387.2459 c 346.7816 387.2459 344.5022 385.0931 344.5022 382.4376 c 344.5022 379.7821 346.7816 377.6293 349.5933 377.6293 c b 0 g 349.5933 382.4376 m F 0 G 0.3 w 10 M 376.2048 382.4376 m S 0.3 g 1 w 4 M 376.2048 377.6293 m 379.0166 377.6293 381.296 379.7821 381.296 382.4376 c 381.296 385.0931 379.0166 387.2459 376.2048 387.2459 c 373.3932 387.2459 371.1138 385.0931 371.1138 382.4376 c 371.1138 379.7821 373.3932 377.6293 376.2048 377.6293 c b 0 g 376.2048 382.4376 m F 0 G 0.3 w 10 M 362.8992 382.4376 m S 1 g 1 w 4 M 362.8992 377.6293 m 365.7108 377.6293 367.9902 379.7821 367.9902 382.4376 c 367.9902 385.0931 365.7108 387.2459 362.8992 387.2459 c 360.0874 387.2459 357.808 385.0931 357.808 382.4376 c 357.808 379.7821 360.0874 377.6293 362.8992 377.6293 c b 0 g 362.8992 382.4376 m F 0 G 0.3 w 10 M 243.1469 382.4376 m S 0.3 g 1 w 4 M 243.1469 377.6293 m 245.9586 377.6293 248.238 379.7821 248.238 382.4376 c 248.238 385.0931 245.9586 387.2459 243.1469 387.2459 c 241.0019 387.2459 238.0558 385.7597 238.0558 382.4376 c 238.0558 379.7821 240.3352 377.6293 243.1469 377.6293 c b 0 g 243.1469 382.4376 m F 0 G 0.3 w 10 M 256.4527 356.5044 m S 243.1469 356.5044 m S 269.7585 356.5044 m S 256.4527 356.5044 m S 269.7585 356.5044 m S 256.4527 356.5044 m S 283.0643 356.5044 m S 269.7585 356.5044 m S 283.0643 356.5044 m S 269.7585 356.5044 m S 256.4527 356.5044 m S 243.1469 356.5044 m S 296.3701 356.5044 m S 283.0643 356.5044 m S 309.6759 356.5044 m S 296.3701 356.5044 m S 309.6759 356.5044 m S 296.3701 356.5044 m S 322.9817 356.5044 m S 309.6759 356.5044 m S 322.9817 356.5044 m S 309.6759 356.5044 m S 296.3701 356.5044 m S 283.0643 356.5044 m S 336.2875 356.5044 m S 322.9817 356.5044 m S 349.5933 356.5044 m S 336.2875 356.5044 m S 349.5933 356.5044 m S 336.2875 356.5044 m S 362.8992 356.5044 m S 349.5933 356.5044 m S 362.8992 356.5044 m S 349.5933 356.5044 m S 336.2875 356.5044 m S 322.9817 356.5044 m S 376.2048 356.5044 m S 362.8992 356.5044 m S 376.2048 356.5044 m S 376.2048 356.5044 m S 376.2048 356.5044 m S 362.8992 356.5044 m S 256.4527 356.5044 m S 1 g 1 w 4 M 256.4527 351.6961 m 259.2644 351.6961 261.5438 353.8489 261.5438 356.5044 c 261.5438 359.1599 259.2644 361.3127 256.4527 361.3127 c 253.641 361.3127 251.3616 359.1599 251.3616 356.5044 c 251.3616 353.8489 253.641 351.6961 256.4527 351.6961 c b 0 g 256.4527 356.5044 m F 0 G 0.3 w 10 M 269.7585 356.5044 m S 1 g 1 w 4 M 269.7585 351.6961 m 272.5702 351.6961 274.8497 353.8489 274.8497 356.5044 c 274.8497 359.1599 272.5702 361.3127 269.7585 361.3127 c 266.9468 361.3127 264.6674 359.1599 264.6674 356.5044 c 264.6674 353.8489 266.9468 351.6961 269.7585 351.6961 c b 0 g 269.7585 356.5044 m F 0 G 0.3 w 10 M 283.0643 356.5044 m S 1 g 1 w 4 M 283.0643 351.6961 m 285.876 351.6961 288.1554 353.8489 288.1554 356.5044 c 288.1554 359.1599 285.876 361.3127 283.0643 361.3127 c 280.2527 361.3127 277.9732 359.1599 277.9732 356.5044 c 277.9732 353.8489 280.2527 351.6961 283.0643 351.6961 c b 0 g 283.0643 356.5044 m F 0 G 0.3 w 10 M 296.3701 356.5044 m S 1 g 1 w 4 M 296.3701 351.6961 m 299.1819 351.6961 301.4612 353.8489 301.4612 356.5044 c 301.4612 359.1599 299.1819 361.3127 296.3701 361.3127 c 293.5585 361.3127 291.279 359.1599 291.279 356.5044 c 291.279 353.8489 293.5585 351.6961 296.3701 351.6961 c b 0 g 296.3701 356.5044 m F 0 G 0.3 w 10 M 309.6759 356.5044 m S 1 g 1 w 4 M 309.6759 351.6961 m 312.4877 351.6961 314.767 353.8489 314.767 356.5044 c 314.767 359.1599 312.4877 361.3127 309.6759 361.3127 c 306.8642 361.3127 304.5848 359.1599 304.5848 356.5044 c 304.5848 353.8489 306.8642 351.6961 309.6759 351.6961 c b 0 g 309.6759 356.5044 m F 0 G 0.3 w 10 M 322.9817 356.5044 m S 1 g 1 w 4 M 322.9817 351.6961 m 325.7934 351.6961 328.0728 353.8489 328.0728 356.5044 c 328.0728 359.1599 325.7934 361.3127 322.9817 361.3127 c 320.17 361.3127 317.8907 359.1599 317.8907 356.5044 c 317.8907 353.8489 320.17 351.6961 322.9817 351.6961 c b 0 g 322.9817 356.5044 m F 0 G 0.3 w 10 M 336.2875 356.5044 m S 1 g 1 w 4 M 336.2875 351.6961 m 339.0992 351.6961 341.3786 353.8489 341.3786 356.5044 c 341.3786 359.1599 339.0992 361.3127 336.2875 361.3127 c 333.4758 361.3127 331.1964 359.1599 331.1964 356.5044 c 331.1964 353.8489 333.4758 351.6961 336.2875 351.6961 c b 0 g 336.2875 356.5044 m F 0 G 0.3 w 10 M 349.5933 356.5044 m S 1 g 1 w 4 M 349.5933 351.6961 m 352.405 351.6961 354.6844 353.8489 354.6844 356.5044 c 354.6844 359.1599 352.405 361.3127 349.5933 361.3127 c 346.7816 361.3127 344.5022 359.1599 344.5022 356.5044 c 344.5022 353.8489 346.7816 351.6961 349.5933 351.6961 c b 0 g 349.5933 356.5044 m F 0 G 0.3 w 10 M 376.2048 356.5044 m S 0.3 g 1 w 4 M 376.2048 351.6961 m 379.0166 351.6961 381.296 353.8489 381.296 356.5044 c 381.296 359.1599 379.0166 361.3127 376.2048 361.3127 c 373.3932 361.3127 371.1138 359.1599 371.1138 356.5044 c 371.1138 353.8489 373.3932 351.6961 376.2048 351.6961 c b 0 g 376.2048 356.5044 m F 0 G 0.3 w 10 M 362.8992 356.5044 m S 1 g 1 w 4 M 362.8992 351.6961 m 365.7108 351.6961 367.9902 353.8489 367.9902 356.5044 c 367.9902 359.1599 365.7108 361.3127 362.8992 361.3127 c 360.0874 361.3127 357.808 359.1599 357.808 356.5044 c 357.808 353.8489 360.0874 351.6961 362.8992 351.6961 c b 0 g 362.8992 356.5044 m F 0 G 0.3 w 10 M 243.1469 356.5044 m S 0.3 g 1 w 4 M 243.1469 351.6961 m 245.9586 351.6961 248.238 353.8489 248.238 356.5044 c 248.238 359.1599 245.9586 361.3127 243.1469 361.3127 c 240.3352 361.3127 238.0558 359.1599 238.0558 356.5044 c 238.0558 353.8489 240.3352 351.6961 243.1469 351.6961 c b 0 g 243.1469 356.5044 m F 0 G 0.3 w 10 M 362.8992 395.4042 m S 1 g 1 w 4 M 362.8992 390.5959 m 365.7108 390.5959 367.9902 392.7487 367.9902 395.4042 c 367.9902 398.0597 365.7108 400.2125 362.8992 400.2125 c 360.0874 400.2125 357.808 398.0597 357.808 395.4042 c 357.808 392.7487 360.0874 390.5959 362.8992 390.5959 c b 0 g 362.8992 395.4042 m F 0 G 0.3 w 10 M 336.2875 395.4042 m S 1 g 1 w 4 M 336.2875 390.5959 m 339.0992 390.5959 341.3786 392.7487 341.3786 395.4042 c 341.3786 398.0597 339.0992 400.2125 336.2875 400.2125 c 333.4758 400.2125 331.1964 398.0597 331.1964 395.4042 c 331.1964 392.7487 333.4758 390.5959 336.2875 390.5959 c b 0 g 336.2875 395.4042 m F 0 G 0.3 w 10 M 362.8992 369.471 m S 1 g 1 w 4 M 362.8992 364.6627 m 365.7108 364.6627 367.9902 366.8155 367.9902 369.471 c 367.9902 372.1265 365.7108 374.2793 362.8992 374.2793 c 360.0874 374.2793 357.808 372.1265 357.808 369.471 c 357.808 366.8155 360.0874 364.6627 362.8992 364.6627 c b 0 g 362.8992 369.471 m F 0 G 0.3 w 10 M 336.2875 369.471 m S 1 g 1 w 4 M 336.2875 364.6627 m 339.0992 364.6627 341.3786 366.8155 341.3786 369.471 c 341.3786 372.1265 339.0992 374.2793 336.2875 374.2793 c 333.4758 374.2793 331.1964 372.1265 331.1964 369.471 c 331.1964 366.8155 333.4758 364.6627 336.2875 364.6627 c b 0 g 336.2875 369.471 m F 0 G 0.3 w 10 M 283.0643 395.4042 m S 1 g 1 w 4 M 283.0643 390.5959 m 285.876 390.5959 288.1554 392.7487 288.1554 395.4042 c 288.1554 398.0597 285.876 400.2125 283.0643 400.2125 c 280.2526 400.2125 277.9732 398.0597 277.9732 395.4042 c 277.9732 392.7487 280.2526 390.5959 283.0643 390.5959 c b 0 g 283.0643 395.4042 m F 0 G 0.3 w 10 M 256.4527 395.4042 m S 1 g 1 w 4 M 256.4527 390.5959 m 259.2644 390.5959 261.5438 392.7487 261.5438 395.4042 c 261.5438 398.0597 259.2644 400.2125 256.4527 400.2125 c 253.641 400.2125 251.3616 398.0597 251.3616 395.4042 c 251.3616 392.7487 253.641 390.5959 256.4527 390.5959 c b 0 g 256.4527 395.4042 m F 0 G 0.3 w 10 M 256.4527 369.471 m S 1 g 1 w 4 M 256.4527 364.6627 m 259.2644 364.6627 261.5438 366.8155 261.5438 369.471 c 261.5438 372.1265 259.2644 374.2793 256.4527 374.2793 c 253.641 374.2793 251.3616 372.1265 251.3616 369.471 c 251.3616 366.8155 253.641 364.6627 256.4527 364.6627 c b 0 g 256.4527 369.471 m F 0 G 0.3 w 10 M 283.0643 369.471 m S 1 g 1 w 4 M 283.0643 364.6627 m 285.876 364.6627 288.1554 366.8155 288.1554 369.471 c 288.1554 372.1265 285.876 374.2793 283.0643 374.2793 c 280.2526 374.2793 277.9732 372.1265 277.9732 369.471 c 277.9732 366.8155 280.2526 364.6627 283.0643 364.6627 c b 0 g 283.0643 369.471 m F 0 G 0.3 w 10 M 309.6759 369.471 m S 1 g 1 w 4 M 309.6759 364.6627 m 312.4876 364.6627 314.767 366.8155 314.767 369.471 c 314.767 372.1265 312.4876 374.2793 309.6759 374.2793 c 306.8642 374.2793 304.5848 372.1265 304.5848 369.471 c 304.5848 366.8155 306.8642 364.6627 309.6759 364.6627 c b 0 g 309.6759 369.471 m F 0 G 0.3 w 10 M 309.6759 395.4042 m S 1 g 1 w 4 M 309.6759 390.5959 m 312.4876 390.5959 314.767 392.7487 314.767 395.4042 c 314.767 398.0597 312.4876 400.2125 309.6759 400.2125 c 306.8642 400.2125 304.5848 398.0597 304.5848 395.4042 c 304.5848 392.7487 306.8642 390.5959 309.6759 390.5959 c b 0 g 309.6759 395.4042 m F 0 G 0.3 w 10 M 256.4527 330.5712 m S 243.1469 330.5712 m S 269.7585 330.5712 m S 256.4527 330.5712 m S 269.7585 330.5712 m S 256.4527 330.5712 m S 283.0643 330.5712 m S 269.7585 330.5712 m S 283.0643 330.5712 m S 269.7585 330.5712 m S 256.4527 330.5712 m S 243.1469 330.5712 m S 296.3701 330.5712 m S 283.0643 330.5712 m S 309.6759 330.5712 m S 296.3701 330.5712 m S 309.6759 330.5712 m S 296.3701 330.5712 m S 322.9817 330.5712 m S 309.6759 330.5712 m S 322.9817 330.5712 m S 309.6759 330.5712 m S 296.3701 330.5712 m S 283.0643 330.5712 m S 336.2875 330.5712 m S 322.9817 330.5712 m S 349.5933 330.5712 m S 336.2875 330.5712 m S 349.5933 330.5712 m S 336.2875 330.5712 m S 362.8992 330.5712 m S 349.5933 330.5712 m S 362.8992 330.5712 m S 349.5933 330.5712 m S 336.2875 330.5712 m S 322.9817 330.5712 m S 376.2048 330.5712 m S 362.8992 330.5712 m S 376.2048 330.5712 m S 376.2048 330.5712 m S 376.2048 330.5712 m S 362.8992 330.5712 m S 256.4527 330.5712 m S 243.1469 330.5712 m S 269.7585 330.5712 m S 256.4527 330.5712 m S 269.7585 330.5712 m S 256.4527 330.5712 m S 283.0643 330.5712 m S 269.7585 330.5712 m S 283.0643 330.5712 m S 269.7585 330.5712 m S 256.4527 330.5712 m S 243.1469 330.5712 m S 296.3701 330.5712 m S 283.0643 330.5712 m S 309.6759 330.5712 m S 296.3701 330.5712 m S 309.6759 330.5712 m S 296.3701 330.5712 m S 322.9817 330.5712 m S 309.6759 330.5712 m S 322.9817 330.5712 m S 309.6759 330.5712 m S 296.3701 330.5712 m S 283.0643 330.5712 m S 336.2875 330.5712 m S 322.9817 330.5712 m S 349.5933 330.5712 m S 336.2875 330.5712 m S 349.5933 330.5712 m S 336.2875 330.5712 m S 362.8992 330.5712 m S 349.5933 330.5712 m S 362.8992 330.5712 m S 349.5933 330.5712 m S 336.2875 330.5712 m S 322.9817 330.5712 m S 376.2048 330.5712 m S 362.8992 330.5712 m S 376.2048 330.5712 m S 376.2048 330.5712 m S 376.2048 330.5712 m S 362.8992 330.5712 m S 256.4527 330.5712 m S 1 g 1 w 4 M 256.4527 325.7629 m 259.2644 325.7629 261.5438 327.9157 261.5438 330.5712 c 261.5438 333.2267 259.2644 335.3795 256.4527 335.3795 c 253.641 335.3795 251.3616 333.2267 251.3616 330.5712 c 251.3616 327.9157 253.641 325.7629 256.4527 325.7629 c b 0 g 256.4527 330.5712 m F 0 G 0.3 w 10 M 269.7585 330.5712 m S 1 g 1 w 4 M 269.7585 325.7629 m 272.5702 325.7629 274.8497 327.9157 274.8497 330.5712 c 274.8497 333.2267 272.5702 335.3795 269.7585 335.3795 c 266.9468 335.3795 264.6674 333.2267 264.6674 330.5712 c 264.6674 327.9157 266.9468 325.7629 269.7585 325.7629 c b 0 g 269.7585 330.5712 m F 0 G 0.3 w 10 M 283.0643 330.5712 m S 1 g 1 w 4 M 283.0643 325.7629 m 285.876 325.7629 288.1554 327.9157 288.1554 330.5712 c 288.1554 333.2267 285.876 335.3795 283.0643 335.3795 c 280.2527 335.3795 277.9732 333.2267 277.9732 330.5712 c 277.9732 327.9157 280.2527 325.7629 283.0643 325.7629 c b 0 g 283.0643 330.5712 m F 0 G 0.3 w 10 M 296.3701 330.5712 m S 1 g 1 w 4 M 296.3701 325.7629 m 299.1819 325.7629 301.4612 327.9157 301.4612 330.5712 c 301.4612 333.2267 299.1819 335.3795 296.3701 335.3795 c 293.5585 335.3795 291.279 333.2267 291.279 330.5712 c 291.279 327.9157 293.5585 325.7629 296.3701 325.7629 c b 0 g 296.3701 330.5712 m F 0 G 0.3 w 10 M 309.6759 330.5712 m S 1 g 1 w 4 M 309.6759 325.7629 m 312.4877 325.7629 314.767 327.9157 314.767 330.5712 c 314.767 333.2267 312.4877 335.3795 309.6759 335.3795 c 306.8642 335.3795 304.5848 333.2267 304.5848 330.5712 c 304.5848 327.9157 306.8642 325.7629 309.6759 325.7629 c b 0 g 309.6759 330.5712 m F 0 G 0.3 w 10 M 322.9817 330.5712 m S 1 g 1 w 4 M 322.9817 325.7629 m 325.7934 325.7629 328.0728 327.9157 328.0728 330.5712 c 328.0728 333.2267 325.7934 335.3795 322.9817 335.3795 c 320.17 335.3795 317.8907 333.2267 317.8907 330.5712 c 317.8907 327.9157 320.17 325.7629 322.9817 325.7629 c b 0 g 322.9817 330.5712 m F 0 G 0.3 w 10 M 336.2875 330.5712 m S 1 g 1 w 4 M 336.2875 325.7629 m 339.0992 325.7629 341.3786 327.9157 341.3786 330.5712 c 341.3786 333.2267 339.0992 335.3795 336.2875 335.3795 c 333.4758 335.3795 331.1964 333.2267 331.1964 330.5712 c 331.1964 327.9157 333.4758 325.7629 336.2875 325.7629 c b 0 g 336.2875 330.5712 m F 0 G 0.3 w 10 M 349.5933 330.5712 m S 1 g 1 w 4 M 349.5933 325.7629 m 352.405 325.7629 354.6844 327.9157 354.6844 330.5712 c 354.6844 333.2267 352.405 335.3795 349.5933 335.3795 c 346.7816 335.3795 344.5022 333.2267 344.5022 330.5712 c 344.5022 327.9157 346.7816 325.7629 349.5933 325.7629 c b 0 g 349.5933 330.5712 m F 0 G 0.3 w 10 M 376.2048 330.5712 m S 0.3 g 1 w 4 M 376.2048 325.7629 m 379.0166 325.7629 381.296 327.9157 381.296 330.5712 c 381.296 333.2267 379.0166 335.3795 376.2048 335.3795 c 373.3932 335.3795 371.1138 333.2267 371.1138 330.5712 c 371.1138 327.9157 373.3932 325.7629 376.2048 325.7629 c b 0 g 376.2048 330.5712 m F 0 G 0.3 w 10 M 362.8992 330.5712 m S 1 g 1 w 4 M 362.8992 325.7629 m 365.7108 325.7629 367.9902 327.9157 367.9902 330.5712 c 367.9902 333.2267 365.7108 335.3795 362.8992 335.3795 c 360.0874 335.3795 357.808 333.2267 357.808 330.5712 c 357.808 327.9157 360.0874 325.7629 362.8992 325.7629 c b 0 g 362.8992 330.5712 m F 0 G 0.3 w 10 M 243.1469 330.5712 m S 0.3 g 1 w 4 M 243.1469 325.7629 m 245.9586 325.7629 248.238 327.9157 248.238 330.5712 c 248.238 333.2267 245.9586 335.3795 243.1469 335.3795 c 240.3352 335.3795 238.0558 333.2267 238.0558 330.5712 c 238.0558 327.9157 240.3352 325.7629 243.1469 325.7629 c b 0 g 243.1469 330.5712 m F 0 G 0.3 w 10 M 256.4527 343.5378 m S 256.4527 343.5378 m S 256.4527 343.5378 m S 283.0643 343.5378 m S 283.0643 343.5378 m S 256.4527 343.5378 m S 283.0643 343.5378 m S 309.6759 343.5378 m S 309.6759 343.5378 m S 309.6759 343.5378 m S 309.6759 343.5378 m S 283.0643 343.5378 m S 336.2875 343.5378 m S 336.2875 343.5378 m S 336.2875 343.5378 m S 362.8992 343.5378 m S 362.8992 343.5378 m S 336.2875 343.5378 m S 362.8992 343.5378 m S 362.8992 343.5378 m S 362.8992 343.5378 m S 1 g 1 w 4 M 362.8992 338.7295 m 365.7108 338.7295 367.9902 340.8823 367.9902 343.5378 c 367.9902 346.1933 365.7108 348.3461 362.8992 348.3461 c 360.0874 348.3461 357.808 346.1933 357.808 343.5378 c 357.808 340.8823 360.0874 338.7295 362.8992 338.7295 c b 0 g 362.8992 343.5378 m F 0 G 0.3 w 10 M 336.2875 343.5378 m S 1 g 1 w 4 M 336.2875 338.7295 m 339.0992 338.7295 341.3786 340.8823 341.3786 343.5378 c 341.3786 346.1933 339.0992 348.3461 336.2875 348.3461 c 333.4758 348.3461 331.1964 346.1933 331.1964 343.5378 c 331.1964 340.8823 333.4758 338.7295 336.2875 338.7295 c b 0 g 336.2875 343.5378 m F 0 G 0.3 w 10 M 283.0643 343.5378 m S 1 g 1 w 4 M 283.0643 338.7295 m 285.876 338.7295 288.1554 340.8823 288.1554 343.5378 c 288.1554 346.1933 285.876 348.3461 283.0643 348.3461 c 280.2526 348.3461 277.9732 346.1933 277.9732 343.5378 c 277.9732 340.8823 280.2526 338.7295 283.0643 338.7295 c b 0 g 283.0643 343.5378 m F 0 G 0.3 w 10 M 256.4527 343.5378 m S 1 g 1 w 4 M 256.4527 338.7295 m 259.2644 338.7295 261.5438 340.8823 261.5438 343.5378 c 261.5438 346.1933 259.2644 348.3461 256.4527 348.3461 c 253.641 348.3461 251.3616 346.1933 251.3616 343.5378 c 251.3616 340.8823 253.641 338.7295 256.4527 338.7295 c b 0 g 256.4527 343.5378 m F 0 G 0.3 w 10 M 309.6759 343.5378 m S 1 g 1 w 4 M 309.6759 338.7295 m 312.4876 338.7295 314.767 340.8823 314.767 343.5378 c 314.767 346.1933 312.4876 348.3461 309.6759 348.3461 c 306.8642 348.3461 304.5848 346.1933 304.5848 343.5378 c 304.5848 340.8823 306.8642 338.7295 309.6759 338.7295 c b 0 g 309.6759 343.5378 m F 0 G 0.3 w 10 M 256.4527 317.6046 m S 249.7998 311.1213 m S 256.4527 317.6046 m S 263.1056 311.1213 m S 283.0643 317.6046 m S 276.4114 311.1213 m S 0 g 1 w 4 M 249.7998 311.1213 m F 276.4114 311.1213 m F 0 G 0.3 w 10 M 283.0643 317.6046 m S 289.7173 311.1213 m S 309.6759 317.6046 m S 303.0231 311.1213 m S 309.6759 317.6046 m S 316.3288 311.1213 m S 0 g 1 w 4 M 289.7173 311.1213 m F 316.3288 311.1213 m F 0 G 0.3 w 10 M 336.2875 317.6046 m S 329.6346 311.1213 m S 336.2875 317.6046 m S 342.9404 311.1213 m S 362.8992 317.6046 m S 356.2462 311.1213 m S 0 g 1 w 4 M 329.6346 311.1213 m F 356.2462 311.1213 m F 0 G 0.3 w 10 M 362.8992 317.6046 m S 369.552 311.1213 m S 382.8578 311.1213 m S 0 g 1 w 4 M 369.552 311.1213 m F 0 G 0.3 w 10 M 249.7998 311.1213 m S 0 g 1 w 4 M 249.7998 311.1213 m F 0 G 0.3 w 10 M 256.4527 317.6046 m S 256.4527 317.6046 m S 256.4527 317.6046 m S 0.3 g 1 w 4 M 256.4527 312.7963 m 259.2644 312.7963 261.5438 314.9491 261.5438 317.6046 c 261.5438 320.2601 259.2644 322.4129 256.4527 322.4129 c 253.641 322.4129 251.3616 320.2601 251.3616 317.6046 c 251.3616 314.9491 253.641 312.7963 256.4527 312.7963 c b 0 g 256.4527 317.6046 m F 0 G 0.3 w 10 M 283.0643 317.6046 m S 0.3 g 1 w 4 M 283.0643 312.7963 m 285.876 312.7963 288.1554 314.9491 288.1554 317.6046 c 288.1554 320.2601 285.876 322.4129 283.0643 322.4129 c 280.2526 322.4129 277.9732 320.2601 277.9732 317.6046 c 277.9732 314.9491 280.2526 312.7963 283.0643 312.7963 c b 0 g 283.0643 317.6046 m F 0 G 0.3 w 10 M 336.2875 317.6046 m S 0.3 g 1 w 4 M 336.2875 312.7963 m 339.0992 312.7963 341.3786 314.9491 341.3786 317.6046 c 341.3786 320.2601 339.0992 322.4129 336.2875 322.4129 c 333.4758 322.4129 331.1964 320.2601 331.1964 317.6046 c 331.1964 314.9491 333.4758 312.7963 336.2875 312.7963 c b 0 g 336.2875 317.6046 m F 0 G 0.3 w 10 M 362.8992 317.6046 m S 0.3 g 1 w 4 M 362.8992 312.7963 m 365.7108 312.7963 367.9902 314.9491 367.9902 317.6046 c 367.9902 320.2601 365.7108 322.4129 362.8992 322.4129 c 360.0874 322.4129 357.808 320.2601 357.808 317.6046 c 357.808 314.9491 360.0874 312.7963 362.8992 312.7963 c b 0 g 362.8992 317.6046 m F 0 G 0.3 w 10 M 309.6759 317.6046 m S 0.3 g 1 w 4 M 309.6759 312.7963 m 312.4876 312.7963 314.767 314.9491 314.767 317.6046 c 314.767 320.2601 312.4876 322.4129 309.6759 322.4129 c 306.8642 322.4129 304.5848 320.2601 304.5848 317.6046 c 304.5848 314.9491 306.8642 312.7963 309.6759 312.7963 c b 0 g 309.6759 317.6046 m F 0 G 0.3 w 10 M 216.5353 434.3038 m S 216.5353 447.2704 m S 223.1882 440.7871 m S 256.4527 421.3372 m S 256.4527 408.3707 m S 243.1469 408.3707 m S 243.1469 421.3372 m S 249.7998 414.854 m S 243.1469 434.3038 m S 243.1469 421.3372 m S 236.494 427.8206 m S 243.1469 447.2704 m S 243.1469 434.3038 m S 236.494 440.7871 m S u 256.4527 447.2704 m S 256.4527 434.3038 m S 243.1469 434.3038 m S 243.1469 447.2704 m S 249.7998 440.7871 m S U u 256.4527 434.3038 m S 256.4527 421.3372 m S 243.1469 421.3372 m S 243.1469 434.3038 m S 249.7998 427.8206 m S U 243.1469 421.3372 m S 243.1469 408.3707 m S 236.494 414.854 m S 216.5353 408.3707 m S 216.5353 421.3372 m S 223.1882 414.854 m S 216.5353 421.3372 m S 216.5353 434.3038 m S 223.1882 427.8206 m S 0 g 1 w 4 M 223.1882 440.7871 m F 223.1882 414.854 m F 0 G 0.3 w 10 M 216.5353 395.4041 m S 216.5353 408.3707 m S 223.1882 401.8874 m S 256.4527 382.4375 m S 256.4527 369.4709 m S 243.1469 382.4375 m S 249.7998 375.9542 m S 243.1469 382.4375 m S 236.494 388.9208 m S 243.1469 408.3707 m S 236.494 401.8874 m S 256.4527 408.3707 m S 256.4527 395.4041 m S 243.1469 408.3707 m S 249.7998 401.8874 m S 243.1469 382.4375 m S 236.494 375.9542 m S 216.5353 369.4709 m S 216.5353 382.4375 m S 223.1882 375.9542 m S 216.5353 382.4375 m S 216.5353 395.4041 m S 223.1882 388.9208 m S 0 g 1 w 4 M 223.1882 401.8874 m F 223.1882 375.9542 m F 223.1882 362.9876 m F 0 G 0.3 w 10 M 216.5353 356.5043 m S 216.5353 369.4709 m S 223.1882 362.9876 m S 243.1469 330.5711 m S 243.1469 356.5043 m S 236.494 350.021 m S 243.1469 356.5043 m S 236.494 362.9876 m S 243.1469 356.5043 m S 243.1469 356.5043 m S 243.1469 330.5711 m S 236.494 337.0544 m S 216.5353 330.5711 m S 216.5353 343.5377 m S 223.1882 337.0544 m S 216.5353 343.5377 m S 216.5353 356.5043 m S 223.1882 350.021 m S 0 g 1 w 4 M 223.1882 362.9876 m F 223.1882 337.0544 m F 0 G 0.3 w 10 M 216.5353 317.6045 m S 216.5353 330.5711 m S 223.1882 324.0878 m S 243.1469 291.6714 m S 236.494 311.1212 m S 243.1469 330.5711 m S 236.494 324.0878 m S 243.1469 330.5711 m S 243.1469 291.6714 m S 229.8411 291.6714 m S 236.494 298.1546 m S 229.8411 291.6714 m S 216.5353 291.6714 m S 216.5353 304.6379 m S 223.1882 298.1546 m S 216.5353 304.6379 m S 216.5353 317.6045 m S 223.1882 311.1212 m S 0 g 1 w 4 M 223.1882 324.0878 m F 223.1882 298.1546 m F 0 G 0.3 w 10 M 256.4527 447.2704 m S 243.1469 447.2704 m S 249.7998 453.7537 m S 229.8411 460.2369 m S 243.1469 447.2704 m S 229.8411 460.2369 m S 236.494 453.7537 m S 229.8411 460.2369 m S 216.5353 447.2704 m S 216.5353 460.2369 m S 223.1882 453.7537 m S 229.8411 460.2369 m S 216.5353 460.2369 m S 223.1882 466.7203 m S 296.3701 447.2704 m S 283.0643 447.2704 m S 289.7172 453.7537 m S 283.0643 447.2704 m S 269.7585 447.2704 m S 276.4114 453.7537 m S 269.7585 447.2704 m S 256.4527 447.2704 m S 263.1056 453.7537 m S 309.6759 447.2704 m S 316.3288 453.7537 m S 309.6759 447.2704 m S 296.3701 447.2704 m S 303.023 453.7537 m S 382.8578 453.7538 m S 402.8166 460.237 m S 396.1637 466.7203 m S 402.8166 460.237 m S 402.8166 447.2704 m S 396.1637 453.7538 m S 0 g 1 w 4 M 396.1637 466.7203 m F 0 G 0.3 w 10 M 216.6603 382.5749 m S 216.6603 395.5415 m S 223.3132 389.0582 m S 243.2719 382.5749 m S 236.619 376.0917 m S 243.2719 382.5749 m S 236.619 389.0582 m S 243.2719 356.6418 m S 236.619 363.1251 m S 216.6603 356.6418 m S 216.6603 369.6083 m S 223.3132 363.1251 m S 216.6603 369.6083 m S 216.6603 382.5749 m S 223.3132 376.0917 m S 216.6603 343.6752 m S 216.6603 356.6418 m S 223.3132 350.1585 m S 243.2719 356.6418 m S 236.619 350.1585 m S 216.6603 395.5415 m S 216.6603 408.508 m S 223.3132 402.0248 m S 216.6603 330.7085 m S 216.6603 343.6751 m S 223.3132 337.1918 m S 243.2719 330.7085 m S 236.619 324.2253 m S 243.2719 330.7085 m S 236.619 337.1918 m S 236.619 311.2587 m S 216.6603 304.7754 m S 216.6603 317.7419 m S 223.3132 311.2587 m S 216.6603 317.7419 m S 216.6603 330.7085 m S 223.3132 324.2253 m S 229.9661 291.8088 m S 216.6603 291.8088 m S 216.6603 304.7754 m S 223.3132 298.2921 m S 243.2719 291.8088 m S 229.9661 291.8088 m S 236.619 298.2921 m S 216.6603 343.6751 m S 216.6603 356.6416 m S 223.3132 350.1584 m S 376.3299 356.617 m S 382.9828 363.1003 m S 376.2049 408.3584 m S 382.8578 401.8751 m S 376.2049 382.4252 m S 382.8578 375.942 m S 376.2049 356.4921 m S 382.8578 362.9754 m S 376.2049 408.3584 m S 382.8578 414.8417 m S 382.9203 453.7915 m S 402.879 460.2748 m S 402.879 447.3082 m S 396.2261 453.7915 m S 376.2674 408.4085 m S 382.9203 414.8918 m S 1 w 4 M 219.218 434.286 m 221.665 455.7155 225.5962 469.6116 230.0286 469.6116 c S 243.4636 382.6374 m S 230.0286 295.6633 m 222.6088 295.6633 216.5936 334.6037 216.5936 382.6374 c 216.5936 401.9771 217.5687 419.8426 219.218 434.286 c S 389.3815 469.3994 m 396.8014 469.3994 402.8165 430.459 402.8165 382.4252 c 402.8165 334.3914 396.8014 295.4511 389.3815 295.4511 c S 375.9465 382.4252 m S u u 0 g /_Times-Italic 36 43 0 0 z [1 0 0 1 176.621 376.5287]e (m)t T U U 0 G 0.3 w 10 M 256.4527 434.3039 m S 243.1469 434.3039 m S 269.7585 434.3039 m S 256.4527 434.3039 m S 269.7585 434.3039 m S 256.4527 434.3039 m S 283.0643 434.3039 m S 269.7585 434.3039 m S 283.0643 434.3039 m S 269.7585 434.3039 m S 256.4527 434.3039 m S 243.1469 434.3039 m S 296.3701 434.3039 m S 283.0643 434.3039 m S 309.6759 434.3039 m S 296.3701 434.3039 m S 309.6759 434.3039 m S 296.3701 434.3039 m S 322.9817 434.3039 m S 309.6759 434.3039 m S 322.9817 434.3039 m S 309.6759 434.3039 m S 296.3701 434.3039 m S 283.0643 434.3039 m S 336.2875 434.3039 m S 322.9817 434.3039 m S 349.5933 434.3039 m S 336.2875 434.3039 m S 349.5933 434.3039 m S 336.2875 434.3039 m S 362.8992 434.3039 m S 349.5933 434.3039 m S 362.8992 434.3039 m S 349.5933 434.3039 m S 336.2875 434.3039 m S 322.9817 434.3039 m S 376.2048 434.3039 m S 362.8992 434.3039 m S 376.2048 434.3039 m S 376.2048 434.3039 m S 376.2048 434.3039 m S 362.8992 434.3039 m S 256.4527 434.3039 m S 1 g 1 w 4 M 256.4527 429.4956 m 259.2644 429.4956 261.5438 431.6484 261.5438 434.3039 c 261.5438 436.9594 259.2644 439.1122 256.4527 439.1122 c 253.641 439.1122 251.3616 436.9594 251.3616 434.3039 c 251.3616 431.6484 253.641 429.4956 256.4527 429.4956 c b 0 g 256.4527 434.3039 m F 0 G 0.3 w 10 M 269.7585 434.3039 m S 1 g 1 w 4 M 269.7585 429.4956 m 272.5702 429.4956 274.8497 431.6484 274.8497 434.3039 c 274.8497 436.9594 272.5702 439.1122 269.7585 439.1122 c 266.9468 439.1122 264.6674 438.2927 264.6674 434.3039 c 264.6674 431.6484 266.9468 429.4956 269.7585 429.4956 c b 0 g 269.7585 434.3039 m F 0 G 0.3 w 10 M 283.0643 434.3039 m S 1 g 1 w 4 M 283.0643 429.4956 m 285.876 429.4956 288.1554 431.6484 288.1554 434.3039 c 288.1554 436.9594 285.876 439.1122 283.0643 439.1122 c 280.2527 439.1122 277.9732 436.9594 277.9732 434.3039 c 277.9732 431.6484 280.2527 429.4956 283.0643 429.4956 c b 0 g 283.0643 434.3039 m F 0 G 0.3 w 10 M 296.3701 434.3039 m S 1 g 1 w 4 M 296.3701 429.4956 m 299.1819 429.4956 301.4612 431.6484 301.4612 434.3039 c 301.4612 436.9594 299.1819 439.1122 296.3701 439.1122 c 293.5585 439.1122 291.279 436.9594 291.279 434.3039 c 291.279 431.6484 293.5585 429.4956 296.3701 429.4956 c b 0 g 296.3701 434.3039 m F 0 G 0.3 w 10 M 309.6759 434.3039 m S 1 g 1 w 4 M 309.6759 429.4956 m 312.4877 429.4956 314.767 431.6484 314.767 434.3039 c 314.767 436.9594 312.4877 439.1122 309.6759 439.1122 c 306.8642 439.1122 304.5848 436.9594 304.5848 434.3039 c 304.5848 431.6484 306.8642 429.4956 309.6759 429.4956 c b 0 g 309.6759 434.3039 m F 0 G 0.3 w 10 M 322.9817 434.3039 m S 1 g 1 w 4 M 322.9817 429.4956 m 325.7934 429.4956 328.0728 431.6484 328.0728 434.3039 c 328.0728 436.9594 325.7934 439.1122 322.9817 439.1122 c 320.17 439.1122 317.8907 436.9594 317.8907 434.3039 c 317.8907 431.6484 320.17 429.4956 322.9817 429.4956 c b 0 g 322.9817 434.3039 m F 0 G 0.3 w 10 M 336.2875 434.3039 m S 1 g 1 w 4 M 336.2875 429.4956 m 339.0992 429.4956 341.3786 431.6484 341.3786 434.3039 c 341.3786 436.9594 339.0992 439.1122 336.2875 439.1122 c 333.4758 439.1122 331.1964 436.9594 331.1964 434.3039 c 331.1964 431.6484 333.4758 429.4956 336.2875 429.4956 c b 0 g 336.2875 434.3039 m F 0 G 0.3 w 10 M 349.5933 434.3039 m S 1 g 1 w 4 M 349.5933 429.4956 m 352.405 429.4956 354.6844 431.6484 354.6844 434.3039 c 354.6844 436.9594 352.405 439.1122 349.5933 439.1122 c 346.7816 439.1122 344.5022 436.9594 344.5022 434.3039 c 344.5022 431.6484 346.7816 429.4956 349.5933 429.4956 c b 0 g 349.5933 434.3039 m F 0 G 0.3 w 10 M 376.2048 434.3039 m S 0.3 g 1 w 4 M 376.2048 429.4956 m 379.0166 429.4956 381.296 431.6484 381.296 434.3039 c 381.296 436.9594 379.0166 439.1122 376.2048 439.1122 c 372.7266 439.1122 371.1138 436.9593 371.1138 434.3039 c 371.1138 431.6484 373.3932 429.4956 376.2048 429.4956 c b 0 g 376.2048 434.3039 m F 0 G 0.3 w 10 M 362.8992 434.3039 m S 1 g 1 w 4 M 362.8992 429.4956 m 365.7108 429.4956 367.9902 431.6484 367.9902 434.3039 c 367.9902 436.9594 365.7108 439.1122 362.8992 439.1122 c 360.0874 439.1122 357.808 436.9594 357.808 434.3039 c 357.808 431.6484 360.0874 429.4956 362.8992 429.4956 c b 0 g 362.8992 434.3039 m F 0 G 0.3 w 10 M 243.1469 434.3039 m S 0.3 g 1 w 4 M 243.1469 429.4956 m 245.9586 429.4956 248.238 431.6484 248.238 434.3039 c 248.238 436.9594 245.9586 439.1122 243.1469 439.1122 c 240.3352 439.1122 238.0558 436.9594 238.0558 434.3039 c 238.0558 431.6484 240.3352 429.4956 243.1469 429.4956 c b 0 g 243.1469 434.3039 m F 0 G 0.3 w 10 M 256.4527 434.3038 m S 243.1469 434.3038 m S 243.1469 434.3038 m S 243.1469 434.3038 m S 256.4527 434.3038 m S 243.1469 434.3038 m S 376.2049 434.2915 m S 376.2049 434.2915 m S 376.2674 434.3416 m S 296.3701 447.2704 m S 0 g 1 w 4 M 296.3701 447.2704 m F 0 G 0.3 w 10 M 296.3701 447.2704 m S 296.3701 447.2704 m S 296.3701 447.2704 m S 0 g 1 w 4 M 296.3701 447.2704 m F 0 G 0.3 w 10 M 296.3701 447.2704 m S 296.3701 447.2704 m S 296.3701 447.2704 m S 0 g 1 w 4 M 296.3701 447.2704 m F 0 G 0.3 w 10 M 296.3701 447.2704 m S 296.3701 447.2704 m S 269.7585 447.2704 m S 0 g 1 w 4 M 269.7585 447.2704 m F 0 G 0.3 w 10 M 269.7585 447.2704 m S 269.7585 447.2704 m S 269.7585 447.2704 m S 0 g 1 w 4 M 269.7585 447.2704 m F 0 G 0.3 w 10 M 269.7585 447.2704 m S 269.7585 447.2704 m S 269.7585 447.2704 m S 0 g 1 w 4 M 269.7585 447.2704 m F 0 G 0.3 w 10 M 269.7585 447.2704 m S 269.7585 447.2704 m S 243.0219 421.1999 m S 0 g 1 w 4 M 243.0219 421.1999 m F 0 G 0.3 w 10 M 243.0219 421.1999 m S 243.0219 421.1999 m S 243.0219 421.1999 m S 0 g 1 w 4 M 243.0219 421.1999 m F 0 G 0.3 w 10 M 243.0219 421.1999 m S 243.0219 421.1999 m S 1 g 1 w 4 M 243.0219 421.1999 m F 0 G 0.3 w 10 M 243.0219 421.1999 m S 0 g 1 w 4 M 243.0219 421.1999 m F 0 G 0.3 w 10 M 243.0219 421.1999 m S 243.0219 421.1999 m S 269.6335 421.1999 m S 0 g 1 w 4 M 269.6335 421.1999 m F 0 G 0.3 w 10 M 269.6335 421.1999 m S 269.6335 421.1999 m S 269.6335 421.1999 m S 0 g 1 w 4 M 269.6335 421.1999 m F 0 G 0.3 w 10 M 269.6335 421.1999 m S 269.6335 421.1999 m S 1 g 1 w 4 M 269.6335 421.1999 m F 0 G 0.3 w 10 M 269.6335 421.1999 m S 0 g 1 w 4 M 269.6335 421.1999 m F 0 G 0.3 w 10 M 269.6335 421.1999 m S 269.6335 421.1999 m S 362.7742 421.1999 m S 1 g 1 w 4 M 362.7742 416.3916 m 365.5858 416.3916 367.8652 418.5444 367.8652 421.1999 c 367.8652 423.8554 365.5858 426.0082 362.7742 426.0082 c 359.9624 426.0082 357.683 423.8554 357.683 421.1999 c 357.683 418.5444 359.9624 416.3916 362.7742 416.3916 c b 0 g 362.7742 421.1999 m F 0 G 0.3 w 10 M 336.1625 421.1999 m S 1 g 1 w 4 M 336.1625 416.3916 m 338.9742 416.3916 341.2536 418.5444 341.2536 421.1999 c 341.2536 423.8554 338.9742 426.0082 336.1625 426.0082 c 333.3508 426.0082 331.0714 423.8554 331.0714 421.1999 c 331.0714 418.5444 333.3508 416.3916 336.1625 416.3916 c b 0 g 336.1625 421.1999 m F 0 G 0.3 w 10 M 256.3277 421.1999 m S 1 w 4 M 256.3277 416.3916 m 259.1394 416.3916 261.4188 418.5444 261.4188 421.1999 c 261.4188 423.8554 259.1394 426.0082 256.3277 426.0082 c 253.516 426.0082 251.2366 423.8554 251.2366 421.1999 c 251.2366 418.5444 253.516 416.3916 256.3277 416.3916 c s 0 g 256.3277 421.1999 m F 0 G 0.3 w 10 M 282.9393 421.1999 m S 1 g 1 w 4 M 282.9393 416.3916 m 285.751 416.3916 288.0304 418.5444 288.0304 421.1999 c 288.0304 423.8554 285.751 426.0082 282.9393 426.0082 c 280.1276 426.0082 277.8482 423.8554 277.8482 421.1999 c 277.8482 418.5444 280.1276 416.3916 282.9393 416.3916 c b 0 g 282.9393 421.1999 m F 0 G 0.3 w 10 M 309.5509 421.1999 m S 1 g 1 w 4 M 309.5509 416.3916 m 312.3626 416.3916 314.642 418.5444 314.642 421.1999 c 314.642 423.8554 312.3626 426.0082 309.5509 426.0082 c 306.7392 426.0082 304.4598 423.8554 304.4598 421.1999 c 304.4598 418.5444 306.7392 416.3916 309.5509 416.3916 c b 0 g 309.5509 421.1999 m F 0 G 0.3 w 10 M 256.3277 421.1998 m S 243.0219 421.1998 m S 243.0219 421.1998 m S 243.0219 421.1998 m S 243.0219 421.1998 m S 243.1469 421.3372 m S 243.1469 421.3372 m S 236.494 414.854 m S 382.8578 414.8292 m S 382.7328 414.7043 m S u 336.2954 314.3216 m S 336.2954 301.3551 m S 322.9896 301.3551 m S 322.9896 314.3216 m S 329.6425 307.8384 m S U u 376.2128 314.3216 m S 376.2128 301.3551 m S 362.907 301.3551 m S 362.907 314.3216 m S 369.5599 307.8384 m S U u 362.907 314.3216 m S 362.907 301.3551 m S 349.6011 301.3551 m S 349.6011 314.3216 m S 356.254 307.8384 m S U u 349.6011 314.3216 m S 349.6011 301.3551 m S 336.2954 301.3551 m S 336.2954 314.3216 m S 342.9482 307.8384 m S U u 376.2128 314.3217 m S 376.2128 301.3551 m S 362.9071 301.3551 m S 362.9071 314.3217 m S 369.5599 307.8385 m S U 0.5 w 4 M 263.1056 311.1213 m 263.1056 305.5883 l S 0.4 G 1 w 262.8556 290.3715 m S 0 G 0.5 w 262.8556 305.5883 m 356.2462 305.5883 l S 0.4 G 1 w 356.2462 290.3715 m S u 1 g 0 G 0.5 w 275.3784 309.0036 m 263.1056 305.5883 L 275.4656 302.5028 L 275.3784 309.0036 L b U u 343.9286 302.338 m 356.2462 305.5883 L 343.9286 308.8393 L 343.9286 302.338 L b U u u 0 g 1 w /_Times-Roman 12 14.5 0 0 z [1 0 0 1 295.75 294.6213]e (\62)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 301.75 294.6213]e (R+)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 317.1777 294.6213]e (\61)t T U U 0 G 0.5 w 263.1056 305.5883 m 263.1056 300.0553 l S 356.2462 305.5883 m 356.2462 300.0553 l S 356.2462 311.1213 m 356.2462 305.5883 l S 1 w 256.4527 452.0788 m 256.5 465.9375 l S u 0 g 0.3 w 1 M 254.6679 457.8701 m 256.4527 452.0788 L 257.9925 457.9401 L 254.6679 457.8701 L b U u u 1 w 4 M /_Times-Italic 12 14.5 0 0 z [1 0 0 1 245.75 467.25]e (h)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 251.75 467.25]e (=)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 258.5176 467.25]e (J)t T U U u u /_Times-Roman 36 43 0 0 z [1 0 0 1 457 375.5]e (=)t T U U 0 G 0.3 w 10 M 108.1469 220.708 m S 0 g 1 w 4 M 108.1469 220.708 m F 0 G 0.3 w 10 M 108.1469 220.708 m S 108.1469 220.708 m S 108.1469 220.708 m S 0 g 1 w 4 M 108.1469 220.708 m F 0 G 0.3 w 10 M 108.1469 220.708 m S 108.1469 220.708 m S 1 g 1 w 4 M 108.1469 220.708 m F 0 G 0.3 w 10 M 108.1469 220.708 m S 0 g 1 w 4 M 108.1469 220.708 m F 0 G 0.3 w 10 M 108.1469 220.708 m S 108.1469 220.708 m S 148.0643 194.7748 m S 0 g 1 w 4 M 148.0643 194.7748 m F 0 G 0.3 w 10 M 174.6759 194.7748 m S 0 g 1 w 4 M 174.6759 194.7748 m F 0 G 0.3 w 10 M 201.2875 194.7748 m S 0 g 1 w 4 M 201.2875 194.7748 m F 0 G 0.3 w 10 M 227.8992 194.7748 m S 0 g 1 w 4 M 227.8992 194.7748 m F 0 G 0.3 w 10 M 121.4527 181.8083 m S 134.7585 181.8083 m S 121.4527 181.8083 m S 134.7585 181.8083 m S 121.4527 181.8083 m S 148.0643 181.8083 m S 134.7585 181.8083 m S 148.0643 181.8083 m S 134.7585 181.8083 m S 121.4527 181.8083 m S 161.3701 181.8083 m S 148.0643 181.8083 m S 174.6759 181.8083 m S 161.3701 181.8083 m S 174.6759 181.8083 m S 161.3701 181.8083 m S 187.9817 181.8083 m S 174.6759 181.8083 m S 187.9817 181.8083 m S 174.6759 181.8083 m S 161.3701 181.8083 m S 148.0643 181.8083 m S 201.2875 181.8083 m S 187.9817 181.8083 m S 214.5933 181.8083 m S 201.2875 181.8083 m S 214.5933 181.8083 m S 201.2875 181.8083 m S 227.8992 181.8083 m S 214.5933 181.8083 m S 227.8992 181.8083 m S 214.5933 181.8083 m S 201.2875 181.8083 m S 187.9817 181.8083 m S 227.8992 181.8083 m S 227.8992 181.8083 m S 121.4527 181.8083 m S 0.5 g 1 w 4 M 121.4527 177 m 124.2644 177 126.5438 179.1528 126.5438 181.8083 c 126.5438 184.4638 124.2644 186.6166 121.4527 186.6166 c 118.641 186.6166 116.3616 184.4638 116.3616 181.8083 c 116.3616 179.1528 118.641 177 121.4527 177 c b 0 g 121.4527 181.8083 m F 0 G 0.3 w 10 M 134.7585 181.8083 m S 0 g 1 w 4 M 134.7585 181.8083 m F 0 G 0.3 w 10 M 148.0643 181.8083 m S 1 g 1 w 4 M 148.0643 177 m 150.876 177 153.1554 179.1528 153.1554 181.8083 c 153.1554 184.4638 150.876 186.6166 148.0643 186.6166 c 145.2527 186.6166 142.9732 184.4638 142.9732 181.8083 c 142.9732 179.1528 145.2527 177 148.0643 177 c b 0 g 148.0643 181.8083 m F 0 G 0.3 w 10 M 161.3701 181.8083 m S 0 g 1 w 4 M 161.3701 181.8083 m F 0 G 0.3 w 10 M 174.6759 181.8083 m S 1 g 1 w 4 M 174.6759 177 m 177.4877 177 179.767 179.1528 179.767 181.8083 c 179.767 184.4638 177.4877 186.6166 174.6759 186.6166 c 171.8642 186.6166 169.5848 184.4638 169.5848 181.8083 c 169.5848 179.1528 171.8642 177 174.6759 177 c b 0 g 174.6759 181.8083 m F 0 G 0.3 w 10 M 187.9817 181.8083 m S 0 g 1 w 4 M 187.9817 181.8083 m F 0 G 0.3 w 10 M 201.2875 181.8083 m S 1 g 1 w 4 M 201.2875 177 m 204.0992 177 206.3786 179.1528 206.3786 181.8083 c 206.3786 184.4638 204.0992 186.6166 201.2875 186.6166 c 198.4758 186.6166 196.1964 184.4638 196.1964 181.8083 c 196.1964 179.1528 198.4758 177 201.2875 177 c b 0 g 201.2875 181.8083 m F 0 G 0.3 w 10 M 214.5933 181.8083 m S 0 g 1 w 4 M 214.5933 181.8083 m F 0 G 0.3 w 10 M 227.8992 181.8083 m S 0.5 g 1 w 4 M 227.8992 177 m 230.7108 177 232.9902 179.1528 232.9902 181.8083 c 232.9902 184.4638 230.7108 186.6166 227.8992 186.6166 c 225.0874 186.6166 222.808 184.4638 222.808 181.8083 c 222.808 179.1528 225.0874 177 227.8992 177 c b 0 g 227.8992 181.8083 m F 0 G 0.3 w 10 M 121.4527 155.8751 m S 134.7585 155.8751 m S 121.4527 155.8751 m S 134.7585 155.8751 m S 121.4527 155.8751 m S 148.0643 155.8751 m S 134.7585 155.8751 m S 148.0643 155.8751 m S 134.7585 155.8751 m S 121.4527 155.8751 m S 161.3701 155.8751 m S 148.0643 155.8751 m S 174.6759 155.8751 m S 161.3701 155.8751 m S 174.6759 155.8751 m S 161.3701 155.8751 m S 187.9817 155.8751 m S 174.6759 155.8751 m S 187.9817 155.8751 m S 174.6759 155.8751 m S 161.3701 155.8751 m S 148.0643 155.8751 m S 201.2875 155.8751 m S 187.9817 155.8751 m S 214.5933 155.8751 m S 201.2875 155.8751 m S 214.5933 155.8751 m S 201.2875 155.8751 m S 227.8992 155.8751 m S 214.5933 155.8751 m S 227.8992 155.8751 m S 214.5933 155.8751 m S 201.2875 155.8751 m S 187.9817 155.8751 m S 227.8992 155.8751 m S 227.8992 155.8751 m S 121.4527 155.8751 m S 0 g 1 w 4 M 121.4527 155.8751 m F 0 G 0.3 w 10 M 134.7585 155.8751 m S 0 g 1 w 4 M 134.7585 155.8751 m F 0 G 0.3 w 10 M 148.0643 155.8751 m S 0 g 1 w 4 M 148.0643 155.8751 m F 0 G 0.3 w 10 M 161.3701 155.8751 m S 0 g 1 w 4 M 161.3701 155.8751 m F 0 G 0.3 w 10 M 174.6759 155.8751 m S 0 g 1 w 4 M 174.6759 155.8751 m F 0 G 0.3 w 10 M 187.9817 155.8751 m S 0 g 1 w 4 M 187.9817 155.8751 m F 0 G 0.3 w 10 M 201.2875 155.8751 m S 0 g 1 w 4 M 201.2875 155.8751 m F 0 G 0.3 w 10 M 214.5933 155.8751 m S 0 g 1 w 4 M 214.5933 155.8751 m F 0 G 0.3 w 10 M 227.8992 155.8751 m S 0 g 1 w 4 M 227.8992 155.8751 m F 0 G 0.3 w 10 M 121.4527 155.8751 m S 134.7585 155.8751 m S 121.4527 155.8751 m S 134.7585 155.8751 m S 121.4527 155.8751 m S 148.0643 155.8751 m S 134.7585 155.8751 m S 148.0643 155.8751 m S 134.7585 155.8751 m S 121.4527 155.8751 m S 161.3701 155.8751 m S 148.0643 155.8751 m S 174.6759 155.8751 m S 161.3701 155.8751 m S 174.6759 155.8751 m S 161.3701 155.8751 m S 187.9817 155.8751 m S 174.6759 155.8751 m S 187.9817 155.8751 m S 174.6759 155.8751 m S 161.3701 155.8751 m S 148.0643 155.8751 m S 201.2875 155.8751 m S 187.9817 155.8751 m S 214.5933 155.8751 m S 201.2875 155.8751 m S 214.5933 155.8751 m S 201.2875 155.8751 m S 227.8992 155.8751 m S 214.5933 155.8751 m S 227.8992 155.8751 m S 214.5933 155.8751 m S 201.2875 155.8751 m S 187.9817 155.8751 m S 227.8992 155.8751 m S 227.8992 155.8751 m S 121.4527 155.8751 m S 0.5 g 1 w 4 M 121.4527 151.0668 m 124.2644 151.0668 126.5438 153.2196 126.5438 155.8751 c 126.5438 158.5306 124.2644 160.6834 121.4527 160.6834 c 118.641 160.6834 116.3616 158.5306 116.3616 155.8751 c 116.3616 153.2196 118.641 151.0668 121.4527 151.0668 c b 0 g 121.4527 155.8751 m F 0 G 0.3 w 10 M 134.7585 155.8751 m S 0 g 1 w 4 M 134.7585 155.8751 m F 0 G 0.3 w 10 M 148.0643 155.8751 m S 1 g 1 w 4 M 148.0643 151.0668 m 150.876 151.0668 153.1554 153.2196 153.1554 155.8751 c 153.1554 158.5306 150.876 160.6834 148.0643 160.6834 c 145.2527 160.6834 142.9732 158.5306 142.9732 155.8751 c 142.9732 153.2196 145.2527 151.0668 148.0643 151.0668 c b 0 g 148.0643 155.8751 m F 0 G 0.3 w 10 M 161.3701 155.8751 m S 0 g 1 w 4 M 161.3701 155.8751 m F 0 G 0.3 w 10 M 174.6759 155.8751 m S 1 g 1 w 4 M 174.6759 151.0668 m 177.4877 151.0668 179.767 153.2196 179.767 155.8751 c 179.767 158.5306 177.4877 160.6834 174.6759 160.6834 c 171.8642 160.6834 169.5848 158.5306 169.5848 155.8751 c 169.5848 153.2196 171.8642 151.0668 174.6759 151.0668 c b 0 g 174.6759 155.8751 m F 0 G 0.3 w 10 M 187.9817 155.8751 m S 0 g 1 w 4 M 187.9817 155.8751 m F 0 G 0.3 w 10 M 201.2875 155.8751 m S 1 g 1 w 4 M 201.2875 151.0668 m 204.0992 151.0668 206.3786 153.2196 206.3786 155.8751 c 206.3786 158.5306 204.0992 160.6834 201.2875 160.6834 c 198.4758 160.6834 196.1964 158.5306 196.1964 155.8751 c 196.1964 153.2196 198.4758 151.0668 201.2875 151.0668 c b 0 g 201.2875 155.8751 m F 0 G 0.3 w 10 M 214.5933 155.8751 m S 0 g 1 w 4 M 214.5933 155.8751 m F 0 G 0.3 w 10 M 227.8992 155.8751 m S 0.5 g 1 w 4 M 227.8992 151.0668 m 230.7108 151.0668 232.9902 153.2196 232.9902 155.8751 c 232.9902 158.5306 230.7108 160.6834 227.8992 160.6834 c 225.0874 160.6834 222.808 158.5306 222.808 155.8751 c 222.808 153.2196 225.0874 151.0668 227.8992 151.0668 c b 0 g 227.8992 155.8751 m F 0 G 0.3 w 10 M 121.4527 129.9419 m S 134.7585 129.9419 m S 121.4527 129.9419 m S 134.7585 129.9419 m S 121.4527 129.9419 m S 148.0643 129.9419 m S 134.7585 129.9419 m S 148.0643 129.9419 m S 134.7585 129.9419 m S 121.4527 129.9419 m S 161.3701 129.9419 m S 148.0643 129.9419 m S 174.6759 129.9419 m S 161.3701 129.9419 m S 174.6759 129.9419 m S 161.3701 129.9419 m S 187.9817 129.9419 m S 174.6759 129.9419 m S 187.9817 129.9419 m S 174.6759 129.9419 m S 161.3701 129.9419 m S 148.0643 129.9419 m S 201.2875 129.9419 m S 187.9817 129.9419 m S 214.5933 129.9419 m S 201.2875 129.9419 m S 214.5933 129.9419 m S 201.2875 129.9419 m S 227.8992 129.9419 m S 214.5933 129.9419 m S 227.8992 129.9419 m S 214.5933 129.9419 m S 201.2875 129.9419 m S 187.9817 129.9419 m S 227.8992 129.9419 m S 227.8992 129.9419 m S 121.4527 129.9419 m S 0.5 g 1 w 4 M 121.4527 125.1336 m 124.2644 125.1336 126.5438 127.2864 126.5438 129.9419 c 126.5438 132.5974 124.2644 134.7502 121.4527 134.7502 c 118.641 134.7502 116.3616 132.5974 116.3616 129.9419 c 116.3616 127.2864 118.641 125.1336 121.4527 125.1336 c b 0 g 121.4527 129.9419 m F 0 G 0.3 w 10 M 134.7585 129.9419 m S 0 g 1 w 4 M 134.7585 129.9419 m F 0 G 0.3 w 10 M 148.0643 129.9419 m S 1 g 1 w 4 M 148.0643 125.1336 m 150.876 125.1336 153.1554 127.2864 153.1554 129.9419 c 153.1554 132.5974 150.876 134.7502 148.0643 134.7502 c 145.2527 134.7502 142.9732 132.5974 142.9732 129.9419 c 142.9732 127.2864 145.2527 125.1336 148.0643 125.1336 c b 0 g 148.0643 129.9419 m F 0 G 0.3 w 10 M 161.3701 129.9419 m S 0 g 1 w 4 M 161.3701 129.9419 m F 0 G 0.3 w 10 M 174.6759 129.9419 m S 1 g 1 w 4 M 174.6759 125.1336 m 177.4877 125.1336 179.767 127.2864 179.767 129.9419 c 179.767 132.5974 177.4877 134.7502 174.6759 134.7502 c 171.8642 134.7502 169.5848 132.5974 169.5848 129.9419 c 169.5848 127.2864 171.8642 125.1336 174.6759 125.1336 c b 0 g 174.6759 129.9419 m F 0 G 0.3 w 10 M 187.9817 129.9419 m S 0 g 1 w 4 M 187.9817 129.9419 m F 0 G 0.3 w 10 M 201.2875 129.9419 m S 1 g 1 w 4 M 201.2875 125.1336 m 204.0992 125.1336 206.3786 127.2864 206.3786 129.9419 c 206.3786 132.5974 204.0992 134.7502 201.2875 134.7502 c 198.4758 134.7502 196.1964 132.5974 196.1964 129.9419 c 196.1964 127.2864 198.4758 125.1336 201.2875 125.1336 c b 0 g 201.2875 129.9419 m F 0 G 0.3 w 10 M 214.5933 129.9419 m S 0 g 1 w 4 M 214.5933 129.9419 m F 0 G 0.3 w 10 M 227.8992 129.9419 m S 0.5 g 1 w 4 M 227.8992 125.1336 m 230.7108 125.1336 232.9902 127.2864 232.9902 129.9419 c 232.9902 132.5974 230.7108 134.7502 227.8992 134.7502 c 225.0874 134.7502 222.808 132.5974 222.808 129.9419 c 222.808 127.2864 225.0874 125.1336 227.8992 125.1336 c b 0 g 227.8992 129.9419 m F 0 G 0.3 w 10 M 227.8992 168.8417 m S 0 g 1 w 4 M 227.8992 168.8417 m F 0 G 0.3 w 10 M 201.2875 168.8417 m S 0 g 1 w 4 M 201.2875 168.8417 m F 0 G 0.3 w 10 M 227.8992 142.9085 m S 0 g 1 w 4 M 227.8992 142.9085 m F 0 G 0.3 w 10 M 201.2875 142.9085 m S 0 g 1 w 4 M 201.2875 142.9085 m F 0 G 0.3 w 10 M 148.0643 168.8417 m S 0 g 1 w 4 M 148.0643 168.8417 m F 0 G 0.3 w 10 M 121.4527 168.8417 m S 0 g 1 w 4 M 121.4527 168.8417 m F 0 G 0.3 w 10 M 121.4527 142.9085 m S 0 g 1 w 4 M 121.4527 142.9085 m F 0 G 0.3 w 10 M 148.0643 142.9085 m S 0 g 1 w 4 M 148.0643 142.9085 m F 0 G 0.3 w 10 M 174.6759 142.9085 m S 0 g 1 w 4 M 174.6759 142.9085 m F 0 G 0.3 w 10 M 174.6759 168.8417 m S 0 g 1 w 4 M 174.6759 168.8417 m F 0 G 0.3 w 10 M 121.4527 104.0087 m S 134.7585 104.0087 m S 121.4527 104.0087 m S 134.7585 104.0087 m S 121.4527 104.0087 m S 148.0643 104.0087 m S 134.7585 104.0087 m S 148.0643 104.0087 m S 134.7585 104.0087 m S 121.4527 104.0087 m S 161.3701 104.0087 m S 148.0643 104.0087 m S 174.6759 104.0087 m S 161.3701 104.0087 m S 174.6759 104.0087 m S 161.3701 104.0087 m S 187.9817 104.0087 m S 174.6759 104.0087 m S 187.9817 104.0087 m S 174.6759 104.0087 m S 161.3701 104.0087 m S 148.0643 104.0087 m S 201.2875 104.0087 m S 187.9817 104.0087 m S 214.5933 104.0087 m S 201.2875 104.0087 m S 214.5933 104.0087 m S 201.2875 104.0087 m S 227.8992 104.0087 m S 214.5933 104.0087 m S 227.8992 104.0087 m S 214.5933 104.0087 m S 201.2875 104.0087 m S 187.9817 104.0087 m S 227.8992 104.0087 m S 227.8992 104.0087 m S 121.4527 104.0087 m S 134.7585 104.0087 m S 121.4527 104.0087 m S 134.7585 104.0087 m S 121.4527 104.0087 m S 148.0643 104.0087 m S 134.7585 104.0087 m S 148.0643 104.0087 m S 134.7585 104.0087 m S 121.4527 104.0087 m S 161.3701 104.0087 m S 148.0643 104.0087 m S 174.6759 104.0087 m S 161.3701 104.0087 m S 174.6759 104.0087 m S 161.3701 104.0087 m S 187.9817 104.0087 m S 174.6759 104.0087 m S 187.9817 104.0087 m S 174.6759 104.0087 m S 161.3701 104.0087 m S 148.0643 104.0087 m S 201.2875 104.0087 m S 187.9817 104.0087 m S 214.5933 104.0087 m S 201.2875 104.0087 m S 214.5933 104.0087 m S 201.2875 104.0087 m S 227.8992 104.0087 m S 214.5933 104.0087 m S 227.8992 104.0087 m S 214.5933 104.0087 m S 201.2875 104.0087 m S 187.9817 104.0087 m S 227.8992 104.0087 m S 227.8992 104.0087 m S 121.4527 104.0087 m S 0 g 1 w 4 M 121.4527 99.2004 m 124.2644 99.2004 126.5438 101.3532 126.5438 104.0087 c 126.5438 106.6642 124.2644 108.817 121.4527 108.817 c 117.9744 108.817 116.3616 106.6641 116.3616 104.0087 c 116.3616 101.3532 118.641 99.2004 121.4527 99.2004 c b 121.4527 104.0087 m F 0 G 0.3 w 10 M 134.7585 104.0087 m S 0 g 1 w 4 M 134.7585 104.0087 m F 0 G 0.3 w 10 M 148.0643 104.0087 m S 0.5 g 1 w 4 M 148.0643 99.2004 m 150.876 99.2004 153.1554 101.3532 153.1554 104.0087 c 153.1554 106.6642 150.876 108.817 148.0643 108.817 c 145.2527 108.817 142.9732 106.6642 142.9732 104.0087 c 142.9732 101.3532 145.2527 99.2004 148.0643 99.2004 c b 0 g 148.0643 104.0087 m F 0 G 0.3 w 10 M 161.3701 104.0087 m S 0 g 1 w 4 M 161.3701 104.0087 m F 0 G 0.3 w 10 M 174.6759 104.0087 m S 0.5 g 1 w 4 M 174.6759 99.2004 m 177.4877 99.2004 179.767 101.3532 179.767 104.0087 c 179.767 106.6642 177.4877 108.817 174.6759 108.817 c 171.8642 108.817 169.5848 106.6642 169.5848 104.0087 c 169.5848 101.3532 171.8642 99.2004 174.6759 99.2004 c b 0 g 174.6759 104.0087 m F 0 G 0.3 w 10 M 187.9817 104.0087 m S 0 g 1 w 4 M 187.9817 104.0087 m F 0 G 0.3 w 10 M 201.2875 104.0087 m S 0.5 g 1 w 4 M 201.2875 99.2004 m 204.0992 99.2004 206.3786 101.3532 206.3786 104.0087 c 206.3786 106.6642 204.0992 108.817 201.2875 108.817 c 198.4758 108.817 196.1964 106.6642 196.1964 104.0087 c 196.1964 101.3532 198.4758 99.2004 201.2875 99.2004 c b 0 g 201.2875 104.0087 m F 0 G 0.3 w 10 M 214.5933 104.0087 m S 0 g 1 w 4 M 214.5933 104.0087 m F 0 G 0.3 w 10 M 227.8992 104.0087 m S 0 g 1 w 4 M 227.8992 99.2004 m 230.7108 99.2004 232.9902 101.3532 232.9902 104.0087 c 232.9902 106.6642 230.7108 108.817 227.8992 108.817 c 225.0874 108.817 222.808 106.6642 222.808 104.0087 c 222.808 101.3532 225.0874 99.2004 227.8992 99.2004 c b 227.8992 104.0087 m F 0 G 0.3 w 10 M 121.4527 116.9753 m S 121.4527 116.9753 m S 121.4527 116.9753 m S 148.0643 116.9753 m S 148.0643 116.9753 m S 121.4527 116.9753 m S 148.0643 116.9753 m S 174.6759 116.9753 m S 174.6759 116.9753 m S 174.6759 116.9753 m S 174.6759 116.9753 m S 148.0643 116.9753 m S 201.2875 116.9753 m S 201.2875 116.9753 m S 201.2875 116.9753 m S 227.8992 116.9753 m S 227.8992 116.9753 m S 201.2875 116.9753 m S 227.8992 116.9753 m S 227.8992 116.9753 m S 227.8992 116.9753 m S 0 g 1 w 4 M 227.8992 116.9753 m F 0 G 0.3 w 10 M 201.2875 116.9753 m S 0 g 1 w 4 M 201.2875 116.9753 m F 0 G 0.3 w 10 M 148.0643 116.9753 m S 0 g 1 w 4 M 148.0643 116.9753 m F 0 G 0.3 w 10 M 121.4527 116.9753 m S 0 g 1 w 4 M 121.4527 116.9753 m F 0 G 0.3 w 10 M 174.6759 116.9753 m S 0 g 1 w 4 M 174.6759 116.9753 m F 0 G 0.3 w 10 M 115.2257 96.6009 m S 115.2257 96.6009 m S 128.5315 96.6009 m S 0 g 1 w 4 M 115.2257 96.6009 m F 128.5315 96.6009 m F 0 G 0.3 w 10 M 155.1432 96.6009 m S 175.1018 103.0842 m S 168.449 96.6009 m S 175.1018 103.0842 m S 181.7547 96.6009 m S 0 g 1 w 4 M 155.1432 96.6009 m F 181.7547 96.6009 m F 0 G 0.3 w 10 M 195.0605 96.6009 m S 221.6721 96.6009 m S 234.9779 96.6009 m S 0 g 1 w 4 M 195.0605 96.6009 m F 234.9779 96.6009 m F 0 G 0.3 w 10 M 234.9779 96.6009 m S 247.8578 84.5588 m S 0 g 1 w 4 M 234.9779 96.6009 m F 0 G 0.3 w 10 M 115.2257 96.6009 m S 0 g 1 w 4 M 115.2257 96.6009 m F 0 G 0.3 w 10 M 175.1018 103.0842 m S 0 g 1 w 4 M 175.1018 103.0842 m F 0 G 0.3 w 10 M 81.5353 207.7413 m S 81.5353 220.7079 m S 88.1882 214.2246 m S 121.4527 194.7747 m S 121.4527 181.8082 m S 114.7998 188.2915 m S 101.494 201.2581 m S 108.1469 220.7079 m S 101.494 214.2246 m S 101.494 188.2915 m S 81.5353 181.8082 m S 81.5353 194.7747 m S 88.1882 188.2915 m S 81.5353 194.7747 m S 81.5353 207.7413 m S 88.1882 201.2581 m S 0 g 1 w 4 M 88.1882 214.2246 m F 88.1882 188.2915 m F 0 G 0.3 w 10 M 81.5353 168.8416 m S 81.5353 181.8082 m S 88.1882 175.3249 m S 121.4527 155.875 m S 121.4527 142.9084 m S 114.7998 149.3917 m S 101.494 162.3583 m S 101.494 175.3249 m S 121.4527 181.8082 m S 121.4527 168.8416 m S 114.7998 175.3249 m S 101.494 149.3917 m S 81.5353 142.9084 m S 81.5353 155.875 m S 88.1882 149.3917 m S 81.5353 155.875 m S 81.5353 168.8416 m S 88.1882 162.3583 m S 0 g 1 w 4 M 88.1882 175.3249 m F 88.1882 149.3917 m F 88.1882 136.4251 m F 0 G 0.3 w 10 M 81.5353 129.9418 m S 81.5353 142.9084 m S 88.1882 136.4251 m S 101.494 123.4585 m S 101.494 136.4251 m S 101.494 110.4919 m S 81.5353 104.0086 m S 81.5353 116.9752 m S 88.1882 110.4919 m S 81.5353 116.9752 m S 81.5353 129.9418 m S 88.1882 123.4585 m S 0 g 1 w 4 M 88.1882 136.4251 m F 88.1882 110.4919 m F 0 G 0.3 w 10 M 81.5353 91.042 m S 81.5353 104.0086 m S 88.1882 97.5253 m S 108.1469 65.1089 m S 101.494 84.5587 m S 101.494 97.5253 m S 108.1469 65.1089 m S 94.8411 65.1089 m S 101.494 71.5921 m S 94.8411 65.1089 m S 81.5353 65.1089 m S 81.5353 78.0754 m S 88.1882 71.5921 m S 81.5353 78.0754 m S 81.5353 91.042 m S 88.1882 84.5587 m S 0 g 1 w 4 M 88.1882 97.5253 m F 88.1882 71.5921 m F 0 G 0.3 w 10 M 108.1469 220.7079 m S 114.7998 214.9412 m S 94.8411 233.6744 m S 108.1469 220.7079 m S 94.8411 233.6744 m S 101.494 227.1912 m S 94.8411 233.6744 m S 81.5353 220.7079 m S 81.5353 233.6744 m S 88.1882 227.1912 m S 94.8411 233.6744 m S 81.5353 233.6744 m S 88.1882 240.1578 m S 154.7172 227.1912 m S 141.4114 227.1912 m S 128.1056 214.9412 m S 181.3288 227.1912 m S 168.023 227.1912 m S 247.8578 227.1913 m S 267.8166 233.6745 m S 261.1637 240.1578 m S 267.8166 233.6745 m S 267.8166 220.7079 m S 261.1637 227.1913 m S 0 g 1 w 4 M 261.1637 240.1578 m F 0 G 0.3 w 10 M 81.6603 156.0124 m S 81.6603 168.979 m S 88.3132 162.4957 m S 101.619 149.5292 m S 101.619 162.4957 m S 101.619 136.5626 m S 81.6603 130.0793 m S 81.6603 143.0458 m S 88.3132 136.5626 m S 81.6603 143.0458 m S 81.6603 156.0124 m S 88.3132 149.5292 m S 81.6603 117.1127 m S 81.6603 130.0793 m S 88.3132 123.596 m S 101.619 123.596 m S 81.6603 168.979 m S 81.6603 181.9455 m S 88.3132 175.4623 m S 81.6603 104.146 m S 81.6603 117.1126 m S 88.3132 110.6293 m S 101.619 97.6628 m S 101.619 110.6293 m S 101.619 84.6962 m S 81.6603 78.2129 m S 81.6603 91.1794 m S 88.3132 84.6962 m S 81.6603 91.1794 m S 81.6603 104.146 m S 88.3132 97.6628 m S 94.9661 65.2463 m S 81.6603 65.2463 m S 81.6603 78.2129 m S 88.3132 71.7296 m S 108.2719 65.2463 m S 94.9661 65.2463 m S 101.619 71.7296 m S 81.6603 117.1126 m S 81.6603 130.0791 m S 88.3132 123.5959 m S 247.9203 227.229 m S 267.879 233.7123 m S 267.879 220.7457 m S 261.2261 227.229 m S 1 w 4 M 84.218 207.7235 m 86.665 229.153 90.5962 243.0491 95.0286 243.0491 c S 95.0286 69.1008 m 87.6088 69.1008 81.5936 108.0412 81.5936 156.0749 c 81.5936 175.4146 82.5687 193.2801 84.218 207.7235 c S 254.3815 242.8369 m 261.8014 242.8369 267.8165 203.8965 267.8165 155.8627 c 267.8165 107.8289 261.8014 68.8886 254.3815 68.8886 c S u u 0 g /_Times-Italic 36 43 0 0 z [1 0 0 1 41.621 149.9662]e (m)t T U U 0 G 0.3 w 10 M 121.4527 207.7414 m S 134.7585 207.7414 m S 121.4527 207.7414 m S 134.7585 207.7414 m S 121.4527 207.7414 m S 148.0643 207.7414 m S 134.7585 207.7414 m S 148.0643 207.7414 m S 134.7585 207.7414 m S 121.4527 207.7414 m S 161.3701 207.7414 m S 148.0643 207.7414 m S 174.6759 207.7414 m S 161.3701 207.7414 m S 174.6759 207.7414 m S 161.3701 207.7414 m S 187.9817 207.7414 m S 174.6759 207.7414 m S 187.9817 207.7414 m S 174.6759 207.7414 m S 161.3701 207.7414 m S 148.0643 207.7414 m S 201.2875 207.7414 m S 187.9817 207.7414 m S 214.5933 207.7414 m S 201.2875 207.7414 m S 214.5933 207.7414 m S 201.2875 207.7414 m S 227.8992 207.7414 m S 214.5933 207.7414 m S 227.8992 207.7414 m S 214.5933 207.7414 m S 201.2875 207.7414 m S 187.9817 207.7414 m S 227.8992 207.7414 m S 227.8992 207.7414 m S 121.4527 207.7414 m S 0 g 1 w 4 M 121.4527 202.9331 m 124.2644 202.9331 126.5438 205.0859 126.5438 207.7414 c 126.5438 210.3969 124.2644 212.5497 121.4527 212.5497 c 118.641 212.5497 116.3616 210.3969 116.3616 207.7414 c 116.3616 205.0859 118.641 202.9331 121.4527 202.9331 c b 121.4527 207.7414 m F 0 G 0.3 w 10 M 134.7585 207.7414 m S 0 g 1 w 4 M 134.7585 207.7414 m F 0 G 0.3 w 10 M 148.0643 207.7414 m S 0.5 g 1 w 4 M 148.0643 202.9331 m 150.876 202.9331 153.1554 205.0859 153.1554 207.7414 c 153.1554 210.3969 150.876 212.5497 148.0643 212.5497 c 145.2527 212.5497 142.9732 210.3969 142.9732 207.7414 c 142.9732 205.0859 145.2527 202.9331 148.0643 202.9331 c b 0 g 148.0643 207.7414 m F 0 G 0.3 w 10 M 161.3701 207.7414 m S 0 g 1 w 4 M 161.3701 207.7414 m F 0 G 0.3 w 10 M 174.6759 207.7414 m S 0.5 g 1 w 4 M 174.6759 202.9331 m 177.4877 202.9331 179.767 205.0859 179.767 207.7414 c 179.767 210.3969 177.4877 212.5497 174.6759 212.5497 c 171.8642 212.5497 169.5848 210.3969 169.5848 207.7414 c 169.5848 205.0859 171.8642 202.9331 174.6759 202.9331 c b 0 g 174.6759 207.7414 m F 0 G 0.3 w 10 M 187.9817 207.7414 m S 0 g 1 w 4 M 187.9817 207.7414 m F 0 G 0.3 w 10 M 201.2875 207.7414 m S 0.5 g 1 w 4 M 201.2875 202.9331 m 204.0992 202.9331 206.3786 205.0859 206.3786 207.7414 c 206.3786 210.3969 204.0992 212.5497 201.2875 212.5497 c 198.4758 212.5497 196.1964 210.3969 196.1964 207.7414 c 196.1964 205.0859 198.4758 202.9331 201.2875 202.9331 c b 0 g 201.2875 207.7414 m F 0 G 0.3 w 10 M 214.5933 207.7414 m S 0 g 1 w 4 M 214.5933 207.7414 m F 0 G 0.3 w 10 M 227.8992 207.7414 m S 0 g 1 w 4 M 227.8992 202.9331 m 230.7108 202.9331 232.9902 205.0859 232.9902 207.7414 c 232.9902 210.3969 230.7108 212.5497 227.8992 212.5497 c 225.0874 212.5497 222.808 210.3969 222.808 207.7414 c 222.808 205.0859 225.0874 202.9331 227.8992 202.9331 c b 227.8992 207.7414 m F 0 G 0.3 w 10 M 121.4527 207.7413 m S 121.4527 207.7413 m S 134.6335 194.6374 m S 0 g 1 w 4 M 134.6335 194.6374 m F 0 G 0.3 w 10 M 134.6335 194.6374 m S 134.6335 194.6374 m S 134.6335 194.6374 m S 0 g 1 w 4 M 134.6335 194.6374 m F 0 G 0.3 w 10 M 134.6335 194.6374 m S 134.6335 194.6374 m S 1 g 1 w 4 M 134.6335 194.6374 m F 0 G 0.3 w 10 M 134.6335 194.6374 m S 0 g 1 w 4 M 134.6335 194.6374 m F 0 G 0.3 w 10 M 134.6335 194.6374 m S 134.6335 194.6374 m S 227.7742 194.6374 m S 0 g 1 w 4 M 227.7742 194.6374 m F 0 G 0.3 w 10 M 201.1625 194.6374 m S 0 g 1 w 4 M 201.1625 194.6374 m F 0 G 0.3 w 10 M 121.3277 194.6374 m S 0 g 1 w 4 M 121.3277 194.6374 m F 0 G 0.3 w 10 M 147.9393 194.6374 m S 0 g 1 w 4 M 147.9393 194.6374 m F 0 G 0.3 w 10 M 174.5509 194.6374 m S 0 g 1 w 4 M 174.5509 194.6374 m F 0 G 0.3 w 10 M 121.3277 194.6373 m S 101.494 188.2915 m S 0.5 w 4 M 115.2257 96.6009 m 115.2257 91.0679 l S 0.4 G 1 w 127.8556 63.809 m S 114.9757 91.0679 m S 234.9779 91.0679 m S 221.2462 63.809 m S u 1 g 0 G 0.5 w 127.4985 94.4832 m 115.2257 91.0679 L 127.5857 87.9824 L 127.4985 94.4832 L b U u 222.6603 87.8176 m 234.9779 91.0679 L 222.6603 94.3189 L 222.6603 87.8176 L b U 234.9779 91.0679 m 234.9779 85.5349 l S 115.2257 85.5349 m 115.2257 91.0679 l 234.9779 91.0679 l 234.9779 96.6009 l S 1 w 121.4527 213.2663 m 121.5 227.125 l S u 0 g 0.3 w 1 M 119.6679 219.0576 m 121.4527 213.2663 L 122.9925 219.1276 L 119.6679 219.0576 L b U u u 1 w 4 M /_Times-Roman 12 14.5 0 0 z [1 0 0 1 284.75 275]e (\(c\))t T U U 0.15 g 0 G 174.6759 91.0421 m B u u 0 g /_Times-Italic 12 14.5 0 0 z [1 0 0 1 163.5 80]e (R)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 170.8301 80]e (+2)t T U U 0 G 0.3 w 10 M 393.1469 221.708 m S 0 g 1 w 4 M 393.1469 221.708 m F 0 G 0.3 w 10 M 393.1469 221.708 m S 393.1469 221.708 m S 393.1469 221.708 m S 0 g 1 w 4 M 393.1469 221.708 m F 0 G 0.3 w 10 M 393.1469 221.708 m S 393.1469 221.708 m S 1 g 1 w 4 M 393.1469 221.708 m F 0 G 0.3 w 10 M 393.1469 221.708 m S 0 g 1 w 4 M 393.1469 221.708 m F 0 G 0.3 w 10 M 393.1469 221.708 m S 393.1469 221.708 m S 433.0643 195.7748 m S 0 g 1 w 4 M 433.0643 195.7748 m F 0 G 0.3 w 10 M 459.6759 195.7748 m S 0 g 1 w 4 M 459.6759 195.7748 m F 0 G 0.3 w 10 M 486.2875 195.7748 m S 0 g 1 w 4 M 486.2875 195.7748 m F 0 G 0.3 w 10 M 512.8992 195.7748 m S 0 g 1 w 4 M 512.8992 195.7748 m F 0 G 0.3 w 10 M 406.4527 182.8083 m S 419.7585 182.8083 m S 406.4527 182.8083 m S 419.7585 182.8083 m S 406.4527 182.8083 m S 433.0643 182.8083 m S 419.7585 182.8083 m S 433.0643 182.8083 m S 419.7585 182.8083 m S 406.4527 182.8083 m S 446.3701 182.8083 m S 433.0643 182.8083 m S 459.6759 182.8083 m S 446.3701 182.8083 m S 459.6759 182.8083 m S 446.3701 182.8083 m S 472.9817 182.8083 m S 459.6759 182.8083 m S 472.9817 182.8083 m S 459.6759 182.8083 m S 446.3701 182.8083 m S 433.0643 182.8083 m S 486.2875 182.8083 m S 472.9817 182.8083 m S 499.5933 182.8083 m S 486.2875 182.8083 m S 499.5933 182.8083 m S 486.2875 182.8083 m S 512.8992 182.8083 m S 499.5933 182.8083 m S 512.8992 182.8083 m S 499.5933 182.8083 m S 486.2875 182.8083 m S 472.9817 182.8083 m S 512.8992 182.8083 m S 512.8992 182.8083 m S 406.4527 182.8083 m S 1 g 1 w 4 M 406.4527 178 m 409.2644 178 411.5438 180.1528 411.5438 182.8083 c 411.5438 185.4638 409.2644 187.6166 406.4527 187.6166 c 403.641 187.6166 401.3616 185.4638 401.3616 182.8083 c 401.3616 180.1528 403.641 178 406.4527 178 c b 0 g 406.4527 182.8083 m F 0 G 0.3 w 10 M 419.7585 182.8083 m S 0 g 1 w 4 M 419.7585 182.8083 m F 0 G 0.3 w 10 M 433.0643 182.8083 m S 1 g 1 w 4 M 433.0643 178 m 435.876 178 438.1554 180.1528 438.1554 182.8083 c 438.1554 185.4638 435.876 187.6166 433.0643 187.6166 c 430.2527 187.6166 427.9732 185.4638 427.9732 182.8083 c 427.9732 180.1528 430.2527 178 433.0643 178 c b 0 g 433.0643 182.8083 m F 0 G 0.3 w 10 M 446.3701 182.8083 m S 0 g 1 w 4 M 446.3701 182.8083 m F 0 G 0.3 w 10 M 459.6759 182.8083 m S 1 g 1 w 4 M 459.6759 178 m 462.4877 178 464.767 180.1528 464.767 182.8083 c 464.767 185.4638 462.4877 187.6166 459.6759 187.6166 c 456.8642 187.6166 454.5848 185.4638 454.5848 182.8083 c 454.5848 180.1528 456.8642 178 459.6759 178 c b 0 g 459.6759 182.8083 m F 0 G 0.3 w 10 M 472.9817 182.8083 m S 0 g 1 w 4 M 472.9817 182.8083 m F 0 G 0.3 w 10 M 486.2875 182.8083 m S 1 g 1 w 4 M 486.2875 178 m 489.0992 178 491.3786 180.1528 491.3786 182.8083 c 491.3786 185.4638 489.0992 187.6166 486.2875 187.6166 c 483.4758 187.6166 481.1964 185.4638 481.1964 182.8083 c 481.1964 180.1528 483.4758 178 486.2875 178 c b 0 g 486.2875 182.8083 m F 0 G 0.3 w 10 M 499.5933 182.8083 m S 0 g 1 w 4 M 499.5933 182.8083 m F 0 G 0.3 w 10 M 512.8992 182.8083 m S 1 g 1 w 4 M 512.8992 178 m 515.7108 178 517.9902 180.1528 517.9902 182.8083 c 517.9902 185.4638 515.7108 187.6166 512.8992 187.6166 c 510.0874 187.6166 507.808 185.4638 507.808 182.8083 c 507.808 180.1528 510.0874 178 512.8992 178 c b 0 g 512.8992 182.8083 m F 0 G 0.3 w 10 M 406.4527 156.8751 m S 419.7585 156.8751 m S 406.4527 156.8751 m S 419.7585 156.8751 m S 406.4527 156.8751 m S 433.0643 156.8751 m S 419.7585 156.8751 m S 433.0643 156.8751 m S 419.7585 156.8751 m S 406.4527 156.8751 m S 446.3701 156.8751 m S 433.0643 156.8751 m S 459.6759 156.8751 m S 446.3701 156.8751 m S 459.6759 156.8751 m S 446.3701 156.8751 m S 472.9817 156.8751 m S 459.6759 156.8751 m S 472.9817 156.8751 m S 459.6759 156.8751 m S 446.3701 156.8751 m S 433.0643 156.8751 m S 486.2875 156.8751 m S 472.9817 156.8751 m S 499.5933 156.8751 m S 486.2875 156.8751 m S 499.5933 156.8751 m S 486.2875 156.8751 m S 512.8992 156.8751 m S 499.5933 156.8751 m S 512.8992 156.8751 m S 499.5933 156.8751 m S 486.2875 156.8751 m S 472.9817 156.8751 m S 512.8992 156.8751 m S 512.8992 156.8751 m S 406.4527 156.8751 m S 0 g 1 w 4 M 406.4527 156.8751 m F 0 G 0.3 w 10 M 419.7585 156.8751 m S 0 g 1 w 4 M 419.7585 156.8751 m F 0 G 0.3 w 10 M 433.0643 156.8751 m S 0 g 1 w 4 M 433.0643 156.8751 m F 0 G 0.3 w 10 M 446.3701 156.8751 m S 0 g 1 w 4 M 446.3701 156.8751 m F 0 G 0.3 w 10 M 459.6759 156.8751 m S 0 g 1 w 4 M 459.6759 156.8751 m F 0 G 0.3 w 10 M 472.9817 156.8751 m S 0 g 1 w 4 M 472.9817 156.8751 m F 0 G 0.3 w 10 M 486.2875 156.8751 m S 0 g 1 w 4 M 486.2875 156.8751 m F 0 G 0.3 w 10 M 499.5933 156.8751 m S 0 g 1 w 4 M 499.5933 156.8751 m F 0 G 0.3 w 10 M 512.8992 156.8751 m S 0 g 1 w 4 M 512.8992 156.8751 m F 0 G 0.3 w 10 M 406.4527 156.8751 m S 419.7585 156.8751 m S 406.4527 156.8751 m S 419.7585 156.8751 m S 406.4527 156.8751 m S 433.0643 156.8751 m S 419.7585 156.8751 m S 433.0643 156.8751 m S 419.7585 156.8751 m S 406.4527 156.8751 m S 446.3701 156.8751 m S 433.0643 156.8751 m S 459.6759 156.8751 m S 446.3701 156.8751 m S 459.6759 156.8751 m S 446.3701 156.8751 m S 472.9817 156.8751 m S 459.6759 156.8751 m S 472.9817 156.8751 m S 459.6759 156.8751 m S 446.3701 156.8751 m S 433.0643 156.8751 m S 486.2875 156.8751 m S 472.9817 156.8751 m S 499.5933 156.8751 m S 486.2875 156.8751 m S 499.5933 156.8751 m S 486.2875 156.8751 m S 512.8992 156.8751 m S 499.5933 156.8751 m S 512.8992 156.8751 m S 499.5933 156.8751 m S 486.2875 156.8751 m S 472.9817 156.8751 m S 512.8992 156.8751 m S 512.8992 156.8751 m S 406.4527 156.8751 m S 1 g 1 w 4 M 406.4527 152.0668 m 409.2644 152.0668 411.5438 154.2196 411.5438 156.8751 c 411.5438 159.5306 409.2644 161.6834 406.4527 161.6834 c 403.641 161.6834 401.3616 159.5306 401.3616 156.8751 c 401.3616 154.2196 403.641 152.0668 406.4527 152.0668 c b 0 g 406.4527 156.8751 m F 0 G 0.3 w 10 M 419.7585 156.8751 m S 0 g 1 w 4 M 419.7585 156.8751 m F 0 G 0.3 w 10 M 433.0643 156.8751 m S 1 g 1 w 4 M 433.0643 152.0668 m 435.876 152.0668 438.1554 154.2196 438.1554 156.8751 c 438.1554 159.5306 435.876 161.6834 433.0643 161.6834 c 430.2527 161.6834 427.9732 159.5306 427.9732 156.8751 c 427.9732 154.2196 430.2527 152.0668 433.0643 152.0668 c b 0 g 433.0643 156.8751 m F 0 G 0.3 w 10 M 446.3701 156.8751 m S 0 g 1 w 4 M 446.3701 156.8751 m F 0 G 0.3 w 10 M 459.6759 156.8751 m S 1 g 1 w 4 M 459.6759 152.0668 m 462.4877 152.0668 464.767 154.2196 464.767 156.8751 c 464.767 159.5306 462.4877 161.6834 459.6759 161.6834 c 456.8642 161.6834 454.5848 159.5306 454.5848 156.8751 c 454.5848 154.2196 456.8642 152.0668 459.6759 152.0668 c b 0 g 459.6759 156.8751 m F 0 G 0.3 w 10 M 472.9817 156.8751 m S 0 g 1 w 4 M 472.9817 156.8751 m F 0 G 0.3 w 10 M 486.2875 156.8751 m S 1 g 1 w 4 M 486.2875 152.0668 m 489.0992 152.0668 491.3786 154.2196 491.3786 156.8751 c 491.3786 159.5306 489.0992 161.6834 486.2875 161.6834 c 483.4758 161.6834 481.1964 159.5306 481.1964 156.8751 c 481.1964 154.2196 483.4758 152.0668 486.2875 152.0668 c b 0 g 486.2875 156.8751 m F 0 G 0.3 w 10 M 499.5933 156.8751 m S 0 g 1 w 4 M 499.5933 156.8751 m F 0 G 0.3 w 10 M 512.8992 156.8751 m S 1 g 1 w 4 M 512.8992 152.0668 m 515.7108 152.0668 517.9902 154.2196 517.9902 156.8751 c 517.9902 159.5306 515.7108 161.6834 512.8992 161.6834 c 510.0874 161.6834 507.808 159.5306 507.808 156.8751 c 507.808 154.2196 510.0874 152.0668 512.8992 152.0668 c b 0 g 512.8992 156.8751 m F 0 G 0.3 w 10 M 406.4527 130.9419 m S 419.7585 130.9419 m S 406.4527 130.9419 m S 419.7585 130.9419 m S 406.4527 130.9419 m S 433.0643 130.9419 m S 419.7585 130.9419 m S 433.0643 130.9419 m S 419.7585 130.9419 m S 406.4527 130.9419 m S 446.3701 130.9419 m S 433.0643 130.9419 m S 459.6759 130.9419 m S 446.3701 130.9419 m S 459.6759 130.9419 m S 446.3701 130.9419 m S 472.9817 130.9419 m S 459.6759 130.9419 m S 472.9817 130.9419 m S 459.6759 130.9419 m S 446.3701 130.9419 m S 433.0643 130.9419 m S 486.2875 130.9419 m S 472.9817 130.9419 m S 499.5933 130.9419 m S 486.2875 130.9419 m S 499.5933 130.9419 m S 486.2875 130.9419 m S 512.8992 130.9419 m S 499.5933 130.9419 m S 512.8992 130.9419 m S 499.5933 130.9419 m S 486.2875 130.9419 m S 472.9817 130.9419 m S 512.8992 130.9419 m S 512.8992 130.9419 m S 406.4527 130.9419 m S 1 g 1 w 4 M 406.4527 126.1336 m 409.2644 126.1336 411.5438 128.2864 411.5438 130.9419 c 411.5438 133.5974 409.2644 135.7502 406.4527 135.7502 c 403.641 135.7502 401.3616 133.5974 401.3616 130.9419 c 401.3616 128.2864 403.641 126.1336 406.4527 126.1336 c b 0 g 406.4527 130.9419 m F 0 G 0.3 w 10 M 419.7585 130.9419 m S 0 g 1 w 4 M 419.7585 130.9419 m F 0 G 0.3 w 10 M 433.0643 130.9419 m S 1 g 1 w 4 M 433.0643 126.1336 m 435.876 126.1336 438.1554 128.2864 438.1554 130.9419 c 438.1554 133.5974 435.876 135.7502 433.0643 135.7502 c 430.2527 135.7502 427.9732 133.5974 427.9732 130.9419 c 427.9732 128.2864 430.2527 126.1336 433.0643 126.1336 c b 0 g 433.0643 130.9419 m F 0 G 0.3 w 10 M 446.3701 130.9419 m S 0 g 1 w 4 M 446.3701 130.9419 m F 0 G 0.3 w 10 M 459.6759 130.9419 m S 1 g 1 w 4 M 459.6759 126.1336 m 462.4877 126.1336 464.767 128.2864 464.767 130.9419 c 464.767 133.5974 462.4877 135.7502 459.6759 135.7502 c 456.8642 135.7502 454.5848 133.5974 454.5848 130.9419 c 454.5848 128.2864 456.8642 126.1336 459.6759 126.1336 c b 0 g 459.6759 130.9419 m F 0 G 0.3 w 10 M 472.9817 130.9419 m S 0 g 1 w 4 M 472.9817 130.9419 m F 0 G 0.3 w 10 M 486.2875 130.9419 m S 1 g 1 w 4 M 486.2875 126.1336 m 489.0992 126.1336 491.3786 128.2864 491.3786 130.9419 c 491.3786 133.5974 489.0992 135.7502 486.2875 135.7502 c 483.4758 135.7502 481.1964 133.5974 481.1964 130.9419 c 481.1964 128.2864 483.4758 126.1336 486.2875 126.1336 c b 0 g 486.2875 130.9419 m F 0 G 0.3 w 10 M 499.5933 130.9419 m S 0 g 1 w 4 M 499.5933 130.9419 m F 0 G 0.3 w 10 M 512.8992 130.9419 m S 1 g 1 w 4 M 512.8992 126.1336 m 515.7108 126.1336 517.9902 128.2864 517.9902 130.9419 c 517.9902 133.5974 515.7108 135.7502 512.8992 135.7502 c 510.0874 135.7502 507.808 133.5974 507.808 130.9419 c 507.808 128.2864 510.0874 126.1336 512.8992 126.1336 c b 0 g 512.8992 130.9419 m F 0 G 0.3 w 10 M 512.8992 169.8417 m S 0 g 1 w 4 M 512.8992 169.8417 m F 0 G 0.3 w 10 M 486.2875 169.8417 m S 0 g 1 w 4 M 486.2875 169.8417 m F 0 G 0.3 w 10 M 512.8992 143.9085 m S 0 g 1 w 4 M 512.8992 143.9085 m F 0 G 0.3 w 10 M 486.2875 143.9085 m S 0 g 1 w 4 M 486.2875 143.9085 m F 0 G 0.3 w 10 M 433.0643 169.8417 m S 0 g 1 w 4 M 433.0643 169.8417 m F 0 G 0.3 w 10 M 406.4527 169.8417 m S 0 g 1 w 4 M 406.4527 169.8417 m F 0 G 0.3 w 10 M 406.4527 143.9085 m S 0 g 1 w 4 M 406.4527 143.9085 m F 0 G 0.3 w 10 M 433.0643 143.9085 m S 0 g 1 w 4 M 433.0643 143.9085 m F 0 G 0.3 w 10 M 459.6759 143.9085 m S 0 g 1 w 4 M 459.6759 143.9085 m F 0 G 0.3 w 10 M 459.6759 169.8417 m S 0 g 1 w 4 M 459.6759 169.8417 m F 0 G 0.3 w 10 M 406.4527 105.0087 m S 419.7585 105.0087 m S 406.4527 105.0087 m S 419.7585 105.0087 m S 406.4527 105.0087 m S 433.0643 105.0087 m S 419.7585 105.0087 m S 433.0643 105.0087 m S 419.7585 105.0087 m S 406.4527 105.0087 m S 446.3701 105.0087 m S 433.0643 105.0087 m S 459.6759 105.0087 m S 446.3701 105.0087 m S 459.6759 105.0087 m S 446.3701 105.0087 m S 472.9817 105.0087 m S 459.6759 105.0087 m S 472.9817 105.0087 m S 459.6759 105.0087 m S 446.3701 105.0087 m S 433.0643 105.0087 m S 486.2875 105.0087 m S 472.9817 105.0087 m S 499.5933 105.0087 m S 486.2875 105.0087 m S 499.5933 105.0087 m S 486.2875 105.0087 m S 512.8992 105.0087 m S 499.5933 105.0087 m S 512.8992 105.0087 m S 499.5933 105.0087 m S 486.2875 105.0087 m S 472.9817 105.0087 m S 512.8992 105.0087 m S 512.8992 105.0087 m S 406.4527 105.0087 m S 419.7585 105.0087 m S 406.4527 105.0087 m S 419.7585 105.0087 m S 406.4527 105.0087 m S 433.0643 105.0087 m S 419.7585 105.0087 m S 433.0643 105.0087 m S 419.7585 105.0087 m S 406.4527 105.0087 m S 446.3701 105.0087 m S 433.0643 105.0087 m S 459.6759 105.0087 m S 446.3701 105.0087 m S 459.6759 105.0087 m S 446.3701 105.0087 m S 472.9817 105.0087 m S 459.6759 105.0087 m S 472.9817 105.0087 m S 459.6759 105.0087 m S 446.3701 105.0087 m S 433.0643 105.0087 m S 486.2875 105.0087 m S 472.9817 105.0087 m S 499.5933 105.0087 m S 486.2875 105.0087 m S 499.5933 105.0087 m S 486.2875 105.0087 m S 512.8992 105.0087 m S 499.5933 105.0087 m S 512.8992 105.0087 m S 499.5933 105.0087 m S 486.2875 105.0087 m S 472.9817 105.0087 m S 512.8992 105.0087 m S 512.8992 105.0087 m S 406.4527 105.0087 m S 1 g 1 w 4 M 406.4527 100.2004 m 409.2644 100.2004 411.5438 102.3532 411.5438 105.0087 c 411.5438 107.6642 409.2644 109.817 406.4527 109.817 c 403.641 109.817 401.3616 107.6642 401.3616 105.0087 c 401.3616 102.3532 403.641 100.2004 406.4527 100.2004 c b 0 g 406.4527 105.0087 m F 0 G 0.3 w 10 M 419.7585 105.0087 m S 0 g 1 w 4 M 419.7585 105.0087 m F 0 G 0.3 w 10 M 433.0643 105.0087 m S 1 g 1 w 4 M 433.0643 100.2004 m 435.876 100.2004 438.1554 102.3532 438.1554 105.0087 c 438.1554 107.6642 435.876 109.817 433.0643 109.817 c 430.2527 109.817 427.9732 107.6642 427.9732 105.0087 c 427.9732 102.3532 430.2527 100.2004 433.0643 100.2004 c b 0 g 433.0643 105.0087 m F 0 G 0.3 w 10 M 446.3701 105.0087 m S 0 g 1 w 4 M 446.3701 105.0087 m F 0 G 0.3 w 10 M 459.6759 105.0087 m S 1 g 1 w 4 M 459.6759 100.2004 m 462.4877 100.2004 464.767 102.3532 464.767 105.0087 c 464.767 107.6642 462.4877 109.817 459.6759 109.817 c 456.8642 109.817 454.5848 107.6642 454.5848 105.0087 c 454.5848 102.3532 456.8642 100.2004 459.6759 100.2004 c b 0 g 459.6759 105.0087 m F 0 G 0.3 w 10 M 472.9817 105.0087 m S 0 g 1 w 4 M 472.9817 105.0087 m F 0 G 0.3 w 10 M 486.2875 105.0087 m S 1 g 1 w 4 M 486.2875 100.2004 m 489.0992 100.2004 491.3786 102.3532 491.3786 105.0087 c 491.3786 107.6642 489.0992 109.817 486.2875 109.817 c 483.4758 109.817 481.1964 107.6642 481.1964 105.0087 c 481.1964 102.3532 483.4758 100.2004 486.2875 100.2004 c b 0 g 486.2875 105.0087 m F 0 G 0.3 w 10 M 499.5933 105.0087 m S 0 g 1 w 4 M 499.5933 105.0087 m F 0 G 0.3 w 10 M 512.8992 105.0087 m S 1 g 1 w 4 M 512.8992 100.2004 m 515.7108 100.2004 517.9902 102.3532 517.9902 105.0087 c 517.9902 107.6642 515.7108 109.817 512.8992 109.817 c 510.0874 109.817 507.808 107.6642 507.808 105.0087 c 507.808 102.3532 510.0874 100.2004 512.8992 100.2004 c b 0 g 512.8992 105.0087 m F 0 G 0.3 w 10 M 406.4527 117.9753 m S 406.4527 117.9753 m S 406.4527 117.9753 m S 433.0643 117.9753 m S 433.0643 117.9753 m S 406.4527 117.9753 m S 433.0643 117.9753 m S 459.6759 117.9753 m S 459.6759 117.9753 m S 459.6759 117.9753 m S 459.6759 117.9753 m S 433.0643 117.9753 m S 486.2875 117.9753 m S 486.2875 117.9753 m S 486.2875 117.9753 m S 512.8992 117.9753 m S 512.8992 117.9753 m S 486.2875 117.9753 m S 512.8992 117.9753 m S 512.8992 117.9753 m S 512.8992 117.9753 m S 0 g 1 w 4 M 512.8992 117.9753 m F 0 G 0.3 w 10 M 486.2875 117.9753 m S 0 g 1 w 4 M 486.2875 117.9753 m F 0 G 0.3 w 10 M 433.0643 117.9753 m S 0 g 1 w 4 M 433.0643 117.9753 m F 0 G 0.3 w 10 M 406.4527 117.9753 m S 0 g 1 w 4 M 406.4527 117.9753 m F 0 G 0.3 w 10 M 459.6759 117.9753 m S 0 g 1 w 4 M 459.6759 117.9753 m F 0 G 0.3 w 10 M 460.1018 104.0842 m S 460.1018 104.0842 m S 532.8578 85.5588 m S 460.1018 104.0842 m S 0 g 1 w 4 M 460.1018 104.0842 m F 0 G 0.3 w 10 M 366.5353 208.7413 m S 366.5353 221.7079 m S 373.1882 215.2246 m S 406.4527 195.7747 m S 406.4527 182.8082 m S 386.494 189.2915 m S 373.1882 202.2581 m S 393.1469 221.7079 m S 373.1882 215.2246 m S 373.1882 189.2915 m S 366.5353 182.8082 m S 366.5353 195.7747 m S 373.1882 189.2915 m S 366.5353 195.7747 m S 366.5353 208.7413 m S 373.1882 202.2581 m S 0 g 1 w 4 M 373.1882 215.2246 m F 373.1882 189.2915 m F 0 G 0.3 w 10 M 366.5353 169.8416 m S 366.5353 182.8082 m S 373.1882 176.3249 m S 406.4527 156.875 m S 406.4527 143.9084 m S 386.494 150.3917 m S 373.1882 163.3583 m S 373.1882 176.3249 m S 406.4527 182.8082 m S 406.4527 169.8416 m S 386.494 176.3249 m S 373.1882 150.3917 m S 366.5353 143.9084 m S 366.5353 156.875 m S 373.1882 150.3917 m S 366.5353 156.875 m S 366.5353 169.8416 m S 373.1882 163.3583 m S 0 g 1 w 4 M 373.1882 176.3249 m F 373.1882 150.3917 m F 373.1882 137.4251 m F 0 G 0.3 w 10 M 366.5353 130.9418 m S 366.5353 143.9084 m S 373.1882 137.4251 m S 373.1882 124.4585 m S 373.1882 137.4251 m S 373.1882 111.4919 m S 366.5353 105.0086 m S 366.5353 117.9752 m S 373.1882 111.4919 m S 366.5353 117.9752 m S 366.5353 130.9418 m S 373.1882 124.4585 m S 0 g 1 w 4 M 373.1882 137.4251 m F 373.1882 111.4919 m F 0 G 0.3 w 10 M 366.5353 92.042 m S 366.5353 105.0086 m S 373.1882 98.5253 m S 393.1469 66.1089 m S 386.494 85.5587 m S 373.1882 98.5253 m S 393.1469 66.1089 m S 379.8411 66.1089 m S 386.494 72.5921 m S 379.8411 66.1089 m S 366.5353 66.1089 m S 366.5353 79.0754 m S 373.1882 72.5921 m S 366.5353 79.0754 m S 366.5353 92.042 m S 373.1882 85.5587 m S 0 g 1 w 4 M 373.1882 98.5253 m F 373.1882 72.5921 m F 0 G 0.3 w 10 M 393.1469 221.7079 m S 379.8411 234.6744 m S 393.1469 221.7079 m S 379.8411 234.6744 m S 386.494 228.1912 m S 379.8411 234.6744 m S 366.5353 221.7079 m S 366.5353 234.6744 m S 373.1882 228.1912 m S 379.8411 234.6744 m S 366.5353 234.6744 m S 373.1882 241.1578 m S 439.7172 241.1577 m S 426.4114 241.1577 m S 466.3288 241.1577 m S 453.023 241.1577 m S 532.8578 228.1913 m S 552.8166 234.6745 m S 546.1637 241.1578 m S 552.8166 234.6745 m S 552.8166 221.7079 m S 546.1637 228.1913 m S 0 g 1 w 4 M 546.1637 241.1578 m F 0 G 0.3 w 10 M 366.6603 157.0124 m S 366.6603 169.979 m S 373.3132 163.4957 m S 373.3132 150.5292 m S 373.3132 163.4957 m S 373.3132 137.5626 m S 366.6603 131.0793 m S 366.6603 144.0458 m S 373.3132 137.5626 m S 366.6603 144.0458 m S 366.6603 157.0124 m S 373.3132 150.5292 m S 366.6603 118.1127 m S 366.6603 131.0793 m S 373.3132 124.596 m S 373.3132 124.596 m S 366.6603 169.979 m S 366.6603 182.9455 m S 373.3132 176.4623 m S 366.6603 105.146 m S 366.6603 118.1126 m S 373.3132 111.6293 m S 373.3132 98.6628 m S 373.3132 111.6293 m S 386.619 85.6962 m S 366.6603 79.2129 m S 366.6603 92.1794 m S 373.3132 85.6962 m S 366.6603 92.1794 m S 366.6603 105.146 m S 373.3132 98.6628 m S 379.9661 66.2463 m S 366.6603 66.2463 m S 366.6603 79.2129 m S 373.3132 72.7296 m S 393.2719 66.2463 m S 379.9661 66.2463 m S 386.619 72.7296 m S 366.6603 118.1126 m S 366.6603 131.0791 m S 373.3132 124.5959 m S 532.9203 228.229 m S 552.879 234.7123 m S 552.879 221.7457 m S 546.2261 228.229 m S 1 w 4 M 369.218 208.7235 m 371.665 230.153 375.5962 244.0491 380.0286 244.0491 c S 380.0286 70.1008 m 372.6088 70.1008 366.5936 109.0412 366.5936 157.0749 c 366.5936 176.4146 367.5687 194.2801 369.218 208.7235 c S 539.3815 243.8369 m 546.8014 243.8369 552.8165 204.8965 552.8165 156.8627 c 552.8165 108.8289 546.8014 69.8886 539.3815 69.8886 c S u u 0 g /_Times-Italic 36 43 0 0 z [1 0 0 1 326.621 150.9662]e (m)t T U U 0 G 0.3 w 10 M 406.4527 208.7414 m S 419.7585 208.7414 m S 406.4527 208.7414 m S 419.7585 208.7414 m S 406.4527 208.7414 m S 433.0643 208.7414 m S 419.7585 208.7414 m S 433.0643 208.7414 m S 419.7585 208.7414 m S 406.4527 208.7414 m S 446.3701 208.7414 m S 433.0643 208.7414 m S 459.6759 208.7414 m S 446.3701 208.7414 m S 459.6759 208.7414 m S 446.3701 208.7414 m S 472.9817 208.7414 m S 459.6759 208.7414 m S 472.9817 208.7414 m S 459.6759 208.7414 m S 446.3701 208.7414 m S 433.0643 208.7414 m S 486.2875 208.7414 m S 472.9817 208.7414 m S 499.5933 208.7414 m S 486.2875 208.7414 m S 499.5933 208.7414 m S 486.2875 208.7414 m S 512.8992 208.7414 m S 499.5933 208.7414 m S 512.8992 208.7414 m S 499.5933 208.7414 m S 486.2875 208.7414 m S 472.9817 208.7414 m S 512.8992 208.7414 m S 512.8992 208.7414 m S 406.4527 208.7414 m S 1 g 1 w 4 M 406.4527 203.9331 m 409.2644 203.9331 411.5438 206.0859 411.5438 208.7414 c 411.5438 211.3969 409.2644 213.5497 406.4527 213.5497 c 403.641 213.5497 401.3616 211.3969 401.3616 208.7414 c 401.3616 206.0859 403.641 203.9331 406.4527 203.9331 c b 0 g 406.4527 208.7414 m F 0 G 0.3 w 10 M 419.7585 208.7414 m S 0 g 1 w 4 M 419.7585 208.7414 m F 0 G 0.3 w 10 M 433.0643 208.7414 m S 1 g 1 w 4 M 433.0643 203.9331 m 435.876 203.9331 438.1554 206.0859 438.1554 208.7414 c 438.1554 211.3969 435.876 213.5497 433.0643 213.5497 c 430.2527 213.5497 427.9732 211.3969 427.9732 208.7414 c 427.9732 206.0859 430.2527 203.9331 433.0643 203.9331 c b 0 g 433.0643 208.7414 m F 0 G 0.3 w 10 M 446.3701 208.7414 m S 0 g 1 w 4 M 446.3701 208.7414 m F 0 G 0.3 w 10 M 459.6759 208.7414 m S 1 g 1 w 4 M 459.6759 203.9331 m 462.4877 203.9331 464.767 206.0859 464.767 208.7414 c 464.767 211.3969 462.4877 213.5497 459.6759 213.5497 c 456.8642 213.5497 454.5848 211.3969 454.5848 208.7414 c 454.5848 206.0859 456.8642 203.9331 459.6759 203.9331 c b 0 g 459.6759 208.7414 m F 0 G 0.3 w 10 M 472.9817 208.7414 m S 0 g 1 w 4 M 472.9817 208.7414 m F 0 G 0.3 w 10 M 486.2875 208.7414 m S 1 g 1 w 4 M 486.2875 203.9331 m 489.0992 203.9331 491.3786 206.0859 491.3786 208.7414 c 491.3786 211.3969 489.0992 213.5497 486.2875 213.5497 c 483.4758 213.5497 481.1964 211.3969 481.1964 208.7414 c 481.1964 206.0859 483.4758 203.9331 486.2875 203.9331 c b 0 g 486.2875 208.7414 m F 0 G 0.3 w 10 M 499.5933 208.7414 m S 0 g 1 w 4 M 499.5933 208.7414 m F 0 G 0.3 w 10 M 512.8992 208.7414 m S 1 g 1 w 4 M 512.8992 203.9331 m 515.7108 203.9331 517.9902 206.0859 517.9902 208.7414 c 517.9902 211.3969 515.7108 213.5497 512.8992 213.5497 c 510.0874 213.5497 507.808 211.3969 507.808 208.7414 c 507.808 206.0859 510.0874 203.9331 512.8992 203.9331 c b 0 g 512.8992 208.7414 m F 0 G 0.3 w 10 M 406.4527 208.7413 m S 406.4527 208.7413 m S 419.6335 195.6374 m S 0 g 1 w 4 M 419.6335 195.6374 m F 0 G 0.3 w 10 M 419.6335 195.6374 m S 419.6335 195.6374 m S 419.6335 195.6374 m S 0 g 1 w 4 M 419.6335 195.6374 m F 0 G 0.3 w 10 M 419.6335 195.6374 m S 419.6335 195.6374 m S 1 g 1 w 4 M 419.6335 195.6374 m F 0 G 0.3 w 10 M 419.6335 195.6374 m S 0 g 1 w 4 M 419.6335 195.6374 m F 0 G 0.3 w 10 M 419.6335 195.6374 m S 419.6335 195.6374 m S 512.7742 195.6374 m S 0 g 1 w 4 M 512.7742 195.6374 m F 0 G 0.3 w 10 M 486.1625 195.6374 m S 0 g 1 w 4 M 486.1625 195.6374 m F 0 G 0.3 w 10 M 406.3277 195.6374 m S 0 g 1 w 4 M 406.3277 195.6374 m F 0 G 0.3 w 10 M 432.9393 195.6374 m S 0 g 1 w 4 M 432.9393 195.6374 m F 0 G 0.3 w 10 M 459.5509 195.6374 m S 0 g 1 w 4 M 459.5509 195.6374 m F 0 G 0.3 w 10 M 406.3277 195.6373 m S 373.1882 189.2915 m S 0.4 G 1 w 4 M 412.8556 64.809 m S 506.2462 64.809 m S u u 0 g /_Symbol 36 43 0 2 z [1 0 0 1 318 149.5]e (\256)t T U U 0 G 0.3 w 10 M 168.023 214.2246 m S 181.3288 214.2246 m S 1 w 4 M 174.6759 212.5497 m 174.7232 226.4084 l S u 0 g 0.3 w 1 M 172.8911 218.341 m 174.6759 212.5497 L 176.2157 218.411 L 172.8911 218.341 L b U u u 1 w 4 M /_Times-Roman 12 14.5 0 2 z [1 0 0 1 160 44]e (\(d\))t T U U u u /_Times-Roman 12 14.5 0 2 z [1 0 0 1 443.5 43]e (\(e\))t T U U 0 G 0.3 w 10 M 539.5106 221.708 m S 0 g 1 w 4 M 539.5106 221.708 m F 0 G 0.3 w 10 M 539.5106 221.708 m S 539.5106 221.708 m S 539.5106 221.708 m S 0 g 1 w 4 M 539.5106 221.708 m F 0 G 0.3 w 10 M 539.5106 221.708 m S 539.5106 221.708 m S 1 g 1 w 4 M 539.5106 221.708 m F 0 G 0.3 w 10 M 539.5106 221.708 m S 0 g 1 w 4 M 539.5106 221.708 m F 0 G 0.3 w 10 M 539.5106 221.708 m S 539.5106 221.708 m S 406.4527 234.6745 m S 0 g 1 w 4 M 406.4527 234.6745 m F 0 G 0.3 w 10 M 406.4527 234.6745 m S 406.4527 234.6745 m S 406.4527 234.6745 m S 0 g 1 w 4 M 406.4527 234.6745 m F 0 G 0.3 w 10 M 406.4527 234.6745 m S 406.4527 234.6745 m S 1 g 1 w 4 M 400.4423 234.6745 m 400.4423 231.4527 403.1333 228.8409 406.4527 228.8409 c 409.7722 228.8409 412.4631 231.4527 412.4631 234.6745 c F 412.4631 234.6745 m 412.4631 237.8963 409.7722 240.5082 406.4527 240.5082 c 403.1333 240.5082 400.4423 237.8963 400.4423 234.6745 c F 406.4527 234.6745 m F 0 G 0.3 w 10 M 406.4527 234.6745 m S 0 g 1 w 4 M 406.4527 234.6745 m F 0 G 0.3 w 10 M 406.4527 234.6745 m S 406.4527 234.6745 m S 0 g 1 w 4 M 405.3676 233.6066 m 405.3676 230.0295 L 407.5378 230.0295 L 407.5378 233.6066 L 411.1234 233.5954 L 411.1234 235.7538 L 407.5378 235.7427 L 407.5378 239.3198 L 405.3676 239.3198 L 405.3676 235.7427 L 401.782 235.7538 L 401.782 233.5954 L 405.3676 233.6066 L f 0 G 0.3 w 10 M 419.7585 234.6745 m S 0 g 1 w 4 M 419.7585 234.6745 m F 0 G 0.3 w 10 M 446.3701 234.6745 m S 0 g 1 w 4 M 446.3701 234.6745 m F 0 G 0.3 w 10 M 406.4527 208.7414 m S 0 g 1 w 4 M 406.4527 208.7414 m F 0 G 0.3 w 10 M 499.5933 234.6745 m S 0 g 1 w 4 M 499.5933 234.6745 m F 0 G 0.3 w 10 M 526.205 221.708 m S 0 g 1 w 4 M 526.205 221.708 m F 0 G 0.3 w 10 M 472.9817 234.6745 m S 0 g 1 w 4 M 472.9817 234.6745 m F u 0 G 0.3 w 10 M 393.1469 208.7413 m S 393.1469 195.7747 m S 379.8411 195.7747 m S 379.8411 208.7413 m S 386.494 202.2581 m S U u 393.1469 221.7079 m S 393.1469 208.7413 m S 379.8411 208.7413 m S 379.8411 221.7079 m S 386.494 215.2246 m S U u 419.7585 234.6744 m S 419.7585 221.7078 m S 406.4527 221.7078 m S 406.4527 234.6744 m S 413.1056 228.1911 m S U u 419.7585 208.7413 m S 419.7585 195.7747 m S 406.4527 195.7747 m S 406.4527 208.7413 m S 413.1056 202.2581 m S U 419.7585 234.6744 m S 406.4527 234.6744 m S 413.1056 241.1577 m S 406.4527 234.6744 m S 399.7998 241.1577 m S 459.6759 234.6744 m S 446.3701 234.6744 m S 453.023 241.1577 m S 446.3701 234.6744 m S 433.0643 234.6744 m S 439.7172 241.1577 m S 433.0643 234.6744 m S 419.7585 234.6744 m S 426.4114 241.1577 m S u 499.5933 247.6409 m S 499.5933 234.6744 m S 486.2875 234.6744 m S 486.2875 247.6409 m S 492.9404 241.1577 m S U 486.2875 234.6744 m S 472.9817 234.6744 m S 479.6346 241.1577 m S 472.9817 234.6744 m S 459.6759 234.6744 m S 466.3288 241.1577 m S u 539.5107 234.6744 m S 539.5107 221.7079 m S 526.2049 221.7079 m S 526.2049 234.6744 m S 532.8578 228.1912 m S U u 526.2049 247.6409 m S 526.2049 234.6744 m S 512.899 234.6744 m S 512.899 247.6409 m S 519.5519 241.1577 m S U u 512.899 247.6409 m S 512.899 234.6744 m S 499.5933 234.6744 m S 499.5933 247.6409 m S 506.2461 241.1577 m S U 539.5107 221.7079 m S 546.1636 228.1913 m S u 552.8166 221.7079 m S 552.8166 208.7415 m S 539.5107 208.7415 m S 539.5107 221.7079 m S 546.1636 215.2247 m S U u 552.6915 221.5705 m S 552.6915 208.6041 m S 539.3858 208.6041 m S 539.3858 221.5705 m S 546.0386 215.0873 m S U u 539.5107 234.6745 m S 539.5107 221.7079 m S 526.205 221.7079 m S 526.205 234.6745 m S 532.8578 228.1913 m S U 539.5732 221.7457 m S 546.2261 228.229 m S u 552.879 208.7791 m S 552.879 195.8126 m S 539.5732 195.8126 m S 539.5732 208.7791 m S 546.2261 202.2959 m S U u 552.879 221.7457 m S 552.879 208.7791 m S 539.5732 208.7791 m S 539.5732 221.7457 m S 546.2261 215.2625 m S U 419.7585 208.7414 m S 406.4527 208.7414 m S 433.0643 208.7414 m S 419.7585 208.7414 m S 433.0643 208.7414 m S 419.7585 208.7414 m S 446.3701 208.7414 m S 433.0643 208.7414 m S 446.3701 208.7414 m S 433.0643 208.7414 m S 419.7585 208.7414 m S 406.4527 208.7414 m S 459.6759 208.7414 m S 446.3701 208.7414 m S 472.9817 208.7414 m S 459.6759 208.7414 m S 472.9817 208.7414 m S 459.6759 208.7414 m S 486.2875 208.7414 m S 472.9817 208.7414 m S 486.2875 208.7414 m S 472.9817 208.7414 m S 459.6759 208.7414 m S 446.3701 208.7414 m S 499.5933 208.7414 m S 486.2875 208.7414 m S 512.8991 208.7414 m S 499.5933 208.7414 m S 512.8991 208.7414 m S 499.5933 208.7414 m S 539.3858 208.604 m S 512.8991 208.7414 m S 539.3858 208.604 m S 512.8991 208.7414 m S 499.5933 208.7414 m S 486.2875 208.7414 m S 539.5106 208.7414 m S 539.3858 208.604 m S 539.5106 208.7414 m S 539.5106 208.7414 m S 539.5106 208.7414 m S 539.3858 208.604 m S 419.7585 208.7414 m S 0 g 1 w 4 M 419.7585 208.7414 m F 0 G 0.3 w 10 M 433.0643 208.7414 m S 0 g 1 w 4 M 433.0643 208.7414 m F 0 G 0.3 w 10 M 446.3701 208.7414 m S 0 g 1 w 4 M 446.3701 208.7414 m F 0 G 0.3 w 10 M 459.6759 208.7414 m S 0 g 1 w 4 M 459.6759 208.7414 m F 0 G 0.3 w 10 M 472.9817 208.7414 m S 0 g 1 w 4 M 472.9817 208.7414 m F 0 G 0.3 w 10 M 486.2875 208.7414 m S 0 g 1 w 4 M 486.2875 208.7414 m F 0 G 0.3 w 10 M 499.5933 208.7414 m S 0 g 1 w 4 M 499.5933 208.7414 m F 0 G 0.3 w 10 M 512.8991 208.7414 m S 0 g 1 w 4 M 512.8991 208.7414 m F 0 G 0.3 w 10 M 539.5106 208.7414 m S 0 g 1 w 4 M 539.5106 208.7414 m F 0 G 0.3 w 10 M 539.3858 208.604 m S 0 g 1 w 4 M 539.3858 208.604 m F 0 G 0.3 w 10 M 406.4527 208.7414 m S 0 g 1 w 4 M 406.4527 208.7414 m F 0 G 0.3 w 10 M 419.7585 208.7413 m S 406.4527 208.7413 m S 406.4527 208.7413 m S 406.4527 208.7413 m S 419.7585 208.7413 m S 406.4527 208.7413 m S 539.5107 208.729 m S 539.5107 208.729 m S 539.5732 208.7791 m S 512.899 234.6744 m S 0 g 1 w 4 M 512.899 234.6744 m F 0 G 0.3 w 10 M 512.899 234.6744 m S 512.899 234.6744 m S 512.899 234.6744 m S 0 g 1 w 4 M 512.899 234.6744 m F 0 G 0.3 w 10 M 512.899 234.6744 m S 512.899 234.6744 m S u 1 g 1 w 4 M 506.8886 234.6744 m 506.8886 231.4526 509.5796 228.8408 512.899 228.8408 c 516.2184 228.8408 518.9094 231.4526 518.9094 234.6744 c F 518.9094 234.6744 m 518.9094 237.8962 516.2184 240.508 512.899 240.508 c 509.5796 240.508 506.8886 237.8962 506.8886 234.6744 c F 512.899 234.6744 m F U 0 G 0.3 w 10 M 512.899 234.6744 m S 0 g 1 w 4 M 512.899 234.6744 m F 0 G 0.3 w 10 M 512.899 234.6744 m S 512.899 234.6744 m S 0 g 1 w 4 M 511.8139 233.6065 m 511.8139 230.0294 L 513.9841 230.0294 L 513.9841 233.6065 L 517.5697 233.5953 L 517.5697 235.7537 L 513.9841 235.7426 L 513.9841 239.3197 L 511.8139 239.3197 L 511.8139 235.7426 L 508.2283 235.7537 L 508.2283 233.5953 L 511.8139 233.6065 L f 0 G 0.3 w 10 M 486.2875 234.6744 m S 0 g 1 w 4 M 486.2875 234.6744 m F 0 G 0.3 w 10 M 486.2875 234.6744 m S 486.2875 234.6744 m S 486.2875 234.6744 m S 0 g 1 w 4 M 486.2875 234.6744 m F 0 G 0.3 w 10 M 486.2875 234.6744 m S 486.2875 234.6744 m S u 1 g 1 w 4 M 480.2771 234.6744 m 480.2771 231.4526 482.9681 228.8408 486.2875 228.8408 c 489.6069 228.8408 492.2979 231.4526 492.2979 234.6744 c F 492.2979 234.6744 m 492.2979 237.8962 489.6069 240.508 486.2875 240.508 c 482.9681 240.508 480.2771 237.8962 480.2771 234.6744 c F 486.2875 234.6744 m F U 0 G 0.3 w 10 M 486.2875 234.6744 m S 0 g 1 w 4 M 486.2875 234.6744 m F 0 G 0.3 w 10 M 486.2875 234.6744 m S 486.2875 234.6744 m S 0 g 1 w 4 M 485.2024 233.6065 m 485.2024 230.0294 L 487.3726 230.0294 L 487.3726 233.6065 L 490.9582 233.5953 L 490.9582 235.7537 L 487.3726 235.7426 L 487.3726 239.3197 L 485.2024 239.3197 L 485.2024 235.7426 L 481.6168 235.7537 L 481.6168 233.5953 L 485.2024 233.6065 L f 0 G 0.3 w 10 M 459.6759 234.6744 m S 0 g 1 w 4 M 459.6759 234.6744 m F 0 G 0.3 w 10 M 459.6759 234.6744 m S 459.6759 234.6744 m S 459.6759 234.6744 m S 0 g 1 w 4 M 459.6759 234.6744 m F 0 G 0.3 w 10 M 459.6759 234.6744 m S 459.6759 234.6744 m S u 1 g 1 w 4 M 453.6655 234.6744 m 453.6655 231.4526 456.3565 228.8408 459.6759 228.8408 c 462.9953 228.8408 465.6863 231.4526 465.6863 234.6744 c F 465.6863 234.6744 m 465.6863 237.8962 462.9953 240.508 459.6759 240.508 c 456.3565 240.508 453.6655 237.8962 453.6655 234.6744 c F 459.6759 234.6744 m F U 0 G 0.3 w 10 M 459.6759 234.6744 m S 0 g 1 w 4 M 459.6759 234.6744 m F 0 G 0.3 w 10 M 459.6759 234.6744 m S 459.6759 234.6744 m S 0 g 1 w 4 M 458.5908 233.6065 m 458.5908 230.0294 L 460.761 230.0294 L 460.761 233.6065 L 464.3466 233.5953 L 464.3466 235.7537 L 460.761 235.7426 L 460.761 239.3197 L 458.5908 239.3197 L 458.5908 235.7426 L 455.0052 235.7537 L 455.0052 233.5953 L 458.5908 233.6065 L f 0 G 0.3 w 10 M 433.0643 234.6744 m S 0 g 1 w 4 M 433.0643 234.6744 m F 0 G 0.3 w 10 M 433.0643 234.6744 m S 433.0643 234.6744 m S 433.0643 234.6744 m S 0 g 1 w 4 M 433.0643 234.6744 m F 0 G 0.3 w 10 M 433.0643 234.6744 m S 433.0643 234.6744 m S u 1 g 1 w 4 M 427.0539 234.6744 m 427.0539 231.4526 429.7449 228.8408 433.0643 228.8408 c 436.3837 228.8408 439.0747 231.4526 439.0747 234.6744 c F 439.0747 234.6744 m 439.0747 237.8962 436.3837 240.508 433.0643 240.508 c 429.7449 240.508 427.0539 237.8962 427.0539 234.6744 c F 433.0643 234.6744 m F U 0 G 0.3 w 10 M 433.0643 234.6744 m S 0 g 1 w 4 M 433.0643 234.6744 m F 0 G 0.3 w 10 M 433.0643 234.6744 m S 433.0643 234.6744 m S 0 g 1 w 4 M 431.9792 233.6065 m 431.9792 230.0294 L 434.1494 230.0294 L 434.1494 233.6065 L 437.735 233.5953 L 437.735 235.7537 L 434.1494 235.7426 L 434.1494 239.3197 L 431.9792 239.3197 L 431.9792 235.7426 L 428.3936 235.7537 L 428.3936 233.5953 L 431.9792 233.6065 L f 0 G 0.3 w 10 M 512.8991 79.0757 m S 0 g 1 w 4 M 512.8991 79.0757 m F 0 G 0.3 w 10 M 512.8991 79.0757 m S 512.8991 79.0757 m S 512.8991 79.0757 m S 0 g 1 w 4 M 512.8991 79.0757 m F 0 G 0.3 w 10 M 512.8991 79.0757 m S 512.8991 79.0757 m S 1 g 1 w 4 M 506.8887 79.0757 m 506.8887 75.8539 509.5797 73.2421 512.8991 73.2421 c 516.2186 73.2421 518.9096 75.8539 518.9096 79.0757 c F 518.9096 79.0757 m 518.9096 82.2975 516.2186 84.9094 512.8991 84.9094 c 509.5797 84.9094 506.8887 82.2975 506.8887 79.0757 c F 512.8991 79.0757 m F 0 G 0.3 w 10 M 512.8991 79.0757 m S 0 g 1 w 4 M 512.8991 79.0757 m F 0 G 0.3 w 10 M 512.8991 79.0757 m S 512.8991 79.0757 m S 0 g 1 w 4 M 511.814 78.0078 m 511.814 74.4307 L 513.9842 74.4307 L 513.9842 78.0078 L 517.5698 77.9966 L 517.5698 80.155 L 513.9842 80.1439 L 513.9842 83.721 L 511.814 83.721 L 511.814 80.1439 L 508.2284 80.155 L 508.2284 77.9966 L 511.814 78.0078 L f 0 G 0.3 w 10 M 379.8412 92.0422 m S 0 g 1 w 4 M 379.8412 92.0422 m F 0 G 0.3 w 10 M 379.8412 92.0422 m S 379.8412 92.0422 m S 379.8412 92.0422 m S 0 g 1 w 4 M 379.8412 92.0422 m F 0 G 0.3 w 10 M 379.8412 92.0422 m S 379.8412 92.0422 m S 1 g 1 w 4 M 379.8412 92.0422 m F 0 G 0.3 w 10 M 379.8412 92.0422 m S 0 g 1 w 4 M 379.8412 92.0422 m F 0 G 0.3 w 10 M 379.8412 92.0422 m S 379.8412 92.0422 m S 393.147 92.0422 m S 0 g 1 w 4 M 393.147 92.0422 m F 0 G 0.3 w 10 M 419.7586 79.0757 m S 0 g 1 w 4 M 419.7586 79.0757 m F 0 G 0.3 w 10 M 379.8412 79.0756 m S 0 g 1 w 4 M 379.8412 79.0756 m F 0 G 0.3 w 10 M 472.9818 79.0757 m S 0 g 1 w 4 M 472.9818 79.0757 m F 0 G 0.3 w 10 M 499.5935 79.0757 m S 0 g 1 w 4 M 499.5935 79.0757 m F 0 G 0.3 w 10 M 446.3702 79.0757 m S 0 g 1 w 4 M 446.3702 79.0757 m F u 0 G 0.3 w 10 M 379.8412 79.0755 m S 379.8412 66.1089 m S 366.5354 66.1089 m S 366.5354 79.0755 m S 373.1883 72.5923 m S U u 379.8412 92.0421 m S 379.8412 79.0755 m S 366.5354 79.0755 m S 366.5354 92.0421 m S 373.1883 85.5588 m S U u 393.147 92.0421 m S 393.147 79.0755 m S 379.8412 79.0755 m S 379.8412 92.0421 m S 386.4941 85.5588 m S U u 393.147 79.0755 m S 393.147 66.1089 m S 379.8412 66.1089 m S 379.8412 79.0755 m S 386.4941 72.5923 m S U 393.147 92.0421 m S 379.8412 92.0421 m S 373.1883 98.5254 m S 379.8412 92.0421 m S 373.1883 98.5254 m S 433.0644 79.0756 m S 419.7586 79.0756 m S 426.4115 85.5589 m S 419.7586 79.0756 m S 406.4528 79.0756 m S 413.1057 85.5589 m S 406.4528 79.0756 m S 393.147 92.0421 m S 399.7999 85.5589 m S u 472.9818 92.0421 m S 472.9818 79.0756 m S 459.676 79.0756 m S 459.676 92.0421 m S 466.3289 85.5589 m S U 459.676 79.0756 m S 446.3702 79.0756 m S 453.0231 85.5589 m S 446.3702 79.0756 m S 433.0644 79.0756 m S 439.7173 85.5589 m S u 512.8992 92.0421 m S 512.8992 79.0756 m S 499.5934 79.0756 m S 499.5934 92.0421 m S 506.2463 85.5589 m S U u 499.5934 92.0421 m S 499.5934 79.0756 m S 486.2875 79.0756 m S 486.2875 92.0421 m S 492.9404 85.5589 m S U u 486.2875 92.0421 m S 486.2875 79.0756 m S 472.9818 79.0756 m S 472.9818 92.0421 m S 479.6346 85.5589 m S U 512.8992 79.0756 m S 532.7329 98.3881 m S u 526.2051 79.0756 m S 526.2051 66.1092 m S 512.8992 66.1092 m S 512.8992 79.0756 m S 519.5521 72.5924 m S U u 512.8992 79.0756 m S 512.8992 66.1092 m S 499.5935 66.1092 m S 499.5935 79.0756 m S 506.2463 72.5924 m S U u 512.8992 92.0422 m S 512.8992 79.0756 m S 499.5935 79.0756 m S 499.5935 92.0422 m S 506.2463 85.559 m S U 512.9617 79.1134 m S 532.7954 98.4258 m S u 526.2675 79.1133 m S 526.2675 66.1468 m S 512.9617 66.1468 m S 512.9617 79.1133 m S 519.6146 72.6301 m S U u 526.2675 79.1134 m S 526.2675 66.1468 m S 512.9617 66.1468 m S 512.9617 79.1134 m S 519.6146 72.6302 m S U 393.147 79.0756 m S 379.8412 79.0756 m S 406.4528 79.0756 m S 393.147 79.0756 m S 406.4528 79.0756 m S 393.147 79.0756 m S 419.7586 79.0756 m S 406.4528 79.0756 m S 419.7586 79.0756 m S 406.4528 79.0756 m S 393.147 79.0756 m S 379.8412 79.0756 m S 433.0644 79.0756 m S 419.7586 79.0756 m S 446.3702 79.0756 m S 433.0644 79.0756 m S 446.3702 79.0756 m S 433.0644 79.0756 m S 459.676 79.0756 m S 446.3702 79.0756 m S 459.676 79.0756 m S 446.3702 79.0756 m S 433.0644 79.0756 m S 419.7586 79.0756 m S 472.9818 79.0756 m S 459.676 79.0756 m S 486.2876 79.0756 m S 472.9818 79.0756 m S 486.2876 79.0756 m S 472.9818 79.0756 m S 499.5935 79.0756 m S 486.2876 79.0756 m S 499.5935 79.0756 m S 486.2876 79.0756 m S 472.9818 79.0756 m S 459.676 79.0756 m S 512.8991 79.0756 m S 499.5935 79.0756 m S 512.8991 79.0756 m S 512.8991 79.0756 m S 512.8991 79.0756 m S 499.5935 79.0756 m S 393.147 79.0756 m S 0 g 1 w 4 M 393.147 79.0756 m F 0 G 0.3 w 10 M 406.4528 79.0756 m S 0 g 1 w 4 M 406.4528 79.0756 m F 0 G 0.3 w 10 M 419.7586 79.0756 m S 0 g 1 w 4 M 419.7586 79.0756 m F 0 G 0.3 w 10 M 433.0644 79.0756 m S 0 g 1 w 4 M 433.0644 79.0756 m F 0 G 0.3 w 10 M 446.3702 79.0756 m S 0 g 1 w 4 M 446.3702 79.0756 m F 0 G 0.3 w 10 M 459.676 79.0756 m S 0 g 1 w 4 M 459.676 79.0756 m F 0 G 0.3 w 10 M 472.9818 79.0756 m S 0 g 1 w 4 M 472.9818 79.0756 m F 0 G 0.3 w 10 M 486.2876 79.0756 m S 0 g 1 w 4 M 486.2876 79.0756 m F 0 G 0.3 w 10 M 512.8991 79.0756 m S 0 g 1 w 4 M 512.8991 79.0756 m F 0 G 0.3 w 10 M 499.5935 79.0756 m S 0 g 1 w 4 M 499.5935 79.0756 m F 0 G 0.3 w 10 M 379.8412 79.0756 m S 0 g 1 w 4 M 379.8412 79.0756 m F 0 G 0.3 w 10 M 393.147 79.0755 m S 379.8412 79.0755 m S 379.8412 79.0755 m S 379.8412 79.0755 m S 393.147 79.0755 m S 379.8412 79.0755 m S 512.8992 79.0632 m S 512.8992 79.0632 m S 512.9617 79.1133 m S 486.2875 79.0756 m S 0 g 1 w 4 M 486.2875 79.0756 m F 0 G 0.3 w 10 M 486.2875 79.0756 m S 486.2875 79.0756 m S 486.2875 79.0756 m S 0 g 1 w 4 M 486.2875 79.0756 m F 0 G 0.3 w 10 M 486.2875 79.0756 m S 486.2875 79.0756 m S u 1 g 1 w 4 M 480.2771 79.0756 m 480.2771 75.8538 482.9681 73.242 486.2875 73.242 c 489.6069 73.242 492.2979 75.8538 492.2979 79.0756 c F 492.2979 79.0756 m 492.2979 82.2974 489.6069 84.9092 486.2875 84.9092 c 482.9681 84.9092 480.2771 82.2974 480.2771 79.0756 c F 486.2875 79.0756 m F U 0 G 0.3 w 10 M 486.2875 79.0756 m S 0 g 1 w 4 M 486.2875 79.0756 m F 0 G 0.3 w 10 M 486.2875 79.0756 m S 486.2875 79.0756 m S 0 g 1 w 4 M 485.2024 78.0077 m 485.2024 74.4306 L 487.3726 74.4306 L 487.3726 78.0077 L 490.9582 77.9965 L 490.9582 80.1549 L 487.3726 80.1438 L 487.3726 83.7209 L 485.2024 83.7209 L 485.2024 80.1438 L 481.6168 80.1549 L 481.6168 77.9965 L 485.2024 78.0077 L f 0 G 0.3 w 10 M 459.676 79.0756 m S 0 g 1 w 4 M 459.676 79.0756 m F 0 G 0.3 w 10 M 459.676 79.0756 m S 459.676 79.0756 m S 459.676 79.0756 m S 0 g 1 w 4 M 459.676 79.0756 m F 0 G 0.3 w 10 M 459.676 79.0756 m S 459.676 79.0756 m S u 1 g 1 w 4 M 453.6656 79.0756 m 453.6656 75.8538 456.3566 73.242 459.676 73.242 c 462.9954 73.242 465.6864 75.8538 465.6864 79.0756 c F 465.6864 79.0756 m 465.6864 82.2974 462.9954 84.9092 459.676 84.9092 c 456.3566 84.9092 453.6656 82.2974 453.6656 79.0756 c F 459.676 79.0756 m F U 0 G 0.3 w 10 M 459.676 79.0756 m S 0 g 1 w 4 M 459.676 79.0756 m F 0 G 0.3 w 10 M 459.676 79.0756 m S 459.676 79.0756 m S 0 g 1 w 4 M 458.5909 78.0077 m 458.5909 74.4306 L 460.7611 74.4306 L 460.7611 78.0077 L 464.3467 77.9965 L 464.3467 80.1549 L 460.7611 80.1438 L 460.7611 83.7209 L 458.5909 83.7209 L 458.5909 80.1438 L 455.0053 80.1549 L 455.0053 77.9965 L 458.5909 78.0077 L f 0 G 0.3 w 10 M 433.0644 79.0756 m S 0 g 1 w 4 M 433.0644 79.0756 m F 0 G 0.3 w 10 M 433.0644 79.0756 m S 433.0644 79.0756 m S 433.0644 79.0756 m S 0 g 1 w 4 M 433.0644 79.0756 m F 0 G 0.3 w 10 M 433.0644 79.0756 m S 433.0644 79.0756 m S u 1 g 1 w 4 M 427.054 79.0756 m 427.054 75.8538 429.745 73.242 433.0644 73.242 c 436.3838 73.242 439.0748 75.8538 439.0748 79.0756 c F 439.0748 79.0756 m 439.0748 82.2974 436.3838 84.9092 433.0644 84.9092 c 429.745 84.9092 427.054 82.2974 427.054 79.0756 c F 433.0644 79.0756 m F U 0 G 0.3 w 10 M 433.0644 79.0756 m S 0 g 1 w 4 M 433.0644 79.0756 m F 0 G 0.3 w 10 M 433.0644 79.0756 m S 433.0644 79.0756 m S 0 g 1 w 4 M 431.9793 78.0077 m 431.9793 74.4306 L 434.1495 74.4306 L 434.1495 78.0077 L 437.7351 77.9965 L 437.7351 80.1549 L 434.1495 80.1438 L 434.1495 83.7209 L 431.9793 83.7209 L 431.9793 80.1438 L 428.3937 80.1549 L 428.3937 77.9965 L 431.9793 78.0077 L f 0 G 0.3 w 10 M 406.4528 79.0756 m S 0 g 1 w 4 M 406.4528 79.0756 m F 0 G 0.3 w 10 M 406.4528 79.0756 m S 406.4528 79.0756 m S 406.4528 79.0756 m S 0 g 1 w 4 M 406.4528 79.0756 m F 0 G 0.3 w 10 M 406.4528 79.0756 m S 406.4528 79.0756 m S u 1 g 1 w 4 M 400.4424 79.0756 m 400.4424 75.8538 403.1334 73.242 406.4528 73.242 c 409.7722 73.242 412.4632 75.8538 412.4632 79.0756 c F 412.4632 79.0756 m 412.4632 82.2974 409.7722 84.9092 406.4528 84.9092 c 403.1334 84.9092 400.4424 82.2974 400.4424 79.0756 c F 406.4528 79.0756 m F U 0 G 0.3 w 10 M 406.4528 79.0756 m S 0 g 1 w 4 M 406.4528 79.0756 m F 0 G 0.3 w 10 M 406.4528 79.0756 m S 406.4528 79.0756 m S 0 g 1 w 4 M 405.3677 78.0077 m 405.3677 74.4306 L 407.5379 74.4306 L 407.5379 78.0077 L 411.1235 77.9965 L 411.1235 80.1549 L 407.5379 80.1438 L 407.5379 83.7209 L 405.3677 83.7209 L 405.3677 80.1438 L 401.7821 80.1549 L 401.7821 77.9965 L 405.3677 78.0077 L f 0 G 0.3 w 10 M 379.8411 156.8751 m S 0 g 1 w 4 M 379.8411 156.8751 m F 0 G 0.3 w 10 M 379.8411 156.8751 m S 379.8411 156.8751 m S 379.8411 156.8751 m S 0 g 1 w 4 M 379.8411 156.8751 m F 0 G 0.3 w 10 M 379.8411 156.8751 m S 379.8411 156.8751 m S 1 g 1 w 4 M 373.8307 156.8751 m 373.8307 153.6533 376.5217 151.0415 379.8411 151.0415 c 383.1606 151.0415 385.8515 153.6533 385.8515 156.8751 c F 385.8515 156.8751 m 385.8515 160.0969 383.1606 162.7088 379.8411 162.7088 c 376.5217 162.7088 373.8307 160.0969 373.8307 156.8751 c F 379.8411 156.8751 m F 0 G 0.3 w 10 M 379.8411 156.8751 m S 0 g 1 w 4 M 379.8411 156.8751 m F 0 G 0.3 w 10 M 379.8411 156.8751 m S 379.8411 156.8751 m S 0 g 1 w 4 M 378.756 155.8072 m 378.756 152.2301 L 380.9262 152.2301 L 380.9262 155.8072 L 384.5118 155.796 L 384.5118 157.9544 L 380.9262 157.9433 L 380.9262 161.5204 L 378.756 161.5204 L 378.756 157.9433 L 375.1704 157.9544 L 375.1704 155.796 L 378.756 155.8072 L f 0 G 0.3 w 10 M 379.8411 130.9419 m S 0 g 1 w 4 M 379.8411 130.9419 m F 0 G 0.3 w 10 M 379.8411 130.9419 m S 379.8411 130.9419 m S 379.8411 130.9419 m S 0 g 1 w 4 M 379.8411 130.9419 m F 0 G 0.3 w 10 M 379.8411 130.9419 m S 379.8411 130.9419 m S 1 g 1 w 4 M 373.8307 130.9419 m 373.8307 127.7201 376.5217 125.1083 379.8411 125.1083 c 383.1606 125.1083 385.8515 127.7201 385.8515 130.9419 c F 385.8515 130.9419 m 385.8515 134.1637 383.1606 136.7756 379.8411 136.7756 c 376.5217 136.7756 373.8307 134.1637 373.8307 130.9419 c F 379.8411 130.9419 m F 0 G 0.3 w 10 M 379.8411 130.9419 m S 0 g 1 w 4 M 379.8411 130.9419 m F 0 G 0.3 w 10 M 379.8411 130.9419 m S 379.8411 130.9419 m S 0 g 1 w 4 M 378.756 129.874 m 378.756 126.2969 L 380.9262 126.2969 L 380.9262 129.874 L 384.5118 129.8628 L 384.5118 132.0212 L 380.9262 132.0101 L 380.9262 135.5872 L 378.756 135.5872 L 378.756 132.0101 L 375.1704 132.0212 L 375.1704 129.8628 L 378.756 129.874 L f 0 G 0.3 w 10 M 379.8411 208.7414 m S 0 g 1 w 4 M 379.8411 208.7414 m F 0 G 0.3 w 10 M 379.8411 208.7414 m S 379.8411 208.7414 m S 379.8411 208.7414 m S 0 g 1 w 4 M 379.8411 208.7414 m F 0 G 0.3 w 10 M 379.8411 208.7414 m S 379.8411 208.7414 m S 1 g 1 w 4 M 373.8307 208.7414 m 373.8307 205.5196 376.5217 202.9078 379.8411 202.9078 c 383.1606 202.9078 385.8515 205.5196 385.8515 208.7414 c F 385.8515 208.7414 m 385.8515 211.9632 383.1606 214.5751 379.8411 214.5751 c 376.5217 214.5751 373.8307 211.9632 373.8307 208.7414 c F 379.8411 208.7414 m F 0 G 0.3 w 10 M 379.8411 208.7414 m S 0 g 1 w 4 M 379.8411 208.7414 m F 0 G 0.3 w 10 M 379.8411 208.7414 m S 379.8411 208.7414 m S 0 g 1 w 4 M 378.756 207.6735 m 378.756 204.0964 L 380.9262 204.0964 L 380.9262 207.6735 L 384.5118 207.6623 L 384.5118 209.8207 L 380.9262 209.8096 L 380.9262 213.3867 L 378.756 213.3867 L 378.756 209.8096 L 375.1704 209.8207 L 375.1704 207.6623 L 378.756 207.6735 L f 0 G 0.3 w 10 M 406.4527 208.7414 m S 0 g 1 w 4 M 406.4527 208.7414 m F 0 G 0.3 w 10 M 379.8411 195.7748 m S 0 g 1 w 4 M 379.8411 195.7748 m F 0 G 0.3 w 10 M 406.4527 169.8417 m S 379.8411 169.8417 m S 406.4527 169.8417 m S 406.4527 169.8417 m S 406.4527 169.8417 m S 379.8411 169.8417 m S 406.4527 169.8417 m S 0 g 1 w 4 M 406.4527 169.8417 m F 0 G 0.3 w 10 M 379.8411 169.8417 m S 0 g 1 w 4 M 379.8411 169.8417 m F 0 G 0.3 w 10 M 406.4527 143.9085 m S 379.8411 143.9085 m S 406.4527 143.9085 m S 406.4527 143.9085 m S 406.4527 143.9085 m S 379.8411 143.9085 m S 406.4527 143.9085 m S 0 g 1 w 4 M 406.4527 143.9085 m F 0 G 0.3 w 10 M 379.8411 143.9085 m S 0 g 1 w 4 M 379.8411 143.9085 m F 0 G 0.3 w 10 M 406.4527 143.9085 m S 379.8411 143.9085 m S 406.4527 143.9085 m S 406.4527 143.9085 m S 406.4527 143.9085 m S 379.8411 143.9085 m S 406.4527 143.9085 m S 0 g 1 w 4 M 406.4527 143.9085 m F 0 G 0.3 w 10 M 379.8411 143.9085 m S 0 g 1 w 4 M 379.8411 143.9085 m F 0 G 0.3 w 10 M 406.4527 117.9753 m S 379.8411 117.9753 m S 406.4527 117.9753 m S 406.4527 117.9753 m S 406.4527 117.9753 m S 379.8411 117.9753 m S 406.4527 117.9753 m S 0 g 1 w 4 M 406.4527 117.9753 m F 0 G 0.3 w 10 M 379.8411 117.9753 m S 0 g 1 w 4 M 379.8411 117.9753 m F 0 G 0.3 w 10 M 406.4527 156.8751 m S 0 g 1 w 4 M 406.4527 156.8751 m F 0 G 0.3 w 10 M 406.4527 130.9419 m S 0 g 1 w 4 M 406.4527 130.9419 m F 0 G 0.3 w 10 M 406.4527 79.0756 m S 393.1469 92.0421 m S 406.4527 79.0756 m S 406.4527 79.0756 m S 406.4527 79.0756 m S 393.1469 92.0421 m S 406.4527 79.0756 m S 393.1469 92.0421 m S 406.4527 79.0756 m S 406.4527 79.0756 m S 406.4527 79.0756 m S 393.1469 92.0421 m S 406.4527 79.0756 m S 0 g 1 w 4 M 406.4527 79.0756 m F 0 G 0.3 w 10 M 393.1469 92.0421 m S 0 g 1 w 4 M 393.1469 92.0421 m F 0 G 0.3 w 10 M 406.4527 105.0087 m S 379.8411 105.0087 m S 406.4527 105.0087 m S 406.4527 105.0087 m S 406.4527 105.0087 m S 379.8411 105.0087 m S 379.8411 105.0087 m S 0 g 1 w 4 M 379.8411 105.0087 m F 0 G 0.3 w 10 M 379.8411 105.0087 m S 379.8411 105.0087 m S 379.8411 105.0087 m S 0 g 1 w 4 M 379.8411 105.0087 m F 0 G 0.3 w 10 M 379.8411 105.0087 m S 379.8411 105.0087 m S 1 g 1 w 4 M 373.8307 105.0087 m 373.8307 101.787 376.5217 99.1751 379.8411 99.1751 c 383.1606 99.1751 385.8515 101.787 385.8515 105.0087 c F 385.8515 105.0087 m 385.8515 108.2305 383.1606 110.8424 379.8411 110.8424 c 376.5217 110.8424 373.8307 108.2305 373.8307 105.0087 c F 379.8411 105.0087 m F 0 G 0.3 w 10 M 379.8411 105.0087 m S 0 g 1 w 4 M 379.8411 105.0087 m F 0 G 0.3 w 10 M 379.8411 105.0087 m S 379.8411 105.0087 m S 0 g 1 w 4 M 378.756 103.9408 m 378.756 100.3637 L 380.9262 100.3637 L 380.9262 103.9408 L 384.5118 103.9296 L 384.5118 106.088 L 380.9262 106.0769 L 380.9262 109.654 L 378.756 109.654 L 378.756 106.0769 L 375.1704 106.088 L 375.1704 103.9296 L 378.756 103.9408 L f 0 G 0.3 w 10 M 406.4527 105.0087 m S 0 g 1 w 4 M 406.4527 105.0087 m F 0 G 0.3 w 10 M 406.4527 79.0755 m S 393.1469 79.0755 m S 399.7998 72.5922 m S 406.4527 79.0755 m S 0 g 1 w 4 M 399.7998 72.5922 m F 0 G 0.3 w 10 M 399.7998 72.5922 m S 0 g 1 w 4 M 399.7998 72.5922 m F 0 G 0.3 w 10 M 406.4527 79.0755 m S 406.4527 79.0755 m S 393.1469 79.0755 m S 0 g 1 w 4 M 393.1469 79.0755 m F 0 G 0.3 w 10 M 393.1469 79.0755 m S 393.1469 79.0755 m S 393.1469 79.0755 m S 0 g 1 w 4 M 393.1469 79.0755 m F 0 G 0.3 w 10 M 393.1469 79.0755 m S 393.1469 79.0755 m S 1 g 1 w 4 M 393.1469 79.0755 m F 0 G 0.3 w 10 M 393.1469 79.0755 m S 0 g 1 w 4 M 393.1469 79.0755 m F 0 G 0.3 w 10 M 393.1469 79.0755 m S 393.1469 79.0755 m S 406.4527 79.0755 m S 0 g 1 w 4 M 406.4527 79.0755 m F 0 G 0.3 w 10 M 406.4527 182.8081 m S 406.4527 169.8416 m S 379.8411 169.8416 m S 379.8411 182.8081 m S 386.494 176.3249 m S u 379.8411 195.7747 m S 379.8411 182.8081 m S 366.5353 182.8081 m S 366.5353 195.7747 m S 373.1882 189.2915 m S U u 379.8411 208.7413 m S 379.8411 195.7747 m S 366.5353 195.7747 m S 366.5353 208.7413 m S 373.1882 202.258 m S U u 393.1469 208.7413 m S 393.1469 195.7747 m S 379.8411 195.7747 m S 379.8411 208.7413 m S 386.494 202.258 m S U u 393.1469 195.7747 m S 393.1469 182.8081 m S 379.8411 182.8081 m S 379.8411 195.7747 m S 386.494 189.2915 m S U 379.8411 182.8081 m S 379.8411 169.8416 m S 373.1882 176.3249 m S 406.4527 143.9084 m S 406.4527 130.9418 m S 379.8411 130.9418 m S 379.8411 143.9084 m S 386.494 137.4251 m S u 379.8411 156.875 m S 379.8411 143.9084 m S 366.5353 143.9084 m S 366.5353 156.875 m S 373.1882 150.3917 m S U 379.8411 169.8416 m S 379.8411 156.875 m S 373.1882 163.3583 m S 406.4527 169.8416 m S 406.4527 156.875 m S 379.8411 156.875 m S 379.8411 169.8416 m S 386.494 163.3583 m S u 393.1469 156.875 m S 393.1469 143.9084 m S 379.8411 143.9084 m S 379.8411 156.875 m S 386.494 150.3917 m S U 379.8411 143.9084 m S 379.8411 130.9418 m S 373.1882 137.4251 m S 393.1469 92.042 m S 379.8411 105.0086 m S 379.8411 117.9752 m S 379.8411 105.0086 m S 373.1882 111.4919 m S 379.8411 130.9418 m S 379.8411 117.9752 m S 373.1882 124.4585 m S 379.8411 117.9752 m S 379.8411 130.9418 m S 379.8411 105.0086 m S 379.8411 117.9752 m S 379.8411 105.0086 m S 393.1469 92.042 m S 373.1882 98.5253 m S 393.1469 79.0754 m S 386.494 72.5921 m S 393.1469 92.042 m S 393.1469 79.0754 m S 386.494 85.5587 m S 393.1469 79.0754 m S 393.1469 92.042 m S 393.1469 79.0754 m S 406.4527 208.7413 m S 379.8411 208.7413 m S 386.494 215.2246 m S 379.8411 208.7413 m S 373.1882 215.2246 m S 406.4527 208.7413 m S 379.9661 144.0458 m S 379.9661 131.0792 m S 373.3132 137.5626 m S u 379.9661 157.0124 m S 379.9661 144.0458 m S 366.6603 144.0458 m S 366.6603 157.0124 m S 373.3132 150.5291 m S U 379.9661 131.0792 m S 379.9661 118.1127 m S 373.3132 124.596 m S u 379.9661 118.1127 m S 379.9661 105.1461 m S 366.6603 105.1461 m S 366.6603 118.1127 m S 373.3132 111.6294 m S U u 393.2719 92.1794 m S 393.2719 79.2128 m S 379.9661 79.2128 m S 379.9661 92.1794 m S 386.619 85.6962 m S U u 379.9661 105.146 m S 379.9661 92.1794 m S 366.6603 92.1794 m S 366.6603 105.146 m S 373.3132 98.6627 m S U 393.2719 79.2128 m S 386.619 72.7296 m S 406.4527 195.7748 m S 379.8411 195.7748 m S 406.4527 195.7748 m S 406.4527 195.7748 m S 406.4527 195.7748 m S 379.8411 195.7748 m S 406.4527 195.7748 m S 0 g 1 w 4 M 406.4527 195.7748 m F 0 G 0.3 w 10 M 379.8411 195.7748 m S 0 g 1 w 4 M 379.8411 195.7748 m F 0 G 0.3 w 10 M 406.4527 195.7747 m S 379.8411 195.7747 m S 379.8411 195.7747 m S 379.8411 195.7747 m S 406.4527 195.7747 m S 379.8411 195.7747 m S 379.7161 182.6708 m S 0 g 1 w 4 M 379.7161 182.6708 m F 0 G 0.3 w 10 M 379.7161 182.6708 m S 379.7161 182.6708 m S 379.7161 182.6708 m S 0 g 1 w 4 M 379.7161 182.6708 m F 0 G 0.3 w 10 M 379.7161 182.6708 m S 379.7161 182.6708 m S 1 g 1 w 4 M 373.7057 182.6708 m 373.7057 179.449 376.3967 176.8372 379.7161 176.8372 c 383.0356 176.8372 385.7265 179.449 385.7265 182.6708 c F 385.7265 182.6708 m 385.7265 185.8926 383.0356 188.5045 379.7161 188.5045 c 376.3967 188.5045 373.7057 185.8926 373.7057 182.6708 c F 379.7161 182.6708 m F 0 G 0.3 w 10 M 379.7161 182.6708 m S 0 g 1 w 4 M 379.7161 182.6708 m F 0 G 0.3 w 10 M 379.7161 182.6708 m S 379.7161 182.6708 m S 0 g 1 w 4 M 378.631 181.6029 m 378.631 178.0258 L 380.8012 178.0258 L 380.8012 181.6029 L 384.3868 181.5917 L 384.3868 183.7501 L 380.8012 183.739 L 380.8012 187.3161 L 378.631 187.3161 L 378.631 183.739 L 375.0454 183.7501 L 375.0454 181.5917 L 378.631 181.6029 L f 0 G 0.3 w 10 M 406.3277 182.6708 m S 0 g 1 w 4 M 406.3277 182.6708 m F 0 G 0.3 w 10 M 406.3277 182.6707 m S 379.7161 182.6707 m S 379.7161 182.6707 m S 379.7161 182.6707 m S 379.7161 182.6707 m S 379.8411 182.8081 m S 379.8411 182.8081 m S 373.1882 176.3249 m S 0 g 1 w 4 M 386.619 85.6962 m F 386.619 72.7296 m F 0 G 0.3 w 10 M 539.3857 156.7378 m S 0 g 1 w 4 M 539.3857 156.7378 m F 0 G 0.3 w 10 M 539.3857 156.7378 m S 539.3857 156.7378 m S 539.3857 156.7378 m S 0 g 1 w 4 M 539.3857 156.7378 m F 0 G 0.3 w 10 M 539.3857 156.7378 m S 539.3857 156.7378 m S 1 g 1 w 4 M 533.3753 156.7378 m 533.3753 153.516 536.0663 150.9042 539.3857 150.9042 c 542.7052 150.9042 545.3961 153.516 545.3961 156.7378 c F 545.3961 156.7378 m 545.3961 159.9596 542.7052 162.5715 539.3857 162.5715 c 536.0663 162.5715 533.3753 159.9596 533.3753 156.7378 c F 539.3857 156.7378 m F 0 G 0.3 w 10 M 539.3857 156.7378 m S 0 g 1 w 4 M 539.3857 156.7378 m F 0 G 0.3 w 10 M 539.3857 156.7378 m S 539.3857 156.7378 m S 0 g 1 w 4 M 538.3006 155.6699 m 538.3006 152.0928 L 540.4708 152.0928 L 540.4708 155.6699 L 544.0564 155.6587 L 544.0564 157.8171 L 540.4708 157.806 L 540.4708 161.3831 L 538.3006 161.3831 L 538.3006 157.806 L 534.715 157.8171 L 534.715 155.6587 L 538.3006 155.6699 L f 0 G 0.3 w 10 M 539.3857 130.8046 m S 0 g 1 w 4 M 539.3857 130.8046 m F 0 G 0.3 w 10 M 539.3857 130.8046 m S 539.3857 130.8046 m S 539.3857 130.8046 m S 0 g 1 w 4 M 539.3857 130.8046 m F 0 G 0.3 w 10 M 539.3857 130.8046 m S 539.3857 130.8046 m S 1 g 1 w 4 M 533.3753 130.8046 m 533.3753 127.5828 536.0663 124.971 539.3857 124.971 c 542.7052 124.971 545.3961 127.5828 545.3961 130.8046 c F 545.3961 130.8046 m 545.3961 134.0264 542.7052 136.6383 539.3857 136.6383 c 536.0663 136.6383 533.3753 134.0264 533.3753 130.8046 c F 539.3857 130.8046 m F 0 G 0.3 w 10 M 539.3857 130.8046 m S 0 g 1 w 4 M 539.3857 130.8046 m F 0 G 0.3 w 10 M 539.3857 130.8046 m S 539.3857 130.8046 m S 0 g 1 w 4 M 538.3006 129.7367 m 538.3006 126.1596 L 540.4708 126.1596 L 540.4708 129.7367 L 544.0564 129.7255 L 544.0564 131.8839 L 540.4708 131.8728 L 540.4708 135.4499 L 538.3006 135.4499 L 538.3006 131.8728 L 534.715 131.8839 L 534.715 129.7255 L 538.3006 129.7367 L f 0 G 0.3 w 10 M 539.3857 208.6041 m S 0 g 1 w 4 M 539.3857 208.6041 m F 0 G 0.3 w 10 M 539.3857 208.6041 m S 539.3857 208.6041 m S 539.3857 208.6041 m S 0 g 1 w 4 M 539.3857 208.6041 m F 0 G 0.3 w 10 M 539.3857 208.6041 m S 539.3857 208.6041 m S 1 g 1 w 4 M 533.3753 208.6041 m 533.3753 205.3823 536.0663 202.7705 539.3857 202.7705 c 542.7052 202.7705 545.3961 205.3823 545.3961 208.6041 c F 545.3961 208.6041 m 545.3961 211.8259 542.7052 214.4378 539.3857 214.4378 c 536.0663 214.4378 533.3753 211.8259 533.3753 208.6041 c F 539.3857 208.6041 m F 0 G 0.3 w 10 M 539.3857 208.6041 m S 0 g 1 w 4 M 539.3857 208.6041 m F 0 G 0.3 w 10 M 539.3857 208.6041 m S 539.3857 208.6041 m S 0 g 1 w 4 M 538.3006 207.5362 m 538.3006 203.9591 L 540.4708 203.9591 L 540.4708 207.5362 L 544.0564 207.525 L 544.0564 209.6834 L 540.4708 209.6723 L 540.4708 213.2494 L 538.3006 213.2494 L 538.3006 209.6723 L 534.715 209.6834 L 534.715 207.525 L 538.3006 207.5362 L f 0 G 0.3 w 10 M 539.5107 208.7415 m S 0 g 1 w 4 M 539.5107 208.7415 m F 0 G 0.3 w 10 M 539.3857 195.6375 m S 0 g 1 w 4 M 539.3857 195.6375 m F 0 G 0.3 w 10 M 539.5107 169.8418 m S 539.3857 169.7044 m S 539.5107 169.8418 m S 539.5107 169.8418 m S 539.5107 169.8418 m S 539.3857 169.7044 m S 539.5107 169.8418 m S 0 g 1 w 4 M 539.5107 169.8418 m F 0 G 0.3 w 10 M 539.3857 169.7044 m S 0 g 1 w 4 M 539.3857 169.7044 m F 0 G 0.3 w 10 M 539.5107 143.9086 m S 539.3857 143.7712 m S 539.5107 143.9086 m S 539.5107 143.9086 m S 539.5107 143.9086 m S 539.3857 143.7712 m S 539.5107 143.9086 m S 0 g 1 w 4 M 539.5107 143.9086 m F 0 G 0.3 w 10 M 539.3857 143.7712 m S 0 g 1 w 4 M 539.3857 143.7712 m F 0 G 0.3 w 10 M 539.5107 143.9086 m S 539.3857 143.7712 m S 539.5107 143.9086 m S 539.5107 143.9086 m S 539.5107 143.9086 m S 539.3857 143.7712 m S 539.5107 143.9086 m S 0 g 1 w 4 M 539.5107 143.9086 m F 0 G 0.3 w 10 M 539.3857 143.7712 m S 0 g 1 w 4 M 539.3857 143.7712 m F 0 G 0.3 w 10 M 539.5107 117.9754 m S 539.3857 117.838 m S 539.5107 117.9754 m S 539.5107 117.9754 m S 539.5107 117.9754 m S 539.3857 117.838 m S 539.5107 117.9754 m S 0 g 1 w 4 M 539.5107 117.9754 m F 0 G 0.3 w 10 M 539.3857 117.838 m S 0 g 1 w 4 M 539.3857 117.838 m F 0 G 0.3 w 10 M 539.5107 156.8752 m S 0 g 1 w 4 M 539.5107 156.8752 m F 0 G 0.3 w 10 M 539.5107 130.942 m S 0 g 1 w 4 M 539.5107 130.942 m F 0 G 0.3 w 10 M 539.5107 92.0422 m S 526.2049 92.0422 m S 539.5107 92.0422 m S 539.5107 92.0422 m S 539.5107 92.0422 m S 526.2049 92.0422 m S 539.5107 92.0422 m S 526.2049 92.0422 m S 539.5107 92.0422 m S 539.5107 92.0422 m S 539.5107 92.0422 m S 526.2049 92.0422 m S 539.5107 92.0422 m S 0 g 1 w 4 M 539.5107 92.0422 m F 0 G 0.3 w 10 M 526.2049 92.0422 m S 0 g 1 w 4 M 526.2049 92.0422 m F 0 G 0.3 w 10 M 539.5107 105.0088 m S 539.3857 104.8714 m S 539.5107 105.0088 m S 539.5107 105.0088 m S 539.5107 105.0088 m S 539.3857 104.8714 m S 539.3857 104.8714 m S 0 g 1 w 4 M 539.3857 104.8714 m F 0 G 0.3 w 10 M 539.3857 104.8714 m S 539.3857 104.8714 m S 539.3857 104.8714 m S 0 g 1 w 4 M 539.3857 104.8714 m F 0 G 0.3 w 10 M 539.3857 104.8714 m S 539.3857 104.8714 m S 1 g 1 w 4 M 533.3753 104.8714 m 533.3753 101.6497 536.0663 99.0378 539.3857 99.0378 c 542.7052 99.0378 545.3961 101.6497 545.3961 104.8714 c F 545.3961 104.8714 m 545.3961 108.0932 542.7052 110.7051 539.3857 110.7051 c 536.0663 110.7051 533.3753 108.0932 533.3753 104.8714 c F 539.3857 104.8714 m F 0 G 0.3 w 10 M 539.3857 104.8714 m S 0 g 1 w 4 M 539.3857 104.8714 m F 0 G 0.3 w 10 M 539.3857 104.8714 m S 539.3857 104.8714 m S 0 g 1 w 4 M 538.3006 103.8035 m 538.3006 100.2264 L 540.4708 100.2264 L 540.4708 103.8035 L 544.0564 103.7923 L 544.0564 105.9507 L 540.4708 105.9396 L 540.4708 109.5167 L 538.3006 109.5167 L 538.3006 105.9396 L 534.715 105.9507 L 534.715 103.7923 L 538.3006 103.8035 L f 0 G 0.3 w 10 M 539.5107 105.0088 m S 0 g 1 w 4 M 539.5107 105.0088 m F 0 G 0.3 w 10 M 539.5107 79.0756 m S 526.2049 79.0756 m S 532.8578 72.5923 m S 539.5107 79.0756 m S 0 g 1 w 4 M 532.8578 72.5923 m F 0 G 0.3 w 10 M 532.8578 72.5923 m S 0 g 1 w 4 M 532.8578 72.5923 m F 0 G 0.3 w 10 M 539.5107 79.0756 m S 539.5107 79.0756 m S 526.2049 79.0756 m S 0 g 1 w 4 M 526.2049 79.0756 m F 0 G 0.3 w 10 M 526.2049 79.0756 m S 526.2049 79.0756 m S 526.2049 79.0756 m S 0 g 1 w 4 M 526.2049 79.0756 m F 0 G 0.3 w 10 M 526.2049 79.0756 m S 526.2049 79.0756 m S 1 g 1 w 4 M 526.2049 79.0756 m F 0 G 0.3 w 10 M 526.2049 79.0756 m S 0 g 1 w 4 M 526.2049 79.0756 m F 0 G 0.3 w 10 M 526.2049 79.0756 m S 526.2049 79.0756 m S 539.5107 79.0756 m S 0 g 1 w 4 M 539.5107 79.0756 m F 0 G 0.3 w 10 M 539.5107 182.8082 m S 539.5107 169.8417 m S 539.3857 169.7043 m S 539.3857 182.6708 m S 546.0386 176.1876 m S u 539.3857 195.6374 m S 539.3857 182.6708 m S 526.0799 182.6708 m S 526.0799 195.6374 m S 532.7328 189.1542 m S U u 539.3857 208.604 m S 539.3857 195.6374 m S 526.0799 195.6374 m S 526.0799 208.604 m S 532.7328 202.1207 m S U u 552.6915 208.604 m S 552.6915 195.6374 m S 539.3857 195.6374 m S 539.3857 208.604 m S 546.0386 202.1207 m S U u 552.6915 195.6374 m S 552.6915 182.6708 m S 539.3857 182.6708 m S 539.3857 195.6374 m S 546.0386 189.1542 m S U 539.3857 182.6708 m S 539.3857 169.7043 m S 532.7328 176.1876 m S 539.5107 143.9085 m S 539.5107 130.9419 m S 539.3857 130.8045 m S 539.3857 143.7711 m S 546.0386 137.2878 m S u 539.3857 156.7377 m S 539.3857 143.7711 m S 526.0799 143.7711 m S 526.0799 156.7377 m S 532.7328 150.2544 m S U 539.3857 169.7043 m S 539.3857 156.7377 m S 532.7328 163.221 m S 539.5107 169.8417 m S 539.5107 156.8751 m S 539.3857 156.7377 m S 539.3857 169.7043 m S 546.0386 163.221 m S u 552.6915 156.7377 m S 552.6915 143.7711 m S 539.3857 143.7711 m S 539.3857 156.7377 m S 546.0386 150.2544 m S U 539.3857 143.7711 m S 539.3857 130.8045 m S 532.7328 137.2878 m S 526.2049 92.0421 m S 539.3857 104.8713 m S 539.3857 117.8379 m S 539.3857 104.8713 m S 532.7328 111.3546 m S 539.3857 130.8045 m S 539.3857 117.8379 m S 532.7328 124.3212 m S 539.3857 117.8379 m S 539.3857 130.8045 m S 539.3857 104.8713 m S 539.3857 117.8379 m S 539.3857 104.8713 m S 526.2049 92.0421 m S 532.7328 98.388 m S 526.2049 79.0755 m S 519.552 72.5922 m S 526.2049 92.0421 m S 526.2049 79.0755 m S 519.552 85.5588 m S 526.2049 79.0755 m S 526.2049 92.0421 m S 526.2049 79.0755 m S 539.5107 208.7414 m S 539.3857 208.604 m S 546.0386 215.0873 m S 539.3857 208.604 m S 519.552 228.1912 m S 539.5107 208.7414 m S 539.5107 143.9085 m S 539.5107 130.9419 m S 532.8578 137.4253 m S u 539.5107 156.8751 m S 539.5107 143.9085 m S 526.2049 143.9085 m S 526.2049 156.8751 m S 532.8578 150.3918 m S U 539.5107 130.9419 m S 539.5107 117.9754 m S 532.8578 124.4587 m S u 539.5107 117.9754 m S 539.5107 105.0088 m S 526.2049 105.0088 m S 526.2049 117.9754 m S 532.8578 111.4921 m S U u 526.3299 79.213 m S 526.3299 66.2464 m S 513.0241 66.2464 m S 513.0241 79.213 m S 519.677 72.7298 m S U u 526.3299 92.1796 m S 526.3299 79.213 m S 513.0241 79.213 m S 513.0241 92.1796 m S 519.677 85.6963 m S U 526.3299 79.2129 m S 519.677 72.7297 m S 539.5107 195.7749 m S 539.3857 195.6375 m S 539.5107 195.7749 m S 539.5107 195.7749 m S 539.5107 195.7749 m S 539.3857 195.6375 m S 539.5107 195.7749 m S 0 g 1 w 4 M 539.5107 195.7749 m F 0 G 0.3 w 10 M 539.3857 195.6375 m S 0 g 1 w 4 M 539.3857 195.6375 m F 0 G 0.3 w 10 M 539.5107 195.7748 m S 539.3857 195.6374 m S 539.3857 195.6374 m S 539.3857 195.6374 m S 539.5107 195.7748 m S 539.3857 195.6374 m S 539.2607 182.5335 m S 0 g 1 w 4 M 539.2607 182.5335 m F 0 G 0.3 w 10 M 539.2607 182.5335 m S 539.2607 182.5335 m S 539.2607 182.5335 m S 0 g 1 w 4 M 539.2607 182.5335 m F 0 G 0.3 w 10 M 539.2607 182.5335 m S 539.2607 182.5335 m S 1 g 1 w 4 M 533.2503 182.5335 m 533.2503 179.3117 535.9413 176.6999 539.2607 176.6999 c 542.5802 176.6999 545.2711 179.3117 545.2711 182.5335 c F 545.2711 182.5335 m 545.2711 185.7553 542.5802 188.3672 539.2607 188.3672 c 535.9413 188.3672 533.2503 185.7553 533.2503 182.5335 c F 539.2607 182.5335 m F 0 G 0.3 w 10 M 539.2607 182.5335 m S 0 g 1 w 4 M 539.2607 182.5335 m F 0 G 0.3 w 10 M 539.2607 182.5335 m S 539.2607 182.5335 m S 0 g 1 w 4 M 538.1756 181.4656 m 538.1756 177.8885 L 540.3458 177.8885 L 540.3458 181.4656 L 543.9314 181.4544 L 543.9314 183.6128 L 540.3458 183.6017 L 540.3458 187.1788 L 538.1756 187.1788 L 538.1756 183.6017 L 534.59 183.6128 L 534.59 181.4544 L 538.1756 181.4656 L f 0 G 0.3 w 10 M 539.3857 182.6709 m S 0 g 1 w 4 M 539.3857 182.6709 m F 0 G 0.3 w 10 M 539.3857 182.6708 m S 539.2607 182.5334 m S 539.2607 182.5334 m S 539.2607 182.5334 m S 539.2607 182.5334 m S 539.3857 182.6708 m S 539.3857 182.6708 m S 532.7328 176.1876 m S 0 g 1 w 4 M 519.677 85.6963 m F 519.677 72.7297 m F 1 g 0 G 427.6509 701.0128 m 427.6036 687.1541 l B u u 0 g /_Times-Italic 12 14.5 0 0 z [1 0 0 1 107 229]e (h')t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 115.5664 229]e (=2)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 128.334 229]e (J')t T U U u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 160.5 229]e (h')t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 169.0664 229]e (=)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 175.834 229]e (J')t T U U 0 G 1 M 153.1554 181.8083 m 169.5848 181.8083 l B u u 4 M /_Times-Italic 12 14.5 0 0 z [1 0 0 1 159 185]e (J')t T U U u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 443.25 185.75]e (J')t T U U 0 G 438.1554 182.8083 m 454.5848 182.8083 l B 1 g 0.5 w 115.2257 91.0679 m 127.4985 94.4832 l 127.5857 87.9824 l 115.2257 91.0679 l b 222.6603 94.3189 m 234.9779 91.0679 l 222.6603 87.8176 l 222.6603 94.3189 l b showpage _E end %%EndDocument @endspecial 220 x FQ(Figure)21 b(4:)33 b(Sequence)20 b(of)i(b)q(ounds)h(pro) o(ving)f(a)g(lo)o(w)o(er)e(b)q(ound)j(on)f(the)g(magnetization)e(for)i(the)60 2611 y(in)o(ternal)15 b(spins.)951 2784 y(98)p eop %%Page: 99 99 bop 426 1178 a @beginspecial 29 @llx 29.500000 @lly 306 @urx 300.500000 @ury 2635 @rwi @setspecial %%BeginDocument: fig5.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n []/_Symbol/Symbol Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Italic/Times-Italic Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 110.0356 221.2557 m S 129.0078 240.0219 m S 90.5078 201.9675 m S 109.754 220.7229 m S 90.5158 202.5109 m S 129.0078 240.0219 m 129.0078 202.5109 L 90.5158 202.5109 L S 109.7618 221.2662 m S 90.5158 202.5109 m 129.0078 202.5109 L S 205.992 240.0219 m S 187.0276 221.7991 m S 225.5196 221.7991 m S 205.992 240.0219 m S 129.0078 240.0219 m S 148.5354 221.7991 m S 264.0116 221.7991 m S 167.4998 202.5109 m 129.0078 202.5109 L 129.0078 240.0219 L S 148.2538 221.2662 m S 205.992 240.0219 m 205.992 202.5109 L 167.4998 202.5109 L S 186.746 221.2662 m S 244.484 202.5109 m 205.992 202.5109 L 205.992 240.0219 L S 225.238 221.2662 m S 244.484 202.5109 m S 263.73 221.2662 m S 244.484 202.5109 m S 90.5158 127.4891 m S 90.5078 126.9457 m S 109.754 145.7011 m S 90.5078 201.9675 m S 109.754 183.2121 m S 90.5158 202.5109 m S 90.5158 127.4891 m S 90.5078 126.9457 m S 109.754 108.1903 m S 90.5158 202.5109 m 129.0078 202.5109 L 129.0078 164.9999 L S 109.7618 183.7555 m S 90.5158 127.4891 m 129.0078 127.4891 L 129.0078 89.9783 L S 109.7618 108.7337 m S 129.0078 164.9999 m 129.0078 127.4891 L 90.5158 127.4891 L S 109.7618 146.2445 m S 109.754 70.6795 m S 129.0078 89.9783 m S 109.7618 71.2229 m S 129.0078 164.9999 m 129.0078 202.5109 L 167.4998 202.5109 L S 148.2538 183.7555 m S 205.992 89.9783 m 205.992 127.4891 L 244.484 127.4891 L S 225.238 108.7337 m S 205.992 164.9999 m 205.992 127.4891 L 167.4998 127.4891 L S 186.746 146.2445 m S 167.4998 202.5109 m 205.992 202.5109 L 205.992 164.9999 L S 186.746 183.7555 m S 205.992 164.9999 m 205.992 202.5109 L 244.484 202.5109 L S 225.238 183.7555 m S 244.484 127.4891 m 205.992 127.4891 L 205.992 164.9999 L S 225.238 146.2445 m S 167.4998 127.4891 m 205.992 127.4891 L 205.992 89.9783 L S 186.746 108.7337 m S 129.0078 89.9783 m 129.0078 127.4891 L 167.4998 127.4891 L S 148.2538 108.7337 m S 167.4998 127.4891 m 129.0078 127.4891 L 129.0078 164.9999 L S 148.2538 146.2445 m S 244.484 202.5109 m S 263.73 183.7555 m S 244.484 127.4891 m S 263.73 108.7337 m S 244.484 127.4891 m S 263.73 146.2445 m S 129.0078 89.9783 m S 148.2538 71.2229 m S 205.992 89.9783 m S 186.746 71.2229 m S 205.992 89.9783 m S 225.238 71.2229 m S 263.73 71.2229 m S 195.992 240.0219 m 205.992 240.0219 L S 205.992 240.0219 m 215.9922 240.0219 L S 119.7576 240.0109 m 129.7578 240.0109 L S 129.7578 240.0109 m 139.7578 240.0109 L S 119.0076 164.9999 m S 129.0078 164.9999 m S 129.0078 164.9999 m S 139.0078 164.9999 m S 195.992 164.9999 m S 205.992 164.9999 m S 205.992 164.9999 m S 218.9922 164.9999 m S 195.992 89.9783 m 205.992 89.9783 L S 205.992 89.9783 m 215.9922 89.9783 L S 119.0076 89.9783 m 129.0078 89.9783 L S 129.0078 89.9783 m 139.0078 89.9783 L S 90.5078 116.9457 m 90.5078 126.9457 L S 90.5078 126.9457 m 90.5078 136.9459 L S 90.5158 117.4891 m 90.5158 127.4891 L S 90.5158 127.4891 m 90.5158 137.4893 L S 167.4998 117.4891 m S 167.4998 127.4891 m S 167.4998 127.4891 m S 167.4998 137.4893 m S 244.484 117.4891 m 244.484 127.4891 L S 244.484 127.4891 m 244.484 137.4893 L S 244.484 192.5109 m 244.484 202.5109 L S 244.484 202.5109 m 244.484 212.5111 L S 167.4998 192.5109 m S 167.4998 202.5109 m S 167.4998 202.5109 m S 167.4998 212.5111 m S 90.5158 192.5109 m 90.5158 202.5109 L S 90.5158 202.5109 m 90.5158 212.5111 L S 90.5078 191.9675 m 90.5078 201.9675 L S 90.5078 201.9675 m 90.5078 211.9677 L S 225.9922 202.5109 m S 225.9922 127.4891 m S 206.0228 107.4889 m S 129.0386 107.4889 m S 225.5196 221.7991 m S 282.9762 240.0219 m S 264.0116 221.7991 m S 244.484 202.5109 m S 244.484 202.5109 m S 225.238 221.2662 m S 282.9762 240.0219 m 282.9762 202.5109 L 244.484 202.5109 L S 263.73 221.2662 m S 244.484 202.5109 m 282.9762 202.5109 L S 244.484 127.4891 m S 225.238 108.7337 m S 244.484 127.4891 m S 244.484 202.5109 m S 244.484 202.5109 m S 225.238 183.7555 m S 244.484 127.4891 m S 225.238 146.2445 m S 244.484 127.4891 m S 244.484 202.5109 m 282.9762 202.5109 L 282.9762 164.9999 L S 263.73 183.7555 m S 244.484 127.4891 m 282.9762 127.4891 L 282.9762 89.9783 L S 263.73 108.7337 m S 282.9762 164.9999 m 282.9762 127.4891 L 244.484 127.4891 L S 263.73 146.2445 m S 225.238 71.2229 m S 282.9762 89.9783 m S 263.73 71.2229 m S 272.976 240.0219 m 282.9762 240.0219 L S 272.976 164.9999 m 282.9762 164.9999 L S 272.976 89.9783 m 282.9762 89.9783 L S 244.484 117.4891 m 244.484 127.4891 L S 244.484 127.4891 m 244.484 137.4893 L S 244.484 192.5109 m 244.484 202.5109 L S 244.484 202.5109 m 244.484 212.5111 L S 272.9762 240.0219 m 282.9762 240.0219 L S 282.9762 240.0219 m 292.9764 240.0219 L S 282.9762 202.5109 m 292.9762 202.5109 L S 292.9762 202.5109 m 302.9764 202.5109 L S 272.9762 164.9999 m 282.9762 164.9999 L S 282.9762 164.9999 m 292.9764 164.9999 L S 272.9762 89.9783 m 282.9762 89.9783 L S 282.9762 89.9783 m 292.9764 89.9783 L S 282.9762 127.4891 m 292.9762 127.4891 L S 292.9762 127.4891 m 302.9764 127.4891 L S 283.007 107.4889 m S 109.754 108.1903 m S 129.0078 89.9783 m S 109.7618 108.7337 m S 129.0078 89.9783 m S 90.5078 51.9241 m S 109.754 70.6795 m S 90.5158 52.4674 m S 129.0078 89.9783 m 129.0078 52.4674 L 90.5158 52.4674 L S 109.7618 71.2229 m S 90.5158 52.4674 m 129.0078 52.4674 L S 205.992 89.9783 m S 225.238 108.7337 m S 205.992 89.9783 m S 205.992 89.9783 m S 205.992 89.9783 m S 186.746 108.7337 m S 129.0078 89.9783 m S 148.2538 108.7337 m S 129.0078 89.9783 m S 263.73 108.7337 m S 167.4998 52.4674 m 129.0078 52.4674 L 129.0078 89.9783 L S 148.2538 71.2229 m S 205.992 89.9783 m 205.992 52.4674 L 167.4998 52.4674 L S 186.746 71.2229 m S 244.484 52.4674 m 205.992 52.4674 L 205.992 89.9783 L S 225.238 71.2229 m S 244.484 52.4674 m S 263.73 71.2229 m S 244.484 52.4674 m S 195.992 89.9783 m 205.992 89.9783 L S 205.992 89.9783 m 215.9922 89.9783 L S 119.0076 89.9783 m 129.0078 89.9783 L S 129.0078 89.9783 m 139.0078 89.9783 L S 90.5078 51.9241 m 90.5078 61.9241 L S 90.5158 52.4674 m 90.5158 62.4674 L S 167.4998 52.4674 m 167.4998 62.4674 L S 244.484 52.4674 m 244.484 62.4674 L S 225.9922 52.4674 m S 206.0228 32.4673 m 206.0074 42.4673 L S 206.0074 42.4673 m 205.992 52.4674 L S 244.4994 42.4674 m 244.484 52.4674 L S 244.484 52.4674 m 244.4686 62.4677 L S 167.5152 42.4674 m 167.4998 52.4674 L S 167.4998 52.4674 m 167.4844 62.4677 L S 129.0386 32.4673 m 129.0232 42.4673 L S 129.0232 42.4673 m 129.0078 52.4674 L S 90.5312 42.4674 m 90.5158 52.4674 L S 90.5158 52.4674 m 90.5004 62.4677 L S 90.5232 41.9241 m 90.5078 51.9241 L S 90.5078 51.9241 m 90.4924 61.9243 L S 225.238 108.7337 m S 282.9762 89.9783 m S 263.73 108.7337 m S 282.9762 89.9783 m S 244.484 52.4674 m S 244.484 52.4674 m S 225.238 71.2229 m S 282.9762 89.9783 m 282.9762 52.4674 L 244.484 52.4674 L S 263.73 71.2229 m S 244.484 52.4674 m 282.9762 52.4674 L S 272.976 89.9783 m 282.9762 89.9783 L S 244.484 52.4674 m 244.484 62.4674 L S 272.9762 89.9783 m 282.9762 89.9783 L S 282.9762 89.9783 m 292.9764 89.9783 L S 282.9762 52.4674 m 292.9762 52.4674 L S 292.9762 52.4674 m 302.9764 52.4674 L S 283.007 32.4673 m 282.9916 42.4673 L S 282.9916 42.4673 m 282.9762 52.4674 L S 244.4994 42.4674 m 244.484 52.4674 L S 244.484 52.4674 m 244.4686 62.4677 L S 4 M 129.0078 164.9999 m 205.992 164.9999 l S 167.4998 202.7609 m 167.4998 127.7391 l S 10 M 167.2497 202.7609 m S 148.0037 202.7609 m S 157.6267 212.1386 m S 186.4958 202.7609 m S 167.2497 202.7609 m S 176.8728 212.1386 m S 157.6267 193.3832 m S 176.8728 193.3832 m S 167.2497 197.7609 m S 167.2497 202.7609 m S 167.2497 202.7609 m S 167.2497 207.761 m S 4 M 167.2497 202.7609 m S 10 M 167.4998 202.5109 m S 167.4998 202.5109 m S 162.4998 202.5109 m S 167.4998 202.5109 m S 167.4998 202.5109 m S 172.4999 202.5109 m S 4 M 163.3436 198.5055 m S 167.2498 202.7609 m S u 0 g 1 M 162.0026 199.3854 m 159.1185 194.0555 L 164.3809 197.0612 L 162.0026 199.3854 L b U 1 w 172.3436 206.7555 m S 167.4998 202.5109 m S 4 M 163.3436 198.5055 m 172.3436 206.7555 l S 0.3 w 10 M 205.617 165.3749 m S 186.371 165.3749 m S 195.9939 174.7526 m S 227.8631 165.3749 m S 205.617 165.3749 m S 215.2401 174.7526 m S 195.9939 155.9972 m S 215.2401 155.9972 m S 205.617 160.3749 m S 205.617 165.3749 m S 205.617 165.3749 m S 205.617 170.375 m S 4 M 205.617 165.3749 m S 10 M 205.8671 165.1249 m S 205.8671 165.1249 m S 200.8671 165.1249 m S 205.8671 165.1249 m S 205.8671 165.1249 m S 210.8671 165.1249 m S 4 M 201.7108 161.1195 m S 205.6171 165.3749 m S u 0 g 1 M 200.3698 161.9994 m 197.4858 156.6695 L 202.7481 159.6752 L 200.3698 161.9994 L b U 1 w 210.7108 169.3695 m S 205.8671 165.1249 m S 4 M 201.7108 161.1195 m 210.7108 169.3695 l S 0.3 w 10 M 167.2497 127.7391 m S 148.0037 127.7391 m S 157.6267 137.1167 m S 186.4958 127.7391 m S 167.2497 127.7391 m S 176.8728 137.1167 m S 157.6267 118.3614 m S 176.8728 118.3614 m S 167.2497 122.7391 m S 167.2497 127.7391 m S 167.2497 127.7391 m S 167.2497 132.7391 m S 4 M 167.2497 127.7391 m S 10 M 167.4998 127.4891 m S 167.4998 127.4891 m S 162.4998 127.4891 m S 167.4998 127.4891 m S 167.4998 127.4891 m S 172.4999 127.4891 m S 4 M 163.3436 123.4837 m S 167.2498 127.7391 m S u 0 g 1 M 162.0026 124.3635 m 159.1185 119.0336 L 164.3809 122.0394 L 162.0026 124.3635 L b U 1 w 172.3436 131.7337 m S 167.4998 127.4891 m S 4 M 163.3436 123.4837 m 172.3436 131.7337 l S 0.3 w 10 M 128.7577 165.2499 m S 109.5117 165.2499 m S 119.1347 174.6275 m S 148.0038 165.2499 m S 128.7577 165.2499 m S 138.3808 174.6275 m S 119.1347 155.8722 m S 138.3808 155.8722 m S 128.7577 160.2499 m S 128.7577 165.2499 m S 128.7577 165.2499 m S 128.7577 170.25 m S 4 M 128.7577 165.2499 m S 10 M 129.0078 164.9999 m S 129.0078 164.9999 m S 124.0078 164.9999 m S 129.0078 164.9999 m S 129.0078 164.9999 m S 134.0079 164.9999 m S 4 M 124.8516 160.9945 m S 128.7578 165.2499 m S u 0 g 1 M 123.5106 161.8743 m 120.6266 156.5444 L 125.8889 159.5502 L 123.5106 161.8743 L b U 1 w 133.8516 169.2445 m S 129.0078 164.9999 m S 4 M 124.8516 160.9945 m 133.8516 169.2445 l S u 0 g /_Times-Italic 12 14.5 0 0 z [1 0 0 1 157.6267 212.1386]e (h)t T /_Times-Roman 12 14.5 0 0 z [1 0 0 1 163.6267 212.1386]e (=)t T /_Symbol 12 14.5 0 0 z [1 0 0 1 170.3943 212.1386]e (-)t T /_Times-Italic 12 14.5 0 0 z [1 0 0 1 176.9802 212.1386]e (J)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 148.2538 108.7337]e (h)t T /_Times-Roman 12 14.5 0 0 z [1 0 0 1 154.2538 108.7337]e (=)t T /_Symbol 12 14.5 0 0 z [1 0 0 1 161.0214 108.7337]e (-)t T /_Times-Italic 12 14.5 0 0 z [1 0 0 1 167.6073 108.7337]e (J)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 213.8671 165.1249]e (h)t T /_Times-Roman 12 14.5 0 0 z [1 0 0 1 219.8671 165.1249]e (=)t T /_Symbol 12 14.5 0 0 z [1 0 0 1 226.6347 165.1249]e (-)t T /_Times-Italic 12 14.5 0 0 z [1 0 0 1 233.2206 165.1249]e (J)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 95.0502 156.0625]e (h)t T /_Times-Roman 12 14.5 0 0 z [1 0 0 1 101.0502 156.0625]e (=)t T /_Symbol 12 14.5 0 0 z [1 0 0 1 107.8178 156.0625]e (-)t T /_Times-Italic 12 14.5 0 0 z [1 0 0 1 114.4037 156.0625]e (J)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 169.9306 180.8125]e (J)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 143.9306 167.3125]e (J)t T U 0 G 0.3 w 10 M 90.5078 276.9893 m S 109.754 258.2339 m S 90.5158 277.5327 m S 109.4724 257.7013 m S 90.5158 277.5327 m 129.0078 277.5327 L 129.0078 240.0219 L S 109.7618 258.7773 m S 109.4802 258.2447 m S 129.0078 240.0219 m 129.0078 277.5327 L 167.4998 277.5327 L S 148.2538 258.7773 m S 224.9564 258.2447 m S 205.992 240.0219 m S 167.4998 277.5327 m 205.992 277.5327 L 205.992 240.0219 L S 186.746 258.7773 m S 205.992 240.0219 m 205.992 277.5327 L 244.484 277.5327 L S 225.238 258.7773 m S 205.992 240.0219 m S 186.4644 258.2447 m S 147.9722 258.2447 m S 129.0078 240.0219 m S 244.484 277.5327 m S 263.73 258.7773 m S 263.4484 258.2447 m S 119.0076 240.0219 m 129.0078 240.0219 L S 129.0078 240.0219 m 139.0078 240.0219 L S 195.992 240.0219 m 205.992 240.0219 L S 205.992 240.0219 m 215.9922 240.0219 L S 90.5078 266.9893 m 90.5078 276.9893 L S 90.5078 266.9893 m 90.5078 276.9893 L S 167.4998 267.5327 m 167.4998 277.5327 L S 244.484 267.5327 m 244.484 277.5327 L S 225.9922 277.5327 m S 90.5232 266.9893 m 90.5078 276.9893 L S 90.5078 276.9893 m 90.4924 286.9895 L S 129.0078 277.5327 m 128.9924 287.5327 L S 128.9924 287.5327 m 128.977 297.5328 L S 90.5232 266.9893 m 90.5078 276.9893 L S 90.5078 276.9893 m 90.4924 286.9895 L S 167.5152 267.5327 m 167.4998 277.5327 L S 167.4998 277.5327 m 167.4844 287.5328 L S 244.4994 267.5327 m 244.484 277.5327 L S 244.484 277.5327 m 244.4686 287.5328 L S 205.992 277.5327 m 205.9766 287.5327 L S 205.9766 287.5327 m 205.9612 297.5328 L S 224.9564 258.2447 m S 244.484 277.5327 m S 244.484 277.5327 m S 225.238 258.7773 m S 244.484 277.5327 m 282.9762 277.5327 L 282.9762 240.0219 L S 263.73 258.7773 m S 263.4484 258.2447 m S 282.9762 240.0219 m S 272.976 240.0219 m 282.9762 240.0219 L S 244.484 267.5327 m 244.484 277.5327 L S 282.9762 277.5327 m 292.9762 277.5327 L S 292.9762 277.5327 m S 272.9762 240.0219 m 282.9762 240.0219 L S 282.9762 240.0219 m 292.9764 240.0219 L S 244.4994 267.5327 m 244.484 277.5327 L S 244.484 277.5327 m 244.4686 287.5328 L S 282.9762 277.5327 m 282.9608 287.5327 L S 282.9608 287.5327 m 282.9454 297.5328 L S 282.9762 277.5327 m 292.9762 277.5327 L S 292.9762 277.5327 m 302.9764 277.5327 L S 52.0238 240.0219 m S 52.3054 240.5545 m S 71.5514 221.7991 m S 90.5158 202.5109 m 52.0238 202.5109 L 52.0238 240.0219 L S 71.2698 221.2662 m S 71.2778 221.8096 m S 52.0238 164.9999 m 52.0238 202.5109 L 90.5158 202.5109 L S 71.2698 183.7555 m S 71.2778 109.277 m S 71.2778 184.2989 m S 71.2778 146.7879 m S 52.0238 89.9783 m 52.0238 127.4891 L 90.5158 127.4891 L S 71.2698 108.7337 m S 90.5158 127.4891 m 52.0238 127.4891 L 52.0238 164.9999 L S 71.2698 146.2445 m S 52.0238 89.9783 m S 71.2698 71.2229 m S 71.2778 71.7662 m S 52.0238 240.0219 m 62.0238 240.0219 L S 52.0238 240.0219 m 62.024 240.0219 L S 52.0238 164.9999 m 62.024 164.9999 L S 52.0238 89.9783 m 62.024 89.9783 L S 42.0238 240.0219 m 52.0238 240.0219 L S 52.0238 240.0219 m 62.024 240.0219 L S 42.0238 240.0219 m 52.0238 240.0219 L S 52.0238 240.0219 m 62.024 240.0219 L S 32.0236 202.5109 m 42.0236 202.5109 L S 42.0236 202.5109 m 52.0238 202.5109 L S 42.0238 164.9999 m 52.0238 164.9999 L S 52.0238 164.9999 m 62.024 164.9999 L S 42.0238 89.9783 m 52.0238 89.9783 L S 52.0238 89.9783 m 62.024 89.9783 L S 32.0236 127.4891 m 42.0236 127.4891 L S 42.0236 127.4891 m 52.0238 127.4891 L S 52.0546 107.4889 m S 71.2778 109.277 m S 52.0238 89.9783 m S 71.2698 108.7337 m S 52.0238 89.9783 m S 90.5158 52.4674 m 52.0238 52.4674 L 52.0238 89.9783 L S 71.2698 71.2229 m S 71.2778 71.7662 m S 52.0238 89.9783 m 62.024 89.9783 L S 42.0238 89.9783 m 52.0238 89.9783 L S 52.0238 89.9783 m 62.024 89.9783 L S 32.0236 52.4674 m 42.0236 52.4674 L S 42.0236 52.4674 m 52.0238 52.4674 L S 52.0546 32.4673 m 52.0392 42.4673 L S 52.0392 42.4673 m 52.0238 52.4674 L S 52.0238 240.0219 m 52.0238 277.5327 L 90.5158 277.5327 L S 71.2698 258.7773 m S 70.9962 258.7881 m S 71.2778 259.3207 m S 70.9882 258.2447 m S 32.0236 277.5327 m 42.0236 277.5327 L S 42.0236 277.5327 m 52.0238 277.5327 L S 52.0238 277.5327 m 52.0084 287.5327 L S 52.0084 287.5327 m 51.993 297.5328 L S u 0 g 1 w 4 M /_Times-Italic 12 14.5 0 0 z [1 0 0 1 271.4306 255.3125]e (J)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 221.1806 267.3125]e (J)t T U _E end %%EndDocument @endspecial 178 1452 a FQ(Figure)16 b(5:)21 b(Decorated)c(lattice)e(when)h (the)g(spin)g(at)h(the)f(origin)g(is)g(free)g(to)g(\015uctuate.)60 1669 y FF(R)g FE(\025)g FF(R)205 1676 y FH(0)225 1669 y FQ(\()p FF(i)261 1676 y FH(1)280 1669 y FF(;)8 b(i)319 1676 y FH(2)338 1669 y FQ(\))18 b(and)g(uniformly)d(in)i(the)g(b)q(oundary)i(condition)e (outside)g(\003)1476 1676 y FD(R)p FH(+2)1550 1669 y FQ(.)25 b(Rep)q(eating)17 b(the)60 1729 y(argumen)o(t)d(but)i(with)f(the)g(image)e (spins)j(in)f(\000)906 1736 y FD(R)p FH(+2)995 1729 y FQ(c)o(hosen)h(as)f(\\) p FE(\000)p FQ(",)1310 1711 y FH(48)1363 1729 y FQ(w)o(e)g(obtain)h(the)f(\\) p FE(\000)p FQ(")h(phase)60 1789 y(for)g(the)f(in)o(ternal)g(spins)h(and)g (th)o(us)f(a)h(strictly)f(negativ)o(e)f(upp)q(er)i(b)q(ound)h(on)f FE(h)p FF(\033)1520 1796 y FD(i)1532 1801 y Fr(1)1549 1796 y FD(;i)1571 1801 y Fr(2)1591 1789 y FE(i)p FQ(.)21 b(This)16 b(pro)o(v)o(es)60 1850 y(that)i(the)f(lo)q(cal)g(magnetization,)f(sa)o(y)h (for)g(the)g(four)h(in)o(ternal)e(spins)i(neigh)o(b)q(oring)f(the)g(origin,)g (is)60 1910 y(determined)d(b)o(y)h(the)h(image)f(spins)i(at)f(fara)o(w)o(a)o (y)h(distances.)133 1995 y FP(Step)j(3.)28 b(Un\014xing)22 b(of)d(the)h(spin)f(at)g(the)h(origin.)28 b FQ(W)l(e)18 b(no)o(w)h(ha)o(v)o (e)e(to)i(mak)o(e)d(a)j(sligh)o(t)f(mo)q(di\014-)60 2055 y(cation)e(in)f(the) g(preceding)g(argumen)o(t,)f(as)i(the)f(system)f(w)o(e)h(really)f(w)o(an)o(t) i(to)f(study)h(is)f(the)g(system)60 2115 y(consisting)f(of)g(the)f(in)o (ternal)g(spins)h(in)f(\003)803 2122 y FD(R)p FH(+2)891 2115 y FP(and)i(the)h(spin)f(at)g(the)h(origin)t FQ(,)d(with)h(the)f(image)g (spins)60 2175 y(in)19 b(\003)154 2152 y FD(imag)q(e)154 2188 y(R)271 2175 y FP(other)h(than)g(the)h(one)g(at)f(the)g(origin)j FQ(\014xed)c(in)g(the)f(alternating)h(con\014guration)i FF(!)1834 2157 y Fy(0)1832 2188 y FD(alt)1876 2175 y FQ(,)60 2236 y(the)15 b(image)g(spins)h(in)f(la)o(y)o(er)g(\000)610 2212 y FD(imag)q(e)610 2248 y(R)p FH(+2)724 2236 y FQ(set)h(to)g(b)q(e)g(\\+",)g(and)g(the)g(spins)f (outside)h(\003)1542 2243 y FD(R)p FH(+2)1632 2236 y FQ(\(b)q(oth)g(image)60 2296 y(and)i(in)o(ternal\))e(\014xed)h(in)g(some)f(arbitrary)h (con\014guration.)26 b(By)16 b(the)h(same)f(reasoning)i(as)g(b)q(efore,)60 2356 y(w)o(e)c(obtain)h(a)g(system)e(on)i(the)f(decorated)g(lattice)g FP(plus)i(the)g(origin)t FQ(,)e(with)h(a)g(coupling)f FF(J)19 b FQ(b)q(et)o(w)o(een)60 2416 y(the)c(origin)g(and)g(its)g(four)g(neigh)o(b)q (ors)h FP(and)g(an)h(additional)f(magnetic)i(\014eld)g FE(\000)p FF(J)i FP(on)d(the)g(neighb)n(ors)60 2476 y(of)d(the)h(origin)i FQ([Figure)12 b(5].)20 b(Denoting)14 b(b)o(y)e FE(h)c(\001)g(i)910 2483 y FH(+)954 2476 y FQ(\(resp.)13 b FE(h)8 b(\001)g(i)1155 2458 y Fy(\030)1155 2489 y FH(+)1185 2476 y FQ(\))13 b(the)g(exp)q(ectation)g (in)g(the)f(old)i(\(resp.)p 60 2526 732 2 v 100 2580 a FA(48)135 2595 y Fz(Because)20 b(w)o(e)f(ha)o(v)o(e)f(\014xed)h(the)f(image)f(spin)h (at)g(the)h(origin)f(to)g(b)q(e)h(+,)g(the)g(t)o(w)o(o)f(situations)g(are)h (not)f(quite)60 2645 y(symmetric.)j(But)16 b(the)h(only)d(c)o(hange)i(is)g(a) f(shift)g(in)g(the)i Fw(lo)n(c)n(ation)h Fz(of)d(the)h(in)o(ternal)f(spins)h (in)f(\000)1587 2651 y Fp(R)p FA(+1)1672 2645 y Fz(whic)o(h)h(feel)f(a)951 2784 y FQ(99)p eop %%Page: 100 100 bop 60 91 a FQ(new\))16 b(decorated)g(system,)f(it)h(is)g(easy)g(to)g(see)g (that)205 233 y FE(h)p FF(\033)252 240 y FH(0)p FD(;)p FH(0)299 233 y FE(i)318 209 y Fy(\030)318 249 y FH(+)389 233 y FQ(=)474 162 y Fx(P)518 205 y FD(\033)538 210 y Fr(0)p Fs(;)p Fr(0)580 205 y FH(=)p Fy(\006)p FH(1)663 195 y FE(h)p FF(\033)710 202 y FH(0)p FD(;)p FH(0)779 195 y FQ(exp)8 b([)p FF(J)d FQ(\()p FF(\033)955 202 y FH(0)p FD(;)p FH(0)1012 195 y FE(\000)11 b FQ(1\)\()p FF(\033)1152 202 y FH(0)p FD(;)p FH(1)1210 195 y FQ(+)g FF(\033)1287 202 y FH(0)p FD(;)p Fy(\000)p FH(1)1373 195 y FQ(+)g FF(\033)1450 202 y FH(1)p FD(;)p FH(0)1507 195 y FQ(+)g FF(\033)1584 202 y Fy(\000)p FH(1)p FD(;)p FH(0)1659 195 y FQ(\)])o FE(i)1711 211 y FH(+)p 474 222 1267 2 v 522 234 a Fx(P)566 278 y FD(\033)586 283 y Fr(0)p Fs(;)p Fr(0)628 278 y FH(=)p Fy(\006)p FH(1)711 267 y FE(h)q FQ(exp)c([)p FF(J)e FQ(\()p FF(\033)906 274 y FH(0)p FD(;)p FH(0)964 267 y FE(\000)10 b FQ(1\)\()p FF(\033)1103 274 y FH(0)p FD(;)p FH(1)1162 267 y FQ(+)h FF(\033)1239 274 y FH(0)p FD(;)p Fy(\000)p FH(1)1324 267 y FQ(+)g FF(\033)1401 274 y FH(1)p FD(;)p FH(0)1459 267 y FQ(+)g FF(\033)1536 274 y Fy(\000)p FH(1)p FD(;)p FH(0)1610 267 y FQ(\)])p FE(i)1662 283 y FH(+)389 379 y FQ(=)474 341 y(1)g FE(\000)g(h)q FQ(exp)c([)p FE(\000)p FQ(2)p FF(J)e FQ(\()p FF(\033)817 348 y FH(0)p FD(;)p FH(1)875 341 y FQ(+)11 b FF(\033)952 348 y FH(0)p FD(;)p Fy(\000)p FH(1)1037 341 y FQ(+)g FF(\033)1114 348 y FH(1)p FD(;)p FH(0)1172 341 y FQ(+)g FF(\033)1249 348 y Fy(\000)p FH(1)p FD(;)p FH(0)1323 341 y FQ(\)])p FE(i)1375 357 y FH(+)p 474 367 931 2 v 474 413 a FQ(1)h(+)f FE(h)p FQ(exp)d([)p FE(\000)p FQ(2)p FF(J)d FQ(\()p FF(\033)817 420 y FH(0)p FD(;)p FH(1)874 413 y FQ(+)11 b FF(\033)951 420 y FH(0)p FD(;)p Fy(\000)p FH(1)1037 413 y FQ(+)g FF(\033)1114 420 y FH(1)p FD(;)p FH(0)1171 413 y FQ(+)g FF(\033)1248 420 y Fy(\000)p FH(1)p FD(;)p FH(0)1323 413 y FQ(\)])o FE(i)1375 429 y FH(+)1423 379 y FF(:)353 b FQ(\(4.7\))60 532 y(Similarly)l(,)12 b(for)k(the)f(analogous)i(system)d(with)h(the)g(image) f(spins)h(in)g(\000)1358 508 y FD(imag)q(e)1358 544 y(R)p FH(+2)1473 532 y FQ(set)g(to)g(\\)p FE(\000)p FQ(",)h(w)o(e)f(ha)o(v)o(e)359 677 y FE(h)q FF(\033)407 684 y FH(0)p FD(;)p FH(0)454 677 y FE(i)473 653 y Fy(\030)473 693 y(\000)544 677 y FQ(=)628 639 y(1)d FE(\000)f(h)p FQ(exp)d([)o FE(\000)p FQ(2)p FF(J)d FQ(\()p FF(\033)971 646 y FH(0)p FD(;)p FH(1)1029 639 y FQ(+)11 b FF(\033)1106 646 y FH(0)p FD(;)p Fy(\000)p FH(1)1191 639 y FQ(+)g FF(\033)1268 646 y FH(1)p FD(;)p FH(0)1326 639 y FQ(+)g FF(\033)1403 646 y Fy(\000)p FH(1)p FD(;)p FH(0)1478 639 y FQ(\)])o FE(i)1530 655 y Fy(\000)p 628 665 V 628 711 a FQ(1)h(+)f FE(h)q FQ(exp)c([)p FE(\000)p FQ(2)p FF(J)e FQ(\()p FF(\033)971 718 y FH(0)p FD(;)p FH(1)1029 711 y FQ(+)11 b FF(\033)1106 718 y FH(0)p FD(;)p Fy(\000)p FH(1)1191 711 y FQ(+)g FF(\033)1268 718 y FH(1)p FD(;)p FH(0)1326 711 y FQ(+)g FF(\033)1403 718 y Fy(\000)p FH(1)p FD(;)p FH(0)1477 711 y FQ(\)])p FE(i)1529 727 y Fy(\000)544 822 y FQ(=)628 784 y(1)h FE(\000)f(h)p FQ(exp)d([)o(+2)p FF(J)d FQ(\()p FF(\033)970 791 y FH(0)p FD(;)p FH(1)1028 784 y FQ(+)11 b FF(\033)1105 791 y FH(0)p FD(;)p Fy(\000)p FH(1)1191 784 y FQ(+)g FF(\033)1268 791 y FH(1)p FD(;)p FH(0)1326 784 y FQ(+)g FF(\033)1403 791 y Fy(\000)p FH(1)p FD(;)p FH(0)1477 784 y FQ(\)])o FE(i)1529 800 y FH(+)p 628 810 930 2 v 628 856 a FQ(1)h(+)f FE(h)q FQ(exp)c([+2)p FF(J)e FQ(\()p FF(\033)970 863 y FH(0)p FD(;)p FH(1)1028 856 y FQ(+)11 b FF(\033)1105 863 y FH(0)p FD(;)p Fy(\000)p FH(1)1190 856 y FQ(+)g FF(\033)1267 863 y FH(1)p FD(;)p FH(0)1325 856 y FQ(+)g FF(\033)1402 863 y Fy(\000)p FH(1)p FD(;)p FH(0)1477 856 y FQ(\)])o FE(i)1528 872 y FH(+)1577 822 y FF(:)1790 930 y FQ(\(4.8\))60 1040 y(Therefore,)583 1125 y FE(h)p FF(\033)630 1132 y FH(0)p FD(;)p FH(0)677 1125 y FE(i)697 1100 y Fy(\030)697 1141 y FH(+)745 1125 y FE(\000)20 b(h)p FF(\033)851 1132 y FH(0)p FD(;)p FH(0)898 1125 y FE(i)917 1100 y Fy(\030)917 1141 y(\000)974 1125 y FQ(=)1106 1091 y(2\()p FF(y)13 b FE(\000)e FF(x)p FQ(\))p 1045 1113 299 2 v 1045 1159 a(\(1)g(+)g FF(x)p FQ(\)\(1)g(+)g FF(y)r FQ(\))1362 1125 y FF(;)414 b FQ(\(4)p FF(:)p FQ(9\))60 1237 y(where)474 1347 y FF(x)41 b FQ(=)g FE(h)q FQ(exp)8 b([)o FE(\000)p FQ(2)p FF(J)d FQ(\()p FF(\033)880 1354 y FH(0)p FD(;)p FH(1)938 1347 y FQ(+)11 b FF(\033)1015 1354 y FH(0)p FD(;)p Fy(\000)p FH(1)1100 1347 y FQ(+)g FF(\033)1177 1354 y FH(1)p FD(;)p FH(0)1235 1347 y FQ(+)g FF(\033)1312 1354 y Fy(\000)p FH(1)p FD(;)p FH(0)1387 1347 y FQ(\)])o FE(i)1438 1363 y FH(+)1765 1347 y FQ(\(4.10\))476 1420 y FF(y)43 b FQ(=)e FE(h)q FQ(exp)8 b([)o(+2)p FF(J)d FQ(\()p FF(\033)879 1427 y FH(0)p FD(;)p FH(1)937 1420 y FQ(+)11 b FF(\033)1014 1427 y FH(0)p FD(;)p Fy(\000)p FH(1)1099 1420 y FQ(+)g FF(\033)1176 1427 y FH(1)p FD(;)p FH(0)1234 1420 y FQ(+)g FF(\033)1311 1427 y Fy(\000)p FH(1)p FD(;)p FH(0)1386 1420 y FQ(\)])o FE(i)1438 1436 y FH(+)1765 1420 y FQ(\(4.11\))60 1530 y(No)o(w)374 1640 y FF(y)h FE(\000)f FF(x)42 b FQ(=)f(2)8 b FE(h)p FQ(sinh)i(2)p FF(J)5 b FQ(\()p FF(\033)860 1647 y FH(0)p FD(;)p FH(1)918 1640 y FQ(+)11 b FF(\033)995 1647 y FH(0)p FD(;)p Fy(\000)p FH(1)1080 1640 y FQ(+)g FF(\033)1157 1647 y FH(1)p FD(;)p FH(0)1215 1640 y FQ(+)g FF(\033)1292 1647 y Fy(\000)p FH(1)p FD(;)p FH(0)1366 1640 y FQ(\))p FE(i)1404 1647 y FH(+)530 1745 y FQ(=)41 b(2)690 1691 y Fy(1)677 1703 y Fx(X)665 1802 y FD(k)11 b FH(=)g(1)663 1844 y FD(k)i FH(o)q(dd)786 1711 y FQ(\(2)p FF(J)5 b FQ(\))880 1693 y FD(k)p 786 1733 116 2 v 823 1779 a FF(k)r FQ(!)914 1745 y FE(h)p FQ(\()p FF(\033)980 1752 y FH(0)p FD(;)p FH(1)1039 1745 y FQ(+)11 b FF(\033)1116 1752 y FH(0)p FD(;)p Fy(\000)p FH(1)1201 1745 y FQ(+)g FF(\033)1278 1752 y FH(1)p FD(;)p FH(0)1336 1745 y FQ(+)g FF(\033)1413 1752 y Fy(\000)p FH(1)p FD(;)p FH(0)1487 1745 y FQ(\))1506 1724 y FD(k)1528 1745 y FE(i)1547 1752 y FH(+)529 1915 y FE(\025)41 b FQ(4)p FF(J)14 b FE(h)p FQ(\()p FF(\033)740 1922 y FH(0)p FD(;)p FH(1)798 1915 y FQ(+)d FF(\033)875 1922 y FH(0)p FD(;)p Fy(\000)p FH(1)960 1915 y FQ(+)g FF(\033)1037 1922 y FH(1)p FD(;)p FH(0)1095 1915 y FQ(+)g FF(\033)1172 1922 y Fy(\000)p FH(1)p FD(;)p FH(0)1247 1915 y FQ(\))p FE(i)1285 1922 y FH(+)530 1988 y FQ(=)41 b(16)p FF(J)14 b FE(h)p FF(\033)745 1995 y FH(0)p FD(;)p FH(1)792 1988 y FE(i)811 1995 y FH(+)855 1988 y FF(;)896 b FQ(\(4.12\))60 2098 y(since)10 b(the)h(con)o(tributions)g(from)e FF(k)16 b FQ(=)e(3)p FF(;)8 b FQ(5)p FF(;)g(:)g(:)g(:)j FQ(are)g(all)f (nonnegativ)o(e)h(b)o(y)f(Gri\016ths')g(\014rst)i(inequalit)o(y)l(.)60 2158 y(On)21 b(the)g(other)g(hand,)h(the)e(denominator)h(in)f(\(4.9\))h(is)g (b)q(ounded)h(b)q(et)o(w)o(een)e(1)h(and)g(\(1)15 b(+)f FF(e)1796 2140 y FH(8)p FD(J)1838 2158 y FQ(\))1857 2140 y FH(2)1876 2158 y FQ(.)60 2218 y(Since)f(w)o(e)g(pro)o(v)o(ed)g(previously)f(that)i(for) g FF(J)847 2200 y Fy(0)872 2218 y FF(>)g(J)951 2225 y FD(c)968 2218 y FQ(,)g(the)f(lo)q(cal)h(magnetization)e FE(h)p FF(\033)1551 2225 y FH(0)p FD(;)p FH(1)1598 2218 y FE(i)1617 2225 y FH(+)1661 2218 y FQ(is)h(b)q(ounded)60 2278 y(b)q(elo)o(w)22 b(b)o(y)f(a)h(strictly)e (p)q(ositiv)o(e)h(constan)o(t,)i(uniformly)d(in)h FF(R)h FQ(\(su\016cien)o (tly)e(large\))i(and)g(in)f(the)60 2338 y(con\014guration)c(outside)g(\003) 558 2345 y FD(R)p FH(+2)631 2338 y FQ(,)f(w)o(e)g(can)g(conclude)g(that)675 2448 y FE(h)p FF(\033)722 2455 y FH(0)p FD(;)p FH(0)770 2448 y FE(i)789 2428 y Fy(\030)789 2461 y FH(+)838 2448 y FE(\000)j(h)p FF(\033)943 2455 y FH(0)p FD(;)p FH(0)990 2448 y FE(i)1009 2428 y Fy(\030)1009 2461 y(\000)1067 2448 y FE(\025)27 b FF(\016)j(>)d FQ(0)491 b(\(4)p FF(:)p FQ(13\))60 2558 y(uniformly)14 b(in)i FF(R)h FQ(\(su\016cien)o(tly)d(large\))i(and)h(in)f(the)g(con\014guration)h (outside)g(\003)1528 2565 y FD(R)p FH(+2)1601 2558 y FQ(.)p 60 2605 732 2 v 60 2657 a Fz(nonzero)e(e\013ectiv)o(e)g(\014eld;)e(and)h (this)g(is)g(irrelev)n(an)o(t,)f(since)i(w)o(e)f(replace)h(these)g(\014elds)f (b)o(y)g(zero)h(an)o(yw)o(a)o(y)m(.)938 2784 y FQ(100)p eop %%Page: 101 101 bop 133 91 a FP(Conclusion)23 b(of)e(the)g(ar)n(gument.)34 b FQ(In)20 b(summary)l(,)e(w)o(e)i(ha)o(v)o(e)g(sho)o(wn)g(that)h(at)g(zero)f (magnetic)60 152 y(\014eld)11 b(and)h(an)o(y)g(su\016cien)o(tly)d(lo)o(w)j (temp)q(erature,)e(giv)o(en)h(an)o(y)g(Gibbs)h(measure)f FF(\026)p FQ(,)h(the)f(renormalized)60 212 y(measure)k FF(\026T)22 b FQ(has)17 b(the)e(follo)o(wing)h(prop)q(ert)o(y:)21 b(Let)16 b FF(!)1043 194 y Fy(0)1041 224 y FD(alt)1102 212 y FQ(b)q(e)g(the)f(fully)g (alternating)h(con\014guration)60 272 y FF(\033)90 254 y Fy(0)88 284 y FD(i)100 289 y Fr(1)117 284 y FD(;i)139 289 y Fr(2)176 272 y FQ(=)i(\()p FE(\000)p FQ(1\))333 254 y FD(i)345 259 y Fr(1)363 254 y FH(+)p FD(i)402 259 y Fr(2)422 272 y FQ(;)h(let)f FF(A)565 279 y FD(R;)p FH(+)649 272 y FE(\021)g(N)747 280 y FD(R=)p FH(2)p FD(;)p FH(\()p FD(R=)p FH(2\)+1)p FD(;)p FH(+)1011 272 y FQ(b)q(e)h(the)g(set)f(of)h(all)g(con\014gurations)h FE(f)p FF(\033)1746 254 y Fy(0)1757 272 y FE(g)f FQ(that)60 332 y(are)e(alternating)g(in)f(\003)483 340 y FD(R=)p FH(2)547 332 y FQ(,)g(\\+")i(in)e(\000)768 340 y FH(\()p FD(R=)p FH(2\)+1)922 332 y FQ(and)h(arbitrary)g(outside;)f(and)i(let)e FF(A)1611 339 y FD(R;)p Fy(\000)1693 332 y FQ(b)q(e)h(analo-)60 392 y(gously)h (de\014ned)f(but)h(with)g(\\)p FE(\000)p FQ(")g(in)f(\000)778 400 y FH(\()p FD(R=)p FH(2\)+1)915 392 y FQ(.)25 b(In)18 b(the)f(pro)q(duct)h (top)q(ology)h FF(A)1525 399 y FD(R;)p FH(+)1608 392 y FQ(and)g FF(A)1742 399 y FD(R;)p Fy(\000)1825 392 y FQ(are)60 452 y(op)q(en)f(sets)f (|)h(in)f(particular,)g(they)f(ha)o(v)o(e)h(strictly)f(p)q(ositiv)o(e)h(\()p FF(\026T)7 b FQ(\)-measure)16 b(|)h(and)h(giv)o(en)e(an)o(y)60 513 y(neigh)o(b)q(orho)q(o)q(d)i(of)d FE(N)21 b(3)15 b FF(!)562 495 y Fy(0)560 525 y FD(alt)620 513 y FQ(w)o(e)g(alw)o(a)o(ys)h(c)o(ho)q(ose) g FF(R)g FQ(large)f(enough)i(so)f(that)g FF(A)1541 520 y FD(R;)p FH(+)1616 513 y FE([)10 b FF(A)1696 520 y FD(R;)p Fy(\000)1776 513 y FE(\032)j(N)7 b FQ(.)60 573 y(Moreo)o(v)o(er,)15 b(w)o(e)g(ha)o(v)o(e)h (pro)o(v)o(en)f(that)i(for)g(all)e FF(!)910 555 y Fy(0)908 585 y FH(1)942 573 y FE(2)f FF(A)1026 580 y FD(R;)p FH(+)1108 573 y FQ(and)j FF(!)1235 555 y Fy(0)1233 585 y FH(2)1267 573 y FE(2)d FF(A)1351 580 y FD(R;)p Fy(\000)1417 573 y FQ(,)h(w)o(e)h(ha)o(v)o (e)109 691 y FF(E)145 698 y FD(\026T)202 642 y Fx(\020)227 691 y FF(\033)257 670 y Fy(0)255 703 y FH(0)p FD(;)p FH(0)310 691 y FE(j)8 b(f)p FF(\033)387 670 y Fy(0)385 703 y FD(i)397 708 y Fr(1)414 703 y FD(;i)436 708 y Fr(2)455 691 y FE(g)480 698 y FH(\()p FD(i)506 703 y Fr(1)523 698 y FD(;i)545 703 y Fr(2)563 698 y FH(\))p Fy(6)p FH(=\(0)p FD(;)p FH(0\))678 642 y Fx(\021)711 691 y FQ(\()p FF(!)762 670 y Fy(0)760 703 y FH(1)780 691 y FQ(\))25 b FE(\000)g FF(E)924 698 y FD(\026T)981 642 y Fx(\020)1006 691 y FF(\033)1036 670 y Fy(0)1034 703 y FH(0)p FD(;)p FH(0)1089 691 y FE(j)8 b(f)p FF(\033)1166 670 y Fy(0)1164 703 y FD(i)1176 708 y Fr(1)1193 703 y FD(;i)1215 708 y Fr(2)1234 691 y FE(g)1259 698 y FH(\()p FD(i)1285 703 y Fr(1)1302 698 y FD(;i)1324 703 y Fr(2)1341 698 y FH(\))p Fy(6)p FH(=\(0)p FD(;)p FH(0\))1457 642 y Fx(\021)1490 691 y FQ(\()p FF(!)1541 670 y Fy(0)1539 703 y FH(2)1559 691 y FQ(\))28 b FE(\025)f FF(\016)j(>)d FQ(0)14 b FF(:)1765 757 y FQ(\(4)p FF(:)p FQ(14\))60 817 y(This)i(means)f(|)g(as)h(\014rst)g(p)q(oin)o(ted)g(out)g(b)o(y)f(Israel) h([207])g(|)f(that)h(the)g(conditional)f(exp)q(ectations)60 877 y(of)22 b FF(\033)151 859 y Fy(0)149 890 y FH(0)p FD(;)p FH(0)218 877 y FQ(are)f(discon)o(tin)o(uous)h(as)g(a)g(function)g(of)g(the)f (b)q(oundary)i(conditions.)38 b(More)21 b(precisely)l(,)60 938 y(they)16 b(are)g FP(essential)r(ly)k(disc)n(ontinuous)t FQ(:)i(no)17 b(mo)q(di\014cation)f(on)h(a)g(set)f(of)h(\()p FF(\026T)7 b FQ(\)-measure)15 b(zero)h(can)60 998 y(mak)o(e)g(them)g(con)o (tin)o(uous)i(at)g FF(!)654 980 y Fy(0)652 1010 y FD(alt)697 998 y FQ(.)27 b(No)o(w,)17 b(for)h(systems)f(with)h(a)g(\014nite)g (single-spin)f(space)h(\(suc)o(h)60 1058 y(as)f(the)f(Ising)g(mo)q(del\),)e (con)o(tin)o(uit)o(y)g(is)i(equiv)m(alen)o(t)f(to)h(quasilo)q(calit)o(y)l(.)k (Therefore,)15 b(what)i(w)o(e)f(ha)o(v)o(e)60 1118 y(really)d(pro)o(v)o(en)h (is)g(that)h FP(the)i(r)n(enormalize)n(d)e(me)n(asur)n(e)g FF(\026T)22 b FP(is)16 b(not)g(c)n(onsistent)h(with)g(any)f(quasilo)n(c)n(al) 60 1178 y(sp)n(e)n(ci\014c)n(ation)t FQ(.)33 b(\(In)20 b(our)h(language,)g FF(\026T)27 b FQ(is)20 b FP(non-quasilo)n(c)n(al)5 b FQ(;)24 b(in)c(the)g(terminology)e(of)j(Sulliv)m(an)60 1239 y([336)q(],)13 b(it)g(is)g FP(non-almost)j(Markovian)t FQ(.\))k(In)13 b(particular,)g FF(\026T)22 b FP(is)14 b(not)i(Gibbsian)f(for)f(any)h(uniformly)60 1299 y(c)n(onver)n(gent)k(inter)n(action.)60 1413 y FM(Theorem)e(4.1)24 b FP(L)n(et)18 b FF(\026)i FP(b)n(e)f(any)g(Gibbs)h(me)n(asur)n(e)e(for)h (the)h(two-dimensional)h(Ising)e(mo)n(del)h(with)60 1473 y(ne)n(ar)n (est-neighb)n(or)25 b(c)n(oupling)g FF(J)30 b(>)751 1453 y FH(1)p 751 1461 18 2 v 751 1490 a(2)782 1473 y FQ(cosh)874 1452 y Fy(\000)p FH(1)921 1473 y FQ(\(1)16 b(+)1034 1432 y FE(p)p 1076 1432 25 2 v 41 x FQ(2\))26 b(=)g(0)p FF(:)p FQ(764285)8 b FF(:)g(:)g(:)27 b FE(\031)f FQ(1)p FF(:)p FQ(73)p FF(J)1662 1480 y FD(c)1704 1473 y FP(and)e(zer)n(o)60 1533 y(magnetic)c(\014eld.)27 b(L)n(et)18 b FF(T)25 b FP(b)n(e)19 b(the)h(de)n(cimation)f(tr)n (ansformation)e(with)i(sp)n(acing)g FF(b)d FQ(=)g(2)p FP(.)26 b(Then)19 b(the)60 1593 y(me)n(asur)n(e)f FF(\026T)25 b FP(is)18 b(not)h(c)n(onsistent)g(with)g(any)f(quasilo)n(c)n(al)h(sp)n(e)n(ci\014c)n (ation.)25 b(In)19 b(p)n(articular,)f(it)g(is)h(not)60 1654 y(the)f(Gibbs)g(me)n(asur)n(e)e(for)h(any)h(uniformly)f(c)n(onver)n(gent)i (inter)n(action.)133 1768 y FQ(In)h(ph)o(ysical)f(terms,)f(w)o(e)i(ha)o(v)o (e)f(sho)o(wn)h(that)h(the)e(v)m(alue)h(of)g(the)g(renormalized)d(spin)j(at)g (the)60 1828 y(origin,)h FF(\033)247 1810 y Fy(0)245 1840 y FH(0)p FD(;)p FH(0)292 1828 y FQ(,)g(dep)q(ends)g(strongly)g(on)g(the)g(v)m (alues)f(of)h(the)g(renormalized)d(spins)j(arbitrarily)f(far)60 1888 y(from)f(the)h(origin,)h(if)f(the)g(renormalized)e(spins)j(in)f(the)g (in)o(termediate)d(region)k(are)f(\014xed)g(to)h(b)q(e)60 1948 y(alternating.)g(Suc)o(h)14 b(a)h(long-range)h(dep)q(endence)e(is)g (incompatible)e(with)j(the)f(measure)g FF(\026T)21 b FQ(b)q(eing)60 2009 y(Gibbsian)c(for)f(an)o(y)g(reasonable)h(in)o(teraction.)60 2153 y FB(4.2)70 b(Gri\016ths-P)n(earce-Israel)21 b(P)n(athologies)h(I)r(I:)h (General)f(Metho)r(d)60 2245 y FQ(In)12 b(this)f(section)h(w)o(e)f(abstract)i (the)e(essen)o(tial)g(features)h(of)g(the)g(Gri\016ths-P)o(earce-Israel)f (argumen)o(t,)60 2306 y(in)16 b(order)g(to)h(prepare)f(the)g(w)o(a)o(y)g(for) g(generalizations)g(to)h(more)e(complicated)f(examples.)60 2416 y FP(Step)k(0.)23 b(Computation)17 b(of)h(the)f(c)n(onditional)i(pr)n (ob)n(abilities.)133 2476 y FQ(This)11 b(step)g(is)g(tec)o(hnical)e(and)i (messy)l(,)f(but)h(the)g(\014nal)g(result)f(is)h(the)f(ob)o(vious)h(one)g ([cf.)f(\(4.22\)/\(4.23\))60 2536 y(b)q(elo)o(w].)21 b(The)16 b(reader)g(is)g(therefore)g(in)o(vited)e(to)j(skip)f(this)g(step)g(on)h(a)f (\014rst)h(reading.)133 2596 y(F)l(or)24 b(decimation,)f(the)h(computation)f (of)h(the)g(conditional)g(probabilities)e(of)j FF(\026T)30 b FQ(w)o(as)25 b(an)60 2656 y(immedi)o(ate)18 b(application)i(of)h(Prop)q (osition)h(2.25.)35 b(F)l(or)20 b(more)g(general)g(R)l(T)h(maps,)f(it)g(will) g(b)q(e)h(a)938 2784 y(101)p eop %%Page: 102 102 bop 60 91 a FQ(more)17 b(complicated)f(application)i(of)g(this)g(same)f(prop) q(osition:)26 b(the)18 b(idea)g(is)g(to)g(consider)g(\014rst)h(a)60 152 y FP(joint)h FQ(system)14 b(of)h(in)o(teracting)f(spins)h FF(!)j FQ(and)d FF(!)931 133 y Fy(0)943 152 y FQ(,)g(and)h(then)e(decimate)f (this)i(system)f(to)h(the)g(space)60 212 y(\012)95 194 y Fy(0)107 212 y FQ(.)133 272 y(If)i FF(\026)g FQ(is)g(an)o(y)g(measure)e(on)j(the)e (system)g(of)h(original)g(spins)g(\(i.e.)e(on)j(\012\),)f(and)g FF(T)24 b FQ(is)16 b(an)o(y)h(prob-)60 332 y(abilit)o(y)i(k)o(ernel)f(from)h (\012)h(to)h(\012)636 314 y Fy(0)647 332 y FQ(,)g(then)f(the)g(join)o(t)f (measure)g FF(\026)14 b FE(\002)f FF(T)27 b FQ(on)20 b(\012)14 b FE(\002)g FQ(\012)1555 314 y Fy(0)1587 332 y FQ(is)19 b(w)o(ell-de\014ned) 60 392 y(b)o(y)502 465 y(\()p FF(\026)11 b FE(\002)g FF(T)c FQ(\)\()p FF(A)p FQ(\))26 b(=)833 406 y Fx(Z)874 465 y FF(d\026)p FQ(\()p FF(!)r FQ(\))1006 406 y Fx(Z)1049 465 y FF(T)7 b FQ(\()p FF(!)r(;)h(d!)1215 444 y Fy(0)1226 465 y FQ(\))g FF(\037)1284 472 y FD(A)1313 465 y FQ(\()p FF(!)r(;)g(!)1418 444 y Fy(0)1430 465 y FQ(\))316 b(\(4)p FF(:)p FQ(15\))60 567 y(for)19 b(measurable)f(sets)h FF(A)f FE(\032)g FQ(\012)13 b FE(\002)g FQ(\012)740 549 y Fy(0)752 567 y FQ(.)29 b(No)o(w,)19 b(if)f(\005)g(=)h FE(f)p FF(\031)1135 574 y FH(\003)1161 567 y FE(g)g FQ(is)g(a)g(sp)q(eci\014cation)g(for)g(the)f (system)60 627 y(of)e(original)g(spins,)g(w)o(e)g(wish)g(to)h(de\014ne)e(a)i (sp)q(eci\014cation)f(\005)10 b FE(\012)g FF(T)21 b FQ(=)13 b FE(f)p FQ(\(\005)d FE(\012)h FF(T)c FQ(\))1522 634 y FH(\003)p FD(;)p FH(\003)1580 625 y Ft(0)1593 627 y FE(g)16 b FQ(for)h(the)e(join)o(t) 60 687 y(system,)f(with)i(the)g(prop)q(ert)o(y)h(that)378 796 y FF(\026)f FQ(consisten)o(t)g(with)g(\005)27 b(=)-8 b FE(\))27 b FF(\026)12 b FE(\002)f FF(T)22 b FQ(consisten)o(t)16 b(with)g(\005)11 b FE(\012)g FF(T)20 b(:)192 b FQ(\(4)p FF(:)p FQ(16\))60 906 y(\(In)15 b(fact,)f(the)h(con)o(v)o(erse)f(should)h(also)h(hold,)f(i.e.)e(a)j (measure)d FF(\027)19 b FQ(on)c(\012)9 b FE(\002)f FQ(\012)1434 888 y Fy(0)1461 906 y FQ(should)15 b(b)q(e)g(consisten)o(t)60 966 y(with)h(\005)11 b FE(\012)g FF(T)22 b FQ(if)16 b(and)h(only)f(if)f FF(\026)g FE(\021)e FF(\027)s Fm(\026)p FE(F)21 b FQ(is)16 b(consisten)o(t)g(with)g(\005)g(and)h FF(\027)g FQ(=)d FF(\026)d FE(\002)g FF(T)c FQ(.\))133 1026 y(F)l(or)17 b(simplici)o(t)o(y)c(let)i(us)i (assume)f(that)g(the)g(probabilit)o(y)g(k)o(ernel)e FF(T)23 b FQ(has)17 b(the)f(follo)o(wing)g(form:)581 1136 y FF(T)7 b FQ(\()p FF(!)r(;)h(d!)747 1115 y Fy(0)759 1136 y FQ(\))27 b(=)884 1094 y Fx(Y)871 1187 y FD(x)p Fy(2L)939 1177 y Ft(0)968 1120 y Fx(e)958 1136 y FF(T)987 1143 y FD(x)1008 1136 y FQ(\()p FF(!)1057 1143 y FD(B)1084 1147 y Fs(x)1106 1136 y FF(;)8 b(!)1160 1115 y Fy(0)1158 1148 y FD(x)1180 1136 y FQ(\))g FF(d\027)1256 1143 y FD(x)1279 1136 y FQ(\()p FF(!)1330 1115 y Fy(0)1328 1148 y FD(x)1350 1136 y FQ(\))396 b(\(4)p FF(:)p FQ(17\))60 1281 y(where)13 b(the)g FF(\027)303 1288 y FD(x)338 1281 y FQ(are)h(probabilit)o(y)e(measures,)h(and)g(the)g FF(B)1093 1288 y FD(x)1129 1281 y FQ(are)g(\014nite)g(sets)g(of)h(original)f(spins)h (whic)o(h)60 1341 y(together)g(determine)d(the)i(image)f(spin)i FF(!)827 1323 y Fy(0)825 1354 y FD(x)847 1341 y FQ(.)21 b(W)l(e)13 b(also)h(assume)f(that)h(the)f(family)f(of)i(sets)f FE(f)p FF(B)1762 1348 y FD(x)1784 1341 y FE(g)1809 1348 y FD(x)p Fy(2L)1877 1339 y Ft(0)60 1401 y FQ(is)19 b(lo)q(cally)g(\014nite)379 1383 y FH(49)416 1401 y FQ(,)g(i.e.)f(only)h(\014nitely)f(man)o(y)g(image)g (spins)i FF(x)f FQ(dep)q(end)g(on)h(an)o(y)g(giv)o(en)e(original)60 1462 y(spin)f FF(y)r FQ(.)25 b(No)o(w,)17 b(to)h(motiv)m(ate)e(the)h (construction,)g(supp)q(ose)i(that)f FF(\026)g FQ(is)f(a)h(Gibbs)g(measure)e (for)i(an)60 1522 y(in)o(teraction)f(\010)h(\(and)h FP(a)g(priori)i FQ(measure)c FF(\026)884 1504 y FH(0)904 1522 y FQ(\).)26 b(Then,)18 b FP(formal)r(ly)23 b FQ(the)18 b(measure)e FF(\026)d FE(\002)f FF(T)24 b FQ(is)18 b(giv)o(en)60 1582 y(b)o(y)432 1691 y(\()p FF(\026)11 b FE(\002)g FF(T)c FQ(\)\()p FF(d!)r(;)h(d!)751 1671 y Fy(0)763 1691 y FQ(\))13 b(\\=")i(const)20 b FE(\002)496 1758 y Fx(Y)480 1850 y FD(X)s Fy(\032L)572 1800 y FF(e)595 1779 y Fy(\000)p FH(\010)647 1785 y Fs(X)677 1779 y FH(\()p FD(!)q FH(\))750 1758 y Fx(Y)737 1850 y FD(x)p Fy(2L)805 1841 y Ft(0)835 1783 y Fx(e)825 1800 y FF(T)854 1807 y FD(x)875 1800 y FQ(\()p FF(!)924 1807 y FD(B)951 1811 y Fs(x)973 1800 y FF(;)8 b(!)1027 1779 y Fy(0)1025 1812 y FD(x)1047 1800 y FQ(\))1081 1758 y Fx(Y)1074 1850 y FD(x)p Fy(2L)1150 1800 y FF(d\026)1204 1779 y FH(0)1204 1812 y FD(x)1227 1800 y FQ(\()p FF(!)1276 1807 y FD(x)1298 1800 y FQ(\))1338 1758 y Fx(Y)1325 1850 y FD(x)p Fy(2L)1393 1841 y Ft(0)1412 1800 y FF(d\027)1461 1807 y FD(x)1484 1800 y FQ(\()p FF(!)1535 1779 y Fy(0)1533 1812 y FD(x)1555 1800 y FQ(\))14 b FF(:)1765 1911 y FQ(\(4.18\))60 2020 y(Of)23 b(course,)h(the)f(\014rst)g(t)o(w)o(o)g(in\014nite)f(pro)q (ducts)i(\(the)f(ones)h(o)o(v)o(er)e(functions)h FF(e)1562 2002 y Fy(\000)p FH(\010)1614 2008 y Fs(X)1643 2002 y FH(\()p FD(!)q FH(\))1719 2020 y FQ(and)1831 2004 y Fx(e)1821 2020 y FF(T)1850 2027 y FD(x)1871 2020 y FQ(\))60 2080 y(are)g(meaningless,)g(but) g(w)o(e)g(kno)o(w)g(what)h(to)f(do:)35 b(to)24 b(describ)q(e)e(the)h FP(c)n(onditional)29 b FQ(probabilit)o(y)60 2141 y(distribution)16 b FF(\026)c FE(\002)f FF(T)c FQ(,)15 b(with)i FF(!)h FQ(\014xed)f(outside)f (a)h(\014nite)f(set)h(\003)f(and)h FF(!)1349 2122 y Fy(0)1377 2141 y FQ(\014xed)g(outside)f(a)h(\014nite)f(set)60 2201 y(\003)94 2183 y Fy(0)105 2201 y FQ(,)g(w)o(e)g(retain)g(in)g(the)g(pro)q(ducts)h(only) f(those)h(terms)d(that)j(in)o(tersect)e(\003)h(and/or)i(\003)1611 2183 y Fy(0)1622 2201 y FQ(,)e(i.e.)219 2310 y(\()p FF(\026)c FE(\002)f FF(T)c FQ(\)\()p FF(d!)458 2317 y FH(\003)484 2310 y FF(;)h(d!)563 2290 y Fy(0)561 2323 y FH(\003)585 2313 y Ft(0)599 2310 y FE(j)p FF(!)643 2317 y FH(\003)667 2308 y Fs(c)686 2310 y FF(;)g(!)740 2290 y Fy(0)738 2323 y FH(\003)762 2313 y Ft(0)p Fs(c)790 2310 y FQ(\))28 b(=)f(const)q(\()p FF(!)1063 2317 y FH(\003)1087 2308 y Fs(c)1106 2310 y FF(;)8 b(!)1160 2290 y Fy(0)1158 2323 y FH(\003)1182 2313 y Ft(0)p Fs(c)1209 2310 y FQ(\))20 b FE(\002)316 2377 y Fx(Y)268 2480 y FD(X)s Fy(\\)p FH(\003)p Fy(6)p FH(=)p Fq(?)424 2418 y FF(e)447 2398 y Fy(\000)p FH(\010)499 2404 y Fs(X)529 2398 y FH(\()p FD(!)q FH(\))782 2377 y Fx(Y)590 2480 y FD(x)p FH(:)9 b FD(x)p Fy(2)p FH(\003)697 2471 y Ft(0)708 2480 y FH(or)i FD(B)778 2484 y Fs(x)797 2480 y Fy(\\)p FH(\003)p Fy(6)p FH(=)p Fq(?)p FH(or)h(b)q(oth)1047 2402 y Fx(e)1036 2418 y FF(T)1065 2425 y FD(x)1087 2418 y FQ(\()p FF(!)1136 2425 y FD(B)1163 2429 y Fs(x)1185 2418 y FF(;)c(!)1239 2398 y Fy(0)1237 2431 y FD(x)1259 2418 y FQ(\))1293 2377 y Fx(Y)1286 2469 y FD(x)p Fy(2)p FH(\003)1362 2418 y FF(d\026)1416 2398 y FH(0)1416 2431 y FD(x)1439 2418 y FQ(\()p FF(!)1488 2425 y FD(x)1510 2418 y FQ(\))1550 2377 y Fx(Y)1537 2469 y FD(x)p Fy(2)p FH(\003)1605 2460 y Ft(0)1625 2418 y FF(d\027)1674 2425 y FD(x)1696 2418 y FQ(\()p FF(!)1747 2398 y Fy(0)1745 2431 y FD(x)1767 2418 y FQ(\))14 b FF(:)1765 2545 y FQ(\(4.19\))p 60 2591 732 2 v 100 2645 a FA(49)135 2660 y Fz(That)f(is,)h(the)g(set)h Fu(f)p Fv(x)p Fz(:)e Fv(B)529 2666 y Fp(x)562 2660 y Fu(3)e Fv(y)q Fu(g)j Fz(is)g(\014nite)g(for)g(eac)o(h)g Fv(y)g Fu(2)d(L)p Fz(.)938 2784 y FQ(102)p eop %%Page: 103 103 bop 60 97 a FQ(No)o(w,)19 b(the)g(\014rst)g(pro)q(duct)h(is)f(just)g FF(e)738 79 y Fy(\000)p FD(H)797 67 y Fr(\010)794 90 y(\003)821 79 y FH(\()p FD(!)857 85 y Fr(\003)879 79 y FD(;!)911 85 y Fr(\003)932 78 y Fs(c)950 79 y FH(\))965 97 y FQ(,)h(and)f(the)g(\014rst)g (and)h(third)f(pro)q(ducts)h(together)60 157 y(yield)14 b(\(when)h(prop)q (erly)g(normalized\))e(the)i(k)o(ernel)e FF(\031)1036 164 y FH(\003)1062 157 y FQ(\()p FF(!)1111 164 y FH(\003)1135 155 y Fs(c)1154 157 y FF(;)8 b(d!)1231 164 y FH(\003)1258 157 y FQ(\).)21 b(Therefore,)14 b(the)h(sp)q(eci\014cation)60 217 y(\005)c FE(\012)f FF(T)23 b FQ(should)17 b(b)q(e)f(de\014ned)g(as)145 327 y(\(\005)11 b FE(\012)g FF(T)c FQ(\)\()p FF(d)366 323 y Fx(e)361 327 y FF(!)391 334 y FH(\003)417 327 y FF(;)h(d)469 323 y Fx(e)464 327 y FF(!)496 306 y Fy(0)494 339 y FH(\003)518 330 y Ft(0)532 327 y FE(j)p FF(!)576 334 y FH(\003)600 325 y Fs(c)619 327 y FF(;)g(!)673 306 y Fy(0)671 339 y FH(\003)695 330 y Ft(0)p Fs(c)723 327 y FQ(\))28 b(=)846 314 y(\026)835 327 y FF(Z)868 334 y FH(\003)p FD(;)p FH(\003)926 325 y Ft(0)941 327 y FQ(\()p FF(!)990 334 y FH(\003)1014 325 y Fs(c)1033 327 y FF(;)8 b(!)1087 306 y Fy(0)1085 339 y FH(\003)1109 330 y Ft(0)p Fs(c)1136 327 y FQ(\))1155 306 y Fy(\000)p FH(1)1222 327 y FE(\002)194 443 y FF(\031)222 450 y FH(\003)248 443 y FQ(\()p FF(!)297 450 y FH(\003)321 441 y Fs(c)340 443 y FF(;)g(d)392 439 y Fx(e)387 443 y FF(!)417 450 y FH(\003)444 443 y FQ(\))676 401 y Fx(Y)471 505 y FD(x)p FH(:)i FD(x)p Fy(2)p FH(\003)579 495 y Ft(0)602 505 y FH(or)h FD(B)672 509 y Fs(x)691 505 y Fy(\\)p FH(\003)p Fy(6)p FH(=)p Fq(?)h FH(or)f(b)q(oth)952 427 y Fx(e)942 443 y FF(T)971 450 y FD(x)992 395 y Fx(\020)1009 443 y FQ(\()p FF(!)1058 450 y FH(\003)1082 441 y Fs(c)1112 443 y FE(\002)1166 439 y Fx(e)1162 443 y FF(!)1192 450 y FH(\003)1219 443 y FQ(\))1238 450 y FD(B)1265 454 y Fs(x)1286 443 y FF(;)d FQ(\()p FF(!)1359 422 y Fy(0)1357 455 y FH(\003)1381 446 y Ft(0)p Fs(c)1420 443 y FE(\002)1474 439 y Fx(e)1469 443 y FF(!)1501 422 y Fy(0)1499 455 y FH(\003)1523 446 y Ft(0)1537 443 y FQ(\))1556 450 y FD(x)1570 395 y Fx(\021)1616 401 y(Y)1603 494 y FD(x)p Fy(2)p FH(\003)1671 484 y Ft(0)1691 443 y FF(d\027)1740 450 y FD(x)1762 443 y FQ(\()p FF(!)1813 422 y Fy(0)1811 455 y FD(x)1833 443 y FQ(\))14 b FF(;)1765 569 y FQ(\(4.20\))60 679 y(where)153 776 y(\026)143 789 y FF(Z)176 796 y FH(\003)p FD(;)p FH(\003)234 787 y Ft(0)248 789 y FQ(\()p FF(!)297 796 y FH(\003)321 787 y Fs(c)340 789 y FF(;)8 b(!)394 769 y Fy(0)392 801 y FH(\003)416 792 y Ft(0)p Fs(c)444 789 y FQ(\))463 769 y Fy(\000)p FH(1)538 789 y FQ(=)239 843 y Fx(Z)183 968 y FH(\012)208 974 y Fr(\003)231 968 y Fy(\002)p FH(\012)283 956 y Ft(0)283 984 y Fr(\003)304 977 y Ft(0)319 902 y FF(\031)347 909 y FH(\003)373 902 y FQ(\()p FF(!)422 909 y FH(\003)446 900 y Fs(c)465 902 y FF(;)g(d)517 898 y Fx(e)512 902 y FF(!)542 909 y FH(\003)569 902 y FQ(\))801 860 y Fx(Y)596 964 y FD(x)p FH(:)i FD(x)p Fy(2)p FH(\003)704 954 y Ft(0)726 964 y FH(or)i FD(B)797 968 y Fs(x)816 964 y Fy(\\)p FH(\003)p Fy(6)p FH(=)p Fq(?)g FH(or)f(b)q(oth)1077 886 y Fx(e)1067 902 y FF(T)1096 909 y FD(x)1117 854 y Fx(\020)1134 902 y FQ(\()p FF(!)1183 909 y FH(\003)1207 900 y Fs(c)1236 902 y FE(\002)1291 898 y Fx(e)1286 902 y FF(!)1316 909 y FH(\003)1343 902 y FQ(\))1362 909 y FD(B)1389 913 y Fs(x)1410 902 y FF(;)d FQ(\()p FF(!)1483 881 y Fy(0)1481 914 y FH(\003)1505 905 y Ft(0)p Fs(c)1544 902 y FE(\002)1599 898 y Fx(e)1594 902 y FF(!)1626 881 y Fy(0)1624 914 y FH(\003)1648 905 y Ft(0)1662 902 y FQ(\))1681 909 y FD(x)1695 854 y Fx(\021)1741 860 y(Y)1728 953 y FD(x)p Fy(2)p FH(\003)1796 943 y Ft(0)1815 902 y FF(d\027)1864 909 y FD(x)1887 902 y FQ(\()p FF(!)1938 881 y Fy(0)1936 914 y FD(x)1958 902 y FQ(\))1852 1042 y(\(4.21\))60 1152 y(and)14 b(w)o(e)f(ha)o(v)o(e)g (assumed,)g(of)g(course,)h(that)864 1139 y(\026)854 1152 y FF(Z)887 1159 y FH(\003)p FD(;)p FH(\003)945 1150 y Ft(0)959 1152 y FQ(\()p FF(!)1008 1159 y FH(\003)1032 1150 y Fs(c)1051 1152 y FF(;)8 b(!)1105 1134 y Fy(0)1103 1164 y FH(\003)1127 1155 y Ft(0)p Fs(c)1155 1152 y FQ(\))14 b FF(>)f FQ(0.)21 b([If)1368 1139 y(\026)1358 1152 y FF(Z)1391 1159 y FH(\003)p FD(;)p FH(\003)1449 1150 y Ft(0)1463 1152 y FQ(\()p FF(!)1512 1159 y FH(\003)1536 1150 y Fs(c)1555 1152 y FF(;)8 b(!)1609 1134 y Fy(0)1607 1164 y FH(\003)1631 1155 y Ft(0)p Fs(c)1659 1152 y FQ(\))13 b(=)h(0,)g(then)60 1212 y(\()p FF(!)109 1219 y FH(\003)133 1210 y Fs(c)152 1212 y FF(;)8 b(!)206 1194 y Fy(0)204 1225 y FH(\003)228 1215 y Ft(0)p Fs(c)256 1212 y FQ(\))18 b(is)g(a)g(\\forbidden)g(b)q(oundary)i (condition",)e(whic)o(h)f(has)i(to)f(b)q(e)g(dealt)g(with)g(as)h(in)e(the)60 1272 y(theory)i(of)h(lattice)e(systems)g(with)h(hard-core)g(constrain)o(ts)h ([299,)f(313)q(].])30 b(W)l(e)18 b(m)o(ust)g(no)o(w)i(c)o(hec)o(k)60 1333 y(that:)95 1434 y(\(a\))25 b(\005)11 b FE(\012)f FF(T)d FQ(,)16 b(th)o(us)g(de\014ned,)f(is)h(indeed)g(a)h(sp)q(eci\014cation.)93 1536 y(\(b\))24 b(If)16 b FF(\026)g FQ(is)g(an)o(y)g(measure)f(consisten)o(t) h(with)g(\005,)g(then)g FF(\026)11 b FE(\002)g FF(T)23 b FQ(is)16 b(consisten)o(t)f(with)i(\005)10 b FE(\012)h FF(T)c FQ(.)60 1638 y(These)20 b(t)o(w)o(o)f(v)o(eri\014cations)g(are)h(messy)e (calculations,)i(whic)o(h)f(the)h(authors)h(are)f(con)o(vinced)e(will)60 1698 y(w)o(ork)11 b(out)g(\(although)h(men)o(tal)d(exhaustion)i(prev)o(en)o (ted)f(them)f(from)h(writing)h(out)g(the)g(full)f(details\).)133 1758 y(Things)j(b)q(ecome)d(m)o(uc)o(h)g(simpler)g(when)i(\005)g(is)f(the)h (Gibbsian)g(sp)q(eci\014cation)g(for)h(an)f(in)o(teraction)60 1818 y(\010)i(and)h FP(a)g(priori)j FQ(measure)13 b FF(\026)599 1800 y FH(0)619 1818 y FQ(,)h(and)h(the)832 1802 y Fx(e)822 1818 y FF(T)851 1825 y FD(x)887 1818 y FQ(are)f(all)f(non)o(v)m(anishing.)21 b(Then)15 b(it)e(is)h(easy)g(to)h(see)f(that)60 1878 y(\005)8 b FE(\012)g FF(T)20 b FQ(is)14 b(the)h(Gibbsian)g(sp)q(eci\014cation)f(for)h (the)f(in)o(teraction)1217 1862 y Fx(e)1211 1878 y FQ(\010)h(\(on)g(the)f (lattice)g FE(L)8 b([)g(L)1693 1860 y Fy(0)1705 1878 y FQ(\))14 b(de\014ned)60 1939 y(b)o(y)245 2028 y Fx(e)239 2044 y FQ(\010)274 2051 y FD(X)q(;X)346 2042 y Ft(0)359 2044 y FQ(\()p FF(!)r(;)8 b(!)464 2023 y Fy(0)475 2044 y FQ(\))28 b(=)588 1957 y Fx(8)588 1994 y(<)588 2069 y(:)633 1990 y FQ(\010)668 1997 y FD(X)702 1990 y FQ(\()p FF(!)r FQ(\))269 b(if)16 b FF(X)1130 1972 y Fy(0)1156 1990 y FQ(=)d Fq(?)633 2050 y FE(\000)8 b FQ(log)761 2034 y Fx(e)751 2050 y FF(T)780 2057 y FD(x)802 2050 y FQ(\()p FF(!)851 2057 y FD(B)878 2061 y Fs(x)899 2050 y FF(;)g(!)953 2032 y Fy(0)951 2062 y FD(x)973 2050 y FQ(\))49 b(if)16 b FF(X)i FQ(=)c FF(B)1233 2057 y FD(x)1271 2050 y FQ(and)j FF(X)1410 2032 y Fy(0)1436 2050 y FQ(=)d FE(f)p FF(x)p FE(g)633 2110 y FQ(0)384 b(otherwise)1765 2044 y(\(4)p FF(:)p FQ(22\))60 2181 y(and)19 b FP(a)g(priori)j FQ(measure)17 b FF(\026)566 2163 y FH(0)599 2181 y FE(\002)12 b FF(\027)s FQ(.)28 b(\(In)18 b(particular,)g(it)g(follo)o(ws)g(immedi)o(ately)d(from)i(the)h(general)60 2241 y(theory)h(in)f(Section)h(2.3.2)g(that)h(\005)12 b FE(\012)h FF(T)25 b FQ(is)19 b(indeed)f(a)h(sp)q(eci\014cation.\))29 b(This)20 b(is)e(the)h(in)o(teraction)60 2301 y(corresp)q(onding)e(to)g(the)f (formal)f(Hamiltonian)414 2411 y FF(H)454 2418 y FD(j)r(oint)536 2411 y FQ(\()p FF(!)r(;)8 b(!)641 2391 y Fy(0)652 2411 y FQ(\))42 b(=)804 2370 y Fx(X)792 2462 y FD(X)s Fy(\032L)884 2411 y FQ(\010)919 2418 y FD(X)953 2411 y FQ(\()p FF(!)r FQ(\))19 b FE(\000)1110 2370 y Fx(X)1100 2462 y FD(x)p Fy(2L)1168 2453 y Ft(0)1188 2411 y FQ(log)1269 2395 y Fx(e)1259 2411 y FF(T)1288 2418 y FD(x)1309 2411 y FQ(\()p FF(!)1358 2418 y FD(B)1385 2422 y Fs(x)1407 2411 y FF(;)8 b(!)1461 2391 y Fy(0)1459 2424 y FD(x)1481 2411 y FQ(\))713 2555 y(=)41 b FF(H)832 2562 y FD(or)q(ig)q(inal)962 2555 y FQ(\()p FF(!)r FQ(\))19 b FE(\000)1119 2513 y Fx(X)1109 2606 y FD(x)p Fy(2L)1177 2596 y Ft(0)1197 2555 y FQ(log)1278 2539 y Fx(e)1268 2555 y FF(T)1297 2562 y FD(x)1318 2555 y FQ(\()p FF(!)1367 2562 y FD(B)1394 2566 y Fs(x)1416 2555 y FF(;)8 b(!)1470 2534 y Fy(0)1468 2567 y FD(x)1490 2555 y FQ(\))14 b FF(:)228 b FQ(\(4.23\))938 2784 y(103)p eop %%Page: 104 104 bop 60 96 a FQ(If)16 b(the)204 80 y Fx(e)194 96 y FF(T)223 103 y FD(x)261 96 y FQ(can)i(v)m(anish,)f(then)634 80 y Fx(e)628 96 y FQ(\010)g(ma)o(y)f(tak)o(e)g(the)h(v)m(alue)f(+)p FE(1)p FQ(,)h(whic)o(h)f(is)h(not)g(\(strictly)f(sp)q(eaking\))60 156 y(p)q(ermitted)21 b(in)h(our)h(form)o(ulation;)h(but)f(the)f(same)g (algebra)h(sho)o(ws)g(that)g(\005)15 b FE(\012)g FF(T)29 b FQ(is)23 b(indeed)f(a)60 216 y(sp)q(eci\014cation,)16 b(at)g(least)g(when)663 204 y(\026)653 216 y FF(Z)686 223 y FH(\003)p FD(;)p FH(\003)744 214 y Ft(0)758 216 y FQ(\()p FF(!)807 223 y FH(\003)831 214 y Fs(c)850 216 y FF(;)8 b(!)904 198 y Fy(0)902 229 y FH(\003)926 219 y Ft(0)p Fs(c)954 216 y FQ(\))14 b FF(>)f FQ(0.)1076 198 y FH(50)133 277 y FQ(Ha)o(ving)h(constructed)h(the)f(sp)q(eci\014cation)h (\005)8 b FE(\012)g FF(T)20 b FQ(on)15 b(the)g(lattice)e FE(L)8 b([)g(L)1473 258 y Fy(0)1485 277 y FQ(,)15 b(w)o(e)f(can)h(no)o(w)g(apply)60 337 y(the)i(same)g(argumen)o(t)f(as)j(in)e(the)g(decimation)f(case,)h(based)h (on)g(Prop)q(osition)h(2.25)f(\(see)g(Section)60 397 y(4.1.2,)j(Step)f(0\).) 34 b(Indeed,)20 b(the)g(renormalized)e(measure)h FF(\026T)27 b FQ(is)20 b(obtained)h(b)o(y)f(decimating)e(the)60 457 y(join)o(t)e(measure) f FF(\026)c FE(\002)g FF(T)c FQ(,)15 b(i.e.)g(restricting)g(it)h(to)g(the)g (lattice)f FE(L)1206 439 y Fy(0)1218 457 y FQ(.)133 517 y(W)l(e)i(hop)q(e)h (that)f(someone)f(will)g(come)f(along)j(and)g(simplify)c(our)k(\\abstract)g (nonsense")g(con-)60 577 y(cerning)f(Step)g(0.)26 b(But)17 b(w)o(e)g(ha)o(v)o(e)g(no)h(doubt)h(that)f(our)g(concrete)e(argumen)o(ts)h (in)g(this)h(pap)q(er)g(are)60 638 y(correct.)60 748 y FP(Step)k(1.)34 b(Sele)n(ction)23 b(of)e(an)h(image-spin)g(c)n(on\014gur)n(ation)g FF(!)1168 730 y Fy(0)1166 760 y FH(sp)q(ecial)1293 748 y FP(for)e(which)i (the)g(c)n(orr)n(esp)n(onding)60 808 y(internal-spin)d(system)f(has)f(a)g (non-unique)j(Gibbs)e(me)n(asur)n(e.)133 868 y FQ(W)l(e)e(need)f(to)i(\014nd) f(an)h(image-spin)d(con\014guration)k FF(!)1126 850 y Fy(0)1124 880 y FH(sp)q(ecial)1245 868 y FQ(suc)o(h)e(that)g(the)g(resulting)f(system) 60 928 y(of)j(in)o(ternal)f(spins)h(\(the)f(\\mo)q(di\014ed)g(ob)s(ject)g (system"\))g(has)h(at)g(least)g(t)o(w)o(o)f(distinct)g(Gibbs)h(mea-)60 988 y(sures,)f(call)f(them)f FF(\026)441 995 y FH(+)488 988 y FQ(and)i FF(\026)612 995 y Fy(\000)642 988 y FQ(.)23 b(Ho)o(w)17 b(w)o(e)f(do)i(this)e(dep)q(ends)i(on)f(the)g(details)f(of)h(the)g(mo)q(del)e (and)60 1049 y(the)j(renormalization)f(transformation.)27 b(F)l(or)19 b(the)f FF(b)f FQ(=)g(2)i(decimation)d(transformation)i(on)h(the)60 1109 y(nearest-neigh)o(b)q(or)j(Ising)e(mo)q(del,)h(the)g(fully)e (alternating)i(con\014guration)i FF(!)1512 1091 y Fy(0)1510 1121 y FD(alt)1575 1109 y FQ(do)q(es)f(the)f(tric)o(k.)60 1169 y(F)l(or)d(the)g(ma)s(jorit)o(y-rule)d(transformation)j(w)o(e)g(shall)g(need) f(a)i(more)d(complicated)g(con\014guration)60 1229 y(\(Section)g(4.3.4\).)133 1289 y(No)o(w)23 b(let)f FF(f)28 b FQ(b)q(e)23 b(a)g(lo)q(cal)g(observ)m (able)g(suc)o(h)g(that)g FF(\026)1124 1296 y FH(+)1154 1289 y FQ(\()p FF(f)5 b FQ(\))25 b FF(>)g(\026)1338 1296 y Fy(\000)1368 1289 y FQ(\()p FF(f)5 b FQ(\);)26 b(w)o(e)c(shall)h(call)f FF(f)28 b FQ(the)60 1350 y(\\in)o(ternal-spin)23 b(order)h(parameter".)44 b(\(F)l(or)24 b(the)f(decimation)f(example,)h FF(f)29 b FQ(is)24 b(the)g(spin)f(at)i(a)60 1410 y(neigh)o(b)q(or)17 b(of)f(the)g(origin.\))60 1520 y FP(Step)i(2.)k(Disc)n(ontinuity)c(of)f(the)h(internal-spin)h(or)n(der) d(p)n(ar)n(ameter)g(as)h(a)g(function)i(of)e(the)h(image-)60 1580 y(spin)g(c)n(on\014gur)n(ation)g(in)f(a)h(neighb)n(orho)n(o)n(d)e(of)i FF(!)938 1562 y Fy(0)936 1592 y FH(sp)q(ecial)1041 1580 y FP(.)133 1640 y FQ(The)h(next)f(step)g(is)h(to)g(study)f(the)h(b)q(eha)o(vior)f(of)h (the)f(in)o(ternal-spin)g(system)f(for)i(image-spin)60 1700 y(con\014gurations)h(in)f(a)g FP(neighb)n(orho)n(o)n(d)k FQ(\(in)c(the)g(pro) q(duct)g(top)q(ology\))h(of)g FF(!)1440 1682 y Fy(0)1438 1713 y FH(sp)q(ecial)1543 1700 y FQ(.)29 b(Our)19 b(goal)h(is)f(to)60 1761 y(sho)o(w)c(that)g(the)g(order)f(parameter)g(for)h(the)f(in)o (ternal-spin)g(system)f(is)h FP(essential)r(ly)k(disc)n(ontinuous)60 1821 y FQ(as)f(a)g(function)f(of)g(the)g(image-spin)f(con\014guration)j FF(!)1063 1803 y Fy(0)1074 1821 y FQ(.)133 1881 y(T)l(o)d(do)f(this,)g(w)o(e) g(\014rst)g(c)o(ho)q(ose)h(image-spin)e(con\014gurations)j FF(!)1283 1863 y Fy(0)1281 1893 y FH(+)1325 1881 y FQ(and)e FF(!)1449 1863 y Fy(0)1447 1893 y(\000)1491 1881 y FQ(whic)o(h)g(w)o(e)f(hop) q(e)i(will)60 1941 y(\\select)g(the)g(phases)i FF(\026)484 1948 y FH(+)529 1941 y FQ(and)f FF(\026)652 1948 y Fy(\000)682 1941 y FQ(".)22 b(W)l(e)15 b(then)g(study)h(image-spin)f(con\014gurations)i FF(!)1659 1923 y Fy(0)1686 1941 y FQ(whic)o(h)e(are)60 2001 y(equal)g(to)h FF(!)279 1983 y Fy(0)277 2014 y FH(sp)q(ecial)399 2001 y FQ(on)g(some)f(large)h(b)q(o)o(x)g(\003)834 2008 y FD(R)862 2001 y FQ(,)g(whic)o(h)f(are)h(equal)f(to)h FF(!)1331 1983 y Fy(0)1329 2014 y FH(+)1375 2001 y FQ([or)g FF(!)1480 1983 y Fy(0)1478 2014 y(\000)1507 2001 y FQ(])g(on)g(some)f(ann)o(ulus)60 2062 y(\003)94 2069 y FD(R)121 2060 y Ft(0)147 2062 y FE(n)f FQ(\003)220 2069 y FD(R)268 2062 y FQ(\()p FF(R)20 b(<)g(R)439 2043 y Fy(0)471 2062 y FF(<)g FE(1)p FQ(\),)g(and)g(whic)o(h)f(are)h (arbitrary)f(outside)h(\003)1374 2069 y FD(R)1401 2060 y Ft(0)1414 2062 y FQ(.)32 b(Our)19 b(goal)i(is)e(to)h(sho)o(w)60 2122 y(that,)e(no)g(matter)e(ho)o(w)i(large)g FF(R)g FQ(is,)g(the)f(in)o (ternal-spin)g(phase)h(is)f(selected)g(b)o(y)g(the)g(b)q(eha)o(vior)h(of)60 2182 y(the)c(image)g(spins)g(in)h(\003)492 2189 y FD(R)519 2180 y Ft(0)539 2182 y FE(n)8 b FQ(\003)606 2189 y FD(R)649 2182 y FQ(|)15 b(for)g(a)g(suitable)f(c)o(hoice)f(of)i FF(R)1239 2164 y Fy(0)1266 2182 y FQ(dep)q(ending)g(on)g FF(R)g FQ(|)f(no)h(matter)60 2242 y(what)i(happ)q(ens)g(outside)g(\003)576 2249 y FD(R)603 2240 y Ft(0)615 2242 y FQ(.)p 60 2286 732 2 v 100 2340 a FA(50)135 2355 y Fz(Man)o(y)g(of)f(our)i(concrete)h(examples)e Fw(do)j Fz(ha)o(v)o(e)d(con\014gurations)h(for)f(whic)o(h)1364 2344 y(\026)1355 2355 y Fv(Z)1383 2361 y FA(\003)p Fp(;)p FA(\003)1439 2353 y Fe(0)1452 2355 y Fz(\()p Fv(!)1494 2361 y FA(\003)1517 2353 y Fn(c)1534 2355 y Fv(;)7 b(!)1580 2340 y Fo(0)1579 2366 y FA(\003)1602 2358 y Fe(0)p Fn(c)1628 2355 y Fz(\))17 b(=)h(0:)25 b(for)17 b(ex-)60 2405 y(ample,)e(in)i(the)g(case)h(of)e(decimation,)g(one)h (ob)o(viously)e(cannot)i(insist)g(that)g(a)g(certain)g(image)e(spin)i(b)q(e)g (+1)g(and)60 2454 y(sim)o(ultaneously)10 b(insist)i(that)h(the)f(corresp)q (onding)i(original)c(spin)i(b)q(e)h Fu(\000)p Fz(1!)k(But)c(eac)o(h)g(of)e (these)j(concrete)g(cases)g(has)60 2504 y(a)e(simple)f(resolution:)17 b(for)c(example,)e(in)h(the)h(case)g(of)f(decimation,)f(w)o(e)i(called)f Fw(internal)h(spin)j Fz(only)c(those)h(original)60 2554 y(spins)j(whic)o(h)g (are)g Fw(not)k Fz(\(lo)q(c)o(k)o(ed)c(to\))f(image)f(spins;)j(of)e(course,)i (the)f(original)e(spins)i(whic)o(h)g(are)g(lo)q(c)o(k)o(ed)f(to)h(image)60 2604 y(spins)e(don't)g(ev)o(en)g(need)h(to)f(b)q(e)g(considered.)938 2784 y FQ(104)p eop %%Page: 105 105 bop 133 91 a FQ(In)17 b(mathematical)d(terms,)h(our)j(goal)g(is)f(to)g(sho)o (w)h(that)f(there)g(exists)f(a)i(n)o(um)o(b)q(er)d FF(\016)i(>)e FQ(0)i(suc)o(h)60 152 y(that)e(in)e(eac)o(h)h(neigh)o(b)q(orho)q(o)q(d)i FE(N)21 b(3)14 b FF(!)771 133 y Fy(0)769 164 y FH(sp)q(ecial)889 152 y FQ(\(in)g(the)g(pro)q(duct)g(top)q(ology\))i(there)d(exist)h(nonempt)o (y)60 212 y(op)q(en)23 b(sets)f FE(N)326 219 y FH(+)355 212 y FF(;)8 b FE(N)418 219 y Fy(\000)471 212 y FE(\032)24 b(N)29 b FQ(and)22 b(n)o(um)o(b)q(ers)f FF(c)928 219 y FH(+)957 212 y FF(;)8 b(c)1000 219 y Fy(\000)1052 212 y FQ(with)22 b FF(c)1190 219 y FH(+)1234 212 y FE(\000)15 b FF(c)1309 219 y Fy(\000)1362 212 y FE(\025)24 b FF(\016)f FQ(suc)o(h)f(that)g(for)h(ev)o(ery)60 272 y FF(!)92 254 y Fy(0)118 272 y FE(2)14 b(N)206 279 y FH(+)252 272 y FQ([resp.)i FF(!)415 254 y Fy(0)441 272 y FE(2)e(N)529 279 y Fy(\000)559 272 y FQ(])i(and)h(ev)o(ery)e(Gibbs)i(measure)e FF(\026)i FQ(for)f(the)h(in)o(ternal-spin)e(system)g(with)60 332 y(image)21 b(spins)h(set)g(to)h FF(!)515 314 y Fy(0)527 332 y FQ(,)g(w)o(e)f(ha)o(v)o(e)f FF(\026)p FQ(\()p FF(f)5 b FQ(\))25 b FE(\025)e FF(c)964 339 y FH(+)1016 332 y FQ([resp.)e FF(\026)p FQ(\()p FF(f)5 b FQ(\))25 b FE(\024)e FF(c)1356 339 y Fy(\000)1386 332 y FQ(].)39 b(No)o(w)22 b(a)g(basis)h(for)f(the)60 392 y(neigh)o(b)q(orho)q(o)q(ds)c FE(N)j(3)15 b FF(!)527 374 y Fy(0)525 405 y FD(alt)586 392 y FQ(is)h(giv)o(en)f(b)o(y)h(sets)g(of)h(the) f(form)350 497 y FE(N)391 504 y FD(R)447 497 y FQ(=)28 b FE(f)p FF(!)570 476 y Fy(0)582 497 y FQ(:)21 b FF(!)649 476 y Fy(0)675 497 y FQ(=)14 b FF(!)759 476 y Fy(0)757 509 y FD(alt)818 497 y FQ(on)j(\003)920 504 y FD(R)948 497 y FF(;)22 b(!)1016 476 y Fy(0)1042 497 y FQ(=)30 b(arbitrary)16 b(outside)g(\003)1519 504 y FD(R)1548 497 y FE(g)e FF(;)164 b FQ(\(4)p FF(:)p FQ(24\))60 601 y(W)l(e)16 b(shall)g(tak)o(e)g FE(N)405 608 y FH(+)434 601 y FF(;)8 b FE(N)497 608 y Fy(\000)543 601 y FQ(to)16 b(b)q(e)h(sets)f(of) h(the)f(form)65 705 y FE(N)106 712 y FD(R;R)170 703 y Ft(0)181 712 y FD(;)p FH(+)262 705 y FQ(=)41 b FE(f)p FF(!)398 684 y Fy(0)410 705 y FQ(:)21 b FF(!)477 684 y Fy(0)503 705 y FQ(=)14 b FF(!)587 684 y Fy(0)585 717 y FD(alt)646 705 y FQ(on)j(\003)748 712 y FD(R)776 705 y FF(;)22 b(!)844 684 y Fy(0)870 705 y FQ(=)13 b FF(!)953 684 y Fy(0)951 717 y FH(+)998 705 y FQ(on)j(\003)1099 712 y FD(R)1126 703 y Ft(0)1150 705 y FE(n)11 b FQ(\003)1220 712 y FD(R)1249 705 y FF(;)22 b(!)1317 684 y Fy(0)1342 705 y FQ(=)30 b(arbitrary)17 b(outside)f(\003)1820 712 y FD(R)1847 703 y Ft(0)1860 705 y FE(g)1741 778 y FQ(\(4.25a\))65 850 y FE(N)106 857 y FD(R;R)170 848 y Ft(0)181 857 y FD(;)p Fy(\000)262 850 y FQ(=)41 b FE(f)p FF(!)398 830 y Fy(0)410 850 y FQ(:)21 b FF(!)477 830 y Fy(0)503 850 y FQ(=)14 b FF(!)587 830 y Fy(0)585 863 y FD(alt)646 850 y FQ(on)j(\003)748 857 y FD(R)776 850 y FF(;)22 b(!)844 830 y Fy(0)870 850 y FQ(=)13 b FF(!)953 830 y Fy(0)951 863 y(\000)998 850 y FQ(on)j(\003)1099 857 y FD(R)1126 848 y Ft(0)1150 850 y FE(n)11 b FQ(\003)1220 857 y FD(R)1249 850 y FF(;)22 b(!)1317 830 y Fy(0)1342 850 y FQ(=)30 b(arbitrary)17 b(outside)f(\003)1820 857 y FD(R)1847 848 y Ft(0)1860 850 y FE(g)1738 923 y FQ(\(4.25b\))60 1027 y(W)l(e)f(then)f(ha)o(v)o(e)g(to)i(pro)o (v)o(e)e(that)h FF(R)693 1009 y Fy(0)720 1027 y FQ(can)g(b)q(e)g(c)o(hosen)g (as)g(a)g(function)g(of)g FF(R)h FQ(\()p FF(R)e(<)g(R)1581 1009 y Fy(0)1607 1027 y FF(<)f FE(1)p FQ(\))i(so)h(that)60 1087 y FF(\026)p FQ(\()p FF(f)5 b FQ(\))17 b(satis\014es)g(the)f(claimed)d(b) q(ounds.)133 1148 y(In)h(practice,)g(the)g(only)g(w)o(a)o(y)g(w)o(e)h(shall)f (b)q(e)h(able)f(to)h(pro)o(v)o(e)e(the)i(existence)d(of)j(suc)o(h)f(an)h FF(R)1762 1130 y Fy(0)1788 1148 y FF(<)f FE(1)60 1208 y FQ(is)i(to)g(pro)o(v) o(e)f(that)i(the)e(in)o(ternal-spin)h(system)e(with)i FF(R)1081 1190 y Fy(0)1107 1208 y FQ(=)e FE(1)i FQ(and)g FF(!)1351 1190 y Fy(0)1377 1208 y FE(2)e(N)1465 1215 y FD(R;)p Fy(1)p FD(;)p FH(+)1592 1208 y FQ(or)i FE(N)1692 1215 y FD(R;)p Fy(1)p FD(;)p Fy(\000)1819 1208 y FQ(has)60 1268 y(a)i FP(unique)24 b FQ(Gibbs)18 b(measure,)f(and)h(that)h(this)f(measure)e(satis\014es)j(the)f(required)f(b)q (ounds.)28 b(It)17 b(will)60 1328 y(then)j(follo)o(w)g(fairly)f(easily)h (that)h(the)f(\(p)q(ossibly)g(non-unique\))g(Gibbs)h(measures)e(for)i FF(R)1749 1310 y Fy(0)1782 1328 y FF(<)f FE(1)60 1388 y FQ(tend)d(to)g(this)g (unique)g(limit)d(as)k FF(R)703 1370 y Fy(0)730 1388 y FE(!)e(1)p FQ(,)g(and)i(satisfy)f(the)g(b)q(ounds)h(\(with)f(a)h(sligh)o(tly)e(reduced) 60 1449 y FF(\016)r FQ(\))g(for)g(some)f(su\016cien)o(tly)g(large)h FF(R)716 1430 y Fy(0)728 1449 y FQ(.)133 1509 y(W)l(e)k(emphasize)e(that)j (since)e(w)o(e)h(kno)o(w)g(only)g(that)g(the)g(conditional)g(distribution)g FE(h)8 b(\001)g(i)1800 1516 y FD(!)1823 1507 y Ft(0)1857 1509 y FQ(is)60 1569 y FP(some)17 b FQ(Gibbs)d(measure)d(for)j(the)f(in)o (ternal-spin)f(system,)g(w)o(e)h(need)g(to)g(pro)o(v)o(e)g(the)g(claimed)e(b) q(ounds)60 1629 y(on)21 b FF(\026)p FQ(\()p FF(f)5 b FQ(\))21 b FP(uniformly)j FQ(for)d FP(al)r(l)26 b FQ(Gibbs)21 b(measures)e(for)h(this) g(system.)32 b(T)l(o)21 b(do)f(this,)h(it)f(su\016ces)g(to)60 1689 y(sho)o(w)g(that)f(the)g(b)q(ounds)h(are)f(satis\014ed)g(for)g(a)g FP(\014nite-volume)26 b FQ(in)o(ternal-spin)18 b(system,)g(for)h(some)60 1749 y(su\016cien)o(tly)g(large)i(v)o(olume,)e(uniformly)g(in)h(the)h(\(in)o (ternal-spin\))f(b)q(oundary)i(conditions;)h(that)60 1810 y(is,)c(it)f (su\016ces)g(to)h(sho)o(w)g(that)g(there)f(exists)g FF(R)939 1792 y Fy(00)978 1810 y FF(<)g FE(1)h FQ(suc)o(h)f(that)h(the)f(Gibbs)h (measure)e(for)i(the)60 1870 y(in)o(ternal-spin)h(system)e(in)j(the)f(v)o (olume)e(\003)869 1852 y FD(int)869 1882 y(R)896 1873 y Ft(00)918 1870 y FQ(,)j(with)f(image)f(spins)i FF(!)1372 1852 y Fy(0)1404 1870 y FE(2)g(N)1499 1877 y FD(R;R)1563 1868 y Ft(0)1574 1877 y FD(;)p FH(+)1634 1870 y FQ(\(or)f FE(N)1757 1877 y FD(R;R)1821 1868 y Ft(0)1832 1877 y FD(;)p Fy(\000)1871 1870 y FQ(\))60 1930 y FP(and)i(arbitr)n(ary)d(internal-spin)24 b(b)n(oundary)d(c)n(ondition) k FE(f)p 1118 1904 30 2 v FF(\033)1147 1937 y FD(l)1160 1930 y FE(g)1185 1941 y FD(l)p Fy(2)p FH(\()p Fl(Z)1255 1931 y Fr(2)1272 1941 y FH(\))1286 1931 y Fs(int)1330 1941 y Fy(n)p FH(\003)1372 1929 y Fs(int)1372 1957 y(R)1395 1950 y Ft(00)1419 1930 y FQ(,)d(satis\014es) f(the)f(claimed)60 1998 y(b)q(ounds.)j(F)l(or)16 b(simplicit)n(y)d(w)o(e)j (shall)g(tak)o(e)g FF(R)887 1980 y Fy(00)923 1998 y FQ(=)d FF(R)1011 1980 y Fy(0)1024 1998 y FQ(.)133 2058 y(Let)24 b(us)g(emphasize)e (once)i(again)h(that)f(b)q(oth)h(the)e(image)g(spins)h(and)g(the)g(in)o (ternal)f(spins)60 2118 y(are)f(arbitrary)g(outside)g(\003)568 2125 y FD(R)595 2116 y Ft(0)607 2118 y FQ(,)h(but)f FP(for)g(di\013er)n(ent)h (r)n(e)n(asons)t FQ(.)37 b(The)22 b(image)e(spins)i(are)g(arbitrary)60 2178 y(outside)d(\003)265 2185 y FD(R)292 2176 y Ft(0)323 2178 y FQ(b)q(ecause)g(our)g(computation)f(of)h(the)g(conditional)f(probabilities) g FF(\026)p FQ(\()8 b FE(\001)g(j)p FF(!)1687 2160 y Fy(0)1699 2178 y FQ(\))19 b(is)f(v)m(alid)60 2238 y(only)f(for)h(\()p FF(\026T)7 b FQ(\)-almost-ev)o(ery)16 b FF(!)683 2220 y Fy(0)695 2238 y FQ(;)h(therefore,)g(to)h(pro)o(v)o(e)f(that)h(these)f(conditional)h (probabilities)60 2299 y(are)k FP(essential)r(ly)j(disc)n(ontinuous)j FQ(\(i.e.)20 b(cannot)j(b)q(e)f(made)f(con)o(tin)o(uous)i(b)o(y)e(mo)q (di\014cation)h(on)h(a)60 2359 y(set)g(of)g(\()p FF(\026T)7 b FQ(\)-measure)22 b(zero\),)i(w)o(e)f(m)o(ust)e(pro)o(v)o(e)i(our)g(b)q (ounds)i(for)e(a)h(nonempt)o(y)d(op)q(en)j(set)f(of)60 2419 y(con\014gurations)f FF(!)411 2401 y Fy(0)423 2419 y FQ(.)33 b(The)21 b(in)o(ternal)e(spins)i(are)f(arbitrary)h(outside)f(\003)1389 2426 y FD(R)1416 2417 y Ft(00)1459 2419 y FQ(\(=)h(\003)1571 2426 y FD(R)1598 2417 y Ft(0)1610 2419 y FQ(\))g(b)q(ecause)f(w)o(e)60 2479 y(kno)o(w)12 b(only)g(that)g(the)g(conditional)f(measure)g FF(\026)p FQ(\()d FE(\001)g(j)p FF(!)1024 2461 y Fy(0)1036 2479 y FQ(\))k(is)g FP(some)k FQ(Gibbs)c(measure)e(for)i(the)g(mo)q(di\014ed) 60 2539 y(ob)s(ject)j(system,)g(but)h(w)o(e)f(ha)o(v)o(e)h(no)g(idea)g(whic)o (h)f(one)i(\(in)e(case)h(it)g(is)g(non-unique\);)f(therefore,)g(w)o(e)60 2600 y(m)o(ust)f(pro)o(v)o(e)g(b)q(ounds)j(v)m(alid)e(for)g FP(al)r(l)22 b FQ(in\014nite-v)o(olume)12 b(Gibbs)k(measures)e(of)h(the)g(mo) q(di\014ed)g(ob)s(ject)60 2660 y(system.)938 2784 y(105)p eop %%Page: 106 106 bop 60 91 a FP(Step)18 b(3.)23 b(Un\014xing)c(of)f(the)f(spin)h(at)g(the)g (origin.)133 152 y FQ(The)i(\014nal)h(step)f(is)g(to)g(sho)o(w)h(that)f(if)g (the)g(system)e(of)j(in)o(ternal)e(spins)h(is)g(sligh)o(tly)f(mo)q(di\014ed) 60 212 y(b)o(y)i(c)o(hanging)i(the)e(in)o(teraction)g(with)h(a)g(few)g(\(in)g (the)g(our)g(examples)e(just)i(one\))g(image)f(spins)60 272 y(close)14 b(to)g(the)g(origin,)g(the)g(order)h(parameter)e(at)h(these)g (extra)g(spins)h(di\013ers)f(little)e(from)h(the)h(v)m(alue)60 332 y(at)19 b(in)o(ternal)f(spins)g(close)h(to)g(the)f(origin.)28 b(This)19 b(is)f(the)h(step)f(of)h(\\un\014xing")h(some)d(image)h(spins)60 392 y(discussed)e(ab)q(o)o(v)o(e.)60 502 y FP(Conclusion)j(of)e(the)h(ar)n (gument.)133 562 y FQ(Com)o(bining)12 b(the)g(conclusions)h(of)g(Steps)f(2)h (and)h(3,)f(w)o(e)f(ha)o(v)o(e)g(that)h(for)g(all)f(p)q(ossible)h(image-spin) 60 623 y(con\014gurations)21 b(outside)f(\003)584 630 y FD(R)611 621 y Ft(0)624 623 y FQ(,)g(the)f(order)h(parameter)e(at)i(image)e(spins)i (close)f(to)h(the)g(origin)f(is)60 683 y(determined)13 b(b)o(y)j(the)g(image) e(spins)i(in)g(the)g(arbitrarily)f(fara)o(w)o(a)o(y)h(ann)o(ulus)g(\003)1497 690 y FD(R)1524 681 y Ft(0)1547 683 y FE(n)10 b FQ(\003)1616 690 y FD(R)1645 683 y FQ(.)21 b(In)16 b(mathe-)60 743 y(matical)f(terms,)g (the)i(conditional)f(probabilit)o(y)g(distribution)g(of)h(the)g(image)f(spin) g(at)h(the)g(origin)60 803 y(is)e(an)h FP(essential)r(ly)j(disc)n(ontinuous)i FQ(function)15 b(of)h(the)f(other)h(image)e(spins,)h(in)g(a)h(neigh)o(b)q (orho)q(o)q(d)i(of)60 863 y FF(!)92 845 y Fy(0)90 876 y FD(specif)t(ic)218 863 y FQ(.)j(Th)o(us,)16 b(the)g(renormalized)e(measure)h(has)i(non-quasilo)q (cal)g(conditional)f(probabilities:)60 924 y(it)e(is)g(not)i(consisten)o(t)e (with)g(an)o(y)h(quasilo)q(cal)f(sp)q(eci\014cation,)g(and)i(in)e(particular) g(is)g(not)h(the)g(Gibbs)60 984 y(measure)g(of)h(an)o(y)h(uniformly)d(con)o (v)o(ergen)o(t)h(in)o(teraction.)60 1128 y FB(4.3)70 b(Gri\016ths-P)n (earce-Israel)13 b(P)n(athologies)i(I)r(I)r(I:)g(Some)e(F)-6 b(urther)16 b(Ex-)217 1203 y(ample)o(s)60 1295 y FQ(In)g(this)g(section)g(w)o (e)f(apply)h(the)g(Gri\016ths-P)o(earce-Israel)f(metho)q(d)h(to)g(pro)o(v)o (e)g(non-Gibbsianness)60 1356 y(of)h(the)f(renormalized)d(measure)i(in)h(the) g(follo)o(wing)g(additional)h(examples:)133 1457 y FE(\017)24 b FF(b)14 b FQ(=)f(2)k(decimation)d(for)j(the)f(Ising)g(mo)q(del)f(in)h (dimension)e FF(d)h FE(\025)e FQ(3.)133 1559 y FE(\017)24 b FQ(Decimation)14 b(with)i(spacing)h FF(b)d FE(\025)f FQ(3,)k(for)f(the)g (Ising)g(mo)q(del)f(in)h(an)o(y)g(dimension)f FF(d)f FE(\025)g FQ(2.)133 1661 y FE(\017)24 b FQ(The)15 b(Kadano\013)h(transformation)f(with) f(\014nite)h FF(p)g FQ(and)g(arbitrary)g(blo)q(c)o(k)f(size)g FF(b)g FE(\025)f FQ(1,)i(for)g(the)182 1721 y(Ising)h(mo)q(del)f(in)h(an)o(y) g(dimension)f FF(d)f FE(\025)f FQ(2.)133 1823 y FE(\017)24 b FQ(Some)14 b(cases)i(of)g(the)g(ma)s(jorit)o(y-rule)d(transformation)j(for) g(the)f(Ising)h(mo)q(del)e(in)i(dimension)182 1883 y FF(d)e FQ(=)g(2.)133 1984 y FE(\017)24 b FQ(Blo)q(c)o(k-a)o(v)o(eraging,)d(with)f FP(even)27 b FQ(blo)q(c)o(k)20 b(size)g FF(b)p FQ(,)h(for)g(the)g(Ising)g(mo) q(del)e(in)i(an)o(y)g(dimension)182 2045 y FF(d)14 b FE(\025)g FQ(2.)60 2146 y(Finally)l(,)20 b(and)h(most)e(strikingly)l(,)h(w)o(e)g(can)g (sho)o(w)h(that)g(in)f(all)g(of)h(these)f(examples)e(except)h(\(and)60 2206 y(this)j(probably)g(only)g(for)h(tec)o(hnical)d(reasons\))j(the)f(ma)s (jorit)o(y-rule)e(case,)j(there)f(is)g(in)f(fact)i(an)60 2267 y FP(op)n(en)17 b(r)n(e)n(gion)f(in)h(the)g FQ(\()p FF(J)o(;)8 b(h)p FQ(\))p FP(-plane)20 b FQ(for)c(whic)o(h)e(the)h(renormalized)e (measures)h(are)h(non-Gibbsian.)60 2327 y(Therefore,)g(the)g(Gri\016ths-P)o (earce-Israel)f(pathologies)i(are)g FP(not)k FQ(asso)q(ciated)d(with)e(the)g (fact)h(that)60 2387 y(the)j(original)h(mo)q(del)e(is)h FP(sitting)j(on)i FQ(a)c(phase-transition)g(surface.)31 b(Rather,)20 b(it)f(su\016ces)h(that)g (a)60 2447 y(\014rst-order)d(phase)g(transition)g(can)g(b)q(e)f(induced)g(in) g(the)g(in)o(ternal-spin)g(system)f(b)o(y)h(c)o(ho)q(osing)i(an)60 2507 y(appropriate)d(blo)q(c)o(k-spin)e(con\014guration.)22 b(F)l(or)14 b(this)g(w)o(e)g(need)f(to)i(w)o(ork)f(at)g(lo)o(w)g(temp)q (erature)f(but)60 2568 y(not)k(necessarily)e(at)h(zero)g(magnetic)f(\014eld.) 938 2784 y(106)p eop %%Page: 107 107 bop 60 91 a FM(4.3.1)55 b(Israel's)18 b(Example)e(in)i(Dimension)f FF(d)d FE(\025)g FQ(3)60 184 y(In)19 b(this)g(section)g(w)o(e)g(study)g(the)g FF(b)g FQ(=)g(2)h(decimation)d(transformation)j(for)f(the)g(Ising)g(mo)q(del) f(in)60 244 y(dimension)d FF(d)f FE(\025)f FQ(3.)133 329 y FP(Step)19 b(0.)j(Computation)17 b(of)h(the)g(c)n(onditional)g(pr)n(ob)n (abilities.)k FQ(This)16 b(has)h(already)f(b)q(een)g(done.)133 414 y FP(Step)e(1.)21 b(Choic)n(e)13 b(of)f FF(!)537 396 y Fy(0)535 426 y FH(sp)q(ecial)641 414 y FP(.)20 b FQ(As)11 b(in)g(the)g(t)o(w) o(o-dimensional)f(case,)i(w)o(e)e(c)o(ho)q(ose)i FF(!)1591 396 y Fy(0)1589 426 y FH(sp)q(ecial)1706 414 y FQ(to)g(b)q(e)f(the)60 474 y(fully)j(alternating)h(con\014guration)h FF(!)744 456 y Fy(0)742 487 y FD(alt)787 474 y FQ(.)k(The)15 b(system)f(of)h(in)o(ternal)f (spins)h(for)g(a)g(fully)f(alternating)60 534 y(image-spin)j(con\014guration) j(again)f(corresp)q(onds)g(to)g(a)g(p)q(erio)q(dically)e(diluted)g (ferromagnet:)25 b(an)60 595 y(in)o(ternal)16 b(spin)g(with)g(all)h(but)f (one)h(of)g(its)f(co)q(ordinates)i(ev)o(en)d(|)h(that)h(is,)f(one)h(whic)o(h) f(is)g(adjacen)o(t)60 655 y(to)h(t)o(w)o(o)f(image)g(spins)g(|)h(has)g(t)o(w) o(o)f(less)h(neigh)o(b)q(ors)g(coupled)f(to)h(itself,)e(while)g(all)h(other)h (in)o(ternal)60 715 y(spins)k(are)g(una\013ected.)34 b(The)21 b(only)f(di\013erence)g(from)g(the)g(t)o(w)o(o-dimensional)f(case)i(is)f (that)h(the)60 775 y(resulting)e(lattice)f(is)i(not)g(merely)d(a)j(decorated) f(v)o(ersion)g(of)h(an)g(exactly)e(soluble)h(Ising)h(mo)q(del,)60 835 y(so)e(w)o(e)f(cannot)h(write)f(an)h(explicit)d(form)o(ula)h(for)h(its)h (critical)d(temp)q(erature.)23 b(Nev)o(ertheless,)15 b(it)i(is)60 896 y(easy)h(to)h(sho)o(w)g(that)f(the)g(in)o(ternal-spin)g(system)f(do)q(es) i(ha)o(v)o(e)e(a)i(phase)g(transition,)f(and)h(that)g(at)60 956 y(lo)o(w)f(enough)h(temp)q(erature)d(there)i(exist)f(distinct)g(Gibbs)i (measures)e FF(\026)1405 963 y FH(+)1453 956 y FQ(and)h FF(\026)1578 963 y Fy(\000)1626 956 y FQ(with)g(strictly)60 1016 y(p)q(ositiv)o(e)c(and)h (strictly)e(negativ)o(e)h(magnetization,)f(resp)q(ectiv)o(ely;)f(these)j (phases)g(can)g(b)q(e)f(selected)60 1076 y(b)o(y)19 b(using,)i(for)g (example,)d(\\+")j(or)f(\\)p FE(\000)p FQ(")g(b)q(oundary)i(conditions.)32 b(These)20 b(claims)e(follo)o(w)i(easily)60 1136 y(from)g(a)h(P)o(eierls)e (argumen)o(t)g(\(for)i(a)g(description)f(of)h(suc)o(h)f(argumen)o(ts,)h(see)f (e.g.)g([169]\).)34 b(They)60 1197 y(can)23 b(alternativ)o(ely)d(b)q(e)j(pro) o(v)o(en)f(b)o(y)g(observing)h(that)g(the)g(diluted)f(system)f(is)h(a)h (collection)f(of)60 1257 y(\()p FF(d)10 b FE(\000)g FQ(1\)-dimensional)15 b(diluted)f(and)j(undiluted)e(Ising)g(mo)q(dels,)f(ferromagnetically)g (coupled.)20 b(In)60 1317 y(particular,)f(the)f FF(d)p FQ(-dimensional)g (diluted)g(system)f(is)h(more)g(ferromagnetic)f(than)i(the)g(\()p FF(d)13 b FE(\000)f FQ(1\)-)60 1377 y(dimensional)e(undiluted)g(Ising)i(mo)q (del,)e(and)i(hence)f([169)q(])g(exhibits)f(sp)q(on)o(taneous)j (magnetization)60 1437 y(for)20 b(all)f(temp)q(eratures)f(b)q(elo)o(w)i(the)f (critical)f(temp)q(erature)g FF(J)1212 1444 y FD(c;d)p Fy(\000)p FH(1)1322 1437 y FQ(of)i(the)f(\()p FF(d)14 b FE(\000)f FQ(1\)-dimensional)60 1498 y(undiluted)i(Ising)i(mo)q(del.)133 1608 y FP(Step)k(2.)30 b(Study)21 b(of)f(a)g(neighb)n(orho)n(o)n(d)f(of)h FF(!)942 1589 y Fy(0)940 1620 y FH(sp)q(ecial)1064 1608 y FQ(=)f FF(!)1153 1589 y Fy(0)1151 1620 y FD(alt)1196 1608 y FP(.)30 b FQ(Next)18 b(w)o(e)h(m)o(ust)f(\014nd)h(image-spin)60 1668 y(con\014gurations)e FF(!)406 1650 y Fy(0)404 1680 y FH(+)450 1668 y FQ(and)g FF(!)577 1650 y Fy(0)575 1680 y(\000)621 1668 y FQ(that)g(will)e(\\select")g(the)h (phases)h FF(\026)1268 1675 y FH(+)1314 1668 y FQ(and)g FF(\026)1438 1675 y Fy(\000)1484 1668 y FQ(of)f(the)g(in)o(ternal-spin)60 1728 y(system.)j(The)12 b(c)o(hoice)g(is)h(ob)o(vious:)19 b(as)14 b(in)e(the)h(t)o(w)o(o-dimensional)e(case,)i(w)o(e)g(tak)o(e)f FF(!)1582 1710 y Fy(0)1580 1740 y FH(+)1623 1728 y FQ(\(resp.)g FF(!)1787 1710 y Fy(0)1785 1740 y(\000)1815 1728 y FQ(\))h(to)60 1788 y(b)q(e)j(the)f(con\014guration)h(with)f(all)g(spins)h(+)f(\(resp.)g (all)g(spins)h FE(\000)p FQ(\).)21 b(W)l(e)15 b(need)g(then)g(to)h(sho)o(w)g (that)g(if)60 1848 y(the)f(image)e(spins)i(in)g(\003)493 1825 y FD(imag)q(e)493 1860 y(R)606 1848 y FQ(are)g(\014xed)g(in)f(a)i(fully)d (alternating)i(con\014guration,)h(and)g(those)f(in)g(an)60 1908 y(ann)o(ulus)g(\003)273 1885 y FD(imag)q(e)273 1921 y(R)300 1912 y Ft(0)380 1908 y FE(n)8 b FQ(\003)447 1885 y FD(imag)q(e)447 1921 y(R)560 1908 y FQ(are)15 b(set)f(to)i(all)e(+)h(\(or)g(all)f FE(\000)p FQ(\),)h(then)f(for)h FF(R)1341 1890 y Fy(0)1368 1908 y FQ(large)g(enough)h(\(dep)q(ending)60 1969 y(on)23 b FF(R)p FQ(\))h(the)e(image)g(spins)h(in)f(the)h(ann)o(ulus)g(are)g(capable)g (of)g(determining)d(the)j(in)o(ternal-spin)60 2029 y(phase.)133 2089 y(In)15 b(t)o(w)o(o)g(dimensions)e(w)o(e)i(w)o(ere)f(able)g(to)i(tak)o (e)e FF(R)1015 2071 y Fy(0)1041 2089 y FQ(=)g FF(R)9 b FQ(+)f(2.)21 b(That)16 b(is,)e(w)o(e)h(w)o(ere)f(able)h(to)g(shield)60 2149 y(o\013)k(a)f(v)o(olume)d(b)o(y)i(\014xing)h(around)h(it)e(a)h FP(single)23 b FQ(la)o(y)o(er)17 b(of)h(image)e(spins:)25 b(namely)l(,)15 b(b)o(y)j(setting)f(the)60 2209 y FP(image)j(spins)f(only)k FQ(in)18 b(la)o(y)o(er)f(\000)650 2216 y FD(R)p FH(+2)743 2209 y FQ(to)i(b)q(e)f(+,)g(w)o(e)g(w)o(ere)g(able)g(to)h(guaran)o(tee)f(that)h (the)f(e\013ectiv)o(e)60 2270 y(magnetic)g(\014elds)h(felt)g(b)o(y)g(the)g (in)o(ternal)g(spins)h(in)f(\003)1051 2252 y FD(int)1051 2282 y(R)p FH(+2)1144 2270 y FQ(are)h(all)f(nonnegativ)o(e,)h(ev)o(en)e(if)h(all)g (the)60 2330 y(spins)g(\(b)q(oth)h(image)e(and)i(in)o(ternal\))d(outside)j (\003)971 2337 y FD(R)p FH(+2)1063 2330 y FQ(are)f(set)g(to)h(b)q(e)f FE(\000)g FQ([see)f(Figures)h(4\(a\){\(b\)].)60 2390 y(This)j(situation)f(do) q(es)i(not,)f(ho)o(w)o(ev)o(er,)g(p)q(ersist)f(in)g(higher)h(dimensions:)30 b(a)22 b(la)o(y)o(er)e(\000)1671 2366 y FD(imag)q(e)1671 2402 y(R)p FH(+2)1791 2390 y FQ(of)i(+)60 2450 y(image)13 b(spins)h(do)q(es)h FP(not)20 b FQ(protect)14 b(all)g(of)g(the)g(in)o(ternal)f(spins)i(in)f(\000) 1266 2432 y FD(int)1266 2463 y(R)p FH(+2)1354 2450 y FQ(from)f(the)h(p)q (ossible)h FE(\000)f FQ(spins)60 2510 y(in)i(la)o(y)o(er)g(\000)266 2517 y FD(R)p FH(+3)357 2510 y FQ([see)f(Figure)h(6].)23 b(Therefore,)16 b(w)o(e)g(ha)o(v)o(e)g(to)h(resort)f(to)h(a)g(more)f(general)g(argumen)o(t)60 2571 y(to)21 b(sho)o(w)g(that)f(there)g(exists)g(a)h(shielding)e(la)o(y)o (er,)h(though)h(thic)o(k)o(er.)32 b(Consider,)21 b(therefore,)f(the)60 2631 y(system)f(of)i(in)o(ternal)f(spins)h(in)f(v)o(olume)e(\003)865 2613 y FD(int)865 2643 y(R)892 2634 y Ft(0)913 2631 y FQ(,)k(with)e(the)g (image)g(spins)h(in)f(\003)1520 2607 y FD(imag)q(e)1520 2643 y(R)1639 2631 y FQ(\014xed)g(in)g(the)938 2784 y(107)p eop %%Page: 108 108 bop 152 1637 a @beginspecial 31 @llx 35.500000 @lly 516 @urx 306.500000 @ury 3952 @rwi @setspecial %%BeginDocument: fig6.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n []/_Symbol/Symbol Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Italic/Times-Italic Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z u 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 273.5 248.8193 m S 227.8797 226.5907 m S 205.0696 226.5907 m S 250.6899 248.8193 m S 239.2847 237.705 m S U u 296.3103 271.048 m S 250.6899 248.8193 m S 227.8797 248.8193 m S 273.5001 271.048 m S 262.0951 259.9337 m S U 341.9306 293.2766 m S 296.3103 271.048 m S 307.7154 282.1623 m S 364.7407 293.2766 m S 319.1204 271.048 m S 296.3103 271.048 m S 341.9306 293.2766 m S 330.5255 282.1623 m S u 319.1204 271.048 m S 273.5 248.8193 m S 250.6899 248.8193 m S 296.3103 271.048 m S 284.9052 259.9337 m S U u 250.6899 248.8193 m S 205.0696 226.5907 m S 182.2594 226.5907 m S 227.8797 248.8193 m S 216.4746 237.705 m S U u 182.2594 248.8193 m S 182.2594 226.5907 m S 159.4493 226.5907 m S 159.4493 248.8193 m S 170.8543 237.705 m S U 0 g 1 w 4 M 330.5255 282.1623 m F 170.8543 237.705 m F 239.2847 237.705 m F 0 G 0.3 w 10 M 387.5508 293.2766 m S 341.9305 271.048 m S 319.1204 271.048 m S 364.7407 293.2766 m S 353.3356 282.1623 m S u 341.9304 248.8193 m S 296.3101 226.5907 m S 273.5 226.5907 m S 319.1203 248.8193 m S 307.7151 237.705 m S U u 364.7407 271.048 m S 319.1203 248.8193 m S 296.3101 248.8193 m S 341.9305 271.048 m S 330.5255 259.9337 m S U 410.361 293.2766 m S 364.7407 271.048 m S 341.9305 271.048 m S 387.5508 293.2766 m S 376.1458 282.1623 m S 433.1711 293.2766 m S 387.5508 271.048 m S 364.7407 271.048 m S 410.361 293.2766 m S 398.9559 282.1623 m S u 387.5508 271.048 m S 341.9304 248.8193 m S 319.1203 248.8193 m S 364.7407 271.048 m S 353.3356 259.9337 m S U u 319.1203 248.8193 m S 273.5 226.5907 m S 250.6898 226.5907 m S 296.3101 248.8193 m S 284.905 237.705 m S U u 296.3101 248.8193 m S 250.6898 226.5907 m S 227.8797 226.5907 m S 273.5 248.8193 m S 262.0948 237.705 m S U u 341.9305 271.048 m S 296.3101 248.8193 m S 273.5 248.8193 m S 319.1204 271.048 m S 307.7153 259.9337 m S U 0 g 1 w 4 M 353.3356 282.1623 m F 398.9559 282.1623 m F 262.0948 237.705 m F 307.7151 237.705 m F 0 G 0.3 w 10 M 455.9812 293.2766 m S 410.3609 271.048 m S 387.5508 271.048 m S 433.1711 293.2766 m S 421.766 282.1623 m S u 410.3608 248.8193 m S 364.7405 226.5907 m S 341.9304 226.5907 m S 387.5507 248.8193 m S 376.1455 237.705 m S U u 433.1711 271.048 m S 387.5507 248.8193 m S 364.7405 248.8193 m S 410.3609 271.048 m S 398.9559 259.9337 m S U 478.7914 293.2766 m S 433.1711 271.048 m S 410.3609 271.048 m S 455.9812 293.2766 m S 444.5762 282.1623 m S 364.7405 293.2766 m S 364.7405 271.048 m S 433.1711 271.048 m S 478.7914 293.2766 m S 467.3863 282.1623 m S u 455.9812 271.048 m S 410.3608 248.8193 m S 387.5507 248.8193 m S 433.1711 271.048 m S 421.766 259.9337 m S U u 387.5507 248.8193 m S 341.9304 226.5907 m S 319.1202 226.5907 m S 364.7405 248.8193 m S 353.3354 237.705 m S U u 364.7405 248.8193 m S 319.1202 226.5907 m S 296.3101 226.5907 m S 341.9304 248.8193 m S 330.5252 237.705 m S U u 410.3609 271.048 m S 364.7405 248.8193 m S 341.9304 248.8193 m S 387.5508 271.048 m S 376.1457 259.9337 m S U 0 g 1 w 4 M 421.766 282.1623 m F 467.3863 282.1623 m F 330.5252 237.705 m F 376.1455 237.705 m F u 0 G 0.3 w 10 M 387.5506 293.2766 m S 387.5506 271.048 m S 364.7405 271.048 m S 364.7405 293.2766 m S 376.1455 282.1623 m S U u 387.5506 248.8193 m S 387.5506 226.5907 m S 364.7405 226.5907 m S 364.7405 248.8193 m S 376.1455 237.705 m S U u 387.5506 271.048 m S 387.5506 248.8193 m S 364.7405 248.8193 m S 364.7405 271.048 m S 376.1455 259.9337 m S U 0 g 1 w 4 M 376.1455 282.1623 m F 376.1455 237.705 m F u 0 G 0.3 w 10 M 182.2594 226.5907 m S 182.2594 204.362 m S 159.4493 204.362 m S 159.4493 226.5907 m S 170.8543 215.4764 m S U u 136.639 182.1334 m S 91.0188 159.9048 m S 68.2087 159.9048 m S 113.8289 182.1334 m S 102.4238 171.0191 m S U u 159.4492 204.362 m S 113.8289 182.1334 m S 91.0187 182.1334 m S 136.639 204.362 m S 125.2341 193.2478 m S U u 205.0696 226.5907 m S 159.4492 204.362 m S 136.639 204.362 m S 182.2594 226.5907 m S 170.8544 215.4764 m S U u 227.8797 226.5907 m S 182.2593 204.362 m S 159.4492 204.362 m S 205.0696 226.5907 m S 193.6645 215.4764 m S U u 182.2593 204.362 m S 136.639 182.1334 m S 113.8289 182.1334 m S 159.4492 204.362 m S 148.0442 193.2478 m S U u 113.8289 182.1334 m S 68.2087 159.9048 m S 45.3985 159.9048 m S 91.0187 182.1334 m S 79.6137 171.0191 m S U u 182.2594 182.1334 m S 182.2594 159.9048 m S 159.4493 159.9048 m S 159.4493 182.1334 m S 170.8543 171.0191 m S U u 182.2594 204.362 m S 182.2594 182.1334 m S 159.4493 182.1334 m S 159.4493 204.362 m S 170.8543 193.2478 m S U 0 g 1 w 4 M 170.8543 215.4764 m F 193.6645 215.4764 m F 170.8543 171.0191 m F 102.4238 171.0191 m F u 0 G 0.3 w 10 M 250.6898 226.5907 m S 205.0694 204.362 m S 182.2593 204.362 m S 227.8797 226.5907 m S 216.4746 215.4764 m S U u 205.0694 182.1334 m S 159.4492 159.9048 m S 136.6391 159.9048 m S 182.2593 182.1334 m S 170.8542 171.0191 m S U u 227.8796 204.362 m S 182.2593 182.1334 m S 159.4491 182.1334 m S 205.0694 204.362 m S 193.6645 193.2478 m S U u 273.5 226.5907 m S 227.8796 204.362 m S 205.0694 204.362 m S 250.6898 226.5907 m S 239.2848 215.4764 m S U u 296.3101 226.5907 m S 250.6897 204.362 m S 227.8796 204.362 m S 273.5 226.5907 m S 262.0949 215.4764 m S U u 250.6897 204.362 m S 205.0694 182.1334 m S 182.2593 182.1334 m S 227.8796 204.362 m S 216.4746 193.2478 m S U u 182.2593 182.1334 m S 136.6391 159.9048 m S 113.8289 159.9048 m S 159.4491 182.1334 m S 148.0441 171.0191 m S U u 159.4491 182.1334 m S 113.8289 159.9048 m S 91.0188 159.9048 m S 136.639 182.1334 m S 125.2339 171.0191 m S U u 205.0694 204.362 m S 159.4491 182.1334 m S 136.639 182.1334 m S 182.2593 204.362 m S 170.8543 193.2478 m S U 0 g 1 w 4 M 216.4746 215.4764 m F 262.0949 215.4764 m F 125.2339 171.0191 m F 170.8542 171.0191 m F u 0 G 0.3 w 10 M 319.1202 226.5907 m S 273.4998 204.362 m S 250.6897 204.362 m S 296.3101 226.5907 m S 284.905 215.4764 m S U u 273.4998 182.1334 m S 227.8796 159.9048 m S 205.0695 159.9048 m S 250.6897 182.1334 m S 239.2846 171.0191 m S U u 296.31 204.362 m S 250.6897 182.1334 m S 227.8795 182.1334 m S 273.4998 204.362 m S 262.0949 193.2478 m S U u 341.9304 226.5907 m S 296.31 204.362 m S 273.4998 204.362 m S 319.1202 226.5907 m S 307.7152 215.4764 m S U u 364.7405 226.5907 m S 319.1201 204.362 m S 296.31 204.362 m S 341.9304 226.5907 m S 330.5253 215.4764 m S U u 319.1201 204.362 m S 273.4998 182.1334 m S 250.6897 182.1334 m S 296.31 204.362 m S 284.905 193.2478 m S U u 250.6897 182.1334 m S 205.0695 159.9048 m S 182.2593 159.9048 m S 227.8795 182.1334 m S 216.4745 171.0191 m S U u 227.8795 182.1334 m S 182.2593 159.9048 m S 159.4492 159.9048 m S 205.0694 182.1334 m S 193.6643 171.0191 m S U u 273.4998 204.362 m S 227.8795 182.1334 m S 205.0694 182.1334 m S 250.6897 204.362 m S 239.2847 193.2478 m S U 0 g 1 w 4 M 284.905 215.4764 m F 330.5253 215.4764 m F 193.6643 171.0191 m F 239.2846 171.0191 m F u 0 G 0.3 w 10 M 387.5506 226.5907 m S 387.5506 204.362 m S 364.7405 204.362 m S 364.7405 226.5907 m S 376.1455 215.4764 m S U u 387.5506 182.1334 m S 387.5506 159.9048 m S 364.7405 159.9048 m S 364.7405 182.1334 m S 376.1455 171.0191 m S U u 387.5506 204.362 m S 387.5506 182.1334 m S 364.7405 182.1334 m S 364.7405 204.362 m S 376.1455 193.2478 m S U 0 g 1 w 4 M 376.1455 215.4764 m F 376.1455 171.0191 m F 170.8543 148.7905 m F 56.8035 148.7905 m F 79.6136 148.7905 m F 125.2339 148.7905 m F 148.044 148.7905 m F 193.6643 148.7905 m F 376.1455 148.7905 m F u 0 G 0.3 w 10 M 227.8797 115.4475 m S 227.8797 93.2189 m S 205.0696 93.2189 m S 205.0696 115.4475 m S 216.4746 104.3332 m S U u 227.8797 137.6761 m S 227.8797 115.4475 m S 205.0696 115.4475 m S 205.0696 137.6761 m S 216.4746 126.5618 m S U u 205.0696 115.4475 m S 205.0696 93.2189 m S 182.2594 93.2189 m S 182.2594 115.4475 m S 193.6645 104.3332 m S U u 182.2594 115.4475 m S 182.2594 93.2189 m S 159.4493 93.2189 m S 159.4493 115.4475 m S 170.8543 104.3332 m S U 0 g 1 w 4 M 170.8543 148.7905 m F 56.8035 148.7905 m F 170.8543 104.3332 m F 216.4746 104.3332 m F u 0 G 0.3 w 10 M 296.3101 115.4475 m S 296.3101 93.2189 m S 273.5 93.2189 m S 273.5 115.4475 m S 284.905 104.3332 m S U u 273.5 137.6761 m S 273.5 115.4475 m S 250.6898 115.4475 m S 250.6898 137.6761 m S 262.0949 126.5618 m S U u 296.3101 137.6761 m S 296.3101 115.4475 m S 273.5 115.4475 m S 273.5 137.6761 m S 284.905 126.5618 m S U u 273.5 115.4475 m S 273.5 93.2189 m S 250.6898 93.2189 m S 250.6898 115.4475 m S 262.0949 104.3332 m S U u 250.6898 115.4475 m S 250.6898 93.2189 m S 227.8797 93.2189 m S 227.8797 115.4475 m S 239.2847 104.3332 m S U u 250.6898 137.6761 m S 250.6898 115.4475 m S 227.8797 115.4475 m S 227.8797 137.6761 m S 239.2847 126.5618 m S U 0 g 1 w 4 M 79.6136 148.7905 m F 125.2339 148.7905 m F 239.2847 104.3332 m F 284.905 104.3332 m F u 0 G 0.3 w 10 M 341.9304 137.6761 m S 341.9304 115.4475 m S 319.1202 115.4475 m S 319.1202 137.6761 m S 330.5253 126.5618 m S U u 364.7405 137.6761 m S 364.7405 115.4475 m S 341.9304 115.4475 m S 341.9304 137.6761 m S 353.3354 126.5618 m S U u 319.1202 115.4475 m S 319.1202 93.2189 m S 296.3101 93.2189 m S 296.3101 115.4475 m S 307.7151 104.3332 m S U u 319.1202 137.6761 m S 319.1202 115.4475 m S 296.3101 115.4475 m S 296.3101 137.6761 m S 307.7151 126.5618 m S U 0 g 1 w 4 M 148.044 148.7905 m F 193.6643 148.7905 m F 307.7151 104.3332 m F 353.3354 104.3332 m F u 0 G 0.3 w 10 M 387.5506 159.9048 m S 387.5506 137.6761 m S 364.7405 137.6761 m S 364.7405 159.9048 m S 376.1455 148.7905 m S U 387.5506 115.4475 m S 364.7405 115.4475 m S 376.1455 104.3332 m S 387.5506 137.6761 m S 387.5506 115.4475 m S 364.7405 115.4475 m S 364.7405 137.6761 m S 376.1455 126.5618 m S 0 g 1 w 4 M 376.1455 148.7905 m F 376.1455 104.3332 m F u 0 G 0.3 w 10 M 182.2594 93.2189 m S 182.2594 70.9902 m S 159.4493 70.9902 m S 159.4493 93.2189 m S 170.8543 82.1046 m S U 319.2658 159.8843 m S 273.6455 137.6557 m S 250.8354 137.6557 m S 296.4557 159.8843 m S 285.0506 148.77 m S 342.076 182.1129 m S 296.4557 159.8843 m S 182.2594 48.7616 m S 182.2594 70.9902 m S 307.8607 170.9987 m S 205.0696 93.2189 m S 342.076 182.1129 m S 182.2594 70.9902 m S 182.2594 93.2189 m S 353.4812 193.2274 m S 227.8797 93.2189 m S 364.8861 182.1129 m S 342.076 182.1129 m S 205.0696 93.2189 m S 376.2913 193.2274 m S 364.8861 182.1129 m S 319.2658 159.8843 m S 296.4557 159.8843 m S 342.076 182.1129 m S 330.6708 170.9987 m S 296.4557 159.8843 m S 250.8354 137.6557 m S 182.2594 48.7616 m S 262.2405 148.77 m S u 182.2594 70.9902 m S 182.2594 48.7616 m S 159.4493 48.7616 m S 159.4493 70.9902 m S 170.8543 59.8759 m S U 0 g 1 w 4 M 170.8543 82.1046 m F 376.2913 193.2274 m F 170.8543 37.6473 m F 285.0506 148.77 m F 0 G 0.3 w 10 M 250.6898 93.2189 m S 387.6962 182.1129 m S 364.8861 182.1129 m S 227.8797 93.2189 m S 399.1014 193.2274 m S 387.6962 159.8843 m S 342.076 137.6557 m S 319.2658 137.6557 m S 364.8861 159.8843 m S 353.481 148.77 m S 410.5064 182.1129 m S 364.8861 159.8843 m S 342.0759 159.8843 m S 387.6962 182.1129 m S 376.2911 170.9987 m S 273.5 93.2189 m S 410.5064 182.1129 m S 387.6962 182.1129 m S 250.6898 93.2189 m S 421.9116 193.2274 m S 296.3101 93.2189 m S 433.3165 182.1129 m S 410.5064 182.1129 m S 273.5 93.2189 m S 444.7217 193.2274 m S 433.3165 182.1129 m S 387.6962 159.8843 m S 364.8861 159.8843 m S 410.5064 182.1129 m S 399.1013 170.9987 m S 364.8861 159.8843 m S 319.2658 137.6557 m S 296.4557 137.6557 m S 342.0759 159.8843 m S 330.6709 148.77 m S 342.0759 159.8843 m S 296.4557 137.6557 m S 273.6455 137.6557 m S 319.2658 159.8843 m S 307.8607 148.77 m S 387.6962 182.1129 m S 342.0759 159.8843 m S 319.2658 159.8843 m S 364.8861 182.1129 m S 353.481 170.9987 m S 0 g 1 w 4 M 399.1014 193.2274 m F 444.7217 193.2274 m F 307.8607 148.77 m F 353.481 148.77 m F 0 G 0.3 w 10 M 319.1202 93.2189 m S 456.1266 182.1129 m S 433.3165 182.1129 m S 296.3101 93.2189 m S 467.5318 193.2274 m S 387.6962 137.6557 m S 433.3165 159.8843 m S 421.9114 148.77 m S 478.9367 182.1129 m S 433.3165 159.8843 m S 410.5063 159.8843 m S 456.1266 182.1129 m S 444.7216 170.9987 m S 478.9367 182.1129 m S 456.1266 182.1129 m S 319.1202 93.2189 m S 490.342 193.2274 m S 478.9367 182.1129 m S 513.1521 193.2274 m S 433.3165 159.8843 m S 478.9367 182.1129 m S 467.5317 170.9987 m S 433.3165 159.8843 m S 387.6962 137.6557 m S 364.886 137.6557 m S 410.5063 159.8843 m S 399.1013 148.77 m S 410.5063 159.8843 m S 364.886 137.6557 m S 342.076 137.6557 m S 387.6962 159.8843 m S 376.2911 148.77 m S 456.1266 182.1129 m S 410.5063 159.8843 m S 387.6962 159.8843 m S 433.3165 182.1129 m S 421.9114 170.9987 m S 0 g 1 w 4 M 467.5318 193.2274 m F 513.1521 193.2274 m F 376.2911 148.77 m F 421.9114 148.77 m F 0 G 0.3 w 10 M 341.9306 293.2766 m S 0 g 1 w 4 M 341.9306 293.2766 m F 0 G 0.3 w 10 M 341.9306 293.2766 m S 0 g 1 w 4 M 341.9306 293.2766 m F 1 g 335.9202 293.2766 m 329.308 290.0548 326.6387 287.443 329.9582 287.443 c 333.2776 287.443 341.3288 290.0548 347.941 293.2766 c F 347.941 293.2766 m 354.5531 296.4984 357.2224 299.1102 353.903 299.1102 c 350.5836 299.1102 342.5323 296.4984 335.9202 293.2766 c F 341.9306 293.2766 m F 0 G 0.3 w 10 M 341.9306 293.2766 m S 0 g 1 w 4 M 341.9306 293.2766 m F 0 G 0.3 w 10 M 341.9306 293.2766 m S 0 g 1 w 4 M 341.9306 293.2766 m F 343.0378 294.3448 m 339.475 294.3559 L 335.0452 292.1975 L 338.6536 292.2086 L F 340.8238 292.2086 m 344.3866 292.1975 L 348.8164 294.3559 L 345.208 294.3448 L F 339.475 294.3559 m 348.8164 294.3559 l 344.3866 292.1975 l 335.0452 292.1975 l 339.475 294.3559 l f 0 G 0.3 w 10 M 387.5508 293.2766 m S 0 g 1 w 4 M 387.5508 293.2766 m F 0 G 0.3 w 10 M 387.5508 293.2766 m S 0 g 1 w 4 M 387.5508 293.2766 m F 1 g 381.5404 293.2766 m 374.9282 290.0548 372.259 287.443 375.5784 287.443 c 378.8978 287.443 386.949 290.0548 393.5612 293.2766 c F 393.5612 293.2766 m 400.1733 296.4984 402.8426 299.1102 399.5232 299.1102 c 396.2038 299.1102 388.1525 296.4984 381.5404 293.2766 c F 387.5508 293.2766 m F 0 G 0.3 w 10 M 387.5508 293.2766 m S 0 g 1 w 4 M 387.5508 293.2766 m F 0 G 0.3 w 10 M 387.5508 293.2766 m S 0 g 1 w 4 M 387.5508 293.2766 m F 388.658 294.3448 m 385.0952 294.3559 L 380.6654 292.1975 L 384.2738 292.2086 L F 386.444 292.2086 m 390.0068 292.1975 L 394.4366 294.3559 L 390.8282 294.3448 L F 385.0952 294.3559 m 394.4366 294.3559 l 390.0068 292.1975 l 380.6654 292.1975 l 385.0952 294.3559 l f 0 G 0.3 w 10 M 433.1711 293.2766 m S 0 g 1 w 4 M 433.1711 293.2766 m F 0 G 0.3 w 10 M 433.1711 293.2766 m S 0 g 1 w 4 M 433.1711 293.2766 m F 1 g 427.1607 293.2766 m 420.5485 290.0548 417.8793 287.443 421.1987 287.443 c 424.5181 287.443 432.5693 290.0548 439.1815 293.2766 c F 439.1815 293.2766 m 445.7936 296.4984 448.4629 299.1102 445.1435 299.1102 c 441.8241 299.1102 433.7728 296.4984 427.1607 293.2766 c F 433.1711 293.2766 m F 0 G 0.3 w 10 M 433.1711 293.2766 m S 0 g 1 w 4 M 433.1711 293.2766 m F 0 G 0.3 w 10 M 433.1711 293.2766 m S 0 g 1 w 4 M 433.1711 293.2766 m F 434.2783 294.3448 m 430.7155 294.3559 L 426.2857 292.1975 L 429.8941 292.2086 L F 432.0643 292.2086 m 435.6271 292.1975 L 440.0569 294.3559 L 436.4485 294.3448 L F 430.7155 294.3559 m 440.0569 294.3559 l 435.6271 292.1975 l 426.2857 292.1975 l 430.7155 294.3559 l f 0 G 0.3 w 10 M 478.7914 293.2766 m S 0 g 1 w 4 M 478.7914 293.2766 m F 0 G 0.3 w 10 M 478.7914 293.2766 m S 0 g 1 w 4 M 478.7914 293.2766 m F 1 g 472.781 293.2766 m 466.1688 290.0548 463.4995 287.443 466.819 287.443 c 470.1383 287.443 478.1896 290.0548 484.8018 293.2766 c F 484.8018 293.2766 m 491.4139 296.4984 494.0832 299.1102 490.7638 299.1102 c 487.4444 299.1102 479.3931 296.4984 472.781 293.2766 c F 478.7914 293.2766 m F 0 G 0.3 w 10 M 478.7914 293.2766 m S 0 g 1 w 4 M 478.7914 293.2766 m F 0 G 0.3 w 10 M 478.7914 293.2766 m S 0 g 1 w 4 M 478.7914 293.2766 m F 479.8986 294.3448 m 476.3358 294.3559 L 471.906 292.1975 L 475.5144 292.2086 L F 477.6846 292.2086 m 481.2474 292.1975 L 485.6772 294.3559 L 482.0688 294.3448 L F 476.3358 294.3559 m 485.6772 294.3559 l 481.2474 292.1975 l 471.906 292.1975 l 476.3358 294.3559 l f 0 G 0.3 w 10 M 250.6899 248.8193 m S 273.5 248.8193 m S 250.6899 248.8193 m S 296.3101 248.8193 m S 273.5 248.8193 m S 319.1203 248.8193 m S 296.3101 248.8193 m S 341.9304 248.8193 m S 319.1203 248.8193 m S 364.7405 248.8193 m S 341.9304 248.8193 m S 387.5507 248.8193 m S 364.7405 248.8193 m S 387.5507 248.8193 m S 250.6899 248.8193 m S 0 g 1 w 4 M 250.6899 248.8193 m F 0 G 0.3 w 10 M 250.6899 248.8193 m S 0 g 1 w 4 M 250.6899 248.8193 m F 1 g 244.6795 248.8193 m 238.0673 245.5975 235.398 242.9857 238.7174 242.9857 c 242.0368 242.9857 250.0881 245.5975 256.7003 248.8193 c F 256.7003 248.8193 m 263.3124 252.0411 265.9817 254.6529 262.6623 254.6529 c 259.3429 254.6529 251.2916 252.0411 244.6795 248.8193 c F 250.6899 248.8193 m F 0 G 0.3 w 10 M 250.6899 248.8193 m S 0 g 1 w 4 M 250.6899 248.8193 m F 0 G 0.3 w 10 M 250.6899 248.8193 m S 0 g 1 w 4 M 250.6899 248.8193 m F 251.797 249.8875 m 248.2342 249.8986 L 243.8045 247.7402 L 247.4129 247.7513 L F 249.5831 247.7513 m 253.1459 247.7402 L 257.5756 249.8986 L 253.9673 249.8875 L F 248.2342 249.8986 m 257.5756 249.8986 l 253.1459 247.7402 l 243.8045 247.7402 l 248.2342 249.8986 l f 0 G 0.3 w 10 M 296.3101 248.8193 m S 0 g 1 w 4 M 296.3101 248.8193 m F 0 G 0.3 w 10 M 296.3101 248.8193 m S 0 g 1 w 4 M 296.3101 248.8193 m F 1 g 290.2997 248.8193 m 283.6875 245.5975 281.0182 242.9857 284.3376 242.9857 c 287.657 242.9857 295.7083 245.5975 302.3205 248.8193 c F 302.3205 248.8193 m 308.9326 252.0411 311.6019 254.6529 308.2825 254.6529 c 304.9631 254.6529 296.9118 252.0411 290.2997 248.8193 c F 296.3101 248.8193 m F 0 G 0.3 w 10 M 296.3101 248.8193 m S 0 g 1 w 4 M 296.3101 248.8193 m F 0 G 0.3 w 10 M 296.3101 248.8193 m S 0 g 1 w 4 M 296.3101 248.8193 m F 297.4172 249.8875 m 293.8545 249.8986 L 289.4247 247.7402 L 293.0331 247.7513 L F 295.2033 247.7513 m 298.7661 247.7402 L 303.1958 249.8986 L 299.5875 249.8875 L F 293.8545 249.8986 m 303.1958 249.8986 l 298.7661 247.7402 l 289.4247 247.7402 l 293.8545 249.8986 l f 0 G 0.3 w 10 M 341.9304 248.8193 m S 0 g 1 w 4 M 341.9304 248.8193 m F 0 G 0.3 w 10 M 341.9304 248.8193 m S 0 g 1 w 4 M 341.9304 248.8193 m F 1 g 335.92 248.8193 m 329.3078 245.5975 326.6385 242.9857 329.9579 242.9857 c 333.2773 242.9857 341.3286 245.5975 347.9408 248.8193 c F 347.9408 248.8193 m 354.5529 252.0411 357.2222 254.6529 353.9028 254.6529 c 350.5834 254.6529 342.5321 252.0411 335.92 248.8193 c F 341.9304 248.8193 m F 0 G 0.3 w 10 M 341.9304 248.8193 m S 0 g 1 w 4 M 341.9304 248.8193 m F 0 G 0.3 w 10 M 341.9304 248.8193 m S 0 g 1 w 4 M 341.9304 248.8193 m F 343.0375 249.8875 m 339.4748 249.8986 L 335.045 247.7402 L 338.6534 247.7513 L F 340.8236 247.7513 m 344.3864 247.7402 L 348.8161 249.8986 L 345.2078 249.8875 L F 339.4748 249.8986 m 348.8161 249.8986 l 344.3864 247.7402 l 335.045 247.7402 l 339.4748 249.8986 l f 0 G 0.3 w 10 M 387.5507 248.8193 m S 0 g 1 w 4 M 387.5507 248.8193 m F 0 G 0.3 w 10 M 387.5507 248.8193 m S 0 g 1 w 4 M 387.5507 248.8193 m F 1 g 381.5403 248.8193 m 374.9281 245.5975 372.2588 242.9857 375.5782 242.9857 c 378.8976 242.9857 386.9489 245.5975 393.5611 248.8193 c F 393.5611 248.8193 m 400.1732 252.0411 402.8425 254.6529 399.5231 254.6529 c 396.2037 254.6529 388.1524 252.0411 381.5403 248.8193 c F 387.5507 248.8193 m F 0 G 0.3 w 10 M 387.5507 248.8193 m S 0 g 1 w 4 M 387.5507 248.8193 m F 0 G 0.3 w 10 M 387.5507 248.8193 m S 0 g 1 w 4 M 387.5507 248.8193 m F 388.6578 249.8875 m 385.095 249.8986 L 380.6653 247.7402 L 384.2737 247.7513 L F 386.4439 247.7513 m 390.0067 247.7402 L 394.4364 249.8986 L 390.828 249.8875 L F 385.095 249.8986 m 394.4364 249.8986 l 390.0067 247.7402 l 380.6653 247.7402 l 385.095 249.8986 l f 0 G 0.3 w 10 M 159.4492 204.362 m S 182.2593 204.362 m S 159.4492 204.362 m S 205.0694 204.362 m S 182.2593 204.362 m S 227.8796 204.362 m S 205.0694 204.362 m S 250.6897 204.362 m S 227.8796 204.362 m S 273.4998 204.362 m S 250.6897 204.362 m S 296.31 204.362 m S 273.4998 204.362 m S 296.31 204.362 m S 159.4492 204.362 m S 0 g 1 w 4 M 159.4492 204.362 m F 0 G 0.3 w 10 M 159.4492 204.362 m S 0 g 1 w 4 M 159.4492 204.362 m F 1 g 153.4388 204.362 m 146.8266 201.1402 144.1573 198.5284 147.4767 198.5284 c 150.7961 198.5284 158.8474 201.1402 165.4596 204.362 c F 165.4596 204.362 m 172.0717 207.5838 174.741 210.1956 171.4216 210.1956 c 168.1022 210.1956 160.0509 207.5838 153.4388 204.362 c F 159.4492 204.362 m F 0 G 0.3 w 10 M 159.4492 204.362 m S 0 g 1 w 4 M 159.4492 204.362 m F 0 G 0.3 w 10 M 159.4492 204.362 m S 0 g 1 w 4 M 159.4492 204.362 m F 160.5563 205.4302 m 156.9936 205.4413 L 152.5638 203.2829 L 156.1722 203.294 L F 158.3424 203.294 m 161.9052 203.2829 L 166.3349 205.4413 L 162.7266 205.4302 L F 156.9936 205.4413 m 166.3349 205.4413 l 161.9052 203.2829 l 152.5638 203.2829 l 156.9936 205.4413 l f 0 G 0.3 w 10 M 205.0694 204.362 m S 0 g 1 w 4 M 205.0694 204.362 m F 0 G 0.3 w 10 M 205.0694 204.362 m S 0 g 1 w 4 M 205.0694 204.362 m F 1 g 199.059 204.362 m 192.4468 201.1402 189.7775 198.5284 193.097 198.5284 c 196.4163 198.5284 204.4676 201.1402 211.0798 204.362 c F 211.0798 204.362 m 217.6919 207.5838 220.3612 210.1956 217.0418 210.1956 c 213.7224 210.1956 205.6711 207.5838 199.059 204.362 c F 205.0694 204.362 m F 0 G 0.3 w 10 M 205.0694 204.362 m S 0 g 1 w 4 M 205.0694 204.362 m F 0 G 0.3 w 10 M 205.0694 204.362 m S 0 g 1 w 4 M 205.0694 204.362 m F 206.1766 205.4302 m 202.6138 205.4413 L 198.184 203.2829 L 201.7924 203.294 L F 203.9626 203.294 m 207.5254 203.2829 L 211.9552 205.4413 L 208.3468 205.4302 L F 202.6138 205.4413 m 211.9552 205.4413 l 207.5254 203.2829 l 198.184 203.2829 l 202.6138 205.4413 l f 0 G 0.3 w 10 M 250.6897 204.362 m S 0 g 1 w 4 M 250.6897 204.362 m F 0 G 0.3 w 10 M 250.6897 204.362 m S 0 g 1 w 4 M 250.6897 204.362 m F 1 g 244.6793 204.362 m 238.0671 201.1402 235.3978 198.5284 238.7173 198.5284 c 242.0366 198.5284 250.0879 201.1402 256.7001 204.362 c F 256.7001 204.362 m 263.3122 207.5838 265.9815 210.1956 262.6621 210.1956 c 259.3427 210.1956 251.2914 207.5838 244.6793 204.362 c F 250.6897 204.362 m F 0 G 0.3 w 10 M 250.6897 204.362 m S 0 g 1 w 4 M 250.6897 204.362 m F 0 G 0.3 w 10 M 250.6897 204.362 m S 0 g 1 w 4 M 250.6897 204.362 m F 251.7969 205.4302 m 248.2341 205.4413 L 243.8043 203.2829 L 247.4127 203.294 L F 249.5829 203.294 m 253.1457 203.2829 L 257.5755 205.4413 L 253.9671 205.4302 L F 248.2341 205.4413 m 257.5755 205.4413 l 253.1457 203.2829 l 243.8043 203.2829 l 248.2341 205.4413 l f 0 G 0.3 w 10 M 296.31 204.362 m S 0 g 1 w 4 M 296.31 204.362 m F 0 G 0.3 w 10 M 296.31 204.362 m S 0 g 1 w 4 M 296.31 204.362 m F 1 g 290.2996 204.362 m 283.6874 201.1402 281.0181 198.5284 284.3375 198.5284 c 287.6569 198.5284 295.7082 201.1402 302.3204 204.362 c F 302.3204 204.362 m 308.9325 207.5838 311.6018 210.1956 308.2824 210.1956 c 304.963 210.1956 296.9117 207.5838 290.2996 204.362 c F 296.31 204.362 m F 0 G 0.3 w 10 M 296.31 204.362 m S 0 g 1 w 4 M 296.31 204.362 m F 0 G 0.3 w 10 M 296.31 204.362 m S 0 g 1 w 4 M 296.31 204.362 m F 297.4171 205.4302 m 293.8544 205.4413 L 289.4246 203.2829 L 293.033 203.294 L F 295.2032 203.294 m 298.766 203.2829 L 303.1957 205.4413 L 299.5874 205.4302 L F 293.8544 205.4413 m 303.1957 205.4413 l 298.766 203.2829 l 289.4246 203.2829 l 293.8544 205.4413 l f 0 G 0.3 w 10 M 68.2087 159.9048 m S 91.0188 159.9048 m S 68.2087 159.9048 m S 113.8289 159.9048 m S 91.0188 159.9048 m S 136.6391 159.9048 m S 113.8289 159.9048 m S 159.4492 159.9048 m S 136.6391 159.9048 m S 182.2593 159.9048 m S 159.4492 159.9048 m S 205.0695 159.9048 m S 182.2593 159.9048 m S 205.0695 159.9048 m S 68.2087 159.9048 m S 0 g 1 w 4 M 68.2087 159.9048 m F 0 G 0.3 w 10 M 68.2087 159.9048 m S 0 g 1 w 4 M 68.2087 159.9048 m F 1 g 62.1983 159.9048 m 55.5861 156.683 52.9168 154.0712 56.2362 154.0712 c 59.5556 154.0712 67.6069 156.683 74.2191 159.9048 c F 74.2191 159.9048 m 80.8312 163.1266 83.5005 165.7384 80.1811 165.7384 c 76.8617 165.7384 68.8104 163.1266 62.1983 159.9048 c F 68.2087 159.9048 m F 0 G 0.3 w 10 M 68.2087 159.9048 m S 0 g 1 w 4 M 68.2087 159.9048 m F 0 G 0.3 w 10 M 68.2087 159.9048 m S 0 g 1 w 4 M 68.2087 159.9048 m F 69.3158 160.973 m 65.753 160.9841 L 61.3233 158.8257 L 64.9317 158.8368 L F 67.1019 158.8368 m 70.6647 158.8257 L 75.0944 160.9841 L 71.486 160.973 L F 65.753 160.9841 m 75.0944 160.9841 l 70.6647 158.8257 l 61.3233 158.8257 l 65.753 160.9841 l f 0 G 0.3 w 10 M 113.8289 159.9048 m S 0 g 1 w 4 M 113.8289 159.9048 m F 0 G 0.3 w 10 M 113.8289 159.9048 m S 0 g 1 w 4 M 113.8289 159.9048 m F 1 g 107.8185 159.9048 m 101.2063 156.683 98.537 154.0712 101.8565 154.0712 c 105.1759 154.0712 113.2271 156.683 119.8393 159.9048 c F 119.8393 159.9048 m 126.4514 163.1266 129.1207 165.7384 125.8013 165.7384 c 122.4819 165.7384 114.4306 163.1266 107.8185 159.9048 c F 113.8289 159.9048 m F 0 G 0.3 w 10 M 113.8289 159.9048 m S 0 g 1 w 4 M 113.8289 159.9048 m F 0 G 0.3 w 10 M 113.8289 159.9048 m S 0 g 1 w 4 M 113.8289 159.9048 m F 114.936 160.973 m 111.3733 160.9841 L 106.9435 158.8257 L 110.5519 158.8368 L F 112.7221 158.8368 m 116.2849 158.8257 L 120.7146 160.9841 L 117.1063 160.973 L F 111.3733 160.9841 m 120.7146 160.9841 l 116.2849 158.8257 l 106.9435 158.8257 l 111.3733 160.9841 l f 0 G 0.3 w 10 M 159.4492 159.9048 m S 0 g 1 w 4 M 159.4492 159.9048 m F 0 G 0.3 w 10 M 159.4492 159.9048 m S 0 g 1 w 4 M 159.4492 159.9048 m F 1 g 153.4388 159.9048 m 146.8266 156.683 144.1573 154.0712 147.4768 154.0712 c 150.7962 154.0712 158.8474 156.683 165.4596 159.9048 c F 165.4596 159.9048 m 172.0717 163.1266 174.741 165.7384 171.4216 165.7384 c 168.1022 165.7384 160.0509 163.1266 153.4388 159.9048 c F 159.4492 159.9048 m F 0 G 0.3 w 10 M 159.4492 159.9048 m S 0 g 1 w 4 M 159.4492 159.9048 m F 0 G 0.3 w 10 M 159.4492 159.9048 m S 0 g 1 w 4 M 159.4492 159.9048 m F 160.5563 160.973 m 156.9936 160.9841 L 152.5638 158.8257 L 156.1722 158.8368 L F 158.3424 158.8368 m 161.9052 158.8257 L 166.3349 160.9841 L 162.7266 160.973 L F 156.9936 160.9841 m 166.3349 160.9841 l 161.9052 158.8257 l 152.5638 158.8257 l 156.9936 160.9841 l f 0 G 0.3 w 10 M 205.0695 159.9048 m S 0 g 1 w 4 M 205.0695 159.9048 m F 0 G 0.3 w 10 M 205.0695 159.9048 m S 0 g 1 w 4 M 205.0695 159.9048 m F 1 g 199.0591 159.9048 m 192.4469 156.683 189.7776 154.0712 193.097 154.0712 c 196.4164 154.0712 204.4677 156.683 211.0799 159.9048 c F 211.0799 159.9048 m 217.692 163.1266 220.3613 165.7384 217.0419 165.7384 c 213.7225 165.7384 205.6712 163.1266 199.0591 159.9048 c F 205.0695 159.9048 m F 0 G 0.3 w 10 M 205.0695 159.9048 m S 0 g 1 w 4 M 205.0695 159.9048 m F 0 G 0.3 w 10 M 205.0695 159.9048 m S 0 g 1 w 4 M 205.0695 159.9048 m F 206.1766 160.973 m 202.6138 160.9841 L 198.1841 158.8257 L 201.7925 158.8368 L F 203.9627 158.8368 m 207.5255 158.8257 L 211.9552 160.9841 L 208.3468 160.973 L F 202.6138 160.9841 m 211.9552 160.9841 l 207.5255 158.8257 l 198.1841 158.8257 l 202.6138 160.9841 l f u 0 G 0.3 w 10 M 182.4048 93.1984 m S 136.7846 70.9698 m S 113.9745 70.9698 m S 159.5947 93.1984 m S 148.1896 82.0841 m S U u 205.2152 115.4271 m S 159.5947 93.1984 m S 136.7845 93.1984 m S 182.405 115.4271 m S 170.9999 104.3128 m S U 250.8354 137.6557 m S 205.2152 115.4271 m S 216.6202 126.5414 m S 273.6455 137.6557 m S 228.0253 115.4271 m S 205.2152 115.4271 m S 250.8354 137.6557 m S 239.4303 126.5414 m S u 228.0253 115.4271 m S 182.4048 93.1984 m S 159.5947 93.1984 m S 205.2152 115.4271 m S 193.81 104.3128 m S U u 159.5947 93.1984 m S 113.9745 70.9698 m S 91.1643 70.9698 m S 136.7845 93.1984 m S 125.3795 82.0841 m S U 0 g 1 w 4 M 239.4303 126.5414 m F 148.1896 82.0841 m F 0 G 0.3 w 10 M 296.4557 137.6557 m S 250.8354 115.4271 m S 228.0253 115.4271 m S 273.6455 137.6557 m S 262.2404 126.5414 m S u 250.8352 93.1984 m S 205.215 70.9698 m S 182.4049 70.9698 m S 228.0251 93.1984 m S 216.62 82.0841 m S U u 273.6456 115.4271 m S 228.0251 93.1984 m S 205.2149 93.1984 m S 250.8354 115.4271 m S 239.4303 104.3128 m S U 319.2658 137.6557 m S 273.6456 115.4271 m S 250.8354 115.4271 m S 296.4557 137.6557 m S 285.0506 126.5414 m S 342.076 137.6557 m S 296.4557 115.4271 m S 273.6456 115.4271 m S 319.2658 137.6557 m S 307.8607 126.5414 m S u 296.4557 115.4271 m S 250.8352 93.1984 m S 228.0251 93.1984 m S 273.6456 115.4271 m S 262.2404 104.3128 m S U u 228.0251 93.1984 m S 182.4049 70.9698 m S 159.5947 70.9698 m S 205.2149 93.1984 m S 193.8099 82.0841 m S U u 205.2149 93.1984 m S 159.5947 70.9698 m S 136.7846 70.9698 m S 182.4048 93.1984 m S 170.9997 82.0841 m S U u 250.8354 115.4271 m S 205.2149 93.1984 m S 182.4048 93.1984 m S 228.0253 115.4271 m S 216.6201 104.3128 m S U 0 g 1 w 4 M 262.2404 126.5414 m F 307.8607 126.5414 m F 170.9997 82.0841 m F 216.62 82.0841 m F 0 G 0.3 w 10 M 364.886 137.6557 m S 319.2658 115.4271 m S 296.4557 115.4271 m S 342.076 137.6557 m S 330.6708 126.5414 m S u 319.2656 93.1984 m S 273.6454 70.9698 m S 250.8353 70.9698 m S 296.4555 93.1984 m S 285.0504 82.0841 m S U u 342.076 115.4271 m S 296.4555 93.1984 m S 273.6453 93.1984 m S 319.2658 115.4271 m S 307.8607 104.3128 m S U 387.6962 137.6557 m S 342.076 115.4271 m S 319.2658 115.4271 m S 364.886 137.6557 m S 353.4185 126.5414 m S 342.076 115.4271 m S 387.6962 137.6557 m S 376.2911 126.5414 m S u 364.8861 115.4271 m S 319.2656 93.1984 m S 296.4555 93.1984 m S 342.076 115.4271 m S 330.6708 104.3128 m S U u 296.4555 93.1984 m S 250.8353 70.9698 m S 228.0251 70.9698 m S 273.6453 93.1984 m S 262.2403 82.0841 m S U u 273.6453 93.1984 m S 228.0251 70.9698 m S 205.215 70.9698 m S 250.8352 93.1984 m S 239.4301 82.0841 m S U u 319.2658 115.4271 m S 273.6453 93.1984 m S 250.8352 93.1984 m S 296.4557 115.4271 m S 285.0505 104.3128 m S U 0 g 1 w 4 M 330.6708 126.5414 m F 376.2911 126.5414 m F 239.4301 82.0841 m F 285.0504 82.0841 m F u 0 G 0.3 w 10 M 113.9745 70.9698 m S 68.354 48.7411 m S 45.5438 48.7411 m S 91.1643 70.9698 m S 79.7592 59.8555 m S U u 136.7846 70.9698 m S 91.1641 48.7411 m S 68.354 48.7411 m S 113.9745 70.9698 m S 102.5693 59.8555 m S U 0 g 1 w 4 M 102.5693 59.8555 m F u 0 G 0.3 w 10 M 159.5947 70.9698 m S 113.9742 48.7411 m S 91.1641 48.7411 m S 136.7846 70.9698 m S 125.3795 59.8555 m S U u 182.4049 70.9698 m S 136.7844 48.7411 m S 113.9742 48.7411 m S 159.5947 70.9698 m S 148.1896 59.8555 m S U u 205.215 70.9698 m S 159.5945 48.7411 m S 136.7844 48.7411 m S 182.4049 70.9698 m S 170.9998 59.8555 m S U 0 g 1 w 4 M 125.3795 59.8555 m F 170.9998 59.8555 m F u 0 G 0.3 w 10 M 228.0251 70.9698 m S 182.4046 48.7411 m S 159.5945 48.7411 m S 205.215 70.9698 m S 193.8099 59.8555 m S U u 250.8353 70.9698 m S 205.2148 48.7411 m S 182.4046 48.7411 m S 228.0251 70.9698 m S 216.6201 59.8555 m S U u 273.6454 70.9698 m S 228.0249 48.7411 m S 205.2148 48.7411 m S 250.8353 70.9698 m S 239.4302 59.8555 m S U 0 g 1 w 4 M 193.8099 59.8555 m F 239.4302 59.8555 m F 0 G 0.3 w 10 M 342.076 182.1129 m S 1 g 1 w 4 M 332.2078 177.3046 m 335.0195 177.3046 341.7171 179.4574 347.167 182.1129 c 352.617 184.7684 354.7558 186.9212 351.9441 186.9212 c 349.1324 186.9212 342.4347 184.7684 336.9848 182.1129 c 331.5349 179.4574 329.3961 177.3046 332.2078 177.3046 c b 0 g 342.076 182.1129 m F 0 G 0.3 w 10 M 387.6962 182.1129 m S 0.5 g 1 w 4 M 377.828 177.3046 m 380.6397 177.3046 387.3373 179.4574 392.7873 182.1129 c 398.2372 184.7684 400.376 186.9212 397.5643 186.9212 c 394.7526 186.9212 388.055 184.7684 382.6051 182.1129 c 377.1551 179.4574 375.0163 177.3046 377.828 177.3046 c b 0 g 387.6962 182.1129 m F 0 G 0.3 w 10 M 433.3165 182.1129 m S 1 g 1 w 4 M 423.4483 177.3046 m 426.26 177.3046 432.9576 179.4574 438.4076 182.1129 c 443.8575 184.7684 445.9963 186.9212 443.1846 186.9212 c 440.3729 186.9212 433.6753 184.7684 428.2254 182.1129 c 422.7754 179.4574 420.6366 177.3046 423.4483 177.3046 c b 0 g 433.3165 182.1129 m F 0 G 0.3 w 10 M 478.9367 182.1129 m S 0.5 g 1 w 4 M 469.0686 177.3046 m 471.8802 177.3046 478.5779 179.4574 484.0278 182.1129 c 489.4777 184.7684 491.6166 186.9212 488.8049 186.9212 c 485.9932 186.9212 479.2955 184.7684 473.8456 182.1129 c 468.3957 179.4574 466.2568 177.3046 469.0686 177.3046 c b 0 g 478.9367 182.1129 m F 0 G 0.3 w 10 M 296.4557 137.6557 m S 1 g 1 w 4 M 286.5875 132.8474 m 289.3992 132.8474 296.0968 135.0002 301.5467 137.6557 c 306.9967 140.3112 309.1355 142.464 306.3238 142.464 c 303.5121 142.464 296.8145 140.3112 291.3645 137.6557 c 285.9146 135.0002 283.7758 132.8474 286.5875 132.8474 c b 0 g 296.4557 137.6557 m F 0 G 0.3 w 10 M 387.6962 137.6557 m S 1 g 1 w 4 M 377.828 132.8474 m 380.6397 132.8474 387.3374 135.0002 392.7873 137.6557 c 398.2373 140.3112 400.3761 142.464 397.5644 142.464 c 394.7527 142.464 388.055 140.3112 382.6051 137.6557 c 377.1552 135.0002 375.0163 132.8474 377.828 132.8474 c b 0 g 387.6962 137.6557 m F 0 G 0.3 w 10 M 250.8354 137.6557 m S 0 g 1 w 4 M 250.8354 137.6557 m F 0 G 0.3 w 10 M 250.8354 137.6557 m S 250.8354 137.6557 m S 250.8354 137.6557 m S 0 g 1 w 4 M 250.8354 137.6557 m F 0 G 0.3 w 10 M 250.8354 137.6557 m S 250.8354 137.6557 m S 1 g 1 w 4 M 244.825 137.6557 m 238.2129 134.4339 235.5436 131.8221 238.863 131.8221 c 242.1824 131.8221 250.2337 134.4339 256.8458 137.6557 c F 256.8458 137.6557 m 263.458 140.8775 266.1272 143.4893 262.8078 143.4893 c 259.4884 143.4893 251.4372 140.8775 244.825 137.6557 c F 250.8354 137.6557 m F 0 G 0.3 w 10 M 250.8354 137.6557 m S 0 g 1 w 4 M 250.8354 137.6557 m F 0 G 0.3 w 10 M 250.8354 137.6557 m S 250.8354 137.6557 m S 0 g 1 w 4 M 247.5587 136.5878 m 240.2173 133.0107 L 242.3875 133.0107 L 249.7289 136.5878 L 253.2915 136.5766 L 257.7212 138.735 L 254.1128 138.7239 L 261.4542 142.301 L 259.284 142.301 L 251.9426 138.7239 L 248.3798 138.735 L 243.9501 136.5766 L 247.5587 136.5878 L f 0 G 0.3 w 10 M 342.076 137.6557 m S 0 g 1 w 4 M 342.076 137.6557 m F 0 G 0.3 w 10 M 342.076 137.6557 m S 342.076 137.6557 m S 342.076 137.6557 m S 0 g 1 w 4 M 342.076 137.6557 m F 0 G 0.3 w 10 M 342.076 137.6557 m S 342.076 137.6557 m S 1 g 1 w 4 M 336.0655 137.6557 m 329.4534 134.4339 326.7841 131.8221 330.1035 131.8221 c 333.4229 131.8221 341.4742 134.4339 348.0863 137.6557 c F 348.0863 137.6557 m 354.6985 140.8775 357.3677 143.4893 354.0484 143.4893 c 350.7289 143.4893 342.6777 140.8775 336.0655 137.6557 c F 342.076 137.6557 m F 0 G 0.3 w 10 M 342.076 137.6557 m S 0 g 1 w 4 M 342.076 137.6557 m F 0 G 0.3 w 10 M 342.076 137.6557 m S 342.076 137.6557 m S 0 g 1 w 4 M 338.7992 136.5878 m 331.4578 133.0107 L 333.628 133.0107 L 340.9694 136.5878 L 344.532 136.5766 L 348.9617 138.735 L 345.3533 138.7239 L 352.6947 142.301 L 350.5245 142.301 L 343.1831 138.7239 L 339.6203 138.735 L 335.1906 136.5766 L 338.7992 136.5878 L f 0 G 0.3 w 10 M 136.7846 70.9698 m S 91.1643 48.7412 m S 68.3542 48.7412 m S 113.9745 70.9698 m S 102.5693 59.8555 m S 159.5947 93.1984 m S 113.9745 70.9698 m S 159.5947 93.1984 m S 182.4048 93.1984 m S 159.5947 93.1984 m S 182.4048 93.1984 m S 136.7846 70.9698 m S 113.9745 70.9698 m S 159.5947 93.1984 m S 148.1896 82.0841 m S 113.9745 70.9698 m S 68.3542 48.7412 m S 0 g 1 w 4 M 102.5693 59.8555 m F 0 G 0.3 w 10 M 205.2149 93.1984 m S 182.4048 93.1984 m S 205.215 70.9698 m S 159.5947 48.7412 m S 136.7846 48.7412 m S 182.4049 70.9698 m S 170.9998 59.8555 m S 228.0251 93.1984 m S 182.4049 70.9698 m S 159.5947 70.9698 m S 205.2149 93.1984 m S 193.8099 82.0841 m S 228.0251 93.1984 m S 205.2149 93.1984 m S 250.8352 93.1984 m S 228.0251 93.1984 m S 250.8352 93.1984 m S 205.215 70.9698 m S 182.4049 70.9698 m S 228.0251 93.1984 m S 216.62 82.0841 m S 182.4049 70.9698 m S 136.7846 48.7412 m S 113.9744 48.7412 m S 159.5947 70.9698 m S 148.1896 59.8555 m S 159.5947 70.9698 m S 113.9744 48.7412 m S 91.1643 48.7412 m S 136.7846 70.9698 m S 125.3795 59.8555 m S 205.2149 93.1984 m S 159.5947 70.9698 m S 136.7846 70.9698 m S 182.4048 93.1984 m S 170.9997 82.0841 m S 0 g 1 w 4 M 125.3795 59.8555 m F 170.9998 59.8555 m F 0 G 0.3 w 10 M 273.6453 93.1984 m S 250.8352 93.1984 m S 205.215 48.7412 m S 250.8353 70.9698 m S 296.4555 93.1984 m S 250.8353 70.9698 m S 228.0251 70.9698 m S 273.6453 93.1984 m S 262.2403 82.0841 m S 296.4555 93.1984 m S 273.6453 93.1984 m S 296.4555 93.1984 m S 250.8353 70.9698 m S 296.4555 93.1984 m S 250.8353 70.9698 m S 205.215 48.7412 m S 182.4048 48.7412 m S 228.0251 70.9698 m S 216.6201 59.8555 m S 228.0251 70.9698 m S 182.4048 48.7412 m S 159.5947 48.7412 m S 205.215 70.9698 m S 193.8099 59.8555 m S 273.6453 93.1984 m S 228.0251 70.9698 m S 205.215 70.9698 m S 250.8352 93.1984 m S 239.4301 82.0841 m S 0 g 1 w 4 M 193.8099 59.8555 m F 0 G 0.3 w 10 M 68.3542 48.7412 m S 91.1643 48.7412 m S 68.3542 48.7412 m S 113.9744 48.7412 m S 91.1643 48.7412 m S 136.7846 48.7412 m S 113.9744 48.7412 m S 159.5947 48.7412 m S 136.7846 48.7412 m S 182.4048 48.7412 m S 159.5947 48.7412 m S 205.215 48.7412 m S 182.4048 48.7412 m S 205.215 48.7412 m S 159.5947 93.1984 m S 1 g 1 w 4 M 149.7265 88.3901 m 152.5382 88.3901 159.2359 90.5429 164.6858 93.1984 c 170.1357 95.8539 172.2746 98.0067 169.4629 98.0067 c 166.6512 98.0067 159.9535 95.8539 154.5036 93.1984 c 149.0537 90.5429 146.9148 88.3901 149.7265 88.3901 c b 0 g 159.5947 93.1984 m F 0 G 0.3 w 10 M 205.2149 93.1984 m S 0.5 g 1 w 4 M 195.3467 88.3901 m 198.1584 88.3901 204.8561 90.5429 210.306 93.1984 c 215.7559 95.8539 217.8948 98.0067 215.0831 98.0067 c 212.2714 98.0067 205.5737 95.8539 200.1238 93.1984 c 194.6739 90.5429 192.535 88.3901 195.3467 88.3901 c b 0 g 205.2149 93.1984 m F 0 G 0.3 w 10 M 250.8352 93.1984 m S 1 g 1 w 4 M 240.967 88.3901 m 243.7787 88.3901 250.4764 90.5429 255.9263 93.1984 c 261.3762 95.8539 263.5151 98.0067 260.7034 98.0067 c 257.8917 98.0067 251.194 95.8539 245.7441 93.1984 c 240.2942 90.5429 238.1553 88.3901 240.967 88.3901 c b 0 g 250.8352 93.1984 m F 0 G 0.3 w 10 M 296.4555 93.1984 m S 0.5 g 1 w 4 M 286.5873 88.3901 m 289.399 88.3901 296.0967 90.5429 301.5466 93.1984 c 306.9965 95.8539 309.1354 98.0067 306.3237 98.0067 c 303.512 98.0067 296.8143 95.8539 291.3644 93.1984 c 285.9145 90.5429 283.7756 88.3901 286.5873 88.3901 c b 0 g 296.4555 93.1984 m F 0 G 0.3 w 10 M 113.9744 48.7412 m S 1 g 1 w 4 M 104.1062 43.9329 m 106.9179 43.9329 113.6156 46.0857 119.0655 48.7412 c 124.5154 51.3967 126.6543 53.5495 123.8426 53.5495 c 121.0309 53.5495 114.3332 51.3967 108.8833 48.7412 c 103.4334 46.0857 101.2945 43.9329 104.1062 43.9329 c b 0 g 113.9744 48.7412 m F 0 G 0.3 w 10 M 205.215 48.7412 m S 1 g 1 w 4 M 195.3468 43.9329 m 198.1585 43.9329 204.8562 46.0857 210.3061 48.7412 c 215.756 51.3967 217.8949 53.5495 215.0832 53.5495 c 212.2715 53.5495 205.5738 51.3967 200.1239 48.7412 c 194.674 46.0857 192.5351 43.9329 195.3468 43.9329 c b 0 g 205.215 48.7412 m F 0 G 0.3 w 10 M 68.3542 48.7412 m S 0 g 1 w 4 M 68.3542 48.7412 m F 0 G 0.3 w 10 M 68.3542 48.7412 m S 68.3542 48.7412 m S 68.3542 48.7412 m S 0 g 1 w 4 M 68.3542 48.7412 m F 0 G 0.3 w 10 M 68.3542 48.7412 m S 68.3542 48.7412 m S 1 g 1 w 4 M 62.3438 48.7412 m 55.7316 45.5194 53.0624 42.9076 56.3818 42.9076 c 59.7012 42.9076 67.7524 45.5194 74.3646 48.7412 c F 74.3646 48.7412 m 80.9768 51.963 83.646 54.5748 80.3266 54.5748 c 77.0072 54.5748 68.956 51.963 62.3438 48.7412 c F 68.3542 48.7412 m F 0 G 0.3 w 10 M 68.3542 48.7412 m S 0 g 1 w 4 M 68.3542 48.7412 m F 0 G 0.3 w 10 M 68.3542 48.7412 m S 68.3542 48.7412 m S 0 g 1 w 4 M 65.0774 47.6733 m 57.7361 44.0962 L 59.9063 44.0962 L 67.2476 47.6733 L 70.8102 47.6621 L 75.24 49.8205 L 71.6316 49.8094 L 78.973 53.3865 L 76.8027 53.3865 L 69.4614 49.8094 L 65.8986 49.8205 L 61.4689 47.6621 L 65.0774 47.6733 L f 0 G 0.3 w 10 M 159.5947 48.7412 m S 0 g 1 w 4 M 159.5947 48.7412 m F 0 G 0.3 w 10 M 159.5947 48.7412 m S 159.5947 48.7412 m S 159.5947 48.7412 m S 0 g 1 w 4 M 159.5947 48.7412 m F 0 G 0.3 w 10 M 159.5947 48.7412 m S 159.5947 48.7412 m S 1 g 1 w 4 M 153.5843 48.7412 m 146.9721 45.5194 144.3029 42.9076 147.6223 42.9076 c 150.9417 42.9076 158.9929 45.5194 165.6051 48.7412 c F 165.6051 48.7412 m 172.2173 51.963 174.8865 54.5748 171.5671 54.5748 c 168.2477 54.5748 160.1965 51.963 153.5843 48.7412 c F 159.5947 48.7412 m F 0 G 0.3 w 10 M 159.5947 48.7412 m S 0 g 1 w 4 M 159.5947 48.7412 m F 0 G 0.3 w 10 M 159.5947 48.7412 m S 159.5947 48.7412 m S 0 g 1 w 4 M 156.3179 47.6733 m 148.9766 44.0962 L 151.1468 44.0962 L 158.4881 47.6733 L 162.0507 47.6621 L 166.4805 49.8205 L 162.8721 49.8094 L 170.2135 53.3865 L 168.0433 53.3865 L 160.7019 49.8094 L 157.1391 49.8205 L 152.7094 47.6621 L 156.3179 47.6733 L f 0 G 0.3 w 353.3356 304.3909 m 33.9934 148.7905 l 193.6643 148.7905 l 513.0065 304.3909 l 353.3356 304.3909 l s 353.4812 193.2274 m 34.139 37.6269 l 193.8099 37.6269 l 513.1521 193.2274 l 353.4812 193.2274 l s u u 0 g 1 w /_Symbol 18 21.5 0 0 z [1 0 0 1 201.5 272.75]e (G)t T U U u u /_Times-Italic 8 9.5 0 0 z [1 0 0 1 207 270.25]e (R)t T U u /_Times-Roman 8 9.5 0 0 z [1 0 0 1 211.8867 270.25]e (+3)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 181.5 258.5]e (\(worst case\))t T U U u u /_Symbol 18 21.5 0 0 z [1 0 0 1 387.5195 110.0625]e (G)t T U U u u /_Times-Italic 8 9.5 0 0 z [1 0 0 1 393.0195 107.8125]e (R)t T U u /_Times-Roman 8 9.5 0 0 z [1 0 0 1 397.9062 107.8125]e (+2)t T U U u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 462.7145 220.9382]e (h)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 468.7145 220.9382]e (=)t T U u /_Symbol 12 14.5 0 0 z [1 0 0 1 475.4821 220.9382]e (-)t T U u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 482.068 220.9382]e (J)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 487.3942 220.9382]e (<0)t T U U 0 G 0.3 w 1 M 478.9367 182.1129 m 482.1892 190.9005 L B 475.1667 190.7955 m 482.1892 190.9005 L 475.1667 190.7955 L 478.9367 182.1129 L 475.1667 190.7955 L b 1 w 4 M 475.1667 190.7955 m 482.1892 190.9005 l 478.9367 182.1129 l 475.1667 190.7955 l f 0 G 478.9367 182.1129 m 478.955 199.9381 l S 478.955 199.9381 m 478.9733 217.7633 l S 0 g 0.3 w 1 M 387.6962 182.1129 m 390.9487 190.9005 L B 383.9262 190.7955 m 390.9487 190.9005 L 383.9262 190.7955 L 387.6962 182.1129 L 383.9262 190.7955 L b 1 w 4 M 383.9262 190.7955 m 390.9487 190.9005 l 387.6962 182.1129 l 383.9262 190.7955 l f 0 G 387.6962 182.1129 m 387.7145 199.9381 l S 387.7145 199.9381 m 387.7328 217.7633 l S 0 g 0.3 w 1 M 296.4555 93.1984 m 299.708 101.986 L B 292.6855 101.881 m 299.708 101.986 L 292.6855 101.881 L 296.4555 93.1984 L 292.6855 101.881 L b 1 w 4 M 292.6855 101.881 m 299.708 101.986 l 296.4555 93.1984 l 292.6855 101.881 l f 0 G 296.4555 93.1984 m 296.4738 111.0236 l S 296.4738 111.0236 m 296.4921 128.8488 l S 0 g 0.3 w 1 M 205.2149 93.1984 m 208.4674 101.986 L B 201.4449 101.881 m 208.4674 101.986 L 201.4449 101.881 L 205.2149 93.1984 L 201.4449 101.881 L b 1 w 4 M 201.4449 101.881 m 208.4674 101.986 l 205.2149 93.1984 l 201.4449 101.881 l f 0 G 205.2149 93.1984 m 205.2332 111.0236 l S 205.2332 111.0236 m 205.2515 128.8488 l S showpage _E end %%EndDocument @endspecial 60 1911 a FQ(Figure)15 b(6:)22 b(Wh)o(y)15 b(a)h(single)g(la)o (y)o(er)e(do)q(es)j(not)f(w)o(ork)g(in)f FF(d)f FE(\025)g FQ(3.)21 b(F)l(or)16 b(the)g(\\w)o(orst")h(con\014guration)g(of)60 1971 y(the)g(next)h(external)e(la)o(y)o(er)h(\(image)f(and)i(in)o(ternal)f(spins)h (all)f(\\)p FE(\000)p FQ("\),)h(some)f(of)h(the)f(in)o(ternal)g(spins)60 2031 y(in)f(la)o(y)o(er)f(\000)265 2013 y FD(int)265 2043 y(R)p FH(+2)355 2031 y FQ(pic)o(k)g(up)i(a)g(negativ)o(e)e(magnetic)g(\014eld.)938 2784 y(108)p eop %%Page: 109 109 bop 60 95 a FQ(alternating)18 b(\()p FE(\006)p FQ(\))g(con\014guration,)h (the)e(image)g(spins)h(in)g(the)f(ann)o(ulus)h(\003)1429 72 y FD(imag)q(e)1429 108 y(R)1456 99 y Ft(0)1540 95 y FE(n)12 b FQ(\003)1611 72 y FD(imag)q(e)1611 108 y(R)1727 95 y FQ(\014xed)18 b(to)60 156 y(b)q(e)j(all)f(+,)h(and)g(the)f(spins)h(outside)g(\003)797 163 y FD(R)824 154 y Ft(0)857 156 y FQ(\(b)q(oth)h(image)d(and)i(in)o (ternal\))f(\014xed)g(in)g(an)h(arbitrary)60 221 y(con\014guration)p 355 195 30 2 v 17 w FF(\033)q FQ(.)h(W)l(e)15 b(denote)h(exp)q(ectations)g (in)f(this)h(system)e(b)o(y)i FE(h)8 b(\001)g(i)1390 198 y FD(R;R)1454 186 y Ft(0)1390 233 y Fy(\006)p FD(;)p FH(+)p FD(;)p 1464 214 22 2 v(\033)1489 221 y FQ(.)21 b(W)l(e)15 b(w)o(an)o(t)h(to)g(sho)o (w)60 282 y(that,)21 b(for)f FF(J)25 b FQ(su\016cien)o(tly)18 b(large,)i(there)g(exists)f FF(c)h(>)g FQ(0)h(suc)o(h)f(that)g(for)g(all)g FF(R)h(>)f FQ(0)g(there)g(exists)60 342 y FF(R)97 324 y Fy(0)123 342 y FF(>)14 b(R)j FQ(\(dep)q(ending)f(on)h FF(R)p FQ(\))f(suc)o(h)g(that) 636 456 y FE(h)p FF(\033)683 463 y FD(i)697 456 y FE(i)716 432 y FD(R;R)780 421 y Ft(0)716 468 y Fy(\006)p FD(;)p FH(+)p FD(;)p 790 449 V(\033)842 456 y FE(\025)27 b(h)p FF(\033)955 463 y FD(i)969 456 y FE(i)988 432 y FD(R;R)1052 421 y Ft(0)988 466 y Fy(\006)p FD(;)p FH(+)p FD(;)p Fy(\000)1120 456 y FE(\025)h FF(c)22 b(>)g FQ(0)451 b(\(4)p FF(:)p FQ(26\))60 565 y(and)17 b(b)o(y)f(symmetr)o(y)603 625 y FE(h)p FF(\033)650 632 y FD(i)664 625 y FE(i)683 601 y FD(R;R)747 590 y Ft(0)683 637 y Fy(\006)p FD(;)p Fy(\000)p FD(;)p 757 618 V(\033)809 625 y FE(\024)27 b(h)p FF(\033)922 632 y FD(i)936 625 y FE(i)955 601 y FD(R;R)1019 590 y Ft(0)955 634 y Fy(\006)p FD(;)p Fy(\000)p FD(;)p FH(+)1087 625 y FE(\024)h(\000)p FF(c)22 b(<)g FQ(0)14 b FF(;)417 b FQ(\(4)p FF(:)p FQ(27\))60 712 y(for)20 b(ev)o(ery)f(con\014guration)p 570 685 30 2 v 21 w FF(\033)i FQ(outside)f(\003)825 719 y FD(R)852 710 y Ft(0)885 712 y FQ(and)h(ev)o(ery)d FF(i)i FE(2)h FQ(\003)1241 693 y FD(int)1241 724 y(R)1289 712 y FQ(.)32 b(This)20 b(will)f(b)q(e)h(pro)o (v)o(en)g(using)60 772 y(correlation)j(inequalities)f(together)i(with)g(the)g (uniqueness)f(of)h(the)g(Gibbs)g(measure)e(for)i(the)60 832 y(in)o(ternal-spin)15 b(system)g(with)h(image)f(spins)i(set)f(to)g(all)g(+)g (or)h(all)f FE(\000)p FQ(.)133 892 y(More)f(precisely)l(,)d(the)j(pro)q(of)g (of)g(\(4.26\))h(will)d(in)o(v)o(olv)o(e)g(a)i(sequence)e(of)i(inequalities)e (comparing)60 952 y(the)j(follo)o(wing)g(systems)f(of)h(in)o(ternal)g(spins:) 133 1053 y FE(\017)24 b FQ(The)14 b(system)f(of)i(in)o(ternal)f(spins)g(in)g (v)o(olume)f(\003)1049 1035 y FD(int)1049 1065 y(R)1076 1056 y Ft(0)1111 1053 y FQ(describ)q(ed)h(ab)q(o)o(v)o(e,)g(whic)o(h)g(w)o(e)g (denote)h(b)o(y)182 1071 y Fx( )227 1114 y FF(R;)43 b(R)358 1095 y Fy(0)227 1174 y FE(\006)p FF(;)e FQ(+)p FF(;)p 414 1147 V 41 w(\033)456 1071 y Fx(!)489 1144 y FQ(.)133 1283 y FE(\017)24 b FQ(The)16 b FP(in\014nite-volume)22 b FQ(system)14 b(of)i(in)o(ternal)f (spins)h(\003)1169 1265 y FD(int)1169 1295 y Fy(1)1231 1283 y FE(\021)d FQ(\()p Fq(Z)1333 1262 y FD(d)1353 1283 y FQ(\))1372 1265 y FD(int)1420 1283 y FQ(,)j(with)f(the)g(image)g(spins)182 1343 y(in)i(\003)274 1320 y FD(imag)q(e)274 1356 y(R)389 1343 y FQ(\014xed)g(in)g(the)g(alternating)g(\()p FE(\006)p FQ(\))g (con\014guration)i(and)f(the)f(image)f(spins)h(outside)182 1435 y(\003)216 1442 y FD(R)261 1435 y FQ(\014xed)f(to)g(b)q(e)h(all)f(+.)21 b(W)l(e)16 b(denote)g(this)g(system)f(b)o(y)1211 1362 y Fx( )1257 1404 y FF(R;)43 b FE(1)1257 1464 y(\006)p FF(;)e FQ(+)1413 1362 y Fx(!)1446 1435 y FQ(.)133 1574 y FE(\017)24 b FQ(The)16 b FP(in\014nite-volume)22 b FQ(system)14 b(of)i(in)o(ternal)f(spins)h(\003) 1169 1556 y FD(int)1169 1586 y Fy(1)1231 1574 y FE(\021)d FQ(\()p Fq(Z)1333 1553 y FD(d)1353 1574 y FQ(\))1372 1556 y FD(int)1420 1574 y FQ(,)j(with)f(the)g(image)g(spins)182 1634 y(ev)o(erywhere)e(\014xed)i (in)g(the)g(alternating)g(\()p FE(\006)p FQ(\))g(con\014guration.)22 b(W)l(e)15 b(denote)h(this)f(system)f(b)o(y)182 1652 y Fx( )227 1695 y FE(1)227 1755 y(\006)290 1652 y Fx(!)345 1725 y FQ(=)405 1652 y Fx( )450 1695 y FF(R;)43 b FE(1)450 1755 y(\006)p FF(;)e FE(\006)606 1652 y Fx(!)639 1725 y FQ(.)60 1854 y(W)l(e)16 b(shall)g(pro)o(v)o(e)f(the)h(follo)o(wing:)-35 1983 y(Step)g(2.1\))25 b FF(\026)211 1960 y FD(R;R)275 1948 y Ft(0)211 1995 y Fy(\006)p FD(;)p FH(+)p FD(;)p 285 1976 22 2 v(\033)325 1983 y FQ(con)o(v)o(erges)16 b(as)h FF(R)641 1965 y Fy(0)667 1983 y FE(!)c(1)j FQ(to)h(a)g(Gibbs)f (measure)f(for)i(the)f(system)1548 1910 y Fx( )1594 1953 y FF(R;)43 b FE(1)1594 2013 y(\006)p FF(;)e FQ(+)1750 1910 y Fx(!)1783 1983 y FQ(.)-35 2153 y(Step)16 b(2.2\))25 b(The)16 b(system)444 2080 y Fx( )489 2122 y FF(R;)43 b FE(1)489 2183 y(\006)p FF(;)e FQ(+)645 2080 y Fx(!)694 2153 y FQ(has)17 b(a)g FP(unique)22 b FQ(Gibbs)16 b(measure,)f(call)g(it)h FF(\026)1494 2129 y FD(R;)p Fy(1)1494 2163 y(\006)p FD(;)p FH(+)1568 2153 y FQ(.)-35 2294 y(Step)g(2.3\))25 b(The)e(measure)f FF(\026)515 2271 y FD(R;)p Fy(1)515 2304 y(\006)p FD(;)p FH(+)612 2294 y FQ(is)h(larger)g(\(in)f(FK)o(G)h(sense\))g(than)g FP(al)r(l)30 b FQ(Gibbs)23 b(measures)f(for)h(the)182 2389 y(system)344 2316 y Fx( )389 2359 y FE(1)389 2419 y(\006)451 2316 y Fx(!)484 2389 y FQ(.)-35 2535 y(Step)16 b(2.4\))25 b(Let)20 b FF(\026)302 2509 y Fy(1)p FH(\(+\))302 2544 y Fy(\006)414 2535 y FQ(b)q(e)g(the)f(+)h (phase)g(\(i.e.)e(the)i(maximal)c(Gibbs)k(measure)e(in)i(FK)o(G)f(sense\))h (for)182 2627 y(the)c(system)428 2554 y Fx( )473 2596 y FE(1)473 2656 y(\006)535 2554 y Fx(!)568 2627 y FQ(.)21 b(Then)c FF(\026)760 2601 y Fy(1)p FH(\(+\))760 2636 y Fy(\006)852 2627 y FQ(\()p FF(\033)899 2634 y FD(i)913 2627 y FQ(\))d FE(\025)f FF(c)h(>)g FQ(0.)938 2784 y(109)p eop %%Page: 110 110 bop 60 91 a FQ(F)l(rom)15 b(these)h(results)g(w)o(e)g(will)f(then)h(deduce)g (\(4.26\).)60 196 y FP(Step)g(2.1.)21 b(The)15 b(limit)g FF(R)514 178 y Fy(0)540 196 y FE(!)f(1)p FP(.)20 b FQ(W)l(e)13 b(wish)g(to)h(consider) f(the)g(limit)e(as)j FF(R)1411 178 y Fy(0)1437 196 y FE(!)f(1)g FQ(of)h(the)f(measures)60 256 y FF(\026)89 233 y FD(R;R)153 221 y Ft(0)89 268 y Fy(\006)p FD(;)p FH(+)p FD(;)p 163 249 22 2 v(\033)203 256 y FQ(\(for)k(\014xed)f FF(R)p FQ(\).)21 b(By)16 b(compactness,)f(this)h(sequence)f(of)h(measures)f(has)i(at)f(least)g (one)h(limit)60 317 y(p)q(oin)o(t)d(in)g(the)h(w)o(eak)f(top)q(ology)h(\(in)f (fact,)g(an)o(y)h(subsequence)e(has)i(a)g(limit)d(p)q(oin)o(t\).)20 b(W)l(e)14 b(claim)f(that)60 382 y(an)o(y)g(limit)d(p)q(oin)o(t)j(of)g(the)f (measures)g FF(\026)753 359 y FD(R;R)817 347 y Ft(0)753 394 y Fy(\006)p FD(;)p FH(+)p FD(;)p 827 375 V(\033)864 382 y FQ(\(with)h (arbitrary)p 1195 356 30 2 v 13 w FF(\033)q FQ(\))g(is)f(necessarily)g(a)h (Gibbs)g(measure)60 480 y(for)18 b(the)f(system)385 407 y Fx( )430 449 y FF(R;)43 b FE(1)430 509 y(\006)p FF(;)e FQ(+)586 407 y Fx(!)619 480 y FQ(.)25 b(The)18 b(pro)q(of)h(is)e(trivial:)23 b(for)18 b(an)o(y)g(v)o(olume)d(\003)h FE(\032)g FQ(\003)1584 487 y FD(R)1611 478 y Ft(0)1622 487 y Fy(\000)p FH(1)1669 480 y FQ(,)i(the)f(DLR)60 608 y(equations)22 b(for)f(the)h(systems)639 535 y Fx( )684 578 y FF(R;)43 b(R)815 560 y Fy(0)684 638 y FE(\006)p FF(;)e FQ(+)p FF(;)p 871 612 V 41 w(\033)913 535 y Fx(!)967 608 y FQ(and)1067 535 y Fx( )1113 578 y FF(R;)h FE(1)1113 638 y(\006)p FF(;)e FQ(+)1269 535 y Fx(!)1323 608 y FQ(are)21 b(iden)o(tical)f(\(i.e.)g(the)h FF(\031)1831 615 y FH(\003)1857 608 y FQ('s)60 712 y(are)d(the)g(same\);)f(so)i(for)f(large)g (enough)h FF(R)852 694 y Fy(0)864 712 y FQ(,)f(the)f(measure)g FF(\026)1202 688 y FD(R;R)1266 676 y Ft(0)1202 724 y Fy(\006)p FD(;)p FH(+)p FD(;)p 1276 704 22 2 v(\033)1318 712 y FQ(satis\014es)i(the)e (DLR)i(equation)60 809 y(in)e(v)o(olume)e(\003)j(also)g(for)f(the)h(system) 761 736 y Fx( )807 778 y FF(R;)43 b FE(1)807 839 y(\006)p FF(;)e FQ(+)963 736 y Fx(!)996 809 y FQ(.)25 b(Since)16 b(the)h(latter)g(system's)f (sp)q(eci\014cation)h(is)60 898 y(F)l(eller,)d(the)i(DLR)h(equations)f(are)h (preserv)o(ed)e(under)h(a)g(w)o(eak)g(limit.)133 958 y(Note)i(that)g(w)o(e)g (ha)o(v)o(e)f(not)i(y)o(et)e(pro)o(v)o(en)h(that)g(the)g(limit)d(as)k FF(R)1291 940 y Fy(0)1320 958 y FE(!)e(1)h FQ(exists;)g(di\013eren)o(t)g (con-)60 1018 y(v)o(ergen)o(t)c(subsequences)g(migh)o(t)f FP(a)j(priori)j FQ(ha)o(v)o(e)14 b(di\013eren)o(t)g(limits.)k(But)d(in)f(the)h(next)f(step)h (w)o(e)f(will)60 1106 y(pro)o(v)o(e)h(that)g(the)h(Gibbs)f(measure)f(for)i (the)f(system)1026 1033 y Fx( )1071 1076 y FF(R;)43 b FE(1)1071 1136 y(\006)p FF(;)e FQ(+)1227 1033 y Fx(!)1276 1106 y FQ(is)15 b FP(unique)t FQ(,)h(so)g(in)f(fact)h(the)f(limit)60 1195 y FP(do)n(es)20 b FQ(exist.)60 1296 y FP(Step)k(2.2.)38 b(Unique)25 b(Gibbs)e(me)n(asur)n(e)f(for)g(the)i(system)1134 1223 y Fx( )1179 1266 y FF(R;)43 b FE(1)1179 1326 y(\006)p FF(;)e FQ(+)1335 1223 y Fx(!)1368 1296 y FP(.)e FQ(Consider)23 b(the)f FP(in\014nite-)60 1396 y(volume)k FQ(system)20 b(of)h(in)o(ternal)f(spins)h(\()p Fq(Z)822 1375 y FD(d)842 1396 y FQ(\))861 1378 y FD(int)909 1396 y FQ(,)h(with)f(the)g(image)e(spins)j(in)f(\003)1519 1372 y FD(imag)q(e)1519 1408 y(R)1638 1396 y FQ(\014xed)g(in)f(the)60 1456 y(alternating)f(\()p FE(\006)p FQ(\))f(con\014guration,)i(and)f(the)f (image)f(spins)i(outside)f(\003)1374 1463 y FD(R)1422 1456 y FQ(\014xed)g(to)h(b)q(e)f(all)g(+.)28 b(W)l(e)60 1516 y(claim)14 b(that)j(this)f(system)e(has)j(a)g FP(unique)k FQ(Gibbs)c(measure.)i(\(W)l(e) d(only)g(need)g(uniqueness)g(at)g(lo)o(w)60 1576 y(enough)d(temp)q(erature,)e (but)h(in)f(fact)h(the)g(Gibbs)g(measure)f(is)g(unique)h(at)g(all)f(temp)q (eratures.\))19 b(This)60 1637 y(uniqueness)c(is)g(in)o(tuitiv)o(ely)d(ob)o (vious:)21 b(the)15 b(e\013ectiv)o(e)e(magnetic)h(\014elds)h(induced)f(b)o(y) h(the)g(+)g(image)60 1697 y(spins)20 b(outside)g(\003)392 1704 y FD(R)440 1697 y FQ(are)g(su\016cien)o(t)e(to)i(push)g(the)g(system)e(in)o (to)h(the)h(+)f(phase.)32 b(Unfortunately)l(,)60 1757 y(the)19 b(pro)q(of)i(w)o(e)f(ha)o(v)o(e)f(to)h(o\013er)g(is)f(a)h(bit)g(to)q(o)h (complicated)c(for)j(our)g(taste.)32 b(It)19 b(go)q(es)i(as)g(follo)o(ws.)60 1817 y(First,)i(w)o(e)g(notice)f(that)h(it)f(is)h(enough)g(to)g(pro)o(v)o(e)f (uniqueness)g(of)h(the)g(Gibbs)g(measure)e(when)60 1877 y FP(al)r(l)26 b FQ(the)19 b(image)f(spins)i(\(including)f(those)h(inside)f(\003)1035 1884 y FD(R)1063 1877 y FQ(\))h(are)f(set)h(in)f(the)g(\\+")h(p)q(osition.)32 b(Indeed,)60 1938 y(c)o(hanging)22 b(the)f(image)f(spins)i(inside)e(\003)810 1945 y FD(R)860 1938 y FQ(amoun)o(ts)h(to)h(a)g(\014nite-v)o(olume)d(p)q (erturbation)j(of)f(the)60 1998 y(system)d(and)i(hence)e(it)h(do)q(es)h(not)f (alter)g(the)g(n)o(um)o(b)q(er)e(of)j(Gibbs)f(measures)g([157,)h(section)f (7.4].)60 2058 y([In)e(fact,)g(ev)o(ery)f(Gibbs)i(measure)e FF(\026)740 2040 y Fy(0)769 2058 y FQ(for)i(the)f(p)q(erturb)q(ed)h(in)o (teraction)e(comes)g(from)h(a)g(uniquely)60 2118 y(de\014ned)c(Gibbs)g (measure)e FF(\026)i FQ(of)h(the)e(unp)q(erturb)q(ed)i(in)o(teraction:)k(if) 13 b FF(W)19 b FQ(is)13 b(the)f(p)q(erturbation,)i(then)60 2178 y FF(\026)89 2160 y Fy(0)101 2178 y FQ(\()8 b FE(\001)g FQ(\))28 b(=)g FF(\026)p FQ(\()8 b FE(\001)g FF(e)364 2160 y Fy(\000)p FD(W)432 2178 y FQ(\))p FF(=\026)p FQ(\()p FF(e)546 2160 y Fy(\000)p FD(W)614 2178 y FQ(\).])133 2238 y(T)l(o)17 b(pro)o(v)o(e)f(the)h(uniqueness)f(of)h(the)g(Gibbs)g(measure)e(for)i(the)f (system)g(with)g(all)g(image)g(spins)60 2299 y(\\+",)27 b(w)o(e)c(pro)o(vide) h(t)o(w)o(o)g(argumen)o(ts.)45 b(First)24 b(argumen)o(t,)g(pro)o(ving)h (uniqueness)e(only)i(at)f(lo)o(w)60 2359 y(temp)q(erature:)h(Pirogo)o (v-Sinai)19 b(theory)g([328)q(,)f(260)q(,)h(322)q(])g(implies)d(that)j(the)g (phase)g(diagram)g(at)60 2419 y(lo)o(w)i(enough)g(temp)q(erature)f(is)g(a)i (small)d(deformation)h(of)h(that)g(at)h(zero)e(temp)q(erature,)g(but)h(in)60 2479 y(this)g(case)f(there)g(is)h(only)f(one)h(ground)h(state)e(\(namely)l(,) g(all)g(spins)h(\\+"\).)35 b(Second)21 b(argumen)o(t,)60 2539 y(pro)o(ving)15 b(uniqueness)g(at)g(all)g(temp)q(eratures:)k(The)d(in)o (ternal-spin)e(system)g(is)h(an)h(Ising)f(mo)q(del)f(on)60 2600 y(a)j(p)q(erio)q(dic)f(lattice,)g(with)g(nearest-neigh)o(b)q(or)h (coupling)g FF(J)i(>)c FQ(0)i(and)g(a)g(p)q(erio)q(dic)f(magnetic)g(\014eld) 60 2660 y FF(h)88 2667 y FD(x)128 2660 y FQ(=)h FF(h\016)235 2642 y FH(n.i.)233 2672 y FD(x)305 2660 y FQ(\(here)h FF(\016)456 2642 y FH(n.i.)454 2672 y FD(x)524 2660 y FQ(=)g(1)h(if)f FF(x)g FQ(neigh)o(b)q(ors)h(an)g(image)e(spin,)i(and)g(0)g(otherwise\),)f(sp)q (ecialized)938 2784 y(110)p eop %%Page: 111 111 bop 60 91 a FQ(to)17 b FF(h)e FQ(=)g(+)p FF(J)5 b FQ(.)22 b(By)17 b(the)f(Lee-Y)l(ang)h(theorem)f(\([160,)h(Section)f(4.5])h(or)g([250)q(])f (and)i(references)d(cited)60 152 y(therein\))j(and)i(a)f(result)g(of)g(Leb)q (o)o(witz)h(and)f(P)o(enrose)g([242)q(])g(\(see)g(also)g([169)q(,)g(Theorem)f (4.4]\),)h(it)60 212 y(can)h(b)q(e)f(sho)o(wn)h(that)g(the)f(pressure)g(of)h (suc)o(h)f(an)h(Ising)f(mo)q(del)f(is)i(a)f(join)o(tly)f(analytic)h(function) 60 272 y(of)g FF(J)24 b FQ(and)19 b FF(h)g FQ(on)g(the)g(domain)f FF(J)o(;)8 b(h)18 b(>)g FQ(0.)30 b(It)18 b(follo)o(ws)h(that)g(all)g(p)q (erio)q(dic)f(Gibbs)h(measures)f(giv)o(e)60 332 y(the)f(same)g(mean)f(v)m (alue)i(to)g(the)f(observ)m(ables)h(conjugate)h(to)f FF(J)k FQ(and)c FF(h)p FQ(:)24 b(these)17 b(observ)m(ables)h(are,)60 392 y(resp)q(ectiv)o(ely)l(,)337 359 y Fx(P)390 392 y FF(\033)418 399 y FD(i)431 392 y FF(\033)459 399 y FD(j)495 392 y FQ(where)g(the)g(sum)f (runs)h(o)o(v)o(er)f(all)g(nearest-neigh)o(b)q(or)i(pairs)f FE(h)p FF(ij)s FE(i)g FQ(in)g(a)g(unit)60 452 y(cell)f(of)i(the)g(p)q(erio)q (dic)f(lattice,)g(and)746 419 y Fx(P)798 452 y FF(\033)826 459 y FD(k)866 452 y FQ(where)g(the)h(sum)e(runs)i(o)o(v)o(er)f(all)g(sites)h FF(k)h FQ(in)f(this)f(unit)60 513 y(cell)c(that)h(are)h(nearest)f(neigh)o(b)q (or)h(to)f(an)h(image)e(spin.)21 b(By)14 b(Gri\016ths')h(comparison)g (inequalit)o(y)l(,)d(it)60 573 y(follo)o(ws)k(that)730 676 y FF(\026)759 683 y Fy(\000)789 676 y FQ(\()p FF(\033)836 683 y FD(i)850 676 y FF(\033)878 683 y FD(j)896 676 y FQ(\))41 b(=)g FF(\026)1064 683 y FH(+)1094 676 y FQ(\()p FF(\033)1141 683 y FD(i)1155 676 y FF(\033)1183 683 y FD(j)1201 676 y FQ(\))521 b(\(4.28a\))769 748 y FF(\026)798 755 y Fy(\000)828 748 y FQ(\()p FF(\033)875 755 y FD(k)896 748 y FQ(\))41 b(=)g FF(\026)1064 755 y FH(+)1094 748 y FQ(\()p FF(\033)1141 755 y FD(k)1162 748 y FQ(\))557 b(\(4.28b\))60 851 y(for)15 b(ev)o(ery)f(pair)h FE(h)p FF(ij)s FE(i)g FQ(of)h(nearest)f(neigh)o(b)q(ors)h(and)f(for)h(ev)o (ery)d(site)i FF(k)i FQ(neigh)o(b)q(oring)e(an)h(image)d(spin;)60 911 y(here)h FF(\026)193 918 y FH(+)238 911 y FQ(and)h FF(\026)360 918 y Fy(\000)405 911 y FQ(are)f(the)h(measures)f(corresp)q(onding)h(to)g (\\+")h(and)f(\\)p FE(\000)p FQ(")g(b)q(oundary)h(conditions,)60 971 y(resp)q(ectiv)o(ely)l(.)j(W)l(e)d(then)g(resort)g(to)h(the)f(inequalit)o (y)e([236)q(])323 1080 y FF(\026)352 1087 y FH(+)382 1080 y FQ(\()p FF(\033)431 1060 y FD(A)459 1080 y FQ(\))d FE(\000)g FF(\026)568 1087 y Fy(\000)598 1080 y FQ(\()p FF(\033)647 1060 y FD(A)675 1080 y FQ(\))27 b FE(\025)788 1030 y Fx(\014)788 1055 y(\014)788 1080 y(\014)o FF(\026)830 1087 y FH(+)860 1080 y FQ(\()p FF(\033)909 1060 y FD(B)939 1080 y FQ(\))p FF(\026)987 1087 y Fy(\000)1017 1080 y FQ(\()p FF(\033)1066 1060 y FD(A)1094 1080 y FF(\033)1124 1060 y FD(B)1154 1080 y FQ(\))11 b FE(\000)g FF(\026)1263 1087 y Fy(\000)1292 1080 y FQ(\()p FF(\033)1341 1060 y FD(B)1371 1080 y FQ(\))p FF(\026)1419 1087 y FH(+)1449 1080 y FQ(\()p FF(\033)1498 1060 y FD(A)1526 1080 y FF(\033)1556 1060 y FD(B)1586 1080 y FQ(\))1605 1030 y Fx(\014)1605 1055 y(\014)1605 1080 y(\014)146 b FQ(\(4)p FF(:)p FQ(29\))60 1196 y(v)m(alid)20 b(for)g(an)o(y)g(sets)g FF(A;)8 b(B)22 b FE(\032)f Fq(Z)663 1175 y FD(d)703 1196 y FQ(\(w)o(e)f(denote)g FF(\033)989 1178 y FD(A)1037 1196 y FQ(=)1096 1163 y Fx(Q)1135 1206 y FD(i)p Fy(2)p FD(A)1207 1196 y FF(\033)1235 1203 y FD(i)1249 1196 y FQ(\).)33 b(F)l(rom)18 b(\(4.28\))j(and)g(\(4.29\))f(w)o(e)60 1256 y(conclude)c(that)774 1316 y FF(\026)803 1323 y Fy(\000)832 1316 y FQ(\()p FF(\033)881 1296 y FD(A)909 1316 y FQ(\))28 b(=)g FF(\026)1051 1323 y FH(+)1081 1316 y FQ(\()p FF(\033)1130 1296 y FD(A)1157 1316 y FQ(\))589 b(\(4)p FF(:)p FQ(30\))60 1400 y(whenev)o(er)21 b FF(\033)310 1382 y FD(A)360 1400 y FQ(is)h(a)h(pro)q(duct)g(of)f(functions)h(of)f(the)g(form)f FF(\033)1229 1407 y FD(i)1243 1400 y FF(\033)1271 1407 y FD(j)1311 1400 y FQ(with)i FF(i;)8 b(j)24 b FQ(nearest)f(neigh)o(b)q(ors)60 1460 y(and)18 b FF(\033)184 1467 y FD(k)222 1460 y FQ(with)g FF(k)h FQ(b)q(eing)f(a)f(neigh)o(b)q(or)h(to)g(a)f(image-spin)g(site.)24 b(\(In)17 b(other)g(w)o(ords,)h FF(A)f FQ(m)o(ust)f(b)q(e)h(the)60 1521 y(symmetri)o(c)d(di\013erence)h(of)i(a)h(family)c(of)j(suc)o(h)g(sets)f FE(f)p FF(i;)8 b(j)s FE(g)17 b FQ(and/or)h FE(f)p FF(k)r FE(g)p FQ(.\))k(But)16 b(it)h(is)f(not)h(hard)h(to)60 1581 y(see)e(that)h FP(al)r(l)g FQ(sets)f FF(A)e FE(\032)f FQ(\()p Fq(Z)561 1560 y FD(d)581 1581 y FQ(\))600 1563 y FD(int)665 1581 y FQ(are)j(of)g(this)h (form,)d(hence)856 1683 y FF(\026)885 1690 y Fy(\000)942 1683 y FQ(=)28 b FF(\026)1037 1690 y FH(+)1081 1683 y FF(:)670 b FQ(\(4)p FF(:)p FQ(31\))60 1786 y(No)o(w)19 b(b)o(y)g(the)h(FK)o(G)f (inequalit)o(y)e FF(\026)717 1793 y Fy(\000)767 1786 y FE(\024)i FF(\032)h FE(\024)f FF(\026)957 1793 y FH(+)1006 1786 y FQ(in)g(FK)o(G)g (sense)1301 1768 y FH(51)1358 1786 y FQ(for)h FP(every)25 b FQ(Gibbs)19 b(measure)60 1846 y FF(\032)p FQ(,)25 b(hence)e(there)g(is)g(a)h (unique)f(Gibbs)g(measure)g(at)h(all)f(temp)q(eratures.)41 b(\(This)24 b(argumen)o(t)e(is)60 1907 y(essen)o(tially)12 b(due)h(to)h(Leb)q(o)o(witz)g([236)q(,)f(237)q(],)g(with)h(minor)e (alterations)h(to)h(accommo)q(date)e(p)q(erio)q(dic)60 1967 y(systems.\))60 2104 y FP(Step)17 b(2.3.)22 b(Comp)n(arison)15 b(to)i(the)678 2031 y Fx( )723 2073 y FE(1)723 2133 y(\006)785 2031 y Fx(!)835 2104 y FP(system.)k FQ(W)l(e)15 b(claim)e(that)j(the)f (measure)f FF(\026)1631 2080 y FD(R;)p Fy(1)1631 2113 y(\006)p FD(;)p FH(+)1720 2104 y FQ(is)h(larger)60 2232 y(\(in)h(FK)o(G)g(sense\))g (than)h FP(al)r(l)23 b FQ(Gibbs)17 b(measures)e(for)i(the)f(system)1263 2159 y Fx( )1308 2202 y FE(1)1308 2262 y(\006)1371 2159 y Fx(!)1403 2232 y FQ(.)22 b(This)17 b(is)f(an)h(imme)o(diate)60 2321 y(consequence)f(of) h(the)f(FK)o(G)g(inequalit)o(y)f(com)o(bined)f(with)j(the)f(uniqueness)g(pro) o(v)o(ed)g(in)h(Step)f(2.2.)60 2410 y(Indeed,)k(b)o(y)g(the)g(FK)o(G)g (inequalit)o(y)l(,)f(the)h(\014nite-v)o(olume)e(Gibbs)i(measure)f(for)i(the) 1656 2336 y Fx( )1701 2379 y FF(R;)43 b FE(1)1701 2439 y(\006)p FF(;)e FQ(+)1857 2336 y Fx(!)p 60 2491 732 2 v 100 2545 a FA(51)135 2560 y Fz(W)m(e)19 b(write)g Fv(\033)j Fu(\024)e Fv(\033)446 2545 y Fo(0)477 2560 y Fz(in)f(case)h Fv(\033)648 2566 y Fp(i)682 2560 y Fu(\024)h Fv(\033)760 2545 y Fo(0)759 2571 y Fp(i)792 2560 y Fz(for)d(all)g(sites)i Fv(i)p Fz(.)35 b(An)19 b(observ)n(able)g Fv(f)24 b Fz(is)19 b(said)g(to)g(b)q(e)h Fw(incr)n(e)n(asing)j Fz(if)60 2610 y Fv(f)t Fz(\()p Fv(\033)q Fz(\))13 b Fu(\024)f Fv(f)t Fz(\()p Fv(\033)263 2595 y Fo(0)275 2610 y Fz(\))h(whenev)o(er)g Fv(\033)g Fu(\024)f Fv(\033)590 2595 y Fo(0)602 2610 y Fz(.)17 b(W)m(e)12 b(sa)o(y)g(that)g Fv(\026)g Fu(\024)g Fv(\027)i Fz(in)e(FK)o(G)f(sense)j(in)e(case)h Fv(\026)p Fz(\()p Fv(f)t Fz(\))g Fu(\024)f Fv(\027)s Fz(\()p Fv(f)t Fz(\))g(for)g(all)f(increasing)60 2660 y(lo)q(cal)i(observ)n(ables)i Fv(f)t Fz(.)938 2784 y FQ(111)p eop %%Page: 112 112 bop 60 91 a FQ(system)18 b(with)h(an)o(y)g(\(in)o(ternal-spin\))f(b)q (oundary)j(condition)e(is)g(larger)g(in)g(FK)o(G)g(sense)g(than)h(the)60 183 y(\014nite-v)o(olume)10 b(Gibbs)j(measure)f(for)h(the)825 110 y Fx( )870 152 y FE(1)870 212 y(\006)933 110 y Fx(!)978 183 y FQ(system)f(with)g(the)h(same)e(b)q(oundary)j(conditions.)60 271 y(This)i(inequalit)o(y)f(passes)i(directly)d(to)j(the)f(in\014nite-v)o (olume)d(limit.)60 385 y FP(Step)i(2.4.)21 b(Sp)n(ontane)n(ous)15 b(magnetization)h(for)d(the)i FQ(+)f FP(phase)h(of)f(the)1321 312 y Fx( )1366 354 y FE(1)1366 414 y(\006)1428 312 y Fx(!)1475 385 y FP(system.)21 b FQ(The)1750 312 y Fx( )1795 354 y FE(1)1795 414 y(\006)1857 312 y Fx(!)60 473 y FQ(system)d(is)g(precisely)g(the)g(Ising) h(mo)q(del)f(on)i(a)f(p)q(erio)q(dically)f(diluted)g(lattice.)29 b(As)18 b(discussed)h(in)60 533 y(Step)d(1,)g(this)g(mo)q(del)f(has)i(sp)q (on)o(taneous)h(magnetization)d(for)i FF(J)k FQ(su\016cien)o(tly)14 b(large.)133 668 y FP(Step)20 b(3.)25 b(Un\014xing)c(of)d(the)h(spin)g(at)g (the)g(origin.)25 b FQ(Finally)l(,)16 b(w)o(e)h(can)h(\\un\014x")g(the)f (spin)g(at)h(the)60 729 y(origin)e(in)g(the)g(same)f(w)o(a)o(y)h(as)h(in)f (the)g(2-dimensional)f(example.)133 814 y FP(Conclusion)k(of)d(the)i(ar)n (gument.)k FQ(W)l(e)15 b(conclude)g(that)i(in)e(ev)o(ery)f(neigh)o(b)q(orho)q (o)q(d)k(of)e FF(!)1723 796 y Fy(0)1721 826 y FD(alt)1782 814 y FQ(there)60 874 y(are)g(op)q(en)h(sets)g FE(N)396 881 y FH(+)425 874 y FF(;)8 b FE(N)488 881 y Fy(\000)533 874 y FQ(suc)o(h)16 b(that)357 984 y FF(E)393 991 y FD(\026T)450 984 y FQ(\()p FF(\033)499 963 y Fy(0)497 996 y FH(0)525 984 y FE(j)8 b(f)p FF(\033)602 963 y Fy(0)600 996 y FD(i)614 984 y FE(g)639 991 y FD(i)p Fy(6)p FH(=0)698 984 y FQ(\))g(\()p FF(!)774 991 y FH(1)794 984 y FQ(\))25 b FE(\000)g FF(E)938 991 y FD(\026T)995 984 y FQ(\()p FF(\033)1044 963 y Fy(0)1042 996 y FH(0)1070 984 y FE(j)8 b(f)p FF(\033)1147 963 y Fy(0)1145 996 y FD(i)1158 984 y FE(g)1183 991 y FD(i)p Fy(6)p FH(=0)1242 984 y FQ(\))h(\()p FF(!)1319 991 y FH(2)1339 984 y FQ(\))27 b FE(\025)h FF(\016)h(>)f FQ(0)172 b(\(4)p FF(:)p FQ(32\))60 1094 y(for)24 b FF(!)172 1101 y FH(1)220 1094 y FE(2)k(N)322 1101 y FH(+)375 1094 y FQ(and)d FF(!)508 1101 y FH(2)556 1094 y FE(2)i(N)657 1101 y Fy(\000)687 1094 y FQ(.)45 b(As)24 b(in)g(the)g(2-dimensional)f(case,)j (this)e(implies)d(the)j(non-)60 1154 y(quasilo)q(calit)o(y)15 b(of)i(the)f(renormalized)e(measure)h FF(\026T)7 b FQ(,)15 b(for)i(an)o(y)f(original)g(Gibbs)g(measure)f FF(\026)p FQ(.)22 b(This)60 1214 y(w)o(orks)f(for)h(an)o(y)f(temp)q(erature)f(b)q(elo)o(w)h (the)g(critical)e(temp)q(erature)h(of)h(the)g(undiluted)f(\()p FF(d)15 b FE(\000)f FQ(1\)-)60 1274 y(dimensional)h(Ising)h(mo)q(del.)k(W)l (e)c(ha)o(v)o(e)f(therefore)h(pro)o(v)o(en:)60 1389 y FM(Theorem)h(4.2)24 b FP(L)n(et)18 b FF(d)g FE(\025)e FQ(2)p FP(.)28 b(Then)20 b(for)f(al)r(l)h FF(J)i(>)16 b(J)1054 1396 y FD(c;d)p Fy(\000)p FH(1)1145 1389 y FP(,)j(the)h(fol)r(lowing)h(holds:)26 b(L)n(et)19 b FF(\026)h FP(b)n(e)f(any)60 1449 y(Gibbs)e(me)n(asur)n(e)f(for)f(the)i FF(d)p FP(-dimensional)i(Ising)e(mo)n(del)f(with)h(ne)n(ar)n(est-neighb)n(or) g(c)n(oupling)h FF(J)j FP(and)60 1509 y(zer)n(o)c(magnetic)i(\014eld.)24 b(L)n(et)17 b FF(T)24 b FP(b)n(e)17 b(the)i(de)n(cimation)e(tr)n (ansformation)g(with)h(sp)n(acing)g FF(b)c FQ(=)f(2)p FP(.)23 b(Then)60 1569 y(the)c(me)n(asur)n(e)f FF(\026T)25 b FP(is)19 b(not)g(c)n(onsistent)h(with)f(any)g(quasilo)n(c)n(al)g(sp)n(e)n(ci\014c)n (ation.)26 b(In)19 b(p)n(articular,)f(it)h(is)60 1629 y(not)f(the)g(Gibbs)g (me)n(asur)n(e)e(for)h(any)h(uniformly)f(c)n(onver)n(gent)i(inter)n(action.) 60 1759 y FM(4.3.2)55 b(Decimation)16 b(with)j(Spacing)g FF(b)13 b FE(\025)h FQ(3)60 1852 y(The)i(conclusions)g(of)g(Theorem)f(4.2)h(for)g (decimation)e(with)i(spacing)h FF(b)c FQ(=)h(2)i(hold)g(also)h(for)f(larger) 60 1912 y(spacings.)36 b(The)21 b(main)e(di\013erence)h(from)g(the)h FF(b)g FQ(=)h(2)f(case)g(is)g(that)g(for)g FF(b)h FE(\025)f FQ(3)h(the)e(system)g(of)60 1972 y(in)o(ternal)d(spins)h(obtained)g(with)g FF(!)713 1954 y Fy(0)741 1972 y FQ(=)e FF(!)827 1954 y Fy(0)825 1984 y FD(alt)888 1972 y FQ(is)i(no)g(longer)g(simply)d(a)k(p)q(erio)q (dically)d(diluted)h(Ising)60 2032 y(mo)q(del)g(in)g(zero)h(magnetic)f (\014eld;)g(rather,)h(it)g(con)o(tains)g(a)g(p)q(erio)q(dic)g(alternating)g (magnetic)f(\014eld)60 2092 y(whic)o(h)f(is)g(nonzero)g(at)h(the)f(sites)f (neigh)o(b)q(oring)i(an)g(image)d(spin.)22 b(As)16 b(a)g(consequence,)f(w)o (e)h(need)g(a)60 2153 y(more)e(sophisticated)h(tec)o(hnique)f(to)h(conclude)g (that)h(there)f(is)g(indeed)f(a)i(phase)g(transition)f(\(Step)60 2213 y(1\).)38 b(The)21 b(appropriate)i(to)q(ol)f(for)g(this)f(purp)q(ose)i (is)e(Pirogo)o(v-Sinai)h(theory)g([328,)f(329)r(],)h(whic)o(h)60 2273 y(is)d(summarized)e(in)i(App)q(endix)f(B.)30 b(The)20 b(upshot)g(of)g(P-S)f(theory)h(is)f(that)h(the)f(phase)h(diagram)60 2333 y(of)e(a)h(lattice)e(system)g(at)h FP(low)24 b FQ(temp)q(erature)17 b(can)h(in)g(some)f(cases)i(b)q(e)f(deduced)g(from)f(the)h(phase)60 2393 y(diagram)f(at)i FP(zer)n(o)h FQ(temp)q(erature.)k(More)18 b(precisely)l(,)e(if)h(there)h(are)f(a)i(\014nite)e(n)o(um)o(b)q(er)f(of)i(p) q(erio)q(dic)60 2453 y(ground)f(states,)g(and)g(these)f(ground)h(states)g (satisfy)g(a)g(suitable)f(\\P)o(eierls)f(condition",)h(then)g(the)60 2514 y(phase)h(diagram)e(of)i(p)q(erio)q(dic)f(Gibbs)g(measures)f(at)i(lo)o (w)f(temp)q(erature)e(is)i(a)h(small)d(p)q(erturbation)60 2574 y(of)21 b(the)f(phase)h(diagram)f(of)h(ground)h(states.)35 b(In)20 b(the)g(case)h(at)g(hand,)h(one)f(can)f(sho)o(w)i(that)f(for)60 2634 y(the)h(fully)e(alternating)i(blo)q(c)o(k-spin)g(con\014guration,)i(the) d(system)g(of)h(in)o(ternal)f(spins)h(has)g(only)938 2784 y(112)p eop %%Page: 113 113 bop 60 91 a FQ(t)o(w)o(o)18 b(p)q(erio)q(dic)g(ground)h(states)f(|)g(namely)l (,)e(the)i(one)g(with)g(all)g(in)o(ternal)f(spins)h(+,)g(and)h(the)f(one)60 152 y(with)e(all)f(in)o(ternal)g(spins)h FE(\000)g FQ(|)f(and)i(that)f(these) g(ground)g(states)h(satisfy)f(the)f(P)o(eierls)g(condition.)60 212 y(It)20 b(follo)o(ws)h(from)e(P-S)i(theory)g(that)g(at)g(lo)o(w)f(temp)q (erature)f(there)h(are)h(precisely)e(t)o(w)o(o)h(p)q(erio)q(dic)60 272 y(Gibbs)15 b(measures,)e FF(\026)450 279 y FH(+)494 272 y FQ(and)i FF(\026)616 279 y Fy(\000)646 272 y FQ(,)f(c)o(haracterized)f (resp)q(ectiv)o(ely)f(b)o(y)i(a)h(strictly)e(p)q(ositiv)o(e)h(or)g(strictly) 60 332 y(negativ)o(e)22 b(magnetization.)40 b(The)23 b(details)f(of)h(this)g (part)g(of)g(the)g(argumen)o(t)e(are)i(presen)o(ted)f(in)60 392 y(the)c(App)q(endix)g(B)f(\(Section)h(B.5.3\).)27 b(Steps)18 b(2)h(and)g(3)f(are)h(then)f(pro)o(v)o(en)f(in)h(a)h(manner)e(exactly)60 452 y(iden)o(tical)c(to)i(the)g FF(b)e FQ(=)h(2)h(case.)21 b(The)15 b(analysis)g(of)g(Section)f(B.5.3)g(yields)g(a)h(\(v)o(ery)e(w)o (eak\))i(estimate)60 513 y(of)i(the)f(range)g(of)h(temp)q(eratures)e(for)h (whic)o(h)g(the)g(pathologies)h(are)f(presen)o(t)g([form)o(ula)e(\(B.79\)].) 133 573 y(W)l(e)i(ha)o(v)o(e)g(th)o(us)g(pro)o(v)o(en)f(the)h(follo)o(wing:) 60 687 y FM(Theorem)h(4.3)24 b FP(L)n(et)f FF(d)i FE(\025)g FQ(2)f FP(and)g FF(b)h FE(\025)g FQ(2)p FP(.)41 b(Then)24 b(for)f(al)r(l)i FF(J)j FP(su\016ciently)d(lar)n(ge)f(\(dep)n(ending)60 747 y(on)d FF(d)g FP(and)g FF(b)p FP(\),)g(the)h(fol)r(lowing)h(holds:)29 b(L)n(et)20 b FF(\026)i FP(b)n(e)f(any)f(Gibbs)i(me)n(asur)n(e)e(for)g(the)h FF(d)p FP(-dimensional)60 807 y(Ising)i(mo)n(del)f(with)h(ne)n(ar)n (est-neighb)n(or)g(c)n(oupling)g FF(J)k FP(and)c(zer)n(o)e(magnetic)j (\014eld.)38 b(L)n(et)22 b FF(T)29 b FP(b)n(e)22 b(the)60 868 y(de)n(cimation)16 b(tr)n(ansformation)f(with)h(sp)n(acing)h FF(b)p FP(.)k(Then)c(the)f(me)n(asur)n(e)f FF(\026T)23 b FP(is)15 b(not)i(c)n(onsistent)g(with)60 928 y(any)d(quasilo)n(c)n(al)g(sp)n(e)n (ci\014c)n(ation.)22 b(In)14 b(p)n(articular,)g(it)g(is)g(not)g(the)h(Gibbs)f (me)n(asur)n(e)f(for)g(any)h(uniformly)60 988 y(c)n(onver)n(gent)19 b(inter)n(action.)133 1152 y FM(Remark.)29 b FQ(Chec)o(k)o(erb)q(oard)19 b(decimation,)f(as)i(sho)o(wn)g(in)f(Figure)g(2\(b\),)h(is)g(a)g(v)o(ery)e (di\013eren)o(t)60 1212 y(situation:)28 b(the)20 b(in)o(ternal)f(spins)h(are) f(not)i(connected,)e(and)h(hence)f(they)h(cannot)g(co)q(op)q(erate)h(to)60 1272 y(ha)o(v)o(e)d(a)h(phase)f(transition.)29 b(In)18 b(fact,)g(in)g(this)h (case)f(the)g(\014rst)h(iteration)f(of)h(the)f(transformation)60 1333 y(is)d(w)o(ell-de\014ned)e([364)q(])h([346)q(,)h(p.)f(193].)22 b(Ho)o(w)o(ev)o(er,)13 b(the)i FP(se)n(c)n(ond)20 b FQ(iteration)14 b(of)h(this)g(transformation)60 1393 y(corresp)q(onds)23 b(to)e(a)h(single)f (iteration)g(of)g(the)g FF(b)i FQ(=)f(2)g(decimation)d(transformation,)j(and) g(so)g(is)60 1453 y(ill-de\014ned)15 b(at)i(lo)o(w)f(enough)h(temp)q (erature.)60 1583 y FM(4.3.3)55 b(Kadano\013)19 b(T)-5 b(ransformation)18 b(with)h FF(p)g FM(Finite)60 1675 y FQ(In)13 b(some)g(sense)g(the)h(results)f (th)o(us)h(far)g(should)g(not)g(b)q(e)g(surprising:)20 b(the)13 b(decimation)f(transforma-)60 1735 y(tion,)17 b(unlik)o(e)e(other)j(R)o(G)f (transformations,)g(do)q(es)h(not)f(in)g(an)o(y)g(sense)g(in)o(tegrate)g(out) g(the)g(\\high-)60 1796 y(momen)o(tum)8 b(mo)q(des")j(and)h(lea)o(v)o(e)e (the)i(\\lo)o(w-momen)o(tum)c(mo)q(des";)k(it)f(merely)e(in)o(tegrates)j(out) g(one)60 1856 y(sublattice)18 b(and)i(lea)o(v)o(es)e(another.)30 b(In)19 b(particular,)g(if)g(the)g(sublattice)f(of)h(in)o(ternal)f(\(in)o (tegrated-)60 1916 y(out\))c(spins)g(is)f FP(c)n(onne)n(cte)n(d)5 b FQ(,)15 b(it)e(is)h(hardly)f(surprising)h(that)g(the)g(in)o(ternal-spin)e (system)h(can)g(exhibit)60 1976 y(a)k(phase)f(transition,)g(and)h(that)g (this)f(can)g(giv)o(e)g(rise)f(to)i(R)o(G)f(pathologies.)133 2036 y(In)22 b(this)g(section)f(w)o(e)h(sho)o(w)h(something)e(considerably)g (more)g(surprising:)33 b(that)22 b(the)g(same)60 2096 y(pathology)i(|)f (non-Gibbsianness)i(after)e(one)h(renormalization)d(step)j(|)f(is)g(presen)o (t)g(at)g(lo)o(w)60 2157 y(temp)q(erature)16 b(for)j(the)e(Kadano\013)j (transformation)e(with)g(an)o(y)g(\014nite)f(\(but)h(nonzero\))h FF(p)p FQ(.)1731 2139 y FH(52)1795 2157 y FQ(This)60 2217 y(result)k(is)g(in) h(clear)e(con\015ict)h(with)h(the)f(R)o(G)g(ideology)l(,)i(whic)o(h)e(states) h(that)g(in)o(tegration)f(o)o(v)o(er)60 2277 y(high-momen)o(tum)c(mo)q(des)k (cannot)g(pro)q(duce)h(singularities.)40 b(\(Indeed,)24 b(our)f(pro)q(of)h (mak)o(es)e(no)60 2337 y(distinction)15 b(b)q(et)o(w)o(een)g(blo)q(c)o(k)g (sizes)g FF(b)e FE(\025)h FQ(2)i(and)g FF(b)e FQ(=)g(1)i(|)f(and)h(for)g FF(b)e FQ(=)g(1)i(one)g(is)f(not)h(in)o(tegrating)60 2397 y(o)o(v)o(er)10 b FP(any)16 b FQ(\\mo)q(des",)c(high-momen)o(tum)c(or)j(otherwise!\))20 b(In)11 b(the)g(next)f(subsection)i(w)o(e)f(shall)g(pro)o(v)o(e)60 2458 y(a)17 b(similar)d(result)i(for)g(some)f(ma)s(jorit)o(y-rule)f (transformations)i(\(i.e.)f(Kadano\013)j(with)e FF(p)e FQ(=)g FE(1)p FQ(\).)p 60 2504 732 2 v 100 2558 a FA(52)135 2573 y Fz(In)h(earlier)g(v)o(ersions)h(of)e(this)i(w)o(ork)e([352)o(,)h(353)o(],)g (w)o(e)g(claimed)e(this)j(result)f(only)g(for)g Fw(smal)r(l)j Fv(p)p Fz(.)k(Subsequen)o(tly)60 2623 y(w)o(e)14 b(found)g(a)f(pro)q(of)h(v)n (alid)e(for)i Fw(al)r(l)j Fz(0)11 b Fv(<)h(p)g(<)g Fu(1)p Fz(,)g(whic)o(h)i (w)o(e)g(presen)o(t)i(here.)938 2784 y FQ(113)p eop %%Page: 114 114 bop 133 91 a FQ(Consider)21 b(the)g(Kadano\013)i(transformation)d(\(3.10\))i (with)f(blo)q(c)o(k)f(size)g FF(b)h FQ(and)g(parameter)f FF(p)p FQ(.)60 152 y(F)l(rom)14 b(\(3.10\))i(one)f(readily)g(concludes)f([55)q(])h (that)g(for)h(eac)o(h)f(c)o(hoice)f(of)h(blo)q(c)o(k)g(spins)g FF(\033)1650 133 y Fy(0)1677 152 y FQ(the)g(condi-)60 212 y(tional)h (probabilities)g(of)g(the)g(in)o(ternal)f(spins)i FF(\033)h FQ(corresp)q(ond)f(to)f(a)h(Hamiltonian)210 327 y FF(H)250 334 y FH(e\013)291 327 y FQ(\()p FF(\033)r FQ(\))27 b(=)h FE(\000)p FF(J)530 285 y Fx(X)532 379 y Fy(h)p FD(ij)r Fy(i)599 327 y FF(\033)627 334 y FD(i)640 327 y FF(\033)668 334 y FD(j)697 327 y FE(\000)11 b FF(p)779 285 y Fx(X)800 373 y FD(x)848 327 y FF(\033)878 306 y Fy(0)876 339 y FD(x)917 285 y Fx(X)906 377 y FD(i)p Fy(2)p FD(B)969 381 y Fs(x)996 327 y FF(\033)1024 334 y FD(i)1049 327 y FQ(+)1098 285 y Fx(X)1118 373 y FD(x)1166 327 y FQ(log)f(2)e(cosh)1363 266 y Fx(\022)1393 327 y FF(p)1437 285 y Fx(X)1426 377 y FD(i)p Fy(2)p FD(B)1489 381 y Fs(x)1516 327 y FF(\033)1544 334 y FD(i)1558 266 y Fx(\023)1602 327 y FF(:)149 b FQ(\(4)p FF(:)p FQ(33\))60 470 y(This)14 b(is)f(the)g(original)h (Ising-mo)q(del)e(Hamiltonian)g(p)q(erturb)q(ed)i(b)o(y)f(a)h(blo)q(c)o (k-dep)q(enden)o(t)f(magnetic)60 530 y(\014eld)20 b(and)h(an)g(an)o (tiferromagnetic)e(m)o(ulti-spin)f(coupling.)34 b(T)l(o)21 b(obtain)g(non-trivial)f(results)g(w)o(e)60 590 y(consider)e(blo)q(c)o(ks)g (at)g(least)g(of)g(size)f(2)i(in)f(eac)o(h)f(co)q(ordinate)i(direction.)25 b(It)18 b(is)g(natural)g(to)h(exp)q(ect)60 650 y(that,)h(for)g(an)o(y)f (\014xed)g FF(p)h(<)f FE(1)p FQ(,)g(for)h(su\016cien)o(tly)d(large)i FF(J)24 b FQ(\(i.e.)18 b(lo)o(w)h(enough)h(temp)q(erature\))e(the)60 711 y(p)q(erturbation)g(b)q(ecome)e(e\013ectiv)o(ely)f(small,)g(and)j(the)f (phase)h(diagram)f(a)h(small)d(deformation)i(to)60 771 y(that)g(of)f(the)g (original)g(Ising)g(mo)q(del.)133 831 y(W)l(e)h(notice,)g(ho)o(w)o(ev)o(er,)f (that)i(there)e(is)h(a)h(small)e(di\013erence)g(with)h(the)h(original)f(p)q (erturbativ)o(e)60 891 y(setting)e(in)f(that)h FP(the)i(last)f(two)h(terms)f (in)g(\(4.33\))g(do)g(not)g(include)i(a)e(temp)n(er)n(atur)n(e)f(factor)5 b FQ(.)21 b(In)14 b(the)60 951 y(study)e(of)g(deformations)f(of)h(phase)g (diagrams,)g(one)g(considers)f(a)h(\014xed)g(v)m(alue)f(of)h FF(\014)i FQ(m)o(ultiplying)9 b FP(al)r(l)60 1011 y FQ(the)15 b(terms)e(of)i(the)g(Hamiltonian,)e(and)i(analyzes)g(the)f(consequences)g(of) i(c)o(hanging)f(\(p)q(erturbing\))60 1072 y(some)c(of)i(the)f(remaining)f (parameters.)19 b(The)12 b(pro)q(of)i(that)f(the)f(deformations)f(are)i(smo)q (oth)f(usually)60 1132 y(requires)i(that)i(the)e(size)h(of)g(this)g(p)q (erturbation)h(not)f(exceed)f(a)i(certain)e FF(\014)s FQ(-dep)q(enden)o(t)g (b)q(ound.)22 b(In)60 1192 y(our)h(case,)g(after)f(pulling)g(out)h(a)f (common)e(factor)j FF(\014)s FQ(,)f(the)h(parameters)e(of)h(the)g(p)q (erturbation)60 1252 y(acquire)16 b(a)i FF(\014)s FQ(-dep)q(endence)e(and)i (one)f(is)g(confron)o(ted)g(with)g(the)g(problem)f(of)h(v)o(erifying)f(that)h (this)60 1312 y FF(\014)s FQ(-dep)q(enden)o(t)h(size)g(is)h(smaller)e(than)i (the)g FF(\014)s FQ(-dep)q(enden)o(t)f(b)q(ound.)30 b(This)19 b(problem)f(is)h(esp)q(ecially)60 1373 y(serious)c(in)g(the)g(case)g(of)g (the)g(last)g(term)e(in)i(\(4.33\),)g(whic)o(h)g(do)q(es)g(not)h(ha)o(v)o(e)e (an)o(y)h(small)e(parameter)60 1433 y(preceding)18 b(it,)g(so)h(that)f(its)h (size)e(decreases)h(only)g(as)h(1)p FF(=\014)s FQ(.)28 b(W)l(e)18 b(conclude)g(that)h(to)f(successfully)60 1493 y(complete)9 b(Step)i(1)g(w)o(e)g(need)f(a)i(sligh)o(t)e(strengthening)i(of)f(the)g(usual) g(PS)h(theory)l(,)f(in)o(v)o(olving)f FP(families)60 1553 y FQ(of)23 b(in)o(teractions,)g(and)g(sho)o(wing)g(that)g(the)f(deformations)g (of)h(the)f(phase)h(diagram)f(are)h(small)60 1613 y FP(uniformly)15 b FQ(in)g(mem)o(b)q(ers)e(of)j(this)f(family)l(.)j(Suc)o(h)e(a)f (strengthening)h(is)f(discussed)h(in)f(App)q(endix)f(B)60 1674 y(\(Corollaries)i(B.25)g(and)h(B.29\).)133 1734 y(F)l(or)h(Step)f(1,)h(then,) g(w)o(e)f(c)o(ho)q(ose)h(a)g(con\014guration)h FF(!)1117 1716 y Fy(0)1115 1746 y FH(sp)q(ecial)1238 1734 y FQ(for)f(the)g(blo)q(c)o(k)f (spins)h(so)g(that)g(the)60 1794 y(middle)d(term)h(in)h(the)h(RHS)f(of)h (\(4.33\))g(do)q(es)g(not)g(fa)o(v)o(or)g(an)o(y)f(o)o(v)o(erall)f(in)o (ternal)h(spin)g(orien)o(tation)60 1854 y(|)f(for)h(example,)d(a)j(fully)e (alternating)i(con\014guration.)23 b(The)17 b(\\uniform")f(v)o(ersion)f(of)i (PS)g(theory)60 1914 y(implies)j(\(App)q(endix)h(B.5.4\))h(that)h(at)g(lo)o (w)f(enough)h(temp)q(erature)e(there)h(are)g(t)o(w)o(o)g(co)q(existing)60 1975 y(phases)d FF(\026)246 1982 y FH(+)294 1975 y FQ(and)g FF(\026)420 1982 y Fy(\000)450 1975 y FQ(.)27 b(This)18 b(is)g(the)g(end)g (of)g(Step)g(1)h(of)g(the)e(Gri\016ths-P)o(earce-Israel)h(argumen)o(t.)60 2035 y(Steps)e(2)h(and)g(3)f(are)h(then)f(completed)e(almost)h(iden)o (tically)f(to)j(the)f(previous)g(examples.)133 2095 y(In)g(this)g(w)o(a)o(y)g (w)o(e)g(conclude:)60 2197 y FM(Theorem)h(4.4)24 b FP(L)n(et)15 b FF(d)f FE(\025)g FQ(2)p FP(,)j FF(b)c FE(\025)h FQ(1)i FP(and)h FQ(0)d FF(<)g(p)g(<)g FE(1)p FP(.)21 b(Then)c(ther)n(e)f(exists)h(a)f FF(J)1557 2204 y FH(0)1593 2197 y FP(\(dep)n(ending)h(on)60 2257 y FF(d)p FP(,)j FF(b)f FP(and)g FF(p)p FP(\))g(such)h(that)f(for)g(al)r (l)h FF(J)h(>)c(J)814 2264 y FH(0)853 2257 y FP(the)j(fol)r(lowing)h(holds:) 26 b(L)n(et)18 b FF(\026)i FP(b)n(e)f(any)g(Gibbs)h(me)n(asur)n(e)60 2317 y(for)d(the)h FF(d)p FP(-dimensional)i(Ising)e(mo)n(del)f(with)h(ne)n (ar)n(est-neighb)n(or)h(c)n(oupling)f FF(J)23 b FP(and)18 b(zer)n(o)e (magnetic)60 2377 y(\014eld.)29 b(L)n(et)18 b FF(T)26 b FP(b)n(e)19 b(the)h(Kadano\013)f(tr)n(ansformation)g(with)g(p)n(ar)n(ameter)f FF(p)h FP(and)h(blo)n(ck)g(size)f FF(b)p FP(.)27 b(Then)60 2438 y(the)c(r)n(enormalize)n(d)f(me)n(asur)n(e)g FF(\026T)30 b FP(is)23 b(not)g(c)n(onsistent)h(with)f(any)g(quasilo)n(c)n(al)g(sp)n(e)n (ci\014c)n(ation.)39 b(In)60 2498 y(p)n(articular,)17 b(it)g(is)h(not)g(the)g (Gibbs)f(me)n(asur)n(e)g(for)g(any)g(uniformly)h(c)n(onver)n(gent)h(inter)n (action.)60 2600 y FQ(A)d(\(p)q(o)q(or\))j(estimate)c(of)i(the)f(smallness)g (of)h(the)f(temp)q(erature)f(is)i(giv)o(en)f(in)g(form)o(ula)g(\(B.87\).)22 b(W)l(e)60 2660 y(emphasize)c(that)i(our)g(estimate)d FF(J)721 2667 y FH(0)761 2660 y FQ(is)i FP(nonuniform)24 b FQ(in)19 b FF(p)p FQ(.)32 b(As)19 b(a)h(result,)g(w)o(e)f(are)h FP(not)k FQ(able)c(to)938 2784 y(114)p eop %%Page: 115 115 bop 60 91 a FQ(tak)o(e)19 b FF(p)i FE(!)e(1)h FQ(at)g(an)o(y)g(\014xed)f FF(J)5 b FQ(,)20 b(and)h(thereb)o(y)d(treat)i(the)g(ma)s(jorit)o(y-rule)d (map.)31 b(\(Our)20 b(partial)60 152 y(results)15 b(on)i(the)e(ma)s(jorit)o (y-rule)e(map,)i(obtained)h(b)o(y)f(a)h FP(di\013er)n(ent)k FQ(metho)q(d,)15 b(will)f(b)q(e)i(describ)q(ed)f(in)60 212 y(the)h(next)g(subsection.\))133 322 y FM(Remarks.)j FQ(1.)j(The)16 b(o)q(ccurrence)f(of)h(\\p)q(eculiarities")f(in)h(the)g(Kadano\013)i (transformation)e(at)60 382 y(small)e FF(p)h FQ(and)h(lo)o(w)f(temp)q (erature)f(w)o(as)h(suggested)h(already)f(b)o(y)g(Gri\016ths)g(and)h(P)o (earce)e([172)q(,)h(173)q(].)133 442 y(2.)23 b(In)o(teresting)15 b(applications)i(of)g(the)f(Kadano\013)j(transformation)d(\(with)h(blo)q(c)o (k)f(size)f FF(b)g FQ(=)f(1!\))60 502 y(arise)19 b(in)f(image)g(pro)q (cessing)i([152)q(,)e(154)q(,)h(63)q(,)f(158)q(,)h(129)q(],)g(sp)q(eec)o(h)f (recognition)h([302)q(])f(and)i(other)60 562 y(\014elds)c(of)h(applied)f (probabilit)o(y)f(theory)l(.)22 b(The)17 b(basic)f(theoretical)f(construct)i (in)f(these)g(\014elds)g(is)h(a)60 623 y(class)j(of)f(mo)q(dels)g(termed)e FP(hidden)k(Markov)g(mo)n(dels)i FQ([302)q(,)c(153)q(,)g(248)q(];)i(in)e(our) h(language)g(these)60 683 y(are)i(simply)d(the)j(images)f(of)h(Mark)o(o)o (vian)f(\(i.e.)f(nearest-neigh)o(b)q(or\))i(spin)g(mo)q(dels)e(under)i(lo)q (cal)60 743 y(renormalization)16 b(transformations.)24 b(It)17 b(has)h(b)q(een)f(long)h(recognized)f(that)g(suc)o(h)h(measures)e(can)60 803 y(b)q(e)g(v)o(ery)e(far)i(from)f(Mark)o(o)o(vian;)f(here)h(w)o(e)h(ha)o (v)o(e)f(sho)o(wn)h(that)g(they)f(can)h(ev)o(en)f(b)q(e)g(non-Gibbsian.)133 863 y(Consider,)23 b(for)f(example,)e(an)i(Ising-mo)q(del)f(Gibbs)g(measure)g (corrupted)g(b)o(y)g(white)h(noise:)60 924 y(with)d(probabilit)o(y)g FF(\017)g FQ(a)h(spin)g(is)f(observ)o(ed)g(incorrectly)l(,)f(indep)q(enden)o (tly)g(at)i(eac)o(h)f(site.)31 b(This)19 b(is)60 984 y(mo)q(del)g(I)i(of)g (Gri\016ths)f(and)i(P)o(earce)e([172,)h(173)q(],)g(and)g(is)g(equiv)m(alen)o (t)e(to)i(the)g(Kadano\013)h(trans-)60 1044 y(formation)d(with)g FF(p)g FQ(=)h(tanh)599 1023 y Fy(\000)p FH(1)646 1044 y FQ(\(1)14 b FE(\000)f FQ(2)p FF(\017)p FQ(\))19 b(on)h(blo)q(c)o(ks)f(of)h(size)e FF(b)h FQ(=)g(1.)31 b(F)l(or)20 b(an)o(y)f FF(\017)g(>)g FQ(0,)h(w)o(e)f(ha)o (v)o(e)60 1104 y(pro)o(v)o(en)i(that)g(the)g(image)f(measure)g(is)h (non-Gibbsian)h(for)g(\()p FF(J)o(;)8 b(h)p FQ(\))21 b(in)g(an)h(\()p FF(\017)p FQ(-dep)q(enden)o(t\))e(op)q(en)60 1164 y(neigh)o(b)q(orho)q(o)q(d) i(of)f(the)f(lo)o(w-temp)q(erature)e(zero-\014eld)i(region.)33 b(This)20 b(system)f(is)h(of)g(in)o(terest)f(in)60 1225 y(applications)d(to)h (image)e(pro)q(cessing)i([152,)f(129)q(].)60 1354 y FM(4.3.4)55 b(Ma)s(jorit)n(y-Rule)18 b(T)-5 b(ransformation)60 1447 y FQ(Next)10 b(w)o(e)g(wish)h(to)g(sho)o(w)h(that)f(Gri\016ths-P)o(earce-Israel)f (pathologies)h(o)q(ccur)g(also)h(for)f(the)f(ma)s(jorit)o(y-)60 1507 y(rule)16 b(transformation)h(\(i.e.)e(the)h(Kadano\013)j(transformation) d(with)h FF(p)e FQ(=)g FE(1)p FQ(\).)22 b(F)l(or)17 b(simplicit)n(y)d(let)60 1567 y(us)i(consider)g(the)f(case)h(of)h(an)f FP(o)n(dd)k FQ(blo)q(c)o(k)c (size)f FF(b)p FQ(,)g(so)h(as)h(to)f(a)o(v)o(oid)g(the)f(complications)f (caused)j(b)o(y)60 1627 y(ties.)27 b(In)18 b(view)g(of)g(the)h(foregoing)g (examples,)d(it)i(is)g(natural)h(to)g(try)f(a)h(fully)e(alternating)h(blo)q (c)o(k-)60 1688 y(spin)h(con\014guration)g FF(!)495 1670 y Fy(0)493 1700 y FD(alt)538 1688 y FQ(.)28 b(Using)19 b(Pirogo)o(v-Sinai)g (theory)l(,)f(one)h(migh)o(t)e(hop)q(e)i(to)g(pro)o(v)o(e)f(that)h(at)60 1748 y(lo)o(w)h(temp)q(erature)f(the)i(in)o(ternal-spin)e(system)g(has)i (precisely)e(t)o(w)o(o)h(extremal)f(p)q(erio)q(dic)h(Gibbs)60 1808 y(measures:)h(a)c(\\+")g(phase)g(in)f(whic)o(h)g(the)h(in)o(ternal)e (spins)i(sho)o(w)g(an)g(o)o(v)o(erwhelming)d(ma)s(jorit)o(y)h(of)60 1868 y(+)g(spins)g(in)f(blo)q(c)o(ks)g(where)h(the)f(blo)q(c)o(k)g(spin)h(is) g(+)f(but)h(only)g(a)g(w)o(eak)f(ma)s(jorit)o(y)f(of)i FE(\000)f FQ(spins)h(where)60 1928 y(the)20 b(blo)q(c)o(k)g(spin)h(is)f FE(\000)p FQ(,)h(and)g(a)f(\\)p FE(\000)p FQ(")h(phase)g(with)g(the)f(rev)o (erse)f(b)q(eha)o(vior.)33 b(This)21 b(result)f(w)o(ould)60 1989 y(in)d(fact)g(follo)o(w)g(if)f(one)h(could)g(sho)o(w)h(that)f(there)g (are)g(precisely)e(t)o(w)o(o)i(p)q(erio)q(dic)g FP(gr)n(ound)22 b FQ(states:)i(a)60 2049 y(\\+"-lik)o(e)13 b(state)i(in)f(whic)o(h)f(the)h (in)o(ternal)f(spins)i(are)f(unanimously)f(+)h(in)g(blo)q(c)o(ks)g(where)g (the)g(blo)q(c)o(k)60 2109 y(spin)i(is)g(+)g(and)h(sho)o(w)g(a)f(bare)h FE(\000)e FQ(ma)s(jorit)o(y)f(where)i(the)g(blo)q(c)o(k)g(spin)g(is)g FE(\000)p FQ(,)f(and)i(a)g(\\)p FE(\000)p FQ("-lik)o(e)e(state)60 2169 y(with)g(the)g(rev)o(erse)e(b)q(eha)o(vior)i([Figure)f(7\(a\)].)21 b(Unfortunately)l(,)14 b(neither)g(the)h(shap)q(e)h(nor)f(the)g(p)q(osi-)60 2229 y(tion)h(within)g(a)g(blo)q(c)o(k)g(of)g(these)g(\\minimal)d(islands")k (of)f(minorit)o(y)e(spins)i(is)g(in)g(general)f(uniquely)60 2290 y(determined)h([Figure)i(7\(b\)];)h(therefore,)f(this)h(family)d(of)j (states)h(is)e(in\014nitely)f(degenerate,)h(and)60 2350 y(w)o(e)g(cannot)h (apply)g(P-S)g(theory)f(\(at)h(least)g(in)f(its)g(usual)h(form\).)27 b(Moreo)o(v)o(er,)18 b(it)g(turns)h(out)g(that)60 2410 y(these)f (con\014gurations)h(are)g(not)f(ev)o(en)f(ground)i(states:)26 b(there)17 b(are)i(\\strip-lik)o(e")e(states)h(of)h(lo)o(w)o(er)60 2470 y(energy)f(densit)o(y)g([Figure)g(7\(c\)].)29 b(W)l(e)19 b(b)q(eliev)o(e)d(that)k(these)e(strip-lik)o(e)f(states)j(are)f(truly)f (ground)60 2530 y(states)c(\(though)h(w)o(e)e(ha)o(v)o(e)g(not)i(pro)o(v)o (en)e(it\);)g(and)i(since)e(they)g(to)q(o)i(are)f(in\014nitely)e(degenerate,) h(P-S)60 2590 y(theory)j(cannot)h(b)q(e)f(applied.)938 2784 y(115)p eop %%Page: 116 116 bop 609 827 a @beginspecial 34 @llx 32.500000 @lly 242 @urx 252.500000 @ury 1756 @rwi @setspecial %%BeginDocument: fig7a.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z u 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 54.2248 249.0688 m S 54.2248 232.5214 m S 37.427 232.5214 m S 37.427 249.0688 m S 45.8259 240.7951 m S U u 87.8205 215.9741 m S 87.8205 199.4268 m S 71.0227 199.4268 m S 71.0227 215.9741 m S 79.4216 207.7004 m S U u 71.0227 232.5214 m S 71.0227 215.9741 m S 54.2248 215.9741 m S 54.2248 232.5214 m S 62.6237 224.2478 m S U u 71.0227 249.0688 m S 71.0227 232.5214 m S 54.2248 232.5214 m S 54.2248 249.0688 m S 62.6237 240.7951 m S U u 87.8205 249.0688 m S 87.8205 232.5214 m S 71.0227 232.5214 m S 71.0227 249.0688 m S 79.4216 240.7951 m S U u 87.8205 232.5214 m S 87.8205 215.9741 m S 71.0227 215.9741 m S 71.0227 232.5214 m S 79.4216 224.2478 m S U u 71.0227 215.9741 m S 71.0227 199.4268 m S 54.2248 199.4268 m S 54.2248 215.9741 m S 62.6237 207.7004 m S U u 54.2248 215.9741 m S 54.2248 199.4268 m S 37.427 199.4268 m S 37.427 215.9741 m S 45.8259 207.7004 m S U u 54.2248 232.5214 m S 54.2248 215.9741 m S 37.427 215.9741 m S 37.427 232.5214 m S 45.8259 224.2478 m S U 0 g 1 w 4 M 45.8259 240.7951 m F 79.4216 240.7951 m F 45.8259 207.7004 m F 79.4216 207.7004 m F u 0 G 0.3 w 10 M 104.6183 249.0688 m S 104.6183 232.5214 m S 87.8205 232.5214 m S 87.8205 249.0688 m S 96.2194 240.7951 m S U 138.214 215.9741 m S 138.214 199.4268 m S 121.4162 199.4268 m S 121.4162 215.9741 m S 129.815 207.7004 m S 121.4162 232.5214 m S 121.4162 215.9741 m S 104.6183 215.9741 m S 104.6183 232.5214 m S 113.0172 224.2478 m S u 121.4162 249.0688 m S 121.4162 232.5214 m S 104.6183 232.5214 m S 104.6183 249.0688 m S 113.0172 240.7951 m S U u 138.214 249.0688 m S 138.214 232.5214 m S 121.4162 232.5214 m S 121.4162 249.0688 m S 129.815 240.7951 m S U 138.214 232.5214 m S 138.214 215.9741 m S 121.4162 215.9741 m S 121.4162 232.5214 m S 129.815 224.2478 m S 121.4162 215.9741 m S 121.4162 199.4268 m S 104.6183 199.4268 m S 104.6183 215.9741 m S 113.0172 207.7004 m S u 104.6183 215.9741 m S 104.6183 199.4268 m S 87.8205 199.4268 m S 87.8205 215.9741 m S 96.2194 207.7004 m S U u 104.6183 232.5214 m S 104.6183 215.9741 m S 87.8205 215.9741 m S 87.8205 232.5214 m S 96.2194 224.2478 m S U 0 g 1 w 4 M 96.2194 240.7951 m F 129.815 240.7951 m F 96.2194 207.7004 m F 129.815 207.7004 m F u 0 G 0.3 w 10 M 155.0118 249.0688 m S 155.0118 232.5214 m S 138.214 232.5214 m S 138.214 249.0688 m S 146.6128 240.7951 m S U u 188.6075 215.9741 m S 188.6075 199.4268 m S 171.8097 199.4268 m S 171.8097 215.9741 m S 180.2085 207.7004 m S U 171.8097 232.5214 m S 171.8097 215.9741 m S 155.0118 215.9741 m S 155.0118 232.5214 m S 163.4107 224.2478 m S u 171.8097 249.0688 m S 171.8097 232.5214 m S 155.0118 232.5214 m S 155.0118 249.0688 m S 163.4107 240.7951 m S U u 188.6075 249.0688 m S 188.6075 232.5214 m S 171.8097 232.5214 m S 171.8097 249.0688 m S 180.2085 240.7951 m S U u 188.6075 232.5214 m S 188.6075 215.9741 m S 171.8097 215.9741 m S 171.8097 232.5214 m S 180.2085 224.2478 m S U 171.8097 215.9741 m S 171.8097 199.4268 m S 155.0118 199.4268 m S 155.0118 215.9741 m S 163.4107 207.7004 m S 155.0118 215.9741 m S 155.0118 199.4268 m S 138.214 199.4268 m S 138.214 215.9741 m S 146.6128 207.7004 m S 155.0118 232.5214 m S 155.0118 215.9741 m S 138.214 215.9741 m S 138.214 232.5214 m S 146.6128 224.2478 m S 0 g 1 w 4 M 146.6128 240.7951 m F 180.2085 240.7951 m F 146.6128 207.7004 m F 180.2085 207.7004 m F u 0 G 0.3 w 10 M 205.4053 249.0688 m S 205.4053 232.5214 m S 188.6075 232.5214 m S 188.6075 249.0688 m S 197.0063 240.7951 m S U u 239.001 215.9741 m S 239.001 199.4268 m S 222.2032 199.4268 m S 222.2032 215.9741 m S 230.602 207.7004 m S U u 222.2032 232.5214 m S 222.2032 215.9741 m S 205.4053 215.9741 m S 205.4053 232.5214 m S 213.8042 224.2478 m S U u 222.2032 249.0688 m S 222.2032 232.5214 m S 205.4053 232.5214 m S 205.4053 249.0688 m S 213.8042 240.7951 m S U u 239.001 249.0688 m S 239.001 232.5214 m S 222.2032 232.5214 m S 222.2032 249.0688 m S 230.602 240.7951 m S U u 239.001 232.5214 m S 239.001 215.9741 m S 222.2032 215.9741 m S 222.2032 232.5214 m S 230.602 224.2478 m S U u 222.2032 215.9741 m S 222.2032 199.4268 m S 205.4053 199.4268 m S 205.4053 215.9741 m S 213.8042 207.7004 m S U u 205.4053 215.9741 m S 205.4053 199.4268 m S 188.6075 199.4268 m S 188.6075 215.9741 m S 197.0063 207.7004 m S U u 205.4053 232.5214 m S 205.4053 215.9741 m S 188.6075 215.9741 m S 188.6075 232.5214 m S 197.0063 224.2478 m S U 0 g 1 w 4 M 197.0063 240.7951 m F 230.602 240.7951 m F 197.0063 207.7004 m F 230.602 207.7004 m F u 0 G 0.3 w 10 M 54.2248 199.4268 m S 54.2248 182.8794 m S 37.427 182.8794 m S 37.427 199.4268 m S 45.8259 191.1531 m S U u 87.8205 166.3321 m S 87.8205 149.7848 m S 71.0227 149.7848 m S 71.0227 166.3321 m S 79.4216 158.0584 m S U u 71.0227 182.8794 m S 71.0227 166.3321 m S 54.2248 166.3321 m S 54.2248 182.8794 m S 62.6237 174.6058 m S U u 71.0227 199.4268 m S 71.0227 182.8794 m S 54.2248 182.8794 m S 54.2248 199.4268 m S 62.6237 191.1531 m S U u 87.8205 199.4268 m S 87.8205 182.8794 m S 71.0227 182.8794 m S 71.0227 199.4268 m S 79.4216 191.1531 m S U u 87.8205 182.8794 m S 87.8205 166.3321 m S 71.0227 166.3321 m S 71.0227 182.8794 m S 79.4216 174.6058 m S U u 71.0227 166.3321 m S 71.0227 149.7848 m S 54.2248 149.7848 m S 54.2248 166.3321 m S 62.6237 158.0584 m S U u 54.2248 166.3321 m S 54.2248 149.7848 m S 37.427 149.7848 m S 37.427 166.3321 m S 45.8259 158.0584 m S U u 54.2248 182.8794 m S 54.2248 166.3321 m S 37.427 166.3321 m S 37.427 182.8794 m S 45.8259 174.6058 m S U 0 g 1 w 4 M 45.8259 191.1531 m F 79.4216 191.1531 m F 45.8259 158.0584 m F 79.4216 158.0584 m F u 0 G 0.3 w 10 M 104.6183 199.4268 m S 104.6183 182.8794 m S 87.8205 182.8794 m S 87.8205 199.4268 m S 96.2194 191.1531 m S U u 138.214 166.3321 m S 138.214 149.7848 m S 121.4162 149.7848 m S 121.4162 166.3321 m S 129.815 158.0584 m S U 121.4162 182.8794 m S 121.4162 166.3321 m S 104.6183 166.3321 m S 104.6183 182.8794 m S 113.0172 174.6058 m S 121.4162 199.4268 m S 121.4162 182.8794 m S 104.6183 182.8794 m S 104.6183 199.4268 m S 113.0172 191.1531 m S 138.214 199.4268 m S 138.214 182.8794 m S 121.4162 182.8794 m S 121.4162 199.4268 m S 129.815 191.1531 m S 138.214 182.8794 m S 138.214 166.3321 m S 121.4162 166.3321 m S 121.4162 182.8794 m S 129.815 174.6058 m S u 121.4162 166.3321 m S 121.4162 149.7848 m S 104.6183 149.7848 m S 104.6183 166.3321 m S 113.0172 158.0584 m S U u 104.6183 166.3321 m S 104.6183 149.7848 m S 87.8205 149.7848 m S 87.8205 166.3321 m S 96.2194 158.0584 m S U u 104.6183 182.8794 m S 104.6183 166.3321 m S 87.8205 166.3321 m S 87.8205 182.8794 m S 96.2194 174.6058 m S U 0 g 1 w 4 M 96.2194 191.1531 m F 129.815 191.1531 m F 96.2194 158.0584 m F 129.815 158.0584 m F 0 G 0.3 w 10 M 155.0118 199.4268 m S 155.0118 182.8794 m S 138.214 182.8794 m S 138.214 199.4268 m S 146.6128 191.1531 m S u 188.6075 166.3321 m S 188.6075 149.7848 m S 171.8097 149.7848 m S 171.8097 166.3321 m S 180.2085 158.0584 m S U 171.8097 182.8794 m S 171.8097 166.3321 m S 155.0118 166.3321 m S 155.0118 182.8794 m S 163.4107 174.6058 m S 171.8097 199.4268 m S 171.8097 182.8794 m S 155.0118 182.8794 m S 155.0118 199.4268 m S 163.4107 191.1531 m S u 188.6075 199.4268 m S 188.6075 182.8794 m S 171.8097 182.8794 m S 171.8097 199.4268 m S 180.2085 191.1531 m S U u 188.6075 182.8794 m S 188.6075 166.3321 m S 171.8097 166.3321 m S 171.8097 182.8794 m S 180.2085 174.6058 m S U u 171.8097 166.3321 m S 171.8097 149.7848 m S 155.0118 149.7848 m S 155.0118 166.3321 m S 163.4107 158.0584 m S U u 155.0118 166.3321 m S 155.0118 149.7848 m S 138.214 149.7848 m S 138.214 166.3321 m S 146.6128 158.0584 m S U 155.0118 182.8794 m S 155.0118 166.3321 m S 138.214 166.3321 m S 138.214 182.8794 m S 146.6128 174.6058 m S 0 g 1 w 4 M 146.6128 191.1531 m F 180.2085 191.1531 m F 146.6128 158.0584 m F 180.2085 158.0584 m F u 0 G 0.3 w 10 M 205.4053 199.4268 m S 205.4053 182.8794 m S 188.6075 182.8794 m S 188.6075 199.4268 m S 197.0063 191.1531 m S U u 239.001 166.3321 m S 239.001 149.7848 m S 222.2032 149.7848 m S 222.2032 166.3321 m S 230.602 158.0584 m S U u 222.2032 182.8794 m S 222.2032 166.3321 m S 205.4053 166.3321 m S 205.4053 182.8794 m S 213.8042 174.6058 m S U u 222.2032 199.4268 m S 222.2032 182.8794 m S 205.4053 182.8794 m S 205.4053 199.4268 m S 213.8042 191.1531 m S U u 239.001 199.4268 m S 239.001 182.8794 m S 222.2032 182.8794 m S 222.2032 199.4268 m S 230.602 191.1531 m S U u 239.001 182.8794 m S 239.001 166.3321 m S 222.2032 166.3321 m S 222.2032 182.8794 m S 230.602 174.6058 m S U u 222.2032 166.3321 m S 222.2032 149.7848 m S 205.4053 149.7848 m S 205.4053 166.3321 m S 213.8042 158.0584 m S U u 205.4053 166.3321 m S 205.4053 149.7848 m S 188.6075 149.7848 m S 188.6075 166.3321 m S 197.0063 158.0584 m S U u 205.4053 182.8794 m S 205.4053 166.3321 m S 188.6075 166.3321 m S 188.6075 182.8794 m S 197.0063 174.6058 m S U 0 g 1 w 4 M 197.0063 191.1531 m F 230.602 191.1531 m F 197.0063 158.0584 m F 230.602 158.0584 m F 45.8259 141.5111 m F 79.4216 141.5111 m F 96.2194 141.5111 m F 129.815 141.5111 m F 146.6128 141.5111 m F 180.2085 141.5111 m F 197.0063 141.5111 m F 230.602 141.5111 m F u 0 G 0.3 w 10 M 54.2248 149.7848 m S 54.2248 133.2374 m S 37.427 133.2374 m S 37.427 149.7848 m S 45.8259 141.5111 m S U u 87.8205 116.6901 m S 87.8205 100.1427 m S 71.0227 100.1427 m S 71.0227 116.6901 m S 79.4216 108.4164 m S U u 71.0227 133.2374 m S 71.0227 116.6901 m S 54.2248 116.6901 m S 54.2248 133.2374 m S 62.6237 124.9637 m S U u 71.0227 149.7848 m S 71.0227 133.2374 m S 54.2248 133.2374 m S 54.2248 149.7848 m S 62.6237 141.5111 m S U u 87.8205 149.7848 m S 87.8205 133.2374 m S 71.0227 133.2374 m S 71.0227 149.7848 m S 79.4216 141.5111 m S U u 87.8205 133.2374 m S 87.8205 116.6901 m S 71.0227 116.6901 m S 71.0227 133.2374 m S 79.4216 124.9637 m S U u 71.0227 116.6901 m S 71.0227 100.1427 m S 54.2248 100.1427 m S 54.2248 116.6901 m S 62.6237 108.4164 m S U u 54.2248 116.6901 m S 54.2248 100.1427 m S 37.427 100.1427 m S 37.427 116.6901 m S 45.8259 108.4164 m S U u 54.2248 133.2374 m S 54.2248 116.6901 m S 37.427 116.6901 m S 37.427 133.2374 m S 45.8259 124.9637 m S U 0 g 1 w 4 M 45.8259 141.5111 m F 79.4216 141.5111 m F 45.8259 108.4164 m F 79.4216 108.4164 m F u 0 G 0.3 w 10 M 104.6183 149.7848 m S 104.6183 133.2374 m S 87.8205 133.2374 m S 87.8205 149.7848 m S 96.2194 141.5111 m S U u 138.214 116.6901 m S 138.214 100.1427 m S 121.4162 100.1427 m S 121.4162 116.6901 m S 129.815 108.4164 m S U u 121.4162 133.2374 m S 121.4162 116.6901 m S 104.6183 116.6901 m S 104.6183 133.2374 m S 113.0172 124.9637 m S U u 121.4162 149.7848 m S 121.4162 133.2374 m S 104.6183 133.2374 m S 104.6183 149.7848 m S 113.0172 141.5111 m S U u 138.214 149.7848 m S 138.214 133.2374 m S 121.4162 133.2374 m S 121.4162 149.7848 m S 129.815 141.5111 m S U u 138.214 133.2374 m S 138.214 116.6901 m S 121.4162 116.6901 m S 121.4162 133.2374 m S 129.815 124.9637 m S U u 121.4162 116.6901 m S 121.4162 100.1427 m S 104.6183 100.1427 m S 104.6183 116.6901 m S 113.0172 108.4164 m S U u 104.6183 116.6901 m S 104.6183 100.1427 m S 87.8205 100.1427 m S 87.8205 116.6901 m S 96.2194 108.4164 m S U u 104.6183 133.2374 m S 104.6183 116.6901 m S 87.8205 116.6901 m S 87.8205 133.2374 m S 96.2194 124.9637 m S U 0 g 1 w 4 M 96.2194 141.5111 m F 129.815 141.5111 m F 96.2194 108.4164 m F 129.815 108.4164 m F u 0 G 0.3 w 10 M 155.0118 149.7848 m S 155.0118 133.2374 m S 138.214 133.2374 m S 138.214 149.7848 m S 146.6128 141.5111 m S U u 188.6075 116.6901 m S 188.6075 100.1427 m S 171.8097 100.1427 m S 171.8097 116.6901 m S 180.2085 108.4164 m S U u 171.8097 133.2374 m S 171.8097 116.6901 m S 155.0118 116.6901 m S 155.0118 133.2374 m S 163.4107 124.9637 m S U u 171.8097 149.7848 m S 171.8097 133.2374 m S 155.0118 133.2374 m S 155.0118 149.7848 m S 163.4107 141.5111 m S U u 188.6075 149.7848 m S 188.6075 133.2374 m S 171.8097 133.2374 m S 171.8097 149.7848 m S 180.2085 141.5111 m S U u 188.6075 133.2374 m S 188.6075 116.6901 m S 171.8097 116.6901 m S 171.8097 133.2374 m S 180.2085 124.9637 m S U u 171.8097 116.6901 m S 171.8097 100.1427 m S 155.0118 100.1427 m S 155.0118 116.6901 m S 163.4107 108.4164 m S U u 155.0118 116.6901 m S 155.0118 100.1427 m S 138.214 100.1427 m S 138.214 116.6901 m S 146.6128 108.4164 m S U u 155.0118 133.2374 m S 155.0118 116.6901 m S 138.214 116.6901 m S 138.214 133.2374 m S 146.6128 124.9637 m S U 0 g 1 w 4 M 146.6128 141.5111 m F 180.2085 141.5111 m F 146.6128 108.4164 m F 180.2085 108.4164 m F u 0 G 0.3 w 10 M 205.4053 149.7848 m S 205.4053 133.2374 m S 188.6075 133.2374 m S 188.6075 149.7848 m S 197.0063 141.5111 m S U u 239.001 116.6901 m S 239.001 100.1427 m S 222.2032 100.1427 m S 222.2032 116.6901 m S 230.602 108.4164 m S U u 222.2032 133.2374 m S 222.2032 116.6901 m S 205.4053 116.6901 m S 205.4053 133.2374 m S 213.8042 124.9637 m S U u 222.2032 149.7848 m S 222.2032 133.2374 m S 205.4053 133.2374 m S 205.4053 149.7848 m S 213.8042 141.5111 m S U u 239.001 149.7848 m S 239.001 133.2374 m S 222.2032 133.2374 m S 222.2032 149.7848 m S 230.602 141.5111 m S U u 239.001 133.2374 m S 239.001 116.6901 m S 222.2032 116.6901 m S 222.2032 133.2374 m S 230.602 124.9637 m S U u 222.2032 116.6901 m S 222.2032 100.1427 m S 205.4053 100.1427 m S 205.4053 116.6901 m S 213.8042 108.4164 m S U u 205.4053 116.6901 m S 205.4053 100.1427 m S 188.6075 100.1427 m S 188.6075 116.6901 m S 197.0063 108.4164 m S U u 205.4053 133.2374 m S 205.4053 116.6901 m S 188.6075 116.6901 m S 188.6075 133.2374 m S 197.0063 124.9637 m S U 0 g 1 w 4 M 197.0063 141.5111 m F 230.602 141.5111 m F 197.0063 108.4164 m F 230.602 108.4164 m F u 0 G 0.3 w 10 M 54.2248 100.1427 m S 54.2248 83.5954 m S 37.427 83.5954 m S 37.427 100.1427 m S 45.8259 91.8691 m S U u 87.8205 67.048 m S 87.8205 50.5007 m S 71.0227 50.5007 m S 71.0227 67.048 m S 79.4216 58.7744 m S U u 71.0227 83.5954 m S 71.0227 67.048 m S 54.2248 67.048 m S 54.2248 83.5954 m S 62.6237 75.3217 m S U u 71.0227 100.1427 m S 71.0227 83.5954 m S 54.2248 83.5954 m S 54.2248 100.1427 m S 62.6237 91.8691 m S U u 87.8205 100.1427 m S 87.8205 83.5954 m S 71.0227 83.5954 m S 71.0227 100.1427 m S 79.4216 91.8691 m S U u 87.8205 83.5954 m S 87.8205 67.048 m S 71.0227 67.048 m S 71.0227 83.5954 m S 79.4216 75.3217 m S U u 71.0227 67.048 m S 71.0227 50.5007 m S 54.2248 50.5007 m S 54.2248 67.048 m S 62.6237 58.7744 m S U u 54.2248 67.048 m S 54.2248 50.5007 m S 37.427 50.5007 m S 37.427 67.048 m S 45.8259 58.7744 m S U u 54.2248 83.5954 m S 54.2248 67.048 m S 37.427 67.048 m S 37.427 83.5954 m S 45.8259 75.3217 m S U 0 g 1 w 4 M 45.8259 91.8691 m F 79.4216 91.8691 m F 45.8259 58.7744 m F 79.4216 58.7744 m F u 0 G 0.3 w 10 M 104.6183 100.1427 m S 104.6183 83.5954 m S 87.8205 83.5954 m S 87.8205 100.1427 m S 96.2194 91.8691 m S U u 138.214 67.048 m S 138.214 50.5007 m S 121.4162 50.5007 m S 121.4162 67.048 m S 129.815 58.7744 m S U u 121.4162 83.5954 m S 121.4162 67.048 m S 104.6183 67.048 m S 104.6183 83.5954 m S 113.0172 75.3217 m S U u 121.4162 100.1427 m S 121.4162 83.5954 m S 104.6183 83.5954 m S 104.6183 100.1427 m S 113.0172 91.8691 m S U u 138.214 100.1427 m S 138.214 83.5954 m S 121.4162 83.5954 m S 121.4162 100.1427 m S 129.815 91.8691 m S U u 138.214 83.5954 m S 138.214 67.048 m S 121.4162 67.048 m S 121.4162 83.5954 m S 129.815 75.3217 m S U u 121.4162 67.048 m S 121.4162 50.5007 m S 104.6183 50.5007 m S 104.6183 67.048 m S 113.0172 58.7744 m S U u 104.6183 67.048 m S 104.6183 50.5007 m S 87.8205 50.5007 m S 87.8205 67.048 m S 96.2194 58.7744 m S U u 104.6183 83.5954 m S 104.6183 67.048 m S 87.8205 67.048 m S 87.8205 83.5954 m S 96.2194 75.3217 m S U 0 g 1 w 4 M 96.2194 91.8691 m F 129.815 91.8691 m F 96.2194 58.7744 m F 129.815 58.7744 m F u 0 G 0.3 w 10 M 155.0118 100.1427 m S 155.0118 83.5954 m S 138.214 83.5954 m S 138.214 100.1427 m S 146.6128 91.8691 m S U u 188.6075 67.048 m S 188.6075 50.5007 m S 171.8097 50.5007 m S 171.8097 67.048 m S 180.2085 58.7744 m S U u 171.8097 83.5954 m S 171.8097 67.048 m S 155.0118 67.048 m S 155.0118 83.5954 m S 163.4107 75.3217 m S U u 171.8097 100.1427 m S 171.8097 83.5954 m S 155.0118 83.5954 m S 155.0118 100.1427 m S 163.4107 91.8691 m S U u 188.6075 100.1427 m S 188.6075 83.5954 m S 171.8097 83.5954 m S 171.8097 100.1427 m S 180.2085 91.8691 m S U u 188.6075 83.5954 m S 188.6075 67.048 m S 171.8097 67.048 m S 171.8097 83.5954 m S 180.2085 75.3217 m S U u 171.8097 67.048 m S 171.8097 50.5007 m S 155.0118 50.5007 m S 155.0118 67.048 m S 163.4107 58.7744 m S U u 155.0118 67.048 m S 155.0118 50.5007 m S 138.214 50.5007 m S 138.214 67.048 m S 146.6128 58.7744 m S U u 155.0118 83.5954 m S 155.0118 67.048 m S 138.214 67.048 m S 138.214 83.5954 m S 146.6128 75.3217 m S U 0 g 1 w 4 M 146.6128 91.8691 m F 180.2085 91.8691 m F 146.6128 58.7744 m F 180.2085 58.7744 m F u 0 G 0.3 w 10 M 205.4053 100.1427 m S 205.4053 83.5954 m S 188.6075 83.5954 m S 188.6075 100.1427 m S 197.0063 91.8691 m S U u 239.001 67.048 m S 239.001 50.5007 m S 222.2032 50.5007 m S 222.2032 67.048 m S 230.602 58.7744 m S U u 222.2032 83.5954 m S 222.2032 67.048 m S 205.4053 67.048 m S 205.4053 83.5954 m S 213.8042 75.3217 m S U u 222.2032 100.1427 m S 222.2032 83.5954 m S 205.4053 83.5954 m S 205.4053 100.1427 m S 213.8042 91.8691 m S U u 239.001 100.1427 m S 239.001 83.5954 m S 222.2032 83.5954 m S 222.2032 100.1427 m S 230.602 91.8691 m S U u 239.001 83.5954 m S 239.001 67.048 m S 222.2032 67.048 m S 222.2032 83.5954 m S 230.602 75.3217 m S U u 222.2032 67.048 m S 222.2032 50.5007 m S 205.4053 50.5007 m S 205.4053 67.048 m S 213.8042 58.7744 m S U u 205.4053 67.048 m S 205.4053 50.5007 m S 188.6075 50.5007 m S 188.6075 67.048 m S 197.0063 58.7744 m S U u 205.4053 83.5954 m S 205.4053 67.048 m S 188.6075 67.048 m S 188.6075 83.5954 m S 197.0063 75.3217 m S U 0 g 1 w 4 M 197.0063 91.8691 m F 230.602 91.8691 m F 197.0063 58.7744 m F 230.602 58.7744 m F 0 G 62.6237 240.7951 m 62.6237 58.7744 l S 113.0172 240.7951 m 113.0172 58.7744 l S 163.4107 240.7951 m 163.4107 58.7744 l S 213.8042 240.7951 m 213.8042 58.7744 l S 45.8259 224.2478 m 230.602 224.2478 l S 45.8259 174.6058 m 230.602 174.6058 l S 45.8259 124.9637 m 230.602 124.9637 l S 45.8259 75.3217 m 230.602 75.3217 l S 0.3 w 127.7104 186.4282 m 133.7109 186.259 137.6089 189.5586 141.0677 194.2457 c 142.0098 195.5223 145.0059 193.9962 147.2138 194.3549 c 148.7117 194.5984 150.3694 195.4375 150.6946 196.8774 c 151.7307 201.4656 152.6021 206.1757 150.9861 210.483 c 150.4603 211.8842 149.5297 213.6194 148.2043 214.4785 c 145.83 216.0175 142.8042 214.3943 140.3173 215.2869 c 138.1236 216.0743 136.2058 218.2084 133.6137 218.0107 c 131.7185 217.8661 130.1973 216.8845 129.3987 215.3285 c 127.8867 212.3826 129.4031 207.9988 126.4288 206.5126 c 124.8022 205.6998 122.4912 205.4416 120.8147 204.1499 c 120.0275 203.5434 119.1847 202.2217 118.8287 201.5053 c 117.551 198.9345 120.3779 196.4819 121.3869 193.9693 c 122.3486 191.5745 123.6243 189.0437 125.3289 186.93 c 125.6557 186.5248 126.8793 186.4517 127.7104 186.4282 c s 1 w 129.3769 186.9626 m S 0.3 w 10 M 144.9338 209.0159 m S 0 g 1 w 4 M 144.9338 209.0159 m F 0 G 0.3 w 10 M 144.9338 209.0159 m S 0 g 1 w 4 M 144.9338 209.0159 m F u 1 g 140.5076 209.0159 m 140.5076 206.6175 142.4893 204.6732 144.9338 204.6732 c 147.3783 204.6732 149.36 206.6175 149.36 209.0159 c F 149.36 209.0159 m 149.36 211.4142 147.3783 213.3585 144.9338 213.3585 c 142.4893 213.3585 140.5076 211.4142 140.5076 209.0159 c F 144.9338 209.0159 m F U 0 G 0.3 w 10 M 144.9338 209.0159 m S 0 g 1 w 4 M 144.9338 209.0159 m F 0 G 0.3 w 10 M 144.9338 209.0159 m S 0 g 1 w 4 M 144.9338 209.0159 m F 144.1347 209.811 m 141.4942 209.8193 L 141.4942 208.2126 L 144.1347 208.2208 L F 145.7329 208.2208 m 148.3734 208.2126 L 148.3734 209.8193 L 145.7329 209.811 L F 141.4942 209.8193 m 148.3734 209.8193 l 148.3734 208.2126 l 141.4942 208.2126 l 141.4942 209.8193 l f 0 G 0.3 w 10 M 129.815 191.1531 m S 0 g 1 w 4 M 129.815 191.1531 m F 0 G 0.3 w 10 M 129.815 191.1531 m S 0 g 1 w 4 M 129.815 191.1531 m F u 1 g 125.3889 191.1531 m 125.3889 188.7547 127.3706 186.8105 129.815 186.8105 c 132.2595 186.8105 134.2412 188.7547 134.2412 191.1531 c F 134.2412 191.1531 m 134.2412 193.5514 132.2595 195.4957 129.815 195.4957 c 127.3706 195.4957 125.3889 193.5514 125.3889 191.1531 c F 129.815 191.1531 m F U 0 G 0.3 w 10 M 129.815 191.1531 m S 0 g 1 w 4 M 129.815 191.1531 m F 0 G 0.3 w 10 M 129.815 191.1531 m S 0 g 1 w 4 M 129.815 191.1531 m F 129.016 191.9483 m 126.3754 191.9565 L 126.3754 190.3498 L 129.016 190.3581 L F 130.6141 190.3581 m 133.2546 190.3498 L 133.2546 191.9565 L 130.6141 191.9483 L F 126.3754 191.9565 m 133.2546 191.9565 l 133.2546 190.3498 l 126.3754 190.3498 l 126.3754 191.9565 l f 0 G 0.3 w 10 M 134.0716 213.1101 m S 0 g 1 w 4 M 134.0716 213.1101 m F 0 G 0.3 w 10 M 134.0716 213.1101 m S 0 g 1 w 4 M 134.0716 213.1101 m F u 1 g 129.6454 213.1101 m 129.6454 210.7118 131.6271 208.7675 134.0716 208.7675 c 136.5161 208.7675 138.4978 210.7118 138.4978 213.1101 c F 138.4978 213.1101 m 138.4978 215.5085 136.5161 217.4528 134.0716 217.4528 c 131.6271 217.4528 129.6454 215.5085 129.6454 213.1101 c F 134.0716 213.1101 m F U 0 G 0.3 w 10 M 134.0716 213.1101 m S 0 g 1 w 4 M 134.0716 213.1101 m F 0 G 0.3 w 10 M 134.0716 213.1101 m S 0 g 1 w 4 M 134.0716 213.1101 m F 133.2725 213.9053 m 130.632 213.9136 L 130.632 212.3069 L 133.2725 212.3151 L F 134.8707 212.3151 m 137.5112 212.3069 L 137.5112 213.9136 L 134.8707 213.9053 L F 130.632 213.9136 m 137.5112 213.9136 l 137.5112 212.3069 l 130.632 212.3069 l 130.632 213.9136 l f 0 G 0.3 w 10 M 139.4107 199.3385 m S 0 g 1 w 4 M 139.4107 199.3385 m F 0 G 0.3 w 10 M 139.4107 199.3385 m S 0 g 1 w 4 M 139.4107 199.3385 m F u 1 g 134.9845 199.3385 m 134.9845 196.9401 136.9662 194.9958 139.4107 194.9958 c 141.8551 194.9958 143.8368 196.9401 143.8368 199.3385 c F 143.8368 199.3385 m 143.8368 201.7368 141.8551 203.6811 139.4107 203.6811 c 136.9662 203.6811 134.9845 201.7368 134.9845 199.3385 c F 139.4107 199.3385 m F U 0 G 0.3 w 10 M 139.4107 199.3385 m S 0 g 1 w 4 M 139.4107 199.3385 m F 0 G 0.3 w 10 M 139.4107 199.3385 m S 0 g 1 w 4 M 139.4107 199.3385 m F 138.6116 200.1336 m 135.9711 200.1419 L 135.9711 198.5352 L 138.6116 198.5434 L F 140.2098 198.5434 m 142.8502 198.5352 L 142.8502 200.1419 L 140.2098 200.1336 L F 135.9711 200.1419 m 142.8502 200.1419 l 142.8502 198.5352 l 135.9711 198.5352 l 135.9711 200.1419 l f 0 G 0.3 w 10 M 126.3392 201.0134 m S 0 g 1 w 4 M 126.3392 201.0134 m F 0 G 0.3 w 10 M 126.3392 201.0134 m S 0 g 1 w 4 M 126.3392 201.0134 m F u 1 g 121.913 201.0134 m 121.913 198.615 123.8947 196.6708 126.3392 196.6708 c 128.7837 196.6708 130.7654 198.615 130.7654 201.0134 c F 130.7654 201.0134 m 130.7654 203.4118 128.7837 205.356 126.3392 205.356 c 123.8947 205.356 121.913 203.4118 121.913 201.0134 c F 126.3392 201.0134 m F U 0 G 0.3 w 10 M 126.3392 201.0134 m S 0 g 1 w 4 M 126.3392 201.0134 m F 0 G 0.3 w 10 M 126.3392 201.0134 m S 0 g 1 w 4 M 126.3392 201.0134 m F 125.5401 201.8086 m 122.8996 201.8168 L 122.8996 200.2101 L 125.5401 200.2184 L F 127.1383 200.2184 m 129.7788 200.2101 L 129.7788 201.8168 L 127.1383 201.8086 L F 122.8996 201.8168 m 129.7788 201.8168 l 129.7788 200.2101 l 122.8996 200.2101 l 122.8996 201.8168 l f 0 G 0.3 w 10 M 121.4162 215.9741 m S 0 g 1 w 4 M 121.4162 215.9741 m F 0 G 0.3 w 10 M 121.4162 215.9741 m S 121.4162 215.9741 m S 121.4162 215.9741 m S 0 g 1 w 4 M 121.4162 215.9741 m F 0 G 0.3 w 10 M 121.4162 215.9741 m S 121.4162 215.9741 m S u 1 g 1 w 4 M 116.99 215.9741 m 116.99 213.5757 118.9717 211.6315 121.4162 211.6315 c 123.8606 211.6315 125.8423 213.5757 125.8423 215.9741 c F 125.8423 215.9741 m 125.8423 218.3724 123.8606 220.3167 121.4162 220.3167 c 118.9717 220.3167 116.99 218.3724 116.99 215.9741 c F 121.4162 215.9741 m F U 0 G 0.3 w 10 M 121.4162 215.9741 m S 0 g 1 w 4 M 121.4162 215.9741 m F 0 G 0.3 w 10 M 121.4162 215.9741 m S 121.4162 215.9741 m S 0 g 1 w 4 M 120.6171 215.1791 m 120.6171 212.5162 L 122.2153 212.5162 L 122.2153 215.1791 L 124.8558 215.1708 L 124.8558 216.7775 L 122.2153 216.7692 L 122.2153 219.4321 L 120.6171 219.4321 L 120.6171 216.7692 L 117.9766 216.7775 L 117.9766 215.1708 L 120.6171 215.1791 L f 0 G 0.3 w 10 M 157.8212 217.0183 m S 0 g 1 w 4 M 157.8212 217.0183 m F 0 G 0.3 w 10 M 157.8212 217.0183 m S 157.8212 217.0183 m S 157.8212 217.0183 m S 0 g 1 w 4 M 157.8212 217.0183 m F 0 G 0.3 w 10 M 157.8212 217.0183 m S 157.8212 217.0183 m S u 1 g 1 w 4 M 153.395 217.0183 m 153.395 214.62 155.3767 212.6757 157.8212 212.6757 c 160.2656 212.6757 162.2473 214.62 162.2473 217.0183 c F 162.2473 217.0183 m 162.2473 219.4167 160.2656 221.3609 157.8212 221.3609 c 155.3767 221.3609 153.395 219.4167 153.395 217.0183 c F 157.8212 217.0183 m F U 0 G 0.3 w 10 M 157.8212 217.0183 m S 0 g 1 w 4 M 157.8212 217.0183 m F 0 G 0.3 w 10 M 157.8212 217.0183 m S 157.8212 217.0183 m S 0 g 1 w 4 M 157.0221 216.2234 m 157.0221 213.5605 L 158.6203 213.5605 L 158.6203 216.2234 L 161.2607 216.215 L 161.2607 217.8218 L 158.6203 217.8135 L 158.6203 220.4764 L 157.0221 220.4764 L 157.0221 217.8135 L 154.3816 217.8218 L 154.3816 216.215 L 157.0221 216.2234 L f 0 G 0.3 w 10 M 153.4026 186.3112 m S 0 g 1 w 4 M 153.4026 186.3112 m F 0 G 0.3 w 10 M 153.4026 186.3112 m S 153.4026 186.3112 m S 153.4026 186.3112 m S 0 g 1 w 4 M 153.4026 186.3112 m F 0 G 0.3 w 10 M 153.4026 186.3112 m S 153.4026 186.3112 m S u 1 g 1 w 4 M 148.9765 186.3112 m 148.9765 183.9128 150.9582 181.9686 153.4026 181.9686 c 155.8471 181.9686 157.8288 183.9128 157.8288 186.3112 c F 157.8288 186.3112 m 157.8288 188.7095 155.8471 190.6538 153.4026 190.6538 c 150.9582 190.6538 148.9765 188.7095 148.9765 186.3112 c F 153.4026 186.3112 m F U 0 G 0.3 w 10 M 153.4026 186.3112 m S 0 g 1 w 4 M 153.4026 186.3112 m F 0 G 0.3 w 10 M 153.4026 186.3112 m S 153.4026 186.3112 m S 0 g 1 w 4 M 152.6035 185.5162 m 152.6035 182.8534 L 154.2017 182.8534 L 154.2017 185.5162 L 156.8422 185.5079 L 156.8422 187.1147 L 154.2017 187.1064 L 154.2017 189.7692 L 152.6035 189.7692 L 152.6035 187.1064 L 149.963 187.1147 L 149.963 185.5079 L 152.6035 185.5162 L f 0 G 0.3 w 10 M 127.2597 179.7976 m S 0 g 1 w 4 M 127.2597 179.7976 m F 0 G 0.3 w 10 M 127.2597 179.7976 m S 127.2597 179.7976 m S 127.2597 179.7976 m S 0 g 1 w 4 M 127.2597 179.7976 m F 0 G 0.3 w 10 M 127.2597 179.7976 m S 127.2597 179.7976 m S u 1 g 1 w 4 M 122.8336 179.7976 m 122.8336 177.3992 124.8153 175.455 127.2597 175.455 c 129.7042 175.455 131.6859 177.3992 131.6859 179.7976 c F 131.6859 179.7976 m 131.6859 182.1959 129.7042 184.1402 127.2597 184.1402 c 124.8153 184.1402 122.8336 182.1959 122.8336 179.7976 c F 127.2597 179.7976 m F U 0 G 0.3 w 10 M 127.2597 179.7976 m S 0 g 1 w 4 M 127.2597 179.7976 m F 0 G 0.3 w 10 M 127.2597 179.7976 m S 127.2597 179.7976 m S 0 g 1 w 4 M 126.4606 179.0026 m 126.4606 176.3398 L 128.0588 176.3398 L 128.0588 179.0026 L 130.6993 178.9943 L 130.6993 180.601 L 128.0588 180.5928 L 128.0588 183.2556 L 126.4606 183.2556 L 126.4606 180.5928 L 123.8201 180.601 L 123.8201 178.9943 L 126.4606 179.0026 L f 0 G 0.3 w 10 M 138.214 116.6901 m S 138.214 100.1427 m S 121.4162 100.1427 m S 121.4162 116.6901 m S 129.815 108.4164 m S 121.4162 116.6901 m S 138.214 116.6901 m S 121.4162 116.6901 m S 121.4162 116.6901 m S 121.4162 100.1427 m S 0 g 1 w 4 M 129.815 108.4164 m F 0 G 0.3 w 10 M 155.0118 116.6901 m S 155.0118 100.1427 m S 155.0118 116.6901 m S 155.0118 116.6901 m S 155.0118 100.1427 m S 138.214 100.1427 m S 138.214 116.6901 m S 146.6128 108.4164 m S 155.0118 116.6901 m S 138.214 116.6901 m S 0 g 1 w 4 M 146.6128 108.4164 m F 0 G 0.3 w 10 M 121.4162 83.5954 m S 121.4162 100.1427 m S 121.4162 83.5954 m S 138.214 100.1427 m S 138.214 83.5954 m S 121.4162 83.5954 m S 121.4162 100.1427 m S 129.815 91.8691 m S 138.214 83.5954 m S 121.4162 83.5954 m S 0 g 1 w 4 M 129.815 91.8691 m F 0 G 0.3 w 10 M 155.0118 100.1427 m S 155.0118 83.5954 m S 138.214 83.5954 m S 138.214 100.1427 m S 146.6128 91.8691 m S 155.0118 83.5954 m S 155.0118 83.5954 m S 155.0118 100.1427 m S 155.0118 83.5954 m S 138.214 83.5954 m S 0 g 1 w 4 M 146.6128 91.8691 m F 0 G 0.3 w 127.7104 87.1442 m 133.7109 86.975 137.6089 90.2745 141.0677 94.9617 c 142.0098 96.2383 145.0059 94.7122 147.2138 95.071 c 148.7117 95.3144 150.3694 96.1535 150.6946 97.5934 c 151.7307 102.1816 152.6021 106.8917 150.9861 111.199 c 150.4603 112.6002 149.5297 114.3354 148.2043 115.1945 c 145.83 116.7335 142.8042 115.1103 140.3173 116.0029 c 138.1236 116.7902 136.2058 118.9244 133.6137 118.7267 c 131.7185 118.5821 130.1973 117.6005 129.3987 116.0445 c 127.8867 113.0986 129.4031 108.7148 126.4288 107.2286 c 124.8022 106.4158 122.4912 106.1576 120.8147 104.8659 c 120.0275 104.2594 119.1847 102.9377 118.8287 102.2213 c 117.551 99.6505 120.3779 97.1979 121.3869 94.6853 c 122.3486 92.2905 123.6243 89.7597 125.3289 87.646 c 125.6557 87.2408 126.8793 87.1677 127.7104 87.1442 c s 1 w 129.3769 87.6786 m S 0.3 w 10 M 144.9338 109.7319 m S 0 g 1 w 4 M 144.9338 109.7319 m F 0 G 0.3 w 10 M 144.9338 109.7319 m S 0 g 1 w 4 M 144.9338 109.7319 m F u 1 g 140.5076 109.7319 m 140.5076 107.3335 142.4893 105.3892 144.9338 105.3892 c 147.3783 105.3892 149.36 107.3335 149.36 109.7319 c F 149.36 109.7319 m 149.36 112.1302 147.3783 114.0745 144.9338 114.0745 c 142.4893 114.0745 140.5076 112.1302 140.5076 109.7319 c F 144.9338 109.7319 m F U 0 G 0.3 w 10 M 144.9338 109.7319 m S 0 g 1 w 4 M 144.9338 109.7319 m F 0 G 0.3 w 10 M 144.9338 109.7319 m S 0 g 1 w 4 M 144.9338 109.7319 m F 144.1347 110.527 m 141.4942 110.5353 L 141.4942 108.9286 L 144.1347 108.9368 L F 145.7329 108.9368 m 148.3734 108.9286 L 148.3734 110.5353 L 145.7329 110.527 L F 141.4942 110.5353 m 148.3734 110.5353 l 148.3734 108.9286 l 141.4942 108.9286 l 141.4942 110.5353 l f 0 G 0.3 w 10 M 129.815 91.8691 m S 0 g 1 w 4 M 129.815 91.8691 m F 0 G 0.3 w 10 M 129.815 91.8691 m S 0 g 1 w 4 M 129.815 91.8691 m F u 1 g 125.3889 91.8691 m 125.3889 89.4707 127.3706 87.5265 129.815 87.5265 c 132.2595 87.5265 134.2412 89.4707 134.2412 91.8691 c F 134.2412 91.8691 m 134.2412 94.2675 132.2595 96.2117 129.815 96.2117 c 127.3706 96.2117 125.3889 94.2675 125.3889 91.8691 c F 129.815 91.8691 m F U 0 G 0.3 w 10 M 129.815 91.8691 m S 0 g 1 w 4 M 129.815 91.8691 m F 0 G 0.3 w 10 M 129.815 91.8691 m S 0 g 1 w 4 M 129.815 91.8691 m F 129.016 92.6643 m 126.3754 92.6725 L 126.3754 91.0658 L 129.016 91.0741 L F 130.6141 91.0741 m 133.2546 91.0658 L 133.2546 92.6725 L 130.6141 92.6643 L F 126.3754 92.6725 m 133.2546 92.6725 l 133.2546 91.0658 l 126.3754 91.0658 l 126.3754 92.6725 l f 0 G 0.3 w 10 M 134.0716 113.8261 m S 0 g 1 w 4 M 134.0716 113.8261 m F 0 G 0.3 w 10 M 134.0716 113.8261 m S 0 g 1 w 4 M 134.0716 113.8261 m F u 1 g 129.6454 113.8261 m 129.6454 111.4278 131.6271 109.4835 134.0716 109.4835 c 136.5161 109.4835 138.4978 111.4278 138.4978 113.8261 c F 138.4978 113.8261 m 138.4978 116.2245 136.5161 118.1688 134.0716 118.1688 c 131.6271 118.1688 129.6454 116.2245 129.6454 113.8261 c F 134.0716 113.8261 m F U 0 G 0.3 w 10 M 134.0716 113.8261 m S 0 g 1 w 4 M 134.0716 113.8261 m F 0 G 0.3 w 10 M 134.0716 113.8261 m S 0 g 1 w 4 M 134.0716 113.8261 m F 133.2725 114.6213 m 130.632 114.6296 L 130.632 113.0228 L 133.2725 113.0311 L F 134.8707 113.0311 m 137.5112 113.0228 L 137.5112 114.6296 L 134.8707 114.6213 L F 130.632 114.6296 m 137.5112 114.6296 l 137.5112 113.0228 l 130.632 113.0228 l 130.632 114.6296 l f 0 G 0.3 w 10 M 139.4107 100.0545 m S 0 g 1 w 4 M 139.4107 100.0545 m F 0 G 0.3 w 10 M 139.4107 100.0545 m S 0 g 1 w 4 M 139.4107 100.0545 m F u 1 g 134.9845 100.0545 m 134.9845 97.6561 136.9662 95.7118 139.4107 95.7118 c 141.8551 95.7118 143.8368 97.6561 143.8368 100.0545 c F 143.8368 100.0545 m 143.8368 102.4528 141.8551 104.3971 139.4107 104.3971 c 136.9662 104.3971 134.9845 102.4528 134.9845 100.0545 c F 139.4107 100.0545 m F U 0 G 0.3 w 10 M 139.4107 100.0545 m S 0 g 1 w 4 M 139.4107 100.0545 m F 0 G 0.3 w 10 M 139.4107 100.0545 m S 0 g 1 w 4 M 139.4107 100.0545 m F 138.6116 100.8497 m 135.9711 100.8579 L 135.9711 99.2512 L 138.6116 99.2594 L F 140.2098 99.2594 m 142.8502 99.2512 L 142.8502 100.8579 L 140.2098 100.8497 L F 135.9711 100.8579 m 142.8502 100.8579 l 142.8502 99.2512 l 135.9711 99.2512 l 135.9711 100.8579 l f 0 G 0.3 w 10 M 126.3392 101.7294 m S 0 g 1 w 4 M 126.3392 101.7294 m F 0 G 0.3 w 10 M 126.3392 101.7294 m S 0 g 1 w 4 M 126.3392 101.7294 m F u 1 g 121.913 101.7294 m 121.913 99.331 123.8947 97.3868 126.3392 97.3868 c 128.7837 97.3868 130.7654 99.331 130.7654 101.7294 c F 130.7654 101.7294 m 130.7654 104.1277 128.7837 106.072 126.3392 106.072 c 123.8947 106.072 121.913 104.1277 121.913 101.7294 c F 126.3392 101.7294 m F U 0 G 0.3 w 10 M 126.3392 101.7294 m S 0 g 1 w 4 M 126.3392 101.7294 m F 0 G 0.3 w 10 M 126.3392 101.7294 m S 0 g 1 w 4 M 126.3392 101.7294 m F 125.5401 102.5246 m 122.8996 102.5328 L 122.8996 100.9261 L 125.5401 100.9344 L F 127.1383 100.9344 m 129.7788 100.9261 L 129.7788 102.5328 L 127.1383 102.5246 L F 122.8996 102.5328 m 129.7788 102.5328 l 129.7788 100.9261 l 122.8996 100.9261 l 122.8996 102.5328 l f 0 G 0.3 w 10 M 121.4162 116.6901 m S 0 g 1 w 4 M 121.4162 116.6901 m F 0 G 0.3 w 10 M 121.4162 116.6901 m S 121.4162 116.6901 m S 121.4162 116.6901 m S 0 g 1 w 4 M 121.4162 116.6901 m F 0 G 0.3 w 10 M 121.4162 116.6901 m S 121.4162 116.6901 m S u 1 g 1 w 4 M 116.99 116.6901 m 116.99 114.2917 118.9717 112.3474 121.4162 112.3474 c 123.8606 112.3474 125.8423 114.2917 125.8423 116.6901 c F 125.8423 116.6901 m 125.8423 119.0884 123.8606 121.0327 121.4162 121.0327 c 118.9717 121.0327 116.99 119.0884 116.99 116.6901 c F 121.4162 116.6901 m F U 0 G 0.3 w 10 M 121.4162 116.6901 m S 0 g 1 w 4 M 121.4162 116.6901 m F 0 G 0.3 w 10 M 121.4162 116.6901 m S 121.4162 116.6901 m S 0 g 1 w 4 M 120.6171 115.8951 m 120.6171 113.2322 L 122.2153 113.2322 L 122.2153 115.8951 L 124.8558 115.8867 L 124.8558 117.4935 L 122.2153 117.4852 L 122.2153 120.1481 L 120.6171 120.1481 L 120.6171 117.4852 L 117.9766 117.4935 L 117.9766 115.8867 L 120.6171 115.8951 L f 0 G 0.3 w 10 M 157.8212 117.7343 m S 0 g 1 w 4 M 157.8212 117.7343 m F 0 G 0.3 w 10 M 157.8212 117.7343 m S 157.8212 117.7343 m S 157.8212 117.7343 m S 0 g 1 w 4 M 157.8212 117.7343 m F 0 G 0.3 w 10 M 157.8212 117.7343 m S 157.8212 117.7343 m S u 1 g 1 w 4 M 153.395 117.7343 m 153.395 115.336 155.3767 113.3917 157.8212 113.3917 c 160.2656 113.3917 162.2473 115.336 162.2473 117.7343 c F 162.2473 117.7343 m 162.2473 120.1327 160.2656 122.0769 157.8212 122.0769 c 155.3767 122.0769 153.395 120.1327 153.395 117.7343 c F 157.8212 117.7343 m F U 0 G 0.3 w 10 M 157.8212 117.7343 m S 0 g 1 w 4 M 157.8212 117.7343 m F 0 G 0.3 w 10 M 157.8212 117.7343 m S 157.8212 117.7343 m S 0 g 1 w 4 M 157.0221 116.9394 m 157.0221 114.2765 L 158.6203 114.2765 L 158.6203 116.9394 L 161.2607 116.931 L 161.2607 118.5378 L 158.6203 118.5295 L 158.6203 121.1924 L 157.0221 121.1924 L 157.0221 118.5295 L 154.3816 118.5378 L 154.3816 116.931 L 157.0221 116.9394 L f 0 G 0.3 w 10 M 153.4026 87.0272 m S 0 g 1 w 4 M 153.4026 87.0272 m F 0 G 0.3 w 10 M 153.4026 87.0272 m S 153.4026 87.0272 m S 153.4026 87.0272 m S 0 g 1 w 4 M 153.4026 87.0272 m F 0 G 0.3 w 10 M 153.4026 87.0272 m S 153.4026 87.0272 m S u 1 g 1 w 4 M 148.9765 87.0272 m 148.9765 84.6288 150.9582 82.6846 153.4026 82.6846 c 155.8471 82.6846 157.8288 84.6288 157.8288 87.0272 c F 157.8288 87.0272 m 157.8288 89.4255 155.8471 91.3698 153.4026 91.3698 c 150.9582 91.3698 148.9765 89.4255 148.9765 87.0272 c F 153.4026 87.0272 m F U 0 G 0.3 w 10 M 153.4026 87.0272 m S 0 g 1 w 4 M 153.4026 87.0272 m F 0 G 0.3 w 10 M 153.4026 87.0272 m S 153.4026 87.0272 m S 0 g 1 w 4 M 152.6035 86.2322 m 152.6035 83.5694 L 154.2017 83.5694 L 154.2017 86.2322 L 156.8422 86.2239 L 156.8422 87.8306 L 154.2017 87.8224 L 154.2017 90.4852 L 152.6035 90.4852 L 152.6035 87.8224 L 149.963 87.8306 L 149.963 86.2239 L 152.6035 86.2322 L f 0 G 0.3 w 10 M 127.2597 80.5136 m S 0 g 1 w 4 M 127.2597 80.5136 m F 0 G 0.3 w 10 M 127.2597 80.5136 m S 127.2597 80.5136 m S 127.2597 80.5136 m S 0 g 1 w 4 M 127.2597 80.5136 m F 0 G 0.3 w 10 M 127.2597 80.5136 m S 127.2597 80.5136 m S u 1 g 1 w 4 M 122.8336 80.5136 m 122.8336 78.1152 124.8153 76.1709 127.2597 76.1709 c 129.7042 76.1709 131.6859 78.1152 131.6859 80.5136 c F 131.6859 80.5136 m 131.6859 82.9119 129.7042 84.8562 127.2597 84.8562 c 124.8153 84.8562 122.8336 82.9119 122.8336 80.5136 c F 127.2597 80.5136 m F U 0 G 0.3 w 10 M 127.2597 80.5136 m S 0 g 1 w 4 M 127.2597 80.5136 m F 0 G 0.3 w 10 M 127.2597 80.5136 m S 127.2597 80.5136 m S 0 g 1 w 4 M 126.4606 79.7186 m 126.4606 77.0557 L 128.0588 77.0557 L 128.0588 79.7186 L 130.6993 79.7103 L 130.6993 81.317 L 128.0588 81.3087 L 128.0588 83.9716 L 126.4606 83.9716 L 126.4606 81.3087 L 123.8201 81.317 L 123.8201 79.7103 L 126.4606 79.7186 L f 0 G 0.3 w 10 M 188.6075 166.3321 m S 188.6075 149.7848 m S 171.8097 149.7848 m S 171.8097 166.3321 m S 180.2085 158.0584 m S 171.8097 166.3321 m S 188.6075 166.3321 m S 171.8097 166.3321 m S 171.8097 166.3321 m S 171.8097 149.7848 m S 0 g 1 w 4 M 180.2085 158.0584 m F 0 G 0.3 w 10 M 205.4053 166.3321 m S 205.4053 149.7848 m S 205.4053 166.3321 m S 205.4053 166.3321 m S 205.4053 149.7848 m S 188.6075 149.7848 m S 188.6075 166.3321 m S 197.0063 158.0584 m S 205.4053 166.3321 m S 188.6075 166.3321 m S 0 g 1 w 4 M 197.0063 158.0584 m F 0 G 0.3 w 10 M 171.8097 133.2374 m S 171.8097 149.7848 m S 171.8097 133.2374 m S 188.6075 149.7848 m S 188.6075 133.2374 m S 171.8097 133.2374 m S 171.8097 149.7848 m S 180.2085 141.5111 m S 188.6075 133.2374 m S 171.8097 133.2374 m S 0 g 1 w 4 M 180.2085 141.5111 m F 0 G 0.3 w 10 M 205.4053 149.7848 m S 205.4053 133.2374 m S 188.6075 133.2374 m S 188.6075 149.7848 m S 197.0063 141.5111 m S 205.4053 133.2374 m S 205.4053 133.2374 m S 205.4053 149.7848 m S 205.4053 133.2374 m S 188.6075 133.2374 m S 0 g 1 w 4 M 197.0063 141.5111 m F 0 G 0.3 w 178.1038 136.7862 m 184.1044 136.617 188.0024 139.9166 191.4612 144.6037 c 192.4033 145.8803 195.3994 144.3542 197.6073 144.7129 c 199.1052 144.9564 200.7629 145.7955 201.0881 147.2354 c 202.1242 151.8236 202.9956 156.5337 201.3796 160.841 c 200.8538 162.2422 199.9232 163.9774 198.5978 164.8365 c 196.2234 166.3755 193.1977 164.7523 190.7108 165.6449 c 188.5171 166.4323 186.5993 168.5664 184.0071 168.3687 c 182.112 168.2241 180.5908 167.2425 179.7922 165.6865 c 178.2801 162.7406 179.7966 158.3568 176.8223 156.8706 c 175.1957 156.0578 172.8847 155.7996 171.2082 154.5079 c 170.421 153.9014 169.5782 152.5797 169.2222 151.8633 c 167.9445 149.2925 170.7714 146.8399 171.7804 144.3273 c 172.742 141.9325 174.0178 139.4017 175.7224 137.288 c 176.0492 136.8828 177.2728 136.8097 178.1038 136.7862 c s 1 w 179.7704 137.3206 m S 0.3 w 10 M 195.3273 159.3739 m S 0 g 1 w 4 M 195.3273 159.3739 m F 0 G 0.3 w 10 M 195.3273 159.3739 m S 0 g 1 w 4 M 195.3273 159.3739 m F u 1 g 190.9011 159.3739 m 190.9011 156.9755 192.8828 155.0312 195.3273 155.0312 c 197.7718 155.0312 199.7535 156.9755 199.7535 159.3739 c F 199.7535 159.3739 m 199.7535 161.7722 197.7718 163.7165 195.3273 163.7165 c 192.8828 163.7165 190.9011 161.7722 190.9011 159.3739 c F 195.3273 159.3739 m F U 0 G 0.3 w 10 M 195.3273 159.3739 m S 0 g 1 w 4 M 195.3273 159.3739 m F 0 G 0.3 w 10 M 195.3273 159.3739 m S 0 g 1 w 4 M 195.3273 159.3739 m F 194.5282 160.169 m 191.8877 160.1773 L 191.8877 158.5706 L 194.5282 158.5788 L F 196.1264 158.5788 m 198.7669 158.5706 L 198.7669 160.1773 L 196.1264 160.169 L F 191.8877 160.1773 m 198.7669 160.1773 l 198.7669 158.5706 l 191.8877 158.5706 l 191.8877 160.1773 l f 0 G 0.3 w 10 M 180.2085 141.5111 m S 0 g 1 w 4 M 180.2085 141.5111 m F 0 G 0.3 w 10 M 180.2085 141.5111 m S 0 g 1 w 4 M 180.2085 141.5111 m F u 1 g 175.7824 141.5111 m 175.7824 139.1127 177.7641 137.1685 180.2085 137.1685 c 182.653 137.1685 184.6347 139.1127 184.6347 141.5111 c F 184.6347 141.5111 m 184.6347 143.9095 182.653 145.8537 180.2085 145.8537 c 177.7641 145.8537 175.7824 143.9095 175.7824 141.5111 c F 180.2085 141.5111 m F U 0 G 0.3 w 10 M 180.2085 141.5111 m S 0 g 1 w 4 M 180.2085 141.5111 m F 0 G 0.3 w 10 M 180.2085 141.5111 m S 0 g 1 w 4 M 180.2085 141.5111 m F 179.4094 142.3063 m 176.7689 142.3145 L 176.7689 140.7078 L 179.4094 140.7161 L F 181.0076 140.7161 m 183.6481 140.7078 L 183.6481 142.3145 L 181.0076 142.3063 L F 176.7689 142.3145 m 183.6481 142.3145 l 183.6481 140.7078 l 176.7689 140.7078 l 176.7689 142.3145 l f 0 G 0.3 w 10 M 184.4651 163.4681 m S 0 g 1 w 4 M 184.4651 163.4681 m F 0 G 0.3 w 10 M 184.4651 163.4681 m S 0 g 1 w 4 M 184.4651 163.4681 m F u 1 g 180.0389 163.4681 m 180.0389 161.0698 182.0206 159.1255 184.4651 159.1255 c 186.9096 159.1255 188.8913 161.0698 188.8913 163.4681 c F 188.8913 163.4681 m 188.8913 165.8665 186.9096 167.8108 184.4651 167.8108 c 182.0206 167.8108 180.0389 165.8665 180.0389 163.4681 c F 184.4651 163.4681 m F U 0 G 0.3 w 10 M 184.4651 163.4681 m S 0 g 1 w 4 M 184.4651 163.4681 m F 0 G 0.3 w 10 M 184.4651 163.4681 m S 0 g 1 w 4 M 184.4651 163.4681 m F 183.666 164.2633 m 181.0255 164.2716 L 181.0255 162.6648 L 183.666 162.6731 L F 185.2642 162.6731 m 187.9047 162.6648 L 187.9047 164.2716 L 185.2642 164.2633 L F 181.0255 164.2716 m 187.9047 164.2716 l 187.9047 162.6648 l 181.0255 162.6648 l 181.0255 164.2716 l f 0 G 0.3 w 10 M 189.8041 149.6965 m S 0 g 1 w 4 M 189.8041 149.6965 m F 0 G 0.3 w 10 M 189.8041 149.6965 m S 0 g 1 w 4 M 189.8041 149.6965 m F u 1 g 185.378 149.6965 m 185.378 147.2981 187.3597 145.3538 189.8041 145.3538 c 192.2486 145.3538 194.2303 147.2981 194.2303 149.6965 c F 194.2303 149.6965 m 194.2303 152.0948 192.2486 154.0391 189.8041 154.0391 c 187.3597 154.0391 185.378 152.0948 185.378 149.6965 c F 189.8041 149.6965 m F U 0 G 0.3 w 10 M 189.8041 149.6965 m S 0 g 1 w 4 M 189.8041 149.6965 m F 0 G 0.3 w 10 M 189.8041 149.6965 m S 0 g 1 w 4 M 189.8041 149.6965 m F 189.0051 150.4916 m 186.3646 150.4999 L 186.3646 148.8932 L 189.0051 148.9014 L F 190.6032 148.9014 m 193.2438 148.8932 L 193.2438 150.4999 L 190.6032 150.4916 L F 186.3646 150.4999 m 193.2438 150.4999 l 193.2438 148.8932 l 186.3646 148.8932 l 186.3646 150.4999 l f 0 G 0.3 w 10 M 176.7327 151.3714 m S 0 g 1 w 4 M 176.7327 151.3714 m F 0 G 0.3 w 10 M 176.7327 151.3714 m S 0 g 1 w 4 M 176.7327 151.3714 m F u 1 g 172.3065 151.3714 m 172.3065 148.973 174.2882 147.0288 176.7327 147.0288 c 179.1772 147.0288 181.1589 148.973 181.1589 151.3714 c F 181.1589 151.3714 m 181.1589 153.7698 179.1772 155.714 176.7327 155.714 c 174.2882 155.714 172.3065 153.7698 172.3065 151.3714 c F 176.7327 151.3714 m F U 0 G 0.3 w 10 M 176.7327 151.3714 m S 0 g 1 w 4 M 176.7327 151.3714 m F 0 G 0.3 w 10 M 176.7327 151.3714 m S 0 g 1 w 4 M 176.7327 151.3714 m F 175.9336 152.1666 m 173.2931 152.1748 L 173.2931 150.5681 L 175.9336 150.5764 L F 177.5318 150.5764 m 180.1723 150.5681 L 180.1723 152.1748 L 177.5318 152.1666 L F 173.2931 152.1748 m 180.1723 152.1748 l 180.1723 150.5681 l 173.2931 150.5681 l 173.2931 152.1748 l f 0 G 0.3 w 10 M 171.8097 166.3321 m S 0 g 1 w 4 M 171.8097 166.3321 m F 0 G 0.3 w 10 M 171.8097 166.3321 m S 171.8097 166.3321 m S 171.8097 166.3321 m S 0 g 1 w 4 M 171.8097 166.3321 m F 0 G 0.3 w 10 M 171.8097 166.3321 m S 171.8097 166.3321 m S u 1 g 1 w 4 M 167.3835 166.3321 m 167.3835 163.9337 169.3652 161.9894 171.8097 161.9894 c 174.2541 161.9894 176.2358 163.9337 176.2358 166.3321 c F 176.2358 166.3321 m 176.2358 168.7304 174.2541 170.6747 171.8097 170.6747 c 169.3652 170.6747 167.3835 168.7304 167.3835 166.3321 c F 171.8097 166.3321 m F U 0 G 0.3 w 10 M 171.8097 166.3321 m S 0 g 1 w 4 M 171.8097 166.3321 m F 0 G 0.3 w 10 M 171.8097 166.3321 m S 171.8097 166.3321 m S 0 g 1 w 4 M 171.0106 165.5371 m 171.0106 162.8742 L 172.6088 162.8742 L 172.6088 165.5371 L 175.2493 165.5288 L 175.2493 167.1355 L 172.6088 167.1272 L 172.6088 169.7901 L 171.0106 169.7901 L 171.0106 167.1272 L 168.3701 167.1355 L 168.3701 165.5288 L 171.0106 165.5371 L f 0 G 0.3 w 10 M 208.2146 167.3763 m S 0 g 1 w 4 M 208.2146 167.3763 m F 0 G 0.3 w 10 M 208.2146 167.3763 m S 208.2146 167.3763 m S 208.2146 167.3763 m S 0 g 1 w 4 M 208.2146 167.3763 m F 0 G 0.3 w 10 M 208.2146 167.3763 m S 208.2146 167.3763 m S u 1 g 1 w 4 M 203.7885 167.3763 m 203.7885 164.978 205.7702 163.0337 208.2146 163.0337 c 210.6591 163.0337 212.6408 164.978 212.6408 167.3763 c F 212.6408 167.3763 m 212.6408 169.7747 210.6591 171.7189 208.2146 171.7189 c 205.7702 171.7189 203.7885 169.7747 203.7885 167.3763 c F 208.2146 167.3763 m F U 0 G 0.3 w 10 M 208.2146 167.3763 m S 0 g 1 w 4 M 208.2146 167.3763 m F 0 G 0.3 w 10 M 208.2146 167.3763 m S 208.2146 167.3763 m S 0 g 1 w 4 M 207.4156 166.5814 m 207.4156 163.9185 L 209.0137 163.9185 L 209.0137 166.5814 L 211.6542 166.573 L 211.6542 168.1798 L 209.0137 168.1715 L 209.0137 170.8344 L 207.4156 170.8344 L 207.4156 168.1715 L 204.7751 168.1798 L 204.7751 166.573 L 207.4156 166.5814 L f 0 G 0.3 w 10 M 203.7961 136.6692 m S 0 g 1 w 4 M 203.7961 136.6692 m F 0 G 0.3 w 10 M 203.7961 136.6692 m S 203.7961 136.6692 m S 203.7961 136.6692 m S 0 g 1 w 4 M 203.7961 136.6692 m F 0 G 0.3 w 10 M 203.7961 136.6692 m S 203.7961 136.6692 m S u 1 g 1 w 4 M 199.37 136.6692 m 199.37 134.2708 201.3516 132.3266 203.7961 132.3266 c 206.2406 132.3266 208.2223 134.2708 208.2223 136.6692 c F 208.2223 136.6692 m 208.2223 139.0675 206.2406 141.0118 203.7961 141.0118 c 201.3516 141.0118 199.37 139.0675 199.37 136.6692 c F 203.7961 136.6692 m F U 0 G 0.3 w 10 M 203.7961 136.6692 m S 0 g 1 w 4 M 203.7961 136.6692 m F 0 G 0.3 w 10 M 203.7961 136.6692 m S 203.7961 136.6692 m S 0 g 1 w 4 M 202.997 135.8742 m 202.997 133.2114 L 204.5952 133.2114 L 204.5952 135.8742 L 207.2357 135.8659 L 207.2357 137.4726 L 204.5952 137.4644 L 204.5952 140.1272 L 202.997 140.1272 L 202.997 137.4644 L 200.3565 137.4726 L 200.3565 135.8659 L 202.997 135.8742 L f 0 G 0.3 w 10 M 177.6532 130.1556 m S 0 g 1 w 4 M 177.6532 130.1556 m F 0 G 0.3 w 10 M 177.6532 130.1556 m S 177.6532 130.1556 m S 177.6532 130.1556 m S 0 g 1 w 4 M 177.6532 130.1556 m F 0 G 0.3 w 10 M 177.6532 130.1556 m S 177.6532 130.1556 m S u 1 g 1 w 4 M 173.2271 130.1556 m 173.2271 127.7572 175.2088 125.8129 177.6532 125.8129 c 180.0977 125.8129 182.0794 127.7572 182.0794 130.1556 c F 182.0794 130.1556 m 182.0794 132.5539 180.0977 134.4982 177.6532 134.4982 c 175.2088 134.4982 173.2271 132.5539 173.2271 130.1556 c F 177.6532 130.1556 m F U 0 G 0.3 w 10 M 177.6532 130.1556 m S 0 g 1 w 4 M 177.6532 130.1556 m F 0 G 0.3 w 10 M 177.6532 130.1556 m S 177.6532 130.1556 m S 0 g 1 w 4 M 176.8541 129.3606 m 176.8541 126.6977 L 178.4523 126.6977 L 178.4523 129.3606 L 181.0928 129.3523 L 181.0928 130.959 L 178.4523 130.9507 L 178.4523 133.6136 L 176.8541 133.6136 L 176.8541 130.9507 L 174.2136 130.959 L 174.2136 129.3523 L 176.8541 129.3606 L f 0 G 0.3 w 10 M 87.8205 166.3321 m S 87.8205 149.7848 m S 71.0227 149.7848 m S 71.0227 166.3321 m S 79.4216 158.0584 m S 71.0227 166.3321 m S 87.8205 166.3321 m S 71.0227 166.3321 m S 71.0227 166.3321 m S 71.0227 149.7848 m S 0 g 1 w 4 M 79.4216 158.0584 m F 0 G 0.3 w 10 M 104.6183 166.3321 m S 104.6183 149.7848 m S 104.6183 166.3321 m S 104.6183 166.3321 m S 104.6183 149.7848 m S 87.8205 149.7848 m S 87.8205 166.3321 m S 96.2194 158.0584 m S 104.6183 166.3321 m S 87.8205 166.3321 m S 0 g 1 w 4 M 96.2194 158.0584 m F 0 G 0.3 w 10 M 71.0227 133.2374 m S 71.0227 149.7848 m S 71.0227 133.2374 m S 87.8205 149.7848 m S 87.8205 133.2374 m S 71.0227 133.2374 m S 71.0227 149.7848 m S 79.4216 141.5111 m S 87.8205 133.2374 m S 71.0227 133.2374 m S 0 g 1 w 4 M 79.4216 141.5111 m F 0 G 0.3 w 10 M 104.6183 149.7848 m S 104.6183 133.2374 m S 87.8205 133.2374 m S 87.8205 149.7848 m S 96.2194 141.5111 m S 104.6183 133.2374 m S 104.6183 133.2374 m S 104.6183 149.7848 m S 104.6183 133.2374 m S 87.8205 133.2374 m S 0 g 1 w 4 M 96.2194 141.5111 m F 0 G 0.3 w 77.3169 136.7862 m 83.3174 136.617 87.2154 139.9166 90.6742 144.6037 c 91.6163 145.8803 94.6124 144.3542 96.8203 144.7129 c 98.3182 144.9564 99.9759 145.7955 100.3011 147.2354 c 101.3372 151.8236 102.2086 156.5337 100.5926 160.841 c 100.0668 162.2422 99.1362 163.9774 97.8108 164.8365 c 95.4364 166.3755 92.4107 164.7523 89.9239 165.6449 c 87.7301 166.4323 85.8123 168.5664 83.2201 168.3687 c 81.3251 168.2241 79.8038 167.2425 79.0052 165.6865 c 77.4932 162.7406 79.0096 158.3568 76.0354 156.8706 c 74.4087 156.0578 72.0977 155.7996 70.4212 154.5079 c 69.634 153.9014 68.7912 152.5797 68.4352 151.8633 c 67.1575 149.2925 69.9844 146.8399 70.9934 144.3273 c 71.9551 141.9325 73.2308 139.4017 74.9354 137.288 c 75.2622 136.8828 76.4858 136.8097 77.3169 136.7862 c s 1 w 78.9835 137.3206 m S 0.3 w 10 M 94.5403 159.3739 m S 0 g 1 w 4 M 94.5403 159.3739 m F 0 G 0.3 w 10 M 94.5403 159.3739 m S 0 g 1 w 4 M 94.5403 159.3739 m F u 1 g 90.1141 159.3739 m 90.1141 156.9755 92.0959 155.0312 94.5403 155.0312 c 96.9848 155.0312 98.9665 156.9755 98.9665 159.3739 c F 98.9665 159.3739 m 98.9665 161.7722 96.9848 163.7165 94.5403 163.7165 c 92.0959 163.7165 90.1141 161.7722 90.1141 159.3739 c F 94.5403 159.3739 m F U 0 G 0.3 w 10 M 94.5403 159.3739 m S 0 g 1 w 4 M 94.5403 159.3739 m F 0 G 0.3 w 10 M 94.5403 159.3739 m S 0 g 1 w 4 M 94.5403 159.3739 m F 93.7412 160.169 m 91.1007 160.1773 L 91.1007 158.5706 L 93.7412 158.5788 L F 95.3394 158.5788 m 97.9799 158.5706 L 97.9799 160.1773 L 95.3394 160.169 L F 91.1007 160.1773 m 97.9799 160.1773 l 97.9799 158.5706 l 91.1007 158.5706 l 91.1007 160.1773 l f 0 G 0.3 w 10 M 79.4216 141.5111 m S 0 g 1 w 4 M 79.4216 141.5111 m F 0 G 0.3 w 10 M 79.4216 141.5111 m S 0 g 1 w 4 M 79.4216 141.5111 m F u 1 g 74.9954 141.5111 m 74.9954 139.1127 76.9771 137.1685 79.4216 137.1685 c 81.866 137.1685 83.8477 139.1127 83.8477 141.5111 c F 83.8477 141.5111 m 83.8477 143.9095 81.866 145.8537 79.4216 145.8537 c 76.9771 145.8537 74.9954 143.9095 74.9954 141.5111 c F 79.4216 141.5111 m F U 0 G 0.3 w 10 M 79.4216 141.5111 m S 0 g 1 w 4 M 79.4216 141.5111 m F 0 G 0.3 w 10 M 79.4216 141.5111 m S 0 g 1 w 4 M 79.4216 141.5111 m F 78.6225 142.3063 m 75.9819 142.3145 L 75.9819 140.7078 L 78.6225 140.7161 L F 80.2206 140.7161 m 82.8611 140.7078 L 82.8611 142.3145 L 80.2206 142.3063 L F 75.9819 142.3145 m 82.8611 142.3145 l 82.8611 140.7078 l 75.9819 140.7078 l 75.9819 142.3145 l f 0 G 0.3 w 10 M 83.6781 163.4681 m S 0 g 1 w 4 M 83.6781 163.4681 m F 0 G 0.3 w 10 M 83.6781 163.4681 m S 0 g 1 w 4 M 83.6781 163.4681 m F u 1 g 79.2519 163.4681 m 79.2519 161.0698 81.2337 159.1255 83.6781 159.1255 c 86.1226 159.1255 88.1043 161.0698 88.1043 163.4681 c F 88.1043 163.4681 m 88.1043 165.8665 86.1226 167.8108 83.6781 167.8108 c 81.2337 167.8108 79.2519 165.8665 79.2519 163.4681 c F 83.6781 163.4681 m F U 0 G 0.3 w 10 M 83.6781 163.4681 m S 0 g 1 w 4 M 83.6781 163.4681 m F 0 G 0.3 w 10 M 83.6781 163.4681 m S 0 g 1 w 4 M 83.6781 163.4681 m F 82.879 164.2633 m 80.2385 164.2716 L 80.2385 162.6648 L 82.879 162.6731 L F 84.4772 162.6731 m 87.1177 162.6648 L 87.1177 164.2716 L 84.4772 164.2633 L F 80.2385 164.2716 m 87.1177 164.2716 l 87.1177 162.6648 l 80.2385 162.6648 l 80.2385 164.2716 l f 0 G 0.3 w 10 M 89.0172 149.6965 m S 0 g 1 w 4 M 89.0172 149.6965 m F 0 G 0.3 w 10 M 89.0172 149.6965 m S 0 g 1 w 4 M 89.0172 149.6965 m F u 1 g 84.591 149.6965 m 84.591 147.2981 86.5727 145.3538 89.0172 145.3538 c 91.4616 145.3538 93.4433 147.2981 93.4433 149.6965 c F 93.4433 149.6965 m 93.4433 152.0948 91.4616 154.0391 89.0172 154.0391 c 86.5727 154.0391 84.591 152.0948 84.591 149.6965 c F 89.0172 149.6965 m F U 0 G 0.3 w 10 M 89.0172 149.6965 m S 0 g 1 w 4 M 89.0172 149.6965 m F 0 G 0.3 w 10 M 89.0172 149.6965 m S 0 g 1 w 4 M 89.0172 149.6965 m F 88.2181 150.4916 m 85.5776 150.4999 L 85.5776 148.8932 L 88.2181 148.9014 L F 89.8163 148.9014 m 92.4568 148.8932 L 92.4568 150.4999 L 89.8163 150.4916 L F 85.5776 150.4999 m 92.4568 150.4999 l 92.4568 148.8932 l 85.5776 148.8932 l 85.5776 150.4999 l f 0 G 0.3 w 10 M 75.9457 151.3714 m S 0 g 1 w 4 M 75.9457 151.3714 m F 0 G 0.3 w 10 M 75.9457 151.3714 m S 0 g 1 w 4 M 75.9457 151.3714 m F u 1 g 71.5195 151.3714 m 71.5195 148.973 73.5012 147.0288 75.9457 147.0288 c 78.3902 147.0288 80.3719 148.973 80.3719 151.3714 c F 80.3719 151.3714 m 80.3719 153.7698 78.3902 155.714 75.9457 155.714 c 73.5012 155.714 71.5195 153.7698 71.5195 151.3714 c F 75.9457 151.3714 m F U 0 G 0.3 w 10 M 75.9457 151.3714 m S 0 g 1 w 4 M 75.9457 151.3714 m F 0 G 0.3 w 10 M 75.9457 151.3714 m S 0 g 1 w 4 M 75.9457 151.3714 m F 75.1466 152.1666 m 72.5061 152.1748 L 72.5061 150.5681 L 75.1466 150.5764 L F 76.7448 150.5764 m 79.3853 150.5681 L 79.3853 152.1748 L 76.7448 152.1666 L F 72.5061 152.1748 m 79.3853 152.1748 l 79.3853 150.5681 l 72.5061 150.5681 l 72.5061 152.1748 l f 0 G 0.3 w 10 M 71.0227 166.3321 m S 0 g 1 w 4 M 71.0227 166.3321 m F 0 G 0.3 w 10 M 71.0227 166.3321 m S 71.0227 166.3321 m S 71.0227 166.3321 m S 0 g 1 w 4 M 71.0227 166.3321 m F 0 G 0.3 w 10 M 71.0227 166.3321 m S 71.0227 166.3321 m S u 1 g 1 w 4 M 66.5965 166.3321 m 66.5965 163.9337 68.5782 161.9894 71.0227 161.9894 c 73.4671 161.9894 75.4489 163.9337 75.4489 166.3321 c F 75.4489 166.3321 m 75.4489 168.7304 73.4671 170.6747 71.0227 170.6747 c 68.5782 170.6747 66.5965 168.7304 66.5965 166.3321 c F 71.0227 166.3321 m F U 0 G 0.3 w 10 M 71.0227 166.3321 m S 0 g 1 w 4 M 71.0227 166.3321 m F 0 G 0.3 w 10 M 71.0227 166.3321 m S 71.0227 166.3321 m S 0 g 1 w 4 M 70.2236 165.5371 m 70.2236 162.8742 L 71.8218 162.8742 L 71.8218 165.5371 L 74.4623 165.5288 L 74.4623 167.1355 L 71.8218 167.1272 L 71.8218 169.7901 L 70.2236 169.7901 L 70.2236 167.1272 L 67.5831 167.1355 L 67.5831 165.5288 L 70.2236 165.5371 L f 0 G 0.3 w 10 M 107.4277 167.3763 m S 0 g 1 w 4 M 107.4277 167.3763 m F 0 G 0.3 w 10 M 107.4277 167.3763 m S 107.4277 167.3763 m S 107.4277 167.3763 m S 0 g 1 w 4 M 107.4277 167.3763 m F 0 G 0.3 w 10 M 107.4277 167.3763 m S 107.4277 167.3763 m S u 1 g 1 w 4 M 103.0015 167.3763 m 103.0015 164.978 104.9832 163.0337 107.4277 163.0337 c 109.8721 163.0337 111.8538 164.978 111.8538 167.3763 c F 111.8538 167.3763 m 111.8538 169.7747 109.8721 171.7189 107.4277 171.7189 c 104.9832 171.7189 103.0015 169.7747 103.0015 167.3763 c F 107.4277 167.3763 m F U 0 G 0.3 w 10 M 107.4277 167.3763 m S 0 g 1 w 4 M 107.4277 167.3763 m F 0 G 0.3 w 10 M 107.4277 167.3763 m S 107.4277 167.3763 m S 0 g 1 w 4 M 106.6286 166.5814 m 106.6286 163.9185 L 108.2268 163.9185 L 108.2268 166.5814 L 110.8673 166.573 L 110.8673 168.1798 L 108.2268 168.1715 L 108.2268 170.8344 L 106.6286 170.8344 L 106.6286 168.1715 L 103.9881 168.1798 L 103.9881 166.573 L 106.6286 166.5814 L f 0 G 0.3 w 10 M 103.0092 136.6692 m S 0 g 1 w 4 M 103.0092 136.6692 m F 0 G 0.3 w 10 M 103.0092 136.6692 m S 103.0092 136.6692 m S 103.0092 136.6692 m S 0 g 1 w 4 M 103.0092 136.6692 m F 0 G 0.3 w 10 M 103.0092 136.6692 m S 103.0092 136.6692 m S u 1 g 1 w 4 M 98.583 136.6692 m 98.583 134.2708 100.5647 132.3266 103.0092 132.3266 c 105.4536 132.3266 107.4353 134.2708 107.4353 136.6692 c F 107.4353 136.6692 m 107.4353 139.0675 105.4536 141.0118 103.0092 141.0118 c 100.5647 141.0118 98.583 139.0675 98.583 136.6692 c F 103.0092 136.6692 m F U 0 G 0.3 w 10 M 103.0092 136.6692 m S 0 g 1 w 4 M 103.0092 136.6692 m F 0 G 0.3 w 10 M 103.0092 136.6692 m S 103.0092 136.6692 m S 0 g 1 w 4 M 102.2101 135.8742 m 102.2101 133.2114 L 103.8082 133.2114 L 103.8082 135.8742 L 106.4487 135.8659 L 106.4487 137.4726 L 103.8082 137.4644 L 103.8082 140.1272 L 102.2101 140.1272 L 102.2101 137.4644 L 99.5695 137.4726 L 99.5695 135.8659 L 102.2101 135.8742 L f 0 G 0.3 w 10 M 76.8663 130.1556 m S 0 g 1 w 4 M 76.8663 130.1556 m F 0 G 0.3 w 10 M 76.8663 130.1556 m S 76.8663 130.1556 m S 76.8663 130.1556 m S 0 g 1 w 4 M 76.8663 130.1556 m F 0 G 0.3 w 10 M 76.8663 130.1556 m S 76.8663 130.1556 m S u 1 g 1 w 4 M 72.4401 130.1556 m 72.4401 127.7572 74.4218 125.8129 76.8663 125.8129 c 79.3107 125.8129 81.2924 127.7572 81.2924 130.1556 c F 81.2924 130.1556 m 81.2924 132.5539 79.3107 134.4982 76.8663 134.4982 c 74.4218 134.4982 72.4401 132.5539 72.4401 130.1556 c F 76.8663 130.1556 m F U 0 G 0.3 w 10 M 76.8663 130.1556 m S 0 g 1 w 4 M 76.8663 130.1556 m F 0 G 0.3 w 10 M 76.8663 130.1556 m S 76.8663 130.1556 m S 0 g 1 w 4 M 76.0672 129.3606 m 76.0672 126.6977 L 77.6653 126.6977 L 77.6653 129.3606 L 80.3058 129.3523 L 80.3058 130.959 L 77.6653 130.9507 L 77.6653 133.6136 L 76.0672 133.6136 L 76.0672 130.9507 L 73.4266 130.959 L 73.4266 129.3523 L 76.0672 129.3606 L f 0 G 0.3 w 10 M 72.0283 217.0183 m S 0 g 1 w 4 M 72.0283 217.0183 m F 0 G 0.3 w 10 M 72.0283 217.0183 m S 72.0283 217.0183 m S 72.0283 217.0183 m S 0 g 1 w 4 M 72.0283 217.0183 m F 0 G 0.3 w 10 M 72.0283 217.0183 m S 72.0283 217.0183 m S u 1 g 1 w 4 M 67.6021 217.0183 m 67.6021 214.62 69.5838 212.6757 72.0283 212.6757 c 74.4727 212.6757 76.4544 214.62 76.4544 217.0183 c F 76.4544 217.0183 m 76.4544 219.4167 74.4727 221.3609 72.0283 221.3609 c 69.5838 221.3609 67.6021 219.4167 67.6021 217.0183 c F 72.0283 217.0183 m F U 0 G 0.3 w 10 M 72.0283 217.0183 m S 0 g 1 w 4 M 72.0283 217.0183 m F 0 G 0.3 w 10 M 72.0283 217.0183 m S 72.0283 217.0183 m S 0 g 1 w 4 M 71.2292 216.2234 m 71.2292 213.5605 L 72.8274 213.5605 L 72.8274 216.2234 L 75.4678 216.215 L 75.4678 217.8218 L 72.8274 217.8135 L 72.8274 220.4764 L 71.2292 220.4764 L 71.2292 217.8135 L 68.5887 217.8218 L 68.5887 216.215 L 71.2292 216.2234 L f 0 G 0.3 w 10 M 103.3261 208.4576 m S 0 g 1 w 4 M 103.3261 208.4576 m F 0 G 0.3 w 10 M 103.3261 208.4576 m S 103.3261 208.4576 m S 103.3261 208.4576 m S 0 g 1 w 4 M 103.3261 208.4576 m F 0 G 0.3 w 10 M 103.3261 208.4576 m S 103.3261 208.4576 m S u 1 g 1 w 4 M 98.8999 208.4576 m 98.8999 206.0592 100.8816 204.1149 103.3261 204.1149 c 105.7706 204.1149 107.7523 206.0592 107.7523 208.4576 c F 107.7523 208.4576 m 107.7523 210.8559 105.7706 212.8002 103.3261 212.8002 c 100.8816 212.8002 98.8999 210.8559 98.8999 208.4576 c F 103.3261 208.4576 m F U 0 G 0.3 w 10 M 103.3261 208.4576 m S 0 g 1 w 4 M 103.3261 208.4576 m F 0 G 0.3 w 10 M 103.3261 208.4576 m S 103.3261 208.4576 m S 0 g 1 w 4 M 102.527 207.6626 m 102.527 204.9998 L 104.1252 204.9998 L 104.1252 207.6626 L 106.7657 207.6543 L 106.7657 209.261 L 104.1252 209.2527 L 104.1252 211.9156 L 102.527 211.9156 L 102.527 209.2527 L 99.8865 209.261 L 99.8865 207.6543 L 102.527 207.6626 L f 0 G 0.3 w 10 M 87.8205 199.4268 m S 0 g 1 w 4 M 87.8205 199.4268 m F 0 G 0.3 w 10 M 87.8205 199.4268 m S 87.8205 199.4268 m S 87.8205 199.4268 m S 0 g 1 w 4 M 87.8205 199.4268 m F 0 G 0.3 w 10 M 87.8205 199.4268 m S 87.8205 199.4268 m S u 1 g 1 w 4 M 83.3943 199.4268 m 83.3943 197.0284 85.376 195.0841 87.8205 195.0841 c 90.265 195.0841 92.2467 197.0284 92.2467 199.4268 c F 92.2467 199.4268 m 92.2467 201.8251 90.265 203.7694 87.8205 203.7694 c 85.376 203.7694 83.3943 201.8251 83.3943 199.4268 c F 87.8205 199.4268 m F U 0 G 0.3 w 10 M 87.8205 199.4268 m S 0 g 1 w 4 M 87.8205 199.4268 m F 0 G 0.3 w 10 M 87.8205 199.4268 m S 87.8205 199.4268 m S 0 g 1 w 4 M 87.0214 198.6318 m 87.0214 195.9689 L 88.6196 195.9689 L 88.6196 198.6318 L 91.2601 198.6235 L 91.2601 200.2302 L 88.6196 200.2219 L 88.6196 202.8848 L 87.0214 202.8848 L 87.0214 200.2219 L 84.3809 200.2302 L 84.3809 198.6235 L 87.0214 198.6318 L f 0 G 0.3 w 10 M 71.2919 191.5221 m S 0 g 1 w 4 M 71.2919 191.5221 m F 0 G 0.3 w 10 M 71.2919 191.5221 m S 71.2919 191.5221 m S 71.2919 191.5221 m S 0 g 1 w 4 M 71.2919 191.5221 m F 0 G 0.3 w 10 M 71.2919 191.5221 m S 71.2919 191.5221 m S u 1 g 1 w 4 M 66.8657 191.5221 m 66.8657 189.1237 68.8474 187.1795 71.2919 187.1795 c 73.7363 187.1795 75.718 189.1237 75.718 191.5221 c F 75.718 191.5221 m 75.718 193.9205 73.7363 195.8647 71.2919 195.8647 c 68.8474 195.8647 66.8657 193.9205 66.8657 191.5221 c F 71.2919 191.5221 m F U 0 G 0.3 w 10 M 71.2919 191.5221 m S 0 g 1 w 4 M 71.2919 191.5221 m F 0 G 0.3 w 10 M 71.2919 191.5221 m S 71.2919 191.5221 m S 0 g 1 w 4 M 70.4927 190.7272 m 70.4927 188.0643 L 72.0909 188.0643 L 72.0909 190.7272 L 74.7314 190.7188 L 74.7314 192.3256 L 72.0909 192.3173 L 72.0909 194.9801 L 70.4927 194.9801 L 70.4927 192.3173 L 67.8522 192.3256 L 67.8522 190.7188 L 70.4927 190.7272 L f 0 G 0.3 w 10 M 104.6183 182.8794 m S 0 g 1 w 4 M 104.6183 182.8794 m F 0 G 0.3 w 10 M 104.6183 182.8794 m S 104.6183 182.8794 m S 104.6183 182.8794 m S 0 g 1 w 4 M 104.6183 182.8794 m F 0 G 0.3 w 10 M 104.6183 182.8794 m S 104.6183 182.8794 m S u 1 g 1 w 4 M 100.1921 182.8794 m 100.1921 180.481 102.1738 178.5367 104.6183 178.5367 c 107.0628 178.5367 109.0445 180.481 109.0445 182.8794 c F 109.0445 182.8794 m 109.0445 185.2777 107.0628 187.222 104.6183 187.222 c 102.1738 187.222 100.1921 185.2777 100.1921 182.8794 c F 104.6183 182.8794 m F U 0 G 0.3 w 10 M 104.6183 182.8794 m S 0 g 1 w 4 M 104.6183 182.8794 m F 0 G 0.3 w 10 M 104.6183 182.8794 m S 104.6183 182.8794 m S 0 g 1 w 4 M 103.8192 182.0844 m 103.8192 179.4216 L 105.4174 179.4216 L 105.4174 182.0844 L 108.0579 182.0761 L 108.0579 183.6828 L 105.4174 183.6746 L 105.4174 186.3374 L 103.8192 186.3374 L 103.8192 183.6746 L 101.1787 183.6828 L 101.1787 182.0761 L 103.8192 182.0844 L f 0 G 0.3 w 10 M 87.8205 182.8794 m S 0 g 1 w 4 M 87.8205 182.8794 m F 0 G 0.3 w 10 M 87.8205 182.8794 m S 87.8205 182.8794 m S 87.8205 182.8794 m S 0 g 1 w 4 M 87.8205 182.8794 m F 0 G 0.3 w 10 M 87.8205 182.8794 m S 87.8205 182.8794 m S u 1 g 1 w 4 M 83.3943 182.8794 m 83.3943 180.481 85.376 178.5367 87.8205 178.5367 c 90.265 178.5367 92.2467 180.481 92.2467 182.8794 c F 92.2467 182.8794 m 92.2467 185.2777 90.265 187.222 87.8205 187.222 c 85.376 187.222 83.3943 185.2777 83.3943 182.8794 c F 87.8205 182.8794 m F U 0 G 0.3 w 10 M 87.8205 182.8794 m S 0 g 1 w 4 M 87.8205 182.8794 m F 0 G 0.3 w 10 M 87.8205 182.8794 m S 87.8205 182.8794 m S 0 g 1 w 4 M 87.0214 182.0844 m 87.0214 179.4216 L 88.6196 179.4216 L 88.6196 182.0844 L 91.2601 182.0761 L 91.2601 183.6828 L 88.6196 183.6746 L 88.6196 186.3374 L 87.0214 186.3374 L 87.0214 183.6746 L 84.3809 183.6828 L 84.3809 182.0761 L 87.0214 182.0844 L f 0 G 0.3 w 10 M 72.5806 205.2938 m S 0 g 1 w 4 M 72.5806 205.2938 m F 0 G 0.3 w 10 M 72.5806 205.2938 m S 72.5806 205.2938 m S 72.5806 205.2938 m S 0 g 1 w 4 M 72.5806 205.2938 m F 0 G 0.3 w 10 M 72.5806 205.2938 m S 72.5806 205.2938 m S u 1 g 1 w 4 M 68.1544 205.2938 m 68.1544 202.8954 70.1361 200.9512 72.5806 200.9512 c 75.0251 200.9512 77.0068 202.8954 77.0068 205.2938 c F 77.0068 205.2938 m 77.0068 207.6921 75.0251 209.6364 72.5806 209.6364 c 70.1361 209.6364 68.1544 207.6921 68.1544 205.2938 c F 72.5806 205.2938 m F U 0 G 0.3 w 10 M 72.5806 205.2938 m S 0 g 1 w 4 M 72.5806 205.2938 m F 0 G 0.3 w 10 M 72.5806 205.2938 m S 72.5806 205.2938 m S 0 g 1 w 4 M 71.7815 204.4988 m 71.7815 201.836 L 73.3797 201.836 L 73.3797 204.4988 L 76.0202 204.4905 L 76.0202 206.0972 L 73.3797 206.089 L 73.3797 208.7518 L 71.7815 208.7518 L 71.7815 206.089 L 69.141 206.0972 L 69.141 204.4905 L 71.7815 204.4988 L f 0 G 0.3 w 10 M 100.3804 194.6859 m S 0 g 1 w 4 M 100.3804 194.6859 m F 0 G 0.3 w 10 M 100.3804 194.6859 m S 100.3804 194.6859 m S 100.3804 194.6859 m S 0 g 1 w 4 M 100.3804 194.6859 m F 0 G 0.3 w 10 M 100.3804 194.6859 m S 100.3804 194.6859 m S u 1 g 1 w 4 M 95.9542 194.6859 m 95.9542 192.2875 97.9359 190.3433 100.3804 190.3433 c 102.8249 190.3433 104.8066 192.2875 104.8066 194.6859 c F 104.8066 194.6859 m 104.8066 197.0842 102.8249 199.0285 100.3804 199.0285 c 97.9359 199.0285 95.9542 197.0842 95.9542 194.6859 c F 100.3804 194.6859 m F U 0 G 0.3 w 10 M 100.3804 194.6859 m S 0 g 1 w 4 M 100.3804 194.6859 m F 0 G 0.3 w 10 M 100.3804 194.6859 m S 100.3804 194.6859 m S 0 g 1 w 4 M 99.5813 193.8909 m 99.5813 191.2281 L 101.1795 191.2281 L 101.1795 193.8909 L 103.82 193.8826 L 103.82 195.4893 L 101.1795 195.4811 L 101.1795 198.1439 L 99.5813 198.1439 L 99.5813 195.4811 L 96.9408 195.4893 L 96.9408 193.8826 L 99.5813 193.8909 L f 0 G 0.3 w 10 M 93.3844 216.8322 m S 0 g 1 w 4 M 93.3844 216.8322 m F 0 G 0.3 w 10 M 93.3844 216.8322 m S 93.3844 216.8322 m S 93.3844 216.8322 m S 0 g 1 w 4 M 93.3844 216.8322 m F 0 G 0.3 w 10 M 93.3844 216.8322 m S 93.3844 216.8322 m S u 1 g 1 w 4 M 88.9583 216.8322 m 88.9583 214.4339 90.94 212.4896 93.3844 212.4896 c 95.8289 212.4896 97.8106 214.4339 97.8106 216.8322 c F 97.8106 216.8322 m 97.8106 219.2306 95.8289 221.1748 93.3844 221.1748 c 90.94 221.1748 88.9583 219.2306 88.9583 216.8322 c F 93.3844 216.8322 m F U 0 G 0.3 w 10 M 93.3844 216.8322 m S 0 g 1 w 4 M 93.3844 216.8322 m F 0 G 0.3 w 10 M 93.3844 216.8322 m S 93.3844 216.8322 m S 0 g 1 w 4 M 92.5853 216.0373 m 92.5853 213.3744 L 94.1835 213.3744 L 94.1835 216.0373 L 96.824 216.0289 L 96.824 217.6357 L 94.1835 217.6274 L 94.1835 220.2903 L 92.5853 220.2903 L 92.5853 217.6274 L 89.9448 217.6357 L 89.9448 216.0289 L 92.5853 216.0373 L f u 0 G 0.3 w 10 M 138.214 166.3321 m S 138.214 149.7848 m S 121.4162 149.7848 m S 121.4162 166.3321 m S 129.815 158.0584 m S U u 121.4162 182.8795 m S 121.4162 166.3321 m S 104.6183 166.3321 m S 104.6183 182.8795 m S 113.0172 174.6058 m S U u 138.214 182.8795 m S 138.214 166.3321 m S 121.4162 166.3321 m S 121.4162 182.8795 m S 129.815 174.6058 m S U u 121.4162 166.3321 m S 121.4162 149.7848 m S 104.6183 149.7848 m S 104.6183 166.3321 m S 113.0172 158.0584 m S U 0 g 1 w 4 M 129.815 158.0584 m F 0 G 0.3 w 10 M 155.0118 166.3321 m S 155.0118 149.7848 m S 155.0118 166.3321 m S u 155.0118 166.3321 m S 155.0118 149.7848 m S 138.214 149.7848 m S 138.214 166.3321 m S 146.6128 158.0584 m S U u 155.0118 182.8795 m S 155.0118 166.3321 m S 138.214 166.3321 m S 138.214 182.8795 m S 146.6128 174.6058 m S U 0 g 1 w 4 M 146.6128 158.0584 m F u 0 G 0.3 w 10 M 121.4162 133.2374 m S 121.4162 116.6901 m S 104.6183 116.6901 m S 104.6183 133.2374 m S 113.0172 124.9638 m S U u 121.4162 149.7848 m S 121.4162 133.2374 m S 104.6183 133.2374 m S 104.6183 149.7848 m S 113.0172 141.5111 m S U u 138.214 149.7848 m S 138.214 133.2374 m S 121.4162 133.2374 m S 121.4162 149.7848 m S 129.815 141.5111 m S U u 138.214 133.2374 m S 138.214 116.6901 m S 121.4162 116.6901 m S 121.4162 133.2374 m S 129.815 124.9638 m S U 0 g 1 w 4 M 129.815 141.5111 m F u 0 G 0.3 w 10 M 155.0118 149.7848 m S 155.0118 133.2374 m S 138.214 133.2374 m S 138.214 149.7848 m S 146.6128 141.5111 m S U 155.0118 133.2374 m S 155.0118 133.2374 m S 155.0118 149.7848 m S u 155.0118 133.2374 m S 155.0118 116.6901 m S 138.214 116.6901 m S 138.214 133.2374 m S 146.6128 124.9638 m S U 0 g 1 w 4 M 146.6128 141.5111 m F 0 G 0.3 w 10 M 122.4217 167.3763 m S 0 g 1 w 4 M 122.4217 167.3763 m F 0 G 0.3 w 10 M 122.4217 167.3763 m S 122.4217 167.3763 m S 122.4217 167.3763 m S 0 g 1 w 4 M 122.4217 167.3763 m F 0 G 0.3 w 10 M 122.4217 167.3763 m S 122.4217 167.3763 m S u 1 g 1 w 4 M 117.9956 167.3763 m 117.9956 164.978 119.9773 163.0337 122.4217 163.0337 c 124.8662 163.0337 126.8479 164.978 126.8479 167.3763 c F 126.8479 167.3763 m 126.8479 169.7747 124.8662 171.7189 122.4217 171.7189 c 119.9773 171.7189 117.9956 169.7747 117.9956 167.3763 c F 122.4217 167.3763 m F U 0 G 0.3 w 10 M 122.4217 167.3763 m S 0 g 1 w 4 M 122.4217 167.3763 m F 0 G 0.3 w 10 M 122.4217 167.3763 m S 122.4217 167.3763 m S 0 g 1 w 4 M 121.6227 166.5814 m 121.6227 163.9185 L 123.2208 163.9185 L 123.2208 166.5814 L 125.8614 166.573 L 125.8614 168.1798 L 123.2208 168.1715 L 123.2208 170.8344 L 121.6227 170.8344 L 121.6227 168.1715 L 118.9822 168.1798 L 118.9822 166.573 L 121.6227 166.5814 L f 0 G 0.3 w 10 M 153.7196 158.8155 m S 0 g 1 w 4 M 153.7196 158.8155 m F 0 G 0.3 w 10 M 153.7196 158.8155 m S 153.7196 158.8155 m S 153.7196 158.8155 m S 0 g 1 w 4 M 153.7196 158.8155 m F 0 G 0.3 w 10 M 153.7196 158.8155 m S 153.7196 158.8155 m S u 1 g 1 w 4 M 149.2934 158.8155 m 149.2934 156.4172 151.2751 154.4729 153.7196 154.4729 c 156.1641 154.4729 158.1458 156.4172 158.1458 158.8155 c F 158.1458 158.8155 m 158.1458 161.2139 156.1641 163.1582 153.7196 163.1582 c 151.2751 163.1582 149.2934 161.2139 149.2934 158.8155 c F 153.7196 158.8155 m F U 0 G 0.3 w 10 M 153.7196 158.8155 m S 0 g 1 w 4 M 153.7196 158.8155 m F 0 G 0.3 w 10 M 153.7196 158.8155 m S 153.7196 158.8155 m S 0 g 1 w 4 M 152.9205 158.0206 m 152.9205 155.3577 L 154.5187 155.3577 L 154.5187 158.0206 L 157.1592 158.0122 L 157.1592 159.619 L 154.5187 159.6107 L 154.5187 162.2736 L 152.9205 162.2736 L 152.9205 159.6107 L 150.28 159.619 L 150.28 158.0122 L 152.9205 158.0206 L f 0 G 0.3 w 10 M 138.214 149.7848 m S 0 g 1 w 4 M 138.214 149.7848 m F 0 G 0.3 w 10 M 138.214 149.7848 m S 138.214 149.7848 m S 138.214 149.7848 m S 0 g 1 w 4 M 138.214 149.7848 m F 0 G 0.3 w 10 M 138.214 149.7848 m S 138.214 149.7848 m S u 1 g 1 w 4 M 133.7878 149.7848 m 133.7878 147.3864 135.7695 145.4421 138.214 145.4421 c 140.6585 145.4421 142.6402 147.3864 142.6402 149.7848 c F 142.6402 149.7848 m 142.6402 152.1831 140.6585 154.1274 138.214 154.1274 c 135.7695 154.1274 133.7878 152.1831 133.7878 149.7848 c F 138.214 149.7848 m F U 0 G 0.3 w 10 M 138.214 149.7848 m S 0 g 1 w 4 M 138.214 149.7848 m F 0 G 0.3 w 10 M 138.214 149.7848 m S 138.214 149.7848 m S 0 g 1 w 4 M 137.4149 148.9898 m 137.4149 146.3269 L 139.0131 146.3269 L 139.0131 148.9898 L 141.6536 148.9815 L 141.6536 150.5882 L 139.0131 150.5799 L 139.0131 153.2428 L 137.4149 153.2428 L 137.4149 150.5799 L 134.7744 150.5882 L 134.7744 148.9815 L 137.4149 148.9898 L f 0 G 0.3 w 10 M 121.6853 141.8801 m S 0 g 1 w 4 M 121.6853 141.8801 m F 0 G 0.3 w 10 M 121.6853 141.8801 m S 121.6853 141.8801 m S 121.6853 141.8801 m S 0 g 1 w 4 M 121.6853 141.8801 m F 0 G 0.3 w 10 M 121.6853 141.8801 m S 121.6853 141.8801 m S u 1 g 1 w 4 M 117.2592 141.8801 m 117.2592 139.4817 119.2409 137.5375 121.6853 137.5375 c 124.1298 137.5375 126.1115 139.4817 126.1115 141.8801 c F 126.1115 141.8801 m 126.1115 144.2785 124.1298 146.2227 121.6853 146.2227 c 119.2409 146.2227 117.2592 144.2785 117.2592 141.8801 c F 121.6853 141.8801 m F U 0 G 0.3 w 10 M 121.6853 141.8801 m S 0 g 1 w 4 M 121.6853 141.8801 m F 0 G 0.3 w 10 M 121.6853 141.8801 m S 121.6853 141.8801 m S 0 g 1 w 4 M 120.8862 141.0851 m 120.8862 138.4223 L 122.4844 138.4223 L 122.4844 141.0851 L 125.1249 141.0768 L 125.1249 142.6835 L 122.4844 142.6753 L 122.4844 145.3381 L 120.8862 145.3381 L 120.8862 142.6753 L 118.2457 142.6835 L 118.2457 141.0768 L 120.8862 141.0851 L f 0 G 0.3 w 10 M 155.0118 133.2374 m S 0 g 1 w 4 M 155.0118 133.2374 m F 0 G 0.3 w 10 M 155.0118 133.2374 m S 155.0118 133.2374 m S 155.0118 133.2374 m S 0 g 1 w 4 M 155.0118 133.2374 m F 0 G 0.3 w 10 M 155.0118 133.2374 m S 155.0118 133.2374 m S u 1 g 1 w 4 M 150.5856 133.2374 m 150.5856 130.839 152.5673 128.8947 155.0118 128.8947 c 157.4562 128.8947 159.438 130.839 159.438 133.2374 c F 159.438 133.2374 m 159.438 135.6357 157.4562 137.58 155.0118 137.58 c 152.5673 137.58 150.5856 135.6357 150.5856 133.2374 c F 155.0118 133.2374 m F U 0 G 0.3 w 10 M 155.0118 133.2374 m S 0 g 1 w 4 M 155.0118 133.2374 m F 0 G 0.3 w 10 M 155.0118 133.2374 m S 155.0118 133.2374 m S 0 g 1 w 4 M 154.2127 132.4424 m 154.2127 129.7796 L 155.8109 129.7796 L 155.8109 132.4424 L 158.4514 132.4341 L 158.4514 134.0408 L 155.8109 134.0325 L 155.8109 136.6954 L 154.2127 136.6954 L 154.2127 134.0325 L 151.5722 134.0408 L 151.5722 132.4341 L 154.2127 132.4424 L f 0 G 0.3 w 10 M 138.214 133.2374 m S 0 g 1 w 4 M 138.214 133.2374 m F 0 G 0.3 w 10 M 138.214 133.2374 m S 138.214 133.2374 m S 138.214 133.2374 m S 0 g 1 w 4 M 138.214 133.2374 m F 0 G 0.3 w 10 M 138.214 133.2374 m S 138.214 133.2374 m S u 1 g 1 w 4 M 133.7878 133.2374 m 133.7878 130.839 135.7695 128.8947 138.214 128.8947 c 140.6585 128.8947 142.6402 130.839 142.6402 133.2374 c F 142.6402 133.2374 m 142.6402 135.6357 140.6585 137.58 138.214 137.58 c 135.7695 137.58 133.7878 135.6357 133.7878 133.2374 c F 138.214 133.2374 m F U 0 G 0.3 w 10 M 138.214 133.2374 m S 0 g 1 w 4 M 138.214 133.2374 m F 0 G 0.3 w 10 M 138.214 133.2374 m S 138.214 133.2374 m S 0 g 1 w 4 M 137.4149 132.4424 m 137.4149 129.7796 L 139.0131 129.7796 L 139.0131 132.4424 L 141.6536 132.4341 L 141.6536 134.0408 L 139.0131 134.0325 L 139.0131 136.6954 L 137.4149 136.6954 L 137.4149 134.0325 L 134.7744 134.0408 L 134.7744 132.4341 L 137.4149 132.4424 L f 0 G 0.3 w 10 M 122.9741 155.6518 m S 0 g 1 w 4 M 122.9741 155.6518 m F 0 G 0.3 w 10 M 122.9741 155.6518 m S 122.9741 155.6518 m S 122.9741 155.6518 m S 0 g 1 w 4 M 122.9741 155.6518 m F 0 G 0.3 w 10 M 122.9741 155.6518 m S 122.9741 155.6518 m S u 1 g 1 w 4 M 118.5479 155.6518 m 118.5479 153.2534 120.5296 151.3092 122.9741 151.3092 c 125.4185 151.3092 127.4002 153.2534 127.4002 155.6518 c F 127.4002 155.6518 m 127.4002 158.0501 125.4185 159.9944 122.9741 159.9944 c 120.5296 159.9944 118.5479 158.0501 118.5479 155.6518 c F 122.9741 155.6518 m F U 0 G 0.3 w 10 M 122.9741 155.6518 m S 0 g 1 w 4 M 122.9741 155.6518 m F 0 G 0.3 w 10 M 122.9741 155.6518 m S 122.9741 155.6518 m S 0 g 1 w 4 M 122.175 154.8568 m 122.175 152.194 L 123.7732 152.194 L 123.7732 154.8568 L 126.4137 154.8485 L 126.4137 156.4552 L 123.7732 156.447 L 123.7732 159.1098 L 122.175 159.1098 L 122.175 156.447 L 119.5345 156.4552 L 119.5345 154.8485 L 122.175 154.8568 L f 0 G 0.3 w 10 M 150.7739 145.0439 m S 0 g 1 w 4 M 150.7739 145.0439 m F 0 G 0.3 w 10 M 150.7739 145.0439 m S 150.7739 145.0439 m S 150.7739 145.0439 m S 0 g 1 w 4 M 150.7739 145.0439 m F 0 G 0.3 w 10 M 150.7739 145.0439 m S 150.7739 145.0439 m S u 1 g 1 w 4 M 146.3477 145.0439 m 146.3477 142.6455 148.3294 140.7012 150.7739 140.7012 c 153.2184 140.7012 155.2001 142.6455 155.2001 145.0439 c F 155.2001 145.0439 m 155.2001 147.4422 153.2184 149.3865 150.7739 149.3865 c 148.3294 149.3865 146.3477 147.4422 146.3477 145.0439 c F 150.7739 145.0439 m F U 0 G 0.3 w 10 M 150.7739 145.0439 m S 0 g 1 w 4 M 150.7739 145.0439 m F 0 G 0.3 w 10 M 150.7739 145.0439 m S 150.7739 145.0439 m S 0 g 1 w 4 M 149.9748 144.2489 m 149.9748 141.5861 L 151.573 141.5861 L 151.573 144.2489 L 154.2135 144.2406 L 154.2135 145.8473 L 151.573 145.839 L 151.573 148.5019 L 149.9748 148.5019 L 149.9748 145.839 L 147.3343 145.8473 L 147.3343 144.2406 L 149.9748 144.2489 L f 0 G 0.3 w 10 M 143.7779 167.1902 m S 0 g 1 w 4 M 143.7779 167.1902 m F 0 G 0.3 w 10 M 143.7779 167.1902 m S 143.7779 167.1902 m S 143.7779 167.1902 m S 0 g 1 w 4 M 143.7779 167.1902 m F 0 G 0.3 w 10 M 143.7779 167.1902 m S 143.7779 167.1902 m S u 1 g 1 w 4 M 139.3518 167.1902 m 139.3518 164.7919 141.3334 162.8476 143.7779 162.8476 c 146.2224 162.8476 148.2041 164.7919 148.2041 167.1902 c F 148.2041 167.1902 m 148.2041 169.5886 146.2224 171.5328 143.7779 171.5328 c 141.3334 171.5328 139.3518 169.5886 139.3518 167.1902 c F 143.7779 167.1902 m F U 0 G 0.3 w 10 M 143.7779 167.1902 m S 0 g 1 w 4 M 143.7779 167.1902 m F 0 G 0.3 w 10 M 143.7779 167.1902 m S 143.7779 167.1902 m S 0 g 1 w 4 M 142.9788 166.3953 m 142.9788 163.7324 L 144.577 163.7324 L 144.577 166.3953 L 147.2175 166.3869 L 147.2175 167.9937 L 144.577 167.9854 L 144.577 170.6483 L 142.9788 170.6483 L 142.9788 167.9854 L 140.3383 167.9937 L 140.3383 166.3869 L 142.9788 166.3953 L f u 0 G 0.3 w 10 M 188.6075 215.9741 m S 188.6075 199.4268 m S 171.8097 199.4268 m S 171.8097 215.9741 m S 180.2085 207.7004 m S U u 171.8097 232.5214 m S 171.8097 215.9741 m S 155.0118 215.9741 m S 155.0118 232.5214 m S 163.4107 224.2478 m S U u 188.6075 232.5214 m S 188.6075 215.9741 m S 171.8097 215.9741 m S 171.8097 232.5214 m S 180.2085 224.2478 m S U u 171.8097 215.9741 m S 171.8097 199.4268 m S 155.0118 199.4268 m S 155.0118 215.9741 m S 163.4107 207.7004 m S U 0 g 1 w 4 M 180.2085 207.7004 m F 0 G 0.3 w 10 M 205.4053 215.9741 m S 205.4053 199.4268 m S 205.4053 215.9741 m S u 205.4053 215.9741 m S 205.4053 199.4268 m S 188.6075 199.4268 m S 188.6075 215.9741 m S 197.0063 207.7004 m S U u 205.4053 232.5214 m S 205.4053 215.9741 m S 188.6075 215.9741 m S 188.6075 232.5214 m S 197.0063 224.2478 m S U 0 g 1 w 4 M 197.0063 207.7004 m F u 0 G 0.3 w 10 M 171.8097 182.8794 m S 171.8097 166.3321 m S 155.0118 166.3321 m S 155.0118 182.8794 m S 163.4107 174.6058 m S U u 171.8097 199.4268 m S 171.8097 182.8794 m S 155.0118 182.8794 m S 155.0118 199.4268 m S 163.4107 191.1531 m S U u 188.6075 199.4268 m S 188.6075 182.8794 m S 171.8097 182.8794 m S 171.8097 199.4268 m S 180.2085 191.1531 m S U u 188.6075 182.8794 m S 188.6075 166.3321 m S 171.8097 166.3321 m S 171.8097 182.8794 m S 180.2085 174.6058 m S U 0 g 1 w 4 M 180.2085 191.1531 m F u 0 G 0.3 w 10 M 205.4053 199.4268 m S 205.4053 182.8794 m S 188.6075 182.8794 m S 188.6075 199.4268 m S 197.0063 191.1531 m S U 205.4053 182.8794 m S 205.4053 182.8794 m S 205.4053 199.4268 m S u 205.4053 182.8794 m S 205.4053 166.3321 m S 188.6075 166.3321 m S 188.6075 182.8794 m S 197.0063 174.6058 m S U 0 g 1 w 4 M 197.0063 191.1531 m F 0 G 0.3 w 10 M 172.8152 217.0183 m S 0 g 1 w 4 M 172.8152 217.0183 m F 0 G 0.3 w 10 M 172.8152 217.0183 m S 172.8152 217.0183 m S 172.8152 217.0183 m S 0 g 1 w 4 M 172.8152 217.0183 m F 0 G 0.3 w 10 M 172.8152 217.0183 m S 172.8152 217.0183 m S u 1 g 1 w 4 M 168.3891 217.0183 m 168.3891 214.62 170.3708 212.6757 172.8152 212.6757 c 175.2597 212.6757 177.2414 214.62 177.2414 217.0183 c F 177.2414 217.0183 m 177.2414 219.4167 175.2597 221.3609 172.8152 221.3609 c 170.3708 221.3609 168.3891 219.4167 168.3891 217.0183 c F 172.8152 217.0183 m F U 0 G 0.3 w 10 M 172.8152 217.0183 m S 0 g 1 w 4 M 172.8152 217.0183 m F 0 G 0.3 w 10 M 172.8152 217.0183 m S 172.8152 217.0183 m S 0 g 1 w 4 M 172.0162 216.2234 m 172.0162 213.5605 L 173.6143 213.5605 L 173.6143 216.2234 L 176.2548 216.215 L 176.2548 217.8218 L 173.6143 217.8135 L 173.6143 220.4764 L 172.0162 220.4764 L 172.0162 217.8135 L 169.3757 217.8218 L 169.3757 216.215 L 172.0162 216.2234 L f 0 G 0.3 w 10 M 204.1131 208.4576 m S 0 g 1 w 4 M 204.1131 208.4576 m F 0 G 0.3 w 10 M 204.1131 208.4576 m S 204.1131 208.4576 m S 204.1131 208.4576 m S 0 g 1 w 4 M 204.1131 208.4576 m F 0 G 0.3 w 10 M 204.1131 208.4576 m S 204.1131 208.4576 m S u 1 g 1 w 4 M 199.6869 208.4576 m 199.6869 206.0592 201.6686 204.1149 204.1131 204.1149 c 206.5576 204.1149 208.5393 206.0592 208.5393 208.4576 c F 208.5393 208.4576 m 208.5393 210.8559 206.5576 212.8002 204.1131 212.8002 c 201.6686 212.8002 199.6869 210.8559 199.6869 208.4576 c F 204.1131 208.4576 m F U 0 G 0.3 w 10 M 204.1131 208.4576 m S 0 g 1 w 4 M 204.1131 208.4576 m F 0 G 0.3 w 10 M 204.1131 208.4576 m S 204.1131 208.4576 m S 0 g 1 w 4 M 203.314 207.6626 m 203.314 204.9998 L 204.9122 204.9998 L 204.9122 207.6626 L 207.5527 207.6543 L 207.5527 209.261 L 204.9122 209.2527 L 204.9122 211.9156 L 203.314 211.9156 L 203.314 209.2527 L 200.6735 209.261 L 200.6735 207.6543 L 203.314 207.6626 L f 0 G 0.3 w 10 M 188.6075 199.4268 m S 0 g 1 w 4 M 188.6075 199.4268 m F 0 G 0.3 w 10 M 188.6075 199.4268 m S 188.6075 199.4268 m S 188.6075 199.4268 m S 0 g 1 w 4 M 188.6075 199.4268 m F 0 G 0.3 w 10 M 188.6075 199.4268 m S 188.6075 199.4268 m S u 1 g 1 w 4 M 184.1813 199.4268 m 184.1813 197.0284 186.163 195.0841 188.6075 195.0841 c 191.0519 195.0841 193.0337 197.0284 193.0337 199.4268 c F 193.0337 199.4268 m 193.0337 201.8251 191.0519 203.7694 188.6075 203.7694 c 186.163 203.7694 184.1813 201.8251 184.1813 199.4268 c F 188.6075 199.4268 m F U 0 G 0.3 w 10 M 188.6075 199.4268 m S 0 g 1 w 4 M 188.6075 199.4268 m F 0 G 0.3 w 10 M 188.6075 199.4268 m S 188.6075 199.4268 m S 0 g 1 w 4 M 187.8084 198.6318 m 187.8084 195.9689 L 189.4066 195.9689 L 189.4066 198.6318 L 192.0471 198.6235 L 192.0471 200.2302 L 189.4066 200.2219 L 189.4066 202.8848 L 187.8084 202.8848 L 187.8084 200.2219 L 185.1679 200.2302 L 185.1679 198.6235 L 187.8084 198.6318 L f 0 G 0.3 w 10 M 172.0788 191.5221 m S 0 g 1 w 4 M 172.0788 191.5221 m F 0 G 0.3 w 10 M 172.0788 191.5221 m S 172.0788 191.5221 m S 172.0788 191.5221 m S 0 g 1 w 4 M 172.0788 191.5221 m F 0 G 0.3 w 10 M 172.0788 191.5221 m S 172.0788 191.5221 m S u 1 g 1 w 4 M 167.6526 191.5221 m 167.6526 189.1237 169.6344 187.1795 172.0788 187.1795 c 174.5233 187.1795 176.505 189.1237 176.505 191.5221 c F 176.505 191.5221 m 176.505 193.9205 174.5233 195.8647 172.0788 195.8647 c 169.6344 195.8647 167.6526 193.9205 167.6526 191.5221 c F 172.0788 191.5221 m F U 0 G 0.3 w 10 M 172.0788 191.5221 m S 0 g 1 w 4 M 172.0788 191.5221 m F 0 G 0.3 w 10 M 172.0788 191.5221 m S 172.0788 191.5221 m S 0 g 1 w 4 M 171.2797 190.7272 m 171.2797 188.0643 L 172.8779 188.0643 L 172.8779 190.7272 L 175.5184 190.7188 L 175.5184 192.3256 L 172.8779 192.3173 L 172.8779 194.9801 L 171.2797 194.9801 L 171.2797 192.3173 L 168.6392 192.3256 L 168.6392 190.7188 L 171.2797 190.7272 L f 0 G 0.3 w 10 M 205.4053 182.8794 m S 0 g 1 w 4 M 205.4053 182.8794 m F 0 G 0.3 w 10 M 205.4053 182.8794 m S 205.4053 182.8794 m S 205.4053 182.8794 m S 0 g 1 w 4 M 205.4053 182.8794 m F 0 G 0.3 w 10 M 205.4053 182.8794 m S 205.4053 182.8794 m S u 1 g 1 w 4 M 200.9791 182.8794 m 200.9791 180.481 202.9608 178.5367 205.4053 178.5367 c 207.8497 178.5367 209.8314 180.481 209.8314 182.8794 c F 209.8314 182.8794 m 209.8314 185.2777 207.8497 187.222 205.4053 187.222 c 202.9608 187.222 200.9791 185.2777 200.9791 182.8794 c F 205.4053 182.8794 m F U 0 G 0.3 w 10 M 205.4053 182.8794 m S 0 g 1 w 4 M 205.4053 182.8794 m F 0 G 0.3 w 10 M 205.4053 182.8794 m S 205.4053 182.8794 m S 0 g 1 w 4 M 204.6062 182.0844 m 204.6062 179.4216 L 206.2044 179.4216 L 206.2044 182.0844 L 208.8449 182.0761 L 208.8449 183.6828 L 206.2044 183.6746 L 206.2044 186.3374 L 204.6062 186.3374 L 204.6062 183.6746 L 201.9657 183.6828 L 201.9657 182.0761 L 204.6062 182.0844 L f 0 G 0.3 w 10 M 188.6075 182.8794 m S 0 g 1 w 4 M 188.6075 182.8794 m F 0 G 0.3 w 10 M 188.6075 182.8794 m S 188.6075 182.8794 m S 188.6075 182.8794 m S 0 g 1 w 4 M 188.6075 182.8794 m F 0 G 0.3 w 10 M 188.6075 182.8794 m S 188.6075 182.8794 m S u 1 g 1 w 4 M 184.1813 182.8794 m 184.1813 180.481 186.163 178.5367 188.6075 178.5367 c 191.0519 178.5367 193.0337 180.481 193.0337 182.8794 c F 193.0337 182.8794 m 193.0337 185.2777 191.0519 187.222 188.6075 187.222 c 186.163 187.222 184.1813 185.2777 184.1813 182.8794 c F 188.6075 182.8794 m F U 0 G 0.3 w 10 M 188.6075 182.8794 m S 0 g 1 w 4 M 188.6075 182.8794 m F 0 G 0.3 w 10 M 188.6075 182.8794 m S 188.6075 182.8794 m S 0 g 1 w 4 M 187.8084 182.0844 m 187.8084 179.4216 L 189.4066 179.4216 L 189.4066 182.0844 L 192.0471 182.0761 L 192.0471 183.6828 L 189.4066 183.6746 L 189.4066 186.3374 L 187.8084 186.3374 L 187.8084 183.6746 L 185.1679 183.6828 L 185.1679 182.0761 L 187.8084 182.0844 L f 0 G 0.3 w 10 M 173.3676 205.2938 m S 0 g 1 w 4 M 173.3676 205.2938 m F 0 G 0.3 w 10 M 173.3676 205.2938 m S 173.3676 205.2938 m S 173.3676 205.2938 m S 0 g 1 w 4 M 173.3676 205.2938 m F 0 G 0.3 w 10 M 173.3676 205.2938 m S 173.3676 205.2938 m S u 1 g 1 w 4 M 168.9414 205.2938 m 168.9414 202.8954 170.9231 200.9512 173.3676 200.9512 c 175.812 200.9512 177.7937 202.8954 177.7937 205.2938 c F 177.7937 205.2938 m 177.7937 207.6921 175.812 209.6364 173.3676 209.6364 c 170.9231 209.6364 168.9414 207.6921 168.9414 205.2938 c F 173.3676 205.2938 m F U 0 G 0.3 w 10 M 173.3676 205.2938 m S 0 g 1 w 4 M 173.3676 205.2938 m F 0 G 0.3 w 10 M 173.3676 205.2938 m S 173.3676 205.2938 m S 0 g 1 w 4 M 172.5685 204.4988 m 172.5685 201.836 L 174.1667 201.836 L 174.1667 204.4988 L 176.8072 204.4905 L 176.8072 206.0972 L 174.1667 206.089 L 174.1667 208.7518 L 172.5685 208.7518 L 172.5685 206.089 L 169.928 206.0972 L 169.928 204.4905 L 172.5685 204.4988 L f 0 G 0.3 w 10 M 201.1674 194.6859 m S 0 g 1 w 4 M 201.1674 194.6859 m F 0 G 0.3 w 10 M 201.1674 194.6859 m S 201.1674 194.6859 m S 201.1674 194.6859 m S 0 g 1 w 4 M 201.1674 194.6859 m F 0 G 0.3 w 10 M 201.1674 194.6859 m S 201.1674 194.6859 m S u 1 g 1 w 4 M 196.7412 194.6859 m 196.7412 192.2875 198.7229 190.3433 201.1674 190.3433 c 203.6119 190.3433 205.5936 192.2875 205.5936 194.6859 c F 205.5936 194.6859 m 205.5936 197.0842 203.6119 199.0285 201.1674 199.0285 c 198.7229 199.0285 196.7412 197.0842 196.7412 194.6859 c F 201.1674 194.6859 m F U 0 G 0.3 w 10 M 201.1674 194.6859 m S 0 g 1 w 4 M 201.1674 194.6859 m F 0 G 0.3 w 10 M 201.1674 194.6859 m S 201.1674 194.6859 m S 0 g 1 w 4 M 200.3683 193.8909 m 200.3683 191.2281 L 201.9665 191.2281 L 201.9665 193.8909 L 204.607 193.8826 L 204.607 195.4893 L 201.9665 195.4811 L 201.9665 198.1439 L 200.3683 198.1439 L 200.3683 195.4811 L 197.7278 195.4893 L 197.7278 193.8826 L 200.3683 193.8909 L f 0 G 0.3 w 10 M 194.1714 216.8322 m S 0 g 1 w 4 M 194.1714 216.8322 m F 0 G 0.3 w 10 M 194.1714 216.8322 m S 194.1714 216.8322 m S 194.1714 216.8322 m S 0 g 1 w 4 M 194.1714 216.8322 m F 0 G 0.3 w 10 M 194.1714 216.8322 m S 194.1714 216.8322 m S u 1 g 1 w 4 M 189.7452 216.8322 m 189.7452 214.4339 191.727 212.4896 194.1714 212.4896 c 196.6159 212.4896 198.5976 214.4339 198.5976 216.8322 c F 198.5976 216.8322 m 198.5976 219.2306 196.6159 221.1748 194.1714 221.1748 c 191.727 221.1748 189.7452 219.2306 189.7452 216.8322 c F 194.1714 216.8322 m F U 0 G 0.3 w 10 M 194.1714 216.8322 m S 0 g 1 w 4 M 194.1714 216.8322 m F 0 G 0.3 w 10 M 194.1714 216.8322 m S 194.1714 216.8322 m S 0 g 1 w 4 M 193.3723 216.0373 m 193.3723 213.3744 L 194.9705 213.3744 L 194.9705 216.0373 L 197.611 216.0289 L 197.611 217.6357 L 194.9705 217.6274 L 194.9705 220.2903 L 193.3723 220.2903 L 193.3723 217.6274 L 190.7318 217.6357 L 190.7318 216.0289 L 193.3723 216.0373 L f u 0 G 0.3 w 10 M 188.6075 116.6901 m S 188.6075 100.1427 m S 171.8097 100.1427 m S 171.8097 116.6901 m S 180.2085 108.4164 m S U u 171.8097 133.2374 m S 171.8097 116.6901 m S 155.0118 116.6901 m S 155.0118 133.2374 m S 163.4107 124.9638 m S U u 188.6075 133.2374 m S 188.6075 116.6901 m S 171.8097 116.6901 m S 171.8097 133.2374 m S 180.2085 124.9638 m S U u 171.8097 116.6901 m S 171.8097 100.1427 m S 155.0118 100.1427 m S 155.0118 116.6901 m S 163.4107 108.4164 m S U 0 g 1 w 4 M 180.2085 108.4164 m F 0 G 0.3 w 10 M 205.4053 116.6901 m S 205.4053 100.1427 m S 205.4053 116.6901 m S u 205.4053 116.6901 m S 205.4053 100.1427 m S 188.6075 100.1427 m S 188.6075 116.6901 m S 197.0063 108.4164 m S U u 205.4053 133.2374 m S 205.4053 116.6901 m S 188.6075 116.6901 m S 188.6075 133.2374 m S 197.0063 124.9638 m S U 0 g 1 w 4 M 197.0063 108.4164 m F u 0 G 0.3 w 10 M 171.8097 83.5954 m S 171.8097 67.048 m S 155.0118 67.048 m S 155.0118 83.5954 m S 163.4107 75.3218 m S U u 171.8097 100.1427 m S 171.8097 83.5954 m S 155.0118 83.5954 m S 155.0118 100.1427 m S 163.4107 91.8691 m S U u 188.6075 100.1427 m S 188.6075 83.5954 m S 171.8097 83.5954 m S 171.8097 100.1427 m S 180.2085 91.8691 m S U u 188.6075 83.5954 m S 188.6075 67.048 m S 171.8097 67.048 m S 171.8097 83.5954 m S 180.2085 75.3218 m S U 0 g 1 w 4 M 180.2085 91.8691 m F u 0 G 0.3 w 10 M 205.4053 100.1427 m S 205.4053 83.5954 m S 188.6075 83.5954 m S 188.6075 100.1427 m S 197.0063 91.8691 m S U 205.4053 83.5954 m S 205.4053 83.5954 m S 205.4053 100.1427 m S u 205.4053 83.5954 m S 205.4053 67.048 m S 188.6075 67.048 m S 188.6075 83.5954 m S 197.0063 75.3218 m S U 0 g 1 w 4 M 197.0063 91.8691 m F 0 G 0.3 w 10 M 172.8152 117.7343 m S 0 g 1 w 4 M 172.8152 117.7343 m F 0 G 0.3 w 10 M 172.8152 117.7343 m S 172.8152 117.7343 m S 172.8152 117.7343 m S 0 g 1 w 4 M 172.8152 117.7343 m F 0 G 0.3 w 10 M 172.8152 117.7343 m S 172.8152 117.7343 m S u 1 g 1 w 4 M 168.3891 117.7343 m 168.3891 115.336 170.3708 113.3917 172.8152 113.3917 c 175.2597 113.3917 177.2414 115.336 177.2414 117.7343 c F 177.2414 117.7343 m 177.2414 120.1327 175.2597 122.0769 172.8152 122.0769 c 170.3708 122.0769 168.3891 120.1327 168.3891 117.7343 c F 172.8152 117.7343 m F U 0 G 0.3 w 10 M 172.8152 117.7343 m S 0 g 1 w 4 M 172.8152 117.7343 m F 0 G 0.3 w 10 M 172.8152 117.7343 m S 172.8152 117.7343 m S 0 g 1 w 4 M 172.0162 116.9394 m 172.0162 114.2765 L 173.6143 114.2765 L 173.6143 116.9394 L 176.2548 116.931 L 176.2548 118.5378 L 173.6143 118.5295 L 173.6143 121.1924 L 172.0162 121.1924 L 172.0162 118.5295 L 169.3757 118.5378 L 169.3757 116.931 L 172.0162 116.9394 L f 0 G 0.3 w 10 M 204.1131 109.1735 m S 0 g 1 w 4 M 204.1131 109.1735 m F 0 G 0.3 w 10 M 204.1131 109.1735 m S 204.1131 109.1735 m S 204.1131 109.1735 m S 0 g 1 w 4 M 204.1131 109.1735 m F 0 G 0.3 w 10 M 204.1131 109.1735 m S 204.1131 109.1735 m S u 1 g 1 w 4 M 199.6869 109.1735 m 199.6869 106.7752 201.6686 104.8309 204.1131 104.8309 c 206.5576 104.8309 208.5393 106.7752 208.5393 109.1735 c F 208.5393 109.1735 m 208.5393 111.5719 206.5576 113.5162 204.1131 113.5162 c 201.6686 113.5162 199.6869 111.5719 199.6869 109.1735 c F 204.1131 109.1735 m F U 0 G 0.3 w 10 M 204.1131 109.1735 m S 0 g 1 w 4 M 204.1131 109.1735 m F 0 G 0.3 w 10 M 204.1131 109.1735 m S 204.1131 109.1735 m S 0 g 1 w 4 M 203.314 108.3786 m 203.314 105.7157 L 204.9122 105.7157 L 204.9122 108.3786 L 207.5527 108.3703 L 207.5527 109.977 L 204.9122 109.9687 L 204.9122 112.6316 L 203.314 112.6316 L 203.314 109.9687 L 200.6735 109.977 L 200.6735 108.3703 L 203.314 108.3786 L f 0 G 0.3 w 10 M 188.6075 100.1427 m S 0 g 1 w 4 M 188.6075 100.1427 m F 0 G 0.3 w 10 M 188.6075 100.1427 m S 188.6075 100.1427 m S 188.6075 100.1427 m S 0 g 1 w 4 M 188.6075 100.1427 m F 0 G 0.3 w 10 M 188.6075 100.1427 m S 188.6075 100.1427 m S u 1 g 1 w 4 M 184.1813 100.1427 m 184.1813 97.7444 186.163 95.8001 188.6075 95.8001 c 191.0519 95.8001 193.0337 97.7444 193.0337 100.1427 c F 193.0337 100.1427 m 193.0337 102.5411 191.0519 104.4854 188.6075 104.4854 c 186.163 104.4854 184.1813 102.5411 184.1813 100.1427 c F 188.6075 100.1427 m F U 0 G 0.3 w 10 M 188.6075 100.1427 m S 0 g 1 w 4 M 188.6075 100.1427 m F 0 G 0.3 w 10 M 188.6075 100.1427 m S 188.6075 100.1427 m S 0 g 1 w 4 M 187.8084 99.3478 m 187.8084 96.6849 L 189.4066 96.6849 L 189.4066 99.3478 L 192.0471 99.3394 L 192.0471 100.9462 L 189.4066 100.9379 L 189.4066 103.6008 L 187.8084 103.6008 L 187.8084 100.9379 L 185.1679 100.9462 L 185.1679 99.3394 L 187.8084 99.3478 L f 0 G 0.3 w 10 M 172.0788 92.2381 m S 0 g 1 w 4 M 172.0788 92.2381 m F 0 G 0.3 w 10 M 172.0788 92.2381 m S 172.0788 92.2381 m S 172.0788 92.2381 m S 0 g 1 w 4 M 172.0788 92.2381 m F 0 G 0.3 w 10 M 172.0788 92.2381 m S 172.0788 92.2381 m S u 1 g 1 w 4 M 167.6526 92.2381 m 167.6526 89.8397 169.6344 87.8955 172.0788 87.8955 c 174.5233 87.8955 176.505 89.8397 176.505 92.2381 c F 176.505 92.2381 m 176.505 94.6365 174.5233 96.5807 172.0788 96.5807 c 169.6344 96.5807 167.6526 94.6365 167.6526 92.2381 c F 172.0788 92.2381 m F U 0 G 0.3 w 10 M 172.0788 92.2381 m S 0 g 1 w 4 M 172.0788 92.2381 m F 0 G 0.3 w 10 M 172.0788 92.2381 m S 172.0788 92.2381 m S 0 g 1 w 4 M 171.2797 91.4431 m 171.2797 88.7803 L 172.8779 88.7803 L 172.8779 91.4431 L 175.5184 91.4348 L 175.5184 93.0415 L 172.8779 93.0333 L 172.8779 95.6961 L 171.2797 95.6961 L 171.2797 93.0333 L 168.6392 93.0415 L 168.6392 91.4348 L 171.2797 91.4431 L f 0 G 0.3 w 10 M 205.4053 83.5954 m S 0 g 1 w 4 M 205.4053 83.5954 m F 0 G 0.3 w 10 M 205.4053 83.5954 m S 205.4053 83.5954 m S 205.4053 83.5954 m S 0 g 1 w 4 M 205.4053 83.5954 m F 0 G 0.3 w 10 M 205.4053 83.5954 m S 205.4053 83.5954 m S u 1 g 1 w 4 M 200.9791 83.5954 m 200.9791 81.197 202.9608 79.2527 205.4053 79.2527 c 207.8497 79.2527 209.8314 81.197 209.8314 83.5954 c F 209.8314 83.5954 m 209.8314 85.9937 207.8497 87.938 205.4053 87.938 c 202.9608 87.938 200.9791 85.9937 200.9791 83.5954 c F 205.4053 83.5954 m F U 0 G 0.3 w 10 M 205.4053 83.5954 m S 0 g 1 w 4 M 205.4053 83.5954 m F 0 G 0.3 w 10 M 205.4053 83.5954 m S 205.4053 83.5954 m S 0 g 1 w 4 M 204.6062 82.8004 m 204.6062 80.1376 L 206.2044 80.1376 L 206.2044 82.8004 L 208.8449 82.7921 L 208.8449 84.3988 L 206.2044 84.3905 L 206.2044 87.0534 L 204.6062 87.0534 L 204.6062 84.3905 L 201.9657 84.3988 L 201.9657 82.7921 L 204.6062 82.8004 L f 0 G 0.3 w 10 M 188.6075 83.5954 m S 0 g 1 w 4 M 188.6075 83.5954 m F 0 G 0.3 w 10 M 188.6075 83.5954 m S 188.6075 83.5954 m S 188.6075 83.5954 m S 0 g 1 w 4 M 188.6075 83.5954 m F 0 G 0.3 w 10 M 188.6075 83.5954 m S 188.6075 83.5954 m S u 1 g 1 w 4 M 184.1813 83.5954 m 184.1813 81.197 186.163 79.2527 188.6075 79.2527 c 191.0519 79.2527 193.0337 81.197 193.0337 83.5954 c F 193.0337 83.5954 m 193.0337 85.9937 191.0519 87.938 188.6075 87.938 c 186.163 87.938 184.1813 85.9937 184.1813 83.5954 c F 188.6075 83.5954 m F U 0 G 0.3 w 10 M 188.6075 83.5954 m S 0 g 1 w 4 M 188.6075 83.5954 m F 0 G 0.3 w 10 M 188.6075 83.5954 m S 188.6075 83.5954 m S 0 g 1 w 4 M 187.8084 82.8004 m 187.8084 80.1376 L 189.4066 80.1376 L 189.4066 82.8004 L 192.0471 82.7921 L 192.0471 84.3988 L 189.4066 84.3905 L 189.4066 87.0534 L 187.8084 87.0534 L 187.8084 84.3905 L 185.1679 84.3988 L 185.1679 82.7921 L 187.8084 82.8004 L f 0 G 0.3 w 10 M 173.3676 106.0098 m S 0 g 1 w 4 M 173.3676 106.0098 m F 0 G 0.3 w 10 M 173.3676 106.0098 m S 173.3676 106.0098 m S 173.3676 106.0098 m S 0 g 1 w 4 M 173.3676 106.0098 m F 0 G 0.3 w 10 M 173.3676 106.0098 m S 173.3676 106.0098 m S u 1 g 1 w 4 M 168.9414 106.0098 m 168.9414 103.6114 170.9231 101.6672 173.3676 101.6672 c 175.812 101.6672 177.7937 103.6114 177.7937 106.0098 c F 177.7937 106.0098 m 177.7937 108.4081 175.812 110.3524 173.3676 110.3524 c 170.9231 110.3524 168.9414 108.4081 168.9414 106.0098 c F 173.3676 106.0098 m F U 0 G 0.3 w 10 M 173.3676 106.0098 m S 0 g 1 w 4 M 173.3676 106.0098 m F 0 G 0.3 w 10 M 173.3676 106.0098 m S 173.3676 106.0098 m S 0 g 1 w 4 M 172.5685 105.2148 m 172.5685 102.552 L 174.1667 102.552 L 174.1667 105.2148 L 176.8072 105.2065 L 176.8072 106.8132 L 174.1667 106.805 L 174.1667 109.4678 L 172.5685 109.4678 L 172.5685 106.805 L 169.928 106.8132 L 169.928 105.2065 L 172.5685 105.2148 L f 0 G 0.3 w 10 M 201.1674 95.4019 m S 0 g 1 w 4 M 201.1674 95.4019 m F 0 G 0.3 w 10 M 201.1674 95.4019 m S 201.1674 95.4019 m S 201.1674 95.4019 m S 0 g 1 w 4 M 201.1674 95.4019 m F 0 G 0.3 w 10 M 201.1674 95.4019 m S 201.1674 95.4019 m S u 1 g 1 w 4 M 196.7412 95.4019 m 196.7412 93.0035 198.7229 91.0592 201.1674 91.0592 c 203.6119 91.0592 205.5936 93.0035 205.5936 95.4019 c F 205.5936 95.4019 m 205.5936 97.8002 203.6119 99.7445 201.1674 99.7445 c 198.7229 99.7445 196.7412 97.8002 196.7412 95.4019 c F 201.1674 95.4019 m F U 0 G 0.3 w 10 M 201.1674 95.4019 m S 0 g 1 w 4 M 201.1674 95.4019 m F 0 G 0.3 w 10 M 201.1674 95.4019 m S 201.1674 95.4019 m S 0 g 1 w 4 M 200.3683 94.6069 m 200.3683 91.944 L 201.9665 91.944 L 201.9665 94.6069 L 204.607 94.5986 L 204.607 96.2053 L 201.9665 96.197 L 201.9665 98.8599 L 200.3683 98.8599 L 200.3683 96.197 L 197.7278 96.2053 L 197.7278 94.5986 L 200.3683 94.6069 L f 0 G 0.3 w 10 M 194.1714 117.5482 m S 0 g 1 w 4 M 194.1714 117.5482 m F 0 G 0.3 w 10 M 194.1714 117.5482 m S 194.1714 117.5482 m S 194.1714 117.5482 m S 0 g 1 w 4 M 194.1714 117.5482 m F 0 G 0.3 w 10 M 194.1714 117.5482 m S 194.1714 117.5482 m S u 1 g 1 w 4 M 189.7452 117.5482 m 189.7452 115.1499 191.727 113.2056 194.1714 113.2056 c 196.6159 113.2056 198.5976 115.1499 198.5976 117.5482 c F 198.5976 117.5482 m 198.5976 119.9466 196.6159 121.8908 194.1714 121.8908 c 191.727 121.8908 189.7452 119.9466 189.7452 117.5482 c F 194.1714 117.5482 m F U 0 G 0.3 w 10 M 194.1714 117.5482 m S 0 g 1 w 4 M 194.1714 117.5482 m F 0 G 0.3 w 10 M 194.1714 117.5482 m S 194.1714 117.5482 m S 0 g 1 w 4 M 193.3723 116.7532 m 193.3723 114.0904 L 194.9705 114.0904 L 194.9705 116.7532 L 197.611 116.7449 L 197.611 118.3517 L 194.9705 118.3434 L 194.9705 121.0063 L 193.3723 121.0063 L 193.3723 118.3434 L 190.7318 118.3517 L 190.7318 116.7449 L 193.3723 116.7532 L f u 0 G 0.3 w 10 M 87.8205 116.6901 m S 87.8205 100.1427 m S 71.0227 100.1427 m S 71.0227 116.6901 m S 79.4216 108.4164 m S U u 71.0227 133.2374 m S 71.0227 116.6901 m S 54.2248 116.6901 m S 54.2248 133.2374 m S 62.6237 124.9638 m S U u 87.8205 133.2374 m S 87.8205 116.6901 m S 71.0227 116.6901 m S 71.0227 133.2374 m S 79.4216 124.9638 m S U u 71.0227 116.6901 m S 71.0227 100.1427 m S 54.2248 100.1427 m S 54.2248 116.6901 m S 62.6237 108.4164 m S U 0 g 1 w 4 M 79.4216 108.4164 m F 0 G 0.3 w 10 M 104.6183 116.6901 m S 104.6183 100.1427 m S 104.6183 116.6901 m S u 104.6183 116.6901 m S 104.6183 100.1427 m S 87.8205 100.1427 m S 87.8205 116.6901 m S 96.2194 108.4164 m S U u 104.6183 133.2374 m S 104.6183 116.6901 m S 87.8205 116.6901 m S 87.8205 133.2374 m S 96.2194 124.9638 m S U 0 g 1 w 4 M 96.2194 108.4164 m F u 0 G 0.3 w 10 M 71.0227 83.5954 m S 71.0227 67.048 m S 54.2248 67.048 m S 54.2248 83.5954 m S 62.6237 75.3218 m S U u 71.0227 100.1427 m S 71.0227 83.5954 m S 54.2248 83.5954 m S 54.2248 100.1427 m S 62.6237 91.8691 m S U u 87.8205 100.1427 m S 87.8205 83.5954 m S 71.0227 83.5954 m S 71.0227 100.1427 m S 79.4216 91.8691 m S U u 87.8205 83.5954 m S 87.8205 67.048 m S 71.0227 67.048 m S 71.0227 83.5954 m S 79.4216 75.3218 m S U 0 g 1 w 4 M 79.4216 91.8691 m F u 0 G 0.3 w 10 M 104.6183 100.1427 m S 104.6183 83.5954 m S 87.8205 83.5954 m S 87.8205 100.1427 m S 96.2194 91.8691 m S U 104.6183 83.5954 m S 104.6183 83.5954 m S 104.6183 100.1427 m S u 104.6183 83.5954 m S 104.6183 67.048 m S 87.8205 67.048 m S 87.8205 83.5954 m S 96.2194 75.3218 m S U 0 g 1 w 4 M 96.2194 91.8691 m F 0 G 0.3 w 10 M 72.0283 117.7343 m S 0 g 1 w 4 M 72.0283 117.7343 m F 0 G 0.3 w 10 M 72.0283 117.7343 m S 72.0283 117.7343 m S 72.0283 117.7343 m S 0 g 1 w 4 M 72.0283 117.7343 m F 0 G 0.3 w 10 M 72.0283 117.7343 m S 72.0283 117.7343 m S u 1 g 1 w 4 M 67.6021 117.7343 m 67.6021 115.336 69.5838 113.3917 72.0283 113.3917 c 74.4727 113.3917 76.4544 115.336 76.4544 117.7343 c F 76.4544 117.7343 m 76.4544 120.1327 74.4727 122.0769 72.0283 122.0769 c 69.5838 122.0769 67.6021 120.1327 67.6021 117.7343 c F 72.0283 117.7343 m F U 0 G 0.3 w 10 M 72.0283 117.7343 m S 0 g 1 w 4 M 72.0283 117.7343 m F 0 G 0.3 w 10 M 72.0283 117.7343 m S 72.0283 117.7343 m S 0 g 1 w 4 M 71.2292 116.9394 m 71.2292 114.2765 L 72.8274 114.2765 L 72.8274 116.9394 L 75.4678 116.931 L 75.4678 118.5378 L 72.8274 118.5295 L 72.8274 121.1924 L 71.2292 121.1924 L 71.2292 118.5295 L 68.5887 118.5378 L 68.5887 116.931 L 71.2292 116.9394 L f 0 G 0.3 w 10 M 103.3261 109.1735 m S 0 g 1 w 4 M 103.3261 109.1735 m F 0 G 0.3 w 10 M 103.3261 109.1735 m S 103.3261 109.1735 m S 103.3261 109.1735 m S 0 g 1 w 4 M 103.3261 109.1735 m F 0 G 0.3 w 10 M 103.3261 109.1735 m S 103.3261 109.1735 m S u 1 g 1 w 4 M 98.8999 109.1735 m 98.8999 106.7752 100.8816 104.8309 103.3261 104.8309 c 105.7706 104.8309 107.7523 106.7752 107.7523 109.1735 c F 107.7523 109.1735 m 107.7523 111.5719 105.7706 113.5162 103.3261 113.5162 c 100.8816 113.5162 98.8999 111.5719 98.8999 109.1735 c F 103.3261 109.1735 m F U 0 G 0.3 w 10 M 103.3261 109.1735 m S 0 g 1 w 4 M 103.3261 109.1735 m F 0 G 0.3 w 10 M 103.3261 109.1735 m S 103.3261 109.1735 m S 0 g 1 w 4 M 102.527 108.3786 m 102.527 105.7157 L 104.1252 105.7157 L 104.1252 108.3786 L 106.7657 108.3703 L 106.7657 109.977 L 104.1252 109.9687 L 104.1252 112.6316 L 102.527 112.6316 L 102.527 109.9687 L 99.8865 109.977 L 99.8865 108.3703 L 102.527 108.3786 L f 0 G 0.3 w 10 M 87.8205 100.1427 m S 0 g 1 w 4 M 87.8205 100.1427 m F 0 G 0.3 w 10 M 87.8205 100.1427 m S 87.8205 100.1427 m S 87.8205 100.1427 m S 0 g 1 w 4 M 87.8205 100.1427 m F 0 G 0.3 w 10 M 87.8205 100.1427 m S 87.8205 100.1427 m S u 1 g 1 w 4 M 83.3943 100.1427 m 83.3943 97.7444 85.376 95.8001 87.8205 95.8001 c 90.265 95.8001 92.2467 97.7444 92.2467 100.1427 c F 92.2467 100.1427 m 92.2467 102.5411 90.265 104.4854 87.8205 104.4854 c 85.376 104.4854 83.3943 102.5411 83.3943 100.1427 c F 87.8205 100.1427 m F U 0 G 0.3 w 10 M 87.8205 100.1427 m S 0 g 1 w 4 M 87.8205 100.1427 m F 0 G 0.3 w 10 M 87.8205 100.1427 m S 87.8205 100.1427 m S 0 g 1 w 4 M 87.0214 99.3478 m 87.0214 96.6849 L 88.6196 96.6849 L 88.6196 99.3478 L 91.2601 99.3394 L 91.2601 100.9462 L 88.6196 100.9379 L 88.6196 103.6008 L 87.0214 103.6008 L 87.0214 100.9379 L 84.3809 100.9462 L 84.3809 99.3394 L 87.0214 99.3478 L f 0 G 0.3 w 10 M 71.2919 92.2381 m S 0 g 1 w 4 M 71.2919 92.2381 m F 0 G 0.3 w 10 M 71.2919 92.2381 m S 71.2919 92.2381 m S 71.2919 92.2381 m S 0 g 1 w 4 M 71.2919 92.2381 m F 0 G 0.3 w 10 M 71.2919 92.2381 m S 71.2919 92.2381 m S u 1 g 1 w 4 M 66.8657 92.2381 m 66.8657 89.8397 68.8474 87.8955 71.2919 87.8955 c 73.7363 87.8955 75.718 89.8397 75.718 92.2381 c F 75.718 92.2381 m 75.718 94.6365 73.7363 96.5807 71.2919 96.5807 c 68.8474 96.5807 66.8657 94.6365 66.8657 92.2381 c F 71.2919 92.2381 m F U 0 G 0.3 w 10 M 71.2919 92.2381 m S 0 g 1 w 4 M 71.2919 92.2381 m F 0 G 0.3 w 10 M 71.2919 92.2381 m S 71.2919 92.2381 m S 0 g 1 w 4 M 70.4927 91.4431 m 70.4927 88.7803 L 72.0909 88.7803 L 72.0909 91.4431 L 74.7314 91.4348 L 74.7314 93.0415 L 72.0909 93.0333 L 72.0909 95.6961 L 70.4927 95.6961 L 70.4927 93.0333 L 67.8522 93.0415 L 67.8522 91.4348 L 70.4927 91.4431 L f 0 G 0.3 w 10 M 104.6183 83.5954 m S 0 g 1 w 4 M 104.6183 83.5954 m F 0 G 0.3 w 10 M 104.6183 83.5954 m S 104.6183 83.5954 m S 104.6183 83.5954 m S 0 g 1 w 4 M 104.6183 83.5954 m F 0 G 0.3 w 10 M 104.6183 83.5954 m S 104.6183 83.5954 m S u 1 g 1 w 4 M 100.1921 83.5954 m 100.1921 81.197 102.1738 79.2527 104.6183 79.2527 c 107.0628 79.2527 109.0445 81.197 109.0445 83.5954 c F 109.0445 83.5954 m 109.0445 85.9937 107.0628 87.938 104.6183 87.938 c 102.1738 87.938 100.1921 85.9937 100.1921 83.5954 c F 104.6183 83.5954 m F U 0 G 0.3 w 10 M 104.6183 83.5954 m S 0 g 1 w 4 M 104.6183 83.5954 m F 0 G 0.3 w 10 M 104.6183 83.5954 m S 104.6183 83.5954 m S 0 g 1 w 4 M 103.8192 82.8004 m 103.8192 80.1376 L 105.4174 80.1376 L 105.4174 82.8004 L 108.0579 82.7921 L 108.0579 84.3988 L 105.4174 84.3905 L 105.4174 87.0534 L 103.8192 87.0534 L 103.8192 84.3905 L 101.1787 84.3988 L 101.1787 82.7921 L 103.8192 82.8004 L f 0 G 0.3 w 10 M 87.8205 83.5954 m S 0 g 1 w 4 M 87.8205 83.5954 m F 0 G 0.3 w 10 M 87.8205 83.5954 m S 87.8205 83.5954 m S 87.8205 83.5954 m S 0 g 1 w 4 M 87.8205 83.5954 m F 0 G 0.3 w 10 M 87.8205 83.5954 m S 87.8205 83.5954 m S u 1 g 1 w 4 M 83.3943 83.5954 m 83.3943 81.197 85.376 79.2527 87.8205 79.2527 c 90.265 79.2527 92.2467 81.197 92.2467 83.5954 c F 92.2467 83.5954 m 92.2467 85.9937 90.265 87.938 87.8205 87.938 c 85.376 87.938 83.3943 85.9937 83.3943 83.5954 c F 87.8205 83.5954 m F U 0 G 0.3 w 10 M 87.8205 83.5954 m S 0 g 1 w 4 M 87.8205 83.5954 m F 0 G 0.3 w 10 M 87.8205 83.5954 m S 87.8205 83.5954 m S 0 g 1 w 4 M 87.0214 82.8004 m 87.0214 80.1376 L 88.6196 80.1376 L 88.6196 82.8004 L 91.2601 82.7921 L 91.2601 84.3988 L 88.6196 84.3905 L 88.6196 87.0534 L 87.0214 87.0534 L 87.0214 84.3905 L 84.3809 84.3988 L 84.3809 82.7921 L 87.0214 82.8004 L f 0 G 0.3 w 10 M 72.5806 106.0098 m S 0 g 1 w 4 M 72.5806 106.0098 m F 0 G 0.3 w 10 M 72.5806 106.0098 m S 72.5806 106.0098 m S 72.5806 106.0098 m S 0 g 1 w 4 M 72.5806 106.0098 m F 0 G 0.3 w 10 M 72.5806 106.0098 m S 72.5806 106.0098 m S u 1 g 1 w 4 M 68.1544 106.0098 m 68.1544 103.6114 70.1361 101.6672 72.5806 101.6672 c 75.0251 101.6672 77.0068 103.6114 77.0068 106.0098 c F 77.0068 106.0098 m 77.0068 108.4081 75.0251 110.3524 72.5806 110.3524 c 70.1361 110.3524 68.1544 108.4081 68.1544 106.0098 c F 72.5806 106.0098 m F U 0 G 0.3 w 10 M 72.5806 106.0098 m S 0 g 1 w 4 M 72.5806 106.0098 m F 0 G 0.3 w 10 M 72.5806 106.0098 m S 72.5806 106.0098 m S 0 g 1 w 4 M 71.7815 105.2148 m 71.7815 102.552 L 73.3797 102.552 L 73.3797 105.2148 L 76.0202 105.2065 L 76.0202 106.8132 L 73.3797 106.805 L 73.3797 109.4678 L 71.7815 109.4678 L 71.7815 106.805 L 69.141 106.8132 L 69.141 105.2065 L 71.7815 105.2148 L f 0 G 0.3 w 10 M 100.3804 95.4019 m S 0 g 1 w 4 M 100.3804 95.4019 m F 0 G 0.3 w 10 M 100.3804 95.4019 m S 100.3804 95.4019 m S 100.3804 95.4019 m S 0 g 1 w 4 M 100.3804 95.4019 m F 0 G 0.3 w 10 M 100.3804 95.4019 m S 100.3804 95.4019 m S u 1 g 1 w 4 M 95.9542 95.4019 m 95.9542 93.0035 97.9359 91.0592 100.3804 91.0592 c 102.8249 91.0592 104.8066 93.0035 104.8066 95.4019 c F 104.8066 95.4019 m 104.8066 97.8002 102.8249 99.7445 100.3804 99.7445 c 97.9359 99.7445 95.9542 97.8002 95.9542 95.4019 c F 100.3804 95.4019 m F U 0 G 0.3 w 10 M 100.3804 95.4019 m S 0 g 1 w 4 M 100.3804 95.4019 m F 0 G 0.3 w 10 M 100.3804 95.4019 m S 100.3804 95.4019 m S 0 g 1 w 4 M 99.5813 94.6069 m 99.5813 91.944 L 101.1795 91.944 L 101.1795 94.6069 L 103.82 94.5986 L 103.82 96.2053 L 101.1795 96.197 L 101.1795 98.8599 L 99.5813 98.8599 L 99.5813 96.197 L 96.9408 96.2053 L 96.9408 94.5986 L 99.5813 94.6069 L f 0 G 0.3 w 10 M 93.3844 117.5482 m S 0 g 1 w 4 M 93.3844 117.5482 m F 0 G 0.3 w 10 M 93.3844 117.5482 m S 93.3844 117.5482 m S 93.3844 117.5482 m S 0 g 1 w 4 M 93.3844 117.5482 m F 0 G 0.3 w 10 M 93.3844 117.5482 m S 93.3844 117.5482 m S u 1 g 1 w 4 M 88.9583 117.5482 m 88.9583 115.1499 90.94 113.2056 93.3844 113.2056 c 95.8289 113.2056 97.8106 115.1499 97.8106 117.5482 c F 97.8106 117.5482 m 97.8106 119.9466 95.8289 121.8908 93.3844 121.8908 c 90.94 121.8908 88.9583 119.9466 88.9583 117.5482 c F 93.3844 117.5482 m F U 0 G 0.3 w 10 M 93.3844 117.5482 m S 0 g 1 w 4 M 93.3844 117.5482 m F 0 G 0.3 w 10 M 93.3844 117.5482 m S 93.3844 117.5482 m S 0 g 1 w 4 M 92.5853 116.7532 m 92.5853 114.0904 L 94.1835 114.0904 L 94.1835 116.7532 L 96.824 116.7449 L 96.824 118.3517 L 94.1835 118.3434 L 94.1835 121.0063 L 92.5853 121.0063 L 92.5853 118.3434 L 89.9448 118.3517 L 89.9448 116.7449 L 92.5853 116.7532 L f u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 131 35.5]e (\(a\))t T U U showpage _E end %%EndDocument @endspecial 243 1411 a @beginspecial 35 @llx 31.500000 @lly 498 @urx 177.500000 @ury 3513 @rwi @setspecial %%BeginDocument: fig7b.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 152.2621 136.9425 m S 152.2621 118.3605 m S 152.2621 174.1067 m S 152.2621 155.5247 m S 152.2621 155.5247 m S 152.2621 136.9425 m S 171.2944 174.1067 m S 171.2944 155.5247 m S 152.2621 155.5247 m S 152.2621 174.1067 m S 161.7782 164.8157 m S 209.3591 136.9425 m S 209.3591 118.3605 m S 190.3268 118.3605 m S 190.3268 136.9425 m S 199.8429 127.6515 m S 190.3268 155.5247 m S 190.3268 136.9425 m S 171.2944 136.9425 m S 171.2944 155.5247 m S 180.8106 146.2336 m S 190.3268 174.1067 m S 190.3268 155.5247 m S 171.2944 155.5247 m S 171.2944 174.1067 m S 180.8106 164.8157 m S 209.3591 174.1067 m S 209.3591 155.5247 m S 190.3268 155.5247 m S 190.3268 174.1067 m S 199.8429 164.8157 m S 209.3591 155.5247 m S 209.3591 136.9425 m S 190.3268 136.9425 m S 190.3268 155.5247 m S 199.8429 146.2336 m S 190.3268 136.9425 m S 190.3268 118.3605 m S 171.2944 118.3605 m S 171.2944 136.9425 m S 180.8106 127.6515 m S 171.2944 136.9425 m S 171.2944 118.3605 m S 152.2621 118.3605 m S 152.2621 136.9425 m S 161.7782 127.6515 m S 171.2944 155.5247 m S 171.2944 136.9425 m S 152.2621 136.9425 m S 152.2621 155.5247 m S 161.7782 146.2336 m S 0 g 1 w 4 M 161.7782 164.8157 m F 199.8429 164.8157 m F 161.7782 127.6515 m F 199.8429 127.6515 m F 0 G 0.3 w 10 M 228.3914 174.1067 m S 228.3914 155.5247 m S 209.3591 155.5247 m S 209.3591 174.1067 m S 218.8752 164.8157 m S 266.4561 136.9425 m S 266.4561 118.3605 m S 247.4238 118.3605 m S 247.4238 136.9425 m S 256.9399 127.6515 m S 247.4238 155.5247 m S 247.4238 136.9425 m S 228.3914 136.9425 m S 228.3914 155.5247 m S 237.9076 146.2336 m S 247.4238 174.1067 m S 247.4238 155.5247 m S 228.3914 155.5247 m S 228.3914 174.1067 m S 237.9076 164.8157 m S 266.4561 174.1067 m S 266.4561 155.5247 m S 247.4238 155.5247 m S 247.4238 174.1067 m S 256.9399 164.8157 m S 266.4561 155.5247 m S 266.4561 136.9425 m S 247.4238 136.9425 m S 247.4238 155.5247 m S 256.9399 146.2336 m S 247.4238 136.9425 m S 247.4238 118.3605 m S 228.3914 118.3605 m S 228.3914 136.9425 m S 237.9076 127.6515 m S 228.3914 136.9425 m S 228.3914 118.3605 m S 209.3591 118.3605 m S 209.3591 136.9425 m S 218.8752 127.6515 m S 228.3914 155.5247 m S 228.3914 136.9425 m S 209.3591 136.9425 m S 209.3591 155.5247 m S 218.8752 146.2336 m S 0 g 1 w 4 M 218.8752 164.8157 m F 256.9399 164.8157 m F 218.8752 127.6515 m F 256.9399 127.6515 m F 0 G 0.3 w 10 M 152.2621 81.1962 m S 152.2621 62.6142 m S 152.2621 118.3605 m S 152.2621 99.7783 m S 152.2621 99.7783 m S 152.2621 81.1962 m S 171.2944 118.3605 m S 171.2944 99.7783 m S 152.2621 99.7783 m S 152.2621 118.3605 m S 161.7782 109.0694 m S 209.3591 81.1962 m S 209.3591 62.6142 m S 190.3268 62.6142 m S 190.3268 81.1962 m S 199.8429 71.9052 m S 190.3268 99.7783 m S 190.3268 81.1962 m S 171.2944 81.1962 m S 171.2944 99.7783 m S 180.8106 90.4874 m S 190.3268 118.3605 m S 190.3268 99.7783 m S 171.2944 99.7783 m S 171.2944 118.3605 m S 180.8106 109.0694 m S 209.3591 118.3605 m S 209.3591 99.7783 m S 190.3268 99.7783 m S 190.3268 118.3605 m S 199.8429 109.0694 m S 209.3591 99.7783 m S 209.3591 81.1962 m S 190.3268 81.1962 m S 190.3268 99.7783 m S 199.8429 90.4874 m S 190.3268 81.1962 m S 190.3268 62.6142 m S 171.2944 62.6142 m S 171.2944 81.1962 m S 180.8106 71.9052 m S 171.2944 81.1962 m S 171.2944 62.6142 m S 152.2621 62.6142 m S 152.2621 81.1962 m S 161.7782 71.9052 m S 171.2944 99.7783 m S 171.2944 81.1962 m S 152.2621 81.1962 m S 152.2621 99.7783 m S 161.7782 90.4874 m S 0 g 1 w 4 M 161.7782 109.0694 m F 199.8429 109.0694 m F 161.7782 71.9052 m F 199.8429 71.9052 m F 0 G 0.3 w 10 M 228.3914 118.3605 m S 228.3914 99.7783 m S 209.3591 99.7783 m S 209.3591 118.3605 m S 218.8752 109.0694 m S 266.4561 81.1962 m S 266.4561 62.6142 m S 247.4238 62.6142 m S 247.4238 81.1962 m S 256.9399 71.9052 m S 247.4238 99.7783 m S 247.4238 81.1962 m S 228.3914 81.1962 m S 228.3914 99.7783 m S 237.9076 90.4874 m S 247.4238 118.3605 m S 247.4238 99.7783 m S 228.3914 99.7783 m S 228.3914 118.3605 m S 237.9076 109.0694 m S 266.4561 118.3605 m S 266.4561 99.7783 m S 247.4238 99.7783 m S 247.4238 118.3605 m S 256.9399 109.0694 m S 266.4561 99.7783 m S 266.4561 81.1962 m S 247.4238 81.1962 m S 247.4238 99.7783 m S 256.9399 90.4874 m S 247.4238 81.1962 m S 247.4238 62.6142 m S 228.3914 62.6142 m S 228.3914 81.1962 m S 237.9076 71.9052 m S 228.3914 81.1962 m S 228.3914 62.6142 m S 209.3591 62.6142 m S 209.3591 81.1962 m S 218.8752 71.9052 m S 228.3914 99.7783 m S 228.3914 81.1962 m S 209.3591 81.1962 m S 209.3591 99.7783 m S 218.8752 90.4874 m S 0 g 1 w 4 M 218.8752 109.0694 m F 256.9399 109.0694 m F 218.8752 71.9052 m F 256.9399 71.9052 m F 0 G 0.3 w 10 M 152.2621 62.6142 m S 171.2944 62.6142 m S 152.2621 62.6142 m S 190.3268 62.6142 m S 171.2944 62.6142 m S 209.3591 62.6142 m S 190.3268 62.6142 m S 228.3914 62.6142 m S 209.3591 62.6142 m S 247.4238 62.6142 m S 228.3914 62.6142 m S 266.4561 62.6142 m S 247.4238 62.6142 m S 171.2944 174.1067 m S 171.2944 155.5247 m S 152.2621 155.5247 m S 152.2621 174.1067 m S 161.7782 164.8157 m S 209.3591 136.9425 m S 209.3591 118.3605 m S 190.3268 118.3605 m S 190.3268 136.9425 m S 190.3268 155.5247 m S 190.3268 136.9425 m S 171.2944 136.9425 m S 171.2944 155.5247 m S 180.8106 146.2336 m S 190.3268 174.1067 m S 190.3268 155.5247 m S 171.2944 155.5247 m S 171.2944 174.1067 m S 180.8106 164.8157 m S 209.3591 174.1067 m S 209.3591 155.5247 m S 190.3268 155.5247 m S 190.3268 174.1067 m S 199.8429 164.8157 m S 209.3591 155.5247 m S 209.3591 136.9425 m S 190.3268 136.9425 m S 190.3268 155.5247 m S 199.8429 146.2336 m S 190.3268 136.9425 m S 190.3268 118.3605 m S 171.2944 118.3605 m S 171.2944 136.9425 m S 180.8106 127.6515 m S 171.2944 136.9425 m S 171.2944 118.3605 m S 152.2621 118.3605 m S 152.2621 136.9425 m S 161.7782 127.6515 m S 171.2944 155.5247 m S 171.2944 136.9425 m S 152.2621 136.9425 m S 152.2621 155.5247 m S 161.7782 146.2336 m S 0 g 1 w 4 M 161.7782 164.8157 m F 199.8429 164.8157 m F 161.7782 127.6515 m F 0 G 0.3 w 10 M 228.3914 174.1067 m S 228.3914 155.5247 m S 209.3591 155.5247 m S 209.3591 174.1067 m S 218.8752 164.8157 m S 266.4561 136.9425 m S 266.4561 118.3605 m S 247.4238 118.3605 m S 247.4238 136.9425 m S 256.9399 127.6515 m S 247.4238 155.5247 m S 247.4238 136.9425 m S 228.3914 136.9425 m S 228.3914 155.5247 m S 237.9076 146.2336 m S 247.4238 174.1067 m S 247.4238 155.5247 m S 228.3914 155.5247 m S 228.3914 174.1067 m S 237.9076 164.8157 m S 266.4561 174.1067 m S 266.4561 155.5247 m S 247.4238 155.5247 m S 247.4238 174.1067 m S 256.9399 164.8157 m S 266.4561 155.5247 m S 266.4561 136.9425 m S 247.4238 136.9425 m S 247.4238 155.5247 m S 256.9399 146.2336 m S 247.4238 136.9425 m S 247.4238 118.3605 m S 228.3914 118.3605 m S 228.3914 136.9425 m S 237.9076 127.6515 m S 228.3914 136.9425 m S 228.3914 118.3605 m S 209.3591 118.3605 m S 209.3591 136.9425 m S 218.8752 127.6515 m S 228.3914 155.5247 m S 228.3914 136.9425 m S 209.3591 136.9425 m S 209.3591 155.5247 m S 218.8752 146.2336 m S 0 g 1 w 4 M 218.8752 164.8157 m F 256.9399 164.8157 m F 218.8752 127.6515 m F 256.9399 127.6515 m F 0 G 0.3 w 10 M 171.2944 118.3605 m S 171.2944 99.7783 m S 152.2621 99.7783 m S 152.2621 118.3605 m S 161.7782 109.0694 m S 209.3591 81.1962 m S 209.3591 62.6142 m S 190.3268 62.6142 m S 190.3268 81.1962 m S 199.8429 71.9052 m S 190.3268 99.7783 m S 190.3268 81.1962 m S 171.2944 81.1962 m S 171.2944 99.7783 m S 180.8106 90.4874 m S 190.3268 118.3605 m S 190.3268 99.7783 m S 171.2944 99.7783 m S 171.2944 118.3605 m S 180.8106 109.0694 m S 209.3591 118.3605 m S 209.3591 99.7783 m S 190.3268 99.7783 m S 190.3268 118.3605 m S 209.3591 99.7783 m S 209.3591 81.1962 m S 190.3268 81.1962 m S 190.3268 99.7783 m S 199.8429 90.4874 m S 190.3268 81.1962 m S 190.3268 62.6142 m S 171.2944 62.6142 m S 171.2944 81.1962 m S 180.8106 71.9052 m S 171.2944 81.1962 m S 171.2944 62.6142 m S 152.2621 62.6142 m S 152.2621 81.1962 m S 161.7782 71.9052 m S 171.2944 99.7783 m S 171.2944 81.1962 m S 152.2621 81.1962 m S 152.2621 99.7783 m S 161.7782 90.4874 m S 0 g 1 w 4 M 161.7782 109.0694 m F 161.7782 71.9052 m F 199.8429 71.9052 m F 0 G 0.3 w 10 M 228.3914 118.3605 m S 228.3914 99.7783 m S 209.3591 99.7783 m S 209.3591 118.3605 m S 218.8752 109.0694 m S 266.4561 81.1962 m S 266.4561 62.6142 m S 247.4238 62.6142 m S 247.4238 81.1962 m S 256.9399 71.9052 m S 247.4238 99.7783 m S 247.4238 81.1962 m S 228.3914 81.1962 m S 228.3914 99.7783 m S 237.9076 90.4874 m S 247.4238 118.3605 m S 247.4238 99.7783 m S 228.3914 99.7783 m S 228.3914 118.3605 m S 237.9076 109.0694 m S 266.4561 118.3605 m S 266.4561 99.7783 m S 247.4238 99.7783 m S 247.4238 118.3605 m S 256.9399 109.0694 m S 266.4561 99.7783 m S 266.4561 81.1962 m S 247.4238 81.1962 m S 247.4238 99.7783 m S 256.9399 90.4874 m S 247.4238 81.1962 m S 247.4238 62.6142 m S 228.3914 62.6142 m S 228.3914 81.1962 m S 237.9076 71.9052 m S 228.3914 81.1962 m S 228.3914 62.6142 m S 209.3591 62.6142 m S 209.3591 81.1962 m S 218.8752 71.9052 m S 228.3914 99.7783 m S 228.3914 81.1962 m S 209.3591 81.1962 m S 209.3591 99.7783 m S 218.8752 90.4874 m S 0 g 1 w 4 M 218.8752 109.0694 m F 256.9399 109.0694 m F 218.8752 71.9052 m F 256.9399 71.9052 m F 0 G 0.3 w 10 M 171.2944 62.6142 m S 152.2621 62.6142 m S 190.3268 62.6142 m S 171.2944 62.6142 m S 209.3591 62.6142 m S 190.3268 62.6142 m S 228.3914 62.6142 m S 209.3591 62.6142 m S 247.4238 62.6142 m S 228.3914 62.6142 m S 266.4561 62.6142 m S 247.4238 62.6142 m S 1 w 4 M 161.7782 146.2336 m 256.9399 146.2336 l S 161.7782 90.4874 m 256.9399 90.4874 l S 180.8106 164.8157 m 180.8106 71.9052 l S 237.9076 164.8157 m 237.9076 71.9052 l S 0.3 w 10 M 190.3268 155.5247 m S 0 g 1 w 4 M 190.3268 155.5247 m F 0 G 0.3 w 10 M 190.3268 155.5247 m S 190.3268 155.5247 m S 190.3268 155.5247 m S 0 g 1 w 4 M 190.3268 155.5247 m F 0 G 0.3 w 10 M 190.3268 155.5247 m S 190.3268 155.5247 m S 1 g 1 w 4 M 185.3118 155.5247 m 185.3118 152.8314 187.5571 150.648 190.3268 150.648 c 193.0964 150.648 195.3417 152.8314 195.3417 155.5247 c F 195.3417 155.5247 m 195.3417 158.2179 193.0964 160.4013 190.3268 160.4013 c 187.5571 160.4013 185.3118 158.2179 185.3118 155.5247 c F 190.3268 155.5247 m F 0 G 0.3 w 10 M 190.3268 155.5247 m S 0 g 1 w 4 M 190.3268 155.5247 m F 0 G 0.3 w 10 M 190.3268 155.5247 m S 190.3268 155.5247 m S 0 g 1 w 4 M 189.4214 154.6319 m 189.4214 151.6417 L 191.2322 151.6417 L 191.2322 154.6319 L 194.2239 154.6226 L 194.2239 156.4269 L 191.2322 156.4176 L 191.2322 159.4079 L 189.4214 159.4079 L 189.4214 156.4176 L 186.4296 156.4269 L 186.4296 154.6226 L 189.4214 154.6319 L f 0 G 0.3 w 10 M 209.3591 155.5247 m S 0 g 1 w 4 M 209.3591 155.5247 m F 0 G 0.3 w 10 M 209.3591 155.5247 m S 209.3591 155.5247 m S 209.3591 155.5247 m S 0 g 1 w 4 M 209.3591 155.5247 m F 0 G 0.3 w 10 M 209.3591 155.5247 m S 209.3591 155.5247 m S 1 g 1 w 4 M 204.3441 155.5247 m 204.3441 152.8314 206.5895 150.648 209.3591 150.648 c 212.1287 150.648 214.3741 152.8314 214.3741 155.5247 c F 214.3741 155.5247 m 214.3741 158.2179 212.1287 160.4013 209.3591 160.4013 c 206.5895 160.4013 204.3441 158.2179 204.3441 155.5247 c F 209.3591 155.5247 m F 0 G 0.3 w 10 M 209.3591 155.5247 m S 0 g 1 w 4 M 209.3591 155.5247 m F 0 G 0.3 w 10 M 209.3591 155.5247 m S 209.3591 155.5247 m S 0 g 1 w 4 M 208.4537 154.6319 m 208.4537 151.6417 L 210.2645 151.6417 L 210.2645 154.6319 L 213.2563 154.6226 L 213.2563 156.4269 L 210.2645 156.4176 L 210.2645 159.4079 L 208.4537 159.4079 L 208.4537 156.4176 L 205.462 156.4269 L 205.462 154.6226 L 208.4537 154.6319 L f 0 G 0.3 w 10 M 228.3914 155.5247 m S 0 g 1 w 4 M 228.3914 155.5247 m F 0 G 0.3 w 10 M 228.3914 155.5247 m S 228.3914 155.5247 m S 228.3914 155.5247 m S 0 g 1 w 4 M 228.3914 155.5247 m F 0 G 0.3 w 10 M 228.3914 155.5247 m S 228.3914 155.5247 m S 1 g 1 w 4 M 223.3765 155.5247 m 223.3765 152.8314 225.6218 150.648 228.3914 150.648 c 231.1611 150.648 233.4064 152.8314 233.4064 155.5247 c F 233.4064 155.5247 m 233.4064 158.2179 231.1611 160.4013 228.3914 160.4013 c 225.6218 160.4013 223.3765 158.2179 223.3765 155.5247 c F 228.3914 155.5247 m F 0 G 0.3 w 10 M 228.3914 155.5247 m S 0 g 1 w 4 M 228.3914 155.5247 m F 0 G 0.3 w 10 M 228.3914 155.5247 m S 228.3914 155.5247 m S 0 g 1 w 4 M 227.486 154.6319 m 227.486 151.6417 L 229.2968 151.6417 L 229.2968 154.6319 L 232.2886 154.6226 L 232.2886 156.4269 L 229.2968 156.4176 L 229.2968 159.4079 L 227.486 159.4079 L 227.486 156.4176 L 224.4943 156.4269 L 224.4943 154.6226 L 227.486 154.6319 L f 0 G 0.3 w 10 M 171.2944 136.9425 m S 0 g 1 w 4 M 171.2944 136.9425 m F 0 G 0.3 w 10 M 171.2944 136.9425 m S 171.2944 136.9425 m S 171.2944 136.9425 m S 0 g 1 w 4 M 171.2944 136.9425 m F 0 G 0.3 w 10 M 171.2944 136.9425 m S 171.2944 136.9425 m S 1 g 1 w 4 M 166.2794 136.9425 m 166.2794 134.2492 168.5247 132.0659 171.2944 132.0659 c 174.064 132.0659 176.3094 134.2492 176.3094 136.9425 c F 176.3094 136.9425 m 176.3094 139.6358 174.064 141.8191 171.2944 141.8191 c 168.5247 141.8191 166.2794 139.6358 166.2794 136.9425 c F 171.2944 136.9425 m F 0 G 0.3 w 10 M 171.2944 136.9425 m S 0 g 1 w 4 M 171.2944 136.9425 m F 0 G 0.3 w 10 M 171.2944 136.9425 m S 171.2944 136.9425 m S 0 g 1 w 4 M 170.389 136.0498 m 170.389 133.0595 L 172.1998 133.0595 L 172.1998 136.0498 L 175.1915 136.0404 L 175.1915 137.8448 L 172.1998 137.8355 L 172.1998 140.8258 L 170.389 140.8258 L 170.389 137.8355 L 167.3972 137.8448 L 167.3972 136.0404 L 170.389 136.0498 L f 0 G 0.3 w 10 M 171.2944 118.3605 m S 0 g 1 w 4 M 171.2944 118.3605 m F 0 G 0.3 w 10 M 171.2944 118.3605 m S 171.2944 118.3605 m S 171.2944 118.3605 m S 0 g 1 w 4 M 171.2944 118.3605 m F 0 G 0.3 w 10 M 171.2944 118.3605 m S 171.2944 118.3605 m S 1 g 1 w 4 M 166.2794 118.3605 m 166.2794 115.6672 168.5247 113.4838 171.2944 113.4838 c 174.064 113.4838 176.3094 115.6672 176.3094 118.3605 c F 176.3094 118.3605 m 176.3094 121.0537 174.064 123.2371 171.2944 123.2371 c 168.5247 123.2371 166.2794 121.0537 166.2794 118.3605 c F 171.2944 118.3605 m F 0 G 0.3 w 10 M 171.2944 118.3605 m S 0 g 1 w 4 M 171.2944 118.3605 m F 0 G 0.3 w 10 M 171.2944 118.3605 m S 171.2944 118.3605 m S 0 g 1 w 4 M 170.389 117.4677 m 170.389 114.4774 L 172.1998 114.4774 L 172.1998 117.4677 L 175.1915 117.4584 L 175.1915 119.2627 L 172.1998 119.2534 L 172.1998 122.2437 L 170.389 122.2437 L 170.389 119.2534 L 167.3972 119.2627 L 167.3972 117.4584 L 170.389 117.4677 L f 0 G 0.3 w 10 M 171.2944 99.7783 m S 0 g 1 w 4 M 171.2944 99.7783 m F 0 G 0.3 w 10 M 171.2944 99.7783 m S 171.2944 99.7783 m S 171.2944 99.7783 m S 0 g 1 w 4 M 171.2944 99.7783 m F 0 G 0.3 w 10 M 171.2944 99.7783 m S 171.2944 99.7783 m S 1 g 1 w 4 M 166.2794 99.7783 m 166.2794 97.085 168.5247 94.9017 171.2944 94.9017 c 174.064 94.9017 176.3094 97.085 176.3094 99.7783 c F 176.3094 99.7783 m 176.3094 102.4716 174.064 104.6549 171.2944 104.6549 c 168.5247 104.6549 166.2794 102.4716 166.2794 99.7783 c F 171.2944 99.7783 m F 0 G 0.3 w 10 M 171.2944 99.7783 m S 0 g 1 w 4 M 171.2944 99.7783 m F 0 G 0.3 w 10 M 171.2944 99.7783 m S 171.2944 99.7783 m S 0 g 1 w 4 M 170.389 98.8856 m 170.389 95.8953 L 172.1998 95.8953 L 172.1998 98.8856 L 175.1915 98.8762 L 175.1915 100.6806 L 172.1998 100.6713 L 172.1998 103.6616 L 170.389 103.6616 L 170.389 100.6713 L 167.3972 100.6806 L 167.3972 98.8762 L 170.389 98.8856 L f 0 G 0.3 w 10 M 190.3268 81.1962 m S 190.3268 81.1962 m S 209.3591 81.1962 m S 190.3268 81.1962 m S 209.3591 81.1962 m S 190.3268 81.1962 m S 228.3914 81.1962 m S 209.3591 81.1962 m S 228.3914 81.1962 m S 228.3914 81.1962 m S 228.3914 81.1962 m S 209.3591 81.1962 m S 190.3268 81.1962 m S 0 g 1 w 4 M 190.3268 81.1962 m F 0 G 0.3 w 10 M 190.3268 81.1962 m S 190.3268 81.1962 m S 190.3268 81.1962 m S 0 g 1 w 4 M 190.3268 81.1962 m F 0 G 0.3 w 10 M 190.3268 81.1962 m S 190.3268 81.1962 m S 1 g 1 w 4 M 185.3118 81.1962 m 185.3118 78.503 187.5571 76.3196 190.3268 76.3196 c 193.0964 76.3196 195.3417 78.503 195.3417 81.1962 c F 195.3417 81.1962 m 195.3417 83.8895 193.0964 86.0729 190.3268 86.0729 c 187.5571 86.0729 185.3118 83.8895 185.3118 81.1962 c F 190.3268 81.1962 m F 0 G 0.3 w 10 M 190.3268 81.1962 m S 0 g 1 w 4 M 190.3268 81.1962 m F 0 G 0.3 w 10 M 190.3268 81.1962 m S 190.3268 81.1962 m S 0 g 1 w 4 M 189.4214 80.3035 m 189.4214 77.3132 L 191.2322 77.3132 L 191.2322 80.3035 L 194.2239 80.2942 L 194.2239 82.0985 L 191.2322 82.0892 L 191.2322 85.0795 L 189.4214 85.0795 L 189.4214 82.0892 L 186.4296 82.0985 L 186.4296 80.2942 L 189.4214 80.3035 L f 0 G 0.3 w 10 M 209.3591 81.1962 m S 0 g 1 w 4 M 209.3591 81.1962 m F 0 G 0.3 w 10 M 209.3591 81.1962 m S 209.3591 81.1962 m S 209.3591 81.1962 m S 0 g 1 w 4 M 209.3591 81.1962 m F 0 G 0.3 w 10 M 209.3591 81.1962 m S 209.3591 81.1962 m S 1 g 1 w 4 M 204.3441 81.1962 m 204.3441 78.503 206.5895 76.3196 209.3591 76.3196 c 212.1287 76.3196 214.3741 78.503 214.3741 81.1962 c F 214.3741 81.1962 m 214.3741 83.8895 212.1287 86.0729 209.3591 86.0729 c 206.5895 86.0729 204.3441 83.8895 204.3441 81.1962 c F 209.3591 81.1962 m F 0 G 0.3 w 10 M 209.3591 81.1962 m S 0 g 1 w 4 M 209.3591 81.1962 m F 0 G 0.3 w 10 M 209.3591 81.1962 m S 209.3591 81.1962 m S 0 g 1 w 4 M 208.4537 80.3035 m 208.4537 77.3132 L 210.2645 77.3132 L 210.2645 80.3035 L 213.2563 80.2942 L 213.2563 82.0985 L 210.2645 82.0892 L 210.2645 85.0795 L 208.4537 85.0795 L 208.4537 82.0892 L 205.462 82.0985 L 205.462 80.2942 L 208.4537 80.3035 L f 0 G 0.3 w 10 M 228.3914 81.1962 m S 0 g 1 w 4 M 228.3914 81.1962 m F 0 G 0.3 w 10 M 228.3914 81.1962 m S 228.3914 81.1962 m S 228.3914 81.1962 m S 0 g 1 w 4 M 228.3914 81.1962 m F 0 G 0.3 w 10 M 228.3914 81.1962 m S 228.3914 81.1962 m S 1 g 1 w 4 M 223.3765 81.1962 m 223.3765 78.503 225.6218 76.3196 228.3914 76.3196 c 231.1611 76.3196 233.4064 78.503 233.4064 81.1962 c F 233.4064 81.1962 m 233.4064 83.8895 231.1611 86.0729 228.3914 86.0729 c 225.6218 86.0729 223.3765 83.8895 223.3765 81.1962 c F 228.3914 81.1962 m F 0 G 0.3 w 10 M 228.3914 81.1962 m S 0 g 1 w 4 M 228.3914 81.1962 m F 0 G 0.3 w 10 M 228.3914 81.1962 m S 228.3914 81.1962 m S 0 g 1 w 4 M 227.486 80.3035 m 227.486 77.3132 L 229.2968 77.3132 L 229.2968 80.3035 L 232.2886 80.2942 L 232.2886 82.0985 L 229.2968 82.0892 L 229.2968 85.0795 L 227.486 85.0795 L 227.486 82.0892 L 224.4943 82.0985 L 224.4943 80.2942 L 227.486 80.3035 L f 0 G 0.3 w 10 M 247.4238 136.9425 m S 247.4238 118.3605 m S 247.4238 136.9425 m S 247.4238 136.9425 m S 247.4238 118.3605 m S 247.4238 136.9425 m S 247.4238 118.3605 m S 247.4238 99.7783 m S 247.4238 99.7783 m S 247.4238 99.7783 m S 247.4238 118.3605 m S 247.4238 99.7783 m S 247.4238 136.9425 m S 0 g 1 w 4 M 247.4238 136.9425 m F 0 G 0.3 w 10 M 247.4238 136.9425 m S 247.4238 136.9425 m S 247.4238 136.9425 m S 0 g 1 w 4 M 247.4238 136.9425 m F 0 G 0.3 w 10 M 247.4238 136.9425 m S 247.4238 136.9425 m S 1 g 1 w 4 M 242.4089 136.9425 m 242.4089 134.2492 244.6542 132.0659 247.4238 132.0659 c 250.1935 132.0659 252.4388 134.2492 252.4388 136.9425 c F 252.4388 136.9425 m 252.4388 139.6358 250.1935 141.8191 247.4238 141.8191 c 244.6542 141.8191 242.4089 139.6358 242.4089 136.9425 c F 247.4238 136.9425 m F 0 G 0.3 w 10 M 247.4238 136.9425 m S 0 g 1 w 4 M 247.4238 136.9425 m F 0 G 0.3 w 10 M 247.4238 136.9425 m S 247.4238 136.9425 m S 0 g 1 w 4 M 246.5184 136.0498 m 246.5184 133.0595 L 248.3292 133.0595 L 248.3292 136.0498 L 251.321 136.0404 L 251.321 137.8448 L 248.3292 137.8355 L 248.3292 140.8258 L 246.5184 140.8258 L 246.5184 137.8355 L 243.5267 137.8448 L 243.5267 136.0404 L 246.5184 136.0498 L f 0 G 0.3 w 10 M 247.4238 118.3605 m S 0 g 1 w 4 M 247.4238 118.3605 m F 0 G 0.3 w 10 M 247.4238 118.3605 m S 247.4238 118.3605 m S 247.4238 118.3605 m S 0 g 1 w 4 M 247.4238 118.3605 m F 0 G 0.3 w 10 M 247.4238 118.3605 m S 247.4238 118.3605 m S 1 g 1 w 4 M 242.4089 118.3605 m 242.4089 115.6672 244.6542 113.4838 247.4238 113.4838 c 250.1935 113.4838 252.4388 115.6672 252.4388 118.3605 c F 252.4388 118.3605 m 252.4388 121.0537 250.1935 123.2371 247.4238 123.2371 c 244.6542 123.2371 242.4089 121.0537 242.4089 118.3605 c F 247.4238 118.3605 m F 0 G 0.3 w 10 M 247.4238 118.3605 m S 0 g 1 w 4 M 247.4238 118.3605 m F 0 G 0.3 w 10 M 247.4238 118.3605 m S 247.4238 118.3605 m S 0 g 1 w 4 M 246.5184 117.4677 m 246.5184 114.4774 L 248.3292 114.4774 L 248.3292 117.4677 L 251.321 117.4584 L 251.321 119.2627 L 248.3292 119.2534 L 248.3292 122.2437 L 246.5184 122.2437 L 246.5184 119.2534 L 243.5267 119.2627 L 243.5267 117.4584 L 246.5184 117.4677 L f 0 G 0.3 w 10 M 247.4238 99.7783 m S 0 g 1 w 4 M 247.4238 99.7783 m F 0 G 0.3 w 10 M 247.4238 99.7783 m S 247.4238 99.7783 m S 247.4238 99.7783 m S 0 g 1 w 4 M 247.4238 99.7783 m F 0 G 0.3 w 10 M 247.4238 99.7783 m S 247.4238 99.7783 m S 1 g 1 w 4 M 242.4089 99.7783 m 242.4089 97.085 244.6542 94.9017 247.4238 94.9017 c 250.1935 94.9017 252.4388 97.085 252.4388 99.7783 c F 252.4388 99.7783 m 252.4388 102.4716 250.1935 104.6549 247.4238 104.6549 c 244.6542 104.6549 242.4089 102.4716 242.4089 99.7783 c F 247.4238 99.7783 m F 0 G 0.3 w 10 M 247.4238 99.7783 m S 0 g 1 w 4 M 247.4238 99.7783 m F 0 G 0.3 w 10 M 247.4238 99.7783 m S 247.4238 99.7783 m S 0 g 1 w 4 M 246.5184 98.8856 m 246.5184 95.8953 L 248.3292 95.8953 L 248.3292 98.8856 L 251.321 98.8762 L 251.321 100.6806 L 248.3292 100.6713 L 248.3292 103.6616 L 246.5184 103.6616 L 246.5184 100.6713 L 243.5267 100.6806 L 243.5267 98.8762 L 246.5184 98.8856 L f 0 G 0.3 w 10 M 199.8429 127.6515 m S 199.8429 127.6515 m S 218.8752 127.6515 m S 199.8429 127.6515 m S 218.8752 127.6515 m S 218.8752 127.6515 m S 218.8752 127.6515 m S 199.8429 127.6515 m S 199.8429 109.0694 m S 199.8429 109.0694 m S 218.8752 109.0694 m S 199.8429 109.0694 m S 218.8752 109.0694 m S 218.8752 109.0694 m S 218.8752 109.0694 m S 199.8429 109.0694 m S 266.4561 118.3605 m S 266.4561 136.9425 m S 266.4561 136.9425 m S 266.4561 155.5247 m S 380.6502 136.9425 m S 380.6502 118.3605 m S 380.6502 174.1067 m S 380.6502 155.5247 m S 380.6502 155.5247 m S 380.6502 136.9425 m S 399.6944 174.1067 m S 399.6944 155.5247 m S 380.6502 155.5247 m S 380.6502 174.1067 m S 390.1722 164.8157 m S 437.7827 136.9425 m S 437.7827 118.3605 m S 418.7386 118.3605 m S 418.7386 136.9425 m S 428.2606 127.6515 m S 418.7386 155.5247 m S 418.7386 136.9425 m S 399.6944 136.9425 m S 399.6944 155.5247 m S 409.2165 146.2336 m S 418.7386 174.1067 m S 418.7386 155.5247 m S 399.6944 155.5247 m S 399.6944 174.1067 m S 409.2165 164.8157 m S 437.7827 174.1067 m S 437.7827 155.5247 m S 418.7386 155.5247 m S 418.7386 174.1067 m S 428.2606 164.8157 m S 437.7827 155.5247 m S 437.7827 136.9425 m S 418.7386 136.9425 m S 418.7386 155.5247 m S 428.2606 146.2336 m S 418.7386 136.9425 m S 418.7386 118.3605 m S 399.6944 118.3605 m S 399.6944 136.9425 m S 409.2165 127.6515 m S 399.6944 136.9425 m S 399.6944 118.3605 m S 380.6502 118.3605 m S 380.6502 136.9425 m S 390.1722 127.6515 m S 399.6944 155.5247 m S 399.6944 136.9425 m S 380.6502 136.9425 m S 380.6502 155.5247 m S 390.1722 146.2336 m S 0 g 1 w 4 M 390.1722 164.8157 m F 428.2606 164.8157 m F 390.1722 127.6515 m F 428.2606 127.6515 m F 0 G 0.3 w 10 M 456.8269 174.1067 m S 456.8269 155.5247 m S 437.7827 155.5247 m S 437.7827 174.1067 m S 447.3048 164.8157 m S 494.9153 136.9425 m S 494.9153 118.3605 m S 475.8711 118.3605 m S 475.8711 136.9425 m S 485.3932 127.6515 m S 475.8711 155.5247 m S 475.8711 136.9425 m S 456.8269 136.9425 m S 456.8269 155.5247 m S 466.349 146.2336 m S 475.8711 174.1067 m S 475.8711 155.5247 m S 456.8269 155.5247 m S 456.8269 174.1067 m S 466.349 164.8157 m S 494.9153 174.1067 m S 494.9153 155.5247 m S 475.8711 155.5247 m S 475.8711 174.1067 m S 485.3932 164.8157 m S 494.9153 155.5247 m S 494.9153 136.9425 m S 475.8711 136.9425 m S 475.8711 155.5247 m S 485.3932 146.2336 m S 475.8711 136.9425 m S 475.8711 118.3605 m S 456.8269 118.3605 m S 456.8269 136.9425 m S 466.349 127.6515 m S 456.8269 136.9425 m S 456.8269 118.3605 m S 437.7827 118.3605 m S 437.7827 136.9425 m S 447.3048 127.6515 m S 456.8269 155.5247 m S 456.8269 136.9425 m S 437.7827 136.9425 m S 437.7827 155.5247 m S 447.3048 146.2336 m S 0 g 1 w 4 M 447.3048 164.8157 m F 485.3932 164.8157 m F 447.3048 127.6515 m F 485.3932 127.6515 m F 0 G 0.3 w 10 M 266.4561 99.7783 m S 266.4561 118.3605 m S 266.4561 81.1962 m S 266.4561 99.7783 m S 380.6502 81.1962 m S 380.6502 62.6142 m S 380.6502 118.3605 m S 380.6502 99.7783 m S 380.6502 99.7783 m S 380.6502 81.1962 m S 399.6944 118.3605 m S 399.6944 99.7783 m S 380.6502 99.7783 m S 380.6502 118.3605 m S 390.1722 109.0694 m S 437.7827 81.1962 m S 437.7827 62.6142 m S 418.7386 62.6142 m S 418.7386 81.1962 m S 428.2606 71.9052 m S 418.7386 99.7783 m S 418.7386 81.1962 m S 399.6944 81.1962 m S 399.6944 99.7783 m S 409.2165 90.4874 m S 418.7386 118.3605 m S 418.7386 99.7783 m S 399.6944 99.7783 m S 399.6944 118.3605 m S 409.2165 109.0694 m S 437.7827 118.3605 m S 437.7827 99.7783 m S 418.7386 99.7783 m S 418.7386 118.3605 m S 428.2606 109.0694 m S 437.7827 99.7783 m S 437.7827 81.1962 m S 418.7386 81.1962 m S 418.7386 99.7783 m S 428.2606 90.4874 m S 418.7386 81.1962 m S 418.7386 62.6142 m S 399.6944 62.6142 m S 399.6944 81.1962 m S 409.2165 71.9052 m S 399.6944 81.1962 m S 399.6944 62.6142 m S 380.6502 62.6142 m S 380.6502 81.1962 m S 390.1722 71.9052 m S 399.6944 99.7783 m S 399.6944 81.1962 m S 380.6502 81.1962 m S 380.6502 99.7783 m S 390.1722 90.4874 m S 0 g 1 w 4 M 390.1722 109.0694 m F 428.2606 109.0694 m F 390.1722 71.9052 m F 428.2606 71.9052 m F 0 G 0.3 w 10 M 456.8269 118.3605 m S 456.8269 99.7783 m S 437.7827 99.7783 m S 437.7827 118.3605 m S 447.3048 109.0694 m S 494.9153 81.1962 m S 494.9153 62.6142 m S 475.8711 62.6142 m S 475.8711 81.1962 m S 485.3932 71.9052 m S 475.8711 99.7783 m S 475.8711 81.1962 m S 456.8269 81.1962 m S 456.8269 99.7783 m S 466.349 90.4874 m S 475.8711 118.3605 m S 475.8711 99.7783 m S 456.8269 99.7783 m S 456.8269 118.3605 m S 466.349 109.0694 m S 494.9153 118.3605 m S 494.9153 99.7783 m S 475.8711 99.7783 m S 475.8711 118.3605 m S 485.3932 109.0694 m S 494.9153 99.7783 m S 494.9153 81.1962 m S 475.8711 81.1962 m S 475.8711 99.7783 m S 485.3932 90.4874 m S 475.8711 81.1962 m S 475.8711 62.6142 m S 456.8269 62.6142 m S 456.8269 81.1962 m S 466.349 71.9052 m S 456.8269 81.1962 m S 456.8269 62.6142 m S 437.7827 62.6142 m S 437.7827 81.1962 m S 447.3048 71.9052 m S 456.8269 99.7783 m S 456.8269 81.1962 m S 437.7827 81.1962 m S 437.7827 99.7783 m S 447.3048 90.4874 m S 0 g 1 w 4 M 447.3048 109.0694 m F 485.3932 109.0694 m F 447.3048 71.9052 m F 485.3932 71.9052 m F 0 G 0.3 w 10 M 380.6502 62.6142 m S 399.6944 62.6142 m S 380.6502 62.6142 m S 418.7386 62.6142 m S 399.6944 62.6142 m S 437.7827 62.6142 m S 418.7386 62.6142 m S 456.8269 62.6142 m S 437.7827 62.6142 m S 475.8711 62.6142 m S 456.8269 62.6142 m S 494.9153 62.6142 m S 475.8711 62.6142 m S 399.6944 174.1067 m S 399.6944 155.5247 m S 380.6502 155.5247 m S 380.6502 174.1067 m S 390.1722 164.8157 m S 437.7827 136.9425 m S 437.7827 118.3605 m S 418.7386 118.3605 m S 418.7386 136.9425 m S 418.7386 155.5247 m S 418.7386 136.9425 m S 399.6944 136.9425 m S 399.6944 155.5247 m S 409.2165 146.2336 m S 418.7386 174.1067 m S 418.7386 155.5247 m S 399.6944 155.5247 m S 399.6944 174.1067 m S 409.2165 164.8157 m S 437.7827 174.1067 m S 437.7827 155.5247 m S 418.7386 155.5247 m S 418.7386 174.1067 m S 428.2606 164.8157 m S 437.7827 155.5247 m S 437.7827 136.9425 m S 418.7386 136.9425 m S 418.7386 155.5247 m S 428.2606 146.2336 m S 418.7386 136.9425 m S 418.7386 118.3605 m S 399.6944 118.3605 m S 399.6944 136.9425 m S 409.2165 127.6515 m S 399.6944 136.9425 m S 399.6944 118.3605 m S 380.6502 118.3605 m S 380.6502 136.9425 m S 390.1722 127.6515 m S 399.6944 155.5247 m S 399.6944 136.9425 m S 380.6502 136.9425 m S 380.6502 155.5247 m S 390.1722 146.2336 m S 0 g 1 w 4 M 390.1722 164.8157 m F 428.2606 164.8157 m F 390.1722 127.6515 m F 0 G 0.3 w 10 M 456.8269 174.1067 m S 456.8269 155.5247 m S 437.7827 155.5247 m S 437.7827 174.1067 m S 447.3048 164.8157 m S 494.9153 136.9425 m S 494.9153 118.3605 m S 475.8711 118.3605 m S 475.8711 136.9425 m S 485.3932 127.6515 m S 475.8711 155.5247 m S 475.8711 136.9425 m S 456.8269 136.9425 m S 456.8269 155.5247 m S 466.349 146.2336 m S 475.8711 174.1067 m S 475.8711 155.5247 m S 456.8269 155.5247 m S 456.8269 174.1067 m S 466.349 164.8157 m S 494.9153 174.1067 m S 494.9153 155.5247 m S 475.8711 155.5247 m S 475.8711 174.1067 m S 485.3932 164.8157 m S 494.9153 155.5247 m S 494.9153 136.9425 m S 475.8711 136.9425 m S 475.8711 155.5247 m S 485.3932 146.2336 m S 475.8711 136.9425 m S 475.8711 118.3605 m S 456.8269 118.3605 m S 456.8269 136.9425 m S 466.349 127.6515 m S 456.8269 136.9425 m S 456.8269 118.3605 m S 437.7827 118.3605 m S 437.7827 136.9425 m S 447.3048 127.6515 m S 456.8269 155.5247 m S 456.8269 136.9425 m S 437.7827 136.9425 m S 437.7827 155.5247 m S 447.3048 146.2336 m S 0 g 1 w 4 M 447.3048 164.8157 m F 485.3932 164.8157 m F 447.3048 127.6515 m F 485.3932 127.6515 m F 0 G 0.3 w 10 M 399.6944 118.3605 m S 399.6944 99.7783 m S 380.6502 99.7783 m S 380.6502 118.3605 m S 390.1722 109.0694 m S 437.7827 81.1962 m S 437.7827 62.6142 m S 418.7386 62.6142 m S 418.7386 81.1962 m S 428.2606 71.9052 m S 418.7386 99.7783 m S 418.7386 81.1962 m S 399.6944 81.1962 m S 399.6944 99.7783 m S 409.2165 90.4874 m S 418.7386 118.3605 m S 418.7386 99.7783 m S 399.6944 99.7783 m S 399.6944 118.3605 m S 409.2165 109.0694 m S 437.7827 118.3605 m S 437.7827 99.7783 m S 418.7386 99.7783 m S 418.7386 118.3605 m S 437.7827 99.7783 m S 437.7827 81.1962 m S 418.7386 81.1962 m S 418.7386 99.7783 m S 428.2606 90.4874 m S 418.7386 81.1962 m S 418.7386 62.6142 m S 399.6944 62.6142 m S 399.6944 81.1962 m S 409.2165 71.9052 m S 399.6944 81.1962 m S 399.6944 62.6142 m S 380.6502 62.6142 m S 380.6502 81.1962 m S 390.1722 71.9052 m S 399.6944 99.7783 m S 399.6944 81.1962 m S 380.6502 81.1962 m S 380.6502 99.7783 m S 390.1722 90.4874 m S 0 g 1 w 4 M 390.1722 109.0694 m F 390.1722 71.9052 m F 428.2606 71.9052 m F 0 G 0.3 w 10 M 456.8269 118.3605 m S 456.8269 99.7783 m S 437.7827 99.7783 m S 437.7827 118.3605 m S 447.3048 109.0694 m S 494.9153 81.1962 m S 494.9153 62.6142 m S 475.8711 62.6142 m S 475.8711 81.1962 m S 485.3932 71.9052 m S 475.8711 99.7783 m S 475.8711 81.1962 m S 456.8269 81.1962 m S 456.8269 99.7783 m S 466.349 90.4874 m S 475.8711 118.3605 m S 475.8711 99.7783 m S 456.8269 99.7783 m S 456.8269 118.3605 m S 466.349 109.0694 m S 494.9153 118.3605 m S 494.9153 99.7783 m S 475.8711 99.7783 m S 475.8711 118.3605 m S 485.3932 109.0694 m S 494.9153 99.7783 m S 494.9153 81.1962 m S 475.8711 81.1962 m S 475.8711 99.7783 m S 485.3932 90.4874 m S 475.8711 81.1962 m S 475.8711 62.6142 m S 456.8269 62.6142 m S 456.8269 81.1962 m S 466.349 71.9052 m S 456.8269 81.1962 m S 456.8269 62.6142 m S 437.7827 62.6142 m S 437.7827 81.1962 m S 447.3048 71.9052 m S 456.8269 99.7783 m S 456.8269 81.1962 m S 437.7827 81.1962 m S 437.7827 99.7783 m S 447.3048 90.4874 m S 0 g 1 w 4 M 447.3048 109.0694 m F 485.3932 109.0694 m F 447.3048 71.9052 m F 485.3932 71.9052 m F 0 G 0.3 w 10 M 399.6944 62.6142 m S 380.6502 62.6142 m S 418.7386 62.6142 m S 399.6944 62.6142 m S 437.7827 62.6142 m S 418.7386 62.6142 m S 456.8269 62.6142 m S 437.7827 62.6142 m S 475.8711 62.6142 m S 456.8269 62.6142 m S 494.9153 62.6142 m S 475.8711 62.6142 m S 1 w 4 M 390.1722 146.2336 m 485.3932 146.2336 l S 390.1722 90.4874 m 485.3932 90.4874 l S 409.2165 164.8157 m 409.2165 71.9052 l S 466.349 164.8157 m 466.349 71.9052 l S 0.3 w 10 M 418.7386 155.5247 m S 0 g 1 w 4 M 418.7386 155.5247 m F 0 G 0.3 w 10 M 418.7386 155.5247 m S 418.7386 155.5247 m S 418.7386 155.5247 m S 0 g 1 w 4 M 418.7386 155.5247 m F 0 G 0.3 w 10 M 418.7386 155.5247 m S 418.7386 155.5247 m S 1 g 1 w 4 M 413.7205 155.5247 m 413.7205 152.8314 415.9672 150.648 418.7386 150.648 c 421.51 150.648 423.7567 152.8314 423.7567 155.5247 c F 423.7567 155.5247 m 423.7567 158.2179 421.51 160.4013 418.7386 160.4013 c 415.9672 160.4013 413.7205 158.2179 413.7205 155.5247 c F 418.7386 155.5247 m F 0 G 0.3 w 10 M 418.7386 155.5247 m S 0 g 1 w 4 M 418.7386 155.5247 m F 0 G 0.3 w 10 M 418.7386 155.5247 m S 418.7386 155.5247 m S 0 g 1 w 4 M 417.8327 154.6319 m 417.8327 151.6417 L 419.6445 151.6417 L 419.6445 154.6319 L 422.6382 154.6226 L 422.6382 156.4269 L 419.6445 156.4176 L 419.6445 159.4079 L 417.8327 159.4079 L 417.8327 156.4176 L 414.839 156.4269 L 414.839 154.6226 L 417.8327 154.6319 L f 0 G 0.3 w 10 M 437.7827 155.5247 m S 0 g 1 w 4 M 437.7827 155.5247 m F 0 G 0.3 w 10 M 437.7827 155.5247 m S 437.7827 155.5247 m S 437.7827 155.5247 m S 0 g 1 w 4 M 437.7827 155.5247 m F 0 G 0.3 w 10 M 437.7827 155.5247 m S 437.7827 155.5247 m S 1 g 1 w 4 M 432.7647 155.5247 m 432.7647 152.8314 435.0114 150.648 437.7827 150.648 c 440.5541 150.648 442.8008 152.8314 442.8008 155.5247 c F 442.8008 155.5247 m 442.8008 158.2179 440.5541 160.4013 437.7827 160.4013 c 435.0114 160.4013 432.7647 158.2179 432.7647 155.5247 c F 437.7827 155.5247 m F 0 G 0.3 w 10 M 437.7827 155.5247 m S 0 g 1 w 4 M 437.7827 155.5247 m F 0 G 0.3 w 10 M 437.7827 155.5247 m S 437.7827 155.5247 m S 0 g 1 w 4 M 436.8768 154.6319 m 436.8768 151.6417 L 438.6887 151.6417 L 438.6887 154.6319 L 441.6823 154.6226 L 441.6823 156.4269 L 438.6887 156.4176 L 438.6887 159.4079 L 436.8768 159.4079 L 436.8768 156.4176 L 433.8832 156.4269 L 433.8832 154.6226 L 436.8768 154.6319 L f 0 G 0.3 w 10 M 456.8269 155.5247 m S 0 g 1 w 4 M 456.8269 155.5247 m F 0 G 0.3 w 10 M 456.8269 155.5247 m S 456.8269 155.5247 m S 456.8269 155.5247 m S 0 g 1 w 4 M 456.8269 155.5247 m F 0 G 0.3 w 10 M 456.8269 155.5247 m S 456.8269 155.5247 m S 1 g 1 w 4 M 451.8088 155.5247 m 451.8088 152.8314 454.0555 150.648 456.8269 150.648 c 459.5983 150.648 461.845 152.8314 461.845 155.5247 c F 461.845 155.5247 m 461.845 158.2179 459.5983 160.4013 456.8269 160.4013 c 454.0555 160.4013 451.8088 158.2179 451.8088 155.5247 c F 456.8269 155.5247 m F 0 G 0.3 w 10 M 456.8269 155.5247 m S 0 g 1 w 4 M 456.8269 155.5247 m F 0 G 0.3 w 10 M 456.8269 155.5247 m S 456.8269 155.5247 m S 0 g 1 w 4 M 455.921 154.6319 m 455.921 151.6417 L 457.7328 151.6417 L 457.7328 154.6319 L 460.7265 154.6226 L 460.7265 156.4269 L 457.7328 156.4176 L 457.7328 159.4079 L 455.921 159.4079 L 455.921 156.4176 L 452.9273 156.4269 L 452.9273 154.6226 L 455.921 154.6319 L f 0 G 0.3 w 10 M 399.6944 136.9425 m S 0 g 1 w 4 M 399.6944 136.9425 m F 0 G 0.3 w 10 M 399.6944 136.9425 m S 399.6944 136.9425 m S 399.6944 136.9425 m S 0 g 1 w 4 M 399.6944 136.9425 m F 0 G 0.3 w 10 M 399.6944 136.9425 m S 399.6944 136.9425 m S 1 g 1 w 4 M 394.6763 136.9425 m 394.6763 134.2492 396.923 132.0659 399.6944 132.0659 c 402.4657 132.0659 404.7124 134.2492 404.7124 136.9425 c F 404.7124 136.9425 m 404.7124 139.6358 402.4657 141.8191 399.6944 141.8191 c 396.923 141.8191 394.6763 139.6358 394.6763 136.9425 c F 399.6944 136.9425 m F 0 G 0.3 w 10 M 399.6944 136.9425 m S 0 g 1 w 4 M 399.6944 136.9425 m F 0 G 0.3 w 10 M 399.6944 136.9425 m S 399.6944 136.9425 m S 0 g 1 w 4 M 398.7884 136.0498 m 398.7884 133.0595 L 400.6003 133.0595 L 400.6003 136.0498 L 403.5939 136.0404 L 403.5939 137.8448 L 400.6003 137.8355 L 400.6003 140.8258 L 398.7884 140.8258 L 398.7884 137.8355 L 395.7948 137.8448 L 395.7948 136.0404 L 398.7884 136.0498 L f 0 G 0.3 w 10 M 399.6944 118.3605 m S 0 g 1 w 4 M 399.6944 118.3605 m F 0 G 0.3 w 10 M 399.6944 118.3605 m S 399.6944 118.3605 m S 399.6944 118.3605 m S 0 g 1 w 4 M 399.6944 118.3605 m F 0 G 0.3 w 10 M 399.6944 118.3605 m S 399.6944 118.3605 m S 1 g 1 w 4 M 394.6763 118.3605 m 394.6763 115.6672 396.923 113.4838 399.6944 113.4838 c 402.4657 113.4838 404.7124 115.6672 404.7124 118.3605 c F 404.7124 118.3605 m 404.7124 121.0537 402.4657 123.2371 399.6944 123.2371 c 396.923 123.2371 394.6763 121.0537 394.6763 118.3605 c F 399.6944 118.3605 m F 0 G 0.3 w 10 M 399.6944 118.3605 m S 0 g 1 w 4 M 399.6944 118.3605 m F 0 G 0.3 w 10 M 399.6944 118.3605 m S 399.6944 118.3605 m S 0 g 1 w 4 M 398.7884 117.4677 m 398.7884 114.4774 L 400.6003 114.4774 L 400.6003 117.4677 L 403.5939 117.4584 L 403.5939 119.2627 L 400.6003 119.2534 L 400.6003 122.2437 L 398.7884 122.2437 L 398.7884 119.2534 L 395.7948 119.2627 L 395.7948 117.4584 L 398.7884 117.4677 L f 0 G 0.3 w 10 M 399.6944 99.7783 m S 0 g 1 w 4 M 399.6944 99.7783 m F 0 G 0.3 w 10 M 399.6944 99.7783 m S 399.6944 99.7783 m S 399.6944 99.7783 m S 0 g 1 w 4 M 399.6944 99.7783 m F 0 G 0.3 w 10 M 399.6944 99.7783 m S 399.6944 99.7783 m S 1 g 1 w 4 M 394.6763 99.7783 m 394.6763 97.085 396.923 94.9017 399.6944 94.9017 c 402.4657 94.9017 404.7124 97.085 404.7124 99.7783 c F 404.7124 99.7783 m 404.7124 102.4716 402.4657 104.6549 399.6944 104.6549 c 396.923 104.6549 394.6763 102.4716 394.6763 99.7783 c F 399.6944 99.7783 m F 0 G 0.3 w 10 M 399.6944 99.7783 m S 0 g 1 w 4 M 399.6944 99.7783 m F 0 G 0.3 w 10 M 399.6944 99.7783 m S 399.6944 99.7783 m S 0 g 1 w 4 M 398.7884 98.8856 m 398.7884 95.8953 L 400.6003 95.8953 L 400.6003 98.8856 L 403.5939 98.8762 L 403.5939 100.6806 L 400.6003 100.6713 L 400.6003 103.6616 L 398.7884 103.6616 L 398.7884 100.6713 L 395.7948 100.6806 L 395.7948 98.8762 L 398.7884 98.8856 L f 0 G 0.3 w 10 M 418.7386 81.1962 m S 418.7386 81.1962 m S 437.7827 81.1962 m S 418.7386 81.1962 m S 437.7827 81.1962 m S 418.7386 81.1962 m S 456.8269 81.1962 m S 437.7827 81.1962 m S 456.8269 81.1962 m S 456.8269 81.1962 m S 456.8269 81.1962 m S 437.7827 81.1962 m S 418.7386 81.1962 m S 0 g 1 w 4 M 418.7386 81.1962 m F 0 G 0.3 w 10 M 418.7386 81.1962 m S 418.7386 81.1962 m S 418.7386 81.1962 m S 0 g 1 w 4 M 418.7386 81.1962 m F 0 G 0.3 w 10 M 418.7386 81.1962 m S 418.7386 81.1962 m S 1 g 1 w 4 M 413.7205 81.1962 m 413.7205 78.503 415.9672 76.3196 418.7386 76.3196 c 421.51 76.3196 423.7567 78.503 423.7567 81.1962 c F 423.7567 81.1962 m 423.7567 83.8895 421.51 86.0729 418.7386 86.0729 c 415.9672 86.0729 413.7205 83.8895 413.7205 81.1962 c F 418.7386 81.1962 m F 0 G 0.3 w 10 M 418.7386 81.1962 m S 0 g 1 w 4 M 418.7386 81.1962 m F 0 G 0.3 w 10 M 418.7386 81.1962 m S 418.7386 81.1962 m S 0 g 1 w 4 M 417.8327 80.3035 m 417.8327 77.3132 L 419.6445 77.3132 L 419.6445 80.3035 L 422.6382 80.2942 L 422.6382 82.0985 L 419.6445 82.0892 L 419.6445 85.0795 L 417.8327 85.0795 L 417.8327 82.0892 L 414.839 82.0985 L 414.839 80.2942 L 417.8327 80.3035 L f 0 G 0.3 w 10 M 437.7827 81.1962 m S 0 g 1 w 4 M 437.7827 81.1962 m F 0 G 0.3 w 10 M 437.7827 81.1962 m S 437.7827 81.1962 m S 437.7827 81.1962 m S 0 g 1 w 4 M 437.7827 81.1962 m F 0 G 0.3 w 10 M 437.7827 81.1962 m S 437.7827 81.1962 m S 1 g 1 w 4 M 432.7647 81.1962 m 432.7647 78.503 435.0114 76.3196 437.7827 76.3196 c 440.5541 76.3196 442.8008 78.503 442.8008 81.1962 c F 442.8008 81.1962 m 442.8008 83.8895 440.5541 86.0729 437.7827 86.0729 c 435.0114 86.0729 432.7647 83.8895 432.7647 81.1962 c F 437.7827 81.1962 m F 0 G 0.3 w 10 M 437.7827 81.1962 m S 0 g 1 w 4 M 437.7827 81.1962 m F 0 G 0.3 w 10 M 437.7827 81.1962 m S 437.7827 81.1962 m S 0 g 1 w 4 M 436.8768 80.3035 m 436.8768 77.3132 L 438.6887 77.3132 L 438.6887 80.3035 L 441.6823 80.2942 L 441.6823 82.0985 L 438.6887 82.0892 L 438.6887 85.0795 L 436.8768 85.0795 L 436.8768 82.0892 L 433.8832 82.0985 L 433.8832 80.2942 L 436.8768 80.3035 L f 0 G 0.3 w 10 M 456.8269 81.1962 m S 0 g 1 w 4 M 456.8269 81.1962 m F 0 G 0.3 w 10 M 456.8269 81.1962 m S 456.8269 81.1962 m S 456.8269 81.1962 m S 0 g 1 w 4 M 456.8269 81.1962 m F 0 G 0.3 w 10 M 456.8269 81.1962 m S 456.8269 81.1962 m S 1 g 1 w 4 M 451.8088 81.1962 m 451.8088 78.503 454.0555 76.3196 456.8269 76.3196 c 459.5983 76.3196 461.845 78.503 461.845 81.1962 c F 461.845 81.1962 m 461.845 83.8895 459.5983 86.0729 456.8269 86.0729 c 454.0555 86.0729 451.8088 83.8895 451.8088 81.1962 c F 456.8269 81.1962 m F 0 G 0.3 w 10 M 456.8269 81.1962 m S 0 g 1 w 4 M 456.8269 81.1962 m F 0 G 0.3 w 10 M 456.8269 81.1962 m S 456.8269 81.1962 m S 0 g 1 w 4 M 455.921 80.3035 m 455.921 77.3132 L 457.7328 77.3132 L 457.7328 80.3035 L 460.7265 80.2942 L 460.7265 82.0985 L 457.7328 82.0892 L 457.7328 85.0795 L 455.921 85.0795 L 455.921 82.0892 L 452.9273 82.0985 L 452.9273 80.2942 L 455.921 80.3035 L f 0 G 0.3 w 10 M 475.8711 136.9425 m S 475.8711 118.3605 m S 475.8711 136.9425 m S 475.8711 136.9425 m S 475.8711 118.3605 m S 475.8711 136.9425 m S 475.8711 118.3605 m S 475.8711 99.7783 m S 475.8711 99.7783 m S 475.8711 99.7783 m S 475.8711 118.3605 m S 475.8711 99.7783 m S 475.8711 136.9425 m S 0 g 1 w 4 M 475.8711 136.9425 m F 0 G 0.3 w 10 M 475.8711 136.9425 m S 475.8711 136.9425 m S 475.8711 136.9425 m S 0 g 1 w 4 M 475.8711 136.9425 m F 0 G 0.3 w 10 M 475.8711 136.9425 m S 475.8711 136.9425 m S 1 g 1 w 4 M 470.853 136.9425 m 470.853 134.2492 473.0998 132.0659 475.8711 132.0659 c 478.6425 132.0659 480.8892 134.2492 480.8892 136.9425 c F 480.8892 136.9425 m 480.8892 139.6358 478.6425 141.8191 475.8711 141.8191 c 473.0998 141.8191 470.853 139.6358 470.853 136.9425 c F 475.8711 136.9425 m F 0 G 0.3 w 10 M 475.8711 136.9425 m S 0 g 1 w 4 M 475.8711 136.9425 m F 0 G 0.3 w 10 M 475.8711 136.9425 m S 475.8711 136.9425 m S 0 g 1 w 4 M 474.9652 136.0498 m 474.9652 133.0595 L 476.7771 133.0595 L 476.7771 136.0498 L 479.7707 136.0404 L 479.7707 137.8448 L 476.7771 137.8355 L 476.7771 140.8258 L 474.9652 140.8258 L 474.9652 137.8355 L 471.9716 137.8448 L 471.9716 136.0404 L 474.9652 136.0498 L f 0 G 0.3 w 10 M 475.8711 118.3605 m S 0 g 1 w 4 M 475.8711 118.3605 m F 0 G 0.3 w 10 M 475.8711 118.3605 m S 475.8711 118.3605 m S 475.8711 118.3605 m S 0 g 1 w 4 M 475.8711 118.3605 m F 0 G 0.3 w 10 M 475.8711 118.3605 m S 475.8711 118.3605 m S 1 g 1 w 4 M 470.853 118.3605 m 470.853 115.6672 473.0998 113.4838 475.8711 113.4838 c 478.6425 113.4838 480.8892 115.6672 480.8892 118.3605 c F 480.8892 118.3605 m 480.8892 121.0537 478.6425 123.2371 475.8711 123.2371 c 473.0998 123.2371 470.853 121.0537 470.853 118.3605 c F 475.8711 118.3605 m F 0 G 0.3 w 10 M 475.8711 118.3605 m S 0 g 1 w 4 M 475.8711 118.3605 m F 0 G 0.3 w 10 M 475.8711 118.3605 m S 475.8711 118.3605 m S 0 g 1 w 4 M 474.9652 117.4677 m 474.9652 114.4774 L 476.7771 114.4774 L 476.7771 117.4677 L 479.7707 117.4584 L 479.7707 119.2627 L 476.7771 119.2534 L 476.7771 122.2437 L 474.9652 122.2437 L 474.9652 119.2534 L 471.9716 119.2627 L 471.9716 117.4584 L 474.9652 117.4677 L f 0 G 0.3 w 10 M 475.8711 99.7783 m S 0 g 1 w 4 M 475.8711 99.7783 m F 0 G 0.3 w 10 M 475.8711 99.7783 m S 475.8711 99.7783 m S 475.8711 99.7783 m S 0 g 1 w 4 M 475.8711 99.7783 m F 0 G 0.3 w 10 M 475.8711 99.7783 m S 475.8711 99.7783 m S 1 g 1 w 4 M 470.853 99.7783 m 470.853 97.085 473.0998 94.9017 475.8711 94.9017 c 478.6425 94.9017 480.8892 97.085 480.8892 99.7783 c F 480.8892 99.7783 m 480.8892 102.4716 478.6425 104.6549 475.8711 104.6549 c 473.0998 104.6549 470.853 102.4716 470.853 99.7783 c F 475.8711 99.7783 m F 0 G 0.3 w 10 M 475.8711 99.7783 m S 0 g 1 w 4 M 475.8711 99.7783 m F 0 G 0.3 w 10 M 475.8711 99.7783 m S 475.8711 99.7783 m S 0 g 1 w 4 M 474.9652 98.8856 m 474.9652 95.8953 L 476.7771 95.8953 L 476.7771 98.8856 L 479.7707 98.8762 L 479.7707 100.6806 L 476.7771 100.6713 L 476.7771 103.6616 L 474.9652 103.6616 L 474.9652 100.6713 L 471.9716 100.6806 L 471.9716 98.8762 L 474.9652 98.8856 L f 0 G 0.3 w 10 M 428.2606 127.6515 m S 428.2606 127.6515 m S 447.3048 127.6515 m S 428.2606 127.6515 m S 447.3048 127.6515 m S 447.3048 127.6515 m S 447.3048 127.6515 m S 428.2606 127.6515 m S 428.2606 109.0694 m S 428.2606 109.0694 m S 447.3048 109.0694 m S 428.2606 109.0694 m S 447.3048 109.0694 m S 447.3048 109.0694 m S 447.3048 109.0694 m S 428.2606 109.0694 m S 190.3268 136.9425 m S 0 g 1 w 4 M 190.3268 136.9425 m F 0 G 0.3 w 10 M 190.3268 136.9425 m S 0 g 1 w 4 M 190.3268 136.9425 m F 1 g 190.3268 136.9425 m F 0 G 0.3 w 10 M 190.3268 136.9425 m S 0 g 1 w 4 M 190.3268 136.9425 m F 0 G 0.3 w 10 M 190.3268 136.9425 m S 0 g 1 w 4 M 190.3268 136.9425 m F 0 G 0.3 w 10 M 190.3268 118.3605 m S 0 g 1 w 4 M 190.3268 118.3605 m F 0 G 0.3 w 10 M 190.3268 118.3605 m S 0 g 1 w 4 M 190.3268 118.3605 m F 1 g 185.3118 118.3605 m 185.3118 115.6672 187.5571 113.4838 190.3268 113.4838 c 193.0964 113.4838 195.3417 115.6672 195.3417 118.3605 c F 195.3417 118.3605 m 195.3417 121.0537 193.0964 123.2371 190.3268 123.2371 c 187.5571 123.2371 185.3118 121.0537 185.3118 118.3605 c F 190.3268 118.3605 m F 0 G 0.3 w 10 M 190.3268 118.3605 m S 0 g 1 w 4 M 190.3268 118.3605 m F 0 G 0.3 w 10 M 190.3268 118.3605 m S 0 g 1 w 4 M 190.3268 118.3605 m F 189.4214 119.2534 m 186.4296 119.2627 L 186.4296 117.4584 L 189.4214 117.4676 L F 191.2322 117.4676 m 194.2239 117.4584 L 194.2239 119.2627 L 191.2322 119.2534 L F 186.4296 119.2627 m 194.2239 119.2627 l 194.2239 117.4584 l 186.4296 117.4584 l 186.4296 119.2627 l f 0 G 0.3 w 10 M 209.3591 118.3605 m S 0 g 1 w 4 M 209.3591 118.3605 m F 0 G 0.3 w 10 M 209.3591 118.3605 m S 0 g 1 w 4 M 209.3591 118.3605 m F 1 g 204.3441 118.3605 m 204.3441 115.6672 206.5895 113.4838 209.3591 113.4838 c 212.1287 113.4838 214.3741 115.6672 214.3741 118.3605 c F 214.3741 118.3605 m 214.3741 121.0537 212.1287 123.2371 209.3591 123.2371 c 206.5895 123.2371 204.3441 121.0537 204.3441 118.3605 c F 209.3591 118.3605 m F 0 G 0.3 w 10 M 209.3591 118.3605 m S 0 g 1 w 4 M 209.3591 118.3605 m F 0 G 0.3 w 10 M 209.3591 118.3605 m S 0 g 1 w 4 M 209.3591 118.3605 m F 208.4537 119.2534 m 205.462 119.2627 L 205.462 117.4584 L 208.4537 117.4676 L F 210.2645 117.4676 m 213.2563 117.4584 L 213.2563 119.2627 L 210.2645 119.2534 L F 205.462 119.2627 m 213.2563 119.2627 l 213.2563 117.4584 l 205.462 117.4584 l 205.462 119.2627 l f 0 G 0.3 w 10 M 209.3591 99.7783 m S 0 g 1 w 4 M 209.3591 99.7783 m F 0 G 0.3 w 10 M 209.3591 99.7783 m S 0 g 1 w 4 M 209.3591 99.7783 m F 1 g 204.3441 99.7783 m 204.3441 97.085 206.5895 94.9017 209.3591 94.9017 c 212.1287 94.9017 214.3741 97.085 214.3741 99.7783 c F 214.3741 99.7783 m 214.3741 102.4716 212.1287 104.6549 209.3591 104.6549 c 206.5895 104.6549 204.3441 102.4716 204.3441 99.7783 c F 209.3591 99.7783 m F 0 G 0.3 w 10 M 209.3591 99.7783 m S 0 g 1 w 4 M 209.3591 99.7783 m F 0 G 0.3 w 10 M 209.3591 99.7783 m S 0 g 1 w 4 M 209.3591 99.7783 m F 208.4537 100.6713 m 205.462 100.6806 L 205.462 98.8762 L 208.4537 98.8855 L F 210.2645 98.8855 m 213.2563 98.8762 L 213.2563 100.6806 L 210.2645 100.6713 L F 205.462 100.6806 m 213.2563 100.6806 l 213.2563 98.8762 l 205.462 98.8762 l 205.462 100.6806 l f 0 G 0.3 w 10 M 190.3268 99.7783 m S 0 g 1 w 4 M 190.3268 99.7783 m F 0 G 0.3 w 10 M 190.3268 99.7783 m S 0 g 1 w 4 M 190.3268 99.7783 m F 1 g 185.3118 99.7783 m 185.3118 97.085 187.5571 94.9017 190.3268 94.9017 c 193.0964 94.9017 195.3417 97.085 195.3417 99.7783 c F 195.3417 99.7783 m 195.3417 102.4716 193.0964 104.6549 190.3268 104.6549 c 187.5571 104.6549 185.3118 102.4716 185.3118 99.7783 c F 190.3268 99.7783 m F 0 G 0.3 w 10 M 190.3268 99.7783 m S 0 g 1 w 4 M 190.3268 99.7783 m F 0 G 0.3 w 10 M 190.3268 99.7783 m S 0 g 1 w 4 M 190.3268 99.7783 m F 189.4214 100.6713 m 186.4296 100.6806 L 186.4296 98.8762 L 189.4214 98.8855 L F 191.2322 98.8855 m 194.2239 98.8762 L 194.2239 100.6806 L 191.2322 100.6713 L F 186.4296 100.6806 m 194.2239 100.6806 l 194.2239 98.8762 l 186.4296 98.8762 l 186.4296 100.6806 l f 0 G 0.3 w 10 M 418.7386 136.9425 m S 0 g 1 w 4 M 418.7386 136.9425 m F 0 G 0.3 w 10 M 418.7386 136.9425 m S 0 g 1 w 4 M 418.7386 136.9425 m F 1 g 418.7386 136.9425 m F 0 G 0.3 w 10 M 418.7386 136.9425 m S 0 g 1 w 4 M 418.7386 136.9425 m F 0 G 0.3 w 10 M 418.7386 136.9425 m S 0 g 1 w 4 M 418.7386 136.9425 m F 0 G 0.3 w 10 M 437.7827 136.9425 m S 0 g 1 w 4 M 437.7827 136.9425 m F 0 G 0.3 w 10 M 437.7827 136.9425 m S 0 g 1 w 4 M 437.7827 136.9425 m F 1 g 437.7827 136.9425 m F 0 G 0.3 w 10 M 437.7827 136.9425 m S 0 g 1 w 4 M 437.7827 136.9425 m F 0 G 0.3 w 10 M 437.7827 136.9425 m S 0 g 1 w 4 M 437.7827 136.9425 m F 0 G 0.3 w 10 M 456.8269 136.9425 m S 0 g 1 w 4 M 456.8269 136.9425 m F 0 G 0.3 w 10 M 456.8269 136.9425 m S 0 g 1 w 4 M 456.8269 136.9425 m F 1 g 451.8088 136.9425 m 451.8088 134.2492 454.0555 132.0659 456.8269 132.0659 c 459.5983 132.0659 461.845 134.2492 461.845 136.9425 c F 461.845 136.9425 m 461.845 139.6358 459.5983 141.8191 456.8269 141.8191 c 454.0555 141.8191 451.8088 139.6358 451.8088 136.9425 c F 456.8269 136.9425 m F 0 G 0.3 w 10 M 456.8269 136.9425 m S 0 g 1 w 4 M 456.8269 136.9425 m F 0 G 0.3 w 10 M 456.8269 136.9425 m S 0 g 1 w 4 M 456.8269 136.9425 m F 455.921 137.8355 m 452.9273 137.8448 L 452.9273 136.0404 L 455.921 136.0497 L F 457.7328 136.0497 m 460.7265 136.0404 L 460.7265 137.8448 L 457.7328 137.8355 L F 452.9273 137.8448 m 460.7265 137.8448 l 460.7265 136.0404 l 452.9273 136.0404 l 452.9273 137.8448 l f 0 G 0.3 w 10 M 456.8269 118.3605 m S 0 g 1 w 4 M 456.8269 118.3605 m F 0 G 0.3 w 10 M 456.8269 118.3605 m S 0 g 1 w 4 M 456.8269 118.3605 m F 1 g 451.8088 118.3605 m 451.8088 115.6672 454.0555 113.4838 456.8269 113.4838 c 459.5983 113.4838 461.845 115.6672 461.845 118.3605 c F 461.845 118.3605 m 461.845 121.0537 459.5983 123.2371 456.8269 123.2371 c 454.0555 123.2371 451.8088 121.0537 451.8088 118.3605 c F 456.8269 118.3605 m F 0 G 0.3 w 10 M 456.8269 118.3605 m S 0 g 1 w 4 M 456.8269 118.3605 m F 0 G 0.3 w 10 M 456.8269 118.3605 m S 0 g 1 w 4 M 456.8269 118.3605 m F 455.921 119.2534 m 452.9273 119.2627 L 452.9273 117.4584 L 455.921 117.4676 L F 457.7328 117.4676 m 460.7265 117.4584 L 460.7265 119.2627 L 457.7328 119.2534 L F 452.9273 119.2627 m 460.7265 119.2627 l 460.7265 117.4584 l 452.9273 117.4584 l 452.9273 119.2627 l f 0 G 0.3 w 10 M 437.7827 118.3605 m S 0 g 1 w 4 M 437.7827 118.3605 m F 0 G 0.3 w 10 M 437.7827 118.3605 m S 0 g 1 w 4 M 437.7827 118.3605 m F 1 g 432.7647 118.3605 m 432.7647 115.6672 435.0114 113.4838 437.7827 113.4838 c 440.5541 113.4838 442.8008 115.6672 442.8008 118.3605 c F 442.8008 118.3605 m 442.8008 121.0537 440.5541 123.2371 437.7827 123.2371 c 435.0114 123.2371 432.7647 121.0537 432.7647 118.3605 c F 437.7827 118.3605 m F 0 G 0.3 w 10 M 437.7827 118.3605 m S 0 g 1 w 4 M 437.7827 118.3605 m F 0 G 0.3 w 10 M 437.7827 118.3605 m S 0 g 1 w 4 M 437.7827 118.3605 m F 436.8768 119.2534 m 433.8832 119.2627 L 433.8832 117.4584 L 436.8768 117.4676 L F 438.6887 117.4676 m 441.6823 117.4584 L 441.6823 119.2627 L 438.6887 119.2534 L F 433.8832 119.2627 m 441.6823 119.2627 l 441.6823 117.4584 l 433.8832 117.4584 l 433.8832 119.2627 l f 0 G 0.3 w 10 M 228.3914 136.9425 m S 0 g 1 w 4 M 228.3914 136.9425 m F 0 G 0.3 w 10 M 228.3914 136.9425 m S 228.3914 136.9425 m S 228.3914 136.9425 m S 0 g 1 w 4 M 228.3914 136.9425 m F 0 G 0.3 w 10 M 228.3914 136.9425 m S 228.3914 136.9425 m S 1 g 1 w 4 M 223.3765 136.9425 m 223.3765 134.2492 225.6218 132.0659 228.3914 132.0659 c 231.1611 132.0659 233.4064 134.2492 233.4064 136.9425 c F 233.4064 136.9425 m 233.4064 139.6358 231.1611 141.8191 228.3914 141.8191 c 225.6218 141.8191 223.3765 139.6358 223.3765 136.9425 c F 228.3914 136.9425 m F 0 G 0.3 w 10 M 228.3914 136.9425 m S 0 g 1 w 4 M 228.3914 136.9425 m F 0 G 0.3 w 10 M 228.3914 136.9425 m S 228.3914 136.9425 m S 0 g 1 w 4 M 227.486 136.0498 m 227.486 133.0595 L 229.2968 133.0595 L 229.2968 136.0498 L 232.2886 136.0404 L 232.2886 137.8448 L 229.2968 137.8355 L 229.2968 140.8258 L 227.486 140.8258 L 227.486 137.8355 L 224.4943 137.8448 L 224.4943 136.0404 L 227.486 136.0498 L f 0 G 0.3 w 10 M 209.3591 136.9425 m S 0 g 1 w 4 M 209.3591 136.9425 m F 0 G 0.3 w 10 M 209.3591 136.9425 m S 209.3591 136.9425 m S 209.3591 136.9425 m S 0 g 1 w 4 M 209.3591 136.9425 m F 0 G 0.3 w 10 M 209.3591 136.9425 m S 209.3591 136.9425 m S 1 g 1 w 4 M 209.3591 136.9425 m F 0 G 0.3 w 10 M 209.3591 136.9425 m S 0 g 1 w 4 M 209.3591 136.9425 m F 0 G 0.3 w 10 M 209.3591 136.9425 m S 209.3591 136.9425 m S 228.3914 118.3605 m S 0 g 1 w 4 M 228.3914 118.3605 m F 0 G 0.3 w 10 M 228.3914 118.3605 m S 228.3914 118.3605 m S 228.3914 118.3605 m S 0 g 1 w 4 M 228.3914 118.3605 m F 0 G 0.3 w 10 M 228.3914 118.3605 m S 228.3914 118.3605 m S 1 g 1 w 4 M 223.3765 118.3605 m 223.3765 115.6672 225.6218 113.4838 228.3914 113.4838 c 231.1611 113.4838 233.4064 115.6672 233.4064 118.3605 c F 233.4064 118.3605 m 233.4064 121.0537 231.1611 123.2371 228.3914 123.2371 c 225.6218 123.2371 223.3765 121.0537 223.3765 118.3605 c F 228.3914 118.3605 m F 0 G 0.3 w 10 M 228.3914 118.3605 m S 0 g 1 w 4 M 228.3914 118.3605 m F 0 G 0.3 w 10 M 228.3914 118.3605 m S 228.3914 118.3605 m S 0 g 1 w 4 M 227.486 117.4677 m 227.486 114.4774 L 229.2968 114.4774 L 229.2968 117.4677 L 232.2886 117.4584 L 232.2886 119.2627 L 229.2968 119.2534 L 229.2968 122.2437 L 227.486 122.2437 L 227.486 119.2534 L 224.4943 119.2627 L 224.4943 117.4584 L 227.486 117.4677 L f 0 G 0.3 w 10 M 228.3914 99.7783 m S 0 g 1 w 4 M 228.3914 99.7783 m F 0 G 0.3 w 10 M 228.3914 99.7783 m S 228.3914 99.7783 m S 228.3914 99.7783 m S 0 g 1 w 4 M 228.3914 99.7783 m F 0 G 0.3 w 10 M 228.3914 99.7783 m S 228.3914 99.7783 m S 1 g 1 w 4 M 223.3765 99.7783 m 223.3765 97.085 225.6218 94.9017 228.3914 94.9017 c 231.1611 94.9017 233.4064 97.085 233.4064 99.7783 c F 233.4064 99.7783 m 233.4064 102.4716 231.1611 104.6549 228.3914 104.6549 c 225.6218 104.6549 223.3765 102.4716 223.3765 99.7783 c F 228.3914 99.7783 m F 0 G 0.3 w 10 M 228.3914 99.7783 m S 0 g 1 w 4 M 228.3914 99.7783 m F 0 G 0.3 w 10 M 228.3914 99.7783 m S 228.3914 99.7783 m S 0 g 1 w 4 M 227.486 98.8856 m 227.486 95.8953 L 229.2968 95.8953 L 229.2968 98.8856 L 232.2886 98.8762 L 232.2886 100.6806 L 229.2968 100.6713 L 229.2968 103.6616 L 227.486 103.6616 L 227.486 100.6713 L 224.4943 100.6806 L 224.4943 98.8762 L 227.486 98.8856 L f 0 G 0.3 w 10 M 418.7386 118.3605 m S 0 g 1 w 4 M 418.7386 118.3605 m F 0 G 0.3 w 10 M 418.7386 118.3605 m S 418.7386 118.3605 m S 418.7386 118.3605 m S 0 g 1 w 4 M 418.7386 118.3605 m F 0 G 0.3 w 10 M 418.7386 118.3605 m S 418.7386 118.3605 m S 1 g 1 w 4 M 413.7205 118.3605 m 413.7205 115.6672 415.9672 113.4838 418.7386 113.4838 c 421.51 113.4838 423.7567 115.6672 423.7567 118.3605 c F 423.7567 118.3605 m 423.7567 121.0537 421.51 123.2371 418.7386 123.2371 c 415.9672 123.2371 413.7205 121.0537 413.7205 118.3605 c F 418.7386 118.3605 m F 0 G 0.3 w 10 M 418.7386 118.3605 m S 0 g 1 w 4 M 418.7386 118.3605 m F 0 G 0.3 w 10 M 418.7386 118.3605 m S 418.7386 118.3605 m S 0 g 1 w 4 M 417.8327 117.4677 m 417.8327 114.4774 L 419.6445 114.4774 L 419.6445 117.4677 L 422.6382 117.4584 L 422.6382 119.2627 L 419.6445 119.2534 L 419.6445 122.2437 L 417.8327 122.2437 L 417.8327 119.2534 L 414.839 119.2627 L 414.839 117.4584 L 417.8327 117.4677 L f 0 G 0.3 w 10 M 437.7827 99.7783 m S 0 g 1 w 4 M 437.7827 99.7783 m F 0 G 0.3 w 10 M 437.7827 99.7783 m S 437.7827 99.7783 m S 437.7827 99.7783 m S 0 g 1 w 4 M 437.7827 99.7783 m F 0 G 0.3 w 10 M 437.7827 99.7783 m S 437.7827 99.7783 m S 1 g 1 w 4 M 437.7827 99.7783 m F 0 G 0.3 w 10 M 437.7827 99.7783 m S 0 g 1 w 4 M 437.7827 99.7783 m F 0 G 0.3 w 10 M 437.7827 99.7783 m S 437.7827 99.7783 m S 456.8269 99.7783 m S 0 g 1 w 4 M 456.8269 99.7783 m F 0 G 0.3 w 10 M 456.8269 99.7783 m S 456.8269 99.7783 m S 456.8269 99.7783 m S 0 g 1 w 4 M 456.8269 99.7783 m F 0 G 0.3 w 10 M 456.8269 99.7783 m S 456.8269 99.7783 m S 1 g 1 w 4 M 456.8269 99.7783 m F 0 G 0.3 w 10 M 456.8269 99.7783 m S 0 g 1 w 4 M 456.8269 99.7783 m F 0 G 0.3 w 10 M 456.8269 99.7783 m S 456.8269 99.7783 m S 418.7386 99.7783 m S 0 g 1 w 4 M 418.7386 99.7783 m F 0 G 0.3 w 10 M 418.7386 99.7783 m S 418.7386 99.7783 m S 418.7386 99.7783 m S 0 g 1 w 4 M 418.7386 99.7783 m F 0 G 0.3 w 10 M 418.7386 99.7783 m S 418.7386 99.7783 m S 1 g 1 w 4 M 413.7205 99.7783 m 413.7205 97.085 415.9672 94.9017 418.7386 94.9017 c 421.51 94.9017 423.7567 97.085 423.7567 99.7783 c F 423.7567 99.7783 m 423.7567 102.4716 421.51 104.6549 418.7386 104.6549 c 415.9672 104.6549 413.7205 102.4716 413.7205 99.7783 c F 418.7386 99.7783 m F 0 G 0.3 w 10 M 418.7386 99.7783 m S 0 g 1 w 4 M 418.7386 99.7783 m F 0 G 0.3 w 10 M 418.7386 99.7783 m S 418.7386 99.7783 m S 0 g 1 w 4 M 417.8327 98.8856 m 417.8327 95.8953 L 419.6445 95.8953 L 419.6445 98.8856 L 422.6382 98.8762 L 422.6382 100.6806 L 419.6445 100.6713 L 419.6445 103.6616 L 417.8327 103.6616 L 417.8327 100.6713 L 414.839 100.6806 L 414.839 98.8762 L 417.8327 98.8856 L f 0 G 0.3 w 10 M 38.068 136.9425 m S 38.068 118.3605 m S 38.068 174.1067 m S 38.068 155.5247 m S 38.068 155.5247 m S 38.068 136.9425 m S 57.1003 174.1067 m S 57.1003 155.5247 m S 38.068 155.5247 m S 38.068 174.1067 m S 47.5841 164.8157 m S 95.1651 136.9425 m S 95.1651 118.3605 m S 76.1327 118.3605 m S 76.1327 136.9425 m S 85.6488 127.6515 m S 76.1327 155.5247 m S 76.1327 136.9425 m S 57.1003 136.9425 m S 57.1003 155.5247 m S 66.6165 146.2336 m S 76.1327 174.1067 m S 76.1327 155.5247 m S 57.1003 155.5247 m S 57.1003 174.1067 m S 66.6165 164.8157 m S 95.1651 174.1067 m S 95.1651 155.5247 m S 76.1327 155.5247 m S 76.1327 174.1067 m S 85.6488 164.8157 m S 95.1651 155.5247 m S 95.1651 136.9425 m S 76.1327 136.9425 m S 76.1327 155.5247 m S 85.6488 146.2336 m S 76.1327 136.9425 m S 76.1327 118.3605 m S 57.1003 118.3605 m S 57.1003 136.9425 m S 66.6165 127.6515 m S 57.1003 136.9425 m S 57.1003 118.3605 m S 38.068 118.3605 m S 38.068 136.9425 m S 47.5841 127.6515 m S 57.1003 155.5247 m S 57.1003 136.9425 m S 38.068 136.9425 m S 38.068 155.5247 m S 47.5841 146.2336 m S 0 g 1 w 4 M 47.5841 164.8157 m F 85.6488 164.8157 m F 47.5841 127.6515 m F 85.6488 127.6515 m F 0 G 0.3 w 10 M 114.1974 174.1067 m S 114.1974 155.5247 m S 95.1651 155.5247 m S 95.1651 174.1067 m S 104.6812 164.8157 m S 152.2621 136.9425 m S 152.2621 118.3605 m S 133.2298 118.3605 m S 133.2298 136.9425 m S 142.7459 127.6515 m S 133.2298 155.5247 m S 133.2298 136.9425 m S 114.1974 136.9425 m S 114.1974 155.5247 m S 123.7136 146.2336 m S 133.2298 174.1067 m S 133.2298 155.5247 m S 114.1974 155.5247 m S 114.1974 174.1067 m S 123.7136 164.8157 m S 152.2621 174.1067 m S 152.2621 155.5247 m S 133.2298 155.5247 m S 133.2298 174.1067 m S 142.7459 164.8157 m S 152.2621 155.5247 m S 152.2621 136.9425 m S 133.2298 136.9425 m S 133.2298 155.5247 m S 142.7459 146.2336 m S 133.2298 136.9425 m S 133.2298 118.3605 m S 114.1974 118.3605 m S 114.1974 136.9425 m S 123.7136 127.6515 m S 114.1974 136.9425 m S 114.1974 118.3605 m S 95.1651 118.3605 m S 95.1651 136.9425 m S 104.6812 127.6515 m S 114.1974 155.5247 m S 114.1974 136.9425 m S 95.1651 136.9425 m S 95.1651 155.5247 m S 104.6812 146.2336 m S 0 g 1 w 4 M 104.6812 164.8157 m F 142.7459 164.8157 m F 104.6812 127.6515 m F 142.7459 127.6515 m F 0 G 0.3 w 10 M 38.068 81.1962 m S 38.068 62.6142 m S 38.068 118.3605 m S 38.068 99.7783 m S 38.068 99.7783 m S 38.068 81.1962 m S 57.1003 118.3605 m S 57.1003 99.7783 m S 38.068 99.7783 m S 38.068 118.3605 m S 47.5841 109.0694 m S 95.1651 81.1962 m S 95.1651 62.6142 m S 76.1327 62.6142 m S 76.1327 81.1962 m S 85.6488 71.9052 m S 76.1327 99.7783 m S 76.1327 81.1962 m S 57.1003 81.1962 m S 57.1003 99.7783 m S 66.6165 90.4874 m S 76.1327 118.3605 m S 76.1327 99.7783 m S 57.1003 99.7783 m S 57.1003 118.3605 m S 66.6165 109.0694 m S 95.1651 118.3605 m S 95.1651 99.7783 m S 76.1327 99.7783 m S 76.1327 118.3605 m S 85.6488 109.0694 m S 95.1651 99.7783 m S 95.1651 81.1962 m S 76.1327 81.1962 m S 76.1327 99.7783 m S 85.6488 90.4874 m S 76.1327 81.1962 m S 76.1327 62.6142 m S 57.1003 62.6142 m S 57.1003 81.1962 m S 66.6165 71.9052 m S 57.1003 81.1962 m S 57.1003 62.6142 m S 38.068 62.6142 m S 38.068 81.1962 m S 47.5841 71.9052 m S 57.1003 99.7783 m S 57.1003 81.1962 m S 38.068 81.1962 m S 38.068 99.7783 m S 47.5841 90.4874 m S 0 g 1 w 4 M 47.5841 109.0694 m F 85.6488 109.0694 m F 47.5841 71.9052 m F 85.6488 71.9052 m F 0 G 0.3 w 10 M 114.1974 118.3605 m S 114.1974 99.7783 m S 95.1651 99.7783 m S 95.1651 118.3605 m S 104.6812 109.0694 m S 152.2621 81.1962 m S 152.2621 62.6142 m S 133.2298 62.6142 m S 133.2298 81.1962 m S 142.7459 71.9052 m S 133.2298 99.7783 m S 133.2298 81.1962 m S 114.1974 81.1962 m S 114.1974 99.7783 m S 123.7136 90.4874 m S 133.2298 118.3605 m S 133.2298 99.7783 m S 114.1974 99.7783 m S 114.1974 118.3605 m S 123.7136 109.0694 m S 152.2621 118.3605 m S 152.2621 99.7783 m S 133.2298 99.7783 m S 133.2298 118.3605 m S 142.7459 109.0694 m S 152.2621 99.7783 m S 152.2621 81.1962 m S 133.2298 81.1962 m S 133.2298 99.7783 m S 142.7459 90.4874 m S 133.2298 81.1962 m S 133.2298 62.6142 m S 114.1974 62.6142 m S 114.1974 81.1962 m S 123.7136 71.9052 m S 114.1974 81.1962 m S 114.1974 62.6142 m S 95.1651 62.6142 m S 95.1651 81.1962 m S 104.6812 71.9052 m S 114.1974 99.7783 m S 114.1974 81.1962 m S 95.1651 81.1962 m S 95.1651 99.7783 m S 104.6812 90.4874 m S 0 g 1 w 4 M 104.6812 109.0694 m F 142.7459 109.0694 m F 104.6812 71.9052 m F 142.7459 71.9052 m F 0 G 0.3 w 10 M 38.068 62.6142 m S 57.1003 62.6142 m S 38.068 62.6142 m S 76.1327 62.6142 m S 57.1003 62.6142 m S 95.1651 62.6142 m S 76.1327 62.6142 m S 114.1974 62.6142 m S 95.1651 62.6142 m S 133.2298 62.6142 m S 114.1974 62.6142 m S 152.2621 62.6142 m S 133.2298 62.6142 m S 57.1003 174.1067 m S 57.1003 155.5247 m S 38.068 155.5247 m S 38.068 174.1067 m S 47.5841 164.8157 m S 95.1651 136.9425 m S 95.1651 118.3605 m S 76.1327 118.3605 m S 76.1327 136.9425 m S 76.1327 155.5247 m S 76.1327 136.9425 m S 57.1003 136.9425 m S 57.1003 155.5247 m S 66.6165 146.2336 m S 76.1327 174.1067 m S 76.1327 155.5247 m S 57.1003 155.5247 m S 57.1003 174.1067 m S 66.6165 164.8157 m S 95.1651 174.1067 m S 95.1651 155.5247 m S 76.1327 155.5247 m S 76.1327 174.1067 m S 85.6488 164.8157 m S 95.1651 155.5247 m S 95.1651 136.9425 m S 76.1327 136.9425 m S 76.1327 155.5247 m S 85.6488 146.2336 m S 76.1327 136.9425 m S 76.1327 118.3605 m S 57.1003 118.3605 m S 57.1003 136.9425 m S 66.6165 127.6515 m S 57.1003 136.9425 m S 57.1003 118.3605 m S 38.068 118.3605 m S 38.068 136.9425 m S 47.5841 127.6515 m S 57.1003 155.5247 m S 57.1003 136.9425 m S 38.068 136.9425 m S 38.068 155.5247 m S 47.5841 146.2336 m S 0 g 1 w 4 M 47.5841 164.8157 m F 85.6488 164.8157 m F 47.5841 127.6515 m F 0 G 0.3 w 10 M 114.1974 174.1067 m S 114.1974 155.5247 m S 95.1651 155.5247 m S 95.1651 174.1067 m S 104.6812 164.8157 m S 152.2621 136.9425 m S 152.2621 118.3605 m S 133.2298 118.3605 m S 133.2298 136.9425 m S 142.7459 127.6515 m S 133.2298 155.5247 m S 133.2298 136.9425 m S 114.1974 136.9425 m S 114.1974 155.5247 m S 123.7136 146.2336 m S 133.2298 174.1067 m S 133.2298 155.5247 m S 114.1974 155.5247 m S 114.1974 174.1067 m S 123.7136 164.8157 m S 152.2621 174.1067 m S 152.2621 155.5247 m S 133.2298 155.5247 m S 133.2298 174.1067 m S 142.7459 164.8157 m S 152.2621 155.5247 m S 152.2621 136.9425 m S 133.2298 136.9425 m S 133.2298 155.5247 m S 142.7459 146.2336 m S 133.2298 136.9425 m S 133.2298 118.3605 m S 114.1974 118.3605 m S 114.1974 136.9425 m S 123.7136 127.6515 m S 114.1974 136.9425 m S 114.1974 118.3605 m S 95.1651 118.3605 m S 95.1651 136.9425 m S 104.6812 127.6515 m S 114.1974 155.5247 m S 114.1974 136.9425 m S 95.1651 136.9425 m S 95.1651 155.5247 m S 104.6812 146.2336 m S 0 g 1 w 4 M 104.6812 164.8157 m F 142.7459 164.8157 m F 104.6812 127.6515 m F 142.7459 127.6515 m F 0 G 0.3 w 10 M 57.1003 118.3605 m S 57.1003 99.7783 m S 38.068 99.7783 m S 38.068 118.3605 m S 47.5841 109.0694 m S 95.1651 81.1962 m S 95.1651 62.6142 m S 76.1327 62.6142 m S 76.1327 81.1962 m S 85.6488 71.9052 m S 76.1327 99.7783 m S 76.1327 81.1962 m S 57.1003 81.1962 m S 57.1003 99.7783 m S 66.6165 90.4874 m S 76.1327 118.3605 m S 76.1327 99.7783 m S 57.1003 99.7783 m S 57.1003 118.3605 m S 66.6165 109.0694 m S 95.1651 118.3605 m S 95.1651 99.7783 m S 76.1327 99.7783 m S 76.1327 118.3605 m S 95.1651 99.7783 m S 95.1651 81.1962 m S 76.1327 81.1962 m S 76.1327 99.7783 m S 85.6488 90.4874 m S 76.1327 81.1962 m S 76.1327 62.6142 m S 57.1003 62.6142 m S 57.1003 81.1962 m S 66.6165 71.9052 m S 57.1003 81.1962 m S 57.1003 62.6142 m S 38.068 62.6142 m S 38.068 81.1962 m S 47.5841 71.9052 m S 57.1003 99.7783 m S 57.1003 81.1962 m S 38.068 81.1962 m S 38.068 99.7783 m S 47.5841 90.4874 m S 0 g 1 w 4 M 47.5841 109.0694 m F 47.5841 71.9052 m F 85.6488 71.9052 m F 0 G 0.3 w 10 M 114.1974 118.3605 m S 114.1974 99.7783 m S 95.1651 99.7783 m S 95.1651 118.3605 m S 104.6812 109.0694 m S 152.2621 81.1962 m S 152.2621 62.6142 m S 133.2298 62.6142 m S 133.2298 81.1962 m S 142.7459 71.9052 m S 133.2298 99.7783 m S 133.2298 81.1962 m S 114.1974 81.1962 m S 114.1974 99.7783 m S 123.7136 90.4874 m S 133.2298 118.3605 m S 133.2298 99.7783 m S 114.1974 99.7783 m S 114.1974 118.3605 m S 123.7136 109.0694 m S 152.2621 118.3605 m S 152.2621 99.7783 m S 133.2298 99.7783 m S 133.2298 118.3605 m S 142.7459 109.0694 m S 152.2621 99.7783 m S 152.2621 81.1962 m S 133.2298 81.1962 m S 133.2298 99.7783 m S 142.7459 90.4874 m S 133.2298 81.1962 m S 133.2298 62.6142 m S 114.1974 62.6142 m S 114.1974 81.1962 m S 123.7136 71.9052 m S 114.1974 81.1962 m S 114.1974 62.6142 m S 95.1651 62.6142 m S 95.1651 81.1962 m S 104.6812 71.9052 m S 114.1974 99.7783 m S 114.1974 81.1962 m S 95.1651 81.1962 m S 95.1651 99.7783 m S 104.6812 90.4874 m S 0 g 1 w 4 M 104.6812 109.0694 m F 142.7459 109.0694 m F 104.6812 71.9052 m F 142.7459 71.9052 m F 0 G 0.3 w 10 M 57.1003 62.6142 m S 38.068 62.6142 m S 76.1327 62.6142 m S 57.1003 62.6142 m S 95.1651 62.6142 m S 76.1327 62.6142 m S 114.1974 62.6142 m S 95.1651 62.6142 m S 133.2298 62.6142 m S 114.1974 62.6142 m S 152.2621 62.6142 m S 133.2298 62.6142 m S 1 w 4 M 47.5841 146.2336 m 142.7459 146.2336 l S 47.5841 90.4874 m 142.7459 90.4874 l S 66.6165 164.8157 m 66.6165 71.9052 l S 123.7136 164.8157 m 123.7136 71.9052 l S 0.3 w 10 M 76.1327 155.5247 m S 0 g 1 w 4 M 76.1327 155.5247 m F 0 G 0.3 w 10 M 76.1327 155.5247 m S 76.1327 155.5247 m S 76.1327 155.5247 m S 0 g 1 w 4 M 76.1327 155.5247 m F 0 G 0.3 w 10 M 76.1327 155.5247 m S 76.1327 155.5247 m S 1 g 1 w 4 M 71.1178 155.5247 m 71.1178 152.8314 73.3631 150.648 76.1327 150.648 c 78.9024 150.648 81.1477 152.8314 81.1477 155.5247 c F 81.1477 155.5247 m 81.1477 158.2179 78.9024 160.4013 76.1327 160.4013 c 73.3631 160.4013 71.1178 158.2179 71.1178 155.5247 c F 76.1327 155.5247 m F 0 G 0.3 w 10 M 76.1327 155.5247 m S 0 g 1 w 4 M 76.1327 155.5247 m F 0 G 0.3 w 10 M 76.1327 155.5247 m S 76.1327 155.5247 m S 0 g 1 w 4 M 75.2273 154.6319 m 75.2273 151.6417 L 77.0381 151.6417 L 77.0381 154.6319 L 80.0299 154.6226 L 80.0299 156.4269 L 77.0381 156.4176 L 77.0381 159.4079 L 75.2273 159.4079 L 75.2273 156.4176 L 72.2356 156.4269 L 72.2356 154.6226 L 75.2273 154.6319 L f 0 G 0.3 w 10 M 95.1651 155.5247 m S 0 g 1 w 4 M 95.1651 155.5247 m F 0 G 0.3 w 10 M 95.1651 155.5247 m S 95.1651 155.5247 m S 95.1651 155.5247 m S 0 g 1 w 4 M 95.1651 155.5247 m F 0 G 0.3 w 10 M 95.1651 155.5247 m S 95.1651 155.5247 m S 1 g 1 w 4 M 90.1501 155.5247 m 90.1501 152.8314 92.3954 150.648 95.1651 150.648 c 97.9347 150.648 100.18 152.8314 100.18 155.5247 c F 100.18 155.5247 m 100.18 158.2179 97.9347 160.4013 95.1651 160.4013 c 92.3954 160.4013 90.1501 158.2179 90.1501 155.5247 c F 95.1651 155.5247 m F 0 G 0.3 w 10 M 95.1651 155.5247 m S 0 g 1 w 4 M 95.1651 155.5247 m F 0 G 0.3 w 10 M 95.1651 155.5247 m S 95.1651 155.5247 m S 0 g 1 w 4 M 94.2597 154.6319 m 94.2597 151.6417 L 96.0704 151.6417 L 96.0704 154.6319 L 99.0622 154.6226 L 99.0622 156.4269 L 96.0704 156.4176 L 96.0704 159.4079 L 94.2597 159.4079 L 94.2597 156.4176 L 91.2679 156.4269 L 91.2679 154.6226 L 94.2597 154.6319 L f 0 G 0.3 w 10 M 114.1974 155.5247 m S 0 g 1 w 4 M 114.1974 155.5247 m F 0 G 0.3 w 10 M 114.1974 155.5247 m S 114.1974 155.5247 m S 114.1974 155.5247 m S 0 g 1 w 4 M 114.1974 155.5247 m F 0 G 0.3 w 10 M 114.1974 155.5247 m S 114.1974 155.5247 m S 1 g 1 w 4 M 109.1824 155.5247 m 109.1824 152.8314 111.4277 150.648 114.1974 150.648 c 116.967 150.648 119.2123 152.8314 119.2123 155.5247 c F 119.2123 155.5247 m 119.2123 158.2179 116.967 160.4013 114.1974 160.4013 c 111.4277 160.4013 109.1824 158.2179 109.1824 155.5247 c F 114.1974 155.5247 m F 0 G 0.3 w 10 M 114.1974 155.5247 m S 0 g 1 w 4 M 114.1974 155.5247 m F 0 G 0.3 w 10 M 114.1974 155.5247 m S 114.1974 155.5247 m S 0 g 1 w 4 M 113.292 154.6319 m 113.292 151.6417 L 115.1027 151.6417 L 115.1027 154.6319 L 118.0945 154.6226 L 118.0945 156.4269 L 115.1027 156.4176 L 115.1027 159.4079 L 113.292 159.4079 L 113.292 156.4176 L 110.3002 156.4269 L 110.3002 154.6226 L 113.292 154.6319 L f 0 G 0.3 w 10 M 57.1003 136.9425 m S 0 g 1 w 4 M 57.1003 136.9425 m F 0 G 0.3 w 10 M 57.1003 136.9425 m S 57.1003 136.9425 m S 57.1003 136.9425 m S 0 g 1 w 4 M 57.1003 136.9425 m F 0 G 0.3 w 10 M 57.1003 136.9425 m S 57.1003 136.9425 m S 1 g 1 w 4 M 52.0854 136.9425 m 52.0854 134.2492 54.3307 132.0659 57.1003 132.0659 c 59.87 132.0659 62.1153 134.2492 62.1153 136.9425 c F 62.1153 136.9425 m 62.1153 139.6358 59.87 141.8191 57.1003 141.8191 c 54.3307 141.8191 52.0854 139.6358 52.0854 136.9425 c F 57.1003 136.9425 m F 0 G 0.3 w 10 M 57.1003 136.9425 m S 0 g 1 w 4 M 57.1003 136.9425 m F 0 G 0.3 w 10 M 57.1003 136.9425 m S 57.1003 136.9425 m S 0 g 1 w 4 M 56.1949 136.0498 m 56.1949 133.0595 L 58.0057 133.0595 L 58.0057 136.0498 L 60.9975 136.0404 L 60.9975 137.8448 L 58.0057 137.8355 L 58.0057 140.8258 L 56.1949 140.8258 L 56.1949 137.8355 L 53.2032 137.8448 L 53.2032 136.0404 L 56.1949 136.0498 L f 0 G 0.3 w 10 M 57.1003 118.3605 m S 0 g 1 w 4 M 57.1003 118.3605 m F 0 G 0.3 w 10 M 57.1003 118.3605 m S 57.1003 118.3605 m S 57.1003 118.3605 m S 0 g 1 w 4 M 57.1003 118.3605 m F 0 G 0.3 w 10 M 57.1003 118.3605 m S 57.1003 118.3605 m S 1 g 1 w 4 M 52.0854 118.3605 m 52.0854 115.6672 54.3307 113.4838 57.1003 113.4838 c 59.87 113.4838 62.1153 115.6672 62.1153 118.3605 c F 62.1153 118.3605 m 62.1153 121.0537 59.87 123.2371 57.1003 123.2371 c 54.3307 123.2371 52.0854 121.0537 52.0854 118.3605 c F 57.1003 118.3605 m F 0 G 0.3 w 10 M 57.1003 118.3605 m S 0 g 1 w 4 M 57.1003 118.3605 m F 0 G 0.3 w 10 M 57.1003 118.3605 m S 57.1003 118.3605 m S 0 g 1 w 4 M 56.1949 117.4677 m 56.1949 114.4774 L 58.0057 114.4774 L 58.0057 117.4677 L 60.9975 117.4584 L 60.9975 119.2627 L 58.0057 119.2534 L 58.0057 122.2437 L 56.1949 122.2437 L 56.1949 119.2534 L 53.2032 119.2627 L 53.2032 117.4584 L 56.1949 117.4677 L f 0 G 0.3 w 10 M 57.1003 99.7783 m S 0 g 1 w 4 M 57.1003 99.7783 m F 0 G 0.3 w 10 M 57.1003 99.7783 m S 57.1003 99.7783 m S 57.1003 99.7783 m S 0 g 1 w 4 M 57.1003 99.7783 m F 0 G 0.3 w 10 M 57.1003 99.7783 m S 57.1003 99.7783 m S 1 g 1 w 4 M 52.0854 99.7783 m 52.0854 97.085 54.3307 94.9017 57.1003 94.9017 c 59.87 94.9017 62.1153 97.085 62.1153 99.7783 c F 62.1153 99.7783 m 62.1153 102.4716 59.87 104.6549 57.1003 104.6549 c 54.3307 104.6549 52.0854 102.4716 52.0854 99.7783 c F 57.1003 99.7783 m F 0 G 0.3 w 10 M 57.1003 99.7783 m S 0 g 1 w 4 M 57.1003 99.7783 m F 0 G 0.3 w 10 M 57.1003 99.7783 m S 57.1003 99.7783 m S 0 g 1 w 4 M 56.1949 98.8856 m 56.1949 95.8953 L 58.0057 95.8953 L 58.0057 98.8856 L 60.9975 98.8762 L 60.9975 100.6806 L 58.0057 100.6713 L 58.0057 103.6616 L 56.1949 103.6616 L 56.1949 100.6713 L 53.2032 100.6806 L 53.2032 98.8762 L 56.1949 98.8856 L f 0 G 0.3 w 10 M 76.1327 81.1962 m S 76.1327 81.1962 m S 95.1651 81.1962 m S 76.1327 81.1962 m S 95.1651 81.1962 m S 76.1327 81.1962 m S 114.1974 81.1962 m S 95.1651 81.1962 m S 114.1974 81.1962 m S 114.1974 81.1962 m S 114.1974 81.1962 m S 95.1651 81.1962 m S 76.1327 81.1962 m S 0 g 1 w 4 M 76.1327 81.1962 m F 0 G 0.3 w 10 M 76.1327 81.1962 m S 76.1327 81.1962 m S 76.1327 81.1962 m S 0 g 1 w 4 M 76.1327 81.1962 m F 0 G 0.3 w 10 M 76.1327 81.1962 m S 76.1327 81.1962 m S 1 g 1 w 4 M 71.1178 81.1962 m 71.1178 78.503 73.3631 76.3196 76.1327 76.3196 c 78.9024 76.3196 81.1477 78.503 81.1477 81.1962 c F 81.1477 81.1962 m 81.1477 83.8895 78.9024 86.0729 76.1327 86.0729 c 73.3631 86.0729 71.1178 83.8895 71.1178 81.1962 c F 76.1327 81.1962 m F 0 G 0.3 w 10 M 76.1327 81.1962 m S 0 g 1 w 4 M 76.1327 81.1962 m F 0 G 0.3 w 10 M 76.1327 81.1962 m S 76.1327 81.1962 m S 0 g 1 w 4 M 75.2273 80.3035 m 75.2273 77.3132 L 77.0381 77.3132 L 77.0381 80.3035 L 80.0299 80.2942 L 80.0299 82.0985 L 77.0381 82.0892 L 77.0381 85.0795 L 75.2273 85.0795 L 75.2273 82.0892 L 72.2356 82.0985 L 72.2356 80.2942 L 75.2273 80.3035 L f 0 G 0.3 w 10 M 95.1651 81.1962 m S 0 g 1 w 4 M 95.1651 81.1962 m F 0 G 0.3 w 10 M 95.1651 81.1962 m S 95.1651 81.1962 m S 95.1651 81.1962 m S 0 g 1 w 4 M 95.1651 81.1962 m F 0 G 0.3 w 10 M 95.1651 81.1962 m S 95.1651 81.1962 m S 1 g 1 w 4 M 90.1501 81.1962 m 90.1501 78.503 92.3954 76.3196 95.1651 76.3196 c 97.9347 76.3196 100.18 78.503 100.18 81.1962 c F 100.18 81.1962 m 100.18 83.8895 97.9347 86.0729 95.1651 86.0729 c 92.3954 86.0729 90.1501 83.8895 90.1501 81.1962 c F 95.1651 81.1962 m F 0 G 0.3 w 10 M 95.1651 81.1962 m S 0 g 1 w 4 M 95.1651 81.1962 m F 0 G 0.3 w 10 M 95.1651 81.1962 m S 95.1651 81.1962 m S 0 g 1 w 4 M 94.2597 80.3035 m 94.2597 77.3132 L 96.0704 77.3132 L 96.0704 80.3035 L 99.0622 80.2942 L 99.0622 82.0985 L 96.0704 82.0892 L 96.0704 85.0795 L 94.2597 85.0795 L 94.2597 82.0892 L 91.2679 82.0985 L 91.2679 80.2942 L 94.2597 80.3035 L f 0 G 0.3 w 10 M 114.1974 81.1962 m S 0 g 1 w 4 M 114.1974 81.1962 m F 0 G 0.3 w 10 M 114.1974 81.1962 m S 114.1974 81.1962 m S 114.1974 81.1962 m S 0 g 1 w 4 M 114.1974 81.1962 m F 0 G 0.3 w 10 M 114.1974 81.1962 m S 114.1974 81.1962 m S 1 g 1 w 4 M 109.1824 81.1962 m 109.1824 78.503 111.4277 76.3196 114.1974 76.3196 c 116.967 76.3196 119.2123 78.503 119.2123 81.1962 c F 119.2123 81.1962 m 119.2123 83.8895 116.967 86.0729 114.1974 86.0729 c 111.4277 86.0729 109.1824 83.8895 109.1824 81.1962 c F 114.1974 81.1962 m F 0 G 0.3 w 10 M 114.1974 81.1962 m S 0 g 1 w 4 M 114.1974 81.1962 m F 0 G 0.3 w 10 M 114.1974 81.1962 m S 114.1974 81.1962 m S 0 g 1 w 4 M 113.292 80.3035 m 113.292 77.3132 L 115.1027 77.3132 L 115.1027 80.3035 L 118.0945 80.2942 L 118.0945 82.0985 L 115.1027 82.0892 L 115.1027 85.0795 L 113.292 85.0795 L 113.292 82.0892 L 110.3002 82.0985 L 110.3002 80.2942 L 113.292 80.3035 L f 0 G 0.3 w 10 M 133.2298 136.9425 m S 133.2298 118.3605 m S 133.2298 136.9425 m S 133.2298 136.9425 m S 133.2298 118.3605 m S 133.2298 136.9425 m S 133.2298 118.3605 m S 133.2298 99.7783 m S 133.2298 99.7783 m S 133.2298 99.7783 m S 133.2298 118.3605 m S 133.2298 99.7783 m S 133.2298 136.9425 m S 0 g 1 w 4 M 133.2298 136.9425 m F 0 G 0.3 w 10 M 133.2298 136.9425 m S 133.2298 136.9425 m S 133.2298 136.9425 m S 0 g 1 w 4 M 133.2298 136.9425 m F 0 G 0.3 w 10 M 133.2298 136.9425 m S 133.2298 136.9425 m S 1 g 1 w 4 M 128.2148 136.9425 m 128.2148 134.2492 130.4601 132.0659 133.2298 132.0659 c 135.9994 132.0659 138.2447 134.2492 138.2447 136.9425 c F 138.2447 136.9425 m 138.2447 139.6358 135.9994 141.8191 133.2298 141.8191 c 130.4601 141.8191 128.2148 139.6358 128.2148 136.9425 c F 133.2298 136.9425 m F 0 G 0.3 w 10 M 133.2298 136.9425 m S 0 g 1 w 4 M 133.2298 136.9425 m F 0 G 0.3 w 10 M 133.2298 136.9425 m S 133.2298 136.9425 m S 0 g 1 w 4 M 132.3244 136.0498 m 132.3244 133.0595 L 134.1351 133.0595 L 134.1351 136.0498 L 137.1269 136.0404 L 137.1269 137.8448 L 134.1351 137.8355 L 134.1351 140.8258 L 132.3244 140.8258 L 132.3244 137.8355 L 129.3326 137.8448 L 129.3326 136.0404 L 132.3244 136.0498 L f 0 G 0.3 w 10 M 133.2298 118.3605 m S 0 g 1 w 4 M 133.2298 118.3605 m F 0 G 0.3 w 10 M 133.2298 118.3605 m S 133.2298 118.3605 m S 133.2298 118.3605 m S 0 g 1 w 4 M 133.2298 118.3605 m F 0 G 0.3 w 10 M 133.2298 118.3605 m S 133.2298 118.3605 m S 1 g 1 w 4 M 128.2148 118.3605 m 128.2148 115.6672 130.4601 113.4838 133.2298 113.4838 c 135.9994 113.4838 138.2447 115.6672 138.2447 118.3605 c F 138.2447 118.3605 m 138.2447 121.0537 135.9994 123.2371 133.2298 123.2371 c 130.4601 123.2371 128.2148 121.0537 128.2148 118.3605 c F 133.2298 118.3605 m F 0 G 0.3 w 10 M 133.2298 118.3605 m S 0 g 1 w 4 M 133.2298 118.3605 m F 0 G 0.3 w 10 M 133.2298 118.3605 m S 133.2298 118.3605 m S 0 g 1 w 4 M 132.3244 117.4677 m 132.3244 114.4774 L 134.1351 114.4774 L 134.1351 117.4677 L 137.1269 117.4584 L 137.1269 119.2627 L 134.1351 119.2534 L 134.1351 122.2437 L 132.3244 122.2437 L 132.3244 119.2534 L 129.3326 119.2627 L 129.3326 117.4584 L 132.3244 117.4677 L f 0 G 0.3 w 10 M 133.2298 99.7783 m S 0 g 1 w 4 M 133.2298 99.7783 m F 0 G 0.3 w 10 M 133.2298 99.7783 m S 133.2298 99.7783 m S 133.2298 99.7783 m S 0 g 1 w 4 M 133.2298 99.7783 m F 0 G 0.3 w 10 M 133.2298 99.7783 m S 133.2298 99.7783 m S 1 g 1 w 4 M 128.2148 99.7783 m 128.2148 97.085 130.4601 94.9017 133.2298 94.9017 c 135.9994 94.9017 138.2447 97.085 138.2447 99.7783 c F 138.2447 99.7783 m 138.2447 102.4716 135.9994 104.6549 133.2298 104.6549 c 130.4601 104.6549 128.2148 102.4716 128.2148 99.7783 c F 133.2298 99.7783 m F 0 G 0.3 w 10 M 133.2298 99.7783 m S 0 g 1 w 4 M 133.2298 99.7783 m F 0 G 0.3 w 10 M 133.2298 99.7783 m S 133.2298 99.7783 m S 0 g 1 w 4 M 132.3244 98.8856 m 132.3244 95.8953 L 134.1351 95.8953 L 134.1351 98.8856 L 137.1269 98.8762 L 137.1269 100.6806 L 134.1351 100.6713 L 134.1351 103.6616 L 132.3244 103.6616 L 132.3244 100.6713 L 129.3326 100.6806 L 129.3326 98.8762 L 132.3244 98.8856 L f 0 G 0.3 w 10 M 85.6488 127.6515 m S 85.6488 127.6515 m S 104.6812 127.6515 m S 85.6488 127.6515 m S 104.6812 127.6515 m S 104.6812 127.6515 m S 104.6812 127.6515 m S 85.6488 127.6515 m S 85.6488 109.0694 m S 85.6488 109.0694 m S 104.6812 109.0694 m S 85.6488 109.0694 m S 104.6812 109.0694 m S 104.6812 109.0694 m S 104.6812 109.0694 m S 85.6488 109.0694 m S 152.2621 118.3605 m S 152.2621 136.9425 m S 152.2621 136.9425 m S 152.2621 155.5247 m S 152.2621 99.7783 m S 152.2621 118.3605 m S 152.2621 81.1962 m S 152.2621 99.7783 m S 76.1327 136.9425 m S 0 g 1 w 4 M 76.1327 136.9425 m F 0 G 0.3 w 10 M 76.1327 136.9425 m S 0 g 1 w 4 M 76.1327 136.9425 m F 1 g 71.1178 136.9425 m 71.1178 134.2492 73.3631 132.0659 76.1327 132.0659 c 78.9024 132.0659 81.1477 134.2492 81.1477 136.9425 c F 81.1477 136.9425 m 81.1477 139.6358 78.9024 141.8191 76.1327 141.8191 c 73.3631 141.8191 71.1178 139.6358 71.1178 136.9425 c F 76.1327 136.9425 m F 0 G 0.3 w 10 M 76.1327 136.9425 m S 0 g 1 w 4 M 76.1327 136.9425 m F 0 G 0.3 w 10 M 76.1327 136.9425 m S 0 g 1 w 4 M 76.1327 136.9425 m F 75.2273 137.8355 m 72.2356 137.8448 L 72.2356 136.0404 L 75.2273 136.0497 L F 77.0381 136.0497 m 80.0299 136.0404 L 80.0299 137.8448 L 77.0381 137.8355 L F 72.2356 137.8448 m 80.0299 137.8448 l 80.0299 136.0404 l 72.2356 136.0404 l 72.2356 137.8448 l f 0 G 0.3 w 10 M 76.1327 118.3605 m S 0 g 1 w 4 M 76.1327 118.3605 m F 0 G 0.3 w 10 M 76.1327 118.3605 m S 0 g 1 w 4 M 76.1327 118.3605 m F 1 g 71.1178 118.3605 m 71.1178 115.6672 73.3631 113.4838 76.1327 113.4838 c 78.9024 113.4838 81.1477 115.6672 81.1477 118.3605 c F 81.1477 118.3605 m 81.1477 121.0537 78.9024 123.2371 76.1327 123.2371 c 73.3631 123.2371 71.1178 121.0537 71.1178 118.3605 c F 76.1327 118.3605 m F 0 G 0.3 w 10 M 76.1327 118.3605 m S 0 g 1 w 4 M 76.1327 118.3605 m F 0 G 0.3 w 10 M 76.1327 118.3605 m S 0 g 1 w 4 M 76.1327 118.3605 m F 75.2273 119.2534 m 72.2356 119.2627 L 72.2356 117.4584 L 75.2273 117.4676 L F 77.0381 117.4676 m 80.0299 117.4584 L 80.0299 119.2627 L 77.0381 119.2534 L F 72.2356 119.2627 m 80.0299 119.2627 l 80.0299 117.4584 l 72.2356 117.4584 l 72.2356 119.2627 l f 0 G 0.3 w 10 M 95.1651 118.3605 m S 0 g 1 w 4 M 95.1651 118.3605 m F 0 G 0.3 w 10 M 95.1651 118.3605 m S 0 g 1 w 4 M 95.1651 118.3605 m F 1 g 90.1501 118.3605 m 90.1501 115.6672 92.3954 113.4838 95.1651 113.4838 c 97.9347 113.4838 100.18 115.6672 100.18 118.3605 c F 100.18 118.3605 m 100.18 121.0537 97.9347 123.2371 95.1651 123.2371 c 92.3954 123.2371 90.1501 121.0537 90.1501 118.3605 c F 95.1651 118.3605 m F 0 G 0.3 w 10 M 95.1651 118.3605 m S 0 g 1 w 4 M 95.1651 118.3605 m F 0 G 0.3 w 10 M 95.1651 118.3605 m S 0 g 1 w 4 M 95.1651 118.3605 m F 94.2597 119.2534 m 91.2679 119.2627 L 91.2679 117.4584 L 94.2597 117.4676 L F 96.0704 117.4676 m 99.0622 117.4584 L 99.0622 119.2627 L 96.0704 119.2534 L F 91.2679 119.2627 m 99.0622 119.2627 l 99.0622 117.4584 l 91.2679 117.4584 l 91.2679 119.2627 l f 0 G 0.3 w 10 M 95.1651 99.7783 m S 0 g 1 w 4 M 95.1651 99.7783 m F 0 G 0.3 w 10 M 95.1651 99.7783 m S 0 g 1 w 4 M 95.1651 99.7783 m F 1 g 90.1501 99.7783 m 90.1501 97.085 92.3954 94.9017 95.1651 94.9017 c 97.9347 94.9017 100.18 97.085 100.18 99.7783 c F 100.18 99.7783 m 100.18 102.4716 97.9347 104.6549 95.1651 104.6549 c 92.3954 104.6549 90.1501 102.4716 90.1501 99.7783 c F 95.1651 99.7783 m F 0 G 0.3 w 10 M 95.1651 99.7783 m S 0 g 1 w 4 M 95.1651 99.7783 m F 0 G 0.3 w 10 M 95.1651 99.7783 m S 0 g 1 w 4 M 95.1651 99.7783 m F 94.2597 100.6713 m 91.2679 100.6806 L 91.2679 98.8762 L 94.2597 98.8855 L F 96.0704 98.8855 m 99.0622 98.8762 L 99.0622 100.6806 L 96.0704 100.6713 L F 91.2679 100.6806 m 99.0622 100.6806 l 99.0622 98.8762 l 91.2679 98.8762 l 91.2679 100.6806 l f 0 G 0.3 w 10 M 76.1327 99.7783 m S 0 g 1 w 4 M 76.1327 99.7783 m F 0 G 0.3 w 10 M 76.1327 99.7783 m S 0 g 1 w 4 M 76.1327 99.7783 m F 1 g 71.1178 99.7783 m 71.1178 97.085 73.3631 94.9017 76.1327 94.9017 c 78.9024 94.9017 81.1477 97.085 81.1477 99.7783 c F 81.1477 99.7783 m 81.1477 102.4716 78.9024 104.6549 76.1327 104.6549 c 73.3631 104.6549 71.1178 102.4716 71.1178 99.7783 c F 76.1327 99.7783 m F 0 G 0.3 w 10 M 76.1327 99.7783 m S 0 g 1 w 4 M 76.1327 99.7783 m F 0 G 0.3 w 10 M 76.1327 99.7783 m S 0 g 1 w 4 M 76.1327 99.7783 m F 75.2273 100.6713 m 72.2356 100.6806 L 72.2356 98.8762 L 75.2273 98.8855 L F 77.0381 98.8855 m 80.0299 98.8762 L 80.0299 100.6806 L 77.0381 100.6713 L F 72.2356 100.6806 m 80.0299 100.6806 l 80.0299 98.8762 l 72.2356 98.8762 l 72.2356 100.6806 l f 0 G 0.3 w 10 M 114.1974 136.9425 m S 0 g 1 w 4 M 114.1974 136.9425 m F 0 G 0.3 w 10 M 114.1974 136.9425 m S 114.1974 136.9425 m S 114.1974 136.9425 m S 0 g 1 w 4 M 114.1974 136.9425 m F 0 G 0.3 w 10 M 114.1974 136.9425 m S 114.1974 136.9425 m S 1 g 1 w 4 M 109.1824 136.9425 m 109.1824 134.2492 111.4277 132.0659 114.1974 132.0659 c 116.967 132.0659 119.2123 134.2492 119.2123 136.9425 c F 119.2123 136.9425 m 119.2123 139.6358 116.967 141.8191 114.1974 141.8191 c 111.4277 141.8191 109.1824 139.6358 109.1824 136.9425 c F 114.1974 136.9425 m F 0 G 0.3 w 10 M 114.1974 136.9425 m S 0 g 1 w 4 M 114.1974 136.9425 m F 0 G 0.3 w 10 M 114.1974 136.9425 m S 114.1974 136.9425 m S 0 g 1 w 4 M 113.292 136.0498 m 113.292 133.0595 L 115.1027 133.0595 L 115.1027 136.0498 L 118.0945 136.0404 L 118.0945 137.8448 L 115.1027 137.8355 L 115.1027 140.8258 L 113.292 140.8258 L 113.292 137.8355 L 110.3002 137.8448 L 110.3002 136.0404 L 113.292 136.0498 L f 0 G 0.3 w 10 M 95.1651 136.9425 m S 0 g 1 w 4 M 95.1651 136.9425 m F 0 G 0.3 w 10 M 95.1651 136.9425 m S 95.1651 136.9425 m S 95.1651 136.9425 m S 0 g 1 w 4 M 95.1651 136.9425 m F 0 G 0.3 w 10 M 95.1651 136.9425 m S 95.1651 136.9425 m S 1 g 1 w 4 M 90.1501 136.9425 m 90.1501 134.2492 92.3954 132.0659 95.1651 132.0659 c 97.9347 132.0659 100.18 134.2492 100.18 136.9425 c F 100.18 136.9425 m 100.18 139.6358 97.9347 141.8191 95.1651 141.8191 c 92.3954 141.8191 90.1501 139.6358 90.1501 136.9425 c F 95.1651 136.9425 m F 0 G 0.3 w 10 M 95.1651 136.9425 m S 0 g 1 w 4 M 95.1651 136.9425 m F 0 G 0.3 w 10 M 95.1651 136.9425 m S 95.1651 136.9425 m S 0 g 1 w 4 M 94.2597 136.0498 m 94.2597 133.0595 L 96.0704 133.0595 L 96.0704 136.0498 L 99.0622 136.0404 L 99.0622 137.8448 L 96.0704 137.8355 L 96.0704 140.8258 L 94.2597 140.8258 L 94.2597 137.8355 L 91.2679 137.8448 L 91.2679 136.0404 L 94.2597 136.0498 L f 0 G 0.3 w 10 M 114.1974 118.3605 m S 0 g 1 w 4 M 114.1974 118.3605 m F 0 G 0.3 w 10 M 114.1974 118.3605 m S 114.1974 118.3605 m S 114.1974 118.3605 m S 0 g 1 w 4 M 114.1974 118.3605 m F 0 G 0.3 w 10 M 114.1974 118.3605 m S 114.1974 118.3605 m S 1 g 1 w 4 M 109.1824 118.3605 m 109.1824 115.6672 111.4277 113.4838 114.1974 113.4838 c 116.967 113.4838 119.2123 115.6672 119.2123 118.3605 c F 119.2123 118.3605 m 119.2123 121.0537 116.967 123.2371 114.1974 123.2371 c 111.4277 123.2371 109.1824 121.0537 109.1824 118.3605 c F 114.1974 118.3605 m F 0 G 0.3 w 10 M 114.1974 118.3605 m S 0 g 1 w 4 M 114.1974 118.3605 m F 0 G 0.3 w 10 M 114.1974 118.3605 m S 114.1974 118.3605 m S 0 g 1 w 4 M 113.292 117.4677 m 113.292 114.4774 L 115.1027 114.4774 L 115.1027 117.4677 L 118.0945 117.4584 L 118.0945 119.2627 L 115.1027 119.2534 L 115.1027 122.2437 L 113.292 122.2437 L 113.292 119.2534 L 110.3002 119.2627 L 110.3002 117.4584 L 113.292 117.4677 L f 0 G 0.3 w 10 M 114.1974 99.7783 m S 0 g 1 w 4 M 114.1974 99.7783 m F 0 G 0.3 w 10 M 114.1974 99.7783 m S 114.1974 99.7783 m S 114.1974 99.7783 m S 0 g 1 w 4 M 114.1974 99.7783 m F 0 G 0.3 w 10 M 114.1974 99.7783 m S 114.1974 99.7783 m S 1 g 1 w 4 M 109.1824 99.7783 m 109.1824 97.085 111.4277 94.9017 114.1974 94.9017 c 116.967 94.9017 119.2123 97.085 119.2123 99.7783 c F 119.2123 99.7783 m 119.2123 102.4716 116.967 104.6549 114.1974 104.6549 c 111.4277 104.6549 109.1824 102.4716 109.1824 99.7783 c F 114.1974 99.7783 m F 0 G 0.3 w 10 M 114.1974 99.7783 m S 0 g 1 w 4 M 114.1974 99.7783 m F 0 G 0.3 w 10 M 114.1974 99.7783 m S 114.1974 99.7783 m S 0 g 1 w 4 M 113.292 98.8856 m 113.292 95.8953 L 115.1027 95.8953 115.0402 95.8953 V 115.1027 95.8953 115.1027 98.8856 Y 118.0945 98.8762 L 118.0945 100.6806 L 115.1027 100.6713 L 115.1027 103.6616 L 113.292 103.6616 L 113.292 100.6713 L 110.3002 100.6806 L 110.3002 98.8762 L 113.292 98.8856 L f 0 G 0.3 w 10 M 266.4561 136.9425 m S 266.4561 118.3605 m S 266.4561 174.1067 m S 266.4561 155.5247 m S 266.4561 155.5247 m S 266.4561 136.9425 m S 285.4884 174.1067 m S 285.4884 155.5247 m S 266.4561 155.5247 m S 266.4561 174.1067 m S 275.9723 164.8157 m S 323.5532 136.9425 m S 323.5532 118.3605 m S 304.5208 118.3605 m S 304.5208 136.9425 m S 314.037 127.6515 m S 304.5208 155.5247 m S 304.5208 136.9425 m S 285.4884 136.9425 m S 285.4884 155.5247 m S 295.0046 146.2336 m S 304.5208 174.1067 m S 304.5208 155.5247 m S 285.4884 155.5247 m S 285.4884 174.1067 m S 295.0046 164.8157 m S 323.5532 174.1067 m S 323.5532 155.5247 m S 304.5208 155.5247 m S 304.5208 174.1067 m S 314.037 164.8157 m S 323.5532 155.5247 m S 323.5532 136.9425 m S 304.5208 136.9425 m S 304.5208 155.5247 m S 314.037 146.2336 m S 304.5208 136.9425 m S 304.5208 118.3605 m S 285.4884 118.3605 m S 285.4884 136.9425 m S 295.0046 127.6515 m S 285.4884 136.9425 m S 285.4884 118.3605 m S 266.4561 118.3605 m S 266.4561 136.9425 m S 275.9723 127.6515 m S 285.4884 155.5247 m S 285.4884 136.9425 m S 266.4561 136.9425 m S 266.4561 155.5247 m S 275.9723 146.2336 m S 0 g 1 w 4 M 275.9723 164.8157 m F 314.037 164.8157 m F 275.9723 127.6515 m F 314.037 127.6515 m F 0 G 0.3 w 10 M 342.5855 174.1067 m S 342.5855 155.5247 m S 323.5532 155.5247 m S 323.5532 174.1067 m S 333.0693 164.8157 m S 380.6502 136.9425 m S 380.6502 118.3605 m S 361.6179 118.3605 m S 361.6179 136.9425 m S 371.134 127.6515 m S 361.6179 155.5247 m S 361.6179 136.9425 m S 342.5855 136.9425 m S 342.5855 155.5247 m S 352.1017 146.2336 m S 361.6179 174.1067 m S 361.6179 155.5247 m S 342.5855 155.5247 m S 342.5855 174.1067 m S 352.1017 164.8157 m S 380.6502 174.1067 m S 380.6502 155.5247 m S 361.6179 155.5247 m S 361.6179 174.1067 m S 371.134 164.8157 m S 380.6502 155.5247 m S 380.6502 136.9425 m S 361.6179 136.9425 m S 361.6179 155.5247 m S 371.134 146.2336 m S 361.6179 136.9425 m S 361.6179 118.3605 m S 342.5855 118.3605 m S 342.5855 136.9425 m S 352.1017 127.6515 m S 342.5855 136.9425 m S 342.5855 118.3605 m S 323.5532 118.3605 m S 323.5532 136.9425 m S 333.0693 127.6515 m S 342.5855 155.5247 m S 342.5855 136.9425 m S 323.5532 136.9425 m S 323.5532 155.5247 m S 333.0693 146.2336 m S 0 g 1 w 4 M 333.0693 164.8157 m F 371.134 164.8157 m F 333.0693 127.6515 m F 371.134 127.6515 m F 0 G 0.3 w 10 M 266.4561 81.1962 m S 266.4561 62.6142 m S 266.4561 118.3605 m S 266.4561 99.7783 m S 266.4561 99.7783 m S 266.4561 81.1962 m S 285.4884 118.3605 m S 285.4884 99.7783 m S 266.4561 99.7783 m S 266.4561 118.3605 m S 275.9723 109.0694 m S 323.5532 81.1962 m S 323.5532 62.6142 m S 304.5208 62.6142 m S 304.5208 81.1962 m S 314.037 71.9052 m S 304.5208 99.7783 m S 304.5208 81.1962 m S 285.4884 81.1962 m S 285.4884 99.7783 m S 295.0046 90.4874 m S 304.5208 118.3605 m S 304.5208 99.7783 m S 285.4884 99.7783 m S 285.4884 118.3605 m S 295.0046 109.0694 m S 323.5532 118.3605 m S 323.5532 99.7783 m S 304.5208 99.7783 m S 304.5208 118.3605 m S 314.037 109.0694 m S 323.5532 99.7783 m S 323.5532 81.1962 m S 304.5208 81.1962 m S 304.5208 99.7783 m S 314.037 90.4874 m S 304.5208 81.1962 m S 304.5208 62.6142 m S 285.4884 62.6142 m S 285.4884 81.1962 m S 295.0046 71.9052 m S 285.4884 81.1962 m S 285.4884 62.6142 m S 266.4561 62.6142 m S 266.4561 81.1962 m S 275.9723 71.9052 m S 285.4884 99.7783 m S 285.4884 81.1962 m S 266.4561 81.1962 m S 266.4561 99.7783 m S 275.9723 90.4874 m S 0 g 1 w 4 M 275.9723 109.0694 m F 314.037 109.0694 m F 275.9723 71.9052 m F 314.037 71.9052 m F 0 G 0.3 w 10 M 342.5855 118.3605 m S 342.5855 99.7783 m S 323.5532 99.7783 m S 323.5532 118.3605 m S 333.0693 109.0694 m S 380.6502 81.1962 m S 380.6502 62.6142 m S 361.6179 62.6142 m S 361.6179 81.1962 m S 371.134 71.9052 m S 361.6179 99.7783 m S 361.6179 81.1962 m S 342.5855 81.1962 m S 342.5855 99.7783 m S 352.1017 90.4874 m S 361.6179 118.3605 m S 361.6179 99.7783 m S 342.5855 99.7783 m S 342.5855 118.3605 m S 352.1017 109.0694 m S 380.6502 118.3605 m S 380.6502 99.7783 m S 361.6179 99.7783 m S 361.6179 118.3605 m S 371.134 109.0694 m S 380.6502 99.7783 m S 380.6502 81.1962 m S 361.6179 81.1962 m S 361.6179 99.7783 m S 371.134 90.4874 m S 361.6179 81.1962 m S 361.6179 62.6142 m S 342.5855 62.6142 m S 342.5855 81.1962 m S 352.1017 71.9052 m S 342.5855 81.1962 m S 342.5855 62.6142 m S 323.5532 62.6142 m S 323.5532 81.1962 m S 333.0693 71.9052 m S 342.5855 99.7783 m S 342.5855 81.1962 m S 323.5532 81.1962 m S 323.5532 99.7783 m S 333.0693 90.4874 m S 0 g 1 w 4 M 333.0693 109.0694 m F 371.134 109.0694 m F 333.0693 71.9052 m F 371.134 71.9052 m F 0 G 0.3 w 10 M 266.4561 62.6142 m S 285.4884 62.6142 m S 266.4561 62.6142 m S 304.5208 62.6142 m S 285.4884 62.6142 m S 323.5532 62.6142 m S 304.5208 62.6142 m S 342.5855 62.6142 m S 323.5532 62.6142 m S 361.6179 62.6142 m S 342.5855 62.6142 m S 380.6502 62.6142 m S 361.6179 62.6142 m S 285.4884 174.1067 m S 285.4884 155.5247 m S 266.4561 155.5247 m S 266.4561 174.1067 m S 275.9723 164.8157 m S 323.5532 136.9425 m S 323.5532 118.3605 m S 304.5208 118.3605 m S 304.5208 136.9425 m S 304.5208 155.5247 m S 304.5208 136.9425 m S 285.4884 136.9425 m S 285.4884 155.5247 m S 295.0046 146.2336 m S 304.5208 174.1067 m S 304.5208 155.5247 m S 285.4884 155.5247 m S 285.4884 174.1067 m S 295.0046 164.8157 m S 323.5532 174.1067 m S 323.5532 155.5247 m S 304.5208 155.5247 m S 304.5208 174.1067 m S 314.037 164.8157 m S 323.5532 155.5247 m S 323.5532 136.9425 m S 304.5208 136.9425 m S 304.5208 155.5247 m S 314.037 146.2336 m S 304.5208 136.9425 m S 304.5208 118.3605 m S 285.4884 118.3605 m S 285.4884 136.9425 m S 295.0046 127.6515 m S 285.4884 136.9425 m S 285.4884 118.3605 m S 266.4561 118.3605 m S 266.4561 136.9425 m S 275.9723 127.6515 m S 285.4884 155.5247 m S 285.4884 136.9425 m S 266.4561 136.9425 m S 266.4561 155.5247 m S 275.9723 146.2336 m S 0 g 1 w 4 M 275.9723 164.8157 m F 314.037 164.8157 m F 275.9723 127.6515 m F 0 G 0.3 w 10 M 342.5855 174.1067 m S 342.5855 155.5247 m S 323.5532 155.5247 m S 323.5532 174.1067 m S 333.0693 164.8157 m S 380.6502 136.9425 m S 380.6502 118.3605 m S 361.6179 118.3605 m S 361.6179 136.9425 m S 371.134 127.6515 m S 361.6179 155.5247 m S 361.6179 136.9425 m S 342.5855 136.9425 m S 342.5855 155.5247 m S 352.1017 146.2336 m S 361.6179 174.1067 m S 361.6179 155.5247 m S 342.5855 155.5247 m S 342.5855 174.1067 m S 352.1017 164.8157 m S 380.6502 174.1067 m S 380.6502 155.5247 m S 361.6179 155.5247 m S 361.6179 174.1067 m S 371.134 164.8157 m S 380.6502 155.5247 m S 380.6502 136.9425 m S 361.6179 136.9425 m S 361.6179 155.5247 m S 371.134 146.2336 m S 361.6179 136.9425 m S 361.6179 118.3605 m S 342.5855 118.3605 m S 342.5855 136.9425 m S 352.1017 127.6515 m S 342.5855 136.9425 m S 342.5855 118.3605 m S 323.5532 118.3605 m S 323.5532 136.9425 m S 333.0693 127.6515 m S 342.5855 155.5247 m S 342.5855 136.9425 m S 323.5532 136.9425 m S 323.5532 155.5247 m S 333.0693 146.2336 m S 0 g 1 w 4 M 333.0693 164.8157 m F 371.134 164.8157 m F 333.0693 127.6515 m F 371.134 127.6515 m F 0 G 0.3 w 10 M 285.4884 118.3605 m S 285.4884 99.7783 m S 266.4561 99.7783 m S 266.4561 118.3605 m S 275.9723 109.0694 m S 323.5532 81.1962 m S 323.5532 62.6142 m S 304.5208 62.6142 m S 304.5208 81.1962 m S 314.037 71.9052 m S 304.5208 99.7783 m S 304.5208 81.1962 m S 285.4884 81.1962 m S 285.4884 99.7783 m S 295.0046 90.4874 m S 304.5208 118.3605 m S 304.5208 99.7783 m S 285.4884 99.7783 m S 285.4884 118.3605 m S 295.0046 109.0694 m S 323.5532 118.3605 m S 323.5532 99.7783 m S 304.5208 99.7783 m S 304.5208 118.3605 m S 323.5532 99.7783 m S 323.5532 81.1962 m S 304.5208 81.1962 m S 304.5208 99.7783 m S 314.037 90.4874 m S 304.5208 81.1962 m S 304.5208 62.6142 m S 285.4884 62.6142 m S 285.4884 81.1962 m S 295.0046 71.9052 m S 285.4884 81.1962 m S 285.4884 62.6142 m S 266.4561 62.6142 m S 266.4561 81.1962 m S 275.9723 71.9052 m S 285.4884 99.7783 m S 285.4884 81.1962 m S 266.4561 81.1962 m S 266.4561 99.7783 m S 275.9723 90.4874 m S 0 g 1 w 4 M 275.9723 109.0694 m F 275.9723 71.9052 m F 314.037 71.9052 m F 0 G 0.3 w 10 M 342.5855 118.3605 m S 342.5855 99.7783 m S 323.5532 99.7783 m S 323.5532 118.3605 m S 333.0693 109.0694 m S 380.6502 81.1962 m S 380.6502 62.6142 m S 361.6179 62.6142 m S 361.6179 81.1962 m S 371.134 71.9052 m S 361.6179 99.7783 m S 361.6179 81.1962 m S 342.5855 81.1962 m S 342.5855 99.7783 m S 352.1017 90.4874 m S 361.6179 118.3605 m S 361.6179 99.7783 m S 342.5855 99.7783 m S 342.5855 118.3605 m S 352.1017 109.0694 m S 380.6502 118.3605 m S 380.6502 99.7783 m S 361.6179 99.7783 m S 361.6179 118.3605 m S 371.134 109.0694 m S 380.6502 99.7783 m S 380.6502 81.1962 m S 361.6179 81.1962 m S 361.6179 99.7783 m S 371.134 90.4874 m S 361.6179 81.1962 m S 361.6179 62.6142 m S 342.5855 62.6142 m S 342.5855 81.1962 m S 352.1017 71.9052 m S 342.5855 81.1962 m S 342.5855 62.6142 m S 323.5532 62.6142 m S 323.5532 81.1962 m S 333.0693 71.9052 m S 342.5855 99.7783 m S 342.5855 81.1962 m S 323.5532 81.1962 m S 323.5532 99.7783 m S 333.0693 90.4874 m S 0 g 1 w 4 M 333.0693 109.0694 m F 371.134 109.0694 m F 333.0693 71.9052 m F 371.134 71.9052 m F 0 G 0.3 w 10 M 285.4884 62.6142 m S 266.4561 62.6142 m S 304.5208 62.6142 m S 285.4884 62.6142 m S 323.5532 62.6142 m S 304.5208 62.6142 m S 342.5855 62.6142 m S 323.5532 62.6142 m S 361.6179 62.6142 m S 342.5855 62.6142 m S 380.6502 62.6142 m S 361.6179 62.6142 m S 1 w 4 M 275.9723 146.2336 m 371.134 146.2336 l S 275.9723 90.4874 m 371.134 90.4874 l S 295.0046 164.8157 m 295.0046 71.9052 l S 352.1017 164.8157 m 352.1017 71.9052 l S 0.3 w 10 M 304.5208 155.5247 m S 0 g 1 w 4 M 304.5208 155.5247 m F 0 G 0.3 w 10 M 304.5208 155.5247 m S 304.5208 155.5247 m S 304.5208 155.5247 m S 0 g 1 w 4 M 304.5208 155.5247 m F 0 G 0.3 w 10 M 304.5208 155.5247 m S 304.5208 155.5247 m S 1 g 1 w 4 M 299.5059 155.5247 m 299.5059 152.8314 301.7512 150.648 304.5208 150.648 c 307.2905 150.648 309.5358 152.8314 309.5358 155.5247 c F 309.5358 155.5247 m 309.5358 158.2179 307.2905 160.4013 304.5208 160.4013 c 301.7512 160.4013 299.5059 158.2179 299.5059 155.5247 c F 304.5208 155.5247 m F 0 G 0.3 w 10 M 304.5208 155.5247 m S 0 g 1 w 4 M 304.5208 155.5247 m F 0 G 0.3 w 10 M 304.5208 155.5247 m S 304.5208 155.5247 m S 0 g 1 w 4 M 303.6155 154.6319 m 303.6155 151.6417 L 305.4263 151.6417 L 305.4263 154.6319 L 308.418 154.6226 L 308.418 156.4269 L 305.4263 156.4176 L 305.4263 159.4079 L 303.6155 159.4079 L 303.6155 156.4176 L 300.6237 156.4269 L 300.6237 154.6226 L 303.6155 154.6319 L f 0 G 0.3 w 10 M 323.5532 155.5247 m S 0 g 1 w 4 M 323.5532 155.5247 m F 0 G 0.3 w 10 M 323.5532 155.5247 m S 323.5532 155.5247 m S 323.5532 155.5247 m S 0 g 1 w 4 M 323.5532 155.5247 m F 0 G 0.3 w 10 M 323.5532 155.5247 m S 323.5532 155.5247 m S 1 g 1 w 4 M 318.5382 155.5247 m 318.5382 152.8314 320.7835 150.648 323.5532 150.648 c 326.3228 150.648 328.5681 152.8314 328.5681 155.5247 c F 328.5681 155.5247 m 328.5681 158.2179 326.3228 160.4013 323.5532 160.4013 c 320.7835 160.4013 318.5382 158.2179 318.5382 155.5247 c F 323.5532 155.5247 m F 0 G 0.3 w 10 M 323.5532 155.5247 m S 0 g 1 w 4 M 323.5532 155.5247 m F 0 G 0.3 w 10 M 323.5532 155.5247 m S 323.5532 155.5247 m S 0 g 1 w 4 M 322.6478 154.6319 m 322.6478 151.6417 L 324.4586 151.6417 L 324.4586 154.6319 L 327.4503 154.6226 L 327.4503 156.4269 L 324.4586 156.4176 L 324.4586 159.4079 L 322.6478 159.4079 L 322.6478 156.4176 L 319.656 156.4269 L 319.656 154.6226 L 322.6478 154.6319 L f 0 G 0.3 w 10 M 342.5855 155.5247 m S 0 g 1 w 4 M 342.5855 155.5247 m F 0 G 0.3 w 10 M 342.5855 155.5247 m S 342.5855 155.5247 m S 342.5855 155.5247 m S 0 g 1 w 4 M 342.5855 155.5247 m F 0 G 0.3 w 10 M 342.5855 155.5247 m S 342.5855 155.5247 m S 1 g 1 w 4 M 337.5705 155.5247 m 337.5705 152.8314 339.8158 150.648 342.5855 150.648 c 345.3551 150.648 347.6004 152.8314 347.6004 155.5247 c F 347.6004 155.5247 m 347.6004 158.2179 345.3551 160.4013 342.5855 160.4013 c 339.8158 160.4013 337.5705 158.2179 337.5705 155.5247 c F 342.5855 155.5247 m F 0 G 0.3 w 10 M 342.5855 155.5247 m S 0 g 1 w 4 M 342.5855 155.5247 m F 0 G 0.3 w 10 M 342.5855 155.5247 m S 342.5855 155.5247 m S 0 g 1 w 4 M 341.6801 154.6319 m 341.6801 151.6417 L 343.4909 151.6417 L 343.4909 154.6319 L 346.4826 154.6226 L 346.4826 156.4269 L 343.4909 156.4176 L 343.4909 159.4079 L 341.6801 159.4079 L 341.6801 156.4176 L 338.6883 156.4269 L 338.6883 154.6226 L 341.6801 154.6319 L f 0 G 0.3 w 10 M 285.4884 136.9425 m S 0 g 1 w 4 M 285.4884 136.9425 m F 0 G 0.3 w 10 M 285.4884 136.9425 m S 285.4884 136.9425 m S 285.4884 136.9425 m S 0 g 1 w 4 M 285.4884 136.9425 m F 0 G 0.3 w 10 M 285.4884 136.9425 m S 285.4884 136.9425 m S 1 g 1 w 4 M 280.4735 136.9425 m 280.4735 134.2492 282.7188 132.0659 285.4884 132.0659 c 288.2581 132.0659 290.5034 134.2492 290.5034 136.9425 c F 290.5034 136.9425 m 290.5034 139.6358 288.2581 141.8191 285.4884 141.8191 c 282.7188 141.8191 280.4735 139.6358 280.4735 136.9425 c F 285.4884 136.9425 m F 0 G 0.3 w 10 M 285.4884 136.9425 m S 0 g 1 w 4 M 285.4884 136.9425 m F 0 G 0.3 w 10 M 285.4884 136.9425 m S 285.4884 136.9425 m S 0 g 1 w 4 M 284.5831 136.0498 m 284.5831 133.0595 L 286.3938 133.0595 L 286.3938 136.0498 L 289.3856 136.0404 L 289.3856 137.8448 L 286.3938 137.8355 L 286.3938 140.8258 L 284.5831 140.8258 L 284.5831 137.8355 L 281.5913 137.8448 L 281.5913 136.0404 L 284.5831 136.0498 L f 0 G 0.3 w 10 M 285.4884 118.3605 m S 0 g 1 w 4 M 285.4884 118.3605 m F 0 G 0.3 w 10 M 285.4884 118.3605 m S 285.4884 118.3605 m S 285.4884 118.3605 m S 0 g 1 w 4 M 285.4884 118.3605 m F 0 G 0.3 w 10 M 285.4884 118.3605 m S 285.4884 118.3605 m S 1 g 1 w 4 M 280.4735 118.3605 m 280.4735 115.6672 282.7188 113.4838 285.4884 113.4838 c 288.2581 113.4838 290.5034 115.6672 290.5034 118.3605 c F 290.5034 118.3605 m 290.5034 121.0537 288.2581 123.2371 285.4884 123.2371 c 282.7188 123.2371 280.4735 121.0537 280.4735 118.3605 c F 285.4884 118.3605 m F 0 G 0.3 w 10 M 285.4884 118.3605 m S 0 g 1 w 4 M 285.4884 118.3605 m F 0 G 0.3 w 10 M 285.4884 118.3605 m S 285.4884 118.3605 m S 0 g 1 w 4 M 284.5831 117.4677 m 284.5831 114.4774 L 286.3938 114.4774 L 286.3938 117.4677 L 289.3856 117.4584 L 289.3856 119.2627 L 286.3938 119.2534 L 286.3938 122.2437 L 284.5831 122.2437 L 284.5831 119.2534 L 281.5913 119.2627 L 281.5913 117.4584 L 284.5831 117.4677 L f 0 G 0.3 w 10 M 285.4884 99.7783 m S 0 g 1 w 4 M 285.4884 99.7783 m F 0 G 0.3 w 10 M 285.4884 99.7783 m S 285.4884 99.7783 m S 285.4884 99.7783 m S 0 g 1 w 4 M 285.4884 99.7783 m F 0 G 0.3 w 10 M 285.4884 99.7783 m S 285.4884 99.7783 m S 1 g 1 w 4 M 280.4735 99.7783 m 280.4735 97.085 282.7188 94.9017 285.4884 94.9017 c 288.2581 94.9017 290.5034 97.085 290.5034 99.7783 c F 290.5034 99.7783 m 290.5034 102.4716 288.2581 104.6549 285.4884 104.6549 c 282.7188 104.6549 280.4735 102.4716 280.4735 99.7783 c F 285.4884 99.7783 m F 0 G 0.3 w 10 M 285.4884 99.7783 m S 0 g 1 w 4 M 285.4884 99.7783 m F 0 G 0.3 w 10 M 285.4884 99.7783 m S 285.4884 99.7783 m S 0 g 1 w 4 M 284.5831 98.8856 m 284.5831 95.8953 L 286.3938 95.8953 L 286.3938 98.8856 L 289.3856 98.8762 L 289.3856 100.6806 L 286.3938 100.6713 L 286.3938 103.6616 L 284.5831 103.6616 L 284.5831 100.6713 L 281.5913 100.6806 L 281.5913 98.8762 L 284.5831 98.8856 L f 0 G 0.3 w 10 M 304.5208 81.1962 m S 304.5208 81.1962 m S 323.5532 81.1962 m S 304.5208 81.1962 m S 323.5532 81.1962 m S 304.5208 81.1962 m S 342.5855 81.1962 m S 323.5532 81.1962 m S 342.5855 81.1962 m S 342.5855 81.1962 m S 342.5855 81.1962 m S 323.5532 81.1962 m S 304.5208 81.1962 m S 0 g 1 w 4 M 304.5208 81.1962 m F 0 G 0.3 w 10 M 304.5208 81.1962 m S 304.5208 81.1962 m S 304.5208 81.1962 m S 0 g 1 w 4 M 304.5208 81.1962 m F 0 G 0.3 w 10 M 304.5208 81.1962 m S 304.5208 81.1962 m S 1 g 1 w 4 M 299.5059 81.1962 m 299.5059 78.503 301.7512 76.3196 304.5208 76.3196 c 307.2905 76.3196 309.5358 78.503 309.5358 81.1962 c F 309.5358 81.1962 m 309.5358 83.8895 307.2905 86.0729 304.5208 86.0729 c 301.7512 86.0729 299.5059 83.8895 299.5059 81.1962 c F 304.5208 81.1962 m F 0 G 0.3 w 10 M 304.5208 81.1962 m S 0 g 1 w 4 M 304.5208 81.1962 m F 0 G 0.3 w 10 M 304.5208 81.1962 m S 304.5208 81.1962 m S 0 g 1 w 4 M 303.6155 80.3035 m 303.6155 77.3132 L 305.4263 77.3132 L 305.4263 80.3035 L 308.418 80.2942 L 308.418 82.0985 L 305.4263 82.0892 L 305.4263 85.0795 L 303.6155 85.0795 L 303.6155 82.0892 L 300.6237 82.0985 L 300.6237 80.2942 L 303.6155 80.3035 L f 0 G 0.3 w 10 M 323.5532 81.1962 m S 0 g 1 w 4 M 323.5532 81.1962 m F 0 G 0.3 w 10 M 323.5532 81.1962 m S 323.5532 81.1962 m S 323.5532 81.1962 m S 0 g 1 w 4 M 323.5532 81.1962 m F 0 G 0.3 w 10 M 323.5532 81.1962 m S 323.5532 81.1962 m S 1 g 1 w 4 M 318.5382 81.1962 m 318.5382 78.503 320.7835 76.3196 323.5532 76.3196 c 326.3228 76.3196 328.5681 78.503 328.5681 81.1962 c F 328.5681 81.1962 m 328.5681 83.8895 326.3228 86.0729 323.5532 86.0729 c 320.7835 86.0729 318.5382 83.8895 318.5382 81.1962 c F 323.5532 81.1962 m F 0 G 0.3 w 10 M 323.5532 81.1962 m S 0 g 1 w 4 M 323.5532 81.1962 m F 0 G 0.3 w 10 M 323.5532 81.1962 m S 323.5532 81.1962 m S 0 g 1 w 4 M 322.6478 80.3035 m 322.6478 77.3132 L 324.4586 77.3132 L 324.4586 80.3035 L 327.4503 80.2942 L 327.4503 82.0985 L 324.4586 82.0892 L 324.4586 85.0795 L 322.6478 85.0795 L 322.6478 82.0892 L 319.656 82.0985 L 319.656 80.2942 L 322.6478 80.3035 L f 0 G 0.3 w 10 M 342.5855 81.1962 m S 0 g 1 w 4 M 342.5855 81.1962 m F 0 G 0.3 w 10 M 342.5855 81.1962 m S 342.5855 81.1962 m S 342.5855 81.1962 m S 0 g 1 w 4 M 342.5855 81.1962 m F 0 G 0.3 w 10 M 342.5855 81.1962 m S 342.5855 81.1962 m S 1 g 1 w 4 M 337.5705 81.1962 m 337.5705 78.503 339.8158 76.3196 342.5855 76.3196 c 345.3551 76.3196 347.6004 78.503 347.6004 81.1962 c F 347.6004 81.1962 m 347.6004 83.8895 345.3551 86.0729 342.5855 86.0729 c 339.8158 86.0729 337.5705 83.8895 337.5705 81.1962 c F 342.5855 81.1962 m F 0 G 0.3 w 10 M 342.5855 81.1962 m S 0 g 1 w 4 M 342.5855 81.1962 m F 0 G 0.3 w 10 M 342.5855 81.1962 m S 342.5855 81.1962 m S 0 g 1 w 4 M 341.6801 80.3035 m 341.6801 77.3132 L 343.4909 77.3132 L 343.4909 80.3035 L 346.4826 80.2942 L 346.4826 82.0985 L 343.4909 82.0892 L 343.4909 85.0795 L 341.6801 85.0795 L 341.6801 82.0892 L 338.6883 82.0985 L 338.6883 80.2942 L 341.6801 80.3035 L f 0 G 0.3 w 10 M 361.6179 136.9425 m S 361.6179 118.3605 m S 361.6179 136.9425 m S 361.6179 136.9425 m S 361.6179 118.3605 m S 361.6179 136.9425 m S 361.6179 118.3605 m S 361.6179 99.7783 m S 361.6179 99.7783 m S 361.6179 99.7783 m S 361.6179 118.3605 m S 361.6179 99.7783 m S 361.6179 136.9425 m S 0 g 1 w 4 M 361.6179 136.9425 m F 0 G 0.3 w 10 M 361.6179 136.9425 m S 361.6179 136.9425 m S 361.6179 136.9425 m S 0 g 1 w 4 M 361.6179 136.9425 m F 0 G 0.3 w 10 M 361.6179 136.9425 m S 361.6179 136.9425 m S 1 g 1 w 4 M 356.6029 136.9425 m 356.6029 134.2492 358.8482 132.0659 361.6179 132.0659 c 364.3875 132.0659 366.6329 134.2492 366.6329 136.9425 c F 366.6329 136.9425 m 366.6329 139.6358 364.3875 141.8191 361.6179 141.8191 c 358.8482 141.8191 356.6029 139.6358 356.6029 136.9425 c F 361.6179 136.9425 m F 0 G 0.3 w 10 M 361.6179 136.9425 m S 0 g 1 w 4 M 361.6179 136.9425 m F 0 G 0.3 w 10 M 361.6179 136.9425 m S 361.6179 136.9425 m S 0 g 1 w 4 M 360.7125 136.0498 m 360.7125 133.0595 L 362.5233 133.0595 L 362.5233 136.0498 L 365.515 136.0404 L 365.515 137.8448 L 362.5233 137.8355 L 362.5233 140.8258 L 360.7125 140.8258 L 360.7125 137.8355 L 357.7207 137.8448 L 357.7207 136.0404 L 360.7125 136.0498 L f 0 G 0.3 w 10 M 361.6179 118.3605 m S 0 g 1 w 4 M 361.6179 118.3605 m F 0 G 0.3 w 10 M 361.6179 118.3605 m S 361.6179 118.3605 m S 361.6179 118.3605 m S 0 g 1 w 4 M 361.6179 118.3605 m F 0 G 0.3 w 10 M 361.6179 118.3605 m S 361.6179 118.3605 m S 1 g 1 w 4 M 356.6029 118.3605 m 356.6029 115.6672 358.8482 113.4838 361.6179 113.4838 c 364.3875 113.4838 366.6329 115.6672 366.6329 118.3605 c F 366.6329 118.3605 m 366.6329 121.0537 364.3875 123.2371 361.6179 123.2371 c 358.8482 123.2371 356.6029 121.0537 356.6029 118.3605 c F 361.6179 118.3605 m F 0 G 0.3 w 10 M 361.6179 118.3605 m S 0 g 1 w 4 M 361.6179 118.3605 m F 0 G 0.3 w 10 M 361.6179 118.3605 m S 361.6179 118.3605 m S 0 g 1 w 4 M 360.7125 117.4677 m 360.7125 114.4774 L 362.5233 114.4774 L 362.5233 117.4677 L 365.515 117.4584 L 365.515 119.2627 L 362.5233 119.2534 L 362.5233 122.2437 L 360.7125 122.2437 L 360.7125 119.2534 L 357.7207 119.2627 L 357.7207 117.4584 L 360.7125 117.4677 L f 0 G 0.3 w 10 M 361.6179 99.7783 m S 0 g 1 w 4 M 361.6179 99.7783 m F 0 G 0.3 w 10 M 361.6179 99.7783 m S 361.6179 99.7783 m S 361.6179 99.7783 m S 0 g 1 w 4 M 361.6179 99.7783 m F 0 G 0.3 w 10 M 361.6179 99.7783 m S 361.6179 99.7783 m S 1 g 1 w 4 M 356.6029 99.7783 m 356.6029 97.085 358.8482 94.9017 361.6179 94.9017 c 364.3875 94.9017 366.6329 97.085 366.6329 99.7783 c F 366.6329 99.7783 m 366.6329 102.4716 364.3875 104.6549 361.6179 104.6549 c 358.8482 104.6549 356.6029 102.4716 356.6029 99.7783 c F 361.6179 99.7783 m F 0 G 0.3 w 10 M 361.6179 99.7783 m S 0 g 1 w 4 M 361.6179 99.7783 m F 0 G 0.3 w 10 M 361.6179 99.7783 m S 361.6179 99.7783 m S 0 g 1 w 4 M 360.7125 98.8856 m 360.7125 95.8953 L 362.5233 95.8953 L 362.5233 98.8856 L 365.515 98.8762 L 365.515 100.6806 L 362.5233 100.6713 L 362.5233 103.6616 L 360.7125 103.6616 L 360.7125 100.6713 L 357.7207 100.6806 L 357.7207 98.8762 L 360.7125 98.8856 L f 0 G 0.3 w 10 M 314.037 127.6515 m S 314.037 127.6515 m S 333.0693 127.6515 m S 314.037 127.6515 m S 333.0693 127.6515 m S 333.0693 127.6515 m S 333.0693 127.6515 m S 314.037 127.6515 m S 314.037 109.0694 m S 314.037 109.0694 m S 333.0693 109.0694 m S 314.037 109.0694 m S 333.0693 109.0694 m S 333.0693 109.0694 m S 333.0693 109.0694 m S 314.037 109.0694 m S 380.6502 118.3605 m S 380.6502 136.9425 m S 380.6502 136.9425 m S 380.6502 155.5247 m S 380.6502 99.7783 m S 380.6502 118.3605 m S 380.6502 81.1962 m S 380.6502 99.7783 m S 304.5208 136.9425 m S 0 g 1 w 4 M 304.5208 136.9425 m F 0 G 0.3 w 10 M 304.5208 136.9425 m S 0 g 1 w 4 M 304.5208 136.9425 m F 1 g 304.5208 136.9425 m F 0 G 0.3 w 10 M 304.5208 136.9425 m S 0 g 1 w 4 M 304.5208 136.9425 m F 0 G 0.3 w 10 M 304.5208 136.9425 m S 0 g 1 w 4 M 304.5208 136.9425 m F 0 G 0.3 w 10 M 304.5208 118.3605 m S 0 g 1 w 4 M 304.5208 118.3605 m F 0 G 0.3 w 10 M 304.5208 118.3605 m S 0 g 1 w 4 M 304.5208 118.3605 m F 1 g 304.5208 118.3605 m F 0 G 0.3 w 10 M 304.5208 118.3605 m S 0 g 1 w 4 M 304.5208 118.3605 m F 0 G 0.3 w 10 M 304.5208 118.3605 m S 0 g 1 w 4 M 304.5208 118.3605 m F 0 G 0.3 w 10 M 323.5532 118.3605 m S 0 g 1 w 4 M 323.5532 118.3605 m F 0 G 0.3 w 10 M 323.5532 118.3605 m S 0 g 1 w 4 M 323.5532 118.3605 m F 1 g 318.5382 118.3605 m 318.5382 115.6672 320.7835 113.4838 323.5532 113.4838 c 326.3228 113.4838 328.5681 115.6672 328.5681 118.3605 c F 328.5681 118.3605 m 328.5681 121.0537 326.3228 123.2371 323.5532 123.2371 c 320.7835 123.2371 318.5382 121.0537 318.5382 118.3605 c F 323.5532 118.3605 m F 0 G 0.3 w 10 M 323.5532 118.3605 m S 0 g 1 w 4 M 323.5532 118.3605 m F 0 G 0.3 w 10 M 323.5532 118.3605 m S 0 g 1 w 4 M 323.5532 118.3605 m F 322.6478 119.2534 m 319.656 119.2627 L 319.656 117.4584 L 322.6478 117.4676 L F 324.4586 117.4676 m 327.4503 117.4584 L 327.4503 119.2627 L 324.4586 119.2534 L F 319.656 119.2627 m 327.4503 119.2627 l 327.4503 117.4584 l 319.656 117.4584 l 319.656 119.2627 l f 0 G 0.3 w 10 M 323.5532 99.7783 m S 0 g 1 w 4 M 323.5532 99.7783 m F 0 G 0.3 w 10 M 323.5532 99.7783 m S 0 g 1 w 4 M 323.5532 99.7783 m F 1 g 318.5382 99.7783 m 318.5382 97.085 320.7835 94.9017 323.5532 94.9017 c 326.3228 94.9017 328.5681 97.085 328.5681 99.7783 c F 328.5681 99.7783 m 328.5681 102.4716 326.3228 104.6549 323.5532 104.6549 c 320.7835 104.6549 318.5382 102.4716 318.5382 99.7783 c F 323.5532 99.7783 m F 0 G 0.3 w 10 M 323.5532 99.7783 m S 0 g 1 w 4 M 323.5532 99.7783 m F 0 G 0.3 w 10 M 323.5532 99.7783 m S 0 g 1 w 4 M 323.5532 99.7783 m F 322.6478 100.6713 m 319.656 100.6806 L 319.656 98.8762 L 322.6478 98.8855 L F 324.4586 98.8855 m 327.4503 98.8762 L 327.4503 100.6806 L 324.4586 100.6713 L F 319.656 100.6806 m 327.4503 100.6806 l 327.4503 98.8762 l 319.656 98.8762 l 319.656 100.6806 l f 0 G 0.3 w 10 M 304.5208 99.7783 m S 0 g 1 w 4 M 304.5208 99.7783 m F 0 G 0.3 w 10 M 304.5208 99.7783 m S 0 g 1 w 4 M 304.5208 99.7783 m F 1 g 304.5208 99.7783 m F 0 G 0.3 w 10 M 304.5208 99.7783 m S 0 g 1 w 4 M 304.5208 99.7783 m F 0 G 0.3 w 10 M 304.5208 99.7783 m S 0 g 1 w 4 M 304.5208 99.7783 m F 0 G 0.3 w 10 M 342.5855 136.9425 m S 0 g 1 w 4 M 342.5855 136.9425 m F 0 G 0.3 w 10 M 342.5855 136.9425 m S 342.5855 136.9425 m S 342.5855 136.9425 m S 0 g 1 w 4 M 342.5855 136.9425 m F 0 G 0.3 w 10 M 342.5855 136.9425 m S 342.5855 136.9425 m S 1 g 1 w 4 M 337.5705 136.9425 m 337.5705 134.2492 339.8158 132.0659 342.5855 132.0659 c 345.3551 132.0659 347.6004 134.2492 347.6004 136.9425 c F 347.6004 136.9425 m 347.6004 139.6358 345.3551 141.8191 342.5855 141.8191 c 339.8158 141.8191 337.5705 139.6358 337.5705 136.9425 c F 342.5855 136.9425 m F 0 G 0.3 w 10 M 342.5855 136.9425 m S 0 g 1 w 4 M 342.5855 136.9425 m F 0 G 0.3 w 10 M 342.5855 136.9425 m S 342.5855 136.9425 m S 0 g 1 w 4 M 341.6801 136.0498 m 341.6801 133.0595 L 343.4909 133.0595 L 343.4909 136.0498 L 346.4826 136.0404 L 346.4826 137.8448 L 343.4909 137.8355 L 343.4909 140.8258 L 341.6801 140.8258 L 341.6801 137.8355 L 338.6883 137.8448 L 338.6883 136.0404 L 341.6801 136.0498 L f 0 G 0.3 w 10 M 323.5532 136.9425 m S 0 g 1 w 4 M 323.5532 136.9425 m F 0 G 0.3 w 10 M 323.5532 136.9425 m S 323.5532 136.9425 m S 323.5532 136.9425 m S 0 g 1 w 4 M 323.5532 136.9425 m F 0 G 0.3 w 10 M 323.5532 136.9425 m S 323.5532 136.9425 m S 1 g 1 w 4 M 323.5532 136.9425 m F 0 G 0.3 w 10 M 323.5532 136.9425 m S 0 g 1 w 4 M 323.5532 136.9425 m F 0 G 0.3 w 10 M 323.5532 136.9425 m S 323.5532 136.9425 m S 342.5855 118.3605 m S 0 g 1 w 4 M 342.5855 118.3605 m F 0 G 0.3 w 10 M 342.5855 118.3605 m S 342.5855 118.3605 m S 342.5855 118.3605 m S 0 g 1 w 4 M 342.5855 118.3605 m F 0 G 0.3 w 10 M 342.5855 118.3605 m S 342.5855 118.3605 m S 1 g 1 w 4 M 342.5855 118.3605 m F 0 G 0.3 w 10 M 342.5855 118.3605 m S 0 g 1 w 4 M 342.5855 118.3605 m F 0 G 0.3 w 10 M 342.5855 118.3605 m S 342.5855 118.3605 m S 342.5855 99.7783 m S 0 g 1 w 4 M 342.5855 99.7783 m F 0 G 0.3 w 10 M 342.5855 99.7783 m S 342.5855 99.7783 m S 342.5855 99.7783 m S 0 g 1 w 4 M 342.5855 99.7783 m F 0 G 0.3 w 10 M 342.5855 99.7783 m S 342.5855 99.7783 m S 1 g 1 w 4 M 342.5855 99.7783 m F 0 G 0.3 w 10 M 342.5855 99.7783 m S 0 g 1 w 4 M 342.5855 99.7783 m F 0 G 0.3 w 10 M 342.5855 99.7783 m S 342.5855 99.7783 m S u u 0 g 1 w 4 M /_Times-Roman 12 14.5 0 0 z [1 0 0 1 236 55.5]e (\(and rotated\))t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 261 34.5]e (\(b\))t T U U 0 G 0.3 w 10 M 209.3591 136.9425 m S 209.3591 136.9425 m S 209.3591 136.9425 m S 209.3591 136.9425 m S 209.3591 136.9425 m S 209.3591 136.9425 m S 209.3591 136.9425 m S 209.3591 136.9425 m S 209.3591 136.9425 m S 0 g 1 w 4 M 209.3591 136.9425 m F 0 G 0.3 w 10 M 209.3591 136.9425 m S 0 g 1 w 4 M 209.3591 136.9425 m F 1 g 204.3441 136.9425 m 204.3441 134.2492 206.5895 132.0659 209.3591 132.0659 c 212.1287 132.0659 214.3741 134.2492 214.3741 136.9425 c F 214.3741 136.9425 m 214.3741 139.6358 212.1287 141.8191 209.3591 141.8191 c 206.5895 141.8191 204.3441 139.6358 204.3441 136.9425 c F 209.3591 136.9425 m F 0 G 0.3 w 10 M 209.3591 136.9425 m S 0 g 1 w 4 M 209.3591 136.9425 m F 0 G 0.3 w 10 M 209.3591 136.9425 m S 0 g 1 w 4 M 209.3591 136.9425 m F 208.4537 137.8355 m 205.462 137.8447 L 205.462 136.0404 L 208.4537 136.0497 L F 210.2645 136.0497 m 213.2563 136.0404 L 213.2563 137.8447 L 210.2645 137.8355 L F 205.462 137.8447 m 213.2563 137.8447 l 213.2563 136.0404 l 205.462 136.0404 l 205.462 137.8447 l f 0 G 0.3 w 10 M 323.5532 136.9425 m S 323.5532 136.9425 m S 323.5532 136.9425 m S 323.5532 136.9425 m S 323.5532 136.9425 m S 323.5532 136.9425 m S 323.5532 136.9425 m S 323.5532 136.9425 m S 323.5532 136.9425 m S 0 g 1 w 4 M 323.5532 136.9425 m F 0 G 0.3 w 10 M 323.5532 136.9425 m S 0 g 1 w 4 M 323.5532 136.9425 m F 1 g 318.5382 136.9425 m 318.5382 134.2492 320.7835 132.0659 323.5532 132.0659 c 326.3228 132.0659 328.5681 134.2492 328.5681 136.9425 c F 328.5681 136.9425 m 328.5681 139.6358 326.3228 141.8191 323.5532 141.8191 c 320.7835 141.8191 318.5382 139.6358 318.5382 136.9425 c F 323.5532 136.9425 m F 0 G 0.3 w 10 M 323.5532 136.9425 m S 0 g 1 w 4 M 323.5532 136.9425 m F 0 G 0.3 w 10 M 323.5532 136.9425 m S 0 g 1 w 4 M 323.5532 136.9425 m F 322.6478 137.8355 m 319.656 137.8447 L 319.656 136.0404 L 322.6478 136.0497 L F 324.4586 136.0497 m 327.4503 136.0404 L 327.4503 137.8447 L 324.4586 137.8355 L F 319.656 137.8447 m 327.4503 137.8447 l 327.4503 136.0404 l 319.656 136.0404 l 319.656 137.8447 l f 0 G 0.3 w 10 M 342.5855 118.3605 m S 342.5855 118.3605 m S 342.5855 99.7783 m S 342.5855 118.3605 m S 342.5855 99.7783 m S 342.5855 99.7783 m S 342.5855 118.3605 m S 342.5855 99.7783 m S 342.5855 118.3605 m S 342.5855 118.3605 m S 342.5855 99.7783 m S 342.5855 118.3605 m S 342.5855 99.7783 m S 342.5855 99.7783 m S 342.5855 118.3605 m S 342.5855 99.7783 m S 342.5855 118.3605 m S 0 g 1 w 4 M 342.5855 118.3605 m F 0 G 0.3 w 10 M 342.5855 118.3605 m S 0 g 1 w 4 M 342.5855 118.3605 m F 1 g 337.5705 118.3605 m 337.5705 115.6672 339.8159 113.4838 342.5855 113.4838 c 345.3552 113.4838 347.6005 115.6672 347.6005 118.3605 c F 347.6005 118.3605 m 347.6005 121.0537 345.3552 123.2371 342.5855 123.2371 c 339.8159 123.2371 337.5705 121.0537 337.5705 118.3605 c F 342.5855 118.3605 m F 0 G 0.3 w 10 M 342.5855 118.3605 m S 0 g 1 w 4 M 342.5855 118.3605 m F 0 G 0.3 w 10 M 342.5855 118.3605 m S 0 g 1 w 4 M 342.5855 118.3605 m F 341.6801 119.2534 m 338.6884 119.2627 L 338.6884 117.4584 L 341.6801 117.4676 L F 343.4909 117.4676 m 346.4826 117.4584 L 346.4826 119.2627 L 343.4909 119.2534 L F 338.6884 119.2627 m 346.4826 119.2627 l 346.4826 117.4584 l 338.6884 117.4584 l 338.6884 119.2627 l f 0 G 0.3 w 10 M 342.5855 99.7783 m S 0 g 1 w 4 M 342.5855 99.7783 m F 0 G 0.3 w 10 M 342.5855 99.7783 m S 0 g 1 w 4 M 342.5855 99.7783 m F 1 g 337.5705 99.7783 m 337.5705 97.085 339.8159 94.9017 342.5855 94.9017 c 345.3552 94.9017 347.6005 97.085 347.6005 99.7783 c F 347.6005 99.7783 m 347.6005 102.4716 345.3552 104.6549 342.5855 104.6549 c 339.8159 104.6549 337.5705 102.4716 337.5705 99.7783 c F 342.5855 99.7783 m F 0 G 0.3 w 10 M 342.5855 99.7783 m S 0 g 1 w 4 M 342.5855 99.7783 m F 0 G 0.3 w 10 M 342.5855 99.7783 m S 0 g 1 w 4 M 342.5855 99.7783 m F 341.6801 100.6713 m 338.6884 100.6806 L 338.6884 98.8762 L 341.6801 98.8855 L F 343.4909 98.8855 m 346.4826 98.8762 L 346.4826 100.6806 L 343.4909 100.6713 L F 338.6884 100.6806 m 346.4826 100.6806 l 346.4826 98.8762 l 338.6884 98.8762 l 338.6884 100.6806 l f 0 G 0.3 w 10 M 304.5208 118.3605 m S 304.5208 136.9425 m S 304.5208 136.9425 m S 304.5208 136.9425 m S 304.5208 136.9425 m S 304.5208 118.3605 m S 304.5208 99.7783 m S 304.5208 118.3605 m S 304.5208 99.7783 m S 304.5208 99.7783 m S 304.5208 118.3605 m S 304.5208 99.7783 m S 304.5208 118.3605 m S 304.5208 136.9425 m S 304.5208 136.9425 m S 304.5208 136.9425 m S 304.5208 136.9425 m S 304.5208 118.3605 m S 304.5208 99.7783 m S 304.5208 118.3605 m S 304.5208 99.7783 m S 304.5208 99.7783 m S 304.5208 118.3605 m S 304.5208 99.7783 m S 304.5208 136.9425 m S 304.5208 118.3605 m S 304.5208 136.9425 m S 304.5208 136.9425 m S 304.5208 118.3605 m S 304.5208 136.9425 m S 304.5208 118.3605 m S 304.5208 99.7783 m S 304.5208 99.7783 m S 304.5208 99.7783 m S 304.5208 118.3605 m S 304.5208 99.7783 m S 304.5208 136.9425 m S 0 g 1 w 4 M 304.5208 136.9425 m F 0 G 0.3 w 10 M 304.5208 136.9425 m S 304.5208 136.9425 m S 304.5208 136.9425 m S 0 g 1 w 4 M 304.5208 136.9425 m F 0 G 0.3 w 10 M 304.5208 136.9425 m S 304.5208 136.9425 m S 1 g 1 w 4 M 299.5059 136.9425 m 299.5059 134.2492 301.7512 132.0659 304.5208 132.0659 c 307.2905 132.0659 309.5358 134.2492 309.5358 136.9425 c F 309.5358 136.9425 m 309.5358 139.6358 307.2905 141.8191 304.5208 141.8191 c 301.7512 141.8191 299.5059 139.6358 299.5059 136.9425 c F 304.5208 136.9425 m F 0 G 0.3 w 10 M 304.5208 136.9425 m S 0 g 1 w 4 M 304.5208 136.9425 m F 0 G 0.3 w 10 M 304.5208 136.9425 m S 304.5208 136.9425 m S 0 g 1 w 4 M 303.6154 136.0498 m 303.6154 133.0595 L 305.4262 133.0595 L 305.4262 136.0498 L 308.418 136.1029 308.418 136.0404 V 308.418 137.8448 L 305.4262 137.8355 L 305.4262 140.8258 L 303.6154 140.8258 L 303.6154 137.8355 L 300.6237 137.8448 L 300.6237 136.0404 L 303.6154 136.0498 L f 0 G 0.3 w 10 M 304.5208 118.3605 m S 0 g 1 w 4 M 304.5208 118.3605 m F 0 G 0.3 w 10 M 304.5208 118.3605 m S 304.5208 118.3605 m S 304.5208 118.3605 m S 0 g 1 w 4 M 304.5208 118.3605 m F 0 G 0.3 w 10 M 304.5208 118.3605 m S 304.5208 118.3605 m S 1 g 1 w 4 M 299.5059 118.3605 m 299.5059 115.6672 301.7512 113.4838 304.5208 113.4838 c 307.2905 113.4838 309.5358 115.6672 309.5358 118.3605 c F 309.5358 118.3605 m 309.5358 121.0537 307.2905 123.2371 304.5208 123.2371 c 301.7512 123.2371 299.5059 121.0537 299.5059 118.3605 c F 304.5208 118.3605 m F 0 G 0.3 w 10 M 304.5208 118.3605 m S 0 g 1 w 4 M 304.5208 118.3605 m F 0 G 0.3 w 10 M 304.5208 118.3605 m S 304.5208 118.3605 m S 0 g 1 w 4 M 303.6154 117.4677 m 303.6154 114.4774 L 305.4262 114.4774 L 305.4262 117.4677 L 308.418 117.4584 L 308.418 119.2627 L 305.4262 119.2534 L 305.4262 122.2437 L 303.6154 122.2437 L 303.6154 119.2534 L 300.6237 119.2627 L 300.6237 117.4584 L 303.6154 117.4677 L f 0 G 0.3 w 10 M 304.5208 99.7783 m S 0 g 1 w 4 M 304.5208 99.7783 m F 0 G 0.3 w 10 M 304.5208 99.7783 m S 304.5208 99.7783 m S 304.5208 99.7783 m S 0 g 1 w 4 M 304.5208 99.7783 m F 0 G 0.3 w 10 M 304.5208 99.7783 m S 304.5208 99.7783 m S 1 g 1 w 4 M 299.5059 99.7783 m 299.5059 97.085 301.7512 94.9017 304.5208 94.9017 c 307.2905 94.9017 309.5358 97.085 309.5358 99.7783 c F 309.5358 99.7783 m 309.5358 102.4716 307.2905 104.6549 304.5208 104.6549 c 301.7512 104.6549 299.5059 102.4716 299.5059 99.7783 c F 304.5208 99.7783 m F 0 G 0.3 w 10 M 304.5208 99.7783 m S 0 g 1 w 4 M 304.5208 99.7783 m F 0 G 0.3 w 10 M 304.5208 99.7783 m S 304.5208 99.7783 m S 0 g 1 w 4 M 303.6154 98.8856 m 303.6154 95.8953 L 305.4262 95.8953 L 305.4262 98.8856 L 308.418 98.8762 L 308.418 100.6806 L 305.4262 100.6713 L 305.4262 103.6616 L 303.6154 103.6616 L 303.6154 100.6713 L 300.6237 100.6806 L 300.6237 98.8762 L 303.6154 98.8856 L f 0 G 0.3 w 10 M 190.3268 136.9425 m S 190.3268 136.9425 m S 190.3268 136.9425 m S 190.3268 136.9425 m S 190.3268 136.9425 m S 190.3268 136.9425 m S 190.3268 136.9425 m S 190.3268 136.9425 m S 190.3268 136.9425 m S 190.3268 136.9425 m S 190.3268 136.9425 m S 190.3268 136.9425 m S 190.3268 136.9425 m S 0 g 1 w 4 M 190.3268 136.9425 m F 0 G 0.3 w 10 M 190.3268 136.9425 m S 190.3268 136.9425 m S 190.3268 136.9425 m S 0 g 1 w 4 M 190.3268 136.9425 m F 0 G 0.3 w 10 M 190.3268 136.9425 m S 190.3268 136.9425 m S 1 g 1 w 4 M 185.3118 136.9425 m 185.3118 134.2492 187.5571 132.0659 190.3268 132.0659 c 193.0964 132.0659 195.3417 134.2492 195.3417 136.9425 c F 195.3417 136.9425 m 195.3417 139.6358 193.0964 141.8191 190.3268 141.8191 c 187.5571 141.8191 185.3118 139.6358 185.3118 136.9425 c F 190.3268 136.9425 m F 0 G 0.3 w 10 M 190.3268 136.9425 m S 0 g 1 w 4 M 190.3268 136.9425 m F 0 G 0.3 w 10 M 190.3268 136.9425 m S 190.3268 136.9425 m S 0 g 1 w 4 M 189.4214 136.0498 m 189.4214 133.0595 L 191.2322 133.0595 L 191.2322 136.0498 L 194.2239 136.0404 L 194.2239 137.8448 L 191.2322 137.8355 L 191.2322 140.8258 L 189.4214 140.8258 L 189.4214 137.8355 L 186.4296 137.8448 L 186.4296 136.0404 L 189.4214 136.0498 L f 0 G 0.3 w 10 M 456.8269 99.7783 m S 437.7828 99.7783 m S 437.7828 99.7783 m S 456.8269 99.7783 m S 437.7828 99.7783 m S 437.7828 99.7783 m S 456.8269 99.7783 m S 456.8269 99.7783 m S 456.8269 99.7783 m S 437.7828 99.7783 m S 437.7828 99.7783 m S 456.8269 99.7783 m S 437.7828 99.7783 m S 437.7828 99.7783 m S 456.8269 99.7783 m S 456.8269 99.7783 m S 437.7828 99.7783 m S 0 g 1 w 4 M 437.7828 99.7783 m F 0 G 0.3 w 10 M 437.7828 99.7783 m S 0 g 1 w 4 M 437.7828 99.7783 m F 1 g 432.7647 99.7783 m 432.7647 97.085 435.0114 94.9017 437.7828 94.9017 c 440.5541 94.9017 442.8008 97.085 442.8008 99.7783 c F 442.8008 99.7783 m 442.8008 102.4716 440.5541 104.6549 437.7828 104.6549 c 435.0114 104.6549 432.7647 102.4716 432.7647 99.7783 c F 437.7828 99.7783 m F 0 G 0.3 w 10 M 437.7828 99.7783 m S 0 g 1 w 4 M 437.7828 99.7783 m F 0 G 0.3 w 10 M 437.7828 99.7783 m S 0 g 1 w 4 M 437.7828 99.7783 m F 436.8768 100.6713 m 433.8832 100.6806 L 433.8832 98.8762 L 436.8768 98.8855 L F 438.6887 98.8855 m 441.6823 98.8762 L 441.6823 100.6806 L 438.6887 100.6713 L F 433.8832 100.6806 m 441.6823 100.6806 l 441.6823 98.8762 l 433.8832 98.8762 l 433.8832 100.6806 l f 0 G 0.3 w 10 M 456.8269 99.7783 m S 0 g 1 w 4 M 456.8269 99.7783 m F 0 G 0.3 w 10 M 456.8269 99.7783 m S 0 g 1 w 4 M 456.8269 99.7783 m F 1 g 451.8088 99.7783 m 451.8088 97.085 454.0555 94.9017 456.8269 94.9017 c 459.5983 94.9017 461.845 97.085 461.845 99.7783 c F 461.845 99.7783 m 461.845 102.4716 459.5983 104.6549 456.8269 104.6549 c 454.0555 104.6549 451.8088 102.4716 451.8088 99.7783 c F 456.8269 99.7783 m F 0 G 0.3 w 10 M 456.8269 99.7783 m S 0 g 1 w 4 M 456.8269 99.7783 m F 0 G 0.3 w 10 M 456.8269 99.7783 m S 0 g 1 w 4 M 456.8269 99.7783 m F 455.921 100.6713 m 452.9273 100.6806 L 452.9273 98.8762 L 455.921 98.8855 L F 457.7329 98.8855 m 460.7265 98.8762 L 460.7265 100.6806 L 457.7329 100.6713 L F 452.9273 100.6806 m 460.7265 100.6806 l 460.7265 98.8762 l 452.9273 98.8762 l 452.9273 100.6806 l f 0 G 0.3 w 10 M 437.7827 136.9425 m S 418.7386 136.9425 m S 418.7386 136.9425 m S 437.7827 136.9425 m S 418.7386 136.9425 m S 418.7386 136.9425 m S 437.7827 136.9425 m S 437.7827 136.9425 m S 437.7827 136.9425 m S 418.7386 136.9425 m S 418.7386 136.9425 m S 437.7827 136.9425 m S 418.7386 136.9425 m S 418.7386 136.9425 m S 437.7827 136.9425 m S 437.7827 136.9425 m S 418.7386 136.9425 m S 418.7386 136.9425 m S 437.7827 136.9425 m S 418.7386 136.9425 m S 437.7827 136.9425 m S 418.7386 136.9425 m S 437.7827 136.9425 m S 437.7827 136.9425 m S 418.7386 136.9425 m S 0 g 1 w 4 M 418.7386 136.9425 m F 0 G 0.3 w 10 M 418.7386 136.9425 m S 418.7386 136.9425 m S 418.7386 136.9425 m S 0 g 1 w 4 M 418.7386 136.9425 m F 0 G 0.3 w 10 M 418.7386 136.9425 m S 418.7386 136.9425 m S 1 g 1 w 4 M 413.7205 136.9425 m 413.7205 134.2492 415.9672 132.0659 418.7386 132.0659 c 421.51 132.0659 423.7567 134.2492 423.7567 136.9425 c F 423.7567 136.9425 m 423.7567 139.6358 421.51 141.8191 418.7386 141.8191 c 415.9672 141.8191 413.7205 139.6358 413.7205 136.9425 c F 418.7386 136.9425 m F 0 G 0.3 w 10 M 418.7386 136.9425 m S 0 g 1 w 4 M 418.7386 136.9425 m F 0 G 0.3 w 10 M 418.7386 136.9425 m S 418.7386 136.9425 m S 0 g 1 w 4 M 417.8327 136.0498 m 417.8327 133.0595 L 419.6445 133.0595 L 419.6445 136.0498 L 422.6382 136.0404 L 422.6382 137.8448 L 419.6445 137.8355 L 419.6445 140.8258 L 417.8327 140.8258 L 417.8327 137.8355 L 414.839 137.8448 L 414.839 136.0404 L 417.8327 136.0498 L f 0 G 0.3 w 10 M 437.7827 136.9425 m S 0 g 1 w 4 M 437.7827 136.9425 m F 0 G 0.3 w 10 M 437.7827 136.9425 m S 437.7827 136.9425 m S 437.7827 136.9425 m S 0 g 1 w 4 M 437.7827 136.9425 m F 0 G 0.3 w 10 M 437.7827 136.9425 m S 437.7827 136.9425 m S 1 g 1 w 4 M 432.7647 136.9425 m 432.7647 134.2492 435.0114 132.0659 437.7827 132.0659 c 440.5541 132.0659 442.8008 134.2492 442.8008 136.9425 c F 442.8008 136.9425 m 442.8008 139.6358 440.5541 141.8191 437.7827 141.8191 c 435.0114 141.8191 432.7647 139.6358 432.7647 136.9425 c F 437.7827 136.9425 m F 0 G 0.3 w 10 M 437.7827 136.9425 m S 0 g 1 w 4 M 437.7827 136.9425 m F 0 G 0.3 w 10 M 437.7827 136.9425 m S 437.7827 136.9425 m S 0 g 1 w 4 M 436.8768 136.0498 m 436.8768 133.0595 L 438.6887 133.0595 L 438.6887 136.0498 L 441.6823 136.0404 L 441.6823 137.8448 L 438.6887 137.8355 L 438.6887 140.8258 L 436.8768 140.8258 L 436.8768 137.8355 L 433.8832 137.8448 L 433.8832 136.0404 L 436.8768 136.0498 L f showpage _E end %%EndDocument @endspecial 517 2127 a @beginspecial 32 @llx 34.500000 @lly 323 @urx 223.500000 @ury 2196 @rwi @setspecial %%BeginDocument: fig7c.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 34.975 127.2563 m S 34.975 108.6743 m S 34.975 164.4206 m S 34.975 145.8385 m S 34.975 145.8385 m S 34.975 127.2563 m S 53.9833 164.4206 m S 53.9833 145.8385 m S 34.975 145.8385 m S 34.975 164.4206 m S 44.4791 155.1295 m S 92 127.2563 m S 92 108.6743 m S 72.9917 108.6743 m S 72.9917 127.2563 m S 82.4958 117.9653 m S 72.9917 145.8385 m S 72.9917 127.2563 m S 53.9833 127.2563 m S 53.9833 145.8385 m S 63.4875 136.5475 m S 72.9917 164.4206 m S 72.9917 145.8385 m S 53.9833 145.8385 m S 53.9833 164.4206 m S 63.4875 155.1295 m S 92 164.4206 m S 92 145.8385 m S 72.9917 145.8385 m S 72.9917 164.4206 m S 82.4958 155.1295 m S 92 145.8385 m S 92 127.2563 m S 72.9917 127.2563 m S 72.9917 145.8385 m S 82.4958 136.5475 m S 72.9917 127.2563 m S 72.9917 108.6743 m S 53.9833 108.6743 m S 53.9833 127.2563 m S 63.4875 117.9653 m S 53.9833 127.2563 m S 53.9833 108.6743 m S 34.975 108.6743 m S 34.975 127.2563 m S 44.4791 117.9653 m S 53.9833 145.8385 m S 53.9833 127.2563 m S 34.975 127.2563 m S 34.975 145.8385 m S 44.4791 136.5475 m S 0 g 1 w 4 M 44.4791 155.1295 m F 82.4958 155.1295 m F 44.4791 117.9653 m F 82.4958 117.9653 m F 0 G 0.3 w 10 M 111.0083 164.4206 m S 111.0083 145.8385 m S 92 145.8385 m S 92 164.4206 m S 101.5041 155.1295 m S 149.025 127.2563 m S 149.025 108.6743 m S 130.0167 108.6743 m S 130.0167 127.2563 m S 139.5208 117.9653 m S 130.0167 145.8385 m S 130.0167 127.2563 m S 111.0083 127.2563 m S 111.0083 145.8385 m S 120.5125 136.5475 m S 130.0167 164.4206 m S 130.0167 145.8385 m S 111.0083 145.8385 m S 111.0083 164.4206 m S 120.5125 155.1295 m S 149.025 164.4206 m S 149.025 145.8385 m S 130.0167 145.8385 m S 130.0167 164.4206 m S 139.5208 155.1295 m S 149.025 145.8385 m S 149.025 127.2563 m S 130.0167 127.2563 m S 130.0167 145.8385 m S 139.5208 136.5475 m S 130.0167 127.2563 m S 130.0167 108.6743 m S 111.0083 108.6743 m S 111.0083 127.2563 m S 120.5125 117.9653 m S 111.0083 127.2563 m S 111.0083 108.6743 m S 92 108.6743 m S 92 127.2563 m S 101.5041 117.9653 m S 111.0083 145.8385 m S 111.0083 127.2563 m S 92 127.2563 m S 92 145.8385 m S 101.5041 136.5475 m S 0 g 1 w 4 M 101.5041 155.1295 m F 139.5208 155.1295 m F 101.5041 117.9653 m F 139.5208 117.9653 m F 0 G 0.3 w 10 M 34.975 71.5101 m S 34.975 52.928 m S 34.975 108.6743 m S 34.975 90.0922 m S 34.975 90.0922 m S 34.975 71.5101 m S 53.9833 108.6743 m S 53.9833 90.0922 m S 34.975 90.0922 m S 34.975 108.6743 m S 44.4791 99.3833 m S 92 71.5101 m S 92 52.928 m S 72.9917 52.928 m S 72.9917 71.5101 m S 82.4958 62.2191 m S 72.9917 90.0922 m S 72.9917 71.5101 m S 53.9833 71.5101 m S 53.9833 90.0922 m S 63.4875 80.8012 m S 72.9917 108.6743 m S 72.9917 90.0922 m S 53.9833 90.0922 m S 53.9833 108.6743 m S 63.4875 99.3833 m S 92 108.6743 m S 92 90.0922 m S 72.9917 90.0922 m S 72.9917 108.6743 m S 82.4958 99.3833 m S 92 90.0922 m S 92 71.5101 m S 72.9917 71.5101 m S 72.9917 90.0922 m S 82.4958 80.8012 m S 72.9917 71.5101 m S 72.9917 52.928 m S 53.9833 52.928 m S 53.9833 71.5101 m S 63.4875 62.2191 m S 53.9833 71.5101 m S 53.9833 52.928 m S 34.975 52.928 m S 34.975 71.5101 m S 44.4791 62.2191 m S 53.9833 90.0922 m S 53.9833 71.5101 m S 34.975 71.5101 m S 34.975 90.0922 m S 44.4791 80.8012 m S 0 g 1 w 4 M 44.4791 99.3833 m F 82.4958 99.3833 m F 44.4791 62.2191 m F 82.4958 62.2191 m F 0 G 0.3 w 10 M 111.0083 108.6743 m S 111.0083 90.0922 m S 92 90.0922 m S 92 108.6743 m S 101.5041 99.3833 m S 149.025 71.5101 m S 149.025 52.928 m S 130.0167 52.928 m S 130.0167 71.5101 m S 139.5208 62.2191 m S 130.0167 90.0922 m S 130.0167 71.5101 m S 111.0083 71.5101 m S 111.0083 90.0922 m S 120.5125 80.8012 m S 130.0167 108.6743 m S 130.0167 90.0922 m S 111.0083 90.0922 m S 111.0083 108.6743 m S 120.5125 99.3833 m S 149.025 108.6743 m S 149.025 90.0922 m S 130.0167 90.0922 m S 130.0167 108.6743 m S 139.5208 99.3833 m S 149.025 90.0922 m S 149.025 71.5101 m S 130.0167 71.5101 m S 130.0167 90.0922 m S 139.5208 80.8012 m S 130.0167 71.5101 m S 130.0167 52.928 m S 111.0083 52.928 m S 111.0083 71.5101 m S 120.5125 62.2191 m S 111.0083 71.5101 m S 111.0083 52.928 m S 92 52.928 m S 92 71.5101 m S 101.5041 62.2191 m S 111.0083 90.0922 m S 111.0083 71.5101 m S 92 71.5101 m S 92 90.0922 m S 101.5041 80.8012 m S 0 g 1 w 4 M 101.5041 99.3833 m F 139.5208 99.3833 m F 101.5041 62.2191 m F 139.5208 62.2191 m F 0 G 0.3 w 10 M 34.975 52.928 m S 53.9833 52.928 m S 34.975 52.928 m S 72.9917 52.928 m S 53.9833 52.928 m S 92 52.928 m S 72.9917 52.928 m S 111.0083 52.928 m S 92 52.928 m S 130.0167 52.928 m S 111.0083 52.928 m S 149.025 52.928 m S 130.0167 52.928 m S 53.9833 164.4206 m S 53.9833 145.8385 m S 34.975 145.8385 m S 34.975 164.4206 m S 44.4791 155.1295 m S 92 127.2563 m S 92 108.6743 m S 72.9917 108.6743 m S 72.9917 127.2563 m S 72.9917 145.8385 m S 72.9917 127.2563 m S 53.9833 127.2563 m S 53.9833 145.8385 m S 63.4875 136.5475 m S 72.9917 164.4206 m S 72.9917 145.8385 m S 53.9833 145.8385 m S 53.9833 164.4206 m S 63.4875 155.1295 m S 92 164.4206 m S 92 145.8385 m S 72.9917 145.8385 m S 72.9917 164.4206 m S 82.4958 155.1295 m S 92 145.8385 m S 92 127.2563 m S 72.9917 127.2563 m S 72.9917 145.8385 m S 82.4958 136.5475 m S 72.9917 127.2563 m S 72.9917 108.6743 m S 53.9833 108.6743 m S 53.9833 127.2563 m S 63.4875 117.9653 m S 53.9833 127.2563 m S 53.9833 108.6743 m S 34.975 108.6743 m S 34.975 127.2563 m S 44.4791 117.9653 m S 53.9833 145.8385 m S 53.9833 127.2563 m S 34.975 127.2563 m S 34.975 145.8385 m S 44.4791 136.5475 m S 0 g 1 w 4 M 44.4791 155.1295 m F 82.4958 155.1295 m F 44.4791 117.9653 m F 0 G 0.3 w 10 M 111.0083 164.4206 m S 111.0083 145.8385 m S 92 145.8385 m S 92 164.4206 m S 101.5041 155.1295 m S 149.025 127.2563 m S 149.025 108.6743 m S 130.0167 108.6743 m S 130.0167 127.2563 m S 139.5208 117.9653 m S 130.0167 145.8385 m S 130.0167 127.2563 m S 111.0083 127.2563 m S 111.0083 145.8385 m S 120.5125 136.5475 m S 130.0167 164.4206 m S 130.0167 145.8385 m S 111.0083 145.8385 m S 111.0083 164.4206 m S 120.5125 155.1295 m S 149.025 164.4206 m S 149.025 145.8385 m S 130.0167 145.8385 m S 130.0167 164.4206 m S 139.5208 155.1295 m S 149.025 145.8385 m S 149.025 127.2563 m S 130.0167 127.2563 m S 130.0167 145.8385 m S 139.5208 136.5475 m S 130.0167 127.2563 m S 130.0167 108.6743 m S 111.0083 108.6743 m S 111.0083 127.2563 m S 120.5125 117.9653 m S 111.0083 127.2563 m S 111.0083 108.6743 m S 92 108.6743 m S 92 127.2563 m S 101.5041 117.9653 m S 111.0083 145.8385 m S 111.0083 127.2563 m S 92 127.2563 m S 92 145.8385 m S 101.5041 136.5475 m S 0 g 1 w 4 M 101.5041 155.1295 m F 139.5208 155.1295 m F 101.5041 117.9653 m F 139.5208 117.9653 m F 0 G 0.3 w 10 M 53.9833 108.6743 m S 53.9833 90.0922 m S 34.975 90.0922 m S 34.975 108.6743 m S 44.4791 99.3833 m S 92 71.5101 m S 92 52.928 m S 72.9917 52.928 m S 72.9917 71.5101 m S 82.4958 62.2191 m S 72.9917 90.0922 m S 72.9917 71.5101 m S 53.9833 71.5101 m S 53.9833 90.0922 m S 63.4875 80.8012 m S 72.9917 108.6743 m S 72.9917 90.0922 m S 53.9833 90.0922 m S 53.9833 108.6743 m S 63.4875 99.3833 m S 92 108.6743 m S 92 90.0922 m S 72.9917 90.0922 m S 72.9917 108.6743 m S 92 90.0922 m S 92 71.5101 m S 72.9917 71.5101 m S 72.9917 90.0922 m S 82.4958 80.8012 m S 72.9917 71.5101 m S 72.9917 52.928 m S 53.9833 52.928 m S 53.9833 71.5101 m S 63.4875 62.2191 m S 53.9833 71.5101 m S 53.9833 52.928 m S 34.975 52.928 m S 34.975 71.5101 m S 44.4791 62.2191 m S 53.9833 90.0922 m S 53.9833 71.5101 m S 34.975 71.5101 m S 34.975 90.0922 m S 44.4791 80.8012 m S 0 g 1 w 4 M 44.4791 99.3833 m F 44.4791 62.2191 m F 82.4958 62.2191 m F 0 G 0.3 w 10 M 111.0083 108.6743 m S 111.0083 90.0922 m S 92 90.0922 m S 92 108.6743 m S 101.5041 99.3833 m S 149.025 71.5101 m S 149.025 52.928 m S 130.0167 52.928 m S 130.0167 71.5101 m S 139.5208 62.2191 m S 130.0167 90.0922 m S 130.0167 71.5101 m S 111.0083 71.5101 m S 111.0083 90.0922 m S 120.5125 80.8012 m S 130.0167 108.6743 m S 130.0167 90.0922 m S 111.0083 90.0922 m S 111.0083 108.6743 m S 120.5125 99.3833 m S 149.025 108.6743 m S 149.025 90.0922 m S 130.0167 90.0922 m S 130.0167 108.6743 m S 139.5208 99.3833 m S 149.025 90.0922 m S 149.025 71.5101 m S 130.0167 71.5101 m S 130.0167 90.0922 m S 139.5208 80.8012 m S 130.0167 71.5101 m S 130.0167 52.928 m S 111.0083 52.928 m S 111.0083 71.5101 m S 120.5125 62.2191 m S 111.0083 71.5101 m S 111.0083 52.928 m S 92 52.928 m S 92 71.5101 m S 101.5041 62.2191 m S 111.0083 90.0922 m S 111.0083 71.5101 m S 92 71.5101 m S 92 90.0922 m S 101.5041 80.8012 m S 0 g 1 w 4 M 101.5041 99.3833 m F 139.5208 99.3833 m F 101.5041 62.2191 m F 139.5208 62.2191 m F 0 G 0.3 w 10 M 53.9833 52.928 m S 34.975 52.928 m S 72.9917 52.928 m S 53.9833 52.928 m S 92 52.928 m S 72.9917 52.928 m S 111.0083 52.928 m S 92 52.928 m S 130.0167 52.928 m S 111.0083 52.928 m S 149.025 52.928 m S 130.0167 52.928 m S 1 w 4 M 44.4791 136.5475 m 139.5208 136.5475 l S 44.4791 80.8012 m 139.5208 80.8012 l S 63.4875 155.1295 m 63.4875 62.2191 l S 0.3 w 10 M 72.9917 145.8385 m S 0 g 1 w 4 M 72.9917 145.8385 m F 0 G 0.3 w 10 M 72.9917 145.8385 m S 72.9917 145.8385 m S 72.9917 145.8385 m S 0 g 1 w 4 M 72.9917 145.8385 m F 0 G 0.3 w 10 M 72.9917 145.8385 m S 72.9917 145.8385 m S 1 g 1 w 4 M 72.9917 145.8385 m F 0 G 0.3 w 10 M 72.9917 145.8385 m S 0 g 1 w 4 M 72.9917 145.8385 m F 0 G 0.3 w 10 M 72.9917 145.8385 m S 72.9917 145.8385 m S 92 145.8385 m S 0 g 1 w 4 M 92 145.8385 m F 0 G 0.3 w 10 M 92 145.8385 m S 92 145.8385 m S 92 145.8385 m S 0 g 1 w 4 M 92 145.8385 m F 0 G 0.3 w 10 M 92 145.8385 m S 92 145.8385 m S 1 g 1 w 4 M 92 145.8385 m F 0 G 0.3 w 10 M 92 145.8385 m S 0 g 1 w 4 M 92 145.8385 m F 0 G 0.3 w 10 M 92 145.8385 m S 92 145.8385 m S 111.0083 145.8385 m S 0 g 1 w 4 M 111.0083 145.8385 m F 0 G 0.3 w 10 M 111.0083 145.8385 m S 111.0083 145.8385 m S 111.0083 145.8385 m S 0 g 1 w 4 M 111.0083 145.8385 m F 0 G 0.3 w 10 M 111.0083 145.8385 m S 111.0083 145.8385 m S 1 g 1 w 4 M 111.0083 145.8385 m F 0 G 0.3 w 10 M 111.0083 145.8385 m S 0 g 1 w 4 M 111.0083 145.8385 m F 0 G 0.3 w 10 M 111.0083 145.8385 m S 111.0083 145.8385 m S 53.9833 127.2563 m S 0 g 1 w 4 M 53.9833 127.2563 m F 0 G 0.3 w 10 M 53.9833 127.2563 m S 53.9833 127.2563 m S 53.9833 127.2563 m S 0 g 1 w 4 M 53.9833 127.2563 m F 0 G 0.3 w 10 M 53.9833 127.2563 m S 53.9833 127.2563 m S 1 g 1 w 4 M 53.9833 127.2563 m F 0 G 0.3 w 10 M 53.9833 127.2563 m S 0 g 1 w 4 M 53.9833 127.2563 m F 0 G 0.3 w 10 M 53.9833 127.2563 m S 53.9833 127.2563 m S 53.9833 108.6743 m S 0 g 1 w 4 M 53.9833 108.6743 m F 0 G 0.3 w 10 M 53.9833 108.6743 m S 53.9833 108.6743 m S 53.9833 108.6743 m S 0 g 1 w 4 M 53.9833 108.6743 m F 0 G 0.3 w 10 M 53.9833 108.6743 m S 53.9833 108.6743 m S 1 g 1 w 4 M 48.9747 108.6743 m 48.9747 105.981 51.2172 103.7977 53.9833 103.7977 c 56.7495 103.7977 58.992 105.981 58.992 108.6743 c F 58.992 108.6743 m 58.992 111.3676 56.7495 113.5509 53.9833 113.5509 c 51.2172 113.5509 48.9747 111.3676 48.9747 108.6743 c F 53.9833 108.6743 m F 0 G 0.3 w 10 M 53.9833 108.6743 m S 0 g 1 w 4 M 53.9833 108.6743 m F 0 G 0.3 w 10 M 53.9833 108.6743 m S 53.9833 108.6743 m S 0 g 1 w 4 M 53.0791 107.7816 m 53.0791 104.7913 L 54.8876 104.7913 L 54.8876 107.7816 L 57.8755 107.7722 L 57.8755 109.5765 L 54.8876 109.5673 L 54.8876 112.5575 L 53.0791 112.5575 L 53.0791 109.5673 L 50.0911 109.5765 L 50.0911 107.7722 L 53.0791 107.7816 L f 0 G 0.3 w 10 M 53.9833 90.0922 m S 0 g 1 w 4 M 53.9833 90.0922 m F 0 G 0.3 w 10 M 53.9833 90.0922 m S 53.9833 90.0922 m S 53.9833 90.0922 m S 0 g 1 w 4 M 53.9833 90.0922 m F 0 G 0.3 w 10 M 53.9833 90.0922 m S 53.9833 90.0922 m S 1 g 1 w 4 M 48.9747 90.0922 m 48.9747 87.3989 51.2172 85.2155 53.9833 85.2155 c 56.7495 85.2155 58.992 87.3989 58.992 90.0922 c F 58.992 90.0922 m 58.992 92.7854 56.7495 94.9688 53.9833 94.9688 c 51.2172 94.9688 48.9747 92.7854 48.9747 90.0922 c F 53.9833 90.0922 m F 0 G 0.3 w 10 M 53.9833 90.0922 m S 0 g 1 w 4 M 53.9833 90.0922 m F 0 G 0.3 w 10 M 53.9833 90.0922 m S 53.9833 90.0922 m S 0 g 1 w 4 M 53.0791 89.1994 m 53.0791 86.2091 L 54.8876 86.2091 L 54.8876 89.1994 L 57.8755 89.1901 L 57.8755 90.9944 L 54.8876 90.9851 L 54.8876 93.9754 L 53.0791 93.9754 L 53.0791 90.9851 L 50.0911 90.9944 L 50.0911 89.1901 L 53.0791 89.1994 L f 0 G 0.3 w 10 M 72.9917 71.5101 m S 72.9917 71.5101 m S 92 71.5101 m S 72.9917 71.5101 m S 92 71.5101 m S 72.9917 71.5101 m S 111.0083 71.5101 m S 92 71.5101 m S 111.0083 71.5101 m S 111.0083 71.5101 m S 111.0083 71.5101 m S 92 71.5101 m S 72.9917 71.5101 m S 0 g 1 w 4 M 72.9917 71.5101 m F 0 G 0.3 w 10 M 72.9917 71.5101 m S 72.9917 71.5101 m S 72.9917 71.5101 m S 0 g 1 w 4 M 72.9917 71.5101 m F 0 G 0.3 w 10 M 72.9917 71.5101 m S 72.9917 71.5101 m S 1 g 1 w 4 M 67.9831 71.5101 m 67.9831 68.8168 70.2256 66.6335 72.9917 66.6335 c 75.7578 66.6335 78.0003 68.8168 78.0003 71.5101 c F 78.0003 71.5101 m 78.0003 74.2034 75.7578 76.3867 72.9917 76.3867 c 70.2256 76.3867 67.9831 74.2034 67.9831 71.5101 c F 72.9917 71.5101 m F 0 G 0.3 w 10 M 72.9917 71.5101 m S 0 g 1 w 4 M 72.9917 71.5101 m F 0 G 0.3 w 10 M 72.9917 71.5101 m S 72.9917 71.5101 m S 0 g 1 w 4 M 72.0874 70.6174 m 72.0874 67.6271 L 73.8959 67.6271 L 73.8959 70.6174 L 76.8839 70.608 L 76.8839 72.4123 L 73.8959 72.4031 L 73.8959 75.3933 L 72.0874 75.3933 L 72.0874 72.4031 L 69.0995 72.4123 L 69.0995 70.608 L 72.0874 70.6174 L f 0 G 0.3 w 10 M 92 71.5101 m S 0 g 1 w 4 M 92 71.5101 m F 0 G 0.3 w 10 M 92 71.5101 m S 92 71.5101 m S 92 71.5101 m S 0 g 1 w 4 M 92 71.5101 m F 0 G 0.3 w 10 M 92 71.5101 m S 92 71.5101 m S 1 g 1 w 4 M 86.9914 71.5101 m 86.9914 68.8168 89.2339 66.6335 92 66.6335 c 94.7661 66.6335 97.0086 68.8168 97.0086 71.5101 c F 97.0086 71.5101 m 97.0086 74.2034 94.7661 76.3867 92 76.3867 c 89.2339 76.3867 86.9914 74.2034 86.9914 71.5101 c F 92 71.5101 m F 0 G 0.3 w 10 M 92 71.5101 m S 0 g 1 w 4 M 92 71.5101 m F 0 G 0.3 w 10 M 92 71.5101 m S 92 71.5101 m S 0 g 1 w 4 M 91.0958 70.6174 m 91.0958 67.6271 L 92.9042 67.6271 L 92.9042 70.6174 L 95.8922 70.608 L 95.8922 72.4123 L 92.9042 72.4031 L 92.9042 75.3933 L 91.0958 75.3933 L 91.0958 72.4031 L 88.1078 72.4123 L 88.1078 70.608 L 91.0958 70.6174 L f 0 G 0.3 w 10 M 111.0083 71.5101 m S 0 g 1 w 4 M 111.0083 71.5101 m F 0 G 0.3 w 10 M 111.0083 71.5101 m S 111.0083 71.5101 m S 111.0083 71.5101 m S 0 g 1 w 4 M 111.0083 71.5101 m F 0 G 0.3 w 10 M 111.0083 71.5101 m S 111.0083 71.5101 m S 1 g 1 w 4 M 105.9997 71.5101 m 105.9997 68.8168 108.2421 66.6335 111.0083 66.6335 c 113.7744 66.6335 116.0169 68.8168 116.0169 71.5101 c F 116.0169 71.5101 m 116.0169 74.2034 113.7744 76.3867 111.0083 76.3867 c 108.2421 76.3867 105.9997 74.2034 105.9997 71.5101 c F 111.0083 71.5101 m F 0 G 0.3 w 10 M 111.0083 71.5101 m S 0 g 1 w 4 M 111.0083 71.5101 m F 0 G 0.3 w 10 M 111.0083 71.5101 m S 111.0083 71.5101 m S 0 g 1 w 4 M 110.1041 70.6174 m 110.1041 67.6271 L 111.9125 67.6271 L 111.9125 70.6174 L 114.9005 70.608 L 114.9005 72.4123 L 111.9125 72.4031 L 111.9125 75.3933 L 110.1041 75.3933 L 110.1041 72.4031 L 107.1161 72.4123 L 107.1161 70.608 L 110.1041 70.6174 L f 0 G 0.3 w 10 M 130.0167 127.2563 m S 130.0167 108.6743 m S 130.0167 127.2563 m S 130.0167 127.2563 m S 130.0167 108.6743 m S 130.0167 127.2563 m S 130.0167 108.6743 m S 130.0167 90.0922 m S 130.0167 90.0922 m S 130.0167 90.0922 m S 130.0167 108.6743 m S 130.0167 90.0922 m S 130.0167 127.2563 m S 0 g 1 w 4 M 130.0167 127.2563 m F 0 G 0.3 w 10 M 130.0167 127.2563 m S 130.0167 127.2563 m S 130.0167 127.2563 m S 0 g 1 w 4 M 130.0167 127.2563 m F 0 G 0.3 w 10 M 130.0167 127.2563 m S 130.0167 127.2563 m S 1 g 1 w 4 M 130.0167 127.2563 m F 0 G 0.3 w 10 M 130.0167 127.2563 m S 0 g 1 w 4 M 130.0167 127.2563 m F 0 G 0.3 w 10 M 130.0167 127.2563 m S 130.0167 127.2563 m S 130.0167 108.6743 m S 0 g 1 w 4 M 130.0167 108.6743 m F 0 G 0.3 w 10 M 130.0167 108.6743 m S 130.0167 108.6743 m S 130.0167 108.6743 m S 0 g 1 w 4 M 130.0167 108.6743 m F 0 G 0.3 w 10 M 130.0167 108.6743 m S 130.0167 108.6743 m S 1 g 1 w 4 M 130.0167 108.6743 m F 0 G 0.3 w 10 M 130.0167 108.6743 m S 0 g 1 w 4 M 130.0167 108.6743 m F 0 G 0.3 w 10 M 130.0167 108.6743 m S 130.0167 108.6743 m S 130.0167 90.0922 m S 0 g 1 w 4 M 130.0167 90.0922 m F 0 G 0.3 w 10 M 130.0167 90.0922 m S 130.0167 90.0922 m S 130.0167 90.0922 m S 0 g 1 w 4 M 130.0167 90.0922 m F 0 G 0.3 w 10 M 130.0167 90.0922 m S 130.0167 90.0922 m S 1 g 1 w 4 M 130.0167 90.0922 m F 0 G 0.3 w 10 M 130.0167 90.0922 m S 0 g 1 w 4 M 130.0167 90.0922 m F 0 G 0.3 w 10 M 130.0167 90.0922 m S 130.0167 90.0922 m S 82.4958 117.9653 m S 82.4958 117.9653 m S 101.5041 117.9653 m S 82.4958 117.9653 m S 101.5041 117.9653 m S 101.5041 117.9653 m S 101.5041 117.9653 m S 82.4958 117.9653 m S 82.4958 99.3833 m S 82.4958 99.3833 m S 101.5041 99.3833 m S 82.4958 99.3833 m S 101.5041 99.3833 m S 101.5041 99.3833 m S 101.5041 99.3833 m S 82.4958 99.3833 m S 72.9917 127.2563 m S 0 g 1 w 4 M 72.9917 127.2563 m F 0 G 0.3 w 10 M 72.9917 127.2563 m S 0 g 1 w 4 M 72.9917 127.2563 m F 1 g 67.9831 127.2563 m 67.9831 124.5631 70.2256 122.3797 72.9917 122.3797 c 75.7578 122.3797 78.0003 124.5631 78.0003 127.2563 c F 78.0003 127.2563 m 78.0003 129.9496 75.7578 132.133 72.9917 132.133 c 70.2256 132.133 67.9831 129.9496 67.9831 127.2563 c F 72.9917 127.2563 m F 0 G 0.3 w 10 M 72.9917 127.2563 m S 0 g 1 w 4 M 72.9917 127.2563 m F 0 G 0.3 w 10 M 72.9917 127.2563 m S 0 g 1 w 4 M 72.9917 127.2563 m F 72.0874 128.1493 m 69.0995 128.1586 L 69.0995 126.3543 L 72.0874 126.3636 L F 73.8959 126.3636 m 76.8839 126.3543 L 76.8839 128.1586 L 73.8959 128.1493 L F 69.0995 128.1586 m 76.8839 128.1586 l 76.8839 126.3543 l 69.0995 126.3543 l 69.0995 128.1586 l f 0 G 0.3 w 10 M 92 127.2563 m S 0 g 1 w 4 M 92 127.2563 m F 0 G 0.3 w 10 M 92 127.2563 m S 0 g 1 w 4 M 92 127.2563 m F 1 g 86.9914 127.2563 m 86.9914 124.5631 89.2339 122.3797 92 122.3797 c 94.7661 122.3797 97.0086 124.5631 97.0086 127.2563 c F 97.0086 127.2563 m 97.0086 129.9496 94.7661 132.133 92 132.133 c 89.2339 132.133 86.9914 129.9496 86.9914 127.2563 c F 92 127.2563 m F 0 G 0.3 w 10 M 92 127.2563 m S 0 g 1 w 4 M 92 127.2563 m F 0 G 0.3 w 10 M 92 127.2563 m S 0 g 1 w 4 M 92 127.2563 m F 91.0958 128.1493 m 88.1078 128.1586 L 88.1078 126.3543 L 91.0958 126.3636 L F 92.9042 126.3636 m 95.8922 126.3543 L 95.8922 128.1586 L 92.9042 128.1493 L F 88.1078 128.1586 m 95.8922 128.1586 l 95.8922 126.3543 l 88.1078 126.3543 l 88.1078 128.1586 l f 0 G 0.3 w 10 M 111.0083 127.2563 m S 0 g 1 w 4 M 111.0083 127.2563 m F 0 G 0.3 w 10 M 111.0083 127.2563 m S 0 g 1 w 4 M 111.0083 127.2563 m F 1 g 105.9997 127.2563 m 105.9997 124.5631 108.2421 122.3797 111.0083 122.3797 c 113.7744 122.3797 116.0169 124.5631 116.0169 127.2563 c F 116.0169 127.2563 m 116.0169 129.9496 113.7744 132.133 111.0083 132.133 c 108.2421 132.133 105.9997 129.9496 105.9997 127.2563 c F 111.0083 127.2563 m F 0 G 0.3 w 10 M 111.0083 127.2563 m S 0 g 1 w 4 M 111.0083 127.2563 m F 0 G 0.3 w 10 M 111.0083 127.2563 m S 0 g 1 w 4 M 111.0083 127.2563 m F 110.1041 128.1493 m 107.1161 128.1586 L 107.1161 126.3543 L 110.1041 126.3636 L F 111.9125 126.3636 m 114.9005 126.3543 L 114.9005 128.1586 L 111.9125 128.1493 L F 107.1161 128.1586 m 114.9005 128.1586 l 114.9005 126.3543 l 107.1161 126.3543 l 107.1161 128.1586 l f 0 G 0.3 w 10 M 111.0083 108.6743 m S 0 g 1 w 4 M 111.0083 108.6743 m F 0 G 0.3 w 10 M 111.0083 108.6743 m S 0 g 1 w 4 M 111.0083 108.6743 m F 1 g 105.9997 108.6743 m 105.9997 105.981 108.2421 103.7977 111.0083 103.7977 c 113.7744 103.7977 116.0169 105.981 116.0169 108.6743 c F 116.0169 108.6743 m 116.0169 111.3676 113.7744 113.5509 111.0083 113.5509 c 108.2421 113.5509 105.9997 111.3676 105.9997 108.6743 c F 111.0083 108.6743 m F 0 G 0.3 w 10 M 111.0083 108.6743 m S 0 g 1 w 4 M 111.0083 108.6743 m F 0 G 0.3 w 10 M 111.0083 108.6743 m S 0 g 1 w 4 M 111.0083 108.6743 m F 110.1041 109.5673 m 107.1161 109.5765 L 107.1161 107.7722 L 110.1041 107.7815 L F 111.9125 107.7815 m 114.9005 107.7722 L 114.9005 109.5765 L 111.9125 109.5673 L F 107.1161 109.5765 m 114.9005 109.5765 l 114.9005 107.7722 l 107.1161 107.7722 l 107.1161 109.5765 l f 0 G 0.3 w 10 M 92 108.6743 m S 0 g 1 w 4 M 92 108.6743 m F 0 G 0.3 w 10 M 92 108.6743 m S 0 g 1 w 4 M 92 108.6743 m F 1 g 86.9914 108.6743 m 86.9914 105.981 89.2339 103.7977 92 103.7977 c 94.7661 103.7977 97.0086 105.981 97.0086 108.6743 c F 97.0086 108.6743 m 97.0086 111.3676 94.7661 113.5509 92 113.5509 c 89.2339 113.5509 86.9914 111.3676 86.9914 108.6743 c F 92 108.6743 m F 0 G 0.3 w 10 M 92 108.6743 m S 0 g 1 w 4 M 92 108.6743 m F 0 G 0.3 w 10 M 92 108.6743 m S 0 g 1 w 4 M 92 108.6743 m F 91.0958 109.5673 m 88.1078 109.5765 L 88.1078 107.7722 L 91.0958 107.7815 L F 92.9042 107.7815 m 95.8922 107.7722 L 95.8922 109.5765 L 92.9042 109.5673 L F 88.1078 109.5765 m 95.8922 109.5765 l 95.8922 107.7722 l 88.1078 107.7722 l 88.1078 109.5765 l f 0 G 0.3 w 10 M 72.9917 108.6743 m S 0 g 1 w 4 M 72.9917 108.6743 m F 0 G 0.3 w 10 M 72.9917 108.6743 m S 72.9917 108.6743 m S 72.9917 108.6743 m S 0 g 1 w 4 M 72.9917 108.6743 m F 0 G 0.3 w 10 M 72.9917 108.6743 m S 72.9917 108.6743 m S 1 g 1 w 4 M 67.9831 108.6743 m 67.9831 105.981 70.2256 103.7977 72.9917 103.7977 c 75.7578 103.7977 78.0003 105.981 78.0003 108.6743 c F 78.0003 108.6743 m 78.0003 111.3676 75.7578 113.5509 72.9917 113.5509 c 70.2256 113.5509 67.9831 111.3676 67.9831 108.6743 c F 72.9917 108.6743 m F 0 G 0.3 w 10 M 72.9917 108.6743 m S 0 g 1 w 4 M 72.9917 108.6743 m F 0 G 0.3 w 10 M 72.9917 108.6743 m S 72.9917 108.6743 m S 0 g 1 w 4 M 72.0874 107.7816 m 72.0874 104.7913 L 73.8959 104.7913 L 73.8959 107.7816 L 76.8839 107.7722 L 76.8839 109.5765 L 73.8959 109.5673 L 73.8959 112.5575 L 72.0874 112.5575 L 72.0874 112.62 72.0874 109.5673 Y 69.0995 109.5765 L 69.0995 107.7722 L 72.0874 107.7816 L f 0 G 0.3 w 10 M 92 90.0922 m S 0 g 1 w 4 M 92 90.0922 m F 0 G 0.3 w 10 M 92 90.0922 m S 92 90.0922 m S 92 90.0922 m S 0 g 1 w 4 M 92 90.0922 m F 0 G 0.3 w 10 M 92 90.0922 m S 92 90.0922 m S 1 g 1 w 4 M 86.9914 90.0922 m 86.9914 87.3989 89.2339 85.2155 92 85.2155 c 94.7661 85.2155 97.0086 87.3989 97.0086 90.0922 c F 97.0086 90.0922 m 97.0086 92.7854 94.7661 94.9688 92 94.9688 c 89.2339 94.9688 86.9914 92.7854 86.9914 90.0922 c F 92 90.0922 m F 0 G 0.3 w 10 M 92 90.0922 m S 0 g 1 w 4 M 92 90.0922 m F 0 G 0.3 w 10 M 92 90.0922 m S 92 90.0922 m S 0 g 1 w 4 M 91.0958 89.1994 m 91.0958 86.2091 L 92.9042 86.2091 L 92.9042 89.1994 L 95.8922 89.1901 L 95.8922 90.9944 L 92.9042 90.9851 L 92.9042 93.9754 L 91.0958 93.9754 L 91.0958 90.9851 L 88.1078 90.9944 L 88.1078 89.1901 L 91.0958 89.1994 L f 0 G 0.3 w 10 M 111.0083 90.0922 m S 0 g 1 w 4 M 111.0083 90.0922 m F 0 G 0.3 w 10 M 111.0083 90.0922 m S 111.0083 90.0922 m S 111.0083 90.0922 m S 0 g 1 w 4 M 111.0083 90.0922 m F 0 G 0.3 w 10 M 111.0083 90.0922 m S 111.0083 90.0922 m S 1 g 1 w 4 M 105.9997 90.0922 m 105.9997 87.3989 108.2421 85.2155 111.0083 85.2155 c 113.7744 85.2155 116.0169 87.3989 116.0169 90.0922 c F 116.0169 90.0922 m 116.0169 92.7854 113.7744 94.9688 111.0083 94.9688 c 108.2421 94.9688 105.9997 92.7854 105.9997 90.0922 c F 111.0083 90.0922 m F 0 G 0.3 w 10 M 111.0083 90.0922 m S 0 g 1 w 4 M 111.0083 90.0922 m F 0 G 0.3 w 10 M 111.0083 90.0922 m S 111.0083 90.0922 m S 0 g 1 w 4 M 110.1041 89.1994 m 110.1041 86.2091 L 111.9125 86.2091 L 111.9125 89.1994 L 114.9005 89.1901 L 114.9005 90.9944 L 111.9125 90.9851 L 111.9125 93.9754 L 110.1041 93.9754 L 110.1041 90.9851 L 107.1161 90.9944 L 107.1161 89.1901 L 110.1041 89.1994 L f 0 G 0.3 w 10 M 72.9917 90.0922 m S 0 g 1 w 4 M 72.9917 90.0922 m F 0 G 0.3 w 10 M 72.9917 90.0922 m S 72.9917 90.0922 m S 72.9917 90.0922 m S 0 g 1 w 4 M 72.9917 90.0922 m F 0 G 0.3 w 10 M 72.9917 90.0922 m S 72.9917 90.0922 m S 1 g 1 w 4 M 67.9831 90.0922 m 67.9831 87.3989 70.2256 85.2155 72.9917 85.2155 c 75.7578 85.2155 78.0003 87.3989 78.0003 90.0922 c F 78.0003 90.0922 m 78.0003 92.7854 75.7578 94.9688 72.9917 94.9688 c 70.2256 94.9688 67.9831 92.7854 67.9831 90.0922 c F 72.9917 90.0922 m F 0 G 0.3 w 10 M 72.9917 90.0922 m S 0 g 1 w 4 M 72.9917 90.0922 m F 0 G 0.3 w 10 M 72.9917 90.0922 m S 72.9917 90.0922 m S 0 g 1 w 4 M 72.0874 89.1994 m 72.0874 86.2091 L 73.8959 86.2091 L 73.8959 89.1994 L 76.8839 89.1901 L 76.8839 90.9944 L 73.8959 90.9851 L 73.8959 93.9754 L 72.0874 93.9754 L 72.0874 90.9851 L 69.0995 90.9944 L 69.0995 89.1901 L 72.0874 89.1994 L f 0 G 0.3 w 10 M 149.025 127.2563 m S 149.025 108.6743 m S 149.025 164.4206 m S 149.025 145.8385 m S 149.025 145.8385 m S 149.025 127.2563 m S 111.0262 164.4206 m S 111.0262 145.8385 m S 149.025 145.8385 m S 149.025 164.4206 m S 101.5041 155.1295 m S 149.1146 127.2564 m S 149.1146 108.6743 m S 130.0705 108.6743 m S 130.0705 127.2564 m S 139.5925 117.9653 m S 130.0705 127.2564 m S 111.0262 127.2564 m S 111.0262 145.8385 m S 120.5484 136.5475 m S 130.0705 164.4206 m S 111.0262 145.8385 m S 111.0262 164.4206 m S 120.5484 155.1295 m S 149.1146 164.4206 m S 130.0705 164.4206 m S 139.5925 155.1295 m S 149.1146 127.2564 m S 130.0705 127.2564 m S 139.5925 136.5475 m S 130.0705 127.2564 m S 130.0705 108.6743 m S 111.0262 108.6743 m S 111.0262 127.2564 m S 120.5484 117.9653 m S 111.0262 127.2564 m S 111.0262 108.6743 m S 149.025 108.6743 m S 149.025 127.2563 m S 101.5041 117.9653 m S 111.0262 145.8385 m S 111.0262 127.2564 m S 149.025 127.2563 m S 149.025 145.8385 m S 101.5041 136.5475 m S 0 g 1 w 4 M 101.5041 155.1295 m F 139.5925 155.1295 m F 101.5041 117.9653 m F 139.5925 117.9653 m F 0 G 0.3 w 10 M 168.1588 164.4206 m S 149.1146 164.4206 m S 158.6366 155.1295 m S 206.2471 127.2564 m S 206.2471 108.6743 m S 187.203 108.6743 m S 187.203 127.2564 m S 196.725 117.9653 m S 187.203 145.8385 m S 187.203 127.2564 m S 168.1588 127.2564 m S 177.6809 136.5475 m S 187.203 164.4206 m S 187.203 145.8385 m S 168.1588 164.4206 m S 177.6809 155.1295 m S 206.2471 164.4206 m S 206.2471 145.8385 m S 187.203 145.8385 m S 187.203 164.4206 m S 196.725 155.1295 m S 206.2471 145.8385 m S 206.2471 127.2564 m S 187.203 127.2564 m S 187.203 145.8385 m S 196.725 136.5475 m S 187.203 127.2564 m S 187.203 108.6743 m S 168.1588 108.6743 m S 168.1588 127.2564 m S 177.6809 117.9653 m S 168.1588 127.2564 m S 168.1588 108.6743 m S 149.1146 108.6743 m S 149.1146 127.2564 m S 158.6366 117.9653 m S 168.1588 127.2564 m S 149.1146 127.2564 m S 158.6366 136.5475 m S 0 g 1 w 4 M 158.6366 155.1295 m F 196.725 155.1295 m F 158.6366 117.9653 m F 196.725 117.9653 m F 0 G 0.3 w 10 M 149.025 71.5101 m S 149.025 52.928 m S 149.025 108.6743 m S 149.025 90.0922 m S 149.025 90.0922 m S 149.025 71.5101 m S 111.0262 108.6743 m S 111.0262 90.0922 m S 149.025 90.0922 m S 149.025 108.6743 m S 101.5041 99.3833 m S 149.1146 71.5101 m S 149.1146 52.9281 m S 130.0705 52.9281 m S 130.0705 71.5101 m S 139.5925 62.2191 m S 130.0705 90.0922 m S 130.0705 71.5101 m S 111.0262 71.5101 m S 111.0262 90.0922 m S 120.5484 80.8012 m S 130.0705 108.6743 m S 130.0705 90.0922 m S 111.0262 90.0922 m S 111.0262 108.6743 m S 120.5484 99.3833 m S 149.1146 108.6743 m S 149.1146 90.0922 m S 130.0705 90.0922 m S 130.0705 108.6743 m S 139.5925 99.3833 m S 149.1146 90.0922 m S 149.1146 71.5101 m S 130.0705 71.5101 m S 130.0705 90.0922 m S 139.5925 80.8012 m S 130.0705 71.5101 m S 130.0705 52.9281 m S 111.0262 52.9281 m S 111.0262 71.5101 m S 120.5484 62.2191 m S 111.0262 71.5101 m S 111.0262 52.9281 m S 149.025 52.928 m S 149.025 71.5101 m S 101.5041 62.2191 m S 111.0262 90.0922 m S 111.0262 71.5101 m S 149.025 71.5101 m S 149.025 90.0922 m S 101.5041 80.8012 m S 0 g 1 w 4 M 101.5041 99.3833 m F 139.5925 99.3833 m F 101.5041 62.2191 m F 139.5925 62.2191 m F 0 G 0.3 w 10 M 168.1588 108.6743 m S 168.1588 90.0922 m S 149.1146 90.0922 m S 149.1146 108.6743 m S 158.6366 99.3833 m S 206.2471 71.5101 m S 206.2471 52.9281 m S 187.203 52.9281 m S 187.203 71.5101 m S 196.725 62.2191 m S 187.203 90.0922 m S 187.203 71.5101 m S 168.1588 71.5101 m S 168.1588 90.0922 m S 177.6809 80.8012 m S 187.203 108.6743 m S 187.203 90.0922 m S 168.1588 90.0922 m S 168.1588 108.6743 m S 177.6809 99.3833 m S 206.2471 108.6743 m S 206.2471 90.0922 m S 187.203 90.0922 m S 187.203 108.6743 m S 196.725 99.3833 m S 206.2471 90.0922 m S 206.2471 71.5101 m S 187.203 71.5101 m S 187.203 90.0922 m S 196.725 80.8012 m S 187.203 71.5101 m S 187.203 52.9281 m S 168.1588 52.9281 m S 168.1588 71.5101 m S 177.6809 62.2191 m S 168.1588 71.5101 m S 168.1588 52.9281 m S 149.1146 52.9281 m S 149.1146 71.5101 m S 158.6366 62.2191 m S 168.1588 90.0922 m S 168.1588 71.5101 m S 149.1146 71.5101 m S 149.1146 90.0922 m S 158.6366 80.8012 m S 0 g 1 w 4 M 158.6366 99.3833 m F 196.725 99.3833 m F 158.6366 62.2191 m F 196.725 62.2191 m F 0 G 0.3 w 10 M 149.025 52.928 m S 111.0262 52.9281 m S 149.025 52.928 m S 130.0705 52.9281 m S 111.0262 52.9281 m S 149.1146 52.9281 m S 130.0705 52.9281 m S 168.1588 52.9281 m S 149.1146 52.9281 m S 187.203 52.9281 m S 168.1588 52.9281 m S 206.2471 52.9281 m S 187.203 52.9281 m S 111.0262 164.4206 m S 111.0262 145.8385 m S 149.025 145.8385 m S 149.025 164.4206 m S 101.5041 155.1295 m S 149.1146 127.2564 m S 149.1146 108.6743 m S 130.0705 108.6743 m S 130.0705 127.2564 m S 130.0705 127.2564 m S 111.0262 127.2564 m S 111.0262 145.8385 m S 120.5484 136.5475 m S 130.0705 164.4206 m S 111.0262 145.8385 m S 111.0262 164.4206 m S 120.5484 155.1295 m S 149.1146 164.4206 m S 130.0705 164.4206 m S 139.5925 155.1295 m S 149.1146 127.2564 m S 130.0705 127.2564 m S 139.5925 136.5475 m S 130.0705 127.2564 m S 130.0705 108.6743 m S 111.0262 108.6743 m S 111.0262 127.2564 m S 120.5484 117.9653 m S 111.0262 127.2564 m S 111.0262 108.6743 m S 149.025 108.6743 m S 149.025 127.2563 m S 101.5041 117.9653 m S 111.0262 145.8385 m S 111.0262 127.2564 m S 149.025 127.2563 m S 149.025 145.8385 m S 101.5041 136.5475 m S 0 g 1 w 4 M 101.5041 155.1295 m F 139.5925 155.1295 m F 101.5041 117.9653 m F 0 G 0.3 w 10 M 168.1588 164.4206 m S 149.1146 164.4206 m S 158.6366 155.1295 m S 206.2471 127.2564 m S 206.2471 108.6743 m S 187.203 108.6743 m S 187.203 127.2564 m S 196.725 117.9653 m S 187.203 145.8385 m S 187.203 127.2564 m S 168.1588 127.2564 m S 177.6809 136.5475 m S 187.203 164.4206 m S 187.203 145.8385 m S 168.1588 164.4206 m S 177.6809 155.1295 m S 206.2471 164.4206 m S 206.2471 145.8385 m S 187.203 145.8385 m S 187.203 164.4206 m S 196.725 155.1295 m S 206.2471 145.8385 m S 206.2471 127.2564 m S 187.203 127.2564 m S 187.203 145.8385 m S 196.725 136.5475 m S 187.203 127.2564 m S 187.203 108.6743 m S 168.1588 108.6743 m S 168.1588 127.2564 m S 177.6809 117.9653 m S 168.1588 127.2564 m S 168.1588 108.6743 m S 149.1146 108.6743 m S 149.1146 127.2564 m S 158.6366 117.9653 m S 168.1588 127.2564 m S 149.1146 127.2564 m S 158.6366 136.5475 m S 0 g 1 w 4 M 158.6366 155.1295 m F 196.725 155.1295 m F 158.6366 117.9653 m F 196.725 117.9653 m F 0 G 0.3 w 10 M 111.0262 108.6743 m S 111.0262 90.0922 m S 149.025 90.0922 m S 149.025 108.6743 m S 101.5041 99.3833 m S 149.1146 71.5101 m S 149.1146 52.9281 m S 130.0705 52.9281 m S 130.0705 71.5101 m S 139.5925 62.2191 m S 130.0705 90.0922 m S 130.0705 71.5101 m S 111.0262 71.5101 m S 111.0262 90.0922 m S 120.5484 80.8012 m S 130.0705 108.6743 m S 130.0705 90.0922 m S 111.0262 90.0922 m S 111.0262 108.6743 m S 120.5484 99.3833 m S 149.1146 108.6743 m S 149.1146 90.0922 m S 130.0705 90.0922 m S 130.0705 108.6743 m S 149.1146 90.0922 m S 149.1146 71.5101 m S 130.0705 71.5101 m S 130.0705 90.0922 m S 139.5925 80.8012 m S 130.0705 71.5101 m S 130.0705 52.9281 m S 111.0262 52.9281 m S 111.0262 71.5101 m S 120.5484 62.2191 m S 111.0262 71.5101 m S 111.0262 52.9281 m S 149.025 52.928 m S 149.025 71.5101 m S 101.5041 62.2191 m S 111.0262 90.0922 m S 111.0262 71.5101 m S 149.025 71.5101 m S 149.025 90.0922 m S 101.5041 80.8012 m S 0 g 1 w 4 M 101.5041 99.3833 m F 101.5041 62.2191 m F 139.5925 62.2191 m F 0 G 0.3 w 10 M 168.1588 108.6743 m S 168.1588 90.0922 m S 149.1146 90.0922 m S 149.1146 108.6743 m S 158.6366 99.3833 m S 206.2471 71.5101 m S 206.2471 52.9281 m S 187.203 52.9281 m S 187.203 71.5101 m S 196.725 62.2191 m S 187.203 90.0922 m S 187.203 71.5101 m S 168.1588 71.5101 m S 168.1588 90.0922 m S 177.6809 80.8012 m S 187.203 108.6743 m S 187.203 90.0922 m S 168.1588 90.0922 m S 168.1588 108.6743 m S 177.6809 99.3833 m S 206.2471 108.6743 m S 206.2471 90.0922 m S 187.203 90.0922 m S 187.203 108.6743 m S 196.725 99.3833 m S 206.2471 90.0922 m S 206.2471 71.5101 m S 187.203 71.5101 m S 187.203 90.0922 m S 196.725 80.8012 m S 187.203 71.5101 m S 187.203 52.9281 m S 168.1588 52.9281 m S 168.1588 71.5101 m S 177.6809 62.2191 m S 168.1588 71.5101 m S 168.1588 52.9281 m S 149.1146 52.9281 m S 149.1146 71.5101 m S 158.6366 62.2191 m S 168.1588 90.0922 m S 168.1588 71.5101 m S 149.1146 71.5101 m S 149.1146 90.0922 m S 158.6366 80.8012 m S 0 g 1 w 4 M 158.6366 99.3833 m F 196.725 99.3833 m F 158.6366 62.2191 m F 196.725 62.2191 m F 0 G 0.3 w 10 M 111.0262 52.9281 m S 149.025 52.928 m S 130.0705 52.9281 m S 111.0262 52.9281 m S 149.1146 52.9281 m S 130.0705 52.9281 m S 168.1588 52.9281 m S 149.1146 52.9281 m S 187.203 52.9281 m S 168.1588 52.9281 m S 206.2471 52.9281 m S 187.203 52.9281 m S 1 w 4 M 101.5041 136.5475 m 196.725 136.5475 l S 101.5041 80.8012 m 196.725 80.8012 l S 177.6809 155.1295 m 177.6809 62.2191 l S 0.3 w 10 M 111.0262 127.2564 m S 0 g 1 w 4 M 111.0262 127.2564 m F 0 G 0.3 w 10 M 111.0262 127.2564 m S 111.0262 127.2564 m S 111.0262 127.2564 m S 0 g 1 w 4 M 111.0262 127.2564 m F 0 G 0.3 w 10 M 111.0262 127.2564 m S 111.0262 127.2564 m S 1 g 1 w 4 M 111.0262 127.2564 m F 0 G 0.3 w 10 M 111.0262 127.2564 m S 0 g 1 w 4 M 111.0262 127.2564 m F 0 G 0.3 w 10 M 111.0262 127.2564 m S 111.0262 127.2564 m S 111.0262 108.6743 m S 0 g 1 w 4 M 111.0262 108.6743 m F 0 G 0.3 w 10 M 111.0262 108.6743 m S 111.0262 108.6743 m S 111.0262 108.6743 m S 0 g 1 w 4 M 111.0262 108.6743 m F 0 G 0.3 w 10 M 111.0262 108.6743 m S 111.0262 108.6743 m S 1 g 1 w 4 M 111.0262 108.6743 m F 0 G 0.3 w 10 M 111.0262 108.6743 m S 0 g 1 w 4 M 111.0262 108.6743 m F 0 G 0.3 w 10 M 111.0262 108.6743 m S 111.0262 108.6743 m S 111.0262 90.0922 m S 0 g 1 w 4 M 111.0262 90.0922 m F 0 G 0.3 w 10 M 111.0262 90.0922 m S 111.0262 90.0922 m S 111.0262 90.0922 m S 0 g 1 w 4 M 111.0262 90.0922 m F 0 G 0.3 w 10 M 111.0262 90.0922 m S 111.0262 90.0922 m S 1 g 1 w 4 M 111.0262 90.0922 m F 0 G 0.3 w 10 M 111.0262 90.0922 m S 0 g 1 w 4 M 111.0262 90.0922 m F 0 G 0.3 w 10 M 111.0262 90.0922 m S 111.0262 90.0922 m S 130.0705 71.5101 m S 130.0705 71.5101 m S 149.1146 71.5101 m S 130.0705 71.5101 m S 149.1146 71.5101 m S 130.0705 71.5101 m S 168.1588 71.5101 m S 149.1146 71.5101 m S 168.1588 71.5101 m S 168.1588 71.5101 m S 168.1588 71.5101 m S 149.1146 71.5101 m S 130.0705 71.5101 m S 0 g 1 w 4 M 130.0705 71.5101 m F 0 G 0.3 w 10 M 130.0705 71.5101 m S 130.0705 71.5101 m S 130.0705 71.5101 m S 0 g 1 w 4 M 130.0705 71.5101 m F 0 G 0.3 w 10 M 130.0705 71.5101 m S 130.0705 71.5101 m S 1 g 1 w 4 M 125.0524 71.5101 m 125.0524 68.8168 127.2991 66.6335 130.0705 66.6335 c 132.8418 66.6335 135.0885 68.8168 135.0885 71.5101 c F 135.0885 71.5101 m 135.0885 74.2034 132.8418 76.3867 130.0705 76.3867 c 127.2991 76.3867 125.0524 74.2034 125.0524 71.5101 c F 130.0705 71.5101 m F 0 G 0.3 w 10 M 130.0705 71.5101 m S 0 g 1 w 4 M 130.0705 71.5101 m F 0 G 0.3 w 10 M 130.0705 71.5101 m S 130.0705 71.5101 m S 0 g 1 w 4 M 129.1645 70.6174 m 129.1645 67.6271 L 130.9764 67.6271 L 130.9764 70.6174 L 133.97 70.608 L 133.97 72.4123 L 130.9764 72.4031 L 130.9764 75.3934 L 129.1645 75.3934 L 129.1645 72.4031 L 126.1709 72.4123 L 126.1709 70.608 L 129.1645 70.6174 L f 0 G 0.3 w 10 M 149.1146 71.5101 m S 0 g 1 w 4 M 149.1146 71.5101 m F 0 G 0.3 w 10 M 149.1146 71.5101 m S 149.1146 71.5101 m S 149.1146 71.5101 m S 0 g 1 w 4 M 149.1146 71.5101 m F 0 G 0.3 w 10 M 149.1146 71.5101 m S 149.1146 71.5101 m S 1 g 1 w 4 M 144.0965 71.5101 m 144.0965 68.8168 146.3432 66.6335 149.1146 66.6335 c 151.886 66.6335 154.1327 68.8168 154.1327 71.5101 c F 154.1327 71.5101 m 154.1327 74.2034 151.886 76.3867 149.1146 76.3867 c 146.3432 76.3867 144.0965 74.2034 144.0965 71.5101 c F 149.1146 71.5101 m F 0 G 0.3 w 10 M 149.1146 71.5101 m S 0 g 1 w 4 M 149.1146 71.5101 m F 0 G 0.3 w 10 M 149.1146 71.5101 m S 149.1146 71.5101 m S 0 g 1 w 4 M 148.2087 70.6174 m 148.2087 67.6271 L 150.0206 67.6271 L 150.0206 70.6174 L 153.0142 70.608 L 153.0142 72.4123 L 150.0206 72.4031 L 150.0206 75.3934 L 148.2087 75.3934 L 148.2087 72.4031 L 145.215 72.4123 L 145.215 70.608 L 148.2087 70.6174 L f 0 G 0.3 w 10 M 168.1588 71.5101 m S 0 g 1 w 4 M 168.1588 71.5101 m F 0 G 0.3 w 10 M 168.1588 71.5101 m S 168.1588 71.5101 m S 168.1588 71.5101 m S 0 g 1 w 4 M 168.1588 71.5101 m F 0 G 0.3 w 10 M 168.1588 71.5101 m S 168.1588 71.5101 m S 1 g 1 w 4 M 163.1407 71.5101 m 163.1407 68.8168 165.3874 66.6335 168.1588 66.6335 c 170.9301 66.6335 173.1768 68.8168 173.1768 71.5101 c F 173.1768 71.5101 m 173.1768 74.2034 170.9301 76.3867 168.1588 76.3867 c 165.3874 76.3867 163.1407 74.2034 163.1407 71.5101 c F 168.1588 71.5101 m F 0 G 0.3 w 10 M 168.1588 71.5101 m S 0 g 1 w 4 M 168.1588 71.5101 m F 0 G 0.3 w 10 M 168.1588 71.5101 m S 168.1588 71.5101 m S 0 g 1 w 4 M 167.2528 70.6174 m 167.2528 67.6271 L 169.0647 67.6271 L 169.0647 70.6174 L 172.0583 70.608 L 172.0583 72.4123 L 169.0647 72.4031 L 169.0647 75.3934 L 167.2528 75.3934 L 167.2528 72.4031 L 164.2592 72.4123 L 164.2592 70.608 L 167.2528 70.6174 L f 0 G 0.3 w 10 M 187.203 127.2564 m S 187.203 108.6743 m S 187.203 127.2564 m S 187.203 127.2564 m S 187.203 108.6743 m S 187.203 127.2564 m S 187.203 108.6743 m S 187.203 90.0922 m S 187.203 90.0922 m S 187.203 90.0922 m S 187.203 108.6743 m S 187.203 90.0922 m S 187.203 127.2564 m S 0 g 1 w 4 M 187.203 127.2564 m F 0 G 0.3 w 10 M 187.203 127.2564 m S 187.203 127.2564 m S 187.203 127.2564 m S 0 g 1 w 4 M 187.203 127.2564 m F 0 G 0.3 w 10 M 187.203 127.2564 m S 187.203 127.2564 m S 1 g 1 w 4 M 187.203 127.2564 m F 0 G 0.3 w 10 M 187.203 127.2564 m S 0 g 1 w 4 M 187.203 127.2564 m F 0 G 0.3 w 10 M 187.203 127.2564 m S 187.203 127.2564 m S 187.203 108.6743 m S 0 g 1 w 4 M 187.203 108.6743 m F 0 G 0.3 w 10 M 187.203 108.6743 m S 187.203 108.6743 m S 187.203 108.6743 m S 0 g 1 w 4 M 187.203 108.6743 m F 0 G 0.3 w 10 M 187.203 108.6743 m S 187.203 108.6743 m S 1 g 1 w 4 M 187.203 108.6743 m F 0 G 0.3 w 10 M 187.203 108.6743 m S 0 g 1 w 4 M 187.203 108.6743 m F 0 G 0.3 w 10 M 187.203 108.6743 m S 187.203 108.6743 m S 187.203 90.0922 m S 0 g 1 w 4 M 187.203 90.0922 m F 0 G 0.3 w 10 M 187.203 90.0922 m S 187.203 90.0922 m S 187.203 90.0922 m S 0 g 1 w 4 M 187.203 90.0922 m F 0 G 0.3 w 10 M 187.203 90.0922 m S 187.203 90.0922 m S 1 g 1 w 4 M 187.203 90.0922 m F 0 G 0.3 w 10 M 187.203 90.0922 m S 0 g 1 w 4 M 187.203 90.0922 m F 0 G 0.3 w 10 M 187.203 90.0922 m S 187.203 90.0922 m S 139.5925 117.9653 m S 139.5925 117.9653 m S 158.6366 117.9653 m S 139.5925 117.9653 m S 158.6366 117.9653 m S 158.6366 117.9653 m S 158.6366 117.9653 m S 139.5925 117.9653 m S 139.5925 99.3833 m S 139.5925 99.3833 m S 158.6366 99.3833 m S 139.5925 99.3833 m S 158.6366 99.3833 m S 158.6366 99.3833 m S 158.6366 99.3833 m S 139.5925 99.3833 m S 130.0705 127.2564 m S 0 g 1 w 4 M 130.0705 127.2564 m F 0 G 0.3 w 10 M 130.0705 127.2564 m S 0 g 1 w 4 M 130.0705 127.2564 m F 1 g 125.0524 127.2564 m 125.0524 124.5631 127.2991 122.3797 130.0705 122.3797 c 132.8418 122.3797 135.0885 124.5631 135.0885 127.2564 c F 135.0885 127.2564 m 135.0885 129.9496 132.8418 132.133 130.0705 132.133 c 127.2991 132.133 125.0524 129.9496 125.0524 127.2564 c F 130.0705 127.2564 m F 0 G 0.3 w 10 M 130.0705 127.2564 m S 0 g 1 w 4 M 130.0705 127.2564 m F 0 G 0.3 w 10 M 130.0705 127.2564 m S 0 g 1 w 4 M 130.0705 127.2564 m F 129.1645 128.1493 m 126.1709 128.1586 L 126.1709 126.3543 L 129.1645 126.3636 L F 130.9764 126.3636 m 133.97 126.3543 L 133.97 128.1586 L 130.9764 128.1493 L F 126.1709 128.1586 m 133.97 128.1586 l 133.97 126.3543 l 126.1709 126.3543 l 126.1709 128.1586 l f 0 G 0.3 w 10 M 149.1146 127.2564 m S 0 g 1 w 4 M 149.1146 127.2564 m F 0 G 0.3 w 10 M 149.1146 127.2564 m S 0 g 1 w 4 M 149.1146 127.2564 m F 1 g 144.0965 127.2564 m 144.0965 124.5631 146.3432 122.3797 149.1146 122.3797 c 151.886 122.3797 154.1327 124.5631 154.1327 127.2564 c F 154.1327 127.2564 m 154.1327 129.9496 151.886 132.133 149.1146 132.133 c 146.3432 132.133 144.0965 129.9496 144.0965 127.2564 c F 149.1146 127.2564 m F 0 G 0.3 w 10 M 149.1146 127.2564 m S 0 g 1 w 4 M 149.1146 127.2564 m F 0 G 0.3 w 10 M 149.1146 127.2564 m S 0 g 1 w 4 M 149.1146 127.2564 m F 148.2087 128.1493 m 145.215 128.1586 L 145.215 126.3543 L 148.2087 126.3636 L F 150.0206 126.3636 m 153.0142 126.3543 L 153.0142 128.1586 L 150.0206 128.1493 L F 145.215 128.1586 m 153.0142 128.1586 l 153.0142 126.3543 l 145.215 126.3543 l 145.215 128.1586 l f 0 G 0.3 w 10 M 168.1588 127.2564 m S 0 g 1 w 4 M 168.1588 127.2564 m F 0 G 0.3 w 10 M 168.1588 127.2564 m S 0 g 1 w 4 M 168.1588 127.2564 m F 1 g 163.1407 127.2564 m 163.1407 124.5631 165.3874 122.3797 168.1588 122.3797 c 170.9301 122.3797 173.1768 124.5631 173.1768 127.2564 c F 173.1768 127.2564 m 173.1768 129.9496 170.9301 132.133 168.1588 132.133 c 165.3874 132.133 163.1407 129.9496 163.1407 127.2564 c F 168.1588 127.2564 m F 0 G 0.3 w 10 M 168.1588 127.2564 m S 0 g 1 w 4 M 168.1588 127.2564 m F 0 G 0.3 w 10 M 168.1588 127.2564 m S 0 g 1 w 4 M 168.1588 127.2564 m F 167.2528 128.1493 m 164.2592 128.1586 L 164.2592 126.3543 L 167.2528 126.3636 L F 169.0647 126.3636 m 172.0583 126.3543 L 172.0583 128.1586 L 169.0647 128.1493 L F 164.2592 128.1586 m 172.0583 128.1586 l 172.0583 126.3543 l 164.2592 126.3543 l 164.2592 128.1586 l f 0 G 0.3 w 10 M 168.1588 108.6743 m S 0 g 1 w 4 M 168.1588 108.6743 m F 0 G 0.3 w 10 M 168.1588 108.6743 m S 0 g 1 w 4 M 168.1588 108.6743 m F 1 g 168.1588 108.6743 m F 0 G 0.3 w 10 M 168.1588 108.6743 m S 0 g 1 w 4 M 168.1588 108.6743 m F 0 G 0.3 w 10 M 168.1588 108.6743 m S 0 g 1 w 4 M 168.1588 108.6743 m F 0 G 0.3 w 10 M 149.1146 108.6743 m S 0 g 1 w 4 M 149.1146 108.6743 m F 0 G 0.3 w 10 M 149.1146 108.6743 m S 0 g 1 w 4 M 149.1146 108.6743 m F 1 g 149.1146 108.6743 m F 0 G 0.3 w 10 M 149.1146 108.6743 m S 0 g 1 w 4 M 149.1146 108.6743 m F 0 G 0.3 w 10 M 149.1146 108.6743 m S 0 g 1 w 4 M 149.1146 108.6743 m F 0 G 0.3 w 10 M 130.0705 108.6743 m S 0 g 1 w 4 M 130.0705 108.6743 m F 0 G 0.3 w 10 M 130.0705 108.6743 m S 130.0705 108.6743 m S 130.0705 108.6743 m S 0 g 1 w 4 M 130.0705 108.6743 m F 0 G 0.3 w 10 M 130.0705 108.6743 m S 130.0705 108.6743 m S 1 g 1 w 4 M 130.0705 108.6743 m F 0 G 0.3 w 10 M 130.0705 108.6743 m S 0 g 1 w 4 M 130.0705 108.6743 m F 0 G 0.3 w 10 M 130.0705 108.6743 m S 130.0705 108.6743 m S 149.1146 90.0922 m S 0 g 1 w 4 M 149.1146 90.0922 m F 0 G 0.3 w 10 M 149.1146 90.0922 m S 149.1146 90.0922 m S 149.1146 90.0922 m S 0 g 1 w 4 M 149.1146 90.0922 m F 0 G 0.3 w 10 M 149.1146 90.0922 m S 149.1146 90.0922 m S 1 g 1 w 4 M 144.0965 90.0922 m 144.0965 87.3989 146.3432 85.2156 149.1146 85.2156 c 151.886 85.2156 154.1327 87.3989 154.1327 90.0922 c F 154.1327 90.0922 m 154.1327 92.7854 151.886 94.9688 149.1146 94.9688 c 146.3432 94.9688 144.0965 92.7854 144.0965 90.0922 c F 149.1146 90.0922 m F 0 G 0.3 w 10 M 149.1146 90.0922 m S 0 g 1 w 4 M 149.1146 90.0922 m F 0 G 0.3 w 10 M 149.1146 90.0922 m S 149.1146 90.0922 m S 0 g 1 w 4 M 148.2087 89.1995 m 148.2087 86.2092 L 150.0206 86.2092 L 150.0206 89.1995 L 153.0142 89.1901 L 153.0142 90.9944 L 150.0206 90.9851 L 150.0206 93.9754 L 148.2087 93.9754 L 148.2087 90.9851 L 145.215 90.9944 L 145.215 89.1901 L 148.2087 89.1995 L f 0 G 0.3 w 10 M 168.1588 90.0922 m S 0 g 1 w 4 M 168.1588 90.0922 m F 0 G 0.3 w 10 M 168.1588 90.0922 m S 168.1588 90.0922 m S 168.1588 90.0922 m S 0 g 1 w 4 M 168.1588 90.0922 m F 0 G 0.3 w 10 M 168.1588 90.0922 m S 168.1588 90.0922 m S 1 g 1 w 4 M 163.1407 90.0922 m 163.1407 87.3989 165.3874 85.2156 168.1588 85.2156 c 170.9301 85.2156 173.1768 87.3989 173.1768 90.0922 c F 173.1768 90.0922 m 173.1768 92.7854 170.9301 94.9688 168.1588 94.9688 c 165.3874 94.9688 163.1407 92.7854 163.1407 90.0922 c F 168.1588 90.0922 m F 0 G 0.3 w 10 M 168.1588 90.0922 m S 0 g 1 w 4 M 168.1588 90.0922 m F 0 G 0.3 w 10 M 168.1588 90.0922 m S 168.1588 90.0922 m S 0 g 1 w 4 M 167.2528 89.1995 m 167.2528 86.2092 L 169.0647 86.2092 L 169.0647 89.1995 L 172.0583 89.1901 L 172.0583 90.9944 L 169.0647 90.9851 L 169.0647 93.9754 L 167.2528 93.9754 L 167.2528 90.9851 L 164.2592 90.9944 L 164.2592 89.1901 L 167.2528 89.1995 L f 0 G 0.3 w 10 M 130.0705 90.0922 m S 0 g 1 w 4 M 130.0705 90.0922 m F 0 G 0.3 w 10 M 130.0705 90.0922 m S 130.0705 90.0922 m S 130.0705 90.0922 m S 0 g 1 w 4 M 130.0705 90.0922 m F 0 G 0.3 w 10 M 130.0705 90.0922 m S 130.0705 90.0922 m S 1 g 1 w 4 M 125.0524 90.0922 m 125.0524 87.3989 127.2991 85.2156 130.0705 85.2156 c 132.8418 85.2156 135.0885 87.3989 135.0885 90.0922 c F 135.0885 90.0922 m 135.0885 92.7854 132.8418 94.9688 130.0705 94.9688 c 127.2991 94.9688 125.0524 92.7854 125.0524 90.0922 c F 130.0705 90.0922 m F 0 G 0.3 w 10 M 130.0705 90.0922 m S 0 g 1 w 4 M 130.0705 90.0922 m F 0 G 0.3 w 10 M 130.0705 90.0922 m S 130.0705 90.0922 m S 0 g 1 w 4 M 129.1645 89.1995 m 129.1645 86.2092 L 130.9764 86.2092 L 130.9764 89.1995 L 133.97 89.1901 L 133.97 90.9944 L 130.9764 90.9851 L 130.9764 93.9754 L 129.1645 93.9754 L 129.1645 90.9851 L 126.1709 90.9944 L 126.1709 89.1901 L 129.1645 89.1995 L f 0 G 0.3 w 10 M 53.9833 127.2563 m S 53.9833 127.2563 m S 53.9833 127.2563 m S 53.9833 127.2563 m S 53.9833 127.2563 m S 53.9833 127.2563 m S 53.9833 127.2563 m S 53.9833 127.2563 m S 53.9833 127.2563 m S 0 g 1 w 4 M 53.9833 127.2563 m F 0 G 0.3 w 10 M 53.9833 127.2563 m S 0 g 1 w 4 M 53.9833 127.2563 m F 1 g 48.9747 127.2563 m 48.9747 124.5631 51.2172 122.3797 53.9833 122.3797 c 56.7495 122.3797 58.992 124.5631 58.992 127.2563 c F 58.992 127.2563 m 58.992 129.9496 56.7495 132.133 53.9833 132.133 c 51.2172 132.133 48.9747 129.9496 48.9747 127.2563 c F 53.9833 127.2563 m F 0 G 0.3 w 10 M 53.9833 127.2563 m S 0 g 1 w 4 M 53.9833 127.2563 m F 0 G 0.3 w 10 M 53.9833 127.2563 m S 0 g 1 w 4 M 53.9833 127.2563 m F 53.0791 128.1493 m 50.0911 128.1586 L 50.0911 126.3543 L 53.0791 126.3636 L F 54.8876 126.3636 m 57.8755 126.3543 L 57.8755 128.1586 L 54.8876 128.1493 L F 50.0911 128.1586 m 57.8755 128.1586 l 57.8755 126.3543 l 50.0911 126.3543 l 50.0911 128.1586 l f 0 G 0.3 w 10 M 130.0705 108.6743 m S 130.0705 108.6743 m S 130.0705 108.6743 m S 130.0705 108.6743 m S 130.0705 108.6743 m S 130.0705 108.6743 m S 130.0705 108.6743 m S 130.0705 108.6743 m S 130.0705 108.6743 m S 0 g 1 w 4 M 130.0705 108.6743 m F 0 G 0.3 w 10 M 130.0705 108.6743 m S 0 g 1 w 4 M 130.0705 108.6743 m F 1 g 125.0618 108.6743 m 125.0618 105.981 127.3043 103.7977 130.0705 103.7977 c 132.8366 103.7977 135.0791 105.981 135.0791 108.6743 c F 135.0791 108.6743 m 135.0791 111.3676 132.8366 113.5509 130.0705 113.5509 c 127.3043 113.5509 125.0618 111.3676 125.0618 108.6743 c F 130.0705 108.6743 m F 0 G 0.3 w 10 M 130.0705 108.6743 m S 0 g 1 w 4 M 130.0705 108.6743 m F 0 G 0.3 w 10 M 130.0705 108.6743 m S 0 g 1 w 4 M 130.0705 108.6743 m F 129.1662 109.5673 m 126.1782 109.5766 L 126.1782 107.7722 L 129.1662 107.7815 L F 130.9747 107.7815 m 133.9627 107.7722 L 133.9627 109.5766 L 130.9747 109.5673 L F 126.1782 109.5766 m 133.9627 109.5766 l 133.9627 107.7722 l 126.1782 107.7722 l 126.1782 109.5766 l f 0 G 0.3 w 10 M 149.025 108.6743 m S 149.025 108.6743 m S 149.025 108.6743 m S 149.025 108.6743 m S 149.025 108.6743 m S 149.025 108.6743 m S 149.025 108.6743 m S 149.1146 108.6743 m S 149.1146 108.6743 m S 149.025 108.6743 m S 168.1588 108.6743 m S 149.1146 108.6743 m S 168.1588 108.6743 m S 168.1588 108.6743 m S 168.1588 108.6743 m S 149.1146 108.6743 m S 149.025 108.6743 m S 149.1146 108.6743 m S 149.1146 108.6743 m S 149.025 108.6743 m S 168.1588 108.6743 m S 149.1146 108.6743 m S 168.1588 108.6743 m S 168.1588 108.6743 m S 168.1588 108.6743 m S 149.1146 108.6743 m S 149.1146 108.6743 m S 0 g 1 w 4 M 149.1146 108.6743 m F 0 G 0.3 w 10 M 149.1146 108.6743 m S 149.1146 108.6743 m S 149.1146 108.6743 m S 0 g 1 w 4 M 149.1146 108.6743 m F 0 G 0.3 w 10 M 149.1146 108.6743 m S 149.1146 108.6743 m S 1 g 1 w 4 M 144.0965 108.6743 m 144.0965 105.981 146.3432 103.7977 149.1146 103.7977 c 151.886 103.7977 154.1327 105.981 154.1327 108.6743 c F 154.1327 108.6743 m 154.1327 111.3676 151.886 113.5509 149.1146 113.5509 c 146.3432 113.5509 144.0965 111.3676 144.0965 108.6743 c F 149.1146 108.6743 m F 0 G 0.3 w 10 M 149.1146 108.6743 m S 0 g 1 w 4 M 149.1146 108.6743 m F 0 G 0.3 w 10 M 149.1146 108.6743 m S 149.1146 108.6743 m S 0 g 1 w 4 M 148.2087 107.7816 m 148.2087 104.7913 L 150.0206 104.7913 L 150.0206 107.7816 L 153.0142 107.7722 L 153.0142 109.5765 L 150.0206 109.5673 L 150.0206 112.5576 L 148.2087 112.5576 L 148.2087 109.5673 L 145.215 109.5765 L 145.215 107.7722 L 148.2087 107.7816 L f 0 G 0.3 w 10 M 168.1588 108.6743 m S 0 g 1 w 4 M 168.1588 108.6743 m F 0 G 0.3 w 10 M 168.1588 108.6743 m S 168.1588 108.6743 m S 168.1588 108.6743 m S 0 g 1 w 4 M 168.1588 108.6743 m F 0 G 0.3 w 10 M 168.1588 108.6743 m S 168.1588 108.6743 m S 1 g 1 w 4 M 163.1407 108.6743 m 163.1407 105.981 165.3874 103.7977 168.1588 103.7977 c 170.9301 103.7977 173.1768 105.981 173.1768 108.6743 c F 173.1768 108.6743 m 173.1768 111.3676 170.9301 113.5509 168.1588 113.5509 c 165.3874 113.5509 163.1407 111.3676 163.1407 108.6743 c F 168.1588 108.6743 m F 0 G 0.3 w 10 M 168.1588 108.6743 m S 0 g 1 w 4 M 168.1588 108.6743 m F 0 G 0.3 w 10 M 168.1588 108.6743 m S 168.1588 108.6743 m S 0 g 1 w 4 M 167.2528 107.7816 m 167.2528 104.7913 L 169.0647 104.7913 L 169.0647 107.7816 L 172.0583 107.7722 L 172.0583 109.5765 L 169.0647 109.5673 L 169.0647 112.5576 L 167.2528 112.5576 L 167.2528 109.5673 L 164.2592 109.5765 L 164.2592 107.7722 L 167.2528 107.7816 L f 0 G 0.3 w 10 M 206.2292 145.8386 m S 206.2292 164.4206 m S 206.2292 108.6744 m S 206.2292 127.2564 m S 206.2292 127.2564 m S 206.2292 145.8386 m S 187.2208 108.6744 m S 187.2208 127.2564 m S 206.2292 127.2564 m S 206.2292 108.6744 m S 196.725 117.9654 m S 149.2042 145.8386 m S 149.2042 164.4206 m S 168.2125 164.4206 m S 168.2125 145.8386 m S 158.7084 155.1296 m S 168.2125 127.2564 m S 168.2125 145.8386 m S 187.2208 145.8386 m S 187.2208 127.2564 m S 177.7166 136.5475 m S 168.2125 108.6744 m S 168.2125 127.2564 m S 187.2208 127.2564 m S 187.2208 108.6744 m S 177.7166 117.9654 m S 149.2042 108.6744 m S 149.2042 127.2564 m S 168.2125 127.2564 m S 168.2125 108.6744 m S 158.7084 117.9654 m S 149.2042 127.2564 m S 149.2042 145.8386 m S 168.2125 145.8386 m S 168.2125 127.2564 m S 158.7084 136.5475 m S 168.2125 145.8386 m S 168.2125 164.4206 m S 187.2208 164.4206 m S 187.2208 145.8386 m S 177.7166 155.1296 m S 187.2208 145.8386 m S 187.2208 164.4206 m S 206.2292 164.4206 m S 206.2292 145.8386 m S 196.725 155.1296 m S 187.2208 127.2564 m S 187.2208 145.8386 m S 206.2292 145.8386 m S 206.2292 127.2564 m S 196.725 136.5475 m S 0 g 1 w 4 M 196.725 117.9654 m F 158.7084 117.9654 m F 196.725 155.1296 m F 158.7084 155.1296 m F 0 G 0.3 w 10 M 130.1959 108.6744 m S 130.1959 127.2564 m S 149.2042 127.2564 m S 149.2042 108.6744 m S 139.7001 117.9654 m S 92.1792 145.8386 m S 92.1792 164.4206 m S 111.1875 164.4206 m S 111.1875 145.8386 m S 101.6834 155.1296 m S 111.1875 127.2564 m S 111.1875 145.8386 m S 130.1959 145.8386 m S 130.1959 127.2564 m S 120.6917 136.5475 m S 111.1875 108.6744 m S 111.1875 127.2564 m S 130.1959 127.2564 m S 130.1959 108.6744 m S 120.6917 117.9654 m S 92.1792 108.6744 m S 92.1792 127.2564 m S 111.1875 127.2564 m S 111.1875 108.6744 m S 101.6834 117.9654 m S 92.1792 127.2564 m S 92.1792 145.8386 m S 111.1875 145.8386 m S 111.1875 127.2564 m S 101.6834 136.5475 m S 111.1875 145.8386 m S 111.1875 164.4206 m S 130.1959 164.4206 m S 130.1959 145.8386 m S 120.6917 155.1296 m S 130.1959 145.8386 m S 130.1959 164.4206 m S 149.2042 164.4206 m S 149.2042 145.8386 m S 139.7001 155.1296 m S 130.1959 127.2564 m S 130.1959 145.8386 m S 149.2042 145.8386 m S 149.2042 127.2564 m S 139.7001 136.5475 m S 0 g 1 w 4 M 139.7001 117.9654 m F 101.6834 117.9654 m F 139.7001 155.1296 m F 101.6834 155.1296 m F 0 G 0.3 w 10 M 206.2292 201.5848 m S 206.2292 220.1669 m S 206.2292 164.4206 m S 206.2292 183.0028 m S 206.2292 183.0028 m S 206.2292 201.5848 m S 187.2208 164.4206 m S 187.2208 183.0028 m S 206.2292 183.0028 m S 206.2292 164.4206 m S 196.725 173.7117 m S 149.2042 201.5848 m S 149.2042 220.1669 m S 168.2125 220.1669 m S 168.2125 201.5848 m S 158.7084 210.8759 m S 168.2125 183.0028 m S 168.2125 201.5848 m S 187.2208 201.5848 m S 187.2208 183.0028 m S 177.7166 192.2937 m S 168.2125 164.4206 m S 168.2125 183.0028 m S 187.2208 183.0028 m S 187.2208 164.4206 m S 177.7166 173.7117 m S 149.2042 164.4206 m S 149.2042 183.0028 m S 168.2125 183.0028 m S 168.2125 164.4206 m S 158.7084 173.7117 m S 149.2042 183.0028 m S 149.2042 201.5848 m S 168.2125 201.5848 m S 168.2125 183.0028 m S 158.7084 192.2937 m S 168.2125 201.5848 m S 168.2125 220.1669 m S 187.2208 220.1669 m S 187.2208 201.5848 m S 177.7166 210.8759 m S 187.2208 201.5848 m S 187.2208 220.1669 m S 206.2292 220.1669 m S 206.2292 201.5848 m S 196.725 210.8759 m S 187.2208 183.0028 m S 187.2208 201.5848 m S 206.2292 201.5848 m S 206.2292 183.0028 m S 196.725 192.2937 m S 0 g 1 w 4 M 196.725 173.7117 m F 158.7084 173.7117 m F 196.725 210.8759 m F 158.7084 210.8759 m F 0 G 0.3 w 10 M 130.1959 164.4206 m S 130.1959 183.0028 m S 149.2042 183.0028 m S 149.2042 164.4206 m S 139.7001 173.7117 m S 92.1792 201.5848 m S 92.1792 220.1669 m S 111.1875 220.1669 m S 111.1875 201.5848 m S 101.6834 210.8759 m S 111.1875 183.0028 m S 111.1875 201.5848 m S 130.1959 201.5848 m S 130.1959 183.0028 m S 120.6917 192.2937 m S 111.1875 164.4206 m S 111.1875 183.0028 m S 130.1959 183.0028 m S 130.1959 164.4206 m S 120.6917 173.7117 m S 92.1792 164.4206 m S 92.1792 183.0028 m S 111.1875 183.0028 m S 111.1875 164.4206 m S 101.6834 173.7117 m S 92.1792 183.0028 m S 92.1792 201.5848 m S 111.1875 201.5848 m S 111.1875 183.0028 m S 101.6834 192.2937 m S 111.1875 201.5848 m S 111.1875 220.1669 m S 130.1959 220.1669 m S 130.1959 201.5848 m S 120.6917 210.8759 m S 130.1959 201.5848 m S 130.1959 220.1669 m S 149.2042 220.1669 m S 149.2042 201.5848 m S 139.7001 210.8759 m S 130.1959 183.0028 m S 130.1959 201.5848 m S 149.2042 201.5848 m S 149.2042 183.0028 m S 139.7001 192.2937 m S 0 g 1 w 4 M 139.7001 173.7117 m F 101.6834 173.7117 m F 139.7001 210.8759 m F 101.6834 210.8759 m F 0 G 0.3 w 10 M 206.2292 220.1669 m S 187.2208 220.1669 m S 206.2292 220.1669 m S 168.2125 220.1669 m S 187.2208 220.1669 m S 149.2042 220.1669 m S 168.2125 220.1669 m S 130.1959 220.1669 m S 149.2042 220.1669 m S 111.1875 220.1669 m S 130.1959 220.1669 m S 92.1792 220.1669 m S 111.1875 220.1669 m S 187.2208 108.6744 m S 187.2208 127.2564 m S 206.2292 127.2564 m S 206.2292 108.6744 m S 196.725 117.9654 m S 149.2042 145.8386 m S 149.2042 164.4206 m S 168.2125 164.4206 m S 168.2125 145.8386 m S 168.2125 127.2564 m S 168.2125 145.8386 m S 187.2208 145.8386 m S 187.2208 127.2564 m S 177.7166 136.5475 m S 168.2125 108.6744 m S 168.2125 127.2564 m S 187.2208 127.2564 m S 187.2208 108.6744 m S 177.7166 117.9654 m S 149.2042 108.6744 m S 149.2042 127.2564 m S 168.2125 127.2564 m S 168.2125 108.6744 m S 158.7084 117.9654 m S 149.2042 127.2564 m S 149.2042 145.8386 m S 168.2125 145.8386 m S 168.2125 127.2564 m S 158.7084 136.5475 m S 168.2125 145.8386 m S 168.2125 164.4206 m S 187.2208 164.4206 m S 187.2208 145.8386 m S 177.7166 155.1296 m S 187.2208 145.8386 m S 187.2208 164.4206 m S 206.2292 164.4206 m S 206.2292 145.8386 m S 196.725 155.1296 m S 187.2208 127.2564 m S 187.2208 145.8386 m S 206.2292 145.8386 m S 206.2292 127.2564 m S 196.725 136.5475 m S 0 g 1 w 4 M 196.725 117.9654 m F 158.7084 117.9654 m F 196.725 155.1296 m F 0 G 0.3 w 10 M 130.1959 108.6744 m S 130.1959 127.2564 m S 149.2042 127.2564 m S 149.2042 108.6744 m S 139.7001 117.9654 m S 92.1792 145.8386 m S 92.1792 164.4206 m S 111.1875 164.4206 m S 111.1875 145.8386 m S 101.6834 155.1296 m S 111.1875 127.2564 m S 111.1875 145.8386 m S 130.1959 145.8386 m S 130.1959 127.2564 m S 120.6917 136.5475 m S 111.1875 108.6744 m S 111.1875 127.2564 m S 130.1959 127.2564 m S 130.1959 108.6744 m S 120.6917 117.9654 m S 92.1792 108.6744 m S 92.1792 127.2564 m S 111.1875 127.2564 m S 111.1875 108.6744 m S 101.6834 117.9654 m S 92.1792 127.2564 m S 92.1792 145.8386 m S 111.1875 145.8386 m S 111.1875 127.2564 m S 101.6834 136.5475 m S 111.1875 145.8386 m S 111.1875 164.4206 m S 130.1959 164.4206 m S 130.1959 145.8386 m S 120.6917 155.1296 m S 130.1959 145.8386 m S 130.1959 164.4206 m S 149.2042 164.4206 m S 149.2042 145.8386 m S 139.7001 155.1296 m S 130.1959 127.2564 m S 130.1959 145.8386 m S 149.2042 145.8386 m S 149.2042 127.2564 m S 139.7001 136.5475 m S 0 g 1 w 4 M 139.7001 117.9654 m F 101.6834 117.9654 m F 139.7001 155.1296 m F 101.6834 155.1296 m F 0 G 0.3 w 10 M 187.2208 164.4206 m S 187.2208 183.0028 m S 206.2292 183.0028 m S 206.2292 164.4206 m S 196.725 173.7117 m S 149.2042 201.5848 m S 149.2042 220.1669 m S 168.2125 220.1669 m S 168.2125 201.5848 m S 158.7084 210.8759 m S 168.2125 183.0028 m S 168.2125 201.5848 m S 187.2208 201.5848 m S 187.2208 183.0028 m S 177.7166 192.2937 m S 168.2125 164.4206 m S 168.2125 183.0028 m S 187.2208 183.0028 m S 187.2208 164.4206 m S 177.7166 173.7117 m S 149.2042 164.4206 m S 149.2042 183.0028 m S 168.2125 183.0028 m S 168.2125 164.4206 m S 149.2042 183.0028 m S 149.2042 201.5848 m S 168.2125 201.5848 m S 168.2125 183.0028 m S 158.7084 192.2937 m S 168.2125 201.5848 m S 168.2125 220.1669 m S 187.2208 220.1669 m S 187.2208 201.5848 m S 177.7166 210.8759 m S 187.2208 201.5848 m S 187.2208 220.1669 m S 206.2292 220.1669 m S 206.2292 201.5848 m S 196.725 210.8759 m S 187.2208 183.0028 m S 187.2208 201.5848 m S 206.2292 201.5848 m S 206.2292 183.0028 m S 196.725 192.2937 m S 0 g 1 w 4 M 196.725 173.7117 m F 196.725 210.8759 m F 158.7084 210.8759 m F 0 G 0.3 w 10 M 130.1959 164.4206 m S 130.1959 183.0028 m S 149.2042 183.0028 m S 149.2042 164.4206 m S 139.7001 173.7117 m S 92.1792 201.5848 m S 92.1792 220.1669 m S 111.1875 220.1669 m S 111.1875 201.5848 m S 101.6834 210.8759 m S 111.1875 183.0028 m S 111.1875 201.5848 m S 130.1959 201.5848 m S 130.1959 183.0028 m S 120.6917 192.2937 m S 111.1875 164.4206 m S 111.1875 183.0028 m S 130.1959 183.0028 m S 130.1959 164.4206 m S 120.6917 173.7117 m S 92.1792 164.4206 m S 92.1792 183.0028 m S 111.1875 183.0028 m S 111.1875 164.4206 m S 101.6834 173.7117 m S 92.1792 183.0028 m S 92.1792 201.5848 m S 111.1875 201.5848 m S 111.1875 183.0028 m S 101.6834 192.2937 m S 111.1875 201.5848 m S 111.1875 220.1669 m S 130.1959 220.1669 m S 130.1959 201.5848 m S 120.6917 210.8759 m S 130.1959 201.5848 m S 130.1959 220.1669 m S 149.2042 220.1669 m S 149.2042 201.5848 m S 139.7001 210.8759 m S 130.1959 183.0028 m S 130.1959 201.5848 m S 149.2042 201.5848 m S 149.2042 183.0028 m S 139.7001 192.2937 m S 0 g 1 w 4 M 139.7001 173.7117 m F 101.6834 173.7117 m F 139.7001 210.8759 m F 101.6834 210.8759 m F 0 G 0.3 w 10 M 187.2208 220.1669 m S 206.2292 220.1669 m S 168.2125 220.1669 m S 187.2208 220.1669 m S 149.2042 220.1669 m S 168.2125 220.1669 m S 130.1959 220.1669 m S 149.2042 220.1669 m S 111.1875 220.1669 m S 130.1959 220.1669 m S 92.1792 220.1669 m S 111.1875 220.1669 m S 1 w 4 M 196.725 136.5475 m 101.6834 136.5475 l S 196.725 192.2937 m 101.6834 192.2937 l S 177.7166 117.9654 m 177.7166 210.8759 l S 0.3 w 10 M 168.2125 127.2564 m S 0 g 1 w 4 M 168.2125 127.2564 m F 0 G 0.3 w 10 M 168.2125 127.2564 m S 168.2125 127.2564 m S 168.2125 127.2564 m S 0 g 1 w 4 M 168.2125 127.2564 m F 0 G 0.3 w 10 M 168.2125 127.2564 m S 168.2125 127.2564 m S 1 g 1 w 4 M 168.2125 127.2564 m F 0 G 0.3 w 10 M 168.2125 127.2564 m S 0 g 1 w 4 M 168.2125 127.2564 m F 0 G 0.3 w 10 M 168.2125 127.2564 m S 168.2125 127.2564 m S 149.2042 127.2564 m S 0 g 1 w 4 M 149.2042 127.2564 m F 0 G 0.3 w 10 M 149.2042 127.2564 m S 149.2042 127.2564 m S 149.2042 127.2564 m S 0 g 1 w 4 M 149.2042 127.2564 m F 0 G 0.3 w 10 M 149.2042 127.2564 m S 149.2042 127.2564 m S 1 g 1 w 4 M 149.2042 127.2564 m F 0 G 0.3 w 10 M 149.2042 127.2564 m S 0 g 1 w 4 M 149.2042 127.2564 m F 0 G 0.3 w 10 M 149.2042 127.2564 m S 149.2042 127.2564 m S 130.1959 127.2564 m S 0 g 1 w 4 M 130.1959 127.2564 m F 0 G 0.3 w 10 M 130.1959 127.2564 m S 130.1959 127.2564 m S 130.1959 127.2564 m S 0 g 1 w 4 M 130.1959 127.2564 m F 0 G 0.3 w 10 M 130.1959 127.2564 m S 130.1959 127.2564 m S 1 g 1 w 4 M 130.1959 127.2564 m F 0 G 0.3 w 10 M 130.1959 127.2564 m S 0 g 1 w 4 M 130.1959 127.2564 m F 0 G 0.3 w 10 M 130.1959 127.2564 m S 130.1959 127.2564 m S 187.2208 145.8386 m S 0 g 1 w 4 M 187.2208 145.8386 m F 0 G 0.3 w 10 M 187.2208 145.8386 m S 187.2208 145.8386 m S 187.2208 145.8386 m S 0 g 1 w 4 M 187.2208 145.8386 m F 0 G 0.3 w 10 M 187.2208 145.8386 m S 187.2208 145.8386 m S 1 g 1 w 4 M 187.2208 145.8386 m F 0 G 0.3 w 10 M 187.2208 145.8386 m S 0 g 1 w 4 M 187.2208 145.8386 m F 0 G 0.3 w 10 M 187.2208 145.8386 m S 187.2208 145.8386 m S 187.2208 164.4206 m S 0 g 1 w 4 M 187.2208 164.4206 m F 0 G 0.3 w 10 M 187.2208 164.4206 m S 187.2208 164.4206 m S 187.2208 164.4206 m S 0 g 1 w 4 M 187.2208 164.4206 m F 0 G 0.3 w 10 M 187.2208 164.4206 m S 187.2208 164.4206 m S 1 g 1 w 4 M 187.2208 164.4206 m F 0 G 0.3 w 10 M 187.2208 164.4206 m S 0 g 1 w 4 M 187.2208 164.4206 m F 0 G 0.3 w 10 M 187.2208 164.4206 m S 187.2208 164.4206 m S 187.2208 183.0028 m S 0 g 1 w 4 M 187.2208 183.0028 m F 0 G 0.3 w 10 M 187.2208 183.0028 m S 187.2208 183.0028 m S 187.2208 183.0028 m S 0 g 1 w 4 M 187.2208 183.0028 m F 0 G 0.3 w 10 M 187.2208 183.0028 m S 187.2208 183.0028 m S 1 g 1 w 4 M 187.2208 183.0028 m F 0 G 0.3 w 10 M 187.2208 183.0028 m S 0 g 1 w 4 M 187.2208 183.0028 m F 0 G 0.3 w 10 M 187.2208 183.0028 m S 187.2208 183.0028 m S 168.2125 201.5848 m S 168.2125 201.5848 m S 149.2042 201.5848 m S 168.2125 201.5848 m S 149.2042 201.5848 m S 168.2125 201.5848 m S 130.1959 201.5848 m S 149.2042 201.5848 m S 130.1959 201.5848 m S 130.1959 201.5848 m S 130.1959 201.5848 m S 149.2042 201.5848 m S 168.2125 201.5848 m S 0 g 1 w 4 M 168.2125 201.5848 m F 0 G 0.3 w 10 M 168.2125 201.5848 m S 168.2125 201.5848 m S 168.2125 201.5848 m S 0 g 1 w 4 M 168.2125 201.5848 m F 0 G 0.3 w 10 M 168.2125 201.5848 m S 168.2125 201.5848 m S 1 g 1 w 4 M 173.2211 201.5848 m 173.2211 204.2781 170.9786 206.4615 168.2125 206.4615 c 165.4463 206.4615 163.2038 204.2781 163.2038 201.5848 c F 163.2038 201.5848 m 163.2038 198.8916 165.4463 196.7082 168.2125 196.7082 c 170.9786 196.7082 173.2211 198.8916 173.2211 201.5848 c F 168.2125 201.5848 m F 0 G 0.3 w 10 M 168.2125 201.5848 m S 0 g 1 w 4 M 168.2125 201.5848 m F 0 G 0.3 w 10 M 168.2125 201.5848 m S 168.2125 201.5848 m S 0 g 1 w 4 M 169.1167 202.4776 m 169.1167 205.4678 L 167.3082 205.4678 L 167.3082 202.4776 L 164.3202 202.4869 L 164.3202 200.6826 L 167.3082 200.6919 L 167.3082 197.7016 L 169.1167 197.7016 L 169.1167 200.6919 L 172.1047 200.6826 L 172.1047 202.4869 L 169.1167 202.4776 L f 0 G 0.3 w 10 M 149.2042 201.5848 m S 0 g 1 w 4 M 149.2042 201.5848 m F 0 G 0.3 w 10 M 149.2042 201.5848 m S 149.2042 201.5848 m S 149.2042 201.5848 m S 0 g 1 w 4 M 149.2042 201.5848 m F 0 G 0.3 w 10 M 149.2042 201.5848 m S 149.2042 201.5848 m S 1 g 1 w 4 M 154.2128 201.5848 m 154.2128 204.2781 151.9703 206.4615 149.2042 206.4615 c 146.438 206.4615 144.1955 204.2781 144.1955 201.5848 c F 144.1955 201.5848 m 144.1955 198.8916 146.438 196.7082 149.2042 196.7082 c 151.9703 196.7082 154.2128 198.8916 154.2128 201.5848 c F 149.2042 201.5848 m F 0 G 0.3 w 10 M 149.2042 201.5848 m S 0 g 1 w 4 M 149.2042 201.5848 m F 0 G 0.3 w 10 M 149.2042 201.5848 m S 149.2042 201.5848 m S 0 g 1 w 4 M 150.1084 202.4776 m 150.1084 205.4678 L 148.2999 205.4678 L 148.2999 202.4776 L 145.3119 202.4869 L 145.3119 200.6826 L 148.2999 200.6919 L 148.2999 197.7016 L 150.1084 197.7016 L 150.1084 200.6919 L 153.0964 200.6826 L 153.0964 202.4869 L 150.1084 202.4776 L f 0 G 0.3 w 10 M 130.1959 201.5848 m S 0 g 1 w 4 M 130.1959 201.5848 m F 0 G 0.3 w 10 M 130.1959 201.5848 m S 130.1959 201.5848 m S 130.1959 201.5848 m S 0 g 1 w 4 M 130.1959 201.5848 m F 0 G 0.3 w 10 M 130.1959 201.5848 m S 130.1959 201.5848 m S 1 g 1 w 4 M 135.2045 201.5848 m 135.2045 204.2781 132.962 206.4615 130.1959 206.4615 c 127.4297 206.4615 125.1872 204.2781 125.1872 201.5848 c F 125.1872 201.5848 m 125.1872 198.8916 127.4297 196.7082 130.1959 196.7082 c 132.962 196.7082 135.2045 198.8916 135.2045 201.5848 c F 130.1959 201.5848 m F 0 G 0.3 w 10 M 130.1959 201.5848 m S 0 g 1 w 4 M 130.1959 201.5848 m F 0 G 0.3 w 10 M 130.1959 201.5848 m S 130.1959 201.5848 m S 0 g 1 w 4 M 131.1001 202.4776 m 131.1001 205.4678 L 129.2916 205.4678 L 129.2916 202.4776 L 126.3036 202.4869 L 126.3036 200.6826 L 129.2916 200.6919 L 129.2916 197.7016 L 131.1001 197.7016 L 131.1001 200.6919 L 134.0881 200.6826 L 134.0881 202.4869 L 131.1001 202.4776 L f 0 G 0.3 w 10 M 111.1875 145.8386 m S 111.1875 164.4206 m S 111.1875 145.8386 m S 111.1875 145.8386 m S 111.1875 164.4206 m S 111.1875 145.8386 m S 111.1875 164.4206 m S 111.1875 183.0028 m S 111.1875 183.0028 m S 111.1875 183.0028 m S 111.1875 164.4206 m S 111.1875 183.0028 m S 111.1875 145.8386 m S 0 g 1 w 4 M 111.1875 145.8386 m F 0 G 0.3 w 10 M 111.1875 145.8386 m S 111.1875 145.8386 m S 111.1875 145.8386 m S 0 g 1 w 4 M 111.1875 145.8386 m F 0 G 0.3 w 10 M 111.1875 145.8386 m S 111.1875 145.8386 m S 1 g 1 w 4 M 111.1875 145.8386 m F 0 G 0.3 w 10 M 111.1875 145.8386 m S 0 g 1 w 4 M 111.1875 145.8386 m F 0 G 0.3 w 10 M 111.1875 145.8386 m S 111.1875 145.8386 m S 111.1875 164.4206 m S 0 g 1 w 4 M 111.1875 164.4206 m F 0 G 0.3 w 10 M 111.1875 164.4206 m S 111.1875 164.4206 m S 111.1875 164.4206 m S 0 g 1 w 4 M 111.1875 164.4206 m F 0 G 0.3 w 10 M 111.1875 164.4206 m S 111.1875 164.4206 m S 1 g 1 w 4 M 111.1875 164.4206 m F 0 G 0.3 w 10 M 111.1875 164.4206 m S 0 g 1 w 4 M 111.1875 164.4206 m F 0 G 0.3 w 10 M 111.1875 164.4206 m S 111.1875 164.4206 m S 111.1875 183.0028 m S 0 g 1 w 4 M 111.1875 183.0028 m F 0 G 0.3 w 10 M 111.1875 183.0028 m S 111.1875 183.0028 m S 111.1875 183.0028 m S 0 g 1 w 4 M 111.1875 183.0028 m F 0 G 0.3 w 10 M 111.1875 183.0028 m S 111.1875 183.0028 m S 1 g 1 w 4 M 111.1875 183.0028 m F 0 G 0.3 w 10 M 111.1875 183.0028 m S 0 g 1 w 4 M 111.1875 183.0028 m F 0 G 0.3 w 10 M 111.1875 183.0028 m S 111.1875 183.0028 m S 158.7084 155.1296 m S 158.7084 155.1296 m S 139.7001 155.1296 m S 158.7084 155.1296 m S 139.7001 155.1296 m S 139.7001 155.1296 m S 139.7001 155.1296 m S 158.7084 155.1296 m S 158.7084 173.7117 m S 158.7084 173.7117 m S 139.7001 173.7117 m S 158.7084 173.7117 m S 139.7001 173.7117 m S 139.7001 173.7117 m S 139.7001 173.7117 m S 158.7084 173.7117 m S 168.2125 145.8386 m S 0 g 1 w 4 M 168.2125 145.8386 m F 0 G 0.3 w 10 M 168.2125 145.8386 m S 0 g 1 w 4 M 168.2125 145.8386 m F 1 g 173.2211 145.8386 m 173.2211 148.5319 170.9786 150.7152 168.2125 150.7152 c 165.4463 150.7152 163.2038 148.5319 163.2038 145.8386 c F 163.2038 145.8386 m 163.2038 143.1453 165.4463 140.962 168.2125 140.962 c 170.9786 140.962 173.2211 143.1453 173.2211 145.8386 c F 168.2125 145.8386 m F 0 G 0.3 w 10 M 168.2125 145.8386 m S 0 g 1 w 4 M 168.2125 145.8386 m F 0 G 0.3 w 10 M 168.2125 145.8386 m S 0 g 1 w 4 M 168.2125 145.8386 m F 169.1167 144.9456 m 172.1047 144.9363 L 172.1047 146.7407 L 169.1167 146.7314 L F 167.3082 146.7314 m 164.3202 146.7407 L 164.3202 144.9363 L 167.3082 144.9456 L F 172.1047 144.9363 m 164.3202 144.9363 l 164.3202 146.7407 l 172.1047 146.7407 l 172.1047 144.9363 l f 0 G 0.3 w 10 M 149.2042 145.8386 m S 0 g 1 w 4 M 149.2042 145.8386 m F 0 G 0.3 w 10 M 149.2042 145.8386 m S 0 g 1 w 4 M 149.2042 145.8386 m F 1 g 154.2128 145.8386 m 154.2128 148.5319 151.9703 150.7152 149.2042 150.7152 c 146.438 150.7152 144.1955 148.5319 144.1955 145.8386 c F 144.1955 145.8386 m 144.1955 143.1453 146.438 140.962 149.2042 140.962 c 151.9703 140.962 154.2128 143.1453 154.2128 145.8386 c F 149.2042 145.8386 m F 0 G 0.3 w 10 M 149.2042 145.8386 m S 0 g 1 w 4 M 149.2042 145.8386 m F 0 G 0.3 w 10 M 149.2042 145.8386 m S 0 g 1 w 4 M 149.2042 145.8386 m F 150.1084 144.9456 m 153.0964 144.9363 L 153.0964 146.7407 L 150.1084 146.7314 L F 148.2999 146.7314 m 145.3119 146.7407 L 145.3119 144.9363 L 148.2999 144.9456 L F 153.0964 144.9363 m 145.3119 144.9363 l 145.3119 146.7407 l 153.0964 146.7407 l 153.0964 144.9363 l f 0 G 0.3 w 10 M 130.1959 145.8386 m S 0 g 1 w 4 M 130.1959 145.8386 m F 0 G 0.3 w 10 M 130.1959 145.8386 m S 0 g 1 w 4 M 130.1959 145.8386 m F 1 g 135.2045 145.8386 m 135.2045 148.5319 132.962 150.7152 130.1959 150.7152 c 127.4297 150.7152 125.1872 148.5319 125.1872 145.8386 c F 125.1872 145.8386 m 125.1872 143.1453 127.4297 140.962 130.1959 140.962 c 132.962 140.962 135.2045 143.1453 135.2045 145.8386 c F 130.1959 145.8386 m F 0 G 0.3 w 10 M 130.1959 145.8386 m S 0 g 1 w 4 M 130.1959 145.8386 m F 0 G 0.3 w 10 M 130.1959 145.8386 m S 0 g 1 w 4 M 130.1959 145.8386 m F 131.1001 144.9456 m 134.0881 144.9363 L 134.0881 146.7407 L 131.1001 146.7314 L F 129.2916 146.7314 m 126.3036 146.7407 L 126.3036 144.9363 L 129.2916 144.9456 L F 134.0881 144.9363 m 126.3036 144.9363 l 126.3036 146.7407 l 134.0881 146.7407 l 134.0881 144.9363 l f 0 G 0.3 w 10 M 130.1959 164.4206 m S 0 g 1 w 4 M 130.1959 164.4206 m F 0 G 0.3 w 10 M 130.1959 164.4206 m S 0 g 1 w 4 M 130.1959 164.4206 m F 1 g 135.2045 164.4206 m 135.2045 167.1139 132.962 169.2973 130.1959 169.2973 c 127.4297 169.2973 125.1872 167.1139 125.1872 164.4206 c F 125.1872 164.4206 m 125.1872 161.7274 127.4297 159.544 130.1959 159.544 c 132.962 159.544 135.2045 161.7274 135.2045 164.4206 c F 130.1959 164.4206 m F 0 G 0.3 w 10 M 130.1959 164.4206 m S 0 g 1 w 4 M 130.1959 164.4206 m F 0 G 0.3 w 10 M 130.1959 164.4206 m S 0 g 1 w 4 M 130.1959 164.4206 m F 131.1001 163.5277 m 134.0881 163.5184 L 134.0881 165.3227 L 131.1001 165.3134 L F 129.2916 165.3134 m 126.3036 165.3227 L 126.3036 163.5184 L 129.2916 163.5277 L F 134.0881 163.5184 m 126.3036 163.5184 l 126.3036 165.3227 l 134.0881 165.3227 l 134.0881 163.5184 l f 0 G 0.3 w 10 M 149.2042 164.4206 m S 0 g 1 w 4 M 149.2042 164.4206 m F 0 G 0.3 w 10 M 149.2042 164.4206 m S 0 g 1 w 4 M 149.2042 164.4206 m F 1 g 154.2128 164.4206 m 154.2128 167.1139 151.9703 169.2973 149.2042 169.2973 c 146.438 169.2973 144.1955 167.1139 144.1955 164.4206 c F 144.1955 164.4206 m 144.1955 161.7274 146.438 159.544 149.2042 159.544 c 151.9703 159.544 154.2128 161.7274 154.2128 164.4206 c F 149.2042 164.4206 m F 0 G 0.3 w 10 M 149.2042 164.4206 m S 0 g 1 w 4 M 149.2042 164.4206 m F 0 G 0.3 w 10 M 149.2042 164.4206 m S 0 g 1 w 4 M 149.2042 164.4206 m F 150.1084 163.5277 m 153.0964 163.5184 L 153.0964 165.3227 L 150.1084 165.3134 L F 148.2999 165.3134 m 145.3119 165.3227 L 145.3119 163.5184 L 148.2999 163.5277 L F 153.0964 163.5184 m 145.3119 163.5184 l 145.3119 165.3227 l 153.0964 165.3227 l 153.0964 163.5184 l f 0 G 0.3 w 10 M 168.2125 164.4206 m S 0 g 1 w 4 M 168.2125 164.4206 m F 0 G 0.3 w 10 M 168.2125 164.4206 m S 168.2125 164.4206 m S 168.2125 164.4206 m S 0 g 1 w 4 M 168.2125 164.4206 m F 0 G 0.3 w 10 M 168.2125 164.4206 m S 168.2125 164.4206 m S 1 g 1 w 4 M 173.2211 164.4206 m 173.2211 167.1139 170.9786 169.2973 168.2125 169.2973 c 165.4463 169.2973 163.2038 167.1139 163.2038 164.4206 c F 163.2038 164.4206 m 163.2038 161.7274 165.4463 159.544 168.2125 159.544 c 170.9786 159.544 173.2211 161.7274 173.2211 164.4206 c F 168.2125 164.4206 m F 0 G 0.3 w 10 M 168.2125 164.4206 m S 0 g 1 w 4 M 168.2125 164.4206 m F 0 G 0.3 w 10 M 168.2125 164.4206 m S 168.2125 164.4206 m S 0 g 1 w 4 M 169.1167 165.3134 m 169.1167 168.3036 L 167.3082 168.3036 L 167.3082 165.3134 L 164.3202 165.3227 L 164.3202 163.5184 L 167.3082 163.5277 L 167.3082 160.5374 L 169.1167 160.5374 L 169.1167 163.5277 L 172.1047 163.5184 L 172.1047 165.3227 L 169.1167 165.3134 L f 0 G 0.3 w 10 M 149.2042 183.0028 m S 0 g 1 w 4 M 149.2042 183.0028 m F 0 G 0.3 w 10 M 149.2042 183.0028 m S 149.2042 183.0028 m S 149.2042 183.0028 m S 0 g 1 w 4 M 149.2042 183.0028 m F 0 G 0.3 w 10 M 149.2042 183.0028 m S 149.2042 183.0028 m S 1 g 1 w 4 M 154.2128 183.0028 m 154.2128 185.6961 151.9703 187.8794 149.2042 187.8794 c 146.438 187.8794 144.1955 185.6961 144.1955 183.0028 c F 144.1955 183.0028 m 144.1955 180.3095 146.438 178.1262 149.2042 178.1262 c 151.9703 178.1262 154.2128 180.3095 154.2128 183.0028 c F 149.2042 183.0028 m F 0 G 0.3 w 10 M 149.2042 183.0028 m S 0 g 1 w 4 M 149.2042 183.0028 m F 0 G 0.3 w 10 M 149.2042 183.0028 m S 149.2042 183.0028 m S 0 g 1 w 4 M 150.1084 183.8955 m 150.1084 186.8858 L 148.2999 186.8858 L 148.2999 183.8955 L 145.3119 183.9049 L 145.3119 182.1005 L 148.2999 182.1098 L 148.2999 179.1195 L 150.1084 179.1195 L 150.1084 182.1098 L 153.0964 182.1005 L 153.0964 183.9049 L 150.1084 183.8955 L f 0 G 0.3 w 10 M 130.1959 183.0028 m S 0 g 1 w 4 M 130.1959 183.0028 m F 0 G 0.3 w 10 M 130.1959 183.0028 m S 130.1959 183.0028 m S 130.1959 183.0028 m S 0 g 1 w 4 M 130.1959 183.0028 m F 0 G 0.3 w 10 M 130.1959 183.0028 m S 130.1959 183.0028 m S 1 g 1 w 4 M 135.2045 183.0028 m 135.2045 185.6961 132.962 187.8794 130.1959 187.8794 c 127.4297 187.8794 125.1872 185.6961 125.1872 183.0028 c F 125.1872 183.0028 m 125.1872 180.3095 127.4297 178.1262 130.1959 178.1262 c 132.962 178.1262 135.2045 180.3095 135.2045 183.0028 c F 130.1959 183.0028 m F 0 G 0.3 w 10 M 130.1959 183.0028 m S 0 g 1 w 4 M 130.1959 183.0028 m F 0 G 0.3 w 10 M 130.1959 183.0028 m S 130.1959 183.0028 m S 0 g 1 w 4 M 131.1001 183.8955 m 131.1001 186.8858 L 129.2916 186.8858 L 129.2916 183.8955 L 126.3036 183.9049 L 126.3036 182.1005 L 129.2916 182.1098 L 129.2916 179.1195 L 131.1001 179.1195 L 131.1001 182.1098 L 134.0881 182.1005 L 134.0881 183.9049 L 131.1001 183.8955 L f 0 G 0.3 w 10 M 168.2125 183.0028 m S 0 g 1 w 4 M 168.2125 183.0028 m F 0 G 0.3 w 10 M 168.2125 183.0028 m S 168.2125 183.0028 m S 168.2125 183.0028 m S 0 g 1 w 4 M 168.2125 183.0028 m F 0 G 0.3 w 10 M 168.2125 183.0028 m S 168.2125 183.0028 m S 1 g 1 w 4 M 173.2211 183.0028 m 173.2211 185.6961 170.9786 187.8794 168.2125 187.8794 c 165.4463 187.8794 163.2038 185.6961 163.2038 183.0028 c F 163.2038 183.0028 m 163.2038 180.3095 165.4463 178.1262 168.2125 178.1262 c 170.9786 178.1262 173.2211 180.3095 173.2211 183.0028 c F 168.2125 183.0028 m F 0 G 0.3 w 10 M 168.2125 183.0028 m S 0 g 1 w 4 M 168.2125 183.0028 m F 0 G 0.3 w 10 M 168.2125 183.0028 m S 168.2125 183.0028 m S 0 g 1 w 4 M 169.1167 183.8955 m 169.1167 186.8858 L 167.3082 186.8858 L 167.3082 183.8955 L 164.3202 183.9049 L 164.3202 182.1005 L 167.3082 182.1098 L 167.3082 179.1195 L 169.1167 179.1195 L 169.1167 182.1098 L 172.1047 182.1005 L 172.1047 183.9049 L 169.1167 183.8955 L f 0 G 0.3 w 10 M 92.1792 145.8386 m S 92.1792 164.4206 m S 92.1792 108.6744 m S 92.1792 127.2564 m S 92.1792 127.2564 m S 92.1792 145.8386 m S 130.1779 108.6744 m S 130.1779 127.2564 m S 92.1792 127.2564 m S 92.1792 108.6744 m S 139.7001 117.9654 m S 92.0895 145.8386 m S 92.0895 164.4206 m S 111.1337 164.4206 m S 111.1337 145.8386 m S 101.6117 155.1296 m S 111.1337 145.8386 m S 130.1779 145.8386 m S 130.1779 127.2564 m S 120.6558 136.5475 m S 111.1337 108.6744 m S 130.1779 127.2564 m S 130.1779 108.6744 m S 120.6558 117.9654 m S 92.0895 108.6744 m S 111.1337 108.6744 m S 101.6117 117.9654 m S 92.0895 145.8386 m S 111.1337 145.8386 m S 101.6117 136.5475 m S 111.1337 145.8386 m S 111.1337 164.4206 m S 130.1779 164.4206 m S 130.1779 145.8386 m S 120.6558 155.1296 m S 130.1779 145.8386 m S 130.1779 164.4206 m S 92.1792 164.4206 m S 92.1792 145.8386 m S 139.7001 155.1296 m S 130.1779 127.2564 m S 130.1779 145.8386 m S 92.1792 145.8386 m S 92.1792 127.2564 m S 139.7001 136.5475 m S 0 g 1 w 4 M 139.7001 117.9654 m F 101.6117 117.9654 m F 139.7001 155.1296 m F 101.6117 155.1296 m F 0 G 0.3 w 10 M 73.0454 108.6744 m S 92.0895 108.6744 m S 82.5675 117.9654 m S 34.957 145.8386 m S 34.957 164.4206 m S 54.0012 164.4206 m S 54.0012 145.8386 m S 44.4791 155.1296 m S 54.0012 127.2564 m S 54.0012 145.8386 m S 73.0454 145.8386 m S 63.5233 136.5475 m S 54.0012 108.6744 m S 54.0012 127.2564 m S 73.0454 108.6744 m S 63.5233 117.9654 m S 34.957 108.6744 m S 34.957 127.2564 m S 54.0012 127.2564 m S 54.0012 108.6744 m S 44.4791 117.9654 m S 34.957 127.2564 m S 34.957 145.8386 m S 54.0012 145.8386 m S 54.0012 127.2564 m S 44.4791 136.5475 m S 54.0012 145.8386 m S 54.0012 164.4206 m S 73.0454 164.4206 m S 73.0454 145.8386 m S 63.5233 155.1296 m S 73.0454 145.8386 m S 73.0454 164.4206 m S 92.0895 164.4206 m S 92.0895 145.8386 m S 82.5675 155.1296 m S 73.0454 145.8386 m S 92.0895 145.8386 m S 82.5675 136.5475 m S 0 g 1 w 4 M 82.5675 117.9654 m F 44.4791 117.9654 m F 82.5675 155.1296 m F 44.4791 155.1296 m F 0 G 0.3 w 10 M 92.1792 201.5848 m S 92.1792 220.1669 m S 92.1792 164.4206 m S 92.1792 183.0028 m S 92.1792 183.0028 m S 92.1792 201.5848 m S 130.1779 164.4206 m S 130.1779 183.0028 m S 92.1792 183.0028 m S 92.1792 164.4206 m S 139.7001 173.7117 m S 92.0895 201.5848 m S 92.0895 220.1669 m S 111.1337 220.1669 m S 111.1337 201.5848 m S 101.6117 210.8759 m S 111.1337 183.0028 m S 111.1337 201.5848 m S 130.1779 201.5848 m S 130.1779 183.0028 m S 120.6558 192.2937 m S 111.1337 164.4206 m S 111.1337 183.0028 m S 130.1779 183.0028 m S 130.1779 164.4206 m S 120.6558 173.7117 m S 92.0895 164.4206 m S 92.0895 183.0028 m S 111.1337 183.0028 m S 111.1337 164.4206 m S 101.6117 173.7117 m S 92.0895 183.0028 m S 92.0895 201.5848 m S 111.1337 201.5848 m S 111.1337 183.0028 m S 101.6117 192.2937 m S 111.1337 201.5848 m S 111.1337 220.1669 m S 130.1779 220.1669 m S 130.1779 201.5848 m S 120.6558 210.8759 m S 130.1779 201.5848 m S 130.1779 220.1669 m S 92.1792 220.1669 m S 92.1792 201.5848 m S 139.7001 210.8759 m S 130.1779 183.0028 m S 130.1779 201.5848 m S 92.1792 201.5848 m S 92.1792 183.0028 m S 139.7001 192.2937 m S 0 g 1 w 4 M 139.7001 173.7117 m F 101.6117 173.7117 m F 139.7001 210.8759 m F 101.6117 210.8759 m F 0 G 0.3 w 10 M 73.0454 164.4206 m S 73.0454 183.0028 m S 92.0895 183.0028 m S 92.0895 164.4206 m S 82.5675 173.7117 m S 34.957 201.5848 m S 34.957 220.1669 m S 54.0012 220.1669 m S 54.0012 201.5848 m S 44.4791 210.8759 m S 54.0012 183.0028 m S 54.0012 201.5848 m S 73.0454 201.5848 m S 73.0454 183.0028 m S 63.5233 192.2937 m S 54.0012 164.4206 m S 54.0012 183.0028 m S 73.0454 183.0028 m S 73.0454 164.4206 m S 63.5233 173.7117 m S 34.957 164.4206 m S 34.957 183.0028 m S 54.0012 183.0028 m S 54.0012 164.4206 m S 44.4791 173.7117 m S 34.957 183.0028 m S 34.957 201.5848 m S 54.0012 201.5848 m S 54.0012 183.0028 m S 44.4791 192.2937 m S 54.0012 201.5848 m S 54.0012 220.1669 m S 73.0454 220.1669 m S 73.0454 201.5848 m S 63.5233 210.8759 m S 73.0454 201.5848 m S 73.0454 220.1669 m S 92.0895 220.1669 m S 92.0895 201.5848 m S 82.5675 210.8759 m S 73.0454 183.0028 m S 73.0454 201.5848 m S 92.0895 201.5848 m S 92.0895 183.0028 m S 82.5675 192.2937 m S 0 g 1 w 4 M 82.5675 173.7117 m F 44.4791 173.7117 m F 82.5675 210.8759 m F 44.4791 210.8759 m F 0 G 0.3 w 10 M 92.1792 220.1669 m S 130.1779 220.1669 m S 92.1792 220.1669 m S 111.1337 220.1669 m S 130.1779 220.1669 m S 92.0895 220.1669 m S 111.1337 220.1669 m S 73.0454 220.1669 m S 92.0895 220.1669 m S 54.0012 220.1669 m S 73.0454 220.1669 m S 34.957 220.1669 m S 54.0012 220.1669 m S 130.1779 108.6744 m S 130.1779 127.2564 m S 92.1792 127.2564 m S 92.1792 108.6744 m S 139.7001 117.9654 m S 92.0895 145.8386 m S 92.0895 164.4206 m S 111.1337 164.4206 m S 111.1337 145.8386 m S 111.1337 145.8386 m S 130.1779 145.8386 m S 130.1779 127.2564 m S 120.6558 136.5475 m S 111.1337 108.6744 m S 130.1779 127.2564 m S 130.1779 108.6744 m S 120.6558 117.9654 m S 92.0895 108.6744 m S 111.1337 108.6744 m S 101.6117 117.9654 m S 92.0895 145.8386 m S 111.1337 145.8386 m S 101.6117 136.5475 m S 111.1337 145.8386 m S 111.1337 164.4206 m S 130.1779 164.4206 m S 130.1779 145.8386 m S 130.1779 145.8386 m S 130.1779 164.4206 m S 92.1792 164.4206 m S 92.1792 145.8386 m S 139.7001 155.1296 m S 130.1779 127.2564 m S 130.1779 145.8386 m S 92.1792 145.8386 m S 92.1792 127.2564 m S 139.7001 136.5475 m S 0 g 1 w 4 M 139.7001 117.9654 m F 101.6117 117.9654 m F 139.7001 155.1296 m F 0 G 0.3 w 10 M 73.0454 108.6744 m S 92.0895 108.6744 m S 82.5675 117.9654 m S 34.957 145.8386 m S 34.957 164.4206 m S 54.0012 164.4206 m S 54.0012 145.8386 m S 44.4791 155.1296 m S 54.0012 127.2564 m S 54.0012 145.8386 m S 73.0454 145.8386 m S 63.5233 136.5475 m S 54.0012 108.6744 m S 54.0012 127.2564 m S 73.0454 108.6744 m S 63.5233 117.9654 m S 34.957 108.6744 m S 34.957 127.2564 m S 54.0012 127.2564 m S 54.0012 108.6744 m S 44.4791 117.9654 m S 34.957 127.2564 m S 34.957 145.8386 m S 54.0012 145.8386 m S 54.0012 127.2564 m S 44.4791 136.5475 m S 54.0012 145.8386 m S 54.0012 164.4206 m S 73.0454 164.4206 m S 73.0454 145.8386 m S 63.5233 155.1296 m S 73.0454 145.8386 m S 73.0454 164.4206 m S 92.0895 164.4206 m S 92.0895 145.8386 m S 82.5675 155.1296 m S 73.0454 145.8386 m S 92.0895 145.8386 m S 82.5675 136.5475 m S 0 g 1 w 4 M 82.5675 117.9654 m F 44.4791 117.9654 m F 82.5675 155.1296 m F 44.4791 155.1296 m F 0 G 0.3 w 10 M 130.1779 164.4206 m S 130.1779 183.0028 m S 92.1792 183.0028 m S 92.1792 164.4206 m S 139.7001 173.7117 m S 92.0895 201.5848 m S 92.0895 220.1669 m S 111.1337 220.1669 m S 111.1337 201.5848 m S 101.6117 210.8759 m S 111.1337 183.0028 m S 111.1337 201.5848 m S 130.1779 201.5848 m S 130.1779 183.0028 m S 120.6558 192.2937 m S 111.1337 164.4206 m S 111.1337 183.0028 m S 130.1779 183.0028 m S 130.1779 164.4206 m S 120.6558 173.7117 m S 92.0895 164.4206 m S 92.0895 183.0028 m S 111.1337 183.0028 m S 111.1337 164.4206 m S 92.0895 183.0028 m S 92.0895 201.5848 m S 111.1337 201.5848 m S 111.1337 183.0028 m S 101.6117 192.2937 m S 111.1337 201.5848 m S 111.1337 220.1669 m S 130.1779 220.1669 m S 130.1779 201.5848 m S 120.6558 210.8759 m S 130.1779 201.5848 m S 130.1779 220.1669 m S 92.1792 220.1669 m S 92.1792 201.5848 m S 139.7001 210.8759 m S 130.1779 183.0028 m S 130.1779 201.5848 m S 92.1792 201.5848 m S 92.1792 183.0028 m S 139.7001 192.2937 m S 0 g 1 w 4 M 139.7001 173.7117 m F 139.7001 210.8759 m F 101.6117 210.8759 m F 0 G 0.3 w 10 M 73.0454 164.4206 m S 73.0454 183.0028 m S 92.0895 183.0028 m S 92.0895 164.4206 m S 82.5675 173.7117 m S 34.957 201.5848 m S 34.957 220.1669 m S 54.0012 220.1669 m S 54.0012 201.5848 m S 44.4791 210.8759 m S 54.0012 183.0028 m S 54.0012 201.5848 m S 73.0454 201.5848 m S 73.0454 183.0028 m S 63.5233 192.2937 m S 54.0012 164.4206 m S 54.0012 183.0028 m S 73.0454 183.0028 m S 73.0454 164.4206 m S 63.5233 173.7117 m S 34.957 164.4206 m S 34.957 183.0028 m S 54.0012 183.0028 m S 54.0012 164.4206 m S 44.4791 173.7117 m S 34.957 183.0028 m S 34.957 201.5848 m S 54.0012 201.5848 m S 54.0012 183.0028 m S 44.4791 192.2937 m S 54.0012 201.5848 m S 54.0012 220.1669 m S 73.0454 220.1669 m S 73.0454 201.5848 m S 63.5233 210.8759 m S 73.0454 201.5848 m S 73.0454 220.1669 m S 92.0895 220.1669 m S 92.0895 201.5848 m S 82.5675 210.8759 m S 73.0454 183.0028 m S 73.0454 201.5848 m S 92.0895 201.5848 m S 92.0895 183.0028 m S 82.5675 192.2937 m S 0 g 1 w 4 M 82.5675 173.7117 m F 44.4791 173.7117 m F 82.5675 210.8759 m F 44.4791 210.8759 m F 0 G 0.3 w 10 M 130.1779 220.1669 m S 92.1792 220.1669 m S 111.1337 220.1669 m S 130.1779 220.1669 m S 92.0895 220.1669 m S 111.1337 220.1669 m S 73.0454 220.1669 m S 92.0895 220.1669 m S 54.0012 220.1669 m S 73.0454 220.1669 m S 34.957 220.1669 m S 54.0012 220.1669 m S 1 w 4 M 139.7001 136.5475 m 44.4791 136.5475 l S 139.7001 192.2937 m 44.4791 192.2937 l S 63.5233 117.9654 m 63.5233 210.8759 l S 0.3 w 10 M 130.1779 145.8386 m S 0 g 1 w 4 M 130.1779 145.8386 m F 0 G 0.3 w 10 M 130.1779 145.8386 m S 130.1779 145.8386 m S 130.1779 145.8386 m S 0 g 1 w 4 M 130.1779 145.8386 m F 0 G 0.3 w 10 M 130.1779 145.8386 m S 130.1779 145.8386 m S 1 g 1 w 4 M 130.1779 145.8386 m F 0 G 0.3 w 10 M 130.1779 145.8386 m S 0 g 1 w 4 M 130.1779 145.8386 m F 0 G 0.3 w 10 M 130.1779 145.8386 m S 130.1779 145.8386 m S 130.1779 164.4206 m S 0 g 1 w 4 M 130.1779 164.4206 m F 0 G 0.3 w 10 M 130.1779 164.4206 m S 130.1779 164.4206 m S 130.1779 164.4206 m S 0 g 1 w 4 M 130.1779 164.4206 m F 0 G 0.3 w 10 M 130.1779 164.4206 m S 130.1779 164.4206 m S 1 g 1 w 4 M 130.1779 164.4206 m F 0 G 0.3 w 10 M 130.1779 164.4206 m S 0 g 1 w 4 M 130.1779 164.4206 m F 0 G 0.3 w 10 M 130.1779 164.4206 m S 130.1779 164.4206 m S 130.1779 183.0028 m S 0 g 1 w 4 M 130.1779 183.0028 m F 0 G 0.3 w 10 M 130.1779 183.0028 m S 130.1779 183.0028 m S 130.1779 183.0028 m S 0 g 1 w 4 M 130.1779 183.0028 m F 0 G 0.3 w 10 M 130.1779 183.0028 m S 130.1779 183.0028 m S 1 g 1 w 4 M 130.1779 183.0028 m F 0 G 0.3 w 10 M 130.1779 183.0028 m S 0 g 1 w 4 M 130.1779 183.0028 m F 0 G 0.3 w 10 M 130.1779 183.0028 m S 130.1779 183.0028 m S 111.1337 201.5848 m S 111.1337 201.5848 m S 92.0895 201.5848 m S 111.1337 201.5848 m S 92.0895 201.5848 m S 111.1337 201.5848 m S 73.0454 201.5848 m S 92.0895 201.5848 m S 73.0454 201.5848 m S 73.0454 201.5848 m S 73.0454 201.5848 m S 92.0895 201.5848 m S 111.1337 201.5848 m S 0 g 1 w 4 M 111.1337 201.5848 m F 0 G 0.3 w 10 M 111.1337 201.5848 m S 111.1337 201.5848 m S 111.1337 201.5848 m S 0 g 1 w 4 M 111.1337 201.5848 m F 0 G 0.3 w 10 M 111.1337 201.5848 m S 111.1337 201.5848 m S 1 g 1 w 4 M 116.1518 201.5848 m 116.1518 204.2781 113.9051 206.4615 111.1337 206.4615 c 108.3623 206.4615 106.1156 204.2781 106.1156 201.5848 c F 106.1156 201.5848 m 106.1156 198.8916 108.3623 196.7082 111.1337 196.7082 c 113.9051 196.7082 116.1518 198.8916 116.1518 201.5848 c F 111.1337 201.5848 m F 0 G 0.3 w 10 M 111.1337 201.5848 m S 0 g 1 w 4 M 111.1337 201.5848 m F 0 G 0.3 w 10 M 111.1337 201.5848 m S 111.1337 201.5848 m S 0 g 1 w 4 M 112.0396 202.4776 m 112.0396 205.4678 L 110.2277 205.4678 L 110.2277 202.4776 L 107.2341 202.4869 L 107.2341 200.6826 L 110.2277 200.6919 L 110.2277 197.7016 L 112.0396 197.7016 L 112.0396 200.6919 L 115.0333 200.6826 L 115.0333 202.4869 L 112.0396 202.4776 L f 0 G 0.3 w 10 M 92.0895 201.5848 m S 0 g 1 w 4 M 92.0895 201.5848 m F 0 G 0.3 w 10 M 92.0895 201.5848 m S 92.0895 201.5848 m S 92.0895 201.5848 m S 0 g 1 w 4 M 92.0895 201.5848 m F 0 G 0.3 w 10 M 92.0895 201.5848 m S 92.0895 201.5848 m S 1 g 1 w 4 M 97.1076 201.5848 m 97.1076 204.2781 94.8609 206.4615 92.0895 206.4615 c 89.3182 206.4615 87.0715 204.2781 87.0715 201.5848 c F 87.0715 201.5848 m 87.0715 198.8916 89.3182 196.7082 92.0895 196.7082 c 94.8609 196.7082 97.1076 198.8916 97.1076 201.5848 c F 92.0895 201.5848 m F 0 G 0.3 w 10 M 92.0895 201.5848 m S 0 g 1 w 4 M 92.0895 201.5848 m F 0 G 0.3 w 10 M 92.0895 201.5848 m S 92.0895 201.5848 m S 0 g 1 w 4 M 92.9955 202.4776 m 92.9955 205.4678 L 91.1836 205.4678 L 91.1836 202.4776 L 88.19 202.4869 L 88.19 200.6826 L 91.1836 200.6919 L 91.1836 197.7016 L 92.9955 197.7016 L 92.9955 200.6919 L 95.9891 200.6826 L 95.9891 202.4869 L 92.9955 202.4776 L f 0 G 0.3 w 10 M 73.0454 201.5848 m S 0 g 1 w 4 M 73.0454 201.5848 m F 0 G 0.3 w 10 M 73.0454 201.5848 m S 73.0454 201.5848 m S 73.0454 201.5848 m S 0 g 1 w 4 M 73.0454 201.5848 m F 0 G 0.3 w 10 M 73.0454 201.5848 m S 73.0454 201.5848 m S 1 g 1 w 4 M 78.0635 201.5848 m 78.0635 204.2781 75.8168 206.4615 73.0454 206.4615 c 70.274 206.4615 68.0273 204.2781 68.0273 201.5848 c F 68.0273 201.5848 m 68.0273 198.8916 70.274 196.7082 73.0454 196.7082 c 75.8168 196.7082 78.0635 198.8916 78.0635 201.5848 c F 73.0454 201.5848 m F 0 G 0.3 w 10 M 73.0454 201.5848 m S 0 g 1 w 4 M 73.0454 201.5848 m F 0 G 0.3 w 10 M 73.0454 201.5848 m S 73.0454 201.5848 m S 0 g 1 w 4 M 73.9513 202.4776 m 73.9513 205.4678 L 72.1394 205.4678 L 72.1394 202.4776 L 69.1458 202.4869 L 69.1458 200.6826 L 72.1394 200.6919 L 72.1394 197.7016 L 73.9513 197.7016 L 73.9513 200.6919 L 76.945 200.6826 L 76.945 202.4869 L 73.9513 202.4776 L f 0 G 0.3 w 10 M 54.0012 145.8386 m S 54.0012 164.4206 m S 54.0012 145.8386 m S 54.0012 145.8386 m S 54.0012 164.4206 m S 54.0012 145.8386 m S 54.0012 164.4206 m S 54.0012 183.0028 m S 54.0012 183.0028 m S 54.0012 183.0028 m S 54.0012 164.4206 m S 54.0012 183.0028 m S 54.0012 145.8386 m S 0 g 1 w 4 M 54.0012 145.8386 m F 0 G 0.3 w 10 M 54.0012 145.8386 m S 54.0012 145.8386 m S 54.0012 145.8386 m S 0 g 1 w 4 M 54.0012 145.8386 m F 0 G 0.3 w 10 M 54.0012 145.8386 m S 54.0012 145.8386 m S 1 g 1 w 4 M 54.0012 145.8386 m F 0 G 0.3 w 10 M 54.0012 145.8386 m S 0 g 1 w 4 M 54.0012 145.8386 m F 0 G 0.3 w 10 M 54.0012 145.8386 m S 54.0012 145.8386 m S 54.0012 164.4206 m S 0 g 1 w 4 M 54.0012 164.4206 m F 0 G 0.3 w 10 M 54.0012 164.4206 m S 54.0012 164.4206 m S 54.0012 164.4206 m S 0 g 1 w 4 M 54.0012 164.4206 m F 0 G 0.3 w 10 M 54.0012 164.4206 m S 54.0012 164.4206 m S 1 g 1 w 4 M 54.0012 164.4206 m F 0 G 0.3 w 10 M 54.0012 164.4206 m S 0 g 1 w 4 M 54.0012 164.4206 m F 0 G 0.3 w 10 M 54.0012 164.4206 m S 54.0012 164.4206 m S 54.0012 183.0028 m S 0 g 1 w 4 M 54.0012 183.0028 m F 0 G 0.3 w 10 M 54.0012 183.0028 m S 54.0012 183.0028 m S 54.0012 183.0028 m S 0 g 1 w 4 M 54.0012 183.0028 m F 0 G 0.3 w 10 M 54.0012 183.0028 m S 54.0012 183.0028 m S 1 g 1 w 4 M 54.0012 183.0028 m F 0 G 0.3 w 10 M 54.0012 183.0028 m S 0 g 1 w 4 M 54.0012 183.0028 m F 0 G 0.3 w 10 M 54.0012 183.0028 m S 54.0012 183.0028 m S 101.6117 155.1296 m S 101.6117 155.1296 m S 82.5675 155.1296 m S 101.6117 155.1296 m S 82.5675 155.1296 m S 82.5675 155.1296 m S 82.5675 155.1296 m S 101.6117 155.1296 m S 101.6117 173.7117 m S 101.6117 173.7117 m S 82.5675 173.7117 m S 101.6117 173.7117 m S 82.5675 173.7117 m S 82.5675 173.7117 m S 82.5675 173.7117 m S 101.6117 173.7117 m S 111.1337 145.8386 m S 0 g 1 w 4 M 111.1337 145.8386 m F 0 G 0.3 w 10 M 111.1337 145.8386 m S 0 g 1 w 4 M 111.1337 145.8386 m F 1 g 116.1518 145.8386 m 116.1518 148.5318 113.9051 150.7152 111.1337 150.7152 c 108.3623 150.7152 106.1156 148.5318 106.1156 145.8386 c F 106.1156 145.8386 m 106.1156 143.1453 108.3623 140.962 111.1337 140.962 c 113.9051 140.962 116.1518 143.1453 116.1518 145.8386 c F 111.1337 145.8386 m F 0 G 0.3 w 10 M 111.1337 145.8386 m S 0 g 1 w 4 M 111.1337 145.8386 m F 0 G 0.3 w 10 M 111.1337 145.8386 m S 0 g 1 w 4 M 111.1337 145.8386 m F 112.0396 144.9456 m 115.0333 144.9363 L 115.0333 146.7406 L 112.0396 146.7314 L F 110.2277 146.7314 m 107.2341 146.7406 L 107.2341 144.9363 L 110.2277 144.9456 L F 115.0333 144.9363 m 107.2341 144.9363 l 107.2341 146.7406 l 115.0333 146.7406 l 115.0333 144.9363 l f 0 G 0.3 w 10 M 92.0895 145.8386 m S 0 g 1 w 4 M 92.0895 145.8386 m F 0 G 0.3 w 10 M 92.0895 145.8386 m S 0 g 1 w 4 M 92.0895 145.8386 m F 1 g 97.1076 145.8386 m 97.1076 148.5318 94.8609 150.7152 92.0895 150.7152 c 89.3182 150.7152 87.0715 148.5318 87.0715 145.8386 c F 87.0715 145.8386 m 87.0715 143.1453 89.3182 140.962 92.0895 140.962 c 94.8609 140.962 97.1076 143.1453 97.1076 145.8386 c F 92.0895 145.8386 m F 0 G 0.3 w 10 M 92.0895 145.8386 m S 0 g 1 w 4 M 92.0895 145.8386 m F 0 G 0.3 w 10 M 92.0895 145.8386 m S 0 g 1 w 4 M 92.0895 145.8386 m F 92.9955 144.9456 m 95.9891 144.9363 L 95.9891 146.7406 L 92.9955 146.7314 L F 91.1836 146.7314 m 88.19 146.7406 L 88.19 144.9363 L 91.1836 144.9456 L F 95.9891 144.9363 m 88.19 144.9363 l 88.19 146.7406 l 95.9891 146.7406 l 95.9891 144.9363 l f 0 G 0.3 w 10 M 73.0454 145.8386 m S 0 g 1 w 4 M 73.0454 145.8386 m F 0 G 0.3 w 10 M 73.0454 145.8386 m S 0 g 1 w 4 M 73.0454 145.8386 m F 1 g 78.0635 145.8386 m 78.0635 148.5318 75.8168 150.7152 73.0454 150.7152 c 70.274 150.7152 68.0273 148.5318 68.0273 145.8386 c F 68.0273 145.8386 m 68.0273 143.1453 70.274 140.962 73.0454 140.962 c 75.8168 140.962 78.0635 143.1453 78.0635 145.8386 c F 73.0454 145.8386 m F 0 G 0.3 w 10 M 73.0454 145.8386 m S 0 g 1 w 4 M 73.0454 145.8386 m F 0 G 0.3 w 10 M 73.0454 145.8386 m S 0 g 1 w 4 M 73.0454 145.8386 m F 73.9513 144.9456 m 76.945 144.9363 L 76.945 146.7406 L 73.9513 146.7314 L F 72.1394 146.7314 m 69.1458 146.7406 L 69.1458 144.9363 L 72.1394 144.9456 L F 76.945 144.9363 m 69.1458 144.9363 l 69.1458 146.7406 l 76.945 146.7406 l 76.945 144.9363 l f 0 G 0.3 w 10 M 73.0454 164.4206 m S 0 g 1 w 4 M 73.0454 164.4206 m F 0 G 0.3 w 10 M 73.0454 164.4206 m S 0 g 1 w 4 M 73.0454 164.4206 m F 1 g 73.0454 164.4206 m F 0 G 0.3 w 10 M 73.0454 164.4206 m S 0 g 1 w 4 M 73.0454 164.4206 m F 0 G 0.3 w 10 M 73.0454 164.4206 m S 0 g 1 w 4 M 73.0454 164.4206 m F 0 G 0.3 w 10 M 92.0895 164.4206 m S 0 g 1 w 4 M 92.0895 164.4206 m F 0 G 0.3 w 10 M 92.0895 164.4206 m S 0 g 1 w 4 M 92.0895 164.4206 m F 1 g 92.0895 164.4206 m F 0 G 0.3 w 10 M 92.0895 164.4206 m S 0 g 1 w 4 M 92.0895 164.4206 m F 0 G 0.3 w 10 M 92.0895 164.4206 m S 0 g 1 w 4 M 92.0895 164.4206 m F 0 G 0.3 w 10 M 111.1337 164.4206 m S 0 g 1 w 4 M 111.1337 164.4206 m F 0 G 0.3 w 10 M 111.1337 164.4206 m S 111.1337 164.4206 m S 111.1337 164.4206 m S 0 g 1 w 4 M 111.1337 164.4206 m F 0 G 0.3 w 10 M 111.1337 164.4206 m S 111.1337 164.4206 m S 1 g 1 w 4 M 111.1337 164.4206 m F 0 G 0.3 w 10 M 111.1337 164.4206 m S 0 g 1 w 4 M 111.1337 164.4206 m F 0 G 0.3 w 10 M 111.1337 164.4206 m S 111.1337 164.4206 m S 92.0895 183.0028 m S 0 g 1 w 4 M 92.0895 183.0028 m F 0 G 0.3 w 10 M 92.0895 183.0028 m S 92.0895 183.0028 m S 92.0895 183.0028 m S 0 g 1 w 4 M 92.0895 183.0028 m F 0 G 0.3 w 10 M 92.0895 183.0028 m S 92.0895 183.0028 m S 1 g 1 w 4 M 97.1076 183.0028 m 97.1076 185.696 94.8609 187.8794 92.0895 187.8794 c 89.3182 187.8794 87.0715 185.696 87.0715 183.0028 c F 87.0715 183.0028 m 87.0715 180.3095 89.3182 178.1262 92.0895 178.1262 c 94.8609 178.1262 97.1076 180.3095 97.1076 183.0028 c F 92.0895 183.0028 m F 0 G 0.3 w 10 M 92.0895 183.0028 m S 0 g 1 w 4 M 92.0895 183.0028 m F 0 G 0.3 w 10 M 92.0895 183.0028 m S 92.0895 183.0028 m S 0 g 1 w 4 M 92.9955 183.8955 m 92.9955 186.8858 L 91.1836 186.8858 L 91.1836 183.8955 L 88.19 183.9048 L 88.19 182.1005 L 91.1836 182.1098 L 91.1836 179.1195 L 92.9955 179.1195 L 92.9955 182.1098 L 95.9891 182.1005 L 95.9891 183.9048 L 92.9955 183.8955 L f 0 G 0.3 w 10 M 73.0454 183.0028 m S 0 g 1 w 4 M 73.0454 183.0028 m F 0 G 0.3 w 10 M 73.0454 183.0028 m S 73.0454 183.0028 m S 73.0454 183.0028 m S 0 g 1 w 4 M 73.0454 183.0028 m F 0 G 0.3 w 10 M 73.0454 183.0028 m S 73.0454 183.0028 m S 1 g 1 w 4 M 78.0635 183.0028 m 78.0635 185.696 75.8168 187.8794 73.0454 187.8794 c 70.274 187.8794 68.0273 185.696 68.0273 183.0028 c F 68.0273 183.0028 m 68.0273 180.3095 70.274 178.1262 73.0454 178.1262 c 75.8168 178.1262 78.0635 180.3095 78.0635 183.0028 c F 73.0454 183.0028 m F 0 G 0.3 w 10 M 73.0454 183.0028 m S 0 g 1 w 4 M 73.0454 183.0028 m F 0 G 0.3 w 10 M 73.0454 183.0028 m S 73.0454 183.0028 m S 0 g 1 w 4 M 73.9513 183.8955 m 73.9513 186.8858 L 72.1394 186.8858 L 72.1394 183.8955 L 69.1458 183.9048 L 69.1458 182.1005 L 72.1394 182.1098 L 72.1394 179.1195 L 73.9513 179.1195 L 73.9513 182.1098 L 76.945 182.1005 L 76.945 183.9048 L 73.9513 183.8955 L f 0 G 0.3 w 10 M 111.1337 183.0028 m S 0 g 1 w 4 M 111.1337 183.0028 m F 0 G 0.3 w 10 M 111.1337 183.0028 m S 111.1337 183.0028 m S 111.1337 183.0028 m S 0 g 1 w 4 M 111.1337 183.0028 m F 0 G 0.3 w 10 M 111.1337 183.0028 m S 111.1337 183.0028 m S 1 g 1 w 4 M 116.1518 183.0028 m 116.1518 185.696 113.9051 187.8794 111.1337 187.8794 c 108.3623 187.8794 106.1156 185.696 106.1156 183.0028 c F 106.1156 183.0028 m 106.1156 180.3095 108.3623 178.1262 111.1337 178.1262 c 113.9051 178.1262 116.1518 180.3095 116.1518 183.0028 c F 111.1337 183.0028 m F 0 G 0.3 w 10 M 111.1337 183.0028 m S 0 g 1 w 4 M 111.1337 183.0028 m F 0 G 0.3 w 10 M 111.1337 183.0028 m S 111.1337 183.0028 m S 0 g 1 w 4 M 112.0396 183.8955 m 112.0396 186.8858 L 110.2277 186.8858 L 110.2277 183.8955 L 107.2341 183.9048 L 107.2341 182.1005 L 110.2277 182.1098 L 110.2277 179.1195 L 112.0396 179.1195 L 112.0396 182.1098 L 115.0333 182.1005 L 115.0333 183.9048 L 112.0396 183.8955 L f 0 G 0.3 w 10 M 187.2208 145.8386 m S 187.2208 145.8386 m S 187.2208 145.8386 m S 187.2208 145.8386 m S 187.2208 145.8386 m S 187.2208 145.8386 m S 187.2208 145.8386 m S 187.2208 145.8386 m S 187.2208 145.8386 m S 0 g 1 w 4 M 187.2208 145.8386 m F 0 G 0.3 w 10 M 187.2208 145.8386 m S 0 g 1 w 4 M 187.2208 145.8386 m F 1 g 187.2208 145.8386 m F 0 G 0.3 w 10 M 187.2208 145.8386 m S 0 g 1 w 4 M 187.2208 145.8386 m F 0 G 0.3 w 10 M 187.2208 145.8386 m S 0 g 1 w 4 M 187.2208 145.8386 m F 0 G 0.3 w 10 M 111.1337 164.4206 m S 111.1337 164.4206 m S 111.1337 164.4206 m S 111.1337 164.4206 m S 111.1337 164.4206 m S 111.1337 164.4206 m S 111.1337 164.4206 m S 111.1337 164.4206 m S 111.1337 164.4206 m S 0 g 1 w 4 M 111.1337 164.4206 m F 0 G 0.3 w 10 M 111.1337 164.4206 m S 0 g 1 w 4 M 111.1337 164.4206 m F 1 g 116.1423 164.4206 m 116.1423 167.1139 113.8998 169.2972 111.1337 169.2972 c 108.3675 169.2972 106.1251 167.1139 106.1251 164.4206 c F 106.1251 164.4206 m 106.1251 161.7273 108.3675 159.544 111.1337 159.544 c 113.8998 159.544 116.1423 161.7273 116.1423 164.4206 c F 111.1337 164.4206 m F 0 G 0.3 w 10 M 111.1337 164.4206 m S 0 g 1 w 4 M 111.1337 164.4206 m F 0 G 0.3 w 10 M 111.1337 164.4206 m S 0 g 1 w 4 M 111.1337 164.4206 m F 112.0379 163.5276 m 115.0259 163.5184 L 115.0259 165.3227 L 112.0379 165.3134 L F 110.2295 165.3134 m 107.2415 165.3227 L 107.2415 163.5184 L 110.2295 163.5276 L F 115.0259 163.5184 m 107.2415 163.5184 l 107.2415 165.3227 l 115.0259 165.3227 l 115.0259 163.5184 l f 0 G 0.3 w 10 M 92.1792 164.4206 m S 92.1792 164.4206 m S 92.1792 164.4206 m S 92.1792 164.4206 m S 92.1792 164.4206 m S 92.1792 164.4206 m S 92.1792 164.4206 m S 92.0895 164.4206 m S 92.0895 164.4206 m S 92.1792 164.4206 m S 73.0454 164.4206 m S 92.0895 164.4206 m S 73.0454 164.4206 m S 73.0454 164.4206 m S 73.0454 164.4206 m S 92.0895 164.4206 m S 92.1792 164.4206 m S 92.0895 164.4206 m S 92.0895 164.4206 m S 92.1792 164.4206 m S 73.0454 164.4206 m S 92.0895 164.4206 m S 73.0454 164.4206 m S 73.0454 164.4206 m S 73.0454 164.4206 m S 92.0895 164.4206 m S 92.0895 164.4206 m S 0 g 1 w 4 M 92.0895 164.4206 m F 0 G 0.3 w 10 M 92.0895 164.4206 m S 92.0895 164.4206 m S 92.0895 164.4206 m S 0 g 1 w 4 M 92.0895 164.4206 m F 0 G 0.3 w 10 M 92.0895 164.4206 m S 92.0895 164.4206 m S 1 g 1 w 4 M 97.1076 164.4206 m 97.1076 167.1139 94.8609 169.2972 92.0895 169.2972 c 89.3182 169.2972 87.0715 167.1139 87.0715 164.4206 c F 87.0715 164.4206 m 87.0715 161.7274 89.3182 159.544 92.0895 159.544 c 94.8609 159.544 97.1076 161.7274 97.1076 164.4206 c F 92.0895 164.4206 m F 0 G 0.3 w 10 M 92.0895 164.4206 m S 0 g 1 w 4 M 92.0895 164.4206 m F 0 G 0.3 w 10 M 92.0895 164.4206 m S 92.0895 164.4206 m S 0 g 1 w 4 M 92.9955 165.3133 m 92.9955 168.3036 L 91.1836 168.3036 L 91.1836 165.3133 L 88.19 165.3227 L 88.19 163.5184 L 91.1836 163.5277 L 91.1836 160.5374 L 92.9955 160.5374 L 92.9955 163.5277 L 95.9891 163.5184 L 95.9891 165.3227 L 92.9955 165.3133 L f 0 G 0.3 w 10 M 73.0454 164.4206 m S 0 g 1 w 4 M 73.0454 164.4206 m F 0 G 0.3 w 10 M 73.0454 164.4206 m S 73.0454 164.4206 m S 73.0454 164.4206 m S 0 g 1 w 4 M 73.0454 164.4206 m F 0 G 0.3 w 10 M 73.0454 164.4206 m S 73.0454 164.4206 m S 1 g 1 w 4 M 78.0635 164.4206 m 78.0635 167.1139 75.8168 169.2972 73.0454 169.2972 c 70.274 169.2972 68.0273 167.1139 68.0273 164.4206 c F 68.0273 164.4206 m 68.0273 161.7274 70.274 159.544 73.0454 159.544 c 75.8168 159.544 78.0635 161.7274 78.0635 164.4206 c F 73.0454 164.4206 m F 0 G 0.3 w 10 M 73.0454 164.4206 m S 0 g 1 w 4 M 73.0454 164.4206 m F 0 G 0.3 w 10 M 73.0454 164.4206 m S 73.0454 164.4206 m S 0 g 1 w 4 M 73.9513 165.3133 m 73.9513 168.3036 L 72.1394 168.3036 L 72.1394 165.3133 L 69.1458 165.3227 L 69.1458 163.5184 L 72.1394 163.5277 L 72.1394 160.5374 L 73.9513 160.5374 L 73.9513 163.5277 L 76.945 163.5184 L 76.945 165.3227 L 73.9513 165.3133 L f 0 G 0.3 w 10 M 53.9833 145.8385 m S 53.9833 164.4206 m S 53.9833 145.8385 m S 53.9833 145.8385 m S 53.9833 164.4206 m S 53.9833 145.8385 m S 53.9833 145.8385 m S 53.9833 164.4206 m S 53.9833 145.8385 m S 53.9833 145.8385 m S 53.9833 164.4206 m S 53.9833 145.8385 m S 54.0012 145.8386 m S 54.0012 164.4206 m S 54.0012 145.8386 m S 54.0012 145.8386 m S 54.0012 164.4206 m S 54.0012 145.8386 m S 54.0012 164.4206 m S 54.0012 183.0028 m S 54.0012 183.0028 m S 54.0012 183.0028 m S 54.0012 164.4206 m S 54.0012 183.0028 m S 54.0012 145.8386 m S 54.0012 164.4206 m S 54.0012 145.8386 m S 54.0012 145.8386 m S 54.0012 164.4206 m S 54.0012 145.8386 m S 54.0012 164.4206 m S 54.0012 183.0028 m S 54.0012 183.0028 m S 54.0012 183.0028 m S 54.0012 164.4206 m S 54.0012 183.0028 m S 54.0012 145.8386 m S 0 g 1 w 4 M 54.0012 145.8386 m F 0 G 0.3 w 10 M 54.0012 145.8386 m S 54.0012 145.8386 m S 54.0012 145.8386 m S 0 g 1 w 4 M 54.0012 145.8386 m F 0 G 0.3 w 10 M 54.0012 145.8386 m S 54.0012 145.8386 m S 1 g 1 w 4 M 54.0012 145.8386 m F 0 G 0.3 w 10 M 54.0012 145.8386 m S 0 g 1 w 4 M 54.0012 145.8386 m F 0 G 0.3 w 10 M 54.0012 145.8386 m S 54.0012 145.8386 m S 54.0012 164.4206 m S 0 g 1 w 4 M 54.0012 164.4206 m F 0 G 0.3 w 10 M 54.0012 164.4206 m S 54.0012 164.4206 m S 54.0012 164.4206 m S 0 g 1 w 4 M 54.0012 164.4206 m F 0 G 0.3 w 10 M 54.0012 164.4206 m S 54.0012 164.4206 m S 1 g 1 w 4 M 59.0098 164.4206 m 59.0098 167.1139 56.7673 169.2972 54.0012 169.2972 c 51.235 169.2972 48.9925 167.1139 48.9925 164.4206 c F 48.9925 164.4206 m 48.9925 161.7274 51.235 159.544 54.0012 159.544 c 56.7673 159.544 59.0098 161.7274 59.0098 164.4206 c F 54.0012 164.4206 m F 0 G 0.3 w 10 M 54.0012 164.4206 m S 0 g 1 w 4 M 54.0012 164.4206 m F 0 G 0.3 w 10 M 54.0012 164.4206 m S 54.0012 164.4206 m S 0 g 1 w 4 M 54.9054 165.3133 m 54.9054 168.3036 L 53.0969 168.3036 L 53.0969 165.3133 L 50.1089 165.3227 L 50.1089 163.5184 L 53.0969 163.5277 L 53.0969 160.5374 L 54.9054 160.5374 L 54.9054 163.5277 L 57.8934 163.5184 L 57.8934 165.3227 L 54.9054 165.3133 L f 0 G 0.3 w 10 M 54.0012 183.0028 m S 0 g 1 w 4 M 54.0012 183.0028 m F 0 G 0.3 w 10 M 54.0012 183.0028 m S 54.0012 183.0028 m S 54.0012 183.0028 m S 0 g 1 w 4 M 54.0012 183.0028 m F 0 G 0.3 w 10 M 54.0012 183.0028 m S 54.0012 183.0028 m S 1 g 1 w 4 M 59.0098 183.0028 m 59.0098 185.696 56.7673 187.8794 54.0012 187.8794 c 51.235 187.8794 48.9925 185.696 48.9925 183.0028 c F 48.9925 183.0028 m 48.9925 180.3095 51.235 178.1262 54.0012 178.1262 c 56.7673 178.1262 59.0098 180.3095 59.0098 183.0028 c F 54.0012 183.0028 m F 0 G 0.3 w 10 M 54.0012 183.0028 m S 0 g 1 w 4 M 54.0012 183.0028 m F 0 G 0.3 w 10 M 54.0012 183.0028 m S 54.0012 183.0028 m S 0 g 1 w 4 M 54.9054 183.8955 m 54.9054 186.8858 L 53.0969 186.8858 L 53.0969 183.8955 L 50.1089 183.9048 L 50.1089 182.1005 L 53.0969 182.1098 L 53.0969 179.1195 L 54.9054 179.1195 L 54.9054 182.1098 L 57.8934 182.1005 L 57.8934 183.9048 L 54.9054 183.8955 L f 0 G 0.3 w 10 M 54.0012 145.8386 m S 54.0012 145.8386 m S 54.0012 145.8386 m S 54.0012 145.8386 m S 54.0012 145.8386 m S 54.0012 145.8386 m S 54.0012 145.8386 m S 54.0012 145.8386 m S 54.0012 145.8386 m S 0 g 1 w 4 M 54.0012 145.8386 m F 0 G 0.3 w 10 M 54.0012 145.8386 m S 0 g 1 w 4 M 54.0012 145.8386 m F 1 g 59.0098 145.8386 m 59.0098 148.5318 56.7673 150.7152 54.0012 150.7152 c 51.235 150.7152 48.9925 148.5318 48.9925 145.8386 c F 48.9925 145.8386 m 48.9925 143.1453 51.235 140.962 54.0012 140.962 c 56.7673 140.962 59.0098 143.1453 59.0098 145.8386 c F 54.0012 145.8386 m F 0 G 0.3 w 10 M 54.0012 145.8386 m S 0 g 1 w 4 M 54.0012 145.8386 m F 0 G 0.3 w 10 M 54.0012 145.8386 m S 0 g 1 w 4 M 54.0012 145.8386 m F 54.9054 144.9456 m 57.8934 144.9363 L 57.8934 146.7406 L 54.9054 146.7314 L F 53.0969 146.7314 m 50.1089 146.7406 L 50.1089 144.9363 L 53.0969 144.9456 L F 57.8934 144.9363 m 50.1089 144.9363 l 50.1089 146.7406 l 57.8934 146.7406 l 57.8934 144.9363 l f 0 G 120.6558 210.8759 m 120.5484 62.2191 l S 0.3 w 10 M 149.2042 127.2564 m S 149.2042 108.6743 m S 149.2042 164.4206 m S 149.2042 145.8385 m S 149.2042 145.8385 m S 149.2042 127.2564 m S 168.2126 164.4206 m S 168.2126 145.8385 m S 149.2042 145.8385 m S 149.2042 164.4206 m S 158.7084 155.1295 m S 206.2292 127.2564 m S 206.2292 108.6743 m S 187.2209 108.6743 m S 187.2209 127.2564 m S 196.725 117.9653 m S 187.2209 145.8385 m S 187.2209 127.2564 m S 168.2126 127.2564 m S 168.2126 145.8385 m S 177.7167 136.5475 m S 187.2209 164.4206 m S 187.2209 145.8385 m S 168.2126 145.8385 m S 168.2126 164.4206 m S 177.7167 155.1295 m S 206.2292 164.4206 m S 206.2292 145.8385 m S 187.2209 145.8385 m S 187.2209 164.4206 m S 196.725 155.1295 m S 206.2292 145.8385 m S 206.2292 127.2564 m S 187.2209 127.2564 m S 187.2209 145.8385 m S 196.725 136.5475 m S 187.2209 127.2564 m S 187.2209 108.6743 m S 168.2126 108.6743 m S 168.2126 127.2564 m S 177.7167 117.9653 m S 168.2126 127.2564 m S 168.2126 108.6743 m S 149.2042 108.6743 m S 149.2042 127.2564 m S 158.7084 117.9653 m S 168.2126 145.8385 m S 168.2126 127.2564 m S 149.2042 127.2564 m S 149.2042 145.8385 m S 158.7084 136.5475 m S 0 g 1 w 4 M 158.7084 155.1295 m F 196.725 155.1295 m F 158.7084 117.9653 m F 196.725 117.9653 m F 0 G 0.3 w 10 M 225.2375 164.4206 m S 225.2375 145.8385 m S 206.2292 145.8385 m S 206.2292 164.4206 m S 215.7333 155.1295 m S 263.2542 127.2564 m S 263.2542 108.6743 m S 244.2459 108.6743 m S 244.2459 127.2564 m S 253.75 117.9653 m S 244.2459 145.8385 m S 244.2459 127.2564 m S 225.2375 127.2564 m S 225.2375 145.8385 m S 234.7417 136.5475 m S 244.2459 164.4206 m S 244.2459 145.8385 m S 225.2375 145.8385 m S 225.2375 164.4206 m S 234.7417 155.1295 m S 263.2542 164.4206 m S 263.2542 145.8385 m S 244.2459 145.8385 m S 244.2459 164.4206 m S 253.75 155.1295 m S 263.2542 145.8385 m S 263.2542 127.2564 m S 244.2459 127.2564 m S 244.2459 145.8385 m S 253.75 136.5475 m S 244.2459 127.2564 m S 244.2459 108.6743 m S 225.2375 108.6743 m S 225.2375 127.2564 m S 234.7417 117.9653 m S 225.2375 127.2564 m S 225.2375 108.6743 m S 206.2292 108.6743 m S 206.2292 127.2564 m S 215.7333 117.9653 m S 225.2375 145.8385 m S 225.2375 127.2564 m S 206.2292 127.2564 m S 206.2292 145.8385 m S 215.7333 136.5475 m S 0 g 1 w 4 M 215.7333 155.1295 m F 253.75 155.1295 m F 215.7333 117.9653 m F 253.75 117.9653 m F 0 G 0.3 w 10 M 149.2042 71.5101 m S 149.2042 52.9281 m S 149.2042 108.6743 m S 149.2042 90.0922 m S 149.2042 90.0922 m S 149.2042 71.5101 m S 168.2126 108.6743 m S 168.2126 90.0922 m S 149.2042 90.0922 m S 149.2042 108.6743 m S 158.7084 99.3833 m S 206.2292 71.5101 m S 206.2292 52.9281 m S 187.2209 52.9281 m S 187.2209 71.5101 m S 196.725 62.2191 m S 187.2209 90.0922 m S 187.2209 71.5101 m S 168.2126 71.5101 m S 168.2126 90.0922 m S 177.7167 80.8012 m S 187.2209 108.6743 m S 187.2209 90.0922 m S 168.2126 90.0922 m S 168.2126 108.6743 m S 177.7167 99.3833 m S 206.2292 108.6743 m S 206.2292 90.0922 m S 187.2209 90.0922 m S 187.2209 108.6743 m S 196.725 99.3833 m S 206.2292 90.0922 m S 206.2292 71.5101 m S 187.2209 71.5101 m S 187.2209 90.0922 m S 196.725 80.8012 m S 187.2209 71.5101 m S 187.2209 52.9281 m S 168.2126 52.9281 m S 168.2126 71.5101 m S 177.7167 62.2191 m S 168.2126 71.5101 m S 168.2126 52.9281 m S 149.2042 52.9281 m S 149.2042 71.5101 m S 158.7084 62.2191 m S 168.2126 90.0922 m S 168.2126 71.5101 m S 149.2042 71.5101 m S 149.2042 90.0922 m S 158.7084 80.8012 m S 0 g 1 w 4 M 158.7084 99.3833 m F 196.725 99.3833 m F 158.7084 62.2191 m F 196.725 62.2191 m F 0 G 0.3 w 10 M 225.2375 108.6743 m S 225.2375 90.0922 m S 206.2292 90.0922 m S 206.2292 108.6743 m S 215.7333 99.3833 m S 263.2542 71.5101 m S 263.2542 52.9281 m S 244.2459 52.9281 m S 244.2459 71.5101 m S 253.75 62.2191 m S 244.2459 90.0922 m S 244.2459 71.5101 m S 225.2375 71.5101 m S 225.2375 90.0922 m S 234.7417 80.8012 m S 244.2459 108.6743 m S 244.2459 90.0922 m S 225.2375 90.0922 m S 225.2375 108.6743 m S 234.7417 99.3833 m S 263.2542 108.6743 m S 263.2542 90.0922 m S 244.2459 90.0922 m S 244.2459 108.6743 m S 253.75 99.3833 m S 263.2542 90.0922 m S 263.2542 71.5101 m S 244.2459 71.5101 m S 244.2459 90.0922 m S 253.75 80.8012 m S 244.2459 71.5101 m S 244.2459 52.9281 m S 225.2375 52.9281 m S 225.2375 71.5101 m S 234.7417 62.2191 m S 225.2375 71.5101 m S 225.2375 52.9281 m S 206.2292 52.9281 m S 206.2292 71.5101 m S 215.7333 62.2191 m S 225.2375 90.0922 m S 225.2375 71.5101 m S 206.2292 71.5101 m S 206.2292 90.0922 m S 215.7333 80.8012 m S 0 g 1 w 4 M 215.7333 99.3833 m F 253.75 99.3833 m F 215.7333 62.2191 m F 253.75 62.2191 m F 0 G 0.3 w 10 M 149.2042 52.9281 m S 168.2126 52.9281 m S 149.2042 52.9281 m S 187.2209 52.9281 m S 168.2126 52.9281 m S 206.2292 52.9281 m S 187.2209 52.9281 m S 225.2375 52.9281 m S 206.2292 52.9281 m S 244.2459 52.9281 m S 225.2375 52.9281 m S 263.2542 52.9281 m S 244.2459 52.9281 m S 168.2126 164.4206 m S 168.2126 145.8385 m S 149.2042 145.8385 m S 149.2042 164.4206 m S 158.7084 155.1295 m S 206.2292 127.2564 m S 206.2292 108.6743 m S 187.2209 108.6743 m S 187.2209 127.2564 m S 187.2209 145.8385 m S 187.2209 127.2564 m S 168.2126 127.2564 m S 168.2126 145.8385 m S 177.7167 136.5475 m S 187.2209 164.4206 m S 187.2209 145.8385 m S 168.2126 145.8385 m S 168.2126 164.4206 m S 177.7167 155.1295 m S 206.2292 164.4206 m S 206.2292 145.8385 m S 187.2209 145.8385 m S 187.2209 164.4206 m S 196.725 155.1295 m S 206.2292 145.8385 m S 206.2292 127.2564 m S 187.2209 127.2564 m S 187.2209 145.8385 m S 196.725 136.5475 m S 187.2209 127.2564 m S 187.2209 108.6743 m S 168.2126 108.6743 m S 168.2126 127.2564 m S 177.7167 117.9653 m S 168.2126 127.2564 m S 168.2126 108.6743 m S 149.2042 108.6743 m S 149.2042 127.2564 m S 158.7084 117.9653 m S 168.2126 145.8385 m S 168.2126 127.2564 m S 149.2042 127.2564 m S 149.2042 145.8385 m S 158.7084 136.5475 m S 0 g 1 w 4 M 158.7084 155.1295 m F 196.725 155.1295 m F 158.7084 117.9653 m F 0 G 0.3 w 10 M 225.2375 164.4206 m S 225.2375 145.8385 m S 206.2292 145.8385 m S 206.2292 164.4206 m S 215.7333 155.1295 m S 263.2542 127.2564 m S 263.2542 108.6743 m S 244.2459 108.6743 m S 244.2459 127.2564 m S 253.75 117.9653 m S 244.2459 145.8385 m S 244.2459 127.2564 m S 225.2375 127.2564 m S 225.2375 145.8385 m S 234.7417 136.5475 m S 244.2459 164.4206 m S 244.2459 145.8385 m S 225.2375 145.8385 m S 225.2375 164.4206 m S 234.7417 155.1295 m S 263.2542 164.4206 m S 263.2542 145.8385 m S 244.2459 145.8385 m S 244.2459 164.4206 m S 253.75 155.1295 m S 263.2542 145.8385 m S 263.2542 127.2564 m S 244.2459 127.2564 m S 244.2459 145.8385 m S 253.75 136.5475 m S 244.2459 127.2564 m S 244.2459 108.6743 m S 225.2375 108.6743 m S 225.2375 127.2564 m S 234.7417 117.9653 m S 225.2375 127.2564 m S 225.2375 108.6743 m S 206.2292 108.6743 m S 206.2292 127.2564 m S 215.7333 117.9653 m S 225.2375 145.8385 m S 225.2375 127.2564 m S 206.2292 127.2564 m S 206.2292 145.8385 m S 215.7333 136.5475 m S 0 g 1 w 4 M 215.7333 155.1295 m F 253.75 155.1295 m F 215.7333 117.9653 m F 253.75 117.9653 m F 0 G 0.3 w 10 M 168.2126 108.6743 m S 168.2126 90.0922 m S 149.2042 90.0922 m S 149.2042 108.6743 m S 158.7084 99.3833 m S 206.2292 71.5101 m S 206.2292 52.9281 m S 187.2209 52.9281 m S 187.2209 71.5101 m S 196.725 62.2191 m S 187.2209 90.0922 m S 187.2209 71.5101 m S 168.2126 71.5101 m S 168.2126 90.0922 m S 177.7167 80.8012 m S 187.2209 108.6743 m S 187.2209 90.0922 m S 168.2126 90.0922 m S 168.2126 108.6743 m S 177.7167 99.3833 m S 206.2292 108.6743 m S 206.2292 90.0922 m S 187.2209 90.0922 m S 187.2209 108.6743 m S 206.2292 90.0922 m S 206.2292 71.5101 m S 187.2209 71.5101 m S 187.2209 90.0922 m S 196.725 80.8012 m S 187.2209 71.5101 m S 187.2209 52.9281 m S 168.2126 52.9281 m S 168.2126 71.5101 m S 177.7167 62.2191 m S 168.2126 71.5101 m S 168.2126 52.9281 m S 149.2042 52.9281 m S 149.2042 71.5101 m S 158.7084 62.2191 m S 168.2126 90.0922 m S 168.2126 71.5101 m S 149.2042 71.5101 m S 149.2042 90.0922 m S 158.7084 80.8012 m S 0 g 1 w 4 M 158.7084 99.3833 m F 158.7084 62.2191 m F 196.725 62.2191 m F 0 G 0.3 w 10 M 225.2375 108.6743 m S 225.2375 90.0922 m S 206.2292 90.0922 m S 206.2292 108.6743 m S 215.7333 99.3833 m S 263.2542 71.5101 m S 263.2542 52.9281 m S 244.2459 52.9281 m S 244.2459 71.5101 m S 253.75 62.2191 m S 244.2459 90.0922 m S 244.2459 71.5101 m S 225.2375 71.5101 m S 225.2375 90.0922 m S 234.7417 80.8012 m S 244.2459 108.6743 m S 244.2459 90.0922 m S 225.2375 90.0922 m S 225.2375 108.6743 m S 234.7417 99.3833 m S 263.2542 108.6743 m S 263.2542 90.0922 m S 244.2459 90.0922 m S 244.2459 108.6743 m S 253.75 99.3833 m S 263.2542 90.0922 m S 263.2542 71.5101 m S 244.2459 71.5101 m S 244.2459 90.0922 m S 253.75 80.8012 m S 244.2459 71.5101 m S 244.2459 52.9281 m S 225.2375 52.9281 m S 225.2375 71.5101 m S 234.7417 62.2191 m S 225.2375 71.5101 m S 225.2375 52.9281 m S 206.2292 52.9281 m S 206.2292 71.5101 m S 215.7333 62.2191 m S 225.2375 90.0922 m S 225.2375 71.5101 m S 206.2292 71.5101 m S 206.2292 90.0922 m S 215.7333 80.8012 m S 0 g 1 w 4 M 215.7333 99.3833 m F 253.75 99.3833 m F 215.7333 62.2191 m F 253.75 62.2191 m F 0 G 0.3 w 10 M 168.2126 52.9281 m S 149.2042 52.9281 m S 187.2209 52.9281 m S 168.2126 52.9281 m S 206.2292 52.9281 m S 187.2209 52.9281 m S 225.2375 52.9281 m S 206.2292 52.9281 m S 244.2459 52.9281 m S 225.2375 52.9281 m S 263.2542 52.9281 m S 244.2459 52.9281 m S 1 w 4 M 158.7084 136.5475 m 253.75 136.5475 l S 158.7084 80.8012 m 253.75 80.8012 l S 177.7167 155.1295 m 177.7167 62.2191 l S 0.3 w 10 M 187.2209 145.8385 m S 0 g 1 w 4 M 187.2209 145.8385 m F 0 G 0.3 w 10 M 187.2209 145.8385 m S 187.2209 145.8385 m S 187.2209 145.8385 m S 0 g 1 w 4 M 187.2209 145.8385 m F 0 G 0.3 w 10 M 187.2209 145.8385 m S 187.2209 145.8385 m S 1 g 1 w 4 M 187.2209 145.8385 m F 0 G 0.3 w 10 M 187.2209 145.8385 m S 0 g 1 w 4 M 187.2209 145.8385 m F 0 G 0.3 w 10 M 187.2209 145.8385 m S 187.2209 145.8385 m S 206.2292 145.8385 m S 0 g 1 w 4 M 206.2292 145.8385 m F 0 G 0.3 w 10 M 206.2292 145.8385 m S 206.2292 145.8385 m S 206.2292 145.8385 m S 0 g 1 w 4 M 206.2292 145.8385 m F 0 G 0.3 w 10 M 206.2292 145.8385 m S 206.2292 145.8385 m S 1 g 1 w 4 M 206.2292 145.8385 m F 0 G 0.3 w 10 M 206.2292 145.8385 m S 0 g 1 w 4 M 206.2292 145.8385 m F 0 G 0.3 w 10 M 206.2292 145.8385 m S 206.2292 145.8385 m S 225.2375 145.8385 m S 0 g 1 w 4 M 225.2375 145.8385 m F 0 G 0.3 w 10 M 225.2375 145.8385 m S 225.2375 145.8385 m S 225.2375 145.8385 m S 0 g 1 w 4 M 225.2375 145.8385 m F 0 G 0.3 w 10 M 225.2375 145.8385 m S 225.2375 145.8385 m S 1 g 1 w 4 M 225.2375 145.8385 m F 0 G 0.3 w 10 M 225.2375 145.8385 m S 0 g 1 w 4 M 225.2375 145.8385 m F 0 G 0.3 w 10 M 225.2375 145.8385 m S 225.2375 145.8385 m S 168.2126 127.2564 m S 0 g 1 w 4 M 168.2126 127.2564 m F 0 G 0.3 w 10 M 168.2126 127.2564 m S 168.2126 127.2564 m S 168.2126 127.2564 m S 0 g 1 w 4 M 168.2126 127.2564 m F 0 G 0.3 w 10 M 168.2126 127.2564 m S 168.2126 127.2564 m S 1 g 1 w 4 M 168.2126 127.2564 m F 0 G 0.3 w 10 M 168.2126 127.2564 m S 0 g 1 w 4 M 168.2126 127.2564 m F 0 G 0.3 w 10 M 168.2126 127.2564 m S 168.2126 127.2564 m S 168.2126 108.6743 m S 0 g 1 w 4 M 168.2126 108.6743 m F 0 G 0.3 w 10 M 168.2126 108.6743 m S 168.2126 108.6743 m S 168.2126 108.6743 m S 0 g 1 w 4 M 168.2126 108.6743 m F 0 G 0.3 w 10 M 168.2126 108.6743 m S 168.2126 108.6743 m S 1 g 1 w 4 M 168.2126 108.6743 m F 0 G 0.3 w 10 M 168.2126 108.6743 m S 0 g 1 w 4 M 168.2126 108.6743 m F 0 G 0.3 w 10 M 168.2126 108.6743 m S 168.2126 108.6743 m S 168.2126 90.0922 m S 0 g 1 w 4 M 168.2126 90.0922 m F 0 G 0.3 w 10 M 168.2126 90.0922 m S 168.2126 90.0922 m S 168.2126 90.0922 m S 0 g 1 w 4 M 168.2126 90.0922 m F 0 G 0.3 w 10 M 168.2126 90.0922 m S 168.2126 90.0922 m S 1 g 1 w 4 M 168.2126 90.0922 m F 0 G 0.3 w 10 M 168.2126 90.0922 m S 0 g 1 w 4 M 168.2126 90.0922 m F 0 G 0.3 w 10 M 168.2126 90.0922 m S 168.2126 90.0922 m S 187.2209 71.5101 m S 187.2209 71.5101 m S 206.2292 71.5101 m S 187.2209 71.5101 m S 206.2292 71.5101 m S 187.2209 71.5101 m S 225.2375 71.5101 m S 206.2292 71.5101 m S 225.2375 71.5101 m S 225.2375 71.5101 m S 225.2375 71.5101 m S 206.2292 71.5101 m S 187.2209 71.5101 m S 0 g 1 w 4 M 187.2209 71.5101 m F 0 G 0.3 w 10 M 187.2209 71.5101 m S 187.2209 71.5101 m S 187.2209 71.5101 m S 0 g 1 w 4 M 187.2209 71.5101 m F 0 G 0.3 w 10 M 187.2209 71.5101 m S 187.2209 71.5101 m S 1 g 1 w 4 M 182.2123 71.5101 m 182.2123 68.8168 184.4548 66.6335 187.2209 66.6335 c 189.9871 66.6335 192.2296 68.8168 192.2296 71.5101 c F 192.2296 71.5101 m 192.2296 74.2034 189.9871 76.3867 187.2209 76.3867 c 184.4548 76.3867 182.2123 74.2034 182.2123 71.5101 c F 187.2209 71.5101 m F 0 G 0.3 w 10 M 187.2209 71.5101 m S 0 g 1 w 4 M 187.2209 71.5101 m F 0 G 0.3 w 10 M 187.2209 71.5101 m S 187.2209 71.5101 m S 0 g 1 w 4 M 186.3167 70.6174 m 186.3167 67.6271 L 188.1252 67.6271 L 188.1252 70.6174 L 191.1132 70.608 L 191.1132 72.4123 L 188.1252 72.4031 L 188.1252 75.3934 L 186.3167 75.3934 L 186.3167 72.4031 L 183.3287 72.4123 L 183.3287 70.608 L 186.3167 70.6174 L f 0 G 0.3 w 10 M 206.2292 71.5101 m S 0 g 1 w 4 M 206.2292 71.5101 m F 0 G 0.3 w 10 M 206.2292 71.5101 m S 206.2292 71.5101 m S 206.2292 71.5101 m S 0 g 1 w 4 M 206.2292 71.5101 m F 0 G 0.3 w 10 M 206.2292 71.5101 m S 206.2292 71.5101 m S 1 g 1 w 4 M 201.2206 71.5101 m 201.2206 68.8168 203.4631 66.6335 206.2292 66.6335 c 208.9954 66.6335 211.2379 68.8168 211.2379 71.5101 c F 211.2379 71.5101 m 211.2379 74.2034 208.9954 76.3867 206.2292 76.3867 c 203.4631 76.3867 201.2206 74.2034 201.2206 71.5101 c F 206.2292 71.5101 m F 0 G 0.3 w 10 M 206.2292 71.5101 m S 0 g 1 w 4 M 206.2292 71.5101 m F 0 G 0.3 w 10 M 206.2292 71.5101 m S 206.2292 71.5101 m S 0 g 1 w 4 M 205.325 70.6174 m 205.325 67.6271 L 207.1335 67.6271 L 207.1335 70.6174 L 210.1215 70.608 L 210.1215 72.4123 L 207.1335 72.4031 L 207.1335 75.3934 L 205.325 75.3934 L 205.325 72.4031 L 202.337 72.4123 L 202.337 70.608 L 205.325 70.6174 L f 0 G 0.3 w 10 M 225.2375 71.5101 m S 0 g 1 w 4 M 225.2375 71.5101 m F 0 G 0.3 w 10 M 225.2375 71.5101 m S 225.2375 71.5101 m S 225.2375 71.5101 m S 0 g 1 w 4 M 225.2375 71.5101 m F 0 G 0.3 w 10 M 225.2375 71.5101 m S 225.2375 71.5101 m S 1 g 1 w 4 M 220.2289 71.5101 m 220.2289 68.8168 222.4714 66.6335 225.2375 66.6335 c 228.0037 66.6335 230.2462 68.8168 230.2462 71.5101 c F 230.2462 71.5101 m 230.2462 74.2034 228.0037 76.3867 225.2375 76.3867 c 222.4714 76.3867 220.2289 74.2034 220.2289 71.5101 c F 225.2375 71.5101 m F 0 G 0.3 w 10 M 225.2375 71.5101 m S 0 g 1 w 4 M 225.2375 71.5101 m F 0 G 0.3 w 10 M 225.2375 71.5101 m S 225.2375 71.5101 m S 0 g 1 w 4 M 224.3333 70.6174 m 224.3333 67.6271 L 226.1418 67.6271 L 226.1418 70.6174 L 229.1298 70.608 L 229.1298 72.4123 L 226.1418 72.4031 L 226.1418 75.3934 L 224.3333 75.3934 L 224.3333 72.4031 L 221.3453 72.4123 L 221.3453 70.608 L 224.3333 70.6174 L f 0 G 0.3 w 10 M 244.2459 127.2564 m S 244.2459 108.6743 m S 244.2459 127.2564 m S 244.2459 127.2564 m S 244.2459 108.6743 m S 244.2459 127.2564 m S 244.2459 108.6743 m S 244.2459 90.0922 m S 244.2459 90.0922 m S 244.2459 90.0922 m S 244.2459 108.6743 m S 244.2459 90.0922 m S 244.2459 127.2564 m S 0 g 1 w 4 M 244.2459 127.2564 m F 0 G 0.3 w 10 M 244.2459 127.2564 m S 244.2459 127.2564 m S 244.2459 127.2564 m S 0 g 1 w 4 M 244.2459 127.2564 m F 0 G 0.3 w 10 M 244.2459 127.2564 m S 244.2459 127.2564 m S 1 g 1 w 4 M 244.2459 127.2564 m F 0 G 0.3 w 10 M 244.2459 127.2564 m S 0 g 1 w 4 M 244.2459 127.2564 m F 0 G 0.3 w 10 M 244.2459 127.2564 m S 244.2459 127.2564 m S 244.2459 108.6743 m S 0 g 1 w 4 M 244.2459 108.6743 m F 0 G 0.3 w 10 M 244.2459 108.6743 m S 244.2459 108.6743 m S 244.2459 108.6743 m S 0 g 1 w 4 M 244.2459 108.6743 m F 0 G 0.3 w 10 M 244.2459 108.6743 m S 244.2459 108.6743 m S 1 g 1 w 4 M 244.2459 108.6743 m F 0 G 0.3 w 10 M 244.2459 108.6743 m S 0 g 1 w 4 M 244.2459 108.6743 m F 0 G 0.3 w 10 M 244.2459 108.6743 m S 244.2459 108.6743 m S 244.2459 90.0922 m S 0 g 1 w 4 M 244.2459 90.0922 m F 0 G 0.3 w 10 M 244.2459 90.0922 m S 244.2459 90.0922 m S 244.2459 90.0922 m S 0 g 1 w 4 M 244.2459 90.0922 m F 0 G 0.3 w 10 M 244.2459 90.0922 m S 244.2459 90.0922 m S 1 g 1 w 4 M 244.2459 90.0922 m F 0 G 0.3 w 10 M 244.2459 90.0922 m S 0 g 1 w 4 M 244.2459 90.0922 m F 0 G 0.3 w 10 M 244.2459 90.0922 m S 244.2459 90.0922 m S 196.725 117.9653 m S 196.725 117.9653 m S 215.7333 117.9653 m S 196.725 117.9653 m S 215.7333 117.9653 m S 215.7333 117.9653 m S 215.7333 117.9653 m S 196.725 117.9653 m S 196.725 99.3833 m S 196.725 99.3833 m S 215.7333 99.3833 m S 196.725 99.3833 m S 215.7333 99.3833 m S 215.7333 99.3833 m S 215.7333 99.3833 m S 196.725 99.3833 m S 187.2209 127.2564 m S 0 g 1 w 4 M 187.2209 127.2564 m F 0 G 0.3 w 10 M 187.2209 127.2564 m S 0 g 1 w 4 M 187.2209 127.2564 m F 1 g 182.2123 127.2564 m 182.2123 124.5631 184.4548 122.3797 187.2209 122.3797 c 189.9871 122.3797 192.2296 124.5631 192.2296 127.2564 c F 192.2296 127.2564 m 192.2296 129.9496 189.9871 132.133 187.2209 132.133 c 184.4548 132.133 182.2123 129.9496 182.2123 127.2564 c F 187.2209 127.2564 m F 0 G 0.3 w 10 M 187.2209 127.2564 m S 0 g 1 w 4 M 187.2209 127.2564 m F 0 G 0.3 w 10 M 187.2209 127.2564 m S 0 g 1 w 4 M 187.2209 127.2564 m F 186.3167 128.1493 m 183.3287 128.1586 L 183.3287 126.3543 L 186.3167 126.3636 L F 188.1252 126.3636 m 191.1132 126.3543 L 191.1132 128.1586 L 188.1252 128.1493 L F 183.3287 128.1586 m 191.1132 128.1586 l 191.1132 126.3543 l 183.3287 126.3543 l 183.3287 128.1586 l f 0 G 0.3 w 10 M 206.2292 127.2564 m S 0 g 1 w 4 M 206.2292 127.2564 m F 0 G 0.3 w 10 M 206.2292 127.2564 m S 0 g 1 w 4 M 206.2292 127.2564 m F 1 g 201.2206 127.2564 m 201.2206 124.5631 203.4631 122.3797 206.2292 122.3797 c 208.9954 122.3797 211.2379 124.5631 211.2379 127.2564 c F 211.2379 127.2564 m 211.2379 129.9496 208.9954 132.133 206.2292 132.133 c 203.4631 132.133 201.2206 129.9496 201.2206 127.2564 c F 206.2292 127.2564 m F 0 G 0.3 w 10 M 206.2292 127.2564 m S 0 g 1 w 4 M 206.2292 127.2564 m F 0 G 0.3 w 10 M 206.2292 127.2564 m S 0 g 1 w 4 M 206.2292 127.2564 m F 205.325 128.1493 m 202.337 128.1586 L 202.337 126.3543 L 205.325 126.3636 L F 207.1335 126.3636 m 210.1215 126.3543 L 210.1215 128.1586 L 207.1335 128.1493 L F 202.337 128.1586 m 210.1215 128.1586 l 210.1215 126.3543 l 202.337 126.3543 l 202.337 128.1586 l f 0 G 0.3 w 10 M 225.2375 127.2564 m S 0 g 1 w 4 M 225.2375 127.2564 m F 0 G 0.3 w 10 M 225.2375 127.2564 m S 0 g 1 w 4 M 225.2375 127.2564 m F 1 g 220.2289 127.2564 m 220.2289 124.5631 222.4714 122.3797 225.2375 122.3797 c 228.0037 122.3797 230.2462 124.5631 230.2462 127.2564 c F 230.2462 127.2564 m 230.2462 129.9496 228.0037 132.133 225.2375 132.133 c 222.4714 132.133 220.2289 129.9496 220.2289 127.2564 c F 225.2375 127.2564 m F 0 G 0.3 w 10 M 225.2375 127.2564 m S 0 g 1 w 4 M 225.2375 127.2564 m F 0 G 0.3 w 10 M 225.2375 127.2564 m S 0 g 1 w 4 M 225.2375 127.2564 m F 224.3333 128.1493 m 221.3453 128.1586 L 221.3453 126.3543 L 224.3333 126.3636 L F 226.1418 126.3636 m 229.1298 126.3543 L 229.1298 128.1586 L 226.1418 128.1493 L F 221.3453 128.1586 m 229.1298 128.1586 l 229.1298 126.3543 l 221.3453 126.3543 l 221.3453 128.1586 l f 0 G 0.3 w 10 M 225.2375 108.6743 m S 0 g 1 w 4 M 225.2375 108.6743 m F 0 G 0.3 w 10 M 225.2375 108.6743 m S 0 g 1 w 4 M 225.2375 108.6743 m F 1 g 220.2289 108.6743 m 220.2289 105.981 222.4714 103.7977 225.2375 103.7977 c 228.0037 103.7977 230.2462 105.981 230.2462 108.6743 c F 230.2462 108.6743 m 230.2462 111.3676 228.0037 113.5509 225.2375 113.5509 c 222.4714 113.5509 220.2289 111.3676 220.2289 108.6743 c F 225.2375 108.6743 m F 0 G 0.3 w 10 M 225.2375 108.6743 m S 0 g 1 w 4 M 225.2375 108.6743 m F 0 G 0.3 w 10 M 225.2375 108.6743 m S 0 g 1 w 4 M 225.2375 108.6743 m F 224.3333 109.5673 m 221.3453 109.5765 L 221.3453 107.7722 L 224.3333 107.7815 L F 226.1418 107.7815 m 229.1298 107.7722 L 229.1298 109.5765 L 226.1418 109.5673 L F 221.3453 109.5765 m 229.1298 109.5765 l 229.1298 107.7722 l 221.3453 107.7722 l 221.3453 109.5765 l f 0 G 0.3 w 10 M 206.2292 108.6743 m S 0 g 1 w 4 M 206.2292 108.6743 m F 0 G 0.3 w 10 M 206.2292 108.6743 m S 0 g 1 w 4 M 206.2292 108.6743 m F 1 g 201.2206 108.6743 m 201.2206 105.981 203.4631 103.7977 206.2292 103.7977 c 208.9954 103.7977 211.2379 105.981 211.2379 108.6743 c F 211.2379 108.6743 m 211.2379 111.3676 208.9954 113.5509 206.2292 113.5509 c 203.4631 113.5509 201.2206 111.3676 201.2206 108.6743 c F 206.2292 108.6743 m F 0 G 0.3 w 10 M 206.2292 108.6743 m S 0 g 1 w 4 M 206.2292 108.6743 m F 0 G 0.3 w 10 M 206.2292 108.6743 m S 0 g 1 w 4 M 206.2292 108.6743 m F 205.325 109.5673 m 202.337 109.5765 L 202.337 107.7722 L 205.325 107.7815 L F 207.1335 107.7815 m 210.1215 107.7722 L 210.1215 109.5765 L 207.1335 109.5673 L F 202.337 109.5765 m 210.1215 109.5765 l 210.1215 107.7722 l 202.337 107.7722 l 202.337 109.5765 l f 0 G 0.3 w 10 M 187.2209 108.6743 m S 0 g 1 w 4 M 187.2209 108.6743 m F 0 G 0.3 w 10 M 187.2209 108.6743 m S 187.2209 108.6743 m S 187.2209 108.6743 m S 0 g 1 w 4 M 187.2209 108.6743 m F 0 G 0.3 w 10 M 187.2209 108.6743 m S 187.2209 108.6743 m S 1 g 1 w 4 M 182.2123 108.6743 m 182.2123 105.981 184.4548 103.7977 187.2209 103.7977 c 189.9871 103.7977 192.2296 105.981 192.2296 108.6743 c F 192.2296 108.6743 m 192.2296 111.3676 189.9871 113.5509 187.2209 113.5509 c 184.4548 113.5509 182.2123 111.3676 182.2123 108.6743 c F 187.2209 108.6743 m F 0 G 0.3 w 10 M 187.2209 108.6743 m S 0 g 1 w 4 M 187.2209 108.6743 m F 0 G 0.3 w 10 M 187.2209 108.6743 m S 187.2209 108.6743 m S 0 g 1 w 4 M 186.3167 107.7816 m 186.3167 104.7913 L 188.1252 104.7913 L 188.1252 107.7816 L 191.1132 107.7722 L 191.1132 109.5765 L 188.1252 109.5673 L 188.1252 112.5576 L 186.3167 112.5576 L 186.3167 109.5673 L 183.3287 109.5765 L 183.3287 107.7722 L 186.3167 107.7816 L f 0 G 0.3 w 10 M 206.2292 90.0922 m S 0 g 1 w 4 M 206.2292 90.0922 m F 0 G 0.3 w 10 M 206.2292 90.0922 m S 206.2292 90.0922 m S 206.2292 90.0922 m S 0 g 1 w 4 M 206.2292 90.0922 m F 0 G 0.3 w 10 M 206.2292 90.0922 m S 206.2292 90.0922 m S 1 g 1 w 4 M 201.2206 90.0922 m 201.2206 87.3989 203.4631 85.2156 206.2292 85.2156 c 208.9954 85.2156 211.2379 87.3989 211.2379 90.0922 c F 211.2379 90.0922 m 211.2379 92.7854 208.9954 94.9688 206.2292 94.9688 c 203.4631 94.9688 201.2206 92.7854 201.2206 90.0922 c F 206.2292 90.0922 m F 0 G 0.3 w 10 M 206.2292 90.0922 m S 0 g 1 w 4 M 206.2292 90.0922 m F 0 G 0.3 w 10 M 206.2292 90.0922 m S 206.2292 90.0922 m S 0 g 1 w 4 M 205.325 89.1995 m 205.325 86.2092 L 207.1335 86.2092 L 207.1335 89.1995 L 210.1215 89.1901 L 210.1215 90.9944 L 207.1335 90.9851 L 207.1335 93.9754 L 205.325 93.9754 L 205.325 90.9851 L 202.337 90.9944 L 202.337 89.1901 L 205.325 89.1995 L f 0 G 0.3 w 10 M 225.2375 90.0922 m S 0 g 1 w 4 M 225.2375 90.0922 m F 0 G 0.3 w 10 M 225.2375 90.0922 m S 225.2375 90.0922 m S 225.2375 90.0922 m S 0 g 1 w 4 M 225.2375 90.0922 m F 0 G 0.3 w 10 M 225.2375 90.0922 m S 225.2375 90.0922 m S 1 g 1 w 4 M 220.2289 90.0922 m 220.2289 87.3989 222.4714 85.2156 225.2375 85.2156 c 228.0037 85.2156 230.2462 87.3989 230.2462 90.0922 c F 230.2462 90.0922 m 230.2462 92.7854 228.0037 94.9688 225.2375 94.9688 c 222.4714 94.9688 220.2289 92.7854 220.2289 90.0922 c F 225.2375 90.0922 m F 0 G 0.3 w 10 M 225.2375 90.0922 m S 0 g 1 w 4 M 225.2375 90.0922 m F 0 G 0.3 w 10 M 225.2375 90.0922 m S 225.2375 90.0922 m S 0 g 1 w 4 M 224.3333 89.1995 m 224.3333 86.2092 L 226.1418 86.2092 L 226.1418 89.1995 L 229.1298 89.1901 L 229.1298 90.9944 L 226.1418 90.9851 L 226.1418 93.9754 L 224.3333 93.9754 L 224.3333 90.9851 L 221.3453 90.9944 L 221.3453 89.1901 L 224.3333 89.1995 L f 0 G 0.3 w 10 M 187.2209 90.0922 m S 0 g 1 w 4 M 187.2209 90.0922 m F 0 G 0.3 w 10 M 187.2209 90.0922 m S 187.2209 90.0922 m S 187.2209 90.0922 m S 0 g 1 w 4 M 187.2209 90.0922 m F 0 G 0.3 w 10 M 187.2209 90.0922 m S 187.2209 90.0922 m S 1 g 1 w 4 M 182.2123 90.0922 m 182.2123 87.3989 184.4548 85.2156 187.2209 85.2156 c 189.9871 85.2156 192.2296 87.3989 192.2296 90.0922 c F 192.2296 90.0922 m 192.2296 92.7854 189.9871 94.9688 187.2209 94.9688 c 184.4548 94.9688 182.2123 92.7854 182.2123 90.0922 c F 187.2209 90.0922 m F 0 G 0.3 w 10 M 187.2209 90.0922 m S 0 g 1 w 4 M 187.2209 90.0922 m F 0 G 0.3 w 10 M 187.2209 90.0922 m S 187.2209 90.0922 m S 0 g 1 w 4 M 186.3167 89.1995 m 186.3167 86.2092 L 188.1252 86.2092 L 188.1252 89.1995 L 191.1132 89.1901 L 191.1132 90.9944 L 188.1252 90.9851 L 188.1252 93.9754 L 186.3167 93.9754 L 186.3167 90.9851 L 183.3287 90.9944 L 183.3287 89.1901 L 186.3167 89.1995 L f 0 G 0.3 w 10 M 263.2542 127.2564 m S 263.2542 108.6743 m S 263.2542 164.4206 m S 263.2542 145.8385 m S 263.2542 145.8385 m S 263.2542 127.2564 m S 225.2555 164.4206 m S 225.2555 145.8385 m S 263.2542 145.8385 m S 263.2542 164.4206 m S 215.7333 155.1296 m S 263.3438 127.2564 m S 263.3438 108.6743 m S 244.2997 108.6743 m S 244.2997 127.2564 m S 253.8217 117.9653 m S 244.2997 127.2564 m S 225.2555 127.2564 m S 225.2555 145.8385 m S 234.7776 136.5475 m S 244.2997 164.4206 m S 225.2555 145.8385 m S 225.2555 164.4206 m S 234.7776 155.1296 m S 263.3438 164.4206 m S 244.2997 164.4206 m S 253.8217 155.1296 m S 263.3438 127.2564 m S 244.2997 127.2564 m S 253.8217 136.5475 m S 244.2997 127.2564 m S 244.2997 108.6743 m S 225.2555 108.6743 m S 225.2555 127.2564 m S 234.7776 117.9653 m S 225.2555 127.2564 m S 225.2555 108.6743 m S 263.2542 108.6743 m S 263.2542 127.2564 m S 215.7333 117.9653 m S 225.2555 145.8385 m S 225.2555 127.2564 m S 263.2542 127.2564 m S 263.2542 145.8385 m S 215.7333 136.5475 m S 0 g 1 w 4 M 215.7333 155.1296 m F 253.8217 155.1296 m F 215.7333 117.9653 m F 253.8217 117.9653 m F 0 G 0.3 w 10 M 282.388 164.4206 m S 263.3438 164.4206 m S 272.8659 155.1296 m S 320.4764 127.2564 m S 320.4764 108.6743 m S 301.4322 108.6743 m S 301.4322 127.2564 m S 310.9543 117.9653 m S 301.4322 145.8385 m S 301.4322 127.2564 m S 282.388 127.2564 m S 291.9101 136.5475 m S 301.4322 164.4206 m S 301.4322 145.8385 m S 282.388 164.4206 m S 291.9101 155.1296 m S 320.4764 164.4206 m S 320.4764 145.8385 m S 301.4322 145.8385 m S 301.4322 164.4206 m S 310.9543 155.1296 m S 320.4764 145.8385 m S 320.4764 127.2564 m S 301.4322 127.2564 m S 301.4322 145.8385 m S 310.9543 136.5475 m S 301.4322 127.2564 m S 301.4322 108.6743 m S 282.388 108.6743 m S 282.388 127.2564 m S 291.9101 117.9653 m S 282.388 127.2564 m S 282.388 108.6743 m S 263.3438 108.6743 m S 263.3438 127.2564 m S 272.8659 117.9653 m S 282.388 127.2564 m S 263.3438 127.2564 m S 272.8659 136.5475 m S 0 g 1 w 4 M 272.8659 155.1296 m F 310.9543 155.1296 m F 272.8659 117.9653 m F 310.9543 117.9653 m F 0 G 0.3 w 10 M 263.2542 71.5101 m S 263.2542 52.9281 m S 263.2542 108.6743 m S 263.2542 90.0922 m S 263.2542 90.0922 m S 263.2542 71.5101 m S 225.2555 108.6743 m S 225.2555 90.0922 m S 263.2542 90.0922 m S 263.2542 108.6743 m S 215.7333 99.3833 m S 263.3438 71.5101 m S 263.3438 52.9281 m S 244.2997 52.9281 m S 244.2997 71.5101 m S 253.8217 62.2191 m S 244.2997 90.0922 m S 244.2997 71.5101 m S 225.2555 71.5101 m S 225.2555 90.0922 m S 234.7776 80.8012 m S 244.2997 108.6743 m S 244.2997 90.0922 m S 225.2555 90.0922 m S 225.2555 108.6743 m S 234.7776 99.3833 m S 263.3438 108.6743 m S 263.3438 90.0922 m S 244.2997 90.0922 m S 244.2997 108.6743 m S 253.8217 99.3833 m S 263.3438 90.0922 m S 263.3438 71.5101 m S 244.2997 71.5101 m S 244.2997 90.0922 m S 253.8217 80.8012 m S 244.2997 71.5101 m S 244.2997 52.9281 m S 225.2555 52.9281 m S 225.2555 71.5101 m S 234.7776 62.2191 m S 225.2555 71.5101 m S 225.2555 52.9281 m S 263.2542 52.9281 m S 263.2542 71.5101 m S 215.7333 62.2191 m S 225.2555 90.0922 m S 225.2555 71.5101 m S 263.2542 71.5101 m S 263.2542 90.0922 m S 215.7333 80.8012 m S 0 g 1 w 4 M 215.7333 99.3833 m F 253.8217 99.3833 m F 215.7333 62.2191 m F 253.8217 62.2191 m F 0 G 0.3 w 10 M 282.388 108.6743 m S 282.388 90.0922 m S 263.3438 90.0922 m S 263.3438 108.6743 m S 272.8659 99.3833 m S 320.4764 71.5101 m S 320.4764 52.9281 m S 301.4322 52.9281 m S 301.4322 71.5101 m S 310.9543 62.2191 m S 301.4322 90.0922 m S 301.4322 71.5101 m S 282.388 71.5101 m S 282.388 90.0922 m S 291.9101 80.8012 m S 301.4322 108.6743 m S 301.4322 90.0922 m S 282.388 90.0922 m S 282.388 108.6743 m S 291.9101 99.3833 m S 320.4764 108.6743 m S 320.4764 90.0922 m S 301.4322 90.0922 m S 301.4322 108.6743 m S 310.9543 99.3833 m S 320.4764 90.0922 m S 320.4764 71.5101 m S 301.4322 71.5101 m S 301.4322 90.0922 m S 310.9543 80.8012 m S 301.4322 71.5101 m S 301.4322 52.9281 m S 282.388 52.9281 m S 282.388 71.5101 m S 291.9101 62.2191 m S 282.388 71.5101 m S 282.388 52.9281 m S 263.3438 52.9281 m S 263.3438 71.5101 m S 272.8659 62.2191 m S 282.388 90.0922 m S 282.388 71.5101 m S 263.3438 71.5101 m S 263.3438 90.0922 m S 272.8659 80.8012 m S 0 g 1 w 4 M 272.8659 99.3833 m F 310.9543 99.3833 m F 272.8659 62.2191 m F 310.9543 62.2191 m F 0 G 0.3 w 10 M 263.2542 52.9281 m S 225.2555 52.9281 m S 263.2542 52.9281 m S 244.2997 52.9281 m S 225.2555 52.9281 m S 263.3438 52.9281 m S 244.2997 52.9281 m S 282.388 52.9281 m S 263.3438 52.9281 m S 301.4322 52.9281 m S 282.388 52.9281 m S 320.4764 52.9281 m S 301.4322 52.9281 m S 225.2555 164.4206 m S 225.2555 145.8385 m S 263.2542 145.8385 m S 263.2542 164.4206 m S 215.7333 155.1296 m S 263.3438 127.2564 m S 263.3438 108.6743 m S 244.2997 108.6743 m S 244.2997 127.2564 m S 244.2997 127.2564 m S 225.2555 127.2564 m S 225.2555 145.8385 m S 234.7776 136.5475 m S 244.2997 164.4206 m S 225.2555 145.8385 m S 225.2555 164.4206 m S 234.7776 155.1296 m S 263.3438 164.4206 m S 244.2997 164.4206 m S 253.8217 155.1296 m S 263.3438 127.2564 m S 244.2997 127.2564 m S 253.8217 136.5475 m S 244.2997 127.2564 m S 244.2997 108.6743 m S 225.2555 108.6743 m S 225.2555 127.2564 m S 234.7776 117.9653 m S 225.2555 127.2564 m S 225.2555 108.6743 m S 263.2542 108.6743 m S 263.2542 127.2564 m S 215.7333 117.9653 m S 225.2555 145.8385 m S 225.2555 127.2564 m S 263.2542 127.2564 m S 263.2542 145.8385 m S 215.7333 136.5475 m S 0 g 1 w 4 M 215.7333 155.1296 m F 253.8217 155.1296 m F 215.7333 117.9653 m F 0 G 0.3 w 10 M 282.388 164.4206 m S 263.3438 164.4206 m S 272.8659 155.1296 m S 320.4764 127.2564 m S 320.4764 108.6743 m S 301.4322 108.6743 m S 301.4322 127.2564 m S 310.9543 117.9653 m S 301.4322 145.8385 m S 301.4322 127.2564 m S 282.388 127.2564 m S 291.9101 136.5475 m S 301.4322 164.4206 m S 301.4322 145.8385 m S 282.388 164.4206 m S 291.9101 155.1296 m S 320.4764 164.4206 m S 320.4764 145.8385 m S 301.4322 145.8385 m S 301.4322 164.4206 m S 310.9543 155.1296 m S 320.4764 145.8385 m S 320.4764 127.2564 m S 301.4322 127.2564 m S 301.4322 145.8385 m S 310.9543 136.5475 m S 301.4322 127.2564 m S 301.4322 108.6743 m S 282.388 108.6743 m S 282.388 127.2564 m S 291.9101 117.9653 m S 282.388 127.2564 m S 282.388 108.6743 m S 263.3438 108.6743 m S 263.3438 127.2564 m S 272.8659 117.9653 m S 282.388 127.2564 m S 263.3438 127.2564 m S 272.8659 136.5475 m S 0 g 1 w 4 M 272.8659 155.1296 m F 310.9543 155.1296 m F 272.8659 117.9653 m F 310.9543 117.9653 m F 0 G 0.3 w 10 M 225.2555 108.6743 m S 225.2555 90.0922 m S 263.2542 90.0922 m S 263.2542 108.6743 m S 215.7333 99.3833 m S 263.3438 71.5101 m S 263.3438 52.9281 m S 244.2997 52.9281 m S 244.2997 71.5101 m S 253.8217 62.2191 m S 244.2997 90.0922 m S 244.2997 71.5101 m S 225.2555 71.5101 m S 225.2555 90.0922 m S 234.7776 80.8012 m S 244.2997 108.6743 m S 244.2997 90.0922 m S 225.2555 90.0922 m S 225.2555 108.6743 m S 234.7776 99.3833 m S 263.3438 108.6743 m S 263.3438 90.0922 m S 244.2997 90.0922 m S 244.2997 108.6743 m S 263.3438 90.0922 m S 263.3438 71.5101 m S 244.2997 71.5101 m S 244.2997 90.0922 m S 253.8217 80.8012 m S 244.2997 71.5101 m S 244.2997 52.9281 m S 225.2555 52.9281 m S 225.2555 71.5101 m S 234.7776 62.2191 m S 225.2555 71.5101 m S 225.2555 52.9281 m S 263.2542 52.9281 m S 263.2542 71.5101 m S 215.7333 62.2191 m S 225.2555 90.0922 m S 225.2555 71.5101 m S 263.2542 71.5101 m S 263.2542 90.0922 m S 215.7333 80.8012 m S 0 g 1 w 4 M 215.7333 99.3833 m F 215.7333 62.2191 m F 253.8217 62.2191 m F 0 G 0.3 w 10 M 282.388 108.6743 m S 282.388 90.0922 m S 263.3438 90.0922 m S 263.3438 108.6743 m S 272.8659 99.3833 m S 320.4764 71.5101 m S 320.4764 52.9281 m S 301.4322 52.9281 m S 301.4322 71.5101 m S 310.9543 62.2191 m S 301.4322 90.0922 m S 301.4322 71.5101 m S 282.388 71.5101 m S 282.388 90.0922 m S 291.9101 80.8012 m S 301.4322 108.6743 m S 301.4322 90.0922 m S 282.388 90.0922 m S 282.388 108.6743 m S 291.9101 99.3833 m S 320.4764 108.6743 m S 320.4764 90.0922 m S 301.4322 90.0922 m S 301.4322 108.6743 m S 310.9543 99.3833 m S 320.4764 90.0922 m S 320.4764 71.5101 m S 301.4322 71.5101 m S 301.4322 90.0922 m S 310.9543 80.8012 m S 301.4322 71.5101 m S 301.4322 52.9281 m S 282.388 52.9281 m S 282.388 71.5101 m S 291.9101 62.2191 m S 282.388 71.5101 m S 282.388 52.9281 m S 263.3438 52.9281 m S 263.3438 71.5101 m S 272.8659 62.2191 m S 282.388 90.0922 m S 282.388 71.5101 m S 263.3438 71.5101 m S 263.3438 90.0922 m S 272.8659 80.8012 m S 0 g 1 w 4 M 272.8659 99.3833 m F 310.9543 99.3833 m F 272.8659 62.2191 m F 310.9543 62.2191 m F 0 G 0.3 w 10 M 225.2555 52.9281 m S 263.2542 52.9281 m S 244.2997 52.9281 m S 225.2555 52.9281 m S 263.3438 52.9281 m S 244.2997 52.9281 m S 282.388 52.9281 m S 263.3438 52.9281 m S 301.4322 52.9281 m S 282.388 52.9281 m S 320.4764 52.9281 m S 301.4322 52.9281 m S 1 w 4 M 215.7333 136.5475 m 310.9543 136.5475 l S 215.7333 80.8012 m 310.9543 80.8012 l S 291.9101 155.1296 m 291.9101 62.2191 l S 0.3 w 10 M 225.2555 127.2564 m S 0 g 1 w 4 M 225.2555 127.2564 m F 0 G 0.3 w 10 M 225.2555 127.2564 m S 225.2555 127.2564 m S 225.2555 127.2564 m S 0 g 1 w 4 M 225.2555 127.2564 m F 0 G 0.3 w 10 M 225.2555 127.2564 m S 225.2555 127.2564 m S 1 g 1 w 4 M 225.2555 127.2564 m F 0 G 0.3 w 10 M 225.2555 127.2564 m S 0 g 1 w 4 M 225.2555 127.2564 m F 0 G 0.3 w 10 M 225.2555 127.2564 m S 225.2555 127.2564 m S 225.2555 108.6743 m S 0 g 1 w 4 M 225.2555 108.6743 m F 0 G 0.3 w 10 M 225.2555 108.6743 m S 225.2555 108.6743 m S 225.2555 108.6743 m S 0 g 1 w 4 M 225.2555 108.6743 m F 0 G 0.3 w 10 M 225.2555 108.6743 m S 225.2555 108.6743 m S 1 g 1 w 4 M 225.2555 108.6743 m F 0 G 0.3 w 10 M 225.2555 108.6743 m S 0 g 1 w 4 M 225.2555 108.6743 m F 0 G 0.3 w 10 M 225.2555 108.6743 m S 225.2555 108.6743 m S 225.2555 90.0922 m S 0 g 1 w 4 M 225.2555 90.0922 m F 0 G 0.3 w 10 M 225.2555 90.0922 m S 225.2555 90.0922 m S 225.2555 90.0922 m S 0 g 1 w 4 M 225.2555 90.0922 m F 0 G 0.3 w 10 M 225.2555 90.0922 m S 225.2555 90.0922 m S 1 g 1 w 4 M 225.2555 90.0922 m F 0 G 0.3 w 10 M 225.2555 90.0922 m S 0 g 1 w 4 M 225.2555 90.0922 m F 0 G 0.3 w 10 M 225.2555 90.0922 m S 225.2555 90.0922 m S 244.2997 71.5101 m S 244.2997 71.5101 m S 263.3438 71.5101 m S 244.2997 71.5101 m S 263.3438 71.5101 m S 244.2997 71.5101 m S 282.388 71.5101 m S 263.3438 71.5101 m S 282.388 71.5101 m S 282.388 71.5101 m S 282.388 71.5101 m S 263.3438 71.5101 m S 244.2997 71.5101 m S 0 g 1 w 4 M 244.2997 71.5101 m F 0 G 0.3 w 10 M 244.2997 71.5101 m S 244.2997 71.5101 m S 244.2997 71.5101 m S 0 g 1 w 4 M 244.2997 71.5101 m F 0 G 0.3 w 10 M 244.2997 71.5101 m S 244.2997 71.5101 m S 1 g 1 w 4 M 239.2816 71.5101 m 239.2816 68.8168 241.5283 66.6335 244.2997 66.6335 c 247.0711 66.6335 249.3178 68.8168 249.3178 71.5101 c F 249.3178 71.5101 m 249.3178 74.2034 247.0711 76.3867 244.2997 76.3867 c 241.5283 76.3867 239.2816 74.2034 239.2816 71.5101 c F 244.2997 71.5101 m F 0 G 0.3 w 10 M 244.2997 71.5101 m S 0 g 1 w 4 M 244.2997 71.5101 m F 0 G 0.3 w 10 M 244.2997 71.5101 m S 244.2997 71.5101 m S 0 g 1 w 4 M 243.3937 70.6174 m 243.3937 67.6271 L 245.2056 67.6271 L 245.2056 70.6174 L 248.1993 70.608 L 248.1993 72.4124 L 245.2056 72.4031 L 245.2056 75.3934 L 243.3937 75.3934 L 243.3937 72.4031 L 240.4001 72.4124 L 240.4001 70.608 L 243.3937 70.6174 L f 0 G 0.3 w 10 M 263.3438 71.5101 m S 0 g 1 w 4 M 263.3438 71.5101 m F 0 G 0.3 w 10 M 263.3438 71.5101 m S 263.3438 71.5101 m S 263.3438 71.5101 m S 0 g 1 w 4 M 263.3438 71.5101 m F 0 G 0.3 w 10 M 263.3438 71.5101 m S 263.3438 71.5101 m S 1 g 1 w 4 M 258.3258 71.5101 m 258.3258 68.8168 260.5725 66.6335 263.3438 66.6335 c 266.1152 66.6335 268.3619 68.8168 268.3619 71.5101 c F 268.3619 71.5101 m 268.3619 74.2034 266.1152 76.3867 263.3438 76.3867 c 260.5725 76.3867 258.3258 74.2034 258.3258 71.5101 c F 263.3438 71.5101 m F 0 G 0.3 w 10 M 263.3438 71.5101 m S 0 g 1 w 4 M 263.3438 71.5101 m F 0 G 0.3 w 10 M 263.3438 71.5101 m S 263.3438 71.5101 m S 0 g 1 w 4 M 262.4379 70.6174 m 262.4379 67.6271 L 264.2498 67.6271 L 264.2498 70.6174 L 267.2434 70.608 L 267.2434 72.4124 L 264.2498 72.4031 L 264.2498 75.3934 L 262.4379 75.3934 L 262.4379 72.4031 L 259.4443 72.4124 L 259.4443 70.608 L 262.4379 70.6174 L f 0 G 0.3 w 10 M 282.388 71.5101 m S 0 g 1 w 4 M 282.388 71.5101 m F 0 G 0.3 w 10 M 282.388 71.5101 m S 282.388 71.5101 m S 282.388 71.5101 m S 0 g 1 w 4 M 282.388 71.5101 m F 0 G 0.3 w 10 M 282.388 71.5101 m S 282.388 71.5101 m S 1 g 1 w 4 M 277.3699 71.5101 m 277.3699 68.8168 279.6166 66.6335 282.388 66.6335 c 285.1594 66.6335 287.4061 68.8168 287.4061 71.5101 c F 287.4061 71.5101 m 287.4061 74.2034 285.1594 76.3867 282.388 76.3867 c 279.6166 76.3867 277.3699 74.2034 277.3699 71.5101 c F 282.388 71.5101 m F 0 G 0.3 w 10 M 282.388 71.5101 m S 0 g 1 w 4 M 282.388 71.5101 m F 0 G 0.3 w 10 M 282.388 71.5101 m S 282.388 71.5101 m S 0 g 1 w 4 M 281.4821 70.6174 m 281.4821 67.6271 L 283.2939 67.6271 L 283.2939 70.6174 L 286.2876 70.608 L 286.2876 72.4124 L 283.2939 72.4031 L 283.2939 75.3934 L 281.4821 75.3934 L 281.4821 72.4031 L 278.4884 72.4124 L 278.4884 70.608 L 281.4821 70.6174 L f 0 G 0.3 w 10 M 301.4322 127.2564 m S 301.4322 108.6743 m S 301.4322 127.2564 m S 301.4322 127.2564 m S 301.4322 108.6743 m S 301.4322 127.2564 m S 301.4322 108.6743 m S 301.4322 90.0922 m S 301.4322 90.0922 m S 301.4322 90.0922 m S 301.4322 108.6743 m S 301.4322 90.0922 m S 301.4322 127.2564 m S 0 g 1 w 4 M 301.4322 127.2564 m F 0 G 0.3 w 10 M 301.4322 127.2564 m S 301.4322 127.2564 m S 301.4322 127.2564 m S 0 g 1 w 4 M 301.4322 127.2564 m F 0 G 0.3 w 10 M 301.4322 127.2564 m S 301.4322 127.2564 m S 1 g 1 w 4 M 301.4322 127.2564 m F 0 G 0.3 w 10 M 301.4322 127.2564 m S 0 g 1 w 4 M 301.4322 127.2564 m F 0 G 0.3 w 10 M 301.4322 127.2564 m S 301.4322 127.2564 m S 301.4322 108.6743 m S 0 g 1 w 4 M 301.4322 108.6743 m F 0 G 0.3 w 10 M 301.4322 108.6743 m S 301.4322 108.6743 m S 301.4322 108.6743 m S 0 g 1 w 4 M 301.4322 108.6743 m F 0 G 0.3 w 10 M 301.4322 108.6743 m S 301.4322 108.6743 m S 1 g 1 w 4 M 301.4322 108.6743 m F 0 G 0.3 w 10 M 301.4322 108.6743 m S 0 g 1 w 4 M 301.4322 108.6743 m F 0 G 0.3 w 10 M 301.4322 108.6743 m S 301.4322 108.6743 m S 301.4322 90.0922 m S 0 g 1 w 4 M 301.4322 90.0922 m F 0 G 0.3 w 10 M 301.4322 90.0922 m S 301.4322 90.0922 m S 301.4322 90.0922 m S 0 g 1 w 4 M 301.4322 90.0922 m F 0 G 0.3 w 10 M 301.4322 90.0922 m S 301.4322 90.0922 m S 1 g 1 w 4 M 301.4322 90.0922 m F 0 G 0.3 w 10 M 301.4322 90.0922 m S 0 g 1 w 4 M 301.4322 90.0922 m F 0 G 0.3 w 10 M 301.4322 90.0922 m S 301.4322 90.0922 m S 253.8217 117.9653 m S 253.8217 117.9653 m S 272.8659 117.9653 m S 253.8217 117.9653 m S 272.8659 117.9653 m S 272.8659 117.9653 m S 272.8659 117.9653 m S 253.8217 117.9653 m S 253.8217 99.3833 m S 253.8217 99.3833 m S 272.8659 99.3833 m S 253.8217 99.3833 m S 272.8659 99.3833 m S 272.8659 99.3833 m S 272.8659 99.3833 m S 253.8217 99.3833 m S 244.2997 127.2564 m S 0 g 1 w 4 M 244.2997 127.2564 m F 0 G 0.3 w 10 M 244.2997 127.2564 m S 0 g 1 w 4 M 244.2997 127.2564 m F 1 g 239.2816 127.2564 m 239.2816 124.5631 241.5283 122.3798 244.2997 122.3798 c 247.0711 122.3798 249.3178 124.5631 249.3178 127.2564 c F 249.3178 127.2564 m 249.3178 129.9497 247.0711 132.133 244.2997 132.133 c 241.5283 132.133 239.2816 129.9497 239.2816 127.2564 c F 244.2997 127.2564 m F 0 G 0.3 w 10 M 244.2997 127.2564 m S 0 g 1 w 4 M 244.2997 127.2564 m F 0 G 0.3 w 10 M 244.2997 127.2564 m S 0 g 1 w 4 M 244.2997 127.2564 m F 243.3937 128.1493 m 240.4001 128.1586 L 240.4001 126.3543 L 243.3937 126.3636 L F 245.2056 126.3636 m 248.1993 126.3543 L 248.1993 128.1586 L 245.2056 128.1493 L F 240.4001 128.1586 m 248.1993 128.1586 l 248.1993 126.3543 l 240.4001 126.3543 l 240.4001 128.1586 l f 0 G 0.3 w 10 M 263.3438 127.2564 m S 0 g 1 w 4 M 263.3438 127.2564 m F 0 G 0.3 w 10 M 263.3438 127.2564 m S 0 g 1 w 4 M 263.3438 127.2564 m F 1 g 258.3258 127.2564 m 258.3258 124.5631 260.5725 122.3798 263.3438 122.3798 c 266.1152 122.3798 268.3619 124.5631 268.3619 127.2564 c F 268.3619 127.2564 m 268.3619 129.9497 266.1152 132.133 263.3438 132.133 c 260.5725 132.133 258.3258 129.9497 258.3258 127.2564 c F 263.3438 127.2564 m F 0 G 0.3 w 10 M 263.3438 127.2564 m S 0 g 1 w 4 M 263.3438 127.2564 m F 0 G 0.3 w 10 M 263.3438 127.2564 m S 0 g 1 w 4 M 263.3438 127.2564 m F 262.4379 128.1493 m 259.4443 128.1586 L 259.4443 126.3543 L 262.4379 126.3636 L F 264.2498 126.3636 m 267.2434 126.3543 L 267.2434 128.1586 L 264.2498 128.1493 L F 259.4443 128.1586 m 267.2434 128.1586 l 267.2434 126.3543 l 259.4443 126.3543 l 259.4443 128.1586 l f 0 G 0.3 w 10 M 282.388 127.2564 m S 0 g 1 w 4 M 282.388 127.2564 m F 0 G 0.3 w 10 M 282.388 127.2564 m S 0 g 1 w 4 M 282.388 127.2564 m F 1 g 277.3699 127.2564 m 277.3699 124.5631 279.6166 122.3798 282.388 122.3798 c 285.1594 122.3798 287.4061 124.5631 287.4061 127.2564 c F 287.4061 127.2564 m 287.4061 129.9497 285.1594 132.133 282.388 132.133 c 279.6166 132.133 277.3699 129.9497 277.3699 127.2564 c F 282.388 127.2564 m F 0 G 0.3 w 10 M 282.388 127.2564 m S 0 g 1 w 4 M 282.388 127.2564 m F 0 G 0.3 w 10 M 282.388 127.2564 m S 0 g 1 w 4 M 282.388 127.2564 m F 281.4821 128.1493 m 278.4884 128.1586 L 278.4884 126.3543 L 281.4821 126.3636 L F 283.2939 126.3636 m 286.2876 126.3543 L 286.2876 128.1586 L 283.2939 128.1493 L F 278.4884 128.1586 m 286.2876 128.1586 l 286.2876 126.3543 l 278.4884 126.3543 l 278.4884 128.1586 l f 0 G 0.3 w 10 M 282.388 108.6743 m S 0 g 1 w 4 M 282.388 108.6743 m F 0 G 0.3 w 10 M 282.388 108.6743 m S 0 g 1 w 4 M 282.388 108.6743 m F 1 g 282.388 108.6743 m F 0 G 0.3 w 10 M 282.388 108.6743 m S 0 g 1 w 4 M 282.388 108.6743 m F 0 G 0.3 w 10 M 282.388 108.6743 m S 0 g 1 w 4 M 282.388 108.6743 m F 0 G 0.3 w 10 M 263.3438 108.6743 m S 0 g 1 w 4 M 263.3438 108.6743 m F 0 G 0.3 w 10 M 263.3438 108.6743 m S 0 g 1 w 4 M 263.3438 108.6743 m F 1 g 263.3438 108.6743 m F 0 G 0.3 w 10 M 263.3438 108.6743 m S 0 g 1 w 4 M 263.3438 108.6743 m F 0 G 0.3 w 10 M 263.3438 108.6743 m S 0 g 1 w 4 M 263.3438 108.6743 m F 0 G 0.3 w 10 M 244.2997 108.6743 m S 0 g 1 w 4 M 244.2997 108.6743 m F 0 G 0.3 w 10 M 244.2997 108.6743 m S 244.2997 108.6743 m S 244.2997 108.6743 m S 0 g 1 w 4 M 244.2997 108.6743 m F 0 G 0.3 w 10 M 244.2997 108.6743 m S 244.2997 108.6743 m S 1 g 1 w 4 M 244.2997 108.6743 m F 0 G 0.3 w 10 M 244.2997 108.6743 m S 0 g 1 w 4 M 244.2997 108.6743 m F 0 G 0.3 w 10 M 244.2997 108.6743 m S 244.2997 108.6743 m S 263.3438 90.0922 m S 0 g 1 w 4 M 263.3438 90.0922 m F 0 G 0.3 w 10 M 263.3438 90.0922 m S 263.3438 90.0922 m S 263.3438 90.0922 m S 0 g 1 w 4 M 263.3438 90.0922 m F 0 G 0.3 w 10 M 263.3438 90.0922 m S 263.3438 90.0922 m S 1 g 1 w 4 M 258.3258 90.0922 m 258.3258 87.3989 260.5725 85.2156 263.3438 85.2156 c 266.1152 85.2156 268.3619 87.3989 268.3619 90.0922 c F 268.3619 90.0922 m 268.3619 92.7854 266.1152 94.9688 263.3438 94.9688 c 260.5725 94.9688 258.3258 92.7854 258.3258 90.0922 c F 263.3438 90.0922 m F 0 G 0.3 w 10 M 263.3438 90.0922 m S 0 g 1 w 4 M 263.3438 90.0922 m F 0 G 0.3 w 10 M 263.3438 90.0922 m S 263.3438 90.0922 m S 0 g 1 w 4 M 262.4379 89.1995 m 262.4379 86.2092 L 264.2498 86.2092 L 264.2498 89.1995 L 267.2434 89.1901 L 267.2434 90.9944 L 264.2498 90.9851 L 264.2498 93.9754 L 262.4379 93.9754 L 262.4379 90.9851 L 259.4443 90.9944 L 259.4443 89.1901 L 262.4379 89.1995 L f 0 G 0.3 w 10 M 282.388 90.0922 m S 0 g 1 w 4 M 282.388 90.0922 m F 0 G 0.3 w 10 M 282.388 90.0922 m S 282.388 90.0922 m S 282.388 90.0922 m S 0 g 1 w 4 M 282.388 90.0922 m F 0 G 0.3 w 10 M 282.388 90.0922 m S 282.388 90.0922 m S 1 g 1 w 4 M 277.3699 90.0922 m 277.3699 87.3989 279.6166 85.2156 282.388 85.2156 c 285.1594 85.2156 287.4061 87.3989 287.4061 90.0922 c F 287.4061 90.0922 m 287.4061 92.7854 285.1594 94.9688 282.388 94.9688 c 279.6166 94.9688 277.3699 92.7854 277.3699 90.0922 c F 282.388 90.0922 m F 0 G 0.3 w 10 M 282.388 90.0922 m S 0 g 1 w 4 M 282.388 90.0922 m F 0 G 0.3 w 10 M 282.388 90.0922 m S 282.388 90.0922 m S 0 g 1 w 4 M 281.4821 89.1995 m 281.4821 86.2092 L 283.2939 86.2092 L 283.2939 89.1995 L 286.2876 89.1901 L 286.2876 90.9944 L 283.2939 90.9851 L 283.2939 93.9754 L 281.4821 93.9754 L 281.4821 90.9851 L 278.4884 90.9944 L 278.4884 89.1901 L 281.4821 89.1995 L f 0 G 0.3 w 10 M 244.2997 90.0922 m S 0 g 1 w 4 M 244.2997 90.0922 m F 0 G 0.3 w 10 M 244.2997 90.0922 m S 244.2997 90.0922 m S 244.2997 90.0922 m S 0 g 1 w 4 M 244.2997 90.0922 m F 0 G 0.3 w 10 M 244.2997 90.0922 m S 244.2997 90.0922 m S 1 g 1 w 4 M 239.2816 90.0922 m 239.2816 87.3989 241.5283 85.2156 244.2997 85.2156 c 247.0711 85.2156 249.3178 87.3989 249.3178 90.0922 c F 249.3178 90.0922 m 249.3178 92.7854 247.0711 94.9688 244.2997 94.9688 c 241.5283 94.9688 239.2816 92.7854 239.2816 90.0922 c F 244.2997 90.0922 m F 0 G 0.3 w 10 M 244.2997 90.0922 m S 0 g 1 w 4 M 244.2997 90.0922 m F 0 G 0.3 w 10 M 244.2997 90.0922 m S 244.2997 90.0922 m S 0 g 1 w 4 M 243.3937 89.1995 m 243.3937 86.2092 L 245.2056 86.2092 L 245.2056 89.1995 L 248.1993 89.1901 L 248.1993 90.9944 L 245.2056 90.9851 L 245.2056 93.9754 L 243.3937 93.9754 L 243.3937 90.9851 L 240.4001 90.9944 L 240.4001 89.1901 L 243.3937 89.1995 L f 0 G 0.3 w 10 M 168.2126 127.2564 m S 168.2126 127.2564 m S 168.2126 127.2564 m S 168.2126 127.2564 m S 168.2126 127.2564 m S 168.2126 127.2564 m S 168.2126 127.2564 m S 168.2126 127.2564 m S 168.2126 127.2564 m S 0 g 1 w 4 M 168.2126 127.2564 m F 0 G 0.3 w 10 M 168.2126 127.2564 m S 0 g 1 w 4 M 168.2126 127.2564 m F 1 g 168.2126 127.2564 m F 0 G 0.3 w 10 M 168.2126 127.2564 m S 0 g 1 w 4 M 168.2126 127.2564 m F 0 G 0.3 w 10 M 168.2126 127.2564 m S 0 g 1 w 4 M 168.2126 127.2564 m F 0 G 0.3 w 10 M 244.2997 108.6743 m S 244.2997 108.6743 m S 244.2997 108.6743 m S 244.2997 108.6743 m S 244.2997 108.6743 m S 244.2997 108.6743 m S 244.2997 108.6743 m S 244.2997 108.6743 m S 244.2997 108.6743 m S 0 g 1 w 4 M 244.2997 108.6743 m F 0 G 0.3 w 10 M 244.2997 108.6743 m S 0 g 1 w 4 M 244.2997 108.6743 m F 1 g 239.2911 108.6743 m 239.2911 105.9811 241.5335 103.7977 244.2997 103.7977 c 247.0658 103.7977 249.3083 105.9811 249.3083 108.6743 c F 249.3083 108.6743 m 249.3083 111.3676 247.0658 113.5509 244.2997 113.5509 c 241.5335 113.5509 239.2911 111.3676 239.2911 108.6743 c F 244.2997 108.6743 m F 0 G 0.3 w 10 M 244.2997 108.6743 m S 0 g 1 w 4 M 244.2997 108.6743 m F 0 G 0.3 w 10 M 244.2997 108.6743 m S 0 g 1 w 4 M 244.2997 108.6743 m F 243.3954 109.5673 m 240.4075 109.5766 L 240.4075 107.7723 L 243.3954 107.7815 L F 245.2039 107.7815 m 248.1919 107.7723 L 248.1919 109.5766 L 245.2039 109.5673 L F 240.4075 109.5766 m 248.1919 109.5766 l 248.1919 107.7723 l 240.4075 107.7723 l 240.4075 109.5766 l f 0 G 0.3 w 10 M 263.2542 108.6743 m S 263.2542 108.6743 m S 263.2542 108.6743 m S 263.2542 108.6743 m S 263.2542 108.6743 m S 263.2542 108.6743 m S 263.2542 108.6743 m S 263.3438 108.6743 m S 263.3438 108.6743 m S 263.2542 108.6743 m S 282.388 108.6743 m S 263.3438 108.6743 m S 282.388 108.6743 m S 282.388 108.6743 m S 282.388 108.6743 m S 263.3438 108.6743 m S 263.2542 108.6743 m S 263.3438 108.6743 m S 263.3438 108.6743 m S 263.2542 108.6743 m S 282.388 108.6743 m S 263.3438 108.6743 m S 282.388 108.6743 m S 282.388 108.6743 m S 282.388 108.6743 m S 263.3438 108.6743 m S 263.3438 108.6743 m S 0 g 1 w 4 M 263.3438 108.6743 m F 0 G 0.3 w 10 M 263.3438 108.6743 m S 263.3438 108.6743 m S 263.3438 108.6743 m S 0 g 1 w 4 M 263.3438 108.6743 m F 0 G 0.3 w 10 M 263.3438 108.6743 m S 263.3438 108.6743 m S 1 g 1 w 4 M 258.3258 108.6743 m 258.3258 105.981 260.5725 103.7977 263.3438 103.7977 c 266.1152 103.7977 268.3619 105.981 268.3619 108.6743 c F 268.3619 108.6743 m 268.3619 111.3676 266.1152 113.5509 263.3438 113.5509 c 260.5725 113.5509 258.3258 111.3676 258.3258 108.6743 c F 263.3438 108.6743 m F 0 G 0.3 w 10 M 263.3438 108.6743 m S 0 g 1 w 4 M 263.3438 108.6743 m F 0 G 0.3 w 10 M 263.3438 108.6743 m S 263.3438 108.6743 m S 0 g 1 w 4 M 262.4379 107.7816 m 262.4379 104.7913 L 264.2498 104.7913 L 264.2498 107.7816 L 267.2434 107.7722 L 267.2434 109.5766 L 264.2498 109.5673 L 264.2498 112.5576 L 262.4379 112.5576 L 262.4379 109.5673 L 259.4443 109.5766 L 259.4443 107.7722 L 262.4379 107.7816 L f 0 G 0.3 w 10 M 282.388 108.6743 m S 0 g 1 w 4 M 282.388 108.6743 m F 0 G 0.3 w 10 M 282.388 108.6743 m S 282.388 108.6743 m S 282.388 108.6743 m S 0 g 1 w 4 M 282.388 108.6743 m F 0 G 0.3 w 10 M 282.388 108.6743 m S 282.388 108.6743 m S 1 g 1 w 4 M 277.3699 108.6743 m 277.3699 105.981 279.6166 103.7977 282.388 103.7977 c 285.1594 103.7977 287.4061 105.981 287.4061 108.6743 c F 287.4061 108.6743 m 287.4061 111.3676 285.1594 113.5509 282.388 113.5509 c 279.6166 113.5509 277.3699 111.3676 277.3699 108.6743 c F 282.388 108.6743 m F 0 G 0.3 w 10 M 282.388 108.6743 m S 0 g 1 w 4 M 282.388 108.6743 m F 0 G 0.3 w 10 M 282.388 108.6743 m S 282.388 108.6743 m S 0 g 1 w 4 M 281.4821 107.7816 m 281.4821 104.7913 L 283.2939 104.7913 L 283.2939 107.7816 L 286.2876 107.7722 L 286.2876 109.5766 L 283.2939 109.5673 L 283.2939 112.5576 L 281.4821 112.5576 L 281.4821 109.5673 L 278.4884 109.5766 L 278.4884 107.7722 L 281.4821 107.7816 L f 0 G 0.3 w 10 M 320.4584 145.8386 m S 320.4584 164.4207 m S 320.4584 108.6744 m S 320.4584 127.2565 m S 320.4584 127.2565 m S 320.4584 145.8386 m S 301.4501 108.6744 m S 301.4501 127.2565 m S 320.4584 127.2565 m S 320.4584 108.6744 m S 310.9543 117.9654 m S 263.4334 145.8386 m S 263.4334 164.4207 m S 282.4417 164.4207 m S 282.4417 145.8386 m S 272.9376 155.1296 m S 282.4417 127.2565 m S 282.4417 145.8386 m S 301.4501 145.8386 m S 301.4501 127.2565 m S 291.9459 136.5475 m S 282.4417 108.6744 m S 282.4417 127.2565 m S 301.4501 127.2565 m S 301.4501 108.6744 m S 291.9459 117.9654 m S 263.4334 108.6744 m S 263.4334 127.2565 m S 282.4417 127.2565 m S 282.4417 108.6744 m S 272.9376 117.9654 m S 263.4334 127.2565 m S 263.4334 145.8386 m S 282.4417 145.8386 m S 282.4417 127.2565 m S 272.9376 136.5475 m S 282.4417 145.8386 m S 282.4417 164.4207 m S 301.4501 164.4207 m S 301.4501 145.8386 m S 291.9459 155.1296 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 320.4584 164.4207 m S 320.4584 145.8386 m S 310.9543 155.1296 m S 301.4501 127.2565 m S 301.4501 145.8386 m S 320.4584 145.8386 m S 320.4584 127.2565 m S 310.9543 136.5475 m S 0 g 1 w 4 M 310.9543 117.9654 m F 272.9376 117.9654 m F 310.9543 155.1296 m F 272.9376 155.1296 m F 0 G 0.3 w 10 M 244.4251 108.6744 m S 244.4251 127.2565 m S 263.4334 127.2565 m S 263.4334 108.6744 m S 253.9293 117.9654 m S 206.4084 145.8386 m S 206.4084 164.4207 m S 225.4167 164.4207 m S 225.4167 145.8386 m S 215.9126 155.1296 m S 225.4167 127.2565 m S 225.4167 145.8386 m S 244.4251 145.8386 m S 244.4251 127.2565 m S 234.9209 136.5475 m S 225.4167 108.6744 m S 225.4167 127.2565 m S 244.4251 127.2565 m S 244.4251 108.6744 m S 234.9209 117.9654 m S 206.4084 108.6744 m S 206.4084 127.2565 m S 225.4167 127.2565 m S 225.4167 108.6744 m S 215.9126 117.9654 m S 206.4084 127.2565 m S 206.4084 145.8386 m S 225.4167 145.8386 m S 225.4167 127.2565 m S 215.9126 136.5475 m S 225.4167 145.8386 m S 225.4167 164.4207 m S 244.4251 164.4207 m S 244.4251 145.8386 m S 234.9209 155.1296 m S 244.4251 145.8386 m S 244.4251 164.4207 m S 263.4334 164.4207 m S 263.4334 145.8386 m S 253.9293 155.1296 m S 244.4251 127.2565 m S 244.4251 145.8386 m S 263.4334 145.8386 m S 263.4334 127.2565 m S 253.9293 136.5475 m S 0 g 1 w 4 M 253.9293 117.9654 m F 215.9126 117.9654 m F 253.9293 155.1296 m F 215.9126 155.1296 m F 0 G 0.3 w 10 M 320.4584 201.5849 m S 320.4584 220.1669 m S 320.4584 164.4207 m S 320.4584 183.0028 m S 320.4584 183.0028 m S 320.4584 201.5849 m S 301.4501 164.4207 m S 301.4501 183.0028 m S 320.4584 183.0028 m S 320.4584 164.4207 m S 310.9543 173.7117 m S 263.4334 201.5849 m S 263.4334 220.1669 m S 282.4417 220.1669 m S 282.4417 201.5849 m S 272.9376 210.8759 m S 282.4417 183.0028 m S 282.4417 201.5849 m S 301.4501 201.5849 m S 301.4501 183.0028 m S 291.9459 192.2937 m S 282.4417 164.4207 m S 282.4417 183.0028 m S 301.4501 183.0028 m S 301.4501 164.4207 m S 291.9459 173.7117 m S 263.4334 164.4207 m S 263.4334 183.0028 m S 282.4417 183.0028 m S 282.4417 164.4207 m S 272.9376 173.7117 m S 263.4334 183.0028 m S 263.4334 201.5849 m S 282.4417 201.5849 m S 282.4417 183.0028 m S 272.9376 192.2937 m S 282.4417 201.5849 m S 282.4417 220.1669 m S 301.4501 220.1669 m S 301.4501 201.5849 m S 291.9459 210.8759 m S 301.4501 201.5849 m S 301.4501 220.1669 m S 320.4584 220.1669 m S 320.4584 201.5849 m S 310.9543 210.8759 m S 301.4501 183.0028 m S 301.4501 201.5849 m S 320.4584 201.5849 m S 320.4584 183.0028 m S 310.9543 192.2937 m S 0 g 1 w 4 M 310.9543 173.7117 m F 272.9376 173.7117 m F 310.9543 210.8759 m F 272.9376 210.8759 m F 0 G 0.3 w 10 M 244.4251 164.4207 m S 244.4251 183.0028 m S 263.4334 183.0028 m S 263.4334 164.4207 m S 253.9293 173.7117 m S 206.4084 201.5849 m S 206.4084 220.1669 m S 225.4167 220.1669 m S 225.4167 201.5849 m S 215.9126 210.8759 m S 225.4167 183.0028 m S 225.4167 201.5849 m S 244.4251 201.5849 m S 244.4251 183.0028 m S 234.9209 192.2937 m S 225.4167 164.4207 m S 225.4167 183.0028 m S 244.4251 183.0028 m S 244.4251 164.4207 m S 234.9209 173.7117 m S 206.4084 164.4207 m S 206.4084 183.0028 m S 225.4167 183.0028 m S 225.4167 164.4207 m S 215.9126 173.7117 m S 206.4084 183.0028 m S 206.4084 201.5849 m S 225.4167 201.5849 m S 225.4167 183.0028 m S 215.9126 192.2937 m S 225.4167 201.5849 m S 225.4167 220.1669 m S 244.4251 220.1669 m S 244.4251 201.5849 m S 234.9209 210.8759 m S 244.4251 201.5849 m S 244.4251 220.1669 m S 263.4334 220.1669 m S 263.4334 201.5849 m S 253.9293 210.8759 m S 244.4251 183.0028 m S 244.4251 201.5849 m S 263.4334 201.5849 m S 263.4334 183.0028 m S 253.9293 192.2937 m S 0 g 1 w 4 M 253.9293 173.7117 m F 215.9126 173.7117 m F 253.9293 210.8759 m F 215.9126 210.8759 m F 0 G 0.3 w 10 M 320.4584 220.1669 m S 301.4501 220.1669 m S 320.4584 220.1669 m S 282.4417 220.1669 m S 301.4501 220.1669 m S 263.4334 220.1669 m S 282.4417 220.1669 m S 244.4251 220.1669 m S 263.4334 220.1669 m S 225.4167 220.1669 m S 244.4251 220.1669 m S 206.4084 220.1669 m S 225.4167 220.1669 m S 301.4501 108.6744 m S 301.4501 127.2565 m S 320.4584 127.2565 m S 320.4584 108.6744 m S 310.9543 117.9654 m S 263.4334 145.8386 m S 263.4334 164.4207 m S 282.4417 164.4207 m S 282.4417 145.8386 m S 282.4417 127.2565 m S 282.4417 145.8386 m S 301.4501 145.8386 m S 301.4501 127.2565 m S 291.9459 136.5475 m S 282.4417 108.6744 m S 282.4417 127.2565 m S 301.4501 127.2565 m S 301.4501 108.6744 m S 291.9459 117.9654 m S 263.4334 108.6744 m S 263.4334 127.2565 m S 282.4417 127.2565 m S 282.4417 108.6744 m S 272.9376 117.9654 m S 263.4334 127.2565 m S 263.4334 145.8386 m S 282.4417 145.8386 m S 282.4417 127.2565 m S 272.9376 136.5475 m S 282.4417 145.8386 m S 282.4417 164.4207 m S 301.4501 164.4207 m S 301.4501 145.8386 m S 291.9459 155.1296 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 320.4584 164.4207 m S 320.4584 145.8386 m S 310.9543 155.1296 m S 301.4501 127.2565 m S 301.4501 145.8386 m S 320.4584 145.8386 m S 320.4584 127.2565 m S 310.9543 136.5475 m S 0 g 1 w 4 M 310.9543 117.9654 m F 272.9376 117.9654 m F 310.9543 155.1296 m F 0 G 0.3 w 10 M 244.4251 108.6744 m S 244.4251 127.2565 m S 263.4334 127.2565 m S 263.4334 108.6744 m S 253.9293 117.9654 m S 206.4084 145.8386 m S 206.4084 164.4207 m S 225.4167 164.4207 m S 225.4167 145.8386 m S 215.9126 155.1296 m S 225.4167 127.2565 m S 225.4167 145.8386 m S 244.4251 145.8386 m S 244.4251 127.2565 m S 234.9209 136.5475 m S 225.4167 108.6744 m S 225.4167 127.2565 m S 244.4251 127.2565 m S 244.4251 108.6744 m S 234.9209 117.9654 m S 206.4084 108.6744 m S 206.4084 127.2565 m S 225.4167 127.2565 m S 225.4167 108.6744 m S 215.9126 117.9654 m S 206.4084 127.2565 m S 206.4084 145.8386 m S 225.4167 145.8386 m S 225.4167 127.2565 m S 215.9126 136.5475 m S 225.4167 145.8386 m S 225.4167 164.4207 m S 244.4251 164.4207 m S 244.4251 145.8386 m S 234.9209 155.1296 m S 244.4251 145.8386 m S 244.4251 164.4207 m S 263.4334 164.4207 m S 263.4334 145.8386 m S 253.9293 155.1296 m S 244.4251 127.2565 m S 244.4251 145.8386 m S 263.4334 145.8386 m S 263.4334 127.2565 m S 253.9293 136.5475 m S 0 g 1 w 4 M 253.9293 117.9654 m F 215.9126 117.9654 m F 253.9293 155.1296 m F 215.9126 155.1296 m F 0 G 0.3 w 10 M 301.4501 164.4207 m S 301.4501 183.0028 m S 320.4584 183.0028 m S 320.4584 164.4207 m S 310.9543 173.7117 m S 263.4334 201.5849 m S 263.4334 220.1669 m S 282.4417 220.1669 m S 282.4417 201.5849 m S 272.9376 210.8759 m S 282.4417 183.0028 m S 282.4417 201.5849 m S 301.4501 201.5849 m S 301.4501 183.0028 m S 291.9459 192.2937 m S 282.4417 164.4207 m S 282.4417 183.0028 m S 301.4501 183.0028 m S 301.4501 164.4207 m S 291.9459 173.7117 m S 263.4334 164.4207 m S 263.4334 183.0028 m S 282.4417 183.0028 m S 282.4417 164.4207 m S 263.4334 183.0028 m S 263.4334 201.5849 m S 282.4417 201.5849 m S 282.4417 183.0028 m S 272.9376 192.2937 m S 282.4417 201.5849 m S 282.4417 220.1669 m S 301.4501 220.1669 m S 301.4501 201.5849 m S 291.9459 210.8759 m S 301.4501 201.5849 m S 301.4501 220.1669 m S 320.4584 220.1669 m S 320.4584 201.5849 m S 310.9543 210.8759 m S 301.4501 183.0028 m S 301.4501 201.5849 m S 320.4584 201.5849 m S 320.4584 183.0028 m S 310.9543 192.2937 m S 0 g 1 w 4 M 310.9543 173.7117 m F 310.9543 210.8759 m F 272.9376 210.8759 m F 0 G 0.3 w 10 M 244.4251 164.4207 m S 244.4251 183.0028 m S 263.4334 183.0028 m S 263.4334 164.4207 m S 253.9293 173.7117 m S 206.4084 201.5849 m S 206.4084 220.1669 m S 225.4167 220.1669 m S 225.4167 201.5849 m S 215.9126 210.8759 m S 225.4167 183.0028 m S 225.4167 201.5849 m S 244.4251 201.5849 m S 244.4251 183.0028 m S 234.9209 192.2937 m S 225.4167 164.4207 m S 225.4167 183.0028 m S 244.4251 183.0028 m S 244.4251 164.4207 m S 234.9209 173.7117 m S 206.4084 164.4207 m S 206.4084 183.0028 m S 225.4167 183.0028 m S 225.4167 164.4207 m S 215.9126 173.7117 m S 206.4084 183.0028 m S 206.4084 201.5849 m S 225.4167 201.5849 m S 225.4167 183.0028 m S 215.9126 192.2937 m S 225.4167 201.5849 m S 225.4167 220.1669 m S 244.4251 220.1669 m S 244.4251 201.5849 m S 234.9209 210.8759 m S 244.4251 201.5849 m S 244.4251 220.1669 m S 263.4334 220.1669 m S 263.4334 201.5849 m S 253.9293 210.8759 m S 244.4251 183.0028 m S 244.4251 201.5849 m S 263.4334 201.5849 m S 263.4334 183.0028 m S 253.9293 192.2937 m S 0 g 1 w 4 M 253.9293 173.7117 m F 215.9126 173.7117 m F 253.9293 210.8759 m F 215.9126 210.8759 m F 0 G 0.3 w 10 M 301.4501 220.1669 m S 320.4584 220.1669 m S 282.4417 220.1669 m S 301.4501 220.1669 m S 263.4334 220.1669 m S 282.4417 220.1669 m S 244.4251 220.1669 m S 263.4334 220.1669 m S 225.4167 220.1669 m S 244.4251 220.1669 m S 206.4084 220.1669 m S 225.4167 220.1669 m S 1 w 4 M 310.9543 136.5475 m 215.9126 136.5475 l S 310.9543 192.2937 m 215.9126 192.2937 l S 291.9459 117.9654 m 291.9459 210.8759 l S 0.3 w 10 M 282.4417 127.2565 m S 0 g 1 w 4 M 282.4417 127.2565 m F 0 G 0.3 w 10 M 282.4417 127.2565 m S 282.4417 127.2565 m S 282.4417 127.2565 m S 0 g 1 w 4 M 282.4417 127.2565 m F 0 G 0.3 w 10 M 282.4417 127.2565 m S 282.4417 127.2565 m S 1 g 1 w 4 M 282.4417 127.2565 m F 0 G 0.3 w 10 M 282.4417 127.2565 m S 0 g 1 w 4 M 282.4417 127.2565 m F 0 G 0.3 w 10 M 282.4417 127.2565 m S 282.4417 127.2565 m S 263.4334 127.2565 m S 0 g 1 w 4 M 263.4334 127.2565 m F 0 G 0.3 w 10 M 263.4334 127.2565 m S 263.4334 127.2565 m S 263.4334 127.2565 m S 0 g 1 w 4 M 263.4334 127.2565 m F 0 G 0.3 w 10 M 263.4334 127.2565 m S 263.4334 127.2565 m S 1 g 1 w 4 M 263.4334 127.2565 m F 0 G 0.3 w 10 M 263.4334 127.2565 m S 0 g 1 w 4 M 263.4334 127.2565 m F 0 G 0.3 w 10 M 263.4334 127.2565 m S 263.4334 127.2565 m S 244.4251 127.2565 m S 0 g 1 w 4 M 244.4251 127.2565 m F 0 G 0.3 w 10 M 244.4251 127.2565 m S 244.4251 127.2565 m S 244.4251 127.2565 m S 0 g 1 w 4 M 244.4251 127.2565 m F 0 G 0.3 w 10 M 244.4251 127.2565 m S 244.4251 127.2565 m S 1 g 1 w 4 M 244.4251 127.2565 m F 0 G 0.3 w 10 M 244.4251 127.2565 m S 0 g 1 w 4 M 244.4251 127.2565 m F 0 G 0.3 w 10 M 244.4251 127.2565 m S 244.4251 127.2565 m S 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 301.4501 145.8386 m S 1 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 0 g 1 w 4 M 301.4501 164.4207 m F 0 G 0.3 w 10 M 301.4501 164.4207 m S 301.4501 164.4207 m S 301.4501 164.4207 m S 0 g 1 w 4 M 301.4501 164.4207 m F 0 G 0.3 w 10 M 301.4501 164.4207 m S 301.4501 164.4207 m S 1 g 1 w 4 M 301.4501 164.4207 m F 0 G 0.3 w 10 M 301.4501 164.4207 m S 0 g 1 w 4 M 301.4501 164.4207 m F 0 G 0.3 w 10 M 301.4501 164.4207 m S 301.4501 164.4207 m S 301.4501 183.0028 m S 0 g 1 w 4 M 301.4501 183.0028 m F 0 G 0.3 w 10 M 301.4501 183.0028 m S 301.4501 183.0028 m S 301.4501 183.0028 m S 0 g 1 w 4 M 301.4501 183.0028 m F 0 G 0.3 w 10 M 301.4501 183.0028 m S 301.4501 183.0028 m S 1 g 1 w 4 M 301.4501 183.0028 m F 0 G 0.3 w 10 M 301.4501 183.0028 m S 0 g 1 w 4 M 301.4501 183.0028 m F 0 G 0.3 w 10 M 301.4501 183.0028 m S 301.4501 183.0028 m S 282.4417 201.5849 m S 282.4417 201.5849 m S 263.4334 201.5849 m S 282.4417 201.5849 m S 263.4334 201.5849 m S 282.4417 201.5849 m S 244.4251 201.5849 m S 263.4334 201.5849 m S 244.4251 201.5849 m S 244.4251 201.5849 m S 244.4251 201.5849 m S 263.4334 201.5849 m S 282.4417 201.5849 m S 0 g 1 w 4 M 282.4417 201.5849 m F 0 G 0.3 w 10 M 282.4417 201.5849 m S 282.4417 201.5849 m S 282.4417 201.5849 m S 0 g 1 w 4 M 282.4417 201.5849 m F 0 G 0.3 w 10 M 282.4417 201.5849 m S 282.4417 201.5849 m S 1 g 1 w 4 M 287.4503 201.5849 m 287.4503 204.2781 285.2078 206.4615 282.4417 206.4615 c 279.6755 206.4615 277.4331 204.2781 277.4331 201.5849 c F 277.4331 201.5849 m 277.4331 198.8916 279.6755 196.7082 282.4417 196.7082 c 285.2078 196.7082 287.4503 198.8916 287.4503 201.5849 c F 282.4417 201.5849 m F 0 G 0.3 w 10 M 282.4417 201.5849 m S 0 g 1 w 4 M 282.4417 201.5849 m F 0 G 0.3 w 10 M 282.4417 201.5849 m S 282.4417 201.5849 m S 0 g 1 w 4 M 283.3459 202.4776 m 283.3459 205.4679 L 281.5375 205.4679 L 281.5375 202.4776 L 278.5495 202.4869 L 278.5495 200.6826 L 281.5375 200.6919 L 281.5375 197.7016 L 283.3459 197.7016 L 283.3459 200.6919 L 286.3339 200.6826 L 286.3339 202.4869 L 283.3459 202.4776 L f 0 G 0.3 w 10 M 263.4334 201.5849 m S 0 g 1 w 4 M 263.4334 201.5849 m F 0 G 0.3 w 10 M 263.4334 201.5849 m S 263.4334 201.5849 m S 263.4334 201.5849 m S 0 g 1 w 4 M 263.4334 201.5849 m F 0 G 0.3 w 10 M 263.4334 201.5849 m S 263.4334 201.5849 m S 1 g 1 w 4 M 268.442 201.5849 m 268.442 204.2781 266.1995 206.4615 263.4334 206.4615 c 260.6672 206.4615 258.4248 204.2781 258.4248 201.5849 c F 258.4248 201.5849 m 258.4248 198.8916 260.6672 196.7082 263.4334 196.7082 c 266.1995 196.7082 268.442 198.8916 268.442 201.5849 c F 263.4334 201.5849 m F 0 G 0.3 w 10 M 263.4334 201.5849 m S 0 g 1 w 4 M 263.4334 201.5849 m F 0 G 0.3 w 10 M 263.4334 201.5849 m S 263.4334 201.5849 m S 0 g 1 w 4 M 264.3376 202.4776 m 264.3376 205.4679 L 262.5292 205.4679 L 262.5292 202.4776 L 259.5412 202.4869 L 259.5412 200.6826 L 262.5292 200.6919 L 262.5292 197.7016 L 264.3376 197.7016 L 264.3376 200.6919 L 267.3256 200.6826 L 267.3256 202.4869 L 264.3376 202.4776 L f 0 G 0.3 w 10 M 244.4251 201.5849 m S 0 g 1 w 4 M 244.4251 201.5849 m F 0 G 0.3 w 10 M 244.4251 201.5849 m S 244.4251 201.5849 m S 244.4251 201.5849 m S 0 g 1 w 4 M 244.4251 201.5849 m F 0 G 0.3 w 10 M 244.4251 201.5849 m S 244.4251 201.5849 m S 1 g 1 w 4 M 249.4337 201.5849 m 249.4337 204.2781 247.1912 206.4615 244.4251 206.4615 c 241.6589 206.4615 239.4165 204.2781 239.4165 201.5849 c F 239.4165 201.5849 m 239.4165 198.8916 241.6589 196.7082 244.4251 196.7082 c 247.1912 196.7082 249.4337 198.8916 249.4337 201.5849 c F 244.4251 201.5849 m F 0 G 0.3 w 10 M 244.4251 201.5849 m S 0 g 1 w 4 M 244.4251 201.5849 m F 0 G 0.3 w 10 M 244.4251 201.5849 m S 244.4251 201.5849 m S 0 g 1 w 4 M 245.3293 202.4776 m 245.3293 205.4679 L 243.5208 205.4679 L 243.5208 202.4776 L 240.5329 202.4869 L 240.5329 200.6826 L 243.5208 200.6919 L 243.5208 197.7016 L 245.3293 197.7016 L 245.3293 200.6919 L 248.3173 200.6826 L 248.3173 202.4869 L 245.3293 202.4776 L f 0 G 0.3 w 10 M 225.4167 145.8386 m S 225.4167 164.4207 m S 225.4167 145.8386 m S 225.4167 145.8386 m S 225.4167 164.4207 m S 225.4167 145.8386 m S 225.4167 164.4207 m S 225.4167 183.0028 m S 225.4167 183.0028 m S 225.4167 183.0028 m S 225.4167 164.4207 m S 225.4167 183.0028 m S 225.4167 145.8386 m S 0 g 1 w 4 M 225.4167 145.8386 m F 0 G 0.3 w 10 M 225.4167 145.8386 m S 225.4167 145.8386 m S 225.4167 145.8386 m S 0 g 1 w 4 M 225.4167 145.8386 m F 0 G 0.3 w 10 M 225.4167 145.8386 m S 225.4167 145.8386 m S 1 g 1 w 4 M 225.4167 145.8386 m F 0 G 0.3 w 10 M 225.4167 145.8386 m S 0 g 1 w 4 M 225.4167 145.8386 m F 0 G 0.3 w 10 M 225.4167 145.8386 m S 225.4167 145.8386 m S 225.4167 164.4207 m S 0 g 1 w 4 M 225.4167 164.4207 m F 0 G 0.3 w 10 M 225.4167 164.4207 m S 225.4167 164.4207 m S 225.4167 164.4207 m S 0 g 1 w 4 M 225.4167 164.4207 m F 0 G 0.3 w 10 M 225.4167 164.4207 m S 225.4167 164.4207 m S 1 g 1 w 4 M 225.4167 164.4207 m F 0 G 0.3 w 10 M 225.4167 164.4207 m S 0 g 1 w 4 M 225.4167 164.4207 m F 0 G 0.3 w 10 M 225.4167 164.4207 m S 225.4167 164.4207 m S 225.4167 183.0028 m S 0 g 1 w 4 M 225.4167 183.0028 m F 0 G 0.3 w 10 M 225.4167 183.0028 m S 225.4167 183.0028 m S 225.4167 183.0028 m S 0 g 1 w 4 M 225.4167 183.0028 m F 0 G 0.3 w 10 M 225.4167 183.0028 m S 225.4167 183.0028 m S 1 g 1 w 4 M 225.4167 183.0028 m F 0 G 0.3 w 10 M 225.4167 183.0028 m S 0 g 1 w 4 M 225.4167 183.0028 m F 0 G 0.3 w 10 M 225.4167 183.0028 m S 225.4167 183.0028 m S 272.9376 155.1296 m S 272.9376 155.1296 m S 253.9293 155.1296 m S 272.9376 155.1296 m S 253.9293 155.1296 m S 253.9293 155.1296 m S 253.9293 155.1296 m S 272.9376 155.1296 m S 272.9376 173.7117 m S 272.9376 173.7117 m S 253.9293 173.7117 m S 272.9376 173.7117 m S 253.9293 173.7117 m S 253.9293 173.7117 m S 253.9293 173.7117 m S 272.9376 173.7117 m S 282.4417 145.8386 m S 0 g 1 w 4 M 282.4417 145.8386 m F 0 G 0.3 w 10 M 282.4417 145.8386 m S 0 g 1 w 4 M 282.4417 145.8386 m F 1 g 287.4503 145.8386 m 287.4503 148.5319 285.2078 150.7152 282.4417 150.7152 c 279.6755 150.7152 277.4331 148.5319 277.4331 145.8386 c F 277.4331 145.8386 m 277.4331 143.1453 279.6755 140.962 282.4417 140.962 c 285.2078 140.962 287.4503 143.1453 287.4503 145.8386 c F 282.4417 145.8386 m F 0 G 0.3 w 10 M 282.4417 145.8386 m S 0 g 1 w 4 M 282.4417 145.8386 m F 0 G 0.3 w 10 M 282.4417 145.8386 m S 0 g 1 w 4 M 282.4417 145.8386 m F 283.3459 144.9456 m 286.3339 144.9364 L 286.3339 146.7407 L 283.3459 146.7314 L F 281.5375 146.7314 m 278.5495 146.7407 L 278.5495 144.9364 L 281.5375 144.9456 L F 286.3339 144.9364 m 278.5495 144.9364 l 278.5495 146.7407 l 286.3339 146.7407 l 286.3339 144.9364 l f 0 G 0.3 w 10 M 263.4334 145.8386 m S 0 g 1 w 4 M 263.4334 145.8386 m F 0 G 0.3 w 10 M 263.4334 145.8386 m S 0 g 1 w 4 M 263.4334 145.8386 m F 1 g 268.442 145.8386 m 268.442 148.5319 266.1995 150.7152 263.4334 150.7152 c 260.6672 150.7152 258.4248 148.5319 258.4248 145.8386 c F 258.4248 145.8386 m 258.4248 143.1453 260.6672 140.962 263.4334 140.962 c 266.1995 140.962 268.442 143.1453 268.442 145.8386 c F 263.4334 145.8386 m F 0 G 0.3 w 10 M 263.4334 145.8386 m S 0 g 1 w 4 M 263.4334 145.8386 m F 0 G 0.3 w 10 M 263.4334 145.8386 m S 0 g 1 w 4 M 263.4334 145.8386 m F 264.3376 144.9456 m 267.3256 144.9364 L 267.3256 146.7407 L 264.3376 146.7314 L F 262.5292 146.7314 m 259.5412 146.7407 L 259.5412 144.9364 L 262.5292 144.9456 L F 267.3256 144.9364 m 259.5412 144.9364 l 259.5412 146.7407 l 267.3256 146.7407 l 267.3256 144.9364 l f 0 G 0.3 w 10 M 244.4251 145.8386 m S 0 g 1 w 4 M 244.4251 145.8386 m F 0 G 0.3 w 10 M 244.4251 145.8386 m S 0 g 1 w 4 M 244.4251 145.8386 m F 1 g 249.4337 145.8386 m 249.4337 148.5319 247.1912 150.7152 244.4251 150.7152 c 241.6589 150.7152 239.4165 148.5319 239.4165 145.8386 c F 239.4165 145.8386 m 239.4165 143.1453 241.6589 140.962 244.4251 140.962 c 247.1912 140.962 249.4337 143.1453 249.4337 145.8386 c F 244.4251 145.8386 m F 0 G 0.3 w 10 M 244.4251 145.8386 m S 0 g 1 w 4 M 244.4251 145.8386 m F 0 G 0.3 w 10 M 244.4251 145.8386 m S 0 g 1 w 4 M 244.4251 145.8386 m F 245.3293 144.9456 m 248.3173 144.9364 L 248.3173 146.7407 L 245.3293 146.7314 L F 243.5208 146.7314 m 240.5329 146.7407 L 240.5329 144.9364 L 243.5208 144.9456 L F 248.3173 144.9364 m 240.5329 144.9364 l 240.5329 146.7407 l 248.3173 146.7407 l 248.3173 144.9364 l f 0 G 0.3 w 10 M 244.4251 164.4207 m S 0 g 1 w 4 M 244.4251 164.4207 m F 0 G 0.3 w 10 M 244.4251 164.4207 m S 0 g 1 w 4 M 244.4251 164.4207 m F 1 g 249.4337 164.4207 m 249.4337 167.1139 247.1912 169.2973 244.4251 169.2973 c 241.6589 169.2973 239.4165 167.1139 239.4165 164.4207 c F 239.4165 164.4207 m 239.4165 161.7274 241.6589 159.544 244.4251 159.544 c 247.1912 159.544 249.4337 161.7274 249.4337 164.4207 c F 244.4251 164.4207 m F 0 G 0.3 w 10 M 244.4251 164.4207 m S 0 g 1 w 4 M 244.4251 164.4207 m F 0 G 0.3 w 10 M 244.4251 164.4207 m S 0 g 1 w 4 M 244.4251 164.4207 m F 245.3293 163.5277 m 248.3173 163.5184 L 248.3173 165.3227 L 245.3293 165.3135 L F 243.5208 165.3135 m 240.5329 165.3227 L 240.5329 163.5184 L 243.5208 163.5277 L F 248.3173 163.5184 m 240.5329 163.5184 l 240.5329 165.3227 l 248.3173 165.3227 l 248.3173 163.5184 l f 0 G 0.3 w 10 M 263.4334 164.4207 m S 0 g 1 w 4 M 263.4334 164.4207 m F 0 G 0.3 w 10 M 263.4334 164.4207 m S 0 g 1 w 4 M 263.4334 164.4207 m F 1 g 268.442 164.4207 m 268.442 167.1139 266.1995 169.2973 263.4334 169.2973 c 260.6672 169.2973 258.4248 167.1139 258.4248 164.4207 c F 258.4248 164.4207 m 258.4248 161.7274 260.6672 159.544 263.4334 159.544 c 266.1995 159.544 268.442 161.7274 268.442 164.4207 c F 263.4334 164.4207 m F 0 G 0.3 w 10 M 263.4334 164.4207 m S 0 g 1 w 4 M 263.4334 164.4207 m F 0 G 0.3 w 10 M 263.4334 164.4207 m S 0 g 1 w 4 M 263.4334 164.4207 m F 264.3376 163.5277 m 267.3256 163.5184 L 267.3256 165.3227 L 264.3376 165.3135 L F 262.5292 165.3135 m 259.5412 165.3227 L 259.5412 163.5184 L 262.5292 163.5277 L F 267.3256 163.5184 m 259.5412 163.5184 l 259.5412 165.3227 l 267.3256 165.3227 l 267.3256 163.5184 l f 0 G 0.3 w 10 M 282.4417 164.4207 m S 0 g 1 w 4 M 282.4417 164.4207 m F 0 G 0.3 w 10 M 282.4417 164.4207 m S 282.4417 164.4207 m S 282.4417 164.4207 m S 0 g 1 w 4 M 282.4417 164.4207 m F 0 G 0.3 w 10 M 282.4417 164.4207 m S 282.4417 164.4207 m S 1 g 1 w 4 M 287.4503 164.4207 m 287.4503 167.1139 285.2078 169.2973 282.4417 169.2973 c 279.6755 169.2973 277.4331 167.1139 277.4331 164.4207 c F 277.4331 164.4207 m 277.4331 161.7274 279.6755 159.544 282.4417 159.544 c 285.2078 159.544 287.4503 161.7274 287.4503 164.4207 c F 282.4417 164.4207 m F 0 G 0.3 w 10 M 282.4417 164.4207 m S 0 g 1 w 4 M 282.4417 164.4207 m F 0 G 0.3 w 10 M 282.4417 164.4207 m S 282.4417 164.4207 m S 0 g 1 w 4 M 283.3459 165.3134 m 283.3459 168.3037 L 281.5375 168.3037 L 281.5375 165.3134 L 278.5495 165.3227 L 278.5495 163.5184 L 281.5375 163.5277 L 281.5375 160.5374 L 283.3459 160.5374 L 283.3459 163.5277 L 286.3339 163.5184 L 286.3339 165.3227 L 283.3459 165.3134 L f 0 G 0.3 w 10 M 263.4334 183.0028 m S 0 g 1 w 4 M 263.4334 183.0028 m F 0 G 0.3 w 10 M 263.4334 183.0028 m S 263.4334 183.0028 m S 263.4334 183.0028 m S 0 g 1 w 4 M 263.4334 183.0028 m F 0 G 0.3 w 10 M 263.4334 183.0028 m S 263.4334 183.0028 m S 1 g 1 w 4 M 268.442 183.0028 m 268.442 185.6961 266.1995 187.8794 263.4334 187.8794 c 260.6672 187.8794 258.4248 185.6961 258.4248 183.0028 c F 258.4248 183.0028 m 258.4248 180.3095 260.6672 178.1262 263.4334 178.1262 c 266.1995 178.1262 268.442 180.3095 268.442 183.0028 c F 263.4334 183.0028 m F 0 G 0.3 w 10 M 263.4334 183.0028 m S 0 g 1 w 4 M 263.4334 183.0028 m F 0 G 0.3 w 10 M 263.4334 183.0028 m S 263.4334 183.0028 m S 0 g 1 w 4 M 264.3376 183.8955 m 264.3376 186.8858 L 262.5292 186.8858 L 262.5292 183.8955 L 259.5412 183.9049 L 259.5412 182.1006 L 262.5292 182.1098 L 262.5292 179.1195 L 264.3376 179.1195 L 264.3376 182.1098 L 267.3256 182.1006 L 267.3256 183.9049 L 264.3376 183.8955 L f 0 G 0.3 w 10 M 244.4251 183.0028 m S 0 g 1 w 4 M 244.4251 183.0028 m F 0 G 0.3 w 10 M 244.4251 183.0028 m S 244.4251 183.0028 m S 244.4251 183.0028 m S 0 g 1 w 4 M 244.4251 183.0028 m F 0 G 0.3 w 10 M 244.4251 183.0028 m S 244.4251 183.0028 m S 1 g 1 w 4 M 249.4337 183.0028 m 249.4337 185.6961 247.1912 187.8794 244.4251 187.8794 c 241.6589 187.8794 239.4165 185.6961 239.4165 183.0028 c F 239.4165 183.0028 m 239.4165 180.3095 241.6589 178.1262 244.4251 178.1262 c 247.1912 178.1262 249.4337 180.3095 249.4337 183.0028 c F 244.4251 183.0028 m F 0 G 0.3 w 10 M 244.4251 183.0028 m S 0 g 1 w 4 M 244.4251 183.0028 m F 0 G 0.3 w 10 M 244.4251 183.0028 m S 244.4251 183.0028 m S 0 g 1 w 4 M 245.3293 183.8955 m 245.3293 186.8858 L 243.5208 186.8858 L 243.5208 183.8955 L 240.5329 183.9049 L 240.5329 182.1006 L 243.5208 182.1098 L 243.5208 179.1195 L 245.3293 179.1195 L 245.3293 182.1098 L 248.3173 182.1006 L 248.3173 183.9049 L 245.3293 183.8955 L f 0 G 0.3 w 10 M 282.4417 183.0028 m S 0 g 1 w 4 M 282.4417 183.0028 m F 0 G 0.3 w 10 M 282.4417 183.0028 m S 282.4417 183.0028 m S 282.4417 183.0028 m S 0 g 1 w 4 M 282.4417 183.0028 m F 0 G 0.3 w 10 M 282.4417 183.0028 m S 282.4417 183.0028 m S 1 g 1 w 4 M 287.4503 183.0028 m 287.4503 185.6961 285.2078 187.8794 282.4417 187.8794 c 279.6755 187.8794 277.4331 185.6961 277.4331 183.0028 c F 277.4331 183.0028 m 277.4331 180.3095 279.6755 178.1262 282.4417 178.1262 c 285.2078 178.1262 287.4503 180.3095 287.4503 183.0028 c F 282.4417 183.0028 m F 0 G 0.3 w 10 M 282.4417 183.0028 m S 0 g 1 w 4 M 282.4417 183.0028 m F 0 G 0.3 w 10 M 282.4417 183.0028 m S 282.4417 183.0028 m S 0 g 1 w 4 M 283.3459 183.8955 m 283.3459 186.8858 L 281.5375 186.8858 L 281.5375 183.8955 L 278.5495 183.9049 L 278.5495 182.1006 L 281.5375 182.1098 L 281.5375 179.1195 L 283.3459 179.1195 L 283.3459 182.1098 L 286.3339 182.1006 L 286.3339 183.9049 L 283.3459 183.8955 L f 0 G 0.3 w 10 M 206.4084 145.8386 m S 206.4084 164.4207 m S 206.4084 108.6744 m S 206.4084 127.2565 m S 206.4084 127.2565 m S 206.4084 145.8386 m S 244.4072 108.6744 m S 244.4072 127.2564 m S 206.4084 127.2565 m S 206.4084 108.6744 m S 253.9293 117.9654 m S 206.3188 145.8386 m S 206.3188 164.4206 m S 225.3629 164.4206 m S 225.3629 145.8386 m S 215.8409 155.1296 m S 225.3629 145.8386 m S 244.4072 145.8386 m S 244.4072 127.2564 m S 234.885 136.5475 m S 225.3629 108.6744 m S 244.4072 127.2564 m S 244.4072 108.6744 m S 234.885 117.9654 m S 206.3188 108.6744 m S 225.3629 108.6744 m S 215.8409 117.9654 m S 206.3188 145.8386 m S 225.3629 145.8386 m S 215.8409 136.5475 m S 225.3629 145.8386 m S 225.3629 164.4206 m S 244.4072 164.4206 m S 244.4072 145.8386 m S 234.885 155.1296 m S 244.4072 145.8386 m S 244.4072 164.4206 m S 206.4084 164.4207 m S 206.4084 145.8386 m S 253.9293 155.1296 m S 244.4072 127.2564 m S 244.4072 145.8386 m S 206.4084 145.8386 m S 206.4084 127.2565 m S 253.9293 136.5475 m S 0 g 1 w 4 M 253.9293 117.9654 m F 215.8409 117.9654 m F 253.9293 155.1296 m F 215.8409 155.1296 m F 0 G 0.3 w 10 M 187.2746 108.6744 m S 206.3188 108.6744 m S 196.7967 117.9654 m S 149.1862 145.8386 m S 149.1862 164.4206 m S 168.2304 164.4206 m S 168.2304 145.8386 m S 158.7084 155.1296 m S 168.2304 127.2564 m S 168.2304 145.8386 m S 187.2746 145.8386 m S 177.7525 136.5475 m S 168.2304 108.6744 m S 168.2304 127.2564 m S 187.2746 108.6744 m S 177.7525 117.9654 m S 149.1862 108.6744 m S 149.1862 127.2564 m S 168.2304 127.2564 m S 168.2304 108.6744 m S 158.7084 117.9654 m S 149.1862 127.2564 m S 149.1862 145.8386 m S 168.2304 145.8386 m S 168.2304 127.2564 m S 158.7084 136.5475 m S 168.2304 145.8386 m S 168.2304 164.4206 m S 187.2746 164.4206 m S 187.2746 145.8386 m S 177.7525 155.1296 m S 187.2746 145.8386 m S 187.2746 164.4206 m S 206.3188 164.4206 m S 206.3188 145.8386 m S 196.7967 155.1296 m S 187.2746 145.8386 m S 206.3188 145.8386 m S 196.7967 136.5475 m S 0 g 1 w 4 M 196.7967 117.9654 m F 158.7084 117.9654 m F 196.7967 155.1296 m F 158.7084 155.1296 m F 0 G 0.3 w 10 M 206.4084 201.5849 m S 206.4084 220.1669 m S 206.4084 164.4207 m S 206.4084 183.0028 m S 206.4084 183.0028 m S 206.4084 201.5849 m S 244.4072 164.4206 m S 244.4072 183.0028 m S 206.4084 183.0028 m S 206.4084 164.4207 m S 253.9293 173.7117 m S 206.3188 201.5848 m S 206.3188 220.1669 m S 225.3629 220.1669 m S 225.3629 201.5848 m S 215.8409 210.8759 m S 225.3629 183.0028 m S 225.3629 201.5848 m S 244.4072 201.5848 m S 244.4072 183.0028 m S 234.885 192.2937 m S 225.3629 164.4206 m S 225.3629 183.0028 m S 244.4072 183.0028 m S 244.4072 164.4206 m S 234.885 173.7117 m S 206.3188 164.4206 m S 206.3188 183.0028 m S 225.3629 183.0028 m S 225.3629 164.4206 m S 215.8409 173.7117 m S 206.3188 183.0028 m S 206.3188 201.5848 m S 225.3629 201.5848 m S 225.3629 183.0028 m S 215.8409 192.2937 m S 225.3629 201.5848 m S 225.3629 220.1669 m S 244.4072 220.1669 m S 244.4072 201.5848 m S 234.885 210.8759 m S 244.4072 201.5848 m S 244.4072 220.1669 m S 206.4084 220.1669 m S 206.4084 201.5849 m S 253.9293 210.8759 m S 244.4072 183.0028 m S 244.4072 201.5848 m S 206.4084 201.5849 m S 206.4084 183.0028 m S 253.9293 192.2937 m S 0 g 1 w 4 M 253.9293 173.7117 m F 215.8409 173.7117 m F 253.9293 210.8759 m F 215.8409 210.8759 m F 0 G 0.3 w 10 M 187.2746 164.4206 m S 187.2746 183.0028 m S 206.3188 183.0028 m S 206.3188 164.4206 m S 196.7967 173.7117 m S 149.1862 201.5848 m S 149.1862 220.1669 m S 168.2304 220.1669 m S 168.2304 201.5848 m S 158.7084 210.8759 m S 168.2304 183.0028 m S 168.2304 201.5848 m S 187.2746 201.5848 m S 187.2746 183.0028 m S 177.7525 192.2937 m S 168.2304 164.4206 m S 168.2304 183.0028 m S 187.2746 183.0028 m S 187.2746 164.4206 m S 177.7525 173.7117 m S 149.1862 164.4206 m S 149.1862 183.0028 m S 168.2304 183.0028 m S 168.2304 164.4206 m S 158.7084 173.7117 m S 149.1862 183.0028 m S 149.1862 201.5848 m S 168.2304 201.5848 m S 168.2304 183.0028 m S 158.7084 192.2937 m S 168.2304 201.5848 m S 168.2304 220.1669 m S 187.2746 220.1669 m S 187.2746 201.5848 m S 177.7525 210.8759 m S 187.2746 201.5848 m S 187.2746 220.1669 m S 206.3188 220.1669 m S 206.3188 201.5848 m S 196.7967 210.8759 m S 187.2746 183.0028 m S 187.2746 201.5848 m S 206.3188 201.5848 m S 206.3188 183.0028 m S 196.7967 192.2937 m S 0 g 1 w 4 M 196.7967 173.7117 m F 158.7084 173.7117 m F 196.7967 210.8759 m F 158.7084 210.8759 m F 0 G 0.3 w 10 M 206.4084 220.1669 m S 244.4072 220.1669 m S 206.4084 220.1669 m S 225.3629 220.1669 m S 244.4072 220.1669 m S 206.3188 220.1669 m S 225.3629 220.1669 m S 187.2746 220.1669 m S 206.3188 220.1669 m S 168.2304 220.1669 m S 187.2746 220.1669 m S 149.1862 220.1669 m S 168.2304 220.1669 m S 244.4072 108.6744 m S 244.4072 127.2564 m S 206.4084 127.2565 m S 206.4084 108.6744 m S 253.9293 117.9654 m S 206.3188 145.8386 m S 206.3188 164.4206 m S 225.3629 164.4206 m S 225.3629 145.8386 m S 225.3629 145.8386 m S 244.4072 145.8386 m S 244.4072 127.2564 m S 234.885 136.5475 m S 225.3629 108.6744 m S 244.4072 127.2564 m S 244.4072 108.6744 m S 234.885 117.9654 m S 206.3188 108.6744 m S 225.3629 108.6744 m S 215.8409 117.9654 m S 206.3188 145.8386 m S 225.3629 145.8386 m S 215.8409 136.5475 m S 225.3629 145.8386 m S 225.3629 164.4206 m S 244.4072 164.4206 m S 244.4072 145.8386 m S 244.4072 145.8386 m S 244.4072 164.4206 m S 206.4084 164.4207 m S 206.4084 145.8386 m S 253.9293 155.1296 m S 244.4072 127.2564 m S 244.4072 145.8386 m S 206.4084 145.8386 m S 206.4084 127.2565 m S 253.9293 136.5475 m S 0 g 1 w 4 M 253.9293 117.9654 m F 215.8409 117.9654 m F 253.9293 155.1296 m F 0 G 0.3 w 10 M 187.2746 108.6744 m S 206.3188 108.6744 m S 196.7967 117.9654 m S 149.1862 145.8386 m S 149.1862 164.4206 m S 168.2304 164.4206 m S 168.2304 145.8386 m S 158.7084 155.1296 m S 168.2304 127.2564 m S 168.2304 145.8386 m S 187.2746 145.8386 m S 177.7525 136.5475 m S 168.2304 108.6744 m S 168.2304 127.2564 m S 187.2746 108.6744 m S 177.7525 117.9654 m S 149.1862 108.6744 m S 149.1862 127.2564 m S 168.2304 127.2564 m S 168.2304 108.6744 m S 158.7084 117.9654 m S 149.1862 127.2564 m S 149.1862 145.8386 m S 168.2304 145.8386 m S 168.2304 127.2564 m S 158.7084 136.5475 m S 168.2304 145.8386 m S 168.2304 164.4206 m S 187.2746 164.4206 m S 187.2746 145.8386 m S 177.7525 155.1296 m S 187.2746 145.8386 m S 187.2746 164.4206 m S 206.3188 164.4206 m S 206.3188 145.8386 m S 196.7967 155.1296 m S 187.2746 145.8386 m S 206.3188 145.8386 m S 196.7967 136.5475 m S 0 g 1 w 4 M 196.7967 117.9654 m F 158.7084 117.9654 m F 196.7967 155.1296 m F 158.7084 155.1296 m F 0 G 0.3 w 10 M 244.4072 164.4206 m S 244.4072 183.0028 m S 206.4084 183.0028 m S 206.4084 164.4207 m S 253.9293 173.7117 m S 206.3188 201.5848 m S 206.3188 220.1669 m S 225.3629 220.1669 m S 225.3629 201.5848 m S 215.8409 210.8759 m S 225.3629 183.0028 m S 225.3629 201.5848 m S 244.4072 201.5848 m S 244.4072 183.0028 m S 234.885 192.2937 m S 225.3629 164.4206 m S 225.3629 183.0028 m S 244.4072 183.0028 m S 244.4072 164.4206 m S 234.885 173.7117 m S 206.3188 164.4206 m S 206.3188 183.0028 m S 225.3629 183.0028 m S 225.3629 164.4206 m S 206.3188 183.0028 m S 206.3188 201.5848 m S 225.3629 201.5848 m S 225.3629 183.0028 m S 215.8409 192.2937 m S 225.3629 201.5848 m S 225.3629 220.1669 m S 244.4072 220.1669 m S 244.4072 201.5848 m S 234.885 210.8759 m S 244.4072 201.5848 m S 244.4072 220.1669 m S 206.4084 220.1669 m S 206.4084 201.5849 m S 253.9293 210.8759 m S 244.4072 183.0028 m S 244.4072 201.5848 m S 206.4084 201.5849 m S 206.4084 183.0028 m S 253.9293 192.2937 m S 0 g 1 w 4 M 253.9293 173.7117 m F 253.9293 210.8759 m F 215.8409 210.8759 m F 0 G 0.3 w 10 M 187.2746 164.4206 m S 187.2746 183.0028 m S 206.3188 183.0028 m S 206.3188 164.4206 m S 196.7967 173.7117 m S 149.1862 201.5848 m S 149.1862 220.1669 m S 168.2304 220.1669 m S 168.2304 201.5848 m S 158.7084 210.8759 m S 168.2304 183.0028 m S 168.2304 201.5848 m S 187.2746 201.5848 m S 187.2746 183.0028 m S 177.7525 192.2937 m S 168.2304 164.4206 m S 168.2304 183.0028 m S 187.2746 183.0028 m S 187.2746 164.4206 m S 177.7525 173.7117 m S 149.1862 164.4206 m S 149.1862 183.0028 m S 168.2304 183.0028 m S 168.2304 164.4206 m S 158.7084 173.7117 m S 149.1862 183.0028 m S 149.1862 201.5848 m S 168.2304 201.5848 m S 168.2304 183.0028 m S 158.7084 192.2937 m S 168.2304 201.5848 m S 168.2304 220.1669 m S 187.2746 220.1669 m S 187.2746 201.5848 m S 177.7525 210.8759 m S 187.2746 201.5848 m S 187.2746 220.1669 m S 206.3188 220.1669 m S 206.3188 201.5848 m S 196.7967 210.8759 m S 187.2746 183.0028 m S 187.2746 201.5848 m S 206.3188 201.5848 m S 206.3188 183.0028 m S 196.7967 192.2937 m S 0 g 1 w 4 M 196.7967 173.7117 m F 158.7084 173.7117 m F 196.7967 210.8759 m F 158.7084 210.8759 m F 0 G 0.3 w 10 M 244.4072 220.1669 m S 206.4084 220.1669 m S 225.3629 220.1669 m S 244.4072 220.1669 m S 206.3188 220.1669 m S 225.3629 220.1669 m S 187.2746 220.1669 m S 206.3188 220.1669 m S 168.2304 220.1669 m S 187.2746 220.1669 m S 149.1862 220.1669 m S 168.2304 220.1669 m S 1 w 4 M 253.9293 136.5475 m 158.7084 136.5475 l S 253.9293 192.2937 m 158.7084 192.2937 l S 177.2525 117.9654 m S 177.2525 210.8759 m S 0.3 w 10 M 244.4072 145.8386 m S 0 g 1 w 4 M 244.4072 145.8386 m F 0 G 0.3 w 10 M 244.4072 145.8386 m S 244.4072 145.8386 m S 244.4072 145.8386 m S 0 g 1 w 4 M 244.4072 145.8386 m F 0 G 0.3 w 10 M 244.4072 145.8386 m S 244.4072 145.8386 m S 1 g 1 w 4 M 244.4072 145.8386 m F 0 G 0.3 w 10 M 244.4072 145.8386 m S 0 g 1 w 4 M 244.4072 145.8386 m F 0 G 0.3 w 10 M 244.4072 145.8386 m S 244.4072 145.8386 m S 244.4072 164.4206 m S 0 g 1 w 4 M 244.4072 164.4206 m F 0 G 0.3 w 10 M 244.4072 164.4206 m S 244.4072 164.4206 m S 244.4072 164.4206 m S 0 g 1 w 4 M 244.4072 164.4206 m F 0 G 0.3 w 10 M 244.4072 164.4206 m S 244.4072 164.4206 m S 1 g 1 w 4 M 244.4072 164.4206 m F 0 G 0.3 w 10 M 244.4072 164.4206 m S 0 g 1 w 4 M 244.4072 164.4206 m F 0 G 0.3 w 10 M 244.4072 164.4206 m S 244.4072 164.4206 m S 244.4072 183.0028 m S 0 g 1 w 4 M 244.4072 183.0028 m F 0 G 0.3 w 10 M 244.4072 183.0028 m S 244.4072 183.0028 m S 244.4072 183.0028 m S 0 g 1 w 4 M 244.4072 183.0028 m F 0 G 0.3 w 10 M 244.4072 183.0028 m S 244.4072 183.0028 m S 1 g 1 w 4 M 244.4072 183.0028 m F 0 G 0.3 w 10 M 244.4072 183.0028 m S 0 g 1 w 4 M 244.4072 183.0028 m F 0 G 0.3 w 10 M 244.4072 183.0028 m S 244.4072 183.0028 m S 225.3629 201.5848 m S 225.3629 201.5848 m S 206.3188 201.5848 m S 225.3629 201.5848 m S 206.3188 201.5848 m S 225.3629 201.5848 m S 187.2746 201.5848 m S 206.3188 201.5848 m S 187.2746 201.5848 m S 187.2746 201.5848 m S 187.2746 201.5848 m S 206.3188 201.5848 m S 225.3629 201.5848 m S 0 g 1 w 4 M 225.3629 201.5848 m F 0 G 0.3 w 10 M 225.3629 201.5848 m S 225.3629 201.5848 m S 225.3629 201.5848 m S 0 g 1 w 4 M 225.3629 201.5848 m F 0 G 0.3 w 10 M 225.3629 201.5848 m S 225.3629 201.5848 m S 1 g 1 w 4 M 230.381 201.5848 m 230.381 204.2781 228.1343 206.4615 225.3629 206.4615 c 222.5916 206.4615 220.3448 204.2781 220.3448 201.5848 c F 220.3448 201.5848 m 220.3448 198.8916 222.5916 196.7082 225.3629 196.7082 c 228.1343 196.7082 230.381 198.8916 230.381 201.5848 c F 225.3629 201.5848 m F 0 G 0.3 w 10 M 225.3629 201.5848 m S 0 g 1 w 4 M 225.3629 201.5848 m F 0 G 0.3 w 10 M 225.3629 201.5848 m S 225.3629 201.5848 m S 0 g 1 w 4 M 226.2689 202.4776 m 226.2689 205.4678 L 224.457 205.4678 L 224.457 202.4776 L 221.4634 202.4869 L 221.4634 200.6826 L 224.457 200.6919 L 224.457 197.7016 L 226.2689 197.7016 L 226.2689 200.6919 L 229.2625 200.6826 L 229.2625 202.4869 L 226.2689 202.4776 L f 0 G 0.3 w 10 M 206.3188 201.5848 m S 0 g 1 w 4 M 206.3188 201.5848 m F 0 G 0.3 w 10 M 206.3188 201.5848 m S 206.3188 201.5848 m S 206.3188 201.5848 m S 0 g 1 w 4 M 206.3188 201.5848 m F 0 G 0.3 w 10 M 206.3188 201.5848 m S 206.3188 201.5848 m S 1 g 1 w 4 M 211.3369 201.5848 m 211.3369 204.2781 209.0901 206.4615 206.3188 206.4615 c 203.5474 206.4615 201.3007 204.2781 201.3007 201.5848 c F 201.3007 201.5848 m 201.3007 198.8916 203.5474 196.7082 206.3188 196.7082 c 209.0901 196.7082 211.3369 198.8916 211.3369 201.5848 c F 206.3188 201.5848 m F 0 G 0.3 w 10 M 206.3188 201.5848 m S 0 g 1 w 4 M 206.3188 201.5848 m F 0 G 0.3 w 10 M 206.3188 201.5848 m S 206.3188 201.5848 m S 0 g 1 w 4 M 207.2247 202.4776 m 207.2247 205.4678 L 205.4128 205.4678 L 205.4128 202.4776 L 202.4192 202.4869 L 202.4192 200.6826 L 205.4128 200.6919 L 205.4128 197.7016 L 207.2247 197.7016 L 207.2247 200.6919 L 210.2183 200.6826 L 210.2183 202.4869 L 207.2247 202.4776 L f 0 G 0.3 w 10 M 187.2746 201.5848 m S 0 g 1 w 4 M 187.2746 201.5848 m F 0 G 0.3 w 10 M 187.2746 201.5848 m S 187.2746 201.5848 m S 187.2746 201.5848 m S 0 g 1 w 4 M 187.2746 201.5848 m F 0 G 0.3 w 10 M 187.2746 201.5848 m S 187.2746 201.5848 m S 1 g 1 w 4 M 192.2927 201.5848 m 192.2927 204.2781 190.046 206.4615 187.2746 206.4615 c 184.5033 206.4615 182.2565 204.2781 182.2565 201.5848 c F 182.2565 201.5848 m 182.2565 198.8916 184.5033 196.7082 187.2746 196.7082 c 190.046 196.7082 192.2927 198.8916 192.2927 201.5848 c F 187.2746 201.5848 m F 0 G 0.3 w 10 M 187.2746 201.5848 m S 0 g 1 w 4 M 187.2746 201.5848 m F 0 G 0.3 w 10 M 187.2746 201.5848 m S 187.2746 201.5848 m S 0 g 1 w 4 M 188.1806 202.4776 m 188.1806 205.4678 L 186.3687 205.4678 L 186.3687 202.4776 L 183.3751 202.4869 L 183.3751 200.6826 L 186.3687 200.6919 L 186.3687 197.7016 L 188.1806 197.7016 L 188.1806 200.6919 L 191.1742 200.6826 L 191.1742 202.4869 L 188.1806 202.4776 L f 0 G 0.3 w 10 M 168.2304 145.8386 m S 168.2304 164.4206 m S 168.2304 145.8386 m S 168.2304 145.8386 m S 168.2304 164.4206 m S 168.2304 145.8386 m S 168.2304 164.4206 m S 168.2304 183.0028 m S 168.2304 183.0028 m S 168.2304 183.0028 m S 168.2304 164.4206 m S 168.2304 183.0028 m S 168.2304 145.8386 m S 0 g 1 w 4 M 168.2304 145.8386 m F 0 G 0.3 w 10 M 168.2304 145.8386 m S 168.2304 145.8386 m S 168.2304 145.8386 m S 0 g 1 w 4 M 168.2304 145.8386 m F 0 G 0.3 w 10 M 168.2304 145.8386 m S 168.2304 145.8386 m S 1 g 1 w 4 M 168.2304 145.8386 m F 0 G 0.3 w 10 M 168.2304 145.8386 m S 0 g 1 w 4 M 168.2304 145.8386 m F 0 G 0.3 w 10 M 168.2304 145.8386 m S 168.2304 145.8386 m S 168.2304 164.4206 m S 0 g 1 w 4 M 168.2304 164.4206 m F 0 G 0.3 w 10 M 168.2304 164.4206 m S 168.2304 164.4206 m S 168.2304 164.4206 m S 0 g 1 w 4 M 168.2304 164.4206 m F 0 G 0.3 w 10 M 168.2304 164.4206 m S 168.2304 164.4206 m S 1 g 1 w 4 M 168.2304 164.4206 m F 0 G 0.3 w 10 M 168.2304 164.4206 m S 0 g 1 w 4 M 168.2304 164.4206 m F 0 G 0.3 w 10 M 168.2304 164.4206 m S 168.2304 164.4206 m S 168.2304 183.0028 m S 0 g 1 w 4 M 168.2304 183.0028 m F 0 G 0.3 w 10 M 168.2304 183.0028 m S 168.2304 183.0028 m S 168.2304 183.0028 m S 0 g 1 w 4 M 168.2304 183.0028 m F 0 G 0.3 w 10 M 168.2304 183.0028 m S 168.2304 183.0028 m S 1 g 1 w 4 M 168.2304 183.0028 m F 0 G 0.3 w 10 M 168.2304 183.0028 m S 0 g 1 w 4 M 168.2304 183.0028 m F 0 G 0.3 w 10 M 168.2304 183.0028 m S 168.2304 183.0028 m S 215.8409 155.1296 m S 215.8409 155.1296 m S 196.7967 155.1296 m S 215.8409 155.1296 m S 196.7967 155.1296 m S 196.7967 155.1296 m S 196.7967 155.1296 m S 215.8409 155.1296 m S 215.8409 173.7117 m S 215.8409 173.7117 m S 196.7967 173.7117 m S 215.8409 173.7117 m S 196.7967 173.7117 m S 196.7967 173.7117 m S 196.7967 173.7117 m S 215.8409 173.7117 m S 225.3629 145.8386 m S 0 g 1 w 4 M 225.3629 145.8386 m F 0 G 0.3 w 10 M 225.3629 145.8386 m S 0 g 1 w 4 M 225.3629 145.8386 m F 1 g 230.381 145.8386 m 230.381 148.5319 228.1343 150.7152 225.3629 150.7152 c 222.5916 150.7152 220.3448 148.5319 220.3448 145.8386 c F 220.3448 145.8386 m 220.3448 143.1453 222.5916 140.962 225.3629 140.962 c 228.1343 140.962 230.381 143.1453 230.381 145.8386 c F 225.3629 145.8386 m F 0 G 0.3 w 10 M 225.3629 145.8386 m S 0 g 1 w 4 M 225.3629 145.8386 m F 0 G 0.3 w 10 M 225.3629 145.8386 m S 0 g 1 w 4 M 225.3629 145.8386 m F 226.2689 144.9456 m 229.2625 144.9363 L 229.2625 146.7407 L 226.2689 146.7314 L F 224.457 146.7314 m 221.4634 146.7407 L 221.4634 144.9363 L 224.457 144.9456 L F 229.2625 144.9363 m 221.4634 144.9363 l 221.4634 146.7407 l 229.2625 146.7407 l 229.2625 144.9363 l f 0 G 0.3 w 10 M 206.3188 145.8386 m S 0 g 1 w 4 M 206.3188 145.8386 m F 0 G 0.3 w 10 M 206.3188 145.8386 m S 0 g 1 w 4 M 206.3188 145.8386 m F 1 g 211.3369 145.8386 m 211.3369 148.5319 209.0901 150.7152 206.3188 150.7152 c 203.5474 150.7152 201.3007 148.5319 201.3007 145.8386 c F 201.3007 145.8386 m 201.3007 143.1453 203.5474 140.962 206.3188 140.962 c 209.0901 140.962 211.3369 143.1453 211.3369 145.8386 c F 206.3188 145.8386 m F 0 G 0.3 w 10 M 206.3188 145.8386 m S 0 g 1 w 4 M 206.3188 145.8386 m F 0 G 0.3 w 10 M 206.3188 145.8386 m S 0 g 1 w 4 M 206.3188 145.8386 m F 207.2247 144.9456 m 210.2183 144.9363 L 210.2183 146.7407 L 207.2247 146.7314 L F 205.4128 146.7314 m 202.4192 146.7407 L 202.4192 144.9363 L 205.4128 144.9456 L F 210.2183 144.9363 m 202.4192 144.9363 l 202.4192 146.7407 l 210.2183 146.7407 l 210.2183 144.9363 l f 0 G 0.3 w 10 M 187.2746 145.8386 m S 0 g 1 w 4 M 187.2746 145.8386 m F 0 G 0.3 w 10 M 187.2746 145.8386 m S 0 g 1 w 4 M 187.2746 145.8386 m F 1 g 192.2927 145.8386 m 192.2927 148.5319 190.046 150.7152 187.2746 150.7152 c 184.5033 150.7152 182.2565 148.5319 182.2565 145.8386 c F 182.2565 145.8386 m 182.2565 143.1453 184.5033 140.962 187.2746 140.962 c 190.046 140.962 192.2927 143.1453 192.2927 145.8386 c F 187.2746 145.8386 m F 0 G 0.3 w 10 M 187.2746 145.8386 m S 0 g 1 w 4 M 187.2746 145.8386 m F 0 G 0.3 w 10 M 187.2746 145.8386 m S 0 g 1 w 4 M 187.2746 145.8386 m F 188.1806 144.9456 m 191.1742 144.9363 L 191.1742 146.7407 L 188.1806 146.7314 L F 186.3687 146.7314 m 183.3751 146.7407 L 183.3751 144.9363 L 186.3687 144.9456 L F 191.1742 144.9363 m 183.3751 144.9363 l 183.3751 146.7407 l 191.1742 146.7407 l 191.1742 144.9363 l f 0 G 0.3 w 10 M 187.2746 164.4206 m S 0 g 1 w 4 M 187.2746 164.4206 m F 0 G 0.3 w 10 M 187.2746 164.4206 m S 0 g 1 w 4 M 187.2746 164.4206 m F 1 g 187.2746 164.4206 m F 0 G 0.3 w 10 M 187.2746 164.4206 m S 0 g 1 w 4 M 187.2746 164.4206 m F 0 G 0.3 w 10 M 187.2746 164.4206 m S 0 g 1 w 4 M 187.2746 164.4206 m F 0 G 0.3 w 10 M 206.3188 164.4206 m S 0 g 1 w 4 M 206.3188 164.4206 m F 0 G 0.3 w 10 M 206.3188 164.4206 m S 0 g 1 w 4 M 206.3188 164.4206 m F 1 g 206.3188 164.4206 m F 0 G 0.3 w 10 M 206.3188 164.4206 m S 0 g 1 w 4 M 206.3188 164.4206 m F 0 G 0.3 w 10 M 206.3188 164.4206 m S 0 g 1 w 4 M 206.3188 164.4206 m F 0 G 0.3 w 10 M 225.3629 164.4206 m S 0 g 1 w 4 M 225.3629 164.4206 m F 0 G 0.3 w 10 M 225.3629 164.4206 m S 225.3629 164.4206 m S 225.3629 164.4206 m S 0 g 1 w 4 M 225.3629 164.4206 m F 0 G 0.3 w 10 M 225.3629 164.4206 m S 225.3629 164.4206 m S 1 g 1 w 4 M 225.3629 164.4206 m F 0 G 0.3 w 10 M 225.3629 164.4206 m S 0 g 1 w 4 M 225.3629 164.4206 m F 0 G 0.3 w 10 M 225.3629 164.4206 m S 225.3629 164.4206 m S 206.3188 183.0028 m S 0 g 1 w 4 M 206.3188 183.0028 m F 0 G 0.3 w 10 M 206.3188 183.0028 m S 206.3188 183.0028 m S 206.3188 183.0028 m S 0 g 1 w 4 M 206.3188 183.0028 m F 0 G 0.3 w 10 M 206.3188 183.0028 m S 206.3188 183.0028 m S 1 g 1 w 4 M 211.3369 183.0028 m 211.3369 185.6961 209.0901 187.8794 206.3188 187.8794 c 203.5474 187.8794 201.3007 185.6961 201.3007 183.0028 c F 201.3007 183.0028 m 201.3007 180.3095 203.5474 178.1262 206.3188 178.1262 c 209.0901 178.1262 211.3369 180.3095 211.3369 183.0028 c F 206.3188 183.0028 m F 0 G 0.3 w 10 M 206.3188 183.0028 m S 0 g 1 w 4 M 206.3188 183.0028 m F 0 G 0.3 w 10 M 206.3188 183.0028 m S 206.3188 183.0028 m S 0 g 1 w 4 M 207.2247 183.8955 m 207.2247 186.8858 L 205.4128 186.8858 L 205.4128 183.8955 L 202.4192 183.9049 L 202.4192 182.1005 L 205.4128 182.1098 L 205.4128 179.1195 L 207.2247 179.1195 L 207.2247 182.1098 L 210.2183 182.1005 L 210.2183 183.9049 L 207.2247 183.8955 L f 0 G 0.3 w 10 M 187.2746 183.0028 m S 0 g 1 w 4 M 187.2746 183.0028 m F 0 G 0.3 w 10 M 187.2746 183.0028 m S 187.2746 183.0028 m S 187.2746 183.0028 m S 0 g 1 w 4 M 187.2746 183.0028 m F 0 G 0.3 w 10 M 187.2746 183.0028 m S 187.2746 183.0028 m S 1 g 1 w 4 M 192.2927 183.0028 m 192.2927 185.6961 190.046 187.8794 187.2746 187.8794 c 184.5033 187.8794 182.2565 185.6961 182.2565 183.0028 c F 182.2565 183.0028 m 182.2565 180.3095 184.5033 178.1262 187.2746 178.1262 c 190.046 178.1262 192.2927 180.3095 192.2927 183.0028 c F 187.2746 183.0028 m F 0 G 0.3 w 10 M 187.2746 183.0028 m S 0 g 1 w 4 M 187.2746 183.0028 m F 0 G 0.3 w 10 M 187.2746 183.0028 m S 187.2746 183.0028 m S 0 g 1 w 4 M 188.1806 183.8955 m 188.1806 186.8858 L 186.3687 186.8858 L 186.3687 183.8955 L 183.3751 183.9049 L 183.3751 182.1005 L 186.3687 182.1098 L 186.3687 179.1195 L 188.1806 179.1195 L 188.1806 182.1098 L 191.1742 182.1005 L 191.1742 183.9049 L 188.1806 183.8955 L f 0 G 0.3 w 10 M 225.3629 183.0028 m S 0 g 1 w 4 M 225.3629 183.0028 m F 0 G 0.3 w 10 M 225.3629 183.0028 m S 225.3629 183.0028 m S 225.3629 183.0028 m S 0 g 1 w 4 M 225.3629 183.0028 m F 0 G 0.3 w 10 M 225.3629 183.0028 m S 225.3629 183.0028 m S 1 g 1 w 4 M 230.381 183.0028 m 230.381 185.6961 228.1343 187.8794 225.3629 187.8794 c 222.5916 187.8794 220.3448 185.6961 220.3448 183.0028 c F 220.3448 183.0028 m 220.3448 180.3095 222.5916 178.1262 225.3629 178.1262 c 228.1343 178.1262 230.381 180.3095 230.381 183.0028 c F 225.3629 183.0028 m F 0 G 0.3 w 10 M 225.3629 183.0028 m S 0 g 1 w 4 M 225.3629 183.0028 m F 0 G 0.3 w 10 M 225.3629 183.0028 m S 225.3629 183.0028 m S 0 g 1 w 4 M 226.2689 183.8955 m 226.2689 186.8858 L 224.457 186.8858 L 224.457 183.8955 L 221.4634 183.9049 L 221.4634 182.1005 L 224.457 182.1098 L 224.457 179.1195 L 226.2689 179.1195 L 226.2689 182.1098 L 229.2625 182.1005 L 229.2625 183.9049 L 226.2689 183.8955 L f 0 G 0.3 w 10 M 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 1 g 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 225.3629 164.4206 m S 225.3629 164.4206 m S 225.3629 164.4206 m S 225.3629 164.4206 m S 225.3629 164.4206 m S 225.3629 164.4206 m S 225.3629 164.4206 m S 225.3629 164.4206 m S 225.3629 164.4206 m S 0 g 1 w 4 M 225.3629 164.4206 m F 0 G 0.3 w 10 M 225.3629 164.4206 m S 0 g 1 w 4 M 225.3629 164.4206 m F 1 g 230.3716 164.4206 m 230.3716 167.1139 228.1291 169.2973 225.3629 169.2973 c 222.5968 169.2973 220.3543 167.1139 220.3543 164.4206 c F 220.3543 164.4206 m 220.3543 161.7274 222.5968 159.544 225.3629 159.544 c 228.1291 159.544 230.3716 161.7274 230.3716 164.4206 c F 225.3629 164.4206 m F 0 G 0.3 w 10 M 225.3629 164.4206 m S 0 g 1 w 4 M 225.3629 164.4206 m F 0 G 0.3 w 10 M 225.3629 164.4206 m S 0 g 1 w 4 M 225.3629 164.4206 m F 226.2672 163.5277 m 229.2552 163.5184 L 229.2552 165.3227 L 226.2672 165.3134 L F 224.4587 165.3134 m 221.4707 165.3227 L 221.4707 163.5184 L 224.4587 163.5277 L F 229.2552 163.5184 m 221.4707 163.5184 l 221.4707 165.3227 l 229.2552 165.3227 l 229.2552 163.5184 l f 0 G 0.3 w 10 M 206.4084 164.4207 m S 206.4084 164.4207 m S 206.4084 164.4207 m S 206.4084 164.4207 m S 206.4084 164.4207 m S 206.4084 164.4207 m S 206.4084 164.4207 m S 206.3188 164.4206 m S 206.3188 164.4206 m S 206.4084 164.4207 m S 187.2746 164.4206 m S 206.3188 164.4206 m S 187.2746 164.4206 m S 187.2746 164.4206 m S 187.2746 164.4206 m S 206.3188 164.4206 m S 206.4084 164.4207 m S 206.3188 164.4206 m S 206.3188 164.4206 m S 206.4084 164.4207 m S 187.2746 164.4206 m S 206.3188 164.4206 m S 187.2746 164.4206 m S 187.2746 164.4206 m S 187.2746 164.4206 m S 206.3188 164.4206 m S 206.3188 164.4206 m S 0 g 1 w 4 M 206.3188 164.4206 m F 0 G 0.3 w 10 M 206.3188 164.4206 m S 206.3188 164.4206 m S 206.3188 164.4206 m S 0 g 1 w 4 M 206.3188 164.4206 m F 0 G 0.3 w 10 M 206.3188 164.4206 m S 206.3188 164.4206 m S 1 g 1 w 4 M 211.3369 164.4206 m 211.3369 167.1139 209.0901 169.2973 206.3188 169.2973 c 203.5474 169.2973 201.3007 167.1139 201.3007 164.4206 c F 201.3007 164.4206 m 201.3007 161.7274 203.5474 159.544 206.3188 159.544 c 209.0901 159.544 211.3369 161.7274 211.3369 164.4206 c F 206.3188 164.4206 m F 0 G 0.3 w 10 M 206.3188 164.4206 m S 0 g 1 w 4 M 206.3188 164.4206 m F 0 G 0.3 w 10 M 206.3188 164.4206 m S 206.3188 164.4206 m S 0 g 1 w 4 M 207.2247 165.3134 m 207.2247 168.3036 L 205.4128 168.3036 L 205.4128 165.3134 L 202.4192 165.3227 L 202.4192 163.5184 L 205.4128 163.5277 L 205.4128 160.5374 L 207.2247 160.5374 L 207.2247 163.5277 L 210.2183 163.5184 L 210.2183 165.3227 L 207.2247 165.3134 L f 0 G 0.3 w 10 M 187.2746 164.4206 m S 0 g 1 w 4 M 187.2746 164.4206 m F 0 G 0.3 w 10 M 187.2746 164.4206 m S 187.2746 164.4206 m S 187.2746 164.4206 m S 0 g 1 w 4 M 187.2746 164.4206 m F 0 G 0.3 w 10 M 187.2746 164.4206 m S 187.2746 164.4206 m S 1 g 1 w 4 M 192.2927 164.4206 m 192.2927 167.1139 190.046 169.2973 187.2746 169.2973 c 184.5033 169.2973 182.2565 167.1139 182.2565 164.4206 c F 182.2565 164.4206 m 182.2565 161.7274 184.5033 159.544 187.2746 159.544 c 190.046 159.544 192.2927 161.7274 192.2927 164.4206 c F 187.2746 164.4206 m F 0 G 0.3 w 10 M 187.2746 164.4206 m S 0 g 1 w 4 M 187.2746 164.4206 m F 0 G 0.3 w 10 M 187.2746 164.4206 m S 187.2746 164.4206 m S 0 g 1 w 4 M 188.1806 165.3134 m 188.1806 168.3036 L 186.3687 168.3036 L 186.3687 165.3134 L 183.3751 165.3227 L 183.3751 163.5184 L 186.3687 163.5277 L 186.3687 160.5374 L 188.1806 160.5374 L 188.1806 163.5277 L 191.1742 163.5184 L 191.1742 165.3227 L 188.1806 165.3134 L f 0 G 0.3 w 10 M 168.2126 145.8385 m S 168.2126 164.4206 m S 168.2126 145.8385 m S 168.2126 145.8385 m S 168.2126 164.4206 m S 168.2126 145.8385 m S 168.2126 145.8385 m S 168.2126 164.4206 m S 168.2126 145.8385 m S 168.2126 145.8385 m S 168.2126 164.4206 m S 168.2126 145.8385 m S 168.2304 145.8386 m S 168.2304 164.4206 m S 168.2304 145.8386 m S 168.2304 145.8386 m S 168.2304 164.4206 m S 168.2304 145.8386 m S 168.2304 164.4206 m S 168.2304 183.0028 m S 168.2304 183.0028 m S 168.2304 183.0028 m S 168.2304 164.4206 m S 168.2304 183.0028 m S 168.2304 145.8386 m S 168.2304 164.4206 m S 168.2304 145.8386 m S 168.2304 145.8386 m S 168.2304 164.4206 m S 168.2304 145.8386 m S 168.2304 164.4206 m S 168.2304 183.0028 m S 168.2304 183.0028 m S 168.2304 183.0028 m S 168.2304 164.4206 m S 168.2304 183.0028 m S 168.2304 145.8386 m S 0 g 1 w 4 M 168.2304 145.8386 m F 0 G 0.3 w 10 M 168.2304 145.8386 m S 168.2304 145.8386 m S 168.2304 145.8386 m S 0 g 1 w 4 M 168.2304 145.8386 m F 0 G 0.3 w 10 M 168.2304 145.8386 m S 168.2304 145.8386 m S 1 g 1 w 4 M 168.2304 145.8386 m F 0 G 0.3 w 10 M 168.2304 145.8386 m S 0 g 1 w 4 M 168.2304 145.8386 m F 0 G 0.3 w 10 M 168.2304 145.8386 m S 168.2304 145.8386 m S 168.2304 164.4206 m S 0 g 1 w 4 M 168.2304 164.4206 m F 0 G 0.3 w 10 M 168.2304 164.4206 m S 168.2304 164.4206 m S 168.2304 164.4206 m S 0 g 1 w 4 M 168.2304 164.4206 m F 0 G 0.3 w 10 M 168.2304 164.4206 m S 168.2304 164.4206 m S 1 g 1 w 4 M 168.2304 164.4206 m F 0 G 0.3 w 10 M 168.2304 164.4206 m S 0 g 1 w 4 M 168.2304 164.4206 m F 0 G 0.3 w 10 M 168.2304 164.4206 m S 168.2304 164.4206 m S 168.2304 183.0028 m S 0 g 1 w 4 M 168.2304 183.0028 m F 0 G 0.3 w 10 M 168.2304 183.0028 m S 168.2304 183.0028 m S 168.2304 183.0028 m S 0 g 1 w 4 M 168.2304 183.0028 m F 0 G 0.3 w 10 M 168.2304 183.0028 m S 168.2304 183.0028 m S 1 g 1 w 4 M 168.2304 183.0028 m F 0 G 0.3 w 10 M 168.2304 183.0028 m S 0 g 1 w 4 M 168.2304 183.0028 m F 0 G 0.3 w 10 M 168.2304 183.0028 m S 168.2304 183.0028 m S 168.2304 145.8386 m S 168.2304 145.8386 m S 168.2304 145.8386 m S 168.2304 145.8386 m S 168.2304 145.8386 m S 168.2304 145.8386 m S 168.2304 145.8386 m S 168.2304 145.8386 m S 168.2304 145.8386 m S 0 g 1 w 4 M 168.2304 145.8386 m F 0 G 0.3 w 10 M 168.2304 145.8386 m S 0 g 1 w 4 M 168.2304 145.8386 m F 1 g 168.2304 145.8386 m F 0 G 0.3 w 10 M 168.2304 145.8386 m S 0 g 1 w 4 M 168.2304 145.8386 m F 0 G 0.3 w 10 M 168.2304 145.8386 m S 0 g 1 w 4 M 168.2304 145.8386 m F 0 G 234.885 210.8759 m 234.7776 62.2191 l S 0.3 w 10 M 301.4322 164.4206 m S 301.4322 145.8385 m S 301.4322 145.8385 m S 301.4322 145.8385 m S 301.4322 164.4206 m S 301.4322 145.8385 m S 301.4322 164.4206 m S 301.4322 145.8385 m S 301.4322 145.8385 m S 301.4322 145.8385 m S 301.4322 164.4206 m S 301.4322 145.8385 m S 301.4501 164.4207 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 301.4501 183.0028 m S 301.4501 164.4207 m S 301.4501 183.0028 m S 301.4501 183.0028 m S 301.4501 164.4207 m S 301.4501 183.0028 m S 301.4501 164.4207 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 301.4501 183.0028 m S 301.4501 164.4207 m S 301.4501 183.0028 m S 301.4501 183.0028 m S 301.4501 164.4207 m S 301.4501 183.0028 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 301.4501 183.0028 m S 301.4501 183.0028 m S 301.4501 183.0028 m S 301.4501 164.4207 m S 301.4501 183.0028 m S 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 301.4501 145.8386 m S 1 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 0 g 1 w 4 M 301.4501 164.4207 m F 0 G 0.3 w 10 M 301.4501 164.4207 m S 301.4501 164.4207 m S 301.4501 164.4207 m S 0 g 1 w 4 M 301.4501 164.4207 m F 0 G 0.3 w 10 M 301.4501 164.4207 m S 301.4501 164.4207 m S 1 g 1 w 4 M 301.4501 164.4207 m F 0 G 0.3 w 10 M 301.4501 164.4207 m S 0 g 1 w 4 M 301.4501 164.4207 m F 0 G 0.3 w 10 M 301.4501 164.4207 m S 301.4501 164.4207 m S 301.4501 183.0028 m S 0 g 1 w 4 M 301.4501 183.0028 m F 0 G 0.3 w 10 M 301.4501 183.0028 m S 301.4501 183.0028 m S 301.4501 183.0028 m S 0 g 1 w 4 M 301.4501 183.0028 m F 0 G 0.3 w 10 M 301.4501 183.0028 m S 301.4501 183.0028 m S 1 g 1 w 4 M 301.4501 183.0028 m F 0 G 0.3 w 10 M 301.4501 183.0028 m S 0 g 1 w 4 M 301.4501 183.0028 m F 0 G 0.3 w 10 M 301.4501 183.0028 m S 301.4501 183.0028 m S 301.4322 145.8385 m S 301.4322 164.4206 m S 301.4322 145.8385 m S 301.4322 145.8385 m S 301.4322 164.4206 m S 301.4322 145.8385 m S 301.4322 145.8385 m S 301.4322 164.4206 m S 301.4322 145.8385 m S 301.4322 145.8385 m S 301.4322 164.4206 m S 301.4322 145.8385 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 301.4501 183.0028 m S 301.4501 183.0028 m S 301.4501 183.0028 m S 301.4501 164.4207 m S 301.4501 183.0028 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 301.4501 183.0028 m S 301.4501 183.0028 m S 301.4501 183.0028 m S 301.4501 164.4207 m S 301.4501 183.0028 m S 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 301.4501 145.8386 m S 1 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 164.4207 m S 0 g 1 w 4 M 301.4501 164.4207 m F 0 G 0.3 w 10 M 301.4501 164.4207 m S 301.4501 164.4207 m S 301.4501 164.4207 m S 0 g 1 w 4 M 301.4501 164.4207 m F 0 G 0.3 w 10 M 301.4501 164.4207 m S 301.4501 164.4207 m S 1 g 1 w 4 M 306.4587 164.4207 m 306.4587 167.1139 304.2162 169.2973 301.4501 169.2973 c 298.6839 169.2973 296.4414 167.1139 296.4414 164.4207 c F 296.4414 164.4207 m 296.4414 161.7274 298.6839 159.544 301.4501 159.544 c 304.2162 159.544 306.4587 161.7274 306.4587 164.4207 c F 301.4501 164.4207 m F 0 G 0.3 w 10 M 301.4501 164.4207 m S 0 g 1 w 4 M 301.4501 164.4207 m F 0 G 0.3 w 10 M 301.4501 164.4207 m S 301.4501 164.4207 m S 0 g 1 w 4 M 302.3543 165.3134 m 302.3543 168.3037 L 300.5458 168.3037 L 300.5458 165.3134 L 297.5579 165.3227 L 297.5579 163.5184 L 300.5458 163.5277 L 300.5458 160.5374 L 302.3543 160.5374 L 302.3543 163.5277 L 305.3423 163.5184 L 305.3423 165.3227 L 302.3543 165.3134 L f 0 G 0.3 w 10 M 301.4501 183.0028 m S 0 g 1 w 4 M 301.4501 183.0028 m F 0 G 0.3 w 10 M 301.4501 183.0028 m S 301.4501 183.0028 m S 301.4501 183.0028 m S 0 g 1 w 4 M 301.4501 183.0028 m F 0 G 0.3 w 10 M 301.4501 183.0028 m S 301.4501 183.0028 m S 1 g 1 w 4 M 306.4587 183.0028 m 306.4587 185.6961 304.2162 187.8794 301.4501 187.8794 c 298.6839 187.8794 296.4414 185.6961 296.4414 183.0028 c F 296.4414 183.0028 m 296.4414 180.3095 298.6839 178.1262 301.4501 178.1262 c 304.2162 178.1262 306.4587 180.3095 306.4587 183.0028 c F 301.4501 183.0028 m F 0 G 0.3 w 10 M 301.4501 183.0028 m S 0 g 1 w 4 M 301.4501 183.0028 m F 0 G 0.3 w 10 M 301.4501 183.0028 m S 301.4501 183.0028 m S 0 g 1 w 4 M 302.3543 183.8955 m 302.3543 186.8858 L 300.5458 186.8858 L 300.5458 183.8955 L 297.5579 183.9049 L 297.5579 182.1006 L 300.5458 182.1098 L 300.5458 179.1195 L 302.3543 179.1195 L 302.3543 182.1098 L 305.3423 182.1006 L 305.3423 183.9049 L 302.3543 183.8955 L f 0 G 0.3 w 10 M 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 1 g 306.4587 145.8386 m 306.4587 148.5319 304.2162 150.7152 301.4501 150.7152 c 298.6839 150.7152 296.4414 148.5319 296.4414 145.8386 c F 296.4414 145.8386 m 296.4414 143.1453 298.6839 140.962 301.4501 140.962 c 304.2162 140.962 306.4587 143.1453 306.4587 145.8386 c F 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 0 G 0.3 w 10 M 301.4501 145.8386 m S 0 g 1 w 4 M 301.4501 145.8386 m F 302.3543 144.9456 m 305.3423 144.9364 L 305.3423 146.7407 L 302.3543 146.7314 L F 300.5458 146.7314 m 297.5578 146.7407 L 297.5578 144.9364 L 300.5458 144.9456 L F 305.3423 144.9364 m 297.5578 144.9364 l 297.5578 146.7407 l 305.3423 146.7407 l 305.3423 144.9364 l f 0 G 0.3 w 10 M 301.4322 127.2564 m S 301.4322 108.6743 m S 301.4322 127.2564 m S 301.4322 127.2564 m S 301.4322 108.6743 m S 301.4322 127.2564 m S 301.4322 108.6743 m S 301.4322 90.0922 m S 301.4322 90.0922 m S 301.4322 90.0922 m S 301.4322 108.6743 m S 301.4322 90.0922 m S 301.4322 127.2564 m S 301.4322 108.6743 m S 301.4322 127.2564 m S 301.4322 127.2564 m S 301.4322 108.6743 m S 301.4322 127.2564 m S 301.4322 108.6743 m S 301.4322 90.0922 m S 301.4322 90.0922 m S 301.4322 90.0922 m S 301.4322 108.6743 m S 301.4322 90.0922 m S 301.4322 127.2564 m S 0 g 1 w 4 M 301.4322 127.2564 m F 0 G 0.3 w 10 M 301.4322 127.2564 m S 301.4322 127.2564 m S 301.4322 127.2564 m S 0 g 1 w 4 M 301.4322 127.2564 m F 0 G 0.3 w 10 M 301.4322 127.2564 m S 301.4322 127.2564 m S 1 g 1 w 4 M 301.4322 127.2564 m F 0 G 0.3 w 10 M 301.4322 127.2564 m S 0 g 1 w 4 M 301.4322 127.2564 m F 0 G 0.3 w 10 M 301.4322 127.2564 m S 301.4322 127.2564 m S 301.4322 108.6743 m S 0 g 1 w 4 M 301.4322 108.6743 m F 0 G 0.3 w 10 M 301.4322 108.6743 m S 301.4322 108.6743 m S 301.4322 108.6743 m S 0 g 1 w 4 M 301.4322 108.6743 m F 0 G 0.3 w 10 M 301.4322 108.6743 m S 301.4322 108.6743 m S 1 g 1 w 4 M 296.4236 108.6743 m 296.4236 105.9811 298.6661 103.7977 301.4322 103.7977 c 304.1984 103.7977 306.4409 105.9811 306.4409 108.6743 c F 306.4409 108.6743 m 306.4409 111.3676 304.1984 113.5509 301.4322 113.5509 c 298.6661 113.5509 296.4236 111.3676 296.4236 108.6743 c F 301.4322 108.6743 m F 0 G 0.3 w 10 M 301.4322 108.6743 m S 0 g 1 w 4 M 301.4322 108.6743 m F 0 G 0.3 w 10 M 301.4322 108.6743 m S 301.4322 108.6743 m S 0 g 1 w 4 M 300.528 107.7816 m 300.528 104.7913 L 302.3365 104.7913 L 302.3365 107.7816 L 305.3244 107.7722 L 305.3244 109.5766 L 302.3365 109.5673 L 302.3365 112.5576 L 300.528 112.5576 L 300.528 109.5673 L 297.54 109.5766 L 297.54 107.7722 L 300.528 107.7816 L f 0 G 0.3 w 10 M 301.4322 90.0922 m S 0 g 1 w 4 M 301.4322 90.0922 m F 0 G 0.3 w 10 M 301.4322 90.0922 m S 301.4322 90.0922 m S 301.4322 90.0922 m S 0 g 1 w 4 M 301.4322 90.0922 m F 0 G 0.3 w 10 M 301.4322 90.0922 m S 301.4322 90.0922 m S 1 g 1 w 4 M 296.4236 90.0922 m 296.4236 87.3989 298.6661 85.2156 301.4322 85.2156 c 304.1984 85.2156 306.4409 87.3989 306.4409 90.0922 c F 306.4409 90.0922 m 306.4409 92.7854 304.1984 94.9688 301.4322 94.9688 c 298.6661 94.9688 296.4236 92.7854 296.4236 90.0922 c F 301.4322 90.0922 m F 0 G 0.3 w 10 M 301.4322 90.0922 m S 0 g 1 w 4 M 301.4322 90.0922 m F 0 G 0.3 w 10 M 301.4322 90.0922 m S 301.4322 90.0922 m S 0 g 1 w 4 M 300.528 89.1995 m 300.528 86.2092 L 302.3365 86.2092 L 302.3365 89.1995 L 305.3244 89.1901 L 305.3244 90.9944 L 302.3365 90.9851 L 302.3365 93.9754 L 300.528 93.9754 L 300.528 90.9851 L 297.54 90.9944 L 297.54 89.1901 L 300.528 89.1995 L f 0 G 0.3 w 10 M 301.4322 127.2564 m S 301.4322 127.2564 m S 301.4322 127.2564 m S 301.4322 127.2564 m S 301.4322 127.2564 m S 301.4322 127.2564 m S 301.4322 127.2564 m S 301.4322 127.2564 m S 301.4322 127.2564 m S 0 g 1 w 4 M 301.4322 127.2564 m F 0 G 0.3 w 10 M 301.4322 127.2564 m S 0 g 1 w 4 M 301.4322 127.2564 m F 1 g 296.4236 127.2564 m 296.4236 124.5631 298.6661 122.3798 301.4322 122.3798 c 304.1984 122.3798 306.4409 124.5631 306.4409 127.2564 c F 306.4409 127.2564 m 306.4409 129.9497 304.1984 132.133 301.4322 132.133 c 298.6661 132.133 296.4236 129.9497 296.4236 127.2564 c F 301.4322 127.2564 m F 0 G 0.3 w 10 M 301.4322 127.2564 m S 0 g 1 w 4 M 301.4322 127.2564 m F 0 G 0.3 w 10 M 301.4322 127.2564 m S 0 g 1 w 4 M 301.4322 127.2564 m F 300.528 128.1493 m 297.54 128.1586 L 297.54 126.3543 L 300.528 126.3636 L F 302.3365 126.3636 m 305.3245 126.3543 L 305.3245 128.1586 L 302.3365 128.1493 L F 297.54 128.1586 m 305.3245 128.1586 l 305.3245 126.3543 l 297.54 126.3543 l 297.54 128.1586 l f 0 G 0.3 w 10 M 301.4501 127.2565 m S 301.4501 108.6744 m S 301.4501 127.2565 m S 301.4501 127.2565 m S 301.4501 108.6744 m S 301.4501 127.2565 m S 301.4501 127.2565 m S 301.4501 108.6744 m S 301.4501 127.2565 m S 301.4501 127.2565 m S 301.4501 108.6744 m S 301.4501 127.2565 m S u u 0 g 1 w 4 M /_Times-Roman 12 14.5 0 0 z [1 0 0 1 172 37.5]e (\(c\))t T U U 0 G 0.3 w 10 M 54.0012 201.5848 m S 54.0012 201.5848 m S 54.0012 201.5848 m S 54.0012 201.5848 m S 54.0012 201.5848 m S 54.0012 201.5848 m S 54.0012 201.5848 m S 54.0012 201.5848 m S 54.0012 201.5848 m S 54.0012 201.5848 m S 54.0012 201.5848 m S 54.0012 201.5848 m S 54.0012 201.5848 m S 0 g 1 w 4 M 54.0012 201.5848 m F 0 G 0.3 w 10 M 54.0012 201.5848 m S 54.0012 201.5848 m S 54.0012 201.5848 m S 0 g 1 w 4 M 54.0012 201.5848 m F 0 G 0.3 w 10 M 54.0012 201.5848 m S 54.0012 201.5848 m S 1 g 1 w 4 M 59.0193 201.5848 m 59.0193 204.2781 56.7726 206.4615 54.0012 206.4615 c 51.2298 206.4615 48.9831 204.2781 48.9831 201.5848 c F 48.9831 201.5848 m 48.9831 198.8916 51.2298 196.7082 54.0012 196.7082 c 56.7726 196.7082 59.0193 198.8916 59.0193 201.5848 c F 54.0012 201.5848 m F 0 G 0.3 w 10 M 54.0012 201.5848 m S 0 g 1 w 4 M 54.0012 201.5848 m F 0 G 0.3 w 10 M 54.0012 201.5848 m S 54.0012 201.5848 m S 0 g 1 w 4 M 54.9071 202.4776 m 54.9071 205.4678 L 53.0952 205.4678 L 53.0952 202.4776 L 50.1016 202.4869 L 50.1016 200.6826 L 53.0952 200.6919 L 53.0952 197.7016 L 54.9071 197.7016 L 54.9071 200.6919 L 57.9008 200.6826 L 57.9008 202.4869 L 54.9071 202.4776 L f 0 G 0.3 w 10 M 53.9833 71.5101 m S 53.9833 71.5101 m S 53.9833 71.5101 m S 53.9833 71.5101 m S 53.9833 71.5101 m S 53.9833 71.5101 m S 53.9833 71.5101 m S 53.9833 71.5101 m S 53.9833 71.5101 m S 53.9833 71.5101 m S 53.9833 71.5101 m S 53.9833 71.5101 m S 53.9833 71.5101 m S 0 g 1 w 4 M 53.9833 71.5101 m F 0 G 0.3 w 10 M 53.9833 71.5101 m S 53.9833 71.5101 m S 53.9833 71.5101 m S 0 g 1 w 4 M 53.9833 71.5101 m F 0 G 0.3 w 10 M 53.9833 71.5101 m S 53.9833 71.5101 m S 1 g 1 w 4 M 59.0014 71.5101 m 59.0014 74.2034 56.7547 76.3868 53.9833 76.3868 c 51.2119 76.3868 48.9652 74.2034 48.9652 71.5101 c F 48.9652 71.5101 m 48.9652 68.8169 51.2119 66.6335 53.9833 66.6335 c 56.7547 66.6335 59.0014 68.8169 59.0014 71.5101 c F 53.9833 71.5101 m F 0 G 0.3 w 10 M 53.9833 71.5101 m S 0 g 1 w 4 M 53.9833 71.5101 m F 0 G 0.3 w 10 M 53.9833 71.5101 m S 53.9833 71.5101 m S 0 g 1 w 4 M 54.8892 72.4029 m 54.8892 75.3931 L 53.0773 75.3931 L 53.0773 72.4029 L 50.0837 72.4122 L 50.0837 70.6079 L 53.0773 70.6172 L 53.0773 67.6269 L 54.8892 67.6269 L 54.8892 70.6172 L 57.8829 70.6079 L 57.8829 72.4122 L 54.8892 72.4029 L f 0 G 0.3 w 10 M 301.4322 71.5101 m S 301.4322 71.5101 m S 301.4322 71.5101 m S 301.4322 71.5101 m S 301.4322 71.5101 m S 301.4322 71.5101 m S 301.4322 71.5101 m S 301.4322 71.5101 m S 301.4322 71.5101 m S 301.4322 71.5101 m S 301.4322 71.5101 m S 301.4322 71.5101 m S 301.4322 71.5101 m S 0 g 1 w 4 M 301.4322 71.5101 m F 0 G 0.3 w 10 M 301.4322 71.5101 m S 301.4322 71.5101 m S 301.4322 71.5101 m S 0 g 1 w 4 M 301.4322 71.5101 m F 0 G 0.3 w 10 M 301.4322 71.5101 m S 301.4322 71.5101 m S 1 g 1 w 4 M 306.4503 71.5101 m 306.4503 74.2034 304.2036 76.3868 301.4322 76.3868 c 298.6608 76.3868 296.4141 74.2034 296.4141 71.5101 c F 296.4141 71.5101 m 296.4141 68.8169 298.6608 66.6335 301.4322 66.6335 c 304.2036 66.6335 306.4503 68.8169 306.4503 71.5101 c F 301.4322 71.5101 m F 0 G 0.3 w 10 M 301.4322 71.5101 m S 0 g 1 w 4 M 301.4322 71.5101 m F 0 G 0.3 w 10 M 301.4322 71.5101 m S 301.4322 71.5101 m S 0 g 1 w 4 M 302.3381 72.4029 m 302.3381 75.3931 L 300.5262 75.3931 L 300.5262 72.4029 L 297.5326 72.4122 L 297.5326 70.6079 L 300.5262 70.6172 L 300.5262 67.6269 L 302.3381 67.6269 L 302.3381 70.6172 L 305.3318 70.6079 L 305.3318 72.4122 L 302.3381 72.4029 L f 0 G 0.3 w 10 M 301.4501 201.5849 m S 301.4501 201.5849 m S 301.4501 201.5849 m S 301.4501 201.5849 m S 301.4501 201.5849 m S 301.4501 201.5849 m S 301.4501 201.5849 m S 301.4501 201.5849 m S 301.4501 201.5849 m S 301.4501 201.5849 m S 301.4501 201.5849 m S 301.4501 201.5849 m S 301.4501 201.5849 m S 0 g 1 w 4 M 301.4501 201.5849 m F 0 G 0.3 w 10 M 301.4501 201.5849 m S 301.4501 201.5849 m S 301.4501 201.5849 m S 0 g 1 w 4 M 301.4501 201.5849 m F 0 G 0.3 w 10 M 301.4501 201.5849 m S 301.4501 201.5849 m S 1 g 1 w 4 M 306.4682 201.5849 m 306.4682 204.2782 304.2215 206.4616 301.4501 206.4616 c 298.6787 206.4616 296.432 204.2782 296.432 201.5849 c F 296.432 201.5849 m 296.432 198.8917 298.6787 196.7083 301.4501 196.7083 c 304.2215 196.7083 306.4682 198.8917 306.4682 201.5849 c F 301.4501 201.5849 m F 0 G 0.3 w 10 M 301.4501 201.5849 m S 0 g 1 w 4 M 301.4501 201.5849 m F 0 G 0.3 w 10 M 301.4501 201.5849 m S 301.4501 201.5849 m S 0 g 1 w 4 M 302.356 202.4777 m 302.356 205.4679 L 300.5441 205.4679 L 300.5441 202.4777 L 297.5505 202.487 L 297.5505 200.6827 L 300.5441 200.692 L 300.5441 197.7017 L 302.356 197.7017 L 302.356 200.692 L 305.3497 200.6827 L 305.3497 202.487 L 302.356 202.4777 L f showpage _E end %%EndDocument @endspecial 60 2342 a FQ(Figure)14 b(7:)21 b(\(a\))16 b(The)f(hop)q(ed-for)h (structure)f(of)g(the)g(\\+"-lik)o(e)f(ground)i(state.)21 b(\(b\))15 b(Indeterminacy)60 2402 y(of)e(the)g(shap)q(e)h(and)f(p)q(osition)h(of)f(the) f(minimal)e(islands)j(of)g FE(\000)g FQ(spins,)g(for)g(the)g(case)g(of)g(a)g (3)t FE(\002)t FQ(3)h(blo)q(c)o(k.)60 2463 y(The)j(energy)f(p)q(er)h(island)g (is)g(20)p FF(J)5 b FQ(,)17 b(irresp)q(ectiv)o(e)d(of)j(its)g(shap)q(e.)24 b(The)17 b(energy)f(densit)o(y)g(is)h(10)p FF(J)22 b FQ(p)q(er)60 2523 y(blo)q(c)o(k.)k(\(c\))17 b(Strip-lik)o(e)g(states)h(with)g(an)g(energy) g(densit)o(y)f(of)h(8)p FF(J)23 b FQ(p)q(er)18 b(blo)q(c)o(k.)26 b(These)18 b(states)g(also)60 2583 y(ha)o(v)o(e)d(an)i(indeterminacy)d(in)h (eac)o(h)h(blo)q(c)o(k.)938 2784 y(116)p eop %%Page: 117 117 bop 133 91 a FQ(W)l(e)17 b(susp)q(ect)g(that)g(for)g(eac)o(h)f(o)q(dd)i FF(b)c FE(\025)g FQ(3)k(there)e(do)h(exist)f(blo)q(c)o(k-spin)g (con\014gurations)i(\(more)60 152 y(complicated)g(than)i FF(!)484 133 y Fy(0)482 164 y FD(alt)527 152 y FQ(\))g(for)g(whic)o(h)f(the)g (Gri\016ths-P)o(earce-Israel)g(argumen)o(t)g(can)h(b)q(e)g(carried)60 212 y(through,)13 b(but)f(for)g FF(b)h FQ(=)h(3)p FF(;)8 b FQ(5)k(w)o(e)f(ha)o(v)o(e)g(b)q(een)g(unable)h(to)g(\014nd)f(an)o(y)l(.)20 b(The)11 b(simplest)f(case)h(in)h(whic)o(h)e(w)o(e)60 272 y(managed)i(to)h(a) o(v)o(oid)f(these)g(problems)f(is)h FF(b)h FQ(=)h(7.)20 b(Here)12 b(a)g(bare)h(ma)s(jorit)o(y)d(in)i(a)h(7)s FE(\002)s FQ(7)g(blo)q(c)o(k)f (consists)60 332 y(of)18 b(25)h(spins,)g(and)f(the)g(unique)f(minimal-ene)o (rgy)f(con\014guration)j(for)f(an)h(island)f(of)g(25)h(or)f(more)60 392 y(spins)c(is)h(a)f(5)7 b FE(\002)g FQ(5)15 b(square.)21 b(By)13 b(taking)i(a)f FP(doubly-alternating)22 b FQ(blo)q(c)o(k-spin)14 b(con\014guration)h([Figure)60 452 y(8\(a\)],)20 b(w)o(e)g(can)g(force)f (these)h(5)13 b FE(\002)h FQ(5)20 b(squares)g(to)g(b)q(e)g(p)q(ositioned)g (in)g(a)g(unique)f(minim)o(al-energy)60 513 y(w)o(a)o(y)c([Figure)f(8\(b\)].) 21 b(The)15 b(energy)g(of)h(this)f(arrangemen)o(t)f(is)h(80)p FF(J)20 b FQ(p)q(er)c(group)g(of)f(eigh)o(t)g(blo)q(c)o(ks,)g(or)60 573 y(10)p FF(J)22 b FQ(p)q(er)17 b(blo)q(c)o(k.)k(On)c(the)f(other)h(hand,)g (strip-lik)o(e)e(states)i(w)o(ould)f(cost)h(at)g(least)f(14)p FF(J)22 b FQ(p)q(er)17 b(blo)q(c)o(k.)60 633 y(Therefore,)24 b(with)f(this)g(blo)q(c)o(k-spin)f(con\014guration)j(the)d(in)o(ternal-spin)h (system)e(has)j(precisely)60 693 y(t)o(w)o(o)14 b(ground)h(states:)21 b(the)14 b(\\+"-lik)o(e)g(state)g(depicted)f(in)h(Figure)g(8\(b\),)g(and)h (the)f(rev)o(erse)f(\\)p FE(\000)p FQ("-lik)o(e)60 753 y(state.)30 b(It)19 b(then)g(follo)o(ws)g(from)f(P-S)h(theory)g(that)h(at)f(lo)o(w)g (enough)h(temp)q(erature)e(the)h(in)o(ternal-)60 814 y(spin)f(system)f(has)i (t)o(w)o(o)f(extremal)e(p)q(erio)q(dic)i(Gibbs)h(measures,)e FF(\026)1303 821 y FH(+)1352 814 y FQ(and)h FF(\026)1477 821 y Fy(\000)1507 814 y FQ(,)h(c)o(haracterized)e(b)o(y)60 874 y(a)g(nonzero)h(p)q(osition-dep)q(enden)o(t)f(magnetization)f(of)h(opp)q (osite)h(signs.)24 b(The)17 b(ingredien)o(ts)f(of)h(the)60 934 y(rigorous)22 b(argumen)o(t)d(sho)o(wing)j(that)f(indeed)f(the)g(\\+"-)i (and)f(\\)p FE(\000)p FQ("-lik)o(e)f(con\014gurations)i(of)f(the)60 994 y(t)o(yp)q(e)d(of)g(Figure)f(8\(b\))i(are)f(the)g(only)f(ground)i (states,)g(and)g(that)f(PS)g(theory)g(is)g(applicable,)f(are)60 1054 y(summarized)g(in)k(Section)e(B.5.5.)34 b(This)20 b(completes)f(Step)h (1,)h(whic)o(h)f(is)g(the)h(hard)g(part)g(of)f(the)60 1115 y(pro)q(of.)133 1175 y(The)f(pro)q(of)g(of)g(Step)f(2)h(relies)e(again)i(on)g (P-S)g(theory)f(and)h(the)g(FK)o(G)f(inequalit)o(y)l(.)25 b(Step)19 b(2.1)60 1235 y(is)j(pro)o(v)o(en)g(in)g(the)g(usual)h(w)o(a)o(y)l(.)39 b(The)22 b(fact)g(that)h(the)f(system)f(with)h(+)g(blo)q(c)o(k)g (magnetization)60 1295 y(outside)d(a)g(square)g(\003)464 1302 y FD(R)512 1295 y FQ(has)g(a)h(unique)e(Gibbs)h(measure)f(is)g(a)i (consequence)e(of)h(P-S)g(theory:)27 b(at)60 1355 y(zero)21 b(temp)q(erature)g(this)g(system)f(has)j(a)f(unique)f(ground)i(state,)g (namely)d(the)h(state)h(with)g(all)60 1416 y(spins)15 b(+,)g(and)g(P-S)h (implies)c(\(see)j(Section)f(B.5.2\))h(that)g(this)g(trivial)e(phase)j (diagram)e(p)q(ersists)i(at)60 1476 y(lo)o(w)f(enough)g(temp)q(erature.)k (This)c(pro)o(v)o(es)f(Step)h(2.2.)21 b(Finally)l(,)13 b(w)o(e)i(claim)d (that)j(the)g(system)e(with)60 1536 y(+)19 b(blo)q(c)o(k)f(spins)i(outside)f (a)g(square)g(\003)778 1543 y FD(R)826 1536 y FQ(\(and)h(doubly)f (alternating)g(blo)q(c)o(k)f(spins)i(inside\))e(has)i(a)60 1596 y(larger)15 b(magnetization)g(than)h(the)f(system)f(with)h(doubly)g (alternating)h(blo)q(c)o(k)f(spins)g(ev)o(erywhere.)60 1656 y(Indeed,)21 b(the)g(constrain)o(t)g(that)h(the)f(ma)s(jorit)o(y)e(of)i(in)o (ternal)f(spins)i(in)e(a)i(blo)q(c)o(k)f FF(B)i FQ(b)q(e)f FE(\000)f FQ(\(resp.)60 1716 y(+\))g(can)g(b)q(e)h(imp)q(osed)e(b)o(y)h (including)f(in)h(the)f(Hamiltonian)g(a)h(term)f FE(\000)p FF(h)1459 1723 y FD(B)1497 1716 y FQ(sgn)9 b(\()1595 1683 y Fx(P)1639 1727 y FD(i)p Fy(2)p FD(B)1713 1716 y FF(\033)1741 1723 y FD(i)1755 1716 y FQ(\))21 b(with)60 1777 y FF(h)88 1784 y FD(B)141 1777 y FE(!)h(\0001)f FQ(\(resp.)g FF(h)492 1784 y FD(B)545 1777 y FE(!)h FQ(+)p FE(1)p FQ(\).)37 b(Since)20 b(sgn)9 b(\()1005 1743 y Fx(P)1049 1787 y FD(i)p Fy(2)p FD(B)1123 1777 y FF(\033)1151 1784 y FD(i)1165 1777 y FQ(\))21 b(is)h(an)f(increasing)g (function)h(of)f(the)60 1837 y(spins,)d(the)f(FK)o(G)h(inequalit)o(y)d (implies)g(that)j(the)g(magnetization)e(at)i(an)o(y)g(site)f(is)g(an)h (increasing)60 1897 y(function)e(of)h FF(h)335 1904 y FD(B)365 1897 y FQ(.)k(This)c(pro)o(v)o(es)e(Step)h(2.3.)133 1957 y(Step)g(3)h(is)f (pro)o(v)o(en)f(in)h(the)g(usual)h(w)o(a)o(y)l(.)k(W)l(e)16 b(therefore)f(conclude:)60 2068 y FM(Theorem)i(4.5)24 b FP(F)l(or)e(al)r(l)i FF(J)k FP(su\016ciently)d(lar)n(ge,)f(the)g(fol)r(lowing)h(holds:)34 b(L)n(et)23 b FF(\026)g FP(b)n(e)h(any)f(Gibbs)60 2128 y(me)n(asur)n(e)14 b(for)h(the)g(two-dimensional)i(Ising)f(mo)n(del)f(with)g(ne)n(ar)n (est-neighb)n(or)h(c)n(oupling)g FF(J)j FP(and)d(zer)n(o)60 2188 y(magnetic)h(\014eld.)23 b(L)n(et)16 b FF(T)22 b FP(b)n(e)16 b(the)g(majority-rule)g(tr)n(ansformation)e(on)i FQ(7)7 b FE(\002)g FQ(7)17 b FP(squar)n(e)f(blo)n(cks.)22 b(Then)60 2248 y(the)d(me)n(asur)n(e)f FF(\026T)25 b FP(is)19 b(not)g(c)n(onsistent)h(with)f(any)g(quasilo)n(c)n(al) g(sp)n(e)n(ci\014c)n(ation.)26 b(In)19 b(p)n(articular,)f(it)h(is)60 2309 y(not)f(the)g(Gibbs)g(me)n(asur)n(e)e(for)h(any)h(uniformly)f(c)n(onver) n(gent)i(inter)n(action.)133 2419 y FQ(It)13 b(is)f(of)i(course)f(unnatural)g (and)h(unpleasan)o(t)f(for)g(this)g(result)f(to)i(b)q(e)f(restricted)e(to)j (the)e(sp)q(ecial)60 2479 y(case)i(of)h(7)7 b FE(\002)g FQ(7)15 b(blo)q(c)o(ks.)20 b(This)15 b(restriction)e(w)o(as)i(necessary)f(only)g(in)g (Step)g(1)h(\(the)f(pro)q(of)h(of)g(a)g(phase)60 2539 y(transition)e(for)g (some)f(\014xed)h(blo)q(c)o(k-spin)f(con\014guration\);)j(it)e(arose)g(from)f (the)h(necessit)o(y)e(to)j(obtain)60 2600 y(a)k(\014nite)f(n)o(um)o(b)q(er)g (of)h(p)q(erio)q(dic)f(ground)i(states)f(in)g(order)g(to)g(apply)g(P-S)g (theory)l(.)26 b(All)16 b(the)i(other)60 2660 y(steps)k(in)g(the)g(pro)q(of)h (remain)e(v)m(alid)h(for)g(blo)q(c)o(ks)g(of)g(arbitrary)h(size)e(and)i(for)f (Ising)g(mo)q(dels)f(in)938 2784 y(117)p eop %%Page: 118 118 bop 517 1060 a @beginspecial 30 @llx 31.500000 @lly 264 @urx 275.500000 @ury 2196 @rwi @setspecial %%BeginDocument: fig8a.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z u 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 48.2759 272.6705 m S 48.2759 257.7421 m S 33.0691 257.7421 m S 33.0691 272.6705 m S 40.6725 265.2063 m S U u 78.6897 242.8137 m S 78.6897 227.8852 m S 63.4828 227.8852 m S 63.4828 242.8137 m S 71.0862 235.3495 m S U u 63.4828 257.7421 m S 63.4828 242.8137 m S 48.2759 242.8137 m S 48.2759 257.7421 m S 55.8794 250.2779 m S U u 63.4828 272.6705 m S 63.4828 257.7421 m S 48.2759 257.7421 m S 48.2759 272.6705 m S 55.8794 265.2063 m S U u 78.6897 272.6705 m S 78.6897 257.7421 m S 63.4828 257.7421 m S 63.4828 272.6705 m S 71.0862 265.2063 m S U u 78.6897 257.7421 m S 78.6897 242.8137 m S 63.4828 242.8137 m S 63.4828 257.7421 m S 71.0862 250.2779 m S U u 63.4828 242.8137 m S 63.4828 227.8852 m S 48.2759 227.8852 m S 48.2759 242.8137 m S 55.8794 235.3495 m S U u 48.2759 242.8137 m S 48.2759 227.8852 m S 33.0691 227.8852 m S 33.0691 242.8137 m S 40.6725 235.3495 m S U u 48.2759 257.7421 m S 48.2759 242.8137 m S 33.0691 242.8137 m S 33.0691 257.7421 m S 40.6725 250.2779 m S U 0 g 1 w 4 M 40.6725 265.2063 m F 71.0862 265.2063 m F 40.6725 235.3495 m F 71.0862 235.3495 m F u 0 G 0.3 w 10 M 93.8965 272.6705 m S 93.8965 257.7421 m S 78.6897 257.7421 m S 78.6897 272.6705 m S 86.2931 265.2063 m S U u 124.3103 242.8137 m S 124.3103 227.8852 m S 109.1034 227.8852 m S 109.1034 242.8137 m S 116.7068 235.3495 m S U u 109.1034 257.7421 m S 109.1034 242.8137 m S 93.8965 242.8137 m S 93.8965 257.7421 m S 101.5 250.2779 m S U u 109.1034 272.6705 m S 109.1034 257.7421 m S 93.8965 257.7421 m S 93.8965 272.6705 m S 101.5 265.2063 m S U u 124.3103 272.6705 m S 124.3103 257.7421 m S 109.1034 257.7421 m S 109.1034 272.6705 m S 116.7068 265.2063 m S U u 124.3103 257.7421 m S 124.3103 242.8137 m S 109.1034 242.8137 m S 109.1034 257.7421 m S 116.7068 250.2779 m S U u 109.1034 242.8137 m S 109.1034 227.8852 m S 93.8965 227.8852 m S 93.8965 242.8137 m S 101.5 235.3495 m S U u 93.8965 242.8137 m S 93.8965 227.8852 m S 78.6897 227.8852 m S 78.6897 242.8137 m S 86.2931 235.3495 m S U u 93.8965 257.7421 m S 93.8965 242.8137 m S 78.6897 242.8137 m S 78.6897 257.7421 m S 86.2931 250.2779 m S U 0 g 1 w 4 M 86.2931 265.2063 m F 116.7068 265.2063 m F 86.2931 235.3495 m F 116.7068 235.3495 m F u 0 G 0.3 w 10 M 139.5171 272.6705 m S 139.5171 257.7421 m S 124.3103 257.7421 m S 124.3103 272.6705 m S 131.9137 265.2063 m S U 169.9309 242.8137 m S 169.9309 227.8852 m S 154.7241 227.8852 m S 154.7241 242.8137 m S 162.3274 235.3495 m S 154.7241 257.7421 m S 154.7241 242.8137 m S 139.5171 242.8137 m S 139.5171 257.7421 m S 147.1206 250.2779 m S u 154.7241 272.6705 m S 154.7241 257.7421 m S 139.5171 257.7421 m S 139.5171 272.6705 m S 147.1206 265.2063 m S U u 169.9309 272.6705 m S 169.9309 257.7421 m S 154.7241 257.7421 m S 154.7241 272.6705 m S 162.3274 265.2063 m S U 169.9309 257.7421 m S 169.9309 242.8137 m S 154.7241 242.8137 m S 154.7241 257.7421 m S 162.3274 250.2779 m S 154.7241 242.8137 m S 154.7241 227.8852 m S 139.5171 227.8852 m S 139.5171 242.8137 m S 147.1206 235.3495 m S u 139.5171 242.8137 m S 139.5171 227.8852 m S 124.3103 227.8852 m S 124.3103 242.8137 m S 131.9137 235.3495 m S U u 139.5171 257.7421 m S 139.5171 242.8137 m S 124.3103 242.8137 m S 124.3103 257.7421 m S 131.9137 250.2779 m S U 0 g 1 w 4 M 131.9137 265.2063 m F 162.3274 265.2063 m F 131.9137 235.3495 m F 162.3274 235.3495 m F 0 G 0.3 w 10 M 169.9309 257.7421 m S 169.9309 272.6705 m S 169.9309 227.8852 m S 169.9309 242.8137 m S 169.9309 242.8137 m S 169.9309 257.7421 m S u 48.2759 227.8852 m S 48.2759 212.9568 m S 33.0691 212.9568 m S 33.0691 227.8852 m S 40.6725 220.421 m S U u 78.6897 198.0284 m S 78.6897 183.1 m S 63.4828 183.1 m S 63.4828 198.0284 m S 71.0862 190.5642 m S U u 63.4828 212.9568 m S 63.4828 198.0284 m S 48.2759 198.0284 m S 48.2759 212.9568 m S 55.8794 205.4927 m S U u 63.4828 227.8852 m S 63.4828 212.9568 m S 48.2759 212.9568 m S 48.2759 227.8852 m S 55.8794 220.421 m S U u 78.6897 227.8852 m S 78.6897 212.9568 m S 63.4828 212.9568 m S 63.4828 227.8852 m S 71.0862 220.421 m S U u 78.6897 212.9568 m S 78.6897 198.0284 m S 63.4828 198.0284 m S 63.4828 212.9568 m S 71.0862 205.4927 m S U u 63.4828 198.0284 m S 63.4828 183.1 m S 48.2759 183.1 m S 48.2759 198.0284 m S 55.8794 190.5642 m S U u 48.2759 198.0284 m S 48.2759 183.1 m S 33.0691 183.1 m S 33.0691 198.0284 m S 40.6725 190.5642 m S U u 48.2759 212.9568 m S 48.2759 198.0284 m S 33.0691 198.0284 m S 33.0691 212.9568 m S 40.6725 205.4927 m S U 0 g 1 w 4 M 40.6725 220.421 m F 71.0862 220.421 m F 40.6725 190.5642 m F 71.0862 190.5642 m F u 0 G 0.3 w 10 M 93.8965 227.8852 m S 93.8965 212.9568 m S 78.6897 212.9568 m S 78.6897 227.8852 m S 86.2931 220.421 m S U u 124.3103 198.0284 m S 124.3103 183.1 m S 109.1034 183.1 m S 109.1034 198.0284 m S 116.7068 190.5642 m S U u 109.1034 212.9568 m S 109.1034 198.0284 m S 93.8965 198.0284 m S 93.8965 212.9568 m S 101.5 205.4927 m S U u 109.1034 227.8852 m S 109.1034 212.9568 m S 93.8965 212.9568 m S 93.8965 227.8852 m S 101.5 220.421 m S U u 124.3103 227.8852 m S 124.3103 212.9568 m S 109.1034 212.9568 m S 109.1034 227.8852 m S 116.7068 220.421 m S U u 124.3103 212.9568 m S 124.3103 198.0284 m S 109.1034 198.0284 m S 109.1034 212.9568 m S 116.7068 205.4927 m S U u 109.1034 198.0284 m S 109.1034 183.1 m S 93.8965 183.1 m S 93.8965 198.0284 m S 101.5 190.5642 m S U u 93.8965 198.0284 m S 93.8965 183.1 m S 78.6897 183.1 m S 78.6897 198.0284 m S 86.2931 190.5642 m S U u 93.8965 212.9568 m S 93.8965 198.0284 m S 78.6897 198.0284 m S 78.6897 212.9568 m S 86.2931 205.4927 m S U 0 g 1 w 4 M 86.2931 220.421 m F 116.7068 220.421 m F 86.2931 190.5642 m F 116.7068 190.5642 m F u 0 G 0.3 w 10 M 139.5171 227.8852 m S 139.5171 212.9568 m S 124.3103 212.9568 m S 124.3103 227.8852 m S 131.9137 220.421 m S U u 169.9309 198.0284 m S 169.9309 183.1 m S 154.7241 183.1 m S 154.7241 198.0284 m S 162.3274 190.5642 m S U 154.7241 212.9568 m S 154.7241 198.0284 m S 139.5171 198.0284 m S 139.5171 212.9568 m S 147.1206 205.4927 m S 154.7241 227.8852 m S 154.7241 212.9568 m S 139.5171 212.9568 m S 139.5171 227.8852 m S 147.1206 220.421 m S 169.9309 227.8852 m S 169.9309 212.9568 m S 154.7241 212.9568 m S 154.7241 227.8852 m S 162.3274 220.421 m S 169.9309 212.9568 m S 169.9309 198.0284 m S 154.7241 198.0284 m S 154.7241 212.9568 m S 162.3274 205.4927 m S u 154.7241 198.0284 m S 154.7241 183.1 m S 139.5171 183.1 m S 139.5171 198.0284 m S 147.1206 190.5642 m S U u 139.5171 198.0284 m S 139.5171 183.1 m S 124.3103 183.1 m S 124.3103 198.0284 m S 131.9137 190.5642 m S U u 139.5171 212.9568 m S 139.5171 198.0284 m S 124.3103 198.0284 m S 124.3103 212.9568 m S 131.9137 205.4927 m S U 0 g 1 w 4 M 131.9137 220.421 m F 162.3274 220.421 m F 131.9137 190.5642 m F 162.3274 190.5642 m F 0 G 0.3 w 10 M 169.9309 212.9568 m S 169.9309 227.8852 m S 169.9309 183.1 m S 169.9309 198.0284 m S 169.9309 198.0284 m S 169.9309 212.9568 m S 0 g 1 w 4 M 40.6725 175.6358 m F 71.0862 175.6358 m F 86.2931 175.6358 m F 116.7068 175.6358 m F 131.9137 175.6358 m F 162.3274 175.6358 m F u 0 G 0.3 w 10 M 48.2759 183.1 m S 48.2759 168.1715 m S 33.0691 168.1715 m S 33.0691 183.1 m S 40.6725 175.6358 m S U u 78.6897 153.2431 m S 78.6897 138.3147 m S 63.4828 138.3147 m S 63.4828 153.2431 m S 71.0862 145.7789 m S U u 63.4828 168.1715 m S 63.4828 153.2431 m S 48.2759 153.2431 m S 48.2759 168.1715 m S 55.8794 160.7073 m S U u 63.4828 183.1 m S 63.4828 168.1715 m S 48.2759 168.1715 m S 48.2759 183.1 m S 55.8794 175.6358 m S U u 78.6897 183.1 m S 78.6897 168.1715 m S 63.4828 168.1715 m S 63.4828 183.1 m S 71.0862 175.6358 m S U u 78.6897 168.1715 m S 78.6897 153.2431 m S 63.4828 153.2431 m S 63.4828 168.1715 m S 71.0862 160.7073 m S U u 63.4828 153.2431 m S 63.4828 138.3147 m S 48.2759 138.3147 m S 48.2759 153.2431 m S 55.8794 145.7789 m S U u 48.2759 153.2431 m S 48.2759 138.3147 m S 33.0691 138.3147 m S 33.0691 153.2431 m S 40.6725 145.7789 m S U u 48.2759 168.1715 m S 48.2759 153.2431 m S 33.0691 153.2431 m S 33.0691 168.1715 m S 40.6725 160.7073 m S U 0 g 1 w 4 M 40.6725 175.6358 m F 71.0862 175.6358 m F 40.6725 145.7789 m F 71.0862 145.7789 m F u 0 G 0.3 w 10 M 93.8965 183.1 m S 93.8965 168.1715 m S 78.6897 168.1715 m S 78.6897 183.1 m S 86.2931 175.6358 m S U u 124.3103 153.2431 m S 124.3103 138.3147 m S 109.1034 138.3147 m S 109.1034 153.2431 m S 116.7068 145.7789 m S U u 109.1034 168.1715 m S 109.1034 153.2431 m S 93.8965 153.2431 m S 93.8965 168.1715 m S 101.5 160.7073 m S U u 109.1034 183.1 m S 109.1034 168.1715 m S 93.8965 168.1715 m S 93.8965 183.1 m S 101.5 175.6358 m S U u 124.3103 183.1 m S 124.3103 168.1715 m S 109.1034 168.1715 m S 109.1034 183.1 m S 116.7068 175.6358 m S U u 124.3103 168.1715 m S 124.3103 153.2431 m S 109.1034 153.2431 m S 109.1034 168.1715 m S 116.7068 160.7073 m S U u 109.1034 153.2431 m S 109.1034 138.3147 m S 93.8965 138.3147 m S 93.8965 153.2431 m S 101.5 145.7789 m S U u 93.8965 153.2431 m S 93.8965 138.3147 m S 78.6897 138.3147 m S 78.6897 153.2431 m S 86.2931 145.7789 m S U u 93.8965 168.1715 m S 93.8965 153.2431 m S 78.6897 153.2431 m S 78.6897 168.1715 m S 86.2931 160.7073 m S U 0 g 1 w 4 M 86.2931 175.6358 m F 116.7068 175.6358 m F 86.2931 145.7789 m F 116.7068 145.7789 m F u 0 G 0.3 w 10 M 139.5171 183.1 m S 139.5171 168.1715 m S 124.3103 168.1715 m S 124.3103 183.1 m S 131.9137 175.6358 m S U u 169.9309 153.2431 m S 169.9309 138.3147 m S 154.7241 138.3147 m S 154.7241 153.2431 m S 162.3274 145.7789 m S U u 154.7241 168.1715 m S 154.7241 153.2431 m S 139.5171 153.2431 m S 139.5171 168.1715 m S 147.1206 160.7073 m S U u 154.7241 183.1 m S 154.7241 168.1715 m S 139.5171 168.1715 m S 139.5171 183.1 m S 147.1206 175.6358 m S U u 169.9309 183.1 m S 169.9309 168.1715 m S 154.7241 168.1715 m S 154.7241 183.1 m S 162.3274 175.6358 m S U u 169.9309 168.1715 m S 169.9309 153.2431 m S 154.7241 153.2431 m S 154.7241 168.1715 m S 162.3274 160.7073 m S U u 154.7241 153.2431 m S 154.7241 138.3147 m S 139.5171 138.3147 m S 139.5171 153.2431 m S 147.1206 145.7789 m S U u 139.5171 153.2431 m S 139.5171 138.3147 m S 124.3103 138.3147 m S 124.3103 153.2431 m S 131.9137 145.7789 m S U u 139.5171 168.1715 m S 139.5171 153.2431 m S 124.3103 153.2431 m S 124.3103 168.1715 m S 131.9137 160.7073 m S U 0 g 1 w 4 M 131.9137 175.6358 m F 162.3274 175.6358 m F 131.9137 145.7789 m F 162.3274 145.7789 m F 0 G 0.3 w 10 M 169.9309 168.1715 m S 169.9309 183.1 m S 169.9309 138.3147 m S 169.9309 153.2431 m S 169.9309 153.2431 m S 169.9309 168.1715 m S 48.2759 138.3147 m S 33.0691 138.3147 m S 63.4828 138.3147 m S 48.2759 138.3147 m S 78.6897 138.3147 m S 63.4828 138.3147 m S 93.8965 138.3147 m S 78.6897 138.3147 m S 109.1034 138.3147 m S 93.8965 138.3147 m S 124.3103 138.3147 m S 109.1034 138.3147 m S 139.5171 138.3147 m S 124.3103 138.3147 m S 154.7241 138.3147 m S 139.5171 138.3147 m S 169.9309 138.3147 m S 154.7241 138.3147 m S 169.9309 138.3147 m S 1 w 4 M 40.6725 250.2779 m 162.3274 250.2779 l S 40.6725 205.4927 m 162.3274 205.4927 l S 40.6725 160.7073 m 162.3274 160.7073 l S 55.8794 265.2063 m 55.8794 145.7789 l S 101.5 265.2063 m 101.5 145.7789 l S 147.1206 265.2063 m 147.1206 145.7789 l S u 0.3 w 10 M 139.5171 272.6705 m S 139.5171 257.7421 m S 124.3103 257.7421 m S 124.3103 272.6705 m S 131.9137 265.2063 m S U 169.9309 242.8137 m S 169.9309 227.8852 m S 154.724 227.8852 m S 154.724 242.8137 m S 162.3274 235.3495 m S 154.724 257.7421 m S 154.724 242.8137 m S 139.5171 242.8137 m S 139.5171 257.7421 m S 147.1206 250.2779 m S u 154.724 272.6705 m S 154.724 257.7421 m S 139.5171 257.7421 m S 139.5171 272.6705 m S 147.1206 265.2063 m S U u 169.9309 272.6705 m S 169.9309 257.7421 m S 154.724 257.7421 m S 154.724 272.6705 m S 162.3274 265.2063 m S U 169.9309 257.7421 m S 169.9309 242.8137 m S 154.724 242.8137 m S 154.724 257.7421 m S 162.3274 250.2779 m S 154.724 242.8137 m S 154.724 227.8852 m S 139.5171 227.8852 m S 139.5171 242.8137 m S 147.1206 235.3495 m S u 139.5171 242.8137 m S 139.5171 227.8852 m S 124.3103 227.8852 m S 124.3103 242.8137 m S 131.9137 235.3495 m S U u 139.5171 257.7421 m S 139.5171 242.8137 m S 124.3103 242.8137 m S 124.3103 257.7421 m S 131.9137 250.2779 m S U 0 g 1 w 4 M 131.9137 265.2063 m F 162.3274 265.2063 m F 131.9137 235.3495 m F 162.3274 235.3495 m F u 0 G 0.3 w 10 M 185.1378 272.6705 m S 185.1378 257.7421 m S 169.9309 257.7421 m S 169.9309 272.6705 m S 177.5343 265.2063 m S U 215.5515 242.8137 m S 215.5515 227.8852 m S 200.3447 227.8852 m S 200.3447 242.8137 m S 207.9481 235.3495 m S 200.3447 257.7421 m S 200.3447 242.8137 m S 185.1378 242.8137 m S 185.1378 257.7421 m S 192.7412 250.2779 m S u 200.3447 272.6705 m S 200.3447 257.7421 m S 185.1378 257.7421 m S 185.1378 272.6705 m S 192.7412 265.2063 m S U u 215.5515 272.6705 m S 215.5515 257.7421 m S 200.3447 257.7421 m S 200.3447 272.6705 m S 207.9481 265.2063 m S U 215.5515 257.7421 m S 215.5515 242.8137 m S 200.3447 242.8137 m S 200.3447 257.7421 m S 207.9481 250.2779 m S 200.3447 242.8137 m S 200.3447 227.8852 m S 185.1378 227.8852 m S 185.1378 242.8137 m S 192.7412 235.3495 m S 185.1378 242.8137 m S 185.1378 227.8852 m S 169.9309 227.8852 m S 169.9309 242.8137 m S 177.5343 235.3495 m S 185.1378 257.7421 m S 185.1378 242.8137 m S 169.9309 242.8137 m S 169.9309 257.7421 m S 177.5343 250.2779 m S 0 g 1 w 4 M 177.5343 265.2063 m F 207.9481 265.2063 m F 177.5343 235.3495 m F 207.9481 235.3495 m F u 0 G 0.3 w 10 M 230.7584 272.6705 m S 230.7584 257.7421 m S 215.5515 257.7421 m S 215.5515 272.6705 m S 223.1549 265.2063 m S U u 261.1721 242.8137 m S 261.1721 227.8852 m S 245.9653 227.8852 m S 245.9653 242.8137 m S 253.5687 235.3495 m S U 245.9653 257.7421 m S 245.9653 242.8137 m S 230.7584 242.8137 m S 230.7584 257.7421 m S 238.3618 250.2779 m S u 245.9653 272.6705 m S 245.9653 257.7421 m S 230.7584 257.7421 m S 230.7584 272.6705 m S 238.3618 265.2063 m S U u 261.1721 272.6705 m S 261.1721 257.7421 m S 245.9653 257.7421 m S 245.9653 272.6705 m S 253.5687 265.2063 m S U u 261.1721 257.7421 m S 261.1721 242.8137 m S 245.9653 242.8137 m S 245.9653 257.7421 m S 253.5687 250.2779 m S U 245.9653 242.8137 m S 245.9653 227.8852 m S 230.7584 227.8852 m S 230.7584 242.8137 m S 238.3618 235.3495 m S 230.7584 242.8137 m S 230.7584 227.8852 m S 215.5515 227.8852 m S 215.5515 242.8137 m S 223.1549 235.3495 m S 230.7584 257.7421 m S 230.7584 242.8137 m S 215.5515 242.8137 m S 215.5515 257.7421 m S 223.1549 250.2779 m S 0 g 1 w 4 M 223.1549 265.2063 m F 253.5687 265.2063 m F 223.1549 235.3495 m F 253.5687 235.3495 m F 0 G 0.3 w 10 M 261.1721 257.7421 m S 261.1721 272.6705 m S 261.1721 227.8852 m S 261.1721 242.8137 m S 261.1721 242.8137 m S 261.1721 257.7421 m S u 139.5171 227.8852 m S 139.5171 212.9568 m S 124.3103 212.9568 m S 124.3103 227.8852 m S 131.9137 220.421 m S U u 169.9309 198.0284 m S 169.9309 183.1 m S 154.724 183.1 m S 154.724 198.0284 m S 162.3274 190.5642 m S U 154.724 212.9568 m S 154.724 198.0284 m S 139.5171 198.0284 m S 139.5171 212.9568 m S 147.1206 205.4927 m S 154.724 227.8852 m S 154.724 212.9568 m S 139.5171 212.9568 m S 139.5171 227.8852 m S 147.1206 220.421 m S 169.9309 227.8852 m S 169.9309 212.9568 m S 154.724 212.9568 m S 154.724 227.8852 m S 162.3274 220.421 m S 169.9309 212.9568 m S 169.9309 198.0284 m S 154.724 198.0284 m S 154.724 212.9568 m S 162.3274 205.4927 m S u 154.724 198.0284 m S 154.724 183.1 m S 139.5171 183.1 m S 139.5171 198.0284 m S 147.1206 190.5642 m S U u 139.5171 198.0284 m S 139.5171 183.1 m S 124.3103 183.1 m S 124.3103 198.0284 m S 131.9137 190.5642 m S U u 139.5171 212.9568 m S 139.5171 198.0284 m S 124.3103 198.0284 m S 124.3103 212.9568 m S 131.9137 205.4927 m S U 0 g 1 w 4 M 131.9137 220.421 m F 162.3274 220.421 m F 131.9137 190.5642 m F 162.3274 190.5642 m F 0 G 0.3 w 10 M 185.1378 227.8852 m S 185.1378 212.9568 m S 169.9309 212.9568 m S 169.9309 227.8852 m S 177.5343 220.421 m S u 215.5515 198.0284 m S 215.5515 183.1 m S 200.3447 183.1 m S 200.3447 198.0284 m S 207.9481 190.5642 m S U 200.3447 212.9568 m S 200.3447 198.0284 m S 185.1378 198.0284 m S 185.1378 212.9568 m S 192.7412 205.4927 m S 200.3447 227.8852 m S 200.3447 212.9568 m S 185.1378 212.9568 m S 185.1378 227.8852 m S 192.7412 220.421 m S 215.5515 227.8852 m S 215.5515 212.9568 m S 200.3447 212.9568 m S 200.3447 227.8852 m S 207.9481 220.421 m S 215.5515 212.9568 m S 215.5515 198.0284 m S 200.3447 198.0284 m S 200.3447 212.9568 m S 207.9481 205.4927 m S u 200.3447 198.0284 m S 200.3447 183.1 m S 185.1378 183.1 m S 185.1378 198.0284 m S 192.7412 190.5642 m S U u 185.1378 198.0284 m S 185.1378 183.1 m S 169.9309 183.1 m S 169.9309 198.0284 m S 177.5343 190.5642 m S U 185.1378 212.9568 m S 185.1378 198.0284 m S 169.9309 198.0284 m S 169.9309 212.9568 m S 177.5343 205.4927 m S 0 g 1 w 4 M 177.5343 220.421 m F 207.9481 220.421 m F 177.5343 190.5642 m F 207.9481 190.5642 m F 0 G 0.3 w 10 M 230.7584 227.8852 m S 230.7584 212.9568 m S 215.5515 212.9568 m S 215.5515 227.8852 m S 223.1549 220.421 m S u 261.1721 198.0284 m S 261.1721 183.1 m S 245.9653 183.1 m S 245.9653 198.0284 m S 253.5687 190.5642 m S U 245.9653 212.9568 m S 245.9653 198.0284 m S 230.7584 198.0284 m S 230.7584 212.9568 m S 238.3618 205.4927 m S 245.9653 227.8852 m S 245.9653 212.9568 m S 230.7584 212.9568 m S 230.7584 227.8852 m S 238.3618 220.421 m S u 261.1721 227.8852 m S 261.1721 212.9568 m S 245.9653 212.9568 m S 245.9653 227.8852 m S 253.5687 220.421 m S U u 261.1721 212.9568 m S 261.1721 198.0284 m S 245.9653 198.0284 m S 245.9653 212.9568 m S 253.5687 205.4927 m S U u 245.9653 198.0284 m S 245.9653 183.1 m S 230.7584 183.1 m S 230.7584 198.0284 m S 238.3618 190.5642 m S U u 230.7584 198.0284 m S 230.7584 183.1 m S 215.5515 183.1 m S 215.5515 198.0284 m S 223.1549 190.5642 m S U 230.7584 212.9568 m S 230.7584 198.0284 m S 215.5515 198.0284 m S 215.5515 212.9568 m S 223.1549 205.4927 m S 0 g 1 w 4 M 223.1549 220.421 m F 253.5687 220.421 m F 223.1549 190.5642 m F 253.5687 190.5642 m F 0 G 0.3 w 10 M 261.1721 212.9568 m S 261.1721 227.8852 m S 261.1721 183.1 m S 261.1721 198.0284 m S 261.1721 198.0284 m S 261.1721 212.9568 m S 0 g 1 w 4 M 131.9137 175.6358 m F 162.3274 175.6358 m F 177.5343 175.6358 m F 207.9481 175.6358 m F 223.1549 175.6358 m F 253.5687 175.6358 m F u 0 G 0.3 w 10 M 139.5171 183.1 m S 139.5171 168.1715 m S 124.3103 168.1715 m S 124.3103 183.1 m S 131.9137 175.6358 m S U u 169.9309 153.2431 m S 169.9309 138.3147 m S 154.724 138.3147 m S 154.724 153.2431 m S 162.3274 145.7789 m S U u 154.724 168.1715 m S 154.724 153.2431 m S 139.5171 153.2431 m S 139.5171 168.1715 m S 147.1206 160.7073 m S U u 154.724 183.1 m S 154.724 168.1715 m S 139.5171 168.1715 m S 139.5171 183.1 m S 147.1206 175.6358 m S U u 169.9309 183.1 m S 169.9309 168.1715 m S 154.724 168.1715 m S 154.724 183.1 m S 162.3274 175.6358 m S U u 169.9309 168.1715 m S 169.9309 153.2431 m S 154.724 153.2431 m S 154.724 168.1715 m S 162.3274 160.7073 m S U u 154.724 153.2431 m S 154.724 138.3147 m S 139.5171 138.3147 m S 139.5171 153.2431 m S 147.1206 145.7789 m S U u 139.5171 153.2431 m S 139.5171 138.3147 m S 124.3103 138.3147 m S 124.3103 153.2431 m S 131.9137 145.7789 m S U u 139.5171 168.1715 m S 139.5171 153.2431 m S 124.3103 153.2431 m S 124.3103 168.1715 m S 131.9137 160.7073 m S U 0 g 1 w 4 M 131.9137 175.6358 m F 162.3274 175.6358 m F 131.9137 145.7789 m F 162.3274 145.7789 m F u 0 G 0.3 w 10 M 185.1378 183.1 m S 185.1378 168.1715 m S 169.9309 168.1715 m S 169.9309 183.1 m S 177.5343 175.6358 m S U u 215.5515 153.2431 m S 215.5515 138.3147 m S 200.3447 138.3147 m S 200.3447 153.2431 m S 207.9481 145.7789 m S U u 200.3447 168.1715 m S 200.3447 153.2431 m S 185.1378 153.2431 m S 185.1378 168.1715 m S 192.7412 160.7073 m S U u 200.3447 183.1 m S 200.3447 168.1715 m S 185.1378 168.1715 m S 185.1378 183.1 m S 192.7412 175.6358 m S U u 215.5515 183.1 m S 215.5515 168.1715 m S 200.3447 168.1715 m S 200.3447 183.1 m S 207.9481 175.6358 m S U u 215.5515 168.1715 m S 215.5515 153.2431 m S 200.3447 153.2431 m S 200.3447 168.1715 m S 207.9481 160.7073 m S U u 200.3447 153.2431 m S 200.3447 138.3147 m S 185.1378 138.3147 m S 185.1378 153.2431 m S 192.7412 145.7789 m S U u 185.1378 153.2431 m S 185.1378 138.3147 m S 169.9309 138.3147 m S 169.9309 153.2431 m S 177.5343 145.7789 m S U u 185.1378 168.1715 m S 185.1378 153.2431 m S 169.9309 153.2431 m S 169.9309 168.1715 m S 177.5343 160.7073 m S U 0 g 1 w 4 M 177.5343 175.6358 m F 207.9481 175.6358 m F 177.5343 145.7789 m F 207.9481 145.7789 m F u 0 G 0.3 w 10 M 230.7584 183.1 m S 230.7584 168.1715 m S 215.5515 168.1715 m S 215.5515 183.1 m S 223.1549 175.6358 m S U u 261.1721 153.2431 m S 261.1721 138.3147 m S 245.9653 138.3147 m S 245.9653 153.2431 m S 253.5687 145.7789 m S U u 245.9653 168.1715 m S 245.9653 153.2431 m S 230.7584 153.2431 m S 230.7584 168.1715 m S 238.3618 160.7073 m S U u 245.9653 183.1 m S 245.9653 168.1715 m S 230.7584 168.1715 m S 230.7584 183.1 m S 238.3618 175.6358 m S U u 261.1721 183.1 m S 261.1721 168.1715 m S 245.9653 168.1715 m S 245.9653 183.1 m S 253.5687 175.6358 m S U u 261.1721 168.1715 m S 261.1721 153.2431 m S 245.9653 153.2431 m S 245.9653 168.1715 m S 253.5687 160.7073 m S U u 245.9653 153.2431 m S 245.9653 138.3147 m S 230.7584 138.3147 m S 230.7584 153.2431 m S 238.3618 145.7789 m S U u 230.7584 153.2431 m S 230.7584 138.3147 m S 215.5515 138.3147 m S 215.5515 153.2431 m S 223.1549 145.7789 m S U u 230.7584 168.1715 m S 230.7584 153.2431 m S 215.5515 153.2431 m S 215.5515 168.1715 m S 223.1549 160.7073 m S U 0 g 1 w 4 M 223.1549 175.6358 m F 253.5687 175.6358 m F 223.1549 145.7789 m F 253.5687 145.7789 m F 0 G 0.3 w 10 M 261.1721 168.1715 m S 261.1721 183.1 m S 261.1721 138.3147 m S 261.1721 153.2431 m S 261.1721 153.2431 m S 261.1721 168.1715 m S 139.5171 138.3147 m S 124.3103 138.3147 m S 154.724 138.3147 m S 139.5171 138.3147 m S 169.9309 138.3147 m S 154.724 138.3147 m S 185.1378 138.3147 m S 169.9309 138.3147 m S 200.3447 138.3147 m S 185.1378 138.3147 m S 215.5515 138.3147 m S 200.3447 138.3147 m S 230.7584 138.3147 m S 215.5515 138.3147 m S 245.9653 138.3147 m S 230.7584 138.3147 m S 261.1721 138.3147 m S 245.9653 138.3147 m S 261.1721 138.3147 m S 1 w 4 M 131.9137 250.2779 m 253.5687 250.2779 l S 131.9137 205.4927 m 253.5687 205.4927 l S 131.9137 160.7073 m 253.5687 160.7073 l S 147.1206 265.2063 m 147.1206 145.7789 l S 192.7412 265.2063 m 192.7412 145.7789 l S 238.3618 265.2063 m 238.3618 145.7789 l S u 0.3 w 10 M 48.2759 183.1 m S 48.2759 168.1716 m S 33.0691 168.1716 m S 33.0691 183.1 m S 40.6725 175.6358 m S U u 78.6897 153.2431 m S 78.6897 138.3147 m S 63.4828 138.3147 m S 63.4828 153.2431 m S 71.0862 145.7789 m S U u 63.4828 168.1716 m S 63.4828 153.2431 m S 48.2759 153.2431 m S 48.2759 168.1716 m S 55.8794 160.7074 m S U u 63.4828 183.1 m S 63.4828 168.1716 m S 48.2759 168.1716 m S 48.2759 183.1 m S 55.8794 175.6358 m S U u 78.6897 183.1 m S 78.6897 168.1716 m S 63.4828 168.1716 m S 63.4828 183.1 m S 71.0862 175.6358 m S U u 78.6897 168.1716 m S 78.6897 153.2431 m S 63.4828 153.2431 m S 63.4828 168.1716 m S 71.0862 160.7074 m S U u 63.4828 153.2431 m S 63.4828 138.3147 m S 48.2759 138.3147 m S 48.2759 153.2431 m S 55.8794 145.7789 m S U u 48.2759 153.2431 m S 48.2759 138.3147 m S 33.0691 138.3147 m S 33.0691 153.2431 m S 40.6725 145.7789 m S U u 48.2759 168.1716 m S 48.2759 153.2431 m S 33.0691 153.2431 m S 33.0691 168.1716 m S 40.6725 160.7074 m S U 0 g 1 w 4 M 40.6725 175.6358 m F 71.0862 175.6358 m F 40.6725 145.7789 m F 71.0862 145.7789 m F u 0 G 0.3 w 10 M 93.8965 183.1 m S 93.8965 168.1716 m S 78.6897 168.1716 m S 78.6897 183.1 m S 86.2931 175.6358 m S U u 124.3103 153.2431 m S 124.3103 138.3147 m S 109.1034 138.3147 m S 109.1034 153.2431 m S 116.7068 145.7789 m S U u 109.1034 168.1716 m S 109.1034 153.2431 m S 93.8965 153.2431 m S 93.8965 168.1716 m S 101.5 160.7074 m S U u 109.1034 183.1 m S 109.1034 168.1716 m S 93.8965 168.1716 m S 93.8965 183.1 m S 101.5 175.6358 m S U u 124.3103 183.1 m S 124.3103 168.1716 m S 109.1034 168.1716 m S 109.1034 183.1 m S 116.7068 175.6358 m S U u 124.3103 168.1716 m S 124.3103 153.2431 m S 109.1034 153.2431 m S 109.1034 168.1716 m S 116.7068 160.7074 m S U u 109.1034 153.2431 m S 109.1034 138.3147 m S 93.8965 138.3147 m S 93.8965 153.2431 m S 101.5 145.7789 m S U u 93.8965 153.2431 m S 93.8965 138.3147 m S 78.6897 138.3147 m S 78.6897 153.2431 m S 86.2931 145.7789 m S U u 93.8965 168.1716 m S 93.8965 153.2431 m S 78.6897 153.2431 m S 78.6897 168.1716 m S 86.2931 160.7074 m S U 0 g 1 w 4 M 86.2931 175.6358 m F 116.7068 175.6358 m F 86.2931 145.7789 m F 116.7068 145.7789 m F u 0 G 0.3 w 10 M 139.5171 183.1 m S 139.5171 168.1716 m S 124.3103 168.1716 m S 124.3103 183.1 m S 131.9137 175.6358 m S U u 169.9309 153.2431 m S 169.9309 138.3147 m S 154.7241 138.3147 m S 154.7241 153.2431 m S 162.3274 145.7789 m S U u 154.7241 168.1716 m S 154.7241 153.2431 m S 139.5171 153.2431 m S 139.5171 168.1716 m S 147.1206 160.7074 m S U u 154.7241 183.1 m S 154.7241 168.1716 m S 139.5171 168.1716 m S 139.5171 183.1 m S 147.1206 175.6358 m S U u 169.9309 183.1 m S 169.9309 168.1716 m S 154.7241 168.1716 m S 154.7241 183.1 m S 162.3274 175.6358 m S U u 169.9309 168.1716 m S 169.9309 153.2431 m S 154.7241 153.2431 m S 154.7241 168.1716 m S 162.3274 160.7074 m S U u 154.7241 153.2431 m S 154.7241 138.3147 m S 139.5171 138.3147 m S 139.5171 153.2431 m S 147.1206 145.7789 m S U u 139.5171 153.2431 m S 139.5171 138.3147 m S 124.3103 138.3147 m S 124.3103 153.2431 m S 131.9137 145.7789 m S U u 139.5171 168.1716 m S 139.5171 153.2431 m S 124.3103 153.2431 m S 124.3103 168.1716 m S 131.9137 160.7074 m S U 0 g 1 w 4 M 131.9137 175.6358 m F 162.3274 175.6358 m F 131.9137 145.7789 m F 162.3274 145.7789 m F 0 G 0.3 w 10 M 169.9309 168.1716 m S 169.9309 183.1 m S 169.9309 138.3147 m S 169.9309 153.2431 m S 169.9309 153.2431 m S 169.9309 168.1716 m S u 48.2759 138.3147 m S 48.2759 123.3863 m S 33.0691 123.3863 m S 33.0691 138.3147 m S 40.6725 130.8505 m S U u 78.6897 108.4579 m S 78.6897 93.5295 m S 63.4828 93.5295 m S 63.4828 108.4579 m S 71.0862 100.9937 m S U u 63.4828 123.3863 m S 63.4828 108.4579 m S 48.2759 108.4579 m S 48.2759 123.3863 m S 55.8794 115.9221 m S U u 63.4828 138.3147 m S 63.4828 123.3863 m S 48.2759 123.3863 m S 48.2759 138.3147 m S 55.8794 130.8505 m S U u 78.6897 138.3147 m S 78.6897 123.3863 m S 63.4828 123.3863 m S 63.4828 138.3147 m S 71.0862 130.8505 m S U u 78.6897 123.3863 m S 78.6897 108.4579 m S 63.4828 108.4579 m S 63.4828 123.3863 m S 71.0862 115.9221 m S U u 63.4828 108.4579 m S 63.4828 93.5295 m S 48.2759 93.5295 m S 48.2759 108.4579 m S 55.8794 100.9937 m S U u 48.2759 108.4579 m S 48.2759 93.5295 m S 33.0691 93.5295 m S 33.0691 108.4579 m S 40.6725 100.9937 m S U u 48.2759 123.3863 m S 48.2759 108.4579 m S 33.0691 108.4579 m S 33.0691 123.3863 m S 40.6725 115.9221 m S U 0 g 1 w 4 M 40.6725 130.8505 m F 71.0862 130.8505 m F 40.6725 100.9937 m F 71.0862 100.9937 m F u 0 G 0.3 w 10 M 93.8965 138.3147 m S 93.8965 123.3863 m S 78.6897 123.3863 m S 78.6897 138.3147 m S 86.2931 130.8505 m S U u 124.3103 108.4579 m S 124.3103 93.5295 m S 109.1034 93.5295 m S 109.1034 108.4579 m S 116.7068 100.9937 m S U u 109.1034 123.3863 m S 109.1034 108.4579 m S 93.8965 108.4579 m S 93.8965 123.3863 m S 101.5 115.9221 m S U u 109.1034 138.3147 m S 109.1034 123.3863 m S 93.8965 123.3863 m S 93.8965 138.3147 m S 101.5 130.8505 m S U u 124.3103 138.3147 m S 124.3103 123.3863 m S 109.1034 123.3863 m S 109.1034 138.3147 m S 116.7068 130.8505 m S U u 124.3103 123.3863 m S 124.3103 108.4579 m S 109.1034 108.4579 m S 109.1034 123.3863 m S 116.7068 115.9221 m S U u 109.1034 108.4579 m S 109.1034 93.5295 m S 93.8965 93.5295 m S 93.8965 108.4579 m S 101.5 100.9937 m S U u 93.8965 108.4579 m S 93.8965 93.5295 m S 78.6897 93.5295 m S 78.6897 108.4579 m S 86.2931 100.9937 m S U u 93.8965 123.3863 m S 93.8965 108.4579 m S 78.6897 108.4579 m S 78.6897 123.3863 m S 86.2931 115.9221 m S U 0 g 1 w 4 M 86.2931 130.8505 m F 116.7068 130.8505 m F 86.2931 100.9937 m F 116.7068 100.9937 m F u 0 G 0.3 w 10 M 139.5171 138.3147 m S 139.5171 123.3863 m S 124.3103 123.3863 m S 124.3103 138.3147 m S 131.9137 130.8505 m S U u 169.9309 108.4579 m S 169.9309 93.5295 m S 154.7241 93.5295 m S 154.7241 108.4579 m S 162.3274 100.9937 m S U u 154.7241 123.3863 m S 154.7241 108.4579 m S 139.5171 108.4579 m S 139.5171 123.3863 m S 147.1206 115.9221 m S U u 154.7241 138.3147 m S 154.7241 123.3863 m S 139.5171 123.3863 m S 139.5171 138.3147 m S 147.1206 130.8505 m S U u 169.9309 138.3147 m S 169.9309 123.3863 m S 154.7241 123.3863 m S 154.7241 138.3147 m S 162.3274 130.8505 m S U u 169.9309 123.3863 m S 169.9309 108.4579 m S 154.7241 108.4579 m S 154.7241 123.3863 m S 162.3274 115.9221 m S U u 154.7241 108.4579 m S 154.7241 93.5295 m S 139.5171 93.5295 m S 139.5171 108.4579 m S 147.1206 100.9937 m S U u 139.5171 108.4579 m S 139.5171 93.5295 m S 124.3103 93.5295 m S 124.3103 108.4579 m S 131.9137 100.9937 m S U u 139.5171 123.3863 m S 139.5171 108.4579 m S 124.3103 108.4579 m S 124.3103 123.3863 m S 131.9137 115.9221 m S U 0 g 1 w 4 M 131.9137 130.8505 m F 162.3274 130.8505 m F 131.9137 100.9937 m F 162.3274 100.9937 m F 0 G 0.3 w 10 M 169.9309 123.3863 m S 169.9309 138.3147 m S 169.9309 93.5295 m S 169.9309 108.4579 m S 169.9309 108.4579 m S 169.9309 123.3863 m S 0 g 1 w 4 M 40.6725 86.0653 m F 71.0862 86.0653 m F 86.2931 86.0653 m F 116.7068 86.0653 m F 131.9137 86.0653 m F 162.3274 86.0653 m F u 0 G 0.3 w 10 M 48.2759 93.5295 m S 48.2759 78.601 m S 33.0691 78.601 m S 33.0691 93.5295 m S 40.6725 86.0653 m S U u 78.6897 63.6726 m S 78.6897 48.7442 m S 63.4828 48.7442 m S 63.4828 63.6726 m S 71.0862 56.2084 m S U u 63.4828 78.601 m S 63.4828 63.6726 m S 48.2759 63.6726 m S 48.2759 78.601 m S 55.8794 71.1368 m S U u 63.4828 93.5295 m S 63.4828 78.601 m S 48.2759 78.601 m S 48.2759 93.5295 m S 55.8794 86.0653 m S U u 78.6897 93.5295 m S 78.6897 78.601 m S 63.4828 78.601 m S 63.4828 93.5295 m S 71.0862 86.0653 m S U u 78.6897 78.601 m S 78.6897 63.6726 m S 63.4828 63.6726 m S 63.4828 78.601 m S 71.0862 71.1368 m S U u 63.4828 63.6726 m S 63.4828 48.7442 m S 48.2759 48.7442 m S 48.2759 63.6726 m S 55.8794 56.2084 m S U u 48.2759 63.6726 m S 48.2759 48.7442 m S 33.0691 48.7442 m S 33.0691 63.6726 m S 40.6725 56.2084 m S U u 48.2759 78.601 m S 48.2759 63.6726 m S 33.0691 63.6726 m S 33.0691 78.601 m S 40.6725 71.1368 m S U 0 g 1 w 4 M 40.6725 86.0653 m F 71.0862 86.0653 m F 40.6725 56.2084 m F 71.0862 56.2084 m F u 0 G 0.3 w 10 M 93.8965 93.5295 m S 93.8965 78.601 m S 78.6897 78.601 m S 78.6897 93.5295 m S 86.2931 86.0653 m S U u 124.3103 63.6726 m S 124.3103 48.7442 m S 109.1034 48.7442 m S 109.1034 63.6726 m S 116.7068 56.2084 m S U u 109.1034 78.601 m S 109.1034 63.6726 m S 93.8965 63.6726 m S 93.8965 78.601 m S 101.5 71.1368 m S U u 109.1034 93.5295 m S 109.1034 78.601 m S 93.8965 78.601 m S 93.8965 93.5295 m S 101.5 86.0653 m S U u 124.3103 93.5295 m S 124.3103 78.601 m S 109.1034 78.601 m S 109.1034 93.5295 m S 116.7068 86.0653 m S U u 124.3103 78.601 m S 124.3103 63.6726 m S 109.1034 63.6726 m S 109.1034 78.601 m S 116.7068 71.1368 m S U u 109.1034 63.6726 m S 109.1034 48.7442 m S 93.8965 48.7442 m S 93.8965 63.6726 m S 101.5 56.2084 m S U u 93.8965 63.6726 m S 93.8965 48.7442 m S 78.6897 48.7442 m S 78.6897 63.6726 m S 86.2931 56.2084 m S U u 93.8965 78.601 m S 93.8965 63.6726 m S 78.6897 63.6726 m S 78.6897 78.601 m S 86.2931 71.1368 m S U 0 g 1 w 4 M 86.2931 86.0653 m F 116.7068 86.0653 m F 86.2931 56.2084 m F 116.7068 56.2084 m F u 0 G 0.3 w 10 M 139.5171 93.5295 m S 139.5171 78.601 m S 124.3103 78.601 m S 124.3103 93.5295 m S 131.9137 86.0653 m S U 169.9309 63.6726 m S 169.9309 48.7442 m S 154.7241 48.7442 m S 154.7241 63.6726 m S 162.3274 56.2084 m S u 154.7241 78.601 m S 154.7241 63.6726 m S 139.5171 63.6726 m S 139.5171 78.601 m S 147.1206 71.1368 m S U u 154.7241 93.5295 m S 154.7241 78.601 m S 139.5171 78.601 m S 139.5171 93.5295 m S 147.1206 86.0653 m S U u 169.9309 93.5295 m S 169.9309 78.601 m S 154.7241 78.601 m S 154.7241 93.5295 m S 162.3274 86.0653 m S U u 169.9309 78.601 m S 169.9309 63.6726 m S 154.7241 63.6726 m S 154.7241 78.601 m S 162.3274 71.1368 m S U 154.7241 63.6726 m S 154.7241 48.7442 m S 139.5171 48.7442 m S 139.5171 63.6726 m S 147.1206 56.2084 m S 139.5171 63.6726 m S 139.5171 48.7442 m S 124.3103 48.7442 m S 124.3103 63.6726 m S 131.9137 56.2084 m S u 139.5171 78.601 m S 139.5171 63.6726 m S 124.3103 63.6726 m S 124.3103 78.601 m S 131.9137 71.1368 m S U 0 g 1 w 4 M 131.9137 86.0653 m F 162.3274 86.0653 m F 131.9137 56.2084 m F 162.3274 56.2084 m F 0 G 0.3 w 10 M 169.9309 78.601 m S 169.9309 93.5295 m S 169.9309 48.7442 m S 169.9309 63.6726 m S 169.9309 63.6726 m S 169.9309 78.601 m S 48.2759 48.7442 m S 33.0691 48.7442 m S 63.4828 48.7442 m S 48.2759 48.7442 m S 78.6897 48.7442 m S 63.4828 48.7442 m S 93.8965 48.7442 m S 78.6897 48.7442 m S 109.1034 48.7442 m S 93.8965 48.7442 m S 124.3103 48.7442 m S 109.1034 48.7442 m S 139.5171 48.7442 m S 124.3103 48.7442 m S 154.7241 48.7442 m S 139.5171 48.7442 m S 169.9309 48.7442 m S 154.7241 48.7442 m S 169.9309 48.7442 m S 1 w 4 M 40.6725 160.7074 m 162.3274 160.7074 l S 40.6725 115.9221 m 162.3274 115.9221 l S 40.6725 71.1368 m 162.3274 71.1368 l S 55.8794 175.6358 m 55.8794 56.2084 l S 101.5 175.6358 m 101.5 56.2084 l S 147.1206 175.6358 m 147.1206 56.2084 l S u 0.3 w 10 M 139.5171 183.1 m S 139.5171 168.1716 m S 124.3103 168.1716 m S 124.3103 183.1 m S 131.9137 175.6358 m S U u 169.9309 153.2431 m S 169.9309 138.3147 m S 154.724 138.3147 m S 154.724 153.2431 m S 162.3274 145.7789 m S U u 154.724 168.1716 m S 154.724 153.2431 m S 139.5171 153.2431 m S 139.5171 168.1716 m S 147.1206 160.7074 m S U u 154.724 183.1 m S 154.724 168.1716 m S 139.5171 168.1716 m S 139.5171 183.1 m S 147.1206 175.6358 m S U u 169.9309 183.1 m S 169.9309 168.1716 m S 154.724 168.1716 m S 154.724 183.1 m S 162.3274 175.6358 m S U u 169.9309 168.1716 m S 169.9309 153.2431 m S 154.724 153.2431 m S 154.724 168.1716 m S 162.3274 160.7074 m S U u 154.724 153.2431 m S 154.724 138.3147 m S 139.5171 138.3147 m S 139.5171 153.2431 m S 147.1206 145.7789 m S U u 139.5171 153.2431 m S 139.5171 138.3147 m S 124.3103 138.3147 m S 124.3103 153.2431 m S 131.9137 145.7789 m S U u 139.5171 168.1716 m S 139.5171 153.2431 m S 124.3103 153.2431 m S 124.3103 168.1716 m S 131.9137 160.7074 m S U 0 g 1 w 4 M 131.9137 175.6358 m F 162.3274 175.6358 m F 131.9137 145.7789 m F 162.3274 145.7789 m F u 0 G 0.3 w 10 M 185.1378 183.1 m S 185.1378 168.1716 m S 169.9309 168.1716 m S 169.9309 183.1 m S 177.5343 175.6358 m S U u 215.5515 153.2431 m S 215.5515 138.3147 m S 200.3447 138.3147 m S 200.3447 153.2431 m S 207.9481 145.7789 m S U u 200.3447 168.1716 m S 200.3447 153.2431 m S 185.1378 153.2431 m S 185.1378 168.1716 m S 192.7412 160.7074 m S U u 200.3447 183.1 m S 200.3447 168.1716 m S 185.1378 168.1716 m S 185.1378 183.1 m S 192.7412 175.6358 m S U u 215.5515 183.1 m S 215.5515 168.1716 m S 200.3447 168.1716 m S 200.3447 183.1 m S 207.9481 175.6358 m S U u 215.5515 168.1716 m S 215.5515 153.2431 m S 200.3447 153.2431 m S 200.3447 168.1716 m S 207.9481 160.7074 m S U u 200.3447 153.2431 m S 200.3447 138.3147 m S 185.1378 138.3147 m S 185.1378 153.2431 m S 192.7412 145.7789 m S U u 185.1378 153.2431 m S 185.1378 138.3147 m S 169.9309 138.3147 m S 169.9309 153.2431 m S 177.5343 145.7789 m S U u 185.1378 168.1716 m S 185.1378 153.2431 m S 169.9309 153.2431 m S 169.9309 168.1716 m S 177.5343 160.7074 m S U 0 g 1 w 4 M 177.5343 175.6358 m F 207.9481 175.6358 m F 177.5343 145.7789 m F 207.9481 145.7789 m F u 0 G 0.3 w 10 M 230.7584 183.1 m S 230.7584 168.1716 m S 215.5515 168.1716 m S 215.5515 183.1 m S 223.1549 175.6358 m S U u 261.1721 153.2431 m S 261.1721 138.3147 m S 245.9653 138.3147 m S 245.9653 153.2431 m S 253.5687 145.7789 m S U u 245.9653 168.1716 m S 245.9653 153.2431 m S 230.7584 153.2431 m S 230.7584 168.1716 m S 238.3618 160.7074 m S U u 245.9653 183.1 m S 245.9653 168.1716 m S 230.7584 168.1716 m S 230.7584 183.1 m S 238.3618 175.6358 m S U u 261.1721 183.1 m S 261.1721 168.1716 m S 245.9653 168.1716 m S 245.9653 183.1 m S 253.5687 175.6358 m S U u 261.1721 168.1716 m S 261.1721 153.2431 m S 245.9653 153.2431 m S 245.9653 168.1716 m S 253.5687 160.7074 m S U u 245.9653 153.2431 m S 245.9653 138.3147 m S 230.7584 138.3147 m S 230.7584 153.2431 m S 238.3618 145.7789 m S U u 230.7584 153.2431 m S 230.7584 138.3147 m S 215.5515 138.3147 m S 215.5515 153.2431 m S 223.1549 145.7789 m S U u 230.7584 168.1716 m S 230.7584 153.2431 m S 215.5515 153.2431 m S 215.5515 168.1716 m S 223.1549 160.7074 m S U 0 g 1 w 4 M 223.1549 175.6358 m F 253.5687 175.6358 m F 223.1549 145.7789 m F 253.5687 145.7789 m F 0 G 0.3 w 10 M 261.1721 168.1716 m S 261.1721 183.1 m S 261.1721 138.3147 m S 261.1721 153.2431 m S 261.1721 153.2431 m S 261.1721 168.1716 m S u 139.5171 138.3147 m S 139.5171 123.3863 m S 124.3103 123.3863 m S 124.3103 138.3147 m S 131.9137 130.8505 m S U u 169.9309 108.4579 m S 169.9309 93.5295 m S 154.724 93.5295 m S 154.724 108.4579 m S 162.3274 100.9937 m S U u 154.724 123.3863 m S 154.724 108.4579 m S 139.5171 108.4579 m S 139.5171 123.3863 m S 147.1206 115.9221 m S U u 154.724 138.3147 m S 154.724 123.3863 m S 139.5171 123.3863 m S 139.5171 138.3147 m S 147.1206 130.8505 m S U u 169.9309 138.3147 m S 169.9309 123.3863 m S 154.724 123.3863 m S 154.724 138.3147 m S 162.3274 130.8505 m S U u 169.9309 123.3863 m S 169.9309 108.4579 m S 154.724 108.4579 m S 154.724 123.3863 m S 162.3274 115.9221 m S U u 154.724 108.4579 m S 154.724 93.5295 m S 139.5171 93.5295 m S 139.5171 108.4579 m S 147.1206 100.9937 m S U u 139.5171 108.4579 m S 139.5171 93.5295 m S 124.3103 93.5295 m S 124.3103 108.4579 m S 131.9137 100.9937 m S U u 139.5171 123.3863 m S 139.5171 108.4579 m S 124.3103 108.4579 m S 124.3103 123.3863 m S 131.9137 115.9221 m S U 0 g 1 w 4 M 131.9137 130.8505 m F 162.3274 130.8505 m F 131.9137 100.9937 m F 162.3274 100.9937 m F u 0 G 0.3 w 10 M 185.1378 138.3147 m S 185.1378 123.3863 m S 169.9309 123.3863 m S 169.9309 138.3147 m S 177.5343 130.8505 m S U u 215.5515 108.4579 m S 215.5515 93.5295 m S 200.3447 93.5295 m S 200.3447 108.4579 m S 207.9481 100.9937 m S U u 200.3447 123.3863 m S 200.3447 108.4579 m S 185.1378 108.4579 m S 185.1378 123.3863 m S 192.7412 115.9221 m S U u 200.3447 138.3147 m S 200.3447 123.3863 m S 185.1378 123.3863 m S 185.1378 138.3147 m S 192.7412 130.8505 m S U u 215.5515 138.3147 m S 215.5515 123.3863 m S 200.3447 123.3863 m S 200.3447 138.3147 m S 207.9481 130.8505 m S U u 215.5515 123.3863 m S 215.5515 108.4579 m S 200.3447 108.4579 m S 200.3447 123.3863 m S 207.9481 115.9221 m S U u 200.3447 108.4579 m S 200.3447 93.5295 m S 185.1378 93.5295 m S 185.1378 108.4579 m S 192.7412 100.9937 m S U u 185.1378 108.4579 m S 185.1378 93.5295 m S 169.9309 93.5295 m S 169.9309 108.4579 m S 177.5343 100.9937 m S U u 185.1378 123.3863 m S 185.1378 108.4579 m S 169.9309 108.4579 m S 169.9309 123.3863 m S 177.5343 115.9221 m S U 0 g 1 w 4 M 177.5343 130.8505 m F 207.9481 130.8505 m F 177.5343 100.9937 m F 207.9481 100.9937 m F u 0 G 0.3 w 10 M 230.7584 138.3147 m S 230.7584 123.3863 m S 215.5515 123.3863 m S 215.5515 138.3147 m S 223.1549 130.8505 m S U u 261.1721 108.4579 m S 261.1721 93.5295 m S 245.9653 93.5295 m S 245.9653 108.4579 m S 253.5687 100.9937 m S U u 245.9653 123.3863 m S 245.9653 108.4579 m S 230.7584 108.4579 m S 230.7584 123.3863 m S 238.3618 115.9221 m S U u 245.9653 138.3147 m S 245.9653 123.3863 m S 230.7584 123.3863 m S 230.7584 138.3147 m S 238.3618 130.8505 m S U u 261.1721 138.3147 m S 261.1721 123.3863 m S 245.9653 123.3863 m S 245.9653 138.3147 m S 253.5687 130.8505 m S U u 261.1721 123.3863 m S 261.1721 108.4579 m S 245.9653 108.4579 m S 245.9653 123.3863 m S 253.5687 115.9221 m S U u 245.9653 108.4579 m S 245.9653 93.5295 m S 230.7584 93.5295 m S 230.7584 108.4579 m S 238.3618 100.9937 m S U u 230.7584 108.4579 m S 230.7584 93.5295 m S 215.5515 93.5295 m S 215.5515 108.4579 m S 223.1549 100.9937 m S U u 230.7584 123.3863 m S 230.7584 108.4579 m S 215.5515 108.4579 m S 215.5515 123.3863 m S 223.1549 115.9221 m S U 0 g 1 w 4 M 223.1549 130.8505 m F 253.5687 130.8505 m F 223.1549 100.9937 m F 253.5687 100.9937 m F 0 G 0.3 w 10 M 261.1721 123.3863 m S 261.1721 138.3147 m S 261.1721 93.5295 m S 261.1721 108.4579 m S 261.1721 108.4579 m S 261.1721 123.3863 m S 0 g 1 w 4 M 131.9137 86.0653 m F 162.3274 86.0653 m F 177.5343 86.0653 m F 207.9481 86.0653 m F 223.1549 86.0653 m F 253.5687 86.0653 m F u 0 G 0.3 w 10 M 139.5171 93.5295 m S 139.5171 78.601 m S 124.3103 78.601 m S 124.3103 93.5295 m S 131.9137 86.0653 m S U 169.9309 63.6726 m S 169.9309 48.7442 m S 154.724 48.7442 m S 154.724 63.6726 m S 162.3274 56.2084 m S u 154.724 78.601 m S 154.724 63.6726 m S 139.5171 63.6726 m S 139.5171 78.601 m S 147.1206 71.1368 m S U u 154.724 93.5295 m S 154.724 78.601 m S 139.5171 78.601 m S 139.5171 93.5295 m S 147.1206 86.0653 m S U u 169.9309 93.5295 m S 169.9309 78.601 m S 154.724 78.601 m S 154.724 93.5295 m S 162.3274 86.0653 m S U u 169.9309 78.601 m S 169.9309 63.6726 m S 154.724 63.6726 m S 154.724 78.601 m S 162.3274 71.1368 m S U 154.724 63.6726 m S 154.724 48.7442 m S 139.5171 48.7442 m S 139.5171 63.6726 m S 147.1206 56.2084 m S 139.5171 63.6726 m S 139.5171 48.7442 m S 124.3103 48.7442 m S 124.3103 63.6726 m S 131.9137 56.2084 m S u 139.5171 78.601 m S 139.5171 63.6726 m S 124.3103 63.6726 m S 124.3103 78.601 m S 131.9137 71.1368 m S U 0 g 1 w 4 M 131.9137 86.0653 m F 162.3274 86.0653 m F 131.9137 56.2084 m F 162.3274 56.2084 m F u 0 G 0.3 w 10 M 185.1378 93.5295 m S 185.1378 78.601 m S 169.9309 78.601 m S 169.9309 93.5295 m S 177.5343 86.0653 m S U u 215.5515 63.6726 m S 215.5515 48.7442 m S 200.3447 48.7442 m S 200.3447 63.6726 m S 207.9481 56.2084 m S U u 200.3447 78.601 m S 200.3447 63.6726 m S 185.1378 63.6726 m S 185.1378 78.601 m S 192.7412 71.1368 m S U u 200.3447 93.5295 m S 200.3447 78.601 m S 185.1378 78.601 m S 185.1378 93.5295 m S 192.7412 86.0653 m S U u 215.5515 93.5295 m S 215.5515 78.601 m S 200.3447 78.601 m S 200.3447 93.5295 m S 207.9481 86.0653 m S U u 215.5515 78.601 m S 215.5515 63.6726 m S 200.3447 63.6726 m S 200.3447 78.601 m S 207.9481 71.1368 m S U u 200.3447 63.6726 m S 200.3447 48.7442 m S 185.1378 48.7442 m S 185.1378 63.6726 m S 192.7412 56.2084 m S U u 185.1378 63.6726 m S 185.1378 48.7442 m S 169.9309 48.7442 m S 169.9309 63.6726 m S 177.5343 56.2084 m S U u 185.1378 78.601 m S 185.1378 63.6726 m S 169.9309 63.6726 m S 169.9309 78.601 m S 177.5343 71.1368 m S U 0 g 1 w 4 M 177.5343 86.0653 m F 207.9481 86.0653 m F 177.5343 56.2084 m F 207.9481 56.2084 m F u 0 G 0.3 w 10 M 230.7584 93.5295 m S 230.7584 78.601 m S 215.5515 78.601 m S 215.5515 93.5295 m S 223.1549 86.0653 m S U u 261.1721 63.6726 m S 261.1721 48.7442 m S 245.9653 48.7442 m S 245.9653 63.6726 m S 253.5687 56.2084 m S U u 245.9653 78.601 m S 245.9653 63.6726 m S 230.7584 63.6726 m S 230.7584 78.601 m S 238.3618 71.1368 m S U u 245.9653 93.5295 m S 245.9653 78.601 m S 230.7584 78.601 m S 230.7584 93.5295 m S 238.3618 86.0653 m S U u 261.1721 93.5295 m S 261.1721 78.601 m S 245.9653 78.601 m S 245.9653 93.5295 m S 253.5687 86.0653 m S U u 261.1721 78.601 m S 261.1721 63.6726 m S 245.9653 63.6726 m S 245.9653 78.601 m S 253.5687 71.1368 m S U u 245.9653 63.6726 m S 245.9653 48.7442 m S 230.7584 48.7442 m S 230.7584 63.6726 m S 238.3618 56.2084 m S U u 230.7584 63.6726 m S 230.7584 48.7442 m S 215.5515 48.7442 m S 215.5515 63.6726 m S 223.1549 56.2084 m S U u 230.7584 78.601 m S 230.7584 63.6726 m S 215.5515 63.6726 m S 215.5515 78.601 m S 223.1549 71.1368 m S U 0 g 1 w 4 M 223.1549 86.0653 m F 253.5687 86.0653 m F 223.1549 56.2084 m F 253.5687 56.2084 m F 0 G 0.3 w 10 M 261.1721 78.601 m S 261.1721 93.5295 m S 261.1721 48.7442 m S 261.1721 63.6726 m S 261.1721 63.6726 m S 261.1721 78.601 m S 139.5171 48.7442 m S 124.3103 48.7442 m S 154.724 48.7442 m S 139.5171 48.7442 m S 169.9309 48.7442 m S 154.724 48.7442 m S 185.1378 48.7442 m S 169.9309 48.7442 m S 200.3447 48.7442 m S 185.1378 48.7442 m S 215.5515 48.7442 m S 200.3447 48.7442 m S 230.7584 48.7442 m S 215.5515 48.7442 m S 245.9653 48.7442 m S 230.7584 48.7442 m S 261.1721 48.7442 m S 245.9653 48.7442 m S 261.1721 48.7442 m S 1 w 4 M 131.9137 160.7074 m 253.5687 160.7074 l S 131.9137 115.9221 m 253.5687 115.9221 l S 131.9137 71.1368 m 253.5687 71.1368 l S 147.1206 175.6358 m 147.1206 56.2084 l S 192.7412 175.6358 m 192.7412 56.2084 l S 238.3618 175.6358 m 238.3618 56.2084 l S u u 0 g /_Times-Roman 12 14.5 0 0 z [1 0 0 1 141.5 34.5]e (\(a\))t T U U 0 G 0.3 w 10 M 78.6897 227.8852 m S 71.0862 235.3495 m S 0 g 1 w 4 M 71.0862 235.3495 m F 0 G 0.3 w 10 M 78.6897 227.8852 m S 86.2931 235.3495 m S 0 g 1 w 4 M 86.2931 235.3495 m F 0 G 0.3 w 10 M 78.6897 227.8852 m S 71.0862 220.421 m S 0 g 1 w 4 M 71.0862 220.421 m F 0 G 0.3 w 10 M 78.6897 227.8852 m S 86.2931 220.421 m S 0 g 1 w 4 M 86.2931 220.421 m F 0 G 0.3 w 10 M 78.6897 227.8852 m S 0 g 1 w 4 M 78.6897 227.8852 m F 0 G 0.3 w 10 M 78.6897 227.8852 m S 78.6897 227.8852 m S 78.6897 227.8852 m S 0 g 1 w 4 M 78.6897 227.8852 m F 0 G 0.3 w 10 M 78.6897 227.8852 m S 78.6897 227.8852 m S u 1 g 1 w 4 M 67.9369 227.8852 m 67.9369 221.8732 72.7512 216.9994 78.6897 216.9994 c 84.6282 216.9994 89.4425 221.8732 89.4425 227.8852 c F 89.4425 227.8852 m 89.4425 233.8973 84.6282 238.7711 78.6897 238.7711 c 72.7512 238.7711 67.9369 233.8973 67.9369 227.8852 c F 78.6897 227.8852 m F U 0 G 0.3 w 10 M 78.6897 227.8852 m S 0 g 1 w 4 M 78.6897 227.8852 m F 0 G 0.3 w 10 M 78.6897 227.8852 m S 78.6897 227.8852 m S 0 g 1 w 4 M 76.7484 225.8925 m 76.7484 219.2174 L 80.6309 219.2174 L 80.6309 225.8925 L 87.0457 225.8716 L 87.0457 229.8993 L 80.6309 229.8786 L 80.6309 236.5536 L 76.7484 236.5536 L 76.7484 229.8786 L 70.3336 229.8993 L 70.3336 225.8716 L 76.7484 225.8925 L f 0 G 0.3 w 10 M 124.3103 227.8852 m S 116.7068 235.3495 m S 0 g 1 w 4 M 116.7068 235.3495 m F 0 G 0.3 w 10 M 124.3103 227.8852 m S 131.9137 235.3495 m S 0 g 1 w 4 M 131.9137 235.3495 m F 0 G 0.3 w 10 M 124.3103 227.8852 m S 116.7068 220.421 m S 0 g 1 w 4 M 116.7068 220.421 m F 0 G 0.3 w 10 M 124.3103 227.8852 m S 131.9137 220.421 m S 0 g 1 w 4 M 131.9137 220.421 m F 0 G 0.3 w 10 M 124.3103 227.8852 m S 0 g 1 w 4 M 124.3103 227.8852 m F 0 G 0.3 w 10 M 124.3103 227.8852 m S 124.3103 227.8852 m S 124.3103 227.8852 m S 0 g 1 w 4 M 124.3103 227.8852 m F 0 G 0.3 w 10 M 124.3103 227.8852 m S 124.3103 227.8852 m S u 1 g 1 w 4 M 113.5575 227.8852 m 113.5575 221.8732 118.3718 216.9994 124.3103 216.9994 c 130.2488 216.9994 135.0631 221.8732 135.0631 227.8852 c F 135.0631 227.8852 m 135.0631 233.8973 130.2488 238.7711 124.3103 238.7711 c 118.3718 238.7711 113.5575 233.8973 113.5575 227.8852 c F 124.3103 227.8852 m F U 0 G 0.3 w 10 M 124.3103 227.8852 m S 0 g 1 w 4 M 124.3103 227.8852 m F 0 G 0.3 w 10 M 124.3103 227.8852 m S 124.3103 227.8852 m S 0 g 1 w 4 M 122.369 225.8925 m 122.369 219.2174 L 126.2516 219.2174 L 126.2516 225.8925 L 132.6663 225.8716 L 132.6663 229.8993 L 126.2516 229.8786 L 126.2516 236.5536 L 122.369 236.5536 L 122.369 229.8786 L 115.9542 229.8993 L 115.9542 225.8716 L 122.369 225.8925 L f 0 G 0.3 w 10 M 78.6897 183.1 m S 71.0862 190.5642 m S 0 g 1 w 4 M 71.0862 190.5642 m F 0 G 0.3 w 10 M 78.6897 183.1 m S 86.2931 190.5642 m S 0 g 1 w 4 M 86.2931 190.5642 m F 0 G 0.3 w 10 M 78.6897 183.1 m S 71.0862 175.6358 m S 0 g 1 w 4 M 71.0862 175.6358 m F 0 G 0.3 w 10 M 78.6897 183.1 m S 86.2931 175.6358 m S 0 g 1 w 4 M 86.2931 175.6358 m F 0 G 0.3 w 10 M 78.6897 183.1 m S 0 g 1 w 4 M 78.6897 183.1 m F 0 G 0.3 w 10 M 78.6897 183.1 m S 78.6897 183.1 m S 78.6897 183.1 m S 0 g 1 w 4 M 78.6897 183.1 m F 0 G 0.3 w 10 M 78.6897 183.1 m S 78.6897 183.1 m S u 1 g 1 w 4 M 67.9369 183.1 m 67.9369 177.0879 72.7512 172.2141 78.6897 172.2141 c 84.6282 172.2141 89.4425 177.0879 89.4425 183.1 c F 89.4425 183.1 m 89.4425 189.1121 84.6282 193.9858 78.6897 193.9858 c 72.7512 193.9858 67.9369 189.1121 67.9369 183.1 c F 78.6897 183.1 m F U 0 G 0.3 w 10 M 78.6897 183.1 m S 0 g 1 w 4 M 78.6897 183.1 m F 0 G 0.3 w 10 M 78.6897 183.1 m S 78.6897 183.1 m S 0 g 1 w 4 M 76.7484 181.1072 m 76.7484 174.4321 L 80.6309 174.4321 L 80.6309 181.1072 L 87.0457 181.0863 L 87.0457 185.114 L 80.6309 185.0933 L 80.6309 191.7684 L 76.7484 191.7684 L 76.7484 185.0933 L 70.3336 185.114 L 70.3336 181.0863 L 76.7484 181.1072 L f 0 G 0.3 w 10 M 124.3103 183.1 m S 116.7068 190.5642 m S 0 g 1 w 4 M 116.7068 190.5642 m F 0 G 0.3 w 10 M 124.3103 183.1 m S 131.9137 190.5642 m S 0 g 1 w 4 M 131.9137 190.5642 m F 0 G 0.3 w 10 M 124.3103 183.1 m S 116.7068 175.6358 m S 0 g 1 w 4 M 116.7068 175.6358 m F 0 G 0.3 w 10 M 124.3103 183.1 m S 131.9137 175.6358 m S 0 g 1 w 4 M 131.9137 175.6358 m F 0 G 0.3 w 10 M 124.3103 183.1 m S 0 g 1 w 4 M 124.3103 183.1 m F 0 G 0.3 w 10 M 124.3103 183.1 m S 124.3103 183.1 m S 124.3103 183.1 m S 0 g 1 w 4 M 124.3103 183.1 m F 0 G 0.3 w 10 M 124.3103 183.1 m S 124.3103 183.1 m S u 1 g 1 w 4 M 113.5575 183.1 m 113.5575 177.0879 118.3718 172.2141 124.3103 172.2141 c 130.2488 172.2141 135.0631 177.0879 135.0631 183.1 c F 135.0631 183.1 m 135.0631 189.1121 130.2488 193.9858 124.3103 193.9858 c 118.3718 193.9858 113.5575 189.1121 113.5575 183.1 c F 124.3103 183.1 m F U 0 G 0.3 w 10 M 124.3103 183.1 m S 0 g 1 w 4 M 124.3103 183.1 m F 0 G 0.3 w 10 M 124.3103 183.1 m S 124.3103 183.1 m S 0 g 1 w 4 M 122.369 181.1072 m 122.369 174.4321 L 126.2516 174.4321 L 126.2516 181.1072 L 132.6663 181.0863 L 132.6663 185.114 L 126.2516 185.0933 L 126.2516 191.7684 L 122.369 191.7684 L 122.369 185.0933 L 115.9542 185.114 L 115.9542 181.0863 L 122.369 181.1072 L f 0 G 0.3 w 10 M 169.9309 138.3147 m S 162.3274 145.7789 m S 0 g 1 w 4 M 162.3274 145.7789 m F 0 G 0.3 w 10 M 169.9309 138.3147 m S 177.5343 145.7789 m S 0 g 1 w 4 M 177.5343 145.7789 m F 0 G 0.3 w 10 M 169.9309 138.3147 m S 162.3274 130.8505 m S 0 g 1 w 4 M 162.3274 130.8505 m F 0 G 0.3 w 10 M 169.9309 138.3147 m S 177.5343 130.8505 m S 0 g 1 w 4 M 177.5343 130.8505 m F 0 G 0.3 w 10 M 169.9309 138.3147 m S 0 g 1 w 4 M 169.9309 138.3147 m F 0 G 0.3 w 10 M 169.9309 138.3147 m S 169.9309 138.3147 m S 169.9309 138.3147 m S 0 g 1 w 4 M 169.9309 138.3147 m F 0 G 0.3 w 10 M 169.9309 138.3147 m S 169.9309 138.3147 m S u 1 g 1 w 4 M 159.1781 138.3147 m 159.1781 132.3027 163.9924 127.4289 169.9309 127.4289 c 175.8694 127.4289 180.6837 132.3027 180.6837 138.3147 c F 180.6837 138.3147 m 180.6837 144.3268 175.8694 149.2006 169.9309 149.2006 c 163.9924 149.2006 159.1781 144.3268 159.1781 138.3147 c F 169.9309 138.3147 m F U 0 G 0.3 w 10 M 169.9309 138.3147 m S 0 g 1 w 4 M 169.9309 138.3147 m F 0 G 0.3 w 10 M 169.9309 138.3147 m S 169.9309 138.3147 m S 0 g 1 w 4 M 167.9896 136.322 m 167.9896 129.6469 L 171.8722 129.6469 L 171.8722 136.322 L 178.2869 136.3011 L 178.2869 140.3288 L 171.8722 140.3081 L 171.8722 146.9831 L 167.9896 146.9831 L 167.9896 140.3081 L 161.5749 140.3288 L 161.5749 136.3011 L 167.9896 136.322 L f 0 G 0.3 w 10 M 215.5515 138.3147 m S 207.9481 145.7789 m S 0 g 1 w 4 M 207.9481 145.7789 m F 0 G 0.3 w 10 M 215.5515 138.3147 m S 223.1549 145.7789 m S 0 g 1 w 4 M 223.1549 145.7789 m F 0 G 0.3 w 10 M 215.5515 138.3147 m S 207.9481 130.8505 m S 0 g 1 w 4 M 207.9481 130.8505 m F 0 G 0.3 w 10 M 215.5515 138.3147 m S 223.1549 130.8505 m S 0 g 1 w 4 M 223.1549 130.8505 m F 0 G 0.3 w 10 M 215.5515 138.3147 m S 0 g 1 w 4 M 215.5515 138.3147 m F 0 G 0.3 w 10 M 215.5515 138.3147 m S 215.5515 138.3147 m S 215.5515 138.3147 m S 0 g 1 w 4 M 215.5515 138.3147 m F 0 G 0.3 w 10 M 215.5515 138.3147 m S 215.5515 138.3147 m S u 1 g 1 w 4 M 204.7987 138.3147 m 204.7987 132.3027 209.613 127.4289 215.5515 127.4289 c 221.49 127.4289 226.3043 132.3027 226.3043 138.3147 c F 226.3043 138.3147 m 226.3043 144.3268 221.49 149.2006 215.5515 149.2006 c 209.613 149.2006 204.7987 144.3268 204.7987 138.3147 c F 215.5515 138.3147 m F U 0 G 0.3 w 10 M 215.5515 138.3147 m S 0 g 1 w 4 M 215.5515 138.3147 m F 0 G 0.3 w 10 M 215.5515 138.3147 m S 215.5515 138.3147 m S 0 g 1 w 4 M 213.6103 136.322 m 213.6103 129.6469 L 217.4928 129.6469 L 217.4928 136.322 L 223.9076 136.3011 L 223.9076 140.3288 L 217.4928 140.3081 L 217.4928 146.9831 L 213.6103 146.9831 L 213.6103 140.3081 L 207.1955 140.3288 L 207.1955 136.3011 L 213.6103 136.322 L f 0 G 0.3 w 10 M 215.5515 93.5295 m S 207.9481 100.9937 m S 0 g 1 w 4 M 207.9481 100.9937 m F 0 G 0.3 w 10 M 215.5515 93.5295 m S 223.1549 100.9937 m S 0 g 1 w 4 M 223.1549 100.9937 m F 0 G 0.3 w 10 M 215.5515 93.5295 m S 207.9481 86.0653 m S 0 g 1 w 4 M 207.9481 86.0653 m F 0 G 0.3 w 10 M 215.5515 93.5295 m S 223.1549 86.0653 m S 0 g 1 w 4 M 223.1549 86.0653 m F 0 G 0.3 w 10 M 215.5515 93.5295 m S 0 g 1 w 4 M 215.5515 93.5295 m F 0 G 0.3 w 10 M 215.5515 93.5295 m S 215.5515 93.5295 m S 215.5515 93.5295 m S 0 g 1 w 4 M 215.5515 93.5295 m F 0 G 0.3 w 10 M 215.5515 93.5295 m S 215.5515 93.5295 m S u 1 g 1 w 4 M 204.7987 93.5295 m 204.7987 87.5174 209.613 82.6436 215.5515 82.6436 c 221.49 82.6436 226.3043 87.5174 226.3043 93.5295 c F 226.3043 93.5295 m 226.3043 99.5416 221.49 104.4153 215.5515 104.4153 c 209.613 104.4153 204.7987 99.5416 204.7987 93.5295 c F 215.5515 93.5295 m F U 0 G 0.3 w 10 M 215.5515 93.5295 m S 0 g 1 w 4 M 215.5515 93.5295 m F 0 G 0.3 w 10 M 215.5515 93.5295 m S 215.5515 93.5295 m S 0 g 1 w 4 M 213.6103 91.5367 m 213.6103 84.8616 L 217.4928 84.8616 L 217.4928 91.5367 L 223.9076 91.5158 L 223.9076 95.5435 L 217.4928 95.5228 L 217.4928 102.1979 L 213.6103 102.1979 L 213.6103 95.5228 L 207.1955 95.5435 L 207.1955 91.5158 L 213.6103 91.5367 L f 0 G 0.3 w 10 M 169.9309 93.5295 m S 162.3274 100.9937 m S 0 g 1 w 4 M 162.3274 100.9937 m F 0 G 0.3 w 10 M 169.9309 93.5295 m S 177.5343 100.9937 m S 0 g 1 w 4 M 177.5343 100.9937 m F 0 G 0.3 w 10 M 169.9309 93.5295 m S 162.3274 86.0653 m S 0 g 1 w 4 M 162.3274 86.0653 m F 0 G 0.3 w 10 M 169.9309 93.5295 m S 177.5343 86.0653 m S 0 g 1 w 4 M 177.5343 86.0653 m F 0 G 0.3 w 10 M 169.9309 93.5295 m S 0 g 1 w 4 M 169.9309 93.5295 m F 0 G 0.3 w 10 M 169.9309 93.5295 m S 169.9309 93.5295 m S 169.9309 93.5295 m S 0 g 1 w 4 M 169.9309 93.5295 m F 0 G 0.3 w 10 M 169.9309 93.5295 m S 169.9309 93.5295 m S u 1 g 1 w 4 M 159.1781 93.5295 m 159.1781 87.5174 163.9924 82.6436 169.9309 82.6436 c 175.8694 82.6436 180.6837 87.5174 180.6837 93.5295 c F 180.6837 93.5295 m 180.6837 99.5416 175.8694 104.4153 169.9309 104.4153 c 163.9924 104.4153 159.1781 99.5416 159.1781 93.5295 c F 169.9309 93.5295 m F U 0 G 0.3 w 10 M 169.9309 93.5295 m S 0 g 1 w 4 M 169.9309 93.5295 m F 0 G 0.3 w 10 M 169.9309 93.5295 m S 169.9309 93.5295 m S 0 g 1 w 4 M 167.9896 91.5367 m 167.9896 84.8616 L 171.8722 84.8616 L 171.8722 91.5367 L 178.2869 91.5158 L 178.2869 95.5435 L 171.8722 95.5228 L 171.8722 102.1979 L 167.9896 102.1979 L 167.9896 95.5228 L 161.5749 95.5435 L 161.5749 91.5158 L 167.9896 91.5367 L f 0 G 0.3 w 10 M 169.9309 227.8852 m S 162.3274 235.3495 m S 0 g 1 w 4 M 162.3274 235.3495 m F 0 G 0.3 w 10 M 169.9309 227.8852 m S 169.9309 227.8852 m S 162.3274 220.421 m S 0 g 1 w 4 M 162.3274 220.421 m F 0 G 0.3 w 10 M 169.9309 227.8852 m S 169.9309 227.8852 m S 162.3274 235.3495 m S 0 g 1 w 4 M 162.3274 235.3495 m F 0 G 0.3 w 10 M 169.9309 227.8852 m S 177.5343 235.3495 m S 0 g 1 w 4 M 177.5343 235.3495 m F 0 G 0.3 w 10 M 169.9309 227.8852 m S 162.3274 220.421 m S 0 g 1 w 4 M 162.3274 220.421 m F 0 G 0.3 w 10 M 169.9309 227.8852 m S 177.5343 220.421 m S 0 g 1 w 4 M 177.5343 220.421 m F 0 G 0.3 w 10 M 169.9309 227.8852 m S 0 g 1 w 4 M 169.9309 227.8852 m F 0 G 0.3 w 10 M 169.9309 227.8852 m S 0 g 1 w 4 M 169.9309 227.8852 m F u 1 g 159.1781 227.8852 m 159.1781 222.2268 163.9924 217.6397 169.9309 217.6397 c 175.8694 217.6397 180.6837 222.2268 180.6837 227.8852 c F 180.6837 227.8852 m 180.6837 233.5437 175.8694 238.1308 169.9309 238.1308 c 163.9924 238.1308 159.1781 233.5437 159.1781 227.8852 c F 169.9309 227.8852 m F U 0 G 0.3 w 10 M 169.9309 227.8852 m S 0 g 1 w 4 M 169.9309 227.8852 m F 0 G 0.3 w 10 M 169.9309 227.8852 m S 0 g 1 w 4 M 169.9309 227.8852 m F 167.9896 229.7613 m 161.5749 229.7808 L 161.5749 225.99 L 167.9896 226.0095 L F 171.8722 226.0095 m 178.2869 225.99 L 178.2869 229.7808 L 171.8722 229.7613 L F 161.5749 229.7808 m 178.2869 229.7808 l 178.2869 225.99 l 161.5749 225.99 l 161.5749 229.7808 l f 0 G 0.3 w 10 M 215.5515 227.8852 m S 207.9481 235.3495 m S 0 g 1 w 4 M 207.9481 235.3495 m F 0 G 0.3 w 10 M 215.5515 227.8852 m S 215.5515 227.8852 m S 207.9481 220.421 m S 0 g 1 w 4 M 207.9481 220.421 m F 0 G 0.3 w 10 M 215.5515 227.8852 m S 215.5515 227.8852 m S 207.9481 235.3495 m S 0 g 1 w 4 M 207.9481 235.3495 m F 0 G 0.3 w 10 M 215.5515 227.8852 m S 223.1549 235.3495 m S 0 g 1 w 4 M 223.1549 235.3495 m F 0 G 0.3 w 10 M 215.5515 227.8852 m S 207.9481 220.421 m S 0 g 1 w 4 M 207.9481 220.421 m F 0 G 0.3 w 10 M 215.5515 227.8852 m S 223.1549 220.421 m S 0 g 1 w 4 M 223.1549 220.421 m F 0 G 0.3 w 10 M 215.5515 227.8852 m S 0 g 1 w 4 M 215.5515 227.8852 m F 0 G 0.3 w 10 M 215.5515 227.8852 m S 0 g 1 w 4 M 215.5515 227.8852 m F u 1 g 204.7987 227.8852 m 204.7987 222.2268 209.613 217.6397 215.5515 217.6397 c 221.49 217.6397 226.3043 222.2268 226.3043 227.8852 c F 226.3043 227.8852 m 226.3043 233.5437 221.49 238.1308 215.5515 238.1308 c 209.613 238.1308 204.7987 233.5437 204.7987 227.8852 c F 215.5515 227.8852 m F U 0 G 0.3 w 10 M 215.5515 227.8852 m S 0 g 1 w 4 M 215.5515 227.8852 m F 0 G 0.3 w 10 M 215.5515 227.8852 m S 0 g 1 w 4 M 215.5515 227.8852 m F 213.6102 229.7613 m 207.1955 229.7808 L 207.1955 225.99 L 213.6102 226.0095 L F 217.4928 226.0095 m 223.9075 225.99 L 223.9075 229.7808 L 217.4928 229.7613 L F 207.1955 229.7808 m 223.9075 229.7808 l 223.9075 225.99 l 207.1955 225.99 l 207.1955 229.7808 l f 0 G 0.3 w 10 M 169.9309 183.1 m S 162.3274 190.5642 m S 0 g 1 w 4 M 162.3274 190.5642 m F 0 G 0.3 w 10 M 169.9309 183.1 m S 169.9309 183.1 m S 162.3274 175.6358 m S 0 g 1 w 4 M 162.3274 175.6358 m F 0 G 0.3 w 10 M 169.9309 183.1 m S 169.9309 183.1 m S 162.3274 190.5642 m S 0 g 1 w 4 M 162.3274 190.5642 m F 0 G 0.3 w 10 M 169.9309 183.1 m S 177.5343 190.5642 m S 0 g 1 w 4 M 177.5343 190.5642 m F 0 G 0.3 w 10 M 169.9309 183.1 m S 162.3274 175.6358 m S 0 g 1 w 4 M 162.3274 175.6358 m F 0 G 0.3 w 10 M 169.9309 183.1 m S 177.5343 175.6358 m S 0 g 1 w 4 M 177.5343 175.6358 m F 0 G 0.3 w 10 M 169.9309 183.1 m S 0 g 1 w 4 M 169.9309 183.1 m F 0 G 0.3 w 10 M 169.9309 183.1 m S 0 g 1 w 4 M 169.9309 183.1 m F u 1 g 159.1781 183.1 m 159.1781 177.4415 163.9924 172.8544 169.9309 172.8544 c 175.8694 172.8544 180.6837 177.4415 180.6837 183.1 c F 180.6837 183.1 m 180.6837 188.7584 175.8694 193.3456 169.9309 193.3456 c 163.9924 193.3456 159.1781 188.7584 159.1781 183.1 c F 169.9309 183.1 m F U 0 G 0.3 w 10 M 169.9309 183.1 m S 0 g 1 w 4 M 169.9309 183.1 m F 0 G 0.3 w 10 M 169.9309 183.1 m S 0 g 1 w 4 M 169.9309 183.1 m F 167.9896 184.9761 m 161.5749 184.9956 L 161.5749 181.2048 L 167.9896 181.2243 L F 171.8722 181.2243 m 178.2869 181.2048 L 178.2869 184.9956 L 171.8722 184.9761 L F 161.5749 184.9956 m 178.2869 184.9956 l 178.2869 181.2048 l 161.5749 181.2048 l 161.5749 184.9956 l f 0 G 0.3 w 10 M 215.5515 183.1 m S 207.9481 190.5642 m S 0 g 1 w 4 M 207.9481 190.5642 m F 0 G 0.3 w 10 M 215.5515 183.1 m S 215.5515 183.1 m S 207.9481 175.6358 m S 0 g 1 w 4 M 207.9481 175.6358 m F 0 G 0.3 w 10 M 215.5515 183.1 m S 215.5515 183.1 m S 207.9481 190.5642 m S 0 g 1 w 4 M 207.9481 190.5642 m F 0 G 0.3 w 10 M 215.5515 183.1 m S 223.1549 190.5642 m S 0 g 1 w 4 M 223.1549 190.5642 m F 0 G 0.3 w 10 M 215.5515 183.1 m S 207.9481 175.6358 m S 0 g 1 w 4 M 207.9481 175.6358 m F 0 G 0.3 w 10 M 215.5515 183.1 m S 223.1549 175.6358 m S 0 g 1 w 4 M 223.1549 175.6358 m F 0 G 0.3 w 10 M 215.5515 183.1 m S 0 g 1 w 4 M 215.5515 183.1 m F 0 G 0.3 w 10 M 215.5515 183.1 m S 0 g 1 w 4 M 215.5515 183.1 m F u 1 g 204.7987 183.1 m 204.7987 177.4415 209.613 172.8544 215.5515 172.8544 c 221.49 172.8544 226.3043 177.4415 226.3043 183.1 c F 226.3043 183.1 m 226.3043 188.7584 221.49 193.3456 215.5515 193.3456 c 209.613 193.3456 204.7987 188.7584 204.7987 183.1 c F 215.5515 183.1 m F U 0 G 0.3 w 10 M 215.5515 183.1 m S 0 g 1 w 4 M 215.5515 183.1 m F 0 G 0.3 w 10 M 215.5515 183.1 m S 0 g 1 w 4 M 215.5515 183.1 m F 213.6102 184.9761 m 207.1955 184.9956 L 207.1955 181.2048 L 213.6102 181.2243 L F 217.4928 181.2243 m 223.9075 181.2048 L 223.9075 184.9956 L 217.4928 184.9761 L F 207.1955 184.9956 m 223.9075 184.9956 l 223.9075 181.2048 l 207.1955 181.2048 l 207.1955 184.9956 l f 0 G 0.3 w 10 M 78.6897 138.3147 m S 71.0862 145.7789 m S 0 g 1 w 4 M 71.0862 145.7789 m F 0 G 0.3 w 10 M 78.6897 138.3147 m S 78.6897 138.3147 m S 71.0862 130.8505 m S 0 g 1 w 4 M 71.0862 130.8505 m F 0 G 0.3 w 10 M 78.6897 138.3147 m S 78.6897 138.3147 m S 71.0862 145.7789 m S 0 g 1 w 4 M 71.0862 145.7789 m F 0 G 0.3 w 10 M 78.6897 138.3147 m S 86.2931 145.7789 m S 0 g 1 w 4 M 86.2931 145.7789 m F 0 G 0.3 w 10 M 78.6897 138.3147 m S 71.0862 130.8505 m S 0 g 1 w 4 M 71.0862 130.8505 m F 0 G 0.3 w 10 M 78.6897 138.3147 m S 86.2931 130.8505 m S 0 g 1 w 4 M 86.2931 130.8505 m F 0 G 0.3 w 10 M 78.6897 138.3147 m S 0 g 1 w 4 M 78.6897 138.3147 m F 0 G 0.3 w 10 M 78.6897 138.3147 m S 0 g 1 w 4 M 78.6897 138.3147 m F u 1 g 67.9369 138.3147 m 67.9369 132.6563 72.7512 128.0692 78.6897 128.0692 c 84.6282 128.0692 89.4425 132.6563 89.4425 138.3147 c F 89.4425 138.3147 m 89.4425 143.9732 84.6282 148.5603 78.6897 148.5603 c 72.7512 148.5603 67.9369 143.9732 67.9369 138.3147 c F 78.6897 138.3147 m F U 0 G 0.3 w 10 M 78.6897 138.3147 m S 0 g 1 w 4 M 78.6897 138.3147 m F 0 G 0.3 w 10 M 78.6897 138.3147 m S 0 g 1 w 4 M 78.6897 138.3147 m F 76.7484 140.1908 m 70.3336 140.2103 L 70.3336 136.4195 L 76.7484 136.439 L F 80.6309 136.439 m 87.0457 136.4195 L 87.0457 140.2103 L 80.6309 140.1908 L F 70.3336 140.2103 m 87.0457 140.2103 l 87.0457 136.4195 l 70.3336 136.4195 l 70.3336 140.2103 l f 0 G 0.3 w 10 M 124.3103 138.3147 m S 116.7068 145.7789 m S 0 g 1 w 4 M 116.7068 145.7789 m F 0 G 0.3 w 10 M 124.3103 138.3147 m S 124.3103 138.3147 m S 116.7068 130.8505 m S 0 g 1 w 4 M 116.7068 130.8505 m F 0 G 0.3 w 10 M 124.3103 138.3147 m S 124.3103 138.3147 m S 116.7068 145.7789 m S 0 g 1 w 4 M 116.7068 145.7789 m F 0 G 0.3 w 10 M 124.3103 138.3147 m S 131.9137 145.7789 m S 0 g 1 w 4 M 131.9137 145.7789 m F 0 G 0.3 w 10 M 124.3103 138.3147 m S 116.7068 130.8505 m S 0 g 1 w 4 M 116.7068 130.8505 m F 0 G 0.3 w 10 M 124.3103 138.3147 m S 131.9137 130.8505 m S 0 g 1 w 4 M 131.9137 130.8505 m F 0 G 0.3 w 10 M 124.3103 138.3147 m S 0 g 1 w 4 M 124.3103 138.3147 m F 0 G 0.3 w 10 M 124.3103 138.3147 m S 0 g 1 w 4 M 124.3103 138.3147 m F u 1 g 113.5575 138.3147 m 113.5575 132.6563 118.3718 128.0692 124.3103 128.0692 c 130.2488 128.0692 135.0631 132.6563 135.0631 138.3147 c F 135.0631 138.3147 m 135.0631 143.9732 130.2488 148.5603 124.3103 148.5603 c 118.3718 148.5603 113.5575 143.9732 113.5575 138.3147 c F 124.3103 138.3147 m F U 0 G 0.3 w 10 M 124.3103 138.3147 m S 0 g 1 w 4 M 124.3103 138.3147 m F 0 G 0.3 w 10 M 124.3103 138.3147 m S 0 g 1 w 4 M 124.3103 138.3147 m F 122.369 140.1908 m 115.9542 140.2103 L 115.9542 136.4195 L 122.369 136.439 L F 126.2516 136.439 m 132.6663 136.4195 L 132.6663 140.2103 L 126.2516 140.1908 L F 115.9542 140.2103 m 132.6663 140.2103 l 132.6663 136.4195 l 115.9542 136.4195 l 115.9542 140.2103 l f 0 G 0.3 w 10 M 78.6897 93.5295 m S 71.0862 100.9937 m S 0 g 1 w 4 M 71.0862 100.9937 m F 0 G 0.3 w 10 M 78.6897 93.5295 m S 78.6897 93.5295 m S 71.0862 86.0653 m S 0 g 1 w 4 M 71.0862 86.0653 m F 0 G 0.3 w 10 M 78.6897 93.5295 m S 78.6897 93.5295 m S 71.0862 100.9937 m S 0 g 1 w 4 M 71.0862 100.9937 m F 0 G 0.3 w 10 M 78.6897 93.5295 m S 86.2931 100.9937 m S 0 g 1 w 4 M 86.2931 100.9937 m F 0 G 0.3 w 10 M 78.6897 93.5295 m S 71.0862 86.0653 m S 0 g 1 w 4 M 71.0862 86.0653 m F 0 G 0.3 w 10 M 78.6897 93.5295 m S 86.2931 86.0653 m S 0 g 1 w 4 M 86.2931 86.0653 m F 0 G 0.3 w 10 M 78.6897 93.5295 m S 0 g 1 w 4 M 78.6897 93.5295 m F 0 G 0.3 w 10 M 78.6897 93.5295 m S 0 g 1 w 4 M 78.6897 93.5295 m F u 1 g 67.9369 93.5295 m 67.9369 87.871 72.7512 83.2839 78.6897 83.2839 c 84.6282 83.2839 89.4425 87.871 89.4425 93.5295 c F 89.4425 93.5295 m 89.4425 99.188 84.6282 103.7751 78.6897 103.7751 c 72.7512 103.7751 67.9369 99.188 67.9369 93.5295 c F 78.6897 93.5295 m F U 0 G 0.3 w 10 M 78.6897 93.5295 m S 0 g 1 w 4 M 78.6897 93.5295 m F 0 G 0.3 w 10 M 78.6897 93.5295 m S 0 g 1 w 4 M 78.6897 93.5295 m F 76.7484 95.4056 m 70.3336 95.4251 L 70.3336 91.6343 L 76.7484 91.6538 L F 80.6309 91.6538 m 87.0457 91.6343 L 87.0457 95.4251 L 80.6309 95.4056 L F 70.3336 95.4251 m 87.0457 95.4251 l 87.0457 91.6343 l 70.3336 91.6343 l 70.3336 95.4251 l f 0 G 0.3 w 10 M 124.3103 93.5295 m S 116.7068 100.9937 m S 0 g 1 w 4 M 116.7068 100.9937 m F 0 G 0.3 w 10 M 124.3103 93.5295 m S 124.3103 93.5295 m S 116.7068 86.0653 m S 0 g 1 w 4 M 116.7068 86.0653 m F 0 G 0.3 w 10 M 124.3103 93.5295 m S 124.3103 93.5295 m S 116.7068 100.9937 m S 0 g 1 w 4 M 116.7068 100.9937 m F 0 G 0.3 w 10 M 124.3103 93.5295 m S 131.9137 100.9937 m S 0 g 1 w 4 M 131.9137 100.9937 m F 0 G 0.3 w 10 M 124.3103 93.5295 m S 116.7068 86.0653 m S 0 g 1 w 4 M 116.7068 86.0653 m F 0 G 0.3 w 10 M 124.3103 93.5295 m S 131.9137 86.0653 m S 0 g 1 w 4 M 131.9137 86.0653 m F 0 G 0.3 w 10 M 124.3103 93.5295 m S 0 g 1 w 4 M 124.3103 93.5295 m F 0 G 0.3 w 10 M 124.3103 93.5295 m S 0 g 1 w 4 M 124.3103 93.5295 m F u 1 g 113.5575 93.5295 m 113.5575 87.871 118.3718 83.2839 124.3103 83.2839 c 130.2488 83.2839 135.0631 87.871 135.0631 93.5295 c F 135.0631 93.5295 m 135.0631 99.188 130.2488 103.7751 124.3103 103.7751 c 118.3718 103.7751 113.5575 99.188 113.5575 93.5295 c F 124.3103 93.5295 m F U 0 G 0.3 w 10 M 124.3103 93.5295 m S 0 g 1 w 4 M 124.3103 93.5295 m F 0 G 0.3 w 10 M 124.3103 93.5295 m S 0 g 1 w 4 M 124.3103 93.5295 m F 122.369 95.4056 m 115.9542 95.4251 L 115.9542 91.6343 L 122.369 91.6538 L F 126.2516 91.6538 m 132.6663 91.6343 L 132.6663 95.4251 L 126.2516 95.4056 L F 115.9542 95.4251 m 132.6663 95.4251 l 132.6663 91.6343 l 115.9542 91.6343 l 115.9542 95.4251 l f showpage _E end %%EndDocument @endspecial 1194 x @beginspecial 31 @llx 30.500000 @lly 265 @urx 274.500000 @ury 2196 @rwi @setspecial %%BeginDocument: fig8b.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z u 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 48.7927 271.6705 m S 48.7927 256.7421 m S 33.5859 256.7421 m S 33.5859 271.6705 m S 41.1893 264.2063 m S U u 79.2065 241.8137 m S 79.2065 226.8852 m S 63.9996 226.8852 m S 63.9996 241.8137 m S 71.6031 234.3495 m S U u 63.9996 256.7421 m S 63.9996 241.8137 m S 48.7927 241.8137 m S 48.7927 256.7421 m S 56.3962 249.2779 m S U u 63.9996 271.6705 m S 63.9996 256.7421 m S 48.7927 256.7421 m S 48.7927 271.6705 m S 56.3962 264.2063 m S U u 79.2065 271.6705 m S 79.2065 256.7421 m S 63.9996 256.7421 m S 63.9996 271.6705 m S 71.6031 264.2063 m S U u 79.2065 256.7421 m S 79.2065 241.8137 m S 63.9996 241.8137 m S 63.9996 256.7421 m S 71.6031 249.2779 m S U u 63.9996 241.8137 m S 63.9996 226.8852 m S 48.7927 226.8852 m S 48.7927 241.8137 m S 56.3962 234.3495 m S U u 48.7927 241.8137 m S 48.7927 226.8852 m S 33.5859 226.8852 m S 33.5859 241.8137 m S 41.1893 234.3495 m S U u 48.7927 256.7421 m S 48.7927 241.8137 m S 33.5859 241.8137 m S 33.5859 256.7421 m S 41.1893 249.2779 m S U 0 g 1 w 4 M 41.1893 264.2063 m F 71.6031 264.2063 m F 41.1893 234.3495 m F 71.6031 234.3495 m F u 0 G 0.3 w 10 M 94.4134 271.6705 m S 94.4134 256.7421 m S 79.2065 256.7421 m S 79.2065 271.6705 m S 86.8099 264.2063 m S U u 124.8271 241.8137 m S 124.8271 226.8852 m S 109.6203 226.8852 m S 109.6203 241.8137 m S 117.2237 234.3495 m S U u 109.6203 256.7421 m S 109.6203 241.8137 m S 94.4134 241.8137 m S 94.4134 256.7421 m S 102.0168 249.2779 m S U u 109.6203 271.6705 m S 109.6203 256.7421 m S 94.4134 256.7421 m S 94.4134 271.6705 m S 102.0168 264.2063 m S U u 124.8271 271.6705 m S 124.8271 256.7421 m S 109.6203 256.7421 m S 109.6203 271.6705 m S 117.2237 264.2063 m S U u 124.8271 256.7421 m S 124.8271 241.8137 m S 109.6203 241.8137 m S 109.6203 256.7421 m S 117.2237 249.2779 m S U u 109.6203 241.8137 m S 109.6203 226.8852 m S 94.4134 226.8852 m S 94.4134 241.8137 m S 102.0168 234.3495 m S U u 94.4134 241.8137 m S 94.4134 226.8852 m S 79.2065 226.8852 m S 79.2065 241.8137 m S 86.8099 234.3495 m S U u 94.4134 256.7421 m S 94.4134 241.8137 m S 79.2065 241.8137 m S 79.2065 256.7421 m S 86.8099 249.2779 m S U 0 g 1 w 4 M 86.8099 264.2063 m F 117.2237 264.2063 m F 86.8099 234.3495 m F 117.2237 234.3495 m F u 0 G 0.3 w 10 M 140.034 271.6705 m S 140.034 256.7421 m S 124.8271 256.7421 m S 124.8271 271.6705 m S 132.4305 264.2063 m S U 170.4477 241.8137 m S 170.4477 226.8852 m S 155.2409 226.8852 m S 162.8443 234.3495 m S 155.2409 256.7421 m S 140.034 241.8137 m S 140.034 256.7421 m S 147.6374 249.2779 m S u 155.2409 271.6705 m S 155.2409 256.7421 m S 140.034 256.7421 m S 140.034 271.6705 m S 147.6374 264.2063 m S U u 170.4477 271.6705 m S 170.4477 256.7421 m S 155.2409 256.7421 m S 155.2409 271.6705 m S 162.8443 264.2063 m S U 170.4477 256.7421 m S 170.4477 241.8137 m S 155.2409 256.7421 m S 162.8443 249.2779 m S 155.2409 226.8852 m S 140.034 226.8852 m S 140.034 241.8137 m S 147.6374 234.3495 m S u 140.034 241.8137 m S 140.034 226.8852 m S 124.8271 226.8852 m S 124.8271 241.8137 m S 132.4305 234.3495 m S U u 140.034 256.7421 m S 140.034 241.8137 m S 124.8271 241.8137 m S 124.8271 256.7421 m S 132.4305 249.2779 m S U 0 g 1 w 4 M 132.4305 264.2063 m F 162.8443 264.2063 m F 132.4305 234.3495 m F 162.8443 234.3495 m F 0 G 0.3 w 10 M 170.4477 256.7421 m S 170.4477 271.6705 m S 170.4477 226.8852 m S 170.4477 241.8137 m S 170.4477 241.8137 m S 170.4477 256.7421 m S u 48.7927 226.8852 m S 48.7927 211.9568 m S 33.5859 211.9568 m S 33.5859 226.8852 m S 41.1893 219.421 m S U u 79.2065 197.0284 m S 79.2065 182.1 m S 63.9996 182.1 m S 63.9996 197.0284 m S 71.6031 189.5642 m S U u 63.9996 211.9568 m S 63.9996 197.0284 m S 48.7927 197.0284 m S 48.7927 211.9568 m S 56.3962 204.4927 m S U u 63.9996 226.8852 m S 63.9996 211.9568 m S 48.7927 211.9568 m S 48.7927 226.8852 m S 56.3962 219.421 m S U u 79.2065 226.8852 m S 79.2065 211.9568 m S 63.9996 211.9568 m S 63.9996 226.8852 m S 71.6031 219.421 m S U u 79.2065 211.9568 m S 79.2065 197.0284 m S 63.9996 197.0284 m S 63.9996 211.9568 m S 71.6031 204.4927 m S U u 63.9996 197.0284 m S 63.9996 182.1 m S 48.7927 182.1 m S 48.7927 197.0284 m S 56.3962 189.5642 m S U u 48.7927 197.0284 m S 48.7927 182.1 m S 33.5859 182.1 m S 33.5859 197.0284 m S 41.1893 189.5642 m S U u 48.7927 211.9568 m S 48.7927 197.0284 m S 33.5859 197.0284 m S 33.5859 211.9568 m S 41.1893 204.4927 m S U 0 g 1 w 4 M 41.1893 219.421 m F 71.6031 219.421 m F 41.1893 189.5642 m F 71.6031 189.5642 m F u 0 G 0.3 w 10 M 94.4134 226.8852 m S 94.4134 211.9568 m S 79.2065 211.9568 m S 79.2065 226.8852 m S 86.8099 219.421 m S U 124.8271 197.0284 m S 124.8271 182.1 m S 109.6203 182.1 m S 109.6203 197.0284 m S 117.2237 189.5642 m S 109.6203 211.9568 m S 109.6203 197.0284 m S 94.4134 197.0284 m S 94.4134 211.9568 m S 102.0168 204.4927 m S u 109.6203 226.8852 m S 109.6203 211.9568 m S 94.4134 211.9568 m S 94.4134 226.8852 m S 102.0168 219.421 m S U u 124.8271 226.8852 m S 124.8271 211.9568 m S 109.6203 211.9568 m S 109.6203 226.8852 m S 117.2237 219.421 m S U 124.8271 211.9568 m S 124.8271 197.0284 m S 109.6203 197.0284 m S 109.6203 211.9568 m S 117.2237 204.4927 m S 109.6203 197.0284 m S 109.6203 182.1 m S 94.4134 182.1 m S 94.4134 197.0284 m S 102.0168 189.5642 m S u 94.4134 197.0284 m S 94.4134 182.1 m S 79.2065 182.1 m S 79.2065 197.0284 m S 86.8099 189.5642 m S U u 94.4134 211.9568 m S 94.4134 197.0284 m S 79.2065 197.0284 m S 79.2065 211.9568 m S 86.8099 204.4927 m S U 0 g 1 w 4 M 86.8099 219.421 m F 117.2237 219.421 m F 86.8099 189.5642 m F 117.2237 189.5642 m F 0 G 0.3 w 10 M 140.034 226.8852 m S 140.034 211.9568 m S 124.8271 211.9568 m S 124.8271 226.8852 m S 132.4305 219.421 m S 170.4477 197.0284 m S 170.4477 182.1 m S 155.2409 182.1 m S 155.2409 197.0284 m S 162.8443 189.5642 m S 155.2409 211.9568 m S 155.2409 197.0284 m S 140.034 197.0284 m S 140.034 211.9568 m S 147.6374 204.4927 m S 155.2409 226.8852 m S 155.2409 211.9568 m S 140.034 211.9568 m S 140.034 226.8852 m S 147.6374 219.421 m S 170.4477 226.8852 m S 170.4477 211.9568 m S 155.2409 211.9568 m S 155.2409 226.8852 m S 162.8443 219.421 m S 170.4477 211.9568 m S 170.4477 197.0284 m S 155.2409 197.0284 m S 155.2409 211.9568 m S 162.8443 204.4927 m S 155.2409 197.0284 m S 155.2409 182.1 m S 140.034 182.1 m S 140.034 197.0284 m S 147.6374 189.5642 m S 140.034 197.0284 m S 140.034 182.1 m S 124.8271 182.1 m S 124.8271 197.0284 m S 132.4305 189.5642 m S 140.034 211.9568 m S 140.034 197.0284 m S 124.8271 197.0284 m S 124.8271 211.9568 m S 132.4305 204.4927 m S 0 g 1 w 4 M 132.4305 219.421 m F 162.8443 219.421 m F 132.4305 189.5642 m F 162.8443 189.5642 m F 0 G 0.3 w 10 M 170.4477 211.9568 m S 170.4477 226.8852 m S 170.4477 182.1 m S 170.4477 197.0284 m S 170.4477 197.0284 m S 170.4477 211.9568 m S 0 g 1 w 4 M 41.1893 174.6358 m F 71.6031 174.6358 m F 86.8099 174.6358 m F 117.2237 174.6358 m F 132.4305 174.6358 m F 162.8443 174.6358 m F u 0 G 0.3 w 10 M 48.7927 182.1 m S 48.7927 167.1715 m S 33.5859 167.1715 m S 33.5859 182.1 m S 41.1893 174.6358 m S U 79.2065 152.2431 m S 79.2065 137.3147 m S 63.9996 137.3147 m S 63.9996 152.2431 m S 71.6031 144.7789 m S u 63.9996 167.1715 m S 63.9996 152.2431 m S 48.7927 152.2431 m S 48.7927 167.1715 m S 56.3962 159.7073 m S U u 63.9996 182.1 m S 63.9996 167.1715 m S 48.7927 167.1715 m S 48.7927 182.1 m S 56.3962 174.6358 m S U u 79.2065 182.1 m S 79.2065 167.1715 m S 63.9996 167.1715 m S 63.9996 182.1 m S 71.6031 174.6358 m S U 79.2065 167.1715 m S 79.2065 152.2431 m S 63.9996 152.2431 m S 63.9996 167.1715 m S 71.6031 159.7073 m S u 63.9996 152.2431 m S 63.9996 137.3147 m S 48.7927 137.3147 m S 48.7927 152.2431 m S 56.3962 144.7789 m S U u 48.7927 152.2431 m S 48.7927 137.3147 m S 33.5859 137.3147 m S 33.5859 152.2431 m S 41.1893 144.7789 m S U u 48.7927 167.1715 m S 48.7927 152.2431 m S 33.5859 152.2431 m S 33.5859 167.1715 m S 41.1893 159.7073 m S U 0 g 1 w 4 M 41.1893 174.6358 m F 71.6031 174.6358 m F 41.1893 144.7789 m F 71.6031 144.7789 m F u 0 G 0.3 w 10 M 94.4134 182.1 m S 94.4134 167.1715 m S 79.2065 167.1715 m S 79.2065 182.1 m S 86.8099 174.6358 m S U u 124.8271 152.2431 m S 124.8271 137.3147 m S 109.6203 137.3147 m S 109.6203 152.2431 m S 117.2237 144.7789 m S U 109.6203 167.1715 m S 109.6203 152.2431 m S 94.4134 152.2431 m S 94.4134 167.1715 m S 102.0168 159.7073 m S 109.6203 182.1 m S 109.6203 167.1715 m S 94.4134 167.1715 m S 94.4134 182.1 m S 102.0168 174.6358 m S 124.8271 182.1 m S 124.8271 167.1715 m S 109.6203 167.1715 m S 109.6203 182.1 m S 117.2237 174.6358 m S 124.8271 167.1715 m S 124.8271 152.2431 m S 109.6203 152.2431 m S 109.6203 167.1715 m S 117.2237 159.7073 m S 109.6203 152.2431 m S 109.6203 137.3147 m S 94.4134 137.3147 m S 94.4134 152.2431 m S 102.0168 144.7789 m S 94.4134 152.2431 m S 94.4134 137.3147 m S 79.2065 137.3147 m S 79.2065 152.2431 m S 86.8099 144.7789 m S 94.4134 167.1715 m S 94.4134 152.2431 m S 79.2065 152.2431 m S 79.2065 167.1715 m S 86.8099 159.7073 m S 0 g 1 w 4 M 86.8099 174.6358 m F 117.2237 174.6358 m F 86.8099 144.7789 m F 117.2237 144.7789 m F 0 G 0.3 w 10 M 140.034 182.1 m S 140.034 167.1715 m S 124.8271 167.1715 m S 124.8271 182.1 m S 132.4305 174.6358 m S u 170.4477 152.2431 m S 170.4477 137.3147 m S 155.2409 137.3147 m S 155.2409 152.2431 m S 162.8443 144.7789 m S U 155.2409 167.1715 m S 155.2409 152.2431 m S 140.034 152.2431 m S 140.034 167.1715 m S 147.6374 159.7073 m S 155.2409 182.1 m S 155.2409 167.1715 m S 140.034 167.1715 m S 140.034 182.1 m S 147.6374 174.6358 m S 170.4477 182.1 m S 170.4477 167.1715 m S 155.2409 167.1715 m S 155.2409 182.1 m S 162.8443 174.6358 m S 170.4477 167.1715 m S 170.4477 152.2431 m S 155.2409 152.2431 m S 155.2409 167.1715 m S 162.8443 159.7073 m S u 155.2409 152.2431 m S 155.2409 137.3147 m S 140.034 137.3147 m S 140.034 152.2431 m S 147.6374 144.7789 m S U u 140.034 152.2431 m S 140.034 137.3147 m S 124.8271 137.3147 m S 124.8271 152.2431 m S 132.4305 144.7789 m S U 140.034 167.1715 m S 140.034 152.2431 m S 124.8271 152.2431 m S 124.8271 167.1715 m S 132.4305 159.7073 m S 0 g 1 w 4 M 132.4305 174.6358 m F 162.8443 174.6358 m F 132.4305 144.7789 m F 162.8443 144.7789 m F 0 G 0.3 w 10 M 170.4477 167.1715 m S 170.4477 182.1 m S 170.4477 137.3147 m S 170.4477 152.2431 m S 170.4477 152.2431 m S 170.4477 167.1715 m S 48.7927 137.3147 m S 33.5859 137.3147 m S 63.9996 137.3147 m S 48.7927 137.3147 m S 79.2065 137.3147 m S 63.9996 137.3147 m S 94.4134 137.3147 m S 79.2065 137.3147 m S 109.6203 137.3147 m S 94.4134 137.3147 m S 124.8271 137.3147 m S 109.6203 137.3147 m S 140.034 137.3147 m S 124.8271 137.3147 m S 155.2409 137.3147 m S 140.034 137.3147 m S 170.4477 137.3147 m S 155.2409 137.3147 m S 170.4477 137.3147 m S 1 w 4 M 41.1893 249.2779 m 162.8443 249.2779 l S 41.1893 204.4927 m 162.8443 204.4927 l S 41.1893 159.7073 m 162.8443 159.7073 l S 56.3962 264.2063 m 56.3962 144.7789 l S 102.0168 264.2063 m 102.0168 144.7789 l S 147.6374 264.2063 m 147.6374 144.7789 l S u 0.3 w 10 M 140.034 271.6705 m S 140.034 256.7421 m S 124.8271 256.7421 m S 124.8271 271.6705 m S 132.4305 264.2063 m S U 170.4477 241.8137 m S 170.4477 226.8852 m S 155.2409 226.8852 m S 162.8443 234.3495 m S 155.2409 256.7421 m S 140.034 241.8137 m S 140.034 256.7421 m S 147.6374 249.2779 m S u 155.2409 271.6705 m S 155.2409 256.7421 m S 140.034 256.7421 m S 140.034 271.6705 m S 147.6374 264.2063 m S U u 170.4477 271.6705 m S 170.4477 256.7421 m S 155.2409 256.7421 m S 155.2409 271.6705 m S 162.8443 264.2063 m S U 170.4477 256.7421 m S 170.4477 241.8137 m S 155.2409 256.7421 m S 162.8443 249.2779 m S 155.2409 226.8852 m S 140.034 226.8852 m S 140.034 241.8137 m S 147.6374 234.3495 m S u 140.034 241.8137 m S 140.034 226.8852 m S 124.8271 226.8852 m S 124.8271 241.8137 m S 132.4305 234.3495 m S U u 140.034 256.7421 m S 140.034 241.8137 m S 124.8271 241.8137 m S 124.8271 256.7421 m S 132.4305 249.2779 m S U 0 g 1 w 4 M 132.4305 264.2063 m F 162.8443 264.2063 m F 132.4305 234.3495 m F 162.8443 234.3495 m F u 0 G 0.3 w 10 M 185.6546 271.6705 m S 185.6546 256.7421 m S 170.4477 256.7421 m S 170.4477 271.6705 m S 178.0511 264.2063 m S U 216.0684 241.8137 m S 216.0684 226.8852 m S 200.8615 226.8852 m S 208.4649 234.3495 m S 200.8615 256.7421 m S 185.6546 241.8137 m S 185.6546 256.7421 m S 193.2581 249.2779 m S 200.8615 271.6705 m S 200.8615 256.7421 m S 185.6546 256.7421 m S 185.6546 271.6705 m S 193.2581 264.2063 m S 216.0684 271.6705 m S 216.0684 256.7421 m S 200.8615 256.7421 m S 200.8615 271.6705 m S 208.4649 264.2063 m S 216.0684 256.7421 m S 216.0684 241.8137 m S 200.8615 256.7421 m S 208.4649 249.2779 m S 200.8615 226.8852 m S 185.6546 226.8852 m S 185.6546 241.8137 m S 193.2581 234.3495 m S u 185.6546 241.8137 m S 185.6546 226.8852 m S 170.4477 226.8852 m S 170.4477 241.8137 m S 178.0511 234.3495 m S U u 185.6546 256.7421 m S 185.6546 241.8137 m S 170.4477 241.8137 m S 170.4477 256.7421 m S 178.0511 249.2779 m S U 0 g 1 w 4 M 178.0511 264.2063 m F 208.4649 264.2063 m F 178.0511 234.3495 m F 208.4649 234.3495 m F 0 G 0.3 w 10 M 231.2752 271.6705 m S 231.2752 256.7421 m S 216.0684 256.7421 m S 216.0684 271.6705 m S 223.6717 264.2063 m S u 261.689 241.8137 m S 261.689 226.8852 m S 246.4821 226.8852 m S 246.4821 241.8137 m S 254.0855 234.3495 m S U 246.4821 256.7421 m S 246.4821 241.8137 m S 231.2752 241.8137 m S 231.2752 256.7421 m S 238.8787 249.2779 m S 246.4821 271.6705 m S 246.4821 256.7421 m S 231.2752 256.7421 m S 231.2752 271.6705 m S 238.8787 264.2063 m S u 261.689 271.6705 m S 261.689 256.7421 m S 246.4821 256.7421 m S 246.4821 271.6705 m S 254.0855 264.2063 m S U u 261.689 256.7421 m S 261.689 241.8137 m S 246.4821 241.8137 m S 246.4821 256.7421 m S 254.0855 249.2779 m S U u 246.4821 241.8137 m S 246.4821 226.8852 m S 231.2752 226.8852 m S 231.2752 241.8137 m S 238.8787 234.3495 m S U u 231.2752 241.8137 m S 231.2752 226.8852 m S 216.0684 226.8852 m S 216.0684 241.8137 m S 223.6717 234.3495 m S U 231.2752 256.7421 m S 231.2752 241.8137 m S 216.0684 241.8137 m S 216.0684 256.7421 m S 223.6717 249.2779 m S 0 g 1 w 4 M 223.6717 264.2063 m F 254.0855 264.2063 m F 223.6717 234.3495 m F 254.0855 234.3495 m F 0 G 0.3 w 10 M 261.689 256.7421 m S 261.689 271.6705 m S 261.689 226.8852 m S 261.689 241.8137 m S 261.689 241.8137 m S 261.689 256.7421 m S 140.034 226.8852 m S 140.034 211.9568 m S 124.8271 211.9568 m S 124.8271 226.8852 m S 132.4305 219.421 m S 170.4477 197.0284 m S 170.4477 182.1 m S 155.2409 182.1 m S 155.2409 197.0284 m S 162.8443 189.5642 m S 155.2409 211.9568 m S 155.2409 197.0284 m S 140.034 197.0284 m S 140.034 211.9568 m S 147.6374 204.4927 m S 155.2409 226.8852 m S 155.2409 211.9568 m S 140.034 211.9568 m S 140.034 226.8852 m S 147.6374 219.421 m S 170.4477 226.8852 m S 170.4477 211.9568 m S 155.2409 211.9568 m S 155.2409 226.8852 m S 162.8443 219.421 m S 170.4477 211.9568 m S 170.4477 197.0284 m S 155.2409 197.0284 m S 155.2409 211.9568 m S 162.8443 204.4927 m S 155.2409 197.0284 m S 155.2409 182.1 m S 140.034 182.1 m S 140.034 197.0284 m S 147.6374 189.5642 m S 140.034 197.0284 m S 140.034 182.1 m S 124.8271 182.1 m S 124.8271 197.0284 m S 132.4305 189.5642 m S 140.034 211.9568 m S 140.034 197.0284 m S 124.8271 197.0284 m S 124.8271 211.9568 m S 132.4305 204.4927 m S 0 g 1 w 4 M 132.4305 219.421 m F 162.8443 219.421 m F 132.4305 189.5642 m F 162.8443 189.5642 m F u 0 G 0.3 w 10 M 185.6546 226.8852 m S 185.6546 211.9568 m S 170.4477 211.9568 m S 170.4477 226.8852 m S 178.0511 219.421 m S U u 216.0684 197.0284 m S 216.0684 182.1 m S 200.8615 182.1 m S 200.8615 197.0284 m S 208.4649 189.5642 m S U 200.8615 211.9568 m S 200.8615 197.0284 m S 185.6546 197.0284 m S 185.6546 211.9568 m S 193.2581 204.4927 m S u 200.8615 226.8852 m S 200.8615 211.9568 m S 185.6546 211.9568 m S 185.6546 226.8852 m S 193.2581 219.421 m S U u 216.0684 226.8852 m S 216.0684 211.9568 m S 200.8615 211.9568 m S 200.8615 226.8852 m S 208.4649 219.421 m S U u 216.0684 211.9568 m S 216.0684 197.0284 m S 200.8615 197.0284 m S 200.8615 211.9568 m S 208.4649 204.4927 m S U 200.8615 197.0284 m S 200.8615 182.1 m S 185.6546 182.1 m S 185.6546 197.0284 m S 193.2581 189.5642 m S 185.6546 197.0284 m S 185.6546 182.1 m S 170.4477 182.1 m S 170.4477 197.0284 m S 178.0511 189.5642 m S 185.6546 211.9568 m S 185.6546 197.0284 m S 170.4477 197.0284 m S 170.4477 211.9568 m S 178.0511 204.4927 m S 0 g 1 w 4 M 178.0511 219.421 m F 208.4649 219.421 m F 178.0511 189.5642 m F 208.4649 189.5642 m F u 0 G 0.3 w 10 M 231.2752 226.8852 m S 231.2752 211.9568 m S 216.0684 211.9568 m S 216.0684 226.8852 m S 223.6717 219.421 m S U u 261.689 197.0284 m S 261.689 182.1 m S 246.4821 182.1 m S 246.4821 197.0284 m S 254.0855 189.5642 m S U u 246.4821 211.9568 m S 246.4821 197.0284 m S 231.2752 197.0284 m S 231.2752 211.9568 m S 238.8787 204.4927 m S U u 246.4821 226.8852 m S 246.4821 211.9568 m S 231.2752 211.9568 m S 231.2752 226.8852 m S 238.8787 219.421 m S U u 261.689 226.8852 m S 261.689 211.9568 m S 246.4821 211.9568 m S 246.4821 226.8852 m S 254.0855 219.421 m S U u 261.689 211.9568 m S 261.689 197.0284 m S 246.4821 197.0284 m S 246.4821 211.9568 m S 254.0855 204.4927 m S U u 246.4821 197.0284 m S 246.4821 182.1 m S 231.2752 182.1 m S 231.2752 197.0284 m S 238.8787 189.5642 m S U u 231.2752 197.0284 m S 231.2752 182.1 m S 216.0684 182.1 m S 216.0684 197.0284 m S 223.6717 189.5642 m S U u 231.2752 211.9568 m S 231.2752 197.0284 m S 216.0684 197.0284 m S 216.0684 211.9568 m S 223.6717 204.4927 m S U 0 g 1 w 4 M 223.6717 219.421 m F 254.0855 219.421 m F 223.6717 189.5642 m F 254.0855 189.5642 m F 0 G 0.3 w 10 M 261.689 211.9568 m S 261.689 226.8852 m S 261.689 182.1 m S 261.689 197.0284 m S 261.689 197.0284 m S 261.689 211.9568 m S 0 g 1 w 4 M 132.4305 174.6358 m F 162.8443 174.6358 m F 178.0511 174.6358 m F 208.4649 174.6358 m F 223.6717 174.6358 m F 254.0855 174.6358 m F 0 G 0.3 w 10 M 140.034 182.1 m S 140.034 167.1715 m S 124.8271 167.1715 m S 124.8271 182.1 m S 132.4305 174.6358 m S u 170.4477 152.2431 m S 170.4477 137.3147 m S 155.2409 137.3147 m S 155.2409 152.2431 m S 162.8443 144.7789 m S U 155.2409 167.1715 m S 155.2409 152.2431 m S 140.034 152.2431 m S 140.034 167.1715 m S 147.6374 159.7073 m S 155.2409 182.1 m S 155.2409 167.1715 m S 140.034 167.1715 m S 140.034 182.1 m S 147.6374 174.6358 m S 170.4477 182.1 m S 170.4477 167.1715 m S 155.2409 167.1715 m S 155.2409 182.1 m S 162.8443 174.6358 m S 170.4477 167.1715 m S 170.4477 152.2431 m S 155.2409 152.2431 m S 155.2409 167.1715 m S 162.8443 159.7073 m S u 155.2409 152.2431 m S 155.2409 137.3147 m S 140.034 137.3147 m S 140.034 152.2431 m S 147.6374 144.7789 m S U u 140.034 152.2431 m S 140.034 137.3147 m S 124.8271 137.3147 m S 124.8271 152.2431 m S 132.4305 144.7789 m S U 140.034 167.1715 m S 140.034 152.2431 m S 124.8271 152.2431 m S 124.8271 167.1715 m S 132.4305 159.7073 m S 0 g 1 w 4 M 132.4305 174.6358 m F 162.8443 174.6358 m F 132.4305 144.7789 m F 162.8443 144.7789 m F 0 G 0.3 w 10 M 185.6546 182.1 m S 185.6546 167.1715 m S 170.4477 167.1715 m S 170.4477 182.1 m S 178.0511 174.6358 m S u 216.0684 152.2431 m S 216.0684 137.3147 m S 200.8615 137.3147 m S 200.8615 152.2431 m S 208.4649 144.7789 m S U 200.8615 167.1715 m S 200.8615 152.2431 m S 185.6546 152.2431 m S 185.6546 167.1715 m S 193.2581 159.7073 m S 200.8615 182.1 m S 200.8615 167.1715 m S 185.6546 167.1715 m S 185.6546 182.1 m S 193.2581 174.6358 m S u 216.0684 182.1 m S 216.0684 167.1715 m S 200.8615 167.1715 m S 200.8615 182.1 m S 208.4649 174.6358 m S U u 216.0684 167.1715 m S 216.0684 152.2431 m S 200.8615 152.2431 m S 200.8615 167.1715 m S 208.4649 159.7073 m S U u 200.8615 152.2431 m S 200.8615 137.3147 m S 185.6546 137.3147 m S 185.6546 152.2431 m S 193.2581 144.7789 m S U u 185.6546 152.2431 m S 185.6546 137.3147 m S 170.4477 137.3147 m S 170.4477 152.2431 m S 178.0511 144.7789 m S U 185.6546 167.1715 m S 185.6546 152.2431 m S 170.4477 152.2431 m S 170.4477 167.1715 m S 178.0511 159.7073 m S 0 g 1 w 4 M 178.0511 174.6358 m F 208.4649 174.6358 m F 178.0511 144.7789 m F 208.4649 144.7789 m F u 0 G 0.3 w 10 M 231.2752 182.1 m S 231.2752 167.1715 m S 216.0684 167.1715 m S 216.0684 182.1 m S 223.6717 174.6358 m S U u 261.689 152.2431 m S 261.689 137.3147 m S 246.4821 137.3147 m S 246.4821 152.2431 m S 254.0855 144.7789 m S U u 246.4821 167.1715 m S 246.4821 152.2431 m S 231.2752 152.2431 m S 231.2752 167.1715 m S 238.8787 159.7073 m S U u 246.4821 182.1 m S 246.4821 167.1715 m S 231.2752 167.1715 m S 231.2752 182.1 m S 238.8787 174.6358 m S U u 261.689 182.1 m S 261.689 167.1715 m S 246.4821 167.1715 m S 246.4821 182.1 m S 254.0855 174.6358 m S U u 261.689 167.1715 m S 261.689 152.2431 m S 246.4821 152.2431 m S 246.4821 167.1715 m S 254.0855 159.7073 m S U u 246.4821 152.2431 m S 246.4821 137.3147 m S 231.2752 137.3147 m S 231.2752 152.2431 m S 238.8787 144.7789 m S U u 231.2752 152.2431 m S 231.2752 137.3147 m S 216.0684 137.3147 m S 216.0684 152.2431 m S 223.6717 144.7789 m S U u 231.2752 167.1715 m S 231.2752 152.2431 m S 216.0684 152.2431 m S 216.0684 167.1715 m S 223.6717 159.7073 m S U 0 g 1 w 4 M 223.6717 174.6358 m F 254.0855 174.6358 m F 223.6717 144.7789 m F 254.0855 144.7789 m F 0 G 0.3 w 10 M 261.689 167.1715 m S 261.689 182.1 m S 261.689 137.3147 m S 261.689 152.2431 m S 261.689 152.2431 m S 261.689 167.1715 m S 140.034 137.3147 m S 124.8271 137.3147 m S 155.2409 137.3147 m S 140.034 137.3147 m S 170.4477 137.3147 m S 155.2409 137.3147 m S 185.6546 137.3147 m S 170.4477 137.3147 m S 200.8615 137.3147 m S 185.6546 137.3147 m S 216.0684 137.3147 m S 200.8615 137.3147 m S 231.2752 137.3147 m S 216.0684 137.3147 m S 246.4821 137.3147 m S 231.2752 137.3147 m S 261.689 137.3147 m S 246.4821 137.3147 m S 261.689 137.3147 m S 1 w 4 M 132.4305 249.2779 m 254.0855 249.2779 l S 132.4305 204.4927 m 254.0855 204.4927 l S 132.4305 159.7073 m 254.0855 159.7073 l S 147.6374 264.2063 m 147.6374 144.7789 l S 193.2581 264.2063 m 193.2581 144.7789 l S 238.8787 264.2063 m 238.8787 144.7789 l S u 0.3 w 10 M 48.7927 182.1 m S 48.7927 167.1716 m S 33.5859 167.1716 m S 33.5859 182.1 m S 41.1893 174.6358 m S U 79.2065 152.2431 m S 79.2065 137.3147 m S 63.9996 137.3147 m S 63.9996 152.2431 m S 71.6031 144.7789 m S u 63.9996 167.1716 m S 63.9996 152.2431 m S 48.7927 152.2431 m S 48.7927 167.1716 m S 56.3962 159.7074 m S U u 63.9996 182.1 m S 63.9996 167.1716 m S 48.7927 167.1716 m S 48.7927 182.1 m S 56.3962 174.6358 m S U u 79.2065 182.1 m S 79.2065 167.1716 m S 63.9996 167.1716 m S 63.9996 182.1 m S 71.6031 174.6358 m S U 79.2065 167.1716 m S 79.2065 152.2431 m S 63.9996 152.2431 m S 63.9996 167.1716 m S 71.6031 159.7074 m S u 63.9996 152.2431 m S 63.9996 137.3147 m S 48.7927 137.3147 m S 48.7927 152.2431 m S 56.3962 144.7789 m S U u 48.7927 152.2431 m S 48.7927 137.3147 m S 33.5859 137.3147 m S 33.5859 152.2431 m S 41.1893 144.7789 m S U u 48.7927 167.1716 m S 48.7927 152.2431 m S 33.5859 152.2431 m S 33.5859 167.1716 m S 41.1893 159.7074 m S U 0 g 1 w 4 M 41.1893 174.6358 m F 71.6031 174.6358 m F 41.1893 144.7789 m F 71.6031 144.7789 m F u 0 G 0.3 w 10 M 94.4134 182.1 m S 94.4134 167.1716 m S 79.2065 167.1716 m S 79.2065 182.1 m S 86.8099 174.6358 m S U u 124.8271 152.2431 m S 124.8271 137.3147 m S 109.6203 137.3147 m S 109.6203 152.2431 m S 117.2237 144.7789 m S U 109.6203 167.1716 m S 109.6203 152.2431 m S 94.4134 152.2431 m S 94.4134 167.1716 m S 102.0168 159.7074 m S 109.6203 182.1 m S 109.6203 167.1716 m S 94.4134 167.1716 m S 94.4134 182.1 m S 102.0168 174.6358 m S 124.8271 182.1 m S 124.8271 167.1716 m S 109.6203 167.1716 m S 109.6203 182.1 m S 117.2237 174.6358 m S 124.8271 167.1716 m S 124.8271 152.2431 m S 109.6203 152.2431 m S 109.6203 167.1716 m S 117.2237 159.7074 m S 109.6203 152.2431 m S 109.6203 137.3147 m S 94.4134 137.3147 m S 94.4134 152.2431 m S 102.0168 144.7789 m S 94.4134 152.2431 m S 94.4134 137.3147 m S 79.2065 137.3147 m S 79.2065 152.2431 m S 86.8099 144.7789 m S 94.4134 167.1716 m S 94.4134 152.2431 m S 79.2065 152.2431 m S 79.2065 167.1716 m S 86.8099 159.7074 m S 0 g 1 w 4 M 86.8099 174.6358 m F 117.2237 174.6358 m F 86.8099 144.7789 m F 117.2237 144.7789 m F 0 G 0.3 w 10 M 140.034 182.1 m S 140.034 167.1716 m S 124.8271 167.1716 m S 124.8271 182.1 m S 132.4305 174.6358 m S u 170.4477 152.2431 m S 170.4477 137.3147 m S 155.2409 137.3147 m S 155.2409 152.2431 m S 162.8443 144.7789 m S U 155.2409 167.1716 m S 155.2409 152.2431 m S 140.034 152.2431 m S 140.034 167.1716 m S 147.6374 159.7074 m S 155.2409 182.1 m S 155.2409 167.1716 m S 140.034 167.1716 m S 140.034 182.1 m S 147.6374 174.6358 m S 170.4477 182.1 m S 170.4477 167.1716 m S 155.2409 167.1716 m S 155.2409 182.1 m S 162.8443 174.6358 m S 170.4477 167.1716 m S 170.4477 152.2431 m S 155.2409 152.2431 m S 155.2409 167.1716 m S 162.8443 159.7074 m S u 155.2409 152.2431 m S 155.2409 137.3147 m S 140.034 137.3147 m S 140.034 152.2431 m S 147.6374 144.7789 m S U u 140.034 152.2431 m S 140.034 137.3147 m S 124.8271 137.3147 m S 124.8271 152.2431 m S 132.4305 144.7789 m S U 140.034 167.1716 m S 140.034 152.2431 m S 124.8271 152.2431 m S 124.8271 167.1716 m S 132.4305 159.7074 m S 0 g 1 w 4 M 132.4305 174.6358 m F 162.8443 174.6358 m F 132.4305 144.7789 m F 162.8443 144.7789 m F 0 G 0.3 w 10 M 170.4477 167.1716 m S 170.4477 182.1 m S 170.4477 137.3147 m S 170.4477 152.2431 m S 170.4477 152.2431 m S 170.4477 167.1716 m S u 48.7927 137.3147 m S 48.7927 122.3863 m S 33.5859 122.3863 m S 33.5859 137.3147 m S 41.1893 129.8505 m S U u 79.2065 107.4579 m S 79.2065 92.5295 m S 63.9996 92.5295 m S 63.9996 107.4579 m S 71.6031 99.9937 m S U u 63.9996 122.3863 m S 63.9996 107.4579 m S 48.7927 107.4579 m S 48.7927 122.3863 m S 56.3962 114.9221 m S U u 63.9996 137.3147 m S 63.9996 122.3863 m S 48.7927 122.3863 m S 48.7927 137.3147 m S 56.3962 129.8505 m S U u 79.2065 137.3147 m S 79.2065 122.3863 m S 63.9996 122.3863 m S 63.9996 137.3147 m S 71.6031 129.8505 m S U u 79.2065 122.3863 m S 79.2065 107.4579 m S 63.9996 107.4579 m S 63.9996 122.3863 m S 71.6031 114.9221 m S U u 63.9996 107.4579 m S 63.9996 92.5295 m S 48.7927 92.5295 m S 48.7927 107.4579 m S 56.3962 99.9937 m S U u 48.7927 107.4579 m S 48.7927 92.5295 m S 33.5859 92.5295 m S 33.5859 107.4579 m S 41.1893 99.9937 m S U u 48.7927 122.3863 m S 48.7927 107.4579 m S 33.5859 107.4579 m S 33.5859 122.3863 m S 41.1893 114.9221 m S U 0 g 1 w 4 M 41.1893 129.8505 m F 71.6031 129.8505 m F 41.1893 99.9937 m F 71.6031 99.9937 m F u 0 G 0.3 w 10 M 94.4134 137.3147 m S 94.4134 122.3863 m S 79.2065 122.3863 m S 79.2065 137.3147 m S 86.8099 129.8505 m S U u 124.8271 107.4579 m S 124.8271 92.5295 m S 109.6203 92.5295 m S 109.6203 107.4579 m S 117.2237 99.9937 m S U u 109.6203 122.3863 m S 109.6203 107.4579 m S 94.4134 107.4579 m S 94.4134 122.3863 m S 102.0168 114.9221 m S U u 109.6203 137.3147 m S 109.6203 122.3863 m S 94.4134 122.3863 m S 94.4134 137.3147 m S 102.0168 129.8505 m S U u 124.8271 137.3147 m S 124.8271 122.3863 m S 109.6203 122.3863 m S 109.6203 137.3147 m S 117.2237 129.8505 m S U u 124.8271 122.3863 m S 124.8271 107.4579 m S 109.6203 107.4579 m S 109.6203 122.3863 m S 117.2237 114.9221 m S U u 109.6203 107.4579 m S 109.6203 92.5295 m S 94.4134 92.5295 m S 94.4134 107.4579 m S 102.0168 99.9937 m S U u 94.4134 107.4579 m S 94.4134 92.5295 m S 79.2065 92.5295 m S 79.2065 107.4579 m S 86.8099 99.9937 m S U u 94.4134 122.3863 m S 94.4134 107.4579 m S 79.2065 107.4579 m S 79.2065 122.3863 m S 86.8099 114.9221 m S U 0 g 1 w 4 M 86.8099 129.8505 m F 117.2237 129.8505 m F 86.8099 99.9937 m F 117.2237 99.9937 m F u 0 G 0.3 w 10 M 140.034 137.3147 m S 140.034 122.3863 m S 124.8271 122.3863 m S 124.8271 137.3147 m S 132.4305 129.8505 m S U u 170.4477 107.4579 m S 170.4477 92.5295 m S 155.2409 92.5295 m S 155.2409 107.4579 m S 162.8443 99.9937 m S U u 155.2409 122.3863 m S 155.2409 107.4579 m S 140.034 107.4579 m S 140.034 122.3863 m S 147.6374 114.9221 m S U u 155.2409 137.3147 m S 155.2409 122.3863 m S 140.034 122.3863 m S 140.034 137.3147 m S 147.6374 129.8505 m S U u 170.4477 137.3147 m S 170.4477 122.3863 m S 155.2409 122.3863 m S 155.2409 137.3147 m S 162.8443 129.8505 m S U u 170.4477 122.3863 m S 170.4477 107.4579 m S 155.2409 107.4579 m S 155.2409 122.3863 m S 162.8443 114.9221 m S U u 155.2409 107.4579 m S 155.2409 92.5295 m S 140.034 92.5295 m S 140.034 107.4579 m S 147.6374 99.9937 m S U u 140.034 107.4579 m S 140.034 92.5295 m S 124.8271 92.5295 m S 124.8271 107.4579 m S 132.4305 99.9937 m S U u 140.034 122.3863 m S 140.034 107.4579 m S 124.8271 107.4579 m S 124.8271 122.3863 m S 132.4305 114.9221 m S U 0 g 1 w 4 M 132.4305 129.8505 m F 162.8443 129.8505 m F 132.4305 99.9937 m F 162.8443 99.9937 m F 0 G 0.3 w 10 M 170.4477 122.3863 m S 170.4477 137.3147 m S 170.4477 92.5295 m S 170.4477 107.4579 m S 170.4477 107.4579 m S 170.4477 122.3863 m S 0 g 1 w 4 M 41.1893 85.0653 m F 71.6031 85.0653 m F 86.8099 85.0653 m F 117.2237 85.0653 m F 132.4305 85.0653 m F 162.8443 85.0653 m F u 0 G 0.3 w 10 M 48.7927 92.5295 m S 48.7927 77.601 m S 33.5859 77.601 m S 33.5859 92.5295 m S 41.1893 85.0653 m S U u 79.2065 62.6726 m S 79.2065 47.7442 m S 63.9996 47.7442 m S 63.9996 62.6726 m S 71.6031 55.2084 m S U u 63.9996 77.601 m S 63.9996 62.6726 m S 48.7927 62.6726 m S 48.7927 77.601 m S 56.3962 70.1368 m S U u 63.9996 92.5295 m S 63.9996 77.601 m S 48.7927 77.601 m S 48.7927 92.5295 m S 56.3962 85.0653 m S U u 79.2065 92.5295 m S 79.2065 77.601 m S 63.9996 77.601 m S 63.9996 92.5295 m S 71.6031 85.0653 m S U u 79.2065 77.601 m S 79.2065 62.6726 m S 63.9996 62.6726 m S 63.9996 77.601 m S 71.6031 70.1368 m S U u 63.9996 62.6726 m S 63.9996 47.7442 m S 48.7927 47.7442 m S 48.7927 62.6726 m S 56.3962 55.2084 m S U u 48.7927 62.6726 m S 48.7927 47.7442 m S 33.5859 47.7442 m S 33.5859 62.6726 m S 41.1893 55.2084 m S U u 48.7927 77.601 m S 48.7927 62.6726 m S 33.5859 62.6726 m S 33.5859 77.601 m S 41.1893 70.1368 m S U 0 g 1 w 4 M 41.1893 85.0653 m F 71.6031 85.0653 m F 41.1893 55.2084 m F 71.6031 55.2084 m F u 0 G 0.3 w 10 M 94.4134 92.5295 m S 94.4134 77.601 m S 79.2065 77.601 m S 79.2065 92.5295 m S 86.8099 85.0653 m S U u 124.8271 62.6726 m S 124.8271 47.7442 m S 109.6203 47.7442 m S 109.6203 62.6726 m S 117.2237 55.2084 m S U u 109.6203 77.601 m S 109.6203 62.6726 m S 94.4134 62.6726 m S 94.4134 77.601 m S 102.0168 70.1368 m S U u 109.6203 92.5295 m S 109.6203 77.601 m S 94.4134 77.601 m S 94.4134 92.5295 m S 102.0168 85.0653 m S U u 124.8271 92.5295 m S 124.8271 77.601 m S 109.6203 77.601 m S 109.6203 92.5295 m S 117.2237 85.0653 m S U u 124.8271 77.601 m S 124.8271 62.6726 m S 109.6203 62.6726 m S 109.6203 77.601 m S 117.2237 70.1368 m S U u 109.6203 62.6726 m S 109.6203 47.7442 m S 94.4134 47.7442 m S 94.4134 62.6726 m S 102.0168 55.2084 m S U u 94.4134 62.6726 m S 94.4134 47.7442 m S 79.2065 47.7442 m S 79.2065 62.6726 m S 86.8099 55.2084 m S U u 94.4134 77.601 m S 94.4134 62.6726 m S 79.2065 62.6726 m S 79.2065 77.601 m S 86.8099 70.1368 m S U 0 g 1 w 4 M 86.8099 85.0653 m F 117.2237 85.0653 m F 86.8099 55.2084 m F 117.2237 55.2084 m F u 0 G 0.3 w 10 M 140.034 92.5295 m S 140.034 77.601 m S 124.8271 77.601 m S 124.8271 92.5295 m S 132.4305 85.0653 m S U u 170.4477 62.6726 m S 170.4477 47.7442 m S 155.2409 47.7442 m S 155.2409 62.6726 m S 162.8443 55.2084 m S U u 155.2409 77.601 m S 155.2409 62.6726 m S 140.034 62.6726 m S 140.034 77.601 m S 147.6374 70.1368 m S U u 155.2409 92.5295 m S 155.2409 77.601 m S 140.034 77.601 m S 140.034 92.5295 m S 147.6374 85.0653 m S U u 170.4477 92.5295 m S 170.4477 77.601 m S 155.2409 77.601 m S 155.2409 92.5295 m S 162.8443 85.0653 m S U u 170.4477 77.601 m S 170.4477 62.6726 m S 155.2409 62.6726 m S 155.2409 77.601 m S 162.8443 70.1368 m S U u 155.2409 62.6726 m S 155.2409 47.7442 m S 140.034 47.7442 m S 140.034 62.6726 m S 147.6374 55.2084 m S U u 140.034 62.6726 m S 140.034 47.7442 m S 124.8271 47.7442 m S 124.8271 62.6726 m S 132.4305 55.2084 m S U u 140.034 77.601 m S 140.034 62.6726 m S 124.8271 62.6726 m S 124.8271 77.601 m S 132.4305 70.1368 m S U 0 g 1 w 4 M 132.4305 85.0653 m F 162.8443 85.0653 m F 132.4305 55.2084 m F 162.8443 55.2084 m F 0 G 0.3 w 10 M 170.4477 77.601 m S 170.4477 92.5295 m S 170.4477 47.7442 m S 170.4477 62.6726 m S 170.4477 62.6726 m S 170.4477 77.601 m S 48.7927 47.7442 m S 33.5859 47.7442 m S 63.9996 47.7442 m S 48.7927 47.7442 m S 79.2065 47.7442 m S 63.9996 47.7442 m S 94.4134 47.7442 m S 79.2065 47.7442 m S 109.6203 47.7442 m S 94.4134 47.7442 m S 124.8271 47.7442 m S 109.6203 47.7442 m S 140.034 47.7442 m S 124.8271 47.7442 m S 155.2409 47.7442 m S 140.034 47.7442 m S 170.4477 47.7442 m S 155.2409 47.7442 m S 170.4477 47.7442 m S 1 w 4 M 41.1893 159.7074 m 162.8443 159.7074 l S 41.1893 114.9221 m 162.8443 114.9221 l S 41.1893 70.1368 m 162.8443 70.1368 l S 56.3962 174.6358 m 56.3962 55.2084 l S 102.0168 174.6358 m 102.0168 55.2084 l S 147.6374 174.6358 m 147.6374 55.2084 l S 0.3 w 10 M 140.034 182.1 m S 140.034 167.1716 m S 124.8271 167.1716 m S 124.8271 182.1 m S 132.4305 174.6358 m S u 170.4477 152.2431 m S 170.4477 137.3147 m S 155.2409 137.3147 m S 155.2409 152.2431 m S 162.8443 144.7789 m S U 155.2409 167.1716 m S 155.2409 152.2431 m S 140.034 152.2431 m S 140.034 167.1716 m S 147.6374 159.7074 m S 155.2409 182.1 m S 155.2409 167.1716 m S 140.034 167.1716 m S 140.034 182.1 m S 147.6374 174.6358 m S 170.4477 182.1 m S 170.4477 167.1716 m S 155.2409 167.1716 m S 155.2409 182.1 m S 162.8443 174.6358 m S 170.4477 167.1716 m S 170.4477 152.2431 m S 155.2409 152.2431 m S 155.2409 167.1716 m S 162.8443 159.7074 m S u 155.2409 152.2431 m S 155.2409 137.3147 m S 140.034 137.3147 m S 140.034 152.2431 m S 147.6374 144.7789 m S U u 140.034 152.2431 m S 140.034 137.3147 m S 124.8271 137.3147 m S 124.8271 152.2431 m S 132.4305 144.7789 m S U 140.034 167.1716 m S 140.034 152.2431 m S 124.8271 152.2431 m S 124.8271 167.1716 m S 132.4305 159.7074 m S 0 g 1 w 4 M 132.4305 174.6358 m F 162.8443 174.6358 m F 132.4305 144.7789 m F 162.8443 144.7789 m F 0 G 0.3 w 10 M 185.6546 182.1 m S 185.6546 167.1716 m S 170.4477 167.1716 m S 170.4477 182.1 m S 178.0511 174.6358 m S u 216.0684 152.2431 m S 216.0684 137.3147 m S 200.8615 137.3147 m S 200.8615 152.2431 m S 208.4649 144.7789 m S U 200.8615 167.1716 m S 200.8615 152.2431 m S 185.6546 152.2431 m S 185.6546 167.1716 m S 193.2581 159.7074 m S 200.8615 182.1 m S 200.8615 167.1716 m S 185.6546 167.1716 m S 185.6546 182.1 m S 193.2581 174.6358 m S u 216.0684 182.1 m S 216.0684 167.1716 m S 200.8615 167.1716 m S 200.8615 182.1 m S 208.4649 174.6358 m S U u 216.0684 167.1716 m S 216.0684 152.2431 m S 200.8615 152.2431 m S 200.8615 167.1716 m S 208.4649 159.7074 m S U u 200.8615 152.2431 m S 200.8615 137.3147 m S 185.6546 137.3147 m S 185.6546 152.2431 m S 193.2581 144.7789 m S U u 185.6546 152.2431 m S 185.6546 137.3147 m S 170.4477 137.3147 m S 170.4477 152.2431 m S 178.0511 144.7789 m S U 185.6546 167.1716 m S 185.6546 152.2431 m S 170.4477 152.2431 m S 170.4477 167.1716 m S 178.0511 159.7074 m S 0 g 1 w 4 M 178.0511 174.6358 m F 208.4649 174.6358 m F 178.0511 144.7789 m F 208.4649 144.7789 m F u 0 G 0.3 w 10 M 231.2752 182.1 m S 231.2752 167.1716 m S 216.0684 167.1716 m S 216.0684 182.1 m S 223.6717 174.6358 m S U u 261.689 152.2431 m S 261.689 137.3147 m S 246.4821 137.3147 m S 246.4821 152.2431 m S 254.0855 144.7789 m S U u 246.4821 167.1716 m S 246.4821 152.2431 m S 231.2752 152.2431 m S 231.2752 167.1716 m S 238.8787 159.7074 m S U u 246.4821 182.1 m S 246.4821 167.1716 m S 231.2752 167.1716 m S 231.2752 182.1 m S 238.8787 174.6358 m S U u 261.689 182.1 m S 261.689 167.1716 m S 246.4821 167.1716 m S 246.4821 182.1 m S 254.0855 174.6358 m S U u 261.689 167.1716 m S 261.689 152.2431 m S 246.4821 152.2431 m S 246.4821 167.1716 m S 254.0855 159.7074 m S U u 246.4821 152.2431 m S 246.4821 137.3147 m S 231.2752 137.3147 m S 231.2752 152.2431 m S 238.8787 144.7789 m S U u 231.2752 152.2431 m S 231.2752 137.3147 m S 216.0684 137.3147 m S 216.0684 152.2431 m S 223.6717 144.7789 m S U u 231.2752 167.1716 m S 231.2752 152.2431 m S 216.0684 152.2431 m S 216.0684 167.1716 m S 223.6717 159.7074 m S U 0 g 1 w 4 M 223.6717 174.6358 m F 254.0855 174.6358 m F 223.6717 144.7789 m F 254.0855 144.7789 m F 0 G 0.3 w 10 M 261.689 167.1716 m S 261.689 182.1 m S 261.689 137.3147 m S 261.689 152.2431 m S 261.689 152.2431 m S 261.689 167.1716 m S u 140.034 137.3147 m S 140.034 122.3863 m S 124.8271 122.3863 m S 124.8271 137.3147 m S 132.4305 129.8505 m S U u 170.4477 107.4579 m S 170.4477 92.5295 m S 155.2409 92.5295 m S 155.2409 107.4579 m S 162.8443 99.9937 m S U u 155.2409 122.3863 m S 155.2409 107.4579 m S 140.034 107.4579 m S 140.034 122.3863 m S 147.6374 114.9221 m S U u 155.2409 137.3147 m S 155.2409 122.3863 m S 140.034 122.3863 m S 140.034 137.3147 m S 147.6374 129.8505 m S U u 170.4477 137.3147 m S 170.4477 122.3863 m S 155.2409 122.3863 m S 155.2409 137.3147 m S 162.8443 129.8505 m S U u 170.4477 122.3863 m S 170.4477 107.4579 m S 155.2409 107.4579 m S 155.2409 122.3863 m S 162.8443 114.9221 m S U u 155.2409 107.4579 m S 155.2409 92.5295 m S 140.034 92.5295 m S 140.034 107.4579 m S 147.6374 99.9937 m S U u 140.034 107.4579 m S 140.034 92.5295 m S 124.8271 92.5295 m S 124.8271 107.4579 m S 132.4305 99.9937 m S U u 140.034 122.3863 m S 140.034 107.4579 m S 124.8271 107.4579 m S 124.8271 122.3863 m S 132.4305 114.9221 m S U 0 g 1 w 4 M 132.4305 129.8505 m F 162.8443 129.8505 m F 132.4305 99.9937 m F 162.8443 99.9937 m F u 0 G 0.3 w 10 M 185.6546 137.3147 m S 185.6546 122.3863 m S 170.4477 122.3863 m S 170.4477 137.3147 m S 178.0511 129.8505 m S U u 216.0684 107.4579 m S 216.0684 92.5295 m S 200.8615 92.5295 m S 200.8615 107.4579 m S 208.4649 99.9937 m S U u 200.8615 122.3863 m S 200.8615 107.4579 m S 185.6546 107.4579 m S 185.6546 122.3863 m S 193.2581 114.9221 m S U u 200.8615 137.3147 m S 200.8615 122.3863 m S 185.6546 122.3863 m S 185.6546 137.3147 m S 193.2581 129.8505 m S U u 216.0684 137.3147 m S 216.0684 122.3863 m S 200.8615 122.3863 m S 200.8615 137.3147 m S 208.4649 129.8505 m S U u 216.0684 122.3863 m S 216.0684 107.4579 m S 200.8615 107.4579 m S 200.8615 122.3863 m S 208.4649 114.9221 m S U u 200.8615 107.4579 m S 200.8615 92.5295 m S 185.6546 92.5295 m S 185.6546 107.4579 m S 193.2581 99.9937 m S U u 185.6546 107.4579 m S 185.6546 92.5295 m S 170.4477 92.5295 m S 170.4477 107.4579 m S 178.0511 99.9937 m S U u 185.6546 122.3863 m S 185.6546 107.4579 m S 170.4477 107.4579 m S 170.4477 122.3863 m S 178.0511 114.9221 m S U 0 g 1 w 4 M 178.0511 129.8505 m F 208.4649 129.8505 m F 178.0511 99.9937 m F 208.4649 99.9937 m F u 0 G 0.3 w 10 M 231.2752 137.3147 m S 231.2752 122.3863 m S 216.0684 122.3863 m S 216.0684 137.3147 m S 223.6717 129.8505 m S U u 261.689 107.4579 m S 261.689 92.5295 m S 246.4821 92.5295 m S 246.4821 107.4579 m S 254.0855 99.9937 m S U u 246.4821 122.3863 m S 246.4821 107.4579 m S 231.2752 107.4579 m S 231.2752 122.3863 m S 238.8787 114.9221 m S U u 246.4821 137.3147 m S 246.4821 122.3863 m S 231.2752 122.3863 m S 231.2752 137.3147 m S 238.8787 129.8505 m S U u 261.689 137.3147 m S 261.689 122.3863 m S 246.4821 122.3863 m S 246.4821 137.3147 m S 254.0855 129.8505 m S U u 261.689 122.3863 m S 261.689 107.4579 m S 246.4821 107.4579 m S 246.4821 122.3863 m S 254.0855 114.9221 m S U u 246.4821 107.4579 m S 246.4821 92.5295 m S 231.2752 92.5295 m S 231.2752 107.4579 m S 238.8787 99.9937 m S U u 231.2752 107.4579 m S 231.2752 92.5295 m S 216.0684 92.5295 m S 216.0684 107.4579 m S 223.6717 99.9937 m S U u 231.2752 122.3863 m S 231.2752 107.4579 m S 216.0684 107.4579 m S 216.0684 122.3863 m S 223.6717 114.9221 m S U 0 g 1 w 4 M 223.6717 129.8505 m F 254.0855 129.8505 m F 223.6717 99.9937 m F 254.0855 99.9937 m F 0 G 0.3 w 10 M 261.689 122.3863 m S 261.689 137.3147 m S 261.689 92.5295 m S 261.689 107.4579 m S 261.689 107.4579 m S 261.689 122.3863 m S 0 g 1 w 4 M 132.4305 85.0653 m F 162.8443 85.0653 m F 178.0511 85.0653 m F 208.4649 85.0653 m F 223.6717 85.0653 m F 254.0855 85.0653 m F u 0 G 0.3 w 10 M 140.034 92.5295 m S 140.034 77.601 m S 124.8271 77.601 m S 124.8271 92.5295 m S 132.4305 85.0653 m S U u 170.4477 62.6726 m S 170.4477 47.7442 m S 155.2409 47.7442 m S 155.2409 62.6726 m S 162.8443 55.2084 m S U u 155.2409 77.601 m S 155.2409 62.6726 m S 140.034 62.6726 m S 140.034 77.601 m S 147.6374 70.1368 m S U u 155.2409 92.5295 m S 155.2409 77.601 m S 140.034 77.601 m S 140.034 92.5295 m S 147.6374 85.0653 m S U u 170.4477 92.5295 m S 170.4477 77.601 m S 155.2409 77.601 m S 155.2409 92.5295 m S 162.8443 85.0653 m S U u 170.4477 77.601 m S 170.4477 62.6726 m S 155.2409 62.6726 m S 155.2409 77.601 m S 162.8443 70.1368 m S U u 155.2409 62.6726 m S 155.2409 47.7442 m S 140.034 47.7442 m S 140.034 62.6726 m S 147.6374 55.2084 m S U u 140.034 62.6726 m S 140.034 47.7442 m S 124.8271 47.7442 m S 124.8271 62.6726 m S 132.4305 55.2084 m S U u 140.034 77.601 m S 140.034 62.6726 m S 124.8271 62.6726 m S 124.8271 77.601 m S 132.4305 70.1368 m S U 0 g 1 w 4 M 132.4305 85.0653 m F 162.8443 85.0653 m F 132.4305 55.2084 m F 162.8443 55.2084 m F u 0 G 0.3 w 10 M 185.6546 92.5295 m S 185.6546 77.601 m S 170.4477 77.601 m S 170.4477 92.5295 m S 178.0511 85.0653 m S U u 216.0684 62.6726 m S 216.0684 47.7442 m S 200.8615 47.7442 m S 200.8615 62.6726 m S 208.4649 55.2084 m S U u 200.8615 77.601 m S 200.8615 62.6726 m S 185.6546 62.6726 m S 185.6546 77.601 m S 193.2581 70.1368 m S U u 200.8615 92.5295 m S 200.8615 77.601 m S 185.6546 77.601 m S 185.6546 92.5295 m S 193.2581 85.0653 m S U u 216.0684 92.5295 m S 216.0684 77.601 m S 200.8615 77.601 m S 200.8615 92.5295 m S 208.4649 85.0653 m S U u 216.0684 77.601 m S 216.0684 62.6726 m S 200.8615 62.6726 m S 200.8615 77.601 m S 208.4649 70.1368 m S U u 200.8615 62.6726 m S 200.8615 47.7442 m S 185.6546 47.7442 m S 185.6546 62.6726 m S 193.2581 55.2084 m S U u 185.6546 62.6726 m S 185.6546 47.7442 m S 170.4477 47.7442 m S 170.4477 62.6726 m S 178.0511 55.2084 m S U u 185.6546 77.601 m S 185.6546 62.6726 m S 170.4477 62.6726 m S 170.4477 77.601 m S 178.0511 70.1368 m S U 0 g 1 w 4 M 178.0511 85.0653 m F 208.4649 85.0653 m F 178.0511 55.2084 m F 208.4649 55.2084 m F u 0 G 0.3 w 10 M 231.2752 92.5295 m S 231.2752 77.601 m S 216.0684 77.601 m S 216.0684 92.5295 m S 223.6717 85.0653 m S U u 261.689 62.6726 m S 261.689 47.7442 m S 246.4821 47.7442 m S 246.4821 62.6726 m S 254.0855 55.2084 m S U u 246.4821 77.601 m S 246.4821 62.6726 m S 231.2752 62.6726 m S 231.2752 77.601 m S 238.8787 70.1368 m S U u 246.4821 92.5295 m S 246.4821 77.601 m S 231.2752 77.601 m S 231.2752 92.5295 m S 238.8787 85.0653 m S U u 261.689 92.5295 m S 261.689 77.601 m S 246.4821 77.601 m S 246.4821 92.5295 m S 254.0855 85.0653 m S U u 261.689 77.601 m S 261.689 62.6726 m S 246.4821 62.6726 m S 246.4821 77.601 m S 254.0855 70.1368 m S U u 246.4821 62.6726 m S 246.4821 47.7442 m S 231.2752 47.7442 m S 231.2752 62.6726 m S 238.8787 55.2084 m S U u 231.2752 62.6726 m S 231.2752 47.7442 m S 216.0684 47.7442 m S 216.0684 62.6726 m S 223.6717 55.2084 m S U u 231.2752 77.601 m S 231.2752 62.6726 m S 216.0684 62.6726 m S 216.0684 77.601 m S 223.6717 70.1368 m S U 0 g 1 w 4 M 223.6717 85.0653 m F 254.0855 85.0653 m F 223.6717 55.2084 m F 254.0855 55.2084 m F 0 G 0.3 w 10 M 261.689 77.601 m S 261.689 92.5295 m S 261.689 47.7442 m S 261.689 62.6726 m S 261.689 62.6726 m S 261.689 77.601 m S 140.034 47.7442 m S 124.8271 47.7442 m S 155.2409 47.7442 m S 140.034 47.7442 m S 170.4477 47.7442 m S 155.2409 47.7442 m S 185.6546 47.7442 m S 170.4477 47.7442 m S 200.8615 47.7442 m S 185.6546 47.7442 m S 216.0684 47.7442 m S 200.8615 47.7442 m S 231.2752 47.7442 m S 216.0684 47.7442 m S 246.4821 47.7442 m S 231.2752 47.7442 m S 261.689 47.7442 m S 246.4821 47.7442 m S 261.689 47.7442 m S 1 w 4 M 132.4305 159.7074 m 254.0855 159.7074 l S 132.4305 114.9221 m 254.0855 114.9221 l S 132.4305 70.1368 m 254.0855 70.1368 l S 147.6374 174.6358 m 147.6374 55.2084 l S 193.2581 174.6358 m 193.2581 55.2084 l S 238.8787 174.6358 m 238.8787 55.2084 l S 0.3 w 162.8443 234.3495 m 223.6717 234.3495 l 223.6717 174.6358 l 162.8443 174.6358 l 162.8443 234.3495 l s 71.6031 144.7789 m 132.4305 144.7789 l 132.4305 85.0653 l 71.6031 85.0653 l 71.6031 144.7789 l s u u 0 g 1 w /_Times-Roman 12 14.5 0 0 z [1 0 0 1 175 238.5]e (\65)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 153 216]e (\65)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 215 253.5]e (\67)t T U U 1 g 0 G 0.5 w 201.6583 259.7431 m 194.9631 256.3282 L B 194.9631 256.3282 m 201.7059 253.243 L 201.6583 259.7431 L 194.9631 256.3282 L b 231.3488 259.757 m 238.0369 256.3282 L B 238.0369 256.3282 m 231.2877 253.2571 L 231.3488 259.757 L 238.0369 256.3282 L b 0.3 w 200.8615 256.7421 m 208 256.5 l S 231.2752 256.7421 m 224 256.5 l S 10 M 168.88 241.2491 m S 168.88 241.2491 m S 168.88 241.2491 m S 168.88 241.2491 m S 1 g 0.5 w 4 M 169.6768 244.25 m 162.9815 240.8351 L B 162.9815 240.8351 m 169.7243 237.75 L 169.6768 244.25 L 162.9815 240.8351 L B 0.3 w 10 M 186.2567 241.2351 m S 186.2567 241.2351 m S 186.2567 241.2351 m S 186.2567 241.2351 m S 1 g 0.5 w 4 M 186.3303 244.25 m 193.0185 240.8212 L B 193.0185 240.8212 m 186.2692 237.75 L 186.3303 244.25 L 193.0185 240.8212 L B 0.3 w 10 M 155.8029 211.405 m S 156.0839 196.2007 m S 155.8029 211.405 m S 156.0839 196.2007 m S 155.8029 211.405 m S 155.8029 211.405 m S 155.8029 211.405 m S 156.0839 196.2007 m S 155.8029 211.405 m S 156.0839 196.2007 m S 155.5219 226.6093 m S 155.5219 226.6093 m S 155.5219 226.6093 m S 155.8029 211.405 m S 155.5219 226.6093 m S 155.8029 211.405 m S 156.0892 227.222 m S 156.0892 227.222 m S 156.0892 227.222 m S 156.0892 227.222 m S 1 g 0.5 w 4 M 153.0735 227.2399 m 156.3781 233.9903 L B 156.3781 233.9903 m 159.5735 227.2989 L 153.0735 227.2399 L 156.3781 233.9903 L B 0.3 w 10 M 155.2409 47.7442 m S 155.2409 47.7442 m S 140.034 47.7442 m S 140.034 47.7442 m S 140.034 47.7442 m S 155.2409 47.7442 m S 140.034 47.7442 m S 155.2409 47.7442 m S 155.2409 47.7442 m S 155.2409 47.7442 m S 140.034 47.7442 m S 140.034 47.7442 m S 140.034 47.7442 m S 155.2409 47.7442 m S 140.034 47.7442 m S 155.2409 47.7442 m S u u 0 g 1 w 4 M /_Times-Roman 12 14.5 0 0 z [1 0 0 1 142.0168 33.5]e (\(b\))t T U U 0 G 0.3 w 10 M 140.034 167.1716 m S 0 g 1 w 4 M 140.034 167.1716 m F 0 G 0.3 w 10 M 140.034 167.1716 m S 140.034 167.1716 m S 140.034 167.1716 m S 0 g 1 w 4 M 140.034 167.1716 m F 0 G 0.3 w 10 M 140.034 167.1716 m S 140.034 167.1716 m S 140.034 167.1716 m S 0 g 1 w 4 M 140.034 167.1716 m F 0 G 0.3 w 10 M 140.034 167.1716 m S 140.034 167.1716 m S 155.2409 197.0284 m S 0 g 1 w 4 M 155.2409 197.0284 m F 0 G 0.3 w 10 M 155.2409 197.0284 m S 155.2409 197.0284 m S 155.2409 197.0284 m S 0 g 1 w 4 M 155.2409 197.0284 m F 0 G 0.3 w 10 M 155.2409 197.0284 m S 155.2409 197.0284 m S 1 g 1 w 4 M 149.2305 197.0284 m 149.2305 193.8066 151.9215 191.1948 155.2409 191.1948 c 158.5603 191.1948 161.2513 193.8066 161.2513 197.0284 c F 161.2513 197.0284 m 161.2513 200.2502 158.5603 202.862 155.2409 202.862 c 151.9215 202.862 149.2305 200.2502 149.2305 197.0284 c F 155.2409 197.0284 m F 0 G 0.3 w 10 M 155.2409 197.0284 m S 0 g 1 w 4 M 155.2409 197.0284 m F 0 G 0.3 w 10 M 155.2409 197.0284 m S 155.2409 197.0284 m S 0 g 1 w 4 M 154.1558 195.9605 m 154.1558 192.3834 L 156.326 192.3834 L 156.326 195.9605 L 159.9116 195.9493 L 159.9116 198.1077 L 156.326 198.0966 L 156.326 201.6737 L 154.1558 201.6737 L 154.1558 198.0966 L 150.5702 198.1077 L 150.5702 195.9493 L 154.1558 195.9605 L f 0 G 0.3 w 10 M 155.2409 167.1716 m S 0 g 1 w 4 M 155.2409 167.1716 m F 0 G 0.3 w 10 M 155.2409 167.1716 m S 155.2409 167.1716 m S 155.2409 167.1716 m S 0 g 1 w 4 M 155.2409 167.1716 m F 0 G 0.3 w 10 M 155.2409 167.1716 m S 155.2409 167.1716 m S 155.2409 167.1716 m S 0 g 1 w 4 M 155.2409 167.1716 m F 0 G 0.3 w 10 M 155.2409 167.1716 m S 155.2409 167.1716 m S 185.6546 167.1716 m S 0 g 1 w 4 M 185.6546 167.1716 m F 0 G 0.3 w 10 M 185.6546 167.1716 m S 185.6546 167.1716 m S 185.6546 167.1716 m S 0 g 1 w 4 M 185.6546 167.1716 m F 0 G 0.3 w 10 M 185.6546 167.1716 m S 185.6546 167.1716 m S 185.6546 167.1716 m S 0 g 1 w 4 M 185.6546 167.1716 m F 0 G 0.3 w 10 M 185.6546 167.1716 m S 185.6546 167.1716 m S 140.034 197.0284 m S 0 g 1 w 4 M 140.034 197.0284 m F 0 G 0.3 w 10 M 140.034 197.0284 m S 140.034 197.0284 m S 140.034 197.0284 m S 0 g 1 w 4 M 140.034 197.0284 m F 0 G 0.3 w 10 M 140.034 197.0284 m S 140.034 197.0284 m S 140.034 197.0284 m S 0 g 1 w 4 M 140.034 197.0284 m F 0 G 0.3 w 10 M 140.034 197.0284 m S 140.034 197.0284 m S 109.6203 197.0284 m S 0 g 1 w 4 M 109.6203 197.0284 m F 0 G 0.3 w 10 M 109.6203 197.0284 m S 109.6203 197.0284 m S 109.6203 197.0284 m S 0 g 1 w 4 M 109.6203 197.0284 m F 0 G 0.3 w 10 M 109.6203 197.0284 m S 109.6203 197.0284 m S 109.6203 197.0284 m S 0 g 1 w 4 M 109.6203 197.0284 m F 0 G 0.3 w 10 M 109.6203 197.0284 m S 109.6203 197.0284 m S 124.8271 182.1 m S 0 g 1 w 4 M 124.8271 182.1 m F 0 G 0.3 w 10 M 124.8271 182.1 m S 124.8271 182.1 m S 124.8271 182.1 m S 0 g 1 w 4 M 124.8271 182.1 m F 0 G 0.3 w 10 M 124.8271 182.1 m S 124.8271 182.1 m S 124.8271 182.1 m S 0 g 1 w 4 M 124.8271 182.1 m F 0 G 0.3 w 10 M 124.8271 182.1 m S 124.8271 182.1 m S 109.6203 167.1716 m S 0 g 1 w 4 M 109.6203 167.1716 m F 0 G 0.3 w 10 M 109.6203 167.1716 m S 109.6203 167.1716 m S 109.6203 167.1716 m S 0 g 1 w 4 M 109.6203 167.1716 m F 0 G 0.3 w 10 M 109.6203 167.1716 m S 109.6203 167.1716 m S 109.6203 167.1716 m S 0 g 1 w 4 M 109.6203 167.1716 m F 0 G 0.3 w 10 M 109.6203 167.1716 m S 109.6203 167.1716 m S 170.4477 182.1 m S 0 g 1 w 4 M 170.4477 182.1 m F 0 G 0.3 w 10 M 170.4477 182.1 m S 0 g 1 w 4 M 170.4477 182.1 m F 0 G 0.3 w 10 M 170.4477 182.1 m S 0 g 1 w 4 M 170.4477 182.1 m F 0 G 0.3 w 10 M 170.4477 182.1 m S 0 g 1 w 4 M 170.4477 182.1 m F 0 G 0.3 w 10 M 185.6546 197.0284 m S 0 g 1 w 4 M 185.6546 197.0284 m F 0 G 0.3 w 10 M 185.6546 197.0284 m S 0 g 1 w 4 M 185.6546 197.0284 m F 0 G 0.3 w 10 M 185.6546 197.0284 m S 0 g 1 w 4 M 185.6546 197.0284 m F 0 G 0.3 w 10 M 185.6546 197.0284 m S 0 g 1 w 4 M 185.6546 197.0284 m F 0 G 0.3 w 10 M 170.4477 197.0284 m S 0 g 1 w 4 M 170.4477 197.0284 m F 0 G 0.3 w 10 M 170.4477 197.0284 m S 0 g 1 w 4 M 170.4477 197.0284 m F 1 g 170.4477 197.0284 m F 0 G 0.3 w 10 M 170.4477 197.0284 m S 0 g 1 w 4 M 170.4477 197.0284 m F 0 G 0.3 w 10 M 170.4477 197.0284 m S 0 g 1 w 4 M 170.4477 197.0284 m F 0 G 0.3 w 10 M 186.5 181.5 m S 0 g 1 w 4 M 186.5 181.5 m F 0 G 0.3 w 10 M 186.5 181.5 m S 0 g 1 w 4 M 186.5 181.5 m F 1 g 180.4896 181.5 m 180.4896 178.2782 183.1806 175.6664 186.5 175.6664 c 189.8194 175.6664 192.5104 178.2782 192.5104 181.5 c F 192.5104 181.5 m 192.5104 184.7218 189.8194 187.3336 186.5 187.3336 c 183.1806 187.3336 180.4896 184.7218 180.4896 181.5 c F 186.5 181.5 m F 0 G 0.3 w 10 M 186.5 181.5 m S 0 g 1 w 4 M 186.5 181.5 m F 0 G 0.3 w 10 M 186.5 181.5 m S 0 g 1 w 4 M 186.5 181.5 m F 185.4149 182.5682 m 181.8293 182.5793 L 181.8293 180.4209 L 185.4149 180.432 L F 187.5851 180.432 m 191.1707 180.4209 L 191.1707 182.5793 L 187.5851 182.5682 L F 181.8293 182.5793 m 191.1707 182.5793 l 191.1707 180.4209 l 181.8293 180.4209 l 181.8293 182.5793 l f 0 G 0.3 w 10 M 169.25 198.25 m S 0 g 1 w 4 M 169.25 198.25 m F 0 G 0.3 w 10 M 169.25 198.25 m S 0 g 1 w 4 M 169.25 198.25 m F 1 g 163.2396 198.25 m 163.2396 195.0282 165.9306 192.4164 169.25 192.4164 c 172.5694 192.4164 175.2604 195.0282 175.2604 198.25 c F 175.2604 198.25 m 175.2604 201.4718 172.5694 204.0836 169.25 204.0836 c 165.9306 204.0836 163.2396 201.4718 163.2396 198.25 c F 169.25 198.25 m F 0 G 0.3 w 10 M 169.25 198.25 m S 0 g 1 w 4 M 169.25 198.25 m F 0 G 0.3 w 10 M 169.25 198.25 m S 0 g 1 w 4 M 169.25 198.25 m F 168.1649 199.3182 m 164.5793 199.3293 L 164.5793 197.1709 L 168.1649 197.182 L F 170.3351 197.182 m 173.9207 197.1709 L 173.9207 199.3293 L 170.3351 199.3182 L F 164.5793 199.3293 m 173.9207 199.3293 l 173.9207 197.1709 l 164.5793 197.1709 l 164.5793 199.3293 l f 0 G 0.3 w 10 M 184.25 193.25 m S 0 g 1 w 4 M 184.25 193.25 m F 0 G 0.3 w 10 M 184.25 193.25 m S 0 g 1 w 4 M 184.25 193.25 m F 1 g 178.2396 193.25 m 178.2396 190.0282 180.9306 187.4164 184.25 187.4164 c 187.5694 187.4164 190.2604 190.0282 190.2604 193.25 c F 190.2604 193.25 m 190.2604 196.4718 187.5694 199.0836 184.25 199.0836 c 180.9306 199.0836 178.2396 196.4718 178.2396 193.25 c F 184.25 193.25 m F 0 G 0.3 w 10 M 184.25 193.25 m S 0 g 1 w 4 M 184.25 193.25 m F 0 G 0.3 w 10 M 184.25 193.25 m S 0 g 1 w 4 M 184.25 193.25 m F 183.1649 194.3182 m 179.5793 194.3293 L 179.5793 192.1709 L 183.1649 192.182 L F 185.3351 192.182 m 188.9207 192.1709 L 188.9207 194.3293 L 185.3351 194.3182 L F 179.5793 194.3293 m 188.9207 194.3293 l 188.9207 192.1709 l 179.5793 192.1709 l 179.5793 194.3293 l f 0 G 0.3 w 10 M 171.5 184.75 m S 0 g 1 w 4 M 171.5 184.75 m F 0 G 0.3 w 10 M 171.5 184.75 m S 0 g 1 w 4 M 171.5 184.75 m F 1 g 165.4896 184.75 m 165.4896 181.5282 168.1806 178.9164 171.5 178.9164 c 174.8194 178.9164 177.5104 181.5282 177.5104 184.75 c F 177.5104 184.75 m 177.5104 187.9718 174.8194 190.5836 171.5 190.5836 c 168.1806 190.5836 165.4896 187.9718 165.4896 184.75 c F 171.5 184.75 m F 0 G 0.3 w 10 M 171.5 184.75 m S 0 g 1 w 4 M 171.5 184.75 m F 0 G 0.3 w 10 M 171.5 184.75 m S 0 g 1 w 4 M 171.5 184.75 m F 170.4149 185.8182 m 166.8293 185.8293 L 166.8293 183.6709 L 170.4149 183.682 L F 172.5851 183.682 m 176.1707 183.6709 L 176.1707 185.8293 L 172.5851 185.8182 L F 166.8293 185.8293 m 176.1707 185.8293 l 176.1707 183.6709 l 166.8293 183.6709 l 166.8293 185.8293 l f 0 G 0.3 w 10 M 135.875 192.625 m S 0 g 1 w 4 M 135.875 192.625 m F 0 G 0.3 w 10 M 135.875 192.625 m S 135.875 192.625 m S 135.875 192.625 m S 0 g 1 w 4 M 135.875 192.625 m F 0 G 0.3 w 10 M 135.875 192.625 m S 135.875 192.625 m S 1 g 1 w 4 M 129.8646 192.625 m 129.8646 189.4032 132.5556 186.7914 135.875 186.7914 c 139.1944 186.7914 141.8854 189.4032 141.8854 192.625 c F 141.8854 192.625 m 141.8854 195.8468 139.1944 198.4586 135.875 198.4586 c 132.5556 198.4586 129.8646 195.8468 129.8646 192.625 c F 135.875 192.625 m F 0 G 0.3 w 10 M 135.875 192.625 m S 0 g 1 w 4 M 135.875 192.625 m F 0 G 0.3 w 10 M 135.875 192.625 m S 135.875 192.625 m S 0 g 1 w 4 M 134.7899 191.5571 m 134.7899 187.98 L 136.9601 187.98 L 136.9601 191.5571 L 140.5457 191.5459 L 140.5457 193.7043 L 136.9601 193.6932 L 136.9601 197.2703 L 134.7899 197.2703 L 134.7899 193.6932 L 131.2043 193.7043 L 131.2043 191.5459 L 134.7899 191.5571 L f 0 G 0.3 w 10 M 111.375 197.125 m S 0 g 1 w 4 M 111.375 197.125 m F 0 G 0.3 w 10 M 111.375 197.125 m S 111.375 197.125 m S 111.375 197.125 m S 0 g 1 w 4 M 111.375 197.125 m F 0 G 0.3 w 10 M 111.375 197.125 m S 111.375 197.125 m S 1 g 1 w 4 M 105.3646 197.125 m 105.3646 193.9032 108.0556 191.2914 111.375 191.2914 c 114.6944 191.2914 117.3854 193.9032 117.3854 197.125 c F 117.3854 197.125 m 117.3854 200.3468 114.6944 202.9586 111.375 202.9586 c 108.0556 202.9586 105.3646 200.3468 105.3646 197.125 c F 111.375 197.125 m F 0 G 0.3 w 10 M 111.375 197.125 m S 0 g 1 w 4 M 111.375 197.125 m F 0 G 0.3 w 10 M 111.375 197.125 m S 111.375 197.125 m S 0 g 1 w 4 M 110.2899 196.0571 m 110.2899 192.48 L 112.4601 192.48 L 112.4601 196.0571 L 116.0457 196.0459 L 116.0457 198.2043 L 112.4601 198.1932 L 112.4601 201.7703 L 110.2899 201.7703 L 110.2899 198.1932 L 106.7043 198.2043 L 106.7043 196.0459 L 110.2899 196.0571 L f 0 G 0.3 w 10 M 132.375 167.625 m S 0 g 1 w 4 M 132.375 167.625 m F 0 G 0.3 w 10 M 132.375 167.625 m S 132.375 167.625 m S 132.375 167.625 m S 0 g 1 w 4 M 132.375 167.625 m F 0 G 0.3 w 10 M 132.375 167.625 m S 132.375 167.625 m S 1 g 1 w 4 M 126.3646 167.625 m 126.3646 164.4032 129.0556 161.7914 132.375 161.7914 c 135.6944 161.7914 138.3854 164.4032 138.3854 167.625 c F 138.3854 167.625 m 138.3854 170.8468 135.6944 173.4586 132.375 173.4586 c 129.0556 173.4586 126.3646 170.8468 126.3646 167.625 c F 132.375 167.625 m F 0 G 0.3 w 10 M 132.375 167.625 m S 0 g 1 w 4 M 132.375 167.625 m F 0 G 0.3 w 10 M 132.375 167.625 m S 132.375 167.625 m S 0 g 1 w 4 M 131.2899 166.5571 m 131.2899 162.98 L 133.4601 162.98 L 133.4601 166.5571 L 137.0457 166.5459 L 137.0457 168.7043 L 133.4601 168.6932 L 133.4601 172.2703 L 131.2899 172.2703 L 131.2899 168.6932 L 127.7043 168.7043 L 127.7043 166.5459 L 131.2899 166.5571 L f 0 G 0.3 w 10 M 122.125 186.625 m S 0 g 1 w 4 M 122.125 186.625 m F 0 G 0.3 w 10 M 122.125 186.625 m S 122.125 186.625 m S 122.125 186.625 m S 0 g 1 w 4 M 122.125 186.625 m F 0 G 0.3 w 10 M 122.125 186.625 m S 122.125 186.625 m S 1 g 1 w 4 M 116.1146 186.625 m 116.1146 183.4032 118.8056 180.7914 122.125 180.7914 c 125.4444 180.7914 128.1354 183.4032 128.1354 186.625 c F 128.1354 186.625 m 128.1354 189.8468 125.4444 192.4586 122.125 192.4586 c 118.8056 192.4586 116.1146 189.8468 116.1146 186.625 c F 122.125 186.625 m F 0 G 0.3 w 10 M 122.125 186.625 m S 0 g 1 w 4 M 122.125 186.625 m F 0 G 0.3 w 10 M 122.125 186.625 m S 122.125 186.625 m S 0 g 1 w 4 M 121.0399 185.5571 m 121.0399 181.98 L 123.2101 181.98 L 123.2101 185.5571 L 126.7957 185.5459 L 126.7957 187.7043 L 123.2101 187.6932 L 123.2101 191.2703 L 121.0399 191.2703 L 121.0399 187.6932 L 117.4543 187.7043 L 117.4543 185.5459 L 121.0399 185.5571 L f 0 G 0.3 w 10 M 114.875 172.125 m S 0 g 1 w 4 M 114.875 172.125 m F 0 G 0.3 w 10 M 114.875 172.125 m S 114.875 172.125 m S 114.875 172.125 m S 0 g 1 w 4 M 114.875 172.125 m F 0 G 0.3 w 10 M 114.875 172.125 m S 114.875 172.125 m S 1 g 1 w 4 M 108.8646 172.125 m 108.8646 168.9032 111.5556 166.2914 114.875 166.2914 c 118.1944 166.2914 120.8854 168.9032 120.8854 172.125 c F 120.8854 172.125 m 120.8854 175.3468 118.1944 177.9586 114.875 177.9586 c 111.5556 177.9586 108.8646 175.3468 108.8646 172.125 c F 114.875 172.125 m F 0 G 0.3 w 10 M 114.875 172.125 m S 0 g 1 w 4 M 114.875 172.125 m F 0 G 0.3 w 10 M 114.875 172.125 m S 114.875 172.125 m S 0 g 1 w 4 M 113.7899 171.0571 m 113.7899 167.48 L 115.9601 167.48 L 115.9601 171.0571 L 119.5457 171.0459 L 119.5457 173.2043 L 115.9601 173.1932 L 115.9601 176.7703 L 113.7899 176.7703 L 113.7899 173.1932 L 110.2043 173.2043 L 110.2043 171.0459 L 113.7899 171.0571 L f 0 G 0.3 w 10 M 177.625 168.125 m S 0 g 1 w 4 M 177.625 168.125 m F 0 G 0.3 w 10 M 177.625 168.125 m S 177.625 168.125 m S 177.625 168.125 m S 0 g 1 w 4 M 177.625 168.125 m F 0 G 0.3 w 10 M 177.625 168.125 m S 177.625 168.125 m S 1 g 1 w 4 M 171.6146 168.125 m 171.6146 164.9032 174.3056 162.2914 177.625 162.2914 c 180.9444 162.2914 183.6354 164.9032 183.6354 168.125 c F 183.6354 168.125 m 183.6354 171.3468 180.9444 173.9586 177.625 173.9586 c 174.3056 173.9586 171.6146 171.3468 171.6146 168.125 c F 177.625 168.125 m F 0 G 0.3 w 10 M 177.625 168.125 m S 0 g 1 w 4 M 177.625 168.125 m F 0 G 0.3 w 10 M 177.625 168.125 m S 177.625 168.125 m S 0 g 1 w 4 M 176.5399 167.0571 m 176.5399 163.48 L 178.7101 163.48 L 178.7101 167.0571 L 182.2957 167.0459 L 182.2957 169.2043 L 178.7101 169.1932 L 178.7101 172.7703 L 176.5399 172.7703 L 176.5399 169.1932 L 172.9543 169.2043 L 172.9543 167.0459 L 176.5399 167.0571 L f 0 G 0.3 w 10 M 155.875 172.125 m S 0 g 1 w 4 M 155.875 172.125 m F 0 G 0.3 w 10 M 155.875 172.125 m S 155.875 172.125 m S 155.875 172.125 m S 0 g 1 w 4 M 155.875 172.125 m F 0 G 0.3 w 10 M 155.875 172.125 m S 155.875 172.125 m S 1 g 1 w 4 M 149.8646 172.125 m 149.8646 168.9032 152.5556 166.2914 155.875 166.2914 c 159.1944 166.2914 161.8854 168.9032 161.8854 172.125 c F 161.8854 172.125 m 161.8854 175.3468 159.1944 177.9586 155.875 177.9586 c 152.5556 177.9586 149.8646 175.3468 149.8646 172.125 c F 155.875 172.125 m F 0 G 0.3 w 10 M 155.875 172.125 m S 0 g 1 w 4 M 155.875 172.125 m F 0 G 0.3 w 10 M 155.875 172.125 m S 155.875 172.125 m S 0 g 1 w 4 M 154.7899 171.0571 m 154.7899 167.48 L 156.9601 167.48 L 156.9601 171.0571 L 160.5457 171.0459 L 160.5457 173.2043 L 156.9601 173.1932 L 156.9601 176.7703 L 154.7899 176.7703 L 154.7899 173.1932 L 151.2043 173.2043 L 151.2043 171.0459 L 154.7899 171.0571 L f 0 G 0.3 w 10 M 156.625 242.875 m S 0 g 1 w 4 M 156.625 242.875 m F 0 G 0.3 w 10 M 156.625 242.875 m S 156.625 242.875 m S 156.625 242.875 m S 0 g 1 w 4 M 156.625 242.875 m F 0 G 0.3 w 10 M 156.625 242.875 m S 156.625 242.875 m S 1 g 1 w 4 M 156.625 242.875 m F 0 G 0.3 w 10 M 156.625 242.875 m S 0 g 1 w 4 M 156.625 242.875 m F 0 G 0.3 w 10 M 156.625 242.875 m S 156.625 242.875 m S 210.875 241.375 m S 0 g 1 w 4 M 210.875 241.375 m F 0 G 0.3 w 10 M 210.875 241.375 m S 210.875 241.375 m S 210.875 241.375 m S 0 g 1 w 4 M 210.875 241.375 m F 0 G 0.3 w 10 M 210.875 241.375 m S 210.875 241.375 m S 210.875 241.375 m S 0 g 1 w 4 M 210.875 241.375 m F 0 G 0.3 w 10 M 210.875 241.375 m S 210.875 241.375 m S 232.125 229.625 m S 0 g 1 w 4 M 232.125 229.625 m F 0 G 0.3 w 10 M 232.125 229.625 m S 232.125 229.625 m S 232.125 229.625 m S 0 g 1 w 4 M 232.125 229.625 m F 0 G 0.3 w 10 M 232.125 229.625 m S 232.125 229.625 m S 232.125 229.625 m S 0 g 1 w 4 M 232.125 229.625 m F 0 G 0.3 w 10 M 232.125 229.625 m S 232.125 229.625 m S 231.875 221.625 m S 0 g 1 w 4 M 231.875 221.625 m F 0 G 0.3 w 10 M 231.875 221.625 m S 231.875 221.625 m S 231.875 221.625 m S 0 g 1 w 4 M 231.875 221.625 m F 0 G 0.3 w 10 M 231.875 221.625 m S 231.875 221.625 m S 231.875 221.625 m S 0 g 1 w 4 M 231.875 221.625 m F 0 G 0.3 w 10 M 231.875 221.625 m S 231.875 221.625 m S 199.875 242.875 m S 0 g 1 w 4 M 199.875 242.875 m F 0 G 0.3 w 10 M 199.875 242.875 m S 199.875 242.875 m S 199.875 242.875 m S 0 g 1 w 4 M 199.875 242.875 m F 0 G 0.3 w 10 M 199.875 242.875 m S 199.875 242.875 m S 1 g 1 w 4 M 199.875 242.875 m F 0 G 0.3 w 10 M 199.875 242.875 m S 0 g 1 w 4 M 199.875 242.875 m F 0 G 0.3 w 10 M 199.875 242.875 m S 199.875 242.875 m S 232.375 198.125 m S 0 g 1 w 4 M 232.375 198.125 m F 0 G 0.3 w 10 M 232.375 198.125 m S 232.375 198.125 m S 232.375 198.125 m S 0 g 1 w 4 M 232.375 198.125 m F 0 G 0.3 w 10 M 232.375 198.125 m S 232.375 198.125 m S 232.375 198.125 m S 0 g 1 w 4 M 232.375 198.125 m F 0 G 0.3 w 10 M 232.375 198.125 m S 232.375 198.125 m S 231.375 172.625 m S 0 g 1 w 4 M 231.375 172.625 m F 0 G 0.3 w 10 M 231.375 172.625 m S 231.375 172.625 m S 231.375 172.625 m S 0 g 1 w 4 M 231.375 172.625 m F 0 G 0.3 w 10 M 231.375 172.625 m S 231.375 172.625 m S 231.375 172.625 m S 0 g 1 w 4 M 231.375 172.625 m F 0 G 0.3 w 10 M 231.375 172.625 m S 231.375 172.625 m S 208.625 166.625 m S 0 g 1 w 4 M 208.625 166.625 m F 0 G 0.3 w 10 M 208.625 166.625 m S 208.625 166.625 m S 208.625 166.625 m S 0 g 1 w 4 M 208.625 166.625 m F 0 G 0.3 w 10 M 208.625 166.625 m S 208.625 166.625 m S 208.625 166.625 m S 0 g 1 w 4 M 208.625 166.625 m F 0 G 0.3 w 10 M 208.625 166.625 m S 208.625 166.625 m S 170.4477 226.8852 m S 170.4477 211.9568 m S 170.4477 226.8852 m S 170.4477 211.9568 m S 170.4477 226.8852 m S 170.4477 226.8852 m S 170.4477 211.9568 m S 170.4477 211.9568 m S 170.4477 226.8852 m S 170.4477 211.9568 m S 170.4477 226.8852 m S 185.6546 226.8852 m S 185.6546 211.9568 m S 185.6546 226.8852 m S 185.6546 226.8852 m S 185.6546 211.9568 m S 170.4477 211.9568 m S 170.4477 226.8852 m S 178.0511 219.421 m S 185.6546 226.8852 m S 170.4477 226.8852 m S 0 g 1 w 4 M 178.0511 219.421 m F 0 G 0.3 w 10 M 170.4477 211.9568 m S 185.6546 211.9568 m S 170.4477 211.9568 m S 185.6546 211.9568 m S 170.4477 211.9568 m S 170.4477 211.9568 m S 170.4477 211.9568 m S 185.6546 211.9568 m S 170.4477 211.9568 m S 185.6546 211.9568 m S 170.4477 211.9568 m S 0 g 1 w 4 M 170.4477 211.9568 m F 0 G 0.3 w 10 M 170.4477 211.9568 m S 0 g 1 w 4 M 170.4477 211.9568 m F 0 G 0.3 w 10 M 170.4477 211.9568 m S 0 g 1 w 4 M 170.4477 211.9568 m F 0 G 0.3 w 10 M 170.4477 211.9568 m S 0 g 1 w 4 M 170.4477 211.9568 m F 0 G 0.3 w 10 M 185.6546 226.8852 m S 0 g 1 w 4 M 185.6546 226.8852 m F 0 G 0.3 w 10 M 185.6546 226.8852 m S 0 g 1 w 4 M 185.6546 226.8852 m F 0 G 0.3 w 10 M 185.6546 226.8852 m S 0 g 1 w 4 M 185.6546 226.8852 m F 0 G 0.3 w 10 M 185.6546 226.8852 m S 0 g 1 w 4 M 185.6546 226.8852 m F 0 G 0.3 w 10 M 170.4477 226.8852 m S 0 g 1 w 4 M 170.4477 226.8852 m F 0 G 0.3 w 10 M 170.4477 226.8852 m S 0 g 1 w 4 M 170.4477 226.8852 m F 1 g 170.4477 226.8852 m F 0 G 0.3 w 10 M 170.4477 226.8852 m S 0 g 1 w 4 M 170.4477 226.8852 m F 0 G 0.3 w 10 M 170.4477 226.8852 m S 0 g 1 w 4 M 170.4477 226.8852 m F 0 G 0.3 w 10 M 186.5 211.3568 m S 0 g 1 w 4 M 186.5 211.3568 m F 0 G 0.3 w 10 M 186.5 211.3568 m S 0 g 1 w 4 M 186.5 211.3568 m F 1 g 180.4896 211.3568 m 180.4896 208.135 183.1806 205.5232 186.5 205.5232 c 189.8194 205.5232 192.5104 208.135 192.5104 211.3568 c F 192.5104 211.3568 m 192.5104 214.5786 189.8194 217.1904 186.5 217.1904 c 183.1806 217.1904 180.4896 214.5786 180.4896 211.3568 c F 186.5 211.3568 m F 0 G 0.3 w 10 M 186.5 211.3568 m S 0 g 1 w 4 M 186.5 211.3568 m F 0 G 0.3 w 10 M 186.5 211.3568 m S 0 g 1 w 4 M 186.5 211.3568 m F 185.4149 212.425 m 181.8293 212.4361 L 181.8293 210.2777 L 185.4149 210.2888 L F 187.5851 210.2888 m 191.1707 210.2777 L 191.1707 212.4361 L 187.5851 212.425 L F 181.8293 212.4361 m 191.1707 212.4361 l 191.1707 210.2777 l 181.8293 210.2777 l 181.8293 212.4361 l f 0 G 0.3 w 10 M 169.25 228.1068 m S 0 g 1 w 4 M 169.25 228.1068 m F 0 G 0.3 w 10 M 169.25 228.1068 m S 0 g 1 w 4 M 169.25 228.1068 m F 1 g 163.2396 228.1068 m 163.2396 224.885 165.9306 222.2732 169.25 222.2732 c 172.5694 222.2732 175.2604 224.885 175.2604 228.1068 c F 175.2604 228.1068 m 175.2604 231.3286 172.5694 233.9404 169.25 233.9404 c F 169.25 233.9404 m 165.9306 233.9404 163.2396 231.3286 163.2396 228.1068 c F 169.25 228.1068 m F 0 G 0.3 w 10 M 169.25 228.1068 m S 0 g 1 w 4 M 169.25 228.1068 m F 0 G 0.3 w 10 M 169.25 228.1068 m S 0 g 1 w 4 M 169.25 228.1068 m F 168.1649 229.175 m 164.5793 229.1861 L 164.5793 227.0277 L 168.1649 227.0388 L F 170.3351 227.0388 m 173.9207 227.0277 L 173.9207 229.1861 L 170.3351 229.175 L F 164.5793 229.1861 m 173.9207 229.1861 l 173.9207 227.0277 l 164.5793 227.0277 l 164.5793 229.1861 l f 0 G 0.3 w 10 M 184.25 223.1068 m S 0 g 1 w 4 M 184.25 223.1068 m F 0 G 0.3 w 10 M 184.25 223.1068 m S 0 g 1 w 4 M 184.25 223.1068 m F 1 g 178.2396 223.1068 m 178.2396 219.885 180.9306 217.2732 184.25 217.2732 c 187.5694 217.2732 190.2604 219.885 190.2604 223.1068 c F 190.2604 223.1068 m 190.2604 226.3286 187.5694 228.9404 184.25 228.9404 c 180.9306 228.9404 178.2396 226.3286 178.2396 223.1068 c F 184.25 223.1068 m F 0 G 0.3 w 10 M 184.25 223.1068 m S 0 g 1 w 4 M 184.25 223.1068 m F 0 G 0.3 w 10 M 184.25 223.1068 m S 0 g 1 w 4 M 184.25 223.1068 m F 183.1649 224.175 m 179.5793 224.1861 L 179.5793 222.0277 L 183.1649 222.0388 L F 185.3351 222.0388 m 188.9207 222.0277 L 188.9207 224.1861 L 185.3351 224.175 L F 179.5793 224.1861 m 188.9207 224.1861 l 188.9207 222.0277 l 179.5793 222.0277 l 179.5793 224.1861 l f 0 G 0.3 w 10 M 171.5 214.6068 m S 0 g 1 w 4 M 171.5 214.6068 m F 0 G 0.3 w 10 M 171.5 214.6068 m S 0 g 1 w 4 M 171.5 214.6068 m F 1 g 165.4896 214.6068 m 165.4896 211.385 168.1806 208.7732 171.5 208.7732 c 174.8194 208.7732 177.5104 211.385 177.5104 214.6068 c F 177.5104 214.6068 m 177.5104 217.8286 174.8194 220.4404 171.5 220.4404 c 168.1806 220.4404 165.4896 217.8286 165.4896 214.6068 c F 171.5 214.6068 m F 0 G 0.3 w 10 M 171.5 214.6068 m S 0 g 1 w 4 M 171.5 214.6068 m F 0 G 0.3 w 10 M 171.5 214.6068 m S 0 g 1 w 4 M 171.5 214.6068 m F 170.4149 215.675 m 166.8293 215.6861 L 166.8293 213.5277 L 170.4149 213.5388 L F 172.5851 213.5388 m 176.1707 213.5277 L 176.1707 215.6861 L 172.5851 215.675 L F 166.8293 215.6861 m 176.1707 215.6861 l 176.1707 213.5277 l 166.8293 213.5277 l 166.8293 215.6861 l f 0 G 0.3 w 10 M 200.8615 226.8852 m S 200.8615 211.9568 m S 200.8615 226.8852 m S 200.8615 211.9568 m S 200.8615 226.8852 m S 200.8615 226.8852 m S 200.8615 211.9568 m S 200.8615 211.9568 m S 200.8615 226.8852 m S 200.8615 211.9568 m S 200.8615 226.8852 m S 216.0684 226.8852 m S 216.0684 211.9568 m S 216.0684 226.8852 m S 216.0684 226.8852 m S 216.0684 211.9568 m S 200.8615 211.9568 m S 200.8615 226.8852 m S 208.4649 219.421 m S 216.0684 226.8852 m S 200.8615 226.8852 m S 0 g 1 w 4 M 208.4649 219.421 m F 0 G 0.3 w 10 M 200.8615 211.9568 m S 216.0684 211.9568 m S 200.8615 211.9568 m S 216.0684 211.9568 m S 200.8615 211.9568 m S 200.8615 211.9568 m S 200.8615 211.9568 m S 216.0684 211.9568 m S 200.8615 211.9568 m S 216.0684 211.9568 m S 200.8615 211.9568 m S 0 g 1 w 4 M 200.8615 211.9568 m F 0 G 0.3 w 10 M 200.8615 211.9568 m S 0 g 1 w 4 M 200.8615 211.9568 m F 0 G 0.3 w 10 M 200.8615 211.9568 m S 0 g 1 w 4 M 200.8615 211.9568 m F 0 G 0.3 w 10 M 200.8615 211.9568 m S 0 g 1 w 4 M 200.8615 211.9568 m F 0 G 0.3 w 10 M 216.0684 226.8852 m S 0 g 1 w 4 M 216.0684 226.8852 m F 0 G 0.3 w 10 M 216.0684 226.8852 m S 0 g 1 w 4 M 216.0684 226.8852 m F 0 G 0.3 w 10 M 216.0684 226.8852 m S 0 g 1 w 4 M 216.0684 226.8852 m F 0 G 0.3 w 10 M 216.0684 226.8852 m S 0 g 1 w 4 M 216.0684 226.8852 m F 0 G 0.3 w 10 M 200.8615 226.8852 m S 0 g 1 w 4 M 200.8615 226.8852 m F 0 G 0.3 w 10 M 200.8615 226.8852 m S 0 g 1 w 4 M 200.8615 226.8852 m F 1 g 200.8615 226.8852 m F 0 G 0.3 w 10 M 200.8615 226.8852 m S 0 g 1 w 4 M 200.8615 226.8852 m F 0 G 0.3 w 10 M 200.8615 226.8852 m S 0 g 1 w 4 M 200.8615 226.8852 m F 0 G 0.3 w 10 M 216.9138 211.3568 m S 0 g 1 w 4 M 216.9138 211.3568 m F 0 G 0.3 w 10 M 216.9138 211.3568 m S 0 g 1 w 4 M 216.9138 211.3568 m F 1 g 210.9034 211.3568 m 210.9034 208.135 213.5944 205.5232 216.9138 205.5232 c 220.2332 205.5232 222.9242 208.135 222.9242 211.3568 c F 222.9242 211.3568 m 222.9242 214.5786 220.2332 217.1904 216.9138 217.1904 c 213.5944 217.1904 210.9034 214.5786 210.9034 211.3568 c F 216.9138 211.3568 m F 0 G 0.3 w 10 M 216.9138 211.3568 m S 0 g 1 w 4 M 216.9138 211.3568 m F 0 G 0.3 w 10 M 216.9138 211.3568 m S 0 g 1 w 4 M 216.9138 211.3568 m F 215.8287 212.425 m 212.2431 212.4361 L 212.2431 210.2777 L 215.8287 210.2888 L F 217.9989 210.2888 m 221.5845 210.2777 L 221.5845 212.4361 L 217.9989 212.425 L F 212.2431 212.4361 m 221.5845 212.4361 l 221.5845 210.2777 l 212.2431 210.2777 l 212.2431 212.4361 l f 0 G 0.3 w 10 M 199.6638 228.1068 m S 0 g 1 w 4 M 199.6638 228.1068 m F 0 G 0.3 w 10 M 199.6638 228.1068 m S 0 g 1 w 4 M 199.6638 228.1068 m F 1 g 193.6534 228.1068 m 193.6534 224.885 196.3444 222.2732 199.6638 222.2732 c 202.9832 222.2732 205.6742 224.885 205.6742 228.1068 c F 205.6742 228.1068 m 205.6742 231.3286 202.9832 233.9404 199.6638 233.9404 c F 199.6638 233.9404 m 196.3444 233.9404 193.6534 231.3286 193.6534 228.1068 c F 199.6638 228.1068 m F 0 G 0.3 w 10 M 199.6638 228.1068 m S 0 g 1 w 4 M 199.6638 228.1068 m F 0 G 0.3 w 10 M 199.6638 228.1068 m S 0 g 1 w 4 M 199.6638 228.1068 m F 198.5787 229.175 m 194.9931 229.1861 L 194.9931 227.0277 L 198.5787 227.0388 L F 200.7489 227.0388 m 204.3345 227.0277 L 204.3345 229.1861 L 200.7489 229.175 L F 194.9931 229.1861 m 204.3345 229.1861 l 204.3345 227.0277 l 194.9931 227.0277 l 194.9931 229.1861 l f 0 G 0.3 w 10 M 214.6638 223.1068 m S 0 g 1 w 4 M 214.6638 223.1068 m F 0 G 0.3 w 10 M 214.6638 223.1068 m S 0 g 1 w 4 M 214.6638 223.1068 m F 1 g 208.6534 223.1068 m 208.6534 219.885 211.3444 217.2732 214.6638 217.2732 c 217.9832 217.2732 220.6742 219.885 220.6742 223.1068 c F 220.6742 223.1068 m 220.6742 226.3286 217.9832 228.9404 214.6638 228.9404 c 211.3444 228.9404 208.6534 226.3286 208.6534 223.1068 c F 214.6638 223.1068 m F 0 G 0.3 w 10 M 214.6638 223.1068 m S 0 g 1 w 4 M 214.6638 223.1068 m F 0 G 0.3 w 10 M 214.6638 223.1068 m S 0 g 1 w 4 M 214.6638 223.1068 m F 213.5787 224.175 m 209.9931 224.1861 L 209.9931 222.0277 L 213.5787 222.0388 L F 215.7489 222.0388 m 219.3345 222.0277 L 219.3345 224.1861 L 215.7489 224.175 L F 209.9931 224.1861 m 219.3345 224.1861 l 219.3345 222.0277 l 209.9931 222.0277 l 209.9931 224.1861 l f 0 G 0.3 w 10 M 201.9138 214.6068 m S 0 g 1 w 4 M 201.9138 214.6068 m F 0 G 0.3 w 10 M 201.9138 214.6068 m S 0 g 1 w 4 M 201.9138 214.6068 m F 1 g 195.9034 214.6068 m 195.9034 211.385 198.5944 208.7732 201.9138 208.7732 c 205.2332 208.7732 207.9242 211.385 207.9242 214.6068 c F 207.9242 214.6068 m 207.9242 217.8286 205.2332 220.4404 201.9138 220.4404 c 198.5944 220.4404 195.9034 217.8286 195.9034 214.6068 c F 201.9138 214.6068 m F 0 G 0.3 w 10 M 201.9138 214.6068 m S 0 g 1 w 4 M 201.9138 214.6068 m F 0 G 0.3 w 10 M 201.9138 214.6068 m S 0 g 1 w 4 M 201.9138 214.6068 m F 200.8287 215.675 m 197.2431 215.6861 L 197.2431 213.5277 L 200.8287 213.5388 L F 202.9989 213.5388 m 206.5845 213.5277 L 206.5845 215.6861 L 202.9989 215.675 L F 197.2431 215.6861 m 206.5845 215.6861 l 206.5845 213.5277 l 197.2431 213.5277 l 197.2431 215.6861 l f 0 G 0.3 w 10 M 200.8615 197.0284 m S 200.8615 182.1 m S 200.8615 197.0284 m S 200.8615 182.1 m S 200.8615 197.0284 m S 200.8615 197.0284 m S 200.8615 182.1 m S 200.8615 182.1 m S 200.8615 197.0284 m S 200.8615 182.1 m S 200.8615 197.0284 m S 216.0684 197.0284 m S 216.0684 182.1 m S 216.0684 197.0284 m S 216.0684 197.0284 m S 216.0684 182.1 m S 200.8615 182.1 m S 200.8615 197.0284 m S 208.4649 189.5642 m S 216.0684 197.0284 m S 200.8615 197.0284 m S 0 g 1 w 4 M 208.4649 189.5642 m F 0 G 0.3 w 10 M 200.8615 182.1 m S 216.0684 182.1 m S 200.8615 182.1 m S 216.0684 182.1 m S 200.8615 182.1 m S 200.8615 182.1 m S 200.8615 182.1 m S 216.0684 182.1 m S 200.8615 182.1 m S 216.0684 182.1 m S 200.8615 182.1 m S 0 g 1 w 4 M 200.8615 182.1 m F 0 G 0.3 w 10 M 200.8615 182.1 m S 0 g 1 w 4 M 200.8615 182.1 m F 0 G 0.3 w 10 M 200.8615 182.1 m S 0 g 1 w 4 M 200.8615 182.1 m F 0 G 0.3 w 10 M 200.8615 182.1 m S 0 g 1 w 4 M 200.8615 182.1 m F 0 G 0.3 w 10 M 216.0684 197.0284 m S 0 g 1 w 4 M 216.0684 197.0284 m F 0 G 0.3 w 10 M 216.0684 197.0284 m S 0 g 1 w 4 M 216.0684 197.0284 m F 0 G 0.3 w 10 M 216.0684 197.0284 m S 0 g 1 w 4 M 216.0684 197.0284 m F 0 G 0.3 w 10 M 216.0684 197.0284 m S 0 g 1 w 4 M 216.0684 197.0284 m F 0 G 0.3 w 10 M 200.8615 197.0284 m S 0 g 1 w 4 M 200.8615 197.0284 m F 0 G 0.3 w 10 M 200.8615 197.0284 m S 0 g 1 w 4 M 200.8615 197.0284 m F 1 g 200.8615 197.0284 m F 0 G 0.3 w 10 M 200.8615 197.0284 m S 0 g 1 w 4 M 200.8615 197.0284 m F 0 G 0.3 w 10 M 200.8615 197.0284 m S 0 g 1 w 4 M 200.8615 197.0284 m F 0 G 0.3 w 10 M 216.9138 181.5 m S 0 g 1 w 4 M 216.9138 181.5 m F 0 G 0.3 w 10 M 216.9138 181.5 m S 0 g 1 w 4 M 216.9138 181.5 m F 1 g 210.9034 181.5 m 210.9034 178.2782 213.5944 175.6664 216.9138 175.6664 c 220.2332 175.6664 222.9242 178.2782 222.9242 181.5 c F 222.9242 181.5 m 222.9242 184.7218 220.2332 187.3336 216.9138 187.3336 c 213.5944 187.3336 210.9034 184.7218 210.9034 181.5 c F 216.9138 181.5 m F 0 G 0.3 w 10 M 216.9138 181.5 m S 0 g 1 w 4 M 216.9138 181.5 m F 0 G 0.3 w 10 M 216.9138 181.5 m S 0 g 1 w 4 M 216.9138 181.5 m F 215.8287 182.5682 m 212.2431 182.5793 L 212.2431 180.4209 L 215.8287 180.432 L F 217.9989 180.432 m 221.5845 180.4209 L 221.5845 182.5793 L 217.9989 182.5682 L F 212.2431 182.5793 m 221.5845 182.5793 l 221.5845 180.4209 l 212.2431 180.4209 l 212.2431 182.5793 l f 0 G 0.3 w 10 M 199.6638 198.25 m S 0 g 1 w 4 M 199.6638 198.25 m F 0 G 0.3 w 10 M 199.6638 198.25 m S 0 g 1 w 4 M 199.6638 198.25 m F 1 g 193.6534 198.25 m 193.6534 195.0282 196.3444 192.4164 199.6638 192.4164 c 202.9832 192.4164 205.6742 195.0282 205.6742 198.25 c F 205.6742 198.25 m 205.6742 201.4718 202.9832 204.0836 199.6638 204.0836 c F 199.6638 204.0836 m 196.3444 204.0836 193.6534 201.4718 193.6534 198.25 c F 199.6638 198.25 m F 0 G 0.3 w 10 M 199.6638 198.25 m S 0 g 1 w 4 M 199.6638 198.25 m F 0 G 0.3 w 10 M 199.6638 198.25 m S 0 g 1 w 4 M 199.6638 198.25 m F 198.5787 199.3182 m 194.9931 199.3293 L 194.9931 197.1709 L 198.5787 197.182 L F 200.7489 197.182 m 204.3345 197.1709 L 204.3345 199.3293 L 200.7489 199.3182 L F 194.9931 199.3293 m 204.3345 199.3293 l 204.3345 197.1709 l 194.9931 197.1709 l 194.9931 199.3293 l f 0 G 0.3 w 10 M 214.6638 193.25 m S 0 g 1 w 4 M 214.6638 193.25 m F 0 G 0.3 w 10 M 214.6638 193.25 m S 0 g 1 w 4 M 214.6638 193.25 m F 1 g 208.6534 193.25 m 208.6534 190.0282 211.3444 187.4164 214.6638 187.4164 c 217.9832 187.4164 220.6742 190.0282 220.6742 193.25 c F 220.6742 193.25 m 220.6742 196.4718 217.9832 199.0836 214.6638 199.0836 c 211.3444 199.0836 208.6534 196.4718 208.6534 193.25 c F 214.6638 193.25 m F 0 G 0.3 w 10 M 214.6638 193.25 m S 0 g 1 w 4 M 214.6638 193.25 m F 0 G 0.3 w 10 M 214.6638 193.25 m S 0 g 1 w 4 M 214.6638 193.25 m F 213.5787 194.3182 m 209.9931 194.3293 L 209.9931 192.1709 L 213.5787 192.182 L F 215.7489 192.182 m 219.3345 192.1709 L 219.3345 194.3293 L 215.7489 194.3182 L F 209.9931 194.3293 m 219.3345 194.3293 l 219.3345 192.1709 l 209.9931 192.1709 l 209.9931 194.3293 l f 0 G 0.3 w 10 M 201.9138 184.75 m S 0 g 1 w 4 M 201.9138 184.75 m F 0 G 0.3 w 10 M 201.9138 184.75 m S 0 g 1 w 4 M 201.9138 184.75 m F 1 g 195.9034 184.75 m 195.9034 181.5282 198.5944 178.9164 201.9138 178.9164 c 205.2332 178.9164 207.9242 181.5282 207.9242 184.75 c F 207.9242 184.75 m 207.9242 187.9718 205.2332 190.5836 201.9138 190.5836 c 198.5944 190.5836 195.9034 187.9718 195.9034 184.75 c F 201.9138 184.75 m F 0 G 0.3 w 10 M 201.9138 184.75 m S 0 g 1 w 4 M 201.9138 184.75 m F 0 G 0.3 w 10 M 201.9138 184.75 m S 0 g 1 w 4 M 201.9138 184.75 m F 200.8287 185.8182 m 197.2431 185.8293 L 197.2431 183.6709 L 200.8287 183.682 L F 202.9989 183.682 m 206.5845 183.6709 L 206.5845 185.8293 L 202.9989 185.8182 L F 197.2431 185.8293 m 206.5845 185.8293 l 206.5845 183.6709 l 197.2431 183.6709 l 197.2431 185.8293 l f 0 G 0.3 w 10 M 79.2065 137.3147 m S 79.2065 122.3863 m S 79.2065 137.3147 m S 79.2065 122.3863 m S 79.2065 137.3147 m S 79.2065 137.3147 m S 79.2065 122.3863 m S 79.2065 122.3863 m S 79.2065 137.3147 m S 79.2065 122.3863 m S 79.2065 137.3147 m S 94.4134 137.3147 m S 94.4134 122.3863 m S 94.4134 137.3147 m S 94.4134 137.3147 m S 94.4134 122.3863 m S 79.2065 122.3863 m S 79.2065 137.3147 m S 86.8099 129.8505 m S 94.4134 137.3147 m S 79.2065 137.3147 m S 0 g 1 w 4 M 86.8099 129.8505 m F 0 G 0.3 w 10 M 79.2065 122.3863 m S 94.4134 122.3863 m S 79.2065 122.3863 m S 94.4134 122.3863 m S 79.2065 122.3863 m S 79.2065 122.3863 m S 79.2065 122.3863 m S 94.4134 122.3863 m S 79.2065 122.3863 m S 94.4134 122.3863 m S 79.2065 122.3863 m S 0 g 1 w 4 M 79.2065 122.3863 m F 0 G 0.3 w 10 M 79.2065 122.3863 m S 0 g 1 w 4 M 79.2065 122.3863 m F 0 G 0.3 w 10 M 79.2065 122.3863 m S 0 g 1 w 4 M 79.2065 122.3863 m F 0 G 0.3 w 10 M 79.2065 122.3863 m S 0 g 1 w 4 M 79.2065 122.3863 m F 0 G 0.3 w 10 M 94.4134 137.3147 m S 0 g 1 w 4 M 94.4134 137.3147 m F 0 G 0.3 w 10 M 94.4134 137.3147 m S 0 g 1 w 4 M 94.4134 137.3147 m F 0 G 0.3 w 10 M 94.4134 137.3147 m S 0 g 1 w 4 M 94.4134 137.3147 m F 0 G 0.3 w 10 M 94.4134 137.3147 m S 0 g 1 w 4 M 94.4134 137.3147 m F 0 G 0.3 w 10 M 79.2065 137.3147 m S 0 g 1 w 4 M 79.2065 137.3147 m F 0 G 0.3 w 10 M 79.2065 137.3147 m S 0 g 1 w 4 M 79.2065 137.3147 m F 1 g 79.2065 137.3147 m F 0 G 0.3 w 10 M 79.2065 137.3147 m S 0 g 1 w 4 M 79.2065 137.3147 m F 0 G 0.3 w 10 M 79.2065 137.3147 m S 0 g 1 w 4 M 79.2065 137.3147 m F 0 G 0.3 w 10 M 95.2588 121.7863 m S 0 g 1 w 4 M 95.2588 121.7863 m F 0 G 0.3 w 10 M 95.2588 121.7863 m S 0 g 1 w 4 M 95.2588 121.7863 m F 1 g 95.2588 121.7863 m F 0 G 0.3 w 10 M 95.2588 121.7863 m S 0 g 1 w 4 M 95.2588 121.7863 m F 0 G 0.3 w 10 M 95.2588 121.7863 m S 0 g 1 w 4 M 95.2588 121.7863 m F 0 G 0.3 w 10 M 78.0088 138.5363 m S 0 g 1 w 4 M 78.0088 138.5363 m F 0 G 0.3 w 10 M 78.0088 138.5363 m S 0 g 1 w 4 M 78.0088 138.5363 m F 1 g 71.9984 138.5363 m 71.9984 135.3145 74.6894 132.7027 78.0088 132.7027 c 81.3282 132.7027 84.0192 135.3145 84.0192 138.5363 c F 84.0192 138.5363 m 84.0192 141.7581 81.3282 144.3699 78.0088 144.3699 c F 78.0088 144.3699 m 74.6894 144.3699 71.9984 141.7581 71.9984 138.5363 c F 78.0088 138.5363 m F 0 G 0.3 w 10 M 78.0088 138.5363 m S 0 g 1 w 4 M 78.0088 138.5363 m F 0 G 0.3 w 10 M 78.0088 138.5363 m S 0 g 1 w 4 M 78.0088 138.5363 m F 76.9237 139.6045 m 73.3381 139.6156 L 73.3381 137.4572 L 76.9237 137.4683 L F 79.0939 137.4683 m 82.6795 137.4572 L 82.6795 139.6156 L 79.0939 139.6045 L F 73.3381 139.6156 m 82.6795 139.6156 l 82.6795 137.4572 l 73.3381 137.4572 l 73.3381 139.6156 l f 0 G 0.3 w 10 M 93.0088 133.5363 m S 0 g 1 w 4 M 93.0088 133.5363 m F 0 G 0.3 w 10 M 93.0088 133.5363 m S 0 g 1 w 4 M 93.0088 133.5363 m F 1 g 86.9984 133.5363 m 86.9984 130.3145 89.6894 127.7027 93.0088 127.7027 c 96.3282 127.7027 99.0192 130.3145 99.0192 133.5363 c F 99.0192 133.5363 m 99.0192 136.7581 96.3282 139.3699 93.0088 139.3699 c 89.6894 139.3699 86.9984 136.7581 86.9984 133.5363 c F 93.0088 133.5363 m F 0 G 0.3 w 10 M 93.0088 133.5363 m S 0 g 1 w 4 M 93.0088 133.5363 m F 0 G 0.3 w 10 M 93.0088 133.5363 m S 0 g 1 w 4 M 93.0088 133.5363 m F 91.9237 134.6045 m 88.3381 134.6156 L 88.3381 132.4572 L 91.9237 132.4683 L F 94.0939 132.4683 m 97.6795 132.4572 L 97.6795 134.6156 L 94.0939 134.6045 L F 88.3381 134.6156 m 97.6795 134.6156 l 97.6795 132.4572 l 88.3381 132.4572 l 88.3381 134.6156 l f 0 G 0.3 w 10 M 80.2588 125.0363 m S 0 g 1 w 4 M 80.2588 125.0363 m F 0 G 0.3 w 10 M 80.2588 125.0363 m S 0 g 1 w 4 M 80.2588 125.0363 m F 1 g 74.2484 125.0363 m 74.2484 121.8145 76.9394 119.2027 80.2588 119.2027 c 83.5782 119.2027 86.2692 121.8145 86.2692 125.0363 c F 86.2692 125.0363 m 86.2692 128.2581 83.5782 130.8699 80.2588 130.8699 c 76.9394 130.8699 74.2484 128.2581 74.2484 125.0363 c F 80.2588 125.0363 m F 0 G 0.3 w 10 M 80.2588 125.0363 m S 0 g 1 w 4 M 80.2588 125.0363 m F 0 G 0.3 w 10 M 80.2588 125.0363 m S 0 g 1 w 4 M 80.2588 125.0363 m F 79.1737 126.1045 m 75.5881 126.1156 L 75.5881 123.9572 L 79.1737 123.9683 L F 81.3439 123.9683 m 84.9295 123.9572 L 84.9295 126.1156 L 81.3439 126.1045 L F 75.5881 126.1156 m 84.9295 126.1156 l 84.9295 123.9572 l 75.5881 123.9572 l 75.5881 126.1156 l f 0 G 0.3 w 10 M 109.6203 137.3147 m S 109.6203 122.3863 m S 109.6203 137.3147 m S 109.6203 122.3863 m S 109.6203 137.3147 m S 109.6203 137.3147 m S 109.6203 122.3863 m S 109.6203 122.3863 m S 109.6203 137.3147 m S 109.6203 122.3863 m S 109.6203 137.3147 m S 124.8272 137.3147 m S 124.8272 122.3863 m S 124.8272 137.3147 m S 124.8272 137.3147 m S 124.8272 122.3863 m S 109.6203 122.3863 m S 109.6203 137.3147 m S 117.2237 129.8505 m S 124.8272 137.3147 m S 109.6203 137.3147 m S 0 g 1 w 4 M 117.2237 129.8505 m F 0 G 0.3 w 10 M 109.6203 122.3863 m S 124.8272 122.3863 m S 109.6203 122.3863 m S 124.8272 122.3863 m S 109.6203 122.3863 m S 109.6203 122.3863 m S 109.6203 122.3863 m S 124.8272 122.3863 m S 109.6203 122.3863 m S 124.8272 122.3863 m S 109.6203 122.3863 m S 0 g 1 w 4 M 109.6203 122.3863 m F 0 G 0.3 w 10 M 109.6203 122.3863 m S 0 g 1 w 4 M 109.6203 122.3863 m F 0 G 0.3 w 10 M 109.6203 122.3863 m S 0 g 1 w 4 M 109.6203 122.3863 m F 0 G 0.3 w 10 M 109.6203 122.3863 m S 0 g 1 w 4 M 109.6203 122.3863 m F 0 G 0.3 w 10 M 124.8272 137.3147 m S 0 g 1 w 4 M 124.8272 137.3147 m F 0 G 0.3 w 10 M 124.8272 137.3147 m S 0 g 1 w 4 M 124.8272 137.3147 m F 0 G 0.3 w 10 M 124.8272 137.3147 m S 0 g 1 w 4 M 124.8272 137.3147 m F 0 G 0.3 w 10 M 124.8272 137.3147 m S 0 g 1 w 4 M 124.8272 137.3147 m F 0 G 0.3 w 10 M 109.6203 137.3147 m S 0 g 1 w 4 M 109.6203 137.3147 m F 0 G 0.3 w 10 M 109.6203 137.3147 m S 0 g 1 w 4 M 109.6203 137.3147 m F 1 g 109.6203 137.3147 m F 0 G 0.3 w 10 M 109.6203 137.3147 m S 0 g 1 w 4 M 109.6203 137.3147 m F 0 G 0.3 w 10 M 109.6203 137.3147 m S 0 g 1 w 4 M 109.6203 137.3147 m F 0 G 0.3 w 10 M 125.6726 121.7863 m S 0 g 1 w 4 M 125.6726 121.7863 m F 0 G 0.3 w 10 M 125.6726 121.7863 m S 0 g 1 w 4 M 125.6726 121.7863 m F 1 g 119.6622 121.7863 m 119.6622 118.5645 122.3532 115.9527 125.6726 115.9527 c 128.992 115.9527 131.683 118.5645 131.683 121.7863 c F 131.683 121.7863 m 131.683 125.0081 128.992 127.6199 125.6726 127.6199 c 122.3532 127.6199 119.6622 125.0081 119.6622 121.7863 c F 125.6726 121.7863 m F 0 G 0.3 w 10 M 125.6726 121.7863 m S 0 g 1 w 4 M 125.6726 121.7863 m F 0 G 0.3 w 10 M 125.6726 121.7863 m S 0 g 1 w 4 M 125.6726 121.7863 m F 124.5875 122.8545 m 121.0019 122.8656 L 121.0019 120.7072 L 124.5875 120.7183 L F 126.7577 120.7183 m 130.3433 120.7072 L 130.3433 122.8656 L 126.7577 122.8545 L F 121.0019 122.8656 m 130.3433 122.8656 l 130.3433 120.7072 l 121.0019 120.7072 l 121.0019 122.8656 l f 0 G 0.3 w 10 M 108.4226 138.5363 m S 0 g 1 w 4 M 108.4226 138.5363 m F 0 G 0.3 w 10 M 108.4226 138.5363 m S 0 g 1 w 4 M 108.4226 138.5363 m F 1 g 102.4122 138.5363 m 102.4122 135.3145 105.1032 132.7027 108.4226 132.7027 c 111.742 132.7027 114.433 135.3145 114.433 138.5363 c F 114.433 138.5363 m 114.433 141.7581 111.742 144.3699 108.4226 144.3699 c F 108.4226 144.3699 m 105.1032 144.3699 102.4122 141.7581 102.4122 138.5363 c F 108.4226 138.5363 m F 0 G 0.3 w 10 M 108.4226 138.5363 m S 0 g 1 w 4 M 108.4226 138.5363 m F 0 G 0.3 w 10 M 108.4226 138.5363 m S 0 g 1 w 4 M 108.4226 138.5363 m F 107.3375 139.6045 m 103.7519 139.6156 L 103.7519 137.4572 L 107.3375 137.4683 L F 109.5077 137.4683 m 113.0933 137.4572 L 113.0933 139.6156 L 109.5077 139.6045 L F 103.7519 139.6156 m 113.0933 139.6156 l 113.0933 137.4572 l 103.7519 137.4572 l 103.7519 139.6156 l f 0 G 0.3 w 10 M 123.4226 133.5363 m S 0 g 1 w 4 M 123.4226 133.5363 m F 0 G 0.3 w 10 M 123.4226 133.5363 m S 0 g 1 w 4 M 123.4226 133.5363 m F 1 g 117.4122 133.5363 m 117.4122 130.3145 120.1032 127.7027 123.4226 127.7027 c 126.742 127.7027 129.433 130.3145 129.433 133.5363 c F 129.433 133.5363 m 129.433 136.7581 126.742 139.3699 123.4226 139.3699 c 120.1032 139.3699 117.4122 136.7581 117.4122 133.5363 c F 123.4226 133.5363 m F 0 G 0.3 w 10 M 123.4226 133.5363 m S 0 g 1 w 4 M 123.4226 133.5363 m F 0 G 0.3 w 10 M 123.4226 133.5363 m S 0 g 1 w 4 M 123.4226 133.5363 m F 122.3375 134.6045 m 118.7519 134.6156 L 118.7519 132.4572 L 122.3375 132.4683 L F 124.5077 132.4683 m 128.0933 132.4572 L 128.0933 134.6156 L 124.5077 134.6045 L F 118.7519 134.6156 m 128.0933 134.6156 l 128.0933 132.4572 l 118.7519 132.4572 l 118.7519 134.6156 l f 0 G 0.3 w 10 M 110.6726 125.0363 m S 0 g 1 w 4 M 110.6726 125.0363 m F 0 G 0.3 w 10 M 110.6726 125.0363 m S 0 g 1 w 4 M 110.6726 125.0363 m F 1 g 104.6622 125.0363 m 104.6622 121.8145 107.3532 119.2027 110.6726 119.2027 c 113.992 119.2027 116.683 121.8145 116.683 125.0363 c F 116.683 125.0363 m 116.683 128.2581 113.992 130.8699 110.6726 130.8699 c 107.3532 130.8699 104.6622 128.2581 104.6622 125.0363 c F 110.6726 125.0363 m F 0 G 0.3 w 10 M 110.6726 125.0363 m S 0 g 1 w 4 M 110.6726 125.0363 m F 0 G 0.3 w 10 M 110.6726 125.0363 m S 0 g 1 w 4 M 110.6726 125.0363 m F 109.5875 126.1045 m 106.0019 126.1156 L 106.0019 123.9572 L 109.5875 123.9683 L F 111.7577 123.9683 m 115.3433 123.9572 L 115.3433 126.1156 L 111.7577 126.1045 L F 106.0019 126.1156 m 115.3433 126.1156 l 115.3433 123.9572 l 106.0019 123.9572 l 106.0019 126.1156 l f 0 G 0.3 w 10 M 79.2065 107.4579 m S 79.2065 92.5295 m S 79.2065 107.4579 m S 79.2065 92.5295 m S 79.2065 107.4579 m S 79.2065 107.4579 m S 79.2065 92.5295 m S 79.2065 92.5295 m S 79.2065 107.4579 m S 79.2065 92.5295 m S 79.2065 107.4579 m S 94.4134 107.4579 m S 94.4134 92.5295 m S 94.4134 107.4579 m S 94.4134 107.4579 m S 94.4134 92.5295 m S 79.2065 92.5295 m S 79.2065 107.4579 m S 86.8099 99.9937 m S 94.4134 107.4579 m S 79.2065 107.4579 m S 0 g 1 w 4 M 86.8099 99.9937 m F 0 G 0.3 w 10 M 79.2065 92.5295 m S 94.4134 92.5295 m S 79.2065 92.5295 m S 94.4134 92.5295 m S 79.2065 92.5295 m S 79.2065 92.5295 m S 79.2065 92.5295 m S 94.4134 92.5295 m S 79.2065 92.5295 m S 94.4134 92.5295 m S 79.2065 92.5295 m S 0 g 1 w 4 M 79.2065 92.5295 m F 0 G 0.3 w 10 M 79.2065 92.5295 m S 0 g 1 w 4 M 79.2065 92.5295 m F 0 G 0.3 w 10 M 79.2065 92.5295 m S 0 g 1 w 4 M 79.2065 92.5295 m F 0 G 0.3 w 10 M 79.2065 92.5295 m S 0 g 1 w 4 M 79.2065 92.5295 m F 0 G 0.3 w 10 M 94.4134 107.4579 m S 0 g 1 w 4 M 94.4134 107.4579 m F 0 G 0.3 w 10 M 94.4134 107.4579 m S 0 g 1 w 4 M 94.4134 107.4579 m F 0 G 0.3 w 10 M 94.4134 107.4579 m S 0 g 1 w 4 M 94.4134 107.4579 m F 0 G 0.3 w 10 M 94.4134 107.4579 m S 0 g 1 w 4 M 94.4134 107.4579 m F 0 G 0.3 w 10 M 79.2065 107.4579 m S 0 g 1 w 4 M 79.2065 107.4579 m F 0 G 0.3 w 10 M 79.2065 107.4579 m S 0 g 1 w 4 M 79.2065 107.4579 m F 1 g 79.2065 107.4579 m F 0 G 0.3 w 10 M 79.2065 107.4579 m S 0 g 1 w 4 M 79.2065 107.4579 m F 0 G 0.3 w 10 M 79.2065 107.4579 m S 0 g 1 w 4 M 79.2065 107.4579 m F 0 G 0.3 w 10 M 95.2588 91.9295 m S 0 g 1 w 4 M 95.2588 91.9295 m F 0 G 0.3 w 10 M 95.2588 91.9295 m S 0 g 1 w 4 M 95.2588 91.9295 m F 1 g 89.2484 91.9295 m 89.2484 88.7077 91.9394 86.0959 95.2588 86.0959 c 98.5782 86.0959 101.2692 88.7077 101.2692 91.9295 c F 101.2692 91.9295 m 101.2692 95.1513 98.5782 97.7631 95.2588 97.7631 c 91.9394 97.7631 89.2484 95.1513 89.2484 91.9295 c F 95.2588 91.9295 m F 0 G 0.3 w 10 M 95.2588 91.9295 m S 0 g 1 w 4 M 95.2588 91.9295 m F 0 G 0.3 w 10 M 95.2588 91.9295 m S 0 g 1 w 4 M 95.2588 91.9295 m F 94.1737 92.9977 m 90.5881 93.0088 L 90.5881 90.8504 L 94.1737 90.8615 L F 96.3439 90.8615 m 99.9295 90.8504 L 99.9295 93.0088 L 96.3439 92.9977 L F 90.5881 93.0088 m 99.9295 93.0088 l 99.9295 90.8504 l 90.5881 90.8504 l 90.5881 93.0088 l f 0 G 0.3 w 10 M 78.0088 108.6795 m S 0 g 1 w 4 M 78.0088 108.6795 m F 0 G 0.3 w 10 M 78.0088 108.6795 m S 0 g 1 w 4 M 78.0088 108.6795 m F 1 g 71.9984 108.6795 m 71.9984 105.4577 74.6894 102.8459 78.0088 102.8459 c 81.3282 102.8459 84.0192 105.4577 84.0192 108.6795 c F 84.0192 108.6795 m 84.0192 111.9013 81.3282 114.5131 78.0088 114.5131 c F 78.0088 114.5131 m 74.6894 114.5131 71.9984 111.9013 71.9984 108.6795 c F 78.0088 108.6795 m F 0 G 0.3 w 10 M 78.0088 108.6795 m S 0 g 1 w 4 M 78.0088 108.6795 m F 0 G 0.3 w 10 M 78.0088 108.6795 m S 0 g 1 w 4 M 78.0088 108.6795 m F 76.9237 109.7477 m 73.3381 109.7588 L 73.3381 107.6004 L 76.9237 107.6115 L F 79.0939 107.6115 m 82.6795 107.6004 L 82.6795 109.7588 L 79.0939 109.7477 L F 73.3381 109.7588 m 82.6795 109.7588 l 82.6795 107.6004 l 73.3381 107.6004 l 73.3381 109.7588 l f 0 G 0.3 w 10 M 93.0088 103.6795 m S 0 g 1 w 4 M 93.0088 103.6795 m F 0 G 0.3 w 10 M 93.0088 103.6795 m S 0 g 1 w 4 M 93.0088 103.6795 m F 1 g 86.9984 103.6795 m 86.9984 100.4577 89.6894 97.8459 93.0088 97.8459 c 96.3282 97.8459 99.0192 100.4577 99.0192 103.6795 c F 99.0192 103.6795 m 99.0192 106.9013 96.3282 109.5131 93.0088 109.5131 c 89.6894 109.5131 86.9984 106.9013 86.9984 103.6795 c F 93.0088 103.6795 m F 0 G 0.3 w 10 M 93.0088 103.6795 m S 0 g 1 w 4 M 93.0088 103.6795 m F 0 G 0.3 w 10 M 93.0088 103.6795 m S 0 g 1 w 4 M 93.0088 103.6795 m F 91.9237 104.7477 m 88.3381 104.7588 L 88.3381 102.6004 L 91.9237 102.6115 L F 94.0939 102.6115 m 97.6795 102.6004 L 97.6795 104.7588 L 94.0939 104.7477 L F 88.3381 104.7588 m 97.6795 104.7588 l 97.6795 102.6004 l 88.3381 102.6004 l 88.3381 104.7588 l f 0 G 0.3 w 10 M 80.2588 95.1795 m S 0 g 1 w 4 M 80.2588 95.1795 m F 0 G 0.3 w 10 M 80.2588 95.1795 m S 0 g 1 w 4 M 80.2588 95.1795 m F 1 g 74.2484 95.1795 m 74.2484 91.9577 76.9394 89.3459 80.2588 89.3459 c 83.5782 89.3459 86.2692 91.9577 86.2692 95.1795 c F 86.2692 95.1795 m 86.2692 98.4013 83.5782 101.0131 80.2588 101.0131 c 76.9394 101.0131 74.2484 98.4013 74.2484 95.1795 c F 80.2588 95.1795 m F 0 G 0.3 w 10 M 80.2588 95.1795 m S 0 g 1 w 4 M 80.2588 95.1795 m F 0 G 0.3 w 10 M 80.2588 95.1795 m S 0 g 1 w 4 M 80.2588 95.1795 m F 79.1737 96.2477 m 75.5881 96.2588 L 75.5881 94.1004 L 79.1737 94.1115 L F 81.3439 94.1115 m 84.9295 94.1004 L 84.9295 96.2588 L 81.3439 96.2477 L F 75.5881 96.2588 m 84.9295 96.2588 l 84.9295 94.1004 l 75.5881 94.1004 l 75.5881 96.2588 l f 0 G 0.3 w 10 M 94.6977 120.2784 m S 94.6977 105.35 m S 94.6977 120.2784 m S 94.6977 105.35 m S 94.6977 120.2784 m S 94.6977 120.2784 m S 94.6977 105.35 m S 94.6977 105.35 m S 94.6977 120.2784 m S 94.6977 105.35 m S 94.6977 120.2784 m S 109.9046 120.2784 m S 109.9046 105.35 m S 109.9046 120.2784 m S 109.9046 120.2784 m S 109.9046 105.35 m S 94.6977 105.35 m S 94.6977 120.2784 m S 102.3011 112.8142 m S 109.9046 120.2784 m S 94.6977 120.2784 m S 0 g 1 w 4 M 102.3011 112.8142 m F 0 G 0.3 w 10 M 94.6977 105.35 m S 109.9046 105.35 m S 94.6977 105.35 m S 109.9046 105.35 m S 94.6977 105.35 m S 94.6977 105.35 m S 94.6977 105.35 m S 109.9046 105.35 m S 94.6977 105.35 m S 109.9046 105.35 m S 94.6977 105.35 m S 0 g 1 w 4 M 94.6977 105.35 m F 0 G 0.3 w 10 M 94.6977 105.35 m S 0 g 1 w 4 M 94.6977 105.35 m F 0 G 0.3 w 10 M 94.6977 105.35 m S 0 g 1 w 4 M 94.6977 105.35 m F 0 G 0.3 w 10 M 94.6977 105.35 m S 0 g 1 w 4 M 94.6977 105.35 m F 0 G 0.3 w 10 M 109.9046 120.2784 m S 0 g 1 w 4 M 109.9046 120.2784 m F 0 G 0.3 w 10 M 109.9046 120.2784 m S 0 g 1 w 4 M 109.9046 120.2784 m F 0 G 0.3 w 10 M 109.9046 120.2784 m S 0 g 1 w 4 M 109.9046 120.2784 m F 0 G 0.3 w 10 M 109.9046 120.2784 m S 0 g 1 w 4 M 109.9046 120.2784 m F 0 G 0.3 w 10 M 94.6977 120.2784 m S 0 g 1 w 4 M 94.6977 120.2784 m F 0 G 0.3 w 10 M 94.6977 120.2784 m S 0 g 1 w 4 M 94.6977 120.2784 m F 1 g 94.6977 120.2784 m F 0 G 0.3 w 10 M 94.6977 120.2784 m S 0 g 1 w 4 M 94.6977 120.2784 m F 0 G 0.3 w 10 M 94.6977 120.2784 m S 0 g 1 w 4 M 94.6977 120.2784 m F 0 G 0.3 w 10 M 110.75 104.75 m S 0 g 1 w 4 M 110.75 104.75 m F 0 G 0.3 w 10 M 110.75 104.75 m S 0 g 1 w 4 M 110.75 104.75 m F 1 g 110.75 104.75 m F 0 G 0.3 w 10 M 110.75 104.75 m S 0 g 1 w 4 M 110.75 104.75 m F 0 G 0.3 w 10 M 110.75 104.75 m S 0 g 1 w 4 M 110.75 104.75 m F 0 G 0.3 w 10 M 93.5 121.5 m S 0 g 1 w 4 M 93.5 121.5 m F 0 G 0.3 w 10 M 93.5 121.5 m S 0 g 1 w 4 M 93.5 121.5 m F 1 g 87.4896 121.5 m 87.4896 118.2782 90.1806 115.6664 93.5 115.6664 c 96.8194 115.6664 99.5104 118.2782 99.5104 121.5 c F 99.5104 121.5 m 99.5104 124.7218 96.8194 127.3336 93.5 127.3336 c F 93.5 127.3336 m 90.1806 127.3336 87.4896 124.7218 87.4896 121.5 c F 93.5 121.5 m F 0 G 0.3 w 10 M 93.5 121.5 m S 0 g 1 w 4 M 93.5 121.5 m F 0 G 0.3 w 10 M 93.5 121.5 m S 0 g 1 w 4 M 93.5 121.5 m F 92.4149 122.5682 m 88.8293 122.5793 L 88.8293 120.4209 L 92.4149 120.432 L F 94.5851 120.432 m 98.1707 120.4209 L 98.1707 122.5793 L 94.5851 122.5682 L F 88.8293 122.5793 m 98.1707 122.5793 l 98.1707 120.4209 l 88.8293 120.4209 l 88.8293 122.5793 l f 0 G 0.3 w 10 M 95.75 108 m S 0 g 1 w 4 M 95.75 108 m F 0 G 0.3 w 10 M 95.75 108 m S 0 g 1 w 4 M 95.75 108 m F 1 g 95.75 108 m F 0 G 0.3 w 10 M 95.75 108 m S 0 g 1 w 4 M 95.75 108 m F 0 G 0.3 w 10 M 95.75 108 m S 0 g 1 w 4 M 95.75 108 m F 0 G 0.3 w 10 M 109.6203 107.4579 m S 109.6203 92.5295 m S 109.6203 107.4579 m S 109.6203 92.5295 m S 109.6203 107.4579 m S 109.6203 107.4579 m S 109.6203 92.5295 m S 109.6203 92.5295 m S 109.6203 107.4579 m S 109.6203 92.5295 m S 109.6203 107.4579 m S 124.8272 107.4579 m S 124.8272 92.5295 m S 124.8272 107.4579 m S 124.8272 107.4579 m S 124.8272 92.5295 m S 109.6203 92.5295 m S 109.6203 107.4579 m S 117.2237 99.9937 m S 124.8272 107.4579 m S 109.6203 107.4579 m S 0 g 1 w 4 M 117.2237 99.9937 m F 0 G 0.3 w 10 M 109.6203 92.5295 m S 124.8272 92.5295 m S 109.6203 92.5295 m S 124.8272 92.5295 m S 109.6203 92.5295 m S 109.6203 92.5295 m S 109.6203 92.5295 m S 124.8272 92.5295 m S 109.6203 92.5295 m S 124.8272 92.5295 m S 109.6203 92.5295 m S 0 g 1 w 4 M 109.6203 92.5295 m F 0 G 0.3 w 10 M 109.6203 92.5295 m S 0 g 1 w 4 M 109.6203 92.5295 m F 0 G 0.3 w 10 M 109.6203 92.5295 m S 0 g 1 w 4 M 109.6203 92.5295 m F 0 G 0.3 w 10 M 109.6203 92.5295 m S 0 g 1 w 4 M 109.6203 92.5295 m F 0 G 0.3 w 10 M 124.8272 107.4579 m S 0 g 1 w 4 M 124.8272 107.4579 m F 0 G 0.3 w 10 M 124.8272 107.4579 m S 0 g 1 w 4 M 124.8272 107.4579 m F 0 G 0.3 w 10 M 124.8272 107.4579 m S 0 g 1 w 4 M 124.8272 107.4579 m F 0 G 0.3 w 10 M 124.8272 107.4579 m S 0 g 1 w 4 M 124.8272 107.4579 m F 0 G 0.3 w 10 M 109.6203 107.4579 m S 0 g 1 w 4 M 109.6203 107.4579 m F 0 G 0.3 w 10 M 109.6203 107.4579 m S 0 g 1 w 4 M 109.6203 107.4579 m F 1 g 109.6203 107.4579 m F 0 G 0.3 w 10 M 109.6203 107.4579 m S 0 g 1 w 4 M 109.6203 107.4579 m F 0 G 0.3 w 10 M 109.6203 107.4579 m S 0 g 1 w 4 M 109.6203 107.4579 m F 0 G 0.3 w 10 M 125.6726 91.9295 m S 0 g 1 w 4 M 125.6726 91.9295 m F 0 G 0.3 w 10 M 125.6726 91.9295 m S 0 g 1 w 4 M 125.6726 91.9295 m F 1 g 119.6622 91.9295 m 119.6622 88.7077 122.3532 86.0959 125.6726 86.0959 c 128.992 86.0959 131.683 88.7077 131.683 91.9295 c F 131.683 91.9295 m 131.683 95.1513 128.992 97.7631 125.6726 97.7631 c 122.3532 97.7631 119.6622 95.1513 119.6622 91.9295 c F 125.6726 91.9295 m F 0 G 0.3 w 10 M 125.6726 91.9295 m S 0 g 1 w 4 M 125.6726 91.9295 m F 0 G 0.3 w 10 M 125.6726 91.9295 m S 0 g 1 w 4 M 125.6726 91.9295 m F 124.5875 92.9977 m 121.0019 93.0088 L 121.0019 90.8504 L 124.5875 90.8615 L F 126.7577 90.8615 m 130.3433 90.8504 L 130.3433 93.0088 L 126.7577 92.9977 L F 121.0019 93.0088 m 130.3433 93.0088 l 130.3433 90.8504 l 121.0019 90.8504 l 121.0019 93.0088 l f 0 G 0.3 w 10 M 108.4226 108.6795 m S 0 g 1 w 4 M 108.4226 108.6795 m F 0 G 0.3 w 10 M 108.4226 108.6795 m S 0 g 1 w 4 M 108.4226 108.6795 m F 1 g 102.4122 108.6795 m 102.4122 105.4577 105.1032 102.8459 108.4226 102.8459 c 111.742 102.8459 114.433 105.4577 114.433 108.6795 c F 114.433 108.6795 m 114.433 111.9013 111.742 114.5131 108.4226 114.5131 c F 108.4226 114.5131 m 105.1032 114.5131 102.4122 111.9013 102.4122 108.6795 c F 108.4226 108.6795 m F 0 G 0.3 w 10 M 108.4226 108.6795 m S 0 g 1 w 4 M 108.4226 108.6795 m F 0 G 0.3 w 10 M 108.4226 108.6795 m S 0 g 1 w 4 M 108.4226 108.6795 m F 107.3375 109.7477 m 103.7519 109.7588 L 103.7519 107.6004 L 107.3375 107.6115 L F 109.5077 107.6115 m 113.0933 107.6004 L 113.0933 109.7588 L 109.5077 109.7477 L F 103.7519 109.7588 m 113.0933 109.7588 l 113.0933 107.6004 l 103.7519 107.6004 l 103.7519 109.7588 l f 0 G 0.3 w 10 M 123.4226 103.6795 m S 0 g 1 w 4 M 123.4226 103.6795 m F 0 G 0.3 w 10 M 123.4226 103.6795 m S 0 g 1 w 4 M 123.4226 103.6795 m F 1 g 117.4122 103.6795 m 117.4122 100.4577 120.1032 97.8459 123.4226 97.8459 c 126.742 97.8459 129.433 100.4577 129.433 103.6795 c F 129.433 103.6795 m 129.433 106.9013 126.742 109.5131 123.4226 109.5131 c 120.1032 109.5131 117.4122 106.9013 117.4122 103.6795 c F 123.4226 103.6795 m F 0 G 0.3 w 10 M 123.4226 103.6795 m S 0 g 1 w 4 M 123.4226 103.6795 m F 0 G 0.3 w 10 M 123.4226 103.6795 m S 0 g 1 w 4 M 123.4226 103.6795 m F 122.3375 104.7477 m 118.7519 104.7588 L 118.7519 102.6004 L 122.3375 102.6115 L F 124.5077 102.6115 m 128.0933 102.6004 L 128.0933 104.7588 L 124.5077 104.7477 L F 118.7519 104.7588 m 128.0933 104.7588 l 128.0933 102.6004 l 118.7519 102.6004 l 118.7519 104.7588 l f 0 G 0.3 w 10 M 110.6726 95.1795 m S 0 g 1 w 4 M 110.6726 95.1795 m F 0 G 0.3 w 10 M 110.6726 95.1795 m S 0 g 1 w 4 M 110.6726 95.1795 m F 1 g 104.6622 95.1795 m 104.6622 91.9577 107.3532 89.3459 110.6726 89.3459 c 113.992 89.3459 116.683 91.9577 116.683 95.1795 c F 116.683 95.1795 m 116.683 98.4013 113.992 101.0131 110.6726 101.0131 c 107.3532 101.0131 104.6622 98.4013 104.6622 95.1795 c F 110.6726 95.1795 m F 0 G 0.3 w 10 M 110.6726 95.1795 m S 0 g 1 w 4 M 110.6726 95.1795 m F 0 G 0.3 w 10 M 110.6726 95.1795 m S 0 g 1 w 4 M 110.6726 95.1795 m F 109.5875 96.2477 m 106.0019 96.2588 L 106.0019 94.1004 L 109.5875 94.1115 L F 111.7577 94.1115 m 115.3433 94.1004 L 115.3433 96.2588 L 111.7577 96.2477 L F 106.0019 96.2588 m 115.3433 96.2588 l 115.3433 94.1004 l 106.0019 94.1004 l 106.0019 96.2588 l f 0 G 0.3 w 10 M 63.9996 92.5295 m S 63.9996 107.4579 m S 63.9996 107.4579 m S 63.9996 107.4579 m S 63.9996 107.4579 m S 63.9996 92.5295 m S 63.9996 77.601 m S 63.9996 92.5295 m S 63.9996 77.601 m S 63.9996 77.601 m S 63.9996 92.5295 m S 63.9996 77.601 m S 63.9996 92.5295 m S 63.9996 107.4579 m S 63.9996 107.4579 m S 63.9996 107.4579 m S 63.9996 107.4579 m S 63.9996 92.5295 m S 63.9996 77.601 m S 63.9996 92.5295 m S 63.9996 77.601 m S 63.9996 77.601 m S 63.9996 92.5295 m S 63.9996 77.601 m S 63.9996 77.6011 m S 63.9996 92.5295 m S 63.9996 77.6011 m S 63.9996 77.6011 m S 63.9996 92.5295 m S 63.9996 77.6011 m S 63.9996 77.6011 m S 63.9996 92.5295 m S 63.9996 77.6011 m S 63.9996 77.6011 m S 63.9996 92.5295 m S 63.9996 77.6011 m S 64.8426 106.6302 m S 64.8426 106.6302 m S 64.8426 106.6302 m S 64.8426 106.6302 m S 63.9996 107.4579 m S 0 g 1 w 4 M 63.9996 107.4579 m F 0 G 0.3 w 10 M 63.9996 107.4579 m S 63.9996 107.4579 m S 63.9996 107.4579 m S 0 g 1 w 4 M 63.9996 107.4579 m F 0 G 0.3 w 10 M 63.9996 107.4579 m S 63.9996 107.4579 m S 1 g 1 w 4 M 57.9892 107.4579 m 57.9892 104.2361 60.6802 101.6243 63.9996 101.6243 c 67.319 101.6243 70.01 104.2361 70.01 107.4579 c F 70.01 107.4579 m 70.01 110.6797 67.319 113.2915 63.9996 113.2915 c 60.6802 113.2915 57.9892 110.6797 57.9892 107.4579 c F 63.9996 107.4579 m F 0 G 0.3 w 10 M 63.9996 107.4579 m S 0 g 1 w 4 M 63.9996 107.4579 m F 0 G 0.3 w 10 M 63.9996 107.4579 m S 63.9996 107.4579 m S 0 g 1 w 4 M 62.9145 106.39 m 62.9145 102.8129 L 65.0847 102.8129 L 65.0847 106.39 L 68.6703 106.3788 L 68.6703 108.5372 L 65.0847 108.5261 L 65.0847 112.1032 L 62.9145 112.1032 L 62.9145 108.5261 L 59.3289 108.5372 L 59.3289 106.3788 L 62.9145 106.39 L f 0 G 0.3 w 10 M 63.9996 77.6011 m S 0 g 1 w 4 M 63.9996 77.6011 m F 0 G 0.3 w 10 M 63.9996 77.6011 m S 63.9996 77.6011 m S 63.9996 77.6011 m S 0 g 1 w 4 M 63.9996 77.6011 m F 0 G 0.3 w 10 M 63.9996 77.6011 m S 63.9996 77.6011 m S 63.9996 77.6011 m S 0 g 1 w 4 M 63.9996 77.6011 m F 0 G 0.3 w 10 M 63.9996 77.6011 m S 63.9996 77.6011 m S 64.6337 82.5545 m S 0 g 1 w 4 M 64.6337 82.5545 m F 0 G 0.3 w 10 M 64.6337 82.5545 m S 64.6337 82.5545 m S 64.6337 82.5545 m S 0 g 1 w 4 M 64.6337 82.5545 m F 0 G 0.3 w 10 M 64.6337 82.5545 m S 64.6337 82.5545 m S 1 g 1 w 4 M 58.6233 82.5545 m 58.6233 79.3327 61.3143 76.7209 64.6337 76.7209 c 67.9531 76.7209 70.6441 79.3327 70.6441 82.5545 c F 70.6441 82.5545 m 70.6441 85.7763 67.9531 88.3881 64.6337 88.3881 c 61.3143 88.3881 58.6233 85.7763 58.6233 82.5545 c F 64.6337 82.5545 m F 0 G 0.3 w 10 M 64.6337 82.5545 m S 0 g 1 w 4 M 64.6337 82.5545 m F 0 G 0.3 w 10 M 64.6337 82.5545 m S 64.6337 82.5545 m S 0 g 1 w 4 M 63.5486 81.4866 m 63.5486 77.9095 L 65.7188 77.9095 L 65.7188 81.4866 L 69.3044 81.4754 L 69.3044 83.6338 L 65.7188 83.6227 L 65.7188 87.1998 L 63.5486 87.1998 L 63.5486 83.6227 L 59.963 83.6338 L 59.963 81.4754 L 63.5486 81.4866 L f 0 G 0.3 w 10 M 63.9996 137.3147 m S 63.9996 152.2431 m S 63.9996 152.2431 m S 63.9996 152.2431 m S 63.9996 152.2431 m S 63.9996 137.3147 m S 63.9996 122.3862 m S 63.9996 137.3147 m S 63.9996 122.3862 m S 63.9996 122.3862 m S 63.9996 137.3147 m S 63.9996 122.3862 m S 63.9996 137.3147 m S 63.9996 152.2431 m S 63.9996 152.2431 m S 63.9996 152.2431 m S 63.9996 152.2431 m S 63.9996 137.3147 m S 63.9996 122.3862 m S 63.9996 137.3147 m S 63.9996 122.3862 m S 63.9996 122.3862 m S 63.9996 137.3147 m S 63.9996 122.3862 m S 63.9996 122.3863 m S 63.9996 137.3147 m S 63.9996 122.3863 m S 63.9996 122.3863 m S 63.9996 137.3147 m S 63.9996 122.3863 m S 63.9996 122.3863 m S 63.9996 137.3147 m S 63.9996 122.3863 m S 63.9996 122.3863 m S 63.9996 137.3147 m S 63.9996 122.3863 m S 64.8426 151.4154 m S 64.8426 151.4154 m S 64.8426 151.4154 m S 64.8426 151.4154 m S 63.9996 152.2431 m S 0 g 1 w 4 M 63.9996 152.2431 m F 0 G 0.3 w 10 M 63.9996 152.2431 m S 63.9996 152.2431 m S 63.9996 152.2431 m S 0 g 1 w 4 M 63.9996 152.2431 m F 0 G 0.3 w 10 M 63.9996 152.2431 m S 63.9996 152.2431 m S 1 g 1 w 4 M 57.9892 152.2431 m 57.9892 149.0213 60.6802 146.4095 63.9996 146.4095 c 67.319 146.4095 70.01 149.0213 70.01 152.2431 c F 70.01 152.2431 m 70.01 155.4649 67.319 158.0767 63.9996 158.0767 c 60.6802 158.0767 57.9892 155.4649 57.9892 152.2431 c F 63.9996 152.2431 m F 0 G 0.3 w 10 M 63.9996 152.2431 m S 0 g 1 w 4 M 63.9996 152.2431 m F 0 G 0.3 w 10 M 63.9996 152.2431 m S 63.9996 152.2431 m S 0 g 1 w 4 M 62.9145 151.1752 m 62.9145 147.5981 L 65.0847 147.5981 L 65.0847 151.1752 L 68.6703 151.164 L 68.6703 153.3224 L 65.0847 153.3113 L 65.0847 156.8884 L 62.9145 156.8884 L 62.9145 153.3113 L 59.3289 153.3224 L 59.3289 151.164 L 62.9145 151.1752 L f 0 G 0.3 w 10 M 63.9996 122.3863 m S 0 g 1 w 4 M 63.9996 122.3863 m F 0 G 0.3 w 10 M 63.9996 122.3863 m S 63.9996 122.3863 m S 63.9996 122.3863 m S 0 g 1 w 4 M 63.9996 122.3863 m F 0 G 0.3 w 10 M 63.9996 122.3863 m S 63.9996 122.3863 m S 63.9996 122.3863 m S 0 g 1 w 4 M 63.9996 122.3863 m F 0 G 0.3 w 10 M 63.9996 122.3863 m S 63.9996 122.3863 m S 64.6337 127.3397 m S 0 g 1 w 4 M 64.6337 127.3397 m F 0 G 0.3 w 10 M 64.6337 127.3397 m S 64.6337 127.3397 m S 64.6337 127.3397 m S 0 g 1 w 4 M 64.6337 127.3397 m F 0 G 0.3 w 10 M 64.6337 127.3397 m S 64.6337 127.3397 m S 1 g 1 w 4 M 58.6233 127.3397 m 58.6233 124.1179 61.3143 121.5061 64.6337 121.5061 c 67.9531 121.5061 70.6441 124.1179 70.6441 127.3397 c F 70.6441 127.3397 m 70.6441 130.5615 67.9531 133.1733 64.6337 133.1733 c 61.3143 133.1733 58.6233 130.5615 58.6233 127.3397 c F 64.6337 127.3397 m F 0 G 0.3 w 10 M 64.6337 127.3397 m S 0 g 1 w 4 M 64.6337 127.3397 m F 0 G 0.3 w 10 M 64.6337 127.3397 m S 64.6337 127.3397 m S 0 g 1 w 4 M 63.5486 126.2718 m 63.5486 122.6947 L 65.7188 122.6947 L 65.7188 126.2718 L 69.3044 126.2606 L 69.3044 128.419 L 65.7188 128.4079 L 65.7188 131.985 L 63.5486 131.985 L 63.5486 128.4079 L 59.963 128.419 L 59.963 126.2606 L 63.5486 126.2718 L f 0 G 0.3 w 10 M 140.034 137.3147 m S 140.034 152.2431 m S 140.034 152.2431 m S 140.034 152.2431 m S 140.034 152.2431 m S 140.034 137.3147 m S 140.034 122.3862 m S 140.034 137.3147 m S 140.034 122.3862 m S 140.034 122.3862 m S 140.034 137.3147 m S 140.034 122.3862 m S 140.034 137.3147 m S 140.034 152.2431 m S 140.034 152.2431 m S 140.034 152.2431 m S 140.034 152.2431 m S 140.034 137.3147 m S 140.034 122.3862 m S 140.034 137.3147 m S 140.034 122.3862 m S 140.034 122.3862 m S 140.034 137.3147 m S 140.034 122.3862 m S 140.034 122.3863 m S 140.034 137.3147 m S 140.034 122.3863 m S 140.034 122.3863 m S 140.034 137.3147 m S 140.034 122.3863 m S 140.034 122.3863 m S 140.034 137.3147 m S 140.034 122.3863 m S 140.034 122.3863 m S 140.034 137.3147 m S 140.034 122.3863 m S 140.877 151.4154 m S 140.877 151.4154 m S 140.877 151.4154 m S 140.877 151.4154 m S 140.034 152.2431 m S 0 g 1 w 4 M 140.034 152.2431 m F 0 G 0.3 w 10 M 140.034 152.2431 m S 140.034 152.2431 m S 140.034 152.2431 m S 0 g 1 w 4 M 140.034 152.2431 m F 0 G 0.3 w 10 M 140.034 152.2431 m S 140.034 152.2431 m S 1 g 1 w 4 M 134.0236 152.2431 m 134.0236 149.0213 136.7146 146.4095 140.034 146.4095 c 143.3534 146.4095 146.0444 149.0213 146.0444 152.2431 c F 146.0444 152.2431 m 146.0444 155.4649 143.3534 158.0767 140.034 158.0767 c 136.7146 158.0767 134.0236 155.4649 134.0236 152.2431 c F 140.034 152.2431 m F 0 G 0.3 w 10 M 140.034 152.2431 m S 0 g 1 w 4 M 140.034 152.2431 m F 0 G 0.3 w 10 M 140.034 152.2431 m S 140.034 152.2431 m S 0 g 1 w 4 M 138.9489 151.1752 m 138.9489 147.5981 L 141.1191 147.5981 L 141.1191 151.1752 L 144.7047 151.164 L 144.7047 153.3224 L 141.1191 153.3113 L 141.1191 156.8884 L 138.9489 156.8884 L 138.9489 153.3113 L 135.3633 153.3224 L 135.3633 151.164 L 138.9489 151.1752 L f 0 G 0.3 w 10 M 140.034 122.3863 m S 0 g 1 w 4 M 140.034 122.3863 m F 0 G 0.3 w 10 M 140.034 122.3863 m S 140.034 122.3863 m S 140.034 122.3863 m S 0 g 1 w 4 M 140.034 122.3863 m F 0 G 0.3 w 10 M 140.034 122.3863 m S 140.034 122.3863 m S 140.034 122.3863 m S 0 g 1 w 4 M 140.034 122.3863 m F 0 G 0.3 w 10 M 140.034 122.3863 m S 140.034 122.3863 m S 140.6681 127.3397 m S 0 g 1 w 4 M 140.6681 127.3397 m F 0 G 0.3 w 10 M 140.6681 127.3397 m S 140.6681 127.3397 m S 140.6681 127.3397 m S 0 g 1 w 4 M 140.6681 127.3397 m F 0 G 0.3 w 10 M 140.6681 127.3397 m S 140.6681 127.3397 m S 1 g 1 w 4 M 134.6577 127.3397 m 134.6577 124.1179 137.3487 121.5061 140.6681 121.5061 c 143.9875 121.5061 146.6785 124.1179 146.6785 127.3397 c F 146.6785 127.3397 m 146.6785 130.5615 143.9875 133.1733 140.6681 133.1733 c 137.3487 133.1733 134.6577 130.5615 134.6577 127.3397 c F 140.6681 127.3397 m F 0 G 0.3 w 10 M 140.6681 127.3397 m S 0 g 1 w 4 M 140.6681 127.3397 m F 0 G 0.3 w 10 M 140.6681 127.3397 m S 140.6681 127.3397 m S 0 g 1 w 4 M 139.583 126.2718 m 139.583 122.6947 L 141.7532 122.6947 L 141.7532 126.2718 L 145.3388 126.2606 L 145.3388 128.419 L 141.7532 128.4079 L 141.7532 131.985 L 139.583 131.985 L 139.583 128.4079 L 135.9974 128.419 L 135.9974 126.2606 L 139.583 126.2718 L f 0 G 0.3 w 10 M 140.034 92.5295 m S 140.034 107.4579 m S 140.034 107.4579 m S 140.034 107.4579 m S 140.034 107.4579 m S 140.034 92.5295 m S 140.034 77.601 m S 140.034 92.5295 m S 140.034 77.601 m S 140.034 77.601 m S 140.034 92.5295 m S 140.034 77.601 m S 140.034 92.5295 m S 140.034 107.4579 m S 140.034 107.4579 m S 140.034 107.4579 m S 140.034 107.4579 m S 140.034 92.5295 m S 140.034 77.601 m S 140.034 92.5295 m S 140.034 77.601 m S 140.034 77.601 m S 140.034 92.5295 m S 140.034 77.601 m S 140.034 77.6011 m S 140.034 92.5295 m S 140.034 77.6011 m S 140.034 77.6011 m S 140.034 92.5295 m S 140.034 77.6011 m S 140.034 77.6011 m S 140.034 92.5295 m S 140.034 77.6011 m S 140.034 77.6011 m S 140.034 92.5295 m S 140.034 77.6011 m S 140.877 106.6302 m S 140.877 106.6302 m S 140.877 106.6302 m S 140.877 106.6302 m S 140.034 107.4579 m S 0 g 1 w 4 M 140.034 107.4579 m F 0 G 0.3 w 10 M 140.034 107.4579 m S 140.034 107.4579 m S 140.034 107.4579 m S 0 g 1 w 4 M 140.034 107.4579 m F 0 G 0.3 w 10 M 140.034 107.4579 m S 140.034 107.4579 m S 1 g 1 w 4 M 134.0236 107.4579 m 134.0236 104.2361 136.7146 101.6243 140.034 101.6243 c 143.3534 101.6243 146.0444 104.2361 146.0444 107.4579 c F 146.0444 107.4579 m 146.0444 110.6797 143.3534 113.2915 140.034 113.2915 c 136.7146 113.2915 134.0236 110.6797 134.0236 107.4579 c F 140.034 107.4579 m F 0 G 0.3 w 10 M 140.034 107.4579 m S 0 g 1 w 4 M 140.034 107.4579 m F 0 G 0.3 w 10 M 140.034 107.4579 m S 140.034 107.4579 m S 0 g 1 w 4 M 138.9489 106.39 m 138.9489 102.8129 L 141.1191 102.8129 L 141.1191 106.39 L 144.7047 106.3788 L 144.7047 108.5372 L 141.1191 108.5261 L 141.1191 112.1032 L 138.9489 112.1032 L 138.9489 108.5261 L 135.3633 108.5372 L 135.3633 106.3788 L 138.9489 106.39 L f 0 G 0.3 w 10 M 140.034 77.6011 m S 0 g 1 w 4 M 140.034 77.6011 m F 0 G 0.3 w 10 M 140.034 77.6011 m S 140.034 77.6011 m S 140.034 77.6011 m S 0 g 1 w 4 M 140.034 77.6011 m F 0 G 0.3 w 10 M 140.034 77.6011 m S 140.034 77.6011 m S 140.034 77.6011 m S 0 g 1 w 4 M 140.034 77.6011 m F 0 G 0.3 w 10 M 140.034 77.6011 m S 140.034 77.6011 m S 140.6681 82.5545 m S 0 g 1 w 4 M 140.6681 82.5545 m F 0 G 0.3 w 10 M 140.6681 82.5545 m S 140.6681 82.5545 m S 140.6681 82.5545 m S 0 g 1 w 4 M 140.6681 82.5545 m F 0 G 0.3 w 10 M 140.6681 82.5545 m S 140.6681 82.5545 m S 1 g 1 w 4 M 134.6577 82.5545 m 134.6577 79.3327 137.3487 76.7209 140.6681 76.7209 c 143.9875 76.7209 146.6785 79.3327 146.6785 82.5545 c F 146.6785 82.5545 m 146.6785 85.7763 143.9875 88.3881 140.6681 88.3881 c 137.3487 88.3881 134.6577 85.7763 134.6577 82.5545 c F 140.6681 82.5545 m F 0 G 0.3 w 10 M 140.6681 82.5545 m S 0 g 1 w 4 M 140.6681 82.5545 m F 0 G 0.3 w 10 M 140.6681 82.5545 m S 140.6681 82.5545 m S 0 g 1 w 4 M 139.583 81.4866 m 139.583 77.9095 L 141.7532 77.9095 L 141.7532 81.4866 L 145.3388 81.4754 L 145.3388 83.6338 L 141.7532 83.6227 L 141.7532 87.1998 L 139.583 87.1998 L 139.583 83.6227 L 135.9974 83.6338 L 135.9974 81.4754 L 139.583 81.4866 L f 0 G 0.3 w 10 M 231.2752 182.1 m S 231.2752 197.0284 m S 231.2752 197.0284 m S 231.2752 197.0284 m S 231.2752 197.0284 m S 231.2752 182.1 m S 231.2752 167.1715 m S 231.2752 182.1 m S 231.2752 167.1715 m S 231.2752 167.1715 m S 231.2752 182.1 m S 231.2752 167.1715 m S 231.2752 182.1 m S 231.2752 197.0284 m S 231.2752 197.0284 m S 231.2752 197.0284 m S 231.2752 197.0284 m S 231.2752 182.1 m S 231.2752 167.1715 m S 231.2752 182.1 m S 231.2752 167.1715 m S 231.2752 167.1715 m S 231.2752 182.1 m S 231.2752 167.1715 m S 231.2752 167.1716 m S 231.2752 182.1 m S 231.2752 167.1716 m S 231.2752 167.1716 m S 231.2752 182.1 m S 231.2752 167.1716 m S 231.2752 167.1716 m S 231.2752 182.1 m S 231.2752 167.1716 m S 231.2752 167.1716 m S 231.2752 182.1 m S 231.2752 167.1716 m S 232.1182 196.2007 m S 232.1182 196.2007 m S 232.1182 196.2007 m S 232.1182 196.2007 m S 231.2752 197.0284 m S 0 g 1 w 4 M 231.2752 197.0284 m F 0 G 0.3 w 10 M 231.2752 197.0284 m S 231.2752 197.0284 m S 231.2752 197.0284 m S 0 g 1 w 4 M 231.2752 197.0284 m F 0 G 0.3 w 10 M 231.2752 197.0284 m S 231.2752 197.0284 m S 1 g 1 w 4 M 225.2648 197.0284 m 225.2648 193.8066 227.9558 191.1948 231.2752 191.1948 c 234.5946 191.1948 237.2856 193.8066 237.2856 197.0284 c F 237.2856 197.0284 m 237.2856 200.2502 234.5946 202.862 231.2752 202.862 c 227.9558 202.862 225.2648 200.2502 225.2648 197.0284 c F 231.2752 197.0284 m F 0 G 0.3 w 10 M 231.2752 197.0284 m S 0 g 1 w 4 M 231.2752 197.0284 m F 0 G 0.3 w 10 M 231.2752 197.0284 m S 231.2752 197.0284 m S 0 g 1 w 4 M 230.1901 195.9605 m 230.1901 192.3834 L 232.3603 192.3834 L 232.3603 195.9605 L 235.9459 195.9493 L 235.9459 198.1077 L 232.3603 198.0966 L 232.3603 201.6737 L 230.1901 201.6737 L 230.1901 198.0966 L 226.6045 198.1077 L 226.6045 195.9493 L 230.1901 195.9605 L f 0 G 0.3 w 10 M 231.2752 167.1716 m S 0 g 1 w 4 M 231.2752 167.1716 m F 0 G 0.3 w 10 M 231.2752 167.1716 m S 231.2752 167.1716 m S 231.2752 167.1716 m S 0 g 1 w 4 M 231.2752 167.1716 m F 0 G 0.3 w 10 M 231.2752 167.1716 m S 231.2752 167.1716 m S 231.2752 167.1716 m S 0 g 1 w 4 M 231.2752 167.1716 m F 0 G 0.3 w 10 M 231.2752 167.1716 m S 231.2752 167.1716 m S 231.9093 172.125 m S 0 g 1 w 4 M 231.9093 172.125 m F 0 G 0.3 w 10 M 231.9093 172.125 m S 231.9093 172.125 m S 231.9093 172.125 m S 0 g 1 w 4 M 231.9093 172.125 m F 0 G 0.3 w 10 M 231.9093 172.125 m S 231.9093 172.125 m S 1 g 1 w 4 M 225.8989 172.125 m 225.8989 168.9032 228.5899 166.2914 231.9093 166.2914 c 235.2287 166.2914 237.9197 168.9032 237.9197 172.125 c F 237.9197 172.125 m 237.9197 175.3468 235.2287 177.9586 231.9093 177.9586 c 228.5899 177.9586 225.8989 175.3468 225.8989 172.125 c F 231.9093 172.125 m F 0 G 0.3 w 10 M 231.9093 172.125 m S 0 g 1 w 4 M 231.9093 172.125 m F 0 G 0.3 w 10 M 231.9093 172.125 m S 231.9093 172.125 m S 0 g 1 w 4 M 230.8242 171.0571 m 230.8242 167.48 L 232.9944 167.48 L 232.9944 171.0571 L 236.58 171.0459 L 236.58 173.2043 L 232.9944 173.1932 L 232.9944 176.7703 L 230.8242 176.7703 L 230.8242 173.1932 L 227.2386 173.2043 L 227.2386 171.0459 L 230.8242 171.0571 L f 0 G 0.3 w 10 M 231.2752 226.8852 m S 231.2752 241.8136 m S 231.2752 241.8136 m S 231.2752 241.8136 m S 231.2752 241.8136 m S 231.2752 226.8852 m S 231.2752 211.9567 m S 231.2752 226.8852 m S 231.2752 211.9567 m S 231.2752 211.9567 m S 231.2752 226.8852 m S 231.2752 211.9567 m S 231.2752 226.8852 m S 231.2752 241.8136 m S 231.2752 241.8136 m S 231.2752 241.8136 m S 231.2752 241.8136 m S 231.2752 226.8852 m S 231.2752 211.9567 m S 231.2752 226.8852 m S 231.2752 211.9567 m S 231.2752 211.9567 m S 231.2752 226.8852 m S 231.2752 211.9567 m S 231.2752 211.9568 m S 231.2752 226.8852 m S 231.2752 211.9568 m S 231.2752 211.9568 m S 231.2752 226.8852 m S 231.2752 211.9568 m S 231.2752 211.9568 m S 231.2752 226.8852 m S 231.2752 211.9568 m S 231.2752 211.9568 m S 231.2752 226.8852 m S 231.2752 211.9568 m S 232.1182 240.9859 m S 232.1182 240.9859 m S 232.1182 240.9859 m S 232.1182 240.9859 m S 231.2752 241.8136 m S 0 g 1 w 4 M 231.2752 241.8136 m F 0 G 0.3 w 10 M 231.2752 241.8136 m S 231.2752 241.8136 m S 231.2752 241.8136 m S 0 g 1 w 4 M 231.2752 241.8136 m F 0 G 0.3 w 10 M 231.2752 241.8136 m S 231.2752 241.8136 m S 1 g 1 w 4 M 225.2648 241.8136 m 225.2648 238.5918 227.9558 235.98 231.2752 235.98 c 234.5946 235.98 237.2856 238.5918 237.2856 241.8136 c F 237.2856 241.8136 m 237.2856 245.0354 234.5946 247.6472 231.2752 247.6472 c 227.9558 247.6472 225.2648 245.0354 225.2648 241.8136 c F 231.2752 241.8136 m F 0 G 0.3 w 10 M 231.2752 241.8136 m S 0 g 1 w 4 M 231.2752 241.8136 m F 0 G 0.3 w 10 M 231.2752 241.8136 m S 231.2752 241.8136 m S 0 g 1 w 4 M 230.1901 240.7457 m 230.1901 237.1686 L 232.3603 237.1686 L 232.3603 240.7457 L 235.9459 240.7345 L 235.9459 242.8929 L 232.3603 242.8818 L 232.3603 246.4589 L 230.1901 246.4589 L 230.1901 242.8818 L 226.6045 242.8929 L 226.6045 240.7345 L 230.1901 240.7457 L f 0 G 0.3 w 10 M 231.2752 211.9568 m S 0 g 1 w 4 M 231.2752 211.9568 m F 0 G 0.3 w 10 M 231.2752 211.9568 m S 231.2752 211.9568 m S 231.2752 211.9568 m S 0 g 1 w 4 M 231.2752 211.9568 m F 0 G 0.3 w 10 M 231.2752 211.9568 m S 231.2752 211.9568 m S 231.2752 211.9568 m S 0 g 1 w 4 M 231.2752 211.9568 m F 0 G 0.3 w 10 M 231.2752 211.9568 m S 231.2752 211.9568 m S 231.9093 216.9102 m S 0 g 1 w 4 M 231.9093 216.9102 m F 0 G 0.3 w 10 M 231.9093 216.9102 m S 231.9093 216.9102 m S 231.9093 216.9102 m S 0 g 1 w 4 M 231.9093 216.9102 m F 0 G 0.3 w 10 M 231.9093 216.9102 m S 231.9093 216.9102 m S 1 g 1 w 4 M 225.8989 216.9102 m 225.8989 213.6884 228.5899 211.0766 231.9093 211.0766 c 235.2287 211.0766 237.9197 213.6884 237.9197 216.9102 c F 237.9197 216.9102 m 237.9197 220.132 235.2287 222.7438 231.9093 222.7438 c 228.5899 222.7438 225.8989 220.132 225.8989 216.9102 c F 231.9093 216.9102 m F 0 G 0.3 w 10 M 231.9093 216.9102 m S 0 g 1 w 4 M 231.9093 216.9102 m F 0 G 0.3 w 10 M 231.9093 216.9102 m S 231.9093 216.9102 m S 0 g 1 w 4 M 230.8242 215.8423 m 230.8242 212.2652 L 232.9944 212.2652 L 232.9944 215.8423 L 236.58 215.8311 L 236.58 217.9895 L 232.9944 217.9784 L 232.9944 221.5555 L 230.8242 221.5555 L 230.8242 217.9784 L 227.2386 217.9895 L 227.2386 215.8311 L 230.8242 215.8423 L f 0 G 0.3 w 10 M 200.8615 167.1715 m S 200.8615 167.1715 m S 200.8615 167.1715 m S 200.8615 167.1715 m S 200.8615 167.1715 m S 200.8615 167.1715 m S 216.0684 167.1715 m S 200.8615 167.1715 m S 216.0684 167.1715 m S 216.0684 167.1715 m S 216.0684 167.1715 m S 200.8615 167.1715 m S 200.8615 167.1716 m S 200.8615 167.1716 m S 200.8615 167.1716 m S 200.8615 167.1716 m S 200.8615 167.1716 m S 200.8615 167.1716 m S 216.0684 167.1716 m S 200.8615 167.1716 m S 216.0684 167.1716 m S 216.0684 167.1716 m S 216.0684 167.1716 m S 200.8615 167.1716 m S 216.0684 167.1716 m S 0 g 1 w 4 M 216.0684 167.1716 m F 0 G 0.3 w 10 M 216.0684 167.1716 m S 216.0684 167.1716 m S 216.0684 167.1716 m S 0 g 1 w 4 M 216.0684 167.1716 m F 0 G 0.3 w 10 M 216.0684 167.1716 m S 216.0684 167.1716 m S 216.0684 167.1716 m S 0 g 1 w 4 M 216.0684 167.1716 m F 0 G 0.3 w 10 M 216.0684 167.1716 m S 216.0684 167.1716 m S 208.0388 168.125 m S 0 g 1 w 4 M 208.0388 168.125 m F 0 G 0.3 w 10 M 208.0388 168.125 m S 208.0388 168.125 m S 208.0388 168.125 m S 0 g 1 w 4 M 208.0388 168.125 m F 0 G 0.3 w 10 M 208.0388 168.125 m S 208.0388 168.125 m S 1 g 1 w 4 M 202.0284 168.125 m 202.0284 164.9032 204.7194 162.2914 208.0388 162.2914 c 211.3582 162.2914 214.0492 164.9032 214.0492 168.125 c F 214.0492 168.125 m 214.0492 171.3468 211.3582 173.9586 208.0388 173.9586 c F 208.0388 173.9586 m 204.7194 173.9586 202.0284 171.3468 202.0284 168.125 c F 208.0388 168.125 m F 0 G 0.3 w 10 M 208.0388 168.125 m S 0 g 1 w 4 M 208.0388 168.125 m F 0 G 0.3 w 10 M 208.0388 168.125 m S 208.0388 168.125 m S 0 g 1 w 4 M 206.9537 167.0571 m 206.9537 163.48 L 209.1239 163.48 L 209.1239 167.0571 L 212.7095 167.0459 L 212.7095 169.2043 L 209.1239 169.1932 L 209.1239 172.7703 L 206.9537 172.7703 L 206.9537 169.1932 L 203.3681 169.2043 L 203.3681 167.0459 L 206.9537 167.0571 L f 0 G 0.3 w 10 M 215.4784 240.1715 m S 215.4784 240.1715 m S 215.4784 240.1715 m S 215.4784 240.1715 m S 215.4784 240.1716 m S 215.4784 240.1716 m S 215.4784 240.1716 m S 215.4784 240.1716 m S 215.4784 240.1716 m S 0 g 1 w 4 M 215.4784 240.1716 m F 0 G 0.3 w 10 M 215.4784 240.1716 m S 215.4784 240.1716 m S 215.4784 240.1716 m S 0 g 1 w 4 M 215.4784 240.1716 m F 0 G 0.3 w 10 M 215.4784 240.1716 m S 215.4784 240.1716 m S 215.4784 240.1716 m S 0 g 1 w 4 M 215.4784 240.1716 m F 0 G 0.3 w 10 M 215.4784 240.1716 m S 215.4784 240.1716 m S 207.4488 241.125 m S 0 g 1 w 4 M 207.4488 241.125 m F 0 G 0.3 w 10 M 207.4488 241.125 m S 207.4488 241.125 m S 207.4488 241.125 m S 0 g 1 w 4 M 207.4488 241.125 m F 0 G 0.3 w 10 M 207.4488 241.125 m S 207.4488 241.125 m S 1 g 1 w 4 M 207.4488 241.125 m F 0 G 0.3 w 10 M 207.4488 241.125 m S 0 g 1 w 4 M 207.4488 241.125 m F 0 G 0.3 w 10 M 207.4488 241.125 m S 207.4488 241.125 m S 79.2065 77.6009 m S 79.2065 77.6009 m S 79.2065 77.6009 m S 79.2065 77.6009 m S 79.2065 77.6009 m S 79.2065 77.6009 m S 94.4134 77.6009 m S 79.2065 77.6009 m S 94.4134 77.6009 m S 94.4134 77.6009 m S 94.4134 77.6009 m S 79.2065 77.6009 m S 79.2065 77.601 m S 79.2065 77.601 m S 79.2065 77.601 m S 79.2065 77.601 m S 79.2065 77.601 m S 79.2065 77.601 m S 94.4134 77.601 m S 79.2065 77.601 m S 94.4134 77.601 m S 94.4134 77.601 m S 94.4134 77.601 m S 79.2065 77.601 m S 94.4134 77.601 m S 0 g 1 w 4 M 94.4134 77.601 m F 0 G 0.3 w 10 M 94.4134 77.601 m S 94.4134 77.601 m S 94.4134 77.601 m S 0 g 1 w 4 M 94.4134 77.601 m F 0 G 0.3 w 10 M 94.4134 77.601 m S 94.4134 77.601 m S 94.4134 77.601 m S 0 g 1 w 4 M 94.4134 77.601 m F 0 G 0.3 w 10 M 94.4134 77.601 m S 94.4134 77.601 m S 86.3838 78.5544 m S 0 g 1 w 4 M 86.3838 78.5544 m F 0 G 0.3 w 10 M 86.3838 78.5544 m S 86.3838 78.5544 m S 86.3838 78.5544 m S 0 g 1 w 4 M 86.3838 78.5544 m F 0 G 0.3 w 10 M 86.3838 78.5544 m S 86.3838 78.5544 m S 1 g 1 w 4 M 80.3734 78.5544 m 80.3734 75.3326 83.0644 72.7208 86.3838 72.7208 c 89.7032 72.7208 92.3942 75.3326 92.3942 78.5544 c F 92.3942 78.5544 m 92.3942 81.7762 89.7032 84.388 86.3838 84.388 c F 86.3838 84.388 m 83.0644 84.388 80.3734 81.7762 80.3734 78.5544 c F 86.3838 78.5544 m F 0 G 0.3 w 10 M 86.3838 78.5544 m S 0 g 1 w 4 M 86.3838 78.5544 m F 0 G 0.3 w 10 M 86.3838 78.5544 m S 86.3838 78.5544 m S 0 g 1 w 4 M 85.2987 77.4865 m 85.2987 73.9094 L 87.4689 73.9094 L 87.4689 77.4865 L 91.0545 77.4753 L 91.0545 79.6337 L 87.4689 79.6226 L 87.4689 83.1997 L 85.2987 83.1997 L 85.2987 79.6226 L 81.7131 79.6337 L 81.7131 77.4753 L 85.2987 77.4865 L f 0 G 0.3 w 10 M 109.6203 77.6009 m S 109.6203 77.6009 m S 109.6203 77.6009 m S 109.6203 77.6009 m S 109.6203 77.6009 m S 109.6203 77.6009 m S 124.8272 77.6009 m S 109.6203 77.6009 m S 124.8272 77.6009 m S 124.8272 77.6009 m S 124.8272 77.6009 m S 109.6203 77.6009 m S 109.6203 77.601 m S 109.6203 77.601 m S 109.6203 77.601 m S 109.6203 77.601 m S 109.6203 77.601 m S 109.6203 77.601 m S 124.8272 77.601 m S 109.6203 77.601 m S 124.8272 77.601 m S 124.8272 77.601 m S 124.8272 77.601 m S 109.6203 77.601 m S 124.8272 77.601 m S 0 g 1 w 4 M 124.8272 77.601 m F 0 G 0.3 w 10 M 124.8272 77.601 m S 124.8272 77.601 m S 124.8272 77.601 m S 0 g 1 w 4 M 124.8272 77.601 m F 0 G 0.3 w 10 M 124.8272 77.601 m S 124.8272 77.601 m S 124.8272 77.601 m S 0 g 1 w 4 M 124.8272 77.601 m F 0 G 0.3 w 10 M 124.8272 77.601 m S 124.8272 77.601 m S 116.7976 78.5544 m S 0 g 1 w 4 M 116.7976 78.5544 m F 0 G 0.3 w 10 M 116.7976 78.5544 m S 116.7976 78.5544 m S 116.7976 78.5544 m S 0 g 1 w 4 M 116.7976 78.5544 m F 0 G 0.3 w 10 M 116.7976 78.5544 m S 116.7976 78.5544 m S 1 g 1 w 4 M 110.7872 78.5544 m 110.7872 75.3326 113.4782 72.7208 116.7976 72.7208 c 120.117 72.7208 122.808 75.3326 122.808 78.5544 c F 122.808 78.5544 m 122.808 81.7762 120.117 84.388 116.7976 84.388 c F 116.7976 84.388 m 113.4782 84.388 110.7872 81.7762 110.7872 78.5544 c F 116.7976 78.5544 m F 0 G 0.3 w 10 M 116.7976 78.5544 m S 0 g 1 w 4 M 116.7976 78.5544 m F 0 G 0.3 w 10 M 116.7976 78.5544 m S 116.7976 78.5544 m S 0 g 1 w 4 M 115.7125 77.4865 m 115.7125 73.9094 L 117.8827 73.9094 L 117.8827 77.4865 L 121.4683 77.4753 L 121.4683 79.6337 L 117.8827 79.6226 L 117.8827 83.1997 L 115.7125 83.1997 L 115.7125 79.6226 L 112.1269 79.6337 L 112.1269 77.4753 L 115.7125 77.4865 L f 0 G 0.3 w 10 M 79.5215 150.1715 m S 79.5215 150.1715 m S 79.5215 150.1715 m S 79.5215 150.1715 m S 79.5215 150.1715 m S 79.5215 150.1715 m S 94.7284 150.1715 m S 79.5215 150.1715 m S 94.7284 150.1715 m S 94.7284 150.1715 m S 94.7284 150.1715 m S 79.5215 150.1715 m S 79.5215 150.1716 m S 79.5215 150.1716 m S 79.5215 150.1716 m S 79.5215 150.1716 m S 79.5215 150.1716 m S 79.5215 150.1716 m S 94.7284 150.1716 m S 79.5215 150.1716 m S 94.7284 150.1716 m S 94.7284 150.1716 m S 94.7284 150.1716 m S 79.5215 150.1716 m S 94.7284 150.1716 m S 0 g 1 w 4 M 94.7284 150.1716 m F 0 G 0.3 w 10 M 94.7284 150.1716 m S 94.7284 150.1716 m S 94.7284 150.1716 m S 0 g 1 w 4 M 94.7284 150.1716 m F 0 G 0.3 w 10 M 94.7284 150.1716 m S 94.7284 150.1716 m S 94.7284 150.1716 m S 0 g 1 w 4 M 94.7284 150.1716 m F 0 G 0.3 w 10 M 94.7284 150.1716 m S 94.7284 150.1716 m S 86.6988 151.125 m S 0 g 1 w 4 M 86.6988 151.125 m F 0 G 0.3 w 10 M 86.6988 151.125 m S 86.6988 151.125 m S 86.6988 151.125 m S 0 g 1 w 4 M 86.6988 151.125 m F 0 G 0.3 w 10 M 86.6988 151.125 m S 86.6988 151.125 m S 1 g 1 w 4 M 80.6884 151.125 m 80.6884 147.9032 83.3794 145.2914 86.6988 145.2914 c 90.0182 145.2914 92.7092 147.9032 92.7092 151.125 c F 92.7092 151.125 m 92.7092 154.3468 90.0182 156.9586 86.6988 156.9586 c F 86.6988 156.9586 m 83.3794 156.9586 80.6884 154.3468 80.6884 151.125 c F 86.6988 151.125 m F 0 G 0.3 w 10 M 86.6988 151.125 m S 0 g 1 w 4 M 86.6988 151.125 m F 0 G 0.3 w 10 M 86.6988 151.125 m S 86.6988 151.125 m S 0 g 1 w 4 M 85.6137 150.0571 m 85.6137 146.48 L 87.7839 146.48 L 87.7839 150.0571 L 91.3695 150.0459 L 91.3695 152.2043 L 87.7839 152.1932 L 87.7839 155.7703 L 85.6137 155.7703 L 85.6137 152.1932 L 82.0281 152.2043 L 82.0281 150.0459 L 85.6137 150.0571 L f 0 G 0.3 w 10 M 109.6203 152.2431 m S 109.6203 152.2431 m S 124.8272 152.2431 m S 124.8272 152.2431 m S 124.8272 152.2431 m S 109.6203 152.2431 m S 124.8272 152.2431 m S 109.6203 152.2431 m S 109.6203 152.2431 m S 109.6203 152.2431 m S 124.8272 152.2431 m S 124.8272 152.2431 m S 124.8272 152.2431 m S 109.6203 152.2431 m S 124.8272 152.2431 m S 109.6203 152.2431 m S 109.9353 150.1715 m S 109.9353 150.1715 m S 109.9353 150.1715 m S 109.9353 150.1715 m S 109.9353 150.1715 m S 109.9353 150.1715 m S 125.1422 150.1715 m S 109.9353 150.1715 m S 125.1422 150.1715 m S 125.1422 150.1715 m S 125.1422 150.1715 m S 109.9353 150.1715 m S 109.9353 150.1716 m S 109.9353 150.1716 m S 109.9353 150.1716 m S 109.9353 150.1716 m S 109.9353 150.1716 m S 109.9353 150.1716 m S 125.1422 150.1716 m S 109.9353 150.1716 m S 125.1422 150.1716 m S 125.1422 150.1716 m S 125.1422 150.1716 m S 109.9353 150.1716 m S 125.1422 150.1716 m S 0 g 1 w 4 M 125.1422 150.1716 m F 0 G 0.3 w 10 M 125.1422 150.1716 m S 125.1422 150.1716 m S 125.1422 150.1716 m S 0 g 1 w 4 M 125.1422 150.1716 m F 0 G 0.3 w 10 M 125.1422 150.1716 m S 125.1422 150.1716 m S 125.1422 150.1716 m S 0 g 1 w 4 M 125.1422 150.1716 m F 0 G 0.3 w 10 M 125.1422 150.1716 m S 125.1422 150.1716 m S 117.1126 151.125 m S 0 g 1 w 4 M 117.1126 151.125 m F 0 G 0.3 w 10 M 117.1126 151.125 m S 117.1126 151.125 m S 117.1126 151.125 m S 0 g 1 w 4 M 117.1126 151.125 m F 0 G 0.3 w 10 M 117.1126 151.125 m S 117.1126 151.125 m S 1 g 1 w 4 M 111.1022 151.125 m 111.1022 147.9032 113.7932 145.2914 117.1126 145.2914 c F 117.1126 145.2914 m 120.432 145.2914 123.123 147.9032 123.123 151.125 c F 123.123 151.125 m 123.123 154.3468 120.432 156.9586 117.1126 156.9586 c F 117.1126 156.9586 m 113.7932 156.9586 111.1022 154.3468 111.1022 151.125 c F 117.1126 151.125 m F 0 G 0.3 w 10 M 117.1126 151.125 m S 0 g 1 w 4 M 117.1126 151.125 m F 0 G 0.3 w 10 M 117.1126 151.125 m S 117.1126 151.125 m S 0 g 1 w 4 M 118.1977 146.48 m 118.1977 150.0571 L 121.7833 150.0459 L 121.7833 152.2043 L 118.1977 152.1932 L 118.1977 155.7703 L 116.0275 155.7703 L 116.0275 152.1932 L 112.4419 152.2043 L 112.4419 150.0459 L 116.0275 150.0571 L 116.0275 146.48 L F 0 G 0.3 w 10 M 199.875 242.875 m S 199.875 242.875 m S 215.0819 242.875 m S 215.0819 242.875 m S 215.0819 242.875 m S 199.875 242.875 m S 215.0819 242.875 m S 199.875 242.875 m S 199.875 242.875 m S 199.875 242.875 m S 215.0819 242.875 m S 215.0819 242.875 m S 215.0819 242.875 m S 199.875 242.875 m S 215.0819 242.875 m S 199.875 242.875 m S 200.19 240.8034 m S 200.19 240.8034 m S 200.19 240.8034 m S 200.19 240.8034 m S 200.19 240.8034 m S 200.19 240.8034 m S 215.3969 240.8034 m S 200.19 240.8034 m S 215.3969 240.8034 m S 215.3969 240.8034 m S 215.3969 240.8034 m S 200.19 240.8034 m S 200.19 240.8035 m S 200.19 240.8035 m S 200.19 240.8035 m S 200.19 240.8035 m S 200.19 240.8035 m S 200.19 240.8035 m S 215.3969 240.8035 m S 200.19 240.8035 m S 215.3969 240.8035 m S 215.3969 240.8035 m S 215.3969 240.8035 m S 200.19 240.8035 m S 215.3969 240.8035 m S 0 g 1 w 4 M 215.3969 240.8035 m F 0 G 0.3 w 10 M 215.3969 240.8035 m S 215.3969 240.8035 m S 215.3969 240.8035 m S 0 g 1 w 4 M 215.3969 240.8035 m F 0 G 0.3 w 10 M 215.3969 240.8035 m S 215.3969 240.8035 m S 215.3969 240.8035 m S 0 g 1 w 4 M 215.3969 240.8035 m F 0 G 0.3 w 10 M 215.3969 240.8035 m S 215.3969 240.8035 m S 207.3673 241.7569 m S 0 g 1 w 4 M 207.3673 241.7569 m F 0 G 0.3 w 10 M 207.3673 241.7569 m S 207.3673 241.7569 m S 207.3673 241.7569 m S 0 g 1 w 4 M 207.3673 241.7569 m F 0 G 0.3 w 10 M 207.3673 241.7569 m S 207.3673 241.7569 m S 1 g 1 w 4 M 201.3569 241.7569 m 201.3569 238.5351 204.0479 235.9233 207.3673 235.9233 c F 207.3673 235.9233 m 210.6867 235.9233 213.3777 238.5351 213.3777 241.7569 c F 213.3777 241.7569 m 213.3777 244.9787 210.6867 247.5905 207.3673 247.5905 c F 207.3673 247.5905 m 204.0479 247.5905 201.3569 244.9787 201.3569 241.7569 c F 207.3673 241.7569 m F 0 G 0.3 w 10 M 207.3673 241.7569 m S 0 g 1 w 4 M 207.3673 241.7569 m F 0 G 0.3 w 10 M 207.3673 241.7569 m S 207.3673 241.7569 m S 0 g 1 w 4 M 208.4524 237.1119 m 208.4524 240.689 L 212.038 240.6778 L 212.038 242.8362 L 208.4524 242.8251 L 208.4524 246.4022 L 206.2822 246.4022 L 206.2822 242.8251 L 202.6966 242.8362 L 202.6966 240.6778 L 206.2822 240.689 L 206.2822 237.1119 L F 0 G 0.3 w 10 M 156.7831 207.8241 m S 156.7831 207.8241 m S 156.7831 207.8241 m S 156.7831 207.8241 m S 156.7831 207.8241 m S 156.7831 207.8241 m S 156.7831 207.8241 m S 156.7831 207.8241 m S 157.197 212.0573 m S 157.197 212.0573 m S 157.197 212.0573 m S 157.197 212.0573 m S 157.197 212.0573 m S 157.197 212.0573 m S 157.197 212.0573 m S 157.197 212.0573 m S 156.9087 212.3256 m S 156.9087 212.3256 m S 156.9087 212.3256 m S 156.9087 212.3256 m S 156.358 211.6981 m S 156.358 211.6981 m S 156.358 211.6981 m S 156.358 211.6981 m S 1 g 0.5 w 4 M 159.3731 211.7603 m 156.2492 204.9244 L B 156.2492 204.9244 m 152.8769 211.5285 L 159.3731 211.7603 L 156.2492 204.9244 L B 0.3 w 10 M 124.8271 241.8136 m S 124.8271 226.8852 m S 109.6203 226.8852 m S 109.6203 241.8136 m S 117.2237 234.3494 m S 109.6203 241.8136 m S 124.8271 241.8136 m S 109.6203 241.8136 m S 109.6203 241.8136 m S 109.6203 226.8852 m S 0 g 1 w 4 M 117.2237 234.3494 m F 0 G 0.3 w 10 M 140.034 241.8136 m S 140.034 226.8852 m S 140.034 241.8136 m S 140.034 241.8136 m S 140.034 226.8852 m S 124.8271 226.8852 m S 124.8271 241.8136 m S 132.4305 234.3494 m S 140.034 241.8136 m S 124.8271 241.8136 m S 0 g 1 w 4 M 132.4305 234.3494 m F 117.2237 219.421 m F 132.4305 219.421 m F 0 G 0.3 w 10 M 109.6203 211.9567 m S 109.6203 226.8852 m S 109.6203 211.9567 m S 124.8271 226.8852 m S 124.8271 211.9567 m S 109.6203 211.9567 m S 109.6203 226.8852 m S 117.2237 219.421 m S 124.8271 211.9567 m S 109.6203 211.9567 m S 0 g 1 w 4 M 117.2237 219.421 m F 0 G 0.3 w 10 M 140.034 226.8852 m S 140.034 211.9567 m S 124.8271 211.9567 m S 124.8271 226.8852 m S 132.4305 219.421 m S 140.034 211.9567 m S 140.034 211.9567 m S 140.034 226.8852 m S 140.034 211.9567 m S 124.8271 211.9567 m S 0 g 1 w 4 M 132.4305 219.421 m F 0 G 0.3 w 10 M 140.034 241.8136 m S 140.034 226.8852 m S 140.034 241.8136 m S 140.034 241.8136 m S 140.034 226.8852 m S 124.8271 226.8852 m S 124.8271 241.8136 m S 132.4305 234.3494 m S 140.034 241.8136 m S 124.8271 241.8136 m S 0 g 1 w 4 M 132.4305 234.3494 m F 132.4305 219.421 m F 0 G 0.3 w 10 M 140.034 226.8852 m S 140.034 211.9567 m S 124.8271 211.9567 m S 124.8271 226.8852 m S 132.4305 219.421 m S 140.034 211.9567 m S 140.034 211.9567 m S 140.034 226.8852 m S 140.034 211.9567 m S 124.8271 211.9567 m S 0 g 1 w 4 M 132.4305 219.421 m F 0 G 0.3 w 10 M 109.6203 211.9568 m S 109.6203 226.8852 m S 109.6203 211.9568 m S 124.8271 226.8852 m S 124.8271 211.9568 m S 109.6203 211.9568 m S 109.6203 226.8852 m S 117.2237 219.421 m S 124.8271 211.9568 m S 109.6203 211.9568 m S 0 g 1 w 4 M 117.2237 219.421 m F 0 G 0.3 w 10 M 140.034 226.8852 m S 140.034 211.9568 m S 124.8271 211.9568 m S 124.8271 226.8852 m S 132.4305 219.421 m S 140.034 211.9568 m S 140.034 211.9568 m S 140.034 226.8852 m S 140.034 211.9568 m S 124.8271 211.9568 m S 0 g 1 w 4 M 132.4305 219.421 m F 0 G 0.3 w 10 M 140.034 226.8852 m S 140.034 211.9568 m S 124.8271 211.9568 m S 124.8271 226.8852 m S 132.4305 219.421 m S 140.034 211.9568 m S 140.034 211.9568 m S 140.034 226.8852 m S 140.034 211.9568 m S 124.8271 211.9568 m S 0 g 1 w 4 M 132.4305 219.421 m F 0 G 0.3 w 10 M 140.034 211.9568 m S 0 g 1 w 4 M 140.034 211.9568 m F 0 G 0.3 w 10 M 140.034 211.9568 m S 140.034 211.9568 m S 140.034 211.9568 m S 0 g 1 w 4 M 140.034 211.9568 m F 0 G 0.3 w 10 M 140.034 211.9568 m S 140.034 211.9568 m S 140.034 211.9568 m S 0 g 1 w 4 M 140.034 211.9568 m F 0 G 0.3 w 10 M 140.034 211.9568 m S 140.034 211.9568 m S 140.034 241.8136 m S 0 g 1 w 4 M 140.034 241.8136 m F 0 G 0.3 w 10 M 140.034 241.8136 m S 140.034 241.8136 m S 140.034 241.8136 m S 0 g 1 w 4 M 140.034 241.8136 m F 0 G 0.3 w 10 M 140.034 241.8136 m S 140.034 241.8136 m S 140.034 241.8136 m S 0 g 1 w 4 M 140.034 241.8136 m F 0 G 0.3 w 10 M 140.034 241.8136 m S 140.034 241.8136 m S 109.6203 241.8136 m S 0 g 1 w 4 M 109.6203 241.8136 m F 0 G 0.3 w 10 M 109.6203 241.8136 m S 109.6203 241.8136 m S 109.6203 241.8136 m S 0 g 1 w 4 M 109.6203 241.8136 m F 0 G 0.3 w 10 M 109.6203 241.8136 m S 109.6203 241.8136 m S 109.6203 241.8136 m S 0 g 1 w 4 M 109.6203 241.8136 m F 0 G 0.3 w 10 M 109.6203 241.8136 m S 109.6203 241.8136 m S 124.8271 226.8852 m S 0 g 1 w 4 M 124.8271 226.8852 m F 0 G 0.3 w 10 M 124.8271 226.8852 m S 124.8271 226.8852 m S 124.8271 226.8852 m S 0 g 1 w 4 M 124.8271 226.8852 m F 0 G 0.3 w 10 M 124.8271 226.8852 m S 124.8271 226.8852 m S 124.8271 226.8852 m S 0 g 1 w 4 M 124.8271 226.8852 m F 0 G 0.3 w 10 M 124.8271 226.8852 m S 124.8271 226.8852 m S 109.6203 211.9568 m S 0 g 1 w 4 M 109.6203 211.9568 m F 0 G 0.3 w 10 M 109.6203 211.9568 m S 109.6203 211.9568 m S 109.6203 211.9568 m S 0 g 1 w 4 M 109.6203 211.9568 m F 0 G 0.3 w 10 M 109.6203 211.9568 m S 109.6203 211.9568 m S 109.6203 211.9568 m S 0 g 1 w 4 M 109.6203 211.9568 m F 0 G 0.3 w 10 M 109.6203 211.9568 m S 109.6203 211.9568 m S 135.875 237.4102 m S 0 g 1 w 4 M 135.875 237.4102 m F 0 G 0.3 w 10 M 135.875 237.4102 m S 135.875 237.4102 m S 135.875 237.4102 m S 0 g 1 w 4 M 135.875 237.4102 m F 0 G 0.3 w 10 M 135.875 237.4102 m S 135.875 237.4102 m S 1 g 1 w 4 M 129.8646 237.4102 m 129.8646 234.1884 132.5556 231.5766 135.875 231.5766 c 139.1944 231.5766 141.8854 234.1884 141.8854 237.4102 c F 141.8854 237.4102 m 141.8854 240.632 139.1944 243.2438 135.875 243.2438 c 132.5556 243.2438 129.8646 240.632 129.8646 237.4102 c F 135.875 237.4102 m F 0 G 0.3 w 10 M 135.875 237.4102 m S 0 g 1 w 4 M 135.875 237.4102 m F 0 G 0.3 w 10 M 135.875 237.4102 m S 135.875 237.4102 m S 0 g 1 w 4 M 134.7899 236.3423 m 134.7899 232.7652 L 136.9601 232.7652 L 136.9601 236.3423 L 140.5457 236.3311 L 140.5457 238.4895 L 136.9601 238.4784 L 136.9601 242.0555 L 134.7899 242.0555 L 134.7899 238.4784 L 131.2043 238.4895 L 131.2043 236.3311 L 134.7899 236.3423 L f 0 G 0.3 w 10 M 111.375 241.9102 m S 0 g 1 w 4 M 111.375 241.9102 m F 0 G 0.3 w 10 M 111.375 241.9102 m S 111.375 241.9102 m S 111.375 241.9102 m S 0 g 1 w 4 M 111.375 241.9102 m F 0 G 0.3 w 10 M 111.375 241.9102 m S 111.375 241.9102 m S 1 g 1 w 4 M 105.3646 241.9102 m 105.3646 238.6884 108.0556 236.0766 111.375 236.0766 c 114.6944 236.0766 117.3854 238.6884 117.3854 241.9102 c F 117.3854 241.9102 m 117.3854 245.132 114.6944 247.7438 111.375 247.7438 c 108.0556 247.7438 105.3646 245.132 105.3646 241.9102 c F 111.375 241.9102 m F 0 G 0.3 w 10 M 111.375 241.9102 m S 0 g 1 w 4 M 111.375 241.9102 m F 0 G 0.3 w 10 M 111.375 241.9102 m S 111.375 241.9102 m S 0 g 1 w 4 M 110.2899 240.8423 m 110.2899 237.2652 L 112.4601 237.2652 L 112.4601 240.8423 L 116.0457 240.8311 L 116.0457 242.9895 L 112.4601 242.9784 L 112.4601 246.5555 L 110.2899 246.5555 L 110.2899 242.9784 L 106.7043 242.9895 L 106.7043 240.8311 L 110.2899 240.8423 L f 0 G 0.3 w 10 M 132.375 212.4102 m S 0 g 1 w 4 M 132.375 212.4102 m F 0 G 0.3 w 10 M 132.375 212.4102 m S 132.375 212.4102 m S 132.375 212.4102 m S 0 g 1 w 4 M 132.375 212.4102 m F 0 G 0.3 w 10 M 132.375 212.4102 m S 132.375 212.4102 m S 1 g 1 w 4 M 126.3646 212.4102 m 126.3646 209.1884 129.0556 206.5766 132.375 206.5766 c 135.6944 206.5766 138.3854 209.1884 138.3854 212.4102 c F 138.3854 212.4102 m 138.3854 215.632 135.6944 218.2438 132.375 218.2438 c 129.0556 218.2438 126.3646 215.632 126.3646 212.4102 c F 132.375 212.4102 m F 0 G 0.3 w 10 M 132.375 212.4102 m S 0 g 1 w 4 M 132.375 212.4102 m F 0 G 0.3 w 10 M 132.375 212.4102 m S 132.375 212.4102 m S 0 g 1 w 4 M 131.2899 211.3423 m 131.2899 207.7652 L 133.4601 207.7652 L 133.4601 211.3423 L 137.0457 211.3311 L 137.0457 213.4895 L 133.4601 213.4784 L 133.4601 217.0555 L 131.2899 217.0555 L 131.2899 213.4784 L 127.7043 213.4895 L 127.7043 211.3311 L 131.2899 211.3423 L f 0 G 0.3 w 10 M 122.125 231.4102 m S 0 g 1 w 4 M 122.125 231.4102 m F 0 G 0.3 w 10 M 122.125 231.4102 m S 122.125 231.4102 m S 122.125 231.4102 m S 0 g 1 w 4 M 122.125 231.4102 m F 0 G 0.3 w 10 M 122.125 231.4102 m S 122.125 231.4102 m S 1 g 1 w 4 M 116.1146 231.4102 m 116.1146 228.1884 118.8056 225.5766 122.125 225.5766 c 125.4444 225.5766 128.1354 228.1884 128.1354 231.4102 c F 128.1354 231.4102 m 128.1354 234.632 125.4444 237.2438 122.125 237.2438 c 118.8056 237.2438 116.1146 234.632 116.1146 231.4102 c F 122.125 231.4102 m F 0 G 0.3 w 10 M 122.125 231.4102 m S 0 g 1 w 4 M 122.125 231.4102 m F 0 G 0.3 w 10 M 122.125 231.4102 m S 122.125 231.4102 m S 0 g 1 w 4 M 121.0399 230.3423 m 121.0399 226.7652 L 123.2101 226.7652 L 123.2101 230.3423 L 126.7957 230.3311 L 126.7957 232.4895 L 123.2101 232.4784 L 123.2101 236.0555 L 121.0399 236.0555 L 121.0399 232.4784 L 117.4543 232.4895 L 117.4543 230.3311 L 121.0399 230.3423 L f 0 G 0.3 w 10 M 114.875 216.9102 m S 0 g 1 w 4 M 114.875 216.9102 m F 0 G 0.3 w 10 M 114.875 216.9102 m S 114.875 216.9102 m S 114.875 216.9102 m S 0 g 1 w 4 M 114.875 216.9102 m F 0 G 0.3 w 10 M 114.875 216.9102 m S 114.875 216.9102 m S 1 g 1 w 4 M 108.8646 216.9102 m 108.8646 213.6884 111.5556 211.0766 114.875 211.0766 c 118.1944 211.0766 120.8854 213.6884 120.8854 216.9102 c F 120.8854 216.9102 m 120.8854 220.132 118.1944 222.7438 114.875 222.7438 c 111.5556 222.7438 108.8646 220.132 108.8646 216.9102 c F 114.875 216.9102 m F 0 G 0.3 w 10 M 114.875 216.9102 m S 0 g 1 w 4 M 114.875 216.9102 m F 0 G 0.3 w 10 M 114.875 216.9102 m S 114.875 216.9102 m S 0 g 1 w 4 M 113.7899 215.8423 m 113.7899 212.2652 L 115.9601 212.2652 L 115.9601 215.8423 L 119.5457 215.8311 L 119.5457 217.9895 L 115.9601 217.9784 L 115.9601 221.5555 L 113.7899 221.5555 L 113.7899 217.9784 L 110.2043 217.9895 L 110.2043 215.8311 L 113.7899 215.8423 L f 0 G 0.3 w 10 M 79.2064 241.8136 m S 79.2064 226.8852 m S 63.9996 226.8852 m S 63.9996 241.8136 m S 71.603 234.3494 m S 63.9996 241.8136 m S 79.2064 241.8136 m S 63.9996 241.8136 m S 63.9996 241.8136 m S 63.9996 226.8852 m S 0 g 1 w 4 M 71.603 234.3494 m F 0 G 0.3 w 10 M 94.4133 241.8136 m S 94.4133 226.8852 m S 94.4133 241.8136 m S 94.4133 241.8136 m S 94.4133 226.8852 m S 79.2064 226.8852 m S 79.2064 241.8136 m S 86.8098 234.3494 m S 94.4133 241.8136 m S 79.2064 241.8136 m S 0 g 1 w 4 M 86.8098 234.3494 m F 71.603 219.421 m F 86.8098 219.421 m F 0 G 0.3 w 10 M 63.9996 211.9567 m S 63.9996 226.8852 m S 63.9996 211.9567 m S 79.2064 226.8852 m S 79.2064 211.9567 m S 63.9996 211.9567 m S 63.9996 226.8852 m S 71.603 219.421 m S 79.2064 211.9567 m S 63.9996 211.9567 m S 0 g 1 w 4 M 71.603 219.421 m F 0 G 0.3 w 10 M 94.4133 226.8852 m S 94.4133 211.9567 m S 79.2064 211.9567 m S 79.2064 226.8852 m S 86.8098 219.421 m S 94.4133 211.9567 m S 94.4133 211.9567 m S 94.4133 226.8852 m S 94.4133 211.9567 m S 79.2064 211.9567 m S 0 g 1 w 4 M 86.8098 219.421 m F 0 G 0.3 w 10 M 94.4133 241.8136 m S 94.4133 226.8852 m S 94.4133 241.8136 m S 94.4133 241.8136 m S 94.4133 226.8852 m S 79.2064 226.8852 m S 79.2064 241.8136 m S 86.8098 234.3494 m S 94.4133 241.8136 m S 79.2064 241.8136 m S 0 g 1 w 4 M 86.8098 234.3494 m F 86.8098 219.421 m F 0 G 0.3 w 10 M 94.4133 226.8852 m S 94.4133 211.9567 m S 79.2064 211.9567 m S 79.2064 226.8852 m S 86.8098 219.421 m S 94.4133 211.9567 m S 94.4133 211.9567 m S 94.4133 226.8852 m S 94.4133 211.9567 m S 79.2064 211.9567 m S 0 g 1 w 4 M 86.8098 219.421 m F 0 G 0.3 w 10 M 63.9996 211.9568 m S 63.9996 226.8852 m S 63.9996 211.9568 m S 79.2064 226.8852 m S 79.2064 211.9568 m S 63.9996 211.9568 m S 63.9996 226.8852 m S 71.603 219.421 m S 79.2064 211.9568 m S 63.9996 211.9568 m S 0 g 1 w 4 M 71.603 219.421 m F 0 G 0.3 w 10 M 94.4133 226.8852 m S 94.4133 211.9568 m S 79.2064 211.9568 m S 79.2064 226.8852 m S 86.8098 219.421 m S 94.4133 211.9568 m S 94.4133 211.9568 m S 94.4133 226.8852 m S 94.4133 211.9568 m S 79.2064 211.9568 m S 0 g 1 w 4 M 86.8098 219.421 m F 0 G 0.3 w 10 M 94.4133 226.8852 m S 94.4133 211.9568 m S 79.2064 211.9568 m S 79.2064 226.8852 m S 86.8098 219.421 m S 94.4133 211.9568 m S 94.4133 211.9568 m S 94.4133 226.8852 m S 94.4133 211.9568 m S 79.2064 211.9568 m S 0 g 1 w 4 M 86.8098 219.421 m F 0 G 0.3 w 10 M 94.4133 211.9568 m S 0 g 1 w 4 M 94.4133 211.9568 m F 0 G 0.3 w 10 M 94.4133 211.9568 m S 94.4133 211.9568 m S 94.4133 211.9568 m S 0 g 1 w 4 M 94.4133 211.9568 m F 0 G 0.3 w 10 M 94.4133 211.9568 m S 94.4133 211.9568 m S 94.4133 211.9568 m S 0 g 1 w 4 M 94.4133 211.9568 m F 0 G 0.3 w 10 M 94.4133 211.9568 m S 94.4133 211.9568 m S 94.4133 241.8136 m S 0 g 1 w 4 M 94.4133 241.8136 m F 0 G 0.3 w 10 M 94.4133 241.8136 m S 94.4133 241.8136 m S 94.4133 241.8136 m S 0 g 1 w 4 M 94.4133 241.8136 m F 0 G 0.3 w 10 M 94.4133 241.8136 m S 94.4133 241.8136 m S 94.4133 241.8136 m S 0 g 1 w 4 M 94.4133 241.8136 m F 0 G 0.3 w 10 M 94.4133 241.8136 m S 94.4133 241.8136 m S 63.9996 241.8136 m S 0 g 1 w 4 M 63.9996 241.8136 m F 0 G 0.3 w 10 M 63.9996 241.8136 m S 63.9996 241.8136 m S 63.9996 241.8136 m S 0 g 1 w 4 M 63.9996 241.8136 m F 0 G 0.3 w 10 M 63.9996 241.8136 m S 63.9996 241.8136 m S 63.9996 241.8136 m S 0 g 1 w 4 M 63.9996 241.8136 m F 0 G 0.3 w 10 M 63.9996 241.8136 m S 63.9996 241.8136 m S 79.2064 226.8852 m S 0 g 1 w 4 M 79.2064 226.8852 m F 0 G 0.3 w 10 M 79.2064 226.8852 m S 79.2064 226.8852 m S 79.2064 226.8852 m S 0 g 1 w 4 M 79.2064 226.8852 m F 0 G 0.3 w 10 M 79.2064 226.8852 m S 79.2064 226.8852 m S 79.2064 226.8852 m S 0 g 1 w 4 M 79.2064 226.8852 m F 0 G 0.3 w 10 M 79.2064 226.8852 m S 79.2064 226.8852 m S 63.9996 211.9568 m S 0 g 1 w 4 M 63.9996 211.9568 m F 0 G 0.3 w 10 M 63.9996 211.9568 m S 63.9996 211.9568 m S 63.9996 211.9568 m S 0 g 1 w 4 M 63.9996 211.9568 m F 0 G 0.3 w 10 M 63.9996 211.9568 m S 63.9996 211.9568 m S 63.9996 211.9568 m S 0 g 1 w 4 M 63.9996 211.9568 m F 0 G 0.3 w 10 M 63.9996 211.9568 m S 63.9996 211.9568 m S 90.2543 237.4102 m S 0 g 1 w 4 M 90.2543 237.4102 m F 0 G 0.3 w 10 M 90.2543 237.4102 m S 90.2543 237.4102 m S 90.2543 237.4102 m S 0 g 1 w 4 M 90.2543 237.4102 m F 0 G 0.3 w 10 M 90.2543 237.4102 m S 90.2543 237.4102 m S 1 g 1 w 4 M 84.2439 237.4102 m 84.2439 234.1884 86.9349 231.5766 90.2543 231.5766 c 93.5737 231.5766 96.2647 234.1884 96.2647 237.4102 c F 96.2647 237.4102 m 96.2647 240.632 93.5737 243.2438 90.2543 243.2438 c 86.9349 243.2438 84.2439 240.632 84.2439 237.4102 c F 90.2543 237.4102 m F 0 G 0.3 w 10 M 90.2543 237.4102 m S 0 g 1 w 4 M 90.2543 237.4102 m F 0 G 0.3 w 10 M 90.2543 237.4102 m S 90.2543 237.4102 m S 0 g 1 w 4 M 89.1692 236.3423 m 89.1692 232.7652 L 91.3394 232.7652 L 91.3394 236.3423 L 94.925 236.3311 L 94.925 238.4895 L 91.3394 238.4784 L 91.3394 242.0555 L 89.1692 242.0555 L 89.1692 238.4784 L 85.5836 238.4895 L 85.5836 236.3311 L 89.1692 236.3423 L f 0 G 0.3 w 10 M 65.7543 241.9102 m S 0 g 1 w 4 M 65.7543 241.9102 m F 0 G 0.3 w 10 M 65.7543 241.9102 m S 65.7543 241.9102 m S 65.7543 241.9102 m S 0 g 1 w 4 M 65.7543 241.9102 m F 0 G 0.3 w 10 M 65.7543 241.9102 m S 65.7543 241.9102 m S 1 g 1 w 4 M 59.7439 241.9102 m 59.7439 238.6884 62.4349 236.0766 65.7543 236.0766 c 69.0737 236.0766 71.7647 238.6884 71.7647 241.9102 c F 71.7647 241.9102 m 71.7647 245.132 69.0737 247.7438 65.7543 247.7438 c 62.4349 247.7438 59.7439 245.132 59.7439 241.9102 c F 65.7543 241.9102 m F 0 G 0.3 w 10 M 65.7543 241.9102 m S 0 g 1 w 4 M 65.7543 241.9102 m F 0 G 0.3 w 10 M 65.7543 241.9102 m S 65.7543 241.9102 m S 0 g 1 w 4 M 64.6692 240.8423 m 64.6692 237.2652 L 66.8394 237.2652 L 66.8394 240.8423 L 70.425 240.8311 L 70.425 242.9895 L 66.8394 242.9784 L 66.8394 246.5555 L 64.6692 246.5555 L 64.6692 242.9784 L 61.0836 242.9895 L 61.0836 240.8311 L 64.6692 240.8423 L f 0 G 0.3 w 10 M 86.7543 212.4102 m S 0 g 1 w 4 M 86.7543 212.4102 m F 0 G 0.3 w 10 M 86.7543 212.4102 m S 86.7543 212.4102 m S 86.7543 212.4102 m S 0 g 1 w 4 M 86.7543 212.4102 m F 0 G 0.3 w 10 M 86.7543 212.4102 m S 86.7543 212.4102 m S 1 g 1 w 4 M 80.7439 212.4102 m 80.7439 209.1884 83.4349 206.5766 86.7543 206.5766 c 90.0737 206.5766 92.7647 209.1884 92.7647 212.4102 c F 92.7647 212.4102 m 92.7647 215.632 90.0737 218.2438 86.7543 218.2438 c 83.4349 218.2438 80.7439 215.632 80.7439 212.4102 c F 86.7543 212.4102 m F 0 G 0.3 w 10 M 86.7543 212.4102 m S 0 g 1 w 4 M 86.7543 212.4102 m F 0 G 0.3 w 10 M 86.7543 212.4102 m S 86.7543 212.4102 m S 0 g 1 w 4 M 85.6692 211.3423 m 85.6692 207.7652 L 87.8394 207.7652 L 87.8394 211.3423 L 91.425 211.3311 L 91.425 213.4895 L 87.8394 213.4784 L 87.8394 217.0555 L 85.6692 217.0555 L 85.6692 213.4784 L 82.0836 213.4895 L 82.0836 211.3311 L 85.6692 211.3423 L f 0 G 0.3 w 10 M 76.5043 231.4102 m S 0 g 1 w 4 M 76.5043 231.4102 m F 0 G 0.3 w 10 M 76.5043 231.4102 m S 76.5043 231.4102 m S 76.5043 231.4102 m S 0 g 1 w 4 M 76.5043 231.4102 m F 0 G 0.3 w 10 M 76.5043 231.4102 m S 76.5043 231.4102 m S 1 g 1 w 4 M 70.4939 231.4102 m 70.4939 228.1884 73.1849 225.5766 76.5043 225.5766 c 79.8237 225.5766 82.5147 228.1884 82.5147 231.4102 c F 82.5147 231.4102 m 82.5147 234.632 79.8237 237.2438 76.5043 237.2438 c 73.1849 237.2438 70.4939 234.632 70.4939 231.4102 c F 76.5043 231.4102 m F 0 G 0.3 w 10 M 76.5043 231.4102 m S 0 g 1 w 4 M 76.5043 231.4102 m F 0 G 0.3 w 10 M 76.5043 231.4102 m S 76.5043 231.4102 m S 0 g 1 w 4 M 75.4192 230.3423 m 75.4192 226.7652 L 77.5894 226.7652 L 77.5894 230.3423 L 81.175 230.3311 L 81.175 232.4895 L 77.5894 232.4784 L 77.5894 236.0555 L 75.4192 236.0555 L 75.4192 232.4784 L 71.8336 232.4895 L 71.8336 230.3311 L 75.4192 230.3423 L f 0 G 0.3 w 10 M 69.2543 216.9102 m S 0 g 1 w 4 M 69.2543 216.9102 m F 0 G 0.3 w 10 M 69.2543 216.9102 m S 69.2543 216.9102 m S 69.2543 216.9102 m S 0 g 1 w 4 M 69.2543 216.9102 m F 0 G 0.3 w 10 M 69.2543 216.9102 m S 69.2543 216.9102 m S 1 g 1 w 4 M 63.2439 216.9102 m 63.2439 213.6884 65.9349 211.0766 69.2543 211.0766 c 72.5737 211.0766 75.2647 213.6884 75.2647 216.9102 c F 75.2647 216.9102 m 75.2647 220.132 72.5737 222.7438 69.2543 222.7438 c 65.9349 222.7438 63.2439 220.132 63.2439 216.9102 c F 69.2543 216.9102 m F 0 G 0.3 w 10 M 69.2543 216.9102 m S 0 g 1 w 4 M 69.2543 216.9102 m F 0 G 0.3 w 10 M 69.2543 216.9102 m S 69.2543 216.9102 m S 0 g 1 w 4 M 68.1692 215.8423 m 68.1692 212.2652 L 70.3394 212.2652 L 70.3394 215.8423 L 73.925 215.8311 L 73.925 217.9895 L 70.3394 217.9784 L 70.3394 221.5555 L 68.1692 221.5555 L 68.1692 217.9784 L 64.5836 217.9895 L 64.5836 215.8311 L 68.1692 215.8423 L f 0 G 0.3 w 10 M 79.2064 197.0284 m S 79.2064 182.1 m S 63.9996 182.1 m S 63.9996 197.0284 m S 71.603 189.5642 m S 63.9996 197.0284 m S 79.2064 197.0284 m S 63.9996 197.0284 m S 63.9996 197.0284 m S 63.9996 182.1 m S 0 g 1 w 4 M 71.603 189.5642 m F 0 G 0.3 w 10 M 94.4133 197.0284 m S 94.4133 182.1 m S 94.4133 197.0284 m S 94.4133 197.0284 m S 94.4133 182.1 m S 79.2064 182.1 m S 79.2064 197.0284 m S 86.8098 189.5642 m S 94.4133 197.0284 m S 79.2064 197.0284 m S 0 g 1 w 4 M 86.8098 189.5642 m F 71.603 174.6358 m F 86.8098 174.6358 m F 0 G 0.3 w 10 M 63.9996 167.1715 m S 63.9996 182.1 m S 63.9996 167.1715 m S 79.2064 182.1 m S 79.2064 167.1715 m S 63.9996 167.1715 m S 63.9996 182.1 m S 71.603 174.6358 m S 79.2064 167.1715 m S 63.9996 167.1715 m S 0 g 1 w 4 M 71.603 174.6358 m F 0 G 0.3 w 10 M 94.4133 182.1 m S 94.4133 167.1715 m S 79.2064 167.1715 m S 79.2064 182.1 m S 86.8098 174.6358 m S 94.4133 167.1715 m S 94.4133 167.1715 m S 94.4133 182.1 m S 94.4133 167.1715 m S 79.2064 167.1715 m S 0 g 1 w 4 M 86.8098 174.6358 m F 0 G 0.3 w 10 M 94.4133 197.0284 m S 94.4133 182.1 m S 94.4133 197.0284 m S 94.4133 197.0284 m S 94.4133 182.1 m S 79.2064 182.1 m S 79.2064 197.0284 m S 86.8098 189.5642 m S 94.4133 197.0284 m S 79.2064 197.0284 m S 0 g 1 w 4 M 86.8098 189.5642 m F 86.8098 174.6358 m F 0 G 0.3 w 10 M 94.4133 182.1 m S 94.4133 167.1715 m S 79.2064 167.1715 m S 79.2064 182.1 m S 86.8098 174.6358 m S 94.4133 167.1715 m S 94.4133 167.1715 m S 94.4133 182.1 m S 94.4133 167.1715 m S 79.2064 167.1715 m S 0 g 1 w 4 M 86.8098 174.6358 m F 0 G 0.3 w 10 M 63.9996 167.1716 m S 63.9996 182.1 m S 63.9996 167.1716 m S 79.2064 182.1 m S 79.2064 167.1716 m S 63.9996 167.1716 m S 63.9996 182.1 m S 71.603 174.6358 m S 79.2064 167.1716 m S 63.9996 167.1716 m S 0 g 1 w 4 M 71.603 174.6358 m F 0 G 0.3 w 10 M 94.4133 182.1 m S 94.4133 167.1716 m S 79.2064 167.1716 m S 79.2064 182.1 m S 86.8098 174.6358 m S 94.4133 167.1716 m S 94.4133 167.1716 m S 94.4133 182.1 m S 94.4133 167.1716 m S 79.2064 167.1716 m S 0 g 1 w 4 M 86.8098 174.6358 m F 0 G 0.3 w 10 M 94.4133 182.1 m S 94.4133 167.1716 m S 79.2064 167.1716 m S 79.2064 182.1 m S 86.8098 174.6358 m S 94.4133 167.1716 m S 94.4133 167.1716 m S 94.4133 182.1 m S 94.4133 167.1716 m S 79.2064 167.1716 m S 0 g 1 w 4 M 86.8098 174.6358 m F 0 G 0.3 w 10 M 94.4133 167.1716 m S 0 g 1 w 4 M 94.4133 167.1716 m F 0 G 0.3 w 10 M 94.4133 167.1716 m S 94.4133 167.1716 m S 94.4133 167.1716 m S 0 g 1 w 4 M 94.4133 167.1716 m F 0 G 0.3 w 10 M 94.4133 167.1716 m S 94.4133 167.1716 m S 94.4133 167.1716 m S 0 g 1 w 4 M 94.4133 167.1716 m F 0 G 0.3 w 10 M 94.4133 167.1716 m S 94.4133 167.1716 m S 94.4133 197.0284 m S 0 g 1 w 4 M 94.4133 197.0284 m F 0 G 0.3 w 10 M 94.4133 197.0284 m S 94.4133 197.0284 m S 94.4133 197.0284 m S 0 g 1 w 4 M 94.4133 197.0284 m F 0 G 0.3 w 10 M 94.4133 197.0284 m S 94.4133 197.0284 m S 94.4133 197.0284 m S 0 g 1 w 4 M 94.4133 197.0284 m F 0 G 0.3 w 10 M 94.4133 197.0284 m S 94.4133 197.0284 m S 63.9996 197.0284 m S 0 g 1 w 4 M 63.9996 197.0284 m F 0 G 0.3 w 10 M 63.9996 197.0284 m S 63.9996 197.0284 m S 63.9996 197.0284 m S 0 g 1 w 4 M 63.9996 197.0284 m F 0 G 0.3 w 10 M 63.9996 197.0284 m S 63.9996 197.0284 m S 63.9996 197.0284 m S 0 g 1 w 4 M 63.9996 197.0284 m F 0 G 0.3 w 10 M 63.9996 197.0284 m S 63.9996 197.0284 m S 79.2064 182.1 m S 0 g 1 w 4 M 79.2064 182.1 m F 0 G 0.3 w 10 M 79.2064 182.1 m S 79.2064 182.1 m S 79.2064 182.1 m S 0 g 1 w 4 M 79.2064 182.1 m F 0 G 0.3 w 10 M 79.2064 182.1 m S 79.2064 182.1 m S 79.2064 182.1 m S 0 g 1 w 4 M 79.2064 182.1 m F 0 G 0.3 w 10 M 79.2064 182.1 m S 79.2064 182.1 m S 63.9996 167.1716 m S 0 g 1 w 4 M 63.9996 167.1716 m F 0 G 0.3 w 10 M 63.9996 167.1716 m S 63.9996 167.1716 m S 63.9996 167.1716 m S 0 g 1 w 4 M 63.9996 167.1716 m F 0 G 0.3 w 10 M 63.9996 167.1716 m S 63.9996 167.1716 m S 63.9996 167.1716 m S 0 g 1 w 4 M 63.9996 167.1716 m F 0 G 0.3 w 10 M 63.9996 167.1716 m S 63.9996 167.1716 m S 90.2543 192.625 m S 0 g 1 w 4 M 90.2543 192.625 m F 0 G 0.3 w 10 M 90.2543 192.625 m S 90.2543 192.625 m S 90.2543 192.625 m S 0 g 1 w 4 M 90.2543 192.625 m F 0 G 0.3 w 10 M 90.2543 192.625 m S 90.2543 192.625 m S 1 g 1 w 4 M 84.2439 192.625 m 84.2439 189.4032 86.9349 186.7914 90.2543 186.7914 c 93.5737 186.7914 96.2647 189.4032 96.2647 192.625 c F 96.2647 192.625 m 96.2647 195.8468 93.5737 198.4586 90.2543 198.4586 c 86.9349 198.4586 84.2439 195.8468 84.2439 192.625 c F 90.2543 192.625 m F 0 G 0.3 w 10 M 90.2543 192.625 m S 0 g 1 w 4 M 90.2543 192.625 m F 0 G 0.3 w 10 M 90.2543 192.625 m S 90.2543 192.625 m S 0 g 1 w 4 M 89.1692 191.5571 m 89.1692 187.98 L 91.3394 187.98 L 91.3394 191.5571 L 94.925 191.5459 L 94.925 193.7043 L 91.3394 193.6932 L 91.3394 197.2703 L 89.1692 197.2703 L 89.1692 193.6932 L 85.5836 193.7043 L 85.5836 191.5459 L 89.1692 191.5571 L f 0 G 0.3 w 10 M 65.7543 197.125 m S 0 g 1 w 4 M 65.7543 197.125 m F 0 G 0.3 w 10 M 65.7543 197.125 m S 65.7543 197.125 m S 65.7543 197.125 m S 0 g 1 w 4 M 65.7543 197.125 m F 0 G 0.3 w 10 M 65.7543 197.125 m S 65.7543 197.125 m S 1 g 1 w 4 M 59.7439 197.125 m 59.7439 193.9032 62.4349 191.2914 65.7543 191.2914 c 69.0737 191.2914 71.7647 193.9032 71.7647 197.125 c F 71.7647 197.125 m 71.7647 200.3468 69.0737 202.9586 65.7543 202.9586 c 62.4349 202.9586 59.7439 200.3468 59.7439 197.125 c F 65.7543 197.125 m F 0 G 0.3 w 10 M 65.7543 197.125 m S 0 g 1 w 4 M 65.7543 197.125 m F 0 G 0.3 w 10 M 65.7543 197.125 m S 65.7543 197.125 m S 0 g 1 w 4 M 64.6692 196.0571 m 64.6692 192.48 L 66.8394 192.48 L 66.8394 196.0571 L 70.425 196.0459 L 70.425 198.2043 L 66.8394 198.1932 L 66.8394 201.7703 L 64.6692 201.7703 L 64.6692 198.1932 L 61.0836 198.2043 L 61.0836 196.0459 L 64.6692 196.0571 L f 0 G 0.3 w 10 M 86.7543 167.625 m S 0 g 1 w 4 M 86.7543 167.625 m F 0 G 0.3 w 10 M 86.7543 167.625 m S 86.7543 167.625 m S 86.7543 167.625 m S 0 g 1 w 4 M 86.7543 167.625 m F 0 G 0.3 w 10 M 86.7543 167.625 m S 86.7543 167.625 m S 1 g 1 w 4 M 80.7439 167.625 m 80.7439 164.4032 83.4349 161.7914 86.7543 161.7914 c 90.0737 161.7914 92.7647 164.4032 92.7647 167.625 c F 92.7647 167.625 m 92.7647 170.8468 90.0737 173.4586 86.7543 173.4586 c 83.4349 173.4586 80.7439 170.8468 80.7439 167.625 c F 86.7543 167.625 m F 0 G 0.3 w 10 M 86.7543 167.625 m S 0 g 1 w 4 M 86.7543 167.625 m F 0 G 0.3 w 10 M 86.7543 167.625 m S 86.7543 167.625 m S 0 g 1 w 4 M 85.6692 166.5571 m 85.6692 162.98 L 87.8394 162.98 L 87.8394 166.5571 L 91.425 166.5459 L 91.425 168.7043 L 87.8394 168.6932 L 87.8394 172.2703 L 85.6692 172.2703 L 85.6692 168.6932 L 82.0836 168.7043 L 82.0836 166.5459 L 85.6692 166.5571 L f 0 G 0.3 w 10 M 76.5043 186.625 m S 0 g 1 w 4 M 76.5043 186.625 m F 0 G 0.3 w 10 M 76.5043 186.625 m S 76.5043 186.625 m S 76.5043 186.625 m S 0 g 1 w 4 M 76.5043 186.625 m F 0 G 0.3 w 10 M 76.5043 186.625 m S 76.5043 186.625 m S 1 g 1 w 4 M 70.4939 186.625 m 70.4939 183.4032 73.1849 180.7914 76.5043 180.7914 c 79.8237 180.7914 82.5147 183.4032 82.5147 186.625 c F 82.5147 186.625 m 82.5147 189.8468 79.8237 192.4586 76.5043 192.4586 c 73.1849 192.4586 70.4939 189.8468 70.4939 186.625 c F 76.5043 186.625 m F 0 G 0.3 w 10 M 76.5043 186.625 m S 0 g 1 w 4 M 76.5043 186.625 m F 0 G 0.3 w 10 M 76.5043 186.625 m S 76.5043 186.625 m S 0 g 1 w 4 M 75.4192 185.5571 m 75.4192 181.98 L 77.5894 181.98 L 77.5894 185.5571 L 81.175 185.5459 L 81.175 187.7043 L 77.5894 187.6932 L 77.5894 191.2703 L 75.4192 191.2703 L 75.4192 187.6932 L 71.8336 187.7043 L 71.8336 185.5459 L 75.4192 185.5571 L f 0 G 0.3 w 10 M 69.2543 172.125 m S 0 g 1 w 4 M 69.2543 172.125 m F 0 G 0.3 w 10 M 69.2543 172.125 m S 69.2543 172.125 m S 69.2543 172.125 m S 0 g 1 w 4 M 69.2543 172.125 m F 0 G 0.3 w 10 M 69.2543 172.125 m S 69.2543 172.125 m S 1 g 1 w 4 M 63.2439 172.125 m 63.2439 168.9032 65.9349 166.2914 69.2543 166.2914 c 72.5737 166.2914 75.2647 168.9032 75.2647 172.125 c F 75.2647 172.125 m 75.2647 175.3468 72.5737 177.9586 69.2543 177.9586 c 65.9349 177.9586 63.2439 175.3468 63.2439 172.125 c F 69.2543 172.125 m F 0 G 0.3 w 10 M 69.2543 172.125 m S 0 g 1 w 4 M 69.2543 172.125 m F 0 G 0.3 w 10 M 69.2543 172.125 m S 69.2543 172.125 m S 0 g 1 w 4 M 68.1692 171.0571 m 68.1692 167.48 L 70.3394 167.48 L 70.3394 171.0571 L 73.925 171.0459 L 73.925 173.2043 L 70.3394 173.1932 L 70.3394 176.7703 L 68.1692 176.7703 L 68.1692 173.1932 L 64.5836 173.2043 L 64.5836 171.0459 L 68.1692 171.0571 L f 0 G 0.3 w 10 M 170.4477 152.2431 m S 170.4477 137.3147 m S 155.2409 137.3147 m S 155.2409 152.2431 m S 162.8443 144.7789 m S 155.2409 152.2431 m S 170.4477 152.2431 m S 155.2409 152.2431 m S 155.2409 152.2431 m S 155.2409 137.3147 m S 0 g 1 w 4 M 162.8443 144.7789 m F 0 G 0.3 w 10 M 185.6546 152.2431 m S 185.6546 137.3147 m S 185.6546 152.2431 m S 185.6546 152.2431 m S 185.6546 137.3147 m S 170.4477 137.3147 m S 170.4477 152.2431 m S 178.0511 144.7789 m S 185.6546 152.2431 m S 170.4477 152.2431 m S 0 g 1 w 4 M 178.0511 144.7789 m F 162.8443 129.8505 m F 178.0511 129.8505 m F 0 G 0.3 w 10 M 155.2409 122.3862 m S 155.2409 137.3147 m S 155.2409 122.3862 m S 170.4477 137.3147 m S 170.4477 122.3862 m S 155.2409 122.3862 m S 155.2409 137.3147 m S 162.8443 129.8505 m S 170.4477 122.3862 m S 155.2409 122.3862 m S 0 g 1 w 4 M 162.8443 129.8505 m F 0 G 0.3 w 10 M 185.6546 137.3147 m S 185.6546 122.3862 m S 170.4477 122.3862 m S 170.4477 137.3147 m S 178.0511 129.8505 m S 185.6546 122.3862 m S 185.6546 122.3862 m S 185.6546 137.3147 m S 185.6546 122.3862 m S 170.4477 122.3862 m S 0 g 1 w 4 M 178.0511 129.8505 m F 0 G 0.3 w 10 M 185.6546 152.2431 m S 185.6546 137.3147 m S 185.6546 152.2431 m S 185.6546 152.2431 m S 185.6546 137.3147 m S 170.4477 137.3147 m S 170.4477 152.2431 m S 178.0511 144.7789 m S 185.6546 152.2431 m S 170.4477 152.2431 m S 0 g 1 w 4 M 178.0511 144.7789 m F 178.0511 129.8505 m F 0 G 0.3 w 10 M 185.6546 137.3147 m S 185.6546 122.3862 m S 170.4477 122.3862 m S 170.4477 137.3147 m S 178.0511 129.8505 m S 185.6546 122.3862 m S 185.6546 122.3862 m S 185.6546 137.3147 m S 185.6546 122.3862 m S 170.4477 122.3862 m S 0 g 1 w 4 M 178.0511 129.8505 m F 0 G 0.3 w 10 M 155.2409 122.3863 m S 155.2409 137.3147 m S 155.2409 122.3863 m S 170.4477 137.3147 m S 170.4477 122.3863 m S 155.2409 122.3863 m S 155.2409 137.3147 m S 162.8443 129.8505 m S 170.4477 122.3863 m S 155.2409 122.3863 m S 0 g 1 w 4 M 162.8443 129.8505 m F 0 G 0.3 w 10 M 185.6546 137.3147 m S 185.6546 122.3863 m S 170.4477 122.3863 m S 170.4477 137.3147 m S 178.0511 129.8505 m S 185.6546 122.3863 m S 185.6546 122.3863 m S 185.6546 137.3147 m S 185.6546 122.3863 m S 170.4477 122.3863 m S 0 g 1 w 4 M 178.0511 129.8505 m F 0 G 0.3 w 10 M 185.6546 137.3147 m S 185.6546 122.3863 m S 170.4477 122.3863 m S 170.4477 137.3147 m S 178.0511 129.8505 m S 185.6546 122.3863 m S 185.6546 122.3863 m S 185.6546 137.3147 m S 185.6546 122.3863 m S 170.4477 122.3863 m S 0 g 1 w 4 M 178.0511 129.8505 m F 0 G 0.3 w 10 M 185.6546 122.3863 m S 0 g 1 w 4 M 185.6546 122.3863 m F 0 G 0.3 w 10 M 185.6546 122.3863 m S 185.6546 122.3863 m S 185.6546 122.3863 m S 0 g 1 w 4 M 185.6546 122.3863 m F 0 G 0.3 w 10 M 185.6546 122.3863 m S 185.6546 122.3863 m S 185.6546 122.3863 m S 0 g 1 w 4 M 185.6546 122.3863 m F 0 G 0.3 w 10 M 185.6546 122.3863 m S 185.6546 122.3863 m S 185.6546 152.2431 m S 0 g 1 w 4 M 185.6546 152.2431 m F 0 G 0.3 w 10 M 185.6546 152.2431 m S 185.6546 152.2431 m S 185.6546 152.2431 m S 0 g 1 w 4 M 185.6546 152.2431 m F 0 G 0.3 w 10 M 185.6546 152.2431 m S 185.6546 152.2431 m S 185.6546 152.2431 m S 0 g 1 w 4 M 185.6546 152.2431 m F 0 G 0.3 w 10 M 185.6546 152.2431 m S 185.6546 152.2431 m S 155.2409 152.2431 m S 0 g 1 w 4 M 155.2409 152.2431 m F 0 G 0.3 w 10 M 155.2409 152.2431 m S 155.2409 152.2431 m S 155.2409 152.2431 m S 0 g 1 w 4 M 155.2409 152.2431 m F 0 G 0.3 w 10 M 155.2409 152.2431 m S 155.2409 152.2431 m S 155.2409 152.2431 m S 0 g 1 w 4 M 155.2409 152.2431 m F 0 G 0.3 w 10 M 155.2409 152.2431 m S 155.2409 152.2431 m S 170.4477 137.3147 m S 0 g 1 w 4 M 170.4477 137.3147 m F 0 G 0.3 w 10 M 170.4477 137.3147 m S 170.4477 137.3147 m S 170.4477 137.3147 m S 0 g 1 w 4 M 170.4477 137.3147 m F 0 G 0.3 w 10 M 170.4477 137.3147 m S 170.4477 137.3147 m S 170.4477 137.3147 m S 0 g 1 w 4 M 170.4477 137.3147 m F 0 G 0.3 w 10 M 170.4477 137.3147 m S 170.4477 137.3147 m S 155.2409 122.3863 m S 0 g 1 w 4 M 155.2409 122.3863 m F 0 G 0.3 w 10 M 155.2409 122.3863 m S 155.2409 122.3863 m S 155.2409 122.3863 m S 0 g 1 w 4 M 155.2409 122.3863 m F 0 G 0.3 w 10 M 155.2409 122.3863 m S 155.2409 122.3863 m S 155.2409 122.3863 m S 0 g 1 w 4 M 155.2409 122.3863 m F 0 G 0.3 w 10 M 155.2409 122.3863 m S 155.2409 122.3863 m S 181.4956 147.8397 m S 0 g 1 w 4 M 181.4956 147.8397 m F 0 G 0.3 w 10 M 181.4956 147.8397 m S 181.4956 147.8397 m S 181.4956 147.8397 m S 0 g 1 w 4 M 181.4956 147.8397 m F 0 G 0.3 w 10 M 181.4956 147.8397 m S 181.4956 147.8397 m S 1 g 1 w 4 M 175.4852 147.8397 m 175.4852 144.6179 178.1762 142.0061 181.4956 142.0061 c 184.815 142.0061 187.506 144.6179 187.506 147.8397 c F 187.506 147.8397 m 187.506 151.0615 184.815 153.6733 181.4956 153.6733 c 178.1762 153.6733 175.4852 151.0615 175.4852 147.8397 c F 181.4956 147.8397 m F 0 G 0.3 w 10 M 181.4956 147.8397 m S 0 g 1 w 4 M 181.4956 147.8397 m F 0 G 0.3 w 10 M 181.4956 147.8397 m S 181.4956 147.8397 m S 0 g 1 w 4 M 180.4105 146.7718 m 180.4105 143.1947 L 182.5807 143.1947 L 182.5807 146.7718 L 186.1663 146.7606 L 186.1663 148.919 L 182.5807 148.9079 L 182.5807 152.485 L 180.4105 152.485 L 180.4105 148.9079 L 176.8249 148.919 L 176.8249 146.7606 L 180.4105 146.7718 L f 0 G 0.3 w 10 M 156.9956 152.3397 m S 0 g 1 w 4 M 156.9956 152.3397 m F 0 G 0.3 w 10 M 156.9956 152.3397 m S 156.9956 152.3397 m S 156.9956 152.3397 m S 0 g 1 w 4 M 156.9956 152.3397 m F 0 G 0.3 w 10 M 156.9956 152.3397 m S 156.9956 152.3397 m S 1 g 1 w 4 M 150.9852 152.3397 m 150.9852 149.1179 153.6762 146.5061 156.9956 146.5061 c 160.315 146.5061 163.006 149.1179 163.006 152.3397 c F 163.006 152.3397 m 163.006 155.5615 160.315 158.1733 156.9956 158.1733 c 153.6762 158.1733 150.9852 155.5615 150.9852 152.3397 c F 156.9956 152.3397 m F 0 G 0.3 w 10 M 156.9956 152.3397 m S 0 g 1 w 4 M 156.9956 152.3397 m F 0 G 0.3 w 10 M 156.9956 152.3397 m S 156.9956 152.3397 m S 0 g 1 w 4 M 155.9105 151.2718 m 155.9105 147.6947 L 158.0807 147.6947 L 158.0807 151.2718 L 161.6663 151.2606 L 161.6663 153.419 L 158.0807 153.4079 L 158.0807 156.985 L 155.9105 156.985 L 155.9105 153.4079 L 152.3249 153.419 L 152.3249 151.2606 L 155.9105 151.2718 L f 0 G 0.3 w 10 M 177.9956 122.8397 m S 0 g 1 w 4 M 177.9956 122.8397 m F 0 G 0.3 w 10 M 177.9956 122.8397 m S 177.9956 122.8397 m S 177.9956 122.8397 m S 0 g 1 w 4 M 177.9956 122.8397 m F 0 G 0.3 w 10 M 177.9956 122.8397 m S 177.9956 122.8397 m S 1 g 1 w 4 M 171.9852 122.8397 m 171.9852 119.6179 174.6762 117.0061 177.9956 117.0061 c 181.315 117.0061 184.006 119.6179 184.006 122.8397 c F 184.006 122.8397 m 184.006 126.0615 181.315 128.6733 177.9956 128.6733 c 174.6762 128.6733 171.9852 126.0615 171.9852 122.8397 c F 177.9956 122.8397 m F 0 G 0.3 w 10 M 177.9956 122.8397 m S 0 g 1 w 4 M 177.9956 122.8397 m F 0 G 0.3 w 10 M 177.9956 122.8397 m S 177.9956 122.8397 m S 0 g 1 w 4 M 176.9105 121.7718 m 176.9105 118.1947 L 179.0807 118.1947 L 179.0807 121.7718 L 182.6663 121.7606 L 182.6663 123.919 L 179.0807 123.9079 L 179.0807 127.485 L 176.9105 127.485 L 176.9105 123.9079 L 173.3249 123.919 L 173.3249 121.7606 L 176.9105 121.7718 L f 0 G 0.3 w 10 M 167.7456 141.8397 m S 0 g 1 w 4 M 167.7456 141.8397 m F 0 G 0.3 w 10 M 167.7456 141.8397 m S 167.7456 141.8397 m S 167.7456 141.8397 m S 0 g 1 w 4 M 167.7456 141.8397 m F 0 G 0.3 w 10 M 167.7456 141.8397 m S 167.7456 141.8397 m S 1 g 1 w 4 M 161.7352 141.8397 m 161.7352 138.6179 164.4262 136.0061 167.7456 136.0061 c 171.065 136.0061 173.756 138.6179 173.756 141.8397 c F 173.756 141.8397 m 173.756 145.0615 171.065 147.6733 167.7456 147.6733 c 164.4262 147.6733 161.7352 145.0615 161.7352 141.8397 c F 167.7456 141.8397 m F 0 G 0.3 w 10 M 167.7456 141.8397 m S 0 g 1 w 4 M 167.7456 141.8397 m F 0 G 0.3 w 10 M 167.7456 141.8397 m S 167.7456 141.8397 m S 0 g 1 w 4 M 166.6605 140.7718 m 166.6605 137.1947 L 168.8307 137.1947 L 168.8307 140.7718 L 172.4163 140.7606 L 172.4163 142.919 L 168.8307 142.9079 L 168.8307 146.485 L 166.6605 146.485 L 166.6605 142.9079 L 163.0749 142.919 L 163.0749 140.7606 L 166.6605 140.7718 L f 0 G 0.3 w 10 M 160.4956 127.3397 m S 0 g 1 w 4 M 160.4956 127.3397 m F 0 G 0.3 w 10 M 160.4956 127.3397 m S 160.4956 127.3397 m S 160.4956 127.3397 m S 0 g 1 w 4 M 160.4956 127.3397 m F 0 G 0.3 w 10 M 160.4956 127.3397 m S 160.4956 127.3397 m S 1 g 1 w 4 M 154.4852 127.3397 m 154.4852 124.1179 157.1762 121.5061 160.4956 121.5061 c 163.815 121.5061 166.506 124.1179 166.506 127.3397 c F 166.506 127.3397 m 166.506 130.5615 163.815 133.1733 160.4956 133.1733 c 157.1762 133.1733 154.4852 130.5615 154.4852 127.3397 c F 160.4956 127.3397 m F 0 G 0.3 w 10 M 160.4956 127.3397 m S 0 g 1 w 4 M 160.4956 127.3397 m F 0 G 0.3 w 10 M 160.4956 127.3397 m S 160.4956 127.3397 m S 0 g 1 w 4 M 159.4105 126.2718 m 159.4105 122.6947 L 161.5807 122.6947 L 161.5807 126.2718 L 165.1663 126.2606 L 165.1663 128.419 L 161.5807 128.4079 L 161.5807 131.985 L 159.4105 131.985 L 159.4105 128.4079 L 155.8249 128.419 L 155.8249 126.2606 L 159.4105 126.2718 L f 0 G 0.3 w 10 M 216.0683 152.2431 m S 216.0683 137.3147 m S 200.8615 137.3147 m S 200.8615 152.2431 m S 208.4649 144.7789 m S 200.8615 152.2431 m S 216.0683 152.2431 m S 200.8615 152.2431 m S 200.8615 152.2431 m S 200.8615 137.3147 m S 0 g 1 w 4 M 208.4649 144.7789 m F 0 G 0.3 w 10 M 231.2752 152.2431 m S 231.2752 137.3147 m S 231.2752 152.2431 m S 231.2752 152.2431 m S 231.2752 137.3147 m S 216.0683 137.3147 m S 216.0683 152.2431 m S 223.6717 144.7789 m S 231.2752 152.2431 m S 216.0683 152.2431 m S 0 g 1 w 4 M 223.6717 144.7789 m F 208.4649 129.8505 m F 223.6717 129.8505 m F 0 G 0.3 w 10 M 200.8615 122.3862 m S 200.8615 137.3147 m S 200.8615 122.3862 m S 216.0683 137.3147 m S 216.0683 122.3862 m S 200.8615 122.3862 m S 200.8615 137.3147 m S 208.4649 129.8505 m S 216.0683 122.3862 m S 200.8615 122.3862 m S 0 g 1 w 4 M 208.4649 129.8505 m F 0 G 0.3 w 10 M 231.2752 137.3147 m S 231.2752 122.3862 m S 216.0683 122.3862 m S 216.0683 137.3147 m S 223.6717 129.8505 m S 231.2752 122.3862 m S 231.2752 122.3862 m S 231.2752 137.3147 m S 231.2752 122.3862 m S 216.0683 122.3862 m S 0 g 1 w 4 M 223.6717 129.8505 m F 0 G 0.3 w 10 M 231.2752 152.2431 m S 231.2752 137.3147 m S 231.2752 152.2431 m S 231.2752 152.2431 m S 231.2752 137.3147 m S 216.0683 137.3147 m S 216.0683 152.2431 m S 223.6717 144.7789 m S 231.2752 152.2431 m S 216.0683 152.2431 m S 0 g 1 w 4 M 223.6717 144.7789 m F 223.6717 129.8505 m F 0 G 0.3 w 10 M 231.2752 137.3147 m S 231.2752 122.3862 m S 216.0683 122.3862 m S 216.0683 137.3147 m S 223.6717 129.8505 m S 231.2752 122.3862 m S 231.2752 122.3862 m S 231.2752 137.3147 m S 231.2752 122.3862 m S 216.0683 122.3862 m S 0 g 1 w 4 M 223.6717 129.8505 m F 0 G 0.3 w 10 M 200.8615 122.3863 m S 200.8615 137.3147 m S 200.8615 122.3863 m S 216.0683 137.3147 m S 216.0683 122.3863 m S 200.8615 122.3863 m S 200.8615 137.3147 m S 208.4649 129.8505 m S 216.0683 122.3863 m S 200.8615 122.3863 m S 0 g 1 w 4 M 208.4649 129.8505 m F 0 G 0.3 w 10 M 231.2752 137.3147 m S 231.2752 122.3863 m S 216.0683 122.3863 m S 216.0683 137.3147 m S 223.6717 129.8505 m S 231.2752 122.3863 m S 231.2752 122.3863 m S 231.2752 137.3147 m S 231.2752 122.3863 m S 216.0683 122.3863 m S 0 g 1 w 4 M 223.6717 129.8505 m F 0 G 0.3 w 10 M 231.2752 137.3147 m S 231.2752 122.3863 m S 216.0683 122.3863 m S 216.0683 137.3147 m S 223.6717 129.8505 m S 231.2752 122.3863 m S 231.2752 122.3863 m S 231.2752 137.3147 m S 231.2752 122.3863 m S 216.0683 122.3863 m S 0 g 1 w 4 M 223.6717 129.8505 m F 0 G 0.3 w 10 M 231.2752 122.3863 m S 0 g 1 w 4 M 231.2752 122.3863 m F 0 G 0.3 w 10 M 231.2752 122.3863 m S 231.2752 122.3863 m S 231.2752 122.3863 m S 0 g 1 w 4 M 231.2752 122.3863 m F 0 G 0.3 w 10 M 231.2752 122.3863 m S 231.2752 122.3863 m S 231.2752 122.3863 m S 0 g 1 w 4 M 231.2752 122.3863 m F 0 G 0.3 w 10 M 231.2752 122.3863 m S 231.2752 122.3863 m S 231.2752 152.2431 m S 0 g 1 w 4 M 231.2752 152.2431 m F 0 G 0.3 w 10 M 231.2752 152.2431 m S 231.2752 152.2431 m S 231.2752 152.2431 m S 0 g 1 w 4 M 231.2752 152.2431 m F 0 G 0.3 w 10 M 231.2752 152.2431 m S 231.2752 152.2431 m S 231.2752 152.2431 m S 0 g 1 w 4 M 231.2752 152.2431 m F 0 G 0.3 w 10 M 231.2752 152.2431 m S 231.2752 152.2431 m S 200.8615 152.2431 m S 0 g 1 w 4 M 200.8615 152.2431 m F 0 G 0.3 w 10 M 200.8615 152.2431 m S 200.8615 152.2431 m S 200.8615 152.2431 m S 0 g 1 w 4 M 200.8615 152.2431 m F 0 G 0.3 w 10 M 200.8615 152.2431 m S 200.8615 152.2431 m S 200.8615 152.2431 m S 0 g 1 w 4 M 200.8615 152.2431 m F 0 G 0.3 w 10 M 200.8615 152.2431 m S 200.8615 152.2431 m S 216.0683 137.3147 m S 0 g 1 w 4 M 216.0683 137.3147 m F 0 G 0.3 w 10 M 216.0683 137.3147 m S 216.0683 137.3147 m S 216.0683 137.3147 m S 0 g 1 w 4 M 216.0683 137.3147 m F 0 G 0.3 w 10 M 216.0683 137.3147 m S 216.0683 137.3147 m S 216.0683 137.3147 m S 0 g 1 w 4 M 216.0683 137.3147 m F 0 G 0.3 w 10 M 216.0683 137.3147 m S 216.0683 137.3147 m S 200.8615 122.3863 m S 0 g 1 w 4 M 200.8615 122.3863 m F 0 G 0.3 w 10 M 200.8615 122.3863 m S 200.8615 122.3863 m S 200.8615 122.3863 m S 0 g 1 w 4 M 200.8615 122.3863 m F 0 G 0.3 w 10 M 200.8615 122.3863 m S 200.8615 122.3863 m S 200.8615 122.3863 m S 0 g 1 w 4 M 200.8615 122.3863 m F 0 G 0.3 w 10 M 200.8615 122.3863 m S 200.8615 122.3863 m S 227.1162 147.8397 m S 0 g 1 w 4 M 227.1162 147.8397 m F 0 G 0.3 w 10 M 227.1162 147.8397 m S 227.1162 147.8397 m S 227.1162 147.8397 m S 0 g 1 w 4 M 227.1162 147.8397 m F 0 G 0.3 w 10 M 227.1162 147.8397 m S 227.1162 147.8397 m S 1 g 1 w 4 M 221.1058 147.8397 m 221.1058 144.6179 223.7968 142.0061 227.1162 142.0061 c 230.4356 142.0061 233.1266 144.6179 233.1266 147.8397 c F 233.1266 147.8397 m 233.1266 151.0615 230.4356 153.6733 227.1162 153.6733 c 223.7968 153.6733 221.1058 151.0615 221.1058 147.8397 c F 227.1162 147.8397 m F 0 G 0.3 w 10 M 227.1162 147.8397 m S 0 g 1 w 4 M 227.1162 147.8397 m F 0 G 0.3 w 10 M 227.1162 147.8397 m S 227.1162 147.8397 m S 0 g 1 w 4 M 226.0311 146.7718 m 226.0311 143.1947 L 228.2013 143.1947 L 228.2013 146.7718 L 231.7869 146.7606 L 231.7869 148.919 L 228.2013 148.9079 L 228.2013 152.485 L 226.0311 152.485 L 226.0311 148.9079 L 222.4455 148.919 L 222.4455 146.7606 L 226.0311 146.7718 L f 0 G 0.3 w 10 M 202.6162 152.3397 m S 0 g 1 w 4 M 202.6162 152.3397 m F 0 G 0.3 w 10 M 202.6162 152.3397 m S 202.6162 152.3397 m S 202.6162 152.3397 m S 0 g 1 w 4 M 202.6162 152.3397 m F 0 G 0.3 w 10 M 202.6162 152.3397 m S 202.6162 152.3397 m S 1 g 1 w 4 M 196.6058 152.3397 m 196.6058 149.1179 199.2968 146.5061 202.6162 146.5061 c 205.9356 146.5061 208.6266 149.1179 208.6266 152.3397 c F 208.6266 152.3397 m 208.6266 155.5615 205.9356 158.1733 202.6162 158.1733 c 199.2968 158.1733 196.6058 155.5615 196.6058 152.3397 c F 202.6162 152.3397 m F 0 G 0.3 w 10 M 202.6162 152.3397 m S 0 g 1 w 4 M 202.6162 152.3397 m F 0 G 0.3 w 10 M 202.6162 152.3397 m S 202.6162 152.3397 m S 0 g 1 w 4 M 201.5311 151.2718 m 201.5311 147.6947 L 203.7013 147.6947 L 203.7013 151.2718 L 207.2869 151.2606 L 207.2869 153.419 L 203.7013 153.4079 L 203.7013 156.985 L 201.5311 156.985 L 201.5311 153.4079 L 197.9455 153.419 L 197.9455 151.2606 L 201.5311 151.2718 L f 0 G 0.3 w 10 M 223.6162 122.8397 m S 0 g 1 w 4 M 223.6162 122.8397 m F 0 G 0.3 w 10 M 223.6162 122.8397 m S 223.6162 122.8397 m S 223.6162 122.8397 m S 0 g 1 w 4 M 223.6162 122.8397 m F 0 G 0.3 w 10 M 223.6162 122.8397 m S 223.6162 122.8397 m S 1 g 1 w 4 M 217.6058 122.8397 m 217.6058 119.6179 220.2968 117.0061 223.6162 117.0061 c 226.9356 117.0061 229.6266 119.6179 229.6266 122.8397 c F 229.6266 122.8397 m 229.6266 126.0615 226.9356 128.6733 223.6162 128.6733 c 220.2968 128.6733 217.6058 126.0615 217.6058 122.8397 c F 223.6162 122.8397 m F 0 G 0.3 w 10 M 223.6162 122.8397 m S 0 g 1 w 4 M 223.6162 122.8397 m F 0 G 0.3 w 10 M 223.6162 122.8397 m S 223.6162 122.8397 m S 0 g 1 w 4 M 222.5311 121.7718 m 222.5311 118.1947 L 224.7013 118.1947 L 224.7013 121.7718 L 228.2869 121.7606 L 228.2869 123.919 L 224.7013 123.9079 L 224.7013 127.485 L 222.5311 127.485 L 222.5311 123.9079 L 218.9455 123.919 L 218.9455 121.7606 L 222.5311 121.7718 L f 0 G 0.3 w 10 M 213.3662 141.8397 m S 0 g 1 w 4 M 213.3662 141.8397 m F 0 G 0.3 w 10 M 213.3662 141.8397 m S 213.3662 141.8397 m S 213.3662 141.8397 m S 0 g 1 w 4 M 213.3662 141.8397 m F 0 G 0.3 w 10 M 213.3662 141.8397 m S 213.3662 141.8397 m S 1 g 1 w 4 M 207.3558 141.8397 m 207.3558 138.6179 210.0468 136.0061 213.3662 136.0061 c 216.6856 136.0061 219.3766 138.6179 219.3766 141.8397 c F 219.3766 141.8397 m 219.3766 145.0615 216.6856 147.6733 213.3662 147.6733 c 210.0468 147.6733 207.3558 145.0615 207.3558 141.8397 c F 213.3662 141.8397 m F 0 G 0.3 w 10 M 213.3662 141.8397 m S 0 g 1 w 4 M 213.3662 141.8397 m F 0 G 0.3 w 10 M 213.3662 141.8397 m S 213.3662 141.8397 m S 0 g 1 w 4 M 212.2811 140.7718 m 212.2811 137.1947 L 214.4513 137.1947 L 214.4513 140.7718 L 218.0369 140.7606 L 218.0369 142.919 L 214.4513 142.9079 L 214.4513 146.485 L 212.2811 146.485 L 212.2811 142.9079 L 208.6955 142.919 L 208.6955 140.7606 L 212.2811 140.7718 L f 0 G 0.3 w 10 M 206.1162 127.3397 m S 0 g 1 w 4 M 206.1162 127.3397 m F 0 G 0.3 w 10 M 206.1162 127.3397 m S 206.1162 127.3397 m S 206.1162 127.3397 m S 0 g 1 w 4 M 206.1162 127.3397 m F 0 G 0.3 w 10 M 206.1162 127.3397 m S 206.1162 127.3397 m S 1 g 1 w 4 M 200.1058 127.3397 m 200.1058 124.1179 202.7968 121.5061 206.1162 121.5061 c 209.4356 121.5061 212.1266 124.1179 212.1266 127.3397 c F 212.1266 127.3397 m 212.1266 130.5615 209.4356 133.1733 206.1162 133.1733 c 202.7968 133.1733 200.1058 130.5615 200.1058 127.3397 c F 206.1162 127.3397 m F 0 G 0.3 w 10 M 206.1162 127.3397 m S 0 g 1 w 4 M 206.1162 127.3397 m F 0 G 0.3 w 10 M 206.1162 127.3397 m S 206.1162 127.3397 m S 0 g 1 w 4 M 205.0311 126.2718 m 205.0311 122.6947 L 207.2013 122.6947 L 207.2013 126.2718 L 210.7869 126.2606 L 210.7869 128.419 L 207.2013 128.4079 L 207.2013 131.985 L 205.0311 131.985 L 205.0311 128.4079 L 201.4455 128.419 L 201.4455 126.2606 L 205.0311 126.2718 L f 0 G 0.3 w 10 M 216.0683 107.4579 m S 216.0683 92.5295 m S 200.8615 92.5295 m S 200.8615 107.4579 m S 208.4649 99.9937 m S 200.8615 107.4579 m S 216.0683 107.4579 m S 200.8615 107.4579 m S 200.8615 107.4579 m S 200.8615 92.5295 m S 0 g 1 w 4 M 208.4649 99.9937 m F 0 G 0.3 w 10 M 231.2752 107.4579 m S 231.2752 92.5295 m S 231.2752 107.4579 m S 231.2752 107.4579 m S 231.2752 92.5295 m S 216.0683 92.5295 m S 216.0683 107.4579 m S 223.6717 99.9937 m S 231.2752 107.4579 m S 216.0683 107.4579 m S 0 g 1 w 4 M 223.6717 99.9937 m F 208.4649 85.0653 m F 223.6717 85.0653 m F 0 G 0.3 w 10 M 200.8615 77.601 m S 200.8615 92.5295 m S 200.8615 77.601 m S 216.0683 92.5295 m S 216.0683 77.601 m S 200.8615 77.601 m S 200.8615 92.5295 m S 208.4649 85.0653 m S 216.0683 77.601 m S 200.8615 77.601 m S 0 g 1 w 4 M 208.4649 85.0653 m F 0 G 0.3 w 10 M 231.2752 92.5295 m S 231.2752 77.601 m S 216.0683 77.601 m S 216.0683 92.5295 m S 223.6717 85.0653 m S 231.2752 77.601 m S 231.2752 77.601 m S 231.2752 92.5295 m S 231.2752 77.601 m S 216.0683 77.601 m S 0 g 1 w 4 M 223.6717 85.0653 m F 0 G 0.3 w 10 M 231.2752 107.4579 m S 231.2752 92.5295 m S 231.2752 107.4579 m S 231.2752 107.4579 m S 231.2752 92.5295 m S 216.0683 92.5295 m S 216.0683 107.4579 m S 223.6717 99.9937 m S 231.2752 107.4579 m S 216.0683 107.4579 m S 0 g 1 w 4 M 223.6717 99.9937 m F 223.6717 85.0653 m F 0 G 0.3 w 10 M 231.2752 92.5295 m S 231.2752 77.601 m S 216.0683 77.601 m S 216.0683 92.5295 m S 223.6717 85.0653 m S 231.2752 77.601 m S 231.2752 77.601 m S 231.2752 92.5295 m S 231.2752 77.601 m S 216.0683 77.601 m S 0 g 1 w 4 M 223.6717 85.0653 m F 0 G 0.3 w 10 M 200.8615 77.6011 m S 200.8615 92.5295 m S 200.8615 77.6011 m S 216.0683 92.5295 m S 216.0683 77.6011 m S 200.8615 77.6011 m S 200.8615 92.5295 m S 208.4649 85.0653 m S 216.0683 77.6011 m S 200.8615 77.6011 m S 0 g 1 w 4 M 208.4649 85.0653 m F 0 G 0.3 w 10 M 231.2752 92.5295 m S 231.2752 77.6011 m S 216.0683 77.6011 m S 216.0683 92.5295 m S 223.6717 85.0653 m S 231.2752 77.6011 m S 231.2752 77.6011 m S 231.2752 92.5295 m S 231.2752 77.6011 m S 216.0683 77.6011 m S 0 g 1 w 4 M 223.6717 85.0653 m F 0 G 0.3 w 10 M 231.2752 92.5295 m S 231.2752 77.6011 m S 216.0683 77.6011 m S 216.0683 92.5295 m S 223.6717 85.0653 m S 231.2752 77.6011 m S 231.2752 77.6011 m S 231.2752 92.5295 m S 231.2752 77.6011 m S 216.0683 77.6011 m S 0 g 1 w 4 M 223.6717 85.0653 m F 0 G 0.3 w 10 M 231.2752 77.6011 m S 0 g 1 w 4 M 231.2752 77.6011 m F 0 G 0.3 w 10 M 231.2752 77.6011 m S 231.2752 77.6011 m S 231.2752 77.6011 m S 0 g 1 w 4 M 231.2752 77.6011 m F 0 G 0.3 w 10 M 231.2752 77.6011 m S 231.2752 77.6011 m S 231.2752 77.6011 m S 0 g 1 w 4 M 231.2752 77.6011 m F 0 G 0.3 w 10 M 231.2752 77.6011 m S 231.2752 77.6011 m S 231.2752 107.4579 m S 0 g 1 w 4 M 231.2752 107.4579 m F 0 G 0.3 w 10 M 231.2752 107.4579 m S 231.2752 107.4579 m S 231.2752 107.4579 m S 0 g 1 w 4 M 231.2752 107.4579 m F 0 G 0.3 w 10 M 231.2752 107.4579 m S 231.2752 107.4579 m S 231.2752 107.4579 m S 0 g 1 w 4 M 231.2752 107.4579 m F 0 G 0.3 w 10 M 231.2752 107.4579 m S 231.2752 107.4579 m S 200.8615 107.4579 m S 0 g 1 w 4 M 200.8615 107.4579 m F 0 G 0.3 w 10 M 200.8615 107.4579 m S 200.8615 107.4579 m S 200.8615 107.4579 m S 0 g 1 w 4 M 200.8615 107.4579 m F 0 G 0.3 w 10 M 200.8615 107.4579 m S 200.8615 107.4579 m S 200.8615 107.4579 m S 0 g 1 w 4 M 200.8615 107.4579 m F 0 G 0.3 w 10 M 200.8615 107.4579 m S 200.8615 107.4579 m S 216.0683 92.5295 m S 0 g 1 w 4 M 216.0683 92.5295 m F 0 G 0.3 w 10 M 216.0683 92.5295 m S 216.0683 92.5295 m S 216.0683 92.5295 m S 0 g 1 w 4 M 216.0683 92.5295 m F 0 G 0.3 w 10 M 216.0683 92.5295 m S 216.0683 92.5295 m S 216.0683 92.5295 m S 0 g 1 w 4 M 216.0683 92.5295 m F 0 G 0.3 w 10 M 216.0683 92.5295 m S 216.0683 92.5295 m S 200.8615 77.6011 m S 0 g 1 w 4 M 200.8615 77.6011 m F 0 G 0.3 w 10 M 200.8615 77.6011 m S 200.8615 77.6011 m S 200.8615 77.6011 m S 0 g 1 w 4 M 200.8615 77.6011 m F 0 G 0.3 w 10 M 200.8615 77.6011 m S 200.8615 77.6011 m S 200.8615 77.6011 m S 0 g 1 w 4 M 200.8615 77.6011 m F 0 G 0.3 w 10 M 200.8615 77.6011 m S 200.8615 77.6011 m S 227.1162 103.0545 m S 0 g 1 w 4 M 227.1162 103.0545 m F 0 G 0.3 w 10 M 227.1162 103.0545 m S 227.1162 103.0545 m S 227.1162 103.0545 m S 0 g 1 w 4 M 227.1162 103.0545 m F 0 G 0.3 w 10 M 227.1162 103.0545 m S 227.1162 103.0545 m S 1 g 1 w 4 M 221.1058 103.0545 m 221.1058 99.8327 223.7968 97.2209 227.1162 97.2209 c 230.4356 97.2209 233.1266 99.8327 233.1266 103.0545 c F 233.1266 103.0545 m 233.1266 106.2763 230.4356 108.8881 227.1162 108.8881 c 223.7968 108.8881 221.1058 106.2763 221.1058 103.0545 c F 227.1162 103.0545 m F 0 G 0.3 w 10 M 227.1162 103.0545 m S 0 g 1 w 4 M 227.1162 103.0545 m F 0 G 0.3 w 10 M 227.1162 103.0545 m S 227.1162 103.0545 m S 0 g 1 w 4 M 226.0311 101.9866 m 226.0311 98.4095 L 228.2013 98.4095 L 228.2013 101.9866 L 231.7869 101.9754 L 231.7869 104.1338 L 228.2013 104.1227 L 228.2013 107.6998 L 226.0311 107.6998 L 226.0311 104.1227 L 222.4455 104.1338 L 222.4455 101.9754 L 226.0311 101.9866 L f 0 G 0.3 w 10 M 202.6162 107.5545 m S 0 g 1 w 4 M 202.6162 107.5545 m F 0 G 0.3 w 10 M 202.6162 107.5545 m S 202.6162 107.5545 m S 202.6162 107.5545 m S 0 g 1 w 4 M 202.6162 107.5545 m F 0 G 0.3 w 10 M 202.6162 107.5545 m S 202.6162 107.5545 m S 1 g 1 w 4 M 196.6058 107.5545 m 196.6058 104.3327 199.2968 101.7209 202.6162 101.7209 c 205.9356 101.7209 208.6266 104.3327 208.6266 107.5545 c F 208.6266 107.5545 m 208.6266 110.7763 205.9356 113.3881 202.6162 113.3881 c 199.2968 113.3881 196.6058 110.7763 196.6058 107.5545 c F 202.6162 107.5545 m F 0 G 0.3 w 10 M 202.6162 107.5545 m S 0 g 1 w 4 M 202.6162 107.5545 m F 0 G 0.3 w 10 M 202.6162 107.5545 m S 202.6162 107.5545 m S 0 g 1 w 4 M 201.5311 106.4866 m 201.5311 102.9095 L 203.7013 102.9095 L 203.7013 106.4866 L 207.2869 106.4754 L 207.2869 108.6338 L 203.7013 108.6227 L 203.7013 112.1998 L 201.5311 112.1998 L 201.5311 108.6227 L 197.9455 108.6338 L 197.9455 106.4754 L 201.5311 106.4866 L f 0 G 0.3 w 10 M 223.6162 78.0545 m S 0 g 1 w 4 M 223.6162 78.0545 m F 0 G 0.3 w 10 M 223.6162 78.0545 m S 223.6162 78.0545 m S 223.6162 78.0545 m S 0 g 1 w 4 M 223.6162 78.0545 m F 0 G 0.3 w 10 M 223.6162 78.0545 m S 223.6162 78.0545 m S 1 g 1 w 4 M 217.6058 78.0545 m 217.6058 74.8327 220.2968 72.2209 223.6162 72.2209 c 226.9356 72.2209 229.6266 74.8327 229.6266 78.0545 c F 229.6266 78.0545 m 229.6266 81.2763 226.9356 83.8881 223.6162 83.8881 c 220.2968 83.8881 217.6058 81.2763 217.6058 78.0545 c F 223.6162 78.0545 m F 0 G 0.3 w 10 M 223.6162 78.0545 m S 0 g 1 w 4 M 223.6162 78.0545 m F 0 G 0.3 w 10 M 223.6162 78.0545 m S 223.6162 78.0545 m S 0 g 1 w 4 M 222.5311 76.9866 m 222.5311 73.4095 L 224.7013 73.4095 L 224.7013 76.9866 L 228.2869 76.9754 L 228.2869 79.1338 L 224.7013 79.1227 L 224.7013 82.6998 L 222.5311 82.6998 L 222.5311 79.1227 L 218.9455 79.1338 L 218.9455 76.9754 L 222.5311 76.9866 L f 0 G 0.3 w 10 M 213.3662 97.0545 m S 0 g 1 w 4 M 213.3662 97.0545 m F 0 G 0.3 w 10 M 213.3662 97.0545 m S 213.3662 97.0545 m S 213.3662 97.0545 m S 0 g 1 w 4 M 213.3662 97.0545 m F 0 G 0.3 w 10 M 213.3662 97.0545 m S 213.3662 97.0545 m S 1 g 1 w 4 M 207.3558 97.0545 m 207.3558 93.8327 210.0468 91.2209 213.3662 91.2209 c 216.6856 91.2209 219.3766 93.8327 219.3766 97.0545 c F 219.3766 97.0545 m 219.3766 100.2763 216.6856 102.8881 213.3662 102.8881 c 210.0468 102.8881 207.3558 100.2763 207.3558 97.0545 c F 213.3662 97.0545 m F 0 G 0.3 w 10 M 213.3662 97.0545 m S 0 g 1 w 4 M 213.3662 97.0545 m F 0 G 0.3 w 10 M 213.3662 97.0545 m S 213.3662 97.0545 m S 0 g 1 w 4 M 212.2811 95.9866 m 212.2811 92.4095 L 214.4513 92.4095 L 214.4513 95.9866 L 218.0369 95.9754 L 218.0369 98.1338 L 214.4513 98.1227 L 214.4513 101.6998 L 212.2811 101.6998 L 212.2811 98.1227 L 208.6955 98.1338 L 208.6955 95.9754 L 212.2811 95.9866 L f 0 G 0.3 w 10 M 206.1162 82.5545 m S 0 g 1 w 4 M 206.1162 82.5545 m F 0 G 0.3 w 10 M 206.1162 82.5545 m S 206.1162 82.5545 m S 206.1162 82.5545 m S 0 g 1 w 4 M 206.1162 82.5545 m F 0 G 0.3 w 10 M 206.1162 82.5545 m S 206.1162 82.5545 m S 1 g 1 w 4 M 200.1058 82.5545 m 200.1058 79.3327 202.7968 76.7209 206.1162 76.7209 c 209.4356 76.7209 212.1266 79.3327 212.1266 82.5545 c F 212.1266 82.5545 m 212.1266 85.7763 209.4356 88.3881 206.1162 88.3881 c 202.7968 88.3881 200.1058 85.7763 200.1058 82.5545 c F 206.1162 82.5545 m F 0 G 0.3 w 10 M 206.1162 82.5545 m S 0 g 1 w 4 M 206.1162 82.5545 m F 0 G 0.3 w 10 M 206.1162 82.5545 m S 206.1162 82.5545 m S 0 g 1 w 4 M 205.0311 81.4866 m 205.0311 77.9095 L 207.2013 77.9095 L 207.2013 81.4866 L 210.7869 81.4754 L 210.7869 83.6338 L 207.2013 83.6227 L 207.2013 87.1998 L 205.0311 87.1998 L 205.0311 83.6227 L 201.4455 83.6338 L 201.4455 81.4754 L 205.0311 81.4866 L f 0 G 0.3 w 10 M 170.4477 107.4579 m S 170.4477 92.5295 m S 155.2409 92.5295 m S 155.2409 107.4579 m S 162.8443 99.9937 m S 155.2409 107.4579 m S 170.4477 107.4579 m S 155.2409 107.4579 m S 155.2409 107.4579 m S 155.2409 92.5295 m S 0 g 1 w 4 M 162.8443 99.9937 m F 0 G 0.3 w 10 M 185.6546 107.4579 m S 185.6546 92.5295 m S 185.6546 107.4579 m S 185.6546 107.4579 m S 185.6546 92.5295 m S 170.4477 92.5295 m S 170.4477 107.4579 m S 178.0511 99.9937 m S 185.6546 107.4579 m S 170.4477 107.4579 m S 0 g 1 w 4 M 178.0511 99.9937 m F 162.8443 85.0653 m F 178.0511 85.0653 m F 0 G 0.3 w 10 M 155.2409 77.601 m S 155.2409 92.5295 m S 155.2409 77.601 m S 170.4477 92.5295 m S 170.4477 77.601 m S 155.2409 77.601 m S 155.2409 92.5295 m S 162.8443 85.0653 m S 170.4477 77.601 m S 155.2409 77.601 m S 0 g 1 w 4 M 162.8443 85.0653 m F 0 G 0.3 w 10 M 185.6546 92.5295 m S 185.6546 77.601 m S 170.4477 77.601 m S 170.4477 92.5295 m S 178.0511 85.0653 m S 185.6546 77.601 m S 185.6546 77.601 m S 185.6546 92.5295 m S 185.6546 77.601 m S 170.4477 77.601 m S 0 g 1 w 4 M 178.0511 85.0653 m F 0 G 0.3 w 10 M 185.6546 107.4579 m S 185.6546 92.5295 m S 185.6546 107.4579 m S 185.6546 107.4579 m S 185.6546 92.5295 m S 170.4477 92.5295 m S 170.4477 107.4579 m S 178.0511 99.9937 m S 185.6546 107.4579 m S 170.4477 107.4579 m S 0 g 1 w 4 M 178.0511 99.9937 m F 178.0511 85.0653 m F 0 G 0.3 w 10 M 185.6546 92.5295 m S 185.6546 77.601 m S 170.4477 77.601 m S 170.4477 92.5295 m S 178.0511 85.0653 m S 185.6546 77.601 m S 185.6546 77.601 m S 185.6546 92.5295 m S 185.6546 77.601 m S 170.4477 77.601 m S 0 g 1 w 4 M 178.0511 85.0653 m F 0 G 0.3 w 10 M 155.2409 77.6011 m S 155.2409 92.5295 m S 155.2409 77.6011 m S 170.4477 92.5295 m S 170.4477 77.6011 m S 155.2409 77.6011 m S 155.2409 92.5295 m S 162.8443 85.0653 m S 170.4477 77.6011 m S 155.2409 77.6011 m S 0 g 1 w 4 M 162.8443 85.0653 m F 0 G 0.3 w 10 M 185.6546 92.5295 m S 185.6546 77.6011 m S 170.4477 77.6011 m S 170.4477 92.5295 m S 178.0511 85.0653 m S 185.6546 77.6011 m S 185.6546 77.6011 m S 185.6546 92.5295 m S 185.6546 77.6011 m S 170.4477 77.6011 m S 0 g 1 w 4 M 178.0511 85.0653 m F 0 G 0.3 w 10 M 185.6546 92.5295 m S 185.6546 77.6011 m S 170.4477 77.6011 m S 170.4477 92.5295 m S 178.0511 85.0653 m S 185.6546 77.6011 m S 185.6546 77.6011 m S 185.6546 92.5295 m S 185.6546 77.6011 m S 170.4477 77.6011 m S 0 g 1 w 4 M 178.0511 85.0653 m F 0 G 0.3 w 10 M 185.6546 77.6011 m S 0 g 1 w 4 M 185.6546 77.6011 m F 0 G 0.3 w 10 M 185.6546 77.6011 m S 185.6546 77.6011 m S 185.6546 77.6011 m S 0 g 1 w 4 M 185.6546 77.6011 m F 0 G 0.3 w 10 M 185.6546 77.6011 m S 185.6546 77.6011 m S 185.6546 77.6011 m S 0 g 1 w 4 M 185.6546 77.6011 m F 0 G 0.3 w 10 M 185.6546 77.6011 m S 185.6546 77.6011 m S 185.6546 107.4579 m S 0 g 1 w 4 M 185.6546 107.4579 m F 0 G 0.3 w 10 M 185.6546 107.4579 m S 185.6546 107.4579 m S 185.6546 107.4579 m S 0 g 1 w 4 M 185.6546 107.4579 m F 0 G 0.3 w 10 M 185.6546 107.4579 m S 185.6546 107.4579 m S 185.6546 107.4579 m S 0 g 1 w 4 M 185.6546 107.4579 m F 0 G 0.3 w 10 M 185.6546 107.4579 m S 185.6546 107.4579 m S 155.2409 107.4579 m S 0 g 1 w 4 M 155.2409 107.4579 m F 0 G 0.3 w 10 M 155.2409 107.4579 m S 155.2409 107.4579 m S 155.2409 107.4579 m S 0 g 1 w 4 M 155.2409 107.4579 m F 0 G 0.3 w 10 M 155.2409 107.4579 m S 155.2409 107.4579 m S 155.2409 107.4579 m S 0 g 1 w 4 M 155.2409 107.4579 m F 0 G 0.3 w 10 M 155.2409 107.4579 m S 155.2409 107.4579 m S 170.4477 92.5295 m S 0 g 1 w 4 M 170.4477 92.5295 m F 0 G 0.3 w 10 M 170.4477 92.5295 m S 170.4477 92.5295 m S 170.4477 92.5295 m S 0 g 1 w 4 M 170.4477 92.5295 m F 0 G 0.3 w 10 M 170.4477 92.5295 m S 170.4477 92.5295 m S 170.4477 92.5295 m S 0 g 1 w 4 M 170.4477 92.5295 m F 0 G 0.3 w 10 M 170.4477 92.5295 m S 170.4477 92.5295 m S 155.2409 77.6011 m S 0 g 1 w 4 M 155.2409 77.6011 m F 0 G 0.3 w 10 M 155.2409 77.6011 m S 155.2409 77.6011 m S 155.2409 77.6011 m S 0 g 1 w 4 M 155.2409 77.6011 m F 0 G 0.3 w 10 M 155.2409 77.6011 m S 155.2409 77.6011 m S 155.2409 77.6011 m S 0 g 1 w 4 M 155.2409 77.6011 m F 0 G 0.3 w 10 M 155.2409 77.6011 m S 155.2409 77.6011 m S 181.4956 103.0545 m S 0 g 1 w 4 M 181.4956 103.0545 m F 0 G 0.3 w 10 M 181.4956 103.0545 m S 181.4956 103.0545 m S 181.4956 103.0545 m S 0 g 1 w 4 M 181.4956 103.0545 m F 0 G 0.3 w 10 M 181.4956 103.0545 m S 181.4956 103.0545 m S 1 g 1 w 4 M 175.4852 103.0545 m 175.4852 99.8327 178.1762 97.2209 181.4956 97.2209 c 184.815 97.2209 187.506 99.8327 187.506 103.0545 c F 187.506 103.0545 m 187.506 106.2763 184.815 108.8881 181.4956 108.8881 c 178.1762 108.8881 175.4852 106.2763 175.4852 103.0545 c F 181.4956 103.0545 m F 0 G 0.3 w 10 M 181.4956 103.0545 m S 0 g 1 w 4 M 181.4956 103.0545 m F 0 G 0.3 w 10 M 181.4956 103.0545 m S 181.4956 103.0545 m S 0 g 1 w 4 M 180.4105 101.9866 m 180.4105 98.4095 L 182.5807 98.4095 L 182.5807 101.9866 L 186.1663 101.9754 L 186.1663 104.1338 L 182.5807 104.1227 L 182.5807 107.6998 L 180.4105 107.6998 L 180.4105 104.1227 L 176.8249 104.1338 L 176.8249 101.9754 L 180.4105 101.9866 L f 0 G 0.3 w 10 M 156.9956 107.5545 m S 0 g 1 w 4 M 156.9956 107.5545 m F 0 G 0.3 w 10 M 156.9956 107.5545 m S 156.9956 107.5545 m S 156.9956 107.5545 m S 0 g 1 w 4 M 156.9956 107.5545 m F 0 G 0.3 w 10 M 156.9956 107.5545 m S 156.9956 107.5545 m S 1 g 1 w 4 M 150.9852 107.5545 m 150.9852 104.3327 153.6762 101.7209 156.9956 101.7209 c 160.315 101.7209 163.006 104.3327 163.006 107.5545 c F 163.006 107.5545 m 163.006 110.7763 160.315 113.3881 156.9956 113.3881 c 153.6762 113.3881 150.9852 110.7763 150.9852 107.5545 c F 156.9956 107.5545 m F 0 G 0.3 w 10 M 156.9956 107.5545 m S 0 g 1 w 4 M 156.9956 107.5545 m F 0 G 0.3 w 10 M 156.9956 107.5545 m S 156.9956 107.5545 m S 0 g 1 w 4 M 155.9105 106.4866 m 155.9105 102.9095 L 158.0807 102.9095 L 158.0807 106.4866 L 161.6663 106.4754 L 161.6663 108.6338 L 158.0807 108.6227 L 158.0807 112.1998 L 155.9105 112.1998 L 155.9105 108.6227 L 152.3249 108.6338 L 152.3249 106.4754 L 155.9105 106.4866 L f 0 G 0.3 w 10 M 177.9956 78.0545 m S 0 g 1 w 4 M 177.9956 78.0545 m F 0 G 0.3 w 10 M 177.9956 78.0545 m S 177.9956 78.0545 m S 177.9956 78.0545 m S 0 g 1 w 4 M 177.9956 78.0545 m F 0 G 0.3 w 10 M 177.9956 78.0545 m S 177.9956 78.0545 m S 1 g 1 w 4 M 171.9852 78.0545 m 171.9852 74.8327 174.6762 72.2209 177.9956 72.2209 c 181.315 72.2209 184.006 74.8327 184.006 78.0545 c F 184.006 78.0545 m 184.006 81.2763 181.315 83.8881 177.9956 83.8881 c 174.6762 83.8881 171.9852 81.2763 171.9852 78.0545 c F 177.9956 78.0545 m F 0 G 0.3 w 10 M 177.9956 78.0545 m S 0 g 1 w 4 M 177.9956 78.0545 m F 0 G 0.3 w 10 M 177.9956 78.0545 m S 177.9956 78.0545 m S 0 g 1 w 4 M 176.9105 76.9866 m 176.9105 73.4095 L 179.0807 73.4095 L 179.0807 76.9866 L 182.6663 76.9754 L 182.6663 79.1338 L 179.0807 79.1227 L 179.0807 82.6998 L 176.9105 82.6998 L 176.9105 79.1227 L 173.3249 79.1338 L 173.3249 76.9754 L 176.9105 76.9866 L f 0 G 0.3 w 10 M 167.7456 97.0545 m S 0 g 1 w 4 M 167.7456 97.0545 m F 0 G 0.3 w 10 M 167.7456 97.0545 m S 167.7456 97.0545 m S 167.7456 97.0545 m S 0 g 1 w 4 M 167.7456 97.0545 m F 0 G 0.3 w 10 M 167.7456 97.0545 m S 167.7456 97.0545 m S 1 g 1 w 4 M 161.7352 97.0545 m 161.7352 93.8327 164.4262 91.2209 167.7456 91.2209 c 171.065 91.2209 173.756 93.8327 173.756 97.0545 c F 173.756 97.0545 m 173.756 100.2763 171.065 102.8881 167.7456 102.8881 c 164.4262 102.8881 161.7352 100.2763 161.7352 97.0545 c F 167.7456 97.0545 m F 0 G 0.3 w 10 M 167.7456 97.0545 m S 0 g 1 w 4 M 167.7456 97.0545 m F 0 G 0.3 w 10 M 167.7456 97.0545 m S 167.7456 97.0545 m S 0 g 1 w 4 M 166.6605 95.9866 m 166.6605 92.4095 L 168.8307 92.4095 L 168.8307 95.9866 L 172.4163 95.9754 L 172.4163 98.1338 L 168.8307 98.1227 L 168.8307 101.6998 L 166.6605 101.6998 L 166.6605 98.1227 L 163.0749 98.1338 L 163.0749 95.9754 L 166.6605 95.9866 L f 0 G 0.3 w 10 M 160.4956 82.5545 m S 0 g 1 w 4 M 160.4956 82.5545 m F 0 G 0.3 w 10 M 160.4956 82.5545 m S 160.4956 82.5545 m S 160.4956 82.5545 m S 0 g 1 w 4 M 160.4956 82.5545 m F 0 G 0.3 w 10 M 160.4956 82.5545 m S 160.4956 82.5545 m S 1 g 1 w 4 M 154.4852 82.5545 m 154.4852 79.3327 157.1762 76.7209 160.4956 76.7209 c 163.815 76.7209 166.506 79.3327 166.506 82.5545 c F 166.506 82.5545 m 166.506 85.7763 163.815 88.3881 160.4956 88.3881 c 157.1762 88.3881 154.4852 85.7763 154.4852 82.5545 c F 160.4956 82.5545 m F 0 G 0.3 w 10 M 160.4956 82.5545 m S 0 g 1 w 4 M 160.4956 82.5545 m F 0 G 0.3 w 10 M 160.4956 82.5545 m S 160.4956 82.5545 m S 0 g 1 w 4 M 159.4105 81.4866 m 159.4105 77.9095 L 161.5807 77.9095 L 161.5807 81.4866 L 165.1663 81.4754 L 165.1663 83.6338 L 161.5807 83.6227 L 161.5807 87.1998 L 159.4105 87.1998 L 159.4105 83.6227 L 155.8249 83.6338 L 155.8249 81.4754 L 159.4105 81.4866 L f 0 G 0.3 w 10 M 153.4909 241.8137 m S 153.4909 241.8137 m S 153.4909 241.8137 m S 153.4909 241.8137 m S 153.4909 241.8137 m S 153.4909 241.8137 m S 153.4909 241.8137 m S 153.4909 241.8137 m S 153.4909 241.8137 m S 154.875 242.875 m S 0 g 1 w 4 M 154.875 242.875 m F 0 G 0.3 w 10 M 154.875 242.875 m S 154.875 242.875 m S 154.875 242.875 m S 0 g 1 w 4 M 154.875 242.875 m F 0 G 0.3 w 10 M 154.875 242.875 m S 154.875 242.875 m S 1 g 1 w 4 M 148.8646 242.875 m 148.8646 239.6532 151.5556 237.0414 154.875 237.0414 c 158.1944 237.0414 160.8854 239.6532 160.8854 242.875 c F 160.8854 242.875 m 160.8854 246.0968 158.1944 248.7086 154.875 248.7086 c F 154.875 248.7086 m 151.5556 248.7086 148.8646 246.0968 148.8646 242.875 c F 154.875 242.875 m F 0 G 0.3 w 10 M 154.875 242.875 m S 0 g 1 w 4 M 154.875 242.875 m F 0 G 0.3 w 10 M 154.875 242.875 m S 154.875 242.875 m S 0 g 1 w 4 M 159.5457 243.9543 m 155.9601 243.9432 L 155.9601 247.5203 L 153.7899 247.5203 L 153.7899 243.9432 L 150.2043 243.9543 L 150.2043 241.7959 L 153.7899 241.8071 L 153.7899 238.23 L 155.9601 238.23 L 155.9601 241.8071 L 159.5457 241.7959 L F showpage _E end %%EndDocument @endspecial 60 2528 a FQ(Figure)15 b(8:)21 b(Ma)s(jorit)o(y)14 b(rule)h(for)g(7)10 b FE(\002)e FQ(7)16 b(blo)q(c)o(ks.)21 b(\(a\))15 b(The)h(doubly-alternating)f(blo)q(c)o(k-spin)g(con\014g-)60 2588 y(uration.)21 b(\(b\))16 b(The)g(unique)f(minim)o(al-energy)e (arrangemen)o(t)h(of)i(islands)g(of)g FE(\000)f FQ(spins)h(in)g(a)g(+)f(sea.) 60 2648 y(The)h(energy)g(is)g(80)p FF(J)22 b FQ(p)q(er)16 b(8)h(blo)q(c)o (ks,)e(or)i(10)p FF(J)k FQ(p)q(er)c(blo)q(c)o(k.)938 2784 y(118)p eop %%Page: 119 119 bop 60 91 a FQ(arbitrary)20 b(dimension.)31 b(Digging)21 b(a)f(little)f(deep) q(er)g(w)o(e)h(see)g(that)g(the)g(\\rigidit)o(y")g(in)f(the)h(shap)q(e)60 152 y(and)14 b(p)q(osition)g(of)f(the)g(islands)h(of)f(minorit)o(y)e(spins,)j (and)f(hence)g(the)g(b)q(oundedness)h(of)g(the)f(n)o(um)o(b)q(er)60 212 y(of)19 b(p)q(erio)q(dic)g(ground)h(states,)g(is)f(a)h(consequence)e(of)h (the)g(follo)o(wing)g(n)o(umerological)e(\\miracle":)60 272 y(the)f(blo)q(c)o(k)g(size)f FF(b)f FQ(=)f(7)k(and)g(the)f(island)g(size)g FF(c)d FQ(=)h(5)j(satisfy)f(the)g(Diophan)o(tine)g(equation)820 382 y(1)11 b(+)g FF(b)925 361 y FH(2)972 382 y FQ(=)28 b(2)p FF(c)1083 361 y FH(2)1117 382 y FF(:)634 b FQ(\(4)p FF(:)p FQ(34\))60 492 y(The)15 b(pro)q(of)h(extends)e(automatically)g(to)h(an)o(y)g (blo)q(c)o(k)f(size)g FF(b)h FQ(for)g(whic)o(h)f FF(c)h FQ(de\014ned)g(b)o(y) f(\(4.34\))i(is)f(an)60 552 y(in)o(teger.)20 b(In)15 b(App)q(endix)g(C)g(w)o (e)g(\014nd)h(the)f(general)h(solution)f(to)h(this)f(Diophan)o(tine)h (equation:)k(the)60 612 y(admissible)14 b(blo)q(c)o(k)i(sizes)g(turn)g(out)h (to)f(b)q(e)562 715 y Fx(e)564 732 y FF(b)585 739 y FD(k)633 732 y FQ(=)704 698 y(1)p 704 720 25 2 v 704 766 a(2)742 684 y Fx(h)761 732 y FQ(\(1)c(+)865 689 y FE(p)p 906 689 V 906 732 a FQ(2)q(\))950 711 y FH(2)p FD(k)q FH(+1)1045 732 y FQ(+)f(\(1)g FE(\000)1198 689 y(p)p 1239 689 V 1239 732 a FQ(2)q(\))1283 711 y FH(2)p FD(k)q FH(+1)1367 684 y Fx(i)1765 732 y FQ(\(4)p FF(:)p FQ(35\))60 867 y(for)i FF(k)i FQ(=)f(1)p FF(;)8 b FQ(2)p FF(;)g FQ(3)p FF(;)g(:)g(:)g(:)g FQ(.)20 b(The)13 b(\014rst)f(few)737 850 y Fx(e)738 867 y FF(b)759 874 y FD(k)793 867 y FQ(are)g(7,)h(41,)g(239,)h (1393,)g(8119,)h FF(:)8 b(:)g(:)13 b FQ(.)20 b(F)l(or)12 b(other)g(blo)q(c)o (k)g(sizes,)60 927 y(a)f(pro)q(of)i(of)e(non-Gibbsianness)i(using)e(our)h (metho)q(ds)e(w)o(ould)h(require)f(either)g(a)h(more)f(clev)o(er)f(c)o(hoice) 60 987 y(of)18 b(blo)q(c)o(k-spin)g(con\014guration)i FF(!)681 969 y Fy(0)679 1000 y FH(sp)q(ecial)784 987 y FQ(,)e(or)h(else)e(a)i(more)d (sophisticated)j(v)o(ersion)e(of)h(P-S)h(theory)60 1047 y(capable)i(of)g (dealing)g(with)g(in\014nitely)e(man)o(y)h(p)q(erio)q(dic)h(ground)h(states)g ([46,)f(179)q(,)f(22)q(,)h(23,)g(48)q(].)60 1108 y(Irresp)q(ectiv)o(e)14 b(of)i(these)g(tec)o(hnical)f(details,)g(it)g(seems)g(plausible)g(to)i(exp)q (ect)e(that)i(the)f FP(c)n(onclusion)60 1168 y FQ(of)h(Theorem)d(4.5)j (remains)e(v)m(alid)h(for)g FP(al)r(l)23 b FQ(blo)q(c)o(k)16 b(sizes)f FF(b)p FQ(.)133 1278 y FM(Remark.)j FQ(Gri\016ths)13 b(and)h(P)o(earce)f([172)q(,)f(173)r(])h(and)g(later)g(Hasenfratz)h(and)g (Hasenfratz)f([189,)60 1338 y(Section)19 b(4])g(ha)o(v)o(e)g(presen)o(ted)g (a)g(rather)h(di\013eren)o(t)f(class)g(of)h(cases)f(in)h(whic)o(h)e(the)i(ma) s(jorit)o(y-rule)60 1398 y(transformation)g(is)g(exp)q(ected)f(to)h(ha)o(v)o (e)f(\\p)q(eculiarities":)28 b(in)20 b(these)g(examples)e(the)h(blo)q(c)o (k-spin)60 1458 y(con\014guration)j FF(!)392 1440 y Fy(0)390 1471 y FH(sp)q(ecial)517 1458 y FQ(is)e(tak)o(en)h(to)g(b)q(e)g(purely)f(+,)i (and)g(the)e(magnetic)g(\014eld)g(is)h(tak)o(en)g(to)g(b)q(e)60 1519 y(negativ)o(e)13 b(\(with)g(an)h(order-1)h(strength)f(c)o(hosen)f(to)h (exactly)f(comp)q(ensate)g(the)g(e\013ect)g(of)h(the)g(blo)q(c)o(k)60 1579 y(spins\).)21 b(Our)14 b(sc)o(heme)e(of)i(pro)q(of)i(do)q(es)f(not)g (apply)f(in)g(these)g(examples,)e(for)i(t)o(w)o(o)g(reasons:)22 b(Firstly)l(,)60 1639 y(there)17 b(are)g(in\014nitely)f(man)o(y)f(p)q(erio)q (dic)i(ground)i(states,)e(so)h(P-S)g(theory)f(in)g(its)g(usual)h(form)e(do)q (es)60 1699 y(not)d(apply)l(.)20 b(Secondly)13 b(\(and)g(p)q(erhaps)h(more)d (seriously\),)i(in)g(the)f(con\014guration)i FF(!)1589 1681 y Fy(0)1587 1711 y FH(sp)q(ecial)1706 1699 y FQ(all)e(of)h(the)60 1759 y(blo)q(c)o(k)i(spins)h(are)f FP(alr)n(e)n(ady)k FQ(+,)c(and)h(b)o(y)f (construction)h(the)f(corresp)q(onding)i(in)o(ternal-spin)d(system)60 1820 y(do)q(es)21 b FP(not)k FQ(ha)o(v)o(e)19 b(a)i(unique)e(Gibbs)i (measure;)f(so)h(it)e(is)h(clearly)f(imp)q(ossible)f(to)j(\\select")e(the)h (+)60 1880 y(phase)h(\(i.e.)e(mak)o(e)g(it)h(unique\))g(b)o(y)h(setting)f (the)h(blo)q(c)o(k)f(spins)h(in)f(an)h(ann)o(ulus)g(to)g(b)q(e)g(+.)35 b(This)60 1940 y(latter)16 b(fact)g(w)o(as)h(already)f(noted)g(b)o(y)g (Israel)g([207,)g(p.)g(597].)60 2070 y FM(4.3.5)55 b(Blo)r(c)n(k-Av)n (eraging)17 b(T)-5 b(ransformations)60 2162 y FQ(In)17 b(con)o(trast)g(to)h (our)g(previous)f(example,)d(in)j(this)g(case)h(our)f(pro)q(of)h(w)o(orks)g (for)f FP(even)23 b FQ(blo)q(c)o(k)17 b(sizes)60 2222 y(\(and)c(only)f (these\))g(precisely)e FP(b)n(e)n(c)n(ause)16 b FQ(of)c(the)g(p)q(ossibilit)o (y)f(of)i(ties.)19 b(W)l(e)12 b(discuss)h(here)e(the)h(simplest)60 2283 y(case,)i(namely)e(the)h(2)6 b FE(\002)g FQ(2)14 b(blo)q(c)o(k-a)o(v)o (eraging)f(transformation)h(for)g(the)g(t)o(w)o(o-dimensional)e(nearest-)60 2343 y(neigh)o(b)q(or)21 b(Ising)f(mo)q(del)f(at)i(lo)o(w)g(temp)q(eratures.) 32 b(W)l(e)21 b(divide)e Fq(Z)1289 2322 y FH(2)1330 2343 y FQ(in)o(to)h(2)14 b FE(\002)g FQ(2)21 b(blo)q(c)o(ks)f FF(B)1758 2350 y FD(j)1776 2343 y FQ(,)h(and)60 2403 y(de\014ne)827 2463 y FF(\033)857 2443 y Fy(0)855 2475 y FD(j)901 2463 y FQ(=)976 2422 y Fx(X)967 2514 y FD(i)p Fy(2)p FD(B)1030 2519 y Fs(j)1053 2463 y FF(\033)1081 2470 y FD(i)1109 2463 y FF(:)642 b FQ(\(4)p FF(:)p FQ(36\))60 2596 y(W)l(e)12 b(notice)g(that)h(although)h(the)e (original)h(v)m(ariables)g FF(\033)h FQ(tak)o(e)e(t)o(w)o(o)g(v)m(alues)h(\() p FE(\006)p FQ(1\),)g(the)f(renormalized)60 2656 y(spins)j FF(\033)211 2638 y Fy(0)237 2656 y FQ(tak)o(e)f(\014v)o(e)g(v)m(alues)h(\(0)p FF(;)8 b FE(\006)p FQ(2)p FF(;)g FE(\006)p FQ(4\).)21 b(Usually)14 b(the)h(a)o(v)o(erage)f(spins)h(are)g(rescaled,)f(but)h(suc)o(h)g(a)938 2784 y(119)p eop %%Page: 120 120 bop 152 439 a @beginspecial 29 @llx 31.500000 @lly 358 @urx 98.500000 @ury 3952 @rwi @setspecial %%BeginDocument: fig9.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 44.1934 94.9406 m S 44.1934 83.4704 m S 32.4335 83.4704 m S 32.4335 94.9406 m S 38.3134 89.2055 m S u 67.7134 72 m S 67.7134 60.5297 m S 55.9534 60.5297 m S 55.9534 72 m S 61.8334 66.2648 m S U 55.9534 83.4704 m S 55.9534 72 m S 44.1934 72 m S 44.1934 83.4704 m S 50.0735 77.7352 m S 55.9534 94.9406 m S 55.9534 83.4704 m S 44.1934 83.4704 m S 44.1934 94.9406 m S 50.0735 89.2055 m S 67.7134 94.9406 m S 67.7134 83.4704 m S 55.9534 83.4704 m S 55.9534 94.9406 m S 61.8334 89.2055 m S 67.7134 83.4704 m S 67.7134 72 m S 55.9534 72 m S 55.9534 83.4704 m S 61.8334 77.7352 m S u 55.9534 72 m S 55.9534 60.5297 m S 44.1934 60.5297 m S 44.1934 72 m S 50.0735 66.2648 m S U u 44.1934 72 m S 44.1934 60.5297 m S 32.4335 60.5297 m S 32.4335 72 m S 38.3134 66.2648 m S U 44.1934 83.4704 m S 44.1934 72 m S 32.4335 72 m S 32.4335 83.4704 m S 38.3134 77.7352 m S 0 g 1 w 4 M 38.3134 89.2055 m F 61.8334 89.2055 m F 38.3134 66.2648 m F 61.8334 66.2648 m F 0 G 0.3 w 10 M 79.4733 94.9406 m S 79.4733 83.4704 m S 67.7134 83.4704 m S 67.7134 94.9406 m S 73.5932 89.2055 m S u 102.9932 72 m S 102.9932 60.5297 m S 91.2332 60.5297 m S 91.2332 72 m S 97.1132 66.2648 m S U u 91.2332 83.4704 m S 91.2332 72 m S 79.4733 72 m S 79.4733 83.4704 m S 85.3533 77.7352 m S U u 91.2332 94.9406 m S 91.2332 83.4704 m S 79.4733 83.4704 m S 79.4733 94.9406 m S 85.3533 89.2055 m S U u 102.9932 94.9406 m S 102.9932 83.4704 m S 91.2332 83.4704 m S 91.2332 94.9406 m S 97.1132 89.2055 m S U u 102.9932 83.4704 m S 102.9932 72 m S 91.2332 72 m S 91.2332 83.4704 m S 97.1132 77.7352 m S U u 91.2332 72 m S 91.2332 60.5297 m S 79.4733 60.5297 m S 79.4733 72 m S 85.3533 66.2648 m S U u 79.4733 72 m S 79.4733 60.5297 m S 67.7134 60.5297 m S 67.7134 72 m S 73.5932 66.2648 m S U 79.4733 83.4704 m S 79.4733 72 m S 67.7134 72 m S 67.7134 83.4704 m S 73.5932 77.7352 m S 0 g 1 w 4 M 73.5932 89.2055 m F 97.1132 89.2055 m F 73.5932 66.2648 m F 97.1132 66.2648 m F u 0 G 0.3 w 10 M 114.7531 94.9406 m S 114.7531 83.4704 m S 102.9932 83.4704 m S 102.9932 94.9406 m S 108.8731 89.2055 m S U u 114.7531 72 m S 114.7531 60.5297 m S 102.9932 60.5297 m S 102.9932 72 m S 108.8731 66.2648 m S U u 114.7531 83.4704 m S 114.7531 72 m S 102.9932 72 m S 102.9932 83.4704 m S 108.8731 77.7352 m S U u 44.1934 60.5297 m S 44.1934 49.0594 m S 32.4335 49.0594 m S 32.4335 60.5297 m S 38.3134 54.7945 m S U 55.9534 49.0594 m S 44.1934 49.0594 m S u 55.9534 60.5297 m S 55.9534 49.0594 m S 44.1934 49.0594 m S 44.1934 60.5297 m S 50.0735 54.7945 m S U u 67.7134 60.5297 m S 67.7134 49.0594 m S 55.9534 49.0594 m S 55.9534 60.5297 m S 61.8334 54.7945 m S U 67.7134 49.0594 m S 55.9534 49.0594 m S 44.1934 49.0594 m S 32.4335 49.0594 m S 0 g 1 w 4 M 38.3134 54.7945 m F 61.8334 54.7945 m F u 0 G 0.3 w 10 M 79.4733 60.5297 m S 79.4733 49.0594 m S 67.7134 49.0594 m S 67.7134 60.5297 m S 73.5932 54.7945 m S U 91.2332 49.0594 m S 79.4733 49.0594 m S u 91.2332 60.5297 m S 91.2332 49.0594 m S 79.4733 49.0594 m S 79.4733 60.5297 m S 85.3533 54.7945 m S U u 102.9932 60.5297 m S 102.9932 49.0594 m S 91.2332 49.0594 m S 91.2332 60.5297 m S 97.1132 54.7945 m S U 102.9932 49.0594 m S 91.2332 49.0594 m S 79.4733 49.0594 m S 67.7134 49.0594 m S 0 g 1 w 4 M 73.5932 54.7945 m F 97.1132 54.7945 m F u 0 G 0.3 w 10 M 114.7531 60.5297 m S 114.7531 49.0594 m S 102.9932 49.0594 m S 102.9932 60.5297 m S 108.8731 54.7945 m S U 102.9932 49.0594 m S 1 w 4 M 38.3134 77.7352 m S 97.1132 77.7352 m S 50.0735 89.2055 m S 85.3533 89.2055 m S 32.4335 94.9406 m 79.4733 94.9406 l 79.4733 49.0594 l 32.4335 49.0594 l 32.4335 94.9406 l s 0.3 w 10 M 44.1934 83.4704 m S 0 g 1 w 4 M 44.1934 83.4704 m F 0 G 0.3 w 10 M 44.1934 83.4704 m S 44.1934 83.4704 m S 44.1934 83.4704 m S 0 g 1 w 4 M 44.1934 83.4704 m F 0 G 0.3 w 10 M 44.1934 83.4704 m S 44.1934 83.4704 m S 1 g 1 w 4 M 44.1934 83.4704 m F 0 G 0.3 w 10 M 44.1934 83.4704 m S 0 g 1 w 4 M 44.1934 83.4704 m F 0 G 0.3 w 10 M 44.1934 83.4704 m S 44.1934 83.4704 m S 1 w 4 M 55.9534 94.9406 m 55.9534 49.0594 l S 32.4335 72 m 79.4733 72 l S 0.3 w 10 M 38.3134 89.2055 m S 0 g 1 w 4 M 38.3134 89.2055 m F 0 G 0.3 w 10 M 38.3134 89.2055 m S 38.3134 89.2055 m S 38.3134 89.2055 m S 0 g 1 w 4 M 38.3134 89.2055 m F 0 G 0.3 w 10 M 38.3134 89.2055 m S 38.3134 89.2055 m S 1 g 1 w 4 M 35.2148 89.2055 m 35.2148 87.543 36.6021 86.1952 38.3134 86.1952 c 40.0248 86.1952 41.4122 87.543 41.4122 89.2055 c F 41.4122 89.2055 m 41.4122 90.868 40.0248 92.2157 38.3134 92.2157 c 36.6021 92.2157 35.2148 90.868 35.2148 89.2055 c F 38.3134 89.2055 m F 0 G 0.3 w 10 M 38.3134 89.2055 m S 0 g 1 w 4 M 38.3134 89.2055 m F 0 G 0.3 w 10 M 38.3134 89.2055 m S 38.3134 89.2055 m S 0 g 1 w 4 M 37.754 88.6545 m 37.754 86.8086 L 38.8729 86.8086 L 38.8729 88.6545 L 40.7215 88.6486 L 40.7215 89.7625 L 38.8729 89.7567 L 38.8729 91.6025 L 37.754 91.6025 L 37.754 89.7567 L 35.9054 89.7625 L 35.9054 88.6486 L 37.754 88.6545 L f 0 G 0.3 w 10 M 38.3134 77.7352 m S 0 g 1 w 4 M 38.3134 77.7352 m F 0 G 0.3 w 10 M 38.3134 77.7352 m S 38.3134 77.7352 m S 38.3134 77.7352 m S 0 g 1 w 4 M 38.3134 77.7352 m F 0 G 0.3 w 10 M 38.3134 77.7352 m S 38.3134 77.7352 m S u 1 g 1 w 4 M 35.2148 77.7352 m 35.2148 76.0727 36.6021 74.725 38.3134 74.725 c 40.0248 74.725 41.4122 76.0727 41.4122 77.7352 c F 41.4122 77.7352 m 41.4122 79.3977 40.0248 80.7455 38.3134 80.7455 c 36.6021 80.7455 35.2148 79.3977 35.2148 77.7352 c F 38.3134 77.7352 m F U 0 G 0.3 w 10 M 38.3134 77.7352 m S 0 g 1 w 4 M 38.3134 77.7352 m F 0 G 0.3 w 10 M 38.3134 77.7352 m S 38.3134 77.7352 m S 0 g 1 w 4 M 37.754 77.1841 m 37.754 75.3383 L 38.8729 75.3383 L 38.8729 77.1841 L 40.7215 77.1784 L 40.7215 78.2921 L 38.8729 78.2864 L 38.8729 80.1322 L 37.754 80.1322 L 37.754 78.2864 L 35.9054 78.2921 L 35.9054 77.1784 L 37.754 77.1841 L f 0 G 0.3 w 10 M 38.3134 66.2648 m S 0 g 1 w 4 M 38.3134 66.2648 m F 0 G 0.3 w 10 M 38.3134 66.2648 m S 38.3134 66.2648 m S 38.3134 66.2648 m S 0 g 1 w 4 M 38.3134 66.2648 m F 0 G 0.3 w 10 M 38.3134 66.2648 m S 38.3134 66.2648 m S u 1 g 1 w 4 M 35.2148 66.2648 m 35.2148 64.6023 36.6021 63.2546 38.3134 63.2546 c 40.0248 63.2546 41.4122 64.6023 41.4122 66.2648 c F 41.4122 66.2648 m 41.4122 67.9274 40.0248 69.2751 38.3134 69.2751 c 36.6021 69.2751 35.2148 67.9274 35.2148 66.2648 c F 38.3134 66.2648 m F U 0 G 0.3 w 10 M 38.3134 66.2648 m S 0 g 1 w 4 M 38.3134 66.2648 m F 0 G 0.3 w 10 M 38.3134 66.2648 m S 38.3134 66.2648 m S 0 g 1 w 4 M 37.754 65.7138 m 37.754 63.8679 L 38.8729 63.8679 L 38.8729 65.7138 L 40.7215 65.708 L 40.7215 66.8218 L 38.8729 66.816 L 38.8729 68.6619 L 37.754 68.6619 L 37.754 66.816 L 35.9054 66.8218 L 35.9054 65.708 L 37.754 65.7138 L f 0 G 0.3 w 10 M 38.3134 54.7945 m S 0 g 1 w 4 M 38.3134 54.7945 m F 0 G 0.3 w 10 M 38.3134 54.7945 m S 38.3134 54.7945 m S 38.3134 54.7945 m S 0 g 1 w 4 M 38.3134 54.7945 m F 0 G 0.3 w 10 M 38.3134 54.7945 m S 38.3134 54.7945 m S u 1 g 1 w 4 M 35.2148 54.7945 m 35.2148 53.1321 36.6021 51.7843 38.3134 51.7843 c 40.0248 51.7843 41.4122 53.1321 41.4122 54.7945 c F 41.4122 54.7945 m 41.4122 56.457 40.0248 57.8048 38.3134 57.8048 c 36.6021 57.8048 35.2148 56.457 35.2148 54.7945 c F 38.3134 54.7945 m F U 0 G 0.3 w 10 M 38.3134 54.7945 m S 0 g 1 w 4 M 38.3134 54.7945 m F 0 G 0.3 w 10 M 38.3134 54.7945 m S 38.3134 54.7945 m S 0 g 1 w 4 M 37.754 54.2435 m 37.754 52.3976 L 38.8729 52.3976 L 38.8729 54.2435 L 40.7215 54.2377 L 40.7215 55.3515 L 38.8729 55.3458 L 38.8729 57.1916 L 37.754 57.1916 L 37.754 55.3458 L 35.9054 55.3515 L 35.9054 54.2377 L 37.754 54.2435 L f 0 G 0.3 w 10 M 73.5932 89.2055 m S 0 g 1 w 4 M 73.5932 89.2055 m F 0 G 0.3 w 10 M 73.5932 89.2055 m S 73.5932 89.2055 m S 73.5932 89.2055 m S 0 g 1 w 4 M 73.5932 89.2055 m F 0 G 0.3 w 10 M 73.5932 89.2055 m S 73.5932 89.2055 m S 1 g 1 w 4 M 70.4946 89.2055 m 70.4946 87.543 71.8819 86.1952 73.5932 86.1952 c 75.3046 86.1952 76.692 87.543 76.692 89.2055 c F 76.692 89.2055 m 76.692 90.868 75.3046 92.2157 73.5932 92.2157 c 71.8819 92.2157 70.4946 90.868 70.4946 89.2055 c F 73.5932 89.2055 m F 0 G 0.3 w 10 M 73.5932 89.2055 m S 0 g 1 w 4 M 73.5932 89.2055 m F 0 G 0.3 w 10 M 73.5932 89.2055 m S 73.5932 89.2055 m S 0 g 1 w 4 M 73.0338 88.6545 m 73.0338 86.8086 L 74.1528 86.8086 L 74.1528 88.6545 L 76.0013 88.6486 L 76.0013 89.7625 L 74.1528 89.7567 L 74.1528 91.6025 L 73.0338 91.6025 L 73.0338 89.7567 L 71.1853 89.7625 L 71.1853 88.6486 L 73.0338 88.6545 L f 0 G 0.3 w 10 M 73.5932 77.7352 m S 0 g 1 w 4 M 73.5932 77.7352 m F 0 G 0.3 w 10 M 73.5932 77.7352 m S 73.5932 77.7352 m S 73.5932 77.7352 m S 0 g 1 w 4 M 73.5932 77.7352 m F 0 G 0.3 w 10 M 73.5932 77.7352 m S 73.5932 77.7352 m S 1 g 1 w 4 M 70.4946 77.7352 m 70.4946 76.0727 71.8819 74.725 73.5932 74.725 c 75.3046 74.725 76.692 76.0727 76.692 77.7352 c F 76.692 77.7352 m 76.692 79.3977 75.3046 80.7455 73.5932 80.7455 c 71.8819 80.7455 70.4946 79.3977 70.4946 77.7352 c F 73.5932 77.7352 m F 0 G 0.3 w 10 M 73.5932 77.7352 m S 0 g 1 w 4 M 73.5932 77.7352 m F 0 G 0.3 w 10 M 73.5932 77.7352 m S 73.5932 77.7352 m S 0 g 1 w 4 M 73.0338 77.1841 m 73.0338 75.3383 L 74.1528 75.3383 L 74.1528 77.1841 L 76.0013 77.1784 L 76.0013 78.2921 L 74.1528 78.2864 L 74.1528 80.1322 L 73.0338 80.1322 L 73.0338 78.2864 L 71.1853 78.2921 L 71.1853 77.1784 L 73.0338 77.1841 L f 0 G 0.3 w 10 M 73.5932 66.2648 m S 0 g 1 w 4 M 73.5932 66.2648 m F 0 G 0.3 w 10 M 73.5932 66.2648 m S 73.5932 66.2648 m S 73.5932 66.2648 m S 0 g 1 w 4 M 73.5932 66.2648 m F 0 G 0.3 w 10 M 73.5932 66.2648 m S 73.5932 66.2648 m S u 1 g 1 w 4 M 70.4946 66.2648 m 70.4946 64.6023 71.8819 63.2546 73.5932 63.2546 c 75.3046 63.2546 76.692 64.6023 76.692 66.2648 c F 76.692 66.2648 m 76.692 67.9274 75.3046 69.2751 73.5932 69.2751 c 71.8819 69.2751 70.4946 67.9274 70.4946 66.2648 c F 73.5932 66.2648 m F U 0 G 0.3 w 10 M 73.5932 66.2648 m S 0 g 1 w 4 M 73.5932 66.2648 m F 0 G 0.3 w 10 M 73.5932 66.2648 m S 73.5932 66.2648 m S 0 g 1 w 4 M 73.0338 65.7138 m 73.0338 63.8679 L 74.1528 63.8679 L 74.1528 65.7138 L 76.0013 65.708 L 76.0013 66.8218 L 74.1528 66.816 L 74.1528 68.6619 L 73.0338 68.6619 L 73.0338 66.816 L 71.1853 66.8218 L 71.1853 65.708 L 73.0338 65.7138 L f 0 G 0.3 w 10 M 73.5932 54.7945 m S 0 g 1 w 4 M 73.5932 54.7945 m F 0 G 0.3 w 10 M 73.5932 54.7945 m S 73.5932 54.7945 m S 73.5932 54.7945 m S 0 g 1 w 4 M 73.5932 54.7945 m F 0 G 0.3 w 10 M 73.5932 54.7945 m S 73.5932 54.7945 m S u 1 g 1 w 4 M 70.4946 54.7945 m 70.4946 53.1321 71.8819 51.7843 73.5932 51.7843 c 75.3046 51.7843 76.692 53.1321 76.692 54.7945 c F 76.692 54.7945 m 76.692 56.457 75.3046 57.8048 73.5932 57.8048 c 71.8819 57.8048 70.4946 56.457 70.4946 54.7945 c F 73.5932 54.7945 m F U 0 G 0.3 w 10 M 73.5932 54.7945 m S 0 g 1 w 4 M 73.5932 54.7945 m F 0 G 0.3 w 10 M 73.5932 54.7945 m S 73.5932 54.7945 m S 0 g 1 w 4 M 73.0338 54.2435 m 73.0338 52.3976 L 74.1528 52.3976 L 74.1528 54.2435 L 76.0013 54.2377 L 76.0013 55.3515 L 74.1528 55.3458 L 74.1528 57.1916 L 73.0338 57.1916 L 73.0338 55.3458 L 71.1853 55.3515 L 71.1853 54.2377 L 73.0338 54.2435 L f 0 G 0.3 w 10 M 61.8334 89.2055 m S 0 g 1 w 4 M 61.8334 89.2055 m F 0 G 0.3 w 10 M 61.8334 89.2055 m S 0 g 1 w 4 M 61.8334 89.2055 m F 1 g 58.7346 89.2055 m 58.7346 87.543 60.122 86.1952 61.8334 86.1952 c 63.5447 86.1952 64.9321 87.543 64.9321 89.2055 c F 64.9321 89.2055 m 64.9321 90.868 63.5447 92.2157 61.8334 92.2157 c 60.122 92.2157 58.7346 90.868 58.7346 89.2055 c F 61.8334 89.2055 m F 0 G 0.3 w 10 M 61.8334 89.2055 m S 0 g 1 w 4 M 61.8334 89.2055 m F 0 G 0.3 w 10 M 61.8334 89.2055 m S 0 g 1 w 4 M 61.8334 89.2055 m F 61.2739 89.7567 m 59.4254 89.7625 L 59.4254 88.6486 L 61.2739 88.6544 L F 62.3928 88.6544 m 64.2414 88.6486 L 64.2414 89.7625 L 62.3928 89.7567 L F 59.4254 89.7625 m 64.2414 89.7625 l 64.2414 88.6486 l 59.4254 88.6486 l 59.4254 89.7625 l f 0 G 0.3 w 10 M 61.8334 77.7352 m S 0 g 1 w 4 M 61.8334 77.7352 m F 0 G 0.3 w 10 M 61.8334 77.7352 m S 0 g 1 w 4 M 61.8334 77.7352 m F 1 g 58.7346 77.7352 m 58.7346 76.0727 60.122 74.725 61.8334 74.725 c 63.5447 74.725 64.9321 76.0727 64.9321 77.7352 c F 64.9321 77.7352 m 64.9321 79.3977 63.5447 80.7455 61.8334 80.7455 c 60.122 80.7455 58.7346 79.3977 58.7346 77.7352 c F 61.8334 77.7352 m F 0 G 0.3 w 10 M 61.8334 77.7352 m S 0 g 1 w 4 M 61.8334 77.7352 m F 0 G 0.3 w 10 M 61.8334 77.7352 m S 0 g 1 w 4 M 61.8334 77.7352 m F 61.2739 78.2864 m 59.4254 78.2921 L 59.4254 77.1784 L 61.2739 77.1841 L F 62.3928 77.1841 m 64.2414 77.1784 L 64.2414 78.2921 L 62.3928 78.2864 L F 59.4254 78.2921 m 64.2414 78.2921 l 64.2414 77.1784 l 59.4254 77.1784 l 59.4254 78.2921 l f 0 G 0.3 w 10 M 61.8334 66.2648 m S 0 g 1 w 4 M 61.8334 66.2648 m F 0 G 0.3 w 10 M 61.8334 66.2648 m S 0 g 1 w 4 M 61.8334 66.2648 m F u 1 g 58.7346 66.2648 m 58.7346 64.6023 60.122 63.2546 61.8334 63.2546 c 63.5447 63.2546 64.9321 64.6023 64.9321 66.2648 c F 64.9321 66.2648 m 64.9321 67.9274 63.5447 69.2751 61.8334 69.2751 c 60.122 69.2751 58.7346 67.9274 58.7346 66.2648 c F 61.8334 66.2648 m F U 0 G 0.3 w 10 M 61.8334 66.2648 m S 0 g 1 w 4 M 61.8334 66.2648 m F 0 G 0.3 w 10 M 61.8334 66.2648 m S 0 g 1 w 4 M 61.8334 66.2648 m F 61.2739 66.816 m 59.4254 66.8218 L 59.4254 65.708 L 61.2739 65.7137 L F 62.3928 65.7137 m 64.2414 65.708 L 64.2414 66.8218 L 62.3928 66.816 L F 59.4254 66.8218 m 64.2414 66.8218 l 64.2414 65.708 l 59.4254 65.708 l 59.4254 66.8218 l f 0 G 0.3 w 10 M 61.8334 54.7945 m S 0 g 1 w 4 M 61.8334 54.7945 m F 0 G 0.3 w 10 M 61.8334 54.7945 m S 0 g 1 w 4 M 61.8334 54.7945 m F u 1 g 58.7346 54.7945 m 58.7346 53.1321 60.122 51.7843 61.8334 51.7843 c 63.5447 51.7843 64.9321 53.1321 64.9321 54.7945 c F 64.9321 54.7945 m 64.9321 56.457 63.5447 57.8048 61.8334 57.8048 c 60.122 57.8048 58.7346 56.457 58.7346 54.7945 c F 61.8334 54.7945 m F U 0 G 0.3 w 10 M 61.8334 54.7945 m S 0 g 1 w 4 M 61.8334 54.7945 m F 0 G 0.3 w 10 M 61.8334 54.7945 m S 0 g 1 w 4 M 61.8334 54.7945 m F 61.2739 55.3458 m 59.4254 55.3515 L 59.4254 54.2377 L 61.2739 54.2434 L F 62.3928 54.2434 m 64.2414 54.2377 L 64.2414 55.3515 L 62.3928 55.3458 L F 59.4254 55.3515 m 64.2414 55.3515 l 64.2414 54.2377 l 59.4254 54.2377 l 59.4254 55.3515 l f 0 G 0.3 w 10 M 50.0735 89.2055 m S 0 g 1 w 4 M 50.0735 89.2055 m F 0 G 0.3 w 10 M 50.0735 89.2055 m S 0 g 1 w 4 M 50.0735 89.2055 m F 1 g 46.9747 89.2055 m 46.9747 87.543 48.3621 86.1952 50.0735 86.1952 c 51.7848 86.1952 53.1721 87.543 53.1721 89.2055 c F 53.1721 89.2055 m 53.1721 90.868 51.7848 92.2157 50.0735 92.2157 c 48.3621 92.2157 46.9747 90.868 46.9747 89.2055 c F 50.0735 89.2055 m F 0 G 0.3 w 10 M 50.0735 89.2055 m S 0 g 1 w 4 M 50.0735 89.2055 m F 0 G 0.3 w 10 M 50.0735 89.2055 m S 0 g 1 w 4 M 50.0735 89.2055 m F 49.514 89.7567 m 47.6654 89.7625 L 47.6654 88.6486 L 49.514 88.6544 L F 50.6329 88.6544 m 52.4815 88.6486 L 52.4815 89.7625 L 50.6329 89.7567 L F 47.6654 89.7625 m 52.4815 89.7625 l 52.4815 88.6486 l 47.6654 88.6486 l 47.6654 89.7625 l f 0 G 0.3 w 10 M 50.0735 77.7352 m S 0 g 1 w 4 M 50.0735 77.7352 m F 0 G 0.3 w 10 M 50.0735 77.7352 m S 0 g 1 w 4 M 50.0735 77.7352 m F u 1 g 46.9747 77.7352 m 46.9747 76.0727 48.3621 74.725 50.0735 74.725 c 51.7848 74.725 53.1721 76.0727 53.1721 77.7352 c F 53.1721 77.7352 m 53.1721 79.3977 51.7848 80.7455 50.0735 80.7455 c 48.3621 80.7455 46.9747 79.3977 46.9747 77.7352 c F 50.0735 77.7352 m F U 0 G 0.3 w 10 M 50.0735 77.7352 m S 0 g 1 w 4 M 50.0735 77.7352 m F 0 G 0.3 w 10 M 50.0735 77.7352 m S 0 g 1 w 4 M 50.0735 77.7352 m F 49.514 78.2864 m 47.6654 78.2921 L 47.6654 77.1784 L 49.514 77.1841 L F 50.6329 77.1841 m 52.4815 77.1784 L 52.4815 78.2921 L 50.6329 78.2864 L F 47.6654 78.2921 m 52.4815 78.2921 l 52.4815 77.1784 l 47.6654 77.1784 l 47.6654 78.2921 l f 0 G 0.3 w 10 M 50.0735 66.2648 m S 0 g 1 w 4 M 50.0735 66.2648 m F 0 G 0.3 w 10 M 50.0735 66.2648 m S 0 g 1 w 4 M 50.0735 66.2648 m F u 1 g 46.9747 66.2648 m 46.9747 64.6023 48.3621 63.2546 50.0735 63.2546 c 51.7848 63.2546 53.1721 64.6023 53.1721 66.2648 c F 53.1721 66.2648 m 53.1721 67.9274 51.7848 69.2751 50.0735 69.2751 c 48.3621 69.2751 46.9747 67.9274 46.9747 66.2648 c F 50.0735 66.2648 m F U 0 G 0.3 w 10 M 50.0735 66.2648 m S 0 g 1 w 4 M 50.0735 66.2648 m F 0 G 0.3 w 10 M 50.0735 66.2648 m S 0 g 1 w 4 M 50.0735 66.2648 m F 49.514 66.816 m 47.6654 66.8218 L 47.6654 65.708 L 49.514 65.7137 L F 50.6329 65.7137 m 52.4815 65.708 L 52.4815 66.8218 L 50.6329 66.816 L F 47.6654 66.8218 m 52.4815 66.8218 l 52.4815 65.708 l 47.6654 65.708 l 47.6654 66.8218 l f 0 G 0.3 w 10 M 50.0735 54.7945 m S 0 g 1 w 4 M 50.0735 54.7945 m F 0 G 0.3 w 10 M 50.0735 54.7945 m S 0 g 1 w 4 M 50.0735 54.7945 m F u 1 g 46.9747 54.7945 m 46.9747 53.1321 48.3621 51.7843 50.0735 51.7843 c 51.7848 51.7843 53.1721 53.1321 53.1721 54.7945 c F 53.1721 54.7945 m 53.1721 56.457 51.7848 57.8048 50.0735 57.8048 c 48.3621 57.8048 46.9747 56.457 46.9747 54.7945 c F 50.0735 54.7945 m F U 0 G 0.3 w 10 M 50.0735 54.7945 m S 0 g 1 w 4 M 50.0735 54.7945 m F 0 G 0.3 w 10 M 50.0735 54.7945 m S 0 g 1 w 4 M 50.0735 54.7945 m F 49.514 55.3458 m 47.6654 55.3515 L 47.6654 54.2377 L 49.514 54.2434 L F 50.6329 54.2434 m 52.4815 54.2377 L 52.4815 55.3515 L 50.6329 55.3458 L F 47.6654 55.3515 m 52.4815 55.3515 l 52.4815 54.2377 l 47.6654 54.2377 l 47.6654 55.3515 l f 0 G 0.3 w 10 M 44.1934 49.0594 m S 67.7134 49.0594 m S 55.9534 49.0594 m S 67.7134 49.0594 m S 55.9534 49.0594 m S 44.1934 49.0594 m S u 102.6767 71.2882 m S 102.6767 60.1738 m S 91.2332 60.1738 m S 91.2332 71.2882 m S 96.9549 65.731 m S U u 102.6767 93.517 m S 102.6767 82.4026 m S 91.2332 82.4026 m S 91.2332 93.517 m S 96.9549 87.9598 m S U u 102.6767 82.4026 m S 102.6767 71.2882 m S 91.2332 71.2882 m S 91.2332 82.4026 m S 96.9549 76.8454 m S U u 114.1201 93.517 m S 114.1201 82.4026 m S 102.6767 82.4026 m S 102.6767 93.517 m S 108.3984 87.9598 m S U u 137.007 71.2882 m S 137.007 60.1738 m S 125.5635 60.1738 m S 125.5635 71.2882 m S 131.2852 65.731 m S U u 125.5635 82.4026 m S 125.5635 71.2882 m S 114.1201 71.2882 m S 114.1201 82.4026 m S 119.8419 76.8454 m S U u 125.5635 93.517 m S 125.5635 82.4026 m S 114.1201 82.4026 m S 114.1201 93.517 m S 119.8419 87.9598 m S U u 137.007 93.517 m S 137.007 82.4026 m S 125.5635 82.4026 m S 125.5635 93.517 m S 131.2852 87.9598 m S U u 137.007 82.4026 m S 137.007 71.2882 m S 125.5635 71.2882 m S 125.5635 82.4026 m S 131.2852 76.8454 m S U u 125.5635 71.2882 m S 125.5635 60.1738 m S 114.1201 60.1738 m S 114.1201 71.2882 m S 119.8419 65.731 m S U u 114.1201 71.2882 m S 114.1201 60.1738 m S 102.6767 60.1738 m S 102.6767 71.2882 m S 108.3984 65.731 m S U u 114.1201 82.4026 m S 114.1201 71.2882 m S 102.6767 71.2882 m S 102.6767 82.4026 m S 108.3984 76.8454 m S U 0 g 1 w 4 M 108.3984 87.9598 m F 131.2852 87.9598 m F 108.3984 65.731 m F 131.2852 65.731 m F u 0 G 0.3 w 10 M 148.4504 93.517 m S 148.4504 82.4026 m S 137.007 82.4026 m S 137.007 93.517 m S 142.7287 87.9598 m S U u 171.3373 71.2882 m S 171.3373 60.1738 m S 159.8939 60.1738 m S 159.8939 71.2882 m S 165.6156 65.731 m S U 159.8939 82.4026 m S 159.8939 71.2882 m S 148.4504 71.2882 m S 148.4504 82.4026 m S 154.1722 76.8454 m S 159.8939 93.517 m S 159.8939 82.4026 m S 148.4504 82.4026 m S 148.4504 93.517 m S 154.1722 87.9598 m S u 171.3373 93.517 m S 171.3373 82.4026 m S 159.8939 82.4026 m S 159.8939 93.517 m S 165.6156 87.9598 m S U 171.3373 82.4026 m S 171.3373 71.2882 m S 159.8939 71.2882 m S 159.8939 82.4026 m S 165.6156 76.8454 m S u 159.8939 71.2882 m S 159.8939 60.1738 m S 148.4504 60.1738 m S 148.4504 71.2882 m S 154.1722 65.731 m S U u 148.4504 71.2882 m S 148.4504 60.1738 m S 137.007 60.1738 m S 137.007 71.2882 m S 142.7287 65.731 m S U u 148.4504 82.4026 m S 148.4504 71.2882 m S 137.007 71.2882 m S 137.007 82.4026 m S 142.7287 76.8454 m S U 0 g 1 w 4 M 142.7287 87.9598 m F 165.6156 87.9598 m F 142.7287 65.731 m F 165.6156 65.731 m F u 0 G 0.3 w 10 M 102.6767 60.1738 m S 102.6767 49.0594 m S 91.2332 49.0594 m S 91.2332 60.1738 m S 96.9549 54.6166 m S U 102.6767 49.0594 m S u 114.1201 60.1738 m S 114.1201 49.0594 m S 102.6767 49.0594 m S 102.6767 60.1738 m S 108.3984 54.6166 m S U 125.5635 49.0594 m S 114.1201 49.0594 m S u 125.5635 60.1738 m S 125.5635 49.0594 m S 114.1201 49.0594 m S 114.1201 60.1738 m S 119.8419 54.6166 m S U u 137.007 60.1738 m S 137.007 49.0594 m S 125.5635 49.0594 m S 125.5635 60.1738 m S 131.2852 54.6166 m S U 137.007 49.0594 m S 125.5635 49.0594 m S 114.1201 49.0594 m S 102.6767 49.0594 m S 0 g 1 w 4 M 108.3984 54.6166 m F 131.2852 54.6166 m F u 0 G 0.3 w 10 M 148.4504 60.1738 m S 148.4504 49.0594 m S 137.007 49.0594 m S 137.007 60.1738 m S 142.7287 54.6166 m S U 159.8939 49.0594 m S 148.4504 49.0594 m S u 159.8939 60.1738 m S 159.8939 49.0594 m S 148.4504 49.0594 m S 148.4504 60.1738 m S 154.1722 54.6166 m S U u 171.3373 60.1738 m S 171.3373 49.0594 m S 159.8939 49.0594 m S 159.8939 60.1738 m S 165.6156 54.6166 m S U 171.3373 49.0594 m S 159.8939 49.0594 m S 148.4504 49.0594 m S 137.007 49.0594 m S 0 g 1 w 4 M 142.7287 54.6166 m F 165.6156 54.6166 m F 0 G 125.5635 93.517 m 125.5635 49.0594 l 171.3373 49.0594 l 171.3373 93.517 l 125.5635 93.517 l s 148.4504 93.517 m 148.4504 49.0594 l S 125.5635 71.2882 m 171.3373 71.2882 l S 0.3 w 10 M 142.7287 87.9598 m S 142.7287 76.8454 m S 0 g 1 w 4 M 142.7287 87.9598 m F 0 G 0.3 w 10 M 142.7287 87.9598 m S 0 g 1 w 4 M 142.7287 87.9598 m F 0 G 0.3 w 10 M 142.7287 87.9598 m S 142.7287 87.9598 m S 142.7287 87.9598 m S 0 g 1 w 4 M 142.7287 87.9598 m F 0 G 0.3 w 10 M 142.7287 87.9598 m S 142.7287 87.9598 m S 1 g 1 w 4 M 139.7134 87.9598 m 139.7134 86.3488 141.0634 85.0429 142.7287 85.0429 c 144.3939 85.0429 145.744 86.3488 145.744 87.9598 c F 145.744 87.9598 m 145.744 89.5707 144.3939 90.8766 142.7287 90.8766 c 141.0634 90.8766 139.7134 89.5707 139.7134 87.9598 c F 142.7287 87.9598 m F 0 G 0.3 w 10 M 142.7287 87.9598 m S 0 g 1 w 4 M 142.7287 87.9598 m F 0 G 0.3 w 10 M 142.7287 87.9598 m S 142.7287 87.9598 m S 0 g 1 w 4 M 142.1843 87.4259 m 142.1843 85.6372 L 143.2731 85.6372 L 143.2731 87.4259 L 145.0719 87.4202 L 145.0719 88.4995 L 143.2731 88.4939 L 143.2731 90.2825 L 142.1843 90.2825 L 142.1843 88.4939 L 140.3854 88.4995 L 140.3854 87.4202 L 142.1843 87.4259 L f 0 G 0.3 w 10 M 142.7287 76.8454 m S 0 g 1 w 4 M 142.7287 76.8454 m F 0 G 0.3 w 10 M 142.7287 76.8454 m S 142.7287 76.8454 m S 142.7287 76.8454 m S 0 g 1 w 4 M 142.7287 76.8454 m F 0 G 0.3 w 10 M 142.7287 76.8454 m S 142.7287 76.8454 m S 1 g 1 w 4 M 139.7134 76.8454 m 139.7134 75.2345 141.0634 73.9286 142.7287 73.9286 c 144.3939 73.9286 145.744 75.2345 145.744 76.8454 c F 145.744 76.8454 m 145.744 78.4563 144.3939 79.7623 142.7287 79.7623 c 141.0634 79.7623 139.7134 78.4563 139.7134 76.8454 c F 142.7287 76.8454 m F 0 G 0.3 w 10 M 142.7287 76.8454 m S 0 g 1 w 4 M 142.7287 76.8454 m F 0 G 0.3 w 10 M 142.7287 76.8454 m S 142.7287 76.8454 m S 0 g 1 w 4 M 142.1843 76.3115 m 142.1843 74.5229 L 143.2731 74.5229 L 143.2731 76.3115 L 145.0719 76.3059 L 145.0719 77.3851 L 143.2731 77.3795 L 143.2731 79.168 L 142.1843 79.168 L 142.1843 77.3795 L 140.3854 77.3851 L 140.3854 76.3059 L 142.1843 76.3115 L f 0 G 0.3 w 10 M 154.1722 87.9598 m S 154.1722 76.8454 m S 0 g 1 w 4 M 154.1722 87.9598 m F 0 G 0.3 w 10 M 154.1722 87.9598 m S 0 g 1 w 4 M 154.1722 87.9598 m F 0 G 0.3 w 10 M 154.1722 87.9598 m S 154.1722 87.9598 m S 154.1722 87.9598 m S 0 g 1 w 4 M 154.1722 87.9598 m F 0 G 0.3 w 10 M 154.1722 87.9598 m S 154.1722 87.9598 m S 1 g 1 w 4 M 151.1568 87.9598 m 151.1568 86.3488 152.5068 85.0429 154.1722 85.0429 c 155.8374 85.0429 157.1874 86.3488 157.1874 87.9598 c F 157.1874 87.9598 m 157.1874 89.5707 155.8374 90.8766 154.1722 90.8766 c 152.5068 90.8766 151.1568 89.5707 151.1568 87.9598 c F 154.1722 87.9598 m F 0 G 0.3 w 10 M 154.1722 87.9598 m S 0 g 1 w 4 M 154.1722 87.9598 m F 0 G 0.3 w 10 M 154.1722 87.9598 m S 154.1722 87.9598 m S 0 g 1 w 4 M 153.6278 87.4259 m 153.6278 85.6372 L 154.7165 85.6372 L 154.7165 87.4259 L 156.5153 87.4202 L 156.5153 88.4995 L 154.7165 88.4939 L 154.7165 90.2825 L 153.6278 90.2825 L 153.6278 88.4939 L 151.829 88.4995 L 151.829 87.4202 L 153.6278 87.4259 L f 0 G 0.3 w 10 M 154.1722 76.8454 m S 0 g 1 w 4 M 154.1722 76.8454 m F 0 G 0.3 w 10 M 154.1722 76.8454 m S 154.1722 76.8454 m S 154.1722 76.8454 m S 0 g 1 w 4 M 154.1722 76.8454 m F 0 G 0.3 w 10 M 154.1722 76.8454 m S 154.1722 76.8454 m S 1 g 1 w 4 M 151.1568 76.8454 m 151.1568 75.2345 152.5068 73.9286 154.1722 73.9286 c 155.8374 73.9286 157.1874 75.2345 157.1874 76.8454 c F 157.1874 76.8454 m 157.1874 78.4563 155.8374 79.7623 154.1722 79.7623 c 152.5068 79.7623 151.1568 78.4563 151.1568 76.8454 c F 154.1722 76.8454 m F 0 G 0.3 w 10 M 154.1722 76.8454 m S 0 g 1 w 4 M 154.1722 76.8454 m F 0 G 0.3 w 10 M 154.1722 76.8454 m S 154.1722 76.8454 m S 0 g 1 w 4 M 153.6278 76.3115 m 153.6278 74.5229 L 154.7165 74.5229 L 154.7165 76.3115 L 156.5153 76.3059 L 156.5153 77.3851 L 154.7165 77.3795 L 154.7165 79.168 L 153.6278 79.168 L 153.6278 77.3795 L 151.829 77.3851 L 151.829 76.3059 L 153.6278 76.3115 L f 0 G 0.3 w 10 M 154.1722 65.731 m S 154.1722 54.6166 m S 0 g 1 w 4 M 154.1722 65.731 m F 0 G 0.3 w 10 M 154.1722 65.731 m S 0 g 1 w 4 M 154.1722 65.731 m F 0 G 0.3 w 10 M 154.1722 65.731 m S 154.1722 65.731 m S 154.1722 65.731 m S 0 g 1 w 4 M 154.1722 65.731 m F 0 G 0.3 w 10 M 154.1722 65.731 m S 154.1722 65.731 m S 1 g 1 w 4 M 151.1568 65.731 m 151.1568 64.1201 152.5068 62.8142 154.1722 62.8142 c 155.8374 62.8142 157.1874 64.1201 157.1874 65.731 c F 157.1874 65.731 m 157.1874 67.3419 155.8374 68.6478 154.1722 68.6478 c 152.5068 68.6478 151.1568 67.3419 151.1568 65.731 c F 154.1722 65.731 m F 0 G 0.3 w 10 M 154.1722 65.731 m S 0 g 1 w 4 M 154.1722 65.731 m F 0 G 0.3 w 10 M 154.1722 65.731 m S 154.1722 65.731 m S 0 g 1 w 4 M 153.6278 65.197 m 153.6278 63.4084 L 154.7165 63.4084 L 154.7165 65.197 L 156.5153 65.1914 L 156.5153 66.2707 L 154.7165 66.2651 L 154.7165 68.0536 L 153.6278 68.0536 L 153.6278 66.2651 L 151.829 66.2707 L 151.829 65.1914 L 153.6278 65.197 L f 0 G 0.3 w 10 M 154.1722 54.6166 m S 0 g 1 w 4 M 154.1722 54.6166 m F 0 G 0.3 w 10 M 154.1722 54.6166 m S 154.1722 54.6166 m S 154.1722 54.6166 m S 0 g 1 w 4 M 154.1722 54.6166 m F 0 G 0.3 w 10 M 154.1722 54.6166 m S 154.1722 54.6166 m S 1 g 1 w 4 M 151.1568 54.6166 m 151.1568 53.0057 152.5068 51.6997 154.1722 51.6997 c 155.8374 51.6997 157.1874 53.0057 157.1874 54.6166 c F 157.1874 54.6166 m 157.1874 56.2275 155.8374 57.5334 154.1722 57.5334 c 152.5068 57.5334 151.1568 56.2275 151.1568 54.6166 c F 154.1722 54.6166 m F 0 G 0.3 w 10 M 154.1722 54.6166 m S 0 g 1 w 4 M 154.1722 54.6166 m F 0 G 0.3 w 10 M 154.1722 54.6166 m S 154.1722 54.6166 m S 0 g 1 w 4 M 153.6278 54.0827 m 153.6278 52.294 L 154.7165 52.294 L 154.7165 54.0827 L 156.5153 54.077 L 156.5153 55.1563 L 154.7165 55.1507 L 154.7165 56.9393 L 153.6278 56.9393 L 153.6278 55.1507 L 151.829 55.1563 L 151.829 54.077 L 153.6278 54.0827 L f 0 G 0.3 w 10 M 142.7287 65.731 m S 142.7287 54.6166 m S 0 g 1 w 4 M 142.7287 65.731 m F 0 G 0.3 w 10 M 142.7287 65.731 m S 0 g 1 w 4 M 142.7287 65.731 m F 0 G 0.3 w 10 M 142.7287 65.731 m S 142.7287 65.731 m S 142.7287 65.731 m S 0 g 1 w 4 M 142.7287 65.731 m F 0 G 0.3 w 10 M 142.7287 65.731 m S 142.7287 65.731 m S 1 g 1 w 4 M 139.7134 65.731 m 139.7134 64.1201 141.0634 62.8142 142.7287 62.8142 c 144.3939 62.8142 145.744 64.1201 145.744 65.731 c F 145.744 65.731 m 145.744 67.3419 144.3939 68.6478 142.7287 68.6478 c 141.0634 68.6478 139.7134 67.3419 139.7134 65.731 c F 142.7287 65.731 m F 0 G 0.3 w 10 M 142.7287 65.731 m S 0 g 1 w 4 M 142.7287 65.731 m F 0 G 0.3 w 10 M 142.7287 65.731 m S 142.7287 65.731 m S 0 g 1 w 4 M 142.1843 65.197 m 142.1843 63.4084 L 143.2731 63.4084 L 143.2731 65.197 L 145.0719 65.1914 L 145.0719 66.2707 L 143.2731 66.2651 L 143.2731 68.0536 L 142.1843 68.0536 L 142.1843 66.2651 L 140.3854 66.2707 L 140.3854 65.1914 L 142.1843 65.197 L f 0 G 0.3 w 10 M 142.7287 54.6166 m S 0 g 1 w 4 M 142.7287 54.6166 m F 0 G 0.3 w 10 M 142.7287 54.6166 m S 142.7287 54.6166 m S 142.7287 54.6166 m S 0 g 1 w 4 M 142.7287 54.6166 m F 0 G 0.3 w 10 M 142.7287 54.6166 m S 142.7287 54.6166 m S 1 g 1 w 4 M 139.7134 54.6166 m 139.7134 53.0057 141.0634 51.6997 142.7287 51.6997 c 144.3939 51.6997 145.744 53.0057 145.744 54.6166 c F 145.744 54.6166 m 145.744 56.2275 144.3939 57.5334 142.7287 57.5334 c 141.0634 57.5334 139.7134 56.2275 139.7134 54.6166 c F 142.7287 54.6166 m F 0 G 0.3 w 10 M 142.7287 54.6166 m S 0 g 1 w 4 M 142.7287 54.6166 m F 0 G 0.3 w 10 M 142.7287 54.6166 m S 142.7287 54.6166 m S 0 g 1 w 4 M 142.1843 54.0827 m 142.1843 52.294 L 143.2731 52.294 L 143.2731 54.0827 L 145.0719 54.077 L 145.0719 55.1563 L 143.2731 55.1507 L 143.2731 56.9393 L 142.1843 56.9393 L 142.1843 55.1507 L 140.3854 55.1563 L 140.3854 54.077 L 142.1843 54.0827 L f 0 G 0.3 w 10 M 165.6156 87.9598 m S 165.6156 76.8454 m S 0 g 1 w 4 M 165.6156 87.9598 m F 0 G 0.3 w 10 M 165.6156 87.9598 m S 0 g 1 w 4 M 165.6156 87.9598 m F 0 G 0.3 w 10 M 165.6156 87.9598 m S 0 g 1 w 4 M 165.6156 87.9598 m F 1 g 162.6003 87.9598 m 162.6003 86.3488 163.9503 85.0429 165.6156 85.0429 c 167.2809 85.0429 168.6309 86.3488 168.6309 87.9598 c F 168.6309 87.9598 m 168.6309 89.5707 167.2809 90.8766 165.6156 90.8766 c 163.9503 90.8766 162.6003 89.5707 162.6003 87.9598 c F 165.6156 87.9598 m F 0 G 0.3 w 10 M 165.6156 87.9598 m S 0 g 1 w 4 M 165.6156 87.9598 m F 0 G 0.3 w 10 M 165.6156 87.9598 m S 0 g 1 w 4 M 165.6156 87.9598 m F 165.0712 88.4939 m 163.2723 88.4995 L 163.2723 87.4202 L 165.0712 87.4258 L F 166.16 87.4258 m 167.9588 87.4202 L 167.9588 88.4995 L 166.16 88.4939 L F 163.2723 88.4995 m 167.9588 88.4995 l 167.9588 87.4202 l 163.2723 87.4202 l 163.2723 88.4995 l f 0 G 0.3 w 10 M 165.6156 76.8454 m S 0 g 1 w 4 M 165.6156 76.8454 m F 0 G 0.3 w 10 M 165.6156 76.8454 m S 0 g 1 w 4 M 165.6156 76.8454 m F 1 g 162.6003 76.8454 m 162.6003 75.2345 163.9503 73.9286 165.6156 73.9286 c 167.2809 73.9286 168.6309 75.2345 168.6309 76.8454 c F 168.6309 76.8454 m 168.6309 78.4563 167.2809 79.7623 165.6156 79.7623 c 163.9503 79.7623 162.6003 78.4563 162.6003 76.8454 c F 165.6156 76.8454 m F 0 G 0.3 w 10 M 165.6156 76.8454 m S 0 g 1 w 4 M 165.6156 76.8454 m F 0 G 0.3 w 10 M 165.6156 76.8454 m S 0 g 1 w 4 M 165.6156 76.8454 m F 165.0712 77.3795 m 163.2723 77.3851 L 163.2723 76.3059 L 165.0712 76.3115 L F 166.16 76.3115 m 167.9588 76.3059 L 167.9588 77.3851 L 166.16 77.3795 L F 163.2723 77.3851 m 167.9588 77.3851 l 167.9588 76.3059 l 163.2723 76.3059 l 163.2723 77.3851 l f 0 G 0.3 w 10 M 131.2852 87.9598 m S 131.2852 76.8454 m S 0 g 1 w 4 M 131.2852 87.9598 m F 0 G 0.3 w 10 M 131.2852 87.9598 m S 0 g 1 w 4 M 131.2852 87.9598 m F 0 G 0.3 w 10 M 131.2852 87.9598 m S 0 g 1 w 4 M 131.2852 87.9598 m F 1 g 128.27 87.9598 m 128.27 86.3488 129.62 85.0429 131.2852 85.0429 c 132.9506 85.0429 134.3006 86.3488 134.3006 87.9598 c F 134.3006 87.9598 m 134.3006 89.5707 132.9506 90.8766 131.2852 90.8766 c 129.62 90.8766 128.27 89.5707 128.27 87.9598 c F 131.2852 87.9598 m F 0 G 0.3 w 10 M 131.2852 87.9598 m S 0 g 1 w 4 M 131.2852 87.9598 m F 0 G 0.3 w 10 M 131.2852 87.9598 m S 0 g 1 w 4 M 131.2852 87.9598 m F 130.7409 88.4939 m 128.9421 88.4995 L 128.9421 87.4202 L 130.7409 87.4258 L F 131.8296 87.4258 m 133.6284 87.4202 L 133.6284 88.4995 L 131.8296 88.4939 L F 128.9421 88.4995 m 133.6284 88.4995 l 133.6284 87.4202 l 128.9421 87.4202 l 128.9421 88.4995 l f 0 G 0.3 w 10 M 131.2852 76.8454 m S 0 g 1 w 4 M 131.2852 76.8454 m F 0 G 0.3 w 10 M 131.2852 76.8454 m S 0 g 1 w 4 M 131.2852 76.8454 m F 1 g 128.27 76.8454 m 128.27 75.2345 129.62 73.9286 131.2852 73.9286 c 132.9506 73.9286 134.3006 75.2345 134.3006 76.8454 c F 134.3006 76.8454 m 134.3006 78.4563 132.9506 79.7623 131.2852 79.7623 c 129.62 79.7623 128.27 78.4563 128.27 76.8454 c F 131.2852 76.8454 m F 0 G 0.3 w 10 M 131.2852 76.8454 m S 0 g 1 w 4 M 131.2852 76.8454 m F 0 G 0.3 w 10 M 131.2852 76.8454 m S 0 g 1 w 4 M 131.2852 76.8454 m F 130.7409 77.3795 m 128.9421 77.3851 L 128.9421 76.3059 L 130.7409 76.3115 L F 131.8296 76.3115 m 133.6284 76.3059 L 133.6284 77.3851 L 131.8296 77.3795 L F 128.9421 77.3851 m 133.6284 77.3851 l 133.6284 76.3059 l 128.9421 76.3059 l 128.9421 77.3851 l f 0 G 0.3 w 10 M 131.2852 65.731 m S 131.2852 54.6166 m S 0 g 1 w 4 M 131.2852 65.731 m F 0 G 0.3 w 10 M 131.2852 65.731 m S 0 g 1 w 4 M 131.2852 65.731 m F 0 G 0.3 w 10 M 131.2852 65.731 m S 0 g 1 w 4 M 131.2852 65.731 m F 1 g 128.27 65.731 m 128.27 64.1201 129.62 62.8142 131.2852 62.8142 c 132.9506 62.8142 134.3006 64.1201 134.3006 65.731 c F 134.3006 65.731 m 134.3006 67.3419 132.9506 68.6478 131.2852 68.6478 c 129.62 68.6478 128.27 67.3419 128.27 65.731 c F 131.2852 65.731 m F 0 G 0.3 w 10 M 131.2852 65.731 m S 0 g 1 w 4 M 131.2852 65.731 m F 0 G 0.3 w 10 M 131.2852 65.731 m S 0 g 1 w 4 M 131.2852 65.731 m F 130.7409 66.2651 m 128.9421 66.2706 L 128.9421 65.1914 L 130.7409 65.197 L F 131.8296 65.197 m 133.6284 65.1914 L 133.6284 66.2706 L 131.8296 66.2651 L F 128.9421 66.2706 m 133.6284 66.2706 l 133.6284 65.1914 l 128.9421 65.1914 l 128.9421 66.2706 l f 0 G 0.3 w 10 M 131.2852 54.6166 m S 0 g 1 w 4 M 131.2852 54.6166 m F 0 G 0.3 w 10 M 131.2852 54.6166 m S 0 g 1 w 4 M 131.2852 54.6166 m F 1 g 128.27 54.6166 m 128.27 53.0057 129.62 51.6997 131.2852 51.6997 c 132.9506 51.6997 134.3006 53.0057 134.3006 54.6166 c F 134.3006 54.6166 m 134.3006 56.2275 132.9506 57.5334 131.2852 57.5334 c 129.62 57.5334 128.27 56.2275 128.27 54.6166 c F 131.2852 54.6166 m F 0 G 0.3 w 10 M 131.2852 54.6166 m S 0 g 1 w 4 M 131.2852 54.6166 m F 0 G 0.3 w 10 M 131.2852 54.6166 m S 0 g 1 w 4 M 131.2852 54.6166 m F 130.7409 55.1507 m 128.9421 55.1563 L 128.9421 54.077 L 130.7409 54.0826 L F 131.8296 54.0826 m 133.6284 54.077 L 133.6284 55.1563 L 131.8296 55.1507 L F 128.9421 55.1563 m 133.6284 55.1563 l 133.6284 54.077 l 128.9421 54.077 l 128.9421 55.1563 l f 0 G 0.3 w 10 M 165.6156 65.731 m S 165.6156 54.6166 m S 0 g 1 w 4 M 165.6156 65.731 m F 0 G 0.3 w 10 M 165.6156 65.731 m S 0 g 1 w 4 M 165.6156 65.731 m F 0 G 0.3 w 10 M 165.6156 65.731 m S 0 g 1 w 4 M 165.6156 65.731 m F 1 g 162.6003 65.731 m 162.6003 64.1201 163.9503 62.8142 165.6156 62.8142 c 167.2809 62.8142 168.6309 64.1201 168.6309 65.731 c F 168.6309 65.731 m 168.6309 67.3419 167.2809 68.6478 165.6156 68.6478 c 163.9503 68.6478 162.6003 67.3419 162.6003 65.731 c F 165.6156 65.731 m F 0 G 0.3 w 10 M 165.6156 65.731 m S 0 g 1 w 4 M 165.6156 65.731 m F 0 G 0.3 w 10 M 165.6156 65.731 m S 0 g 1 w 4 M 165.6156 65.731 m F 165.0712 66.2651 m 163.2723 66.2706 L 163.2723 65.1914 L 165.0712 65.197 L F 166.16 65.197 m 167.9588 65.1914 L 167.9588 66.2706 L 166.16 66.2651 L F 163.2723 66.2706 m 167.9588 66.2706 l 167.9588 65.1914 l 163.2723 65.1914 l 163.2723 66.2706 l f 0 G 0.3 w 10 M 165.6156 54.6166 m S 0 g 1 w 4 M 165.6156 54.6166 m F 0 G 0.3 w 10 M 165.6156 54.6166 m S 0 g 1 w 4 M 165.6156 54.6166 m F 1 g 162.6003 54.6166 m 162.6003 53.0057 163.9503 51.6997 165.6156 51.6997 c 167.2809 51.6997 168.6309 53.0057 168.6309 54.6166 c F 168.6309 54.6166 m 168.6309 56.2275 167.2809 57.5334 165.6156 57.5334 c 163.9503 57.5334 162.6003 56.2275 162.6003 54.6166 c F 165.6156 54.6166 m F 0 G 0.3 w 10 M 165.6156 54.6166 m S 0 g 1 w 4 M 165.6156 54.6166 m F 0 G 0.3 w 10 M 165.6156 54.6166 m S 0 g 1 w 4 M 165.6156 54.6166 m F 165.0712 55.1507 m 163.2723 55.1563 L 163.2723 54.077 L 165.0712 54.0826 L F 166.16 54.0826 m 167.9588 54.077 L 167.9588 55.1563 L 166.16 55.1507 L F 163.2723 55.1563 m 167.9588 55.1563 l 167.9588 54.077 l 163.2723 54.077 l 163.2723 55.1563 l f u 0 G 0.3 w 10 M 205.6676 82.4026 m S 205.6676 71.2882 m S 194.2242 71.2882 m S 194.2242 82.4026 m S 199.9459 76.8454 m S U u 194.2242 93.517 m S 194.2242 82.4026 m S 182.7807 82.4026 m S 182.7807 93.517 m S 188.5025 87.9598 m S U u 205.6676 93.517 m S 205.6676 82.4026 m S 194.2242 82.4026 m S 194.2242 93.517 m S 199.9459 87.9598 m S U u 194.2242 82.4026 m S 194.2242 71.2882 m S 182.7807 71.2882 m S 182.7807 82.4026 m S 188.5025 76.8454 m S U u 182.7807 82.4026 m S 182.7807 71.2882 m S 171.3373 71.2882 m S 171.3373 82.4026 m S 177.059 76.8454 m S U u 182.7807 93.517 m S 182.7807 82.4026 m S 171.3373 82.4026 m S 171.3373 93.517 m S 177.059 87.9598 m S U 0 g 1 w 4 M 177.059 76.8454 m F 199.9459 76.8454 m F 0 G 0.3 w 10 M 239.9979 82.4026 m S 239.9979 71.2882 m S 228.5545 71.2882 m S 228.5545 82.4026 m S 234.2762 76.8454 m S 228.5545 93.517 m S 228.5545 82.4026 m S 217.1111 82.4026 m S 217.1111 93.517 m S 222.8328 87.9598 m S 239.9979 93.517 m S 239.9979 82.4026 m S 228.5545 82.4026 m S 228.5545 93.517 m S 234.2762 87.9598 m S 228.5545 82.4026 m S 228.5545 71.2882 m S 217.1111 71.2882 m S 217.1111 82.4026 m S 222.8328 76.8454 m S 217.1111 82.4026 m S 217.1111 71.2882 m S 205.6676 71.2882 m S 205.6676 82.4026 m S 211.3893 76.8454 m S 217.1111 93.517 m S 217.1111 82.4026 m S 205.6676 82.4026 m S 205.6676 93.517 m S 211.3893 87.9598 m S 0 g 1 w 4 M 211.3893 76.8454 m F 234.2762 76.8454 m F 0 G 0.3 w 10 M 274.3282 82.4026 m S 274.3282 71.2882 m S 262.8849 71.2882 m S 262.8849 82.4026 m S 268.6065 76.8454 m S 262.8849 93.517 m S 262.8849 82.4026 m S 251.4414 82.4026 m S 251.4414 93.517 m S 257.1631 87.9598 m S 274.3282 93.517 m S 274.3282 82.4026 m S 262.8849 82.4026 m S 262.8849 93.517 m S 268.6065 87.9598 m S 262.8849 82.4026 m S 262.8849 71.2882 m S 251.4414 71.2882 m S 251.4414 82.4026 m S 257.1631 76.8454 m S 251.4414 82.4026 m S 251.4414 71.2882 m S 239.9979 71.2882 m S 239.9979 82.4026 m S 245.7196 76.8454 m S 251.4414 93.517 m S 251.4414 82.4026 m S 239.9979 82.4026 m S 239.9979 93.517 m S 245.7196 87.9598 m S 0 g 1 w 4 M 245.7196 76.8454 m F 268.6065 76.8454 m F 0 G 0.3 w 10 M 308.6585 82.4026 m S 308.6585 71.2882 m S 297.2152 71.2882 m S 297.2152 82.4026 m S 302.9369 76.8454 m S 297.2152 93.517 m S 297.2152 82.4026 m S 285.7717 82.4026 m S 285.7717 93.517 m S 291.4934 87.9598 m S 308.6585 93.517 m S 308.6585 82.4026 m S 297.2152 82.4026 m S 297.2152 93.517 m S 302.9369 87.9598 m S 297.2152 82.4026 m S 297.2152 71.2882 m S 285.7717 71.2882 m S 285.7717 82.4026 m S 291.4934 76.8454 m S 285.7717 82.4026 m S 285.7717 71.2882 m S 274.3282 71.2882 m S 274.3282 82.4026 m S 280.0499 76.8454 m S 285.7717 93.517 m S 285.7717 82.4026 m S 274.3282 82.4026 m S 274.3282 93.517 m S 280.0499 87.9598 m S 0 g 1 w 4 M 280.0499 76.8454 m F 302.9369 76.8454 m F u 0 G 0.3 w 10 M 182.7807 71.2882 m S 182.7807 60.1738 m S 171.3373 60.1738 m S 171.3373 71.2882 m S 177.059 65.731 m S U 205.6676 49.0594 m S 194.2242 49.0594 m S u 194.2242 60.1738 m S 194.2242 49.0594 m S 182.7807 49.0594 m S 182.7807 60.1738 m S 188.5025 54.6166 m S U u 194.2242 71.2882 m S 194.2242 60.1738 m S 182.7807 60.1738 m S 182.7807 71.2882 m S 188.5025 65.731 m S U u 205.6676 71.2882 m S 205.6676 60.1738 m S 194.2242 60.1738 m S 194.2242 71.2882 m S 199.9459 65.731 m S U u 205.6676 60.1738 m S 205.6676 49.0594 m S 194.2242 49.0594 m S 194.2242 60.1738 m S 199.9459 54.6166 m S U 194.2242 49.0594 m S 182.7807 49.0594 m S 182.7807 49.0594 m S 171.3373 49.0594 m S u 182.7807 60.1738 m S 182.7807 49.0594 m S 171.3373 49.0594 m S 171.3373 60.1738 m S 177.059 54.6166 m S U 0 g 1 w 4 M 177.059 65.731 m F 199.9459 65.731 m F 0 G 0.3 w 10 M 217.1111 71.2882 m S 217.1111 60.1738 m S 205.6676 60.1738 m S 205.6676 71.2882 m S 211.3893 65.731 m S 239.9979 49.0594 m S 228.5545 49.0594 m S 228.5545 60.1738 m S 228.5545 49.0594 m S 217.1111 49.0594 m S 217.1111 60.1738 m S 222.8328 54.6166 m S 228.5545 71.2882 m S 228.5545 60.1738 m S 217.1111 60.1738 m S 217.1111 71.2882 m S 222.8328 65.731 m S 239.9979 71.2882 m S 239.9979 60.1738 m S 228.5545 60.1738 m S 228.5545 71.2882 m S 234.2762 65.731 m S 239.9979 60.1738 m S 239.9979 49.0594 m S 228.5545 49.0594 m S 228.5545 60.1738 m S 234.2762 54.6166 m S 228.5545 49.0594 m S 217.1111 49.0594 m S 217.1111 49.0594 m S 205.6676 49.0594 m S 217.1111 60.1738 m S 217.1111 49.0594 m S 205.6676 49.0594 m S 205.6676 60.1738 m S 211.3893 54.6166 m S 0 g 1 w 4 M 211.3893 65.731 m F 234.2762 65.731 m F 0 G 0.3 w 10 M 251.4414 71.2882 m S 251.4414 60.1738 m S 239.9979 60.1738 m S 239.9979 71.2882 m S 245.7196 65.731 m S 274.3282 49.0594 m S 262.8849 49.0594 m S 262.8849 60.1738 m S 262.8849 49.0594 m S 251.4414 49.0594 m S 251.4414 60.1738 m S 257.1631 54.6166 m S 262.8849 71.2882 m S 262.8849 60.1738 m S 251.4414 60.1738 m S 251.4414 71.2882 m S 257.1631 65.731 m S 274.3282 71.2882 m S 274.3282 60.1738 m S 262.8849 60.1738 m S 262.8849 71.2882 m S 268.6065 65.731 m S 274.3282 60.1738 m S 274.3282 49.0594 m S 262.8849 49.0594 m S 262.8849 60.1738 m S 268.6065 54.6166 m S 262.8849 49.0594 m S 251.4414 49.0594 m S 251.4414 49.0594 m S 239.9979 49.0594 m S 251.4414 60.1738 m S 251.4414 49.0594 m S 239.9979 49.0594 m S 239.9979 60.1738 m S 245.7196 54.6166 m S 0 g 1 w 4 M 245.7196 65.731 m F 268.6065 65.731 m F 0 G 0.3 w 10 M 285.7717 71.2882 m S 285.7717 60.1738 m S 274.3282 60.1738 m S 274.3282 71.2882 m S 280.0499 65.731 m S 308.6585 49.0594 m S 297.2152 49.0594 m S 297.2152 60.1738 m S 297.2152 49.0594 m S 285.7717 49.0594 m S 285.7717 60.1738 m S 291.4934 54.6166 m S 297.2152 71.2882 m S 297.2152 60.1738 m S 285.7717 60.1738 m S 285.7717 71.2882 m S 291.4934 65.731 m S 308.6585 71.2882 m S 308.6585 60.1738 m S 297.2152 60.1738 m S 297.2152 71.2882 m S 302.9369 65.731 m S 308.6585 60.1738 m S 308.6585 49.0594 m S 297.2152 49.0594 m S 297.2152 60.1738 m S 302.9369 54.6166 m S 297.2152 49.0594 m S 285.7717 49.0594 m S 285.7717 49.0594 m S 274.3282 49.0594 m S 285.7717 60.1738 m S 285.7717 49.0594 m S 274.3282 49.0594 m S 274.3282 60.1738 m S 280.0499 54.6166 m S 0 g 1 w 4 M 280.0499 65.731 m F 302.9369 65.731 m F 0 G 217.1111 93.517 m 217.1111 49.0594 l 262.8849 49.0594 l 262.8849 93.517 l 217.1111 93.517 l s 239.9979 93.517 m 239.9979 49.0594 l S 217.1111 71.2882 m 262.8849 71.2882 l S 0.3 w 10 M 331.5455 82.4026 m S 331.5455 71.2882 m S 320.102 71.2882 m S 320.102 82.4026 m S 325.8237 76.8454 m S 320.102 93.517 m S 320.102 82.4026 m S 308.6585 82.4026 m S 308.6585 93.517 m S 314.3803 87.9598 m S 331.5455 93.517 m S 331.5455 82.4026 m S 320.102 82.4026 m S 320.102 93.517 m S 325.8237 87.9598 m S 320.102 82.4026 m S 320.102 71.2882 m S 308.6585 71.2882 m S 308.6585 82.4026 m S 314.3803 76.8454 m S 308.6585 82.4026 m S 308.6585 71.2882 m S 308.6585 93.517 m S 308.6585 82.4026 m S 0 g 1 w 4 M 325.8237 76.8454 m F 0 G 0.3 w 10 M 354.4324 71.2882 m S 354.4324 82.4026 m S 354.4324 93.517 m S 354.4324 82.4026 m S 342.9889 82.4026 m S 342.9889 93.517 m S 348.7106 87.9598 m S 354.4324 82.4026 m S 354.4324 93.517 m S 354.4324 82.4026 m S 354.4324 71.2882 m S 342.9889 71.2882 m S 342.9889 82.4026 m S 348.7106 76.8454 m S 342.9889 82.4026 m S 342.9889 71.2882 m S 331.5455 71.2882 m S 331.5455 82.4026 m S 337.2672 76.8454 m S 342.9889 93.517 m S 342.9889 82.4026 m S 331.5455 82.4026 m S 331.5455 93.517 m S 337.2672 87.9598 m S 0 g 1 w 4 M 337.2672 76.8454 m F 0 G 0.3 w 10 M 308.6585 71.2882 m S 308.6585 60.1738 m S 331.5455 49.0594 m S 320.102 49.0594 m S 320.102 60.1738 m S 320.102 49.0594 m S 308.6585 49.0594 m S 308.6585 60.1738 m S 314.3803 54.6166 m S 320.102 71.2882 m S 320.102 60.1738 m S 308.6585 60.1738 m S 308.6585 71.2882 m S 314.3803 65.731 m S 331.5455 71.2882 m S 331.5455 60.1738 m S 320.102 60.1738 m S 320.102 71.2882 m S 325.8237 65.731 m S 331.5455 60.1738 m S 331.5455 49.0594 m S 320.102 49.0594 m S 320.102 60.1738 m S 325.8237 54.6166 m S 320.102 49.0594 m S 308.6585 49.0594 m S 308.6585 49.0594 m S 308.6585 60.1738 m S 308.6585 49.0594 m S 0 g 1 w 4 M 325.8237 65.731 m F 0 G 0.3 w 10 M 342.9889 71.2882 m S 342.9889 60.1738 m S 331.5455 60.1738 m S 331.5455 71.2882 m S 337.2672 65.731 m S 354.4324 49.0594 m S 354.4324 60.1738 m S 354.4324 49.0594 m S 342.9889 49.0594 m S 342.9889 60.1738 m S 348.7106 54.6166 m S 354.4324 71.2882 m S 354.4324 60.1738 m S 342.9889 60.1738 m S 342.9889 71.2882 m S 348.7106 65.731 m S 354.4324 60.1738 m S 354.4324 71.2882 m S 354.4324 49.0594 m S 354.4324 60.1738 m S 354.4324 49.0594 m S 342.9889 49.0594 m S 342.9889 49.0594 m S 331.5455 49.0594 m S 342.9889 60.1738 m S 342.9889 49.0594 m S 331.5455 49.0594 m S 331.5455 60.1738 m S 337.2672 54.6166 m S 0 g 1 w 4 M 337.2672 65.731 m F 0 G 308.6585 93.517 m 308.6585 49.0594 l 354.4324 49.0594 l 354.4324 93.517 l 308.6585 93.517 l s 331.5455 93.517 m 331.5455 49.0594 l S 308.6585 71.2882 m 354.4324 71.2882 l S 0.3 w 10 M 228.5545 49.0594 m S 251.4415 49.0594 m S 239.9979 49.0594 m S 251.4415 49.0594 m S 239.9979 49.0594 m S 228.5545 49.0594 m S 320.1021 49.0594 m S 342.9889 49.0594 m S 331.5455 49.0594 m S 342.9889 49.0594 m S 331.5455 49.0594 m S 320.1021 49.0594 m S 137.007 49.0594 m S 159.8939 49.0594 m S 148.4504 49.0594 m S 159.8939 49.0594 m S 148.4504 49.0594 m S 137.007 49.0594 m S 222.8328 87.9598 m S 222.8328 87.9598 m S 0 g 1 w 4 M 222.8328 87.9598 m F 0 G 0.3 w 10 M 222.8328 87.9598 m S 0 g 1 w 4 M 222.8328 87.9598 m F 0 G 0.3 w 10 M 222.8328 87.9598 m S 222.8328 87.9598 m S 222.8328 87.9598 m S 0 g 1 w 4 M 222.8328 87.9598 m F 0 G 0.3 w 10 M 222.8328 87.9598 m S 222.8328 87.9598 m S 1 g 1 w 4 M 219.8174 87.9598 m 219.8174 86.3488 221.1675 85.0429 222.8328 85.0429 c 224.498 85.0429 225.8481 86.3488 225.8481 87.9598 c F 225.8481 87.9598 m 225.8481 89.5707 224.498 90.8766 222.8328 90.8766 c 221.1675 90.8766 219.8174 89.5707 219.8174 87.9598 c F 222.8328 87.9598 m F 0 G 0.3 w 10 M 222.8328 87.9598 m S 0 g 1 w 4 M 222.8328 87.9598 m F 0 G 0.3 w 10 M 222.8328 87.9598 m S 222.8328 87.9598 m S 0 g 1 w 4 M 222.2884 87.4259 m 222.2884 85.6372 L 223.3771 85.6372 L 223.3771 87.4259 L 225.176 87.4202 L 225.176 88.4995 L 223.3771 88.4939 L 223.3771 90.2825 L 222.2884 90.2825 L 222.2884 88.4939 L 220.4896 88.4995 L 220.4896 87.4202 L 222.2884 87.4259 L f 0 G 0.3 w 10 M 234.2762 87.9598 m S 234.2762 87.9598 m S 0 g 1 w 4 M 234.2762 87.9598 m F 0 G 0.3 w 10 M 234.2762 87.9598 m S 0 g 1 w 4 M 234.2762 87.9598 m F 0 G 0.3 w 10 M 234.2762 87.9598 m S 234.2762 87.9598 m S 234.2762 87.9598 m S 0 g 1 w 4 M 234.2762 87.9598 m F 0 G 0.3 w 10 M 234.2762 87.9598 m S 234.2762 87.9598 m S 1 g 1 w 4 M 231.2609 87.9598 m 231.2609 86.3488 232.6109 85.0429 234.2762 85.0429 c 235.9415 85.0429 237.2915 86.3488 237.2915 87.9598 c F 237.2915 87.9598 m 237.2915 89.5707 235.9415 90.8766 234.2762 90.8766 c 232.6109 90.8766 231.2609 89.5707 231.2609 87.9598 c F 234.2762 87.9598 m F 0 G 0.3 w 10 M 234.2762 87.9598 m S 0 g 1 w 4 M 234.2762 87.9598 m F 0 G 0.3 w 10 M 234.2762 87.9598 m S 234.2762 87.9598 m S 0 g 1 w 4 M 233.7318 87.4259 m 233.7318 85.6372 L 234.8206 85.6372 L 234.8206 87.4259 L 236.6194 87.4202 L 236.6194 88.4995 L 234.8206 88.4939 L 234.8206 90.2825 L 233.7318 90.2825 L 233.7318 88.4939 L 231.933 88.4995 L 231.933 87.4202 L 233.7318 87.4259 L f 0 G 0.3 w 10 M 245.7196 87.9598 m S 257.1631 87.9598 m S 245.7196 87.9598 m S 245.7196 87.9598 m S 0 g 1 w 4 M 245.7196 87.9598 m F 0 G 0.3 w 10 M 245.7196 87.9598 m S 0 g 1 w 4 M 245.7196 87.9598 m F 0 G 0.3 w 10 M 245.7196 87.9598 m S 245.7196 87.9598 m S 245.7196 87.9598 m S 0 g 1 w 4 M 245.7196 87.9598 m F 0 G 0.3 w 10 M 245.7196 87.9598 m S 245.7196 87.9598 m S 1 g 1 w 4 M 242.7043 87.9598 m 242.7043 86.3488 244.0544 85.0429 245.7196 85.0429 c 247.3849 85.0429 248.735 86.3488 248.735 87.9598 c F 248.735 87.9598 m 248.735 89.5707 247.3849 90.8766 245.7196 90.8766 c 244.0544 90.8766 242.7043 89.5707 242.7043 87.9598 c F 245.7196 87.9598 m F 0 G 0.3 w 10 M 245.7196 87.9598 m S 0 g 1 w 4 M 245.7196 87.9598 m F 0 G 0.3 w 10 M 245.7196 87.9598 m S 245.7196 87.9598 m S 0 g 1 w 4 M 245.1753 87.4259 m 245.1753 85.6372 L 246.264 85.6372 L 246.264 87.4259 L 248.0628 87.4202 L 248.0628 88.4995 L 246.264 88.4939 L 246.264 90.2825 L 245.1753 90.2825 L 245.1753 88.4939 L 243.3764 88.4995 L 243.3764 87.4202 L 245.1753 87.4259 L f 0 G 0.3 w 10 M 257.1631 87.9598 m S 257.1631 87.9598 m S 0 g 1 w 4 M 257.1631 87.9598 m F 0 G 0.3 w 10 M 257.1631 87.9598 m S 0 g 1 w 4 M 257.1631 87.9598 m F 0 G 0.3 w 10 M 257.1631 87.9598 m S 257.1631 87.9598 m S 257.1631 87.9598 m S 0 g 1 w 4 M 257.1631 87.9598 m F 0 G 0.3 w 10 M 257.1631 87.9598 m S 257.1631 87.9598 m S 1 g 1 w 4 M 254.1477 87.9598 m 254.1477 86.3488 255.4978 85.0429 257.1631 85.0429 c 258.8283 85.0429 260.1783 86.3488 260.1783 87.9598 c F 260.1783 87.9598 m 260.1783 89.5707 258.8283 90.8766 257.1631 90.8766 c 255.4978 90.8766 254.1477 89.5707 254.1477 87.9598 c F 257.1631 87.9598 m F 0 G 0.3 w 10 M 257.1631 87.9598 m S 0 g 1 w 4 M 257.1631 87.9598 m F 0 G 0.3 w 10 M 257.1631 87.9598 m S 257.1631 87.9598 m S 0 g 1 w 4 M 256.6186 87.4259 m 256.6186 85.6372 L 257.7075 85.6372 L 257.7075 87.4259 L 259.5063 87.4202 L 259.5063 88.4995 L 257.7075 88.4939 L 257.7075 90.2825 L 256.6186 90.2825 L 256.6186 88.4939 L 254.8198 88.4995 L 254.8198 87.4202 L 256.6186 87.4259 L f 0 G 0.3 w 10 M 245.7196 54.6166 m S 257.1631 54.6166 m S 245.7196 54.6166 m S 245.7196 54.6166 m S 0 g 1 w 4 M 245.7196 54.6166 m F 0 G 0.3 w 10 M 245.7196 54.6166 m S 0 g 1 w 4 M 245.7196 54.6166 m F 0 G 0.3 w 10 M 245.7196 54.6166 m S 245.7196 54.6166 m S 245.7196 54.6166 m S 0 g 1 w 4 M 245.7196 54.6166 m F 0 G 0.3 w 10 M 245.7196 54.6166 m S 245.7196 54.6166 m S 1 g 1 w 4 M 242.7043 54.6166 m 242.7043 53.0057 244.0544 51.6997 245.7196 51.6997 c 247.3849 51.6997 248.735 53.0057 248.735 54.6166 c F 248.735 54.6166 m 248.735 56.2275 247.3849 57.5334 245.7196 57.5334 c 244.0544 57.5334 242.7043 56.2275 242.7043 54.6166 c F 245.7196 54.6166 m F 0 G 0.3 w 10 M 245.7196 54.6166 m S 0 g 1 w 4 M 245.7196 54.6166 m F 0 G 0.3 w 10 M 245.7196 54.6166 m S 245.7196 54.6166 m S 0 g 1 w 4 M 245.1753 54.0827 m 245.1753 52.294 L 246.264 52.294 L 246.264 54.0827 L 248.0628 54.077 L 248.0628 55.1563 L 246.264 55.1507 L 246.264 56.9393 L 245.1753 56.9393 L 245.1753 55.1507 L 243.3764 55.1563 L 243.3764 54.077 L 245.1753 54.0827 L f 0 G 0.3 w 10 M 257.1631 54.6166 m S 257.1631 54.6166 m S 0 g 1 w 4 M 257.1631 54.6166 m F 0 G 0.3 w 10 M 257.1631 54.6166 m S 0 g 1 w 4 M 257.1631 54.6166 m F 0 G 0.3 w 10 M 257.1631 54.6166 m S 257.1631 54.6166 m S 257.1631 54.6166 m S 0 g 1 w 4 M 257.1631 54.6166 m F 0 G 0.3 w 10 M 257.1631 54.6166 m S 257.1631 54.6166 m S 1 g 1 w 4 M 254.1477 54.6166 m 254.1477 53.0057 255.4978 51.6997 257.1631 51.6997 c 258.8283 51.6997 260.1783 53.0057 260.1783 54.6166 c F 260.1783 54.6166 m 260.1783 56.2275 258.8283 57.5334 257.1631 57.5334 c 255.4978 57.5334 254.1477 56.2275 254.1477 54.6166 c F 257.1631 54.6166 m F 0 G 0.3 w 10 M 257.1631 54.6166 m S 0 g 1 w 4 M 257.1631 54.6166 m F 0 G 0.3 w 10 M 257.1631 54.6166 m S 257.1631 54.6166 m S 0 g 1 w 4 M 256.6186 54.0827 m 256.6186 52.294 L 257.7075 52.294 L 257.7075 54.0827 L 259.5063 54.077 L 259.5063 55.1563 L 257.7075 55.1507 L 257.7075 56.9393 L 256.6186 56.9393 L 256.6186 55.1507 L 254.8198 55.1563 L 254.8198 54.077 L 256.6186 54.0827 L f 0 G 0.3 w 10 M 222.8328 54.6166 m S 234.2762 54.6166 m S 222.8328 54.6166 m S 222.8328 54.6166 m S 0 g 1 w 4 M 222.8328 54.6166 m F 0 G 0.3 w 10 M 222.8328 54.6166 m S 0 g 1 w 4 M 222.8328 54.6166 m F 0 G 0.3 w 10 M 222.8328 54.6166 m S 222.8328 54.6166 m S 222.8328 54.6166 m S 0 g 1 w 4 M 222.8328 54.6166 m F 0 G 0.3 w 10 M 222.8328 54.6166 m S 222.8328 54.6166 m S 1 g 1 w 4 M 219.8174 54.6166 m 219.8174 53.0057 221.1675 51.6997 222.8328 51.6997 c 224.498 51.6997 225.8481 53.0057 225.8481 54.6166 c F 225.8481 54.6166 m 225.8481 56.2275 224.498 57.5334 222.8328 57.5334 c 221.1675 57.5334 219.8174 56.2275 219.8174 54.6166 c F 222.8328 54.6166 m F 0 G 0.3 w 10 M 222.8328 54.6166 m S 0 g 1 w 4 M 222.8328 54.6166 m F 0 G 0.3 w 10 M 222.8328 54.6166 m S 222.8328 54.6166 m S 0 g 1 w 4 M 222.2884 54.0827 m 222.2884 52.294 L 223.3771 52.294 L 223.3771 54.0827 L 225.176 54.077 L 225.176 55.1563 L 223.3771 55.1507 L 223.3771 56.9393 L 222.2884 56.9393 L 222.2884 55.1507 L 220.4896 55.1563 L 220.4896 54.077 L 222.2884 54.0827 L f 0 G 0.3 w 10 M 234.2762 54.6166 m S 234.2762 54.6166 m S 0 g 1 w 4 M 234.2762 54.6166 m F 0 G 0.3 w 10 M 234.2762 54.6166 m S 0 g 1 w 4 M 234.2762 54.6166 m F 0 G 0.3 w 10 M 234.2762 54.6166 m S 234.2762 54.6166 m S 234.2762 54.6166 m S 0 g 1 w 4 M 234.2762 54.6166 m F 0 G 0.3 w 10 M 234.2762 54.6166 m S 234.2762 54.6166 m S 1 g 1 w 4 M 231.2609 54.6166 m 231.2609 53.0057 232.6109 51.6997 234.2762 51.6997 c 235.9415 51.6997 237.2915 53.0057 237.2915 54.6166 c F 237.2915 54.6166 m 237.2915 56.2275 235.9415 57.5334 234.2762 57.5334 c 232.6109 57.5334 231.2609 56.2275 231.2609 54.6166 c F 234.2762 54.6166 m F 0 G 0.3 w 10 M 234.2762 54.6166 m S 0 g 1 w 4 M 234.2762 54.6166 m F 0 G 0.3 w 10 M 234.2762 54.6166 m S 234.2762 54.6166 m S 0 g 1 w 4 M 233.7318 54.0827 m 233.7318 52.294 L 234.8206 52.294 L 234.8206 54.0827 L 236.6194 54.077 L 236.6194 55.1563 L 234.8206 55.1507 L 234.8206 56.9393 L 233.7318 56.9393 L 233.7318 55.1507 L 231.933 55.1563 L 231.933 54.077 L 233.7318 54.0827 L f 0 G 0.3 w 10 M 314.3803 76.8454 m S 325.8237 76.8454 m S 314.3803 76.8454 m S 314.3803 76.8454 m S 0 g 1 w 4 M 314.3803 76.8454 m F 0 G 0.3 w 10 M 314.3803 76.8454 m S 0 g 1 w 4 M 314.3803 76.8454 m F 0 G 0.3 w 10 M 314.3803 76.8454 m S 314.3803 76.8454 m S 314.3803 76.8454 m S 0 g 1 w 4 M 314.3803 76.8454 m F 0 G 0.3 w 10 M 314.3803 76.8454 m S 314.3803 76.8454 m S 1 g 1 w 4 M 311.365 76.8454 m 311.365 75.2345 312.715 73.9286 314.3803 73.9286 c 316.0456 73.9286 317.3957 75.2345 317.3957 76.8454 c F 317.3957 76.8454 m 317.3957 78.4563 316.0456 79.7623 314.3803 79.7623 c 312.715 79.7623 311.365 78.4563 311.365 76.8454 c F 314.3803 76.8454 m F 0 G 0.3 w 10 M 314.3803 76.8454 m S 0 g 1 w 4 M 314.3803 76.8454 m F 0 G 0.3 w 10 M 314.3803 76.8454 m S 314.3803 76.8454 m S 0 g 1 w 4 M 313.8359 76.3115 m 313.8359 74.5229 L 314.9247 74.5229 L 314.9247 76.3115 L 316.7235 76.3058 L 316.7235 77.3851 L 314.9247 77.3795 L 314.9247 79.168 L 313.8359 79.168 L 313.8359 77.3795 L 312.0371 77.3851 L 312.0371 76.3058 L 313.8359 76.3115 L f 0 G 0.3 w 10 M 325.8237 76.8454 m S 325.8237 76.8454 m S 0 g 1 w 4 M 325.8237 76.8454 m F 0 G 0.3 w 10 M 325.8237 76.8454 m S 0 g 1 w 4 M 325.8237 76.8454 m F 0 G 0.3 w 10 M 325.8237 76.8454 m S 325.8237 76.8454 m S 325.8237 76.8454 m S 0 g 1 w 4 M 325.8237 76.8454 m F 0 G 0.3 w 10 M 325.8237 76.8454 m S 325.8237 76.8454 m S 1 g 1 w 4 M 322.8084 76.8454 m 322.8084 75.2345 324.1585 73.9286 325.8237 73.9286 c 327.489 73.9286 328.839 75.2345 328.839 76.8454 c F 328.839 76.8454 m 328.839 78.4563 327.489 79.7623 325.8237 79.7623 c 324.1585 79.7623 322.8084 78.4563 322.8084 76.8454 c F 325.8237 76.8454 m F 0 G 0.3 w 10 M 325.8237 76.8454 m S 0 g 1 w 4 M 325.8237 76.8454 m F 0 G 0.3 w 10 M 325.8237 76.8454 m S 325.8237 76.8454 m S 0 g 1 w 4 M 325.2793 76.3115 m 325.2793 74.5229 L 326.3681 74.5229 L 326.3681 76.3115 L 328.167 76.3058 L 328.167 77.3851 L 326.3681 77.3795 L 326.3681 79.168 L 325.2793 79.168 L 325.2793 77.3795 L 323.4805 77.3851 L 323.4805 76.3058 L 325.2793 76.3115 L f 0 G 0.3 w 10 M 314.3803 54.6166 m S 325.8237 54.6166 m S 314.3803 54.6166 m S 314.3803 54.6166 m S 0 g 1 w 4 M 314.3803 54.6166 m F 0 G 0.3 w 10 M 314.3803 54.6166 m S 0 g 1 w 4 M 314.3803 54.6166 m F 0 G 0.3 w 10 M 314.3803 54.6166 m S 314.3803 54.6166 m S 314.3803 54.6166 m S 0 g 1 w 4 M 314.3803 54.6166 m F 0 G 0.3 w 10 M 314.3803 54.6166 m S 314.3803 54.6166 m S 1 g 1 w 4 M 314.3803 54.6166 m F 0 G 0.3 w 10 M 314.3803 54.6166 m S 0 g 1 w 4 M 314.3803 54.6166 m F 0 G 0.3 w 10 M 314.3803 54.6166 m S 314.3803 54.6166 m S 325.8237 54.6166 m S 325.8237 54.6166 m S 0 g 1 w 4 M 325.8237 54.6166 m F 0 G 0.3 w 10 M 325.8237 54.6166 m S 0 g 1 w 4 M 325.8237 54.6166 m F 0 G 0.3 w 10 M 325.8237 54.6166 m S 325.8237 54.6166 m S 325.8237 54.6166 m S 0 g 1 w 4 M 325.8237 54.6166 m F 0 G 0.3 w 10 M 325.8237 54.6166 m S 325.8237 54.6166 m S 1 g 1 w 4 M 325.8237 54.6166 m F 0 G 0.3 w 10 M 325.8237 54.6166 m S 0 g 1 w 4 M 325.8237 54.6166 m F 0 G 0.3 w 10 M 325.8237 54.6166 m S 325.8237 54.6166 m S 337.2672 54.6166 m S 348.7106 54.6166 m S 337.2672 54.6166 m S 337.2672 54.6166 m S 0 g 1 w 4 M 337.2672 54.6166 m F 0 G 0.3 w 10 M 337.2672 54.6166 m S 0 g 1 w 4 M 337.2672 54.6166 m F 0 G 0.3 w 10 M 337.2672 54.6166 m S 337.2672 54.6166 m S 337.2672 54.6166 m S 0 g 1 w 4 M 337.2672 54.6166 m F 0 G 0.3 w 10 M 337.2672 54.6166 m S 337.2672 54.6166 m S 1 g 1 w 4 M 337.2672 54.6166 m F 0 G 0.3 w 10 M 337.2672 54.6166 m S 0 g 1 w 4 M 337.2672 54.6166 m F 0 G 0.3 w 10 M 337.2672 54.6166 m S 337.2672 54.6166 m S 348.7106 54.6166 m S 348.7106 54.6166 m S 0 g 1 w 4 M 348.7106 54.6166 m F 0 G 0.3 w 10 M 348.7106 54.6166 m S 0 g 1 w 4 M 348.7106 54.6166 m F 0 G 0.3 w 10 M 348.7106 54.6166 m S 348.7106 54.6166 m S 348.7106 54.6166 m S 0 g 1 w 4 M 348.7106 54.6166 m F 0 G 0.3 w 10 M 348.7106 54.6166 m S 348.7106 54.6166 m S 1 g 1 w 4 M 348.7106 54.6166 m F 0 G 0.3 w 10 M 348.7106 54.6166 m S 0 g 1 w 4 M 348.7106 54.6166 m F 0 G 0.3 w 10 M 348.7106 54.6166 m S 348.7106 54.6166 m S 337.2672 76.8454 m S 348.7106 76.8454 m S 337.2672 76.8454 m S 337.2672 76.8454 m S 0 g 1 w 4 M 337.2672 76.8454 m F 0 G 0.3 w 10 M 337.2672 76.8454 m S 0 g 1 w 4 M 337.2672 76.8454 m F 0 G 0.3 w 10 M 337.2672 76.8454 m S 337.2672 76.8454 m S 337.2672 76.8454 m S 0 g 1 w 4 M 337.2672 76.8454 m F 0 G 0.3 w 10 M 337.2672 76.8454 m S 337.2672 76.8454 m S 1 g 1 w 4 M 334.2518 76.8454 m 334.2518 75.2345 335.6018 73.9286 337.2672 73.9286 c 338.9324 73.9286 340.2824 75.2345 340.2824 76.8454 c F 340.2824 76.8454 m 340.2824 78.4563 338.9324 79.7623 337.2672 79.7623 c 335.6018 79.7623 334.2518 78.4563 334.2518 76.8454 c F 337.2672 76.8454 m F 0 G 0.3 w 10 M 337.2672 76.8454 m S 0 g 1 w 4 M 337.2672 76.8454 m F 0 G 0.3 w 10 M 337.2672 76.8454 m S 337.2672 76.8454 m S 0 g 1 w 4 M 336.7228 76.3115 m 336.7228 74.5229 L 337.8115 74.5229 L 337.8115 76.3115 L 339.6104 76.3058 L 339.6104 77.3851 L 337.8115 77.3795 L 337.8115 79.168 L 336.7228 79.168 L 336.7228 77.3795 L 334.924 77.3851 L 334.924 76.3058 L 336.7228 76.3115 L f 0 G 0.3 w 10 M 348.7106 76.8454 m S 348.7106 76.8454 m S 0 g 1 w 4 M 348.7106 76.8454 m F 0 G 0.3 w 10 M 348.7106 76.8454 m S 0 g 1 w 4 M 348.7106 76.8454 m F 0 G 0.3 w 10 M 348.7106 76.8454 m S 348.7106 76.8454 m S 348.7106 76.8454 m S 0 g 1 w 4 M 348.7106 76.8454 m F 0 G 0.3 w 10 M 348.7106 76.8454 m S 348.7106 76.8454 m S 1 g 1 w 4 M 345.6953 76.8454 m 345.6953 75.2345 347.0453 73.9286 348.7106 73.9286 c 350.3759 73.9286 351.7259 75.2345 351.7259 76.8454 c F 351.7259 76.8454 m 351.7259 78.4563 350.3759 79.7623 348.7106 79.7623 c 347.0453 79.7623 345.6953 78.4563 345.6953 76.8454 c F 348.7106 76.8454 m F 0 G 0.3 w 10 M 348.7106 76.8454 m S 0 g 1 w 4 M 348.7106 76.8454 m F 0 G 0.3 w 10 M 348.7106 76.8454 m S 348.7106 76.8454 m S 0 g 1 w 4 M 348.1662 76.3115 m 348.1662 74.5229 L 349.2549 74.5229 L 349.2549 76.3115 L 351.0538 76.3058 L 351.0538 77.3851 L 349.2549 77.3795 L 349.2549 79.168 L 348.1662 79.168 L 348.1662 77.3795 L 346.3674 77.3851 L 346.3674 76.3058 L 348.1662 76.3115 L f 0 G 0.3 w 10 M 222.8328 76.8454 m S 222.8328 76.8454 m S 222.8328 76.8454 m S 0 g 1 w 4 M 222.8328 76.8454 m F 0 G 0.3 w 10 M 222.8328 76.8454 m S 0 g 1 w 4 M 222.8328 76.8454 m F 1 g 219.8174 76.8454 m 219.8174 75.2345 221.1675 73.9286 222.8328 73.9286 c 224.4981 73.9286 225.8481 75.2345 225.8481 76.8454 c F 225.8481 76.8454 m 225.8481 78.4563 224.4981 79.7622 222.8328 79.7622 c 221.1675 79.7622 219.8174 78.4563 219.8174 76.8454 c F 222.8328 76.8454 m F 0 G 0.3 w 10 M 222.8328 76.8454 m S 0 g 1 w 4 M 222.8328 76.8454 m F 0 G 0.3 w 10 M 222.8328 76.8454 m S 0 g 1 w 4 M 222.8328 76.8454 m F 222.2884 77.3795 m 220.4896 77.3851 L 220.4896 76.3058 L 222.2884 76.3114 L F 223.3771 76.3114 m 225.176 76.3058 L 225.176 77.3851 L 223.3771 77.3795 L F 220.4896 77.3851 m 225.176 77.3851 l 225.176 76.3058 l 220.4896 76.3058 l 220.4896 77.3851 l f 0 G 0.3 w 10 M 234.2762 76.8454 m S 234.2762 76.8454 m S 234.2762 76.8454 m S 0 g 1 w 4 M 234.2762 76.8454 m F 0 G 0.3 w 10 M 234.2762 76.8454 m S 0 g 1 w 4 M 234.2762 76.8454 m F 1 g 231.2609 76.8454 m 231.2609 75.2345 232.6109 73.9286 234.2762 73.9286 c 235.9415 73.9286 237.2915 75.2345 237.2915 76.8454 c F 237.2915 76.8454 m 237.2915 78.4563 235.9415 79.7622 234.2762 79.7622 c 232.6109 79.7622 231.2609 78.4563 231.2609 76.8454 c F 234.2762 76.8454 m F 0 G 0.3 w 10 M 234.2762 76.8454 m S 0 g 1 w 4 M 234.2762 76.8454 m F 0 G 0.3 w 10 M 234.2762 76.8454 m S 0 g 1 w 4 M 234.2762 76.8454 m F 233.7319 77.3795 m 231.933 77.3851 L 231.933 76.3058 L 233.7319 76.3114 L F 234.8206 76.3114 m 236.6194 76.3058 L 236.6194 77.3851 L 234.8206 77.3795 L F 231.933 77.3851 m 236.6194 77.3851 l 236.6194 76.3058 l 231.933 76.3058 l 231.933 77.3851 l f 0 G 0.3 w 10 M 257.1631 76.8454 m S 245.7196 76.8454 m S 0 g 1 w 4 M 257.1631 76.8454 m F 0 G 0.3 w 10 M 245.7196 76.8454 m S 245.7196 76.8454 m S 245.7196 76.8454 m S 0 g 1 w 4 M 245.7196 76.8454 m F 0 G 0.3 w 10 M 245.7196 76.8454 m S 0 g 1 w 4 M 245.7196 76.8454 m F 1 g 242.7043 76.8454 m 242.7043 75.2345 244.0544 73.9286 245.7196 73.9286 c 247.3849 73.9286 248.735 75.2345 248.735 76.8454 c F 248.735 76.8454 m 248.735 78.4563 247.3849 79.7622 245.7196 79.7622 c 244.0544 79.7622 242.7043 78.4563 242.7043 76.8454 c F 245.7196 76.8454 m F 0 G 0.3 w 10 M 245.7196 76.8454 m S 0 g 1 w 4 M 245.7196 76.8454 m F 0 G 0.3 w 10 M 245.7196 76.8454 m S 0 g 1 w 4 M 245.7196 76.8454 m F 245.1753 77.3795 m 243.3764 77.3851 L 243.3764 76.3058 L 245.1753 76.3114 L F 246.264 76.3114 m 248.0628 76.3058 L 248.0628 77.3851 L 246.264 77.3795 L F 243.3764 77.3851 m 248.0628 77.3851 l 248.0628 76.3058 l 243.3764 76.3058 l 243.3764 77.3851 l f 0 G 0.3 w 10 M 257.1631 76.8454 m S 257.1631 76.8454 m S 257.1631 76.8454 m S 0 g 1 w 4 M 257.1631 76.8454 m F 0 G 0.3 w 10 M 257.1631 76.8454 m S 0 g 1 w 4 M 257.1631 76.8454 m F 1 g 254.1477 76.8454 m 254.1477 75.2345 255.4978 73.9286 257.1631 73.9286 c 258.8283 73.9286 260.1783 75.2345 260.1783 76.8454 c F 260.1783 76.8454 m 260.1783 78.4563 258.8283 79.7622 257.1631 79.7622 c 255.4978 79.7622 254.1477 78.4563 254.1477 76.8454 c F 257.1631 76.8454 m F 0 G 0.3 w 10 M 257.1631 76.8454 m S 0 g 1 w 4 M 257.1631 76.8454 m F 0 G 0.3 w 10 M 257.1631 76.8454 m S 0 g 1 w 4 M 257.1631 76.8454 m F 256.6186 77.3795 m 254.8198 77.3851 L 254.8198 76.3058 L 256.6186 76.3114 L F 257.7075 76.3114 m 259.5063 76.3058 L 259.5063 77.3851 L 257.7075 77.3795 L F 254.8198 77.3851 m 259.5063 77.3851 l 259.5063 76.3058 l 254.8198 76.3058 l 254.8198 77.3851 l f 0 G 0.3 w 10 M 257.1631 65.731 m S 245.7196 65.731 m S 0 g 1 w 4 M 257.1631 65.731 m F 0 G 0.3 w 10 M 245.7196 65.731 m S 245.7196 65.731 m S 245.7196 65.731 m S 0 g 1 w 4 M 245.7196 65.731 m F 0 G 0.3 w 10 M 245.7196 65.731 m S 0 g 1 w 4 M 245.7196 65.731 m F 1 g 242.7043 65.731 m 242.7043 64.1201 244.0544 62.8142 245.7196 62.8142 c 247.3849 62.8142 248.735 64.1201 248.735 65.731 c F 248.735 65.731 m 248.735 67.3419 247.3849 68.6479 245.7196 68.6479 c 244.0544 68.6479 242.7043 67.3419 242.7043 65.731 c F 245.7196 65.731 m F 0 G 0.3 w 10 M 245.7196 65.731 m S 0 g 1 w 4 M 245.7196 65.731 m F 0 G 0.3 w 10 M 245.7196 65.731 m S 0 g 1 w 4 M 245.7196 65.731 m F 245.1753 66.2651 m 243.3764 66.2707 L 243.3764 65.1915 L 245.1753 65.197 L F 246.264 65.197 m 248.0628 65.1915 L 248.0628 66.2707 L 246.264 66.2651 L F 243.3764 66.2707 m 248.0628 66.2707 l 248.0628 65.1915 l 243.3764 65.1915 l 243.3764 66.2707 l f 0 G 0.3 w 10 M 257.1631 65.731 m S 257.1631 65.731 m S 257.1631 65.731 m S 0 g 1 w 4 M 257.1631 65.731 m F 0 G 0.3 w 10 M 257.1631 65.731 m S 0 g 1 w 4 M 257.1631 65.731 m F 1 g 254.1477 65.731 m 254.1477 64.1201 255.4978 62.8142 257.1631 62.8142 c 258.8283 62.8142 260.1783 64.1201 260.1783 65.731 c F 260.1783 65.731 m 260.1783 67.3419 258.8283 68.6479 257.1631 68.6479 c 255.4978 68.6479 254.1477 67.3419 254.1477 65.731 c F 257.1631 65.731 m F 0 G 0.3 w 10 M 257.1631 65.731 m S 0 g 1 w 4 M 257.1631 65.731 m F 0 G 0.3 w 10 M 257.1631 65.731 m S 0 g 1 w 4 M 257.1631 65.731 m F 256.6186 66.2651 m 254.8198 66.2707 L 254.8198 65.1915 L 256.6186 65.197 L F 257.7075 65.197 m 259.5063 65.1915 L 259.5063 66.2707 L 257.7075 66.2651 L F 254.8198 66.2707 m 259.5063 66.2707 l 259.5063 65.1915 l 254.8198 65.1915 l 254.8198 66.2707 l f 0 G 0.3 w 10 M 234.2762 65.731 m S 222.8328 65.731 m S 0 g 1 w 4 M 234.2762 65.731 m F 0 G 0.3 w 10 M 222.8328 65.731 m S 222.8328 65.731 m S 222.8328 65.731 m S 0 g 1 w 4 M 222.8328 65.731 m F 0 G 0.3 w 10 M 222.8328 65.731 m S 0 g 1 w 4 M 222.8328 65.731 m F 1 g 219.8174 65.731 m 219.8174 64.1201 221.1675 62.8142 222.8328 62.8142 c 224.4981 62.8142 225.8481 64.1201 225.8481 65.731 c F 225.8481 65.731 m 225.8481 67.3419 224.4981 68.6479 222.8328 68.6479 c 221.1675 68.6479 219.8174 67.3419 219.8174 65.731 c F 222.8328 65.731 m F 0 G 0.3 w 10 M 222.8328 65.731 m S 0 g 1 w 4 M 222.8328 65.731 m F 0 G 0.3 w 10 M 222.8328 65.731 m S 0 g 1 w 4 M 222.8328 65.731 m F 222.2884 66.2651 m 220.4896 66.2707 L 220.4896 65.1915 L 222.2884 65.197 L F 223.3771 65.197 m 225.176 65.1915 L 225.176 66.2707 L 223.3771 66.2651 L F 220.4896 66.2707 m 225.176 66.2707 l 225.176 65.1915 l 220.4896 65.1915 l 220.4896 66.2707 l f 0 G 0.3 w 10 M 234.2762 65.731 m S 234.2762 65.731 m S 234.2762 65.731 m S 0 g 1 w 4 M 234.2762 65.731 m F 0 G 0.3 w 10 M 234.2762 65.731 m S 0 g 1 w 4 M 234.2762 65.731 m F 1 g 231.2609 65.731 m 231.2609 64.1201 232.6109 62.8142 234.2762 62.8142 c 235.9415 62.8142 237.2915 64.1201 237.2915 65.731 c F 237.2915 65.731 m 237.2915 67.3419 235.9415 68.6479 234.2762 68.6479 c 232.6109 68.6479 231.2609 67.3419 231.2609 65.731 c F 234.2762 65.731 m F 0 G 0.3 w 10 M 234.2762 65.731 m S 0 g 1 w 4 M 234.2762 65.731 m F 0 G 0.3 w 10 M 234.2762 65.731 m S 0 g 1 w 4 M 234.2762 65.731 m F 233.7319 66.2651 m 231.933 66.2707 L 231.933 65.1915 L 233.7319 65.197 L F 234.8206 65.197 m 236.6194 65.1915 L 236.6194 66.2707 L 234.8206 66.2651 L F 231.933 66.2707 m 236.6194 66.2707 l 236.6194 65.1915 l 231.933 65.1915 l 231.933 66.2707 l f 0 G 0.3 w 10 M 325.8237 87.9598 m S 314.3803 87.9598 m S 0 g 1 w 4 M 325.8237 87.9598 m F 0 G 0.3 w 10 M 314.3803 87.9598 m S 314.3803 87.9598 m S 314.3803 87.9598 m S 0 g 1 w 4 M 314.3803 87.9598 m F 0 G 0.3 w 10 M 314.3803 87.9598 m S 0 g 1 w 4 M 314.3803 87.9598 m F 1 g 311.365 87.9598 m 311.365 86.3488 312.715 85.0429 314.3803 85.0429 c 316.0456 85.0429 317.3957 86.3488 317.3957 87.9598 c F 317.3957 87.9598 m 317.3957 89.5707 316.0456 90.8766 314.3803 90.8766 c 312.715 90.8766 311.365 89.5707 311.365 87.9598 c F 314.3803 87.9598 m F 0 G 0.3 w 10 M 314.3803 87.9598 m S 0 g 1 w 4 M 314.3803 87.9598 m F 0 G 0.3 w 10 M 314.3803 87.9598 m S 0 g 1 w 4 M 314.3803 87.9598 m F 313.8359 88.4939 m 312.0371 88.4995 L 312.0371 87.4202 L 313.8359 87.4258 L F 314.9247 87.4258 m 316.7235 87.4202 L 316.7235 88.4995 L 314.9247 88.4939 L F 312.0371 88.4995 m 316.7235 88.4995 l 316.7235 87.4202 l 312.0371 87.4202 l 312.0371 88.4995 l f 0 G 0.3 w 10 M 325.8237 87.9598 m S 325.8237 87.9598 m S 325.8237 87.9598 m S 0 g 1 w 4 M 325.8237 87.9598 m F 0 G 0.3 w 10 M 325.8237 87.9598 m S 0 g 1 w 4 M 325.8237 87.9598 m F 1 g 322.8084 87.9598 m 322.8084 86.3488 324.1585 85.0429 325.8237 85.0429 c 327.489 85.0429 328.839 86.3488 328.839 87.9598 c F 328.839 87.9598 m 328.839 89.5707 327.489 90.8766 325.8237 90.8766 c 324.1585 90.8766 322.8084 89.5707 322.8084 87.9598 c F 325.8237 87.9598 m F 0 G 0.3 w 10 M 325.8237 87.9598 m S 0 g 1 w 4 M 325.8237 87.9598 m F 0 G 0.3 w 10 M 325.8237 87.9598 m S 0 g 1 w 4 M 325.8237 87.9598 m F 325.2793 88.4939 m 323.4805 88.4995 L 323.4805 87.4202 L 325.2793 87.4258 L F 326.3681 87.4258 m 328.167 87.4202 L 328.167 88.4995 L 326.3681 88.4939 L F 323.4805 88.4995 m 328.167 88.4995 l 328.167 87.4202 l 323.4805 87.4202 l 323.4805 88.4995 l f 0 G 0.3 w 10 M 348.7106 87.9598 m S 337.2672 87.9598 m S 0 g 1 w 4 M 348.7106 87.9598 m F 0 G 0.3 w 10 M 337.2672 87.9598 m S 337.2672 87.9598 m S 337.2672 87.9598 m S 0 g 1 w 4 M 337.2672 87.9598 m F 0 G 0.3 w 10 M 337.2672 87.9598 m S 0 g 1 w 4 M 337.2672 87.9598 m F 1 g 334.2518 87.9598 m 334.2518 86.3488 335.6018 85.0429 337.2672 85.0429 c 338.9324 85.0429 340.2824 86.3488 340.2824 87.9598 c F 340.2824 87.9598 m 340.2824 89.5707 338.9324 90.8766 337.2672 90.8766 c 335.6018 90.8766 334.2518 89.5707 334.2518 87.9598 c F 337.2672 87.9598 m F 0 G 0.3 w 10 M 337.2672 87.9598 m S 0 g 1 w 4 M 337.2672 87.9598 m F 0 G 0.3 w 10 M 337.2672 87.9598 m S 0 g 1 w 4 M 337.2672 87.9598 m F 336.7228 88.4939 m 334.924 88.4995 L 334.924 87.4202 L 336.7228 87.4258 L F 337.8115 87.4258 m 339.6104 87.4202 L 339.6104 88.4995 L 337.8115 88.4939 L F 334.924 88.4995 m 339.6104 88.4995 l 339.6104 87.4202 l 334.924 87.4202 l 334.924 88.4995 l f 0 G 0.3 w 10 M 348.7106 87.9598 m S 348.7106 87.9598 m S 348.7106 87.9598 m S 0 g 1 w 4 M 348.7106 87.9598 m F 0 G 0.3 w 10 M 348.7106 87.9598 m S 0 g 1 w 4 M 348.7106 87.9598 m F 1 g 345.6953 87.9598 m 345.6953 86.3488 347.0453 85.0429 348.7106 85.0429 c 350.3759 85.0429 351.7259 86.3488 351.7259 87.9598 c F 351.7259 87.9598 m 351.7259 89.5707 350.3759 90.8766 348.7106 90.8766 c 347.0453 90.8766 345.6953 89.5707 345.6953 87.9598 c F 348.7106 87.9598 m F 0 G 0.3 w 10 M 348.7106 87.9598 m S 0 g 1 w 4 M 348.7106 87.9598 m F 0 G 0.3 w 10 M 348.7106 87.9598 m S 0 g 1 w 4 M 348.7106 87.9598 m F 348.1662 88.4939 m 346.3674 88.4995 L 346.3674 87.4202 L 348.1662 87.4258 L F 349.2549 87.4258 m 351.0538 87.4202 L 351.0538 88.4995 L 349.2549 88.4939 L F 346.3674 88.4995 m 351.0538 88.4995 l 351.0538 87.4202 l 346.3674 87.4202 l 346.3674 88.4995 l f 0 G 0.3 w 10 M 348.7106 65.731 m S 337.2672 65.731 m S 337.2672 65.731 m S 348.7106 65.731 m S 337.2672 65.731 m S 337.2672 65.731 m S 0 g 1 w 4 M 337.2672 65.731 m F 0 G 0.3 w 10 M 337.2672 65.731 m S 0 g 1 w 4 M 337.2672 65.731 m F 0 G 0.3 w 10 M 337.2672 65.731 m S 337.2672 65.731 m S 337.2672 65.731 m S 0 g 1 w 4 M 337.2672 65.731 m F 0 G 0.3 w 10 M 337.2672 65.731 m S 337.2672 65.731 m S 1 g 1 w 4 M 334.2518 65.731 m 334.2518 64.1201 335.6018 62.8142 337.2672 62.8142 c 338.9324 62.8142 340.2824 64.1201 340.2824 65.731 c F 340.2824 65.731 m 340.2824 67.342 338.9324 68.6479 337.2672 68.6479 c 335.6018 68.6479 334.2518 67.342 334.2518 65.731 c F 337.2672 65.731 m F 0 G 0.3 w 10 M 337.2672 65.731 m S 0 g 1 w 4 M 337.2672 65.731 m F 0 G 0.3 w 10 M 337.2672 65.731 m S 337.2672 65.731 m S 0 g 1 w 4 M 336.7228 65.197 m 336.7228 63.4085 L 337.8115 63.4085 L 337.8115 65.197 L 339.6104 65.1915 L 339.6104 66.2707 L 337.8115 66.2651 L 337.8115 68.0537 L 336.7228 68.0537 L 336.7228 66.2651 L 334.924 66.2707 L 334.924 65.1915 L 336.7228 65.197 L f 0 G 0.3 w 10 M 348.7106 65.731 m S 348.7106 65.731 m S 0 g 1 w 4 M 348.7106 65.731 m F 0 G 0.3 w 10 M 348.7106 65.731 m S 0 g 1 w 4 M 348.7106 65.731 m F 0 G 0.3 w 10 M 348.7106 65.731 m S 348.7106 65.731 m S 348.7106 65.731 m S 0 g 1 w 4 M 348.7106 65.731 m F 0 G 0.3 w 10 M 348.7106 65.731 m S 348.7106 65.731 m S 1 g 1 w 4 M 345.6953 65.731 m 345.6953 64.1201 347.0453 62.8142 348.7106 62.8142 c 350.3759 62.8142 351.7259 64.1201 351.7259 65.731 c F 351.7259 65.731 m 351.7259 67.342 350.3759 68.6479 348.7106 68.6479 c 347.0453 68.6479 345.6953 67.342 345.6953 65.731 c F 348.7106 65.731 m F 0 G 0.3 w 10 M 348.7106 65.731 m S 0 g 1 w 4 M 348.7106 65.731 m F 0 G 0.3 w 10 M 348.7106 65.731 m S 348.7106 65.731 m S 0 g 1 w 4 M 348.1662 65.197 m 348.1662 63.4085 L 349.2549 63.4085 L 349.2549 65.197 L 351.0538 65.1915 L 351.0538 66.2707 L 349.2549 66.2651 L 349.2549 68.0537 L 348.1662 68.0537 L 348.1662 66.2651 L 346.3674 66.2707 L 346.3674 65.1915 L 348.1662 65.197 L f 0 G 0.3 w 10 M 325.8238 65.731 m S 314.3803 65.731 m S 314.3803 65.731 m S 325.8237 65.731 m S 314.3803 65.731 m S 314.3803 65.731 m S 0 g 1 w 4 M 314.3803 65.731 m F 0 G 0.3 w 10 M 314.3803 65.731 m S 0 g 1 w 4 M 314.3803 65.731 m F 0 G 0.3 w 10 M 314.3803 65.731 m S 314.3803 65.731 m S 314.3803 65.731 m S 0 g 1 w 4 M 314.3803 65.731 m F 0 G 0.3 w 10 M 314.3803 65.731 m S 314.3803 65.731 m S 1 g 1 w 4 M 311.365 65.731 m 311.365 64.1201 312.715 62.8142 314.3803 62.8142 c 316.0456 62.8142 317.3957 64.1201 317.3957 65.731 c F 317.3957 65.731 m 317.3957 67.342 316.0456 68.6479 314.3803 68.6479 c 312.715 68.6479 311.365 67.342 311.365 65.731 c F 314.3803 65.731 m F 0 G 0.3 w 10 M 314.3803 65.731 m S 0 g 1 w 4 M 314.3803 65.731 m F 0 G 0.3 w 10 M 314.3803 65.731 m S 314.3803 65.731 m S 0 g 1 w 4 M 313.8359 65.197 m 313.8359 63.4085 L 314.9247 63.4085 L 314.9247 65.197 L 316.7235 65.1915 L 316.7235 66.2707 L 314.9247 66.2651 L 314.9247 68.0537 L 313.8359 68.0537 L 313.8359 66.2651 L 312.0371 66.2707 L 312.0371 65.1915 L 313.8359 65.197 L f 0 G 0.3 w 10 M 325.8237 65.731 m S 325.8237 65.731 m S 0 g 1 w 4 M 325.8237 65.731 m F 0 G 0.3 w 10 M 325.8237 65.731 m S 0 g 1 w 4 M 325.8237 65.731 m F 0 G 0.3 w 10 M 325.8237 65.731 m S 325.8237 65.731 m S 325.8237 65.731 m S 0 g 1 w 4 M 325.8237 65.731 m F 0 G 0.3 w 10 M 325.8237 65.731 m S 325.8237 65.731 m S 1 g 1 w 4 M 322.8084 65.731 m 322.8084 64.1201 324.1585 62.8142 325.8237 62.8142 c 327.489 62.8142 328.839 64.1201 328.839 65.731 c F 328.839 65.731 m 328.839 67.342 327.489 68.6479 325.8237 68.6479 c 324.1585 68.6479 322.8084 67.342 322.8084 65.731 c F 325.8237 65.731 m F 0 G 0.3 w 10 M 325.8237 65.731 m S 0 g 1 w 4 M 325.8237 65.731 m F 0 G 0.3 w 10 M 325.8237 65.731 m S 325.8237 65.731 m S 0 g 1 w 4 M 325.2793 65.197 m 325.2793 63.4085 L 326.3681 63.4085 L 326.3681 65.197 L 328.167 65.1915 L 328.167 66.2707 L 326.3681 66.2651 L 326.3681 68.0537 L 325.2793 68.0537 L 325.2793 66.2651 L 323.4805 66.2707 L 323.4805 65.1915 L 325.2793 65.197 L f 0 G 0.3 w 10 M 325.8238 54.6166 m S 314.3803 54.6166 m S 325.8237 54.6166 m S 314.3803 54.6166 m S 0 g 1 w 4 M 325.8237 54.6166 m F 0 G 0.3 w 10 M 314.3803 54.6166 m S 314.3803 54.6166 m S 314.3803 54.6166 m S 0 g 1 w 4 M 314.3803 54.6166 m F 0 G 0.3 w 10 M 314.3803 54.6166 m S 0 g 1 w 4 M 314.3803 54.6166 m F 1 g 311.365 54.6166 m 311.365 53.0057 312.715 51.6997 314.3803 51.6997 c 316.0456 51.6997 317.3957 53.0057 317.3957 54.6166 c F 317.3957 54.6166 m 317.3957 56.2275 316.0456 57.5334 314.3803 57.5334 c 312.715 57.5334 311.365 56.2275 311.365 54.6166 c F 314.3803 54.6166 m F 0 G 0.3 w 10 M 314.3803 54.6166 m S 0 g 1 w 4 M 314.3803 54.6166 m F 0 G 0.3 w 10 M 314.3803 54.6166 m S 0 g 1 w 4 M 314.3803 54.6166 m F 313.8359 55.1507 m 312.0371 55.1563 L 312.0371 54.077 L 313.8359 54.0826 L F 314.9247 54.0826 m 316.7235 54.077 L 316.7235 55.1563 L 314.9247 55.1507 L F 312.0371 55.1563 m 316.7235 55.1563 l 316.7235 54.077 l 312.0371 54.077 l 312.0371 55.1563 l f 0 G 0.3 w 10 M 325.8237 54.6166 m S 325.8237 54.6166 m S 325.8237 54.6166 m S 0 g 1 w 4 M 325.8237 54.6166 m F 0 G 0.3 w 10 M 325.8237 54.6166 m S 0 g 1 w 4 M 325.8237 54.6166 m F 1 g 322.8084 54.6166 m 322.8084 53.0057 324.1585 51.6997 325.8237 51.6997 c 327.489 51.6997 328.839 53.0057 328.839 54.6166 c F 328.839 54.6166 m 328.839 56.2275 327.489 57.5334 325.8237 57.5334 c 324.1585 57.5334 322.8084 56.2275 322.8084 54.6166 c F 325.8237 54.6166 m F 0 G 0.3 w 10 M 325.8237 54.6166 m S 0 g 1 w 4 M 325.8237 54.6166 m F 0 G 0.3 w 10 M 325.8237 54.6166 m S 0 g 1 w 4 M 325.8237 54.6166 m F 325.2793 55.1507 m 323.4805 55.1563 L 323.4805 54.077 L 325.2793 54.0826 L F 326.3681 54.0826 m 328.167 54.077 L 328.167 55.1563 L 326.3681 55.1507 L F 323.4805 55.1563 m 328.167 55.1563 l 328.167 54.077 l 323.4805 54.077 l 323.4805 55.1563 l f 0 G 0.3 w 10 M 348.7106 54.6166 m S 337.2672 54.6166 m S 348.7106 54.6166 m S 337.2672 54.6166 m S 0 g 1 w 4 M 348.7106 54.6166 m F 0 G 0.3 w 10 M 337.2672 54.6166 m S 337.2672 54.6166 m S 337.2672 54.6166 m S 0 g 1 w 4 M 337.2672 54.6166 m F 0 G 0.3 w 10 M 337.2672 54.6166 m S 0 g 1 w 4 M 337.2672 54.6166 m F 1 g 334.2518 54.6166 m 334.2518 53.0057 335.6018 51.6997 337.2672 51.6997 c 338.9324 51.6997 340.2824 53.0057 340.2824 54.6166 c F 340.2824 54.6166 m 340.2824 56.2275 338.9324 57.5334 337.2672 57.5334 c 335.6018 57.5334 334.2518 56.2275 334.2518 54.6166 c F 337.2672 54.6166 m F 0 G 0.3 w 10 M 337.2672 54.6166 m S 0 g 1 w 4 M 337.2672 54.6166 m F 0 G 0.3 w 10 M 337.2672 54.6166 m S 0 g 1 w 4 M 337.2672 54.6166 m F 336.7228 55.1507 m 334.924 55.1563 L 334.924 54.077 L 336.7228 54.0826 L F 337.8115 54.0826 m 339.6104 54.077 L 339.6104 55.1563 L 337.8115 55.1507 L F 334.924 55.1563 m 339.6104 55.1563 l 339.6104 54.077 l 334.924 54.077 l 334.924 55.1563 l f 0 G 0.3 w 10 M 348.7106 54.6166 m S 348.7106 54.6166 m S 348.7106 54.6166 m S 0 g 1 w 4 M 348.7106 54.6166 m F 0 G 0.3 w 10 M 348.7106 54.6166 m S 0 g 1 w 4 M 348.7106 54.6166 m F 1 g 345.6953 54.6166 m 345.6953 53.0057 347.0453 51.6997 348.7106 51.6997 c 350.3759 51.6997 351.7259 53.0057 351.7259 54.6166 c F 351.7259 54.6166 m 351.7259 56.2275 350.3759 57.5334 348.7106 57.5334 c 347.0453 57.5334 345.6953 56.2275 345.6953 54.6166 c F 348.7106 54.6166 m F 0 G 0.3 w 10 M 348.7106 54.6166 m S 0 g 1 w 4 M 348.7106 54.6166 m F 0 G 0.3 w 10 M 348.7106 54.6166 m S 0 g 1 w 4 M 348.7106 54.6166 m F 348.1662 55.1507 m 346.3674 55.1563 L 346.3674 54.077 L 348.1662 54.0826 L F 349.2549 54.0826 m 351.0538 54.077 L 351.0538 55.1563 L 349.2549 55.1507 L F 346.3674 55.1563 m 351.0538 55.1563 l 351.0538 54.077 l 346.3674 54.077 l 346.3674 55.1563 l f 0 G 0.3 w 10 M 55.9534 49.0594 m S 55.9534 49.0594 m S 55.9534 49.0594 m S 55.9534 49.0594 m S 55.9534 34.2402 m S 55.9534 49.0594 m S 63.5568 41.6498 m S 55.9534 34.2402 m S 55.9534 34.2402 m S 55.9534 49.0594 m S 55.9534 34.2402 m S 48.3499 41.6498 m S u 0 g 1 w 4 M /_Times-Roman 12 14.5 0 0 z [1 0 0 1 49.2373 34.3082]e (\(1\))t T U 0 G 0.3 w 10 M 148.4504 49.0594 m S 148.4504 49.0594 m S 148.4504 49.0594 m S 148.4504 49.0594 m S 148.4504 34.2402 m S 148.4504 49.0594 m S 156.0538 41.6498 m S 148.4504 34.2402 m S 148.4504 34.2402 m S 148.4504 49.0594 m S 148.4504 34.2402 m S 140.8469 41.6498 m S u 0 g 1 w 4 M /_Times-Roman 12 14.5 0 0 z [1 0 0 1 141.7343 34.3082]e (\(2\))t T U 0 G 0.3 w 10 M 239.9979 49.0594 m S 239.9979 49.0594 m S 239.9979 49.0594 m S 239.9979 49.0594 m S 239.9979 34.2402 m S 239.9979 49.0594 m S 247.6013 41.6498 m S 239.9979 34.2402 m S 239.9979 34.2402 m S 239.9979 49.0594 m S 239.9979 34.2402 m S 232.3944 41.6498 m S u 0 g 1 w 4 M /_Times-Roman 12 14.5 0 0 z [1 0 0 1 233.2818 34.3082]e (\(3\))t T U 0 G 0.3 w 10 M 331.5455 49.0594 m S 331.5455 49.0594 m S 331.5455 49.0594 m S 331.5455 49.0594 m S 331.5455 34.2402 m S 331.5455 49.0594 m S 339.1489 41.6498 m S 331.5455 34.2402 m S 331.5455 34.2402 m S 331.5455 49.0594 m S 331.5455 34.2402 m S 323.942 41.6498 m S u 0 g 1 w 4 M /_Times-Roman 12 14.5 0 0 z [1 0 0 1 324.8294 34.3082]e (\(4\))t T U showpage _E end %%EndDocument @endspecial 60 595 a FQ(Figure)22 b(9:)35 b(The)23 b(four)h(p)q(erio)q(dic)e (ground)i(states)g(of)f(the)g(in)o(ternal-spin)f(system)f(obtained)j(b)o(y)60 655 y(constraining)17 b(the)f(blo)q(c)o(k)f(spins)i(to)f(b)q(e)h(zero.)60 860 y(rescaling)g(is)f(irrelev)m(an)o(t)g(for)h(our)g(discussion)h(b)q (ecause)f(w)o(e)f(only)h(consider)g(a)g FP(single)22 b FQ(application)60 920 y(of)17 b(the)f(transformation)g(and)h(do)f(not)h(iterate.)133 980 y FP(Step)25 b(1.)41 b FQ(W)l(e)23 b(c)o(ho)q(ose)h(the)e (con\014guration)i FF(!)1006 962 y Fy(0)1004 992 y FH(sp)q(ecial)1133 980 y FQ(de\014ned)f(b)o(y)f FF(\033)1412 962 y Fy(0)1410 992 y FD(j)1453 980 y FQ(=)j(0)f(for)f(all)g FF(j)28 b FE(2)d Fq(Z)1857 959 y FH(2)1876 980 y FQ(.)60 1040 y(The)19 b(resulting)g(system)f(of)h(in)o (ternal)f(spins)i(has,)g(at)f(lo)o(w)g(temp)q(eratures,)f(four)i(p)q(erio)q (dic)f(Gibbs)60 1101 y(measures)k(corresp)q(onding)i(to)g(four)f(ground)h (states)g(formed)e(b)o(y)h(in\014nite)f(alternating)h(strips)60 1161 y(of)c(thic)o(kness)f(2)h(\(see)f(Fig.)g(9\).)32 b(This)20 b(follo)o(ws)f(immedi)o(ately)d(from)j(Pirogo)o(v-Sinai)h(theory)f(\(see)60 1221 y(App)q(endix)d(B.5.7\).)133 1281 y FP(Step)24 b(2.)41 b FQ(Let)23 b(\003)f(b)q(e)h(a)g(4)p FF(N)e FE(\002)15 b FQ(4)p FF(N)28 b FQ(square.)40 b(T)l(ak)o(e)23 b(blo)q(c)o(k-spin)f(b)q(oundary)i (conditions)e(as)60 1341 y(follo)o(ws:)29 b(+4)20 b(for)g(the)g(ro)o(ws)g(of) h(blo)q(c)o(k)e(spins)h(immediatel)o(y)d(ab)q(o)o(v)o(e)j(and)g(b)q(elo)o(w)g (\003,)h(+2)f(for)g(the)60 1402 y(columns)11 b(immedi)o(ately)e(to)k(the)g (righ)o(t)f(and)h(left)e(of)i(\003,)g(and)g(+4)g(for)g(the)f(columns)f(just)i (to)g(the)f(righ)o(t)60 1462 y(and)19 b(left)e(of)h(these)f([see)g(Fig.)h (10\(a\)].)27 b(A)17 b(sligh)o(t)g(mo)q(di\014cation)h(of)g(the)f(usual)i(P)o (eierls)d(argumen)o(t)60 1522 y(pro)o(v)o(es)h(that)h(these)g(b)q(oundary)h (conditions)f(induce)f(at)h(lo)o(w)f(temp)q(erature)g(the)g(Gibbs)h(measure) 60 1582 y(asso)q(ciated)f(to)g(ground-state)h(#3)e(in)g(Fig.)f(9)i([see)e (Fig.)h(10\(b\)].)133 1642 y FP(Step)k(3.)27 b FQ(W)l(e)18 b(un\014x)g FP(two)j FQ(nearest-neigh)o(b)q(or)e(blo)q(c)o(k)e(spins:)25 b(the)18 b(one)g(at)h(the)f(origin)g(and)g(the)60 1702 y(one)i(immedi)o (ately)d(ab)q(o)o(v)o(e)i(it.)32 b(Then,)21 b(at)f(su\016cien)o(tly)e(lo)o(w) h(temp)q(erature,)g(one)h(has)h(with)f(high)60 1763 y(probabilit)o(y)d(the)g (b)q(oundary)i(condition)e(of)h(Fig.)e(11)j(for)f(the)f(t)o(w)o(o-blo)q(c)o (k)g(system)f(\(0)1645 1745 y Fy(0)1657 1763 y FF(;)8 b FQ(0)1703 1745 y Fy(0)1715 1763 y FQ(\){\(0)1801 1745 y Fy(0)1813 1763 y FF(;)g FQ(1)1859 1745 y Fy(0)1871 1763 y FQ(\))60 1823 y(\(for)17 b(a)g(suitable)g(p)q(ositioning)g(of)h(the)e(v)o(olume)f(\003\).)23 b(Notice)15 b(that)j(this)e(b)q(oundary)j(condition)d(has)60 1883 y(eigh)o(t)f(+)h(spins)g(and)h(only)f(four)g FE(\000)g FQ(spins;)g(therefore,)e(it)i(is)g(clear)f(that)h(the)g(spins)g(inside)f(the) h(t)o(w)o(o)60 1943 y(blo)q(c)o(ks)g(are)g(biased)h(to)o(w)o(ards)f(+,)g(so)h (that)237 2031 y FF(\026)266 2011 y Fy(0)266 2044 y FH(\003)p FD(;!)323 2032 y Ft(0)322 2056 y Fr(sp)q(ecial)415 2044 y FH(;)p FD(@)r FH(\003)470 2049 y Fr(4;4)p Fs(;)p Fr(2)538 2031 y FQ(\()p FF(\033)587 2011 y Fy(0)585 2044 y FH(\(0)617 2034 y Ft(0)627 2044 y FD(;)p FH(0)655 2034 y Ft(0)665 2044 y FH(\))681 2031 y FQ(\))28 b(=)f FF(\026)822 2011 y Fy(0)822 2044 y FH(\003)p FD(;!)879 2032 y Ft(0)878 2056 y Fr(sp)q(ecial)971 2044 y FH(;)p FD(@)r FH(\003)1026 2049 y Fr(4;4)p Fs(;)p Fr(2)1094 2031 y FQ(\()p FF(\033)1143 2011 y Fy(0)1141 2044 y FH(\(0)1173 2034 y Ft(0)1183 2044 y FD(;)p FH(1)1211 2034 y Ft(0)1222 2044 y FH(\))1237 2031 y FQ(\))h FE(\025)f FF(c)1371 2038 y FH(+)1401 2031 y FQ(\()p FF(J)5 b FQ(\))27 b FF(>)h FQ(0)177 b(\(4)p FF(:)p FQ(37\))60 2134 y(at)14 b(zero)f(magnetic)g(\014eld.)19 b([Indeed,)13 b(at)h(lo)o(w)g(temp)q(erature)e(there)h(is)g(a)h(probabilit)o (y)f FE(\031)1660 2115 y FH(1)p 1660 2123 18 2 v 1660 2151 a(2)1696 2134 y FQ(of)h(ha)o(ving)60 2194 y(a)h(strip)f(con\014guration)i (with)f FF(\033)645 2176 y Fy(0)643 2208 y FH(\(0)675 2198 y Ft(0)685 2208 y FD(;)p FH(0)713 2198 y Ft(0)723 2208 y FH(\))753 2194 y FQ(=)f FF(\033)835 2176 y Fy(0)833 2208 y FH(\(0)865 2198 y Ft(0)875 2208 y FD(;)p FH(1)903 2198 y Ft(0)914 2208 y FH(\))943 2194 y FQ(=)g(0)h(and)g(a)g(probabilit)o(y)f FE(\031)1472 2175 y FH(1)p 1472 2183 V 1472 2212 a(2)1509 2194 y FQ(of)h(ha)o(ving)f(an)h (all-+)60 2255 y(con\014guration)20 b(with)e FF(\033)501 2237 y Fy(0)499 2268 y FH(\(0)531 2259 y Ft(0)542 2268 y FD(;)p FH(0)570 2259 y Ft(0)580 2268 y FH(\))614 2255 y FQ(=)g FF(\033)700 2237 y Fy(0)698 2268 y FH(\(0)730 2259 y Ft(0)741 2268 y FD(;)p FH(1)769 2259 y Ft(0)779 2268 y FH(\))813 2255 y FQ(=)g(+4,)h(so)h(that)f (lim)1203 2262 y FD(J)s Fy(!1)1306 2255 y FF(c)1327 2262 y FH(+)1356 2255 y FQ(\()p FF(J)5 b FQ(\))18 b(=)g(+2.])29 b(Similarly)l(,)16 b(b)o(y)60 2315 y(rev)o(ersing)f(the)h(sign)h(of)f(the)g(blo)q(c)o(k)g(spins) g(on)h(the)f(b)q(oundary)l(,)h(w)o(e)f(obtain)237 2403 y FF(\026)266 2382 y Fy(0)266 2415 y FH(\003)p FD(;!)323 2404 y Ft(0)322 2428 y Fr(sp)q(ecial)415 2415 y FH(;)p FD(@)r FH(\003)470 2420 y Fr(4;4)p Fs(;)p Fr(2)538 2403 y FQ(\()p FF(\033)587 2382 y Fy(0)585 2415 y FH(\(0)617 2406 y Ft(0)627 2415 y FD(;)p FH(0)655 2406 y Ft(0)665 2415 y FH(\))681 2403 y FQ(\))28 b(=)f FF(\026)822 2382 y Fy(0)822 2415 y FH(\003)p FD(;!)879 2404 y Ft(0)878 2428 y Fr(sp)q(ecial)971 2415 y FH(;)p FD(@)r FH(\003)1026 2420 y Fr(4;4)p Fs(;)p Fr(2)1094 2403 y FQ(\()p FF(\033)1143 2382 y Fy(0)1141 2415 y FH(\(0)1173 2406 y Ft(0)1183 2415 y FD(;)p FH(1)1211 2406 y Ft(0)1222 2415 y FH(\))1237 2403 y FQ(\))h FE(\024)f FF(c)1371 2410 y Fy(\000)1401 2403 y FQ(\()p FF(J)5 b FQ(\))27 b FF(<)h FQ(0)177 b(\(4)p FF(:)p FQ(38\))60 2502 y(where)16 b(of)g(course)h FF(c)427 2509 y Fy(\000)456 2502 y FQ(\()p FF(J)5 b FQ(\))14 b(=)f FE(\000)p FF(c)651 2509 y FH(+)681 2502 y FQ(\()p FF(J)5 b FQ(\))15 b(b)o(y)h(symmetry)l(.)i(This)e (completes)e(the)i(argumen)o(t.)133 2600 y FM(Remark.)j FQ(Notice)c(that)h (it)f(do)q(es)i(not)f(su\016ce)f(to)h(un\014x)g(a)g(single)f(blo)q(c)o(k)g (spin)h(to)g(distinguish)60 2660 y(among)h(the)f(four)h(Gibbs)g(measures,)e (b)q(ecause)i(in)g(all)f(four)h(measures)f(the)g(b)q(oundary)i(condition)938 2784 y(120)p eop %%Page: 121 121 bop 152 1054 a @beginspecial 25 @llx 31.500000 @lly 355 @urx 192.500000 @ury 3952 @rwi @setspecial %%BeginDocument: fig10.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n []/_Symbol/Symbol Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 56.0282 166.7379 m S 56.0282 155.7024 m S 44.7351 155.7024 m S 44.7351 166.7379 m S 50.3816 161.2201 m S 44.7351 177.7733 m S 44.7351 166.7379 m S 33.442 166.7379 m S 33.442 177.7733 m S 39.0886 172.2556 m S 44.7351 188.8088 m S 44.7351 177.7733 m S 33.442 177.7733 m S 33.442 188.8088 m S 39.0886 183.2911 m S 56.0282 188.8088 m S 56.0282 177.7733 m S 44.7351 177.7733 m S 44.7351 188.8088 m S 50.3816 183.2911 m S 56.0282 177.7733 m S 56.0282 166.7379 m S 44.7351 166.7379 m S 44.7351 177.7733 m S 50.3816 172.2556 m S 44.7351 166.7379 m S 44.7351 155.7024 m S 33.442 155.7024 m S 33.442 166.7379 m S 39.0886 161.2201 m S 0 g 1 w 4 M 50.3816 183.2911 m F 50.3816 161.2201 m F 0 G 0.3 w 10 M 67.3212 188.8088 m S 67.3212 177.7733 m S 56.0282 177.7733 m S 56.0282 188.8088 m S 61.6746 183.2911 m S 89.9074 166.7379 m S 89.9074 155.7024 m S 78.6143 155.7024 m S 78.6143 166.7379 m S 84.2608 161.2201 m S 78.6143 177.7733 m S 78.6143 166.7379 m S 67.3212 166.7379 m S 67.3212 177.7733 m S 72.9678 172.2556 m S 78.6143 188.8088 m S 78.6143 177.7733 m S 67.3212 177.7733 m S 67.3212 188.8088 m S 72.9678 183.2911 m S 89.9074 188.8088 m S 89.9074 177.7733 m S 78.6143 177.7733 m S 78.6143 188.8088 m S 84.2608 183.2911 m S 89.9074 177.7733 m S 89.9074 166.7379 m S 78.6143 166.7379 m S 78.6143 177.7733 m S 84.2608 172.2556 m S 78.6143 166.7379 m S 78.6143 155.7024 m S 67.3212 155.7024 m S 67.3212 166.7379 m S 72.9678 161.2201 m S 67.3212 166.7379 m S 67.3212 155.7024 m S 56.0282 155.7024 m S 56.0282 166.7379 m S 61.6746 161.2201 m S 67.3212 177.7733 m S 67.3212 166.7379 m S 56.0282 166.7379 m S 56.0282 177.7733 m S 61.6746 172.2556 m S 0 g 1 w 4 M 61.6746 183.2911 m F 84.2608 183.2911 m F 61.6746 161.2201 m F 84.2608 161.2201 m F 0 G 0.3 w 10 M 101.2004 188.8088 m S 101.2004 177.7733 m S 89.9074 177.7733 m S 89.9074 188.8088 m S 95.5539 183.2911 m S 123.7866 166.7379 m S 123.7866 155.7024 m S 112.4935 155.7024 m S 112.4935 166.7379 m S 118.1401 161.2201 m S 112.4935 177.7733 m S 112.4935 166.7379 m S 101.2004 166.7379 m S 101.2004 177.7733 m S 106.847 172.2556 m S 112.4935 188.8088 m S 112.4935 177.7733 m S 101.2004 177.7733 m S 101.2004 188.8088 m S 106.847 183.2911 m S 123.7866 188.8088 m S 123.7866 177.7733 m S 112.4935 177.7733 m S 112.4935 188.8088 m S 118.1401 183.2911 m S 123.7866 177.7733 m S 123.7866 166.7379 m S 112.4935 166.7379 m S 112.4935 177.7733 m S 118.1401 172.2556 m S 112.4935 166.7379 m S 112.4935 155.7024 m S 101.2004 155.7024 m S 101.2004 166.7379 m S 106.847 161.2201 m S 101.2004 166.7379 m S 101.2004 155.7024 m S 89.9074 155.7024 m S 89.9074 166.7379 m S 95.5539 161.2201 m S 101.2004 177.7733 m S 101.2004 166.7379 m S 89.9074 166.7379 m S 89.9074 177.7733 m S 95.5539 172.2556 m S 0 g 1 w 4 M 95.5539 183.2911 m F 118.1401 183.2911 m F 95.5539 161.2201 m F 118.1401 161.2201 m F 0 G 0.3 w 10 M 56.0282 133.6314 m S 56.0282 122.5959 m S 44.7351 122.5959 m S 44.7351 133.6314 m S 50.3816 128.1137 m S 44.7351 144.6668 m S 44.7351 133.6314 m S 33.442 133.6314 m S 33.442 144.6668 m S 39.0886 139.1492 m S 44.7351 155.7024 m S 44.7351 144.6668 m S 33.442 144.6668 m S 33.442 155.7024 m S 39.0886 150.1846 m S 56.0282 155.7024 m S 56.0282 144.6668 m S 44.7351 144.6668 m S 44.7351 155.7024 m S 50.3816 150.1846 m S 56.0282 144.6668 m S 56.0282 133.6314 m S 44.7351 133.6314 m S 44.7351 144.6668 m S 50.3816 139.1492 m S 44.7351 133.6314 m S 44.7351 122.5959 m S 33.442 122.5959 m S 33.442 133.6314 m S 39.0886 128.1137 m S 0 g 1 w 4 M 50.3816 150.1846 m F 50.3816 128.1137 m F 0 G 0.3 w 10 M 67.3212 155.7024 m S 67.3212 144.6668 m S 56.0282 144.6668 m S 56.0282 155.7024 m S 61.6746 150.1846 m S 89.9074 133.6314 m S 89.9074 122.5959 m S 78.6143 122.5959 m S 78.6143 133.6314 m S 84.2608 128.1137 m S 78.6143 144.6668 m S 78.6143 133.6314 m S 67.3212 133.6314 m S 67.3212 144.6668 m S 72.9678 139.1492 m S 78.6143 155.7024 m S 78.6143 144.6668 m S 67.3212 144.6668 m S 67.3212 155.7024 m S 72.9678 150.1846 m S 89.9074 155.7024 m S 89.9074 144.6668 m S 78.6143 144.6668 m S 78.6143 155.7024 m S 84.2608 150.1846 m S 89.9074 144.6668 m S 89.9074 133.6314 m S 78.6143 133.6314 m S 78.6143 144.6668 m S 84.2608 139.1492 m S 78.6143 133.6314 m S 78.6143 122.5959 m S 67.3212 122.5959 m S 67.3212 133.6314 m S 72.9678 128.1137 m S 67.3212 133.6314 m S 67.3212 122.5959 m S 56.0282 122.5959 m S 56.0282 133.6314 m S 61.6746 128.1137 m S 67.3212 144.6668 m S 67.3212 133.6314 m S 56.0282 133.6314 m S 56.0282 144.6668 m S 61.6746 139.1492 m S 0 g 1 w 4 M 61.6746 150.1846 m F 84.2608 150.1846 m F 61.6746 128.1137 m F 84.2608 128.1137 m F 0 G 0.3 w 10 M 101.2004 155.7024 m S 101.2004 144.6668 m S 89.9074 144.6668 m S 89.9074 155.7024 m S 95.5539 150.1846 m S 123.7866 133.6314 m S 123.7866 122.5959 m S 112.4935 122.5959 m S 112.4935 133.6314 m S 118.1401 128.1137 m S 112.4935 144.6668 m S 112.4935 133.6314 m S 101.2004 133.6314 m S 101.2004 144.6668 m S 106.847 139.1492 m S 112.4935 155.7024 m S 112.4935 144.6668 m S 101.2004 144.6668 m S 101.2004 155.7024 m S 106.847 150.1846 m S 123.7866 155.7024 m S 123.7866 144.6668 m S 112.4935 144.6668 m S 112.4935 155.7024 m S 118.1401 150.1846 m S 123.7866 144.6668 m S 123.7866 133.6314 m S 112.4935 133.6314 m S 112.4935 144.6668 m S 118.1401 139.1492 m S 112.4935 133.6314 m S 112.4935 122.5959 m S 101.2004 122.5959 m S 101.2004 133.6314 m S 106.847 128.1137 m S 101.2004 133.6314 m S 101.2004 122.5959 m S 89.9074 122.5959 m S 89.9074 133.6314 m S 95.5539 128.1137 m S 101.2004 144.6668 m S 101.2004 133.6314 m S 89.9074 133.6314 m S 89.9074 144.6668 m S 95.5539 139.1492 m S 0 g 1 w 4 M 95.5539 150.1846 m F 118.1401 150.1846 m F 95.5539 128.1137 m F 118.1401 128.1137 m F 50.3816 117.0782 m F 61.6746 117.0782 m F 84.2608 117.0782 m F 95.5539 117.0782 m F 118.1401 117.0782 m F 0 G 0.3 w 10 M 56.0282 100.525 m S 56.0282 89.4895 m S 44.7351 89.4895 m S 44.7351 100.525 m S 50.3816 95.0072 m S 44.7351 111.5604 m S 44.7351 100.525 m S 33.442 100.525 m S 33.442 111.5604 m S 39.0886 106.0427 m S 44.7351 122.5959 m S 44.7351 111.5604 m S 33.442 111.5604 m S 33.442 122.5959 m S 39.0886 117.0782 m S 56.0282 122.5959 m S 56.0282 111.5604 m S 44.7351 111.5604 m S 44.7351 122.5959 m S 50.3816 117.0782 m S 56.0282 111.5604 m S 56.0282 100.525 m S 44.7351 100.525 m S 44.7351 111.5604 m S 50.3816 106.0427 m S 44.7351 100.525 m S 44.7351 89.4895 m S 33.442 89.4895 m S 33.442 100.525 m S 39.0886 95.0072 m S 0 g 1 w 4 M 50.3816 117.0782 m F 50.3816 95.0072 m F 0 G 0.3 w 10 M 67.3212 122.5959 m S 67.3212 111.5604 m S 56.0282 111.5604 m S 56.0282 122.5959 m S 61.6746 117.0782 m S 89.9074 100.525 m S 89.9074 89.4895 m S 78.6143 89.4895 m S 78.6143 100.525 m S 84.2608 95.0072 m S 78.6143 111.5604 m S 78.6143 100.525 m S 67.3212 100.525 m S 67.3212 111.5604 m S 72.9678 106.0427 m S 78.6143 122.5959 m S 78.6143 111.5604 m S 67.3212 111.5604 m S 67.3212 122.5959 m S 72.9678 117.0782 m S 89.9074 122.5959 m S 89.9074 111.5604 m S 78.6143 111.5604 m S 78.6143 122.5959 m S 84.2608 117.0782 m S 89.9074 111.5604 m S 89.9074 100.525 m S 78.6143 100.525 m S 78.6143 111.5604 m S 84.2608 106.0427 m S 78.6143 100.525 m S 78.6143 89.4895 m S 67.3212 89.4895 m S 67.3212 100.525 m S 72.9678 95.0072 m S 67.3212 100.525 m S 67.3212 89.4895 m S 56.0282 89.4895 m S 56.0282 100.525 m S 61.6746 95.0072 m S 67.3212 111.5604 m S 67.3212 100.525 m S 56.0282 100.525 m S 56.0282 111.5604 m S 61.6746 106.0427 m S 0 g 1 w 4 M 61.6746 117.0782 m F 84.2608 117.0782 m F 61.6746 95.0072 m F 84.2608 95.0072 m F 0 G 0.3 w 10 M 101.2004 122.5959 m S 101.2004 111.5604 m S 89.9074 111.5604 m S 89.9074 122.5959 m S 95.5539 117.0782 m S 123.7866 100.525 m S 123.7866 89.4895 m S 112.4935 89.4895 m S 112.4935 100.525 m S 118.1401 95.0072 m S 112.4935 111.5604 m S 112.4935 100.525 m S 101.2004 100.525 m S 101.2004 111.5604 m S 106.847 106.0427 m S 112.4935 122.5959 m S 112.4935 111.5604 m S 101.2004 111.5604 m S 101.2004 122.5959 m S 106.847 117.0782 m S 123.7866 122.5959 m S 123.7866 111.5604 m S 112.4935 111.5604 m S 112.4935 122.5959 m S 118.1401 117.0782 m S 123.7866 111.5604 m S 123.7866 100.525 m S 112.4935 100.525 m S 112.4935 111.5604 m S 118.1401 106.0427 m S 112.4935 100.525 m S 112.4935 89.4895 m S 101.2004 89.4895 m S 101.2004 100.525 m S 106.847 95.0072 m S 101.2004 100.525 m S 101.2004 89.4895 m S 89.9074 89.4895 m S 89.9074 100.525 m S 95.5539 95.0072 m S 101.2004 111.5604 m S 101.2004 100.525 m S 89.9074 100.525 m S 89.9074 111.5604 m S 95.5539 106.0427 m S 0 g 1 w 4 M 95.5539 117.0782 m F 118.1401 117.0782 m F 95.5539 95.0072 m F 118.1401 95.0072 m F 0 G 0.3 w 10 M 56.0282 67.4185 m S 56.0282 56.383 m S 44.7351 56.383 m S 44.7351 67.4185 m S 50.3816 61.9008 m S 44.7351 78.4539 m S 44.7351 67.4185 m S 33.442 67.4185 m S 33.442 78.4539 m S 39.0886 72.9362 m S 44.7351 89.4895 m S 44.7351 78.4539 m S 33.442 78.4539 m S 33.442 89.4895 m S 39.0886 83.9717 m S 56.0282 89.4895 m S 56.0282 78.4539 m S 44.7351 78.4539 m S 44.7351 89.4895 m S 50.3816 83.9717 m S 56.0282 78.4539 m S 56.0282 67.4185 m S 44.7351 67.4185 m S 44.7351 78.4539 m S 50.3816 72.9362 m S 44.7351 67.4185 m S 44.7351 56.383 m S 33.442 56.383 m S 33.442 67.4185 m S 39.0886 61.9008 m S 0 g 1 w 4 M 50.3816 83.9717 m F 50.3816 61.9008 m F 0 G 0.3 w 10 M 67.3212 89.4895 m S 67.3212 78.4539 m S 56.0282 78.4539 m S 56.0282 89.4895 m S 61.6746 83.9717 m S 89.9074 67.4185 m S 89.9074 56.383 m S 78.6143 56.383 m S 78.6143 67.4185 m S 84.2608 61.9008 m S 78.6143 78.4539 m S 78.6143 67.4185 m S 67.3212 67.4185 m S 67.3212 78.4539 m S 72.9678 72.9362 m S 78.6143 89.4895 m S 78.6143 78.4539 m S 67.3212 78.4539 m S 67.3212 89.4895 m S 72.9678 83.9717 m S 89.9074 89.4895 m S 89.9074 78.4539 m S 78.6143 78.4539 m S 78.6143 89.4895 m S 84.2608 83.9717 m S 89.9074 78.4539 m S 89.9074 67.4185 m S 78.6143 67.4185 m S 78.6143 78.4539 m S 84.2608 72.9362 m S 78.6143 67.4185 m S 78.6143 56.383 m S 67.3212 56.383 m S 67.3212 67.4185 m S 72.9678 61.9008 m S 67.3212 67.4185 m S 67.3212 56.383 m S 56.0282 56.383 m S 56.0282 67.4185 m S 61.6746 61.9008 m S 67.3212 78.4539 m S 67.3212 67.4185 m S 56.0282 67.4185 m S 56.0282 78.4539 m S 61.6746 72.9362 m S 0 g 1 w 4 M 61.6746 83.9717 m F 84.2608 83.9717 m F 61.6746 61.9008 m F 84.2608 61.9008 m F 0 G 0.3 w 10 M 101.2004 89.4895 m S 101.2004 78.4539 m S 89.9074 78.4539 m S 89.9074 89.4895 m S 95.5539 83.9717 m S 123.7866 67.4185 m S 123.7866 56.383 m S 112.4935 56.383 m S 112.4935 67.4185 m S 118.1401 61.9008 m S 112.4935 78.4539 m S 112.4935 67.4185 m S 101.2004 67.4185 m S 101.2004 78.4539 m S 106.847 72.9362 m S 112.4935 89.4895 m S 112.4935 78.4539 m S 101.2004 78.4539 m S 101.2004 89.4895 m S 106.847 83.9717 m S 123.7866 89.4895 m S 123.7866 78.4539 m S 112.4935 78.4539 m S 112.4935 89.4895 m S 118.1401 83.9717 m S 123.7866 78.4539 m S 123.7866 67.4185 m S 112.4935 67.4185 m S 112.4935 78.4539 m S 118.1401 72.9362 m S 112.4935 67.4185 m S 112.4935 56.383 m S 101.2004 56.383 m S 101.2004 67.4185 m S 106.847 61.9008 m S 101.2004 67.4185 m S 101.2004 56.383 m S 89.9074 56.383 m S 89.9074 67.4185 m S 95.5539 61.9008 m S 101.2004 78.4539 m S 101.2004 67.4185 m S 89.9074 67.4185 m S 89.9074 78.4539 m S 95.5539 72.9362 m S 0 g 1 w 4 M 95.5539 83.9717 m F 118.1401 83.9717 m F 95.5539 61.9008 m F 118.1401 61.9008 m F 0 G 50.3816 172.2556 m S 50.3816 139.1492 m S 0.3 w 10 M 146.3728 166.7379 m S 146.3728 155.7024 m S 135.0797 155.7024 m S 135.0797 166.7379 m S 140.7262 161.2201 m S 135.0797 177.7733 m S 135.0797 166.7379 m S 123.7866 166.7379 m S 123.7866 177.7733 m S 129.4331 172.2556 m S 135.0797 188.8088 m S 135.0797 177.7733 m S 123.7866 177.7733 m S 123.7866 188.8088 m S 129.4331 183.2911 m S 146.3728 188.8088 m S 146.3728 177.7733 m S 135.0797 177.7733 m S 135.0797 188.8088 m S 140.7262 183.2911 m S 146.3728 177.7733 m S 146.3728 166.7379 m S 135.0797 166.7379 m S 135.0797 177.7733 m S 140.7262 172.2556 m S 135.0797 166.7379 m S 135.0797 155.7024 m S 123.7866 155.7024 m S 123.7866 166.7379 m S 129.4331 161.2201 m S 0 g 1 w 4 M 140.7262 183.2911 m F 140.7262 161.2201 m F 0 G 0.3 w 10 M 157.6659 188.8088 m S 157.6659 177.7733 m S 146.3728 177.7733 m S 146.3728 188.8088 m S 152.0193 183.2911 m S 180.2521 166.7379 m S 180.2521 155.7024 m S 168.959 155.7024 m S 168.959 166.7379 m S 174.6055 161.2201 m S 168.959 177.7733 m S 168.959 166.7379 m S 157.6659 166.7379 m S 157.6659 177.7733 m S 163.3125 172.2556 m S 168.959 188.8088 m S 168.959 177.7733 m S 157.6659 177.7733 m S 157.6659 188.8088 m S 163.3125 183.2911 m S 180.2521 188.8088 m S 180.2521 177.7733 m S 168.959 177.7733 m S 168.959 188.8088 m S 174.6055 183.2911 m S 180.2521 177.7733 m S 180.2521 166.7379 m S 168.959 166.7379 m S 168.959 177.7733 m S 174.6055 172.2556 m S 168.959 166.7379 m S 168.959 155.7024 m S 157.6659 155.7024 m S 157.6659 166.7379 m S 163.3125 161.2201 m S 157.6659 166.7379 m S 157.6659 155.7024 m S 146.3728 155.7024 m S 146.3728 166.7379 m S 152.0193 161.2201 m S 157.6659 177.7733 m S 157.6659 166.7379 m S 146.3728 166.7379 m S 146.3728 177.7733 m S 152.0193 172.2556 m S 0 g 1 w 4 M 152.0193 183.2911 m F 174.6055 183.2911 m F 152.0193 161.2201 m F 174.6055 161.2201 m F 0 G 0.3 w 10 M 191.5451 188.8088 m S 191.5451 177.7733 m S 180.2521 177.7733 m S 180.2521 188.8088 m S 185.8986 183.2911 m S 214.1313 166.7379 m S 214.1313 155.7024 m S 202.8382 155.7024 m S 202.8382 166.7379 m S 208.4847 161.2201 m S 202.8382 177.7733 m S 202.8382 166.7379 m S 191.5451 166.7379 m S 191.5451 177.7733 m S 197.1917 172.2556 m S 202.8382 188.8088 m S 202.8382 177.7733 m S 191.5451 177.7733 m S 191.5451 188.8088 m S 197.1917 183.2911 m S 214.1313 188.8088 m S 214.1313 177.7733 m S 202.8382 177.7733 m S 202.8382 188.8088 m S 208.4847 183.2911 m S 214.1313 177.7733 m S 214.1313 166.7379 m S 202.8382 166.7379 m S 202.8382 177.7733 m S 208.4847 172.2556 m S 202.8382 166.7379 m S 202.8382 155.7024 m S 191.5451 155.7024 m S 191.5451 166.7379 m S 197.1917 161.2201 m S 191.5451 166.7379 m S 191.5451 155.7024 m S 180.2521 155.7024 m S 180.2521 166.7379 m S 185.8986 161.2201 m S 191.5451 177.7733 m S 191.5451 166.7379 m S 180.2521 166.7379 m S 180.2521 177.7733 m S 185.8986 172.2556 m S 0 g 1 w 4 M 185.8986 183.2911 m F 208.4847 183.2911 m F 185.8986 161.2201 m F 208.4847 161.2201 m F 0 G 0.3 w 10 M 146.3728 133.6314 m S 146.3728 122.5959 m S 135.0797 122.5959 m S 135.0797 133.6314 m S 140.7262 128.1137 m S 135.0797 144.6668 m S 135.0797 133.6314 m S 123.7866 133.6314 m S 123.7866 144.6668 m S 129.4331 139.1492 m S 135.0797 155.7024 m S 135.0797 144.6668 m S 123.7866 144.6668 m S 123.7866 155.7024 m S 129.4331 150.1846 m S 146.3728 155.7024 m S 146.3728 144.6668 m S 135.0797 144.6668 m S 135.0797 155.7024 m S 140.7262 150.1846 m S 146.3728 144.6668 m S 146.3728 133.6314 m S 135.0797 133.6314 m S 135.0797 144.6668 m S 140.7262 139.1492 m S 135.0797 133.6314 m S 135.0797 122.5959 m S 123.7866 122.5959 m S 123.7866 133.6314 m S 129.4331 128.1137 m S 0 g 1 w 4 M 140.7262 150.1846 m F 140.7262 128.1137 m F 0 G 0.3 w 10 M 157.6659 155.7024 m S 157.6659 144.6668 m S 146.3728 144.6668 m S 146.3728 155.7024 m S 152.0193 150.1846 m S 180.2521 133.6314 m S 180.2521 122.5959 m S 168.959 122.5959 m S 168.959 133.6314 m S 174.6055 128.1137 m S 168.959 144.6668 m S 168.959 133.6314 m S 157.6659 133.6314 m S 157.6659 144.6668 m S 163.3125 139.1492 m S 168.959 155.7024 m S 168.959 144.6668 m S 157.6659 144.6668 m S 157.6659 155.7024 m S 163.3125 150.1846 m S 180.2521 155.7024 m S 180.2521 144.6668 m S 168.959 144.6668 m S 168.959 155.7024 m S 174.6055 150.1846 m S 180.2521 144.6668 m S 180.2521 133.6314 m S 168.959 133.6314 m S 168.959 144.6668 m S 174.6055 139.1492 m S 168.959 133.6314 m S 168.959 122.5959 m S 157.6659 122.5959 m S 157.6659 133.6314 m S 163.3125 128.1137 m S 157.6659 133.6314 m S 157.6659 122.5959 m S 146.3728 122.5959 m S 146.3728 133.6314 m S 152.0193 128.1137 m S 157.6659 144.6668 m S 157.6659 133.6314 m S 146.3728 133.6314 m S 146.3728 144.6668 m S 152.0193 139.1492 m S 0 g 1 w 4 M 152.0193 150.1846 m F 174.6055 150.1846 m F 152.0193 128.1137 m F 174.6055 128.1137 m F 0 G 0.3 w 10 M 191.5451 155.7024 m S 191.5451 144.6668 m S 180.2521 144.6668 m S 180.2521 155.7024 m S 185.8986 150.1846 m S 214.1313 133.6314 m S 214.1313 122.5959 m S 202.8382 122.5959 m S 202.8382 133.6314 m S 208.4847 128.1137 m S 202.8382 144.6668 m S 202.8382 133.6314 m S 191.5451 133.6314 m S 191.5451 144.6668 m S 197.1917 139.1492 m S 202.8382 155.7024 m S 202.8382 144.6668 m S 191.5451 144.6668 m S 191.5451 155.7024 m S 197.1917 150.1846 m S 214.1313 155.7024 m S 214.1313 144.6668 m S 202.8382 144.6668 m S 202.8382 155.7024 m S 208.4847 150.1846 m S 214.1313 144.6668 m S 214.1313 133.6314 m S 202.8382 133.6314 m S 202.8382 144.6668 m S 208.4847 139.1492 m S 202.8382 133.6314 m S 202.8382 122.5959 m S 191.5451 122.5959 m S 191.5451 133.6314 m S 197.1917 128.1137 m S 191.5451 133.6314 m S 191.5451 122.5959 m S 180.2521 122.5959 m S 180.2521 133.6314 m S 185.8986 128.1137 m S 191.5451 144.6668 m S 191.5451 133.6314 m S 180.2521 133.6314 m S 180.2521 144.6668 m S 185.8986 139.1492 m S 0 g 1 w 4 M 185.8986 150.1846 m F 208.4847 150.1846 m F 185.8986 128.1137 m F 208.4847 128.1137 m F 140.7262 117.0782 m F 152.0193 117.0782 m F 174.6055 117.0782 m F 185.8986 117.0782 m F 208.4847 117.0782 m F 0 G 0.3 w 10 M 146.3728 100.525 m S 146.3728 89.4895 m S 135.0797 89.4895 m S 135.0797 100.525 m S 140.7262 95.0072 m S 135.0797 111.5604 m S 135.0797 100.525 m S 123.7866 100.525 m S 123.7866 111.5604 m S 129.4331 106.0427 m S 135.0797 122.5959 m S 135.0797 111.5604 m S 123.7866 111.5604 m S 123.7866 122.5959 m S 129.4331 117.0782 m S 146.3728 122.5959 m S 146.3728 111.5604 m S 135.0797 111.5604 m S 135.0797 122.5959 m S 140.7262 117.0782 m S 146.3728 111.5604 m S 146.3728 100.525 m S 135.0797 100.525 m S 135.0797 111.5604 m S 140.7262 106.0427 m S 135.0797 100.525 m S 135.0797 89.4895 m S 123.7866 89.4895 m S 123.7866 100.525 m S 129.4331 95.0072 m S 0 g 1 w 4 M 140.7262 117.0782 m F 140.7262 95.0072 m F 0 G 0.3 w 10 M 157.6659 122.5959 m S 157.6659 111.5604 m S 146.3728 111.5604 m S 146.3728 122.5959 m S 152.0193 117.0782 m S 180.2521 100.525 m S 180.2521 89.4895 m S 168.959 89.4895 m S 168.959 100.525 m S 174.6055 95.0072 m S 168.959 111.5604 m S 168.959 100.525 m S 157.6659 100.525 m S 157.6659 111.5604 m S 163.3125 106.0427 m S 168.959 122.5959 m S 168.959 111.5604 m S 157.6659 111.5604 m S 157.6659 122.5959 m S 163.3125 117.0782 m S 180.2521 122.5959 m S 180.2521 111.5604 m S 168.959 111.5604 m S 168.959 122.5959 m S 174.6055 117.0782 m S 180.2521 111.5604 m S 180.2521 100.525 m S 168.959 100.525 m S 168.959 111.5604 m S 174.6055 106.0427 m S 168.959 100.525 m S 168.959 89.4895 m S 157.6659 89.4895 m S 157.6659 100.525 m S 163.3125 95.0072 m S 157.6659 100.525 m S 157.6659 89.4895 m S 146.3728 89.4895 m S 146.3728 100.525 m S 152.0193 95.0072 m S 157.6659 111.5604 m S 157.6659 100.525 m S 146.3728 100.525 m S 146.3728 111.5604 m S 152.0193 106.0427 m S 0 g 1 w 4 M 152.0193 117.0782 m F 174.6055 117.0782 m F 152.0193 95.0072 m F 174.6055 95.0072 m F 0 G 0.3 w 10 M 191.5451 122.5959 m S 191.5451 111.5604 m S 180.2521 111.5604 m S 180.2521 122.5959 m S 185.8986 117.0782 m S 214.1313 100.525 m S 214.1313 89.4895 m S 202.8382 89.4895 m S 202.8382 100.525 m S 208.4847 95.0072 m S 202.8382 111.5604 m S 202.8382 100.525 m S 191.5451 100.525 m S 191.5451 111.5604 m S 197.1917 106.0427 m S 202.8382 122.5959 m S 202.8382 111.5604 m S 191.5451 111.5604 m S 191.5451 122.5959 m S 197.1917 117.0782 m S 214.1313 122.5959 m S 214.1313 111.5604 m S 202.8382 111.5604 m S 202.8382 122.5959 m S 208.4847 117.0782 m S 214.1313 111.5604 m S 214.1313 100.525 m S 202.8382 100.525 m S 202.8382 111.5604 m S 208.4847 106.0427 m S 202.8382 100.525 m S 202.8382 89.4895 m S 191.5451 89.4895 m S 191.5451 100.525 m S 197.1917 95.0072 m S 191.5451 100.525 m S 191.5451 89.4895 m S 180.2521 89.4895 m S 180.2521 100.525 m S 185.8986 95.0072 m S 191.5451 111.5604 m S 191.5451 100.525 m S 180.2521 100.525 m S 180.2521 111.5604 m S 185.8986 106.0427 m S 0 g 1 w 4 M 185.8986 117.0782 m F 208.4847 117.0782 m F 185.8986 95.0072 m F 208.4847 95.0072 m F 0 G 0.3 w 10 M 146.3728 67.4185 m S 146.3728 56.383 m S 135.0797 56.383 m S 135.0797 67.4185 m S 140.7262 61.9008 m S 135.0797 78.4539 m S 135.0797 67.4185 m S 123.7866 67.4185 m S 123.7866 78.4539 m S 129.4331 72.9362 m S 135.0797 89.4895 m S 135.0797 78.4539 m S 123.7866 78.4539 m S 123.7866 89.4895 m S 129.4331 83.9717 m S 146.3728 89.4895 m S 146.3728 78.4539 m S 135.0797 78.4539 m S 135.0797 89.4895 m S 140.7262 83.9717 m S 146.3728 78.4539 m S 146.3728 67.4185 m S 135.0797 67.4185 m S 135.0797 78.4539 m S 140.7262 72.9362 m S 135.0797 67.4185 m S 135.0797 56.383 m S 123.7866 56.383 m S 123.7866 67.4185 m S 129.4331 61.9008 m S 0 g 1 w 4 M 140.7262 83.9717 m F 140.7262 61.9008 m F 0 G 0.3 w 10 M 157.6659 89.4895 m S 157.6659 78.4539 m S 146.3728 78.4539 m S 146.3728 89.4895 m S 152.0193 83.9717 m S 180.2521 67.4185 m S 180.2521 56.383 m S 168.959 56.383 m S 168.959 67.4185 m S 174.6055 61.9008 m S 168.959 78.4539 m S 168.959 67.4185 m S 157.6659 67.4185 m S 157.6659 78.4539 m S 163.3125 72.9362 m S 168.959 89.4895 m S 168.959 78.4539 m S 157.6659 78.4539 m S 157.6659 89.4895 m S 163.3125 83.9717 m S 180.2521 89.4895 m S 180.2521 78.4539 m S 168.959 78.4539 m S 168.959 89.4895 m S 174.6055 83.9717 m S 180.2521 78.4539 m S 180.2521 67.4185 m S 168.959 67.4185 m S 168.959 78.4539 m S 174.6055 72.9362 m S 168.959 67.4185 m S 168.959 56.383 m S 157.6659 56.383 m S 157.6659 67.4185 m S 163.3125 61.9008 m S 157.6659 67.4185 m S 157.6659 56.383 m S 146.3728 56.383 m S 146.3728 67.4185 m S 152.0193 61.9008 m S 157.6659 78.4539 m S 157.6659 67.4185 m S 146.3728 67.4185 m S 146.3728 78.4539 m S 152.0193 72.9362 m S 0 g 1 w 4 M 152.0193 83.9717 m F 174.6055 83.9717 m F 152.0193 61.9008 m F 174.6055 61.9008 m F 0 G 0.3 w 10 M 191.5451 89.4895 m S 191.5451 78.4539 m S 180.2521 78.4539 m S 180.2521 89.4895 m S 185.8986 83.9717 m S 214.1313 67.4185 m S 214.1313 56.383 m S 202.8382 56.383 m S 202.8382 67.4185 m S 208.4847 61.9008 m S 202.8382 78.4539 m S 202.8382 67.4185 m S 191.5451 67.4185 m S 191.5451 78.4539 m S 197.1917 72.9362 m S 202.8382 89.4895 m S 202.8382 78.4539 m S 191.5451 78.4539 m S 191.5451 89.4895 m S 197.1917 83.9717 m S 214.1313 89.4895 m S 214.1313 78.4539 m S 202.8382 78.4539 m S 202.8382 89.4895 m S 208.4847 83.9717 m S 214.1313 78.4539 m S 214.1313 67.4185 m S 202.8382 67.4185 m S 202.8382 78.4539 m S 208.4847 72.9362 m S 202.8382 67.4185 m S 202.8382 56.383 m S 191.5451 56.383 m S 191.5451 67.4185 m S 197.1917 61.9008 m S 191.5451 67.4185 m S 191.5451 56.383 m S 180.2521 56.383 m S 180.2521 67.4185 m S 185.8986 61.9008 m S 191.5451 78.4539 m S 191.5451 67.4185 m S 180.2521 67.4185 m S 180.2521 78.4539 m S 185.8986 72.9362 m S 0 g 1 w 4 M 185.8986 83.9717 m F 208.4847 83.9717 m F 185.8986 61.9008 m F 208.4847 61.9008 m F 0 G 140.7262 172.2556 m S 140.7262 139.1492 m S 2 w 78.6143 166.7379 m 168.959 166.7379 l 168.959 78.4539 l 78.6143 78.4539 l 78.6143 166.7379 l s 1 w 33.442 166.7379 m 78.6143 166.7379 l 78.6143 188.8088 l 168.959 188.8088 l 168.959 166.7379 l 214.1313 166.7379 l 214.1313 78.4539 l 168.959 78.4539 l 168.959 56.383 l 78.6143 56.383 l 78.6143 78.4539 l 33.442 78.4539 l 33.442 166.7379 l s 56.0282 166.7379 m 56.0282 78.4539 l S 191.5451 166.7379 m 191.5451 78.4539 l S 0.3 w 10 M 67.3212 122.5959 m S 72.9677 128.1137 m S 67.3212 122.5959 m S 61.6746 128.1137 m S 0 g 1 w 4 M 72.9677 128.1137 m F 72.9677 117.0782 m F 0 G 0.3 w 10 M 67.3212 122.5959 m S 61.6746 117.0782 m S 67.3212 122.5959 m S 72.9677 117.0782 m S 0 g 1 w 4 M 72.9677 117.0782 m F 0 G 0.3 w 10 M 180.2521 122.5959 m S 185.8986 128.1137 m S 180.2521 122.5959 m S 174.6055 128.1137 m S 0 g 1 w 4 M 185.8986 128.1137 m F 185.8986 117.0782 m F 0 G 0.3 w 10 M 180.2521 122.5959 m S 174.6055 117.0782 m S 180.2521 122.5959 m S 185.8986 117.0782 m S 0 g 1 w 4 M 185.8986 117.0782 m F 0 G 0.3 w 10 M 202.8382 122.5959 m S 208.4847 128.1137 m S 202.8382 122.5959 m S 197.1917 128.1137 m S 0 g 1 w 4 M 208.4847 128.1137 m F 208.4847 117.0782 m F 0 G 0.3 w 10 M 202.8382 122.5959 m S 197.1917 117.0782 m S 202.8382 122.5959 m S 208.4847 117.0782 m S 0 g 1 w 4 M 208.4847 117.0782 m F 0 G 0.3 w 10 M 123.7866 177.7733 m S 129.4331 183.2911 m S 123.7866 177.7733 m S 118.1401 183.2911 m S 0 g 1 w 4 M 129.4331 183.2911 m F 129.4331 172.2556 m F 0 G 0.3 w 10 M 123.7866 177.7733 m S 118.1401 172.2556 m S 123.7866 177.7733 m S 129.4331 172.2556 m S 0 g 1 w 4 M 129.4331 172.2556 m F 0 G 0.3 w 10 M 123.7866 67.4185 m S 129.4331 72.9362 m S 123.7866 67.4185 m S 118.1401 72.9362 m S 0 g 1 w 4 M 129.4331 72.9362 m F 129.4331 61.9008 m F 0 G 0.3 w 10 M 123.7866 67.4185 m S 118.1401 61.9008 m S 123.7866 67.4185 m S 129.4331 61.9008 m S 0 g 1 w 4 M 129.4331 61.9008 m F 0 G 0.3 w 10 M 225.4243 177.7733 m S 225.4243 166.7379 m S 214.1313 166.7379 m S 214.1313 177.7733 m S 219.7778 172.2556 m S 225.4243 188.8088 m S 225.4243 177.7733 m S 214.1313 177.7733 m S 214.1313 188.8088 m S 219.7778 183.2911 m S 0 g 1 w 4 M 219.7778 172.2556 m F 0 G 0.3 w 10 M 259.3035 177.7733 m S 259.3035 166.7379 m S 248.0105 166.7379 m S 248.0105 177.7733 m S 253.657 172.2556 m S 248.0105 188.8088 m S 248.0105 177.7733 m S 236.7174 177.7733 m S 236.7174 188.8088 m S 242.3639 183.2911 m S 259.3035 188.8088 m S 259.3035 177.7733 m S 248.0105 177.7733 m S 248.0105 188.8088 m S 253.657 183.2911 m S 248.0105 177.7733 m S 248.0105 166.7379 m S 236.7174 166.7379 m S 236.7174 177.7733 m S 242.3639 172.2556 m S 236.7174 177.7733 m S 236.7174 166.7379 m S 225.4243 166.7379 m S 225.4243 177.7733 m S 231.0708 172.2556 m S 236.7174 188.8088 m S 236.7174 177.7733 m S 225.4243 177.7733 m S 225.4243 188.8088 m S 231.0708 183.2911 m S 0 g 1 w 4 M 231.0708 172.2556 m F 253.657 172.2556 m F 0 G 0.3 w 10 M 270.5967 166.7379 m S 270.5967 155.7024 m S 259.3036 155.7024 m S 259.3036 166.7379 m S 264.9501 161.2201 m S 259.3036 177.7733 m S 259.3036 166.7379 m S 248.0105 166.7379 m S 248.0105 177.7733 m S 253.657 172.2556 m S 259.3036 188.8088 m S 259.3036 177.7733 m S 248.0105 177.7733 m S 248.0105 188.8088 m S 253.657 183.2911 m S 270.5967 188.8088 m S 270.5967 177.7733 m S 259.3036 177.7733 m S 259.3036 188.8088 m S 264.9501 183.2911 m S 270.5967 177.7733 m S 270.5967 166.7379 m S 259.3036 166.7379 m S 259.3036 177.7733 m S 264.9501 172.2556 m S 259.3036 166.7379 m S 259.3036 155.7024 m S 248.0105 155.7024 m S 248.0105 166.7379 m S 253.657 161.2201 m S 0 g 1 w 4 M 264.9501 183.2911 m F 264.9501 161.2201 m F 0 G 0.3 w 10 M 281.8897 188.8088 m S 281.8897 177.7733 m S 270.5967 177.7733 m S 270.5967 188.8088 m S 276.2432 183.2911 m S 304.4759 166.7379 m S 304.4759 155.7024 m S 293.1828 155.7024 m S 293.1828 166.7379 m S 298.8294 161.2201 m S 293.1828 177.7733 m S 293.1828 166.7379 m S 281.8897 166.7379 m S 281.8897 177.7733 m S 287.5363 172.2556 m S 293.1828 188.8088 m S 293.1828 177.7733 m S 281.8897 177.7733 m S 281.8897 188.8088 m S 287.5363 183.2911 m S 304.4759 188.8088 m S 304.4759 177.7733 m S 293.1828 177.7733 m S 293.1828 188.8088 m S 298.8294 183.2911 m S 304.4759 177.7733 m S 304.4759 166.7379 m S 293.1828 166.7379 m S 293.1828 177.7733 m S 298.8294 172.2556 m S 293.1828 166.7379 m S 293.1828 155.7024 m S 281.8897 155.7024 m S 281.8897 166.7379 m S 287.5363 161.2201 m S 281.8897 166.7379 m S 281.8897 155.7024 m S 270.5967 155.7024 m S 270.5967 166.7379 m S 276.2432 161.2201 m S 281.8897 177.7733 m S 281.8897 166.7379 m S 270.5967 166.7379 m S 270.5967 177.7733 m S 276.2432 172.2556 m S 0 g 1 w 4 M 276.2432 183.2911 m F 298.8294 183.2911 m F 276.2432 161.2201 m F 298.8294 161.2201 m F 0 G 0.3 w 10 M 315.769 188.8088 m S 315.769 177.7733 m S 304.4759 177.7733 m S 304.4759 188.8088 m S 310.1224 183.2911 m S 338.3552 166.7379 m S 338.3552 155.7024 m S 327.0621 155.7024 m S 327.0621 166.7379 m S 332.7086 161.2201 m S 327.0621 177.7733 m S 327.0621 166.7379 m S 315.769 166.7379 m S 315.769 177.7733 m S 321.4156 172.2556 m S 327.0621 188.8088 m S 327.0621 177.7733 m S 315.769 177.7733 m S 315.769 188.8088 m S 321.4156 183.2911 m S 338.3552 188.8088 m S 338.3552 177.7733 m S 327.0621 177.7733 m S 327.0621 188.8088 m S 332.7086 183.2911 m S 338.3552 177.7733 m S 338.3552 166.7379 m S 327.0621 166.7379 m S 327.0621 177.7733 m S 332.7086 172.2556 m S 327.0621 166.7379 m S 327.0621 155.7024 m S 315.769 155.7024 m S 315.769 166.7379 m S 321.4156 161.2201 m S 315.769 166.7379 m S 315.769 155.7024 m S 304.4759 155.7024 m S 304.4759 166.7379 m S 310.1224 161.2201 m S 315.769 177.7733 m S 315.769 166.7379 m S 304.4759 166.7379 m S 304.4759 177.7733 m S 310.1224 172.2556 m S 0 g 1 w 4 M 310.1224 183.2911 m F 332.7086 183.2911 m F 310.1224 161.2201 m F 332.7086 161.2201 m F 0 G 0.3 w 10 M 270.5967 133.6314 m S 270.5967 122.5959 m S 259.3036 122.5959 m S 259.3036 133.6314 m S 264.9501 128.1137 m S 259.3036 144.6668 m S 259.3036 133.6314 m S 248.0105 133.6314 m S 248.0105 144.6668 m S 253.657 139.1492 m S 259.3036 155.7024 m S 259.3036 144.6668 m S 248.0105 144.6668 m S 248.0105 155.7024 m S 253.657 150.1846 m S 270.5967 155.7024 m S 270.5967 144.6668 m S 259.3036 144.6668 m S 259.3036 155.7024 m S 264.9501 150.1846 m S 270.5967 144.6668 m S 270.5967 133.6314 m S 259.3036 133.6314 m S 259.3036 144.6668 m S 264.9501 139.1492 m S 259.3036 133.6314 m S 259.3036 122.5959 m S 248.0105 122.5959 m S 248.0105 133.6314 m S 253.657 128.1137 m S 0 g 1 w 4 M 264.9501 150.1846 m F 264.9501 128.1137 m F 0 G 0.3 w 10 M 281.8897 155.7024 m S 281.8897 144.6668 m S 270.5967 144.6668 m S 270.5967 155.7024 m S 276.2432 150.1846 m S 304.4759 133.6314 m S 304.4759 122.5959 m S 293.1828 122.5959 m S 293.1828 133.6314 m S 298.8294 128.1137 m S 293.1828 144.6668 m S 293.1828 133.6314 m S 281.8897 133.6314 m S 281.8897 144.6668 m S 287.5363 139.1492 m S 293.1828 155.7024 m S 293.1828 144.6668 m S 281.8897 144.6668 m S 281.8897 155.7024 m S 287.5363 150.1846 m S 304.4759 155.7024 m S 304.4759 144.6668 m S 293.1828 144.6668 m S 293.1828 155.7024 m S 298.8294 150.1846 m S 304.4759 144.6668 m S 304.4759 133.6314 m S 293.1828 133.6314 m S 293.1828 144.6668 m S 298.8294 139.1492 m S 293.1828 133.6314 m S 293.1828 122.5959 m S 281.8897 122.5959 m S 281.8897 133.6314 m S 287.5363 128.1137 m S 281.8897 133.6314 m S 281.8897 122.5959 m S 270.5967 122.5959 m S 270.5967 133.6314 m S 276.2432 128.1137 m S 281.8897 144.6668 m S 281.8897 133.6314 m S 270.5967 133.6314 m S 270.5967 144.6668 m S 276.2432 139.1492 m S 0 g 1 w 4 M 276.2432 150.1846 m F 298.8294 150.1846 m F 276.2432 128.1137 m F 298.8294 128.1137 m F 0 G 0.3 w 10 M 315.769 155.7024 m S 315.769 144.6668 m S 304.4759 144.6668 m S 304.4759 155.7024 m S 310.1224 150.1846 m S 338.3552 133.6314 m S 338.3552 122.5959 m S 327.0621 122.5959 m S 327.0621 133.6314 m S 332.7086 128.1137 m S 327.0621 144.6668 m S 327.0621 133.6314 m S 315.769 133.6314 m S 315.769 144.6668 m S 321.4156 139.1492 m S 327.0621 155.7024 m S 327.0621 144.6668 m S 315.769 144.6668 m S 315.769 155.7024 m S 321.4156 150.1846 m S 338.3552 155.7024 m S 338.3552 144.6668 m S 327.0621 144.6668 m S 327.0621 155.7024 m S 332.7086 150.1846 m S 338.3552 144.6668 m S 338.3552 133.6314 m S 327.0621 133.6314 m S 327.0621 144.6668 m S 332.7086 139.1492 m S 327.0621 133.6314 m S 327.0621 122.5959 m S 315.769 122.5959 m S 315.769 133.6314 m S 321.4156 128.1137 m S 315.769 133.6314 m S 315.769 122.5959 m S 304.4759 122.5959 m S 304.4759 133.6314 m S 310.1224 128.1137 m S 315.769 144.6668 m S 315.769 133.6314 m S 304.4759 133.6314 m S 304.4759 144.6668 m S 310.1224 139.1492 m S 0 g 1 w 4 M 310.1224 150.1846 m F 332.7086 150.1846 m F 310.1224 128.1137 m F 332.7086 128.1137 m F 264.9501 117.0782 m F 276.2432 117.0782 m F 298.8294 117.0782 m F 310.1224 117.0782 m F 332.7086 117.0782 m F 0 G 0.3 w 10 M 259.3036 111.5604 m S 248.0105 111.5604 m S 259.3036 122.5959 m S 259.3036 111.5604 m S 248.0105 111.5604 m S 248.0105 122.5959 m S 253.657 117.0782 m S 270.5967 122.5959 m S 270.5967 111.5604 m S 259.3036 111.5604 m S 259.3036 122.5959 m S 264.9501 117.0782 m S 270.5967 111.5604 m S 259.3036 111.5604 m S 0 g 1 w 4 M 264.9501 117.0782 m F 0 G 0.3 w 10 M 281.8897 122.5959 m S 281.8897 111.5604 m S 270.5967 111.5604 m S 270.5967 122.5959 m S 276.2432 117.0782 m S 293.1828 111.5604 m S 281.8897 111.5604 m S 293.1828 122.5959 m S 293.1828 111.5604 m S 281.8897 111.5604 m S 281.8897 122.5959 m S 287.5363 117.0782 m S 304.4759 122.5959 m S 304.4759 111.5604 m S 293.1828 111.5604 m S 293.1828 122.5959 m S 298.8294 117.0782 m S 304.4759 111.5604 m S 293.1828 111.5604 m S 281.8897 111.5604 m S 270.5967 111.5604 m S 0 g 1 w 4 M 276.2432 117.0782 m F 298.8294 117.0782 m F 0 G 0.3 w 10 M 315.769 122.5959 m S 315.769 111.5604 m S 304.4759 111.5604 m S 304.4759 122.5959 m S 310.1224 117.0782 m S 327.0621 111.5604 m S 315.769 111.5604 m S 327.0621 122.5959 m S 327.0621 111.5604 m S 315.769 111.5604 m S 315.769 122.5959 m S 321.4156 117.0782 m S 338.3552 122.5959 m S 338.3552 111.5604 m S 327.0621 111.5604 m S 327.0621 122.5959 m S 332.7086 117.0782 m S 338.3552 111.5604 m S 327.0621 111.5604 m S 315.769 111.5604 m S 304.4759 111.5604 m S 0 g 1 w 4 M 310.1224 117.0782 m F 332.7086 117.0782 m F 0 G 264.9501 172.2556 m S 264.9501 139.1492 m S 0.3 w 10 M 349.6483 155.7024 m S 349.6483 166.7379 m S 349.6483 177.7733 m S 349.6483 166.7379 m S 338.3552 166.7379 m S 338.3552 177.7733 m S 344.0017 172.2556 m S 349.6483 188.8088 m S 349.6483 177.7733 m S 338.3552 177.7733 m S 338.3552 188.8088 m S 344.0017 183.2911 m S 349.6483 177.7733 m S 349.6483 188.8088 m S 349.6483 166.7379 m S 349.6483 177.7733 m S 349.6483 166.7379 m S 349.6483 155.7024 m S 338.3552 155.7024 m S 338.3552 166.7379 m S 344.0017 161.2201 m S 349.6483 122.5959 m S 349.6483 133.6314 m S 349.6483 144.6668 m S 349.6483 133.6314 m S 338.3552 133.6314 m S 338.3552 144.6668 m S 344.0017 139.1492 m S 349.6483 155.7024 m S 349.6483 144.6668 m S 338.3552 144.6668 m S 338.3552 155.7024 m S 344.0017 150.1846 m S 349.6483 144.6668 m S 349.6483 155.7024 m S 349.6483 133.6314 m S 349.6483 144.6668 m S 349.6483 133.6314 m S 349.6483 122.5959 m S 338.3552 122.5959 m S 338.3552 133.6314 m S 344.0017 128.1137 m S 349.6483 111.5604 m S 338.3552 111.5604 m S 349.6483 122.5959 m S 349.6483 111.5604 m S 338.3552 111.5604 m S 338.3552 122.5959 m S 344.0017 117.0782 m S 349.6483 111.5604 m S 349.6483 122.5959 m S 349.6483 111.5604 m S 2 w 4 M 293.1828 166.7379 m S 1 w 248.0105 111.5604 m 248.0105 166.7379 l 293.1828 166.7379 l 293.1828 188.8088 l 349.6483 188.8088 l S 270.5967 166.7379 m S 0.3 w 10 M 281.8897 122.5959 m S 287.5363 128.1137 m S 281.8897 122.5959 m S 276.2432 128.1137 m S 0 g 1 w 4 M 287.5363 128.1137 m F 287.5363 117.0782 m F 0 G 0.3 w 10 M 281.8897 122.5959 m S 276.2432 117.0782 m S 281.8897 122.5959 m S 287.5363 117.0782 m S 0 g 1 w 4 M 287.5363 117.0782 m F 0 G 0.3 w 10 M 338.3552 177.7733 m S 344.0017 183.2911 m S 338.3552 177.7733 m S 332.7086 183.2911 m S 0 g 1 w 4 M 344.0017 183.2911 m F 344.0017 172.2556 m F 0 G 0.3 w 10 M 338.3552 177.7733 m S 332.7086 172.2556 m S 338.3552 177.7733 m S 344.0017 172.2556 m S 0 g 1 w 4 M 344.0017 172.2556 m F 0 G 315.769 188.8088 m 315.769 111.5604 l S 338.3552 188.8088 m 338.3552 111.5604 l S 248.0105 144.6668 m 349.6483 144.6668 l S 248.0105 122.5959 m 349.6483 122.5959 l S 270.5967 166.7379 m 270.5967 111.5604 l S 2 w 293.1828 111.5604 m 293.1828 166.7379 l 349.6483 166.7379 l S 0.3 w 10 M 276.2432 150.1846 m S 0 g 1 w 4 M 276.2432 150.1846 m F 0 G 0.3 w 10 M 276.2432 150.1846 m S 0 g 1 w 4 M 276.2432 150.1846 m F 0 G 0.3 w 10 M 276.2432 150.1846 m S 276.2432 150.1846 m S 276.2432 150.1846 m S 0 g 1 w 4 M 276.2432 150.1846 m F 0 G 0.3 w 10 M 276.2432 150.1846 m S 276.2432 150.1846 m S 1 g 1 w 4 M 273.2675 150.1846 m 273.2675 148.5851 274.5998 147.2885 276.2432 147.2885 c 277.8866 147.2885 279.2189 148.5851 279.2189 150.1846 c F 279.2189 150.1846 m 279.2189 151.7841 277.8866 153.0807 276.2432 153.0807 c 274.5998 153.0807 273.2675 151.7841 273.2675 150.1846 c F 276.2432 150.1846 m F 0 G 0.3 w 10 M 276.2432 150.1846 m S 0 g 1 w 4 M 276.2432 150.1846 m F 0 G 0.3 w 10 M 276.2432 150.1846 m S 276.2432 150.1846 m S 0 g 1 w 4 M 275.7059 149.6545 m 275.7059 147.8786 L 276.7804 147.8786 L 276.7804 149.6545 L 278.5556 149.6489 L 278.5556 150.7204 L 276.7804 150.7149 L 276.7804 152.4908 L 275.7059 152.4908 L 275.7059 150.7149 L 273.9308 150.7204 L 273.9308 149.6489 L 275.7059 149.6545 L f 0 G 0.3 w 10 M 276.2432 139.1492 m S 0 g 1 w 4 M 276.2432 139.1492 m F 0 G 0.3 w 10 M 276.2432 139.1492 m S 0 g 1 w 4 M 276.2432 139.1492 m F 0 G 0.3 w 10 M 276.2432 139.1492 m S 276.2432 139.1492 m S 276.2432 139.1492 m S 0 g 1 w 4 M 276.2432 139.1492 m F 0 G 0.3 w 10 M 276.2432 139.1492 m S 276.2432 139.1492 m S 1 g 1 w 4 M 273.2675 139.1492 m 273.2675 137.5497 274.5998 136.253 276.2432 136.253 c 277.8866 136.253 279.2189 137.5497 279.2189 139.1492 c F 279.2189 139.1492 m 279.2189 140.7486 277.8866 142.0453 276.2432 142.0453 c 274.5998 142.0453 273.2675 140.7486 273.2675 139.1492 c F 276.2432 139.1492 m F 0 G 0.3 w 10 M 276.2432 139.1492 m S 0 g 1 w 4 M 276.2432 139.1492 m F 0 G 0.3 w 10 M 276.2432 139.1492 m S 276.2432 139.1492 m S 0 g 1 w 4 M 275.7059 138.619 m 275.7059 136.8431 L 276.7804 136.8431 L 276.7804 138.619 L 278.5556 138.6134 L 278.5556 139.685 L 276.7804 139.6795 L 276.7804 141.4553 L 275.7059 141.4553 L 275.7059 139.6795 L 273.9308 139.685 L 273.9308 138.6134 L 275.7059 138.619 L f 0 G 0.3 w 10 M 276.2432 161.2201 m S 0 g 1 w 4 M 276.2432 161.2201 m F 0 G 0.3 w 10 M 276.2432 161.2201 m S 0 g 1 w 4 M 276.2432 161.2201 m F 0 G 0.3 w 10 M 276.2432 161.2201 m S 276.2432 161.2201 m S 276.2432 161.2201 m S 0 g 1 w 4 M 276.2432 161.2201 m F 0 G 0.3 w 10 M 276.2432 161.2201 m S 276.2432 161.2201 m S 1 g 1 w 4 M 273.2675 161.2201 m 273.2675 159.6206 274.5998 158.324 276.2432 158.324 c 277.8866 158.324 279.2189 159.6206 279.2189 161.2201 c F 279.2189 161.2201 m 279.2189 162.8196 277.8866 164.1162 276.2432 164.1162 c 274.5998 164.1162 273.2675 162.8196 273.2675 161.2201 c F 276.2432 161.2201 m F 0 G 0.3 w 10 M 276.2432 161.2201 m S 0 g 1 w 4 M 276.2432 161.2201 m F 0 G 0.3 w 10 M 276.2432 161.2201 m S 276.2432 161.2201 m S 0 g 1 w 4 M 275.7059 160.6899 m 275.7059 158.9141 L 276.7804 158.9141 L 276.7804 160.6899 L 278.5556 160.6844 L 278.5556 161.7559 L 276.7804 161.7504 L 276.7804 163.5263 L 275.7059 163.5263 L 275.7059 161.7504 L 273.9308 161.7559 L 273.9308 160.6844 L 275.7059 160.6899 L f 0 G 0.3 w 10 M 287.5363 161.2201 m S 0 g 1 w 4 M 287.5363 161.2201 m F 0 G 0.3 w 10 M 287.5363 161.2201 m S 0 g 1 w 4 M 287.5363 161.2201 m F 0 G 0.3 w 10 M 287.5363 161.2201 m S 287.5363 161.2201 m S 287.5363 161.2201 m S 0 g 1 w 4 M 287.5363 161.2201 m F 0 G 0.3 w 10 M 287.5363 161.2201 m S 287.5363 161.2201 m S 1 g 1 w 4 M 284.5606 161.2201 m 284.5606 159.6206 285.8929 158.324 287.5363 158.324 c 289.1797 158.324 290.512 159.6206 290.512 161.2201 c F 290.512 161.2201 m 290.512 162.8196 289.1797 164.1162 287.5363 164.1162 c 285.8929 164.1162 284.5606 162.8196 284.5606 161.2201 c F 287.5363 161.2201 m F 0 G 0.3 w 10 M 287.5363 161.2201 m S 0 g 1 w 4 M 287.5363 161.2201 m F 0 G 0.3 w 10 M 287.5363 161.2201 m S 287.5363 161.2201 m S 0 g 1 w 4 M 286.9991 160.6899 m 286.9991 158.9141 L 288.0736 158.9141 L 288.0736 160.6899 L 289.8487 160.6844 L 289.8487 161.7559 L 288.0736 161.7504 L 288.0736 163.5263 L 286.9991 163.5263 L 286.9991 161.7504 L 285.2238 161.7559 L 285.2238 160.6844 L 286.9991 160.6899 L f 0 G 0.3 w 10 M 287.5363 128.1137 m S 276.2432 128.1137 m S 0 g 1 w 4 M 276.2432 128.1137 m F 0 G 0.3 w 10 M 276.2432 128.1137 m S 0 g 1 w 4 M 276.2432 128.1137 m F 0 G 0.3 w 10 M 276.2432 128.1137 m S 0 g 1 w 4 M 276.2432 128.1137 m F 0 G 0.3 w 10 M 276.2432 128.1137 m S 276.2432 128.1137 m S 276.2432 128.1137 m S 0 g 1 w 4 M 276.2432 128.1137 m F 0 G 0.3 w 10 M 276.2432 128.1137 m S 276.2432 128.1137 m S 1 g 1 w 4 M 273.2675 128.1137 m 273.2675 126.5142 274.5998 125.2176 276.2432 125.2176 c 277.8866 125.2176 279.2189 126.5142 279.2189 128.1137 c F 279.2189 128.1137 m 279.2189 129.7132 277.8866 131.0098 276.2432 131.0098 c 274.5998 131.0098 273.2675 129.7132 273.2675 128.1137 c F 276.2432 128.1137 m F 0 G 0.3 w 10 M 276.2432 128.1137 m S 0 g 1 w 4 M 276.2432 128.1137 m F 0 G 0.3 w 10 M 276.2432 128.1137 m S 276.2432 128.1137 m S 0 g 1 w 4 M 275.7059 127.5835 m 275.7059 125.8076 L 276.7804 125.8076 L 276.7804 127.5835 L 278.5556 127.5779 L 278.5556 128.6495 L 276.7804 128.6439 L 276.7804 130.4198 L 275.7059 130.4198 L 275.7059 128.6439 L 273.9308 128.6495 L 273.9308 127.5779 L 275.7059 127.5835 L f 0 G 0.3 w 10 M 287.5363 128.1137 m S 0 g 1 w 4 M 287.5363 128.1137 m F 0 G 0.3 w 10 M 287.5363 128.1137 m S 0 g 1 w 4 M 287.5363 128.1137 m F 0 G 0.3 w 10 M 287.5363 128.1137 m S 287.5363 128.1137 m S 287.5363 128.1137 m S 0 g 1 w 4 M 287.5363 128.1137 m F 0 G 0.3 w 10 M 287.5363 128.1137 m S 287.5363 128.1137 m S 1 g 1 w 4 M 284.5606 128.1137 m 284.5606 126.5142 285.8929 125.2176 287.5363 125.2176 c 289.1797 125.2176 290.512 126.5142 290.512 128.1137 c F 290.512 128.1137 m 290.512 129.7132 289.1797 131.0098 287.5363 131.0098 c 285.8929 131.0098 284.5606 129.7132 284.5606 128.1137 c F 287.5363 128.1137 m F 0 G 0.3 w 10 M 287.5363 128.1137 m S 0 g 1 w 4 M 287.5363 128.1137 m F 0 G 0.3 w 10 M 287.5363 128.1137 m S 287.5363 128.1137 m S 0 g 1 w 4 M 286.9991 127.5835 m 286.9991 125.8076 L 288.0736 125.8076 L 288.0736 127.5835 L 289.8487 127.5779 L 289.8487 128.6495 L 288.0736 128.6439 L 288.0736 130.4198 L 286.9991 130.4198 L 286.9991 128.6439 L 285.2238 128.6495 L 285.2238 127.5779 L 286.9991 127.5835 L f 0 G 0.3 w 10 M 310.1224 128.1137 m S 298.8294 128.1137 m S 0 g 1 w 4 M 298.8294 128.1137 m F 0 G 0.3 w 10 M 298.8294 128.1137 m S 0 g 1 w 4 M 298.8294 128.1137 m F 0 G 0.3 w 10 M 298.8294 128.1137 m S 0 g 1 w 4 M 298.8294 128.1137 m F 0 G 0.3 w 10 M 298.8294 128.1137 m S 298.8294 128.1137 m S 298.8294 128.1137 m S 0 g 1 w 4 M 298.8294 128.1137 m F 0 G 0.3 w 10 M 298.8294 128.1137 m S 298.8294 128.1137 m S 1 g 1 w 4 M 295.8536 128.1137 m 295.8536 126.5142 297.186 125.2176 298.8294 125.2176 c 300.4728 125.2176 301.8051 126.5142 301.8051 128.1137 c F 301.8051 128.1137 m 301.8051 129.7132 300.4728 131.0098 298.8294 131.0098 c 297.186 131.0098 295.8536 129.7132 295.8536 128.1137 c F 298.8294 128.1137 m F 0 G 0.3 w 10 M 298.8294 128.1137 m S 0 g 1 w 4 M 298.8294 128.1137 m F 0 G 0.3 w 10 M 298.8294 128.1137 m S 298.8294 128.1137 m S 0 g 1 w 4 M 298.2921 127.5835 m 298.2921 125.8076 L 299.3666 125.8076 L 299.3666 127.5835 L 301.1418 127.5779 L 301.1418 128.6495 L 299.3666 128.6439 L 299.3666 130.4198 L 298.2921 130.4198 L 298.2921 128.6439 L 296.5169 128.6495 L 296.5169 127.5779 L 298.2921 127.5835 L f 0 G 0.3 w 10 M 310.1224 128.1137 m S 0 g 1 w 4 M 310.1224 128.1137 m F 0 G 0.3 w 10 M 310.1224 128.1137 m S 0 g 1 w 4 M 310.1224 128.1137 m F 0 G 0.3 w 10 M 310.1224 128.1137 m S 310.1224 128.1137 m S 310.1224 128.1137 m S 0 g 1 w 4 M 310.1224 128.1137 m F 0 G 0.3 w 10 M 310.1224 128.1137 m S 310.1224 128.1137 m S 1 g 1 w 4 M 307.1468 128.1137 m 307.1468 126.5142 308.4791 125.2176 310.1224 125.2176 c 311.7659 125.2176 313.0982 126.5142 313.0982 128.1137 c F 313.0982 128.1137 m 313.0982 129.7132 311.7659 131.0098 310.1224 131.0098 c 308.4791 131.0098 307.1468 129.7132 307.1468 128.1137 c F 310.1224 128.1137 m F 0 G 0.3 w 10 M 310.1224 128.1137 m S 0 g 1 w 4 M 310.1224 128.1137 m F 0 G 0.3 w 10 M 310.1224 128.1137 m S 310.1224 128.1137 m S 0 g 1 w 4 M 309.5852 127.5835 m 309.5852 125.8076 L 310.6597 125.8076 L 310.6597 127.5835 L 312.4349 127.5779 L 312.4349 128.6495 L 310.6597 128.6439 L 310.6597 130.4198 L 309.5852 130.4198 L 309.5852 128.6439 L 307.8101 128.6495 L 307.8101 127.5779 L 309.5852 127.5835 L f 0 G 0.3 w 10 M 332.7087 128.1137 m S 321.4156 128.1137 m S 0 g 1 w 4 M 321.4156 128.1137 m F 0 G 0.3 w 10 M 321.4156 128.1137 m S 0 g 1 w 4 M 321.4156 128.1137 m F 0 G 0.3 w 10 M 321.4156 128.1137 m S 0 g 1 w 4 M 321.4156 128.1137 m F 0 G 0.3 w 10 M 321.4156 128.1137 m S 321.4156 128.1137 m S 321.4156 128.1137 m S 0 g 1 w 4 M 321.4156 128.1137 m F 0 G 0.3 w 10 M 321.4156 128.1137 m S 321.4156 128.1137 m S 1 g 1 w 4 M 318.4398 128.1137 m 318.4398 126.5142 319.7721 125.2176 321.4156 125.2176 c 323.0589 125.2176 324.3912 126.5142 324.3912 128.1137 c F 324.3912 128.1137 m 324.3912 129.7132 323.0589 131.0098 321.4156 131.0098 c 319.7721 131.0098 318.4398 129.7132 318.4398 128.1137 c F 321.4156 128.1137 m F 0 G 0.3 w 10 M 321.4156 128.1137 m S 0 g 1 w 4 M 321.4156 128.1137 m F 0 G 0.3 w 10 M 321.4156 128.1137 m S 321.4156 128.1137 m S 0 g 1 w 4 M 320.8783 127.5835 m 320.8783 125.8076 L 321.9528 125.8076 L 321.9528 127.5835 L 323.728 127.5779 L 323.728 128.6495 L 321.9528 128.6439 L 321.9528 130.4198 L 320.8783 130.4198 L 320.8783 128.6439 L 319.1031 128.6495 L 319.1031 127.5779 L 320.8783 127.5835 L f 0 G 0.3 w 10 M 332.7087 128.1137 m S 0 g 1 w 4 M 332.7087 128.1137 m F 0 G 0.3 w 10 M 332.7087 128.1137 m S 0 g 1 w 4 M 332.7087 128.1137 m F 0 G 0.3 w 10 M 332.7087 128.1137 m S 332.7087 128.1137 m S 332.7087 128.1137 m S 0 g 1 w 4 M 332.7087 128.1137 m F 0 G 0.3 w 10 M 332.7087 128.1137 m S 332.7087 128.1137 m S 1 g 1 w 4 M 329.7329 128.1137 m 329.7329 126.5142 331.0653 125.2176 332.7087 125.2176 c 334.352 125.2176 335.6843 126.5142 335.6843 128.1137 c F 335.6843 128.1137 m 335.6843 129.7132 334.352 131.0098 332.7087 131.0098 c 331.0653 131.0098 329.7329 129.7132 329.7329 128.1137 c F 332.7087 128.1137 m F 0 G 0.3 w 10 M 332.7087 128.1137 m S 0 g 1 w 4 M 332.7087 128.1137 m F 0 G 0.3 w 10 M 332.7087 128.1137 m S 332.7087 128.1137 m S 0 g 1 w 4 M 332.1714 127.5835 m 332.1714 125.8076 L 333.2459 125.8076 L 333.2459 127.5835 L 335.0211 127.5779 L 335.0211 128.6495 L 333.2459 128.6439 L 333.2459 130.4198 L 332.1714 130.4198 L 332.1714 128.6439 L 330.3963 128.6495 L 330.3963 127.5779 L 332.1714 127.5835 L f 0 G 0.3 w 10 M 310.1224 161.2201 m S 298.8294 161.2201 m S 0 g 1 w 4 M 298.8294 161.2201 m F 0 G 0.3 w 10 M 298.8294 161.2201 m S 0 g 1 w 4 M 298.8294 161.2201 m F 0 G 0.3 w 10 M 298.8294 161.2201 m S 0 g 1 w 4 M 298.8294 161.2201 m F 0 G 0.3 w 10 M 298.8294 161.2201 m S 298.8294 161.2201 m S 298.8294 161.2201 m S 0 g 1 w 4 M 298.8294 161.2201 m F 0 G 0.3 w 10 M 298.8294 161.2201 m S 298.8294 161.2201 m S 1 g 1 w 4 M 295.8536 161.2201 m 295.8536 159.6206 297.186 158.324 298.8294 158.324 c 300.4728 158.324 301.8051 159.6206 301.8051 161.2201 c F 301.8051 161.2201 m 301.8051 162.8196 300.4728 164.1162 298.8294 164.1162 c 297.186 164.1162 295.8536 162.8196 295.8536 161.2201 c F 298.8294 161.2201 m F 0 G 0.3 w 10 M 298.8294 161.2201 m S 0 g 1 w 4 M 298.8294 161.2201 m F 0 G 0.3 w 10 M 298.8294 161.2201 m S 298.8294 161.2201 m S 0 g 1 w 4 M 298.2921 160.6899 m 298.2921 158.9141 L 299.3666 158.9141 L 299.3666 160.6899 L 301.1418 160.6844 L 301.1418 161.7559 L 299.3666 161.7504 L 299.3666 163.5263 L 298.2921 163.5263 L 298.2921 161.7504 L 296.5169 161.7559 L 296.5169 160.6844 L 298.2921 160.6899 L f 0 G 0.3 w 10 M 310.1224 161.2201 m S 0 g 1 w 4 M 310.1224 161.2201 m F 0 G 0.3 w 10 M 310.1224 161.2201 m S 0 g 1 w 4 M 310.1224 161.2201 m F 0 G 0.3 w 10 M 310.1224 161.2201 m S 310.1224 161.2201 m S 310.1224 161.2201 m S 0 g 1 w 4 M 310.1224 161.2201 m F 0 G 0.3 w 10 M 310.1224 161.2201 m S 310.1224 161.2201 m S 1 g 1 w 4 M 307.1468 161.2201 m 307.1468 159.6206 308.4791 158.324 310.1224 158.324 c 311.7659 158.324 313.0982 159.6206 313.0982 161.2201 c F 313.0982 161.2201 m 313.0982 162.8196 311.7659 164.1162 310.1224 164.1162 c 308.4791 164.1162 307.1468 162.8196 307.1468 161.2201 c F 310.1224 161.2201 m F 0 G 0.3 w 10 M 310.1224 161.2201 m S 0 g 1 w 4 M 310.1224 161.2201 m F 0 G 0.3 w 10 M 310.1224 161.2201 m S 310.1224 161.2201 m S 0 g 1 w 4 M 309.5852 160.6899 m 309.5852 158.9141 L 310.6597 158.9141 L 310.6597 160.6899 L 312.4349 160.6844 L 312.4349 161.7559 L 310.6597 161.7504 L 310.6597 163.5263 L 309.5852 163.5263 L 309.5852 161.7504 L 307.8101 161.7559 L 307.8101 160.6844 L 309.5852 160.6899 L f 0 G 0.3 w 10 M 332.7087 161.2201 m S 321.4156 161.2201 m S 0 g 1 w 4 M 321.4156 161.2201 m F 0 G 0.3 w 10 M 321.4156 161.2201 m S 0 g 1 w 4 M 321.4156 161.2201 m F 0 G 0.3 w 10 M 321.4156 161.2201 m S 0 g 1 w 4 M 321.4156 161.2201 m F 0 G 0.3 w 10 M 321.4156 161.2201 m S 321.4156 161.2201 m S 321.4156 161.2201 m S 0 g 1 w 4 M 321.4156 161.2201 m F 0 G 0.3 w 10 M 321.4156 161.2201 m S 321.4156 161.2201 m S 1 g 1 w 4 M 318.4398 161.2201 m 318.4398 159.6206 319.7721 158.324 321.4156 158.324 c 323.0589 158.324 324.3912 159.6206 324.3912 161.2201 c F 324.3912 161.2201 m 324.3912 162.8196 323.0589 164.1162 321.4156 164.1162 c 319.7721 164.1162 318.4398 162.8196 318.4398 161.2201 c F 321.4156 161.2201 m F 0 G 0.3 w 10 M 321.4156 161.2201 m S 0 g 1 w 4 M 321.4156 161.2201 m F 0 G 0.3 w 10 M 321.4156 161.2201 m S 321.4156 161.2201 m S 0 g 1 w 4 M 320.8783 160.6899 m 320.8783 158.9141 L 321.9528 158.9141 L 321.9528 160.6899 L 323.728 160.6844 L 323.728 161.7559 L 321.9528 161.7504 L 321.9528 163.5263 L 320.8783 163.5263 L 320.8783 161.7504 L 319.1031 161.7559 L 319.1031 160.6844 L 320.8783 160.6899 L f 0 G 0.3 w 10 M 332.7087 161.2201 m S 0 g 1 w 4 M 332.7087 161.2201 m F 0 G 0.3 w 10 M 332.7087 161.2201 m S 0 g 1 w 4 M 332.7087 161.2201 m F 0 G 0.3 w 10 M 332.7087 161.2201 m S 332.7087 161.2201 m S 332.7087 161.2201 m S 0 g 1 w 4 M 332.7087 161.2201 m F 0 G 0.3 w 10 M 332.7087 161.2201 m S 332.7087 161.2201 m S 1 g 1 w 4 M 329.7329 161.2201 m 329.7329 159.6206 331.0653 158.324 332.7087 158.324 c 334.352 158.324 335.6843 159.6206 335.6843 161.2201 c F 335.6843 161.2201 m 335.6843 162.8196 334.352 164.1162 332.7087 164.1162 c 331.0653 164.1162 329.7329 162.8196 329.7329 161.2201 c F 332.7087 161.2201 m F 0 G 0.3 w 10 M 332.7087 161.2201 m S 0 g 1 w 4 M 332.7087 161.2201 m F 0 G 0.3 w 10 M 332.7087 161.2201 m S 332.7087 161.2201 m S 0 g 1 w 4 M 332.1714 160.6899 m 332.1714 158.9141 L 333.2459 158.9141 L 333.2459 160.6899 L 335.0211 160.6844 L 335.0211 161.7559 L 333.2459 161.7504 L 333.2459 163.5263 L 332.1714 163.5263 L 332.1714 161.7504 L 330.3963 161.7559 L 330.3963 160.6844 L 332.1714 160.6899 L f 0 G 0.3 w 10 M 310.1224 172.2556 m S 298.8294 172.2556 m S 0 g 1 w 4 M 298.8294 172.2556 m F 0 G 0.3 w 10 M 298.8294 172.2556 m S 0 g 1 w 4 M 298.8294 172.2556 m F 0 G 0.3 w 10 M 298.8294 172.2556 m S 0 g 1 w 4 M 298.8294 172.2556 m F 0 G 0.3 w 10 M 298.8294 172.2556 m S 298.8294 172.2556 m S 298.8294 172.2556 m S 0 g 1 w 4 M 298.8294 172.2556 m F 0 G 0.3 w 10 M 298.8294 172.2556 m S 298.8294 172.2556 m S 1 g 1 w 4 M 295.8536 172.2556 m 295.8536 170.6562 297.186 169.3595 298.8294 169.3595 c 300.4728 169.3595 301.8051 170.6562 301.8051 172.2556 c F 301.8051 172.2556 m 301.8051 173.8551 300.4728 175.1517 298.8294 175.1517 c 297.186 175.1517 295.8536 173.8551 295.8536 172.2556 c F 298.8294 172.2556 m F 0 G 0.3 w 10 M 298.8294 172.2556 m S 0 g 1 w 4 M 298.8294 172.2556 m F 0 G 0.3 w 10 M 298.8294 172.2556 m S 298.8294 172.2556 m S 0 g 1 w 4 M 298.2921 171.7255 m 298.2921 169.9496 L 299.3666 169.9496 L 299.3666 171.7255 L 301.1418 171.7199 L 301.1418 172.7915 L 299.3666 172.786 L 299.3666 174.5618 L 298.2921 174.5618 L 298.2921 172.786 L 296.5169 172.7915 L 296.5169 171.7199 L 298.2921 171.7255 L f 0 G 0.3 w 10 M 310.1224 172.2556 m S 0 g 1 w 4 M 310.1224 172.2556 m F 0 G 0.3 w 10 M 310.1224 172.2556 m S 0 g 1 w 4 M 310.1224 172.2556 m F 0 G 0.3 w 10 M 310.1224 172.2556 m S 310.1224 172.2556 m S 310.1224 172.2556 m S 0 g 1 w 4 M 310.1224 172.2556 m F 0 G 0.3 w 10 M 310.1224 172.2556 m S 310.1224 172.2556 m S 1 g 1 w 4 M 307.1468 172.2556 m 307.1468 170.6562 308.4791 169.3595 310.1224 169.3595 c 311.7659 169.3595 313.0982 170.6562 313.0982 172.2556 c F 313.0982 172.2556 m 313.0982 173.8551 311.7659 175.1517 310.1224 175.1517 c 308.4791 175.1517 307.1468 173.8551 307.1468 172.2556 c F 310.1224 172.2556 m F 0 G 0.3 w 10 M 310.1224 172.2556 m S 0 g 1 w 4 M 310.1224 172.2556 m F 0 G 0.3 w 10 M 310.1224 172.2556 m S 310.1224 172.2556 m S 0 g 1 w 4 M 309.5852 171.7255 m 309.5852 169.9496 L 310.6597 169.9496 L 310.6597 171.7255 L 312.4349 171.7199 L 312.4349 172.7915 L 310.6597 172.786 L 310.6597 174.5618 L 309.5852 174.5618 L 309.5852 172.786 L 307.8101 172.7915 L 307.8101 171.7199 L 309.5852 171.7255 L f 0 G 0.3 w 10 M 310.1224 183.2911 m S 298.8294 183.2911 m S 0 g 1 w 4 M 298.8294 183.2911 m F 0 G 0.3 w 10 M 298.8294 183.2911 m S 0 g 1 w 4 M 298.8294 183.2911 m F 0 G 0.3 w 10 M 298.8294 183.2911 m S 0 g 1 w 4 M 298.8294 183.2911 m F 0 G 0.3 w 10 M 298.8294 183.2911 m S 298.8294 183.2911 m S 298.8294 183.2911 m S 0 g 1 w 4 M 298.8294 183.2911 m F 0 G 0.3 w 10 M 298.8294 183.2911 m S 298.8294 183.2911 m S 1 g 1 w 4 M 295.8536 183.2911 m 295.8536 181.6916 297.186 180.395 298.8294 180.395 c 300.4728 180.395 301.8051 181.6916 301.8051 183.2911 c F 301.8051 183.2911 m 301.8051 184.8906 300.4728 186.1872 298.8294 186.1872 c 297.186 186.1872 295.8536 184.8906 295.8536 183.2911 c F 298.8294 183.2911 m F 0 G 0.3 w 10 M 298.8294 183.2911 m S 0 g 1 w 4 M 298.8294 183.2911 m F 0 G 0.3 w 10 M 298.8294 183.2911 m S 298.8294 183.2911 m S 0 g 1 w 4 M 298.2921 182.7609 m 298.2921 180.985 L 299.3666 180.985 L 299.3666 182.7609 L 301.1418 182.7554 L 301.1418 183.8269 L 299.3666 183.8214 L 299.3666 185.5973 L 298.2921 185.5973 L 298.2921 183.8214 L 296.5169 183.8269 L 296.5169 182.7554 L 298.2921 182.7609 L f 0 G 0.3 w 10 M 310.1224 183.2911 m S 0 g 1 w 4 M 310.1224 183.2911 m F 0 G 0.3 w 10 M 310.1224 183.2911 m S 0 g 1 w 4 M 310.1224 183.2911 m F 0 G 0.3 w 10 M 310.1224 183.2911 m S 310.1224 183.2911 m S 310.1224 183.2911 m S 0 g 1 w 4 M 310.1224 183.2911 m F 0 G 0.3 w 10 M 310.1224 183.2911 m S 310.1224 183.2911 m S 1 g 1 w 4 M 307.1468 183.2911 m 307.1468 181.6916 308.4791 180.395 310.1224 180.395 c 311.7659 180.395 313.0982 181.6916 313.0982 183.2911 c F 313.0982 183.2911 m 313.0982 184.8906 311.7659 186.1872 310.1224 186.1872 c 308.4791 186.1872 307.1468 184.8906 307.1468 183.2911 c F 310.1224 183.2911 m F 0 G 0.3 w 10 M 310.1224 183.2911 m S 0 g 1 w 4 M 310.1224 183.2911 m F 0 G 0.3 w 10 M 310.1224 183.2911 m S 310.1224 183.2911 m S 0 g 1 w 4 M 309.5852 182.7609 m 309.5852 180.985 L 310.6597 180.985 L 310.6597 182.7609 L 312.4349 182.7554 L 312.4349 183.8269 L 310.6597 183.8214 L 310.6597 185.5973 L 309.5852 185.5973 L 309.5852 183.8214 L 307.8101 183.8269 L 307.8101 182.7554 L 309.5852 182.7609 L f 0 G 0.3 w 10 M 332.7087 183.2911 m S 321.4156 183.2911 m S 0 g 1 w 4 M 321.4156 183.2911 m F 0 G 0.3 w 10 M 321.4156 183.2911 m S 0 g 1 w 4 M 321.4156 183.2911 m F 0 G 0.3 w 10 M 321.4156 183.2911 m S 0 g 1 w 4 M 321.4156 183.2911 m F 0 G 0.3 w 10 M 321.4156 183.2911 m S 321.4156 183.2911 m S 321.4156 183.2911 m S 0 g 1 w 4 M 321.4156 183.2911 m F 0 G 0.3 w 10 M 321.4156 183.2911 m S 321.4156 183.2911 m S 1 g 1 w 4 M 318.4398 183.2911 m 318.4398 181.6916 319.7721 180.395 321.4156 180.395 c 323.0589 180.395 324.3912 181.6916 324.3912 183.2911 c F 324.3912 183.2911 m 324.3912 184.8906 323.0589 186.1872 321.4156 186.1872 c 319.7721 186.1872 318.4398 184.8906 318.4398 183.2911 c F 321.4156 183.2911 m F 0 G 0.3 w 10 M 321.4156 183.2911 m S 0 g 1 w 4 M 321.4156 183.2911 m F 0 G 0.3 w 10 M 321.4156 183.2911 m S 321.4156 183.2911 m S 0 g 1 w 4 M 320.8783 182.7609 m 320.8783 180.985 L 321.9528 180.985 L 321.9528 182.7609 L 323.728 182.7554 L 323.728 183.8269 L 321.9528 183.8214 L 321.9528 185.5973 L 320.8783 185.5973 L 320.8783 183.8214 L 319.1031 183.8269 L 319.1031 182.7554 L 320.8783 182.7609 L f 0 G 0.3 w 10 M 332.7087 183.2911 m S 0 g 1 w 4 M 332.7087 183.2911 m F 0 G 0.3 w 10 M 332.7087 183.2911 m S 0 g 1 w 4 M 332.7087 183.2911 m F 0 G 0.3 w 10 M 332.7087 183.2911 m S 332.7087 183.2911 m S 332.7087 183.2911 m S 0 g 1 w 4 M 332.7087 183.2911 m F 0 G 0.3 w 10 M 332.7087 183.2911 m S 332.7087 183.2911 m S 1 g 1 w 4 M 329.7329 183.2911 m 329.7329 181.6916 331.0653 180.395 332.7087 180.395 c 334.352 180.395 335.6843 181.6916 335.6843 183.2911 c F 335.6843 183.2911 m 335.6843 184.8906 334.352 186.1872 332.7087 186.1872 c 331.0653 186.1872 329.7329 184.8906 329.7329 183.2911 c F 332.7087 183.2911 m F 0 G 0.3 w 10 M 332.7087 183.2911 m S 0 g 1 w 4 M 332.7087 183.2911 m F 0 G 0.3 w 10 M 332.7087 183.2911 m S 332.7087 183.2911 m S 0 g 1 w 4 M 332.1714 182.7609 m 332.1714 180.985 L 333.2459 180.985 L 333.2459 182.7609 L 335.0211 182.7554 L 335.0211 183.8269 L 333.2459 183.8214 L 333.2459 185.5973 L 332.1714 185.5973 L 332.1714 183.8214 L 330.3963 183.8269 L 330.3963 182.7554 L 332.1714 182.7609 L f 0 G 0.3 w 10 M 332.7087 172.2556 m S 321.4156 172.2556 m S 0 g 1 w 4 M 321.4156 172.2556 m F 0 G 0.3 w 10 M 321.4156 172.2556 m S 0 g 1 w 4 M 321.4156 172.2556 m F 0 G 0.3 w 10 M 321.4156 172.2556 m S 0 g 1 w 4 M 321.4156 172.2556 m F 0 G 0.3 w 10 M 321.4156 172.2556 m S 321.4156 172.2556 m S 321.4156 172.2556 m S 0 g 1 w 4 M 321.4156 172.2556 m F 0 G 0.3 w 10 M 321.4156 172.2556 m S 321.4156 172.2556 m S 1 g 1 w 4 M 318.4398 172.2556 m 318.4398 170.6562 319.7721 169.3595 321.4156 169.3595 c 323.0589 169.3595 324.3912 170.6562 324.3912 172.2556 c F 324.3912 172.2556 m 324.3912 173.8551 323.0589 175.1517 321.4156 175.1517 c 319.7721 175.1517 318.4398 173.8551 318.4398 172.2556 c F 321.4156 172.2556 m F 0 G 0.3 w 10 M 321.4156 172.2556 m S 0 g 1 w 4 M 321.4156 172.2556 m F 0 G 0.3 w 10 M 321.4156 172.2556 m S 321.4156 172.2556 m S 0 g 1 w 4 M 320.8783 171.7255 m 320.8783 169.9496 L 321.9528 169.9496 L 321.9528 171.7255 L 323.728 171.7199 L 323.728 172.7915 L 321.9528 172.786 L 321.9528 174.5618 L 320.8783 174.5618 L 320.8783 172.786 L 319.1031 172.7915 L 319.1031 171.7199 L 320.8783 171.7255 L f 0 G 0.3 w 10 M 332.7087 172.2556 m S 0 g 1 w 4 M 332.7087 172.2556 m F 0 G 0.3 w 10 M 332.7087 172.2556 m S 0 g 1 w 4 M 332.7087 172.2556 m F 0 G 0.3 w 10 M 332.7087 172.2556 m S 332.7087 172.2556 m S 332.7087 172.2556 m S 0 g 1 w 4 M 332.7087 172.2556 m F 0 G 0.3 w 10 M 332.7087 172.2556 m S 332.7087 172.2556 m S 1 g 1 w 4 M 329.7329 172.2556 m 329.7329 170.6562 331.0653 169.3595 332.7087 169.3595 c 334.352 169.3595 335.6843 170.6562 335.6843 172.2556 c F 335.6843 172.2556 m 335.6843 173.8551 334.352 175.1517 332.7087 175.1517 c 331.0653 175.1517 329.7329 173.8551 329.7329 172.2556 c F 332.7087 172.2556 m F 0 G 0.3 w 10 M 332.7087 172.2556 m S 0 g 1 w 4 M 332.7087 172.2556 m F 0 G 0.3 w 10 M 332.7087 172.2556 m S 332.7087 172.2556 m S 0 g 1 w 4 M 332.1714 171.7255 m 332.1714 169.9496 L 333.2459 169.9496 L 333.2459 171.7255 L 335.0211 171.7199 L 335.0211 172.7915 L 333.2459 172.786 L 333.2459 174.5618 L 332.1714 174.5618 L 332.1714 172.786 L 330.3963 172.7915 L 330.3963 171.7199 L 332.1714 171.7255 L f 0 G 0.3 w 10 M 264.9502 128.1137 m S 253.657 128.1137 m S 0 g 1 w 4 M 253.657 128.1137 m F 0 G 0.3 w 10 M 253.657 128.1137 m S 0 g 1 w 4 M 253.657 128.1137 m F 0 G 0.3 w 10 M 253.657 128.1137 m S 0 g 1 w 4 M 253.657 128.1137 m F 0 G 0.3 w 10 M 253.657 128.1137 m S 253.657 128.1137 m S 253.657 128.1137 m S 0 g 1 w 4 M 253.657 128.1137 m F 0 G 0.3 w 10 M 253.657 128.1137 m S 253.657 128.1137 m S 1 g 1 w 4 M 250.6814 128.1137 m 250.6814 126.5142 252.0137 125.2176 253.657 125.2176 c 255.3005 125.2176 256.6327 126.5142 256.6327 128.1137 c F 256.6327 128.1137 m 256.6327 129.7132 255.3005 131.0098 253.657 131.0098 c 252.0137 131.0098 250.6814 129.7132 250.6814 128.1137 c F 253.657 128.1137 m F 0 G 0.3 w 10 M 253.657 128.1137 m S 0 g 1 w 4 M 253.657 128.1137 m F 0 G 0.3 w 10 M 253.657 128.1137 m S 253.657 128.1137 m S 0 g 1 w 4 M 253.1198 127.5835 m 253.1198 125.8076 L 254.1942 125.8076 L 254.1942 127.5835 L 255.9695 127.5779 L 255.9695 128.6495 L 254.1942 128.6439 L 254.1942 130.4198 L 253.1198 130.4198 L 253.1198 128.6439 L 251.3446 128.6495 L 251.3446 127.5779 L 253.1198 127.5835 L f 0 G 0.3 w 10 M 264.9502 128.1137 m S 0 g 1 w 4 M 264.9502 128.1137 m F 0 G 0.3 w 10 M 264.9502 128.1137 m S 0 g 1 w 4 M 264.9502 128.1137 m F 0 G 0.3 w 10 M 264.9502 128.1137 m S 264.9502 128.1137 m S 264.9502 128.1137 m S 0 g 1 w 4 M 264.9502 128.1137 m F 0 G 0.3 w 10 M 264.9502 128.1137 m S 264.9502 128.1137 m S 1 g 1 w 4 M 261.9745 128.1137 m 261.9745 126.5142 263.3068 125.2176 264.9502 125.2176 c 266.5936 125.2176 267.9259 126.5142 267.9259 128.1137 c F 267.9259 128.1137 m 267.9259 129.7132 266.5936 131.0098 264.9502 131.0098 c 263.3068 131.0098 261.9745 129.7132 261.9745 128.1137 c F 264.9502 128.1137 m F 0 G 0.3 w 10 M 264.9502 128.1137 m S 0 g 1 w 4 M 264.9502 128.1137 m F 0 G 0.3 w 10 M 264.9502 128.1137 m S 264.9502 128.1137 m S 0 g 1 w 4 M 264.413 127.5835 m 264.413 125.8076 L 265.4874 125.8076 L 265.4874 127.5835 L 267.2626 127.5779 L 267.2626 128.6495 L 265.4874 128.6439 L 265.4874 130.4198 L 264.413 130.4198 L 264.413 128.6439 L 262.6377 128.6495 L 262.6377 127.5779 L 264.413 127.5835 L f 0 G 0.3 w 10 M 264.9502 139.1492 m S 253.657 139.1492 m S 0 g 1 w 4 M 253.657 139.1492 m F 0 G 0.3 w 10 M 253.657 139.1492 m S 0 g 1 w 4 M 253.657 139.1492 m F 0 G 0.3 w 10 M 253.657 139.1492 m S 0 g 1 w 4 M 253.657 139.1492 m F 0 G 0.3 w 10 M 253.657 139.1492 m S 253.657 139.1492 m S 253.657 139.1492 m S 0 g 1 w 4 M 253.657 139.1492 m F 0 G 0.3 w 10 M 253.657 139.1492 m S 253.657 139.1492 m S 1 g 1 w 4 M 250.6814 139.1492 m 250.6814 137.5497 252.0137 136.253 253.657 136.253 c 255.3005 136.253 256.6327 137.5497 256.6327 139.1492 c F 256.6327 139.1492 m 256.6327 140.7486 255.3005 142.0453 253.657 142.0453 c 252.0137 142.0453 250.6814 140.7486 250.6814 139.1492 c F 253.657 139.1492 m F 0 G 0.3 w 10 M 253.657 139.1492 m S 0 g 1 w 4 M 253.657 139.1492 m F 0 G 0.3 w 10 M 253.657 139.1492 m S 253.657 139.1492 m S 0 g 1 w 4 M 253.1198 138.619 m 253.1198 136.8431 L 254.1942 136.8431 L 254.1942 138.619 L 255.9695 138.6134 L 255.9695 139.685 L 254.1942 139.6795 L 254.1942 141.4553 L 253.1198 141.4553 L 253.1198 139.6795 L 251.3446 139.685 L 251.3446 138.6134 L 253.1198 138.619 L f 0 G 0.3 w 10 M 264.9502 139.1492 m S 0 g 1 w 4 M 264.9502 139.1492 m F 0 G 0.3 w 10 M 264.9502 139.1492 m S 0 g 1 w 4 M 264.9502 139.1492 m F 0 G 0.3 w 10 M 264.9502 139.1492 m S 264.9502 139.1492 m S 264.9502 139.1492 m S 0 g 1 w 4 M 264.9502 139.1492 m F 0 G 0.3 w 10 M 264.9502 139.1492 m S 264.9502 139.1492 m S 1 g 1 w 4 M 261.9745 139.1492 m 261.9745 137.5497 263.3068 136.253 264.9502 136.253 c 266.5936 136.253 267.9259 137.5497 267.9259 139.1492 c F 267.9259 139.1492 m 267.9259 140.7486 266.5936 142.0453 264.9502 142.0453 c 263.3068 142.0453 261.9745 140.7486 261.9745 139.1492 c F 264.9502 139.1492 m F 0 G 0.3 w 10 M 264.9502 139.1492 m S 0 g 1 w 4 M 264.9502 139.1492 m F 0 G 0.3 w 10 M 264.9502 139.1492 m S 264.9502 139.1492 m S 0 g 1 w 4 M 264.413 138.619 m 264.413 136.8431 L 265.4874 136.8431 L 265.4874 138.619 L 267.2626 138.6134 L 267.2626 139.685 L 265.4874 139.6795 L 265.4874 141.4553 L 264.413 141.4553 L 264.413 139.6795 L 262.6377 139.685 L 262.6377 138.6134 L 264.413 138.619 L f 0 G 0.3 w 10 M 264.9502 150.1846 m S 253.657 150.1846 m S 0 g 1 w 4 M 253.657 150.1846 m F 0 G 0.3 w 10 M 253.657 150.1846 m S 0 g 1 w 4 M 253.657 150.1846 m F 0 G 0.3 w 10 M 253.657 150.1846 m S 0 g 1 w 4 M 253.657 150.1846 m F 0 G 0.3 w 10 M 253.657 150.1846 m S 253.657 150.1846 m S 253.657 150.1846 m S 0 g 1 w 4 M 253.657 150.1846 m F 0 G 0.3 w 10 M 253.657 150.1846 m S 253.657 150.1846 m S 1 g 1 w 4 M 250.6814 150.1846 m 250.6814 148.5851 252.0137 147.2885 253.657 147.2885 c 255.3005 147.2885 256.6327 148.5851 256.6327 150.1846 c F 256.6327 150.1846 m 256.6327 151.7841 255.3005 153.0807 253.657 153.0807 c 252.0137 153.0807 250.6814 151.7841 250.6814 150.1846 c F 253.657 150.1846 m F 0 G 0.3 w 10 M 253.657 150.1846 m S 0 g 1 w 4 M 253.657 150.1846 m F 0 G 0.3 w 10 M 253.657 150.1846 m S 253.657 150.1846 m S 0 g 1 w 4 M 253.1198 149.6545 m 253.1198 147.8786 L 254.1942 147.8786 L 254.1942 149.6545 L 255.9695 149.6489 L 255.9695 150.7204 L 254.1942 150.7149 L 254.1942 152.4908 L 253.1198 152.4908 L 253.1198 150.7149 L 251.3446 150.7204 L 251.3446 149.6489 L 253.1198 149.6545 L f 0 G 0.3 w 10 M 264.9502 150.1846 m S 0 g 1 w 4 M 264.9502 150.1846 m F 0 G 0.3 w 10 M 264.9502 150.1846 m S 0 g 1 w 4 M 264.9502 150.1846 m F 0 G 0.3 w 10 M 264.9502 150.1846 m S 264.9502 150.1846 m S 264.9502 150.1846 m S 0 g 1 w 4 M 264.9502 150.1846 m F 0 G 0.3 w 10 M 264.9502 150.1846 m S 264.9502 150.1846 m S 1 g 1 w 4 M 261.9745 150.1846 m 261.9745 148.5851 263.3068 147.2885 264.9502 147.2885 c 266.5936 147.2885 267.9259 148.5851 267.9259 150.1846 c F 267.9259 150.1846 m 267.9259 151.7841 266.5936 153.0807 264.9502 153.0807 c 263.3068 153.0807 261.9745 151.7841 261.9745 150.1846 c F 264.9502 150.1846 m F 0 G 0.3 w 10 M 264.9502 150.1846 m S 0 g 1 w 4 M 264.9502 150.1846 m F 0 G 0.3 w 10 M 264.9502 150.1846 m S 264.9502 150.1846 m S 0 g 1 w 4 M 264.413 149.6545 m 264.413 147.8786 L 265.4874 147.8786 L 265.4874 149.6545 L 267.2626 149.6489 L 267.2626 150.7204 L 265.4874 150.7149 L 265.4874 152.4908 L 264.413 152.4908 L 264.413 150.7149 L 262.6377 150.7204 L 262.6377 149.6489 L 264.413 149.6545 L f 0 G 0.3 w 10 M 264.9502 161.2201 m S 253.657 161.2201 m S 0 g 1 w 4 M 253.657 161.2201 m F 0 G 0.3 w 10 M 253.657 161.2201 m S 0 g 1 w 4 M 253.657 161.2201 m F 0 G 0.3 w 10 M 253.657 161.2201 m S 0 g 1 w 4 M 253.657 161.2201 m F 0 G 0.3 w 10 M 253.657 161.2201 m S 253.657 161.2201 m S 253.657 161.2201 m S 0 g 1 w 4 M 253.657 161.2201 m F 0 G 0.3 w 10 M 253.657 161.2201 m S 253.657 161.2201 m S 1 g 1 w 4 M 250.6814 161.2201 m 250.6814 159.6206 252.0137 158.324 253.657 158.324 c 255.3005 158.324 256.6327 159.6206 256.6327 161.2201 c F 256.6327 161.2201 m 256.6327 162.8196 255.3005 164.1162 253.657 164.1162 c 252.0137 164.1162 250.6814 162.8196 250.6814 161.2201 c F 253.657 161.2201 m F 0 G 0.3 w 10 M 253.657 161.2201 m S 0 g 1 w 4 M 253.657 161.2201 m F 0 G 0.3 w 10 M 253.657 161.2201 m S 253.657 161.2201 m S 0 g 1 w 4 M 253.1198 160.6899 m 253.1198 158.9141 L 254.1942 158.9141 L 254.1942 160.6899 L 255.9695 160.6844 L 255.9695 161.7559 L 254.1942 161.7504 L 254.1942 163.5263 L 253.1198 163.5263 L 253.1198 161.7504 L 251.3446 161.7559 L 251.3446 160.6844 L 253.1198 160.6899 L f 0 G 0.3 w 10 M 264.9502 161.2201 m S 0 g 1 w 4 M 264.9502 161.2201 m F 0 G 0.3 w 10 M 264.9502 161.2201 m S 0 g 1 w 4 M 264.9502 161.2201 m F 0 G 0.3 w 10 M 264.9502 161.2201 m S 264.9502 161.2201 m S 264.9502 161.2201 m S 0 g 1 w 4 M 264.9502 161.2201 m F 0 G 0.3 w 10 M 264.9502 161.2201 m S 264.9502 161.2201 m S 1 g 1 w 4 M 261.9745 161.2201 m 261.9745 159.6206 263.3068 158.324 264.9502 158.324 c 266.5936 158.324 267.9259 159.6206 267.9259 161.2201 c F 267.9259 161.2201 m 267.9259 162.8196 266.5936 164.1162 264.9502 164.1162 c 263.3068 164.1162 261.9745 162.8196 261.9745 161.2201 c F 264.9502 161.2201 m F 0 G 0.3 w 10 M 264.9502 161.2201 m S 0 g 1 w 4 M 264.9502 161.2201 m F 0 G 0.3 w 10 M 264.9502 161.2201 m S 264.9502 161.2201 m S 0 g 1 w 4 M 264.413 160.6899 m 264.413 158.9141 L 265.4874 158.9141 L 265.4874 160.6899 L 267.2626 160.6844 L 267.2626 161.7559 L 265.4874 161.7504 L 265.4874 163.5263 L 264.413 163.5263 L 264.413 161.7504 L 262.6377 161.7559 L 262.6377 160.6844 L 264.413 160.6899 L f 0 G 0.3 w 10 M 112.4935 56.383 m S 135.0797 56.383 m S 123.7866 56.383 m S 123.7866 56.383 m S 112.4935 56.383 m S 281.8898 100.525 m S 281.8898 89.4895 m S 281.8898 111.5604 m S 281.8898 100.525 m S 304.4759 111.5604 m S 304.4759 100.525 m S 293.1828 100.525 m S 293.1828 111.5604 m S 298.8294 106.0427 m S 304.4759 100.525 m S 304.4759 89.4895 m S 293.1828 89.4895 m S 293.1828 100.525 m S 298.8294 95.0072 m S 293.1828 100.525 m S 293.1828 89.4895 m S 281.8898 89.4895 m S 281.8898 100.525 m S 287.5363 95.0072 m S 293.1828 111.5604 m S 293.1828 100.525 m S 281.8898 100.525 m S 281.8898 111.5604 m S 287.5363 106.0427 m S 0 g 1 w 4 M 287.5363 95.0072 m F 0 G 0.3 w 10 M 281.8898 78.454 m S 281.8898 67.4185 m S 281.8898 89.4895 m S 281.8898 78.454 m S 304.4759 89.4895 m S 304.4759 78.454 m S 293.1828 78.454 m S 293.1828 89.4895 m S 298.8294 83.9717 m S 304.4759 78.454 m S 304.4759 67.4185 m S 293.1828 67.4185 m S 293.1828 78.454 m S 298.8294 72.9363 m S 293.1828 78.454 m S 293.1828 67.4185 m S 281.8898 67.4185 m S 281.8898 78.454 m S 287.5363 72.9363 m S 293.1828 89.4895 m S 293.1828 78.454 m S 281.8898 78.454 m S 281.8898 89.4895 m S 287.5363 83.9717 m S 0 g 1 w 4 M 287.5363 72.9363 m F 0 G 0.3 w 10 M 281.8898 56.3831 m S 281.8898 67.4185 m S 281.8898 56.3831 m S 304.4759 67.4185 m S 304.4759 56.3831 m S 293.1828 56.3831 m S 293.1828 67.4185 m S 298.8294 61.9008 m S 304.4759 56.3831 m S 293.1828 56.3831 m S 293.1828 56.3831 m S 281.8898 56.3831 m S 293.1828 67.4185 m S 293.1828 56.3831 m S 281.8898 56.3831 m S 281.8898 67.4185 m S 287.5363 61.9008 m S 287.5363 150.1846 m S 1 w 4 M 287.5363 150.1846 m S 0.3 w 10 M 287.5363 150.1846 m S 0 g 1 w 4 M 287.5363 150.1846 m F 0 G 0.3 w 10 M 287.5363 150.1846 m S 0 g 1 w 4 M 287.5363 150.1846 m F 1 g 284.5606 150.1846 m 284.5606 148.5851 285.8929 147.2885 287.5363 147.2885 c 289.1797 147.2885 290.512 148.5851 290.512 150.1846 c F 290.512 150.1846 m 290.512 151.7841 289.1797 153.0807 287.5363 153.0807 c 285.8929 153.0807 284.5606 151.7841 284.5606 150.1846 c F 287.5363 150.1846 m F 0 G 0.3 w 10 M 287.5363 150.1846 m S 0 g 1 w 4 M 287.5363 150.1846 m F 0 G 0.3 w 10 M 287.5363 150.1846 m S 0 g 1 w 4 M 287.5363 150.1846 m F 286.9991 150.7149 m 285.2238 150.7204 L 285.2238 149.6489 L 286.9991 149.6544 L F 288.0736 149.6544 m 289.8487 149.6489 L 289.8487 150.7204 L 288.0736 150.7149 L F 285.2238 150.7204 m 289.8487 150.7204 l 289.8487 149.6489 l 285.2238 149.6489 l 285.2238 150.7204 l f 0 G 0.3 w 10 M 287.5363 139.1492 m S 1 w 4 M 287.5363 139.1492 m S 0.3 w 10 M 287.5363 139.1492 m S 0 g 1 w 4 M 287.5363 139.1492 m F 0 G 0.3 w 10 M 287.5363 139.1492 m S 0 g 1 w 4 M 287.5363 139.1492 m F 1 g 284.5606 139.1492 m 284.5606 137.5497 285.8929 136.253 287.5363 136.253 c 289.1797 136.253 290.512 137.5497 290.512 139.1492 c F 290.512 139.1492 m 290.512 140.7486 289.1797 142.0453 287.5363 142.0453 c 285.8929 142.0453 284.5606 140.7486 284.5606 139.1492 c F 287.5363 139.1492 m F 0 G 0.3 w 10 M 287.5363 139.1492 m S 0 g 1 w 4 M 287.5363 139.1492 m F 0 G 0.3 w 10 M 287.5363 139.1492 m S 0 g 1 w 4 M 287.5363 139.1492 m F 286.9991 139.6795 m 285.2238 139.685 L 285.2238 138.6134 L 286.9991 138.619 L F 288.0736 138.619 m 289.8487 138.6134 L 289.8487 139.685 L 288.0736 139.6795 L F 285.2238 139.685 m 289.8487 139.685 l 289.8487 138.6134 l 285.2238 138.6134 l 285.2238 139.685 l f 0 G 0.3 w 10 M 321.4156 150.1846 m S 1 w 4 M 321.4156 150.1846 m S 0.3 w 10 M 321.4156 150.1846 m S 0 g 1 w 4 M 321.4156 150.1846 m F 0 G 0.3 w 10 M 321.4156 150.1846 m S 0 g 1 w 4 M 321.4156 150.1846 m F 1 g 318.4398 150.1846 m 318.4398 148.5851 319.7721 147.2885 321.4156 147.2885 c 323.0589 147.2885 324.3912 148.5851 324.3912 150.1846 c F 324.3912 150.1846 m 324.3912 151.7841 323.0589 153.0807 321.4156 153.0807 c 319.7721 153.0807 318.4398 151.7841 318.4398 150.1846 c F 321.4156 150.1846 m F 0 G 0.3 w 10 M 321.4156 150.1846 m S 0 g 1 w 4 M 321.4156 150.1846 m F 0 G 0.3 w 10 M 321.4156 150.1846 m S 0 g 1 w 4 M 321.4156 150.1846 m F 320.8783 150.7149 m 319.1031 150.7204 L 319.1031 149.6489 L 320.8783 149.6544 L F 321.9528 149.6544 m 323.728 149.6489 L 323.728 150.7204 L 321.9528 150.7149 L F 319.1031 150.7204 m 323.728 150.7204 l 323.728 149.6489 l 319.1031 149.6489 l 319.1031 150.7204 l f 0 G 0.3 w 10 M 332.7086 150.1846 m S 1 w 4 M 332.7086 150.1846 m S 0.3 w 10 M 332.7086 150.1846 m S 0 g 1 w 4 M 332.7086 150.1846 m F 0 G 0.3 w 10 M 332.7086 150.1846 m S 0 g 1 w 4 M 332.7086 150.1846 m F 1 g 329.7329 150.1846 m 329.7329 148.5851 331.0652 147.2885 332.7086 147.2885 c 334.352 147.2885 335.6843 148.5851 335.6843 150.1846 c F 335.6843 150.1846 m 335.6843 151.7841 334.352 153.0807 332.7086 153.0807 c 331.0652 153.0807 329.7329 151.7841 329.7329 150.1846 c F 332.7086 150.1846 m F 0 G 0.3 w 10 M 332.7086 150.1846 m S 0 g 1 w 4 M 332.7086 150.1846 m F 0 G 0.3 w 10 M 332.7086 150.1846 m S 0 g 1 w 4 M 332.7086 150.1846 m F 332.1714 150.7149 m 330.3962 150.7204 L 330.3962 149.6489 L 332.1714 149.6544 L F 333.2458 149.6544 m 335.021 149.6489 L 335.021 150.7204 L 333.2458 150.7149 L F 330.3962 150.7204 m 335.021 150.7204 l 335.021 149.6489 l 330.3962 149.6489 l 330.3962 150.7204 l f 0 G 0.3 w 10 M 321.4156 139.1492 m S 1 w 4 M 321.4156 139.1492 m S 0.3 w 10 M 321.4156 139.1492 m S 0 g 1 w 4 M 321.4156 139.1492 m F 0 G 0.3 w 10 M 321.4156 139.1492 m S 0 g 1 w 4 M 321.4156 139.1492 m F 1 g 318.4398 139.1492 m 318.4398 137.5497 319.7721 136.253 321.4156 136.253 c 323.0589 136.253 324.3912 137.5497 324.3912 139.1492 c F 324.3912 139.1492 m 324.3912 140.7486 323.0589 142.0453 321.4156 142.0453 c 319.7721 142.0453 318.4398 140.7486 318.4398 139.1492 c F 321.4156 139.1492 m F 0 G 0.3 w 10 M 321.4156 139.1492 m S 0 g 1 w 4 M 321.4156 139.1492 m F 0 G 0.3 w 10 M 321.4156 139.1492 m S 0 g 1 w 4 M 321.4156 139.1492 m F 320.8783 139.6795 m 319.1031 139.685 L 319.1031 138.6134 L 320.8783 138.619 L F 321.9528 138.619 m 323.728 138.6134 L 323.728 139.685 L 321.9528 139.6795 L F 319.1031 139.685 m 323.728 139.685 l 323.728 138.6134 l 319.1031 138.6134 l 319.1031 139.685 l f 0 G 0.3 w 10 M 332.7086 139.1492 m S 1 w 4 M 332.7086 139.1492 m S 0.3 w 10 M 332.7086 139.1492 m S 0 g 1 w 4 M 332.7086 139.1492 m F 0 G 0.3 w 10 M 332.7086 139.1492 m S 0 g 1 w 4 M 332.7086 139.1492 m F 1 g 329.7329 139.1492 m 329.7329 137.5497 331.0652 136.253 332.7086 136.253 c 334.352 136.253 335.6843 137.5497 335.6843 139.1492 c F 335.6843 139.1492 m 335.6843 140.7486 334.352 142.0453 332.7086 142.0453 c 331.0652 142.0453 329.7329 140.7486 329.7329 139.1492 c F 332.7086 139.1492 m F 0 G 0.3 w 10 M 332.7086 139.1492 m S 0 g 1 w 4 M 332.7086 139.1492 m F 0 G 0.3 w 10 M 332.7086 139.1492 m S 0 g 1 w 4 M 332.7086 139.1492 m F 332.1714 139.6795 m 330.3962 139.685 L 330.3962 138.6134 L 332.1714 138.619 L F 333.2458 138.619 m 335.021 138.6134 L 335.021 139.685 L 333.2458 139.6795 L F 330.3962 139.685 m 335.021 139.685 l 335.021 138.6134 l 330.3962 138.6134 l 330.3962 139.685 l f 0 G 0.3 w 10 M 310.1224 150.1846 m S 1 w 4 M 310.1224 150.1846 m S 0.3 w 10 M 310.1224 150.1846 m S 0 g 1 w 4 M 310.1224 150.1846 m F 0 G 0.3 w 10 M 310.1224 150.1846 m S 0 g 1 w 4 M 310.1224 150.1846 m F 1 g 307.1467 150.1846 m 307.1467 148.5851 308.479 147.2885 310.1224 147.2885 c 311.7658 147.2885 313.0981 148.5851 313.0981 150.1846 c F 313.0981 150.1846 m 313.0981 151.7841 311.7658 153.0807 310.1224 153.0807 c 308.479 153.0807 307.1467 151.7841 307.1467 150.1846 c F 310.1224 150.1846 m F 0 G 0.3 w 10 M 310.1224 150.1846 m S 0 g 1 w 4 M 310.1224 150.1846 m F 0 G 0.3 w 10 M 310.1224 150.1846 m S 0 g 1 w 4 M 310.1224 150.1846 m F 309.5852 150.7149 m 307.81 150.7204 L 307.81 149.6489 L 309.5852 149.6544 L F 310.6597 149.6544 m 312.4349 149.6489 L 312.4349 150.7204 L 310.6597 150.7149 L F 307.81 150.7204 m 312.4349 150.7204 l 312.4349 149.6489 l 307.81 149.6489 l 307.81 150.7204 l f 0 G 0.3 w 10 M 298.8294 150.1846 m S 1 w 4 M 298.8294 150.1846 m S 0.3 w 10 M 298.8294 150.1846 m S 0 g 1 w 4 M 298.8294 150.1846 m F 0 G 0.3 w 10 M 298.8294 150.1846 m S 0 g 1 w 4 M 298.8294 150.1846 m F 1 g 295.8536 150.1846 m 295.8536 148.5851 297.186 147.2885 298.8294 147.2885 c 300.4727 147.2885 301.8051 148.5851 301.8051 150.1846 c F 301.8051 150.1846 m 301.8051 151.7841 300.4727 153.0807 298.8294 153.0807 c 297.186 153.0807 295.8536 151.7841 295.8536 150.1846 c F 298.8294 150.1846 m F 0 G 0.3 w 10 M 298.8294 150.1846 m S 0 g 1 w 4 M 298.8294 150.1846 m F 0 G 0.3 w 10 M 298.8294 150.1846 m S 0 g 1 w 4 M 298.8294 150.1846 m F 298.2921 150.7149 m 296.5169 150.7204 L 296.5169 149.6489 L 298.2921 149.6544 L F 299.3666 149.6544 m 301.1418 149.6489 L 301.1418 150.7204 L 299.3666 150.7149 L F 296.5169 150.7204 m 301.1418 150.7204 l 301.1418 149.6489 l 296.5169 149.6489 l 296.5169 150.7204 l f 0 G 0.3 w 10 M 298.8294 139.1492 m S 1 w 4 M 298.8294 139.1492 m S 0.3 w 10 M 298.8294 139.1492 m S 0 g 1 w 4 M 298.8294 139.1492 m F 0 G 0.3 w 10 M 298.8294 139.1492 m S 0 g 1 w 4 M 298.8294 139.1492 m F 1 g 295.8536 139.1492 m 295.8536 137.5497 297.186 136.253 298.8294 136.253 c 300.4727 136.253 301.8051 137.5497 301.8051 139.1492 c F 301.8051 139.1492 m 301.8051 140.7486 300.4727 142.0453 298.8294 142.0453 c 297.186 142.0453 295.8536 140.7486 295.8536 139.1492 c F 298.8294 139.1492 m F 0 G 0.3 w 10 M 298.8294 139.1492 m S 0 g 1 w 4 M 298.8294 139.1492 m F 0 G 0.3 w 10 M 298.8294 139.1492 m S 0 g 1 w 4 M 298.8294 139.1492 m F 298.2921 139.6795 m 296.5169 139.685 L 296.5169 138.6134 L 298.2921 138.619 L F 299.3666 138.619 m 301.1418 138.6134 L 301.1418 139.685 L 299.3666 139.6795 L F 296.5169 139.685 m 301.1418 139.685 l 301.1418 138.6134 l 296.5169 138.6134 l 296.5169 139.685 l f 0 G 0.3 w 10 M 310.1224 139.1492 m S 1 w 4 M 310.1224 139.1492 m S 0.3 w 10 M 310.1224 139.1492 m S 0 g 1 w 4 M 310.1224 139.1492 m F 0 G 0.3 w 10 M 310.1224 139.1492 m S 0 g 1 w 4 M 310.1224 139.1492 m F 1 g 307.1467 139.1492 m 307.1467 137.5497 308.479 136.253 310.1224 136.253 c 311.7658 136.253 313.0981 137.5497 313.0981 139.1492 c F 313.0981 139.1492 m 313.0981 140.7486 311.7658 142.0453 310.1224 142.0453 c 308.479 142.0453 307.1467 140.7486 307.1467 139.1492 c F 310.1224 139.1492 m F 0 G 0.3 w 10 M 310.1224 139.1492 m S 0 g 1 w 4 M 310.1224 139.1492 m F 0 G 0.3 w 10 M 310.1224 139.1492 m S 0 g 1 w 4 M 310.1224 139.1492 m F 309.5852 139.6795 m 307.81 139.685 L 307.81 138.6134 L 309.5852 138.619 L F 310.6597 138.619 m 312.4349 138.6134 L 312.4349 139.685 L 310.6597 139.6795 L F 307.81 139.685 m 312.4349 139.685 l 312.4349 138.6134 l 307.81 138.6134 l 307.81 139.685 l f 0 G 0.3 w 10 M 123.3364 68.1562 m S 123.3364 68.1562 m S 123.3364 68.1562 m S 123.3364 68.1562 m S 123.3364 68.1562 m S 123.3364 68.1562 m S 123.3364 68.1562 m S 123.3364 68.1562 m S u 0 g 1 w 4 M /_Symbol 12 14.5 0 0 z [1 0 0 1 117.957 63.6562]e (+4)t T U 0 G 0.3 w 10 M 123.7866 177.7734 m S 118.1401 172.2557 m S 123.7866 177.7734 m S 118.1401 183.2911 m S 0 g 1 w 4 M 118.1401 172.2557 m F 0 G 0.3 w 10 M 123.7866 177.7734 m S 129.4331 183.2911 m S 123.7866 177.7734 m S 129.4331 172.2557 m S 123.7866 177.7734 m S 129.4331 183.2911 m S 123.7866 177.7734 m S 118.1401 183.2911 m S 0 g 1 w 4 M 129.4331 183.2911 m F 129.4331 172.2557 m F 0 G 0.3 w 10 M 123.7866 177.7734 m S 118.1401 172.2557 m S 123.7866 177.7734 m S 129.4331 172.2557 m S 0 g 1 w 4 M 129.4331 172.2557 m F 0 G 0.3 w 10 M 123.3364 178.5111 m S 123.3364 178.5111 m S 123.3364 178.5111 m S 123.3364 178.5111 m S 123.3364 178.5111 m S 123.3364 178.5111 m S 123.3364 178.5111 m S 123.3364 178.5111 m S u 0 g 1 w 4 M /_Symbol 12 14.5 0 0 z [1 0 0 1 117.957 174.0111]e (+4)t T U 0 G 0.3 w 10 M 202.8383 122.596 m S 197.1917 117.0783 m S 202.8383 122.596 m S 197.1917 128.1137 m S 0 g 1 w 4 M 197.1917 117.0783 m F 0 G 0.3 w 10 M 202.8383 122.596 m S 208.4848 128.1137 m S 202.8383 122.596 m S 208.4848 117.0783 m S 202.8383 122.596 m S 208.4848 128.1137 m S 202.8383 122.596 m S 197.1917 128.1137 m S 0 g 1 w 4 M 208.4848 128.1137 m F 208.4848 117.0783 m F 0 G 0.3 w 10 M 202.8383 122.596 m S 197.1917 117.0783 m S 202.8383 122.596 m S 208.4848 117.0783 m S 0 g 1 w 4 M 208.4848 117.0783 m F 0 G 0.3 w 10 M 202.3881 123.3337 m S 202.3881 123.3337 m S 202.3881 123.3337 m S 202.3881 123.3337 m S 202.3881 123.3337 m S 202.3881 123.3337 m S 202.3881 123.3337 m S 202.3881 123.3337 m S u 0 g 1 w 4 M /_Symbol 12 14.5 0 0 z [1 0 0 1 197.0086 118.8337]e (+4)t T U 0 G 0.3 w 10 M 44.7351 122.596 m S 39.0886 117.0783 m S 44.7351 122.596 m S 39.0886 128.1137 m S 0 g 1 w 4 M 39.0886 117.0783 m F 0 G 0.3 w 10 M 44.7351 122.596 m S 50.3816 128.1137 m S 44.7351 122.596 m S 50.3816 117.0783 m S 44.7351 122.596 m S 50.3816 128.1137 m S 44.7351 122.596 m S 39.0886 128.1137 m S 0 g 1 w 4 M 50.3816 128.1137 m F 50.3816 117.0783 m F 0 G 0.3 w 10 M 44.7351 122.596 m S 39.0886 117.0783 m S 44.7351 122.596 m S 50.3816 117.0783 m S 0 g 1 w 4 M 50.3816 117.0783 m F 0 G 0.3 w 10 M 44.2849 123.3337 m S 44.2849 123.3337 m S 44.2849 123.3337 m S 44.2849 123.3337 m S 44.2849 123.3337 m S 44.2849 123.3337 m S 44.2849 123.3337 m S 44.2849 123.3337 m S u 0 g 1 w 4 M /_Symbol 12 14.5 0 0 z [1 0 0 1 38.9055 118.8337]e (+4)t T U 0 G 0.3 w 10 M 180.2521 122.596 m S 174.6055 117.0783 m S 180.2521 122.596 m S 174.6055 128.1137 m S 0 g 1 w 4 M 174.6055 117.0783 m F 0 G 0.3 w 10 M 180.2521 122.596 m S 185.8986 128.1137 m S 180.2521 122.596 m S 185.8986 117.0783 m S 180.2521 122.596 m S 185.8986 128.1137 m S 180.2521 122.596 m S 174.6055 128.1137 m S 0 g 1 w 4 M 185.8986 128.1137 m F 185.8986 117.0783 m F 0 G 0.3 w 10 M 180.2521 122.596 m S 174.6055 117.0783 m S 180.2521 122.596 m S 185.8986 117.0783 m S 0 g 1 w 4 M 185.8986 117.0783 m F 0 G 0.3 w 10 M 179.8019 123.3337 m S 179.8019 123.3337 m S 179.8019 123.3337 m S 179.8019 123.3337 m S 179.8019 123.3337 m S 179.8019 123.3337 m S 179.8019 123.3337 m S 179.8019 123.3337 m S u 0 g 1 w 4 M /_Symbol 12 14.5 0 0 z [1 0 0 1 174.4225 118.8337]e (+2)t T U 0 G 0.3 w 10 M 67.3212 122.596 m S 61.6746 117.0783 m S 67.3212 122.596 m S 61.6746 128.1137 m S 0 g 1 w 4 M 61.6746 117.0783 m F 0 G 0.3 w 10 M 67.3212 122.596 m S 72.9677 128.1137 m S 67.3212 122.596 m S 72.9677 117.0783 m S 67.3212 122.596 m S 72.9677 128.1137 m S 67.3212 122.596 m S 61.6746 128.1137 m S 0 g 1 w 4 M 72.9677 128.1137 m F 72.9677 117.0783 m F 0 G 0.3 w 10 M 67.3212 122.596 m S 61.6746 117.0783 m S 67.3212 122.596 m S 72.9677 117.0783 m S 0 g 1 w 4 M 72.9677 117.0783 m F 0 G 0.3 w 10 M 66.871 123.3337 m S 66.871 123.3337 m S 66.871 123.3337 m S 66.871 123.3337 m S 66.871 123.3337 m S 66.871 123.3337 m S 66.871 123.3337 m S 66.871 123.3337 m S u 0 g 1 w 4 M /_Symbol 12 14.5 0 0 z [1 0 0 1 61.4916 118.8337]e (+2)t T U 0 G 0.3 w 10 M 123.7866 56.383 m S 123.7866 56.383 m S 123.7866 41.5638 m S 123.7866 56.383 m S 131.39 48.9734 m S 123.7866 41.5638 m S 131.39 34.1542 m S 123.7866 41.5638 m S 116.1831 34.1542 m S 123.7866 56.383 m S 123.7866 41.5638 m S 116.1831 48.9734 m S 0 g 1 w 4 M 116.1831 34.1542 m F u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 117.4591 34.7982]e (\(a\))t T U U 0 G 0.3 w 10 M 293.1828 56.3831 m S 293.1828 56.3831 m S 293.1828 41.5639 m S 293.1828 56.3831 m S 300.7862 48.9735 m S 293.1828 41.5639 m S 300.7862 34.1543 m S 293.1828 41.5639 m S 285.5793 34.1543 m S 293.1828 56.3831 m S 293.1828 41.5639 m S 285.5793 48.9735 m S 0 g 1 w 4 M 285.5793 34.1543 m F u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 286.8553 34.7983]e (\(b\))t T U U showpage _E end %%EndDocument @endspecial 320 1210 a FQ(Figure)16 b(10:)22 b(Blo)q(c)o(k-spin)15 b(b)q(oundary)j(conditions)e(c)o(hosen)g(for)h(Step)f(2.)746 2289 y @beginspecial 28 @llx 31.500000 @lly 71 @urx 95.500000 @ury 1098 @rwi @setspecial %%BeginDocument: fig11.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n u 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 43.9957 68.8072 m S 43.9957 57.6928 m S 32.5906 57.6928 m S 32.5906 68.8072 m S 38.293 63.25 m S U u 43.9957 91.036 m S 43.9957 79.9216 m S 32.5906 79.9216 m S 32.5906 91.036 m S 38.293 85.4788 m S U u 43.9957 79.9216 m S 43.9957 68.8072 m S 32.5906 68.8072 m S 32.5906 79.9216 m S 38.293 74.3644 m S U u 55.4008 91.036 m S 55.4008 79.9216 m S 43.9957 79.9216 m S 43.9957 91.036 m S 49.6982 85.4788 m S U 66.806 57.6928 m S 66.806 68.8072 m S u 66.806 79.9216 m S 66.806 68.8072 m S 55.4008 68.8072 m S 55.4008 79.9216 m S 61.1034 74.3644 m S U u 66.806 91.036 m S 66.806 79.9216 m S 55.4008 79.9216 m S 55.4008 91.036 m S 61.1034 85.4788 m S U 66.806 79.9216 m S 66.806 91.036 m S 66.806 68.8072 m S 66.806 79.9216 m S u 66.806 68.8072 m S 66.806 57.6928 m S 55.4008 57.6928 m S 55.4008 68.8072 m S 61.1034 63.25 m S U u 55.4008 68.8072 m S 55.4008 57.6928 m S 43.9957 57.6928 m S 43.9957 68.8072 m S 49.6982 63.25 m S U u 55.4008 79.9216 m S 55.4008 68.8072 m S 43.9957 68.8072 m S 43.9957 79.9216 m S 49.6982 74.3644 m S U 0 g 1 w 4 M 49.6982 85.4788 m F 49.6982 63.25 m F 0 G 0.3 w 10 M 43.9957 35.464 m S 32.5906 35.464 m S u 43.9957 57.6928 m S 43.9957 46.5783 m S 32.5906 46.5783 m S 32.5906 57.6928 m S 38.293 52.1356 m S U u 43.9957 46.5783 m S 43.9957 35.464 m S 32.5906 35.464 m S 32.5906 46.5783 m S 38.293 41.0212 m S U u 55.4008 57.6928 m S 55.4008 46.5783 m S 43.9957 46.5783 m S 43.9957 57.6928 m S 49.6982 52.1356 m S U 66.806 35.464 m S u 66.806 46.5783 m S 66.806 35.464 m S 55.4008 35.464 m S 55.4008 46.5783 m S 61.1034 41.0212 m S U u 66.806 57.6928 m S 66.806 46.5783 m S 55.4008 46.5783 m S 55.4008 57.6928 m S 61.1034 52.1356 m S U 66.806 46.5783 m S 66.806 57.6928 m S 66.806 35.464 m S 66.806 46.5783 m S 66.806 35.464 m S 55.4008 35.464 m S 55.4008 35.464 m S 43.9957 35.464 m S u 55.4008 46.5783 m S 55.4008 35.464 m S 43.9957 35.464 m S 43.9957 46.5783 m S 49.6982 41.0212 m S U 0 g 1 w 4 M 49.6982 52.1356 m F 0 G 38.293 85.4788 m 61.1034 85.4788 l 61.1034 41.0212 l 38.293 41.0212 l 38.293 85.4788 l s 38.293 63.25 m 61.1034 63.25 l S 0.3 w 10 M 32.5906 68.8072 m S 1 w 4 M 32.5906 68.8072 m S 0.3 w 10 M 32.5906 68.8072 m S 0 g 1 w 4 M 32.5906 68.8072 m F 0 G 0.3 w 10 M 32.5906 68.8072 m S 0 g 1 w 4 M 32.5906 68.8072 m F 1 g 29.5853 68.8072 m 29.5853 67.1963 30.9308 65.8904 32.5906 65.8904 c 34.2502 65.8904 35.5957 67.1963 35.5957 68.8072 c F 35.5957 68.8072 m 35.5957 70.4181 34.2502 71.724 32.5906 71.724 c 30.9308 71.724 29.5853 70.4181 29.5853 68.8072 c F 32.5906 68.8072 m F 0 G 0.3 w 10 M 32.5906 68.8072 m S 0 g 1 w 4 M 32.5906 68.8072 m F 0 G 0.3 w 10 M 32.5906 68.8072 m S 0 g 1 w 4 M 32.5906 68.8072 m F 32.0479 69.3413 m 30.2551 69.3468 L 30.2551 68.2677 L 32.0479 68.2732 L F 33.1331 68.2732 m 34.9259 68.2677 L 34.9259 69.3468 L 33.1331 69.3413 L F 30.2551 69.3468 m 34.9259 69.3468 l 34.9259 68.2677 l 30.2551 68.2677 l 30.2551 69.3468 l f 0 G 0.3 w 10 M 32.5906 57.6928 m S 1 w 4 M 32.5906 57.6928 m S 0.3 w 10 M 32.5906 57.6928 m S 0 g 1 w 4 M 32.5906 57.6928 m F 0 G 0.3 w 10 M 32.5906 57.6928 m S 0 g 1 w 4 M 32.5906 57.6928 m F 1 g 29.5853 57.6928 m 29.5853 56.0819 30.9308 54.776 32.5906 54.776 c 34.2502 54.776 35.5957 56.0819 35.5957 57.6928 c F 35.5957 57.6928 m 35.5957 59.3037 34.2502 60.6096 32.5906 60.6096 c 30.9308 60.6096 29.5853 59.3037 29.5853 57.6928 c F 32.5906 57.6928 m F 0 G 0.3 w 10 M 32.5906 57.6928 m S 0 g 1 w 4 M 32.5906 57.6928 m F 0 G 0.3 w 10 M 32.5906 57.6928 m S 0 g 1 w 4 M 32.5906 57.6928 m F 32.0479 58.2269 m 30.2551 58.2324 L 30.2551 57.1532 L 32.0479 57.1588 L F 33.1331 57.1588 m 34.9259 57.1532 L 34.9259 58.2324 L 33.1331 58.2269 L F 30.2551 58.2324 m 34.9259 58.2324 l 34.9259 57.1532 l 30.2551 57.1532 l 30.2551 58.2324 l f 0 G 0.3 w 10 M 66.806 68.8072 m S 1 w 4 M 66.806 68.8072 m S 0.3 w 10 M 66.806 68.8072 m S 0 g 1 w 4 M 66.806 68.8072 m F 0 G 0.3 w 10 M 66.806 68.8072 m S 0 g 1 w 4 M 66.806 68.8072 m F 1 g 63.8008 68.8072 m 63.8008 67.1963 65.1463 65.8904 66.806 65.8904 c 68.4657 65.8904 69.8112 67.1963 69.8112 68.8072 c F 69.8112 68.8072 m 69.8112 70.4181 68.4657 71.724 66.806 71.724 c 65.1463 71.724 63.8008 70.4181 63.8008 68.8072 c F 66.806 68.8072 m F 0 G 0.3 w 10 M 66.806 68.8072 m S 0 g 1 w 4 M 66.806 68.8072 m F 0 G 0.3 w 10 M 66.806 68.8072 m S 0 g 1 w 4 M 66.806 68.8072 m F 66.2635 69.3413 m 64.4706 69.3468 L 64.4706 68.2677 L 66.2635 68.2732 L F 67.3486 68.2732 m 69.1414 68.2677 L 69.1414 69.3468 L 67.3486 69.3413 L F 64.4706 69.3468 m 69.1414 69.3468 l 69.1414 68.2677 l 64.4706 68.2677 l 64.4706 69.3468 l f 0 G 0.3 w 10 M 66.806 57.6928 m S 1 w 4 M 66.806 57.6928 m S 0.3 w 10 M 66.806 57.6928 m S 0 g 1 w 4 M 66.806 57.6928 m F 0 G 0.3 w 10 M 66.806 57.6928 m S 0 g 1 w 4 M 66.806 57.6928 m F 1 g 63.8008 57.6928 m 63.8008 56.0819 65.1463 54.776 66.806 54.776 c 68.4657 54.776 69.8112 56.0819 69.8112 57.6928 c F 69.8112 57.6928 m 69.8112 59.3037 68.4657 60.6096 66.806 60.6096 c 65.1463 60.6096 63.8008 59.3037 63.8008 57.6928 c F 66.806 57.6928 m F 0 G 0.3 w 10 M 66.806 57.6928 m S 0 g 1 w 4 M 66.806 57.6928 m F 0 G 0.3 w 10 M 66.806 57.6928 m S 0 g 1 w 4 M 66.806 57.6928 m F 66.2635 58.2269 m 64.4706 58.2324 L 64.4706 57.1532 L 66.2635 57.1588 L F 67.3486 57.1588 m 69.1414 57.1532 L 69.1414 58.2324 L 67.3486 58.2269 L F 64.4706 58.2324 m 69.1414 58.2324 l 69.1414 57.1532 l 64.4706 57.1532 l 64.4706 58.2324 l f 0 G 0.3 w 10 M 32.5906 79.9216 m S 0 g 1 w 4 M 32.5906 79.9216 m F 0 G 0.3 w 10 M 32.5906 79.9216 m S 0 g 1 w 4 M 32.5906 79.9216 m F 0 G 0.3 w 10 M 32.5906 79.9216 m S 32.5906 79.9216 m S 32.5906 79.9216 m S 0 g 1 w 4 M 32.5906 79.9216 m F 0 G 0.3 w 10 M 32.5906 79.9216 m S 32.5906 79.9216 m S 1 g 1 w 4 M 29.5853 79.9216 m 29.5853 78.3107 30.9308 77.0048 32.5906 77.0048 c 34.2502 77.0048 35.5957 78.3107 35.5957 79.9216 c F 35.5957 79.9216 m 35.5957 81.5325 34.2502 82.8384 32.5906 82.8384 c 30.9308 82.8384 29.5853 81.5325 29.5853 79.9216 c F 32.5906 79.9216 m F 0 G 0.3 w 10 M 32.5906 79.9216 m S 0 g 1 w 4 M 32.5906 79.9216 m F 0 G 0.3 w 10 M 32.5906 79.9216 m S 32.5906 79.9216 m S 0 g 1 w 4 M 32.0479 79.3877 m 32.0479 77.5991 L 33.1331 77.5991 L 33.1331 79.3877 L 34.9259 79.382 L 34.9259 80.4613 L 33.1331 80.4557 L 33.1331 82.2443 L 32.0479 82.2443 L 32.0479 80.4557 L 30.2551 80.4613 L 30.2551 79.382 L 32.0479 79.3877 L f 0 G 0.3 w 10 M 32.5906 46.5783 m S 0 g 1 w 4 M 32.5906 46.5783 m F 0 G 0.3 w 10 M 32.5906 46.5783 m S 0 g 1 w 4 M 32.5906 46.5783 m F 0 G 0.3 w 10 M 32.5906 46.5783 m S 32.5906 46.5783 m S 32.5906 46.5783 m S 0 g 1 w 4 M 32.5906 46.5783 m F 0 G 0.3 w 10 M 32.5906 46.5783 m S 32.5906 46.5783 m S 1 g 1 w 4 M 29.5853 46.5783 m 29.5853 44.9675 30.9308 43.6615 32.5906 43.6615 c 34.2502 43.6615 35.5957 44.9675 35.5957 46.5783 c F 35.5957 46.5783 m 35.5957 48.1893 34.2502 49.4951 32.5906 49.4951 c 30.9308 49.4951 29.5853 48.1893 29.5853 46.5783 c F 32.5906 46.5783 m F 0 G 0.3 w 10 M 32.5906 46.5783 m S 0 g 1 w 4 M 32.5906 46.5783 m F 0 G 0.3 w 10 M 32.5906 46.5783 m S 32.5906 46.5783 m S 0 g 1 w 4 M 32.0479 46.0444 m 32.0479 44.2559 L 33.1331 44.2559 L 33.1331 46.0444 L 34.9259 46.0388 L 34.9259 47.118 L 33.1331 47.1125 L 33.1331 48.901 L 32.0479 48.901 L 32.0479 47.1125 L 30.2551 47.118 L 30.2551 46.0388 L 32.0479 46.0444 L f 0 G 0.3 w 10 M 66.806 79.9216 m S 0 g 1 w 4 M 66.806 79.9216 m F 0 G 0.3 w 10 M 66.806 79.9216 m S 0 g 1 w 4 M 66.806 79.9216 m F 0 G 0.3 w 10 M 66.806 79.9216 m S 66.806 79.9216 m S 66.806 79.9216 m S 0 g 1 w 4 M 66.806 79.9216 m F 0 G 0.3 w 10 M 66.806 79.9216 m S 66.806 79.9216 m S 1 g 1 w 4 M 63.8008 79.9216 m 63.8008 78.3107 65.1463 77.0048 66.806 77.0048 c 68.4657 77.0048 69.8112 78.3107 69.8112 79.9216 c F 69.8112 79.9216 m 69.8112 81.5325 68.4657 82.8384 66.806 82.8384 c 65.1463 82.8384 63.8008 81.5325 63.8008 79.9216 c F 66.806 79.9216 m F 0 G 0.3 w 10 M 66.806 79.9216 m S 0 g 1 w 4 M 66.806 79.9216 m F 0 G 0.3 w 10 M 66.806 79.9216 m S 66.806 79.9216 m S 0 g 1 w 4 M 66.2635 79.3877 m 66.2635 77.5991 L 67.3486 77.5991 L 67.3486 79.3877 L 69.1414 79.382 L 69.1414 80.4613 L 67.3486 80.4557 L 67.3486 82.2443 L 66.2635 82.2443 L 66.2635 80.4557 L 64.4707 80.4613 L 64.4707 79.382 L 66.2635 79.3877 L f 0 G 0.3 w 10 M 66.806 46.5783 m S 0 g 1 w 4 M 66.806 46.5783 m F 0 G 0.3 w 10 M 66.806 46.5783 m S 0 g 1 w 4 M 66.806 46.5783 m F 0 G 0.3 w 10 M 66.806 46.5783 m S 66.806 46.5783 m S 66.806 46.5783 m S 0 g 1 w 4 M 66.806 46.5783 m F 0 G 0.3 w 10 M 66.806 46.5783 m S 66.806 46.5783 m S 1 g 1 w 4 M 63.8008 46.5783 m 63.8008 44.9675 65.1463 43.6615 66.806 43.6615 c 68.4657 43.6615 69.8112 44.9675 69.8112 46.5783 c F 69.8112 46.5783 m 69.8112 48.1893 68.4657 49.4951 66.806 49.4951 c 65.1463 49.4951 63.8008 48.1893 63.8008 46.5783 c F 66.806 46.5783 m F 0 G 0.3 w 10 M 66.806 46.5783 m S 0 g 1 w 4 M 66.806 46.5783 m F 0 G 0.3 w 10 M 66.806 46.5783 m S 66.806 46.5783 m S 0 g 1 w 4 M 66.2635 46.0444 m 66.2635 44.2559 L 67.3486 44.2559 L 67.3486 46.0444 L 69.1414 46.0388 L 69.1414 47.118 L 67.3486 47.1125 L 67.3486 48.901 L 66.2635 48.901 L 66.2635 47.1125 L 64.4707 47.118 L 64.4707 46.0388 L 66.2635 46.0444 L f 0 G 0.3 w 10 M 43.9957 91.036 m S 0 g 1 w 4 M 43.9957 91.036 m F 0 G 0.3 w 10 M 43.9957 91.036 m S 0 g 1 w 4 M 43.9957 91.036 m F 0 G 0.3 w 10 M 43.9957 91.036 m S 43.9957 91.036 m S 43.9957 91.036 m S 0 g 1 w 4 M 43.9957 91.036 m F 0 G 0.3 w 10 M 43.9957 91.036 m S 43.9957 91.036 m S 1 g 1 w 4 M 40.9905 91.036 m 40.9905 89.4251 42.336 88.1192 43.9957 88.1192 c 45.6554 88.1192 47.0009 89.4251 47.0009 91.036 c F 47.0009 91.036 m 47.0009 92.6469 45.6554 93.9528 43.9957 93.9528 c 42.336 93.9528 40.9905 92.6469 40.9905 91.036 c F 43.9957 91.036 m F 0 G 0.3 w 10 M 43.9957 91.036 m S 0 g 1 w 4 M 43.9957 91.036 m F 0 G 0.3 w 10 M 43.9957 91.036 m S 43.9957 91.036 m S 0 g 1 w 4 M 43.4531 90.5021 m 43.4531 88.7135 L 44.5382 88.7135 L 44.5382 90.5021 L 46.331 90.4964 L 46.331 91.5756 L 44.5382 91.5701 L 44.5382 93.3587 L 43.4531 93.3587 L 43.4531 91.5701 L 41.6603 91.5756 L 41.6603 90.4964 L 43.4531 90.5021 L f 0 G 0.3 w 10 M 55.4008 91.036 m S 0 g 1 w 4 M 55.4008 91.036 m F 0 G 0.3 w 10 M 55.4008 91.036 m S 0 g 1 w 4 M 55.4008 91.036 m F 0 G 0.3 w 10 M 55.4008 91.036 m S 55.4008 91.036 m S 55.4008 91.036 m S 0 g 1 w 4 M 55.4008 91.036 m F 0 G 0.3 w 10 M 55.4008 91.036 m S 55.4008 91.036 m S 1 g 1 w 4 M 52.3956 91.036 m 52.3956 89.4251 53.7411 88.1192 55.4008 88.1192 c 57.0605 88.1192 58.406 89.4251 58.406 91.036 c F 58.406 91.036 m 58.406 92.6469 57.0605 93.9528 55.4008 93.9528 c 53.7411 93.9528 52.3956 92.6469 52.3956 91.036 c F 55.4008 91.036 m F 0 G 0.3 w 10 M 55.4008 91.036 m S 0 g 1 w 4 M 55.4008 91.036 m F 0 G 0.3 w 10 M 55.4008 91.036 m S 55.4008 91.036 m S 0 g 1 w 4 M 54.8583 90.5021 m 54.8583 88.7135 L 55.9434 88.7135 L 55.9434 90.5021 L 57.7362 90.4964 L 57.7362 91.5756 L 55.9434 91.5701 L 55.9434 93.3587 L 54.8583 93.3587 L 54.8583 91.5701 L 53.0654 91.5756 L 53.0654 90.4964 L 54.8583 90.5021 L f 0 G 0.3 w 10 M 43.9957 35.464 m S 0 g 1 w 4 M 43.9957 35.464 m F 0 G 0.3 w 10 M 43.9957 35.464 m S 0 g 1 w 4 M 43.9957 35.464 m F 0 G 0.3 w 10 M 43.9957 35.464 m S 43.9957 35.464 m S 43.9957 35.464 m S 0 g 1 w 4 M 43.9957 35.464 m F 0 G 0.3 w 10 M 43.9957 35.464 m S 43.9957 35.464 m S 1 g 1 w 4 M 40.9905 35.464 m 40.9905 33.8531 42.336 32.5472 43.9957 32.5472 c 45.6554 32.5472 47.0009 33.8531 47.0009 35.464 c F 47.0009 35.464 m 47.0009 37.0749 45.6554 38.3808 43.9957 38.3808 c 42.336 38.3808 40.9905 37.0749 40.9905 35.464 c F 43.9957 35.464 m F 0 G 0.3 w 10 M 43.9957 35.464 m S 0 g 1 w 4 M 43.9957 35.464 m F 0 G 0.3 w 10 M 43.9957 35.464 m S 43.9957 35.464 m S 0 g 1 w 4 M 43.4531 34.93 m 43.4531 33.1415 L 44.5382 33.1415 L 44.5382 34.93 L 46.331 34.9244 L 46.331 36.0036 L 44.5382 35.9981 L 44.5382 37.7867 L 43.4531 37.7867 L 43.4531 35.9981 L 41.6603 36.0036 L 41.6603 34.9244 L 43.4531 34.93 L f 0 G 0.3 w 10 M 55.4008 35.464 m S 0 g 1 w 4 M 55.4008 35.464 m F 0 G 0.3 w 10 M 55.4008 35.464 m S 0 g 1 w 4 M 55.4008 35.464 m F 0 G 0.3 w 10 M 55.4008 35.464 m S 55.4008 35.464 m S 55.4008 35.464 m S 0 g 1 w 4 M 55.4008 35.464 m F 0 G 0.3 w 10 M 55.4008 35.464 m S 55.4008 35.464 m S 1 g 1 w 4 M 52.3956 35.464 m 52.3956 33.8531 53.7411 32.5472 55.4008 32.5472 c 57.0605 32.5472 58.406 33.8531 58.406 35.464 c F 58.406 35.464 m 58.406 37.0749 57.0605 38.3808 55.4008 38.3808 c 53.7411 38.3808 52.3956 37.0749 52.3956 35.464 c F 55.4008 35.464 m F 0 G 0.3 w 10 M 55.4008 35.464 m S 0 g 1 w 4 M 55.4008 35.464 m F 0 G 0.3 w 10 M 55.4008 35.464 m S 55.4008 35.464 m S 0 g 1 w 4 M 54.8583 34.93 m 54.8583 33.1415 L 55.9434 33.1415 L 55.9434 34.93 L 57.7362 34.9244 L 57.7362 36.0036 L 55.9434 35.9981 L 55.9434 37.7867 L 54.8583 37.7867 L 54.8583 35.9981 L 53.0654 36.0036 L 53.0654 34.9244 L 54.8583 34.93 L f showpage _E end %%EndDocument @endspecial 210 2504 a(Figure)g(11:)22 b(Boundary)17 b(conditions)f(for)h (the)f(blo)q(c)o(k-spin)g(observ)m(able)g(of)h(Step)f(3.)938 2784 y(121)p eop %%Page: 122 122 bop 60 91 a FQ(on)16 b(the)f(un\014xed)g(blo)q(c)o(k)f(w)o(ould)h(b)q(e)h (symmetri)o(c)c(b)q(et)o(w)o(een)i(+)i(and)f FE(\000)g FQ(\(i.e.)f(four)h(+)g (spins)h(and)g(four)60 152 y FE(\000)g FQ(spins\),)g(and)h(the)f(exp)q (ectation)g(of)g(the)g(blo)q(c)o(k)g(spin)g(w)o(ould)g(b)q(e)h(zero.)133 262 y(The)e(argumen)o(t)f(giv)o(en)h(here)f(clearly)g(w)o(orks)i(for)f(an)o (y)g FP(even)21 b FQ(blo)q(c)o(k)14 b(size)h FF(b)e FE(\025)h FQ(2,)h(in)g(an)o(y)g(lattice)60 322 y(dimension)g FF(d)f FE(\025)f FQ(2.)22 b(In)16 b(this)g(w)o(a)o(y)g(w)o(e)g(conclude:)60 423 y FM(Theorem)h(4.6)24 b FP(L)n(et)e FF(d)h FE(\025)g FQ(2)p FP(,)h(and)f(let)h FF(b)f FE(\025)g FQ(2)g FP(b)n(e)f FQ(ev)o(en)p FP(.)37 b(Then)23 b(for)f(al)r(l)i FF(J)j FP(su\016ciently)d(lar)n(ge)60 484 y(\(dep)n(ending)e(on)f FF(d)h FP(and)f FF(b)p FP(\),)h(the)f(fol)r (lowing)i(holds:)30 b(L)n(et)21 b FF(\026)g FP(b)n(e)h(any)f(Gibbs)g(me)n (asur)n(e)f(for)h(the)g FF(d)p FP(-)60 544 y(dimensional)d(Ising)f(mo)n(del)g (with)h(ne)n(ar)n(est-neighb)n(or)f(c)n(oupling)i FF(J)i FP(and)c(zer)n(o)f (magnetic)j(\014eld.)k(L)n(et)60 604 y FF(T)g FP(b)n(e)17 b(the)g(blo)n (ck-aver)n(aging)i(tr)n(ansformation)d(with)h(blo)n(ck)h(size)f FF(b)p FP(.)k(Then)d(the)f(me)n(asur)n(e)f FF(\026T)23 b FP(is)17 b(not)60 664 y(c)n(onsistent)j(with)f(any)g(quasilo)n(c)n(al)g(sp)n(e)n (ci\014c)n(ation.)26 b(In)19 b(p)n(articular,)g(it)g(is)f(not)h(the)h(Gibbs)f (me)n(asur)n(e)60 724 y(for)e(any)g(uniformly)h(c)n(onver)n(gent)h(inter)n (action.)60 854 y FM(4.3.6)55 b(Generalization)17 b(to)i(Nonzero)f(Magnetic)g (Field)60 947 y FQ(It)13 b(migh)o(t)f(app)q(ear)i(from)e(our)i(results)f(th)o (us)h(far)g(that)f(the)g(R)o(G)h(pathology)g(is)f(someho)o(w)g(asso)q(ciated) 60 1007 y(with)23 b(the)h(fact)f(that)h(the)f(original)h(Hamiltonian)d FF(H)28 b FQ(lies)22 b FP(on)28 b FQ(the)23 b(phase-co)q(existence)g(curv)o (e)60 1067 y(\(whic)o(h)16 b(in)g(the)h(Ising)f(mo)q(del)g(means)g(zero)g (magnetic)f(\014eld\).)22 b(This)17 b(is)f(in)h(fact)f FP(not)22 b FQ(the)17 b(case.)22 b(In)60 1127 y(this)13 b(section)g(w)o(e)g(include)f (a)i(magnetic)d(\014eld)i FF(h)p FQ(,)g(and)h(sho)o(w)g(that)g(in)f (dimension)e FF(d)k FE(\025)e FQ(3)h(there)e(is)i(an)60 1187 y FP(op)n(en)19 b(r)n(e)n(gion)f(in)h(the)g FQ(\()p FF(J)o(;)8 b(h)p FQ(\))p FP(-plane)22 b FQ(|)c(namely)l(,)d(lo)o(w)i(enough)h(temp)q (erature)e(and)i(small)e(enough)60 1248 y(\014eld)h(|)h(where)g(the)f (decimation)f(transformation)i(pro)q(duces)h(a)f(non-Gibbsian)h(measure)e (after)60 1308 y(one)h(iteration.)26 b(\(W)l(e)17 b(susp)q(ect)h(that)h(the)e (result)h(is)f(true)h(also)g(for)g FF(d)f FQ(=)g(2,)h(but)g(it)f(will)g (require)g(a)60 1368 y(di\013eren)o(t)d(pro)q(of.\))22 b(Our)15 b(argumen)o(t)f(w)o(orks)i(for)f(decimation)e(with)i(arbitrary)h(scale)e (factor)i FF(b)p FQ(,)e(and)60 1428 y(for)19 b(the)g(Kadano\013)i (transformation)f(with)f(an)o(y)g FF(p)g(<)g FE(1)p FQ(.)30 b(Moreo)o(v)o(er,)18 b(for)i(blo)q(c)o(k-a)o(v)o(eraging)e(w)o(e)60 1488 y(ha)o(v)o(e)12 b(an)h(ev)o(en)f(stronger)i(result:)19 b(the)12 b(renormalized)f(measures)g(are)i(non-Gibbsian)h FP(for)g(arbitr)n (ary)60 1549 y(str)n(ength)19 b(of)g(the)h(\014eld)f FQ(in)e(dimensions)f FF(d)h FE(\025)g FQ(2,)h(at)g(lo)o(w)g(temp)q(eratures.)24 b(W)l(e)18 b(conclude)f(that)h(the)60 1609 y(Gri\016ths-P)o(earce-Israel)i (pathologies)i(are)f FP(not)27 b FQ(asso)q(ciated)22 b(with)f(the)g(fact)g (that)h(the)f(original)60 1669 y(mo)q(del)13 b(is)g FP(sitting)k(on)h FQ(a)c(phase-transition)h(surface.)20 b(Rather,)14 b(it)g(is)g(the)f(system)g (of)h(in)o(ternal)f(spins)60 1729 y(constrained)20 b(b)o(y)g(the)f (con\014guration)i FF(!)814 1711 y Fy(0)812 1741 y FH(sp)q(ecial)938 1729 y FQ(whic)o(h)e(m)o(ust)g(ha)o(v)o(e)g(a)h(phase)h(transition.)33 b(If)19 b(this)60 1789 y(transition)14 b(is)g(of)g(a)g(similar)d(t)o(yp)q(e)j (as)g(that)g(of)g(the)g(original)g(system,)e(then)i(it)f(is)g(natural)i(to)f (exp)q(ect)60 1849 y(that)20 b(the)f(original)g(system)f(m)o(ust)f(at)j (least)f(b)q(e)h FP(close)k FQ(to)19 b(a)h(phase)g(transition,)f(in)g(some)g (sense.)60 1910 y(But)c(ev)o(en)f(this)h(need)g(not)g(b)q(e)h(the)f(case,)g (as)h(the)e(example)f(of)j(blo)q(c)o(k-a)o(v)o(eraging)f(transformations)60 1970 y(will)g(sho)o(w,)i(if)e(these)h(t)o(w)o(o)g(transitions)h(are)f(of)h (di\013eren)o(t)e(nature.)1271 1952 y FH(53)133 2030 y FQ(Let)k(us)h(\014rst) f(treat)g(the)g(case)g(of)g(decimation)e(transformations.)30 b(Consider,)20 b(therefore,)f(an)60 2090 y(in)o(teraction)672 2150 y FF(H)31 b FQ(=)d FE(\000)p FF(J)888 2109 y Fx(X)890 2203 y Fy(h)p FD(ij)r Fy(i)956 2150 y FF(\033)984 2157 y FD(i)998 2150 y FF(\033)1026 2157 y FD(j)1055 2150 y FE(\000)11 b FF(h)1141 2109 y Fx(X)1165 2200 y FD(i)1209 2150 y FF(\033)1237 2157 y FD(i)1265 2150 y FF(:)486 b FQ(\(4)p FF(:)p FQ(39\))60 2284 y(\(Note)16 b(that)g(in)g(our)g(normalization,)f(the)h(magnetic)e(\014eld)i (is)g FP(not)21 b FQ(explicitly)13 b(m)o(ultiplie)o(d)h(b)o(y)h(an)o(y)60 2344 y(factor)i(of)g FF(J)k FQ(or)d FF(\014)s FQ(.\))k(The)16 b(idea)h(is)f(that)i(for)f(suitable)f(\(small\))f(v)m(alues)i(of)1437 2327 y Fx(e)1436 2344 y FF(h)e FE(\021)f FF(h=J)5 b FQ(,)16 b(w)o(e)h(can)g(\014nd)60 2404 y(an)j(image-spin)f(con\014guration)h FF(!)709 2386 y Fy(0)707 2417 y FH(sp)q(ecial)833 2404 y FQ(for)g(whic)o(h)f (the)g(corresp)q(onding)i(in)o(ternal-spin)d(system)60 2465 y(has)24 b(a)g(non-unique)g(Gibbs)f(measure.)42 b(Roughly)23 b(sp)q(eaking,)j FF(!)1299 2446 y Fy(0)1297 2477 y FH(sp)q(ecial)1426 2465 y FQ(m)o(ust)c(b)q(e)h(suc)o(h)h(that)f(it)60 2525 y(\\comp)q(ensates")e (the)g(e\013ect)g(of)g(the)g(magnetic)e(\014eld,)j(so)f(that)h(the)f(system)e (of)j(in)o(ternal)e(spins)p 60 2568 732 2 v 100 2622 a FA(53)135 2637 y Fz(F)m(or)13 b(this)h(reason,)g(the)h(title)e(of)h(our)f(earlier)i (rep)q(ort)f([353)o(])g(is)f(in)h(retrosp)q(ect)i(somewhat)d(misleading.)938 2784 y FQ(122)p eop %%Page: 123 123 bop 60 91 a FQ(sub)s(jected)16 b(b)q(oth)h(to)g(the)f(homogeneous)g(\014eld)g FF(h)g FQ(and)h(to)g(the)f(inhomogeneous)g(\014eld)g(due)h(to)f(the)60 152 y(image)f(spins)h(has)h(t)o(w)o(o)f(or)h(more)e(extremal)f(Gibbs)i (measures.)133 212 y(As)22 b(in)g(all)g(the)g(previous)g(cases,)i(w)o(e)e (formalize)e(this)i(idea)g(in)g(t)o(w)o(o)g(steps:)34 b(w)o(e)22 b(\014rst)g(sho)o(w)60 272 y(that)d(it)f(w)o(orks)g(at)h(zero)f(temp)q (erature,)f(namely)g(that)i(there)f(are)g(c)o(hoices)f(of)1535 255 y Fx(e)1534 272 y FF(h)i FQ(and)g FF(!)1710 254 y Fy(0)1708 284 y FH(sp)q(ecial)1832 272 y FQ(for)60 332 y(whic)o(h)f(the)g FP(gr)n(ound)h(state)k FQ(is)18 b(not)h(unique;)f(and)h(second)g(w)o(e)f(sho) o(w)h(that)g(Pirogo)o(v-Sinai)f(theory)60 392 y(is)h(applicable)f(so)i(that)g (it)f(implies)d(non)o(uniqueness)j(of)h(Gibbs)f(measures)g(at)g(lo)o(w)g(but) h(nonzero)60 452 y(temp)q(eratures.)29 b(The)19 b(simplest)e(case)i(is)g(to)h (let)e FF(!)1007 434 y Fy(0)1005 465 y FH(sp)q(ecial)1130 452 y FQ(b)q(e)h FP(p)n(erio)n(dic)s FQ(.)1382 434 y FH(54)1448 452 y FQ(In)g(this)g(situation)h(one)60 522 y(can)c(\014nd)h(the)e(\\comp)q (ensating")i(\014eld)793 505 y Fx(e)792 522 y FF(h)820 529 y FH(0)856 522 y FQ(needed)f(to)g(obtain)h(more)d(than)j(one)f(ground)h (state)g(b)o(y)60 582 y(studying)d(con\014gurations)g(inside)f(a)h(p)q(erio)q (d.)20 b(W)l(e)13 b(do)h(not)g(w)o(an)o(t)f(to)h(en)o(ter)e(in)o(to)h(the)h (details,)e(as)i(w)o(e)60 642 y(later)e(o\013er)h(a)g(b)q(etter)g(and)g(more) e(general)i(pro)q(cedure,)g(but)g(w)o(e)f(mak)o(e)f(the)h(rather)h(ob)o (vious)g(remark)60 703 y(that)j(the)g(\014eld)g(m)o(ust)e(b)q(e)i(tak)o(en)g (in)g(a)g(direction)f(opp)q(osite)i(to)f(that)h(of)f(the)g(ma)s(jorit)o(y)e (of)i(in)o(ternal)60 763 y(spins)k(within)e(a)i(p)q(erio)q(d.)31 b(The)19 b(v)m(alue)g(of)h(the)f(\014eld)g(m)o(ust)f(b)q(e)h(suc)o(h)g(that)h (if)e(the)i(in)o(ternal)e(spins)60 823 y(follo)o(w)f(it,)h(the)f(energy)h (gain)g(is)f(exactly)g(comp)q(ensated)g(b)o(y)g(the)h(p)q(enalt)o(y)f(paid)h (b)o(y)g(the)f(in)o(ternal)60 883 y(spins)k(neigh)o(b)q(oring)g(the)f(image)f (spins)i(of)g(opp)q(osite)g(sign.)35 b(\(In)20 b(other)h(w)o(ords,)h(the)e (sum)g(of)h(all)60 943 y(the)e(\014elds)g(|)h(external)e(or)i(due)f(to)h (image)e(spins)i(|)f(felt)g(b)o(y)g(the)g(in)o(ternal)g(spins)g(in)h(a)g(p)q (erio)q(d)60 1004 y(m)o(ust)15 b(b)q(e)h(zero.\))21 b(This)16 b(\014eld)g(strength)798 987 y Fx(e)797 1004 y FF(h)825 1011 y FH(0)861 1004 y FQ(is)g(to)q(o)h(w)o(eak)f(to)g(fa)o(v)o(or)g(the)g (\015ipping)g(of)g(small)f(regions)60 1064 y(of)j(in)o(ternal)e(spins,)i(and) g(only)f(a)h(collectiv)o(e)d(\015ip)i(is)h(energetically)d(acceptable.)24 b(Of)18 b(course,)f(this)60 1124 y(delicate)f(balance)i(is)g(brok)o(en)f(if)h (the)f(\014eld)g(is)h(c)o(hanged,)g(no)g(matter)f(ho)o(w)h(little.)24 b(Therefore,)17 b(w)o(e)60 1184 y(conclude)i(that)h(this)f(v)m(alue)602 1167 y Fx(e)601 1184 y FF(h)629 1191 y FH(0)668 1184 y FE(\021)727 1167 y Fx(e)726 1184 y FF(h)754 1191 y FH(0)774 1184 y FQ(\()p FF(!)825 1166 y Fy(0)823 1197 y FH(sp)q(ecial)928 1184 y FQ(\))h(is)f(suc)o (h)h(that)g(for)1321 1167 y Fx(e)1319 1184 y FF(h)g(>)1426 1167 y Fx(e)1424 1184 y FF(h)1452 1191 y FH(0)1492 1184 y FQ(\(resp.)1632 1167 y Fx(e)1631 1184 y FF(h)f(<)1737 1167 y Fx(e)1736 1184 y FF(h)1764 1191 y FH(0)1784 1184 y FQ(\))g(the)60 1244 y(in)o(ternal-spin)e (system)e(has)k(only)e(one)g(p)q(erio)q(dic)g(ground)i(state,)e(namely)f(all) h(spins)g(+)h(\(resp.)f(all)60 1305 y(spins)i FE(\000)p FQ(\),)f(while)g(for) 482 1288 y Fx(e)481 1305 y FF(h)g FQ(=)584 1288 y Fx(e)583 1305 y FF(h)611 1312 y FH(0)649 1305 y FQ(there)g(are)g(precisely)f(t)o(w)o (o)h(p)q(erio)q(dic)g(ground)i(states,)f(namely)e(all)60 1365 y(spins)f(+)h(and)g(all)e(spins)i FE(\000)p FQ(.)133 1425 y(F)l(or)h(the)g (second)g(step)g(|)g(relying)f(on)h(Pirogo)o(v-Sinai)g(theory)g(|)g(w)o(e)f (already)h(ha)o(v)o(e)f(t)o(w)o(o)h(of)60 1485 y(the)e(required)f(conditions) h(\(see)f(App)q(endix)h(B\):)k(a)d(p)q(erio)q(dic)f(\(in)o(ternal-spin\))f (in)o(teraction)g(and)i(a)60 1545 y(\014nite)c(n)o(um)o(b)q(er)f(of)i(ground) g(states.)21 b(W)l(e)14 b(need)f(in)g(addition)h(to)g(v)o(erify)e(the)h(P)o (eierls)f(condition,)i(but)60 1606 y(this)g(can)g(b)q(e)g(done)g(basically)f (follo)o(wing)g(the)h(same)f(energy-cost)h(argumen)o(ts)f(outlined)g(ab)q(o)o (v)o(e)h(for)60 1666 y(the)f(determination)e(of)j(ground)g(states.)21 b(The)13 b(conclusion)g(is)h(that)f(there)g(exists)g FF(J)1584 1673 y FH(0)1617 1666 y FE(\021)h FF(J)1697 1673 y FH(0)1717 1666 y FQ(\()p FF(!)1768 1648 y Fy(0)1766 1678 y FH(sp)q(ecial)1871 1666 y FQ(\))60 1735 y(suc)o(h)i(that)g(for)g FF(J)j(>)13 b(J)473 1742 y FH(0)509 1735 y FQ(there)i(is)h(a)g(con)o(tin)o(uous)g(curv)o(e)1097 1719 y Fx(e)1096 1735 y FF(h)e FQ(=)1191 1719 y Fx(e)1190 1735 y FF(h)1218 1717 y Fy(\003)1237 1735 y FQ(\()p FF(J)5 b FQ(\),)15 b(with)h(lim)1515 1742 y FD(J)s Fy(!)p FH(+)p Fy(1)1647 1719 y Fx(e)1646 1735 y FF(h)1674 1717 y Fy(\003)1694 1735 y FQ(\()p FF(J)5 b FQ(\))13 b(=)1830 1719 y Fx(e)1829 1735 y FF(h)1857 1742 y FH(0)1876 1735 y FQ(,)60 1796 y(on)i(whic)o(h)e(the)h(in)o (ternal-spin)g(system)f(has)i(precisely)d(t)o(w)o(o)i(p)q(erio)q(dic)g (extremal)e(Gibbs)j(measures,)60 1856 y(namely)i(a)i(\\+")g(phase)g(and)g(a)g (\\)p FE(\000)p FQ(")g(phase.)29 b(As)18 b(long)h(as)h FF(!)1203 1838 y Fy(0)1201 1868 y FH(sp)q(ecial)1325 1856 y FQ(is)e(not)h(all)f(+)h(or) g(all)f FE(\000)p FQ(,)g(Step)60 1916 y(2)f(can)g(b)q(e)g(pro)o(v)o(en)f (using)h(the)g(FK)o(G)f(inequalit)o(y)l(,)f(as)i(in)g(Section)f(4.3.1.)23 b(W)l(e)17 b(therefore)f(conclude)60 1976 y(that)h(for)241 1959 y Fx(e)240 1976 y FF(h)d FQ(=)335 1959 y Fx(e)334 1976 y FF(h)362 1958 y Fy(\003)382 1976 y FQ(\()p FF(J)5 b FQ(\))15 b(the)h(renormalized)e(measure)h FF(\026T)23 b FQ(is)16 b(non-Gibbsian.)133 2036 y(The)21 b(c)o(hief)f(limitation)e(of)j(this)g(pro)q(cedure)g(is)g(that) g(it)g(pro)q(duces)g(only)g FP(r)n(ational)g FQ(v)m(alues)g(of)61 2080 y Fx(e)60 2096 y FF(h)88 2103 y FH(0)126 2096 y FQ(and)f(that)f(there)f (is)g(no)h(uniformit)o(y)d(in)883 2080 y Fx(e)882 2096 y FF(h)910 2103 y FH(0)948 2096 y FQ(for)j(the)f(range)h(of)g(temp)q(eratures)e(for)i (whic)o(h)f(the)60 2157 y(non)o(uniqueness)13 b(p)q(ersists.)20 b(Hence,)12 b(b)o(y)h(letting)f FF(!)977 2139 y Fy(0)975 2169 y FH(sp)q(ecial)1093 2157 y FQ(range)i(o)o(v)o(er)e FP(al)r(l)19 b FQ(p)q(erio)q(dic)13 b(con\014gurations,)60 2217 y(w)o(e)g(pro)o(v)o(e)g (non-Gibbsianness)i(only)e(for)h(a)g(region)f(of)h(the)f(phase)h(diagram)f (formed)f(b)o(y)h(coun)o(tably)60 2277 y(man)o(y)e(curv)o(es)336 2260 y Fx(e)335 2277 y FF(h)j FQ(=)430 2260 y Fx(e)429 2277 y FF(h)457 2259 y Fy(\003)476 2277 y FQ(\()p FF(J)5 b FQ(\).)20 b(W)l(e)12 b(can)h(pro)o(v)o(e)f(that)h(the)g(set)f(of)1182 2260 y Fx(e)1181 2277 y FF(h)1209 2284 y FH(0)1242 2277 y FQ(v)m(alues)g(is)h (dense)f(in)g(some)g(in)o(terv)m(al)60 2337 y FE(j)75 2321 y Fx(e)74 2337 y FF(h)p FE(j)i FF(<)f(\017)j FQ(but,)g(unfortunately)l(,)g(w) o(e)f FP(c)n(annot)22 b FQ(conclude)15 b(non-Gibbsianness)j(for)e(an)o(y)g (dense)g(subset)60 2397 y(of)i(an)g(op)q(en)h(set)e(in)h(the)f(\()p FF(J)o(;)8 b(h)p FQ(\)-plane:)24 b(the)18 b(trouble)f(is)h(that)g(the)f(curv) o(es)1459 2381 y Fx(e)1458 2397 y FF(h)1486 2379 y Fy(\003)1506 2397 y FQ(\()p FF(J)5 b FQ(\))17 b(corresp)q(onding)60 2458 y(to)d(con\014gurations)h FF(!)461 2440 y Fy(0)459 2470 y FH(sp)q(ecial)578 2458 y FQ(of)f(v)o(ery)f(high)g(p)q(erio)q(d)i(ma)o(y)d(surviv)o(e)g(only)h (to)h(v)o(ery)f(lo)o(w)g(temp)q(eratures)60 2518 y(\(i.e.)i(w)o(e)g(ha)o(v)o (e)h(no)h(uniform)d(con)o(trol)i(on)h FF(J)851 2525 y FH(0)871 2518 y FQ(\).)p 60 2564 732 2 v 100 2618 a FA(54)135 2633 y Fz(This)d(construction)g(w)o(as)g(already)g(suggested)h(b)o(y)f(Israel)g ([207)o(].)938 2784 y FQ(123)p eop %%Page: 124 124 bop 133 91 a FQ(If)24 b(w)o(e)g(w)o(an)o(t)g(to)h(extend)e(this)h(argumen)o (t)f(to)i(more)e(general)h(c)o(hoices)f(of)i FF(!)1602 73 y Fy(0)1600 104 y FH(sp)q(ecial)1705 91 y FQ(,)h(w)o(e)e(are)60 152 y(confron)o(ted)19 b(with)g(the)g(limitation)d(imp)q(osed)i(b)o(y)h(the)g (presen)o(t)f(v)o(ersions)g(of)i(Pirogo)o(v-Sinai)f(the-)60 212 y(ory)l(.)24 b(One)17 b(p)q(ossible)h(generalization)f(of)g(this)g (construction)h(is)f(to)g(let)g FF(!)1412 194 y Fy(0)1410 224 y FH(sp)q(ecial)1533 212 y FQ(b)q(e)g FP(quasip)n(erio)n(dic)s FQ(.)60 272 y(Then)i(one)g(can)g(use)f(an)i(extension)e(of)h(Pirogo)o (v-Sinai)g(theory)f(due)h(to)g(Koukiou,)g(P)o(etritis)e(and)60 332 y(Zahradn)-5 b(\023)-19 b(\020k)15 b([221].)20 b(\(Actually)l(,)13 b(these)h(authors)i(require)d(the)h(quasip)q(erio)q(dic)g(part)h(of)g(the)f (in)o(terac-)60 392 y(tion)i(to)g(b)q(e)g(small;)e(so)j(w)o(e)e(cannot)i (handle)f(decimation,)e(but)i(can)g(handle)g(the)f(Kadano\013)j(trans-)60 452 y(formation)13 b(with)h FF(p)g FQ(small.\))19 b(In)14 b(this)f(w)o(a)o(y) h(w)o(e)f(obtain)i(uncoun)o(tably)e(man)o(y)g(curv)o(es)1615 436 y Fx(e)1614 452 y FF(h)h FQ(=)1708 436 y Fx(e)1707 452 y FF(h)1735 434 y Fy(\003)1755 452 y FQ(\()p FF(J)5 b FQ(\))14 b(on)60 513 y(whic)o(h)h(the)h(renormalized)d(measure)i(is)g(non-Gibbsian.)23 b(\(If)15 b(the)h(results)f(of)h(Koukiou)g FP(et)i(al.)k FQ(can)60 573 y(b)q(e)13 b(extended)e(to)i(frequencies)e(whic)o(h)h(are)g(Diophan)o (tine)h(of)f(arbitrary)h(t)o(yp)q(e)f FF(l)i(<)g FE(1)e FQ(|)h(at)g(presen)o (t)60 633 y(they)18 b(treat)g(only)g FF(l)h FQ(=)e(2)i(|)f(then)g(the)g (corresp)q(onding)i(set)e(of)1253 616 y Fx(e)1252 633 y FF(h)1280 640 y FH(0)1318 633 y FQ(v)m(alues)g(w)o(ould)h(con)o(tain)f(some)60 693 y(in)o(terv)m(al)12 b FE(j)248 677 y Fx(e)247 693 y FF(h)p FE(j)h FF(<)h(\017)f FQ(except)f(for)h(a)h(subset)f(of)g(Leb)q(esgue)h (measure)e(zero.\))20 b(Ho)o(w)o(ev)o(er,)11 b(w)o(e)i(still)e(cannot)60 753 y(conclude)j(non-Gibbsianness)j(for)e(an)o(y)g(dense)g(subset)h(of)f(an)h (op)q(en)g(set)f(in)g(the)f(\()p FF(J)o(;)8 b(h)p FQ(\)-plane:)21 b(the)60 814 y(trouble)16 b(is)g(again)h(that)g(w)o(e)f(lac)o(k)f(uniform)g (con)o(trol)h(on)g FF(J)1126 821 y FH(0)1146 814 y FQ(.)133 874 y(A)o(t)i(an)o(y)g(rate,)g(w)o(e)g(are)g(able)g(to)h(o)o(v)o(ercome)c (these)j(tec)o(hnicalities,)e(and)i(w)o(e)g(presen)o(t)g(here)g(an)60 934 y(argumen)o(t)12 b(pro)o(ving)h(the)g(existence)e(of)i(Gri\016ths-P)o (earce-Israel)f(pathologies)i(for)f(an)h FP(op)n(en)g(r)n(e)n(gion)60 994 y FE(f)p FF(J)k(>)c(J)209 1001 y FH(0)229 994 y FF(;)i FE(j)p FF(h)p FE(j)e FF(<)f(\016)402 1001 y FH(0)422 994 y FF(J)5 b FE(g)10 b FQ(in)h(the)f(\()p FF(J)o(;)e(h)p FQ(\)-plane,)k(as)g (originally)e(conjectured)g(b)o(y)h(Gri\016ths)f(and)i(P)o(earce)60 1054 y([172)q(,)h(173)q(])h(and)h(Israel)e([207)q(].)20 b(The)14 b(k)o(ey)f(ingredien)o(t)f(is)i(a)h(mec)o(hanism)10 b(to)15 b(generate)f(a)g(con)o(tin)o(uum)60 1115 y(of)i(image-spin)f (con\014gurations)i FF(!)705 1096 y Fy(0)703 1127 y FH(sp)q(ecial)824 1115 y FQ(suc)o(h)f(that)g(P-S)h(theory)e(is)h(applicable)f(to)h(the)f (resulting)60 1175 y(in)o(ternal-spin)24 b(system.)43 b(A)o(t)24 b(presen)o(t)g(this)g(is)g(only)g(p)q(ossible)h(if)e(w)o(e)h(resort)h(to)g (randomness:)60 1235 y(Zahradn)-5 b(\023)-19 b(\020k)18 b([369)q(,)g(370)q(,) g(371)q(],)g(and)h(with)f(less)g(generalit)o(y)f(Bricmon)o(t)f(and)j (Kupiainen)f([43,)g(44)q(],)60 1295 y(extended)i(P-S)i(theory)g(to)f(systems) f(with)i(sup)q(erimp)q(osed)f(\(small\))e(random)i(in)o(teractions)g(for)60 1355 y(dimensions)c FF(d)i FE(\025)f FQ(3.)29 b(Our)19 b(construction)g (will,)f(therefore,)g(b)q(e)h(based)g(on)h(a)f(\(sligh)o(tly\))e(random)60 1416 y(c)o(hoice)e(of)i(the)f(con\014guration)h FF(!)672 1397 y Fy(0)670 1428 y FH(sp)q(ecial)792 1416 y FQ(and)g(will)e(b)q(e)h(limited)d (to)k FF(d)d FE(\025)g FQ(3.)133 1476 y(Consider,)23 b(for)e(starters,)i (decimation)c(with)i(some)g(spacing)h FF(b)g FE(\025)g FQ(2,)h(applied)e(to)g (an)h(Ising)60 1536 y(mo)q(del)14 b(with)h(ferromagnetic)e(nearest-neigh)o(b) q(or)j(in)o(teraction)e FF(J)20 b FQ(and)c(magnetic)d(\014eld)i FF(h)f FQ(=)g FF(J)1812 1519 y Fx(e)1811 1536 y FF(h)f(>)60 1596 y FQ(0.)25 b(W)l(e)17 b(consider)g(a)h(blo)q(c)o(k-spin)f (con\014guration)i(whic)o(h)e(is)g(equal)g(to)h(the)f(fully)f(alternating)i (con-)60 1656 y(\014guration)k(except)d(that)i(the)g(spins)f(that)h(w)o(ould) g(corresp)q(ond)h(to)f(a)g(\\+")g(ha)o(v)o(e)f(a)h(probabilit)o(y)60 1716 y FF(\017=)p FQ(2)p FF(J)27 b FQ(of)21 b(b)q(ecoming)g(a)g(\\)p FE(\000)p FQ(",)i(indep)q(enden)o(tly)d(for)i(eac)o(h)f(suc)o(h)g(spin.)37 b(W)l(e)21 b(wish)h(to)g(sho)o(w)g(that)60 1777 y(for)17 b(eac)o(h)e (su\016cien)o(tly)g(small)g(p)q(ositiv)o(e)798 1760 y Fx(e)797 1777 y FF(h)p FQ(,)h(there)g(exists)g(an)h FF(\017)f FQ(suc)o(h)g(that)h(the) f(random)g(magnetic)60 1837 y(\014eld)e(induced)h(b)o(y)f(the)h(blo)q(c)o(k)g (spins)g(\(whose)h(net)e(e\013ect)h(is)g(negativ)o(e\))f(exactly)g(comp)q (ensates)g(the)60 1897 y(p)q(ositiv)o(e)j(uniform)g(\014eld,)h(in)g(the)g (sense)g(that)g(for)h(almost)e(all)h(suc)o(h)g(image-spin)f(con\014gurations) 60 1957 y(there)j(are)h(t)o(w)o(o)g(distinct)e(Gibbs)j(measures)d FF(\026)941 1964 y FH(+)992 1957 y FQ(and)i FF(\026)1120 1964 y Fy(\000)1150 1957 y FQ(.)35 b(T)l(o)21 b(do)g(this,)h(w)o(e)e(apply)h(an)g (as-y)o(et-)60 2017 y(unpublished)d(theorem)f(of)i(Zahradn)-5 b(\023)-19 b(\020k)19 b([370)q(,)f(371)q(],)g(whic)o(h)g(generalizes)f (Pirogo)o(v-Sinai)i(theory)60 2078 y(to)h(small)d(random)i(in)o(teractions,)g (if)f(the)h(lattice)f(dimension)g(is)h FE(\025)g FQ(3.)30 b(\(In)19 b(the)g(preprin)o(t)f([370)q(],)60 2138 y(the)h(random)h(in)o(teractions)f (are)g(assumed)g(to)h(b)q(e)g(small)e(uniformly)g(in)h(all)g(realizations)g (of)h(the)60 2198 y(randomness.)37 b(This)22 b(condition)f(is)g(not)h (satis\014ed)g(in)f(our)h(case,)h(as)f(one)g(has)g(large)g(terms)e(\(of)60 2258 y(strength)e FE(\030)d FF(J)5 b FQ(\),)17 b(alb)q(eit)g(o)q(ccurring)g (with)g(small)f(probabilit)o(y)g(\()p FF(\017=)p FQ(2)p FF(J)5 b FQ(\).)24 b(In)17 b(a)h(priv)m(ate)f(comm)o(uni-)60 2318 y(cation)g([371)q(],)f(Zahradn)-5 b(\023)-19 b(\020k)17 b(has)h(informed)e (us)h(that)h(minor)d(mo)q(di\014cations)i(of)g(his)g(pro)q(ofs)i(su\016ce)60 2379 y(to)e(co)o(v)o(er)e(also)h(this)h(case.\))133 2439 y(W)l(e)k(apply)h (Zahradn)-5 b(\023)-19 b(\020k's)21 b(theory)h(with)f(the)h(original)f (Hamiltonian)f FF(H)1506 2446 y FH(0)1548 2439 y FQ(tak)o(en)h(to)h(b)q(e)f (the)60 2499 y(system)12 b(of)h(in)o(ternal)f(spins)h(with)g(fully)f (alternating)h(image)e(spins)j(\(i.e.)d(a)i(ferromagnetic)f(nearest-)60 2559 y(neigh)o(b)q(or)h(Ising)g(mo)q(del)f(in)h(a)g(p)q(erio)q(dically)f (diluted)g(lattice)g(and)i(with)f(a)g(p)q(erio)q(dic)g(magnetic)f(\014eld)60 2619 y(of)19 b(mean)f(zero,)h(see)f(Section)h(4.3.2\);)h(the)e (symmetry-breaking)e(\\\014elds")k(are)e(tak)o(en)h(to)g(b)q(e)g(the)938 2784 y(124)p eop %%Page: 125 125 bop 60 91 a FQ(uniform)19 b(magnetic)f(\014eld,)i(and)g(the)g(random)f (negativ)o(e)g(magnetic)g(\014elds)g(coming)g(from)g(those)60 152 y(blo)q(c)o(k)f(spins)g(that)h(w)o(ere)f(\015ipp)q(ed)g(from)f(\\+")i(to) g(\\)p FE(\000)p FQ(")g(according)f(to)h(the)f(pro)q(cedure)g(explained)60 212 y(ab)q(o)o(v)o(e.)26 b(The)17 b(analysis)h(of)g(the)g(ground-state)h (structure)f(of)g FF(H)1245 219 y FH(0)1265 212 y FQ(,)f(and)i(the)e(pro)q (of)i(of)f(the)g(P)o(eierls)60 272 y(condition)11 b(for)g(it,)g(w)o(ere)g (already)g(carried)f(out)i(in)e(Sections)h(4.3.2)h(and)f(B.5.3.)19 b(Zahradn)-5 b(\023)-19 b(\020k's)11 b(theory)60 332 y(\(Theorem)16 b(B.31\))i(then)f(assures)i(us)f(\(Section)f(B.5.7\))g(that)h(for)g(eac)o(h)f FF(J)22 b FQ(su\016cien)o(tly)16 b(large)h(and)60 392 y(eac)o(h)e FF(\017)g FQ(su\016cien)o(tly)e(small,)g(the)i(phase)h(diagram)f(is,)g(with)g (probabilit)o(y)f(1,)i(a)f(small)f(deformation)60 452 y(of)k(that)h(of)f(the) g(Hamiltonian)f FF(H)691 459 y FH(0)711 452 y FQ(;)i(that)f(is,)g(for)h(eac)o (h)e(suc)o(h)h(pair)g(\()p FF(J)o(;)8 b(\017)p FQ(\))18 b(there)g(exists)f(a) i(unique)61 496 y Fx(e)60 513 y FF(h)88 495 y Fy(\003)108 513 y FQ(\()p FF(J)o(;)8 b(\017)p FQ(\))15 b FF(>)g FQ(0)j(suc)o(h)f(that)g(the)g (system)f(has)i(t)o(w)o(o)f(distinct)f(Gibbs)i(measures)e FF(\026)1529 520 y FH(+)1576 513 y FQ(and)i FF(\026)1701 520 y Fy(\000)1748 513 y FQ(\(whic)o(h)60 573 y(can)e(b)q(e)h(obtained,)f(for)h(example,)c(b)o (y)j(taking)929 556 y Fx(e)928 573 y FF(h)e FE(#)1010 556 y Fx(e)1008 573 y FF(h)1036 555 y Fy(\003)1072 573 y FQ(or)1133 556 y Fx(e)1132 573 y FF(h)g FE(")1214 556 y Fx(e)1213 573 y FF(h)1241 555 y Fy(\003)1261 573 y FQ(,)i(resp)q(ectiv)o(ely\).)j(Moreo)o (v)o(er,)14 b(the)60 633 y(v)m(alue)186 616 y Fx(e)185 633 y FF(h)213 640 y FH(0)232 633 y FQ(\()p FF(\017)p FQ(\))h(at)g(whic)o(h)f (the)h(\\+")g(and)h(\\)p FE(\000)p FQ(")f(con\014gurations)h(are)f(sim)o (ultaneously)e(ground)j(states)60 693 y(is)21 b(a)g(strictly)f(increasing)h (linear)f(function)h(of)h FF(\017)p FQ(.)35 b(\(This)21 b(follo)o(ws)g(from)f (an)i(argumen)o(t)e(similar)60 753 y(to,)f(alb)q(eit)g(more)f(elab)q(orate)h (than,)h(the)e(one)h(presen)o(ted)f(at)i(the)e(b)q(eginning)h(of)h(the)e (section)h(for)60 814 y(p)q(erio)q(dic)11 b(c)o(hoices)g(of)h FF(!)485 796 y Fy(0)483 826 y FH(sp)q(ecial)588 814 y FQ(.)20 b(The)11 b(slop)q(e)h(dep)q(ends)g(on)g(the)g(blo)q(c)o(k-size)e FF(b)h FQ(and)i(the)e(dimensionalit)o(y)60 874 y FF(d)p FQ(.\))21 b(As)13 b(Zahradn)-5 b(\023)-19 b(\020k's)13 b(theory)h(tells)e(us)i(that)g (the)f(lo)o(w-temp)q(erature)f(phase)i(diagram)f(is)g(a)h(smo)q(oth)60 934 y(deformation)f(of)i(the)f(zero-temp)q(erature)f(one,)h(w)o(e)g(conclude) f(that)i(that)1423 917 y Fx(e)1422 934 y FF(h)1450 916 y Fy(\003)1484 934 y FQ(is)f(a)g(con)o(tin)o(uous)g(and)60 994 y(strictly)g(increasing)h (function)f(of)i FF(\017)p FQ(.)k(Ob)o(viously)15 b(the)f(case)i FF(h)e(<)f FQ(0)j(can)f(b)q(e)g(handled)h(b)o(y)e(the)h(same)60 1054 y(argumen)o(t)g(with)h(\\+")h(and)g(\\)p FE(\000)p FQ(")g(rev)o(ersed.) 133 1115 y(The)f(b)q(ottom)g(line)f(is,)g(therefore,)g(that)i(there)e(exists) h(|)f(for)i(eac)o(h)e FF(J)21 b FQ(su\016cien)o(tly)14 b(large)i(|)g(a)60 1175 y(con)o(tin)o(uous)j(and)g(monotonic)f(curv)o(e)g FF(\017)798 1157 y Fy(\003)817 1175 y FQ(\()837 1158 y Fx(e)836 1175 y FF(h)p FQ(\))h(through)g(the)g(origin,)g(de\014ned)f(for)h FE(j)1592 1158 y Fx(e)1591 1175 y FF(h)p FE(j)g FQ(small,)e(suc)o(h)60 1235 y(that)f(for)h(almost)e(all)g(c)o(hoices)g(of)h(the)g(random)g(blo)q(c)o (k-spin)f(con\014guration)i(the)f(system)e(presen)o(ts)60 1295 y(m)o(ultiple)e(Gibbs)k(measures)f(on)h(the)f(curv)o(e)g(and)h(a)g(unique)f (Gibbs)h(measure)e(to)i(eac)o(h)f(side)g(of)h(the)60 1355 y(curv)o(e)11 b(\(Figure)h(12\).)21 b(Th)o(us,)13 b(for)f(the)g(Ising)g(mo)q(del)g(with)g FF(J)17 b FQ(su\016cien)o(tly)10 b(large)i(and)h FE(j)1609 1339 y Fx(e)1608 1355 y FF(h)p FE(j)f FQ(su\016cien)o(tly)60 1416 y(small,)h(w)o(e)h(can)h(pro)o(v)o(e)f(Step)g(1)h(b)o(y)f(c)o(hosing)h (as)g FF(!)963 1397 y Fy(0)961 1428 y FH(sp)q(ecial)1081 1416 y FQ(an)o(y)g(one)g(of)f(the)h(con\014gurations)h(from)d(the)60 1485 y(probabilit)o(y-1)k(set)g(corresp)q(onding)h(to)g FF(\017)d FQ(=)h FF(\017)912 1467 y Fy(\003)931 1485 y FQ(\()951 1468 y Fx(e)950 1485 y FF(h)p FQ(\).)24 b(The)17 b(pro)q(of)i(of)e(the)g(v)m (alidit)o(y)f(of)h(Steps)h(2)f(and)60 1545 y(3)e(is)g(essen)o(tially)e(iden)o (tical)h(to)h(that)g(of)h(the)e(case)h FF(h)f FQ(=)g(0)h(\(Sections)g(4.3.1)g (and)h(4.3.2\).)21 b(W)l(e)15 b(notice)60 1606 y(that)i(due)g(to)g(the)g(smo) q(othness)g(of)g(the)g(phase)h(diagram)e(deformations,)g(the)g(b)q(ound)i FE(j)1688 1589 y Fx(e)1687 1606 y FF(h)p FE(j)d FF(<)g(\016)r FQ(\()p FF(J)5 b FQ(\))60 1666 y(for)22 b(whic)o(h)e(these)h(steps,)h(and)g (hence)f(the)g(existence)e(of)j(R)o(G)f(pathologies,)i(can)e(b)q(e)h(pro)o(v) o(en)e(is)60 1726 y(giv)o(en)15 b(b)o(y)h(a)h FP(c)n(ontinuous)k FQ(function)16 b FF(\016)r FQ(\()p FF(J)5 b FQ(\).)20 b(Moreo)o(v)o(er,)15 b(w)o(e)h(ha)o(v)o(e)f(lim)8 b(inf)1410 1733 y FD(J)s Fy(!1)1514 1726 y FF(\016)r FQ(\()p FF(J)d FQ(\))12 b FE(\025)i FF(\016)1695 1733 y FH(0)1728 1726 y FF(>)g FQ(0.)133 1786 y(The)i(\014nal)h(result)f(is)g (the)g(follo)o(wing:)60 1892 y FM(Theorem)h(4.7)24 b FP(F)l(or)15 b(e)n(ach)h FF(d)e FE(\025)f FQ(3)j FP(and)g FF(b)e FE(\025)g FQ(2)p FP(,)i(ther)n(e)g(exists)g(a)g FF(J)1277 1899 y FH(0)1310 1892 y FF(<)e FE(1)i FP(and)g(a)f FF(\016)1583 1899 y FH(0)1616 1892 y FF(>)f FQ(0)i FP(\(dep)n(end-)60 1952 y(ing)j(on)g FF(d)f FP(and)h FF(b)p FP(\))e(such)i(that)f(for)g(al)r(l)i FF(J)g(>)15 b(J)900 1959 y FH(0)938 1952 y FP(and)j FE(j)p FF(h)p FE(j)d FF(<)g(\016)1179 1959 y FH(0)1199 1952 y FF(J)23 b FP(the)18 b(fol)r(lowing)j(is)d(true:)24 b(L)n(et)18 b FF(\026)h FP(b)n(e)60 2012 y(any)e(Gibbs)g(me)n(asur)n(e)e(for)h(the)h FF(d)p FP(-dimensional)i (Ising)e(mo)n(del)f(with)h(ne)n(ar)n(est-neighb)n(or)h(c)n(oupling)f FF(J)60 2072 y FP(and)h(magnetic)h(\014eld)g FF(h)p FP(.)j(Then)d(the)f(r)n (enormalize)n(d)e(me)n(asur)n(e)h FF(\026T)25 b FP(arising)17 b(fr)n(om)g(the)h(de)n(cimation)60 2133 y(tr)n(ansformation)j(with)i(sp)n (acing)f FF(b)g FP(is)g(not)h(c)n(onsistent)g(with)f(any)h(quasilo)n(c)n(al)f (sp)n(e)n(ci\014c)n(ation.)37 b(In)60 2193 y(p)n(articular,)17 b(it)g(is)h(not)g(the)g(Gibbs)f(me)n(asur)n(e)g(for)g(any)g(uniformly)h(c)n (onver)n(gent)h(inter)n(action.)133 2299 y FQ(Similar)e(results)j(are)f(v)m (alid,)g(b)o(y)g(a)h(similar)d(argumen)o(t,)i(for)h(the)f(Kadano\013)i (transformation)60 2359 y(with)e(an)o(y)f(\014xed)h(0)f FF(<)g(p)h(<)f FE(1)p FQ(.)28 b(Ho)o(w)o(ev)o(er,)18 b(w)o(e)g(are)h(not)g(able)f(to)i (apply)e(suc)o(h)h(an)g(argumen)o(t)f(to)60 2419 y(the)e(ma)s(jorit)o(y-rule) e(example)g(b)q(ecause)j(w)o(e)f(need)g(dimension)e FF(d)h FE(\025)f FQ(3.)22 b(This)16 b(seems)f(to)i(b)q(e)f(only)h(a)60 2479 y(tec)o(hnical)e(reason.)133 2539 y(The)f(pro)q(of)i(for)e(blo)q(c)o (k-a)o(v)o(eraging)g(transformations)g(in)g(a)h(\014eld)e(is)h(m)o(uc)o(h)e (simpler:)18 b(w)o(e)c(do)h(not)60 2600 y(need)j(randomness)h(in)g(the)f(c)o (hoice)g(of)h FF(!)829 2582 y Fy(0)827 2612 y FH(sp)q(ecial)933 2600 y FQ(.)29 b(In)18 b(fact,)h(the)g(same)f(steps)h(detailed)f(in)h (Section)60 2660 y(4.3.5)14 b(ab)q(o)o(v)o(e)f(can)h(b)q(e)g(applied)f FP(r)n(e)n(gar)n(d)r(less)h(of)h(whether)h(or)e(not)i(a)f(\014eld)h(is)e(pr)n (esent)5 b FQ(.)21 b(Steps)14 b(1)f(and)i(2)938 2784 y(125)p eop %%Page: 126 126 bop 60 1852 a @beginspecial 21 @llx 30.500000 @lly 310 @urx 205.500000 @ury 4392 @rwi @setspecial %%BeginDocument: fig12.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n []/_Symbol/Symbol Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Italic/Times-Italic Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 1 w 4 M []0 d 47 49.3589 m 168.655 49.3589 l S 168.655 49.3589 m 290.31 49.3589 l S 2 w 47 196.5 m S 1 w 280 49.3589 m S u u 0 g /_Times-Italic 12 14.5 0 0 z [1 0 0 1 33 181.5]e (h)t T U U u u /_Symbol 12 14.5 0 0 z [1 0 0 1 279 34.5]e (e)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 72 168.5]e (unique Gibbs measure)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 123.3442 73.5625]e (unique Gibbs measure)t T U U 0 G 238 195.5 m 238 174.5 l 280 174.5 l S u u 0 g /_Times-Italic 12 14.5 0 0 z [1 0 0 1 248 182.5]e (J)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 256.3262 182.5]e (large)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 178 99.5]e (multiple Gibbs measures)t T U U 0 G 47 49.3589 m 47 196.5 l S 0.3 w 10 M 46.1984 195.872 m S 46.7657 196.4847 m S 46.7657 196.4847 m S 46.7657 196.4847 m S 46.7657 196.4847 m S 0 g 0.5 w 4 M 43.75 196.5026 m 47.0546 203.253 L B 47.0546 203.253 m 50.2499 196.5616 L 43.75 196.5026 L B 43.75 196.5026 m 47.0546 203.253 L B 0.3 w 10 M 289.9157 50.2328 m S 290.5201 49.6566 m S 290.5201 49.6566 m S 290.5201 49.6566 m S 290.5201 49.6566 m S 0 g 0.5 w 4 M 290.5821 52.6717 m 297.2834 49.2688 L B 297.2834 49.2688 m 290.546 46.1716 L 290.5821 52.6717 L B 290.5821 52.6717 m 297.2834 49.2688 L B 3 w 267.0003 131.9291 m 170.3953 132.0709 69.1547 92.4393 47 49.3589 c S 0.3 w 10 M 237.6984 120.1106 m S 238.2657 120.7233 m S 238.2657 120.7233 m S 238.2657 120.7233 m S 238.2657 120.7233 m S 1 g 0.5 w 4 M 235.25 120.9912 m 238.5546 127.7416 L B 238.5546 127.4916 m 241.9999 120.8002 L 235.5 120.7412 L B 238.2657 120.7233 m 238.4794 110.0084 l S showpage _E end %%EndDocument @endspecial 155 x FQ(Figure)15 b(12:)21 b(Phase)15 b(diagram)g(for)g(a)h (random-\014eld)e(Ising)h(mo)q(del)e(at)j(lo)o(w)f(temp)q(eratures)e(\()p FF(d)i FE(\025)e FQ(3\).)938 2784 y(126)p eop %%Page: 127 127 bop 60 91 a FQ(are)13 b(exactly)e(the)h(same)g(for)g(all)g(v)m(alues)h(of)g (the)f(\014eld,)g(b)q(ecause)h(the)f(constrain)o(t)h(of)g(zero)f(blo)q(c)o(k) g(spins)60 152 y(remo)o(v)o(es)17 b(all)i(\014eld-dep)q(endence)f(inside)h (suc)o(h)g(blo)q(c)o(ks.)30 b(\(The)19 b(p)q(oin)o(t)h(is)f(that)g(the)g (ground-state)60 212 y(con\014gurations,)i(as)f(w)o(ell)f(as)h(the)f(blo)q(c) o(k-spin)g(b)q(oundary)i(conditions)f(needed)f(to)h(select)e(them,)60 272 y(are)i(the)f FP(same)24 b FQ(for)c(all)f(v)m(alues)h(of)g(the)f (magnetic)f(\014eld.\))32 b(In)19 b(Step)h(3,)g(the)g(presence)e(of)i(a)h (\014eld)60 332 y(causes)c(an)g(asymmetry)d(b)q(et)o(w)o(een)h(\\+")j(and)f (\\)p FE(\000)p FQ(")g(b)q(oundary)h(conditions)e(|)h(i.e.)e(w)o(e)h(no)h (longer)60 392 y(ha)o(v)o(e)i FF(c)197 399 y Fy(\000)227 392 y FQ(\()p FF(J)5 b FQ(\))19 b(=)h FE(\000)p FF(c)434 399 y FH(+)463 392 y FQ(\()p FF(J)5 b FQ(\))20 b(|)f(as)i(w)o(ell)d(as)j(a)f (smaller)e(v)m(alue)i(for)g(the)f(di\013erence)g FF(c)1605 399 y FH(+)1635 392 y FQ(\()p FF(J)5 b FQ(\))13 b FE(\000)g FF(c)1791 399 y Fy(\000)1820 392 y FQ(\()p FF(J)5 b FQ(\))60 452 y(b)q(et)o(w)o(een)18 b(the)g(t)o(w)o(o)h(magnetizations.)27 b(But)18 b(this)h(di\013erence)e(is)h(still)g(b)q(ounded)h(a)o(w)o(a)o(y)g (from)e(zero)60 513 y(uniformly)11 b(in)j(\003)f(\(the)g(extra)h(factor)f(in) o(v)o(olv)o(ed)f(dep)q(ends)i(only)f(on)h(the)f(\014elds)g(at)h(the)g(eigh)o (t)e(sites)i(of)60 573 y(the)j(t)o(w)o(o-blo)q(c)o(k)g(observ)m(able\),)g(so) h(the)f(result)g(is)g(still)f(v)m(alid.)24 b(Alternativ)o(ely)l(,)14 b(one)j(could)g(\\un\014x")60 633 y(a)g(strip)f(of)g FF(N)h FE(\002)10 b FQ(2)17 b(blo)q(c)o(ks.)133 693 y(Therefore,)f(w)o(e)f(ha)o(v)o (e:)60 795 y FM(Theorem)i(4.8)24 b FP(F)l(or)16 b(e)n(ach)i FF(d)c FE(\025)g FQ(2)j FP(and)h(e)n(ach)g FQ(ev)o(en)e FF(b)d FE(\025)h FQ(2)p FP(,)k(ther)n(e)f(exists)h(a)f FF(J)1511 802 y FH(0)1548 795 y FP(\(dep)n(ending)i(on)f FF(d)60 855 y FP(and)h FF(b)p FP(\))f(such)g(that)h(the)g(fol)r(lowing)h(is)f(true:)24 b(F)l(or)18 b(any)g(Gibbs)h(me)n(asur)n(e)e FF(\026)i FP(of)f(the)h FF(d)p FP(-dimensional)60 915 y(Ising)25 b(mo)n(del)f(with)g(ne)n(ar)n (est-neighb)n(or)h(c)n(oupling)g FF(J)31 b(>)26 b(J)1160 922 y FH(0)1204 915 y FP(and)e FQ(arbitrary)h FP(magnetic)h(\014eld)f FF(h)p FP(,)60 976 y(the)d(r)n(enormalize)n(d)f(me)n(asur)n(e)g FF(\026T)28 b FP(arising)22 b(fr)n(om)e(the)i(blo)n(ck-aver)n(aging)i(tr)n (ansformation)d(is)h(not)60 1036 y(c)n(onsistent)e(with)f(any)g(quasilo)n(c)n (al)g(sp)n(e)n(ci\014c)n(ation.)26 b(In)19 b(p)n(articular,)g(it)g(is)f(not)h (the)h(Gibbs)f(me)n(asur)n(e)60 1096 y(for)e(any)g(uniformly)h(c)n(onver)n (gent)h(inter)n(action.)133 1198 y FQ(This)11 b(result)f(is)h(in)g(con)o (trast)g(with)f(the)h(results)g(obtained)g(ab)q(o)o(v)o(e)f(for)i(decimation) c(and)k(Kadano\013)60 1258 y(transformations,)h(where)e(w)o(e)h(w)o(ere)f (able)h(to)g(pro)o(v)o(e)g(non-Gibbsianness)h(for)g FF(h)g FE(6)p FQ(=)h(0)f(only)f(for)g FF(d)i FE(\025)g FQ(3)60 1318 y(and)19 b(only)e(for)h FE(j)p FF(h)p FE(j)p FF(=J)23 b FQ(small.)i(The)18 b(restriction)f(to)h(w)o(eak)g(\014elds)f(is,)h(for)g(these)g(examples,)e (essen-)60 1378 y(tial,)i(b)q(ecause)h(it)g(is)f(kno)o(wn)h(that)g(in)g(a)g (strong)h(\014eld)e(the)g(renormalized)f(measure)g(is)i(Gibbsian)60 1438 y([172)q(,)14 b(173)r(,)g(207)q(].)21 b(Moreo)o(v)o(er,)14 b(Martinelli)f(and)j(Olivieri)c([258)q(])j(ha)o(v)o(e)f(pro)o(v)o(en)g(that)i (for)f FP(any)20 b FQ(\()p FF(J)o(;)8 b(h)p FQ(\))60 1499 y(with)20 b FF(h)h FE(6)p FQ(=)g(0,)h(the)e(decimation)e(transformation)j(results)f(in) g(a)h(Gibbsian)g(measure)e(when)h(the)60 1559 y(spacing)d FF(b)f FQ(is)g FP(lar)n(ge)h(enough)22 b FQ(\(ho)o(w)16 b(large)g(dep)q(ends,)h(of)f (course,)g(on)h FF(J)k FQ(and)16 b FF(h)p FQ(\).)133 1619 y(Finally)l(,)c(w)o (e)i(note)f(an)h(in)o(teresting)f(consequence)f(of)i(our)g(Theorem)e(4.7:)21 b(for)14 b(the)f(Ising)g(mo)q(del)60 1679 y(in)f(dimension)f FF(d)j FE(\025)g FQ(3,)f(in)g(the)f(region)h FE(f)p FF(J)18 b(>)c(J)909 1686 y FH(0)928 1679 y FF(;)j FE(j)p FF(h)p FE(j)c FF(<)h(\016)1102 1686 y FH(0)1121 1679 y FF(J)5 b FE(g)p FQ(,)13 b(the)f(Dobrushin-Shlosman)h([94,)g(96])60 1739 y(complete)h(analyticit)o(y)g (condition)j(is)f(violated.)60 1884 y FB(4.4)70 b(Large-Cell)21 b(Renormal)o(iz)o(ati)o(on)g(Maps)j(in)e(Dim)o(e)o(nsion)e Fc(d)1718 1887 y FC(\()28 b(\))1724 1875 y Fb(\025)1787 1884 y FN(4)60 1976 y FQ(F)l(our)-98 b Fa(\030)102 1966 y(\030)116 1962 y(\030)181 1976 y FQ(Fiv)o(e)14 b(y)o(ears)h(ago,)i(Leb)q(o)o(witz)f (and)g(Maes)g([239])f(constructed)h(a)g(v)o(ery)e(di\013eren)o(t)h(example)f (of)60 2036 y(a)20 b(non-Gibbsian)h(measure,)d(arising)i(in)f(the)g(study)h (of)g(en)o(tropic)e(repulsion)h(of)h(a)g(surface)g(b)o(y)f(a)60 2096 y(w)o(all.)j(Subsequen)o(tly)l(,)15 b(Dorlas)i(and)h(v)m(an)f(En)o(ter)f ([103)q(])g(generalized)f(this)i(example,)d(and)j(p)q(oin)o(ted)60 2157 y(out)d(its)f(relev)m(ance)f(for)h(the)g(renormalization-group)g(theory) g(of)h(Ising-lik)o(e)d(mo)q(dels)i(in)g(dimension)60 2217 y FF(d)94 2220 y FC(\()29 b(\))101 2209 y FE(\025)154 2217 y FQ(4.)c(In)16 b(this)h(section)g(w)o(e)f(presen)o(t)h(a)g(sligh)o(tly)f (generalized)g(v)o(ersion)g(of)i(the)e(Leb)q(o)o(witz-Maes-)60 2277 y(Dorlas-v)m(an)h(En)o(ter)f(theorem)e(on)j(non-Gibbsianness,)f(and)h (then)f(discuss)g(its)f(relev)m(ance)g(for)h(R)o(G)60 2337 y(theory)l(.)25 b(The)17 b(reader)h(in)o(terested)e(primarily)f(in)i(the)g (results)h(\(resp.)f(in)g(the)g(application)g(to)h(R)o(G)60 2397 y(theory\))f(should)g(read)g(up)g(through)g(the)g(statemen)o(t)e(of)i (Theorem)f(4.9,)g(and)i(then)e(skip)h(directly)60 2458 y(to)g(Section)e (4.4.3)i(\(resp.)f(to)g(Section)g(4.4.4\).)938 2784 y(127)p eop %%Page: 128 128 bop 60 91 a FM(4.4.1)55 b(Non-Gibbsianness)18 b(of)h(the)f(Sign)h(Field)f(of) g(an)i(\(An\)harmonic)d(Crystal)60 184 y FQ(Consider)i(a)h(system)d(of)j FP(r)n(e)n(al-value)n(d)k FQ(spins)c FE(f)p FF(')963 191 y FD(x)984 184 y FE(g)1009 193 y FD(x)p Fy(2)p Fl(Z)1074 184 y Fs(d)t FQ(,)f(and)h(de\014ne)f FF(\033)1397 191 y FD(x)1437 184 y FQ(=)f(sgn)q(\()p FF(')1615 191 y FD(x)1637 184 y FQ(\).)1670 166 y FH(55)1737 184 y FQ(Clearly)60 244 y FE(f)p FF(\033)113 251 y FD(x)135 244 y FE(g)160 254 y FD(x)p Fy(2)p Fl(Z)224 244 y Fs(d)e FQ(is)11 b(a)g(\014eld)g(of)h(Ising)f(spins.)20 b(W)l(e)11 b(shall)g(sho)o(w)h(that)g(for)f(certain)g(massless)f(Gibbs)i (measures)60 304 y(on)17 b(the)f(system)f(of)h FE(f)p FF(')p FE(g)g FQ(spins,)h(the)f(pro)s(jection)f(of)i(suc)o(h)f(a)h(measure)e(on)i (the)f FE(f)p FF(\033)r FE(g)f FQ(spins)i(is)f(non-)60 364 y(Gibbsian.)133 424 y(The)g(measures)f(w)o(e)g(ha)o(v)o(e)g(in)h(mind)e(are)i (those)h(p)q(ossessing)g(a)f(sp)q(on)o(taneously)h(brok)o(en)f(global)60 485 y(shift)h(symmetry)c FF(')i FE(!)g FF(')c FQ(+)h FF(c)p FQ(.)23 b(More)16 b(precisely)l(,)f(consider)i(a)g(system)e(de\014ned)i (formally)e(b)o(y)h(the)60 545 y(Hamiltonian)662 615 y FF(H)t FQ(\()p FF(')p FQ(\))28 b(=)874 581 y(1)p 874 603 25 2 v 874 649 a(2)915 573 y Fx(X)912 666 y FD(x)p Fy(6)p FH(=)p FD(y)986 615 y FF(V)1014 622 y FD(xy)1055 615 y FQ(\()p FF(')1106 622 y FD(x)1139 615 y FE(\000)11 b FF(')1221 622 y FD(y)1242 615 y FQ(\))i FF(;)477 b FQ(\(4)p FF(:)p FQ(40\))60 751 y(where)14 b(the)f(functions)h FF(V)516 758 y FD(xy)571 751 y FQ(are)g(ev)o(en,)f(and)h FF(V)893 758 y FD(xy)948 751 y FQ(=)g FF(V)1028 758 y FD(x)p FH(+)p FD(a;y)q FH(+)p FD(a)1185 751 y FQ(for)g(all)f FF(x;)8 b(y)r(;)g(a)13 b FE(2)h Fq(Z)1536 730 y FD(d)1556 751 y FQ(.)21 b(Suc)o(h)13 b(a)h(system)60 811 y(is)i(termed)d(an)j FP(anharmonic)i (crystal)j FQ(\(or)16 b(if)f(the)g(functions)h FF(V)1214 818 y FD(xy)1271 811 y FQ(are)g(all)f(quadratic,)g(a)h FP(harmonic)60 872 y(crystal)5 b FQ(\).)21 b([More)16 b(rigorously)l(,)g(suc)o(h)g(a)h (system)d(is)i(de\014ned)g(b)o(y)g(the)g(in)o(teraction)534 1000 y(\010)569 1007 y FD(A)597 1000 y FQ(\()p FF(')p FQ(\))28 b(=)761 940 y Fx(\032)800 976 y FF(V)828 983 y FD(xy)869 976 y FQ(\()p FF(')920 983 y FD(x)953 976 y FE(\000)11 b FF(')1035 983 y FD(y)1055 976 y FQ(\))49 b(if)16 b FF(A)d FQ(=)h FE(f)p FF(x;)8 b(y)r FE(g)800 1037 y FQ(0)299 b(otherwise)1765 1000 y(\(4)p FF(:)p FQ(41\))60 1131 y(where)16 b(the)h FP(a)g(priori)j FQ(measure)c FF(d\026)715 1113 y FH(0)715 1143 y FD(x)737 1131 y FQ(\()p FF(')788 1138 y FD(x)810 1131 y FQ(\))h(is)f(tak)o(en)g(to)h(b)q(e) g(Leb)q(esgue)g(measure.)k(Leb)q(esgue)c(mea-)60 1191 y(sure)j(is)g(not)h (normalizable,)e(but)h(if)g(the)g(p)q(oten)o(tials)g FF(V)1104 1198 y FD(xy)1165 1191 y FQ(are)g(c)o(hosen)g(suitably)l(,)h(then)f(one)g (has)60 1251 y FF(Z)93 1258 y FH(\003)120 1251 y FQ(\()p FF(')171 1258 y FH(\003)195 1249 y Fs(c)213 1251 y FQ(\))14 b FF(<)g FE(1)p FQ(,)e(and)g(the)g(sp)q(eci\014cation)g(is)f(then)h(w)o (ell-de\014ned.)18 b(In)12 b(the)f(in\014nite-range)h(case)g(there)60 1312 y(are)k(some)e(subtleties)h(asso)q(ciated)i(with)e(rapidly)g(gro)o(wing) i(b)q(oundary)f(conditions,)g(as)g(discussed)60 1372 y(in)g(Example)e(4)j(of) g(Section)e(2.3.3.])133 1432 y(F)l(or)24 b(an)h(\(an\)harmonic)e(crystal,)i (an)g(in\014nite-v)o(olume)c(Gibbs)j(measure)f(need)h(not)g(exist;)60 1492 y(and)g(indeed,)h(it)e(will)g(not)i(exist)e(in)g(lo)o(w)h(enough)h (dimension,)e(e.g.)g FF(d)28 b FE(\024)e FQ(2)e(for)h(short-range)60 1552 y(in)o(teractions)16 b([39,)h(92,)g(133)q(].)22 b(Ho)o(w)o(ev)o(er,)15 b(if)h(a)i(Gibbs)f(measure)e FF(\026)i FQ(do)q(es)h(exist,)e(then)g(it)h(p)q (ossesses)60 1613 y(a)k(sp)q(on)o(taneously)h(brok)o(en)e(global)h(shift)g (symmetry)c(in)k(the)f(sense)h(that)g FF(\034)1496 1620 y FD(c)1514 1613 y FF(\026)g FQ(is)f(also)i(a)f(Gibbs)60 1673 y(measure)14 b(for)h(the)g(same)e(in)o(teraction)h(\(here)h FF(\034)914 1680 y FD(c)946 1673 y FQ(is)g(the)g(map)f(that)h(shifts)g(all)g(spins)g(b)o (y)f(a)i(constan)o(t)60 1733 y FF(c)p FQ(\),)h(but)h FF(\034)243 1740 y FD(c)261 1733 y FF(\026)e FE(6)p FQ(=)g FF(\026)i FQ(for)g FF(c)e FE(6)p FQ(=)g(0.)25 b(That)18 b FF(\034)781 1740 y FD(c)799 1733 y FF(\026)g FQ(is)f(a)h(Gibbs)g(measure)e(is)h(an)h(immedi)o(ate)d (consequence)60 1793 y(of)i(the)g(DLR)h(equations,)f(while)f FF(\034)704 1800 y FD(c)722 1793 y FF(\026)g FE(6)p FQ(=)f FF(\026)i FQ(follo)o(ws)g(from)f(the)h(imp)q(ossibilit)o(y)e(of)i(the)g (probabilit)o(y)60 1853 y(distribution)d(of)h FF(')410 1860 y FH(0)444 1853 y FQ(b)q(eing)g(in)o(v)m(arian)o(t)f(under)g(a)h(non-trivial) f(shift.)21 b(F)l(urther)14 b(information)f(on)i(the)60 1914 y(prop)q(erties)h(of)h(\(an\)harmonic)e(crystals)h(can)h(b)q(e)f(found)h(in)f (references)f([39,)h(42)q(].)133 1974 y(Ev)o(ery)22 b(harmonic)f(crystal)i (is)f(a)i(massless)e(Gaussian)i(mo)q(del,)e(and)i(the)e(con)o(v)o(erse)g(is)g (v)o(ery)60 2034 y(nearly)c(true.)27 b(T)l(o)20 b(see)e(this,)g(consider)g(a) h(translation-in)o(v)m(arian)o(t)g(Gaussian)g(measure)f FF(\026)g FQ(on)h Fq(R)1849 2013 y Fl(Z)1870 2001 y Fs(d)60 2094 y FQ(with)d(mean)f FF(m)h FQ(and)h(co)o(v)m(ariance)460 2204 y FE(h)p FF(')511 2211 y FD(x)533 2204 y FQ(;)8 b FF(')587 2211 y FD(y)608 2204 y FE(i)28 b FQ(=)g FF(C)756 2211 y FD(xy)824 2204 y FQ(=)f(\(2)p FF(\031)r FQ(\))981 2184 y Fy(\000)p FD(d)1075 2146 y Fx(Z)1028 2271 y FH([)p Fy(\000)p FD(\031)q(;\031)q FH(])1127 2262 y Fs(d)1157 2200 y Fx(b)1155 2204 y FF(c)p FQ(\()p FF(p)p FQ(\))8 b FF(e)1269 2184 y FD(ip)p Fy(\001)p FH(\()p FD(x)p Fy(\000)p FD(y)q FH(\))1413 2204 y FF(dp)14 b(;)275 b FQ(\(4)p FF(:)p FQ(42\))p 60 2318 732 2 v 100 2372 a FA(55)135 2387 y Fz(Strictly)13 b(sp)q(eaking)g(w)o(e)h(m)o(ust)e(de\014ne)j Fv(\033)760 2393 y Fp(x)794 2387 y Fz(also)d(in)h(the)h(am)o(biguous)d(case)k Fv(')1316 2393 y Fp(x)1348 2387 y Fz(=)d(0.)18 b(The)c(simplest)e(c)o(hoice)i (is)f(to)60 2437 y(set)k Fv(\033)151 2443 y Fp(x)187 2437 y Fz(=)f(+1)g(b)o(y)g(\014at;)g(the)h(most)e(elegan)o(t)h(c)o(hoice)h(is)f(to)g (set)h Fv(\033)1088 2443 y Fp(x)1124 2437 y Fz(=)f Fu(\006)p Fz(1)g(with)g(probabilities)1583 2420 y FA(1)p 1583 2427 17 2 v 1583 2451 a(2)1604 2437 y Fz(.)25 b(Ho)o(w)o(ev)o(er,)17 b(this)60 2487 y(c)o(hoice)f(will)e(in)h(fact)h(pla)o(y)f(no)g(role,)h(as)f (ev)o(ery)i(measure)e(that)h(w)o(e)g(will)e(consider)i(has)g(the)g(prop)q (ert)o(y)h(Prob\()p Fv(')1822 2493 y Fp(x)1858 2487 y Fz(=)60 2536 y(0)d(for)f(at)h(least)g(one)g Fv(x)p Fz(\))d(=)h(0.)938 2784 y FQ(128)p eop %%Page: 129 129 bop 60 91 a FQ(where)199 87 y Fx(b)198 91 y FF(c)p FQ(\()p FF(p)p FQ(\))13 b(is)g(a)g(nonnegativ)o(e,)g(ev)o(en,)f(in)o(tegrable)g (function)h(of)h FF(p)g FE(2)g FQ([)p FE(\000)p FF(\031)r(;)8 b(\031)r FQ(])1479 73 y FD(d)1497 91 y FQ(.)20 b(No)o(w)13 b(let)f(us)h(de\014ne)566 210 y FF(B)603 217 y FD(xy)671 210 y FQ(=)28 b(\(2)p FF(\031)r FQ(\))829 189 y Fy(\000)p FD(d)923 151 y Fx(Z)875 277 y FH([)p Fy(\000)p FD(\031)q(;\031)q FH(])974 268 y Fs(d)1004 206 y Fx(b)1002 210 y FF(c)p FQ(\()p FF(p)p FQ(\))1085 189 y Fy(\000)p FH(1)1141 210 y FF(e)1164 189 y FD(ip)p Fy(\001)p FH(\()p FD(x)p Fy(\000)p FD(y)q FH(\))1307 210 y FF(dp)15 b(;)380 b FQ(\(4)p FF(:)p FQ(43\))60 376 y(assuming)18 b(that)384 372 y Fx(b)382 376 y FF(c)p FQ(\()p FF(p)p FQ(\))465 358 y Fy(\000)p FH(1)532 376 y FQ(is)g(an)h(in)o(tegrable)f(function)g(of)h FF(p)p FQ(.)29 b(Then)19 b FF(B)i FQ(is)e(the)f(in)o(v)o(erse)f(matrix)g(of) 60 437 y(the)f(co)o(v)m(ariance)g(matrix)e FF(C)t FQ(.)21 b(No)o(w,)16 b(supp)q(ose)h(that)807 499 y Fx(X)828 586 y FD(y)875 540 y FE(j)p FF(B)926 547 y FD(xy)967 540 y FE(j)27 b FF(<)h FE(1)14 b FF(;)613 b FQ(\(4)p FF(:)p FQ(44\))60 683 y(as)13 b(will)f(o)q(ccur)h(if) 376 679 y Fx(b)374 683 y FF(c)p FQ(\()p FF(p)p FQ(\))457 665 y Fy(\000)p FH(1)517 683 y FQ(is)g(at)g(least)f(mo)q(destly)g(smo)q(oth.)1105 665 y FH(56)1162 683 y FQ(In)h(that)g(case,)g(there)f(is)g(a)h(w)o (ell-de\014ned)60 743 y(sp)q(eci\014cation)j(corresp)q(onding)h(to)g(the)f (formal)f(Hamiltonian)609 847 y FF(H)t FQ(\()p FF(')p FQ(\))28 b(=)822 827 y FH(1)p 822 835 18 2 v 822 864 a(2)852 805 y Fx(X)858 892 y FD(x;y)921 847 y FF(B)958 854 y FD(xy)998 847 y FF(')1030 854 y FD(x)1052 847 y FF(')1084 854 y FD(y)1124 847 y FE(\000)19 b FF(h)1218 805 y Fx(X)1239 892 y FD(x)1287 847 y FF(')1319 854 y FD(x)1765 847 y FQ(\(4)p FF(:)p FQ(45\))60 988 y(with)13 b FF(h)h FQ(=)g FF(m=)331 984 y Fx(b)329 988 y FF(c)p FQ(\(0\))g(and)g FP(a)h(priori)i FQ(measure)c(tak)o(en)g(to)h(b)q(e)f(Leb)q(esgue)i(measure;)d (and)j FF(\026)e FQ(is)h(a)g(Gibbs)60 1048 y(measure)g(for)i(this)g(sp)q (eci\014cation.)k(In)c(particular,)f(if)1058 1044 y Fx(b)1057 1048 y FF(c)p FQ(\(0\))f(=)g FE(1)h FQ(|)g(this)h(is)f(the)g(\\massless")h (case)60 1108 y(|)g(then)g(the)g(couplings)g FF(B)571 1115 y FD(xy)628 1108 y FQ(satisfy)834 1170 y Fx(X)854 1257 y FD(y)902 1212 y FF(B)939 1219 y FD(xy)1007 1212 y FQ(=)28 b(0)14 b FF(:)640 b FQ(\(4)p FF(:)p FQ(46\))60 1350 y(This)16 b(means)g(that)g(the)g (Hamiltonian)f(can)h(b)q(e)h(rewritten)e(as)665 1453 y FF(H)t FQ(\()p FF(')p FQ(\))28 b(=)877 1434 y FH(1)p 877 1442 V 877 1470 a(4)919 1420 y Fx(P)908 1492 y FD(x)p Fy(6)p FH(=)p FD(y)982 1453 y FF(B)1019 1460 y FD(xy)1060 1453 y FQ(\()p FF(')1111 1460 y FD(x)1144 1453 y FE(\000)11 b FF(')1226 1460 y FD(y)1246 1453 y FQ(\))1265 1435 y FH(2)1765 1453 y FQ(\(4)p FF(:)p FQ(47\))60 1587 y(\(note)18 b(that)h(here)e FF(h)h FQ(=)f(0\).)27 b(Th)o(us,)18 b(ev)o(ery)f(massless)g(Gaussian)j(measure)d(\(satisfying)h(mild)e(reg-)60 1647 y(ularit)o(y)k(conditions\))h(is)f(the)h(Gibbs)g(measure)e(for)j(some)d (harmonic)h(crystal,)h(and)g(con)o(v)o(ersely)l(.)60 1707 y(F)l(urther)h (details)h(on)g(the)g(Gibbs)g(represen)o(tation)f(of)h(Gaussian)h(measures)e (can)h(b)q(e)g(found)g(in)60 1768 y(references)15 b([86,)h(227)q(])g(and)h ([157,)f(Chapter)h(13].)133 1828 y(No)o(w)e(let)g FF(\026)g FQ(b)q(e)h(an)o(y)f(translation-in)o(v)m(arian)o(t)g(Gibbs)h(measure)e(of)h (the)g(\(an\)harmonic)g(crystal,)60 1888 y(and)21 b(let)238 1884 y Fx(e)233 1888 y FF(\026)g FQ(b)q(e)f(its)g(Ising)g(pro)s(jection.)32 b(Under)20 b(mild)e(tec)o(hnical)g(conditions)j(on)f(the)g(p)q(oten)o(tials) 60 1948 y FF(V)88 1955 y FD(xy)129 1948 y FQ(,)c(w)o(e)g(will)f(pro)o(v)o(e)g (that)564 1944 y Fx(e)560 1948 y FF(\026)h FQ(is)g(a)h FP(non-Gibbsian)22 b FQ(measure.)e(The)c(basic)g(idea)g(of)g(the)g(pro)q(of)i(is)e(to)60 2008 y(use)g(the)g(sp)q(on)o(taneously)h(brok)o(en)f(shift)g(symmetry)d(to)k (sho)o(w)g(that)560 2112 y(Prob)664 2119 y FD(\026)687 2112 y FQ(\()p FF(')738 2119 y FD(x)774 2112 y FF(>)d FQ(0)i(for)h(all)f FF(x)d FE(2)h FF(A)p FQ(\))28 b FE(\025)f FF(e)1270 2091 y Fy(\000)p FD(o)p FH(\()p Fy(j)p FD(A)p Fy(j)p FH(\))1765 2112 y FQ(\(4)p FF(:)p FQ(48\))60 2215 y(as)19 b FF(A)f FE(\045)g(1)h FQ(\(v)m(an)g(Ho)o(v)o(e\).)27 b(That)20 b(is,)f(the)f(probabilit)o(y)g(that) h FP(al)r(l)26 b FQ(the)18 b(spins)h(in)g(a)g(region)g FF(A)f FQ(are)60 2275 y(sim)o(ultaneously)e(p)q(ositiv)o(e)h(is)h(exp)q(onen)o (tially)f(suppressed)h(at)g(a)h(rate)f FP(slower)24 b FQ(than)18 b(the)g(v)o(olume)60 2336 y(of)f FF(A)e FQ(\(roughly)i(sp)q(eaking,)f(it)g (is)g(suppressed)h(b)o(y)e(a)i(\\surface)g(term"\).)i(This)e(means)e(that)827 2439 y FF(i)p FQ(\()p FF(\016)887 2418 y FH(+)916 2439 y FE(j)934 2435 y Fx(e)930 2439 y FF(\026)p FQ(\))28 b(=)f(0)14 b FF(;)642 b FQ(\(4)p FF(:)p FQ(49\))p 60 2484 732 2 v 100 2537 a FA(56)135 2553 y Fz(A)20 b(necessary)i(condition)d(for)634 2521 y Fx(P)678 2565 y Fp(y)705 2553 y Fu(j)p Fv(B)748 2559 y Fp(xy)786 2553 y Fu(j)j Fv(<)g Fu(1)d Fz(to)h(hold)g(is)g(that)f Fx(b)-22 b Fv(c)p Fz(\()p Fv(p)p Fz(\))1306 2537 y Fo(\000)p FA(1)1370 2553 y Fz(b)q(e)21 b(a)f(con)o(tin)o(uous)g(function)g(of)60 2610 y Fv(p)11 b Fu(2)h Fz([)p Fu(\000)p Fv(\031)q(;)7 b(\031)q Fz(])257 2595 y Fp(d)275 2610 y Fz(.)18 b(Ho)o(w)o(ev)o(er,)12 b(this)h(condition)f(is)h(not)f(su\016cien)o(t;)h(for)g(some)e(su\016cien)o (t)i(conditions)g(in)f(the)h(case)h Fv(d)d Fz(=)h(1,)60 2660 y(see)j([108)o(,)e(Section)i(10.6])d(and)h([211)o(].)938 2784 y FQ(129)p eop %%Page: 130 130 bop 60 91 a FQ(where)15 b FF(\016)224 73 y FH(+)268 91 y FQ(is)g(the)g(delta) g(measure)f(concen)o(trated)h(on)h(the)f(con\014guration)h(with)g(all)e (spins)i(+.)21 b(If)1865 87 y Fx(e)1861 91 y FF(\026)60 152 y FQ(w)o(ere)c(Gibbsian,)g(then)h(b)o(y)f(Prop)q(osition)i(2.67,)f FF(\016)983 133 y FH(+)1029 152 y FQ(w)o(ould)g(ha)o(v)o(e)f(to)g(b)q(e)h (Gibbsian)g(for)g(the)f(same)60 212 y(in)o(teraction.)35 b(But)21 b FF(\016)465 194 y FH(+)515 212 y FQ(is)h(ob)o(viously)e(non-Gibbsian)j (\(no)e(absolutely)g(summable)e(in)o(teraction)60 272 y(can)d(force)g(a)h (spin)f(to)h(b)q(e)f(+\),)g(so)688 268 y Fx(e)684 272 y FF(\026)g FQ(m)o(ust)f(also)i(b)q(e)f(non-Gibbsian.)1312 254 y FH(57)133 332 y FQ(The)g(pro)q(of)i(of)e(\(4.48\))h(pro)q(ceeds)g(in)f(three)f(steps:) 133 392 y FP(Step)k(1.)i FQ(Using)16 b(the)g(DLR)h(equations,)f(one)g(pro)o (v)o(es)g(the)g(iden)o(tit)o(y)414 456 y Fx(Z)464 515 y FF(F)7 b FQ(\()p FF(')p FQ(\))h FF(d\026)p FQ(\()p FF(')p FQ(\))28 b(=)799 456 y Fx(Z)848 515 y FF(F)7 b FQ(\()p FF(')k FQ(+)g FF(k)r(\037)1056 522 y FD(A)1084 515 y FQ(\))d FF(e)1134 494 y Fy(\000)p FD(H)1190 500 y Fs(r)q(el)1232 494 y FH(\()p FD(')p FH(+)p FD(k)q(\037)1337 500 y Fs(A)1363 494 y FH(;)p FD(')p FH(\))1419 515 y FF(d\026)p FQ(\()p FF(')p FQ(\))222 b(\(4)p FF(:)p FQ(50\))60 637 y(for)14 b(an)o(y)f(b)q(ounded)i(function)e FF(F)20 b FQ(and)14 b(an)o(y)g(Gibbs)g(measure)e FF(\026)p FQ(.)20 b(Here)13 b FF(A)g FQ(is)g(an)i(arbitrary)e(\014nite)g(set)60 697 y(of)h(sites,)f FF(\037)264 704 y FD(A)305 697 y FQ(is)g(its)g(indicator) g(function,)g FF(k)i FQ(is)f(an)f(arbitrary)h(real)e(n)o(um)o(b)q(er,)g(and)i FF(H)1589 704 y FD(r)q(el)1649 697 y FQ(denotes)f(the)60 757 y(energy)k(di\013erence)f(b)q(et)o(w)o(een)g(the)h(t)o(w)o(o)g (con\014gurations.)25 b(\(Since)17 b(the)g(t)o(w)o(o)g(con\014gurations)h (di\013er)60 817 y(on)h(a)g(\014nite)f(set)g(of)h(sites,)f(this)g(energy)g (di\013erence)g(is)g(\014nite)g FF(\026)p FQ(-a.e.\))28 b(In)18 b(essence,)g(this)g(iden)o(tit)o(y)60 877 y(sa)o(ys)i(that)g(a)g (con\014guration)g FF(')14 b FQ(+)f FF(k)r(\037)773 884 y FD(A)821 877 y FQ(has)20 b(a)g(probabilit)o(y)e FF(e)1230 859 y Fy(\000)p FD(H)1286 865 y Fs(r)q(el)1328 859 y FH(\()p FD(')p FH(+)p FD(k)q(\037)1433 865 y Fs(A)1459 859 y FH(;)p FD(')p FH(\))1527 877 y FQ(times)g(as)i(large)f(as)60 938 y(that)e(of)f(the)g(con\014guration)i FF(')p FQ(.)133 998 y FP(Step)d(2.)21 b FQ(One)13 b(estimates)e(the)i(energy) f(di\013erence)g FF(H)1098 1005 y FD(r)q(el)1145 998 y FQ(,)h(and)g(attempts) f(to)i(remo)o(v)o(e)c(the)j(factor)60 1058 y FF(e)83 1040 y Fy(\000)p FD(H)139 1046 y Fs(r)q(el)199 1058 y FQ(from)j(the)g(righ)o(t-hand) g(side)g(of)h(\(4.50\))g(at)f(the)g(price)f(of)i(a)g(prefactor)f FF(e)1522 1040 y Fy(\000)p FD(o)p FH(\()p Fy(j)p FD(A)p Fy(j)p FH(\))1642 1058 y FQ(.)133 1118 y FP(Step)21 b(3.)28 b FQ(Sp)q(ecializing)18 b(to)h(the)f(case)h FF(F)7 b FQ(\()p FF(')p FQ(\))17 b(=)h FF(\037)p FQ(\()p FF(')f(>)h FQ(0)e(on)h FF(A)p FQ(\),)h(one)h(attempts)f(to) h(pro)o(v)o(e)f(a)60 1178 y(lo)o(w)o(er)g(b)q(ound)j(on)415 1143 y Fx(R)442 1178 y FF(F)7 b FQ(\()p FF(')13 b FQ(+)g FF(k)r(\037)654 1185 y FD(A)682 1178 y FQ(\))8 b FF(d\026)p FQ(\()p FF(')p FQ(\))20 b(that)g(is)f(of)g(the)g(form)g FF(e)1301 1160 y Fy(\000j)p FD(A)p Fy(j)p FD(f)t FH(\()p FD(k)q FH(\))1443 1178 y FQ(,)h(where)f FF(f)5 b FQ(\()p FF(k)r FQ(\))19 b FE(!)g FQ(0)g(as)60 1239 y FF(k)d FE(!)e FQ(+)p FE(1)p FQ(.)20 b(Since)15 b(the)h(left-hand)f(side)h (of)g(\(4.50\))g(is)f(indep)q(enden)o(t)g(of)h FF(k)r FQ(,)g(w)o(e)f(can)h (tak)o(e)f FF(k)h FE(!)d FQ(+)p FE(1)60 1299 y FQ(and)k(th)o(us)f(complete)e (the)i(pro)q(of.)133 1359 y(Unfortunately)l(,)f(Steps)i(2)f(and)h(3)g(are)f (sligh)o(tly)f(tric)o(ky)g(\(though)i(not)g(terribly)e(complicated\),)60 1419 y(and)k(the)f(details)g(of)h(the)g(pro)q(of)g(dep)q(end)g(on)g(the)f (exact)g(form)g(of)g(the)h(p)q(oten)o(tials)f FF(V)1650 1426 y FD(xy)1691 1419 y FQ(.)28 b(In)19 b(fact,)60 1479 y(w)o(e)d(ha)o(v)o(e)f FP(thr)n(e)n(e)20 b FQ(distinct)15 b(pro)q(ofs,)i(eac)o(h)f(one)g(v)m(alid)g (for)h(a)f(distinct)g(class)g(of)h FF(V)1509 1486 y FD(xy)1550 1479 y FQ(:)95 1581 y(\(a\))25 b(Eac)o(h)16 b FF(V)331 1588 y FD(xy)388 1581 y FQ(is)g(con)o(v)o(ex,)f(and)715 1548 y Fx(P)706 1619 y FD(z)q Fy(6)p FH(=0)777 1581 y FE(k)p FF(V)841 1563 y Fy(0)830 1593 y FH(0)p FD(z)868 1581 y FE(k)893 1588 y Fy(1)944 1581 y FF(<)f FE(1)p FQ(.)93 1713 y(\(b\))24 b(Eac)o(h)16 b FF(V)331 1720 y FD(xy)388 1713 y FQ(is)g(quadratic)g(\(of)g(either)f(sign\),) h(and)h(the)f(measure)f FF(\026)h FQ(is)g(a)g(massless)g(Gaussian)182 1773 y(satisfying)g(\(4.44\))h(and)g(\(4.46\).)98 1875 y(\(c\))24 b(Eac)o(h)19 b FF(V)334 1882 y FD(xy)394 1875 y FQ(is)f(con)o(v)o(ex,)g(the)g (mo)q(del)g(is)h(\014nite-range)g(\(i.e.)e(only)h(\014nitely)g(man)o(y)f(of)i (the)g FF(V)1852 1882 y FH(0)p FD(z)182 1935 y FQ(are)c(nonzero\),)g(and)h (the)f(mo)q(del)f(is)g(dominated)g(b)o(y)h(a)h(stable)f(Gaussian)h(in)f(the)g (sense)g(that)182 1995 y(the)h(v)o(ectors)g FE(f)p FF(z)r FQ(:)21 b(inf)535 2020 y FD(')584 1995 y FF(V)624 1977 y Fy(00)612 2008 y FH(0)p FD(z)650 1995 y FQ(\()p FF(')p FQ(\))14 b FF(>)g FQ(0)p FE(g)i FQ(span)h(a)g(subspace)g(of)f Fq(R)1299 1974 y FD(d)1335 1995 y FQ(of)h(dimension)d FF(>)g FQ(2.)60 2114 y(\(W)l(e)j(conjecture)e(that)j(these)e(tec)o(hnical)f(conditions)i(can)g(b)q (e)g(remo)o(v)o(ed)e(or)i(at)g(least)g(w)o(eak)o(ened.\))60 2174 y(Case)i(\(a\))h(is)e(the)h(easiest)g(case,)g(as)g(the)g(energy)g(shift) f(is)h(uniformly)e(b)q(ounded;)k(unfortunately)l(,)60 2234 y(the)15 b(sup)g(norm)f(condition)h(on)h FF(V)676 2216 y Fy(0)703 2234 y FQ(do)q(es)f(not)h(allo)o(w)f(p)q(oten)o(tials)g(gro)o(wing)g(faster)h (than)f(linearly)f(at)60 2294 y(in\014nit)o(y)f(\(suc)o(h)g(as)h (Gaussians!\).)22 b(All)12 b(the)i(tec)o(hnical)e(details)h(in)h(cases)g (\(b\))f(and)i(\(c\))e(are)h(attempts)p 60 2341 732 2 v 100 2395 a FA(57)135 2410 y Fw(A)o(lternative)d(ar)n(gument:)19 b Fz(If)12 b Fx(e)-25 b Fv(\026)10 b Fz(w)o(ere)i(Gibbsian,)d(then)j(b)o(y)e (Prop)q(osition)g(2.67,)f Fv(\016)1379 2395 y FA(+)1417 2410 y Fz(w)o(ould)h(ha)o(v)o(e)h(to)f(b)q(e)h(Gibbsian)60 2460 y(for)f(the)g(same)g(in)o(teraction,)g(and)g(moreo)o(v)o(er)f Fv(i)p Fz(\()r Fx(e)-25 b Fv(\026)q Fu(j)p Fv(\016)845 2445 y FA(+)872 2460 y Fz(\))10 b(w)o(ould)f(ha)o(v)o(e)h(to)g(b)q(e)h(zero.)17 b(But)11 b(in)f(fact)g Fv(i)p Fz(\()r Fx(e)-25 b Fv(\026)p Fu(j)p Fv(\016)1598 2445 y FA(+)1625 2460 y Fz(\))12 b(=)g Fu(1)p Fz(.)k Fw(Se)n(c)n(ond)60 2509 y(alternative)c(ar)n(gument:)20 b Fz(If)14 b Fx(e)-25 b Fv(\026)11 b Fz(w)o(ere)i(Gibbsian,)e(then)h(b)o(y)g (Prop)q(osition)g(2.59,)e(the)j(pressure)h Fv(p)p Fz(\()p Fv(g)q Fu(j)r Fx(e)-25 b Fv(\026)o Fz(\))12 b(w)o(ould)f(ha)o(v)o(e)h(to)60 2559 y(b)q(e)g Fw(strictly)h Fz(con)o(v)o(ex)f(in)e(directions)i Fv(g)h Fz(=)f Fv(f)716 2565 y FA(\010)758 2559 y Fv(=)-26 b Fu(2)12 b(I)7 b Fz(+)t Fv(const)k Fz(arising)f(from)g(in)o(teractions)h(\010) h Fu(2)f(B)1525 2544 y FA(1)1544 2559 y Fz(.)17 b(But)12 b(for)f Fv(g)q Fz(\()p Fv(\033)q Fz(\))h(=)g Fv(\033)1872 2565 y FA(0)60 2609 y Fz(\(i.e.)i(a)h(magnetic)f(\014eld\),)h(it)g(is)g(easy)h(to)f(see)h (from)e(\(4.48\))g(that)h Fv(p)p Fz(\()p Fv(\025g)q Fu(j)r Fx(e)-25 b Fv(\026)p Fz(\))14 b(=)g Fv(\025)h Fz(for)g(all)f Fv(\025)g Fu(\025)g Fz(0,)g(con)o(tradicting)h(the)60 2659 y(strict)g(con)o(v)o(exit)o(y)m(.)i(\(F)m(or)d(a)f(more)g(general)h(v)o (ersion)g(of)f(this)h(latter)g(argumen)o(t,)f(see)i(Section)f(4.4.2.\))938 2784 y FQ(130)p eop %%Page: 131 131 bop 60 91 a FQ(to)20 b(con)o(trol)f(an)g(energy)g(shift)g(that)h(is)f(b)q (ounded)h(only)f(in)g(some)f FP(aver)n(age)24 b FQ(sense.)30 b(W)l(e)19 b(urge)g(the)60 152 y(reader)i(to)h(study)g(\014rst)g(the)g(pro)q (of)g(for)g(case)g(\(a\),)h(b)q(efore)e(pro)q(ceeding)h(to)g(cases)g(\(b\))g (and)g(\(c\).)60 212 y(Case)15 b(\(b\))f(is)h(the)f(one)g(treated)h(b)o(y)f (Dorlas)h(and)g(v)m(an)g(En)o(ter)f([103];)h(w)o(e)f(follo)o(w)g(their)f(pro) q(of)j(almost)60 272 y(v)o(erbatim.)j(Case)d(\(c\))f(is)g(a)h(minor)f (generalization)g(of)h(the)f(one)h(treated)f(b)o(y)g(Leb)q(o)o(witz)h(and)g (Maes)60 332 y([239)q(];)h(the)h(pro)q(of)h(w)o(e)e(giv)o(e)g(is)h(sligh)o (tly)e(di\013eren)o(t)h(from)g(theirs,)g(but)h(the)g(underlying)f(ideas)g (and)60 392 y(tric)o(ks)e(are)h(the)g(same.)60 490 y FM(Theorem)h(4.9)24 b FP(L)n(et)e FF(\026)g FP(b)n(e)h(a)f(tr)n(anslation-invariant)i(Gibbs)f(me) n(asur)n(e)e(for)h(an)h(\(an\)harmonic)60 550 y(crystal)f(satisfying)g(one)h (of)f(the)g(c)n(onditions)h(\(a\){\(c\))f(liste)n(d)g(ab)n(ove.)37 b(In)22 b(c)n(ase)g(\(c\),)h(assume)g(in)60 610 y(addition)18 b(that)f FF(\026)h FP(is)f(symmetric)g(ar)n(ound)g(its)h(me)n(an.)k(Then)c (for)f(e)n(ach)h FF(M)h(<)14 b FE(1)p FP(,)j(we)h(have)543 706 y FQ(Prob)647 713 y FD(\026)670 706 y FQ(\()p FF(')721 713 y FD(x)757 706 y FF(>)c(M)22 b FP(for)17 b(al)r(l)i FF(x)14 b FE(2)g FF(A)p FQ(\))27 b FE(\025)g FF(e)1287 686 y Fy(\000)p FD(o)p FH(\()p Fy(j)p FD(A)p Fy(j)p FH(\))1765 706 y FQ(\(4)p FF(:)p FQ(51\))60 802 y FP(as)d FF(A)j FE(\045)f(1)e FP(\(van)h(Hove\).)44 b(It)25 b(fol)r(lows)h(that)986 798 y Fx(e)981 802 y FF(\026)q FP(,)g(the)e(pr)n(oje)n(ction)g(of)h FF(\026)f FP(on)h(the)g(Ising)g(spins)60 862 y FF(\033)88 869 y FD(x)123 862 y FE(\021)14 b FQ(sgn)q(\()p FF(')298 869 y FD(x)320 862 y FQ(\))p FP(,)j(is)g(not)h(the)g(Gibbs)g(me)n (asur)n(e)f(for)g(any)g(inter)n(action)h(in)g FE(B)1427 844 y FH(1)1446 862 y FP(.)133 960 y FM(Remarks.)h FQ(1.)j(One)15 b(consequence)g(of)h(this)g(theorem)f(is)g(that)i(an)f(arbitrarily)f(w)o(eak) h(p)q(ertur-)60 1020 y(bation)k(of)g(the)g(form)f FF(H)24 b FE(!)c FF(H)e FE(\000)725 987 y Fx(P)769 1030 y FD(x)799 1020 y FF(f)5 b FQ(\()p FF(')879 1027 y FD(x)901 1020 y FQ(\),)20 b(where)g FF(f)25 b FQ(is)20 b(nondecreasing)g(and)g(nonconstan)o(t,)60 1080 y(will)f(driv)o(e)g(the)h(spins)h FF(')529 1087 y FD(x)571 1080 y FQ(to)g(+)p FE(1)p FQ(.)33 b(As)20 b(a)h(result,)f(th)o(us)h(the)f(p)q (erturb)q(ed)h(mo)q(del)e(will)g(ha)o(v)o(e)h(no)60 1140 y(in\014nite-v)o (olume)c(translation-in)o(v)m(arian)o(t)i(Gibbs)h(measures.)28 b(This)18 b(is)h(the)f(phenomenon)g(of)h(en-)60 1201 y(tropic)d(repulsion)g (of)g(a)h(surface)f(b)o(y)g(a)h(soft)f(w)o(all,)g(studied)g(b)o(y)f(Leb)q(o)o (witz)i(and)f(Maes)h([239].)133 1261 y(2.)22 b(It)16 b(is)g(natural)h(to)f (ask)h(whether)803 1257 y Fx(e)798 1261 y FF(\026)g FQ(is)f(non-quasilo)q (cal)h(\(and)g(not)g(merely)c(non-Gibbsian\).)60 1321 y(W)l(e)j(discuss)g (this)g(question,)g(in)g(somewhat)g(greater)g(generalit)o(y)l(,)f(in)g (Section)h(4.4.3.)60 1423 y Fd(Pr)o(oof)g(of)g(Theorem)g(4.9.)69 b FQ(Since)14 b(the)g(h)o(yp)q(otheses)h(of)g(the)f(theorem)f(are)i(in)o(v)m (arian)o(t)f(under)60 1483 y(a)20 b(uniform)f(shift)g FF(')h FE(!)g FF(')13 b FQ(+)g FF(c)p FQ(,)21 b(it)e(su\016ces)g(to)h(consider)g (the)f(case)h FF(M)25 b FQ(=)20 b(0;)i(this)d(ligh)o(tens)g(the)60 1543 y(notation.)j(\(F)l(or)17 b(our)f(application)g(to)h(the)f(sign)h (function,)e(w)o(e)h(need)g(only)g FF(M)j FQ(=)14 b(0)j(an)o(yw)o(a)o(y)l(.)j (But)60 1603 y(w)o(e)c(will)f(exploit)g(the)h(form)o(ulation)f(with)h (general)g FF(M)22 b FQ(in)16 b(Section)f(4.4.2.\))133 1663 y FP(Step)j(1.)j FQ(Let)16 b FF(\026)f FQ(b)q(e)h(an)o(y)f(Gibbs)h(measure)e (for)i FP(any)k FQ(mo)q(del)14 b(of)i(real-v)m(alued)f(spins)g(\(not)h (neces-)60 1724 y(sarily)g(an)g(anharmonic)g(crystal\).)21 b(Then)16 b(the)g(DLR)h(equations)f(for)h(v)o(olume)d(\003)i(sa)o(y)g(that) 497 1819 y FF(d\026)551 1826 y FH(\003)579 1819 y FQ(\()p FF(')630 1826 y FH(\003)656 1819 y FE(j)p FF(')702 1826 y FH(\003)726 1817 y Fs(c)744 1819 y FQ(\))28 b(=)g FF(Z)890 1826 y FH(\003)917 1819 y FQ(\()p FF(')968 1826 y FH(\003)992 1817 y Fs(c)1010 1819 y FQ(\))1029 1799 y Fy(\000)p FH(1)1084 1819 y FF(e)1107 1799 y Fy(\000)p FD(H)1163 1805 y Fr(\003)1186 1799 y FH(\()p FD(')1223 1805 y Fr(\003)1246 1799 y FD(;')1279 1805 y Fr(\003)1300 1798 y Fs(c)1317 1799 y FH(\))1341 1819 y FF(d')1398 1826 y FH(\003)1439 1819 y FF(:)312 b FQ(\(4)p FF(:)p FQ(52\))60 1915 y(No)o(w)15 b(let)f FF(F)21 b FQ(b)q(e)15 b(an)o(y)f(b)q(ounded)i(\(for)f (simplicit)o(y)o(\))d(measurable)i(function,)g(and)i(let)e FF( )i FQ(b)q(e)f(an)o(y)g(\014eld)60 1975 y(whic)o(h)h(v)m(anishes)g (outside)g(\003.)21 b(Then)131 2012 y Fx(Z)180 2071 y FF(F)7 b FQ(\()p FF(')p FQ(\))h FF(d\026)351 2078 y FH(\003)378 2071 y FQ(\()p FF(')429 2078 y FH(\003)456 2071 y FE(j)p FF(')502 2078 y FH(\003)526 2069 y Fs(c)544 2071 y FQ(\))41 b(=)h FF(Z)717 2078 y FH(\003)744 2071 y FQ(\()p FF(')795 2078 y FH(\003)819 2069 y Fs(c)837 2071 y FQ(\))856 2050 y Fy(\000)p FH(1)912 2012 y Fx(Z)962 2071 y FF(F)7 b FQ(\()p FF(')p FQ(\))h FF(e)1102 2050 y Fy(\000)p FD(H)1158 2056 y Fr(\003)1180 2050 y FH(\()p FD(')1217 2056 y Fr(\003)1239 2050 y FD(;')1272 2056 y Fr(\003)1293 2049 y Fs(c)1311 2050 y FH(\))1335 2071 y FF(d')1392 2078 y FH(\003)604 2180 y FQ(=)42 b FF(Z)717 2187 y FH(\003)744 2180 y FQ(\()p FF(')795 2187 y FH(\003)819 2178 y Fs(c)837 2180 y FQ(\))856 2159 y Fy(\000)p FH(1)912 2121 y Fx(Z)962 2180 y FF(F)7 b FQ(\()p FF(')j FQ(+)h FF( )r FQ(\))d FF(e)1195 2159 y Fy(\000)p FD(H)1251 2165 y Fr(\003)1273 2159 y FH(\()p FD(')1310 2165 y Fr(\003)1333 2159 y FH(+)p FD( )1383 2165 y Fr(\003)1406 2159 y FD(;')1439 2165 y Fr(\003)1460 2158 y Fs(c)1478 2159 y FH(\))1502 2180 y FF(d')1559 2187 y FH(\003)604 2289 y FQ(=)684 2230 y Fx(Z)734 2289 y FF(F)f FQ(\()p FF(')j FQ(+)h FF( )r FQ(\))d FF(e)967 2268 y Fy(\000)p FH([)p FD(H)1033 2274 y Fr(\003)1055 2268 y FH(\()p FD(')1092 2274 y Fr(\003)1115 2268 y FH(+)p FD( )1165 2274 y Fr(\003)1188 2268 y FD(;')1221 2274 y Fr(\003)1242 2267 y Fs(c)1260 2268 y FH(\))p Fy(\000)p FD(H)1330 2274 y Fr(\003)1353 2268 y FH(\()p FD(')1390 2274 y Fr(\003)1412 2268 y FD(;')1445 2274 y Fr(\003)1466 2267 y Fs(c)1484 2268 y FH(\)])1518 2289 y FF(d\026)1572 2296 y FH(\003)1599 2289 y FQ(\()p FF(')1650 2296 y FH(\003)1676 2289 y FE(j)p FF(')1722 2296 y FH(\003)1746 2287 y Fs(c)1765 2289 y FQ(\))14 b FF(;)1765 2376 y FQ(\(4.53\))60 2472 y(where)24 b(in)g(the)f(middle)f(line)h(w)o(e)h(used)g(the)g(shift)g(in) o(v)m(ariance)f(of)i(Leb)q(esgue)g(measure.)43 b(No)o(w)60 2532 y(in)o(tegrate)16 b(o)o(v)o(er)f FF(d\026)423 2539 y FH(\003)447 2530 y Fs(c)466 2532 y FQ(\()p FF(')517 2539 y FH(\003)541 2530 y Fs(c)560 2532 y FQ(\):)21 b(w)o(e)16 b(obtain)448 2584 y Fx(Z)498 2643 y FF(F)7 b FQ(\()p FF(')p FQ(\))h FF(d\026)p FQ(\()p FF(')p FQ(\))28 b(=)832 2584 y Fx(Z)882 2643 y FF(F)7 b FQ(\()p FF(')j FQ(+)h FF( )r FQ(\))d FF(e)1115 2622 y Fy(\000)p FD(H)1171 2628 y Fs(r)q(el)1213 2622 y FH(\()p FD(')p FH(+)p FD( )q FH(;)p FD(')p FH(\))1358 2643 y FF(d\026)p FQ(\()p FF(')p FQ(\))15 b FF(;)254 b FQ(\(4)p FF(:)p FQ(54\))938 2784 y(131)p eop %%Page: 132 132 bop 60 91 a FQ(where)413 152 y FF(H)453 159 y FD(r)q(el)500 152 y FQ(\()p FF(')11 b FQ(+)g FF( )r FQ(;)d FF(')p FQ(\))27 b FE(\021)g FF(H)851 159 y FH(\003)878 152 y FQ(\()p FF(')929 159 y FH(\003)966 152 y FQ(+)11 b FF( )1047 159 y FH(\003)1074 152 y FF(;)d(')1128 159 y FH(\003)1152 150 y Fs(c)1170 152 y FQ(\))j FE(\000)g FF(H)1290 159 y FH(\003)1317 152 y FQ(\()p FF(')1368 159 y FH(\003)1394 152 y FF(;)d(')1448 159 y FH(\003)1472 150 y Fs(c)1491 152 y FQ(\))14 b FF(:)227 b FQ(\(4)p FF(:)p FQ(55\))60 233 y(Note)16 b(that)h FF(H)324 240 y FD(r)q(el)388 233 y FQ(is)f(indep)q(enden)o(t)g(of)h(\003)g(as)g(so)q(on)h(as)f(\003)e FE(\033)f FQ(supp)q FF( )r FQ(.)22 b(The)16 b(iden)o(tit)o(y)f(\(4.54\))i(is) g(th)o(us)60 293 y(v)m(alid)k(for)g(an)o(y)g FF( )i FQ(of)e(b)q(ounded)h (supp)q(ort.)38 b(In)20 b(particular,)i(if)f(w)o(e)f(tak)o(e)h FF( )j FQ(=)e FF(k)r(\037)1614 300 y FD(A)1642 293 y FQ(,)g(w)o(e)f(obtain)60 353 y(\(4.50\).)27 b(In)17 b(the)h(case)g(of)g(the)g(anharmonic)f(crystal)g (\(4.40\))i(w)o(e)e(ha)o(v)o(e)g(the)h(follo)o(wing)f(expression)60 413 y(for)g FF(H)175 420 y FD(r)q(el)221 413 y FQ(:)301 509 y FF(H)341 516 y FD(r)q(el)388 509 y FQ(\()p FF(')11 b FQ(+)g FF(k)r(\037)557 516 y FD(A)585 509 y FQ(;)d FF(')p FQ(\))42 b(=)822 468 y Fx(X)807 566 y FD(x)10 b Fy(2)f FD(A)800 608 y(y)i Fy(2)e FD(A)887 597 y Fs(c)925 509 y FQ([)p FF(V)967 516 y FD(xy)1007 509 y FQ(\()p FF(')1058 516 y FD(x)1091 509 y FQ(+)i FF(k)i FE(\000)e FF(')1260 516 y FD(y)1281 509 y FQ(\))g FE(\000)g FF(V)1389 516 y FD(xy)1430 509 y FQ(\()p FF(')1481 516 y FD(x)1514 509 y FE(\000)f FF(')1595 516 y FD(y)1616 509 y FQ(\)])92 b(\(4.56a\))700 710 y(=)822 669 y Fx(X)807 768 y FD(x)10 b Fy(2)f FD(A)800 810 y(y)i Fy(2)e FD(A)887 798 y Fs(c)933 652 y Fx(Z)974 665 y FD(k)956 746 y FH(0)1004 710 y FF(V)1043 690 y Fy(0)1032 723 y FD(xy)1073 710 y FQ(\()p FF(')1124 717 y FD(x)1157 710 y FE(\000)i FF(')1239 717 y FD(y)1271 710 y FQ(+)g FF( )r FQ(\))d FF(d )15 b(:)271 b FQ(\(4.56b\))133 922 y FP(Step)19 b(2.)i FQ(The)16 b(goal)h(of)g(this)f(step)g(is)g(to)h(pro)o (v)o(e)e(that)483 971 y Fx(Z)533 1030 y FF(F)7 b FQ(\()p FF(')p FQ(\))h FF(d\026)p FQ(\()p FF(')p FQ(\))28 b FE(\025)f FF(e)891 1009 y Fy(\000)p FD(o)935 1015 y Fs(k)954 1009 y FH(\()p Fy(j)p FD(A)p Fy(j)p FH(\))1038 971 y Fx(Z)1088 1030 y FF(F)7 b FQ(\()p FF(')j FQ(+)h FF(k)r(\037)1295 1037 y FD(A)1323 1030 y FQ(\))d FF(d\026)p FQ(\()p FF(')p FQ(\))291 b(\(4)p FF(:)p FQ(57\))60 1141 y(\(or)22 b(some)e(similar)f(form)o(ula\))g(for)j(some)e(suitable)h (class)g(of)h(nonnegativ)o(e)f(functions)g FF(F)7 b FQ(.)35 b(Here)60 1201 y FF(o)83 1208 y FD(k)105 1201 y FQ(\()p FE(j)p FF(A)p FE(j)p FQ(\))15 b(denotes)i(a)g(term)d(that)j(ma)o(y)e(dep)q(end)h(in) g(an)h(arbitrary)f(w)o(a)o(y)g(on)h FF(k)r FQ(,)f(but)h(for)f(eac)o(h)g(real) g FF(k)60 1261 y FQ(it)g(should)g(b)q(e)h FF(o)p FQ(\()p FE(j)p FF(A)p FE(j)p FQ(\))f(as)h FF(A)c FE(\045)h(1)p FQ(.)133 1321 y FP(Case)19 b(\(a\):)28 b FQ(This)18 b(is)g(the)f(easy)h(case,)g(as)h(the)e (energy)h(shift)f(\(4.56\))i(can)f(b)q(e)g(b)q(ounded)h(in)f(sup)60 1382 y(norm:)597 1478 y FE(k)p FF(H)662 1485 y FD(r)q(el)708 1478 y FE(k)733 1485 y Fy(1)812 1478 y FE(\024)935 1436 y Fx(X)920 1535 y FD(x)10 b Fy(2)f FD(A)913 1577 y(y)i Fy(2)f FD(A)1001 1565 y Fs(c)1046 1478 y FE(j)p FF(k)r FE(j)e(k)p FF(V)1173 1457 y Fy(0)1162 1490 y FD(xy)1203 1478 y FE(k)1228 1485 y Fy(1)812 1648 y FE(\024)41 b(j)p FF(k)r FE(j)8 b FF(o)p FQ(\()p FE(j)p FF(A)p FE(j)p FQ(\))49 b(as)17 b FF(A)c FE(\045)h(1)411 b FQ(\(4.58\))60 1744 y(b)o(y)13 b(the)h(usual)g(argumen)o(t)f(based)i(on)757 1710 y Fx(P)747 1782 y FD(z)q Fy(6)p FH(=0)818 1744 y FE(k)p FF(V)882 1726 y Fy(0)871 1756 y FH(0)p FD(z)909 1744 y FE(k)934 1751 y Fy(1)985 1744 y FF(<)f FE(1)g FQ(\(see)f(e.g.)g(the)h(pro)q(of)h(of)f (Prop)q(osition)h(2.45)60 1834 y(in)h(App)q(endix)f(A.3.8\).)21 b(Substituting)16 b(\(4.58\))h(in)o(to)f(the)g(iden)o(tit)o(y)e(\(4.50\),)j (w)o(e)f(conclude)f(that)470 1886 y Fx(Z)520 1945 y FF(F)7 b FQ(\()p FF(')p FQ(\))h FF(d\026)p FQ(\()p FF(')p FQ(\))28 b FE(\025)f FF(e)878 1924 y Fy(\000j)p FD(k)q Fy(j)6 b FD(o)p FH(\()p Fy(j)p FD(A)p Fy(j)p FH(\))1051 1886 y Fx(Z)1101 1945 y FF(F)h FQ(\()p FF(')j FQ(+)h FF(k)r(\037)1308 1952 y FD(A)1336 1945 y FQ(\))d FF(d\026)p FQ(\()p FF(')p FQ(\))278 b(\(4)p FF(:)p FQ(59\))60 2053 y(uniformly)14 b(for)j(all)e(nonnegativ)o(e)h(b)q (ounded)i(functions)e FF(F)7 b FQ(.)133 2113 y FP(Case)13 b(\(b\):)22 b FQ(Here)10 b(w)o(e)h(apply)g(the)g(Sc)o(h)o(w)o(arz)f(inequalit)o(y)f(to)j (the)e(righ)o(t-hand)i(side)f(of)g(the)g(iden)o(tit)o(y)60 2173 y(\(4.50\):)223 2268 y Fx(Z)273 2327 y FF(F)c FQ(\()p FF(')k FQ(+)g FF(k)r(\037)481 2334 y FD(A)509 2327 y FQ(\))d FF(e)559 2306 y Fy(\000)p FD(H)615 2312 y Fs(r)q(el)657 2306 y FH(\()p FD(')p FH(+)p FD(k)q(\037)762 2312 y Fs(A)787 2306 y FH(;)p FD(')p FH(\))844 2327 y FF(d\026)p FQ(\()p FF(')p FQ(\))29 b FE(\025)1068 2236 y Fx(h)1088 2248 y(R)1124 2284 y FF(F)7 b FQ(\()p FF(')j FQ(+)h FF(k)r(\037)1331 2291 y FD(A)1359 2284 y FQ(\))1378 2266 y FH(1)p FD(=)p FH(2)1441 2284 y FF(d\026)p FQ(\()p FF(')p FQ(\))1565 2236 y Fx(i)1585 2247 y FH(2)p 1068 2315 538 2 v 1102 2326 a Fx(R)1138 2361 y FF(e)1161 2347 y FH(+)p FD(H)1217 2353 y Fs(r)q(el)1259 2347 y FH(\()p FD(')p FH(+)p FD(k)q(\037)1364 2353 y Fs(A)1390 2347 y FH(;)p FD(')p FH(\))1446 2361 y FF(d\026)p FQ(\()p FF(')p FQ(\))1765 2327 y(\(4)p FF(:)p FQ(60\))60 2457 y(for)k(an)o(y)g FF(F)20 b FE(\025)14 b FQ(0.)21 b(In)14 b(particular,)h(if)f FF(F)21 b FQ(is)15 b(the)g(indicator)f(function)h(of)g(some)f(set,)g(then)h FF(F)1718 2438 y FH(1)p FD(=)p FH(2)1786 2457 y FQ(=)f FF(F)7 b FQ(.)60 2517 y(No)o(w)16 b(in)g(case)g(\(b\))h(w)o(e)e(ha)o(v)o(e)452 2642 y FF(H)492 2649 y FD(r)q(el)539 2642 y FQ(\()p FF(')c FQ(+)g FF(k)r(\037)708 2649 y FD(A)736 2642 y FQ(;)d FF(')p FQ(\))27 b(=)h FF(k)r FQ(\()p FF(';)8 b(B)s(\037)1073 2649 y FD(A)1101 2642 y FQ(\))19 b(+)1201 2609 y FF(k)1228 2590 y FH(2)p 1201 2631 47 2 v 1212 2676 a FQ(2)1253 2642 y(\()p FF(\037)1303 2649 y FD(A)1331 2642 y FF(;)8 b(B)s(\037)1424 2649 y FD(A)1451 2642 y FQ(\))14 b FF(;)267 b FQ(\(4)p FF(:)p FQ(61\))938 2784 y(132)p eop %%Page: 133 133 bop 60 91 a FQ(and)18 b FF(\026)g FQ(is)g(a)g(Gaussian)h(measure)d(with)i (mean)e FF(m)i FQ(and)g(co)o(v)m(ariance)f(matrix)f FF(C)k FQ(=)c FF(B)1645 73 y Fy(\000)p FH(1)1692 91 y FQ(.)25 b(W)l(e)18 b(can)60 152 y(therefore)e(calculate)f(exactly)332 203 y Fx(Z)382 262 y FF(e)405 241 y FH(+)p FD(H)461 247 y Fs(r)q(el)503 241 y FH(\()p FD(')p FH(+)p FD(k)q(\037)608 247 y Fs(A)633 241 y FH(;)p FD(')p FH(\))690 262 y FF(d\026)p FQ(\()p FF(')p FQ(\))42 b(=)g(exp)o([)p FF(k)1051 241 y FH(2)1071 262 y FQ(\()p FF(\037)1121 269 y FD(A)1149 262 y FF(;)8 b(B)s(\037)1242 269 y FD(A)1269 262 y FQ(\))j(+)g FF(k)r(m)p FQ(\()p FM(1)p FF(;)d(B)s(\037)1558 269 y FD(A)1585 262 y FQ(\)])856 354 y(=)42 b(exp)o([)p FF(k)1051 333 y FH(2)1071 354 y FQ(\()p FF(\037)1121 361 y FD(A)1149 354 y FF(;)8 b(B)s(\037)1242 361 y FD(A)1269 354 y FQ(\)])463 b(\(4.62\))60 452 y(since)15 b FF(B)s FM(1)f FQ(=)g(0)i(b)o(y)g(\(4.46\).)22 b(No)o(w)555 550 y FF(k)582 529 y FH(2)602 550 y FQ(\()p FF(\037)652 557 y FD(A)680 550 y FF(;)8 b(B)s(\037)773 557 y FD(A)801 550 y FQ(\))42 b(=)f(2)p FF(k)992 529 y FH(2)1064 508 y Fx(X)1049 607 y FD(x)10 b Fy(2)f FD(A)1042 649 y(y)i Fy(2)e FD(A)1129 637 y Fs(c)1175 550 y FF(B)1212 557 y FD(xy)861 724 y FE(\024)41 b FF(k)968 704 y FH(2)996 724 y FF(o)p FQ(\()p FE(j)p FF(A)p FE(j)p FQ(\))49 b(as)17 b FF(A)c FE(\045)h(1)370 b FQ(\(4.63\))60 822 y(b)o(y)16 b(the)g(usual)g(argumen)o(t)g(based)g(on)771 789 y Fx(P)761 860 y FD(z)q Fy(6)p FH(=0)832 822 y FE(j)p FF(B)883 829 y FH(0)p FD(z)921 822 y FE(j)d FF(<)h FE(1)p FQ(.)21 b(Hence)443 925 y Fx(Z)492 983 y FF(F)7 b FQ(\()p FF(')p FQ(\))h FF(d\026)p FQ(\()p FF(')p FQ(\))28 b FE(\025)g FF(e)851 963 y Fy(\000)p FD(k)897 951 y Fr(2)914 963 y FD(o)p FH(\()p Fy(j)p FD(A)p Fy(j)p FH(\))1015 923 y Fx(\024)1037 925 y(Z)1087 983 y FF(F)7 b FQ(\()p FF(')j FQ(+)h FF(k)r(\037)1294 990 y FD(A)1322 983 y FQ(\))d FF(d\026)p FQ(\()p FF(')p FQ(\))1473 923 y Fx(\025)1496 934 y FH(2)1765 983 y FQ(\(4)p FF(:)p FQ(64\))60 1100 y(uniformly)14 b(for)j(all)e(indicator)h(functions)h FF(F)7 b FQ(.)20 b(This)d(is)f(a)g (sligh)o(t)g(v)m(arian)o(t)g(of)h(\(4.57\).)133 1160 y FP(Case)23 b(\(c\):)38 b FQ(This)22 b(case)h(is)f(a)h(little)e(bit)h(tric)o(kier.)38 b(Let)22 b FF(F)29 b FQ(b)q(e)23 b(an)o(y)f(nonnegativ)o(e)g(function)60 1220 y(supp)q(orted)j(on)g(the)e(set)h FE(f)p FF(')p FQ(:)16 b FF(a)27 b FE(\024)g FF(')g FE(\024)f FF(b)16 b FQ(on)h FF(A)f FQ(and)h FF(a)1157 1202 y Fy(0)1195 1220 y FE(\024)27 b FF(')g FE(\024)g FF(b)1407 1202 y Fy(0)1434 1220 y FQ(on)17 b FF(@)1531 1202 y FH(+)1528 1233 y FD(r)1560 1220 y FF(A)p FE(g)p FQ(,)25 b(where)f FF(r)h FQ(is)60 1280 y(the)20 b(range)g(of)h(the)f(in)o(teraction.) 31 b(Then)21 b(on)f(the)g(righ)o(t-hand)h(side)e(of)i(\(4.50\))f(the)g(in)o (tegrand)g(is)60 1341 y(non)o(v)m(anishing)d(only)g(when)f FF(a)11 b FE(\000)h FF(k)k FE(\024)e FF(')802 1348 y FD(x)839 1341 y FE(\024)g FF(b)d FE(\000)g FF(k)19 b FQ(for)e FF(x)d FE(2)h FF(A)p FQ(,)h(and)h FF(a)1371 1323 y Fy(0)1397 1341 y FE(\024)d FF(')1482 1348 y FD(y)1517 1341 y FE(\024)g FF(b)1591 1323 y Fy(0)1619 1341 y FQ(for)j FF(y)f FE(2)f FF(@)1811 1323 y FH(+)1808 1353 y FD(r)1840 1341 y FF(A)p FQ(.)60 1401 y(No)o(w,)j(since)f FF(V)336 1408 y FD(xy)395 1401 y FQ(is)h(con)o(v)o(ex,)e FF(V)660 1383 y Fy(0)649 1413 y FD(xy)708 1401 y FQ(is)i(increasing,)f(so)i FF(V)1092 1408 y FD(xy)1133 1401 y FQ(\()p FF(')1184 1408 y FD(x)1218 1401 y FE(\000)12 b FF(')1301 1408 y FD(y)1334 1401 y FQ(+)g FF(k)r FQ(\))g FE(\000)g FF(V)1521 1408 y FD(xy)1562 1401 y FQ(\()p FF(')1613 1408 y FD(x)1647 1401 y FE(\000)g FF(')1730 1408 y FD(y)1751 1401 y FQ(\))18 b(is)g(an)60 1461 y(increasing)e(\(resp.)g(decreasing\))g(function)h(of)g FF(')959 1468 y FD(x)992 1461 y FE(\000)11 b FF(')1074 1468 y FD(y)1111 1461 y FQ(for)17 b FF(k)f FE(\025)e FQ(0)j(\(resp.)f FF(k)g FE(\024)e FQ(0\),)j(as)g(seen)f(from)60 1521 y(\(4.56b\).)22 b(Therefore,)15 b(for)i FF(k)f FE(\025)d FQ(0)k(\(whic)o(h)e(is)i(the)f(case) g(that)g(will)g(in)o(terest)f(us\))h(w)o(e)g(ha)o(v)o(e)333 1619 y FF(H)373 1626 y FD(r)q(el)420 1619 y FQ(\()p FF(')11 b FQ(+)g FF(k)r(\037)589 1626 y FD(A)617 1619 y FQ(;)d FF(')p FQ(\))41 b FE(\024)870 1578 y Fx(X)832 1677 y FD(x)10 b Fy(2)f FD(@)916 1663 y Ft(\000)914 1683 y Fs(r)942 1677 y FD(A)833 1721 y(y)j Fy(2)d FD(@)916 1706 y Fr(+)914 1727 y Fs(r)941 1721 y FD(A)989 1619 y FQ([)p FF(V)1031 1626 y FD(xy)1072 1619 y FQ(\()p FF(b)h FE(\000)h FF(a)1198 1598 y Fy(0)1210 1619 y FQ(\))g FE(\000)f FF(V)1317 1626 y FD(xy)1358 1619 y FQ(\()p FF(b)h FE(\000)g FF(a)1485 1598 y Fy(0)1507 1619 y FE(\000)g FF(k)r FQ(\)])731 1819 y FE(\024)42 b FF(C)t FQ(\()p FF(a)896 1798 y Fy(0)906 1819 y FF(;)8 b(b;)g(k)r FQ(\))g FE(j)p FF(@)1068 1798 y Fy(\000)1065 1831 y FD(r)1097 1819 y FF(A)p FE(j)13 b FF(;)590 b FQ(\(4.65\))60 1916 y(where)17 b FF(C)t FQ(\()p FF(a)286 1898 y Fy(0)297 1916 y FF(;)8 b(b;)g(k)r FQ(\))16 b FE(\021)479 1883 y Fx(P)523 1927 y FD(z)543 1916 y FQ([)p FF(V)585 1923 y FH(0)p FD(z)622 1916 y FQ(\()p FF(b)c FE(\000)g FF(a)751 1898 y Fy(0)762 1916 y FQ(\))g FE(\000)g FF(V)872 1923 y FH(0)p FD(z)910 1916 y FQ(\()p FF(b)g FE(\000)g FF(a)1039 1898 y Fy(0)1062 1916 y FE(\000)g FF(k)r FQ(\)])18 b(is)f(\014nite)g(for)h (all)g FF(a)1539 1898 y Fy(0)1550 1916 y FF(;)8 b(b;)g(k)19 b FQ(\(since)e(only)60 1977 y(\014nitely)e(man)o(y)g(terms)f(in)i(this)g(sum) g(are)g(nonzero\).)22 b(Hence)419 2031 y Fx(Z)469 2089 y FF(F)7 b FQ(\()p FF(')p FQ(\))h FF(d\026)p FQ(\()p FF(')p FQ(\))28 b FE(\025)f FF(e)827 2069 y Fy(\000)p FD(C)r FH(\()p FD(a)914 2057 y Ft(0)925 2069 y FD(;b;k)q FH(\))6 b Fy(j)p FD(@)1030 2054 y Ft(\000)1028 2075 y Fs(r)1055 2069 y FD(A)p Fy(j)1102 2031 y Fx(Z)1152 2089 y FF(F)h FQ(\()p FF(')j FQ(+)h FF(k)r(\037)1359 2096 y FD(A)1387 2089 y FQ(\))d FF(d\026)p FQ(\()p FF(')p FQ(\))227 b(\(4)p FF(:)p FQ(66\))60 2200 y(uniformly)11 b(for)i(all)g(nonnegativ)o(e)g FF(F)19 b FQ(satisfying)14 b(the)e(supp)q(ort)j(condition.)20 b(This,)13 b(to)q(o,)i(is)d(a)i(v)m(arian)o(t)60 2260 y(of)j(\(4.57\).)133 2341 y FP(Step)f(3,)f(Case)g(\(a\):)23 b FQ(W)l(e)14 b(apply)f(\(4.59\))h(to) g FF(F)7 b FQ(\()p FF(')p FQ(\))13 b(=)h FF(\037)p FQ(\()p FF(')f(>)h FQ(0)j(on)f FF(A)p FQ(\),)e(so)g(that)g FF(F)7 b FQ(\()p FF(')f FQ(+)g FF(k)r(\037)1793 2348 y FD(A)1819 2341 y FQ(\))14 b(=)60 2402 y FF(\037)p FQ(\()p FF(')24 b(>)g FE(\000)p FF(k)18 b FQ(on)f FF(A)p FQ(\).)39 b(Since)21 b(the)h FF(V)738 2409 y FD(xy)802 2402 y FQ(are)g(con)o(v)o(ex,)g(it)g(follo)o(ws)g(immedi)o (ately)d(from)i(the)h(DLR)60 2462 y(equation)16 b(that)g(the)g(FK)o(G)g (inequalit)o(y)e([24])h(holds)i(for)f(ev)o(ery)f(Gibbs)h(measure)e FF(\026)p FQ(.)22 b(Therefore)15 b(w)o(e)60 2522 y(ha)o(v)o(e)221 2620 y FE(h)p FF(\037)p FQ(\()p FF(')f(>)f FE(\000)p FF(k)18 b FQ(on)f FF(A)p FQ(\))p FE(i)612 2627 y FD(\026)663 2620 y FE(\025)738 2578 y Fx(Y)729 2670 y FD(x)p Fy(2)p FD(A)799 2620 y FE(h)p FF(\037)p FQ(\()p FF(')900 2627 y FD(x)936 2620 y FF(>)d FE(\000)p FF(k)r FQ(\))p FE(i)1092 2627 y FD(\026)1143 2620 y FQ(=)27 b(Prob)1312 2627 y FD(\026)1335 2620 y FQ(\()p FF(')1386 2627 y FH(0)1420 2620 y FF(>)14 b FE(\000)p FF(k)r FQ(\))1557 2599 y Fy(j)p FD(A)p Fy(j)1765 2620 y FQ(\(4)p FF(:)p FQ(67\))938 2784 y(133)p eop %%Page: 134 134 bop 60 91 a FQ(Com)o(bining)15 b(this)h(with)g(\(4.59\),)h(w)o(e)e(get)357 224 y(lim)8 b(inf)376 254 y FD(A)p Fy(\0451)525 190 y FQ(1)p 505 212 65 2 v 505 258 a FE(j)p FF(A)p FE(j)582 224 y FQ(log)i(Prob)757 231 y FD(\026)781 224 y FQ(\()p FF(')j(>)h FQ(0)j(on)g FF(A)p FQ(\))27 b FE(\025)g FQ(log)9 b(Prob)1330 231 y FD(\026)1353 224 y FQ(\()p FF(')1404 231 y FH(0)1438 224 y FF(>)14 b FE(\000)p FF(k)r FQ(\))f FF(:)163 b FQ(\(4)p FF(:)p FQ(68\))60 359 y(But)16 b(taking)g FF(k)g FE(!)e FQ(+)p FE(1)p FQ(,)h(the)h(righ)o(t-hand)h(side)f (go)q(es)h(to)g(zero.)133 419 y FP(Step)d(3,)g(Case)f(\(b\):)22 b FQ(W)l(e)11 b(apply)g(\(4.64\))h(to)g FF(F)7 b FQ(\()p FF(')p FQ(\))13 b(=)h FF(\037)p FQ(\()p FF(')f(>)h FQ(0)i(on)h FF(A)p FQ(\).)i(W)l(e)11 b(con)o(trol)g(Prob)1764 426 y FD(\026)1787 419 y FQ(\()p FF(')j(>)60 479 y FE(\000)p FF(k)k FQ(on)f FF(A)p FQ(\))23 b(using)g(the)g(Brascamp-Lieb)f(inequalit)o(y)f([37)q(,)h(38)q(],)i (whic)o(h)f(is)g(v)m(alid)g(for)g(arbitrary)60 539 y(Gaussian)18 b(measures,)c(com)o(bined)g(with)i(the)g(Cheb)o(yshev)g(inequalit)o(y:)60 649 y(Prob)164 656 y FD(\026)187 649 y FQ(\()p FF(')e(>)f FE(\000)p FF(k)19 b FQ(on)d FF(A)p FQ(\))41 b FE(\025)h FQ(Prob)734 656 y FD(\026)757 649 y FQ(\()p FE(j)p FF(')11 b FE(\000)g FF(m)p FE(j)i FF(<)h(m)d FQ(+)g FF(k)18 b FQ(on)f FF(A)p FQ(\))551 776 y(=)648 722 y FD(n)633 734 y Fx(Y)631 825 y FD(i)p FH(=1)696 776 y FQ(Prob)800 783 y FD(\026)823 728 y Fx(\020)848 776 y FE(j)p FF(')894 783 y FD(x)914 788 y Fs(i)940 776 y FE(\000)10 b FF(m)p FE(j)k FF(<)g(m)c FQ(+)h FF(k)1241 726 y Fx(\014)1241 751 y(\014)1241 776 y(\014)p FE(j)p FF(')1301 783 y FD(x)1321 788 y Fs(j)1350 776 y FE(\000)g FF(m)p FE(j)i FF(<)h(m)d FQ(+)g FF(k)18 b FQ(for)f(1)d FE(\024)g FF(j)i(<)e(i)1939 728 y Fx(\021)728 884 y FQ([where)i FF(A)d FQ(=)h FE(f)p FF(x)1038 891 y FH(1)1057 884 y FF(;)8 b(:)g(:)g(:)f(;)h(x)1194 891 y FD(n)1218 884 y FE(g)p FQ(])550 1029 y FE(\025)648 975 y FD(n)633 988 y Fx(Y)631 1079 y FD(i)p FH(=1)696 944 y Fx(0)696 1018 y(@)732 1029 y FQ(1)k FE(\000)823 986 y FF(E)859 993 y FD(\026)882 938 y Fx(\020)907 986 y FQ(\()p FF(')958 993 y FD(x)978 998 y Fs(i)1004 986 y FE(\000)f FF(m)p FQ(\))1116 968 y FH(2)1135 936 y Fx(\014)1135 961 y(\014)1135 986 y(\014)p FE(j)p FF(')1195 993 y FD(x)1215 998 y Fs(j)1244 986 y FE(\000)g FF(m)p FE(j)i FF(<)h(m)d FQ(+)g FF(k)18 b FQ(for)e(1)f FE(\024)e FF(j)k(<)d(i)1833 938 y Fx(\021)p 823 1018 1035 2 v 1246 1063 a FQ(\()p FF(m)d FQ(+)g FF(k)r FQ(\))1414 1049 y FH(2)1862 944 y Fx(1)1862 1018 y(A)728 1146 y FQ([b)o(y)k(Cheb)o(yshev])551 1291 y(=)648 1237 y FD(n)633 1250 y Fx(Y)631 1341 y FD(i)p FH(=1)696 1206 y Fx(0)696 1280 y(@)732 1291 y FQ(1)d FE(\000)823 1248 y FQ(v)m(ar)889 1255 y FD(\026)912 1200 y Fx(\020)937 1248 y FF(')969 1255 y FD(x)989 1260 y Fs(i)1004 1198 y Fx(\014)1004 1223 y(\014)1004 1248 y(\014)p FE(j)p FF(')1064 1255 y FD(x)1084 1260 y Fs(j)1113 1248 y FE(\000)f FF(m)p FE(j)i FF(<)h(m)d FQ(+)g FF(k)18 b FQ(for)e(1)f FE(\024)e FF(j)k(<)d(i)1702 1200 y Fx(\021)p 823 1280 904 2 v 1181 1325 a FQ(\()p FF(m)c FQ(+)h FF(k)r FQ(\))1348 1311 y FH(2)1731 1206 y Fx(1)1731 1280 y(A)728 1407 y FQ([since)k (conditioning)h(a)h(Gaussian)g(on)g(a)g(set)742 1456 y(symmetri)o(c)c(ab)q (out)18 b(the)e(mean)f(preserv)o(es)g(the)h(mean)o(])550 1584 y FE(\025)648 1530 y FD(n)633 1542 y Fx(Y)631 1633 y FD(i)p FH(=1)696 1511 y Fx( )729 1584 y FQ(1)11 b FE(\000)819 1550 y FQ(v)m(ar)885 1557 y FD(\026)909 1550 y FQ(\()p FF(')960 1557 y FD(x)980 1562 y Fs(i)995 1550 y FQ(\))p 819 1572 195 2 v 823 1618 a(\()p FF(m)f FQ(+)h FF(k)r FQ(\))990 1604 y FH(2)1019 1511 y Fx(!)728 1692 y FQ([b)o(y)k(Brascamp-Lieb)o(])551 1831 y(=)631 1758 y Fx( )663 1831 y FQ(1)d FE(\000)811 1797 y FF(C)846 1804 y FH(00)p 754 1819 188 2 v 754 1865 a FQ(\()p FF(m)e FQ(+)h FF(k)r FQ(\))921 1851 y FH(2)946 1758 y Fx(!)979 1769 y Fy(j)p FD(A)p Fy(j)1049 1831 y FF(:)776 b FQ(\(4.69\))60 1972 y(Com)o(bining)15 b(this)h(with)g(\(4.64\),)h(w)o(e)e(get)336 2113 y(lim)8 b(inf)355 2143 y FD(A)p Fy(\0451)504 2079 y FQ(1)p 484 2101 65 2 v 484 2147 a FE(j)p FF(A)p FE(j)562 2113 y FQ(log)h(Prob)737 2120 y FD(\026)760 2113 y FQ(\()p FF(')14 b(>)f FQ(0)k(on)g FF(A)p FQ(\))27 b FE(\025)g FQ(2)8 b(log)1238 2040 y Fx( )1271 2113 y FQ(1)k FE(\000)1419 2079 y FF(C)1454 2086 y FH(00)p 1362 2101 188 2 v 1362 2147 a FQ(\()p FF(m)e FQ(+)h FF(k)r FQ(\))1529 2133 y FH(2)1554 2040 y Fx(!)1609 2113 y FF(:)142 b FQ(\(4)p FF(:)p FQ(70\))60 2251 y(No)o(w)16 b(tak)o(e)g FF(k)g FE(!)d FQ(+)p FE(1)p FQ(.)133 2312 y FP(Step)22 b(3,)g(Case)f(\(c\):)33 b FQ(W)l(e)20 b(apply)g(\(4.66\))h(to)g FF(F)7 b FQ(\()p FF(')p FQ(\))19 b(=)i FF(\037)p FQ(\()p FF(a)f FE(\024)g FF(')h FE(\024)f FF(b)c FQ(on)h FF(A)f FQ(and)g FF(a)1707 2293 y Fy(0)1739 2312 y FE(\024)21 b FF(')f FE(\024)60 2372 y FF(b)81 2354 y Fy(0)109 2372 y FQ(on)c FF(@)205 2354 y FH(+)202 2384 y FD(r)234 2372 y FF(A)p FQ(\),)i(with)h(the)f(c)o(hoices)f FF(a)g FQ(=)h(0,)h FF(b)e FQ(=)h(2)p FF(m)12 b FQ(+)h(2)p FF(k)r FQ(,)19 b FF(a)1178 2354 y Fy(0)1206 2372 y FQ(=)f FE(\000)p FF(k)r FQ(,)g FF(b)1381 2354 y Fy(0)1410 2372 y FQ(=)g(2)p FF(m)12 b FQ(+)h FF(k)r FQ(,)18 b FF(k)i FE(\025)d FQ(0.)28 b(W)l(e)60 2432 y(therefore)16 b(need)f(to)i(con)o(trol)418 2542 y(Prob)522 2549 y FD(\026)545 2542 y FQ(\()p FF(a)11 b FE(\000)g FF(k)16 b FE(\024)d FF(')h FE(\024)f FF(b)e FE(\000)g FF(k)18 b FQ(on)f FF(A)f FQ(and)h FF(a)1209 2521 y Fy(0)1234 2542 y FE(\024)c FF(')h FE(\024)g FF(b)1406 2521 y Fy(0)1433 2542 y FQ(on)j FF(@)1530 2521 y FH(+)1527 2554 y FD(r)1559 2542 y FF(A)p FQ(\))516 2615 y(=)27 b(Prob)685 2622 y FD(\026)708 2615 y FQ(\()p FE(j)p FF(')11 b FE(\000)g FF(m)p FE(j)i(\024)h FF(m)d FQ(+)g FF(k)18 b FQ(on)f FF(A)10 b FE([)i FF(@)1292 2594 y FH(+)1289 2627 y FD(r)1321 2615 y FF(A)p FQ(\))h FF(:)361 b FQ(\(4.71\))938 2784 y(134)p eop %%Page: 135 135 bop 60 91 a FQ(T)l(o)13 b(do)f(this,)h(w)o(e)e(emplo)o(y)f(the)i (Brascamp-Lieb)f(and)i(Cheb)o(yshev)e(inequalities)f(as)j(in)f(case)g(\(b\))g ([the)60 152 y(Brascamp-Lieb)i(inequalit)o(y)f(is)h(v)m(alid)h(b)q(ecause)g (all)f(the)h FF(V)1140 159 y FD(xy)1195 152 y FQ(are)g(con)o(v)o(ex].)k(Here) 14 b(it)g(is)h(imp)q(ortan)o(t)60 212 y(that)h FF(\026)f FQ(b)q(e)h(ev)o(en)e (ab)q(out)j(its)e(mean,)f(b)q(ecause)h(Brascamp-Lieb)f(refers)h(to)h(v)m (ariances)f(rather)g(than)60 272 y(to)k(exp)q(ectations)g(of)g(squares;)h(w)o (e)f(need)f(to)h(kno)o(w)g(that)h(conditioning)e FF(\026)h FQ(on)h(a)f(set)g(symmetri)o(c)60 332 y(around)f(the)e(mean)g(do)q(es)h(not)g (displace)f(the)h(mean.)k(The)c(only)g(other)f(c)o(hange)h(from)f(case)g (\(b\))h(is)60 392 y(that)i(v)m(ar)235 399 y FD(\026)258 392 y FQ(\()p FF(')309 399 y FD(x)329 404 y Fs(i)344 392 y FE(j)d(\001)8 b(\001)g(\001)h FQ(\))19 b(is)f(b)q(ounded)i(ab)q(o)o(v)o(e)e(not)i(b)o(y)e (v)m(ar)1098 399 y FD(\026)1122 392 y FQ(\()p FF(')1173 399 y FD(x)1193 404 y Fs(i)1208 392 y FQ(\),)h(but)g(rather)f(b)o(y)h(the)f(v)m (ariance)h(of)60 452 y FF(')92 459 y FD(x)112 464 y Fs(i)145 452 y FQ(in)f(the)f(dominating)g(Gaussian,)j(whic)o(h)d(b)o(y)g(h)o(yp)q (othesis)h(is)g(\014nite)f(\(call)g(it)h FF(C)1599 459 y FH(00)1636 452 y FQ(\).)26 b(Th)o(us,)18 b(w)o(e)60 513 y(ha)o(v)o(e)204 659 y(Prob)308 666 y FD(\026)331 659 y FQ(\()p FE(j)p FF(')11 b FE(\000)g FF(m)p FE(j)i(\024)h FF(m)c FQ(+)h FF(k)19 b FQ(on)e FF(A)10 b FE([)h FF(@)914 638 y FH(+)911 671 y FD(r)943 659 y FF(A)p FQ(\))28 b FE(\025)1093 586 y Fx( )1126 659 y FQ(1)11 b FE(\000)1274 625 y FF(C)1309 632 y FH(00)p 1216 647 188 2 v 1216 693 a FQ(\()p FF(m)g FQ(+)g FF(k)r FQ(\))1384 679 y FH(2)1409 586 y Fx(!)1441 597 y Fy(j)p FD(A)p Fy([)p FD(@)1522 583 y Fr(+)1520 603 y Fs(r)1547 597 y FD(A)p Fy(j)1608 659 y FF(:)143 b FQ(\(4)p FF(:)p FQ(72\))60 800 y(Com)o(bining)15 b(this)h(with)g(\(4.66\),)h(w)o(e)e(get)143 932 y(lim)8 b(inf)162 962 y FD(A)p Fy(\0451)311 899 y FQ(1)p 291 921 65 2 v 291 967 a FE(j)p FF(A)p FE(j)369 932 y FQ(log)h(Prob)544 939 y FD(\026)567 932 y FQ(\()p FF(')14 b(>)g FQ(0)i(on)h FF(A)p FQ(\))241 1061 y FE(\025)27 b FQ(lim)8 b(inf)326 1091 y FD(A)p Fy(\0451)475 1028 y FQ(1)p 455 1050 V 455 1096 a FE(j)p FF(A)p FE(j)533 1061 y FQ(log)h(Prob)708 1068 y FD(\026)731 1061 y FQ(\(0)14 b FF(<)g(')g(<)g FQ(2)p FF(m)d FQ(+)g(2)p FF(k)18 b FQ(on)f FF(A)f FQ(and)28 b FE(\000)11 b FF(k)16 b(<)d(')h(<)g FQ(2)p FF(m)d FQ(+)g FF(k)18 b FQ(on)f FF(@)1866 1041 y FH(+)1863 1074 y FD(r)1895 1061 y FF(A)p FQ(\))241 1199 y FE(\025)27 b FQ(log)378 1126 y Fx( )411 1199 y FQ(1)12 b FE(\000)559 1166 y FF(C)594 1173 y FH(00)p 501 1188 188 2 v 501 1234 a FQ(\()p FF(m)f FQ(+)g FF(k)r FQ(\))669 1219 y FH(2)694 1126 y Fx(!)749 1199 y FF(:)1063 b FQ(\(4.73\))60 1338 y(No)o(w)16 b(tak)o(e)g FF(k)g FE(!)d FQ(+)p FE(1)p FQ(.)p 622 1342 25 34 v 133 1448 a FM(Remark.)36 b FQ(W)l(e)21 b(do)i(not)f(kno)o(w)g(whether)g(there)f(can)h (exist)f(translation-in)o(v)m(arian)o(t)h(Gibbs)60 1508 y(measures)15 b(for)g(the)h(anharmonic)f(crystal)g(that)h(fail)f(to)h(b)q(e)f(symmetric)d (around)17 b(their)e(mean.)k(\(In)60 1568 y(the)j(Gaussian)i(case)e(suc)o(h)g (measures)f(cannot)i(exist.\))38 b(That)23 b(is,)h(w)o(e)d(do)i(not)g(kno)o (w)f(whether)60 1628 y(the)d(re\015ection)g(symmetry)d(can)k(b)q(e)f(sp)q(on) o(taneously)i(brok)o(en.)30 b(If)19 b(the)h(answ)o(er)g(is)f(no,)h(then)g (our)60 1688 y(additional)c(h)o(yp)q(othesis)h(in)f(case)g(\(c\))g(is)g(sup)q (er\015uous.)133 1798 y(The)21 b(tec)o(hnical)e(condition)h(in)h(case)f (\(c\))g(|)h(that)g(the)f(mo)q(del)g(b)q(e)g(dominated)g(b)o(y)g(a)h(stable) 60 1859 y(Gaussian)15 b(|)e(unfortunately)h(excludes)e(some)h(in)o(teresting) f(mo)q(dels,)h(suc)o(h)g(as)i(the)e(\()p FE(r)p FF(')p FQ(\))1715 1841 y FH(4)1748 1859 y FQ(mo)q(del.)60 1919 y(The)i(need)f(for)g(this)h(tec) o(hnical)e(condition)h(arises)g(from)g(the)g(use)h(of)f(Brascamp-Lieb)g (inequalities)60 1979 y(to)e(b)q(ound)h(the)e(conditional)g(probabilit)o(y)g (Prob)936 1986 y FD(\026)959 1979 y FQ(\()p FE(j)p FF(')1024 1986 y FD(x)1044 1991 y Fs(i)1060 1979 y FE(\000)r FF(m)p FE(j)i FF(<)h(m)r FQ(+)r FF(k)9 b FE(j)f(j)p FF(')1410 1986 y FD(x)1430 1991 y Fs(j)1449 1979 y FE(\000)r FF(m)p FE(j)13 b FF(<)h(m)r FQ(+)r FF(k)j FQ(for)f(1)e FE(\024)60 2039 y FF(j)j(<)d(i)p FQ(\))o(.)21 b(An)14 b(alternate)g(approac)o(h)h(w)o(ould)f(b)q(e)h(to)g(use) f(the)g(FK)o(G)g(inequalities)f(as)i(in)f(case)g(\(a\),)h(but)60 2099 y(then)i(w)o(e)g(w)o(ould)h(b)q(e)f(forced)g(to)h(w)o(ork)f(with)g (increasing)g(functions,)h(i.e.)d(to)j(tak)o(e)f FF(b)e FQ(=)h FF(b)1708 2081 y Fy(0)1735 2099 y FQ(=)g(+)p FE(1)p FQ(.)60 2160 y(Unfortunately)l(,)d(the)f(cuto\013)i FF(b)f(<)h FE(1)f FQ(w)o(as)g(necessary)g(in)g(case)g(\(c\))f(in)h(order)g(to)g(con)o(trol)g (the)f(energy)60 2220 y(shift)k FF(H)210 2227 y FD(r)q(el)257 2220 y FQ(,)g(whic)o(h)f(otherwise)h(could)g(b)q(e)h(un)o(b)q(ounded)g(ab)q (o)o(v)o(e.)133 2280 y(Ho)o(w)22 b(can)g(w)o(e)f(escap)q(e)h(from)e(this)i (dilemm)o(a?)35 b(Let)22 b(us)g(\014rst)g(note)g(that)g(the)g(large)f(energy) 60 2340 y(shift)15 b(arises)g(from)f(applying)h(the)g(shift)g FF(')837 2347 y FD(x)873 2340 y FE(!)f FF(')969 2347 y FD(x)999 2340 y FQ(+)9 b FF(k)18 b FQ(to)d(\014elds)g FF(')1303 2347 y FD(x)1340 2340 y FQ(that)h(are)f FP(alr)n(e)n(ady)j FQ(large)d(and)60 2400 y(p)q(ositiv)o(e,)d(hence)g(ha)o(v)o(e)g FP(no)j(ne)n(e)n(d)j FQ(to)13 b(b)q(e)g(shifted)f(farther)h(up)o(w)o(ards)g(in)f(order)h(to)g (bring)g(them)e(ab)q(o)o(v)o(e)60 2461 y(the)k(lev)o(el)e FF(')h FQ(=)g(0.)21 b(This)15 b(suggests)i(that)f(instead)f(of)h(applying)f(a)h (uniform)e(shift)h FF(')1598 2468 y FD(x)1633 2461 y FE(!)f FF(')1729 2468 y FD(x)1760 2461 y FQ(+)9 b FF(k)17 b FQ(in)60 2521 y(the)c(region)g FF(A)p FQ(,)g(w)o(e)f(should)i(apply)f(a)g FP(nonline)n(ar)20 b FQ(map)12 b FF(')1092 2528 y FD(x)1128 2521 y FE(!)h FF(f)5 b FQ(\()p FF(')1271 2528 y FD(x)1294 2521 y FQ(\))13 b(that)g(w)o(ould)g(pro)q(duce)h(a)f(large)60 2581 y(up)o(w)o(ard)i(shift)g(when)g FF(')499 2588 y FD(x)536 2581 y FQ(is)g(negativ)o(e,)f(but)h(a)g(smaller)e(shift)i(when)g FF(')1350 2588 y FD(x)1387 2581 y FQ(is)g(large)g(and)g(p)q(ositiv)o(e.)20 b(In)60 2641 y(this)f(w)o(a)o(y)g(w)o(e)f(ma)o(y)g(hop)q(e)i(to)f(ha)o(v)o(e) g(an)g(energy)g(shift)g(that)g(is)g(uniformly)e(b)q(ounded)j(ab)q(o)o(v)o(e.) 30 b(Of)938 2784 y(135)p eop %%Page: 136 136 bop 60 91 a FQ(course,)18 b(in)f(the)h(case)g(of)g(a)g(nonlinear)g(map)f FF(f)23 b FQ(w)o(e)17 b(m)o(ust)g(also)h(deal)g(with)f(a)i(Jacobian,)f(but)g (this)60 152 y(turns)e(out)g(to)g(b)q(e)g(manageable.)k(The)c(idea)f(ma)o(y)f (b)q(e)i(crazy)l(,)f(but)h(it)f(seems)f(to)i(w)o(ork,)f(at)h(least)g(for)60 212 y(some)c(rather)i(large)f(class)g(of)h(p)q(oten)o(tials)f FF(V)853 219 y FD(xy)894 212 y FQ(.)20 b(Ho)o(w)o(ev)o(er,)12 b(this)h(pap)q(er)h(is)f(already)g(m)o(uc)o(h)f(to)q(o)i(long,)60 272 y(and)i(w)o(e)f(ha)o(v)o(e)g(not)h(had)g(time)e(to)i(w)o(ork)f(out)h(all) f(the)h(details,)f(so)h(w)o(e)f(lea)o(v)o(e)f(further)h(dev)o(elopmen)o(t)60 332 y(of)i(this)f(circle)e(of)j(ideas)f(to)g(the)g(in)o(terested)f(reader.)60 462 y FM(4.4.2)55 b(Non-Gibbsianness)16 b(of)h(Lo)r(cal)f(Nonlinear)f(F)-5 b(unctions)17 b(of)g(an)g(\(An\)harmonic)231 522 y(Crystal)60 615 y FQ(The)d(metho)q(d)g(of)g(the)g(preceding)g(section)f(applies,)h(in)g (fact,)g(to)h(lo)q(cal)f(nonlinear)g(functions)g(m)o(uc)o(h)60 675 y(more)g(general)h(than)i(the)e(sign.)21 b(Indeed,)14 b(let)h(\012)940 657 y Fy(0)940 687 y FH(0)976 675 y FQ(b)q(e)g(a)h(compact)f(metric)e(space,) i(and)h(let)f FF(f)5 b FQ(:)16 b Fq(R)e FE(!)60 735 y FQ(\012)95 717 y Fy(0)95 747 y FH(0)133 735 y FQ(b)q(e)j(an)o(y)h(function)f(\(not)h (necessarily)e(con)o(tin)o(uous\))i(suc)o(h)f(that)h(lim)1388 742 y FD(')p Fy(!)p FH(+)p Fy(1)1519 735 y FF(f)5 b FQ(\()p FF(')p FQ(\))17 b(=)f FF(!)1721 717 y Fy(\003)1758 735 y FQ(exists.)60 795 y(W)l(e)d(shall)h(sho)o(w)g(that)g(for)g(the)g(class)g(of)g(massless)f (Gibbs)h(measures)e(on)j(the)e(system)f(of)i FE(f)p FF(')p FE(g)g FQ(spins)60 855 y(considered)h(in)g(the)g(preceding)f(section,)h(the)g (pro)s(jection)g(of)g(suc)o(h)g(a)h(measure)e(on)i(the)f FE(f)p FF(!)r FE(g)g FQ(spins)60 915 y(is)h(non-Gibbsian.)60 1036 y FM(Theorem)h(4.10)24 b FP(L)n(et)18 b FF(\026)h FP(b)n(e)g(any)f(tr)n (anslation-invariant)i(me)n(asur)n(e)e(on)h Fq(R)1461 1015 y(Z)1492 991 y Fs(d)1530 1036 y FP(satisfying)g(the)g(es-)60 1096 y(timate)e(\(4.51\))f(for)g(al)r(l)i FF(M)h(<)14 b FE(1)p FP(.)22 b(L)n(et)16 b FQ(\012)826 1078 y Fy(0)826 1108 y FH(0)863 1096 y FP(b)n(e)h(a)f(c)n(omp)n(act)g(metric)h(sp)n(ac)n(e,)g(and)f(let)i FF(f)5 b FQ(:)16 b Fq(R)e FE(!)g FQ(\012)1811 1078 y Fy(0)1811 1108 y FH(0)1848 1096 y FP(b)n(e)60 1156 y(a)k(function)h(\(not)g(ne)n(c)n (essarily)f(c)n(ontinuous\))h(such)g(that)f FQ(lim)1192 1163 y FD(')p Fy(!)p FH(+)p Fy(1)1323 1156 y FF(f)5 b FQ(\()p FF(')p FQ(\))15 b(=)g FF(!)1522 1138 y Fy(\003)1560 1156 y FP(exists.)25 b(L)n(et)1805 1152 y Fx(e)1800 1156 y FF(\026)19 b FP(b)n(e)60 1216 y(the)d(image)h(me)n(asur)n(e)e(of)h FF(\026)g FP(under)g(the)h(map)e FF(f)21 b FP(applie)n(d)16 b(to)g(e)n(ach)g(spin.)22 b(Then)1517 1212 y Fx(e)1513 1216 y FF(\026)16 b FP(is)g(not)g(the)h(Gibbs)60 1276 y(for)f(any)g(inter)n(action)h(in)g FE(B)569 1258 y FH(1)587 1276 y FP(,)g(with)g(r)n(esp)n(e)n(ct)e(to)i(any)f FQ(a)f(priori)h FP(me)n(asur)n(e)f(supp)n(orte)n(d)h(on)g(mor)n(e)g(than)60 1337 y(one)i(p)n(oint.)60 1500 y Fd(Pr)o(oof.)48 b FQ(Let)16 b FF(U;)8 b(V)27 b FQ(b)q(e)17 b(op)q(en)g(sets)f(in)g(\012)850 1482 y Fy(0)850 1513 y FH(0)886 1500 y FQ(satisfying)g FF(!)1135 1482 y Fy(\003)1169 1500 y FE(2)e FF(U)19 b FE(\032)1329 1488 y FQ(\026)1321 1500 y FF(U)g FE(\032)14 b FF(V)d FQ(.)21 b(Then)c(let)e FF(g)1721 1507 y FH(0)1741 1500 y FQ(:)h(\012)1806 1482 y Fy(0)1806 1513 y FH(0)1840 1500 y FE(!)60 1561 y FQ([0)p FF(;)8 b FQ(1])20 b(b)q(e)g(a)h(con)o(tin)o(uous)f(function)g(satisfying)g FF(g)980 1568 y FH(0)1000 1561 y Fm(\026)1033 1548 y FQ(\026)1025 1561 y FF(U)26 b FE(\021)20 b FQ(1)h(and)g FF(g)1310 1568 y FH(0)1330 1561 y Fm(\026)p FF(V)1394 1543 y FD(c)1432 1561 y FE(\021)f FQ(0;)i(the)e(existence)f(of)60 1630 y(suc)o(h)h(a)h(function)g(is)f(guaran)o (teed)h(b)o(y)f(Urysohn's)g(lemma.)31 b(No)o(w)20 b(de\014ne)h FF(g)r FQ(:)16 b(\012)1567 1612 y Fy(0)1567 1642 y FH(0)1587 1606 y Fl(Z)1608 1595 y Fs(d)1649 1630 y FE(!)21 b FQ([0)p FF(;)8 b FQ(1])21 b(b)o(y)60 1690 y FF(g)r FQ(\()p FE(f)p FF(!)159 1697 y FD(x)181 1690 y FE(g)206 1700 y FD(x)p Fy(2)p Fl(Z)271 1690 y Fs(d)t FQ(\))14 b(=)g FF(g)399 1697 y FH(0)419 1690 y FQ(\()p FF(!)468 1697 y FH(0)488 1690 y FQ(\).)21 b(That)c(is,)e FF(g)k FQ(is)d(the)g(function)g FF(g)1115 1697 y FH(0)1151 1690 y FQ(applied)g(to)h(the)f(spin)g(at)g(the)g(origin.)133 1750 y(No)o(w)g(let)g(us)g(compute)f(the)h(pressure)g FF(p)p FQ(\()p FF(\025g)r FE(j)963 1746 y Fx(e)959 1750 y FF(\026)r FQ(\))g(for)g FF(\025)f FE(\025)e FQ(0:)377 1904 y FF(p)p FQ(\()p FF(\025g)r FE(j)491 1900 y Fx(e)487 1904 y FF(\026)q FQ(\))42 b FE(\021)53 b FQ(lim)658 1929 y FD(n)p Fy(!1)767 1904 y FF(n)796 1883 y Fy(\000)p FD(d)852 1904 y FQ(log)923 1845 y Fx(Z)965 1904 y FQ(exp)1039 1818 y Fx(2)1039 1893 y(4)1067 1904 y FF(\025)1119 1862 y Fx(X)1104 1954 y FD(x)p Fy(2)p FD(C)1173 1958 y Fs(n)1202 1904 y FF(g)1225 1911 y FH(0)1245 1904 y FQ(\()p FF(!)1294 1911 y FD(x)1316 1904 y FQ(\))1335 1818 y Fx(3)1335 1893 y(5)1379 1904 y FF(d)1408 1900 y Fx(e)1404 1904 y FF(\026)q FQ(\()p FF(!)r FQ(\))578 2093 y(=)h(lim)658 2118 y FD(n)p Fy(!1)767 2093 y FF(n)796 2073 y Fy(\000)p FD(d)852 2093 y FQ(log)923 2035 y Fx(Z)965 2093 y FQ(exp)1039 2008 y Fx(2)1039 2083 y(4)1067 2093 y FF(\025)1119 2052 y Fx(X)1104 2144 y FD(x)p Fy(2)p FD(C)1173 2148 y Fs(n)1202 2093 y FF(g)1225 2100 y FH(0)1245 2093 y FQ(\()p FF(f)5 b FQ(\()p FF(')1344 2100 y FD(x)1366 2093 y FQ(\)\))1404 2008 y Fx(3)1404 2083 y(5)1448 2093 y FF(d\026)p FQ(\()p FF(')p FQ(\))193 b(\(4.74\))60 2244 y(if)18 b(this)h(limit)d(exists.)28 b(Since)18 b FF(g)638 2251 y FH(0)676 2244 y FE(\024)g FQ(1,)i(clearly)d(the) h(lim)8 b(sup)18 b(is)g FE(\024)g FF(\025)p FQ(.)29 b(On)19 b(the)g(other)g(hand,)g(the)60 2304 y(lim)8 b(inf)17 b(is)390 2414 y FE(\025)41 b FQ(lim)8 b(inf)492 2439 y FD(n)p Fy(!1)622 2414 y FF(n)651 2394 y Fy(\000)p FD(d)707 2414 y FQ(log)778 2366 y Fx(h)798 2414 y FF(e)821 2394 y FD(\025n)863 2382 y Fs(d)883 2414 y FQ(Prob)986 2421 y FD(\026)1010 2414 y FQ(\()p FF(f)d FQ(\()p FF(')1109 2421 y FD(x)1131 2414 y FQ(\))14 b FE(2)g FF(U)21 b FQ(for)c(all)f FF(x)d FE(2)h FF(C)1531 2421 y FD(n)1555 2414 y FQ(\))1574 2366 y Fx(i)390 2533 y FE(\025)41 b FQ(lim)8 b(inf)492 2558 y FD(n)p Fy(!1)622 2533 y FF(n)651 2513 y Fy(\000)p FD(d)707 2533 y FQ(log)778 2485 y Fx(h)798 2533 y FF(e)821 2513 y FD(\025n)863 2501 y Fs(d)883 2533 y FQ(Prob)986 2540 y FD(\026)1010 2533 y FQ(\()p FF(')1061 2540 y FD(x)1096 2533 y FF(>)14 b(M)22 b FQ(for)16 b(all)g FF(x)e FE(2)g FF(C)1483 2540 y FD(n)1506 2533 y FQ(\))1525 2485 y Fx(i)390 2640 y FQ(=)42 b FF(\025)15 b(;)1238 b FQ(\(4.75\))938 2784 y(136)p eop %%Page: 137 137 bop 60 91 a FQ(where)18 b FF(M)23 b FQ(is)17 b(c)o(hosen)h(so)h(that)f FF(')f(>)f(M)23 b FQ(implies)16 b FF(f)5 b FQ(\()p FF(')p FQ(\))16 b FE(2)h FF(U)5 b FQ(;)19 b(here)e(the)h(\014nal)g(equalit)o(y)e(uses)i(the) 60 152 y(fundamen)o(tal)d(estimate)f(\(4.51\).)22 b(So)17 b(w)o(e)f(ha)o(v)o (e)641 262 y FF(p)p FQ(\()p FF(\025g)r FE(j)755 258 y Fx(e)751 262 y FF(\026)r FQ(\))27 b(=)h FF(\025)98 b FQ(for)16 b(all)g FF(\025)e FE(\025)g FQ(0)g FF(:)456 b FQ(\(4)p FF(:)p FQ(76\))60 372 y(But)18 b(this)f(violates)h(the)g(strict)f(con)o(v)o(exit)o(y)f(of)i (the)g(pressure)g(whic)o(h)f(m)o(ust)g(hold)h(if)1629 368 y Fx(e)1624 372 y FF(\026)h FQ(is)e(a)i(Gibbs)60 432 y(measure)e(for)i(an)g(in) o(teraction)f(in)g FE(B)741 414 y FH(1)779 432 y FQ(\(Gri\016ths-Ruelle)f (theorem,)g(Prop)q(osition)i(2.59\).)29 b(Hence)64 488 y Fx(e)60 492 y FF(\026)17 b FQ(is)f(non-Gibbsian.)p 593 496 25 34 v 60 672 a FM(4.4.3)55 b(Ph)n(ysical)19 b(In)n(terpretation)60 764 y FQ(W)l(e)j(ha)o(v)o(e)f(pro)o(v)o(en)h(that)549 760 y Fx(e)545 764 y FF(\026)g FQ(is)g(not)h(the)f(Gibbs)h(measure)e(for)h(an)o(y)g (in)o(teraction)g(in)f FE(B)1705 746 y FH(1)1724 764 y FQ(,)j(but)e(is)60 824 y(this)c(enough?)29 b(W)l(e)18 b(kno)o(w)g(that)h(non-Gibbsianness)g(can) g(sometime)o(s)d(o)q(ccur)i(for)h(\\trivial")f(rea-)60 884 y(sons,)24 b(e.g.)e(if)g(there)g(are)g(hard-core)h(exclusions,)g(or)f(for)h (\\semi-trivial")d(reasons,)25 b(e.g.)c(if)h(the)60 945 y(Hamiltonian)14 b FF(H)384 926 y FH(\010)380 957 y(\003)429 945 y FQ(is)i(quasilo)q(cal)g (but)g(un)o(b)q(ounded.)22 b(\(This)17 b(latter)e(can)i(happ)q(en)g(only)f (when)g(the)60 1005 y(single-spin)k(space)h(is)g(in\014nite.\))33 b(If)20 b(w)o(e)h(con)o(tend)f(that)1140 1001 y Fx(e)1135 1005 y FF(\026)h FQ(is)g(\\pathological",)h(then)f(w)o(e)f(really)60 1065 y(ough)o(t)d(to)f(pro)o(v)o(e)g(not)h(merely)c(that)743 1061 y Fx(e)739 1065 y FF(\026)j FQ(is)g(non-Gibbsian,)h(but)g(also)g(that)f (it)g(is)g FP(non-quasilo)n(c)n(al)5 b FQ(.)133 1125 y(W)l(e)12 b(are)h(not)g(able)f(at)h(presen)o(t)f(to)h(pro)o(v)o(e)f(non-quasilo)q (calit)o(y)l(,)g(but)h(w)o(e)f(can)h(argue)g(heuristically)60 1185 y(that)k(in)e(at)i(least)f(some)f(cases)h(the)g(non-Gibbsianness)h(do)q (es)g(in)o(v)o(olv)o(e)d(some)h(strongly)h(non-lo)q(cal)60 1246 y(e\013ect.)21 b(Consider)16 b(the)g(sign)h(of)g(the)f(\(an\)harmonic)f (crystal.)21 b(Recalling)15 b(Theorem)g(4.9)i(together)60 1306 y(with)f(Remark)f(1)h(follo)o(wing)g(it,)g(it)f(is)h(natural)h(to)g (conjecture)e(that)275 1432 y(lim)255 1462 y FD(R)282 1452 y Ft(0)293 1462 y Fy(!1)372 1432 y FF(E)408 1439 y FD(\026)431 1371 y Fx(\022)461 1432 y FQ(sgn)q(\()p FF(')583 1439 y FH(0)603 1432 y FQ(\))630 1369 y Fx(\014)630 1394 y(\014)630 1419 y(\014)630 1444 y(\014)652 1432 y FF(')684 1439 y FD(x)720 1432 y FF(>)f FQ(0)i(for)h(all)f FF(x)g FQ(ha)o(ving)g FF(R)e FE(\024)g(j)p FF(x)p FE(j)f(\024)h FF(R)1419 1411 y Fy(0)1431 1371 y Fx(\023)1489 1432 y FQ(=)28 b(1)186 b(\(4)p FF(:)p FQ(77\))60 1560 y(for)12 b(all)g FF(R)p FQ(,)h(no)g(matter)d(ho)o(w)j(large.)20 b(\(A)o(t)11 b(least)h(in)g(case)g(\(c\))g(of)g(Section)g(4.4.1,)h(w)o(e)e(are)h(able)g (to)h(pro)o(v)o(e)60 1620 y(this)h(using)h(the)g(FK)o(G)f(inequalit)o(y)l(,)e (via)i(a)h(sligh)o(t)f(extension)g(of)h(the)f(argumen)o(ts)g(of)h(Leb)q(o)o (witz)f(and)60 1681 y(Maes)h([239)q(].\))20 b(That)15 b(is,)g(if)f(w)o(e)h (condition)f(on)i(the)e(spins)i(in)e(an)i(ann)o(ulus)f FF(R)f FE(\024)g(j)p FF(x)p FE(j)f(\024)g FF(R)1681 1663 y Fy(0)1708 1681 y FQ(b)q(eing)j(all)60 1741 y FF(>)e FQ(0,)g(as)g FF(R)258 1723 y Fy(0)284 1741 y FE(!)g(1)g FQ(this)f(driv)o(es)g(all)g(the)h(spins)g (to)g(+)p FE(1)p FQ(,)f(and)i(in)e(particular)h FP(for)n(c)n(es)j FQ(the)c(sign)h(of)g(the)60 1801 y(spin)k(at)g(the)f(origin)h(to)g(b)q(e)g(+) f(\(with)h(probabilit)o(y)f(1!\).)25 b(F)l(or)18 b(the)f(Ising)h(measure)1604 1797 y Fx(e)1599 1801 y FF(\026)q FQ(,)f(this)h(means)60 1861 y(heuristically)g(that)j(the)f(spin)g(at)h(the)f(origin)g(is)g(feeling)f(an)i (in\014nite)e(energy)l(.)33 b(Ho)o(w)o(ev)o(er,)19 b(since)60 1921 y(the)g(e\013ect)g(o)q(ccurs)g(for)g(all)g FF(R)p FQ(,)h(no)g(matter)e (ho)o(w)h(large,)g(this)g(in\014nite)g(energy)f(m)o(ust)g(arise)h(from)60 1982 y(the)f(in)o(teraction)e(b)q(et)o(w)o(een)h(the)h(spin)f(at)h(the)g (origin)g(and)g FP(arbitr)n(arily)f(distant)j(spins)t FQ(.)26 b(\(Crudely)60 2042 y(sp)q(eaking,)21 b(the)e(in)o(teraction,)g(if)g(it)g (exists,)g(is)h(non-summable.\))29 b(Th)o(us,)20 b(w)o(e)g(do)g(not)g(ha)o(v) o(e)f(here)60 2102 y(merely)10 b(the)j(\\semi-trivial")e(situation)i(of)g(a)g (Hamiltonian)e(whic)o(h)i(is)f(quasilo)q(cal)h(but)g(un)o(b)q(ounded)60 2162 y(\(whic)o(h)k(an)o(yw)o(a)o(y)g(is)h(imp)q(ossible)e(for)i(a)g(mo)q (del)e(with)i(\014nite)f(single-spin)g(space\);)h(some)f(strongly)60 2222 y(non-lo)q(cal)i(e\013ect)e(is)h(taking)h(place.)26 b(It)17 b(ma)o(y)g(ev)o(en)g(b)q(e)h(that)h(\(4.77\))f(implies)e(non-quasilo)q(calit) o(y;)60 2283 y(or)h(it)f(ma)o(y)g(b)q(e)h(that)g(non-quasilo)q(calit)o(y)f (can)h(b)q(e)g(pro)o(v)o(en)f(b)o(y)g(a)i(di\013eren)o(t)e(argumen)o(t.)21 b(These)c(are)60 2343 y(op)q(en)g(questions.)133 2403 y(A)c(similar)e (situation)i(probably)g(holds)g(in)g(the)g(setup)g(of)g(Section)f(4.4.2,)i (whenev)o(er)e(the)g(image)60 2463 y(single-spin)k(space)g(\012)464 2445 y Fy(0)464 2475 y FH(0)501 2463 y FQ(is)g(\014nite.)133 2523 y(A)h(v)o(ery)g(di\013eren)o(t)g(situation)h(arises)f(if)g FF(f)23 b FQ(is)18 b(a)g FP(bije)n(ctive)23 b FQ(map)17 b(of)h Fq(R)g FQ(on)o(to)g(\012)1571 2505 y Fy(0)1571 2536 y FH(0)1608 2523 y FQ(\(of)g(course)g(\012)1870 2505 y Fy(0)1870 2536 y FH(0)60 2584 y FQ(m)o(ust)e(then)i(b)q(e)g(uncoun)o(tably)g(in\014nite!\).)24 b(In)18 b(this)f(case)h FF(f)23 b FQ(is)18 b(merely)d(a)j(one-to-one)h(relab) q(elling)60 2644 y(of)d(spin)g(v)m(alues;)f(the)g(ph)o(ysics)g(of)h(the)g (image)e(measure)1100 2640 y Fx(e)1096 2644 y FF(\026)i FQ(is)f(ob)o(viously) g FP(identic)n(al)22 b FQ(to)16 b(that)g(of)g(the)938 2784 y(137)p eop %%Page: 138 138 bop 60 91 a FQ(original)16 b(measure)g FF(\026)p FQ(.)22 b(In)17 b(particular,)f(if)g(the)g(original)h(\(an\)harmonic)f(crystal)g(has)h FP(\014nite-r)n(ange)60 152 y FQ(in)o(teractions,)g(then)457 148 y Fx(e)453 152 y FF(\026)h FQ(is)g(consisten)o(t)f(with)h(a)g FP(Gibbsian)23 b FQ(sp)q(eci\014cation)17 b(for)h(a)h(particular)e(\014nite-) 60 212 y(range)c(but)f FP(unb)n(ounde)n(d)18 b FQ(in)o(teraction,)11 b(namely)g(the)h(one)g(gotten)h(b)o(y)e(mapping)h(the)g(\(an\)harmonic-)60 272 y(crystal)18 b(sp)q(eci\014cation)f(via)h(the)g(function)g FF(f)5 b FQ(.)26 b(Suc)o(h)18 b(a)g(sp)q(eci\014cation)g(is)g(alw)o(a)o(ys)g (quasilo)q(cal;)g(the)60 332 y(in)o(teraction)d(is)h(uniformly)e(con)o(v)o (ergen)o(t)h(but)i(not)f(absolutely)g(summable.)133 441 y(Finally)l(,)22 b(let)g(us)h(remark)e(that)i(the)f(lo)q(cal)h(nonlinear)f(maps)g(considered)g (here)g(are)g(a)h(sp)q(e-)60 501 y(cial)17 b(case)g(of)h(the)f (renormalization)f(transformations)h(considered)g(in)g(Sections)h(3)f(and)h (4.1{4.3:)60 561 y(namely)l(,)g(one)h(in)g(whic)o(h)g(the)g(blo)q(c)o(ks)g (are)g(single)g(sites,)g(the)g(transformation)h(is)f(deterministic)o(,)60 622 y(and)f(the)g(image)e(space)i(is)g(in)f(general)h(di\013eren)o(t)f(from)f (the)i(original)g(space.)25 b(Suc)o(h)18 b(transforma-)60 682 y(tions)f(trivially)f(ob)q(ey)h(prop)q(erties)g(\(T1\){\(T3\))i(of)e(Section) g(3.1.)24 b(Of)17 b(course,)g(if)g FF(f)22 b FQ(is)17 b(one-to-one,)60 742 y(then)g(the)g(transformation)g(is)g(trivial)e(\(just)j(a)f(relab)q (elling)f(of)h(spin)g(con\014gurations\).)25 b(Ho)o(w)o(ev)o(er,)60 802 y(if)13 b FF(f)19 b FQ(is)13 b(man)o(y-to-one,)g(then)g(the)g (transformation)h(is)f(not)h(so)g(di\013eren)o(t)e(in)i(nature)f(from)f(the)i (usual)60 862 y(\(blo)q(c)o(k-spin\))h(renormalization)f(transformations:)21 b(b)q(oth)16 b(\\discard)g(details")g(from)e(the)h(original)60 923 y(spin)k(con\014guration.)32 b(These)19 b(details)g(ma)o(y)f(b)q(e)h(in)g (the)g(\014ne)h(structure)f(of)g(a)h(single)f(spin,)h(or)f(in)60 983 y(the)c(lo)q(cal)h(\014ne)f(structure)g(of)h(a)g(small)e(blo)q(c)o(k)h (of)h(spins,)g(but)f(qualitativ)o(ely)e(there)i(do)q(es)i(not)f(seem)60 1043 y(to)h(b)q(e)g(an)o(y)f(great)h(in)o(trinsic)e(di\013erence.)21 b(Our)c(theorems)e(b)q(oth)j(in)e(Sections)g(4.1{4.3)i(and)f(in)f(the)60 1103 y(curren)o(t)21 b(subsection)g(are)h(of)f(the)h(general)f(t)o(yp)q(e:)31 b(an)22 b(R)l(T)g(map)e(whic)o(h)h(discards)h(\(imp)q(ortan)o(t\))60 1163 y(information)d(mak)o(es)f(the)i(image)e(measure)h(\(sometimes\))e (non-Gibbsian)k(\(and)f(p)q(ossibly)g(ev)o(en)60 1224 y(non-quasilo)q(cal\).) 60 1353 y FM(4.4.4)55 b(Application)18 b(to)h(the)f(Renormalization)e(Group) 60 1446 y FQ(In)22 b(this)h(section)f(w)o(e)g(apply)h(Theorem)e(4.9)i(to)g (the)f(R)o(G,)g(follo)o(wing)g(closely)g(Dorlas)h(and)g(v)m(an)60 1506 y(En)o(ter)18 b([103)q(].)26 b(Let)19 b(us)f(consider)g(an)h(Ising)f(mo) q(del)f(in)h(dimension)f FF(d)g(>)g FQ(4)i(at)g(the)f(critical)e(p)q(oin)o (t,)60 1566 y(and)i(apply)f(blo)q(c)o(k-a)o(v)o(eraging)g(transformations)g (on)h(v)m(arious)g(blo)q(c)o(k)f(sizes)f FF(b)p FQ(.)24 b(Then)18 b(DeConinc)o(k)60 1626 y(and)j(Newman)e([71)q(])h(and)h(Shlosman)f([323,)i (and)f(priv)m(ate)f(comm)o(unic)o(ation])e(ha)o(v)o(e)h(sho)o(wn)j(that)60 1686 y(there)c(exists)g(a)g FF(b)p FQ(-dep)q(enden)o(t)g(c)o(hoice)f(of)i (normalization)e(suc)o(h)h(that)h(the)f(blo)q(c)o(k-spin)g(measures)60 1747 y(con)o(v)o(erge)g(as)i FF(b)g FE(!)f(1)g FQ(to)h(a)g(massless)e (Gaussian)j(measure)1195 1728 y FH(58)1231 1747 y FQ(;)g(this)e(is)g(a)h (sligh)o(t)f(v)m(arian)o(t)g(of)h(the)60 1807 y(Aizenman-F)l(r\177)-24 b(ohlic)o(h)13 b(trivialit)o(y)h(theorem.)133 1867 y(No)o(w)22 b(the)f(k)o(ey)g(observ)m(ation)h(is)g(that)g(a)g(blo)q(c)o(k-a)o(v)o (eraging)f(transformation)h(follo)o(w)o(ed)e(b)o(y)i(a)60 1927 y(pro)s(jection)e(on)h(Ising)g(con\014gurations)h(is)e(iden)o(tical)f(to)i(a) g(ma)s(jorit)o(y-rule)d(transformation.)35 b(So)60 1987 y(consider)16 b(applying)h(the)g(ma)s(jorit)o(y-rule)d(transformation)j(using)g(larger)f (and)i(larger)e(blo)q(c)o(k)h(sizes)60 2047 y FF(b)p FQ(.)j(Since)13 b(the)g(blo)q(c)o(k-a)o(v)o(eraged)f(spins)i(\(with)f(a)h(suitable)f FF(b)p FQ(-dep)q(enden)o(t)g(normalization\))f(con)o(v)o(erge)60 2108 y(as)g FF(b)i FE(!)g(1)d FQ(to)h(a)h(massless)e(Gaussian,)i(it)e(is)h (not)g(di\016cult)f(to)h(sho)o(w)g(that)h(the)e(ma)s(jorit)o(y-rule)e(image) 60 2168 y(spins)16 b(con)o(v)o(erge)e(as)i FF(b)e FE(!)g(1)h FQ(to)h(the)f(sign)h(of)g(this)f(same)g(massless)g(Gaussian.)22 b(But)15 b(b)o(y)g(Theorem)60 2228 y(4.9,)h(this)g(latter)g(measure)f(is)h (non-Gibbsian!)22 b(\(F)l(or)17 b(details,)e(see)h([103)q(].\))133 2288 y(This)24 b(non-Gibbsian)h(scaling)f(limit)e(is)i(not)g(a)g(\014xed)g(p) q(oin)o(t)g(in)g(the)g(strict)f(sense,)j(as)e(the)60 2348 y(sequence)15 b(of)i(ma)s(jorit)o(y-rule)d(transformations)j(lac)o(ks)f(the)g(semigroup)f (prop)q(ert)o(y:)22 b(the)16 b(ma)s(jorit)o(y)p 60 2392 732 2 v 100 2445 a FA(58)135 2461 y Fz(Con)o(v)o(en)o(tional)d(wisdom)g(holds)h (that)h(the)g(normalization)d(can)j(b)q(e)g(c)o(hosen)g(to)g(b)q(e)g Fv(b)1468 2445 y Fo(\000)p Fp(p)1528 2461 y Fz(for)f(a)g(suitable)h(p)q(o)o (w)o(er)60 2510 y Fv(p)g Fz([in)f(fact)i(one)f(predicts)i Fv(p)c Fz(=)h(\()p Fv(d)c Fz(+)h(2)f Fu(\000)g Fv(\021)q Fz(\))p Fv(=)p Fz(2)k(=)g(\()p Fv(d)c Fz(+)g(2\))p Fv(=)p Fz(2].)21 b(If)15 b(this)g(is)g(the)h(case,)g(then)g(the)g(limiting)c(measure)60 2560 y(can)h(also)f(b)q(e)h(obtained)f(b)o(y)g(rep)q(eated)j(application)c (of)h(the)h(blo)q(c)o(k-a)o(v)o(eraging)e(transformation)f(with)j(a)f Fw(\014xe)n(d)17 b Fz(blo)q(c)o(k)60 2610 y(size)d Fv(b)p Fz(,)f(and)g(hence) i(is)e(a)g Fw(self-similar)j Fz(Gaussian)d(measure)g([327)o(,)f(17,)h(32)o (].)18 b(Ho)o(w)o(ev)o(er,)13 b(this)g(con)o(v)o(en)o(tional)g(wisdom)60 2660 y(has)h(not)g(y)o(et)g(\(as)g(far)g(as)g(w)o(e)g(kno)o(w\))f(b)q(een)i (pro)o(v)o(en)f(rigorously)m(.)938 2784 y FQ(138)p eop %%Page: 139 139 bop 60 91 a FQ(rule)15 b(on)i(blo)q(c)o(k)f(size)f FF(b)467 73 y FH(2)503 91 y FQ(is)h(not)g(equal)g(to)h(the)e(second)i(iteration)f(of)g (ma)s(jorit)o(y)e(rule)i(on)g(blo)q(c)o(k)g(size)60 152 y FF(b)e FQ(\(as)h(p)q(oliticians)f(w)o(ell)f(kno)o(w!\).)20 b(Therefore,)14 b(the)g(existence)f(of)i(pathologies)g(for)g(the)f(\014xed)g(p)q(oin)o(t)60 212 y(arising)19 b(from)e(the)h FF(b)g FE(!)f(1)h FQ(limit)e(do)q(es)j(not)g FP(guar)n(ante)n(e)k FQ(that)c(the)f(corresp)q(onding)h(pathologies)60 272 y(will)j(o)q(ccur)h(for)h(the)e(\014xed)h(p)q(oin)o(t)g(arising)g(from)f (iteration)h(of)g(a)h(ma)s(jorit)o(y-rule)c(map)j(with)g(a)60 332 y(\014xed)18 b(blo)q(c)o(k)f(size)h FF(b)p FQ(.)26 b(But)18 b(it)g(do)q(es)h(mak)o(e)d(it)i(plausible:)24 b(there)18 b(do)q(es)h(not)f (seem)f(to)h(b)q(e)h FP(so)g(much)60 392 y FQ(di\013erence)i(b)q(et)o(w)o (een)h(ma)s(jorit)o(y)e(rule)i(on)g(a)h(blo)q(c)o(k)f(of)h(size)e FF(b)1224 374 y FD(n)1270 392 y FQ(and)i FF(n)f FQ(iterations)g(of)h(ma)s (jorit)o(y)60 452 y(rule)d(on)h(a)h(blo)q(c)o(k)e(of)h(size)f FF(b)p FQ(.)35 b(And,)21 b(in)g(an)o(y)f(case,)i(the)f(\\large-cell)f(ma)s (jorit)o(y-rule")e(approac)o(h)60 513 y(is)i(clearly)f(part)i(of)f(the)g(R)o (G)h(en)o(terprise)d([128)q(,)i(249)q(],)h(so)g(it)e(is)i(in)o(teresting)e (to)h(see)g(that)h(it)f(can)60 573 y(fail.)27 b(Finally)l(,)17 b(as)h(w)o(e)g(discuss)h(in)f(Section)f(5.2,)i(there)f(are)g(other)g(reasons) h(to)g(exp)q(ect)e(that)i(this)60 633 y(b)q(eha)o(vior)c(is)h(in)f(some)g (sense)g(t)o(ypical.)20 b(Indeed,)14 b(w)o(e)h(conjecture)g(that)h(the)g (\014xed-p)q(oin)o(t)f(measures)60 693 y(of)h(nonlinear)g(R)o(G)g (transformations)g(for)g FF(d)876 696 y FC(\()28 b(\))882 685 y FE(\025)935 693 y FF(d)960 700 y FD(u)998 693 y FQ(\()p FE(\021)16 b FQ(upp)q(er)g(critical)e(dimension)h(of)h(the)f(mo)q(del\))60 753 y(will)g(b)q(e)i(non-Gibbsian)g(in)f(considerable)f(generalit)o(y)l(.)133 814 y(Finally)l(,)i(w)o(e)i(remark)d(that)j(the)g(results)f(discussed)g(here) g(for)h FF(d)f(>)g FQ(4)h(are)f(exp)q(ected)g(to)h(hold)60 874 y(also)e(for)f FF(d)f FQ(=)e(4,)j(pro)o(vided)g(that)h(the)f(\\trivialit) o(y)e(conjecture")i([365,)g(115)q(])g(is)g(true.)60 1018 y FB(4.5)70 b(Other)14 b(Results)g(on)i(Non-Gibbsianness)e(and)j(Non-Quasilo)r (calit)n(y)60 1111 y FQ(In)g(Sections)g(4.1{4.4,)h(w)o(e)f(ha)o(v)o(e)f(giv)o (en)h(a)g(n)o(um)o(b)q(er)f(of)h(examples)f(of)h(non-Gibbsian)i(\(or)e(what)h (is)60 1171 y(sligh)o(tly)11 b(stronger,)i(non-quasilo)q(cal\))h(measures,)d (with)h(particular)g(atten)o(tion)g(to)h(those)g(arising)f(in)60 1231 y(R)o(G)j(theory)l(.)20 b(It)14 b(is)h(natural)g(to)g(ask)h(whether)e (the)h(phenomenon)f(of)h(non-Gibbsianness)h(\(or)f(non-)60 1291 y(quasilo)q(calit)o(y\))e(is)i(more)e(widespread.)20 b(Unfortunately)l (,)14 b(v)o(ery)f(little)g(is)h(kno)o(wn)h(at)g(presen)o(t)f(ab)q(out)60 1351 y(the)22 b(prop)q(erties)g(of)g(non-quasilo)q(cal)h(measures,)f(and)g(v) o(ery)f(few)h(examples)e(of)i(non-quasilo)q(cal)60 1412 y(measures)c(are)h (kno)o(wn.)30 b(In)18 b(this)h(section)g(w)o(e)g(try)f(to)i(mak)o(e)d(a)i (complete)e(surv)o(ey)h(of)h(all)g(kno)o(wn)60 1472 y(ph)o(ysically)11 b(in)o(teresting)h(examples)e(of)j(non-quasilo)q(calit)o(y)l(.)20 b(\(The)13 b(list)f(is)g(short)i(enough)f(that)g(suc)o(h)60 1532 y(a)k(comprehensiv)o(e)c(surv)o(ey)i(is)h(feasible.\))60 1662 y FM(4.5.1)55 b(T)-5 b(rivial)22 b(Example:)30 b(Con)n(v)n(ex)23 b(Com)n(bination)f(of)h(Gibbs)f(Measures)h(for)g(Dif-)231 1722 y(feren)n(t)18 b(In)n(teractions)60 1814 y FQ(These)f(are)f(p)q(erhaps)i (rather)f(silly)e(examples:)21 b(if)16 b(one)h(mak)o(es)e(a)i(con)o(v)o(ex)e (com)o(bination)h(of)h(Gibbs)60 1875 y(measures)c(for)i(the)e(Ising)h(mo)q (del)f(at)i(t)o(w)o(o)f(di\013eren)o(t)f(temp)q(eratures,)g(then)h(it)g(is)g (hardly)g(surprising)60 1935 y(that)e(the)f(resulting)g(measure)f(will)g(not) i(b)q(e)f(Gibbsian)h(at)g(all.)19 b(The)11 b(pro)q(of)i(sa)o(ys)e(roughly)h (that)f(if)g(the)60 1995 y(resulting)h(measure)f FP(wer)n(e)16 b FQ(Gibbsian)d(for)g(some)e(in)o(teraction)g(\010,)i(then)f(the)h(t)o(w)o(o) f(original)g(measures)60 2055 y(w)o(ould)19 b(also)h(ha)o(v)o(e)f(to)h(b)q(e) f(Gibbsian)h(for)f(\010.)31 b(But)19 b(this)g(is)g(imp)q(ossible,)f(b)q (ecause)i(the)f(Gri\016ths-)60 2115 y(Ruelle)g(theorem)f(tells)h(us)i(that)f (a)h(measure)e(can)h(b)q(e)g(Gibbsian)h(for)f(at)g(most)g(one)g(in)o (teraction)60 2176 y(\(mo)q(dulo)c(ph)o(ysical)f(equiv)m(alence\).)133 2236 y(W)l(e)i(need)f(a)i(preliminary)c(result,)i(concerning)h(the)g (conditions)g(under)g(whic)o(h)f(a)i(\\rew)o(eigh)o(t-)60 2296 y(ing")f(of)f(a)h(Gibbs)f(measure)f(remains)g(a)i(Gibbs)f(measure:)60 2410 y FM(Lemma)g(4.11)24 b FP(L)n(et)17 b FQ(\005)h FP(b)n(e)g(a)g(sp)n(e)n (ci\014c)n(ation)g(and)h FF(\026)f FP(a)g(me)n(asur)n(e)f(in)i FE(G)s FQ(\(\005\))p FP(.)k(A)18 b(me)n(asur)n(e)f FF(\027)22 b FP(of)17 b(the)60 2470 y(form)i FF(\027)j FQ(=)c FF(f)5 b(\026)21 b FP(b)n(elongs)g(also)g(to)f FE(G)s FQ(\(\005\))f FP(if)h(and)g(only)g(if)g FF(f)25 b FP(is)1245 2454 y Fx(b)1230 2470 y FE(F)1266 2477 y Fy(1)1303 2470 y FP(-me)n(asur)n(able)c(\(mo)n(dulo)e FF(\026)p FP(-nul)r(l)60 2530 y(sets\).)938 2784 y FQ(139)p eop %%Page: 140 140 bop 60 96 a FQ(\(W)l(e)22 b(recall)f(that)431 80 y Fx(b)417 96 y FE(F)453 103 y Fy(1)514 96 y FE(\021)596 63 y Fx(T)578 134 y FH(\003)p Fy(2S)658 96 y FE(F)694 103 y FH(\003)718 94 y Fs(c)758 96 y FQ(is)i(the)f FF(\033)r FQ(-\014eld)f(of)i(observ)m(ables)g (at)f(in\014nit)o(y:)33 b(see)22 b(Section)60 182 y(2.3.6.\))f(The)15 b(pro)q(of)h(of)f(this)g(lemma)d(is)j(giv)o(en,)e(for)j(instance,)e(in)h ([299,)g(Lemma)e(2.4])i(and)g(in)g([157,)60 242 y(Theorem)g(7.7].)133 302 y(W)l(e)h(can)h(no)o(w)f(pro)o(v)o(e)g(the)g(main)f(result:)60 406 y FM(Prop)r(osition)j(4.12)24 b FP(L)n(et)c FF(\026)603 413 y FH(1)623 406 y FF(;)8 b(\026)674 413 y FH(2)694 406 y FF(;)g(:)g(:)g(:)20 b FP(b)n(e)h(a)f(\014nite)i(or)e(c)n(ountably)i (in\014nite)g(family)e(of)h(me)n(asur)n(es)60 466 y(\(not)k(ne)n(c)n (essarily)g(tr)n(anslation-invariant\))g(which)h(ar)n(e)e(ar)n(e)f (distinguishable)k(at)e(in\014nity,)i(i.e.)60 526 y(ther)n(e)22 b(exist)h(disjoint)f(sets)g FF(F)616 533 y FH(1)636 526 y FF(;)8 b(F)690 533 y FH(2)709 526 y FF(;)g(:)g(:)g(:)21 b FE(2)880 510 y Fx(b)866 526 y FE(F)902 533 y Fy(1)961 526 y FP(such)h(that)h FF(\026)1210 533 y FD(k)1231 526 y FQ(\()p FF(F)1282 533 y FD(k)1303 526 y FQ(\))f(=)h(1)f FP(for)f(e)n(ach)h FF(k)r FP(.)37 b(Assume)60 586 y(further)16 b(that)g(e)n(ach)h(of)f(the)h(me)n(asur)n(es)e FF(\026)801 593 y FH(1)821 586 y FF(;)8 b(\026)872 593 y FH(2)892 586 y FF(;)g(:)g(:)g(:)15 b FP(gives)j(nonzer)n(o)e(me)n(asur)n(e)f(to)i (every)g(op)n(en)f(set)h(in)60 646 y FQ(\012)p FP(.)22 b(Now)17 b(form)f(a)g(c)n(onvex)i(c)n(ombination)f FF(\026)d FQ(=)925 613 y Fx(P)937 685 y FD(k)977 646 y FF(c)998 653 y FD(k)1019 646 y FF(\026)1048 653 y FD(k)1086 646 y FP(with)j(al)r(l)h FF(c)1281 653 y FD(k)1316 646 y FF(>)c FQ(0)p FP(.)22 b(If)16 b FF(\026)h FP(is)f(c)n(onsistent)i(with)60 728 y(a)f(sp)n(e)n(ci\014c)n (ation)g FQ(\005)p FP(,)g(then)h(so)f(ar)n(e)g FF(\026)725 735 y FH(1)745 728 y FF(;)8 b(\026)796 735 y FH(2)816 728 y FF(;)g(:)g(:)g(:)o FP(;)17 b(and)g(if)g FQ(\005)g FP(is)g(F)l(el)r(ler,)i (then)f(this)f(is)g(the)h FQ(only)f FP(F)l(el)r(ler)60 788 y(sp)n(e)n(ci\014c)n(ation)h(with)g(which)g(any)f(of)g(these)i(me)n(asur)n (es)d(is)h(c)n(onsistent.)60 891 y FQ(Th)o(us,)24 b(if)f(some)e(t)o(w)o(o)i (of)g(the)g FE(f)p FF(\026)691 898 y FD(k)713 891 y FE(g)f FQ(|)h(sa)o(y)l(,)h FF(\026)963 898 y FD(i)1000 891 y FQ(and)g FF(\026)1131 898 y FD(j)1172 891 y FQ(|)f(happ)q(en)h(to)f(b)q(e)g(consisten) o(t)f(with)60 952 y FP(di\013er)n(ent)h FQ(F)l(eller)17 b(sp)q (eci\014cations)i(\(\005)751 959 y FD(i)782 952 y FE(6)p FQ(=)e(\005)874 959 y FD(j)892 952 y FQ(\),)i(then)f(it)g(follo)o(ws)g(that)h FF(\026)g FQ(is)f(not)h(consisten)o(t)f(with)60 1012 y FP(any)23 b FQ(F)l(eller)18 b(sp)q(eci\014cation.)29 b(In)19 b(particular,)f FF(\026)i FQ(is)f(not)g(a)g(Gibbs)h(measure)d(for)j(an)o(y)f(con)o(tin)o (uous,)60 1072 y(uniformly)c(con)o(v)o(ergen)o(t)g(in)o(teraction.)21 b(If)16 b(the)h(single-spin)f(space)h(\012)1331 1079 y FH(0)1367 1072 y FQ(is)g(\014nite,)e(this)i(means)f(that)60 1132 y FF(\026)i FQ(is)e(not)i(consisten)o(t)f(with)g(an)o(y)g(quasilo)q(cal)g(sp)q (eci\014cation,)g(and)g(in)g(particular)g(that)h FF(\026)f FQ(is)g(not)h(a)60 1192 y(Gibbs)f(measure)d(for)j(an)o(y)f(uniformly)e(con)o (v)o(ergen)o(t)h(in)o(teraction.)133 1275 y FM(Remark.)32 b FQ(It)20 b(is)h(not)g(di\016cult)e(to)i(sho)o(w)g(that)g(if)f(the)h(measures) e FF(\026)1441 1282 y FH(1)1461 1275 y FF(;)8 b(\026)1512 1282 y FH(2)1532 1275 y FF(;)g(:)g(:)g(:)20 b FQ(are)h FP(p)n(airwise)60 1335 y FQ(distinguishable)15 b(at)h(in\014nit)o(y)l(,)e(then)i(they)f(are)g (join)o(tly)g(distinguishable)g(at)h(in\014nit)o(y)e(in)i(the)f(sense)60 1395 y(of)i(Prop)q(osition)g(4.12.)22 b(Here)15 b(it)h(is)g(crucial)f(that)i (w)o(e)f(are)g(dealing)g(with)g(a)h FP(c)n(ountable)k FQ(family)l(.)60 1500 y Fd(Pr)o(oof)g(of)g(Pr)o(oposition)g(4.12.)78 b FQ(Supp)q(ose)21 b(that)f FF(\026)f FQ(is)g(consisten)o(t)g(with)g(a)h(sp)q(eci\014cation)60 1560 y(\005.)g(Then,)c(b)o(y)e(Lemma)f(4.11,)j(the)f(measures)f FF(\026)947 1567 y FD(k)983 1560 y FQ(=)g FF(c)1056 1539 y Fy(\000)p FH(1)1056 1573 y FD(k)1103 1560 y FF(\037)1134 1567 y FD(F)1156 1573 y Fs(k)1177 1560 y FF(\026)h FQ(are)h(also)g(consisten)o(t)e (with)i(\005.)k(The)60 1620 y(uniqueness)c(follo)o(ws)g(from)f(Theorem)g (2.15.)p 1027 1624 25 34 v 133 1725 a(In)i(order)h(to)g(apply)f(Prop)q (osition)i(4.12,)f(w)o(e)f(need)g(to)h(v)o(erify)e(that)i(the)f(measures)g FF(\026)1720 1732 y FH(1)1740 1725 y FF(;)8 b(\026)1791 1732 y FH(2)1811 1725 y FF(;)g(:)g(:)g(:)60 1785 y FQ(are)15 b(distinguishable)g (at)g(in\014nit)o(y)f(\(the)h(supp)q(ort)h(h)o(yp)q(othesis)f(is)g(usually)g (trivial)f(to)h(c)o(hec)o(k\).)k(One)60 1845 y(easy)14 b(w)o(a)o(y)f(to)h (obtain)h(suc)o(h)e(measures)g(is)h(to)g(recall)e(that)j(distinct)e FP(er)n(go)n(dic)j FQ(translation-in)o(v)m(arian)o(t)60 1906 y(measures)i(are)i(distinguishable)f(at)g(in\014nit)o(y)f(\(Theorem)g(2.33)i (and)g(the)f(remark)f(follo)o(wing)h(it\).)60 1966 y(W)l(e)d(therefore)g(ha)o (v)o(e:)60 2069 y FM(Corollary)i(4.13)24 b FP(L)n(et)12 b FF(\026)541 2076 y FH(1)561 2069 y FF(;)c(\026)612 2076 y FH(2)632 2069 y FF(;)g(:)g(:)g(:)k FP(b)n(e)g(a)h(\014nite)h(or)d(c)n(ountably)j (in\014nite)g(family)e(of)h(er)n(go)n(dic)f(tr)n(anslation-)60 2130 y(invariant)21 b(Gibbs)g(me)n(asur)n(es)e(for)h(inter)n(actions)h FQ(\010)1009 2137 y FH(1)1029 2130 y FF(;)8 b FQ(\010)1086 2137 y FH(2)1106 2130 y FF(;)g(:)g(:)g(:)18 b FE(2)i(B)1292 2111 y FH(1)1311 2130 y FP(,)h(r)n(esp)n(e)n(ctively.)32 b(Now)20 b(form)g(a)60 2190 y(c)n(onvex)e(c)n(ombination)g FF(\026)c FQ(=)586 2157 y Fx(P)598 2228 y FD(k)638 2190 y FF(c)659 2197 y FD(k)680 2190 y FF(\026)709 2197 y FD(k)747 2190 y FP(with)k(al)r(l)g FF(c)943 2197 y FD(k)978 2190 y FF(>)13 b FQ(0)p FP(.)23 b(If)16 b FF(\026)h FP(is)g(c)n(onsistent)h(with)f(a)g FQ(F)l(eller)e FP(sp)n(e)n(ci\014-)60 2271 y(c)n(ation)k FQ(\005)p FP(,)f(then)h(al)r(l)h (the)f(inter)n(actions)g FQ(\010)842 2278 y FD(k)882 2271 y FP(must)g(b)n(e)f(physic)n(al)r(ly)h(e)n(quivalent)i(in)e(the)g(DLR)e(sense) 60 2331 y(\(and)h(henc)n(e)g(also)g(in)f(the)h(R)o(uel)r(le)i(sense\).)60 2479 y Fd(Pr)o(oof.)48 b FQ(If)16 b FF(\026)359 2486 y FD(i)389 2479 y FQ(=)g FF(\026)472 2486 y FD(j)491 2479 y FQ(,)h(then)g(\010)669 2486 y FD(i)701 2479 y FQ(and)h(\010)832 2486 y FD(j)867 2479 y FQ(m)o(ust)e(b)q(e)i(ph)o(ysically)d(equiv)m(alen)o(t)h(in)h(the)g(DLR)h (sense)60 2539 y(\(Corollary)25 b(2.18\).)48 b(So)25 b(w)o(e)f(can)h(assume)f (without)h(loss)h(of)f(generalit)o(y)e(that)j(the)e(measures)60 2600 y FF(\026)89 2607 y FH(1)109 2600 y FF(;)8 b(\026)160 2607 y FH(2)180 2600 y FF(;)g(:)g(:)g(:)20 b FQ(are)g(all)g(distinct.)34 b(Since)19 b(distinct)h(ergo)q(dic)h(measures)e(are)i(distinguishable)f(at)h (in-)60 2660 y(\014nit)o(y)l(,)13 b(and)i(Gibbs)f(measures)f(for)h(an)h (absolutely)e(summable)f(in)o(teraction)h(alw)o(a)o(ys)h(giv)o(e)f(nonzero) 938 2784 y(140)p eop %%Page: 141 141 bop 60 91 a FQ(measure)18 b(to)i(ev)o(ery)d(op)q(en)j(set,)f(w)o(e)g(can)h (apply)f(the)g(preceding)f(prop)q(osition)i(to)g(conclude)f(that)60 152 y(\005)13 b(=)h(\005)199 133 y FH(\010)224 138 y Fr(1)257 152 y FQ(=)g(\005)346 133 y FH(\010)371 138 y Fr(2)404 152 y FQ(=)g FF(:)8 b(:)g(:)13 b FQ(.)22 b(The)16 b(rest)g(follo)o(ws)g(from)f (Theorems)g(2.17)i(and)g(2.42.)p 1696 156 25 34 v 133 260 a(Therefore,)g FP(\(non-trivial\))k(\014nite)f(or)e(c)n(ountably)i(in\014nite)g(c)n(onvex)g (c)n(ombinations)g(of)e(er)n(go)n(dic)60 320 y(tr)n(anslation-invariant)h (Gibbs)f(me)n(asur)n(es)e(for)h(non-physic)n(al)r(ly-e)n(quivalen)q(t)j (inter)n(actions)e(c)n(annot)60 380 y(b)n(e)g(Gibbsian)t FQ(;)e(and)h(for)f (\014nite)g(single-spin)g(space)g(they)g(cannot)h(ev)o(en)e(b)q(e)h(quasilo)q (cal.)60 510 y FM(4.5.2)55 b(Restriction)17 b(of)i(the)f(Tw)n(o-Dimensional)f (Ising)h(Mo)r(del)g(to)g(an)h(Axis)60 602 y FQ(Sc)o(honmann)10 b([318)q(])h(ga)o(v)o(e)g(another)g(example)e(of)j(a)f(non-Gibbsian)i (measure)c(that)j(can)f(b)q(e)h(obtained)60 662 y(b)o(y)20 b(applying)g(a)h(simple)d(transformation)i(to)h(a)f(w)o(ell-kno)o(wn)g (Gibbsian)g(measure.)32 b(He)20 b(pro)o(v)o(ed)60 723 y(that)h(if)e FF(\026)247 730 y FH(+)297 723 y FQ(is)h(the)g(\\+")h(phase)g(of)f(the)g(t)o (w)o(o-dimensional)f(Ising)h(mo)q(del)f(at)h(zero)g(\014eld)g(and)h(at)60 783 y(an)o(y)16 b(temp)q(erature)f(b)q(elo)o(w)h(critical,)e(then)i(its)g (restriction)f FF(\026)1185 790 y FH(+)1215 783 y FF(P)23 b FQ(to)17 b(the)f(axis)g FE(f)p FQ(\()p FF(i;)8 b FQ(0\):)16 b FF(i)d FE(2)h Fq(Z)q FE(g)i FQ(is)g(a)60 843 y FP(non-Gibbsian)22 b FQ(one-dimensional)15 b(Ising)h(mo)q(del.)k(His)15 b(argumen)o(t)h(is)g (based)g(on)h(t)o(w)o(o)f(results:)133 927 y(R1\))g(F)l(or)g(all)g(temp)q (eratures)f(b)q(elo)o(w)g(the)h(critical)e(temp)q(erature)h(for)h(the)g FF(d)e FQ(=)g(2)i(Ising)g(mo)q(del,)60 987 y FF(i)p FQ(\()p FF(\026)125 994 y Fy(\000)154 987 y FF(P)7 b FE(j)p FF(\026)235 994 y FH(+)265 987 y FF(P)g FQ(\))14 b FE(6)p FQ(=)g(0.)133 1072 y(R2\))j(Let)f FF(\033)346 1054 y Fy(0)344 1084 y FD(n;N)425 1072 y FQ(denote)g(the)g(spin)g(con\014guration)h(on)g(the)f(\\ann)o(ulus")h FE(f)p FQ(\()p FF(i;)8 b FQ(0\):)16 b FF(n)e FE(\024)g(j)p FF(i)p FE(j)f(\024)g FF(N)5 b FE(g)p FQ(.)60 1132 y(Then)16 b(for)h(eac)o(h)f FF(n)g FQ(there)g(exists)f(an)i FF(N)5 b FQ(\()p FF(n)p FQ(\))17 b(suc)o(h)f(that)545 1239 y FF(\026)p FQ(\()8 b FE(\001)g(j)p FF(\033)667 1219 y Fy(0)665 1252 y FD(n;N)t FH(\()p FD(n)p FH(\))793 1239 y FQ(=)14 b FE(\000)p FQ(1\))28 b FE(!)f FF(\026)1061 1246 y Fy(\000)1188 1239 y FQ(as)17 b FF(n)d FE(!)g(1)360 b FQ(\(4)p FF(:)p FQ(78\))60 1347 y(for)17 b(all)e(Gibbs)i(measures)e FF(\026)i FQ(of)f(the)g(original)g (mo)q(del.)1058 1328 y FH(59)1116 1347 y FQ(As)g(a)g(consequence)460 1454 y(\()p FF(\026)508 1461 y FH(+)537 1454 y FF(P)7 b FQ(\)\()h FE(\001)g(j)p FF(\033)687 1433 y Fy(0)685 1466 y FD(n;N)t FH(\()p FD(n)p FH(\))813 1454 y FQ(=)14 b FE(\000)p FQ(1\))28 b FE(!)f FF(\026)1081 1461 y Fy(\000)1111 1454 y FF(P)105 b FQ(as)17 b FF(n)d FE(!)f(1)h FF(:)274 b FQ(\(4)p FF(:)p FQ(79\))133 1645 y(Result)23 b(\(4.79\))i(implies)c(that)j(if)f FF(\026)809 1652 y FH(+)839 1645 y FF(P)31 b FQ(is)24 b(consisten)o(t)f(with)h(some)e (quasilo)q(cal)i(\(=)g(F)l(eller\))60 1706 y(sp)q(eci\014cation,)15 b(then)g FF(\026)490 1713 y Fy(\000)520 1706 y FF(P)22 b FQ(m)o(ust)14 b(b)q(e)h(consisten)o(t)g(with)g(that)h FP(same)j FQ(sp)q(eci\014cation.)h (Heuristically)60 1766 y(this)j(is)g(due)f(to)i(the)e(fact)h(that)h(a)f (measure)e(obtained)j(just)f(b)o(y)f(a)i(c)o(hange)f(in)f(the)h(b)q(oundary) 60 1826 y(conditions)13 b(m)o(ust)e(b)q(e)i(a)g(di\013eren)o(t)f(phase)i(for) f(the)f(same)g(in)o(teraction.)19 b(T)l(o)14 b(see)e(it)g(mathematically)-5 b(,)60 1886 y(let)14 b(\005)g(=)f(\()p FF(\031)278 1893 y FH(\003)305 1886 y FQ(\))i(b)q(e)g(a)g(quasilo)q(cal)g(sp)q(eci\014cation)g(with)g(whic)o (h)f FF(\026)1221 1893 y FH(+)1251 1886 y FF(P)22 b FQ(is)15 b(consisten)o(t.)20 b(Then)15 b(for)h(eac)o(h)60 1946 y(set)g(\003)g(con)o (tained)g(in)g(the)g(in)o(terv)m(al)f(\()p FE(\000)p FF(n;)8 b(n)p FQ(\))16 b(w)o(e)g(ha)o(v)o(e)f(that)412 2054 y(\()p FF(\026)460 2061 y FH(+)490 2054 y FF(P)7 b FQ(\)\()h FE(\001)g(j)p FF(\033)640 2033 y Fy(0)638 2066 y FD(n;N)t FH(\()p FD(n)p FH(\))766 2054 y FQ(=)14 b FE(\000)p FQ(1\))8 b FF(\031)936 2061 y FH(\003)990 2054 y FQ(=)22 b(\()p FF(\026)1098 2061 y FH(+)1128 2054 y FF(P)7 b FQ(\)\()h FE(\001)g(j)p FF(\033)1278 2033 y Fy(0)1276 2066 y FD(n;N)t FH(\()p FD(n)p FH(\))1404 2054 y FQ(=)13 b FE(\000)p FQ(1\))228 b(\(4)p FF(:)p FQ(80\))60 2161 y(b)o(y)17 b(prop)q(ert)o(y)h(\(b\))g(of)g(De\014nition)g(2.5;)h(and)f (passing)h(to)f(the)g(limit)d FF(n)i FE(!)g(1)g FQ(\(since)h(\005)f(is)h(F)l (eller\))60 2221 y(w)o(e)e(obtain)772 2281 y(\()p FF(\026)820 2288 y Fy(\000)849 2281 y FF(P)7 b FQ(\))p FF(\031)934 2288 y FH(\003)988 2281 y FQ(=)28 b FF(\026)1083 2288 y Fy(\000)1113 2281 y FF(P)21 b(:)586 b FQ(\(4)p FF(:)p FQ(81\))60 2367 y(Therefore,)16 b(if)h FF(\026)370 2374 y FH(+)400 2367 y FF(P)24 b FQ(w)o(ere)17 b(a)g(Gibbs)g(measure)f(for)i(some)e(\(uniformly)f(con)o(v)o(ergen)o(t\))g (in)o(teraction,)60 2428 y(then)i(so)h(w)o(ould)f(b)q(e)g FF(\026)472 2435 y Fy(\000)502 2428 y FF(P)7 b FQ(.)24 b(But)16 b(this)h(con)o(tradicts)g (the)g(result)f(\(R1\),)h(b)q(ecause)h(Gibbs)f(measures)60 2488 y(for)d(the)g(same)f(\(absolutely)h(summable)d(translation-in)o(v)m (arian)o(t\))j(in)o(teraction)f(ha)o(v)o(e)g(zero)h(relativ)o(e)60 2548 y(en)o(trop)o(y)h(densit)o(y)l(.)p 60 2591 732 2 v 100 2645 a FA(59)135 2660 y Fz(This)f(statemen)o(t)f(easily)h(follo)o(ws)e(from)g (Sc)o(honmann's)h(Lemma)e(1.)938 2784 y FQ(141)p eop %%Page: 142 142 bop 133 91 a FQ(Sc)o(honmann's)19 b(restriction)h FF(P)27 b FQ(do)q(es)21 b(not)f(\014t)h(in)o(to)e(the)h(framew)o(ork)f(considered)h(in) g(Section)60 152 y(3,)h(b)q(ecause)f(the)g(v)o(olume)e(compression)h(factor)i FF(K)j FQ(is)c(not)h(\014nite)e(\(see)h(Example)e(7)j(in)f(Section)60 212 y(3.1\).)27 b(On)18 b(the)f(other)i(hand,)f(Sc)o(honmann's)f(pro)q(of)i (of)g(non-Gibbsianness)g(seems)d(to)j(b)q(e)f(rather)60 272 y(di\013eren)o(t)j(from)g(our)i(pro)q(ofs)g(in)e(Sections)h(4.1{4.3.)40 b(W)l(e)21 b(sho)o(w)i(here)e(that,)j(nev)o(ertheless,)d(his)60 332 y(result)f(can)h(b)q(e)f(obtained)h(b)o(y)f(follo)o(wing)g(basically)g (the)g(steps)g(discussed)h(in)f(Sections)g(4.1{4.3)60 392 y(\(although)c(at)g (presen)o(t)f(w)o(e)g(are)g(able)g(to)h(do)f(it)g(only)g(for)h(temp)q (eratures)e(lo)o(w)h(enough\).)22 b(This)15 b(will)60 452 y(pro)o(v)o(e)f (that)i FF(\026)324 459 y FH(+)354 452 y FF(P)22 b FQ(is)15 b(not)g(merely)d(non-Gibbsian,)k(but)g(in)e(fact)h(non-quasilo)q(cal.)22 b(The)15 b(pro)q(of)h(will)60 513 y(use)g(\(R2\))h(but)f(not)h(\(R1\).)133 573 y(In)f(our)h(language,)g(the)g(image)e(spins)h(for)h(this)g (transformation)f(are)h(the)f(spins)h(on)g(the)f(hori-)60 633 y(zon)o(tal)e(line,)f(and)h(the)g(in)o(ternal)f(spins)h(are)g(all)g(the)g (spins)g(of)g(the)g(plane)g(except)f(those)h(of)h(the)f(line.)60 693 y(W)l(e)j(\014rst)g(notice)f(that)i(Sc)o(honmann's)e(result)g(\(R2\))h (corresp)q(onds)h(exactly)e(to)h(our)h(Step)f(2:)23 b(that)60 753 y(is,)15 b(\(4.78\))i(sho)o(ws)g(that)f(the)g(ann)o(ulus)g([)p FE(\000)p FF(N)r(;)8 b FE(\000)p FF(n)p FQ(])i FE([)g FQ([)p FF(n;)e(N)d FQ(])16 b(of)g(image)e(spins)j(selects)e(the)g(phase)i(of)60 814 y(the)e(in)o(ternal)f(spins.)21 b(Ph)o(ysically)l(,)13 b(this)i(is)f(a)i(kind)e(of)h(w)o(etting)g(phenomenon:)20 b(imp)q(osing)14 b FE(\000)h FQ(spins)60 874 y(on)i(a)g(large)f(segmen)o(t)f(of)i(the)f(axis)h (\(of)g(size)e FE(\030)g FF(N)5 b FQ(\))16 b(giv)o(e)g(rise)g(to)h(a)g (droplet)f(of)h(the)f FE(\000)g FQ(phase)h(in)g(a)60 934 y(neigh)o(b)q(orho)q (o)q(d)j(of)e(the)g(axis,)f FP(even)k(when)f(the)f(bulk)i(b)n(oundary)d(c)n (onditions)i(ar)n(e)e(+)r FQ(;)g(as)h FF(N)j FE(!)16 b(1)60 994 y FQ(the)d(width)h(of)f(the)h(droplet)f(gro)o(ws)h(to)g(in\014nit)o(y)l (,)e(and)i(moreo)o(v)o(er)d(the)i(left)g(and)h(righ)o(t)f(droplets)h(join,)60 1054 y(thereb)o(y)h(enforcing)h(the)g FE(\000)g FQ(phase)h(throughout)h(the)e (in\014nite)f(system.)133 1115 y(W)l(e)22 b(sk)o(etc)o(h)f(no)o(w)h(ho)o(w)h (our)f(Step)g(1)h(can)f(b)q(e)h(pro)o(v)o(en)e(via)h(a)g(con)o(tour)h (argumen)o(t,)f(so)h(that)60 1175 y(w)o(e)16 b(obtain)i(the)e(non-quasilo)q (calit)o(y)h(of)g(the)f(image)g(system)f(without)i(making)e(use)i(of)g(the)g (large-)60 1235 y(deviation)22 b(estimate)e(\(R1\).)40 b(W)l(e)22 b(consider)f(the)h(origin)h(un\014xed)f(from)f(the)h(start)h(\(so)g(Step)f(3) 60 1295 y(is)d(sup)q(er\015uous\),)h(and)g(consider)f FF(!)727 1277 y Fy(0)725 1307 y FH(sp)q(ecial)849 1295 y FQ(to)g(b)q(e)h(an)f (alternating)g(con\014guration)h(suc)o(h)f(that)g(the)60 1355 y(neigh)o(b)q(ors)e(of)f(the)g(origin)h(are)f(of)g(opp)q(osite)h(sign:)586 1494 y(\()p FF(!)637 1473 y Fy(0)635 1506 y FH(sp)q(ecial)740 1494 y FQ(\))759 1501 y FH(\()p FD(i;)p FH(0\))856 1494 y FQ(=)921 1421 y Fx(\()963 1465 y FQ(\()p FE(\000)p FQ(1\))1064 1447 y FD(i)1172 1465 y FQ(if)f FF(i)d(>)h FQ(0)963 1525 y(\()p FE(\000)p FQ(1\))1064 1507 y FD(i)p FH(+1)1172 1525 y FQ(if)i FF(i)d(<)h FQ(0)1351 1494 y FF(:)400 b FQ(\(4)p FF(:)p FQ(82\))60 1635 y(W)l(e)14 b(shall)h(pro)o(v)o(e)f(the)g(follo)o(wing:)20 b(there)15 b(exists)f FF(\017)f(>)h FQ(0)h(suc)o(h)g(that)g(for)g(all)f FF(k)j FQ(there)d(exist)g FF(n)p FQ(\()p FF(k)r FQ(\))g(and)60 1695 y FF(N)5 b FQ(\()p FF(k)r FQ(\))16 b(suc)o(h)h(that)429 1805 y FF(\026)458 1812 y FH(+)488 1805 y FQ(\()p FF(\033)535 1812 y FH(0)555 1805 y FE(j)p FF(\033)599 1784 y Fy(0)597 1817 y FH(1)p FD(;k)659 1805 y FQ(=)c FF(!)742 1784 y Fy(0)740 1817 y FH(sp)q(ecial)846 1805 y FF(;)j(\033)906 1784 y Fy(0)904 1817 y FD(n)p FH(\()p FD(k)q FH(\))p FD(;N)t FH(\()p FD(k)q FH(\))1076 1805 y FQ(=)e(+1\))42 b FE(\025)f FF(\017)27 b(>)h FQ(0)273 b(\(4.83a\))428 1921 y FF(\026)457 1928 y FH(+)487 1921 y FQ(\()p FF(\033)534 1928 y FH(0)554 1921 y FE(j)p FF(\033)598 1900 y Fy(0)596 1933 y FH(1)p FD(;k)658 1921 y FQ(=)14 b FF(!)742 1900 y Fy(0)740 1933 y FH(sp)q(ecial)845 1921 y FF(;)i(\033)905 1900 y Fy(0)903 1933 y FD(n)p FH(\()p FD(k)q FH(\))p FD(;N)t FH(\()p FD(k)q FH(\))1075 1921 y FQ(=)e FE(\000)p FQ(1\))42 b FE(\024)f(\000)1377 1887 y FF(\017)p 1375 1909 25 2 v 1375 1955 a FQ(2)1432 1921 y FF(<)27 b FQ(0)217 b(\(4.83b\))60 2047 y(It)19 b(is)h(clear)f(that)h(\(4.83a\))h(and)f(\(4.83b\))h(together)f(imply) d(the)j(non-quasilo)q(calit)o(y)f(of)h FF(\026)1729 2054 y FH(+)1759 2047 y FF(P)7 b FQ(,)21 b(for)60 2107 y(they)g(sho)o(w)h(that)g(in) f(an)h(arbitrarily)e(small)g(neigh)o(b)q(orho)q(o)q(d)j(of)f FF(!)1323 2089 y Fy(0)1321 2119 y FH(sp)q(ecial)1449 2107 y FE(2)h(f\000)p FQ(1)p FF(;)8 b FQ(1)p FE(g)1664 2089 y Fl(Z)1708 2107 y FQ(\(namely)l(,)60 2167 y FE(N)101 2174 y FD(k)136 2167 y FE(\021)14 b(f)p FF(\033)244 2149 y Fy(0)255 2167 y FQ(:)i FF(\033)315 2149 y Fy(0)313 2179 y FH(1)p FD(;k)375 2167 y FQ(=)e FF(!)459 2149 y Fy(0)457 2179 y FH(sp)q(ecial)563 2167 y FE(g)p FQ(\),)h(there)h(exist)f(op)q(en)i(subsets)450 2277 y FE(N)491 2284 y FD(k)q(;)p FH(+)591 2277 y FQ(=)41 b FE(f)p FF(\033)725 2256 y Fy(0)736 2277 y FQ(:)22 b FF(\033)802 2256 y Fy(0)800 2289 y FH(1)p FD(;k)862 2277 y FQ(=)14 b FF(!)946 2256 y Fy(0)944 2289 y FH(sp)q(ecial)1066 2277 y FQ(and)j FF(\033)1191 2256 y Fy(0)1189 2289 y FD(n)p FH(\()p FD(k)q FH(\))p FD(;N)t FH(\()p FD(k)q FH(\))1360 2277 y FQ(=)d(+1)p FE(g)242 b FQ(\(4.84a\))450 2373 y FE(N)491 2380 y FD(k)q(;)p Fy(\000)591 2373 y FQ(=)41 b FE(f)p FF(\033)725 2353 y Fy(0)736 2373 y FQ(:)22 b FF(\033)802 2353 y Fy(0)800 2385 y FH(1)p FD(;k)862 2373 y FQ(=)14 b FF(!)946 2353 y Fy(0)944 2385 y FH(sp)q(ecial)1066 2373 y FQ(and)j FF(\033)1191 2353 y Fy(0)1189 2385 y FD(n)p FH(\()p FD(k)q FH(\))p FD(;N)t FH(\()p FD(k)q FH(\))1360 2373 y FQ(=)d FE(\000)p FQ(1)p FE(g)238 b FQ(\(4.84b\))60 2483 y(suc)o(h)17 b(that)h(the)f(\()p FF(\026)411 2490 y FH(+)441 2483 y FF(P)7 b FQ(\)-a)o(v)o(erage)18 b(v)m(alue)f(of)h FF(E)911 2490 y FD(\026)932 2494 y Fr(+)957 2490 y FD(P)987 2483 y FQ(\()p FF(\033)1036 2465 y Fy(0)1034 2495 y FH(0)1053 2483 y FE(jf)p FF(\033)1122 2465 y Fy(0)1120 2495 y FD(x)1142 2483 y FE(g)1167 2490 y FD(x)p Fy(6)p FH(=0)1233 2483 y FQ(\))g(o)o(v)o(er)f FE(N)1417 2490 y FD(k)q(;)p FH(+)1492 2483 y FQ(\(resp.)g FE(N)1670 2490 y FD(k)q(;)p Fy(\000)1729 2483 y FQ(\))g(is)h FE(\025)d FF(\017)60 2543 y FQ(\(resp.)20 b FE(\024)f(\000)p FF(\017=)p FQ(2\).)33 b(This)20 b(is)g(incompatible)e(with)i FF(E)1044 2550 y FD(\026)1065 2554 y Fr(+)1090 2550 y FD(P)1120 2543 y FQ(\()p FF(\033)1169 2525 y Fy(0)1167 2556 y FH(0)1186 2543 y FE(jf)p FF(\033)1255 2525 y Fy(0)1253 2556 y FD(x)1274 2543 y FE(g)1299 2550 y FD(x)p Fy(6)p FH(=0)1366 2543 y FQ(\))g(ha)o(ving)g(an)o (y)g(con)o(tin)o(uous)60 2604 y(\()p FE(\021)c FQ(quasilo)q(cal\))g(v)o (ersion.)938 2784 y(142)p eop %%Page: 143 143 bop 133 91 a FQ(In)21 b(order)h(to)f(pro)o(v)o(e)g(\(4.83a\))h(and)g (\(4.83b\),)h(w)o(e)e(shall)g(pro)o(v)o(e)f(the)h(follo)o(wing)g(in)o (termediate)60 152 y(result:)g(there)15 b(exists)h FF(\017)e(>)f FQ(0)k(suc)o(h)f(that)700 262 y FF(\026)729 269 y FH(+)759 262 y FQ(\()p FF(\033)806 269 y FH(0)826 262 y FE(j)p FF(\033)870 241 y Fy(0)868 274 y FH(1)p FD(;k)930 262 y FQ(=)d FF(!)1013 241 y Fy(0)1011 274 y FH(sp)q(ecial)1117 262 y FQ(\))28 b FE(\025)f FF(\017)515 b FQ(\(4)p FF(:)p FQ(85\))60 372 y(for)15 b(all)g FF(k)r FQ(.)20 b(This)15 b(trivially)e(implies)f(\(4.83a\),)k(b)o(y)e(the)h (FK)o(G)g(inequalit)o(y)l(,)d(for)j FP(any)20 b FQ(c)o(hoice)13 b(of)i FF(n)g FQ(and)60 432 y FF(N)5 b FQ(.)26 b(T)l(o)18 b(see)f(that)h(it)f (also)h(implies)d(\(4.83b\),)j(w)o(e)g(use)f(\(4.78\))i(with)e FF(\026)f FQ(=)h FF(\026)1446 439 y FH(+)1493 432 y FQ(and)h(applied)f(to)h (the)60 492 y(functions)691 602 y FF(f)715 609 y FD(k)778 602 y FQ(=)41 b FF(\037)p FQ(\()p FF(\033)937 581 y Fy(0)935 614 y FH(1)p FD(;k)997 602 y FQ(=)14 b FF(!)1081 581 y Fy(0)1079 614 y FH(sp)q(ecial)1184 602 y FQ(\))538 b(\(4.86a\))692 675 y FF(g)715 682 y FD(k)778 675 y FQ(=)41 b FF(\033)885 682 y FH(0)913 675 y FF(\037)p FQ(\()p FF(\033)993 654 y Fy(0)991 687 y FH(1)p FD(;k)1053 675 y FQ(=)14 b FF(!)1137 654 y Fy(0)1135 687 y FH(sp)q(ecial)1240 675 y FQ(\))479 b(\(4.86b\))60 785 y(W)l(e)16 b(obtain)592 895 y(lim)580 919 y FD(n)p Fy(!1)680 895 y FF(\026)709 902 y FH(+)739 895 y FQ(\()p FF(f)782 902 y FD(k)804 895 y FE(j)p FF(\033)848 874 y Fy(0)846 907 y FD(n;N)t FH(\()p FD(n)p FH(\))973 895 y FQ(=)e FE(\000)p FQ(1\))41 b(=)h FF(\026)1257 902 y Fy(\000)1286 895 y FQ(\()p FF(f)1329 902 y FD(k)1351 895 y FQ(\))371 b(\(4.87a\))593 1003 y(lim)581 1028 y FD(n)p Fy(!1)681 1003 y FF(\026)710 1010 y FH(+)740 1003 y FQ(\()p FF(g)782 1010 y FD(k)804 1003 y FE(j)p FF(\033)848 982 y Fy(0)846 1015 y FD(n;N)t FH(\()p FD(n)p FH(\))973 1003 y FQ(=)14 b FE(\000)p FQ(1\))41 b(=)h FF(\026)1257 1010 y Fy(\000)1286 1003 y FQ(\()p FF(g)1328 1010 y FD(k)1350 1003 y FQ(\))369 b(\(4.87b\))60 1123 y(Dividing)15 b(\(4.87b\))i(b)o(y)f(\(4.87a\))i(w)o(e)d (get)233 1233 y(lim)220 1258 y FD(n)p Fy(!1)321 1233 y FF(\026)350 1240 y FH(+)380 1233 y FQ(\()p FF(\033)427 1240 y FH(0)446 1233 y FE(j)p FF(\033)490 1213 y Fy(0)488 1246 y FH(1)p FD(;k)550 1233 y FQ(=)f FF(!)634 1213 y Fy(0)632 1246 y FH(sp)q(ecial)738 1233 y FF(;)i(\033)798 1213 y Fy(0)796 1246 y FD(n;N)t FH(\()p FD(n)p FH(\))923 1233 y FQ(=)e FE(\000)p FQ(1\))27 b(=)h FF(\026)1179 1240 y Fy(\000)1209 1233 y FQ(\()p FF(\033)1256 1240 y FH(0)1275 1233 y FE(j)p FF(\033)1319 1213 y Fy(0)1317 1246 y FH(1)p FD(;k)1380 1233 y FQ(=)13 b FF(!)1463 1213 y Fy(0)1461 1246 y FH(sp)q(ecial)1567 1233 y FQ(\))h FF(:)151 b FQ(\(4)p FF(:)p FQ(88\))60 1356 y(No)o(w,)14 b(b)o(y)g(\(4.85\))h(and)f(spin-\015ip)h(symmetry)-5 b(,)12 b(the)h(RHS)h(is)g FE(\024)g(\000)p FF(\017)p FQ(.)1270 1338 y FH(60)1327 1356 y FQ(Therefore,)g(for)h(eac)o(h)e FF(k)k FQ(there)60 1416 y(exists)f(an)g FF(n)p FQ(\()p FF(k)r FQ(\))h(suc)o(h)f (that)463 1538 y FF(\026)492 1545 y FH(+)522 1538 y FQ(\()p FF(\033)569 1545 y FH(0)588 1538 y FE(j)p FF(\033)632 1517 y Fy(0)630 1550 y FH(1)p FD(;k)692 1538 y FQ(=)e FF(!)776 1517 y Fy(0)774 1550 y FH(sp)q(ecial)880 1538 y FF(;)i(\033)940 1517 y Fy(0)938 1550 y FD(n)p FH(\()p FD(k)q FH(\))p FD(;N)t FH(\()p FD(n)p FH(\()p FD(k)q FH(\)\))1159 1538 y FQ(=)d FE(\000)p FQ(1\))28 b FE(\024)g(\000)1433 1504 y FF(\017)p 1431 1526 25 2 v 1431 1572 a FQ(2)1473 1538 y FF(;)278 b FQ(\(4)p FF(:)p FQ(89\))60 1663 y(whic)o(h)16 b(is)g(\(4.83b\).)133 1723 y(So)22 b(no)o(w)g(let)f(us)h(pro)o(v)o(e)f(\(4.85\))h(|)g(at)g(lo)o(w)f(enough)i (temp)q(eratures)d(|)i(b)o(y)f(a)h(more-or-less)60 1783 y(standard)d(P)o (eierls)d(argumen)o(t)h([169].)25 b(Here)17 b(the)g(con)o(tours)h(are)g (de\014ned)f(as)h(the)g(b)q(oundaries)g(\(in)60 1844 y(the)f(dual)g (lattice\))f(of)i(regions)g(where)e(the)h(spins)h(di\013er)f(from)f(the)h (ground-state)i(con\014guration)60 1904 y(\(that)12 b(is,)f(all)g(\\+")h (except)e(for)h(the)g(required)g(alternating)g(\\)p FE(\000)p FQ("\).)20 b(In)11 b(coun)o(ting)g(the)g(energy)g(of)g(suc)o(h)60 1964 y(con)o(tours)18 b(one)f(m)o(ust)f(subtract)h(the)g(energy)g(of)g(the)g (con)o(tours)h(already)f(existing)f(in)h(the)g(ground)60 2024 y(state)i(\(squares)h(surrounding)g(the)e(alternating)h(\\)p FE(\000)p FQ("\).)30 b(After)18 b(some)g(though)o(t,)i(one)g(concludes)60 2084 y(that)13 b(the)g(energy)f(of)h(the)g(con)o(tours)g(is)g(at)g(least)g (prop)q(ortional)h(to)f FF(N)1306 2091 y FD(v)1331 2084 y FQ(+)1378 2065 y FH(1)p 1378 2073 18 2 v 1378 2102 a(2)1401 2084 y FF(N)1440 2091 y FD(h)1466 2084 y FE(\000)t FQ(2,)h(where)e FF(N)1737 2091 y FD(v)1771 2084 y FQ(\(resp.)60 2145 y FF(N)99 2152 y FD(h)121 2145 y FQ(\))j(is)f(the)f(the)h(n)o(um)o(b)q(er)f(of)h(v)o(ertical)e (\(resp.)i(horizon)o(tal\))g(b)q(onds)h(in)f(the)g(con)o(tour.)21 b(On)14 b(the)g(other)60 2205 y(hand,)g(the)e(n)o(um)o(b)q(er)f(of)i(p)q (ossible)g(con)o(tours)g(is)f(ev)o(en)g(less)g(than)h(that)g(for)g(the)g (unconditioned)f(Ising)60 2265 y(mo)q(del.)21 b(As)16 b(in)h(the)f(standard)i (P)o(eierls)d(argumen)o(t,)g(these)i(facts)f(imply)f(that)i(the)f(probabilit) o(y)g(of)60 2325 y(\014nding)j(a)g(con)o(tour)f(surrounding)i(the)e(origin)g (|)g(that)h(is,)f(of)h(ha)o(ving)f(a)h(\\)p FE(\000)p FQ(")g(at)g(the)f (origin)g(|)60 2385 y(go)q(es)f(to)g(zero)f(as)h FF(\014)h FQ(go)q(es)g(to)e(in\014nit)o(y)l(.)p 60 2429 732 2 v 100 2483 a FA(60)135 2498 y Fz(If)c(w)o(e)g(apply)g(spin-\015ip)g(symmetry)e(to)j (\(4.85\),)e(w)o(e)i(not)f(only)f(c)o(hange)i Fv(\026)1259 2504 y FA(+)1299 2498 y Fz(to)f Fv(\026)1373 2504 y Fo(\000)1414 2498 y Fz(and)g Fv(\017)g Fz(to)g Fu(\000)p Fv(\017)p Fz(,)h(but)f(m)o(ust)g (also)60 2548 y(c)o(hange)h Fv(!)223 2533 y Fo(0)222 2559 y FA(sp)q(ecial)333 2548 y Fz(to)f Fu(\000)p Fv(!)441 2533 y Fo(0)440 2559 y FA(sp)q(ecial)540 2548 y Fz(.)17 b(But)c(this)g(latter)f(is)g (just)h Fv(!)989 2533 y Fo(0)988 2559 y FA(sp)q(ecial)1099 2548 y Fz(re\015ected)i(in)d(the)h Fv(x)1405 2554 y FA(2)1423 2548 y Fz(-axis)f(\(i.e.)f Fv(x)1625 2554 y FA(1)1655 2548 y Fu(!)g(\000)p Fv(x)1764 2554 y FA(1)1783 2548 y Fz(\),)h(and)60 2604 y(the)i(measures)h Fv(\026)335 2610 y FA(+)376 2604 y Fz(and)f Fv(\026)482 2610 y Fo(\000)524 2604 y Fz(are)g(in)o(v)n(arian)o(t)e (under)j(this)f(re\015ection.)938 2784 y FQ(143)p eop %%Page: 144 144 bop 133 91 a FM(Remarks.)24 b FQ(1.)i(In)17 b(con)o(trast)h(to)g(the)g(R)o(G) f(examples)f(giv)o(en)h(in)g(Sections)g(4.1{4.3,)i(here)e(the)60 152 y(non-Gibbsianness)e(o)q(ccurs)f(only)f(for)h(in)o(teractions)e FP(on)18 b FQ(the)13 b(\014rst-order)h(phase-transition)h(curv)o(e,)60 212 y(i.e.)e(zero)h(magnetic)f(\014eld.)20 b(Indeed,)13 b(Maes)i(and)g(v)m (an)f(de)h(V)l(elde)e([256])h(ha)o(v)o(e)g(pro)o(v)o(en)f(that)i(if)f(either) 60 272 y FF(h)j FE(6)p FQ(=)g(0)i(or)f FF(\014)i FQ(is)e(su\016cien)o(tly)e (small,)h(the)h(restriction)f(of)h(the)g(t)o(w)o(o-dimensional)f(Ising)h(mo)q (del)f(to)60 332 y(an)g(axis)f FP(is)k FQ(Gibbsian.)133 392 y(2.)31 b(It)19 b(is)g(natural)h(to)g(generalize)e(this)h(example:)26 b(consider)19 b(a)h FF(d)p FQ(-dimensional)e(Ising)h(mo)q(del)60 452 y(and)f(a)f FF(d)222 434 y Fy(0)234 452 y FQ(-dimensional)f(co)q (ordinate)h(plane)g(\(1)f FE(\024)f FF(d)1029 434 y Fy(0)1056 452 y FF(<)g(d)p FQ(\).)24 b(It)16 b(seems)g(to)h(b)q(e)g(an)h(op)q(en)g (question,)60 513 y(for)d(all)g(cases)g(other)g(than)g(\()p FF(d;)8 b(d)650 495 y Fy(0)663 513 y FQ(\))13 b(=)h(\(2)p FF(;)8 b FQ(1\),)15 b(whether)g(the)g(restricted)e(measure)h(is)h(non-Gibbsian)60 573 y(at)i(lo)o(w)f(temp)q(eratures.)60 702 y FM(4.5.3)55 b(F)-5 b(ortuin-Kasteleyn)17 b(Random-Cluster)g(Mo)r(del)60 795 y FQ(In)i(1972)h(F)l(ortuin)f(and)g(Kasteleyn)f([127)q(])g(in)o(tro)q(duced)h (a)g(correlated)f(b)q(ond-p)q(ercolation)i(mo)q(del)60 855 y(whic)o(h)c(has)h(since)e(b)q(ecome)g(kno)o(wn)i(as)g(the)f FP(F)l(ortuin-Kasteleyn)k(r)n(andom-cluster)e(mo)n(del)5 b FQ(.)22 b(F)l(or)17 b(a)60 915 y FP(\014nite)24 b FQ(graph)19 b FF(G)g FQ(=)f(\()p FF(V)s(;)8 b(B)s FQ(\))18 b(ha)o(ving)g(v)o(ertex)f(set) i FF(V)30 b FQ(and)19 b(edge)g(\(or)g(\\b)q(ond"\))h(set)f FF(B)s FQ(,)f(the)g(mo)q(del)60 975 y(is)f(de\014ned)f(as)i(follo)o(ws:)k(On) 17 b(eac)o(h)g(b)q(ond)g FF(b)g FQ(there)f(is)h(a)g(v)m(ariable)g FF(n)1302 982 y FD(b)1336 975 y FQ(taking)g(the)g(v)m(alue)f(0)i(\(\\b)q(ond) 60 1035 y(v)m(acan)o(t"\))12 b(or)h(1)f(\(\\b)q(ond)h(o)q(ccupied"\).)20 b(The)12 b(probabilit)o(y)f(of)h(a)g(con\014guration)h FM(n)h FQ(=)g FE(f)p FF(n)1640 1042 y FD(b)1657 1035 y FE(g)e FQ(is)f(de\014ned)60 1096 y(to)17 b(b)q(e)507 1156 y(Prob)q(\()p FM(n)p FQ(\))27 b(=)h(const)11 b FE(\002)g FF(p)969 1135 y Fy(N)998 1140 y Fr(1)1016 1135 y FH(\()p Fj(n)p FH(\))1070 1156 y FQ(\(1)g FE(\000)g FF(p)p FQ(\))1217 1135 y Fy(N)1246 1140 y Fr(0)1264 1135 y FH(\()p Fj(n)p FH(\))1318 1156 y FF(q)1342 1135 y Fy(C)r FH(\()p Fj(n)p FH(\))1430 1156 y FF(;)321 b FQ(\(4)p FF(:)p FQ(90\))60 1242 y(where)16 b(0)f FF(<)f(p)h(<)f FQ(1)j(and)g FF(q)e(>)g FQ(0)h(are)h(parameters;)e(here)h FE(N)1144 1249 y FH(0)1164 1242 y FQ(\()p FM(n)p FQ(\))g([resp.)g FE(N)1421 1249 y FH(1)1440 1242 y FQ(\()p FM(n)p FQ(\)])g(is)h(the)f(n)o(um)o(b)q(er)f (of)60 1302 y(b)q(onds)g FF(b)f FQ(with)f FF(n)372 1309 y FD(b)404 1302 y FQ(=)g(0)i([resp.)e FF(n)651 1309 y FD(b)682 1302 y FQ(=)g(1],)h(and)h FE(C)s FQ(\()p FM(n)p FQ(\))f(is)g(the)f(n)o(um)o(b)q(er)f (of)i(\\clusters")g(\(i.e.)f(connected)60 1362 y(comp)q(onen)o(ts)g(of)h(v)o (ertices\))e(in)h(the)h(graph)g FF(G)881 1369 y Fj(n)922 1362 y FQ(whose)h(v)o(ertex)d(set)h(is)h FF(V)25 b FQ(and)14 b(whose)h(edges)e (are)h(the)60 1422 y FP(o)n(c)n(cupie)n(d)k FQ(\()p FF(n)302 1429 y FD(b)333 1422 y FQ(=)c(1\))g(b)q(onds.)22 b(F)l(or)14 b FF(q)h FQ(=)f(1)g(this)f(mo)q(del)f(reduces)h(to)h(ordinary)g(\(indep)q (enden)o(t\))f(b)q(ond)60 1483 y(p)q(ercolation,)22 b(while)f(for)h(in)o (teger)e FF(q)k FE(\025)e FQ(2)g(there)f(are)g(iden)o(tities)f(relating)h (the)g(random-cluster)60 1543 y(mo)q(del)15 b(to)i(the)f FF(q)r FQ(-state)g(P)o(otts)g(mo)q(del)f([127)q(,)h(125)q(,)g(109)q(].)133 1603 y(Let)e(us)g(no)o(w)g(try)f(to)h(form)o(ulate)d(the)j(random-cluster)e (mo)q(del)g(on)i(a)g FP(c)n(ountably)i(in\014nite)j FQ(graph)60 1663 y FF(G)h FQ(=)f(\()p FF(V)s(;)8 b(B)s FQ(\))19 b([for)g(example,)f FF(V)30 b FQ(=)19 b Fq(Z)771 1642 y FD(d)810 1663 y FQ(and)h FF(B)i FQ(=)e(nearest-neigh)o(b)q(or)g(b)q(onds)g(in)f Fq(Z)1633 1642 y FD(d)1653 1663 y FQ(],)g(follo)o(wing)60 1723 y(the)h(DLR)g(approac)o (h.)34 b(The)20 b(\\lattice")f(is)h(here)f FF(B)s FQ(,)h(and)h(the)f (con\014guration)h(space)f(is)g FE(f)p FQ(0)p FF(;)8 b FQ(1)p FE(g)1846 1705 y FD(B)1876 1723 y FQ(.)60 1783 y(Let)20 b(\003)f(b)q(e)h(a)g FP(\014nite)25 b FQ(subset)20 b(of)g FF(B)s FQ(,)f(and)h(let)f(\003)941 1765 y Fy(\003)980 1783 y FE(\032)h FF(V)31 b FQ(b)q(e)19 b(the)h(set)f(of)h (all)f(v)o(ertices)f(touc)o(hing)i(at)60 1844 y(least)14 b(one)g(b)q(ond)h FF(b)f FE(2)g FQ(\003.)20 b(W)l(e)14 b(need)g(to)h(sp)q(ecify)e(the)h (conditional)g(probabilities)f(of)h FE(f)p FF(n)1657 1851 y FD(b)1675 1844 y FE(g)1700 1851 y FD(b)p Fy(2)p FH(\003)1779 1844 y FQ(giv)o(en)60 1904 y FE(f)p FF(n)114 1911 y FD(b)129 1902 y Ft(0)142 1904 y FE(g)167 1912 y FD(b)182 1902 y Ft(0)194 1912 y Fy(2)p FD(B)r Fy(n)p FH(\003)290 1904 y FQ(.)22 b(But)17 b(this)f(is)h(easy)l(,)f(b)o(y)h(the)f(same)g(metho)q(d)g(as)h(for)g(spin)g (systems:)k(w)o(e)16 b(write)h(do)o(wn)60 1964 y(the)i FP(formal)24 b FQ(\(meaningless\))17 b(Boltzmann)h(factor)h(for)g(the)g(in\014nite)f (lattice,)g(and)i(then)f(drop)h(all)60 2024 y(terms)15 b(that)h(don't)h(in)o (v)o(olv)o(e)d FE(f)p FF(n)647 2031 y FD(b)664 2024 y FE(g)689 2031 y FD(b)p Fy(2)p FH(\003)754 2024 y FQ(.)21 b(The)16 b(result)g(is)g (simple:)j(it)d(is)85 2131 y(Prob)q(\()p FE(f)p FF(n)262 2138 y FD(b)279 2131 y FE(g)304 2138 y FD(b)p Fy(2)p FH(\003)369 2131 y FE(jf)p FF(n)437 2138 y FD(b)452 2129 y Ft(0)465 2131 y FE(g)490 2139 y FD(b)505 2130 y Ft(0)516 2139 y Fy(2)p FD(B)r Fy(n)p FH(\003)612 2131 y FQ(\))28 b(=)f(const)q(\()p FE(f)p FF(n)909 2138 y FD(b)924 2129 y Ft(0)937 2131 y FE(g)962 2139 y FD(b)977 2130 y Ft(0)988 2139 y Fy(2)p FD(B)r Fy(n)p FH(\003)1084 2131 y FQ(\))14 b FE(\002)f FF(p)1193 2111 y Fy(N)1222 2116 y Fr(1)1240 2111 y FH(\()p Fj(n)1279 2117 y Fr(\003)1301 2111 y FH(\))1317 2131 y FQ(\(1)5 b FE(\000)g FF(p)p FQ(\))1452 2111 y Fy(N)1481 2116 y Fr(0)1499 2111 y FH(\()p Fj(n)1538 2117 y Fr(\003)1560 2111 y FH(\))1576 2131 y FF(q)1600 2111 y Fy(C)1619 2118 y Fr(\003)1640 2111 y Ft(\003)s FH(\()p Fj(n)p FH(\))1727 2131 y FF(;)24 b FQ(\(4)p FF(:)p FQ(91\))60 2238 y(where)16 b FE(N)242 2245 y FH(0)262 2238 y FQ(\()p FM(n)312 2245 y FH(\003)338 2238 y FQ(\))h([resp.)e FE(N)545 2245 y FH(1)565 2238 y FQ(\()p FM(n)615 2245 y FH(\003)641 2238 y FQ(\)])h(is)g(the)g(n)o(um)o(b)q(er)f(of)i(b)q(onds)g FF(b)d FE(2)g FQ(\003)j(with)f FF(n)1472 2245 y FD(b)1503 2238 y FQ(=)e(0)j([resp.)e FF(n)1755 2245 y FD(b)1787 2238 y FQ(=)f(1],)60 2299 y(while)19 b FE(C)217 2306 y FH(\003)241 2297 y Ft(\003)262 2299 y FQ(\()p FM(n)p FQ(\))h(is)g(the)g(n)o(um)o(b)q(er)f(of)h(clusters)g FP(c)n(ontaining)i(at)g(le)n(ast)f(one)h(element)h(of)e FQ(\003)1707 2281 y Fy(\003)1727 2299 y FQ(,)f(in)g(the)60 2359 y(graph)d(whose)f(edges)g (are)f(the)h FP(o)n(c)n(cupie)n(d)k FQ(\()p FF(n)879 2366 y FD(b)910 2359 y FQ(=)14 b(1\))i(b)q(onds)h(\(b)q(oth)g(those)f(inside)f(and)h (outside)g(\003\).)133 2419 y(It)h(is)f(easy)i(to)f(see)f(that)i(\(4.91\))g (de\014nes)e(a)i(sp)q(eci\014cation)f(\(i.e.)e(it)h(is)h(consisten)o(t)g(for) g(di\013eren)o(t)60 2479 y(\003\).)36 b(It)21 b(is)g(also)h(easy)g(to)f(see)g (that)h(the)f(dep)q(endence)g(on)g FE(f)p FF(n)1232 2486 y FD(b)1247 2477 y Ft(0)1261 2479 y FE(g)1286 2487 y FD(b)1301 2478 y Ft(0)1312 2487 y Fy(2)p FD(B)r Fy(n)p FH(\003)1429 2479 y FQ(is)g(only)g(via)g(the)g(set)h(of)60 2539 y(answ)o(ers)15 b(to)g(the)f(follo)o(wing)g(questions:)20 b(for)15 b(eac)o(h)f(pair)h FF(x;)8 b(y)15 b FE(2)f FQ(\003)1264 2521 y Fy(\003)1283 2539 y FQ(,)h(one)f(w)o(an)o(ts)h(to)g(kno)o(w)f(whether)60 2600 y FF(x)i FQ(and)g FF(y)i FQ(can)e(b)q(e)g(connected)f(b)o(y)h(a)g(path)h(of)f (o)q(ccupied)g(b)q(onds)h(lying)e(in)h FF(B)d FE(n)e FQ(\003.)21 b(Note,)15 b(ho)o(w)o(ev)o(er,)60 2660 y(that)j(the)f(answ)o(er)h(to)g(this)f (question)g(could)g(dep)q(end)h(on)g(b)q(onds)h FF(n)1311 2667 y FD(b)1326 2658 y Ft(0)1357 2660 y FQ(arbitrarily)d(far)i(a)o(w)o(a)o(y)f (from)938 2784 y(144)p eop %%Page: 145 145 bop 60 91 a FQ(\003)18 b(\(pro)o(vided)g(that)h(the)f(graph)i FF(G)f FQ(con)o(tains)f(arbitrarily)g(large)g(closed)h(lo)q(ops\).)29 b(Therefore,)18 b(for)60 152 y FF(q)f FE(6)p FQ(=)e(1,)j FP(the)h(sp)n(e)n (ci\014c)n(ation)f(de\014ne)n(d)i(by)e(\(4.91\))g(is)g(not)h(quasilo)n(c)n (al)k FQ(\(as)18 b(w)o(as)g(previously)e(noted)h(in)60 212 y([5]\).)133 272 y(Aizenman,)26 b(Cha)o(y)o(es,)i(Cha)o(y)o(es)f(and)g (Newman)e([5)o(])h(ha)o(v)o(e)g(pro)o(v)o(en)g(the)g(existence)f(of)h(the)60 332 y(in\014nite-v)o(olume)11 b(limit)g(for)j(the)g(\\Gibbs")h(measures)e(of) h(the)f(random-cluster)g(mo)q(del)g(tak)o(en)g(with)60 392 y(either)f(free)g(\()p FF(n)333 399 y FD(b)348 390 y Ft(0)376 392 y FE(\021)h FQ(0\))h(or)f(wired)g(\()p FF(n)719 399 y FD(b)734 390 y Ft(0)761 392 y FE(\021)h FQ(1\))f(b)q(oundary)h(conditions.)20 b(Ho)o(w)o(ev)o(er,)12 b(since)g(the)h(sp)q(eci\014-)60 452 y(cation)g(\(4.91\))h(is)f(not)g(quasilo)q(cal)g(\(hence)f(not)i(F)l (eller\),)d(it)i(is)g(not)g(immedi)o(ate)e(that)i(these)g(limiting)60 513 y(measures)i FF(\026)298 520 y FD(f)337 513 y FQ(and)h FF(\026)460 520 y FD(w)505 513 y FQ(are)g(indeed)f(consisten)o(t)g(with)h (the)g(sp)q(eci\014cation)f(\(4.91\))i([since)e(Prop)q(osi-)60 573 y(tion)g(2.22)h(do)q(es)g(not)g(apply],)e(although)j(it)d(seems)g(v)o (ery)g(plausible.)20 b(Indeed,)15 b(it)f(is)h(not)h(clear)f(that)60 633 y(there)k(exist)g FP(any)k FQ(measures)c(consisten)o(t)g(with)g(the)g(sp) q(eci\014cation)h(\(4.91\).)31 b(W)l(e)19 b(therefore)g(p)q(ose)60 693 y(the)d(follo)o(wing)g FP(op)n(en)h(question)t FQ(:)22 b(Pro)o(v)o(e)16 b(that)g(the)g(in\014nite-v)o(olume)d(limit)h(measures)h (tak)o(en)g(with)60 753 y(free)g(or)i(wired)f(b)q(oundary)h(conditions)g(are) f(consisten)o(t)g(with)g(the)g(sp)q(eci\014cation)g(\(4.91\).)133 814 y(Assuming)f(that)i(there)f(do)g(exist)g(measures)f(consisten)o(t)h(with) g(the)g(sp)q(eci\014cation)g(\(4.91\),)g(w)o(e)60 874 y(can)g(no)o(w)h(pro)o (v)o(e)e(that)i(all)f(these)g(measures)f(are)h(non-quasilo)q(cal)h(\(hence)f (non-Gibbsian\).)60 988 y FM(De\014nition)i(4.14)24 b FP(L)n(et)e FQ(\012)i FP(b)n(e)g(a)f(metric)g(sp)n(ac)n(e.)40 b(We)23 b(c)n(al)r(l)i(a)e (function)h FF(f)5 b FQ(:)17 b(\012)25 b FE(!)f Fq(R)g FQ(strongly)60 1048 y(discon)o(tin)o(uous)d FP(if)h(every)g(c)n(ontinuous)g(function)h (di\013ers)f(fr)n(om)e FF(f)27 b FP(on)22 b(a)g(set)g(having)g(nonempty)60 1108 y(interior.)40 b([In)23 b(detail:)35 b(for)23 b(every)h FF(g)j FE(2)e FF(C)t FQ(\(\012\))p FP(,)f(the)g(set)g FE(f)p FF(!)r FQ(:)16 b FF(f)5 b FQ(\()p FF(!)r FQ(\))25 b FE(6)p FQ(=)g FF(g)r FQ(\()p FF(!)r FQ(\))p FE(g)e FP(has)g(nonempty)60 1169 y(interior.])133 1229 y(We)17 b(c)n(al)r(l)h(a)e(sp)n(e)n(ci\014c)n (ation)h FQ(strongly)f(non-F)l(eller)f FP(if)i(ther)n(e)g(exists)g FQ(\003)d FE(2)g(S)20 b FP(and)d FF(f)i FE(2)14 b FF(C)t FQ(\(\012\))j FP(such)60 1289 y(that)h FF(\031)188 1296 y FH(\003)214 1289 y FF(f)23 b FP(is)17 b(str)n(ongly)g(disc)n(ontinuous.)60 1403 y FQ(A)i(su\016cien)o(t)f(condition)h(for)h(strong)h(discon)o(tin)o(uit)o(y)c (of)j(a)g(function)f FF(f)25 b FQ(is)19 b(the)g(follo)o(wing:)28 b(there)60 1463 y(exists)18 b(an)h FF(!)299 1445 y Fy(\003)336 1463 y FE(2)e FQ(\012)i(and)g(an)g FF(\017)e(>)g FQ(0)i(suc)o(h)f(that)h(for) g(ev)o(ery)d(neigh)o(b)q(orho)q(o)q(d)21 b FE(N)j(3)18 b FF(!)1626 1445 y Fy(\003)1664 1463 y FQ(there)g(exist)60 1523 y(op)q(en)f(sets)f FE(N)314 1530 y FH(+)344 1523 y FF(;)8 b FE(N)407 1530 y Fy(\000)450 1523 y FE(\032)13 b(N)24 b FQ(suc)o(h)16 b(that)37 b(inf)782 1553 y FD(!)q Fy(2N)858 1557 y Fr(+)892 1523 y FF(f)5 b FQ(\()p FF(!)r FQ(\))11 b FE(\000)25 b FQ(sup)1052 1563 y FD(!)q Fy(2N)1128 1567 y Ft(\000)1162 1523 y FF(f)5 b FQ(\()p FF(!)r FQ(\))14 b FE(\025)g FF(\017)p FQ(.)133 1616 y(It)g(is)h(no)o(w)g(easy)f(to)h(pro)o(v) o(e)f(that)h(the)f(sp)q(eci\014cation)g(\(4.91\))i(is)e(strongly)h(non-F)l (eller.)k(T)l(o)d(a)o(v)o(oid)60 1677 y(unin)o(teresting)h(graph-theoretic)i (complexitie)o(s,)d(w)o(e)i(pro)o(v)o(e)g(the)g(theorem)e(for)j(the)f(sp)q (ecial)g(case)60 1737 y FF(V)27 b FQ(=)16 b Fq(Z)200 1716 y FD(d)238 1737 y FQ(and)i FF(B)g FQ(=)g(nearest-neigh)o(b)q(or)g(b)q(onds)h (in)e Fq(Z)1047 1716 y FD(d)1068 1737 y FQ(.)25 b(The)17 b(reader)h(can)f (easily)g(generalize)f(this)60 1797 y(to)h(a)f(suitable)g(class)g(of)h(coun)o (tably)f(in\014nite)f(graphs)j FF(G)p FQ(.)60 1911 y FM(Prop)r(osition)g (4.15)24 b FP(L)n(et)e FF(q)i FE(6)p FQ(=)e(1)p FP(.)37 b(Then)23 b(the)f(sp)n(e)n(ci\014c)n(ation)h(\(4.91\))e(for)h(the)g(r)n(andom-cluster) 60 1971 y(mo)n(del)17 b(is)h(str)n(ongly)f(non-F)l(el)r(le)q(r,)j(when)e FF(V)25 b FQ(=)14 b Fq(Z)944 1950 y FD(d)982 1971 y FP(and)k FF(B)e FQ(=)i FP(ne)n(ar)n(est-neighb)n(or)g(b)n(onds)f(in)h Fq(Z)1771 1950 y FD(d)1792 1971 y FP(.)60 2135 y Fd(Pr)o(oof.)48 b FQ(Let)18 b(\003)h(b)q(e)f(a)h(set)g(con)o(taining)f(a)h(single)f(b)q(ond)h FF(b)1179 2142 y FH(0)1217 2135 y FQ(=)e FE(f)p FF(x)1325 2142 y FH(0)1344 2135 y FF(;)8 b(x)1394 2142 y FH(1)1414 2135 y FE(g)p FQ(,)18 b(and)h(let)f FF(f)5 b FQ(\()p FM(n)p FQ(\))18 b(=)g FF(n)1842 2142 y FD(b)1857 2147 y Fr(0)1876 2135 y FQ(.)60 2195 y(No)o(w)c(let)f FF(!)269 2177 y Fy(\003)302 2195 y FQ(b)q(e)h(the)g (con\014guration)h(whic)o(h)e(sets)h FF(n)1000 2202 y FD(b)1031 2195 y FQ(=)g(1)g(on)g(parallel)f(ra)o(ys)h(running)g(from)f FF(x)1778 2202 y FH(0)1811 2195 y FQ(and)60 2256 y FF(x)88 2263 y FH(1)124 2256 y FQ(to)j(in\014nit)o(y)l(,)e(p)q(erp)q(endicular)i(to)h (the)f(b)q(ond)h FF(b)957 2263 y FH(0)976 2256 y FQ(,)f(and)h(whic)o(h)e (sets)h FF(n)1364 2263 y FD(b)1395 2256 y FQ(=)e(0)j(on)f(all)g(other)g(b)q (onds.)60 2316 y(No)o(w)23 b(an)o(y)h(neigh)o(b)q(orho)q(o)q(d)h FE(N)34 b(3)26 b FF(!)757 2298 y Fy(\003)800 2316 y FQ(\(in)d(the)h(pro)q (duct)g(top)q(ology\))h(con)o(tains)e(the)g(particular)60 2376 y(neigh)o(b)q(orho)q(o)q(d)674 2436 y FE(N)715 2443 y FD(R)771 2436 y FQ(=)28 b FE(f)p FM(n)p FQ(:)22 b FM(n)14 b FQ(=)f FF(!)1057 2416 y Fy(\003)1093 2436 y FQ(on)k(\003)1195 2443 y FD(R)1224 2436 y FE(g)d FF(;)488 b FQ(\(4)p FF(:)p FQ(92\))60 2523 y(where)16 b(\003)235 2530 y FD(R)280 2523 y FQ(is)h(the)f(set)g(of)h(all)f(b)q(onds)i (in)e(a)h(square)g(of)g(side)f(2)p FF(R)c FQ(+)f(1)17 b(cen)o(tered)e(at)i (the)f(origin.)22 b(W)l(e)60 2584 y(then)f(c)o(ho)q(ose)g FE(N)376 2591 y FD(R;)p FH(+)463 2584 y FQ(to)g(b)q(e)g(the)g(subset)g(of)g FE(N)942 2591 y FD(R)992 2584 y FQ(in)g(whic)o(h)f(an)h(o)q(ccupied)g(b)q (ond)h(in)e(\003)1700 2591 y FD(R)p FH(+1)1788 2584 y FE(n)14 b FQ(\003)1861 2591 y FD(R)60 2644 y FQ(connects)g(the)h(t)o(w)o(o)f (parallel)g(ra)o(ys;)g(and)h(w)o(e)g(c)o(ho)q(ose)g FE(N)1074 2651 y FD(R;)p Fy(\000)1154 2644 y FQ(to)g(b)q(e)g(the)f(subset)h(of)f FE(N)1601 2651 y FD(R)1645 2644 y FQ(in)g(whic)o(h)g FP(al)r(l)938 2784 y FQ(145)p eop %%Page: 146 146 bop 60 91 a FQ(the)15 b(b)q(onds)i(in)f(\003)376 98 y FD(R)p FH(+1)459 91 y FE(n)10 b FQ(\003)528 98 y FD(R)572 91 y FQ(are)16 b(v)m(acan)o(t)g(\(so)g(that)g(the)f(t)o(w)o(o)h(parallel)e(ra)o(ys)i(cannot) g(b)q(e)g(connected,)60 152 y(no)h(matter)e(what)i(happ)q(ens)g(outside)f (\003)803 159 y FD(R)p FH(+1)877 152 y FQ(\).)21 b(It)16 b(is)g(easy)g(to)h (see)f(that)531 294 y(\()p FF(\031)578 302 y Fy(f)p FD(b)611 307 y Fr(0)628 302 y Fy(g)648 294 y FF(f)5 b FQ(\)\()p FF(!)r FQ(\))802 221 y Fx(\()844 248 y FF(p)187 b FQ(for)17 b(all)e FF(!)h FE(2)e(N)1331 255 y FD(R;)p FH(+)916 303 y FD(p)p 849 313 153 2 v 849 342 a(p)p FH(+\(1)p Fy(\000)p FD(p)p FH(\))p FD(q)1055 325 y FQ(for)j(all)e FF(!)h FE(2)e(N)1331 332 y FD(R;)p Fy(\000)1765 294 y FQ(\(4)p FF(:)p FQ(93\))60 434 y(for)k(all)f FF(R)p FQ(.)25 b(Since)17 b(0)f FF(<)g(p)h(<)f FQ(1)i(and)g FF(q)f FE(6)p FQ(=)f(1,)i(it)f(follo)o(ws)g(that)h FF(\031)1232 442 y Fy(f)p FD(b)1265 447 y Fr(0)1282 442 y Fy(g)1302 434 y FF(f)23 b FQ(is)17 b(strongly)h(discon)o(tin)o(uous.)p 178 498 25 34 v 60 650 a FM(Prop)r(osition)g(4.16)24 b FP(\(a\))19 b(L)n(et)h FQ(\005)f FP(b)n(e)i(a)e(str)n(ongly)h(non-F)l(el)r(le)q(r)i(sp)n (e)n(ci\014c)n(ation,)f(and)f(let)h FF(\026)f FP(b)n(e)g(any)60 711 y(me)n(asur)n(e)15 b(c)n(onsistent)h(with)g FQ(\005)f FP(that)h(gives)h (nonzer)n(o)e(me)n(asur)n(e)g(to)g(every)h(op)n(en)g(set.)22 b(Then)16 b FF(\026)g FP(is)g(not)60 771 y(c)n(onsistent)j(with)f(any)f(F)l (el)r(ler)i(sp)n(e)n(ci\014c)n(ation.)133 831 y(\(b\))13 b(L)n(et)g FQ(\005)f FP(b)n(e)h(a)g(str)n(ongly)g(non-F)l(el)r(ler)j(sp)n(e)n(ci\014c)n (ation,)e(and)f(assume)g(further)f(that)h FQ(\005)g FP(is)f(nonnul)r(l)60 891 y(with)21 b(r)n(esp)n(e)n(ct)e(to)h(an)h FQ(a)f(priori)f FP(me)n(asur)n(e)h FF(\026)865 873 y FH(0)905 891 y FP(that)g(gives)i(nonzer) n(o)e(me)n(asur)n(e)f(to)i(every)f(op)n(en)h(set.)60 951 y(L)n(et)i FF(\026)g FP(b)n(e)g(any)g(me)n(asur)n(e)f(c)n(onsistent)i(with)f FQ(\005)p FP(.)38 b(Then)24 b FF(\026)f FP(is)g(not)g(c)n(onsistent)h(with)f (any)g(F)l(el)r(ler)60 1011 y(sp)n(e)n(ci\014c)n(ation.)60 1168 y Fd(Pr)o(oof.)48 b FQ(\(a\))17 b(Let)f(\003)f FE(2)g(S)21 b FQ(and)c FF(f)j FE(2)15 b FF(C)t FQ(\(\012\))h(b)q(e)h(suc)o(h)g(that)g FF(\031)1222 1175 y FH(\003)1248 1168 y FF(f)22 b FQ(is)17 b(strongly)g(discon)o(tin)o(uous.)23 b(If)60 1228 y(no)o(w)c(\005)201 1210 y Fy(0)230 1228 y FQ(is)g(a)g(F)l(eller)d(sp)q(eci\014cation,)j(b)o(y)e (de\014nition)h FF(\031)1073 1210 y Fy(0)1071 1240 y FH(\003)1098 1228 y FF(f)23 b FQ(is)c(con)o(tin)o(uous,)f(and)h(therefore)f(di\013ers)60 1288 y(from)h FF(\031)207 1295 y FH(\003)233 1288 y FF(f)25 b FQ(on)c(a)f(set)g(ha)o(ving)g(nonempt)o(y)e(in)o(terior.)31 b(But)19 b(since)g FF(\026)i FQ(giv)o(es)e(nonzero)h(measure)f(to)60 1348 y(ev)o(ery)14 b(op)q(en)i(set,)f FF(\031)422 1355 y FH(\003)448 1348 y FF(f)21 b FQ(and)16 b FF(\031)617 1330 y Fy(0)615 1360 y FH(\003)641 1348 y FF(f)21 b FQ(cannot)16 b(b)q(e)f(equal)g FF(\026)p FQ(-a.e.;)g FF(\026)h FQ(cannot)g(b)q(e)f(consisten)o(t)g(with)g(b) q(oth)60 1408 y(\005)h(and)h(\005)245 1390 y Fy(0)256 1408 y FQ(.)133 1468 y(\(b\))d(is)f(an)h(imme)o(diate)d(consequence)h(of)i(\(a\),) g(once)f(w)o(e)g(realize)f(that)i(an)o(y)f(measure)f(consisten)o(t)60 1529 y(with)i(a)h(nonn)o(ull)e(sp)q(eci\014cation)h(\(De\014nition)g(2.11\))h (m)o(ust)e(giv)o(e)g(nonzero)h(measure)f(to)i(ev)o(ery)d(op)q(en)60 1589 y(set.)p 273 1593 V 133 1696 a(Since)17 b(the)h(FK)f(sp)q(eci\014cation) h(\(4.91\))g(is)g(clearly)e(nonn)o(ull)h(\(for)h(0)f FF(<)f(p)h(<)g FQ(1)h(and)g FF(q)g(>)e FQ(0\),)i(w)o(e)60 1756 y(conclude:)60 1865 y FM(Corollary)g(4.17)24 b FP(L)n(et)d FF(q)h FE(6)p FQ(=)e(1)p FP(,)j(and)e(let)h FF(\026)f FP(b)n(e)h(any)f(me)n(asur)n(e)f(c)n(onsistent)j (with)e(the)h(FK)f(sp)n(e)n(ci-)60 1925 y(\014c)n(ation)h(\(4.91\))g([for)f FF(V)33 b FQ(=)21 b Fq(Z)637 1905 y FD(d)679 1925 y FP(and)h FF(B)i FQ(=)e FP(ne)n(ar)n(est-neighb)n(or)g(b)n(onds)g(in)g Fq(Z)1497 1905 y FD(d)1517 1925 y FP(].)36 b(Then)22 b FF(\026)g FP(is)g(not)60 1986 y(c)n(onsistent)d(with)f(any)f(F)l(el)r(ler)i(\()p FE(\021)e FP(quasilo)n(c)n(al\))h(sp)n(e)n(ci\014c)n(ation.)133 2118 y FQ(W)l(e)12 b(note)f(that)h(the)g(metho)q(d)f(used)g(here)g(to)h(pro)o (v)o(e)f(non-quasilo)q(calit)o(y)g(is)h(essen)o(tially)e(the)h(same)60 2178 y(as)h(that)g(used)g(in)f(Sections)h(4.1{4.3)g(on)h(the)e(R)o(G)h (examples.)17 b(The)12 b(only)f(di\013erence)g(is)g(that)h(here)f(w)o(e)60 2238 y(are)k(w)o(orking)h(with)f(an)h(explicit)d(sp)q(eci\014cation,)i(so)h (that)g(w)o(e)f(can)h(pro)o(v)o(e)e(b)q(ounds)j(o)o(v)o(er)e(the)g FP(whole)60 2299 y FQ(sets)21 b FE(N)201 2306 y FH(+)250 2299 y FQ(and)h FE(N)391 2306 y Fy(\000)420 2299 y FQ(;)g(whereas)f(in)f(Sections) g(4.1{4.3)i(w)o(e)e(w)o(ere)f(w)o(orking)i(with)f(the)g(conditional)60 2359 y(probabilities)e(of)h(a)g(giv)o(en)f(measure)f FF(\026)794 2341 y Fy(0)806 2359 y FQ(,)i(whic)o(h)f(are)h(de\014ned)f(only)h(up)g(to)g (mo)q(di\014cation)f(on)h FF(\026)1862 2341 y Fy(0)1874 2359 y FQ(-)60 2419 y(n)o(ull)14 b(sets,)i(and)g(therefore)f(w)o(e)g(could)g(only) g(pro)o(v)o(e)g(the)g(b)q(ounds)i(o)o(v)o(er)d FE(N)1395 2426 y FH(+)1440 2419 y FQ(and)i FE(N)1575 2426 y Fy(\000)1620 2419 y FQ(in)f(the)h FF(\026)1789 2401 y Fy(0)1801 2419 y FQ(-a.e.)60 2479 y(sense.)133 2539 y(Finally)l(,)f(w)o(e)i(remark)e(that)i(for)g(in)o (teger)f FF(q)g FE(\025)e FQ(2,)j(there)f(exists)g(a)i FP(joint)j FQ(mo)q(del)16 b(of)h(in)o(teracting)60 2600 y(P)o(otts)k(spins)g(and)g(b)q (ond)h(o)q(ccupation)g(v)m(ariables)e(|)h(that)g(is,)g(a)g(mo)q(del)f(whose)h (state)g(space)g(is)60 2660 y FE(f)p FQ(1)p FF(;)8 b(:)g(:)g(:)g(;)g(q)r FE(g)268 2642 y FD(V)306 2660 y FE(\002)g(f)p FQ(0)p FF(;)g FQ(1)p FE(g)473 2642 y FD(B)519 2660 y FQ(|)14 b(whose)i(marginals)e(on)i (the)e(spin)h(and)h(b)q(ond)g(v)m(ariables)f(are)g(the)g(P)o(otts)938 2784 y(146)p eop %%Page: 147 147 bop 60 91 a FQ(and)15 b(random-cluster)f(mo)q(dels,)g(resp)q(ectiv)o(ely)e ([109)q(].)20 b(This)15 b(join)o(t)g(mo)q(del)e(has)j FP(lo)n(c)n(al)k FQ(in)o(teractions,)60 152 y(so)14 b(its)e(sp)q(eci\014cation)h(ob)o(viously) f(quasilo)q(cal.)20 b(\(The)13 b(only)g(reason)h(it)e(isn't)g(Gibbsian)i(is)e (that)i(there)60 212 y(are)d(some)g(exclusions.\))18 b(The)12 b(iden)o(tities)d(relating)i(the)g(join)o(t,)g(P)o(otts)h(and)g (random-cluster)e(mo)q(dels)60 272 y(are)j(easily)f(pro)o(v)o(en)g(in)g (\014nite)h(v)o(olume,)d(but)j(they)g(can)g(presumably)e(b)q(e)i(made)f (rigorous)h(in)g(in\014nite)60 332 y(v)o(olume)j(b)o(y)j(metho)q(ds)f(lik)o (e)f(those)i(sk)o(etc)o(hed)e(in)h(Section)g(4.2,)i(Step)e(0.)29 b(If)18 b(so,)i(then)e(an)o(y)h(Gibbs)60 392 y(measure)13 b(of)h(the)g(join)o (t)f(mo)q(del)g(w)o(ould)h(pro)q(duce,)h(up)q(on)g(\\decimation")d(to)j(the)f (b)q(ond)h(v)m(ariables,)f(a)60 452 y(non-quasilo)q(cal)k(measure)d(\(namely) l(,)g(a)i(measure)e(consisten)o(t)i(with)f(the)h(random-cluster-mo)q(del)60 513 y(sp)q(eci\014cation\).)355 495 y FH(61)437 513 y FQ(This)24 b(w)o(ould)g(then)g(b)q(e)g(another)h(example)c(in)j(whic)o(h)f (\\decimation")g(of)i(a)60 573 y(quasilo)q(cal)16 b(measure)f(yields)g(a)i (non-quasilo)q(cal)g(measure.)60 703 y FM(4.5.4)55 b(Stationary)18 b(Measures)h(in)f(Nonequilibrium)d(Statistical)j(Mec)n(hanics)60 795 y FQ(Consider)d(an)h(in\014nite-v)o(olume)c(lattice)h(system)h(ev)o (olving)g(sto)q(c)o(hastically)l(,)g(in)g(either)g(con)o(tin)o(uous)60 855 y(time)21 b(or)i(discrete)e(time,)h(according)h(to)g(\(quasi\)lo)q(cal)g (rules)f(whic)o(h)g(do)h FP(not)28 b FQ(satisfy)23 b(detailed)60 915 y(balance.)41 b(Th)o(us,)24 b(in)e(con)o(tin)o(uous)h(time)e(w)o(e)h(ha)o (v)o(e)g(in)g(mind)f(an)j FP(inter)n(acting)g(p)n(article)g(system)60 976 y FQ([251)q(]:)d(for)c(example,)d(a)k(system)d(of)i(the)f(spin-\015ip)h (\(resp.)f(spin-exc)o(hange\))g(t)o(yp)q(e,)g(in)h(whic)o(h)f(eac)o(h)60 1036 y(spin)d(\015ips)h(\(resp.)f(eac)o(h)g(nearest-neigh)o(b)q(or)h(pair)g (of)f(spins)h(exc)o(hanges)f(v)m(alues\))h(indep)q(enden)o(tly)l(,)e(at)60 1096 y(P)o(oisson)18 b(random)e(times,)f(with)h(rates)h(dep)q(ending)g(in)g (a)g(\(quasi\)lo)q(cal)g(w)o(a)o(y)f(on)i(the)e(other)h(spins.)60 1156 y(Examples)e(of)h(suc)o(h)g(dynamics)f(include:)95 1258 y(\(a\))25 b(The)19 b(v)o(oter)g(mo)q(del)f([251)q(]:)27 b(indep)q(enden)o (tly)18 b(at)i(eac)o(h)f(site)g FF(x)p FQ(,)g(at)h(P)o(oisson)g(random)f (times)182 1318 y(the)d(spin)g(\(\\v)o(oter"\))g(at)h FF(x)e FQ(c)o(hanges)i(its)f(v)m(alue)f(to)i(that)f(of)h(a)f(randomly)f(c)o(hosen)h (neigh)o(b)q(or.)93 1420 y(\(b\))24 b(An)13 b(Ising)g(mo)q(del)f(with)h(comp) q(eting)f(dynamics:)18 b(for)c(example,)d(a)j(mixture)d(of)i(Glaub)q(er)h (dy-)182 1480 y(namics)d(for)i(t)o(w)o(o)g(di\013eren)o(t)f(temp)q(eratures)f ([144)q(],)h(or)h(a)g(mixture)e(of)i(Glaub)q(er)g(dynamics)e(for)182 1540 y(one)k(temp)q(erature)f(and)h(Ka)o(w)o(asaki)g(dynamics)f(for)h(a)g (di\013eren)o(t)f(temp)q(erature)g([362)q(].)20 b(\(The)182 1600 y(latter)13 b(mo)q(del)e(has)j(b)q(een)f(considered)g(b)o(y)f(Leb)q(o)o (witz)i(and)f(his)g(collab)q(orators)i(in)d(connection)182 1661 y(with)k(the)g(h)o(ydro)q(dynamic)f(limit)e([238)q(].\))60 1762 y(In)k(discrete)f(time)f(w)o(e)i(ha)o(v)o(e)f(in)h(mind)e(a)j FP(pr)n(ob)n(abilistic)g(c)n(el)r(lular)i(automaton)h FQ(\(PCA\))c([162)q(,)g (240)q(]:)60 1823 y(sim)o(ultaneously)12 b(at)j(eac)o(h)g(clo)q(c)o(k)e(tic)o (k,)g(eac)o(h)h(spin)h(attempts)f(indep)q(enden)o(tly)f(to)i(\015ip,)f(again) h(with)60 1883 y(rates)h(dep)q(ending)h(in)f(a)g(\(quasi\)lo)q(cal)h(w)o(a)o (y)e(on)i(the)f(other)h(spins.)k(An)16 b(example)e(is:)98 1984 y(\(c\))24 b(The)18 b(T)l(o)q(om)g(mo)q(del)f([347)q(,)g(240)r(]:)24 b(eac)o(h)18 b(spin)g(c)o(hanges)g(its)g(v)m(alue,)g(with)g(probabilit)o(y)f FF(p)p FQ(,)i(to)182 2045 y(the)f(ma)s(jorit)o(y)d(of)j(its)g(northern)g (neigh)o(b)q(or,)g(its)g(eastern)g(neigh)o(b)q(or,)g(and)g(itself,)f(and)h (with)182 2105 y(probabilities)d(\(1)d FE(\000)f FF(p)p FQ(\))p FF(=)p FQ(2)17 b(to)g FE(\006)p FQ(1.)60 2206 y(Th)o(us,)24 b(the)f(PCAs)g(are)f(the)h(discrete-time)c(analogue)24 b(of)f(the)g FP(spin-\015ip)i FQ(in)o(teracting)d(particle)60 2267 y(systems.)133 2327 y(Leb)q(o)o(witz)14 b(and)g(Sc)o(honmann)e([246)q(,)h(p.)g(50])h(ha)o(v) o(e)f(argued)h(that)g(in)f(b)q(oth)h(the)f(con)o(tin)o(uous-time)60 2387 y(and)k(discrete-time)d(cases,)i(the)h(stationary)g(measure\(s\))f (should)h(generally)e(b)q(e)i(exp)q(ected)f(to)h(b)q(e)60 2447 y(non-Gibbsian)f(and)f(indeed)g(non-quasilo)q(cal:)21 b(for)15 b(\\systems)f(main)o(tained)f(in)i(a)g(nonequilibrium)p 60 2491 732 2 v 100 2545 a FA(61)135 2560 y Fz(This)k(w)o(ould)f(probably)h (also)g(giv)o(e)f(a)h(metho)q(d)g(for)g(pro)o(ving)f(that)h Fv(\026)1261 2566 y Fp(f)1302 2560 y Fz(and)g Fv(\026)1413 2566 y Fp(w)1459 2560 y Fz(are)h(consisten)o(t)g(with)f(the)60 2610 y(random-cluster-mo)q(del)12 b(sp)q(eci\014cation,)i(at)g(least)g(for)f Fw(inte)n(ger)18 b Fv(q)q Fz(.)938 2784 y FQ(147)p eop %%Page: 148 148 bop 60 91 a FQ(state)21 b(b)o(y)e(con)o(tacts)i(with)f(outside)g(sources)g FF(:)8 b(:)g(:)28 b FQ([the)20 b(measures)f(describing])g(stationary)i(non-) 60 152 y(equilibrium)9 b(states)k(cannot)h(b)q(e)e(exp)q(ected)g(to)h(b)q (eha)o(v)o(e)f(in)g(a)h(quasi-Mark)o(o)o(vian)g([in)e(our)i(language,)60 212 y(quasilo)q(cal])k(w)o(a)o(y)g(|)h(isolating)f(a)h(part)g([of)g(the)f (system)f(from)h(the)g(rest])g(will)f(generally)h(c)o(hange)60 272 y(its)f(b)q(eha)o(vior)g(drastically)l(.")133 332 y(This)c(conjecture)e (has)j(b)q(een)e(pro)o(v)o(en)g(b)o(y)g(Leb)q(o)o(witz)g(and)h(Sc)o(honmann)f ([246)q(])g(in)g(the)g(case)g(of)h(the)60 392 y(v)o(oter)17 b(mo)q(del.)23 b(More)18 b(precisely)l(,)d(they)i(ha)o(v)o(e)g(pro)o(v)o(en)f ([246)q(,)i(equation)f(\(3.8\)])g(that)h FF(i)p FQ(\()p FF(\016)1690 399 y FH(+)1719 392 y FE(j)p FF(\027)1757 399 y FD(\032)1777 392 y FQ(\))e(=)g(0)60 452 y(where)j FF(\027)228 459 y FD(\032)268 452 y FQ(\(0)g FF(<)h(\032)f(<)g FQ(1\))h(is)f(an)h(extremal)e (translation-in)o(v)m(arian)o(t)h(stationary)h(measure)e(of)i(the)60 513 y(v)o(oter)h(mo)q(del)g(in)h Fq(Z)434 492 y FD(d)476 513 y FQ(\()p FF(d)i FE(\025)f FQ(3\).)39 b(This)22 b(sho)o(ws)h(that)f FF(\027)1100 520 y FD(\032)1142 513 y FQ(is)g(non-Gibbsian)h(\(as)g(remark)o (ed)c(also)60 573 y(in)k([240]\).)41 b(It)22 b(is)h(in)o(teresting)f(to)h (note)g(that)g(this)g(is)g(the)f(same)g(large-deviations)h(argumen)o(t)60 633 y(emplo)o(y)o(ed)13 b(in)j(the)g(Leb)q(o)o(witz-Maes-Dorlas-v)m(an)j(En)o (ter)d(examples)e(\(Section)h(4.4\).)133 693 y(Martinelli)g(and)j(Scopp)q (ola)g([259)q(])e(ha)o(v)o(e)h(giv)o(en)f(another)i(example)d(of)i(a)g (dynamics)f(in)h(whic)o(h)60 753 y(the)f(stationary)h(measure)e(is)h (non-Gibbsian:)22 b(again)17 b(the)f(probabilit)o(y)g(of)g(a)h(region)f(in)g (whic)o(h)g FP(al)r(l)60 814 y FQ(the)g(spins)g(are)g(+)g(deca)o(ys)g(more)f (slo)o(wly)g(than)i(exp)q(onen)o(tially)e(in)h(the)f(v)o(olume)f(of)j(the)f (region,)f(so)60 874 y(the)f(measure)f(cannot)h(b)q(e)h(Gibbsian.)21 b(Ho)o(w)o(ev)o(er,)12 b(the)i(Martinelli-Scopp)q(ola)f(dynamics)g(is)h (highly)60 934 y(non-lo)q(cal)21 b(|)e(it)h(in)o(v)o(olv)o(es)d(collectiv)o (e)g(\015ips)j(of)g(arbitrarily)f(large)h(clusters)f(|)h(so)g(p)q(erhaps)h (the)60 994 y(non-Gibbsianness)15 b(is)e(not)g(so)h(surprising.)21 b(\(The)13 b(Martinelli-Scopp)q(ola)f(dynamics)g(sup)q(er\014cially)60 1054 y(resem)o(bles)j(the)i(Sw)o(endsen-W)l(ang)h([340)q(])f(dynamics;)e(but) j(in)f(truth)g(the)g(resem)o(blance)e(is)i(not)g(so)60 1115 y(close,)e(since)f(the)h(stationary)h(measure)e(of)h(the)g(former)f(is)h (non-Gibbsian,)h(while)e(the)h(stationary)60 1175 y(measure)g(of)h(the)h (latter)e(is)h(the)g(nearest-neigh)o(b)q(or)h(Ising)f(mo)q(del!\))133 1235 y(Finally)l(,)g(Maes)i(and)g(Redig)f([255)q(])g(ha)o(v)o(e)g(describ)q (ed)g(an)h(\(anisotropic\))g(lo)q(cal)f(spin-)p FP(exchange)60 1295 y FQ(dynamics)j(in)h(whic)o(h)g(the)g(stationary)h(measure)e(is)h(exp)q (ected)f(to)i(ha)o(v)o(e)f(non-summable)e(long-)60 1355 y(range)24 b(correlations)g(in)f(the)h(\\high-noise")g(regime)e(\(i.e.)g(at)i(what)h (ough)o(t)f(to)g(corresp)q(ond)h(to)60 1416 y(\\high)13 b(temp)q(erature"\).) 19 b(Suc)o(h)12 b(un)o(usual)g(b)q(eha)o(vior)h(w)o(ould)f(suggest,)i(though) f(it)f(w)o(ould)g(not)h(pro)o(v)o(e,)60 1476 y(that)19 b(the)f(stationary)h (measure)e(is)h(non-Gibbsian.)28 b(The)19 b(long-range)g(spatial)g (correlations)f(are)60 1536 y(indicated)k(in)g(this)g(mo)q(del)f(b)o(y)h(a)h (p)q(erturbation)g(calculation,)g(but)g(a)g(more)e(general)h(ph)o(ysical)60 1596 y(in)o(tuition)17 b(seems)f(to)j(b)q(e)f(the)g(follo)o(wing:)24 b(T)l(ransp)q(ort)c(prop)q(erties)e(for)g(spin-exc)o(hange)f(pro)q(cesses)60 1656 y(are)j(di\013usiv)o(e,)g(and)h(the)e(correlation)h(functions)g(are)g (exp)q(ected)g(to)g(exhibit)f(slo)o(w)h(\(p)q(o)o(w)o(er-la)o(w\))60 1716 y(deca)o(y)c(in)g(time)e(\(\\long-time)i(tails"\).)22 b(No)o(w,)16 b(one)h(exp)q(ects)f(spatial)g(and)i(temp)q(oral)d(correlations) 60 1777 y(to)21 b(ha)o(v)o(e)f(roughly)h(similar)d(deca)o(y)i(|)h(i.e.)e(b)q (oth)i(exp)q(onen)o(tial)f(or)h(b)q(oth)h(p)q(o)o(w)o(er-la)o(w)f(|)f(except) 60 1837 y(in)g(v)o(ery)g(sp)q(ecial)g(cases)h(suc)o(h)g(as)g(mo)q(dels)f (satisfying)g(detailed)g(balance.)35 b(This)21 b(suggests)h(that)60 1897 y(spin-exc)o(hange)e(pro)q(cesses)h(not)g(satisfying)f(detailed)g (balance)g(should)h(ha)o(v)o(e,)f(quite)f(generally)l(,)60 1957 y(stationary)e(measures)e(with)g(long-range)j(correlations,)d(and)i(v)o (ery)d(lik)o(ely)l(,)f(stationary)k(measures)60 2017 y(that)g(are)f (non-Gibbsian.)133 2078 y(In)23 b(the)g(PCA)h(mo)q(dels,)f(the)g(probabilit)o (y)g(measure)f(on)i(the)f(space-time)e(histories)i(is)g(the)60 2138 y(Gibbs)17 b(measure)e(for)i(a)f(\()p FF(d)c FQ(+)f(1\)-dimensional)k (lattice)g(mo)q(del)h(with)g(in)o(teractions)g(whic)o(h)f(can)i(b)q(e)60 2198 y(expressed)h(in)g(terms)e(of)j(the)f(transition)h(rules)e(of)i(the)f (PCA)g(mo)q(del)f([162)q(,)h(240)q(].)27 b(The)18 b(station-)60 2258 y(ary)g(measure)f(of)h(the)f(PCA)h(mo)q(del)f(th)o(us)h(corresp)q(onds)h (to)f(the)g(restriction)f(of)h(this)g(space-time)60 2318 y(measure)e(to)h(a)h FF(d)p FQ(-dimensional)e(\(equal-time\))e(h)o(yp)q(erplane.)24 b(When)17 b(the)g(PCA)g(is)g(in)f(the)h(\\high-)60 2379 y(noise")e(regime)d (|)i(so)h(that)g(the)f(asso)q(ciated)h(\()p FF(d)7 b FQ(+)g(1\)-dimensional) 14 b(equilibrium)d(mo)q(del)i(is)h(in)g(the)60 2439 y(Dobrushin-Shlosman)k (high-temp)q(erature)e(regime)g(|)h(the)g(stationary)h(measure)f(is)g(kno)o (wn)h(to)60 2499 y(b)q(e)h(unique)g(and)h(Gibbsian)f([240)q(].)30 b(\(A)19 b(similar)e(theorem)h(has)i(recen)o(tly)d(b)q(een)i(pro)o(v)o(en)g (also)h(for)60 2559 y(con)o(tin)o(uous-time)f FP(spin-\015ip)k FQ(systems)d([257].\))34 b(Ho)o(w)o(ev)o(er,)19 b(b)o(y)i(analogy)g(with)f (the)h(Sc)o(honmann)60 2619 y(example)13 b(\(Section)i(4.5.2\),)h(one)f(ma)o (y)f(susp)q(ect)i(that)g(in)g(the)f(\\non-ergo)q(dic")i(\(phase-transition\)) 938 2784 y(148)p eop %%Page: 149 149 bop 60 91 a FQ(regime)15 b(of)i(the)f(PCA)h(mo)q(del)e(|)i(where)f(the)h (stationary)g(measure)f(is)g(not)h(unique)f(|)h(eac)o(h)f(sta-)60 152 y(tionary)j(measure)e(w)o(ould)i(t)o(ypically)d(b)q(e)j(non-Gibbsian.)30 b(In)18 b(particular,)h(one)g(ma)o(y)e(conjecture)60 212 y(that)f(this)g(is)g (so)h(for)f(the)g(T)l(o)q(om)g(mo)q(del.)k(W)l(e)c(th)o(us)g(susp)q(ect)g (that)h(Liggett's)f(conjecture)f([251)q(,)g(p.)60 272 y(224],)20 b(to)f(the)f(e\013ect)g(that)h(ev)o(ery)e(translation-in)o(v)m(arian)o(t)i (\014nite-range)g(dynamics)e(with)i FP(strictly)60 332 y(p)n(ositive)h FQ(rates)d(has)g(a)f(Gibbsian)h(stationary)g(measure,)d(is)i(most)g(lik)o (ely)e(false.)133 392 y FM(Remark.)28 b FQ(The)20 b(foregoing)g (considerations)f(are)h(for)f(rates)h(that)f(do)h FP(not)25 b FQ(satisfy)19 b(detailed)60 452 y(balance.)i(If)15 b(the)h(rates)g(satisfy) g(detailed)f(balance,)g(then)h(one)g(exp)q(ects)f(all)h(the)f(stationary)i (mea-)60 513 y(sures)f(to)h(b)q(e)f(Gibbsian)h(\(for)f(an)h(explicit)d (Gibbsian)i(sp)q(eci\014cation)g(that)g(is)g(easy)h(to)f(write)g(do)o(wn)60 573 y(giv)o(en)f(the)g(rates\);)h(ho)o(w)o(ev)o(er,)e(this)h(has)h(not)h(y)o (et)d(b)q(een)i(pro)o(v)o(en)f(rigorously)h(ev)o(en)e(in)h(the)h(Glaub)q(er) 60 633 y(dynamics)23 b(for)h(the)g(nearest-neigh)o(b)q(or)h(Ising)f(mo)q(del) f(in)g(dimension)g FF(d)k FE(\025)h FQ(3)c([251)q(,)h(Problem)60 693 y(IV.7.1].)133 753 y(Finally)l(,)d(let)g(us)h(quote)f(a)g(result)g(of)h (K)q(\177)-26 b(unsc)o(h)23 b([229)q(])f(for)g(con)o(tin)o(uous-time)f(lo)q (cal)h(spin-\015ip)60 814 y(pro)q(cesses)c(with)f(strictly)f(p)q(ositiv)o(e)g (rates:)23 b(if)17 b(there)g(exists)f(a)i(translation-in)o(v)m(arian)o(t)f (stationary)60 874 y(measure)k(whic)o(h)h(is)h(Gibbsian)g(for)f(some)g (\(absolutely)g(summable\))e(in)o(teraction,)j(then)g(ev)o(ery)60 934 y(other)16 b(translation-in)o(v)m(arian)o(t)g(stationary)g(measure)e(m)o (ust)g(b)q(e)i(Gibbsian)g(for)g(the)f(same)g(in)o(terac-)60 994 y(tion.)60 1123 y FM(4.5.5)55 b(Comparison)18 b(of)h(Metho)r(ds)f(for)h (Pro)n(ving)f(Non-Gibbsianness)60 1215 y FQ(An)o(y)12 b(theorem)f(of)i(the)g (form)f(\\ev)o(ery)g(Gibbs)h(measure)e(has)j(the)e(prop)q(ert)o(y)h FE(P)t FQ(")g(pro)o(vides)g(a)g(metho)q(d)60 1275 y(for)f(pro)o(ving)f (non-Gibbsianness)j(via)d(the)g(con)o(trap)q(ositiv)o(e:)19 b(a)12 b(measure)e(not)i(ha)o(ving)g(the)f(prop)q(ert)o(y)60 1335 y FE(P)20 b FQ(m)o(ust)15 b(b)q(e)h(non-Gibbsian.)23 b(W)l(e)16 b(ha)o(v)o(e)f(seen)h(four)h(prop)q(erties)f(of)g(this)g(sort:)106 1428 y(\(i\))24 b(A)c(Gibbs)h(measure)e(\(for)i(an)g(absolutely)f(summable)e (in)o(teraction\))h(m)o(ust)g(b)q(e)i(uniformly)182 1488 y(non-n)o(ull.)30 b(This)20 b(is)f(a)g(consequence)g(of)g(the)g(\\easy)h(half)s(")g(of)g(the)f (Gibbs)h(represen)o(tation)182 1548 y(theorem)15 b([Theorem)f(2.12)j(\(a\))g (=)-8 b FE(\))15 b FQ(\(b\)].)93 1647 y(\(ii\))23 b(A)f(Gibbs)h(measure)e (\(for)i(a)g(uniformly)d(con)o(v)o(ergen)o(t)i(in)o(teraction\))f(m)o(ust)g (b)q(e)i(quasilo)q(cal)182 1707 y([Theorem)14 b(2.10].)79 1806 y(\(iii\))23 b(A)17 b(measure)f(can)i(b)q(e)g(Gibbsian)f(for)h(at)g(most)f (one)h(\(uniformly)d(con)o(v)o(ergen)o(t,)h(con)o(tin)o(uous\))182 1866 y(in)o(teraction,)f(up)h(to)h(\\ph)o(ysical)e(equiv)m(alence")g ([Corollary)h(2.18].)80 1965 y(\(iv\))24 b(T)l(ranslation-in)o(v)m(arian)o(t) 11 b(Gibbs)g(measures)f(\(for)h(translation-in)o(v)m(arian)o(t)g(absolutely)g (summable)182 2025 y(in)o(teractions\))g(ha)o(v)o(e)g(\\go)q(o)q(d")j (large-deviation)e(prop)q(erties:)19 b(the)11 b(probabilit)o(y)g(that)h (spins)g(in)182 2085 y(a)f(certain)f(region)h(\015uctuate)g(in)o(to)g(a)g (con\014guration)h(c)o(haracteristic)d(of)i(another)h(translation-)182 2146 y(in)o(v)m(arian)o(t)17 b(measure)f(decreases)h(exp)q(onen)o(tially)f (in)i(the)f(v)o(olume)e(of)j(the)f(region,)h FP(exc)n(ept)24 b FQ(if)182 2206 y(this)16 b(other)g(measure)f(is)h(also)h(Gibbsian)g(for)f (the)g(same)f(\(absolutely)h(summable\))e(in)o(terac-)182 2266 y(tion.)22 b(In)17 b(precise)e(mathematical)f(terms:)21 b(a)c(translation-in) o(v)m(arian)o(t)f(measure)g FF(\026)h FQ(has)g(zero)182 2326 y(relativ)o(e)12 b(en)o(trop)o(y)g(densit)o(y)h(resp)q(ect)g(to)h(another)g (translation-in)o(v)m(arian)o(t)g(measure)e FF(\027)17 b FQ(whic)o(h)182 2386 y(is)i(Gibbsian)g(for)g(an)h(in)o(teraction)e(\010,)h(if)g(and)h(only)e (if)h FF(\026)g FQ(is)g(also)h(Gibbsian)f(for)g(the)g(same)182 2447 y(in)o(teraction)c(\010.)22 b(This)16 b(is)g(one)h(of)f(the)g (consequences)g(of)g(the)g(discussion)h(of)f(Section)g(2.6.6.)182 2507 y(It)e(is)h(also)h(closely)d(related)h(to)i(the)e(strict)h(con)o(v)o (exit)o(y)d(of)j(the)g(pressure)g([Prop)q(osition)g(2.59].)133 2600 y(F)l(or)g(eac)o(h)f(of)h(these)f(conditions,)g(w)o(e)g(ha)o(v)o(e)g (seen)g(examples)e(in)j(whic)o(h)e(the)i(non-Gibbsianness)60 2660 y(is)h(pro)o(v)o(en)g(b)o(y)f(its)h(violation:)938 2784 y(149)p eop %%Page: 150 150 bop 133 91 a FQ(\(i\))23 b FP(L)n(ack)g(of)h(uniform)f(nonnul)r(lne)q(ss.)45 b FQ(This)23 b(has)h(t)o(w)o(o)f(manifestations:)33 b(A)23 b(measure)f(can)60 152 y(b)q(e)d(nonn)o(ull)e(but)i(not)g(uniformly)d(so)j (\(see)f(De\014nition)g(2.11\).)28 b(This)19 b(t)o(ypically)d(means)h(that)i (the)60 212 y(Hamiltonians)f(are)j(un)o(b)q(ounded)f(functions)g(and)h(one)f (cannot)h(use)f(the)g(formalism)d(dev)o(elop)q(ed)60 272 y(for)22 b(absolutely)g(summable)e(in)o(teractions.)37 b(This)23 b(is)e(the)h(generic) f(situation)i(for)f(un)o(b)q(ounded-)60 332 y(spin)d(mo)q(dels,)f(and)i(it)f (gets)g(delicate)f(for)h(in\014nite-range)g(in)o(teractions.)29 b(In)19 b(these)f(cases,)i(often)60 392 y(the)g(notion)i(of)f(Gibbsianness)g (can)g(b)q(e)g(preserv)o(ed)e(if)h(one)h(excludes)f(\\b)o(y)g(hand")i (problematic)60 452 y(con\014gurations)j([245)q(,)e(60)q(].)43 b(On)23 b(the)h(other)g(hand,)h(the)f(measure)e(ma)o(y)g(fail)h(to)h(b)q(e)g (nonn)o(ull,)60 513 y(whic)o(h)17 b(means)g(that)h(some)e(cylinder)g(sets)i (ha)o(v)o(e)f(zero)g(measure.)24 b(This)18 b(is)f(a)h(rather)g(simple)d(case) 60 573 y(of)i(non-Gibbsianness)i(in)e(whic)o(h)f(the)h(Gibbsianness)g(can)h (b)q(e)f(restored)g(b)o(y)g(allo)o(wing)f(hard-core)60 633 y(in)o(teractions)c(or)g(w)o(orking)g(on)h(a)g(more)e(restricted)g (con\014guration)i(space)g(\(see)f(for)g(example)e([313)q(]\).)60 693 y(W)l(e)i(men)o(tion)f(that,)i(in)f(the)g(setting)h(of)g FP(c)n(omplex)19 b FQ(in)o(teractions,)12 b(there)g(are)g(examples)f(of)i (Gibbsian)60 753 y(measures)19 b(that)i(after)f(one)g(renormalization)f(step) h(remain)f(quasilo)q(cal)h(but)g(lose)g(nonn)o(ullness)60 814 y([14].)133 874 y(\(ii\))h FP(Violation)i(of)f(quasilo)n(c)n(ality.)38 b FQ(Most)22 b(of)g(the)g(cases)g(of)g(pathological)g(renormalization)60 934 y(transformations)12 b(analyzed)f(ab)q(o)o(v)o(e)g(\(Sections)g(4.1{4.3)i (and)f(4.5.2\))g(fall)f(in)o(to)g(this)g(category)l(.)20 b(This)60 994 y(phenomenon)e(app)q(ears)i(when)f(there)g(are)g(some)f(\\hidden)g (spins")i(that)f(transmit)f(information)60 1054 y(from)g(arbitrarily)h(far)h (a)o(w)o(a)o(y)f(ev)o(en)g(if)f(the)i(\\non-hidden")h(spins)e(are)h(\014xed.) 31 b(In)19 b(the)g(renormal-)60 1115 y(ization)g(transformations)g(the)h (\\hidden)f(v)m(ariables")g(are)h(the)f(\015uctuations)h(of)f(the)g(original) h(or)60 1175 y(in)o(ternal)g(spins)h(that)g(remain)e(once)i(the)g(blo)q(c)o (k)f(spins)h(are)g(\014xed.)35 b(In)20 b(Sc)o(honmann's)g(example)60 1235 y(\(Section)e(4.5.2\),)g(the)g(\\hidden)h(v)m(ariables")f(are)g(all)g (the)g(spins)h(outside)f(the)g FF(x)p FQ(-axis,)g(whic)o(h)g(are)60 1295 y(\\hidden")f(b)o(y)e(the)h(pro)q(cess)h(of)g(restriction.)133 1355 y(\(iii\))12 b FP(Thr)n(e)n(atene)n(d)i(violation)h(of)g(uniqueness.)22 b FQ(W)l(e)13 b(used)g(this)g(metho)q(d)f(to)i(study)f(the)g(\\trivial")60 1416 y(examples)e(of)i(non-Gibbsianness)i(discussed)e(in)g(Section)f(4.5.1.) 21 b(Consider)13 b(a)g(\014nite)g(or)g(coun)o(table)60 1476 y(family)f(of)j(di\013eren)o(t)f(\(non-ph)o(ysically-equiv)m(alen)o(t\))e(in) o(teractions)i(and)h(pic)o(k)e(for)i(eac)o(h)f(one)h(an)g(er-)60 1536 y(go)q(dic)20 b(translation-in)o(v)m(arian)o(t)f(Gibbs)g(measure.)29 b(Then)19 b(a)h(non)o(trivial)e(con)o(v)o(ex)g(com)o(bination)g(of)60 1596 y(these)13 b(measures)g(cannot)h(b)q(e)g(Gibbsian)f(for)h(an)o(y)g (\(uniformly)d(con)o(v)o(ergen)o(t,)h(con)o(tin)o(uous\))i(in)o(terac-)60 1656 y(tion,)i(b)q(ecause)h(if)f(it)g(w)o(ere,)g(then)g(eac)o(h)h(of)f(the)h (original)f(measures)g(w)o(ould)h(b)q(e)f(a)h(Gibbs)g(measure)60 1716 y(also)j(for)f(this)g(new)h(in)o(teraction,)e(violating)h(uniqueness.)29 b(In)19 b(the)g(case)h(of)f(a)h(\014nite)e(single-spin)60 1777 y(space,)e(this)g(metho)q(d)f(also)i(pro)o(v)o(es)f(non-quasilo)q(calit)o(y)l (.)133 1837 y(\(iv\))g FP(Wr)n(ong)h(lar)n(ge)h(deviation)g(pr)n(op)n (erties.)j FQ(There)c(seem)d(to)j(b)q(e)g(t)o(w)o(o)f(rather)h(di\013eren)o (t)e(t)o(yp)q(es)60 1897 y(of)i(\\bad")g(large-deviation)f(prop)q(erties:)88 1999 y(\()p FF(\013)p FQ(\))25 b(Sub-exp)q(onen)o(tial)13 b(deca)o(y)f(for)h (ev)o(en)o(ts)f(whose)i(probabilit)o(y)e(\\should")i(deca)o(y)e(exp)q(onen)o (tially)182 2059 y(in)i(the)h(v)o(olume.)j(This)d(applies)f(to)h(the)g(sign)g (\014eld)f(of)h(the)f(\(an\)harmonic)g(crystal)h(\(Section)182 2119 y(4.4\),)j(and)h(the)e(stationary)i(measures)e(for)h(the)g(v)o(oter)f (and)i(Martinelli-Scopp)q(ola)e(mo)q(dels)182 2179 y(men)o(tioned)10 b(in)i(Section)g(4.5.4.)20 b(Here)11 b(one)i(sho)o(ws)g(that)g(the)f (probabilit)o(y)f(of)i FP(al)r(l)19 b FQ(the)12 b(spins)g(in)182 2240 y(a)k(large)g(region)f(b)q(ecoming)g(+)g(deca)o(ys)g(sub-exp)q(onen)o (tially)g(in)g(the)h(v)o(olume)d(of)j(the)f(region;)182 2300 y(this)c(is)h(incompatible)d(with)i(b)q(eing)h(Gibbsian)g(for)g(an)o(y)f (absolutely)h(summable)c(in)o(teraction.)182 2360 y(In)17 b(other)h(w)o (ords,)g(one)g(sho)o(ws)g(that)g(the)f(measure)g FF(\026)h FQ(satis\014es)f FF(i)p FQ(\()p FF(\016)1429 2367 y FH(+)1458 2360 y FE(j)p FF(\026)p FQ(\))f(=)g(0,)i(where)g FF(\016)1811 2367 y FH(+)1857 2360 y FQ(is)182 2420 y(the)i(delta-measure)e(concen)o (trated)i(on)g(the)g(all-+)g(con\014guration.)34 b(As)20 b(this)f(measure)g (is)182 2480 y(ob)o(viously)d(non-Gibbsian)h(\(it)f(is)g FP(not)21 b FQ(nonn)o(ull!\),)15 b(neither)g(is)h FF(\026)p FQ(.)89 2582 y(\()p FF(\014)s FQ(\))24 b(Exp)q(onen)o(tial)11 b(deca)o(y)g(for)g(ev)o(en)o (ts)g(whose)h(probabilit)o(y)e(\\should")j(deca)o(y)d(sub-exp)q(onen)o (tially)l(.)182 2642 y(The)k(original)g(pro)q(of)i(of)e(Sc)o(honmann's)g (example)e([318])i(is)g(based)h(on)g(an)f(argumen)o(t)g(of)g(this)938 2784 y(150)p eop %%Page: 151 151 bop 182 91 a FQ(kind.)42 b(Here)22 b(one)i(sho)o(ws)g(that,)h(in)e(the)g(+)g (phase,)i(the)e(probabilit)o(y)g(of)g(ha)o(ving)h(a)f(net)182 152 y(negativ)o(e)18 b(magnetization)g(in)h(a)g(large)h(region)f(deca)o(ys)f (exp)q(onen)o(tially)g(in)h(the)g(v)o(olume)e(of)182 212 y(the)i(region.)29 b(In)19 b(other)g(w)o(ords,)h(the)e(measures)g(obtained)h(via)g(\\+")h(and)f (\\)p FE(\000)p FQ(")h(b)q(oundary)182 272 y(conditions)g(ha)o(v)o(e)f(a)h (strictly)f(p)q(ositiv)o(e)g(relativ)o(e)f(en)o(trop)o(y)l(.)32 b(If)19 b(either)g(of)h(these)g(measures)182 332 y(w)o(ere)f(Gibbsian)h (\(for)g(an)h(absolutely)f(summable)d(in)o(teraction\),)i(the)h(other)g(w)o (ould)g(ha)o(v)o(e)182 392 y(to)g(b)q(e)f(Gibbsian)h(for)f(the)g(same)f(in)o (teraction)h(\(b)q(ecause)g(they)g(di\013er)g(only)g(b)o(y)g(b)q(oundary)182 452 y(conditions\);)c(but)f(then)g(the)h(relativ)o(e)d(en)o(trop)o(y)i(w)o (ould)g(ha)o(v)o(e)g(to)h(b)q(e)f(zero)h(\(Theorem)e(2.66\).)182 513 y(Therefore,)i(they)h(cannot)h(b)q(e)f(Gibbsian.)133 614 y(Often)d(w)o(e)g(w)o(ould)g(lik)o(e)e(to)j(pro)o(v)o(e)e(not)i(only)f(that)g (a)h(measure)e(is)h(non-Gibbsian,)h(but)g(also)g(that)60 675 y(it)e(is)g(non-quasilo)q(cal)i(\(whic)o(h)d(is)i(stronger\).)20 b(In)12 b(nearly)g(all)g(cases)h(w)o(e)f(ha)o(v)o(e)g(done)h(this)f(\\b)o(y)g (hand":)60 735 y(that)h(is,)g(b)o(y)f(pro)o(ving)h(b)q(ounds)h(on)g(the)e (conditional)h(probabilities)f(whic)o(h)g(are)h(incompatible)d(with)60 795 y(their)17 b(ha)o(ving)h(an)o(y)g(quasilo)q(cal)g(v)o(ersion)f(\(see)h (Sections)g(4.1{4.3)h(and)f(4.5.2\).)27 b(In)18 b(only)g(one)g(case)60 855 y(w)o(ere)f(w)o(e)g(able)g(to)h(pro)o(v)o(e)f(non-quasilo)q(calit)o(y)g (b)o(y)g(an)h(abstract)g(\\tric)o(k":)23 b(this)17 b(w)o(as)h(the)g (\\trivial")60 915 y(con)o(v)o(ex-com)o(bination)i(example)f(\(Section)j (4.5.1\),)i(where)d(w)o(e)h(used)g(metho)q(d)g(\(iii\))f(ab)q(o)o(v)o(e.)38 b(It)60 976 y(w)o(ould)16 b(b)q(e)h(in)o(teresting)e(to)h(ha)o(v)o(e)g(a)o(v) m(ailable)f(other)i(metho)q(ds)e(for)i(pro)o(ving)f(non-quasilo)q(calit)o(y)l (.)60 1105 y FM(4.5.6)55 b(Are)19 b(\\Most")f(Measures)h(Non-Gibbsian?)60 1198 y FQ(The)f(traditional)g(b)q(elief)f(among)h(ph)o(ysicists)f (\(including)g(ourselv)o(es)g(un)o(til)g(recen)o(tly\))f(is)i(that)h(all)60 1258 y(\(or)h(nearly)f(all\))f(ph)o(ysically)g(in)o(teresting)g(measures)h (are)g(Gibbsian.)31 b(Indeed,)19 b(this)g(b)q(elief)f(is)h(so)60 1318 y(m)o(uc)o(h)13 b(tak)o(en)i(for)h(gran)o(ted)556 1300 y FH(62)609 1318 y FQ(that)g(it)f(is)g(rarely)g(stated)h(explicitly)l(.)1302 1300 y FH(63)1358 1318 y FQ(The)f(profound)i(message)e(of)60 1378 y(Israel's)i(pioneering)f(w)o(ork)i([207],)f(and)h(of)g(the)f(examples)e (giv)o(en)h(here,)h(is)g(that)h(this)f(traditional)60 1439 y(b)q(elief)d(is)h(false:)20 b FP(many)c(physic)n(al)r(ly)h(inter)n(esting)g (me)n(asur)n(es)f(ar)n(e)f(non-Gibbsian)t FQ(.)23 b(In)14 b(fact,)h(w)o(e)g (no)o(w)60 1499 y(susp)q(ect)20 b(that)g(Gibbsianness)h(should)f(b)q(e)g (considered)f(to)h(b)q(e)g(the)f(exception)g(rather)h(than)g(the)60 1559 y(rule)c(|)g(that,)g(in)g(some)f(sense,)h FP(most)21 b FQ(measures)15 b(are)h(non-Gibbsian.)133 1619 y(It)g(is)g(therefore)g(of)h (at)g(least)f(mathematical)d(in)o(terest)i(to)i(study)g(the)f(set)g FE(G)h(\021)1634 1586 y Fx(S)1606 1660 y FH(\010)p Fy(2B)1679 1650 y Fr(1)1704 1619 y FE(G)1734 1626 y FD(inv)1788 1619 y FQ(\(\005)1844 1601 y FH(\010)1871 1619 y FQ(\))60 1705 y(of)e(all)f (translation-in)o(v)m(arian)o(t)h(measures)f(whic)o(h)g(are)h(Gibbsian)g(for) g(some)f(translation-in)o(v)m(arian)o(t)60 1765 y(absolutely)k(summable)e (con)o(tin)o(uous)j(in)o(teraction.)28 b(Is)18 b FE(G)k FQ(a)d(\\big")g(or)g (a)g(\\small")f(subset)h(of)g(the)60 1825 y(space)d FF(M)237 1832 y FH(+1)p FD(;inv)346 1825 y FQ(\(\012\))h(of)f(all)g(translation-in)o (v)m(arian)o(t)g(measures?)p 60 1873 732 2 v 100 1927 a FA(62)135 1942 y Fz(There)f(are)f(man)o(y)e(examples)h(of)g(this)h(in)g(the)g(ph)o (ysics)h(literature:)j(see,)d(for)e(example,)f([54)o(,)i(49)o(].)100 2000 y FA(63)135 2015 y Fz(One)i(exception)f(is)g(the)h(recen)o(t)h(statemen) o(t)e(b)o(y)g(a)g(noted)g(mathematical)d(ph)o(ysicist)k(that)f(\\ev)o(ery)g (go)q(o)q(d)g(ran-)60 2065 y(dom)g(\014eld)i(is)f(Gibbsian")f([324)o(].)26 b(In)16 b(a)h(similar)d(v)o(ein,)i(a)h(mathematicia)o(n)d(sa)o(ys:)24 b(\\the)17 b(Gibbsian)e(form)g(of)h(lo)q(cal)60 2115 y(conditional)f (distributions)i(is)f(a)h(rather)g(w)o(eak)g(condition,)f(but)h(it)g(is)f (di\016cult)g(to)h(c)o(hec)o(k)h(it.")25 b([229)o(,)17 b(p.)f(410])g(A)60 2165 y(related)h(though)f(somewhat)g(w)o(eak)o(er)h(in)o(tuition)e(can)h(b)q (e)h(found)f(in)g(a)g(w)o(ell-kno)o(wn)f(monograph)g(on)h(in)o(teracting)60 2221 y(particle)e(systems:)20 b(\\Is)14 b(it)g(true)h(that)g(ev)o(ery)g (translation)e(in)o(v)n(arian)o(t)g(strictly)i(p)q(ositiv)o(e)f(spin)g (system)g(on)g Fq(Z)1776 2197 y Fp(d)1809 2221 y Fz(with)60 2271 y(\014nite)f(range)g(has)g(an)f(in)o(v)n(arian)o(t)f(measure)h(whic)o(h) h(is)f(a)h(Gibbs)f(state?)19 b(This)12 b(is)h(plausible)f Fv(:)7 b(:)g(:)17 b Fz([b)q(ecause])d(the)f(strict)60 2320 y(p)q(ositivit)o(y)j(of)g (the)i(rates)f(should)g(imply)e(that)i(an)f(in)o(v)n(arian)o(t)g(measure)g (is)h(somewhat)f(smo)q(oth.")26 b([251)o(,)17 b(p.)f(224])60 2370 y(On)h(this)f(same)f(conjecture,)j(another)f(mathematician)c(sa)o(ys:)23 b(\\W)m(e)15 b(couldn't)h(pro)o(v)o(e)g(in)g(general)g(the)h(existence)60 2420 y(of)g(a)g(stationary)g(Gibbs)g(measure,)h(although)e(this)i(is)f(v)o (ery)h(lik)o(ely)e(to)h(hold.")28 b([229)o(,)17 b(p.)g(408])f(As)i(discussed) h(in)60 2470 y(Section)d(4.5.4,)d(this)j(conjecture)h(is)e(still)g(an)g(op)q (en)h(problem,)e(but)h(there)i(is)e(go)q(o)q(d)g(reason)h(to)f(susp)q(ect)j (that)d(it)g(is)60 2520 y(false.)i(\(These)12 b(examples,)f(together)h(with)e (those)i(of)e(the)i(preceding)g(fo)q(otnote,)f(illustrate)g(the)h (di\013erence)h(b)q(et)o(w)o(een)60 2569 y(ph)o(ysicists)k(and)f (mathematicia)o(ns:)k(b)q(oth)c(often)g(ha)o(v)o(e)g(erroneous)i(in)o (tuitions,)d(but)h(the)h(mathematicians)c(state)60 2619 y(them)g(explicitly)m (.\))938 2784 y FQ(151)p eop %%Page: 152 152 bop 133 91 a FQ(It)14 b(is)f(a)i(\\big")g(set)e(in)h(a)g(v)o(ery)f(w)o(eak)h (sense,)g(namely)e(that)i(of)g(b)q(eing)g(dense)g(in)g(the)f(w)o(eak)h(top)q (ol-)60 152 y(ogy)l(.)30 b(In)19 b(fact,)g(the)g(Gibbs)h(measures)e(for)h FP(\014nite-r)n(ange)25 b FQ(con)o(tin)o(uous)19 b(in)o(teractions)f(are)h (already)60 212 y(dense:)60 318 y FM(Prop)r(osition)f(4.18)24 b FP(Assume)e(that)f(the)h(single-spin)h(sp)n(ac)n(e)e FQ(\012)1272 325 y FH(0)1313 318 y FP(is)h(a)f(c)n(omp)n(act)g(metric)g(sp)n(ac)n(e,)60 378 y(and)f(that)g(the)g FQ(a)f(priori)g FP(single-spin)i(me)n(asur)n(e)e FF(\026)984 360 y FH(0)984 390 y FD(x)1026 378 y FP(gives)i(nonzer)n(o)e(me)n (asur)n(e)g(to)h(every)g(op)n(en)f(set)60 438 y(of)e FQ(\012)152 445 y FH(0)172 438 y FP(.)23 b(Then)691 498 y FE(G)721 505 y FD(f)t(inite)845 498 y FE(\021)965 457 y Fx([)912 549 y FH(\010)p Fy(2B)984 560 y Fk(\014nite)1074 498 y FE(G)1104 505 y FD(inv)1157 498 y FQ(\(\005)1213 478 y FH(\010)1240 498 y FQ(\))60 636 y FP(is)17 b(dense)i(in)f FF(M)354 643 y FH(+1)p FD(;inv)463 636 y FQ(\(\012\))f FP(in)h(the)g(we)n(ak)g(top)n(olo)n(gy.)60 788 y Fd(Pr)o(oof.)48 b FQ(The)17 b(pro)q(of)h(go)q(es)h(in)e(three)g(steps:) 23 b(First,)17 b(the)g(ergo)q(dic)h(measures)e(of)i(\014nite)f(en)o(trop)o(y) 60 848 y(densit)o(y)f(\(relativ)o(e)f(to)i FF(\026)511 830 y FH(0)531 848 y FQ(\))g(are)g(dense)g(in)f FF(M)887 855 y FH(+1)p FD(;inv)996 848 y FQ(\(\012\))h([Prop)q(osition)h(2.61\(e\)].)23 b(Secondly)l(,)16 b(Israel)60 908 y([206)q(])f(has)h(sho)o(wn,)g(using)g(the) f(Bishop-Phelps)h(theorem,)d(that)j(eac)o(h)f(ergo)q(dic)h(measure)e(of)i (\014nite)60 968 y(en)o(trop)o(y)k(densit)o(y)h(is)g(an)h(\(extremal\))c (equilibrium)g(measure)i(for)i(some)e(in)o(teraction)g(\010)1738 950 y Fy(\003)1780 968 y FE(2)j(B)1871 950 y FH(0)60 1028 y FQ(\(see)15 b(item)f(2)i(in)g(Section)f(2.6.7\).)21 b(Finally)l(,)14 b(the)i(\014nite-range)g(in)o(teractions)f(form)g(a)h(dense)g(subset)60 1089 y FE(B)93 1096 y Fk(\014nite)188 1089 y FE(\032)d(B)275 1071 y FH(0)294 1089 y FQ(;)g(and)g(it)f(follo)o(ws)g(from)f(a)h(theorem)f (of)h(Lanford)h(and)g(Robinson)g([231)q(])e(\(see)h(also)h(Sok)m(al)60 1149 y([332)q(]\))f(that)h(ev)o(ery)f(extremal)e(equilibrium)g(measure)h(for) i(\010)1166 1131 y Fy(\003)1200 1149 y FE(2)h(B)1282 1131 y FH(0)1314 1149 y FQ(can)f(b)q(e)g(appro)o(ximated)f(in)g(the)60 1209 y(w)o(eak)f(top)q(ology)i(b)o(y)f(equilibrium)c(measures)i(for)i(in)o (teractions)f(\010)1260 1216 y FD(n)1298 1209 y FE(2)j(B)1378 1216 y Fk(\014nite)1471 1209 y FQ(with)d FE(k)p FQ(\010)1637 1216 y FD(n)1663 1209 y FE(\000)r FQ(\010)1739 1191 y Fy(\003)1758 1209 y FE(k)1783 1217 y Fy(B)1807 1208 y Fr(0)1840 1209 y FE(!)60 1269 y FQ(0.)p 238 1273 25 34 v 133 1375 a(W)l(e)k(emphasize)f(that)h(densit) o(y)g(in)f(the)i(w)o(eak)f(top)q(ology)h(is)f(an)h(extremely)c(w)o(eak)j (prop)q(ert)o(y:)20 b(it)60 1435 y(means)d(only)g(that)h(an)g(arbitrary)g (measure)e FF(\026)h FE(2)f FF(M)1037 1442 y FH(+1)p FD(;inv)1146 1435 y FQ(\(\012\))i(can)g(b)q(e)f FP(appr)n(oximate)n(d)22 b FQ(arbitrary)60 1495 y(closely)l(,)c(with)g(regard)i(to)f(an)o(y)g FP(\014nite)24 b FQ(family)16 b(of)j FP(lo)n(c)n(al)25 b FQ(observ)m(ables,) 19 b(b)o(y)f(a)i(measure)d(in)i FE(G)1780 1502 y FD(f)t(inite)1876 1495 y FQ(.)60 1556 y(In)h(particular,)g(the)f(long-range-order)j(prop)q (erties)e(of)g(the)g(appro)o(ximating)f(measures)g(can)h(b)q(e)60 1616 y(totally)d(di\013eren)o(t)g(from)g(those)h(of)f(the)h(limiting)d (measure)h FF(\026)p FQ(.)26 b(Th)o(us,)18 b(Prop)q(osition)g(4.18)h(is)e(v)o (ery)60 1676 y(far)g(from)e(sa)o(ying)h(that)h(\\most")f(measures)f(are)h (Gibbsian.)133 1736 y(In)k(a)h(more)e(profound)i(sense)g(w)o(e)f(exp)q(ect)f (that)i FE(G)i FQ(is)d(in)g(fact)g(a)h(rather)g(\\small")e(subset)i(of)60 1796 y FF(M)107 1803 y FH(+1)p FD(;inv)216 1796 y FQ(\(\012\).)g(F)l(or)c (example,)c(w)o(e)j(conjecture:)60 1892 y FM(Conjecture)i(4.19)57 b FP(\(a\))24 b FE(G)19 b FP(is)d(a)g(set)h(of)e(\014rst)i(Bair)n(e)e(c)n (ate)n(gory)h(in)g FF(M)1389 1899 y FH(+1)p FD(;inv)1498 1892 y FQ(\(\012\))p FP(.)22 b([That)16 b(is,)g FE(G)j FP(is)182 1952 y(a)e(c)n(ountable)i(union)g(of)e(sets)h(which)g(ar)n(e)f(nowher)n(e)h (dense)g(in)g FF(M)1381 1959 y FH(+1)p FD(;inv)1490 1952 y FQ(\(\012\))p FP(.])95 2052 y(\(b\))25 b FE(G)17 b(\\)e FQ(ex)p FF(M)372 2059 y FH(+1)p FD(;inv)481 2052 y FQ(\(\012\))22 b FP(is)h(a)f(set)h(of)f(\014rst)h(Bair)n(e)f(c)n(ate)n(gory)g(in)g FQ(ex)p FF(M)1422 2059 y FH(+1)p FD(;inv)1531 2052 y FQ(\(\012\))p FP(.)37 b([Her)n(e)23 b(\\)p FQ(ex)p FP(")182 2112 y(denotes)c(the)e(extr)n (eme)i(p)n(oints,)e(i.e.)h(the)f(er)n(go)n(dic)g(me)n(asur)n(es.])60 2207 y FQ(First)f(Baire)f(category)i(is)f(a)g(classic)g(notion)h(of)f (\\smallness")g(in)g(top)q(ology)h([285)q(].)133 2268 y(W)l(e)f(can)h(mak)o (e)d(some)h(small)g(steps)h(to)o(w)o(ard)h(pro)o(ving)f(Conjecture)g (4.19\(a\):)60 2373 y FM(Prop)r(osition)i(4.20)24 b FE(G)c FP(has)d(empty)g(interior.)60 2479 y FM(Prop)r(osition)h(4.21)24 b FP(Assume)e(that)f(the)h(single-spin)h(sp)n(ac)n(e)e FQ(\012)1272 2486 y FH(0)1313 2479 y FP(is)h(a)f(c)n(omp)n(act)g(metric)g(sp)n(ac)n(e,)60 2539 y(and)f(that)g(the)g FQ(a)f(priori)g FP(single-spin)i(me)n(asur)n(e)e FF(\026)984 2521 y FH(0)984 2552 y FD(x)1026 2539 y FP(gives)i(nonzer)n(o)e (me)n(asur)n(e)g(to)h(every)g(op)n(en)f(set)60 2600 y(of)f FQ(\012)153 2607 y FH(0)173 2600 y FP(.)24 b(L)n(et)17 b FF(S)k FP(b)n(e)d(a)g FQ(compact)f FP(subset)i(of)f FE(B)885 2582 y FH(0)904 2600 y FP(,)g(and)g(let)h FE(E)1127 2607 y FD(S)1170 2600 y FP(b)n(e)f(the)h(set)f(of)g(e)n(quilibrium)h(me)n(asur)n(es)60 2660 y(for)e(inter)n(actions)h(in)g FF(S)s FP(.)k(Then)c FE(E)688 2667 y FD(S)731 2660 y FP(is)f(a)h(c)n(omp)n(act)f(subset)h(of)g FF(M)1263 2667 y FH(+1)p FD(;inv)1372 2660 y FQ(\(\012\))p FP(.)938 2784 y FQ(152)p eop %%Page: 153 153 bop 60 91 a FM(Corollary)18 b(4.22)24 b FP(Assume)18 b(that)f(the)h (single-spin)h(sp)n(ac)n(e)e FQ(\012)1198 98 y FH(0)1235 91 y FP(is)g(a)h(c)n(omp)n(act)e(metric)i(sp)n(ac)n(e,)f(and)60 152 y(that)22 b(the)h FQ(a)f(priori)g FP(single-spin)i(me)n(asur)n(e)e FF(\026)904 133 y FH(0)904 164 y FD(x)948 152 y FP(gives)h(nonzer)n(o)g(me)n (asur)n(e)e(to)h(every)h(op)n(en)f(set)h(of)60 212 y FQ(\012)95 219 y FH(0)115 212 y FP(.)35 b(If)21 b FF(S)k FP(is)c(a)h FF(\033)r FQ(-compact)e FP(subset)i(of)g FE(B)869 194 y FH(0)888 212 y FP(,)g(with)g FF(S)j FE(\032)c(B)1185 194 y FH(1)1204 212 y FP(,)i(then)f FE(E)1380 219 y FD(S)1427 212 y FQ(=)g FE(G)1517 219 y FD(S)1564 212 y FE(\021)1643 178 y Fx(S)1624 250 y FH(\010)p Fy(2)p FD(S)1704 212 y FE(G)1734 219 y FD(inv)1788 212 y FQ(\(\005)1844 194 y FH(\010)1871 212 y FQ(\))60 297 y FP(is)e FF(\033)r FP(-c)n(omp)n(act)f (and)h(of)g(\014rst)g(Bair)n(e)f(c)n(ate)n(gory)h(in)g FF(M)1049 304 y FH(+1)p FD(;inv)1158 297 y FQ(\(\012\))p FP(.)30 b(In)20 b(p)n(articular,)g(this)f(o)n(c)n(curs)h(for)60 358 y FF(S)d FQ(=)d FE(B)192 365 y FD(h)231 358 y FP(with)k FF(h)379 370 y FE(\030)379 349 y(\035)442 358 y FQ(1)p FP(.)60 503 y Fd(Pr)o(oof)12 b(of)h(Pr)o(oposition)f(4.20.)68 b FQ(Let)11 b FF(\026)j FE(2)h(G)e FQ(and)f FF(\027)18 b FE(2)c FF(M)1242 510 y FH(+1)p FD(;inv)1352 503 y FE(n)q(G)s FQ(.)19 b(Then,)12 b(b)o(y)f(Prop)q(osition)60 563 y(2.48\(b\),)j(\(1)t FE(\000)t FF(\025)p FQ(\))p FF(\026)t FQ(+)t FF(\025\027)23 b(=)-30 b FE(2)14 b(G)i FQ(for)d(0)h FF(<)g(\025)g FE(\024)g FQ(1.)20 b(But)12 b(\(1)t FE(\000)t FF(\025)p FQ(\))p FF(\026)t FQ(+)t FF(\025\027)18 b FE(!)c FF(\026)f FQ(w)o(eakly)e(as)j FF(\025)g FE(#)g FQ(0.)20 b(Hence)60 623 y FE(G)15 b FQ(cannot)f(con)o(tain)f(an)o(y)f(op)q(en)i(neigh)o(b)q(orho) q(o)q(d)g(of)g FF(\026)p FQ(.)20 b([In)12 b(this)h(pro)q(of)h(w)o(e)e(could)h (equally)e(w)o(ell)h(ha)o(v)o(e)60 684 y(tak)o(en)k FF(\027)k FQ(to)d(b)q(e)g(a)g(Gibbs)g(measure)e(for)i(an)g(in)o(teraction)f(not)h(ph)o (ysically)e(equiv)m(alen)o(t)g(to)i(the)g(one)60 744 y(for)i(whic)o(h)e FF(\026)i FQ(is)f(Gibbsian,)h(and)g(then)f(apply)g(Prop)q(osition)h (2.48\(b\))h(and)e(the)h(Gri\016ths-Ruelle)60 804 y(theorem.])p 400 808 25 34 v 60 951 a Fd(Pr)o(oof)f(of)h(Pr)o(oposition)f(4.21.)70 b FF(M)867 958 y FH(+1)p FD(;inv)976 951 y FQ(\(\012\))17 b(is)f(compact,)g (so)h(w)o(e)f(need)h(only)f(sho)o(w)i(that)60 1012 y FE(E)86 1019 y FD(S)125 1012 y FQ(is)c(closed.)20 b(Let)13 b FF(\026)447 1019 y FD(n)485 1012 y FQ(b)q(e)g(an)h(equilibrium)c(measure)j(for)g(\010) 1163 1019 y FD(n)1201 1012 y FE(2)h FF(S)s FQ(,)g(with)f FF(\026)1446 1019 y FD(n)1484 1012 y FE(!)g FF(\026)h FQ(w)o(eakly)l(.)19 b(Then,)60 1072 y(since)13 b FF(S)j FQ(is)d(compact,)g(there)f(exists)h(a)h (subsequence)f(\010)1075 1079 y FD(n)1096 1084 y Fs(i)1125 1072 y FQ(that)h(con)o(v)o(erges)e(\(in)h FE(B)1551 1054 y FH(0)1584 1072 y FQ(norm\))f(to)i(some)60 1132 y(\010)g FE(2)g FF(S)s FQ(.)21 b(But)16 b(then)g FF(\026)h FQ(is)f(an)h(equilibrium)12 b(measure)j(for)i(\010.)p 1306 1136 V 60 1280 a Fd(Pr)o(oof)j(of)h(Pr)o (oposition)f(4.22.)77 b FQ(The)19 b(\014rst)g(statemen)o(t)e(is)i(an)g(imme)o (diate)d(consequence)60 1340 y(of)f(Prop)q(ositions)h(4.20)g(and)g(4.21.)21 b(The)15 b(second)g(statemen)o(t)e(follo)o(ws)i(from)f(Prop)q(osition)i (2.39\(b\).)p 178 1404 V 133 1504 a(W)l(e)22 b(thank)h(S.R.S.)d(V)l(aradhan)k (for)e(suggesting)h(these)f(latter)g(results)g(and)g(sk)o(etc)o(hing)f(the)60 1564 y(pro)q(ofs.)60 1772 y FG(5)83 b(Discussion)60 1896 y FB(5.1)70 b(Nume)o(ric)o(all)o(y)20 b(Observ)n(ed)j(Discon)n(tin)n(uiti)o(es) d(of)j(the)f(R)n(G)h(Map)60 1989 y FM(5.1.1)55 b(Statemen)n(t)17 b(of)i(the)f(Problem)60 2081 y FQ(In)13 b(sev)o(eral)e(Mon)o(te)i(Carlo)g (renormalization)e(group)j(\(MCR)o(G\))f(studies)f([33)q(,)g(233)q(,)h(72)q (,)f(163)q(],)h(it)f(has)60 2141 y(b)q(een)g(found)h(that)g(the)f(n)o (umerically)d(computed)i(renormalization)g(transformation)h FE(R)p FQ(:)k FF(H)i FE(7!)c FF(H)1878 2123 y Fy(0)60 2202 y FQ(is)k FP(disc)n(ontinuous)24 b FQ(at)19 b(a)g(\014rst-order)g (phase-transition)h(surface.)1280 2183 y FH(64)1345 2202 y FQ(Ho)o(w)o(ev)o(er,)d(this)i(b)q(eha)o(vior)f(is)p 60 2242 732 2 v 100 2296 a FA(64)135 2311 y Fz(The)i(mo)q(dels)f(in)h(whic)o(h)g (this)h(b)q(eha)o(vior)f(has)g(b)q(een)h(\(at)g(least)f(ten)o(tativ)o(ely\))g (observ)o(ed)h(include)g(the)g(t)o(w)o(o-)60 2361 y(dimensional)10 b(Ising)i(mo)q(del)f(at)h(lo)o(w)f(temp)q(erature)i([72)o(],)f(the)g (10-state)h(P)o(otts)f(mo)q(del)f(in)h(t)o(w)o(o)g(dimensions)f([72)o(],)g (the)60 2411 y(3-state)i(P)o(otts)g(mo)q(del)f(in)g(three)i(dimensions)d([33) o(],)h(the)i Fv(Z)978 2417 y FA(2)1009 2411 y Fz(lattice)f(gauge)g(theory)g (in)f(four)h(dimensions)e([163)o(])h(and)60 2461 y(the)g Fv(U)5 b Fz(\(1\))11 b(lattice)g(gauge)g(theory)g(in)g(four)g(dimensions)f([233)o(,) g(72].)16 b(Ho)o(w)o(ev)o(er,)c(in)f(a)g(more)f(recen)o(t)j(study)e(of)g(the) h(t)o(w)o(o-)60 2510 y(dimensional)j(Ising)i(mo)q(del)e(at)i(lo)o(w)f(temp)q (erature)i([165)o(],)f(the)h(observ)o(ed)g(discon)o(tin)o(uit)o(y)e(w)o(as)h (alw)o(a)o(ys)f(less)i(than)60 2560 y(the)h(estimated)e(truncation)h(error,)i (and)d(it)h(decreased)i(as)e(more)f(terms)h(w)o(ere)h(included)f(in)f(the)i (renormalized)60 2610 y(Hamiltonian;)d(this)i(w)o(as)g(in)o(terpreted)h(as)f (evidence)h(against)e(a)h(discon)o(tin)o(uit)o(y)f(in)g(the)i(exact)f (renormalization)60 2660 y(map.)938 2784 y FQ(153)p eop %%Page: 154 154 bop 60 91 a FP(rigor)n(ously)17 b(exclude)n(d)24 b FQ(b)o(y)17 b(our)g(Second)g(F)l(undamen)o(tal)f(Theorem)g(\(Theorem)f(3.6\).)24 b(In)17 b(this)g(sec-)60 152 y(tion)11 b(w)o(e)g(w)o(ould)g(lik)o(e)e(to)j (o\013er)g(our)f(in)o(terpretation)g(of)g(the)g(n)o(umerically)d(observ)o(ed) i(discon)o(tin)o(uities.)133 212 y(A)16 b(MCR)o(G)f(study)h([337)q(,)f(338)r (])g(pro)q(ceeds)h(as)h(follo)o(ws:)k(W)l(e)15 b(c)o(ho)q(ose)i(an)f (original)g(Hamiltonian)60 272 y FF(H)t FQ(,)e(and)h(generate)e(a)i(long)f (sequence)f(of)h(random)f(samples)g FF(!)1198 279 y FH(1)1218 272 y FF(;)8 b(!)1270 279 y FH(2)1290 272 y FF(;)g(:)g(:)g(:)13 b FQ(from)g(the)g(Gibbs)h(measure)60 332 y FF(\026)g FQ(=)g(const)d FE(\002)g FF(e)350 314 y Fy(\000)p FD(H)427 332 y FQ(using)17 b(some)e(Mon)o(te)h(Carlo)g(pro)q(cedure.)22 b(On)16 b(eac)o(h)g(of)g(these)g (\\original-spin")60 392 y(con\014gurations)j FF(!)406 399 y FD(i)439 392 y FQ(w)o(e)e(apply)h(the)g(renormalization)e(map)i FF(T)24 b FQ(to)18 b(generate)g(the)g(corresp)q(onding)60 452 y(blo)q(c)o(k-spin)c(con\014guration)h FF(!)615 434 y Fy(0)613 465 y FD(i)628 452 y FQ(.)20 b(In)15 b(this)f(w)o(a)o(y)g(w)o(e)g(ha)o(v)o(e) f(generated)h(a)h(random)f(sample)f FF(!)1721 434 y Fy(0)1719 465 y FH(1)1739 452 y FF(;)8 b(!)1793 434 y Fy(0)1791 465 y FH(2)1811 452 y FF(;)g(:)g(:)g(:)60 513 y FQ(from)22 b(the)g(renormalized)f (measure)h FF(\026)795 495 y Fy(0)832 513 y FQ(=)j FF(\026T)7 b FQ(.)41 b(It)22 b(is)h(no)o(w)g FP(assume)n(d)28 b FQ(that)23 b FF(\026)1583 495 y Fy(0)1618 513 y FQ(is)g(the)g(Gibbs)60 573 y(measure)17 b(for)i(some)e(renormalized)f(Hamiltonian)g FF(H)1071 555 y Fy(0)1101 573 y FQ(b)q(elonging)j(to)g(a)g(\014xed)f (\014nite-parameter)60 633 y(family)10 b FF(H)t FQ(\()p FF(\025)296 640 y FH(1)317 633 y FF(;)e(:)g(:)g(:)f(;)h(\025)454 640 y FD(N)488 633 y FQ(\),)13 b(and)g(some)e(statistical)h(metho)q(d)g([339)q(,)g (164)q(,)g(9])g(is)g(emplo)o(y)o(ed)e(to)j(estimate)60 693 y(the)j(unkno)o(wn)h(parameters)e FF(\025)633 700 y FH(1)653 693 y FF(;)8 b(:)g(:)g(:)f(;)h(\025)790 700 y FD(N)824 693 y FQ(.)133 753 y(Suc)o(h)16 b(a)h(pro)q(cedure)f(has)h(three)f(sources)g(of)h (error:)114 855 y(1\))25 b(Statistical)16 b(error)g(arising)g(from)f(the)h (\014nite)g(Mon)o(te)g(Carlo)h(sample.)114 957 y(2\))25 b(Systematic)16 b(error)i(arising)g(from)f(the)h(\014nite)g(lattice)e(size.)26 b(\(W)l(e)18 b(tak)o(e)f(the)h(p)q(oin)o(t)g(of)h(view)182 1017 y(that)e(our)f(goal)h(is)f(to)h(learn)f(ab)q(out)h(the)f(b)q(eha)o(vior) h(of)f(the)g FP(in\014nite-volume)23 b FQ(system.\))114 1119 y(3\))i(Systematic)9 b(error)j(arising)f(from)g(truncation)g(of)h(the)f (renormalized)e(Hamiltonian:)17 b FF(\026)1777 1101 y Fy(0)1801 1119 y FQ(ma)o(y)182 1179 y(not)g(b)q(e)g(\(in)f(fact,)h(in)f(almost)g(all)g (cases)h(is)g(not\))g(a)g(Gibbs)g(measure)e(for)i(an)o(y)g(Hamiltonian)182 1239 y(in)g(the)h(assumed)f FF(N)5 b FQ(-parameter)17 b(family)l(.)24 b(W)l(e)17 b(include)g(here)g(the)h(p)q(ossibilit)o(y)f(|)g(studied)182 1299 y(in)k(detail)f(in)h(Section)g(4)g(|)g(that)h FF(\026)877 1281 y Fy(0)910 1299 y FQ(is)f(not)h(the)f(Gibbs)h(measure)d(for)j FP(any)k FQ(reasonable)182 1359 y(Hamiltonian.)60 1461 y(It)14 b(is)f(useful)h(to)g(study)g(these)g(three)f(sources)i(of)f(error)g FP(sep)n(ar)n(ately)t FQ(.)20 b(In)14 b(particular,)f(w)o(e)h(w)o(ould)g(lik) o(e)60 1521 y(to)i(study)f(the)g(problem)f(of)i(truncation)f(of)h(the)f (renormalized)e(Hamiltonian,)g(indep)q(enden)o(tly)h(of)60 1582 y(the)19 b(problems)f(of)h(statistical)g(and)g(\014nite-size)f(errors.) 30 b(Therefore,)19 b(w)o(e)g(b)q(egin)g(b)o(y)f(form)o(ulating)60 1642 y(an)g FP(ide)n(alize)n(d)g(mo)n(del)23 b FQ(of)17 b(the)h (parameter-estimation)c(problem)i(in)h(whic)o(h)g(w)o(e)g(assume)f(that)i (the)60 1702 y(exp)q(erimen)o(ter)11 b(kno)o(ws)j FP(exactly)20 b FQ(the)13 b(exp)q(ectation)h(v)m(alues)g(of)g(an)g(appropriate)h(set)e(of)i (observ)m(ables)60 1762 y(\(to)k(b)q(e)f(sp)q(eci\014ed)g(later\))g(in)g(the) g FP(in\014nite-volume)25 b FQ(renormalized)16 b(measure)h FF(\026)1539 1744 y Fy(0)1551 1762 y FQ(.)27 b(This)19 b(idealized)60 1822 y(situation)j(can)f(b)q(e)h(appro)o(ximated)e(to)i(arbitrary)f(accuracy) g(with)h(su\016cien)o(t)e(computer)g(time,)60 1883 y(b)o(y)j(making)e(long)j (Mon)o(te)f(Carlo)g(runs)h(on)f(large)g(systems.)41 b(\(In)23 b(principle)e(w)o(e)i(should)g(then)60 1943 y(discuss)17 b(the)f FP(stability)21 b FQ(of)c(our)g(theory)f(relativ)o(e)f(to)i(small)d (statistical)i(or)h(\014nite-size)e(errors.)22 b(But)60 2003 y(w)o(e)d(feel)g(that)h(our)g(considerations)g(are)g(still)f(to)q(o)i (preliminary)c(to)j(justify)f(en)o(tering)g(in)o(to)g(suc)o(h)60 2063 y(tec)o(hnicalities.\))60 2193 y FM(5.1.2)55 b(An)19 b(Idealized)f(Mo)r (del)f(of)i(P)n(arameter)e(Estimation)60 2285 y FQ(Let)j(us)h(\014rst)f (consider)g(the)g(parameter-estimation)d(problem)i(in)h(a)g(general)g (probabilistic)f(\(=)60 2346 y(statistical-mec)o(hanical\))8 b(con)o(text,)j(without)g(regard)g(\(for)g(the)g(momen)o(t\))d(to)j(the)f (renormalization-)60 2406 y(group)20 b(application.)30 b(Let,)20 b(therefore,)f(\(\012)p FF(;)8 b FE(F)d FQ(\))19 b(b)q(e)h(an)f(arbitrary)h (measurable)e(space,)h(let)g Fi(F)g FQ(b)q(e)60 2466 y(some)d(family)e(of)j (probabilit)o(y)f(measures)g(on)h(\(\012)p FF(;)8 b FE(F)d FQ(\),)17 b(and)g(let)f FF(\032)h FQ(b)q(e)g(another)g(probabilit)o(y)f(mea-) 60 2526 y(sure)h(on)h(\(\012)p FF(;)8 b FE(F)d FQ(\).)24 b(W)l(e)17 b(wish)h(to)g(\014nd)f(the)g(measure)f(in)h Fi(F)g FQ(whic)o(h)g(is)g(in)g (some)g(sense)g(\\closest)g(to")60 2586 y(\(or)i(\\b)q(est)g(appro)o (ximates"\))e FF(\032)p FQ(.)28 b(Ho)o(w)18 b(should)h(w)o(e)f(de\014ne)g (\\closeness"?)29 b(An)o(y)18 b(de\014nition)f(is,)i(of)60 2646 y(course,)c(somewhat)h(arbitrary)l(,)f(but)h(w)o(e)g(claim)d(that)j(the) g(follo)o(wing)g(de\014nition)f(is)g(v)o(ery)g(natural:)938 2784 y(154)p eop %%Page: 155 155 bop 182 97 a FQ(The)23 b(measure)e(in)h Fi(F)h FQ(closest)f(to)h FF(\032)p FQ(,)h(denoted)f FF(\032)1105 79 y Fh(F)1131 97 y FQ(,)h(is)e(the)h(one)f(whic)o(h)g(minimi)o(zes)182 157 y(the)17 b(relativ)o(e)e(en)o(trop)o(y)i FF(I)t FQ(\()p FF(\032)p FE(j)8 b(\001)g FQ(\),)17 b(assuming)f(that)i(a)g(minim)o(iz)o(er)c(with)j(\014nite) g(relativ)o(e)182 217 y(en)o(trop)o(y)e(exists)h(\(it)g(ma)o(y)f(or)h(ma)o(y) f(not)i(b)q(e)f(unique\).)60 319 y(Note)21 b(that)g(the)g(unkno)o(wn)g (measure)f(is)h(tak)o(en)f(here)h(as)g(the)g(reference)f(measure)f(\(second)i (ar-)60 379 y(gumen)o(t\))c(in)h(the)g(relativ)o(e)f(en)o(trop)o(y)l(.)749 361 y FH(65)813 379 y FQ(In)h(supp)q(ort)h(of)g(this)f(de\014nition,)g(w)o(e) g(cite)f(the)h(follo)o(wing)60 439 y(prop)q(erties:)133 499 y(1\))i(If)f FF(\032)g FE(2)h Fi(F)p FQ(,)f(then)h FF(\032)546 481 y Fh(F)591 499 y FQ(=)f FF(\032)p FQ(,)h(uniquely)l(.)29 b(This)20 b(is)f(a)h(rather)f(trivial)f(prop)q(ert)o(y)l(,)i(but)f(it)g(is)h (at)60 560 y(least)c(a)h FP(ne)n(c)n(essary)j FQ(condition)c(for)h(an)o(y)f (reasonable)g(de\014nition)g(of)h(\\closeness".)133 620 y(2\))26 b(Supp)q(ose)g(that)g(one)g(generates)f(a)h(large)g(random)f(sample)f(from)g FF(\032)p FQ(,)k(and)e(constructs)60 680 y(maxim)o(um)n(-lik)n(el)o(iho)q(o)q (d)21 b(estimates)h([325])h(based)g(on)g(the)g(\(false\))f(assumption)h(that) g(the)f(sam-)60 740 y(ple)15 b(arose)h(from)f(some)g(measure)f(in)h Fi(F)p FQ(.)21 b(In)15 b(the)h(large-sample)e(limit,)f(this)i(maxim)o(um)o (-li)o(k)o(e)o(li)o(ho)q(o)q(d)60 800 y(estimate)g(will)i(con)o(v)o(erge)f (to)i FF(\032)636 782 y Fh(F)661 800 y FQ(.)25 b(This)17 b(can)h(b)q(e)f(pro) o(v)o(en)g(under)g(suitable)g(tec)o(hnical)f(h)o(yp)q(otheses)60 861 y([196)q(],)g(but)h(it)g(is)f(easy)h(to)h(see)e(in)o(tuitiv)o(ely)e(wh)o (y)j(it)f(is)h(true:)23 b(the)16 b(relativ)o(e)f(en)o(trop)o(y)i FF(I)t FQ(\()p FF(\032)p FE(j)p FF(\027)s FQ(\))f(is,)h(up)60 921 y(to)i(an)g(additiv)o(e)e(constan)o(t,)i(precisely)e(min)o(us)f(the)j (mean)e(\(under)h(the)h(true)f(measure)f FF(\032)p FQ(\))h(of)h(the)60 981 y(log)e(lik)o(eliho)q(o)q(d)e(function:)605 1113 y FF(I)t FQ(\()p FF(\032)p FE(j)p FF(\027)s FQ(\))41 b(=)856 1054 y Fx(Z)905 1113 y FF(d\032)18 b FQ(log)1050 1079 y FF(d\032)p 1049 1101 53 2 v 1049 1147 a(d\027)776 1222 y FQ(=)42 b(const)11 b FE(\000)1028 1164 y Fx(Z)1078 1222 y FF(d\032)17 b FQ(log)9 b(\\)p FF(d\027)s FQ(")15 b FF(;)445 b FQ(\(5.1\))60 1344 y(so)20 b(maximi)o(zing)c(the)j(lik)o(eliho)q(o)q(d)g(is)g(equiv)m(alen)o(t)e(to)j (minimi)o(zi)o(ng)d(the)i(relativ)o(e)f(en)o(trop)o(y)l(.)29 b(Th)o(us,)60 1405 y FF(\032)85 1387 y Fh(F)128 1405 y FQ(is)18 b(the)f(estimate)f(that)i(w)o(ould)f(b)q(e)h(generated)g(b)o(y)f(an)h(exp)q (erimen)o(ter)c(p)q(ossessing)19 b(an)f FP(in\014nite)60 1465 y FQ(random)g(sample)e(from)h FF(\032)h FQ(and)h(using)g(the)e FP(optimal)24 b FQ(estimation)16 b(metho)q(d)i(\(namely)l(,)e(maxim)n(um)60 1525 y(lik)o(eliho)q(o)q(d\).)300 1507 y FH(66)376 1525 y FQ(\(Note)22 b(also)h(that)f(the)g(maxim)o(um)o(-li)o(k)n(eli)o(ho)q(o)q(d)f(estimate)g (for)h(a)h FP(\014nite)k FQ(sample)60 1585 y FF(!)90 1592 y FH(1)110 1585 y FF(;)8 b(:)g(:)g(:)f(;)h(!)249 1592 y FD(n)296 1585 y FQ(is)23 b(the)f(measure)g(in)g Fi(F)g FQ(closest)h(to)g(the)g FP(empiric)n(al)28 b FQ(measure)21 b FF(L)1523 1592 y FD(n)1572 1585 y FE(\021)j FF(n)1664 1567 y Fy(\000)p FH(1)1720 1552 y Fx(P)1764 1565 y FD(n)1764 1597 y(i)p FH(=1)1831 1585 y FF(\016)1853 1592 y FD(!)1875 1597 y Fs(i)60 1645 y FQ(for)17 b(the)e(giv)o(en)h(sample.)k (This)c(close)g(relation)g(b)q(et)o(w)o(een)f(maxim)o(um)n(-lik)n(el)o(iho)q (o)q(d)g(estimation)f(and)60 1706 y(relativ)o(e)g(en)o(trop)o(y)i(has)h(b)q (een)f(noticed)g(b)o(y)g(previous)g(authors.\))133 1766 y(Supp)q(ose)f(no)o (w)g(that)g(the)f(set)g Fi(F)g FQ(is)g(of)g(the)g(Boltzmann-Gibbs)f(form)h (\(=)g(exp)q(onen)o(tial)f(family\))429 1913 y Fi(F)28 b FQ(=)550 1840 y Fx(\()584 1913 y FF(\027)608 1920 y FD(\025)653 1913 y FE(\021)21 b FF(Z)t FQ(\()p FF(\025)p FQ(\))816 1892 y Fy(\000)p FH(1)881 1913 y FQ(exp)955 1840 y Fx(")979 1913 y FE(\000)1041 1859 y FD(N)1026 1871 y Fx(X)1028 1963 y FD(i)p FH(=1)1095 1913 y FF(\025)1123 1920 y FD(i)1137 1913 y FF(H)1177 1920 y FD(i)1192 1840 y Fx(#)1233 1913 y FF(\026)1262 1892 y FH(0)1282 1913 y FQ(:)35 b FF(\025)14 b FE(2)g Fq(R)1454 1892 y FD(N)1487 1840 y Fx(\))1790 1913 y FQ(\(5)p FF(:)p FQ(2\))60 2060 y(for)g(some)e(sp)q (eci\014ed)h(family)f FF(H)632 2067 y FH(1)652 2060 y FF(;)c(:)g(:)g(:)f(;)h (H)801 2067 y FD(N)849 2060 y FQ(and)14 b FP(a)h(priori)i FQ(measure)12 b FF(\026)1336 2042 y FH(0)1356 2060 y FQ(.)21 b(W)l(e)13 b(can)h(assume)f (without)60 2120 y(loss)20 b(of)f(generalit)o(y)f(that)h(the)g(functions)g(1) p FF(;)8 b(H)936 2127 y FH(1)957 2120 y FF(;)g(:)g(:)g(:)f(;)h(H)1106 2127 y FD(N)1159 2120 y FQ(are)19 b(linearly)f(indep)q(enden)o(t)g(\()p FF(\026)1748 2102 y FH(0)1768 2120 y FQ(-a.e.\).)p 60 2167 732 2 v 100 2221 a FA(65)135 2236 y Fz(This)c(follo)o(ws)372 2225 y(\024)368 2236 y(Cenco)o(v)h([61)o(].)20 b(\(Note,)15 b(ho)o(w)o(ev)o(er,)g(that)1007 2225 y(\024)1003 2236 y(Cenco)o(v's)g (notation)e(for)i(the)g(argumen)o(ts)f(of)g Fv(I)s Fz(\()7 b Fu(\001)g(j)g(\001)g Fz(\))14 b(is)60 2286 y(the)i(rev)o(erse)g(of)f (ours.\))21 b(By)16 b(con)o(trast,)f(Csiszar)h([68)o(,)e(69])g(considers)i (the)g(quite)f(di\013eren)o(t)h(problem)d(in)i(whic)o(h)f(the)60 2335 y(unkno)o(wn)g(measure)f(is)h(the)h(\014rst)f(argumen)o(t)f(in)g(the)i (relativ)o(e)f(en)o(trop)o(y)m(.)100 2393 y FA(66)135 2408 y Fz(This)20 b(assertion)i(is)e(p)q(erhaps)i(somewhat)e(misleading:)29 b(The)21 b(maxim)n(um)o(-)o(lik)n(eliho)q(o)q(d)c(metho)q(d)j(is)h(optimal)60 2458 y(as)c(regards)h Fw(statistic)n(al)i Fz(errors)f(\(in)d(the)i (large-sample)e(limit\))e([325)o(],)j(while)f(here)j(w)o(e)e(are)h(concerned) h(with)d(the)60 2508 y Fw(systematic)21 b Fz(errors)e(due)g(to)g(truncation.) 32 b(Indeed,)20 b(the)f(problem)e(here)j(is)e(to)g Fw(de\014ne)23 b Fz(what)18 b(w)o(e)h(mean)e(b)o(y)h(the)60 2558 y(\\optimal")7 b(truncation.)17 b(In)10 b(an)o(y)g(case,)h(w)o(e)f(claim)e(that)i(maxim)n (um)o(-l)o(ik)o(eli)o(ho)q(o)q(d)d(estimation)i(is)h(a)f(sensible)i (idealized)60 2608 y(mo)q(del)h(of)i(what)f(a)h(go)q(o)q(d)f(exp)q(erimen)o (ter)i(w)o(ould)e(actually)g(do)h(if)f(he/she)i(could.)938 2784 y FQ(155)p eop %%Page: 156 156 bop 60 91 a FQ(Then)16 b(the)g(relativ)o(e)f(en)o(trop)o(y)497 234 y FF(I)t FQ(\()p FF(\032)p FE(j)p FF(\027)605 241 y FD(\025)627 234 y FQ(\))28 b(=)g(log)9 b FF(Z)t FQ(\()p FF(\025)p FQ(\))20 b(+)1005 180 y FD(N)991 193 y Fx(X)992 284 y FD(i)p FH(=1)1059 234 y FF(\025)1087 241 y FD(i)1110 176 y Fx(Z)1151 234 y FF(H)1191 241 y FD(i)1214 234 y FF(d\032)g FQ(+)f(const)338 b(\(5)p FF(:)p FQ(3\))60 387 y(is)16 b(a)g(strictly)e(con)o(v)o(ex)h(function)g(of)i FF(\025)p FQ(;)f(in)f(particular,)g(the)h(measure)e FF(\032)1371 369 y Fh(F)1413 387 y FQ(is)i(unique)f(if)g(it)g(exists)h(at)60 447 y(all)112 429 y FH(67)149 447 y FQ(,)g(and)g(it)g(is)g(de\014ned)g(b)o(y) g(the)g(conditions)566 556 y FE(h)p FF(H)625 563 y FD(i)640 556 y FE(i)659 563 y FD(\027)676 569 y Fs(\025)727 556 y FQ(=)27 b FE(h)p FF(H)851 563 y FD(i)866 556 y FE(i)885 563 y FD(\032)954 556 y FQ(for)17 b(all)f FF(i)d FQ(=)h(1)p FF(;)8 b(:)g(:)g(:)g(;)g(N)19 b(:)405 b FQ(\(5)p FF(:)p FQ(4\))133 713 y(The)13 b(foregoing)g(theory)f(is)g (adequate)h(for)f(parameter)g(estimation)e(in)j FP(\014nite-volume)19 b FQ(systems;)60 773 y(but)f(for)h(in\014nite-v)o(olume)c(systems)i(it)g(is)h (inapplicable,)f(b)q(ecause)h(the)g(relativ)o(e)e(en)o(trop)o(y)i(of)g(t)o(w) o(o)60 833 y(translation-in)o(v)m(arian)o(t)e(measures)f(is)g(in)h(nearly)f (all)h(cases)g(+)p FE(1)p FQ(.)k(The)c(problem)f(here)g(is)g(that,)h(as)60 893 y(discussed)c(in)f(Section)h(2.6,)g(the)g(relativ)o(e)e(en)o(trop)o(y)h (in)h(v)o(olume)d(\003)j(t)o(ypically)e(gro)o(ws)j(prop)q(ortionally)60 954 y(to)21 b(the)f(v)o(olume)e(\(unless)i(the)g(t)o(w)o(o)g(measures)f(happ) q(en)j(to)e(b)q(e)h(Gibbs)f(measures)f(for)i(the)f(same)60 1014 y(in)o(teraction\).)f(This)13 b(v)o(olume)e(factor)i(is)g(unin)o (teresting)f(in)h(the)g(presen)o(t)f(con)o(text,)g(b)q(ecause)i(it)e(do)q(es) 60 1074 y(not)17 b(dep)q(end)f(on)h(the)f(parameters)f FF(\025)i FQ(o)o(v)o(er)e(whic)o(h)h(w)o(e)g(w)o(an)o(t)g(to)h(optimize.)h(Therefore,)e (it)g(mak)o(es)60 1134 y(sense)h(to)g(just)g(divide)f(out)h(this)g(v)o(olume) e(factor)i(and)g(minimi)o(ze)d(the)i(relativ)o(e)f(en)o(trop)o(y)i FP(density)t FQ(.)60 1194 y(That)g(is,)f(if)f Fi(F)f FE(\032)f FF(M)430 1201 y FH(+1)p FD(;inv)539 1194 y FQ(\(\012\))k(and)g FF(\032)d FE(2)g FF(M)857 1201 y FH(+1)p FD(;inv)966 1194 y FQ(\(\012\),)i(w)o(e)f(de\014ne:)182 1299 y(The)23 b(measure)e(in)h Fi(F)h FQ(closest)f(to)h FF(\032)p FQ(,)h(denoted)f FF(\032)1105 1281 y Fh(F)1131 1299 y FQ(,)h(is)e(the)h(one)f(whic)o(h)g(minimi)o(zes)182 1360 y(the)g(relativ)o(e)e(en)o(trop)o(y)h(densit)o(y)g FF(i)p FQ(\()p FF(\032)p FE(j)8 b(\001)g FQ(\),)22 b(assuming)g(that)g(these)g (relativ)o(e)e(en)o(trop)o(y)182 1420 y(densities)15 b(are)i(w)o (ell-de\014ned)e(and)h(that)h(a)g(minim)o(ize)o(r)d(with)i(\014nite)f (relativ)o(e)g(en)o(trop)o(y)182 1480 y(densit)o(y)g(exists)h(\(it)g(ma)o(y)e (or)j(ma)o(y)e(not)h(b)q(e)h(unique\).)133 1580 y(Supp)q(ose)h(no)o(w)g(that) g Fi(F)f FQ(is)g(the)g(set)g(of)g(translation-in)o(v)m(arian)o(t)h(Gibbs)f (measures)f(for)i(in)o(terac-)60 1640 y(tions)e(\010)e FE(2)g FF(V)26 b FQ(\(and)16 b FP(a)h(priori)i FQ(measure)14 b FF(\026)843 1622 y FH(0)863 1640 y FQ(\),)h(where)g FF(V)25 b FQ(=)14 b(span)q(\(\010) 1308 1647 y FH(1)1328 1640 y FF(;)8 b(:)g(:)g(:)f(;)h FQ(\010)1472 1647 y FD(N)1506 1640 y FQ(\))15 b(is)g(some)g(sp)q(eci\014ed)60 1701 y(\014nite-dimensional)f(linear)i(subspace)g(of)h FE(B)883 1683 y FH(1)902 1701 y FQ(.)k(Then,)16 b(from)f(\(2.96\))i(w)o(e)f(ha)o(v)o (e)522 1824 y FF(i)p FQ(\()p FF(\032)p FE(j)p FF(\027)s FQ(\))42 b(=)g FF(p)p FQ(\()p FE(\000)p FF(f)871 1831 y FH(\010)898 1824 y FE(j)p FF(\026)941 1803 y FH(0)961 1824 y FQ(\))20 b(+)1057 1765 y Fx(Z)1098 1824 y FF(f)1122 1831 y FH(\010)1158 1824 y FF(d\032)g FQ(+)f FF(i)p FQ(\()p FF(\032)p FE(j)p FF(\026)1389 1803 y FH(0)1409 1824 y FQ(\))684 1912 y FE(\021)42 b FF(F)797 1919 y FD(\032)816 1912 y FQ(\(\010\))901 b(\(5.5\))60 2020 y(whenev)o(er)11 b FF(\027)k FQ(is)c(a)h(Gibbs)g(measure)f(for)h(\010.)20 b(Th)o(us,)12 b FF(i)p FQ(\()p FF(\032)p FE(j)p FF(\027)s FQ(\))g(dep)q(ends) g(on)g FF(\027)j FQ(only)d(via)f(the)h(in)o(teraction)60 2080 y(\010;)19 b(in)g(fact,)f FF(F)332 2087 y FD(\032)352 2080 y FQ(\(\010\))h(is)f(precisely)e(the)j(amoun)o(t)e(b)o(y)h(whic)o(h)g(the)h (pair)f(\()p FF(\032;)8 b FQ(\010\))19 b(fails)f(to)h(satisfy)f(the)60 2140 y(v)m(ariational)24 b(principle.)42 b(Therefore,)25 b(if)e(one)h(Gibbs)f (measure)g(for)h(\010)g(happ)q(ens)h(to)f(minim)o(iz)o(e)60 2201 y FF(i)p FQ(\()p FF(\032)p FE(j)8 b(\001)g FQ(\),)16 b(then)g(all)f (Gibbs)i(measures)e(for)h(\010)h(do)f(so.)22 b(So)17 b(the)f FP(me)n(asur)n(e)j FQ(in)c Fi(F)h FQ(closest)g(to)h FF(\032)f FQ(ma)o(y)f(not)60 2261 y(b)q(e)j(unique.)25 b(Nev)o(ertheless,)15 b(the)j(corresp)q(onding)g FP(inter)n(action)k FQ(is)c(necessarily)f(unique)g (\(mo)q(dulo)60 2321 y(ph)o(ysical)22 b(equiv)m(alence\))f(if)h(it)g(exists)g (at)h(all)902 2303 y FH(68)939 2321 y FQ(,)h(b)q(ecause)f FF(F)1196 2328 y FD(\032)1239 2321 y FQ(is)f(strictly)g(con)o(v)o(ex)f(on)i FF(V)36 b FE(\032)25 b(B)1871 2303 y FH(1)p 60 2368 732 2 v 100 2422 a FA(67)135 2437 y Fz(The)17 b(minim)o(izer)d Fv(\032)440 2422 y Fh(F)483 2437 y Fz(could)i(fail)g(to)g(exist:)24 b(Consider,)17 b(for)f(example,)g(\012)g(=)g Fu(f\000)p Fz(1)p Fv(;)7 b Fz(1)p Fu(g)p Fz(,)16 b Fv(\026)1557 2422 y FA(0)1591 2437 y Fz(=)1645 2421 y FA(1)p 1645 2428 17 2 v 1645 2452 a(2)1666 2437 y Fz(\()p Fv(\016)1700 2443 y Fo(\000)p FA(1)1756 2437 y Fz(+)c Fv(\016)1818 2443 y FA(+1)1862 2437 y Fz(\),)60 2487 y Fv(\032)h Fz(=)f Fv(\016)156 2493 y Fo(\000)p FA(1)201 2487 y Fz(,)i Fv(N)j Fz(=)12 b(1)i(and)g Fv(H)472 2493 y FA(1)490 2487 y Fz(\()p Fv(!)q Fz(\))f(=)f Fv(!)q Fz(.)19 b(Then)c(the)g(minim)n(um)10 b(is)k(\\at)g Fv(\025)e Fz(=)h(+)p Fu(1)p Fz(";)g(there)i(is)g(no)f(minim)o (i)o(zer)f(at)h(\014nite)60 2537 y Fv(\025)p Fz(.)100 2595 y FA(68)135 2610 y Fz(Again,)f(a)h(minim)o(i)o(zer)f(could)h(fail)e(to)i (exist,)h(if)e(the)i(minim)n(um)10 b(is)k(\\at)g(in\014nit)o(y".)k(This)c(o)q (ccurs,)h(for)f(example,)60 2660 y(if)f Fv(\032)h Fz(is)g(a)g Fw(gr)n(ound-state)j Fz(measure)d(for)f(some)g(in)o(teraction)h(\010)e Fu(2)f Fv(V)e Fz(:)18 b(then)d Fv(F)1253 2666 y Fp(\032)1272 2660 y Fz(\()p Fv(\014)r Fz(\010\))d Fu(!)f Fz(0)j(as)g Fv(\014)g Fu(!)d Fz(+)p Fu(1)p Fz(.)938 2784 y FQ(156)p eop %%Page: 157 157 bop 60 91 a FQ(\(Prop)q(osition)19 b(2.59\).)25 b(This)18 b(is)f(go)q(o)q(d,) j(b)q(ecause)d(it)g(is)h(after)f(all)g(the)g(in)o(teraction)g(that)h(w)o(e)f (w)o(ould)60 152 y(lik)o(e)i(to)h(estimate.)32 b(No)o(w,)21 b(an)g(in)o(teraction)e(\010)930 133 y Fy(\003)970 152 y FQ(minimi)o(zes)e FF(F)1234 159 y FD(\032)1254 152 y Fm(\026)p FF(V)32 b FQ(if)19 b(and)i(only)f(if)g FF(\032)p Fm(\026)p FF(f)5 b FQ([)p FF(V)12 b FQ(])19 b(is)i(a)60 212 y(tangen)o(t)f(functional)f(at)h FF(f)560 219 y FH(\010)585 210 y Ft(\003)626 212 y FQ(to)g(the)f(pressure)h (restricted)e(to)i FF(f)5 b FQ([)p FF(V)12 b FQ(].)31 b([Here)18 b FF(f)5 b FQ([)p FF(V)11 b FQ(])19 b(denotes)h(the)60 272 y(image)12 b(of)h FF(V)24 b FQ(under)13 b(the)f(map)h(\011)g FE(7!)h FF(f)762 279 y FH(\011)791 272 y FQ(;)g(it)f(is)f(a)i(linear)e (subspace)h(of)g FF(C)t FQ(\(\012\).])20 b(No)o(w,)13 b(b)o(y)f(the)h(Hahn-) 60 332 y(Banac)o(h)19 b(theorem)412 314 y FH(69)448 332 y FQ(,)g(ev)o(ery)f (tangen)o(t)h(functional)g(to)g FF(p)p Fm(\026)p FF(f)5 b FQ([)p FF(V)12 b FQ(])18 b(can)i(b)q(e)f(extended)f(to)h(a)h(tangen)o(t)60 392 y(functional)13 b(to)h FF(p)p FQ(,)g(i.e.)e(to)i(an)g(equilibrium)c(\(=)k (Gibbs\))f(measure.)19 b(It)14 b(follo)o(ws)f(that)h(an)g(in)o(teraction)60 452 y(\010)95 434 y Fy(\003)131 452 y FQ(minim)o(ize)o(s)g FF(F)391 459 y FD(\032)410 452 y Fm(\026)p FF(V)28 b FQ(if)15 b(and)i(only)f(if)f(there)h(exists)f(a)h(translation-in)o(v)m(arian)o(t)h (Gibbs)f(measure)f FF(\027)60 513 y FQ(for)i(\010)170 495 y Fy(\003)206 513 y FQ(suc)o(h)f(that)564 573 y FE(h)p FF(f)607 580 y FH(\010)635 585 y FD(i)649 573 y FE(i)668 580 y FD(\027)717 573 y FQ(=)28 b FE(h)p FF(f)826 580 y FH(\010)854 585 y FD(i)868 573 y FE(i)887 580 y FD(\032)956 573 y FQ(for)17 b(all)f FF(i)d FQ(=)h(1)p FF(;)8 b(:)g(:)g(:)g(;)g(N)19 b(:)403 b FQ(\(5)p FF(:)p FQ(6\))133 696 y(What)16 b(happ)q(ens)h(if)e(w)o(e)g(consider)g (larger)g(and)h(larger)g(subspaces)g(of)g(in)o(teractions?)21 b(Let)15 b FF(V)1817 703 y FH(1)1851 696 y FE(\032)60 757 y FF(V)88 764 y FH(2)122 757 y FE(\032)f FF(:)8 b(:)g(:)16 b FQ(b)q(e)h(an)g(increasing)f(sequence)f(of)i(\014nite-dimensional)e(linear)g (subspaces)j(of)e FE(B)1713 739 y FH(1)1732 757 y FQ(,)g(whose)60 817 y(union)i(is)f(dense)g(in)h FE(B)475 799 y FH(1)494 817 y FQ(.)25 b(Let)17 b(\010)656 799 y Fy(\003)656 829 y FD(n)698 817 y FQ(b)q(e)g(the)h(in)o(teraction)e(in)h FF(V)1183 824 y FD(n)1225 817 y FQ(that)h(minim)o(ize)o(s)d FF(F)1593 824 y FD(\032)1613 817 y Fm(\026)p FF(V)1666 824 y FD(n)1690 817 y FQ(.)25 b(Then)17 b(it)60 877 y(is)f(natural)h(to)f(conjecture)g(the)g (follo)o(wing:)60 967 y FM(Conjecture)i(5.1)67 b FP(\(i\))24 b(If)g FF(\032)g FP(is)g(a)f(Gibbs)i(me)n(asur)n(e)e(for)g(some)h(inter)n (action)h FQ(\010)h FE(2)g(B)1740 949 y FH(1)1759 967 y FP(,)f(then)182 1027 y FQ(\010)217 1009 y Fy(\003)217 1040 y FD(n)254 1027 y FE(!)14 b FQ(\010)k FP(in)g FE(B)466 1009 y FH(1)502 1027 y FP(norm)f(as)g FF(n)d FE(!)g(1)p FP(.)88 1125 y(\(ii\))24 b(If)e FF(\032)h FP(is)g(not)g(a)g(Gibbs)g(me)n(asur)n(e)f(for)g(any)h(inter) n(action)h(in)f FE(B)1352 1107 y FH(1)1371 1125 y FP(,)h(then)f FE(k)p FQ(\010)1583 1107 y Fy(\003)1583 1138 y FD(n)1607 1125 y FE(k)1632 1134 y Fy(B)1656 1124 y Fr(1)1699 1125 y FE(!)h(1)e FP(as)182 1186 y FF(n)14 b FE(!)g(1)p FP(.)60 1276 y FQ(W)l(e)j(are)h(not)f (able)g(to)h(pro)o(v)o(e)f(this)g(m)o(uc)o(h)e(\(and)j(w)o(e)f(susp)q(ect)h (that)g(it)e(ma)o(y)g(not)i(b)q(e)g(true)f(without)60 1336 y(additional)f(h)o(yp)q(otheses\).)22 b(Regarding)16 b(conjecture)g(\(i\),)f (what)i(w)o(e)f(can)g(pro)o(v)o(e)g(is)g(the)g(follo)o(wing:)60 1435 y FM(Prop)r(osition)i(5.2)24 b FP(L)n(et)c FF(\032)g FP(b)n(e)h(an)f(er) n(go)n(dic)g(tr)n(anslation-invariant)h(me)n(asur)n(e)f(of)g(\014nite)h(entr) n(opy)60 1495 y(density)e(\(r)n(elative)h(to)e FF(\026)509 1477 y FH(0)529 1495 y FP(\);)i(and)e(let)i FF(V)777 1502 y FH(1)814 1495 y FE(\032)15 b FF(V)896 1502 y FH(2)933 1495 y FE(\032)h FF(:)8 b(:)g(:)18 b FP(b)n(e)h(an)g(incr)n(e)n(asing)g(se)n (quenc)n(e)h(of)f(subsets)g(of)60 1555 y FE(B)95 1537 y FH(0)114 1555 y FP(,)e(whose)h(union)h(is)e(dense)h(in)g FE(B)708 1537 y FH(0)727 1555 y FP(.)k(Then:)93 1645 y(\(a\))i(Ther)n(e)d(exists)h(an)f (inter)n(action)793 1629 y Fx(b)787 1645 y FQ(\010)g FE(2)f(B)931 1627 y FH(0)971 1645 y FP(\(not)i(ne)n(c)n(essarily)f(in)g FE(B)1426 1627 y FH(1)1445 1645 y FP(!\))33 b(for)21 b(which)h FF(\032)f FP(is)g(an)182 1706 y(e)n(quilibrium)d(me)n(asur)n(e.)95 1803 y(\(b\))25 b(L)n(et)270 1787 y Fx(b)264 1803 y FQ(\010)15 b FP(b)n(e)h(any)f(inter)n(action)h(in)g FE(B)801 1785 y FH(0)835 1803 y FP(for)f(which)g FF(\032)h FP(is)f(an)g(e)n(quilibrium)h(me)n(asur)n (e.)21 b(Then)16 b(ther)n(e)182 1864 y(exists)k(a)f(se)n(quenc)n(e)566 1848 y Fx(b)560 1864 y FQ(\010)595 1871 y FD(n)636 1864 y FE(2)e FF(V)714 1871 y FD(n)757 1864 y FP(which)i(c)n(onver)n(ges)h(to)1180 1848 y Fx(b)1174 1864 y FQ(\010)g FP(in)f FE(B)1325 1846 y FH(0)1363 1864 y FP(norm.)27 b(If,)19 b(in)g(addition,)1861 1848 y Fx(b)1855 1864 y FQ(\010)182 1924 y FP(b)n(elongs)i(to)f(some)g(sp)n (ac)n(e)g FE(B)702 1931 y FD(h)743 1924 y FE(\032)e(B)835 1906 y FH(0)874 1924 y FP(and)i FE([)1004 1906 y Fy(1)1004 1936 y FD(n)p FH(=1)1073 1924 y FF(V)1101 1931 y FD(n)1144 1924 y FP(is)g(dense)h(in)g FE(B)1432 1931 y FD(h)1474 1924 y FP(\(in)f FE(B)1589 1931 y FD(h)1631 1924 y FP(norm\),)g(then)182 1984 y(ther)n(e)d(exists)i(a)e(se)n(quenc)n(e)683 1968 y Fx(b)677 1984 y FQ(\010)712 1991 y FD(n)750 1984 y FE(2)d FF(V)825 1991 y FD(n)866 1984 y FP(which)k(c)n(onver)n(ges)g(to)1285 1968 y Fx(b)1279 1984 y FQ(\010)f FP(in)h FE(B)1424 1991 y FD(h)1464 1984 y FP(norm.)95 2082 y(\(c\))25 b(L)n(et)269 2066 y Fx(b)263 2082 y FQ(\010)14 b FP(b)n(e)g(any)g(inter)n(action)h(in)f FE(B)793 2064 y FH(0)826 2082 y FP(for)f(which)i FF(\032)f FP(is)f(an)i(e)n(quilibrium)f(me)n(asur)n(e,)g(and)g(let)h FQ(\()1818 2066 y Fx(b)1812 2082 y FQ(\010)1847 2089 y FD(n)1871 2082 y FQ(\))182 2142 y FP(b)n(e)j(any)g(se)n(quenc)n(e)i(c)n(onver)n(ging)f (to)840 2126 y Fx(b)834 2142 y FQ(\010)f FP(in)h FE(B)983 2124 y FH(0)1020 2142 y FP(norm.)k(Then)c FF(F)1331 2149 y FD(\032)1351 2142 y FQ(\()1376 2126 y Fx(b)1370 2142 y FQ(\010)1405 2149 y FD(n)1428 2142 y FQ(\))c FE(!)g FQ(0)p FP(.)24 b([In)19 b(p)n(articular,) 182 2202 y(we)f(have)30 b FQ(lim)366 2227 y FD(n)p Fy(!1)482 2202 y FQ(inf)467 2232 y FH(\010)p Fy(2)p FD(V)537 2236 y Fs(n)566 2202 y FF(F)598 2209 y FD(\032)617 2202 y FQ(\(\010\))14 b(=)g(0)p FP(.])93 2328 y(\(d\))24 b(Conversely,)18 b(let)g FQ(\()538 2312 y Fx(b)532 2328 y FQ(\010)567 2335 y FD(n)591 2328 y FQ(\))f FP(b)n(e)h(any)f(se)n(quenc)n(e)h(for)f(which)h FF(F)1224 2335 y FD(\032)1243 2328 y FQ(\()1268 2312 y Fx(b)1262 2328 y FQ(\010)1297 2335 y FD(n)1321 2328 y FQ(\))c FE(!)g FQ(0)j FP(and)g(which)h(c)n(onver)n (ges)182 2388 y(in)e FE(B)275 2370 y FH(0)309 2388 y FP(norm,)g(say)f(to)599 2372 y Fx(b)593 2388 y FQ(\010)628 2395 y Fy(1)666 2388 y FP(.)21 b(Then)16 b FF(\032)g FP(is)f(an)h(e)n(quilibrium)g(me)n(asur)n(e)f(for)1505 2372 y Fx(b)1499 2388 y FQ(\010)1534 2395 y Fy(1)1571 2388 y FP(.)22 b(In)16 b(p)n(articular,)182 2449 y(if)h FQ(\()p FE(k)279 2432 y Fx(b)273 2449 y FQ(\010)308 2456 y FD(n)332 2449 y FE(k)357 2457 y Fy(B)381 2448 y Fr(1)400 2449 y FQ(\))g FP(is)h(b)n(ounde)n(d,)f(then)804 2432 y Fx(b)798 2449 y FQ(\010)833 2456 y Fy(1)884 2449 y FE(2)d(B)966 2431 y FH(1)1002 2449 y FP(and)k FF(\032)g FP(is)f(a)g(Gibbs)h(me)n(asur)n(e)f(for)1642 2432 y Fx(b)1636 2449 y FQ(\010)1671 2456 y Fy(1)1708 2449 y FP(.)p 60 2491 732 2 v 100 2545 a FA(69)135 2560 y Fz(The)12 b(required)i(v)o(ersion)e(of)g(the)h(Hahn-Banac)o(h)f(theorem)g([313)o(,)g (p.)g(157,)f(A.3.2])g(can)h(b)q(e)h(deduced)h(easily)e(from)60 2610 y(the)17 b(separating-h)o(yp)q(erplane)h(v)o(ersion)f(\([315)o(,)g(p.)f (46,)h(Theorem)f(I)q(I.3.1])f(or)i([310)n(,)g(p.)g(58,)f(Theorem)h (3.4\(a\)]\))e(b)o(y)60 2660 y(considering)f(epigraphs.)938 2784 y FQ(157)p eop %%Page: 158 158 bop 133 91 a FQ(This)19 b(sho)o(ws)g(that)g(if)f FF(\032)g FQ(is)h(a)g(Gibbs)f(measure)f(for)i(\010)f FE(2)g(B)1233 73 y FH(1)1252 91 y FQ(,)g(then)h(there)e(exists)h(a)h(sequence)66 135 y Fx(b)60 152 y FQ(\010)95 159 y FD(n)133 152 y FE(2)14 b FF(V)208 159 y FD(n)245 152 y FQ(of)g FP(appr)n(oximate)j FQ(minim)o(iz)o(ers)11 b(whic)o(h)i(con)o(v)o(erges)f(\(in)i FE(B)1279 133 y FH(1)1311 152 y FQ(norm\))f(to)h(\010.)20 b(Unfortunately)l (,)60 212 y(there)c(is)g(no)g(guaran)o(tee)h(that)f(the)g FP(exact)22 b FQ(minimi)o(zers)13 b(\010)1125 194 y Fy(\003)1125 224 y FD(n)1165 212 y FQ(\(if)j(suc)o(h)g(exist\))f(con)o(v)o(erge)g(to)i(\010;)f (they)60 272 y(migh)o(t)d(fail)i(to)g(con)o(v)o(erge,)f(or)h(they)g(migh)o(t) e(con)o(v)o(erge)h(instead)h(to)h(some)e(in)o(teraction)1650 256 y Fx(b)1644 272 y FQ(\010)g FE(2)g(B)1775 254 y FH(0)1803 272 y FE(n)8 b(B)1871 254 y FH(1)60 332 y FQ(for)k(whic)o(h)f FF(\032)g FQ(is)h(an)g(equilibrium)c(\(but)j(not)h(Gibbs!\))20 b(measure.)f(It)11 b(is)g(an)h(imp)q(ortan)o(t)f FP(op)n(en)i(pr)n(oblem)60 392 y FQ(to)k(\014nd)f(conditions)g(under)h(whic)o(h)e(conjecture)h(\(i\),)f (or)i(something)e(lik)o(e)f(it,)i(can)g(b)q(e)g(pro)o(v)o(en.)133 452 y FM(Remark.)24 b FQ(It)18 b(is)f(certainly)g(p)q(ossible)h(for)g(a)g (sequence)1191 436 y Fx(b)1185 452 y FQ(\010)1220 459 y FD(n)1262 452 y FQ(of)g(appro)o(ximate)e(minimi)o(zers)f(of)60 513 y FF(F)92 520 y FD(\032)134 513 y FQ(to)22 b(fail)g(to)g(con)o(v)o(erge)f(ev)o (en)g(when)h FF(\032)h FQ(is)f(a)g(Gibbs)g(measure)f(for)i(some)e(in)o (teraction)g(in)h FE(B)1858 495 y FH(1)1876 513 y FQ(.)60 573 y(Consider,)e(for)g(example,)d(an)j(Ising)g(mo)q(del:)26 b(tak)o(e)19 b FF(\032)g FQ(=)g FF(\026)1169 555 y FH(0)1209 573 y FQ(=)g(pro)q(duct)h (measure,)f(and)h(let)1837 557 y Fx(b)1831 573 y FQ(\010)1866 580 y FD(n)60 633 y FQ(b)q(e)c(a)g(ferromagnetic)f(t)o(w)o(o-b)q(o)q(dy)i(in) o(teraction)d FF(n)962 615 y Fy(\000)p FD(d)1010 633 y FF(f)5 b FQ(\()p FF(n)1087 615 y Fy(\000)p FH(1)1135 633 y FQ(\()p FF(x)10 b FE(\000)g FF(y)r FQ(\)\))p FF(\033)1333 640 y FD(x)1354 633 y FF(\033)1382 640 y FD(y)1403 633 y FQ(,)15 b(where)h FF(f)21 b FQ(is)16 b(some)e(\014xed)60 693 y(nonnegativ)o(e)k(smo)q(oth)g (function)g(with)g(0)f FF(<)909 658 y Fx(R)936 693 y FF(f)5 b FQ(\()p FF(x)p FQ(\))j FF(d)1064 675 y FD(d)1085 693 y FF(x)17 b FE(\024)g FQ(1.)27 b(In)17 b(suc)o(h)h(a)h(situation,)f FF(F)1719 700 y FD(\032)1739 693 y FQ(\()1764 677 y Fx(b)1758 693 y FQ(\010)1793 700 y FD(n)1816 693 y FQ(\))f(=)60 753 y FF(F)92 760 y FD(\026)113 765 y Fr(0)132 753 y FQ(\()157 737 y Fx(b)151 753 y FQ(\010)186 760 y FD(n)210 753 y FQ(\))d(=)f FF(p)p FQ(\()p FE(\000)p FF(f)401 766 y Fx(b)400 771 y FH(\010)425 775 y Fs(n)449 753 y FE(j)p FF(\026)492 735 y FH(0)512 753 y FQ(\).)21 b(But)16 b(then)f FF(F)805 760 y FD(\026)826 765 y Fr(0)846 753 y FQ(\()871 737 y Fx(b)865 753 y FQ(\010)900 760 y FD(n)923 753 y FQ(\))f FE(!)g FQ(0)i(b)o(y)f(the)h(Leb)q(o)o(witz-P)o(enrose)g(theorem)e([241])60 819 y([345)q(,)21 b(App)q(endix)e(C],)h(whic)o(h)f(tells)h(us)g(that)h(the)f (so-called)g(\\Kac)h(limit")d(lim)1551 826 y FD(n)p Fy(!1)1653 819 y FF(p)p FQ(\()p FE(\000)p FF(f)1759 826 y FH(\010)1784 830 y Fs(n)1808 819 y FE(j)p FF(\026)1851 801 y FH(0)1871 819 y FQ(\))60 879 y(is)g(the)f(high-temp)q(erature)g(mean-\014eld)f(pressure,)i (whic)o(h)f(is)g(0)h(in)g(our)g(normalization.)24 b(On)18 b(the)60 939 y(other)j(hand)h(it)e(is)h(ob)o(vious)g(that)h FF(\026)747 946 y FH(0)788 939 y FQ(is)e(the)h(Gibbs)g(measure)f(for)h(the)g(absolutely)g (summable)60 999 y(in)o(teraction)16 b(\010)f(=)g(0,)i(and)g(that)g(nev)o (ertheless)f(the)g(in)o(teractions)1293 983 y Fx(b)1287 999 y FQ(\010)1322 1006 y FD(n)1363 999 y FQ(do)h(not)h(con)o(v)o(erge)d(in)i FE(B)1811 981 y FH(0)1847 999 y FQ(or)60 1060 y(an)o(y)j(of)g(its)f (subspaces)i FE(B)546 1067 y FD(h)568 1060 y FQ(.)32 b([Moreo)o(v)o(er,)19 b(the)g(measures)g FF(\026)1189 1067 y FD(n)1233 1060 y FQ(de\014ned)g(b)o(y) h(the)f(in)o(teractions)1837 1043 y Fx(b)1831 1060 y FQ(\010)1866 1067 y FD(n)60 1120 y FQ(con)o(v)o(erge)g(to)h(the)g(pro)q(duct)g(measure)f FF(\026)823 1127 y FH(0)843 1120 y FQ(.])32 b(W)l(e)19 b(fear)h(that)h (something)e(similar)e(could)j(happ)q(en)60 1180 y(also)d(for)f(the)g(exact)g (minimi)o(ze)o(rs)e(\010)727 1162 y Fy(\003)727 1192 y FD(n)751 1180 y FQ(,)h(unless)i(the)f(spaces)g FF(V)1186 1187 y FD(n)1226 1180 y FQ(are)h(v)o(ery)e(carefully)f(c)o(hosen.)133 1290 y(On)i(the)g(other) h(hand,)f(w)o(e)g(can)h(almost)e(pro)o(v)o(e)g(conjecture)h(\(ii\):)60 1404 y FM(Prop)r(osition)i(5.3)24 b FP(L)n(et)19 b FF(h)p FQ(:)27 b FE(S)c(!)18 b FQ([1)p FF(;)8 b FE(1)p FQ(\))20 b FP(b)n(e)g(a)g(tr)n (anslation-invariant)i(weight)f(function,)h(and)60 1464 y(let)f FF(\032)f FP(b)n(e)g(a)g(tr)n(anslation-invariant)h(me)n(asur)n(e)e(which)h (is)g FQ(not)g FP(an)g(e)n(quilibrium)h(me)n(asur)n(e)e(for)g(any)60 1525 y(inter)n(action)d(in)f FE(B)395 1532 y FD(h)417 1525 y FP(.)22 b(L)n(et)15 b FQ(\()561 1508 y Fx(b)555 1525 y FQ(\010)590 1532 y FD(n)613 1525 y FQ(\))g FP(b)n(e)h(any)f(se)n(quenc)n(e)h(in)g FE(B)1082 1532 y FD(h)1119 1525 y FP(for)e(which)i FF(F)1361 1532 y FD(\032)1381 1525 y FQ(\()1406 1508 y Fx(b)1400 1525 y FQ(\010)1435 1532 y FD(n)1458 1525 y FQ(\))e FE(!)g FQ(0)p FP(.)22 b(Then)15 b(at)h(le)n(ast)60 1585 y(one)i(\(and)g(p)n(ossibly)f(b)n (oth\))g(of)g(the)h(fol)r(lowing)i(two)e(statements)h(is)e(true:)93 1686 y(\(a\))36 b FQ(lim)182 1711 y FD(n)p Fy(!1)282 1686 y FE(k)313 1670 y Fx(b)307 1686 y FQ(\010)342 1693 y FD(n)366 1686 y FE(k)391 1693 y Fy(B)414 1699 y Fs(h)450 1686 y FQ(=)14 b FE(1)p FP(.)95 1807 y(\(b\))25 b FQ(\()207 1791 y Fx(b)201 1807 y FQ(\010)236 1814 y FD(n)260 1807 y FQ(\))17 b FP(do)n(es)g(not)h(c)n (onver)n(ge)g(in)g FE(B)781 1789 y FH(0)818 1807 y FP(norm.)60 1909 y(Mor)n(e)n(over,)e(if)h(the)g(single-spin)i(sp)n(ac)n(e)d FQ(\012)818 1916 y FH(0)855 1909 y FP(is)h(\014nite)h(and)f FF(h)1168 1921 y FE(\030)1168 1901 y(\035)1232 1909 y FQ(1)p FP(,)g(then)h(statement)g(\(a\))f(is)g(always)60 1969 y(true.)133 2083 y FQ(This)k(comes)d(v)o(ery)h(close)h(to)h(pro)o(ving)f(conjecture)f (\(ii\):)29 b(the)20 b(only)g(p)q(ossible)g(escap)q(e)g(clause)60 2144 y(is)e(that)h(the)f(sequence)g(\()535 2127 y Fx(b)529 2144 y FQ(\010)564 2151 y FD(n)587 2144 y FQ(\))h(migh)o(t)d(ha)o(v)o(e)i(no) h(limit)d(at)i(all)g(\(ev)o(en)g(in)g FE(B)1428 2125 y FH(0)1465 2144 y FQ(norm\),)g(ev)o(en)f(though)60 2204 y(\()p FE(k)110 2188 y Fx(b)104 2204 y FQ(\010)139 2211 y FD(n)163 2204 y FE(k)188 2212 y Fy(B)212 2203 y Fr(1)231 2204 y FQ(\))d(is)g(b)q(ounded.)21 b(This)15 b(can)f(happ)q(en,)h(for)f(example,)e(if)i(the)g(in)o(teractions)f (b)q(ecome)g(longer-)60 2264 y(and-longer-ranged)21 b(but)f(with)f(b)q (ounded)h(total)f(strength.)1182 2246 y FH(70)1250 2264 y FQ(In)g(suc)o(h)h (a)f(case)g(one)h(m)o(ust)e(ha)o(v)o(e)60 2324 y FE(k)91 2308 y Fx(b)85 2324 y FQ(\010)120 2331 y FD(n)144 2324 y FE(k)169 2331 y Fy(B)192 2337 y Fs(h)236 2324 y FE(!)j(1)g FQ(in)g(ev)o(ery)e(space)i FE(B)741 2331 y FD(h)784 2324 y FQ(of)h(\\short-range)g(in)o(teractions")f (\(De\014nition)f(2.38\),)j(e.g.)60 2384 y FF(h)p FQ(\()p FF(X)t FQ(\))14 b(=)g(diam)o(\()p FF(X)t FQ(\))424 2366 y FD(\017)457 2384 y FQ(with)i FF(\017)d(>)h FQ(0.)p 60 2431 732 2 v 100 2485 a FA(70)135 2500 y Fz(This)j(situation)g(is)g(reminiscen)o(t)g(of)f (\\mean-\014eld-lik)o(e")f(in)o(teractions.)29 b(Ho)o(w)o(ev)o(er,)18 b(in)f(suc)o(h)h(situations)f(one)60 2550 y(usually)c(exp)q(ects)i(\(and)f (in)f(some)f(cases)j(can)f(pro)o(v)o(e,)f(as)h(in)f(the)h(previous)g (remark\))e(that)i(the)g(limiting)c(measure)k Fv(\032)60 2599 y Fw(is)i Fz(Gibbsian)11 b(for)i(some)f(in)o(teraction)g(\010)g Fu(2)f(B)762 2584 y FA(1)794 2599 y Fz(whic)o(h)i(has)f(pic)o(k)o(ed)h(up)g (a)f(magnetic)g(\014eld.)18 b(W)m(e)12 b(wish)h(to)f(thank)h(Bob)60 2649 y(Gri\016ths)g(and)h(Bob)g(Sw)o(endsen)h(for)f(a)f(discussion)i(of)e (this)h(p)q(oin)o(t.)938 2784 y FQ(158)p eop %%Page: 159 159 bop 60 91 a Fd(Pr)o(oof)24 b(of)h(Pr)o(oposition)e(5.2.)88 b FQ(\(a\))22 b(is)g(a)h(sp)q(ecial)f(case)g(of)g(a)h(theorem)e(of)h(Israel)g ([206,)60 152 y(Theorem)17 b(V.2.2\(a\)].)25 b(\(b\))18 b(follo)o(ws)g(from)f (the)h(densit)o(y)f(of)h FE([)1204 133 y Fy(1)1204 164 y FD(n)p FH(=1)1273 152 y FF(V)1301 159 y FD(n)1343 152 y FQ(in)g FE(B)1437 133 y FH(0)1474 152 y FQ(\(or)g FE(B)1587 159 y FD(h)1609 152 y FQ(\).)27 b(\(c\))17 b(follo)o(ws)60 212 y(from)12 b(the)h(\(Lipsc)o (hitz\))f(con)o(tin)o(uit)o(y)f(of)i(the)g(function)g FF(F)1076 219 y FD(\032)1109 212 y FQ(in)g FE(B)1198 194 y FH(0)1230 212 y FQ(norm.)19 b(\(d\))13 b(is)g(also)g(a)h(consequence)60 272 y(of)d(the)g(con)o(tin)o(uit)o(y)f(of)h FF(F)497 279 y FD(\032)517 272 y FQ(,)g(since)g(the)g(h)o(yp)q(otheses)g(imply)e(that)i FF(F)1243 279 y FD(\032)1263 272 y FQ(\()1288 256 y Fx(b)1282 272 y FQ(\010)1317 279 y Fy(1)1355 272 y FQ(\))j(=)f(0.)20 b(The)11 b(last)h(statemen)o(t)60 332 y(is)k(a)h(consequence)e(of)i(Prop)q (osition)g(2.39\(a\))g(applied)f(to)h FE(B)1172 339 y FD(h)1208 332 y FQ(=)c FE(B)1294 314 y FH(1)1313 332 y FQ(.)p 1467 336 25 34 v 60 492 a Fd(Pr)o(oof)23 b(of)h(Pr)o(oposition)e(5.3.)85 b FQ(Supp)q(ose)22 b(that)g(\()1153 476 y Fx(b)1147 492 y FQ(\010)1182 499 y FD(n)1206 492 y FQ(\))f(con)o(v)o(erges)g(in)f FE(B)1566 474 y FH(0)1607 492 y FQ(norm)g(to)1810 476 y Fx(b)1804 492 y FQ(\010)1839 499 y Fy(1)1876 492 y FQ(.)60 552 y(Then)e FF(F)221 559 y FD(\032)240 552 y FQ(\()265 536 y Fx(b)259 552 y FQ(\010)294 559 y Fy(1)332 552 y FQ(\))e(=)g(0,)i(so)h FF(\032)f FQ(is)f(an)h (equilibrium)c(measure)j(for)1235 536 y Fx(b)1229 552 y FQ(\010)1264 559 y Fy(1)1301 552 y FQ(.)26 b(By)17 b(h)o(yp)q(othesis)g(this)h(means)60 612 y(that)176 596 y Fx(b)170 612 y FQ(\010)205 619 y Fy(1)270 612 y FF(=)-30 b FE(2)21 b(B)351 619 y FD(h)373 612 y FQ(,)h(i.e.)c FE(k)522 596 y Fx(b)516 612 y FQ(\010)551 619 y Fy(1)589 612 y FE(k)614 619 y Fy(B)637 625 y Fs(h)680 612 y FQ(=)j FE(1)p FQ(.)34 b(No)o(w)21 b(assume)f(that)h FE(k)1267 596 y Fx(b)1261 612 y FQ(\010)1296 619 y FD(n)1319 612 y FE(k)1344 619 y Fy(B)1367 625 y Fs(h)1411 612 y FE(6!)g(1)p FQ(;)h(then)e(there)g(is)h(a)60 672 y(subsequence)15 b(of)i(\()416 656 y Fx(b)410 672 y FQ(\010)445 679 y FD(n)468 672 y FQ(\))f(on)h(whic)o(h)e(the)h FE(B)827 679 y FD(h)865 672 y FQ(norm)f(is)h(b)q(ounded,)h(sa)o(y)f(b)o(y)f FF(M)5 b FQ(;)16 b(but)g(b)o(y)g(Prop)q(osition)60 733 y(2.39\(a\))h(this)f (implies)d(that)k FE(k)622 717 y Fx(b)616 733 y FQ(\010)651 740 y Fy(1)688 733 y FE(k)713 740 y Fy(B)736 746 y Fs(h)772 733 y FE(\024)d FF(M)5 b FQ(,)16 b(a)g(con)o(tradiction.)21 b(This)16 b(pro)o(v)o(es)g(that)g(either)f(\(a\))i(or)60 793 y(\(b\))f([or)g(b)q(oth])h(m)o(ust)e(b)q(e)h(true.)133 853 y(Finally)l(,)e(supp)q(ose)i(that)g(the)f(single-spin)g(space)h(is)f (\014nite,)f(that)i FF(h)1378 866 y FE(\030)1378 845 y(\035)1442 853 y FQ(1,)f(and)h(that)g(there)e(is)i(a)60 913 y(subsequence)c(of)i(\()410 897 y Fx(b)404 913 y FQ(\010)439 920 y FD(n)462 913 y FQ(\))f(on)h(whic)o(h)e (the)g FE(B)808 920 y FD(h)844 913 y FQ(norm)g(is)g(b)q(ounded,)i(sa)o(y)f(b) o(y)g FF(M)5 b FQ(.)20 b(Then)13 b(b)o(y)g(Prop)q(osition)60 973 y(2.39\(b\))18 b(there)g(exists)f(a)h(sub-subsequence)f(whic)o(h)g(con)o (v)o(erges)g(in)h FE(B)1355 955 y FH(0)1391 973 y FQ(norm)f(to)h(some)1711 957 y Fx(b)1705 973 y FQ(\010)1740 980 y Fy(1)1795 973 y FQ(with)60 1034 y FE(k)91 1017 y Fx(b)85 1034 y FQ(\010)120 1041 y Fy(1)157 1034 y FE(k)182 1041 y Fy(B)205 1047 y Fs(h)255 1034 y FE(\024)27 b FF(M)5 b FQ(;)29 b(and)c FF(\032)f FQ(is)g(an)h(equilibrium)c(measure)i (for)1254 1017 y Fx(b)1248 1034 y FQ(\010)1283 1041 y Fy(1)1321 1034 y FQ(;)28 b(but)c(this)g(con)o(tradicts)g(the)60 1094 y(h)o(yp)q(othesis)16 b(of)h(the)f(prop)q(osition.)p 833 1098 V 133 1229 a FM(Remarks.)j FQ(1.)j(Similar)14 b(ideas)i(app)q(ear)h(in)f(the) g(w)o(ork)g(of)h(Hugenholtz)f([199].)133 1289 y(2.)42 b(A)23 b(partially)f(alternate)h(pro)q(of)h(of)f(the)g(second)g(half)g(of)g(Prop)q (osition)h(5.3,)h(when)e FF(\032)g FQ(is)60 1349 y(ergo)q(dic)18 b(\(or)g(a)f FP(\014nite)23 b FQ(con)o(v)o(ex)16 b(com)o(bination)g(of)i (ergo)q(dic)g(measures\),)e(go)q(es)j(as)f(follo)o(ws:)23 b(By)17 b(the)60 1409 y(Bishop-Phelps)c(theorem)f([206)q(,)h(Corollary)h(V.2.1])e (there)h(exists)1289 1393 y Fx(e)1283 1409 y FQ(\010)1318 1416 y FD(n)1356 1409 y FE(2)h(B)1438 1391 y FH(0)1470 1409 y FQ(with)f FE(k)1609 1393 y Fx(e)1603 1409 y FQ(\010)1638 1416 y FD(n)1667 1409 y FE(\000)1717 1393 y Fx(b)1711 1409 y FQ(\010)1746 1416 y FD(n)1769 1409 y FE(k)1794 1418 y Fy(B)1818 1408 y Fr(0)1851 1409 y FE(\024)60 1486 y FF(C)95 1493 y FD(\032)115 1486 y FF(F)147 1493 y FD(\032)167 1486 y FQ(\()192 1470 y Fx(b)186 1486 y FQ(\010)221 1493 y FD(n)244 1486 y FQ(\))19 b(suc)o(h)f(that)h FF(\032)f FQ(is)g(an)h(equilibrium)c(measure)i(for)1202 1470 y Fx(e)1196 1486 y FQ(\010)1231 1493 y FD(n)1273 1486 y FQ([if)g FF(\032)h FQ(=)1444 1444 y FD(m)1438 1453 y Fx(P)1431 1523 y FD(i)p FH(=1)1497 1486 y FF(\013)1528 1493 y FD(i)1542 1486 y FF(\032)1567 1493 y FD(i)1600 1486 y FQ(is)g(the)g(ergo)q(dic)60 1577 y(decomp)q(osition)c(of)h FF(\032)p FQ(,)f(then)h FF(C)632 1584 y FD(\032)666 1577 y FQ(=)e(\(2)26 b(min)768 1607 y FH(1)p Fy(\024)p FD(i)p Fy(\024)p FD(m)893 1577 y FF(\013)924 1584 y FD(i)938 1577 y FQ(\))957 1559 y Fy(\000)p FH(1)1004 1577 y FQ(].)20 b(No)o(w)15 b(assume)f(that)h FE(k)1464 1561 y Fx(b)1458 1577 y FQ(\010)1493 1584 y FD(n)1516 1577 y FE(k)1541 1584 y Fy(B)1564 1590 y Fs(h)1600 1577 y FE(6!)f(1)p FQ(,)g(so)i(that)60 1667 y(there)g(is)g(a)g(subsequence)g(of)g(\()630 1650 y Fx(b)624 1667 y FQ(\010)659 1674 y FD(n)683 1667 y FQ(\))g(on)h(whic)o(h)f(the)g FE(B)1043 1674 y FD(h)1081 1667 y FQ(norm)f(is)h(b)q(ounded,)h(sa)o(y)f(b)o (y)g FF(M)5 b FQ(.)22 b(W)l(e)16 b(ha)o(v)o(e)60 1727 y(then)c(sho)o(wn)i (that)f(there)f(exist)f(in)o(teractions)913 1711 y Fx(e)907 1727 y FQ(\010)942 1734 y FD(n)978 1727 y FQ(in)i FE(B)1067 1709 y FH(0)1086 1727 y FQ(,)f(arbitrarily)g(close)g(to)h FE(f)p FQ(\010:)j FE(k)p FQ(\010)p FE(k)1687 1734 y Fy(B)1710 1740 y Fs(h)1747 1727 y FE(\024)d FF(M)5 b FE(g)p FQ(,)60 1787 y(for)12 b(whic)o(h)g FF(\032)g FQ(is)g(an)h(equilibrium)c(measure.)18 b(When)13 b(this)f FE(B)1137 1794 y FD(h)1159 1787 y FQ(-ball)g(is)g(compact) f(in)h FE(B)1590 1769 y FH(0)1621 1787 y FQ(\(i.e.)e(\012)1749 1794 y FH(0)1782 1787 y FQ(\014nite)60 1847 y(and)j FF(h)193 1860 y FE(\030)193 1839 y(\035)256 1847 y FQ(1\),)g(then)f(it)g(is)g(easy)g (to)h(sho)o(w)g(that)f(there)g(exists)f(an)i(in)o(teraction)e FP(in)16 b FQ(this)c(ball)g(for)h(whic)o(h)60 1907 y FF(\032)18 b FQ(is)f(an)h(equilibrium)c(measure)i([w)o(e'v)o(e)f(done)j(it)f(ab)q(o)o(v) o(e,)g(b)o(y)g(extracting)g(a)h(sub-subsequence)g(of)60 1968 y(\()85 1951 y Fx(b)79 1968 y FQ(\010)114 1975 y FD(n)138 1968 y FQ(\))13 b(con)o(v)o(ergen)o(t)f(to)473 1951 y Fx(b)467 1968 y FQ(\010)502 1975 y Fy(1)540 1968 y FQ(;)i(for)f(what)h(it's)f(w)o(orth,)g (the)g(corresp)q(onding)i(sub-subsequence)e(of)g(\()1818 1951 y Fx(e)1812 1968 y FQ(\010)1847 1975 y FD(n)1871 1968 y FQ(\))60 2028 y(also)j(con)o(v)o(erges)e(to)439 2012 y Fx(b)433 2028 y FQ(\010)468 2035 y Fy(1)506 2028 y FQ(].)20 b(Unfortunately)l(,)15 b(if)f(the)h FE(B)1038 2035 y FD(h)1061 2028 y FQ(-ball)g(is)g(not)h (compact,)e(w)o(e)h(do)g(not)h(see)f(an)o(y)60 2088 y(w)o(a)o(y)i(to)h (conclude)e(that)i(there)f(exists)f(an)i(in)o(teraction)f FP(in)k FQ(the)c(ball)g(\(or)h(ev)o(en)e(in)h FE(B)1633 2095 y FD(h)1655 2088 y FQ(\))g(for)h(whic)o(h)60 2148 y FF(\032)f FQ(is)g(an)h(equilibrium)c (measure.)23 b(So)18 b(this)f(metho)q(d)f(still)g(do)q(es)i(not)g(su\016ce)f (to)g(pro)o(v)o(e)g(conjecture)60 2208 y(\(ii\).)60 2338 y FM(5.1.3)55 b(Application)18 b(to)h(the)f(Renormalization)e(Group)60 2431 y FQ(No)o(w)23 b(let)f(us)i(apply)f(these)g(ideas)g(to)h(the)f (renormalization)e(group,)26 b(b)o(y)d(taking)g FF(\032)g FQ(to)h(b)q(e)f (the)60 2491 y(renormalized)12 b(measure)i FF(\026)566 2473 y Fy(0)578 2491 y FQ(.)20 b(W)l(e)15 b(assume)f(that)h(the)f(exp)q(erimen)o (ter)e(uses)j(the)f(sc)o(heme)f(describ)q(ed)60 2551 y(in)19 b(the)h(previous)g(section)f(to)h(construct)g(an)g(estimated)e(renormalized)g (in)o(teraction)h(\010)1728 2533 y Fy(0)1728 2563 y FD(n)1771 2551 y FE(2)i FF(V)1853 2558 y FD(n)1876 2551 y FQ(.)60 2611 y(W)l(e)16 b(con)o(tin)o(ue)f(to)i(ignore)f(statistical)g(and)h (\014nite-size)e(errors.)938 2784 y(159)p eop %%Page: 160 160 bop 133 91 a FQ(The)24 b(exp)q(ected)f(b)q(eha)o(vior)g(of)h(the)g(estimates) e(\010)1070 73 y Fy(0)1070 104 y FD(n)1117 91 y FQ(dep)q(ends)i(critically)e (on)i(whether)f FF(\026)1821 73 y Fy(0)1857 91 y FQ(is)60 152 y(Gibbsian)16 b(or)g(non-Gibbsian.)22 b(Assuming)14 b(the)i(v)m(alidit)o(y)e (of)i(Conjecture)f(5.1)h(\(or)g(something)f(lik)o(e)60 212 y(it\),)g(w)o(e)h(ha)o(v)o(e)g(the)g(follo)o(wing)f(scenario:)133 272 y FP(Case)k(\(i\):)24 b FF(\026)377 254 y Fy(0)408 272 y FP(is)18 b(Gibbsian)i(for)e FQ(\010)779 254 y Fy(0)806 272 y FE(2)f(B)891 254 y FH(1)910 272 y FP(.)25 b FQ(Then)18 b(w)o(e)f(exp)q(ect) f(the)i(estimated)d(renormalized)60 332 y(in)o(teractions)d(\010)356 314 y Fy(0)356 344 y FD(n)393 332 y FQ(to)h(con)o(v)o(erge)f(in)g FE(B)733 314 y FH(1)765 332 y FQ(norm)g(to)i(\010)981 314 y Fy(0)992 332 y FQ(.)21 b(No)o(w,)12 b(b)o(y)h(the)g(First)f(F)l(undamen)o (tal)f(Theorem)60 392 y(\(Theorem)16 b(3.4\),)g(the)h(renormalized)e (measures)h(arising)h(from)f(distinct)g(phases)h(of)g(the)g(original)60 452 y(mo)q(del)g(m)o(ust)f(b)q(e)i(Gibbsian)g(for)g(the)g FP(same)j FQ(in)o(teraction)c(\010)1177 434 y Fy(0)1189 452 y FQ(.)26 b(Therefore,)17 b(an)o(y)h(observ)o(ed)f(m)o(ulti-)60 513 y(v)m(aluedness)h (of)f(the)h(R)o(G)f(map)g(m)o(ust)f(disapp)q(ear)i(asymptotically)e(as)i(the) f(assumed)g(in)o(teraction)60 573 y(space)f FF(V)218 580 y FD(n)259 573 y FQ(gro)o(ws.)133 633 y FP(Case)k(\(ii\):)26 b FF(\026)395 615 y Fy(0)427 633 y FP(is)20 b(non-Gibbsian.)30 b FQ(In)19 b(this)f(case)h(w)o(e)f(exp)q(ect)g(the)g(estimated)f (renormalized)60 693 y(in)o(teractions)j(\010)364 675 y Fy(0)364 706 y FD(n)409 693 y FQ(to)i(div)o(erge)e(in)h FE(B)744 675 y FH(1)784 693 y FQ(norm,)g(i.e.)36 b FE(k)p FQ(\010)1091 675 y Fy(0)1091 706 y FD(n)1114 693 y FE(k)1139 702 y Fy(B)1163 692 y Fr(1)1205 693 y FE(!)22 b(1)p FQ(.)36 b(This)22 b(b)q(eha)o(vior)f(is)g FP(almost)60 753 y FQ(rigorously)c(pro)o(v)o(en)e(\(Prop)q(osition)i(5.3\).) 133 814 y(This)k(dic)o(hotom)o(y)e(pro)o(vides,)i(at)g(least)f(in)h (principle,)f(a)h(clear)f(metho)q(d)g(for)h(distinguishing)60 874 y(exp)q(erimen)o(tally)13 b(the)i(Gibbsianness)i(or)g(non-Gibbsianness)g (of)g(the)f(renormalized)e(measure)g FF(\026)1864 856 y Fy(0)1876 874 y FQ(.)60 934 y(Whether)f(it)h(will)e(w)o(ork)i(in)f(practice)g(is)h (less)f(clear:)19 b(the)14 b(pro)q(ofs)h(of)f(non-Gibbsianness)h(in)f (Section)60 994 y(4)e(\(and)g(of)f(the)h(F)l(undamen)o(tal)d(Theorems)i(in)g (Section)g(3\))g(in)o(v)o(olv)o(e)e(extremely)f(rare)k(ev)o(en)o(ts)e(in)h (large)60 1054 y(v)o(olumes;)g(so)i(the)f(distinction)f(b)q(et)o(w)o(een)g (Gibbsianness)i(and)f(non-Gibbsianness)i(migh)o(t)c(turn)j(out)60 1115 y(to)21 b(b)q(e)f(visible)f(only)h(with)g(extremely)d(high)j(statistics) g(and)h(when)g(using)f(an)h(extremely)c(large)60 1175 y(space)d(of)h (renormalized)c(in)o(teractions)j(\(that)g(is,)g(including)f(in)o(teractions) h(in)o(v)o(olving)e(man)o(y)h(spins)60 1235 y(sim)o(ultaneously\).)19 b(On)c(the)h(other)f(hand,)h(it)f(is)h(at)g(least)f(conceiv)m(able)f(that)i (this)g(dep)q(endence)f(on)60 1295 y(rare)k(ev)o(en)o(ts)e(is)i(an)g (artifact)g(of)g(the)g FP(pr)n(o)n(of)27 b FQ(and)20 b(not)f(of)g(the)g (result.)28 b(It)19 b(w)o(ould)g(b)q(e)g(in)o(teresting,)60 1355 y(therefore,)14 b(to)i(p)q(erform)f(a)h(high-precision)f(MCR)o(G)g (test,)g(using)h(a)g(large)f(space)h(of)f(renormalized)60 1416 y(in)o(teractions,)g(to)i(compare)f(a)h(case)g(in)f(whic)o(h)g FF(\026)965 1397 y Fy(0)993 1416 y FQ(is)h(exp)q(ected)f(to)h(b)q(e)f (Gibbsian)h(\(e.g.)f(the)g FF(d)f FQ(=)g(2)60 1476 y(Ising)21 b(mo)q(del)f(at)i(a)g(temp)q(erature)d(not)j(to)q(o)h(far)e(b)q(elo)o(w)g (critical\))f(with)h(a)h(case)f(in)g(whic)o(h)g FF(\026)1824 1458 y Fy(0)1857 1476 y FQ(is)60 1536 y(exp)q(ected)12 b(or)h(pro)o(v)o(en)e (to)i(b)q(e)g(non-Gibbsian)h(\(e.g.)e(the)g FF(d)i FQ(=)g(2)f(Ising)f(mo)q (del)g(at)h(lo)o(w)f(temp)q(erature\).)60 1596 y(W)l(e)i(are)h(somewhat)f(p)q (essimistic)e(ab)q(out)k(whether)e(the)g(asymptotic)f(\()p FF(n)h FE(!)g(1)p FQ(\))g(b)q(eha)o(vior)g(can)h(b)q(e)60 1656 y(seen)h(with)g(an)o(y)g(curren)o(tly)f(feasible)g(exp)q(enditure)g(of)i (resources,)f(but)g(it)g(cannot)h(h)o(urt)f(to)g(try)l(.)133 1716 y(In)f(the)h(existing)e(MCR)o(G)h(studies,)g(the)h(in)o(teraction)e (space)i FF(V)26 b FQ(is)15 b(usually)h(tak)o(en)f(to)g(b)q(e)h(quite)60 1777 y(small:)27 b(t)o(ypically)18 b(1)i FE(\024)g FQ(dim)7 b FF(V)669 1789 y FE(\030)669 1768 y FF(<)727 1777 y FQ(10.)33 b(Can)21 b(w)o(e)e(explain)g(the)h(observ)o(ed)f(discon)o(tin)o(uit)o(y)f(of) i(the)60 1837 y(R)o(G)i(map)g(as)h(an)g(artifact)f(of)h(this)f(truncation)h (to)g(a)g(small)e(space)h(of)h(in)o(teractions?)39 b(In)23 b(our)60 1897 y(opinion)15 b(the)f(answ)o(er)h(is)g FP(yes)t FQ(.)21 b(Note)14 b(\014rst)h(that)g(the)g(estimated)e(renormalized)f(in)o (teraction)i(\010)1817 1879 y Fy(0)1844 1897 y FQ(is,)60 1957 y(according)19 b(to)g(\(5.4\)/\(5.6\),)g(just)g(a)g(pro)o(xy)f(for)h(the)f (renormalized)e(exp)q(ectation)i(v)m(alues)h FE(h)p FF(f)1793 1964 y FH(\011)1823 1957 y FE(i)1842 1964 y FD(\026)1863 1955 y Ft(0)1876 1957 y FQ(,)60 2017 y(\011)f FE(2)h FF(V)11 b FQ(.)30 b(These)18 b(latter)h(exp)q(ectation)f(v)m(alues)h(are,)h(of)f(course,)g (discon)o(tin)o(uous)g(at)g(a)g(\014rst-order)60 2078 y(phase-transition)j (surface)e(\(and)i(m)o(ulti-v)m(alued)c(on)j(that)h(surface\).)34 b(That)22 b(in)e(itself)g(do)q(es)i(not)60 2138 y(imply)13 b(the)h(discon)o(tin)o(uit)o(y)f(and)j(m)o(ulti-v)m(aluedness)d(of)i(\010) 1118 2120 y Fy(0)1130 2138 y FQ(,)g(b)q(ecause)g(the)g(map)f(from)g(in)o (teractions)60 2198 y(to)f(exp)q(ectation)f(v)m(alues)h(is)g(itself)e(discon) o(tin)o(uous)i(and)g(m)o(ulti-v)m(alued.)18 b(Ho)o(w)o(ev)o(er,)11 b(for)i(most)f(renor-)60 2258 y(malization)j(transformations)h(w)o(e)g(exp)q (ect)f(the)h(renormalized)e(exp)q(ectation)i(v)m(alues)h(to)f(b)q(e)h FP(mor)n(e)60 2318 y FQ(discon)o(tin)o(uous)j(than)g(the)f(original)h(exp)q (ectation)f(v)m(alues;)i(and)g(it)e(is)g(far)h(from)f(clear)g(that)h(this)60 2379 y(larger)c(discon)o(tin)o(uit)o(y)f(can)i(b)q(e)f(realized,)f(sim)o (ultaneously)g(for)h(all)g(observ)m(ables)h FF(f)1593 2386 y FH(\011)1639 2379 y FQ(\(\011)e FE(2)f FF(V)e FQ(\),)k(at)60 2439 y(an)o(y)i(in)o(teraction)f(in)h(the)f(giv)o(en)h(space)g FF(V)11 b FQ(.)27 b(If)17 b(it)h(cannot,)g(then)g(the)g(R)o(G)g(map)f(on)i (the)f(space)g(of)60 2499 y(in)o(teractions)d(will)h FP(app)n(e)n(ar)k FQ(to)c(b)q(e)h(discon)o(tin)o(uous.)133 2559 y(Consider,)g(for)g(example,)d (an)j(Ising)f(mo)q(del)g(at)h FF(h)d FQ(=)h(0)i(and)g FF(\014)g(>)d(\014)1379 2566 y FD(c)1396 2559 y FQ(,)j(and)g(use)f(the)h(ma)s(jorit)o(y-)60 2619 y(rule)k(transformation.)37 b(Then)21 b(the)g(renormalized)e (magnetization)i FF(M)1421 2601 y Fy(0)1454 2619 y FQ(will)g(undoubtedly)g(b) q(e)938 2784 y(160)p eop %%Page: 161 161 bop 60 91 a FQ(larger)22 b(than)g(the)f(original)h(magnetization)e FF(M)28 b FQ(=)23 b FF(M)5 b FQ(\()p FF(\014)s(;)j FQ(0)1200 73 y FH(+)1230 91 y FQ(\),)22 b(since)f(minorities)e(tend)j(to)g(get)60 152 y(outv)o(oted.)31 b(No)o(w)20 b(supp)q(ose)h(that)f(one)f(is)h(using,)g (as)g(in)g(the)f(w)o(ork)h(of)g(Dec)o(k)o(er,)e(Hasenfratz)h(and)60 212 y(Hasenfratz)13 b([72,)h(Section)e(4],)h(only)g(a)h(single)e (renormalized)f(coupling)i FF(h)1404 194 y Fy(0)1416 212 y FQ(,)g(with)g FF(\014)1582 194 y Fy(0)1606 212 y FQ(\014xed)g(to)h(equal)60 272 y FF(\014)s FQ(.)24 b(\(That)18 b(is,)g FF(V)28 b FQ(is)18 b(a)g FP(one-dimensional)25 b FQ(a\016ne)17 b(subspace.\))25 b(Then)18 b(one)g(will)e FP(inevitably)24 b FQ(\014nd)18 b(a)60 332 y(renormalized)11 b(coupling)i FF(h)567 314 y Fy(0)592 332 y FF(>)h FQ(0)g(for)f(the)g(image)f(measure)g FF(\026)1188 314 y Fy(0)1188 344 y FH(+)1231 332 y FQ(\(resp.)g FF(h)1391 314 y Fy(0)1417 332 y FF(<)i FQ(0)f(for)h FF(\026)1607 314 y Fy(0)1607 344 y(\000)1637 332 y FQ(\),)f(since)f(only)60 392 y(in)19 b(this)h(w)o(a)o(y)f(can)g(one)h(accoun)o(t)f(for)h(a)g (renormalized)d(magnetization)i FF(M)1477 374 y Fy(0)1508 392 y FQ(=)g FF(M)5 b FQ(\()p FF(\014)s(;)j(h)1717 374 y Fy(0)1728 392 y FQ(\))20 b FF(>)f(M)5 b FQ(.)60 452 y(Dec)o(k)o(er)18 b FP(et)k(al.)33 b FQ(do)21 b(recognize)e(this)h(ob)s(jection,)g(and)g(try)g (to)h(argue)f(that)h(allo)o(wing)e FF(\014)1703 434 y Fy(0)1734 452 y FQ(to)i(v)m(ary)60 513 y(w)o(ould)16 b(not)h(pro)q(duce)g(an)g (e\013ect)f(large)g(enough)h(to)g(accoun)o(t)f(for)h(the)f(observ)o(ed)g (discon)o(tin)o(uit)o(y)e(in)60 573 y FF(h)88 555 y Fy(0)100 573 y FQ(,)i(but)g(w)o(e)g(do)h(not)f(\014nd)h(their)e(argumen)o(t)g(con)o (vincing.)133 633 y(The)e(situation)g(is)g(more)f(subtle)g(if)h(one)g (considers)g(the)g FP(two-dimensional)20 b FQ(space)13 b(of)g(couplings)60 693 y FF(\014)91 675 y Fy(0)126 693 y FQ(and)25 b FF(h)257 675 y Fy(0)269 693 y FQ(.)46 b(Then)24 b(one)h(has)g(to)g(c)o(ho)q(ose)f(the) h(pair)f(\()p FF(\014)1138 675 y Fy(0)1149 693 y FF(;)8 b(h)1199 675 y Fy(0)1210 693 y FQ(\))25 b(so)g(as)g(to)g(matc)o(h)d(the)i(observ)o(ed) 60 753 y(renormalized)14 b(magnetization)g FF(M)718 735 y Fy(0)746 753 y FP(and)21 b FQ(the)16 b(observ)o(ed)f(renormalized)f(energy)h FF(E)1612 735 y Fy(0)1624 753 y FQ(.)21 b(T)l(o)16 b(do)h(this,)60 814 y(let)i(us)h(determine)e(\014rst)i(the)g(unique)f(v)m(alue)h FF(\014)947 796 y Fy(0)944 826 y(\003)983 814 y FQ(suc)o(h)g(that)g(the)g (renormalized)d(energy)j(can)g(b)q(e)60 874 y(matc)o(hed)14 b(at)j(zero)f(magnetic)e(\014eld,)h(i.e.)g FF(E)864 856 y Fy(0)889 874 y FQ(=)f FF(E)s FQ(\()p FF(\014)1030 856 y Fy(0)1027 886 y(\003)1046 874 y FF(;)8 b FQ(0\).)22 b(Then)16 b(w)o(e)f(ask)i(ho)o(w)f(the) g(renormalized)60 934 y(magnetization)f FF(M)429 916 y Fy(0)457 934 y FQ(compares)h(to)g(the)g(sp)q(on)o(taneous)i(magnetization)d(at)i FF(\014)1500 916 y Fy(0)1497 946 y(\003)1516 934 y FQ(:)95 1030 y(\(a\))25 b(If)e FF(M)290 1012 y Fy(0)330 1030 y FF(>)j(M)5 b FQ(\()p FF(\014)496 1012 y Fy(0)493 1042 y(\003)513 1030 y FF(;)j FQ(0)559 1012 y FH(+)589 1030 y FQ(\),)25 b(then)f(it)g(is)f(imp)q (ossible)g(to)h(matc)o(h)f(b)q(oth)i FF(M)1523 1012 y Fy(0)1559 1030 y FQ(and)f FF(E)1700 1012 y Fy(0)1736 1030 y FQ(at)g(zero)182 1090 y(magnetic)16 b(\014eld.)24 b(Therefore,)16 b(the)i(renormalized)d (coupling)i FF(h)1356 1072 y Fy(0)1385 1090 y FQ(will)f(b)q(e)i(found)g(to)f (b)q(e)h FF(>)e FQ(0)182 1150 y(\(resp.)g FF(<)d FQ(0\))k(for)g(the)f(image)f (measure)f FF(\026)947 1132 y Fy(0)947 1163 y FH(+)994 1150 y FQ(\(resp.)h FF(\026)1158 1132 y Fy(0)1158 1163 y(\000)1188 1150 y FQ(\).)93 1250 y(\(b\))24 b(If)14 b FF(M)281 1232 y Fy(0)307 1250 y FE(\024)f FF(M)5 b FQ(\()p FF(\014)461 1232 y Fy(0)458 1262 y(\003)478 1250 y FF(;)j FQ(0)524 1232 y FH(+)554 1250 y FQ(\),)14 b(then)g FF(M)762 1232 y Fy(0)789 1250 y FQ(and)h FF(E)921 1232 y Fy(0)947 1250 y FQ(can)f(b)q(e)h(matc)o(hed)e(b)o(y)h(taking) g FF(\014)i FQ(=)e FF(\014)1635 1232 y Fy(0)1632 1262 y(\003)1651 1250 y FQ(,)h FF(h)1708 1232 y Fy(0)1733 1250 y FQ(=)f(0.)21 b([If)182 1310 y FF(M)234 1292 y Fy(0)260 1310 y FF(<)14 b(M)5 b FQ(\()p FF(\014)414 1292 y Fy(0)411 1323 y(\003)430 1310 y FF(;)j FQ(0)476 1292 y FH(+)506 1310 y FQ(\),)14 b(this)h(en)o(tails)f (using)h(a)g FP(mixe)n(d)k FQ(phase)c FF(\027)j FQ(in)c(\(5.6\),)h(but)g (that)g(is)f(p)q(erfectly)182 1371 y(legitimate.)k(It)e(corresp)q(onds)h(to)g (the)f(minim)n(um)c(of)k FF(F)1197 1378 y FD(\032)1217 1371 y Fm(\026)p FF(V)27 b FQ(o)q(ccurring)17 b(at)f(a)h(p)q(oin)o(t)f(of)g(non-) 182 1431 y(di\013eren)o(tiabilit)o(y)l(.])60 1527 y(W)l(e)22 b(are)h(unable)f(to)h(decide)e FP(a)i(priori)j FQ(b)q(et)o(w)o(een)c(these)g (t)o(w)o(o)g(p)q(ossibilities;)i(it)e(seems)f(to)i(b)q(e)g(a)60 1587 y(detailed)15 b(dynamical)g(question.)133 1647 y(One)22 b(approac)o(h)h(is)f(to)g(compute)f(the)h(lo)o(w-temp)q(erature)e(expansion)j (of)f FF(M)1589 1629 y Fy(0)1623 1647 y FQ(and)h FF(E)1763 1629 y Fy(0)1774 1647 y FQ(,)g(and)60 1707 y(compare)17 b(them)g(to)i(the)f (corresp)q(onding)i(expansions)f(for)g FF(E)s FQ(\()p FF(\014)s(;)8 b FQ(0\))18 b(and)h FF(M)5 b FQ(\()p FF(\014)s(;)j FQ(0\).)27 b(This)19 b(w)o(ould)60 1767 y(answ)o(er)g(the)g(question)g(at)g(su\016cien)o (tly)e(lo)o(w)i(temp)q(erature.)28 b(W)l(e)19 b(are)g(indebted)g(to)g(Jes)q (\023)-26 b(us)20 b(Salas)60 1828 y([314)q(])e(for)h(p)q(erforming)f(this)g (computation,)h(for)g(the)f(t)o(w)o(o-dimensional)f(Ising)i(mo)q(del)e(at)i FF(h)g FQ(=)f(0)60 1888 y(using)i(ma)s(jorit)o(y)e(rule)i(on)g(2)14 b FE(\002)f FQ(2)21 b(blo)q(c)o(ks)f(\(with)f(a)i(random)e(tie-break)o(er\).) 31 b(Setting)20 b FF(u)g FQ(=)g FF(e)1808 1870 y Fy(\000)p FH(4)p FD(\014)1876 1888 y FQ(,)60 1948 y FF(M)f FQ(=)14 b FE(h)p FF(\033)225 1955 y FH(0)245 1948 y FE(i)i FQ(and)h FF(E)g FQ(=)d FE(h)p FF(\033)527 1955 y FH(0)547 1948 y FF(\033)575 1956 y FH(\(1)p FD(;)p FH(0\))649 1948 y FE(i)p FQ(,)i(Salas)h(\014nds:)538 2051 y FF(M)590 2031 y Fy(0)602 2051 y FQ(\()p FF(u;)8 b FQ(0)695 2031 y FH(+)724 2051 y FQ(\))42 b(=)f(1)20 b FE(\000)f FQ(4)p FF(u)1018 2031 y FH(3)1057 2051 y FE(\000)g FQ(32)p FF(u)1191 2031 y FH(4)1231 2051 y FQ(+)g FF(O)q FQ(\()p FF(u)1373 2031 y FH(5)1393 2051 y FQ(\))353 b(\(5.7a\))581 2124 y FF(E)620 2103 y Fy(0)631 2124 y FQ(\()p FF(u;)8 b FQ(0\))42 b(=)f(1)20 b FE(\000)f FQ(8)p FF(u)1018 2103 y FH(3)1057 2124 y FE(\000)g FQ(63)p FF(u)1191 2103 y FH(4)1231 2124 y FQ(+)g FF(O)q FQ(\()p FF(u)1373 2103 y FH(5)1393 2124 y FQ(\))351 b(\(5.7b\))60 2227 y(These)16 b(are)g(to)h(b)q(e)f(compared)g(with)g(the)g(w)o(ell-kno)o(wn)f (results)457 2331 y FF(M)5 b FQ(\()p FF(u;)j FQ(0)602 2310 y FH(+)632 2331 y FQ(\))41 b(=)g(1)20 b FE(\000)f FQ(2)p FF(u)925 2310 y FH(2)965 2331 y FE(\000)g FQ(8)p FF(u)1075 2310 y FH(3)1114 2331 y FE(\000)g FQ(34)p FF(u)1248 2310 y FH(4)1288 2331 y FQ(+)g FF(O)q FQ(\()p FF(u)1430 2310 y FH(5)1450 2331 y FQ(\))296 b(\(5.8a\))500 2403 y FF(E)s FQ(\()p FF(u;)8 b FQ(0\))41 b(=)g(1)20 b FE(\000)f FQ(4)p FF(u)925 2383 y FH(2)965 2403 y FE(\000)g FQ(12)p FF(u)1099 2383 y FH(3)1138 2403 y FE(\000)g FQ(36)p FF(u)1272 2383 y FH(4)1312 2403 y FQ(+)g FF(O)q FQ(\()p FF(u)1454 2383 y FH(5)1474 2403 y FQ(\))270 b(\(5.8b\))60 2507 y(Matc)o(hing)16 b(the)g(energies,)f(w)o(e)h(\014nd)482 2642 y FF(u)510 2622 y Fy(0)510 2655 y(\003)557 2642 y FQ(=)623 2599 y FE(p)p 664 2599 25 2 v 664 2642 a FQ(2)q FF(u)717 2622 y FH(3)p FD(=)p FH(2)791 2642 y FQ(+)853 2609 y(63)901 2568 y FE(p)p 943 2568 V 41 x FQ(2)p 853 2631 115 2 v 886 2676 a(16)973 2642 y FF(u)1001 2622 y FH(5)p FD(=)p FH(2)1075 2642 y FE(\000)j FQ(3)p FF(u)1185 2622 y FH(3)1224 2642 y FQ(+)g FF(O)q FQ(\()p FF(u)1366 2622 y FH(7)p FD(=)p FH(2)1422 2642 y FQ(\))14 b FF(:)321 b FQ(\(5)p FF(:)p FQ(9\))938 2784 y(161)p eop %%Page: 162 162 bop 60 91 a FQ(Plugging)17 b(this)f(in)o(to)g FF(M)5 b FQ(,)16 b(w)o(e)g(ha)o(v)o(e)404 201 y FF(M)5 b FQ(\()p FF(u)503 181 y Fy(0)503 214 y(\003)522 201 y FF(;)j FQ(0)568 181 y FH(+)598 201 y FQ(\))28 b(=)f(1)20 b FE(\000)f FQ(4)p FF(u)864 181 y FH(3)903 201 y FE(\000)967 168 y FQ(63)p 967 190 49 2 v 979 236 a(2)1020 201 y FF(u)1048 181 y FH(4)1087 201 y FE(\000)g FQ(4)1169 158 y FE(p)p 1211 158 25 2 v 43 x FQ(2)q FF(u)1264 181 y FH(9)p FD(=)p FH(2)1338 201 y FQ(+)g FF(O)q FQ(\()p FF(u)1480 181 y FH(5)1500 201 y FQ(\))14 b FF(;)218 b FQ(\(5)p FF(:)p FQ(10\))60 310 y(whic)o(h)18 b(is)g(equal)g(to)h FF(M)498 292 y Fy(0)510 310 y FQ(\()p FF(u;)8 b FQ(0)603 292 y FH(+)633 310 y FQ(\))18 b(at)h(leading)g(order)f(and)h(greater)g(than)g FF(M)1465 292 y Fy(0)1477 310 y FQ(\()p FF(u;)8 b FQ(0)1570 292 y FH(+)1600 310 y FQ(\))18 b(at)h(order)g FF(u)1857 292 y FH(4)1876 310 y FQ(.)60 370 y(W)l(e)i(conclude)g(that)h(at)g(lo)o(w)g(temp) q(erature)e FF(M)960 352 y Fy(0)993 370 y FQ(and)j FF(E)1133 352 y Fy(0)1166 370 y FP(c)n(an)j FQ(b)q(e)21 b(matc)o(hed)f(at)i FF(h)h FQ(=)g(0)f(in)f(the)60 430 y(t)o(w)o(o-dimensional)12 b(Ising)i(mo)q(del)f(with)h(the)f(2)6 b FE(\002)g FQ(2)15 b(ma)s(jorit)o (y-rule)d(transformation.)20 b(Ho)o(w)o(ev)o(er,)12 b(w)o(e)60 490 y(do)17 b(not)f(kno)o(w)h(what)g(will)e(happ)q(en)i(with)f(other)g (transformations.)133 550 y(Similar)10 b(remarks)h(apply)g(in)h(the)g(case)g (of)g(higher-dimensional)f(in)o(teraction)g(spaces)h FF(V)f FQ(.)20 b(While)60 611 y(w)o(e)c(are)h(unable)f(to)h(pro)o(v)o(e)e(that)i(a)g (discon)o(tin)o(uit)o(y)e(will)g(inevitably)g(b)q(e)h(observ)o(ed,)g(neither) f(do)i(w)o(e)60 671 y(see)h(an)o(y)g(reason)i(to)e(b)q(eliev)o(e)f(that)i (the)f(renormalized)e(exp)q(ectation)i(v)m(alues)g FE(h)p FF(f)1556 678 y FH(\011)1586 671 y FE(i)1605 678 y FD(\026)1626 669 y Ft(0)1659 671 y FQ(can)g(alw)o(a)o(ys)60 731 y(b)q(e)24 b(matc)o(hed,)f(sim)o (ultaneously)f(for)i(all)f(\011)k FE(2)f FF(V)35 b FP(and)25 b(al)r(l)h(phases)e FF(\026)1405 713 y Fy(0)1417 731 y FQ(,)h(b)o(y)e(some)g (in)o(teraction)60 791 y(\010)95 773 y Fy(0)134 791 y FE(2)28 b FF(V)11 b FQ(.)45 b(Therefore,)25 b(w)o(e)f(m)o(ust)f(exp)q(ect)g(that)i FP(typic)n(al)r(ly)k FQ(the)24 b(observ)o(ed)g(R)o(G)g(map)f(will)g(b)q(e)60 851 y(m)o(ulti-v)m(alued)16 b(and)j(discon)o(tin)o(uous)g(at)f(a)h (\014rst-order)h(phase-transition)f(surface,)g(purely)e(as)j(an)60 912 y(artifact)j(of)h(the)f(truncation)g(of)h(the)f(renormalized)e(in)o (teraction.)42 b(Of)23 b(course,)h(if)f(the)g(image)60 972 y(measure)d FF(\026)284 954 y Fy(0)318 972 y FQ(is)h(Gibbsian,)h(then)f(this) h(discon)o(tin)o(uit)o(y)d(should)j(go)g(to)g(zero)f(asymptotically)e(as)60 1032 y(the)i(assumed)g(in)o(teraction)f(space)h FF(V)763 1039 y FD(n)808 1032 y FQ(gro)o(ws.)37 b(If)21 b FF(\026)1062 1014 y Fy(0)1095 1032 y FQ(is)g(non-Gibbsian,)i(then)e(w)o(e)g(exp)q(ect)f(the)60 1092 y(estimated)13 b(renormalized)f(in)o(teractions)h(\010)866 1074 y Fy(0)866 1104 y FD(n)904 1092 y FQ(to)i(div)o(erge)e(in)h FE(B)1218 1074 y FH(1)1251 1092 y FQ(norm,)g(and)h(it)e(is)i(p)q(erfectly)e (lik)o(ely)60 1152 y(that)k(the)f(\010)285 1134 y Fy(0)285 1165 y FD(n)325 1152 y FQ(corresp)q(onding)h(to)g(di\013eren)o(t)e(phases)i (will)e(div)o(erge)g FP(in)j(di\013er)n(ent)f(ways)t FQ(.)133 1212 y(W)l(e)12 b(think)g(that)h(this)f(explains)f(the)i(n)o(umericall)o(y)c (observ)o(ed)j(discon)o(tin)o(uities)f(of)h(the)g(R)o(G)g(map,)60 1273 y(irresp)q(ectiv)o(e)i(of)j(whether)f(the)g(renormalized)e(measure)g FF(\026)1154 1255 y Fy(0)1183 1273 y FQ(is)i(Gibbsian)g(or)h(not.)60 1414 y FB(5.2)70 b(A)22 b(Remark)f(on)i(Dangerous)h(Irrelev)l(an)n(t)f(V)-6 b(ariables)60 1507 y FQ(The)18 b(renormalization-group)g(description)g(of)h (critical)e(b)q(eha)o(vior)h(in)g(its)h(simplest)d(form)i(seems)60 1567 y(to)f(imply)c(h)o(yp)q(erscaling)j(relations)g(suc)o(h)g(as)785 1657 y FF(d\027)45 b FQ(=)d FF(\015)987 1637 y Fy(0)1009 1657 y FQ(+)11 b(2)p FF(\014)655 b FQ(\(5.11\))785 1730 y FF(d\027)45 b FQ(=)d(2\001)1024 1737 y FH(4)1054 1730 y FE(\000)11 b FF(\015)636 b FQ(\(5.12\))785 1803 y FF(d\027)45 b FQ(=)d(2)11 b FE(\000)g FF(\013)690 b FQ(\(5.13\))814 1900 y FF(\016)43 b FQ(=)964 1866 y FF(d)11 b FQ(+)g(2)g FE(\000)g FF(\021)p 964 1888 197 2 v 964 1934 a(d)g FE(\000)g FQ(2)g(+)g FF(\021)1765 1900 y FQ(\(5.14\))60 2015 y(where)18 b FF(\027;)8 b(\013;)g(\014)s(;)g(\015)s(;)g (\015)433 1997 y Fy(0)444 2015 y FF(;)g(\016)o(;)g FQ(\001)550 2022 y FH(4)569 2015 y FF(;)g(\021)19 b FQ(are)f(critical)f(exp)q(onen)o(ts)h (and)g FF(d)g FQ(is)g(the)g(spatial)g(dimension.)25 b(It)17 b(is)60 2075 y(a)j(w)o(ell-kno)o(wn)e(fact,)h(ho)o(w)o(ev)o(er,)g(that)g(h)o (yp)q(erscaling)g(do)q(es)h FP(not)25 b FQ(hold)19 b(for)h(systems)e(ab)q(o)o (v)o(e)h(their)60 2135 y(upp)q(er)d(critical)d(dimension)h FF(d)615 2142 y FD(u)637 2135 y FQ(:)21 b(for)16 b FF(d)e(>)g(d)862 2142 y FD(u)900 2135 y FQ(the)h(critical)e(exp)q(onen)o(ts)i(are)h(exp)q (ected)e(to)h(b)q(e)h(those)60 2196 y(of)22 b(mean-\014eld)f(theory)l(,)h (and)h(these)e(exp)q(onen)o(ts)h(satisfy)g(the)g(h)o(yp)q(erscaling)f (relations)h(only)g FP(at)60 2256 y FF(d)d FQ(=)f FF(d)185 2263 y FD(u)208 2256 y FQ(.)29 b(Indeed,)18 b(the)h(h)o(yp)q(erscaling)f (relations)h(\(5.11\){\(5.14\))h(ha)o(v)o(e)e(b)q(een)h FP(pr)n(oven)h(rigor) n(ously)60 2316 y(to)e(fail)j FQ(for)c(Ising-lik)o(e)d(mo)q(dels)h(in)h (dimension)f FF(d)f(>)g FQ(4)j([2,)e(130)q(,)h(7)q(,)f(13)q(,)h(6,)g(115)q (].)133 2376 y(The)g(traditional)g(explanation)f(of)h(h)o(yp)q(erscaling)g(|) f(and)h(of)g(its)g(failure)f(|)g(is)h(the)f(follo)o(wing)60 2436 y([117)q(,)e(118)r(,)g(254)q(]:)20 b(Under)14 b(an)g(R)o(G)g (transformation)g FF(H)1068 2418 y Fy(0)1094 2436 y FQ(=)g FE(R)p FQ(\()p FF(H)t FQ(\))g(with)g(linear)f(scale)h(factor)h FF(l)q FQ(,)e(the)60 2497 y(correlation)j(length)g FF(\030)j FQ(and)e(free)e(energy)h(densit)o(y)f FF(f)22 b FQ(transform)16 b(as)679 2587 y FF(\030)r FQ(\()p FF(H)t FQ(\))43 b(=)e FF(l)q(\030)r FQ(\()p FF(H)1008 2567 y Fy(0)1020 2587 y FQ(\))702 b(\(5.15a\))673 2660 y FF(f)5 b FQ(\()p FF(H)t FQ(\))43 b(=)e FF(g)r FQ(\()p FF(H)t FQ(\))20 b(+)f FF(l)1106 2639 y Fy(\000)p FD(d)1153 2660 y FF(f)5 b FQ(\()p FF(H)1245 2639 y Fy(0)1258 2660 y FQ(\))461 b(\(5.15b\))938 2784 y(162)p eop %%Page: 163 163 bop 60 91 a FQ(where)17 b FF(g)i FQ(is)e(nonsingular.)26 b(\(In)16 b(fact,)h(for)h(most)f(R)o(G)g(maps)f(these)h(iden)o(tities)f(are)h(only)g (appro)o(xi-)60 152 y(mate.\))h(Near)11 b(a)h(\014xed)g(p)q(oin)o(t)f FF(H)647 133 y Fy(\003)679 152 y FQ(w)o(e)g(parametrize)e(the)j(Hamiltonian)d (b)o(y)i(scaling)h(\014elds)f FF(g)1726 159 y FH(1)1746 152 y FF(;)d(g)1791 159 y FH(2)1811 152 y FF(;)g(:)g(:)g(:)60 212 y FQ(with)19 b(eigen)o(v)m(alues)g FF(l)446 194 y FD(y)463 199 y Fr(1)482 212 y FF(;)8 b(l)520 194 y FD(y)537 199 y Fr(2)556 212 y FF(;)g(:)g(:)g(:)o FQ(;)21 b(the)e(v)m(ariable)g FF(g)966 219 y FD(i)1000 212 y FQ(is)g(said)g(to)h(b)q(e)g FP(r)n(elevant)25 b FQ(\(resp.)19 b FP(irr)n(elevant)5 b FQ(\))20 b(if)60 272 y FF(y)84 279 y FD(i)112 272 y FF(>)13 b FQ(0)i(\(resp.)e FF(y)359 279 y FD(i)387 272 y FF(<)h FQ(0\).)21 b(The)14 b(critical)e(surface)i (corresp)q(onds)h(to)f(setting)g(all)f(the)h(relev)m(an)o(t)f(scaling)60 332 y(\014elds)k(to)h(zero.)25 b(W)l(e)17 b(can)h(assume)e(without)i(loss)g (of)g(generalit)o(y)e(that)i FF(g)1408 339 y FH(1)1446 332 y FQ(is)f(a)h(relev)m(an)o(t)e(v)m(ariable)60 392 y(\()p FF(y)103 399 y FH(1)136 392 y FF(>)e FQ(0\).)22 b(The)16 b(asymptotic)f(scaling)h(la)o (ws)g(then)g(read)581 496 y FF(\030)r FQ(\()p FF(g)646 503 y FH(1)667 496 y FF(;)8 b(g)712 503 y FH(2)732 496 y FF(;)g(:)g(:)g(:)o FQ(\))42 b FE(\031)f FF(l)q(\030)r FQ(\()p FF(l)1026 475 y FD(y)1043 480 y Fr(1)1063 496 y FF(g)1086 503 y FH(1)1106 496 y FF(;)8 b(l)1144 475 y FD(y)1161 480 y Fr(2)1180 496 y FF(g)1203 503 y FH(2)1223 496 y FF(;)g(:)g(:)g(:)o FQ(\))420 b(\(5.16a\))511 568 y FF(f)535 575 y FD(sing)605 568 y FQ(\()p FF(g)647 575 y FH(1)667 568 y FF(;)8 b(g)712 575 y FH(2)732 568 y FF(;)g(:)g(:)g(:)o FQ(\))42 b FE(\031)f FF(l)968 548 y Fy(\000)p FD(d)1015 568 y FF(f)1039 575 y FD(sing)1109 568 y FQ(\()p FF(l)1144 548 y FD(y)1161 553 y Fr(1)1180 568 y FF(g)1203 575 y FH(1)1223 568 y FF(;)8 b(l)1261 548 y FD(y)1278 553 y Fr(2)1298 568 y FF(g)1321 575 y FH(2)1341 568 y FF(;)g(:)g(:)g(:)o FQ(\))299 b(\(5.16b\))60 680 y(Making)16 b(the)g(c)o(hoice)f FF(l)g FQ(=)e FF(g)571 655 y Fy(\000)p FH(1)p FD(=y)651 660 y Fr(1)569 691 y FH(1)671 680 y FQ(,)685 662 y FH(71)738 680 y FQ(w)o(e)j(obtain)374 813 y FF(\030)r FQ(\()p FF(g)439 820 y FH(1)460 813 y FF(;)8 b(g)505 820 y FH(2)525 813 y FF(;)g(g)570 820 y FH(3)589 813 y FF(;)g(:)g(:)g(:)p FQ(\))41 b FE(\031)g(j)p FF(g)846 820 y FH(1)866 813 y FE(j)880 793 y Fy(\000)p FH(1)p FD(=y)960 798 y Fr(1)980 813 y FF(\030)1003 740 y Fx( )1036 813 y FE(\006)p FQ(1)p FF(;)1185 780 y(g)1208 787 y FH(2)p 1126 802 160 2 v 1126 847 a FE(j)p FF(g)1163 854 y FH(1)1183 847 y FE(j)1197 833 y FD(y)1214 838 y Fr(2)1232 833 y FD(=y)1267 838 y Fr(1)1291 813 y FF(;)1376 780 y(g)1399 787 y FH(3)p 1318 802 V 1318 847 a FE(j)p FF(g)1355 854 y FH(1)1375 847 y FE(j)1389 833 y FD(y)1406 838 y Fr(3)1423 833 y FD(=y)1458 838 y Fr(1)1483 813 y FF(;)8 b(:)g(:)g(:)1562 740 y Fx(!)1741 813 y FQ(\(5.17a\))304 954 y FF(f)328 961 y FD(sing)398 954 y FQ(\()p FF(g)440 961 y FH(1)460 954 y FF(;)g(g)505 961 y FH(2)525 954 y FF(;)g(g)570 961 y FH(3)589 954 y FF(;)g(:)g(:)g(:)p FQ(\))41 b FE(\031)g(j)p FF(g)846 961 y FH(1)866 954 y FE(j)880 934 y FD(d=y)933 939 y Fr(1)953 954 y FF(f)977 961 y FD(sing)1046 881 y Fx( )1079 954 y FE(\006)p FQ(1)p FF(;)1228 921 y(g)1251 928 y FH(2)p 1169 943 V 1169 989 a FE(j)p FF(g)1206 996 y FH(1)1226 989 y FE(j)1240 974 y FD(y)1257 979 y Fr(2)1275 974 y FD(=y)1310 979 y Fr(1)1334 954 y FF(;)1420 921 y(g)1443 928 y FH(3)p 1361 943 V 1361 989 a FE(j)p FF(g)1398 996 y FH(1)1418 989 y FE(j)1432 974 y FD(y)1449 979 y Fr(3)1467 974 y FD(=y)1502 979 y Fr(1)1526 954 y FF(;)8 b(:)g(:)g(:)1605 881 y Fx(!)1738 954 y FQ(\(5.17b\))60 1095 y(If)k(no)o(w)h FF(g)226 1102 y FD(i)253 1095 y FQ(is)f(an)h FP(irr)n(elevant)19 b FQ(v)m(ariable)12 b(\()p FF(y)804 1102 y FD(i)831 1095 y FF(<)i FQ(0\),)f(then)g FF(g)1084 1102 y FD(i)1098 1095 y FF(=)p FE(j)p FF(g)1159 1102 y FH(1)1180 1095 y FE(j)1194 1077 y FD(y)1211 1082 y Fs(i)1224 1077 y FD(=y)1259 1082 y Fr(1)1292 1095 y FE(!)h FQ(0)f(as)g FF(g)1472 1102 y FH(1)1506 1095 y FE(!)h FQ(0.)20 b(It)12 b FP(app)n(e)n(ars)h(at)60 1155 y(\014rst)i(glanc)n(e)t FQ(,)f(therefore,)f(that)h(for)f(the)g(purp)q (ose)h(of)g(determining)d(the)i(leading)f(scaling)i(b)q(eha)o(vior,)60 1215 y(the)i(quan)o(tit)o(y)f FF(g)362 1222 y FD(i)377 1215 y FF(=)p FE(j)p FF(g)438 1222 y FH(1)458 1215 y FE(j)472 1197 y FD(y)489 1202 y Fs(i)503 1197 y FD(=y)538 1202 y Fr(1)574 1215 y FQ(on)h(the)h(righ)o(t-hand)g(sides)f(of)h(\(5.17\))g(can)f(b)q(e)h (replaced)e(b)o(y)h(zero.)22 b(F)l(or)60 1275 y(example,)12 b(if)i(only)g(the)h(\014rst)g(t)o(w)o(o)f(\014elds)g(are)h(relev)m(an)o(t)e (\(the)h(case)h(of)g(an)g(ordinary)g(critical)d(p)q(oin)o(t\),)60 1335 y(w)o(e)k(w)o(ould)g(obtain)391 1458 y FF(\030)r FQ(\()p FF(g)456 1465 y FH(1)477 1458 y FF(;)8 b(g)522 1465 y FH(2)542 1458 y FF(;)g(g)587 1465 y FH(3)607 1458 y FF(;)g(g)652 1465 y FH(4)672 1458 y FF(;)g(:)g(:)g(:)o FQ(\))41 b FE(\031)g(j)p FF(g)928 1465 y FH(1)948 1458 y FE(j)962 1437 y Fy(\000)p FH(1)p FD(=y)1042 1442 y Fr(1)1062 1458 y FF(\030)1085 1384 y Fx( )1118 1458 y FE(\006)p FQ(1)p FF(;)1267 1424 y(g)1290 1431 y FH(2)p 1208 1446 V 1208 1492 a FE(j)p FF(g)1245 1499 y FH(1)1265 1492 y FE(j)1279 1477 y FD(y)1296 1482 y Fr(2)1314 1477 y FD(=y)1349 1482 y Fr(1)1373 1458 y FF(;)8 b FQ(0)p FF(;)g FQ(0)p FF(;)g(:)g(:)g(:)1545 1384 y Fx(!)1741 1458 y FQ(\(5.18a\))321 1599 y FF(f)345 1606 y FD(sing)415 1599 y FQ(\()p FF(g)457 1606 y FH(1)477 1599 y FF(;)g(g)522 1606 y FH(2)542 1599 y FF(;)g(g)587 1606 y FH(3)607 1599 y FF(;)g(g)652 1606 y FH(4)672 1599 y FF(;)g(:)g(:)g(:)o FQ(\))41 b FE(\031)g(j)p FF(g)928 1606 y FH(1)948 1599 y FE(j)962 1578 y FD(d=y)1015 1583 y Fr(1)1035 1599 y FF(f)1059 1606 y FD(sing)1129 1526 y Fx( )1161 1599 y FE(\006)p FQ(1)p FF(;)1310 1565 y(g)1333 1572 y FH(2)p 1251 1587 V 1251 1633 a FE(j)p FF(g)1288 1640 y FH(1)1308 1633 y FE(j)1322 1618 y FD(y)1339 1623 y Fr(2)1357 1618 y FD(=y)1392 1623 y Fr(1)1416 1599 y FF(;)8 b FQ(0)p FF(;)g FQ(0)p FF(;)g(:)g(:)g(:)1588 1526 y Fx(!)1738 1599 y FQ(\(5.18b\))60 1733 y(In)17 b(particular,)h(supp)q(ose)g (that)g(w)o(e)g(set)f FF(g)828 1740 y FH(1)864 1733 y FQ(=)f FF(t)i FQ(\(the)f(temp)q(erature)f(deviation)h(from)g(criticalit)o(y\))60 1793 y(and)24 b FF(g)185 1800 y FH(2)232 1793 y FQ(=)j FF(h)c FQ(\(the)h(magnetic)e(\014eld\).)43 b(Then)24 b(\(5.18a\))h(yields)d(the)i (scaling)g(b)q(eha)o(vior)f(of)h(the)60 1854 y(correlation)16 b(length:)130 1986 y FF(\030)r FQ(\()p FF(t;)8 b(h)14 b FQ(=)g(0)p FF(;)8 b(g)375 1993 y FH(3)396 1986 y FF(;)g(g)441 1993 y FH(4)460 1986 y FF(;)g(:)g(:)g(:)p FQ(\))27 b FE(\030)653 1912 y Fx(\()707 1954 y FF(t)725 1936 y Fy(\000)p FD(\027)903 1954 y FQ(as)17 b FF(t)c FE(!)h FQ(0)1082 1936 y FH(+)707 2016 y FQ(\()p FE(\000)p FF(t)p FQ(\))802 1998 y Fy(\000)p FD(\027)848 1986 y Ft(0)903 2016 y FQ(as)j FF(t)c FE(!)h FQ(0)1082 1998 y Fy(\000)1132 1912 y Fx(\))1272 1986 y FQ(with)i FF(\027)h FQ(=)d FF(\027)1503 1965 y Fy(0)1528 1986 y FQ(=)g(1)p FF(=y)1652 1993 y FD(t)1681 1986 y FF(:)70 b FQ(\(5)p FF(:)p FQ(19\))60 2120 y(Lik)o(ewise,)14 b(\(5.18b\))j(and)f(its)f(deriv)m(ativ)o(es)f(yield)h(the)g(scaling)h(b)q (eha)o(vior)f(for)h(the)g(thermo)q(dynamic)60 2180 y(quan)o(tities:)95 2276 y(\(a\))25 b(Di\013eren)o(tiating)17 b(\(5.18b\))h(t)o(wice)f(with)h (resp)q(ect)f(to)h FF(t)g FQ(and)g(setting)g FF(h)e FQ(=)h(0,)h(w)o(e)f (obtain)h(the)182 2337 y(critical)d(exp)q(onen)o(ts)i(for)g(the)f(sp)q (eci\014c)g(heat:)22 b FF(\013)15 b FQ(=)g FF(\013)1162 2319 y Fy(0)1188 2337 y FQ(=)g(2)c FE(\000)g FF(d=y)1399 2344 y FD(t)1415 2337 y FQ(.)22 b(Com)o(bining)16 b(this)g(with)182 2397 y(\(5.19\))h(yields)e(the)h(h)o(yp)q(erscaling)g(la)o(w)g FF(d\027)h FQ(=)d(2)d FE(\000)g FF(\013)p FQ(.)p 60 2441 732 2 v 100 2495 a FA(71)135 2510 y Fz(F)m(or)k(a)g(p)q(osition-space)h(R)o(G)e (map,)g(this)i(can)g(of)e(course)j(b)q(e)f(done)g(only)f(appro)o(ximately)m (,)e(since)j Fv(l)h Fz(m)o(ust)d(b)q(e)i(a)60 2560 y(p)q(o)o(w)o(er)h(of)f (the)i(basic)f(blo)q(c)o(k)f(size)i Fv(b)p Fz(.)26 b(Ho)o(w)o(ev)o(er,)18 b(this)f(is)g(go)q(o)q(d)f(enough)h(for)f(the)i(purp)q(ose)g(of)e(obtaining)f (critical)60 2610 y(exp)q(onen)o(ts:)j(b)o(y)12 b(c)o(ho)q(osing)g Fv(l)h Fz(within)e(a)h(factor)g Fv(b)g Fz(of)f(the)i(desired)g(v)n(alue,)e (one)h(obtains)g(the)g(desired)i(equalit)o(y)d Fw(within)60 2660 y(a)k(b)n(ounde)n(d)h(multiplic)n(ative)e(c)n(onstant)t Fz(.)938 2784 y FQ(163)p eop %%Page: 164 164 bop 93 91 a FQ(\(b\))24 b(Di\013eren)o(tiating)18 b(\(5.18b\))j(once)e(or)g (t)o(wice)f(with)i(resp)q(ect)f(to)g FF(h)p FQ(,)h(then)f(setting)g FF(h)g FQ(=)g(0,)h(w)o(e)182 152 y(obtain)c(the)g(critical)e(exp)q(onen)o(ts) i(for)g(the)g(sp)q(on)o(taneous)i(magnetization)c(and)j(the)f(suscep-)182 212 y(tibilit)o(y:)k FF(\014)e FQ(=)d(\()p FF(d)d FE(\000)f FF(y)591 219 y FD(h)613 212 y FQ(\))p FF(=y)680 219 y FD(t)712 212 y FQ(and)18 b FF(\015)g FQ(=)d FF(\015)932 194 y Fy(0)959 212 y FQ(=)g(\(2)p FF(y)1079 219 y FD(h)1114 212 y FE(\000)c FF(d)p FQ(\))p FF(=y)1256 219 y FD(t)1271 212 y FQ(.)24 b(Com)o(bining)16 b(this)g(with)h(\(5.19\))182 272 y(yields)e(the)h(h)o(yp)q(erscaling)g(la)o (w)g FF(d\027)h FQ(=)d FF(\015)918 254 y Fy(0)941 272 y FQ(+)d(2)p FF(\014)s FQ(.)98 374 y(\(c\))24 b(Di\013eren)o(tiating)c(\(5.18b\))i(four)f (times)e(with)i(resp)q(ect)g(to)g FF(h)p FQ(,)h(then)e(setting)h FF(h)h FQ(=)g(0)f(\(with)182 434 y FF(t)26 b(>)h FQ(0\),)f(w)o(e)d(obtain)i (the)e(critical)g(exp)q(onen)o(t)g(for)h(the)g(four-p)q(oin)o(t)h(cum)o(ulan) o(t:)34 b(2\001)1816 441 y FH(4)1852 434 y FQ(+)182 494 y FF(\015)21 b FQ(=)d(\(4)p FF(y)351 501 y FD(h)387 494 y FE(\000)12 b FF(d)p FQ(\))p FF(=y)530 501 y FD(t)545 494 y FQ(.)29 b(Com)o(bining)18 b(this)g(with)h(\(5.19\))g(and)h(the)e(form)o(ula)g(for)h FF(\015)j FQ(yields)17 b(the)182 554 y(h)o(yp)q(erscaling)f(la)o(w)g FF(d\027)h FQ(=)d(2\001)734 561 y FH(4)765 554 y FE(\000)d FF(\015)s FQ(.)60 656 y(\(Relations)16 b(for)h(exp)q(onen)o(ts)f(on)h(the)g (critical)e(isotherm)g(can)h(b)q(e)h(obtained)g(in)f(a)h(similar)d(manner)60 716 y(b)o(y)21 b(setting)h FF(g)322 723 y FH(1)365 716 y FQ(=)h FF(h)f FQ(and)g FF(g)599 723 y FH(2)642 716 y FQ(=)h FF(t)f FQ(=)h(0.\))38 b(Ho)o(w)o(ev)o(er,)21 b(Fisher)g([117)q(])1371 698 y FH(72)1429 716 y FQ(p)q(oin)o(ted)h(out)g(that)g FP(this)60 776 y(r)n(e)n(asoning)c(is)f(c)n(orr)n(e)n(ct)g(only)h(if)g FF(f)5 b FQ(\()p FF(g)715 783 y FH(1)735 776 y FF(;)j(g)780 783 y FH(2)800 776 y FF(;)g(g)845 783 y FH(3)865 776 y FF(;)g(g)910 783 y FH(4)930 776 y FF(;)g(:)g(:)g(:)o FQ(\))18 b FP(and)g(its)g(low-or)n (der)f(derivatives)i(have)g(\014nite)60 836 y(limits)13 b(as)g FF(g)272 843 y FH(3)292 836 y FF(;)8 b(g)337 843 y FH(4)357 836 y FF(;)g(:)g(:)g(:)13 b FE(!)h FQ(0)f FP(when)h FF(g)694 843 y FH(1)728 836 y FQ(=)g FE(\006)p FQ(1.)20 b(If)11 b FF(f)17 b FQ(or)12 b(one)f(of)h(its)f(lo)o(w-order)h(deriv)m(ativ)o(es)e(div)o(erges) g(as)60 897 y FF(g)83 904 y FH(3)103 897 y FF(;)e(g)148 904 y FH(4)168 897 y FF(;)g(:)g(:)g(:)13 b FE(!)h FQ(0,)f(then)h(the)f(h)o(yp)q (erscaling)g(relations)g(can)g(fail.)20 b(A)13 b(v)m(ariable)g FF(g)1479 904 y FD(i)1507 897 y FQ(whic)o(h)f(is)h(irrelev)m(an)o(t)60 957 y(in)20 b(the)g(R)o(G)g(sense)g(but)g(whic)o(h)g(pro)o(v)o(ok)o(es)f(a)h (div)o(ergence)f(of)h(the)g(free)f(energy)h(densit)o(y)f(\(or)i(one)60 1017 y(of)d(its)g(lo)o(w-order)g(deriv)m(ativ)o(es\))e(is)i(termed)e(a)i FP(danger)n(ous)i(irr)n(elevant)f(variable)t FQ(.)27 b(W)l(e)18 b(emphasize)60 1077 y(that)f(the)g(free)f(energy)h(is)g(here)f(b)q(eing)h(ev) m(aluated)g FP(wel)r(l)k(away)d(fr)n(om)e(the)j(critic)n(al)g(p)n(oint)5 b FQ(,)16 b(namely)60 1137 y(at)h FF(g)143 1144 y FH(1)177 1137 y FQ(=)c FE(\006)p FQ(1.)133 1198 y(The)h(standard)i(example)c(of)j(suc) o(h)f(a)g(b)q(eha)o(vior)h(is)f(the)g FF(')1181 1180 y FH(4)1215 1198 y FQ(mo)q(del)f(in)h(dimension)e FF(d)i(>)g FQ(4.)21 b(Here)60 1258 y(the)f(\014xed)f(p)q(oin)o(t)h(is)g(Gaussian,)h(with)f(relev)m(an)o(t)f (\014elds)g FF(g)1134 1265 y FH(1)1174 1258 y FQ(=)h FF(t)g FQ(and)g FF(g)1391 1265 y FH(2)1431 1258 y FQ(=)g FF(h)p FQ(;)h(the)f FF(')1672 1240 y FH(4)1711 1258 y FQ(coupling)60 1318 y(constan)o(t)14 b FF(g)277 1325 y FH(3)311 1318 y FQ(=)f FF(u)g FQ(is)h(irrelev)m(an)o(t)d (in)i(the)g(R)o(G)g(sense.)21 b(Ho)o(w)o(ev)o(er,)11 b(the)i(Gaussian)i(mo)q (del)d(is)h(unstable)60 1378 y(at)g(nonzero)h(magnetic)d(\014eld)h(on)i(the)e (critical)g(isotherm,)f(and)j(also)f(at)h(zero)e(magnetic)g(\014eld)g(b)q (elo)o(w)60 1438 y(the)k(critical)f(temp)q(erature,)f(and)j(the)f(irrelev)m (an)o(t)f FF(')1026 1420 y FH(4)1062 1438 y FQ(term)f(is)i(needed)g(to)g (stabilize)f(it.)21 b(A)16 b(mean-)60 1499 y(\014eld)g(calculation)f(\(whic)o (h)h(is)g(exp)q(ected)f(to)i(giv)o(e)e(the)i(correct)e(scaling)h(for)h FF(d)d(>)g FQ(4\))j(predicts)f(that)60 1559 y(the)g(free)f(energy)h(div)o (erges)g(as)g FF(u)e FE(#)g FQ(0,)i(as)619 1669 y FF(f)5 b FQ(\()p FF(t)14 b FQ(=)g FE(\000)p FQ(1)p FF(;)8 b(h;)g(u)p FQ(\))41 b FE(\031)g FF(u)1082 1648 y Fy(\000)p FH(1)1129 1669 y FF(W)7 b FQ(\()p FF(hu)1257 1648 y FH(1)p FD(=)p FH(2)1312 1669 y FQ(\))434 b(\(5.20\))658 1741 y FF(f)5 b FQ(\()p FF(t)14 b FQ(=)g(0)p FF(;)8 b(h;)g(u)p FQ(\))41 b FE(\031)g FF(u)1082 1721 y Fy(\000)p FH(1)p FD(=)p FH(3)1164 1741 y FF(h)1192 1721 y FH(4)p FD(=)p FH(3)1765 1741 y FQ(\(5.21\))60 1851 y(where)20 b FF(W)28 b FQ(is)20 b(a)h(w)o(ell-b)q(eha)o(v)o(ed)e(function.)34 b(Inserting)20 b(this)h(b)q(eha)o(vior)f(in)o(to)h(\(5.17b\),)h(one)e (\014nds)60 1912 y FP(mo)n(di\014e)n(d)26 b FQ(h)o(yp)q(erscaling)20 b(la)o(ws)i(whic)o(h)e(di\013er)h(from)f(\(5.11\){\(5.14\))j(and)f(whic)o(h)e (are)h(consisten)o(t)60 1972 y(with)16 b(the)g(mean-\014eld)f(exp)q(onen)o (ts.)21 b(This)16 b(b)q(eha)o(vior)g(o)q(ccurs)h(b)q(ecause)f(the)g(\014xed)g (p)q(oin)o(t)g FF(H)1753 1954 y Fy(\003)1790 1972 y FQ(is)g(on)60 2032 y(the)h FP(b)n(oundary)22 b FQ(of)c(the)f(stabilit)o(y)g(region,)h(and)g (the)f(free)g(energy)h(div)o(erges)e(as)j(this)e(b)q(oundary)i(is)60 2092 y(approac)o(hed.)316 2074 y FH(73)133 2152 y FQ(Here)j(w)o(e)h(w)o(ould) g(lik)o(e)f(to)h(mak)o(e)f(the)h(trivial)f(observ)m(ation)i(that)f(suc)o(h)g (a)h(blo)o(w-up)g(of)f(the)60 2213 y(free)18 b(energy)g(is)g(p)q(ossible)h FP(only)24 b FQ(in)18 b(mo)q(dels)f(with)i(un)o(b)q(ounded)g(Hamiltonians)e (\(suc)o(h)i(as)g(the)f FF(')1870 2194 y FH(4)60 2273 y FQ(mo)q(del\).)i (Indeed,)14 b(w)o(e)h(kno)o(w)g(that)g(for)h(absolutely)f(summable)d(in)o (teractions)j(\(\010)f FE(2)g(B)1663 2255 y FH(1)1682 2273 y FQ(\),)h(the)g(free)60 2333 y(energy)h(densit)o(y)f(is)h(a)g FP(Lipschitz)h(c)n(ontinuous)k FQ(function)16 b(of)h(the)f(in)o(teraction)f (\(Prop)q(ositions)i(2.56)p 60 2379 732 2 v 100 2433 a FA(72)135 2448 y Fz(See)e(also)e(Fisher)h([118)o(,)g(App)q(endix)g(D])f(and)h(Ma)f ([254)o(,)g(Section)i(VI)q(I.4].)100 2506 y FA(73)135 2521 y Fz(A)d(qualitativ)o(ely)e(similar)g(b)q(eha)o(vior)i(is)h(exp)q(ected)h(to) e(o)q(ccur)i(also)d(in)h(dimension)f Fv(d)g Fz(=)h(4.)17 b(Here)d(the)e (dangerous)60 2571 y(irrelev)n(an)o(t)j(v)n(ariable)e Fv(g)422 2577 y FA(3)453 2571 y Fz(=)g Fv(u)i Fz(is)f(only)g Fw(mar)n(ginal)r(ly)h (irr)n(elevant)j Fz(\(i.e.)13 b Fv(y)1171 2577 y FA(3)1203 2571 y Fz(=)g(0,)h(but)h(second-order)i(e\013ects)f(mak)o(e)e Fv(g)1872 2577 y FA(3)60 2621 y Fz(irrelev)n(an)o(t\),)f(so)h(that)g(the)h (violations)d(of)h(h)o(yp)q(erscaling)h(are)h(only)e Fw(lo)n(garithmic)r Fz(.)938 2784 y FQ(164)p eop %%Page: 165 165 bop 60 91 a FQ(and)17 b(2.58\).)23 b(This)17 b(means)e(that)i FP(the)h(fr)n(e)n(e)f(ener)n(gy)h(density)h(and)e(its)h(\014rst)g (derivatives)h(ar)n(e)e(always)60 152 y(b)n(ounde)n(d)5 b FQ(.)22 b(This)16 b(situation)g(prev)m(ails)g(in)g(all)g(ph)o(ysically)e(sensible)i (mo)q(dels)f(of)h FP(b)n(ounde)n(d)22 b FQ(spins.)133 212 y(These)d (considerations)h(do)g(not)f(quite)g(rule)f(out)i(the)f(p)q(ossibilit)o(y)f (of)i(dangerous)g(irrelev)m(an)o(t)60 272 y(v)m(ariables:)29 b(in)20 b(principle)f(it)h(could)g(happ)q(en)h(that)g FF(f)5 b FQ(\()p FE(\006)p FQ(1)p FF(;)j(g)1184 279 y FH(2)1204 272 y FF(;)g(g)1249 279 y FH(3)1269 272 y FF(;)g(:)g(:)g(:)o FQ(\))21 b(and)g(its)f(\014rst)g(deriv)m(ativ)o(es)60 332 y(are)h(b)q(ounded,)h(but)e (that)h FP(higher)26 b FQ(deriv)m(ativ)o(es)19 b(blo)o(w)i(up.)34 b(This)20 b(w)o(ould)h(cause)f(some)g(or)h(all)f(of)60 392 y(the)d(h)o(yp)q(erscaling)f(relations)h(to)h(fail.)767 374 y FH(74)828 392 y FQ(This)f(is)g(indeed)f(what)i(happ)q(ens)g(in)f(the)g FF(X)t(Y)28 b FQ(mo)q(del)16 b(in)60 452 y(dimension)d FF(d)h FQ(=)g(4)8 b FE(\000)g FF(\017)15 b FQ(\(and)h(probably)f(also)g FF(d)f FQ(=)g(3\))h(if)g(w)o(e)f(let)g FF(g)1261 459 y FH(3)1296 452 y FQ(b)q(e)h(the)g(co)q(e\016cien)o(t)e(of)i(a)g(cos)9 b FF(n\022)60 513 y FQ(single-site)18 b(term,)g(where)h FF(n)h FQ(is)f(ev)o(en)f(and)i FE(\025)e FQ(4)i([271)q(,)f(10].)30 b(Suc)o(h)19 b(a)h(term)d(is)j(irrelev)m(an)o(t)d(in)i(the)60 573 y(R)o(G)g(sense)g(\(at)g(least)g(if)g FF(\017)g FQ(is)g(small)e (enough\),)j(but)g(for)f FF(T)25 b(<)19 b(T)1261 580 y FD(c)1297 573 y FQ(it)g(suppresses)g(the)g(Goldstone)60 633 y(mo)q(des.)h(In)15 b FF(d)f(<)g FQ(4)i(these)e(mo)q(des)h(giv)o(e)f(rise)h(to)g(a)h(div)o(ergen) o(t)d(longitudinal)i(as)h(w)o(ell)e(as)h(transv)o(erse)60 693 y(susceptibilit)o(y)i(in)i(the)g(pure)h FF(X)t(Y)31 b FQ(mo)q(del)18 b([106)q(,)h(243)q(,)g(105)q(],)g(so)i(that)e(\()p FF(@)1438 675 y FH(2)1458 693 y FF(f)5 b(=@)s(h)1568 675 y FH(2)1588 693 y FQ(\)\()p FF(t)18 b FQ(=)i FE(\000)p FQ(1)p FF(;)8 b(h)19 b FQ(=)60 760 y(0)p FF(;)8 b(g)129 767 y FH(3)149 760 y FQ(\))21 b(is)g(\014nite)g(for)h FF(g)476 767 y FH(3)518 760 y FE(6)p FQ(=)g(0)g(but)f(blo)o(ws)g(up)h(as)f FF(g)1020 767 y FH(3)1063 760 y FE(!)h FQ(0)f(\(presumably)f(at)i(the)f(rate)g FE(\030)h FF(g)1811 735 y Fy(\000)p FD(\017=)p FH(2)1809 771 y(3)60 820 y FQ([271)q(]\).)e(This)c(means)f(that)h(the)g(mo)q(del)e(with)i FF(g)941 827 y FH(3)975 820 y FE(6)p FQ(=)e(0)i(b)q(elongs)h(to)f(a)g FF(Z)1374 827 y FD(n)1398 820 y FQ(-symmetri)o(c)d(but)j FF(S)s(O)q FQ(\(2\)-)60 881 y(nonsymmetric)e(univ)o(ersalit)o(y)i(class)i(|)f(whic)o(h)h (naiv)o(ely)e(w)o(ould)h(not)i(exist)e(|)g(and)i(that)f(in)f(this)60 941 y(univ)o(ersalit)o(y)11 b(class)i(the)g(relation)g FF(\015)716 923 y Fy(0)741 941 y FQ(=)h(\(2)p FF(y)860 948 y FD(h)887 941 y FE(\000)5 b FF(d)p FQ(\))p FF(=y)1023 948 y FD(t)1051 941 y FQ([step)12 b(\(b\))i(ab)q(o)o(v)o(e])e(fails.)20 b(As)13 b(a)g(consequence,)60 1001 y(the)j(scaling)g(la)o(w)g FF(\015)420 983 y Fy(0)446 1001 y FQ(=)d FF(\015)20 b FQ(fails,)15 b(and)i(is)f(replaced) f(b)o(y)h FF(\015)1089 983 y Fy(0)1115 1001 y FQ(=)d FF(\015)i FE(\000)1260 981 y FH(1)p 1260 989 18 2 v 1260 1018 a(2)1283 1001 y FF(\017y)1327 1008 y FH(3)1346 1001 y FF(=y)1394 1008 y FD(t)1423 1001 y FF(>)f(\015)19 b FQ([271)q(].)133 1061 y(Other)e(cases)g (in)g(whic)o(h)f(an)i(apparen)o(tly)f(irrelev)m(an)o(t)e(term)h(\(in)g(the)h (R)o(G)g(sense\))g(c)o(hanges)g(the)60 1121 y(phase)g(diagram)e(ha)o(v)o(e)h (b)q(een)g(studied)g(in)g([50,)g(10)q(,)g(350)q(].)133 1182 y(Ho)o(w)o(ev)o(er,)h(w)o(e)h(ha)o(v)o(e)g(not)h(b)q(een)f(able)g(to)h (construct)g(an)o(y)f(plausible)g(Ansatz)h(for)f(suc)o(h)h(a)g(b)q(e-)60 1242 y(ha)o(vior)g(in)g(an)g(Ising-to-Ising)h(R)o(G)f(map)f(for)i(the)e (Ising)h(mo)q(del)f(in)h(dimension)f FF(d)h(>)f FQ(4.)30 b(Nor)20 b(do)60 1302 y(w)o(e)15 b(kno)o(w)g(of)g(an)o(y)g(plausible)f(candidate)h (for)g(the)g(dangerous)h(irrelev)m(an)o(t)d(v)m(ariable.)21 b(\(In)14 b(the)h(Ising)60 1362 y(language)g(there)e(is)h(no)h(term)d(in)i (the)f(Hamiltonian)g(corresp)q(onding)i(to)f(the)g(\\)p FF(')1531 1344 y FH(4)1565 1362 y FQ(coupling";)g(suc)o(h)60 1422 y(a)j(term)d(is)i (built)g(in)o(to)g(the)g FP(a)h(priori)j FQ(single-spin)c(measure.\))133 1482 y(W)l(e)k(conclude)f(that)i(the)f(dangerous-irrelev)m(an)o(t-v)m (ariables)g(scenario)g(is)g(probably)h FP(not)k FQ(the)60 1543 y(correct)20 b(description)g(of)h(what)g(is)g(happ)q(ening)h(in)e(the)g (Ising)h(mo)q(del)e(in)i(dimension)e FF(d)j(>)f FQ(4,)h(at)60 1603 y(least)d(in)g(the)g(con)o(text)f(of)h(an)h(Ising-to-Ising)g(R)o(G)e (map.)29 b(On)20 b(the)e(other)i(hand,)g(w)o(e)e(kno)o(w)i(that)60 1663 y(the)g(h)o(yp)q(erscaling)f(relations)h(\(5.11\){\(5.14\))i(do)e(fail)f (for)i(Ising)f(mo)q(dels)e(in)i(dimension)e FF(d)j(>)f FQ(4.)60 1723 y(Therefore,)14 b(one)h(of)f(the)g FP(other)20 b FQ(assumptions)15 b(made)e(in)h(the)g(con)o(v)o(en)o(tional)f(R)o(G)h(theory)h(m)o(ust)e(fail) 60 1783 y(when)j(applied)g(to)h(Ising-to-Ising)g(R)o(G)f(maps)f(in)h (dimension)f FF(d)f(>)g FQ(4.)133 1844 y(F)l(or)24 b(large-cell)e(R)o(G)i (maps)f(\()p FF(b)k FE(!)f(1)p FQ(\),)f(the)e(results)h(summarized)d(in)i (Section)g(4.4)h(sho)o(w)60 1904 y(that)f(what)h(fails)e(is)h(the)g (Gibbsianness)g(of)g(the)g(\014xed-p)q(oin)o(t)f(measure)g FF(\026)1486 1886 y Fy(\003)1506 1904 y FQ(.)41 b(No)o(w)23 b(there)f(is)h(a)60 1964 y(v)o(ery)16 b(close)g(similarit)o(y)e(b)q(et)o(w)o (een)i(the)h(dangerous-irrelev)m(an)o(t-v)m(ariables)g(scenario)g(and)g(the)g (non-)60 2024 y(Gibbsianness)22 b(pro)q(of)h(for)f(large-cell)e(R)o(G)i (maps:)31 b(b)q(oth)23 b(hinge)e(on)i(the)e(fact)h(that)g(a)g(massless)60 2084 y(Gaussian)i(\014eld)e(is)g(unstable)h(to)g(magnetic-\014eld)e(p)q (erturbations.)41 b(This)22 b(reasoning)i(suggests)60 2145 y(that)d(non-Gibbsianness)i(of)e(the)g(\014xed-p)q(oin)o(t)g(measure)e(ma)o (y)h(o)q(ccur)h(also)g(for)h(iterated)e(Ising-)60 2205 y(to-Ising)j (transformations)f(with)g(\014xed)g(blo)q(c)o(k)g(size)f FF(b)h FQ(\(e.g.)f(ma)s(jorit)o(y)f(rule)i(or)g(the)g(Kadano\013)60 2265 y(transformation\).)40 b(If)21 b(this)i(w)o(ere)e(the)h(case,)i(then)e (the)g(R)o(G)g(map)g FE(R)h FQ(from)e(Hamiltonians)g(to)60 2325 y(Hamiltonians)c(w)o(ould)h(b)q(e)g(ill-de\014ned)f(at)i(the)f(critical) f(Ising)h(mo)q(del,)f(and)i(the)f(putativ)o(e)f(\014xed-)p 60 2369 732 2 v 100 2423 a FA(74)135 2438 y Fz(Fisher)c([118)o(,)g(p.)f(134]) g(states)i(that)f(the)g(deriv)n(ation)f(of)g(the)i(h)o(yp)q(erscaling)f (relations)g(relies)g(implicitly)d(on)i(the)60 2488 y(assumption)i(that)i (the)g(free)g(energy)g Fv(f)t Fz(\()p Fu(\006)p Fz(1)p Fv(;)7 b(g)793 2494 y FA(2)812 2488 y Fv(;)g(g)851 2494 y FA(3)869 2488 y Fv(;)g(g)908 2494 y FA(4)926 2488 y Fv(;)g(:)g(:)g(:)n Fz(\))15 b(has)h(a)f(w)o(ell-de\014ned)h(\014nite)f(limit)e(as)j Fv(g)1646 2494 y FA(3)1664 2488 y Fv(;)7 b(g)1703 2494 y FA(4)1721 2488 y Fv(;)g(:)g(:)g(:)12 b Fu(!)i Fz(0.)60 2537 y(Ho)o(w)o(ev)o(er,)f(this) g(statemen)o(t)g(is)g(sligh)o(tly)f(misleading,)e(b)q(ecause)15 b(it)e(is)g(to)q(o)g(w)o(eak:)k(in)c(fact,)g(as)g(is)g(clear)g(from)e (\(a\){\(c\))60 2587 y(ab)q(o)o(v)o(e,)17 b(to)f(deriv)o(e)h(a)g(h)o(yp)q (erscaling)g(relation)f(one)h(needs)h(to)e(kno)o(w)g(that)h(at)g(least)f(the) i Fw(se)n(c)n(ond)g(derivative)h Fz(of)d Fv(f)60 2637 y Fz(with)e(resp)q(ect) i(to)d Fv(t)h Fz(or)g Fv(h)g Fz(has)g(a)g(go)q(o)q(d)f(limit.)938 2784 y FQ(165)p eop %%Page: 166 166 bop 60 91 a FQ(p)q(oin)o(t)16 b(Hamiltonian)f FF(H)512 73 y Fy(\003)548 91 y FQ(w)o(ould)h(simply)e(not)j(exist.)60 258 y FG(6)83 b(Conclusions)25 b(and)j(Op)r(en)f(Questions)60 382 y FB(6.1)70 b(Conclusions)60 474 y FM(6.1.1)55 b(Ho)n(w)20 b(Muc)n(h)f(of)g(the)f(Standard)h(Picture)f(of)h(the)f(R)n(G)h(Map)g(is)g(T) -5 b(rue?)60 566 y FQ(W)l(e)18 b(can)h(classify)f(the)g(evidence)f(regarding) i(the)f(v)m(alidit)o(y)f(or)i(failure)f(of)h(the)f(standard)i(picture)60 627 y(of)d(R)o(G)f(transformations)g(in)g(three)g(categories:)133 712 y(1\))d FP(Positive)i(r)n(esults.)20 b FQ(Some)12 b(R)o(G)g(maps)g(are)g (w)o(ell-de\014ned)g(in)g(parts)h(of)g(the)f(one-phase)h(region.)60 772 y(The)j(published)g(pro)q(ofs)i(refer)d(to)i(the)f(follo)o(wing)g(cases:) 106 874 y(\(i\))24 b FP(High-\014eld)18 b(r)n(esults.)k FQ(Decimation)13 b(and)i(Kadano\013)i(transformations)e(for)g(absolutely)g(sum-)182 934 y(mable)g(lattice-gas)h([173)q(])f(and)i(Ising-spin)g([207])f(in)o (teractions.)93 1036 y(\(ii\))23 b FP(High-temp)n(er)n(atur)n(e)e(r)n (esults.)33 b FQ(Decimation)18 b([207)q(,)h(212)q(],)i(Kadano\013)g([207)q(]) f(and)g(a)o(v)o(eraging)182 1096 y([212)q(,)15 b(56)q(])h(transformations)g (for)h(absolutely)f(summable)e(Ising-spin)i(in)o(teractions.)79 1197 y(\(iii\))23 b FP(Smal)r(l-\014eld)c(r)n(esults.)i FQ(These)15 b(results)f(refer)g(to)h(decimation)d(transformations)j(of)g(the)f(Ising)182 1258 y(mo)q(del)j(in)h(an)o(y)h(dimension)e([258)q(]:)25 b(F)l(or)19 b(an)o(y)f FP(\014xe)n(d)25 b FQ(temp)q(erature)17 b(and)i FP(nonzer)n(o)i FQ(v)m(alue)e(of)182 1318 y(the)j(magnetic)f(\014eld,)i (there)f(exists)g(a)h(minim)n(um)18 b(blo)q(c)o(k)k(size)g FF(b)1412 1325 y FD(min)1501 1318 y FQ(b)q(ey)o(ond)g(whic)o(h)g(the)182 1378 y(renormalization)14 b(transformation)i(is)g(w)o(ell-de\014ned)e(\(the)i (minim)n(um)c(blo)q(c)o(k)j(size)g(div)o(erges)182 1438 y(as)i(a)f(p)q(o)o(w) o(er)h(of)f(1)p FF(=h)h FQ(when)g FF(h)d FE(!)f FQ(0\).)80 1540 y(\(iv\))24 b FP(R)n(esults)19 b(in)h(one)g(dimension.)28 b FQ(The)19 b(decimation)d(transformation)i(is)g(w)o(ell-de\014ned)f(in)h (di-)182 1600 y(mension)f FF(d)g FQ(=)g(1)i(for)g(lattice-gas)f(in)o (teractions)f(with)h(man)o(y-b)q(o)q(dy)g(and)h(long-range)h(cou-)182 1660 y(plings)c(satisfying)g(the)g(summabilit)o(y)d(condition)1118 1627 y Fx(P)1162 1671 y FD(A)p Fy(3)p FH(0)1231 1660 y FQ(\(diam)o FF(A)d FQ(+)h(1\))p FE(j)p FF(A)p FE(j)1560 1642 y Fy(\000)p FH(1)1607 1660 y FE(k)p FQ(\010)1667 1667 y FD(A)1696 1660 y FE(k)1721 1667 y Fy(1)1780 1660 y FF(<)22 b FE(1)182 1720 y FQ([59].)34 b(F)l(or)21 b(instance,)g(this)g(includes)e(all)i(the)f(t)o(w)o (o-b)q(o)q(dy)i(Ising)e(in)o(teractions)g(decreasing)182 1781 y(strictly)15 b(faster)h(than)h(1)p FF(=r)668 1763 y FH(2)689 1781 y FQ(.)60 1882 y(These)g(results)h(are,)f(ho)o(w)o(ev)o(er,)f(of)i (limited)c(in)o(terest,)i(as)i(they)f(corresp)q(ond)i(to)e(w)o(ell-understo)q (o)q(d)60 1943 y(regions)e(of)f(the)g(phase)h(diagram,)e(deep)h(within)g(the) g(regime)e(in)i(whic)o(h)f(uniqueness)h(of)h(the)f(Gibbs)60 2003 y(measure,)23 b(and)h(ev)o(en)e(analyticit)o(y)g(of)h(the)g(free)g (energy)f(and)i(correlation)f(functions,)h(can)g(b)q(e)60 2063 y(pro)o(v)o(en.)c(If)c(these)f(w)o(ere)g(the)h(only)f(p)q(ositiv)o(e)g (results,)g(then)h(one)g(w)o(ould)g(conclude,)e(in)i(agreemen)o(t)60 2123 y(with)d(Gri\016ths)g(and)i(P)o(earce's)d(p)q(essimist)g([172)q(],)h (that)h(the)f(metho)q(d)g(only)g(w)o(orks)h(where)f(one)g(do)q(es)60 2183 y(not)k(really)e(need)h(it)f(\(and,)i(w)o(e)f(ma)o(y)e(add,)j(sometime)o (s)d(not)j(ev)o(en)e(there,)g(giv)o(en)g(Theorem)g(4.8\).)133 2244 y(W)l(e)h(can)g(also)h(men)o(tion,)c(as)k(p)q(ositiv)o(e)e(results)h (\(of)g(a)h(sort\),)f(our)g(F)l(undamen)o(tal)f(Theorems)g(of)60 2304 y(Section)f(3)h(whic)o(h)f(sa)o(y)g(that)h(the)f(R)o(G)h(map)f(is)g (single-v)m(alued)g(and)h(con)o(tin)o(uous)f(|)h(in)f(accordance)60 2364 y(with)i(the)g(standard)i(picture)d(|)h FP(if)h(it)h(exists)g(at)g(al)r (l)5 b FQ(.)133 2449 y(2\))19 b FP(Non-ne)n(gative)i(r)n(esults.)28 b FQ(There)18 b(is)g(at)g(presen)o(t)g(no)g(evidence)f(of)h(R)o(G)g (pathologies)h(ab)q(o)o(v)o(e)60 2509 y(or)c(at)g(the)f(critical)f(temp)q (erature)g(for)i(mo)q(dels)e(strictly)h(b)q(elo)o(w)g(the)g(upp)q(er)h (critical)e(dimension)g FF(d)1867 2516 y FD(u)60 2569 y FQ(\(=)j(4)h(for)f (Ising-lik)o(e)e(mo)q(dels\).)20 b(In)c(fact,)g(there)f(exist)h(mo)q(dels)f (for)h(whic)o(h)g(the)g(critical)e(p)q(oin)o(t)i(has)60 2630 y(b)q(een)j(rigorously)h(studied)e(using)i(the)f(standard)h(R)o(G)f (prescription:)27 b(the)19 b(hierarc)o(hical)e(mo)q(dels)938 2784 y(166)p eop %%Page: 167 167 bop 60 91 a FQ([218)q(,)17 b(32)q(,)h(219)q(])f(and)i(the)f(Gross-Nev)o(eu)g (mo)q(del)f([149].)26 b(The)19 b(hierarc)o(hical)d(mo)q(dels)h(presen)o(t)g (the)60 152 y(most)h(faithful)h(transcription)g(of)g(Wilson's)g (prescription,)g(but)g(from)f(our)i(p)q(oin)o(t)f(of)g(view)g(they)60 212 y(are)14 b(somewhat)g(arti\014cial)f(as)i(the)f(p)q(ossible)h (pathologies)g(are)f(remo)o(v)o(ed)e(\\b)o(y)i(hand".)21 b(The)15 b(Gross-)60 272 y(Nev)o(eu)f(mo)q(del)g(is)i(fermionic,)c(and)17 b(th)o(us)e(has)i(no)f(direct)e(probabilistic)h(in)o(terpretation.)20 b(W)l(e)15 b(also)60 332 y(should)h(men)o(tion)d(here)h(some)g(v)o(ery)g(in)o (teresting)g(preliminary)f(results)h([214)q(])h(indicating)f(that)i(for)60 392 y(the)g(t)o(w)o(o-dimensional)f(Ising)i(mo)q(del)e(at)i(zero)g(\014eld,)f (the)g(ma)s(jorit)o(y-rule)e(transformation)j(migh)o(t)60 452 y(b)q(e)d(w)o(ell-de\014ned)e(at)i(\(as)g(w)o(ell)e(as)i(sligh)o(tly)f(b)q (elo)o(w\))g(the)g(critical)f(temp)q(erature.)19 b(These)14 b(results)f(are)60 513 y(partially)j(rigorous)i(and)f(partially)f(n)o (umerical,)d(and)18 b(so)f(far)g(they)f(concern)g(only)h(some)e(selected)60 573 y(\(alb)q(eit)g(judiciously)g(selected\))f(blo)q(c)o(k-spin)i (con\014gurations.)22 b(W)l(e)16 b(feel)e(that)i(this)g(w)o(ork)g(pro)o (vides)60 633 y(some)f(supp)q(ort)j(for)e(the)g(standard)i(picture,)d(but)h (its)g(results)g(are)g(still)f(inconclusiv)o(e.)133 718 y(3\))22 b FP(Ne)n(gative)h(r)n(esults.)36 b FQ(There)21 b(are)g(pathologies)h(at)f (lo)o(w)g(temp)q(erature)f(\(not)h(only)g(at)g(zero)60 778 y(magnetic)f(\014eld\))g(in)h(all)g(dimensions,)g(and)g(quite)g(p)q(ossibly)g (at)h(the)f(critical)e(p)q(oin)o(t)j(in)f(dimen-)60 839 y(sion)h FF(d)209 842 y FC(\()29 b(\))216 830 y FE(\025)278 839 y FF(d)303 846 y FD(u)326 839 y FQ(.)39 b(In)22 b(the)g(former)f(case)h(these)g (pathologies)h(consist)f(in)g(the)g(non-Gibbsianness)60 899 y(of)c(the)g(renormalized)d(measure,)i(that)h(is,)g(in)f(the)h(imp)q (ossibilit)o(y)d(of)j(constructing)g(a)g(renormal-)60 959 y(ized)f (Hamiltonian)e(after)j(ev)o(en)e(a)i FP(single)23 b FQ(R)o(G)17 b(transformation.)26 b(In)17 b(Sections)g(4.1{4.3)i(w)o(e)e(ha)o(v)o(e)60 1019 y(sho)o(wn)23 b(examples)d(of)j(suc)o(h)f(pathologies)h(for)g(all)f(the) g(standard)i(real-space)e(transformations)60 1079 y(\(decimation,)d (Kadano\013,)24 b(ma)s(jorit)o(y-rule,)18 b(a)o(v)o(eraging\).)35 b(The)21 b(range)g(of)g(temp)q(eratures)e(where)60 1139 y(these)c (pathologies)i(are)e(pro)o(v)o(en)g(to)h(exist)f(do)q(es)h(not)g(include)f (the)g(critical)f(temp)q(erature,)g(but)i(on)60 1200 y(the)g(other)h(hand)h (the)e(pathological)h(region)g(extends)f(o\013)i(the)e(phase-co)q(existence)g (curv)o(e,)g(i.e.)f(to)60 1260 y(nonzero)k(\(and)g(in)f(some)f(cases)i (large\))f(magnetic)f(\014eld)h(\(Section)f(4.3.6\).)28 b(Finally)l(,)17 b(in)h(Sections)60 1320 y(4.4)13 b(and)h(5.2)f(w)o(e)f(ha)o(v)o(e)h(giv)o(en) f(argumen)o(ts)g(indicating)g(that)h(for)g FF(d)1268 1323 y FC(\()29 b(\))1275 1312 y FE(\025)1327 1320 y FQ(4)14 b(there)e(ma)o(y)f(b)q (e)i(pathologies)60 1380 y(at)19 b(the)f(critical)f(p)q(oin)o(t.)28 b(In)18 b(these)g(latter)g(cases)h(our)g(argumen)o(ts)e(suggest)j(that)f(the) f FP(\014xe)n(d-p)n(oint)60 1440 y FQ(Hamiltonian)c(ma)o(y)h(b)q(e)i (ill-de\014ned.)133 1501 y(T)l(ak)o(en)22 b(together,)g(these)g(results)f (suggest)i(that)f(non-Gibbsianness)h(ma)o(y)d(b)q(e)i(the)f(normal)60 1561 y(situation)e(for)g(R)o(G)g(maps)f(at)h(lo)o(w)g(temp)q(erature)e (and/or)j(near)f(a)h(\014rst-order)f(phase-transition)60 1621 y(surface,)e(or)h(at)g(the)f(critical)f(p)q(oin)o(t)h(in)g(high)h (dimensions.)23 b(This)18 b(is)f(in)g(direct)f(con\015ict)h(with)g(the)60 1681 y(con)o(v)o(en)o(tional)e(R)o(G)h(ideology)g(\(compare)f(the)h(\014rst)h (paragraph)h(of)e(the)g(In)o(tro)q(duction\).)60 1811 y FM(6.1.2)55 b(Resp)r(onses)18 b(to)h(Some)e(Ob)s(jections)60 1903 y FQ(Man)o(y)f(of)h (our)f(colleagues,)g(up)q(on)h(hearing)g(our)g(results,)e(ha)o(v)o(e)h (initially)e(reacted)i(b)o(y)g(sa)o(ying:)21 b(\\If)60 1964 y FF(\026)89 1946 y Fy(0)119 1964 y FQ(is)c(not)h(Gibbsian)g(for)g(some)f(in) o(teraction)f(in)i FE(B)1005 1946 y FH(1)1024 1964 y FQ(,)f(then)h(that)g (just)f(means)g(it)g(is)h(Gibbsian)g(for)60 2024 y(some)j(in)o(teraction)g FP(not)27 b FQ(in)22 b FE(B)632 2006 y FH(1)651 2024 y FQ(.)38 b(Y)l(ou)22 b(ha)o(v)o(e)f(to)h(use)g(a)h(larger)f(space)g(of)g(in)o (teractions.")38 b(This)60 2084 y(view)17 b(seems)g FP(a)h(priori)k FQ(reasonable)d(|)e(and)i(it)e(is)h(ev)o(en)f(conceiv)m(able)f(that)j(it)e (is)h(correct)f(|)h(but)60 2144 y(unfortunately)g(things)g(are)g(not)g(quite) e(so)j(simple.)k(Before)17 b(asserting)h(that)g FF(\026)1543 2126 y Fy(0)1573 2144 y FQ(is)g(Gibbsian)g(for)60 2204 y(some)g(in)o (teraction)g(\010)468 2186 y Fy(0)505 2204 y FF(=)-30 b FE(2)19 b(B)586 2186 y FH(1)605 2204 y FQ(,)h(one)f(\014rst)h(has)g(to)f(de\014ne)g (what)h(it)f FP(me)n(ans)k FQ(for)d(a)f(measure)f(to)i(b)q(e)60 2265 y(\\Gibbsian")f(for)f(a)g(non-absolutely-summable)d(in)o(teraction.)25 b(Our)17 b(notion)h(of)g(Gibbs)g(measure)60 2325 y(relies)h(on)i(the)g(DLR)g (equations,)h(and)f(if)f(the)g(in)o(teraction)g(fails)g(to)h(b)q(e)g (absolutely)g(summable)60 2385 y(\(or)g(at)g(least)g(con)o(v)o(ergen)o(t\),)e (then)i(these)f(equations)h(simply)e(do)i(not)g(mak)o(e)e(sense.)34 b(It)20 b(is)h(th)o(us)60 2445 y(incum)o(b)q(en)o(t)15 b(on)i(the)g(adv)o(o)q (cate)g(of)h(\\larger)f(in)o(teraction)f(spaces")i(to)f(mak)o(e)f(precise)g (what)h(is)g(the)60 2505 y(corresp)q(ondence)i(b)q(et)o(w)o(een)f(measures)g (and)h(in)o(teractions)f(that)h(is)g(to)g(substitute)g(for)g(the)f(DLR)60 2566 y(equations)e(\(and)h(b)q(e)g(equiv)m(alen)o(t)d(to)j(them)e(when)h(the) g(in)o(teraction)f(is)h(absolutely)g(summable\).)133 2626 y(No)o(w,)g(as)g (is)g(usual)h(when)f(one)g(is)g(lo)q(oking)h(for)f(the)g(solution)h(of)f(an)h (equation,)e(there)h(are)g(t)o(w)o(o)938 2784 y(167)p eop %%Page: 168 168 bop 60 91 a FQ(compleme)o(n)o(tary)16 b(asp)q(ects)k(|)e(existence)g(and)h (uniqueness)f(|)h(and)h(one)f(w)o(an)o(ts)g(preferably)f(for)60 152 y(b)q(oth)13 b(prop)q(erties)e(to)h(hold.)20 b(The)12 b(existence)d(is)j (fa)o(v)o(ored)f(b)o(y)g(enlarging)h(the)f(space)h(of)g(p)q(ossible)f(solu-) 60 212 y(tions,)j(while)f(the)h(uniqueness)g(is)g(fa)o(v)o(ored)f(b)o(y)h (narro)o(wing)h(it;)f(and)g(it)g(is)g(far)g(from)f(clear,)g FP(a)j(priori)5 b FQ(,)60 272 y(whether)17 b(there)g(exists)g(a)h(space)f(in) g(whic)o(h)g(the)g(solutions)h(b)q(oth)h(exist)d(and)i(are)g(unique.)24 b(These)60 332 y(general)16 b(remarks)g(can)g(b)q(e)h(exempli\014ed)d(in)i (our)h(statistical-mec)o(hanical)d(problem.)20 b(Within)c(the)60 392 y(class)g(of)h(F)l(eller)d(sp)q(eci\014cations)i(\(and)h(hence)f FP(a)h(fortiori)j FQ(within)c FE(B)1312 374 y FH(1)1331 392 y FQ(\),)f(the)h(Gri\016ths-Ruelle)f(the-)60 452 y(orem)h(\(Theorem)g(2.15,)i (Corollary)g(2.18)g(and)g(Prop)q(osition)h(2.59\))f(guaran)o(tees)g(the)f (uniqueness)60 513 y(of)g(the)g(sp)q(eci\014cation)g(for)g(a)g(giv)o(en)f (measure)g FF(\026)i FQ(\(and)f(hence)f(the)h(uniqueness)g(mo)q(dulo)f(ph)o (ysical)60 573 y(equiv)m(alence)f(of)i(the)f(in)o(teraction\).)22 b(But)16 b(the)g(existence)f(ma)o(y)g(fail,)h(as)h(w)o(e)g(sho)o(w)o(ed)f (through)i(n)o(u-)60 633 y(merous)f(examples)e(in)j(Section)f(4.)26 b(On)17 b(the)h(other)g(hand,)g(if)f(w)o(e)g(enlarge)h(the)f(space)h(of)g (allo)o(w)o(ed)60 693 y(sp)q(eci\014cations)23 b(b)o(y)g(dropping)h(the)f(F)l (eller)e(\()p FE(\031)i FQ(quasilo)q(calit)o(y\))f(prop)q(ert)o(y)l(,)j(then) e(the)g(existence)60 753 y(holds)f(but)h(the)e(uniqueness)h(fails)f(sp)q (ectacularly)h(\(see)f(the)h(Remark)e(at)j(the)e(end)h(of)h(Section)60 814 y(2.3.4\).)32 b(Similarly)l(,)17 b(if)j(w)o(e)f(enlarge)h(the)f(space)h (of)g(allo)o(w)o(ed)f(in)o(teractions)g(from)g FE(B)1621 796 y FH(1)1660 814 y FQ(to)h FE(B)1758 796 y FH(0)1777 814 y FQ(,)g(and)60 874 y(generalize)c(\\Gibbs)j(measure")e(to)h(\\equilibrium)d(measure",)h (then)i(ev)o(ery)e(ergo)q(dic)i(measure)f(of)60 934 y(\014nite)e(en)o(trop)o (y)g(densit)o(y)f(is)h(the)g(equilibrium)d(measure)i(for)i(some)f(in)o (teraction,)f(but)h(the)g(unique-)60 994 y(ness)d(again)g(fails)g(sp)q (ectacularly)f(\(see)g(item)e(2)j(in)f(Section)g(2.6.7\).)20 b(One)12 b(certainly)e(cannot)i(dev)o(elop)60 1054 y(a)17 b(satisfactory)f(R) o(G)g(theory)g(in)g(suc)o(h)g(pathological)h(spaces.)133 1115 y(F)l(urthermore,)12 b(w)o(e)i(ha)o(v)o(e)f(giv)o(en)h(strong)h(argumen)o(ts) e(that)h(an)o(y)g(ph)o(ysically)f(reasonable)h(sp)q(eci-)60 1175 y(\014cation)f(m)o(ust)f(b)q(e)h FP(quasilo)n(c)n(al)5 b FQ(,)14 b(at)f(least)g(in)f(systems)g(of)i(b)q(ounded)f(spins)h(\(see)e (Section)h(2.3.3\).)20 b(On)60 1235 y(the)e(other)f(hand,)i(in)e(Sections)h (4.1{4.3)h(and)f(4.5.2)g(w)o(e)g(ha)o(v)o(e)f(pro)o(v)o(en)g(directly)f(that) i(the)g(renor-)60 1295 y(malized)13 b(measures)g(are)i(not)h(consisten)o(t)e (with)h FP(any)k FQ(quasilo)q(cal)c(sp)q(eci\014cation.)21 b(So)15 b(ev)o(en)f(if)h(there)60 1355 y(w)o(ere)21 b(to)h(exist)f(quasilo)q (cal)h(sp)q(eci\014cations)f(corresp)q(onding)i(to)f(in)o(teractions)f(not)h (in)g FE(B)1741 1337 y FH(1)1760 1355 y FQ(,)g(suc)o(h)60 1416 y(sp)q(eci\014cations)16 b(could)g(not)h(b)q(e)f(of)h(an)o(y)f(relev)m(ance)f (for)i(our)f(renormalization-group)g(problem.)1836 1397 y FH(75)133 1476 y FQ(Our)i(\014nal)g(ob)s(jection)f(to)h(considering)g(spaces)g(of)g(in) o(teractions)f(larger)h(than)g FE(B)1641 1458 y FH(1)1678 1476 y FQ(is)g(that)g FE(B)1871 1458 y FH(1)60 1536 y FQ(is)e(already)g(to)q(o)h (big!)22 b(Indeed,)15 b(the)g(standard)j(R)o(G)e(ideology)g([365)q(])f(is)h (that)h(the)f(R)o(G)g(\015o)o(w)h(should)60 1596 y(tak)o(e)i(place)g(in)g (some)g(space)g(of)h(\\short-range")i(in)o(teractions,)d(e.g.)g(in)o (teractions)g(whic)o(h)g(deca)o(y)60 1656 y(exp)q(onen)o(tially)13 b(or)i(at)g(least)f(lik)o(e)f(a)i(su\016cien)o(tly)d(large)j(p)q(o)o(w)o(er)f (\(e.g.)g FE(j)p FF(x)p FE(j)1377 1638 y Fy(\000)p FD(p)1438 1656 y FQ(with)h FF(p)f FE(\025)f FF(d)8 b FQ(+)g(1\).)21 b(This)60 1716 y(ideology)12 b(is)h(not)g(a)g(mere)d(whim,)i(but)g(results)h(from)e (the)i(need)f(to)h(explain)e(univ)o(ersalit)o(y)g(of)i(critical)60 1777 y(b)q(eha)o(vior:)29 b(one)21 b(needs)f(to)h(ha)o(v)o(e)e(an)i(in)o (teraction)e(space)i(in)f(whic)o(h)f(the)h(unstable)h(manifold)e(of)60 1837 y(a)h(giv)o(en)e(\014xed)h(p)q(oin)o(t)h(is)f FP(\014nite-dimensional)28 b FQ(\(i.e.)17 b(there)i(are)h(\014nitely)e(man)o(y)g(relev)m(an)o(t)g (scaling)60 1897 y(\014elds\).)k(No)o(w,)16 b(suc)o(h)h(a)g(b)q(eha)o(vior)g (is)f(imp)q(ossible)f(in)i(a)g(space)f(of)h(long-range)h(in)o(teractions)e (\(suc)o(h)60 1957 y(as)g FE(B)154 1939 y FH(1)173 1957 y FQ(\),)f(since)g (in)h(general)f(the)g(critical)f(exp)q(onen)o(ts)i(will)e(b)q(e)i(altered)f (b)o(y)g(an)o(y)g(p)q(erturbation)i(that)60 2017 y(deca)o(ys)22 b(lik)o(e)f FE(j)p FF(x)p FE(j)373 1999 y Fy(\000)p FH(\()p FD(d)p FH(+2)p Fy(\000)p FD(\017)p FH(\))557 2017 y FQ(with)h FF(\017)j(>)d FQ(the)h(critical)e(exp)q(onen)o(t)h FF(\021)j FQ(of)d(the)h(original)f(mo)q(del)g([292,)60 2078 y(Section)16 b(10.2].)23 b(Moreo)o(v)o(er,)16 b(ev)o(en)f(the)i(qualitativ)o(e)e(phase)i (diagram)f(is)h(unstable)g(to)g(long-range)60 2138 y(but)i(summable)d(pair)i (in)o(teractions)g([349)q(,)g(332)q(,)g(208)q(]:)26 b(that)19 b(is,)f(the)h(Gibbs)f(phase)i(rule)d(cannot)60 2198 y(hold)f(in)f FE(B)259 2180 y FH(1)294 2198 y FQ(or)h(ev)o(en)f(in)g(an)o(y)h FE(B)647 2180 y FD(n)669 2198 y FQ(.)21 b(In)16 b(order)g(to)g(ha)o(v)o(e)f (an)o(y)g(hop)q(e)i(of)f(constructing)f(a)i(satisfactory)60 2258 y(R)o(G)e(theory)l(,)f(it)h(is)f(necessary)h(to)g(w)o(ork)g(in)g(a)g (space)g(of)g(\\short-range")i(in)o(teractions,)d(suc)o(h)h(as)g(the)60 2318 y(space)h FE(B)223 2325 y FD(h)262 2318 y FQ(for)g(some)f FF(h)500 2331 y FE(\030)500 2310 y(\035)564 2318 y FQ(1.)133 2403 y(A)j(second)g(commen)o(t)d(whic)o(h)i(is)h(often)g(made)e(is)i(the)g (follo)o(wing:)24 b(\\The)19 b(R)o(G)e(map)g(is)h(alw)o(a)o(ys)p 60 2447 732 2 v 100 2501 a FA(75)135 2516 y Fz(Note)f(also)g(that)g(Sulliv)n (an)e([336)o(])i(and)g(Kozlo)o(v)f([222)o(])h(ha)o(v)o(e)g Fw(almost)k Fz(pro)o(v)o(en)c(that)g(ev)o(ery)h(quasilo)q(cal)e(sp)q(eci-)60 2566 y(\014cation)g(arises)i(from)d(an)h(in)o(teraction)h(in)g Fu(B)780 2551 y FA(1)799 2566 y Fz(:)23 b(see)18 b(Theorem)f(2.12)e(and)i (the)g(Remarks)f(follo)o(wing)e(it,)j(plus)f(the)60 2616 y(Remark)c(at)i(the) h(end)f(of)f(Section)i(2.4.9.)938 2784 y FQ(168)p eop %%Page: 169 169 bop 60 91 a FQ(w)o(ell-de\014ned)18 b(as)i(a)g(map)f(from)f(measures)g(to)i (measures;)g(the)f(pathologies)h(come)e(from)g(trying)60 152 y(to)e(lift)f(it)h(to)g(a)h(map)e(from)g(Hamiltonians)f(to)i(Hamiltonians.)k (So)c(wh)o(y)g(not)g(just)h(stic)o(k)d(with)i(the)60 212 y(R)o(G)g(map)f (\(1.1\))i(on)g(the)f(space)g(of)h(measures?")133 272 y(This)g(is)g(a)g (sensible)g(question,)f(whic)o(h)g(w)o(as)i(already)f(raised)g(b)o(y)f (Gri\016ths)h(and)h(P)o(earce)e([173,)60 332 y(p.)g(534{535],)j(and)e(our)g (answ)o(er)g(is)f(essen)o(tially)f(the)i(same)e(as)j(theirs:)j(Man)o(y)16 b(in)o(teresting)g(things)60 392 y FP(c)n(an)t FQ(,)21 b(indeed,)f(b)q(e)h (learned)e(b)o(y)h(studying)h(the)f(action)g(of)h(R)o(G)f(transformations)h (on)g(measures.)60 452 y(F)l(or)h(linear)e(R)o(G)h(transformations,)i(this)e (is)g(an)h(ancien)o(t)f(branc)o(h)g(of)h(probabilit)o(y)e(theory)i(that)60 513 y(go)q(es)17 b(bac)o(k)e(to)i(Gauss')f(and)h(DeMoivre's)e(in)o(v)o (estigations)g(of)h(the)g(cen)o(tral)e(limit)g(theorem)g(for)i(in-)60 573 y(dep)q(enden)o(t)f(random)g(v)m(ariables,)g(and)h(whic)o(h)e(con)o(tin)o (ues)h(to)h(this)f(da)o(y)g(in)g(studies)g(of)h(cen)o(tral)e(and)60 633 y(non-cen)o(tral)19 b(limit)d(theorems)h(for)i(dep)q(enden)o(t)g(random)f (\014elds)h([201)q(,)f(180)q(,)h(273)q(,)f(274)q(,)h(58)q(];)g(it)f(is)60 693 y(closely)e(related)g(to)h(studies)f(of)h(trivialit)o(y)e(and)i (non-trivialit)o(y)e(for)i(scaling)g(limits)d(in)j(statistical)60 753 y(mec)o(hanics)12 b(and)j(quan)o(tum)f(\014eld)g(theory)g([323)q(,)g(71,) h(115)q(].)20 b(F)l(or)15 b(nonlinear)f(R)o(G)g(transformations,)60 814 y(this)j(study)g(is)g(only)g(b)q(eginning)h([281,)f(193)q(],)g(but)g(w)o (e)g(exp)q(ect)f(it)h(to)g(b)q(e)g(fruitful)g(as)g(w)o(ell.)23 b(Unfor-)60 874 y(tunately)l(,)16 b(not)i(all)e(of)i(the)f(R)o(G)g(theory)g (can)g(b)q(e)g(carried)g(out)g(on)h(the)f(space)g(of)g(measures)f(alone.)60 934 y(F)l(or)e(example,)e(the)i(critical)e(exp)q(onen)o(t)i FF(\015)j FQ(measures)c(the)g(rate)h(of)h(div)o(ergence)d(of)i(the)g (susceptibil-)60 994 y(it)o(y)h(as)j(the)e(temp)q(erature)f(approac)o(hes)i (the)f(critical)f(temp)q(erature.)21 b(No)o(w,)16 b(the)g(susceptibilit)o(y)e (is)60 1054 y(the)i(in)o(tegral)g(of)h(the)g(2-p)q(oin)o(t)g(correlation)f (function,)g(and)i(th)o(us)e(can)h(b)q(e)g(read)g(o\013)g(the)g(measure;)60 1115 y(while)c(the)h(\(in)o(v)o(erse\))f(temp)q(erature)f(is)i(the)g(co)q (e\016cien)o(t)f(of)h(some)f(term)g(in)h(the)g(Hamiltonian)e(\(e.g.)60 1175 y(the)17 b(nearest-neigh)o(b)q(or)h(term)e(in)h(the)h(case)f(of)h(the)f (Ising)h(mo)q(del\).)23 b(Therefore,)17 b(the)h(exp)q(onen)o(t)f FF(\015)60 1235 y FQ(can)j(b)q(e)f(deduced)g(only)h(from)e(a)i(theory)f(that) h FP(r)n(elates)k FQ(the)c(measure)e(to)i(the)f(Hamiltonian)f(\(or)60 1295 y(in)o(teraction\);)c(it)h(cannot)h(b)q(e)f(deduced)g(solely)f(from)h (an)g(R)o(G)g(map)g(acting)g(on)h(the)f(space)g(of)h(mea-)60 1355 y(sures.)21 b(The)15 b(same)f(go)q(es)i(for)f(the)g(exp)q(onen)o(t)g FF(\027)s FQ(,)g(whic)o(h)g(measures)e(the)i(rate)g(of)h(div)o(ergence)d(of)i (the)60 1416 y(correlation)j(length)h(as)h(the)e(temp)q(erature)f(approac)o (hes)j(criticalit)o(y)l(.)26 b(On)19 b(the)g(other)g(hand,)g(the)60 1476 y(exp)q(onen)o(t)d FP(r)n(atio)i FF(\015)s(=\027)h FQ(measures)c(the)h FP(r)n(elative)k FQ(rate)c(of)g(div)o(ergence)e(of)i(t)o(w)o(o)g(di\013eren)o (t)f(asp)q(ects)i(of)60 1536 y(the)g(2-p)q(oin)o(t)i(correlation)e(function,) g(and)h(so)h FP(c)n(an)i FQ(p)q(oten)o(tially)c(b)q(e)g(deduced)g(from)g(a)h (measures-)60 1596 y(to-measures)j(R)o(G)f(map.)35 b(Lik)o(ewise,)21 b(the)g(critical)e(exp)q(onen)o(t)i FF(\021)i FQ(measures)d(the)g(rate)h(of)h (deca)o(y)60 1656 y(of)f(the)f(2-p)q(oin)o(t)i(function)e(at)h(the)g (critical)e(p)q(oin)o(t,)i(making)f(no)h(reference)e(whatso)q(ev)o(er)i(to)g (the)60 1716 y(temp)q(erature;)13 b(therefore,)g(it)h(to)q(o)h(can)f(p)q (oten)o(tially)f(b)q(e)h(deduced)f(from)g(a)h(measures-to-measures)60 1777 y(R)o(G)k(map.)27 b(It)18 b(follo)o(ws)h(that)f(the)h(scaling)f(la)o(w)g FF(\015)s(=\027)j FQ(=)d(2)13 b FE(\000)f FF(\021)20 b FQ(also)f(lies)f(p)q (oten)o(tially)f(within)h(the)60 1837 y(purview)e(of)g(a)h (measures-to-measures)e(R)o(G)h(theory)l(.)60 1966 y FM(6.1.3)55 b(Where)18 b(Do)r(es)g(All)g(This)g(Lea)n(v)n(e)h(R)n(G)g(Theory?)60 2058 y FQ(After)14 b(the)g(more-or-less)g(cold)g(exp)q(osition)h(of)g(facts)g (of)g(Section)f(6.1.1,)h(and)g(the)f(additional)h(clar-)60 2118 y(i\014cation)i(\(pre-emptiv)o(e)c(defense\))k(of)g(the)g(previous)f (subsection,)h(let)f(us)h(presen)o(t)f(some)g(general)60 2178 y(remarks)f(ab)q(out)i(the)f(consequences)g(of)h(the)f(presen)o(t)f(w)o(ork)h (for)h(the)f(R)o(G)g(en)o(terprise.)133 2238 y(W)l(e)i(think)g(that)h(there)f (is)g(already)g(a)h(substan)o(tial)f(b)q(o)q(dy)i(of)e(evidence)f(indicating) g(that)i(the)60 2299 y FP(c)n(onventional)32 b FQ(R)o(G)24 b(theory)l(,)i(in)e(its)h(narro)o(w)g(sense)f(of)h (Hamiltonian-to-Hamiltonian)d(maps,)60 2359 y(needs)e(to)i(b)q(e)e (reexamined.)32 b(Ho)o(w)o(ev)o(er,)20 b(this)h(do)q(es)g(not,)h(in)e (itself,)g(detract)h(in)f(an)o(y)h(w)o(a)o(y)f(from)60 2419 y(the)c(v)m(alue)h(and)g(signi\014cance)f(of)h(the)f(R)o(G)g(ideas)h(that)g (ha)o(v)o(e)e(p)q(erv)m(aded)i(m)o(uc)o(h)e(of)h(to)q(da)o(y's)h(statis-)60 2479 y(tical)f(mec)o(hanics)f(and)i(quan)o(tum)f(\014eld)g(theory)l(.)23 b(The)17 b(R)o(G)f FP(philosophy)21 b FQ(|)c(in)o(terpreted)e(broadly)60 2539 y(to)21 b(include)f(v)m(arious)h(kinds)g(of)g(\\m)o(ulti-length-scale")e (and)j(\\coarse-graining")g(argumen)o(ts)e(|)60 2600 y(has)d(b)q(een,)g(and)g (will)e(con)o(tin)o(ue)h(to)h(b)q(e,)f(our)h(main)e(to)q(ol)j(to)f(analyze)f (the)g(otherwise)h(inaccessible)60 2660 y(\\in)o(termediate)f(temp)q (erature")h(regions,)i(whic)o(h)e(fall)h(b)q(ey)o(ond)g(the)g(reac)o(h)g(of)h (series)e(expansions)938 2784 y(169)p eop %%Page: 170 170 bop 60 91 a FQ(or)18 b(p)q(erturbativ)o(e)e(argumen)o(ts)h(and)g(y)o(et)g (are)g(the)g(regions)h(in)f(whic)o(h)f(the)h(most)g(in)o(teresting)f(phe-)60 152 y(nomena)g(tak)o(e)f(place.)133 212 y(The)j(main)f(issue)g(in)h(the)g (prop)q(er)g(application)g(of)g(R)o(G)g(theory)g(to)g(a)g(particular)g (problem)e(is)60 272 y(the)g(c)o(hoice)e(of)i(v)m(ariables)g(in)f(whic)o(h)g (to)h(express)g(the)f(mo)q(del,)f(along)j(with)f(the)f(c)o(hoice)g(of)h(the)f (R)o(G)60 332 y(map.)20 b(This)15 b(w)o(as)h(already)f(understo)q(o)q(d)i(b)o (y)d(the)h(founding)h(fathers)f(of)h(the)f(\014eld.)20 b(It)15 b(corresp)q(onds)60 392 y(to)k(what)g(Mic)o(hael)e(Fisher)g(calls)h (\\aptness)i(or)f(fo)q(cusabilit)o(y")f(of)g(the)h(transformation,)f(and)h (his)60 452 y(o)o(wn)e(w)o(ords)f(are)h(esp)q(ecially)d(clear:)182 546 y(F)l(or)20 b(an)o(y)f(giv)o(en)g(Hamiltonian)e(or)j(class)g(of)g (Hamiltonians)e(there)h(is)g(not)h(just)g(one)182 606 y(renormalization)9 b(group)j(|)e(\\)p FP(the)16 b FQ(renormalization)9 b(group")j(as)g(some)d(p) q(eople)i(sa)o(y)g(|)182 667 y(but)h(rather)g(there)f(are)g(man)o(y)g(that)h (migh)o(t)e(b)q(e)i(in)o(tro)q(duced,)f(and)i(one)e(m)o(ust)g(question,)182 727 y(for)19 b(example,)f(whether)h(the)g(pro)q(cess)h(is)f(b)q(est)h (carried)e(out)i(in)f(real)g(space)g(or)h(mo-)182 787 y(men)o(tum)14 b(space)j(and)g(so)h(on.)23 b(A)17 b(\\go)q(o)q(d")i(renormalization)c(group) j(m)o(ust)e(b)q(e)h(\\apt")182 847 y(or)f(appropriate)g(for)f(the)g(problem)f (at)i(hand,)f(and)h(it)f(m)o(ust,)f(in)h(particular,)g(\\fo)q(cus")182 907 y(prop)q(erly)h(on)h(the)f(critical)e(phenomena)i(of)g(in)o(terest.)k ([118)q(,)c(page)h(82])60 1001 y(Let)d(us)h(men)o(tion)d(an)j(illustrativ)o (e)d(example:)18 b(The)c(usual)g(transformations)h(in)o(v)o(olving)d(a)o(v)o (eraging)60 1061 y(\(or)18 b(other)g(kinds)f(of)h(\\v)o(oting"\))g(o)o(v)o (er)f(square)h(blo)q(c)o(ks)f(are)h(designed)g(mostly)e(ha)o(ving)h (ferromag-)60 1121 y(netic)k(systems)g(in)h(mind.)38 b(They)22 b(are)g(e\016cien)o(t)e(for)j(selecting)e(the)h(zero-momen)o(tum)c(mo)q(des,) 60 1182 y(whic)o(h)e(are)h(indeed)g(the)g(mo)q(des)f(that)i(b)q(ecome)d (critical)h(in)g(an)i(ordinary)f(ferromagnetic)f(transi-)60 1242 y(tion.)25 b(On)18 b(the)f(other)h(hand,)g(these)f(transformations)h (are)f(unsuitable)h(for)f(studying)h(an)o(tiferro-)60 1302 y(magnets)f(b)q(ecause)h(they)f(do)h(not)g(distinguish)f(the)g(opp)q(ositely) h(magnetized)d(sublattices.)25 b(This)60 1362 y(w)o(as)d(remark)o(ed)c(b)o(y) j(v)m(an)h(Leeu)o(w)o(en)e([357)q(],)h(who)h(sho)o(w)o(ed)f(ho)o(w)g(a)h (more)d(careful)i(design)g(of)g(the)60 1422 y(blo)q(c)o(k)c(shap)q(es)i (could)e(o)o(v)o(ercome)e(this)i(de\014ciency)f(\(his)h(prop)q(osal)i(is)f (depicted)e(in)h(Figure)g(2\(d\)\).)60 1483 y(Th)o(us,)g(while)e(most)h(p)q (eople)h(imagine)e(R)o(G)i(maps)f(as)h(acting)g(in)f(a)h(h)o(uge)g(space)g (of)g(Hamiltonians)60 1543 y(|)g(including)g(regions)h(exhibiting)f(v)m (arious)h(di\013eren)o(t)f(t)o(yp)q(es)g(of)h(phase)g(transitions)g (\(ferromag-)60 1603 y(netic,)13 b(an)o(tiferromagnetic)e(and)j(man)o(y)f (others\))h(|)f(it)g(is)h(unlik)o(ely)d(that)j(an)o(y)f(single)h(R)o(G)f(map) g(can)60 1663 y(exhibit)g(w)o(ell-b)q(eha)o(v)o(ed)g(\014xed)h(p)q(oin)o(ts)h (corresp)q(onding)g(to)g(all)f(of)g(these)g(transitions.)22 b(Rather,)14 b(one)60 1723 y(m)o(ust)h(\\custom-mak)o(e")f(the)i(R)o(G)g(map) g(for)g(eac)o(h)g(new)g(ph)o(ysical)f(situation.)133 1784 y(In)e(this)g (regard,)h(our)f(w)o(ork)g(|)g(building)f(on)i(that)f(of)h(Gri\016ths,)f(P)o (earce)f(and)i(Israel)e([172)q(,)g(173)q(,)60 1844 y(171)q(,)17 b(207)r(])g(|)g(can)h(b)q(e)g(considered)f(an)h(extension)f(of)h(the)g (preceding)e(observ)m(ations:)26 b(\\aptness")60 1904 y(and)14 b(\\fo)q(cusabilit)o(y")g(are)g(needed)f(not)h(just)g(to)g(ensure)f(the)h (usefulness)f(of)h(the)g(map,)f(but)h(ev)o(en)e(its)60 1964 y(v)o(ery)j FP(existenc)n(e)t FQ(.)23 b(On)16 b(the)f(other)h(hand,)g(the)g (success)g(stories)g(of)g(rigorous)h(R)o(G)f(studies)f(teac)o(h)h(us)60 2024 y(that)c(the)g(searc)o(h)g(for)g(this)g(\\aptness")h(ma)o(y)e(require)f (a)j(v)o(ery)e(op)q(en-minded)g(attitude,)h(in)f(the)h(sense)60 2085 y(that,)i(in)g(man)o(y)e(cases,)i(the)g(appropriate)g(v)m(ariables)g (are)g(not)h(necessarily)d(spin)i(v)m(ariables)g(and,)g(in)60 2145 y(fact,)e(not)g(ev)o(en)f(lo)q(cal)h(ob)s(jects.)19 b(Indeed,)12 b(with)f(the)h(exception)f(of)h(hierarc)o(hical)e([218,)i(32)q(,)f(219)q(])g (and)60 2205 y(fermionic)17 b([149])i(mo)q(dels,)g(rigorous)h(R)o(G)f (studies)g(ha)o(v)o(e)f FP(not)25 b FQ(implem)o(en)o(t)o(ed)16 b(the)j(strict)g(Wilson)60 2265 y(prescription)d(in)o(v)o(olving)f(an)i(R)o (G)f(transformation)g(of)h(Hamiltonians)e(written)h(in)g(terms)f(of)i(spin)60 2325 y(v)m(ariables.)32 b(Rather,)20 b(they)f(ha)o(v)o(e)g(emplo)o(y)o(ed)e (a)j(com)o(bination)f(of)h(spin)g(v)m(ariables)f(and)i(p)q(olymer)60 2385 y(ensem)o(bles)11 b([147)q(,)i(148)q(,)g(150)q(,)g(151)q(,)g(181)q(,)g (188)q(])g(or)h(a)g(pure)f(p)q(olymer)f(ensem)o(ble)f([53])i(when)h(studying) 60 2446 y(critical)d(phenomena,)h(or)g(an)h(ensem)o(ble)d(of)j(P)o (eierls-lik)o(e)c(con)o(tours)k([145)q(,)e(146)r(,)h(44])g(when)h(studying)60 2506 y(\014rst-order)h(phase)h(transitions.)21 b(More)13 b(generally)l(,)g (\\m)o(ulti-scale")f(and)i(\\coarse-graining")i(ideas)60 2566 y(ha)o(v)o(e)f(b)q(een)i(used)f(in)g(a)h(wide)e(v)m(ariet)o(y)h(of)g (problems,)f(including:)133 2660 y FE(\017)24 b FQ(ultra)o(violet)9 b(stabilit)o(y)h(of)h(the)g FF(')758 2642 y FH(4)758 2672 y(3)789 2660 y FQ([159)q(,)f(28)q(])g(and)i(Y)l(ang-Mills)1293 2667 y FH(4)1323 2660 y FQ([19])f(quan)o(tum)e(\014eld)i(theories;)938 2784 y(170)p eop %%Page: 171 171 bop 133 91 a FE(\017)24 b FQ(the)12 b(Kosterlitz-Thouless)g(transition)h(in)f (the)g(t)o(w)o(o-dimensional)f FF(X)t(Y)24 b FQ(and)13 b(related)f(mo)q(dels) 182 152 y([134)q(,)j(135)r(];)133 253 y FE(\017)24 b FQ(the)16 b(ferromagnetic)e(transition)j(in)f(the)g(one-dimensional)f(1)p FF(=r)1366 235 y FH(2)1403 253 y FQ(Ising)h(mo)q(del)f([137)q(];)133 355 y FE(\017)24 b FQ(con\014nemen)o(t)14 b(in)i(the)g(three-dimensional)e FF(U)5 b FQ(\(1\))17 b(lattice)e(gauge)i(theory)g([166];)133 457 y FE(\017)24 b FQ(lo)q(calization)16 b(for)g(random)g(Sc)o(hr\177)-24 b(odinger)16 b(op)q(erators)i([138];)133 558 y FE(\017)24 b FQ(the)16 b(phase)h(transition)f(in)g(plaquette)f(p)q(ercolation)i([4];)133 660 y FE(\017)24 b FQ(the)d(in)o(tersection)f(prop)q(erties)h(of)g(ordinary)h (random)f(w)o(alks)g(and)g(of)h(Bro)o(wnian)f(motion)182 720 y([3,)16 b(112)q(,)g(115)q(];)f(and)133 822 y FE(\017)24 b FQ(the)18 b(critical)f(b)q(eha)o(vior)i(of)g(self-a)o(v)o(oiding)e(w)o(alks)i ([52,)f(185)q(,)g(187)r(,)g(186)q(],)g(p)q(ercolation)h([183,)182 882 y(182)q(])d(and)h(branc)o(hed)f(p)q(olymers)f([184])h(in)g(high)g (dimensions.)60 984 y(In)e(man)o(y)f(of)h(these)g(examples,)e(the)i (\\coarse-graining")i(is)e(applied)f(at)i(the)f(lev)o(el)e(of)i(ob)s(jects)g (with)60 1044 y(some)h(geometric)f(con)o(ten)o(t,)h(suc)o(h)h(as)h(random)f (w)o(alks,)g(clusters,)f(surfaces,)h(con)o(tours,)g(etc.)133 1104 y(Th)o(us,)e(our)f(w)o(ork)h(is)e(in)h(no)h(w)o(a)o(y)f(an)g(attac)o(k)g (on)h(the)f(essen)o(tial)f(ph)o(ysical)g(ideas)h(b)q(ehind)g(the)g(R)o(G)60 1164 y(approac)o(h.)22 b(It)16 b(simply)e(p)q(oin)o(ts)i(out)h(the)f(need)g (for)h(a)f(more)f(general)h(de\014nition)g(of)g(their)g(scop)q(e.)60 1294 y FM(6.1.4)55 b(T)-5 b(o)n(w)n(ards)21 b(a)e(Non-Gibbsian)f(P)n(oin)n(t) i(of)e(View)60 1387 y FQ(Let)f(us)g(close)f(with)h(some)f(general)g(remarks)f (on)j(the)e(signi\014cance)g(of)h(\(non-\)Gibbsianness)h(and)60 1447 y(\(non-\)quasilo)q(calit)o(y)j(in)g(statistical)g(ph)o(ysics.)35 b(Our)22 b(\014rst)f(observ)m(ation)i(is)e(that)g(Gibbsianness)60 1507 y(has)15 b(heretofore)e(b)q(een)h(ubiquitous)f(in)h(equilibrium)c (statistical)k(mec)o(hanics)d(b)q(ecause)j(it)g(has)g(b)q(een)60 1567 y(put)g(in)f FP(by)i(hand)5 b FQ(:)20 b(nearly)13 b(all)h(the)f (measures)g(that)h(ph)o(ysicists)e(encoun)o(ter)h(are)h(Gibbsian)g(b)q (ecause)60 1627 y(ph)o(ysicists)g(ha)o(v)o(e)h FP(de)n(cide)n(d)20 b FQ(to)c(study)f(Gibbs)h(measures!)k(Ho)o(w)o(ev)o(er,)13 b(w)o(e)i(no)o(w)g(kno)o(w)h(that)g(natural)60 1688 y(op)q(erations)k(on)g (Gibbs)f(measures)f(can)h(sometimes)e(lead)h(out)i(of)f(this)g(class:)27 b(among)19 b(suc)o(h)g(op-)60 1748 y(erations)f(are)g(some)g(renormalization) e(transformations)i(\(Sections)g(4.1{4.3)h(and)g(4.5.2\),)f(some)60 1808 y(nonlinear)d(lo)q(cal)h(functions)g(\(Section)f(4.4\),)g(con)o(v)o(ex)f (com)o(binations)h(\(Section)g(4.5.1\),)g(and)h(w)o(eak)60 1868 y(limits)h(\(Section)h(4.5.6\).)30 b(It)19 b(is)g(th)o(us)g(of)h(great)f (in)o(terest)f(to)i(study)f(whic)o(h)g(t)o(yp)q(es)f(of)i(op)q(erations)60 1928 y(preserv)o(e,)g(or)h(fail)f(to)h(preserv)o(e,)f(the)g(Gibbsianness)i (\(or)e(quasilo)q(calit)o(y\))g(of)h(a)g(measure.)33 b(This)60 1989 y(study)16 b(is)g(curren)o(tly)f(in)h(its)g(infancy)l(.)133 2049 y(More)24 b(generally)l(,)h(in)e(areas)i(of)g(ph)o(ysics)e(where)h (Gibbsianness)h(is)e(not)i(put)f(in)g(b)o(y)g(hand,)60 2109 y(one)d(should)g(exp)q(ect)f(non-Gibbsianness)j(to)e(b)q(e)g(ubiquitous.)35 b(This)21 b(is)g(probably)g(the)f(case)h(in)60 2169 y(nonequilibrium)13 b(statistical)j(mec)o(hanics)e(\(Section)i(4.5.4\).)133 2229 y(Since)f(one)i(cannot)g(exp)q(ect)e(all)h(measures)f(of)h(in)o(terest)f(to)i (b)q(e)f(Gibbsian,)g(the)g(question)g(then)60 2290 y(arises)j(whether)f (there)g(are)h FP(we)n(aker)25 b FQ(conditions)18 b(that)i(capture)e(some)g (or)h(most)f(of)h(the)f(\\go)q(o)q(d")60 2350 y(ph)o(ysical)13 b(prop)q(erties)h(c)o(haracteristic)e(of)i(Gibbs)g(measures.)19 b(F)l(or)14 b(example,)e(the)i(stationary)g(mea-)60 2410 y(sure)20 b(of)h(the)e(v)o(oter)h(mo)q(del)f(app)q(ears)i(to)g(ha)o(v)o(e)e(the)h (critical)e(exp)q(onen)o(ts)i(predicted)f(\(under)h(the)60 2470 y(h)o(yp)q(othesis)j(of)h(Gibbsianness\))g(b)o(y)f(the)g(Mon)o(te)g (Carlo)g(renormalization)f(group)i([362)q(],)g(ev)o(en)60 2530 y(though)17 b(this)f(measure)f(is)h(pro)o(v)m(ably)h(non-Gibbsian)g([246)q (].)133 2590 y(One)k(ma)o(y)e(also)i(inquire)f(whether)g(there)h(is)f(a)h (classi\014cation)g(of)g(non-Gibbsian)h(measures)60 2651 y(according)e(to)g (their)f(\\degree)h(of)g(non-Gibbsianness".)34 b(Jo)q(el)20 b(Leb)q(o)o(witz)f(has)i(suggested)g(to)f(us)938 2784 y(171)p eop %%Page: 172 172 bop 60 91 a FQ(the)18 b(analogy)g(with)g(the)g(rational)g(and)g(real)g(n)o (um)o(b)q(ers:)23 b(although)c(the)e(set)h(of)g(rationals)h(is)e(v)o(ery)60 152 y(\\small")e(in)g(man)o(y)f(senses)h(\(e.g.)g(\014rst)g(Baire)g(category) l(,)g(zero)g(Leb)q(esgue)h(measure\),)e(it)h(is)g(\\large")60 212 y(in)f(the)h(w)o(eak)f(sense)h(that)g(an)o(y)f(real)g(n)o(um)o(b)q(er)f (can)i(b)q(e)g(appro)o(ximated)e(b)o(y)h(a)h(sequence)f(of)h(rational)60 272 y(n)o(um)o(b)q(ers;)i(and)i(the)e(irrational)h(n)o(um)o(b)q(ers)f(can)h (b)q(e)g(classi\014ed)g(according)g(to)g(the)g(rate)g(at)h(whic)o(h)60 332 y(they)c(can)h(b)q(e)g(appro)o(ximated)f(b)o(y)g(rationals)h(\(Diophan)o (tine)g(appro)o(ximation\).)k(In)15 b(Section)h(4.5.6)60 392 y(w)o(e)21 b(conjectured)f(a)h(similar)e(scenario)i(for)g(the)g(Gibbsian)g (measures)f(within)g(the)h(space)g(of)h(all)60 452 y(measures.)28 b(It)18 b(w)o(ould)h(then)f(b)q(e)h(natural)g(to)h(classify)e(the)g (non-Gibbsian)i(measures)e(according)60 513 y(to)f(ho)o(w)f(w)o(ell)f(\(or)i (ho)o(w)f(rapidly\))g(they)g(can)g(b)q(e)g(appro)o(ximated)f(b)o(y)h (Gibbsian)h(ones.)133 573 y(Finally)l(,)f(there)h(is)h(a)g(philosophical)f (question,)g(raised)h(b)o(y)f(one)h(of)g(our)g(colleagues)f(in)g(Rome)60 633 y(\(to)22 b(whom)g(w)o(e)f(ap)q(ologize)i(b)q(ecause)f(w)o(e)g(cannot)g (remem)o(b)q(er)d(his)j(name\):)31 b(All)21 b(mathematical)60 693 y(mo)q(delling,)g(in)g(an)o(y)h(branc)o(h)g(of)g(science,)f(in)o(v)o(olv) o(es)f(selecting)h(the)g(\\imp)q(ortan)o(t")h(v)m(ariables)f(in)60 753 y(the)d(description)g(of)h(a)g(system)e(and)i(neglecting)e(the)h(v)m (ariables)h(judged)g(\\unimp)q(ortan)o(t".)27 b(In)19 b(a)60 814 y(statistical)d(system)f(this)h(means)f(that)i(the)f(\\unimp)q(ortan)o (t")g(v)m(ariables)g(are)h(in)o(tegrated)e(out,)i(i.e.)60 874 y(one)g(p)q(erforms)f(a)i(kind)e(of)h(\\decimation")f(transformation.)24 b(No)o(w,)16 b(if)h(the)f(decimated)f(v)m(ariables)60 934 y(are)20 b(only)h(w)o(eakly)e(coupled)h(to)h(the)f(others,)h(then)f(one)h(ma)o(y)e (hop)q(e)i(that)g(the)f(decimation)e(will)60 994 y(lead)j(to)h(a)g(Gibbs)g (measure)e(\(although)j(rigorous)f(theorems)f(guaran)o(teeing)h(this)f(seem)f (to)i(b)q(e)60 1054 y(lac)o(king\).)31 b(Ho)o(w)o(ev)o(er,)19 b(one)h(could)f(also)i(fear)f(that)g(the)f(result)h(of)g(the)g(decimation)d (migh)o(t)i(b)q(e)h(a)60 1115 y FP(non-Gibbsian)27 b FQ(measure,)20 b(esp)q(ecially)g(if)g(the)h(decimated)e(v)m(ariables)i(are)g(strongly)g (coupled)g(to)60 1175 y(the)15 b(others.)22 b(\(Suc)o(h)15 b(v)m(ariables)g(migh)o(t)f(still)g(b)q(e)i(deemed)e(\\unimp)q(ortan)o(t")h (if)g(they)g(w)o(ere)g(b)q(eliev)o(ed)60 1235 y(to)j(a\013ect)f(only)g(unin)o (teresting)g(quan)o(titativ)o(e)f(details)g(of)i(the)f(problem,)f(without)i (c)o(hanging)f(the)60 1295 y(features)g(of)g(in)o(terest.\))k(In)c(this)f (case,)h(not)g(only)f(w)o(ould)h(one)g(b)q(e)g(making)e(an)j(appro)o (ximation)d(in)60 1355 y(describing)i(the)g(system)f(b)o(y)h(a)h(particular)g (\\mo)q(del)e(Hamiltonian",)g(but)i(ev)o(en)e(the)i(description)60 1416 y(of)g(the)g(decimated)d(system)h(b)o(y)i FP(any)k FQ(Hamiltonian)16 b(w)o(ould)i(itself)e(b)q(e)i(an)h(appro)o(ximation.)24 b(And)60 1476 y(one)16 b(w)o(ould)h(ha)o(v)o(e)e(to)i(in)o(v)o(estigate)e(ho)o(w)h(go) q(o)q(d)i(this)e(appro)o(ximation)g(is.)60 1618 y FB(6.2)70 b(Some)20 b(Op)r(en)i(Questions)60 1710 y FQ(W)l(e)16 b(end)g(with)g(a)h (list)e(of)i(op)q(en)g(questions)f(for)h(future)f(researc)o(h:)133 1790 y(1\))f(Clean)f(up)h(the)f(circle)e(of)j(results)f(connected)g(with)g (the)g(Gibbs)h(Represen)o(tation)e(Theorem)60 1850 y(\(Theorem)f(2.12\),)j (particularly)e(in)g(the)g(translation-in)o(v)m(arian)o(t)h(case)g (\(Sections)f(2.3.3,)h(2.4.9)g(and)60 1911 y(A.2\).)133 1991 y(2\))h(Determine)e(whether)h FE(f)p FQ(\010:)22 b FE(k)p FQ(\010)p FE(k)794 1998 y Fy(B)817 2004 y Fs(h)853 1991 y FE(\024)14 b FF(M)5 b FE(g)j FQ(+)g FE(J)24 b FQ(is)15 b(a)g(closed)g(subset)g(of)g FE(B)1562 1973 y FH(0)1581 1991 y FQ(,)f(if)h FF(h)f FE(6)1695 2003 y(\030)1695 1983 y(\035)1758 1991 y FQ(1,)h(and)60 2051 y(in)f(particular)h(for)g FE(B)445 2058 y FD(h)481 2051 y FQ(=)e FE(B)567 2033 y FH(1)601 2051 y FQ(\(Sections)i(2.4.4)g(and)g(2.4.6\).)21 b(This)15 b(a\013ects)g(the)f(w)o(a)o(ys)h(in)f(whic)o(h)g(the)60 2111 y(R)l(T)19 b(map)e(can)i(blo)o(w)f(up)h(at)g(the)f(b)q(oundary)h(of)g (its)f(domain)g(\(Section)g(3.3\),)h(and)g(arises)f(also)h(in)60 2171 y(our)e(theory)f(of)g(parameter)f(estimation)g(\(Section)h(5.1.2\).)133 2252 y(3\))h(Devise)f(a)h(clean)f(general)g(theory)g(for)h(systems)e(of)i(un) o(b)q(ounded)h(spins,)e(analogous)i(to)f(the)60 2312 y(spaces)g FE(B)245 2294 y FH(0)280 2312 y FQ(and)g FE(B)410 2294 y FH(1)445 2312 y FQ(for)f(systems)f(of)i(b)q(ounded)g(spins)g(\(Sections)e(2.4.4)i(and) g(3.1.4\).)133 2392 y(4\))e(In)o(v)o(estigate)e(rigorously)i(the)f (Gibbsianness)h(or)g(non-Gibbsianness)h(of)f(the)f(renormalized)60 2452 y(measure)h(in)h(the)g(follo)o(wing)g(mo)q(dels:)203 2539 y(\(a\))24 b(F)l(erromagnetic)14 b(Ising)h(mo)q(del,)f(using)h(the)h (decimation)d(transformation)i(with)289 2600 y(spacing)k FF(b)p FQ(:)26 b(do)q(es)19 b(the)f(cuto\013)i(temp)q(erature)d(for)h (non-Gibbsianness)i(tend)f(to)289 2660 y FF(J)316 2667 y FD(c)350 2660 y FQ(as)e FF(b)c FE(!)h(1)p FQ(?)21 b(\(See)16 b(Section)g(4.3.2.\))938 2784 y(172)p eop %%Page: 173 173 bop 200 91 a FQ(\(b\))24 b(F)l(erromagnetic)g(Ising)h(mo)q(del,)h(using)g (the)f(ma)s(jorit)o(y-rule)e(transformation)289 152 y(with)e(blo)q(c)o(k)g (sizes)g FF(b)g FQ(not)h(co)o(v)o(ered)e(b)o(y)h(the)g(construction)g(in)g (Section)g(4.3.4.)289 212 y(\(F)l(or)c(dimension)e FF(d)f FE(\025)g FQ(3,)j(it)f(app)q(ears)i(that)f FP(no)j FQ(blo)q(c)o(k)c(sizes)g FF(b)g FQ(are)h(co)o(v)o(ered)e(b)o(y)289 272 y(this)h(construction:)22 b(see)16 b(App)q(endix)f(C.\))205 350 y(\(c\))24 b(F)l(erromagnetic)15 b(Ising)h(mo)q(del)f(at)i(lo)o(w)f(temp)q(erature)f(and)i(nonzero)g(magnetic) 289 410 y(\014eld,)d(in)g(dimension)f FF(d)h FQ(=)f(2,)i(using)g(the)f (decimation,)e(Kadano\013)k(or)f(ma)s(jorit)o(y-)289 471 y(rule)h (transformation.)200 549 y(\(d\))24 b(An)o(tiferromagnetic)10 b(nearest-neigh)o(b)q(or)i(Ising)g(mo)q(del)f(in)h(a)h(uniform)e(magnetic)289 609 y(\014eld,)j(on)h(the)f(paramagnetic-an)o(tiferromagnetic)d(critical)i (surface:)20 b(compare)289 669 y(the)12 b(ma)s(jorit)o(y-rule)d(\(or)j (Kadano\013)s(\))i(transformation)e(on)g(square)g(\()p FF(b)r FE(\002)r FF(b)p FQ(\))e(blo)q(c)o(ks)289 730 y(to)17 b(the)f(same)f (transformation)h(on)h(v)m(an)g(Leeu)o(w)o(en's)e(5-spin)i(blo)q(c)o(ks)f ([357)q(,)f(55)q(].)205 808 y(\(e\))24 b FF(q)r FQ(-state)e(P)o(otts)h(mo)q (del)d(with)i FF(q)h FQ(large,)g(at)g(\(or)f(near\))g(the)g(\014rst-order)h (phase)289 868 y(transition,)j(using)f(either)e(the)h(ordinary)g(\\pluralit)o (y-rule")f(\(or)i(Kadano\013)s(\))289 928 y(transformation)17 b([305)q(])g(or)h(the)f(mo)q(di\014ed)f(transformation)h(including)f(v)m (acan-)289 989 y(cies)g([279,)g(305)q(].)209 1067 y(\(f)s(\))24 b(Other)16 b(mo)q(dels)f(at)i(or)g(near)f(a)h(\014rst-order)g(phase)f (transition.)203 1145 y(\(g\))24 b(F)l(erromagnetic)18 b(Ising)i(mo)q(del)f (at)h(the)g(critical)e(p)q(oin)o(t)i(in)f(dimension)g FF(d)h(>)g FQ(4,)289 1206 y(using)h(a)f(ma)s(jorit)o(y-rule)d(\(or)j(Kadano\013)s(\))i (transformation)e(with)g(\014xed)g(blo)q(c)o(k)289 1266 y(size)c FF(b)g FQ(\(Section)f(4.4\).)133 1382 y(5\))20 b(Impro)o(v)o(e/generalize)d (the)j(theorems)e(on)j(non-Gibbsianness)g(of)f(lo)q(cal)g(nonlinear)g(func-) 60 1442 y(tions)12 b(of)h(an)f(anharmonic)g(crystal,)g(and)h(in)e(particular) h(try)g(to)g(pro)o(v)o(e)g(non-quasilo)q(calit)o(y)g(\(Section)60 1502 y(4.4\).)133 1585 y(6\))k(T)l(ry)f(to)h(generalize)d(Sc)o(honmann's)i (example)e(\(Section)h(4.5.2\))i(to)g(dimensions)d FF(d;)8 b(d)1751 1567 y Fy(0)1779 1585 y FQ(other)60 1645 y(than)17 b FF(d)d FQ(=)g(2,)i FF(d)344 1627 y Fy(0)370 1645 y FQ(=)e(1.)133 1728 y(7\))d(Pro)o(v)o(e)f(\(or)i(dispro)o(v)o(e\))d(the)i(existence)e(of)i (measures)f(consisten)o(t)g(with)h(the)g(F)l(ortuin-Kasteleyn)60 1788 y(random-cluster-mo)q(del)17 b(sp)q(eci\014cation)i(\(4.91\);)h(in)f (particular,)g(pro)o(v)o(e)f(\(or)i(dispro)o(v)o(e\))e(that)h(the)60 1848 y(in\014nite-v)o(olume)c(limit)g(measures)i(tak)o(en)g(with)h(free)f(or) h(wired)g(b)q(oundary)h(conditions)f(are)g(con-)60 1908 y(sisten)o(t)e(with)g (this)g(sp)q(eci\014cation)g(\(Section)g(4.5.3\).)133 1991 y(8\))j(In)o(v)o(estigate)e(the)i(Gibbsianness)g(or)g(non-Gibbsianness)h(of)f (the)g(stationary)g(measure\(s\))60 2051 y(in)d(v)m(arious)h(sto)q(c)o (hastic)f(ev)o(olutions)g(not)h(satisfying)f(detailed)f(balance)h(\(Section)g (4.5.4\).)133 2134 y(9\))i(In)o(v)o(estigate)f(the)g(abstract)i(prop)q (erties)f(of)g(the)f(set)h FE(G)i FQ(of)e(Gibbsian)h(measures)d(\(Sections)60 2194 y(4.5.6)h(and)f(6.1.4\).)133 2276 y(10\))g(In)o(v)o(estigate)e (rigorously)h(the)g(mo)q(del)e(of)j(parameter)e(estimation)f(in)o(tro)q (duced)i(in)g(Section)60 2337 y(5.1.2;)h(in)g(particular,)f(try)h(to)h(pro)o (v)o(e)e(Conjecture)h(5.1)h(or)g(some)e(w)o(eak)o(ened)g(v)o(ersion)g(of)i (it.)133 2419 y(11\))f(Mak)o(e)e(a)i(high-precision)f(MCR)o(G)f(test,)h (using)h(a)f(large)g(space)h(of)f(renormalized)e(in)o(terac-)60 2479 y(tions,)h(to)h(compare)e(a)h(case)g(in)g(whic)o(h)f(the)h(renormalized) e(measure)g(is)i(exp)q(ected)f(to)i(b)q(e)f(Gibbsian)60 2539 y(\(e.g.)19 b(the)g FF(d)h FQ(=)f(2)h(Ising)f(mo)q(del)f(at)i(a)g(temp)q (erature)e(not)i(to)q(o)h(far)f(b)q(elo)o(w)f(critical\))f(with)h(a)h(case)60 2600 y(in)c(whic)o(h)f(the)g(renormalized)f(measure)h(is)g(exp)q(ected)g(or)i (pro)o(v)o(en)e(to)h(b)q(e)g(non-Gibbsian)h(\(e.g.)e(the)60 2660 y FF(d)f FQ(=)g(2)j(Ising)f(mo)q(del)f(at)h(lo)o(w)g(temp)q(erature\))f ([Section)g(5.1.3].)938 2784 y(173)p eop %%Page: 174 174 bop 133 91 a FQ(12\))19 b(Clarify)f(the)g(relationship)g(b)q(et)o(w)o(een)f (R)o(G)h(transformations)h(acting)f(on)h(con)o(tours)g([145,)60 152 y(146)q(])14 b(or)h(p)q(olymers)f([147,)h(148)q(,)f(150)q(,)g(151)q(,)h (181)q(,)f(188)q(,)g(53)q(],)g(and)h(the)g(traditional)f(R)o(G)h(transforma-) 60 212 y(tions)h(acting)h(on)g(spins.)133 297 y(13\))25 b(Discuss)e(the)h (Gibbsianness)g(or)g(non-Gibbsianness)h(of)f(v)m(arious)g(states)g(of)g FP(quantum)60 357 y FQ(lattice)15 b(systems)h([253)q(,)g(355)q(].)22 b(Here)16 b(one)g(problem)f(is)i(to)g(understand)g(b)q(etter)g(the)f (relationships)60 417 y(b)q(et)o(w)o(een)f(the)h(v)m(arious)h(alternativ)o(e) e(notions)i(of)g(\\Gibbsianness")g(in)f(the)g(quan)o(tum)f(case.)133 502 y(14\))i(Pro)o(v)o(e)f(Conjecture)g(C.5.)60 669 y FG(A)83 b(Pro)r(ofs)28 b(of)g(Some)d(Theorems)g(from)h(Section)h(2)60 793 y FB(A.1)69 b(Pro)r(ofs)24 b(and)g(References)d(for)i(Section)f(2.1)60 885 y FQ(The)12 b(remarks)g(made)f(in)h(Section)g(2.1.2)h(are)f(all)g(w)o (ell-kno)o(wn)g(results.)20 b(Here)11 b(are)h(some)g(references:)133 945 y(\(a\))21 b(\012)251 952 y FH(0)292 945 y FQ(compact)f(=)-8 b FE(\))20 b FQ(\012)h(compact)f(=)-8 b FE(\))20 b FQ(ev)o(ery)f(con)o(tin)o (uous)i(function)f(on)i(\012)f(is)f(b)q(ounded)60 1005 y([309)q(,)e(Prop)q (osition)i(9.4].)29 b(The)18 b(densit)o(y)g(of)h FF(C)929 1012 y FD(loc)974 1005 y FQ(\(\012\))g(in)f FF(C)t FQ(\(\012\))g(is)h(an)g(easy)g (consequence)e(of)i(the)60 1066 y(Stone-W)l(eierstrass)e(theorem)d([309)q(,)i (Theorem)f(9.28].)133 1126 y(\(b\))24 b(If)f(\012)313 1133 y FH(0)357 1126 y FQ(is)g(discrete,)i(then)e(ev)o(ery)f(lo)q(cal)i(function)g (is)f(con)o(tin)o(uous;)k(and)d(con)o(tin)o(uit)o(y)e(is)60 1186 y(preserv)o(ed)15 b(under)h(uniform)f(con)o(v)o(ergence.)133 1246 y(\(c\))h(This)g(is)g(an)h(immedi)o(ate)d(consequence)h(of)i(\(a\))f (and)h(\(b\).)133 1356 y FM(F)-5 b(urther)26 b(Remark.)37 b FQ(If)22 b(the)g(single-spin)g(space)h(\012)1156 1363 y FH(0)1198 1356 y FQ(is)f(noncompact,)h(there)f(ma)o(y)f(exist)60 1416 y(b)q(ounded)f(con)o(tin)o(uous)e(functions)h(whic)o(h)f(are)h FP(not)k FQ(quasilo)q(cal.)29 b(Hans-Otto)19 b(Georgii)g(pro)o(vided)60 1477 y(us)e(with)g(the)g(follo)o(wing)f(example:)21 b(tak)o(e)16 b FE(L)g FQ(=)f(\012)982 1484 y FH(0)1016 1477 y FQ(=)g Fq(Z)j FQ(and)f(let)g FF(f)5 b FQ(\()p FF(\033)r FQ(\))14 b(=)h FF(\033)1476 1484 y FD(\033)1496 1489 y Fr(0)1533 1477 y FQ(\(!\);)h(then)h(let)f FF(g)j FQ(b)q(e)60 1537 y(a)e(b)q(ounded)g(function)f(of)g FF(f)5 b FQ(,)17 b(sa)o(y)f FF(g)g FQ(=)e FE(j)p FF(f)5 b FE(j)p FF(=)p FQ(\(1)11 b(+)g FE(j)p FF(f)5 b FE(j)p FQ(\).)133 1597 y(In)22 b(fact,)i(this)e(construction)h(can)g(b)q(e)f(imitated)f(whenev)o(er) g(\012)1330 1604 y FH(0)1372 1597 y FQ(is)i(a)g(noncompact)f(metric)60 1657 y(space)d(and)g FE(L)g FQ(is)g(in\014nite:)25 b(Let)19 b FF(f)698 1664 y FH(1)718 1657 y FF(;)8 b(f)764 1664 y FH(2)784 1657 y FF(;)g(:)g(:)g(:)17 b FE(2)h FF(C)t FQ(\(\012)1025 1664 y FH(0)1045 1657 y FQ(\))g(ha)o(v)o(e)g(disjoin)o(t)h(supp)q(orts)h FF(S)1606 1664 y FH(1)1626 1657 y FF(;)8 b(S)1678 1664 y FH(2)1697 1657 y FF(;)g(:)g(:)g(:)18 b FQ(with)60 1717 y FF(S)90 1724 y FD(i)116 1717 y FE(\\)p 160 1678 113 2 v 171 1684 a Fx(S)160 1756 y FD(j)r Fy(6)p FH(=)p FD(i)224 1717 y FF(S)254 1724 y FD(j)288 1717 y FQ(=)d Fq(?)h FQ(and)i FE(k)p FF(f)543 1724 y FD(i)557 1717 y FE(k)582 1724 y Fy(1)634 1717 y FQ(=)d(1)i(\(suc)o(h)g (functions)g(are)g(easily)f(constructed)h(using)g(Urysohn's)60 1808 y(lemma\);)h(let)h FF(x)357 1815 y FH(0)377 1808 y FF(;)8 b(x)427 1815 y FH(1)446 1808 y FF(;)g(x)496 1815 y FH(2)515 1808 y FF(;)g(:)g(:)g(:)19 b FQ(b)q(e)h(distinct)f(sites)h(in)f FE(L)p FQ(;)j(let)d FF(g)j FE(2)f FF(C)t FQ(\(\012)1373 1815 y FH(0)1392 1808 y FQ(\))f(b)q(e)g(non-constan)o(t;)i(and)60 1868 y(de\014ne)16 b FF(h)p FQ(\()p FF(\033)r FQ(\))d(=)362 1835 y Fx(P)406 1848 y Fy(1)406 1880 y FD(n)p FH(=1)483 1868 y FF(g)r FQ(\()p FF(\033)555 1875 y FD(x)575 1879 y Fs(n)598 1868 y FQ(\))p FF(f)641 1875 y FD(n)664 1868 y FQ(\()p FF(\033)711 1875 y FD(x)731 1880 y Fr(0)750 1868 y FQ(\).)133 1978 y(Standard)23 b(references)e(for)h(the)f(theory)h(of)g(probabilit)o(y)f(measures)g(on)h (metric)e(spaces)i(are)60 2038 y(the)15 b(b)q(o)q(oks)i(of)e(P)o(arthasarath) o(y)h([289)q(])e(and)i(Billingsley)d([29].)20 b(Probabilit)o(y)15 b(measures)f(on)h(general)60 2098 y(\(not)f(necessarily)f(metrizable\))e(top) q(ological)k(spaces)f(are)g(treated)g(in)g([358)q(,)f(73)q(,)h(320)q(].)20 b(The)14 b(Riesz-)60 2159 y(Mark)o(o)o(v)23 b(theorem)f(is)h([309)q(,)h (Theorem)f(14.8])g(or)h([289)q(,)h(Theorems)d(I)q(I.5.7)h(and)h(I)q(I.5.8].) 42 b(The)60 2219 y(theorem)15 b(on)h(supp)q(ort)i(of)e(a)h(measure)e(is)h ([289)q(,)g(Theorem)f(I)q(I.2.1].)133 2279 y(The)f(b)q(ounded)h(measurable)e (top)q(ology)j(on)e FF(M)5 b FQ(\(\012\))15 b(and)g FF(M)1225 2286 y FH(+1)1272 2279 y FQ(\(\012\))f(is)g(discussed)g(in)g([143)q(].)20 b(The)60 2339 y(w)o(eak)h(top)q(ology)h(on)g FF(M)512 2346 y FH(+1)559 2339 y FQ(\(\012\))f(is)g(discussed)g(in)g(detail)f(in)h([289,)g (29)q(,)f(358)r(];)i(in)f(particular,)g(the)60 2399 y(top)q(ological)16 b(prop)q(erties)f(of)g FF(M)636 2406 y FH(+1)683 2399 y FQ(\(\012\))h(for)f (di\013eren)o(t)f(classes)h(of)g(spaces)h(\012)f(are)g(discussed)g(in)g ([358,)60 2460 y(P)o(art)h(I)q(I],)f([289)q(,)h(Section)g(I)q(I.6])f(and)i ([73,)f(Theorem)f(I)q(I)q(I{60].)133 2520 y(If)g(\012)216 2527 y FH(0)251 2520 y FQ(is)g(a)g(separable)h(metric)c(space,)j(then)g(ev)o(ery)f FP(uniformly)19 b FQ(con)o(tin)o(uous)c(function)g(on)h(\012)f(is)60 2580 y(quasilo)q(cal)c([157)q(,)h(Remark)d(2.21\(2\)].)21 b(Since)10 b(the)h(b)q(ounded)h(uniformly)d(con)o(tin)o(uous)j(functions)f(are)60 2640 y(su\016cien)o(t)16 b(to)j(generate)e(the)h(\(ordinary\))g(w)o(eak)f (top)q(ology)j(\(this)d(is)h(the)f(famous)h(\\p)q(ortman)o(teau)938 2784 y(174)p eop %%Page: 175 175 bop 60 91 a FQ(theorem")10 b([29)q(,)i(Theorem)e(2.1]\),)i(it)g(follo)o(ws)f (that)h(the)g(b)q(ounded)g(quasilo)q(cal)g(top)q(ology)h(is)e(stronger)60 152 y(than)19 b(the)f(w)o(eak)g(top)q(ology)l(.)28 b(On)19 b(the)f(other)g(hand,)h(if)f(\012)1126 159 y FH(0)1164 152 y FQ(is)g(also)h(discrete)e(\(hence)h(coun)o(table\),)60 212 y(then)c(ev)o(ery)e(quasilo)q(cal)i(function)g(is)g(con)o(tin)o(uous,)g(so)g (the)g(t)o(w)o(o)g(top)q(ologies)h(in)e(fact)h(coincide.)20 b(See)60 272 y([155)q(,)c(Remark)e(0.3].)60 416 y FB(A.2)69 b(Pro)r(ofs)24 b(and)g(References)d(for)i(Section)f(2.3)60 509 y FQ(Prop)q(osition)e(2.7)g(is)f(essen)o(tially)e([157)q(,)j(Remark)d (1.24].)31 b(Examples)17 b(1)j(and)g(2)f(in)g(Section)g(2.3.3)60 569 y(are)h([157,)g(Prop)q(osition)h(2.24)f(and)h(Example)c(2.25].)32 b(Theorem)18 b(2.10)j(and)f(related)f(results)g(are)60 629 y(discussed)11 b(in)h([157,)g(Section)f(2.2].)20 b(Theorem)10 b(2.12)i(is)g(pro)o(v)o(en)f(b)o(y)g(Kozlo)o(v)f([222)q(];)i(see)g(also)g (Sulliv)m(an)60 689 y([336)q(].)133 799 y FM(Remarks.)20 b FQ(1.)j(The)17 b(follo)o(wing)f(conjectured)g(extensions)h(of)g(Theorem)e (2.12)i(app)q(ear)h(to)f(b)q(e)60 859 y(op)q(en)g(questions:)133 920 y(\(a\))e(If)g(\005)g(is)f(quasilo)q(cal)h(and)h(nonn)o(ull)e(\(but)h (not)h FP(uniformly)j FQ(nonn)o(ull\),)14 b(and)i(\012)1600 927 y FH(0)1635 920 y FQ(is)f(not)g(\014nite,)60 980 y(do)q(es)e(there)e (exist)g(a)h FP(uniformly)h(c)n(onver)n(gent)19 b FQ(in)o(teraction)10 b(\010)j(suc)o(h)e(that)h(\005)i(=)g(\005)1526 962 y FH(\010)1553 980 y FQ(?)20 b([This)12 b(theorem)60 1040 y(migh)o(t)j(b)q(e)h(relev)m(an)o (t)f(to)i(mo)q(dels)e(of)i(un)o(b)q(ounded)g(spins)f(with)g FP(\014nite-r)n(ange)22 b FQ(in)o(teractions.])133 1100 y(\(b\))c(If)f(\005)g (is)g(quasilo)q(cal,)h(uniformly)d(nonn)o(ull)j(and)g FP(str)n(ongly)g(F)l (el)r(ler)25 b FQ(in)17 b(the)h(sense)f(that)h FF(f)k FE(2)60 1160 y FF(B)s FQ(\(\012)p FF(;)8 b FE(F)212 1167 y FH(\003)238 1160 y FQ(\))21 b(implies)e FF(\031)477 1167 y FH(\003)503 1160 y FF(f)28 b FE(2)23 b FF(C)646 1167 y FD(q)q(l)675 1160 y FQ(\(\012\),)g(and)f(\012)920 1167 y FH(0)961 1160 y FQ(is)f(not)h (\014nite,)f(do)q(es)h(there)f(exist)f(a)i FP(c)n(ontinuous)60 1221 y FQ(absolutely)16 b(summable)e(in)o(teraction)h(\010)h(suc)o(h)g(that)h (\005)c(=)h(\005)1174 1203 y FH(\010)1201 1221 y FQ(?)133 1281 y(2.)35 b(Regarding)20 b(the)h(relation)f(b)q(et)o(w)o(een)f(quasilo)q(calit) o(y)h(and)h(the)f(F)l(eller)f(prop)q(ert)o(y)l(,)i(the)f(fol-)60 1341 y(lo)o(wing)f(app)q(ears)h(to)f(b)q(e)g(an)h(op)q(en)f(question:)27 b(If)18 b(\012)1026 1348 y FH(0)1065 1341 y FQ(is)h(compact)e(but)i(not)h (\014nite,)e(can)h(a)h(F)l(eller)60 1401 y(sp)q(eci\014cation)c(fail)g(to)g (b)q(e)h(quasilo)q(cal?)60 1511 y Fd(Pr)o(oof)j(of)h(Theorem)f(2.15.)75 b FQ(Let)19 b FF(\026)g FQ(b)q(e)f(consisten)o(t)g(with)h(F)l(eller)d(sp)q (eci\014cations)j(\005)1774 1518 y FH(1)1811 1511 y FQ(and)60 1571 y(\005)97 1578 y FH(2)116 1571 y FQ(.)j(Then)444 1632 y FF(E)480 1639 y FD(\026)504 1632 y FQ(\()p FF(f)5 b FE(jF)602 1639 y FH(\003)626 1630 y Fs(c)644 1632 y FQ(\)\()p FF(!)r FQ(\))28 b(=)f(\()p FF(\031)873 1639 y FH(1\003)917 1632 y FF(f)5 b FQ(\)\()p FF(!)r FQ(\))28 b(=)g(\()p FF(\031)1176 1639 y FH(2\003)1220 1632 y FF(f)5 b FQ(\)\()p FF(!)r FQ(\))49 b FF(\026)p FQ(-a.e.)272 b(\(A)p FF(:)p FQ(1\))60 1719 y(for)19 b(eac)o(h)f FF(f)24 b FE(2)18 b FF(C)t FQ(\(\012\).)29 b(No)o(w,)18 b(since)h FF(\026)g FQ(giv)o(es)f(nonzero)h(measure)e(to)i(ev)o(ery)f(op)q (en)h(set,)g(t)o(w)o(o)g(con-)60 1779 y(tin)o(uous)e(functions)h(whic)o(h)e (agree)i FF(\026)p FQ(-a.e.)f(m)o(ust)e(in)i(fact)h(agree)f(ev)o(erywhere.)22 b(So)c(w)o(e)f(m)o(ust)f(ha)o(v)o(e)60 1839 y(\()p FF(\031)107 1846 y FH(1\003)151 1839 y FF(f)5 b FQ(\)\()p FF(!)r FQ(\))14 b(=)g(\()p FF(\031)382 1846 y FH(2\003)426 1839 y FF(f)5 b FQ(\)\()p FF(!)r FQ(\))16 b(for)g(all)f FF(!)r FQ(.)21 b(But)15 b(if)g(the)h(t)o(w)o(o)f(measures)g FF(\031)1320 1846 y FH(1\003)1364 1839 y FQ(\()p FF(!)r(;)h FE(\001)8 b FQ(\))16 b(and)g FF(\031)1624 1846 y FH(2\003)1668 1839 y FQ(\()p FF(!)r(;)g FE(\001)8 b FQ(\))16 b(giv)o(e)60 1899 y(equal)g(exp)q(ectations)g(to)g(eac)o(h)g(con)o (tin)o(uous)g(function)g FF(f)5 b FQ(,)16 b(then)h(they)e(m)o(ust)g(b)q(e)i (equal.)p 1808 1903 25 34 v 133 2009 a(F)l(urther)k(examples)e(of)i (pathological)h(non-quasilo)q(cal)g(sp)q(eci\014cations,)g(along)g(the)e (lines)h(of)60 2069 y(the)16 b(Remark)f(at)h(the)g(end)g(of)h(Section)f (2.3.4,)g(are)g(giv)o(en)f(b)o(y)h(Georgii)g([157)q(,)g(pp.)g(34{35].)133 2180 y(Theorem)g(2.17)i(and)g(Corollary)g(2.18)g(are)f(pro)o(v)o(en)g(in)g ([157)q(,)g(Theorem)f(2.34].)25 b(Prop)q(ositions)60 2240 y(2.19)18 b(and)h(2.20)f(are)g([157)q(,)f(Prop)q(osition)i(7.9)f(and)h(Theorem)d(7.7].) 26 b(Prop)q(osition)19 b(2.22)f(is)g(almost)60 2300 y(immedi)o(ate)12 b(from)i(the)h(de\014nition)g(of)g(F)l(eller)f(sp)q(eci\014cation)g(and)i(w)o (eak)f(con)o(v)o(ergence;)e(for)j(related)60 2360 y(results,)k(see)f([157)q (,)h(Sections)g(4.3)g(and)g(4.4].)32 b(Prop)q(osition)21 b(2.23)f(is)g(pro)o (v)o(en)f(in)g([157)q(,)h(Theorem)60 2420 y(7.12].)60 2530 y Fd(Pr)o(oof)c(of)g(Pr)o(oposition)g(2.25.)68 b FQ(Recall)13 b(that)i FF(\026)1089 2512 y FD(!)1115 2530 y FQ(\()8 b FE(\001)g FQ(\))15 b(is)f(a)h(regular)f(conditional)h(probabil-)60 2590 y(it)o(y)f(for)h FF(\026)g FQ(giv)o(en)g FE(F)412 2597 y FH(\001)443 2590 y FQ(,)g(i.e.)e(it)h(dep)q(ends)i(on)f FF(!)i FQ(only)e(through)h FF(!)1216 2597 y FH(\001)1248 2590 y FQ(;)f(and)g(w)o(e)g(are)g(in)o (terested)f(only)g(in)938 2784 y(175)p eop %%Page: 176 176 bop 60 91 a FQ(its)16 b(restriction)f(to)h FE(F)456 98 y FH(\001)485 89 y Fs(c)504 91 y FQ(,)f(i.e.)g(w)o(e)g(w)o(an)o(t)h(to)h(study)f(the)g (measure)e FF(\026)1298 73 y FD(!)1320 79 y Fr(\001)1350 91 y FQ(\()p FF(d!)1426 73 y Fy(0)1424 104 y FH(\001)1453 94 y Fs(c)1472 91 y FQ(\).)21 b(The)16 b(claim)e(is)i(no)o(w)60 152 y(that)h(for)f FF(\026)p FQ(-a.e.)g FF(!)405 159 y FH(\001)437 152 y FQ(,)g(w)o(e)g(ha)o(v)o(e)592 208 y Fx(Z)634 267 y FF(\026)663 246 y FD(!)685 252 y Fr(\001)714 267 y FQ(\()p FF(d!)790 246 y Fy(0)788 279 y FH(\001)817 270 y Fs(c)836 267 y FQ(\))8 b FF(\031)893 244 y FD(!)915 250 y Fr(\001)891 279 y FH(\003)944 267 y FQ(\()p FF(!)995 246 y Fy(0)993 279 y FH(\001)1022 270 y Fs(c)1041 267 y FF(;)g(A)p FQ(\))27 b(=)g FF(\026)1240 246 y FD(!)1262 252 y Fr(\001)1292 267 y FQ(\()p FF(A)p FQ(\))411 b(\(A)p FF(:)p FQ(2\))60 382 y(for)17 b(all)f FF(A)e FE(2)g(F)337 389 y FH(\001)366 380 y Fs(c)401 382 y FQ(and)j(all)f(\003)f FE(\032)f FQ(\001)707 364 y FD(c)724 382 y FQ(.)22 b(Both)16 b(sides)h(of)g(this)f(equation)g(are)h FE(F)1467 389 y FH(\001)1498 382 y FQ(-measurable.)k(So)c(it)60 442 y(su\016ces)f(to)g(pro)o(v)o(e)g(that) h(for)f(all)g FF(f)j FE(2)14 b FF(B)s FQ(\(\012)p FF(;)8 b FE(F)907 449 y FH(\001)938 442 y FQ(\))16 b(w)o(e)g(ha)o(v)o(e)140 502 y Fx(Z)181 560 y FF(d\026)235 567 y FH(\001)268 560 y FQ(\()p FF(!)317 567 y FH(\001)348 560 y FQ(\))8 b FF(f)d FQ(\(\012)458 567 y FH(\001)491 560 y FQ(\))526 502 y Fx(Z)568 560 y FF(\026)597 540 y FD(!)619 546 y Fr(\001)648 560 y FQ(\()p FF(d!)724 540 y Fy(0)722 573 y FH(\001)751 563 y Fs(c)770 560 y FQ(\))j FF(\031)827 538 y FD(!)849 544 y Fr(\001)825 573 y FH(\003)878 560 y FQ(\()p FF(!)929 540 y Fy(0)927 573 y FH(\001)956 563 y Fs(c)975 560 y FF(;)g(A)p FQ(\))27 b(=)1146 502 y Fx(Z)1187 560 y FF(d\026)1241 567 y FH(\001)1273 560 y FQ(\()p FF(!)1322 567 y FH(\001)1354 560 y FQ(\))8 b FF(f)d FQ(\(\012)1464 567 y FH(\001)1496 560 y FQ(\))j FF(\026)1552 540 y FD(!)1574 546 y Fr(\001)1604 560 y FQ(\()p FF(A)p FQ(\))13 b FF(:)72 b FQ(\(A)p FF(:)p FQ(3\))60 679 y(No)o(w)15 b(the)g(righ)o(t-hand)g(side)g(of)g(\(A.3\))f(is)817 643 y Fx(R)845 679 y FF(f)5 b(\037)905 686 y FD(A)942 679 y FF(d\026)p FQ(,)15 b(b)o(y)g(de\014nition)f(of)h(regular)g(conditional)g (prob-)60 739 y(abilit)o(y)l(.)20 b(As)c(for)g(the)g(left-hand)h(side,)e(let) g(us)i(rewrite)e(it)h(as)525 795 y Fx(Z)558 854 y FQ([)p FF(d\026)626 861 y FH(\001)658 854 y FQ(\()p FF(!)707 861 y FH(\001)739 854 y FQ(\))8 b FF(\026)795 833 y FD(!)817 839 y Fr(\001)846 854 y FQ(\()p FF(d!)922 833 y Fy(0)920 866 y FH(\001)949 857 y Fs(c)968 854 y FQ(\)])g FF(f)d FQ(\(\012)1092 861 y FH(\001)1124 854 y FQ(\))j FF(\031)1181 831 y FD(!)1203 837 y Fr(\001)1179 866 y FH(\003)1232 854 y FQ(\()p FF(!)1283 833 y Fy(0)1281 866 y FH(\001)1310 857 y Fs(c)1329 854 y FF(;)g(A)p FQ(\))13 b(;)344 b(\(A)p FF(:)p FQ(4\))60 969 y(this)24 b(passage)h(from)d(an)j (iterated)e(in)o(tegral)g(to)h(a)g(single)f(in)o(tegral)g(on)h(the)g(pro)q (duct)g(space)g(is)60 1030 y(justi\014ed)16 b(b)o(y)f([272)q(,)g(Prop)q (osition)j(I)q(I)q(I{2{1].)j(But)16 b(the)g(measure)e(in)i(brac)o(k)o(ets)f (in)h(A.4)f(is)h(precisely)60 1090 y FF(d\026)p FQ(\()p FF(!)163 1097 y FH(\001)196 1090 y FF(;)8 b(!)250 1072 y Fy(0)248 1102 y FH(\001)277 1093 y Fs(c)295 1090 y FQ(\);)16 b(so)h(the)f(left-hand)g(side) g(of)h(\(A.3\))e(equals)567 1149 y Fx(Z)608 1208 y FF(d\026)p FQ(\()p FF(!)711 1215 y FH(\001)744 1208 y FF(;)8 b(!)798 1187 y Fy(0)796 1220 y FH(\001)825 1211 y Fs(c)843 1208 y FQ(\))g FF(f)d FQ(\(\012)953 1215 y FH(\001)986 1208 y FQ(\))j FF(\031)1041 1215 y FH(\003)1067 1208 y FQ(\()p FF(!)1116 1215 y FH(\001)1159 1208 y FE(\002)j FF(!)1241 1187 y Fy(0)1239 1220 y FH(\001)1268 1211 y Fs(c)1287 1208 y FF(;)d(A)p FQ(\))13 b FF(;)386 b FQ(\(A)p FF(:)p FQ(5\))60 1326 y(where)14 b(w)o(e)g(ha)o(v)o(e)g(no)o(w)h(inserted)f (the)g(de\014nition)g(\(2.37\))h(of)g FF(\031)1183 1303 y FD(!)1205 1309 y Fr(\001)1181 1338 y FH(\003)1233 1326 y FQ(.)21 b(W)l(e)14 b(no)o(w)h(use)g(the)f(fact)g(that)h FF(\026)g FQ(is)60 1386 y(consisten)o(t)f(with)h(\005,)f(and)h(that)g(\003)f FE(\032)g FQ(\001)799 1368 y FD(c)830 1386 y FQ(\(so)i(\001)d FE(\032)h FQ(\003)1049 1368 y FD(c)1066 1386 y FQ(\);)h(it)f(follo)o(ws)h(that)g (\(A.5\))f(equals)1697 1351 y Fx(R)1725 1386 y FF(f)5 b(\037)1785 1393 y FD(A)1822 1386 y FF(d\026)p FQ(.)p 178 1450 25 34 v 60 1636 a FB(A.3)69 b(Pro)r(ofs)24 b(and)g(References)d(for)i(Section)f(2.4) 60 1728 y FM(A.3.1)56 b(V)-5 b(an)19 b(Ho)n(v)n(e)g(Con)n(v)n(ergence)60 1866 y Fd(Pr)o(oof)f(of)g(Pr)o(oposition)f(2.27.)69 b FQ(It)16 b(is)g(easy)g(to)h(see)f(that)562 1969 y FF(x)e FE(2)g FQ(\003)41 b(=)-8 b FE(\))41 b FQ(dist\()p FF(x;)8 b FQ(\003)1029 1949 y FD(c)1046 1969 y FQ(\))22 b(=)g(dist\()p FF(x;)8 b(@)1324 1949 y FH(+)1321 1982 y(1)1352 1969 y FQ(\003\))348 b(\(A.6a\))545 2042 y FF(x)13 b FE(2)h FQ(\003)667 2021 y FD(c)726 2042 y FQ(=)-8 b FE(\))41 b FQ(dist\()p FF(x;)8 b FQ(\003\))22 b(=)g(dist)o(\()p FF(x;)8 b(@)1306 2021 y Fy(\000)1303 2054 y FH(1)1335 2042 y FQ(\003\))362 b(\(A.6b\))60 2145 y(Therefore,)699 2248 y FE(j)p FF(@)742 2228 y Fy(\000)739 2260 y FD(r)771 2248 y FQ(\003)p FE(j)41 b(\024)h FQ(\(2)p FF(r)12 b FQ(+)f(1\))1110 2228 y FD(d)1131 2248 y FE(j)p FF(@)1174 2228 y FH(+)1171 2260 y(1)1203 2248 y FQ(\003)p FE(j)502 b FQ(\(A.7a\))699 2321 y FE(j)p FF(@)742 2300 y FH(+)739 2333 y FD(r)771 2321 y FQ(\003)p FE(j)41 b(\024)h FQ(\(2)p FF(r)12 b FQ(+)f(1\))1110 2300 y FD(d)1131 2321 y FE(j)p FF(@)1174 2300 y Fy(\000)1171 2333 y FH(1)1203 2321 y FQ(\003)p FE(j)499 b FQ(\(A.7b\))60 2424 y(It)16 b(follo)o(ws)g(that)h (\(a\){\(c\))f(are)h(equiv)m(alen)o(t.)133 2484 y(Next)e(notice)h(that)445 2587 y FF(x)d FE(2)h FQ(\003)d FE(n)g FQ(\(\003)g(+)g FF(a)p FQ(\))41 b(=)-8 b FE(\))41 b FF(x)14 b FE(2)g FQ(\003)i(and)h(dist\()p FF(x;)8 b FQ(\003)1350 2567 y FD(c)1366 2587 y FQ(\))14 b FE(\024)g(j)p FF(a)p FE(j)247 b FQ(\(A.8a\))445 2660 y FF(x)13 b FE(2)h FQ(\(\003)d(+)g FF(a)p FQ(\))g FE(n)g FQ(\003)41 b(=)-8 b FE(\))41 b FF(x)14 b FE(2)g FQ(\003)1057 2639 y FD(c)1090 2660 y FQ(and)j(dist\()p FF(x;)8 b FQ(\003\))13 b FE(\024)h(j)p FF(a)p FE(j)244 b FQ(\(A.8b\))938 2784 y(176)p eop %%Page: 177 177 bop 60 91 a FQ(Therefore)16 b(\(c\))g(implies)d(\(d\))k(and)f(\(e\).)21 b(Con)o(v)o(ersely)l(,)694 201 y FF(@)723 181 y Fy(\000)720 214 y FH(1)752 201 y FQ(\003)41 b(=)926 160 y Fx([)907 254 y Fy(j)p FD(a)p Fy(j)p FH(=1)990 201 y FQ([\003)11 b FE(n)g FQ(\(\003)g(+)g FF(a)p FQ(\)])496 b(\(A.9a\))694 352 y FF(@)723 332 y FH(+)720 365 y(1)752 352 y FQ(\003)41 b(=)926 311 y Fx([)907 405 y Fy(j)p FD(a)p Fy(j)p FH(=1)990 352 y FQ([\(\003)11 b(+)g FF(a)p FQ(\))f FE(n)h FQ(\003])494 b(\(A.9b\))60 509 y(so)17 b(\(d\))f(=)-8 b FE(\))16 b FQ(\(a\))g(and)h(\(e\))f(=)-8 b FE(\))16 b FQ(\(b\).)133 569 y(Finally)l(,)600 629 y(\003)p FE(4)p FQ(\(\003)10 b(+)h FF(A)p FQ(\))28 b FE(\032)952 587 y Fx([)941 679 y FD(a)p Fy(2)p FD(A)1010 629 y FQ([\003)p FE(4)p FQ(\(\003)9 b(+)i FE(f)p FF(a)p FE(g)p FQ(\)])i FF(;)403 b FQ(\(A)p FF(:)p FQ(10\))60 754 y(so)18 b(\(d\))f(and)h(\(e\))e(together)i (imply)c(\(f)s(\).)24 b(On)18 b(the)e(other)i(hand,)f(taking)g FF(A)e FQ(=)h FE(f)p FF(a)p FE(g)g FQ(sho)o(ws)i(trivially)60 814 y(that)f(\(f)s(\))f(implies)e(\(d\))i(and)h(\(e\).)133 874 y(This)g(completes)d(the)i(pro)q(of)h(of)g(equiv)m(alence)d(of)j (\(a\){\(f)s(\).)133 935 y(Next)h(w)o(e)g(pro)o(v)o(e)f(that)i(lim)638 942 y FD(n)p Fy(!1)740 935 y FE(j)p FQ(\003)788 942 y FD(n)811 935 y FE(j)f FQ(=)f FE(1)p FQ(:)26 b(this)18 b(follo)o(ws)g(immedi)o(ately)d (from)i(\(a\))i(and)g(the)60 995 y(fact)d(that)h FE(j)p FF(@)305 974 y Fy(\000)302 1006 y FH(1)334 995 y FQ(\003)p FE(j)c(\025)h FQ(1)i(whenev)o(er)g(\003)g(and)g(\003)881 977 y FD(c)915 995 y FQ(are)g(b)q(oth)h(nonempt)o(y)l(.)133 1055 y(Finally)l(,)i(let)g(us)i(pro) o(v)o(e)e(statemen)o(t)f(\()p FF(\014)s FQ(\):)28 b(F)l(or)20 b(eac)o(h)f FF(n)p FQ(,)i(c)o(ho)q(ose)f FF(a)1382 1062 y FD(n)1425 1055 y FE(2)h Fq(Z)1509 1034 y FD(d)1549 1055 y FQ(and)g FF(r)1670 1062 y FD(n)1713 1055 y FE(2)f Fq(Z)1797 1062 y FH(+)1846 1055 y FQ(so)60 1115 y(that)i FF(B)208 1122 y FD(r)224 1126 y Fs(n)247 1115 y FQ(\()p FF(a)292 1122 y FD(n)315 1115 y FQ(\))h FE(\021)f(f)p FF(x)h FE(2)f Fq(Z)580 1094 y FD(d)600 1115 y FQ(:)16 b FE(j)p FF(x)e FE(\000)h FF(a)766 1122 y FD(n)789 1115 y FE(j)22 b(\024)h FF(r)909 1122 y FD(n)932 1115 y FE(g)f FQ(is)f(a)h(maxim)n(um)o(-size)o(d)d (ball)i(con)o(tained)g(in)g(\003)1853 1122 y FD(n)1876 1115 y FQ(.)60 1175 y(W)l(e)i(claim)e(that)i(lim)468 1182 y FD(n)p Fy(!1)570 1175 y FF(r)592 1182 y FD(n)641 1175 y FQ(=)j FE(1)p FQ(.)41 b FP(Pr)n(o)n(of:)c FQ(Fix)22 b(an)o(y)h FF(r)k(>)e FQ(0.)42 b(Since)22 b(lim)1564 1182 y FD(n)p Fy(!1)1666 1175 y FE(j)p FQ(\003)1714 1182 y FD(n)1737 1175 y FE(j)k FQ(=)f FE(1)60 1236 y FQ(and)19 b(lim)225 1243 y FD(n)p Fy(!1)327 1236 y FE(j)p FF(@)370 1218 y Fy(\000)367 1248 y FD(r)399 1236 y FQ(\003)433 1243 y FD(n)456 1236 y FE(j)p FF(=)p FE(j)p FQ(\003)542 1243 y FD(n)565 1236 y FE(j)f FQ(=)f(0,)h(w)o(e)g(clearly)f(ha)o(v)o(e)g(lim) 1122 1243 y FD(n)p Fy(!1)1225 1236 y FE(j)p FQ(\003)1273 1243 y FD(n)1308 1236 y FE(n)12 b FF(@)1374 1218 y Fy(\000)1371 1248 y FD(r)1403 1236 y FQ(\003)1437 1243 y FD(n)1461 1236 y FE(j)17 b FQ(=)g FE(1)h FQ(and)h(hence)e(in)60 1296 y(particular)c(\003)316 1303 y FD(n)344 1296 y FE(n)5 b FF(@)403 1278 y Fy(\000)400 1308 y FD(r)432 1296 y FQ(\003)466 1303 y FD(n)504 1296 y FE(6)p FQ(=)13 b Fq(?)g FQ(for)h(all)f(su\016cien)o(tly)e(large)i FF(n)p FQ(.)21 b(But)12 b(\003)1294 1303 y FD(n)1323 1296 y FE(n)5 b FF(@)1382 1278 y Fy(\000)1379 1308 y FD(r)1411 1296 y FQ(\003)1445 1303 y FD(n)1482 1296 y FE(6)p FQ(=)14 b Fq(?)f FQ(is)g(just)g(another)60 1356 y(w)o(a)o(y)j(of)g(sa)o(ying)h(that)f FF(r)491 1363 y FD(n)529 1356 y FE(\025)d FF(r)q FQ(.)p 758 1360 25 34 v 133 1466 a FM(Remarks.)20 b FQ(1.)j(Man)o(y)16 b(b)q(o)q(oks)i([312,)f(206)q(,)f(40)q(])g(use)g(a)h(more)e(complicated)g (de\014nition)h(of)g(v)m(an)60 1526 y(Ho)o(v)o(e)h(con)o(v)o(ergence,)g (based)j(on)f(a)g(pa)o(ving)f(of)h Fq(Z)969 1505 y FD(d)1008 1526 y FQ(b)o(y)f(cub)q(es)h(of)g(side)f FF(a)p FQ(.)28 b(It)18 b(is)h(easy)f(to)h(see)g(that)60 1586 y(this)d(de\014nition)g(is)g(equiv)m (alen)o(t)f(to)h(conditions)h(\(a\){\(f)s(\).)133 1647 y(2.)39 b(What)23 b(ph)o(ysicists)e(call)h(v)m(an)g(Ho)o(v)o(e)f(con)o(v)o(ergence)g (is)g(termed)g FP(F\034lner)i(c)n(onver)n(genc)n(e)28 b FQ(b)o(y)60 1707 y(mathematicians.)k(Muc)o(h)21 b(of)g(the)f(theory)h(extends,)g(in)g (fact,)g(to)h(lo)q(cally)e(compact)f(amenable)60 1767 y(\(semi\)groups)c ([167)q(].)21 b(See)16 b([223,)g(Section)g(6.4])g(for)h(ergo)q(dic)f (theorems)f(in)h(this)g(con)o(text.)60 1897 y FM(A.3.2)56 b(T)-5 b(ranslation-In)n(v)m(arian)n(t)18 b(Measures)60 1989 y FQ(Prop)q(osition)e (2.30)f(is)g([157,)g(Theorem)e(14.5)j(and)f(Prop)q(osition)h(14.7].)21 b(Prop)q(osition)16 b(2.31)f(is)g([157,)60 2049 y(Corollary)24 b(14.A5)f(and)h(Theorem)e(14.A8].)43 b(F)l(or)23 b(more)f(information)g(on)i (ergo)q(dic)g(theorems,)60 2110 y(along)17 b(with)g(some)e(relev)m(an)o(t)h (coun)o(terexamples,)d(see)j([223)q(,)g(pp.)g(222{226].)24 b(Prop)q(osition)18 b(2.32)f(is)60 2170 y(pro)o(v)o(en)d(in)h([157,)g (Theorem)e(14.12])j(or)f([206)q(,)f(Lemma)f(IV.3.2];)h(a)h(stronger)g(form)f (will)g(b)q(e)h(pro)o(v)o(en)60 2230 y(as)22 b(Prop)q(osition)h(2.61\(e\))f (b)q(elo)o(w.)38 b(Information)20 b(on)i(the)g(P)o(oulsen)f(simplex)e(can)j (b)q(e)g(found)g(in)60 2290 y([252)q(,)16 b(284)q(].)60 2420 y FM(A.3.3)56 b(A)19 b(Digression)e(on)i(Subadditivit)n(y)60 2512 y FQ(An)g(imp)q(ortan)o(t)g(role)g(in)g(the)h(theory)f(of)h (translation-in)o(v)m(arian)o(t)g(lattice)e(systems)h(is)g(pla)o(y)o(ed)g(b)o (y)60 2573 y(the)j(concept)f(of)h(a)g FP(sub)n(additive)i(set)f(function)t FQ(.)39 b(Subadditivit)o(y)20 b(argumen)o(ts)h(will)g(b)q(e)h(used)g(to)60 2633 y(pro)o(v)o(e)c(the)h(existence)e(of)i(the)g(in\014nite-v)o(olume)d (limit)g(for)j(the)g(pressure,)g(the)f(en)o(trop)o(y)h(densit)o(y)l(,)938 2784 y(177)p eop %%Page: 178 178 bop 60 91 a FQ(and)14 b(quan)o(tities)f(connected)g(with)h(the)f(quotien)o(t) g(norm.)20 b(W)l(e)13 b(therefore)h(collect)e(here)h(the)h(needed)60 152 y(results.)60 263 y FM(De\014nition)k(A.1)24 b FP(L)n(et)18 b FE(S)k FP(b)n(e)d(the)g(class)g(of)f(al)r(l)h(nonempty)h(\014nite)f (subsets)h(of)e Fq(Z)1564 242 y FD(d)1584 263 y FP(,)h(and)g(let)g FE(S)1817 245 y Fy(\003)1852 263 y FQ(=)60 324 y FE(S)c([)c(f)p Fq(?)p FE(g)p FP(.)22 b(A)c(function)h FF(F)7 b FQ(:)15 b FE(S)625 305 y Fy(\003)658 324 y FE(!)f FQ([)p FE(\0001)p FF(;)8 b FE(1)p FQ(\))16 b FP(is)i(c)n(al)r(le)n(d)133 424 y FE(\017)24 b FQ(subadditiv)o(e) 14 b FP(if)g FF(F)7 b FQ(\()p FF(A)580 431 y FH(1)603 424 y FE([)t FF(A)677 431 y FH(2)697 424 y FQ(\))13 b FE(\024)h FF(F)7 b FQ(\()p FF(A)877 431 y FH(1)896 424 y FQ(\))t(+)t FF(F)g FQ(\()p FF(A)1056 431 y FH(2)1075 424 y FQ(\))14 b FP(whenever)j FF(A)1355 431 y FH(1)1374 424 y FF(;)8 b(A)1433 431 y FH(2)1466 424 y FE(2)14 b(S)1547 405 y Fy(\003)1581 424 y FP(with)h FF(A)1721 431 y FH(1)1744 424 y FE(\\)t FF(A)1818 431 y FH(2)1852 424 y FQ(=)182 484 y Fq(?)133 585 y FE(\017)24 b FQ(completely)14 b(subadditiv)o(e)j FP(if)g FF(F)7 b FQ(\()p FF(A)p FQ(\))14 b FE(\024)936 543 y FD(n)925 552 y Fx(P)918 622 y FD(i)p FH(=1)984 585 y FF(\025)1012 592 y FD(i)1026 585 y FF(F)7 b FQ(\()p FF(A)1121 592 y FD(i)1134 585 y FQ(\))18 b FP(whenever)i FF(A;)8 b(A)1480 592 y FH(1)1498 585 y FF(;)g(:)g(:)g(:)g(;)g(A)1645 592 y FD(n)1682 585 y FE(2)15 b(S)1764 567 y Fy(\003)1802 585 y FP(with)182 690 y FF(\037)213 697 y FD(A)255 690 y FQ(=)324 649 y FD(n)313 657 y Fx(P)307 727 y FD(i)p FH(=1)372 690 y FF(\025)400 697 y FD(i)415 690 y FF(\037)446 697 y FD(A)472 702 y Fs(i)504 690 y FP(and)j(al)r(l)h FF(\025)697 697 y FD(i)725 690 y FE(\025)14 b FQ(0)133 814 y FE(\017)24 b FQ(strongly)d(subadditiv)o(e)g FP(if)h FF(F)7 b FQ(\()p FF(A)788 821 y FH(1)820 814 y FE([)15 b FF(A)905 821 y FH(2)924 814 y FQ(\))f(+)g FF(F)7 b FQ(\()p FF(A)1104 821 y FH(1)1137 814 y FE(\\)15 b FF(A)1222 821 y FH(2)1241 814 y FQ(\))22 b FE(\024)f FF(F)7 b FQ(\()p FF(A)1437 821 y FH(1)1456 814 y FQ(\))14 b(+)g FF(F)7 b FQ(\()p FF(A)1636 821 y FH(2)1654 814 y FQ(\))22 b FP(whenever)182 874 y FF(A)219 881 y FH(1)238 874 y FF(;)8 b(A)297 881 y FH(2)330 874 y FE(2)14 b(S)411 856 y Fy(\003)133 986 y FQ(Clearly)l(,)h(complete)f(subadditivit)o(y) h(implies)e(subadditivit)o(y)l(.)20 b(The)d(k)o(ey)e(non)o(trivial)g(fact)h (is:)60 1098 y FM(Lemma)g(A.2)i(\([268,)g(Th)o(\023)-27 b(eor)o(\022)g(eme)16 b(2]\))24 b FP(If)17 b FF(F)24 b FP(is)17 b(str)n(ongly)h(sub)n(additive)g (and)g FF(F)7 b FQ(\()p Fq(?)o FQ(\))14 b FE(\025)g FQ(0)p FP(,)k(then)60 1158 y FF(F)24 b FP(is)17 b(c)n(ompletely)i(sub)n(additive.) 133 1270 y FM(Remark.)34 b FQ(If)21 b FF(F)27 b FQ(is)21 b(subadditiv)o(e,)g (then)g(either)g FF(F)7 b FQ(\()p Fq(?)o FQ(\))22 b FE(\025)g FQ(0)f(or)h(else)e FF(F)29 b FE(\021)22 b(\0001)p FQ(.)36 b(In)21 b(our)60 1330 y(applications)16 b(w)o(e)g(will)f(alw)o(a)o(ys)h(ha)o(v)o(e)g FF(F)7 b FQ(\()p Fq(?)o FQ(\))14 b(=)f(0.)133 1439 y(W)l(e)g(can)g(no)o(w)h (state)f(the)g(t)o(w)o(o)f(principal)h(theorems)e(on)j(the)f(existence)e(of)i (the)g(in\014nite-v)o(olume)60 1499 y(limit:)60 1611 y FM(Prop)r(osition)18 b(A.3)24 b FP(L)n(et)15 b FF(F)7 b FQ(:)21 b FE(S)663 1593 y Fy(\003)696 1611 y FE(!)14 b FQ([)p FE(\0001)p FF(;)8 b FE(1)p FQ(\))13 b FP(b)n(e)j(tr)n(anslation-invariant)g(and)f(c)n(ompletely)h(sub-) 60 1671 y(additive.)23 b(Then)32 b FQ(lim)390 1701 y FH(\003)p Fy(\0451)493 1671 y FE(j)p FQ(\003)p FE(j)555 1653 y Fy(\000)p FH(1)602 1671 y FF(F)7 b FQ(\(\003\))17 b FP(exists)h(and)g(e)n(quals)24 b FQ(inf)1101 1701 y FH(\003)p Fy(2S)1181 1671 y FE(j)p FQ(\003)p FE(j)1243 1653 y Fy(\000)p FH(1)1290 1671 y FF(F)7 b FQ(\(\003\))p FP(.)60 1805 y FM(Prop)r(osition)18 b(A.4)24 b FP(L)n(et)f FF(F)7 b FQ(:)32 b FE(S)682 1787 y Fy(\003)726 1805 y FE(!)24 b FQ([)p FE(\0001)p FF(;)8 b FE(1)p FQ(\))22 b FP(b)n(e)h(tr)n (anslation-invariant)i(and)e(sub)n(additive.)60 1865 y(Then)38 b FQ(lim)195 1890 y FD(n)p Fy(!1)295 1865 y FE(j)p FQ(\003)343 1872 y FD(n)366 1865 y FE(j)380 1847 y Fy(\000)p FH(1)427 1865 y FF(F)7 b FQ(\(\003)519 1872 y FD(n)542 1865 y FQ(\))25 b FP(exists)h(for)e(any)h(van)h(Hove)g(se)n(quenc)n(e)h FQ(\(\003)1403 1872 y FD(n)1426 1865 y FQ(\))e FP(satisfying)g(the)h(addi-)60 1940 y(tional)20 b(c)n(ondition)f FE(j)p FQ(\003)462 1947 y FD(n)485 1940 y FE(j)p FF(=)p FQ(diam)o(\(\003)682 1947 y FD(n)706 1940 y FQ(\))725 1921 y FD(d)761 1940 y FE(\025)e FF(\016)h(>)e FQ(0)k FP(for)e(some)h FF(\016)f(>)f FQ(0)p FP(.)27 b(Mor)n(e)n(over,)18 b(this)h(limit)g(e)n(quals)64 2000 y FQ(inf)60 2029 y FD(n)p Fy(\025)p FH(1)135 2000 y FE(j)p FF(C)184 2007 y FD(n)207 2000 y FE(j)221 1982 y Fy(\000)p FH(1)268 2000 y FF(F)7 b FQ(\()p FF(C)361 2007 y FD(n)384 2000 y FQ(\))p FP(.)133 2129 y FQ(W)l(e)19 b(note)h(that)g(ordinary)g(subadditivit)o(y)e(is)h FP(not)25 b FQ(su\016cien)o(t)18 b(for)i(the)f(existence)f(of)h(the)g(v)m(an)60 2189 y(Ho)o(v)o(e)c(limit;)e(a)k(coun)o(terexample)c(has)k(b)q(een)f(giv)o (en)g(in)g([175].)60 2298 y Fd(Pr)o(oof)e(of)g(Pr)o(oposition)f(A.3.)68 b FQ(This)12 b(result)g(is)g(stated)h(in)f([267)q(,)h(Th)o(\023)-23 b(eor)o(\022)g(eme)10 b(0])j(and)g(pro)o(v)o(en)60 2358 y(in)k([268,)g (Corollaire)f(10],)h(but)g(the)g(pro)q(of)h(is)f(rather)g(di\016cult)e(to)i (follo)o(w.)23 b(F)l(or)17 b(completeness)e(let)60 2418 y(us)i(giv)o(e)e(an)i (elemen)o(tary)c(pro)q(of)k([333)q(]:)133 2479 y(Let)h FF(A;)8 b(B)18 b FE(2)e(S)t FQ(;)h(without)h(loss)g(of)f(generalit)o(y)g(let)f(us)i (supp)q(ose)h(that)e(0)g FE(2)f FF(B)s FQ(.)24 b(No)o(w)17 b(consider)60 2539 y(the)f(decomp)q(osition)575 2618 y FF(\037)606 2625 y FD(A)661 2618 y FQ(=)778 2577 y Fx(X)727 2669 y FD(a)p FH(:)5 b FD(B)r FH(+)p FD(a)p Fy(\032)p FD(A)924 2585 y FQ(1)p 903 2607 68 2 v 903 2653 a FE(j)p FF(B)s FE(j)975 2618 y FF(\037)1006 2625 y FD(B)r FH(+)p FD(a)1102 2618 y FQ(+)1164 2577 y Fx(X)1159 2669 y FD(x)p Fy(2)p FD(A)1237 2618 y FF(\025)1265 2625 y FD(x)1288 2618 y FF(\037)1319 2626 y Fy(f)p FD(x)p Fy(g)1753 2618 y FQ(\(A)p FF(:)p FQ(11\))938 2784 y(178)p eop %%Page: 179 179 bop 60 91 a FQ(where)539 167 y FF(\025)567 174 y FD(x)617 167 y FQ(=)687 133 y FE(jf)p FF(a)p FQ(:)21 b FF(B)14 b FQ(+)d FF(a)i FE(3)h FF(x)i FQ(and)h FF(B)d FQ(+)d FF(a)i FE(6\032)h FF(A)p FE(gj)p 687 155 692 2 v 1000 201 a(j)p FF(B)s FE(j)1398 167 y FF(:)341 b FQ(\(A)p FF(:)p FQ(12\))60 288 y(Clearly)15 b(0)g FE(\024)e FF(\025)348 295 y FD(x)384 288 y FE(\024)h FQ(1;)i(and)h(b)o(y)f(summing)e(\(A.11\))i(o)o(v)o(er)f FF(y)g FE(2)g Fq(Z)1237 267 y FD(d)1273 288 y FQ(w)o(e)h(\014nd)454 363 y Fx(X)449 455 y FD(x)p Fy(2)p FD(A)528 404 y FF(\025)556 411 y FD(x)620 404 y FQ(=)42 b FE(j)p FF(A)p FE(j)18 b(\000)841 355 y Fx(\014)841 380 y(\014)841 404 y(\014)866 363 y(\\)855 455 y FD(b)p Fy(2)p FD(B)922 404 y FQ(\()p FF(A)11 b FE(\000)g FF(b)p FQ(\))1079 355 y Fx(\014)1079 380 y(\014)1079 404 y(\014)620 528 y FQ(=)700 478 y Fx(\014)700 503 y(\014)700 528 y(\014)p FF(A)f FE(n)808 486 y Fx(\\)797 579 y FD(b)p Fy(2)p FD(B)864 528 y FQ(\()p FF(A)h FE(\000)f FF(b)p FQ(\))1020 478 y Fx(\014)1020 503 y(\014)1020 528 y(\014)195 b FQ([since)15 b(0)f FE(2)g FF(B)s FQ(])619 642 y FE(\021)42 b FF(m)743 622 y Fy(\000)743 654 y FD(B)773 642 y FQ(\()p FF(A)p FQ(\))13 b FF(:)878 b FQ(\(A.13\))60 752 y(By)13 b(complete)d(subadditivit)o(y)i(and)i(translation-in)o(v)m (ariance)f(it)g(follo)o(ws)g(from)f(\(A.11\))h(and)h(\(A.13\))60 812 y(that)434 937 y FF(F)7 b FQ(\()p FF(A)p FQ(\))40 b FE(\024)720 896 y Fx(X)668 988 y FD(a)p FH(:)6 b FD(B)r FH(+)p FD(a)p Fy(\032)p FD(A)844 904 y FF(F)h FQ(\()p FF(B)13 b FQ(+)e FF(a)p FQ(\))p 844 926 202 2 v 911 971 a FE(j)p FF(B)s FE(j)1070 937 y FQ(+)1132 896 y Fx(X)1128 988 y FD(x)p Fy(2)p FD(A)1206 937 y FF(\025)1234 944 y FD(x)1256 937 y FF(F)c FQ(\()p FE(f)p FF(x)p FE(g)p FQ(\))588 1087 y(=)673 1053 y FF(F)g FQ(\()p FF(B)s FQ(\))p 673 1075 116 2 v 698 1121 a FE(j)p FF(B)s FE(j)794 1037 y Fx(\014)794 1062 y(\014)794 1087 y(\014)818 1045 y(\\)808 1137 y FD(b)p Fy(2)p FD(B)875 1087 y FQ(\()p FF(A)j FE(\000)h FF(b)p FQ(\))1031 1037 y Fx(\014)1031 1062 y(\014)1031 1087 y(\014)19 b FQ(+)1121 1014 y Fx( )1159 1045 y(X)1154 1137 y FD(x)p Fy(2)p FD(A)1232 1087 y FF(\025)1260 1094 y FD(x)1283 1014 y Fx(!)1324 1087 y FF(F)7 b FQ(\()p FE(f)p FQ(0)p FE(g)p FQ(\))588 1231 y(=)673 1198 y FF(F)g FQ(\()p FF(B)s FQ(\))p 673 1220 V 698 1265 a FE(j)p FF(B)s FE(j)802 1183 y Fx(h)822 1231 y FE(j)p FF(A)p FE(j)j(\000)h FF(m)990 1211 y Fy(\000)990 1244 y FD(B)1020 1231 y FQ(\()p FF(A)p FQ(\))1095 1183 y Fx(i)1134 1231 y FQ(+)19 b FF(m)1234 1211 y Fy(\000)1234 1244 y FD(B)1264 1231 y FQ(\()p FF(A)p FQ(\))p FF(F)7 b FQ(\()p FE(f)p FQ(0)p FE(g)p FQ(\))13 b FF(:)236 b FQ(\(A.14\))60 1369 y(No)o(w)22 b(divide)g(b)o(y)g FE(j)p FF(A)p FE(j)f FQ(and)j(tak)o(e)d FF(A)k FE(\045)f(1)e FQ(\(v)m(an)h(Ho)o(v)o(e\):)33 b(b)o(y)22 b(Prop)q(osition)h(2.27\(d\))h(w)o (e)e(ha)o(v)o(e)75 1429 y(lim)60 1459 y FD(A)p Fy(\0451)165 1429 y FF(m)208 1409 y Fy(\000)208 1442 y FD(B)238 1429 y FQ(\()p FF(A)p FQ(\))p FF(=)p FE(j)p FF(A)p FE(j)13 b FQ(=)h(0.)22 b(Therefore)715 1595 y(lim)8 b(sup)741 1635 y FD(A)p Fy(\0451)878 1561 y FF(F)f FQ(\()p FF(A)p FQ(\))p 878 1583 113 2 v 902 1629 a FE(j)p FF(A)p FE(j)1023 1595 y(\024)1095 1561 y FF(F)g FQ(\()p FF(B)s FQ(\))p 1095 1583 116 2 v 1119 1629 a FE(j)p FF(B)s FE(j)1230 1595 y FF(:)509 b FQ(\(A)p FF(:)p FQ(15\))60 1734 y(Since)15 b(this)h(holds)h(for)g(all)e FF(B)i FE(2)d(S)t FQ(,)i(w)o(e)f(ha)o (v)o(e)492 1869 y(lim)8 b(sup)518 1908 y FD(A)p Fy(\0451)654 1835 y FF(F)f FQ(\()p FF(A)p FQ(\))p 654 1857 113 2 v 679 1903 a FE(j)p FF(A)p FE(j)800 1869 y(\024)36 b FQ(inf)866 1898 y FD(B)r Fy(2S)955 1835 y FF(F)7 b FQ(\()p FF(B)s FQ(\))p 955 1857 116 2 v 979 1903 a FE(j)p FF(B)s FE(j)1104 1869 y(\024)27 b FQ(lim)8 b(inf)1188 1899 y FD(B)r Fy(\0451)1318 1835 y FF(F)f FQ(\()p FF(B)s FQ(\))p 1318 1857 V 1343 1903 a FE(j)p FF(B)s FE(j)1453 1869 y FF(:)286 b FQ(\(A)p FF(:)p FQ(16\))p 178 2006 25 34 v 60 2162 a Fd(Pr)o(oof)18 b(of)h(Pr)o(oposition)f(A.4.)72 b FQ(This)17 b(is)g(essen)o(tially)e([198)q(,)h(Prop)q(osition)i(4.10].)24 b(See)16 b(also)60 2222 y([175)q(,)g(333)q(].)p 417 2226 V 133 2332 a FM(Remarks.)32 b FQ(1.)i(The)21 b(imp)q(ortan)o(t)e(concept)h(of)h (complete)d(subadditivit)o(y)h(w)o(as)i(apparen)o(tly)60 2392 y(\014rst)c(in)o(tro)q(duced)e(b)o(y)h(Moulin-Ollagnier)f(and)i(Pinc)o(hon)f ([267)q(,)f(268)r(].)133 2452 y(2.)44 b(The)24 b(pro)q(ofs)h(giv)o(en)e(here) h(actually)f(w)o(ork)h(\(after)f(sligh)o(t)g(notational)i(c)o(hanges\))f(in)g (an)60 2512 y(arbitrary)17 b(discrete)e(amenable)g(group)i([333)q(].)22 b(A)16 b(sligh)o(tly)f(di\013eren)o(t)h(pro)q(of)h(of)g(Prop)q(osition)h (A.3,)60 2573 y(also)g(v)m(alid)f(for)g(discrete)f(amenable)g(groups,)i(is)g (implici)o(t)c(in)j([266)q(,)g(pro)q(of)h(of)g(Th)o(\023)-23 b(eor)o(\022)g(eme)16 b(2].)24 b(F)l(or)60 2633 y(an)17 b(extension)e(to)i (lo)q(cally)f(compact)f(amenable)f(groups,)j(see)f([268)q(].)938 2784 y(179)p eop %%Page: 180 180 bop 60 91 a FM(A.3.4)56 b(A)19 b(Lemm)o(a)d(on)j(Sums)f(of)g(T)-5 b(ranslates)60 184 y FQ(Next)21 b(w)o(e)g(use)h(subadditivit)o(y)f(argumen)o (ts)g(to)h(pro)o(v)o(e)f(an)i(imp)q(ortan)o(t)e(lemm)o(a)f(concerning)h(the) 60 244 y(in\014nite-v)o(olume)c(limit)g(of)j(sums)e(of)i(translates)g(of)g(a) g(function)g FF(f)5 b FQ(.)32 b(This)19 b(lemma)e(will)h(pla)o(y)i(an)60 304 y(imp)q(ortan)o(t)15 b(role)h(in)g(our)h(study)f(of)h(the)f(quotien)o(t)f (seminorms.)133 364 y(First)k(let)g(us)g(in)o(tro)q(duce)g(a)h(con)o(v)o (enien)o(t)d(notation:)29 b(for)19 b(an)o(y)h FF(g)h FE(2)e FF(B)s FQ(\(\012\),)h(let)e(us)i(de\014ne)f(the)60 424 y FP(maximum,)e (minimum)h(and)f(midp)n(oint)g(values)i(of)e FF(g)i FQ(b)o(y)604 527 y(sup)8 b FF(g)44 b FE(\021)d FQ(sup)833 566 y FD(!)q Fy(2)p FH(\012)914 527 y FF(g)r FQ(\()p FF(!)r FQ(\))720 b(\(A.17a\))618 650 y(inf)11 b FF(g)44 b FE(\021)k FQ(inf)832 679 y FD(!)q Fy(2)p FH(\012)913 650 y FF(g)r FQ(\()p FF(!)r FQ(\))718 b(\(A.17b\))596 800 y(mid)6 b FF(g)44 b FE(\021)837 781 y FH(1)p 837 789 18 2 v 837 818 a(2)868 727 y Fx(")892 800 y FQ(sup)893 840 y FD(!)q Fy(2)p FH(\012)974 800 y FF(g)r FQ(\()p FF(!)r FQ(\))20 b(+)26 b(inf)1146 830 y FD(!)q Fy(2)p FH(\012)1226 800 y FF(g)r FQ(\()p FF(!)r FQ(\))1321 727 y Fx(#)752 908 y FQ(=)837 888 y FH(1)p 837 896 V 837 925 a(2)860 908 y FQ(\(sup)9 b FF(g)k FQ(+)e(inf)g FF(g)r FQ(\))574 b(\(A.17c\))60 1010 y(Clearly)15 b(w)o(e)h(ha)o(v)o(e)564 1112 y FE(k)p FF(g)r FE(k)639 1119 y Fy(1)718 1112 y FQ(=)42 b(max)n(\(sup)9 b FF(g)r(;)f FE(\000)g FQ(inf)j FF(g)r FQ(\))535 b(\(A.18a\))418 1208 y FE(k)p FF(g)r FE(k)493 1216 y FD(B)r FH(\(\012\))p FD(=const)718 1208 y FQ(=)803 1189 y FH(1)p 803 1197 V 803 1225 a(2)825 1208 y FQ(\(sup)9 b FF(g)k FE(\000)e FQ(inf)g FF(g)r FQ(\))28 b(=)g FE(k)p FF(g)13 b FE(\000)e FQ(mid)6 b FF(g)r FE(k)1467 1215 y Fy(1)1518 1208 y FF(:)194 b FQ(\(A.18b\))60 1313 y FM(Lemma)16 b(A.5)24 b FP(L)n(et)17 b FF(f)i FE(2)14 b FF(B)s FQ(\(\012\))p FP(.)22 b(Then:)93 1408 y(\(a\))38 b FQ(lim)182 1438 y FH(\003)p Fy(\0451)285 1408 y FE(j)p FQ(\003)p FE(j)347 1390 y Fy(\000)p FH(1)402 1408 y FQ(sup)495 1375 y Fx(P)484 1446 y FD(a)p Fy(2)p FH(\003)559 1408 y FF(T)588 1415 y FD(a)608 1408 y FF(f)23 b FP(exists)18 b(and)g(e)n(quals)25 b FQ(inf)1026 1438 y FH(\003)p Fy(2S)1106 1408 y FE(j)p FQ(\003)p FE(j)1168 1390 y Fy(\000)p FH(1)1223 1408 y FQ(sup)1317 1375 y Fx(P)1305 1446 y FD(a)p Fy(2)p FH(\003)1380 1408 y FF(T)1409 1415 y FD(a)1430 1408 y FF(f)5 b FP(.)95 1535 y(\(b\))39 b FQ(lim)182 1565 y FH(\003)p Fy(\0451)285 1535 y FE(j)p FQ(\003)p FE(j)347 1517 y Fy(\000)p FH(1)402 1535 y FQ(inf)481 1502 y Fx(P)470 1573 y FD(a)p Fy(2)p FH(\003)545 1535 y FF(T)574 1542 y FD(a)594 1535 y FF(f)23 b FP(exists)18 b(and)g(e)n(quals)g FQ(sup)1013 1575 y FH(\003)p Fy(2S)1094 1535 y FE(j)p FQ(\003)p FE(j)1156 1517 y Fy(\000)p FH(1)1211 1535 y FQ(inf)1289 1502 y Fx(P)1278 1573 y FD(a)p Fy(2)p FH(\003)1353 1535 y FF(T)1382 1542 y FD(a)1402 1535 y FF(f)5 b FP(.)95 1674 y(\(c\))39 b FQ(lim)182 1704 y FH(\003)p Fy(\0451)285 1674 y FE(j)p FQ(\003)p FE(j)347 1656 y Fy(\000)p FH(1)402 1624 y Fx(\015)402 1649 y(\015)402 1674 y(\015)437 1641 y(P)425 1712 y FD(a)p Fy(2)p FH(\003)500 1674 y FF(T)529 1681 y FD(a)550 1674 y FF(f)579 1624 y Fx(\015)579 1649 y(\015)579 1674 y(\015)602 1701 y Fy(1)657 1674 y FP(exists)18 b(and)g(e)n(quals)24 b FQ(inf)1028 1704 y FH(\003)p Fy(2S)1108 1674 y FE(j)p FQ(\003)p FE(j)1170 1656 y Fy(\000)p FH(1)1225 1624 y Fx(\015)1225 1649 y(\015)1225 1674 y(\015)1260 1641 y(P)1248 1712 y FD(a)p Fy(2)p FH(\003)1323 1674 y FF(T)1352 1681 y FD(a)1373 1674 y FF(f)1402 1624 y Fx(\015)1402 1649 y(\015)1402 1674 y(\015)1425 1701 y Fy(1)1462 1674 y FP(.)93 1811 y(\(d\))38 b FQ(lim)182 1841 y FH(\003)p Fy(\0451)285 1811 y FE(j)p FQ(\003)p FE(j)347 1793 y Fy(\000)p FH(1)402 1762 y Fx(\015)402 1786 y(\015)402 1811 y(\015)437 1778 y(P)425 1849 y FD(a)p Fy(2)p FH(\003)500 1811 y FF(T)529 1818 y FD(a)550 1811 y FF(f)579 1762 y Fx(\015)579 1786 y(\015)579 1811 y(\015)602 1838 y FD(B)r FH(\(\012\))p FD(=const)803 1811 y FP(exists)19 b(and)e(e)n(quals)25 b FQ(inf)1174 1841 y FH(\003)p Fy(2S)1255 1811 y FE(j)p FQ(\003)p FE(j)1317 1793 y Fy(\000)p FH(1)1372 1762 y Fx(\015)1372 1786 y(\015)1372 1811 y(\015)1406 1778 y(P)1395 1849 y FD(a)p Fy(2)p FH(\003)1470 1811 y FF(T)1499 1818 y FD(a)1519 1811 y FF(f)1548 1762 y Fx(\015)1548 1786 y(\015)1548 1811 y(\015)1571 1838 y FD(B)r FH(\(\012\))p FD(=const)1755 1811 y FP(.)95 1974 y(\(e\))39 b FQ(lim)182 2004 y FH(\003)p Fy(\0451)285 1974 y FE(j)p FQ(\003)p FE(j)347 1956 y Fy(\000)p FH(1)402 1974 y FQ(mid)484 1901 y Fx( )528 1940 y(P)516 2012 y FD(a)p Fy(2)p FH(\003)591 1974 y FF(T)620 1981 y FD(a)641 1974 y FF(f)670 1901 y Fx(!)721 1974 y FP(exists)18 b(and)f(lies)i(in)e(the)h (interval)h FQ([inf)11 b FF(f)s(;)d FQ(sup)g FF(f)d FQ(])p FP(.)60 2155 y Fd(Pr)o(oof.)48 b FQ(\(a\))17 b(Consider)g(the)g(set)g (function)f FF(F)949 2162 y FH(+)978 2155 y FQ(\(\003\))f FE(\021)g FQ(sup)1201 2122 y Fx(P)1244 2165 y FD(a)p Fy(2)p FH(\003)1322 2155 y FF(T)1351 2162 y FD(a)1371 2155 y FF(f)5 b FQ(,)17 b(de\014ned)g(for)g (\014nite)f(sub-)60 2215 y(sets)23 b(\003)j FE(\032)f Fq(Z)317 2194 y FD(d)337 2215 y FQ(.)42 b(Clearly)23 b FF(F)29 b FQ(is)23 b(\014nite-v)m(alued)g(and)h(translation-in)o(v)m(arian)o(t.)42 b(Moreo)o(v)o(er,)23 b(it)g(is)60 2289 y(completely)13 b(subadditiv)o(e)i (\(De\014nition)h(A.1\):)21 b(if)15 b FF(A;)8 b(A)1080 2296 y FH(1)1099 2289 y FF(;)g(:)g(:)g(:)g(;)g(A)1246 2296 y FD(n)1282 2289 y FE(2)14 b(S)20 b FQ(with)c FF(\037)1521 2296 y FD(A)1563 2289 y FQ(=)1633 2248 y FD(n)1622 2256 y Fx(P)1615 2326 y FD(i)p FH(=1)1680 2289 y FF(\025)1708 2296 y FD(i)1723 2289 y FF(\037)1754 2296 y FD(A)1780 2301 y Fs(i)1811 2289 y FQ(and)60 2369 y(all)g FF(\025)156 2376 y FD(i)184 2369 y FE(\025)e FQ(0,)i(then)619 2471 y FF(F)7 b FQ(\()p FF(A)p FQ(\))40 b FE(\021)h FQ(sup)854 2510 y FD(!)q Fy(2)p FH(\012)940 2430 y Fx(X)935 2522 y FD(a)p Fy(2)p FD(A)1004 2471 y FQ(\()p FF(T)1052 2478 y FD(a)1072 2471 y FF(f)5 b FQ(\)\()p FF(!)r FQ(\))774 2617 y(=)41 b(sup)854 2656 y FD(!)q Fy(2)p FH(\012)954 2563 y FD(n)935 2575 y Fx(X)937 2666 y FD(i)p FH(=1)1003 2617 y FF(\025)1031 2624 y FD(i)1065 2575 y Fx(X)1054 2667 y FD(a)p Fy(2)p FD(A)1123 2672 y Fs(i)1136 2617 y FQ(\()p FF(T)1184 2624 y FD(a)1204 2617 y FF(f)5 b FQ(\)\()p FF(!)r FQ(\))938 2784 y(180)p eop %%Page: 181 181 bop 773 122 a FE(\024)873 68 y FD(n)853 81 y Fx(X)855 172 y FD(i)p FH(=1)922 122 y FF(\025)950 129 y FD(i)981 122 y FQ(sup)981 162 y FD(!)q Fy(2)p FH(\012)1074 81 y Fx(X)1063 173 y FD(a)p Fy(2)p FD(A)1132 178 y Fs(i)1144 122 y FQ(\()p FF(T)1192 129 y FD(a)1213 122 y FF(f)5 b FQ(\)\()p FF(!)r FQ(\))773 271 y FE(\021)873 217 y FD(n)853 229 y Fx(X)855 320 y FD(i)p FH(=1)922 271 y FF(\025)950 278 y FD(i)973 271 y FF(F)1005 278 y FH(+)1034 271 y FQ(\()p FF(A)1090 278 y FD(i)1103 271 y FQ(\))14 b FF(:)603 b FQ(\(A.19\))60 418 y(Prop)q(osition)17 b(A.3)f(then)g(implies)e(that)30 b(lim)796 448 y FH(\003)p Fy(\0451)899 418 y FE(j)p FQ(\003)p FE(j)961 400 y Fy(\000)p FH(1)1008 418 y FF(F)1040 425 y FH(+)1069 418 y FQ(\(\003\))16 b(exists)f(and)i(equals)23 b(inf)1534 448 y FH(\003)p Fy(2S)1614 418 y FE(j)p FQ(\003)p FE(j)1676 400 y Fy(\000)p FH(1)1723 418 y FF(F)1755 425 y FH(+)1784 418 y FQ(\(\003\).)133 500 y(\(b\))16 b(is)g(simply)f(\(a\))h(applied)g(to)g(the) g(function)h FE(\000)p FF(f)5 b FQ(.)133 560 y(\(c\))16 b(Consider)h(the)f (set)g(function)g FF(F)7 b FQ(\(\003\))13 b FE(\021)g(k)973 527 y Fx(P)1017 571 y FD(a)p Fy(2)p FH(\003)1094 560 y FF(T)1123 567 y FD(a)1144 560 y FF(f)5 b FE(k)1198 567 y Fy(1)1235 560 y FQ(;)16 b(the)g(pro)q(of)i(is)e(then)g(as)h(in)f(\(a\).)133 621 y(\(d\))h(This)f(is)g(an)h(immedi)o(ate)d(consequence)h(of)i(\(a\))f(and) h(\(b\))g(together)f(with)g(\(A.18b\).)22 b([Or)15 b(it)60 681 y(can)c(b)q(e)g(pro)o(v)o(en)f(directly)f(b)o(y)h(applying)h(complete)e (subadditivit)o(y)g(to)i FF(F)1364 688 y FD(c)1381 681 y FQ(\(\003\))j FE(\021)g(k)1553 648 y Fx(P)1597 691 y FD(a)p Fy(2)p FH(\003)1674 681 y FF(T)1703 688 y FD(a)1723 681 y FF(f)5 b FE(k)1777 688 y FD(B)r FH(\(\012\))p FD(=const)1961 681 y FQ(.])133 741 y(\(e\))16 b(This)g(is)g(an)h(immedi)o(ate)d(consequence)h(of)i(\(a\))f(and)h(\(b\).)p 1398 745 25 34 v 133 851 a FM(Remark.)h FQ(F)l(or)c FF(f)20 b FE(2)14 b FF(B)576 858 y FD(q)q(l)606 851 y FQ(\(\012\))g(w)o(e)f(can)h (pro)o(v)o(e)f(this)h(lemma)d(b)o(y)i(a)h(sligh)o(tly)f(di\013eren)o(t)g (argumen)o(t)60 911 y(based)k(on)g(the)g(fact)f(that)h(the)g(set)f(functions) h FF(F)955 918 y FH(+)984 911 y FQ(,)f FF(F)23 b FQ(and)17 b FF(F)1196 918 y FD(c)1230 911 y FQ(are)f(\\almost)h(additiv)o(e")e(\(and)j (not)60 971 y(merely)f FP(sub)s FQ(additiv)o(e\).)29 b(Since)18 b(the)i(argumen)o(t)e(is)h(virtually)f(iden)o(tical)f(to)j(that)f(used)h(b)o (y)f(Israel)60 1031 y(in)c(pro)o(ving)h(the)f(existence)f(of)h(the)h (pressure)f([206)q(,)g(Theorems)f(I.2.3)h(and)i(I.2.4],)d(w)o(e)h(giv)o(e)f (only)i(a)60 1092 y(brief)f(sk)o(etc)o(h.)20 b(F)l(or)d(simplicit)n(y)c(let)j (us)g(consider)g(part)h(\(c\);)e(the)h(other)h(parts)g(are)f(similar.)133 1152 y(Supp)q(ose)23 b(\014rst)f(that)g FF(f)28 b FQ(is)21 b(a)h(b)q(ounded)h FP(lo)n(c)n(al)k FQ(function,)c(i.e.)d(that)i FF(f)29 b FE(2)23 b FF(B)s FQ(\(\012)p FF(;)8 b FE(F)1691 1159 y FD(X)1725 1152 y FQ(\))21 b(where)60 1212 y(diam)o(\()p FF(X)t FQ(\))26 b FF(<)g(D)q FQ(.)44 b(Then)23 b(it)g(is)g(easily)g(seen)g(that)h FF(F)7 b FQ(\(\003)15 b FE([)h FQ(\003)1241 1194 y Fy(0)1252 1212 y FQ(\))26 b(=)g(2)p FF(F)7 b FQ(\(\003\))23 b(whenev)o(er)g(\003)1775 1194 y Fy(0)1809 1212 y FQ(is)h(a)60 1272 y(translate)16 b(of)g(\003)f(with)h (dist)o(\(\003)p FF(;)8 b FQ(\003)665 1254 y Fy(0)677 1272 y FQ(\))13 b FE(\025)h FF(D)q FQ(.)22 b([Here)14 b(it)h(is)g(imp)q(ortan)o(t) g(that)h(the)f(con\014guration)i(space)60 1332 y(is)d(a)h(pro)q(duct)g (space,)g(so)g(that)f(arbitrary)h(pairs)g(of)f(con\014gurations)i(in)e(\003)h (and)g(\003)1552 1314 y Fy(0)1577 1332 y FQ(are)g(compatible)60 1393 y(\(i.e.)k(there)h(are)g(no)h(hard-core)g(exclusions\).)33 b(It)20 b(also)h(seems)e(to)h(b)q(e)h(imp)q(ortan)o(t)e(that)i(\003)1763 1375 y Fy(0)1795 1393 y FQ(b)q(e)g(a)60 1453 y(translate)15 b(of)g(\003:)20 b(this)14 b(guaran)o(tees)h(that)g(w)o(e)f(can)h(c)o(ho)q (ose)g(con\014gurations)h(in)e(\003)g(and)h(\003)1676 1435 y Fy(0)1702 1453 y FQ(that)g(giv)o(e)60 1480 y Fx(P)104 1523 y FD(a)p Fy(2)p FH(\003)181 1513 y FF(T)210 1520 y FD(a)230 1513 y FF(f)24 b FQ(and)376 1480 y Fx(P)420 1523 y FD(a)p Fy(2)p FH(\003)487 1514 y Ft(0)508 1513 y FF(T)537 1520 y FD(a)557 1513 y FF(f)h FQ(near-maxim)o(um)14 b(v)m(alues)19 b FP(of)g(the)i(same)f (sign)t FQ(.])28 b(Moreo)o(v)o(er,)18 b(for)h(an)o(y)60 1573 y(t)o(w)o(o)e(sets)g(\003)283 1580 y FH(1)303 1573 y FF(;)8 b FQ(\003)359 1580 y FH(2)396 1573 y FQ(w)o(e)16 b(ob)o(viously)h(ha)o(v)o(e) f FE(j)p FF(F)7 b FQ(\(\003)904 1580 y FH(1)923 1573 y FQ(\))12 b FE(\000)f FF(F)c FQ(\(\003)1096 1580 y FH(2)1115 1573 y FQ(\))p FE(j)15 b(\024)g(j)p FQ(\003)1265 1580 y FH(1)1285 1573 y FE(4)p FQ(\003)1364 1580 y FH(2)1383 1573 y FE(j)8 b(k)p FF(f)d FE(k)1484 1580 y Fy(1)1521 1573 y FQ(.)24 b(F)l(rom)16 b(these)h(t)o(w)o(o)60 1633 y(facts)e(one)g(can)g(pro)o(v)o(e)f(the)g(v)m(an)h(Ho)o(v)o(e)f(con)o(v) o(ergence)f(of)i FE(j)p FQ(\003)p FE(j)1156 1615 y Fy(\000)p FH(1)1203 1633 y FF(F)7 b FQ(\(\003\):)19 b(the)c(idea)f(is)h(to)g(pa)o(v)o (e)f(a)h(large)60 1694 y(set)h(\003)g(b)o(y)g(medium-size)o(d)e(cub)q(es)i (\(of)h(side)f FF(a)g FQ(whic)o(h)f(will)h(ev)o(en)o(tually)e(go)j(to)f (in\014nit)o(y\))g(separated)60 1754 y(b)o(y)k(corridors)g(of)h(width)f FF(D)q FQ(.)34 b(See)20 b([206)q(,)h(pp.)f(10{13])h(for)g(details.)33 b(The)20 b(extension)g(to)g(general)60 1814 y FF(f)f FE(2)14 b FF(B)187 1821 y FD(q)q(l)217 1814 y FQ(\(\012\))j(is)f(no)o(w)g(a)h (routine)f(appro)o(ximation)f(argumen)o(t.)60 1944 y FM(A.3.5)56 b(The)18 b(Quotien)n(t)g(Seminorm)60 2036 y FQ(In)c(Section)g(2.4.3)h(w)o(e)e (stated)i(Prop)q(osition)h(2.34)f(for)f(the)h(case)f(of)h(a)f FP(c)n(omp)n(act)i(metric)h FQ(single-spin)60 2096 y(space)c(\012)222 2103 y FH(0)255 2096 y FQ(and)h(for)f(a)g FP(c)n(ontinuous)18 b FQ(function)13 b FF(f)5 b FQ(.)20 b(Here)12 b(w)o(e)h(pro)o(v)o(e)f(a)h (more)f(general)h(result)f(in)h(whic)o(h)60 2157 y(these)j(t)o(w)o(o)g (restrictions)g(are)g(lifted:)60 2271 y FM(Prop)r(osition)i(A.6)g(\(=)g(Prop) r(osition)g(2.34)954 2253 y Fy(0)965 2271 y FM(\))25 b FP(L)n(et)g FF(f)33 b FE(2)c FF(B)s FQ(\(\012\))p FP(.)46 b(Consider)25 b(the)h(fol)r(lowing)60 2331 y(pr)n(op)n(erties:)93 2433 y(\(a\))e FF(f)g FP(has)19 b(zer)n(o)f(me)n(an)g(with)i(r)n(esp)n(e)n(ct)e(to)g(every)i (tr)n(anslation-invariant)g(pr)n(ob)n(ability)e(me)n(asur)n(e,)182 2493 y(i.e.)267 2457 y Fx(R)294 2493 y FF(f)c(d\026)g FQ(=)g(0)k FP(for)f(al)r(l)i FF(\026)14 b FE(2)g FF(M)779 2500 y FH(+1)p FD(;inv)888 2493 y FQ(\(\012\))p FP(.)95 2595 y(\(b\))25 b FF(f)20 b FP(has)15 b(zer)n(o)g(me)n(an)g(with)h(r)n(esp)n(e)n(ct)e(to)h (every)h(tr)n(anslation-invariant)h(\014nite)f(signe)n(d)g(me)n(asur)n(e,)182 2655 y(i.e.)267 2619 y Fx(R)294 2655 y FF(f)e(d\026)g FQ(=)g(0)k FP(for)f(al)r(l)i FF(\026)14 b FE(2)g FF(M)779 2662 y FD(inv)833 2655 y FQ(\(\012\))p FP(.)938 2784 y FQ(181)p eop %%Page: 182 182 bop 84 94 a FP(\(c)126 76 y Fy(0)138 94 y FP(\))24 b FF(f)f FP(lies)18 b(in)g FE(I)403 101 y FD(f)439 94 y FE(\021)g FP(close)n(d)f(line) n(ar)h(sp)n(an)f(of)g FE(f)p FF(f)g FE(\000)11 b FF(T)1089 101 y FD(a)1109 94 y FF(f)5 b FQ(:)22 b FF(a)13 b FE(2)i Fq(Z)1291 73 y FD(d)1311 94 y FE(g)p FP(.)72 194 y(\(c)114 176 y Fy(0)r(0)138 194 y FP(\))24 b FF(f)f FP(lies)18 b(in)g FE(I)403 202 y FD(B)r FH(\(\012\))500 194 y FE(\021)f FP(close)n(d)h(line)n(ar)g(sp)n(an)f(of)g FE(f)p FF(g)c FE(\000)e FF(T)1145 201 y FD(a)1165 194 y FF(g)r FQ(:)22 b FF(g)16 b FE(2)e FF(B)s FQ(\(\012\))p FF(;)i(a)e FE(2)g Fq(Z)1572 173 y FD(d)1592 194 y FE(g)p FP(.)93 304 y(\(d\))36 b FQ(lim)182 329 y FD(n)p Fy(!1)282 304 y FF(n)311 286 y Fy(\000)p FD(d)359 255 y Fx(\015)359 280 y(\015)359 304 y(\015)404 271 y(P)382 342 y FD(a)p Fy(2)p FD(C)450 346 y Fs(n)479 304 y FF(T)508 311 y FD(a)528 304 y FF(f)557 255 y Fx(\015)557 280 y(\015)557 304 y(\015)581 331 y Fy(1)640 304 y FQ(=)22 b(0)p FP(.)95 445 y(\(e\))39 b FQ(lim)182 475 y FH(\003)p Fy(\0451)285 445 y FE(j)p FQ(\003)p FE(j)347 427 y Fy(\000)p FH(1)402 395 y Fx(\015)402 420 y(\015)402 445 y(\015)437 412 y(P)425 483 y FD(a)p Fy(2)p FH(\003)500 445 y FF(T)529 452 y FD(a)550 445 y FF(f)579 395 y Fx(\015)579 420 y(\015)579 445 y(\015)602 472 y Fy(1)662 445 y FQ(=)22 b(0)p FP(.)60 568 y(Then)h(\(a\))e FE(\()-8 b(\))22 b FP(\(b\))g FE(\()-8 b FQ(=)21 b FP(\(c)619 550 y Fy(0)631 568 y FP(\))h FE(\()-8 b(\))21 b FP(\(c)828 550 y Fy(0)r(0)852 568 y FP(\))h FE(\()-8 b(\))21 b FP(\(d\))h FE(\()-8 b(\))21 b FP(\(e\).)36 b(Mor)n(e)n(over,)22 b(if)g FQ(\012)1642 575 y FH(0)1684 568 y FP(is)g(a)g(c)n(om-)60 628 y(p)n(act)h(metric)h(sp)n(ac)n (e)f(and)h FF(f)30 b FE(2)25 b FF(C)t FQ(\(\012\))p FP(,)g(then)f(al)r(l)h (these)f(pr)n(op)n(erties)e(ar)n(e)h(e)n(quivalent.)43 b([In)23 b(this)60 689 y(c)n(ase)17 b(pr)n(op)n(erty)f(\(c\))i(of)f(Pr)n(op)n(osition) f(2.34)h(is)g(interme)n(diate)h(b)n(etwe)n(en)h(\(c)1412 671 y Fy(0)1424 689 y FP(\))e(and)h(\(c)1598 671 y Fy(0)r(0)1621 689 y FP(\),)f(henc)n(e)i(also)60 749 y(e)n(quivalent.])60 905 y Fd(Pr)o(oof.)48 b FQ(\(a\))18 b(=)-8 b FE(\))17 b FQ(\(b\):)25 b(If)17 b FF(\026)g FE(2)g FF(M)755 912 y FD(inv)809 905 y FQ(\(\012\),)h(then)g FF(\026)1056 912 y FH(+)1086 905 y FF(;)8 b(\026)1137 912 y Fy(\000)1183 905 y FE(2)17 b FF(M)1280 912 y FD(inv)1334 905 y FQ(\(\012\))h([otherwise)f(the)h(Jordan)60 965 y(decomp)q(osition)j(of)h FF(\026)g FQ(in)o(to)f(p)q(ositiv)o(e)g(and)i (negativ)o(e)d(parts)j(w)o(ouldn't)e(b)q(e)h(unique].)36 b(So)23 b(ev)o(ery)60 1026 y FF(\026)14 b FE(2)g FF(M)197 1033 y FD(inv)251 1026 y FQ(\(\012\))j(is)f(a)g(linear)g(com)o(bination)f(of)h(t)o(w)o(o)g (measures)f(in)h FF(M)1304 1033 y FH(+1)p FD(;inv)1413 1026 y FQ(\(\012\).)133 1086 y(\(b\))g(=)-8 b FE(\))16 b FQ(\(a\):)22 b(T)l(rivial.)133 1146 y(\(c)174 1128 y Fy(0)185 1146 y FQ(\))17 b(=)-8 b FE(\))15 b FQ(\(c)357 1128 y Fy(0)r(0)380 1146 y FQ(\):)22 b(T)l(rivial.)133 1206 y(\(c)174 1188 y Fy(0)q(0)197 1206 y FQ(\))16 b(=)-8 b FE(\))16 b FQ(\(e\):)21 b(Assume)15 b(that)h FF(f)j FQ(=)14 b FF(g)f FE(\000)e FF(T)919 1213 y FD(a)940 1206 y FF(g)18 b FQ(with)e FF(g)g FE(2)e FF(B)s FQ(\(\012\).)21 b(Then)527 1312 y FE(k)564 1270 y Fx(X)560 1362 y FD(x)p Fy(2)p FH(\003)636 1312 y FF(T)665 1319 y FD(x)687 1312 y FF(f)5 b FE(k)741 1319 y Fy(1)820 1312 y FQ(=)42 b FE(k)937 1270 y Fx(X)933 1362 y FD(x)p Fy(2)p FH(\003)1010 1312 y FF(T)1039 1319 y FD(x)1060 1312 y FF(g)22 b FE(\000)1190 1270 y Fx(X)1163 1362 y FD(x)p Fy(2)p FH(\003+)p FD(a)1285 1312 y FF(T)1314 1319 y FD(x)1336 1312 y FF(g)r FE(k)1386 1319 y Fy(1)820 1424 y FE(\024)41 b(j)p FQ(\003)p FE(4)p FQ(\(\003)10 b(+)h FF(a)p FQ(\))p FE(j)d(k)p FF(g)r FE(k)1247 1431 y Fy(1)1753 1424 y FQ(\(A.20\))60 1529 y(where)17 b FE(4)f FQ(denotes)h(symmetri)o(c)d(di\013erence.)22 b(By)16 b(Prop)q(osition)j(2.27,)e FE(j)p FQ(\003)p FE(4)p FQ(\(\003)10 b(+)i FF(a)p FQ(\))p FE(j)p FF(=)p FE(j)p FQ(\003)p FE(j)i(!)h FQ(0)i(as)60 1589 y(\003)d FE(\045)f(1)h FQ(\(v)m(an)h(Ho)o(v)o (e\).)k(This)14 b(pro)o(v)o(es)f(the)h(claim)e(for)i(functions)g FF(f)20 b FQ(of)14 b(the)g(giv)o(en)f(form.)19 b(The)14 b(same)60 1649 y(ob)o(viously)f(holds)i(for)f(\014nite)f(linear)g(com)o(binations.)20 b(It)13 b(is)h(then)g(routine)f(to)i(pass)g(to)f(norm)f(limits.)133 1710 y(\(e\))j(=)-8 b FE(\))16 b FQ(\(d\):)21 b(T)l(rivial.)133 1770 y(\(d\))c(=)-8 b FE(\))16 b FQ(\(c)352 1752 y Fy(0)363 1770 y FQ(\):)22 b FF(h)446 1777 y FD(n)484 1770 y FE(\021)14 b FF(f)i FE(\000)11 b FF(n)656 1752 y Fy(\000)p FD(d)713 1737 y Fx(P)756 1780 y FD(a)p Fy(2)p FD(C)824 1784 y Fs(n)855 1770 y FF(T)884 1777 y FD(a)905 1770 y FF(f)22 b FQ(lies)15 b(in)i(the)f(linear)g (span)h(of)g FE(f)p FF(f)f FE(\000)11 b FF(T)1627 1777 y FD(a)1648 1770 y FF(f)5 b FQ(:)22 b FF(a)14 b FE(2)h Fq(Z)1831 1749 y FD(d)1852 1770 y FE(g)p FQ(,)60 1830 y(and)i(lim)223 1837 y FD(n)p Fy(!1)325 1830 y FE(k)p FF(h)378 1837 y FD(n)412 1830 y FE(\000)11 b FF(f)5 b FE(k)516 1837 y Fy(1)568 1830 y FQ(=)14 b(0.)133 1890 y(\(d\))20 b(=)-8 b FE(\))20 b FQ(\(b\):)28 b(Since)20 b FF(\026)g FQ(is)g(translation-in)o(v)m(arian)o(t,)g FF(\026)p FQ(\()p FF(f)5 b FQ(\))21 b(=)g FF(n)1333 1872 y Fy(\000)p FD(d)1389 1857 y Fx(P)1432 1901 y FD(a)p Fy(2)p FD(C)1500 1905 y Fs(n)1531 1890 y FF(\026)p FQ(\()p FF(T)1608 1897 y FD(a)1629 1890 y FF(f)5 b FQ(\))21 b(for)f(all)f FF(n)p FQ(.)60 1950 y(Hence)c FE(j)p FF(\026)p FQ(\()p FF(f)5 b FQ(\))p FE(j)14 b(\024)g(k)p FF(\026)p FE(k)8 b(k)p FF(n)537 1932 y Fy(\000)p FD(d)593 1917 y Fx(P)637 1961 y FD(a)p Fy(2)p FD(C)705 1965 y Fs(n)736 1950 y FF(T)765 1957 y FD(a)785 1950 y FF(f)d FE(k)839 1957 y Fy(1)877 1950 y FQ(.)21 b(No)o(w)16 b(let)g FF(n)e FE(!)f(1)p FQ(.)133 2011 y(\(b\))19 b(=)-8 b FE(\))18 b FQ(\(c\))g(=)-8 b FE(\))18 b FQ(\(c)532 1993 y Fy(0)r(0)555 2011 y FQ(\),)h(if)f(\012)689 2018 y FH(0)728 2011 y FQ(is)g(compact)g(and)h FF(f)k FE(2)18 b FF(C)t FQ(\(\012\):)26 b(Supp)q(ose)19 b(that)g FF(f)29 b(=)-29 b FE(2)18 b(I)1751 2018 y FD(C)r FH(\(\012\))1851 2011 y FE(\021)60 2071 y FQ(closed)23 b(linear)h(span)g(of)g FE(f)p FF(g)19 b FE(\000)d FF(T)690 2078 y FD(a)710 2071 y FF(g)r FQ(:)35 b FF(g)29 b FE(2)e FF(C)t FQ(\(\012\))p FF(;)15 b(a)27 b FE(2)g Fq(Z)1180 2050 y FD(d)1201 2071 y FE(g)p FQ(.)43 b(Then,)26 b(b)o(y)d(the)h(Hahn-Banac)o(h)60 2131 y(theorem,)18 b(there)h(exists)g FF(l)i FE(2)e FF(C)t FQ(\(\012\))733 2113 y Fy(\003)772 2131 y FQ(suc)o(h)h(that)g FF(l)q Fm(\026)o FE(I)1062 2139 y FD(C)r FH(\(\012\))1164 2131 y FE(\021)g FQ(0)g(and)g FF(l)q FQ(\()p FF(f)5 b FQ(\))19 b(=)h(1.)31 b(By)19 b(the)h(Riesz-)60 2191 y(Mark)o(o)o(v)d(theorem,)f FF(l)i FQ(arises)g(from)e(some)h FF(\026)f FE(2)h FF(M)5 b FQ(\(\012\))18 b(and)g FF(l)q Fm(\026)o FE(I)1253 2199 y FD(C)r FH(\(\012\))1352 2191 y FE(\021)e FQ(0)i(means)f (precisely)f(that)60 2251 y FF(\026)e FE(2)g FF(M)197 2258 y FD(inv)251 2251 y FQ(\(\012\).)22 b(But)16 b(then)g(\(b\))g(implies)d(that) k FF(l)q FQ(\()p FF(f)5 b FQ(\))14 b(=)g(0,)i(a)h(con)o(tradiction.)p 1597 2255 25 34 v 133 2359 a FM(Remarks.)30 b FQ(1.)h(V)l(arian)o(ts)20 b(of)g(this)f(Prop)q(osition)i(seems)d(to)i(b)q(e)g(w)o(ell)e(kno)o(wn)i ([198)q(,)g(p.)f(454])60 2419 y(\(see)e(also)h([66,)g(pp.)f(39{40])i(for)e(a) h(similar)d(argumen)o(t\),)i(but)g(w)o(e)g(ha)o(v)o(e)g(not)h(b)q(een)f(able) g(to)h(\014nd)g(a)60 2479 y(published)e(pro)q(of.)22 b(See)16 b(also)h([313,)f(Exercise)f(7.2])h(for)h(a)f(related)g(result.)133 2539 y(2.)23 b(W)l(e)16 b(do)h(not)g(kno)o(w)g(whether)f(\(a\){\(b\))h(are)g (equiv)m(alen)o(t)e(to)i(\(c)1331 2521 y Fy(0)1342 2539 y FQ(\){\(e\))g(in)f (general;)g(or)h(if)f(not,)60 2600 y(under)21 b(what)g(minimal)d(extra)i (conditions)h(this)g(equiv)m(alence)e(can)i(b)q(e)g(pro)o(v)o(en.)35 b(F)l(or)21 b(aesthetic)60 2660 y(reasons,)c(if)f(no)g(other,)g(it)g(w)o (ould)g(b)q(e)h(desirable)e(to)i(resolv)o(e)e(this)h(question.)938 2784 y(182)p eop %%Page: 183 183 bop 133 91 a FQ(Next)17 b(w)o(e)h(pro)o(v)o(e)g(an)h(analogue)g(of)g(Prop)q (osition)g(A.6)f(in)g(whic)o(h)f(w)o(e)h(quotien)o(t)g(out)h(constan)o(t)60 152 y(functions:)60 247 y FM(Prop)r(osition)f(A.7)24 b FP(L)n(et)17 b FF(f)i FE(2)14 b FF(B)s FQ(\(\012\))p FP(.)22 b(Consider)c(the)g(fol)r (lowing)i(pr)n(op)n(erties:)93 334 y(\(a\))k FF(f)e FP(has)17 b(the)g(same)g(me)n(an)g(with)h(r)n(esp)n(e)n(ct)e(to)h(every)g(tr)n (anslation-invariant)i(pr)n(ob)n(ability)d(me)n(a-)182 395 y(sur)n(e,)h(i.e.)386 359 y Fx(R)413 395 y FF(f)d(d\026)g FQ(=)571 359 y Fx(R)599 395 y FF(f)g(d\027)21 b FP(for)16 b(al)r(l)j FF(\026;)8 b(\027)17 b FE(2)d FF(M)1040 402 y FH(+1)p FD(;inv)1149 395 y FQ(\(\012\))p FP(.)95 492 y(\(b\))25 b FF(f)d FP(has)16 b(zer)n(o)g(me)n(an)h(with)f(r)n(esp)n(e)n(ct)g(to)h(every)g(tr)n (anslation-invariant)h(\014nite)g(signe)n(d)f(me)n(asur)n(e)182 552 y(of)g(zer)n(o)g(total)h(mass,)f(i.e.)676 516 y Fx(R)703 552 y FF(f)d(d\026)h FQ(=)e(0)18 b FP(for)f(al)r(l)i FF(\026)14 b FE(2)g FF(M)1188 559 y FD(inv)1242 552 y FQ(\(\012\))k FP(satisfying)f FF(\026)p FQ(\(\012\))e(=)e(0)p FP(.)84 649 y(\(c)126 631 y Fy(0)138 649 y FP(\))24 b FF(f)j FP(lies)c(in)f FE(I)416 656 y FD(f)453 649 y FQ(+)15 b FF(const)22 b FE(\021)f FP(close)n(d)i(line)n(ar)f (sp)n(an)f(of)h FE(f)p FF(f)e FE(\000)14 b FF(T)1320 656 y FD(a)1340 649 y FF(f)5 b FQ(:)31 b FF(a)21 b FE(2)i Fq(Z)1547 628 y FD(d)1567 649 y FE(g)f FP(and)g(c)n(onstant)182 709 y(functions.)72 806 y(\(c)114 788 y Fy(0)r(0)138 806 y FP(\))i FF(f)f FP(lies)18 b(in)g FE(I)403 814 y FD(B)r FH(\(\012\))498 806 y FQ(+)11 b FF(const)j FE(\021)k FP(close)n(d)g(line)n(ar)f(sp)n(an)h(of)f FE(f)p FF(g)c FE(\000)e FF(T)1321 813 y FD(a)1342 806 y FF(g)r FQ(:)22 b FF(g)16 b FE(2)f FF(B)s FQ(\(\012\))p FF(;)g(a)f FE(2)h Fq(Z)1750 785 y FD(d)1770 806 y FE(g)j FP(and)182 866 y(c)n(onstant)g(functions.)93 963 y(\(d\))36 b FQ(lim)182 988 y FD(n)p Fy(!1)282 963 y FF(n)311 945 y Fy(\000)p FD(d)359 913 y Fx(\015)359 938 y(\015)359 963 y(\015)404 930 y(P)382 1001 y FD(a)p Fy(2)p FD(C)450 1005 y Fs(n)479 963 y FF(T)508 970 y FD(a)528 963 y FF(f)557 913 y Fx(\015)557 938 y(\015)557 963 y(\015)581 990 y FD(B)r FH(\(\012\))p FD(=const)787 963 y FQ(=)22 b(0)p FP(.)95 1100 y(\(e\))39 b FQ(lim)182 1130 y FH(\003)p Fy(\0451)285 1100 y FE(j)p FQ(\003)p FE(j)347 1082 y Fy(\000)p FH(1)402 1050 y Fx(\015)402 1075 y(\015)402 1100 y(\015)437 1067 y(P)425 1138 y FD(a)p Fy(2)p FH(\003)500 1100 y FF(T)529 1107 y FD(a)550 1100 y FF(f)579 1050 y Fx(\015)579 1075 y(\015)579 1100 y(\015)602 1127 y FD(B)r FH(\(\012\))p FD(=const)808 1100 y FQ(=)22 b(0)p FP(.)60 1213 y(Then)d(\(a\))f FE(\()-8 b(\))18 b FP(\(b\))h FE(\()-8 b FQ(=)17 b FP(\(c)601 1195 y Fy(0)613 1213 y FP(\))i FE(\()-8 b(\))18 b FP(\(c)804 1195 y Fy(0)q(0)827 1213 y FP(\))g FE(\()-8 b(\))18 b FP(\(d\))g FE(\()-8 b(\))18 b FP(\(e\).)26 b(Mor)n(e)n(over,)17 b(if)h FQ(\012)1584 1220 y FH(0)1623 1213 y FP(is)g(a)g(c)n(omp)n(act)60 1273 y(metric)g(sp)n(ac)n(e)f(and)g FF(f)j FE(2)14 b FF(C)t FQ(\(\012\))p FP(,)j(then)h(al)r(l)h(these)f(pr)n(op)n(erties)e(ar)n(e)h(e)n (quivalent.)60 1409 y Fd(Pr)o(oof.)48 b FQ(\(a\))20 b(=)-8 b FE(\))19 b FQ(\(b\):)29 b(If)19 b FF(\026)i FE(2)f FF(M)772 1416 y FD(inv)826 1409 y FQ(\(\012\))g(with)g FF(\026)p FQ(\(\012\))g(=)g(0,) h(then)f FF(\026)1417 1416 y FH(+)1447 1409 y FF(;)8 b(\026)1498 1416 y Fy(\000)1548 1409 y FE(2)20 b FF(M)1648 1416 y FD(inv)1702 1409 y FQ(\(\012\))g(with)60 1469 y FF(\026)89 1476 y FH(+)119 1469 y FQ(\(\012\))e(=)f FF(\026)294 1476 y Fy(\000)324 1469 y FQ(\(\012\))h(=)g FF(\025)g FE(\025)f FQ(0.)28 b(If)18 b FF(\025)h FQ(=)e(0)i(w)o(e)f(are)h(done;)g(if)f FF(\025)g(>)g FQ(0,)h(apply)f(\(a\))h(to)g(the)f(measures)60 1529 y FF(\025)88 1511 y Fy(\000)p FH(1)136 1529 y FF(\026)165 1536 y FH(+)194 1529 y FF(;)8 b(\025)244 1511 y Fy(\000)p FH(1)292 1529 y FF(\026)321 1536 y Fy(\000)365 1529 y FE(2)14 b FF(M)459 1536 y FH(+1)p FD(;inv)568 1529 y FQ(\(\012\).)133 1590 y(\(b\))i(=)-8 b FE(\))16 b FQ(\(a\):)22 b(Just)16 b(apply)g(\(b\))h(to)f FF(\026)c FE(\000)f FF(\027)s FQ(.)133 1650 y(\(c)174 1632 y Fy(0)185 1650 y FQ(\))17 b(=)-8 b FE(\))15 b FQ(\(c)357 1632 y Fy(0)r(0)380 1650 y FQ(\):)22 b(T)l(rivial.)133 1710 y(\(c)174 1692 y Fy(0)q(0)197 1710 y FQ(\))16 b(=)-8 b FE(\))16 b FQ(\(e\):)21 b(Assume)15 b(that)h FF(f)j FQ(=)14 b FF(g)f FE(\000)e FF(T)919 1717 y FD(a)940 1710 y FF(g)i FQ(+)e FF(c)16 b FQ(with)g FF(g)g FE(2)e FF(B)s FQ(\(\012\))i(and)h FF(c)d FE(2)g Fq(R)p FQ(.)21 b(Then)313 1760 y Fx(\015)313 1785 y(\015)313 1810 y(\015)340 1768 y(X)336 1860 y FD(x)p Fy(2)p FH(\003)412 1810 y FF(T)441 1817 y FD(x)463 1810 y FF(f)492 1760 y Fx(\015)492 1785 y(\015)492 1810 y(\015)515 1837 y FD(B)r FH(\(\012\))p FD(=const)741 1810 y FQ(=)821 1760 y Fx(\015)821 1785 y(\015)821 1810 y(\015)848 1768 y(X)844 1860 y FD(x)p Fy(2)p FH(\003)920 1810 y FF(T)949 1817 y FD(x)970 1810 y FF(g)h FE(\000)1100 1768 y Fx(X)1073 1860 y FD(x)p Fy(2)p FH(\003+)p FD(a)1195 1810 y FF(T)1224 1817 y FD(x)1246 1810 y FF(g)f FQ(+)f FF(c)p FE(j)p FQ(\003)p FE(j)1431 1760 y Fx(\015)1431 1785 y(\015)1431 1810 y(\015)1453 1837 y FD(B)r FH(\(\012\))p FD(=const)740 1934 y FE(\024)821 1884 y Fx(\015)821 1909 y(\015)821 1934 y(\015)848 1893 y(X)844 1985 y FD(x)p Fy(2)p FH(\003)920 1934 y FF(T)949 1941 y FD(x)970 1934 y FF(g)i FE(\000)1100 1893 y Fx(X)1073 1985 y FD(x)p Fy(2)p FH(\003+)p FD(a)1195 1934 y FF(T)1224 1941 y FD(x)1246 1934 y FF(g)1271 1884 y Fx(\015)1271 1909 y(\015)1271 1934 y(\015)1294 1961 y Fy(1)740 2046 y FE(\024)42 b(j)p FQ(\003)p FE(4)p FQ(\(\003)10 b(+)h FF(a)p FQ(\))p FE(j)d(k)p FF(g)r FE(k)1168 2053 y Fy(1)1218 2046 y FF(:)521 b FQ(\(A.21\))60 2140 y(The)16 b(rest)g(is)g(as)h(in)f(Prop)q(osition)i(A.6.)133 2200 y(\(e\))e(=)-8 b FE(\))16 b FQ(\(d\):)21 b(T)l(rivial.)133 2260 y(\(d\))14 b(=)-8 b FE(\))13 b FQ(\(c)346 2242 y Fy(0)357 2260 y FQ(\):)20 b(Let)14 b FF(c)g FE(\021)f FQ(lim)650 2267 y FD(n)p Fy(!1)752 2260 y FF(n)781 2242 y Fy(\000)p FD(d)838 2260 y FQ(mid)6 b(\()946 2227 y Fx(P)990 2270 y FD(a)p Fy(2)p FD(C)1058 2274 y Fs(n)1089 2260 y FF(T)1118 2267 y FD(a)1138 2260 y FF(f)f FQ(\))14 b(as)h(guaran)o(teed)f(b)o(y)f(Lemma)e(A.5\(e\).)60 2320 y(Then)16 b FF(h)215 2327 y FD(n)253 2320 y FE(\021)d FF(f)k FE(\000)11 b FF(n)425 2302 y Fy(\000)p FD(d)481 2287 y Fx(P)524 2331 y FD(a)p Fy(2)p FD(C)592 2335 y Fs(n)624 2320 y FF(T)653 2327 y FD(a)673 2320 y FF(f)22 b FQ(lies)15 b(in)h(the)g(linear)f (span)i(of)g FE(f)p FF(f)f FE(\000)11 b FF(T)1393 2327 y FD(a)1413 2320 y FF(f)5 b FQ(:)22 b FF(a)14 b FE(2)g Fq(Z)1595 2299 y FD(d)1616 2320 y FE(g)p FQ(,)h(and)341 2422 y(lim)8 b(sup)370 2457 y FD(n)p Fy(!1)499 2422 y FE(k)p FQ(\()p FF(h)571 2429 y FD(n)605 2422 y FQ(+)j FF(c)p FQ(\))g FE(\000)g FF(f)5 b FE(k)809 2429 y Fy(1)889 2422 y FQ(=)42 b(lim)8 b(sup)997 2457 y FD(n)p Fy(!1)1126 2372 y Fx(\015)1126 2397 y(\015)1126 2422 y(\015)q FF(n)1179 2402 y Fy(\000)p FD(d)1249 2381 y Fx(X)1235 2472 y FD(a)p Fy(2)p FD(C)1303 2476 y Fs(n)1332 2422 y FF(T)1361 2429 y FD(a)1381 2422 y FF(f)25 b FE(\000)19 b FF(c)1509 2372 y Fx(\015)1509 2397 y(\015)1509 2422 y(\015)1532 2449 y Fy(1)888 2547 y FE(\024)42 b FQ(lim)8 b(sup)997 2582 y FD(n)p Fy(!1)1126 2547 y FF(n)1155 2527 y Fy(\000)p FD(d)1203 2497 y Fx(\015)1203 2522 y(\015)1203 2547 y(\015)1241 2506 y(X)1226 2598 y FD(a)p Fy(2)p FD(C)1294 2602 y Fs(n)1323 2547 y FF(T)1352 2554 y FD(a)1373 2547 y FF(f)1402 2497 y Fx(\015)1402 2522 y(\015)1402 2547 y(\015)1425 2574 y FD(B)r FH(\(\012\))p FD(=const)889 2660 y FQ(=)42 b(0)14 b FF(:)732 b FQ(\(A.22\))938 2784 y(183)p eop %%Page: 184 184 bop 133 91 a FQ(\(d\))16 b(=)-8 b FE(\))16 b FQ(\(b\):)21 b(A)16 b(trivial)f(mo)q(di\014cation)h(of)g(the)g(corresp)q(onding)h(pro)q(of)h(in)e (Prop)q(osition)h(A.6.)133 152 y(\(b\))g(=)-8 b FE(\))16 b FQ(\(c\))g(=)-8 b FE(\))16 b FQ(\(c)524 133 y Fy(0)q(0)547 152 y FQ(\),)g(if)g(\012)676 159 y FH(0)713 152 y FQ(is)g(compact)f(and)j FF(f)h FE(2)c FF(C)t FQ(\(\012\):)21 b(Same)16 b(as)h(in)f(Prop)q(osition)i (A.6,)60 212 y(but)h(use)f(the)h(subspace)g FE(I)558 219 y FD(C)r FH(\(\012\))653 212 y FQ(+)12 b FF(const)19 b FQ(in)f(place)g(of)h FE(I)1107 219 y FD(C)r FH(\(\012\))1190 212 y FQ(;)g(the)f(signed)h(measure)e FF(\026)i FQ(will)e(then)60 272 y(ha)o(v)o(e)e(zero)h(total)h(mass.)p 649 276 25 34 v 133 409 a(Next)k(w)o(e)h(pro)o(v)o(e)g(a)g(strengthened)h(v)o (ersion)e(of)i(Prop)q(osition)g(2.35.)41 b(Again)22 b(w)o(e)g(can)g(allo)o(w) 60 469 y(an)i(arbitrary)f(\(not)h(necessarily)e(compact\))g(single-spin)h (space)g(\012)1351 476 y FH(0)1371 469 y FQ(,)i(and)f(an)f(arbitrary)h(\(not) 60 529 y(necessarily)15 b(con)o(tin)o(uous)g(or)i(quasilo)q(cal\))e(function) h FF(f)5 b FQ(.)21 b(The)16 b(only)g(subtlet)o(y)f(is)h(that)g(in)f(this)h (case)60 589 y(w)o(e)d(m)o(ust)e(c)o(ho)q(ose)i(the)g(correct)f(de\014nition) h(of)g FE(I)t FQ(,)g(since)f(\(a\){\(b\))i(and)g(\(c)1375 571 y Fy(0)1386 589 y FQ(\){\(e\))f(are)g(not)g(necessarily)60 649 y(equiv)m(alen)o(t.)20 b(The)c(righ)o(t)g(de\014nition)g(turns)g(out)h (to)g(b)q(e)f(\(c)1127 631 y Fy(0)1138 649 y FQ(\){\(e\).)60 741 y FM(Prop)r(osition)i(A.8)g(\(=)g(Prop)r(osition)g(2.35)954 723 y Fy(0)965 741 y FM(\))25 b FP(L)n(et)17 b FF(f)i FE(2)14 b FF(B)s FQ(\(\012\))p FP(.)22 b(Then)486 837 y FQ(lim)473 867 y FH(\003)p Fy(\0451)576 837 y FE(j)p FQ(\003)p FE(j)638 816 y Fy(\000)p FH(1)693 787 y Fx(\015)693 812 y(\015)693 837 y(\015)719 795 y(X)716 887 y FD(a)p Fy(2)p FH(\003)791 837 y FF(T)820 844 y FD(a)841 837 y FF(f)870 787 y Fx(\015)870 812 y(\015)870 837 y(\015)893 864 y Fy(1)972 837 y FQ(=)48 b(inf)1051 866 y FH(\003)p Fy(2S)1131 837 y FE(j)p FQ(\003)p FE(j)1193 816 y Fy(\000)p FH(1)1248 787 y Fx(\015)1248 812 y(\015)1248 837 y(\015)1275 795 y(X)1271 887 y FD(a)p Fy(2)p FH(\003)1346 837 y FF(T)1375 844 y FD(a)1396 837 y FF(f)1425 787 y Fx(\015)1425 812 y(\015)1425 837 y(\015)1448 864 y Fy(1)1729 837 y FQ(\(A.23a\))972 971 y(=)41 b FE(k)p FF(f)5 b FE(k)1130 989 y FD(B)r FH(\(\012\))p FD(=)1230 984 y Fx(e)1230 989 y Fy(I)1726 971 y FQ(\(A.23b\))60 1065 y FP(and)340 1155 y FQ(lim)326 1185 y FH(\003)p Fy(\0451)430 1155 y FE(j)p FQ(\003)p FE(j)492 1135 y Fy(\000)p FH(1)547 1105 y Fx(\015)547 1130 y(\015)547 1155 y(\015)573 1114 y(X)570 1206 y FD(a)p Fy(2)p FH(\003)645 1155 y FF(T)674 1162 y FD(a)694 1155 y FF(f)723 1105 y Fx(\015)723 1130 y(\015)723 1155 y(\015)747 1182 y FD(B)r FH(\(\012\))p FD(=const)972 1155 y FQ(=)48 b(inf)1051 1185 y FH(\003)p Fy(2S)1131 1155 y FE(j)p FQ(\003)p FE(j)1193 1135 y Fy(\000)p FH(1)1248 1105 y Fx(\015)1248 1130 y(\015)1248 1155 y(\015)1275 1114 y(X)1271 1206 y FD(a)p Fy(2)p FH(\003)1346 1155 y FF(T)1375 1162 y FD(a)1396 1155 y FF(f)1425 1105 y Fx(\015)1425 1130 y(\015)1425 1155 y(\015)1448 1182 y FD(B)r FH(\(\012\))p FD(=const)1729 1155 y FQ(\(A.24a\))972 1289 y(=)41 b FE(k)p FF(f)5 b FE(k)1130 1307 y FD(B)r FH(\(\012\))p FD(=)p FH(\()1244 1302 y Fx(e)1244 1307 y Fy(I)r FH(+)p FD(const)p FH(\))1726 1289 y FQ(\(A.24b\))60 1395 y FP(for)17 b(al)r(l)i(close)n(d)f(line)n(ar)f(subsp)n(ac)n(es)708 1379 y Fx(e)703 1395 y FE(I)k FP(satisfying)d FE(I)995 1402 y FD(f)1031 1395 y FE(\032)1089 1379 y Fx(e)1084 1395 y FE(I)f(\032)d(I)1208 1403 y FD(B)r FH(\(\012\))1291 1395 y FP(.)60 1525 y Fd(Pr)o(oof.)48 b FQ(In)22 b(Lemma)f(A.5\(c,d\))g(w)o(e)i(ha)o(v)o(e)f(pro)o(v)o(en)g(the)g (existence)f(of)i(the)g(limits)d(and)k(their)60 1585 y(equalit)o(y)c(to)i (the)g(corresp)q(onding)g(in\014ma.)37 b(No)o(w)21 b(w)o(e)g(w)o(an)o(t)h(to) g(iden)o(tify)e(the)i(limits)d(with)i(the)60 1645 y(quotien)o(t)15 b(seminorms.)133 1705 y(Let)h(us)g(denote)g(b)o(y)f FF(L)539 1712 y FD(f)578 1705 y FQ(the)h(limit)d(\(A.23a\).)21 b(Clearly)15 b FF(L)1176 1712 y FD(f)1213 1705 y FE(\024)e(k)p FF(f)5 b FE(k)1344 1712 y Fy(1)1382 1705 y FQ(.)21 b(Moreo)o(v)o(er,)14 b(b)o(y)i(Prop)q(osi-)60 1766 y(tion)i(A.6)f(\(c)295 1747 y Fy(0)306 1766 y FQ(\))h(=)-8 b FE(\))17 b FQ(\(e\),)g FF(L)564 1773 y FD(f)603 1766 y FQ(=)g FF(L)691 1773 y FD(f)712 1764 y Ft(0)742 1766 y FQ(whenev)o(er)g FF(f)g FE(\000)12 b FF(f)1079 1747 y Fy(0)1107 1766 y FE(2)17 b(I)1184 1773 y FD(B)r FH(\(\012\))1267 1766 y FQ(;)h(hence)f FF(L)1469 1773 y FD(f)1508 1766 y FE(\024)f(k)p FF(f)5 b FE(k)1642 1773 y FD(B)r FH(\(\012\))p FD(=)p Fy(I)1761 1780 y Fs(B)q Fr(\(\012\))1851 1766 y FE(\024)60 1826 y(k)p FF(f)g FE(k)139 1843 y FD(B)r FH(\(\012\))p FD(=)239 1838 y Fx(e)239 1843 y Fy(I)262 1826 y FQ(.)133 1890 y(T)l(o)16 b(pro)o(v)o(e)e(the) h(rev)o(erse)e(inequalit)o(y)l(,)g(note)i(that)g(b)o(y)g(an)g(easy)g (corollary)g(of)g(the)g(Hahn-Banac)o(h)60 1951 y(theorem)i([306)q(,)i (Corollary)g(3)g(of)g(Section)f(I)q(I)q(I.3])g(there)g(exists)g FF(l)h FE(2)g FF(B)s FQ(\(\012\))1453 1932 y Fy(\003)1491 1951 y FQ(suc)o(h)f(that)i FE(k)p FF(l)q FE(k)d(\024)h FQ(1,)60 2011 y FF(l)q FQ(\()p FF(f)5 b FQ(\))14 b(=)g FE(k)p FF(f)5 b FE(k)288 2028 y FD(B)r FH(\(\012\))p FD(=)388 2023 y Fx(e)388 2028 y Fy(I)424 2011 y FQ(and)15 b FF(l)q Fm(\026)563 1995 y Fx(e)558 2011 y FE(I)i(\021)d FQ(0.)21 b(On)14 b(the)g(other)g(hand,)h(for) f(ev)o(ery)f FF(l)h FE(2)g FF(B)s FQ(\(\012\))1522 1993 y Fy(\003)1556 2011 y FQ(that)g(annihilates)65 2071 y Fx(e)60 2087 y FE(I)k(\033)13 b(I)184 2094 y FD(f)223 2087 y FQ(w)o(e)j(ha)o(v)o(e)544 2180 y FF(l)q FQ(\()p FF(f)5 b FQ(\))28 b(=)f FF(l)736 2107 y Fx( )769 2180 y FF(n)798 2159 y Fy(\000)p FD(d)868 2138 y Fx(X)854 2230 y FD(a)p Fy(2)p FD(C)922 2234 y Fs(n)951 2180 y FF(T)980 2187 y FD(a)1000 2180 y FF(f)1029 2107 y Fx(!)1090 2153 y FD(n)p Fy(!1)1096 2180 y FE(\000)-8 b(!)19 b(\024)14 b FF(L)1282 2187 y FD(f)1313 2180 y FE(k)p FF(l)q FE(k)f FF(:)347 b FQ(\(A)p FF(:)p FQ(25\))60 2298 y(Hence)15 b FE(k)p FF(f)5 b FE(k)284 2316 y FD(B)r FH(\(\012\))p FD(=)384 2311 y Fx(e)384 2316 y Fy(I)421 2298 y FE(\024)13 b FF(L)506 2305 y FD(f)529 2298 y FQ(.)21 b(This)c(pro)o(v)o(es)e(\(A.23b\).)133 2375 y(A)f(completely)d (analogous)16 b(argumen)o(t)d(handles)h(\(A.24\):)20 b(it)14 b(su\016ces)f(to)i(replace)1647 2358 y Fx(e)1642 2375 y FE(I)j FQ(and)d FE(I)1807 2382 y FD(B)r FH(\(\012\))60 2441 y FQ(ev)o(erywhere)f(b)o (y)386 2425 y Fx(e)381 2441 y FE(I)h FQ(+)c FF(const)16 b FQ(and)h FE(I)724 2449 y FD(B)r FH(\(\012\))819 2441 y FQ(+)11 b FF(const)p FQ(,)16 b(resp)q(ectiv)o(ely)l(.)p 1410 2445 V 133 2539 a FM(Remark.)j FQ(The)c(pro)q(of)h(giv)o(en)f(here)f(of)i(\(A.23\))f(is)g(a)g(sligh)o(t)g (elab)q(oration)h(of)f(one)h(sk)o(etc)o(hed)e(b)o(y)60 2600 y(Hugenholtz)19 b([198,)h(p.)f(454];)h(b)o(y)f(using)h FP(c)n(omplete)k FQ(subadditivit)o(y)17 b(w)o(e)i(are)g(able)g(to)h(deduce)e(the)60 2660 y(full)d(v)m(an)i(Ho)o(v)o(e)e(con)o(v)o(ergence.)938 2784 y(184)p eop %%Page: 185 185 bop 60 91 a FM(A.3.6)56 b(Closed)18 b(and)h(Compact)f(Sets)g(in)h FE(B)994 73 y FH(0)60 222 y Fd(Pr)o(oof)26 b(of)g(Pr)o(oposition)f(2.39.)91 b FQ(\(a\))25 b(W)l(e)e(shall)h(actually)f(pro)o(v)o(e)f(something)h(sligh)o (tly)60 282 y(stronger,)14 b(namely)e(that)i FE(f)p FQ(\010:)22 b FE(k)p FQ(\010)p FE(k)712 289 y Fy(B)735 295 y Fs(h)771 282 y FE(\024)14 b FF(M)5 b FE(g)14 b FQ(is)f(closed)g(in)h(the)f(pro)q(duct)h (top)q(ology)1616 249 y Fx(Q)1655 293 y FD(X)s Fy(2S)1745 282 y FF(C)t FQ(\(\012)1838 289 y FD(X)1871 282 y FQ(\))60 342 y(\(whic)o(h)d(is)g(w)o(eak)o(er)f(than)i(the)g FE(B)638 324 y FH(0)668 342 y FQ(norm)f(top)q(ology\).)21 b(So)12 b(let)e(\(\010)1210 349 y FD(n)1234 342 y FQ(\))h(b)q(e)h(a)g(sequence)e(in)h FE(f)p FQ(\010:)22 b FE(k)p FQ(\010)p FE(k)1792 349 y Fy(B)1815 355 y Fs(h)1851 342 y FE(\024)60 403 y FF(M)5 b FE(g)p FQ(,)18 b(and)g(let)e(\010)i(b)q(e)g(another)g(in)o(teraction;)f(and)h(supp)q(ose)g (that)g FE(k)p FQ(\(\010)1364 410 y FD(n)1388 403 y FQ(\))1407 410 y FD(X)1453 403 y FE(\000)11 b FQ(\010)1538 410 y FD(X)1572 403 y FE(k)16 b(!)g FQ(0)i(for)g(eac)o(h)60 463 y FF(X)t FQ(.)k(\(This)16 b(w)o(ould)g(o)q(ccur,)g(in)g(particular,)g(if)f(\010)932 470 y FD(n)970 463 y FE(!)e FQ(\010)k(in)f FE(B)1177 445 y FH(0)1212 463 y FQ(norm.\))k(Then)371 580 y FE(k)p FQ(\010)p FE(k)456 587 y Fy(B)479 593 y Fs(h)529 580 y FQ(=)601 539 y Fx(X)595 631 y FD(X)s Fy(3)p FH(0)681 547 y FF(h)p FQ(\()p FF(X)t FQ(\))p 681 569 111 2 v 700 614 a FE(j)p FF(X)t FE(j)805 580 y(k)p FQ(\010)865 587 y FD(X)899 580 y FE(k)41 b FQ(=)1052 539 y Fx(X)1045 631 y FD(X)s Fy(3)p FH(0)1131 547 y FF(h)p FQ(\()p FF(X)t FQ(\))p 1131 569 V 1151 614 a FE(j)p FF(X)t FE(j)1275 580 y FQ(lim)1263 605 y FD(n)p Fy(!1)1364 580 y FE(k)p FQ(\(\010)1443 587 y FD(n)1466 580 y FQ(\))1485 587 y FD(X)1519 580 y FE(k)965 725 y(\024)g FQ(lim)8 b(inf)1067 749 y FD(n)p Fy(!1)1195 683 y Fx(X)1189 775 y FD(X)s Fy(3)p FH(0)1275 691 y FF(h)p FQ(\()p FF(X)t FQ(\))p 1275 713 V 1294 759 a FE(j)p FF(X)t FE(j)1398 725 y(k)p FQ(\(\010)1477 732 y FD(n)1501 725 y FQ(\))1520 732 y FD(X)1554 725 y FE(k)965 835 y FQ(=)42 b(lim)8 b(inf)1067 860 y FD(n)p Fy(!1)1189 835 y FE(k)p FQ(\010)1249 842 y FD(n)1272 835 y FE(k)1297 842 y Fy(B)1320 848 y Fs(h)965 918 y FE(\024)41 b FF(M)20 b(;)627 b FQ(\(A.26\))60 1008 y(where)16 b(in)g(the)g(k)o(ey)f (inequalit)o(y)f(w)o(e)i(ha)o(v)o(e)f(used)i(F)l(atou's)f(lemma.)133 1068 y(\(b\))21 b(Let)g(\(\010)365 1075 y FD(n)389 1068 y FQ(\))g(b)q(e)g(a)g (sequence)f(in)h FE(f)p FQ(\010:)30 b FE(k)p FQ(\010)p FE(k)1003 1075 y Fy(B)1026 1081 y Fs(h)1070 1068 y FE(\024)22 b FF(M)5 b FE(g)p FQ(.)36 b(Since)20 b(the)g(single-spin)h(space)g(is)60 1129 y(\014nite,)f(eac)o(h)f(space)h FF(C)t FQ(\(\012)543 1136 y FD(X)577 1129 y FQ(\),)g FF(X)25 b FQ(\014nite,)19 b(is)h (\014nite-dimensional.)30 b(Therefore,)20 b(b)o(y)g(compactness)60 1189 y(of)i(the)g(ball)g(in)g FF(C)t FQ(\(\012)468 1196 y FD(X)501 1189 y FQ(\))g(together)g(with)g(the)g(usual)g(diagonal)h(argumen)o(t,)f(w)o (e)g(can)g(extract)g(a)60 1249 y(subsequence)14 b(\(\010)388 1256 y FD(n)409 1247 y Ft(0)423 1249 y FQ(\))h(suc)o(h)g(that)g(\(\010)724 1256 y FD(n)745 1247 y Ft(0)759 1249 y FQ(\))778 1256 y FD(X)826 1249 y FQ(con)o(v)o(erges)f(\(in)h FE(k)h(\001)h(k)1215 1256 y Fy(1)1267 1249 y FQ(norm\))d(for)h(eac)o(h)f FF(X)t FQ(,)h(sa)o(y)g(to)h (\010)1843 1256 y FD(X)1876 1249 y FQ(.)60 1309 y(Let)j(\010)f(=)g FE(f)p FQ(\010)319 1316 y FD(X)353 1309 y FE(g)p FQ(.)29 b(In)18 b(part)h(\(a\))g(w)o(e)g(ha)o(v)o(e)f(sho)o(wn)h(that)g FE(k)p FQ(\010)p FE(k)1206 1316 y Fy(B)1229 1322 y Fs(h)1270 1309 y FE(\024)e FF(M)5 b FQ(.)30 b(No)o(w)18 b(w)o(e)g(wish)h(to)g(sho)o(w)60 1369 y(that)e(\010)201 1376 y FD(n)222 1367 y Ft(0)249 1369 y FE(!)d FQ(\010)j(in)e FE(B)456 1351 y FH(0)492 1369 y FQ(norm.)20 b(So)d(\014x)f FF(K)i(<)c FE(1)p FQ(;)h(w)o(e)h(then)g(ha)o(v)o(e)121 1479 y FE(k)p FQ(\010)181 1486 y FD(n)202 1477 y Ft(0)227 1479 y FE(\000)11 b FQ(\010)p FE(k)337 1487 y Fy(B)361 1478 y Fr(0)422 1479 y FQ(=)572 1437 y Fx(X)556 1536 y FD(X)h Fy(3)d FH(0)523 1578 y FD(h)p FH(\()p FD(X)s FH(\))g FD(<)h(K)739 1445 y FQ(1)p 715 1467 73 2 v 715 1513 a FE(j)p FF(X)t FE(j)800 1479 y(k)p FQ(\(\010)879 1486 y FD(n)900 1477 y Ft(0)914 1479 y FQ(\))933 1486 y FD(X)978 1479 y FE(\000)h FQ(\010)1063 1486 y FD(X)1097 1479 y FE(k)24 b FQ(+)1279 1437 y Fx(X)1263 1536 y FD(X)13 b Fy(3)c FH(0)1230 1578 y FD(h)p FH(\()p FD(X)s FH(\))g Fy(\025)i FD(K)1447 1445 y FQ(1)p 1423 1467 V 1423 1513 a FE(j)p FF(X)t FE(j)1508 1479 y(k)p FQ(\(\010)1587 1486 y FD(n)1608 1477 y Ft(0)1622 1479 y FQ(\))1641 1486 y FD(X)1686 1479 y FE(\000)f FQ(\010)1770 1486 y FD(X)1804 1479 y FE(k)422 1677 y(\024)572 1636 y Fx(X)556 1734 y FD(X)i Fy(3)d FH(0)523 1777 y FD(h)p FH(\()p FD(X)s FH(\))g FD(<)h(K)739 1644 y FQ(1)p 715 1666 V 715 1711 a FE(j)p FF(X)t FE(j)800 1677 y(k)p FQ(\(\010)879 1684 y FD(n)900 1675 y Ft(0)914 1677 y FQ(\))933 1684 y FD(X)978 1677 y FE(\000)h FQ(\010)1063 1684 y FD(X)1097 1677 y FE(k)24 b FQ(+)h(2)p FF(M)r(=K)20 b(:)372 b FQ(\(A.27\))60 1865 y(Since)15 b FF(h)229 1877 y FE(\030)229 1856 y(\035)292 1865 y FQ(1,)h(the)f(\014rst)h (sum)f(is)g(\014nite;)g(and)h(since)f FE(k)p FQ(\(\010)1110 1872 y FD(n)1131 1863 y Ft(0)1144 1865 y FQ(\))1163 1872 y FD(X)1207 1865 y FE(\000)9 b FQ(\010)1290 1872 y FD(X)1324 1865 y FE(k)14 b(!)f FQ(0)j(for)g(eac)o(h)f FF(X)t FQ(,)h(w)o(e)f(ha)o(v)o(e) 634 1955 y(lim)8 b(sup)692 1995 y FD(n)713 1985 y Ft(0)800 1955 y FE(k)p FQ(\010)860 1962 y FD(n)881 1953 y Ft(0)906 1955 y FE(\000)j FQ(\010)p FE(k)1016 1963 y Fy(B)1040 1954 y Fr(0)1087 1955 y FE(\024)27 b FQ(2)p FF(M)r(=K)20 b(:)428 b FQ(\(A)p FF(:)p FQ(28\))60 2067 y(Since)15 b FF(K)21 b FQ(ma)o(y)14 b(b)q(e)j(tak)o(en)f(arbitrarily)f(large,)h(w)o(e)g(are)g(done.)p 1327 2071 25 34 v 133 2166 a FM(Remarks.)j FQ(1.)j(F)l(or)16 b(a)h(con)o(v)o(erse)e(to)i(part)f(\(b\),)g(see)g(Prop)q(osition)h(A.10)g(b)q (elo)o(w.)133 2226 y(2.)38 b(One)22 b(migh)o(t)e(ask)i(whether)f(\(a\))h(and) g(\(b\))g(can)g(b)q(e)g(extended)e(to)j(more)d(general)h(closed)60 2286 y(b)q(ounded)f(sets)f(in)g FE(B)453 2293 y FD(h)494 2286 y FQ(\(not)g(just)g(balls\).)29 b(The)19 b(answ)o(er)h(is)e(no,)i(in)f (general:)26 b(a)19 b(closed)g(b)q(ounded)60 2346 y(con)o(v)o(ex)f(set)h(in)g FE(B)395 2353 y FD(h)436 2346 y FQ(need)g(not)h(b)q(e)f(closed)g(\(m)o(uc)o (h)e(less)i(compact!\))29 b(in)19 b FE(B)1441 2328 y FH(0)1460 2346 y FQ(,)h(if)e FF(h)i FQ(is)f(un)o(b)q(ounded.)60 2407 y FP(Example:)33 b FQ(Let)20 b FE(f)p FF(A)440 2414 y FD(n)463 2407 y FE(g)f FQ(b)q(e)i(a)f(sequence)f(of)h(\014nite)f(subsets)i(of)f Fq(Z)1277 2386 y FD(d)1297 2407 y FQ(,)h(in)e(whic)o(h)g(eac)o(h)h(equiv)m (alence)60 2467 y(class)13 b(mo)q(dulo)g(translation)h(o)q(ccurs)f(at)h(most) e(once,)h(and)h(satisfying)f(lim)1403 2474 y FD(n)p Fy(!1)1505 2467 y FF(h)p FQ(\()p FF(A)1589 2474 y FD(n)1612 2467 y FQ(\))h(=)g(+)p FE(1)p FQ(.)20 b(Let)60 2527 y(\010)95 2534 y FD(n)135 2527 y FQ(b)q(e)c(de\014ned)g(b)o(y)470 2636 y(\(\010)524 2643 y FD(n)548 2636 y FQ(\))567 2643 y FD(A)623 2636 y FQ(=)689 2575 y Fx(\032)728 2608 y FQ(1)p FF(=h)p FQ(\()p FF(A)860 2615 y FD(n)884 2608 y FQ(\))49 b(if)16 b FF(A)f FQ(is)i(a)f(translate)h(of)f FF(A)1435 2615 y FD(n)728 2676 y FQ(0)200 b(otherwise)1753 2636 y(\(A)p FF(:)p FQ(29\))938 2784 y(185)p eop %%Page: 186 186 bop 60 91 a FQ(No)o(w,)15 b(for)h(eac)o(h)f(sequence)f FF(\025)h FE(2)f FF(`)678 73 y FH(1)698 91 y FQ(,)h(let)g(\010)832 73 y FD(\025)868 91 y FQ(=)920 58 y Fx(P)964 71 y Fy(1)964 104 y FD(n)p FH(=1)1041 91 y FF(\025)1069 98 y FD(n)1093 91 y FQ(\010)1128 98 y FD(n)1167 91 y FQ(\(this)g(sum)g(is)g(absolutely)g(con)o(v)o(ergen)o(t) 60 152 y(in)h FE(B)150 159 y FD(h)173 152 y FQ(\).)22 b(Then)17 b FE(k)p FQ(\010)416 133 y FD(\025)439 152 y FE(k)464 159 y Fy(B)487 165 y Fs(h)524 152 y FQ(=)d FE(k)p FF(\025)p FE(k)654 160 y FD(`)668 150 y Fr(1)705 152 y FQ(and)k FE(k)p FQ(\010)861 133 y FD(\025)895 152 y FE(\000)11 b FQ(\010)980 133 y FD(\025)1001 122 y Ft(0)1014 152 y FE(k)1039 159 y Fy(B)1062 165 y Fs(h)1099 152 y FQ(=)k FE(k)p FF(\025)c FE(\000)g FF(\025)1294 133 y Fy(0)1307 152 y FE(k)1332 160 y FD(`)1346 150 y Fr(1)1365 152 y FQ(.)23 b(\(That)17 b(is,)g FF(\025)e FE(7!)f FQ(\010)1749 133 y FD(\025)1789 152 y FQ(is)j(an)60 212 y(isometric)e(isomorphism)h(of)h FF(`)633 194 y FH(1)671 212 y FQ(on)o(to)h(a)g(closed)f(linear)g(subspace)h (of)g FE(B)1401 219 y FD(h)1423 212 y FQ(.\))25 b(No)o(w)17 b(let)g FF(S)i FQ(=)d FE(f)p FQ(\010)1828 219 y FD(n)1852 212 y FE(g)p FQ(,)60 272 y(and)h(let)553 348 y FF(T)34 b FQ(=)27 b FE(f)p FQ(\010)741 328 y FD(\025)764 348 y FQ(:)22 b(0)14 b FE(\024)f FF(\025)918 355 y FD(n)956 348 y FE(\024)h FQ(1)8 b FE(8)p FF(n;)1144 294 y Fy(1)1132 307 y Fx(X)1128 398 y FD(n)p FH(=1)1203 348 y FF(\025)1231 355 y FD(n)1269 348 y FQ(=)14 b(1)p FE(g)g FF(:)355 b FQ(\(A)p FF(:)p FQ(30\))60 470 y FF(T)24 b FQ(is)18 b(the)f(closed)h(con)o(v)o(ex)e(h)o(ull)h(of)h FF(S)i FQ(in)e FE(B)853 477 y FD(h)875 470 y FQ(.)26 b(No)o(w,)17 b FE(k)p FQ(\010)p FE(k)1126 477 y Fy(B)1149 483 y Fs(h)1188 470 y FQ(=)f(1)i(for)g(all)g(\010)e FE(2)h FF(T)7 b FQ(,)17 b(so)h(0)23 b FF(=)-30 b FE(2)17 b FF(T)7 b FQ(.)25 b(On)60 530 y(the)16 b(other)g(hand,)h(0)f FP(do)n(es)21 b FQ(b)q(elong)16 b(to)h(the)f(closure)g(of)g FF(T)23 b FQ(in)16 b FE(B)1219 512 y FH(0)1238 530 y FQ(,)g(since)f(lim)1455 537 y FD(n)p Fy(!1)1557 530 y FE(k)p FQ(\010)1617 537 y FD(n)1641 530 y FE(k)1666 539 y Fy(B)1690 529 y Fr(0)1723 530 y FQ(=)f(0.)133 640 y(The)h(natural)f(setting)h(for)f(discussing)h(the)f(spaces)h FE(B)1123 622 y FH(0)1156 640 y FQ(and)g FE(B)1282 647 y FD(h)1319 640 y FQ(is)f(that)h(of)g FP(weighte)n(d)i FF(`)1738 622 y FH(1)1774 640 y FP(dir)n(e)n(ct)60 701 y(sums)e(of)h(Banach)g(sp)n(ac)n(es)t FQ(.)21 b(Let)14 b FF(Y)693 708 y FH(1)713 701 y FF(;)8 b(Y)763 708 y FH(2)783 701 y FF(;)g(:)g(:)g(:)13 b FQ(b)q(e)i(Banac)o(h)f(spaces,)g (and)h(let)f FF(h)p FQ(:)i Fq(N)e FE(!)f FQ(\(0)p FF(;)8 b FE(1)p FQ(\).)21 b(Then)60 761 y(w)o(e)15 b(de\014ne)f FM(Y)312 768 y FD(h)350 761 y FQ(to)h(b)q(e)g(the)g(space)g(of)g(sequences)f FF(y)i FQ(=)e(\()p FF(y)1094 768 y FH(1)1113 761 y FF(;)8 b(y)1159 768 y FH(2)1178 761 y FF(;)g(:)g(:)g(:)p FQ(\),)14 b(with)h(eac)o(h)g FF(y)1548 768 y FD(i)1575 761 y FE(2)f FF(Y)1650 768 y FD(i)1665 761 y FQ(,)g(for)i(whic)o(h)60 821 y(the)g(norm)721 898 y FE(k)p FF(y)r FE(k)797 906 y Fj(Y)830 912 y Fs(h)880 898 y FE(\021)959 844 y Fy(1)946 856 y Fx(X)948 947 y FD(i)p FH(=1)1014 898 y FF(h)p FQ(\()p FF(i)p FQ(\))8 b FE(k)p FF(y)1154 905 y FD(i)1168 898 y FE(k)1193 905 y FD(Y)1213 910 y Fs(i)1753 898 y FQ(\(A)p FF(:)p FQ(31\))60 1017 y(is)18 b(\014nite.)27 b(F)l(or)18 b FF(h)f FE(\021)g FQ(1)i(w)o(e)f(write)g FM(Y)737 1024 y FD(h)777 1017 y FQ(=)f FM(Y)q FQ(.)28 b(It)18 b(is)g(easy)g(to)h(pro)o(v)o(e)e(that)i (all)e(the)h(spaces)h FM(Y)1784 1024 y FD(h)1825 1017 y FQ(are)60 1077 y(Banac)o(h)e(spaces.)23 b(The)16 b(canonical)h(pro)s(jection)f FF(p)976 1084 y FD(i)991 1077 y FQ(:)22 b FM(Y)1069 1084 y FD(h)1107 1077 y FE(!)14 b FF(Y)1199 1084 y FD(i)1231 1077 y FQ(de\014ned)i(b)o(y)g FF(p)1491 1084 y FD(i)1506 1077 y FQ(\()p FF(y)r FQ(\))e(=)h FF(y)1661 1084 y FD(i)1691 1077 y FQ(has)j(norm)60 1137 y(1)p FF(=h)p FQ(\()p FF(i)p FQ(\).)133 1198 y(W)l(e)e(then)g(ha)o(v)o(e)g(the)g(follo)o(wing)g(results:)60 1312 y FM(Prop)r(osition)i(A.9)24 b FP(The)c(close)n(d)g(b)n(al)r(l)h FE(f)p FF(y)r FQ(:)k FE(k)p FF(y)r FE(k)977 1320 y Fj(Y)1010 1326 y Fs(h)1049 1312 y FE(\024)18 b FF(M)5 b FE(g)20 b FP(is)f(close)n(d)h (in)g(the)g(pr)n(o)n(duct)f(top)n(olo)n(gy)60 1339 y Fx(Q)74 1409 y FD(i)108 1372 y FF(Y)136 1379 y FD(i)150 1372 y FP(.)60 1506 y FM(Prop)r(osition)f(A.10)24 b FP(L)n(et)17 b FF(S)g FE(\032)c FM(Y)q FP(.)24 b(Then)18 b(the)g(fol)r(lowing)h(ar)n(e)e(e)n (quivalent:)93 1608 y(\(a\))24 b FF(S)c FP(has)d(c)n(omp)n(act)g(closur)n(e)h (in)g FM(Y)q FP(.)95 1709 y(\(b\))25 b FF(S)20 b FP(is)e(b)n(ounde)n(d,)f FF(p)509 1716 y FD(i)524 1709 y FQ([)p FF(S)s FQ(])f FP(has)h(c)n(omp)n(act)g (closur)n(e)h(in)g FF(Y)1128 1716 y FD(i)1160 1709 y FP(for)e(e)n(ach)i FF(i)p FP(,)f(and)779 1848 y FQ(lim)762 1878 y FD(N)t Fy(!1)881 1848 y FQ(sup)885 1888 y FD(y)q Fy(2)p FD(S)988 1794 y Fy(1)976 1807 y Fx(X)971 1899 y FD(i)p FH(=)p FD(N)1050 1848 y FE(k)p FF(y)1099 1855 y FD(i)1113 1848 y FE(k)1138 1855 y FD(Y)1158 1860 y Fs(i)1201 1848 y FQ(=)28 b(0)14 b FF(:)434 b FQ(\(A)p FF(:)p FQ(32\))95 2015 y FP(\(c\))25 b FF(S)16 b FP(is)c(b)n(ounde)n(d,)i FF(p)496 2022 y FD(i)511 2015 y FQ([)p FF(S)s FQ(])e FP(has)g(c)n(omp)n(act)g (closur)n(e)i(in)f FF(Y)1092 2022 y FD(i)1119 2015 y FP(for)f(e)n(ach)h FF(i)p FP(,)g(and)h(ther)n(e)e(exists)i(a)f(function)182 2075 y FF(h)p FQ(:)j Fq(N)e FE(!)f FQ([1)p FF(;)8 b FE(1)p FQ(\))17 b FP(such)h(that)25 b FQ(lim)713 2104 y FD(i)p Fy(!1)804 2075 y FF(h)p FQ(\()p FF(i)p FQ(\))13 b(=)h(+)p FE(1)j FP(and)849 2199 y FQ(sup)853 2239 y FD(y)q Fy(2)p FD(S)930 2199 y FE(k)p FF(y)r FE(k)1006 2208 y Fj(Y)1039 2214 y Fs(h)1089 2199 y FF(<)28 b FE(1)13 b FF(:)521 b FQ(\(A)p FF(:)p FQ(33\))60 2361 y(Note)16 b(that)g(if)g FF(Y)356 2368 y FD(i)386 2361 y FQ(is)g(\014nite-dimensional,)d (then)j FF(S)j FQ(b)q(ounded)e(=)-8 b FE(\))16 b FF(p)1320 2368 y FD(i)1334 2361 y FQ([)p FF(S)s FQ(])f(b)q(ounded)i(=)-8 b FE(\))16 b FF(p)1729 2368 y FD(i)1743 2361 y FQ([)p FF(S)s FQ(])f(has)60 2422 y(compact)g(closure)h(in)g FF(Y)503 2429 y FD(i)517 2422 y FQ(.)133 2482 y(The)d(pro)q(of)g(of)g(Prop)q(osition)h(A.9) e(is)g(completely)e(analogous)k(to)f(that)g(of)g(Prop)q(osition)g(2.39\(a\).) 60 2542 y(Let)j(us)h(sk)o(etc)o(h)e(the)h(pro)q(of)h(of)g(Prop)q(osition)g (A.10:)938 2784 y(186)p eop %%Page: 187 187 bop 133 91 a FQ(\(a\))22 b(=)-8 b FE(\))20 b FQ(\(b\):)31 b(Let)528 79 y(\026)520 91 y FF(S)24 b FQ(b)q(e)d(compact)f(in)h FM(Y)q FQ(.)37 b(Then)21 b(clearly)f FF(p)1318 98 y FD(i)1332 91 y FQ([)1354 79 y(\026)1346 91 y FF(S)s FQ(])i FE(\033)g FF(p)1500 98 y FD(i)1514 91 y FQ([)p FF(S)s FQ(])e(is)h(compact)f(in)60 152 y FF(Y)88 159 y FD(i)102 152 y FQ(.)41 b(Moreo)o(v)o(er,)22 b(for)h(eac)o(h)g FF(\017)h(>)h FQ(0)e(there)f(exists)g(a)h(\014nite)f(set)h FF(y)1303 133 y FH(\(1\))1349 152 y FF(;)8 b(:)g(:)g(:)g(;)g(y)1485 133 y FH(\()p FD(n)p FH(\))1560 152 y FE(2)25 b FM(Y)f FQ(suc)o(h)f(that)60 225 y FF(S)17 b FE(\032)181 184 y FD(n)174 192 y Fx(S)159 264 y FD(k)q FH(=1)232 225 y FF(B)s FQ(\()p FF(y)317 207 y FH(\()p FD(k)q FH(\))365 225 y FF(;)8 b(\017)p FQ(\).)21 b(It)15 b(follo)o(ws)i(that) 548 394 y(sup)552 433 y FD(y)q Fy(2)p FD(S)647 340 y Fy(1)635 353 y Fx(X)629 444 y FD(i)p FH(=)p FD(N)709 394 y FE(k)p FF(y)758 401 y FD(i)772 394 y FE(k)797 401 y FD(Y)817 406 y Fs(i)860 394 y FE(\024)27 b FF(\017)19 b FQ(+)31 b(max)1023 424 y FH(1)p Fy(\024)p FD(k)q Fy(\024)p FD(n)1162 340 y Fy(1)1150 353 y Fx(X)1144 444 y FD(i)p FH(=)p FD(N)1223 394 y FE(k)p FF(y)1274 369 y FH(\()p FD(k)q FH(\))1272 406 y FD(i)1323 394 y FE(k)1348 401 y FD(Y)1368 406 y Fs(i)1397 394 y FF(:)342 b FQ(\(A)p FF(:)p FQ(34\))60 537 y(T)l(aking)17 b FF(N)i FE(!)13 b(1)p FQ(,)j(w)o(e)g(get)679 623 y(lim)8 b(sup)703 663 y FD(N)t Fy(!1)845 623 y FQ(sup)849 663 y FD(y)q Fy(2)p FD(S)953 569 y Fy(1)941 582 y Fx(X)935 674 y FD(i)p FH(=)p FD(N)1015 623 y FE(k)p FF(y)1064 630 y FD(i)1077 623 y FE(k)1102 630 y FD(Y)1122 635 y Fs(i)1166 623 y FE(\024)27 b FF(\017)14 b(:)473 b FQ(\(A)p FF(:)p FQ(35\))60 744 y(Since)15 b FF(\017)h FQ(w)o(as)h(arbitrary)l(,)f(the)g(pro)q(of)h(is)f (complete.)133 804 y(\(b\))g(=)-8 b FE(\))16 b FQ(\(c\):)21 b(Cho)q(ose)d FF(N)614 811 y FH(1)647 804 y FF(<)c(N)738 811 y FH(2)772 804 y FF(<)f(:)8 b(:)g(:)16 b FQ(suc)o(h)g(that)717 943 y(sup)721 982 y FD(y)q Fy(2)p FD(S)837 889 y Fy(1)825 901 y Fx(X)807 993 y FD(i)p FH(=)p FD(N)874 997 y Fs(m)912 943 y FE(k)p FF(y)961 950 y FD(i)974 943 y FE(k)999 950 y FD(Y)1019 955 y Fs(i)1063 943 y FE(\024)27 b FQ(3)1153 922 y Fy(\000)p FD(m)1228 943 y FF(:)511 b FQ(\(A)p FF(:)p FQ(36\))60 1090 y(No)o(w)16 b(de\014ne)597 1159 y FF(h)p FQ(\()p FF(i)p FQ(\))27 b(=)773 1099 y Fx(\032)812 1129 y FQ(1)83 b(for)16 b FF(i)e(<)g(N)1115 1136 y FH(1)812 1189 y FQ(2)836 1171 y FD(m)919 1189 y FQ(for)i FF(N)1032 1196 y FD(m)1080 1189 y FE(\024)d FF(i)h(<)f(N)1253 1196 y FD(m)p FH(+1)1753 1159 y FQ(\(A)p FF(:)p FQ(37\))60 1266 y(Then,)j(for)g(all)g FF(y)g FE(2)e FF(S)s FQ(,)299 1414 y FE(k)p FF(y)r FE(k)375 1423 y Fj(Y)408 1429 y Fs(h)458 1414 y FE(\021)537 1360 y Fy(1)524 1373 y Fx(X)526 1464 y FD(i)p FH(=1)593 1414 y FF(h)p FQ(\()p FF(i)p FQ(\))8 b FE(k)p FF(y)733 1421 y FD(i)746 1414 y FE(k)771 1421 y FD(Y)791 1426 y Fs(i)849 1414 y FQ(=)929 1359 y FD(N)957 1364 y Fr(1)974 1359 y Fy(\000)p FH(1)944 1373 y Fx(X)945 1464 y FD(i)p FH(=1)1027 1414 y FE(k)p FF(y)1076 1421 y FD(i)1090 1414 y FE(k)1115 1421 y FD(Y)1135 1426 y Fs(i)1170 1414 y FQ(+)1248 1360 y Fy(1)1236 1373 y Fx(X)1227 1463 y FD(m)p FH(=1)1312 1414 y FQ(2)1336 1394 y FD(m)1378 1356 y(N)1406 1361 y Fs(m)p Fr(+1)1474 1356 y Fy(\000)p FH(1)1419 1373 y Fx(X)1400 1465 y FD(i)p FH(=)p FD(N)1467 1469 y Fs(m)1527 1414 y FE(k)p FF(y)1576 1421 y FD(i)1590 1414 y FE(k)1615 1421 y FD(Y)1635 1426 y Fs(i)848 1571 y FE(\024)929 1516 y FD(N)957 1521 y Fr(1)974 1516 y Fy(\000)p FH(1)944 1530 y Fx(X)945 1621 y FD(i)p FH(=1)1027 1571 y FE(k)p FF(y)1076 1578 y FD(i)1090 1571 y FE(k)1115 1578 y FD(Y)1135 1583 y Fs(i)1170 1571 y FQ(+)1248 1517 y Fy(1)1236 1530 y Fx(X)1227 1620 y FD(m)p FH(=1)1312 1511 y Fx(\022)1348 1538 y FQ(2)p 1348 1560 25 2 v 1348 1606 a(3)1377 1511 y Fx(\023)1402 1519 y FD(m)848 1679 y FE(\024)42 b(k)p FF(y)r FE(k)1005 1688 y Fj(Y)1060 1679 y FQ(+)19 b(2)c FF(:)583 b FQ(\(A.38\))60 1789 y(Since)15 b FF(S)20 b FQ(is,)15 b(b)o(y)h(h)o(yp)q(othesis,)g(b)q(ounded)h(in)f FM(Y)q FQ(,)g(this)g(pro)o(v) o(es)g(the)g(claim.)133 1849 y(\(c\))d(=)-8 b FE(\))13 b FQ(\(a\):)20 b(The)13 b(pro)q(of)h(is)f(essen)o(tially)f(iden)o(tical)f(to)i(that)h(of)g (Prop)q(osition)g(2.39\(b\).)p 1861 1853 25 34 v 133 1959 a(T)l(o)e(apply)f (this)g(to)h(our)g(statistical-mec)o(hanical)c(setup,)k(let)f(\()p FF(X)1289 1966 y FD(i)1303 1959 y FQ(\))h(b)q(e)f(a)h(sequence)e(of)i (nonempt)o(y)60 2020 y(\014nite)18 b(subsets)g(of)h Fq(Z)445 1999 y FD(d)483 2020 y FQ(in)f(whic)o(h)g(eac)o(h)f(equiv)m(alence)g(class)h (mo)q(dulo)g(translation)g(is)g(represen)o(ted)60 2080 y(once)c(and)g(only)g (once.)20 b(Setting)14 b FF(Y)689 2087 y FD(i)717 2080 y FQ(=)g FF(C)t FQ(\(\012)862 2087 y FD(X)891 2092 y Fs(i)906 2080 y FQ(\),)g(it)g(is)f(easy)h(to)h(see)e(that)i FE(B)1424 2062 y FH(0)1457 2080 y FQ(and)f FE(B)1582 2087 y FD(h)1618 2080 y FQ(are)g(isometric)60 2140 y(to)e(the)f(direct-sum)f(spaces)h FM(Y)i FQ(and)f FM(Y)762 2147 y FD(h)785 2140 y FQ(,)g(resp)q(ectiv)o(ely)l (.)17 b(Therefore,)12 b(Prop)q(osition)g(A.10)g(\(a\)=)-8 b FE(\))p FQ(\(c\))60 2200 y(tells)18 b(us)h(that)g(an)o(y)f(compact)g(subset)h (of)g FE(B)876 2182 y FH(0)913 2200 y FQ(is)g(con)o(tained)f(in)g(the)h(ball) f FE(f)p FQ(\010:)26 b FE(k)p FQ(\010)p FE(k)1616 2207 y Fy(B)1639 2213 y Fs(h)1679 2200 y FE(\024)18 b FF(M)5 b FE(g)19 b FQ(for)60 2260 y(some)d FF(h)226 2273 y FE(\030)226 2252 y(\035)290 2260 y FQ(1)i(and)f(some)f FF(M)k(<)15 b FE(1)p FQ(.)23 b(A)16 b(similar)f(result) h(can)h(b)q(e)g(found)h(in)e([208)q(,)g(Lemmas)f(1)i(and)60 2320 y(2].)60 2430 y Fd(Pr)o(oof)j(of)h(Pr)o(oposition)f(2.43.)76 b FQ(This)19 b(is)f(an)h(immedi)o(ate)d(consequence)i(of)h(Prop)q(osition)60 2491 y(2.39\(b\),)13 b(together)f(with)f(the)h(follo)o(wing)f(w)o(ell-kno)o (wn)g(fact:)18 b(if)12 b FF(A)f FQ(and)h FF(B)i FQ(are)e(subsets)g(of)g(a)g (Banac)o(h)60 2551 y(space)k FF(X)t FQ(,)h(with)f FF(A)f FQ(compact)h(and)g FF(B)j FQ(closed,)d(then)g FF(A)10 b FQ(+)h FF(B)19 b FQ(is)d(closed.)p 1525 2555 V 938 2784 a(187)p eop %%Page: 188 188 bop 60 91 a FM(A.3.7)56 b(Ph)n(ysical)18 b(Equiv)m(alence)60 184 y FQ(Here)e(w)o(e)i(pro)o(v)o(e)e(Theorem)g(2.42)j(on)f(the)f(equiv)m (alence)f(of)i(the)f(t)o(w)o(o)g(notions)i(of)e(ph)o(ysical)g(equiv-)60 244 y(alence)j(\(DLR)i(and)g(Ruelle\).)34 b(Since)21 b(b)q(oth)h(senses)f(of) h(ph)o(ysical)e(equiv)m(alence)f(are)i(statemen)o(ts)60 304 y(ab)q(out)d(the)e(di\013erence)f(\010)c FE(\000)g FQ(\010)633 286 y Fy(0)645 304 y FQ(,)k(it)h(su\016ces)g(to)h(consider)f(the)g(case)g (\010)1361 286 y Fy(0)1387 304 y FQ(=)d(0.)60 414 y Fd(Pr)o(oof)k(of)g (Theorem)g(2.42,)f(DLR)i FQ(=)-8 b FE(\))17 b Fd(R)o(uelle.)68 b FQ(W)l(e)15 b(wish)g(to)h(measure)e(ho)o(w)i(strongly)60 474 y FF(H)104 456 y FH(\010)100 487 y(\003)132 474 y FQ(\()p FF(!)181 481 y FH(\003)208 474 y FF(;)8 b(!)260 481 y FH(\003)284 472 y Fs(c)302 474 y FQ(\))15 b(dep)q(ends)g(on)g FF(!)619 481 y FH(\003)643 472 y Fs(c)662 474 y FQ(.)20 b(Let)15 b(us)g(therefore)f (de\014ne)g(the)g FP(oscil)r(lation)k(of)e FF(H)1601 456 y FH(\010)1597 487 y(\003)1644 474 y FP(with)h(r)n(esp)n(e)n(ct)60 534 y(to)h FF(!)149 541 y FH(\003)173 532 y Fs(c)208 534 y FQ(b)o(y)389 644 y(osc)454 651 y FH(\003)478 642 y Fs(c)497 644 y FQ(\()p FF(H)560 624 y FH(\010)556 657 y(\003)587 644 y FQ(\))42 b FE(\021)96 b FQ(sup)749 690 y FD(!)q(;)6 b(!)811 679 y Ft(0)832 690 y Fy(2)j FH(\012)752 733 y FD(!)774 739 y Fr(\003)806 733 y FH(=)h FD(!)866 721 y Ft(0)865 744 y Fr(\003)920 644 y FE(j)p FF(H)978 624 y FH(\010)974 657 y(\003)1005 644 y FQ(\()p FF(!)r FQ(\))i FE(\000)e FF(H)1180 624 y FH(\010)1176 657 y(\003)1208 644 y FQ(\()p FF(!)1259 624 y Fy(0)1271 644 y FQ(\))p FE(j)648 845 y FQ(=)98 b(sup)728 887 y FD(!)750 893 y Fr(\003)773 887 y FD(;!)805 893 y Fr(\003)826 886 y Fs(c)843 887 y FD(;!)876 875 y Ft(0)875 900 y Fr(\003)896 893 y Fs(c)922 845 y FE(j)p FF(H)980 824 y FH(\010)976 857 y(\003)1008 845 y FQ(\()p FF(!)1057 852 y FH(\003)1084 845 y FF(;)8 b(!)1136 852 y FH(\003)1160 843 y Fs(c)1179 845 y FQ(\))j FE(\000)f FF(H)1302 824 y FH(\010)1298 857 y(\003)1330 845 y FQ(\()p FF(!)1379 852 y FH(\003)1406 845 y FF(;)e(!)1460 824 y Fy(0)1458 857 y FH(\003)1482 847 y Fs(c)1501 845 y FQ(\))p FE(j)14 b FF(:)191 b FQ(\(A.39\))60 998 y(Considering)25 b(no)o(w)g(the)g(de\014nition) f FF(H)809 980 y FH(\010)805 1011 y(\003)837 998 y FQ(\()p FF(!)r FQ(\))k(=)1001 965 y Fx(P)1045 1015 y FD(A)p FH(:)6 b FD(A)p Fy(\\)p FH(\003)p Fy(6)p FH(=)p Fq(?)1240 998 y FQ(\010)1275 1005 y FD(A)1304 998 y FQ(\()p FF(!)r FQ(\),)26 b(it)f(is)f(easy)h(to)g(see)g (that)60 1067 y(osc)125 1074 y FH(\003)149 1065 y Fs(c)168 1067 y FQ(\()p FF(H)231 1049 y FH(\010)227 1079 y(\003)259 1067 y FQ(\))16 b(gets)g(con)o(tributions)g(only)g(from)g(sets)g FF(A)g FQ(that)g(in)o(tersect)f(b)q(oth)i(\003)f(and)h(\003)1658 1049 y FD(c)1676 1067 y FQ(,)e(so)i(that)692 1177 y(osc)758 1184 y FH(\003)782 1175 y Fs(c)800 1177 y FQ(\()p FF(H)863 1156 y FH(\010)859 1189 y(\003)891 1177 y FQ(\))28 b FE(\024)f FQ(2)p FE(k)p FF(W)1106 1156 y FH(\010)1099 1189 y(\003)p FD(;)p FH(\003)1157 1179 y Fs(c)1176 1177 y FE(k)1201 1184 y Fy(1)1252 1177 y FF(:)487 b FQ(\(A)p FF(:)p FQ(40\))60 1286 y(In)16 b(particular,)f (for)i(\010)d FE(2)g(B)565 1268 y FH(1)600 1286 y FQ(w)o(e)i(ha)o(v)o(e)459 1396 y(osc)525 1403 y FH(\003)549 1394 y Fs(c)567 1396 y FQ(\()p FF(H)630 1376 y FH(\010)626 1409 y(\003)658 1396 y FQ(\))28 b FE(\024)f FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))98 b(as)16 b(\003)e FE(\045)g(1)i FQ(\(v)m(an)h(Ho)o(v)o(e\))12 b FF(;)262 b FQ(\(A)p FF(:)p FQ(41\))60 1506 y(b)o(y)16 b(\(2.62a\).)133 1566 y(Supp)q(ose)k(no)o(w)g(that)f(\010)h(is)f(ph)o(ysically)e(equiv)m(alen) o(t)h(to)h(0)h(in)e(the)h(DLR)h(sense,)f(i.e.)f(that)h FF(H)1862 1548 y FH(\010)1858 1579 y(\003)60 1627 y FQ(is)h FE(F)149 1634 y FH(\003)173 1625 y Fs(c)191 1627 y FQ(-measurable)f(for)i(all)e(\003.) 33 b(\(Actually)l(,)19 b(it)h(su\016ces)f(to)i(assume)e(this)h(for)h(some)e (v)m(an)h(Ho)o(v)o(e)60 1687 y(sequence)15 b(of)i(sets)f(\003.\))22 b(Then)16 b FF(H)673 1669 y FH(\010)669 1699 y(\003)701 1687 y FQ(\()p FF(!)750 1694 y FH(\003)777 1687 y FF(;)8 b(!)829 1694 y FH(\003)853 1685 y Fs(c)871 1687 y FQ(\))17 b(is)f(indep)q(enden)o(t)f (of)i FF(!)1318 1694 y FH(\003)1345 1687 y FQ(,)f(so)h(osc)1500 1694 y FH(\003)1524 1685 y Fs(c)1543 1687 y FQ(\()p FF(H)1606 1669 y FH(\010)1602 1699 y(\003)1633 1687 y FQ(\))g(is)f(equal)g(to)60 1747 y(the)g FP(unr)n(estricte)n(d)21 b FQ(oscillation)641 1857 y(osc)q(\()p FF(H)770 1836 y FH(\010)766 1869 y(\003)798 1857 y FQ(\))41 b FE(\021)g FQ(sup)9 b FF(H)1064 1836 y FH(\010)1060 1869 y(\003)1111 1857 y FE(\000)19 b FQ(inf)12 b FF(H)1281 1836 y FH(\010)1277 1869 y(\003)1753 1857 y FQ(\(A.42\))858 1930 y FE(\021)41 b FQ(2)p FE(k)p FF(H)1031 1909 y FH(\010)1027 1942 y(\003)1059 1930 y FE(k)1084 1937 y FD(B)r FH(\(\012\))p FD(=const)1282 1930 y FF(:)457 b FQ(\(A.43\))60 2040 y(Com)o(bining)15 b(\(A.41\))h(and)h(\(A.43\),)e(w)o(e)h(conclude)g(that)416 2149 y FE(k)p FF(H)485 2129 y FH(\010)481 2162 y(\003)512 2149 y FE(k)537 2157 y FD(B)r FH(\(\012\))p FD(=const)749 2149 y FE(\024)27 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))97 b(as)17 b(\003)d FE(\045)g(1)i FQ(\(v)m(an)g(Ho)o(v)o(e\))d FF(:)218 b FQ(\(A)p FF(:)p FQ(44\))60 2259 y(By)16 b(Prop)q(osition)j (2.45\(c\),)e(w)o(e)g(conclude)f(that)i FE(k)p FQ(\010)p FE(k)1044 2268 y Fy(B)1068 2258 y Fr(0)1085 2268 y FD(=)p FH(\()p Fy(J)6 b FH(+)p FD(C)r(onst)p FH(\))1300 2259 y FQ(=)16 b(0,)h(i.e.)f(\010)f FE(2)h(J)21 b FQ(+)11 b FF(C)t(onst)17 b FQ(|)60 2320 y(that)g(is,)e(\010)i (is)f(ph)o(ysically)e(equiv)m(alen)o(t)h(to)i(zero)f(in)g(the)g(Ruelle)e (sense.)p 1502 2324 25 34 v 60 2479 a Fd(Pr)o(oof)i(of)g(Theorem)g(2.42,)f(R) o(uelle)g FQ(=)-8 b FE(\))16 b Fd(DLR.)63 b FQ(Supp)q(ose)16 b(that)f(the)f(single-spin)g(space)60 2539 y(\012)95 2546 y FH(0)129 2539 y FQ(is)g(a)g(standard)i(Borel)d(space)h(\(e.g.)g(a)g(complete) e(separable)i(metric)e(space\),)i(and)g(that)h(\010)p FF(;)8 b FQ(\010)1831 2521 y Fy(0)1857 2539 y FE(2)60 2600 y(B)95 2582 y FH(1)127 2600 y FQ(are)14 b(ph)o(ysically)e(equiv)m(alen)o(t)g(in)h (the)g(Ruelle)f(sense.)20 b(Then)14 b(b)o(y)f([157)q(,)g(Theorems)g(4.22)h (and)g(5.19)60 2660 y(and)k(the)f(commen)o(ts)e(after)i(them],)e(there)i (exists)g(a)h(translation-in)o(v)m(arian)o(t)g(Gibbs)g(measure)e(for)938 2784 y(188)p eop %%Page: 189 189 bop 60 91 a FQ(\010,)14 b(call)e(it)h FF(\026)p FQ(.)21 b(By)12 b(Corollary)i(2.68,)g FF(\026)g FQ(is)f(an)h(equilibrium)9 b(measure)k(for)g(\010.)21 b(By)12 b(Prop)q(osition)j(2.65,)60 152 y FF(\026)g FQ(is)f(an)i(equilibrium)11 b(measure)i(also)i(for)g(\010)867 133 y Fy(0)879 152 y FQ(.)21 b(By)14 b(Corollary)g(2.68)i(again,)f FF(\026)g FQ(is)f(a)h(Gibbs)g(measure)60 212 y(for)i(\010)170 194 y Fy(0)182 212 y FQ(.)k(But)16 b(then)g(Corollary)h(2.18)g(implies)d (that)i(\010)h(and)g(\010)1197 194 y Fy(0)1225 212 y FQ(are)g(ph)o(ysically)d (equiv)m(alen)o(t)h(in)h(the)60 272 y(DLR)h(sense.)p 442 276 25 34 v 133 382 a FM(Remark.)30 b FQ(The)20 b(pro)q(of)g(giv)o(en)f(here)g (of)i(Ruelle)d(=)-8 b FE(\))19 b FQ(DLR)h(is)g(aesthetically)e(unsatisfying:) 60 442 y(the)g(t)o(w)o(o)g(notions)h(of)g(ph)o(ysical)e(equiv)m(alence)g(are) h(statemen)o(ts)f(purely)g(ab)q(out)j(in)o(teractions)d(and)60 502 y(Hamiltonians,)23 b(so)g(there)g(ough)o(t)g(to)h(b)q(e)f(a)g(purely)g (\\algebraic")g(pro)q(of)h(of)g(their)e(equiv)m(alence)60 562 y(in)o(v)o(olving)f FP(only)j(these)g(c)n(onc)n(epts)t FQ(,)g(without)f (dragging)h(in)e(the)h(whole)f(theory)h(of)f(equilibrium)60 623 y(measures,)15 b(Gibbs)h(measures)f(and)i(their)e(equiv)m(alence.)20 b(In)c(particular,)f(it)h(is)g(galling)g(to)g(ha)o(v)o(e)g(to)60 683 y(assume)i(that)h(\012)374 690 y FH(0)413 683 y FQ(is)f(a)h(standard)h (Borel)e(space,)h(for)g(a)g(result)f(that)h(ob)o(viously)f(has)h(nothing)h (to)60 743 y(do)f(with)f(top)q(ology)l(.)28 b(Ho)o(w)o(ev)o(er,)16 b(w)o(e)i(ha)o(v)o(e)f(b)q(een)h(unable)g(to)h(\014nd)f(suc)o(h)g(an)h (algebraic)f(pro)q(of;)h(w)o(e)60 803 y(hop)q(e)e(that)g(some)e(reader)h (will)f(do)i(so.)60 933 y FM(A.3.8)56 b(Estimates)16 b(on)j(Hamiltonians)d (and)j(Gibbs)g(Measures)60 1025 y FQ(In)14 b(Section)g(2.4.5)h(w)o(e)e (stated)i(Prop)q(osition)h(2.40)f(for)f(the)h(case)f(of)h(a)f FP(c)n(omp)n(act)i(metric)h FQ(single-spin)60 1086 y(space.)j(Here)13 b(w)o(e)g(pro)o(v)o(e)g(a)i(more)d(general)i(theorem)e(in)h(whic)o(h)g(this)h (restriction)f(is)g(remo)o(v)o(ed.)18 b(\(W)l(e)60 1146 y(still)13 b(consider)h(only)g FP(c)n(ontinuous)20 b FQ(in)o(teractions)13 b(and)i(functions,)f(but)h(that)f(restriction)g(to)q(o)h(could)60 1206 y(b)q(e)h(remo)o(v)o(ed)e(if)i(w)o(e)g(really)f(cared.\))60 1320 y FM(Prop)r(osition)j(A.11)g(\(=)g(Prop)r(osition)g(2.40)982 1302 y Fy(0)993 1320 y FM(\))25 b FP(The)d(map)g FQ([\010])g FE(7!)g FQ([)p FF(f)1451 1327 y FH(\010)1478 1320 y FQ(])g FP(is)g(an)h(isometry)e(of)60 1380 y FE(B)95 1362 y FH(0)114 1380 y FF(=)p FE(J)27 b FP(onto)19 b FF(C)346 1387 y FD(q)q(l)376 1380 y FQ(\(\012\))p FF(=)p FE(I)500 1387 y FD(q)q(l)530 1380 y FP(,)g(and)f(of)g FE(B)752 1362 y FH(0)771 1380 y FF(=)p FQ(\()p FE(J)j FQ(+)11 b FP(Const)p FQ(\))18 b FP(onto)h FF(C)1225 1387 y FD(q)q(l)1255 1380 y FQ(\(\012\))p FF(=)p FQ(\()p FE(I)1398 1387 y FD(q)q(l)1440 1380 y FQ(+)11 b FF(const)p FQ(\))p FP(.)25 b(Her)n(e)18 b FE(I)1806 1387 y FD(q)q(l)1851 1380 y FE(\021)60 1441 y(I)d(\\)c FF(C)181 1448 y FD(q)q(l)211 1441 y FQ(\(\012\))p FP(.)60 1605 y Fd(Pr)o(oof.)48 b FQ(It)11 b(is)g(con)o(v)o(enien)o(t)f (\(follo)o(wing)h(Ruelle)f([313)q(,)i(Section)f(3.2]\))h(to)g(in)o(tro)q (duce)f(the)g(mo)q(di\014ed)60 1665 y(observ)m(able)785 1725 y FF(f)814 1704 y Fy(00)809 1737 y FH(\010)865 1725 y FE(\021)966 1683 y Fx(X)931 1775 y FD(X)s Fy(3)987 1781 y Fs(mid)1043 1775 y FH(0)1068 1725 y FQ(\010)1103 1732 y FD(X)1151 1725 y FF(;)588 b FQ(\(A)p FF(:)p FQ(45\))60 1858 y(where)18 b FF(X)23 b FE(3)299 1865 y FD(mid)380 1858 y FQ(0)d(denotes)e(that)i(0)f(is)f(the)h FE(b)p FQ(\()p FE(j)p FF(X)t FE(j)13 b FQ(+)f(1\))p FF(=)p FQ(2)p FE(c)1181 1840 y FD(th)1236 1858 y FQ(elemen)o(t)k(\(\\middle)h (elemen)o(t"\))f(of)60 1918 y FF(X)21 b FQ(in)c(lexicographic)e(order.)23 b(Clearly)16 b FF(f)815 1925 y FH(\010)854 1918 y FE(\000)11 b FF(f)933 1900 y Fy(00)928 1930 y FH(\010)970 1918 y FE(2)k(I)1045 1925 y FD(q)q(l)1075 1918 y FQ(.)23 b(The)17 b(adv)m(an)o(tages)h(of)f FF(f)1548 1900 y Fy(00)1543 1930 y FH(\010)1588 1918 y FQ(are)f(due)h(to)g (the)60 1978 y(follo)o(wing)f(easily)f(v)o(eri\014ed)g(facts)h([313)q(,)g(p.) g(37]:)114 2080 y(a\))25 b FE(f)p FF(f)236 2062 y Fy(00)231 2092 y FH(\010)258 2080 y FQ(:)d(\010)14 b FE(2)g(B)423 2087 y Fk(\014nite)504 2080 y FE(g)22 b FQ(=)g FF(C)646 2087 y FD(loc)692 2080 y FQ(\(\012\).)111 2181 y(b\))j FE(f)p FF(f)236 2163 y Fy(00)231 2194 y FH(\010)258 2181 y FQ(:)d(\010)14 b FE(2)g(B)425 2163 y FH(0)444 2181 y FE(g)22 b FQ(=)g FF(C)586 2188 y FD(q)q(l)616 2181 y FQ(\(\012\).)117 2283 y(c\))i(F)l(or)16 b(all)g FF(f)j FE(2)14 b FF(C)462 2290 y FD(q)q(l)492 2283 y FQ(\(\012\),)750 2343 y FE(k)p FF(f)5 b FE(k)829 2350 y Fy(1)894 2343 y FQ(=)97 b(inf)959 2376 y FH(\010)p Fy(2B)1032 2366 y Fr(0)1050 2376 y FH(:)9 b FD(f)1090 2364 y Ft(00)1086 2388 y Fr(\010)1110 2376 y FH(=)p FD(f)1167 2343 y FE(k)p FQ(\010)p FE(k)1252 2352 y Fy(B)1276 2342 y Fr(0)1309 2343 y FF(:)430 b FQ(\(A)p FF(:)p FQ(46\))182 2461 y(Moreo)o(v)o(er,)15 b(for)h FF(f)j FE(2)14 b FF(C)609 2468 y FD(loc)655 2461 y FQ(\(\012\))i(there)g(exists)f(a)i(\010)d FE(2)g(B)1173 2468 y Fk(\014nite)1270 2461 y FQ(that)j(attains)g(this)f (minim)n(um)o(.)938 2784 y(189)p eop %%Page: 190 190 bop 60 91 a FQ(In)16 b(particular,)f(the)h(map)g(\010)e FE(7!)g FQ([)p FF(f)703 98 y FH(\010)730 91 y FQ(])f(=)h([)p FF(f)852 73 y Fy(00)847 104 y FH(\010)874 91 y FQ(])i(is)g FP(onto)k FF(C)1101 98 y FD(q)q(l)1130 91 y FQ(\(\012\))p FF(=)p FE(I)1254 98 y FD(q)q(l)1285 91 y FQ(.)133 152 y(No)o(w,)c(from)f FE(k)p FF(f)422 159 y FH(\010)449 152 y FE(k)474 159 y Fy(1)526 152 y FE(\024)e(k)p FQ(\010)p FE(k)663 160 y Fy(B)687 150 y Fr(0)723 152 y FQ(w)o(e)j(easily)f(deduce)h(that)687 254 y FE(k)p FQ([)p FF(f)750 261 y FH(\010)778 254 y FQ(])p FE(k)817 261 y FD(C)r FH(\(\012\))p FD(=)p Fy(I)966 254 y FE(\024)27 b(k)p FQ([\010])p FE(k)1145 262 y Fy(B)1169 253 y Fr(0)1185 262 y FD(=)p Fy(J)1249 254 y FF(:)490 b FQ(\(A)p FF(:)p FQ(47\))60 356 y(T)l(o)21 b(pro)o(v)o(e)f(the)g(rev)o(erse)f(inequalit)o(y)l(,)g(note)i(that)f(b)o(y)g (Prop)q(osition)i(A.8)e(w)o(e)g(ha)o(v)o(e,)g(for)h(an)o(y)f FF(f)27 b FE(2)60 416 y FF(C)95 423 y FD(q)q(l)125 416 y FQ(\(\012\),)18 b FE(k)p FQ([)p FF(f)5 b FQ(])p FE(k)337 424 y FD(C)r FH(\(\012\))p FD(=)p Fy(I)475 416 y FQ(=)17 b(lim)598 423 y FH(\003)p Fy(\0451)695 366 y Fx(\015)695 391 y(\015)695 416 y(\015)p FE(j)p FQ(\003)p FE(j)780 398 y Fy(\000)p FH(1)847 383 y Fx(P)835 454 y FD(a)p Fy(2)p FH(\003)910 416 y FF(T)939 423 y FD(a)960 416 y FF(f)989 366 y Fx(\015)989 391 y(\015)989 416 y(\015)1012 443 y Fy(1)1050 416 y FQ(.)26 b(No)o(w,)18 b(b)o(y)g(prop)q(ert)o(y)g(\(c\))g(ab)q(o)o(v)o (e,)g(for)h(eac)o(h)60 504 y(\003)g(and)g(eac)o(h)g FF(\017)f(>)g FQ(0)h(w)o(e)g(can)g(c)o(ho)q(ose)g(\011)g FE(2)f(B)927 486 y FH(0)965 504 y FQ(suc)o(h)h(that)g FF(f)1215 486 y Fy(00)1210 516 y FH(\011)1258 504 y FQ(=)g FE(j)p FQ(\003)p FE(j)1377 486 y Fy(\000)p FH(1)1443 471 y Fx(P)1432 542 y FD(a)p Fy(2)p FH(\003)1507 504 y FF(T)1536 511 y FD(a)1556 504 y FF(f)24 b FQ(and)c FE(k)p FQ(\011)p FE(k)1790 512 y Fy(B)1814 503 y Fr(0)1851 504 y FE(\024)60 552 y Fx(\015)60 577 y(\015)60 602 y(\015)p FE(j)p FQ(\003)p FE(j)145 584 y Fy(\000)p FH(1)212 569 y Fx(P)200 640 y FD(a)p Fy(2)p FH(\003)275 602 y FF(T)304 609 y FD(a)324 602 y FF(f)353 552 y Fx(\015)353 577 y(\015)353 602 y(\015)377 629 y Fy(1)429 602 y FQ(+)15 b FF(\017)p FQ(.)37 b(\(In)21 b(particular,)i(w)o(e)e(ha)o(v)o(e)g([)p FF(f)5 b FQ(])22 b(=)h([)p FF(f)1262 584 y Fy(00)1257 614 y FH(\011)1286 602 y FQ(])g(=)g([)p FF(f)1422 609 y FH(\011)1451 602 y FQ(].\))37 b(Then,)23 b(b)o(y)e(taking)60 688 y(\003)14 b FE(\045)f(1)j FQ(and)h FF(\017)d FE(#)g FQ(0)i(w)o(e)g(conclude)f(that)i(for)g(all)e FF(f)20 b FE(2)14 b FF(C)1091 695 y FD(q)q(l)1121 688 y FQ(\(\012\),)610 790 y FE(k)p FQ([)p FF(f)5 b FQ(])p FE(k)717 797 y FD(C)r FH(\(\012\))p FD(=)p Fy(I)866 790 y FE(\025)118 b FQ(inf)932 822 y FH(\011)p Fy(2B)1007 813 y Fr(0)1024 822 y FH(:)10 b([)p FD(f)1075 811 y Ft(00)1071 834 y Fr(\011)1096 822 y FH(]=[)p FD(f)t FH(])1182 790 y FE(k)p FQ(\011)p FE(k)1270 798 y Fy(B)1294 789 y Fr(0)1327 790 y FF(:)412 b FQ(\(A)p FF(:)p FQ(48\))60 919 y(In)16 b(particular,)f (taking)i FF(f)i FQ(=)14 b FF(f)629 926 y FH(\010)656 919 y FQ(,)i(w)o(e)g(get)687 1021 y FE(k)p FQ([)p FF(f)750 1028 y FH(\010)778 1021 y FQ(])p FE(k)817 1029 y FD(C)r FH(\(\012\))p FD(=)p Fy(I)966 1021 y FE(\025)27 b(k)p FQ([\010])p FE(k)1145 1030 y Fy(B)1169 1020 y Fr(0)1185 1030 y FD(=)p Fy(J)1249 1021 y FF(:)490 b FQ(\(A)p FF(:)p FQ(49\))60 1123 y(This)16 b(pro)o(v)o(es)g(that) h(the)f(map)f([\010])e FE(7!)h FQ([)p FF(f)798 1130 y FH(\010)825 1123 y FQ(])i(is)g(an)h(isometry)d(of)j FE(B)1262 1105 y FH(0)1281 1123 y FF(=)p FE(J)25 b FQ(in)o(to)16 b FF(C)t FQ(\(\012\))p FF(=)p FE(I)t FQ(.)133 1184 y(Rep)q(eating)e(the)f(same)g(argumen)o(t)g(with) g FF(f)19 b FQ(replaced)13 b(b)o(y)g FF(f)f FQ(+)6 b FF(c)p FQ(,)13 b(and)h(then)g(optimizing)e(o)o(v)o(er)g FF(c)p FQ(,)60 1244 y(w)o(e)e(conclude)h(that)g([\010])i FE(7!)h FQ([)p FF(f)600 1251 y FH(\010)627 1244 y FQ(])c(is)h(also)h(an)f(isometry)e(of)i FE(B)1129 1226 y FH(0)1148 1244 y FF(=)p FQ(\()p FE(J)f FQ(+)p FP(Const)p FQ(\))h(in)o(to)f FF(C)t FQ(\(\012\))p FF(=)p FQ(\()p FE(I)t FQ(+)p FF(const)p FQ(\).)p 178 1308 25 34 v 60 1500 a Fd(Pr)o(oof)18 b(of)g(Pr)o(oposition)f(2.44.)133 1560 y FQ(\(a\))g(is)f (easy)g(and)h(w)o(ell)e(kno)o(wn:)21 b(see)16 b([206)q(,)g(p.)g(9].)133 1620 y(\(d\))g(By)g(de\014nition)g(w)o(e)g(ha)o(v)o(e)774 1681 y FF(H)818 1660 y FH(\010)814 1693 y(\003)p FD(;f)t(r)q(ee)949 1681 y FQ(=)1027 1639 y Fx(X)1015 1731 y FD(X)s Fy(\032)p FH(\003)1107 1681 y FQ(\010)1142 1688 y FD(X)1753 1681 y FQ(\(A)p FF(:)p FQ(50\))60 1800 y(and)631 1860 y Fx(X)627 1952 y FD(x)p Fy(2)p FH(\003)704 1902 y FF(T)733 1909 y FD(x)754 1902 y FF(f)778 1909 y FH(\010)847 1902 y FQ(=)931 1860 y Fx(X)927 1952 y FD(x)p Fy(2)p FH(\003)1009 1860 y Fx(X)1003 1952 y FD(X)s Fy(3)p FH(0)1084 1902 y FE(j)p FF(X)t FE(j)1156 1881 y Fy(\000)p FH(1)1203 1902 y FF(T)1232 1909 y FD(x)1254 1902 y FQ(\010)1289 1909 y FD(X)847 2021 y FQ(=)931 1979 y Fx(X)927 2071 y FD(x)p Fy(2)p FH(\003)1009 1979 y Fx(X)1003 2071 y FD(X)s Fy(3)p FH(0)1084 2021 y FE(j)p FF(X)t FE(j)1156 2000 y Fy(\000)p FH(1)1203 2021 y FQ(\010)1238 2028 y FD(X)s FH(+)p FD(x)847 2139 y FQ(=)931 2098 y Fx(X)927 2190 y FD(x)p Fy(2)p FH(\003)1009 2098 y Fx(X)1003 2190 y FD(Y)8 b Fy(3)p FD(x)1083 2139 y FE(j)p FF(Y)j FE(j)1150 2119 y Fy(\000)p FH(1)1197 2139 y FQ(\010)1232 2146 y FD(Y)847 2284 y FQ(=)927 2242 y Fx(X)943 2334 y FD(Y)1000 2250 y FE(j)p FF(Y)22 b FE(\\)11 b FQ(\003)p FE(j)p 1000 2272 157 2 v 1045 2318 a(j)p FF(Y)f FE(j)1161 2284 y FQ(\010)1196 2291 y FD(Y)1753 2284 y FQ(\(A.51\))60 2422 y(\(the)16 b(double)g(sum)f(is)h(absolutely)g(con)o(v)o(ergen)o(t)f(and) i(hence)f(can)g(b)q(e)g(rearranged)h(freely\).)j(Th)o(us)454 2551 y FF(H)498 2531 y FH(\010)494 2564 y(\003)p FD(;f)t(r)q(ee)612 2551 y FE(\000)665 2510 y Fx(X)661 2602 y FD(x)p Fy(2)p FH(\003)738 2551 y FF(T)767 2558 y FD(x)788 2551 y FF(f)812 2558 y FH(\010)867 2551 y FQ(=)28 b FE(\000)1070 2510 y Fx(X)1009 2613 y FD(X)10 b Fy(\\)e FH(\003)i Fy(6)p FH(=)g Fq(?)1001 2660 y FD(X)g Fy(\\)e FH(\003)1096 2648 y Fs(c)1122 2660 y Fy(6)p FH(=)i Fq(?)1234 2518 y FE(j)p FF(X)15 b FE(\\)c FQ(\003)p FE(j)p 1234 2540 162 2 v 1278 2585 a(j)p FF(X)t FE(j)1400 2551 y FQ(\010)1435 2558 y FD(X)1483 2551 y FF(:)256 b FQ(\(A)p FF(:)p FQ(52\))938 2784 y(190)p eop %%Page: 191 191 bop 60 91 a FQ(T)l(aking)17 b(norms,)e(w)o(e)h(ha)o(v)o(e)338 226 y FE(k)p FF(H)407 205 y FH(\010)403 238 y(\003)p FD(;f)t(r)q(ee)521 226 y FE(\000)575 185 y Fx(X)571 276 y FD(x)p Fy(2)p FH(\003)647 226 y FF(T)676 233 y FD(x)698 226 y FF(f)722 233 y FH(\010)749 226 y FE(k)774 233 y Fy(1)853 226 y FE(\024)1023 185 y Fx(X)962 288 y FD(X)10 b Fy(\\)e FH(\003)i Fy(6)p FH(=)g Fq(?)954 334 y FD(X)g Fy(\\)e FH(\003)1049 323 y Fs(c)1075 334 y Fy(6)p FH(=)i Fq(?)1187 192 y FE(j)p FF(X)15 b FE(\\)d FQ(\003)p FE(j)p 1187 214 162 2 v 1232 260 a(j)p FF(X)t FE(j)1353 226 y(k)p FQ(\010)1413 233 y FD(X)1447 226 y FE(k)1472 233 y Fy(1)853 413 y FQ(=)937 372 y Fx(X)933 464 y FD(x)p Fy(2)p FH(\003)1100 372 y Fx(X)1082 471 y FD(X)h Fy(3)c FD(x)1030 517 y(X)i Fy(\\)c FH(\003)1125 506 y Fs(c)1151 517 y Fy(6)p FH(=)j Fq(?)1258 413 y FE(j)p FF(X)t FE(j)1330 393 y Fy(\000)p FH(1)1377 413 y FE(k)p FQ(\010)1437 420 y FD(X)1471 413 y FE(k)1496 420 y Fy(1)853 596 y FQ(=)937 555 y Fx(X)933 647 y FD(x)p Fy(2)p FH(\003)1143 555 y Fx(X)1129 654 y FD(Y)18 b Fy(3)9 b FH(0)1030 700 y(\()p FD(Y)16 b FH(+)8 b FD(x)p FH(\))g Fy(\\)f FH(\003)1212 689 y Fs(c)1238 700 y Fy(6)p FH(=)j Fq(?)1345 596 y FE(j)p FF(Y)h FE(j)1412 576 y Fy(\000)p FH(1)1459 596 y FE(k)p FQ(\010)1519 603 y FD(Y)1550 596 y FE(k)1575 603 y Fy(1)853 805 y FQ(=)938 763 y Fx(X)933 855 y FD(Y)d Fy(3)p FH(0)1016 771 y FE(j)p FQ(\(\003)1083 753 y FD(c)1111 771 y FE(\000)j FF(Y)g FQ(\))g FE(\\)g FQ(\003)p FE(j)p 1016 793 307 2 v 1135 839 a(j)p FF(Y)g FE(j)1327 805 y(k)p FQ(\010)1387 812 y FD(Y)1417 805 y FE(k)1442 812 y Fy(1)1753 805 y FQ(\(A.53\))60 953 y(No)o(w)16 b(divide)f(b)o(y)h FE(j)p FQ(\003)p FE(j)p FQ(:)345 1090 y FE(j)p FQ(\003)p FE(j)407 1070 y Fy(\000)p FH(1)454 1090 y FE(k)p FF(H)523 1070 y FH(\010)519 1102 y(\003)p FD(;f)t(r)q(ee)637 1090 y FE(\000)690 1049 y Fx(X)686 1140 y FD(x)p Fy(2)p FH(\003)763 1090 y FF(T)792 1097 y FD(x)813 1090 y FF(f)837 1097 y FH(\010)865 1090 y FE(k)890 1097 y Fy(1)955 1090 y FE(\024)1026 1049 y Fx(X)1021 1140 y FD(Y)8 b Fy(3)p FH(0)1104 1056 y FE(j)p FQ(\(\003)1171 1038 y FD(c)1199 1056 y FE(\000)j FF(Y)g FQ(\))g FE(\\)g FQ(\003)p FE(j)p 1104 1078 V 1226 1124 a(j)p FQ(\003)p FE(j)1420 1056 y(k)p FQ(\010)1480 1063 y FD(Y)1510 1056 y FE(k)1535 1063 y Fy(1)p 1420 1078 153 2 v 1463 1124 a FE(j)p FF(Y)g FE(j)1591 1090 y FF(:)148 b FQ(\(A)p FF(:)p FQ(54\))60 1240 y(This)17 b(sum)f(is)h(dominated)f(uniformly)f(in)i(\003,)g(since)f FE(j)p FQ(\(\003)1101 1222 y FD(c)1130 1240 y FE(\000)11 b FF(Y)g FQ(\))h FE(\\)f FQ(\003)p FE(j)p FF(=)p FE(j)p FQ(\003)p FE(j)k(\024)g FQ(1)j(and)f(\010)f FE(2)f(B)1768 1222 y FH(0)1787 1240 y FQ(.)24 b(On)60 1300 y(the)16 b(other)g(hand,)h(for)f(eac)o(h)g(\014xed)g(\014nite)g (set)g FF(Y)11 b FQ(,)16 b(w)o(e)g(ha)o(v)o(e)570 1401 y FE(j)p FQ(\(\003)637 1383 y FD(c)665 1401 y FE(\000)11 b FF(Y)g FQ(\))g FE(\\)g FQ(\003)p FE(j)p 570 1423 307 2 v 692 1469 a(j)p FQ(\003)p FE(j)922 1435 y(\024)1008 1394 y Fx(X)1002 1485 y FD(y)q Fy(2)p FD(Y)1086 1401 y FE(j)p FQ(\003)g FE(\\)g FQ(\(\003)1242 1383 y FD(c)1270 1401 y FE(\000)g FF(y)r FQ(\))p FE(j)p 1086 1423 293 2 v 1202 1469 a(j)p FQ(\003)p FE(j)923 1584 y FQ(=)1008 1542 y Fx(X)1002 1634 y FD(y)q Fy(2)p FD(Y)1086 1550 y FE(j)p FQ(\003)g FE(n)g FQ(\(\003)g FE(\000)g FF(y)r FQ(\))p FE(j)p 1086 1572 267 2 v 1189 1618 a(j)p FQ(\003)p FE(j)1372 1584 y FF(;)367 b FQ(\(A.55\))60 1736 y(whic)o(h)20 b(tends)i(to)f(zero)g(as)h (\003)g FE(\045)g(1)f FQ(\(v)m(an)g(Ho)o(v)o(e\).)35 b(Hence,)20 b(b)o(y)h(the)g(dominated)f(con)o(v)o(ergence)60 1796 y(theorem,)14 b(\(A.54\))i(tends)h(to)f(zero)g(as)h(\003)d FE(\045)f(1)k FQ(\(v)m(an)f(Ho)o(v)o(e\).)133 1856 y(\(b\))g(and)h(\(c\))f(are)g(immedi)o (ate)e(consequences)h(of)i(\(d\))f(together)g(with)g(Prop)q(ositions)i(A.8)d (and)60 1917 y(A.11.)p 312 1921 25 34 v 133 2027 a FM(Remark.)j FQ(See)10 b([313)q(,)i(p.)f(41])h(for)f(an)h(alternate)f(pro)q(of)i(of)e (\(c\),)h(carried)f(out)h(\014rst)f(for)h(\010)i FE(2)g(B)1809 2034 y Fk(\014nite)60 2087 y FQ(and)j(then)f(extended)f(to)i FE(B)568 2069 y FH(0)603 2087 y FQ(b)o(y)f(densit)o(y)l(.)60 2247 y Fd(Pr)o(oof)i(of)g(Pr)o(oposition)f(2.45.)133 2307 y FQ(\(a\))g(is)f(easy)g(and)h(w)o(ell)e(kno)o(wn:)21 b(see)16 b([206)q(,)g(p.)g(14])g(or)h([157,)f(p.)g(29].)133 2367 y(\(d\))g(By)g (de\014nition,)508 2477 y FF(H)552 2456 y FH(\010)548 2489 y(\003)591 2477 y FE(\000)11 b FF(H)685 2456 y FH(\010)681 2489 y(\003)p FD(;f)t(r)q(ee)815 2477 y FQ(=)28 b FF(W)934 2456 y FH(\010)927 2489 y(\003)p FD(;)p FH(\003)985 2480 y Fs(c)1031 2477 y FQ(=)1187 2435 y Fx(X)1126 2539 y FD(X)10 b Fy(\\)e FH(\003)i Fy(6)p FH(=)g Fq(?)1118 2585 y FD(X)g Fy(\\)e FH(\003)1213 2574 y Fs(c)1239 2585 y Fy(6)p FH(=)i Fq(?)1346 2477 y FQ(\010)1381 2484 y FD(X)1429 2477 y FF(:)310 b FQ(\(A)p FF(:)p FQ(56\))938 2784 y(191)p eop %%Page: 192 192 bop 60 91 a FQ(T)l(aking)17 b(norms,)e(w)o(e)h(ha)o(v)o(e)445 201 y FE(k)p FF(H)514 181 y FH(\010)510 214 y(\003)552 201 y FE(\000)11 b FF(H)646 181 y FH(\010)642 214 y(\003)p FD(;f)t(r)q(ee)749 201 y FE(k)774 208 y Fy(1)853 201 y FE(\024)1023 160 y Fx(X)962 263 y FD(X)f Fy(\\)e FH(\003)i Fy(6)p FH(=)g Fq(?)954 310 y FD(X)g Fy(\\)e FH(\003)1049 298 y Fs(c)1075 310 y Fy(6)p FH(=)i Fq(?)1182 201 y FE(k)p FQ(\010)1242 208 y FD(X)1276 201 y FE(k)1301 208 y Fy(1)853 389 y FE(\024)937 347 y Fx(X)933 439 y FD(x)p Fy(2)p FH(\003)1100 347 y Fx(X)1082 446 y FD(X)j Fy(3)c FD(x)1030 493 y(X)i Fy(\\)c FH(\003)1125 481 y Fs(c)1151 493 y Fy(6)p FH(=)j Fq(?)1258 389 y FE(k)p FQ(\010)1318 396 y FD(X)1352 389 y FE(k)1377 396 y Fy(1)853 572 y FQ(=)937 530 y Fx(X)933 622 y FD(x)p Fy(2)p FH(\003)1143 530 y Fx(X)1129 629 y FD(Y)18 b Fy(3)9 b FH(0)1030 676 y(\()p FD(Y)16 b FH(+)8 b FD(x)p FH(\))g Fy(\\)f FH(\003)1212 664 y Fs(c)1238 676 y Fy(6)p FH(=)k Fq(?)1345 572 y FE(k)p FQ(\010)1405 579 y FD(Y)1436 572 y FE(k)1461 579 y Fy(1)853 755 y FQ(=)938 713 y Fx(X)933 805 y FD(Y)d Fy(3)p FH(0)1011 755 y FE(j)p FQ(\(\003)1078 734 y FD(c)1106 755 y FE(\000)j FF(Y)g FQ(\))g FE(\\)g FQ(\003)p FE(j)d(k)p FQ(\010)1385 762 y FD(Y)1416 755 y FE(k)1441 762 y Fy(1)1492 755 y FF(:)247 b FQ(\(A.57\))60 900 y(The)25 b(remainder)d(of)j(the)g(argumen)o(t)e(is)i (completely)d(parallel)i(to)h(the)f(pro)q(of)i(of)f(Prop)q(osition)60 960 y(2.44\(d\),)17 b(but)f(using)h(\010)d FE(2)g(B)590 942 y FH(1)625 960 y FQ(rather)i(than)h(\010)d FE(2)g(B)1016 942 y FH(0)1035 960 y FQ(.)21 b(This)c(pro)o(v)o(es)e(\(2.62a\).)133 1020 y(As)i(for)g(\(2.62b\),)g(the)f(leftmost)f(term)g(is)h FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))h(as)g(an)g(immediate)c (consequence)j(of)h(\(2.62a\))60 1080 y(and)g(\(2.58\).)k(The)16 b(middle)e(term)g(is)i(pro)o(v)o(en)g(to)g(b)q(e)g FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))g(in)g([157,)g(pp.)g(320{321].)23 b(\(That)17 b(pro)q(of)60 1141 y(is)f(stated)h(only)f(for)g(cub)q(es,)g(but)h (it)e(is)h(v)m(alid)g(for)h(arbitrary)f(v)m(an)h(Ho)o(v)o(e)e(sequences.\)) 133 1201 y(\(b\))23 b(is)g(then)g(an)h(imme)o(diate)c(consequence)i(of)i (\(2.62a\))g(and)f(\(2.56\).)43 b(\(c\))23 b(is)g(lik)o(ewise)e(an)60 1261 y(immedi)o(ate)13 b(consequence)j(of)g(\(2.62a\))i(and)e(\(2.57\).)p 1167 1265 25 34 v 60 1471 a Fd(Pr)o(oof)f(of)g(Pr)o(oposition)f(2.46.)68 b FQ(Let)13 b FF(\026)h FQ(b)q(e)g(a)f(Gibbs)h(measure)e(for)i(an)g(in)o (teraction)e(\010)i FE(2)g(B)1871 1452 y FH(1)60 1531 y FQ(and)j FP(a)g(priori)j FQ(measure)15 b FF(\026)558 1513 y FH(0)578 1531 y FQ(.)21 b(Then)c(the)f(DLR)h(equation)f(\(2.22\))h(states)g(that)407 1632 y FF(d\026)461 1639 y FH(\003)p 407 1654 82 2 v 407 1700 a FF(d\026)461 1682 y FH(0)461 1712 y(\003)493 1665 y FQ(\()p FF(!)542 1672 y FH(\003)569 1665 y FQ(\))28 b(=)681 1607 y Fx(Z)731 1665 y FF(d\026)p FQ(\()p FF(\034)6 b FQ(\))i FF(Z)895 1645 y FH(\010)891 1678 y(\003)923 1665 y FQ(\()p FF(\034)963 1672 y FH(\003)987 1663 y Fs(c)1006 1665 y FQ(\))1025 1645 y Fy(\000)p FH(1)1089 1665 y FQ(exp)o([)p FE(\000)p FF(H)1260 1645 y FH(\010)1256 1678 y(\003)1288 1665 y FQ(\()p FF(!)1337 1672 y FH(\003)1374 1665 y FE(\002)j FF(\034)1445 1672 y FH(\003)1469 1663 y Fs(c)1488 1665 y FQ(\)])i FF(;)205 b FQ(\(A)p FF(:)p FQ(58\))60 1800 y(where)461 1861 y FF(Z)498 1840 y FH(\010)494 1873 y(\003)526 1861 y FQ(\()p FF(\034)566 1868 y FH(\003)590 1859 y Fs(c)608 1861 y FQ(\))28 b(=)720 1802 y Fx(Z)770 1861 y FQ(exp[)p FE(\000)p FF(H)942 1840 y FH(\010)938 1873 y(\003)969 1861 y FQ(\()p FF(!)1018 1868 y FH(\003)1056 1861 y FE(\002)11 b FF(\034)1127 1868 y FH(\003)1151 1859 y Fs(c)1169 1861 y FQ(\)])1226 1819 y Fx(Y)1219 1911 y FD(x)p Fy(2)p FH(\003)1295 1861 y FF(d\026)1349 1840 y FH(0)1349 1873 y FD(x)1371 1861 y FQ(\()p FF(!)1420 1868 y FD(x)1443 1861 y FQ(\))i FF(:)264 b FQ(\(A)p FF(:)p FQ(59\))60 1989 y(No)o(w,)15 b(b)o(y)f(Prop)q(osition)i (2.45\(d\),)g(w)o(e)e(can)i(replace)e FF(H)1059 1971 y FH(\010)1055 2001 y(\003)1087 1989 y FQ(\()p FF(!)1136 1996 y FH(\003)1171 1989 y FE(\002)8 b FF(\034)1239 1996 y FH(\003)1263 1987 y Fs(c)1282 1989 y FQ(\))15 b(ev)o(erywhere)e(b)o(y)i FF(H)1679 1971 y FH(\010)1675 2001 y(\003)p FD(;f)t(r)q(ee)1782 1989 y FQ(\()p FF(!)1831 1996 y FH(\003)1857 1989 y FQ(\),)60 2049 y(incurring)h(an)g(error)h(whic)o(h)e(is)h FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))g(uniformly)f(in)g FF(!)k FQ(and)e FF(\034)6 b FQ(.)21 b(Therefore,)495 2116 y Fx(\015)495 2141 y(\015)495 2165 y(\015)495 2190 y(\015)495 2215 y(\015)518 2190 y FQ(log)594 2157 y FF(d\026)648 2164 y FH(\003)p 594 2179 V 594 2225 a FF(d\026)648 2207 y FH(0)648 2237 y(\003)691 2190 y FQ(+)11 b FF(H)784 2170 y FH(\010)780 2203 y(\003)p FD(;f)t(r)q(ee)898 2190 y FQ(+)g(log)f FF(Z)1056 2170 y FH(\010)1052 2203 y(\003)p FD(;f)t(r)q(ee)1159 2116 y Fx(\015)1159 2141 y(\015)1159 2165 y(\015)1159 2190 y(\015)1159 2215 y(\015)1182 2242 y Fy(1)1247 2190 y FE(\024)27 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))14 b FF(:)289 b FQ(\(A)p FF(:)p FQ(60\))60 2337 y(But)10 b FE(k)p FF(H)220 2319 y FH(\010)216 2349 y(\003)p FD(;f)t(r)q(ee)323 2337 y FE(\000)362 2304 y Fx(P)406 2347 y FD(x)p Fy(2)p FH(\003)484 2337 y FF(T)513 2344 y FD(x)535 2337 y FF(f)559 2344 y FH(\010)586 2337 y FE(k)611 2344 y Fy(1)662 2337 y FE(\024)k FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))d(b)o(y)f(Prop)q(osition)i(2.44\(c\),)g(and)f FE(j)d FQ(log)i FF(Z)1560 2319 y FH(\010)1556 2349 y(\003)p FD(;f)t(r)q(ee)1663 2337 y FE(\000j)p FQ(\003)p FE(j)p FF(p)p FQ(\(\010)p FE(j)p FF(\026)1885 2319 y FH(0)1905 2337 y FQ(\))p FE(j)j(\024)60 2397 y FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))j(b)o(y)g(Prop)q(osition)h(2.58\(a\).)23 b(Hence)474 2464 y Fx(\015)474 2489 y(\015)474 2513 y(\015)474 2538 y(\015)474 2563 y(\015)497 2538 y FQ(log)573 2505 y FF(d\026)627 2512 y FH(\003)p 573 2527 V 573 2572 a FF(d\026)627 2555 y FH(0)627 2585 y(\003)670 2538 y FQ(+)723 2497 y Fx(X)719 2589 y FD(x)p Fy(2)p FH(\003)796 2538 y FF(T)825 2545 y FD(x)846 2538 y FF(f)870 2545 y FH(\010)909 2538 y FQ(+)11 b FE(j)p FQ(\003)p FE(j)p FF(p)p FQ(\(\010)p FE(j)p FF(\026)1141 2518 y FH(0)1161 2538 y FQ(\))1180 2464 y Fx(\015)1180 2489 y(\015)1180 2513 y(\015)1180 2538 y(\015)1180 2563 y(\015)1203 2597 y Fy(1)1268 2538 y FE(\024)27 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))14 b FF(:)268 b FQ(\(A)p FF(:)p FQ(61\))938 2784 y(192)p eop %%Page: 193 193 bop 60 91 a FQ(In)16 b(particular,)542 105 y Fx(\015)542 130 y(\015)542 155 y(\015)542 180 y(\015)542 205 y(\015)565 180 y FQ(log)641 146 y FF(d\026)695 153 y FH(\003)p 641 168 82 2 v 641 214 a FF(d\026)695 197 y FH(0)695 226 y(\003)739 180 y FQ(+)792 138 y Fx(X)788 230 y FD(x)p Fy(2)p FH(\003)864 180 y FF(T)893 187 y FD(x)914 180 y FF(f)938 187 y FH(\010)966 105 y Fx(\015)966 130 y(\015)966 155 y(\015)966 180 y(\015)966 205 y(\015)989 239 y FD(C)r FH(\(\012\))p FD(=const)1200 180 y FE(\024)27 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))14 b FF(:)336 b FQ(\(A)p FF(:)p FQ(62\))60 318 y(This)16 b(pro)o(v)o(es)g (\(2.63\).)22 b(This)16 b(b)q(ound)i(is)e(uniform)f(for)h(all)g FF(\026)e FE(2)g(G)s FQ(\(\005)1297 300 y FH(\010)1324 318 y FQ(\).)133 378 y(No)o(w)20 b(let)g FF(\026)352 385 y FH(1)392 378 y FQ(\(resp.)g FF(\026)561 385 y FH(2)581 378 y FQ(\))g(b)q(e)h(Gibbsian) f(for)h(in)o(teractions)e(\010)1283 385 y FH(1)1323 378 y FQ(\(resp.)h(\010) 1498 385 y FH(2)1518 378 y FQ(\))g(in)g FE(B)1653 360 y FH(1)1672 378 y FQ(,)h(with)f(the)60 438 y(same)15 b FP(a)j(priori)i FQ(measure)15 b FF(\026)586 420 y FH(0)606 438 y FQ(.)21 b(Com)o(bining)15 b(\(A.61\))h(for)g(the)g(t)o(w)o(o)h(cases,)f(w)o(e)f(get)151 502 y Fx(\015)151 527 y(\015)151 552 y(\015)151 577 y(\015)151 602 y(\015)174 577 y FQ(log)250 543 y FF(d\026)304 550 y FH(1\003)p 250 565 99 2 v 250 611 a FF(d\026)304 618 y FH(2\003)354 502 y Fx(\015)354 527 y(\015)354 552 y(\015)354 577 y(\015)354 602 y(\015)377 629 y Fy(1)442 577 y FQ(=)508 502 y Fx(\015)508 527 y(\015)508 552 y(\015)508 577 y(\015)508 602 y(\015)535 535 y(X)531 627 y FD(x)p Fy(2)p FH(\003)607 577 y FF(T)636 584 y FD(x)657 577 y FF(f)681 584 y FH(\010)706 589 y Fr(1)724 584 y Fy(\000)p FH(\010)776 589 y Fr(2)816 577 y FQ(+)k FE(j)p FQ(\003)p FE(j)p FQ([)p FF(p)p FQ(\(\010)1027 584 y FH(1)1047 577 y FE(j)p FF(\026)1090 556 y FH(0)1110 577 y FQ(\))11 b FE(\000)f FF(p)p FQ(\(\010)1267 584 y FH(2)1288 577 y FE(j)p FF(\026)1331 556 y FH(0)1351 577 y FQ(\)])1384 502 y Fx(\015)1384 527 y(\015)1384 552 y(\015)1384 577 y(\015)1384 602 y(\015)1406 635 y Fy(1)1463 577 y FQ(+)19 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))14 b FF(:)82 b FQ(\(A)p FF(:)p FQ(63\))60 721 y(But)467 725 y Fx(\015)467 750 y(\015)467 775 y(\015)467 800 y(\015)467 825 y(\015)494 758 y(X)490 850 y FD(x)p Fy(2)p FH(\003)567 800 y FF(T)596 807 y FD(x)617 800 y FF(f)641 807 y FH(\010)666 812 y Fr(1)684 807 y Fy(\000)p FH(\010)736 812 y Fr(2)756 725 y Fx(\015)756 750 y(\015)756 775 y(\015)756 800 y(\015)756 825 y(\015)779 858 y Fy(1)844 800 y FQ(=)28 b FE(j)p FQ(\003)p FE(j)8 b(k)p FQ(\010)1040 807 y FH(1)1071 800 y FE(\000)i FQ(\010)1155 807 y FH(2)1175 800 y FE(k)1200 808 y Fy(B)1224 799 y Fr(0)1242 808 y FD(=)p Fy(J)1311 800 y FQ(+)19 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))262 b(\(A)p FF(:)p FQ(64\))60 923 y(b)o(y)16 b(Prop)q(ositions)h(A.8)f(and)h(A.11,)f(while)552 981 y Fx(\014)552 1006 y(\014)552 1031 y(\014)p FF(p)p FQ(\(\010)644 1038 y FH(1)664 1031 y FE(j)p FF(\026)707 1010 y FH(0)727 1031 y FQ(\))11 b FE(\000)g FF(p)p FQ(\(\010)885 1038 y FH(2)905 1031 y FE(j)p FF(\026)948 1010 y FH(0)968 1031 y FQ(\))987 981 y Fx(\014)987 1006 y(\014)987 1031 y(\014)27 b FE(\024)h(k)p FQ(\010)1155 1038 y FH(1)1186 1031 y FE(\000)11 b FQ(\010)1271 1038 y FH(2)1291 1031 y FE(k)1316 1039 y Fy(B)1340 1030 y Fr(0)1357 1039 y FD(=)p Fy(J)1753 1031 y FQ(\(A)p FF(:)p FQ(65\))60 1144 y(b)o(y)16 b(Prop)q(ositions)h(2.56\(d,e\))g(and)f(2.58\(a\).)23 b(Hence)484 1208 y Fx(\015)484 1233 y(\015)484 1258 y(\015)484 1283 y(\015)484 1308 y(\015)507 1283 y FQ(log)583 1249 y FF(d\026)637 1256 y FH(1\003)p 583 1271 V 583 1317 a FF(d\026)637 1324 y FH(2\003)687 1208 y Fx(\015)687 1233 y(\015)687 1258 y(\015)687 1283 y(\015)687 1308 y(\015)710 1335 y Fy(1)775 1283 y FE(\024)28 b FQ(2)p FE(j)p FQ(\003)p FE(j)8 b(k)p FQ(\010)996 1290 y FH(1)1027 1283 y FE(\000)j FQ(\010)1112 1290 y FH(2)1131 1283 y FE(k)1156 1291 y Fy(B)1180 1282 y Fr(0)1198 1291 y FD(=)p Fy(J)1267 1283 y FQ(+)19 b FF(o)p FQ(\()p FE(j)p FQ(\003)p FE(j)p FQ(\))14 b FF(:)278 b FQ(\(A)p FF(:)p FQ(66\))60 1424 y(But)16 b(b)o(y)f(Prop)q (ositions)j(2.56\(c\))e(and)h(2.58\(a\),)f(the)g(righ)o(t-hand)h(side)e(of)i (\(A.63\))e(is)h(unc)o(hanged)h(if)60 1484 y(w)o(e)g(replace)f(\010)334 1491 y FH(1)371 1484 y FQ(b)o(y)g(\010)474 1491 y FH(1)506 1484 y FQ(+)11 b(\011)17 b(with)g(\011)e FE(2)g FP(Const)i FQ(\(i.e.)f(if)g FF(f)1131 1491 y FH(\011)1176 1484 y FE(2)f FF(const)p FQ(\).)24 b(Th)o(us,)17 b(in)f(\(A.66\))h(w)o(e)g(can)60 1544 y(replace)e(the)h FE(B)344 1526 y FH(0)363 1544 y FF(=)p FE(J)26 b FQ(norm)15 b(b)o(y)h FE(B)677 1526 y FH(0)696 1544 y FF(=)p FQ(\()p FE(J)k FQ(+)11 b FP(Const)q FQ(\).)21 b(This)16 b(pro)o(v)o(es)g(\(2.64\).)133 1604 y(In)c(a)h(similar)e(w)o(a)o(y)h(w)o(e)g (deduce)g(\(2.65\))h(from)f(the)g(t)o(w)o(o)g(cases)h(of)g(\(A.61\))g (together)f(with)h(\(A.64\).)p 178 1669 25 34 v 133 1773 a FM(Remarks.)25 b FQ(1.)i(W)l(e)17 b(wish)h(to)h(emphasize)d(that)i(\(2.65\))h (is)f(an)g FP(e)n(quality)t FQ(.)28 b(This)18 b(fact)g(pla)o(ys)g(a)60 1833 y(crucial)d(role)h(in)g(our)h(pro)q(of)g(of)g(the)f(Second)g(F)l (undamen)o(tal)e(Theorem)h(\(Section)h(3.3\).)133 1893 y(2.)39 b(The)22 b(pro)q(ofs)h(of)f(Prop)q(ositions)i(2.56)f(and)f(2.58)h(do)f(not)h (use)f(these)f(estimates,)h(so)g(the)60 1954 y(reasoning)17 b(is)f(not)h(circular.)60 2098 y FB(A.4)69 b(Pro)r(ofs)24 b(and)g(References) d(for)i(Section)f(2.5)60 2190 y FQ(Prop)q(osition)17 b(2.51)g(is)f(easy)h(to) f(pro)o(v)o(e:)21 b(see)16 b(e.g.)f([206)q(,)h(Lemma)e(I.2.2].)60 2299 y Fd(Pr)o(oof)k(of)g(Pr)o(oposition)f(2.53.)133 2359 y FQ(\(a\),)f(\(b\),)g(\(c\))g(and)h(\(g\))f(are)h(pro)o(v)o(en)e(in)h([157)q (,)g(Prop)q(osition)h(15.5].)133 2419 y(\(d\))f(is)g(a)h(trivial)e (generalization)h(of)g(what)h(is)f(pro)o(v)o(en)g(in)g([157,)g(Prop)q (osition)i(15.14\(1\)].)133 2479 y(\(e\))23 b(is)h(pro)o(v)o(en)f(for)g(the)h (b)q(ounded)g(measurable)f(top)q(ology)h(in)g([157,)h(Corollary)f(15.7)g(and) 60 2539 y(pro)q(of)e(of)f(Prop)q(osition)g(15.14\(2\)].)36 b(F)l(or)20 b(the)h(w)o(eak)f(top)q(ology)l(,)j(see)d([206)q(,)h(pp.)f (42{43];)k(though)60 2600 y(stated)15 b(there)e(for)i(compact)e(metric)e (spaces,)k(the)f(pro)q(of)h(is)f(in)g(fact)g(v)m(alid)g(for)g(arbitrary)g (complete)60 2660 y(separable)i(metric)e(spaces.)22 b(See)15 b(also)i([157)q(,)f(p.)g(316].)938 2784 y(193)p eop %%Page: 194 194 bop 133 91 a FQ(\(f)s(\))21 b(W)l(e)g(kno)o(w)g(from)e(part)j(\(e\))e(that)h FE(f)p FF(\026)p FQ(:)30 b FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))21 b FE(\024)h FF(c)p FE(g)e FQ(is)h(closed)f(in)h(the)f(b)q (ounded)i(mea-)60 152 y(surable)g(top)q(ology)l(.)40 b(In)22 b([157)q(,)h(pro)q(of)g(of)f(Prop)q(osition)i(15.6])e(it)g(is)g(sho)o(wn)g (that)h(the)f(densities)60 212 y FE(f)p FF(d\026=d\027)s FQ(:)30 b FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))20 b FE(\024)g FF(c)p FE(g)g FQ(are)g(uniformly)f FF(\027)s FQ(-in)o(tegrable)g(\(see)h (also)h([73,)f(Theorem)f(I)q(I{22]\);)j(this)60 272 y(implies,)d(b)o(y)h(the) g(Dunford-P)o(ettis)h(theorem,)f(that)h FE(f)p FF(\026)p FQ(:)29 b FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))21 b FE(\024)g FF(c)p FE(g)g FQ(is)f(relativ)o(ely)e(compact)60 332 y(and)i(relativ)o(ely)c (sequen)o(tially)h(compact)h(in)h(the)g(b)q(ounded)h(measurable)d(top)q (ology)k(\([73,)e(Theo-)60 392 y(rem)c(I)q(I{25])i(or)h([272,)f(Prop)q (osition)h(IV{2{3]\).)23 b(Since)16 b(the)h(w)o(eak)f(top)q(ology)i(is)f(w)o (eak)o(er)f(than)h(the)60 452 y(b)q(ounded)g(measurable)e(top)q(ology)l(,)i (the)f(last)h(statemen)o(t)d(is)i(an)h(imme)o(diate)c(consequence.)133 513 y(\(h\))j(is)g(pro)o(v)o(en)g(in)g([102)q(,)f(Theorem)g(2.1)i(and)g (Lemma)d(2.3].)133 573 y(\(i\))h(is)f(an)i(abstraction)g(of)f(the)g(usual)g (statemen)o(t)e(of)i(strong)h(sup)q(eradditivit)o(y)e([157)q(,)h(Prop)q(osi-) 60 633 y(tion)h(15.10].)p 438 637 25 34 v 133 743 a FM(Remarks.)22 b FQ(1.)j(Statemen)o(t)16 b(\(d\))h(is)g FP(not)23 b FQ(true)17 b(join)o(tly)f(in)h FF(\026)g FQ(and)h FF(\027)s FQ(.)25 b(Coun)o (terexample:)c(Let)60 803 y(\012)14 b(=)g FE(f)p FF(a;)8 b(b)p FE(g)p FQ(,)15 b FF(\026)338 810 y FH(1)372 803 y FQ(=)f FF(\027)448 810 y FH(2)481 803 y FQ(=)g FF(\016)555 810 y FD(a)576 803 y FQ(,)i FF(\026)635 810 y FH(2)669 803 y FQ(=)d FF(\027)744 810 y FH(1)778 803 y FQ(=)h FF(\016)852 810 y FD(b)869 803 y FQ(,)i FF(\025)927 810 y FH(1)961 803 y FQ(=)e FF(\025)1041 810 y FH(2)1075 803 y FQ(=)1132 784 y FH(1)p 1132 792 18 2 v 1132 820 a(2)1154 803 y FQ(.)22 b(Then)16 b FF(I)t FQ(\()p FF(\026)1391 810 y FH(1)1410 803 y FE(j)p FF(\027)1448 810 y FH(1)1468 803 y FQ(\))e(=)g FF(I)t FQ(\()p FF(\026)1627 810 y FH(2)1646 803 y FE(j)p FF(\027)1684 810 y FH(2)1704 803 y FQ(\))g(=)g(+)p FE(1)p FQ(,)60 863 y(while)h FF(I)t FQ(\()237 844 y FH(1)p 237 852 V 237 881 a(2)259 863 y FF(\026)288 870 y FH(1)319 863 y FQ(+)373 844 y FH(1)p 373 852 V 373 881 a(2)396 863 y FF(\026)425 870 y FH(2)445 863 y FE(j)464 844 y FH(1)p 464 852 V 464 881 a(2)487 863 y FF(\027)511 870 y FH(1)541 863 y FQ(+)595 844 y FH(1)p 595 852 V 595 881 a(2)618 863 y FF(\027)642 870 y FH(2)662 863 y FQ(\))f(=)f(0.)133 924 y(2.)22 b(F)l(or)15 b(some)g(impro)o(v)o(em)o(e)o(n)o(ts)e(of)j(\(d\))f(if)g(the)g FF(\026)1003 931 y FD(i)1033 924 y FQ(ha)o(v)o(e)g(\\almost)g(disjoin)o(t")g (supp)q(orts,)i(see)e([26,)60 984 y(Prop)q(osition)i(5.1)g(and)g(Corollary)f (5.2])g(and)h([326)q(,)f(Theorem)f(2.1].)133 1044 y(3.)28 b(If)17 b(the)h FF(\033)r FQ(-\014eld)g(\006)g(is)g(coun)o(tably)g(generated,)h(then) f(the)g(set)g FE(f)p FF(\026)p FQ(:)25 b FF(I)t FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))17 b FE(\024)g FF(c)p FE(g)h FQ(is)g(in)g(fact)60 1104 y(compact)h FP(and)i(metrizable)j FQ(in)c(the)g(b)q(ounded)g(measurable) f(top)q(ology:)30 b(this)20 b(follo)o(ws)f(from)g([73,)60 1164 y(Theorem)c(I)q(I{24].)133 1225 y(4.)21 b(Additional)12 b(useful)h(prop)q (erties)g(of)h(the)f(relativ)o(e)f(en)o(trop)o(y)g(are)h(giv)o(en)g(in)g ([157,)h(Prop)q(osition)60 1285 y(15.6)j(and)g(Corollary)f(15.7].)133 1395 y(The)f(\014nite-v)o(olume)d(v)m(ariational)j(principle)e(\(Theorem)g (2.54\))j(is)e(w)o(ell)g(kno)o(wn:)20 b(see)15 b(e.g.)f([206,)60 1455 y(p.)i(46])g(or)h([99,)f(Lemma)e(2.1].)60 1599 y FB(A.5)69 b(Pro)r(ofs)24 b(and)g(References)d(for)i(Section)f(2.6)60 1692 y FM(A.5.1)56 b(The)18 b(In\014nite-V)-5 b(olume)16 b(Limit:)22 b(Pro)r(ofs)60 1834 y Fd(Pr)o(oof)d(of)h(Pr)o(oposition)f(2.56.)74 b FQ(F)l(or)18 b(all)f(but)h(part)g(\(e\),)g(see)f([206)q(,)g(Theorems)g (I.2.3)g(and)60 1894 y(I.2.4].)j(P)o(art)d(\(e\))f(is)g(an)g(immedi)o(ate)e (consequence)h(of)i(Prop)q(osition)g(2.34\(e\).)p 1637 1898 25 34 v 133 2004 a(Prop)q(osition)h(2.57)f(is)f([313)q(,)g(Prop)q(osition)h (4.4].)22 b(Prop)q(osition)17 b(2.58)g(is)f(an)h(immedi)o(ate)d(conse-)60 2064 y(quence)h(of)i(Prop)q(ositions)g(2.56)g(and)g(2.57)g(together)g(with)f (the)g(estimates)e(\(2.58\))j(and)g(\(2.62b\).)60 2174 y Fd(Pr)o(oof)c(of)h (Pr)o(oposition)f(2.59.)68 b FQ(When)12 b FF(\027)k FQ(is)c(a)g(pro)q(duct)h (measure,)e(this)h(is)h([157,)g(Corollary)60 2235 y(16.15\(b\)].)37 b(When)21 b FF(\027)j FQ(is)d(a)h(Gibbs)f(measure,)g(this)g(follo)o(ws)g (from)f(the)h(pro)q(duct-measure)g(case)60 2295 y(together)16 b(with)g(\(2.90\).)p 641 2299 V 60 2455 a Fd(Pr)o(oof)i(of)g(Pr)o(oposition)f (2.61.)133 2515 y FQ(The)e(existence)f(of)h(the)g(v)m(an)g(Ho)o(v)o(e)f (limit,)e(and)k(its)f(equalit)o(y)e(to)j(the)e(suprem)o(um,)e(b)q(oth)k (follo)o(w)60 2575 y(from)k(the)h(strong)h(sup)q(eradditivit)o(y)e(of)i FF(I)850 2582 y FH(\003)876 2575 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))g(as)g(a)f(function)g(of)h(\003,)g(when)f FF(\027)k FQ(is)c(a)g(pro)q(duct)60 2635 y(measure)11 b([Prop)q(osition)h(2.53\(i\)].) 20 b(One)12 b(w)o(a)o(y)f(to)h(see)g(this)g(is)g(to)g(note)g(that)g(strong)h (sup)q(eradditivit)o(y)938 2784 y(194)p eop %%Page: 195 195 bop 60 91 a FQ(implies)9 b(complete)h(sup)q(eradditivit)o(y)g(\(Lemma)g (A.2\);)i(the)f(claim)f(then)i(follo)o(ws)f(from)g(Prop)q(osition)60 152 y(A.3.)27 b(Alternativ)o(ely)l(,)16 b(one)i(can)h(mak)o(e)d(a)j(direct)f (argumen)o(t)f(using)i(the)f(strong)h(sup)q(eradditivit)o(y)60 212 y([206)q(,)d(Theorem)e(I)q(I.2.2].)133 272 y(The)h(a\016neness)g(is)f(an) i(imm)o(ediate)c(consequence)h(of)i(Prop)q(osition)h(2.53\(c,d\),)f(and)g (the)g(lo)o(w)o(er)60 332 y(semicon)o(tin)o(uit)n(y)8 b(is)j(an)g(imme)o (diate)d(consequence)i(of)h(Prop)q(osition)h(2.53\(e\))f(and)h(equation)e (\(2.93b\);)60 392 y(see)16 b([206)q(,)f(Theorem)g(I)q(I.2.3])h(or)g([157)q (,)g(Prop)q(osition)h(15.14].)133 452 y(The)f(pro)q(of)g(of)g(\(d\))f(emplo)o (ys)f(the)h(follo)o(wing)g(construction:)21 b(P)o(a)o(v)o(e)14 b Fq(Z)1414 432 y FD(d)1449 452 y FQ(b)o(y)h(a)h(cub)q(e)f FF(C)1705 459 y FD(n)1744 452 y FQ(and)h(its)60 513 y(disjoin)o(t)g (translates.)23 b(No)o(w,)16 b(giv)o(en)g(a)h(translation-in)o(v)m(arian)o(t) g(measure)e FF(\026)p FQ(,)h(let)g FF(\032)1568 520 y FD(n)1609 513 y FQ(b)q(e)g(a)h(measure)60 573 y(whic)o(h)f(equals)h FF(\026)g FQ(when)g(restricted)f(to)i(eac)o(h)e(of)h(these)g(cub)q(es,)g(and)h(in)e (whic)o(h)h(the)f(copies)h(of)g(the)60 633 y(spins)c(in)f(the)g(v)m(arious)h (cub)q(es)f(are)h FP(rigid)r(ly)k FQ(forced)12 b(to)h(b)q(e)g(equal.)19 b(Then)12 b(let)g FF(\026)1461 640 y FD(n)1499 633 y FQ(=)h FF(n)1579 615 y Fy(\000)p FD(d)1636 600 y Fx(P)1679 643 y FD(a)p Fy(2)p FD(C)1747 647 y Fs(n)1778 633 y FF(T)1807 640 y FD(a)1828 633 y FF(\032)1853 640 y FD(n)1876 633 y FQ(.)60 693 y(By)j(construction)h FF(\026)446 700 y FD(n)487 693 y FQ(is)g(translation-in)o(v)m(arian)o(t;)g (and)g(with)g(a)g(little)e(w)o(ork)i(one)g(can)g(pro)o(v)o(e)g(that)60 753 y FF(i)p FQ(\()p FF(\026)125 760 y FD(n)148 753 y FE(j)p FF(\027)s FQ(\))e(=)g FF(i)293 760 y FD(max)364 753 y FQ(.)23 b(On)17 b(the)g(other)g(hand,)g(it)f(is)h(easy)f(to)i(see)e(that)h(lim)1352 760 y FD(n)p Fy(!1)1454 753 y FF(\026)1483 760 y FD(n)1522 753 y FQ(=)d(lim)1642 760 y FD(n)p Fy(!1)1745 753 y FF(\032)1770 760 y FD(n)1808 753 y FQ(=)h FF(\026)60 814 y FQ(in)h(the)g(b)q(ounded)h (quasilo)q(cal)f(top)q(ology)l(.)133 874 y(\(e\))g(is)g(pro)o(v)o(en)g(in)g ([206,)g(Lemma)e(IV.3.2].)133 934 y(When)19 b(\012)313 941 y FH(0)352 934 y FQ(is)g(a)h(standard)g(Borel)f(space)g(\(e.g.)f(a)i (complete)d(separable)i(metric)e(space,)i(or)h(a)60 994 y(Borel)e(subset)h (thereof)s(\),)g(the)f(compactness)g(in)h(the)f(b)q(ounded)i(quasilo)q(cal)e (top)q(ology)i(is)f(pro)o(v)o(en)60 1054 y(in)g([157)q(,)g(Prop)q(osition)h (15.14\(3\)].)32 b(\(W)l(e)19 b(do)g(not)h(kno)o(w)f(whether)g(the)g(result)g (is)g(true)g(for)g(more)60 1115 y(general)h(spaces)g(\012)420 1122 y FH(0)440 1115 y FQ(.\))33 b(Since)19 b(the)h(w)o(eak)f(quasilo)q(cal)h (top)q(ology)i(is)e(w)o(eak)o(er)f(than)h(the)g(b)q(ounded)60 1175 y(quasilo)q(cal)c(top)q(ology)l(,)h(the)f(last)h(statemen)o(t)d(is)i(an) h(imme)o(diate)c(corollary)l(.)p 1588 1179 25 34 v 133 1285 a(Prop)q(osition)18 b(2.62)f(is)f(pro)o(v)o(en)f(in)h([157)q(,)g(Theorem)e (15.30\(b\)].)133 1370 y FM(Remark.)31 b FQ(F\177)-24 b(ollmer)17 b([122)q(])j(has)g(giv)o(en)f(a)i(b)q(eautiful)f(form)o(ula)e(for)j FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))f(in)f(terms)g(of)h(the)60 1430 y(relativ)o(e)10 b(en)o(trop)o(y)i(\()p FP(not)18 b FQ(relativ)o(e)10 b(en)o(trop)o(y)i FP(density)t FQ(!\))20 b(of)13 b(the)f(conditional)g (distributions)g(of)h FF(\026)f FQ(and)60 1490 y FF(\027)19 b FQ(giv)o(en)d(the)g(lexicographic)f(past.)22 b(See)15 b(also)i([157)q(,)f (Prop)q(osition)h(15.16)h(and)e(Theorem)f(15.20].)133 1600 y(Theorem)g(2.63)i(is)f(essen)o(tially)f([157,)h(Theorems)f(15.30\(b\))j(and) f(15.39].)133 1710 y FM(Remark.)25 b FQ(A)17 b(rather)h(w)o(eak)g(con)o(v)o (erse)f(to)h(Theorem)f(2.66)i(is)f(the)f(follo)o(wing:)25 b(Let)18 b FF(\026)1749 1717 y FH(1)1769 1710 y FF(;)8 b(\026)1820 1717 y FH(2)1857 1710 y FE(2)60 1770 y FF(M)107 1777 y FH(+1)p FD(;inv)216 1770 y FQ(\(\012\))19 b(with)f FF(\026)450 1777 y FH(2)489 1770 y FQ(Gibbsian)h(for)g(\010)810 1777 y FH(2)848 1770 y FE(2)f(B)934 1752 y FH(1)953 1770 y FQ(,)h FF(i)p FQ(\()p FF(\026)1051 1777 y FH(1)1071 1770 y FE(j)p FF(\026)1114 1777 y FH(2)1134 1770 y FQ(\))f FE(\024)f FF(K)23 b FQ(and)c FF(\026)1417 1777 y FH(1)1456 1770 y FQ(ergo)q(dic.)29 b(Then)19 b(there)60 1831 y(exists)i(an)h(in)o(teraction)f(\010)559 1838 y FH(1)602 1831 y FE(2)j(B)694 1813 y FH(0)735 1831 y FQ(\()p FP(not)j FE(B)884 1813 y FH(1)903 1831 y FQ(!\))37 b(with)22 b FE(k)p FQ(\010)1150 1838 y FH(1)1185 1831 y FE(\000)14 b FQ(\010)1273 1838 y FH(2)1293 1831 y FE(k)1318 1839 y Fy(B)1342 1830 y Fr(0)1385 1831 y FE(\024)23 b FF(K)q(=)p FQ(2)g(suc)o(h)e(that)h FF(\026)1815 1838 y FH(1)1857 1831 y FQ(is)60 1891 y(an)c(equilibrium)c(measure)i(for)i(\010)691 1898 y FH(1)711 1891 y FQ(.)25 b(This)18 b(can)f(b)q(e)h(pro)o(v)o(en)f (using)h(the)f(Bishop-Phelps)h(theorem)60 1951 y([206)q(,)d(Corollary)h (V.2.1].)k(The)c(same)e(is)i(true)f(if)g FF(\026)997 1958 y FH(1)1033 1951 y FQ(is)g(a)h(\014nite)f(con)o(v)o(ex)g(com)o(bination)f(of)i (ergo)q(dic)60 2011 y(measures,)f(but)h(then)g(the)g(constan)o(t)h FF(K)q(=)p FQ(2)g(is)f(replaced)g(b)o(y)g(a)g(w)o(orse)h(one.)133 2121 y(Theorem)j(2.67)h(is)g(pro)o(v)o(en)f(in)g([157)q(,)h(Theorem)f (15.37].)35 b(The)21 b(pro)q(of)h(is)f(giv)o(en)e(there)i(for)g(a)60 2181 y(sequence)15 b(of)i(cub)q(es,)f(but)g(the)g(same)f(pro)q(of)j(w)o(orks) e(for)h(an)f(arbitrary)h(v)m(an)f(Ho)o(v)o(e)f(sequence.)60 2291 y Fd(Pr)o(oof)k(of)g(Cor)o(ollar)m(y)e(2.68.)72 b FE(G)822 2298 y FD(inv)876 2291 y FQ(\(\005)932 2273 y FH(\010)959 2291 y FQ(\))16 b FE(6)p FQ(=)f Fq(?)p FQ(,)i(so)h(let)f FF(\027)h FE(2)e(G)1373 2298 y FD(inv)1427 2291 y FQ(\(\005)1483 2273 y FH(\010)1510 2291 y FQ(\))h(and)h(use)f(\(2.110\).)60 2352 y(Then)g(Gibbs)g(=)-8 b FE(\))16 b FQ(equilibrium)d(is)k(Theorem)e(2.66,)i (and)g(equilibrium)d(=)-8 b FE(\))16 b FQ(Gibbs)h(is)f(Theorem)60 2412 y(2.67.)p 300 2416 V 938 2784 a(195)p eop %%Page: 196 196 bop 60 91 a FM(A.5.2)56 b(The)18 b(In\014nite-V)-5 b(olume)16 b(Limit:)22 b(Coun)n(terexamples)60 184 y FQ(As)11 b(men)o(tioned)e(in)i (Sections)g(2.6.1)h(and)g(2.6.2,)g(the)f(existence)f(of)h(the)g(limits)e (de\014ning)j(the)f(in\014nite-)60 244 y(v)o(olume)21 b(pressure)i FF(p)p FQ(\()p FF(f)5 b FE(j)p FF(\027)s FQ(\))24 b(and)g(the)f(in\014nite-v) o(olume)d(relativ)o(e)i(en)o(trop)o(y)g(densit)o(y)g FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))i(is)f(a)60 304 y(highly)18 b(non)o(trivial)f(problem:)24 b(con)o(trary)18 b(to)g(what)h(migh)o(t)e(b)q (e)h(supp)q(osed)i(at)f(\014rst)f(glance,)g(these)60 364 y(limits)13 b(do)j FP(not)21 b FQ(alw)o(a)o(ys)16 b(exist.)k(The)15 b(\014rst)h(coun)o (terexamples)e(b)q(earing)i(on)g(this)f(problem)f(are)i(due)60 424 y(to)i(Kie\013er)e([216)q(].)24 b(Here)17 b(w)o(e)g(giv)o(e)f(a)i (simpli\014ed)d(v)o(ersion)i(of)g(Kie\013er's)g(coun)o(terexample,)d(due)k (to)60 485 y(Sok)m(al)f([331]:)133 545 y(Let)23 b(\012)i(=)g FE(f\000)p FQ(1)p FF(;)8 b FQ(1)p FE(g)509 527 y Fl(Z)532 545 y FQ(.)41 b(Let)23 b FF(\027)705 552 y FD(n)751 545 y FQ(b)q(e)g(the)f (measure)g(whic)o(h)g(giv)o(es)g(w)o(eigh)o(t)f(1)p FF(=)p FQ(2)p FF(n)j FQ(to)g(eac)o(h)e(of)60 605 y(the)d(p)q(erio)q(dic)f(sequences) g(of)h(p)q(erio)q(d)h(2)p FF(n)f FQ(consisting)g(of)g FF(n)g FQ(1's)g(follo)o(w)o(ed)f(b)o(y)h FF(n)g FE(\000)p FQ(1's.)29 b(Let)19 b FF(\027)j FQ(b)q(e)60 665 y(the)e(con)o(v)o(ex)g(com)o(bination) 595 632 y Fx(P)639 645 y Fy(1)639 678 y FD(n)p FH(=1)715 665 y FF(a)741 672 y FD(n)765 665 y FF(\027)789 672 y FD(n)812 665 y FQ(.)35 b(W)l(e)20 b(shall)g(sho)o(w)i(that)f(for)g(a)g(suitable)f(c)o (hoice)f(of)i(the)60 725 y(co)q(e\016cien)o(ts)15 b FE(f)p FF(a)358 732 y FD(n)381 725 y FE(g)p FQ(:)95 845 y(\(a\))25 b(F)l(or)20 b(the)g(function)f FF(f)5 b FQ(\()p FF(!)r FQ(\))21 b(=)f FF(!)763 852 y FH(0)783 845 y FQ(,)g(the)g(pressure)31 b(lim)1099 875 y FD(k)q Fy(!1)1197 845 y FF(k)1224 827 y Fy(\000)p FH(1)1280 845 y FQ(log)1351 810 y Fx(R)1387 845 y FQ(exp)1461 772 y Fx( )1513 804 y FD(k)1501 812 y Fx(P)1494 882 y FD(i)p FH(=1)1560 845 y FF(!)1590 852 y FD(i)1604 772 y Fx(!)1654 845 y FF(d\027)s FQ(\()p FF(!)r FQ(\))20 b(do)q(es)182 932 y(not)d(exist.)93 1030 y(\(b\))24 b(F)l(or)d(the)f(measure)f FF(\026)j FQ(=)f FF(\016)688 1037 y FH(+)739 1030 y FE(\021)f FQ(delta)g(measure)g(concen)o(trated)g(on)h(the)f(sequence)g(of)h(all)182 1090 y(+1's,)16 b(the)g(relativ)o(e)e(en)o(trop)o(y)i(densit)o(y)26 b(lim)910 1120 y FD(k)q Fy(!1)1008 1090 y FF(k)1035 1072 y Fy(\000)p FH(1)1082 1090 y FF(I)1104 1098 y Fy(f)p FH(1)p FD(;:::)n(;k)q Fy(g)1227 1090 y FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))17 b(do)q(es)g(not)f(exist.)60 1273 y Fd(Pr)o(oof)22 b(of)g(\(a\).)82 b FQ(Let)20 b FF(g)607 1280 y FD(n)631 1273 y FQ(\()p FF(k)r FQ(\))g FE(\021)776 1237 y Fx(R)812 1273 y FQ(exp)886 1200 y Fx( )938 1231 y FD(k)926 1239 y Fx(P)919 1310 y FD(i)p FH(=1)984 1273 y FF(!)1014 1280 y FD(i)1029 1200 y Fx(!)1078 1273 y FF(d\027)1127 1280 y FD(n)1151 1273 y FQ(\()p FF(!)r FQ(\).)33 b(It)20 b(is)g(easy)h(to)f (see)g(that)h FF(g)1769 1280 y FD(n)1813 1273 y FQ(is)f(a)60 1364 y(p)q(erio)q(dic)c(function)g(of)h(p)q(erio)q(d)f(2)p FF(n)p FQ(,)h(and)f(satis\014es)h(the)f(\(crude\))g(b)q(ounds)684 1447 y(1)p 670 1469 54 2 v 670 1515 a(2)p FF(n)728 1481 y(e)751 1461 y FD(F)773 1465 y Fs(n)794 1461 y FH(\()p FD(k)q FH(\))871 1481 y FE(\024)27 b FF(g)960 1488 y FD(n)984 1481 y FQ(\()p FF(k)r FQ(\))h FE(\024)f FF(e)1166 1461 y FD(F)1188 1465 y Fs(n)1209 1461 y FH(\()p FD(k)q FH(\))1272 1481 y FF(;)467 b FQ(\(A)p FF(:)p FQ(67\))60 1589 y(where)642 1649 y FF(F)674 1656 y FD(n)697 1649 y FQ(\()p FF(k)r FQ(\))27 b FE(\021)h FF(n)19 b FE(\000)g(j)p FF(k)10 b FQ(\(mo)q(d)e(2)p FF(n)p FQ(\))k FE(\000)f FF(n)p FE(j)444 b FQ(\(A)p FF(:)p FQ(68\))60 1730 y(is)21 b(the)f(sa)o(wto)q(oth)j(function)d(taking)h(the)g(v)m(alue)f(0) i(at)f FF(k)j FQ(=)d(0)p FF(;)8 b FQ(2)p FF(n;)g FQ(4)p FF(n;)g(:)g(:)g(:)21 b FQ(and)h(the)e(v)m(alue)h FF(n)g FQ(at)60 1790 y FF(k)16 b FQ(=)e FF(n;)8 b FQ(3)p FF(n;)g FQ(5)p FF(n;)g(:)g(:)g(:)13 b FQ(.)22 b(Hence)449 1919 y FF(g)r FQ(\()p FF(k)r FQ(\))28 b FE(\021)633 1861 y Fx(Z)683 1919 y FQ(exp)758 1846 y Fx( )811 1866 y FD(k)791 1878 y Fx(X)792 1969 y FD(i)p FH(=1)859 1919 y FF(!)889 1926 y FD(i)903 1846 y Fx(!)953 1919 y FF(d\027)s FQ(\()p FF(!)r FQ(\))75 b(=)1231 1866 y Fy(1)1219 1878 y Fx(X)1216 1969 y FD(n)p FH(=1)1291 1919 y FF(a)1317 1926 y FD(n)1348 1919 y FF(g)1371 1926 y FD(n)1395 1919 y FQ(\()p FF(k)r FQ(\))1150 2021 y Fx(8)1150 2058 y(>)1150 2071 y(>)1150 2083 y(<)1150 2158 y(>)1150 2170 y(>)1150 2183 y(:)1195 2073 y FE(\025)1263 2032 y Fy(1)1259 2040 y Fx(P)1248 2110 y FD(n)p FH(=1)1328 2054 y FD(a)1347 2058 y Fs(n)p 1328 2062 40 2 v 1328 2091 a FH(2)p FD(n)1381 2073 y FF(e)1404 2055 y FD(F)1426 2059 y Fs(n)1447 2055 y FH(\()p FD(k)q FH(\))1195 2187 y FE(\024)1263 2145 y Fy(1)1259 2153 y Fx(P)1248 2223 y FD(n)p FH(=1)1323 2187 y FF(a)1349 2194 y FD(n)1380 2187 y FF(e)1403 2169 y FD(F)1425 2173 y Fs(n)1446 2169 y FH(\()p FD(k)q FH(\))1753 2133 y FQ(\(A.69\))60 2304 y(No)o(w)16 b(c)o(ho)q(ose)h(the)f(sequence)f FE(f)p FF(a)663 2311 y FD(n)686 2304 y FE(g)h FQ(to)h(ha)o(v)o(e)e(h)o(uge)h(gaps:)432 2418 y FF(a)458 2425 y FD(n)508 2418 y FQ(=)28 b(const)11 b FE(\002)746 2357 y Fx(\032)786 2396 y FF(e)809 2378 y Fy(\000)p FD(\013n)931 2396 y FQ(if)k FF(n)f FQ(=)g(2)1094 2378 y FD(l)1124 2396 y FQ(for)i(some)f(in)o(teger)h FF(l)786 2456 y FQ(0)121 b(otherwise)1753 2418 y(\(A)p FF(:)p FQ(70\))60 2536 y(where)16 b FF(\013)e(>)g FQ(0)j(will)e(b)q(e)h(c)o(hosen)g(later.)21 b(Then)16 b(for)h FF(k)f FQ(=)d(2)1104 2518 y FD(l)1134 2536 y FQ(w)o(e)j(ha)o(v)o(e)f(the)h(lo)o(w)o(er)g(b)q(ound)511 2642 y FF(g)r FQ(\()p FF(k)r FQ(\))28 b FE(\025)f FF(a)721 2649 y FD(k)751 2642 y FF(g)774 2649 y FD(k)795 2642 y FQ(\()p FF(k)r FQ(\))h FE(\025)962 2609 y FF(a)988 2616 y FD(k)p 959 2631 52 2 v 959 2676 a FQ(2)p FF(k)1024 2642 y(e)1047 2622 y FD(F)1069 2628 y Fs(k)1088 2622 y FH(\()p FD(k)q FH(\))1164 2642 y FQ(=)1249 2609 y(1)p 1235 2631 V 1235 2676 a(2)p FF(k)1300 2642 y(e)1323 2622 y FH(\(1)p Fy(\000)p FD(\013)p FH(\))p FD(k)1753 2642 y FQ(\(A)p FF(:)p FQ(71\))938 2784 y(196)p eop %%Page: 197 197 bop 60 91 a FQ(and)17 b(hence)675 161 y(lim)8 b(inf)701 191 y FD(l)p Fy(!1)830 128 y FQ(1)p 823 150 38 2 v 823 195 a(2)847 181 y FD(l)874 161 y FQ(log)h FF(g)r FQ(\(2)1013 141 y FD(l)1027 161 y FQ(\))27 b FE(\025)h FQ(1)11 b FE(\000)g FF(\013)j(:)469 b FQ(\(A)p FF(:)p FQ(72\))60 264 y(On)16 b(the)g(other)h(hand,)f(for)h(2)587 246 y FD(l)614 264 y FF(<)d(k)i(<)d FQ(2)782 246 y FD(l)p FH(+1)857 264 y FQ(w)o(e)j(ha)o(v)o(e)f(the)h(upp)q(er)h(b)q(ound)497 405 y FF(g)r FQ(\()p FF(k)r FQ(\))41 b FE(\024)727 351 y FH(2)745 340 y Fs(l)712 364 y Fx(X)709 454 y FD(n)p FH(=1)783 405 y FF(a)809 412 y FD(n)841 405 y FF(e)864 385 y FD(n)912 405 y FQ(+)1016 351 y Fy(1)1003 364 y Fx(X)975 460 y FD(n)p FH(=2)1041 450 y Fs(l)p Fr(+1)1100 405 y FF(a)1126 412 y FD(n)1157 405 y FF(e)1180 385 y FD(k)904 518 y FQ([using)16 b FF(F)1077 525 y FD(n)1100 518 y FQ(\()p FF(k)r FQ(\))e FE(\024)f FQ(min)o(\()p FF(n;)8 b(k)r FQ(\)])628 658 y FE(\024)709 585 y Fx( )757 604 y Fy(1)745 616 y Fx(X)742 707 y FD(n)p FH(=1)816 658 y FF(a)842 665 y FD(n)865 585 y Fx(!)907 658 y FF(e)930 637 y FH(2)948 625 y Fs(l)986 658 y FQ(+)1049 572 y Fx(0)1049 647 y(@)1126 604 y Fy(1)1114 616 y Fx(X)1085 712 y FD(n)p FH(=2)1151 703 y Fs(l)p Fr(+1)1210 658 y FF(a)1236 665 y FD(n)1260 572 y Fx(1)1260 647 y(A)1304 658 y FF(e)1327 637 y FD(k)628 810 y FE(\024)42 b FF(e)732 789 y FH(2)750 778 y Fs(l)788 810 y FQ(+)25 b(const)11 b FE(\002)g FF(e)1046 789 y Fy(\000)p FD(\013)p FH(2)1114 778 y Fs(l)p Fr(+1)1166 810 y FF(e)1189 789 y FD(k)904 882 y FQ([const)16 b(dep)q(ends)h(on)f FF(\013)h FQ(only])628 979 y FE(\024)42 b FQ(const)11 b FE(\002)g FQ(exp)o([max)o(\(2)1103 958 y FD(l)1116 979 y FF(;)d(k)13 b FE(\000)e FF(\013)p FQ(2)1281 958 y FD(l)p FH(+1)1340 979 y FQ(\)])i FF(:)353 b FQ(\(A.73\))60 1080 y(De\014ning)16 b FF(\014)h FQ(=)c FF(k)r(=)p FQ(2)425 1061 y FD(l)455 1080 y FQ(\(so)k(that)g(1)d FF(<)g(\014)i(<)e FQ(2\),)i(w)o(e)g(\014nd)529 1178 y(1)p 528 1200 28 2 v 528 1246 a FF(k)568 1211 y FQ(log)10 b FF(g)r FQ(\()p FF(k)r FQ(\))27 b FE(\024)829 1178 y FQ(const)p 829 1200 112 2 v 871 1246 a FF(k)964 1211 y FQ(+)20 b(max)1113 1138 y Fx( )1153 1178 y FQ(1)p 1150 1200 31 2 v 1150 1246 a FF(\014)1186 1211 y(;)8 b FQ(1)j FE(\000)1298 1178 y FQ(2)p FF(\013)p 1298 1200 56 2 v 1310 1246 a(\014)1358 1138 y Fx(!)1413 1211 y FF(:)326 b FQ(\(A)p FF(:)p FQ(74\))60 1347 y(No)o(w)13 b(c)o(ho)q(ose)i(an)o(y)e(0)h FF(<)g(\013)g(<)602 1327 y FH(1)p 602 1335 18 2 v 602 1364 a(2)625 1347 y FQ(.)20 b(Then)14 b(max)n(\(1)p FF(=\014)s(;)8 b FQ(1)e FE(\000)g FQ(2)p FF(\013=\014)s FQ(\))14 b(is)f(minimi)o(zed)d(at)k FF(\014)i FQ(=)e FF(\014)1675 1329 y Fy(\003)1708 1347 y FE(\021)g FQ(2)p FF(\013)6 b FQ(+)g(1)60 1407 y(\(whic)o(h)23 b(satis\014es)h(1)j FF(<)g(\014)560 1389 y Fy(\003)605 1407 y FF(<)g FQ(2\))d(and)h(tak)o(es)e(the)g(v)m(alue)h(1)p FF(=)p FQ(\(2)p FF(\013)18 b FQ(+)e(1\))24 b(there.)43 b(By)23 b(c)o(ho)q(osing)60 1467 y FF(k)16 b FQ(=)e FE(b)p FQ(2)199 1449 y FD(l)212 1467 y FF(\014)243 1449 y Fy(\003)262 1467 y FE(c)j FQ(and)f(letting)g FF(l)e FE(!)g(1)p FQ(,)i(w)o(e)f(conclude)h(that) 556 1590 y(lim)8 b(sup)590 1630 y FD(l)p Fy(!1)773 1557 y FQ(1)p 719 1579 132 2 v 719 1625 a FE(b)p FQ(2)765 1610 y FD(l)779 1625 y FF(\014)810 1610 y Fy(\003)829 1625 y FE(c)864 1590 y FQ(log)h FF(g)r FQ(\()p FE(b)p FQ(2)1025 1570 y FD(l)1039 1590 y FF(\014)1070 1570 y Fy(\003)1089 1590 y FE(c)p FQ(\))28 b FE(\024)1287 1557 y FQ(1)p 1229 1579 141 2 v 1229 1625 a(2)p FF(\013)12 b FQ(+)f(1)1388 1590 y FF(:)351 b FQ(\(A)p FF(:)p FQ(75\))60 1723 y(Since)19 b(1)p FF(=)p FQ(\(2)p FF(\013)c FQ(+)f(1\))21 b FF(<)g FQ(1)14 b FE(\000)f FF(\013)21 b FQ(when)f(0)h FF(<)f(\013)h(<)995 1703 y FH(1)p 995 1711 18 2 v 995 1740 a(2)1017 1723 y FQ(,)g(it)f(follo)o(ws)g(from)f(\(A.72\))h(and)h(\(A.75\))f (that)71 1783 y(lim)60 1813 y FD(k)q Fy(!1)158 1783 y FF(k)185 1765 y Fy(\000)p FH(1)241 1783 y FQ(log)9 b FF(g)r FQ(\()p FF(k)r FQ(\))16 b(do)q(es)h(not)g(exist.)p 868 1787 25 34 v 60 1948 a Fd(Pr)o(oof)h(of)g(\(b\).)70 b FQ(It)15 b(is)h(easy)h(to)f(see)g (that)383 2049 y FF(h)p FQ(\()p FF(k)r FQ(\))27 b FE(\021)h FF(I)592 2056 y Fy(f)p FH(1)p FD(;:::)n(;k)q Fy(g)715 2049 y FQ(\()p FF(\016)756 2056 y FH(+)785 2049 y FE(j)p FF(\027)s FQ(\))41 b(=)h FE(\000)8 b FQ(log)h FF(\027)s FQ(\()p FF(!)1160 2056 y FH(1)1194 2049 y FQ(=)14 b FF(:)8 b(:)g(:)13 b FQ(=)h FF(!)1399 2056 y FD(k)1434 2049 y FQ(=)g(+1\))886 2166 y(=)42 b FE(\000)8 b FQ(log)1100 2112 y Fy(1)1088 2124 y Fx(X)1084 2216 y FD(n)p FH(=)p FD(k)1160 2166 y FF(a)1186 2173 y FD(n)1223 2132 y FF(n)j FE(\000)g FF(k)i FQ(+)e(1)p 1223 2154 202 2 v 1297 2200 a(2)p FF(n)1443 2166 y(:)296 b FQ(\(A.76\))60 2300 y(Let)16 b(us)h(again)g(tak)o(e)432 2417 y FF(a)458 2424 y FD(n)508 2417 y FQ(=)28 b(const)11 b FE(\002)746 2357 y Fx(\032)786 2395 y FF(e)809 2377 y Fy(\000)p FD(\013n)931 2395 y FQ(if)k FF(n)f FQ(=)g(2)1094 2377 y FD(l)1124 2395 y FQ(for)i(some)f(in)o(teger)h FF(l)786 2456 y FQ(0)121 b(otherwise)1753 2417 y(\(A)p FF(:)p FQ(77\))60 2541 y(Then)16 b(for)h FF(k)f FQ(=)e(2)379 2523 y FD(l)408 2541 y FQ(w)o(e)i(ha)o(v)o(e)596 2642 y FF(h)p FQ(\()p FF(k)r FQ(\))28 b FE(\024)f(\000)8 b FQ(log)909 2609 y FF(a)935 2616 y FD(k)p 906 2631 52 2 v 906 2676 a FQ(2)p FF(k)990 2642 y FQ(=)28 b FF(\013k)13 b FQ(+)e(log)q(\(2)p FF(k)r FQ(\))k FF(:)398 b FQ(\(A)p FF(:)p FQ(78\))938 2784 y(197)p eop %%Page: 198 198 bop 60 91 a FQ(On)16 b(the)g(other)h(hand,)f(for)h(2)587 73 y FD(l)614 91 y FF(<)d(k)i(<)d FQ(2)782 73 y FD(l)p FH(+1)857 91 y FQ(w)o(e)j(ha)o(v)o(e)495 226 y FF(h)p FQ(\()p FF(k)r FQ(\))42 b(=)g FE(\000)8 b FQ(log)868 172 y Fy(1)856 184 y Fx(X)828 276 y FD(m)p FH(=)p FD(l)p FH(+1)951 226 y FF(e)974 205 y Fy(\000)p FD(\013)p FH(2)1042 193 y Fs(m)1086 192 y FQ(2)1110 174 y FD(m)1155 192 y FE(\000)j FF(k)i FQ(+)e(1)p 1086 214 231 2 v 1150 260 a(2)1174 245 y FD(m)p FH(+1)630 397 y FE(\025)41 b(\000)8 b FQ(log)868 343 y Fy(1)856 355 y Fx(X)828 447 y FD(m)p FH(=)p FD(l)p FH(+1)951 397 y FF(e)974 376 y Fy(\000)p FD(\013)p FH(2)1042 364 y Fs(m)630 539 y FE(\025)41 b FQ(const)25 b(+)g FF(\013)p FQ(2)964 518 y FD(l)p FH(+1)1753 539 y FQ(\(A.79\))905 611 y([const)16 b(dep)q(ends)h(on)g FF(\013)f FQ(only])60 720 y(Th)o(us)809 838 y(lim)8 b(sup)843 877 y FD(l)p Fy(!1)979 804 y FQ(1)p 972 826 38 2 v 972 872 a(2)996 857 y FD(l)1014 838 y FF(h)p FQ(\(2)1085 817 y FD(l)1099 838 y FQ(\))41 b FE(\024)h FF(\013)458 b FQ(\(A.80a\))655 987 y(lim)8 b(inf)682 1017 y FD(l)p Fy(!1)852 954 y FQ(1)p 803 976 122 2 v 803 1022 a(2)827 1007 y FD(l)852 1022 y FQ(+)j(1)930 987 y FF(h)p FQ(\(2)1001 967 y FD(l)1025 987 y FQ(+)g(1\))42 b FE(\025)g FQ(2)p FF(\013)431 b FQ(\(A.80b\))60 1117 y(So)17 b(for)f(an)o(y)g FF(\013)f(>)e FQ(0)k(w)o(e)f(conclude)f(that)28 b(lim)810 1147 y FD(k)q Fy(!1)908 1117 y FF(k)935 1099 y Fy(\000)p FH(1)982 1117 y FF(h)p FQ(\()p FF(k)r FQ(\))17 b(do)q(es)g(not)f(exist.)p 1541 1121 25 34 v 133 1242 a(W)l(e)i(note)h(also)g(that)g(V)l(aradhan)g([359)q(])f(and)h (Newman)e([275)q(])h(ha)o(v)o(e)f(giv)o(en)h(an)h(example)d(of)j(a)60 1302 y(mixing)14 b(Gaussian)k(pro)q(cess)f(for)f(whic)o(h)g(the)g(pressure)g (do)q(es)h(not)g(exist.)60 1468 y FG(B)82 b(Lo)n(w-T)-7 b(emp)r(erature)16 b(Phase)i(Diagrams)e(and)i(Pirogo)n(v-)201 1559 y(Sinai)27 b(Theory)60 1683 y FB(B.1)69 b(Generalities)20 b(on)j(Phase)g(Diagrams)60 1776 y FQ(The)18 b(cen)o(tral)g(problem)f(in)h(equilibrium)d(statistical)j (mec)o(hanics)e(is)i(the)g(description)g(of)h(the)f(set)60 1836 y(of)23 b(Gibbs)g(measures)f(for)h(a)g(giv)o(en)f(in)o(teraction.)39 b(More)23 b(generally)l(,)g FP(families)k FQ(of)c(in)o(teractions)60 1896 y(\(or)g(of)h(sp)q(eci\014cations\))e(are)h(considered,)h(with)f(mem)o (b)q(ers)d(lab)q(elled)i(b)o(y)g(certain)g(parameters:)60 1956 y(in)o(v)o(erse)e(temp)q(erature)490 1938 y FH(76)547 1956 y FF(\014)s FQ(,)i(magnetic)e(\014eld,)i(c)o(hemical)c(p)q(oten)o(tial,)k (etc.)36 b(The)22 b(ultimate)d(goal)60 2016 y(is)h(then)g(to)h(describ)q(e)e (the)h(set)h(of)f(Gibbs)h(measures,)e(in)h(particular)g(the)g(n)o(um)o(b)q (er)f(of)h(extremal)60 2077 y(Gibbs)h(measures,)f(as)h(a)g(function)g(of)g (these)f(parameters.)34 b(The)20 b(partition)h(of)g(the)f(parameter)60 2137 y(space)15 b(in)o(to)f(regions)i(with)e(di\013eren)o(t)g(n)o(um)o(b)q (ers)g(of)h(extremal)d(Gibbs)j(measures)f(is)h(called)f(a)h FP(phase)60 2197 y(diagr)n(am)23 b FQ(of)d(the)g(family)e(of)i(in)o (teractions,)g(and)h(the)f(manifolds)f(delimiti)o(ng)f(suc)o(h)i(regions)g (are)60 2257 y(called)15 b FP(phase-tr)n(ansition)j(manifolds)t FQ(.)133 2317 y(A)e(natural)i(approac)o(h)f(to)g(the)g(di\016cult)e(problem)g (of)i(determining)e(the)h(full)g(phase)i(diagram)60 2377 y(is)f(to)g(\014x)g (\014rst)h(some)e(of)h(the)g(parameters)f(so)i(that)g(the)f(resulting)f (\\restricted")h(phase)h(diagram)60 2438 y(is)e(amenable)f(to)h(a)h (comparativ)o(ely)c(simple)h(analysis.)21 b(Then,)16 b(one)h(studies)f (whether)g(this)g(phase)60 2498 y(diagram)g(is)g(\\stable",)h(that)g(is,)f (whether)g(a)h(small)e(c)o(hange)h(in)h(the)f(\014xed)g(parameters)f(pro)q (duces)p 60 2541 732 2 v 100 2595 a FA(76)135 2610 y Fz(As)c(w)o(e)g(w)o(an)o (t)f(to)g(explicitly)g(discuss)i(the)f(role)g(of)f(this)g(parameter,)h (throughout)g(this)f(app)q(endix)h(w)o(e)g(un-absorb)60 2660 y Fv(\014)17 b Fz(from)12 b(in)o(teractions)i(and)g(Hamiltonia)o(ns.)938 2784 y FQ(198)p eop %%Page: 199 199 bop 60 91 a FQ(only)16 b(a)h(small)e(deformation)g(of)i(the)f(diagram)g(k)o (eeping)f(unaltered)h(the)g(main)f(prop)q(erties)i(of)f(the)60 152 y(extremal)e(Gibbs)i(measures.)133 212 y(The)c(most)e(widely)h(used)g (\\restricted")g(phase)h(diagrams)g(are)f(the)g(high-temp)q(erature)g(\()p FF(\014)16 b FQ(=)e(0\))60 272 y(and)e(lo)o(w-temp)q(erature)e(\()p FF(\014)16 b FQ(=)e FE(1)p FQ(\))d(limits.)17 b(In)11 b(the)g(former,)g(the)g (situation)g(is)g(particularly)g(simple:)60 332 y(The)g(\014nite-v)o(olume)e (Gibbs)j(distribution)f(\(2.20\))h(b)q(ecomes)e(for)i FF(\014)k FQ(=)e(0)d(just)h(the)f(pro)q(duct)h(measure)60 359 y Fx(Q)99 403 y FD(x)p Fy(2)p FH(\003)177 392 y FF(d\026)231 374 y FH(0)231 405 y FD(x)274 392 y FQ(indep)q(enden)o(tly)19 b(of)i(the)f(b)q(oundary)i (condition.)33 b(Hence,)20 b(there)g(is)g(a)h(unique)f(Gibbs)60 452 y(measure,)d(namely)f FF(\026)466 434 y FH(0)502 452 y FQ(=)557 419 y Fx(Q)596 463 y FD(x)p Fy(2L)674 452 y FF(d\026)728 434 y FH(0)728 465 y FD(x)751 452 y FQ(,)h(whic)o(h)h(corresp)q(onds)h(to)f (indep)q(enden)o(t)f(spins,)h(the)g(one)g(at)60 513 y(site)j FF(x)g FQ(distributed)f(according)i(to)f(the)g(a)h(priori)f(measure)f FF(\026)1244 495 y FH(0)1244 525 y FD(x)1266 513 y FQ(.)36 b([Note)21 b(that)h(for)f(translation-)60 573 y(in)o(v)m(arian)o(t)f(Gibbs)h (measures)f(the)h(same)f(conclusion)g(follo)o(ws)h(from)f(the)h(v)m (ariational)g(principle)60 633 y(\(2.105a\),)i(whic)o(h)d(for)h FF(f)516 640 y FH(\010)564 633 y FQ(=)h(0)f(requires)e FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\026)964 615 y FH(0)984 633 y FQ(\))i(=)h(inf)11 b FF(i)p FQ(\()d FE(\001)g(j)p FF(\026)1260 615 y FH(0)1280 633 y FQ(\))21 b(=)h(0,)f(hence)f FF(\026)i FQ(=)f FF(\026)1718 615 y FH(0)1738 633 y FQ(.])34 b(It)20 b(is)60 693 y(w)o(ell)d(kno)o(wn)h (that)h(this)f(in\014nite-temp)q(erature)e(phase)j(diagram)e(is)h(stable)h (in)f(a)g(suitable)g(space)60 753 y(of)h(in)o(teractions:)25 b(for)19 b FF(\014)i FQ(small)16 b(the)j(Gibbs)g(measure)e(remains)g(unique)h (and)h(it)f(corresp)q(onds)i(to)60 814 y(w)o(eakly)15 b(dep)q(enden)o(t)h (spins.)21 b(This)c(has)g(b)q(een)f(pro)o(v)o(en)f(for)i(lattice-gas)f([140)q (])f(or,)i(more)d(generally)l(,)60 874 y(spin-1/2)k([205])e(in)o(teractions)g (in)g FE(B)726 856 y FH(1)745 874 y FQ(,)f(and)i(for)g(general)f(in)o (teractions)f(in)h FE(B)1468 856 y FH(2)1503 874 y FQ([84)q(,)g(177)q(].)21 b(It)15 b(is)i(not)60 934 y(kno)o(wn)f(whether)g(it)g(is)g(true)g(for)h (general)f(in)o(teractions)f(in)h FE(B)1201 916 y FH(1)1220 934 y FQ(.)133 994 y(The)g(phase)h(diagram)e(for)i(the)e(zero-temp)q(erature) g(limit)e(is,)j(in)f(general,)h(more)e(complicated)60 1054 y(to)f(describ)q(e;)h(its)e(stabilit)o(y)g(is)h(the)g(sub)s(ject)g(of)g (Pirogo)o(v-Sinai)g(theory)l(.)20 b(In)13 b(this)g(app)q(endix)g(w)o(e)g(giv) o(e)60 1115 y(a)g(brief)f(o)o(v)o(erview)f(of)i(the)f(conclusions)h(of)g (this)f(theory)h(with)f(an)h(ey)o(e)f(on)h(the)f(applications)h(needed)60 1175 y(in)i(Section)g(4.)22 b(Its)15 b(understanding)i(requires,)d(of)i (course,)f(a)h(prop)q(er)h(grasp)f(of)g(the)g(basic)f(notions)60 1235 y(in)o(v)o(olv)o(ed)d(in)h(the)g(construction)h(of)g(zero-temp)q (erature)f(phase)h(diagrams.)20 b(As)14 b(remark)o(ed)d(already)60 1295 y(in)24 b(the)f(seminal)f(w)o(ork)i(of)g(Ruelle)f([311],)i(the)f (formalism)d(for)j(zero-temp)q(erature)f(statistical)60 1355 y(mec)o(hanics)10 b(has)j(some)e(imp)q(ortan)o(t)h(di\013erences)f(with)h (the)g(one)h(for)f(\014nite)g(temp)q(eratures)f(review)o(ed)60 1416 y(in)i(Section)h(2.)20 b(Moreo)o(v)o(er,)13 b(the)g(nomenclature)f (adopted)j(throughout)g(the)f(existing)f(literature)f(is)60 1476 y(often)17 b(a)g(source)g(of)h(confusion,)f(with)g(di\013eren)o(t)f (authors)i(assigning)g(di\013eren)o(t)e(meanings)g(to)h(the)60 1536 y(same)12 b(w)o(ords.)21 b(Therefore,)13 b(for)g(the)g(con)o(v)o (enience)d(of)k(the)e(reader)h(and)h(to)f(\014x)g(the)g(terminology)l(,)e(w)o (e)60 1596 y(start)17 b(with)g(a)g(review)e(of)i(the)g(zero-temp)q(erature)e (formalism.)20 b(F)l(or)c(this)h(part)g(of)g(the)f(app)q(endix,)60 1656 y(the)g(reference)e(closest)i(to)g(our)h(needs)f(|)g(and)g(from)f(whic)o (h)h(w)o(e)f(ha)o(v)o(e)h(tak)o(en)f(man)o(y)g(of)h(the)g(ideas)60 1716 y(|)e(is)h(the)f(review)f(b)o(y)h(Dobrushin)h(and)h(Shlosman)e([95].)20 b(Ho)o(w)o(ev)o(er,)13 b(for)h(the)h(sak)o(e)f(of)h(consistency)60 1777 y(with)i(the)f(rest)h(of)g(our)g(w)o(ork,)g(w)o(e)f(adopt)i(a)f (nomenclature)e(sligh)o(tly)h(di\013eren)o(t)g(from)g(theirs.)22 b(W)l(e)60 1837 y(shall)11 b(paren)o(thetically)f(con)o(trast)i(these)f (di\013erences)g(b)q(oth)i(for)e(the)h(b)q(ene\014t)f(of)h(the)g(reader)f (familiar)60 1897 y(with)16 b([95])g(and)h(as)g(a)g(tok)o(en)e(of)i(the)f (confusing)h(state)f(of)h(the)f(nomenclature.)133 1957 y(Let)21 b(us)g(state)g(once)f(and)h(for)g(all)f(that)h FP(in)h(this)f(app)n(endix,)i (we)f(c)n(onsider)g(only)g(the)g(c)n(ase)f(of)60 2017 y(p)n(erio)n(dic)d (inter)n(actions)i(and)f(\014nite)i(single-spin)g(sp)n(ac)n(e,)e(i.e.)g FE(j)p FQ(\012)1259 2024 y FH(0)1279 2017 y FE(j)g FP(\014nite)t FQ(.)28 b(Moreo)o(v)o(er,)16 b(except)h(in)60 2078 y(Sections)f(B.2.9)g(and)g (B.4.4,)g FP(the)i(inter)n(actions)g(ar)n(e)f(assume)n(d)g(to)g(b)n(e)h(of)f (\014nite)i(r)n(ange)t FQ(.)60 2222 y FB(B.2)69 b(Zero-T)-6 b(emp)r(erature)17 b(Lattice)h(Systems.)27 b(General)19 b(F)-6 b(ormalism)60 2314 y FQ(Heuristically)l(,)12 b(as)i FF(\014)j FE(!)c(1)h FQ(only)g(con\014gurations)i(with)e(minim)o(al)d(energy)j (\\surviv)o(e",)g(the)g(others)60 2375 y(b)q(eing)i(exp)q(onen)o(tially)f (damp)q(ed)g(b)o(y)h(the)f(Boltzmann)g(factor.)21 b(Ho)o(w)o(ev)o(er,)14 b(in)i(the)f(general)h(theory)60 2435 y(of)f(zero-temp)q(erature)f (statistical)g(mec)o(hanics)f(|)i(as)h(in)f(statistical)f(mec)o(hanics)f (quite)h(generally)60 2495 y(|)21 b(the)g(cen)o(tral)f(ob)s(jects)h(are)g (not)g(individual)f(con\014gurations)i(but)g(rather)f(probabilit)o(y)f(mea-) 60 2555 y(sures)h(describing)g(a)g(random)g(distribution)g(of)g (con\014gurations)i([303].)36 b(Just)21 b(as)h(for)f(non-zero)60 2615 y(temp)q(erature,)13 b(suc)o(h)g(measures)g(can)h(b)q(e)h(de\014ned)e (either)g(via)h(sp)q(eci\014cations)g(or)h(via)e(a)i(v)m(ariational)938 2784 y(199)p eop %%Page: 200 200 bop 60 91 a FQ(principle.)60 221 y FM(B.2.1)55 b(Zero-T)-5 b(emp)r(erature)15 b(Gibbs)k(Measures)60 314 y FQ(Let)13 b(us)h(start)g(with) f(the)g(approac)o(h)h(based)f(on)h(sp)q(eci\014cations.)20 b(W)l(e)13 b(see)g(that)g(the)g FF(\014)k FE(!)c(1)g FQ(limit)e(of)60 374 y(the)j(\014nite-v)o(olume)d(Gibbs)j(distribution)f(\(2.20\))h(with)g(a)g (\014xed)g(b)q(oundary)h(condition)e(pro)q(duces)i(a)60 434 y(measure)10 b(concen)o(trated)h(on)h(the)f(con\014gurations)h(of)g (\\minimal)c(energy")k(for)f(the)g(giv)o(en)g(b)q(oundary)60 494 y(condition)21 b(and)h(giving)f(equal)f(probabilit)o(y)g(to)i(eac)o(h)e (suc)o(h)h(con\014guration.)37 b(That)22 b(is,)g(for)f(an)o(y)60 554 y(in)o(teraction)15 b(\010,)h(an)o(y)g(\014nite)g(v)o(olume)e(\003)i(and) h(an)o(y)f(b)q(oundary)i(condition)e FF(\034)j FE(2)14 b FQ(\012)1548 561 y FH(\003)1572 552 y Fs(c)1591 554 y FQ(,)i(w)o(e)g(ha)o(v)o(e)519 696 y(lim)507 726 y FD(\014)r Fy(!1)607 696 y FF(\031)637 672 y FD(\014)r FH(\010)635 708 y(\003)p FD(;\034)691 696 y FQ(\()p FF(A)p FQ(\))27 b(=)864 659 y FF(\026)893 641 y FH(0)893 671 y(\003)920 659 y FQ(\()p FF(A)10 b FE(\\)h FQ(\012)1065 641 y FH(\010)1065 671 y(\003)p FD(;\034)1121 659 y FQ(\))p 864 684 277 2 v 910 730 a FF(\026)939 713 y FH(0)939 742 y(\003)965 730 y FQ(\(\012)1019 713 y FH(\010)1019 742 y(\003)p FD(;\034)1075 730 y FQ(\))1173 696 y FE(\021)27 b FF(\031)1269 672 y FH(\010)p FD(;T)5 b FH(=0)1267 708 y(\003)p FD(;\034)1377 696 y FQ(\()p FF(A)p FQ(\))328 b(\(B)p FF(:)p FQ(1\))60 843 y(for)21 b(all)e(sets)i FF(A)f FE(2)h(F)457 850 y FH(\003)483 843 y FQ(,)g(where)f(\012)698 825 y FH(\010)698 856 y(\003)p FD(;\034)774 843 y FQ(is)g(the)h(set)f(of)g (con\014gurations)i FF(!)1404 850 y FH(\003)1451 843 y FQ(in)e(\003)g(minimi) o(zi)o(ng)e(the)60 904 y(energy)e FF(H)260 885 y FH(\010)256 916 y(\003)288 904 y FQ(\()p FF(!)337 911 y FH(\003)375 904 y FE(\002)10 b FF(\034)445 911 y FH(\003)469 902 y Fs(c)488 904 y FQ(\):)419 1032 y(\012)454 1012 y FH(\010)454 1045 y(\003)p FD(;\034)524 1032 y FQ(=)576 972 y Fx(\032)607 1032 y FF(!)637 1039 y FH(\003)664 1032 y FQ(:)21 b FF(H)743 1012 y FH(\010)739 1045 y(\003)771 1032 y FQ(\()p FF(!)820 1039 y FH(\003)858 1032 y FE(\002)11 b FF(\034)929 1039 y FH(\003)953 1030 y Fs(c)972 1032 y FQ(\))j(=)42 b(inf)1056 1069 y Fx(e)-23 b FD(!)1078 1075 y Fr(\003)1101 1069 y Fy(2)p FH(\012)1150 1075 y Fr(\003)1181 1032 y FF(H)1225 1012 y FH(\010)1221 1045 y(\003)1253 1032 y FQ(\()1277 1028 y Fx(e)1272 1032 y FF(!)1302 1039 y FH(\003)1340 1032 y FE(\002)11 b FF(\034)1411 1039 y FH(\003)1435 1030 y Fs(c)1453 1032 y FQ(\))1472 972 y Fx(\033)1517 1032 y FF(:)249 b FQ(\(B)p FF(:)p FQ(2\))60 1179 y(W)l(e)14 b(call)f(\005)266 1161 y FH(\010)p FD(;T)5 b FH(=0)387 1179 y FQ(=)14 b(\()p FF(\031)488 1156 y FH(\010)p FD(;T)5 b FH(=0)486 1191 y(\003)p FD(;\034)595 1179 y FQ(\))614 1186 y FH(\003)p Fy(2S)702 1179 y FQ(the)14 b FP(zer)n(o-temp)n(er)n(atur)n(e)g(sp)n(e)n(ci\014c)n(ation)k FQ(\(or)c(ground-state)i(sp)q(ec-)60 1239 y(i\014cation)g([95]\))g(for)h(the) f(in)o(teraction)f(\010.)60 1341 y FM(De\014nition)j(B.1)23 b FP(A)15 b FQ(zero-temp)q(erature)10 b(Gibbs)j(measure)g FP(for)g FQ(\010)h FP(is)g(a)g(me)n(asur)n(e)f(c)n(onsistent)j(with)60 1401 y(the)i(sp)n(e)n(ci\014c)n(ation)g(\(B.1\).)60 1503 y FQ(W)l(e)g(remark)f(that)i(the)f(sp)q(eci\014cations)h(\(B.1\))f(are)h (quasilo)q(cal)f(\(since)g(w)o(e)g(only)g(consider)g(\014nite-)60 1563 y(range)12 b(in)o(teractions\),)g(but)g(not)g(uniformly)e(nonn)o(ull,)i (hence)f(they)h(are)f(not)i(Gibbsian.)20 b(Therefore,)60 1623 y(zero-temp)q(erature)d(Gibbs)j(measures)d(happ)q(en)j(not)g(to)f(b)q(e)g (honest)g(Gibbs)h(measures.)28 b(In)19 b(fact,)60 1683 y(the)i(p)q(ossibilit) o(y)e(of)j(including)e(\(B.1\))g(in)g(the)h(general)g(framew)o(ork)e(is)i (one)g(of)g(the)g(adv)m(an)o(tages)60 1744 y(of)d(in)o(tro)q(ducing)f(the)g (general)g(notion)h(of)g(sp)q(eci\014cation)f(\(Section)g(2.3.1\),)g(rather)h (than)g(just)f(the)60 1804 y(more)k(restricted)h(\(and)h(p)q(opular\))g (class)g(of)g(Gibbsian)g(sp)q(eci\014cations)f(\(Section)g(2.3.2\).)41 b(The)60 1864 y(zero-temp)q(erature)22 b(Gibbs)h(measures)f(for)i(a)f(giv)o (en)g(in)o(teraction)f(\010)h(form)g(a)g(\(w)o(eakly\))f(closed)60 1924 y(|)c(hence)f(\(w)o(eakly\))g(compact)g(|)h(con)o(v)o(ex)e(subset)i(of)h (the)f(compact)e(metric)g(space)i FF(M)1714 1931 y FH(+1)1761 1924 y FQ(\(\012\))f FE(\032)60 1984 y FF(M)5 b FQ(\(\012\).)21 b(Therefore,)15 b(b)o(y)f(Cho)q(quet's)h(theorem)f([293])h(an)o(y)g(suc)o(h)f (measure)g(can)h(b)q(e)g(written)g(as)g(the)60 2045 y(barycen)o(ter)i(of)h(a) g(probabilit)o(y)f(measure)g(concen)o(trated)g(on)h(the)g(extreme)d(p)q(oin)o (ts.)27 b(In)17 b(fact,)h(the)60 2105 y(general)i(theory)h(of)g(sp)q (eci\014cations)g(guaran)o(tees)g(us)g(that)g(this)f(decomp)q(osition)g(in)o (to)g(extremal)60 2165 y(measures)f(is)i FP(unique)26 b FQ([157,)c(Theorem)d (7.26],)i(i.e.)e(that)i(the)f(set)h(of)g(zero-temp)q(erature)e(Gibbs)60 2225 y(measures)c(is)h(a)h(simplex.)60 2355 y FM(B.2.2)55 b(Ground-State)12 b(Con\014gurations.)23 b(Supp)r(ort)12 b(Prop)r(erties)f(of)i(Zero-T)-5 b(emp)r(erature)243 2415 y(Gibbs)19 b(Measures)60 2508 y FQ(The)d(sp)q (eci\014cations)h(\(B.1\))e(satisfy)563 2618 y FF(\031)591 2625 y FH(\003)617 2618 y FQ(\()p FF(!)666 2625 y FH(\003)693 2618 y FE(j)p FF(!)737 2625 y FH(\003)761 2616 y Fs(c)780 2618 y FQ(\))28 b(=)f(0)49 b(unless)16 b FF(!)1139 2625 y FH(\003)1180 2618 y FE(2)e FQ(\012)1262 2597 y FH(\010)1262 2630 y(\003)p FD(;!)1318 2636 y Fr(\003)1339 2629 y Fs(c)1373 2618 y FF(:)393 b FQ(\(B)p FF(:)p FQ(3\))938 2784 y(200)p eop %%Page: 201 201 bop 60 91 a FQ(This)11 b(prop)q(ert)o(y)g(implies)d(that)j(the)g(zero-temp)q (erature)e(Gibbs)i(measures)f(|)h(whic)o(h)f(satisfy)h FF(\026\031)1812 98 y FH(\003)1852 91 y FQ(=)60 152 y FF(\026)23 b FQ(for)h(ev)o(ery)d (\014nite)i(set)g(\003)g(|)f(are)h(supp)q(orted)i(b)o(y)d(the)h(set)g(of)g (con\014gurations)i FF(!)g FQ(suc)o(h)e(that)60 212 y FF(!)90 219 y FH(\003)133 212 y FE(2)16 b FQ(\012)217 194 y FH(\010)217 224 y(\003)p FD(;!)273 230 y Fr(\003)294 223 y Fs(c)332 212 y FQ(for)i FP(every)g FQ(\014nite)f(\003,)g(i.e.)f(is)i(of)g (con\014gurations)h(that)f(minim)o(iz)o(e)d(the)i(lo)q(cal)g(energy)60 272 y(when)g(they)g(themselv)o(es)e(are)i(the)g(b)q(oundary)i(condition.)24 b(Con\014gurations)c(with)d(this)g(prop)q(ert)o(y)60 332 y(are)k(called)f FP(gr)n(ound-state)j(c)n(on\014gur)n(ations)t FQ(.)36 b(By)20 b(\(B.2\))h(they)f(can)h(b)q(e)g(c)o(haracterized)f(as)i(those)60 392 y(con\014gurations)e(whose)f(energy)f(cannot)h(b)q(e)g(lo)o(w)o(ered)e(b) o(y)h(an)o(y)h(c)o(hange)f(in)o(v)o(olving)f(only)i(a)g(\014nite)60 452 y(n)o(um)o(b)q(er)14 b(of)h(spins.)22 b(That)16 b(is,)f FF(!)h FE(2)e FQ(\012)h(is)h(a)f(ground-state)i(con\014guration)g(for)f(an)f (in)o(teraction)g(\010)h(if)60 513 y(and)h(only)f(if)g(for)g(ev)o(ery)f(\003) h(and)h(ev)o(ery)d(con\014guration)k FF(!)1111 495 y Fy(0)1139 513 y FQ(suc)o(h)e(that)h FF(!)1385 520 y FH(\003)1409 511 y Fs(c)1441 513 y FQ(=)d FF(!)1525 495 y Fy(0)1523 525 y FH(\003)1547 516 y Fs(c)1566 513 y FQ(,)i(w)o(e)g(ha)o(v)o(e)384 623 y FF(H)428 602 y FH(\010)424 635 y(\003)455 623 y FQ(\()p FF(!)506 602 y Fy(0)518 623 y FQ(\))11 b FE(\000)g FF(H)642 602 y FH(\010)638 635 y(\003)670 623 y FQ(\()p FF(!)r FQ(\))28 b FE(\021)914 581 y Fx(X)895 680 y FD(A)10 b Fy(\032)h FD(S)855 727 y(A)d Fy(\\)f FH(\003)k Fy(6)p FH(=)f Fq(?)1053 623 y FQ([\010)1102 630 y FD(A)1131 623 y FQ(\()p FF(!)1182 602 y Fy(0)1193 623 y FQ(\))h FE(\000)g FQ(\010)1308 630 y FD(A)1337 623 y FQ(\()p FF(!)r FQ(\)])27 b FE(\025)h FQ(0)14 b FF(:)213 b FQ(\(B)p FF(:)p FQ(4\))60 835 y(The)20 b(set)g(of)h(ground-state)g(con\014gurations)h (is)e(closed)f(\(hence)h(compact\))f(b)q(ecause)h(the)g(condi-)60 895 y(tions)f(\(B.4\))g(in)o(v)o(olv)o(e)e(\014nite-v)o(olume)f(Hamiltonians) i(whic)o(h)g(are)i(con)o(tin)o(uous)f(functions)g(of)g(the)60 955 y(con\014gurations.)k(This)16 b(fact)g(of)g(b)q(eing)h(a)f(closed)g(set)g (justi\014es)g(the)g(use)g(ab)q(o)o(v)o(e)g(of)g(the)g(expression)60 1015 y(\\is)k(supp)q(orted)h(b)o(y")f(\(=)f(\\its)h(supp)q(ort)h(is)f(a)g (subset)g(of)s("\).)33 b(W)l(e)20 b(recall)f(that)h(the)f(supp)q(ort)i(of)g (a)60 1075 y(measure)15 b FF(\026)i FQ(is)f(the)g(smallest)e(closed)i(set)g (of)h(full)e(measure)g(\(Section)h(2.1.3\).)133 1136 y(The)h(fact)g(of)g(b)q (eing)g(supp)q(orted)h(on)f(con\014gurations)h(satisfying)f(\(B.4\))f(is)h (not)g(equiv)m(alen)o(t)f(to)60 1196 y(b)q(eing)h(consisten)o(t)g(with)g(the) g(sp)q(eci\014cations)g(\(B.1\))g(|)g(it)f(is)h FP(we)n(aker)5 b FQ(.)25 b(The)17 b(more)f(general)h(mea-)60 1256 y(sures)h(c)o (haracterized)f(only)h(b)o(y)f(this)h(supp)q(ort)i(prop)q(ert)o(y)e(turn)g (out)h(to)f(pla)o(y)g(an)g(imp)q(ortan)o(t)f(role)60 1316 y(in)i(the)h(study) f(of)h(the)f(stabilit)o(y)g(of)h(zero-temp)q(erature)e(phase)i(diagrams)f (\(Theorem)f(B.12)i(b)q(e-)60 1376 y(lo)o(w\).)g(Inspired)13 b(b)o(y)g([95],)g(w)o(e)g(call)f(these)h(measures)g FP(w-)h FQ(\(for)g(w)o(eak\))f FP(zer)n(o-temp)n(er)n(atur)n(e)g(me)n(asur)n(es)t FQ(.)60 1437 y(F)l(ormally:)60 1538 y FM(De\014nition)18 b(B.2)23 b FP(A)f(w-zer)n(o-temp)n(er)n(atur)n(e)f(me)n(asur)n(e)f(for)h(an)h(inter)n (action)g FQ(\010)g FP(is)f(a)g(me)n(asur)n(e)g FF(\026)60 1598 y FP(satisfying)489 1659 y FF(\026)p FQ(\()q FE(f)p FQ(ground-state)c (con\014gurations)h(for)e(\010)p FE(g)p FQ(\))28 b(=)g(1)14 b FF(:)319 b FQ(\(B)p FF(:)p FQ(5\))60 1760 y(In)17 b(Section)g(B.2.7)g(w)o (e)g(discuss)g(a)h(natural)g(limit)c(pro)q(cess)k(that)g(pro)q(duces)g (w-zero-temp)q(erature)60 1821 y(measures,)f(and)h(w)o(e)f(presen)o(t)g(an)h (example)e(\(for)i(the)f(Ising)h(an)o(tiferromagnet)e(with)i(a)g(magnetic)60 1881 y(\014eld\))f(in)h(whic)o(h)f(this)h(limit)d(pro)q(cess)j(pro)q(duces)h (a)f(translation-in)o(v)m(arian)o(t)g(w-zero-temp)q(erature)60 1941 y(measure)d(whic)o(h)h(is)g FP(not)g FQ(a)h(zero-temp)q(erature)e FP(Gibbs)h FQ(measure.)133 2001 y(Ob)o(viously)24 b(the)h(set)g(of)h (w-zero-temp)q(erature)e(measures)g(for)i(a)f(giv)o(en)g(in)o(teraction)f (\010)h(is)60 2061 y(\(w)o(eakly\))12 b(closed)h(|)g(hence)f(\(w)o(eakly\))g (compact)g(and)i(con)o(v)o(ex.)19 b(The)13 b(extreme)d(p)q(oin)o(ts)k(are)f (simply)60 2121 y(the)j(delta)g(measures)f FF(\016)497 2128 y FD(!)538 2121 y FQ(concen)o(trated)h(on)h(a)f(single)g(ground-state)i (con\014guration)f FF(!)r FQ(.)22 b(This)16 b(set)60 2182 y(is)g(therefore)g (trivially)e(a)j(simplex.)133 2242 y(The)f(previous)g(discussion)h(can)f(b)q (e)h(summarized)c(in)j(the)g(follo)o(wing)g(w)o(a)o(y:)60 2344 y FM(Theorem)h(B.3)23 b FP(Every)13 b(zer)n(o-temp)n(er)n(atur)n(e)f(Gibbs)h (me)n(asur)n(e)f(is)h(a)f(w-zer)n(o-temp)n(er)n(atur)n(e)h(me)n(asur)n(e)60 2404 y(for)k(the)h(c)n(orr)n(esp)n(onding)e(inter)n(action,)j(i.e.)e(it)h (satis\014es)g(\(B.5\).)60 2505 y FQ(This)f(theorem)e(constitutes)i(the)g (precise)e(v)o(ersion)i(of)g(the)f(idea)h(that)g(only)g(con\014gurations)h (with)60 2566 y(minim)o(al)c(energy)h(\\surviv)o(e")h(at)h(zero)f(temp)q (erature.)938 2784 y(201)p eop %%Page: 202 202 bop 60 91 a FM(B.2.3)55 b(Rigid)18 b(Ground-State)g(Con\014gurations)60 184 y FQ(The)i(set)h(of)f(ground-state)i(con\014gurations)g(is)e(in)g (general)g(rather)g(large.)33 b(Already)20 b(the)g(ferro-)60 244 y(magnetic)13 b(Ising)i(mo)q(del)f(pro)o(vides)g(a)i(ric)o(h)e (illustration.)20 b(This)15 b(mo)q(del)f(has)i(exactly)d(t)o(w)o(o)i(p)q (erio)q(dic)60 304 y(\(in)f(fact)f(translation-in)o(v)m(arian)o(t\))i (ground-state)g(con\014gurations:)21 b(the)14 b(all-\\+")h(and)f(the)g (all-\\)p FE(\000)p FQ(")60 364 y(con\014gurations.)22 b(But)16 b(in)f(addition)h(it)f(presen)o(ts)g(in\014nitely)f(man)o(y)g(non-p)q(erio)q (dic)j(con\014gurations)60 424 y(exhibiting)f(in)o(terfaces)h(b)q(et)o(w)o (een)f(\\+")i(and)h(\\)p FE(\000)p FQ(")f(spins.)25 b(In)17 b(all)g(dimensions)f(w)o(e)h(ha)o(v)o(e)g(the)g(\015at-)60 485 y(in)o(terface)e(con\014gurations:)699 573 y FF(!)729 580 y FD(x)779 573 y FQ(=)845 500 y Fx(\()899 543 y FQ(+1)43 b(for)16 b FF(x)1106 550 y FH(1)1140 543 y FE(\025)d FQ(0)899 603 y FE(\000)p FQ(1)42 b(for)16 b FF(x)1106 610 y FH(1)1140 603 y FF(<)d FQ(0)1780 573 y(\(B)p FF(:)p FQ(6\))60 692 y(\(and)19 b(translated,)g(90)471 673 y Fy(\016)491 692 y FQ(-rotated)g(and)g(180)849 673 y Fy(\016)870 692 y FQ(-rotated)g(v)o(ersions)f(of)g(this\).)27 b(In)18 b(higher)g(dimensions)60 752 y(w)o(e)g(ha)o(v)o(e)g(a)g(gro)o(wing)h (zo)q(o:)27 b(F)l(or)18 b(dimensions)f FF(d)h FE(\025)f FQ(2)i(w)o(e)f(ha)o (v)o(e)f(con\014gurations)j(with)e(in)o(terfaces)60 812 y(in)f(the)h(form)e (of)i(staircases;)g(for)g FF(d)e FE(\025)g FQ(3)i(there)f(app)q(ear)i (con\014gurations)g(resem)o(bling)c(\\b)q(o)q(oks)20 b(on)60 872 y(a)d(table")f(or)h(\\b)q(o)q(oks)h(on)f(a)f(staircase")h([95].)k(See)16 b(this)g(last)g(reference)f(for)h(a)h(partial)f(catalogue.)133 932 y(Not)11 b(all)g(these)g(con\014gurations)i(are)e(equally)f(relev)m(an)o (t)h(for)g(zero-)h(and)g(lo)o(w-temp)q(erature)e(phase)60 992 y(diagrams.)20 b(W)l(e)14 b(can)h(distinguish)f(three)g(m)o(utually)e (exclusiv)o(e)g(categories)i(roughly)h(represen)o(ting)60 1053 y(di\013eren)o(t)21 b(\(for)h(us)h(decreasing\))f(lev)o(els)e(of)i(relev)m (ance.)37 b(W)l(e)22 b(shall)g(call)f(them)g FP(rigid)5 b FQ(,)23 b FP(c)n(onvivial)60 1113 y FQ(and)17 b FP(sup)n(er\015uous)t FQ(.)j(The)d(rigid)e(con\014gurations)j(are)e(usually)g(the)g(most)g(imp)q (ortan)o(t)f(ones)h(\(alb)q(eit)60 1173 y(not)h(the)g(most)e(n)o(umerous\);)h (they)g(are)h(asso)q(ciated)g(to)g(deterministic)d(zero-temp)q(erature)h (Gibbs)60 1233 y(measures:)60 1335 y FM(De\014nition)j(B.4)23 b FP(F)l(or)g(a)f(given)i(inter)n(action)g FQ(\010)p FP(,)g(a)f(gr)n (ound-state)g(c)n(on\014gur)n(ation)h FF(!)g FP(is)f(c)n(al)r(le)n(d)60 1395 y FQ(rigid)18 b FP([8])g(if)h(the)g(me)n(asur)n(e)e FF(\016)591 1402 y FD(!)635 1395 y FP(c)n(onc)n(entr)n(ate)n(d)h(on)h FF(!)i FP(is)d(a)h(zer)n(o-temp)n(er)n(atur)n(e)e(Gibbs)i(me)n(asur)n(e)f(for)60 1455 y FQ(\010)p FP(,)g(i.e.)f(is)h(c)n(onsistent)g(with)g(the)g(sp)n(e)n (ci\014c)n(ation)g(\(B.1\).)60 1557 y FQ(A)e(simple)e(calculation)h(pro)o(v)o (es)h(the)g(follo)o(wing:)60 1659 y FM(Prop)r(osition)i(B.5)24 b FP(A)17 b(gr)n(ound-state)i(c)n(on\014gur)n(ation)f FF(!)h FP(is)e(rigid)h(if)f(and)h(only)g(if)850 1769 y FE(j)p FQ(\012)899 1748 y FH(\010)899 1781 y(\003)p FD(;!)955 1787 y Fr(\003)976 1780 y Fs(c)996 1769 y FE(j)c FQ(=)g(1)680 b(\(B)p FF(:)p FQ(7\))60 1879 y FP(for)17 b(al)r(l)i(\014nite)f FQ(\003)p FP(.)60 1980 y FQ(In)13 b(w)o(ords,)h(this)e(theorem)g(sa)o(ys)h(that)h FF(!)h FQ(placed)e(as)g(a)h(b)q(oundary)g(condition)f(determines)d(uniquely) 60 2041 y(the)k(minim)o(al-energy)d(con\014guration)k(inside)e(an)o(y)h(giv)o (en)f(v)o(olume)f(\(thereb)o(y)h(justifying)g(the)h(qual-)60 2101 y(i\014er)f(\\rigid"\).)21 b(Equiv)m(alen)o(tly)l(,)12 b(an)o(y)i(lo)q(cal)g(c)o(hange)h(of)f FF(!)i FQ(pro)q(duces)f(a)g(strictly)d (p)q(ositiv)o(e)i(c)o(hange)g(of)60 2161 y(energy)l(.)20 b(Usual)13 b(phase-diagram)h(studies)g(|)f(in)h(particular)f(Pirogo)o(v-Sinai)h(theory)f (|)h(deal)f(only)60 2221 y(with)k(these)g(deterministic)d(zero-temp)q (erature)i(Gibbs)i(measures)e(and)i(their)e(lo)o(w-temp)q(erature)60 2281 y(p)q(erturbations.)30 b(\()p FP(Warning)t FQ(:)e(Reference)17 b([95)q(])h(reserv)o(es)g(the)h(name)f(\\ground-state)j(con\014gura-)60 2342 y(tions")c(only)f(for)g(the)g(rigid)g(ones.\))133 2402 y(F)l(or)e(the)g(Ising)g(mo)q(del)f(\(ferromagnetic,)g(zero)h(magnetic)e (\014eld\),)i(it)g(is)g(clear)f(that)i(the)f(all-\\+")60 2462 y(and)f(all-\\)p FE(\000)p FQ(")g(con\014gurations)g(satisfy)g(\(B.7\))f(and) h(hence)e(they)h(are)g(rigid)g(in)g(an)o(y)h(dimension.)18 b(The)60 2522 y(case)e(of)f(the)h(non-p)q(erio)q(dic)g(ground-state)h (con\014gurations)g(\(\015at-in)o(terface,)e(staircase-in)o(terface,)60 2582 y(etc.\))32 b(is)20 b(more)e(delicate.)31 b(There)20 b(is,)g(ho)o(w)o (ev)o(er,)f(a)i(simple)d(argumen)o(t)g([95)q(])h(sho)o(wing)i(that)f(if)g FF(!)60 2643 y FQ(is)d(a)h(ground-state)h(con\014guration)g(for)f(the)f FF(d)p FQ(-dimensional)g(Ising)g(mo)q(del,)f(then)i(its)f(cylindrical)938 2784 y(202)p eop %%Page: 203 203 bop 60 91 a FQ(extension)18 b(to)i(an)f(extra)f(dimension)g(|)g(de\014ned)h (b)o(y)1086 87 y Fx(e)1081 91 y FF(!)1111 99 y FH(\()p FD(x)1145 104 y Fr(1)1163 99 y FD(;:::)o(;x)1232 105 y Fs(d)1249 99 y FD(;x)1279 105 y Fs(d)p Fr(+1)1336 99 y FH(\))1370 91 y FE(\021)f FF(!)1457 99 y FH(\()p FD(x)1491 104 y Fr(1)1508 99 y FD(;:::)o(;x)1577 105 y Fs(d)1595 99 y FH(\))1630 91 y FQ(|)g(is)h(a)g FP(rigid)60 152 y FQ(ground-state)d(con\014guration)f(for)g(the)f(\()p FF(d)7 b FQ(+)g(1\)-dimensional)15 b(Ising)f(mo)q(del.)19 b(Indeed,)14 b(if)g(w)o(e)g(think)60 212 y(of)20 b(the)g(extra)g(dimension)e(as)j(\\v)o (ertical",)e(an)o(y)h(lo)q(cal)g(c)o(hange)g(of)1318 208 y Fx(e)1314 212 y FF(!)i FQ(consists)e(of)h(a)f FP(\014nite)h FQ(stac)o(k)60 272 y(of)f(lo)q(cal)f(c)o(hanges)h(of)g FF(!)r FQ(.)31 b(The)19 b(b)q(ottom)g(and)i(top)e FF(d)p FQ(-dimensional)g(sections) g(of)h(this)f(stac)o(k)g(face)60 332 y(sections)i(where)g(the)g (con\014guration)i(is)e(equal)g(to)h FF(!)h FQ(without)f(c)o(hanges.)37 b(Th)o(us,)22 b(some)f(of)g(the)60 392 y(corresp)q(onding)12 b(\\v)o(ertical")e(b)q(onds)i(join)f(an)o(tiparallel)e(spins,)j(whic)o(h)e (pro)q(duces)i(a)f(strictly)f(p)q(ositiv)o(e)60 452 y(con)o(tribution)16 b(to)g(the)g(c)o(hange)h(in)e(energy)l(.)21 b(This)c(pro)o(v)o(es)e(\(B.7\))h (and)h(hence)e(the)h(rigidit)o(y)f(of)1804 448 y Fx(e)1799 452 y FF(!)s FQ(.)133 513 y(As)c(a)g(consequence)f(of)h(this)g(argumen)o(t,)f (w)o(e)h(conclude)f(that)h(the)g(\015at-in)o(terface)f(con\014gurations)60 573 y(are)j(rigid)g(for)g FF(d)i FE(\025)e FQ(2,)h(the)f(staircase-in)o (terface)f(ones)i(are)f(rigid)f(for)i FF(d)g FE(\025)g FQ(3,)f(and)h(so)g (on.)21 b(The)13 b(pro)q(of)60 633 y(that)20 b(the)f(rigidit)o(y)f(do)q(es)j FP(not)j FQ(extend)19 b FP(b)n(elow)26 b FQ(suc)o(h)20 b(dimensions)e (requires)g(further)h(argumen)o(ts.)60 693 y(W)l(e)d(shall)g(commen)o(t)d(on) k(this)f(b)q(elo)o(w.)133 753 y FM(Remark.)i FQ(Rigidit)o(y)12 b(of)h(a)h(ground-state)h(con\014guration)f FF(!)i FQ(do)q(es)e(not)g (exclude)d(its)i(b)q(elonging)60 814 y FP(also)18 b FQ(to)d(the)g(supp)q(ort) h(of)f(some)f(zero-temp)q(erature)f(Gibbs)i(measure)f(that)h(is)g(not)g (deterministic)o(.)60 874 y(F)l(or)23 b(instance,)h(if)f(there)f(is)h(more)f (than)i(one)f(rigid)g(con\014guration,)i(one)f(can)f(of)g(course)h(tak)o(e)60 934 y(con)o(v)o(ex)d(com)o(binations)f(of)i(the)g(corresp)q(onding)h (delta-measures.)37 b(The)22 b(p)q(ossibilit)o(y)f(of)h(a)g(less)60 994 y(trivial)15 b(example)f(will)h(b)q(e)i(discussed)f(b)q(elo)o(w,)f(after) i(\(B.10\).)60 1124 y FM(B.2.4)55 b(Con)n(vivial)18 b(Con\014gurations.)25 b(Zero-T)-5 b(emp)r(erature)15 b(En)n(trop)n(y)60 1216 y FQ(Ho)o(w)o(ev)o (er,)f(not)j(all)f(is)g(deterministic)d(in)i(zero-temp)q(erature)g(life.)20 b(Our)d(next)e(t)o(yp)q(e)h(of)h(con\014gura-)60 1277 y(tions)c(are)g(those)h (that)f(b)q(elong)g(only)g(to)h(the)e(supp)q(ort)i(of)g(a)f (non-deterministic)e(zero-temp)q(erature)60 1337 y(Gibbs)i(measure.)18 b(W)l(e)12 b(recall)g(that)h(the)f(supp)q(ort)h(of)g(a)g(measure)e(is)h(the)g (complemen)n(t)e(of)j(the)f(union)60 1397 y(of)17 b(all)e(the)h(zero-measure) f(op)q(en)i(sets)f(\(that)h(is,)f(the)g(smallest)e(closed)i(set)g(with)g (full)g(measure\).)60 1499 y FM(De\014nition)i(B.6)23 b FP(F)l(or)17 b(a)h(given)h(inter)n(action,)f(a)f(gr)n(ound-state)h(c)n(on\014gur)n(ation)g FF(!)i FP(is)d(c)n(al)r(le)n(d)i FQ(con-)60 1559 y(vivial)14 b FP(if)i FF(\016)260 1566 y FD(!)301 1559 y FP(is)g(not)g(a)g(zer)n(o-temp)n (er)n(atur)n(e)f(Gibbs)h(me)n(asur)n(e)f(but)i(ther)n(e)f(exists)g(a)g(zer)n (o-temp)n(er)n(atur)n(e)60 1619 y(Gibbs)i(me)n(asur)n(e)e(having)j FF(!)h FP(in)d(its)h(supp)n(ort.)60 1721 y FQ(These)e(ground-state)i (con\014gurations,)g(whic)o(h)e(individually)e(ha)o(v)o(e)i(little)f(or)i(no) g(w)o(eigh)o(t)e(but)i(are)60 1781 y(relev)m(an)o(t)11 b(as)h(an)g(ensem)o (ble,)d(and)j(the)f(asso)q(ciated)i(non-deterministic)c(Gibbs)j(measure)e (supp)q(orted)60 1841 y(on)21 b(suc)o(h)g(an)g(ensem)o(ble,)e(are)h(probably) h(not)h(what)f(the)g(ph)o(ysicist-in-the-street)e(has)i(in)g(mind)60 1901 y(when)11 b(thinking)g(ab)q(out)h(zero)f(temp)q(erature.)18 b(One)11 b(exp)q(ects)f(them)g(in)g(cases)i(where)e(there)h(is)g(a)g(large)60 1962 y(degeneracy)j(in)h(the)f(ground)i(state.)21 b(The)15 b(precise)f(concept)h(measuring)f(suc)o(h)g(degeneracy)h(is)f(the)60 2022 y FP(zer)n(o-temp)n(er)n(atur)n(e)j(entr)n(opy)k FQ(\(also)c(called)f FP(r)n(esidual)h(entr)n(opy)t FQ(\).)23 b(F)l(or)17 b(the)g(sak)o(e)f(of)i (completeness,)60 2082 y(w)o(e)i(brie\015y)g(review)f(the)h(de\014nition)h (and)g(principal)e(prop)q(erties)i(of)g(this)f(quan)o(tit)o(y)l(.)33 b(Our)20 b(main)60 2142 y(reference)15 b(is)h(the)g(classic)f(article)g(b)o (y)h(Aizenman)e(and)j(Lieb)f([8].)133 2202 y(There)f(are)g(some)f(subtleties) g(in)o(v)o(olv)o(ed)f(in)i(the)f(righ)o(t)h(notion)g(of)h(zero-temp)q (erature)d(en)o(trop)o(y)l(.)60 2263 y(Heuristically)l(,)e(its)j(computation) f(requires)g(a)h(limit)d(pro)q(cess:)21 b(one)13 b(m)o(ust)g(compute)f(\(or)i (measure\))60 2323 y(a)20 b(sequence)f(of)h(lo)o(w-temp)q(erature)f(en)o (tropies)g(and)i(tak)o(e)e(the)h(limit)d(as)k(the)e(temp)q(erature)g(go)q(es) 60 2383 y(to)g(zero.)29 b(The)19 b(so-called)g(\\third)g(la)o(w)g(of)g (thermo)q(dynamics")e(claims)g(that)i(suc)o(h)g(a)g(limit)d(m)o(ust)60 2443 y(b)q(e)22 b(zero;)j(suc)o(h)c(b)q(eha)o(vior)h(is)g(indeed)g(seen)f(in) h(simple)e(mo)q(dels,)i(but)g FP(not)28 b FQ(alw)o(a)o(ys.)38 b(Its)22 b(viola-)60 2503 y(tion)d(m)o(ust)f(b)q(e)h(in)o(terpreted)e(as)j (signaling)f(a)h(large)f(\\degeneracy)g(of)g(the)g(ground)h(state".)30 b(The)60 2563 y(formalization)16 b(of)i(these)g(ideas)f(requires)g(a)h (consideration)g(of)g(the)f(role)h(of)g(the)f(in\014nite-v)o(olume)60 2624 y(limit.)35 b(As)22 b(p)q(oin)o(ted)g(out)g(b)o(y)g(some)e(authors)j (\(see)f(references)e(in)i([8]\),)g(the)g(v)o(olume)d(m)o(ust)i(b)q(e)938 2784 y(203)p eop %%Page: 204 204 bop 60 91 a FQ(sen)o(t)20 b(to)h(in\014nit)o(y)e FP(b)n(efor)n(e)24 b FQ(taking)d(the)f(limit)e FF(T)28 b FE(!)21 b FQ(0.)34 b(But)21 b(in)f(this)g(case,)h(one)g(m)o(ust)e(consider)60 152 y(with)f(some)f(care)h (the)f(b)q(oundary)j(conditions.)26 b(If,)18 b(motiv)m(ated)f(b)o(y)g(the)h (\\ground-state-energy")60 212 y(\(=)j(v)m(ariational\))g(approac)o(h)h([see) e(eq.)g(\(B.14\))g(b)q(elo)o(w],)i(one)f(w)o(orks)g(with)g(pre-\014xed)f(|)h (for)g(in-)60 272 y(stance)15 b(free)g(|)f(b)q(oundary)j(conditions,)e(then)g (there)f(are)h(examples)e(where)i(the)g(con)o(tribution)g(of)60 332 y(some)j(excited)g(con\014gurations)i(surviv)o(es)f(the)f(zero-temp)q (erature)g(limit,)f(so)j(that)f(the)g(residual)60 392 y(en)o(trop)o(y)e (seems)f(to)i(b)q(e)g(measuring)e(more)g(than)j(just)e(the)h(\\degeneracy)f (of)h(the)f(ground)i(state".)60 452 y(The)g(correct)g(w)o(a)o(y)f(to)i (consider)f(the)g(b)q(oundary)h(conditions,)g(and)f(hence)g(the)g(righ)o(t)f (de\014nition)60 513 y(of)g(\\degeneracy",)g(w)o(as)g(p)q(oin)o(ted)f(out)h (b)o(y)f(Aizenman)f(and)i(Lieb)f([8].)25 b(A)o(t)17 b(the)h(same)e(time,)g (they)60 573 y(pro)o(vided)21 b(a)h(remark)m(able)e(form)o(ula)h(for)h(the)f (zero-temp)q(erature)f(en)o(trop)o(y)h(purely)g(in)g(terms)g(of)60 633 y(zero-temp)q(erature)d(concepts,)h(with)g(no)g(reference)f(to)h(limits)e (from)h(\014nite)h(temp)q(eratures.)28 b(W)l(e)60 693 y(shall)15 b(tak)o(e)g(this)h(form)o(ula)e(as)i(the)f(de\014nition.)21 b(F)l(or)15 b(a)h(\014nite)f(set)h(\003)f(and)h(an)g(in)o(teraction)f(\010,)g (let)g(us)60 753 y(denote)h FE(G)250 735 y FH(\010)247 766 y(\003)294 753 y FQ(the)g(set)g(of)g(restrictions)g(to)g(\003)h(of)f(the)g (ground-state)i(con\014gurations)f(for)g(\010.)60 866 y FM(De\014nition)h (B.7)23 b FP(The)18 b FQ(zero-temp)q(erature)d(en)o(trop)o(y)h FP(for)h(an)h(inter)n(action)g FQ(\010)g FP(is)f(the)h(limit)718 994 y FF(s)741 1001 y FH(\010)796 994 y FQ(=)42 b(lim)862 1024 y FH(\003)p Fy(\0451)989 961 y FQ(1)p 970 983 62 2 v 970 1029 a FE(j)p FQ(\003)p FE(j)1045 994 y FQ(log)10 b FE(jG)1164 974 y FH(\010)1161 1007 y(\003)1191 994 y FE(j)j FF(:)548 b FQ(\(B)p FF(:)p FQ(8\))60 1132 y(In)18 b(w)o(ords,)i(this)e(form)o(ula)f(sa)o(ys)i (that)g(a)g(system)f(has)h(non-zero)g(residual)f(en)o(trop)o(y)g(i\013)h(the) f(n)o(um-)60 1193 y(b)q(er)k(of)f(distinct)g(ground-state)i (con\014gurations,)h(as)e(view)o(ed)e(within)h(a)h(\014nite)f(v)o(olume,)f (gro)o(ws)60 1253 y(exp)q(onen)o(tially)e(with)i(this)g(v)o(olume.)30 b(F)l(ollo)o(wing)19 b([244)q(],)h(it)f(is)h(suggestiv)o(e)f(to)h(call)f(suc) o(h)h(mo)q(dels)60 1313 y FP(sup)n(er-de)n(gener)n(ate)t FQ(.)27 b(In)o(tuitiv)o(ely)l(,)15 b(this)i(feature)h(requires)f(the)h(presence)f(of) h(comp)q(eting)f(in)o(terac-)60 1373 y(tions)j(to)g(pro)q(duce)g(a)g (su\016cien)o(t)e(large)i(n)o(um)o(b)q(er)d(of)j(ground-state)i (con\014gurations.)32 b(Indeed,)19 b(it)60 1433 y(can)d(b)q(e)h(pro)o(v)o(en) e([8])h(that)h(all)e(ferromagnetic)g(mo)q(dels)g(ha)o(v)o(e)h(zero)g (residual)f(en)o(trop)o(y)l(.)133 1494 y(The)j(k)o(ey)e(result)i (establishing)f(the)h(connection)f(b)q(et)o(w)o(een)g(non-zero)h(residual)f (en)o(trop)o(y)g(and)60 1554 y(existence)f(of)j(con)o(vivial)d(ground-state)k (con\014gurations)f(is)f(the)f(follo)o(wing.)27 b(T)l(o)18 b(abbreviate,)g(for)60 1614 y(a)g(translation-in)o(v)m(arian)o(t)g(\(or)g(p)q (erio)q(dic\))g(measure)e FF(\026)i FQ(w)o(e)f(denote)h FF(s)p FQ(\()p FF(\026)p FQ(\))f FE(\021)f(\000)p FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\026)1622 1596 y FH(0)1641 1614 y FQ(\))d(+)f(log)d FE(j)p FQ(\012)1843 1621 y FH(0)1863 1614 y FE(j)p FQ(,)60 1674 y(where)22 b FF(i)p FQ(\()p FF(\026)p FE(j)p FF(\027)s FQ(\))h(is)g(the)f(relativ)o(e)f(en)o(trop)o(y)h(densit)o(y)g(de\014ned)h(in) f(Section)g(2.6.2,)i(and)g FF(\026)1724 1656 y FH(0)1767 1674 y FQ(is)e(the)60 1734 y(pro)q(duct)c(o)o(v)o(er)e(all)g(sites)h(of)g (normalized)e(coun)o(ting)i(measure.)22 b(\(This)17 b(the)f(the)h(ph)o (ysicists')f(usual)60 1795 y(en)o(trop)o(y)l(,)e(whic)o(h)g(is)h(de\014ned)f (relativ)o(e)f(to)j FP(unnormalize)n(d)k FQ(coun)o(ting)15 b(measure)e(on)j(the)e(single-spin)60 1855 y(space)i(\012)225 1862 y FH(0)262 1855 y FQ(|)g(this)g(accoun)o(ts)g(for)h(the)f(additiv)o(e)f (constan)o(t)h(log)10 b FE(j)p FQ(\012)1284 1862 y FH(0)1303 1855 y FE(j)p FQ(.\))60 1955 y FM(Prop)r(osition)18 b(B.8)24 b FP(Fix)17 b(an)h(inter)n(action)g FQ(\010)p FP(.)23 b(Then:)93 2056 y(\(a\))h(If)15 b FF(\026)g FP(is)g(a)g(tr)n(anslation-invariant)h (w-zer)n(o-temp)n(er)n(atur)n(e)f(me)n(asur)n(e)f(for)g FQ(\010)p FP(,)i(then)g FF(s)p FQ(\()p FF(\026)p FQ(\))e FE(\024)g FF(s)1848 2063 y FH(\010)1875 2056 y FP(.)95 2157 y(\(b\))25 b(Ther)n(e)14 b(exists)i(for)e FQ(\010)h FP(a)g(tr)n(anslation-invariant)h(zer)n(o-temp)n (er)n(atur)n(e)d(Gibbs)j(me)n(asur)n(e)e FF(\026)h FP(such)182 2218 y(that)j FF(s)p FQ(\()p FF(\026)p FQ(\))c(=)f FF(s)460 2225 y FH(\010)488 2218 y FP(.)60 2318 y FQ(W)l(e)j(summarize)e(b)q(elo)o(w)i (the)g(results)h(on)g(whic)o(h)e(this)i(prop)q(osition)g(is)g(based)g(\(Prop) q(osition)g(B.13)60 2379 y(and)c(Theorems)e(B.11,)h(B.15)g(and)h(B.17)f(part) h(\(b\)\).)20 b(W)l(e)12 b(note)g(that)h(if)f(the)f(supp)q(ort)j(of)e FF(\026)h FQ(is)f(a)h(\014nite)60 2439 y(set,)k(then)h FF(s)p FQ(\()p FF(\026)p FQ(\))e(=)g(0)h([)p FF(\026)h FQ(is)f(of)h(the)f(form)834 2406 y Fx(P)878 2449 y FD(i)901 2439 y FF(\025)929 2446 y FD(i)943 2439 y FF(\016)965 2446 y FD(!)987 2451 y Fs(i)1002 2439 y FQ(,)g(hence)g FF(s)p FQ(\()p FF(\026)p FQ(\))f FE(\024)g(\000)p FQ(\(1)p FF(=)p FE(j)p FQ(\003)p FE(j)p FQ(\))1526 2406 y Fx(P)1570 2449 y FD(i)1592 2439 y FF(\025)1620 2446 y FD(i)1643 2439 y FQ(log)9 b FF(\025)1742 2446 y FD(i)1773 2439 y FE(!)16 b FQ(0].)60 2499 y(Therefore,)f(w)o(e)h(conclude)g(the)g(follo)o(wing:)60 2600 y FM(Prop)r(osition)i(B.9)24 b FP(A)i(sup)n(er-de)n(gener)n(ate)h (system)g(with)f(\014nitely)i(many)e(rigid)g(gr)n(ound-state)60 2660 y(c)n(on\014gur)n(ations)18 b(exhibits)h(in\014nitely)g(many)e(c)n (onvivial)i(gr)n(ound-state)f(c)n(on\014gur)n(ations.)938 2784 y FQ(204)p eop %%Page: 205 205 bop 133 91 a FQ(This)15 b(prop)q(osition)h(co)o(v)o(ers)e(all)h(the)g(cases)g (w)o(e)g(kno)o(w)g(of)g(in)g(whic)o(h)f(the)h(existence)e(of)j(con)o(vivial) 60 152 y(ground-state)k(con\014gurations)g(has)g(b)q(een)e(pro)o(v)o(en.)28 b(Consider,)20 b(for)f(example,)d(the)j(mo)q(del)e(with)60 212 y(spins)f FF(!)212 219 y FD(i)241 212 y FQ(=)e FE(\000)p FQ(1)p FF(;)8 b FQ(0)p FF(;)g FQ(1)16 b(and)h(Hamiltonian)724 317 y FF(H)764 324 y FH(\003)805 317 y FQ(=)886 276 y Fx(X)856 370 y Fy(j)p FD(i)p Fy(\000)p FD(j)r Fy(j)p FH(=1)977 317 y FQ(\()p FF(!)1028 297 y FH(2)1026 329 y FD(i)1059 317 y FE(\000)10 b FF(!)1140 297 y FH(2)1138 329 y FD(j)1160 317 y FQ(\))1179 297 y FH(2)1213 317 y FF(:)553 b FQ(\(B)p FF(:)p FQ(9\))60 466 y(The)16 b(ground-state)i(con\014gurations)g(for)f(this)f(mo)q(del)f(are) i(all)f(the)g(con\014gurations)i(with)e(no)h(spin)60 526 y(equal)j(to)i (zero,)f(and)h(the)f(all-\\0")h(con\014guration.)36 b(The)21 b(zero-temp)q(erature)f(en)o(trop)o(y)g(for)h(this)60 587 y(mo)q(del)15 b(is)h(exactly)f(log)10 b(2.)22 b(As)16 b(the)g(all-\\0")h(con\014guration)h (is)e(the)g(only)g(rigid)g(one,)g(w)o(e)g(conclude,)60 647 y(b)o(y)e(the)h(previous)g(prop)q(osition,)h(that)f(there)g(m)o(ust)e(b)q(e)i (in\014nitely)f(man)o(y)f(con)o(vivial)g(ground-state)60 707 y(con\014gurations.)29 b(Another)18 b(imp)q(ortan)o(t)g(example)e(is)i(the)h (Ising)f(mo)q(del)f(with)h(nearest-neigh)o(b)q(or)60 767 y(an)o (tiferromagnetic)10 b(coupling)i(of)g(strength)h FF(J)j FQ(and)d(magnetic)e (\014eld)g FF(h)j FQ(=)g(2)p FF(d)p FE(j)p FF(J)5 b FE(j)p FQ(.)20 b(Its)11 b(ground-state)60 827 y(con\014gurations)i(are)e(those)h(in) f(whic)o(h)f(no)i(t)o(w)o(o)f(nearest-neigh)o(b)q(or)h(spins)f(are)h(sim)o (ultaneously)d(\\)p FE(\000)p FQ(",)60 887 y(a)21 b(fact)f(that)g(pro)q (duces)h(a)f(non-zero)h(residual)f(en)o(trop)o(y)l(.)32 b(There)20 b(are)g(no)g(rigid)g(con\014gurations,)60 948 y(hence)f(the)h(prop)q(osition) h(implies)c(the)j(existence)e(of)i(man)o(y)f(con)o(vivial)f(ones.)33 b(F)l(or)20 b(this)g(mo)q(del,)60 1008 y(suc)o(h)f(a)g(fact)g(can)g(b)q(e)h (pro)o(v)o(en)e(also)i(b)o(y)e(a)i(di\013eren)o(t)e(argumen)o(t)g(whic)o(h)g (yields)g(some)g(additional)60 1068 y(insigh)o(t.)i(Indeed,)13 b(b)o(y)h(iden)o(tifying)e(a)i(\\)p FE(\000)p FQ(")h(spin)f(with)g(the)f (presence)g(of)i(a)f(particle,)f(the)h(ensem)o(ble)60 1128 y(of)19 b(ground-state)h(con\014gurations)g(|)f(with)g(the)f(asso)q(ciated)i (conditional)e(probabilities)g(giving)60 1188 y(equal)f(w)o(eigh)o(t)h(to)g (all)f(of)i(them)d(|)i(is)g(seen)f(to)i(corresp)q(ond)g(to)f(the)g (grand-canonical)h(ensem)o(ble)60 1249 y(for)f(the)g(ideal)f(lattice)g(gas)i (with)f(nearest-neigh)o(b)q(or)g(exclusion)f(and)i(c)o(hemical)c(p)q(oten)o (tial)j(equal)60 1309 y(to)g(zero.)26 b(Using)18 b(a)h(b)q(eautiful)e (computer-assisted)h(pro)q(of,)h(Dobrushin,)f(Kolafa)h(and)g(Shlosman)60 1369 y([87])e(pro)o(v)o(ed)e(that)j(suc)o(h)e(a)h(system)e(has)j(an)f FP(unique)h FQ(Gibbs)f(measure.)k(As)16 b(none)h(of)g(the)g(ground-)60 1429 y(state)j(con\014gurations)i(are)e(rigid,)h(this)f(Gibbs)g(measure)f(is) h(non-deterministic)e(and)j(therefore)60 1489 y(supp)q(orted)g(on)f(con)o (vivial)f(con\014gurations.)33 b(This)20 b(example)e(sho)o(ws)j(a)f(w)o(a)o (y)g(\(in)f(fact,)i(the)e(only)60 1550 y(one)f(w)o(e)g(kno)o(w)h(of)s(\))g (to)f(in)o(terpret)f(and)i(understand)g(the)f(c)o(haracteristics)f(of)h (non-deterministic)60 1610 y(zero-temp)q(erature)j(Gibbs)i(measures)e(supp)q (orted)j(on)f(\(v)o(ery)e(man)o(y\))h(con)o(vivial)e(ground-state)60 1670 y(con\014gurations:)26 b(One)18 b(maps)f(it)g(in)o(to)h(a)g (statistical-mec)o(hanical)d(problem)i(for)h(another,)g(b)q(etter)60 1730 y(understo)q(o)q(d,)j(equiv)m(alen)o(t)d(system.)28 b(As)19 b(the)g(original)g(ensem)o(ble)e(in)o(v)o(olv)o(es)g(con\014gurations)j(sat-) 60 1790 y(isfying)f(some)f(condition)h(deriv)o(ed)f(from)g(the)h (minimal-energy)d(requiremen)o(t,)g(this)k(equiv)m(alen)o(t)60 1851 y(system)f(will,)g(in)h(general,)g(b)q(e)g(a)h(mo)q(del)d(with)i (exclusions.)32 b(That)21 b(is,)f(it)g(will)f(not)h(\014t)h(in)o(to)e(the)60 1911 y(general)d(formalism)e(dev)o(elop)q(ed)h(in)h(Chapter)g(2.)133 1971 y(Prop)q(osition)21 b(B.9)e(do)q(es)i(not)f(yield)e(an)o(y)i (information)f(on)h(mo)q(dels)f(with)g(zero)h(residual)f(en-)60 2031 y(trop)o(y)l(,)h(for)h(instance)f(on)g(ferromagnetic)f(systems.)31 b(In)20 b(particular,)g(the)g(question)g(remains)f(of)60 2091 y(whether)11 b(con)o(vivialit)o(y)e FP(r)n(e)n(quir)n(es)14 b FQ(sup)q(er-degeneracy)l(.)20 b(A)11 b(p)q(ossible)h(coun)o(terexample)d (is)i(presen)o(ted)60 2151 y(in)19 b(reference)f([95]:)27 b(Consider,)20 b(for)g(the)f(three-dimensional)f(ferromagnetic)f(Ising)j(mo)q(del,)e(the)60 2212 y(ensem)o(ble)c(of)j(ground-state)h(con\014gurations)g(that)g(di\013er)e (only)h(lo)q(cally)f(\(i.e.)f(in)h(\014nite)g(v)o(olumes\))60 2272 y(from)f(the)h(\\zig-zag)h(in)o(terface")e(one:)548 2406 y FF(!)580 2382 y FH(zig)p Fy(\000)p FH(zag)578 2420 y(\()p FD(t)605 2425 y Fr(1)622 2420 y FD(;t)645 2425 y Fr(2)662 2420 y FD(;t)685 2425 y Fr(3)702 2420 y FH(\))745 2406 y FQ(=)811 2333 y Fx(\()865 2375 y FQ(+1)43 b(if)19 b FF(t)1036 2382 y FH(1)1066 2375 y FQ(+)11 b FF(t)1133 2382 y FH(2)1164 2375 y FQ(+)g FF(t)1231 2382 y FH(3)1264 2375 y FF(>)j FQ(0)865 2435 y FE(\000)p FQ(1)42 b(if)19 b FF(t)1036 2442 y FH(1)1066 2435 y FQ(+)11 b FF(t)1133 2442 y FH(2)1164 2435 y FQ(+)g FF(t)1231 2442 y FH(3)1264 2435 y FE(\024)i FQ(0)i FF(:)1755 2406 y FQ(\(B)p FF(:)p FQ(10\))60 2539 y(Suc)o(h)21 b(an)g(ensem)o(ble)e(can)i(b)q(e)g(mapp)q (ed)g(on)o(to)g(an)h(appropriate)f(solid-on-solid)h(mo)q(del.)35 b(If)20 b(this)60 2600 y(mo)q(del)c(can)h(b)q(e)h(pro)o(v)o(en)e(to)i(ha)o(v) o(e)e(at)i(least)f(one)g(Gibbs)g(measure)f(\(a)i(problem)e(still)g(op)q (en\),)h(then)60 2660 y(it)d(w)o(ould)h(imply)d(that)j(the)f(ab)q(o)o(v)o(e)g (con\014gurations)i(are)f(con)o(vivial.)k(W)l(e)14 b(m)o(ust)f(ac)o(kno)o (wledge)h(that)938 2784 y(205)p eop %%Page: 206 206 bop 60 91 a FQ(the)18 b(standing)h(conjecture)e([85)q(,)g(95)q(])h(is)g(that) h(suc)o(h)f(Gibbs)g(measures)f(do)i(not)g(exist.)26 b(Note)18 b(that)60 152 y(if)f(this)g(Gibbs)g(measure)f(exists,)g(then)h(the)g (all-\\+")h(and)f(all-\\)p FE(\000)p FQ(")h(con\014gurations)g(w)o(ould)f(b)q (e)h(at)60 212 y(the)c(same)f(time)f(rigid)i(and)g(in)g(the)g(\(b)q(oundary)h (of)g(the\))f(supp)q(ort)h(of)f(a)h(highly)e(non-deterministic)60 272 y(zero-temp)q(erature)i(Gibbs)h(measure.)133 332 y(Nev)o(ertheless,)g (there)i(is)g(an)h(in)o(teresting)e(result)h(\(Prop)q(osition)i(4)f(of)f ([8]\))g(in)o(v)o(olving)f(mo)q(dels)60 392 y(with)f(zero)g(residual)g(en)o (trop)o(y:)60 483 y FM(Prop)r(osition)i(B.10)24 b FP(If)16 b FF(s)572 490 y FH(\010)613 483 y FQ(=)e(0)p FP(,)j(every)g FQ(translation-in)o(v)m(arian)o(t)g FP(w-zer)n(o-temp)n(er)n(atur)n(e)f(me)n (asur)n(e)60 543 y(for)h FQ(\010)g FP(is)h(supp)n(orte)n(d)e(on)i(the)g(set)g (of)f(rigid)g(gr)n(ound-state)i(c)n(on\014gur)n(ations.)60 634 y FQ(That)12 b(is,)g(if)g(a)g(mo)q(del)e(with)i(zero)f(residual)h(en)o (trop)o(y)f(do)q(es)h(in)f(fact)h(p)q(ossess)h(con)o(vivial)d(ground-state)60 694 y(con\014gurations,)16 b(then)f(suc)o(h)g(con\014gurations)h(can)f(lie)f (in)g(the)h(supp)q(ort)h(only)f(of)g FP(non-tr)n(anslation-)60 755 y(invariant)22 b FQ(zero-temp)q(erature)14 b(Gibbs)j(measures.)133 815 y FM(Remark.)h FQ(On)c(the)g(other)g(hand,)h(Radin)f([304)q(])f(has)i (sho)o(wn)f(examples)e(of)j(sup)q(er-degenerate)60 875 y(systems)g(with)h(a)g (unique)g(translation-in)o(v)m(arian)o(t)g(w-zero-temp)q(erature)f(measure)g (en)o(tirely)f(sup-)60 935 y(p)q(orted)20 b(on)g(the)f(set)h(of)f(rigid)h (ground-state)h(con\014gurations.)32 b(In)19 b(these)g(examples,)f(the)h(set) h(of)60 995 y(ground-state)d(con\014gurations)f(do)q(es)g(not)f(ha)o(v)o(e)f (an)o(y)h(closed)g(translation-in)o(v)m(arian)o(t)g(prop)q(er)g(sub-)60 1055 y(set,)e(hence)g(it)f(is)h(formed)f(b)o(y)h(all)f(the)h(translates)h(of) f(a)h FP(single)k FQ(\(non-p)q(erio)q(dic\))c(con\014guration,)g(and)60 1116 y(limits)c(of)k(suc)o(h.)20 b(The)13 b(non-zero)g(residual)g(en)o(trop)o (y)f(implies)e(that)k(an)o(y)e(t)o(w)o(o)h(suc)o(h)g(translates)g(m)o(ust)60 1176 y(di\013er)g(in)g(in\014nitely)f(man)o(y)g(sites,)h(and)h(hence)e(they)h (all)g(m)o(ust)f(b)q(e)h(rigid)g(ground)i(states.)20 b(Ho)o(w)o(ev)o(er,)60 1236 y(this)15 b(phenomenon)e(can)i(happ)q(en)h(only)e(in)h(the)f(presence)g (of)h FP(in\014nite-r)n(ange)21 b FQ(in)o(teractions)13 b(\(alb)q(eit)60 1296 y(decreasing)j(arbitrarily)f(fast)i(with)f(the)g(range\))h([304)q(].)60 1424 y FM(B.2.5)55 b(Sup)r(er\015uous)19 b(Ground-State)f(Con\014gurations)60 1517 y FQ(The)g(last)h(t)o(yp)q(e)f(of)g(ground-state)i(con\014gurations)g (are)e(those)h(that)g(are)f(not)h(in)f(the)g(supp)q(ort)i(of)60 1577 y(an)o(y)e(zero-temp)q(erature)f(Gibbs)h(measure.)27 b(These)18 b(are)g(ob)o(viously)g(the)g(least)g(in)o(teresting)f(ones,)60 1637 y(and)h(w)o(e)g(shall)f(call)g(them)f FP(sup)n(er\015uous)21 b FQ(ground-state)e(con\014gurations.)27 b(The)18 b(most)f(imme)o(diate)60 1697 y(example)9 b(is)h(pro)o(vided)g(b)o(y)h(the)f(one-dimensional)g (ferromagnetic)f(Ising)i(mo)q(del.)18 b(Its)10 b(ground-state)60 1757 y(con\014gurations)18 b(are)f(the)f(all-\\+",)h(all-\\)p FE(\000)p FQ(")f(and)i(the)e(\015at-in)o(terface)g(con\014gurations.)23 b(Ho)o(w)o(ev)o(er,)60 1818 y FP(al)r(l)k FQ(the)20 b(zero-temp)q(erature)g (Gibbs)g(measures)g(are)h(of)f(the)h(form)e FF(\025\016)1374 1825 y FH(+)1418 1818 y FQ(+)14 b(\(1)g FE(\000)g FF(\025)p FQ(\))p FF(\016)1649 1825 y Fy(\000)1679 1818 y FQ(;)22 b(the)e(\015at-)60 1878 y(in)o(terface)10 b(con\014gurations)k(\(B.6\))d(are)h(sup)q (er\015uous.)21 b(Heuristically)9 b(this)j(is)g(b)q(ecause)g(the)f(in)o (terface)60 1938 y(is)j(free)f(to)h(w)o(ander)g(at)h(no)f(energy)g(cost;)g (in)g(the)g(in\014nite-v)o(olume)d(limit)g(it)i(w)o(anders)i(to)f FE(\0061)p FQ(.)20 b(The)60 1998 y(pro)q(of)k(go)q(es)f(as)g(follo)o(ws:)34 b(Denote)22 b(b)o(y)g FF(\037)843 2005 y FH(+)p Fy(\000)p FD(x)917 2010 y Fr(0)959 1998 y FQ(the)h(indicator)f(function)g(of)h(the)f (con\014guration)60 2058 y(whic)o(h)14 b(is)h(+1)g(for)h FF(x)d(<)h(x)518 2065 y FH(0)553 2058 y FQ(and)h FE(\000)p FQ(1)g(for)h FF(x)d FE(\025)h FF(x)920 2065 y FH(0)939 2058 y FQ(.)21 b(Then,)15 b(for)g(\003)f(=)g([)p FE(\000)p FF(N)r(;)8 b(N)d FQ(],)14 b(the)h(measures)f(\(B.1\))60 2119 y(yield)215 2302 y FF(\031)245 2278 y FH(\010)p FD(;T)5 b FH(=0)243 2314 y(\003)353 2302 y FQ(\()p FF(\037)403 2309 y FH(+)p Fy(\000)p FD(x)477 2314 y Fr(0)496 2302 y FE(j)p FF(\034)h FQ(\))27 b(=)649 2177 y Fx(8)649 2215 y(>)649 2227 y(>)649 2239 y(>)649 2252 y(<)649 2327 y(>)649 2339 y(>)649 2352 y(>)649 2364 y(:)707 2212 y FQ(1)p FF(=)p FQ(\(2)p FF(N)17 b FQ(+)11 b(2\))42 b(if)16 b FF(\034)1054 2219 y Fy(\000)p FH(\()p FD(N)t FH(+1\))1201 2212 y FQ(=)e(+1)p FF(;)j(\034)1367 2219 y FD(N)t FH(+1)1459 2212 y FQ(=)d FE(\000)p FQ(1)1004 2272 y(and)28 b FE(\000)11 b FF(N)19 b FE(\024)14 b FF(x)1299 2279 y FH(0)1332 2272 y FE(\024)g FF(N)i FQ(+)11 b(1)707 2391 y(0)257 b(otherwise)1755 2302 y(\(B)p FF(:)p FQ(11\))60 2488 y([The)12 b(\014rst)h(line)e(is)i(due)f(to)h(the)g(2)p FF(N)c FQ(+)t(2)j(p)q(ossible)h(p)q(ositions)g FF(x)1185 2495 y FH(0)1217 2488 y FQ(for)g(the)g(\\kink")f(\(lac)o(k)g(of)g(rigidit)o(y\).]) 60 2548 y(Therefore,)j(if)h FF(\026)h FQ(is)f(a)g(zero-temp)q(erature)f (Gibbs)i(measure,)d(then)i(for)h(ev)o(ery)d FF(N)20 b FE(\025)13 b(j)p FF(x)1667 2555 y FH(0)1686 2548 y FE(j)j FQ(w)o(e)g(ha)o(v)o(e)383 2652 y FF(\026)p FQ(\()p FF(\037)462 2659 y FH(+)p Fy(\000)p FD(x)536 2664 y Fr(0)556 2652 y FQ(\))41 b(=)h FF(\026)725 2603 y Fx(\020)750 2652 y FF(\031)780 2628 y FH(\010)p FD(;T)5 b FH(=0)778 2664 y(\003)888 2652 y FQ(\()p FF(\037)938 2659 y FH(+)p Fy(\000)p FD(x)1012 2664 y Fr(0)1031 2652 y FE(j)j(\001)g FQ(\))1094 2603 y Fx(\021)938 2784 y FQ(206)p eop %%Page: 207 207 bop 616 116 a FQ(=)766 82 y(1)p 701 104 154 2 v 701 150 a(2)p FF(N)17 b FQ(+)11 b(2)859 116 y FF(\026)p FQ(\()p FF(!)937 123 y Fy(\000)p FH(\()p FD(N)t FH(+1\))1085 116 y FQ(=)j(+1)j(and)g FF(!)1341 123 y FD(N)t FH(+1)1434 116 y FQ(=)c FE(\000)p FQ(1\))616 236 y FE(\024)766 202 y FQ(1)p 701 224 V 701 270 a(2)p FF(N)k FQ(+)11 b(2)873 236 y FF(:)868 b FQ(\(B.12\))60 365 y(Letting)19 b FF(N)k FE(!)18 b(1)g FQ(w)o(e)g(conclude)g(that)h FF(\026)p FQ(\()p FF(\037)896 372 y FH(+)p Fy(\000)p FD(x)970 377 y Fr(0)990 365 y FQ(\))f(=)g(0.)29 b(The)19 b(same)e(holds,)j(of)e(course,)h(for)g(the) 60 425 y(\015at-in)o(terface)14 b(con\014gurations)i(whic)o(h)e(go)i(from)d FE(\000)i FQ(to)g(+.)20 b(As)15 b(the)f(ground-state)j(con\014gurations)60 486 y(here)f(form)f(a)i FP(c)n(ountable)22 b FQ(set)16 b(\(lab)q(elled)g(b)o (y)f FF(x)910 493 y FH(0)944 486 y FE(2)f FQ([)p FE(\0001)p FF(;)8 b FE(1)p FQ(])15 b(and)i(the)f(p)q(olarit)o(y)g(of)h(the)f(kink\),)f (its)60 546 y(measure)e(is)i(the)g(sum)e(of)j(the)e(measure)g(of)h(eac)o(h)f (of)h(its)g(p)q(oin)o(ts.)21 b(Therefore,)14 b(\(B.12\))g(implies)f(that)60 606 y FF(\026)j FQ(giv)o(es)g(full)f(measure)g(to)h(the)g(set)g(formed)f (only)h(b)o(y)g(the)f(all-\\+")i(and)g(all-\\)p FE(\000)p FQ(")f (con\014gurations;)60 666 y(the)c(\015at-in)o(terface)g(con\014gurations)i (are)f(sup)q(er\015uous.)21 b(Com)o(bining)12 b(this)g(with)h(the)f(results)h (stated)60 726 y(ab)q(o)o(v)o(e,)g(w)o(e)g(conclude)f(that)i(the)f(\015at-in) o(terface)f(con\014gurations)j(\(B.6\))e(are)g(sup)q(er\015uous)h(in)f FF(d)h FQ(=)g(1,)60 787 y(and)j(rigid)f(in)g FF(d)e FE(\025)f FQ(2.)133 847 y(The)19 b(preceding)f(argumen)o(t)g(requires)f(not)j(only)e (that)h(there)g(b)q(e)g(a)g(gro)o(wing)g(degeneracy)f(in)60 907 y(the)f(p)q(osition)i(of)e(the)h(in)o(terface,)e(but)h(also)i(that)f(the) f(n)o(um)o(b)q(er)f(of)i(ground-state)h(con\014gurations)60 967 y(b)q(e)d(not)f(to)q(o)i(large,)e(i.e.)f(at)i(most)e(coun)o(table.)21 b(This)15 b(second)h(fact)f(is)h(not)g(true)f(for)g(higher)h(dimen-)60 1027 y(sions.)23 b(In)17 b(dimension)e(t)o(w)o(o,)h(for)h(instance,)f(the)g (\\staircase-in)o(terface")h(con\014gurations)h(form)e(an)60 1088 y(uncoun)o(table)d(set.)21 b(T)l(o)14 b(b)q(e)f(sure,)h(the)f(set)h(of)f (staircases)h(with)g FP(\014nitely)i(many)i FQ(stairs)c(is)f(coun)o(table,)60 1148 y(and)20 b(the)g(ab)q(o)o(v)o(e)f(argumen)o(t)g(can)g(b)q(e)h(used)g(to) g(pro)o(v)o(e)f(that)h(this)f(set)h(has)g(measure)e(zero)i(for)g(all)60 1208 y(zero-temp)q(erature)f(Gibbs)i(measures.)33 b(This)21 b(w)o(ould)f(pro)o(v)o(e)g(that)h(the)f(supp)q(ort)i(of)f(suc)o(h)f(mea-)60 1268 y(sures)e(is)f(alw)o(a)o(ys)g(con)o(tained)g(in)g(the)h(set)f(formed)f (b)o(y)h(the)g(all-\\+",)h(all-\\)p FE(\000)p FQ(",)g(\015at-in)o(terface)e (and)60 1328 y(in\014nite-staircase)d(con\014gurations)i(\(this)e(b)q(eing)g (a)h FP(close)n(d)g FQ(set)g(whose)g(complem)o(en)o(t)c(has)k(measure)60 1389 y(zero\).)27 b(But)18 b(it)g(do)q(es)i(not)e(rule)g(out)h(the)f(o)q (ccurrence)g(of)h(non-deterministic)d(zero-temp)q(erature)60 1449 y(Gibbs)j(measures)e(supp)q(orted)i(on)g(in\014nite-staircase)f (con\014gurations,)i(similarly)c(to)i(what)i(ma)o(y)60 1509 y(happ)q(en)d(in)f(the)h(three-dimensional)d(Ising)i(mo)q(del)g(for)g (con\014gurations)i(close)e(to)h FF(!)1629 1491 y FH(zig)p Fy(\000)p FH(zag)1754 1509 y FQ(.)22 b(Nev-)60 1569 y(ertheless,)c(w)o(e)g(m) o(ust)f(k)o(eep)g(in)h(mind)f(that)h(w)o(e)g(are)h(primarily)d(in)o(terested) h(in)h(those)g(features)h(of)60 1629 y(zero-temp)q(erature)h(phase)i (diagrams)f(that)g(surviv)o(e)f(at)i(\(can)g(tell)e(us)h(something)g(ab)q (out\))h FP(low)60 1689 y(but)c(nonzer)n(o)h FQ(temp)q(erature.)h(Therefore,) 15 b(for)i(the)f(t)o(w)o(o-dimensional)e(Ising)i(mo)q(del)f(the)h(p)q (ossible)60 1750 y(existence)e(of)j(suc)o(h)e(a)i(zero-temp)q(erature)d (Gibbs)i(measure)f(with)h(supp)q(ort)h(on)g(in\014nite-staircase)60 1810 y(con\014gurations)j(is)f(a)g(rather)g(irrelev)m(an)o(t)e(issue,)i (since)f(it)g(has)i(b)q(een)e(pro)o(v)o(en)g([1,)h(192)q(])f(that)h(only)60 1870 y(the)e(Gibbs)h(measures)e(of)i(the)f(form)f FF(\025\016)806 1877 y FH(+)848 1870 y FQ(+)11 b(\(1)i FE(\000)e FF(\025)p FQ(\))p FF(\016)1072 1877 y Fy(\000)1119 1870 y FQ(\\surviv)o(e")17 b(at)h(non-zero)g(temp)q(eratures.)60 1930 y(The)g(question)g(of)g (non-deterministic)e(Gibbs)i(measures)f(b)q(ecomes)g(really)g(imp)q(ortan)o (t)g(only)h(for)60 1990 y(dimension)d FF(d)f FE(\025)f FQ(3.)60 2120 y FM(B.2.6)55 b(Non)n(uniqueness)18 b(of)h(Sp)r(eci\014cations)e(and)j (In)n(teractions)60 2213 y FQ(W)l(e)14 b(shall)h(no)o(w)g(commen)o(t)d(on)j (one)g(imp)q(ortan)o(t)e(di\013erence)h(b)q(et)o(w)o(een)g(the)g(zero-temp)q (erature)f(and)60 2273 y(nonzero-temp)q(erature)i(formalisms:)j(A)o(t)d(zero) g(temp)q(erature)f(the)i(\\in)o(v)o(erse)e(problem")g(|)i(giv)o(en)60 2333 y(a)c(measure,)e(determine)f(the)i(sp)q(eci\014cation)h(and/or)g(the)f (in)o(teraction)g(|)g(is)g(no)h(longer)g(w)o(ell-p)q(osed:)60 2393 y(the)19 b(map)f(from)f(in)o(teractions)h(\(or)i(sp)q(eci\014cations\))e (to)i(zero-temp)q(erature)d(Gibbs)i(measures)f(is,)60 2453 y(in)e(general,)f(man)o(y-to-one.)21 b(This)c(lac)o(k)e(of)h(uniqueness)g (app)q(ears)i(at)e(three)g(di\013eren)o(t)f(lev)o(els:)133 2539 y(A\))20 b(There)g(are)g(measures)f(consisten)o(t)g(with)h(sev)o(eral)f (di\013eren)o(t)g(zero-temp)q(erature)g(sp)q(eci\014-)60 2599 y(cations)k(sim)o(ultaneously)l(.)37 b(Theorem)21 b(2.15)j(do)q(es)f(not)g (apply)f(at)h(zero)f(temp)q(erature)f(b)q(ecause)938 2784 y(207)p eop %%Page: 208 208 bop 60 91 a FQ(there)19 b(are)g(\(large\))g(op)q(en)h(sets)f(ha)o(ving)h (zero)f(measure)f(for)h(all)g(zero-temp)q(erature)f(Gibbs)h(mea-)60 152 y(sures.)24 b(Therefore,)17 b(b)o(y)g(rede\014ning)g(the)g(sp)q (eci\014cation)g(more)f(or)h(less)g(arbitrarily)g(on)g(suc)o(h)g(op)q(en)60 212 y(sets)e(w)o(e)f(can)i(obtain)f(sev)o(eral)f(di\013eren)o(t)g(sp)q (eci\014cations)h(for)g(the)g(same)e(zero-temp)q(erature)h(Gibbs)60 272 y(measure.)40 b(Let)23 b(us)g(presen)o(t)g(an)g(explicit)e(example.)39 b(Consider)23 b(the)g(nearest-neigh)o(b)q(or)g(Ising)60 332 y(mo)q(del)18 b(with)h(formal)f(Hamiltonian)f FE(\000)p FF(J)839 299 y Fx(P)883 342 y Fy(h)p FD(xy)q Fy(i)960 332 y FF(!)990 339 y FD(x)1012 332 y FF(!)1042 339 y FD(y)1076 332 y FE(\000)c FF(h)1164 299 y Fx(P)1208 342 y FD(x)1238 332 y FF(!)1268 339 y FD(x)1290 332 y FQ(.)30 b(Then)19 b(the)g(measure)f FF(\016)1766 339 y FH(+)1814 332 y FQ(is)h(a)60 392 y(zero-temp)q(erature)c(Gibbs)h (measure)f(for)i(the)f(follo)o(wing)g(zero-temp)q(erature)e(sp)q (eci\014cations:)120 494 y(1.)24 b(The)16 b(sp)q(eci\014cation)g FF(\031)590 476 y FH(\010)615 481 y Fr(1)632 476 y FD(;T)5 b FH(=0)731 494 y FQ(where)16 b(\010)907 501 y FH(1)943 494 y FQ(is)g(de\014ned)g(b)o(y)g FF(J)i FQ(=)c(0)j(and)g(some)e FF(h)f(>)g FQ(0.)120 596 y(2.)24 b(The)16 b(sp)q(eci\014cation)g FF(\031)590 578 y FH(\010)615 583 y Fr(2)632 578 y FD(;T)5 b FH(=0)731 596 y FQ(where)16 b(\010)907 603 y FH(2)943 596 y FQ(is)g(de\014ned)g(b)o(y)g(some)f FF(J)k(>)13 b FQ(0)k(and)g FF(h)d FQ(=)g(0.)60 697 y(Nev)o(ertheless,)c(\005)388 679 y FH(\010)413 684 y Fr(1)430 679 y FD(;T)5 b FH(=0)527 697 y FE(6)p FQ(=)13 b(\005)615 679 y FH(\010)640 684 y Fr(2)658 679 y FD(;T)5 b FH(=0)752 697 y FQ(b)q(ecause)12 b(the)f(former)g(has)h FF(\016)1263 704 y FH(+)1304 697 y FQ(as)g(its)g(only)g(zero-temp)q(erature) 60 758 y(Gibbs)18 b(measure,)f(while)g(the)h(latter)g(has)g(b)q(oth)h FF(\016)986 765 y FH(+)1034 758 y FQ(and)f FF(\016)1152 765 y Fy(\000)1199 758 y FQ(as)h(zero-temp)q(erature)e(Gibbs)h(mea-)60 818 y(sures.)133 903 y(B\))11 b(There)f(are)h(zero-temp)q(erature)e(sp)q (eci\014cations)i(whic)o(h)f(arise)h(from)f(sev)o(eral)f(non-ph)o(ysically-) 60 963 y(equiv)m(alen)o(t)21 b(in)o(teractions)h(\(in)g(other)g(w)o(ords,)i (the)e(notion)h(of)g(ph)o(ysical)f(equiv)m(alence)e(b)q(ecomes)60 1023 y(meaningless)15 b(at)h FF(T)21 b FQ(=)13 b(0\).)22 b(W)l(e)16 b(giv)o(e)f(t)o(w)o(o)h(examples:)120 1125 y(1.)24 b(T)l(rivial)19 b(example:)27 b(Consider)20 b(an)o(y)g(in)o(teraction)f(\010)i(and)f(an)o(y)g (n)o(um)o(b)q(er)f FF(\025)i(>)f FQ(0.)34 b(Then)20 b(\010)182 1185 y(and)i FF(\025)p FQ(\010)h(are)f(not)g(\(usually\))f(ph)o(ysically)f (equiv)m(alen)o(t,)i(but)f(they)h(ha)o(v)o(e)f(the)g(same)g(zero-)182 1245 y(temp)q(erature)15 b(sp)q(eci\014cations.)120 1347 y(2.)24 b(Less)19 b(trivial)e(example:)23 b(All)17 b(Ising-t)o(yp)q(e)h(pair)g(in)o (teractions)g(\(not)g(necessarily)f(ferromag-)182 1407 y(netic\))h(suc)o(h)h (that)h FF(h)573 1414 y FD(x)614 1407 y FF(>)671 1374 y Fx(P)715 1418 y FD(y)744 1407 y FE(j)p FF(J)785 1414 y FD(xy)826 1407 y FE(j)f FQ(for)g(all)g FF(x)g FQ(giv)o(e)g(rise)f(to)i(the)f(same)g (zero-temp)q(erature)182 1467 y(sp)q(eci\014cation,)d(namely)e(the)i(one)g (that)h(for)g(eac)o(h)e(\014nite)h(set)g(\003)g(and)h(ev)o(ery)e(b)q(oundary) j(con-)182 1528 y(dition)e(giv)o(es,)f(inside)g(\003,)h(the)g(measure)f (concen)o(trated)h(in)f(the)h(all-\\+")h(con\014guration.)133 1629 y(C\))24 b(The)g(v)m(ariational)f(principle)f(\(Section)h(B.2.8)g(b)q (elo)o(w\))h(reduces)f(to)h(the)f(minim)o(ization)60 1689 y(of)f(the)f(sp)q (eci\014c)g(energy)l(,)h(whic)o(h)f(is)g(not)i(a)e(strictly)g(con)o(v)o(ex)f (functional)h(on)h FE(B)1574 1671 y FH(1)1615 1689 y FQ(or)g(an)o(y)f(of)h (its)60 1750 y(subspaces)17 b FE(B)316 1757 y FD(h)338 1750 y FQ(.)60 1880 y FM(B.2.7)55 b(Stabilit)n(y)18 b(and)h(w-Stabilit)n(y)60 1972 y FQ(Zero)h(temp)q(erature)f(is)h(in)g(itself)g(unattainable.)33 b(So)21 b(one)g(really)e(is)h(in)o(terested)f(in)h(those)h(zero-)60 2032 y(temp)q(erature)d(features)h(that)h(\\surviv)o(e")f(at)h(lo)o(w)f(but)h (nonzero)g(temp)q(eratures.)29 b(F)l(or)20 b(instance,)60 2092 y(one)i(is)g(in)o(terested)e(in)i(determining)e(whic)o(h)h(are)h(the)f (measures)g(that)i(can)f(b)q(e)g(obtained)g(as)h(a)60 2153 y FF(\014)f FE(!)e(1)g FQ(limit)d(of)k(p)q(ositiv)o(e-temp)q(erature)c(Gibbs) k(measures)e(for)h(a)g FP(\014xe)n(d)26 b FQ(in)o(teraction)19 b(\010.)32 b(W)l(e)60 2213 y(shall)18 b(refer)f(to)i(these)e(measures)g(as)i FP(stable)i(me)n(asur)n(es)g FQ(for)d(the)g(in)o(teraction)f(\010.)27 b(It)18 b(is)g(simple)e(to)60 2273 y(c)o(hec)o(k)e(that)j(all)f(these)g (stable)g(measures)f(m)o(ust)g(b)q(e)h(zero-temp)q(erature)f(Gibbs)i (measures)e(for)h(\010:)60 2375 y FM(Theorem)h(B.11)23 b FP(L)n(et)f FF(\026)551 2382 y FD(n)596 2375 y FP(b)n(e)g(Gibbs)g(me)n(asur)n(es)f(for)f (a)i(\014xe)n(d)g(inter)n(action)g FQ(\010)g FP(and)g(a)f(se)n(quenc)n(e)60 2435 y(of)j(inverse)h(temp)n(er)n(atur)n(es)e FF(\014)619 2442 y FD(n)665 2435 y FP(with)i FF(\014)806 2442 y FD(n)854 2435 y FE(!)h FQ(+)p FE(1)p FP(.)41 b(If)24 b FF(\026)1161 2442 y FD(n)1211 2435 y FE(!)h FF(\026)p FP(,)h(then)f(the)f(me)n(asur)n(e)f FF(\026)h FP(is)g(a)60 2495 y(zer)n(o-temp)n(er)n(atur)n(e)16 b(Gibbs)i(me)n(asur)n(e)f(for)g FQ(\010)p FP(.)133 2597 y FQ(Ho)o(w)o(ev)o (er,)d(not)i(ev)o(ery)e(zero-temp)q(erature)g(Gibbs)i(measure)f(for)h(a)g (giv)o(en)e(p)q(oten)o(tial)i(is)f(neces-)60 2657 y(sarily)d(stable.)20 b(W)l(e)12 b(can)h(illustrate)e(this)h(concept)g(with)h(the)f(case)g(of)h (the)f(Ising)h(mo)q(del.)19 b(F)l(or)12 b FF(d)i FQ(=)g(1,)938 2784 y(208)p eop %%Page: 209 209 bop 60 91 a FQ(none)16 b(of)g(the)g(deterministic)d(zero-temp)q(erature)h (Gibbs)i(measures)f(\()p FF(\016)1379 98 y FH(+)1424 91 y FQ(and)h FF(\016)1540 98 y Fy(\000)1569 91 y FQ(\))g(are)g(stable.)21 b(In)60 152 y(fact,)16 b(the)g(only)f(stable)h(measure)f(is)h(\()p FF(\016)781 159 y FH(+)821 152 y FQ(+)11 b FF(\016)892 159 y Fy(\000)921 152 y FQ(\))p FF(=)p FQ(2.)22 b(F)l(or)16 b(the)g(Ising)g(mo)q (del)f(in)h(dimension)e(2,)i(only)60 212 y(the)e(measures)e(of)i(the)g(form)f FF(\025\016)646 219 y FH(+)681 212 y FQ(+)6 b(\(1)g FE(\000)g FF(\025)p FQ(\))p FF(\016)888 219 y Fy(\000)932 212 y FQ(are)13 b(stable.)21 b(The)14 b(deterministic)c(Gibbs)k(measures)60 272 y(asso)q(ciated)g(with)e(the)h(rigid)f(\015at-in)o(terface)g (con\014gurations)i(are)f(unstable:)20 b(at)13 b(an)o(y)f(nonzero)h(tem-)60 332 y(p)q(erature,)19 b(the)f(in)o(terface)f(\\w)o(anders")j(to)f FE(\0061)f FQ(and)h(w)o(e)f(are)g(left)g(with)g(a)h(con)o(v)o(ex)f(com)o (bination)60 392 y(of)e(the)g(\\+")h(and)g(\\)p FE(\000)p FQ(")f(phases)h ([1,)f(192)q(].)21 b(F)l(or)16 b(dimension)e(3,)j(the)e(\015at-in)o(terface)h (measures)f(w)o(ere)60 452 y(pro)o(v)o(en)e(to)i(b)q(e)f(stable)g(b)o(y)f (Dobrushin)i([85])f(\(see)f(also)i([348)q(]\).)20 b FM(Remark:)d FQ(The)d(lo)o(w-temp)q(erature)60 513 y(Gibbs)20 b(measure)f(for)i(the)e (\015at-in)o(terface)h(phase)g(seems,)g(at)g(least)g(in)g(n)o(umerical)d(exp) q(erimen)o(ts,)60 573 y(to)k(disapp)q(ear)g(at)g(a)f(temp)q(erature)f (strictly)g(b)q(elo)o(w)i(the)f(critical)e(temp)q(erature,)i(giving)g(rise)g (to)60 633 y(a)d(roughening)g(transition.)23 b(If)16 b(the)h(ab)q(o)o(v)o (e-men)o(tioned)e(zero-temp)q(erature)g(measure)g(supp)q(orted)60 693 y(near)i(the)f(con\014guration)i FF(!)581 675 y FH(zig)p Fy(\000)p FH(zag)722 693 y FQ(happ)q(ens)g(to)f(exist,)f(w)o(e)g(could)g(ask) h(t)o(w)o(o)g(questions:)22 b(\(i\))16 b(Do)q(es)60 753 y(it)i(surviv)o(e)f (for)h FF(T)24 b(>)17 b FQ(0)h(\(stabilit)o(y\)?;)g(and,)h(if)e(so,)i(\(ii\)) e(Do)q(es)i(it)f(fail)g(to)g(surviv)o(e)f(to)i FF(T)k FQ(=)17 b FF(T)1776 760 y FD(c)1793 753 y FQ(?.)28 b(If)60 814 y(the)19 b(answ)o(er)g(to)h(b)q(oth)g(questions)g(w)o(ere)e(y)o(es,)h(then)g(the)g (Ising)g(mo)q(del)f(w)o(ould)h(exhibit)f(a)i(second)60 874 y(roughening)d(transition.)133 934 y(Ho)o(w)o(ev)o(er,)f(as)i(our)g(ev)o(en)o (tual)e(goal)i(is)f(the)g(study)h(of)g(ho)o(w)f(the)h(full)e(phase)i(diagram) f(deforms)60 994 y(as)i(the)e(temp)q(erature)g(is)g(raised,)h(w)o(e)g(m)o (ust)e(consider)i(a)g(more)f(general)g(situation)h(in)g(whic)o(h)f(the)60 1054 y(in)o(teraction)22 b(is)i(also)f(v)m(aried)h(as)g(the)f(temp)q(erature) f(go)q(es)i(to)g(zero.)42 b(That)24 b(is,)h(w)o(e)e(m)o(ust)f(con-)60 1115 y(sider)d(the)h(more)f(general)h(class)g(of)g(measures)f(that)h(can)g(b) q(e)g(obtained)g(as)h(a)f FF(\014)j FE(!)d(1)f FQ(limit)f(of)60 1175 y(p)q(ositiv)o(e-temp)q(erature)d(Gibbs)i(measures)f(for)h(in)o (teractions)g(\010)1247 1182 y FD(n)1285 1175 y FE(!)e FQ(\010.)24 b(W)l(e)17 b(shall)g(refer)f(to)h(suc)o(h)60 1235 y(measures)g(as)j FP(w-stable)h(me)n(asur)n(es)h FQ(for)d(the)f(in)o(teraction)f(\010)i([95].) 28 b(\()p FP(Warning)t FQ(:)e(Reference)17 b([328])60 1295 y(calls)h(these)g(measures)f FP(stable)t FQ(.\))28 b(In)18 b(general,)h(suc)o(h)f(measures)f FP(ne)n(e)n(d)i(not)h(b)n(e)j FQ(zero-temp)q(erature)60 1355 y(Gibbs)17 b(measures)e(for)h(\010.)22 b(F)l(or)16 b(example,)e(if)h(to)i(the)f(an)o(tiferromagnetic)e(Ising)i(mo)q (del)f(with)i(\014eld)60 1416 y FF(h)h FQ(=)g(2)p FF(d)p FE(j)p FF(J)5 b FE(j)19 b FQ(considered)f(ab)q(o)o(v)o(e)h(w)o(e)f(add)i(an)f (additional)g(\014eld)f FF(h)1283 1423 y FD(n)1324 1416 y FQ(=)g FF(\013=\014)1463 1423 y FD(n)1487 1416 y FQ(,)h(w)o(e)f(obtain,)i(in)e(the) 60 1476 y(limit)12 b FF(\014)203 1483 y FD(n)240 1476 y FE(!)i(1)p FQ(,)h(a)g(Gibbs)g(measure)f(corresp)q(onding)i(to)g(a)f(lattice)f(gas)i (with)f(c)o(hemical)d(p)q(oten)o(tial)60 1536 y FF(\013)p FQ(.)28 b(All)17 b(these)i(measures)e(are)i(di\013eren)o(t)e(among)i(themselv)o(es,)c (and)k(di\013eren)o(t)f(from)f(the)i(unique)60 1596 y(zero-temp)q(erature)h (Gibbs)h(measure)f(for)i(the)f(Ising)g(an)o(tiferromagnet)f(in)h(a)g(\014eld) g FF(h)h FQ(=)g(2)p FF(d)p FE(j)p FF(J)5 b FE(j)p FQ(,)60 1656 y(whic)o(h)16 b(corresp)q(onds)i(to)f FF(\013)e FQ(=)f(0.)23 b(A)17 b(more)e(dramatic)g(example)g(w)o(ould)i(b)q(e)g(to)g(add,)g(to)g(the) f(same)60 1716 y(mo)q(del,)j(a)h(\014eld)f FF(h)h FQ(=)g(1)p FF(=)530 1679 y FE(p)p 573 1679 52 2 v 573 1716 a FF(\014)601 1723 y FD(n)624 1716 y FQ(.)31 b(The)20 b(measure)f(obtained)h(in)f(the)h (limit)d FF(\014)1467 1723 y FD(n)1510 1716 y FE(!)j(1)f FQ(w)o(ould)h(then) 60 1777 y(b)q(e)h(the)f(measure)f FF(\016)435 1784 y FH(+)485 1777 y FQ(\(all)g(the)i(conditional)f(probabilities)g FF(\031)1234 1759 y FD(T)5 b FH(=0)1232 1789 y(\003)1326 1777 y FQ(are)21 b(equal)e(to)i FF(\016)1630 1784 y FH(+)1659 1777 y FQ(\),)g(whic)o(h)f(is)60 1837 y(not)i(a)f(zero-temp)q(erature)f(Gibbs)i(measure)e(for)h(\010)h(b)q (ecause)f(there)g(is)g(no)h(rigid)e(ground-state)60 1897 y(con\014guration)c (for)g(this)f(mo)q(del.)k(This)c(example)e(sho)o(ws)j(that)g(the)e(notion)i (of)f(w-stabilit)o(y)g(is)g(p)q(er-)60 1957 y(haps)j(a)g(little)e(to)q(o)j (general;)e(for)h(in)o(teresting)f(applications)g(one)h(usually)f(constrains) i(oneself)e(to)60 2017 y FP(w-stability)h(with)f(r)n(esp)n(e)n(ct)f(to)h(a)f (pr)n(e-\014xe)n(d)i(set)f(of)f(p)n(erturb)n(e)n(d)g(inter)n(actions)t FQ(.)22 b(In)15 b(Section)g(B.3.2)f(w)o(e)60 2078 y(shall)i(mak)o(e)e (precise)i(the)g(desirable)f(prop)q(erties)h(of)h(suc)o(h)f(p)q (erturbations.)133 2138 y(A)o(t)e(an)o(y)g(rate,)g(it)g(is)g(imme)o(diate)d (that)k(all)f(w-stable)h(measures)e(ha)o(v)o(e)g(the)h(w)o(eak)o(er)g(prop)q (ert)o(y)g(of)60 2198 y(b)q(eing)j(supp)q(orted)g(on)g(the)f(ground-state)i (con\014gurations)g(for)e(the)g(giv)o(en)g(in)o(teraction,)f(i.e.)g(they)60 2258 y(are)h FP(we)n(ak)23 b FQ(zero-temp)q(erature)14 b(measures:)60 2360 y FM(Theorem)j(B.12)23 b FP(L)n(et)g FF(\026)552 2367 y FD(n)598 2360 y FP(b)n(e)g(Gibbs)g(me)n(asur)n(es)e(for)h(a)h(se)n(quenc)n (e)h(of)e(inter)n(actions)h FQ(\010)1719 2367 y FD(n)1765 2360 y FP(and)g(a)60 2420 y(se)n(quenc)n(e)f(of)f(inverse)h(temp)n(er)n(atur)n(es) d FF(\014)810 2427 y FD(n)854 2420 y FP(such)i(that)g FQ(\010)1106 2427 y FD(n)1150 2420 y FE(!)e FQ(\010)i FP(and)g FF(\014)1401 2427 y FD(n)1444 2420 y FE(!)f FQ(+)p FE(1)p FP(.)32 b(If)20 b FF(\026)1732 2427 y FD(n)1776 2420 y FE(!)g FF(\026)p FP(,)60 2480 y(then)489 2540 y FF(\026)p FQ(\()q FE(f)p FQ(ground-state)d (con\014gurations)h(for)e(\010)p FE(g)p FQ(\))28 b(=)g(1)14 b FF(;)294 b FQ(\(B)p FF(:)p FQ(13\))60 2628 y FP(i.e.)18 b FF(\026)f FP(is)h(a)f(we)n(ak)h(zer)n(o-temp)n(er)n(atur)n(e)e(me)n(asur)n(e) h(for)g FQ(\010)p FP(.)938 2784 y FQ(209)p eop %%Page: 210 210 bop 133 91 a FQ(The)20 b(notion)h(of)g(zero-temp)q(erature)e(en)o(trop)o(y)g (in)o(v)o(olv)o(es)f(a)j(zero-temp)q(erature)e(limit,)f(hence)60 152 y(it)i(m)o(ust)e(ha)o(v)o(e)h(something)g(to)i(sa)o(y)f(ab)q(out)h (stabilit)o(y)l(.)31 b(Indeed,)20 b(Aizenman)e(and)i(Lieb)g([8])g(ha)o(v)o(e) 60 212 y(pro)o(v)o(en)c(the)g(follo)o(wing:)60 313 y FM(Prop)r(osition)i (B.13)24 b FP(If)17 b FF(\026)h FP(is)f(a)h(stable)h(tr)n (anslation-invariant)g(zer)n(o-temp)n(er)n(atur)n(e)d(Gibbs)i(me)n(a-)60 374 y(sur)n(e)f(for)g FQ(\010)p FP(,)g(then)858 434 y FF(s)p FQ(\()p FF(\026)p FQ(\))d(=)g FF(s)1037 441 y FH(\010)1078 434 y FF(:)60 535 y FQ(This)24 b(result,)h(together)f(with)g(Theorem)f(B.11)h (and)h(the)f(fact)g(that)g(the)g(set)g(of)g(translation-)60 596 y(in)o(v)m(arian)o(t)d(Gibbs)h(measures)f(is)h(non-empt)o(y)f(at)h(all)f (temp)q(eratures,)h(pro)o(v)o(es)f(Prop)q(osition)j(B.8)60 656 y(\(b\))c(ab)q(o)o(v)o(e.)33 b(In)19 b(the)h(case)g(of)g(sup)q (er-degenerate)h(systems)d(\(i.e.)h(systems)g(for)h(whic)o(h)f FF(s)1727 663 y FH(\010)1775 656 y FF(>)h FQ(0\),)60 716 y(Prop)q(osition)d (B.13)g(can)f(b)q(e)g(used)h(to)f(rule)g(out)h(the)f(stabilit)o(y)f(of)h (some)f(measures:)60 818 y FM(Corollary)j(B.14)24 b FP(F)l(or)12 b(a)g(sup)n(er-de)n(gener)n(ate)h(system,)h(every)f(tr)n(anslation-invariant) h(zer)n(o-temp)n(er)n(atur)n(e)60 878 y(Gibbs)k(me)n(asur)n(e)e(supp)n(orte)n (d)h(on)h(a)f(\014nite)i(set)f(is)f(unstable.)60 980 y FQ(F)l(or)f(instance,) g(for)g(the)g(system)f(\(B.9\),)g(the)h(all-\\0")i(Gibbs)e(state)h(is)f (unstable.)60 1110 y FM(B.2.8)55 b(V)-5 b(ariational-Principle)17 b(Approac)n(h)60 1202 y FQ(The)f(v)m(ariational-principle)f(approac)o(h)i (for)g(zero-temp)q(erature)d(measures)i(w)o(as)g(historically)f(the)60 1262 y(\014rst)h(one)f(to)g(b)q(e)h(considered)f([311].)21 b(A)o(t)14 b(zero)h(temp)q(erature)f(it)h(pro)o(vides)f(an)i(ev)o(en)e (simpler)f(crite-)60 1322 y(rion)j(than)h(at)g(non-zero)g(temp)q(eratures,)e (b)q(ecause)h(it)g(reduces)g(to)h(a)g(minim)o(al-energy)c(condition)60 1382 y(\()p FF(F)22 b FQ(=)17 b FF(E)e FE(\000)c FF(T)c(S)20 b FQ(reduces)d(to)h FF(F)23 b FQ(=)16 b FF(E)21 b FQ(if)c FF(T)22 b FQ(=)16 b(0\).)26 b(F)l(or)18 b(a)g(translation-in)o(v)m(arian)o(t)g(in)o (teraction)e(\010,)60 1443 y(it)g(is)g(not)h(hard)f(to)h(sho)o(w)g(that)f (the)g(limit)649 1562 y FF(e)672 1569 y FH(\010)727 1562 y FE(\021)41 b FQ(lim)794 1592 y FH(\003)p Fy(\0451)921 1529 y FQ(1)p 902 1551 62 2 v 902 1597 a FE(j)p FQ(\003)p FE(j)995 1562 y FQ(inf)977 1592 y FD(!)q Fy(2)p FH(\012)1049 1598 y Fr(\003)1089 1521 y Fx(X)1080 1613 y FD(A)p Fy(\032)p FH(\003)1167 1562 y FQ(\010)1202 1569 y FD(A)1230 1562 y FQ(\()p FF(!)r FQ(\))455 b(\(B)p FF(:)p FQ(14\))60 1710 y(exists;)18 b(w)o(e)g(call)g(it)f (the)i FP(minimal)g(sp)n(e)n(ci\014c)h(ener)n(gy)f FQ(\(or)f FP(gr)n(ound-state)j(ener)n(gy)p FQ(\).)27 b(A)18 b(translation-)60 1771 y(in)o(v)m(arian)o(t)e(measure)f FF(\026)h FQ(satisfying)844 1831 y FF(\026)p FQ(\()p FF(f)916 1838 y FH(\010)944 1831 y FQ(\))27 b(=)h FF(e)1079 1838 y FH(\010)1755 1831 y FQ(\(B)p FF(:)p FQ(15\))60 1918 y(is)17 b(called)f(a)i FP(zer)n(o-temp)n(er)n(atur)n (e)g(e)n(quilibrium)h(me)n(asur)n(e)h FQ(for)e(the)f(in)o(teraction)f(\010.) 25 b(The)17 b(de\014nition)60 1978 y(can)h(b)q(e)g(extended)f(to)h(p)q(erio)q (dic)f(measures)g(if)g FF(f)958 1985 y FH(\010)1003 1978 y FQ(includes)g(an)h(a)o(v)o(erage)g(o)o(v)o(er)e(all)i(the)f(sites)h(of)g(a)60 2038 y(basic)h(p)q(erio)q(d:)26 b(If)18 b(\010)h(is)g(in)o(v)m(arian)o(t)f (under)g(a)h(subgroup)h FF(S)i FQ(of)d Fq(Z)1261 2017 y FD(d)1281 2038 y FQ(,)g(with)g Fq(Z)1458 2017 y FD(d)1478 2038 y FF(=S)j FQ(isomorphic)c(to)h(a)60 2099 y(\014nite)f(set)g FF(P)25 b FE(\032)17 b Fq(Z)408 2078 y FD(d)428 2099 y FQ(,)i(then)f(one)g(m)o(ust)g (de\014ne)g FF(f)956 2106 y FH(\010)1018 2099 y FE(\021)35 b(j)p FF(P)7 b FE(j)1158 2080 y Fy(\000)p FH(1)1214 2065 y Fx(P)1257 2109 y FD(x)p Fy(2)p FD(P)1339 2065 y Fx(P)1382 2109 y FD(X)s Fy(3)p FD(x)1468 2099 y FE(j)p FF(X)t FE(j)1540 2080 y Fy(\000)p FH(1)1595 2099 y FQ(\010)1630 2106 y FD(X)1664 2099 y FQ(.)28 b(W)l(e)18 b(shall)60 2159 y(assume)e(this)g(extension)f(in)h (the)g(sequel.)k(Sc)o(hrader)c(has)h(pro)o(v)o(en)f([319)q(]:)60 2260 y FM(Theorem)h(B.15)93 2375 y FP(\(a\))24 b(Every)12 b(tr)n (anslation-invariant)i(w-zer)n(o-temp)n(er)n(atur)n(e)e(me)n(asur)n(e)g(for)g FQ(\010)h FP(is)f(a)g(zer)n(o-temp)n(er)n(atur)n(e)182 2435 y(e)n(quilibrium)18 b(me)n(asur)n(e)f(for)g FQ(\010)p FP(,)g(i.e.)h (satis\014es)g(\(B.15\).)95 2536 y(\(b\))25 b(Conversely,)14 b(every)f(zer)n(o-temp)n(er)n(atur)n(e)f(e)n(quilibrium)h(me)n(asur)n(e)e (for)h FQ(\010)h FP(is)f(a)h(w-zer)n(o-temp)n(er)n(atur)n(e)182 2597 y(me)n(asur)n(e)k(for)f FQ(\010)p FP(.)938 2784 y FQ(210)p eop %%Page: 211 211 bop 60 91 a FQ(That)23 b(is,)h(for)f(translation-in)o(v)m(arian)o(t)g (measures)e(to)i(b)q(e)g(supp)q(orted)h(on)f(\(lo)q(cal\))f(ground-state)60 152 y(con\014gurations)16 b(is)f(equiv)m(alen)o(t)e(to)i(ha)o(ving)f(minimal) d(a)o(v)o(erage)k(energy)f(densit)o(y)l(.)20 b(W)l(e)14 b(notice)g(that,)60 212 y(unlik)o(e)j(the)g(\014nite-temp)q(erature)g(case,)h(w)o(e)g(do)g FP(not)24 b FQ(ha)o(v)o(e)17 b(an)i(equiv)m(alence)d(b)q(et)o(w)o(een)h(the)h (v)m(aria-)60 272 y(tional)g(and)h(the)f(Gibbsian-sp)q(eci\014cations)h (approac)o(hes;)g(only)g(the)f(more)f(general)h(w-measures)60 332 y(app)q(ear)23 b(in)f(the)g(previous)g(theorem.)37 b(The)22 b(relationship)g(b)q(et)o(w)o(een)f(zero-temp)q(erature)g(Gibbs)60 392 y(measures)15 b(and)i(equilibrium)c(measures)i(is)h(m)o(uc)o(h)e(more)h (problematic.)133 452 y(The)24 b(v)m(ariational)g(approac)o(h)g(yields)f (also)h(a)g(c)o(haracterization)f(of)h FP(p)n(erio)n(dic)e FQ(ground-state)60 513 y(con\014gurations:)60 627 y FM(Theorem)17 b(B.16)118 741 y FP(1.)24 b(F)l(or)17 b(any)g(p)n(erio)n(dic)g(c)n(on\014gur) n(ation)h FF(!)e FE(2)e FQ(\012)p FP(,)j(the)h(sp)n(e)n(ci\014c)g(ener)n(gy)g (\(ener)n(gy)g(p)n(er)f(site\))727 873 y FF(e)750 880 y FH(\010)778 873 y FQ(\()p FF(!)r FQ(\))27 b(=)42 b(lim)941 903 y FH(\003)p Fy(\0451)1068 839 y FQ(1)p 1049 862 62 2 v 1049 907 a FE(j)p FQ(\003)p FE(j)1133 832 y Fx(X)1124 924 y FD(A)p Fy(\032)p FH(\003)1211 873 y FQ(\010)1246 880 y FD(A)1274 873 y FQ(\()p FF(!)r FQ(\))411 b(\(B)p FF(:)p FQ(16\))182 1016 y FP(exists.)118 1118 y(2.)24 b(The)19 b(in\014mum)h(of)e FF(e)559 1125 y FH(\010)587 1118 y FQ(\()p FF(!)r FQ(\))h FP(over)g(al)r(l)h(p)n(erio)n(dic)e(c)n (on\014gur)n(ations)h FF(!)j FP(is)c(\014nite)j(and)e(e)n(quals)g(the)182 1178 y(value)g FF(e)331 1185 y FH(\010)375 1178 y FP(de\014ne)n(d)g(in)e (\(B.14\).)118 1280 y(3.)24 b FF(!)c FP(is)d(a)g(p)n(erio)n(dic)g(gr)n (ound-state)h(c)n(on\014gur)n(ation)g(if)f(and)h(only)g(if)f FF(e)1397 1287 y FH(\010)1424 1280 y FQ(\()p FF(!)r FQ(\))d(=)g FF(e)1583 1287 y FH(\010)1628 1280 y FP([328)o(,)k(95)o(].)133 1394 y FQ(F)l(or)d(completeness,)d(w)o(e)j(men)o(tion)d(also)k(t)o(w)o(o)e(v) m(ariational)h(principles)e(in)o(v)o(olving)g(the)i(minim)o(al)60 1454 y(energy)h(densit)o(y)f(and)i(the)f(residual)g(en)o(trop)o(y:)60 1556 y FM(Theorem)h(B.17)93 1670 y FP(\(a\))769 1730 y FF(e)792 1737 y FH(\010)847 1730 y FQ(=)130 b(inf)913 1762 y FD(\026)p Fy(2)p FD(M)992 1767 y Fr(+1)p Fs(;)p Fr(p)q(er)1084 1762 y FH(\(\012)p FD(;)p Fy(F)s FH(\))1184 1730 y FF(\026)p FQ(\()p FF(f)1256 1737 y FH(\010)1284 1730 y FQ(\))452 b(\(B)p FF(:)p FQ(17\))95 1865 y FP(\(b\))25 b([8])383 1975 y FF(s)406 1982 y FH(\010)475 1975 y FQ(=)42 b(sup)p FE(f)p FF(s)p FQ(\()p FF(\026)p FQ(\))8 b FE(j)g FF(\026)15 b FE(2)f FF(M)911 1982 y FH(+1)p FD(;)p FH(p)q(er)1018 1975 y FQ(\(\012)p FF(;)8 b FE(F)d FQ(\))16 b(and)h FF(\026)p FQ(\()p FF(f)1337 1982 y FH(\010)1365 1975 y FQ(\))d(=)g FF(e)1473 1982 y FH(\010)1500 1975 y FE(g)206 b FQ(\(B.18a\))475 2047 y(=)42 b(sup)p FE(f)p FF(s)p FQ(\()p FF(\026)p FQ(\))8 b FE(j)g FF(\026)19 b FP(is)e(a)g(w-zer)n(o) h(temp)n(er)n(atur)n(e)e(me)n(asur)n(e)h(for)g FQ(\010)p FE(g)d FF(:)39 b FQ(\(B.18b\))60 2178 y(In)16 b(particular,)g(\(B.18b\))g(pro)o(v)o (es)g(Prop)q(osition)i(B.8\(a\).)j(The)c(\\inf)s(")g(in)f(part)h(\(a\))g(and) g(the)f(\\sup")60 2238 y(in)h(part)h(\(b\))f(are)h(in)f(fact)g(\\min")g(and)h (\\max",)e(resp)q(ectiv)o(ely)l(.)22 b(They)c(are)f(realized)f(b)o(y)h(the)g (zero-)60 2299 y(temp)q(erature)e(equilibrium)e(measures.)938 2784 y(211)p eop %%Page: 212 212 bop 60 91 a FM(B.2.9)55 b(In\014nite)18 b(Range)g(and)i(Lac)n(k)e(of)h (Quasilo)r(calit)n(y)60 184 y FQ(The)j(v)m(ariational-principle)f(approac)o (h)h(to)h(zero-temp)q(erature)d(classical)h(lattice)g(systems)g(can)60 244 y(b)q(e)h(extended)g(without)h(di\016cult)o(y)d(to)j(in)o(teractions)e (in)h FE(B)1177 226 y FH(0)1218 244 y FQ([319)q(,)g(8].)39 b(The)23 b(extension)f(of)g(the)60 304 y(DLR)14 b(approac)o(h)h(to)f (in\014nite-range)f(in)o(teractions)g(\(e.g.)g(in)g FE(B)1194 286 y FH(1)1213 304 y FQ(\))h(is,)g(ho)o(w)o(ev)o(er,)e(more)g(problematic.) 60 364 y(In)23 b(particular,)h(the)f(v)m(alidit)o(y)f(of)h(the)g(imp)q(ortan) o(t)f(Theorem)g(B.11)h(is)g(an)h(op)q(en)g(question:)34 b(A)60 424 y(sequence)22 b(of)i(p)q(ositiv)o(e-temp)q(erature)d(Gibbs)j(measures)e (for)i(\010)g(could)f(conceiv)m(ably)f(con)o(v)o(erge)60 485 y(to)f(a)h(limiting)c(measure)i(that)h(is)g(not)h(consisten)o(t)e(with)h(the) g(zero-temp)q(erature)e(sp)q(eci\014cation)60 545 y(\(B.1\).)k(If)17 b(this)g(latter)f(sp)q(eci\014cation)h(w)o(ere)f(quasilo)q(cal,)h(suc)o(h)g (a)g(phenomenon)f(could)h(not)h(o)q(ccur)60 605 y([157)q(,)g(Theorem)e (4.17];)j(ho)o(w)o(ev)o(er,)e(for)h(long-range)h(in)o(teractions)f(the)f(sp)q (eci\014cation)h(\(B.1\))g(is)f(in)60 665 y(general)e(not)h(quasilo)q(cal.)21 b(Let)15 b(us)h(conclude)e(this)h(section)g(with)g(an)h(example)d(sho)o(wing) j(this)f(lac)o(k)60 725 y(of)i(quasilo)q(calit)o(y)l(.)133 786 y(Consider)g(an)o(y)g(long-range)h(one-dimensional)e(Ising)g(mo)q(del)g (with)h(pair)g(in)o(teractions)f FF(J)1797 793 y FD(xy)1852 786 y FQ(=)60 846 y FF(J)87 854 y Fy(j)p FD(x)p Fy(\000)p FD(y)q Fy(j)197 846 y FQ(satisfying)421 813 y Fx(P)465 856 y FD(n)496 846 y FE(j)p FF(J)537 853 y FD(n)561 846 y FE(j)24 b FF(<)h FE(1)p FQ(.)40 b(The)22 b(mo)q(del)g(has)h(to)g(b)q(e)g(truly)f(long-range)h (in)g(the)f(sense)60 906 y(that)16 b(there)g(m)o(ust)e(b)q(e)i(in\014nitely)e (man)o(y)h(nonzero)h(couplings)g FF(J)1235 913 y FD(n)1259 906 y FQ(;)f(for)h(simplicit)o(y)c(of)17 b(notation)f(w)o(e)60 966 y(assume)e(that)h FF(J)358 973 y FD(n)395 966 y FE(6)p FQ(=)f(0)h(for)g(all)f FF(n)p FQ(.)21 b(W)l(e)15 b(claim)d(that)j(the)g (zero-temp)q(erature)e(sp)q(eci\014cation)h(of)h(suc)o(h)60 1026 y(a)f(mo)q(del)e(is)i(non-quasilo)q(cal.)21 b(Indeed,)13 b(the)g(zero-temp)q(erature)f(conditional)i(probabilit)o(y)e(for)i(the)60 1087 y(spin)i(at)h(the)f(origin)g(satis\014es:)437 1253 y FF(\031)467 1229 y FH(\010)p FD(;T)5 b FH(=0)465 1267 y Fy(f)p FH(0)p Fy(g)575 1253 y FQ(\()p FF(!)624 1260 y FH(0)658 1253 y FQ(=)13 b(+1)p FE(j)p FF(\034)6 b FQ(\))28 b(=)925 1153 y Fx(8)925 1191 y(>)925 1203 y(<)925 1278 y(>)925 1290 y(:)982 1192 y FQ(1)91 b(if)1150 1159 y Fx(P)1194 1203 y FD(x)p Fy(6)p FH(=0)1269 1192 y FF(J)1296 1199 y FD(x)1318 1192 y FF(\034)1339 1199 y FD(x)1375 1192 y FF(>)14 b FQ(0)982 1253 y(1)p FF(=)p FQ(2)43 b(if)1150 1219 y Fx(P)1194 1263 y FD(x)p Fy(6)p FH(=0)1269 1253 y FF(J)1296 1260 y FD(x)1318 1253 y FF(\034)1339 1260 y FD(x)1375 1253 y FQ(=)14 b(0)982 1313 y(0)91 b(if)1150 1280 y Fx(P)1194 1323 y FD(x)p Fy(6)p FH(=0)1269 1313 y FF(J)1296 1320 y FD(x)1318 1313 y FF(\034)1339 1320 y FD(x)1375 1313 y FF(<)14 b FQ(0)g FF(:)1755 1253 y FQ(\(B)p FF(:)p FQ(19\))60 1419 y(T)l(o)19 b(pro)o(v)o(e)f(that)h(this)f(is)g(not)h(a)g(quasilo)q(cal)g(function)f(of)h (the)f(b)q(oundary)i(condition)e FF(\034)6 b FQ(,)18 b(w)o(e)g(need)60 1480 y(to)h(sho)o(w)h(that)g(there)e(exists)g(some)g FF(")h(>)f FQ(0)i(for)f(whic)o(h)f(the)h(follo)o(wing)g(is)g(true:)26 b(F)l(or)19 b(an)h(in\014nite)60 1540 y(sequence)13 b(of)g(nested)h(\014nite) f(sets)h(\003)f(there)g(exist)g(t)o(w)o(o)h(op)q(en)g(sets)g(of)g (con\014gurations,)h FE(N)1677 1547 y FH(\003)1717 1540 y FQ(and)f FE(N)1857 1522 y Fy(0)1850 1552 y FH(\003)1876 1540 y FQ(,)60 1600 y(formed)h(b)o(y)h(con\014gurations)h(whic)o(h)f(are)g(all)g(iden)o (tical)e(inside)i(\003,)f(but)i(suc)o(h)f(that)477 1660 y Fx(\014)477 1685 y(\014)477 1710 y(\014)p FF(\031)521 1686 y FH(\010)p FD(;T)5 b FH(=0)519 1724 y Fy(f)p FH(0)p Fy(g)628 1710 y FQ(\()p FF(!)677 1717 y FH(0)711 1710 y FQ(=)14 b(+1)p FE(j)p FF(\034)6 b FQ(\))k FE(\000)h FF(\031)975 1686 y FH(\010)p FD(;T)5 b FH(=0)973 1724 y Fy(f)p FH(0)p Fy(g)1083 1710 y FQ(\()p FF(!)1132 1717 y FH(0)1166 1710 y FQ(=)13 b(+1)p FE(j)p FF(\034)1320 1689 y Fy(0)1332 1710 y FQ(\))1351 1660 y Fx(\014)1351 1685 y(\014)1351 1710 y(\014)27 b FE(\025)h FF(")273 b FQ(\(B)p FF(:)p FQ(20\))60 1825 y(if)20 b FF(\034)26 b FE(2)c(N)252 1832 y FH(\003)298 1825 y FQ(and)f FF(\034)424 1807 y Fy(0)457 1825 y FE(2)g(N)559 1807 y Fy(0)552 1838 y FH(\003)578 1825 y FQ(.)34 b(Suc)o(h)20 b(sets)g FE(N)888 1832 y FH(\003)915 1825 y FQ(,)h FE(N)998 1807 y Fy(0)991 1838 y FH(\003)1038 1825 y FQ(are)f(constructed)g(as)h(follo)o(ws:)30 b(T)l(ak)o(e)20 b(\003)1798 1832 y FD(N)1852 1825 y FQ(=)60 1885 y([)p FE(\000)p FF(N)r(;)8 b(N)d FQ(])16 b(and)h(\014x)f FF(N)453 1892 y FH(0)486 1885 y FF(>)e(N)22 b FQ(suc)o(h)16 b(that)776 1954 y Fx(X)759 2046 y FD(x>N)834 2051 y Fr(0)860 1995 y FE(j)p FF(J)901 2002 y FD(x)923 1995 y FE(j)27 b FF(<)h FE(j)p FF(J)1071 2002 y FD(N)t FH(+1)1150 1995 y FE(j)13 b FF(;)564 b FQ(\(B)p FF(:)p FQ(21\))60 2143 y(and)17 b(let)e FE(N)266 2150 y FH(\003)309 2143 y FQ(b)q(e)h(the)g(set)g(of)h(con\014gurations)h FF(\034)k FQ(suc)o(h)16 b(that)541 2340 y FF(\034)562 2347 y FD(x)611 2340 y FQ(=)677 2215 y Fx(8)677 2252 y(>)677 2265 y(>)677 2277 y(>)677 2290 y(<)677 2365 y(>)677 2377 y(>)677 2389 y(>)677 2402 y(:)735 2249 y FQ(+1)166 b(if)16 b(1)e FE(\024)g FF(x)f FE(\024)h FF(N)735 2309 y FE(\000)p FQ(1)165 b(if)27 b FE(\000)11 b FF(N)19 b FE(\024)13 b FF(x)h FE(\024)g(\000)p FQ(1)735 2369 y(sgn)9 b FF(J)841 2376 y FD(x)963 2369 y FQ(if)16 b FF(N)g FQ(+)11 b(1)j FE(\024)g(j)p FF(x)p FE(j)f(\024)h FF(N)1364 2376 y FH(0)735 2430 y FQ(an)o(ything)41 b(if)16 b FE(j)p FF(x)p FE(j)d FF(>)h(N)1168 2437 y FH(0)1202 2430 y FF(:)1755 2340 y FQ(\(B)p FF(:)p FQ(22\))938 2784 y(212)p eop %%Page: 213 213 bop 60 91 a FQ(The)15 b(set)g(set)h FE(N)358 73 y Fy(0)351 104 y FH(\003)392 91 y FQ(is)f(de\014ned)h(analogously)g(but)g(replacing)e (sgn)9 b FF(J)1273 98 y FD(x)1310 91 y FQ(b)o(y)15 b FE(\000)8 b FQ(sgn)h FF(J)1530 98 y FD(x)1552 91 y FQ(.)21 b(W)l(e)15 b(then)g(ha)o(v)o(e:)154 305 y Fx(X)152 398 y FD(x)p Fy(6)p FH(=0)225 347 y FF(J)252 354 y FD(x)274 347 y FF(\034)295 354 y FD(x)344 347 y FQ(=)429 305 y Fx(X)410 399 y Fy(j)p FD(x)p Fy(j)p FD(>N)517 347 y FF(J)544 354 y FD(x)566 347 y FF(\034)587 354 y FD(x)637 347 y FQ(=)702 160 y Fx(8)702 197 y(>)702 210 y(>)702 222 y(>)702 235 y(>)702 247 y(>)702 260 y(>)702 272 y(>)702 285 y(>)702 297 y(<)702 372 y(>)702 384 y(>)702 397 y(>)702 409 y(>)702 422 y(>)702 434 y(>)702 447 y(>)702 459 y(>)702 471 y(:)760 239 y FQ(2)842 184 y FD(N)870 189 y Fr(0)834 198 y Fx(X)792 292 y Fy(j)p FD(x)p Fy(j)p FH(=)p FD(N)t FH(+1)944 239 y FE(j)p FF(J)985 246 y FD(x)1007 239 y FE(j)c FQ(+)g(2)1140 198 y Fx(X)1114 292 y Fy(j)p FD(x)p Fy(j)p FD(>N)1209 297 y Fr(0)1234 239 y FF(J)1261 246 y FD(x)1283 239 y FF(\034)1304 246 y FD(x)1354 239 y FF(>)27 b FQ(0)81 b(for)17 b FF(\034)i FE(2)14 b(N)1727 246 y FH(\003)760 446 y FE(\000)p FQ(2)880 391 y FD(N)908 396 y Fr(0)873 405 y Fx(X)831 499 y Fy(j)p FD(x)p Fy(j)p FH(=)p FD(N)t FH(+1)983 446 y FE(j)p FF(J)1024 453 y FD(x)1046 446 y FE(j)d FQ(+)g(2)1179 405 y Fx(X)1152 499 y Fy(j)p FD(x)p Fy(j)p FD(>N)1247 504 y Fr(0)1273 446 y FF(J)1300 453 y FD(x)1322 446 y FF(\034)1343 453 y FD(x)1393 446 y FF(<)27 b FQ(0)42 b(for)17 b FF(\034)i FE(2)14 b(N)1734 428 y Fy(0)1727 459 y FH(\003)1767 446 y FF(;)1755 553 y FQ(\(B)p FF(:)p FQ(23\))60 613 y(where)i(the)g(last)g(inequalities)f(follo)o(w)h(from)f(\(B.21\).)21 b(Therefore,)15 b(b)o(y)h(\(B.19\),)476 679 y Fx(\014)476 704 y(\014)476 729 y(\014)p FF(\031)520 706 y FH(\010)p FD(;T)5 b FH(=0)518 744 y Fy(f)p FH(0)p Fy(g)628 729 y FQ(\()p FF(!)677 736 y FH(0)710 729 y FQ(=)14 b(+1)p FE(j)p FF(\034)6 b FQ(\))11 b FE(\000)g FF(\031)975 706 y FH(\010)p FD(;T)5 b FH(=0)973 744 y Fy(f)p FH(0)p Fy(g)1082 729 y FQ(\()p FF(!)1131 736 y FH(0)1165 729 y FQ(=)14 b(+1)p FE(j)p FF(\034)1320 709 y Fy(0)1331 729 y FQ(\))1350 679 y Fx(\014)1350 704 y(\014)1350 729 y(\014)28 b FQ(=)g(1)273 b(\(B)p FF(:)p FQ(24\))60 845 y(if)16 b FF(\034)j FE(2)14 b(N)233 852 y FH(\003)276 845 y FQ(and)j FF(\034)398 827 y Fy(0)423 845 y FE(2)d(N)518 827 y Fy(0)511 857 y FH(\003)538 845 y FQ(,)h(and)i(the)f(sp)q(eci\014cation)g(is)g(not)h(quasilo)q(cal.)60 989 y FB(B.3)69 b(Phase)23 b(Diagrams)60 1081 y FM(B.3.1)55 b(Regular)18 b(Phase)h(Diagrams)60 1174 y FQ(The)j(w)o(ords)g(\\phase)h (diagram")f(are)g(usually)f(asso)q(ciated)i(with)f(nice)e(pictures)h(in)h (whic)o(h)f(t)o(w)o(o)60 1234 y(conditions)16 b(are)h(satis\014ed:)133 1319 y(1\))25 b(Only)e FP(p)n(erio)n(dic)j FQ(extremal)c(Gibbs)i(measures)f (are)h(considered.)45 b(W)l(e)23 b(emphasize)g(that)60 1379 y(the)c(order)h(of)g(the)g(quali\014ers)f(has)h(b)q(een)g(carefully)e(c)o (hosen:)28 b(the)19 b(measures)g(relev)m(an)o(t)g(here)g(are)60 1439 y(those)24 b FP(extr)n(emal)g(Gibbs)k FQ(measures)22 b(that)h FP(happ)n(en)h(to)g(b)n(e)g(p)n(erio)n(dic)s FQ(;)h(w)o(e)e(are)g FP(not)28 b FQ(referring)23 b(to)60 1500 y(the)d(measures)f(that)i(are)g (extremal)d(among)i(the)g(p)q(erio)q(dic)g(ones)h(\(this)f(latter)g(is)g(a)h (larger)f(and)60 1560 y(less-w)o(ell-b)q(eha)o(v)o(ed)d(class\).)30 b(F)l(or)19 b(short,)h(w)o(e)e(shall)h(call)f(these)h(measures)f FP(pur)n(e)h(phases)t FQ(,)g(but)g(w)o(e)60 1620 y(emphasize)11 b(that)j(this)f(em)o(b)q(o)q(dies)e(a)j(double)f(c)o(hange)g(with)g(resp)q (ect)g(to)g(the)g(terminology)e(adopted)60 1680 y(in)18 b(the)g(rest)g(of)g (this)g(pap)q(er:)26 b(First,)17 b(w)o(e)h(consider)g(all)f(p)q(erio)q(dic)h (Gibbs)h(measures)e(on)h(the)g(same)60 1740 y(fo)q(oting,)g(whether)f(they)g (are)g(in)o(v)m(arian)o(t)g(under)g(the)g(whole)g(translation)h(group)g Fq(Z)1608 1720 y FD(d)1645 1740 y FQ(or)g(merely)d(a)60 1801 y(non)o(trivial)h FF(d)p FQ(-dimensional)h(subgroup)h(of)g(it.)24 b(Second,)18 b(w)o(e)f(in)o(v)o(ert)f(the)h(order)g(of)h(the)f(quali\014ers,) 60 1861 y(that)j(is,)f(w)o(e)g(call)g FP(pur)n(e)h(phase)j FQ(an)d(extremal)d(measure)h(in)h(the)g(sense)g(of)h(\(ii\))e(in)h(Section)g (2.4.9,)60 1921 y(rather)d(than)h(in)f(the)g(more)f(customary)g(sense)i (\(iii\).)133 1981 y(W)l(e)24 b(shall)f(ful\014ll)g(this)g(condition)h (throughout)h(the)e(rest)h(of)g(this)g(app)q(endix:)36 b(b)o(y)23 b(\\phase)60 2041 y(diagram")17 b(w)o(e)g(will)f(mean)g(the)h(partition)g(of) g(a)h(certain)e(parameter)g(space)h(in)o(to)g(regions)h(with)f(a)60 2102 y(giv)o(en)e(n)o(um)o(b)q(er)g(and)i(t)o(yp)q(e)e(of)i(pure)f(phases.) 133 2187 y(2\))23 b(The)f(Gibbs)g(phase)h(rule)e([363)q(])g(is)h(ob)q(ey)o (ed.)39 b(Let)22 b(us)g(explain)f(in)h(a)h(little)d(more)h(detail)60 2247 y(what)f(this)e(means.)29 b(An)18 b(example)f(of)i(a)h(phase)f(diagram)g (satisfying)g(the)f(Gibbs)i(phase)f(rule)f(is)60 2307 y(presen)o(ted)d(in)i (Figure)e(13)i(b)q(elo)o(w:)22 b(There)16 b(is)g(a)h(p)q(oin)o(t)f(where)g (three)g(pure)g(phases)h(co)q(exist)f(\()p FP(p)n(oint)60 2367 y(of)h(maximal)h(c)n(o)n(existenc)n(e)t FQ(\),)f(from)e(whic)o(h)h(there)f (emanate)g(three)h(lines)f(where)h(t)o(w)o(o)g(pure)g(phases)60 2427 y(co)q(exist,)k(whic)o(h)f(in)h(turn)g(b)q(ound)h(three)f(op)q(en)g (regions)g(in)g(whic)o(h)f(there)h(is)f(only)h(one)g(p)q(erio)q(dic)60 2488 y(extremal)13 b(Gibbs)i(measure.)k(Suc)o(h)c(a)g(phase)g(diagram)g(will) e(b)q(e)i(called)f FP(r)n(e)n(gular)5 b FQ(.)21 b(More)14 b(generally)l(,)60 2548 y(an)j FF(r)q FP(-r)n(e)n(gular)g(phase)h(diagr)n(am)d FQ(consists)i(of)f([170)q(,)g(App)q(endix)f(A]:)95 2650 y(\(1\))25 b(a)17 b(p)q(oin)o(t)f(of)g(maximal)e(co)q(existence)h(where)h FF(r)h FQ(pure)f(phases)h(co)q(exist;)938 2784 y(213)p eop %%Page: 214 214 bop 95 91 a FQ(\(2\))25 b FF(r)e FQ(one-dimensional)e(op)q(en)i(manifolds,)f (eac)o(h)g(b)q(ounded)h(b)o(y)e(this)h(maximal-co)q(existenc)o(e)182 152 y(p)q(oin)o(t,)16 b(where)g(exactly)f FF(r)d FE(\000)f FQ(1)17 b(phases)g(co)q(exist;)95 247 y(\(3\))25 b FF(r)q FQ(\()p FF(r)5 b FE(\000)s FQ(1\))p FF(=)p FQ(2)13 b(t)o(w)o(o-dimensional)e(op)q(en) i(manifolds,)f(eac)o(h)g(b)q(ounded)h(b)o(y)f(pairs)g(of)h(the)f(previous)182 307 y(one-dimensional)j(manifolds,)g(where)g(exactly)g FF(r)e FE(\000)e FQ(2)16 b(pure)g(phases)h(co)q(exist;)125 387 y(.)125 403 y(.)125 420 y(.)96 516 y(\()p FF(r)q FQ(\))25 b FF(r)18 b FQ(op)q(en)g(\()p FF(r)13 b FE(\000)e FQ(1\)-dimensional)16 b(manifolds,)g(eac)o(h)g(b)q(ounded)i(b)o(y)f(the)g(\()p FF(r)c FE(\000)e FQ(2\)-dimensional)182 576 y(2-phase-co)q(existence)22 b(manifolds,)f(and)h(suc)o(h)g(that)g(the)f(closure)g(of)h(their)f(union)h (is)f(the)182 636 y(whole)16 b(parameter)f(space,)h(where)g(there)g(is)g (only)g(one)g(pure)g(phase.)60 720 y(Usually)l(,)j(the)h(pure)f(phases)i(are) f(de\014ned)f(b)o(y)h(\014xing)f(the)h(b)q(oundary)h(conditions)f(according)g (to)60 780 y(some)12 b FP(p)n(ar)n(ameter-indep)n(endent)18 b FQ(set)12 b FE(K)i FQ(of)f(reference)e(con\014gurations)j(\(or,)f(more)e (generally)l(,)h(mea-)60 840 y(sures\).)40 b(T)o(ypically)l(,)21 b FE(K)i FQ(is)f(the)g(set)g(of)h(ground-state)h(con\014gurations)f(at)g(the) f(p)q(oin)o(t)g(of)h(max-)60 900 y(imal)e(co)q(existence)h(at)h FF(T)31 b FQ(=)25 b(0.)42 b(One)22 b(can)h(then)g(lab)q(el)g(eac)o(h)f(pure)h (phase)g(according)g(to)g(the)60 961 y(b)q(oundary)h(condition)e(emplo)o(y)o (ed)d(in)j(its)g(de\014nition.)39 b(One)23 b(calls)e(the)h FF(K)t FQ(-)p FP(str)n(atum)k FQ(\()p FF(K)i FE(\032)c(K)q FQ(\))60 1021 y(the)c(manifold)g(in)g(parameter)g(space)g(where)h(the)f(co)q (existing)h(phases)g(are)g(precisely)e(those)i(la-)60 1081 y(b)q(elled)d(b)o(y)g(elemen)o(ts)e(of)j FF(K)t FQ(.)29 b(F)l(or)19 b(instance,)g(in)f(Figure)g(13,)i(the)f(di\013eren)o(t)f(strata)h(are)g(lab)q (elled)60 1141 y(b)o(y)i(the)g(b)q(oundary)i(conditions)f(\\+",)h(\\0")g(and) f(\\)p FE(\000)p FQ(".)38 b(There)21 b(are,)i(therefore,)f(sev)o(en)f (strata:)60 1201 y FE(f)p FQ(+)p FE(g)p FF(;)8 b FE(f)p FQ(0)p FE(g)p FF(;)g FE(f\000g)p FF(;)g FE(f)p FQ(+)p FF(;)g FQ(0)p FE(g)p FF(;)g FE(f)p FQ(+)p FF(;)g FE(\000g)p FF(;)g FE(f)p FQ(0)p FF(;)g FE(\000g)p FF(;)g FE(f)p FQ(+)p FF(;)g FQ(0)p FF(;)g FE(\000g)p FQ(.)133 1262 y(A)16 b(more)f(abstract)i(\(top)q (ological\))h(w)o(a)o(y)e(of)g(visualizing)g(suc)o(h)g(a)h(phase)g(diagram)f (is)g(pro)o(vided)60 1322 y(b)o(y)i(the)h(follo)o(wing)f(equiv)m(alen)o(t)g (c)o(haracterization:)25 b(a)20 b FF(r)q FQ(-regular)f(phase)g(diagram)g(is)f (a)i(diagram)60 1382 y(that)e(can)f(b)q(e)g(homeomorphically)d(mapp)q(ed)j (on)o(to)h(the)f(b)q(oundary)h(of)g(the)f(p)q(ositiv)o(e)f(o)q(ctan)o(t)i(in) f FF(r)60 1442 y FQ(dimensions,)529 1502 y FF(@)s(Q)597 1509 y FD(r)643 1502 y FQ(=)709 1454 y Fx(n)736 1502 y FQ(\()p FF(t)773 1509 y FH(1)793 1502 y FF(;)8 b(:)g(:)g(:)f(;)h(t)920 1509 y FD(r)938 1502 y FQ(\))14 b FE(2)g Fq(R)1051 1481 y FD(d)1051 1515 y Fy(\025)p FH(0)1099 1502 y FQ(:)31 b(min)1134 1531 y FH(1)p Fy(\024)p FD(i)p Fy(\024)p FD(r)1244 1502 y FF(t)1262 1509 y FD(i)1290 1502 y FQ(=)13 b(0)1365 1454 y Fx(o)1407 1502 y FF(;)334 b FQ(\(B)p FF(:)p FQ(25\))60 1598 y(in)21 b(suc)o(h)f(a)i(w)o(a)o (y)e(that)h(the)g(p)q(oin)o(t)g(of)g(maximal)d(co)q(existence)i(corresp)q (onds)i(to)f(the)g(origin,)g(the)60 1658 y(curv)o(es)12 b(of)h(\()p FF(r)5 b FE(\000)t FQ(1\)-phase)13 b(co)q(existence)f(corresp)q(ond)i(to)f (the)f(p)q(ositiv)o(e)g(co)q(ordinate)h(axes)g(excluding)60 1718 y(the)21 b(origin,)h FF(:)8 b(:)g(:)21 b FQ(,)h(the)f(op)q(en)h(sets)g (with)f(only)g(one)g(pure)g(phase)h(corresp)q(ond)g(to)f(the)g(\()p FF(r)16 b FE(\000)e FQ(1\)-)60 1779 y(dimensional)e(co)q(ordinate)i(h)o(yp)q (erplanes)g(excluding)e(their)h(\()p FF(r)7 b FE(\000)f FQ(2\)-dimensional)13 b(b)q(oundaries.)21 b(In)60 1839 y(brief,)16 b(the)g(di\013eren)o(t)g(strata) i(are)f(mapp)q(ed)f(in)o(to)g(the)h(di\013eren)o(t)f(submanifolds)g(of)h(the) g(b)q(oundary)60 1899 y(of)g(the)f FF(r)q FQ(-o)q(ctan)o(t.)133 1959 y(General)f(phase)h(diagrams)e(need)h(not)h(ob)q(ey)f(the)g(Gibbs)g (phase)h(rule.)k(A)15 b(t)o(ypical)f(situation)h(is)60 2019 y(for)i(some)f(of)h(the)g(pure)f(phases)i(to)f(alw)o(a)o(ys)g(app)q(ear)h (together)f(throughout)h(the)f(diagram.)22 b(Suc)o(h)60 2079 y(a)e(situation)h(is)f(called)f(a)h FP(de)n(gener)n(acy)t FQ(,)i(and)e(it)g (is)g(usually)f(asso)q(ciated)j(to)e(some)f(symmetry)e(of)60 2140 y(the)h(system)f(\(if)h(no)h(symmetry)c(can)k(explain)f(it,)g(the)g (degeneracy)g(is)h(called)e FP(fortuitous)t FQ(\).)28 b(The)60 2200 y(addition)21 b(of)g(further)g(in)o(teractions)f(\(not)h(resp)q(ecting)f (the)h(symmetry)o(\))d(can)j(pro)q(duce)g(a)h(phase)60 2260 y(diagram)14 b(without)h(degeneracy)l(.)20 b(These)15 b(extra)g(in)o (teractions)f(are)h(said)g(to)g FP(br)n(e)n(ak)h(the)g(de)n(gener)n(acy)60 2320 y FQ(of)d(the)f(pure)g(phases)h(in)f(question.)20 b(An)12 b(in)o(teraction)f(is)h(said)h(to)g FP(c)n(ompletely)i(br)n(e)n(ak)e(the)h (de)n(gener)n(acy)60 2380 y FQ(of)j(the)f(pure)g(phases)h(if)e(its)h (addition)h(yields)e(a)i(regular)f(phase)h(diagram.)60 2507 y FM(B.3.2)55 b(Zero-T)-5 b(emp)r(erature)15 b(Regular)j(Phase)h(Diagrams)60 2600 y FQ(F)l(or)e(zero-temp)q(erature)f(phase)i(diagrams,)f(it)f(is)i (relativ)o(ely)c(simple)h(to)j(giv)o(e)e(conditions)h(on)h(the)60 2660 y(extra)k(in)o(teractions)f(needed)g(to)i(ensure)f(a)g(regular)g(phase)h (diagram.)38 b(Indeed,)22 b(at)h(zero)e(tem-)938 2784 y(214)p eop %%Page: 215 215 bop 60 91 a FQ(p)q(erature)17 b(degeneracy)f(means)g(equal)h(sp)q(eci\014c)f (energy)g(for)i(all)e(v)m(alues)h(of)g(the)g(parameters,)e(and)60 152 y(its)j(breaking)g(in)o(v)o(olv)o(es)f(adding)i(in)o(teractions)e(pro)q (ducing)j(a)e(di\013eren)o(t)g(set)g(of)h(sp)q(eci\014c)f(energies)60 212 y(for)h(eac)o(h)g(of)g(the)g(initially)e(degenerate)i(pure)g(phases.)31 b(This)19 b(is)g(usually)g(done)g(p)q(erturbativ)o(ely)l(,)60 272 y(that)i(is,)g(eac)o(h)f(additional)h(in)o(teraction)f(is)g(m)o(ultiplie) o(d)e(b)o(y)i(an)h(o)o(v)o(erall)e(\\turn-on")k(parameter.)60 332 y(Supp)q(ose)e(w)o(e)e(start)h(with)g(an)g(in)o(teraction)f(\010)920 339 y FH(0)960 332 y FQ(ha)o(ving)g FF(r)j FQ(degenerate)d(zero-temp)q (erature)f(pure)60 392 y(phases)d FF(\026)242 399 y FH(1)262 392 y FF(;)8 b(:)g(:)g(:)f(\026)378 399 y FD(r)397 392 y FQ(.)21 b(Then,)14 b(to)g(completely)d(break)j(the)f(degeneracy)h(one)g(usually)f (considers)h FF(r)8 b FE(\000)e FQ(1)60 452 y(additional)16 b(in)o(teractions)g(\010)590 459 y FH(1)610 452 y FF(;)8 b(:)g(:)g(:)f(;)h FQ(\010)754 459 y FD(r)q Fy(\000)p FH(1)835 452 y FQ(and)16 b(constructs)h(the)f(\\p)q(erturb)q(ed")h(in)o(teractions)747 589 y(\010)p 782 576 23 2 v 15 x FD(\025)833 589 y FQ(=)27 b(\010)933 596 y FH(0)964 589 y FQ(+)1013 536 y FD(r)q Fy(\000)p FH(1)1014 548 y Fx(X)1016 639 y FD(i)p FH(=1)1084 589 y FF(\025)1112 596 y FD(i)1126 589 y FQ(\010)1161 596 y FD(i)1189 589 y FF(:)552 b FQ(\(B)p FF(:)p FQ(26\))60 727 y([Examples:)31 b(\(i\))21 b(F)l(or)h(the)g(Ising)g(mo)q(del)e(at)j(zero)e(\014eld,)i FF(\025)1185 734 y FH(1)1228 727 y FQ(=)h FF(h)p FQ(;)g(\(ii\))d(for)h(the)g (Blume-Cap)q(el)60 787 y(in)o(teraction)15 b(de\014ned)h(b)o(y)g(\(B.34\))g (b)q(elo)o(w,)g FF(\025)872 794 y FH(1)906 787 y FQ(=)e FF(g)k FQ(and)f FF(\025)1122 794 y FH(2)1156 787 y FQ(=)d FF(h)i FQ(in)g(the)g(\\p)q (erturbation")i(\(B.35\).])60 848 y(The)i(parameters)p 421 808 29 2 v 20 w FF(\025)h FQ(=)g(\()p FF(\025)576 855 y FH(1)596 848 y FF(;)8 b(:)g(:)g(:)g(;)g(\025)734 855 y FD(r)q Fy(\000)p FH(1)798 848 y FQ(\))20 b(usually)g(tak)o(e)g(v)m(alues)h(in)f(a)h(certain)e (neigh)o(b)q(orho)q(o)q(d)k(of)60 908 y(the)16 b(origin.)21 b(The)c(degree)f(of)g(degeneracy)g(for)h(the)f(p)q(erturb)q(ed)g(in)o (teraction)g(\010)p 1527 894 23 2 v 14 x FD(\025)1566 908 y FQ(dep)q(ends)g(on)h(the)60 968 y FF(r)q FQ(-tuple)f(of)h(sp)q(eci\014c)e (energies)p 653 1044 V 653 1071 a FF(e)p FQ(\()p 695 1031 29 2 v FF(\025)p FQ(\))f(=)g(\()p FF(e)850 1078 y FH(\010)p 875 1070 21 2 v 14 x Fs(\025)897 1071 y FQ(\()p FF(\026)945 1078 y FH(1)965 1071 y FQ(\))p FF(;)8 b(:)g(:)g(:)g(;)g(e)1117 1078 y FH(\010)p 1142 1070 V 14 x Fs(\025)1164 1071 y FQ(\()p FF(\026)1212 1078 y FD(r)1231 1071 y FQ(\)\))14 b FF(:)458 b FQ(\(B)p FF(:)p FQ(27\))60 1173 y(In)16 b(fact,)g(if)f(w)o(e)h(denote)597 1233 y FF(Q)p FQ(\()p 655 1194 29 2 v FF(\025)p FQ(\))28 b(=)f FE(f)p FF(i)8 b FQ(:)16 b FF(\026)904 1240 y FD(i)935 1233 y FQ(minim)o(ize)o(s)e FF(e)1186 1240 y FH(\010)p 1211 1233 21 2 v 15 x Fs(\025)1233 1233 y FQ(\()p FF(\026)p FQ(\))p FE(g)g FF(:)402 b FQ(\(B)p FF(:)p FQ(28\))60 1317 y(then)16 b(the)g(strata)h(of)g(the)f(zero-temp)q (erature)f(phase)h(diagram)g(are)g(the)g(sets)730 1420 y FF(S)760 1427 y FD(K)822 1420 y FQ(=)28 b FE(f)p 912 1380 29 2 v -1 w FF(\025)9 b FQ(:)16 b FF(Q)p FQ(\()p 1037 1380 V FF(\025)p FQ(\))e(=)g FF(K)t FE(g)535 b FQ(\(B)p FF(:)p FQ(29\))60 1523 y(for)16 b(eac)o(h)f(subset)h(of)g(lab)q(els)g FF(K)h FE(\032)d(f)p FQ(1)p FF(;)8 b(:)g(:)g(:)g(;)g(r)q FE(g)p FQ(.)21 b(The)16 b(p)q(erturb)q(ed)g(in)o(teraction)e(completely)f(breaks)60 1583 y(the)j(degeneracy)g(if)f(the)h(phase)h(diagram)f(formed)f(b)o(y)g(the)h (strata)i(\(B.28\))e(is)g FF(r)q FQ(-regular.)133 1643 y(It)21 b(is)f(of)i(in)o(terest)d(to)j(translate)f(the)g(requiremen)n(t)d(of)j (regularit)o(y)f(in)o(to)h(conditions)g(on)g(the)60 1703 y(p)q(erturbations)f (\010)403 1710 y FD(i)417 1703 y FQ(.)30 b(One)19 b(w)o(a)o(y)g(to)g(do)h(it) e(is)h(to)h(notice)e(that,)i(as)g(the)f(sp)q(eci\014c)f(energy)h(dep)q(ends) 60 1763 y(linearly)c(on)i(the)f(parameters)f FF(\025)667 1770 y FD(i)681 1763 y FQ(,)h(it)g(can)g(b)q(e)h(written)e(in)h(the)g(form)p 769 1873 23 2 v 769 1899 a FF(e)o FQ(\()p 810 1860 29 2 v FF(\025)q FQ(\))d(=)923 1845 y FD(r)q Fy(\000)p FH(1)924 1858 y Fx(X)926 1949 y FD(i)p FH(=1)993 1899 y FF(\025)1021 1906 y FD(i)p 1036 1873 23 2 v 1036 1899 a FF(e)p FQ(\(\010)1113 1906 y FD(i)1127 1899 y FQ(\))h FF(;)581 b FQ(\(B)p FF(:)p FQ(30\))60 2034 y(with)p 636 2068 V 636 2094 a FF(e)p FQ(\(\010)713 2101 y FD(i)727 2094 y FQ(\))28 b(=)f(\()p FF(e)881 2101 y FH(\010)906 2106 y Fs(i)922 2094 y FQ(\()p FF(\026)970 2101 y FH(1)990 2094 y FQ(\))p FF(;)8 b(:)g(:)g(:)f(;)h(e)1141 2101 y FH(\010)1166 2106 y Fs(i)1181 2094 y FQ(\()p FF(\026)1229 2101 y FD(r)1249 2094 y FQ(\)\))13 b FF(:)441 b FQ(\(B)p FF(:)p FQ(31\))60 2178 y(One)18 b(of)h(the)g(conditions)f(for)h(the)g(phase)g(diagram)f(to)h(b)q(e)g FF(r)q FQ(-regular)g(is)f(that)h(the)g(origin)p 1763 2139 29 2 v 18 w FF(\025)g FQ(=)f(0)60 2238 y(b)q(e)f(the)g(only)g(p)q(oin)o(t)h(of)f (maximal)d(co)q(existence.)23 b(This)17 b(implies)e(that)i(no)h(nonzero)g(v)o (ector)e(of)h(the)60 2299 y(form)d(\(B.30\))h(can)g(ha)o(v)o(e)f(all)h(its)g (co)q(ordinates)h(equal.)k(A)14 b(little)g(bit)g(of)i(linear)e(algebra)i(sho) o(ws)g(that)60 2359 y(all)k(the)h(other)g(conditions)g(for)g(regularit)o(y)e (are)i(satis\014ed)g(if)g(the)f(v)o(ectors)g FE(f)p 1507 2332 23 2 v FF(e)p FQ(\(\010)1584 2366 y FD(i)1598 2359 y FQ(\))p FE(g)1642 2366 y FH(1)p Fy(\024)p FD(i)p Fy(\024)p FD(r)q Fy(\000)p FH(1)1811 2359 y FQ(are,)60 2419 y(in)d(addition,)g(linearly)f(indep)q(enden) o(t.)23 b(Therefore,)16 b FP(the)j(p)n(erturb)n(ations)f FQ(\010)1446 2426 y FH(1)1466 2419 y FF(;)8 b(:)g(:)g(:)f FQ(\010)1588 2426 y FD(r)q Fy(\000)p FH(1)1671 2419 y FP(c)n(ompletely)60 2479 y(br)n(e)n(ak)16 b(the)g(de)n(gener)n(acy)g(of)g FQ(\010)598 2486 y FH(0)634 2479 y FP(if)g(and)g(only)g(if)g(the)h(ve)n(ctors)p 1165 2453 V 16 w FF(e)o FQ(\(\010)1241 2486 y FD(i)1256 2479 y FQ(\))f FP(ar)n(e)f(line)n(arly)h(indep)n(endent)i(and)60 2539 y(they)g(do)f(not)h(sp)n(an)f(the)h(ve)n(ctor)g FQ(\(1)p FF(;)8 b(:)g(:)g(:)f(;)h FQ(1\))14 b FE(2)g Fq(R)945 2519 y FD(r)964 2539 y FQ(.)133 2600 y(Alternativ)o(ely)l(,)g(if)i(w)o(e)g(resort)i (to)f(the)f(previous)h(geometrical)e(description)h(of)h(regularit)o(y)l(,)e (w)o(e)60 2660 y(conclude)f(that)g(it)g(is)h(equiv)m(alen)o(t)d(to)j(require) e(that)i(the)f(v)o(ector)p 1237 2633 V 14 w FF(e)o FQ(\()p 1278 2620 29 2 v FF(\025)q FQ(\))g(|)g(shifted)g(so)h(it)f(alw)o(a)o(ys)g (has)938 2784 y(215)p eop %%Page: 216 216 bop 60 91 a FQ(at)16 b(least)g(one)h(co)q(ordinate)f(equal)g(to)g(zero)g(|)g (sw)o(eeps)g(o)o(v)o(er)f(the)h(b)q(oundary)h FF(@)s(Q)1552 98 y FD(r)1587 91 y FQ(of)f(the)g(p)q(ositiv)o(e)60 152 y(o)q(ctan)o(t.)22 b(Precisely)14 b(stated,)i(if)g(w)o(e)g(denote)608 258 y Fx(e)606 262 y FF(e)p 629 248 23 2 v 14 x FD(\025)651 262 y FQ(\()p FF(\026)699 269 y FD(i)713 262 y FQ(\))28 b(=)g FF(e)849 269 y FH(\010)p 874 261 21 2 v 14 x Fs(\025)896 262 y FQ(\()p FF(\026)944 269 y FD(i)959 262 y FQ(\))11 b FE(\000)23 b FQ(min)1039 291 y FH(1)p Fy(\024)p FD(j)r Fy(\024)p FD(r)1152 262 y FF(e)1175 269 y FH(\010)p 1200 261 V 14 x Fs(\025)1223 262 y FQ(\()p FF(\026)1271 269 y FD(j)1290 262 y FQ(\))13 b FF(;)419 b FQ(\(B)p FF(:)p FQ(32\))60 390 y FP(the)18 b(p)n(erturb)n(ation)f FQ(\010)p 450 376 23 2 v 14 x FD(\025)490 390 y FP(c)n(ompletely)i(br)n(e)n(aks)e(the)h (de)n(gener)n(acy)g(of)f FQ(\010)1291 397 y FH(0)1329 390 y FP(if)g(and)g(only)h(if)g(the)g(map)p 727 460 29 2 v 727 500 a FF(\025)d FE(7!)e FQ(\()855 496 y Fx(e)852 500 y FF(e)p 875 486 23 2 v 14 x FD(\025)898 500 y FQ(\()p FF(\026)946 507 y FH(1)966 500 y FQ(\))p FF(;)8 b(:)g(:)g(:)1075 496 y Fx(e)1072 500 y FF(e)p 1095 486 V 14 x FD(\025)1117 500 y FQ(\()p FF(\026)1165 507 y FD(r)1185 500 y FQ(\)\))532 b(\(B)p FF(:)p FQ(33\))60 610 y FP(is)22 b(one-to-one.)40 b(In)23 b(other)g(wor)n(ds,)f(if)h(such)g(a)f (map)g(is)h(a)f(bije)n(ction)i(fr)n(om)d(a)i(neighb)n(orho)n(o)n(d)e(of)60 670 y FQ(0)16 b FE(2)f Fq(R)181 649 y FD(d)p Fy(\000)p FH(1)265 670 y FP(to)j(a)g(neighb)n(orho)n(o)n(d)f(of)h FQ(0)e FE(2)f FF(@)s(Q)871 677 y FD(r)889 670 y FQ(.)24 b(F)l(or)17 b(eac)o(h)g(particular) f(v)m(alue)h(of)p 1534 630 29 2 v 17 w FF(\025)q FQ(,)g(the)f(co)q(existing) 60 730 y(pure)g(phases)h(are)f(those)h FF(\026)564 737 y FD(i)595 730 y FQ(with)708 726 y Fx(e)706 730 y FF(e)p 729 716 23 2 v 14 x FD(\025)751 730 y FQ(\()p FF(\026)799 737 y FD(i)813 730 y FQ(\))d(=)g(0.)60 860 y FM(B.3.3)55 b(Lo)n(w-T)-5 b(emp)r(erature)16 b(Phase)j(Diagrams.)24 b(Scop)r(e)18 b(of)g(Pirogo)n(v-Sinai)g(Theory)60 952 y FQ(If)h(nature)h(is)f(fair,)h(one)g(exp)q(ects)f(that)g(lo)o(w-temp)q (erature)g(phase)h(diagrams)f(lo)q(ok)h(v)o(ery)e(similar)60 1013 y(to)g(the)g(corresp)q(onding)h(zero-temp)q(erature)d(ones.)27 b(This)18 b(is)g(not)h(alw)o(a)o(ys)e(so,)i(ho)o(w)o(ev)o(er,)e(and)h(the)60 1073 y(question)f(of)h(stabilit)o(y)f(or)h(w-stabilit)o(y)f(of)h(Gibbs)g (measures)f(is)g(an)h(imp)q(ortan)o(t)f(issue.)25 b(Pirogo)o(v-)60 1133 y(Sinai)17 b(theory)h(has)g(b)q(een)g(precisely)e(designed)h(to)h (single)f(out)h(some)f(imp)q(ortan)o(t)g(cases)g(in)h(whic)o(h)60 1193 y(indeed)d(the)g(lo)o(w-temp)q(erature)g(diagrams)g(are)h(only)f(a)i (small)d(deformation)h(of)h(the)f(ones)h(at)g(zero)60 1253 y(temp)q(erature.)31 b(When)20 b(the)g(theory)f(applies,)i(one)f(is)f(guaran) o(teed)i(that)f(the)g(regularit)o(y)f(of)h(the)60 1314 y(diagram)d(is)h (preserv)o(ed)e(at)i(least)g(for)g(small)e(temp)q(eratures;)g(and,)i (furthermore,)e(that)j(the)e(lo)o(w-)60 1374 y(temp)q(erature)e(pure)h (phases)h(lo)q(ok)g(v)o(ery)e(\\similar")f(to)j(the)f(zero-temp)q(erature)f (ones.)133 1434 y(As)h(an)h(input)g(to)g(the)f(Pirogo)o(v-Sinai)g(theory)h (one)f(m)o(ust)f(determine)f(the)j(zero-temp)q(erature)60 1494 y(phase)j(diagram)e(and)i(sho)o(w)g(that)g(t)o(w)o(o)f(k)o(ey)f(h)o(yp)q (otheses)h(are)h(satis\014ed.)30 b(The)19 b(\014rst)h(h)o(yp)q(othesis)60 1554 y(refers)i(to)h(the)f(n)o(um)o(b)q(er)f(of)h(zero-temp)q(erature)f (deterministic)e(pure)j(phases:)35 b(In)22 b(its)g(original)60 1615 y(v)o(ersion)d([296)q(,)g(297)r(],)g(Pirogo)o(v-Sinai)i(\(PS\))f(theory) f(applies)h(to)g(a)g(system)f(with)h(a)g(\014nite-range)60 1675 y(p)q(erio)q(dic)e(in)o(teraction,)e(exhibiting)h(a)h FP(\014nite)j(numb)n(er)e(of)g(p)n(erio)n(dic)f(rigid)h(gr)n(ound-state)g(c)n (on\014gu-)60 1735 y(r)n(ations)t FQ(.)27 b(\(This)18 b(has)h(subsequen)o (tly)e(b)q(een)h(generalized)g(to)g(some)f(exten)o(t:)24 b(see)18 b(Section)g(B.4.4.\))60 1795 y(The)e(second)g(h)o(yp)q(othesis)g(is)g(that)g (the)g(in)o(teraction)f(satisfy)h(the)g(so-called)f(\\P)o(eierls)g (condition",)60 1855 y(to)i(b)q(e)g(stated)h(more)d(precisely)h(b)q(elo)o(w,) g(whic)o(h)h(roughly)g(requires)f(that)h(for)g(eac)o(h)g(rigid)f(p)q(erio)q (dic)60 1916 y(ground-state)23 b(con\014guration)f(the)f(energy)g(cost)h(of)f (in)o(tro)q(ducing)g(a)h(droplet)f(of)h(spins)f(aligned)60 1976 y(as)d(in)f(a)h FP(di\013er)n(ent)23 b FQ(ground)18 b(state)g(m)o(ust)e (gro)o(w)j(t)o(ypically)c(as)j(the)f(area)h(of)g(the)g(b)q(oundary)g(of)g (the)60 2036 y(droplet.)26 b(This)18 b(condition)g(allo)o(ws)g(the)g(energy)f (cost)h(of)h(creating)e(excitations)g(to)i(b)q(eat)f(the)g(en-)60 2096 y(trop)o(y)i(gain,)g(preserving)f(the)h(long-range)h(order)e(observ)o (ed)h(at)g(zero)f(temp)q(erature.)30 b(Ho)o(w)o(ev)o(er,)60 2156 y(the)13 b(P)o(eierls)e(condition)i(has)h(this)f(desired)f(e\013ect)g (only)h(for)g FF(d)h FE(\025)g FQ(2.)21 b(The)13 b(trouble)f(is)h(that)g(for) h FF(d)g FQ(=)g(1)60 2216 y(the)k(size)f(of)h(the)g(b)q(oundary)i(of)e(a)g (set)g(do)q(es)h(not)g(gro)o(w)f(with)g(its)g(v)o(olume.)25 b(Therefore,)17 b FP(Pir)n(o)n(gov-)60 2277 y(Sinai)f(the)n(ory)e(is)i(not)f (applic)n(able)i(to)e(one-dimensional)j(mo)n(dels)t FQ(.)i(On)14 b(the)g(other)g(hand,)h(for)f FF(d)g FE(\025)g FQ(2)60 2337 y(the)20 b(P)o(eierls)f(condition)h(is)g(certainly)f(stronger)i(than)g (necessary)1298 2319 y FH(77)1335 2337 y FQ(:)30 b(there)19 b(exist)h(mo)q(dels)f(with)60 2397 y(a)f(\014nite)f(n)o(um)o(b)q(er)f(of)i (rigid)f(p)q(erio)q(dic)g(ground-state)j(con\014gurations)f(whic)o(h)e(ha)o (v)o(e)f(a)i(non-trivial)60 2457 y(phase)e(diagram)f(and)h(whic)o(h)f(do)h (not)g(satisfy)g(the)f(P)o(eierls)f(condition)h([290)q(,)g(264)q(].)21 b(Nev)o(ertheless,)p 60 2504 732 2 v 100 2558 a FA(77)135 2573 y Fz(In)12 b(some)f(sense)j(it)e(is)g(the)h Fw(str)n(ongest)g(p)n(ossible)i Fz(condition:)h(see)e(the)f(commen)o(ts)d(after)j(De\014nition)e(B.19)h(b)q (elo)o(w.)938 2784 y FQ(216)p eop %%Page: 217 217 bop 60 91 a FQ(the)14 b(P)o(eierls)f(condition)h(applies)g(in)g(a)h(large)f (n)o(um)o(b)q(er)e(of)j(in)o(teresting)e(mo)q(dels,)g(and)i(allo)o(ws)g(a)f (v)o(ery)60 152 y(precise)h(description)h(of)g(the)g(lo)o(w-temp)q(erature)f (b)q(eha)o(vior.)133 212 y(The)22 b(output)g(of)g(the)f(theory)h(is)f(a)h (family)e(of)i(results)f(in)o(v)o(olving)f(extensions)h(to)h(non-zero)60 272 y(temp)q(eratures.)e(The)15 b(main)f(result)h(of)h(the)f(theory)h(is)f (that)h(for)g(a)g(system)e(satisfying)h(the)h(P)o(eierls)60 332 y(condition)g(the)f(phase)i(diagram)e(in)o(v)o(olving)f(these)i(p)q(erio) q(dic)f(deterministic)e(measures)i(is)h(stable:)60 392 y(As)i(the)f(temp)q (erature)f(increases,)i(the)f(co)q(existence)g(manifolds)f(deform)h(con)o (tin)o(uously)g(\(in)g(fact)60 452 y(analytically\).)24 b(Moreo)o(v)o(er,)16 b(the)h(theory)g(mak)o(es)f(rigorous)j(the)e(in)o(tuitiv)o(e)e(picture)i(of)g (what)i(eac)o(h)60 513 y(lo)o(w-temp)q(erature)d(pure)h(phase)h(lo)q(oks)g (lik)o(e:)k(its)17 b(t)o(ypical)f(con\014gurations)j(consist)f(of)f(a)h (\\sea")h(of)60 573 y(spins)g(aligned)f(as)i(in)e(the)h(ground-state)h (con\014guration)g(with)e(small)f(and)j(sparse)f(\\islands")h(of)60 633 y(o)o(v)o(erturned)15 b(spins.)133 693 y(W)l(e)20 b(remark)f(that)h(the)g (theory)g(do)q(es)h(not)f(ha)o(v)o(e)g(an)o(ything)g(to)g(sa)o(y)h(ab)q(out)g (the)f(stabilit)o(y)f(of)60 753 y(the)f(\(p)q(ossibly)h(in\014nitely)e(man)o (y\))g FP(non-p)n(erio)n(dic)22 b FQ(ground-state)e(con\014gurations)g(and)f (the)f(zero-)60 814 y(temp)q(erature)f(Gibbs)h(measures)g(they)g(supp)q(ort)h (\(but)g(see)f(Section)g(B.4.4\).)27 b(Other)18 b(tec)o(hniques)60 874 y(are)k(needed)e(to)i(sho)o(w,)h(for)f(example,)e(that)i(the)g(\015at-in) o(terface)f(ground-state)i(con\014gurations)60 934 y(\(B.6\))15 b(|)f(whic)o(h)h(are)g(rigid)g(for)g FF(d)f FE(\025)g FQ(2)h(|)g(are)h (unstable)f(for)g FF(d)f FQ(=)g(2)i([141,)f(1,)g(192)q(])g(and)h(stable)f (for)60 994 y FF(d)f FE(\025)g FQ(3)i([85)q(,)g(348)q(].)133 1054 y(Moreo)o(v)o(er,)c(the)g(original)g(v)o(ersion)g(of)h(PS)g(theory)f (giv)o(es)g(only)g(v)o(ery)g(limite)o(d)e(information)i(as)h(to)60 1115 y(the)h(sp)q(eci\014cs)f(of)i(the)f(deformation)f(of)h(the)g(phase)h (diagram;)e(in)h(particular)g(it)f(do)q(es)i(not)g(pro)q(duce)60 1175 y(a)20 b(useful)e(criterion)h(to)g(determine)e(whic)o(h)h(pure)h(phases) h(are)g(stable)f(for)g(the)g(di\013eren)o(t)g(regions)60 1235 y(of)e(the)g(zero-temp)q(erature)e(phase)i(diagram.)22 b(That)c(is,)e(it)g (do)q(es)i(not)f(tell)e(us)j FP(in)g(which)g(dir)n(e)n(ction)60 1295 y FQ(the)24 b(phase)g(b)q(oundaries)h(mo)o(v)o(e)d(when)i(the)g(temp)q (erature)f(is)h(raised)g(from)f(zero.)44 b(Therefore,)60 1355 y(for)17 b(in)o(teractions)f(\010)h(lying)f FP(on)21 b FQ(a)c (phase-transition)h(manifold)e(of)h(the)f(zero-temp)q(erature)g(phase)60 1416 y(diagram,)h(the)g(original)h(PS)g(theory)f(do)q(es)h(not)h(tell)d(us)i (in)f(whic)o(h)g(phase\(s\))h(\010)g(ends)g(up)g(at)g FF(T)k(>)60 1476 y FQ(0;)j(that)d(is,)h(it)f(do)q(es)h(not)f(tell)f(us)i(whic)o(h)e (one\(s\))i(of)f(the)g(co)q(existing)g(zero-temp)q(erature)e(pure)60 1536 y(phases)13 b(is/are)g(stable,)g(and)h(whic)o(h)e(are)g(only)h(w-stable) g(for)g(the)f(family)f(of)i(in)o(teractions)f(adopted.)60 1596 y(Ho)o(w)o(ev)o(er,)i(Sla)o(wn)o(y's)h(extension)h(of)h(PS)f(theory)g([329)q (])g(pro)o(vides)f(this)i(additional)f(information.)133 1656 y(T)l(o)i(clarify)e(this)i(p)q(oin)o(t,)f(let)g(us)h(b)q(orro)o(w)g(a)g(v)o (ery)f(instructiv)o(e)e(example)h(from)g(the)h(review)g(b)o(y)60 1716 y(Sla)o(wn)o(y)e([329)q(].)21 b(Consider)16 b(the)g(spin-1)g(Blume-Cap)q (el)e(mo)q(del)h(de\014ned)h(b)o(y)f(the)h(formal)f(Hamilto-)60 1777 y(nian)719 1837 y FF(H)759 1844 y FH(0)806 1837 y FQ(=)877 1817 y FH(1)p 877 1825 18 2 v 877 1854 a(2)911 1795 y Fx(X)908 1889 y Fy(h)p FD(xy)q Fy(i)974 1837 y FQ(\()p FF(!)1023 1844 y FD(x)1056 1837 y FE(\000)c FF(!)1136 1844 y FD(y)1157 1837 y FQ(\))1176 1816 y FH(2)1210 1837 y FF(;)531 b FQ(\(B)p FF(:)p FQ(34\))60 1977 y(where)18 b FF(!)233 1984 y FD(x)273 1977 y FQ(=)g FE(\000)p FQ(1)p FF(;)8 b FQ(0)p FF(;)g FQ(1)19 b(and)g(the)f(sum)g (is)g(o)o(v)o(er)f(pairs)i(of)g(nearest-neigh)o(b)q(or)g(sites)f(in)g Fq(Z)1701 1956 y FD(d)1721 1977 y FQ(,)h FF(d)e(>)h FQ(1.)60 2037 y(Suc)o(h)h(a)h(mo)q(del)e(has)j(three)d(p)q(erio)q(dic)i(\(in)f(fact)g (translation-in)o(v)m(arian)o(t\))h(ground-state)h(con\014gu-)60 2097 y(rations:)j(all-\\+",)18 b(all-\\0")h(and)f(all-\\)p FE(\000)p FQ(".)25 b(They)18 b(are)f(all)g(rigid.)25 b(T)l(o)18 b(obtain)g(a)g(3-regular)h(phase)60 2158 y(diagram)13 b(one)h(can)g (consider,)g(for)g(instance,)g(the)f(family)f(of)i(in)o(teractions)f (de\014ned)h(b)o(y)g(the)f(formal)60 2218 y(Hamiltonians)590 2278 y FF(H)t FQ(\()p FF(g)r(;)8 b(h)p FQ(\))28 b(=)f FF(H)880 2285 y FH(0)911 2278 y FE(\000)11 b FF(g)995 2236 y Fx(X)1015 2324 y FD(x)1063 2278 y FF(!)1095 2257 y FH(2)1093 2290 y FD(x)1126 2278 y FE(\000)g FF(h)1212 2236 y Fx(X)1232 2324 y FD(x)1281 2278 y FF(!)1311 2285 y FD(x)1347 2278 y FF(:)394 b FQ(\(B)p FF(:)p FQ(35\))60 2396 y(The)11 b(corresp)q(onding)h(zero-temp)q(erature)d (phase)i(diagram)g(is)f(presen)o(ted)g(in)h(Figure)f(13\(a\).)21 b(Pirogo)o(v-)60 2456 y(Sinai)15 b(theory)g(tells)g(us)h(that)f(for)h FF(T)k(>)14 b FQ(0)i(lo)o(w)f(enough)h(the)g(phase)g(diagram)e(is)i(just)f(a) h(con)o(tin)o(uous)60 2517 y(deformation)k(of)g(the)h(one)g(depicted,)f(but)g (to)h(conclude)f(that)h(suc)o(h)f(deformations)g(lo)q(ok)h(as)g(in)60 2577 y(Figure)14 b(13\(b\))i(w)o(e)e(need)h(some)f(extra)g(information)g (whic)o(h)g(is)h(not)g(directly)e(obtainable)i(from)f(PS)60 2637 y(theory)l(,)h(although)g(it)g(is)f(probably)i(con)o(tained)e(in)h(it.) 20 b(This)15 b(extra)g(information)f(is)g(presen)o(ted)g(ex-)938 2784 y(217)p eop %%Page: 218 218 bop 60 91 a FQ(plicitly)l(,)13 b(for)j(instance,)f(in)h(Sla)o(wn)o(y's)f (theory)h(of)g(asymptotics)f(of)h(phase)g(diagrams)g([329)q(].)k(F)l(rom)60 152 y(the)d(latter)g(diagram)f(w)o(e)h(see,)f(for)i(instance,)e(that)i(of)g (the)e(three)h(deterministic)d(pure)j(phases)h(of)60 212 y FF(H)t FQ(\()p FF(g)e FQ(=)e(0)p FF(;)8 b(h)14 b FQ(=)g(0\))f(only)g(the)f (all-\\0")i(is)f(stable,)g(while)f(the)g(other)h(t)o(w)o(o)g(pure)g(phases)g (are)g(w-stable.)60 272 y(The)i(w)o(ell-studied)f(ferromagnetic)g(Ising)h(mo) q(del)g(pro)o(vides)f(an)i(example)d(of)j(an)g(exceptional)e(na-)60 332 y(ture:)21 b(its)16 b(phase)g(diagram)f(remains)g(undeformed)g(at)h(lo)o (w)g(temp)q(eratures;)e(for)i(all)g(v)m(alues)g(of)g(the)60 392 y(magnetic)f(\014eld)g(the)h(p)q(erio)q(dic)g(zero-temp)q(erature)f (Gibbs)i(measures)e(are)h(stable.)60 537 y FB(B.4)69 b(Pirogo)n(v-Sinai)23 b(Theory)60 629 y FQ(W)l(e)e(summarize)d(no)o(w)j(the)g(main)e(asp)q(ects)j (of)f(PS)g(theory)l(.)36 b(In)20 b(the)h(\014rst)g(t)o(w)o(o)g(subsections)g (w)o(e)60 689 y(carefully)c(discuss)h(the)f(basic)h(h)o(yp)q(otheses)h (required)d(b)o(y)i(the)g(theory;)g(in)g(the)f(third)h(subsection)60 749 y(w)o(e)g(presen)o(t)h(a)g(somewhat)g(detailed)f(accoun)o(t)g(of)i(the)e (results)h(\(for)g(\014nite-range)g(in)o(teractions\).)60 810 y(Of)f(course,)h(w)o(e)e(omit)g(all)h(pro)q(ofs;)i(these)e(can)h(b)q(e)f (found)h(in)f(the)g(references)f(cited.)26 b(As)18 b(already)60 870 y(p)q(oin)o(ted)e(out,)f(the)h(theory)f(do)q(es)i(not)f(apply)f(for)h FF(d)e FQ(=)g(1,)i(therefore)f FP(in)i(the)h(r)n(est)e(of)h(this)g(app)n (endix)60 930 y(we)h(r)n(estrict)f(ourselves)i(to)e FF(d)e FE(\025)e FQ(2.)60 1060 y FM(B.4.1)55 b(Boundary)19 b(of)g(a)f (Con\014guration.)25 b(The)19 b(P)n(eierls)e(Condition)60 1152 y FQ(T)o(ypical)e(con\014gurations)j(of)e(a)h(lo)o(w-temp)q(erature)e(pure)h (phase)h(are)f(exp)q(ected)f(to)i(b)q(e)f(small)f(\015uc-)60 1212 y(tuations)h(around)g(those)f(of)g(a)g(corresp)q(onding)h(zero-temp)q (erature)e(pure)g(phase.)22 b(These)14 b(\015uctua-)60 1273 y(tions)i(result)e(in)h(the)h(app)q(earance)g(of)f(\\droplets")h (\(\\bubbles",)g(\\islands"\))g(of)g(spins)g(aligned)f(ac-)60 1333 y(cording)e(to)h(a)f(di\013eren)o(t)g(zero-temp)q(erature)e(pure)i (phase)h(|)f(or,)g(more)f(generally)l(,)g(a)i(\\metastable)60 1393 y(phase")k([369)q(])e(as)i(w)o(e)e(discuss)h(b)q(elo)o(w.)24 b(These)17 b(droplets)f(are)h(surrounded)h(b)o(y)f(a)g(transitional)g(re-)60 1453 y(gion)d(or)g(\\b)q(oundary")i(of)e(sets)f(of)h(spins)g(not)g(aligned)g (according)g(to)g(an)o(y)f(zero-temp)q(erature)f(pure)60 1513 y(phase,)17 b(whic)o(h)g(therefore)f(raises)h(the)g(energy)f(of)i(the)e (con\014guration.)25 b(The)17 b(probabilit)o(y)f(of)h(suc)o(h)60 1574 y(\015uctuations)22 b(is)e(determined)f(b)o(y)h(the)h(comp)q(etition)e (b)q(et)o(w)o(een)h(t)o(w)o(o)h(factors:)31 b(the)21 b(energy)g(cost)60 1634 y(of)f(in)o(tro)q(ducing)f(a)h(b)q(oundary)g(and)g(the)f(en)o(trop)o(y)g (gain)h(due)f(to)h(the)f(di\013eren)o(t)f(p)q(ossible)i(shap)q(es)60 1694 y(and)f(lo)q(cations)h(of)f(the)f(droplets.)28 b(If)19 b(the)f(energy)g(cost)h(is)g(large)f(enough)i(to)f(o)o(v)o(ercome,)d(at)j(lo) o(w)60 1754 y(temp)q(eratures,)g(the)g(en)o(trop)o(y)g(gain,)h(then)f(eac)o (h)g(zero-temp)q(erature)f(pure)i(phase)g(giv)o(es)f(rise)g(to)60 1814 y(a)j(lo)o(w-temp)q(erature)e(one)i(whic)o(h)f(di\013ers)g(only)h(in)f (the)g(presence)g(of)h(few)f(and)h(small)e(droplets)60 1875 y(of)f(o)o(v)o(erturned)e(spins.)28 b(In)18 b(particular,)g(this)g(w)o(ould)g (pro)o(v)o(e)g(that)h(there)f(are)g(precisely)e(as)j(man)o(y)60 1935 y(co)q(existing)k(pure)h(phases)h(at)f(lo)o(w)g(temp)q(eratures)e(as)j (there)e(are)h(at)g(zero)g(temp)q(erature,)f(and)60 1995 y(hence)16 b(that)i(there)e(is)h(a)h(phase)f(transition.)24 b(This)17 b(t)o(yp)q(e)g(of)g(argumen)o(t)f(w)o(as)i(\014rst)f(in)o(tro)q(duced)g(b)o (y)60 2055 y(P)o(eierls)e([291)q(,)h(82)q(,)g(168)q(])g(to)h(pro)o(v)o(e)e (the)i(existence)d(of)j(a)g(phase)g(transition)g(in)f(the)g FF(d)p FQ(-dimensional)60 2115 y(Ising)21 b(mo)q(del)f(for)i FF(d)h FE(\025)f FQ(2,)h(and)f(hence)e(it)h(is)g(often)h(referred)e(to)i(as)g (the)f(\\P)o(eierls)f(argumen)o(t".)60 2176 y(Pirogo)o(v-Sinai)g(theory)f(is) g(a)h(generalization)f(\(and,)h(th)o(us,)g(a)g(more)e(abstract)i(v)o (ersion\))f(of)g(suc)o(h)60 2236 y(an)e(argumen)o(t.)133 2296 y(T)l(o)g(form)o(ulate)e(the)h(P)o(eierls)f(argumen)o(t)g(in)h(a)g(rigorous)i (form)d(w)o(e)h(need)g(a)g(criterion)g(to)g(deter-)60 2356 y(mine)c(when)j(the)f(energy)g(cost)h(of)g(a)g(b)q(oundary)g(is)g(\\large)f (enough")i(to)f(defeat)f(the)g(en)o(trop)o(y)g(gain.)60 2416 y(The)g(P)o(eierls)e(condition)i(is)f(precisely)f(one)i(suc)o(h)g (\(su\016cien)o(t\))e(criterion.)19 b(It)13 b(relies,)g(ho)o(w)o(ev)o(er,)f (on)j(a)60 2476 y(suitable)d(de\014nition)g(of)h(the)f(\\b)q(oundary")j(of)e (a)g(con\014guration,)h(whic)o(h)e(is)g(not)h(a)g(uniquely)e(de\014ned)60 2537 y(concept.)22 b(In)17 b(fact,)f(t)o(w)o(o)h(compleme)o(n)o(tary)d (notions)k(are)e(in)o(tro)q(duced)h(at)g(this)g(stage:)23 b(the)16 b FP(b)n(ound-)60 2597 y(ary)p FQ(,)c(whic)o(h)g(roughly)h(corresp)q(onds)h (to)f(the)f(collection)g(of)h(sites)f(where)g(the)h(spins)g(are)f (misaligned,)60 2657 y(and)19 b(the)f FP(c)n(ontours)t FQ(,)g(whic)o(h)f(are) h(the)g(di\013eren)o(t)f(comp)q(onen)o(ts)h(of)g(this)g(b)q(oundary)i FP(to)n(gether)e FQ(with)938 2784 y(218)p eop %%Page: 219 219 bop 517 1035 a @beginspecial 21 @llx 33.500000 @lly 250 @urx 266.500000 @ury 2196 @rwi @setspecial %%BeginDocument: fig13a.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n []/_Symbol/Symbol Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Italic/Times-Italic Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 1 w 4 M []0 d 132.6725 158 m 231.9998 158 l S 33.3452 158 m 132.6725 158 l S 0.3 w 10 M 231.9882 158.2349 m S 231.9882 158.2349 m S 231.9882 158.2349 m S 231.9882 158.2349 m S 0 g 0.5 w 4 M 232.0502 161.25 m 238.7515 157.8471 L B 238.7515 157.8471 m 232.0142 154.75 L 232.0502 161.25 L B 232.0502 161.25 m 238.7515 157.8471 L B 1 w 132.6725 158 m 132.3436 257.3273 l S 3 w 72 222.5 m 132.6725 158 l S 133.0014 58.6727 m S 0.3 w 10 M 132.1087 257.3149 m S 132.1087 257.3149 m S 132.1087 257.3149 m S 132.1087 257.3149 m S 0 g 0.5 w 4 M 129.0934 257.3669 m 132.4741 264.0795 L B 132.4741 264.0795 m 135.5936 257.3524 L 129.0934 257.3669 L B 129.0934 257.3669 m 132.4741 264.0795 L B u u 1 w /_Times-Italic 12 14.5 0 0 z [1 0 0 1 118 244.5]e (h)t T U U u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 219 146.5]e (g)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 127 36.5]e (\(a\))t T U U 0 G 2 w 72 222.5 m S 1 w 67.7319 97.7998 m S 3 w 67.7319 97.7998 m 132.6725 158 l 214 157.5 l S 1 w 132.6725 158 m 133.0014 58.6727 l S u u 0 g /_Times-Roman 12 14.5 0 0 z [1 0 0 1 115 194.5]e (")t T U u /_Symbol 12 14.5 0 0 z [1 0 0 1 119.8955 194.5]e (+)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 126.4814 194.5]e ("-pure phase)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 115.2886 100.5625]e (")t T U u /_Symbol 12 14.5 0 0 z [1 0 0 1 120.1841 100.5625]e (-)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 126.77 100.5625]e ("-pure phase)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 33.2886 163.5625]e ("0"-pure phase)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 36 229.5]e (two-phase coexistence)t T U U 0 G 0.3 w 10 M 88.183 218.6101 m S 87.3647 218.4437 m S 87.3647 218.4437 m S 87.3647 218.4437 m S 87.3647 218.4437 m S 1 g 0.5 w 4 M 89.803 216.669 m 83.1796 213.1166 L B 83.1796 213.1166 m 84.4907 220.4149 L 89.803 216.669 L B 89.803 216.669 m 83.1796 213.1166 L B 87.3647 218.4437 m 93.4453 227.2687 l S u u 0 g 1 w /_Times-Roman 12 14.5 0 0 z [1 0 0 1 123 130.5]e (three-phase coexistence)t T U U 0 G 0.3 w 10 M 138.3083 148.8824 m S 138.4093 149.7113 m S 138.4093 149.7113 m S 138.4093 149.7113 m S 138.4093 149.7113 m S 1 g 0.5 w 4 M 135.9544 147.9597 m 134.6796 155.3666 L B 134.6796 155.3666 m 141.1884 151.8141 L 135.9544 147.9597 L B 135.9544 147.9597 m 134.6796 155.3666 L B 138.4093 149.7113 m 144.8577 141.1513 l S showpage _E end %%EndDocument @endspecial 1304 x @beginspecial 31 @llx 31.500000 @lly 244 @urx 265.500000 @ury 2196 @rwi @setspecial %%BeginDocument: fig13b.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n []/_Symbol/Symbol Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Italic/Times-Italic Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 1 w 4 M []0 d 133.6241 156.5227 m 232.9515 156.5227 l S 34.2968 156.5227 m 133.6241 156.5227 l S 0.3 w 10 M 232.9398 156.7577 m S 232.9398 156.7577 m S 232.9398 156.7577 m S 232.9398 156.7577 m S 0 g 0.5 w 4 M 233.0018 159.7728 m 239.7032 156.3699 L B 239.7032 156.3699 m 232.9658 153.2727 L 233.0018 159.7728 L B 233.0018 159.7728 m 239.7032 156.3699 L B 1 w 133.6241 156.5227 m 133.2953 255.8501 l S 133.953 57.1954 m 133.6241 156.5227 l S 0.3 w 10 M 133.0603 255.8376 m S 133.0603 255.8376 m S 133.0603 255.8376 m S 133.0603 255.8376 m S 0 g 0.5 w 4 M 130.045 255.8896 m 133.4258 262.6023 L B 133.4258 262.6023 m 136.5452 255.8751 L 130.045 255.8896 L B 130.045 255.8896 m 133.4258 262.6023 L B u u 1 w /_Times-Italic 12 14.5 0 0 z [1 0 0 1 118.9516 243.0227]e (h)t T U U u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 219.9516 145.0227]e (g)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 127.9516 35.0227]e (\(b\))t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 46.2886 161.5625]e ("0"-pure phase)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 158.9956 185.9062]e (")t T U u /_Symbol 12 14.5 0 0 z [1 0 0 1 163.8911 185.9062]e (+)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 170.477 185.9062]e ("-pure phase)t T U U u u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 158.9956 111.9062]e (")t T U u /_Symbol 12 14.5 0 0 z [1 0 0 1 163.8911 111.9062]e (-)t T U u /_Times-Roman 12 14.5 0 0 z [1 0 0 1 170.477 111.9062]e ("-pure phase)t T U U 0 G 3 w 134.6241 156.5227 m S 215.9516 156.0227 m S 95.9998 216.5 m 95.9998 183.376 131.6495 156.5227 175.6241 156.5227 c S 93.0521 95.4825 m 92.6542 128.6043 127.979 155.8838 171.9506 156.412 c S 215.9516 156.0227 m S 216.2283 156.5163 m 170.7742 156.4886 l S showpage _E end %%EndDocument @endspecial 60 2613 a FQ(Figure)13 b(13:)20 b(Phase)14 b(diagrams)f(of)g (the)g(mo)q(del)f(with)h(in)o(teraction)f(\(B.35\).)20 b(\(a\))13 b(Zero)g(temp)q(erature.)60 2673 y(\(b\))j(Lo)o(w)h(temp)q(erature.)938 2784 y(219)p eop %%Page: 220 220 bop 60 91 a FQ(the)19 b(corresp)q(onding)h(spin)g(con\014gurations.)31 b(The)20 b(latter)f(allo)o(w)g(a)g(complete)e(determination)h(of)60 152 y(the)e(energy)g(of)g(a)h(giv)o(en)e(con\014guration.)133 212 y(Let)f(us)h(motiv)m(ate)e(the)h(general)g(de\014nitions)f(via)h (examples.)19 b(In)14 b(the)g(original)g(case)g(of)g(the)g(fer-)60 272 y(romagnetic)d(Ising)h(mo)q(del,)f(the)h(b)q(oundary)h(of)f(a)g (con\014guration)i(can,)e(for)g(instance,)g(b)q(e)h(de\014ned)e(as)60 332 y(all)h(the)g(pairs)g(of)g(nearest-neigh)o(b)q(or)h(sites)f(with)g(opp)q (osite)h(spins.)20 b(As)12 b(eac)o(h)g(suc)o(h)f(pair)i(con)o(tributes)60 392 y(equally)f(to)i(the)f(energy)f(of)i(the)f(con\014guration,)h(regardless) g(of)f(whic)o(h)g(spin)g(of)h(the)f(pair)g(is)g(up)g(and)60 452 y(whic)o(h)i(is)h(do)o(wn,)g(one)h(do)q(es)f(not)h(need)f(to)g(sp)q (ecify)f(the)h(actual)g(con\014guration)h(on)g(the)f(b)q(oundary)60 513 y(to)g(compute)f(the)h(energy)l(.)k(Therefore)c(con)o(tours)g(are)g (de\014ned)g(with)g(no)g(reference)e(to)j(con\014gura-)60 573 y(tions,)e(b)o(y)f(considering)g(the)h(p)q(olyhedral)f(surface)h(formed)e(b)o (y)h(plaquettes)g(p)q(erp)q(endicular)g(to)h(the)60 633 y(b)q(onds)21 b(joining)e(misaligned)f(spins,)h(and)h(taking)g(its)f(connected)g(comp)q (onen)o(ts)f([82)q(,)h(168)q(].)30 b(The)60 693 y(same)14 b(de\014nition)h (of)g(b)q(oundary)h(w)o(orks)f(for)h(the)e(Blume-Cap)q(el)g(mo)q(del)f (\(B.34\),)i(but)g(to)g(compute)60 753 y(the)22 b(energy)f(w)o(e)g(no)o(w)i (m)o(ust)d(sp)q(ecify)h(the)h(con\014guration)h(of)f(eac)o(h)f(pair)h(of)g (misaligned)e(spins,)60 814 y(as)g(di\013eren)o(t)e(com)o(binations)g(ha)o(v) o(e)h(di\013eren)o(t)f(energies.)30 b(The)19 b(de\014nition)g(of)g(con)o (tours)h(requires)60 874 y(hence)15 b(to)h(consider)g(p)q(olyhedra)g(lab)q (eled)f(b)o(y)g(the)h(con\014guration)h(on)f(the)g(imme)o(diately)c(adjacen)o (t)60 934 y(\(in)o(ternal)i(and)i(external\))f(shells)f(of)i(spins.)21 b(The)15 b(next)g(complication)f(app)q(ears)i(for)g(mo)q(dels)e(with)60 994 y(in)o(teractions)f(extending)h(b)q(ey)o(ond)g(nearest)g(neigh)o(b)q(ors) h(and/or)h(in)o(v)o(olving)c(more)h(than)i(t)o(w)o(o)f(spins)60 1054 y(at)k(a)h(time.)24 b(An)17 b(example)f(of)i(practical)f(in)o(terest)g (is)h(the)f(an)o(tiferromagnet)g(on)h(a)h(face-cen)o(tered)60 1115 y(cubic)12 b(lattice)h([329,)h(p.)f(145)h(and)g(references)e(therein].) 19 b(Suc)o(h)13 b(mo)q(dels)f(require)g(\\thic)o(k)o(er")h(b)q(ound-)60 1175 y(aries)j(and)h(con)o(tours)g(de\014ned)f(sp)q(ecifying)f(the)h (con\014gurations)i(of)e(larger)h(groups)g(of)g(spins.)133 1235 y(Therefore,)k(to)g(de\014ne)g(b)q(oundary)h(and)f(con)o(tours)h(in)e(a) h(general)g(fashion,)h(w)o(e)e(m)o(ust)g(c)o(hec)o(k)60 1295 y(whether)f(sets)g(of)h(spins)f(are)g(aligned)g(or)g(misaligned,)f(but)h (this)g(c)o(hec)o(king)f(has)h(to)h(b)q(e)f(done)h(on)60 1355 y(su\016cien)o(tly)15 b(large)h(collections)g(of)g(spins)h(at)g(a)g(time.)j (F)l(ollo)o(wing)d(closely)e([328)q(,)h(Chapter)h(I)q(I],)e(w)o(e)60 1416 y(consider)g(a)g(set)g FE(K)g FQ(=)e FE(f)p FF(!)p 492 1423 33 2 v 524 1397 a FH(\(1\))572 1416 y FF(;)8 b(:)g(:)g(:)f(;)h(!)p 681 1423 V 713 1397 a FH(\()p FD(r)q FH(\))759 1416 y FE(g)15 b FQ(of)h FP(p)n(erio)n(dic)e FQ(con\014gurations)i(\()p FF(r)f FE(\025)f FQ(1\).)21 b(F)l(or)15 b(the)g(standard)60 1476 y(statemen)o(t)e (of)i(the)g(P)o(eierls)e(condition)i FE(K)g FQ(will)f(b)q(e)h(the)f(set)h(of) g(p)q(erio)q(dic)f(\(deterministic\))e(ground-)60 1536 y(state)18 b(con\014gurations)g(of)g(some)e(in)o(teraction,)g(but)i(the)f(de\014nition)g (can)g(b)q(e)h(done)f(\(and)h FP(must)g FQ(b)q(e)60 1596 y(done,)h(as)h(w)o (e)f(shall)f(discuss)h(in)g(next)f(section\),)h(for)g(general)g(sets)g(of)g (p)q(erio)q(dic)g(con\014gurations.)60 1656 y(Let)d(us)h(call)e FE(K)i FQ(the)f(set)g(of)g FP(r)n(efer)n(enc)n(e)h(c)n(on\014gur)n(ations)g FQ([369)q(].)k(W)l(e)15 b(also)i(consider)f(for)g(some)f(\014xed)60 1716 y FF(a)e FE(\025)h FQ(0)j(the)f(cub)q(es)g FF(W)457 1723 y FD(a)478 1716 y FQ(\()p FF(x)p FQ(\))d(=)h FE(f)p FF(y)i FE(2)e Fq(Z)751 1696 y FD(d)771 1716 y FQ(:)8 b FF(;)g FE(j)p FF(y)853 1723 y FD(i)878 1716 y FE(\000)j FF(x)956 1723 y FD(i)969 1716 y FE(j)j(\024)g FF(a)h FQ(for)i(1)d FE(\024)g FF(i)f FE(\024)h FF(d)p FE(g)i FQ(|)g(the)g FP(sampling)j(cub)n(es)t FQ(.)60 1810 y FM(De\014nition)f(B.18)23 b FP(The)18 b(b)n(oundary)g(of)f(a)h(c)n (on\014gur)n(ation)g FF(!)i FP(|)e(with)g(r)n(esp)n(e)n(ct)f(to)h(the)g(set)h (of)e(r)n(ef-)60 1871 y(er)n(enc)n(e)h(c)n(on\014gur)n(ations)g FE(K)g FP(and)g(sampling)g(cub)n(es)g FF(W)1051 1878 y FD(a)1072 1871 y FQ(\()p FF(x)p FQ(\))f FP(|)g(is)h(the)g(set)g(of)f(sites)464 1978 y FF(@)s(!)30 b FQ(=)636 1936 y Fx([)618 2032 y FD(x)p Fy(2)p Fl(Z)683 2023 y Fs(d)701 1929 y Fx(n)729 1978 y FF(W)775 1985 y FD(a)795 1978 y FQ(\()p FF(x)p FQ(\):)22 b FF(!)r FE(j)943 1985 y FD(W)976 1989 y Fs(a)995 1985 y FH(\()p FD(x)p FH(\))1058 1978 y FE(6)p FQ(=)14 b FF(!)p 1110 1985 V 2 w FE(j)1156 1985 y FD(W)1189 1989 y Fs(a)1208 1985 y FH(\()p FD(x)p FH(\))1271 1978 y FE(8)p FF(!)p 1300 1985 V 15 w FE(2)g(K)1431 1929 y Fx(o)1472 1978 y FF(:)269 b FQ(\(B)p FF(:)p FQ(36\))60 2118 y(T)o(ypically)13 b(w)o(e)i(will)f(consider)h(con\014gurations)i FF(!)g FQ(equal)e(to)h(some)e FF(!)p 1294 2125 V 16 w FE(2)g(K)i FQ(except)e(for)i(a)f(\014nite)g(set)60 2178 y(of)i(spins.)k(In)16 b(this)g(situation)h(the)f(b)q(oundary)h(is)f(a)h(\014nite)e(set.)133 2238 y(Let)h(us)f(no)o(w)h(state)f(the)g(simplest)f(and)i(most)e(p)q(opular)i (v)o(ersion)f(of)h(P)o(eierls)d(condition;)i(in)g(the)60 2298 y(follo)o(wing)i(section)g(w)o(e)g(discuss)h(a)g(more)e(general)h (de\014nition.)25 b(W)l(e)17 b(consider)h(an)g(in)o(teraction)e(\010)1870 2305 y FH(0)60 2359 y FQ(and,)g(for)h(eac)o(h)f(\014xed)g FF(!)p 471 2366 V 16 w FE(2)e(K)i FQ(construct)h(the)f(relativ)o(e)e(Hamiltonian)515 2459 y FF(H)559 2439 y FH(\010)584 2444 y Fr(0)605 2459 y FQ(\()p FF(!)r FE(j)p FF(!)p 670 2466 V 2 w FQ(\))g(=)871 2418 y Fx(X)786 2514 y FD(A)p FH(:)6 b FD(A)p Fy(\032)p Fl(Z)903 2504 y Fs(d)938 2514 y FH(\014nite)1016 2459 y FQ([\010)1065 2466 y FH(0)p FD(A)1111 2459 y FQ(\()p FF(!)r FQ(\))11 b FE(\000)g FQ(\010)1277 2466 y FH(0)p FD(A)1324 2459 y FQ(\()p FF(!)p 1343 2466 V 2 w FQ(\)])i FF(;)320 b FQ(\(B)p FF(:)p FQ(37\))60 2600 y(de\014ned)13 b(only)g(for)g(con\014gurations)i FF(!)g FQ(coinciding)d(with)h FF(!)p 1092 2607 V 16 w FQ(except)f(on)h(a)h(\014nite)e(set.)20 b(Let)14 b(us)f(denote)60 2660 y FE(G)93 2636 y FH(p)q(er)90 2672 y FD(T)5 b FH(=0)162 2660 y FQ(\(\010)216 2667 y FH(0)236 2660 y FQ(\))16 b(the)g(set)h(of)f(p)q(erio)q(dic)g(ground-state)i (con\014gurations)f(of)g(\010)1364 2667 y FH(0)1384 2660 y FQ(.)938 2784 y(220)p eop %%Page: 221 221 bop 60 91 a FM(De\014nition)18 b(B.19)23 b FP(The)18 b(inter)n(action)h FQ(\010)840 98 y FH(0)877 91 y FP(satis\014es)g(the)f(\(original\))g(Peierls) g(c)n(ondition)g(if)g(ther)n(e)60 152 y(exists)g(a)g(c)n(onstant)g FF(\032)455 159 y FH(0)489 152 y FF(>)13 b FQ(0)18 b FP(such)g(that)g(for)e (e)n(ach)i FF(!)p 980 159 33 2 v 16 w FE(2)c(G)1106 128 y FH(p)q(er)1103 164 y FD(T)5 b FH(=0)1175 152 y FQ(\(\010)1229 159 y FH(0)1249 152 y FQ(\))759 261 y FF(H)803 240 y FH(\010)828 245 y Fr(0)848 261 y FQ(\()p FF(!)r FE(j)p FF(!)p 913 268 V 2 w FQ(\))28 b FE(\025)f FF(\032)1083 268 y FH(0)1103 261 y FE(j)p FF(@)s(!)r FE(j)563 b FQ(\(B)p FF(:)p FQ(38\))60 370 y FP(for)15 b(every)h(c)n (on\014gur)n(ation)f FF(!)j FP(c)n(oinciding)e(with)g FF(!)p 933 377 V 18 w FP(exc)n(ept)g(p)n(ossibly)f(on)h(a)f(\014nite)i(set)f(of)f (sites.)22 b(Her)n(e)60 431 y FF(@)s(!)e FP(is)f(the)g(b)n(oundary)g(of)f FF(!)j FP(with)f(r)n(esp)n(e)n(ct)e(to)h FE(K)e FQ(=)f FE(G)1066 407 y FH(p)q(er)1063 443 y FD(T)5 b FH(=0)1135 431 y FQ(\(\010)1189 438 y FH(0)1209 431 y FQ(\))19 b FP(and)g(sampling)h(cub)n(es)f(de\014ne)n(d) h(by)60 491 y(some)e(\014xe)n(d)g(choic)n(e)g(of)f FF(a)c FE(\025)h FQ(0)p FP(.)60 592 y FQ(W)l(e)j(shall)h(call)f(a)h(constan)o(t)g FF(\032)617 599 y FH(0)655 592 y FQ(satisfying)f(\(B.38\))h(a)g FP(Peierls)h(c)n(onstant)g FQ(for)f(the)f(in)o(teraction)g(\010)1870 599 y FH(0)60 652 y FQ(\(and)12 b(the)g(c)o(hosen)g FE(K)g FQ(and)h FF(a)p FQ(\).)19 b(The)12 b(P)o(eierls)e(condition)i(immedi)o(ately) c(implies)i(that)i(eac)o(h)f(p)q(erio)q(dic)60 712 y(ground-state)16 b(con\014guration)f(is)f(rigid,)g(and)g(hence)g(de\014nes)g(a)g FP(deterministic)19 b FQ(zero-temp)q(erature)60 773 y(pure)f(phase)i (\(Section)e(B.2.3\).)27 b(The)19 b(con)o(v)o(erse)e(is)i(not)g(true)f([290)q (,)g(264)q(].)28 b(W)l(e)18 b(also)i(notice)e(that)60 833 y(an)j(upp)q(er)g (b)q(ound)h(of)g(the)e(form)g FF(H)744 815 y FH(\010)769 820 y Fr(0)789 833 y FQ(\()p FF(!)r FE(j)p FF(!)p 854 840 V 2 w FQ(\))43 b FE(\024)1035 829 y Fx(e)1030 833 y FF(\032)1055 840 y FH(0)1075 833 y FE(j)p FF(@)s(!)r FE(j)20 b FQ(is)h(alw)o(a)o(ys)g (true,)g(hence)f(the)h(P)o(eierls)60 893 y(condition)h(is)g(basically)f(a)i (requiremen)o(t)c(for)j(the)g(energy)g(cost)g(to)h(gro)o(w)g(as)f(fast)h(as)g (p)q(ossible)60 953 y(with)15 b(the)g(size)g(of)g(the)g(b)q(oundary)i(of)e (the)g(con\014guration.)22 b(There)15 b(are)h(imp)q(ortan)o(t)e(mo)q(dels)g (where)60 1013 y(this)k(is)g(not)h(true,)f(i.e.)f(in)g(whic)o(h)h(the)g (energy)g(cost)g(gro)o(ws)i(more)d(slo)o(wly)g(than)i(the)f(area)h(of)f(the) 60 1074 y(b)q(oundary:)24 b(for)17 b(example,)e(the)h(balanced)h(mo)q(del)f ([132)q(,)g(48)q(])h(and)g(the)g(ANNNI)e(mo)q(del)g([48)q(,)h(and)60 1134 y(references)f(therein]\).)133 1194 y(W)l(e)c(notice)g(that)h(the)f FP(validity)h FQ(of)g(the)f(P)o(eierls)f(condition)h(do)q(es)h(not)g(dep)q (end)f(on)h(the)f(particular)60 1254 y(c)o(hoice)20 b(of)j(the)e(parameter)g FF(a)h FE(\025)h FQ(0)g(adopted)f(for)g(the)g(de\014nition)f(of)h(the)f(b)q (oundary)l(,)j(but)e(the)60 1314 y(actual)17 b(v)m(alue)f(of)g(the)h(P)o (eierls)e(constan)o(t)h(do)q(es.)23 b(Indeed,)15 b(follo)o(wing)h([328)q(])g (w)o(e)g(notice)g(that)h(if)f FF(@)1847 1296 y Fy(0)1858 1314 y FF(!)60 1374 y FQ(indicates)e(the)h(b)q(oundary)i(de\014ned)e(via)g (sampling)f(cub)q(es)h FF(W)1194 1381 y FD(a)1213 1373 y Ft(0)1241 1374 y FQ(with)g FF(a)1377 1356 y Fy(0)1402 1374 y FE(\025)f FF(a)h FQ(\(other)g(cases)g(left)g(to)60 1435 y(the)h(reader\),)g(then)709 1495 y FF(@)s(!)g FE(\032)d FF(@)865 1474 y Fy(0)876 1495 y FF(!)j FE(\032)e([)1008 1502 y FD(x)p Fy(2)p FD(@)r(!)1097 1495 y FF(W)1143 1502 y FD(a)1162 1493 y Ft(0)1175 1495 y FQ(\()p FF(x)p FQ(\))514 b(\(B)p FF(:)p FQ(39\))60 1582 y(th)o(us,)627 1642 y FE(j)p FF(@)s(!)r FE(j)27 b(\024)g(j)p FF(@)852 1621 y Fy(0)863 1642 y FF(!)r FE(j)h(\024)f FQ(\(2)p FF(a)1072 1621 y Fy(0)1095 1642 y FQ(+)11 b(1\))1187 1621 y FD(d)1208 1642 y FE(j)p FF(@)s(!)r FE(j)i FF(:)431 b FQ(\(B)p FF(:)p FQ(40\))60 1729 y(Therefore,)15 b(di\013eren)o(t)h(c)o(hoices)f(of)i FF(a)e FQ(c)o(hange)i(the)f(actual)g(v)m(alue)g(of)h FF(\032)1347 1736 y FH(0)1366 1729 y FQ(:)641 1829 y FF(\032)666 1836 y FH(0)p 561 1851 205 2 v 561 1897 a FQ(\(2)p FF(a)630 1883 y Fy(0)653 1897 y FQ(+)11 b(1\))745 1883 y FD(d)798 1863 y FE(\024)27 b FF(\032)889 1843 y Fy(0)889 1875 y FH(0)923 1863 y FQ(=)14 b FF(\032)1000 1870 y FH(0)1028 1863 y FQ(sup)1053 1898 y FD(!)1120 1829 y FE(j)p FF(@)s(!)r FE(j)p 1115 1851 100 2 v 1115 1897 a(j)p FF(@)1158 1883 y Fy(0)1169 1897 y FF(!)r FE(j)1247 1863 y(\024)28 b FF(\032)1339 1870 y FH(0)1372 1863 y FF(;)369 b FQ(\(B)p FF(:)p FQ(41\))60 1998 y(but)16 b(not)g(its)g(nonzero)g(c)o (haracter.)21 b(One)15 b(has)i(the)e(freedom)g(of)h(adjusting)g FF(a)g FQ(according)g(to)g(future)60 2058 y(con)o(v)o(enience.)26 b(Ho)o(w)o(ev)o(er,)17 b(the)i(actual)f(v)m(alue)h(of)g FF(\032)1013 2065 y FH(0)1051 2058 y FQ(is)g(related)f(to)h(the)f(range)h(of)g(temp)q (eratures)60 2118 y(where)13 b(PS)h(theory)f(is)h(v)m(alid)f(\(this)g(range)h (is)f(prop)q(ortional)i(to)f FF(\032)1231 2125 y FH(0)1251 2118 y FQ(\).)20 b(Hence,)12 b(for)i(the)f(sak)o(e)h(of)f(quan-)60 2178 y(titativ)o(e)i(predictions)h(one)h(should)g(emplo)o(y)d(a)j(v)m(alue)g (of)g FF(\032)1143 2185 y FH(0)1179 2178 y FQ(as)h(large)e(as)i(p)q(ossible,) e(whic)o(h)g(means)60 2238 y FF(a)e FQ(as)g(small)f(as)i(p)q(ossible.)20 b(An)14 b(extremely)d(fa)o(v)o(orable)i(case)h(is)g(exempli\014ed)d(b)o(y)j (the)g(ferromagnetic)60 2299 y(Ising)i(mo)q(del,)f(and)i(its)f (generalizations)g(to)g(higher)h(spins,)f(for)g(whic)o(h)g(the)g(b)q(oundary) h(of)g(con\014g-)60 2359 y(urations)f(can)f(b)q(e)g(de\014ned)g(via)g(p)q (olyhedra)h(of)f(\\zero)g(width")h([and)f(w)o(e)g(ma)o(y)e(ev)o(en)h(ha)o(v)o (e)h(equalit)o(y)60 2419 y(in)20 b(\(B.38\)].)33 b(Strictly)19 b(sp)q(eaking,)i(the)f(corresp)q(onding)i(\\zero-width")f(\(or)g FP(thin)t FQ(\))f(con)o(tours)h(are)60 2479 y(not)d(included)e(in)g(the)h (formalism)e(to)i(b)q(e)g(in)o(tro)q(duced)g(b)q(elo)o(w,)g(but)g(w)o(e)g (shall)g(k)o(eep)f(them)g(within)60 2539 y(our)h(discussion)f(through)h (appropriate)g(commen)o(ts.)133 2600 y(The)24 b(actual)f(v)o(eri\014cation)f (of)i(the)f(P)o(eierls)f(condition)h(is)g(a)h(mo)q(del-dep)q(enden)o(t,)f (generally)60 2660 y(non)o(trivial,)h(pro)q(cedure.)43 b(The)24 b(starting)g(p)q(oin)o(t)f(is,)i(in)e(principle,)h(the)f(determination)f(of)i (all)938 2784 y(221)p eop %%Page: 222 222 bop 60 91 a FQ(p)q(erio)q(dic)12 b(ground-state)h(con\014gurations)h(|)e(an)g (often)g(tedious)h(pro)q(cess.)20 b(A)12 b(sligh)o(t)f(simpli\014cation)60 152 y(follo)o(ws)17 b(from)f(the)g(observ)m(ation)i(that)f FP(if)h(we)h(\014nd)g(that)f(\(B.38\))g(is)f(satis\014e)n(d)i(for)e(some)h (\014nite)h(set)60 212 y FE(K)d FP(of)f(p)n(erio)n(dic)g(c)n(on\014gur)n (ations,)h(automatic)n(al)r(ly)g(these)g(must)g(b)n(e)g(al)r(l)g(the)g(p)n (erio)n(dic)f(gr)n(ound)g(states)p FQ(.)60 272 y(Indeed,)g(\(B.38\))i (implies)c(that)k(suc)o(h)g(con\014gurations)h FF(!)p 1081 279 33 2 v 18 w FQ(are)f(ground)g(states,)g(and)g(if)f(there)g(w)o(ere)60 332 y(others)25 b(\(B.38\))e(w)o(ould)i(not)f(b)q(e)h(satis\014ed)f(b)q (ecause)g(arbitrarily)g(large)g(b)q(oundaries)h(could)f(b)q(e)60 392 y(constructed)17 b(without)h(extra)e(energy)h(cost,)g(simply)e(b)o(y)i (in)o(terp)q(osing)g(regions)h(o)q(ccupied)f(b)o(y)f(the)60 452 y(ground)j(states)g(not)g(accoun)o(ted)f(for.)28 b(In)19 b(practice,)e(this)h(observ)m(ation)i(is)e(of)h(little)d(help,)i(as)h(the)60 513 y(determination)10 b(of)i(ground)g(states)g(is)g(made)e(using)i(some)f (sort)h(of)g(con)o(tour)g(ideas,)g(so)g(c)o(hec)o(king)e(the)60 573 y(P)o(eierls)15 b(condition)i(and)g(\014nding)g(the)f(ground-state)j (con\014gurations)f(are)f(almost)e(sim)o(ultaneous)60 633 y(pro)q(cesses)g (\(ho)o(w)o(ev)o(er,)e(see)h([215)q(]\).)20 b(The)14 b(only)g(real)g (shortcut)h(a)o(v)m(ailable)e(is)i(a)f(su\016cien)o(t)f(condition)60 693 y(due)k(to)h(Holszt)o(ynski)d(and)j(Sla)o(wn)o(y)f([195])g(whic)o(h)g(w)o (e)f(will)g(use)i(for)f(almost)f(all)h(the)g(applications)60 753 y(in)f(this)g(pap)q(er.)60 850 y FM(De\014nition)i(B.20)23 b FP(A)h(p)n(otential)h FQ(\010)f FP(is)g(an)g FF(m)p FQ(-p)q(oten)o(tial)f FP(if)h(ther)n(e)g(exists)h(a)e(c)n(on\014gur)n(ation)i FF(!)60 910 y FP(simultane)n(ously)18 b(minimizing)g(e)n(ach)g FE(j)p FF(A)p FE(j)p FP(-b)n(o)n(dy)e(function:)607 1014 y FQ(\010)642 1021 y FD(A)670 1014 y FQ(\()p FF(!)r FQ(\))28 b(=)g(min)838 1051 y Fx(e)-23 b FD(!)r Fy(2)p FH(\012)923 1014 y FQ(\010)958 1021 y FD(A)987 1014 y FQ(\()1011 1010 y Fx(e)1006 1014 y FF(!)r FQ(\))100 b FE(8)p FF(A)12 b FE(2)i(S)k FF(:)411 b FQ(\(B)p FF(:)p FQ(42\))60 1143 y(F)l(or)16 b(suc)o(h)f(an)h(in)o(teraction)e(let)h (us)h(denote)f(b)o(y)g FE(G)952 1150 y FD(T)5 b FH(=0)1025 1143 y FQ(\(\010\))15 b(the)h(\(nonempt)o(y\))d(set)j(of)g(con\014gurations) 60 1203 y(minim)o(izi)o(ng)e(all)i(\010)415 1210 y FD(A)443 1203 y FQ(.)22 b(The)16 b(su\016cien)o(t)f(condition)h(is:)60 1299 y FM(Theorem)h(B.21)h(\(Holszt)n(ynski-Sla)n(wn)n(y\))23 b FP(A)e(\014nite-r)n(ange)h FF(m)p FP(-p)n(otential)g FQ(\010)f FP(with)g FE(G)1745 1306 y FD(T)5 b FH(=0)1817 1299 y FQ(\(\010\))60 1359 y FP(\014nite)19 b(satis\014es)f(the)g(Peierls)g(c)n(ondition.)133 1456 y FQ(Resorting)h(to)f(an)h(alternativ)o(e)e(|)h(and)h(suggestiv)o(e)f(|) g(terminology)l(,)f(w)o(e)h(can)g(sa)o(y)h(that)g(an)60 1516 y FF(m)p FQ(-p)q(oten)o(tial)h(is)f(one)i(for)f(whic)o(h)f(there)h(are)g (ground)h(states)g(\\satisfying")f(all)g(b)q(onds.)34 b(An)20 b(im-)60 1576 y(mediate)g(example)f(is)i(an)o(y)h(Ising)g(mo)q(del)e(with)h (ferromagnetic)f(in)o(teractions)h(\(\010)1625 1583 y FD(A)1677 1576 y FQ(=)i FE(\000)p FF(J)1804 1583 y FD(A)1832 1576 y FF(\033)1862 1558 y FD(A)60 1637 y FQ(with)17 b FF(J)199 1644 y FD(A)242 1637 y FE(\025)d FQ(0)j(for)g(all)f FF(A)p FQ(\):)22 b(clearly)15 b(the)i(all-\\+")g(con\014guration)h(sim)o(ultaneously)c(minimi)o(zes)g(all) 60 1697 y(\010)95 1704 y FD(A)124 1697 y FQ(.)21 b(The)15 b(opp)q(osite)i (case)f(is)f(that)h(of)g(the)g(p)q(oten)o(tials)f(with)h(\\frustration",)h (i.e.)d(for)i(whic)o(h)f(ev)o(ery)60 1757 y(con\014guration)23 b(has)f(b)q(onds)h(that)f(giv)o(e)f(an)h(energy)g(con)o(tribution)f(larger)g (than)i(the)e(minim)n(um)60 1817 y(p)q(ossible)g(\(\\frustrated)g(b)q (onds"\).)36 b(Ho)o(w)o(ev)o(er,)19 b(these)h(notions)h(of)g FF(m)p FQ(-p)q(oten)o(tials)g(and)g(\\frustra-)60 1877 y(tion")d(m)o(ust)f(b) q(e)h(tak)o(en)g(mo)q(dulo)g(ph)o(ysical)f(equiv)m(alence,)f(b)q(ecause)i (equiv)m(alen)o(t)f(p)q(oten)o(tials)h(ha)o(v)o(e)60 1938 y(the)e(same)g (statistical-mec)o(hanical)d(prop)q(erties.)22 b(This)17 b(adds)g(an)g(extra) f(t)o(wist)g(to)h(the)f(matter.)k(A)60 1998 y(p)q(opular)c(example)d(is)i (the)g(an)o(tiferromagnetic)e(Ising)i(mo)q(del)f(in)h(a)g(triangular)h (lattice.)j(It)c(is)g(easy)60 2058 y(to)k(see)f(that)h(when)g(the)f(mo)q(del) g(is)g(giv)o(en)g(its)g(usual)h(form)o(ulation)f(in)g(terms)f(of)i(t)o(w)o (o-spin)g(in)o(ter-)60 2118 y(actions,)e(no)g(con\014guration)h(can)f (\\satisfy")h(sim)o(ultaneously)d(the)i(three)f(b)q(onds)i(of)f(a)h (triangular)60 2178 y(plaquette.)i(But)15 b(this)h(seemingly)d(frustrated)j (p)q(oten)o(tial)f(can)h(equiv)m(alen)o(tly)d(b)q(e)j(written)f(b)o(y)g(con-) 60 2238 y(sidering)d(the)h(triangular)g(plaquettes)f(themselv)o(es)e(as)j (the)f(b)q(onds,)j(with)d(an)h(energy)g(con)o(tribution)60 2299 y(obtained)i(b)o(y)g(a)h(suitable)f(com)o(bination)e(of)j(the)f(con)o (tributions)g(of)g(the)g(original)g(t)o(w)o(o-spin)h(b)q(onds)60 2359 y(around)i(the)f(plaquette.)22 b(In)17 b(this)f(form)o(ulation)g(the)h (mo)q(del)e(is)i(no)o(w)g(an)h FF(m)p FQ(-p)q(oten)o(tial)e(\(although)60 2419 y(one)g(cannot)h(use)f(Theorem)f(B.21)h(b)q(ecause)g(there)g(are)g (in\014nitely)e(man)o(y)h(p)q(erio)q(dic)g(ground-state)60 2479 y(con\014gurations\).)22 b(In)15 b(this)g(regard,)g(probably)h(the)f (most)f(di\016cult)g(asp)q(ect)h(of)h(the)f(application)g(of)60 2539 y(this)f(v)o(ery)f(con)o(v)o(enien)o(t)g(theorem)g(is)h(the)g(v)o (eri\014cation)f(of)i(whether)f(the)g(p)q(oten)o(tial)g(of)h(in)o(terest)e (can)60 2600 y(b)q(e)k(rewritten)e(as)j(\(i.e.)c(is)j(ph)o(ysically)e(equiv)m (alen)o(t)g(to\))h(an)i FF(m)p FQ(-p)q(oten)o(tial.)j(It)16 b(w)o(ould)h(b)q(e)g(v)o(ery)e(nice)60 2660 y(to)f(complem)o(en)o(t)c (Theorem)i(B.21)h(with)g(some)f(simple)f(su\016cien)o(t)g(criterion)h(for)i (an)g(in)o(teraction)e(to)938 2784 y(222)p eop %%Page: 223 223 bop 60 91 a FQ(b)q(e)17 b(ph)o(ysically)e(equiv)m(alen)o(t)h(to)h(an)h FF(m)p FQ(-p)q(oten)o(tial,)e(but)h(this)g(ma)o(y)f(not)h(b)q(e)g(an)h(easy)f (task.)24 b(F)l(or)17 b(in-)60 152 y(stance,)g(the)f(natural)i(conjecture)e (that)h(ev)o(ery)f(\014nite-range)h(translation-in)o(v)m(arian)o(t)g(in)o (teraction)60 212 y(is)f(equiv)m(alen)o(t)f(to)h(a)h(\(translation-in)o(v)m (arian)o(t)f(\014nite-range\))h FF(m)p FQ(-p)q(oten)o(tial)f(is)g(false)g ([263].)133 272 y(A)o(t)g(an)o(y)g(rate,)g(once)g(the)g FF(m)p FQ(-p)q(oten)o(tial)g(c)o(haracter)g(has)h(b)q(een)g(v)o(eri\014ed,)d (Theorem)h(B.21)h(is)h(an)60 332 y(extremely)f(con)o(v)o(enien)o(t)h(to)q (ol.)30 b(It)18 b(has,)i(ho)o(w)o(ev)o(er,)e(an)h(imp)q(ortan)o(t)f(dra)o (wbac)o(k:)27 b(its)19 b(pro)q(of)h(is)f(not)60 392 y(constructiv)o(e,)h(so)i (it)e(do)q(es)h(not)h(pro)o(vide)e(an)o(y)g(explicit)f(expression)h(for)h (the)g(P)o(eierls)e(constan)o(t.)60 452 y(Therefore,)i(argumen)o(ts)g(based)g (on)h(this)f(theorem)f(do)h(not)h(allo)o(w)f(an)o(y)g(determination)e(of)i (the)60 513 y(range)c(of)f(temp)q(eratures)f(where)h(the)g(PS)h(theory)f (remains)f(v)m(alid.)60 641 y FM(B.4.2)55 b(Con)n(tours.)26 b(The)18 b(Generalized)f(P)n(eierls)g(Condition)60 734 y FQ(In)11 b(the)h(presence)f(of)h(the)f(P)o(eierls)f(condition)i(for)g(an)g(in)o (teraction)e(\010)1287 741 y FH(0)1307 734 y FQ(,)i(the)g(usual)g(P)o(eierls) e(argumen)o(t)60 794 y(can)19 b(b)q(e)h(rep)q(eated)f(for)h(those)g (zero-temp)q(erature)d(pure)i(phases)i(of)e(\010)1382 801 y FH(0)1421 794 y FQ(for)h(whic)o(h)f(the)g(en)o(trop)o(y)60 854 y(factor)k(can)g(b)q(e)g(sho)o(wn)g(to)g(gro)o(w)g(at)g(most)f(exp)q (onen)o(tially)f(with)i(the)f(size)g(of)h(the)f(b)q(oundary)l(.)60 914 y(Indeed,)d(the)h(P)o(eierls)e(condition)h(ensures)h(that)g(the)f(energy) g(cost)h(gro)o(ws)h(as)f(least)f(as)i(fast)f(but)60 974 y(with)e(an)i(exp)q (onen)o(t)e(including)g(a)h(factor)g FF(\014)s FQ(,)f(hence)g(the)g(energy)g (cost)h(b)q(eats)g(the)g(en)o(trop)o(y)f(gain)60 1035 y(for)c(large)f(enough) i FF(\014)s FQ(,)e(and)h(only)f(small)f(b)q(oundaries)j(are)e(presen)o(t.)20 b(Ho)o(w)o(ev)o(er,)12 b(this)h(energy-b)q(eats-)60 1095 y(en)o(trop)o(y)j (phenomenon)g(is)h(in)g(general)f FP(not)i FQ(true)e(for)h(all)g(the)f(pure)h (phases,)h(only)e(for)h(the)g(stable)60 1155 y(ones.)34 b(It)20 b(turns)g(out)h(that)g(to)g(obtain)f(a)h(situation)g(in)f(whic)o(h)f(the)h (en)o(trop)o(y)g(is)g(b)q(eaten)g(b)o(y)g(the)60 1215 y(energy)d(for)g FP(al)r(l)24 b FQ(the)17 b(rigid)f(p)q(erio)q(dic)h(ground-state)i (con\014gurations)f(of)g(\010)1447 1222 y FH(0)1484 1215 y FQ(|)f(and)h(hence)e(all)h(of)60 1275 y(them)e(co)q(exist)i(|)g(one)g(m)o (ust)e(consider)i(a)g(p)q(erturb)q(ed)h(in)o(teraction)d(\010)h(=)f(\010)1471 1282 y FH(0)1502 1275 y FQ(+)1558 1259 y Fx(e)1552 1275 y FQ(\010)i(for)g(a)g (suitably)60 1336 y(adjusted)262 1319 y Fx(e)256 1336 y FQ(\010)f(\(shift)f (in)g(the)h(p)q(oin)o(t)f(of)h(maximal)c(co)q(existence\).)20 b(In)15 b(general,)g(not)h(all)f(the)h(ground-)60 1396 y(state)21 b(con\014gurations)g(for)g(\010)616 1403 y FH(0)656 1396 y FQ(are)f(ground-state)i(con\014gurations)g(for)f(\010,)g(hence)e(this)h(pro)q (cess)60 1456 y(of)e(\\tuning")g(\010)g(requires)e(us)i(to)g(consider)f(a)h (set)g FE(K)g FQ(not)g(reduced)f(just)g(to)h(con\014gurations)h(with)60 1516 y(minim)o(al)14 b(\010-energy)l(.)133 1576 y(Another)21 b(reason)g(to)g(generalize)f(the)g(P)o(eierls)g(condition)g(app)q(ears)i (when)f(studying)g(whole)60 1637 y(regions)d(of)h(the)f(phase)g(diagram.)27 b(In)17 b(suc)o(h)h(a)h(situation)f(one)h(is)e(in)o(terested)g(in)h (estimates)e(v)m(alid)60 1697 y FP(uniformly)24 b FQ(throughout)d(the)e (region;)i(but)f(a)g(uniform)e(P)o(eierls)g(condition,)i(as)g(stated)g(in)g (De\014-)60 1757 y(nition)f(B.19,)g(is)g(not)g(in)g(general)g(p)q(ossible.)29 b(F)l(or)19 b(example,)e(consider)i(the)g(Ising)g(mo)q(del)f(in)g(the)60 1817 y(presence)g(of)i(a)f(strictly)f(p)q(ositiv)o(e)g(magnetic)g(\014eld.)29 b(The)19 b(only)g(ground-state)i(con\014guration)f(is)60 1877 y(the)c(all-\\+")h(|)g(to)g(b)q(e)f(denoted)h FF(!)724 1859 y FH(\(+\))797 1877 y FQ(|)g(and)g(hence)f FE(j)p FF(@)s(!)r FE(j)g FQ(is)g(prop)q(ortional)i(to)f(the)f(n)o(um)o(b)q(er)f(of)60 1938 y(\\)p FE(\000)p FQ(")k(presen)o(t.)26 b(F)l(or)19 b(instance,)e(for)i (the)f(con\014gurations)h FF(!)1166 1919 y FD(W)1225 1938 y FQ(equal)f(to)g(+1)h(ev)o(erywhere)d(except)60 1998 y(inside)22 b(a)g(cub)q(e)h FF(W)7 b FQ(,)23 b(the)f(relativ)o(e)f(energy)h(is)g FF(H)t FQ(\()p FF(!)1045 1980 y FD(W)1086 1998 y FE(j)p FF(!)1132 1980 y FH(\(+\))1189 1998 y FQ(\))i(=)g(2)p FF(J)5 b FE(j)p FF(@)s(W)i FE(j)14 b FQ(+)i(2)p FF(h)8 b FQ(v)o(ol\()p FF(W)f FQ(\),)23 b(while)60 2058 y FE(j)p FF(@)s(!)135 2040 y FD(W)175 2058 y FE(j)13 b(\030)h FQ(v)o(ol)o(\()p FF(W)7 b FQ(\).)21 b(A)15 b(simple)f(calculation)h(sho)o(ws)h(that)g(for)g(the)f(P)o(eierls)f (condition)i(to)g(b)q(e)f(v)m(alid)60 2118 y(for)j(all)g(these)g FF(!)365 2100 y FD(W)423 2118 y FQ(w)o(e)g(need)f FF(\032)654 2131 y FE(\030)654 2110 y FF(<)709 2118 y(h)p FQ(.)27 b(Th)o(us)18 b(the)g(\(original\))g(P)o(eierls)f(condition)g(is)h(not)h(satis\014ed)60 2178 y(uniformly)12 b(in)i(a)h(neigh)o(b)q(orho)q(o)q(d)h(of)e(the)g(p)q(oin) o(t)h FF(h)e FQ(=)h(0,)h(whic)o(h)e(is)h(precisely)f(the)h(most)f(in)o (teresting)60 2238 y(region.)133 2299 y(A)19 b(generalized)f(P)o(eierls)f (condition)i(m)o(ust,)g(therefore,)f(allo)o(w)h(con\014gurations)i(that)e (are)h(not)60 2359 y(necessarily)13 b(ground)h(states)h(and)f(also)g(m)o(ust) f(satisfy)g(some)g(\\uniformit)o(y")f(requiremen)o(t.)17 b(Suc)o(h)d(a)60 2419 y(condition)e(is)h(already)f(con)o(tained)h(in)f(the)g(w)o(ork)h(b)o(y)f (Pirogo)o(v)h(and)h(Sinai,)e(where)g(the)h(main)e(results)60 2479 y(are)h(sho)o(wn)i(to)e(b)q(e)h(consequence)e(of)i(a)g(further)f (generalized)f(condition)h(for)h(the)f(p)q(erturb)q(ed)h(\010)g(that)60 2539 y(follo)o(ws)18 b(from)f(the)h(the)g(P)o(eierls)f(condition)h (satis\014ed)g(b)o(y)g(\010)1180 2546 y FH(0)1200 2539 y FQ(.)27 b(Zahradn)-5 b(\023)-19 b(\020k)18 b([366)q(])g(w)o(as,)h(ho)o(w)o(ev)o(er,) 60 2600 y(the)f(\014rst)h(to)g(p)q(oin)o(t)f(out)h(that)g(this)f(generalized) f(condition)h(is)g(a)h(more)e(natural)i(starting)g(p)q(oin)o(t)60 2660 y(from)e(the)h(conceptual)f(p)q(oin)o(t)h(of)g(view.)26 b(W)l(e)17 b(initially)f(had)j(a)f(more)f(concrete)g(motiv)m(ation:)23 b(the)938 2784 y(223)p eop %%Page: 224 224 bop 60 91 a FQ(uniformit)o(y)16 b(requiremen)o(t)f(is)j(imp)q(ortan)o(t)g (for)h(our)g(example)d(of)j(the)f(Kadano\013)i(transformation)60 152 y(\(Section)c(4.3.3\).)24 b(In)16 b(fact,)h(this)g(application)g(demands) f(only)g(a)i(particular)e(case)h(of)g(uniformit)o(y)60 212 y(\(Corollary)c(B.25)f(b)q(elo)o(w\),)g(and,)i(moreo)o(v)o(er,)c(the)i (result)g(w)o(e)g(need)g(is)g(exactly)f(giv)o(en)h(b)o(y)g(a)h(theorem)60 272 y(due)22 b(to)g(Zahradn)-5 b(\023)-19 b(\020k)22 b(\(Theorem)e(B.30)i(b)q (elo)o(w\).)37 b(Ho)o(w)o(ev)o(er,)21 b(w)o(e)h(shall)f(tak)o(e)g(here)h(the) f(time)f(to)60 332 y(discuss)g(the)f(uniformit)o(y)e(issue)i(in)g(some)f (generalit)o(y)l(,)h(b)q(ecause)g(w)o(e)g(feel)f(that)i(it)f(has)h(not)g(b)q (een)60 392 y(su\016cien)o(tly)14 b(emphasized)h(in)g(the)h(literature.)133 452 y(Let)h(us)g(\014rst)g(in)o(tro)q(duce)f(the)g(notion)h(of)g(con)o(tour.) 22 b(W)l(e)17 b(\014x)f(a)h(set)g FE(K)g FQ(of)g(reference)e(con\014gura-)60 513 y(tions)f(and)g(a)h(c)o(hoice)d(of)i(sampling)f(cub)q(es)h(\(v)m(alue)f (of)h FF(a)p FQ(\).)20 b(The)14 b(idea)f(is)h(to)g(decomp)q(ose)f(the)h(b)q (ound-)60 573 y(ary)19 b(in)f(comp)q(onen)o(ts:)26 b(t)o(w)o(o)19 b(sets)g FF(A)f FQ(and)i FF(B)h FQ(of)e(sites)g(are)f(called)g FP(c)n(onne)n(cte)n(d)i FQ(if)e(dist)9 b(\()p FF(A;)f(B)s FQ(\))17 b FE(\024)h FQ(1)60 633 y(in)g(lattice)g(units.)28 b(A)18 b FP(c)n(ontour)g FQ(of)h(a)g(con\014guration)h FF(!)g FQ(is)f(a)g(pair)f(\000) h(=)e(\()p FF(M)r(;)8 b(!)1522 640 y FD(M)1563 633 y FQ(\))18 b(where)g FF(M)24 b FQ(is)19 b(a)60 693 y(maximall)o(y)14 b(connected)i(comp) q(onen)o(t)g(of)h(the)g(b)q(oundary)h(of)f FF(!)r FQ(.)23 b(The)17 b(set)g FF(M)22 b FQ(is)17 b(often)f(called)g(the)60 753 y FP(supp)n(ort)f FQ(of)i(the)f(con)o(tour)h(\000.)22 b(A)o(t)16 b(this)g(p)q(oin)o(t)g(w)o(e)g(start)h(in)o(tro)q(ducing)g(constrain)o(ts)f (on)h(the)f(size)g(of)60 814 y(the)g(sampling)f(cub)q(es.)22 b(W)l(e)16 b(require:)60 908 y(\(C1\))25 b(The)c(v)m(alue)h(2)p FF(a)14 b FQ(+)h(1)21 b(m)o(ust)g(b)q(e)g(strictly)f(larger)i(than)g(all)e (the)i(p)q(erio)q(ds)g(of)f(the)h(reference)182 968 y(con\014gurations)c FF(!)p 497 975 33 2 v 16 w FE(2)c(K)q FQ(.)60 1062 y(Suc)o(h)g(a)h (requiremen)o(t)c(implies)h(the)i(follo)o(wing)g FP(extension)k(pr)n(op)n (erty)f FQ(\(nomenclature)12 b(tak)o(en)i(from)60 1123 y([329)q(]\):)33 b(if)22 b(a)h(con\014guration)h FF(!)h FQ(coincides)d(with)g(a)h(reference)e (con\014guration)j FF(!)p 1572 1130 V 27 w FE(2)h(K)e FQ(on)g(the)60 1183 y(sampling)18 b(cub)q(e)h FF(W)433 1190 y FD(a)454 1183 y FQ(\()p FF(x)p FQ(\))g(and)g(with)g FF(!)p 750 1190 V 782 1165 a Fy(0)813 1183 y FE(2)g(K)g FQ(on)h(the)f(cub)q(e)g FF(W)1244 1190 y FD(a)1265 1183 y FQ(\()p FF(y)r FQ(\))f(with)h(dist)8 b(\()p FF(x;)g(y)r FQ(\))18 b FE(\024)g FQ(1,)i(then)60 1243 y FF(!)p 60 1250 V 16 w FQ(=)14 b FF(!)p 158 1250 V 190 1225 a Fy(0)202 1243 y FQ(.)20 b(This)13 b(has)i(the)e(k)o(ey)f(consequence)g (that)i(w)o(e)f(can)h(reconstruct)f(uniquely)f(a)i(con\014guration)60 1303 y FF(!)k FQ(starting)f(from)e(its)h(family)e(of)j(con)o(tours.)133 1363 y(Eac)o(h)h(con)o(tour)g(with)g(a)g(\014nite)g(supp)q(ort)h(divides)e Fq(Z)1095 1342 y FD(d)1128 1363 y FE(n)12 b FF(M)23 b FQ(in)o(to)18 b(sev)o(eral)f(disconnected)g(com-)60 1424 y(p)q(onen)o(ts:)33 b(One)21 b(of)h(them)e(is)i(un)o(b)q(ounded,)h(and)g(is)e(called)g(the)g FP(exterior)h FQ(of)h(the)e(con)o(tour;)j(the)60 1484 y(others)e(are)f(b)q (ounded)i(and)f(are)g(collectiv)o(el)o(y)d(called)h(the)h FP(interior)h FQ(of)g(the)f(con)o(tour.)37 b(Eac)o(h)22 b(of)60 1544 y(these)f(comp)q(onen) o(ts)f(has)h(a)h(reference)d(con\014guration)j(asso)q(ciated)g(to)f(it,)g (namely)e(that)i(of)g(the)60 1604 y(sampling)15 b(cub)q(es)i(cen)o(tered)e (on)i(sites)f(adjacen)o(t)g(to)h(the)f(supp)q(ort)i(of)e(the)g(con)o(tour.)22 b(The)17 b(con)o(tour)60 1664 y(is)d(a)g FF(!)p 145 1671 V 2 w FQ(-)p FP(c)n(ontour)g FQ(if)f(its)h(exterior)f(corresp)q(onds)i(to)f (the)g(reference)e(con\014guration)j FF(!)p 1552 1671 V 2 w FQ(.)20 b(On)14 b(the)g(other)60 1724 y(hand,)19 b(the)e FF(!)p 283 1731 V 316 1706 a FH(\()p FD(i)p FH(\))357 1724 y FQ(-in)o(terior)g(|)h (denoted)g(In)o(t)862 1736 y FD(!)p 862 1743 24 2 v 885 1726 a Fr(\()p Fs(i)p Fr(\))925 1724 y FQ(\(\000\))g(|)g(is)g(the)f(union)i(of)f (the)g(comp)q(onen)o(ts)f(of)h(the)60 1791 y(in)o(terior)e(of)h(\000)g(asso)q (ciated)g(to)h(a)f(reference)e(con\014guration)j FF(!)p 1171 1798 33 2 v 1203 1773 a FH(\()p FD(i)p FH(\))1244 1791 y FQ(.)23 b(In)16 b(general,)g FF(!)p 1524 1798 V 19 w FQ(will)g(ha)o(v)o(e)g(other)60 1851 y(con)o(tours)c(b)q(esides)g(\000,)g(some)f(of)h(whic)o(h)f(ma)o(y)f(b)q (e)i(in)f(the)g(in)o(terior)g(of)h(\000.)20 b(Hence)10 b FF(!)p 1492 1858 V 14 w FQ(ma)o(y)g(not)i(coincide)60 1912 y(with)j FF(!)p 170 1919 V 202 1894 a FH(\()p FD(i)p FH(\))258 1912 y FQ(on)g(the)g(whole)f(In)o(t)606 1923 y FD(!)p 606 1930 24 2 v 629 1914 a Fr(\()p Fs(i)p Fr(\))683 1912 y FQ(The)h(generalized)e(P)o (eierls)g(condition)i(is)f(a)i(requiremen)n(t)c(on)j(the)60 1972 y(minim)n(um)e(energy)j(cost)h(of)g(in)o(tro)q(ducing)g(a)g(con)o(tour.) 23 b(This)16 b(can)h(b)q(e)g(estimated)e(b)o(y)h(considering)60 2032 y(the)f(con\014guration)h FF(!)469 2014 y FH(\000)508 2032 y FQ(that)g(has)g(\000)f(as)h(its)f FP(only)h FQ(con)o(tour.)21 b(If)14 b(\000)h(=)e(\()p FF(M)r(;)8 b(!)1433 2039 y FD(M)1474 2032 y FQ(\))15 b(is)g(a)g FF(!)p 1595 2039 33 2 v 2 w FQ(-con)o(tour,)h FF(!)1866 2014 y FH(\000)60 2092 y FQ(coincides)h(with)g FF(!)p 380 2099 V 20 w FQ(on)i(the)e(exterior)g(of)h(\000,)g(with)g FF(!)p 999 2099 V 1031 2074 a FH(\()p FD(i)p FH(\))1091 2092 y FQ(on)g(the)g(whole)f(In)o(t)1448 2104 y FD(!)p 1448 2111 24 2 v 1471 2094 a Fr(\()p Fs(i)p Fr(\))1510 2092 y FQ(,)h(and)g(with)g FF(!)1781 2099 y FD(M)1839 2092 y FQ(on)60 2152 y(the)e(supp)q(ort)h FF(M)133 2213 y FQ(Let)f(us)g(in)o(tro)q(duce)f(no)o(w)h(a)g(p)q(erio)q(dic)g (in)o(teraction)f(\010.)21 b(The)15 b(energy)h(cost)g(of)g(the)f FF(!)p 1634 2220 33 2 v 2 w FQ(-con)o(tour)i(\000)60 2273 y(is)f(giv)o(en)f (b)o(y)h(the)g(relativ)o(e)f(energy)g FF(H)761 2255 y FH(\010)789 2273 y FQ(\()p FF(!)840 2255 y FH(\000)864 2273 y FE(j)p FF(!)p 878 2280 V 2 w FQ(\),)h(whic)o(h)g(can)g(b)q(e)h(decomp)q(osed)e(in)h(the)g (form:)434 2403 y FF(H)478 2382 y FH(\010)506 2403 y FQ(\()p FF(!)557 2382 y FH(\000)581 2403 y FE(j)p FF(!)p 595 2410 V 2 w FQ(\))28 b(=)g(\011\(\000\))11 b(+)928 2349 y FD(r)906 2361 y Fx(X)907 2453 y FD(i)p FH(=1)966 2403 y FQ([)p FF(e)1003 2410 y FH(\010)1030 2403 y FQ(\()p FF(!)p 1049 2410 V 1081 2382 a FH(\()p FD(i)p FH(\))1122 2403 y FQ(\))g FE(\000)g FF(e)1225 2410 y FH(\010)1252 2403 y FQ(\()p FF(!)p 1271 2410 V 2 w FQ(\)])p FE(j)p FQ(In)o(t)1412 2414 y FD(!)p 1412 2421 24 2 v 1435 2405 a Fr(\()p Fs(i)p Fr(\))1475 2403 y FE(j)i FF(:)239 b FQ(\(B)p FF(:)p FQ(43\))60 2539 y(The)17 b(second)g(term)f(in)g(the)h(RHS)g(is,)g(up)g (to)g(terms)f(prop)q(ortional)i(to)g FE(j)p FF(@)s(M)5 b FE(j)p FQ(,)16 b(the)h(energy)f(con)o(tri-)60 2600 y(bution)g(due)f(to)h(the)g (con\014gurations)h(in)e(the)h(in)o(terior)e(of)i(\000.)22 b(This)15 b(term)f(is)i(absen)o(t)g(if)f(all)g(the)g FF(!)p 1816 2607 33 2 v 1848 2582 a FH(\()p FD(i)p FH(\))60 2660 y FQ(are)20 b(ground-state)h(con\014gurations)g(of)f(\010.)31 b(The)20 b FP(c)n(ontour)h(functional)g FQ(\011\(\000\))f(is)g FP(de\014ne)n(d)g FQ(b)o(y)f(the)938 2784 y(224)p eop %%Page: 225 225 bop 60 91 a FQ(iden)o(tit)o(y)13 b(\(B.43\);)i(it)g(is)g(roughly)g(equal)g (to)862 58 y Fx(P)905 102 y FD(A)p Fy(\032)p FD(M)999 91 y FQ([)o(\010)1047 98 y FD(A)1076 91 y FQ(\()p FF(!)1127 73 y FH(\000)1151 91 y FQ(\))9 b FE(\000)g FQ(\010)1262 98 y FD(A)1291 91 y FQ(\()p FF(!)p 1310 98 33 2 v 2 w FQ(\)])o(,)15 b(but)h(it)e(also)i (includes)e(the)60 152 y(just)i(men)o(tioned)f(terms)f(prop)q(ortional)k(to)e FE(j)p FF(@)s(M)5 b FE(j)p FQ(.)60 235 y FM(De\014nition)18 b(B.22)23 b FP(A)o(n)c(inter)n(action)h FQ(\010)e FP(satis\014es)i(the)f (gener)n(alize)n(d)g(Peierls)g(c)n(ondition)g(|)g(with)60 296 y(r)n(esp)n(e)n(ct)f(to)i(a)f(set)g FE(K)h FP(of)f(r)n(efer)n(enc)n(e)g(c)n (on\014gur)n(ations)h(|)f(if)g(ther)n(e)g(exists)h(a)f(c)n(onstant)h FF(\032)d(>)g FQ(0)j FP(such)60 356 y(that)e(for)e(e)n(ach)i(c)n(ontour)g FQ(\000)c(=)g(\()p FF(M)r(;)8 b(!)741 363 y FD(M)781 356 y FQ(\))p FP(.)822 445 y FQ(\011\(\000\))28 b FE(\025)g FF(\032)p FE(j)p FF(M)5 b FE(j)627 b FQ(\(B)p FF(:)p FQ(44\))60 534 y(The)23 b(\(original\))g(P)o(eierls)e(condition)i(\(B.38\))g(corresp)q(onds)h(to)g (the)e(particular)h(case)g(in)g(whic)o(h)60 594 y FE(K)i FQ(=)f FE(G)218 571 y FH(p)q(er)215 606 y FD(T)5 b FH(=0)287 594 y FQ(\(\010\).)40 b(W)l(e)22 b(remark)f(that)i(this)f(generalized)f(condition)h (is)g(sometimes)e(called)h(just)60 654 y(\\P)o(eierls)c(condition",)i(or)g (\\Gerzik-Pirogo)o(v-Sinai")f(condition.)28 b(W)l(e)18 b(shall)g(also)h(call) e(a)i FP(Peierls)60 715 y(c)n(onstant)e FQ(|)f(for)h(the)f(in)o(teraction)f (\010)h(|)g(a)h(constan)o(t)g FF(\032)f FQ(satisfying)h(\(B.44\).)133 775 y(T)l(o)23 b(understand)g(wh)o(y)f(De\014nition)h(B.22)f(has)h(the)f (desired)g(uniformit)o(y)l(,)f(let)h(us)g(return)h(to)60 835 y(the)e(example)e(of)j(the)f(Ising)g(mo)q(del)f(with)h(magnetic)f(\014eld)h FF(h)h(>)h FQ(0.)37 b(W)l(e)21 b(m)o(ust)f(no)o(w)h(consider)60 895 y FE(K)27 b FQ(=)f FE(f)p FF(!)246 877 y FH(\(+\))303 895 y FF(;)8 b(!)357 877 y FH(\()p Fy(\000)p FH(\))414 895 y FE(g)p FQ(,)25 b(where)e FF(!)658 877 y FH(\(+\))738 895 y FQ(and)i FF(!)873 877 y FH(\()p Fy(\000)p FH(\))953 895 y FQ(are)f(the)f(all-\\+")h (and)g(all-\\)p FE(\000)p FQ(")g(con\014gurations)60 955 y(resp)q(ectiv)o (ely)l(.)d(W)l(e)16 b(notice,)g(ho)o(w)o(ev)o(er,)f(that)j FF(!)925 937 y FH(\()p Fy(\000)p FH(\))999 955 y FQ(is)e(not)h(a)h(ground)g (state.)23 b(With)16 b(this)h(c)o(hoice)f(of)60 1015 y FE(K)q FQ(,)h(the)g(con)o(tours)h(can)f(b)q(e)h(tak)o(en)f(to)h(b)q(e)f(\\thin")h (as)g(in)f(the)g(zero-\014eld)g(case,)g(and)h(w)o(e)f(ha)o(v)o(e)g(that)60 1076 y(for)g(an)o(y)f FF(!)259 1058 y FH(\(+\))316 1076 y FQ(-con)o(tour)h (\000)520 1165 y FF(H)564 1144 y FH(\010)592 1165 y FQ(\()p FF(!)643 1144 y FH(\000)668 1165 y FE(j)p FF(!)714 1144 y FH(\(+\))770 1165 y FQ(\))28 b(=)g(2)p FF(J)5 b FE(j)p FF(@)s(W)i FE(j)j FQ(+)h(2)p FF(h)p FE(j)p FQ(In)o(t)1236 1176 y FD(!)1259 1166 y Fr(\()p Ft(\000)p Fr(\))1312 1165 y FQ(\(\000\))p FE(j)j FF(;)333 b FQ(\(B)p FF(:)p FQ(45\))60 1254 y(while)15 b(for)i(an)g FF(!)362 1236 y FH(\()p Fy(\000)p FH(\))419 1254 y FQ(-con)o(tour)525 1343 y FF(H)569 1322 y FH(\010)596 1343 y FQ(\()p FF(!)647 1322 y FH(\000)672 1343 y FE(j)p FF(!)718 1322 y FH(\()p Fy(\000)p FH(\))775 1343 y FQ(\))27 b(=)h(2)p FF(J)5 b FE(j)p FF(@)s(W)i FE(j)j(\000)h FQ(2)p FF(h)p FE(j)p FQ(In)o(t)1241 1354 y FD(!)1264 1345 y Fr(\(+\))1316 1343 y FQ(\(\000\))p FE(j)j FF(:)329 b FQ(\(B)p FF(:)p FQ(46\))60 1432 y(So,)23 b(comparing)e(with)g(\(B.43\))g(w)o (e)g(see)h(that)f(the)h(generalized)e(P)o(eierls)g(condition)h(is)h (satis\014ed)60 1492 y(with)c FF(\032)g FQ(=)g(2)p FF(J)5 b FQ(,)19 b(uniformly)d(in)j FF(h)p FQ(.)28 b(W)l(e)18 b(see)h(that)g(this)f (uniformit)o(y)e(is)j(gained)f(b)o(y)h(including)e(the)60 1553 y(extra)h(con\014guration)h FF(!)517 1534 y FH(\()p Fy(\000)p FH(\))592 1553 y FQ(whic)o(h)e(is)h(not)g(a)h(ground)f(state,)h(but)f(rather) g(could)g(b)q(e)g(in)o(terpreted)60 1613 y(as)f(a)g(\\metastable)e(state".) 133 1673 y(In)i(general,)f(the)h(uniformit)o(y)e(prop)q(ert)o(y)h(of)i(the)e (generalized)g(P)o(eierls)g(condition)h(is)f(a)i(conse-)60 1733 y(quence)c(of)h(an)g(estimate)e(v)m(alid)i(for)g(sampling)e(cub)q(es)i (larger)g(than)h(the)e(p)q(erio)q(d)h(and)h(range)f(of)g(the)60 1793 y(in)o(teraction;)g(that)h(is,)g(w)o(e)g(imp)q(ose)f(the)h(follo)o(wing) g(extra)g(condition)g(on)h(the)f(sampling)f(cub)q(es:)60 1877 y(\(C2\))25 b(The)20 b(v)m(alue)f(2)p FF(a)14 b FQ(+)f(1)20 b(m)o(ust)f(b)q(e)h(strictly)e(larger)i(than)g(the)g(p)q(erio)q(d)g(and)g (the)g(range)g(of)g(the)182 1937 y(in)o(teraction)15 b(\010.)60 2021 y(W)l(e)d(emphasize)d(that)k(due)e(to)h(requiremen)o(ts)d(\(C1\))k(and)f (\(C2\),)h(the)e(v)m(alue)h(c)o(hosen)f(for)h FF(a)g FQ(|)f(that)i(is,)60 2081 y(the)f(de\014nition)g(of)g(the)g(con)o(tours)h(|)f(dep)q(ends)h(on)g (the)f(set)g FE(K)h FQ(and)g(on)g(the)f(in)o(teraction\(s\))f(presen)o(t.)60 2141 y(The)21 b(reader)f(should)i(k)o(eep)d(this)i(in)f(mind)g(esp)q(ecially) f(b)q(ecause,)j(to)f(k)o(eep)e(form)o(ulas)h(simple)f(to)60 2202 y(read,)g(the)f(notation)h(will)e(not)i(mak)o(e)e(this)h(dep)q(endence)g (explicit.)25 b(In)18 b(particular,)g(a)h(c)o(hange)f(in)60 2262 y(the)d(in)o(teraction)f(|)g(for)h(instance)g(the)g(addition)g(of)g(an)g (arbitrarily)g(small)e(p)q(erturbation)i(|)g(will)60 2322 y(require)g(the)h (rede\014nition)f(of)i(the)f(con)o(tours.)133 2382 y(Under)g(condition)g (\(C2\),)467 2428 y Fx(\014)467 2453 y(\014)467 2478 y(\014)467 2502 y(\014)695 2449 y(X)481 2563 y FD(A)p FH(:)p FD(A)p Fy(\\)567 2519 y Fx(h)587 2563 y FH(In)o(t)632 2579 y Fs(!)p 632 2586 21 2 v 652 2570 a Fr(\()p Fs(i)p Fr(\))691 2563 y Fy([)p FD(@)734 2567 y Fr(ext)777 2563 y FH(In)o(t)822 2579 y Fs(!)p 822 2586 V 843 2570 a Fr(\()p Fs(i)p Fr(\))882 2519 y Fx(i)901 2563 y Fy(6)p FH(=)p Fq(?)978 2490 y FQ(\010)1013 2497 y FD(A)1042 2490 y FQ(\()p FF(!)1093 2469 y FH(\000)1117 2490 y FQ(\))11 b FE(\000)g(j)p FQ(In)o(t)1273 2501 y FD(!)p 1273 2508 24 2 v 1296 2492 a Fr(\()p Fs(i)p Fr(\))1335 2490 y FE(j)d FF(e)1380 2497 y FH(\010)1407 2490 y FQ(\()p FF(!)p 1426 2497 33 2 v 1459 2469 a FH(\()p FD(i)p FH(\))1500 2490 y FQ(\))1533 2428 y Fx(\014)1533 2453 y(\014)1533 2478 y(\014)1533 2502 y(\014)550 2657 y FE(\024)28 b FQ(2\(2)p FF(a)11 b FQ(+)g(1\))813 2636 y FD(d)834 2657 y FE(k)p FQ(\010)p FE(k)919 2665 y Fy(B)943 2656 y Fr(0)962 2657 y FE(j)p FF(@)1002 2664 y FH(ext)1052 2657 y FQ(In)o(t)1114 2668 y FD(!)p 1114 2675 24 2 v 1137 2659 a Fr(\()p Fs(i)p Fr(\))1176 2657 y FE(j)565 b FQ(\(B.47\))938 2784 y(225)p eop %%Page: 226 226 bop 60 91 a FQ(whic)o(h)18 b(implies)f(the)i(follo)o(wing)f(k)o(ey)g (estimate.)28 b(If)19 b(\000)g(=)g(\()p FF(M)r(;)8 b(!)1258 98 y FD(M)1298 91 y FQ(\))19 b(is)g(a)g(a)h FF(!)p 1475 98 33 2 v 2 w FQ(-con)o(tour,)g(then)f(for)60 152 y(an)o(y)d(p)q(erio)q(dic)g (in)o(teraction)590 135 y Fx(e)584 152 y FQ(\010)202 235 y Fx(\014)202 260 y(\014)202 285 y(\014)p FF(H)261 260 y Fx(e)260 265 y FH(\010)288 285 y FQ(\()p FF(!)339 264 y FH(\000)363 285 y FE(j)p FF(!)p 377 292 V 2 w FQ(\))11 b FE(\000)511 231 y FD(r)489 243 y Fx(X)491 335 y FD(i)p FH(=1)557 285 y FE(j)p FQ(In)o(t)634 296 y FD(!)p 634 303 24 2 v 657 287 a Fr(\()p Fs(i)p Fr(\))696 285 y FE(j)p FQ([)o FF(e)747 298 y Fx(e)746 303 y FH(\010)773 285 y FQ(\()p FF(!)p 792 292 33 2 v 825 264 a FH(\()p FD(i)p FH(\))866 285 y FQ(\))g FE(\000)g FF(e)970 298 y Fx(e)969 303 y FH(\010)996 285 y FQ(\()p FF(!)p 1015 292 V 2 w FQ(\)])1080 235 y Fx(\014)1080 260 y(\014)1080 285 y(\014)i FE(\024)h FQ(2\(2)p FF(a)d FQ(+)g(1\))1356 264 y FD(d)1377 285 y FE(k)1408 269 y Fx(e)1402 285 y FQ(\010)p FE(k)1462 293 y Fy(B)1486 284 y Fr(0)1505 285 y FE(j)p FF(M)5 b FE(j)14 b FF(:)142 b FQ(\(B)p FF(:)p FQ(48\))60 425 y(Therefore:)60 524 y FM(Theorem)17 b(B.23)h(\(Uniformit)n(y)e(prop)r(ert)n(y\))23 b FP(If)j(a)g(p)n(erio)n(dic)e(inter)n(action)j FQ(\010)1589 531 y FH(0)1635 524 y FP(satis\014es)f(the)60 584 y(gener)n(alize)n(d)17 b(Peierls)f(c)n(ondition)h(with)f(c)n(onstant)h FF(\032)p FP(,)g(then)f(for)g (any)g(inter)n(action)1560 568 y Fx(e)1553 584 y FQ(\010)h FP(with)f FE(k)1740 568 y Fx(e)1734 584 y FQ(\010)p FE(k)1794 593 y Fy(B)1818 583 y Fr(0)1851 584 y FE(\024)60 645 y FF(c\032=)p FQ(\(2)p FF(a)c FQ(+)g(1\))304 626 y FD(d)325 645 y FP(,)18 b(the)h(sum)f FQ(\010)579 652 y FH(0)611 645 y FQ(+)667 628 y Fx(e)661 645 y FQ(\010)g FP(satis\014es)h(the)g(gener)n(alize)n(d)g (Peierls)g(c)n(ondition)g(with)g(c)n(onstant)60 705 y FF(\032)p FQ(\(1)12 b FE(\000)e FQ(2)p FF(c)p FQ(\))p FP(.)60 804 y FQ(Another)i (useful)g(result,)h(whic)o(h)f(basically)f(follo)o(ws)i(from)e(\(B.48\),)i (is)f(the)g(follo)o(wing)h([328,)g(Lemma)60 864 y(2.2]:)60 964 y FM(Prop)r(osition)18 b(B.24)24 b FP(Consider)19 b(a)g(p)n(erio)n(dic)g (inter)n(action)h FQ(\010)1221 971 y FH(0)1261 964 y FP(satisfying)f(the)h (original)g(Peierls)60 1024 y(c)n(ondition)e(\(B.38\))f(with)h(c)n(onstant)g FF(\032)754 1031 y FH(0)774 1024 y FP(.)23 b(Then,)18 b(for)e(any)i(other)f (p)n(erio)n(dic)g(inter)n(action)1687 1008 y Fx(e)1681 1024 y FQ(\010)400 1131 y FE(k)431 1115 y Fx(e)425 1131 y FQ(\010)p FE(k)485 1140 y Fy(B)509 1130 y Fr(0)542 1131 y FF(<)d(\032=)p FQ(\(2)p FF(a)d FQ(+)g(1\))815 1111 y FD(d)864 1131 y FQ(=)-8 b FE(\))27 b(G)1004 1108 y FH(p)q(er)1001 1144 y FD(T)5 b FH(=0)1073 1131 y FQ(\(\010)1127 1138 y FH(0)1158 1131 y FQ(+)1213 1115 y Fx(e)1207 1131 y FQ(\010\))14 b FE(\032)g(G)1361 1108 y FH(p)q(er)1358 1144 y FD(T)5 b FH(=0)1430 1131 y FQ(\(\010)1484 1138 y FH(0)1504 1131 y FQ(\))14 b FF(:)204 b FQ(\(B)p FF(:)p FQ(49\))60 1239 y(W)l(e)17 b(presen)o(t)g(t)o(w)o(o)h(corollaries)e(of)i(Theorem)e(B.23.)25 b(F)l(or)18 b(our)g(study)g(of)f(the)h(Kadano\013)h(transfor-)60 1299 y(mation)c(w)o(e)h(need)g(the)g(follo)o(wing)g(trivial)f(consequence:)60 1398 y FM(Corollary)j(B.25)24 b FP(Consider)i(a)g(p)n(erio)n(dic)f(inter)n (action)i FQ(\010)1194 1405 y FH(0)1240 1398 y FP(satisfying)g(the)g (original)f(Peierls)60 1459 y(c)n(ondition)c(\(B.38\))f(with)h(c)n(onstant)h FF(\032)771 1466 y FH(0)790 1459 y FP(,)g(and)e(another)h(inter)n(action)1367 1442 y Fx(e)1360 1459 y FQ(\010)g FP(such)g(that)g FE(G)1669 1435 y FH(p)q(er)1666 1471 y FD(T)5 b FH(=0)1738 1459 y FQ(\(\010)1792 1466 y FH(0)1812 1459 y FQ(\))21 b(=)60 1519 y FE(G)93 1495 y FH(p)q(er)90 1531 y FD(T)5 b FH(=0)162 1519 y FQ(\(\010)216 1526 y FH(0)249 1519 y FQ(+)305 1503 y Fx(e)299 1519 y FQ(\010\))p FP(.)29 b(Then)20 b(if)f FE(k)606 1503 y Fx(e)600 1519 y FQ(\010)p FE(k)660 1527 y Fy(B)684 1518 y Fr(0)721 1519 y FE(\024)f FF(c\032)824 1526 y FH(0)843 1519 y FF(=)p FQ(\(2)p FF(a)13 b FQ(+)g(1\))1043 1501 y FD(d)1063 1519 y FP(,)20 b(the)g(sum)g FQ(\010)1322 1526 y FH(0)1354 1519 y FQ(+)1411 1503 y Fx(e)1405 1519 y FQ(\010)f FP(satis\014es)i(the)e(original)60 1579 y(Peierls)f(c)n(ondition)g(with)g(c)n (onstant)g FF(\032)761 1586 y FH(0)781 1579 y FQ(\(1)12 b FE(\000)e FQ(2)p FF(c)p FQ(\))p FP(.)60 1678 y FQ(Ho)o(w)o(ev)o(er,)k(the)i(corollary)g (more)f(often)h(used)g(is:)60 1778 y FM(Corollary)i(B.26)24 b FP(If)e FQ(\010)536 1785 y FH(0)578 1778 y FP(satis\014es)g(the)h(original) g(Peierls)g(c)n(ondition)f(with)h(c)n(onstant)g FF(\032)1756 1785 y FH(0)1798 1778 y FP([and)60 1838 y FE(K)e FQ(=)g FE(G)211 1814 y FH(p)q(er)208 1850 y FD(T)5 b FH(=0)280 1838 y FQ(\(\010)334 1845 y FH(0)354 1838 y FQ(\))p FP(],)22 b(then)g(a)f(\\p)n(erturb)n(e)n(d")f (inter)n(action)i FQ(\010)f(=)f(\010)1247 1845 y FH(0)1281 1838 y FQ(+)1339 1822 y Fx(e)1333 1838 y FQ(\010)h FP(satis\014es)h(the)f (gener)n(alize)n(d)60 1898 y(Peierls)d(c)n(ondition)g(with)g(c)n(onstant)g FF(\032)761 1905 y FH(0)781 1898 y FQ(\(1)11 b FE(\000)f FQ(2)p FF(c)p FQ(\))18 b FP([and)g(the)f FQ(same)g FE(K)q FP(])g(if)g FE(k)1429 1882 y Fx(e)1423 1898 y FQ(\010)p FE(k)1483 1907 y Fy(B)1507 1897 y Fr(0)1540 1898 y FE(\024)d FF(c\032)1639 1905 y FH(0)1659 1898 y FF(=)p FQ(\(2)p FF(a)d FQ(+)f(1\))1854 1880 y FD(d)1875 1898 y FP(.)60 1998 y FQ(This)21 b(corollary)g(generalizes)f (what)i(w)o(as)g(observ)o(ed)e(regarding)i(the)f(Ising)g(mo)q(del)f(in)g (non-zero)60 2058 y(\014eld.)133 2118 y(As)11 b(the)g(inclusion)g(in)g (\(B.49\))g(is)g(in)g(general)g(strict,)h(the)f(last)g(corollary)g(implies)e (that,)j(from)e(the)60 2178 y(p)q(oin)o(t)j(of)f(view)g(of)h(\010)h(=)f(\010) 531 2185 y FH(0)555 2178 y FQ(+)602 2162 y Fx(e)596 2178 y FQ(\010,)g(the)f(uniformit)o(y)e(is)i(gained)h(at)g(the)f(cost)h(of)f (including)g(some)f(extra)60 2238 y(reference)17 b(con\014gurations)k(that)e (are)g(not)h(ground)g(states)f(\(e.g.)f FF(!)1319 2220 y FH(\()p Fy(\000)p FH(\))1395 2238 y FQ(in)h(the)g(ab)q(o)o(v)o(e)g(example\).)60 2299 y(These)d(extra)g(con\014gurations)i(can)e(b)q(e)g(in)o(terpreted)f(as)i (\\metastable)e(states")i(or)f(\\lo)q(cal)h(ground)60 2359 y(states")j(for)f(\010)g([369].)29 b(On)18 b(the)h(other)g(hand,)g(an)o(y)g (system)e(with)i(a)g(\014nite)f(n)o(um)o(b)q(er)f(of)i(p)q(erio)q(dic)60 2419 y(ground-state)24 b(con\014gurations)f(ough)o(t)f(to)h(satisfy)f(the)f (generalized)g(P)o(eierls)g(condition)g(if)h(one)60 2479 y(adds)16 b FP(al)r(l)g FQ(the)e(lo)q(cal)h(ground)h(states)f(of)g(the)f(mo)q(del)g ([369])h(\(or)g(allo)o(w)f(more)g(complicated)e(t)o(yp)q(es)j(of)60 2539 y(reference)g(states\).)133 2600 y(A)o(t)k(the)h(risk)g(of)g(b)q(eing)g (considered)g(almost)f(patronizing,)h(w)o(e)g(emphasize)e(again)j(that)f(the) 60 2660 y(size)h FF(a)g FQ(in)h(the)f(previous)h(results)f(is)h(c)o(hosen)f (so)i(as)f(to)g(satisfy)g(\(C1\))g(and)h(\(C2\))f(for)g(the)f FP(total)938 2784 y FQ(226)p eop %%Page: 227 227 bop 60 96 a FQ(in)o(teraction)22 b(\010)347 103 y FH(0)383 96 y FQ(+)443 80 y Fx(e)437 96 y FQ(\010.)42 b(Often,)24 b(\010)722 103 y FH(0)765 96 y FQ(is)f(a)g(simpler)e(or)j(more)e(standard)i(in)o (teraction)e(that)i(one)60 156 y(studies)d(indep)q(enden)o(tly)e(or)i(for)g (whic)o(h)f(one)h(can)f(b)q(orro)o(w)i(results)f(from)e(the)i(literature.)33 b(The)60 216 y(P)o(eierls)13 b(constan)o(t)i(determined)e(in)h(this)h(manner) e(corresp)q(onds,)j(hence,)e(to)h(a)g(v)m(alues)g(of)g FF(a)f FQ(c)o(hosen)60 277 y(without)j(reference)d(to)j(an)o(ything)f(but)h(\010)834 284 y FH(0)854 277 y FQ(.)k(When)c(considering)f(in)g(addition)g(p)q (erturbations)1847 260 y Fx(e)1841 277 y FQ(\010,)60 337 y(no)h(matter)d(ho)o (w)j(small,)d(this)i(size)f(ma)o(y)g(need)g(to)i(b)q(e)f(rede\014ned)g(to)g (a)h(new)f(v)m(alue)g FF(a)1623 319 y Fy(0)1650 337 y FQ(suitable)g(for)60 397 y(the)g(total)g(in)o(teraction.)k(If)15 b(so,)h(the)g(P)o(eierls)f (constan)o(t)h FF(\032)1107 404 y FH(0)1143 397 y FQ(app)q(earing)h(in)e(the) h(previous)g(results)f(is)60 457 y FP(smal)r(ler)h FQ(than)g(the)f(one)g (initially)f(determined.)k(The)d(simplest)e(pro)q(cedure)i(at)h(this)f(p)q (oin)o(t,)g(if)g(one)60 517 y(do)q(es)g(not)f(w)o(an)o(t)f(to)i(completely)10 b(redo)k(the)g(analysis)g(with)f(the)h(new)f(de\014nition)h(of)g(con)o (tours,)g(is)g(to)60 577 y(adopt)i(for)f FF(\032)295 584 y FH(0)329 577 y FQ(the)g(initial)e(v)m(alue)h(divided)g(b)o(y)g(\(2)p FF(a)981 559 y Fy(0)1001 577 y FQ(+)8 b(1\))1090 559 y FD(d)1125 577 y FQ([leftmost)k(inequalit)o(y)h(in)h(\(B.41\)].)20 b(Note)60 638 y(that)e(the)f(P)o(eierls)e(constan)o(t)j(c)o(hosen)f(in)g(this)g(w)o(a)o (y)g(go)q(es)h(to)g(zero)f(with)g(increasing)g(range)h(of)f(the)60 698 y(p)q(erturbations.)22 b(In)15 b(fact,)g(in)g(general)h(one)f(can)h(not)g (do)g(m)o(uc)o(h)d(b)q(etter)j(than)g(this.)21 b(In)15 b(particular,)60 758 y(it)k(is)g(kno)o(wn)h(\(cf.)f(Remark)f(4)i(in)f(Section)g(2.6.7\))h (that)g(arbitrarily)e(w)o(eak)i(p)q(erturbations)g(with)60 818 y(long-range)d(in)o(teractions)f(can)g(destro)o(y)g(the)g(phase)h (diagram.)133 903 y(T)l(o)e(conclude)f(this)h(section,)f(w)o(e)g(observ)o(e)g (that)h(the)g(notion)g(of)g(con)o(tour)g(can)g(b)q(e)g(presen)o(ted)e(in)60 964 y(a)18 b(sligh)o(tly)e(more)g(general)i(\(and)g(abstract\))g(fashion.)26 b(Indeed,)17 b(the)g(k)o(ey)f(prop)q(erties)i(supp)q(orting)60 1024 y(the)h(rest)h(of)g(the)f(theory)h(are)g(the)f(unique)g(reconstruction)h (of)g(a)g(con\014guration)g(from)f(a)h(set)g(of)60 1084 y(con)o(tours)f ([here)f(a)g(consequence)g(of)h(the)f(extension)g(prop)q(ert)o(y)l(,)h (requiremen)n(t)d(\(C1\)],)j(estimates)60 1144 y(\(B.44\))14 b(and)i(\(B.48\),)e(and)h(that)g(the)f(en)o(trop)o(y)g(gain)h(b)q(e)g(b)q (eaten)g(b)o(y)f(the)g(energy)g(cost)h(at)g(lo)o(w)f(tem-)60 1204 y(p)q(eratures.)27 b(As)18 b(long)g(as)g(these)g(prop)q(erties)g(are)g (satis\014ed,)g(con)o(tours)h(need)e(not)i(b)q(e)f(de\014ned)f(via)60 1264 y(sampling)11 b(cub)q(es.)19 b(An)12 b(illustration)f(of)g(this)h (observ)m(ation)g(is)g(the)f(use)h(of)f(\\thin")i(con)o(tours)f(in)f(ferro-) 60 1325 y(magnetic)i(nearest-neigh)o(b)q(or)h(Ising)g(mo)q(dels)f(or,)i(more) e(generally)l(,)g(mo)q(dels)g(whose)h(ground-state)60 1385 y(con\014gurations)k(are)f(constan)o(t.)22 b(The)17 b(b)q(oundary)h(in)e(suc) o(h)h(a)g(mo)q(del)e(can)i(b)q(e)g(de\014ned)f(as)h(a)g(set)g(of)60 1445 y(p)q(olyhedra,)g(and)g(the)f(con)o(tours)h(are)g(non-self-in)o (tersecting)f(closed)g(\(h)o(yp)q(er\)surfaces)g(\(uniquely)60 1505 y(de\014ned)f(via)g(suitable)g(\014xed)g(prescriptions)g(to)h(handle)g (in)o(tersections\),)e(lab)q(elled)g(b)o(y)h(the)g(con\014g-)60 1565 y(urations)i(of)g(the)g(adjacen)o(t)f(spins.)22 b(The)17 b(lab)q(elling)f(allo)o(ws)g(for)h(a)g(unique)f(reconstruction)g(of)h(the)60 1626 y(con\014guration,)d(and)f(the)f(thin)g(con)o(tours)h(satisfy)f (estimate)f(\(B.44\))h(with)g FE(j)p FF(M)5 b FE(j)12 b FQ(replaced)g(b)o(y)g FE(j)p FQ(\000)p FE(j)26 b FQ(=)60 1686 y(area)19 b(of)g(the)f(p)q(olyhedra)h (=)f(n)o(um)o(b)q(er)f(of)i(plaquettes)f(forming)g(its)g(faces,)g(and)i (estimate)c(\(B.48\))60 1746 y(with)j FF(a)g FQ(determined)d(on)k(the)f (basis)h(of)821 1730 y Fx(e)815 1746 y FQ(\010)q(.)30 b(Moreo)o(v)o(er,)18 b(they)g(ha)o(v)o(e)h(smaller)e(en)o(trop)o(y)i(than)g(the)60 1806 y(\\thic)o(k")c(con)o(tours.)21 b(Note,)15 b(ho)o(w)o(ev)o(er,)f(that)i (the)f(remark)f(discussed)h(in)g(the)g(previous)g(paragraph)60 1866 y(is)20 b(esp)q(ecially)e(relev)m(an)o(t)h(in)h(connection)g(with)g (thin)f(con)o(tours:)30 b(in)19 b(general,)i(if)e(the)h(in)o(teraction)60 1927 y(is)e(p)q(erturb)q(ed,)g(one)h FP(c)n(annot)f FQ(use)g(the)g(v)m(alue)g (of)h FF(\032)987 1934 y FH(0)1024 1927 y FQ(determined)d(via)i(thin)g(con)o (tours;)h(one)f(m)o(ust,)60 1987 y(for)h(instance,)g(divide)f(it)g(b)o(y)h(a) g(factor)h(\(2)p FF(a)13 b FQ(+)f(1\))975 1969 y FD(d)996 1987 y FQ(,)19 b(where)g FF(a)g FQ(dep)q(ends)g(on)g(the)g(p)q(erturbation)1861 1971 y Fx(e)1855 1987 y FQ(\010)60 2047 y(considered.)60 2177 y FM(B.4.3)55 b(Results)18 b(of)h(the)f(Theory)60 2269 y FQ(W)l(e)i(presen)o (t)f(here)g(the)h(main)e(results)i(of)g(PS)g(theory)l(.)32 b(W)l(e)20 b(include)f(some)f(general)i(commen)o(ts)60 2329 y(on)g(the)g(underlying)f(ideas,)h(but)h(w)o(e)e(do)h(not)h(discuss)f(the)f (details)h(of)g(the)g(pro)q(ofs.)33 b(These)20 b(can)60 2390 y(b)q(e)h(consulted)f(in)g(the)g(bibliograph)o(y)l(.)33 b(W)l(e)20 b(men)o(tion)f(that)h(there)g(are)h(t)o(w)o(o)f(approac)o(hes)h(to)g(PS)60 2450 y(theory:)27 b(the)19 b(original)g(one,)g(based)h(on)g(\\con)o(tour)g (mo)q(dels)e(with)h(parameters",)g(and)g(the)g(more)60 2510 y(recen)o(t)12 b(one,)h(due)g(to)h(Zahradn)-5 b(\023)-19 b(\020k,)13 b(based)h(instead)f(on)g(a)h(classi\014cation)f(of)g(con)o(tours)h(in)o(to)e (\\stable")60 2570 y(and)21 b(\\unstable")g(ones.)33 b(References)19 b(for)i(the)f(\014rst)g(approac)o(h)h(are)f(the)g(seminal)f(pap)q(ers)i ([296,)60 2630 y(297)q(],)d(Sinai's)g(b)q(o)q(ok)i([328],)f(and)f(Sla)o(wn)o (y's)g(review)f(article)g([329)q(].)27 b(The)19 b(second)f(approac)o(h)i(w)o (as)938 2784 y(227)p eop %%Page: 228 228 bop 60 91 a FQ(in)o(tro)q(duced)11 b(in)g([366)q(];)h(a)g(concise)f(presen)o (tation)g(is)g(giv)o(en)g(in)g([35])g(and)h(a)g(p)q(edagogical)g(one)g(in)f ([369)q(].)60 152 y(This)19 b(second)g(approac)o(h)h(is)f(in)o(tuitiv)o(ely)d (more)h(app)q(ealing,)j(pro)o(vides)e(some)g(more)g(information)60 212 y(|)d(as)g(for)g(instance)f(the)h(completeness)e([366])i(and)g (analyticit)o(y)e([368)q(])h(of)h(the)g(phase)g(diagram)f(|)60 272 y(and)f(has)g(serv)o(ed)f(as)h(a)g(basis)g(for)f(further)h(extensions)f (and)h(applications)f(of)h(the)f(theory)h([367,)f(287)q(,)60 332 y(288)q(,)k(194)q(,)g(35)q(,)g(36].)21 b(In)16 b(the)g(commen)o(ts)d(b)q (elo)o(w)j(w)o(e)g(mostly)f(ha)o(v)o(e)h(in)f(mind)g(suc)o(h)h(an)h(approac)o (h.)133 392 y(The)i(essence)g(of)g(Pirogo)o(v-Sinai)h(theory)f(|)g(inherited) f(from)g(the)h(P)o(eierls)e(argumen)o(t)h(|)h(is)60 452 y(the)c(de\014nition) h(of)g(maps)f(from)f(the)i(original)f(spin)h(ensem)o(ble)d(in)o(to)i(ensem)o (bles)e(of)j(con)o(tours)h(that)60 513 y FP(inter)n(act)h(only)f(by)g (volume-exclu)q(sion)t FQ(,)h(that)e(is,)f(in)o(to)h FP(gases)h(of)g(c)n (ontours)t FQ(.)k(The)16 b(families)d(of)k(con-)60 573 y(tours)g(in)f(the)h (latter)f(do)h(not)g(necessarily)e(corresp)q(ond)i(to)g(an)g(actual)g (collection)e(of)i(con)o(tours)g(of)60 633 y(a)d(spin)g(con\014guration,)h(b) q(ecause)f(they)g(are)g(not)g(required)f(to)h(\\matc)o(h")f(exteriors)h(with) f(in)o(teriors.)60 693 y(F)l(or)20 b(instance,)g(a)g(set)g(of)g(t)o(w)o(o)g (\\)p FE(\000)p FQ("-con)o(tours,)i(one)e(inside)f(the)g(other,)i(is)f(an)g (allo)o(w)o(ed)f(elemen)o(t)60 753 y(of)i(one)f(of)h(the)f(con)o(tour)h (ensem)o(bles,)d(ev)o(en)i(when)g(there)g(is)g(no)h(spin)g(con\014guration)g (ha)o(ving)f(it)60 814 y(as)d(its)f(family)e(of)i(con)o(tours)h(\(in)e(a)i (spin)f(con\014guration)h(there)f(w)o(ould)g(b)q(e)g(an)h(in)o(termediate)c (\\+"-)60 874 y(con)o(tour\).)38 b(This)22 b(lac)o(k)f(of)h(\\matc)o(hing")f (requiremen)n(t)e(mak)o(es)h(the)i(con)o(tour)g(ensem)o(bles)d(m)o(uc)o(h)60 934 y(simpler)e(systems)h(to)h(w)o(ork)g(with.)30 b(The)19 b(maps)f(are)h(de\014ned)g(so)h(that)f(eac)o(h)g(stable)g(pure)g(phase)60 994 y(is)e(equiv)m(alen)o(t)f(to)h(a)h(con)o(tour)f(ensem)o(ble)d(in)j(the)g (sense)g(that)h(b)q(oth)g(ha)o(v)o(e)e(the)h FP(same)i(distribution)60 1054 y(of)k FQ(external)e FP(c)n(ontours)t FQ(.)39 b(The)22 b(lo)o(w-temp)q(erature)e(picture)h(of)h(only)g(small)f(\\islands")h(of)h(o)o (v)o(er-)60 1115 y(turned)15 b(spins)h(can)g(then)f(b)q(e)g(precisely)f(pro)o (v)o(en)h(b)o(y)g(estimating)f(the)h(probabilities)f(of)i(\(external\))60 1175 y(b)q(oundaries)h(using)g(the)f(con)o(tour)g(ensem)o(bles.)133 1235 y(One)k(considers)g FF(r)h FQ(di\013eren)o(t)e(con)o(tour)h(ensem)o (bles,)e(one)i(for)g(eac)o(h)g(reference)e(con\014guration)60 1295 y FF(!)p 60 1302 33 2 v 92 1277 a FH(\()p FD(i)p FH(\))148 1295 y FE(2)c(K)q FQ(.)20 b(The)d FF(i)p FQ(-th)f(ensem)o(ble)d(is)j(formed)f (b)o(y)h(all)g(the)g FF(!)p 1104 1302 V 1136 1277 a FH(\()p FD(i)p FH(\))1177 1295 y FQ(-con)o(tours)h(in)o(teracting)e(only)h(via)g(the) 60 1355 y(restriction)e(of)h(b)q(eing)h(separated)f(b)o(y)g(2)g(or)g(more)f (lattice)g(units.)21 b(The)15 b(statistical)f(w)o(eigh)o(t)g(of)i(eac)o(h)60 1416 y(con)o(tour)d(is)f(giv)o(en)g(b)o(y)g(an)i(activit)o(y)d(exp)o([)p FE(\000)p FF(F)872 1390 y FH(\()p FD(i)p FH(\))865 1428 y FD(\014)912 1416 y FQ(\(\000\)])i(with)g(a)g(functional)f FF(F)1416 1390 y FH(\()p FD(i)p FH(\))1409 1428 y FD(\014)1457 1416 y FQ(\(\000\))h (determined)d(via)j(a)60 1476 y(relation)g(\(form)o(ulas)g(\(1.14\))i(or)f (\(1.19\))g(in)g([366)q(]\))f(that)h(roughly)h(compares)e(the)g(\\w)o(ork)h (needed)g(to)60 1536 y(install)i(a)h(con)o(tour")g([369)q(])f(in)g(the)g (spin)h(and)g(con)o(tour)g(ensem)o(bles.)i([In)d(the)g(original)h(PS)g (theory)l(,)60 1596 y(some)j(extra)g(w)o(eigh)o(ts)g(exp[)p FF(b)605 1578 y FH(\()p FD(i)p FH(\))645 1596 y FE(j)p FQ(In)o(t)8 b(\(\000\))p FE(j)p FQ(])20 b(are)h(assigned)g(to)h(the)e(external)g(con)o (tours)h([328)q(],)f(and)60 1656 y(b)q(oth)f(the)f(\\parameters")g FF(b)587 1638 y FH(\()p FD(i)p FH(\))647 1656 y FQ(and)g(the)g(functional)g FF(F)1099 1638 y FH(\()p FD(i)p FH(\))1158 1656 y FQ(are)h(also)f(determined) e(b)o(y)i(comparing)60 1716 y(\\w)o(orks")i(\(form)o(ula)e(\(2.43\))j(in)e ([328]\).)31 b(W)l(e)19 b(prefer)g(to)h(follo)o(w)f(here)g(Zahradn)-5 b(\023)-19 b(\020k's)19 b(approac)o(h)h(in)60 1783 y(whic)o(h)c(the)g (\\parameter)f(degree)h(of)g(freedom")f(is)h(absorb)q(ed)i(in)o(to)e(the)g (functional)g FF(F)1666 1758 y FH(\()p FD(i)p FH(\))1659 1796 y FD(\014)1707 1783 y FQ(.])133 1844 y(Eac)o(h)h(con)o(tour)g(ensem)o(ble)d (is)j(a)g(statistical-mec)o(hanical)d(system)i(of)h(its)g(o)o(wn,)g(whic)o(h) f(can)h(b)q(e)60 1904 y(studied)f(without)h(an)o(y)f(reference)e(to)j(the)f (original)g(spin)g(system.)k(Prop)q(erties)c(of)h(these)f(con)o(tour)60 1964 y(mo)q(dels)h(can)h(then)g(b)q(e)g(transcrib)q(ed)g(in)o(to)g(results)g (for)g(the)g(spin)g(system)f(via)g(the)h(iden)o(ti\014cation)60 2024 y(b)q(et)o(w)o(een)i(the)h(ensem)o(bles.)34 b(This)22 b(is)f(the)g(usual)h(p)q(olicy)e(in)h(the)g(standard)i(exp)q(ositions)f(of)f (the)60 2084 y(theory)l(,)h(all)e(of)i(whic)o(h)e(include)g(an)i(\\in)o (terlude")e(in)h(whic)o(h)f(abstract)i(con)o(tour)f(ensem)o(bles)e(are)60 2145 y(analyzed)12 b FP(p)n(er)i(se)j FQ(\(Sections)12 b(7)i(to)f(9)g(in)f (Chapter)i(2)f(of)g([328)q(],)f(Section)h(2)g(in)f([366)q(],)h(etc\).)19 b(Basically)l(,)60 2205 y(con)o(tour)j(mo)q(dels)f(are)h(studied)g(via)g (cluster-expansion)g(tec)o(hniques:)31 b(this)22 b(is)g(the)f(metho)q(d)h(of) 60 2265 y(c)o(hoice)15 b(for)h(systems)f(at)i(\\high)g(temp)q(erature")e(or)h (\\lo)o(w)h(densit)o(y".)j(All)15 b(the)h(con)o(tour)g(ensem)o(bles)60 2325 y(satisfy)h(one)f(of)h(the)g(k)o(ey)e(ingredien)o(ts)h(of)h(the)f(P)o (eierls)f(argumen)o(t:)21 b FP(the)d(entr)n(opy)g(factor)f(gr)n(ows)h(at)60 2385 y(most)f(exp)n(onential)r(ly)i(with)e(the)h(size)f(of)g(the)g(c)n (ontours)f FQ([328,)g(Lemma)d(2.7])j(\(this)f(fact)h(is)f(false)h(for)60 2446 y FF(d)j FQ(=)f(1!\).)29 b(Therefore,)19 b(there)f(is)h(a)g(mark)o(ed)e (di\013erence)h(according)h(to)g(whether)g(the)f(functional)60 2513 y FF(F)99 2487 y FH(\()p FD(i)p FH(\))92 2525 y FD(\014)156 2513 y FQ(de\014ning)e(the)g(con)o(tour)h(activit)o(y)d(satis\014es)j(a)g(b)q (ound)g(of)g(the)f(form)780 2636 y FF(F)819 2610 y FH(\()p FD(i)p FH(\))812 2648 y FD(\014)860 2636 y FQ(\(\000\))28 b FE(\025)f FF(\034)1049 2610 y FH(\()p FD(i)p FH(\))1043 2648 y FD(\014)1090 2636 y FE(j)p FF(M)5 b FE(j)585 b FQ(\(B)p FF(:)p FQ(50\))938 2784 y(228)p eop %%Page: 229 229 bop 60 100 a FQ(with)12 b FF(\034)194 75 y FH(\()p FD(i)p FH(\))188 113 y FD(\014)249 100 y FF(>)i FQ(0.)20 b(If)12 b(this)g(is)h(the)f(case,)g (it)g(is)g(customary)g(to)h(sa)o(y)f(that)h FF(F)1335 75 y FH(\()p FD(i)p FH(\))1328 113 y FD(\014)1388 100 y FQ(is)f(a)h FF(\034)1497 75 y FH(\()p FD(i)p FH(\))1491 113 y FD(\014)1538 100 y FQ(-)p FP(functional)5 b FQ(.)22 b([F)l(or)60 160 y(the)d(original)h (PS)f(approac)o(h,)i(the)e(big)h(di\013erence)e(is)h(whether)h(the)f(corresp) q(onding)h(parameter)60 221 y FF(b)81 202 y FH(\()p FD(i)p FH(\))139 221 y FQ(is)c(zero;)f(all)h(the)g(functionals)g FF(F)743 202 y FH(\()p FD(i)p FH(\))800 221 y FQ(in)g(the)g(PS)h(approac)o(h)g(are)f FF(\034)6 b FQ(-functionals.])133 281 y(The)15 b(con)o(tour)h(mo)q(dels)e (de\014ned)h(b)o(y)g FF(\034)6 b FQ(-functionals)15 b(enjo)o(y)f(sev)o(eral)g (remark)m(able)g(prop)q(erties)h FP(if)60 341 y FF(\034)23 b FP(is)18 b(lar)n(ge)g(enough)h(to)f(over)n(c)n(ome)g(the)g(entr)n(opy)f(gr) n(owth)t FQ(.)22 b(This)17 b(gro)o(wth)g(is)f(c)o(haracterized)f(b)o(y)i(an) 60 401 y(exp)q(onen)o(tial)e(factor)i(b)q(ounded)g(b)o(y)f([328)q(,)f(Lemma)g (2.7])537 517 y FF(\013)28 b FQ(=)g(max)753 469 y Fx(n)780 517 y FF(d)8 b FQ(log)r(\(2)p FF(a)j FQ(+)g(1\))j FF(;)22 b FQ(log)9 b FE(j)p FQ(\012)1219 524 y FH(0)1239 517 y FE(j)i FQ(+)g(3)1337 497 y FD(d)1358 469 y Fx(o)1399 517 y FF(:)342 b FQ(\(B)p FF(:)p FQ(51\))60 634 y(If)16 b(the)f(con)o(tour)i(mo)q(del)d(has) j(a)f(con)o(v)o(ergen)o(t)f(cluster)g(expansion,)h(whic)o(h)g(o)q(ccurs)g(at) g(least)g(if)g([328,)60 694 y(Lemma)e(2.8)j(and)g(Prop)q(ositions)g(2.1)g (and)g(2.2])848 811 y FF(\034)875 785 y FH(\()p FD(i)p FH(\))869 823 y FD(\014)944 811 y FE(\025)27 b FQ(4)p FF(\013)15 b(;)661 b FQ(\(B)p FF(:)p FQ(52\))60 921 y(then)26 b(it)f(has)i(a)f(w)o (ell-de\014ned)f(thermo)q(dynamic)e(limit,)i(with)h(a)g(w)o(ell-de\014ned)f (pressure)g(and)60 981 y(in\014nite-v)o(olume)c(probabilit)o(y)j(measure.)44 b(F)l(or)25 b(this)f(measure,)g(in\014nite)g(con)o(tours)h(ha)o(v)o(e)e(zero) 60 1041 y(probabilit)o(y)e(of)h(o)q(ccurrence,)f(more)g(generally)l(,)g(the)h (probabilit)o(y)e(for)i(a)g(giv)o(en)f(con)o(tour)h(to)g(b)q(e)60 1101 y(presen)o(t)e(decreases)f(exp)q(onen)o(tially)g(with)h(the)g(size)f(of) i(its)f(supp)q(ort.)34 b(Moreo)o(v)o(er,)19 b(the)h(measure)60 1161 y(satis\014es)d(exp)q(onen)o(tial)f(mixing)f(conditions)i(for)g(disjoin) o(t)f(families)e(of)j(external)f(con)o(tours.)23 b(\(See,)60 1222 y(for)f(instance,)g(Sections)g(7-9)h(of)f([328].\))38 b(F)l(urthermore,)21 b(eac)o(h)g(of)h(suc)o(h)g(con)o(tour)g(measures)e(is)60 1289 y(equiv)m(alen)o(t)g(to)j(a)f(Gibbs)g(measure)f(in)g(the)h(spin)g (system:)31 b FP(if)23 b FF(F)1297 1263 y FH(\()p FD(i)p FH(\))1290 1301 y FD(\014)1360 1289 y FP(is)g(a)f FF(\034)1492 1263 y FH(\()p FD(i)p FH(\))1486 1301 y FD(\014)1534 1289 y FP(-functional,)k(with) 60 1362 y FF(\034)87 1337 y FH(\()p FD(i)p FH(\))81 1375 y FD(\014)153 1362 y FE(\025)e FQ(4)p FF(\013)p FP(,)i(then)e(the)f (\(in\014nite-volume)q(\))j(pr)n(ob)n(ability)c(density)i(of)f(external)i(c)n (ontours)e(of)g(the)60 1422 y(c)n(ontour)17 b(ensemble)i(is)e(e)n(qual)h(to)f (that)g(of)g(the)g(Gibbs)h(me)n(asur)n(e)e(|)h(at)g(inverse)h(temp)n(er)n (atur)n(e)e FF(\014)j FP(|)60 1482 y(of)i(the)g(spin)g(mo)n(del)g(de\014ne)n (d)h(by)f(the)h FF(!)p 776 1489 33 2 v 808 1464 a FH(\()p FD(i)p FH(\))871 1482 y FP(b)n(oundary)e(c)n(ondition)t FQ(.)33 b(Th)o(us,)21 b(this)f(Gibbs)g(measure)60 1543 y(inherits)14 b(the)g(sparsit)o(y)g(of)h (\(external\))e(con)o(tours)i(c)o(haracterizing)e(the)i(con)o(tour)f(ensem)o (ble)e(and)j(its)60 1603 y(mixing)h(prop)q(erties.)28 b(It)19 b(is,)f(therefore,)g(an)h(extremal)d(p)q(erio)q(dic)i(Gibbs)h(measure)e (\(pure)i(phase\))60 1663 y(whic)o(h)14 b(is)g(only)h(a)g(small)e(p)q (erturbation)i(of)g(the)g(reference)e(\(in)h(fact)h(ground-state\))h (con\014guration)60 1723 y FF(!)p 60 1730 V 92 1705 a FH(\()p FD(i)p FH(\))134 1723 y FQ(.)21 b(The)16 b(precise)f(result)h(of)h(this)f (argumen)o(t)f(is:)60 1837 y FM(Theorem)i(B.27)h(\(Pirogo)n(v-Sinai-Zahradn) -6 b(\023)-22 b(\020k\))23 b FP(Assume)f FF(d)g FE(\025)g FQ(2)p FP(.)36 b(If)22 b(a)g(\014nite-r)n(ange)i(p)n(e-)60 1898 y(rio)n(dic)d(inter) n(action)h FQ(\010)f FP(satis\014es)h(the)g(gener)n(alize)n(d)g(Peierls)g(c)n (ondition)g(\(B.44\))f(with)h(r)n(esp)n(e)n(ct)f(ot)60 1958 y(a)g(\014nite)h(set)g(of)f(p)n(erio)n(dic)f(r)n(efer)n(enc)n(e)h(c)n (on\014gur)n(ations)g FE(K)g FQ(=)f FE(f)p FF(!)p 1228 1965 V 1261 1940 a FH(\(1\))1308 1958 y FF(;)8 b(:)g(:)g(:)f(;)h(!)p 1417 1965 V 1449 1940 a FH(\()p FD(r)q FH(\))1496 1958 y FE(g)p FP(,)21 b(then)h(ther)n(e)f(exist)60 2018 y FF(\014)88 2025 y FH(0)121 2018 y FF(<)14 b FE(1)j FP(such)h(that)g(for)e(e)n(ach)i FF(\014)e FE(\025)e FF(\014)763 2025 y FH(0)133 2078 y FP(\(a\))j(A)o(l)r(l)i (the)g(pur)n(e)e(phases)g(ar)n(e)g(Gibbs)h(me)n(asur)n(es)f FF(\026)1096 2053 y FH(\()p FD(i)p FH(\))1096 2091 y FD(\014)1155 2078 y FP(de\014ne)n(d)i(by)e(the)i(b)n(oundary)e(c)n(onditions)60 2152 y FF(!)p 60 2159 V 92 2134 a FH(\()p FD(i)p FH(\))151 2152 y FP(with)h FF(F)296 2126 y FH(\()p FD(i)p FH(\))289 2164 y FD(\014)354 2152 y FP(b)n(eing)h(a)e FF(\034)548 2126 y FH(\()p FD(i)p FH(\))542 2164 y FD(\014)589 2152 y FP(-functional.)25 b(In)18 b(this)f(c)n(ase,)h FF(\034)1160 2126 y FH(\()p FD(i)p FH(\))1154 2164 y FD(\014)1215 2152 y FE(!)13 b(1)18 b FP(as)f FF(\014)f FE(!)e(1)p FP(.)133 2225 y(\(b\))g(Each)g(pur)n(e)g(phase)g FF(\026)594 2200 y FH(\()p FD(i)p FH(\))594 2238 y FD(\014)649 2225 y FP(is)g(c)n(onc)n(entr)n(ate)n(d)g(on)g(c)n(on\014gur)n(ations)h(with) f(\014nite)h(b)n(oundaries)f(and)60 2285 y(mor)n(e)n(over,)21 b(the)g(pr)n(ob)n(ability)f(that)h(a)g(given)h(b)n(oundary)e(b)n(e)i(pr)n (esent)f(tends)g(to)g(zer)n(o)f(as)h FF(\014)h FE(!)e(1)p FP(.)60 2346 y(Mor)n(e)c(pr)n(e)n(cisely,)i(if)f FQ(\000)d(=)g(\()p FF(M)r(;)8 b(!)661 2353 y FD(M)701 2346 y FQ(\))583 2471 y FF(\026)612 2446 y FH(\()p FD(i)p FH(\))612 2484 y FD(\014)654 2471 y FE(f)p FQ(\000)p FP(external)19 b(c)n(ontour)p FE(g)28 b(\024)f FF(e)1197 2448 y Fy(\000)p FD(\034)1244 2431 y Fr(\()p Fs(i)p Fr(\))1240 2461 y Fs(\014)1281 2448 y Fy(j)p FD(M)t Fy(j)1354 2471 y FF(:)387 b FQ(\(B)p FF(:)p FQ(53\))133 2585 y(This)23 b(theorem)f(w)o(as)h(pro)o(v)o(ed)f(b)o(y)h(Pirogo)o(v)g(and)h (Sinai)e(\(see)h(for)g(instance)g([328,)i(Prop)q(osi-)60 2645 y(tions)19 b(2.6)f(and)h(2.2]\),)g(except)e(for)i(the)f(w)o(ord)h(\\all")f (in)g(P)o(art)h(\(a\),)g(whic)o(h)f(w)o(as)g(incorp)q(orated)i(b)o(y)938 2784 y(229)p eop %%Page: 230 230 bop 60 91 a FQ(Zahradn)-5 b(\023)-19 b(\020k)13 b([366])f (\(\\completeness"\).)19 b(One)12 b(of)h(the)f(consequences)g(of)h(this)f (completeness)e(is)j(that)60 152 y(if)18 b(the)h(in)o(teraction)f(\010)h(has) h(a)f FP(unique)i FQ(p)q(erio)q(dic)e(ground-state)h(con\014guration,)h(and)e (it)g(satis\014es)60 212 y(the)g(P)o(eierls)e(condition,)i(then)g(there)f(is) h(also)h(a)f(unique)f(pure)h(phase)g(at)h(lo)o(w)e(temp)q(erature.)28 b(In)60 272 y(fact,)17 b(Martirosy)o(an)h([260])f(has)h(pro)o(v)o(en)f(that,) h(in)f(this)g(situation,)g(in)g FF(d)g FE(\025)e FQ(2)j(there)f(are)g(no)h (other)60 332 y(extremal)c(Gibbs)i(measures,)f(p)q(erio)q(dic)h(or)h(not.)133 392 y(The)i(parameters)e FF(\034)517 367 y FH(\()p FD(i)p FH(\))511 405 y FD(\014)577 392 y FQ(c)o(haracterizing)g(the)h(pure)g(phases)h(are)g (of)f(the)h(form)e(\(see)h(the)g(pro)q(of)60 452 y(of)f(Prop)q(osition)g(2.3) g(in)e([328)q(]\))534 570 y FF(\034)561 544 y FH(\()p FD(i)p FH(\))555 582 y FD(\014)630 570 y FE(\025)28 b FF(\014)s(\032)10 b FE(\000)h FF(\017)833 549 y FH(\()p FD(i)p FH(\))972 570 y FQ(with)16 b FF(\017)1103 549 y FH(\()p FD(i)p FH(\))1158 570 y FE(\024)e FQ(2)p FF(e)1258 547 y Fy(\000)p FD(\034)1305 529 y Fr(\()p Fs(i)p Fr(\))1301 559 y Fs(\014)1344 570 y FQ(3)1368 549 y FD(d)1402 570 y FF(;)339 b FQ(\(B)p FF(:)p FQ(54\))60 671 y(where)17 b FF(\032)g FQ(is)g(the)g(PS-constan)o(t)h(of)f(the)g(in)o (teraction)f(\010.)24 b(F)l(rom)16 b(this)h(expression)g(one)g(can)h(obtain) 60 731 y(some)c(\(far)i(from)f(optimal\))f(estimates)g(of)h(the)h(parameters) e(in)o(v)o(olv)o(ed.)19 b(Indeed,)14 b(for)i(example)d(w)o(e)60 792 y(can)j(c)o(ho)q(ose)872 852 y FF(\034)899 826 y FH(\()p FD(i)p FH(\))893 864 y FD(\014)968 852 y FQ(=)27 b FF(\034)1054 859 y FD(\014)1755 852 y FQ(\(B)p FF(:)p FQ(55\))60 935 y(with)16 b FF(\034)192 942 y FD(\014)232 935 y FQ(satisfying)755 996 y FF(\034)776 1003 y FD(\014)828 996 y FQ(=)27 b FF(\014)s(\032)11 b FE(\000)g FQ(2)p FF(e)1057 975 y Fy(\000)p FD(\034)1100 981 y Fs(\014)1123 996 y FQ(3)1147 975 y FD(d)1181 996 y FF(:)560 b FQ(\(B)p FF(:)p FQ(56\))60 1079 y(Then,)16 b(b)o(y)g(the)g(requiremen)n(t)e (\(B.52\))i(w)o(e)f(obtain)i(the)f(b)q(ound)744 1203 y FF(\034)765 1210 y FD(\014)816 1203 y FE(\025)28 b FF(\014)s(\032)10 b FE(\000)1015 1169 y FQ(1)p 1004 1191 47 2 v 1004 1237 a(2)p FF(e)1084 1203 y FE(\025)27 b FQ(4)p FF(\013)550 b FQ(\(B)p FF(:)p FQ(57\))60 1317 y(and)17 b(hence,)761 1402 y FF(\014)789 1409 y FH(0)836 1402 y FQ(=)907 1368 y(4)p FF(\013)12 b FQ(+)f(1)p FF(=)p FQ(\(2)p FF(e)p FQ(\))p 907 1391 250 2 v 1019 1436 a FF(\032)1175 1402 y(:)566 b FQ(\(B)p FF(:)p FQ(58\))60 1511 y(Note)16 b(that)h(as)f FF(\014)h FE(!)c(1)j FQ(one)h(also)g(obtains,)f(from) f(\(B.56\))750 1613 y FF(\034)771 1620 y FD(\014)823 1613 y FQ(=)27 b FF(\014)s(\032)11 b FQ(+)g FF(O)q FQ(\()p FF(e)1084 1592 y Fy(\000)p FD(\014)r(\032)1153 1613 y FQ(\))j FF(:)555 b FQ(\(B)p FF(:)p FQ(59\))133 1714 y(In)13 b(principle,)e(Theorem)g (B.27\(a\))i(pro)o(vides)f(a)i(criterion)d(for)i(the)g(stabilit)o(y)e(of)i(a) g(ground-state)60 1774 y(con\014guration,)j(but)g(it)g(is)f(quite)g(useless)g (for)h(practical)f(applications.)21 b(The)16 b(w)o(ork)g(of)g(Zahradn)-5 b(\023)-19 b(\020k)60 1835 y([366)q(,)14 b(369)r(])g(pro)o(vides)h(a)g (di\013eren)o(t)g(criterion)f(whic)o(h)g(could)h(b)q(e)g(emplo)o(y)o(ed)e (for)i(a)h(computer-based)60 1902 y(pro)q(cedure.)24 b(It)16 b(is)h(based)h(on)g(the)e(computation)h(of)g(the)g(pressure)1324 1898 y Fx(e)1319 1902 y FF(p)q FQ(\()p FF(F)1402 1876 y FH(\()p FD(i)p FH(\))1395 1914 y FD(\014)1443 1902 y FQ(\))g(for)g(the)g FF(!)p 1639 1909 33 2 v 1671 1883 a FH(\()p FD(i)p FH(\))1713 1902 y FQ(-con)o(tour)60 1962 y(ensem)o(ble)j(but)j(including)f(only)h FP(smal)r(l)g FQ(\(or)h(stable\))e(con)o(tours.)42 b(These)22 b(are)h(con)o(tours)g(whose)60 2022 y(in)o(terior)13 b(v)o(olume)f(is)i(at)h (most)e(prop)q(ortional)i(to)g(the)f(size)f(of)i(the)f(supp)q(ort.)22 b(A)o(t)13 b(lo)o(w)h(temp)q(erature,)60 2082 y(the)i(co)q(existing)g(pure)g (phases)h(are)f(those)h(minim)o(izi)o(ng)697 2184 y FF(h)725 2158 y FH(\()p FD(i)p FH(\))725 2196 y FD(\014)794 2184 y FE(\021)28 b FF(e)884 2191 y FH(\010)911 2184 y FQ(\()p FF(!)p 930 2191 V 962 2163 a FH(\()p FD(i)p FH(\))1003 2184 y FQ(\))12 b FE(\000)1088 2180 y Fx(e)1083 2184 y FF(p)q FQ(\()p FF(F)1166 2158 y FH(\()p FD(i)p FH(\))1159 2196 y FD(\014)1207 2184 y FQ(\))h FF(:)502 b FQ(\(B)p FF(:)p FQ(60\))60 2299 y(It)14 b(can)h(b)q(e)f(pro)o(v)o(en)g ([366)q(])g(that)644 2295 y Fx(e)639 2299 y FF(p)p FQ(\()p FF(F)721 2273 y FH(\()p FD(i)p FH(\))714 2311 y FD(\014)762 2299 y FQ(\))g FE(!)g FQ(0)g(as)i FF(\034)983 2273 y FH(\()p FD(i)p FH(\))977 2311 y FD(\014)1038 2299 y FE(!)d(1)i FQ(\(i.e.)d FF(\014)17 b FE(!)c(1)p FQ(\),)h(th)o(us)h(the)f(minimi)o(zing)60 2359 y(con\014gurations)22 b(are)f(ground)g(states.)35 b(Hence,)20 b(\(B.60\))g(means)g(that)h(the)f(stable)g(ground-state)60 2419 y(con\014gurations)e(are)f(those)h(maximi)o(zing)c(the)j(con)o (tour-ensem)o(ble)e(pressure;)i(that)g(is,)g(those)g(ad-)60 2479 y(mitting)g(the)h(larger)h(n)o(um)o(b)q(er)d(of)j(lo)o(w-energy)f(small) f(con)o(tours.)29 b(A)18 b(related)g(stabilit)o(y)f(criterion)60 2539 y(w)o(as)g(dev)o(elop)q(ed)f(b)o(y)g(Sla)o(wn)o(y)h([329],)f(emplo)o (ying)f(the)i FP(pr)n(essur)n(e)f(of)i(a)g(gas)g(of)g(elementary)h(excita-)60 2600 y(tions)e FQ(instead)f(of)h(the)f(con)o(tour-ensem)o(ble)e(pressure.)22 b(The)16 b(stable)g(phases)h(are)g(therefore)e(deter-)60 2660 y(mined)e(as)j(those)f(with)g(the)f(larger)h(n)o(um)o(b)q(er)e(of)i(lo)o (w-energy)g(excited)e(con\014gurations)k(\()p FP(dominant)938 2784 y FQ(230)p eop %%Page: 231 231 bop 60 91 a FP(gr)n(ound-state)22 b(c)n(on\014gur)n(ations)t FQ(\).)35 b(This)20 b(criterion)g(is)g(simpler)e(to)j(apply)g(for)f(pap)q (er-and-p)q(encil)60 152 y(calculations.)133 212 y(The)g(preceding)g(theorem) f(is)h(the)g(main)e(to)q(ol)j(used)g(to)f(pro)o(v)o(e)g(the)g(stabilit)o(y)f (of)h(the)g(whole)60 272 y(phase)d(diagram.)j(Let)d(us)f(denote)h FF(U)745 279 y FD(")763 272 y FQ(\()p 782 232 29 2 v FF(\025)810 242 y Fy(0)822 272 y FQ(\))d(=)g FE(f)p 932 232 V FF(\025)g FE(2)g Fq(R)1054 251 y FD(d)p Fy(\000)p FH(1)1128 272 y FQ(:)1158 239 y Fx(P)1202 252 y FD(r)q Fy(\000)p FH(1)1202 284 y FD(i)p FH(=1)1274 272 y FE(j)p FF(\025)1316 279 y FD(i)1342 272 y FE(\000)c FF(\025)1419 254 y Fy(0)1419 284 y FD(i)1434 272 y FE(j)k FF(<)f(")p FE(g)p FQ(.)60 374 y FM(Theorem)k(B.28)h(\(Pirogo)n (v-Sinai-Zahradn)-6 b(\023)-22 b(\020k\))23 b FP(Consider)14 b(a)g(\014nite-r)n(ange)j(p)n(erio)n(dic)c(inter-)60 434 y(action)25 b FQ(\010)250 441 y FH(0)295 434 y FP(in)g(dimension)g FF(d)i FE(\025)g FQ(2)d FP(such)h(that:)37 b(\(i\))24 b(it)h(has)f FF(r)k(<)f FE(1)e FP(p)n(erio)n(dic)e(gr)n(ound-state)60 494 y(c)n(on\014gur)n(ations)f(and)h(\(ii\))e(it)i(satis\014es)f(the)h(original)f (Peierls)h(c)n(ondition)f(\(B.38\).)36 b(Consider)22 b(a)60 554 y(p)n(erturb)n(ation)f FQ(\010)p 373 540 23 2 v 14 x FD(\025)438 554 y FQ(=)43 b(\010)554 561 y FH(0)588 554 y FQ(+)640 521 y Fx(P)683 534 y FD(r)q Fy(\000)p FH(1)683 566 y FD(i)p FH(=1)756 554 y FF(\025)784 561 y FD(i)798 554 y FQ(\010)833 561 y FD(i)848 554 y FP(,)22 b(with)g(e)n(ach)f FQ(\010)1143 561 y FD(i)1179 554 y FP(p)n(erio)n(dic)g(and)g(of)g(\014nite)i(r)n(ange,)g(that)60 614 y(c)n(ompletely)18 b(br)n(e)n(aks)e(the)g(de)n(gener)n(acy)h(of)g FQ(\010)856 621 y FH(0)876 614 y FP(.)22 b(Then)17 b(ther)n(e)f(exist)h(p)n (ositive)g(c)n(onstants)g FF(\014)1687 621 y FH(0)1706 614 y FP(,)g FF(")1761 621 y FH(0)1797 614 y FP(such)60 675 y(that)133 735 y(\(a\))22 b(F)l(or)g(e)n(ach)g FF(\014)j FE(\025)d FF(\014)572 742 y FH(0)613 735 y FP(ther)n(e)h(exists)f(a)h(nonempty)f(op)n(en)h(set)f FF(V)1381 742 y FD(\014)1428 735 y FE(\032)g Fq(R)1522 714 y FD(d)p Fy(\000)p FH(1)1610 735 y FP(such)g(that)h(for)60 795 y(p)n(ar)n(ameters)p 310 755 29 2 v 17 w FF(\025)17 b FE(2)f FF(V)432 802 y FD(\014)475 795 y FP(the)j(phase)f(diagr)n(am)g(at)h(inverse)g (temp)n(er)n(atur)n(e)f FF(\014)j FP(is)e FF(r)q FP(-r)n(e)n(gular.)26 b(F)l(or)18 b(e)n(ach)p 60 816 V 60 855 a FF(\025)26 b FE(2)f FF(V)200 862 y FD(\014)248 855 y FP(r)n(esults)f(\(a\))f(and)h(\(b\))g(of)f (The)n(or)n(em)g(B.27)g(hold)h(for)f(the)h(inter)n(action)h FQ(\010)p 1647 841 23 2 v 14 x FD(\025)1693 855 y FP(taking)g(as)60 915 y(r)n(efer)n(enc)n(e)17 b(c)n(on\014gur)n(ations)h(the)g(gr)n(ound-state) h(c)n(on\014gur)n(ations)f(of)f FQ(\010)1341 922 y FH(0)1361 915 y FP(.)133 976 y(\(b\))h(Mor)n(e)n(over,)e(ther)n(e)i(exists)g(an)g (invertible)h(map)783 1086 y FF(I)805 1093 y FD(\014)837 1086 y FQ(:)25 b FF(U)909 1093 y FD(")925 1098 y Fr(0)945 1086 y FQ(\()p 964 1048 25 2 v(0\))14 b FE(\000)-9 b(!)14 b FF(V)1143 1093 y FD(\014)1755 1086 y FQ(\(B)p FF(:)p FQ(61\))60 1196 y FP(\(the)21 b(\\underlying)h(deformation)f(of)g(the)g(p)n(ar)n(ameter)f(sp) n(ac)n(e")g([369]\),)h(which)h(maps)e(e)n(ach)h(zer)n(o-)60 1256 y(temp)n(er)n(atur)n(e)12 b(c)n(o)n(existenc)n(e)i(manifold)f(onto)g (the)g(c)n(orr)n(esp)n(onding)e(c)n(o)n(existenc)n(e)j(manifold)f(at)g (inverse)60 1316 y(temp)n(er)n(atur)n(e)19 b FF(\014)j FP(\(mor)n(e)d(gener)n (al)r(ly,)j(str)n(atum)e(onto)g(str)n(atum\).)29 b(The)20 b(map)g FF(I)1503 1323 y FD(\014)1546 1316 y FP(c)n(onver)n(ges)g(to)g(the)60 1376 y(identity)e(as)f FF(\014)f FE(!)e(1)p FP(.)22 b(In)c(fact,)g(it)f(is)h (an)f(home)n(omorphism,)f(and)i(even)h FF(C)1463 1358 y Fy(1)1500 1376 y FP(.)133 1436 y(\(c\))e(The)g(phase)g(diagr)n(am)f(deforms)h(analytic) n(al)r(ly)h(with)f(temp)n(er)n(atur)n(e)f(in)h(the)h(fol)r(lowing)h FQ(lo)q(cal)60 1501 y FP(sense:)j(Consider)14 b(a)g(p)n(oint)f FQ(\()p 589 1462 29 2 v FF(\025)618 1471 y Fy(0)629 1501 y FF(;)8 b(\014)682 1483 y Fy(0)693 1501 y FQ(\))14 b FP(of)g(the)g(phase)h (diagr)n(am,)e(with)i FE(j)p 1305 1462 V FF(\025)1333 1471 y Fy(0)1344 1501 y FE(j)f FF(<)g(")1447 1508 y FH(0)1480 1501 y FP(and)h FF(\014)1603 1483 y Fy(0)1628 1501 y FP(lar)n(ge)f(enough)60 1566 y([its)j(minimum)g(value)h(dep)n(ends)f(on)g(the)h(distanc)n(e)f(fr)n (om)p 1121 1526 V 16 w FF(\025)1149 1536 y Fy(0)1178 1566 y FP(to)g(the)g(c)n(omplement)h(of)f FF(U)1673 1573 y FD(")1689 1578 y Fr(0)1709 1566 y FQ(\()p 1728 1529 25 2 v(0\))p FP(].)22 b(L)n(et)60 1626 y FF(K)c FP(b)n(e)c(the)h(set)f(of)g(r)n(efer)n(enc)n(e)g(c) n(on\014gur)n(ations)g(giving)i(rise)e(to)g(the)g(pur)n(e)g(phases)f(for)h (the)g(inter)n(action)60 1686 y FQ(\010)p 95 1676 21 2 v 18 x FD(\025)116 1683 y Ft(0)147 1686 y FP(at)j(inverse)i(temp)n(er)n(atur)n(e)d FF(\014)670 1668 y Fy(0)681 1686 y FP(.)22 b(Then)c(ther)n(e)g(exists)g(an)g (analytic)g(function)859 1801 y FF(\014)30 b FE(7!)p 994 1761 29 2 v 27 w FF(\025)q FQ(\()p FF(\014)s FQ(\))663 b(\(B)p FF(:)p FQ(62\))60 1916 y FP(such)20 b(that)h(for)e FF(\014)j FP(close)f(to)g FF(\014)621 1897 y Fy(0)651 1916 y FP(and)p 749 1876 V 21 w FF(\025)p FQ(\()p FF(\014)s FQ(\))e FP(close)j(to)p 1049 1876 V 20 w FF(\025)1077 1886 y Fy(0)1089 1916 y FP(,)e(the)h(pur)n(e)e(phases)h (for)g(the)g(inter)n(actions)60 1976 y FQ(\010)p 95 1962 21 2 v 14 x FD(\025)p FH(\()p FD(\014)r FH(\))180 1976 y FP(at)14 b(inverse)g(temp)n(er)n(atur)n(e)f FF(\014)i FP(c)n(orr)n(esp)n(ond)d(to)i (the)g(same)f(set)h FF(K)k FP(of)13 b(r)n(efer)n(enc)n(e)h(c)n(on\014gur)n (ations.)133 2077 y FQ(Pirogo)o(v)22 b(and)g(Sinai)f(pro)o(v)o(ed)g(P)o(arts) h(\(a\))g(and)g(\(b\))g(of)f(the)h(theorem)e(except)g(for)i(the)f(com-)60 2138 y(pleteness)15 b(of)h(the)f(phase)h(diagram)f(and)h(the)f(homeomorphic)f (and)i FF(C)1366 2120 y Fy(1)1418 2138 y FQ(c)o(haracter)f(of)h FF(I)1707 2145 y FD(\014)1730 2138 y FQ(.)21 b(These)60 2198 y(additional)16 b(results)g(are)h(due)f(to)g(Zahradn)-5 b(\023)-19 b(\020k)17 b([366,)f(369)q(],)g(who)h(also)g(pro)o(v)o(ed)e(P)o(art)i(\(c\))e ([368)q(].)133 2258 y(As)i(remark)o(ed)e(in)h([369)q(],)g(maps)g(other)h (than)g(\(B.62\))g(need)g(not)g(b)q(e)g(analytic.)22 b(In)17 b(particular,)60 2318 y(the)i(\()p FF(\014)s FQ(-dep)q(enden)o(t\))g(maps)g FF(V)630 2325 y FD(\014)674 2318 y FE(!)g FF(@)s(Q)811 2325 y FD(r)849 2318 y FQ(establishing)g(the)h(regularit)o(y)e(of)i(the)f(phase)i (diagram)60 2378 y(at)g(in)o(v)o(erse)e(temp)q(erature)g FF(\014)k FQ(are,)f(in)e(general,)h FP(not)h FQ(analytic.)34 b(Suc)o(h)20 b(a)h(map)f(can)h(b)q(e)g(de\014ned,)60 2439 y(for)g(example)e([366)q(,)i (369)q(],)h(analogously)g(to)g(the)f(zero-temp)q(erature)e(map)i (\(B.32\){\(B.33\))g(but)60 2506 y(replacing)16 b FF(e)292 2513 y FH(\010)p 317 2505 V 14 x Fs(\025)339 2506 y FQ(\()p FF(\026)387 2513 y FD(i)402 2506 y FQ(\))g(b)o(y)g FF(h)533 2480 y FH(\()p FD(i)p FH(\))533 2518 y FD(\014)590 2506 y FQ([see)g (\(B.60\)]:)p 366 2592 29 2 v 366 2631 a FF(\025)e FE(7\000)-8 b(!)502 2583 y Fx(\020)527 2631 y FF(h)555 2606 y FH(\(1\))555 2644 y FD(\014)602 2631 y FQ(\()p 621 2592 V FF(\025)q FQ(\))11 b FE(\000)21 b FQ(min)729 2661 y FH(1)p Fy(\024)p FD(i)p Fy(\024)p FD(r)839 2631 y FF(h)867 2606 y FH(\()p FD(i)p FH(\))867 2644 y FD(\014)909 2631 y FQ(\()p 928 2592 V FF(\025)p FQ(\))p FF(;)8 b(:)g(:)g(:)g(;)g(h)1113 2606 y FH(\()p FD(r)q FH(\))1113 2644 y FD(\014)1159 2631 y FQ(\()p 1178 2592 V FF(\025)p FQ(\))j FE(\000)21 b FQ(min)1286 2661 y FH(1)p Fy(\024)p FD(i)p Fy(\024)p FD(r)1396 2631 y FF(h)1424 2606 y FH(\()p FD(i)p FH(\))1424 2644 y FD(\014)1466 2631 y FQ(\()p 1485 2592 V FF(\025)p FQ(\))1532 2583 y Fx(\021)1571 2631 y FF(:)170 b FQ(\(B)p FF(:)p FQ(63\))938 2784 y(231)p eop %%Page: 232 232 bop 60 93 a FQ([In)19 b(the)h(original)g(PS)g(form)o(ulation,)f(the)h (parameters)f FF(b)1132 75 y FH(\()p FD(i)p FH(\))1193 93 y FQ(pla)o(y)o(ed)g(the)h(role)g(of)g(the)g FF(h)1712 75 y FH(\()p FD(i)p FH(\))1773 93 y FQ(here.])60 153 y(Suc)o(h)e(a)h(map)e(is)h(in)g (general)g(not)h(analytic)f(b)q(ecause)h(if)e(it)h(w)o(ere)g(it)g(w)o(ould)g (imply)e(that)j(the)f(free)60 213 y(energy)k(of)i(a)f(pure)f(phase)i(could)f (b)q(e)f(analytically)g(con)o(tin)o(ued)g(in)p 1363 174 29 2 v 22 w FF(\025)i FQ(in)o(to)e(the)h(metastabilit)o(y)60 273 y(region;)17 b(and)h(already)f(for)g(the)g(Ising)g(mo)q(del)f(it)h(has)g(b)q (een)g(sho)o(wn)h([204)q(])f(that)g(suc)o(h)g(an)h(analytic)60 334 y(metastable)e(extension)g(do)q(es)i(not)f(exist.)22 b(On)17 b(the)g(other)g(hand,)h(the)e(map)g(\(B.63\))h(is)g(of)g(limited)60 394 y(ph)o(ysical)22 b(signi\014cance,)h(b)q(ecause)g(for)g FF(!)p 801 401 33 2 v 833 376 a FH(\()p FD(i)p FH(\))897 394 y FQ(not)g(de\014ning)g(a)g(pure)f(phase,)j(the)d(corresp)q(onding)60 454 y(quan)o(tit)o(y)f FF(h)289 436 y FH(\()p FD(i)p FH(\))330 454 y FQ(\()p 349 414 29 2 v FF(\025)q FQ(\))h(is)f(only)h(an)g(auxiliary)f (concept,)i(not)f(ev)o(en)f(uniquely)f(de\014ned)i([369].)38 b(The)60 514 y(ph)o(ysically)15 b(in)o(teresting)g(ob)s(jects)h(are)g(the)g (strata)684 621 y FF(S)714 628 y FD(K)748 621 y FQ(\()p FF(\014)s FQ(\))27 b(=)h FE(f)p 935 582 V FF(\025)9 b FQ(:)16 b FF(Q)1041 628 y FD(\014)1064 621 y FQ(\()p 1083 582 V FF(\025)p FQ(\))e(=)g FF(K)t FE(g)489 b FQ(\(B)p FF(:)p FQ(64\))60 728 y(for)17 b(eac)o(h)e FF(K)j FE(\032)c(K)q FQ(,)h(where)567 835 y FF(Q)606 842 y FD(\014)630 835 y FQ(\()p 649 796 V FF(\025)p FQ(\))28 b(=)789 787 y Fx(n)817 835 y FF(i)8 b FQ(:)16 b FF(h)900 810 y FH(\()p FD(i)p FH(\))900 848 y FD(\014)942 835 y FQ(\()p 961 796 V FF(\025)p FQ(\))e(=)26 b(min)1074 865 y FH(1)p Fy(\024)p FD(j)r Fy(\024)p FD(r)1187 835 y FF(h)1215 810 y FH(\()p FD(j)r FH(\))1215 848 y FD(\014)1261 835 y FQ(\()p 1280 796 V FF(\025)q FQ(\))1328 787 y Fx(o)1369 835 y FF(:)372 b FQ(\(B)p FF(:)p FQ(65\))60 964 y(These)11 b(strata)i(deform)d(\(lo)q(cally\))g(analytically)g(with)i (the)f(temp)q(erature,)f(b)o(y)h(P)o(art)h(\(c\))f(of)g(Theorem)60 1024 y(B.28.)133 1084 y(Non-optimal)22 b(estimations)f(of)i(the)f(limit)e(v)m (alues)j FF(\014)1142 1091 y FH(0)1184 1084 y FQ(and)g FF(")1308 1091 y FH(0)1350 1084 y FQ(of)g(Theorem)f(B.28)g(can)h(b)q(e)60 1144 y(obtained)d(com)o(bining)f(Corollary)h(B.26)g(with)g(\(B.58\):)29 b(If)20 b(\010)1220 1151 y FH(0)1260 1144 y FQ(satis\014es)h(the)f(P)o (eierls)e(condition)60 1204 y(with)e(constan)o(t)h FF(\032)393 1211 y FH(0)413 1204 y FQ(,)f(then)g(at)g(most)775 1336 y FF(\014)803 1343 y FH(0)850 1336 y FQ(=)921 1303 y(4)p FF(\013)11 b FQ(+)g(1)p FF(=)p FQ(\(2)p FF(e)p FQ(\))p 921 1325 250 2 v 939 1370 a FF(\032)964 1377 y FH(0)983 1370 y FQ(\(1)h FE(\000)f FQ(2)p FF(c)p FQ(\))1755 1336 y(\(B)p FF(:)p FQ(66\))60 1469 y(if)16 b(at)g(least)792 1529 y FF(")815 1536 y FH(0)862 1529 y FQ(=)996 1495 y FF(c\032)1042 1502 y FH(0)p 933 1517 193 2 v 933 1563 a FQ(\(2)p FF(a)11 b FQ(+)g(1\))1105 1549 y FD(d)1144 1529 y FF(:)597 b FQ(\(B)p FF(:)p FQ(67\))60 1640 y(These)20 b(b)q(ounds)h(are)f (an)g(explicit)e(example)g(of)i(a)g(general)g(fact)f(ab)q(out)j(the)d(pro)q (of)i(of)f(Theorem)60 1700 y(B.28.)34 b(As)21 b(all)f(the)g(results)h(follo)o (w)f(from)f(studying)i(the)g(equiv)m(alen)o(t)e(con)o(tour)h(ensem)o(bles,)f (the)60 1760 y(relev)m(an)o(t)d(magnitudes)g(are)i(those)f(actually)f(used)i (to)f(construct)g(these)g(ensem)o(bles:)k(the)c(P)o(eierls)60 1820 y(constan)o(t)j FF(\032)285 1827 y FH(0)324 1820 y FQ(and)g(the)f(exp)q (onen)o(tial)f(en)o(trop)o(y)h(factor)h FF(\013)p FQ(.)30 b(In)19 b(addition,)h(the)f(dimension)f FF(d)h FQ(and)60 1881 y(the)14 b(size)e FF(a)i FQ(of)g(the)g(sampling)e(cub)q(es)i(app)q(ear)h(via)e(the)h (uniformit)o(y)d(prop)q(ert)o(y)l(.)21 b(As)13 b(a)h(consequence,)60 1941 y(w)o(e)i(ha)o(v)o(e:)60 2040 y FM(Corollary)i(B.29)24 b FP(Consider)18 b(a)g FQ(family)f FP(of)h(original)h(inter)n(actions)g FE(f)p FQ(\010)1415 2047 y FH(0)1435 2040 y FQ(\()p 1454 2014 25 2 v FF(p)p FQ(\))p FE(g)p 1522 2035 18 2 v 15 x FD(p)p Fy(2)p FD(P)5 b Fy(\032)p Fl(R)1641 2045 y Fs(m)1691 2040 y FP(satisfying)60 2100 y(the)13 b(Peierls)g(c)n(ondition)g FQ(uniformly)e FP(that)h(is,)i(with) e(the)h(same)g(c)n(onstant)g FF(\032)1389 2107 y FH(0)1422 2100 y FP(and)f(the)h(same)g(family)f(of)60 2160 y(p)n(erio)n(dic)i(gr)n (ound-state)i(c)n(on\014gur)n(ations)f FE(K)h FP(for)e(al)r(l)p 1022 2134 25 2 v 17 w FF(p)g FE(2)g FF(P)22 b FP(\(e.g.)16 b(in)f(the)h(c)n(onditions)f(of)g(Cor)n(ol)r(lary)60 2221 y(B.25\).)21 b(Then)15 b(The)n(or)n(em)e(B.28)i(holds)f(also)g(uniformly)h(for)e(al)r(l)j (the)f(inter)n(actions)g FQ(\010)1607 2228 y FH(0)1627 2221 y FQ(\()p 1646 2194 V FF(p)p FQ(\))f FP([i.e.,)h(one)60 2281 y(c)n(an)k(chose)f(the)h(same)g FF(\014)519 2288 y FH(0)556 2281 y FP(and)g FF(")675 2288 y FH(0)713 2281 y FP(in)f(Parts)g(\(a\))g(and)h (\(b\),)f(and)h(the)g(same)f FF(\014)s FP(-)g(and)p 1645 2241 29 2 v 19 w FF(\025)p FP(-)h(intervals)60 2341 y(in)f(Part)f(\(c\)].)133 2440 y FQ(More)j(generally)l(,)g(Theorem)f(B.28)i(can)f(b)q(e)h(extended)e (to)i(situations)g(in)f(whic)o(h)g(there)f(is)i(a)60 2500 y(further)16 b(smo)q(oth)g(dep)q(endence)g(of)g(the)g(in)o(teractions)g(on)h(the)f(extra)g (parameters)p 1592 2474 25 2 v 15 w FF(p)p FQ(.)60 2600 y FM(Theorem)h(B.30) 23 b FP(Assume)i FF(d)i FE(\025)f FQ(2)f FP(and)f(c)n(onsider)h(inter)n (actions)f FQ(\010)1397 2607 y FH(0)1417 2600 y FQ(\()p 1436 2573 V FF(p)q FQ(\))p FF(;)8 b FQ(\010)1537 2607 y FH(1)1557 2600 y FQ(\()p 1576 2573 V FF(p)p FQ(\))p FF(;)g(:)g(:)g(:)f(;)h FQ(\010)1763 2607 y FD(r)q Fy(\000)p FH(1)1828 2600 y FQ(\()p 1847 2573 V FF(p)p FQ(\))60 2660 y FP(dep)n(ending)17 b(analytic)n(al)r(ly)g (on)f(p)n(ar)n(ameters)p 856 2633 V 14 w FF(p)g FP(taking)h(values)g(on)f(an) g(op)n(en)g(set)g FF(P)21 b FE(\032)13 b Fq(R)1645 2639 y FD(m)1678 2660 y FP(,)j(and)g(with)938 2784 y FQ(232)p eop %%Page: 233 233 bop 60 91 a FP(b)n(ounde)n(d)18 b(p)n(erio)n(d)e(and)i(r)n(ange.)24 b(Assume)18 b(that)g(ther)n(e)g(exists)g(a)p 1220 65 25 2 v 18 w FF(p)1244 103 y FH(0)1278 91 y FE(2)d FF(P)25 b FP(such)18 b(that)g(\(i\))f FQ(\010)1700 98 y FH(0)1720 91 y FQ(\()p 1739 65 V FF(p)1764 103 y FH(0)1784 91 y FQ(\))g FP(has)60 152 y FF(r)e(<)f FE(1)h FP(p)n(erio)n(dic)f(gr)n(ound-state)h(c)n(on\014gur)n (ations)h(and)f(\(ii\))g FQ(\010)1191 159 y FH(0)1211 152 y FQ(\()p 1230 125 V FF(p)1254 163 y FH(0)1274 152 y FQ(\))g FP(satis\014es)g(the)h(original)f(Peierls)60 212 y(c)n(ondition)j(\(B.38\).)k (Assume)17 b(also)h(that)f(for)g(e)n(ach)p 1016 185 V 17 w FF(p)d FE(2)g FF(P)24 b FP(the)18 b(p)n(erturb)n(ation)f FQ(\010)p 1546 198 23 2 v 14 x FD(\025)1569 212 y FQ(\()p 1588 185 25 2 v FF(p)p FQ(\))28 b(=)f(\010)1759 219 y FH(0)1779 212 y FQ(\()p 1798 185 V FF(p)q FQ(\))10 b(+)60 239 y Fx(P)104 252 y FD(r)q Fy(\000)p FH(1)104 284 y FD(i)p FH(=1)176 272 y FF(\025)204 279 y FD(i)219 272 y FQ(\010)254 279 y FD(i)268 272 y FQ(\()p 287 245 V FF(p)p FQ(\))15 b FP(c)n(ompletely)h(br)n(e)n(aks)e(the)h(de)n (gener)n(acy)g(of)f FQ(\010)1131 279 y FH(0)1151 272 y FQ(\()p 1170 245 V FF(p)p FQ(\))p FP(.)22 b(Denote)p 1414 232 31 2 v 15 w FF(\014)16 b FE(\021)e FQ(\()p FF(\014)s(;)p 1583 245 25 2 v 8 w(p)p FQ(\))p FP(.)21 b(Then)15 b(ther)n(e)60 332 y(exist)j(p)n(ositive)f(c)n(onstants)h FF(\014)590 339 y FH(0)609 332 y FP(,)g FF(")665 339 y FH(0)701 332 y FP(and)g FF(")819 339 y FH(1)855 332 y FP(such)g(that)f(the)h(r)n(esults)f(\(a\),)g(\(b\))g (and)h(\(c\))f(of)g(The)n(or)n(em)60 392 y(B.28)g(hold)h(r)n(eplacing)g FF(\014)i FP(by)p 600 353 31 2 v 18 w FF(\014)f FP(and)f(the)g(c)n(ondition)g (\\)p FF(\014)e FE(\025)e FF(\014)1186 399 y FH(0)1205 392 y FP(")j(by)h(\\)p FF(\014)e FE(\025)d FF(\014)1460 399 y FH(0)1480 392 y FF(;)8 b FE(j)p 1516 366 25 2 v FF(p)j FE(\000)p 1601 366 V 11 w FF(p)1625 404 y FH(0)1645 392 y FE(j)i(\024)h FF(")1748 399 y FH(1)1768 392 y FP(".)60 494 y FQ(There)i(are)g(no)h(simple)d(explicit) g(form)o(ulas)h(for)i(the)f(v)m(alues)g FF(\014)1204 501 y FH(0)1223 494 y FQ(,)g FF(")1276 501 y FH(0)1312 494 y FQ(and)h FF(")1430 501 y FH(1)1449 494 y FQ(.)133 579 y(As)e(men)o(tioned)d(at)j(the)g (end)f(of)h(the)g(preceding)f(Section)g(B.4.2,)g(the)g(theory)h(can)f(b)q(e)h (adapted)60 639 y(to)22 b(sligh)o(tly)e(more)g(general)h(notions)h(of)f(con)o (tours.)37 b(In)21 b(particular)g(it)g(applies)g(for)g(the)h(\\thin")60 699 y(\(p)q(olyhedral-lik)o(e\))e(con)o(tours)j(of)f(mo)q(dels)f(with)h (constan)o(t)g(ground-state)i(con\014gurations)f(\(e.g.)60 760 y(the)17 b(ferromagnetic)g(Ising)g(mo)q(del,)f(Blume-Cap)q(el)g(mo)q (dels,)h(etc\).)25 b(Suc)o(h)17 b(con)o(tours)h(pro)o(vide)f(the)60 820 y(b)q(est)k(\(largest\))g(estimate)e(of)i FF(\032)654 827 y FH(0)694 820 y FQ(\(e.g.)f(for)h(Ising)g(mo)q(dels)e FF(\032)1202 827 y FH(0)1244 820 y FQ(=)i(2)p FF(J)5 b FQ(\),)21 b(and)h(ha)o(v)o(e)d(and) j(en)o(trop)o(y)60 880 y(gro)o(wth)17 b(with)f(an)h(exp)q(onen)o(tial)e (factor)i(b)q(ounded)g(b)o(y)f(\(see,)f(for)i(instance,)e([169)q(]\))753 990 y FF(\013)784 997 y Fr(thin)868 990 y FQ(=)28 b(log)q(\(2)p FF(d)12 b FE(\000)e FQ(1\))15 b FF(:)557 b FQ(\(B)p FF(:)p FQ(68\))60 1100 y(This)14 b(b)q(ound)i(is)e(smaller)e(than)j(\(B.51\),)f(and) g(therefore)g(yields)f(another)i(source)f(of)h(impro)o(v)o(em)o(e)o(n)o(t)60 1160 y(on)k(the)e(estimates)g(of)h FF(\014)517 1167 y FH(0)555 1160 y FQ(in)g(\(B.58\))f(or)i(\(B.66\).)27 b(Moreo)o(v)o(er,)17 b(in)g(the)h(b)q(ound)h(\(B.67\))f(for)h FF(")1783 1167 y FH(0)1802 1160 y FQ(,)f(w)o(e)60 1220 y(can)e(use)h(2)p FF(a)30 b FQ(=)16 b(range)h(of)f(the)g(p)q(erturbation)926 1187 y Fx(P)978 1220 y FF(\025)1006 1227 y FD(i)1021 1220 y FQ(\010)1056 1227 y FD(i)1070 1220 y FQ(;)g(whic)o(h)g(is)g(the)g(minim)o(al)d(p)q(ossible)k(c)o (hoice.)60 1350 y FM(B.4.4)55 b(Extensions)18 b(of)g(the)h(Theory)-5 b(.)23 b(The)c(Random)f(Case)60 1443 y FQ(Pirogo)o(v-Sinai)c(theory)f(has)h (b)q(een)g(extended)e(in)h(sev)o(eral)f(directions.)20 b(F)l(or)14 b(example,)d(w)o(e)i(men)o(tion)60 1503 y(the)j(extensions)h(to)g(systems)e (with)i(long-range)h([287,)f(288)q(],)f(quasip)q(erio)q(dic)g([221)q(])g(and) h(complex)60 1563 y([21,)i(295)q(,)f(368)q(,)h(35])g(in)o(teractions;)f (systems)g(with)g(con)o(tin)o(uous)h(spins)g([97,)g(367)q(];)g(systems)e(on)j (a)60 1623 y(con)o(tin)o(uous)h(space)h([45,)f(46)q(];)i(\014eld-theoretical) d(systems)g([202,)h(203)q(,)g(35)q(];)i(and)f(systems)e(with)60 1683 y(in\014nitely)e(man)o(y)g(p)q(erio)q(dic)i(ground-state)h (con\014gurations)g([46)q(,)e(47)q(,)g(80)q(,)g(79)q(,)g(77)q(,)h(179)q(,)f (78)q(,)g(48)q(].)60 1744 y(Among)11 b(these)g(are)h(mo)q(dels)f(with)h (energy)f(cost)h(gro)o(wing)g(slo)o(w)o(er)g(than)g(the)f(area)i(of)f(the)f (b)q(oundary)l(,)60 1804 y(suc)o(h)h(as)g(the)g(balanced)g(mo)q(del)f([132)q (,)g(48)q(])h(and)g(the)g(ANNNI)e(mo)q(del)h([48,)i(and)f(references)f (therein].)60 1864 y(Also)18 b(w)o(orth)g(men)o(tioning)e(are)h(the)h (applications)g(to)g(the)f(study)h(of)h(in)o(terfaces)d([367)q(,)h(369)q(,)h (194)q(],)60 1924 y(random)e(surfaces)g([261)q(])g(and)h(\014nite-size)e (scaling)h([36].)133 1984 y(These)j(extensions)g(generalize)e(the)i(theory)g (c)o(hie\015y)e(in)i(t)o(w)o(o)g(directions.)29 b(First,)18 b(ensem)o(bles)60 2045 y(of)k FP(inter)n(acting)h FQ(con)o(tours)f(are)g(in)o (tro)q(duced)f([202)q(,)g(203)r(,)g(21)q(,)g(46)q(,)g(79)q(,)g(77)q(,)g(287)q (,)h(288)q(,)f(48)q(].)37 b(The)60 2105 y(in)o(teraction)17 b(among)i(con)o(tours)g(\(on)f(top)h(of)g(v)o(olume)d(exclusion\))i(m)o(ust)f (b)q(e)h(w)o(eak,)g(to)h(allo)o(w)f(the)60 2165 y(con)o(v)o(ergence)h(of)h (the)g(cluster)f(expansions.)34 b(Second,)21 b(the)f(set)g(of)g(reference)f (con\014gurations)i(is)60 2225 y(replaced)h(b)o(y)g(a)h(set)f(of)h FP(r)n(efer)n(enc)n(e)g(me)n(asur)n(es)p FQ(.)40 b(These)22 b(can)h(b)q(e)g(supp)q(orted)g(on)g(whole)g(classes)60 2285 y(of)e(ground-state)h(con\014gurations)g([179)q(])e(or,)i(more)e(generally)l (,)g(on)h(families)e(of)i(con\014gurations)60 2346 y(|)d FP(r)n(estricte)n(d) h(ensembles)25 b FQ(|)18 b(suitably)g(c)o(hosen)g(so)h(as)g(to)g(include)e (en)o(trop)o(y)h(con)o(tributions.)27 b(In)60 2406 y(man)o(y)13 b(cases,)i(these)g(restricted)f(ensem)o(bles)e(are)j(formed)f(b)o(y)g(lo)o (w-energy)h(excitations)f(of)h(ground)60 2466 y(states)23 b([80,)g(79,)g(77,) f(78)q(,)g(48)q(,)g(261)q(],)i(but)f(other)f(de\014nitions)h(are)f(in)h (principle)d(p)q(ossible.)41 b(F)l(or)60 2526 y(instance,)24 b(the)e(ensem)o(ble)f(for)i(the)f(disordered)h(phase)g(of)h(the)e(large-)p FF(q)j FQ(P)o(otts)e(mo)q(del)f(|)g(and)60 2586 y(for)f(other)g(examples)e(p) q(ertaining)i(to)h(the)e(study)i(of)f(liquid-gas)g(phase)g(transitions)h ([46])e(|)h(is)60 2646 y(supp)q(orted)g(on)f(\\maximally)d(disordered")j (con\014gurations)h([46].)32 b(The)20 b(latter)g(corresp)q(onds)h(to)938 2784 y(233)p eop %%Page: 234 234 bop 60 91 a FQ(a)19 b(\\pure-en)o(trop)o(y")g(restricted)e(ensem)o(ble)f ([46],)i(as)h(opp)q(osed)h(to)f(the)f(\\pure-energy")h(\(just)g(one)60 152 y(ground)k(state)f(con\014guration\))g(or)g(\\almost-pure-energy")g (\(ground)g(state)g(plus)g(excitations\))60 212 y(used)16 b(in)g(most)g(of)h (the)f(applications.)21 b(In)16 b(general,)g(the)g(restricted)f(ensem)o(bles) f(are)i(c)o(hosen)h(so)g(to)60 272 y(ha)o(v)o(e)c(minim)o(al)e (\(restricted\))i FP(fr)n(e)n(e)g FQ(energy)g(at)h(the)g(temp)q(erature)e(of) i(in)o(terest.)20 b(Often,)13 b(in)o(teracting)60 332 y(con)o(tours)18 b(and)h(reference)d(measures)h(are)h(alternativ)o(e)f(pro)q(cedures;)i(it)e (is)h(a)g(matter)f(of)h(taste)h(to)60 392 y(c)o(ho)q(ose)e(one)f(or)h(the)f (other.)133 452 y(A)e(third)f(direction)g(in)h(whic)o(h)f(PS)h(theory)g(has)g (b)q(een)g(extended)f(|)h(and)g(one)g(whic)o(h)f(is)h(crucial)60 513 y(for)k(our)g(application)g(to)g(the)g(pro)q(of)g(of)h(R)o(G)e (pathologies)i(in)e(nonzero)h(magnetic)e(\014eld)i(\(Section)60 573 y(4.3.6\))e(|)g(is)g(to)o(w)o(ards)g(the)g(incorp)q(oration)h(of)f (random)g(in)o(teractions.)k(In)c(w)o(ork)g(unpublished)f(so)60 633 y(far,)d(Zahradn)-5 b(\023)-19 b(\020k)11 b([370)q(,)g(371)q(])g(|)g (generalizing)f(the)h(w)o(ork)h(of)f(Bricmon)o(t)e(and)j(Kupiainen)e([43)q(,) h(44])g(|)60 693 y(has)22 b(pro)o(v)o(en)f(that)h(for)g FF(d)i FE(\025)f FQ(3)f(the)f(addition)h(of)g(a)g(small)e(enough)i(random)g(in)o (teraction)e(only)60 753 y(pro)q(duces)15 b(small)e(deformations)h(in)g(the)h (phase)g(diagram.)20 b(An)14 b(imp)q(ortan)o(t)g(issue)g(is)h(the)f(meaning) 60 814 y(of)j(\\small)e(enough".)23 b(In)17 b(the)f(original)g(w)o(ork)h ([370)q(],)e(the)i(random)f(in)o(teraction)f(w)o(as)i(required)f(to)60 874 y(b)q(e)g(uniformly)e(small)g(resp)q(ect)i(to)g(the)g(nonrandom)g(part.) 21 b(Later)c(w)o(e)e(w)o(ere)g(informed)f([371)q(])i(that)60 934 y(the)h(pro)q(of)g(also)h(applies)e(to)h(random)g(con)o(tributions)f (that)i(are)f(small)e FP(in)j(pr)n(ob)n(ability)p FQ(.)k(W)l(e)17 b(state)60 994 y(the)f(later)g(v)o(ersion,)f(whic)o(h)g(is)i(the)f(one)g (suited)g(to)g(our)h(applications.)60 1096 y FM(Theorem)g(B.31)23 b FP(Consider)h(the)g(lattic)n(e)h Fq(Z)915 1075 y FD(d)935 1096 y FP(,)g FF(d)h FE(\025)f FQ(3)p FP(,)h(and)d(an)h(inter)n(action)h FQ(\010)p 1620 1082 23 2 v 14 x FD(\025)1693 1096 y FQ(=)50 b(\010)1816 1103 y FH(0)1852 1096 y FQ(+)60 1123 y Fx(P)104 1136 y FD(r)q Fy(\000)p FH(1)104 1168 y FD(i)p FH(=1)176 1156 y FF(\025)204 1163 y FD(i)219 1156 y FQ(\010)254 1163 y FD(i)289 1156 y FP(satisfying)20 b(the)h(hyp)n(othesis)f(of)h(The)n(or)n(em)e(B.28.)32 b(A)n(dd)20 b(a)g(\014nite-r)n(ange)j(r)n(andom)c(in-)60 1222 y(ter)n(action)g FQ(\010)301 1204 y Fr(rdom)387 1222 y FQ(=)440 1174 y Fx(n)468 1222 y FQ(\010)503 1204 y Fr(rdom)503 1235 y FD(A)574 1222 y FQ(\()8 b FE(\001)g FF(;)g(\024)p FQ(\))692 1174 y Fx(o)720 1249 y FD(A)p Fy(2S)796 1222 y FP(,)18 b(wher)n(e)g FF(\024)g FP(is)g(a)h(r)n(andom)e(variable)i(with)f(pr)n(ob)n(ability)g(dis-) 60 1293 y(tribution)h FF(P)7 b FP(,)18 b(such)h(that)f(the)h(r)n(andom)e (variables)i FQ(\010)1043 1275 y Fr(rdom)1043 1305 y FD(A)1114 1293 y FQ(\()8 b FE(\001)g FF(;)g(\024)p FQ(\))19 b FP(and)f FQ(\010)1381 1275 y Fr(rdom)1381 1305 y FD(A)1407 1296 y Ft(0)1452 1293 y FQ(\()8 b FE(\001)g FF(;)g(\024)p FQ(\))19 b FP(have)f(the)h(same)60 1353 y(distribution)j(if)g FF(A)414 1335 y Fy(0)448 1353 y FP(is)f(a)h(tr)n(anslate)h(of)f FF(A)f FP(and)h(ar)n(e)g(indep)n(endent)i(if) d FF(A)14 b FE(\\)h FF(A)1525 1335 y Fy(0)1559 1353 y FQ(=)22 b Fq(?)p FP(.)36 b(Assume,)60 1413 y(in)19 b(addition,)h(the)g(fol)r(lowing)h (smal)r(lness)g(c)n(ondition:)26 b(F)l(or)19 b(e)n(ach)g FF(\016)f(>)f FQ(0)j FP(ther)n(e)f(exists)h FF(\017)p FQ(\()p FF(\016)r FQ(\))e FP(smal)r(l)60 1474 y(enough)h(such)e(that)709 1534 y FF(P)7 b FQ(\()p FE(j)p FQ(\010)815 1513 y Fr(rdom)815 1546 y FD(A)886 1534 y FQ(\()p FF(!)r(;)h(\024)p FQ(\))p FE(j)13 b FF(>)h(\016)r FQ(\))27 b FE(\024)h FF(\017)513 b FQ(\(B)p FF(:)p FQ(69\))60 1621 y FP(for)23 b(al)r(l)i FF(A)g FE(2)h(S)t FP(,)f FF(!)i FE(2)f FQ(\012)p FP(.)41 b(Then,)26 b(for)d FF(\014)j FP(lar)n(ge)e(enough)h (the)f(phase)g(diagr)n(ams)e(for)h FQ(\010)p 1766 1607 V 14 x FD(\025)1813 1621 y FP(and)60 1681 y FQ(\010)p 95 1667 V 14 x FD(\025)126 1681 y FQ(+)8 b(\010)207 1663 y Fr(rdom)294 1681 y FP(ar)n(e)15 b(home)n(omorphic.)21 b(Mor)n(e)15 b(pr)n(e)n(cisely,)h (for)f FF(\014)k FP(lar)n(ge)d(and)g FF(\017)g FP(uniformly)g(smal)r(l,)h (ther)n(e)60 1741 y(exists)h(an)g(home)n(omorphism)783 1801 y FF(L)816 1808 y FD(\014)r(;\017)872 1801 y FQ(:)j FF(V)947 1781 y Fy(0)935 1814 y FD(\014)r(;\017)997 1801 y FE(\000)-8 b(!)13 b FF(V)1131 1781 y Fy(00)1119 1814 y FD(\014)r(;\017)1755 1801 y FQ(\(B)p FF(:)p FQ(70\))60 1894 y FP(b)n(etwe)n(en)22 b(two)e(op)n(en)g(sets)g FF(V)588 1876 y Fy(0)577 1906 y FD(\014)r(;\017)625 1894 y FF(;)8 b(V)686 1876 y Fy(00)675 1906 y FD(\014)r(;\017)741 1894 y FE(\032)19 b Fq(R)832 1873 y FD(r)q Fy(\000)p FH(1)916 1894 y FP(mapping)h(an)g FF(r)q FP(-r)n(e)n(gular)g FQ(\010)p 1427 1880 V 14 x FD(\025)1470 1894 y FP(phase)g(diagr)n(am)f(onto)60 1954 y(an)e FF(r)q FP(-r)n(e)n(gular)g FQ(\010)p 366 1940 V 14 x FD(\025)397 1954 y FQ(+)9 b(\010)479 1936 y Fr(rdom)567 1954 y FP(phase)17 b(diagr)n(am.)k(The)16 b(home)n(omorphism)f FF(L)1400 1961 y FD(\014)r(;\017)1464 1954 y FP(tends)j(to)e(the)h(identity) 60 2014 y(as)g FF(\017)d FE(!)f FQ(0)18 b FP(uniformly.)60 2158 y FB(B.5)69 b(Application)21 b(to)i(the)f(Examples)e(of)k(Section)d(4)60 2251 y FM(B.5.1)55 b(General)18 b(Strategies)60 2343 y FQ(In)h(principle,)e (the)i(v)o(eri\014cation)f(of)i(the)f(P)o(eierls)e(condition)i(for)h(a)f (certain)g(in)o(teraction)f(\010)1775 2350 y FH(0)1814 2343 y FQ(is)h(a)60 2403 y(t)o(w)o(o-stage)e(pro)q(cess:)133 2476 y(\(A\))22 b(Find)g(all)g(the)g(p)q(erio)q(dic)g(ground-state)i (con\014gurations)g(of)e(\010)1417 2483 y FH(0)1437 2476 y FQ(.)40 b(This)22 b(stage)h(usually)60 2536 y(in)o(v)o(olv)o(es)11 b(coun)o(ting)h(ho)o(w)h(man)o(y)f(\\frustrated)h(b)q(onds")h(eac)o(h)f (candidate)f(con\014guration)i(has.)21 b(This)60 2596 y(should)16 b(b)q(e)g(follo)o(w)o(ed)e(b)o(y)h(a)h(pro)q(of)h(sho)o(wing)f(that)g(indeed) f(no)h(other)f(p)q(erio)q(dic)h(con\014guration)g(has)60 2657 y(the)i(same)f(or)i(less)f(energy)g(densit)o(y)l(,)f(but)i(this)f(pro)q(of)h (is)f(usually)g(omitted)f(b)q(ecause)h(it)g(is)g(either)938 2784 y(234)p eop %%Page: 235 235 bop 60 91 a FQ(considered)13 b(to)h(b)q(e)g(ob)o(vious)g(or)g(to)q(o)h(messy) d(to)i(write)f(do)o(wn.)21 b(F)l(urthermore,)12 b(as)i(remark)o(ed)e(b)q (efore)60 152 y(De\014nition)17 b(B.20,)g(this)g(pro)q(of)h(is)f(not)h (really)e(necessary)h(if)f(the)h(P)o(eierls)f(condition)h(\(next)f(stage\))60 212 y(can)c(b)q(e)g(successfully)f(v)o(eri\014ed.)18 b(In)12 b(this)g(regard,)h(the)f(tedious)g(pro)q(cess)g(of)h(\014nding)f(these)g (reference)60 272 y(con\014gurations)k(is)f(a)g(natural)g(candidate)g(for)g (a)h(computer-assisted)e(pro)q(cedure.)20 b(Ho)o(w)o(ev)o(er,)13 b(this)60 332 y(ma)o(y)20 b(not)i(b)q(e)g(p)q(ossible,)h(in)f(general:)32 b(the)21 b(problem)g(of)h(c)o(hec)o(king)e(whether)h(a)h(giv)o(en)f(p)q(erio) q(dic)60 392 y(con\014guration)16 b(is)f(a)g(ground)h(state)f(ma)o(y)e(not)j (b)q(e)f(algorithmically)d(decidable)i(\(see)g([313)q(,)h(Section)60 452 y(4.15])j(and)g([316)q(])f(and)h(references)e(therein)h(for)g(some)g (related)g(undecidabilit)o(y)e(results,)i(and)h(see)60 513 y(also)e([263)q(]\).)21 b(In)15 b(an)o(y)h(case,)f(this)g(problem)g(ma)o(y)f (b)q(e)i(alleviated)e(in)h(practice)g(if)g(one)h(w)o(orks)g(in)f(the)60 573 y(framew)o(ork)h(of)i(PS)g(theory)l(.)26 b(Indeed,)17 b(the)g(further)g (steps)h(of)g(the)g(theory)f(w)o(ork)h(as)h(a)f(correcting)60 633 y(mec)o(hanism:)23 b(if)c(to)q(o)h(few)f(con\014gurations)h(ha)o(v)o(e)e (b)q(een)h(found,)h(the)f(P)o(eierls)e(condition)i(will)f(fail)60 693 y(and)h(the)g(the)f(con\014gurations)i(of)f(large)g(con)o(tours)g(with)f (v)o(ery)g(lo)o(w)g(energy)h(densit)o(y)e(will)h(giv)o(e)g(a)60 753 y(hin)o(t)c(of)i(ho)o(w)f(additional)g(ground-state)i(con\014gurations)f (lo)q(ok)g(lik)o(e.)j(On)c(the)g(other)g(hand,)g(if)g(to)q(o)60 814 y(man)o(y)f(con\014gurations)i(ha)o(v)o(e)f(b)q(een)g(selected,)e(the)i (spurious)h(ones)g(will)e(b)q(e)h(ev)o(en)o(tually)e(ruled)i(out)60 874 y(in)g(the)f(sense)h(that)h(they)e(will)g(not)h(giv)o(e)f(rise)h(to)g (pure)g(phases;)h(they)e(lead)h(to)g(con)o(tour)g(ensem)o(bles)60 934 y(with)21 b(high)g(free-energy)f(cost,)i(whic)o(h)e(are)h(not)g(asso)q (ciated)h(to)f FF(\034)6 b FQ(-functionals.)35 b([W)l(e)21 b(o)o(w)o(e)f(this)60 994 y(insigh)o(t)c(to)g(con)o(v)o(ersations)g(with)g (Milo)m(\024)-22 b(s)17 b(Zahradn)-5 b(\023)-19 b(\020k.])133 1054 y(\(B\))20 b(Devise)f(a)h(suitable)g(notion)g(of)h(con)o(tour)f(and)g (sho)o(w)h(that)f(the)g(energy)g(gro)o(ws)g(prop)q(or-)60 1115 y(tionally)15 b(to)i(its)f(supp)q(ort.)23 b(This)16 b(is)g(an)h(extremely)c (mo)q(del-dep)q(enden)o(t)h(pro)q(cess.)133 1175 y(Often,)23 b(the)f(determination)f(of)i(ground-state)h(con\014gurations)f(and)g(of)g (con)o(tour)g(energies)60 1235 y(are)18 b(done)f(sim)o(ultaneously:)22 b(The)17 b(comparison)g(b)q(et)o(w)o(een)g(the)g(energies)g(of)g(di\013eren)o (t)g(candidate)60 1295 y(con\014gurations)c(is)e(done)h(already)g(with)f(the) h(help)f(of)h(con)o(tours.)20 b(This)11 b(is)h(a)g(manifestation)e(of)i(what) 60 1355 y(w)o(e)i(ha)o(v)o(e)h(rep)q(eatedly)f(commen)o(t)o(ed)e(up)q(on:)22 b(the)14 b(con)o(tour)i(energy)e(is)h(the)g(essen)o(tial)e(quan)o(tit)o(y;)h (the)60 1416 y(crucial)g(stage)i(is)f(\(B\).)g(If)f(w)o(e)h(manage)g(to)h (sho)o(w)g(that)f(con)o(tour)h(energies)f(are)g(large)g(enough)h(then)60 1476 y(w)o(e)c(do)g(not)g(need)g(to)g(care)g(ab)q(out)h(the)f(nature)g(of)h (the)e(reference)g(con\014gurations,)i(they)f(are)g(ground)60 1536 y(states)19 b(b)o(y)f(force.)27 b(Y)l(et)17 b(again,)j(the)e(same)f (argumen)o(t)g(used)i(to)g(pro)o(v)o(e)e(the)h(appropriate)h(gro)o(wth)60 1596 y(of)j(con)o(tour)h(energies,)f(usually)f(sho)o(ws)i(the)f(ground-state) i(c)o(haracter)d(of)h(the)g(con\014gurations.)60 1656 y(Pro)o(ving)16 b(\(B\))g(directly)e(is)i(not)h(a)g(substan)o(tial)f(sa)o(ving)h(of)f(misery) l(.)133 1741 y(Belo)o(w,)21 b(w)o(e)g(shall)g(use)g(this)h(canonical)f (approac)o(h)h(for)f(decimation)e(and)j(Kadano\013-)p FF(p)i FQ(pre-)60 1802 y(scriptions,)16 b(where)g(w)o(e)g(can)g(resort)h(to)g(the)f (Ising)g(t)o(yp)q(e)g(of)h(con)o(tours:)22 b(p)q(olyhedra)17 b(dra)o(wn)f(on)h(the)60 1862 y(dual)f(lattice)e(with)i(plaquettes)f(p)q(erp) q(endicular)g(to)h(eac)o(h)g(frustrated)g(b)q(ond.)22 b(F)l(or)15 b(the)h(studies)g(on)60 1922 y(other)g(R)o(G)g(transformations)g(w)o(e)g (shall)g(use)g(instead)g(the)g(Holszt)o(ynski-Sla)o(wn)o(y)e(criterion)h (\(The-)60 1982 y(orem)g(B.21\))h(based)h(on)g(the)g(notion)g(of)f FF(m)p FQ(-p)q(oten)o(tials)h(\(De\014nition)f(B.20\).)22 b(The)16 b(corresp)q(onding)60 2042 y(pro)q(cedure)h(usually)g(starts)h(b)o(y)e (rewriting)g(the)h(in)o(teraction)f(in)o(to)h(an)g(equiv)m(alen)o(t)f(form)g (whic)o(h)g(is)60 2103 y(indeed)g(an)h FF(m)p FQ(-p)q(oten)o(tial.)22 b(This)17 b(is)f(the)g(hard)i(part)f(of)f(the)h(game;)e(it)h(in)o(v)o(olv)o (es)f(some)h(kno)o(wledge)60 2163 y(of)h(what)h(the)f(ground-state)i (con\014gurations)f(lo)q(ok)f(lik)o(e.)22 b(Once)17 b(the)f(rewriting)h(is)g (done,)g(the)g(ac-)60 2223 y(tual)f(v)o(eri\014cation)f(of)h(whic)o(h)f (con\014gurations)j(ha)o(v)o(e)d(minimal)e(energy)i(is)h(in)g(general)f (simple;)f(one)60 2283 y(studies)k(one)h(b)q(ond)g(at)g(a)g(time.)26 b(As)18 b(already)g(remark)o(ed,)f(the)h(disadv)m(an)o(tage)h(of)g(this)f (approac)o(h)60 2343 y(is)j(that)g(it)f(do)q(es)i(not)f(supply)g(a)g(v)m (alue)g(for)g(the)g(P)o(eierls)e(constan)o(t,)j(a)g(fact)f(that,)h(in)e(our)h (case,)60 2403 y(prev)o(en)o(ts)d(us)h(from)f(pro)q(ducing)i(an)o(y)e (estimate)f(of)j(the)e(range)i(of)f(temp)q(eratures)f(for)h(whic)o(h)f(the)60 2464 y(pathologies)f(of)g(the)f(R)o(G)g(transformations)g(o)q(ccur.)133 2524 y(W)l(e)c(observ)o(e)f(that)h(for)g(the)g(Steps)g(1{3)h(in)f(the)f(pro)q (ofs)i(of)f(existence)f(of)h(pathologies,)h(w)o(e)e(do)i(not)60 2584 y(need)e(the)g(full)g(information)f(on)i(phase)g(diagrams)f(pro)o(vided) g(b)o(y)g(PS)g(theory)l(.)20 b(Rather,)12 b(w)o(e)f(are)g(only)60 2644 y(in)o(terested)i(in)h(the)g(p)q(oin)o(t)h(of)f(maxim)o(um)c(co)q (existence)j(\(for)i(Step)f(1\),)h(and)g(regions)g(of)f(uniqueness)938 2784 y(235)p eop %%Page: 236 236 bop 60 91 a FQ(of)21 b(Gibbs)g(measure)f(\(for)h(Step)g(2\).)35 b(Moreo)o(v)o(er,)21 b(b)q(oth)h(t)o(yp)q(es)e(of)h(questions)g(refer)g(to)g FP(di\013er)n(ent)60 152 y FQ(systems:)d(The)11 b(maxim)o(um)c(co)q (existence)j(p)q(oin)o(t)i(m)o(ust)e(b)q(e)i(determined)d(for)j(in)o (ternal-spin)e(systems)60 212 y(obtained)22 b(when)g(the)f(image)f(spins)i (do)g(not)g(fa)o(v)o(or)g(an)o(y)f(phase)h(of)g(the)g(original)f(system)f (\(this)60 272 y(amoun)o(ts,)15 b(in)h(general,)f(to)h(blo)q(c)o(k)f(spins)i (c)o(hosen)e(in)h(an)g(alternating)g(or)h(random)e(w)o(a)o(y\).)21 b(In)15 b(these)60 332 y(cases,)23 b(the)f(symmetry-breaking)d(p)q (erturbation)k(is)f(c)o(hosen)g(simply)e(as)i(a)h(uniform)e(magnetic)60 392 y(\014eld)d(and)h(symmetry)c(considerations)k(imply)d(that)j(maxim)o(um) 14 b(co)q(existence)j(is)i(ac)o(hiev)o(ed)d(only)60 452 y(when)g(this)g (\014eld)f(is)g(zero.)21 b(Therefore,)15 b(this)h(symmetry)o(-breaking)d(in)o (teraction)i(pla)o(ys)h(an)g(almost)60 513 y(in)o(visible)e(role,)i(and)i(it) e(is)g(only)h(brie\015y)e(men)o(tioned.)21 b(The)16 b(only)h(case)f(in)h (whic)o(h)f(the)g(symmetry-)60 573 y(breaking)h(deserv)o(es)e(careful)h (consideration)h(is)f(that)h(of)g(systems)f(whic)o(h)g(already)g(initially)f (ha)o(v)o(e)60 633 y(a)23 b(magnetic)d(\014eld)i(\(Sections)g(4.3.6)h(and)g (B.5.7\).)39 b(On)22 b(the)g(other)h(hand,)h(the)e(uniqueness)g(of)60 693 y(Gibbs)f(measures)f(is)h(of)h(in)o(terest)d(for)j(in)o(ternal-spin)e (systems)g(corresp)q(onding)i(to)f(blo)q(c)o(k)g(spins)60 753 y(c)o(hosen)c(so)h(as)g(to)f(de\014nitely)f(fa)o(v)o(or)g(one)i(of)f(the)g (phases.)25 b(It)16 b(is)h(not)h(wise)f(to)g(think)g(of)g(these)g(t)o(w)o(o) 60 814 y(in)o(ternal-spin)i(systems)g(\(determined)e(b)o(y)j(blo)q(c)o(k)f (spins)i(either)e(fa)o(v)o(oring)g(or)i(not)f(fa)o(v)o(oring)g(one)60 874 y(pure)14 b(phase\))h(as)g(living)e(in)h(the)g(same)f(phase)i(diagram)f (with)g(blo)q(c)o(k-spin)g(\015ipping)g(as)h(symmetry-)60 934 y(breaking)h(in)o(teraction.)k(The)15 b(problem)g(is)g(that)h(suc)o(h)g(an)g (in)o(teraction)f(can)g(not)i(b)q(e)e(considered)h(a)60 994 y(p)q(erturbation:)k(it)12 b(go)q(es)h(b)o(y)f(\014nite)f(steps)i(and)f (hence)g(ma)o(y)e(thro)o(w)j(us)f(out)h(of)g(the)f(small-parameter)60 1054 y(region)k FF(V)234 1061 y FD(\014)275 1054 y FQ(\(see)f(Theorem)g (B.28\))h(of)h(the)f(phase)h(diagram)e(where)h(PS)h(theory)f(holds.)133 1115 y(Let)h(us)f(no)o(w)h(discuss)f(the)g(di\013eren)o(t)g(applications)g (starting)h(from)e(the)h(simplest)e(ones.)60 1244 y FM(B.5.2)55 b(In)n(ternal-Spin)18 b(Systems)f(with)h(Unique)g(Ground-State)g (Con\014gurations)60 1337 y FQ(In)h(all)f(the)h(applications)g(of)g(Section)g (4)g(there)g(is)g(a)g(step)g(\(Step)g(2.2\))g(whic)o(h)f(in)o(v)o(olv)o(es)f (sho)o(wing)60 1397 y(that)d(at)g(lo)o(w)g(temp)q(erature)e(the)h(ensem)o (ble)e(of)j(in)o(ternal)f(\(or)h(original\))f(spins)h(has)h(a)f(unique)f (Gibbs)60 1457 y(measure)g(for)h(some)f(particular)h(c)o(hoice)f(of)h(image)f (spins.)21 b(These)14 b(are)g(all)f(cases)i(in)e(whic)o(h)h(there)f(is)60 1517 y(only)g(one)h(\(p)q(erio)q(dic\))e(ground-state)j(con\014guration,)g (due)e(to)h(the)f(presence)f(of)i(a)f(p)q(erio)q(dic)g(single-)60 1578 y(sign)f(magnetic)f(\014eld.)19 b(The)12 b(uniqueness)g(of)g(the)g (Gibbs)g(state)h(is,)f(basically)l(,)g(a)g(consequence)f(of)i(PS)60 1638 y(theory)18 b(plus)g(Zahradn)-5 b(\023)-19 b(\020k's)19 b(completeness)d(result)i(\(see)f(the)i(commen)n(t)d(imm)o(ediatel)o(y)f (follo)o(wing)60 1698 y(Theorem)g(B.27\).)22 b(Ho)o(w)o(ev)o(er,)14 b(this)j(w)o(ould)f(only)h(pro)o(v)o(e)e(uniqueness)i FP(among)h(the)g(p)n (erio)n(dic)f(Gibbs)60 1758 y(me)n(asur)n(es)t FQ(;)24 b(w)o(e)f(need)f (Martirosy)o(an's)g(extension)g(of)h(this)f(result)g([260)q(])g(to)h(pro)o(v) o(e)e(uniqueness)60 1818 y(among)16 b(the)g(set)g(of)h FP(al)r(l)g FQ(Gibbs)g(measures.)60 1948 y FM(B.5.3)55 b(In)n(ternal)18 b(Spins)h(under)g(Decimation)60 2041 y FQ(In)h(this)h(case)g(w)o(e)f(can)h (apply)f(the)h(canonical)f(t)o(w)o(o-stage)i(pro)q(cess)f(describ)q(ed)f(ab)q (o)o(v)o(e)h(to)g(v)o(erify)60 2101 y(the)f(P)o(eierls)g(condition.)34 b(As)20 b(discussed)h(in)f(detail)g(in)h(Sections)f(4.1.2)h(and)g(4.2)g (\(Step)g(0\),)g(the)60 2161 y(ensem)o(ble)14 b(of)j(in)o(ternal)f(spins)h (for)g(a)g(giv)o(en)e(image-spin)h(con\014guration)i(is)e(just)h(the)g(ensem) o(ble)d(of)60 2221 y(con\014gurations)k(of)f(original)f(spins)h(with)f(some)f (of)i(the)f(spins)h(constrained)f(to)h(b)q(e)g(\014xed.)k(T)l(o)c(the)60 2281 y(latter)j(w)o(e)g(can)h(apply)f(the)h(usual)f(P)o(eierls)f (construction)i(of)g(p)q(olyhedral)f(con)o(tours.)35 b(W)l(e)20 b(shall)60 2342 y(therefore)f(use)g(the)g(\\thin")h(notion)g(of)g(con)o (tours)g(discussed)f(at)h(the)f(end)g(of)h(the)f(t)o(w)o(o)g(previous)60 2402 y(Sections)f(B.4.2)g(and)i(B.4.3.)28 b(The)18 b FP(internal-spin)j FQ(con)o(tours)e(are)g(obtained)g(from)e(the)i(original-)60 2462 y(spin)j(con)o(tours)h(b)o(y)f(remo)o(ving)e(the)i(plaquettes)g(adjacen) o(t)g(to)h(an)f(image)f(spin)h([thic)o(k)f(lines)g(in)60 2522 y(Figure)g(14\(a\)].)37 b(The)22 b(argumen)o(t)e(that)i(follo)o(ws)f(is)g(th) o(us)g(based)h(on)g(comparing)f(in)o(ternal-spin)60 2582 y(with)16 b(original-spin)g(\(=)h(in)o(ternal)e(+)h(image\))f(quan)o(tities.)938 2784 y(236)p eop %%Page: 237 237 bop 133 91 a FQ(W)l(e)13 b(\014x)g(the)g(image)f(spin)h(in)g(the)g(fully)f (alternating)h(\\+)p FF(=)p FE(\000)p FQ(")h(con\014guration,)h(so)e(the)g(t) o(w)o(o)g(ob)o(vi-)60 152 y(ous)j(candidates)g(to)g(ground-state)h (con\014gurations)g(in)e(the)h(resulting)f(system)f(of)i FP(internal)i(spins) 60 212 y FQ(are)f(the)g(same)f(as)i(for)g(the)f(original)g(system:)k FF(!)p 931 219 33 2 v 963 194 a FH(\(+\))1038 212 y FQ(equal)16 b(to)i(+1)f(ev)o(erywhere,)e(and)j FF(!)p 1671 219 V 1703 194 a FH(\()p Fy(\000)p FH(\))1778 212 y FQ(equal)60 272 y(to)e FE(\000)p FQ(1)g(ev)o(erywhere.)j(That)d(is,)f(in)g(terms)g(of)g(original)h (spins,)f FF(!)p 1210 279 V 1243 254 a FH(\(+\))1315 272 y FQ(\(resp.)21 b FF(!)p 1456 279 V 1488 254 a FH(\()p Fy(\000)p FH(\))1545 272 y FQ(\))16 b(corresp)q(onds)h(to)60 332 y(all)d(spins)h(\\+")g (\(\\)p FE(\000)p FQ("\))g(except)f(for)h(a)g(sublattice)f(of)h(p)q(erio)q(d) g(2)p FF(b)g FQ(|)f(with)g FF(b)h FQ(b)q(eing)g(the)f(decimation)60 392 y(spacing)g(|)g(where)g(the)g(spins)g(are)g(\015ipp)q(ed.)20 b(The)14 b(symmetry-breaking)d(p)q(erturbation)k FF(\025)1728 399 y FH(1)1748 392 y FQ(\010)1783 399 y FH(1)1817 392 y FQ(can)60 452 y(b)q(e)i(tak)o(en)f(to)h(b)q(e)g(a)g(magnetic)e(\014eld)i(at)g(eac)o(h)f (\(in)o(ternal\))g(site.)22 b(Ho)o(w)o(ev)o(er,)14 b(the)j(symmetry)c(of)k (the)60 513 y(problem)d(\(i.e.)g(of)h(the)g(c)o(hoice)g(of)g(blo)q(c)o(k)g (spins\),)h(implies)c(that)k(the)f(co)q(existence)f(of)i(the)f(\\+")h(and)60 573 y(\\)p FE(\000)p FQ(")h(measures)f(o)q(ccurs)i(at)f(zero)g(v)m(alues)f (of)i(this)e(\014eld.)23 b(W)l(e)17 b(therefore)f(forget)h(ab)q(out)h(this)f (extra)60 633 y(\014eld,)k(and)h(concen)o(trate)e(on)h(pro)o(ving)g(that)g (the)g(zero-temp)q(erature)e(phase)j(diagram)e(deforms)60 693 y(little)15 b(for)h(lo)o(w)g(temp)q(eratures.)133 753 y(If)i(w)o(e)g(wish)h (only)f(to)h(pro)o(v)o(e)e(that)i FF(!)p 784 760 V 816 735 a FH(\(+\))892 753 y FQ(and)g FF(!)p 989 760 V 1021 735 a FH(\()p Fy(\000)p FH(\))1096 753 y FQ(are)g(all)f(the)g(in)o(ternal-spin)f (ground-state)60 814 y(con\014gurations,)f(w)o(e)e(can)h(for)g(instance)g (consider)f(the)h(corresp)q(onding)h(set)f(of)g FP(original-spin)h FQ(con-)60 874 y(tours,)22 b(whic)o(h)e(is)g(just)h(an)g(arra)o(y)f(of)h(2)p FF(b)p FQ(-spaced)g(unit)g(cub)q(es)f(surrounding)i(eac)o(h)e(\015ipp)q(ed)g (spin,)60 934 y(and)d(sho)o(w)f(that)h(all)e(other)i(original-spin)f (con\014gurations)h(lead)f(to)g(a)h(system)e(of)h(\(original-spin\))60 994 y(con)o(tours)d(with)g(a)g(larger)f(area.)20 b(This)13 b(is)g(not)g(hard)g(to)g(do,)g(for)g(instance)f(w)o(e)g(can)h(argue)g(as)h (follo)o(ws:)60 1054 y(Observ)o(e)19 b(that)i(ev)o(ery)d(in)o(terv)m(al)h (parallel)g(to)i(the)f(axis)g(b)q(et)o(w)o(een)f(t)o(w)o(o)h(nearest-neigh)o (b)q(or)g(image)60 1115 y(spins)j(necessarily)e(con)o(tains)h(at)h(least)f (one)g(brok)o(en)g(b)q(ond,)i(as)f(t)o(w)o(o)g(nearest-neigh)o(b)q(or)f (image)60 1175 y(spins)17 b(alw)o(a)o(ys)g(ha)o(v)o(e)e(opp)q(osite)j(signs.) 23 b(The)17 b(c)o(hoice)e(of)i(all)g(in)o(ternal)e(spins)i(either)f(all)g(+)h (or)g(all)f FE(\000)60 1235 y FQ(has)i(precisely)e(this)h(minim)o(al)d(c)o (hoice)i(of)i(exactly)e(one)i(brok)o(en)f(b)q(ond)h(in)f(eac)o(h)g(in)o(terv) m(al,)f(and)i(no)60 1295 y(other)e(brok)o(en)g(b)q(onds.)133 1355 y(Ho)o(w)o(ev)o(er,)c(suc)o(h)h(an)h(argumen)o(t)e(is)h(not)h(really)e (needed.)20 b(As)13 b(commen)n(ted)d(ab)q(o)o(v)o(e,)k(a)g(more)e(con-)60 1416 y(v)o(enien)o(t)17 b(approac)o(h)i(for)g(our)g(purp)q(oses)g(is)g(to)g (sho)o(w)g(directly)e(that)i(the)f(insertion)g(of)h(a)g(con)o(tour)60 1476 y(in)e FF(!)p 118 1483 V 150 1458 a FH(\(+\))225 1476 y FQ(has)h(an)g(energy)g(cost)f(prop)q(ortional)i(to)f(its)g(area.)25 b(Consider)18 b(then)g(the)f(\(in)o(ternal-spin\))60 1536 y(con\014guration)g FF(!)387 1518 y FH(\000)427 1536 y FQ(obtained)e(b)o(y)g(inserting)h(a)g (\\+")g(\(in)o(ternal-spin\))f(con)o(tour)g(\000)h(inside)f(the)h(con-)60 1596 y(\014guration)d FF(!)p 278 1603 V 311 1578 a FH(\(+\))368 1596 y FQ(,)f(that)h(is,)g(a)g(region)g(of)f(\\)p FE(\000)p FQ(")i(b)q(ounded)f(b)o(y)f(\000)h([Figure)f(14\(a\)].)20 b(Its)13 b(relativ)o(e)d(energy)60 1656 y(can)16 b(b)q(e)h(written)f(in)f(the)h(form:) 566 1766 y FF(H)t FQ(\()p FF(!)661 1746 y FH(\000)685 1766 y FE(j)p FF(!)p 699 1773 V 731 1746 a FH(\(+\))788 1766 y FQ(\))28 b(=)g(2)p FF(J)5 b FE(j)p FQ(\000)p FE(j)11 b(\000)g FQ(\001)p FF(E)1153 1773 y Fy(\000)1193 1766 y FQ(+)g(\001)p FF(E)1319 1773 y FH(+)1362 1766 y FF(;)379 b FQ(\(B)p FF(:)p FQ(71\))60 1876 y(where)16 b FE(j)p FQ(\000)p FE(j)g FQ(is)g(the)g(area)h(of)f(the)g (con)o(tour)h([n)o(um)o(b)q(er)c(of)k(plaquettes,)e(or)i(length)f(of)g(the)g (thic)o(k)f(lines)60 1936 y(for)j(the)f(t)o(w)o(o-dimensional)f(example)g(of) i(Figure)f(14\(a\)],)h(\001)p FF(E)1221 1943 y Fy(\000)1268 1936 y FQ(is)f(the)h(energy)f(gain)h(due)f(to)h(the)60 1997 y(fact)c(that)h(the)e(\\)p FE(\000)p FQ(")i(image)e(spins)h(inside)f(of,)i (or)f(visited)f(b)o(y)l(,)h(\000)g(acquire)f(\\)p FE(\000)p FQ(")i(neigh)o(b)q(ors)f([e.g.)f(the)60 2057 y(sites)j FF(a)195 2064 y FD(i)225 2057 y FQ(in)h(Figure)f(14\(a\)],)h(and)g(\001)p FF(E)764 2064 y FH(+)809 2057 y FQ(is)g(the)f(additional)h(energy)f(due)g(to) h(\\+")g(image)f(spins)g(in)60 2117 y(\000.)133 2177 y(T)l(o)f(pro)o(v)o(e)f (the)g(P)o(eierls)f(condition)i(w)o(e)f(ha)o(v)o(e)f(to)i(c)o(hec)o(k)e(that) i(the)f(extra)g(con)o(tribution)g(\001)p FF(E)1814 2184 y Fy(\000)1851 2177 y FE(\000)60 2237 y FQ(\001)p FF(E)137 2244 y FH(+)186 2237 y FQ(is)19 b(prop)q(ortional)i(to)f(the)g(area)g(of)g(the)f(con)o(tour)h (with)f(a)h(not)h(to)q(o)f(large)g(prop)q(ortionalit)o(y)60 2298 y(constan)o(t.)38 b(The)21 b(in)o(tuition)g(is)g(clear:)31 b(The)22 b(con)o(tributions)f(corresp)q(onding)i(to)f(\\+")g(and)g(\\)p FE(\000)p FQ(")60 2358 y(image)17 b(spins)h(inside)f(the)h(v)o(olume)e (cancel)h(eac)o(h)g(other,)h(except)f(p)q(ossibly)i(for)f(a)g(la)o(y)o(er)f (of)h(image)60 2418 y(spins)13 b(placed)f(close)g(to)h(the)f(con)o(tour.)20 b(This)13 b(correction)f(is)g(hence)g(of)h(the)f(order)h(of)g(the)f(area)h (of)g(the)60 2478 y(con)o(tour,)18 b(with)f(prop)q(ortionalit)o(y)h(constan)o (t)g(giv)o(en)f(roughly)h(b)o(y)f(the)h(in)o(v)o(erse)e(of)i(the)f (separation)60 2538 y(b)q(et)o(w)o(een)g(these)h(image)f(spins.)28 b(Ho)o(w)o(ev)o(er,)16 b(this)i(last)h(b)q(ound)g(is)f(not)h(applicable)e(if) h(the)g(con)o(tour)60 2599 y(in)o(v)o(olv)o(es)d(few)i(\(e.g.)g(one\))g (image)f(spins.)25 b(In)17 b(this)g(sense,)g(it)g(is)g(natural)h(to)g (distinguish)f(b)q(et)o(w)o(een)60 2659 y(con)o(tours)g(surrounding)h(and)g (con)o(tours)f(a)o(v)o(oiding)f(the)h(image)e(spins.)24 b(While)15 b(the)i(former)e(\\feel")938 2784 y(237)p eop %%Page: 238 238 bop 517 959 a @beginspecial 29 @llx 31.500000 @lly 286 @urx 265.500000 @ury 2196 @rwi @setspecial %%BeginDocument: fig14a.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Italic/Times-Italic Z [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 49.5236 257.6162 m S 49.5236 246.1712 m S 37.8651 246.1712 m S 37.8651 257.6162 m S 43.6943 251.8937 m S u 72.8407 234.7261 m S 72.8407 223.281 m S 61.1821 223.281 m S 61.1821 234.7261 m S 67.0114 229.0036 m S U 61.1821 246.1712 m S 61.1821 234.7261 m S 49.5236 234.7261 m S 49.5236 246.1712 m S 55.3529 240.4486 m S 61.1821 257.6162 m S 61.1821 246.1712 m S 49.5236 246.1712 m S 49.5236 257.6162 m S 55.3529 251.8937 m S 72.8407 257.6162 m S 72.8407 246.1712 m S 61.1821 246.1712 m S 61.1821 257.6162 m S 67.0114 251.8937 m S u 72.8407 246.1712 m S 72.8407 234.7261 m S 61.1821 234.7261 m S 61.1821 246.1712 m S 67.0114 240.4486 m S U u 61.1821 234.7261 m S 61.1821 223.281 m S 49.5236 223.281 m S 49.5236 234.7261 m S 55.3529 229.0036 m S U u 49.5236 234.7261 m S 49.5236 223.281 m S 37.8651 223.281 m S 37.8651 234.7261 m S 43.6943 229.0036 m S U 49.5236 246.1712 m S 49.5236 234.7261 m S 37.8651 234.7261 m S 37.8651 246.1712 m S 43.6943 240.4486 m S 0 g 1 w 4 M 43.6943 251.8937 m F 67.0114 251.8937 m F 43.6943 229.0036 m F 67.0114 229.0036 m F 0 G 0.3 w 10 M 84.4992 257.6162 m S 84.4992 246.1712 m S 72.8407 246.1712 m S 72.8407 257.6162 m S 78.6699 251.8937 m S u 107.8163 234.7261 m S 107.8163 223.281 m S 96.1577 223.281 m S 96.1577 234.7261 m S 101.987 229.0036 m S U u 96.1577 246.1712 m S 96.1577 234.7261 m S 84.4992 234.7261 m S 84.4992 246.1712 m S 90.3285 240.4486 m S U 96.1577 257.6162 m S 96.1577 246.1712 m S 84.4992 246.1712 m S 84.4992 257.6162 m S 90.3285 251.8937 m S 107.8163 257.6162 m S 107.8163 246.1712 m S 96.1577 246.1712 m S 96.1577 257.6162 m S 101.987 251.8937 m S u 107.8163 246.1712 m S 107.8163 234.7261 m S 96.1577 234.7261 m S 96.1577 246.1712 m S 101.987 240.4486 m S U u 96.1577 234.7261 m S 96.1577 223.281 m S 84.4992 223.281 m S 84.4992 234.7261 m S 90.3285 229.0036 m S U u 84.4992 234.7261 m S 84.4992 223.281 m S 72.8407 223.281 m S 72.8407 234.7261 m S 78.6699 229.0036 m S U u 84.4992 246.1712 m S 84.4992 234.7261 m S 72.8407 234.7261 m S 72.8407 246.1712 m S 78.6699 240.4486 m S U 0 g 1 w 4 M 78.6699 251.8937 m F 101.987 251.8937 m F 78.6699 229.0036 m F 101.987 229.0036 m F 0 G 0.3 w 10 M 119.4748 257.6162 m S 119.4748 246.1712 m S 107.8163 246.1712 m S 107.8163 257.6162 m S 113.6455 251.8937 m S 142.7919 234.7261 m S 142.7919 223.281 m S 131.1334 223.281 m S 131.1334 234.7261 m S 136.9626 229.0036 m S u 131.1334 246.1712 m S 131.1334 234.7261 m S 119.4748 234.7261 m S 119.4748 246.1712 m S 125.3041 240.4486 m S U 131.1334 257.6162 m S 131.1334 246.1712 m S 119.4748 246.1712 m S 119.4748 257.6162 m S 125.3041 251.8937 m S 142.7919 257.6162 m S 142.7919 246.1712 m S 131.1334 246.1712 m S 131.1334 257.6162 m S 136.9626 251.8937 m S u 142.7919 246.1712 m S 142.7919 234.7261 m S 131.1334 234.7261 m S 131.1334 246.1712 m S 136.9626 240.4486 m S U 131.1334 234.7261 m S 131.1334 223.281 m S 119.4748 223.281 m S 119.4748 234.7261 m S 125.3041 229.0036 m S u 119.4748 234.7261 m S 119.4748 223.281 m S 107.8163 223.281 m S 107.8163 234.7261 m S 113.6455 229.0036 m S U u 119.4748 246.1712 m S 119.4748 234.7261 m S 107.8163 234.7261 m S 107.8163 246.1712 m S 113.6455 240.4486 m S U 0 g 1 w 4 M 113.6455 251.8937 m F 136.9626 251.8937 m F 113.6455 229.0036 m F 136.9626 229.0036 m F 0 G 0.3 w 10 M 142.7919 246.1712 m S 142.7919 257.6162 m S 142.7919 223.281 m S 142.7919 234.7261 m S 142.7919 234.7261 m S 142.7919 246.1712 m S u 49.5236 223.281 m S 49.5236 211.8359 m S 37.8651 211.8359 m S 37.8651 223.281 m S 43.6943 217.5585 m S U 72.8407 200.3909 m S 72.8407 188.9459 m S 61.1821 188.9459 m S 61.1821 200.3909 m S 67.0114 194.6684 m S 61.1821 211.8359 m S 61.1821 200.3909 m S 49.5236 200.3909 m S 49.5236 211.8359 m S 55.3529 206.1135 m S 61.1821 223.281 m S 61.1821 211.8359 m S 49.5236 211.8359 m S 49.5236 223.281 m S 55.3529 217.5585 m S 72.8407 223.281 m S 72.8407 211.8359 m S 61.1821 211.8359 m S 61.1821 223.281 m S 67.0114 217.5585 m S 72.8407 211.8359 m S 72.8407 200.3909 m S 61.1821 200.3909 m S 61.1821 211.8359 m S 67.0114 206.1135 m S 61.1821 200.3909 m S 61.1821 188.9459 m S 49.5236 188.9459 m S 49.5236 200.3909 m S 55.3529 194.6684 m S u 49.5236 200.3909 m S 49.5236 188.9459 m S 37.8651 188.9459 m S 37.8651 200.3909 m S 43.6943 194.6684 m S U u 49.5236 211.8359 m S 49.5236 200.3909 m S 37.8651 200.3909 m S 37.8651 211.8359 m S 43.6943 206.1135 m S U 0 g 1 w 4 M 43.6943 217.5585 m F 67.0114 217.5585 m F 43.6943 194.6684 m F 67.0114 194.6684 m F 0 G 0.3 w 10 M 84.4992 223.281 m S 84.4992 211.8359 m S 72.8407 211.8359 m S 72.8407 223.281 m S 78.6699 217.5585 m S u 107.8163 200.3909 m S 107.8163 188.9459 m S 96.1577 188.9459 m S 96.1577 200.3909 m S 101.987 194.6684 m S U 96.1577 211.8359 m S 96.1577 200.3909 m S 84.4992 200.3909 m S 84.4992 211.8359 m S 90.3285 206.1135 m S 96.1577 223.281 m S 96.1577 211.8359 m S 84.4992 211.8359 m S 84.4992 223.281 m S 90.3285 217.5585 m S u 107.8163 223.281 m S 107.8163 211.8359 m S 96.1577 211.8359 m S 96.1577 223.281 m S 101.987 217.5585 m S U u 107.8163 211.8359 m S 107.8163 200.3909 m S 96.1577 200.3909 m S 96.1577 211.8359 m S 101.987 206.1135 m S U u 96.1577 200.3909 m S 96.1577 188.9459 m S 84.4992 188.9459 m S 84.4992 200.3909 m S 90.3285 194.6684 m S U u 84.4992 200.3909 m S 84.4992 188.9459 m S 72.8407 188.9459 m S 72.8407 200.3909 m S 78.6699 194.6684 m S U 84.4992 211.8359 m S 84.4992 200.3909 m S 72.8407 200.3909 m S 72.8407 211.8359 m S 78.6699 206.1135 m S 0 g 1 w 4 M 78.6699 217.5585 m F 101.987 217.5585 m F 78.6699 194.6684 m F 101.987 194.6684 m F u 0 G 0.3 w 10 M 119.4748 223.281 m S 119.4748 211.8359 m S 107.8163 211.8359 m S 107.8163 223.281 m S 113.6455 217.5585 m S U u 142.7919 200.3909 m S 142.7919 188.9459 m S 131.1334 188.9459 m S 131.1334 200.3909 m S 136.9626 194.6684 m S U u 131.1334 211.8359 m S 131.1334 200.3909 m S 119.4748 200.3909 m S 119.4748 211.8359 m S 125.3041 206.1135 m S U u 131.1334 223.281 m S 131.1334 211.8359 m S 119.4748 211.8359 m S 119.4748 223.281 m S 125.3041 217.5585 m S U u 142.7919 223.281 m S 142.7919 211.8359 m S 131.1334 211.8359 m S 131.1334 223.281 m S 136.9626 217.5585 m S U u 142.7919 211.8359 m S 142.7919 200.3909 m S 131.1334 200.3909 m S 131.1334 211.8359 m S 136.9626 206.1135 m S U u 131.1334 200.3909 m S 131.1334 188.9459 m S 119.4748 188.9459 m S 119.4748 200.3909 m S 125.3041 194.6684 m S U u 119.4748 200.3909 m S 119.4748 188.9459 m S 107.8163 188.9459 m S 107.8163 200.3909 m S 113.6455 194.6684 m S U u 119.4748 211.8359 m S 119.4748 200.3909 m S 107.8163 200.3909 m S 107.8163 211.8359 m S 113.6455 206.1135 m S U 0 g 1 w 4 M 113.6455 217.5585 m F 136.9626 217.5585 m F 113.6455 194.6684 m F 136.9626 194.6684 m F 0 G 0.3 w 10 M 142.7919 211.8359 m S 142.7919 223.281 m S 142.7919 188.9459 m S 142.7919 200.3909 m S 142.7919 200.3909 m S 142.7919 211.8359 m S 0 g 1 w 4 M 43.6943 183.2233 m F 67.0114 183.2233 m F 78.6699 183.2233 m F 101.987 183.2233 m F 113.6455 183.2233 m F 136.9626 183.2233 m F u 0 G 0.3 w 10 M 49.5236 188.9459 m S 49.5236 177.5007 m S 37.8651 177.5007 m S 37.8651 188.9459 m S 43.6943 183.2233 m S U u 72.8407 166.0557 m S 72.8407 154.6107 m S 61.1821 154.6107 m S 61.1821 166.0557 m S 67.0114 160.3332 m S U u 61.1821 177.5007 m S 61.1821 166.0557 m S 49.5236 166.0557 m S 49.5236 177.5007 m S 55.3529 171.7782 m S U u 61.1821 188.9459 m S 61.1821 177.5007 m S 49.5236 177.5007 m S 49.5236 188.9459 m S 55.3529 183.2233 m S U u 72.8407 188.9459 m S 72.8407 177.5007 m S 61.1821 177.5007 m S 61.1821 188.9459 m S 67.0114 183.2233 m S U u 72.8407 177.5007 m S 72.8407 166.0557 m S 61.1821 166.0557 m S 61.1821 177.5007 m S 67.0114 171.7782 m S U u 61.1821 166.0557 m S 61.1821 154.6107 m S 49.5236 154.6107 m S 49.5236 166.0557 m S 55.3529 160.3332 m S U u 49.5236 166.0557 m S 49.5236 154.6107 m S 37.8651 154.6107 m S 37.8651 166.0557 m S 43.6943 160.3332 m S U u 49.5236 177.5007 m S 49.5236 166.0557 m S 37.8651 166.0557 m S 37.8651 177.5007 m S 43.6943 171.7782 m S U 0 g 1 w 4 M 43.6943 183.2233 m F 67.0114 183.2233 m F 43.6943 160.3332 m F 67.0114 160.3332 m F u 0 G 0.3 w 10 M 84.4992 188.9459 m S 84.4992 177.5007 m S 72.8407 177.5007 m S 72.8407 188.9459 m S 78.6699 183.2233 m S U u 107.8163 166.0557 m S 107.8163 154.6107 m S 96.1577 154.6107 m S 96.1577 166.0557 m S 101.987 160.3332 m S U u 96.1577 177.5007 m S 96.1577 166.0557 m S 84.4992 166.0557 m S 84.4992 177.5007 m S 90.3285 171.7782 m S U u 96.1577 188.9459 m S 96.1577 177.5007 m S 84.4992 177.5007 m S 84.4992 188.9459 m S 90.3285 183.2233 m S U u 107.8163 188.9459 m S 107.8163 177.5007 m S 96.1577 177.5007 m S 96.1577 188.9459 m S 101.987 183.2233 m S U u 107.8163 177.5007 m S 107.8163 166.0557 m S 96.1577 166.0557 m S 96.1577 177.5007 m S 101.987 171.7782 m S U u 96.1577 166.0557 m S 96.1577 154.6107 m S 84.4992 154.6107 m S 84.4992 166.0557 m S 90.3285 160.3332 m S U u 84.4992 166.0557 m S 84.4992 154.6107 m S 72.8407 154.6107 m S 72.8407 166.0557 m S 78.6699 160.3332 m S U u 84.4992 177.5007 m S 84.4992 166.0557 m S 72.8407 166.0557 m S 72.8407 177.5007 m S 78.6699 171.7782 m S U 0 g 1 w 4 M 78.6699 183.2233 m F 101.987 183.2233 m F 78.6699 160.3332 m F 101.987 160.3332 m F u 0 G 0.3 w 10 M 119.4748 188.9459 m S 119.4748 177.5007 m S 107.8163 177.5007 m S 107.8163 188.9459 m S 113.6455 183.2233 m S U u 142.7919 166.0557 m S 142.7919 154.6107 m S 131.1334 154.6107 m S 131.1334 166.0557 m S 136.9626 160.3332 m S U u 131.1334 177.5007 m S 131.1334 166.0557 m S 119.4748 166.0557 m S 119.4748 177.5007 m S 125.3041 171.7782 m S U u 131.1334 188.9459 m S 131.1334 177.5007 m S 119.4748 177.5007 m S 119.4748 188.9459 m S 125.3041 183.2233 m S U u 142.7919 188.9459 m S 142.7919 177.5007 m S 131.1334 177.5007 m S 131.1334 188.9459 m S 136.9626 183.2233 m S U u 142.7919 177.5007 m S 142.7919 166.0557 m S 131.1334 166.0557 m S 131.1334 177.5007 m S 136.9626 171.7782 m S U u 131.1334 166.0557 m S 131.1334 154.6107 m S 119.4748 154.6107 m S 119.4748 166.0557 m S 125.3041 160.3332 m S U u 119.4748 166.0557 m S 119.4748 154.6107 m S 107.8163 154.6107 m S 107.8163 166.0557 m S 113.6455 160.3332 m S U u 119.4748 177.5007 m S 119.4748 166.0557 m S 107.8163 166.0557 m S 107.8163 177.5007 m S 113.6455 171.7782 m S U 0 g 1 w 4 M 113.6455 183.2233 m F 136.9626 183.2233 m F 113.6455 160.3332 m F 136.9626 160.3332 m F 0 G 0.3 w 10 M 142.7919 177.5007 m S 142.7919 188.9459 m S 142.7919 154.6107 m S 142.7919 166.0557 m S 142.7919 166.0557 m S 142.7919 177.5007 m S 49.5236 154.6107 m S 37.8651 154.6107 m S 61.1821 154.6107 m S 49.5236 154.6107 m S 72.8407 154.6107 m S 61.1821 154.6107 m S 84.4992 154.6107 m S 72.8407 154.6107 m S 96.1577 154.6107 m S 84.4992 154.6107 m S 107.8163 154.6107 m S 96.1577 154.6107 m S 119.4748 154.6107 m S 107.8163 154.6107 m S 131.1334 154.6107 m S 119.4748 154.6107 m S 142.7919 154.6107 m S 131.1334 154.6107 m S 142.7919 154.6107 m S 119.4748 257.6162 m S 119.4748 246.1712 m S 107.8163 246.1712 m S 107.8163 257.6162 m S 113.6455 251.8937 m S 142.7919 234.7261 m S 142.7919 223.281 m S 131.1334 223.281 m S 131.1334 234.7261 m S 136.9626 229.0036 m S u 131.1334 246.1712 m S 131.1334 234.7261 m S 119.4748 234.7261 m S 119.4748 246.1712 m S 125.3041 240.4486 m S U 131.1334 257.6162 m S 131.1334 246.1712 m S 119.4748 246.1712 m S 119.4748 257.6162 m S 125.3041 251.8937 m S 142.7919 257.6162 m S 142.7919 246.1712 m S 131.1334 246.1712 m S 131.1334 257.6162 m S 136.9626 251.8937 m S u 142.7919 246.1712 m S 142.7919 234.7261 m S 131.1334 234.7261 m S 131.1334 246.1712 m S 136.9626 240.4486 m S U 131.1334 234.7261 m S 131.1334 223.281 m S 119.4748 223.281 m S 119.4748 234.7261 m S 125.3041 229.0036 m S u 119.4748 234.7261 m S 119.4748 223.281 m S 107.8163 223.281 m S 107.8163 234.7261 m S 113.6455 229.0036 m S U u 119.4748 246.1712 m S 119.4748 234.7261 m S 107.8163 234.7261 m S 107.8163 246.1712 m S 113.6455 240.4486 m S U 0 g 1 w 4 M 113.6455 251.8937 m F 136.9626 251.8937 m F 113.6455 229.0036 m F 136.9626 229.0036 m F 0 G 0.3 w 10 M 154.4505 257.6162 m S 154.4505 246.1712 m S 142.7919 246.1712 m S 142.7919 257.6162 m S 148.6211 251.8937 m S u 177.7675 234.7261 m S 177.7675 223.281 m S 166.109 223.281 m S 166.109 234.7261 m S 171.9383 229.0036 m S U u 166.109 246.1712 m S 166.109 234.7261 m S 154.4505 234.7261 m S 154.4505 246.1712 m S 160.2797 240.4486 m S U 166.109 257.6162 m S 166.109 246.1712 m S 154.4505 246.1712 m S 154.4505 257.6162 m S 160.2797 251.8937 m S 177.7675 257.6162 m S 177.7675 246.1712 m S 166.109 246.1712 m S 166.109 257.6162 m S 171.9383 251.8937 m S u 177.7675 246.1712 m S 177.7675 234.7261 m S 166.109 234.7261 m S 166.109 246.1712 m S 171.9383 240.4486 m S U u 166.109 234.7261 m S 166.109 223.281 m S 154.4505 223.281 m S 154.4505 234.7261 m S 160.2797 229.0036 m S U u 154.4505 234.7261 m S 154.4505 223.281 m S 142.7919 223.281 m S 142.7919 234.7261 m S 148.6211 229.0036 m S U u 154.4505 246.1712 m S 154.4505 234.7261 m S 142.7919 234.7261 m S 142.7919 246.1712 m S 148.6211 240.4486 m S U 0 g 1 w 4 M 148.6211 251.8937 m F 171.9383 251.8937 m F 148.6211 229.0036 m F 171.9383 229.0036 m F 0 G 0.3 w 10 M 189.4261 257.6162 m S 189.4261 246.1712 m S 177.7675 246.1712 m S 177.7675 257.6162 m S 183.5967 251.8937 m S u 212.7431 234.7261 m S 212.7431 223.281 m S 201.0846 223.281 m S 201.0846 234.7261 m S 206.9139 229.0036 m S U u 201.0846 246.1712 m S 201.0846 234.7261 m S 189.4261 234.7261 m S 189.4261 246.1712 m S 195.2553 240.4486 m S U 201.0846 257.6162 m S 201.0846 246.1712 m S 189.4261 246.1712 m S 189.4261 257.6162 m S 195.2553 251.8937 m S 212.7431 257.6162 m S 212.7431 246.1712 m S 201.0846 246.1712 m S 201.0846 257.6162 m S 206.9139 251.8937 m S u 212.7431 246.1712 m S 212.7431 234.7261 m S 201.0846 234.7261 m S 201.0846 246.1712 m S 206.9139 240.4486 m S U u 201.0846 234.7261 m S 201.0846 223.281 m S 189.4261 223.281 m S 189.4261 234.7261 m S 195.2553 229.0036 m S U u 189.4261 234.7261 m S 189.4261 223.281 m S 177.7675 223.281 m S 177.7675 234.7261 m S 183.5967 229.0036 m S U u 189.4261 246.1712 m S 189.4261 234.7261 m S 177.7675 234.7261 m S 177.7675 246.1712 m S 183.5967 240.4486 m S U 0 g 1 w 4 M 183.5967 251.8937 m F 206.9139 251.8937 m F 183.5967 229.0036 m F 206.9139 229.0036 m F 0 G 0.3 w 10 M 212.7431 246.1712 m S 212.7431 257.6162 m S 212.7431 223.281 m S 212.7431 234.7261 m S 212.7431 234.7261 m S 212.7431 246.1712 m S u 119.4748 223.281 m S 119.4748 211.8359 m S 107.8163 211.8359 m S 107.8163 223.281 m S 113.6455 217.5585 m S U u 142.7919 200.3909 m S 142.7919 188.9459 m S 131.1334 188.9459 m S 131.1334 200.3909 m S 136.9626 194.6684 m S U u 131.1334 211.8359 m S 131.1334 200.3909 m S 119.4748 200.3909 m S 119.4748 211.8359 m S 125.3041 206.1135 m S U u 131.1334 223.281 m S 131.1334 211.8359 m S 119.4748 211.8359 m S 119.4748 223.281 m S 125.3041 217.5585 m S U u 142.7919 223.281 m S 142.7919 211.8359 m S 131.1334 211.8359 m S 131.1334 223.281 m S 136.9626 217.5585 m S U u 142.7919 211.8359 m S 142.7919 200.3909 m S 131.1334 200.3909 m S 131.1334 211.8359 m S 136.9626 206.1135 m S U u 131.1334 200.3909 m S 131.1334 188.9459 m S 119.4748 188.9459 m S 119.4748 200.3909 m S 125.3041 194.6684 m S U u 119.4748 200.3909 m S 119.4748 188.9459 m S 107.8163 188.9459 m S 107.8163 200.3909 m S 113.6455 194.6684 m S U u 119.4748 211.8359 m S 119.4748 200.3909 m S 107.8163 200.3909 m S 107.8163 211.8359 m S 113.6455 206.1135 m S U 0 g 1 w 4 M 113.6455 217.5585 m F 136.9626 217.5585 m F 113.6455 194.6684 m F 136.9626 194.6684 m F u 0 G 0.3 w 10 M 154.4505 223.281 m S 154.4505 211.8359 m S 142.7919 211.8359 m S 142.7919 223.281 m S 148.6211 217.5585 m S U u 177.7675 200.3909 m S 177.7675 188.9459 m S 166.109 188.9459 m S 166.109 200.3909 m S 171.9383 194.6684 m S U u 166.109 211.8359 m S 166.109 200.3909 m S 154.4505 200.3909 m S 154.4505 211.8359 m S 160.2797 206.1135 m S U u 166.109 223.281 m S 166.109 211.8359 m S 154.4505 211.8359 m S 154.4505 223.281 m S 160.2797 217.5585 m S U u 177.7675 223.281 m S 177.7675 211.8359 m S 166.109 211.8359 m S 166.109 223.281 m S 171.9383 217.5585 m S U u 177.7675 211.8359 m S 177.7675 200.3909 m S 166.109 200.3909 m S 166.109 211.8359 m S 171.9383 206.1135 m S U u 166.109 200.3909 m S 166.109 188.9459 m S 154.4505 188.9459 m S 154.4505 200.3909 m S 160.2797 194.6684 m S U u 154.4505 200.3909 m S 154.4505 188.9459 m S 142.7919 188.9459 m S 142.7919 200.3909 m S 148.6211 194.6684 m S U u 154.4505 211.8359 m S 154.4505 200.3909 m S 142.7919 200.3909 m S 142.7919 211.8359 m S 148.6211 206.1135 m S U 0 g 1 w 4 M 148.6211 217.5585 m F 171.9383 217.5585 m F 148.6211 194.6684 m F 171.9383 194.6684 m F u 0 G 0.3 w 10 M 189.4261 223.281 m S 189.4261 211.8359 m S 177.7675 211.8359 m S 177.7675 223.281 m S 183.5967 217.5585 m S U u 212.7431 200.3909 m S 212.7431 188.9459 m S 201.0846 188.9459 m S 201.0846 200.3909 m S 206.9139 194.6684 m S U u 201.0846 211.8359 m S 201.0846 200.3909 m S 189.4261 200.3909 m S 189.4261 211.8359 m S 195.2553 206.1135 m S U u 201.0846 223.281 m S 201.0846 211.8359 m S 189.4261 211.8359 m S 189.4261 223.281 m S 195.2553 217.5585 m S U u 212.7431 223.281 m S 212.7431 211.8359 m S 201.0846 211.8359 m S 201.0846 223.281 m S 206.9139 217.5585 m S U u 212.7431 211.8359 m S 212.7431 200.3909 m S 201.0846 200.3909 m S 201.0846 211.8359 m S 206.9139 206.1135 m S U u 201.0846 200.3909 m S 201.0846 188.9459 m S 189.4261 188.9459 m S 189.4261 200.3909 m S 195.2553 194.6684 m S U u 189.4261 200.3909 m S 189.4261 188.9459 m S 177.7675 188.9459 m S 177.7675 200.3909 m S 183.5967 194.6684 m S U u 189.4261 211.8359 m S 189.4261 200.3909 m S 177.7675 200.3909 m S 177.7675 211.8359 m S 183.5967 206.1135 m S U 0 g 1 w 4 M 183.5967 217.5585 m F 206.9139 217.5585 m F 183.5967 194.6684 m F 206.9139 194.6684 m F 0 G 0.3 w 10 M 212.7431 211.8359 m S 212.7431 223.281 m S 212.7431 188.9459 m S 212.7431 200.3909 m S 212.7431 200.3909 m S 212.7431 211.8359 m S 0 g 1 w 4 M 113.6455 183.2233 m F 136.9626 183.2233 m F 148.6211 183.2233 m F 171.9383 183.2233 m F 183.5967 183.2233 m F 206.9139 183.2233 m F u 0 G 0.3 w 10 M 119.4748 188.9459 m S 119.4748 177.5007 m S 107.8163 177.5007 m S 107.8163 188.9459 m S 113.6455 183.2233 m S U u 142.7919 166.0557 m S 142.7919 154.6107 m S 131.1334 154.6107 m S 131.1334 166.0557 m S 136.9626 160.3332 m S U u 131.1334 177.5007 m S 131.1334 166.0557 m S 119.4748 166.0557 m S 119.4748 177.5007 m S 125.3041 171.7782 m S U u 131.1334 188.9459 m S 131.1334 177.5007 m S 119.4748 177.5007 m S 119.4748 188.9459 m S 125.3041 183.2233 m S U u 142.7919 188.9459 m S 142.7919 177.5007 m S 131.1334 177.5007 m S 131.1334 188.9459 m S 136.9626 183.2233 m S U u 142.7919 177.5007 m S 142.7919 166.0557 m S 131.1334 166.0557 m S 131.1334 177.5007 m S 136.9626 171.7782 m S U u 131.1334 166.0557 m S 131.1334 154.6107 m S 119.4748 154.6107 m S 119.4748 166.0557 m S 125.3041 160.3332 m S U u 119.4748 166.0557 m S 119.4748 154.6107 m S 107.8163 154.6107 m S 107.8163 166.0557 m S 113.6455 160.3332 m S U u 119.4748 177.5007 m S 119.4748 166.0557 m S 107.8163 166.0557 m S 107.8163 177.5007 m S 113.6455 171.7782 m S U 0 g 1 w 4 M 113.6455 183.2233 m F 136.9626 183.2233 m F 113.6455 160.3332 m F 136.9626 160.3332 m F u 0 G 0.3 w 10 M 154.4505 188.9459 m S 154.4505 177.5007 m S 142.7919 177.5007 m S 142.7919 188.9459 m S 148.6211 183.2233 m S U u 177.7675 166.0557 m S 177.7675 154.6107 m S 166.109 154.6107 m S 166.109 166.0557 m S 171.9383 160.3332 m S U u 166.109 177.5007 m S 166.109 166.0557 m S 154.4505 166.0557 m S 154.4505 177.5007 m S 160.2797 171.7782 m S U u 166.109 188.9459 m S 166.109 177.5007 m S 154.4505 177.5007 m S 154.4505 188.9459 m S 160.2797 183.2233 m S U u 177.7675 188.9459 m S 177.7675 177.5007 m S 166.109 177.5007 m S 166.109 188.9459 m S 171.9383 183.2233 m S U u 177.7675 177.5007 m S 177.7675 166.0557 m S 166.109 166.0557 m S 166.109 177.5007 m S 171.9383 171.7782 m S U u 166.109 166.0557 m S 166.109 154.6107 m S 154.4505 154.6107 m S 154.4505 166.0557 m S 160.2797 160.3332 m S U u 154.4505 166.0557 m S 154.4505 154.6107 m S 142.7919 154.6107 m S 142.7919 166.0557 m S 148.6211 160.3332 m S U u 154.4505 177.5007 m S 154.4505 166.0557 m S 142.7919 166.0557 m S 142.7919 177.5007 m S 148.6211 171.7782 m S U 0 g 1 w 4 M 148.6211 183.2233 m F 171.9383 183.2233 m F 148.6211 160.3332 m F 171.9383 160.3332 m F u 0 G 0.3 w 10 M 189.4261 188.9459 m S 189.4261 177.5007 m S 177.7675 177.5007 m S 177.7675 188.9459 m S 183.5967 183.2233 m S U 212.7431 166.0557 m S 212.7431 154.6107 m S 201.0846 154.6107 m S 201.0846 166.0557 m S 206.9139 160.3332 m S u 201.0846 177.5007 m S 201.0846 166.0557 m S 189.4261 166.0557 m S 189.4261 177.5007 m S 195.2553 171.7782 m S U u 201.0846 188.9459 m S 201.0846 177.5007 m S 189.4261 177.5007 m S 189.4261 188.9459 m S 195.2553 183.2233 m S U u 212.7431 188.9459 m S 212.7431 177.5007 m S 201.0846 177.5007 m S 201.0846 188.9459 m S 206.9139 183.2233 m S U u 212.7431 177.5007 m S 212.7431 166.0557 m S 201.0846 166.0557 m S 201.0846 177.5007 m S 206.9139 171.7782 m S U 201.0846 166.0557 m S 201.0846 154.6107 m S 189.4261 154.6107 m S 189.4261 166.0557 m S 195.2553 160.3332 m S u 189.4261 166.0557 m S 189.4261 154.6107 m S 177.7675 154.6107 m S 177.7675 166.0557 m S 183.5967 160.3332 m S U u 189.4261 177.5007 m S 189.4261 166.0557 m S 177.7675 166.0557 m S 177.7675 177.5007 m S 183.5967 171.7782 m S U 0 g 1 w 4 M 183.5967 183.2233 m F 206.9139 183.2233 m F 183.5967 160.3332 m F 206.9139 160.3332 m F 0 G 0.3 w 10 M 212.7431 177.5007 m S 212.7431 188.9459 m S 212.7431 154.6107 m S 212.7431 166.0557 m S 212.7431 166.0557 m S 212.7431 177.5007 m S 119.4748 154.6107 m S 107.8163 154.6107 m S 131.1334 154.6107 m S 119.4748 154.6107 m S 142.7919 154.6107 m S 131.1334 154.6107 m S 154.4505 154.6107 m S 142.7919 154.6107 m S 166.109 154.6107 m S 154.4505 154.6107 m S 177.7675 154.6107 m S 166.109 154.6107 m S 189.4261 154.6107 m S 177.7675 154.6107 m S 201.0846 154.6107 m S 189.4261 154.6107 m S 212.7431 154.6107 m S 201.0846 154.6107 m S 212.7431 154.6107 m S u 49.5236 188.9459 m S 49.5236 177.5008 m S 37.8651 177.5008 m S 37.8651 188.9459 m S 43.6943 183.2233 m S U u 72.8407 166.0557 m S 72.8407 154.6107 m S 61.1821 154.6107 m S 61.1821 166.0557 m S 67.0114 160.3332 m S U u 61.1821 177.5008 m S 61.1821 166.0557 m S 49.5236 166.0557 m S 49.5236 177.5008 m S 55.3529 171.7783 m S U u 61.1821 188.9459 m S 61.1821 177.5008 m S 49.5236 177.5008 m S 49.5236 188.9459 m S 55.3529 183.2233 m S U u 72.8407 188.9459 m S 72.8407 177.5008 m S 61.1821 177.5008 m S 61.1821 188.9459 m S 67.0114 183.2233 m S U u 72.8407 177.5008 m S 72.8407 166.0557 m S 61.1821 166.0557 m S 61.1821 177.5008 m S 67.0114 171.7783 m S U u 61.1821 166.0557 m S 61.1821 154.6107 m S 49.5236 154.6107 m S 49.5236 166.0557 m S 55.3529 160.3332 m S U u 49.5236 166.0557 m S 49.5236 154.6107 m S 37.8651 154.6107 m S 37.8651 166.0557 m S 43.6943 160.3332 m S U u 49.5236 177.5008 m S 49.5236 166.0557 m S 37.8651 166.0557 m S 37.8651 177.5008 m S 43.6943 171.7783 m S U 0 g 1 w 4 M 43.6943 183.2233 m F 67.0114 183.2233 m F 43.6943 160.3332 m F 67.0114 160.3332 m F u 0 G 0.3 w 10 M 84.4992 188.9459 m S 84.4992 177.5008 m S 72.8407 177.5008 m S 72.8407 188.9459 m S 78.6699 183.2233 m S U u 107.8163 166.0557 m S 107.8163 154.6107 m S 96.1577 154.6107 m S 96.1577 166.0557 m S 101.987 160.3332 m S U u 96.1577 177.5008 m S 96.1577 166.0557 m S 84.4992 166.0557 m S 84.4992 177.5008 m S 90.3285 171.7783 m S U u 96.1577 188.9459 m S 96.1577 177.5008 m S 84.4992 177.5008 m S 84.4992 188.9459 m S 90.3285 183.2233 m S U u 107.8163 188.9459 m S 107.8163 177.5008 m S 96.1577 177.5008 m S 96.1577 188.9459 m S 101.987 183.2233 m S U u 107.8163 177.5008 m S 107.8163 166.0557 m S 96.1577 166.0557 m S 96.1577 177.5008 m S 101.987 171.7783 m S U u 96.1577 166.0557 m S 96.1577 154.6107 m S 84.4992 154.6107 m S 84.4992 166.0557 m S 90.3285 160.3332 m S U u 84.4992 166.0557 m S 84.4992 154.6107 m S 72.8407 154.6107 m S 72.8407 166.0557 m S 78.6699 160.3332 m S U u 84.4992 177.5008 m S 84.4992 166.0557 m S 72.8407 166.0557 m S 72.8407 177.5008 m S 78.6699 171.7783 m S U 0 g 1 w 4 M 78.6699 183.2233 m F 101.987 183.2233 m F 78.6699 160.3332 m F 101.987 160.3332 m F u 0 G 0.3 w 10 M 119.4748 188.9459 m S 119.4748 177.5008 m S 107.8163 177.5008 m S 107.8163 188.9459 m S 113.6455 183.2233 m S U u 142.7919 166.0557 m S 142.7919 154.6107 m S 131.1334 154.6107 m S 131.1334 166.0557 m S 136.9626 160.3332 m S U u 131.1334 177.5008 m S 131.1334 166.0557 m S 119.4748 166.0557 m S 119.4748 177.5008 m S 125.3041 171.7783 m S U u 131.1334 188.9459 m S 131.1334 177.5008 m S 119.4748 177.5008 m S 119.4748 188.9459 m S 125.3041 183.2233 m S U u 142.7919 188.9459 m S 142.7919 177.5008 m S 131.1334 177.5008 m S 131.1334 188.9459 m S 136.9626 183.2233 m S U u 142.7919 177.5008 m S 142.7919 166.0557 m S 131.1334 166.0557 m S 131.1334 177.5008 m S 136.9626 171.7783 m S U u 131.1334 166.0557 m S 131.1334 154.6107 m S 119.4748 154.6107 m S 119.4748 166.0557 m S 125.3041 160.3332 m S U u 119.4748 166.0557 m S 119.4748 154.6107 m S 107.8163 154.6107 m S 107.8163 166.0557 m S 113.6455 160.3332 m S U u 119.4748 177.5008 m S 119.4748 166.0557 m S 107.8163 166.0557 m S 107.8163 177.5008 m S 113.6455 171.7783 m S U 0 g 1 w 4 M 113.6455 183.2233 m F 136.9626 183.2233 m F 113.6455 160.3332 m F 136.9626 160.3332 m F 0 G 0.3 w 10 M 142.7919 177.5008 m S 142.7919 188.9459 m S 142.7919 154.6107 m S 142.7919 166.0557 m S 142.7919 166.0557 m S 142.7919 177.5008 m S u 49.5236 154.6107 m S 49.5236 143.1656 m S 37.8651 143.1656 m S 37.8651 154.6107 m S 43.6943 148.8881 m S U u 72.8407 131.7206 m S 72.8407 120.2755 m S 61.1821 120.2755 m S 61.1821 131.7206 m S 67.0114 125.998 m S U u 61.1821 143.1656 m S 61.1821 131.7206 m S 49.5236 131.7206 m S 49.5236 143.1656 m S 55.3529 137.4431 m S U u 61.1821 154.6107 m S 61.1821 143.1656 m S 49.5236 143.1656 m S 49.5236 154.6107 m S 55.3529 148.8881 m S U u 72.8407 154.6107 m S 72.8407 143.1656 m S 61.1821 143.1656 m S 61.1821 154.6107 m S 67.0114 148.8881 m S U u 72.8407 143.1656 m S 72.8407 131.7206 m S 61.1821 131.7206 m S 61.1821 143.1656 m S 67.0114 137.4431 m S U u 61.1821 131.7206 m S 61.1821 120.2755 m S 49.5236 120.2755 m S 49.5236 131.7206 m S 55.3529 125.998 m S U u 49.5236 131.7206 m S 49.5236 120.2755 m S 37.8651 120.2755 m S 37.8651 131.7206 m S 43.6943 125.998 m S U u 49.5236 143.1656 m S 49.5236 131.7206 m S 37.8651 131.7206 m S 37.8651 143.1656 m S 43.6943 137.4431 m S U 0 g 1 w 4 M 43.6943 148.8881 m F 67.0114 148.8881 m F 43.6943 125.998 m F 67.0114 125.998 m F u 0 G 0.3 w 10 M 84.4992 154.6107 m S 84.4992 143.1656 m S 72.8407 143.1656 m S 72.8407 154.6107 m S 78.6699 148.8881 m S U u 107.8163 131.7206 m S 107.8163 120.2755 m S 96.1577 120.2755 m S 96.1577 131.7206 m S 101.987 125.998 m S U u 96.1577 143.1656 m S 96.1577 131.7206 m S 84.4992 131.7206 m S 84.4992 143.1656 m S 90.3285 137.4431 m S U u 96.1577 154.6107 m S 96.1577 143.1656 m S 84.4992 143.1656 m S 84.4992 154.6107 m S 90.3285 148.8881 m S U u 107.8163 154.6107 m S 107.8163 143.1656 m S 96.1577 143.1656 m S 96.1577 154.6107 m S 101.987 148.8881 m S U u 107.8163 143.1656 m S 107.8163 131.7206 m S 96.1577 131.7206 m S 96.1577 143.1656 m S 101.987 137.4431 m S U u 96.1577 131.7206 m S 96.1577 120.2755 m S 84.4992 120.2755 m S 84.4992 131.7206 m S 90.3285 125.998 m S U u 84.4992 131.7206 m S 84.4992 120.2755 m S 72.8407 120.2755 m S 72.8407 131.7206 m S 78.6699 125.998 m S U u 84.4992 143.1656 m S 84.4992 131.7206 m S 72.8407 131.7206 m S 72.8407 143.1656 m S 78.6699 137.4431 m S U 0 g 1 w 4 M 78.6699 148.8881 m F 101.987 148.8881 m F 78.6699 125.998 m F 101.987 125.998 m F u 0 G 0.3 w 10 M 119.4748 154.6107 m S 119.4748 143.1656 m S 107.8163 143.1656 m S 107.8163 154.6107 m S 113.6455 148.8881 m S U u 142.7919 131.7206 m S 142.7919 120.2755 m S 131.1334 120.2755 m S 131.1334 131.7206 m S 136.9626 125.998 m S U u 131.1334 143.1656 m S 131.1334 131.7206 m S 119.4748 131.7206 m S 119.4748 143.1656 m S 125.3041 137.4431 m S U u 131.1334 154.6107 m S 131.1334 143.1656 m S 119.4748 143.1656 m S 119.4748 154.6107 m S 125.3041 148.8881 m S U u 142.7919 154.6107 m S 142.7919 143.1656 m S 131.1334 143.1656 m S 131.1334 154.6107 m S 136.9626 148.8881 m S U u 142.7919 143.1656 m S 142.7919 131.7206 m S 131.1334 131.7206 m S 131.1334 143.1656 m S 136.9626 137.4431 m S U u 131.1334 131.7206 m S 131.1334 120.2755 m S 119.4748 120.2755 m S 119.4748 131.7206 m S 125.3041 125.998 m S U u 119.4748 131.7206 m S 119.4748 120.2755 m S 107.8163 120.2755 m S 107.8163 131.7206 m S 113.6455 125.998 m S U u 119.4748 143.1656 m S 119.4748 131.7206 m S 107.8163 131.7206 m S 107.8163 143.1656 m S 113.6455 137.4431 m S U 0 g 1 w 4 M 113.6455 148.8881 m F 136.9626 148.8881 m F 113.6455 125.998 m F 136.9626 125.998 m F 0 G 0.3 w 10 M 142.7919 143.1656 m S 142.7919 154.6107 m S 142.7919 120.2755 m S 142.7919 131.7206 m S 142.7919 131.7206 m S 142.7919 143.1656 m S 0 g 1 w 4 M 43.6943 114.553 m F 67.0114 114.553 m F 78.6699 114.553 m F 101.987 114.553 m F 113.6455 114.553 m F 136.9626 114.553 m F u 0 G 0.3 w 10 M 49.5236 120.2755 m S 49.5236 108.8304 m S 37.8651 108.8304 m S 37.8651 120.2755 m S 43.6943 114.553 m S U u 72.8407 97.3853 m S 72.8407 85.9403 m S 61.1821 85.9403 m S 61.1821 97.3853 m S 67.0114 91.6628 m S U u 61.1821 108.8304 m S 61.1821 97.3853 m S 49.5236 97.3853 m S 49.5236 108.8304 m S 55.3529 103.1079 m S U u 61.1821 120.2755 m S 61.1821 108.8304 m S 49.5236 108.8304 m S 49.5236 120.2755 m S 55.3529 114.553 m S U u 72.8407 120.2755 m S 72.8407 108.8304 m S 61.1821 108.8304 m S 61.1821 120.2755 m S 67.0114 114.553 m S U u 72.8407 108.8304 m S 72.8407 97.3853 m S 61.1821 97.3853 m S 61.1821 108.8304 m S 67.0114 103.1079 m S U u 61.1821 97.3853 m S 61.1821 85.9403 m S 49.5236 85.9403 m S 49.5236 97.3853 m S 55.3529 91.6628 m S U u 49.5236 97.3853 m S 49.5236 85.9403 m S 37.8651 85.9403 m S 37.8651 97.3853 m S 43.6943 91.6628 m S U u 49.5236 108.8304 m S 49.5236 97.3853 m S 37.8651 97.3853 m S 37.8651 108.8304 m S 43.6943 103.1079 m S U 0 g 1 w 4 M 43.6943 114.553 m F 67.0114 114.553 m F 43.6943 91.6628 m F 67.0114 91.6628 m F u 0 G 0.3 w 10 M 84.4992 120.2755 m S 84.4992 108.8304 m S 72.8407 108.8304 m S 72.8407 120.2755 m S 78.6699 114.553 m S U u 107.8163 97.3853 m S 107.8163 85.9403 m S 96.1577 85.9403 m S 96.1577 97.3853 m S 101.987 91.6628 m S U u 96.1577 108.8304 m S 96.1577 97.3853 m S 84.4992 97.3853 m S 84.4992 108.8304 m S 90.3285 103.1079 m S U u 96.1577 120.2755 m S 96.1577 108.8304 m S 84.4992 108.8304 m S 84.4992 120.2755 m S 90.3285 114.553 m S U u 107.8163 120.2755 m S 107.8163 108.8304 m S 96.1577 108.8304 m S 96.1577 120.2755 m S 101.987 114.553 m S U u 107.8163 108.8304 m S 107.8163 97.3853 m S 96.1577 97.3853 m S 96.1577 108.8304 m S 101.987 103.1079 m S U u 96.1577 97.3853 m S 96.1577 85.9403 m S 84.4992 85.9403 m S 84.4992 97.3853 m S 90.3285 91.6628 m S U u 84.4992 97.3853 m S 84.4992 85.9403 m S 72.8407 85.9403 m S 72.8407 97.3853 m S 78.6699 91.6628 m S U u 84.4992 108.8304 m S 84.4992 97.3853 m S 72.8407 97.3853 m S 72.8407 108.8304 m S 78.6699 103.1079 m S U 0 g 1 w 4 M 78.6699 114.553 m F 101.987 114.553 m F 78.6699 91.6628 m F 101.987 91.6628 m F u 0 G 0.3 w 10 M 119.4748 120.2755 m S 119.4748 108.8304 m S 107.8163 108.8304 m S 107.8163 120.2755 m S 113.6455 114.553 m S U u 142.7919 97.3853 m S 142.7919 85.9403 m S 131.1334 85.9403 m S 131.1334 97.3853 m S 136.9626 91.6628 m S U u 131.1334 108.8304 m S 131.1334 97.3853 m S 119.4748 97.3853 m S 119.4748 108.8304 m S 125.3041 103.1079 m S U u 131.1334 120.2755 m S 131.1334 108.8304 m S 119.4748 108.8304 m S 119.4748 120.2755 m S 125.3041 114.553 m S U u 142.7919 120.2755 m S 142.7919 108.8304 m S 131.1334 108.8304 m S 131.1334 120.2755 m S 136.9626 114.553 m S U u 142.7919 108.8304 m S 142.7919 97.3853 m S 131.1334 97.3853 m S 131.1334 108.8304 m S 136.9626 103.1079 m S U u 131.1334 97.3853 m S 131.1334 85.9403 m S 119.4748 85.9403 m S 119.4748 97.3853 m S 125.3041 91.6628 m S U u 119.4748 97.3853 m S 119.4748 85.9403 m S 107.8163 85.9403 m S 107.8163 97.3853 m S 113.6455 91.6628 m S U u 119.4748 108.8304 m S 119.4748 97.3853 m S 107.8163 97.3853 m S 107.8163 108.8304 m S 113.6455 103.1079 m S U 0 g 1 w 4 M 113.6455 114.553 m F 136.9626 114.553 m F 113.6455 91.6628 m F 136.9626 91.6628 m F 0 G 0.3 w 10 M 142.7919 108.8304 m S 142.7919 120.2755 m S 142.7919 85.9403 m S 142.7919 97.3853 m S 142.7919 97.3853 m S 142.7919 108.8304 m S 49.5236 85.9403 m S 37.8651 85.9403 m S 61.1821 85.9403 m S 49.5236 85.9403 m S 72.8407 85.9403 m S 61.1821 85.9403 m S 84.4992 85.9403 m S 72.8407 85.9403 m S 96.1577 85.9403 m S 84.4992 85.9403 m S 107.8163 85.9403 m S 96.1577 85.9403 m S 119.4748 85.9403 m S 107.8163 85.9403 m S 131.1334 85.9403 m S 119.4748 85.9403 m S 142.7919 85.9403 m S 131.1334 85.9403 m S 142.7919 85.9403 m S u 119.4748 188.9459 m S 119.4748 177.5008 m S 107.8163 177.5008 m S 107.8163 188.9459 m S 113.6455 183.2233 m S U u 142.7919 166.0557 m S 142.7919 154.6107 m S 131.1334 154.6107 m S 131.1334 166.0557 m S 136.9626 160.3332 m S U u 131.1334 177.5008 m S 131.1334 166.0557 m S 119.4748 166.0557 m S 119.4748 177.5008 m S 125.3041 171.7783 m S U u 131.1334 188.9459 m S 131.1334 177.5008 m S 119.4748 177.5008 m S 119.4748 188.9459 m S 125.3041 183.2233 m S U u 142.7919 188.9459 m S 142.7919 177.5008 m S 131.1334 177.5008 m S 131.1334 188.9459 m S 136.9626 183.2233 m S U u 142.7919 177.5008 m S 142.7919 166.0557 m S 131.1334 166.0557 m S 131.1334 177.5008 m S 136.9626 171.7783 m S U u 131.1334 166.0557 m S 131.1334 154.6107 m S 119.4748 154.6107 m S 119.4748 166.0557 m S 125.3041 160.3332 m S U u 119.4748 166.0557 m S 119.4748 154.6107 m S 107.8163 154.6107 m S 107.8163 166.0557 m S 113.6455 160.3332 m S U u 119.4748 177.5008 m S 119.4748 166.0557 m S 107.8163 166.0557 m S 107.8163 177.5008 m S 113.6455 171.7783 m S U 0 g 1 w 4 M 113.6455 183.2233 m F 136.9626 183.2233 m F 113.6455 160.3332 m F 136.9626 160.3332 m F u 0 G 0.3 w 10 M 154.4505 188.9459 m S 154.4505 177.5008 m S 142.7919 177.5008 m S 142.7919 188.9459 m S 148.6211 183.2233 m S U u 177.7675 166.0557 m S 177.7675 154.6107 m S 166.109 154.6107 m S 166.109 166.0557 m S 171.9383 160.3332 m S U u 166.109 177.5008 m S 166.109 166.0557 m S 154.4505 166.0557 m S 154.4505 177.5008 m S 160.2797 171.7783 m S U u 166.109 188.9459 m S 166.109 177.5008 m S 154.4505 177.5008 m S 154.4505 188.9459 m S 160.2797 183.2233 m S U u 177.7675 188.9459 m S 177.7675 177.5008 m S 166.109 177.5008 m S 166.109 188.9459 m S 171.9383 183.2233 m S U u 177.7675 177.5008 m S 177.7675 166.0557 m S 166.109 166.0557 m S 166.109 177.5008 m S 171.9383 171.7783 m S U u 166.109 166.0557 m S 166.109 154.6107 m S 154.4505 154.6107 m S 154.4505 166.0557 m S 160.2797 160.3332 m S U u 154.4505 166.0557 m S 154.4505 154.6107 m S 142.7919 154.6107 m S 142.7919 166.0557 m S 148.6211 160.3332 m S U u 154.4505 177.5008 m S 154.4505 166.0557 m S 142.7919 166.0557 m S 142.7919 177.5008 m S 148.6211 171.7783 m S U 0 g 1 w 4 M 148.6211 183.2233 m F 171.9383 183.2233 m F 148.6211 160.3332 m F 171.9383 160.3332 m F u 0 G 0.3 w 10 M 189.4261 188.9459 m S 189.4261 177.5008 m S 177.7675 177.5008 m S 177.7675 188.9459 m S 183.5967 183.2233 m S U 212.7431 166.0557 m S 212.7431 154.6107 m S 201.0846 154.6107 m S 201.0846 166.0557 m S 206.9139 160.3332 m S u 201.0846 177.5008 m S 201.0846 166.0557 m S 189.4261 166.0557 m S 189.4261 177.5008 m S 195.2553 171.7783 m S U u 201.0846 188.9459 m S 201.0846 177.5008 m S 189.4261 177.5008 m S 189.4261 188.9459 m S 195.2553 183.2233 m S U u 212.7431 188.9459 m S 212.7431 177.5008 m S 201.0846 177.5008 m S 201.0846 188.9459 m S 206.9139 183.2233 m S U u 212.7431 177.5008 m S 212.7431 166.0557 m S 201.0846 166.0557 m S 201.0846 177.5008 m S 206.9139 171.7783 m S U 201.0846 166.0557 m S 201.0846 154.6107 m S 189.4261 154.6107 m S 189.4261 166.0557 m S 195.2553 160.3332 m S u 189.4261 166.0557 m S 189.4261 154.6107 m S 177.7675 154.6107 m S 177.7675 166.0557 m S 183.5967 160.3332 m S U u 189.4261 177.5008 m S 189.4261 166.0557 m S 177.7675 166.0557 m S 177.7675 177.5008 m S 183.5967 171.7783 m S U 0 g 1 w 4 M 183.5967 183.2233 m F 206.9139 183.2233 m F 183.5967 160.3332 m F 206.9139 160.3332 m F 0 G 0.3 w 10 M 212.7431 177.5008 m S 212.7431 188.9459 m S 212.7431 154.6107 m S 212.7431 166.0557 m S 212.7431 166.0557 m S 212.7431 177.5008 m S u 119.4748 154.6107 m S 119.4748 143.1656 m S 107.8163 143.1656 m S 107.8163 154.6107 m S 113.6455 148.8881 m S U u 142.7919 131.7206 m S 142.7919 120.2755 m S 131.1334 120.2755 m S 131.1334 131.7206 m S 136.9626 125.998 m S U u 131.1334 143.1656 m S 131.1334 131.7206 m S 119.4748 131.7206 m S 119.4748 143.1656 m S 125.3041 137.4431 m S U u 131.1334 154.6107 m S 131.1334 143.1656 m S 119.4748 143.1656 m S 119.4748 154.6107 m S 125.3041 148.8881 m S U u 142.7919 154.6107 m S 142.7919 143.1656 m S 131.1334 143.1656 m S 131.1334 154.6107 m S 136.9626 148.8881 m S U u 142.7919 143.1656 m S 142.7919 131.7206 m S 131.1334 131.7206 m S 131.1334 143.1656 m S 136.9626 137.4431 m S U u 131.1334 131.7206 m S 131.1334 120.2755 m S 119.4748 120.2755 m S 119.4748 131.7206 m S 125.3041 125.998 m S U u 119.4748 131.7206 m S 119.4748 120.2755 m S 107.8163 120.2755 m S 107.8163 131.7206 m S 113.6455 125.998 m S U u 119.4748 143.1656 m S 119.4748 131.7206 m S 107.8163 131.7206 m S 107.8163 143.1656 m S 113.6455 137.4431 m S U 0 g 1 w 4 M 113.6455 148.8881 m F 136.9626 148.8881 m F 113.6455 125.998 m F 136.9626 125.998 m F u 0 G 0.3 w 10 M 154.4505 154.6107 m S 154.4505 143.1656 m S 142.7919 143.1656 m S 142.7919 154.6107 m S 148.6211 148.8881 m S U u 177.7675 131.7206 m S 177.7675 120.2755 m S 166.109 120.2755 m S 166.109 131.7206 m S 171.9383 125.998 m S U u 166.109 143.1656 m S 166.109 131.7206 m S 154.4505 131.7206 m S 154.4505 143.1656 m S 160.2797 137.4431 m S U u 166.109 154.6107 m S 166.109 143.1656 m S 154.4505 143.1656 m S 154.4505 154.6107 m S 160.2797 148.8881 m S U u 177.7675 154.6107 m S 177.7675 143.1656 m S 166.109 143.1656 m S 166.109 154.6107 m S 171.9383 148.8881 m S U u 177.7675 143.1656 m S 177.7675 131.7206 m S 166.109 131.7206 m S 166.109 143.1656 m S 171.9383 137.4431 m S U u 166.109 131.7206 m S 166.109 120.2755 m S 154.4505 120.2755 m S 154.4505 131.7206 m S 160.2797 125.998 m S U u 154.4505 131.7206 m S 154.4505 120.2755 m S 142.7919 120.2755 m S 142.7919 131.7206 m S 148.6211 125.998 m S U u 154.4505 143.1656 m S 154.4505 131.7206 m S 142.7919 131.7206 m S 142.7919 143.1656 m S 148.6211 137.4431 m S U 0 g 1 w 4 M 148.6211 148.8881 m F 171.9383 148.8881 m F 148.6211 125.998 m F 171.9383 125.998 m F u 0 G 0.3 w 10 M 189.4261 154.6107 m S 189.4261 143.1656 m S 177.7675 143.1656 m S 177.7675 154.6107 m S 183.5967 148.8881 m S U u 212.7431 131.7206 m S 212.7431 120.2755 m S 201.0846 120.2755 m S 201.0846 131.7206 m S 206.9139 125.998 m S U 201.0846 143.1656 m S 201.0846 131.7206 m S 189.4261 131.7206 m S 189.4261 143.1656 m S 195.2553 137.4431 m S 201.0846 154.6107 m S 201.0846 143.1656 m S 189.4261 143.1656 m S 189.4261 154.6107 m S 195.2553 148.8881 m S 212.7431 154.6107 m S 212.7431 143.1656 m S 201.0846 143.1656 m S 201.0846 154.6107 m S 206.9139 148.8881 m S 212.7431 143.1656 m S 212.7431 131.7206 m S 201.0846 131.7206 m S 201.0846 143.1656 m S 206.9139 137.4431 m S u 201.0846 131.7206 m S 201.0846 120.2755 m S 189.4261 120.2755 m S 189.4261 131.7206 m S 195.2553 125.998 m S U u 189.4261 131.7206 m S 189.4261 120.2755 m S 177.7675 120.2755 m S 177.7675 131.7206 m S 183.5967 125.998 m S U u 189.4261 143.1656 m S 189.4261 131.7206 m S 177.7675 131.7206 m S 177.7675 143.1656 m S 183.5967 137.4431 m S U 0 g 1 w 4 M 183.5967 148.8881 m F 206.9139 148.8881 m F 183.5967 125.998 m F 206.9139 125.998 m F 0 G 0.3 w 10 M 212.7431 143.1656 m S 212.7431 154.6107 m S 212.7431 120.2755 m S 212.7431 131.7206 m S 212.7431 131.7206 m S 212.7431 143.1656 m S 0 g 1 w 4 M 113.6455 114.553 m F 136.9626 114.553 m F 148.6211 114.553 m F 171.9383 114.553 m F 183.5967 114.553 m F 206.9139 114.553 m F u 0 G 0.3 w 10 M 119.4748 120.2755 m S 119.4748 108.8304 m S 107.8163 108.8304 m S 107.8163 120.2755 m S 113.6455 114.553 m S U u 142.7919 97.3853 m S 142.7919 85.9403 m S 131.1334 85.9403 m S 131.1334 97.3853 m S 136.9626 91.6628 m S U u 131.1334 108.8304 m S 131.1334 97.3853 m S 119.4748 97.3853 m S 119.4748 108.8304 m S 125.3041 103.1079 m S U u 131.1334 120.2755 m S 131.1334 108.8304 m S 119.4748 108.8304 m S 119.4748 120.2755 m S 125.3041 114.553 m S U u 142.7919 120.2755 m S 142.7919 108.8304 m S 131.1334 108.8304 m S 131.1334 120.2755 m S 136.9626 114.553 m S U u 142.7919 108.8304 m S 142.7919 97.3853 m S 131.1334 97.3853 m S 131.1334 108.8304 m S 136.9626 103.1079 m S U u 131.1334 97.3853 m S 131.1334 85.9403 m S 119.4748 85.9403 m S 119.4748 97.3853 m S 125.3041 91.6628 m S U u 119.4748 97.3853 m S 119.4748 85.9403 m S 107.8163 85.9403 m S 107.8163 97.3853 m S 113.6455 91.6628 m S U u 119.4748 108.8304 m S 119.4748 97.3853 m S 107.8163 97.3853 m S 107.8163 108.8304 m S 113.6455 103.1079 m S U 0 g 1 w 4 M 113.6455 114.553 m F 136.9626 114.553 m F 113.6455 91.6628 m F 136.9626 91.6628 m F u 0 G 0.3 w 10 M 154.4505 120.2755 m S 154.4505 108.8304 m S 142.7919 108.8304 m S 142.7919 120.2755 m S 148.6211 114.553 m S U u 177.7675 97.3853 m S 177.7675 85.9403 m S 166.109 85.9403 m S 166.109 97.3853 m S 171.9383 91.6628 m S U u 166.109 108.8304 m S 166.109 97.3853 m S 154.4505 97.3853 m S 154.4505 108.8304 m S 160.2797 103.1079 m S U u 166.109 120.2755 m S 166.109 108.8304 m S 154.4505 108.8304 m S 154.4505 120.2755 m S 160.2797 114.553 m S U u 177.7675 120.2755 m S 177.7675 108.8304 m S 166.109 108.8304 m S 166.109 120.2755 m S 171.9383 114.553 m S U u 177.7675 108.8304 m S 177.7675 97.3853 m S 166.109 97.3853 m S 166.109 108.8304 m S 171.9383 103.1079 m S U u 166.109 97.3853 m S 166.109 85.9403 m S 154.4505 85.9403 m S 154.4505 97.3853 m S 160.2797 91.6628 m S U u 154.4505 97.3853 m S 154.4505 85.9403 m S 142.7919 85.9403 m S 142.7919 97.3853 m S 148.6211 91.6628 m S U u 154.4505 108.8304 m S 154.4505 97.3853 m S 142.7919 97.3853 m S 142.7919 108.8304 m S 148.6211 103.1079 m S U 0 g 1 w 4 M 148.6211 114.553 m F 171.9383 114.553 m F 148.6211 91.6628 m F 171.9383 91.6628 m F u 0 G 0.3 w 10 M 189.4261 120.2755 m S 189.4261 108.8304 m S 177.7675 108.8304 m S 177.7675 120.2755 m S 183.5967 114.553 m S U u 212.7431 97.3853 m S 212.7431 85.9403 m S 201.0846 85.9403 m S 201.0846 97.3853 m S 206.9139 91.6628 m S U u 201.0846 108.8304 m S 201.0846 97.3853 m S 189.4261 97.3853 m S 189.4261 108.8304 m S 195.2553 103.1079 m S U u 201.0846 120.2755 m S 201.0846 108.8304 m S 189.4261 108.8304 m S 189.4261 120.2755 m S 195.2553 114.553 m S U u 212.7431 120.2755 m S 212.7431 108.8304 m S 201.0846 108.8304 m S 201.0846 120.2755 m S 206.9139 114.553 m S U u 212.7431 108.8304 m S 212.7431 97.3853 m S 201.0846 97.3853 m S 201.0846 108.8304 m S 206.9139 103.1079 m S U u 201.0846 97.3853 m S 201.0846 85.9403 m S 189.4261 85.9403 m S 189.4261 97.3853 m S 195.2553 91.6628 m S U u 189.4261 97.3853 m S 189.4261 85.9403 m S 177.7675 85.9403 m S 177.7675 97.3853 m S 183.5967 91.6628 m S U u 189.4261 108.8304 m S 189.4261 97.3853 m S 177.7675 97.3853 m S 177.7675 108.8304 m S 183.5967 103.1079 m S U 0 g 1 w 4 M 183.5967 114.553 m F 206.9139 114.553 m F 183.5967 91.6628 m F 206.9139 91.6628 m F 0 G 0.3 w 10 M 212.7431 108.8304 m S 212.7431 120.2755 m S 212.7431 85.9403 m S 212.7431 97.3853 m S 212.7431 97.3853 m S 212.7431 108.8304 m S 119.4748 85.9403 m S 107.8163 85.9403 m S 131.1334 85.9403 m S 119.4748 85.9403 m S 142.7919 85.9403 m S 131.1334 85.9403 m S 154.4505 85.9403 m S 142.7919 85.9403 m S 166.109 85.9403 m S 154.4505 85.9403 m S 177.7675 85.9403 m S 166.109 85.9403 m S 189.4261 85.9403 m S 177.7675 85.9403 m S 201.0846 85.9403 m S 189.4261 85.9403 m S 212.7431 85.9403 m S 201.0846 85.9403 m S 212.7431 85.9403 m S 61.1821 234.7261 m S 0 g 1 w 4 M 61.1821 234.7261 m F 0 G 0.3 w 10 M 61.1821 234.7261 m S 61.1821 234.7261 m S 61.1821 234.7261 m S 0 g 1 w 4 M 61.1821 234.7261 m F 0 G 0.3 w 10 M 61.1821 234.7261 m S 61.1821 234.7261 m S 61.1821 234.7261 m S 0 g 1 w 4 M 61.1821 234.7261 m F 0 G 0.3 w 10 M 61.1821 234.7261 m S 61.1821 234.7261 m S 72.8407 223.281 m S 0 g 1 w 4 M 72.8407 223.281 m F 0 G 0.3 w 10 M 72.8407 223.281 m S 72.8407 223.281 m S 72.8407 223.281 m S 0 g 1 w 4 M 72.8407 223.281 m F 0 G 0.3 w 10 M 72.8407 223.281 m S 72.8407 223.281 m S 72.8407 223.281 m S 0 g 1 w 4 M 72.8407 223.281 m F 0 G 0.3 w 10 M 72.8407 223.281 m S 72.8407 223.281 m S 72.8407 223.281 m S 0 g 1 w 4 M 72.8407 223.281 m F 0 G 0.3 w 10 M 72.8407 223.281 m S 72.8407 223.281 m S 72.8407 223.281 m S 0 g 1 w 4 M 72.8407 223.281 m F 0 G 0.3 w 10 M 72.8407 223.281 m S 72.8407 223.281 m S u 1 g 1 w 4 M 72.8407 223.281 m F U 0 G 0.3 w 10 M 72.8407 223.281 m S 0 g 1 w 4 M 72.8407 223.281 m F 0 G 0.3 w 10 M 72.8407 223.281 m S 72.8407 223.281 m S 72.8407 234.7261 m S 0 g 1 w 4 M 72.8407 234.7261 m F 0 G 0.3 w 10 M 72.8407 234.7261 m S 72.8407 234.7261 m S 72.8407 234.7261 m S 0 g 1 w 4 M 72.8407 234.7261 m F 0 G 0.3 w 10 M 72.8407 234.7261 m S 72.8407 234.7261 m S 72.8407 234.7261 m S 0 g 1 w 4 M 72.8407 234.7261 m F 0 G 0.3 w 10 M 72.8407 234.7261 m S 72.8407 234.7261 m S 61.1821 223.281 m S 0 g 1 w 4 M 61.1821 223.281 m F 0 G 0.3 w 10 M 61.1821 223.281 m S 61.1821 223.281 m S 61.1821 223.281 m S 0 g 1 w 4 M 61.1821 223.281 m F 0 G 0.3 w 10 M 61.1821 223.281 m S 61.1821 223.281 m S 61.1821 223.281 m S 0 g 1 w 4 M 61.1821 223.281 m F 0 G 0.3 w 10 M 61.1821 223.281 m S 61.1821 223.281 m S 61.1821 211.8359 m S 0 g 1 w 4 M 61.1821 211.8359 m F 0 G 0.3 w 10 M 61.1821 211.8359 m S 61.1821 211.8359 m S 61.1821 211.8359 m S 0 g 1 w 4 M 61.1821 211.8359 m F 0 G 0.3 w 10 M 61.1821 211.8359 m S 61.1821 211.8359 m S 61.1821 211.8359 m S 0 g 1 w 4 M 61.1821 211.8359 m F 0 G 0.3 w 10 M 61.1821 211.8359 m S 61.1821 211.8359 m S 61.1821 200.3909 m S 0 g 1 w 4 M 61.1821 200.3909 m F 0 G 0.3 w 10 M 61.1821 200.3909 m S 61.1821 200.3909 m S 61.1821 200.3909 m S 0 g 1 w 4 M 61.1821 200.3909 m F 0 G 0.3 w 10 M 61.1821 200.3909 m S 61.1821 200.3909 m S 1 g 0.5 w 4 M 61.1821 200.3909 m B 0.3 w 10 M 61.1821 200.3909 m S 0 g 1 w 4 M 61.1821 200.3909 m F 0 G 0.3 w 10 M 61.1821 200.3909 m S 61.1821 200.3909 m S 72.8407 188.9459 m S 0 g 1 w 4 M 72.8407 188.9459 m F 0 G 0.3 w 10 M 72.8407 188.9459 m S 0 g 1 w 4 M 72.8407 188.9459 m F 0 G 0.3 w 10 M 72.8407 188.9459 m S 0 g 1 w 4 M 72.8407 188.9459 m F 0 G 0.3 w 10 M 72.8407 188.9459 m S 0 g 1 w 4 M 72.8407 188.9459 m F 0 G 0.3 w 10 M 72.8407 188.9459 m S 0 g 1 w 4 M 72.8407 188.9459 m F 0 G 0.3 w 10 M 72.8407 188.9459 m S 72.8407 188.9459 m S 72.8407 188.9459 m S 0 g 1 w 4 M 72.8407 188.9459 m F 0 G 0.3 w 10 M 72.8407 188.9459 m S 72.8407 188.9459 m S 1 g 1 w 4 M 72.8407 188.9459 m F 0 G 0.3 w 10 M 72.8407 188.9459 m S 0 g 1 w 4 M 72.8407 188.9459 m F 0 G 0.3 w 10 M 72.8407 188.9459 m S 72.8407 188.9459 m S 1 g 0.5 w 4 M 72.8407 188.9459 m B 0.3 w 10 M 72.8407 188.9459 m S 0 g 1 w 4 M 72.8407 188.9459 m F 0 G 0.3 w 10 M 72.8407 188.9459 m S 72.8407 188.9459 m S 72.8407 188.9459 m S 0 g 1 w 4 M 72.8407 188.9459 m F 0 G 0.3 w 10 M 72.8407 188.9459 m S 72.8407 188.9459 m S u 1 g 1 w 4 M 72.8407 188.9459 m F U 0 G 0.3 w 10 M 72.8407 188.9459 m S 0 g 1 w 4 M 72.8407 188.9459 m F 0 G 0.3 w 10 M 72.8407 188.9459 m S 72.8407 188.9459 m S 72.8407 188.9459 m S 0 g 1 w 4 M 72.8407 188.9459 m F 0 G 0.3 w 10 M 72.8407 188.9459 m S 72.8407 188.9459 m S 72.8407 188.9459 m S 0 g 1 w 4 M 72.8407 188.9459 m F 0 G 0.3 w 10 M 72.8407 188.9459 m S 72.8407 188.9459 m S u 1 g 1 w 4 M 72.8407 188.9459 m F U 0 G 0.3 w 10 M 72.8407 188.9459 m S 0 g 1 w 4 M 72.8407 188.9459 m F 0 G 0.3 w 10 M 72.8407 188.9459 m S 72.8407 188.9459 m S 72.8407 211.8359 m S 0 g 1 w 4 M 72.8407 211.8359 m F 0 G 0.3 w 10 M 72.8407 211.8359 m S 72.8407 211.8359 m S 72.8407 211.8359 m S 0 g 1 w 4 M 72.8407 211.8359 m F 0 G 0.3 w 10 M 72.8407 211.8359 m S 72.8407 211.8359 m S 72.8407 211.8359 m S 0 g 1 w 4 M 72.8407 211.8359 m F 0 G 0.3 w 10 M 72.8407 211.8359 m S 72.8407 211.8359 m S 61.1821 188.9459 m S 0 g 1 w 4 M 61.1821 188.9459 m F 0 G 0.3 w 10 M 61.1821 188.9459 m S 61.1821 188.9459 m S 61.1821 188.9459 m S 0 g 1 w 4 M 61.1821 188.9459 m F 0 G 0.3 w 10 M 61.1821 188.9459 m S 61.1821 188.9459 m S 61.1821 188.9459 m S 0 g 1 w 4 M 61.1821 188.9459 m F 0 G 0.3 w 10 M 61.1821 188.9459 m S 61.1821 188.9459 m S 72.8407 200.3909 m S 0 g 1 w 4 M 72.8407 200.3909 m F 0 G 0.3 w 10 M 72.8407 200.3909 m S 0 g 1 w 4 M 72.8407 200.3909 m F 0 G 0.3 w 10 M 72.8407 200.3909 m S 0 g 1 w 4 M 72.8407 200.3909 m F 0 G 0.3 w 10 M 72.8407 200.3909 m S 0 g 1 w 4 M 72.8407 200.3909 m F 0 G 0.3 w 10 M 224.4016 257.6162 m S 224.4016 246.1712 m S 212.7431 246.1712 m S 212.7431 257.6162 m S 218.5723 251.8937 m S u 247.7187 234.7261 m S 247.7187 223.281 m S 236.0601 223.281 m S 236.0601 234.7261 m S 241.8894 229.0036 m S U 236.0601 246.1712 m S 236.0601 234.7261 m S 224.4016 234.7261 m S 224.4016 246.1712 m S 230.2309 240.4486 m S 236.0601 257.6162 m S 236.0601 246.1712 m S 224.4016 246.1712 m S 224.4016 257.6162 m S 230.2309 251.8937 m S 247.7187 257.6162 m S 247.7187 246.1712 m S 236.0601 246.1712 m S 236.0601 257.6162 m S 241.8894 251.8937 m S u 247.7187 246.1712 m S 247.7187 234.7261 m S 236.0601 234.7261 m S 236.0601 246.1712 m S 241.8894 240.4486 m S U u 236.0601 234.7261 m S 236.0601 223.281 m S 224.4016 223.281 m S 224.4016 234.7261 m S 230.2309 229.0036 m S U u 224.4016 234.7261 m S 224.4016 223.281 m S 212.7431 223.281 m S 212.7431 234.7261 m S 218.5723 229.0036 m S U 224.4016 246.1712 m S 224.4016 234.7261 m S 212.7431 234.7261 m S 212.7431 246.1712 m S 218.5723 240.4486 m S 0 g 1 w 4 M 218.5723 251.8937 m F 241.8894 251.8937 m F 218.5723 229.0036 m F 241.8894 229.0036 m F 0 G 0.3 w 10 M 259.3772 257.6162 m S 259.3772 246.1712 m S 247.7187 246.1712 m S 247.7187 257.6162 m S 253.5479 251.8937 m S u 282.6943 234.7261 m S 282.6943 223.281 m S 271.0358 223.281 m S 271.0358 234.7261 m S 276.865 229.0036 m S U u 271.0358 246.1712 m S 271.0358 234.7261 m S 259.3772 234.7261 m S 259.3772 246.1712 m S 265.2065 240.4486 m S U 271.0358 257.6162 m S 271.0358 246.1712 m S 259.3772 246.1712 m S 259.3772 257.6162 m S 265.2065 251.8937 m S 282.6943 257.6162 m S 282.6943 246.1712 m S 271.0358 246.1712 m S 271.0358 257.6162 m S 276.865 251.8937 m S u 282.6943 246.1712 m S 282.6943 234.7261 m S 271.0358 234.7261 m S 271.0358 246.1712 m S 276.865 240.4486 m S U u 271.0358 234.7261 m S 271.0358 223.281 m S 259.3772 223.281 m S 259.3772 234.7261 m S 265.2065 229.0036 m S U u 259.3772 234.7261 m S 259.3772 223.281 m S 247.7187 223.281 m S 247.7187 234.7261 m S 253.5479 229.0036 m S U u 259.3772 246.1712 m S 259.3772 234.7261 m S 247.7187 234.7261 m S 247.7187 246.1712 m S 253.5479 240.4486 m S U 0 g 1 w 4 M 253.5479 251.8937 m F 276.865 251.8937 m F 253.5479 229.0036 m F 276.865 229.0036 m F u 0 G 0.3 w 10 M 224.4016 223.281 m S 224.4016 211.8359 m S 212.7431 211.8359 m S 212.7431 223.281 m S 218.5723 217.5585 m S U 247.7187 200.3909 m S 247.7187 188.9459 m S 236.0601 188.9459 m S 236.0601 200.3909 m S 241.8894 194.6684 m S 236.0601 211.8359 m S 236.0601 200.3909 m S 224.4016 200.3909 m S 224.4016 211.8359 m S 230.2309 206.1135 m S u 236.0601 223.281 m S 236.0601 211.8359 m S 224.4016 211.8359 m S 224.4016 223.281 m S 230.2309 217.5585 m S U u 247.7187 223.281 m S 247.7187 211.8359 m S 236.0601 211.8359 m S 236.0601 223.281 m S 241.8894 217.5585 m S U 247.7187 211.8359 m S 247.7187 200.3909 m S 236.0601 200.3909 m S 236.0601 211.8359 m S 241.8894 206.1135 m S 236.0601 200.3909 m S 236.0601 188.9459 m S 224.4016 188.9459 m S 224.4016 200.3909 m S 230.2309 194.6684 m S u 224.4016 200.3909 m S 224.4016 188.9459 m S 212.7431 188.9459 m S 212.7431 200.3909 m S 218.5723 194.6684 m S U u 224.4016 211.8359 m S 224.4016 200.3909 m S 212.7431 200.3909 m S 212.7431 211.8359 m S 218.5723 206.1135 m S U 0 g 1 w 4 M 218.5723 217.5585 m F 241.8894 217.5585 m F 218.5723 194.6684 m F 241.8894 194.6684 m F u 0 G 0.3 w 10 M 259.3772 223.281 m S 259.3772 211.8359 m S 247.7187 211.8359 m S 247.7187 223.281 m S 253.5479 217.5585 m S U u 282.6943 200.3909 m S 282.6943 188.9459 m S 271.0358 188.9459 m S 271.0358 200.3909 m S 276.865 194.6684 m S U u 271.0358 211.8359 m S 271.0358 200.3909 m S 259.3772 200.3909 m S 259.3772 211.8359 m S 265.2065 206.1135 m S U u 271.0358 223.281 m S 271.0358 211.8359 m S 259.3772 211.8359 m S 259.3772 223.281 m S 265.2065 217.5585 m S U u 282.6943 223.281 m S 282.6943 211.8359 m S 271.0358 211.8359 m S 271.0358 223.281 m S 276.865 217.5585 m S U u 282.6943 211.8359 m S 282.6943 200.3909 m S 271.0358 200.3909 m S 271.0358 211.8359 m S 276.865 206.1135 m S U u 271.0358 200.3909 m S 271.0358 188.9459 m S 259.3772 188.9459 m S 259.3772 200.3909 m S 265.2065 194.6684 m S U u 259.3772 200.3909 m S 259.3772 188.9459 m S 247.7187 188.9459 m S 247.7187 200.3909 m S 253.5479 194.6684 m S U u 259.3772 211.8359 m S 259.3772 200.3909 m S 247.7187 200.3909 m S 247.7187 211.8359 m S 253.5479 206.1135 m S U 0 g 1 w 4 M 253.5479 217.5585 m F 276.865 217.5585 m F 253.5479 194.6684 m F 276.865 194.6684 m F 218.5723 183.2233 m F 241.8894 183.2233 m F 253.5479 183.2233 m F 276.865 183.2233 m F u 0 G 0.3 w 10 M 224.4016 188.9459 m S 224.4016 177.5007 m S 212.7431 177.5007 m S 212.7431 188.9459 m S 218.5723 183.2233 m S U u 247.7187 166.0557 m S 247.7187 154.6107 m S 236.0601 154.6107 m S 236.0601 166.0557 m S 241.8894 160.3332 m S U u 236.0601 177.5007 m S 236.0601 166.0557 m S 224.4016 166.0557 m S 224.4016 177.5007 m S 230.2309 171.7782 m S U u 236.0601 188.9459 m S 236.0601 177.5007 m S 224.4016 177.5007 m S 224.4016 188.9459 m S 230.2309 183.2233 m S U u 247.7187 188.9459 m S 247.7187 177.5007 m S 236.0601 177.5007 m S 236.0601 188.9459 m S 241.8894 183.2233 m S U u 247.7187 177.5007 m S 247.7187 166.0557 m S 236.0601 166.0557 m S 236.0601 177.5007 m S 241.8894 171.7782 m S U u 236.0601 166.0557 m S 236.0601 154.6107 m S 224.4016 154.6107 m S 224.4016 166.0557 m S 230.2309 160.3332 m S U u 224.4016 166.0557 m S 224.4016 154.6107 m S 212.7431 154.6107 m S 212.7431 166.0557 m S 218.5723 160.3332 m S U u 224.4016 177.5007 m S 224.4016 166.0557 m S 212.7431 166.0557 m S 212.7431 177.5007 m S 218.5723 171.7782 m S U 0 g 1 w 4 M 218.5723 183.2233 m F 241.8894 183.2233 m F 218.5723 160.3332 m F 241.8894 160.3332 m F u 0 G 0.3 w 10 M 259.3772 188.9459 m S 259.3772 177.5007 m S 247.7187 177.5007 m S 247.7187 188.9459 m S 253.5479 183.2233 m S U u 282.6943 166.0557 m S 282.6943 154.6107 m S 271.0358 154.6107 m S 271.0358 166.0557 m S 276.865 160.3332 m S U u 271.0358 177.5007 m S 271.0358 166.0557 m S 259.3772 166.0557 m S 259.3772 177.5007 m S 265.2065 171.7782 m S U u 271.0358 188.9459 m S 271.0358 177.5007 m S 259.3772 177.5007 m S 259.3772 188.9459 m S 265.2065 183.2233 m S U u 282.6943 188.9459 m S 282.6943 177.5007 m S 271.0358 177.5007 m S 271.0358 188.9459 m S 276.865 183.2233 m S U u 282.6943 177.5007 m S 282.6943 166.0557 m S 271.0358 166.0557 m S 271.0358 177.5007 m S 276.865 171.7782 m S U u 271.0358 166.0557 m S 271.0358 154.6107 m S 259.3772 154.6107 m S 259.3772 166.0557 m S 265.2065 160.3332 m S U u 259.3772 166.0557 m S 259.3772 154.6107 m S 247.7187 154.6107 m S 247.7187 166.0557 m S 253.5479 160.3332 m S U u 259.3772 177.5007 m S 259.3772 166.0557 m S 247.7187 166.0557 m S 247.7187 177.5007 m S 253.5479 171.7782 m S U 0 g 1 w 4 M 253.5479 183.2233 m F 276.865 183.2233 m F 253.5479 160.3332 m F 276.865 160.3332 m F 0 G 0.3 w 10 M 224.4016 154.6107 m S 212.7431 154.6107 m S 236.0601 154.6107 m S 224.4016 154.6107 m S 247.7187 154.6107 m S 236.0601 154.6107 m S 259.3772 154.6107 m S 247.7187 154.6107 m S 271.0358 154.6107 m S 259.3772 154.6107 m S 282.6943 154.6107 m S 271.0358 154.6107 m S 282.6943 154.6107 m S 282.6943 154.6107 m S u 224.4016 188.9459 m S 224.4016 177.5008 m S 212.7431 177.5008 m S 212.7431 188.9459 m S 218.5723 183.2233 m S U u 247.7187 166.0557 m S 247.7187 154.6107 m S 236.0601 154.6107 m S 236.0601 166.0557 m S 241.8894 160.3332 m S U u 236.0601 177.5008 m S 236.0601 166.0557 m S 224.4016 166.0557 m S 224.4016 177.5008 m S 230.2309 171.7783 m S U u 236.0601 188.9459 m S 236.0601 177.5008 m S 224.4016 177.5008 m S 224.4016 188.9459 m S 230.2309 183.2233 m S U u 247.7187 188.9459 m S 247.7187 177.5008 m S 236.0601 177.5008 m S 236.0601 188.9459 m S 241.8894 183.2233 m S U u 247.7187 177.5008 m S 247.7187 166.0557 m S 236.0601 166.0557 m S 236.0601 177.5008 m S 241.8894 171.7783 m S U u 236.0601 166.0557 m S 236.0601 154.6107 m S 224.4016 154.6107 m S 224.4016 166.0557 m S 230.2309 160.3332 m S U u 224.4016 166.0557 m S 224.4016 154.6107 m S 212.7431 154.6107 m S 212.7431 166.0557 m S 218.5723 160.3332 m S U u 224.4016 177.5008 m S 224.4016 166.0557 m S 212.7431 166.0557 m S 212.7431 177.5008 m S 218.5723 171.7783 m S U 0 g 1 w 4 M 218.5723 183.2233 m F 241.8894 183.2233 m F 218.5723 160.3332 m F 241.8894 160.3332 m F u 0 G 0.3 w 10 M 259.3772 188.9459 m S 259.3772 177.5008 m S 247.7187 177.5008 m S 247.7187 188.9459 m S 253.5479 183.2233 m S U u 282.6943 166.0557 m S 282.6943 154.6107 m S 271.0358 154.6107 m S 271.0358 166.0557 m S 276.865 160.3332 m S U u 271.0358 177.5008 m S 271.0358 166.0557 m S 259.3772 166.0557 m S 259.3772 177.5008 m S 265.2065 171.7783 m S U u 271.0358 188.9459 m S 271.0358 177.5008 m S 259.3772 177.5008 m S 259.3772 188.9459 m S 265.2065 183.2233 m S U u 282.6943 188.9459 m S 282.6943 177.5008 m S 271.0358 177.5008 m S 271.0358 188.9459 m S 276.865 183.2233 m S U u 282.6943 177.5008 m S 282.6943 166.0557 m S 271.0358 166.0557 m S 271.0358 177.5008 m S 276.865 171.7783 m S U u 271.0358 166.0557 m S 271.0358 154.6107 m S 259.3772 154.6107 m S 259.3772 166.0557 m S 265.2065 160.3332 m S U u 259.3772 166.0557 m S 259.3772 154.6107 m S 247.7187 154.6107 m S 247.7187 166.0557 m S 253.5479 160.3332 m S U u 259.3772 177.5008 m S 259.3772 166.0557 m S 247.7187 166.0557 m S 247.7187 177.5008 m S 253.5479 171.7783 m S U 0 g 1 w 4 M 253.5479 183.2233 m F 276.865 183.2233 m F 253.5479 160.3332 m F 276.865 160.3332 m F 0 G 0.3 w 10 M 224.4016 154.6107 m S 224.4016 143.1656 m S 212.7431 143.1656 m S 212.7431 154.6107 m S 218.5723 148.8881 m S u 247.7187 131.7206 m S 247.7187 120.2755 m S 236.0601 120.2755 m S 236.0601 131.7206 m S 241.8894 125.998 m S U 236.0601 143.1656 m S 236.0601 131.7206 m S 224.4016 131.7206 m S 224.4016 143.1656 m S 230.2309 137.4431 m S 236.0601 154.6107 m S 236.0601 143.1656 m S 224.4016 143.1656 m S 224.4016 154.6107 m S 230.2309 148.8881 m S u 247.7187 154.6107 m S 247.7187 143.1656 m S 236.0601 143.1656 m S 236.0601 154.6107 m S 241.8894 148.8881 m S U u 247.7187 143.1656 m S 247.7187 131.7206 m S 236.0601 131.7206 m S 236.0601 143.1656 m S 241.8894 137.4431 m S U u 236.0601 131.7206 m S 236.0601 120.2755 m S 224.4016 120.2755 m S 224.4016 131.7206 m S 230.2309 125.998 m S U u 224.4016 131.7206 m S 224.4016 120.2755 m S 212.7431 120.2755 m S 212.7431 131.7206 m S 218.5723 125.998 m S U 224.4016 143.1656 m S 224.4016 131.7206 m S 212.7431 131.7206 m S 212.7431 143.1656 m S 218.5723 137.4431 m S 0 g 1 w 4 M 218.5723 148.8881 m F 241.8894 148.8881 m F 218.5723 125.998 m F 241.8894 125.998 m F u 0 G 0.3 w 10 M 259.3772 154.6107 m S 259.3772 143.1656 m S 247.7187 143.1656 m S 247.7187 154.6107 m S 253.5479 148.8881 m S U u 282.6943 131.7206 m S 282.6943 120.2755 m S 271.0358 120.2755 m S 271.0358 131.7206 m S 276.865 125.998 m S U u 271.0358 143.1656 m S 271.0358 131.7206 m S 259.3772 131.7206 m S 259.3772 143.1656 m S 265.2065 137.4431 m S U u 271.0358 154.6107 m S 271.0358 143.1656 m S 259.3772 143.1656 m S 259.3772 154.6107 m S 265.2065 148.8881 m S U u 282.6943 154.6107 m S 282.6943 143.1656 m S 271.0358 143.1656 m S 271.0358 154.6107 m S 276.865 148.8881 m S U u 282.6943 143.1656 m S 282.6943 131.7206 m S 271.0358 131.7206 m S 271.0358 143.1656 m S 276.865 137.4431 m S U u 271.0358 131.7206 m S 271.0358 120.2755 m S 259.3772 120.2755 m S 259.3772 131.7206 m S 265.2065 125.998 m S U u 259.3772 131.7206 m S 259.3772 120.2755 m S 247.7187 120.2755 m S 247.7187 131.7206 m S 253.5479 125.998 m S U u 259.3772 143.1656 m S 259.3772 131.7206 m S 247.7187 131.7206 m S 247.7187 143.1656 m S 253.5479 137.4431 m S U 0 g 1 w 4 M 253.5479 148.8881 m F 276.865 148.8881 m F 253.5479 125.998 m F 276.865 125.998 m F 218.5723 114.553 m F 241.8894 114.553 m F 253.5479 114.553 m F 276.865 114.553 m F u 0 G 0.3 w 10 M 224.4016 120.2755 m S 224.4016 108.8304 m S 212.7431 108.8304 m S 212.7431 120.2755 m S 218.5723 114.553 m S U u 247.7187 97.3853 m S 247.7187 85.9403 m S 236.0601 85.9403 m S 236.0601 97.3853 m S 241.8894 91.6628 m S U u 236.0601 108.8304 m S 236.0601 97.3853 m S 224.4016 97.3853 m S 224.4016 108.8304 m S 230.2309 103.1079 m S U u 236.0601 120.2755 m S 236.0601 108.8304 m S 224.4016 108.8304 m S 224.4016 120.2755 m S 230.2309 114.553 m S U u 247.7187 120.2755 m S 247.7187 108.8304 m S 236.0601 108.8304 m S 236.0601 120.2755 m S 241.8894 114.553 m S U u 247.7187 108.8304 m S 247.7187 97.3853 m S 236.0601 97.3853 m S 236.0601 108.8304 m S 241.8894 103.1079 m S U u 236.0601 97.3853 m S 236.0601 85.9403 m S 224.4016 85.9403 m S 224.4016 97.3853 m S 230.2309 91.6628 m S U u 224.4016 97.3853 m S 224.4016 85.9403 m S 212.7431 85.9403 m S 212.7431 97.3853 m S 218.5723 91.6628 m S U u 224.4016 108.8304 m S 224.4016 97.3853 m S 212.7431 97.3853 m S 212.7431 108.8304 m S 218.5723 103.1079 m S U 0 g 1 w 4 M 218.5723 114.553 m F 241.8894 114.553 m F 218.5723 91.6628 m F 241.8894 91.6628 m F u 0 G 0.3 w 10 M 259.3772 120.2755 m S 259.3772 108.8304 m S 247.7187 108.8304 m S 247.7187 120.2755 m S 253.5479 114.553 m S U u 282.6943 97.3853 m S 282.6943 85.9403 m S 271.0358 85.9403 m S 271.0358 97.3853 m S 276.865 91.6628 m S U u 271.0358 108.8304 m S 271.0358 97.3853 m S 259.3772 97.3853 m S 259.3772 108.8304 m S 265.2065 103.1079 m S U u 271.0358 120.2755 m S 271.0358 108.8304 m S 259.3772 108.8304 m S 259.3772 120.2755 m S 265.2065 114.553 m S U u 282.6943 120.2755 m S 282.6943 108.8304 m S 271.0358 108.8304 m S 271.0358 120.2755 m S 276.865 114.553 m S U u 282.6943 108.8304 m S 282.6943 97.3853 m S 271.0358 97.3853 m S 271.0358 108.8304 m S 276.865 103.1079 m S U u 271.0358 97.3853 m S 271.0358 85.9403 m S 259.3772 85.9403 m S 259.3772 97.3853 m S 265.2065 91.6628 m S U u 259.3772 97.3853 m S 259.3772 85.9403 m S 247.7187 85.9403 m S 247.7187 97.3853 m S 253.5479 91.6628 m S U u 259.3772 108.8304 m S 259.3772 97.3853 m S 247.7187 97.3853 m S 247.7187 108.8304 m S 253.5479 103.1079 m S U 0 g 1 w 4 M 253.5479 114.553 m F 276.865 114.553 m F 253.5479 91.6628 m F 276.865 91.6628 m F 0 G 0.3 w 10 M 224.4016 85.9403 m S 212.7431 85.9403 m S 236.0601 85.9403 m S 224.4016 85.9403 m S 247.7187 85.9403 m S 236.0601 85.9403 m S 259.3772 85.9403 m S 247.7187 85.9403 m S 271.0358 85.9403 m S 259.3772 85.9403 m S 282.6943 85.9403 m S 271.0358 85.9403 m S 282.6943 85.9403 m S 282.6943 85.9403 m S 236.0601 234.7261 m S 0 g 1 w 4 M 236.0601 234.7261 m F 0 G 0.3 w 10 M 236.0601 234.7261 m S 236.0601 234.7261 m S 236.0601 234.7261 m S 0 g 1 w 4 M 236.0601 234.7261 m F 0 G 0.3 w 10 M 236.0601 234.7261 m S 236.0601 234.7261 m S 236.0601 234.7261 m S 0 g 1 w 4 M 236.0601 234.7261 m F 0 G 0.3 w 10 M 236.0601 234.7261 m S 236.0601 234.7261 m S 247.7187 223.281 m S 0 g 1 w 4 M 247.7187 223.281 m F 0 G 0.3 w 10 M 247.7187 223.281 m S 247.7187 223.281 m S 247.7187 223.281 m S 0 g 1 w 4 M 247.7187 223.281 m F 0 G 0.3 w 10 M 247.7187 223.281 m S 247.7187 223.281 m S 247.7187 223.281 m S 0 g 1 w 4 M 247.7187 223.281 m F 0 G 0.3 w 10 M 247.7187 223.281 m S 247.7187 223.281 m S 247.7187 223.281 m S 0 g 1 w 4 M 247.7187 223.281 m F 0 G 0.3 w 10 M 247.7187 223.281 m S 247.7187 223.281 m S 247.7187 223.281 m S 0 g 1 w 4 M 247.7187 223.281 m F 0 G 0.3 w 10 M 247.7187 223.281 m S 247.7187 223.281 m S u 1 g 1 w 4 M 247.7187 223.281 m F U 0 G 0.3 w 10 M 247.7187 223.281 m S 0 g 1 w 4 M 247.7187 223.281 m F 0 G 0.3 w 10 M 247.7187 223.281 m S 247.7187 223.281 m S 247.7187 234.7261 m S 0 g 1 w 4 M 247.7187 234.7261 m F 0 G 0.3 w 10 M 247.7187 234.7261 m S 247.7187 234.7261 m S 247.7187 234.7261 m S 0 g 1 w 4 M 247.7187 234.7261 m F 0 G 0.3 w 10 M 247.7187 234.7261 m S 247.7187 234.7261 m S 247.7187 234.7261 m S 0 g 1 w 4 M 247.7187 234.7261 m F 0 G 0.3 w 10 M 247.7187 234.7261 m S 247.7187 234.7261 m S 236.0601 223.281 m S 0 g 1 w 4 M 236.0601 223.281 m F 0 G 0.3 w 10 M 236.0601 223.281 m S 236.0601 223.281 m S 236.0601 223.281 m S 0 g 1 w 4 M 236.0601 223.281 m F 0 G 0.3 w 10 M 236.0601 223.281 m S 236.0601 223.281 m S 236.0601 223.281 m S 0 g 1 w 4 M 236.0601 223.281 m F 0 G 0.3 w 10 M 236.0601 223.281 m S 236.0601 223.281 m S 236.0601 211.8359 m S 0 g 1 w 4 M 236.0601 211.8359 m F 0 G 0.3 w 10 M 236.0601 211.8359 m S 236.0601 211.8359 m S 236.0601 211.8359 m S 0 g 1 w 4 M 236.0601 211.8359 m F 0 G 0.3 w 10 M 236.0601 211.8359 m S 236.0601 211.8359 m S 236.0601 211.8359 m S 0 g 1 w 4 M 236.0601 211.8359 m F 0 G 0.3 w 10 M 236.0601 211.8359 m S 236.0601 211.8359 m S 236.0601 200.3909 m S 0 g 1 w 4 M 236.0601 200.3909 m F 0 G 0.3 w 10 M 236.0601 200.3909 m S 236.0601 200.3909 m S 236.0601 200.3909 m S 0 g 1 w 4 M 236.0601 200.3909 m F 0 G 0.3 w 10 M 236.0601 200.3909 m S 236.0601 200.3909 m S 1 g 0.5 w 4 M 236.0601 200.3909 m B 0.3 w 10 M 236.0601 200.3909 m S 0 g 1 w 4 M 236.0601 200.3909 m F 0 G 0.3 w 10 M 236.0601 200.3909 m S 236.0601 200.3909 m S 247.7187 188.9459 m S 0 g 1 w 4 M 247.7187 188.9459 m F 0 G 0.3 w 10 M 247.7187 188.9459 m S 0 g 1 w 4 M 247.7187 188.9459 m F 0 G 0.3 w 10 M 247.7187 188.9459 m S 0 g 1 w 4 M 247.7187 188.9459 m F 0 G 0.3 w 10 M 247.7187 188.9459 m S 0 g 1 w 4 M 247.7187 188.9459 m F 0 G 0.3 w 10 M 247.7187 188.9459 m S 0 g 1 w 4 M 247.7187 188.9459 m F 0 G 0.3 w 10 M 247.7187 188.9459 m S 247.7187 188.9459 m S 247.7187 188.9459 m S 0 g 1 w 4 M 247.7187 188.9459 m F 0 G 0.3 w 10 M 247.7187 188.9459 m S 247.7187 188.9459 m S 1 g 1 w 4 M 247.7187 188.9459 m F 0 G 0.3 w 10 M 247.7187 188.9459 m S 0 g 1 w 4 M 247.7187 188.9459 m F 0 G 0.3 w 10 M 247.7187 188.9459 m S 247.7187 188.9459 m S 1 g 0.5 w 4 M 247.7187 188.9459 m B 0.3 w 10 M 247.7187 188.9459 m S 0 g 1 w 4 M 247.7187 188.9459 m F 0 G 0.3 w 10 M 247.7187 188.9459 m S 247.7187 188.9459 m S 247.7187 188.9459 m S 0 g 1 w 4 M 247.7187 188.9459 m F 0 G 0.3 w 10 M 247.7187 188.9459 m S 247.7187 188.9459 m S u 1 g 1 w 4 M 247.7187 188.9459 m F U 0 G 0.3 w 10 M 247.7187 188.9459 m S 0 g 1 w 4 M 247.7187 188.9459 m F 0 G 0.3 w 10 M 247.7187 188.9459 m S 247.7187 188.9459 m S 247.7187 188.9459 m S 0 g 1 w 4 M 247.7187 188.9459 m F 0 G 0.3 w 10 M 247.7187 188.9459 m S 247.7187 188.9459 m S 247.7187 188.9459 m S 0 g 1 w 4 M 247.7187 188.9459 m F 0 G 0.3 w 10 M 247.7187 188.9459 m S 247.7187 188.9459 m S u 1 g 1 w 4 M 247.7187 188.9459 m F U 0 G 0.3 w 10 M 247.7187 188.9459 m S 0 g 1 w 4 M 247.7187 188.9459 m F 0 G 0.3 w 10 M 247.7187 188.9459 m S 247.7187 188.9459 m S 247.7187 211.8359 m S 0 g 1 w 4 M 247.7187 211.8359 m F 0 G 0.3 w 10 M 247.7187 211.8359 m S 247.7187 211.8359 m S 247.7187 211.8359 m S 0 g 1 w 4 M 247.7187 211.8359 m F 0 G 0.3 w 10 M 247.7187 211.8359 m S 247.7187 211.8359 m S 247.7187 211.8359 m S 0 g 1 w 4 M 247.7187 211.8359 m F 0 G 0.3 w 10 M 247.7187 211.8359 m S 247.7187 211.8359 m S 236.0601 188.9459 m S 0 g 1 w 4 M 236.0601 188.9459 m F 0 G 0.3 w 10 M 236.0601 188.9459 m S 236.0601 188.9459 m S 236.0601 188.9459 m S 0 g 1 w 4 M 236.0601 188.9459 m F 0 G 0.3 w 10 M 236.0601 188.9459 m S 236.0601 188.9459 m S 236.0601 188.9459 m S 0 g 1 w 4 M 236.0601 188.9459 m F 0 G 0.3 w 10 M 236.0601 188.9459 m S 236.0601 188.9459 m S 247.7187 200.3909 m S 0 g 1 w 4 M 247.7187 200.3909 m F 0 G 0.3 w 10 M 247.7187 200.3909 m S 0 g 1 w 4 M 247.7187 200.3909 m F 0 G 0.3 w 10 M 247.7187 200.3909 m S 0 g 1 w 4 M 247.7187 200.3909 m F 0 G 0.3 w 10 M 247.7187 200.3909 m S 0 g 1 w 4 M 247.7187 200.3909 m F u 0 G 0.3 w 10 M 72.8407 85.9403 m S 72.8407 74.4953 m S 61.1821 74.4953 m S 61.1821 85.9403 m S 67.0114 80.2178 m S U u 61.1821 85.9403 m S 61.1821 74.4953 m S 49.5236 74.4953 m S 49.5236 85.9403 m S 55.3529 80.2178 m S U u 49.5236 85.9403 m S 49.5236 74.4953 m S 37.8651 74.4953 m S 37.8651 85.9403 m S 43.6943 80.2178 m S U u 107.8163 85.9403 m S 107.8163 74.4953 m S 96.1577 74.4953 m S 96.1577 85.9403 m S 101.987 80.2178 m S U u 96.1577 85.9403 m S 96.1577 74.4953 m S 84.4992 74.4953 m S 84.4992 85.9403 m S 90.3285 80.2178 m S U u 84.4992 85.9403 m S 84.4992 74.4953 m S 72.8407 74.4953 m S 72.8407 85.9403 m S 78.6699 80.2178 m S U u 142.7919 85.9403 m S 142.7919 74.4953 m S 131.1334 74.4953 m S 131.1334 85.9403 m S 136.9626 80.2178 m S U u 131.1334 85.9403 m S 131.1334 74.4953 m S 119.4748 74.4953 m S 119.4748 85.9403 m S 125.3041 80.2178 m S U u 119.4748 85.9403 m S 119.4748 74.4953 m S 107.8163 74.4953 m S 107.8163 85.9403 m S 113.6455 80.2178 m S U 142.7919 74.4953 m S u 49.5236 74.4953 m S 49.5236 63.0501 m S 37.8651 63.0501 m S 37.8651 74.4953 m S 43.6943 68.7727 m S U u 61.1821 74.4953 m S 61.1821 63.0501 m S 49.5236 63.0501 m S 49.5236 74.4953 m S 55.3529 68.7727 m S U u 72.8407 74.4953 m S 72.8407 63.0501 m S 61.1821 63.0501 m S 61.1821 74.4953 m S 67.0114 68.7727 m S U u 84.4992 74.4953 m S 84.4992 63.0501 m S 72.8407 63.0501 m S 72.8407 74.4953 m S 78.6699 68.7727 m S U u 96.1577 74.4953 m S 96.1577 63.0501 m S 84.4992 63.0501 m S 84.4992 74.4953 m S 90.3285 68.7727 m S U u 107.8163 74.4953 m S 107.8163 63.0501 m S 96.1577 63.0501 m S 96.1577 74.4953 m S 101.987 68.7727 m S U u 119.4748 74.4953 m S 119.4748 63.0501 m S 107.8163 63.0501 m S 107.8163 74.4953 m S 113.6455 68.7727 m S U u 131.1334 74.4953 m S 131.1334 63.0501 m S 119.4748 63.0501 m S 119.4748 74.4953 m S 125.3041 68.7727 m S U u 142.7919 74.4953 m S 142.7919 63.0501 m S 131.1334 63.0501 m S 131.1334 74.4953 m S 136.9626 68.7727 m S U 142.7919 74.4953 m S u 142.7919 85.9403 m S 142.7919 74.4953 m S 131.1334 74.4953 m S 131.1334 85.9403 m S 136.9626 80.2178 m S U u 131.1334 85.9403 m S 131.1334 74.4953 m S 119.4748 74.4953 m S 119.4748 85.9403 m S 125.3041 80.2178 m S U u 119.4748 85.9403 m S 119.4748 74.4953 m S 107.8163 74.4953 m S 107.8163 85.9403 m S 113.6455 80.2178 m S U u 177.7675 85.9403 m S 177.7675 74.4953 m S 166.109 74.4953 m S 166.109 85.9403 m S 171.9383 80.2178 m S U u 166.109 85.9403 m S 166.109 74.4953 m S 154.4505 74.4953 m S 154.4505 85.9403 m S 160.2797 80.2178 m S U u 154.4505 85.9403 m S 154.4505 74.4953 m S 142.7919 74.4953 m S 142.7919 85.9403 m S 148.6211 80.2178 m S U u 212.7431 85.9403 m S 212.7431 74.4953 m S 201.0846 74.4953 m S 201.0846 85.9403 m S 206.9139 80.2178 m S U u 201.0846 85.9403 m S 201.0846 74.4953 m S 189.4261 74.4953 m S 189.4261 85.9403 m S 195.2553 80.2178 m S U u 189.4261 85.9403 m S 189.4261 74.4953 m S 177.7675 74.4953 m S 177.7675 85.9403 m S 183.5967 80.2178 m S U 212.7431 74.4953 m S u 119.4748 74.4953 m S 119.4748 63.0501 m S 107.8163 63.0501 m S 107.8163 74.4953 m S 113.6455 68.7727 m S U u 131.1334 74.4953 m S 131.1334 63.0501 m S 119.4748 63.0501 m S 119.4748 74.4953 m S 125.3041 68.7727 m S U u 142.7919 74.4953 m S 142.7919 63.0501 m S 131.1334 63.0501 m S 131.1334 74.4953 m S 136.9626 68.7727 m S U u 154.4505 74.4953 m S 154.4505 63.0501 m S 142.7919 63.0501 m S 142.7919 74.4953 m S 148.6211 68.7727 m S U u 166.109 74.4953 m S 166.109 63.0501 m S 154.4505 63.0501 m S 154.4505 74.4953 m S 160.2797 68.7727 m S U u 177.7675 74.4953 m S 177.7675 63.0501 m S 166.109 63.0501 m S 166.109 74.4953 m S 171.9383 68.7727 m S U u 189.4261 74.4953 m S 189.4261 63.0501 m S 177.7675 63.0501 m S 177.7675 74.4953 m S 183.5967 68.7727 m S U u 201.0846 74.4953 m S 201.0846 63.0501 m S 189.4261 63.0501 m S 189.4261 74.4953 m S 195.2553 68.7727 m S U u 212.7431 74.4953 m S 212.7431 63.0501 m S 201.0846 63.0501 m S 201.0846 74.4953 m S 206.9139 68.7727 m S U 212.7431 74.4953 m S u 247.7187 85.9403 m S 247.7187 74.4953 m S 236.0601 74.4953 m S 236.0601 85.9403 m S 241.8894 80.2178 m S U u 236.0601 85.9403 m S 236.0601 74.4953 m S 224.4016 74.4953 m S 224.4016 85.9403 m S 230.2309 80.2178 m S U u 224.4016 85.9403 m S 224.4016 74.4953 m S 212.7431 74.4953 m S 212.7431 85.9403 m S 218.5723 80.2178 m S U u 282.6943 85.9403 m S 282.6943 74.4953 m S 271.0358 74.4953 m S 271.0358 85.9403 m S 276.865 80.2178 m S U u 271.0358 85.9403 m S 271.0358 74.4953 m S 259.3772 74.4953 m S 259.3772 85.9403 m S 265.2065 80.2178 m S U u 259.3772 85.9403 m S 259.3772 74.4953 m S 247.7187 74.4953 m S 247.7187 85.9403 m S 253.5479 80.2178 m S U u 224.4016 74.4953 m S 224.4016 63.0501 m S 212.7431 63.0501 m S 212.7431 74.4953 m S 218.5723 68.7727 m S U u 236.0601 74.4953 m S 236.0601 63.0501 m S 224.4016 63.0501 m S 224.4016 74.4953 m S 230.2309 68.7727 m S U u 247.7187 74.4953 m S 247.7187 63.0501 m S 236.0601 63.0501 m S 236.0601 74.4953 m S 241.8894 68.7727 m S U u 259.3772 74.4953 m S 259.3772 63.0501 m S 247.7187 63.0501 m S 247.7187 74.4953 m S 253.5479 68.7727 m S U u 271.0358 74.4953 m S 271.0358 63.0501 m S 259.3772 63.0501 m S 259.3772 74.4953 m S 265.2065 68.7727 m S U u 282.6943 74.4953 m S 282.6943 63.0501 m S 271.0358 63.0501 m S 271.0358 74.4953 m S 276.865 68.7727 m S U 61.1821 234.7261 m S 0 g 1 w 4 M 61.1821 234.7261 m F 0 G 0.3 w 10 M 61.1821 234.7261 m S 61.1821 234.7261 m S 61.1821 234.7261 m S 0 g 1 w 4 M 61.1821 234.7261 m F 0 G 0.3 w 10 M 61.1821 234.7261 m S 61.1821 234.7261 m S 61.1821 234.7261 m S 0 g 1 w 4 M 61.1821 234.7261 m F 0 G 0.3 w 10 M 61.1821 234.7261 m S 61.1821 234.7261 m S 0 g 1 w 4 M 60.097 233.6582 m 60.097 230.0811 L 62.2672 230.0811 L 62.2672 233.6582 L 65.8528 233.647 L 65.8528 235.8054 L 62.2672 235.7943 L 62.2672 239.3714 L 60.097 239.3714 L 60.097 235.7943 L 56.5114 235.8054 L 56.5114 233.647 L 60.097 233.6582 L f 0 G 0.3 w 10 M 61.1821 234.7261 m S 0 g 1 w 4 M 61.1821 234.7261 m F 0 G 0.3 w 10 M 61.1821 234.7261 m S 61.1821 234.7261 m S 61.1821 234.7261 m S 0 g 1 w 4 M 61.1821 234.7261 m F 0 G 0.3 w 10 M 61.1821 234.7261 m S 61.1821 234.7261 m S u 1 g 1 w 4 M 61.1821 234.7261 m F U 0 G 0.3 w 10 M 61.1821 234.7261 m S 0 g 1 w 4 M 61.1821 234.7261 m F 0 G 0.3 w 10 M 61.1821 234.7261 m S 61.1821 234.7261 m S 61.1821 234.7261 m S 0 g 1 w 4 M 61.1821 234.7261 m F 0 G 0.3 w 10 M 61.1821 234.7261 m S 0 g 1 w 4 M 61.1821 234.7261 m F 0 G 0.3 w 10 M 49.5236 246.1712 m S 72.8407 223.281 m S 61.1821 234.7261 m S 61.1821 234.7261 m S 49.5236 246.1712 m S 49.5236 246.1712 m S 72.8407 246.1712 m S 72.8407 246.1712 m S 61.1821 234.7261 m S 61.1821 234.7261 m S 49.5236 223.281 m S 49.5236 223.281 m S 49.5236 246.1712 m S 72.8407 246.1712 m S 72.8407 223.281 m S 72.8407 246.1712 m S 49.5236 223.281 m S 49.5236 223.281 m S 72.8407 223.281 m S 72.8407 223.281 m S 61.1821 234.7261 m S 0 g 1 w 4 M 61.1821 234.7261 m F 0 G 0.3 w 10 M 61.1821 234.7261 m S 61.1821 234.7261 m S 61.1821 234.7261 m S 0 g 1 w 4 M 61.1821 234.7261 m F 0 G 0.3 w 10 M 61.1821 234.7261 m S 61.1821 234.7261 m S 61.1821 234.7261 m S 0 g 1 w 4 M 61.1821 234.7261 m F 0 G 0.3 w 10 M 61.1821 234.7261 m S 61.1821 234.7261 m S 72.8407 223.281 m S 0 g 1 w 4 M 72.8407 223.281 m F 0 G 0.3 w 10 M 72.8407 223.281 m S 72.8407 223.281 m S 72.8407 223.281 m S 0 g 1 w 4 M 72.8407 223.281 m F 0 G 0.3 w 10 M 72.8407 223.281 m S 72.8407 223.281 m S 72.8407 223.281 m S 0 g 1 w 4 M 72.8407 223.281 m F 0 G 0.3 w 10 M 72.8407 223.281 m S 72.8407 223.281 m S 72.8407 223.281 m S 0 g 1 w 4 M 72.8407 223.281 m F 0 G 0.3 w 10 M 72.8407 223.281 m S 72.8407 223.281 m S 72.8407 223.281 m S 0 g 1 w 4 M 72.8407 223.281 m F 0 G 0.3 w 10 M 72.8407 223.281 m S 72.8407 223.281 m S 1 g 1 w 4 M 72.8407 223.281 m F 0 G 0.3 w 10 M 72.8407 223.281 m S 0 g 1 w 4 M 72.8407 223.281 m F 0 G 0.3 w 10 M 72.8407 223.281 m S 72.8407 223.281 m S 0.5 w 4 M 49.5236 246.1712 m 72.8407 246.1712 l 72.8407 223.281 l 49.5236 223.281 l 49.5236 246.1712 l s 0.3 w 10 M 61.1821 257.6162 m S 0 g 1 w 4 M 61.1821 257.6162 m F 0 G 0.3 w 10 M 61.1821 257.6162 m S 61.1821 257.6162 m S 61.1821 257.6162 m S 0 g 1 w 4 M 61.1821 257.6162 m F 0 G 0.3 w 10 M 61.1821 257.6162 m S 61.1821 257.6162 m S 1 g 0.5 w 4 M 55.1717 257.6162 m 55.1717 254.3944 57.8627 251.7826 61.1821 251.7826 c 64.5015 251.7826 67.1925 254.3944 67.1925 257.6162 c B 67.1925 257.6162 m 67.1925 260.838 64.5015 263.4498 61.1821 263.4498 c 57.8627 263.4498 55.1717 260.838 55.1717 257.6162 c B 61.1821 257.6162 m B 0.3 w 10 M 61.1821 257.6162 m S 0 g 1 w 4 M 61.1821 257.6162 m F 0 G 0.3 w 10 M 61.1821 257.6162 m S 61.1821 257.6162 m S 0 g 1 w 4 M 60.097 256.5483 m 60.097 252.9712 L 62.2672 252.9712 L 62.2672 256.5483 L 65.8528 256.5371 L 65.8528 258.6955 L 62.2672 258.6844 L 62.2672 262.2615 L 60.097 262.2615 L 60.097 258.6844 L 56.5114 258.6955 L 56.5114 256.5371 L 60.097 256.5483 L f 0 G 0.3 w 10 M 37.8651 234.7261 m S 0 g 1 w 4 M 37.8651 234.7261 m F 0 G 0.3 w 10 M 37.8651 234.7261 m S 37.8651 234.7261 m S 37.8651 234.7261 m S 0 g 1 w 4 M 37.8651 234.7261 m F 0 G 0.3 w 10 M 37.8651 234.7261 m S 37.8651 234.7261 m S u 1 g 0.5 w 4 M 31.8547 234.7261 m 31.8547 231.5043 34.5457 228.8925 37.8651 228.8925 c 41.1845 228.8925 43.8755 231.5043 43.8755 234.7261 c B 43.8755 234.7261 m 43.8755 237.9479 41.1845 240.5597 37.8651 240.5597 c 34.5457 240.5597 31.8547 237.9479 31.8547 234.7261 c B 37.8651 234.7261 m B U 0.3 w 10 M 37.8651 234.7261 m S 0 g 1 w 4 M 37.8651 234.7261 m F 0 G 0.3 w 10 M 37.8651 234.7261 m S 37.8651 234.7261 m S 0 g 1 w 4 M 36.78 233.6582 m 36.78 230.0811 L 38.9502 230.0811 L 38.9502 233.6582 L 42.5358 233.647 L 42.5358 235.8054 L 38.9502 235.7943 L 38.9502 239.3714 L 36.78 239.3714 L 36.78 235.7943 L 33.1944 235.8054 L 33.1944 233.647 L 36.78 233.6582 L f 0 G 0.3 w 10 M 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 130.0483 235.7943 m 126.4627 235.8054 L 126.4627 233.647 L 130.0483 233.6581 L F 132.2184 233.6581 m 135.8041 233.647 L 135.8041 235.8054 L 132.2184 235.7943 L F 126.4627 235.8054 m 135.8041 235.8054 l 135.8041 233.647 l 126.4627 233.647 l 126.4627 235.8054 l f 0 G 0.3 w 10 M 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 131.1334 234.7261 m S 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 131.1334 234.7261 m S 1 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 131.1334 234.7261 m S 1 g 0.5 w 4 M 131.1334 234.7261 m B 0.3 w 10 M 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 131.1334 234.7261 m S 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 131.1334 234.7261 m S u 1 g 1 w 4 M 131.1334 234.7261 m F U 0 G 0.3 w 10 M 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 131.1334 234.7261 m S 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 131.1334 234.7261 m S 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 131.1334 234.7261 m S u 1 g 1 w 4 M 131.1334 234.7261 m F U 0 G 0.3 w 10 M 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 131.1334 234.7261 m S 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 119.4748 246.1712 m S 142.7919 223.281 m S 131.1334 234.7261 m S 131.1334 234.7261 m S 119.4748 246.1712 m S 119.4748 246.1712 m S 142.7919 246.1712 m S 142.7919 246.1712 m S 131.1334 234.7261 m S 131.1334 234.7261 m S 119.4748 223.281 m S 119.4748 223.281 m S 119.4748 246.1712 m S 142.7919 246.1712 m S 142.7919 223.281 m S 142.7919 246.1712 m S 119.4748 223.281 m S 119.4748 223.281 m S 142.7919 223.281 m S 142.7919 223.281 m S 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 131.1334 234.7261 m S 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 131.1334 234.7261 m S 131.1334 234.7261 m S 0 g 1 w 4 M 131.1334 234.7261 m F 0 G 0.3 w 10 M 131.1334 234.7261 m S 131.1334 234.7261 m S 142.7919 223.281 m S 0 g 1 w 4 M 142.7919 223.281 m F 0 G 0.3 w 10 M 142.7919 223.281 m S 142.7919 223.281 m S 142.7919 223.281 m S 0 g 1 w 4 M 142.7919 223.281 m F 0 G 0.3 w 10 M 142.7919 223.281 m S 142.7919 223.281 m S 142.7919 223.281 m S 0 g 1 w 4 M 142.7919 223.281 m F 0 G 0.3 w 10 M 142.7919 223.281 m S 142.7919 223.281 m S 142.7919 223.281 m S 0 g 1 w 4 M 142.7919 223.281 m F 0 G 0.3 w 10 M 142.7919 223.281 m S 142.7919 223.281 m S 142.7919 223.281 m S 0 g 1 w 4 M 142.7919 223.281 m F 0 G 0.3 w 10 M 142.7919 223.281 m S 142.7919 223.281 m S 1 g 1 w 4 M 142.7919 223.281 m F 0 G 0.3 w 10 M 142.7919 223.281 m S 0 g 1 w 4 M 142.7919 223.281 m F 0 G 0.3 w 10 M 142.7919 223.281 m S 142.7919 223.281 m S 0.5 w 4 M 119.4748 246.1712 m 142.7919 246.1712 l 142.7919 223.281 l 119.4748 223.281 l 119.4748 246.1712 l s 0.3 w 10 M 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 60.097 167.1239 m 56.5114 167.135 L 56.5114 164.9766 L 60.097 164.9877 L F 62.2672 164.9877 m 65.8528 164.9766 L 65.8528 167.135 L 62.2672 167.1239 L F 56.5114 167.135 m 65.8528 167.135 l 65.8528 164.9766 l 56.5114 164.9766 l 56.5114 167.135 l f 0 G 0.3 w 10 M 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 61.1821 166.0557 m S 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 61.1821 166.0557 m S 1 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 61.1821 166.0557 m S 1 g 0.5 w 4 M 61.1821 166.0557 m B 0.3 w 10 M 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 61.1821 166.0557 m S 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 61.1821 166.0557 m S u 1 g 1 w 4 M 61.1821 166.0557 m F U 0 G 0.3 w 10 M 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 61.1821 166.0557 m S 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 61.1821 166.0557 m S 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 61.1821 166.0557 m S u 1 g 1 w 4 M 61.1821 166.0557 m F U 0 G 0.3 w 10 M 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 61.1821 166.0557 m S 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 49.5236 177.5007 m S 72.8407 154.6106 m S 61.1821 166.0557 m S 61.1821 166.0557 m S 49.5236 177.5007 m S 49.5236 177.5007 m S 72.8407 177.5007 m S 72.8407 177.5007 m S 61.1821 166.0557 m S 61.1821 166.0557 m S 49.5236 154.6106 m S 49.5236 154.6106 m S 49.5236 177.5007 m S 72.8407 177.5007 m S 72.8407 154.6106 m S 72.8407 177.5007 m S 49.5236 154.6106 m S 49.5236 154.6106 m S 72.8407 154.6106 m S 72.8407 154.6106 m S 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 61.1821 166.0557 m S 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 61.1821 166.0557 m S 61.1821 166.0557 m S 0 g 1 w 4 M 61.1821 166.0557 m F 0 G 0.3 w 10 M 61.1821 166.0557 m S 61.1821 166.0557 m S 72.8407 154.6106 m S 0 g 1 w 4 M 72.8407 154.6106 m F 0 G 0.3 w 10 M 72.8407 154.6106 m S 72.8407 154.6106 m S 72.8407 154.6106 m S 0 g 1 w 4 M 72.8407 154.6106 m F 0 G 0.3 w 10 M 72.8407 154.6106 m S 72.8407 154.6106 m S 72.8407 154.6106 m S 0 g 1 w 4 M 72.8407 154.6106 m F 0 G 0.3 w 10 M 72.8407 154.6106 m S 72.8407 154.6106 m S 72.8407 154.6106 m S 0 g 1 w 4 M 72.8407 154.6106 m F 0 G 0.3 w 10 M 72.8407 154.6106 m S 72.8407 154.6106 m S 72.8407 154.6106 m S 0 g 1 w 4 M 72.8407 154.6106 m F 0 G 0.3 w 10 M 72.8407 154.6106 m S 72.8407 154.6106 m S 1 g 1 w 4 M 72.8407 154.6106 m F 0 G 0.3 w 10 M 72.8407 154.6106 m S 0 g 1 w 4 M 72.8407 154.6106 m F 0 G 0.3 w 10 M 72.8407 154.6106 m S 72.8407 154.6106 m S 0.5 w 4 M 49.5236 177.5007 m 72.8407 177.5007 l 72.8407 154.6106 l 49.5236 154.6106 l 49.5236 177.5007 l s 0.3 w 10 M 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 199.9995 167.1239 m 196.4139 167.135 L 196.4139 164.9766 L 199.9995 164.9877 L F 202.1697 164.9877 m 205.7553 164.9766 L 205.7553 167.135 L 202.1697 167.1239 L F 196.4139 167.135 m 205.7553 167.135 l 205.7553 164.9766 l 196.4139 164.9766 l 196.4139 167.135 l f 0 G 0.3 w 10 M 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 201.0846 166.0557 m S 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 201.0846 166.0557 m S 1 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 201.0846 166.0557 m S 1 g 0.5 w 4 M 201.0846 166.0557 m B 0.3 w 10 M 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 201.0846 166.0557 m S 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 201.0846 166.0557 m S u 1 g 1 w 4 M 201.0846 166.0557 m F U 0 G 0.3 w 10 M 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 201.0846 166.0557 m S 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 201.0846 166.0557 m S 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 201.0846 166.0557 m S u 1 g 1 w 4 M 201.0846 166.0557 m F U 0 G 0.3 w 10 M 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 201.0846 166.0557 m S 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 189.4261 177.5007 m S 212.7432 154.6106 m S 201.0846 166.0557 m S 201.0846 166.0557 m S 189.4261 177.5007 m S 189.4261 177.5007 m S 212.7432 177.5007 m S 212.7432 177.5007 m S 201.0846 166.0557 m S 201.0846 166.0557 m S 189.4261 154.6106 m S 189.4261 154.6106 m S 189.4261 177.5007 m S 212.7432 177.5007 m S 212.7432 154.6106 m S 212.7432 177.5007 m S 189.4261 154.6106 m S 189.4261 154.6106 m S 212.7432 154.6106 m S 212.7432 154.6106 m S 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 201.0846 166.0557 m S 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 201.0846 166.0557 m S 201.0846 166.0557 m S 0 g 1 w 4 M 201.0846 166.0557 m F 0 G 0.3 w 10 M 201.0846 166.0557 m S 201.0846 166.0557 m S 212.7432 154.6106 m S 0 g 1 w 4 M 212.7432 154.6106 m F 0 G 0.3 w 10 M 212.7432 154.6106 m S 212.7432 154.6106 m S 212.7432 154.6106 m S 0 g 1 w 4 M 212.7432 154.6106 m F 0 G 0.3 w 10 M 212.7432 154.6106 m S 212.7432 154.6106 m S 212.7432 154.6106 m S 0 g 1 w 4 M 212.7432 154.6106 m F 0 G 0.3 w 10 M 212.7432 154.6106 m S 212.7432 154.6106 m S 212.7432 154.6106 m S 0 g 1 w 4 M 212.7432 154.6106 m F 0 G 0.3 w 10 M 212.7432 154.6106 m S 212.7432 154.6106 m S 212.7432 154.6106 m S 0 g 1 w 4 M 212.7432 154.6106 m F 0 G 0.3 w 10 M 212.7432 154.6106 m S 212.7432 154.6106 m S 1 g 1 w 4 M 212.7432 154.6106 m F 0 G 0.3 w 10 M 212.7432 154.6106 m S 0 g 1 w 4 M 212.7432 154.6106 m F 0 G 0.3 w 10 M 212.7432 154.6106 m S 212.7432 154.6106 m S 0.5 w 4 M 189.4261 177.5007 m 212.7432 177.5007 l 212.7432 154.6106 l 189.4261 154.6106 l 189.4261 177.5007 l s 0.3 w 10 M 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 130.0483 98.4535 m 126.4627 98.4646 L 126.4627 96.3062 L 130.0483 96.3173 L F 132.2184 96.3173 m 135.8041 96.3062 L 135.8041 98.4646 L 132.2184 98.4535 L F 126.4627 98.4646 m 135.8041 98.4646 l 135.8041 96.3062 l 126.4627 96.3062 l 126.4627 98.4646 l f 0 G 0.3 w 10 M 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 131.1334 97.3853 m S 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 131.1334 97.3853 m S 1 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 131.1334 97.3853 m S 1 g 0.5 w 4 M 131.1334 97.3853 m B 0.3 w 10 M 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 131.1334 97.3853 m S 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 131.1334 97.3853 m S u 1 g 1 w 4 M 131.1334 97.3853 m F U 0 G 0.3 w 10 M 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 131.1334 97.3853 m S 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 131.1334 97.3853 m S 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 131.1334 97.3853 m S u 1 g 1 w 4 M 131.1334 97.3853 m F U 0 G 0.3 w 10 M 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 131.1334 97.3853 m S 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 119.4748 108.8304 m S 142.7919 85.9402 m S 131.1334 97.3853 m S 131.1334 97.3853 m S 119.4748 108.8304 m S 119.4748 108.8304 m S 142.7919 108.8304 m S 142.7919 108.8304 m S 131.1334 97.3853 m S 131.1334 97.3853 m S 119.4748 85.9402 m S 119.4748 85.9402 m S 119.4748 108.8304 m S 142.7919 108.8304 m S 142.7919 85.9402 m S 142.7919 108.8304 m S 119.4748 85.9402 m S 119.4748 85.9402 m S 142.7919 85.9402 m S 142.7919 85.9402 m S 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 131.1334 97.3853 m S 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 131.1334 97.3853 m S 131.1334 97.3853 m S 0 g 1 w 4 M 131.1334 97.3853 m F 0 G 0.3 w 10 M 131.1334 97.3853 m S 131.1334 97.3853 m S 142.7919 85.9402 m S 0 g 1 w 4 M 142.7919 85.9402 m F 0 G 0.3 w 10 M 142.7919 85.9402 m S 142.7919 85.9402 m S 142.7919 85.9402 m S 0 g 1 w 4 M 142.7919 85.9402 m F 0 G 0.3 w 10 M 142.7919 85.9402 m S 142.7919 85.9402 m S 142.7919 85.9402 m S 0 g 1 w 4 M 142.7919 85.9402 m F 0 G 0.3 w 10 M 142.7919 85.9402 m S 142.7919 85.9402 m S 142.7919 85.9402 m S 0 g 1 w 4 M 142.7919 85.9402 m F 0 G 0.3 w 10 M 142.7919 85.9402 m S 142.7919 85.9402 m S 142.7919 85.9402 m S 0 g 1 w 4 M 142.7919 85.9402 m F 0 G 0.3 w 10 M 142.7919 85.9402 m S 142.7919 85.9402 m S 1 g 1 w 4 M 142.7919 85.9402 m F 0 G 0.3 w 10 M 142.7919 85.9402 m S 0 g 1 w 4 M 142.7919 85.9402 m F 0 G 0.3 w 10 M 142.7919 85.9402 m S 142.7919 85.9402 m S 0.5 w 4 M 119.4748 108.8304 m 142.7919 108.8304 l 142.7919 85.9402 l 119.4748 85.9402 l 119.4748 108.8304 l s 0.3 w 10 M 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 269.9507 98.4535 m 266.3651 98.4646 L 266.3651 96.3062 L 269.9507 96.3173 L F 272.1209 96.3173 m 275.7065 96.3062 L 275.7065 98.4646 L 272.1209 98.4535 L F 266.3651 98.4646 m 275.7065 98.4646 l 275.7065 96.3062 l 266.3651 96.3062 l 266.3651 98.4646 l f 0 G 0.3 w 10 M 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 271.0358 97.3853 m S 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 271.0358 97.3853 m S 1 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 271.0358 97.3853 m S 1 g 0.5 w 4 M 271.0358 97.3853 m B 0.3 w 10 M 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 271.0358 97.3853 m S 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 271.0358 97.3853 m S u 1 g 1 w 4 M 271.0358 97.3853 m F U 0 G 0.3 w 10 M 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 271.0358 97.3853 m S 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 271.0358 97.3853 m S 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 271.0358 97.3853 m S u 1 g 1 w 4 M 271.0358 97.3853 m F U 0 G 0.3 w 10 M 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 271.0358 97.3853 m S 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 259.3772 108.8304 m S 282.6943 85.9402 m S 271.0358 97.3853 m S 271.0358 97.3853 m S 259.3772 108.8304 m S 259.3772 108.8304 m S 282.6943 108.8304 m S 282.6943 108.8304 m S 271.0358 97.3853 m S 271.0358 97.3853 m S 259.3772 85.9402 m S 259.3772 85.9402 m S 259.3772 108.8304 m S 282.6943 108.8304 m S 282.6943 85.9402 m S 282.6943 108.8304 m S 259.3772 85.9402 m S 259.3772 85.9402 m S 282.6943 85.9402 m S 282.6943 85.9402 m S 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 271.0358 97.3853 m S 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 271.0358 97.3853 m S 271.0358 97.3853 m S 0 g 1 w 4 M 271.0358 97.3853 m F 0 G 0.3 w 10 M 271.0358 97.3853 m S 271.0358 97.3853 m S 282.6943 85.9402 m S 0 g 1 w 4 M 282.6943 85.9402 m F 0 G 0.3 w 10 M 282.6943 85.9402 m S 282.6943 85.9402 m S 282.6943 85.9402 m S 0 g 1 w 4 M 282.6943 85.9402 m F 0 G 0.3 w 10 M 282.6943 85.9402 m S 282.6943 85.9402 m S 282.6943 85.9402 m S 0 g 1 w 4 M 282.6943 85.9402 m F 0 G 0.3 w 10 M 282.6943 85.9402 m S 282.6943 85.9402 m S 282.6943 85.9402 m S 0 g 1 w 4 M 282.6943 85.9402 m F 0 G 0.3 w 10 M 282.6943 85.9402 m S 282.6943 85.9402 m S 282.6943 85.9402 m S 0 g 1 w 4 M 282.6943 85.9402 m F 0 G 0.3 w 10 M 282.6943 85.9402 m S 282.6943 85.9402 m S 1 g 1 w 4 M 282.6943 85.9402 m F 0 G 0.3 w 10 M 282.6943 85.9402 m S 0 g 1 w 4 M 282.6943 85.9402 m F 0 G 0.3 w 10 M 282.6943 85.9402 m S 282.6943 85.9402 m S 0.5 w 4 M 259.3772 108.8304 m 282.6943 108.8304 l 282.6943 85.9402 l 259.3772 85.9402 l 259.3772 108.8304 l s 0.3 w 10 M 201.0846 234.7261 m S 0 g 1 w 4 M 201.0846 234.7261 m F 0 G 0.3 w 10 M 201.0846 234.7261 m S 201.0846 234.7261 m S 201.0846 234.7261 m S 0 g 1 w 4 M 201.0846 234.7261 m F 0 G 0.3 w 10 M 201.0846 234.7261 m S 201.0846 234.7261 m S 201.0846 234.7261 m S 0 g 1 w 4 M 201.0846 234.7261 m F 0 G 0.3 w 10 M 201.0846 234.7261 m S 201.0846 234.7261 m S 0 g 1 w 4 M 199.9995 233.6582 m 199.9995 230.0811 L 202.1697 230.0811 L 202.1697 233.6582 L 205.7553 233.647 L 205.7553 235.8054 L 202.1697 235.7943 L 202.1697 239.3714 L 199.9995 239.3714 L 199.9995 235.7943 L 196.4139 235.8054 L 196.4139 233.647 L 199.9995 233.6582 L f 0 G 0.3 w 10 M 201.0846 234.7261 m S 0 g 1 w 4 M 201.0846 234.7261 m F 0 G 0.3 w 10 M 201.0846 234.7261 m S 201.0846 234.7261 m S 201.0846 234.7261 m S 0 g 1 w 4 M 201.0846 234.7261 m F 0 G 0.3 w 10 M 201.0846 234.7261 m S 201.0846 234.7261 m S u 1 g 1 w 4 M 201.0846 234.7261 m F U 0 G 0.3 w 10 M 201.0846 234.7261 m S 0 g 1 w 4 M 201.0846 234.7261 m F 0 G 0.3 w 10 M 201.0846 234.7261 m S 201.0846 234.7261 m S 201.0846 234.7261 m S 0 g 1 w 4 M 201.0846 234.7261 m F 0 G 0.3 w 10 M 201.0846 234.7261 m S 0 g 1 w 4 M 201.0846 234.7261 m F 0 G 0.3 w 10 M 189.4261 246.1712 m S 212.7432 223.281 m S 201.0846 234.7261 m S 201.0846 234.7261 m S 189.4261 246.1712 m S 189.4261 246.1712 m S 212.7432 246.1712 m S 212.7432 246.1712 m S 201.0846 234.7261 m S 201.0846 234.7261 m S 189.4261 223.281 m S 189.4261 223.281 m S 189.4261 246.1712 m S 212.7432 246.1712 m S 212.7432 223.281 m S 212.7432 246.1712 m S 189.4261 223.281 m S 189.4261 223.281 m S 212.7432 223.281 m S 212.7432 223.281 m S 201.0846 234.7261 m S 0 g 1 w 4 M 201.0846 234.7261 m F 0 G 0.3 w 10 M 201.0846 234.7261 m S 201.0846 234.7261 m S 201.0846 234.7261 m S 0 g 1 w 4 M 201.0846 234.7261 m F 0 G 0.3 w 10 M 201.0846 234.7261 m S 201.0846 234.7261 m S 201.0846 234.7261 m S 0 g 1 w 4 M 201.0846 234.7261 m F 0 G 0.3 w 10 M 201.0846 234.7261 m S 201.0846 234.7261 m S 212.7432 223.281 m S 0 g 1 w 4 M 212.7432 223.281 m F 0 G 0.3 w 10 M 212.7432 223.281 m S 212.7432 223.281 m S 212.7432 223.281 m S 0 g 1 w 4 M 212.7432 223.281 m F 0 G 0.3 w 10 M 212.7432 223.281 m S 212.7432 223.281 m S 212.7432 223.281 m S 0 g 1 w 4 M 212.7432 223.281 m F 0 G 0.3 w 10 M 212.7432 223.281 m S 212.7432 223.281 m S 212.7432 223.281 m S 0 g 1 w 4 M 212.7432 223.281 m F 0 G 0.3 w 10 M 212.7432 223.281 m S 212.7432 223.281 m S 212.7432 223.281 m S 0 g 1 w 4 M 212.7432 223.281 m F 0 G 0.3 w 10 M 212.7432 223.281 m S 212.7432 223.281 m S 1 g 1 w 4 M 212.7432 223.281 m F 0 G 0.3 w 10 M 212.7432 223.281 m S 0 g 1 w 4 M 212.7432 223.281 m F 0 G 0.3 w 10 M 212.7432 223.281 m S 212.7432 223.281 m S 0.5 w 4 M 189.4261 246.1712 m 212.7432 246.1712 l 212.7432 223.281 l 189.4261 223.281 l 189.4261 246.1712 l s 0.3 w 10 M 131.1334 166.0557 m S 0 g 1 w 4 M 131.1334 166.0557 m F 0 G 0.3 w 10 M 131.1334 166.0557 m S 131.1334 166.0557 m S 131.1334 166.0557 m S 0 g 1 w 4 M 131.1334 166.0557 m F 0 G 0.3 w 10 M 131.1334 166.0557 m S 131.1334 166.0557 m S 131.1334 166.0557 m S 0 g 1 w 4 M 131.1334 166.0557 m F 0 G 0.3 w 10 M 131.1334 166.0557 m S 131.1334 166.0557 m S 0 g 1 w 4 M 130.0483 164.9878 m 130.0483 161.4107 L 132.2184 161.4107 L 132.2184 164.9878 L 135.8041 164.9766 L 135.8041 167.135 L 132.2184 167.1239 L 132.2184 170.701 L 130.0483 170.701 L 130.0483 167.1239 L 126.4627 167.135 L 126.4627 164.9766 L 130.0483 164.9878 L f 0 G 0.3 w 10 M 131.1334 166.0557 m S 0 g 1 w 4 M 131.1334 166.0557 m F 0 G 0.3 w 10 M 131.1334 166.0557 m S 131.1334 166.0557 m S 131.1334 166.0557 m S 0 g 1 w 4 M 131.1334 166.0557 m F 0 G 0.3 w 10 M 131.1334 166.0557 m S 131.1334 166.0557 m S u 1 g 1 w 4 M 131.1334 166.0557 m F U 0 G 0.3 w 10 M 131.1334 166.0557 m S 0 g 1 w 4 M 131.1334 166.0557 m F 0 G 0.3 w 10 M 131.1334 166.0557 m S 131.1334 166.0557 m S 131.1334 166.0557 m S 0 g 1 w 4 M 131.1334 166.0557 m F 0 G 0.3 w 10 M 131.1334 166.0557 m S 0 g 1 w 4 M 131.1334 166.0557 m F 0 G 0.3 w 10 M 119.4748 177.5007 m S 142.7919 154.6106 m S 131.1334 166.0557 m S 131.1334 166.0557 m S 119.4748 177.5007 m S 119.4748 177.5007 m S 142.7919 177.5007 m S 142.7919 177.5007 m S 131.1334 166.0557 m S 131.1334 166.0557 m S 119.4748 154.6106 m S 119.4748 154.6106 m S 119.4748 177.5007 m S 142.7919 177.5007 m S 142.7919 154.6106 m S 142.7919 177.5007 m S 119.4748 154.6106 m S 119.4748 154.6106 m S 142.7919 154.6106 m S 142.7919 154.6106 m S 131.1334 166.0557 m S 0 g 1 w 4 M 131.1334 166.0557 m F 0 G 0.3 w 10 M 131.1334 166.0557 m S 131.1334 166.0557 m S 131.1334 166.0557 m S 0 g 1 w 4 M 131.1334 166.0557 m F 0 G 0.3 w 10 M 131.1334 166.0557 m S 131.1334 166.0557 m S 131.1334 166.0557 m S 0 g 1 w 4 M 131.1334 166.0557 m F 0 G 0.3 w 10 M 131.1334 166.0557 m S 131.1334 166.0557 m S 142.7919 154.6106 m S 0 g 1 w 4 M 142.7919 154.6106 m F 0 G 0.3 w 10 M 142.7919 154.6106 m S 142.7919 154.6106 m S 142.7919 154.6106 m S 0 g 1 w 4 M 142.7919 154.6106 m F 0 G 0.3 w 10 M 142.7919 154.6106 m S 142.7919 154.6106 m S 142.7919 154.6106 m S 0 g 1 w 4 M 142.7919 154.6106 m F 0 G 0.3 w 10 M 142.7919 154.6106 m S 142.7919 154.6106 m S 142.7919 154.6106 m S 0 g 1 w 4 M 142.7919 154.6106 m F 0 G 0.3 w 10 M 142.7919 154.6106 m S 142.7919 154.6106 m S 142.7919 154.6106 m S 0 g 1 w 4 M 142.7919 154.6106 m F 0 G 0.3 w 10 M 142.7919 154.6106 m S 142.7919 154.6106 m S 1 g 1 w 4 M 142.7919 154.6106 m F 0 G 0.3 w 10 M 142.7919 154.6106 m S 0 g 1 w 4 M 142.7919 154.6106 m F 0 G 0.3 w 10 M 142.7919 154.6106 m S 142.7919 154.6106 m S 0.5 w 4 M 119.4748 177.5007 m 142.7919 177.5007 l 142.7919 154.6106 l 119.4748 154.6106 l 119.4748 177.5007 l s 0.3 w 10 M 271.0358 166.0557 m S 0 g 1 w 4 M 271.0358 166.0557 m F 0 G 0.3 w 10 M 271.0358 166.0557 m S 271.0358 166.0557 m S 271.0358 166.0557 m S 0 g 1 w 4 M 271.0358 166.0557 m F 0 G 0.3 w 10 M 271.0358 166.0557 m S 271.0358 166.0557 m S 271.0358 166.0557 m S 0 g 1 w 4 M 271.0358 166.0557 m F 0 G 0.3 w 10 M 271.0358 166.0557 m S 271.0358 166.0557 m S 0 g 1 w 4 M 269.9507 164.9878 m 269.9507 161.4107 L 272.1209 161.4107 L 272.1209 164.9878 L 275.7065 164.9766 L 275.7065 167.135 L 272.1209 167.1239 L 272.1209 170.701 L 269.9507 170.701 L 269.9507 167.1239 L 266.3651 167.135 L 266.3651 164.9766 L 269.9507 164.9878 L f 0 G 0.3 w 10 M 271.0358 166.0557 m S 0 g 1 w 4 M 271.0358 166.0557 m F 0 G 0.3 w 10 M 271.0358 166.0557 m S 271.0358 166.0557 m S 271.0358 166.0557 m S 0 g 1 w 4 M 271.0358 166.0557 m F 0 G 0.3 w 10 M 271.0358 166.0557 m S 271.0358 166.0557 m S u 1 g 1 w 4 M 271.0358 166.0557 m F U 0 G 0.3 w 10 M 271.0358 166.0557 m S 0 g 1 w 4 M 271.0358 166.0557 m F 0 G 0.3 w 10 M 271.0358 166.0557 m S 271.0358 166.0557 m S 271.0358 166.0557 m S 0 g 1 w 4 M 271.0358 166.0557 m F 0 G 0.3 w 10 M 271.0358 166.0557 m S 0 g 1 w 4 M 271.0358 166.0557 m F 0 G 0.3 w 10 M 259.3772 177.5007 m S 282.6943 154.6106 m S 271.0358 166.0557 m S 271.0358 166.0557 m S 259.3772 177.5007 m S 259.3772 177.5007 m S 282.6943 177.5007 m S 282.6943 177.5007 m S 271.0358 166.0557 m S 271.0358 166.0557 m S 259.3772 154.6106 m S 259.3772 154.6106 m S 259.3772 177.5007 m S 282.6943 177.5007 m S 282.6943 154.6106 m S 282.6943 177.5007 m S 259.3772 154.6106 m S 259.3772 154.6106 m S 282.6943 154.6106 m S 282.6943 154.6106 m S 271.0358 166.0557 m S 0 g 1 w 4 M 271.0358 166.0557 m F 0 G 0.3 w 10 M 271.0358 166.0557 m S 271.0358 166.0557 m S 271.0358 166.0557 m S 0 g 1 w 4 M 271.0358 166.0557 m F 0 G 0.3 w 10 M 271.0358 166.0557 m S 271.0358 166.0557 m S 271.0358 166.0557 m S 0 g 1 w 4 M 271.0358 166.0557 m F 0 G 0.3 w 10 M 271.0358 166.0557 m S 271.0358 166.0557 m S 282.6943 154.6106 m S 0 g 1 w 4 M 282.6943 154.6106 m F 0 G 0.3 w 10 M 282.6943 154.6106 m S 282.6943 154.6106 m S 282.6943 154.6106 m S 0 g 1 w 4 M 282.6943 154.6106 m F 0 G 0.3 w 10 M 282.6943 154.6106 m S 282.6943 154.6106 m S 282.6943 154.6106 m S 0 g 1 w 4 M 282.6943 154.6106 m F 0 G 0.3 w 10 M 282.6943 154.6106 m S 282.6943 154.6106 m S 282.6943 154.6106 m S 0 g 1 w 4 M 282.6943 154.6106 m F 0 G 0.3 w 10 M 282.6943 154.6106 m S 282.6943 154.6106 m S 282.6943 154.6106 m S 0 g 1 w 4 M 282.6943 154.6106 m F 0 G 0.3 w 10 M 282.6943 154.6106 m S 282.6943 154.6106 m S 1 g 1 w 4 M 282.6943 154.6106 m F 0 G 0.3 w 10 M 282.6943 154.6106 m S 0 g 1 w 4 M 282.6943 154.6106 m F 0 G 0.3 w 10 M 282.6943 154.6106 m S 282.6943 154.6106 m S 0.5 w 4 M 259.3772 177.5007 m 282.6943 177.5007 l 282.6943 154.6106 l 259.3772 154.6106 l 259.3772 177.5007 l s 0.3 w 10 M 201.0846 97.3853 m S 0 g 1 w 4 M 201.0846 97.3853 m F 0 G 0.3 w 10 M 201.0846 97.3853 m S 201.0846 97.3853 m S 201.0846 97.3853 m S 0 g 1 w 4 M 201.0846 97.3853 m F 0 G 0.3 w 10 M 201.0846 97.3853 m S 201.0846 97.3853 m S 201.0846 97.3853 m S 0 g 1 w 4 M 201.0846 97.3853 m F 0 G 0.3 w 10 M 201.0846 97.3853 m S 201.0846 97.3853 m S 0 g 1 w 4 M 199.9995 96.3174 m 199.9995 92.7403 L 202.1697 92.7403 L 202.1697 96.3174 L 205.7553 96.3062 L 205.7553 98.4646 L 202.1697 98.4535 L 202.1697 102.0306 L 199.9995 102.0306 L 199.9995 98.4535 L 196.4139 98.4646 L 196.4139 96.3062 L 199.9995 96.3174 L f 0 G 0.3 w 10 M 201.0846 97.3853 m S 0 g 1 w 4 M 201.0846 97.3853 m F 0 G 0.3 w 10 M 201.0846 97.3853 m S 201.0846 97.3853 m S 201.0846 97.3853 m S 0 g 1 w 4 M 201.0846 97.3853 m F 0 G 0.3 w 10 M 201.0846 97.3853 m S 201.0846 97.3853 m S u 1 g 1 w 4 M 201.0846 97.3853 m F U 0 G 0.3 w 10 M 201.0846 97.3853 m S 0 g 1 w 4 M 201.0846 97.3853 m F 0 G 0.3 w 10 M 201.0846 97.3853 m S 201.0846 97.3853 m S 201.0846 97.3853 m S 0 g 1 w 4 M 201.0846 97.3853 m F 0 G 0.3 w 10 M 201.0846 97.3853 m S 0 g 1 w 4 M 201.0846 97.3853 m F 0 G 0.3 w 10 M 189.4261 108.8304 m S 212.7432 85.9402 m S 201.0846 97.3853 m S 201.0846 97.3853 m S 189.4261 108.8304 m S 189.4261 108.8304 m S 212.7432 108.8304 m S 212.7432 108.8304 m S 201.0846 97.3853 m S 201.0846 97.3853 m S 189.4261 85.9402 m S 189.4261 85.9402 m S 189.4261 108.8304 m S 212.7432 108.8304 m S 212.7432 85.9402 m S 212.7432 108.8304 m S 189.4261 85.9402 m S 189.4261 85.9402 m S 212.7432 85.9402 m S 212.7432 85.9402 m S 201.0846 97.3853 m S 0 g 1 w 4 M 201.0846 97.3853 m F 0 G 0.3 w 10 M 201.0846 97.3853 m S 201.0846 97.3853 m S 201.0846 97.3853 m S 0 g 1 w 4 M 201.0846 97.3853 m F 0 G 0.3 w 10 M 201.0846 97.3853 m S 201.0846 97.3853 m S 201.0846 97.3853 m S 0 g 1 w 4 M 201.0846 97.3853 m F 0 G 0.3 w 10 M 201.0846 97.3853 m S 201.0846 97.3853 m S 212.7432 85.9402 m S 0 g 1 w 4 M 212.7432 85.9402 m F 0 G 0.3 w 10 M 212.7432 85.9402 m S 212.7432 85.9402 m S 212.7432 85.9402 m S 0 g 1 w 4 M 212.7432 85.9402 m F 0 G 0.3 w 10 M 212.7432 85.9402 m S 212.7432 85.9402 m S 212.7432 85.9402 m S 0 g 1 w 4 M 212.7432 85.9402 m F 0 G 0.3 w 10 M 212.7432 85.9402 m S 212.7432 85.9402 m S 212.7432 85.9402 m S 0 g 1 w 4 M 212.7432 85.9402 m F 0 G 0.3 w 10 M 212.7432 85.9402 m S 212.7432 85.9402 m S 212.7432 85.9402 m S 0 g 1 w 4 M 212.7432 85.9402 m F 0 G 0.3 w 10 M 212.7432 85.9402 m S 212.7432 85.9402 m S 1 g 1 w 4 M 212.7432 85.9402 m F 0 G 0.3 w 10 M 212.7432 85.9402 m S 0 g 1 w 4 M 212.7432 85.9402 m F 0 G 0.3 w 10 M 212.7432 85.9402 m S 212.7432 85.9402 m S 0.5 w 4 M 189.4261 108.8304 m 212.7432 108.8304 l 212.7432 85.9402 l 189.4261 85.9402 l 189.4261 108.8304 l s 0.3 w 10 M 61.1821 97.3853 m S 0 g 1 w 4 M 61.1821 97.3853 m F 0 G 0.3 w 10 M 61.1821 97.3853 m S 61.1821 97.3853 m S 61.1821 97.3853 m S 0 g 1 w 4 M 61.1821 97.3853 m F 0 G 0.3 w 10 M 61.1821 97.3853 m S 61.1821 97.3853 m S 61.1821 97.3853 m S 0 g 1 w 4 M 61.1821 97.3853 m F 0 G 0.3 w 10 M 61.1821 97.3853 m S 61.1821 97.3853 m S 0 g 1 w 4 M 60.097 96.3174 m 60.097 92.7403 L 62.2672 92.7403 L 62.2672 96.3174 L 65.8528 96.3062 L 65.8528 98.4646 L 62.2672 98.4535 L 62.2672 102.0306 L 60.097 102.0306 L 60.097 98.4535 L 56.5114 98.4646 L 56.5114 96.3062 L 60.097 96.3174 L f 0 G 0.3 w 10 M 61.1821 97.3853 m S 0 g 1 w 4 M 61.1821 97.3853 m F 0 G 0.3 w 10 M 61.1821 97.3853 m S 61.1821 97.3853 m S 61.1821 97.3853 m S 0 g 1 w 4 M 61.1821 97.3853 m F 0 G 0.3 w 10 M 61.1821 97.3853 m S 61.1821 97.3853 m S u 1 g 1 w 4 M 61.1821 97.3853 m F U 0 G 0.3 w 10 M 61.1821 97.3853 m S 0 g 1 w 4 M 61.1821 97.3853 m F 0 G 0.3 w 10 M 61.1821 97.3853 m S 61.1821 97.3853 m S 61.1821 97.3853 m S 0 g 1 w 4 M 61.1821 97.3853 m F 0 G 0.3 w 10 M 61.1821 97.3853 m S 0 g 1 w 4 M 61.1821 97.3853 m F 0 G 0.3 w 10 M 49.5236 108.8304 m S 72.8407 85.9402 m S 61.1821 97.3853 m S 61.1821 97.3853 m S 49.5236 108.8304 m S 49.5236 108.8304 m S 72.8407 108.8304 m S 72.8407 108.8304 m S 61.1821 97.3853 m S 61.1821 97.3853 m S 49.5236 85.9402 m S 49.5236 85.9402 m S 49.5236 108.8304 m S 72.8407 108.8304 m S 72.8407 85.9402 m S 72.8407 108.8304 m S 49.5236 85.9402 m S 49.5236 85.9402 m S 72.8407 85.9402 m S 72.8407 85.9402 m S 61.1821 97.3853 m S 0 g 1 w 4 M 61.1821 97.3853 m F 0 G 0.3 w 10 M 61.1821 97.3853 m S 61.1821 97.3853 m S 61.1821 97.3853 m S 0 g 1 w 4 M 61.1821 97.3853 m F 0 G 0.3 w 10 M 61.1821 97.3853 m S 61.1821 97.3853 m S 61.1821 97.3853 m S 0 g 1 w 4 M 61.1821 97.3853 m F 0 G 0.3 w 10 M 61.1821 97.3853 m S 61.1821 97.3853 m S 72.8407 85.9402 m S 0 g 1 w 4 M 72.8407 85.9402 m F 0 G 0.3 w 10 M 72.8407 85.9402 m S 72.8407 85.9402 m S 72.8407 85.9402 m S 0 g 1 w 4 M 72.8407 85.9402 m F 0 G 0.3 w 10 M 72.8407 85.9402 m S 72.8407 85.9402 m S 72.8407 85.9402 m S 0 g 1 w 4 M 72.8407 85.9402 m F 0 G 0.3 w 10 M 72.8407 85.9402 m S 72.8407 85.9402 m S 72.8407 85.9402 m S 0 g 1 w 4 M 72.8407 85.9402 m F 0 G 0.3 w 10 M 72.8407 85.9402 m S 72.8407 85.9402 m S 72.8407 85.9402 m S 0 g 1 w 4 M 72.8407 85.9402 m F 0 G 0.3 w 10 M 72.8407 85.9402 m S 72.8407 85.9402 m S 1 g 1 w 4 M 72.8407 85.9402 m F 0 G 0.3 w 10 M 72.8407 85.9402 m S 0 g 1 w 4 M 72.8407 85.9402 m F 0 G 0.3 w 10 M 72.8407 85.9402 m S 72.8407 85.9402 m S 0.5 w 4 M 49.5236 108.8304 m 72.8407 108.8304 l 72.8407 85.9402 l 49.5236 85.9402 l 49.5236 108.8304 l s 0.3 w 10 M 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 269.9507 235.7943 m 266.3651 235.8054 L 266.3651 233.647 L 269.9507 233.6581 L F 272.1209 233.6581 m 275.7065 233.647 L 275.7065 235.8054 L 272.1209 235.7943 L F 266.3651 235.8054 m 275.7065 235.8054 l 275.7065 233.647 l 266.3651 233.647 l 266.3651 235.8054 l f 0 G 0.3 w 10 M 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 271.0358 234.7261 m S 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 271.0358 234.7261 m S 1 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 271.0358 234.7261 m S 1 g 0.5 w 4 M 271.0358 234.7261 m B 0.3 w 10 M 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 271.0358 234.7261 m S 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 271.0358 234.7261 m S u 1 g 1 w 4 M 271.0358 234.7261 m F U 0 G 0.3 w 10 M 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 271.0358 234.7261 m S 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 271.0358 234.7261 m S 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 271.0358 234.7261 m S u 1 g 1 w 4 M 271.0358 234.7261 m F U 0 G 0.3 w 10 M 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 271.0358 234.7261 m S 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 259.3772 246.1712 m S 282.6943 223.281 m S 271.0358 234.7261 m S 271.0358 234.7261 m S 259.3772 246.1712 m S 259.3772 246.1712 m S 282.6943 246.1712 m S 282.6943 246.1712 m S 271.0358 234.7261 m S 271.0358 234.7261 m S 259.3772 223.281 m S 259.3772 223.281 m S 259.3772 246.1712 m S 282.6943 246.1712 m S 282.6943 223.281 m S 282.6943 246.1712 m S 259.3772 223.281 m S 259.3772 223.281 m S 282.6943 223.281 m S 282.6943 223.281 m S 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 271.0358 234.7261 m S 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 271.0358 234.7261 m S 271.0358 234.7261 m S 0 g 1 w 4 M 271.0358 234.7261 m F 0 G 0.3 w 10 M 271.0358 234.7261 m S 271.0358 234.7261 m S 282.6943 223.281 m S 0 g 1 w 4 M 282.6943 223.281 m F 0 G 0.3 w 10 M 282.6943 223.281 m S 282.6943 223.281 m S 282.6943 223.281 m S 0 g 1 w 4 M 282.6943 223.281 m F 0 G 0.3 w 10 M 282.6943 223.281 m S 282.6943 223.281 m S 282.6943 223.281 m S 0 g 1 w 4 M 282.6943 223.281 m F 0 G 0.3 w 10 M 282.6943 223.281 m S 282.6943 223.281 m S 282.6943 223.281 m S 0 g 1 w 4 M 282.6943 223.281 m F 0 G 0.3 w 10 M 282.6943 223.281 m S 282.6943 223.281 m S 282.6943 223.281 m S 0 g 1 w 4 M 282.6943 223.281 m F 0 G 0.3 w 10 M 282.6943 223.281 m S 282.6943 223.281 m S 1 g 1 w 4 M 282.6943 223.281 m F 0 G 0.3 w 10 M 282.6943 223.281 m S 0 g 1 w 4 M 282.6943 223.281 m F 0 G 0.3 w 10 M 282.6943 223.281 m S 282.6943 223.281 m S 0.5 w 4 M 259.3772 246.1712 m 282.6943 246.1712 l 282.6943 223.281 l 259.3772 223.281 l 259.3772 246.1712 l s 0.3 w 10 M 37.8651 257.6162 m S 0 g 1 w 4 M 37.8651 257.6162 m F 0 G 0.3 w 10 M 37.8651 257.6162 m S 37.8651 257.6162 m S 37.8651 257.6162 m S 0 g 1 w 4 M 37.8651 257.6162 m F 0 G 0.3 w 10 M 37.8651 257.6162 m S 37.8651 257.6162 m S 1 g 0.5 w 4 M 31.8547 257.6162 m 31.8547 254.3944 34.5457 251.7826 37.8651 251.7826 c 41.1845 251.7826 43.8755 254.3944 43.8755 257.6162 c B 43.8755 257.6162 m 43.8755 260.838 41.1845 263.4498 37.8651 263.4498 c 34.5457 263.4498 31.8547 260.838 31.8547 257.6162 c B 37.8651 257.6162 m B 0.3 w 10 M 37.8651 257.6162 m S 0 g 1 w 4 M 37.8651 257.6162 m F 0 G 0.3 w 10 M 37.8651 257.6162 m S 37.8651 257.6162 m S 0 g 1 w 4 M 36.78 256.5483 m 36.78 252.9712 L 38.9502 252.9712 L 38.9502 256.5483 L 42.5358 256.5371 L 42.5358 258.6955 L 38.9502 258.6844 L 38.9502 262.2615 L 36.78 262.2615 L 36.78 258.6844 L 33.1944 258.6955 L 33.1944 256.5371 L 36.78 256.5483 L f 0 G 0.3 w 10 M 84.4992 257.6162 m S 0 g 1 w 4 M 84.4992 257.6162 m F 0 G 0.3 w 10 M 84.4992 257.6162 m S 84.4992 257.6162 m S 84.4992 257.6162 m S 0 g 1 w 4 M 84.4992 257.6162 m F 0 G 0.3 w 10 M 84.4992 257.6162 m S 84.4992 257.6162 m S 1 g 0.5 w 4 M 78.4888 257.6162 m 78.4888 254.3944 81.1798 251.7826 84.4992 251.7826 c 87.8186 251.7826 90.5096 254.3944 90.5096 257.6162 c B 90.5096 257.6162 m 90.5096 260.838 87.8186 263.4498 84.4992 263.4498 c 81.1798 263.4498 78.4888 260.838 78.4888 257.6162 c B 84.4992 257.6162 m B 0.3 w 10 M 84.4992 257.6162 m S 0 g 1 w 4 M 84.4992 257.6162 m F 0 G 0.3 w 10 M 84.4992 257.6162 m S 84.4992 257.6162 m S 0 g 1 w 4 M 83.4141 256.5483 m 83.4141 252.9712 L 85.5843 252.9712 L 85.5843 256.5483 L 89.1699 256.5371 L 89.1699 258.6955 L 85.5843 258.6844 L 85.5843 262.2615 L 83.4141 262.2615 L 83.4141 258.6844 L 79.8285 258.6955 L 79.8285 256.5371 L 83.4141 256.5483 L f 0 G 0.3 w 10 M 37.8651 211.8359 m S 0 g 1 w 4 M 37.8651 211.8359 m F 0 G 0.3 w 10 M 37.8651 211.8359 m S 37.8651 211.8359 m S 37.8651 211.8359 m S 0 g 1 w 4 M 37.8651 211.8359 m F 0 G 0.3 w 10 M 37.8651 211.8359 m S 37.8651 211.8359 m S u 1 g 0.5 w 4 M 31.8547 211.8359 m 31.8547 208.6141 34.5457 206.0023 37.8651 206.0023 c 41.1845 206.0023 43.8755 208.6141 43.8755 211.8359 c B 43.8755 211.8359 m 43.8755 215.0578 41.1845 217.6696 37.8651 217.6696 c 34.5457 217.6696 31.8547 215.0578 31.8547 211.8359 c B 37.8651 211.8359 m B U 0.3 w 10 M 37.8651 211.8359 m S 0 g 1 w 4 M 37.8651 211.8359 m F 0 G 0.3 w 10 M 37.8651 211.8359 m S 37.8651 211.8359 m S 0 g 1 w 4 M 36.78 210.768 m 36.78 207.1909 L 38.9502 207.1909 L 38.9502 210.768 L 42.5358 210.7568 L 42.5358 212.9152 L 38.9502 212.9042 L 38.9502 216.4812 L 36.78 216.4812 L 36.78 212.9042 L 33.1944 212.9152 L 33.1944 210.7568 L 36.78 210.768 L f 0 G 0.3 w 10 M 61.1821 211.8359 m S 0 g 1 w 4 M 61.1821 211.8359 m F 0 G 0.3 w 10 M 61.1821 211.8359 m S 61.1821 211.8359 m S 61.1821 211.8359 m S 0 g 1 w 4 M 61.1821 211.8359 m F 0 G 0.3 w 10 M 61.1821 211.8359 m S 61.1821 211.8359 m S 1 g 0.5 w 4 M 55.1717 211.8359 m 55.1717 208.6141 57.8627 206.0023 61.1821 206.0023 c 64.5015 206.0023 67.1925 208.6141 67.1925 211.8359 c B 67.1925 211.8359 m 67.1925 215.0578 64.5015 217.6696 61.1821 217.6696 c 57.8627 217.6696 55.1717 215.0578 55.1717 211.8359 c B 61.1821 211.8359 m B 0.3 w 10 M 61.1821 211.8359 m S 0 g 1 w 4 M 61.1821 211.8359 m F 0 G 0.3 w 10 M 61.1821 211.8359 m S 61.1821 211.8359 m S 0 g 1 w 4 M 60.097 210.768 m 60.097 207.1909 L 62.2672 207.1909 L 62.2672 210.768 L 65.8528 210.7568 L 65.8528 212.9152 L 62.2672 212.9042 L 62.2672 216.4812 L 60.097 216.4812 L 60.097 212.9042 L 56.5114 212.9152 L 56.5114 210.7568 L 60.097 210.768 L f 0 G 0.3 w 10 M 84.4992 211.8359 m S 0 g 1 w 4 M 84.4992 211.8359 m F 0 G 0.3 w 10 M 84.4992 211.8359 m S 84.4992 211.8359 m S 84.4992 211.8359 m S 0 g 1 w 4 M 84.4992 211.8359 m F 0 G 0.3 w 10 M 84.4992 211.8359 m S 84.4992 211.8359 m S 1 g 0.5 w 4 M 78.4888 211.8359 m 78.4888 208.6141 81.1798 206.0023 84.4992 206.0023 c 87.8186 206.0023 90.5096 208.6141 90.5096 211.8359 c B 90.5096 211.8359 m 90.5096 215.0578 87.8186 217.6696 84.4992 217.6696 c 81.1798 217.6696 78.4888 215.0578 78.4888 211.8359 c B 84.4992 211.8359 m B 0.3 w 10 M 84.4992 211.8359 m S 0 g 1 w 4 M 84.4992 211.8359 m F 0 G 0.3 w 10 M 84.4992 211.8359 m S 84.4992 211.8359 m S 0 g 1 w 4 M 83.4141 210.768 m 83.4141 207.1909 L 85.5843 207.1909 L 85.5843 210.768 L 89.1699 210.7568 L 89.1699 212.9152 L 85.5843 212.9042 L 85.5843 216.4812 L 83.4141 216.4812 L 83.4141 212.9042 L 79.8285 212.9152 L 79.8285 210.7568 L 83.4141 210.768 L f 0 G 0.3 w 10 M 84.4992 234.7261 m S 96.1577 234.7261 m S 84.4992 234.7261 m S 107.8162 234.7261 m S 96.1577 234.7261 m S 107.8162 234.7261 m S 84.4992 234.7261 m S 0 g 1 w 4 M 84.4992 234.7261 m F 0 G 0.3 w 10 M 84.4992 234.7261 m S 84.4992 234.7261 m S 84.4992 234.7261 m S 0 g 1 w 4 M 84.4992 234.7261 m F 0 G 0.3 w 10 M 84.4992 234.7261 m S 84.4992 234.7261 m S 1 g 0.5 w 4 M 78.4888 234.7261 m 78.4888 231.5043 81.1798 228.8925 84.4992 228.8925 c 87.8186 228.8925 90.5096 231.5043 90.5096 234.7261 c B 90.5096 234.7261 m 90.5096 237.9479 87.8186 240.5597 84.4992 240.5597 c 81.1798 240.5597 78.4888 237.9479 78.4888 234.7261 c B 84.4992 234.7261 m B 0.3 w 10 M 84.4992 234.7261 m S 0 g 1 w 4 M 84.4992 234.7261 m F 0 G 0.3 w 10 M 84.4992 234.7261 m S 84.4992 234.7261 m S 0 g 1 w 4 M 83.4141 233.6582 m 83.4141 230.0811 L 85.5843 230.0811 L 85.5843 233.6582 L 89.1699 233.647 L 89.1699 235.8054 L 85.5843 235.7943 L 85.5843 239.3714 L 83.4141 239.3714 L 83.4141 235.7943 L 79.8285 235.8054 L 79.8285 233.647 L 83.4141 233.6582 L f 0 G 0.3 w 10 M 107.8162 234.7261 m S 0 g 1 w 4 M 107.8162 234.7261 m F 0 G 0.3 w 10 M 107.8162 234.7261 m S 107.8162 234.7261 m S 107.8162 234.7261 m S 0 g 1 w 4 M 107.8162 234.7261 m F 0 G 0.3 w 10 M 107.8162 234.7261 m S 107.8162 234.7261 m S 1 g 0.5 w 4 M 101.8058 234.7261 m 101.8058 231.5043 104.4968 228.8925 107.8162 228.8925 c 111.1356 228.8925 113.8266 231.5043 113.8266 234.7261 c B 113.8266 234.7261 m 113.8266 237.9479 111.1356 240.5597 107.8162 240.5597 c 104.4968 240.5597 101.8058 237.9479 101.8058 234.7261 c B 107.8162 234.7261 m B 0.3 w 10 M 107.8162 234.7261 m S 0 g 1 w 4 M 107.8162 234.7261 m F 0 G 0.3 w 10 M 107.8162 234.7261 m S 107.8162 234.7261 m S 0 g 1 w 4 M 106.7311 233.6582 m 106.7311 230.0811 L 108.9013 230.0811 L 108.9013 233.6582 L 112.4869 233.647 L 112.4869 235.8054 L 108.9013 235.7943 L 108.9013 239.3714 L 106.7311 239.3714 L 106.7311 235.7943 L 103.1455 235.8054 L 103.1455 233.647 L 106.7311 233.6582 L f 0 G 0.3 w 10 M 107.8162 257.6162 m S 119.4748 257.6162 m S 107.8162 257.6162 m S 131.1333 257.6162 m S 119.4748 257.6162 m S 131.1333 257.6162 m S 107.8162 257.6162 m S 0 g 1 w 4 M 107.8162 257.6162 m F 0 G 0.3 w 10 M 107.8162 257.6162 m S 107.8162 257.6162 m S 107.8162 257.6162 m S 0 g 1 w 4 M 107.8162 257.6162 m F 0 G 0.3 w 10 M 107.8162 257.6162 m S 107.8162 257.6162 m S 1 g 0.5 w 4 M 101.8058 257.6162 m 101.8058 254.3944 104.4968 251.7826 107.8162 251.7826 c 111.1356 251.7826 113.8266 254.3944 113.8266 257.6162 c B 113.8266 257.6162 m 113.8266 260.838 111.1356 263.4498 107.8162 263.4498 c 104.4968 263.4498 101.8058 260.838 101.8058 257.6162 c B 107.8162 257.6162 m B 0.3 w 10 M 107.8162 257.6162 m S 0 g 1 w 4 M 107.8162 257.6162 m F 0 G 0.3 w 10 M 107.8162 257.6162 m S 107.8162 257.6162 m S 0 g 1 w 4 M 106.7311 256.5483 m 106.7311 252.9712 L 108.9013 252.9712 L 108.9013 256.5483 L 112.4869 256.5371 L 112.4869 258.6955 L 108.9013 258.6844 L 108.9013 262.2615 L 106.7311 262.2615 L 106.7311 258.6844 L 103.1455 258.6955 L 103.1455 256.5371 L 106.7311 256.5483 L f 0 G 0.3 w 10 M 131.1333 257.6162 m S 0 g 1 w 4 M 131.1333 257.6162 m F 0 G 0.3 w 10 M 131.1333 257.6162 m S 131.1333 257.6162 m S 131.1333 257.6162 m S 0 g 1 w 4 M 131.1333 257.6162 m F 0 G 0.3 w 10 M 131.1333 257.6162 m S 131.1333 257.6162 m S 1 g 0.5 w 4 M 125.1229 257.6162 m 125.1229 254.3944 127.8139 251.7826 131.1333 251.7826 c 134.4527 251.7826 137.1437 254.3944 137.1437 257.6162 c B 137.1437 257.6162 m 137.1437 260.838 134.4527 263.4498 131.1333 263.4498 c 127.8139 263.4498 125.1229 260.838 125.1229 257.6162 c B 131.1333 257.6162 m B 0.3 w 10 M 131.1333 257.6162 m S 0 g 1 w 4 M 131.1333 257.6162 m F 0 G 0.3 w 10 M 131.1333 257.6162 m S 131.1333 257.6162 m S 0 g 1 w 4 M 130.0482 256.5483 m 130.0482 252.9712 L 132.2184 252.9712 L 132.2184 256.5483 L 135.804 256.5371 L 135.804 258.6955 L 132.2184 258.6844 L 132.2184 262.2615 L 130.0482 262.2615 L 130.0482 258.6844 L 126.4626 258.6955 L 126.4626 256.5371 L 130.0482 256.5483 L f 0 G 0.3 w 10 M 154.4505 234.7261 m S 166.109 234.7261 m S 154.4505 234.7261 m S 177.7675 234.7261 m S 166.109 234.7261 m S 177.7675 234.7261 m S 154.4505 234.7261 m S 0 g 1 w 4 M 154.4505 234.7261 m F 0 G 0.3 w 10 M 154.4505 234.7261 m S 154.4505 234.7261 m S 154.4505 234.7261 m S 0 g 1 w 4 M 154.4505 234.7261 m F 0 G 0.3 w 10 M 154.4505 234.7261 m S 154.4505 234.7261 m S 1 g 0.5 w 4 M 148.4401 234.7261 m 148.4401 231.5043 151.1311 228.8925 154.4505 228.8925 c 157.7699 228.8925 160.4609 231.5043 160.4609 234.7261 c B 160.4609 234.7261 m 160.4609 237.9479 157.7699 240.5597 154.4505 240.5597 c 151.1311 240.5597 148.4401 237.9479 148.4401 234.7261 c B 154.4505 234.7261 m B 0.3 w 10 M 154.4505 234.7261 m S 0 g 1 w 4 M 154.4505 234.7261 m F 0 G 0.3 w 10 M 154.4505 234.7261 m S 154.4505 234.7261 m S 0 g 1 w 4 M 153.3654 233.6582 m 153.3654 230.0811 L 155.5356 230.0811 L 155.5356 233.6582 L 159.1212 233.647 L 159.1212 235.8054 L 155.5356 235.7943 L 155.5356 239.3714 L 153.3654 239.3714 L 153.3654 235.7943 L 149.7798 235.8054 L 149.7798 233.647 L 153.3654 233.6582 L f 0 G 0.3 w 10 M 177.7675 234.7261 m S 0 g 1 w 4 M 177.7675 234.7261 m F 0 G 0.3 w 10 M 177.7675 234.7261 m S 177.7675 234.7261 m S 177.7675 234.7261 m S 0 g 1 w 4 M 177.7675 234.7261 m F 0 G 0.3 w 10 M 177.7675 234.7261 m S 177.7675 234.7261 m S 1 g 0.5 w 4 M 171.7571 234.7261 m 171.7571 231.5043 174.4481 228.8925 177.7675 228.8925 c 181.0869 228.8925 183.7779 231.5043 183.7779 234.7261 c B 183.7779 234.7261 m 183.7779 237.9479 181.0869 240.5597 177.7675 240.5597 c 174.4481 240.5597 171.7571 237.9479 171.7571 234.7261 c B 177.7675 234.7261 m B 0.3 w 10 M 177.7675 234.7261 m S 0 g 1 w 4 M 177.7675 234.7261 m F 0 G 0.3 w 10 M 177.7675 234.7261 m S 177.7675 234.7261 m S 0 g 1 w 4 M 176.6824 233.6582 m 176.6824 230.0811 L 178.8526 230.0811 L 178.8526 233.6582 L 182.4382 233.647 L 182.4382 235.8054 L 178.8526 235.7943 L 178.8526 239.3714 L 176.6824 239.3714 L 176.6824 235.7943 L 173.0968 235.8054 L 173.0968 233.647 L 176.6824 233.6582 L f 0 G 0.3 w 10 M 154.4505 257.6162 m S 166.109 257.6162 m S 154.4505 257.6162 m S 177.7675 257.6162 m S 166.109 257.6162 m S 177.7675 257.6162 m S 154.4505 257.6162 m S 0 g 1 w 4 M 154.4505 257.6162 m F 0 G 0.3 w 10 M 154.4505 257.6162 m S 154.4505 257.6162 m S 154.4505 257.6162 m S 0 g 1 w 4 M 154.4505 257.6162 m F 0 G 0.3 w 10 M 154.4505 257.6162 m S 154.4505 257.6162 m S 1 g 0.5 w 4 M 148.4401 257.6162 m 148.4401 254.3944 151.1311 251.7826 154.4505 251.7826 c 157.7699 251.7826 160.4609 254.3944 160.4609 257.6162 c B 160.4609 257.6162 m 160.4609 260.838 157.7699 263.4498 154.4505 263.4498 c 151.1311 263.4498 148.4401 260.838 148.4401 257.6162 c B 154.4505 257.6162 m B 0.3 w 10 M 154.4505 257.6162 m S 0 g 1 w 4 M 154.4505 257.6162 m F 0 G 0.3 w 10 M 154.4505 257.6162 m S 154.4505 257.6162 m S 0 g 1 w 4 M 153.3654 256.5483 m 153.3654 252.9712 L 155.5356 252.9712 L 155.5356 256.5483 L 159.1212 256.5371 L 159.1212 258.6955 L 155.5356 258.6844 L 155.5356 262.2615 L 153.3654 262.2615 L 153.3654 258.6844 L 149.7798 258.6955 L 149.7798 256.5371 L 153.3654 256.5483 L f 0 G 0.3 w 10 M 177.7675 257.6162 m S 0 g 1 w 4 M 177.7675 257.6162 m F 0 G 0.3 w 10 M 177.7675 257.6162 m S 177.7675 257.6162 m S 177.7675 257.6162 m S 0 g 1 w 4 M 177.7675 257.6162 m F 0 G 0.3 w 10 M 177.7675 257.6162 m S 177.7675 257.6162 m S 1 g 0.5 w 4 M 171.7571 257.6162 m 171.7571 254.3944 174.4481 251.7826 177.7675 251.7826 c 181.0869 251.7826 183.7779 254.3944 183.7779 257.6162 c B 183.7779 257.6162 m 183.7779 260.838 181.0869 263.4498 177.7675 263.4498 c 174.4481 263.4498 171.7571 260.838 171.7571 257.6162 c B 177.7675 257.6162 m B 0.3 w 10 M 177.7675 257.6162 m S 0 g 1 w 4 M 177.7675 257.6162 m F 0 G 0.3 w 10 M 177.7675 257.6162 m S 177.7675 257.6162 m S 0 g 1 w 4 M 176.6824 256.5483 m 176.6824 252.9712 L 178.8526 252.9712 L 178.8526 256.5483 L 182.4382 256.5371 L 182.4382 258.6955 L 178.8526 258.6844 L 178.8526 262.2615 L 176.6824 262.2615 L 176.6824 258.6844 L 173.0968 258.6955 L 173.0968 256.5371 L 176.6824 256.5483 L f 0 G 0.3 w 10 M 224.4016 234.7261 m S 236.0601 234.7261 m S 224.4016 234.7261 m S 247.7186 234.7261 m S 236.0601 234.7261 m S 247.7186 234.7261 m S 224.4016 234.7261 m S 0 g 1 w 4 M 224.4016 234.7261 m F 0 G 0.3 w 10 M 224.4016 234.7261 m S 224.4016 234.7261 m S 224.4016 234.7261 m S 0 g 1 w 4 M 224.4016 234.7261 m F 0 G 0.3 w 10 M 224.4016 234.7261 m S 224.4016 234.7261 m S 1 g 0.5 w 4 M 218.3912 234.7261 m 218.3912 231.5043 221.0822 228.8925 224.4016 228.8925 c 227.721 228.8925 230.412 231.5043 230.412 234.7261 c B 230.412 234.7261 m 230.412 237.9479 227.721 240.5597 224.4016 240.5597 c 221.0822 240.5597 218.3912 237.9479 218.3912 234.7261 c B 224.4016 234.7261 m B 0.3 w 10 M 224.4016 234.7261 m S 0 g 1 w 4 M 224.4016 234.7261 m F 0 G 0.3 w 10 M 224.4016 234.7261 m S 224.4016 234.7261 m S 0 g 1 w 4 M 223.3165 233.6582 m 223.3165 230.0811 L 225.4867 230.0811 L 225.4867 233.6582 L 229.0723 233.647 L 229.0723 235.8054 L 225.4867 235.7943 L 225.4867 239.3714 L 223.3165 239.3714 L 223.3165 235.7943 L 219.7309 235.8054 L 219.7309 233.647 L 223.3165 233.6582 L f 0 G 0.3 w 10 M 247.7186 234.7261 m S 0 g 1 w 4 M 247.7186 234.7261 m F 0 G 0.3 w 10 M 247.7186 234.7261 m S 247.7186 234.7261 m S 247.7186 234.7261 m S 0 g 1 w 4 M 247.7186 234.7261 m F 0 G 0.3 w 10 M 247.7186 234.7261 m S 247.7186 234.7261 m S 1 g 0.5 w 4 M 241.7082 234.7261 m 241.7082 231.5043 244.3992 228.8925 247.7186 228.8925 c 251.038 228.8925 253.729 231.5043 253.729 234.7261 c B 253.729 234.7261 m 253.729 237.9479 251.038 240.5597 247.7186 240.5597 c 244.3992 240.5597 241.7082 237.9479 241.7082 234.7261 c B 247.7186 234.7261 m B 0.3 w 10 M 247.7186 234.7261 m S 0 g 1 w 4 M 247.7186 234.7261 m F 0 G 0.3 w 10 M 247.7186 234.7261 m S 247.7186 234.7261 m S 0 g 1 w 4 M 246.6335 233.6582 m 246.6335 230.0811 L 248.8037 230.0811 L 248.8037 233.6582 L 252.3893 233.647 L 252.3893 235.8054 L 248.8037 235.7943 L 248.8037 239.3714 L 246.6335 239.3714 L 246.6335 235.7943 L 243.0479 235.8054 L 243.0479 233.647 L 246.6335 233.6582 L f 0 G 0.3 w 10 M 201.0845 257.6162 m S 212.7431 257.6162 m S 201.0845 257.6162 m S 224.4016 257.6162 m S 212.7431 257.6162 m S 224.4016 257.6162 m S 201.0845 257.6162 m S 0 g 1 w 4 M 201.0845 257.6162 m F 0 G 0.3 w 10 M 201.0845 257.6162 m S 201.0845 257.6162 m S 201.0845 257.6162 m S 0 g 1 w 4 M 201.0845 257.6162 m F 0 G 0.3 w 10 M 201.0845 257.6162 m S 201.0845 257.6162 m S 1 g 0.5 w 4 M 195.0741 257.6162 m 195.0741 254.3944 197.7651 251.7826 201.0845 251.7826 c 204.4039 251.7826 207.0949 254.3944 207.0949 257.6162 c B 207.0949 257.6162 m 207.0949 260.838 204.4039 263.4498 201.0845 263.4498 c 197.7651 263.4498 195.0741 260.838 195.0741 257.6162 c B 201.0845 257.6162 m B 0.3 w 10 M 201.0845 257.6162 m S 0 g 1 w 4 M 201.0845 257.6162 m F 0 G 0.3 w 10 M 201.0845 257.6162 m S 201.0845 257.6162 m S 0 g 1 w 4 M 199.9994 256.5483 m 199.9994 252.9712 L 202.1696 252.9712 L 202.1696 256.5483 L 205.7552 256.5371 L 205.7552 258.6955 L 202.1696 258.6844 L 202.1696 262.2615 L 199.9994 262.2615 L 199.9994 258.6844 L 196.4138 258.6955 L 196.4138 256.5371 L 199.9994 256.5483 L f 0 G 0.3 w 10 M 224.4016 257.6162 m S 0 g 1 w 4 M 224.4016 257.6162 m F 0 G 0.3 w 10 M 224.4016 257.6162 m S 224.4016 257.6162 m S 224.4016 257.6162 m S 0 g 1 w 4 M 224.4016 257.6162 m F 0 G 0.3 w 10 M 224.4016 257.6162 m S 224.4016 257.6162 m S 1 g 0.5 w 4 M 218.3912 257.6162 m 218.3912 254.3944 221.0822 251.7826 224.4016 251.7826 c 227.721 251.7826 230.412 254.3944 230.412 257.6162 c B 230.412 257.6162 m 230.412 260.838 227.721 263.4498 224.4016 263.4498 c 221.0822 263.4498 218.3912 260.838 218.3912 257.6162 c B 224.4016 257.6162 m B 0.3 w 10 M 224.4016 257.6162 m S 0 g 1 w 4 M 224.4016 257.6162 m F 0 G 0.3 w 10 M 224.4016 257.6162 m S 224.4016 257.6162 m S 0 g 1 w 4 M 223.3165 256.5483 m 223.3165 252.9712 L 225.4867 252.9712 L 225.4867 256.5483 L 229.0723 256.5371 L 229.0723 258.6955 L 225.4867 258.6844 L 225.4867 262.2615 L 223.3165 262.2615 L 223.3165 258.6844 L 219.7309 258.6955 L 219.7309 256.5371 L 223.3165 256.5483 L f 0 G 0.3 w 10 M 247.7186 257.6162 m S 259.3772 257.6162 m S 247.7186 257.6162 m S 271.0357 257.6162 m S 259.3772 257.6162 m S 271.0357 257.6162 m S 247.7186 257.6162 m S 0 g 1 w 4 M 247.7186 257.6162 m F 0 G 0.3 w 10 M 247.7186 257.6162 m S 247.7186 257.6162 m S 247.7186 257.6162 m S 0 g 1 w 4 M 247.7186 257.6162 m F 0 G 0.3 w 10 M 247.7186 257.6162 m S 247.7186 257.6162 m S 1 g 0.5 w 4 M 241.7082 257.6162 m 241.7082 254.3944 244.3992 251.7826 247.7186 251.7826 c 251.038 251.7826 253.729 254.3944 253.729 257.6162 c B 253.729 257.6162 m 253.729 260.838 251.038 263.4498 247.7186 263.4498 c 244.3992 263.4498 241.7082 260.838 241.7082 257.6162 c B 247.7186 257.6162 m B 0.3 w 10 M 247.7186 257.6162 m S 0 g 1 w 4 M 247.7186 257.6162 m F 0 G 0.3 w 10 M 247.7186 257.6162 m S 247.7186 257.6162 m S 0 g 1 w 4 M 246.6335 256.5483 m 246.6335 252.9712 L 248.8037 252.9712 L 248.8037 256.5483 L 252.3893 256.5371 L 252.3893 258.6955 L 248.8037 258.6844 L 248.8037 262.2615 L 246.6335 262.2615 L 246.6335 258.6844 L 243.0479 258.6955 L 243.0479 256.5371 L 246.6335 256.5483 L f 0 G 0.3 w 10 M 271.0357 257.6162 m S 0 g 1 w 4 M 271.0357 257.6162 m F 0 G 0.3 w 10 M 271.0357 257.6162 m S 271.0357 257.6162 m S 271.0357 257.6162 m S 0 g 1 w 4 M 271.0357 257.6162 m F 0 G 0.3 w 10 M 271.0357 257.6162 m S 271.0357 257.6162 m S 1 g 0.5 w 4 M 265.0253 257.6162 m 265.0253 254.3944 267.7163 251.7826 271.0357 251.7826 c 274.3551 251.7826 277.0461 254.3944 277.0461 257.6162 c B 277.0461 257.6162 m 277.0461 260.838 274.3551 263.4498 271.0357 263.4498 c 267.7163 263.4498 265.0253 260.838 265.0253 257.6162 c B 271.0357 257.6162 m B 0.3 w 10 M 271.0357 257.6162 m S 0 g 1 w 4 M 271.0357 257.6162 m F 0 G 0.3 w 10 M 271.0357 257.6162 m S 271.0357 257.6162 m S 0 g 1 w 4 M 269.9506 256.5483 m 269.9506 252.9712 L 272.1208 252.9712 L 272.1208 256.5483 L 275.7064 256.5371 L 275.7064 258.6955 L 272.1208 258.6844 L 272.1208 262.2615 L 269.9506 262.2615 L 269.9506 258.6844 L 266.365 258.6955 L 266.365 256.5371 L 269.9506 256.5483 L f 0 G 0.3 w 10 M 247.7186 211.8359 m S 259.3772 211.8359 m S 247.7186 211.8359 m S 271.0357 211.8359 m S 259.3772 211.8359 m S 271.0357 211.8359 m S 247.7186 211.8359 m S 0 g 1 w 4 M 247.7186 211.8359 m F 0 G 0.3 w 10 M 247.7186 211.8359 m S 247.7186 211.8359 m S 247.7186 211.8359 m S 0 g 1 w 4 M 247.7186 211.8359 m F 0 G 0.3 w 10 M 247.7186 211.8359 m S 247.7186 211.8359 m S 1 g 0.5 w 4 M 241.7082 211.8359 m 241.7082 208.6141 244.3992 206.0023 247.7186 206.0023 c 251.038 206.0023 253.729 208.6141 253.729 211.8359 c B 253.729 211.8359 m 253.729 215.0578 251.038 217.6696 247.7186 217.6696 c 244.3992 217.6696 241.7082 215.0578 241.7082 211.8359 c B 247.7186 211.8359 m B 0.3 w 10 M 247.7186 211.8359 m S 0 g 1 w 4 M 247.7186 211.8359 m F 0 G 0.3 w 10 M 247.7186 211.8359 m S 247.7186 211.8359 m S 0 g 1 w 4 M 246.6335 210.768 m 246.6335 207.1909 L 248.8037 207.1909 L 248.8037 210.768 L 252.3893 210.7568 L 252.3893 212.9152 L 248.8037 212.9042 L 248.8037 216.4812 L 246.6335 216.4812 L 246.6335 212.9042 L 243.0479 212.9152 L 243.0479 210.7568 L 246.6335 210.768 L f 0 G 0.3 w 10 M 271.0357 211.8359 m S 0 g 1 w 4 M 271.0357 211.8359 m F 0 G 0.3 w 10 M 271.0357 211.8359 m S 271.0357 211.8359 m S 271.0357 211.8359 m S 0 g 1 w 4 M 271.0357 211.8359 m F 0 G 0.3 w 10 M 271.0357 211.8359 m S 271.0357 211.8359 m S 1 g 0.5 w 4 M 265.0253 211.8359 m 265.0253 208.6141 267.7163 206.0023 271.0357 206.0023 c 274.3551 206.0023 277.0461 208.6141 277.0461 211.8359 c B 277.0461 211.8359 m 277.0461 215.0578 274.3551 217.6696 271.0357 217.6696 c 267.7163 217.6696 265.0253 215.0578 265.0253 211.8359 c B 271.0357 211.8359 m B 0.3 w 10 M 271.0357 211.8359 m S 0 g 1 w 4 M 271.0357 211.8359 m F 0 G 0.3 w 10 M 271.0357 211.8359 m S 271.0357 211.8359 m S 0 g 1 w 4 M 269.9506 210.768 m 269.9506 207.1909 L 272.1208 207.1909 L 272.1208 210.768 L 275.7064 210.7568 L 275.7064 212.9152 L 272.1208 212.9042 L 272.1208 216.4812 L 269.9506 216.4812 L 269.9506 212.9042 L 266.365 212.9152 L 266.365 210.7568 L 269.9506 210.768 L f 0 G 0.3 w 10 M 247.7186 188.9459 m S 259.3772 188.9459 m S 247.7186 188.9459 m S 271.0357 188.9459 m S 259.3772 188.9459 m S 271.0357 188.9459 m S 247.7186 188.9459 m S 0 g 1 w 4 M 247.7186 188.9459 m F 0 G 0.3 w 10 M 247.7186 188.9459 m S 247.7186 188.9459 m S 247.7186 188.9459 m S 0 g 1 w 4 M 247.7186 188.9459 m F 0 G 0.3 w 10 M 247.7186 188.9459 m S 247.7186 188.9459 m S 1 g 0.5 w 4 M 241.7082 188.9459 m 241.7082 185.7241 244.3992 183.1123 247.7186 183.1123 c 251.038 183.1123 253.729 185.7241 253.729 188.9459 c B 253.729 188.9459 m 253.729 192.1677 251.038 194.7795 247.7186 194.7795 c 244.3992 194.7795 241.7082 192.1677 241.7082 188.9459 c B 247.7186 188.9459 m B 0.3 w 10 M 247.7186 188.9459 m S 0 g 1 w 4 M 247.7186 188.9459 m F 0 G 0.3 w 10 M 247.7186 188.9459 m S 247.7186 188.9459 m S 0 g 1 w 4 M 246.6335 187.878 m 246.6335 184.3009 L 248.8037 184.3009 L 248.8037 187.878 L 252.3893 187.8668 L 252.3893 190.0252 L 248.8037 190.0141 L 248.8037 193.5912 L 246.6335 193.5912 L 246.6335 190.0141 L 243.0479 190.0252 L 243.0479 187.8668 L 246.6335 187.878 L f 0 G 0.3 w 10 M 271.0357 188.9459 m S 0 g 1 w 4 M 271.0357 188.9459 m F 0 G 0.3 w 10 M 271.0357 188.9459 m S 271.0357 188.9459 m S 271.0357 188.9459 m S 0 g 1 w 4 M 271.0357 188.9459 m F 0 G 0.3 w 10 M 271.0357 188.9459 m S 271.0357 188.9459 m S 1 g 0.5 w 4 M 265.0253 188.9459 m 265.0253 185.7241 267.7163 183.1123 271.0357 183.1123 c 274.3551 183.1123 277.0461 185.7241 277.0461 188.9459 c B 277.0461 188.9459 m 277.0461 192.1677 274.3551 194.7795 271.0357 194.7795 c 267.7163 194.7795 265.0253 192.1677 265.0253 188.9459 c B 271.0357 188.9459 m B 0.3 w 10 M 271.0357 188.9459 m S 0 g 1 w 4 M 271.0357 188.9459 m F 0 G 0.3 w 10 M 271.0357 188.9459 m S 271.0357 188.9459 m S 0 g 1 w 4 M 269.9506 187.878 m 269.9506 184.3009 L 272.1208 184.3009 L 272.1208 187.878 L 275.7064 187.8668 L 275.7064 190.0252 L 272.1208 190.0141 L 272.1208 193.5912 L 269.9506 193.5912 L 269.9506 190.0141 L 266.365 190.0252 L 266.365 187.8668 L 269.9506 187.878 L f 0 G 0.3 w 10 M 247.7186 143.1656 m S 259.3772 143.1656 m S 247.7186 143.1656 m S 271.0357 143.1656 m S 259.3772 143.1656 m S 271.0357 143.1656 m S 247.7186 143.1656 m S 0 g 1 w 4 M 247.7186 143.1656 m F 0 G 0.3 w 10 M 247.7186 143.1656 m S 247.7186 143.1656 m S 247.7186 143.1656 m S 0 g 1 w 4 M 247.7186 143.1656 m F 0 G 0.3 w 10 M 247.7186 143.1656 m S 247.7186 143.1656 m S 1 g 0.5 w 4 M 241.7082 143.1656 m 241.7082 139.9438 244.3992 137.332 247.7186 137.332 c 251.038 137.332 253.729 139.9438 253.729 143.1656 c B 253.729 143.1656 m 253.729 146.3874 251.038 148.9992 247.7186 148.9992 c 244.3992 148.9992 241.7082 146.3874 241.7082 143.1656 c B 247.7186 143.1656 m B 0.3 w 10 M 247.7186 143.1656 m S 0 g 1 w 4 M 247.7186 143.1656 m F 0 G 0.3 w 10 M 247.7186 143.1656 m S 247.7186 143.1656 m S 0 g 1 w 4 M 246.6335 142.0977 m 246.6335 138.5206 L 248.8037 138.5206 L 248.8037 142.0977 L 252.3893 142.0865 L 252.3893 144.2449 L 248.8037 144.2338 L 248.8037 147.8109 L 246.6335 147.8109 L 246.6335 144.2338 L 243.0479 144.2449 L 243.0479 142.0865 L 246.6335 142.0977 L f 0 G 0.3 w 10 M 271.0357 143.1656 m S 0 g 1 w 4 M 271.0357 143.1656 m F 0 G 0.3 w 10 M 271.0357 143.1656 m S 271.0357 143.1656 m S 271.0357 143.1656 m S 0 g 1 w 4 M 271.0357 143.1656 m F 0 G 0.3 w 10 M 271.0357 143.1656 m S 271.0357 143.1656 m S 1 g 0.5 w 4 M 265.0253 143.1656 m 265.0253 139.9438 267.7163 137.332 271.0357 137.332 c 274.3551 137.332 277.0461 139.9438 277.0461 143.1656 c B 277.0461 143.1656 m 277.0461 146.3874 274.3551 148.9992 271.0357 148.9992 c 267.7163 148.9992 265.0253 146.3874 265.0253 143.1656 c B 271.0357 143.1656 m B 0.3 w 10 M 271.0357 143.1656 m S 0 g 1 w 4 M 271.0357 143.1656 m F 0 G 0.3 w 10 M 271.0357 143.1656 m S 271.0357 143.1656 m S 0 g 1 w 4 M 269.9506 142.0977 m 269.9506 138.5206 L 272.1208 138.5206 L 272.1208 142.0977 L 275.7064 142.0865 L 275.7064 144.2449 L 272.1208 144.2338 L 272.1208 147.8109 L 269.9506 147.8109 L 269.9506 144.2338 L 266.365 144.2449 L 266.365 142.0865 L 269.9506 142.0977 L f 0 G 0.3 w 10 M 247.7186 120.2755 m S 259.3772 120.2755 m S 247.7186 120.2755 m S 271.0357 120.2755 m S 259.3772 120.2755 m S 271.0357 120.2755 m S 247.7186 120.2755 m S 0 g 1 w 4 M 247.7186 120.2755 m F 0 G 0.3 w 10 M 247.7186 120.2755 m S 247.7186 120.2755 m S 247.7186 120.2755 m S 0 g 1 w 4 M 247.7186 120.2755 m F 0 G 0.3 w 10 M 247.7186 120.2755 m S 247.7186 120.2755 m S 1 g 0.5 w 4 M 241.7082 120.2755 m 241.7082 117.0537 244.3992 114.4419 247.7186 114.4419 c 251.038 114.4419 253.729 117.0537 253.729 120.2755 c B 253.729 120.2755 m 253.729 123.4973 251.038 126.1091 247.7186 126.1091 c 244.3992 126.1091 241.7082 123.4973 241.7082 120.2755 c B 247.7186 120.2755 m B 0.3 w 10 M 247.7186 120.2755 m S 0 g 1 w 4 M 247.7186 120.2755 m F 0 G 0.3 w 10 M 247.7186 120.2755 m S 247.7186 120.2755 m S 0 g 1 w 4 M 246.6335 119.2076 m 246.6335 115.6305 L 248.8037 115.6305 L 248.8037 119.2076 L 252.3893 119.1964 L 252.3893 121.3548 L 248.8037 121.3437 L 248.8037 124.9208 L 246.6335 124.9208 L 246.6335 121.3437 L 243.0479 121.3548 L 243.0479 119.1964 L 246.6335 119.2076 L f 0 G 0.3 w 10 M 271.0357 120.2755 m S 0 g 1 w 4 M 271.0357 120.2755 m F 0 G 0.3 w 10 M 271.0357 120.2755 m S 271.0357 120.2755 m S 271.0357 120.2755 m S 0 g 1 w 4 M 271.0357 120.2755 m F 0 G 0.3 w 10 M 271.0357 120.2755 m S 271.0357 120.2755 m S 1 g 0.5 w 4 M 265.0253 120.2755 m 265.0253 117.0537 267.7163 114.4419 271.0357 114.4419 c 274.3551 114.4419 277.0461 117.0537 277.0461 120.2755 c B 277.0461 120.2755 m 277.0461 123.4973 274.3551 126.1091 271.0357 126.1091 c 267.7163 126.1091 265.0253 123.4973 265.0253 120.2755 c B 271.0357 120.2755 m B 0.3 w 10 M 271.0357 120.2755 m S 0 g 1 w 4 M 271.0357 120.2755 m F 0 G 0.3 w 10 M 271.0357 120.2755 m S 271.0357 120.2755 m S 0 g 1 w 4 M 269.9506 119.2076 m 269.9506 115.6305 L 272.1208 115.6305 L 272.1208 119.2076 L 275.7064 119.1964 L 275.7064 121.3548 L 272.1208 121.3437 L 272.1208 124.9208 L 269.9506 124.9208 L 269.9506 121.3437 L 266.365 121.3548 L 266.365 119.1964 L 269.9506 119.2076 L f 0 G 0.3 w 10 M 224.4016 97.3853 m S 236.0601 97.3853 m S 224.4016 97.3853 m S 247.7186 97.3853 m S 236.0601 97.3853 m S 247.7186 97.3853 m S 224.4016 97.3853 m S 0 g 1 w 4 M 224.4016 97.3853 m F 0 G 0.3 w 10 M 224.4016 97.3853 m S 224.4016 97.3853 m S 224.4016 97.3853 m S 0 g 1 w 4 M 224.4016 97.3853 m F 0 G 0.3 w 10 M 224.4016 97.3853 m S 224.4016 97.3853 m S 1 g 0.5 w 4 M 218.3912 97.3853 m 218.3912 94.1635 221.0822 91.5517 224.4016 91.5517 c 227.721 91.5517 230.412 94.1635 230.412 97.3853 c B 230.412 97.3853 m 230.412 100.6071 227.721 103.2189 224.4016 103.2189 c 221.0822 103.2189 218.3912 100.6071 218.3912 97.3853 c B 224.4016 97.3853 m B 0.3 w 10 M 224.4016 97.3853 m S 0 g 1 w 4 M 224.4016 97.3853 m F 0 G 0.3 w 10 M 224.4016 97.3853 m S 224.4016 97.3853 m S 0 g 1 w 4 M 223.3165 96.3174 m 223.3165 92.7403 L 225.4867 92.7403 L 225.4867 96.3174 L 229.0723 96.3062 L 229.0723 98.4646 L 225.4867 98.4535 L 225.4867 102.0306 L 223.3165 102.0306 L 223.3165 98.4535 L 219.7309 98.4646 L 219.7309 96.3062 L 223.3165 96.3174 L f 0 G 0.3 w 10 M 247.7186 97.3853 m S 0 g 1 w 4 M 247.7186 97.3853 m F 0 G 0.3 w 10 M 247.7186 97.3853 m S 247.7186 97.3853 m S 247.7186 97.3853 m S 0 g 1 w 4 M 247.7186 97.3853 m F 0 G 0.3 w 10 M 247.7186 97.3853 m S 247.7186 97.3853 m S 1 g 0.5 w 4 M 241.7082 97.3853 m 241.7082 94.1635 244.3992 91.5517 247.7186 91.5517 c 251.038 91.5517 253.729 94.1635 253.729 97.3853 c B 253.729 97.3853 m 253.729 100.6071 251.038 103.2189 247.7186 103.2189 c 244.3992 103.2189 241.7082 100.6071 241.7082 97.3853 c B 247.7186 97.3853 m B 0.3 w 10 M 247.7186 97.3853 m S 0 g 1 w 4 M 247.7186 97.3853 m F 0 G 0.3 w 10 M 247.7186 97.3853 m S 247.7186 97.3853 m S 0 g 1 w 4 M 246.6335 96.3174 m 246.6335 92.7403 L 248.8037 92.7403 L 248.8037 96.3174 L 252.3893 96.3062 L 252.3893 98.4646 L 248.8037 98.4535 L 248.8037 102.0306 L 246.6335 102.0306 L 246.6335 98.4535 L 243.0479 98.4646 L 243.0479 96.3062 L 246.6335 96.3174 L f 0 G 0.3 w 10 M 84.4992 97.3853 m S 96.1577 97.3853 m S 84.4992 97.3853 m S 107.8162 97.3853 m S 96.1577 97.3853 m S 107.8162 97.3853 m S 84.4992 97.3853 m S 0 g 1 w 4 M 84.4992 97.3853 m F 0 G 0.3 w 10 M 84.4992 97.3853 m S 84.4992 97.3853 m S 84.4992 97.3853 m S 0 g 1 w 4 M 84.4992 97.3853 m F 0 G 0.3 w 10 M 84.4992 97.3853 m S 84.4992 97.3853 m S 1 g 0.5 w 4 M 78.4888 97.3853 m 78.4888 94.1635 81.1798 91.5517 84.4992 91.5517 c 87.8186 91.5517 90.5096 94.1635 90.5096 97.3853 c B 90.5096 97.3853 m 90.5096 100.6071 87.8186 103.2189 84.4992 103.2189 c 81.1798 103.2189 78.4888 100.6071 78.4888 97.3853 c B 84.4992 97.3853 m B 0.3 w 10 M 84.4992 97.3853 m S 0 g 1 w 4 M 84.4992 97.3853 m F 0 G 0.3 w 10 M 84.4992 97.3853 m S 84.4992 97.3853 m S 0 g 1 w 4 M 83.4141 96.3174 m 83.4141 92.7403 L 85.5843 92.7403 L 85.5843 96.3174 L 89.1699 96.3062 L 89.1699 98.4646 L 85.5843 98.4535 L 85.5843 102.0306 L 83.4141 102.0306 L 83.4141 98.4535 L 79.8285 98.4646 L 79.8285 96.3062 L 83.4141 96.3174 L f 0 G 0.3 w 10 M 107.8162 97.3853 m S 0 g 1 w 4 M 107.8162 97.3853 m F 0 G 0.3 w 10 M 107.8162 97.3853 m S 107.8162 97.3853 m S 107.8162 97.3853 m S 0 g 1 w 4 M 107.8162 97.3853 m F 0 G 0.3 w 10 M 107.8162 97.3853 m S 107.8162 97.3853 m S 1 g 0.5 w 4 M 101.8058 97.3853 m 101.8058 94.1635 104.4968 91.5517 107.8162 91.5517 c 111.1356 91.5517 113.8266 94.1635 113.8266 97.3853 c B 113.8266 97.3853 m 113.8266 100.6071 111.1356 103.2189 107.8162 103.2189 c 104.4968 103.2189 101.8058 100.6071 101.8058 97.3853 c B 107.8162 97.3853 m B 0.3 w 10 M 107.8162 97.3853 m S 0 g 1 w 4 M 107.8162 97.3853 m F 0 G 0.3 w 10 M 107.8162 97.3853 m S 107.8162 97.3853 m S 0 g 1 w 4 M 106.7311 96.3174 m 106.7311 92.7403 L 108.9013 92.7403 L 108.9013 96.3174 L 112.4869 96.3062 L 112.4869 98.4646 L 108.9013 98.4535 L 108.9013 102.0306 L 106.7311 102.0306 L 106.7311 98.4535 L 103.1455 98.4646 L 103.1455 96.3062 L 106.7311 96.3174 L f 0 G 0.3 w 10 M 37.865 120.2755 m S 49.5236 120.2755 m S 37.865 120.2755 m S 61.1821 120.2755 m S 49.5236 120.2755 m S 61.1821 120.2755 m S 37.865 120.2755 m S 0 g 1 w 4 M 37.865 120.2755 m F 0 G 0.3 w 10 M 37.865 120.2755 m S 37.865 120.2755 m S 37.865 120.2755 m S 0 g 1 w 4 M 37.865 120.2755 m F 0 G 0.3 w 10 M 37.865 120.2755 m S 37.865 120.2755 m S 1 g 0.5 w 4 M 31.8546 120.2755 m 31.8546 117.0537 34.5456 114.4419 37.865 114.4419 c 41.1844 114.4419 43.8754 117.0537 43.8754 120.2755 c B 43.8754 120.2755 m 43.8754 123.4973 41.1844 126.1091 37.865 126.1091 c 34.5456 126.1091 31.8546 123.4973 31.8546 120.2755 c B 37.865 120.2755 m B 0.3 w 10 M 37.865 120.2755 m S 0 g 1 w 4 M 37.865 120.2755 m F 0 G 0.3 w 10 M 37.865 120.2755 m S 37.865 120.2755 m S 0 g 1 w 4 M 36.7799 119.2076 m 36.7799 115.6305 L 38.9501 115.6305 L 38.9501 119.2076 L 42.5357 119.1964 L 42.5357 121.3548 L 38.9501 121.3437 L 38.9501 124.9208 L 36.7799 124.9208 L 36.7799 121.3437 L 33.1943 121.3548 L 33.1943 119.1964 L 36.7799 119.2076 L f 0 G 0.3 w 10 M 61.1821 120.2755 m S 0 g 1 w 4 M 61.1821 120.2755 m F 0 G 0.3 w 10 M 61.1821 120.2755 m S 61.1821 120.2755 m S 61.1821 120.2755 m S 0 g 1 w 4 M 61.1821 120.2755 m F 0 G 0.3 w 10 M 61.1821 120.2755 m S 61.1821 120.2755 m S 1 g 0.5 w 4 M 55.1717 120.2755 m 55.1717 117.0537 57.8627 114.4419 61.1821 114.4419 c 64.5015 114.4419 67.1925 117.0537 67.1925 120.2755 c B 67.1925 120.2755 m 67.1925 123.4973 64.5015 126.1091 61.1821 126.1091 c 57.8627 126.1091 55.1717 123.4973 55.1717 120.2755 c B 61.1821 120.2755 m B 0.3 w 10 M 61.1821 120.2755 m S 0 g 1 w 4 M 61.1821 120.2755 m F 0 G 0.3 w 10 M 61.1821 120.2755 m S 61.1821 120.2755 m S 0 g 1 w 4 M 60.097 119.2076 m 60.097 115.6305 L 62.2672 115.6305 L 62.2672 119.2076 L 65.8528 119.1964 L 65.8528 121.3548 L 62.2672 121.3437 L 62.2672 124.9208 L 60.097 124.9208 L 60.097 121.3437 L 56.5114 121.3548 L 56.5114 119.1964 L 60.097 119.2076 L f 0 G 0.3 w 10 M 37.8651 188.9459 m S 37.8651 188.9459 m S 37.8651 188.9459 m S 0 g 1 w 4 M 37.8651 188.9459 m F 0 G 0.3 w 10 M 37.8651 188.9459 m S 37.8651 188.9459 m S 37.8651 188.9459 m S 0 g 1 w 4 M 37.8651 188.9459 m F 0 G 0.3 w 10 M 37.8651 188.9459 m S 37.8651 188.9459 m S 1 g 0.5 w 4 M 31.8547 188.9459 m 31.8547 185.7241 34.5457 183.1123 37.8651 183.1123 c 41.1845 183.1123 43.8755 185.7241 43.8755 188.9459 c B 43.8755 188.9459 m 43.8755 192.1677 41.1845 194.7795 37.8651 194.7795 c 34.5457 194.7795 31.8547 192.1677 31.8547 188.9459 c B 37.8651 188.9459 m B 0.3 w 10 M 37.8651 188.9459 m S 0 g 1 w 4 M 37.8651 188.9459 m F 0 G 0.3 w 10 M 37.8651 188.9459 m S 37.8651 188.9459 m S 0 g 1 w 4 M 36.78 187.878 m 36.78 184.3009 L 38.9502 184.3009 L 38.9502 187.878 L 42.5358 187.8668 L 42.5358 190.0252 L 38.9502 190.0141 L 38.9502 193.5912 L 36.78 193.5912 L 36.78 190.0141 L 33.1944 190.0252 L 33.1944 187.8668 L 36.78 187.878 L f 0 G 0.3 w 10 M 37.8651 166.0557 m S 37.8651 166.0557 m S 37.8651 166.0557 m S 0 g 1 w 4 M 37.8651 166.0557 m F 0 G 0.3 w 10 M 37.8651 166.0557 m S 37.8651 166.0557 m S 37.8651 166.0557 m S 0 g 1 w 4 M 37.8651 166.0557 m F 0 G 0.3 w 10 M 37.8651 166.0557 m S 37.8651 166.0557 m S 1 g 0.5 w 4 M 31.8547 166.0557 m 31.8547 162.8339 34.5457 160.2221 37.8651 160.2221 c 41.1845 160.2221 43.8755 162.8339 43.8755 166.0557 c B 43.8755 166.0557 m 43.8755 169.2775 41.1845 171.8893 37.8651 171.8893 c 34.5457 171.8893 31.8547 169.2775 31.8547 166.0557 c B 37.8651 166.0557 m B 0.3 w 10 M 37.8651 166.0557 m S 0 g 1 w 4 M 37.8651 166.0557 m F 0 G 0.3 w 10 M 37.8651 166.0557 m S 37.8651 166.0557 m S 0 g 1 w 4 M 36.78 164.9878 m 36.78 161.4107 L 38.9502 161.4107 L 38.9502 164.9878 L 42.5358 164.9766 L 42.5358 167.135 L 38.9502 167.1239 L 38.9502 170.701 L 36.78 170.701 L 36.78 167.1239 L 33.1944 167.135 L 33.1944 164.9766 L 36.78 164.9878 L f 0 G 0.3 w 10 M 37.8651 143.1656 m S 37.8651 143.1656 m S 37.8651 143.1656 m S 0 g 1 w 4 M 37.8651 143.1656 m F 0 G 0.3 w 10 M 37.8651 143.1656 m S 37.8651 143.1656 m S 37.8651 143.1656 m S 0 g 1 w 4 M 37.8651 143.1656 m F 0 G 0.3 w 10 M 37.8651 143.1656 m S 37.8651 143.1656 m S 1 g 0.5 w 4 M 31.8547 143.1656 m 31.8547 139.9438 34.5457 137.332 37.8651 137.332 c 41.1845 137.332 43.8755 139.9438 43.8755 143.1656 c B 43.8755 143.1656 m 43.8755 146.3874 41.1845 148.9992 37.8651 148.9992 c 34.5457 148.9992 31.8547 146.3874 31.8547 143.1656 c B 37.8651 143.1656 m B 0.3 w 10 M 37.8651 143.1656 m S 0 g 1 w 4 M 37.8651 143.1656 m F 0 G 0.3 w 10 M 37.8651 143.1656 m S 37.8651 143.1656 m S 0 g 1 w 4 M 36.78 142.0977 m 36.78 138.5206 L 38.9502 138.5206 L 38.9502 142.0977 L 42.5358 142.0865 L 42.5358 144.2449 L 38.9502 144.2338 L 38.9502 147.8109 L 36.78 147.8109 L 36.78 144.2338 L 33.1944 144.2449 L 33.1944 142.0865 L 36.78 142.0977 L f 0 G 0.3 w 10 M 37.8651 97.3853 m S 37.8651 97.3853 m S 37.8651 97.3853 m S 0 g 1 w 4 M 37.8651 97.3853 m F 0 G 0.3 w 10 M 37.8651 97.3853 m S 37.8651 97.3853 m S 37.8651 97.3853 m S 0 g 1 w 4 M 37.8651 97.3853 m F 0 G 0.3 w 10 M 37.8651 97.3853 m S 37.8651 97.3853 m S 1 g 0.5 w 4 M 31.8547 97.3853 m 31.8547 94.1635 34.5457 91.5517 37.8651 91.5517 c 41.1845 91.5517 43.8755 94.1635 43.8755 97.3853 c B 43.8755 97.3853 m 43.8755 100.6071 41.1845 103.2189 37.8651 103.2189 c 34.5457 103.2189 31.8547 100.6071 31.8547 97.3853 c B 37.8651 97.3853 m B 0.3 w 10 M 37.8651 97.3853 m S 0 g 1 w 4 M 37.8651 97.3853 m F 0 G 0.3 w 10 M 37.8651 97.3853 m S 37.8651 97.3853 m S 0 g 1 w 4 M 36.78 96.3174 m 36.78 92.7403 L 38.9502 92.7403 L 38.9502 96.3174 L 42.5358 96.3062 L 42.5358 98.4646 L 38.9502 98.4535 L 38.9502 102.0306 L 36.78 102.0306 L 36.78 98.4535 L 33.1944 98.4646 L 33.1944 96.3062 L 36.78 96.3174 L f 0 G 0.3 w 10 M 177.7675 97.3853 m S 177.7675 97.3853 m S 177.7675 97.3853 m S 0 g 1 w 4 M 177.7675 97.3853 m F 0 G 0.3 w 10 M 177.7675 97.3853 m S 177.7675 97.3853 m S 177.7675 97.3853 m S 0 g 1 w 4 M 177.7675 97.3853 m F 0 G 0.3 w 10 M 177.7675 97.3853 m S 177.7675 97.3853 m S 1 g 0.5 w 4 M 171.7571 97.3853 m 171.7571 94.1635 174.4481 91.5517 177.7675 91.5517 c 181.0869 91.5517 183.7779 94.1635 183.7779 97.3853 c B 183.7779 97.3853 m 183.7779 100.6071 181.0869 103.2189 177.7675 103.2189 c 174.4481 103.2189 171.7571 100.6071 171.7571 97.3853 c B 177.7675 97.3853 m B 0.3 w 10 M 177.7675 97.3853 m S 0 g 1 w 4 M 177.7675 97.3853 m F 0 G 0.3 w 10 M 177.7675 97.3853 m S 177.7675 97.3853 m S 0 g 1 w 4 M 176.6824 96.3174 m 176.6824 92.7403 L 178.8526 92.7403 L 178.8526 96.3174 L 182.4382 96.3062 L 182.4382 98.4646 L 178.8526 98.4535 L 178.8526 102.0306 L 176.6824 102.0306 L 176.6824 98.4535 L 173.0968 98.4646 L 173.0968 96.3062 L 176.6824 96.3174 L f 0 G 0.3 w 10 M 247.7187 166.0557 m S 247.7187 166.0557 m S 247.7187 166.0557 m S 0 g 1 w 4 M 247.7187 166.0557 m F 0 G 0.3 w 10 M 247.7187 166.0557 m S 247.7187 166.0557 m S 247.7187 166.0557 m S 0 g 1 w 4 M 247.7187 166.0557 m F 0 G 0.3 w 10 M 247.7187 166.0557 m S 247.7187 166.0557 m S 1 g 0.5 w 4 M 241.7083 166.0557 m 241.7083 162.8339 244.3993 160.2221 247.7187 160.2221 c 251.0381 160.2221 253.7291 162.8339 253.7291 166.0557 c B 253.7291 166.0557 m 253.7291 169.2775 251.0381 171.8893 247.7187 171.8893 c 244.3993 171.8893 241.7083 169.2775 241.7083 166.0557 c B 247.7187 166.0557 m B 0.3 w 10 M 247.7187 166.0557 m S 0 g 1 w 4 M 247.7187 166.0557 m F 0 G 0.3 w 10 M 247.7187 166.0557 m S 247.7187 166.0557 m S 0 g 1 w 4 M 246.6336 164.9878 m 246.6336 161.4107 L 248.8038 161.4107 L 248.8038 164.9878 L 252.3894 164.9766 L 252.3894 167.135 L 248.8038 167.1239 L 248.8038 170.701 L 246.6336 170.701 L 246.6336 167.1239 L 243.048 167.135 L 243.048 164.9766 L 246.6336 164.9878 L f 0 G 0.3 w 10 M 49.5236 74.4953 m S 37.8651 74.4953 m S 43.6943 68.7727 m S 61.1821 74.4953 m S 49.5236 74.4953 m S 55.3529 68.7727 m S 72.8407 74.4953 m S 61.1821 74.4953 m S 67.0114 68.7727 m S 0 g 1 w 4 M 43.6943 68.7727 m F 67.0114 68.7727 m F 0 G 0.3 w 10 M 84.4992 74.4953 m S 72.8407 74.4953 m S 78.6699 68.7727 m S 96.1577 74.4953 m S 84.4992 74.4953 m S 90.3285 68.7727 m S 107.8163 74.4953 m S 96.1577 74.4953 m S 101.987 68.7727 m S 0 g 1 w 4 M 78.6699 68.7727 m F 101.987 68.7727 m F 0 G 0.3 w 10 M 119.4748 74.4953 m S 107.8163 74.4953 m S 113.6455 68.7727 m S 131.1334 74.4953 m S 119.4748 74.4953 m S 125.3041 68.7727 m S 142.7919 74.4953 m S 131.1334 74.4953 m S 136.9626 68.7727 m S 0 g 1 w 4 M 113.6455 68.7727 m F 136.9626 68.7727 m F 0 G 0.3 w 10 M 142.7919 74.4953 m S 119.4748 74.4953 m S 107.8163 74.4953 m S 113.6455 68.7727 m S 131.1334 74.4953 m S 119.4748 74.4953 m S 125.3041 68.7727 m S 142.7919 74.4953 m S 131.1334 74.4953 m S 136.9626 68.7727 m S 0 g 1 w 4 M 113.6455 68.7727 m F 136.9626 68.7727 m F 0 G 0.3 w 10 M 154.4505 74.4953 m S 142.7919 74.4953 m S 148.6211 68.7727 m S 166.109 74.4953 m S 154.4505 74.4953 m S 160.2797 68.7727 m S 177.7675 74.4953 m S 166.109 74.4953 m S 171.9383 68.7727 m S 0 g 1 w 4 M 148.6211 68.7727 m F 171.9383 68.7727 m F 0 G 0.3 w 10 M 189.4261 74.4953 m S 177.7675 74.4953 m S 183.5967 68.7727 m S 201.0846 74.4953 m S 189.4261 74.4953 m S 195.2553 68.7727 m S 212.7431 74.4953 m S 201.0846 74.4953 m S 206.9139 68.7727 m S 0 g 1 w 4 M 183.5967 68.7727 m F 206.9139 68.7727 m F 0 G 0.3 w 10 M 212.7431 74.4953 m S 224.4016 74.4953 m S 212.7431 74.4953 m S 218.5723 68.7727 m S 236.0601 74.4953 m S 224.4016 74.4953 m S 230.2309 68.7727 m S 247.7187 74.4953 m S 236.0601 74.4953 m S 241.8894 68.7727 m S 0 g 1 w 4 M 218.5723 68.7727 m F 241.8894 68.7727 m F 0 G 0.3 w 10 M 259.3772 74.4953 m S 247.7187 74.4953 m S 253.5479 68.7727 m S 271.0358 74.4953 m S 259.3772 74.4953 m S 265.2065 68.7727 m S 271.0358 74.4953 m S 276.865 68.7727 m S 0 g 1 w 4 M 253.5479 68.7727 m F 276.865 68.7727 m F 0 G 0.3 w 10 M 61.1821 74.4953 m S 0 g 1 w 4 M 61.1821 74.4953 m F 0 G 0.3 w 10 M 61.1821 74.4953 m S 61.1821 74.4953 m S 61.1821 74.4953 m S 0 g 1 w 4 M 61.1821 74.4953 m F 0 G 0.3 w 10 M 61.1821 74.4953 m S 61.1821 74.4953 m S 1 g 0.5 w 4 M 55.1717 74.4953 m 55.1717 71.2734 57.8627 68.6616 61.1821 68.6616 c 64.5015 68.6616 67.1925 71.2734 67.1925 74.4953 c B 67.1925 74.4953 m 67.1925 77.7171 64.5015 80.3289 61.1821 80.3289 c 57.8627 80.3289 55.1717 77.7171 55.1717 74.4953 c B 61.1821 74.4953 m B 0.3 w 10 M 61.1821 74.4953 m S 0 g 1 w 4 M 61.1821 74.4953 m F 0 G 0.3 w 10 M 61.1821 74.4953 m S 61.1821 74.4953 m S 0 g 1 w 4 M 60.097 73.4273 m 60.097 69.8502 L 62.2672 69.8502 L 62.2672 73.4273 L 65.8528 73.4161 L 65.8528 75.5746 L 62.2672 75.5635 L 62.2672 79.1405 L 60.097 79.1405 L 60.097 75.5635 L 56.5114 75.5746 L 56.5114 73.4161 L 60.097 73.4273 L f 0 G 0.3 w 10 M 37.8651 74.4953 m S 0 g 1 w 4 M 37.8651 74.4953 m F 0 G 0.3 w 10 M 37.8651 74.4953 m S 37.8651 74.4953 m S 37.8651 74.4953 m S 0 g 1 w 4 M 37.8651 74.4953 m F 0 G 0.3 w 10 M 37.8651 74.4953 m S 37.8651 74.4953 m S 1 g 0.5 w 4 M 31.8547 74.4953 m 31.8547 71.2734 34.5457 68.6616 37.8651 68.6616 c 41.1845 68.6616 43.8755 71.2734 43.8755 74.4953 c B 43.8755 74.4953 m 43.8755 77.7171 41.1845 80.3289 37.8651 80.3289 c 34.5457 80.3289 31.8547 77.7171 31.8547 74.4953 c B 37.8651 74.4953 m B 0.3 w 10 M 37.8651 74.4953 m S 0 g 1 w 4 M 37.8651 74.4953 m F 0 G 0.3 w 10 M 37.8651 74.4953 m S 37.8651 74.4953 m S 0 g 1 w 4 M 36.78 73.4273 m 36.78 69.8502 L 38.9502 69.8502 L 38.9502 73.4273 L 42.5358 73.4161 L 42.5358 75.5746 L 38.9502 75.5635 L 38.9502 79.1405 L 36.78 79.1405 L 36.78 75.5635 L 33.1944 75.5746 L 33.1944 73.4161 L 36.78 73.4273 L f 0 G 0.3 w 10 M 84.4992 74.4953 m S 0 g 1 w 4 M 84.4992 74.4953 m F 0 G 0.3 w 10 M 84.4992 74.4953 m S 84.4992 74.4953 m S 84.4992 74.4953 m S 0 g 1 w 4 M 84.4992 74.4953 m F 0 G 0.3 w 10 M 84.4992 74.4953 m S 84.4992 74.4953 m S 1 g 0.5 w 4 M 78.4888 74.4953 m 78.4888 71.2734 81.1798 68.6616 84.4992 68.6616 c 87.8186 68.6616 90.5096 71.2734 90.5096 74.4953 c B 90.5096 74.4953 m 90.5096 77.7171 87.8186 80.3289 84.4992 80.3289 c 81.1798 80.3289 78.4888 77.7171 78.4888 74.4953 c B 84.4992 74.4953 m B 0.3 w 10 M 84.4992 74.4953 m S 0 g 1 w 4 M 84.4992 74.4953 m F 0 G 0.3 w 10 M 84.4992 74.4953 m S 84.4992 74.4953 m S 0 g 1 w 4 M 83.4141 73.4273 m 83.4141 69.8502 L 85.5843 69.8502 L 85.5843 73.4273 L 89.1699 73.4161 L 89.1699 75.5746 L 85.5843 75.5635 L 85.5843 79.1405 L 83.4141 79.1405 L 83.4141 75.5635 L 79.8285 75.5746 L 79.8285 73.4161 L 83.4141 73.4273 L f 0 G 0.3 w 10 M 107.8162 74.4953 m S 119.4748 74.4953 m S 107.8162 74.4953 m S 131.1333 74.4953 m S 119.4748 74.4953 m S 131.1333 74.4953 m S 107.8162 74.4953 m S 0 g 1 w 4 M 107.8162 74.4953 m F 0 G 0.3 w 10 M 107.8162 74.4953 m S 107.8162 74.4953 m S 107.8162 74.4953 m S 0 g 1 w 4 M 107.8162 74.4953 m F 0 G 0.3 w 10 M 107.8162 74.4953 m S 107.8162 74.4953 m S 1 g 0.5 w 4 M 101.8058 74.4953 m 101.8058 71.2734 104.4968 68.6616 107.8162 68.6616 c 111.1356 68.6616 113.8266 71.2734 113.8266 74.4953 c B 113.8266 74.4953 m 113.8266 77.7171 111.1356 80.3289 107.8162 80.3289 c 104.4968 80.3289 101.8058 77.7171 101.8058 74.4953 c B 107.8162 74.4953 m B 0.3 w 10 M 107.8162 74.4953 m S 0 g 1 w 4 M 107.8162 74.4953 m F 0 G 0.3 w 10 M 107.8162 74.4953 m S 107.8162 74.4953 m S 0 g 1 w 4 M 106.7311 73.4273 m 106.7311 69.8502 L 108.9013 69.8502 L 108.9013 73.4273 L 112.4869 73.4161 L 112.4869 75.5746 L 108.9013 75.5635 L 108.9013 79.1405 L 106.7311 79.1405 L 106.7311 75.5635 L 103.1455 75.5746 L 103.1455 73.4161 L 106.7311 73.4273 L f 0 G 0.3 w 10 M 131.1333 74.4953 m S 0 g 1 w 4 M 131.1333 74.4953 m F 0 G 0.3 w 10 M 131.1333 74.4953 m S 131.1333 74.4953 m S 131.1333 74.4953 m S 0 g 1 w 4 M 131.1333 74.4953 m F 0 G 0.3 w 10 M 131.1333 74.4953 m S 131.1333 74.4953 m S 1 g 0.5 w 4 M 125.1229 74.4953 m 125.1229 71.2734 127.8139 68.6616 131.1333 68.6616 c 134.4527 68.6616 137.1437 71.2734 137.1437 74.4953 c B 137.1437 74.4953 m 137.1437 77.7171 134.4527 80.3289 131.1333 80.3289 c 127.8139 80.3289 125.1229 77.7171 125.1229 74.4953 c B 131.1333 74.4953 m B 0.3 w 10 M 131.1333 74.4953 m S 0 g 1 w 4 M 131.1333 74.4953 m F 0 G 0.3 w 10 M 131.1333 74.4953 m S 131.1333 74.4953 m S 0 g 1 w 4 M 130.0482 73.4273 m 130.0482 69.8502 L 132.2184 69.8502 L 132.2184 73.4273 L 135.804 73.4161 L 135.804 75.5746 L 132.2184 75.5635 L 132.2184 79.1405 L 130.0482 79.1405 L 130.0482 75.5635 L 126.4626 75.5746 L 126.4626 73.4161 L 130.0482 73.4273 L f 0 G 0.3 w 10 M 154.4505 74.4953 m S 166.109 74.4953 m S 154.4505 74.4953 m S 177.7675 74.4953 m S 166.109 74.4953 m S 177.7675 74.4953 m S 154.4505 74.4953 m S 0 g 1 w 4 M 154.4505 74.4953 m F 0 G 0.3 w 10 M 154.4505 74.4953 m S 154.4505 74.4953 m S 154.4505 74.4953 m S 0 g 1 w 4 M 154.4505 74.4953 m F 0 G 0.3 w 10 M 154.4505 74.4953 m S 154.4505 74.4953 m S 1 g 0.5 w 4 M 148.4401 74.4953 m 148.4401 71.2734 151.1311 68.6616 154.4505 68.6616 c 157.7699 68.6616 160.4609 71.2734 160.4609 74.4953 c B 160.4609 74.4953 m 160.4609 77.7171 157.7699 80.3289 154.4505 80.3289 c 151.1311 80.3289 148.4401 77.7171 148.4401 74.4953 c B 154.4505 74.4953 m B 0.3 w 10 M 154.4505 74.4953 m S 0 g 1 w 4 M 154.4505 74.4953 m F 0 G 0.3 w 10 M 154.4505 74.4953 m S 154.4505 74.4953 m S 0 g 1 w 4 M 153.3654 73.4273 m 153.3654 69.8502 L 155.5356 69.8502 L 155.5356 73.4273 L 159.1212 73.4161 L 159.1212 75.5746 L 155.5356 75.5635 L 155.5356 79.1405 L 153.3654 79.1405 L 153.3654 75.5635 L 149.7798 75.5746 L 149.7798 73.4161 L 153.3654 73.4273 L f 0 G 0.3 w 10 M 177.7675 74.4953 m S 0 g 1 w 4 M 177.7675 74.4953 m F 0 G 0.3 w 10 M 177.7675 74.4953 m S 177.7675 74.4953 m S 177.7675 74.4953 m S 0 g 1 w 4 M 177.7675 74.4953 m F 0 G 0.3 w 10 M 177.7675 74.4953 m S 177.7675 74.4953 m S 1 g 0.5 w 4 M 171.7571 74.4953 m 171.7571 71.2734 174.4481 68.6616 177.7675 68.6616 c 181.0869 68.6616 183.7779 71.2734 183.7779 74.4953 c B 183.7779 74.4953 m 183.7779 77.7171 181.0869 80.3289 177.7675 80.3289 c 174.4481 80.3289 171.7571 77.7171 171.7571 74.4953 c B 177.7675 74.4953 m B 0.3 w 10 M 177.7675 74.4953 m S 0 g 1 w 4 M 177.7675 74.4953 m F 0 G 0.3 w 10 M 177.7675 74.4953 m S 177.7675 74.4953 m S 0 g 1 w 4 M 176.6824 73.4273 m 176.6824 69.8502 L 178.8526 69.8502 L 178.8526 73.4273 L 182.4382 73.4161 L 182.4382 75.5746 L 178.8526 75.5635 L 178.8526 79.1405 L 176.6824 79.1405 L 176.6824 75.5635 L 173.0968 75.5746 L 173.0968 73.4161 L 176.6824 73.4273 L f 0 G 0.3 w 10 M 201.0845 74.4953 m S 212.7431 74.4953 m S 201.0845 74.4953 m S 224.4016 74.4953 m S 212.7431 74.4953 m S 224.4016 74.4953 m S 201.0845 74.4953 m S 0 g 1 w 4 M 201.0845 74.4953 m F 0 G 0.3 w 10 M 201.0845 74.4953 m S 201.0845 74.4953 m S 201.0845 74.4953 m S 0 g 1 w 4 M 201.0845 74.4953 m F 0 G 0.3 w 10 M 201.0845 74.4953 m S 201.0845 74.4953 m S 1 g 0.5 w 4 M 195.0741 74.4953 m 195.0741 71.2734 197.7651 68.6616 201.0845 68.6616 c 204.4039 68.6616 207.0949 71.2734 207.0949 74.4953 c B 207.0949 74.4953 m 207.0949 77.7171 204.4039 80.3289 201.0845 80.3289 c 197.7651 80.3289 195.0741 77.7171 195.0741 74.4953 c B 201.0845 74.4953 m B 0.3 w 10 M 201.0845 74.4953 m S 0 g 1 w 4 M 201.0845 74.4953 m F 0 G 0.3 w 10 M 201.0845 74.4953 m S 201.0845 74.4953 m S 0 g 1 w 4 M 199.9994 73.4273 m 199.9994 69.8502 L 202.1696 69.8502 L 202.1696 73.4273 L 205.7552 73.4161 L 205.7552 75.5746 L 202.1696 75.5635 L 202.1696 79.1405 L 199.9994 79.1405 L 199.9994 75.5635 L 196.4138 75.5746 L 196.4138 73.4161 L 199.9994 73.4273 L f 0 G 0.3 w 10 M 224.4016 74.4953 m S 0 g 1 w 4 M 224.4016 74.4953 m F 0 G 0.3 w 10 M 224.4016 74.4953 m S 224.4016 74.4953 m S 224.4016 74.4953 m S 0 g 1 w 4 M 224.4016 74.4953 m F 0 G 0.3 w 10 M 224.4016 74.4953 m S 224.4016 74.4953 m S 1 g 0.5 w 4 M 218.3912 74.4953 m 218.3912 71.2734 221.0822 68.6616 224.4016 68.6616 c 227.721 68.6616 230.412 71.2734 230.412 74.4953 c B 230.412 74.4953 m 230.412 77.7171 227.721 80.3289 224.4016 80.3289 c 221.0822 80.3289 218.3912 77.7171 218.3912 74.4953 c B 224.4016 74.4953 m B 0.3 w 10 M 224.4016 74.4953 m S 0 g 1 w 4 M 224.4016 74.4953 m F 0 G 0.3 w 10 M 224.4016 74.4953 m S 224.4016 74.4953 m S 0 g 1 w 4 M 223.3165 73.4273 m 223.3165 69.8502 L 225.4867 69.8502 L 225.4867 73.4273 L 229.0723 73.4161 L 229.0723 75.5746 L 225.4867 75.5635 L 225.4867 79.1405 L 223.3165 79.1405 L 223.3165 75.5635 L 219.7309 75.5746 L 219.7309 73.4161 L 223.3165 73.4273 L f 0 G 0.3 w 10 M 247.7186 74.4953 m S 259.3772 74.4953 m S 247.7186 74.4953 m S 271.0357 74.4953 m S 259.3772 74.4953 m S 271.0357 74.4953 m S 247.7186 74.4953 m S 0 g 1 w 4 M 247.7186 74.4953 m F 0 G 0.3 w 10 M 247.7186 74.4953 m S 247.7186 74.4953 m S 247.7186 74.4953 m S 0 g 1 w 4 M 247.7186 74.4953 m F 0 G 0.3 w 10 M 247.7186 74.4953 m S 247.7186 74.4953 m S 1 g 0.5 w 4 M 241.7082 74.4953 m 241.7082 71.2734 244.3992 68.6616 247.7186 68.6616 c 251.038 68.6616 253.729 71.2734 253.729 74.4953 c B 253.729 74.4953 m 253.729 77.7171 251.038 80.3289 247.7186 80.3289 c 244.3992 80.3289 241.7082 77.7171 241.7082 74.4953 c B 247.7186 74.4953 m B 0.3 w 10 M 247.7186 74.4953 m S 0 g 1 w 4 M 247.7186 74.4953 m F 0 G 0.3 w 10 M 247.7186 74.4953 m S 247.7186 74.4953 m S 0 g 1 w 4 M 246.6335 73.4273 m 246.6335 69.8502 L 248.8037 69.8502 L 248.8037 73.4273 L 252.3893 73.4161 L 252.3893 75.5746 L 248.8037 75.5635 L 248.8037 79.1405 L 246.6335 79.1405 L 246.6335 75.5635 L 243.0479 75.5746 L 243.0479 73.4161 L 246.6335 73.4273 L f 0 G 0.3 w 10 M 271.0357 74.4953 m S 0 g 1 w 4 M 271.0357 74.4953 m F 0 G 0.3 w 10 M 271.0357 74.4953 m S 271.0357 74.4953 m S 271.0357 74.4953 m S 0 g 1 w 4 M 271.0357 74.4953 m F 0 G 0.3 w 10 M 271.0357 74.4953 m S 271.0357 74.4953 m S 1 g 0.5 w 4 M 265.0253 74.4953 m 265.0253 71.2734 267.7163 68.6616 271.0357 68.6616 c 274.3551 68.6616 277.0461 71.2734 277.0461 74.4953 c B 277.0461 74.4953 m 277.0461 77.7171 274.3551 80.3289 271.0357 80.3289 c 267.7163 80.3289 265.0253 77.7171 265.0253 74.4953 c B 271.0357 74.4953 m B 0.3 w 10 M 271.0357 74.4953 m S 0 g 1 w 4 M 271.0357 74.4953 m F 0 G 0.3 w 10 M 271.0357 74.4953 m S 271.0357 74.4953 m S 0 g 1 w 4 M 269.9506 73.4273 m 269.9506 69.8502 L 272.1208 69.8502 L 272.1208 73.4273 L 275.7064 73.4161 L 275.7064 75.5746 L 272.1208 75.5635 L 272.1208 79.1405 L 269.9506 79.1405 L 269.9506 75.5635 L 266.365 75.5746 L 266.365 73.4161 L 269.9506 73.4273 L f 0 G 0.3 w 10 M 154.4505 97.3853 m S 0 g 1 w 4 M 154.4505 97.3853 m F 0 G 0.3 w 10 M 154.4505 97.3853 m S 0 g 1 w 4 M 154.4505 97.3853 m F u 1 g 0 G 0.5 w 148.4401 97.3853 m 148.4401 94.1635 151.1311 91.5517 154.4505 91.5517 c 157.7699 91.5517 160.4609 94.1635 160.4609 97.3853 c B 160.4609 97.3853 m 160.4609 100.6071 157.7699 103.2189 154.4505 103.2189 c 151.1311 103.2189 148.4401 100.6071 148.4401 97.3853 c B 154.4505 97.3853 m B U 0.3 w 10 M 154.4505 97.3853 m S 0 g 1 w 4 M 154.4505 97.3853 m F 0 G 0.3 w 10 M 154.4505 97.3853 m S 0 g 1 w 4 M 154.4505 97.3853 m F 153.3654 98.4535 m 149.7798 98.4646 L 149.7798 96.3062 L 153.3654 96.3173 L F 155.5356 96.3173 m 159.1212 96.3062 L 159.1212 98.4646 L 155.5356 98.4535 L F 149.7798 98.4646 m 159.1212 98.4646 l 159.1212 96.3062 l 149.7798 96.3062 l 149.7798 98.4646 l f 0 G 0.3 w 10 M 224.4016 166.0557 m S 0 g 1 w 4 M 224.4016 166.0557 m F 0 G 0.3 w 10 M 224.4016 166.0557 m S 0 g 1 w 4 M 224.4016 166.0557 m F u 1 g 0 G 0.5 w 218.3912 166.0557 m 218.3912 162.8339 221.0822 160.2221 224.4016 160.2221 c 227.721 160.2221 230.412 162.8339 230.412 166.0557 c B 230.412 166.0557 m 230.412 169.2775 227.721 171.8893 224.4016 171.8893 c 221.0822 171.8893 218.3912 169.2775 218.3912 166.0557 c B 224.4016 166.0557 m B U 0.3 w 10 M 224.4016 166.0557 m S 0 g 1 w 4 M 224.4016 166.0557 m F 0 G 0.3 w 10 M 224.4016 166.0557 m S 0 g 1 w 4 M 224.4016 166.0557 m F 223.3165 167.1239 m 219.7309 167.135 L 219.7309 164.9766 L 223.3165 164.9877 L F 225.4867 164.9877 m 229.0723 164.9766 L 229.0723 167.135 L 225.4867 167.1239 L F 219.7309 167.135 m 229.0723 167.135 l 229.0723 164.9766 l 219.7309 164.9766 l 219.7309 167.135 l f 0 G 0.3 w 10 M 224.4016 143.1656 m S 0 g 1 w 4 M 224.4016 143.1656 m F 0 G 0.3 w 10 M 224.4016 143.1656 m S 0 g 1 w 4 M 224.4016 143.1656 m F 1 g 0 G 0.5 w 218.3912 143.1656 m 218.3912 139.9438 221.0822 137.332 224.4016 137.332 c 227.721 137.332 230.412 139.9438 230.412 143.1656 c B 230.412 143.1656 m 230.412 146.3874 227.721 148.9992 224.4016 148.9992 c 221.0822 148.9992 218.3912 146.3874 218.3912 143.1656 c B 224.4016 143.1656 m B 0.3 w 10 M 224.4016 143.1656 m S 0 g 1 w 4 M 224.4016 143.1656 m F 0 G 0.3 w 10 M 224.4016 143.1656 m S 0 g 1 w 4 M 224.4016 143.1656 m F 223.3165 144.2338 m 219.7309 144.2449 L 219.7309 142.0865 L 223.3165 142.0976 L F 225.4867 142.0976 m 229.0723 142.0865 L 229.0723 144.2449 L 225.4867 144.2338 L F 219.7309 144.2449 m 229.0723 144.2449 l 229.0723 142.0865 l 219.7309 142.0865 l 219.7309 144.2449 l f 0 G 0.3 w 10 M 201.0846 143.1656 m S 0 g 1 w 4 M 201.0846 143.1656 m F 0 G 0.3 w 10 M 201.0846 143.1656 m S 0 g 1 w 4 M 201.0846 143.1656 m F 1 g 0 G 0.5 w 195.0742 143.1656 m 195.0742 139.9438 197.7652 137.332 201.0846 137.332 c 204.404 137.332 207.095 139.9438 207.095 143.1656 c B 207.095 143.1656 m 207.095 146.3874 204.404 148.9992 201.0846 148.9992 c 197.7652 148.9992 195.0742 146.3874 195.0742 143.1656 c B 201.0846 143.1656 m B 0.3 w 10 M 201.0846 143.1656 m S 0 g 1 w 4 M 201.0846 143.1656 m F 0 G 0.3 w 10 M 201.0846 143.1656 m S 0 g 1 w 4 M 201.0846 143.1656 m F 199.9995 144.2338 m 196.4139 144.2449 L 196.4139 142.0865 L 199.9995 142.0976 L F 202.1697 142.0976 m 205.7553 142.0865 L 205.7553 144.2449 L 202.1697 144.2338 L F 196.4139 144.2449 m 205.7553 144.2449 l 205.7553 142.0865 l 196.4139 142.0865 l 196.4139 144.2449 l f 0 G 0.3 w 10 M 201.0846 120.2755 m S 195.2553 114.553 m S 201.0846 120.2755 m S 195.2553 125.9981 m S 212.7431 120.2755 m S 201.0846 120.2755 m S 206.9139 125.9981 m S 212.7431 120.2755 m S 201.0846 120.2755 m S 206.9139 114.553 m S 0 g 1 w 4 M 206.9139 125.9981 m F 0 G 0.3 w 10 M 212.7431 120.2755 m S 212.7431 120.2755 m S 224.4016 120.2755 m S 212.7431 120.2755 m S 218.5723 125.9981 m S 224.4016 120.2755 m S 230.2309 114.553 m S 224.4016 120.2755 m S 230.2309 125.9981 m S 224.4016 120.2755 m S 212.7431 120.2755 m S 218.5723 114.553 m S 0 g 1 w 4 M 218.5723 125.9981 m F 0 G 0.3 w 10 M 224.4016 120.2755 m S 0 g 1 w 4 M 224.4016 120.2755 m F 0 G 0.3 w 10 M 224.4016 120.2755 m S 0 g 1 w 4 M 224.4016 120.2755 m F 1 g 0 G 0.5 w 218.3912 120.2755 m 218.3912 117.0537 221.0822 114.4419 224.4016 114.4419 c 227.721 114.4419 230.412 117.0537 230.412 120.2755 c B 230.412 120.2755 m 230.412 123.4973 227.721 126.1091 224.4016 126.1091 c 221.0822 126.1091 218.3912 123.4973 218.3912 120.2755 c B 224.4016 120.2755 m B 0.3 w 10 M 224.4016 120.2755 m S 0 g 1 w 4 M 224.4016 120.2755 m F 0 G 0.3 w 10 M 224.4016 120.2755 m S 0 g 1 w 4 M 224.4016 120.2755 m F 223.3165 121.3437 m 219.7309 121.3548 L 219.7309 119.1964 L 223.3165 119.2075 L F 225.4867 119.2075 m 229.0723 119.1964 L 229.0723 121.3548 L 225.4867 121.3437 L F 219.7309 121.3548 m 229.0723 121.3548 l 229.0723 119.1964 l 219.7309 119.1964 l 219.7309 121.3548 l f 0 G 0.3 w 10 M 201.0846 120.2755 m S 0 g 1 w 4 M 201.0846 120.2755 m F 0 G 0.3 w 10 M 201.0846 120.2755 m S 0 g 1 w 4 M 201.0846 120.2755 m F 1 g 0 G 0.5 w 195.0742 120.2755 m 195.0742 117.0537 197.7652 114.4419 201.0846 114.4419 c 204.404 114.4419 207.095 117.0537 207.095 120.2755 c B 207.095 120.2755 m 207.095 123.4973 204.404 126.1091 201.0846 126.1091 c 197.7652 126.1091 195.0742 123.4973 195.0742 120.2755 c B 201.0846 120.2755 m B 0.3 w 10 M 201.0846 120.2755 m S 0 g 1 w 4 M 201.0846 120.2755 m F 0 G 0.3 w 10 M 201.0846 120.2755 m S 0 g 1 w 4 M 201.0846 120.2755 m F 199.9995 121.3437 m 196.4139 121.3548 L 196.4139 119.1964 L 199.9995 119.2075 L F 202.1697 119.2075 m 205.7553 119.1964 L 205.7553 121.3548 L 202.1697 121.3437 L F 196.4139 121.3548 m 205.7553 121.3548 l 205.7553 119.1964 l 196.4139 119.1964 l 196.4139 121.3548 l f 0 G 0.3 w 10 M 154.4506 166.0557 m S 148.6212 160.3332 m S 154.4506 166.0557 m S 148.6212 171.7782 m S 166.109 166.0557 m S 154.4506 166.0557 m S 160.2798 171.7782 m S 166.109 166.0557 m S 154.4506 166.0557 m S 160.2798 160.3332 m S 0 g 1 w 4 M 160.2798 171.7782 m F 0 G 0.3 w 10 M 166.109 166.0557 m S 166.109 166.0557 m S 177.7675 166.0557 m S 166.109 166.0557 m S 171.9383 171.7782 m S 177.7675 166.0557 m S 183.5968 160.3332 m S 177.7675 166.0557 m S 183.5968 171.7782 m S 177.7675 166.0557 m S 166.109 166.0557 m S 171.9383 160.3332 m S 0 g 1 w 4 M 171.9383 171.7782 m F 0 G 0.3 w 10 M 177.7675 166.0557 m S 0 g 1 w 4 M 177.7675 166.0557 m F 0 G 0.3 w 10 M 177.7675 166.0557 m S 0 g 1 w 4 M 177.7675 166.0557 m F 1 g 0 G 0.5 w 171.7571 166.0557 m 171.7571 162.8339 174.4481 160.2221 177.7675 160.2221 c 181.0869 160.2221 183.7779 162.8339 183.7779 166.0557 c B 183.7779 166.0557 m 183.7779 169.2775 181.0869 171.8893 177.7675 171.8893 c 174.4481 171.8893 171.7571 169.2775 171.7571 166.0557 c B 177.7675 166.0557 m B 0.3 w 10 M 177.7675 166.0557 m S 0 g 1 w 4 M 177.7675 166.0557 m F 0 G 0.3 w 10 M 177.7675 166.0557 m S 0 g 1 w 4 M 177.7675 166.0557 m F 176.6824 167.1239 m 173.0968 167.135 L 173.0968 164.9766 L 176.6824 164.9877 L F 178.8526 164.9877 m 182.4382 164.9766 L 182.4382 167.135 L 178.8526 167.1239 L F 173.0968 167.135 m 182.4382 167.135 l 182.4382 164.9766 l 173.0968 164.9766 l 173.0968 167.135 l f 0 G 0.3 w 10 M 154.4506 166.0557 m S 0 g 1 w 4 M 154.4506 166.0557 m F 0 G 0.3 w 10 M 154.4506 166.0557 m S 0 g 1 w 4 M 154.4506 166.0557 m F 1 g 0 G 0.5 w 148.4402 166.0557 m 148.4402 162.8339 151.1312 160.2221 154.4506 160.2221 c 157.7699 160.2221 160.461 162.8339 160.461 166.0557 c B 160.461 166.0557 m 160.461 169.2775 157.7699 171.8893 154.4506 171.8893 c 151.1312 171.8893 148.4402 169.2775 148.4402 166.0557 c B 154.4506 166.0557 m B 0.3 w 10 M 154.4506 166.0557 m S 0 g 1 w 4 M 154.4506 166.0557 m F 0 G 0.3 w 10 M 154.4506 166.0557 m S 0 g 1 w 4 M 154.4506 166.0557 m F 153.3655 167.1239 m 149.7799 167.135 L 149.7799 164.9766 L 153.3655 164.9877 L F 155.5356 164.9877 m 159.1213 164.9766 L 159.1213 167.135 L 155.5356 167.1239 L F 149.7799 167.135 m 159.1213 167.135 l 159.1213 164.9766 l 149.7799 164.9766 l 149.7799 167.135 l f 0 G 0.3 w 10 M 84.4993 166.0557 m S 78.6699 160.3332 m S 84.4993 166.0557 m S 78.6699 171.7782 m S 96.1577 166.0557 m S 84.4993 166.0557 m S 90.3285 171.7782 m S 96.1577 166.0557 m S 84.4993 166.0557 m S 90.3285 160.3332 m S 0 g 1 w 4 M 90.3285 171.7782 m F 0 G 0.3 w 10 M 96.1577 166.0557 m S 96.1577 166.0557 m S 107.8162 166.0557 m S 96.1577 166.0557 m S 101.987 171.7782 m S 107.8162 166.0557 m S 113.6455 160.3332 m S 107.8162 166.0557 m S 113.6455 171.7782 m S 107.8162 166.0557 m S 96.1577 166.0557 m S 101.987 160.3332 m S 0 g 1 w 4 M 101.987 171.7782 m F 0 G 0.3 w 10 M 107.8162 166.0557 m S 0 g 1 w 4 M 107.8162 166.0557 m F 0 G 0.3 w 10 M 107.8162 166.0557 m S 0 g 1 w 4 M 107.8162 166.0557 m F 1 g 0 G 0.5 w 101.8058 166.0557 m 101.8058 162.8339 104.4968 160.2221 107.8162 160.2221 c 111.1356 160.2221 113.8266 162.8339 113.8266 166.0557 c B 113.8266 166.0557 m 113.8266 169.2775 111.1356 171.8893 107.8162 171.8893 c 104.4968 171.8893 101.8058 169.2775 101.8058 166.0557 c B 107.8162 166.0557 m B 0.3 w 10 M 107.8162 166.0557 m S 0 g 1 w 4 M 107.8162 166.0557 m F 0 G 0.3 w 10 M 107.8162 166.0557 m S 0 g 1 w 4 M 107.8162 166.0557 m F 106.7311 167.1239 m 103.1455 167.135 L 103.1455 164.9766 L 106.7311 164.9877 L F 108.9013 164.9877 m 112.4869 164.9766 L 112.4869 167.135 L 108.9013 167.1239 L F 103.1455 167.135 m 112.4869 167.135 l 112.4869 164.9766 l 103.1455 164.9766 l 103.1455 167.135 l f 0 G 0.3 w 10 M 84.4993 166.0557 m S 0 g 1 w 4 M 84.4993 166.0557 m F 0 G 0.3 w 10 M 84.4993 166.0557 m S 0 g 1 w 4 M 84.4993 166.0557 m F 1 g 0 G 0.5 w 78.4889 166.0557 m 78.4889 162.8339 81.1799 160.2221 84.4993 160.2221 c 87.8187 160.2221 90.5097 162.8339 90.5097 166.0557 c B 90.5097 166.0557 m 90.5097 169.2775 87.8187 171.8893 84.4993 171.8893 c 81.1799 171.8893 78.4889 169.2775 78.4889 166.0557 c B 84.4993 166.0557 m B 0.3 w 10 M 84.4993 166.0557 m S 0 g 1 w 4 M 84.4993 166.0557 m F 0 G 0.3 w 10 M 84.4993 166.0557 m S 0 g 1 w 4 M 84.4993 166.0557 m F 83.4142 167.1239 m 79.8286 167.135 L 79.8286 164.9766 L 83.4142 164.9877 L F 85.5844 164.9877 m 89.17 164.9766 L 89.17 167.135 L 85.5844 167.1239 L F 79.8286 167.135 m 89.17 167.135 l 89.17 164.9766 l 79.8286 164.9766 l 79.8286 167.135 l f 0 G 0.3 w 10 M 154.4506 143.1656 m S 148.6212 137.4431 m S 154.4506 143.1656 m S 148.6212 148.8881 m S 166.109 143.1656 m S 154.4506 143.1656 m S 160.2798 148.8881 m S 166.109 143.1656 m S 154.4506 143.1656 m S 160.2798 137.4431 m S 0 g 1 w 4 M 160.2798 148.8881 m F 0 G 0.3 w 10 M 166.109 143.1656 m S 166.109 143.1656 m S 177.7675 143.1656 m S 166.109 143.1656 m S 171.9383 148.8881 m S 177.7675 143.1656 m S 183.5968 137.4431 m S 177.7675 143.1656 m S 183.5968 148.8881 m S 177.7675 143.1656 m S 166.109 143.1656 m S 171.9383 137.4431 m S 0 g 1 w 4 M 171.9383 148.8881 m F 0 G 0.3 w 10 M 177.7675 143.1656 m S 0 g 1 w 4 M 177.7675 143.1656 m F 0 G 0.3 w 10 M 177.7675 143.1656 m S 0 g 1 w 4 M 177.7675 143.1656 m F 1 g 0 G 0.5 w 171.7571 143.1656 m 171.7571 139.9438 174.4481 137.332 177.7675 137.332 c 181.0869 137.332 183.7779 139.9438 183.7779 143.1656 c B 183.7779 143.1656 m 183.7779 146.3874 181.0869 148.9992 177.7675 148.9992 c 174.4481 148.9992 171.7571 146.3874 171.7571 143.1656 c B 177.7675 143.1656 m B 0.3 w 10 M 177.7675 143.1656 m S 0 g 1 w 4 M 177.7675 143.1656 m F 0 G 0.3 w 10 M 177.7675 143.1656 m S 0 g 1 w 4 M 177.7675 143.1656 m F 176.6824 144.2338 m 173.0968 144.2449 L 173.0968 142.0865 L 176.6824 142.0976 L F 178.8526 142.0976 m 182.4382 142.0865 L 182.4382 144.2449 L 178.8526 144.2338 L F 173.0968 144.2449 m 182.4382 144.2449 l 182.4382 142.0865 l 173.0968 142.0865 l 173.0968 144.2449 l f 0 G 0.3 w 10 M 154.4506 143.1656 m S 0 g 1 w 4 M 154.4506 143.1656 m F 0 G 0.3 w 10 M 154.4506 143.1656 m S 0 g 1 w 4 M 154.4506 143.1656 m F 1 g 0 G 0.5 w 148.4402 143.1656 m 148.4402 139.9438 151.1312 137.332 154.4506 137.332 c 157.7699 137.332 160.461 139.9438 160.461 143.1656 c B 160.461 143.1656 m 160.461 146.3874 157.7699 148.9992 154.4506 148.9992 c 151.1312 148.9992 148.4402 146.3874 148.4402 143.1656 c B 154.4506 143.1656 m B 0.3 w 10 M 154.4506 143.1656 m S 0 g 1 w 4 M 154.4506 143.1656 m F 0 G 0.3 w 10 M 154.4506 143.1656 m S 0 g 1 w 4 M 154.4506 143.1656 m F 153.3655 144.2338 m 149.7799 144.2449 L 149.7799 142.0865 L 153.3655 142.0976 L F 155.5356 142.0976 m 159.1213 142.0865 L 159.1213 144.2449 L 155.5356 144.2338 L F 149.7799 144.2449 m 159.1213 144.2449 l 159.1213 142.0865 l 149.7799 142.0865 l 149.7799 144.2449 l f 0 G 0.3 w 10 M 107.8163 143.1656 m S 101.987 137.4431 m S 107.8163 143.1656 m S 101.987 148.8881 m S 119.4748 143.1656 m S 107.8163 143.1656 m S 113.6456 148.8881 m S 119.4748 143.1656 m S 107.8163 143.1656 m S 113.6456 137.4431 m S 0 g 1 w 4 M 113.6456 148.8881 m F 0 G 0.3 w 10 M 119.4748 143.1656 m S 119.4748 143.1656 m S 131.1333 143.1656 m S 119.4748 143.1656 m S 125.304 148.8881 m S 131.1333 143.1656 m S 136.9626 137.4431 m S 131.1333 143.1656 m S 136.9626 148.8881 m S 131.1333 143.1656 m S 119.4748 143.1656 m S 125.304 137.4431 m S 0 g 1 w 4 M 125.304 148.8881 m F 0 G 0.3 w 10 M 131.1333 143.1656 m S 0 g 1 w 4 M 131.1333 143.1656 m F 0 G 0.3 w 10 M 131.1333 143.1656 m S 0 g 1 w 4 M 131.1333 143.1656 m F 1 g 0 G 0.5 w 125.1229 143.1656 m 125.1229 139.9438 127.8139 137.332 131.1333 137.332 c 134.4527 137.332 137.1437 139.9438 137.1437 143.1656 c B 137.1437 143.1656 m 137.1437 146.3874 134.4527 148.9992 131.1333 148.9992 c 127.8139 148.9992 125.1229 146.3874 125.1229 143.1656 c B 131.1333 143.1656 m B 0.3 w 10 M 131.1333 143.1656 m S 0 g 1 w 4 M 131.1333 143.1656 m F 0 G 0.3 w 10 M 131.1333 143.1656 m S 0 g 1 w 4 M 131.1333 143.1656 m F 130.0482 144.2338 m 126.4626 144.2449 L 126.4626 142.0865 L 130.0482 142.0976 L F 132.2184 142.0976 m 135.804 142.0865 L 135.804 144.2449 L 132.2184 144.2338 L F 126.4626 144.2449 m 135.804 144.2449 l 135.804 142.0865 l 126.4626 142.0865 l 126.4626 144.2449 l f 0 G 0.3 w 10 M 107.8163 143.1656 m S 0 g 1 w 4 M 107.8163 143.1656 m F 0 G 0.3 w 10 M 107.8163 143.1656 m S 0 g 1 w 4 M 107.8163 143.1656 m F 1 g 0 G 0.5 w 101.8059 143.1656 m 101.8059 139.9438 104.4969 137.332 107.8163 137.332 c 111.1357 137.332 113.8267 139.9438 113.8267 143.1656 c B 113.8267 143.1656 m 113.8267 146.3874 111.1357 148.9992 107.8163 148.9992 c 104.4969 148.9992 101.8059 146.3874 101.8059 143.1656 c B 107.8163 143.1656 m B 0.3 w 10 M 107.8163 143.1656 m S 0 g 1 w 4 M 107.8163 143.1656 m F 0 G 0.3 w 10 M 107.8163 143.1656 m S 0 g 1 w 4 M 107.8163 143.1656 m F 106.7312 144.2338 m 103.1456 144.2449 L 103.1456 142.0865 L 106.7312 142.0976 L F 108.9014 142.0976 m 112.487 142.0865 L 112.487 144.2449 L 108.9014 144.2338 L F 103.1456 144.2449 m 112.487 144.2449 l 112.487 142.0865 l 103.1456 142.0865 l 103.1456 144.2449 l f 0 G 0.3 w 10 M 61.1822 143.1656 m S 55.3529 137.4431 m S 61.1822 143.1656 m S 55.3529 148.8881 m S 72.8407 143.1656 m S 61.1822 143.1656 m S 67.0115 148.8881 m S 72.8407 143.1656 m S 61.1822 143.1656 m S 67.0115 137.4431 m S 0 g 1 w 4 M 67.0115 148.8881 m F 0 G 0.3 w 10 M 72.8407 143.1656 m S 72.8407 143.1656 m S 84.4992 143.1656 m S 72.8407 143.1656 m S 78.6699 148.8881 m S 84.4992 143.1656 m S 90.3285 137.4431 m S 84.4992 143.1656 m S 90.3285 148.8881 m S 84.4992 143.1656 m S 72.8407 143.1656 m S 78.6699 137.4431 m S 0 g 1 w 4 M 78.6699 148.8881 m F 0 G 0.3 w 10 M 84.4992 143.1656 m S 0 g 1 w 4 M 84.4992 143.1656 m F 0 G 0.3 w 10 M 84.4992 143.1656 m S 0 g 1 w 4 M 84.4992 143.1656 m F 1 g 0 G 0.5 w 78.4888 143.1656 m 78.4888 139.9438 81.1798 137.332 84.4992 137.332 c 87.8186 137.332 90.5096 139.9438 90.5096 143.1656 c B 90.5096 143.1656 m 90.5096 146.3874 87.8186 148.9992 84.4992 148.9992 c 81.1798 148.9992 78.4888 146.3874 78.4888 143.1656 c B 84.4992 143.1656 m B 0.3 w 10 M 84.4992 143.1656 m S 0 g 1 w 4 M 84.4992 143.1656 m F 0 G 0.3 w 10 M 84.4992 143.1656 m S 0 g 1 w 4 M 84.4992 143.1656 m F 83.4141 144.2338 m 79.8285 144.2449 L 79.8285 142.0865 L 83.4141 142.0976 L F 85.5843 142.0976 m 89.1699 142.0865 L 89.1699 144.2449 L 85.5843 144.2338 L F 79.8285 144.2449 m 89.1699 144.2449 l 89.1699 142.0865 l 79.8285 142.0865 l 79.8285 144.2449 l f 0 G 0.3 w 10 M 61.1822 143.1656 m S 0 g 1 w 4 M 61.1822 143.1656 m F 0 G 0.3 w 10 M 61.1822 143.1656 m S 0 g 1 w 4 M 61.1822 143.1656 m F 1 g 0 G 0.5 w 55.1718 143.1656 m 55.1718 139.9438 57.8628 137.332 61.1822 137.332 c 64.5016 137.332 67.1926 139.9438 67.1926 143.1656 c B 67.1926 143.1656 m 67.1926 146.3874 64.5016 148.9992 61.1822 148.9992 c 57.8628 148.9992 55.1718 146.3874 55.1718 143.1656 c B 61.1822 143.1656 m B 0.3 w 10 M 61.1822 143.1656 m S 0 g 1 w 4 M 61.1822 143.1656 m F 0 G 0.3 w 10 M 61.1822 143.1656 m S 0 g 1 w 4 M 61.1822 143.1656 m F 60.0971 144.2338 m 56.5115 144.2449 L 56.5115 142.0865 L 60.0971 142.0976 L F 62.2673 142.0976 m 65.8529 142.0865 L 65.8529 144.2449 L 62.2673 144.2338 L F 56.5115 144.2449 m 65.8529 144.2449 l 65.8529 142.0865 l 56.5115 142.0865 l 56.5115 144.2449 l f 0 G 0.3 w 10 M 154.4506 120.2755 m S 148.6212 114.553 m S 154.4506 120.2755 m S 148.6212 125.9981 m S 166.109 120.2755 m S 154.4506 120.2755 m S 160.2798 125.9981 m S 166.109 120.2755 m S 154.4506 120.2755 m S 160.2798 114.553 m S 0 g 1 w 4 M 160.2798 125.9981 m F 0 G 0.3 w 10 M 166.109 120.2755 m S 166.109 120.2755 m S 177.7675 120.2755 m S 166.109 120.2755 m S 171.9383 125.9981 m S 177.7675 120.2755 m S 183.5968 114.553 m S 177.7675 120.2755 m S 183.5968 125.9981 m S 177.7675 120.2755 m S 166.109 120.2755 m S 171.9383 114.553 m S 0 g 1 w 4 M 171.9383 125.9981 m F 0 G 0.3 w 10 M 177.7675 120.2755 m S 0 g 1 w 4 M 177.7675 120.2755 m F 0 G 0.3 w 10 M 177.7675 120.2755 m S 0 g 1 w 4 M 177.7675 120.2755 m F 1 g 0 G 0.5 w 171.7571 120.2755 m 171.7571 117.0537 174.4481 114.4419 177.7675 114.4419 c 181.0869 114.4419 183.7779 117.0537 183.7779 120.2755 c B 183.7779 120.2755 m 183.7779 123.4973 181.0869 126.1091 177.7675 126.1091 c 174.4481 126.1091 171.7571 123.4973 171.7571 120.2755 c B 177.7675 120.2755 m B 0.3 w 10 M 177.7675 120.2755 m S 0 g 1 w 4 M 177.7675 120.2755 m F 0 G 0.3 w 10 M 177.7675 120.2755 m S 0 g 1 w 4 M 177.7675 120.2755 m F 176.6824 121.3437 m 173.0968 121.3548 L 173.0968 119.1964 L 176.6824 119.2075 L F 178.8526 119.2075 m 182.4382 119.1964 L 182.4382 121.3548 L 178.8526 121.3437 L F 173.0968 121.3548 m 182.4382 121.3548 l 182.4382 119.1964 l 173.0968 119.1964 l 173.0968 121.3548 l f 0 G 0.3 w 10 M 154.4506 120.2755 m S 0 g 1 w 4 M 154.4506 120.2755 m F 0 G 0.3 w 10 M 154.4506 120.2755 m S 0 g 1 w 4 M 154.4506 120.2755 m F 1 g 0 G 0.5 w 148.4402 120.2755 m 148.4402 117.0537 151.1312 114.4419 154.4506 114.4419 c 157.7699 114.4419 160.461 117.0537 160.461 120.2755 c B 160.461 120.2755 m 160.461 123.4973 157.7699 126.1091 154.4506 126.1091 c 151.1312 126.1091 148.4402 123.4973 148.4402 120.2755 c B 154.4506 120.2755 m B 0.3 w 10 M 154.4506 120.2755 m S 0 g 1 w 4 M 154.4506 120.2755 m F 0 G 0.3 w 10 M 154.4506 120.2755 m S 0 g 1 w 4 M 154.4506 120.2755 m F 153.3655 121.3437 m 149.7799 121.3548 L 149.7799 119.1964 L 153.3655 119.2075 L F 155.5356 119.2075 m 159.1213 119.1964 L 159.1213 121.3548 L 155.5356 121.3437 L F 149.7799 121.3548 m 159.1213 121.3548 l 159.1213 119.1964 l 149.7799 119.1964 l 149.7799 121.3548 l f 0 G 0.3 w 10 M 107.8163 120.2755 m S 101.987 114.553 m S 107.8163 120.2755 m S 101.987 125.9981 m S 119.4748 120.2755 m S 107.8163 120.2755 m S 113.6456 125.9981 m S 119.4748 120.2755 m S 107.8163 120.2755 m S 113.6456 114.553 m S 0 g 1 w 4 M 113.6456 125.9981 m F 0 G 0.3 w 10 M 119.4748 120.2755 m S 119.4748 120.2755 m S 131.1333 120.2755 m S 119.4748 120.2755 m S 125.304 125.9981 m S 131.1333 120.2755 m S 136.9626 114.553 m S 131.1333 120.2755 m S 136.9626 125.9981 m S 131.1333 120.2755 m S 119.4748 120.2755 m S 125.304 114.553 m S 0 g 1 w 4 M 125.304 125.9981 m F 0 G 0.3 w 10 M 131.1333 120.2755 m S 0 g 1 w 4 M 131.1333 120.2755 m F 0 G 0.3 w 10 M 131.1333 120.2755 m S 0 g 1 w 4 M 131.1333 120.2755 m F 1 g 0 G 0.5 w 125.1229 120.2755 m 125.1229 117.0537 127.8139 114.4419 131.1333 114.4419 c 134.4527 114.4419 137.1437 117.0537 137.1437 120.2755 c B 137.1437 120.2755 m 137.1437 123.4973 134.4527 126.1091 131.1333 126.1091 c 127.8139 126.1091 125.1229 123.4973 125.1229 120.2755 c B 131.1333 120.2755 m B 0.3 w 10 M 131.1333 120.2755 m S 0 g 1 w 4 M 131.1333 120.2755 m F 0 G 0.3 w 10 M 131.1333 120.2755 m S 0 g 1 w 4 M 131.1333 120.2755 m F 130.0482 121.3437 m 126.4626 121.3548 L 126.4626 119.1964 L 130.0482 119.2075 L F 132.2184 119.2075 m 135.804 119.1964 L 135.804 121.3548 L 132.2184 121.3437 L F 126.4626 121.3548 m 135.804 121.3548 l 135.804 119.1964 l 126.4626 119.1964 l 126.4626 121.3548 l f 0 G 0.3 w 10 M 107.8163 120.2755 m S 0 g 1 w 4 M 107.8163 120.2755 m F 0 G 0.3 w 10 M 107.8163 120.2755 m S 0 g 1 w 4 M 107.8163 120.2755 m F 1 g 0 G 0.5 w 101.8059 120.2755 m 101.8059 117.0537 104.4969 114.4419 107.8163 114.4419 c 111.1357 114.4419 113.8267 117.0537 113.8267 120.2755 c B 113.8267 120.2755 m 113.8267 123.4973 111.1357 126.1091 107.8163 126.1091 c 104.4969 126.1091 101.8059 123.4973 101.8059 120.2755 c B 107.8163 120.2755 m B 0.3 w 10 M 107.8163 120.2755 m S 0 g 1 w 4 M 107.8163 120.2755 m F 0 G 0.3 w 10 M 107.8163 120.2755 m S 0 g 1 w 4 M 107.8163 120.2755 m F 106.7312 121.3437 m 103.1456 121.3548 L 103.1456 119.1964 L 106.7312 119.2075 L F 108.9014 119.2075 m 112.487 119.1964 L 112.487 121.3548 L 108.9014 121.3437 L F 103.1456 121.3548 m 112.487 121.3548 l 112.487 119.1964 l 103.1456 119.1964 l 103.1456 121.3548 l f 0 G 0.3 w 10 M 61.1822 188.9459 m S 55.3529 183.2234 m S 61.1822 188.9459 m S 55.3529 194.6684 m S 72.8407 188.9459 m S 61.1822 188.9459 m S 67.0115 194.6684 m S 72.8407 188.9459 m S 61.1822 188.9459 m S 67.0115 183.2234 m S 0 g 1 w 4 M 67.0115 194.6684 m F 0 G 0.3 w 10 M 72.8407 188.9459 m S 72.8407 188.9459 m S 84.4992 188.9459 m S 72.8407 188.9459 m S 78.6699 194.6684 m S 84.4992 188.9459 m S 90.3285 183.2234 m S 84.4992 188.9459 m S 90.3285 194.6684 m S 84.4992 188.9459 m S 72.8407 188.9459 m S 78.6699 183.2234 m S 0 g 1 w 4 M 78.6699 194.6684 m F 0 G 0.3 w 10 M 84.4992 188.9459 m S 0 g 1 w 4 M 84.4992 188.9459 m F 0 G 0.3 w 10 M 84.4992 188.9459 m S 0 g 1 w 4 M 84.4992 188.9459 m F 1 g 0 G 0.5 w 78.4888 188.9459 m 78.4888 185.7241 81.1798 183.1123 84.4992 183.1123 c 87.8186 183.1123 90.5096 185.7241 90.5096 188.9459 c B 90.5096 188.9459 m 90.5096 192.1677 87.8186 194.7795 84.4992 194.7795 c 81.1798 194.7795 78.4888 192.1677 78.4888 188.9459 c B 84.4992 188.9459 m B 0.3 w 10 M 84.4992 188.9459 m S 0 g 1 w 4 M 84.4992 188.9459 m F 0 G 0.3 w 10 M 84.4992 188.9459 m S 0 g 1 w 4 M 84.4992 188.9459 m F 83.4141 190.0141 m 79.8285 190.0252 L 79.8285 187.8668 L 83.4141 187.8779 L F 85.5843 187.8779 m 89.1699 187.8668 L 89.1699 190.0252 L 85.5843 190.0141 L F 79.8285 190.0252 m 89.1699 190.0252 l 89.1699 187.8668 l 79.8285 187.8668 l 79.8285 190.0252 l f 0 G 0.3 w 10 M 61.1822 188.9459 m S 0 g 1 w 4 M 61.1822 188.9459 m F 0 G 0.3 w 10 M 61.1822 188.9459 m S 0 g 1 w 4 M 61.1822 188.9459 m F 1 g 0 G 0.5 w 55.1718 188.9459 m 55.1718 185.7241 57.8628 183.1123 61.1822 183.1123 c 64.5016 183.1123 67.1926 185.7241 67.1926 188.9459 c B 67.1926 188.9459 m 67.1926 192.1677 64.5016 194.7795 61.1822 194.7795 c 57.8628 194.7795 55.1718 192.1677 55.1718 188.9459 c B 61.1822 188.9459 m B 0.3 w 10 M 61.1822 188.9459 m S 0 g 1 w 4 M 61.1822 188.9459 m F 0 G 0.3 w 10 M 61.1822 188.9459 m S 0 g 1 w 4 M 61.1822 188.9459 m F 60.0971 190.0141 m 56.5115 190.0252 L 56.5115 187.8668 L 60.0971 187.8779 L F 62.2673 187.8779 m 65.8529 187.8668 L 65.8529 190.0252 L 62.2673 190.0141 L F 56.5115 190.0252 m 65.8529 190.0252 l 65.8529 187.8668 l 56.5115 187.8668 l 56.5115 190.0252 l f 0 G 0.3 w 10 M 107.8163 211.8359 m S 101.987 206.1134 m S 107.8163 211.8359 m S 101.987 217.5585 m S 119.4748 211.8359 m S 107.8163 211.8359 m S 113.6456 217.5585 m S 119.4748 211.8359 m S 107.8163 211.8359 m S 113.6456 206.1134 m S 0 g 1 w 4 M 113.6456 217.5585 m F 0 G 0.3 w 10 M 119.4748 211.8359 m S 119.4748 211.8359 m S 131.1333 211.8359 m S 119.4748 211.8359 m S 125.304 217.5585 m S 131.1333 211.8359 m S 136.9626 206.1134 m S 131.1333 211.8359 m S 136.9626 217.5585 m S 131.1333 211.8359 m S 119.4748 211.8359 m S 125.304 206.1134 m S 0 g 1 w 4 M 125.304 217.5585 m F 0 G 0.3 w 10 M 131.1333 211.8359 m S 0 g 1 w 4 M 131.1333 211.8359 m F 0 G 0.3 w 10 M 131.1333 211.8359 m S 0 g 1 w 4 M 131.1333 211.8359 m F 1 g 0 G 0.5 w 125.1229 211.8359 m 125.1229 208.6141 127.8139 206.0023 131.1333 206.0023 c 134.4527 206.0023 137.1437 208.6141 137.1437 211.8359 c B 137.1437 211.8359 m 137.1437 215.0578 134.4527 217.6696 131.1333 217.6696 c 127.8139 217.6696 125.1229 215.0578 125.1229 211.8359 c B 131.1333 211.8359 m B 0.3 w 10 M 131.1333 211.8359 m S 0 g 1 w 4 M 131.1333 211.8359 m F 0 G 0.3 w 10 M 131.1333 211.8359 m S 0 g 1 w 4 M 131.1333 211.8359 m F 130.0482 212.9042 m 126.4626 212.9152 L 126.4626 210.7568 L 130.0482 210.768 L F 132.2184 210.768 m 135.804 210.7568 L 135.804 212.9152 L 132.2184 212.9042 L F 126.4626 212.9152 m 135.804 212.9152 l 135.804 210.7568 l 126.4626 210.7568 l 126.4626 212.9152 l f 0 G 0.3 w 10 M 107.8163 211.8359 m S 0 g 1 w 4 M 107.8163 211.8359 m F 0 G 0.3 w 10 M 107.8163 211.8359 m S 0 g 1 w 4 M 107.8163 211.8359 m F 1 g 0 G 0.5 w 101.8059 211.8359 m 101.8059 208.6141 104.4969 206.0023 107.8163 206.0023 c 111.1357 206.0023 113.8267 208.6141 113.8267 211.8359 c B 113.8267 211.8359 m 113.8267 215.0578 111.1357 217.6696 107.8163 217.6696 c 104.4969 217.6696 101.8059 215.0578 101.8059 211.8359 c B 107.8163 211.8359 m B 0.3 w 10 M 107.8163 211.8359 m S 0 g 1 w 4 M 107.8163 211.8359 m F 0 G 0.3 w 10 M 107.8163 211.8359 m S 0 g 1 w 4 M 107.8163 211.8359 m F 106.7312 212.9042 m 103.1456 212.9152 L 103.1456 210.7568 L 106.7312 210.768 L F 108.9014 210.768 m 112.487 210.7568 L 112.487 212.9152 L 108.9014 212.9042 L F 103.1456 212.9152 m 112.487 212.9152 l 112.487 210.7568 l 103.1456 210.7568 l 103.1456 212.9152 l f 0 G 0.3 w 10 M 107.8163 188.9459 m S 101.987 183.2234 m S 107.8163 188.9459 m S 101.987 194.6684 m S 119.4748 188.9459 m S 107.8163 188.9459 m S 113.6456 194.6684 m S 119.4748 188.9459 m S 107.8163 188.9459 m S 113.6456 183.2234 m S 0 g 1 w 4 M 113.6456 194.6684 m F 0 G 0.3 w 10 M 119.4748 188.9459 m S 119.4748 188.9459 m S 131.1333 188.9459 m S 119.4748 188.9459 m S 125.304 194.6684 m S 131.1333 188.9459 m S 136.9626 183.2234 m S 131.1333 188.9459 m S 136.9626 194.6684 m S 131.1333 188.9459 m S 119.4748 188.9459 m S 125.304 183.2234 m S 0 g 1 w 4 M 125.304 194.6684 m F 0 G 0.3 w 10 M 131.1333 188.9459 m S 0 g 1 w 4 M 131.1333 188.9459 m F 0 G 0.3 w 10 M 131.1333 188.9459 m S 0 g 1 w 4 M 131.1333 188.9459 m F 1 g 0 G 0.5 w 125.1229 188.9459 m 125.1229 185.7241 127.8139 183.1123 131.1333 183.1123 c 134.4527 183.1123 137.1437 185.7241 137.1437 188.9459 c B 137.1437 188.9459 m 137.1437 192.1677 134.4527 194.7795 131.1333 194.7795 c 127.8139 194.7795 125.1229 192.1677 125.1229 188.9459 c B 131.1333 188.9459 m B 0.3 w 10 M 131.1333 188.9459 m S 0 g 1 w 4 M 131.1333 188.9459 m F 0 G 0.3 w 10 M 131.1333 188.9459 m S 0 g 1 w 4 M 131.1333 188.9459 m F 130.0482 190.0141 m 126.4626 190.0252 L 126.4626 187.8668 L 130.0482 187.8779 L F 132.2184 187.8779 m 135.804 187.8668 L 135.804 190.0252 L 132.2184 190.0141 L F 126.4626 190.0252 m 135.804 190.0252 l 135.804 187.8668 l 126.4626 187.8668 l 126.4626 190.0252 l f 0 G 0.3 w 10 M 107.8163 188.9459 m S 0 g 1 w 4 M 107.8163 188.9459 m F 0 G 0.3 w 10 M 107.8163 188.9459 m S 0 g 1 w 4 M 107.8163 188.9459 m F 1 g 0 G 0.5 w 101.8059 188.9459 m 101.8059 185.7241 104.4969 183.1123 107.8163 183.1123 c 111.1357 183.1123 113.8267 185.7241 113.8267 188.9459 c B 113.8267 188.9459 m 113.8267 192.1677 111.1357 194.7795 107.8163 194.7795 c 104.4969 194.7795 101.8059 192.1677 101.8059 188.9459 c B 107.8163 188.9459 m B 0.3 w 10 M 107.8163 188.9459 m S 0 g 1 w 4 M 107.8163 188.9459 m F 0 G 0.3 w 10 M 107.8163 188.9459 m S 0 g 1 w 4 M 107.8163 188.9459 m F 106.7312 190.0141 m 103.1456 190.0252 L 103.1456 187.8668 L 106.7312 187.8779 L F 108.9014 187.8779 m 112.487 187.8668 L 112.487 190.0252 L 108.9014 190.0141 L F 103.1456 190.0252 m 112.487 190.0252 l 112.487 187.8668 l 103.1456 187.8668 l 103.1456 190.0252 l f 0 G 0.3 w 10 M 154.4506 211.8359 m S 148.6212 206.1134 m S 154.4506 211.8359 m S 148.6212 217.5585 m S 166.109 211.8359 m S 154.4506 211.8359 m S 160.2798 217.5585 m S 166.109 211.8359 m S 154.4506 211.8359 m S 160.2798 206.1134 m S 0 g 1 w 4 M 160.2798 217.5585 m F 0 G 0.3 w 10 M 166.109 211.8359 m S 166.109 211.8359 m S 177.7675 211.8359 m S 166.109 211.8359 m S 171.9383 217.5585 m S 177.7675 211.8359 m S 183.5968 206.1134 m S 177.7675 211.8359 m S 183.5968 217.5585 m S 177.7675 211.8359 m S 166.109 211.8359 m S 171.9383 206.1134 m S 0 g 1 w 4 M 171.9383 217.5585 m F 0 G 0.3 w 10 M 177.7675 211.8359 m S 0 g 1 w 4 M 177.7675 211.8359 m F 0 G 0.3 w 10 M 177.7675 211.8359 m S 0 g 1 w 4 M 177.7675 211.8359 m F 1 g 0 G 0.5 w 171.7571 211.8359 m 171.7571 208.6141 174.4481 206.0023 177.7675 206.0023 c 181.0869 206.0023 183.7779 208.6141 183.7779 211.8359 c B 183.7779 211.8359 m 183.7779 215.0578 181.0869 217.6696 177.7675 217.6696 c 174.4481 217.6696 171.7571 215.0578 171.7571 211.8359 c B 177.7675 211.8359 m B 0.3 w 10 M 177.7675 211.8359 m S 0 g 1 w 4 M 177.7675 211.8359 m F 0 G 0.3 w 10 M 177.7675 211.8359 m S 0 g 1 w 4 M 177.7675 211.8359 m F 176.6824 212.9042 m 173.0968 212.9152 L 173.0968 210.7568 L 176.6824 210.768 L F 178.8526 210.768 m 182.4382 210.7568 L 182.4382 212.9152 L 178.8526 212.9042 L F 173.0968 212.9152 m 182.4382 212.9152 l 182.4382 210.7568 l 173.0968 210.7568 l 173.0968 212.9152 l f 0 G 0.3 w 10 M 154.4506 211.8359 m S 0 g 1 w 4 M 154.4506 211.8359 m F 0 G 0.3 w 10 M 154.4506 211.8359 m S 0 g 1 w 4 M 154.4506 211.8359 m F 1 g 0 G 0.5 w 148.4402 211.8359 m 148.4402 208.6141 151.1312 206.0023 154.4506 206.0023 c 157.7699 206.0023 160.461 208.6141 160.461 211.8359 c B 160.461 211.8359 m 160.461 215.0578 157.7699 217.6696 154.4506 217.6696 c 151.1312 217.6696 148.4402 215.0578 148.4402 211.8359 c B 154.4506 211.8359 m B 0.3 w 10 M 154.4506 211.8359 m S 0 g 1 w 4 M 154.4506 211.8359 m F 0 G 0.3 w 10 M 154.4506 211.8359 m S 0 g 1 w 4 M 154.4506 211.8359 m F 153.3655 212.9042 m 149.7799 212.9152 L 149.7799 210.7568 L 153.3655 210.768 L F 155.5356 210.768 m 159.1213 210.7568 L 159.1213 212.9152 L 155.5356 212.9042 L F 149.7799 212.9152 m 159.1213 212.9152 l 159.1213 210.7568 l 149.7799 210.7568 l 149.7799 212.9152 l f 0 G 0.3 w 10 M 201.0846 211.8359 m S 195.2553 206.1134 m S 201.0846 211.8359 m S 195.2553 217.5585 m S 212.7431 211.8359 m S 201.0846 211.8359 m S 206.9139 217.5585 m S 212.7431 211.8359 m S 201.0846 211.8359 m S 206.9139 206.1134 m S 0 g 1 w 4 M 206.9139 217.5585 m F 0 G 0.3 w 10 M 212.7431 211.8359 m S 212.7431 211.8359 m S 224.4016 211.8359 m S 212.7431 211.8359 m S 218.5723 217.5585 m S 224.4016 211.8359 m S 230.2309 206.1134 m S 224.4016 211.8359 m S 230.2309 217.5585 m S 224.4016 211.8359 m S 212.7431 211.8359 m S 218.5723 206.1134 m S 0 g 1 w 4 M 218.5723 217.5585 m F 0 G 0.3 w 10 M 224.4016 211.8359 m S 0 g 1 w 4 M 224.4016 211.8359 m F 0 G 0.3 w 10 M 224.4016 211.8359 m S 0 g 1 w 4 M 224.4016 211.8359 m F 1 g 0 G 0.5 w 218.3912 211.8359 m 218.3912 208.6141 221.0822 206.0023 224.4016 206.0023 c 227.721 206.0023 230.412 208.6141 230.412 211.8359 c B 230.412 211.8359 m 230.412 215.0578 227.721 217.6696 224.4016 217.6696 c 221.0822 217.6696 218.3912 215.0578 218.3912 211.8359 c B 224.4016 211.8359 m B 0.3 w 10 M 224.4016 211.8359 m S 0 g 1 w 4 M 224.4016 211.8359 m F 0 G 0.3 w 10 M 224.4016 211.8359 m S 0 g 1 w 4 M 224.4016 211.8359 m F 223.3165 212.9042 m 219.7309 212.9152 L 219.7309 210.7568 L 223.3165 210.768 L F 225.4867 210.768 m 229.0723 210.7568 L 229.0723 212.9152 L 225.4867 212.9042 L F 219.7309 212.9152 m 229.0723 212.9152 l 229.0723 210.7568 l 219.7309 210.7568 l 219.7309 212.9152 l f 0 G 0.3 w 10 M 201.0846 211.8359 m S 0 g 1 w 4 M 201.0846 211.8359 m F 0 G 0.3 w 10 M 201.0846 211.8359 m S 0 g 1 w 4 M 201.0846 211.8359 m F 1 g 0 G 0.5 w 195.0742 211.8359 m 195.0742 208.6141 197.7652 206.0023 201.0846 206.0023 c 204.404 206.0023 207.095 208.6141 207.095 211.8359 c B 207.095 211.8359 m 207.095 215.0578 204.404 217.6696 201.0846 217.6696 c 197.7652 217.6696 195.0742 215.0578 195.0742 211.8359 c B 201.0846 211.8359 m B 0.3 w 10 M 201.0846 211.8359 m S 0 g 1 w 4 M 201.0846 211.8359 m F 0 G 0.3 w 10 M 201.0846 211.8359 m S 0 g 1 w 4 M 201.0846 211.8359 m F 199.9995 212.9042 m 196.4139 212.9152 L 196.4139 210.7568 L 199.9995 210.768 L F 202.1697 210.768 m 205.7553 210.7568 L 205.7553 212.9152 L 202.1697 212.9042 L F 196.4139 212.9152 m 205.7553 212.9152 l 205.7553 210.7568 l 196.4139 210.7568 l 196.4139 212.9152 l f 0 G 0.3 w 10 M 154.4506 188.9459 m S 148.6212 183.2234 m S 154.4506 188.9459 m S 148.6212 194.6684 m S 166.109 188.9459 m S 154.4506 188.9459 m S 160.2798 194.6684 m S 166.109 188.9459 m S 154.4506 188.9459 m S 160.2798 183.2234 m S 0 g 1 w 4 M 160.2798 194.6684 m F 0 G 0.3 w 10 M 166.109 188.9459 m S 166.109 188.9459 m S 177.7675 188.9459 m S 166.109 188.9459 m S 171.9383 194.6684 m S 177.7675 188.9459 m S 183.5968 183.2234 m S 177.7675 188.9459 m S 183.5968 194.6684 m S 177.7675 188.9459 m S 166.109 188.9459 m S 171.9383 183.2234 m S 0 g 1 w 4 M 171.9383 194.6684 m F 0 G 0.3 w 10 M 177.7675 188.9459 m S 0 g 1 w 4 M 177.7675 188.9459 m F 0 G 0.3 w 10 M 177.7675 188.9459 m S 0 g 1 w 4 M 177.7675 188.9459 m F 1 g 0 G 0.5 w 171.7571 188.9459 m 171.7571 185.7241 174.4481 183.1123 177.7675 183.1123 c 181.0869 183.1123 183.7779 185.7241 183.7779 188.9459 c B 183.7779 188.9459 m 183.7779 192.1677 181.0869 194.7795 177.7675 194.7795 c 174.4481 194.7795 171.7571 192.1677 171.7571 188.9459 c B 177.7675 188.9459 m B 0.3 w 10 M 177.7675 188.9459 m S 0 g 1 w 4 M 177.7675 188.9459 m F 0 G 0.3 w 10 M 177.7675 188.9459 m S 0 g 1 w 4 M 177.7675 188.9459 m F 176.6824 190.0141 m 173.0968 190.0252 L 173.0968 187.8668 L 176.6824 187.8779 L F 178.8526 187.8779 m 182.4382 187.8668 L 182.4382 190.0252 L 178.8526 190.0141 L F 173.0968 190.0252 m 182.4382 190.0252 l 182.4382 187.8668 l 173.0968 187.8668 l 173.0968 190.0252 l f 0 G 0.3 w 10 M 154.4506 188.9459 m S 0 g 1 w 4 M 154.4506 188.9459 m F 0 G 0.3 w 10 M 154.4506 188.9459 m S 0 g 1 w 4 M 154.4506 188.9459 m F 1 g 0 G 0.5 w 148.4402 188.9459 m 148.4402 185.7241 151.1312 183.1123 154.4506 183.1123 c 157.7699 183.1123 160.461 185.7241 160.461 188.9459 c B 160.461 188.9459 m 160.461 192.1677 157.7699 194.7795 154.4506 194.7795 c 151.1312 194.7795 148.4402 192.1677 148.4402 188.9459 c B 154.4506 188.9459 m B 0.3 w 10 M 154.4506 188.9459 m S 0 g 1 w 4 M 154.4506 188.9459 m F 0 G 0.3 w 10 M 154.4506 188.9459 m S 0 g 1 w 4 M 154.4506 188.9459 m F 153.3655 190.0141 m 149.7799 190.0252 L 149.7799 187.8668 L 153.3655 187.8779 L F 155.5356 187.8779 m 159.1213 187.8668 L 159.1213 190.0252 L 155.5356 190.0141 L F 149.7799 190.0252 m 159.1213 190.0252 l 159.1213 187.8668 l 149.7799 187.8668 l 149.7799 190.0252 l f 0 G 0.3 w 10 M 201.0846 188.9459 m S 195.2553 183.2234 m S 201.0846 188.9459 m S 195.2553 194.6684 m S 212.7431 188.9459 m S 201.0846 188.9459 m S 206.9139 194.6684 m S 212.7431 188.9459 m S 201.0846 188.9459 m S 206.9139 183.2234 m S 0 g 1 w 4 M 206.9139 194.6684 m F 0 G 0.3 w 10 M 212.7431 188.9459 m S 212.7431 188.9459 m S 224.4016 188.9459 m S 212.7431 188.9459 m S 218.5723 194.6684 m S 224.4016 188.9459 m S 230.2309 183.2234 m S 224.4016 188.9459 m S 230.2309 194.6684 m S 224.4016 188.9459 m S 212.7431 188.9459 m S 218.5723 183.2234 m S 0 g 1 w 4 M 218.5723 194.6684 m F 0 G 0.3 w 10 M 224.4016 188.9459 m S 0 g 1 w 4 M 224.4016 188.9459 m F 0 G 0.3 w 10 M 224.4016 188.9459 m S 0 g 1 w 4 M 224.4016 188.9459 m F 1 g 0 G 0.5 w 218.3912 188.9459 m 218.3912 185.7241 221.0822 183.1123 224.4016 183.1123 c 227.721 183.1123 230.412 185.7241 230.412 188.9459 c B 230.412 188.9459 m 230.412 192.1677 227.721 194.7795 224.4016 194.7795 c 221.0822 194.7795 218.3912 192.1677 218.3912 188.9459 c B 224.4016 188.9459 m B 0.3 w 10 M 224.4016 188.9459 m S 0 g 1 w 4 M 224.4016 188.9459 m F 0 G 0.3 w 10 M 224.4016 188.9459 m S 0 g 1 w 4 M 224.4016 188.9459 m F 223.3165 190.0141 m 219.7309 190.0252 L 219.7309 187.8668 L 223.3165 187.8779 L F 225.4867 187.8779 m 229.0723 187.8668 L 229.0723 190.0252 L 225.4867 190.0141 L F 219.7309 190.0252 m 229.0723 190.0252 l 229.0723 187.8668 l 219.7309 187.8668 l 219.7309 190.0252 l f 0 G 0.3 w 10 M 201.0846 188.9459 m S 0 g 1 w 4 M 201.0846 188.9459 m F 0 G 0.3 w 10 M 201.0846 188.9459 m S 0 g 1 w 4 M 201.0846 188.9459 m F 1 g 0 G 0.5 w 195.0742 188.9459 m 195.0742 185.7241 197.7652 183.1123 201.0846 183.1123 c 204.404 183.1123 207.095 185.7241 207.095 188.9459 c B 207.095 188.9459 m 207.095 192.1677 204.404 194.7795 201.0846 194.7795 c 197.7652 194.7795 195.0742 192.1677 195.0742 188.9459 c B 201.0846 188.9459 m B 0.3 w 10 M 201.0846 188.9459 m S 0 g 1 w 4 M 201.0846 188.9459 m F 0 G 0.3 w 10 M 201.0846 188.9459 m S 0 g 1 w 4 M 201.0846 188.9459 m F 199.9995 190.0141 m 196.4139 190.0252 L 196.4139 187.8668 L 199.9995 187.8779 L F 202.1697 187.8779 m 205.7553 187.8668 L 205.7553 190.0252 L 202.1697 190.0141 L F 196.4139 190.0252 m 205.7553 190.0252 l 205.7553 187.8668 l 196.4139 187.8668 l 196.4139 190.0252 l f 0 G 0.3 w 10 M 84.4992 120.2755 m S 0 g 1 w 4 M 84.4992 120.2755 m F 0 G 0.3 w 10 M 84.4992 120.2755 m S 0 g 1 w 4 M 84.4992 120.2755 m F u 1 g 0 G 0.5 w 78.4888 120.2755 m 78.4888 117.0537 81.1798 114.4419 84.4992 114.4419 c 87.8186 114.4419 90.5096 117.0537 90.5096 120.2755 c B 90.5096 120.2755 m 90.5096 123.4973 87.8186 126.1091 84.4992 126.1091 c 81.1798 126.1091 78.4888 123.4973 78.4888 120.2755 c B 84.4992 120.2755 m B U 0.3 w 10 M 84.4992 120.2755 m S 0 g 1 w 4 M 84.4992 120.2755 m F 0 G 0.3 w 10 M 84.4992 120.2755 m S 0 g 1 w 4 M 84.4992 120.2755 m F 83.4141 121.3437 m 79.8285 121.3548 L 79.8285 119.1964 L 83.4141 119.2075 L F 85.5843 119.2075 m 89.1699 119.1964 L 89.1699 121.3548 L 85.5843 121.3437 L F 79.8285 121.3548 m 89.1699 121.3548 l 89.1699 119.1964 l 79.8285 119.1964 l 79.8285 121.3548 l f 0 G 4 w 49.5236 177.5007 m 49.5236 200.3909 l 96.1577 200.3909 l 96.1577 223.281 l 119.4748 223.281 l S 142.7919 223.281 m 189.4261 223.281 l S 212.7432 223.281 m 236.0601 223.281 l 236.0601 108.8304 l 212.7432 108.8304 l S 189.4261 108.8304 m 166.109 108.8304 l 166.109 85.9403 l 142.7919 85.9402 l S 119.4748 108.8304 m 72.8407 108.8304 l 72.8407 131.7206 l 49.5236 131.7206 l 49.5236 154.6106 l S u u 0 g 1 w /_Times-Italic 12 14.5 0 0 z [1 0 0 1 127.1334 226.781]e (a)t T U U u u /_Times-Roman 7 8.5 0 0 z [1 0 0 1 133 225.5]e (\61)t T U U 0 G 0.3 w 10 M 206.9138 160.3332 m S 195.2553 160.3332 m S 0 g 1 w 4 M 206.9138 160.3332 m F 0 G 0.3 w 10 M 206.9138 160.3332 m S 195.2553 160.3332 m S 0 g 1 w 4 M 206.9138 160.3332 m F u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 197.0846 158.1106]e (a)t T U U u u /_Times-Roman 7 8.5 0 0 z [1 0 0 1 203.9512 156.3296]e (\62)t T U U 0 G 0.3 w 10 M 67.0115 160.3332 m S 55.3529 160.3332 m S 0 g 1 w 4 M 67.0115 160.3332 m F 0 G 0.3 w 10 M 67.0115 160.3332 m S 55.3529 160.3332 m S 0 g 1 w 4 M 67.0115 160.3332 m F 0 G 0.3 w 10 M 67.0114 160.3332 m S 55.3529 160.3332 m S 0 g 1 w 4 M 67.0114 160.3332 m F 0 G 0.3 w 10 M 67.0114 160.3332 m S 55.3529 160.3332 m S 0 g 1 w 4 M 67.0114 160.3332 m F u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 57.1822 158.1106]e (a)t T U U u u /_Times-Roman 7 8.5 0 0 z [1 0 0 1 63.0488 156.3296]e (\64)t T U U 0 G 0.3 w 10 M 136.9627 91.6628 m S 125.3041 91.6628 m S 0 g 1 w 4 M 136.9627 91.6628 m F 0 G 0.3 w 10 M 136.9627 91.6628 m S 125.3041 91.6628 m S 0 g 1 w 4 M 136.9627 91.6628 m F 0 G 0.3 w 10 M 136.9626 91.6628 m S 125.3041 91.6628 m S 0 g 1 w 4 M 136.9626 91.6628 m F 0 G 0.3 w 10 M 136.9626 91.6628 m S 125.3041 91.6628 m S 0 g 1 w 4 M 136.9626 91.6628 m F u u /_Times-Italic 12 14.5 0 0 z [1 0 0 1 127.1334 89.4402]e (a)t T U U u u /_Times-Roman 7 8.5 0 0 z [1 0 0 1 134 87.6592]e (\63)t T U U 0 G 0.3 w 10 M 154.4505 63.0501 m S 154.4505 74.4951 m S 154.4505 74.4951 m S 154.4505 74.4951 m S 154.4505 74.4951 m S 154.4505 63.0501 m S 154.4505 63.0501 m S 154.4505 63.0501 m S 154.4505 51.605 m S 154.4505 63.0501 m S 154.4505 63.0501 m S 154.4505 51.605 m S 154.4505 74.4951 m S 154.4505 74.4951 m S 154.4505 74.4951 m S 154.4505 74.4951 m S 154.4505 74.4951 m S 154.4505 74.4951 m S 154.4505 74.4951 m S 154.4505 74.4951 m S u u 0 g 1 w 4 M /_Times-Roman 12 14.5 0 0 z [1 0 0 1 148.3294 34.5551]e (\(a\))t T U U showpage _E end %%EndDocument @endspecial 1215 x @beginspecial 31 @llx 32.500000 @lly 294 @urx 295.500000 @ury 2196 @rwi @setspecial %%BeginDocument: fig14b.ps /Adobe_Illustrator_1.1 dup 100 dict def load begin /Version 0 def /Revision 0 def /bdef {bind def} bind def /ldef {load def} bdef /xdef {exch def} bdef /_K {3 index add neg dup 0 lt {pop 0} if 3 1 roll} bdef /_k /setcmybcolor where {/setcmybcolor get} {{1 sub 4 1 roll _K _K _K setrgbcolor pop} bind} ifelse def /g {/_b xdef /p {_b setgray} def} bdef /G {/_B xdef /P {_B setgray} def} bdef /k {/_b xdef /_y xdef /_m xdef /_c xdef /p {_c _m _y _b _k} def} bdef /K {/_B xdef /_Y xdef /_M xdef /_C xdef /P {_C _M _Y _B _k} def} bdef /d /setdash ldef /_i currentflat def /i {dup 0 eq {pop _i} if setflat} bdef /j /setlinejoin ldef /J /setlinecap ldef /M /setmiterlimit ldef /w /setlinewidth ldef /_R {.25 sub round .25 add} bdef /_r {transform _R exch _R exch itransform} bdef /c {_r curveto} bdef /C /c ldef /v {currentpoint 6 2 roll _r curveto} bdef /V /v ldef /y {_r 2 copy curveto} bdef /Y /y ldef /l {_r lineto} bdef /L /l ldef /m {_r moveto} bdef /_e [] def /_E {_e length 0 ne {gsave 0 g 0 G 0 i 0 J 0 j 1 w 10 M [] 0 d /Courier 20 0 0 1 z [0.966 0.259 -0.259 0.966 _e 0 get _e 2 get add 2 div _e 1 get _e 3 get add 2 div] e _f t T grestore} if} bdef /_fill {{fill} stopped {/_e [pathbbox] def /_f (ERROR: can't fill, increase flatness) def n _E} if} bdef /_stroke {{stroke} stopped {/_e [pathbbox] def /_f (ERROR: can't stroke, increase flatness) def n _E} if} bdef /n /newpath ldef /N /n ldef /F {p _fill} bdef /f {closepath F} bdef /S {P _stroke} bdef /s {closepath S} bdef /B {gsave F grestore S} bdef /b {closepath B} bdef /_s /ashow ldef /_S {(?) exch {2 copy 0 exch put pop dup false charpath currentpoint _g setmatrix _stroke _G setmatrix moveto 3 copy pop rmoveto} forall pop pop pop n} bdef /_A {_a moveto _t exch 0 exch} bdef /_L {0 _l neg translate _G currentmatrix pop} bdef /_w {dup stringwidth exch 3 -1 roll length 1 sub _t mul add exch} bdef /_z [{0 0} bind {dup _w exch neg 2 div exch neg 2 div} bind {dup _w exch neg exch neg} bind] def /z {_z exch get /_a xdef /_t xdef /_l xdef exch findfont exch scalefont setfont} bdef /_g matrix def /_G matrix def /_D {_g currentmatrix pop gsave concat _G currentmatrix pop} bdef /e {_D p /t {_A _s _L} def} bdef /r {_D P /t {_A _S _L} def} bdef /a {_D /t {dup p _A _s P _A _S _L} def} bdef /o {_D /t {pop _L} def} bdef /T {grestore} bdef /u {} bdef /U {} bdef /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bdef end Adobe_Illustrator_1.1 begin n [39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron ]/_Times-Roman/Times-Roman Z 0 G 0 i 0 J 0 j 0.3 w 10 M []0 d 46.0357 235.6709 m S 46.0357 224.2259 m S 34.3772 224.2259 m S 34.3772 235.6709 m S 40.2064 229.9484 m S u 69.3528 212.7808 m S 69.3528 201.3357 m S 57.6942 201.3357 m S 57.6942 212.7808 m S 63.5235 207.0583 m S U 57.6942 224.2259 m S 57.6942 212.7808 m S 46.0357 212.7808 m S 46.0357 224.2259 m S 51.865 218.5033 m S 57.6942 235.6709 m S 57.6942 224.2259 m S 46.0357 224.2259 m S 46.0357 235.6709 m S 51.865 229.9484 m S u 69.3528 235.6709 m S 69.3528 224.2259 m S 57.6942 224.2259 m S 57.6942 235.6709 m S 63.5235 229.9484 m S U u 69.3528 224.2259 m S 69.3528 212.7808 m S 57.6942 212.7808 m S 57.6942 224.2259 m S 63.5235 218.5033 m S U u 57.6942 212.7808 m S 57.6942 201.3357 m S 46.0357 201.3357 m S 46.0357 212.7808 m S 51.865 207.0583 m S U u 46.0357 212.7808 m S 46.0357 201.3357 m S 34.3772 201.3357 m S 34.3772 212.7808 m S 40.2064 207.0583 m S U 46.0357 224.2259 m S 46.0357 212.7808 m S 34.3772 212.7808 m S 34.3772 224.2259 m S 40.2064 218.5033 m S 0 g 1 w 4 M 40.2064 229.9484 m F 63.5235 229.9484 m F 40.2064 207.0583 m F 63.5235 207.0583 m F u 0 G 0.3 w 10 M 81.0113 235.6709 m S 81.0113 224.2259 m S 69.3528 224.2259 m S 69.3528 235.6709 m S 75.182 229.9484 m S U 104.3284 212.7808 m S 104.3284 201.3357 m S 92.6698 201.3357 m S 92.6698 212.7808 m S 98.4991 207.0583 m S 92.6698 224.2259 m S 92.6698 212.7808 m S 81.0113 212.7808 m S 81.0113 224.2259 m S 86.8406 218.5033 m S u 92.6698 235.6709 m S 92.6698 224.2259 m S 81.0113 224.2259 m S 81.0113 235.6709 m S 86.8406 229.9484 m S U u 104.3284 235.6709 m S 104.3284 224.2259 m S 92.6698 224.2259 m S 92.6698 235.6709 m S 98.4991 229.9484 m S U 104.3284 224.2259 m S 104.3284 212.7808 m S 92.6698 212.7808 m S 92.6698 224.2259 m S 98.4991 218.5033 m S 92.6698 212.7808 m S 92.6698 201.3357 m S 81.0113 201.3357 m S 81.0113 212.7808 m S 86.8406 207.0583 m S 81.0113 212.7808 m S 81.0113 201.3357 m S 69.3528 201.3357 m S 69.3528 212.7808 m S 75.182 207.0583 m S 81.0113 224.2259 m S 81.0113 212.7808 m S 69.3528 212.7808 m S 69.3528 224.2259 m S 75.182 218.5033 m S 0 g 1 w 4 M 75.182 229.9484 m F 98.4991 229.9484 m F 75.182 207.0583 m F 98.4991 207.0583 m F u 0 G 0.3 w 10 M 115.9869 235.6709 m S 115.9869 224.2259 m S 104.3284 224.2259 m S 104.3284 235.6709 m S 110.1576 229.9484 m S U u 139.304 212.7808 m S 139.304 201.3357 m S 127.6455 201.3357 m S 127.6455 212.7808 m S 133.4747 207.0583 m S U u 127.6455 224.2259 m S 127.6455 212.7808 m S 115.9869 212.7808 m S 115.9869 224.2259 m S 121.8162 218.5033 m S U u 127.6455 235.6709 m S 127.6455 224.2259 m S 115.9869 224.2259 m S 115.9869 235.6709 m S 121.8162 229.9484 m S U u 139.304 235.6709 m S 139.304 224.2259 m S 127.6455 224.2259 m S 127.6455 235.6709 m S 133.4747 229.9484 m S U u 139.304 224.2259 m S 139.304 212.7808 m S 127.6455 212.7808 m S 127.6455 224.2259 m S 133.4747 218.5033 m S U u 127.6455 212.7808 m S 127.6455 201.3357 m S 115.9869 201.3357 m S 115.9869 212.7808 m S 121.8162 207.0583 m S U 115.9869 212.7808 m S 115.9869 201.3357 m S 104.3284 201.3357 m S 104.3284 212.7808 m S 110.1576 207.0583 m S 115.9869 224.2259 m S 115.9869 212.7808 m S 104.3284 212.7808 m S 104.3284 224.2259 m S 110.1576 218.5033 m S 0 g 1 w 4 M 110.1576 229.9484 m F 133.4747 229.9484 m F 110.1576 207.0583 m F 133.4747 207.0583 m F 0 G 0.3 w 10 M 139.304 224.2259 m S 139.304 235.6709 m S 139.304 201.3357 m S 139.304 212.7808 m S 139.304 212.7808 m S 139.304 224.2259 m S u 46.0357 201.3357 m S 46.0357 189.8906 m S 34.3772 189.8906 m S 34.3772 201.3357 m S 40.2064 195.6132 m S U 69.3528 178.4456 m S 69.3528 167.0006 m S 57.6942 167.0006 m S 57.6942 178.4456 m S 63.5235 172.7231 m S 57.6942 189.8906 m S 57.6942 178.4456 m S 46.0357 178.4456 m S 46.0357 189.8906 m S 51.865 184.1682 m S 57.6942 201.3357 m S 57.6942 189.8906 m S 46.0357 189.8906 m S 46.0357 201.3357 m S 51.865 195.6132 m S 69.3528 201.3357 m S 69.3528 189.8906 m S 57.6942 189.8906 m S 57.6942 201.3357 m S 63.5235 195.6132 m S 69.3528 189.8906 m S 69.3528 178.4456 m S 57.6942 178.4456 m S 57.6942 189.8906 m S 63.5235 184.1682 m S 57.6942 178.4456 m S 57.6942 167.0006 m S 46.0357 167.0006 m S 46.0357 178.4456 m S 51.865 172.7231 m S u 46.0357 178.4456 m S 46.0357 167.0006 m S 34.3772 167.0006 m S 34.3772 178.4456 m S 40.2064 172.7231 m S U u 46.0357 189.8906 m S 46.0357 178.4456 m S 34.3772 178.4456 m S 34.3772 189.8906 m S 40.2064 184.1682 m S U 0 g 1 w 4 M 40.2064 195.6132 m F 63.5235 195.6132 m F 40.2064 172.7231 m F 63.5235 172.7231 m F 0 G 0.3 w 10 M 81.0113 201.3357 m S 81.0113 189.8906 m S 69.3528 189.8906 m S 69.3528 201.3357 m S 75.182 195.6132 m S 104.3284 178.4456 m S 104.3284 167.0006 m S 92.6698 167.0006 m S 92.6698 178.4456 m S 98.4991 172.7231 m S 92.6698 189.8906 m S 92.6698 178.4456 m S 81.0113 178.4456 m S 81.0113 189.8906 m S 86.8406 184.1682 m S 92.6698 201.3357 m S 92.6698 189.8906 m S 81.0113 189.8906 m S 81.0113 201.3357 m S 86.8406 195.6132 m S 104.3284 201.3357 m S 104.3284 189.8906 m S 92.6698 189.8906 m S 92.6698 201.3357 m S 98.4991 195.6132 m S 104.3284 189.8906 m S 104.3284 178.4456 m S 92.6698 178.4456 m S 92.6698 189.8906 m S 98.4991 184.1682 m S 92.6698 178.4456 m S 92.6698 167.0006 m S 81.0113 167.0006 m S 81.0113 178.4456 m S 86.8406 172.7231 m S 81.0113 178.4456 m S 81.0113 167.0006 m S 69.3528 167.0006 m S 69.3528 178.4456 m S 75.182 172.7231 m S 81.0113 189.8906 m S 81.0113 178.4456 m S 69.3528 178.4456 m S 69.3528 189.8906 m S 75.182 184.1682 m S 0 g 1 w 4 M 75.182 195.6132 m F 98.4991 195.6132 m F 75.182 172.7231 m F 98.4991 172.7231 m F 0 G 0.3 w 10 M 115.9869 201.3357 m S 115.9869 189.8906 m S 104.3284 189.8906 m S 104.3284 201.3357 m S 110.1576 195.6132 m S u 139.304 178.4456 m S 139.304 167.0006 m S 127.6455 167.0006 m S 127.6455 178.4456 m S 133.4747 172.7231 m S U 127.6455 189.8906 m S 127.6455 178.4456 m S 115.9869 178.4456 m S 115.9869 189.8906 m S 121.8162 184.1682 m S 127.6455 201.3357 m S 127.6455 189.8906 m S 115.9869 189.8906 m S 115.9869 201.3357 m S 121.8162 195.6132 m S 139.304 201.3357 m S 139.304 189.8906 m S 127.6455 189.8906 m S 127.6455 201.3357 m S 133.4747 195.6132 m S 139.304 189.8906 m S 139.304 178.4456 m S 127.6455 178.4456 m S 127.6455 189.8906 m S 133.4747 184.1682 m S u 127.6455 178.4456 m S 127.6455 167.0006 m S 115.9869 167.0006 m S 115.9869 178.4456 m S 121.8162 172.7231 m S U 115.9869 178.4456 m S 115.9869 167.0006 m S 104.3284 167.0006 m S 104.3284 178.4456 m S 110.1576 172.7231 m S 115.9869 189.8906 m S 115.9869 178.4456 m S 104.3284 178.4456 m S 104.3284 189.8906 m S 110.1576 184.1682 m S 0 g 1 w 4 M 110.1576 195.6132 m F 133.4747 195.6132 m F 110.1576 172.7231 m F 133.4747 172.7231 m F 0 G 0.3 w 10 M 139.304 189.8906 m S 139.304 201.3357 m S 139.304 167.0006 m S 139.304 178.4456 m S 139.304 178.4456 m S 139.304 189.8906 m S 0 g 1 w 4 M 40.2064 161.278 m F 63.5235 161.278 m F 75.182 161.278 m F 98.4991 161.278 m F 110.1576 161.278 m F 133.4747 161.278 m F 0 G 0.3 w 10 M 46.0357 167.0006 m S 46.0357 155.5554 m S 34.3772 155.5554 m S 34.3772 167.0006 m S 40.2064 161.278 m S 69.3528 144.1104 m S 69.3528 132.6653 m S 57.6942 132.6653 m S 57.6942 144.1104 m S 63.5235 138.3879 m S 57.6942 155.5554 m S 57.6942 144.1104 m S 46.0357 144.1104 m S 46.0357 155.5554 m S 51.865 149.8329 m S 57.6942 167.0006 m S 57.6942 155.5554 m S 46.0357 155.5554 m S 46.0357 167.0006 m S 51.865 161.278 m S 69.3528 167.0006 m S 69.3528 155.5554 m S 57.6942 155.5554 m S 57.6942 167.0006 m S 63.5235 161.278 m S 69.3528 155.5554 m S 69.3528 144.1104 m S 57.6942 144.1104 m S 57.6942 155.5554 m S 63.5235 149.8329 m S 57.6942 144.1104 m S 57.6942 132.6653 m S 46.0357 132.6653 m S 46.0357 144.1104 m S 51.865 138.3879 m S 46.0357 144.1104 m S 46.0357 132.6653 m S 34.3772 132.6653 m S 34.3772 144.1104 m S 40.2064 138.3879 m S 46.0357 155.5554 m S 46.0357 144.1104 m S 34.3772 144.1104 m S 34.3772 155.5554 m S 40.2064 149.8329 m S 0 g 1 w 4 M 40.2064 161.278 m F 63.5235 161.278 m F 40.2064 138.3879 m F 63.5235 138.3879 m F 0 G 0.3 w 10 M 81.0113 167.0006 m S 81.0113 155.5554 m S 69.3528 155.5554 m S 69.3528 167.0006 m S 75.182 161.278 m S 104.3284 144.1104 m S 104.3284 132.6653 m S 92.6698 132.6653 m S 92.6698 144.1104 m S 98.4991 138.3879 m S 92.6698 155.5554 m S 92.6698 144.1104 m S 81.0113 144.1104 m S 81.0113 155.5554 m S 86.8406 149.8329 m S 92.6698 167.0006 m S 92.6698 155.5554 m S 81.0113 155.5554 m S 81.0113 167.0006 m S 86.8406 161.278 m S 104.3284 167.0006 m S 104.3284 155.5554 m S 92.6698 155.5554 m S 92.6698 167.0006 m S 98.4991 161.278 m S 104.3284 155.5554 m S 104.3284 144.1104 m S 92.6698 144.1104 m S 92.6698 155.5554 m S 98.4991 149.8329 m S 92.6698 144.1104 m S 92.6698 132.6653 m S 81.0113 132.6653 m S 81.0113 144.1104 m S 86.8406 138.3879 m S 81.0113 144.1104 m S 81.0113 132.6653 m S 69.3528 132.6653 m S 69.3528 144.1104 m S 75.182 138.3879 m S 81.0113 155.5554 m S 81.0113 144.1104 m S 69.3528 144.1104 m S 69.3528 155.5554 m S 75.182 149.8329 m S 0 g 1 w 4 M 75.182 161.278 m F 98.4991 161.278 m F 75.182 138.3879 m F 98.4991 138.3879 m F 0 G 0.3 w 10 M 115.9869 167.0006 m S 115.9869 155.5554 m S 104.3284 155.5554 m S 104.3284 167.0006 m S 110.1576 161.278 m S 139.304 144.1104 m S 139.304 132.6653 m S 127.6455 132.6653 m S 127.6455 144.1104 m S 133.4747 138.3879 m S 127.6455 155.5554 m S 127.6455 144.1104 m S 115.9869 144.1104 m S 115.9869 155.5554 m S 121.8162 149.8329 m S 127.6455 167.0006 m S 127.6455 155.5554 m S 115.9869 155.5554 m S 115.9869 167.0006 m S 121.8162 161.278 m S 139.304 167.0006 m S 139.304 155.5554 m S 127.6455 155.5554 m S 127.6455 167.0006 m S 133.4747 161.278 m S 139.304 155.5554 m S 139.304 144.1104 m S 127.6455 144.1104 m S 127.6455 155.5554 m S 133.4747 149.8329 m S 127.6455 144.1104 m S 127.6455 132.6653 m S 115.9869 132.6653 m S 115.9869 144.1104 m S 121.8162 138.3879 m S 115.9869 144.1104 m S 115.9869 132.6653 m S 104.3284 132.6653 m S 104.3284 144.1104 m S 110.1576 138.3879 m S 115.9869 155.5554 m S 115.9869 144.1104 m S 104.3284 144.1104 m S 104.3284 155.5554 m S 110.1576 149.8329 m S 0 g 1 w 4 M 110.1576 161.278 m F 133.4747 161.278 m F 110.1576 138.3879 m F 133.4747 138.3879 m F 0 G 0.3 w 10 M 139.304 155.5554 m S 139.304 167.0006 m S 139.304 132.6653 m S 139.304 144.1104 m S 139.304 144.1104 m S 139.304 155.5554 m S 46.0357 132.6653 m S 34.3772 132.6653 m S 57.6942 132.6653 m S 46.0357 132.6653 m S 69.3528 132.6653 m S 57.6942 132.6653 m S 81.0113 132.6653 m S 69.3528 132.6653 m S 92.6698 132.6653 m S 81.0113 132.6653 m S 104.3284 132.6653 m S 92.6698 132.6653 m S 115.9869 132.6653 m S 104.3284 132.6653 m S 127.6455 132.6653 m S 115.9869 132.6653 m S 139.304 132.6653 m S 127.6455 132.6653 m S 139.304 132.6653 m S u 115.9869 235.6709 m S 115.9869 224.2259 m S 104.3284 224.2259 m S 104.3284 235.6709 m S 110.1576 229.9484 m S U u 139.304 212.7808 m S 139.304 201.3357 m S 127.6455 201.3357 m S 127.6455 212.7808 m S 133.4747 207.0583 m S U u 127.6455 224.2259 m S 127.6455 212.7808 m S 115.9869 212.7808 m S 115.9869 224.2259 m S 121.8162 218.5033 m S U u 127.6455 235.6709 m S 127.6455 224.2259 m S 115.9869 224.2259 m S 115.9869 235.6709 m S 121.8162 229.9484 m S U u 139.304 235.6709 m S 139.304 224.2259 m S 127.6455 224.2259 m S 127.6455 235.6709 m S 133.4747 229.9484 m S U u 139.304 224.2259 m S 139.304 212.7808 m S 127.6455 212.7808 m S 127.6455 224.2259 m S 133.4747 218.5033 m S U u 127.6455 212.7808 m S 127.6455 201.3357 m S 115.9869 201.3357 m S 115.9869 212.7808 m S 121.8162 207.0583 m S U 115.9869 212.7808 m S 115.9869 201.3357 m S 104.3284 201.3357 m S 104.3284 212.7808 m S 110.1576 207.0583 m S 115.9869 224.2259 m S 115.9869 212.7808 m S 104.3284 212.7808 m S 104.3284 224.2259 m S 110.1576 218.5033 m S 0 g 1 w 4 M 110.1576 229.9484 m F 133.4747 229.9484 m F 110.1576 207.0583 m F 133.4747 207.0583 m F u 0 G 0.3 w 10 M 150.9626 235.6709 m S 150.9626 224.2259 m S 139.304 224.2259 m S 139.304 235.6709 m S 145.1333 229.9484 m S U 174.2796 212.7808 m S 174.2796 201.3357 m S 162.6211 201.3357 m S 162.6211 212.7808 m S 168.4504 207.0583 m S 162.6211 224.2259 m S 162.6211 212.7808 m S 150.9626 212.7808 m S 150.9626 224.2259 m S 156.7918 218.5033 m S u 162.6211 235.6709 m S 162.6211 224.2259 m S 150.9626 224.2259 m S 150.9626 235.6709 m S 156.7918 229.9484 m S U u 174.2796 235.6709 m S 174.2796 224.2259 m S 162.6211 224.2259 m S 162.6211 235.6709 m S 168.4504 229.9484 m S U 174.2796 224.2259 m S 174.2796 212.7808 m S 162.6211 212.7808 m S 162.6211 224.2259 m S 168.4504 218.5033 m S 162.6211 212.7808 m S 162.6211 201.3357 m S 150.9626 201.3357 m S 150.9626 212.7808 m S 156.7918 207.0583 m S 150.9626 212.7808 m S 150.9626 201.3357 m S 139.304 201.3357 m S 139.304 212.7808 m S 145.1333 207.0583 m S 150.9626 224.2259 m S 150.9626 212.7808 m S 139.304 212.7808 m S 139.304 224.2259 m S 145.1333 218.5033 m S 0 g 1 w 4 M 145.1333 229.9484 m F 168.4504 229.9484 m F 145.1333 207.0583 m F 168.4504 207.0583 m F u 0 G 0.3 w 10 M 185.9382 235.6709 m S 185.9382 224.2259 m S 174.2796 224.2259 m S 174.2796 235.6709 m S 180.1089 229.9484 m S U u 209.2552 212.7808 m S 209.2552 201.3357 m S 197.5967 201.3357 m S 197.5967 212.7808 m S 203.426 207.0583 m S U u 197.5967 224.2259 m S 197.5967 212.7808 m S 185.9382 212.7808 m S 185.9382 224.2259 m S 191.7674 218.5033 m S U u 197.5967 235.6709 m S 197.5967 224.2259 m S 185.9382 224.2259 m S 185.9382 235.6709 m S 191.7674 229.9484 m S U u 209.2552 235.6709 m S 209.2552 224.2259 m S 197.5967 224.2259 m S 197.5967 235.6709 m S 203.426 229.9484 m S U u 209.2552 224.2259 m S 209.2552 212.7808 m S 197.5967 212.7808 m S 197.5967 224.2259 m S 203.426 218.5033 m S U u 197.5967 212.7808 m S 197.5967 201.3357 m S 185.9382 201.3357 m S 185.9382 212.7808 m S 191.7674 207.0583 m S U 185.9382 212.7808 m S 185.9382 201.3357 m S 174.2796 201.3357 m S 174.2796 212.7808 m S 180.1089 207.0583 m S 185.9382 224.2259 m S 185.9382 212.7808 m S 174.2796 212.7808 m S 174.2796 224.2259 m S 180.1089 218.5033 m S 0 g 1 w 4 M 180.1089 229.9484 m F 203.426 229.9484 m F 180.1089 207.0583 m F 203.426 207.0583 m F 0 G 0.3 w 10 M 209.2552 224.2259 m S 209.2552 235.6709 m S 209.2552 201.3357 m S 209.2552 212.7808 m S 209.2552 212.7808 m S 209.2552 224.2259 m S 115.9869 201.3357 m S 115.9869 189.8906 m S 104.3284 189.8906 m S 104.3284 201.3357 m S 110.1576 195.6132 m S u 139.304 178.4456 m S 139.304 167.0006 m S 127.6455 167.0006 m S 127.6455 178.4456 m S 133.4747 172.7231 m S U 127.6455 189.8906 m S 127.6455 178.4456 m S 115.9869 178.4456 m S 115.9869 189.8906 m S 121.8162 184.1682 m S 127.6455 201.3357 m S 127.6455 189.8906 m S 115.9869 189.8906 m S 115.9869 201.3357 m S 121.8162 195.6132 m S 139.304 201.3357 m S 139.304 189.8906 m S 127.6455 189.8906 m S 127.6455 201.3357 m S 133.4747 195.6132 m S 139.304 189.8906 m S 139.304 178.4456 m S 127.6455 178.4456 m S 127.6455 189.8906 m S 133.4747 184.1682 m S u 127.6455 178.4456 m S 127.6455 167.0006 m S 115.9869 167.0006 m S 115.9869 178.4456 m S 121.8162 172.7231 m S U 115.9869 178.4456 m S 115.9869 167.0006 m S 104.3284 167.0006 m S 104.3284 178.4456 m S 110.1576 172.7231 m S 115.9869 189.8906 m S 115.9869 178.4456 m S 104.3284 178.4456 m S 104.3284 189.8906 m S 110.1576 184.1682 m S 0 g 1 w 4 M 110.1576 195.6132 m F 133.4747 195.6132 m F 110.1576 172.7231 m F 133.4747 172.7231 m F 0 G 0.3 w 10 M 150.9626 201.3357 m S 150.9626 189.8906 m S 139.304 189.8906 m S 139.304 201.3357 m S 145.1333 195.6132 m S u 174.2796 178.4456 m S 174.2796 167.0006 m S 162.6211 167.0006 m S 162.6211 178.4456 m S 168.4504 172.7231 m S U 162.6211 189.8906 m S 162.6211 178.4456 m S 150.9626 178.4456 m S 150.9626 189.8906 m S 156.7918 184.1682 m S 162.6211 201.3357 m S 162.6211 189.8906 m S 150.9626 189.8906 m S 150.9626 201.3357 m S 156.7918 195.6132 m S 174.2796 201.3357 m S 174.2796 189.8906 m S 162.6211 189.8906 m S 162.6211 201.3357 m S 168.4504 195.6132 m S 174.2796 189.8906 m S 174.2796 178.4456 m S 162.6211 178.4456 m S 162.6211 189.8906 m S 168.4504 184.1682 m S u 162.6211 178.4456 m S 162.6211 167.0006 m S 150.9626 167.0006 m S 150.9626 178.4456 m S 156.7918 172.7231 m S U u 150.9626 178.4456 m S 150.9626 167.0006 m S 139.304 167.0006 m S 139.304 178.4456 m S 145.1333 172.7231 m S U 150.9626 189.8906 m S 150.9626 178.4456 m S 139.304 178.4456 m S 139.304 189.8906 m S 145.1333 184.1682 m S 0 g 1 w 4 M 145.1333 195.6132 m F 168.4504 195.6132 m F 145.1333 172.7231 m F 168.4504 172.7231 m F 0 G 0.3 w 10 M 185.9382 201.3357 m S 185.9382 189.8906 m S 174.2796 189.8906 m S 174.2796 201.3357 m S 180.1089 195.6132 m S u 209.2552 178.4456 m S 209.2552 167.0006 m S 197.5967 167.0006 m S 197.5967 178.4456 m S 203.426 172.7231 m S U 197.5967 189.8906 m S 197.5967 178.4456 m S 185.9382 178.4456 m S 185.9382 189.8906 m S 191.7674 184.1682 m S 197.5967 201.3357 m S 197.5967 189.8906 m S 185.9382 189.8906 m S 185.9382 201.3357 m S 191.7674 195.6132 m S 209.2552 201.3357 m S 209.2552 189.8906 m S 197.5967 189.8906 m S 197.5967 201.3357 m S 203.426 195.6132 m S 209.2552 189.8906 m S 209.2552 178.4456 m S 197.5967 178.4456 m S 197.5967 189.8906 m S 203.426 184.1682 m S u 197.5967 178.4456 m S 197.5967 167.0006 m S 185.9382 167.0006 m S 185.9382 178.4456 m S 191.7674 172.7231 m S U u 185.9382 178.4456 m S 185.9382 167.0006 m S 174.2796 167.0006 m S 174.2796 178.4456 m S 180.1089 172.7231 m S U 185.9382 189.8906 m S 185.9382 178.4456 m S 174.2796 178.4456 m S 174.2796 189.8906 m S 180.1089 184.1682 m S 0 g 1 w 4 M 180.1089 195.6132 m F 203.426 195.6132 m F 180.1089 172.7231 m F 203.426 172.7231 m F 0 G 0.3 w 10 M 209.2552 189.8906 m S 209.2552 201.3357 m S 209.2552 167.0006 m S 209.2552 178.4456 m S 209.2552 178.4456 m S 209.2552 189.8906 m S 0 g 1 w 4 M 110.1576 161.278 m F 133.4747 161.278 m F 145.1333 161.278 m F 168.4504 161.278 m F 180.1089 161.278 m F 203.426 161.278 m F 0 G 0.3 w 10 M 115.9869 167.0006 m S 115.9869 155.5554 m S 104.3284 155.5554 m S 104.3284 167.0006 m S 110.1576 161.278 m S 139.304 144.1104 m S 139.304 132.6653 m S 127.6455 132.6653 m S 127.6455 144.1104 m S 133.4747 138.3879 m S 127.6455 155.5554 m S 127.6455 144.1104 m S 115.9869 144.1104 m S 115.9869 155.5554 m S 121.8162 149.8329 m S 127.6455 167.0006 m S 127.6455 155.5554 m S 115.9869 155.5554 m S 115.9869 167.0006 m S 121.8162 161.278 m S 139.304 167.0006 m S 139.304 155.5554 m S 127.6455 155.5554 m S 127.6455 167.0006 m S 133.4747 161.278 m S 139.304 155.5554 m S 139.304 144.1104 m S 127.6455 144.1104 m S 127.6455 155.5554 m S 133.4747 149.8329 m S 127.6455 144.1104 m S 127.6455 132.6653 m S 115.9869 132.6653 m S 115.9869 144.1104 m S 121.8162 138.3879 m S 115.9869 144.1104 m S 115.9869 132.6653 m S 104.3284 132.6653 m S 104.3284 144.1104 m S 110.1576 138.3879 m S 115.9869 155.5554 m S 115.9869 144.1104 m S 104.3284 144.1104 m S 104.3284 155.5554 m S 110.1576 149.8329 m S 0 g 1 w 4 M 110.1576 161.278 m F 133.4747 161.278 m F 110.1576 138.3879 m F 133.4747 138.3879 m F 0 G 0.3 w 10 M 150.9626 167.0006 m S 150.9626 155.5554 m S 139.304 155.5554 m S 139.304 167.0006 m S 145.1333 161.278 m S 174.2796 144.1104 m S 174.2796 132.6653 m S 162.6211 132.6653 m S 162.6211 144.1104 m S 168.4504 138.3879 m S 162.6211 155.5554 m S 162.6211 144.1104 m S 150.9626 144.1104 m S 150.9626 155.5554 m S 156.7918 149.8329 m S 162.6211 167.0006 m S 162.6211 155.5554 m S 150.9626 155.5554 m S 150.9626 167.0006 m S 156.7918 161.278 m S 174.2796 167.0006 m S 174.2796 155.5554 m S 162.6211 155.5554 m S 162.6211 167.0006 m S 168.4504 161.278 m S 174.2796 155.5554 m S 174.2796 144.1104 m S 162.6211 144.1104 m S 162.6211 155.5554 m S 168.4504 149.8329 m S 162.6211 144.1104 m S 162.6211 132.6653 m S 150.9626 132.6653 m S 150.9626 144.1104 m S 156.7918 138.3879 m S 150.9626 144.1104 m S 150.9626 132.6653 m S 139.304 132.6653 m S 139.304 144.1104 m S 145.1333 138.3879 m S 150.9626 155.5554 m S 150.9626 144.1104 m S 139.304 144.1104 m S 139.304 155.5554 m S 145.1333 149.8329 m S 0 g 1 w 4 M 145.1333 161.278 m F 168.4504 161.278 m F 145.1333 138.3879 m F 168.4504 138.3879 m F 0 G 0.3 w 10 M 185.9382 167.0006 m S 185.9382 155.5554 m S 174.2796 155.5554 m S 174.2796 167.0006 m S 180.1089 161.278 m S 209.2552 144.1104 m S 209.2552 132.6653 m S 197.5967 132.6653 m S 197.5967 144.1104 m S 203.426 138.3879 m S 197.5967 155.5554 m S 197.5967 144.1104 m S 185.9382 144.1104 m S 185.9382 155.5554 m S 191.7674 149.8329 m S 197.5967 167.0006 m S 197.5967 155.5554 m S 185.9382 155.5554 m S 185.9382 167.0006 m S 191.7674 161.278 m S 209.2552 167.0006 m S 209.2552 155.5554 m S 197.5967 155.5554 m S 197.5967 167.0006 m S 203.426 161.278 m S 209.2552 155.5554 m S 209.2552 144.1104 m S 197.5967 144.1104 m S 197.5967 155.5554 m S 203.426 149.8329 m S 197.5967 144.1104 m S 197.5967 132.6653 m S 185.9382 132.6653 m S 185.9382 144.1104 m S 191.7674 138.3879 m S 185.9382 144.1104 m S 185.9382 132.6653 m S 174.2796 132.6653 m S 174.2796 144.1104 m S 180.1089 138.3879 m S 185.9382 155.5554 m S 185.9382 144.1104 m S 174.2796 144.1104 m S 174.2796 155.5554 m S 180.1089 149.8329 m S 0 g 1 w 4 M 180.1089 161.278 m F 203.426 161.278 m F 180.1089 138.3879 m F 203.426 138.3879 m F 0 G 0.3 w 10 M 209.2552 155.5554 m S 209.2552 167.0006 m S 209.2552 132.6653 m S 209.2552 144.1104 m S 209.2552 144.1104 m S 209.2552 155.5554 m S 115.9869 132.6653 m S 104.3284 132.6653 m S 127.6455 132.6653 m S 115.9869 132.6653 m S 139.304 132.6653 m S 127.6455 132.6653 m S 150.9626 132.6653 m S 139.304 132.6653 m S 162.6211 132.6653 m S 150.9626 132.6653 m S 174.2796 132.6653 m S 162.6211 132.6653 m S 185.9382 132.6653 m S 174.2796 132.6653 m S 197.5967 132.6653 m S 185.9382 132.6653 m S 209.2552 132.6653 m S 197.5967 132.6653 m S 209.2552 132.6653 m S 46.0357 167.0006 m S 46.0357 155.5555 m S 34.3772 155.5555 m S 34.3772 167.0006 m S 40.2064 161.278 m S 69.3528 144.1104 m S 69.3528 132.6653 m S 57.6942 132.6653 m S 57.6942 144.1104 m S 63.5235 138.3879 m S 57.6942 155.5555 m S 57.6942 144.1104 m S 46.0357 144.1104 m S 46.0357 155.5555 m S 51.865 149.833 m S 57.6942 167.0006 m S 57.6942 155.5555 m S 46.0357 155.5555 m S 46.0357 167.0006 m S 51.865 161.278 m S 69.3528 167.0006 m S 69.3528 155.5555 m S 57.6942 155.5555 m S 57.6942 167.0006 m S 63.5235 161.278 m S 69.3528 155.5555 m S 69.3528 144.1104 m S 57.6942 144.1104 m S 57.6942 155.5555 m S 63.5235 149.833 m S 57.6942 144.1104 m S 57.6942 132.6653 m S 46.0357 132.6653 m S 46.0357 144.1104 m S 51.865 138.3879 m S 46.0357 144.1104 m S 46.0357 132.6653 m S 34.3772 132.6653 m S 34.3772 144.1104 m S 40.2064 138.3879 m S 46.0357 155.5555 m S 46.0357 144.1104 m S 34.3772 144.1104 m S 34.3772 155.5555 m S 40.2064 149.833 m S 0 g 1 w 4 M 40.2064 161.278 m F 63.5235 161.278 m F 40.2064 138.3879 m F 63.5235 138.3879 m F 0 G 0.3 w 10 M 81.0113 167.0006 m S 81.0113 155.5555 m S 69.3528 155.5555 m S 69.3528 167.0006 m S 75.182 161.278 m S 104.3284 144.1104 m S 104.3284 132.6653 m S 92.6698 132.6653 m S 92.6698 144.1104 m S 98.4991 138.3879 m S 92.6698 155.5555 m S 92.6698 144.1104 m S 81.0113 144.1104 m S 81.0113 155.5555 m S 86.8406 149.833 m S 92.6698 167.0006 m S 92.6698 155.5555 m S 81.0113 155.5555 m S 81.0113 167.0006 m S 86.8406 161.278 m S 104.3284 167.0006 m S 104.3284 155.5555 m S 92.6698 155.5555 m S 92.6698 167.0006 m S 98.4991 161.278 m S 104.3284 155.5555 m S 104.3284 144.1104 m S 92.6698 144.1104 m S 92.6698 155.5555 m S 98.4991 149.833 m S 92.6698 144.1104 m S 92.6698 132.6653 m S 81.0113 132.6653 m S 81.0113 144.1104 m S 86.8406 138.3879 m S 81.0113 144.1104 m S 81.0113 132.6653 m S 69.3528 132.6653 m S 69.3528 144.1104 m S 75.182 138.3879 m S 81.0113 155.5555 m S 81.0113 144.1104 m S 69.3528 144.1104 m S 69.3528 155.5555 m S 75.182 149.833 m S 0 g 1 w 4 M 75.182 161.278 m F 98.4991 161.278 m F 75.182 138.3879 m F 98.4991 138.3879 m F 0 G 0.3 w 10 M 115.9869 167.0006 m S 115.9869 155.5555 m S 104.3284 155.5555 m S 104.3284 167.0006 m S 110.1576 161.278 m S 139.304 144.1104 m S 139.304 132.6653 m S 127.6455 132.6653 m S 127.6455 144.1104 m S 133.4747 138.3879 m S 127.6455 155.5555 m S 127.6455 144.1104 m S 115.9869 144.1104 m S 115.9869 155.5555 m S 121.8162 149.833 m S 127.6455 167.0006 m S 127.6455 155.5555 m S 115.9869 155.5555 m S 115.9869 167.0006 m S 121.8162 161.278 m S 139.304 167.0006 m S 139.304 155.5555 m S 127.6455 155.5555 m S 127.6455 167.0006 m S 133.4747 161.278 m S 139.304 155.5555 m S 139.304 144.1104 m S 127.6455 144.1104 m S 127.6455 155.5555 m S 133.4747 149.833 m S 127.6455 144.1104 m S 127.6455 132.6653 m S 115.9869 132.6653 m S 115.9869 144.1104 m S 121.8162 138.3879 m S 115.9869 144.1104 m S 115.9869 132.6653 m S 104.3284 132.6653 m S 104.3284 144.1104 m S 110.1576 138.3879 m S 115.9869 155.5555 m S 115.9869 144.1104 m S 104.3284 144.1104 m S 104.3284 155.5555 m S 110.1576 149.833 m S 0 g 1 w 4 M 110.1576 161.278 m F 133.4747 161.278 m F 110.1576 138.3879 m F 133.4747 138.3879 m F 0 G 0.3 w 10 M 139.304 155.5555 m S 139.304 167.0006 m S 139.304 132.6653 m S 139.304 144.1104 m S 139.304 144.1104 m S 139.304 155.5555 m S 46.0357 132.6653 m S 46.0357 121.2203 m S 34.3772 121.2203 m S 34.3772 132.6653 m S 40.2064 126.9428 m S 69.3528 109.7752 m S 69.3528 98.3302 m S 57.6942 98.3302 m S 57.6942 109.7752 m S 63.5235 104.0527 m S 57.6942 121.2203 m S 57.6942 109.7752 m S 46.0357 109.7752 m S 46.0357 121.2203 m S 51.865 115.4978 m S 57.6942 132.6653 m S 57.6942 121.2203 m S 46.0357 121.2203 m S 46.0357 132.6653 m S 51.865 126.9428 m S 69.3528 132.6653 m S 69.3528 121.2203 m S 57.6942 121.2203 m S 57.6942 132.6653 m S 63.5235 126.9428 m S 69.3528 121.2203 m S 69.3528 109.7752 m S 57.6942 109.7752 m S 57.6942 121.2203 m S 63.5235 115.4978 m S 57.6942 109.7752 m S 57.6942 98.3302 m S 46.0357 98.3302 m S 46.0357 109.7752 m S 51.865 104.0527 m S 46.0357 109.7752 m S 46.0357 98.3302 m S 34.3772 98.3302 m S 34.3772 109.7752 m S 40.2064 104.0527 m S 46.0357 121.2203 m S 46.0357 109.7752 m S 34.3772 109.7752 m S 34.3772 121.2203 m S 40.2064 115.4978 m S 0 g 1 w 4 M 40.2064 126.9428 m F 63.5235 126.9428 m F 40.2064 104.0527 m F 63.5235 104.0527 m F 0 G 0.3 w 10 M 81.0113 132.6653 m S 81.0113 121.2203 m S 69.3528 121.2203 m S 69.3528 132.6653 m S 75.182 126.9428 m S 104.3284 109.7752 m S 104.3284 98.3302 m S 92.6698 98.3302 m S 92.6698 109.7752 m S 98.4991 104.0527 m S 92.6698 121.2203 m S 92.6698 109.7752 m S 81.0113 109.7752 m S 81.0113 121.2203 m S 86.8406 115.4978 m S 92.6698 132.6653 m S 92.6698 121.2203 m S 81.0113 121.2203 m S 81.0113 132.6653 m S 86.8406 126.9428 m S 104.3284 132.6653 m S 104.3284 121.2203 m S 92.6698 121.2203 m S 92.6698 132.6653 m S 98.4991 126.9428 m S 104.3284 121.2203 m S 104.3284 109.7752 m S 92.6698 109.7752 m S 92.6698 121.2203 m S 98.4991 115.4978 m S 92.6698 109.7752 m S 92.6698 98.3302 m S 81.0113 98.3302 m S 81.0113 109.7752 m S 86.8406 104.0527 m S 81.0113 109.7752 m S 81.0113 98.3302 m S 69.3528 98.3302 m S 69.3528 109.7752 m S 75.182 104.0527 m S 81.0113 121.2203 m S 81.0113 109.7752 m S 69.3528 109.7752 m S 69.3528 121.2203 m S 75.182 115.4978 m S 0 g 1 w 4 M 75.182 126.9428 m F 98.4991 126.9428 m F 75.182 104.0527 m F 98.4991 104.0527 m F 0 G 0.3 w 10 M 115.9869 132.6653 m S 115.9869 121.2203 m S 104.3284 121.2203 m S 104.3284 132.6653 m S 110.1576 126.9428 m S 139.304 109.7752 m S 139.304 98.3302 m S 127.6455 98.3302 m S 127.6455 109.7752 m S 133.4747 104.0527 m S 127.6455 121.2203 m S 127.6455 109.7752 m S 115.9869 109.7752 m S 115.9869 121.2203 m S 121.8162 115.4978 m S 127.6455 132.6653 m S 127.6455 121.2203 m S 115.9869 121.2203 m S 115.9869 132.6653 m S 121.8162 126.9428 m S 139.304 132.6653 m S 139.304 121.2203 m S 127.6455 121.2203 m S 127.6455 132.6653 m S 133.4747 126.9428 m S 139.304 121.2203 m S 139.304 109.7752 m S 127.6455 109.7752 m S 127.6455 121.2203 m S 133.4747 115.4978 m S 127.6455 109.7752 m S 127.6455 98.3302 m S 115.9869 98.3302 m S 115.9869 109.7752 m S 121.8162 104.0527 m S 115.9869 109.7752 m S 115.9869 98.3302 m S 104.3284 98.3302 m S 104.3284 109.7752 m S 110.1576 104.0527 m S 115.9869 121.2203 m S 115.9869 109.7752 m S 104.3284 109.7752 m S 104.3284 121.2203 m S 110.1576 115.4978 m S 0 g 1 w 4 M 110.1576 126.9428 m F 133.4747 126.9428 m F 110.1576 104.0527 m F 133.4747 104.0527 m F 0 G 0.3 w 10 M 139.304 121.2203 m S 139.304 132.6653 m S 139.304 98.3302 m S 139.304 109.7752 m S 139.304 109.7752 m S 139.304 121.2203 m S 0 g 1 w 4 M 40.2064 92.6077 m F 63.5235 92.6077 m F 75.182 92.6077 m F 98.4991 92.6077 m F 110.1576 92.6077 m F 133.4747 92.6077 m F 0 G 0.3 w 10 M 46.0357 98.3302 m S 46.0357 86.8851 m S 34.3772 86.8851 m S 34.3772 98.3302 m S 40.2064 92.6077 m S u 69.3528 75.44 m S 69.3528 63.995 m S 57.6942 63.995 m S 57.6942 75.44 m S 63.5235 69.7175 m S U u 57.6942 86.8851 m S 57.6942 75.44 m S 46.0357 75.44 m S 46.0357 86.8851 m S 51.865 81.1626 m S U 57.6942 98.3302 m S 57.6942 86.8851 m S 46.0357 86.8851 m S 46.0357 98.3302 m S 51.865 92.6077 m S 69.3528 98.3302 m S 69.3528 86.8851 m S 57.6942 86.8851 m S 57.6942 98.3302 m S 63.5235 92.6077 m S u 69.3528 86.8851 m S 69.3528 75.44 m S 57.6942 75.44 m S 57.6942 86.8851 m S 63.5235 81.1626 m S U u 57.6942 75.44 m S 57.6942 63.995 m S 46.0357 63.995 m S 46.0357 75.44 m S 51.865 69.7175 m S U u 46.0357 75.44 m S 46.0357 63.995 m S 34.3772 63.995 m S 34.3772 75.44 m S 40.2064 69.7175 m S U u 46.0357 86.8851 m S 46.0357 75.44 m S 34.3772 75.44 m S 34.3772 86.8851 m S 40.2064 81.1626 m S U 0 g 1 w 4 M 40.2064 92.6077 m F 63.5235 92.6077 m F 40.2064 69.7175 m F 63.5235 69.7175 m F 0 G 0.3 w 10 M 81.0113 98.3302 m S 81.0113 86.8851 m S 69.3528 86.8851 m S 69.3528 98.3302 m S 75.182 92.6077 m S u 104.3284 75.44 m S 104.3284 63.995 m S 92.6698 63.995 m S 92.6698 75.44 m S 98.4991 69.7175 m S U u 92.6698 86.8851 m S 92.6698 75.44 m S 81.0113 75.44 m S 81.0113 86.8851 m S 86.8406 81.1626 m S U 92.6698 98.3302 m S 92.6698 86.8851 m S 81.0113 86.8851 m S 81.0113 98.3302 m S 86.8406 92.6077 m S 104.3284 98.3302 m S 104.3284 86.8851 m S 92.6698 86.8851 m S 92.6698 98.3302 m S 98.4991 92.6077 m S u 104.3284 86.8851 m S 104.3284 75.44 m S 92.6698 75.44 m S 92.6698 86.8851 m S 98.4991 81.1626 m S U u 92.6698 75.44 m S 92.6698 63.995 m S 81.0113 63.995 m S 81.0113 75.44 m S 86.8406 69.7175 m S U u 81.0113 75.44 m S 81.0113 63.995 m S 69.3528 63.995 m S 69.3528 75.44 m S 75.182 69.7175 m S U u 81.0113 86.8851 m S 81.0113 75.44 m S 69.3528 75.44 m S 69.3528 86.8851 m S 75.182 81.1626 m S U 0 g 1 w 4 M 75.182 92.6077 m F 98.4991 92.6077 m F 75.182 69.7175 m F 98.4991 69.7175 m F 0 G 0.3 w 10 M 115.9869 98.3302 m S 115.9869 86.8851 m S 104.3284 86.8851 m S 104.3284 98.3302 m S 110.1576 92.6077 m S u 139.304 75.44 m S 139.304 63.995 m S 127.6455 63.995 m S 127.6455 75.44 m S 133.4747 69.7175 m S U u 127.6455 86.8851 m S 127.6455 75.44 m S 115.9869 75.44 m S 115.9869 86.8851 m S 121.8162 81.1626 m S U 127.6455 98.3302 m S 127.6455 86.8851 m S 115.9869 86.8851 m S 115.9869 98.3302 m S 121.8162 92.6077 m S 139.304 98.3302 m S 139.304 86.8851 m S 127.6455 86.8851 m S 127.6455 98.3302 m S 133.4747 92.6077 m S u 139.304 86.8851 m S 139.304 75.44 m S 127.6455 75.44 m S 127.6455 86.8851 m S 133.4747 81.1626 m S U u 127.6455 75.44 m S 127.6455 63.995 m S 115.9869 63.995 m S 115.9869 75.44 m S 121.8162 69.7175 m S U u 115.9869 75.44 m S 115.9869 63.995 m S 104.3284 63.995 m S 104.3284 75.44 m S 110.1576 69.7175 m S U u 115.9869 86.8851 m S 115.9869 75.44 m S 104.3284 75.44 m S 104.3284 86.8851 m S 110.1576 81.1626 m S U 0 g 1 w 4 M 110.1576 92.6077 m F 133.4747 92.6077 m F 110.1576 69.7175 m F 133.4747 69.7175 m F 0 G 0.3 w 10 M 139.304 86.8851 m S 139.304 98.3302 m S 139.304 63.995 m S 139.304 75.44 m S 139.304 75.44 m S 139.304 86.8851 m S 46.0357 63.995 m S 34.3772 63.995 m S 57.6942 63.995 m S 46.0357 63.995 m S 69.3528 63.995 m S 57.6942 63.995 m S 81.0113 63.995 m S 69.3528 63.995 m S 92.6698 63.995 m S 81.0113 63.995 m S 104.3284 63.995 m S 92.6698 63.995 m S 115.9869 63.995 m S 104.3284 63.995 m S 127.6455 63.995 m S 115.9869 63.995 m S 139.304 63.995 m S 127.6455 63.995 m S 139.304 63.995 m S 115.9869 167.0006 m S 115.9869 155.5555 m S 104.3284 155.5555 m S 104.3284 167.0006 m S 110.1576 161.278 m S 139.304 144.1104 m S 139.304 132.6653 m S 127.6455 132.6653 m S 127.6455 144.1104 m S 133.4747 138.3879 m S 127.6455 155.5555 m S 127.6455 144.1104 m S 115.9869 144.1104 m S 115.9869 155.5555 m S 121.8162 149.833 m S 127.6455 167.0006 m S 127.6455 155.5555 m S 115.9869 155.5555 m S 115.9869 167.0006 m S 121.8162 161.278 m S 139.304 167.0006 m S 139.304 155.5555 m S 127.6455 155.5555 m S 127.6455 167.0006 m S 133.4747 161.278 m S 139.304 155.5555 m S 139.304 144.1104 m S 127.6455 144.1104 m S 127.6455 155.5555 m S 133.4747 149.833 m S 127.6455 144.1104 m S 127.6455 132.6653 m S 115.9869 132.6653 m S 115.9869 144.1104 m S 121.8162 138.3879 m S 115.9869 144.1104 m S 115.9869 132.6653 m S 104.3284 132.6653 m S 104.3284 144.1104 m S 110.1576 138.3879 m S 115.9869 155.5555 m S 115.9869 144.1104 m S 104.3284 144.1104 m S 104.3284 155.5555 m S 110.1576 149.833 m S 0 g 1 w 4 M 110.1576 161.278 m F 133.4747 161.278 m F 110.1576 138.3879 m F 133.4747 138.3879 m F 0 G 0.3 w 10 M 150.9626 167.0006 m S 150.9626 155.5555 m S 139.304 155.5555 m S 139.304 167.0006 m S 145.1333 161.278 m S 174.2796 144.1104 m S 174.2796 132.6653 m S 162.6211 132.6653 m S 162.6211 144.1104 m S 168.4504 138.3879 m S 162.6211 155.5555 m S 162.6211 144.1104 m S 150.9626 144.1104 m S 150.9626 155.5555 m S 156.7918 149.833 m S 162.6211 167.0006 m S 162.6211 155.5555 m S 150.9626 155.5555 m S 150.9626 167.0006 m S 156.7918 161.278 m S 174.2796 167.0006 m S 174.2796 155.5555 m S 162.6211 155.5555 m S 162.6211 167.0006 m S 168.4504 161.278 m S 174.2796 155.5555 m S 174.2796 144.1104 m S 162.6211 144.1104 m S 162.6211 155.5555 m S 168.4504 149.833 m S 162.6211 144.1104 m S 162.6211 132.6653 m S 150.9626 132.6653 m S 150.9626 144.1104 m S 156.7918 138.3879 m S 150.9626 144.1104 m S 150.9626 132.6653 m S 139.304 132.6653 m S 139.304 144.1104 m S 145.1333 138.3879 m S 150.9626 155.5555 m S 150.9626 144.1104 m S 139.304 144.1104 m S 139.304 155.5555 m S 145.1333 149.833 m S 0 g 1 w 4 M 145.1333 161.278 m F 168.4504 161.278 m F 145.1333 138.3879 m F 168.4504 138.3879 m F 0 G 0.3 w 10 M 185.9382 167.0006 m S 185.9382 155.5555 m S 174.2796 155.5555 m S 174.2796 167.0006 m S 180.1089 161.278 m S 209.2552 144.1104 m S 209.2552 132.6653 m S 197.5967 132.6653 m S 197.5967 144.1104 m S 203.426 138.3879 m S 197.5967 155.5555 m S 197.5967 144.1104 m S 185.9382 144.1104 m S 185.9382 155.5555 m S 191.7674 149.833 m S 197.5967 167.0006 m S 197.5967 155.5555 m S 185.9382 155.5555 m S 185.9382 167.0006 m S 191.7674 161.278 m S 209.2552 167.0006 m S 209.2552 155.5555 m S 197.5967 155.5555 m S 197.5967 167.0006 m S 203.426 161.278 m S 209.2552 155.5555 m S 209.2552 144.1104 m S 197.5967 144.1104 m S 197.5967 155.5555 m S 203.426 149.833 m S 197.5967 144.1104 m S 197.5967 132.6653 m S 185.9382 132.6653 m S 185.9382 144.1104 m S 191.7674 138.3879 m S 185.9382 144.1104 m S 185.9382 132.6653 m S 174.2796 132.6653 m S 174.2796 144.1104 m S 180.1089 138.3879 m S 185.9382 155.5555 m S 185.9382 144.1104 m S 174.2796 144.1104 m S 174.2796 155.5555 m S 180.1089 149.833 m S 0 g 1 w 4 M 180.1089 161.278 m F 203.426 161.278 m F 180.1089 138.3879 m F 203.426 138.3879 m F 0 G 0.3 w 10 M 209.2552 155.5555 m S 209.2552 167.0006 m S 209.2552 132.6653 m S 209.2552 144.1104 m S 209.2552 144.1104 m S 209.2552 155.5555 m S 115.9869 132.6653 m S 115.9869 121.2203 m S 104.3284 121.2203 m S 104.3284 132.6653 m S 110.1576 126.9428 m S 139.304 109.7752 m S 139.304 98.3302 m S 127.6455 98.3302 m S 127.6455 109.7752 m S 133.4747 104.0527 m S 127.6455 121.2203 m S 127.6455 109.7752 m S 115.9869 109.7752 m S 115.9869 121.2203 m S 121.8162 115.4978 m S 127.6455 132.6653 m S 127.6455 121.2203 m S 115.9869 121.2203 m S 115.9869 132.6653 m S 121.8162 126.9428 m S 139.304 132.6653 m S 139.304 121.2203 m S 127.6455 121.2203 m S 127.6455 132.6653 m S 133.4747 126.9428 m S 139.304 121.2203 m S 139.304 109.7752 m S 127.6455 109.7752 m S 127.6455 121.2203 m S 133.4747 115.4978 m S 127.6455 109.7752 m S 127.6455 98.3302 m S 115.9869 98.3302 m S 115.9869 109.7752 m S 121.8162 104.0527 m S 115.9869 109.7752 m S 115.9869 98.3302 m S 104.3284 98.3302 m S 104.3284 109.7752 m S 110.1576 104.0527 m S 115.9869 121.2203 m S 115.9869 109.7752 m S 104.3284 109.7752 m S 104.3284 121.2203 m S 110.1576 115.4978 m S 0 g 1 w 4 M 110.1576 126.9428 m F 133.4747 126.9428 m F 110.1576 104.0527 m F 133.4747 104.0527 m F 0 G 0.3 w 10 M 150.9626 132.6653 m S 150.9626 121.2203 m S 139.304 121.2203 m S 139.304 132.6653 m S 145.1333 126.9428 m S 174.2796 109.7752 m S 174.2796 98.3302 m S 162.6211 98.3302 m S 162.6211 109.7752 m S 168.4504 104.0527 m S 162.6211 121.2203 m S 162.6211 109.7752 m S 150.9626 109.7752 m S 150.9626 121.2203 m S 156.7918 115.4978 m S 162.6211 132.6653 m S 162.6211 121.2203 m S 150.9626 121.2203 m S 150.9626 132.6653 m S 156.7918 126.9428 m S 174.2796 132.6653 m S 174.2796 121.2203 m S 162.6211 121.2203 m S 162.6211 132.6653 m S 168.4504 126.9428 m S 174.2796 121.2203 m S 174.2796 109.7752 m S 162.6211 109.7752 m S 162.6211 121.2203 m S 168.4504 115.4978 m S 162.6211 109.7752 m S 162.6211 98.3302 m S 150.9626 98.3302 m S 150.9626 109.7752 m S 156.7918 104.0527 m S 150.9626 109.7752 m S 150.9626 98.3302 m S 139.304 98.3302 m S 139.304 109.7752 m S 145.1333 104.0527 m S 150.9626 121.2203 m S 150.9626 109.7752 m S 139.304 109.7752 m S 139.304 121.2203 m S 145.1333 115.4978 m S 0 g 1 w 4 M 145.1333 126.9428 m F 168.4504 126.9428 m F 145.1333 104.0527 m F 168.4504 104.0527 m F 0 G 0.3 w 10 M 185.9382 132.6653 m S 185.9382 121.2203 m S 174.2796 121.2203 m S 174.2796 132.6653 m S 180.1089 126.9428 m S 209.2552 109.7752 m S 209.2552 98.3302 m S 197.5967 98.3302 m S 197.5967 109.7752 m S 203.426 104.0527 m S 197.5967 121.2203 m S 197.5967 109.7752 m S 185.9382 109.7752 m S 185.9382 121.2203 m S 191.7674 115.4978 m S 197.5967 132.6653 m S 197.5967 121.2203 m S 185.9382 121.2203 m S 185.9382 132.6653 m S 191.7674 126.9428 m S 209.2552 132.6653 m S 209.2552 121.2203 m S 197.5967 121.2203 m S 197.5967 132.6653 m S 203.426 126.9428 m S 209.2552 121.2203 m S 209.2552 109.7752 m S 197.5967 109.7752 m S 197.5967 121.2203 m S 203.426 115.4978 m S 197.5967 109.7752 m S 197.5967 98.3302 m S 185.9382 98.3302 m S 185.9382 109.7752 m S 191.7674 104.0527 m S 185.9382 109.7752 m S 185.9382 98.3302 m S 174.2796 98.3302 m S 174.2796 109.7752 m S 180.1089 104.0527 m S 185.9382 121.2203 m S 185.9382 109.7752 m S 174.2796 109.7752 m S 174.2796 121.2203 m S 180.1089 115.4978 m S 0 g 1 w 4 M 180.1089 126.9428 m F 203.426 126.9428 m F 180.1089 104.0527 m F 203.426 104.0527 m F 0 G 0.3 w 10 M 209.2552 121.2203 m S 209.2552 132.6653 m S 209.2552 98.3302 m S 209.2552 109.7752 m S 209.2552 109.7752 m S 209.2552 121.2203 m S 0 g 1 w 4 M 110.1576 92.6077 m F 133.4747 92.6077 m F 145.1333 92.6077 m F 168.4504 92.6077 m F 180.1089 92.6077 m F 203.426 92.6077 m F 0 G 0.3 w 10 M 115.9869 98.3302 m S 115.9869 86.8851 m S 104.3284 86.8851 m S 104.3284 98.3302 m S 110.1576 92.6077 m S u 139.304 75.44 m S 139.304 63.995 m S 127.6455 63.995 m S 127.6455 75.44 m S 133.4747 69.7175 m S U u 127.6455 86.8851 m S 127.6455 75.44 m S 115.9869 75.44 m S 115.9869 86.8851 m S 121.8162 81.1626 m S U 127.6455 98.3302 m S 127.6455 86.8851 m S 115.9869 86.8851 m S 115.9869 98.3302 m S 121.8162 92.6077 m S 139.304 98.3302 m S 139.304 86.8851 m S 127.6455 86.8851 m S 127.6455 98.3302 m S 133.4747 92.6077 m S u 139.304 86.8851 m S 139.304 75.44 m S 127.6455 75.44 m S 127.6455 86.8851 m S 133.4747 81.1626 m S U u 127.6455 75.44 m S 127.6455 63.995 m S 115.9869 63.995 m S 115.9869 75.44 m S 121.8162 69.7175 m S U u 115.9869 75.44 m S 115.9869 63.995 m S 104.3284 63.995 m S 104.3284 75.44 m S 110.1576 69.7175 m S U u 115.9869 86.8851 m S 115.9869 75.44 m S 104.3284 75.44 m S 104.3284 86.8851 m S 110.1576 81.1626 m S U 0 g 1 w 4 M 110.1576 92.6077 m F 133.4747 92.6077 m F 110.1576 69.7175 m F 133.4747 69.7175 m F 0 G 0.3 w 10 M 150.9626 98.3302 m S 150.9626 86.8851 m S 139.304 86.8851 m S 139.304 98.3302 m S 145.1333 92.6077 m S u 174.2796 75.44 m S 174.2796 63.995 m S 162.6211 63.995 m S 162.6211 75.44 m S 168.4504 69.7175 m S U u 162.6211 86.8851 m S 162.6211 75.44 m S 150.9626 75.44 m S 150.9626 86.8851 m S 156.7918 81.1626 m S U 162.6211 98.3302 m S 162.6211 86.8851 m S 150.9626 86.8851 m S 150.9626 98.3302 m S 156.7918 92.6077 m S 174.2796 98.3302 m S 174.2796 86.8851 m S 162.6211 86.8851 m S 162.6211 98.3302 m S 168.4504 92.6077 m S u 174.2796 86.8851 m S 174.2796 75.44 m S 162.6211 75.44 m S 162.6211 86.8851 m S 168.4504 81.1626 m S U u 162.6211 75.44 m S 162.6211 63.995 m S 150.9626 63.995 m S 150.9626 75.44 m S 156.7918 69.7175 m S U u 150.9626 75.44 m S 150.9626 63.995 m S 139.304 63.995 m S 139.304 75.44 m S 145.1333 69.7175 m S U u 150.9626 86.8851 m S 150.9626 75.44 m S 139.304 75.44 m S 139.304 86.8851 m S 145.1333 81.1626 m S U 0 g 1 w 4 M 145.1333 92.6077 m F 168.4504 92.6077 m F 145.1333 69.7175 m F 168.4504 69.7175 m F 0 G 0.3 w 10 M 185.9382 98.3302 m S 185.9382 86.8851 m S 174.2796 86.8851 m S 174.2796 98.3302 m S 180.1089 92.6077 m S u 209.2552 75.44 m S 209.2552 63.995 m S 197.5967 63.995 m S 197.5967 75.44 m S 203.426 69.7175 m S U u 197.5967 86.8851 m S 197.5967 75.44 m S 185.9382 75.44 m S 185.9382 86.8851 m S 191.7674 81.1626 m S U 197.5967 98.3302 m S 197.5967 86.8851 m S 185.9382 86.8851 m S 185.9382 98.3302 m S 191.7674 92.6077 m S 209.2552 98.3302 m S 209.2552 86.8851 m S 197.5967 86.8851 m S 197.5967 98.3302 m S 203.426 92.6077 m S u 209.2552 86.8851 m S 209.2552 75.44 m S 197.5967 75.44 m S 197.5967 86.8851 m S 203.426 81.1626 m S U u 197.5967 75.44 m S 197.5967 63.995 m S 185.9382 63.995 m S 185.9382 75.44 m S 191.7674 69.7175 m S U u 185.9382 75.44 m S 185.9382 63.995 m S 174.2796 63.995 m S 174.2796 75.44 m S 180.1089 69.7175 m S U u 185.9382 86.8851 m S 185.9382 75.44 m S 174.2796 75.44 m S 174.2796 86.8851 m S 180.1089 81.1626 m S U 0 g 1 w 4 M 180.1089 92.6077 m F 203.426 92.6077 m F 180.1089 69.7175 m F 203.426 69.7175 m F 0 G 0.3 w 10 M 209.2552 86.8851 m S 209.2552 98.3302 m S 209.2552 63.995 m S 209.2552 75.44 m S 209.2552 75.44 m S 209.2552 86.8851 m S 115.9869 63.995 m S 104.3284 63.995 m S 127.6455 63.995 m S 115.9869 63.995 m S 139.304 63.995 m S 127.6455 63.995 m S 150.9626 63.995 m S 139.304 63.995 m S 162.6211 63.995 m S 150.9626 63.995 m S 174.2796 63.995 m S 162.6211 63.995 m S 185.9382 63.995 m S 174.2796 63.995 m S 197.5967 63.995 m S 185.9382 63.995 m S 209.2552 63.995 m S 197.5967 63.995 m S 209.2552 63.995 m S 57.6942 212.7808 m S 0 g 1 w 4 M 57.6942 212.7808 m F 0 G 0.3 w 10 M 57.6942 212.7808 m S 57.6942 212.7808 m S 57.6942 212.7808 m S 0 g 1 w 4 M 57.6942 212.7808 m F 0 G 0.3 w 10 M 57.6942 212.7808 m S 57.6942 212.7808 m S 57.6942 212.7808 m S 0 g 1 w 4 M 57.6942 212.7808 m F 0 G 0.3 w 10 M 57.6942 212.7808 m S 57.6942 212.7808 m S 69.3528 201.3357 m S 0 g 1 w 4 M 69.3528 201.3357 m F 0 G 0.3 w 10 M 69.3528 201.3357 m S 69.3528 201.3357 m S 69.3528 201.3357 m S 0 g 1 w 4 M 69.3528 201.3357 m F 0 G 0.3 w 10 M 69.3528 201.3357 m S 69.3528 201.3357 m S 69.3528 201.3357 m S 0 g 1 w 4 M 69.3528 201.3357 m F 0 G 0.3 w 10 M 69.3528 201.3357 m S 69.3528 201.3357 m S 69.3528 201.3357 m S 0 g 1 w 4 M 69.3528 201.3357 m F 0 G 0.3 w 10 M 69.3528 201.3357 m S 69.3528 201.3357 m S 69.3528 201.3357 m S 0 g 1 w 4 M 69.3528 201.3357 m F 0 G 0.3 w 10 M 69.3528 201.3357 m S 69.3528 201.3357 m S u 1 g 1 w 4 M 69.3528 201.3357 m F U 0 G 0.3 w 10 M 69.3528 201.3357 m S 0 g 1 w 4 M 69.3528 201.3357 m F 0 G 0.3 w 10 M 69.3528 201.3357 m S 69.3528 201.3357 m S 69.3528 212.7808 m S 0 g 1 w 4 M 69.3528 212.7808 m F 0 G 0.3 w 10 M 69.3528 212.7808 m S 69.3528 212.7808 m S 69.3528 212.7808 m S 0 g 1 w 4 M 69.3528 212.7808 m F 0 G 0.3 w 10 M 69.3528 212.7808 m S 69.3528 212.7808 m S 69.3528 212.7808 m S 0 g 1 w 4 M 69.3528 212.7808 m F 0 G 0.3 w 10 M 69.3528 212.7808 m S 69.3528 212.7808 m S 57.6942 201.3357 m S 0 g 1 w 4 M 57.6942 201.3357 m F 0 G 0.3 w 10 M 57.6942 201.3357 m S 57.6942 201.3357 m S 57.6942 201.3357 m S 0 g 1 w 4 M 57.6942 201.3357 m F 0 G 0.3 w 10 M 57.6942 201.3357 m S 57.6942 201.3357 m S 57.6942 201.3357 m S 0 g 1 w 4 M 57.6942 201.3357 m F 0 G 0.3 w 10 M 57.6942 201.3357 m S 57.6942 201.3357 m S 57.6942 189.8906 m S 0 g 1 w 4 M 57.6942 189.8906 m F 0 G 0.3 w 10 M 57.6942 189.8906 m S 57.6942 189.8906 m S 57.6942 189.8906 m S 0 g 1 w 4 M 57.6942 189.8906 m F 0 G 0.3 w 10 M 57.6942 189.8906 m S 57.6942 189.8906 m S 57.6942 189.8906 m S 0 g 1 w 4 M 57.6942 189.8906 m F 0 G 0.3 w 10 M 57.6942 189.8906 m S 57.6942 189.8906 m S 57.6942 178.4456 m S 0 g 1 w 4 M 57.6942 178.4456 m F 0 G 0.3 w 10 M 57.6942 178.4456 m S 57.6942 178.4456 m S 57.6942 178.4456 m S 0 g 1 w 4 M 57.6942 178.4456 m F 0 G 0.3 w 10 M 57.6942 178.4456 m S 57.6942 178.4456 m S 1 g 0.5 w 4 M 57.6942 178.4456 m B 0.3 w 10 M 57.6942 178.4456 m S 0 g 1 w 4 M 57.6942 178.4456 m F 0 G 0.3 w 10 M 57.6942 178.4456 m S 57.6942 178.4456 m S 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 69.3528 167.0006 m S 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 69.3528 167.0006 m S 1 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 69.3528 167.0006 m S 1 g 0.5 w 4 M 69.3528 167.0006 m B 0.3 w 10 M 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 69.3528 167.0006 m S 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 69.3528 167.0006 m S u 1 g 1 w 4 M 69.3528 167.0006 m F U 0 G 0.3 w 10 M 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 69.3528 167.0006 m S 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 69.3528 167.0006 m S 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 69.3528 167.0006 m S u 1 g 1 w 4 M 69.3528 167.0006 m F U 0 G 0.3 w 10 M 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 69.3528 167.0006 m S 69.3528 189.8906 m S 0 g 1 w 4 M 69.3528 189.8906 m F 0 G 0.3 w 10 M 69.3528 189.8906 m S 69.3528 189.8906 m S 69.3528 189.8906 m S 0 g 1 w 4 M 69.3528 189.8906 m F 0 G 0.3 w 10 M 69.3528 189.8906 m S 69.3528 189.8906 m S 69.3528 189.8906 m S 0 g 1 w 4 M 69.3528 189.8906 m F 0 G 0.3 w 10 M 69.3528 189.8906 m S 69.3528 189.8906 m S 57.6942 167.0006 m S 0 g 1 w 4 M 57.6942 167.0006 m F 0 G 0.3 w 10 M 57.6942 167.0006 m S 57.6942 167.0006 m S 57.6942 167.0006 m S 0 g 1 w 4 M 57.6942 167.0006 m F 0 G 0.3 w 10 M 57.6942 167.0006 m S 57.6942 167.0006 m S 57.6942 167.0006 m S 0 g 1 w 4 M 57.6942 167.0006 m F 0 G 0.3 w 10 M 57.6942 167.0006 m S 57.6942 167.0006 m S 69.3528 178.4456 m S 0 g 1 w 4 M 69.3528 178.4456 m F 0 G 0.3 w 10 M 69.3528 178.4456 m S 0 g 1 w 4 M 69.3528 178.4456 m F 0 G 0.3 w 10 M 69.3528 178.4456 m S 0 g 1 w 4 M 69.3528 178.4456 m F 0 G 0.3 w 10 M 69.3528 178.4456 m S 0 g 1 w 4 M 69.3528 178.4456 m F 0 G 0.3 w 10 M 220.9137 235.6709 m S 220.9137 224.2259 m S 209.2552 224.2259 m S 209.2552 235.6709 m S 215.0844 229.9484 m S u 244.2308 212.7808 m S 244.2308 201.3357 m S 232.5722 201.3357 m S 232.5722 212.7808 m S 238.4015 207.0583 m S U 232.5722 224.2259 m S 232.5722 212.7808 m S 220.9137 212.7808 m S 220.9137 224.2259 m S 226.743 218.5033 m S 232.5722 235.6709 m S 232.5722 224.2259 m S 220.9137 224.2259 m S 220.9137 235.6709 m S 226.743 229.9484 m S u 244.2308 235.6709 m S 244.2308 224.2259 m S 232.5722 224.2259 m S 232.5722 235.6709 m S 238.4015 229.9484 m S U u 244.2308 224.2259 m S 244.2308 212.7808 m S 232.5722 212.7808 m S 232.5722 224.2259 m S 238.4015 218.5033 m S U u 232.5722 212.7808 m S 232.5722 201.3357 m S 220.9137 201.3357 m S 220.9137 212.7808 m S 226.743 207.0583 m S U u 220.9137 212.7808 m S 220.9137 201.3357 m S 209.2552 201.3357 m S 209.2552 212.7808 m S 215.0844 207.0583 m S U 220.9137 224.2259 m S 220.9137 212.7808 m S 209.2552 212.7808 m S 209.2552 224.2259 m S 215.0844 218.5033 m S 0 g 1 w 4 M 215.0844 229.9484 m F 238.4015 229.9484 m F 215.0844 207.0583 m F 238.4015 207.0583 m F u 0 G 0.3 w 10 M 255.8893 235.6709 m S 255.8893 224.2259 m S 244.2308 224.2259 m S 244.2308 235.6709 m S 250.0601 229.9484 m S U u 279.2064 212.7808 m S 279.2064 201.3357 m S 267.5479 201.3357 m S 267.5479 212.7808 m S 273.3771 207.0583 m S U u 267.5479 224.2259 m S 267.5479 212.7808 m S 255.8893 212.7808 m S 255.8893 224.2259 m S 261.7186 218.5033 m S U u 267.5479 235.6709 m S 267.5479 224.2259 m S 255.8893 224.2259 m S 255.8893 235.6709 m S 261.7186 229.9484 m S U u 279.2064 235.6709 m S 279.2064 224.2259 m S 267.5479 224.2259 m S 267.5479 235.6709 m S 273.3771 229.9484 m S U u 279.2064 224.2259 m S 279.2064 212.7808 m S 267.5479 212.7808 m S 267.5479 224.2259 m S 273.3771 218.5033 m S U u 267.5479 212.7808 m S 267.5479 201.3357 m S 255.8893 201.3357 m S 255.8893 212.7808 m S 261.7186 207.0583 m S U u 255.8893 212.7808 m S 255.8893 201.3357 m S 244.2308 201.3357 m S 244.2308 212.7808 m S 250.0601 207.0583 m S U u 255.8893 224.2259 m S 255.8893 212.7808 m S 244.2308 212.7808 m S 244.2308 224.2259 m S 250.0601 218.5033 m S U 0 g 1 w 4 M 250.0601 229.9484 m F 273.3771 229.9484 m F 250.0601 207.0583 m F 273.3771 207.0583 m F u 0 G 0.3 w 10 M 290.8649 235.6709 m S 290.8649 224.2259 m S 279.2064 224.2259 m S 279.2064 235.6709 m S 285.0357 229.9484 m S U u 290.8649 212.7808 m S 290.8649 201.3357 m S 279.2064 201.3357 m S 279.2064 212.7808 m S 285.0357 207.0583 m S U u 290.8649 224.2259 m S 290.8649 212.7808 m S 279.2064 212.7808 m S 279.2064 224.2259 m S 285.0357 218.5033 m S U 0 g 1 w 4 M 285.0357 229.9484 m F 285.0357 207.0583 m F 0 G 0.3 w 10 M 220.9137 201.3357 m S 220.9137 189.8906 m S 209.2552 189.8906 m S 209.2552 201.3357 m S 215.0844 195.6132 m S 244.2308 178.4456 m S 244.2308 167.0006 m S 232.5722 167.0006 m S 232.5722 178.4456 m S 238.4015 172.7231 m S 232.5722 189.8906 m S 232.5722 178.4456 m S 220.9137 178.4456 m S 220.9137 189.8906 m S 226.743 184.1682 m S 232.5722 201.3357 m S 232.5722 189.8906 m S 220.9137 189.8906 m S 220.9137 201.3357 m S 226.743 195.6132 m S 244.2308 201.3357 m S 244.2308 189.8906 m S 232.5722 189.8906 m S 232.5722 201.3357 m S 238.4015 195.6132 m S 244.2308 189.8906 m S 244.2308 178.4456 m S 232.5722 178.4456 m S 232.5722 189.8906 m S 238.4015 184.1682 m S 232.5722 178.4456 m S 232.5722 167.0006 m S 220.9137 167.0006 m S 220.9137 178.4456 m S 226.743 172.7231 m S u 220.9137 178.4456 m S 220.9137 167.0006 m S 209.2552 167.0006 m S 209.2552 178.4456 m S 215.0844 172.7231 m S U 220.9137 189.8906 m S 220.9137 178.4456 m S 209.2552 178.4456 m S 209.2552 189.8906 m S 215.0844 184.1682 m S 0 g 1 w 4 M 215.0844 195.6132 m F 238.4015 195.6132 m F 215.0844 172.7231 m F 238.4015 172.7231 m F 0 G 0.3 w 10 M 255.8893 201.3357 m S 255.8893 189.8906 m S 244.2308 189.8906 m S 244.2308 201.3357 m S 250.0601 195.6132 m S u 279.2064 178.4456 m S 279.2064 167.0006 m S 267.5479 167.0006 m S 267.5479 178.4456 m S 273.3771 172.7231 m S U 267.5479 189.8906 m S 267.5479 178.4456 m S 255.8893 178.4456 m S 255.8893 189.8906 m S 261.7186 184.1682 m S 267.5479 201.3357 m S 267.5479 189.8906 m S 255.8893 189.8906 m S 255.8893 201.3357 m S 261.7186 195.6132 m S 279.2064 201.3357 m S 279.2064 189.8906 m S 267.5479 189.8906 m S 267.5479 201.3357 m S 273.3771 195.6132 m S 279.2064 189.8906 m S 279.2064 178.4456 m S 267.5479 178.4456 m S 267.5479 189.8906 m S 273.3771 184.1682 m S u 267.5479 178.4456 m S 267.5479 167.0006 m S 255.8893 167.0006 m S 255.8893 178.4456 m S 261.7186 172.7231 m S U u 255.8893 178.4456 m S 255.8893 167.0006 m S 244.2308 167.0006 m S 244.2308 178.4456 m S 250.0601 172.7231 m S U 255.8893 189.8906 m S 255.8893 178.4456 m S 244.2308 178.4456 m S 244.2308 189.8906 m S 250.0601 184.1682 m S 0 g 1 w 4 M 250.0601 195.6132 m F 273.3771 195.6132 m F 250.0601 172.7231 m F 273.3771 172.7231 m F u 0 G 0.3 w 10 M 290.8649 201.3357 m S 290.8649 189.8906 m S 279.2064 189.8906 m S 279.2064 201.3357 m S 285.0357 195.6132 m S U u 290.8649 178.4456 m S 290.8649 167.0006 m S 279.2064 167.0006 m S 279.2064 178.4456 m S 285.0357 172.7231 m S U u 290.8649 189.8906 m S 290.8649 178.4456 m S 279.2064 178.4456 m S 279.2064 189.8906 m S 285.0357 184.1682 m S U 0 g 1 w 4 M 285.0357 195.6132 m F 285.0357 172.7231 m F 215.0844 161.278 m F 238.4015 161.278 m F 250.0601 161.278 m F 273.3771 161.278 m F 285.0357 161.278 m F 0 G 0.3 w 10 M 220.9137 167.0006 m S 220.9137 155.5554 m S 209.2552 155.5554 m S 209.2552 167.0006 m S 215.0844 161.278 m S 244.2308 144.1104 m S 244.2308 132.6653 m S 232.5722 132.6653 m S 232.5722 144.1104 m S 238.4015 138.3879 m S 232.5722 155.5554 m S 232.5722 144.1104 m S 220.9137 144.1104 m S 220.9137 155.5554 m S 226.743 149.8329 m S 232.5722 167.0006 m S 232.5722 155.5554 m S 220.9137 155.5554 m S 220.9137 167.0006 m S 226.743 161.278 m S 244.2308 167.0006 m S 244.2308 155.5554 m S 232.5722 155.5554 m S 232.5722 167.0006 m S 238.4015 161.278 m S 244.2308 155.5554 m S 244.2308 144.1104 m S 232.5722 144.1104 m S 232.5722 155.5554 m S 238.4015 149.8329 m S 232.5722 144.1104 m S 232.5722 132.6653 m S 220.9137 132.6653 m S 220.9137 144.1104 m S 226.743 138.3879 m S 220.9137 144.1104 m S 220.9137 132.6653 m S 209.2552 132.6653 m S 209.2552 144.1104 m S 215.0844 138.3879 m S 220.9137 155.5554 m S 220.9137 144.1104 m S 209.2552 144.1104 m S 209.2552 155.5554 m S 215.0844 149.8329 m S 0 g 1 w 4 M 215.0844 161.278 m F 238.4015 161.278 m F 215.0844 138.3879 m F 238.4015 138.3879 m F 0 G 0.3 w 10 M 255.8893 167.0006 m S 255.8893 155.5554 m S 244.2308 155.5554 m S 244.2308 167.0006 m S 250.0601 161.278 m S 279.2064 144.1104 m S 279.2064 132.6653 m S 267.5479 132.6653 m S 267.5479 144.1104 m S 273.3771 138.3879 m S 267.5479 155.5554 m S 267.5479 144.1104 m S 255.8893 144.1104 m S 255.8893 155.5554 m S 261.7186 149.8329 m S 267.5479 167.0006 m S 267.5479 155.5554 m S 255.8893 155.5554 m S 255.8893 167.0006 m S 261.7186 161.278 m S 279.2064 167.0006 m S 279.2064 155.5554 m S 267.5479 155.5554 m S 267.5479 167.0006 m S 273.3771 161.278 m S 279.2064 155.5554 m S 279.2064 144.1104 m S 267.5479 144.1104 m S 267.5479 155.5554 m S 273.3771 149.8329 m S 267.5479 144.1104 m S 267.5479 132.6653 m S 255.8893 132.6653 m S 255.8893 144.1104 m S 261.7186 138.3879 m S 255.8893 144.1104 m S 255.8893 132.6653 m S 244.2308 132.6653 m S 244.2308 144.1104 m S 250.0601 138.3879 m S 255.8893 155.5554 m S 255.8893 144.1104 m S 244.2308 144.1104 m S 244.2308 155.5554 m S 250.0601 149.8329 m S 0 g 1 w 4 M 250.0601 161.278 m F 273.3771 161.278 m F 250.0601 138.3879 m F 273.3771 138.3879 m F 0 G 0.3 w 10 M 290.8649 167.0006 m S 290.8649 155.5554 m S 279.2064 155.5554 m S 279.2064 167.0006 m S 285.0357 161.278 m S 290.8649 144.1104 m S 290.8649 155.5554 m S 290.8649 155.5554 m S 290.8649 167.0006 m S 290.8649 132.6653 m S 290.8649 144.1104 m S 290.8649 144.1104 m S 290.8649 132.6653 m S 279.2064 132.6653 m S 279.2064 144.1104 m S 285.0357 138.3879 m S 290.8649 155.5554 m S 290.8649 144.1104 m S 279.2064 144.1104 m S 279.2064 155.5554 m S 285.0357 149.8329 m S 0 g 1 w 4 M 285.0357 161.278 m F 285.0357 138.3879 m F 0 G 0.3 w 10 M 220.9137 132.6653 m S 209.2552 132.6653 m S 232.5722 132.6653 m S 220.9137 132.6653 m S 244.2308 132.6653 m S 232.5722 132.6653 m S 255.8893 132.6653 m S 244.2308 132.6653 m S 267.5479 132.6653 m S 255.8893 132.6653 m S 279.2064 132.6653 m S 267.5479 132.6653 m S 290.8649 132.6653 m S 279.2064 132.6653 m S 290.8649 132.6653 m S u 290.8649 235.6709 m S 290.8649 224.2259 m S 279.2064 224.2259 m S 279.2064 235.6709 m S 285.0357 229.9484 m S U u 290.8649 212.7808 m S 290.8649 201.3357 m S 279.2064 201.3357 m S 279.2064 212.7808 m S 285.0357 207.0583 m S U u 290.8649 224.2259 m S 290.8649 212.7808 m S 279.2064 212.7808 m S 279.2064 224.2259 m S 285.0357 218.5033 m S U 0 g 1 w 4 M 285.0357 229.9484 m F 285.0357 207.0583 m F u 0 G 0.3 w 10 M 290.8649 201.3357 m S 290.8649 189.8906 m S 279.2064 189.8906 m S 279.2064 201.3357 m S 285.0357 195.6132 m S U u 290.8649 178.4456 m S 290.8649 167.0006 m S 279.2064 167.0006 m S 279.2064 178.4456 m S 285.0357 172.7231 m S U u 290.8649 189.8906 m S 290.8649 178.4456 m S 279.2064 178.4456 m S 279.2064 189.8906 m S 285.0357 184.1682 m S U 0 g 1 w 4 M 285.0357 195.6132 m F 285.0357 172.7231 m F 285.0357 161.278 m F 0 G 0.3 w 10 M 290.8649 167.0006 m S 290.8649 155.5554 m S 279.2064 155.5554 m S 279.2064 167.0006 m S 285.0357 161.278 m S 290.8649 144.1104 m S 290.8649 155.5554 m S 290.8649 155.5554 m S 290.8649 167.0006 m S 290.8649 132.6653 m S 290.8649 144.1104 m S 290.8649 144.1104 m S 290.8649 132.6653 m S 279.2064 132.6653 m S 279.2064 144.1104 m S 285.0357 138.3879 m S 290.8649 155.5554 m S 290.8649 144.1104 m S 279.2064 144.1104 m S 279.2064 155.5554 m S 285.0357 149.8329 m S 0 g 1 w 4 M 285.0357 161.278 m F 285.0357 138.3879 m F 0 G 0.3 w 10 M 290.8649 132.6653 m S 279.2064 132.6653 m S 290.8649 132.6653 m S 220.9137 167.0006 m S 220.9137 155.5555 m S 209.2552 155.5555 m S 209.2552 167.0006 m S 215.0844 161.278 m S 244.2308 144.1104 m S 244.2308 132.6653 m S 232.5722 132.6653 m S 232.5722 144.1104 m S 238.4015 138.3879 m S 232.5722 155.5555 m S 232.5722 144.1104 m S 220.9137 144.1104 m S 220.9137 155.5555 m S 226.743 149.833 m S 232.5722 167.0006 m S 232.5722 155.5555 m S 220.9137 155.5555 m S 220.9137 167.0006 m S 226.743 161.278 m S 244.2308 167.0006 m S 244.2308 155.5555 m S 232.5722 155.5555 m S 232.5722 167.0006 m S 238.4015 161.278 m S 244.2308 155.5555 m S 244.2308 144.1104 m S 232.5722 144.1104 m S 232.5722 155.5555 m S 238.4015 149.833 m S 232.5722 144.1104 m S 232.5722 132.6653 m S 220.9137 132.6653 m S 220.9137 144.1104 m S 226.743 138.3879 m S 220.9137 144.1104 m S 220.9137 132.6653 m S 209.2552 132.6653 m S 209.2552 144.1104 m S 215.0844 138.3879 m S 220.9137 155.5555 m S 220.9137 144.1104 m S 209.2552 144.1104 m S 209.2552 155.5555 m S 215.0844 149.833 m S 0 g 1 w 4 M 215.0844 161.278 m F 238.4015 161.278 m F 215.0844 138.3879 m F 238.4015 138.3879 m F 0 G 0.3 w 10 M 255.8893 167.0006 m S 255.8893 155.5555 m S 244.2308 155.5555 m S 244.2308 167.0006 m S 250.0601 161.278 m S 279.2064 144.1104 m S 279.2064 132.6653 m S 267.5479 132.6653 m S 267.5479 144.1104 m S 273.3771 138.3879 m S 267.5479 155.5555 m S 267.5479 144.1104 m S 255.8893 144.1104 m S 255.8893 155.5555 m S 261.7186 149.833 m S 267.5479 167.0006 m S 267.5479 155.5555 m S 255.8893 155.5555 m S 255.8893 167.0006 m S 261.7186 161.278 m S 279.2064 167.0006 m S 279.2064 155.5555 m S 267.5479 155.5555 m S 267.5479 167.0006 m S 273.3771 161.278 m S 279.2064 155.5555 m S 279.2064 144.1104 m S 267.5479 144.1104 m S 267.5479 155.5555 m S 273.3771 149.833 m S 267.5479 144.1104 m S 267.5479 132.6653 m S 255.8893 132.6653 m S 255.8893 144.1104 m S 261.7186 138.3879 m S 255.8893 144.1104 m S 255.8893 132.6653 m S 244.2308 132.6653 m S 244.2308 144.1104 m S 250.0601 138.3879 m S 255.8893 155.5555 m S 255.8893 144.1104 m S 244.2308 144.1104 m S 244.2308 155.5555 m S 250.0601 149.833 m S 0 g 1 w 4 M 250.0601 161.278 m F 273.3771 161.278 m F 250.0601 138.3879 m F 273.3771 138.3879 m F 0 G 0.3 w 10 M 290.8649 167.0006 m S 290.8649 155.5555 m S 279.2064 155.5555 m S 279.2064 167.0006 m S 285.0357 161.278 m S 290.8649 144.1104 m S 290.8649 155.5555 m S 290.8649 155.5555 m S 290.8649 167.0006 m S 290.8649 132.6653 m S 290.8649 144.1104 m S 290.8649 144.1104 m S 290.8649 132.6653 m S 279.2064 132.6653 m S 279.2064 144.1104 m S 285.0357 138.3879 m S 290.8649 155.5555 m S 290.8649 144.1104 m S 279.2064 144.1104 m S 279.2064 155.5555 m S 285.0357 149.833 m S 0 g 1 w 4 M 285.0357 161.278 m F 285.0357 138.3879 m F 0 G 0.3 w 10 M 220.9137 132.6653 m S 220.9137 121.2203 m S 209.2552 121.2203 m S 209.2552 132.6653 m S 215.0844 126.9428 m S 244.2308 109.7752 m S 244.2308 98.3302 m S 232.5722 98.3302 m S 232.5722 109.7752 m S 238.4015 104.0527 m S 232.5722 121.2203 m S 232.5722 109.7752 m S 220.9137 109.7752 m S 220.9137 121.2203 m S 226.743 115.4978 m S 232.5722 132.6653 m S 232.5722 121.2203 m S 220.9137 121.2203 m S 220.9137 132.6653 m S 226.743 126.9428 m S 244.2308 132.6653 m S 244.2308 121.2203 m S 232.5722 121.2203 m S 232.5722 132.6653 m S 238.4015 126.9428 m S 244.2308 121.2203 m S 244.2308 109.7752 m S 232.5722 109.7752 m S 232.5722 121.2203 m S 238.4015 115.4978 m S 232.5722 109.7752 m S 232.5722 98.3302 m S 220.9137 98.3302 m S 220.9137 109.7752 m S 226.743 104.0527 m S 220.9137 109.7752 m S 220.9137 98.3302 m S 209.2552 98.3302 m S 209.2552 109.7752 m S 215.0844 104.0527 m S 220.9137 121.2203 m S 220.9137 109.7752 m S 209.2552 109.7752 m S 209.2552 121.2203 m S 215.0844 115.4978 m S 0 g 1 w 4 M 215.0844 126.9428 m F 238.4015 126.9428 m F 215.0844 104.0527 m F 238.4015 104.0527 m F 0 G 0.3 w 10 M 255.8893 132.6653 m S 255.8893 121.2203 m S 244.2308 121.2203 m S 244.2308 132.6653 m S 250.0601 126.9428 m S 279.2064 109.7752 m S 279.2064 98.3302 m S 267.5479 98.3302 m S 267.5479 109.7752 m S 273.3771 104.0527 m S 267.5479 121.2203 m S 267.5479 109.7752 m S 255.8893 109.7752 m S 255.8893 121.2203 m S 261.7186 115.4978 m S 267.5479 132.6653 m S 267.5479 121.2203 m S 255.8893 121.2203 m S 255.8893 132.6653 m S 261.7186 126.9428 m S 279.2064 132.6653 m S 279.2064 121.2203 m S 267.5479 121.2203 m S 267.5479 132.6653 m S 273.3771 126.9428 m S 279.2064 121.2203 m S 279.2064 109.7752 m S 267.5479 109.7752 m S 267.5479 121.2203 m S 273.3771 115.4978 m S 267.5479 109.7752 m S 267.5479 98.3302 m S 255.8893 98.3302 m S 255.8893 109.7752 m S 261.7186 104.0527 m S 255.8893 109.7752 m S 255.8893 98.3302 m S 244.2308 98.3302 m S 244.2308 109.7752 m S 250.0601 104.0527 m S 255.8893 121.2203 m S 255.8893 109.7752 m S 244.2308 109.7752 m S 244.2308 121.2203 m S 250.0601 115.4978 m S 0 g 1 w 4 M 250.0601 126.9428 m F 273.3771 126.9428 m F 250.0601 104.0527 m F 273.3771 104.0527 m F 0 G 0.3 w 10 M 290.8649 132.6653 m S 290.8649 121.2203 m S 279.2064 121.2203 m S 279.2064 132.6653 m S 285.0357 126.9428 m S 290.8649 109.7752 m S 290.8649 121.2203 m S 290.8649 121.2203 m S 290.8649 132.6653 m S 290.8649 98.3302 m S 290.8649 109.7752 m S 290.8649 109.7752 m S 290.8649 98.3302 m S 279.2064 98.3302 m S 279.2064 109.7752 m S 285.0357 104.0527 m S 290.8649 121.2203 m S 290.8649 109.7752 m S 279.2064 109.7752 m S 279.2064 121.2203 m S 285.0357 115.4978 m S 0 g 1 w 4 M 285.0357 126.9428 m F 285.0357 104.0527 m F 215.0844 92.6077 m F 238.4015 92.6077 m F 250.0601 92.6077 m F 273.3771 92.6077 m F 285.0357 92.6077 m F 0 G 0.3 w 10 M 220.9137 98.3302 m S 220.9137 86.8851 m S 209.2552 86.8851 m S 209.2552 98.3302 m S 215.0844 92.6077 m S u 244.2308 75.44 m S 244.2308 63.995 m S 232.5722 63.995 m S 232.5722 75.44 m S 238.4015 69.7175 m S U u 232.5722 86.8851 m S 232.5722 75.44 m S 220.9137 75.44 m S 220.9137 86.8851 m S 226.743 81.1626 m S U 232.5722 98.3302 m S 232.5722 86.8851 m S 220.9137 86.8851 m S 220.9137 98.3302 m S 226.743 92.6077 m S 244.2308 98.3302 m S 244.2308 86.8851 m S 232.5722 86.8851 m S 232.5722 98.3302 m S 238.4015 92.6077 m S u 244.2308 86.8851 m S 244.2308 75.44 m S 232.5722 75.44 m S 232.5722 86.8851 m S 238.4015 81.1626 m S U u 232.5722 75.44 m S 232.5722 63.995 m S 220.9137 63.995 m S 220.9137 75.44 m S 226.743 69.7175 m S U u 220.9137 75.44 m S 220.9137 63.995 m S 209.2552 63.995 m S 209.2552 75.44 m S 215.0844 69.7175 m S U u 220.9137 86.8851 m S 220.9137 75.44 m S 209.2552 75.44 m S 209.2552 86.8851 m S 215.0844 81.1626 m S U 0 g 1 w 4 M 215.0844 92.6077 m F 238.4015 92.6077 m F 215.0844 69.7175 m F 238.4015 69.7175 m F 0 G 0.3 w 10 M 255.8893 98.3302 m S 255.8893 86.8851 m S 244.2308 86.8851 m S 244.2308 98.3302 m S 250.0601 92.6077 m S u 279.2064 75.44 m S 279.2064 63.995 m S 267.5479 63.995 m S 267.5479 75.44 m S 273.3771 69.7175 m S U u 267.5479 86.8851 m S 267.5479 75.44 m S 255.8893 75.44 m S 255.8893 86.8851 m S 261.7186 81.1626 m S U 267.5479 98.3302 m S 267.5479 86.8851 m S 255.8893 86.8851 m S 255.8893 98.3302 m S 261.7186 92.6077 m S 279.2064 98.3302 m S 279.2064 86.8851 m S 267.5479 86.8851 m S 267.5479 98.3302 m S 273.3771 92.6077 m S u 279.2064 86.8851 m S 279.2064 75.44 m S 267.5479 75.44 m S 267.5479 86.8851 m S 273.3771 81.1626 m S U u 267.5479 75.44 m S 267.5479 63.995 m S 255.8893 63.995 m S 255.8893 75.44 m S 261.7186 69.7175 m S U u 255.8893 75.44 m S 255.8893 63.995 m S 244.2308 63.995 m S 244.2308 75.44 m S 250.0601 69.7175 m S U u 255.8893 86.8851 m S 255.8893 75.44 m S 244.2308 75.44 m S 244.2308 86.8851 m S 250.0601 81.1626 m S U 0 g 1 w 4 M 250.0601 92.6077 m F 273.3771 92.6077 m F 250.0601 69.7175 m F 273.3771 69.7175 m F 0 G 0.3 w 10 M 290.8649 98.3302 m S 290.8649 86.8851 m S 279.2064 86.8851 m S 279.2064 98.3302 m S 285.0357 92.6077 m S 290.8649 86.8851 m S 290.8649 98.3302 m S u 290.8649 75.44 m S 290.8649 63.995 m S 279.2064 63.995 m S 279.2064 75.44 m S 285.0357 69.7175 m S U u 290.8649 86.8851 m S 290.8649 75.44 m S 279.2064 75.44 m S 279.2064 86.8851 m S 285.0357 81.1626 m S U 0 g 1 w 4 M 285.0357 92.6077 m F 285.0357 69.7175 m F 0 G 0.3 w 10 M 220.9137 63.995 m S 209.2552 63.995 m S 232.5722 63.995 m S 220.9137 63.995 m S 244.2308 63.995 m S 232.5722 63.995 m S 255.8893 63.995 m S 244.2308 63.995 m S 267.5479 63.995 m S 255.8893 63.995 m S 279.2064 63.995 m S 267.5479 63.995 m S 290.8649 63.995 m S 279.2064 63.995 m S 290.8649 63.995 m S 290.8649 167.0006 m S 290.8649 155.5555 m S 279.2064 155.5555 m S 279.2064 167.0006 m S 285.0357 161.278 m S 290.8649 144.1104 m S 290.8649 155.5555 m S 290.8649 155.5555 m S 290.8649 167.0006 m S 290.8649 132.6653 m S 290.8649 144.1104 m S 290.8649 144.1104 m S 290.8649 132.6653 m S 279.2064 132.6653 m S 279.2064 144.1104 m S 285.0357 138.3879 m S 290.8649 155.5555 m S 290.8649 144.1104 m S 279.2064 144.1104 m S 279.2064 155.5555 m S 285.0357 149.833 m S 0 g 1 w 4 M 285.0357 161.278 m F 285.0357 138.3879 m F 0 G 0.3 w 10 M 290.8649 132.6653 m S 290.8649 121.2203 m S 279.2064 121.2203 m S 279.2064 132.6653 m S 285.0357 126.9428 m S 290.8649 109.7752 m S 290.8649 121.2203 m S 290.8649 121.2203 m S 290.8649 132.6653 m S 290.8649 98.3302 m S 290.8649 109.7752 m S 290.8649 109.7752 m S 290.8649 98.3302 m S 279.2064 98.3302 m S 279.2064 109.7752 m S 285.0357 104.0527 m S 290.8649 121.2203 m S 290.8649 109.7752 m S 279.2064 109.7752 m S 279.2064 121.2203 m S 285.0357 115.4978 m S 0 g 1 w 4 M 285.0357 126.9428 m F 285.0357 104.0527 m F 285.0357 92.6077 m F 0 G 0.3 w 10 M 290.8649 98.3302 m S 290.8649 86.8851 m S 279.2064 86.8851 m S 279.2064 98.3302 m S 285.0357 92.6077 m S 290.8649 86.8851 m S 290.8649 98.3302 m S u 290.8649 75.44 m S 290.8649 63.995 m S 279.2064 63.995 m S 279.2064 75.44 m S 285.0357 69.7175 m S U u 290.8649 86.8851 m S 290.8649 75.44 m S 279.2064 75.44 m S 279.2064 86.8851 m S 285.0357 81.1626 m S U 0 g 1 w 4 M 285.0357 92.6077 m F 285.0357 69.7175 m F 0 G 0.3 w 10 M 290.8649 63.995 m S 279.2064 63.995 m S 290.8649 63.995 m S 232.5722 212.7808 m S 0 g 1 w 4 M 232.5722 212.7808 m F 0 G 0.3 w 10 M 232.5722 212.7808 m S 232.5722 212.7808 m S 232.5722 212.7808 m S 0 g 1 w 4 M 232.5722 212.7808 m F 0 G 0.3 w 10 M 232.5722 212.7808 m S 232.5722 212.7808 m S 232.5722 212.7808 m S 0 g 1 w 4 M 232.5722 212.7808 m F 0 G 0.3 w 10 M 232.5722 212.7808 m S 232.5722 212.7808 m S 244.2308 201.3357 m S 0 g 1 w 4 M 244.2308 201.3357 m F 0 G 0.3 w 10 M 244.2308 201.3357 m S 244.2308 201.3357 m S 244.2308 201.3357 m S 0 g 1 w 4 M 244.2308 201.3357 m F 0 G 0.3 w 10 M 244.2308 201.3357 m S 244.2308 201.3357 m S 244.2308 201.3357 m S 0 g 1 w 4 M 244.2308 201.3357 m F 0 G 0.3 w 10 M 244.2308 201.3357 m S 244.2308 201.3357 m S 244.2308 201.3357 m S 0 g 1 w 4 M 244.2308 201.3357 m F 0 G 0.3 w 10 M 244.2308 201.3357 m S 244.2308 201.3357 m S 244.2308 201.3357 m S 0 g 1 w 4 M 244.2308 201.3357 m F 0 G 0.3 w 10 M 244.2308 201.3357 m S 244.2308 201.3357 m S u 1 g 1 w 4 M 244.2308 201.3357 m F U 0 G 0.3 w 10 M 244.2308 201.3357 m S 0 g 1 w 4 M 244.2308 201.3357 m F 0 G 0.3 w 10 M 244.2308 201.3357 m S 244.2308 201.3357 m S 244.2308 212.7808 m S 0 g 1 w 4 M 244.2308 212.7808 m F 0 G 0.3 w 10 M 244.2308 212.7808 m S 244.2308 212.7808 m S 244.2308 212.7808 m S 0 g 1 w 4 M 244.2308 212.7808 m F 0 G 0.3 w 10 M 244.2308 212.7808 m S 244.2308 212.7808 m S 244.2308 212.7808 m S 0 g 1 w 4 M 244.2308 212.7808 m F 0 G 0.3 w 10 M 244.2308 212.7808 m S 244.2308 212.7808 m S 232.5722 201.3357 m S 0 g 1 w 4 M 232.5722 201.3357 m F 0 G 0.3 w 10 M 232.5722 201.3357 m S 232.5722 201.3357 m S 232.5722 201.3357 m S 0 g 1 w 4 M 232.5722 201.3357 m F 0 G 0.3 w 10 M 232.5722 201.3357 m S 232.5722 201.3357 m S 232.5722 201.3357 m S 0 g 1 w 4 M 232.5722 201.3357 m F 0 G 0.3 w 10 M 232.5722 201.3357 m S 232.5722 201.3357 m S 232.5722 189.8906 m S 0 g 1 w 4 M 232.5722 189.8906 m F 0 G 0.3 w 10 M 232.5722 189.8906 m S 232.5722 189.8906 m S 232.5722 189.8906 m S 0 g 1 w 4 M 232.5722 189.8906 m F 0 G 0.3 w 10 M 232.5722 189.8906 m S 232.5722 189.8906 m S 232.5722 189.8906 m S 0 g 1 w 4 M 232.5722 189.8906 m F 0 G 0.3 w 10 M 232.5722 189.8906 m S 232.5722 189.8906 m S 232.5722 178.4456 m S 0 g 1 w 4 M 232.5722 178.4456 m F 0 G 0.3 w 10 M 232.5722 178.4456 m S 232.5722 178.4456 m S 232.5722 178.4456 m S 0 g 1 w 4 M 232.5722 178.4456 m F 0 G 0.3 w 10 M 232.5722 178.4456 m S 232.5722 178.4456 m S 1 g 0.5 w 4 M 232.5722 178.4456 m B 0.3 w 10 M 232.5722 178.4456 m S 0 g 1 w 4 M 232.5722 178.4456 m F 0 G 0.3 w 10 M 232.5722 178.4456 m S 232.5722 178.4456 m S 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 244.2308 167.0006 m S 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 244.2308 167.0006 m S 1 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 244.2308 167.0006 m S 1 g 0.5 w 4 M 244.2308 167.0006 m B 0.3 w 10 M 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 244.2308 167.0006 m S 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 244.2308 167.0006 m S u 1 g 1 w 4 M 244.2308 167.0006 m F U 0 G 0.3 w 10 M 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 244.2308 167.0006 m S 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 244.2308 167.0006 m S 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 244.2308 167.0006 m S u 1 g 1 w 4 M 244.2308 167.0006 m F U 0 G 0.3 w 10 M 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 244.2308 167.0006 m S 244.2308 189.8906 m S 0 g 1 w 4 M 244.2308 189.8906 m F 0 G 0.3 w 10 M 244.2308 189.8906 m S 244.2308 189.8906 m S 244.2308 189.8906 m S 0 g 1 w 4 M 244.2308 189.8906 m F 0 G 0.3 w 10 M 244.2308 189.8906 m S 244.2308 189.8906 m S 244.2308 189.8906 m S 0 g 1 w 4 M 244.2308 189.8906 m F 0 G 0.3 w 10 M 244.2308 189.8906 m S 244.2308 189.8906 m S 232.5722 167.0006 m S 0 g 1 w 4 M 232.5722 167.0006 m F 0 G 0.3 w 10 M 232.5722 167.0006 m S 232.5722 167.0006 m S 232.5722 167.0006 m S 0 g 1 w 4 M 232.5722 167.0006 m F 0 G 0.3 w 10 M 232.5722 167.0006 m S 232.5722 167.0006 m S 232.5722 167.0006 m S 0 g 1 w 4 M 232.5722 167.0006 m F 0 G 0.3 w 10 M 232.5722 167.0006 m S 232.5722 167.0006 m S 244.2308 178.4456 m S 0 g 1 w 4 M 244.2308 178.4456 m F 0 G 0.3 w 10 M 244.2308 178.4456 m S 0 g 1 w 4 M 244.2308 178.4456 m F 0 G 0.3 w 10 M 244.2308 178.4456 m S 0 g 1 w 4 M 244.2308 178.4456 m F 0 G 0.3 w 10 M 244.2308 178.4456 m S 0 g 1 w 4 M 244.2308 178.4456 m F u 0 G 0.3 w 10 M 69.3528 63.995 m S 69.3528 52.5499 m S 57.6942 52.5499 m S 57.6942 63.995 m S 63.5235 58.2725 m S U u 57.6942 63.995 m S 57.6942 52.5499 m S 46.0357 52.5499 m S 46.0357 63.995 m S 51.865 58.2725 m S U u 46.0357 63.995 m S 46.0357 52.5499 m S 34.3772 52.5499 m S 34.3772 63.995 m S 40.2064 58.2725 m S U u 104.3284 63.995 m S 104.3284 52.5499 m S 92.6698 52.5499 m S 92.6698 63.995 m S 98.4991 58.2725 m S U u 92.6698 63.995 m S 92.6698 52.5499 m S 81.0113 52.5499 m S 81.0113 63.995 m S 86.8406 58.2725 m S U u 81.0113 63.995 m S 81.0113 52.5499 m S 69.3528 52.5499 m S 69.3528 63.995 m S 75.182 58.2725 m S U u 139.304 63.995 m S 139.304 52.5499 m S 127.6455 52.5499 m S 127.6455 63.995 m S 133.4747 58.2725 m S U u 127.6455 63.995 m S 127.6455 52.5499 m S 115.9869 52.5499 m S 115.9869 63.995 m S 121.8162 58.2725 m S U u 115.9869 63.995 m S 115.9869 52.5499 m S 104.3284 52.5499 m S 104.3284 63.995 m S 110.1576 58.2725 m S U 139.304 52.5499 m S 139.304 52.5499 m S u 139.304 63.995 m S 139.304 52.5499 m S 127.6455 52.5499 m S 127.6455 63.995 m S 133.4747 58.2725 m S U u 127.6455 63.995 m S 127.6455 52.5499 m S 115.9869 52.5499 m S 115.9869 63.995 m S 121.8162 58.2725 m S U u 115.9869 63.995 m S 115.9869 52.5499 m S 104.3284 52.5499 m S 104.3284 63.995 m S 110.1576 58.2725 m S U u 174.2796 63.995 m S 174.2796 52.5499 m S 162.6211 52.5499 m S 162.6211 63.995 m S 168.4504 58.2725 m S U u 162.6211 63.995 m S 162.6211 52.5499 m S 150.9626 52.5499 m S 150.9626 63.995 m S 156.7918 58.2725 m S U u 150.9626 63.995 m S 150.9626 52.5499 m S 139.304 52.5499 m S 139.304 63.995 m S 145.1333 58.2725 m S U u 209.2552 63.995 m S 209.2552 52.5499 m S 197.5967 52.5499 m S 197.5967 63.995 m S 203.426 58.2725 m S U u 197.5967 63.995 m S 197.5967 52.5499 m S 185.9382 52.5499 m S 185.9382 63.995 m S 191.7674 58.2725 m S U u 185.9382 63.995 m S 185.9382 52.5499 m S 174.2796 52.5499 m S 174.2796 63.995 m S 180.1089 58.2725 m S U 209.2552 52.5499 m S 209.2552 52.5499 m S u 244.2308 63.995 m S 244.2308 52.5499 m S 232.5722 52.5499 m S 232.5722 63.995 m S 238.4015 58.2725 m S U u 232.5722 63.995 m S 232.5722 52.5499 m S 220.9137 52.5499 m S 220.9137 63.995 m S 226.743 58.2725 m S U u 220.9137 63.995 m S 220.9137 52.5499 m S 209.2552 52.5499 m S 209.2552 63.995 m S 215.0844 58.2725 m S U u 279.2064 63.995 m S 279.2064 52.5499 m S 267.5479 52.5499 m S 267.5479 63.995 m S 273.3771 58.2725 m S U u 267.5479 63.995 m S 267.5479 52.5499 m S 255.8893 52.5499 m S 255.8893 63.995 m S 261.7186 58.2725 m S U u 255.8893 63.995 m S 255.8893 52.5499 m S 244.2308 52.5499 m S 244.2308 63.995 m S 250.0601 58.2725 m S U u 290.8649 63.995 m S 290.8649 52.5499 m S 279.2064 52.5499 m S 279.2064 63.995 m S 285.0357 58.2725 m S U u 290.8649 63.995 m S 290.8649 52.5499 m S 279.2064 52.5499 m S 279.2064 63.995 m S 285.0357 58.2725 m S U 57.6942 212.7808 m S 0 g 1 w 4 M 57.6942 212.7808 m F 0 G 0.3 w 10 M 57.6942 212.7808 m S 57.6942 212.7808 m S 57.6942 212.7808 m S 0 g 1 w 4 M 57.6942 212.7808 m F 0 G 0.3 w 10 M 57.6942 212.7808 m S 57.6942 212.7808 m S 57.6942 212.7808 m S 0 g 1 w 4 M 57.6942 212.7808 m F 0 G 0.3 w 10 M 57.6942 212.7808 m S 57.6942 212.7808 m S 0 g 1 w 4 M 56.6091 211.7129 m 56.6091 208.1358 L 58.7793 208.1358 L 58.7793 211.7129 L 62.3649 211.7017 L 62.3649 213.8601 L 58.7793 213.849 L 58.7793 217.4261 L 56.6091 217.4261 L 56.6091 213.849 L 53.0235 213.8601 L 53.0235 211.7017 L 56.6091 211.7129 L f 0 G 0.3 w 10 M 57.6942 212.7808 m S 0 g 1 w 4 M 57.6942 212.7808 m F 0 G 0.3 w 10 M 57.6942 212.7808 m S 57.6942 212.7808 m S 57.6942 212.7808 m S 0 g 1 w 4 M 57.6942 212.7808 m F 0 G 0.3 w 10 M 57.6942 212.7808 m S 57.6942 212.7808 m S u 1 g 1 w 4 M 57.6942 212.7808 m F U 0 G 0.3 w 10 M 57.6942 212.7808 m S 0 g 1 w 4 M 57.6942 212.7808 m F 0 G 0.3 w 10 M 57.6942 212.7808 m S 57.6942 212.7808 m S 57.6942 212.7808 m S 0 g 1 w 4 M 57.6942 212.7808 m F 0 G 0.3 w 10 M 57.6942 212.7808 m S 0 g 1 w 4 M 57.6942 212.7808 m F 0 G 0.3 w 10 M 46.0357 224.2259 m S 69.3528 201.3357 m S 57.6942 212.7808 m S 57.6942 212.7808 m S 46.0357 224.2259 m S 46.0357 224.2259 m S 69.3528 224.2259 m S 69.3528 224.2259 m S 57.6942 212.7808 m S 57.6942 212.7808 m S 46.0357 201.3357 m S 46.0357 201.3357 m S 46.0357 224.2259 m S 69.3528 224.2259 m S 69.3528 201.3357 m S 69.3528 224.2259 m S 46.0357 201.3357 m S 46.0357 201.3357 m S 69.3528 201.3357 m S 69.3528 201.3357 m S 57.6942 212.7808 m S 0 g 1 w 4 M 57.6942 212.7808 m F 0 G 0.3 w 10 M 57.6942 212.7808 m S 57.6942 212.7808 m S 57.6942 212.7808 m S 0 g 1 w 4 M 57.6942 212.7808 m F 0 G 0.3 w 10 M 57.6942 212.7808 m S 57.6942 212.7808 m S 57.6942 212.7808 m S 0 g 1 w 4 M 57.6942 212.7808 m F 0 G 0.3 w 10 M 57.6942 212.7808 m S 57.6942 212.7808 m S 69.3528 201.3357 m S 0 g 1 w 4 M 69.3528 201.3357 m F 0 G 0.3 w 10 M 69.3528 201.3357 m S 69.3528 201.3357 m S 69.3528 201.3357 m S 0 g 1 w 4 M 69.3528 201.3357 m F 0 G 0.3 w 10 M 69.3528 201.3357 m S 69.3528 201.3357 m S 69.3528 201.3357 m S 0 g 1 w 4 M 69.3528 201.3357 m F 0 G 0.3 w 10 M 69.3528 201.3357 m S 69.3528 201.3357 m S 69.3528 201.3357 m S 0 g 1 w 4 M 69.3528 201.3357 m F 0 G 0.3 w 10 M 69.3528 201.3357 m S 69.3528 201.3357 m S 69.3528 201.3357 m S 0 g 1 w 4 M 69.3528 201.3357 m F 0 G 0.3 w 10 M 69.3528 201.3357 m S 69.3528 201.3357 m S 1 g 1 w 4 M 69.3528 201.3357 m F 0 G 0.3 w 10 M 69.3528 201.3357 m S 0 g 1 w 4 M 69.3528 201.3357 m F 0 G 0.3 w 10 M 69.3528 201.3357 m S 69.3528 201.3357 m S 0.5 w 4 M 46.0357 224.2259 m 69.3528 224.2259 l 69.3528 201.3357 l 46.0357 201.3357 l 46.0357 224.2259 l s 0.3 w 10 M 57.6942 235.6709 m S 0 g 1 w 4 M 57.6942 235.6709 m F 0 G 0.3 w 10 M 57.6942 235.6709 m S 57.6942 235.6709 m S 57.6942 235.6709 m S 0 g 1 w 4 M 57.6942 235.6709 m F 0 G 0.3 w 10 M 57.6942 235.6709 m S 57.6942 235.6709 m S 57.6942 235.6709 m S 0 g 1 w 4 M 57.6942 235.6709 m F 0 G 0.3 w 10 M 57.6942 235.6709 m S 57.6942 235.6709 m S 34.3772 212.7808 m S 0 g 1 w 4 M 34.3772 212.7808 m F 0 G 0.3 w 10 M 34.3772 212.7808 m S 34.3772 212.7808 m S 34.3772 212.7808 m S 0 g 1 w 4 M 34.3772 212.7808 m F 0 G 0.3 w 10 M 34.3772 212.7808 m S 34.3772 212.7808 m S 34.3772 212.7808 m S 0 g 1 w 4 M 34.3772 212.7808 m F 0 G 0.3 w 10 M 34.3772 212.7808 m S 34.3772 212.7808 m S 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 126.5604 213.849 m 122.9748 213.8601 L 122.9748 211.7017 L 126.5604 211.7128 L F 128.7306 211.7128 m 132.3162 211.7017 L 132.3162 213.8601 L 128.7306 213.849 L F 122.9748 213.8601 m 132.3162 213.8601 l 132.3162 211.7017 l 122.9748 211.7017 l 122.9748 213.8601 l f 0 G 0.3 w 10 M 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 127.6455 212.7808 m S 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 127.6455 212.7808 m S 1 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 127.6455 212.7808 m S 1 g 0.5 w 4 M 127.6455 212.7808 m B 0.3 w 10 M 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 127.6455 212.7808 m S 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 127.6455 212.7808 m S u 1 g 1 w 4 M 127.6455 212.7808 m F U 0 G 0.3 w 10 M 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 127.6455 212.7808 m S 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 127.6455 212.7808 m S 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 127.6455 212.7808 m S u 1 g 1 w 4 M 127.6455 212.7808 m F U 0 G 0.3 w 10 M 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 127.6455 212.7808 m S 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 115.9869 224.2259 m S 139.304 201.3357 m S 127.6455 212.7808 m S 127.6455 212.7808 m S 115.9869 224.2259 m S 115.9869 224.2259 m S 139.304 224.2259 m S 139.304 224.2259 m S 127.6455 212.7808 m S 127.6455 212.7808 m S 115.9869 201.3357 m S 115.9869 201.3357 m S 115.9869 224.2259 m S 139.304 224.2259 m S 139.304 201.3357 m S 139.304 224.2259 m S 115.9869 201.3357 m S 115.9869 201.3357 m S 139.304 201.3357 m S 139.304 201.3357 m S 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 127.6455 212.7808 m S 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 127.6455 212.7808 m S 127.6455 212.7808 m S 0 g 1 w 4 M 127.6455 212.7808 m F 0 G 0.3 w 10 M 127.6455 212.7808 m S 127.6455 212.7808 m S 139.304 201.3357 m S 0 g 1 w 4 M 139.304 201.3357 m F 0 G 0.3 w 10 M 139.304 201.3357 m S 139.304 201.3357 m S 139.304 201.3357 m S 0 g 1 w 4 M 139.304 201.3357 m F 0 G 0.3 w 10 M 139.304 201.3357 m S 139.304 201.3357 m S 139.304 201.3357 m S 0 g 1 w 4 M 139.304 201.3357 m F 0 G 0.3 w 10 M 139.304 201.3357 m S 139.304 201.3357 m S 139.304 201.3357 m S 0 g 1 w 4 M 139.304 201.3357 m F 0 G 0.3 w 10 M 139.304 201.3357 m S 139.304 201.3357 m S 139.304 201.3357 m S 0 g 1 w 4 M 139.304 201.3357 m F 0 G 0.3 w 10 M 139.304 201.3357 m S 139.304 201.3357 m S 1 g 1 w 4 M 139.304 201.3357 m F 0 G 0.3 w 10 M 139.304 201.3357 m S 0 g 1 w 4 M 139.304 201.3357 m F 0 G 0.3 w 10 M 139.304 201.3357 m S 139.304 201.3357 m S 0.5 w 4 M 115.9869 224.2259 m 139.304 224.2259 l 139.304 201.3357 l 115.9869 201.3357 l 115.9869 224.2259 l s 0.3 w 10 M 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 56.6091 145.1786 m 53.0235 145.1897 L 53.0235 143.0313 L 56.6091 143.0424 L F 58.7793 143.0424 m 62.3649 143.0313 L 62.3649 145.1897 L 58.7793 145.1786 L F 53.0235 145.1897 m 62.3649 145.1897 l 62.3649 143.0313 l 53.0235 143.0313 l 53.0235 145.1897 l f 0 G 0.3 w 10 M 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 57.6942 144.1104 m S 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 57.6942 144.1104 m S 1 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 57.6942 144.1104 m S 1 g 0.5 w 4 M 57.6942 144.1104 m B 0.3 w 10 M 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 57.6942 144.1104 m S 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 57.6942 144.1104 m S 1 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 57.6942 144.1104 m S 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 57.6942 144.1104 m S 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 57.6942 144.1104 m S 1 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 57.6942 144.1104 m S 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 46.0357 155.5554 m S 69.3528 132.6652 m S 57.6942 144.1104 m S 57.6942 144.1104 m S 46.0357 155.5554 m S 46.0357 155.5554 m S 69.3528 155.5554 m S 69.3528 155.5554 m S 57.6942 144.1104 m S 57.6942 144.1104 m S 46.0357 132.6652 m S 46.0357 132.6652 m S 46.0357 155.5554 m S 69.3528 155.5554 m S 69.3528 132.6652 m S 69.3528 155.5554 m S 46.0357 132.6652 m S 46.0357 132.6652 m S 69.3528 132.6652 m S 69.3528 132.6652 m S 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 57.6942 144.1104 m S 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 57.6942 144.1104 m S 57.6942 144.1104 m S 0 g 1 w 4 M 57.6942 144.1104 m F 0 G 0.3 w 10 M 57.6942 144.1104 m S 57.6942 144.1104 m S 69.3528 132.6652 m S 0 g 1 w 4 M 69.3528 132.6652 m F 0 G 0.3 w 10 M 69.3528 132.6652 m S 69.3528 132.6652 m S 69.3528 132.6652 m S 0 g 1 w 4 M 69.3528 132.6652 m F 0 G 0.3 w 10 M 69.3528 132.6652 m S 69.3528 132.6652 m S 69.3528 132.6652 m S 0 g 1 w 4 M 69.3528 132.6652 m F 0 G 0.3 w 10 M 69.3528 132.6652 m S 69.3528 132.6652 m S 69.3528 132.6652 m S 0 g 1 w 4 M 69.3528 132.6652 m F 0 G 0.3 w 10 M 69.3528 132.6652 m S 69.3528 132.6652 m S 69.3528 132.6652 m S 0 g 1 w 4 M 69.3528 132.6652 m F 0 G 0.3 w 10 M 69.3528 132.6652 m S 69.3528 132.6652 m S 1 g 1 w 4 M 69.3528 132.6652 m F 0 G 0.3 w 10 M 69.3528 132.6652 m S 0 g 1 w 4 M 69.3528 132.6652 m F 0 G 0.3 w 10 M 69.3528 132.6652 m S 69.3528 132.6652 m S 0.5 w 4 M 46.0357 155.5554 m 69.3528 155.5554 l 69.3528 132.6652 l 46.0357 132.6652 l 46.0357 155.5554 l s 0.3 w 10 M 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 196.5116 145.1786 m 192.926 145.1897 L 192.926 143.0313 L 196.5116 143.0424 L F 198.6818 143.0424 m 202.2674 143.0313 L 202.2674 145.1897 L 198.6818 145.1786 L F 192.926 145.1897 m 202.2674 145.1897 l 202.2674 143.0313 l 192.926 143.0313 l 192.926 145.1897 l f 0 G 0.3 w 10 M 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 197.5967 144.1104 m S 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 197.5967 144.1104 m S 1 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 197.5967 144.1104 m S 1 g 0.5 w 4 M 197.5967 144.1104 m B 0.3 w 10 M 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 197.5967 144.1104 m S 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 197.5967 144.1104 m S 1 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 197.5967 144.1104 m S 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 197.5967 144.1104 m S 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 197.5967 144.1104 m S 1 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 197.5967 144.1104 m S 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 185.9382 155.5554 m S 209.2553 132.6652 m S 197.5967 144.1104 m S 197.5967 144.1104 m S 185.9382 155.5554 m S 185.9382 155.5554 m S 209.2553 155.5554 m S 209.2553 155.5554 m S 197.5967 144.1104 m S 197.5967 144.1104 m S 185.9382 132.6652 m S 185.9382 132.6652 m S 185.9382 155.5554 m S 209.2553 155.5554 m S 209.2553 132.6652 m S 209.2553 155.5554 m S 185.9382 132.6652 m S 185.9382 132.6652 m S 209.2553 132.6652 m S 209.2553 132.6652 m S 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 197.5967 144.1104 m S 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 197.5967 144.1104 m S 197.5967 144.1104 m S 0 g 1 w 4 M 197.5967 144.1104 m F 0 G 0.3 w 10 M 197.5967 144.1104 m S 197.5967 144.1104 m S 209.2553 132.6652 m S 0 g 1 w 4 M 209.2553 132.6652 m F 0 G 0.3 w 10 M 209.2553 132.6652 m S 209.2553 132.6652 m S 209.2553 132.6652 m S 0 g 1 w 4 M 209.2553 132.6652 m F 0 G 0.3 w 10 M 209.2553 132.6652 m S 209.2553 132.6652 m S 209.2553 132.6652 m S 0 g 1 w 4 M 209.2553 132.6652 m F 0 G 0.3 w 10 M 209.2553 132.6652 m S 209.2553 132.6652 m S 209.2553 132.6652 m S 0 g 1 w 4 M 209.2553 132.6652 m F 0 G 0.3 w 10 M 209.2553 132.6652 m S 209.2553 132.6652 m S 209.2553 132.6652 m S 0 g 1 w 4 M 209.2553 132.6652 m F 0 G 0.3 w 10 M 209.2553 132.6652 m S 209.2553 132.6652 m S 1 g 1 w 4 M 209.2553 132.6652 m F 0 G 0.3 w 10 M 209.2553 132.6652 m S 0 g 1 w 4 M 209.2553 132.6652 m F 0 G 0.3 w 10 M 209.2553 132.6652 m S 209.2553 132.6652 m S 0.5 w 4 M 185.9382 155.5554 m 209.2553 155.5554 l 209.2553 132.6652 l 185.9382 132.6652 l 185.9382 155.5554 l s 0.3 w 10 M 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 126.5604 76.5082 m 122.9748 76.5193 L 122.9748 74.3609 L 126.5604 74.372 L F 128.7306 74.372 m 132.3162 74.3609 L 132.3162 76.5193 L 128.7306 76.5082 L F 122.9748 76.5193 m 132.3162 76.5193 l 132.3162 74.3609 l 122.9748 74.3609 l 122.9748 76.5193 l f 0 G 0.3 w 10 M 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 127.6455 75.44 m S 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 127.6455 75.44 m S 1 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 127.6455 75.44 m S 1 g 0.5 w 4 M 127.6455 75.44 m B 0.3 w 10 M 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 127.6455 75.44 m S 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 127.6455 75.44 m S u 1 g 1 w 4 M 127.6455 75.44 m F U 0 G 0.3 w 10 M 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 127.6455 75.44 m S 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 127.6455 75.44 m S 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 127.6455 75.44 m S u 1 g 1 w 4 M 127.6455 75.44 m F U 0 G 0.3 w 10 M 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 127.6455 75.44 m S 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 115.9869 86.8851 m S 139.304 63.9949 m S 127.6455 75.44 m S 127.6455 75.44 m S 115.9869 86.8851 m S 115.9869 86.8851 m S 139.304 86.8851 m S 139.304 86.8851 m S 127.6455 75.44 m S 127.6455 75.44 m S 115.9869 63.9949 m S 115.9869 63.9949 m S 115.9869 86.8851 m S 139.304 86.8851 m S 139.304 63.9949 m S 139.304 86.8851 m S 115.9869 63.9949 m S 115.9869 63.9949 m S 139.304 63.9949 m S 139.304 63.9949 m S 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 127.6455 75.44 m S 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 127.6455 75.44 m S 127.6455 75.44 m S 0 g 1 w 4 M 127.6455 75.44 m F 0 G 0.3 w 10 M 127.6455 75.44 m S 127.6455 75.44 m S 139.304 63.9949 m S 0 g 1 w 4 M 139.304 63.9949 m F 0 G 0.3 w 10 M 139.304 63.9949 m S 139.304 63.9949 m S 139.304 63.9949 m S 0 g 1 w 4 M 139.304 63.9949 m F 0 G 0.3 w 10 M 139.304 63.9949 m S 139.304 63.9949 m S 139.304 63.9949 m S 0 g 1 w 4 M 139.304 63.9949 m F 0 G 0.3 w 10 M 139.304 63.9949 m S 139.304 63.9949 m S 139.304 63.9949 m S 0 g 1 w 4 M 139.304 63.9949 m F 0 G 0.3 w 10 M 139.304 63.9949 m S 139.304 63.9949 m S 139.304 63.9949 m S 0 g 1 w 4 M 139.304 63.9949 m F 0 G 0.3 w 10 M 139.304 63.9949 m S 139.304 63.9949 m S 1 g 1 w 4 M 139.304 63.9949 m F 0 G 0.3 w 10 M 139.304 63.9949 m S 0 g 1 w 4 M 139.304 63.9949 m F 0 G 0.3 w 10 M 139.304 63.9949 m S 139.304 63.9949 m S 0.5 w 4 M 115.9869 86.8851 m 139.304 86.8851 l 139.304 63.9949 l 115.9869 63.9949 l 115.9869 86.8851 l s 0.3 w 10 M 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 266.4628 76.5082 m 262.8772 76.5193 L 262.8772 74.3609 L 266.4628 74.372 L F 268.633 74.372 m 272.2186 74.3609 L 272.2186 76.5193 L 268.633 76.5082 L F 262.8772 76.5193 m 272.2186 76.5193 l 272.2186 74.3609 l 262.8772 74.3609 l 262.8772 76.5193 l f 0 G 0.3 w 10 M 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 267.5479 75.44 m S 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 267.5479 75.44 m S 1 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 267.5479 75.44 m S 1 g 0.5 w 4 M 267.5479 75.44 m B 0.3 w 10 M 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 267.5479 75.44 m S 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 267.5479 75.44 m S u 1 g 1 w 4 M 267.5479 75.44 m F U 0 G 0.3 w 10 M 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 267.5479 75.44 m S 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 267.5479 75.44 m S 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 267.5479 75.44 m S u 1 g 1 w 4 M 267.5479 75.44 m F U 0 G 0.3 w 10 M 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 267.5479 75.44 m S 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 255.8893 86.8851 m S 279.2064 63.9949 m S 267.5479 75.44 m S 267.5479 75.44 m S 255.8893 86.8851 m S 255.8893 86.8851 m S 279.2064 86.8851 m S 279.2064 86.8851 m S 267.5479 75.44 m S 267.5479 75.44 m S 255.8893 63.9949 m S 255.8893 63.9949 m S 255.8893 86.8851 m S 279.2064 86.8851 m S 279.2064 63.9949 m S 279.2064 86.8851 m S 255.8893 63.9949 m S 255.8893 63.9949 m S 279.2064 63.9949 m S 279.2064 63.9949 m S 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 267.5479 75.44 m S 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 267.5479 75.44 m S 267.5479 75.44 m S 0 g 1 w 4 M 267.5479 75.44 m F 0 G 0.3 w 10 M 267.5479 75.44 m S 267.5479 75.44 m S 279.2064 63.9949 m S 0 g 1 w 4 M 279.2064 63.9949 m F 0 G 0.3 w 10 M 279.2064 63.9949 m S 279.2064 63.9949 m S 279.2064 63.9949 m S 0 g 1 w 4 M 279.2064 63.9949 m F 0 G 0.3 w 10 M 279.2064 63.9949 m S 279.2064 63.9949 m S 279.2064 63.9949 m S 0 g 1 w 4 M 279.2064 63.9949 m F 0 G 0.3 w 10 M 279.2064 63.9949 m S 279.2064 63.9949 m S 279.2064 63.9949 m S 0 g 1 w 4 M 279.2064 63.9949 m F 0 G 0.3 w 10 M 279.2064 63.9949 m S 279.2064 63.9949 m S 279.2064 63.9949 m S 0 g 1 w 4 M 279.2064 63.9949 m F 0 G 0.3 w 10 M 279.2064 63.9949 m S 279.2064 63.9949 m S 1 g 1 w 4 M 279.2064 63.9949 m F 0 G 0.3 w 10 M 279.2064 63.9949 m S 0 g 1 w 4 M 279.2064 63.9949 m F 0 G 0.3 w 10 M 279.2064 63.9949 m S 279.2064 63.9949 m S 0.5 w 4 M 255.8893 86.8851 m 279.2064 86.8851 l 279.2064 63.9949 l 255.8893 63.9949 l 255.8893 86.8851 l s 0.3 w 10 M 197.5967 212.7808 m S 0 g 1 w 4 M 197.5967 212.7808 m F 0 G 0.3 w 10 M 197.5967 212.7808 m S 197.5967 212.7808 m S 197.5967 212.7808 m S 0 g 1 w 4 M 197.5967 212.7808 m F 0 G 0.3 w 10 M 197.5967 212.7808 m S 197.5967 212.7808 m S 197.5967 212.7808 m S 0 g 1 w 4 M 197.5967 212.7808 m F 0 G 0.3 w 10 M 197.5967 212.7808 m S 197.5967 212.7808 m S 0 g 1 w 4 M 196.5116 211.7129 m 196.5116 208.1358 L 198.6818 208.1358 L 198.6818 211.7129 L 202.2674 211.7017 L 202.2674 213.8601 L 198.6818 213.849 L 198.6818 217.4261 L 196.5116 217.4261 L 196.5116 213.849 L 192.926 213.8601 L 192.926 211.7017 L 196.5116 211.7129 L f 0 G 0.3 w 10 M 197.5967 212.7808 m S 0 g 1 w 4 M 197.5967 212.7808 m F 0 G 0.3 w 10 M 197.5967 212.7808 m S 197.5967 212.7808 m S 197.5967 212.7808 m S 0 g 1 w 4 M 197.5967 212.7808 m F 0 G 0.3 w 10 M 197.5967 212.7808 m S 197.5967 212.7808 m S u 1 g 1 w 4 M 197.5967 212.7808 m F U 0 G 0.3 w 10 M 197.5967 212.7808 m S 0 g 1 w 4 M 197.5967 212.7808 m F 0 G 0.3 w 10 M 197.5967 212.7808 m S 197.5967 212.7808 m S 197.5967 212.7808 m S 0 g 1 w 4 M 197.5967 212.7808 m F 0 G 0.3 w 10 M 197.5967 212.7808 m S 0 g 1 w 4 M 197.5967 212.7808 m F 0 G 0.3 w 10 M 185.9382 224.2259 m S 209.2553 201.3357 m S 197.5967 212.7808 m S 197.5967 212.7808 m S 185.9382 224.2259 m S 185.9382 224.2259 m S 209.2553 224.2259 m S 209.2553 224.2259 m S 197.5967 212.7808 m S 197.5967 212.7808 m S 185.9382 201.3357 m S 185.9382 201.3357 m S 185.9382 224.2259 m S 209.2553 224.2259 m S 209.2553 201.3357 m S 209.2553 224.2259 m S 185.9382 201.3357 m S 185.9382 201.3357 m S 209.2553 201.3357 m S 209.2553 201.3357 m S 197.5967 212.7808 m S 0 g 1 w 4 M 197.5967 212.7808 m F 0 G 0.3 w 10 M 197.5967 212.7808 m S 197.5967 212.7808 m S 197.5967 212.7808 m S 0 g 1 w 4 M 197.5967 212.7808 m F 0 G 0.3 w 10 M 197.5967 212.7808 m S 197.5967 212.7808 m S 197.5967 212.7808 m S 0 g 1 w 4 M 197.5967 212.7808 m F 0 G 0.3 w 10 M 197.5967 212.7808 m S 197.5967 212.7808 m S 209.2553 201.3357 m S 0 g 1 w 4 M 209.2553 201.3357 m F 0 G 0.3 w 10 M 209.2553 201.3357 m S 209.2553 201.3357 m S 209.2553 201.3357 m S 0 g 1 w 4 M 209.2553 201.3357 m F 0 G 0.3 w 10 M 209.2553 201.3357 m S 209.2553 201.3357 m S 209.2553 201.3357 m S 0 g 1 w 4 M 209.2553 201.3357 m F 0 G 0.3 w 10 M 209.2553 201.3357 m S 209.2553 201.3357 m S 209.2553 201.3357 m S 0 g 1 w 4 M 209.2553 201.3357 m F 0 G 0.3 w 10 M 209.2553 201.3357 m S 209.2553 201.3357 m S 209.2553 201.3357 m S 0 g 1 w 4 M 209.2553 201.3357 m F 0 G 0.3 w 10 M 209.2553 201.3357 m S 209.2553 201.3357 m S 1 g 1 w 4 M 209.2553 201.3357 m F 0 G 0.3 w 10 M 209.2553 201.3357 m S 0 g 1 w 4 M 209.2553 201.3357 m F 0 G 0.3 w 10 M 209.2553 201.3357 m S 209.2553 201.3357 m S 0.5 w 4 M 185.9382 224.2259 m 209.2553 224.2259 l 209.2553 201.3357 l 185.9382 201.3357 l 185.9382 224.2259 l s 0.3 w 10 M 127.6455 144.1104 m S 0 g 1 w 4 M 127.6455 144.1104 m F 0 G 0.3 w 10 M 127.6455 144.1104 m S 127.6455 144.1104 m S 127.6455 144.1104 m S 0 g 1 w 4 M 127.6455 144.1104 m F 0 G 0.3 w 10 M 127.6455 144.1104 m S 127.6455 144.1104 m S 127.6455 144.1104 m S 0 g 1 w 4 M 127.6455 144.1104 m F 0 G 0.3 w 10 M 127.6455 144.1104 m S 127.6455 144.1104 m S 0 g 1 w 4 M 126.5604 143.0425 m 126.5604 139.4654 L 128.7306 139.4654 L 128.7306 143.0425 L 132.3162 143.0313 L 132.3162 145.1897 L 128.7306 145.1786 L 128.7306 148.7557 L 126.5604 148.7557 L 126.5604 145.1786 L 122.9748 145.1897 L 122.9748 143.0313 L 126.5604 143.0425 L f 0 G 0.3 w 10 M 127.6455 144.1104 m S 0 g 1 w 4 M 127.6455 144.1104 m F 0 G 0.3 w 10 M 127.6455 144.1104 m S 127.6455 144.1104 m S 127.6455 144.1104 m S 0 g 1 w 4 M 127.6455 144.1104 m F 0 G 0.3 w 10 M 127.6455 144.1104 m S 127.6455 144.1104 m S 1 g 1 w 4 M 127.6455 144.1104 m F 0 G 0.3 w 10 M 127.6455 144.1104 m S 0 g 1 w 4 M 127.6455 144.1104 m F 0 G 0.3 w 10 M 127.6455 144.1104 m S 127.6455 144.1104 m S 127.6455 144.1104 m S 0 g 1 w 4 M 127.6455 144.1104 m F 0 G 0.3 w 10 M 127.6455 144.1104 m S 0 g 1 w 4 M 127.6455 144.1104 m F 0 G 0.3 w 10 M 115.9869 155.5554 m S 139.304 132.6652 m S 127.6455 144.1104 m S 127.6455 144.1104 m S 115.9869 155.5554 m S 115.9869 155.5554 m S 139.304 155.5554 m S 139.304 155.5554 m S 127.6455 144.1104 m S 127.6455 144.1104 m S 115.9869 132.6652 m S 115.9869 132.6652 m S 115.9869 155.5554 m S 139.304 155.5554 m S 139.304 132.6652 m S 139.304 155.5554 m S 115.9869 132.6652 m S 115.9869 132.6652 m S 139.304 132.6652 m S 139.304 132.6652 m S 127.6455 144.1104 m S 0 g 1 w 4 M 127.6455 144.1104 m F 0 G 0.3 w 10 M 127.6455 144.1104 m S 127.6455 144.1104 m S 127.6455 144.1104 m S 0 g 1 w 4 M 127.6455 144.1104 m F 0 G 0.3 w 10 M 127.6455 144.1104 m S 127.6455 144.1104 m S 127.6455 144.1104 m S 0 g 1 w 4 M 127.6455 144.1104 m F 0 G 0.3 w 10 M 127.6455 144.1104 m S 127.6455 144.1104 m S 139.304 132.6652 m S 0 g 1 w 4 M 139.304 132.6652 m F 0 G 0.3 w 10 M 139.304 132.6652 m S 139.304 132.6652 m S 139.304 132.6652 m S 0 g 1 w 4 M 139.304 132.6652 m F 0 G 0.3 w 10 M 139.304 132.6652 m S 139.304 132.6652 m S 139.304 132.6652 m S 0 g 1 w 4 M 139.304 132.6652 m F 0 G 0.3 w 10 M 139.304 132.6652 m S 139.304 132.6652 m S 139.304 132.6652 m S 0 g 1 w 4 M 139.304 132.6652 m F 0 G 0.3 w 10 M 139.304 132.6652 m S 139.304 132.6652 m S 139.304 132.6652 m S 0 g 1 w 4 M 139.304 132.6652 m F 0 G 0.3 w 10 M 139.304 132.6652 m S 139.304 132.6652 m S 1 g 1 w 4 M 139.304 132.6652 m F 0 G 0.3 w 10 M 139.304 132.6652 m S 0 g 1 w 4 M 139.304 132.6652 m F 0 G 0.3 w 10 M 139.304 132.6652 m S 139.304 132.6652 m S 0.5 w 4 M 115.9869 155.5554 m 139.304 155.5554 l 139.304 132.6652 l 115.9869 132.6652 l 115.9869 155.5554 l s 0.3 w 10 M 267.5479 144.1104 m S 0 g 1 w 4 M 267.5479 144.1104 m F 0 G 0.3 w 10 M 267.5479 144.1104 m S 267.5479 144.1104 m S 267.5479 144.1104 m S 0 g 1 w 4 M 267.5479 144.1104 m F 0 G 0.3 w 10 M 267.5479 144.1104 m S 267.5479 144.1104 m S 267.5479 144.1104 m S 0 g 1 w 4 M 267.5479 144.1104 m F 0 G 0.3 w 10 M 267.5479 144.1104 m S 267.5479 144.1104 m S 0 g 1 w 4 M 266.4628 143.0425 m 266.4628 139.4654 L 268.633 139.4654 L 268.633 143.0425 L 272.2186 143.0313 L 272.2186 145.1897 L 268.633 145.1786 L 268.633 148.7557 L 266.4628 148.7557 L 266.4628 145.1786 L 262.8772 145.1897 L 262.8772 143.0313 L 266.4628 143.0425 L f 0 G 0.3 w 10 M 267.5479 144.1104 m S 0 g 1 w 4 M 267.5479 144.1104 m F 0 G 0.3 w 10 M 267.5479 144.1104 m S 267.5479 144.1104 m S 267.5479 144.1104 m S 0 g 1 w 4 M 267.5479 144.1104 m F 0 G 0.3 w 10 M 267.5479 144.1104 m S 267.5479 144.1104 m S 1 g 1 w 4 M 267.5479 144.1104 m F 0 G 0.3 w 10 M 267.5479 144.1104 m S 0 g 1 w 4 M 267.5479 144.1104 m F 0 G 0.3 w 10 M 267.5479 144.1104 m S 267.5479 144.1104 m S 267.5479 144.1104 m S 0 g 1 w 4 M 267.5479 144.1104 m F 0 G 0.3 w 10 M 267.5479 144.1104 m S 0 g 1 w 4 M 267.5479 144.1104 m F 0 G 0.3 w 10 M 255.8893 155.5554 m S 279.2064 132.6652 m S 267.5479 144.1104 m S 267.5479 144.1104 m S 255.8893 155.5554 m S 255.8893 155.5554 m S 279.2064 155.5554 m S 279.2064 155.5554 m S 267.5479 144.1104 m S 267.5479 144.1104 m S 255.8893 132.6652 m S 255.8893 132.6652 m S 255.8893 155.5554 m S 279.2064 155.5554 m S 279.2064 132.6652 m S 279.2064 155.5554 m S 255.8893 132.6652 m S 255.8893 132.6652 m S 279.2064 132.6652 m S 279.2064 132.6652 m S 267.5479 144.1104 m S 0 g 1 w 4 M 267.5479 144.1104 m F 0 G 0.3 w 10 M 267.5479 144.1104 m S 267.5479 144.1104 m S 267.5479 144.1104 m S 0 g 1 w 4 M 267.5479 144.1104 m F 0 G 0.3 w 10 M 267.5479 144.1104 m S 267.5479 144.1104 m S 267.5479 144.1104 m S 0 g 1 w 4 M 267.5479 144.1104 m F 0 G 0.3 w 10 M 267.5479 144.1104 m S 267.5479 144.1104 m S 279.2064 132.6652 m S 0 g 1 w 4 M 279.2064 132.6652 m F 0 G 0.3 w 10 M 279.2064 132.6652 m S 279.2064 132.6652 m S 279.2064 132.6652 m S 0 g 1 w 4 M 279.2064 132.6652 m F 0 G 0.3 w 10 M 279.2064 132.6652 m S 279.2064 132.6652 m S 279.2064 132.6652 m S 0 g 1 w 4 M 279.2064 132.6652 m F 0 G 0.3 w 10 M 279.2064 132.6652 m S 279.2064 132.6652 m S 279.2064 132.6652 m S 0 g 1 w 4 M 279.2064 132.6652 m F 0 G 0.3 w 10 M 279.2064 132.6652 m S 279.2064 132.6652 m S 279.2064 132.6652 m S 0 g 1 w 4 M 279.2064 132.6652 m F 0 G 0.3 w 10 M 279.2064 132.6652 m S 279.2064 132.6652 m S 1 g 1 w 4 M 279.2064 132.6652 m F 0 G 0.3 w 10 M 279.2064 132.6652 m S 0 g 1 w 4 M 279.2064 132.6652 m F 0 G 0.3 w 10 M 279.2064 132.6652 m S 279.2064 132.6652 m S 0.5 w 4 M 255.8893 155.5554 m 279.2064 155.5554 l 279.2064 132.6652 l 255.8893 132.6652 l 255.8893 155.5554 l s 0.3 w 10 M 197.5967 75.44 m S 0 g 1 w 4 M 197.5967 75.44 m F 0 G 0.3 w 10 M 197.5967 75.44 m S 197.5967 75.44 m S 197.5967 75.44 m S 0 g 1 w 4 M 197.5967 75.44 m F 0 G 0.3 w 10 M 197.5967 75.44 m S 197.5967 75.44 m S 197.5967 75.44 m S 0 g 1 w 4 M 197.5967 75.44 m F 0 G 0.3 w 10 M 197.5967 75.44 m S 197.5967 75.44 m S 0 g 1 w 4 M 196.5116 74.3721 m 196.5116 70.795 L 198.6818 70.795 L 198.6818 74.3721 L 202.2674 74.3609 L 202.2674 76.5193 L 198.6818 76.5082 L 198.6818 80.0853 L 196.5116 80.0853 L 196.5116 76.5082 L 192.926 76.5193 L 192.926 74.3609 L 196.5116 74.3721 L f 0 G 0.3 w 10 M 197.5967 75.44 m S 0 g 1 w 4 M 197.5967 75.44 m F 0 G 0.3 w 10 M 197.5967 75.44 m S 197.5967 75.44 m S 197.5967 75.44 m S 0 g 1 w 4 M 197.5967 75.44 m F 0 G 0.3 w 10 M 197.5967 75.44 m S 197.5967 75.44 m S u 1 g 1 w 4 M 197.5967 75.44 m F U 0 G 0.3 w 10 M 197.5967 75.44 m S 0 g 1 w 4 M 197.5967 75.44 m F 0 G 0.3 w 10 M 197.5967 75.44 m S 197.5967 75.44 m S 197.5967 75.44 m S 0 g 1 w 4 M 197.5967 75.44 m F 0 G 0.3 w 10 M 197.5967 75.44 m S 0 g 1 w 4 M 197.5967 75.44 m F 0 G 0.3 w 10 M 185.9382 86.8851 m S 209.2553 63.9949 m S 197.5967 75.44 m S 197.5967 75.44 m S 185.9382 86.8851 m S 185.9382 86.8851 m S 209.2553 86.8851 m S 209.2553 86.8851 m S 197.5967 75.44 m S 197.5967 75.44 m S 185.9382 63.9949 m S 185.9382 63.9949 m S 185.9382 86.8851 m S 209.2553 86.8851 m S 209.2553 63.9949 m S 209.2553 86.8851 m S 185.9382 63.9949 m S 185.9382 63.9949 m S 209.2553 63.9949 m S 209.2553 63.9949 m S 197.5967 75.44 m S 0 g 1 w 4 M 197.5967 75.44 m F 0 G 0.3 w 10 M 197.5967 75.44 m S 197.5967 75.44 m S 197.5967 75.44 m S 0 g 1 w 4 M 197.5967 75.44 m F 0 G 0.3 w 10 M 197.5967 75.44 m S 197.5967 75.44 m S 197.5967 75.44 m S 0 g 1 w 4 M 197.5967 75.44 m F 0 G 0.3 w 10 M 197.5967 75.44 m S 197.5967 75.44 m S 209.2553 63.9949 m S 0 g 1 w 4 M 209.2553 63.9949 m F 0 G 0.3 w 10 M 209.2553 63.9949 m S 209.2553 63.9949 m S 209.2553 63.9949 m S 0 g 1 w 4 M 209.2553 63.9949 m F 0 G 0.3 w 10 M 209.2553 63.9949 m S 209.2553 63.9949 m S 209.2553 63.9949 m S 0 g 1 w 4 M 209.2553 63.9949 m F 0 G 0.3 w 10 M 209.2553 63.9949 m S 209.2553 63.9949 m S 209.2553 63.9949 m S 0 g 1 w 4 M 209.2553 63.9949 m F 0 G 0.3 w 10 M 209.2553 63.9949 m S 209.2553 63.9949 m S 209.2553 63.9949 m S 0 g 1 w 4 M 209.2553 63.9949 m F 0 G 0.3 w 10 M 209.2553 63.9949 m S 209.2553 63.9949 m S 1 g 1 w 4 M 209.2553 63.9949 m F 0 G 0.3 w 10 M 209.2553 63.9949 m S 0 g 1 w 4 M 209.2553 63.9949 m F 0 G 0.3 w 10 M 209.2553 63.9949 m S 209.2553 63.9949 m S 0.5 w 4 M 185.9382 86.8851 m 209.2553 86.8851 l 209.2553 63.9949 l 185.9382 63.9949 l 185.9382 86.8851 l s 0.3 w 10 M 57.6942 75.44 m S 0 g 1 w 4 M 57.6942 75.44 m F 0 G 0.3 w 10 M 57.6942 75.44 m S 57.6942 75.44 m S 57.6942 75.44 m S 0 g 1 w 4 M 57.6942 75.44 m F 0 G 0.3 w 10 M 57.6942 75.44 m S 57.6942 75.44 m S 57.6942 75.44 m S 0 g 1 w 4 M 57.6942 75.44 m F 0 G 0.3 w 10 M 57.6942 75.44 m S 57.6942 75.44 m S 0 g 1 w 4 M 56.6091 74.3721 m 56.6091 70.795 L 58.7793 70.795 L 58.7793 74.3721 L 62.3649 74.3609 L 62.3649 76.5193 L 58.7793 76.5082 L 58.7793 80.0853 L 56.6091 80.0853 L 56.6091 76.5082 L 53.0235 76.5193 L 53.0235 74.3609 L 56.6091 74.3721 L f 0 G 0.3 w 10 M 57.6942 75.44 m S 0 g 1 w 4 M 57.6942 75.44 m F 0 G 0.3 w 10 M 57.6942 75.44 m S 57.6942 75.44 m S 57.6942 75.44 m S 0 g 1 w 4 M 57.6942 75.44 m F 0 G 0.3 w 10 M 57.6942 75.44 m S 57.6942 75.44 m S u 1 g 1 w 4 M 57.6942 75.44 m F U 0 G 0.3 w 10 M 57.6942 75.44 m S 0 g 1 w 4 M 57.6942 75.44 m F 0 G 0.3 w 10 M 57.6942 75.44 m S 57.6942 75.44 m S 57.6942 75.44 m S 0 g 1 w 4 M 57.6942 75.44 m F 0 G 0.3 w 10 M 57.6942 75.44 m S 0 g 1 w 4 M 57.6942 75.44 m F 0 G 0.3 w 10 M 46.0357 86.8851 m S 69.3528 63.9949 m S 57.6942 75.44 m S 57.6942 75.44 m S 46.0357 86.8851 m S 46.0357 86.8851 m S 69.3528 86.8851 m S 69.3528 86.8851 m S 57.6942 75.44 m S 57.6942 75.44 m S 46.0357 63.9949 m S 46.0357 63.9949 m S 46.0357 86.8851 m S 69.3528 86.8851 m S 69.3528 63.9949 m S 69.3528 86.8851 m S 46.0357 63.9949 m S 46.0357 63.9949 m S 69.3528 63.9949 m S 69.3528 63.9949 m S 57.6942 75.44 m S 0 g 1 w 4 M 57.6942 75.44 m F 0 G 0.3 w 10 M 57.6942 75.44 m S 57.6942 75.44 m S 57.6942 75.44 m S 0 g 1 w 4 M 57.6942 75.44 m F 0 G 0.3 w 10 M 57.6942 75.44 m S 57.6942 75.44 m S 57.6942 75.44 m S 0 g 1 w 4 M 57.6942 75.44 m F 0 G 0.3 w 10 M 57.6942 75.44 m S 57.6942 75.44 m S 69.3528 63.9949 m S 0 g 1 w 4 M 69.3528 63.9949 m F 0 G 0.3 w 10 M 69.3528 63.9949 m S 69.3528 63.9949 m S 69.3528 63.9949 m S 0 g 1 w 4 M 69.3528 63.9949 m F 0 G 0.3 w 10 M 69.3528 63.9949 m S 69.3528 63.9949 m S 69.3528 63.9949 m S 0 g 1 w 4 M 69.3528 63.9949 m F 0 G 0.3 w 10 M 69.3528 63.9949 m S 69.3528 63.9949 m S 69.3528 63.9949 m S 0 g 1 w 4 M 69.3528 63.9949 m F 0 G 0.3 w 10 M 69.3528 63.9949 m S 69.3528 63.9949 m S 69.3528 63.9949 m S 0 g 1 w 4 M 69.3528 63.9949 m F 0 G 0.3 w 10 M 69.3528 63.9949 m S 69.3528 63.9949 m S 1 g 1 w 4 M 69.3528 63.9949 m F 0 G 0.3 w 10 M 69.3528 63.9949 m S 0 g 1 w 4 M 69.3528 63.9949 m F 0 G 0.3 w 10 M 69.3528 63.9949 m S 69.3528 63.9949 m S 0.5 w 4 M 46.0357 86.8851 m 69.3528 86.8851 l 69.3528 63.9949 l 46.0357 63.9949 l 46.0357 86.8851 l s 0.3 w 10 M 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 266.4628 213.849 m 262.8772 213.8601 L 262.8772 211.7017 L 266.4628 211.7128 L F 268.633 211.7128 m 272.2186 211.7017 L 272.2186 213.8601 L 268.633 213.849 L F 262.8772 213.8601 m 272.2186 213.8601 l 272.2186 211.7017 l 262.8772 211.7017 l 262.8772 213.8601 l f 0 G 0.3 w 10 M 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 267.5479 212.7808 m S 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 267.5479 212.7808 m S 1 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 267.5479 212.7808 m S 1 g 0.5 w 4 M 267.5479 212.7808 m B 0.3 w 10 M 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 267.5479 212.7808 m S 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 267.5479 212.7808 m S u 1 g 1 w 4 M 267.5479 212.7808 m F U 0 G 0.3 w 10 M 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 267.5479 212.7808 m S 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 267.5479 212.7808 m S 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 267.5479 212.7808 m S u 1 g 1 w 4 M 267.5479 212.7808 m F U 0 G 0.3 w 10 M 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 267.5479 212.7808 m S 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 255.8893 224.2259 m S 279.2064 201.3357 m S 267.5479 212.7808 m S 267.5479 212.7808 m S 255.8893 224.2259 m S 255.8893 224.2259 m S 279.2064 224.2259 m S 279.2064 224.2259 m S 267.5479 212.7808 m S 267.5479 212.7808 m S 255.8893 201.3357 m S 255.8893 201.3357 m S 255.8893 224.2259 m S 279.2064 224.2259 m S 279.2064 201.3357 m S 279.2064 224.2259 m S 255.8893 201.3357 m S 255.8893 201.3357 m S 279.2064 201.3357 m S 279.2064 201.3357 m S 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 267.5479 212.7808 m S 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 267.5479 212.7808 m S 267.5479 212.7808 m S 0 g 1 w 4 M 267.5479 212.7808 m F 0 G 0.3 w 10 M 267.5479 212.7808 m S 267.5479 212.7808 m S 279.2064 201.3357 m S 0 g 1 w 4 M 279.2064 201.3357 m F 0 G 0.3 w 10 M 279.2064 201.3357 m S 279.2064 201.3357 m S 279.2064 201.3357 m S 0 g 1 w 4 M 279.2064 201.3357 m F 0 G 0.3 w 10 M 279.2064 201.3357 m S 279.2064 201.3357 m S 279.2064 201.3357 m S 0 g 1 w 4 M 279.2064 201.3357 m F 0 G 0.3 w 10 M 279.2064 201.3357 m S 279.2064 201.3357 m S 279.2064 201.3357 m S 0 g 1 w 4 M 279.2064 201.3357 m F 0 G 0.3 w 10 M 279.2064 201.3357 m S 279.2064 201.3357 m S 279.2064 201.3357 m S 0 g 1 w 4 M 279.2064 201.3357 m F 0 G 0.3 w 10 M 279.2064 201.3357 m S 279.2064 201.3357 m S 1 g 1 w 4 M 279.2064 201.3357 m F 0 G 0.3 w 10 M 279.2064 201.3357 m S 0 g 1 w 4 M 279.2064 201.3357 m F 0 G 0.3 w 10 M 279.2064 201.3357 m S 279.2064 201.3357 m S 0.5 w 4 M 255.8893 224.2259 m 279.2064 224.2259 l 279.2064 201.3357 l 255.8893 201.3357 l 255.8893 224.2259 l s 0.3 w 10 M 81.0113 212.7808 m S 0 g 1 w 4 M 81.0113 212.7808 m F 0 G 0.3 w 10 M 81.0113 212.7808 m S 81.0113 212.7808 m S 81.0113 212.7808 m S 0 g 1 w 4 M 81.0113 212.7808 m F 0 G 0.3 w 10 M 81.0113 212.7808 m S 81.0113 212.7808 m S 1 g 0.5 w 4 M 75.0009 212.7808 m 75.0009 209.559 77.6919 206.9472 81.0113 206.9472 c 84.3307 206.9472 87.0217 209.559 87.0217 212.7808 c B 87.0217 212.7808 m 87.0217 216.0026 84.3307 218.6144 81.0113 218.6144 c 77.6919 218.6144 75.0009 216.0026 75.0009 212.7808 c B 81.0113 212.7808 m B 0.3 w 10 M 81.0113 212.7808 m S 0 g 1 w 4 M 81.0113 212.7808 m F 0 G 0.3 w 10 M 81.0113 212.7808 m S 81.0113 212.7808 m S 104.3284 212.7808 m S 0 g 1 w 4 M 104.3284 212.7808 m F 0 G 0.3 w 10 M 104.3284 212.7808 m S 104.3284 212.7808 m S 104.3284 212.7808 m S 0 g 1 w 4 M 104.3284 212.7808 m F 0 G 0.3 w 10 M 104.3284 212.7808 m S 104.3284 212.7808 m S 1 g 0.5 w 4 M 98.318 212.7808 m 98.318 209.559 101.009 206.9472 104.3284 206.9472 c 107.6478 206.9472 110.3388 209.559 110.3388 212.7808 c B 110.3388 212.7808 m 110.3388 216.0026 107.6478 218.6144 104.3284 218.6144 c 101.009 218.6144 98.318 216.0026 98.318 212.7808 c B 104.3284 212.7808 m B 0.3 w 10 M 104.3284 212.7808 m S 0 g 1 w 4 M 104.3284 212.7808 m F 0 G 0.3 w 10 M 104.3284 212.7808 m S 104.3284 212.7808 m S 81.0113 189.8906 m S 69.3528 189.8906 m S 75.182 184.1681 m S 69.3528 189.8906 m S 57.6942 189.8906 m S 63.5236 195.6132 m S 81.0113 189.8906 m S 69.3528 189.8906 m S 75.182 195.6132 m S 69.3528 189.8906 m S 57.6942 189.8906 m S 63.5236 184.1681 m S 57.6942 189.8906 m S 51.865 184.1681 m S 57.6942 189.8906 m S 51.865 195.6132 m S 0 g 1 w 4 M 51.865 184.1681 m F 75.182 184.1681 m F 0 G 0.3 w 10 M 81.0113 189.8906 m S 86.8406 184.1681 m S 81.0113 189.8906 m S 86.8406 195.6132 m S 0 g 1 w 4 M 86.8406 184.1681 m F 0 G 0.3 w 10 M 81.0113 189.8906 m S 86.8406 184.1681 m S 81.0113 189.8906 m S 86.8406 195.6132 m S 0 g 1 w 4 M 86.8406 184.1681 m F 0 G 0.3 w 10 M 57.6942 189.8906 m S 0 g 1 w 4 M 57.6942 189.8906 m F 0 G 0.3 w 10 M 57.6942 189.8906 m S 57.6942 189.8906 m S 57.6942 189.8906 m S 0 g 1 w 4 M 57.6942 189.8906 m F 0 G 0.3 w 10 M 57.6942 189.8906 m S 57.6942 189.8906 m S 1 g 0.5 w 4 M 51.6838 189.8906 m 51.6838 186.6688 54.3748 184.057 57.6942 184.057 c 61.0136 184.057 63.7046 186.6688 63.7046 189.8906 c B 63.7046 189.8906 m 63.7046 193.1124 61.0136 195.7242 57.6942 195.7242 c 54.3748 195.7242 51.6838 193.1124 51.6838 189.8906 c B 57.6942 189.8906 m B 0.3 w 10 M 57.6942 189.8906 m S 0 g 1 w 4 M 57.6942 189.8906 m F 0 G 0.3 w 10 M 57.6942 189.8906 m S 57.6942 189.8906 m S 81.0113 189.8906 m S 0 g 1 w 4 M 81.0113 189.8906 m F 0 G 0.3 w 10 M 81.0113 189.8906 m S 81.0113 189.8906 m S 81.0113 189.8906 m S 0 g 1 w 4 M 81.0113 189.8906 m F 0 G 0.3 w 10 M 81.0113 189.8906 m S 81.0113 189.8906 m S 1 g 0.5 w 4 M 75.001 189.8906 m 75.001 186.6688 77.692 184.057 81.0113 184.057 c 84.3307 184.057 87.0218 186.6688 87.0218 189.8906 c B 87.0218 189.8906 m 87.0218 193.1124 84.3307 195.7242 81.0113 195.7242 c 77.692 195.7242 75.001 193.1124 75.001 189.8906 c B 81.0113 189.8906 m B 0.3 w 10 M 81.0113 189.8906 m S 0 g 1 w 4 M 81.0113 189.8906 m F 0 G 0.3 w 10 M 81.0113 189.8906 m S 81.0113 189.8906 m S 174.2797 212.7808 m S 162.6211 212.7808 m S 168.4504 207.0583 m S 162.6211 212.7808 m S 150.9626 212.7808 m S 156.7919 218.5033 m S 174.2797 212.7808 m S 162.6211 212.7808 m S 168.4504 218.5033 m S 162.6211 212.7808 m S 150.9626 212.7808 m S 156.7919 207.0583 m S 150.9626 212.7808 m S 145.1333 207.0583 m S 150.9626 212.7808 m S 145.1333 218.5033 m S 0 g 1 w 4 M 145.1333 207.0583 m F 168.4504 207.0583 m F 0 G 0.3 w 10 M 174.2797 212.7808 m S 180.1089 207.0583 m S 174.2797 212.7808 m S 180.1089 218.5033 m S 0 g 1 w 4 M 180.1089 207.0583 m F 0 G 0.3 w 10 M 174.2797 212.7808 m S 180.1089 207.0583 m S 174.2797 212.7808 m S 180.1089 218.5033 m S 0 g 1 w 4 M 180.1089 207.0583 m F 0 G 0.3 w 10 M 150.9626 212.7808 m S 0 g 1 w 4 M 150.9626 212.7808 m F 0 G 0.3 w 10 M 150.9626 212.7808 m S 150.9626 212.7808 m S 150.9626 212.7808 m S 0 g 1 w 4 M 150.9626 212.7808 m F 0 G 0.3 w 10 M 150.9626 212.7808 m S 150.9626 212.7808 m S 1 g 0.5 w 4 M 144.9522 212.7808 m 144.9522 209.559 147.6432 206.9472 150.9626 206.9472 c 154.282 206.9472 156.973 209.559 156.973 212.7808 c B 156.973 212.7808 m 156.973 216.0026 154.282 218.6144 150.9626 218.6144 c 147.6432 218.6144 144.9522 216.0026 144.9522 212.7808 c B 150.9626 212.7808 m B 0.3 w 10 M 150.9626 212.7808 m S 0 g 1 w 4 M 150.9626 212.7808 m F 0 G 0.3 w 10 M 150.9626 212.7808 m S 150.9626 212.7808 m S 174.2797 212.7808 m S 0 g 1 w 4 M 174.2797 212.7808 m F 0 G 0.3 w 10 M 174.2797 212.7808 m S 174.2797 212.7808 m S 174.2797 212.7808 m S 0 g 1 w 4 M 174.2797 212.7808 m F 0 G 0.3 w 10 M 174.2797 212.7808 m S 174.2797 212.7808 m S 1 g 0.5 w 4 M 168.2693 212.7808 m 168.2693 209.559 170.9603 206.9472 174.2797 206.9472 c 177.5991 206.9472 180.2901 209.559 180.2901 212.7808 c B 180.2901 212.7808 m 180.2901 216.0026 177.5991 218.6144 174.2797 218.6144 c 170.9603 218.6144 168.2693 216.0026 168.2693 212.7808 c B 174.2797 212.7808 m B 0.3 w 10 M 174.2797 212.7808 m S 0 g 1 w 4 M 174.2797 212.7808 m F 0 G 0.3 w 10 M 174.2797 212.7808 m S 174.2797 212.7808 m S 127.6454 189.8906 m S 115.9869 189.8906 m S 121.8161 184.1681 m S 115.9869 189.8906 m S 104.3283 189.8906 m S 110.1576 195.6132 m S 127.6454 189.8906 m S 115.9869 189.8906 m S 121.8161 195.6132 m S 115.9869 189.8906 m S 104.3283 189.8906 m S 110.1576 184.1681 m S 104.3283 189.8906 m S 98.4991 184.1681 m S 104.3283 189.8906 m S 98.4991 195.6132 m S 0 g 1 w 4 M 98.4991 184.1681 m F 121.8161 184.1681 m F 0 G 0.3 w 10 M 127.6454 189.8906 m S 133.4747 184.1681 m S 127.6454 189.8906 m S 133.4747 195.6132 m S 0 g 1 w 4 M 133.4747 184.1681 m F 0 G 0.3 w 10 M 127.6454 189.8906 m S 133.4747 184.1681 m S 127.6454 189.8906 m S 133.4747 195.6132 m S 0 g 1 w 4 M 133.4747 184.1681 m F 0 G 0.3 w 10 M 104.3283 189.8906 m S 0 g 1 w 4 M 104.3283 189.8906 m F 0 G 0.3 w 10 M 104.3283 189.8906 m S 104.3283 189.8906 m S 104.3283 189.8906 m S 0 g 1 w 4 M 104.3283 189.8906 m F 0 G 0.3 w 10 M 104.3283 189.8906 m S 104.3283 189.8906 m S 1 g 0.5 w 4 M 98.3179 189.8906 m 98.3179 186.6688 101.0089 184.057 104.3283 184.057 c 107.6477 184.057 110.3387 186.6688 110.3387 189.8906 c B 110.3387 189.8906 m 110.3387 193.1124 107.6477 195.7242 104.3283 195.7242 c 101.0089 195.7242 98.3179 193.1124 98.3179 189.8906 c B 104.3283 189.8906 m B 0.3 w 10 M 104.3283 189.8906 m S 0 g 1 w 4 M 104.3283 189.8906 m F 0 G 0.3 w 10 M 104.3283 189.8906 m S 104.3283 189.8906 m S 127.6454 189.8906 m S 0 g 1 w 4 M 127.6454 189.8906 m F 0 G 0.3 w 10 M 127.6454 189.8906 m S 127.6454 189.8906 m S 127.6454 189.8906 m S 0 g 1 w 4 M 127.6454 189.8906 m F 0 G 0.3 w 10 M 127.6454 189.8906 m S 127.6454 189.8906 m S 1 g 0.5 w 4 M 121.6351 189.8906 m 121.6351 186.6688 124.326 184.057 127.6454 184.057 c 130.9648 184.057 133.6558 186.6688 133.6558 189.8906 c B 133.6558 189.8906 m 133.6558 193.1124 130.9648 195.7242 127.6454 195.7242 c 124.326 195.7242 121.6351 193.1124 121.6351 189.8906 c B 127.6454 189.8906 m B 0.3 w 10 M 127.6454 189.8906 m S 0 g 1 w 4 M 127.6454 189.8906 m F 0 G 0.3 w 10 M 127.6454 189.8906 m S 127.6454 189.8906 m S 174.2797 189.8906 m S 162.6211 189.8906 m S 168.4504 184.1681 m S 162.6211 189.8906 m S 150.9626 189.8906 m S 156.7919 195.6132 m S 174.2797 189.8906 m S 162.6211 189.8906 m S 168.4504 195.6132 m S 162.6211 189.8906 m S 150.9626 189.8906 m S 156.7919 184.1681 m S 150.9626 189.8906 m S 145.1333 184.1681 m S 150.9626 189.8906 m S 145.1333 195.6132 m S 0 g 1 w 4 M 145.1333 184.1681 m F 168.4504 184.1681 m F 0 G 0.3 w 10 M 174.2797 189.8906 m S 180.1089 184.1681 m S 174.2797 189.8906 m S 180.1089 195.6132 m S 0 g 1 w 4 M 180.1089 184.1681 m F 0 G 0.3 w 10 M 174.2797 189.8906 m S 180.1089 184.1681 m S 174.2797 189.8906 m S 180.1089 195.6132 m S 0 g 1 w 4 M 180.1089 184.1681 m F 0 G 0.3 w 10 M 150.9626 189.8906 m S 0 g 1 w 4 M 150.9626 189.8906 m F 0 G 0.3 w 10 M 150.9626 189.8906 m S 150.9626 189.8906 m S 150.9626 189.8906 m S 0 g 1 w 4 M 150.9626 189.8906 m F 0 G 0.3 w 10 M 150.9626 189.8906 m S 150.9626 189.8906 m S 1 g 0.5 w 4 M 144.9522 189.8906 m 144.9522 186.6688 147.6432 184.057 150.9626 184.057 c 154.282 184.057 156.973 186.6688 156.973 189.8906 c B 156.973 189.8906 m 156.973 193.1124 154.282 195.7242 150.9626 195.7242 c 147.6432 195.7242 144.9522 193.1124 144.9522 189.8906 c B 150.9626 189.8906 m B 0.3 w 10 M 150.9626 189.8906 m S 0 g 1 w 4 M 150.9626 189.8906 m F 0 G 0.3 w 10 M 150.9626 189.8906 m S 150.9626 189.8906 m S 174.2797 189.8906 m S 0 g 1 w 4 M 174.2797 189.8906 m F 0 G 0.3 w 10 M 174.2797 189.8906 m S 174.2797 189.8906 m S 174.2797 189.8906 m S 0 g 1 w 4 M 174.2797 189.8906 m F 0 G 0.3 w 10 M 174.2797 189.8906 m S 174.2797 189.8906 m S 1 g 0.5 w 4 M 168.2693 189.8906 m 168.2693 186.6688 170.9603 184.057 174.2797 184.057 c 177.5991 184.057 180.2901 186.6688 180.2901 189.8906 c B 180.2901 189.8906 m 180.2901 193.1124 177.5991 195.7242 174.2797 195.7242 c 170.9603 195.7242 168.2693 193.1124 168.2693 189.8906 c B 174.2797 189.8906 m B 0.3 w 10 M 174.2797 189.8906 m S 0 g 1 w 4 M 174.2797 189.8906 m F 0 G 0.3 w 10 M 174.2797 189.8906 m S 174.2797 189.8906 m S 244.2308 212.7808 m S 232.5722 212.7808 m S 238.4015 207.0583 m S 232.5722 212.7808 m S 220.9137 212.7808 m S 226.743 218.5033 m S 244.2308 212.7808 m S 232.5722 212.7808 m S 238.4015 218.5033 m S 232.5722 212.7808 m S 220.9137 212.7808 m S 226.743 207.0583 m S 220.9137 212.7808 m S 215.0844 207.0583 m S 220.9137 212.7808 m S 215.0844 218.5033 m S 0 g 1 w 4 M 215.0844 207.0583 m F 238.4015 207.0583 m F 0 G 0.3 w 10 M 244.2308 212.7808 m S 250.0601 207.0583 m S 244.2308 212.7808 m S 250.0601 218.5033 m S 0 g 1 w 4 M 250.0601 207.0583 m F 0 G 0.3 w 10 M 244.2308 212.7808 m S 250.0601 207.0583 m S 244.2308 212.7808 m S 250.0601 218.5033 m S 0 g 1 w 4 M 250.0601 207.0583 m F 0 G 0.3 w 10 M 220.9137 212.7808 m S 0 g 1 w 4 M 220.9137 212.7808 m F 0 G 0.3 w 10 M 220.9137 212.7808 m S 220.9137 212.7808 m S 220.9137 212.7808 m S 0 g 1 w 4 M 220.9137 212.7808 m F 0 G 0.3 w 10 M 220.9137 212.7808 m S 220.9137 212.7808 m S 1 g 0.5 w 4 M 214.9033 212.7808 m 214.9033 209.559 217.5943 206.9472 220.9137 206.9472 c 224.2331 206.9472 226.9241 209.559 226.9241 212.7808 c B 220.9137 212.7808 m B 0.3 w 10 M 220.9137 212.7808 m S 0 g 1 w 4 M 220.9137 212.7808 m F 0 G 0.3 w 10 M 220.9137 212.7808 m S 220.9137 212.7808 m S 244.2308 212.7808 m S 0 g 1 w 4 M 244.2308 212.7808 m F 0 G 0.3 w 10 M 244.2308 212.7808 m S 244.2308 212.7808 m S 244.2308 212.7808 m S 0 g 1 w 4 M 244.2308 212.7808 m F 0 G 0.3 w 10 M 244.2308 212.7808 m S 244.2308 212.7808 m S 1 g 0.5 w 4 M 238.2204 212.7808 m 238.2204 209.559 240.9114 206.9472 244.2308 206.9472 c 247.5502 206.9472 250.2412 209.559 250.2412 212.7808 c B 214.9033 212.7808 m 214.9033 216.0026 217.5943 218.6144 220.9137 218.6144 c 224.2331 218.6144 226.9241 216.0026 226.6741 212.7808 c B 237.9704 212.7808 m 238.2204 216.0026 240.9114 218.6144 244.2308 218.6144 c 247.5502 218.6144 250.2412 216.0026 250.2412 212.7808 c B 244.2308 212.7808 m B 0.3 w 10 M 244.2308 212.7808 m S 0 g 1 w 4 M 244.2308 212.7808 m F 0 G 0.3 w 10 M 244.2308 212.7808 m S 244.2308 212.7808 m S 220.9138 189.8906 m S 209.2552 189.8906 m S 215.0845 184.1681 m S 209.2552 189.8906 m S 197.5967 189.8906 m S 203.426 195.6132 m S 220.9138 189.8906 m S 209.2552 189.8906 m S 215.0845 195.6132 m S 209.2552 189.8906 m S 197.5967 189.8906 m S 203.426 184.1681 m S 197.5967 189.8906 m S 191.7674 184.1681 m S 197.5967 189.8906 m S 191.7674 195.6132 m S 0 g 1 w 4 M 191.7674 184.1681 m F 215.0845 184.1681 m F 0 G 0.3 w 10 M 220.9138 189.8906 m S 226.743 184.1681 m S 220.9138 189.8906 m S 226.743 195.6132 m S 0 g 1 w 4 M 226.743 184.1681 m F 0 G 0.3 w 10 M 220.9138 189.8906 m S 226.743 184.1681 m S 220.9138 189.8906 m S 226.743 195.6132 m S 0 g 1 w 4 M 226.743 184.1681 m F 0 G 0.3 w 10 M 197.5967 189.8906 m S 0 g 1 w 4 M 197.5967 189.8906 m F 0 G 0.3 w 10 M 197.5967 189.8906 m S 197.5967 189.8906 m S 197.5967 189.8906 m S 0 g 1 w 4 M 197.5967 189.8906 m F 0 G 0.3 w 10 M 197.5967 189.8906 m S 197.5967 189.8906 m S 1 g 0.5 w 4 M 191.5863 189.8906 m 191.5863 186.6688 194.2773 184.057 197.5967 184.057 c 200.9161 184.057 203.6071 186.6688 203.6071 189.8906 c B 203.6071 189.8906 m 203.6071 193.1124 200.9161 195.7242 197.5967 195.7242 c 194.2773 195.7242 191.5863 193.1124 191.5863 189.8906 c B 197.5967 189.8906 m B 0.3 w 10 M 197.5967 189.8906 m S 0 g 1 w 4 M 197.5967 189.8906 m F 0 G 0.3 w 10 M 197.5967 189.8906 m S 197.5967 189.8906 m S 220.9138 189.8906 m S 0 g 1 w 4 M 220.9138 189.8906 m F 0 G 0.3 w 10 M 220.9138 189.8906 m S 220.9138 189.8906 m S 220.9138 189.8906 m S 0 g 1 w 4 M 220.9138 189.8906 m F 0 G 0.3 w 10 M 220.9138 189.8906 m S 220.9138 189.8906 m S 1 g 0.5 w 4 M 214.9034 189.8906 m 214.9034 186.6688 217.5944 184.057 220.9138 184.057 c 224.2332 184.057 226.9242 186.6688 226.9242 189.8906 c B 226.9242 189.8906 m 226.9242 193.1124 224.2332 195.7242 220.9138 195.7242 c 217.5944 195.7242 214.9034 193.1124 214.9034 189.8906 c B 220.9138 189.8906 m B 0.3 w 10 M 220.9138 189.8906 m S 0 g 1 w 4 M 220.9138 189.8906 m F 0 G 0.3 w 10 M 220.9138 189.8906 m S 220.9138 189.8906 m S 3 w 267.5479 189.8906 m S 255.8893 189.8906 m S 261.7185 184.1681 m S 255.8893 189.8906 m S 244.2308 189.8906 m S 250.0601 195.6132 m S 267.5479 189.8906 m S 255.8893 189.8906 m S 261.7185 195.6132 m S 255.8893 189.8906 m S 244.2308 189.8906 m S 250.0601 184.1681 m S 244.2308 189.8906 m S 238.4015 184.1681 m S 244.2308 189.8906 m S 238.4015 195.6132 m S 4 M 238.4015 184.1681 m S 261.7185 184.1681 m S 10 M 267.5479 189.8906 m S 273.3771 184.1681 m S 267.5479 189.8906 m S 273.3771 195.6132 m S 4 M 273.3771 184.1681 m S 10 M 267.5479 189.8906 m S 273.3771 184.1681 m S 267.5479 189.8906 m S 273.3771 195.6132 m S 4 M 273.3771 184.1681 m S 10 M 244.2308 189.8906 m S 4 M 244.2308 189.8906 m S 10 M 244.2308 189.8906 m S 244.2308 189.8906 m S 244.2308 189.8906 m S 4 M 244.2308 189.8906 m S 10 M 244.2308 189.8906 m S 244.2308 189.8906 m S 1 g 0.5 w 4 M 238.2204 189.8906 m 238.2204 186.6688 240.9114 184.057 244.2308 184.057 c 246.8835 184.057 250.2412 186.6688 250.2412 189.8906 c B 250.2412 189.8906 m 250.2412 193.1124 247.5502 195.7242 244.2308 195.7242 c 240.9114 195.7242 238.2204 193.1124 238.2204 189.8906 c B 3 w 244.2308 189.8906 m S 10 M 244.2308 189.8906 m S 4 M 244.2308 189.8906 m S 10 M 244.2308 189.8906 m S 244.2308 189.8906 m S 267.5479 189.8906 m S 4 M 267.5479 189.8906 m S 10 M 267.5479 189.8906 m S 267.5479 189.8906 m S 267.5479 189.8906 m S 4 M 267.5479 189.8906 m S 10 M 267.5479 189.8906 m S 267.5479 189.8906 m S 1 g 0.5 w 4 M 261.5375 189.8906 m 261.5375 186.6688 264.2285 184.057 267.5479 184.057 c 270.8673 184.057 273.5583 186.6688 273.5583 189.8906 c B 273.5583 189.8906 m 273.5583 193.1124 270.8673 195.7242 267.5479 195.7242 c 264.2285 195.7242 261.5375 193.1124 261.5375 189.8906 c S 3 w 267.5479 189.8906 m S 10 M 267.5479 189.8906 m S 4 M 267.5479 189.8906 m S 10 M 267.5479 189.8906 m S 267.5479 189.8906 m S 1 g 4 M 226.6741 212.7808 m 237.9704 212.7808 l B 226.9242 189.8906 m 238.2205 189.8906 l B 87.0217 212.7808 m 98.318 212.7808 l B 87.0218 189.8906 m 98.3181 189.8906 l B 0.3 w 10 M 57.6942 167.0006 m S 51.865 161.2781 m S 57.6942 167.0006 m S 51.865 172.7231 m S 69.3528 167.0006 m S 57.6942 167.0006 m S 63.5235 172.7231 m S 69.3528 167.0006 m S 57.6942 167.0006 m S 63.5235 161.2781 m S 0 g 1 w 4 M 63.5235 172.7231 m F 0 G 0.3 w 10 M 81.0113 167.0006 m S 69.3528 167.0006 m S 75.182 172.7231 m S 92.6698 167.0006 m S 81.0113 167.0006 m S 86.8406 161.2781 m S 92.6698 167.0006 m S 81.0113 167.0006 m S 86.8406 172.7231 m S 104.3284 167.0006 m S 92.6698 167.0006 m S 98.4991 172.7231 m S 104.3284 167.0006 m S 92.6698 167.0006 m S 98.4991 161.2781 m S 81.0113 167.0006 m S 69.3528 167.0006 m S 75.182 161.2781 m S 0 g 1 w 4 M 75.182 172.7231 m F 98.4991 172.7231 m F 0 G 0.3 w 10 M 115.9869 167.0006 m S 104.3284 167.0006 m S 110.1576 172.7231 m S 127.6455 167.0006 m S 115.9869 167.0006 m S 121.8162 161.2781 m S 127.6455 167.0006 m S 115.9869 167.0006 m S 121.8162 172.7231 m S 139.304 167.0006 m S 127.6455 167.0006 m S 133.4747 172.7231 m S 139.304 167.0006 m S 127.6455 167.0006 m S 133.4747 161.2781 m S 115.9869 167.0006 m S 104.3284 167.0006 m S 110.1576 161.2781 m S 0 g 1 w 4 M 110.1576 172.7231 m F 133.4747 172.7231 m F 0 G 0.3 w 10 M 139.304 167.0006 m S 139.304 167.0006 m S 115.9869 167.0006 m S 104.3284 167.0006 m S 110.1576 172.7231 m S 127.6454 167.0006 m S 115.9869 167.0006 m S 121.8162 161.2781 m S 127.6454 167.0006 m S 115.9869 167.0006 m S 121.8162 172.7231 m S 139.304 167.0006 m S 127.6454 167.0006 m S 133.4747 172.7231 m S 139.304 167.0006 m S 127.6454 167.0006 m S 133.4747 161.2781 m S 115.9869 167.0006 m S 104.3284 167.0006 m S 110.1576 161.2781 m S 0 g 1 w 4 M 110.1576 172.7231 m F 133.4747 172.7231 m F 0 G 0.3 w 10 M 150.9626 167.0006 m S 139.304 167.0006 m S 145.1332 172.7231 m S 162.6211 167.0006 m S 150.9626 167.0006 m S 156.7918 161.2781 m S 162.6211 167.0006 m S 150.9626 167.0006 m S 156.7918 172.7231 m S 174.2796 167.0006 m S 162.6211 167.0006 m S 168.4504 172.7231 m S 174.2796 167.0006 m S 162.6211 167.0006 m S 168.4504 161.2781 m S 150.9626 167.0006 m S 139.304 167.0006 m S 145.1332 161.2781 m S 0 g 1 w 4 M 145.1332 172.7231 m F 168.4504 172.7231 m F 0 G 0.3 w 10 M 185.9382 167.0006 m S 174.2796 167.0006 m S 180.1088 172.7231 m S 197.5967 167.0006 m S 185.9382 167.0006 m S 191.7674 161.2781 m S 197.5967 167.0006 m S 185.9382 167.0006 m S 191.7674 172.7231 m S 209.2552 167.0006 m S 197.5967 167.0006 m S 203.426 172.7231 m S 209.2552 167.0006 m S 197.5967 167.0006 m S 203.426 161.2781 m S 185.9382 167.0006 m S 174.2796 167.0006 m S 180.1088 161.2781 m S 0 g 1 w 4 M 180.1088 172.7231 m F 203.426 172.7231 m F 0 G 0.3 w 10 M 209.2552 167.0006 m S 209.2552 167.0006 m S 57.6942 167.0006 m S 0 g 1 w 4 M 57.6942 167.0006 m F 0 G 0.3 w 10 M 57.6942 167.0006 m S 57.6942 167.0006 m S 57.6942 167.0006 m S 0 g 1 w 4 M 57.6942 167.0006 m F 0 G 0.3 w 10 M 57.6942 167.0006 m S 57.6942 167.0006 m S 57.6942 167.0006 m S 0 g 1 w 4 M 57.6942 167.0006 m F 0 G 0.3 w 10 M 57.6942 167.0006 m S 57.6942 167.0006 m S 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 69.3528 167.0006 m S 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 69.3528 167.0006 m S 69.3528 167.0006 m S 0 g 1 w 4 M 69.3528 167.0006 m F 0 G 0.3 w 10 M 69.3528 167.0006 m S 69.3528 167.0006 m S 220.9137 167.0006 m S 209.2552 167.0006 m S 215.0844 172.7231 m S 232.5722 167.0006 m S 220.9137 167.0006 m S 226.743 161.2781 m S 232.5722 167.0006 m S 220.9137 167.0006 m S 226.743 172.7231 m S 244.2308 167.0006 m S 232.5722 167.0006 m S 238.4015 172.7231 m S 244.2308 167.0006 m S 232.5722 167.0006 m S 238.4015 161.2781 m S 220.9137 167.0006 m S 209.2552 167.0006 m S 215.0844 161.2781 m S 0 g 1 w 4 M 215.0844 172.7231 m F 238.4015 172.7231 m F 0 G 0.3 w 10 M 255.8893 167.0006 m S 244.2308 167.0006 m S 250.06 172.7231 m S 267.5478 167.0006 m S 255.8893 167.0006 m S 261.7186 161.2781 m S 267.5478 167.0006 m S 255.8893 167.0006 m S 261.7186 172.7231 m S 267.5478 167.0006 m S 273.3771 172.7231 m S 267.5478 167.0006 m S 273.3771 161.2781 m S 255.8893 167.0006 m S 244.2308 167.0006 m S 250.06 161.2781 m S 0 g 1 w 4 M 250.06 172.7231 m F 273.3771 172.7231 m F 0 G 0.3 w 10 M 232.5722 167.0006 m S 0 g 1 w 4 M 232.5722 167.0006 m F 0 G 0.3 w 10 M 232.5722 167.0006 m S 232.5722 167.0006 m S 232.5722 167.0006 m S 0 g 1 w 4 M 232.5722 167.0006 m F 0 G 0.3 w 10 M 232.5722 167.0006 m S 232.5722 167.0006 m S 232.5722 167.0006 m S 0 g 1 w 4 M 232.5722 167.0006 m F 0 G 0.3 w 10 M 232.5722 167.0006 m S 232.5722 167.0006 m S 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 244.2308 167.0006 m S 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 244.2308 167.0006 m S 244.2308 167.0006 m S 0 g 1 w 4 M 244.2308 167.0006 m F 0 G 0.3 w 10 M 244.2308 167.0006 m S 244.2308 167.0006 m S 81.0113 167.0006 m S 69.3528 167.0006 m S 75.182 161.278 m S 69.3528 167.0006 m S 57.6942 167.0006 m S 63.5235 172.7231 m S 81.0113 167.0006 m S 69.3528 167.0006 m S 75.182 172.7231 m S 69.3528 167.0006 m S 57.6942 167.0006 m S 63.5235 161.278 m S 57.6942 167.0006 m S 51.865 161.278 m S 57.6942 167.0006 m S 51.865 172.7231 m S 0 g 1 w 4 M 51.865 161.278 m F 75.182 161.278 m F 0 G 0.3 w 10 M 81.0113 167.0006 m S 86.8406 161.278 m S 81.0113 167.0006 m S 86.8406 172.7231 m S 0 g 1 w 4 M 86.8406 161.278 m F 0 G 0.3 w 10 M 81.0113 167.0006 m S 86.8406 161.278 m S 81.0113 167.0006 m S 86.8406 172.7231 m S 0 g 1 w 4 M 86.8406 161.278 m F 0 G 0.3 w 10 M 57.6942 167.0006 m S 0 g 1 w 4 M 57.6942 167.0006 m F 0 G 0.3 w 10 M 57.6942 167.0006 m S 57.6942 167.0006 m S 57.6942 167.0006 m S 0 g 1 w 4 M 57.6942 167.0006 m F 0 G 0.3 w 10 M 57.6942 167.0006 m S 57.6942 167.0006 m S 1 g 0.5 w 4 M 51.6838 167.0006 m 51.6838 163.7788 54.3748 161.167 57.6942 161.167 c 61.0136 161.167 63.7046 163.7788 63.7046 167.0006 c B 63.7046 167.0006 m 63.7046 170.2224 61.0136 172.8342 57.6942 172.8342 c 54.3748 172.8342 51.6838 170.2224 51.6838 167.0006 c B 57.6942 167.0006 m B 0.3 w 10 M 57.6942 167.0006 m S 0 g 1 w 4 M 57.6942 167.0006 m F 0 G 0.3 w 10 M 57.6942 167.0006 m S 57.6942 167.0006 m S 81.0113 167.0006 m S 0 g 1 w 4 M 81.0113 167.0006 m F 0 G 0.3 w 10 M 81.0113 167.0006 m S 81.0113 167.0006 m S 81.0113 167.0006 m S 0 g 1 w 4 M 81.0113 167.0006 m F 0 G 0.3 w 10 M 81.0113 167.0006 m S 81.0113 167.0006 m S 1 g 0.5 w 4 M 75.0009 167.0006 m 75.0009 163.7788 77.6919 161.167 81.0113 161.167 c 84.3307 161.167 87.0217 163.7788 87.0217 167.0006 c B 87.0217 167.0006 m 87.0217 170.2224 84.3307 172.8342 81.0113 172.8342 c 77.6919 172.8342 75.0009 170.2224 75.0009 167.0006 c B 81.0113 167.0006 m B 0.3 w 10 M 81.0113 167.0006 m S 0 g 1 w 4 M 81.0113 167.0006 m F 0 G 0.3 w 10 M 81.0113 167.0006 m S 81.0113 167.0006 m S 127.6454 167.0006 m S 115.9869 167.0006 m S 121.8161 161.278 m S 115.9869 167.0006 m S 104.3283 167.0006 m S 110.1576 172.7231 m S 127.6454 167.0006 m S 115.9869 167.0006 m S 121.8161 172.7231 m S 115.9869 167.0006 m S 104.3283 167.0006 m S 110.1576 161.278 m S 104.3283 167.0006 m S 98.4991 161.278 m S 104.3283 167.0006 m S 98.4991 172.7231 m S 0 g 1 w 4 M 98.4991 161.278 m F 121.8161 161.278 m F 0 G 0.3 w 10 M 127.6454 167.0006 m S 133.4747 161.278 m S 127.6454 167.0006 m S 133.4747 172.7231 m S 0 g 1 w 4 M 133.4747 161.278 m F 0 G 0.3 w 10 M 127.6454 167.0006 m S 133.4747 161.278 m S 127.6454 167.0006 m S 133.4747 172.7231 m S 0 g 1 w 4 M 133.4747 161.278 m F 0 G 0.3 w 10 M 104.3283 167.0006 m S 0 g 1 w 4 M 104.3283 167.0006 m F 0 G 0.3 w 10 M 104.3283 167.0006 m S 104.3283 167.0006 m S 104.3283 167.0006 m S 0 g 1 w 4 M 104.3283 167.0006 m F 0 G 0.3 w 10 M 104.3283 167.0006 m S 104.3283 167.0006 m S 1 g 0.5 w 4 M 98.3179 167.0006 m 98.3179 163.7788 101.0089 161.167 104.3283 161.167 c 107.6477 161.167 110.3387 163.7788 110.3387 167.0006 c B 110.3387 167.0006 m 110.3387 170.2224 107.6477 172.8342 104.3283 172.8342 c 101.0089 172.8342 98.3179 170.2224 98.3179 167.0006 c B 104.3283 167.0006 m B 0.3 w 10 M 104.3283 167.0006 m S 0 g 1 w 4 M 104.3283 167.0006 m F 0 G 0.3 w 10 M 104.3283 167.0006 m S 104.3283 167.0006 m S 127.6454 167.0006 m S 0 g 1 w 4 M 127.6454 167.0006 m F 0 G 0.3 w 10 M 127.6454 167.0006 m S 127.6454 167.0006 m S 127.6454 167.0006 m S 0 g 1 w 4 M 127.6454 167.0006 m F 0 G 0.3 w 10 M 127.6454 167.0006 m S 127.6454 167.0006 m S 1 g 0.5 w 4 M 121.635 167.0006 m 121.635 163.7788 124.326 161.167 127.6454 161.167 c 130.9648 161.167 133.6558 163.7788 133.6558 167.0006 c B 133.6558 167.0006 m 133.6558 170.2224 130.9648 172.8342 127.6454 172.8342 c 124.326 172.8342 121.635 170.2224 121.635 167.0006 c B 127.6454 167.0006 m B 0.3 w 10 M 127.6454 167.0006 m S 0 g 1 w 4 M 127.6454 167.0006 m F 0 G 0.3 w 10 M 127.6454 167.0006 m S 127.6454 167.0006 m S 174.2797 167.0006 m S 162.6211 167.0006 m S 168.4504 161.278 m S 162.6211 167.0006 m S 150.9626 167.0006 m S 156.7919 172.7231 m S 174.2797 167.0006 m S 162.6211 167.0006 m S 168.4504 172.7231 m S 162.6211 167.0006 m S 150.9626 167.0006 m S 156.7919 161.278 m S 150.9626 167.0006 m S 145.1333 161.278 m S 150.9626 167.0006 m S 145.1333 172.7231 m S 0 g 1 w 4 M 145.1333 161.278 m F 168.4504 161.278 m F 0 G 0.3 w 10 M 174.2797 167.0006 m S 180.1089 161.278 m S 174.2797 167.0006 m S 180.1089 172.7231 m S 0 g 1 w 4 M 180.1089 161.278 m F 0 G 0.3 w 10 M 174.2797 167.0006 m S 180.1089 161.278 m S 174.2797 167.0006 m S 180.1089 172.7231 m S 0 g 1 w 4 M 180.1089 161.278 m F 0 G 0.3 w 10 M 150.9626 167.0006 m S 0 g 1 w 4 M 150.9626 167.0006 m F 0 G 0.3 w 10 M 150.9626 167.0006 m S 150.9626 167.0006 m S 150.9626 167.0006 m S 0 g 1 w 4 M 150.9626 167.0006 m F 0 G 0.3 w 10 M 150.9626 167.0006 m S 150.9626 167.0006 m S 1 g 0.5 w 4 M 144.9522 167.0006 m 144.9522 163.7788 147.6432 161.167 150.9626 161.167 c 154.282 161.167 156.973 163.7788 156.973 167.0006 c B 156.973 167.0006 m 156.973 170.2224 154.282 172.8342 150.9626 172.8342 c 147.6432 172.8342 144.9522 170.2224 144.9522 167.0006 c B 150.9626 167.0006 m B 0.3 w 10 M 150.9626 167.0006 m S 0 g 1 w 4 M 150.9626 167.0006 m F 0 G 0.3 w 10 M 150.9626 167.0006 m S 150.9626 167.0006 m S 174.2797 167.0006 m S 0 g 1 w 4 M 174.2797 167.0006 m F 0 G 0.3 w 10 M 174.2797 167.0006 m S 174.2797 167.0006 m S 174.2797 167.0006 m S 0 g 1 w 4 M 174.2797 167.0006 m F 0 G 0.3 w 10 M 174.2797 167.0006 m S 174.2797 167.0006 m S 1 g 0.5 w 4 M 168.2693 167.0006 m 168.2693 163.7788 170.9603 161.167 174.2797 161.167 c 177.5991 161.167 180.2901 163.7788 180.2901 167.0006 c B 180.2901 167.0006 m 180.2901 170.2224 177.5991 172.8342 174.2797 172.8342 c 170.9603 172.8342 168.2693 170.2224 168.2693 167.0006 c B 174.2797 167.0006 m B 0.3 w 10 M 174.2797 167.0006 m S 0 g 1 w 4 M 174.2797 167.0006 m F 0 G 0.3 w 10 M 174.2797 167.0006 m S 174.2797 167.0006 m S 220.9138 167.0006 m S 209.2552 167.0006 m S 215.0844 161.278 m S 209.2552 167.0006 m S 197.5966 167.0006 m S 203.426 172.7231 m S 220.9138 167.0006 m S 209.2552 167.0006 m S 215.0844 172.7231 m S 209.2552 167.0006 m S 197.5966 167.0006 m S 203.426 161.278 m S 197.5966 167.0006 m S 191.7674 161.278 m S 197.5966 167.0006 m S 191.7674 172.7231 m S 0 g 1 w 4 M 191.7674 161.278 m F 215.0844 161.278 m F 0 G 0.3 w 10 M 220.9138 167.0006 m S 226.743 161.278 m S 220.9138 167.0006 m S 226.743 172.7231 m S 0 g 1 w 4 M 226.743 161.278 m F 0 G 0.3 w 10 M 220.9138 167.0006 m S 226.743 161.278 m S 220.9138 167.0006 m S 226.743 172.7231 m S 0 g 1 w 4 M 226.743 161.278 m F 0 G 0.3 w 10 M 197.5966 167.0006 m S 0 g 1 w 4 M 197.5966 167.0006 m F 0 G 0.3 w 10 M 197.5966 167.0006 m S 197.5966 167.0006 m S 197.5966 167.0006 m S 0 g 1 w 4 M 197.5966 167.0006 m F 0 G 0.3 w 10 M 197.5966 167.0006 m S 197.5966 167.0006 m S 1 g 0.5 w 4 M 191.5863 167.0006 m 191.5863 163.7788 194.2772 161.167 197.5966 161.167 c 200.916 161.167 203.6071 163.7788 203.6071 167.0006 c B 203.6071 167.0006 m 203.6071 170.2224 200.916 172.8342 197.5966 172.8342 c 194.2772 172.8342 191.5863 170.2224 191.5863 167.0006 c B 197.5966 167.0006 m B 0.3 w 10 M 197.5966 167.0006 m S 0 g 1 w 4 M 197.5966 167.0006 m F 0 G 0.3 w 10 M 197.5966 167.0006 m S 197.5966 167.0006 m S 220.9138 167.0006 m S 0 g 1 w 4 M 220.9138 167.0006 m F 0 G 0.3 w 10 M 220.9138 167.0006 m S 220.9138 167.0006 m S 220.9138 167.0006 m S 0 g 1 w 4 M 220.9138 167.0006 m F 0 G 0.3 w 10 M 220.9138 167.0006 m S 220.9138 167.0006 m S 1 g 0.5 w 4 M 214.9034 167.0006 m 214.9034 163.7788 217.5944 161.167 220.9138 161.167 c 224.2332 161.167 226.9242 163.7788 226.9242 167.0006 c B 226.9242 167.0006 m 226.9242 170.2224 224.2332 172.8342 220.9138 172.8342 c 217.5944 172.8342 214.9034 170.2224 214.9034 167.0006 c B 220.9138 167.0006 m B 0.3 w 10 M 220.9138 167.0006 m S 0 g 1 w 4 M 220.9138 167.0006 m F 0 G 0.3 w 10 M 220.9138 167.0006 m S 220.9138 167.0006 m S 3 w 267.5478 167.0006 m S 255.8893 167.0006 m S 261.7185 161.278 m S 255.8893 167.0006 m S 244.2307 167.0006 m S 250.0601 172.7231 m S 267.5478 167.0006 m S 255.8893 167.0006 m S 261.7185 172.7231 m S 255.8893 167.0006 m S 244.2307 167.0006 m S 250.0601 161.278 m S 244.2307 167.0006 m S 238.4015 161.278 m S 244.2307 167.0006 m S 238.4015 172.7231 m S 4 M 238.4015 161.278 m S 261.7185 161.278 m S 10 M 267.5478 167.0006 m S 273.3771 161.278 m S 267.5478 167.0006 m S 273.3771 172.7231 m S 4 M 273.3771 161.278 m S 10 M 267.5478 167.0006 m S 273.3771 161.278 m S 267.5478 167.0006 m S 273.3771 172.7231 m S 4 M 273.3771 161.278 m S 10 M 244.2307 167.0006 m S 4 M 244.2307 167.0006 m S 10 M 244.2307 167.0006 m S 244.2307 167.0006 m S 244.2307 167.0006 m S 4 M 244.2307 167.0006 m S 10 M 244.2307 167.0006 m S 244.2307 167.0006 m S 1 g 0.5 w 4 M 238.2203 167.0006 m 238.2203 163.7788 240.9113 161.167 244.2307 161.167 c 246.8835 161.167 250.2411 163.7788 250.2411 167.0006 c B 250.2411 167.0006 m 250.2411 170.2224 247.5501 172.8342 244.2307 172.8342 c 240.9113 172.8342 238.2203 170.2224 238.2203 167.0006 c B 3 w 244.2307 167.0006 m S 10 M 244.2307 167.0006 m S 4 M 244.2307 167.0006 m S 10 M 244.2307 167.0006 m S 244.2307 167.0006 m S 267.5478 167.0006 m S 4 M 267.5478 167.0006 m S 10 M 267.5478 167.0006 m S 267.5478 167.0006 m S 267.5478 167.0006 m S 4 M 267.5478 167.0006 m S 10 M 267.5478 167.0006 m S 267.5478 167.0006 m S 1 g 0.5 w 4 M 261.5375 167.0006 m 261.5375 163.7788 264.2285 161.167 267.5478 161.167 c 270.8672 161.167 273.5583 163.7788 273.5583 167.0006 c B 273.5583 167.0006 m 273.5583 170.2224 270.8672 172.8342 267.5478 172.8342 c 264.2285 172.8342 261.5375 170.2224 261.5375 167.0006 c S 3 w 267.5478 167.0006 m S 10 M 267.5478 167.0006 m S 4 M 267.5478 167.0006 m S 10 M 267.5478 167.0006 m S 267.5478 167.0006 m S 1 g 4 M 226.9242 167.0006 m 238.2205 167.0006 l B 87.0217 167.0006 m 98.318 167.0006 l B 0.3 w 10 M 57.6942 121.2203 m S 51.865 115.4978 m S 57.6942 121.2203 m S 51.865 126.9428 m S 69.3528 121.2203 m S 57.6942 121.2203 m S 63.5235 126.9428 m S 69.3528 121.2203 m S 57.6942 121.2203 m S 63.5235 115.4978 m S 0 g 1 w 4 M 63.5235 126.9428 m F 0 G 0.3 w 10 M 81.0113 121.2203 m S 69.3528 121.2203 m S 75.182 126.9428 m S 92.6698 121.2203 m S 81.0113 121.2203 m S 86.8406 115.4978 m S 92.6698 121.2203 m S 81.0113 121.2203 m S 86.8406 126.9428 m S 104.3284 121.2203 m S 92.6698 121.2203 m S 98.4991 126.9428 m S 104.3284 121.2203 m S 92.6698 121.2203 m S 98.4991 115.4978 m S 81.0113 121.2203 m S 69.3528 121.2203 m S 75.182 115.4978 m S 0 g 1 w 4 M 75.182 126.9428 m F 98.4991 126.9428 m F 0 G 0.3 w 10 M 115.9869 121.2203 m S 104.3284 121.2203 m S 110.1576 126.9428 m S 127.6455 121.2203 m S 115.9869 121.2203 m S 121.8162 115.4978 m S 127.6455 121.2203 m S 115.9869 121.2203 m S 121.8162 126.9428 m S 139.304 121.2203 m S 127.6455 121.2203 m S 133.4747 126.9428 m S 139.304 121.2203 m S 127.6455 121.2203 m S 133.4747 115.4978 m S 115.9869 121.2203 m S 104.3284 121.2203 m S 110.1576 115.4978 m S 0 g 1 w 4 M 110.1576 126.9428 m F 133.4747 126.9428 m F 0 G 0.3 w 10 M 139.304 121.2203 m S 139.304 121.2203 m S 115.9869 121.2203 m S 104.3284 121.2203 m S 110.1576 126.9428 m S 127.6454 121.2203 m S 115.9869 121.2203 m S 121.8162 115.4978 m S 127.6454 121.2203 m S 115.9869 121.2203 m S 121.8162 126.9428 m S 139.304 121.2203 m S 127.6454 121.2203 m S 133.4747 126.9428 m S 139.304 121.2203 m S 127.6454 121.2203 m S 133.4747 115.4978 m S 115.9869 121.2203 m S 104.3284 121.2203 m S 110.1576 115.4978 m S 0 g 1 w 4 M 110.1576 126.9428 m F 133.4747 126.9428 m F 0 G 0.3 w 10 M 150.9626 121.2203 m S 139.304 121.2203 m S 145.1332 126.9428 m S 162.6211 121.2203 m S 150.9626 121.2203 m S 156.7918 115.4978 m S 162.6211 121.2203 m S 150.9626 121.2203 m S 156.7918 126.9428 m S 174.2796 121.2203 m S 162.6211 121.2203 m S 168.4504 126.9428 m S 174.2796 121.2203 m S 162.6211 121.2203 m S 168.4504 115.4978 m S 150.9626 121.2203 m S 139.304 121.2203 m S 145.1332 115.4978 m S 0 g 1 w 4 M 145.1332 126.9428 m F 168.4504 126.9428 m F 0 G 0.3 w 10 M 185.9382 121.2203 m S 174.2796 121.2203 m S 180.1088 126.9428 m S 197.5967 121.2203 m S 185.9382 121.2203 m S 191.7674 115.4978 m S 197.5967 121.2203 m S 185.9382 121.2203 m S 191.7674 126.9428 m S 209.2552 121.2203 m S 197.5967 121.2203 m S 203.426 126.9428 m S 209.2552 121.2203 m S 197.5967 121.2203 m S 203.426 115.4978 m S 185.9382 121.2203 m S 174.2796 121.2203 m S 180.1088 115.4978 m S 0 g 1 w 4 M 180.1088 126.9428 m F 203.426 126.9428 m F 0 G 0.3 w 10 M 209.2552 121.2203 m S 209.2552 121.2203 m S 57.6942 121.2203 m S 0 g 1 w 4 M 57.6942 121.2203 m F 0 G 0.3 w 10 M 57.6942 121.2203 m S 57.6942 121.2203 m S 57.6942 121.2203 m S 0 g 1 w 4 M 57.6942 121.2203 m F 0 G 0.3 w 10 M 57.6942 121.2203 m S 57.6942 121.2203 m S 57.6942 121.2203 m S 0 g 1 w 4 M 57.6942 121.2203 m F 0 G 0.3 w 10 M 57.6942 121.2203 m S 57.6942 121.2203 m S 69.3528 121.2203 m S 0 g 1 w 4 M 69.3528 121.2203 m F 0 G 0.3 w 10 M 69.3528 121.2203 m S 69.3528 121.2203 m S 69.3528 121.2203 m S 0 g 1 w 4 M 69.3528 121.2203 m F 0 G 0.3 w 10 M 69.3528 121.2203 m S 69.3528 121.2203 m S 69.3528 121.2203 m S 0 g 1 w 4 M 69.3528 121.2203 m F 0 G 0.3 w 10 M 69.3528 121.2203 m S 69.3528 121.2203 m S 220.9137 121.2203 m S 209.2552 121.2203 m S 215.0844 126.9428 m S 232.5722 121.2203 m S 220.9137 121.2203 m S 226.743 115.4978 m S 232.5722 121.2203 m S 220.9137 121.2203 m S 226.743 126.9428 m S 244.2308 121.2203 m S 232.5722 121.2203 m S 238.4015 126.9428 m S 244.2308 121.2203 m S 232.5722 121.2203 m S 238.4015 115.4978 m S 220.9137 121.2203 m S 209.2552 121.2203 m S 215.0844 115.4978 m S 0 g 1 w 4 M 215.0844 126.9428 m F 238.4015 126.9428 m F 0 G 0.3 w 10 M 255.8893 121.2203 m S 244.2308 121.2203 m S 250.06 126.9428 m S 267.5478 121.2203 m S 255.8893 121.2203 m S 261.7186 115.4978 m S 267.5478 121.2203 m S 255.8893 121.2203 m S 261.7186 126.9428 m S 267.5478 121.2203 m S 273.3771 126.9428 m S 267.5478 121.2203 m S 273.3771 115.4978 m S 255.8893 121.2203 m S 244.2308 121.2203 m S 250.06 115.4978 m S 0 g 1 w 4 M 250.06 126.9428 m F 273.3771 126.9428 m F 0 G 0.3 w 10 M 232.5722 121.2203 m S 0 g 1 w 4 M 232.5722 121.2203 m F 0 G 0.3 w 10 M 232.5722 121.2203 m S 232.5722 121.2203 m S 232.5722 121.2203 m S 0 g 1 w 4 M 232.5722 121.2203 m F 0 G 0.3 w 10 M 232.5722 121.2203 m S 232.5722 121.2203 m S 232.5722 121.2203 m S 0 g 1 w 4 M 232.5722 121.2203 m F 0 G 0.3 w 10 M 232.5722 121.2203 m S 232.5722 121.2203 m S 244.2308 121.2203 m S 0 g 1 w 4 M 244.2308 121.2203 m F 0 G 0.3 w 10 M 244.2308 121.2203 m S 244.2308 121.2203 m S 244.2308 121.2203 m S 0 g 1 w 4 M 244.2308 121.2203 m F 0 G 0.3 w 10 M 244.2308 121.2203 m S 244.2308 121.2203 m S 244.2308 121.2203 m S 0 g 1 w 4 M 244.2308 121.2203 m F 0 G 0.3 w 10 M 244.2308 121.2203 m S 244.2308 121.2203 m S 81.0113 121.2203 m S 69.3528 121.2203 m S 75.182 115.4978 m S 69.3528 121.2203 m S 57.6942 121.2203 m S 63.5235 126.9428 m S 81.0113 121.2203 m S 69.3528 121.2203 m S 75.182 126.9428 m S 69.3528 121.2203 m S 57.6942 121.2203 m S 63.5235 115.4978 m S 57.6942 121.2203 m S 51.865 115.4978 m S 57.6942 121.2203 m S 51.865 126.9428 m S 0 g 1 w 4 M 51.865 115.4978 m F 75.182 115.4978 m F 0 G 0.3 w 10 M 81.0113 121.2203 m S 86.8406 115.4978 m S 81.0113 121.2203 m S 86.8406 126.9428 m S 0 g 1 w 4 M 86.8406 115.4978 m F 0 G 0.3 w 10 M 81.0113 121.2203 m S 86.8406 115.4978 m S 81.0113 121.2203 m S 86.8406 126.9428 m S 0 g 1 w 4 M 86.8406 115.4978 m F 0 G 0.3 w 10 M 57.6942 121.2203 m S 0 g 1 w 4 M 57.6942 121.2203 m F 0 G 0.3 w 10 M 57.6942 121.2203 m S 57.6942 121.2203 m S 57.6942 121.2203 m S 0 g 1 w 4 M 57.6942 121.2203 m F 0 G 0.3 w 10 M 57.6942 121.2203 m S 57.6942 121.2203 m S 1 g 0.5 w 4 M 51.6838 121.2203 m 51.6838 117.9985 54.3748 115.3867 57.6942 115.3867 c 61.0136 115.3867 63.7046 117.9985 63.7046 121.2203 c B 63.7046 121.2203 m 63.7046 124.4421 61.0136 127.0539 57.6942 127.0539 c 54.3748 127.0539 51.6838 124.4421 51.6838 121.2203 c B 57.6942 121.2203 m B 0.3 w 10 M 57.6942 121.2203 m S 0 g 1 w 4 M 57.6942 121.2203 m F 0 G 0.3 w 10 M 57.6942 121.2203 m S 57.6942 121.2203 m S 81.0113 121.2203 m S 0 g 1 w 4 M 81.0113 121.2203 m F 0 G 0.3 w 10 M 81.0113 121.2203 m S 81.0113 121.2203 m S 81.0113 121.2203 m S 0 g 1 w 4 M 81.0113 121.2203 m F 0 G 0.3 w 10 M 81.0113 121.2203 m S 81.0113 121.2203 m S 1 g 0.5 w 4 M 75.0009 121.2203 m 75.0009 117.9985 77.6919 115.3867 81.0113 115.3867 c 84.3307 115.3867 87.0217 117.9985 87.0217 121.2203 c B 87.0217 121.2203 m 87.0217 124.4421 84.3307 127.0539 81.0113 127.0539 c 77.6919 127.0539 75.0009 124.4421 75.0009 121.2203 c B 81.0113 121.2203 m B 0.3 w 10 M 81.0113 121.2203 m S 0 g 1 w 4 M 81.0113 121.2203 m F 0 G 0.3 w 10 M 81.0113 121.2203 m S 81.0113 121.2203 m S 127.6454 121.2203 m S 115.9869 121.2203 m S 121.8161 115.4978 m S 115.9869 121.2203 m S 104.3283 121.2203 m S 110.1576 126.9428 m S 127.6454 121.2203 m S 115.9869 121.2203 m S 121.8161 126.9428 m S 115.9869 121.2203 m S 104.3283 121.2203 m S 110.1576 115.4978 m S 104.3283 121.2203 m S 98.4991 115.4978 m S 104.3283 121.2203 m S 98.4991 126.9428 m S 0 g 1 w 4 M 98.4991 115.4978 m F 121.8161 115.4978 m F 0 G 0.3 w 10 M 127.6454 121.2203 m S 133.4747 115.4978 m S 127.6454 121.2203 m S 133.4747 126.9428 m S 0 g 1 w 4 M 133.4747 115.4978 m F 0 G 0.3 w 10 M 127.6454 121.2203 m S 133.4747 115.4978 m S 127.6454 121.2203 m S 133.4747 126.9428 m S 0 g 1 w 4 M 133.4747 115.4978 m F 0 G 0.3 w 10 M 104.3283 121.2203 m S 0 g 1 w 4 M 104.3283 121.2203 m F 0 G 0.3 w 10 M 104.3283 121.2203 m S 104.3283 121.2203 m S 104.3283 121.2203 m S 0 g 1 w 4 M 104.3283 121.2203 m F 0 G 0.3 w 10 M 104.3283 121.2203 m S 104.3283 121.2203 m S 1 g 0.5 w 4 M 98.3179 121.2203 m 98.3179 117.9985 101.0089 115.3867 104.3283 115.3867 c 107.6477 115.3867 110.3387 117.9985 110.3387 121.2203 c B 110.3387 121.2203 m 110.3387 124.4421 107.6477 127.0539 104.3283 127.0539 c 101.0089 127.0539 98.3179 124.4421 98.3179 121.2203 c B 104.3283 121.2203 m B 0.3 w 10 M 104.3283 121.2203 m S 0 g 1 w 4 M 104.3283 121.2203 m F 0 G 0.3 w 10 M 104.3283 121.2203 m S 104.3283 121.2203 m S 127.6454 121.2203 m S 0 g 1 w 4 M 127.6454 121.2203 m F 0 G 0.3 w 10 M 127.6454 121.2203 m S 127.6454 121.2203 m S 127.6454 121.2203 m S 0 g 1 w 4 M 127.6454 121.2203 m F 0 G 0.3 w 10 M 127.6454 121.2203 m S 127.6454 121.2203 m S 1 g 0.5 w 4 M 121.635 121.2203 m 121.635 117.9985 124.326 115.3867 127.6454 115.3867 c 130.9648 115.3867 133.6558 117.9985 133.6558 121.2203 c B 133.6558 121.2203 m 133.6558 124.4421 130.9648 127.0539 127.6454 127.0539 c 124.326 127.0539 121.635 124.4421 121.635 121.2203 c B 127.6454 121.2203 m B 0.3 w 10 M 127.6454 121.2203 m S 0 g 1 w 4 M 127.6454 121.2203 m F 0 G 0.3 w 10 M 127.6454 121.2203 m S 127.6454 121.2203 m S 174.2797 121.2203 m S 162.6211 121.2203 m S 168.4504 115.4978 m S 162.6211 121.2203 m S 150.9626 121.2203 m S 156.7919 126.9428 m S 174.2797 121.2203 m S 162.6211 121.2203 m S 168.4504 126.9428 m S 162.6211 121.2203 m S 150.9626 121.2203 m S 156.7919 115.4978 m S 150.9626 121.2203 m S 145.1333 115.4978 m S 150.9626 121.2203 m S 145.1333 126.9428 m S 0 g 1 w 4 M 145.1333 115.4978 m F 168.4504 115.4978 m F 0 G 0.3 w 10 M 174.2797 121.2203 m S 180.1089 115.4978 m S 174.2797 121.2203 m S 180.1089 126.9428 m S 0 g 1 w 4 M 180.1089 115.4978 m F 0 G 0.3 w 10 M 174.2797 121.2203 m S 180.1089 115.4978 m S 174.2797 121.2203 m S 180.1089 126.9428 m S 0 g 1 w 4 M 180.1089 115.4978 m F 0 G 0.3 w 10 M 150.9626 121.2203 m S 0 g 1 w 4 M 150.9626 121.2203 m F 0 G 0.3 w 10 M 150.9626 121.2203 m S 150.9626 121.2203 m S 150.9626 121.2203 m S 0 g 1 w 4 M 150.9626 121.2203 m F 0 G 0.3 w 10 M 150.9626 121.2203 m S 150.9626 121.2203 m S 1 g 0.5 w 4 M 144.9522 121.2203 m 144.9522 117.9985 147.6432 115.3867 150.9626 115.3867 c 154.282 115.3867 156.973 117.9985 156.973 121.2203 c B 156.973 121.2203 m 156.973 124.4421 154.282 127.0539 150.9626 127.0539 c 147.6432 127.0539 144.9522 124.4421 144.9522 121.2203 c B 150.9626 121.2203 m B 0.3 w 10 M 150.9626 121.2203 m S 0 g 1 w 4 M 150.9626 121.2203 m F 0 G 0.3 w 10 M 150.9626 121.2203 m S 150.9626 121.2203 m S 174.2797 121.2203 m S 0 g 1 w 4 M 174.2797 121.2203 m F 0 G 0.3 w 10 M 174.2797 121.2203 m S 174.2797 121.2203 m S 174.2797 121.2203 m S 0 g 1 w 4 M 174.2797 121.2203 m F 0 G 0.3 w 10 M 174.2797 121.2203 m S 174.2797 121.2203 m S 1 g 0.5 w 4 M 168.2693 121.2203 m 168.2693 117.9985 170.9603 115.3867 174.2797 115.3867 c 177.5991 115.3867 180.2901 117.9985 180.2901 121.2203 c B 180.2901 121.2203 m 180.2901 124.4421 177.5991 127.0539 174.2797 127.0539 c 170.9603 127.0539 168.2693 124.4421 168.2693 121.2203 c B 174.2797 121.2203 m B 0.3 w 10 M 174.2797 121.2203 m S 0 g 1 w 4 M 174.2797 121.2203 m F 0 G 0.3 w 10 M 174.2797 121.2203 m S 174.2797 121.2203 m S 220.9138 121.2203 m S 209.2552 121.2203 m S 215.0844 115.4978 m S 209.2552 121.2203 m S 197.5966 121.2203 m S 203.426 126.9428 m S 220.9138 121.2203 m S 209.2552 121.2203 m S 215.0844 126.9428 m S 209.2552 121.2203 m S 197.5966 121.2203 m S 203.426 115.4978 m S 197.5966 121.2203 m S 191.7674 115.4978 m S 197.5966 121.2203 m S 191.7674 126.9428 m S 0 g 1 w 4 M 191.7674 115.4978 m F 215.0844 115.4978 m F 0 G 0.3 w 10 M 220.9138 121.2203 m S 226.743 115.4978 m S 220.9138 121.2203 m S 226.743 126.9428 m S 0 g 1 w 4 M 226.743 115.4978 m F 0 G 0.3 w 10 M 220.9138 121.2203 m S 226.743 115.4978 m S 220.9138 121.2203 m S 226.743 126.9428 m S 0 g 1 w 4 M 226.743 115.4978 m F 0 G 0.3 w 10 M 197.5966 121.2203 m S 0 g 1 w 4 M 197.5966 121.2203 m F 0 G 0.3 w 10 M 197.5966 121.2203 m S 197.5966 121.2203 m S 197.5966 121.2203 m S 0 g 1 w 4 M 197.5966 121.2203 m F 0 G 0.3 w 10 M 197.5966 121.2203 m S 197.5966 121.2203 m S 1 g 0.5 w 4 M 191.5863 121.2203 m 191.5863 117.9985 194.2772 115.3867 197.5966 115.3867 c 200.916 115.3867 203.6071 117.9985 203.6071 121.2203 c B 203.6071 121.2203 m 203.6071 124.4421 200.916 127.0539 197.5966 127.0539 c 194.2772 127.0539 191.5863 124.4421 191.5863 121.2203 c B 197.5966 121.2203 m B 0.3 w 10 M 197.5966 121.2203 m S 0 g 1 w 4 M 197.5966 121.2203 m F 0 G 0.3 w 10 M 197.5966 121.2203 m S 197.5966 121.2203 m S 220.9138 121.2203 m S 0 g 1 w 4 M 220.9138 121.2203 m F 0 G 0.3 w 10 M 220.9138 121.2203 m S 220.9138 121.2203 m S 220.9138 121.2203 m S 0 g 1 w 4 M 220.9138 121.2203 m F 0 G 0.3 w 10 M 220.9138 121.2203 m S 220.9138 121.2203 m S 1 g 0.5 w 4 M 214.9034 121.2203 m 214.9034 117.9985 217.5944 115.3867 220.9138 115.3867 c 224.2332 115.3867 226.9242 117.9985 226.9242 121.2203 c B 226.9242 121.2203 m 226.9242 124.4421 224.2332 127.0539 220.9138 127.0539 c 217.5944 127.0539 214.9034 124.4421 214.9034 121.2203 c B 220.9138 121.2203 m B 0.3 w 10 M 220.9138 121.2203 m S 0 g 1 w 4 M 220.9138 121.2203 m F 0 G 0.3 w 10 M 220.9138 121.2203 m S 220.9138 121.2203 m S 3 w 267.5478 121.2203 m S 255.8893 121.2203 m S 261.7185 115.4978 m S 255.8893 121.2203 m S 244.2307 121.2203 m S 250.0601 126.9428 m S 267.5478 121.2203 m S 255.8893 121.2203 m S 261.7185 126.9428 m S 255.8893 121.2203 m S 244.2307 121.2203 m S 250.0601 115.4978 m S 244.2307 121.2203 m S 238.4015 115.4978 m S 244.2307 121.2203 m S 238.4015 126.9428 m S 4 M 238.4015 115.4978 m S 261.7185 115.4978 m S 10 M 267.5478 121.2203 m S 273.3771 115.4978 m S 267.5478 121.2203 m S 273.3771 126.9428 m S 4 M 273.3771 115.4978 m S 10 M 267.5478 121.2203 m S 273.3771 115.4978 m S 267.5478 121.2203 m S 273.3771 126.9428 m S 4 M 273.3771 115.4978 m S 10 M 244.2307 121.2203 m S 4 M 244.2307 121.2203 m S 10 M 244.2307 121.2203 m S 244.2307 121.2203 m S 244.2307 121.2203 m S 4 M 244.2307 121.2203 m S 10 M 244.2307 121.2203 m S 244.2307 121.2203 m S 1 g 0.5 w 4 M 238.2203 121.2203 m 238.2203 117.9985 240.9113 115.3867 244.2307 115.3867 c 246.8835 115.3867 250.2411 117.9985 250.2411 121.2203 c B 250.2411 121.2203 m 250.2411 124.4421 247.5501 127.0539 244.2307 127.0539 c 240.9113 127.0539 238.2203 124.4421 238.2203 121.2203 c B 3 w 244.2307 121.2203 m S 10 M 244.2307 121.2203 m S 4 M 244.2307 121.2203 m S 10 M 244.2307 121.2203 m S 244.2307 121.2203 m S 267.5478 121.2203 m S 4 M 267.5478 121.2203 m S 10 M 267.5478 121.2203 m S 267.5478 121.2203 m S 267.5478 121.2203 m S 4 M 267.5478 121.2203 m S 10 M 267.5478 121.2203 m S 267.5478 121.2203 m S 1 g 0.5 w 4 M 261.5375 121.2203 m 261.5375 117.9985 264.2285 115.3867 267.5478 115.3867 c 270.8672 115.3867 273.5583 117.9985 273.5583 121.2203 c B 273.5583 121.2203 m 273.5583 124.4421 270.8672 127.0539 267.5478 127.0539 c 264.2285 127.0539 261.5375 124.4421 261.5375 121.2203 c S 3 w 267.5478 121.2203 m S 10 M 267.5478 121.2203 m S 4 M 267.5478 121.2203 m S 10 M 267.5478 121.2203 m S 267.5478 121.2203 m S 1 g 4 M 226.9242 121.2203 m 238.2205 121.2203 l B 87.0217 121.2203 m 98.318 121.2203 l B 0.3 w 10 M 57.6942 98.3302 m S 51.865 92.6078 m S 57.6942 98.3302 m S 51.865 104.0527 m S 69.3528 98.3302 m S 57.6942 98.3302 m S 63.5235 104.0527 m S 69.3528 98.3302 m S 57.6942 98.3302 m S 63.5235 92.6078 m S 0 g 1 w 4 M 63.5235 104.0527 m F 0 G 0.3 w 10 M 81.0113 98.3302 m S 69.3528 98.3302 m S 75.182 104.0527 m S 92.6698 98.3302 m S 81.0113 98.3302 m S 86.8406 92.6078 m S 92.6698 98.3302 m S 81.0113 98.3302 m S 86.8406 104.0527 m S 104.3284 98.3302 m S 92.6698 98.3302 m S 98.4991 104.0527 m S 104.3284 98.3302 m S 92.6698 98.3302 m S 98.4991 92.6078 m S 81.0113 98.3302 m S 69.3528 98.3302 m S 75.182 92.6078 m S 0 g 1 w 4 M 75.182 104.0527 m F 98.4991 104.0527 m F 0 G 0.3 w 10 M 115.9869 98.3302 m S 104.3284 98.3302 m S 110.1576 104.0527 m S 127.6455 98.3302 m S 115.9869 98.3302 m S 121.8162 92.6078 m S 127.6455 98.3302 m S 115.9869 98.3302 m S 121.8162 104.0527 m S 139.304 98.3302 m S 127.6455 98.3302 m S 133.4747 104.0527 m S 139.304 98.3302 m S 127.6455 98.3302 m S 133.4747 92.6078 m S 115.9869 98.3302 m S 104.3284 98.3302 m S 110.1576 92.6078 m S 0 g 1 w 4 M 110.1576 104.0527 m F 133.4747 104.0527 m F 0 G 0.3 w 10 M 139.304 98.3302 m S 139.304 98.3302 m S 115.9869 98.3302 m S 104.3284 98.3302 m S 110.1576 104.0527 m S 127.6454 98.3302 m S 115.9869 98.3302 m S 121.8162 92.6078 m S 127.6454 98.3302 m S 115.9869 98.3302 m S 121.8162 104.0527 m S 139.304 98.3302 m S 127.6454 98.3302 m S 133.4747 104.0527 m S 139.304 98.3302 m S 127.6454 98.3302 m S 133.4747 92.6078 m S 115.9869 98.3302 m S 104.3284 98.3302 m S 110.1576 92.6078 m S 0 g 1 w 4 M 110.1576 104.0527 m F 133.4747 104.0527 m F 0 G 0.3 w 10 M 150.9626 98.3302 m S 139.304 98.3302 m S 145.1332 104.0527 m S 162.6211 98.3302 m S 150.9626 98.3302 m S 156.7918 92.6078 m S 162.6211 98.3302 m S 150.9626 98.3302 m S 156.7918 104.0527 m S 174.2796 98.3302 m S 162.6211 98.3302 m S 168.4504 104.0527 m S 174.2796 98.3302 m S 162.6211 98.3302 m S 168.4504 92.6078 m S 150.9626 98.3302 m S 139.304 98.3302 m S 145.1332 92.6078 m S 0 g 1 w 4 M 145.1332 104.0527 m F 168.4504 104.0527 m F 0 G 0.3 w 10 M 185.9382 98.3302 m S 174.2796 98.3302 m S 180.1088 104.0527 m S 197.5967 98.3302 m S 185.9382 98.3302 m S 191.7674 92.6078 m S 197.5967 98.3302 m S 185.9382 98.3302 m S 191.7674 104.0527 m S 209.2552 98.3302 m S 197.5967 98.3302 m S 203.426 104.0527 m S 209.2552 98.3302 m S 197.5967 98.3302 m S 203.426 92.6078 m S 185.9382 98.3302 m S 174.2796 98.3302 m S 180.1088 92.6078 m S 0 g 1 w 4 M 180.1088 104.0527 m F 203.426 104.0527 m F 0 G 0.3 w 10 M 209.2552 98.3302 m S 209.2552 98.3302 m S 57.6942 98.3302 m S 0 g 1 w 4 M 57.6942 98.3302 m F 0 G 0.3 w 10 M 57.6942 98.3302 m S 57.6942 98.3302 m S 57.6942 98.3302 m S 0 g 1 w 4 M 57.6942 98.3302 m F 0 G 0.3 w 10 M 57.6942 98.3302 m S 57.6942 98.3302 m S 57.6942 98.3302 m S 0 g 1 w 4 M 57.6942 98.3302 m F 0 G 0.3 w 10 M 57.6942 98.3302 m S 57.6942 98.3302 m S 69.3528 98.3302 m S 0 g 1 w 4 M 69.3528 98.3302 m F 0 G 0.3 w 10 M 69.3528 98.3302 m S 69.3528 98.3302 m S 69.3528 98.3302 m S 0 g 1 w 4 M 69.3528 98.3302 m F 0 G 0.3 w 10 M 69.3528 98.3302 m S 69.3528 98.3302 m S 69.3528 98.3302 m S 0 g 1 w 4 M 69.3528 98.3302 m F 0 G 0.3 w 10 M 69.3528 98.3302 m S 69.3528 98.3302 m S 220.9137 98.3302 m S 209.2552 98.3302 m S 215.0844 104.0527 m S 232.5722 98.3302 m S 220.9137 98.3302 m S 226.743 92.6078 m S 232.5722 98.3302 m S 220.9137 98.3302 m S 226.743 104.0527 m S 244.2308 98.3302 m S 232.5722 98.3302 m S 238.4015 104.0527 m S 244.2308 98.3302 m S 232.5722 98.3302 m S 238.4015 92.6078 m S 220.9137 98.3302 m S 209.2552 98.3302 m S 215.0844 92.6078 m S 0 g 1 w 4 M 215.0844 104.0527 m F 238.4015 104.0527 m F 0 G 0.3 w 10 M 255.8893 98.3302 m S 244.2308 98.3302 m S 250.06 104.0527 m S 267.5478 98.3302 m S 255.8893 98.3302 m S 261.7186 92.6078 m S 267.5478 98.3302 m S 255.8893 98.3302 m S 261.7186 104.0527 m S 267.5478 98.3302 m S 273.3771 104.0527 m S 267.5478 98.3302 m S 273.3771 92.6078 m S 255.8893 98.3302 m S 244.2308 98.3302 m S 250.06 92.6078 m S 0 g 1 w 4 M 250.06 104.0527 m F 273.3771 104.0527 m F 0 G 0.3 w 10 M 232.5722 98.3302 m S 0 g 1 w 4 M 232.5722 98.3302 m F 0 G 0.3 w 10 M 232.5722 98.3302 m S 232.5722 98.3302 m S 232.5722 98.3302 m S 0 g 1 w 4 M 232.5722 98.3302 m F 0 G 0.3 w 10 M 232.5722 98.3302 m S 232.5722 98.3302 m S 232.5722 98.3302 m S 0 g 1 w 4 M 232.5722 98.3302 m F 0 G 0.3 w 10 M 232.5722 98.3302 m S 232.5722 98.3302 m S 244.2308 98.3302 m S 0 g 1 w 4 M 244.2308 98.3302 m F 0 G 0.3 w 10 M 244.2308 98.3302 m S 244.2308 98.3302 m S 244.2308 98.3302 m S 0 g 1 w 4 M 244.2308 98.3302 m F 0 G 0.3 w 10 M 244.2308 98.3302 m S 244.2308 98.3302 m S 244.2308 98.3302 m S 0 g 1 w 4 M 244.2308 98.3302 m F 0 G 0.3 w 10 M 244.2308 98.3302 m S 244.2308 98.3302 m S 81.0113 98.3302 m S 69.3528 98.3302 m S 75.182 92.6077 m S 69.3528 98.3302 m S 57.6942 98.3302 m S 63.5235 104.0527 m S 81.0113 98.3302 m S 69.3528 98.3302 m S 75.182 104.0527 m S 69.3528 98.3302 m S 57.6942 98.3302 m S 63.5235 92.6077 m S 57.6942 98.3302 m S 51.865 92.6077 m S 57.6942 98.3302 m S 51.865 104.0527 m S 0 g 1 w 4 M 51.865 92.6077 m F 75.182 92.6077 m F 0 G 0.3 w 10 M 81.0113 98.3302 m S 86.8406 92.6077 m S 81.0113 98.3302 m S 86.8406 104.0527 m S 0 g 1 w 4 M 86.8406 92.6077 m F 0 G 0.3 w 10 M 81.0113 98.3302 m S 86.8406 92.6077 m S 81.0113 98.3302 m S 86.8406 104.0527 m S 0 g 1 w 4 M 86.8406 92.6077 m F 0 G 0.3 w 10 M 57.6942 98.3302 m S 0 g 1 w 4 M 57.6942 98.3302 m F 0 G 0.3 w 10 M 57.6942 98.3302 m S 57.6942 98.3302 m S 57.6942 98.3302 m S 0 g 1 w 4 M 57.6942 98.3302 m F 0 G 0.3 w 10 M 57.6942 98.3302 m S 57.6942 98.3302 m S 1 g 0.5 w 4 M 51.6838 98.3302 m 51.6838 95.1084 54.3748 92.4966 57.6942 92.4966 c 61.0136 92.4966 63.7046 95.1084 63.7046 98.3302 c B 63.7046 98.3302 m 63.7046 101.552 61.0136 104.1638 57.6942 104.1638 c 54.3748 104.1638 51.6838 101.552 51.6838 98.3302 c B 57.6942 98.3302 m B 0.3 w 10 M 57.6942 98.3302 m S 0 g 1 w 4 M 57.6942 98.3302 m F 0 G 0.3 w 10 M 57.6942 98.3302 m S 57.6942 98.3302 m S 81.0113 98.3302 m S 0 g 1 w 4 M 81.0113 98.3302 m F 0 G 0.3 w 10 M 81.0113 98.3302 m S 81.0113 98.3302 m S 81.0113 98.3302 m S 0 g 1 w 4 M 81.0113 98.3302 m F 0 G 0.3 w 10 M 81.0113 98.3302 m S 81.0113 98.3302 m S 1 g 0.5 w 4 M 75.0009 98.3302 m 75.0009 95.1084 77.6919 92.4966 81.0113 92.4966 c 84.3307 92.4966 87.0217 95.1084 87.0217 98.3302 c B 87.0217 98.3302 m 87.0217 101.552 84.3307 104.1638 81.0113 104.1638 c 77.6919 104.1638 75.0009 101.552 75.0009 98.3302 c B 81.0113 98.3302 m B 0.3 w 10 M 81.0113 98.3302 m S 0 g 1 w 4 M 81.0113 98.3302 m F 0 G 0.3 w 10 M 81.0113 98.3302 m S 81.0113 98.3302 m S 127.6454 98.3302 m S 115.9869 98.3302 m S 121.8161 92.6077 m S 115.9869 98.3302 m S 104.3283 98.3302 m S 110.1576 104.0527 m S 127.6454 98.3302 m S 115.9869 98.3302 m S 121.8161 104.0527 m S 115.9869 98.3302 m S 104.3283 98.3302 m S 110.1576 92.6077 m S 104.3283 98.3302 m S 98.4991 92.6077 m S 104.3283 98.3302 m S 98.4991 104.0527 m S 0 g 1 w 4 M 98.4991 92.6077 m F 121.8161 92.6077 m F 0 G 0.3 w 10 M 127.6454 98.3302 m S 133.4747 92.6077 m S 127.6454 98.3302 m S 133.4747 104.0527 m S 0 g 1 w 4 M 133.4747 92.6077 m F 0 G 0.3 w 10 M 127.6454 98.3302 m S 133.4747 92.6077 m S 127.6454 98.3302 m S 133.4747 104.0527 m S 0 g 1 w 4 M 133.4747 92.6077 m F 0 G 0.3 w 10 M 104.3283 98.3302 m S 0 g 1 w 4 M 104.3283 98.3302 m F 0 G 0.3 w 10 M 104.3283 98.3302 m S 104.3283 98.3302 m S 104.3283 98.3302 m S 0 g 1 w 4 M 104.3283 98.3302 m F 0 G 0.3 w 10 M 104.3283 98.3302 m S 104.3283 98.3302 m S 1 g 0.5 w 4 M 98.3179 98.3302 m 98.3179 95.1084 101.0089 92.4966 104.3283 92.4966 c 107.6477 92.4966 110.3387 95.1084 110.3387 98.3302 c B 110.3387 98.3302 m 110.3387 101.552 107.6477 104.1638 104.3283 104.1638 c 101.0089 104.1638 98.3179 101.552 98.3179 98.3302 c B 104.3283 98.3302 m B 0.3 w 10 M 104.3283 98.3302 m S 0 g 1 w 4 M 104.3283 98.3302 m F 0 G 0.3 w 10 M 104.3283 98.3302 m S 104.3283 98.3302 m S 127.6454 98.3302 m S 0 g 1 w 4 M 127.6454 98.3302 m F 0 G 0.3 w 10 M 127.6454 98.3302 m S 127.6454 98.3302 m S 127.6454 98.3302 m S 0 g 1 w 4 M 127.6454 98.3302 m F 0 G 0.3 w 10 M 127.6454 98.3302 m S 127.6454 98.3302 m S 1 g 0.5 w 4 M 121.635 98.3302 m 121.635 95.1084 124.326 92.4966 127.6454 92.4966 c 130.9648 92.4966 133.6558 95.1084 133.6558 98.3302 c B 133.6558 98.3302 m 133.6558 101.552 130.9648 104.1638 127.6454 104.1638 c 124.326 104.1638 121.635 101.552 121.635 98.3302 c B 127.6454 98.3302 m B 0.3 w 10 M 127.6454 98.3302 m S 0 g 1 w 4 M 127.6454 98.3302 m F 0 G 0.3 w 10 M 127.6454 98.3302 m S 127.6454 98.3302 m S 174.2797 98.3302 m S 162.6211 98.3302 m S 168.4504 92.6077 m S 162.6211 98.3302 m S 150.9626 98.3302 m S 156.7919 104.0527 m S 174.2797 98.3302 m S 162.6211 98.3302 m S 168.4504 104.0527 m S 162.6211 98.3302 m S 150.9626 98.3302 m S 156.7919 92.6077 m S 150.9626 98.3302 m S 145.1333 92.6077 m S 150.9626 98.3302 m S 145.1333 104.0527 m S 0 g 1 w 4 M 145.1333 92.6077 m F 168.4504 92.6077 m F 0 G 0.3 w 10 M 174.2797 98.3302 m S 180.1089 92.6077 m S 174.2797 98.3302 m S 180.1089 104.0527 m S 0 g 1 w 4 M 180.1089 92.6077 m F 0 G 0.3 w 10 M 174.2797 98.3302 m S 180.1089 92.6077 m S 174.2797 98.3302 m S 180.1089 104.0527 m S 0 g 1 w 4 M 180.1089 92.6077 m F 0 G 0.3 w 10 M 150.9626 98.3302 m S 0 g 1 w 4 M 150.9626 98.3302 m F 0 G 0.3 w 10 M 150.9626 98.3302 m S 150.9626 98.3302 m S 150.9626 98.3302 m S 0 g 1 w 4 M 150.9626 98.3302 m F 0 G 0.3 w 10 M 150.9626 98.3302 m S 150.9626 98.3302 m S 1 g 0.5 w 4 M 144.9522 98.3302 m 144.9522 95.1084 147.6432 92.4966 150.9626 92.4966 c 154.282 92.4966 156.973 95.1084 156.973 98.3302 c B 156.973 98.3302 m 156.973 101.552 154.282 104.1638 150.9626 104.1638 c 147.6432 104.1638 144.9522 101.552 144.9522 98.3302 c B 150.9626 98.3302 m B 0.3 w 10 M 150.9626 98.3302 m S 0 g 1 w 4 M 150.9626 98.3302 m F 0 G 0.3 w 10 M 150.9626 98.3302 m S 150.9626 98.3302 m S 174.2797 98.3302 m S 0 g 1 w 4 M 174.2797 98.3302 m F 0 G 0.3 w 10 M 174.2797 98.3302 m S 174.2797 98.3302 m S 174.2797 98.3302 m S 0 g 1 w 4 M 174.2797 98.3302 m F 0 G 0.3 w 10 M 174.2797 98.3302 m S 174.2797 98.3302 m S 1 g 0.5 w 4 M 168.2693 98.3302 m 168.2693 95.1084 170.9603 92.4966 174.2797 92.4966 c 177.5991 92.4966 180.2901 95.1084 180.2901 98.3302 c B 180.2901 98.3302 m 180.2901 101.552 177.5991 104.1638 174.2797 104.1638 c 170.9603 104.1638 168.2693 101.552 168.2693 98.3302 c B 174.2797 98.3302 m B 0.3 w 10 M 174.2797 98.3302 m S 0 g 1 w 4 M 174.2797 98.3302 m F 0 G 0.3 w 10 M 174.2797 98.3302 m S 174.2797 98.3302 m S 220.9138 98.3302 m S 209.2552 98.3302 m S 215.0844 92.6077 m S 209.2552 98.3302 m S 197.5966 98.3302 m S 203.426 104.0527 m S 220.9138 98.3302 m S 209.2552 98.3302 m S 215.0844 104.0527 m S 209.2552 98.3302 m S 197.5966 98.3302 m S 203.426 92.6077 m S 197.5966 98.3302 m S 191.7674 92.6077 m S 197.5966 98.3302 m S 191.7674 104.0527 m S 0 g 1 w 4 M 191.7674 92.6077 m F 215.0844 92.6077 m F 0 G 0.3 w 10 M 220.9138 98.3302 m S 226.743 92.6077 m S 220.9138 98.3302 m S 226.743 104.0527 m S 0 g 1 w 4 M 226.743 92.6077 m F 0 G 0.3 w 10 M 220.9138 98.3302 m S 226.743 92.6077 m S 220.9138 98.3302 m S 226.743 104.0527 m S 0 g 1 w 4 M 226.743 92.6077 m F 0 G 0.3 w 10 M 197.5966 98.3302 m S 0 g 1 w 4 M 197.5966 98.3302 m F 0 G 0.3 w 10 M 197.5966 98.3302 m S 197.5966 98.3302 m S 197.5966 98.3302 m S 0 g 1 w 4 M 197.5966 98.3302 m F 0 G 0.3 w 10 M 197.5966 98.3302 m S 197.5966 98.3302 m S 1 g 0.5 w 4 M 191.5863 98.3302 m 191.5863 95.1084 194.2772 92.4966 197.5966 92.4966 c 200.916 92.4966 203.6071 95.1084 203.6071 98.3302 c B 203.6071 98.3302 m 203.6071 101.552 200.916 104.1638 197.5966 104.1638 c 194.2772 104.1638 191.5863 101.552 191.5863 98.3302 c B 197.5966 98.3302 m B 0.3 w 10 M 197.5966 98.3302 m S 0 g 1 w 4 M 197.5966 98.3302 m F 0 G 0.3 w 10 M 197.5966 98.3302 m S 197.5966 98.3302 m S 220.9138 98.3302 m S 0 g 1 w 4 M 220.9138 98.3302 m F 0 G 0.3 w 10 M 220.9138 98.3302 m S 220.9138 98.3302 m S 220.9138 98.3302 m S 0 g 1 w 4 M 220.9138 98.3302 m F 0 G 0.3 w 10 M 220.9138 98.3302 m S 220.9138 98.3302 m S 1 g 0.5 w 4 M 214.9034 98.3302 m 214.9034 95.1084 217.5944 92.4966 220.9138 92.4966 c 224.2332 92.4966 226.9242 95.1084 226.9242 98.3302 c B 226.9242 98.3302 m 226.9242 101.552 224.2332 104.1638 220.9138 104.1638 c 217.5944 104.1638 214.9034 101.552 214.9034 98.3302 c B 220.9138 98.3302 m B 0.3 w 10 M 220.9138 98.3302 m S 0 g 1 w 4 M 220.9138 98.3302 m F 0 G 0.3 w 10 M 220.9138 98.3302 m S 220.9138 98.3302 m S 3 w 267.5478 98.3302 m S 255.8893 98.3302 m S 261.7185 92.6077 m S 255.8893 98.3302 m S 244.2307 98.3302 m S 250.0601 104.0527 m S 267.5478 98.3302 m S 255.8893 98.3302 m S 261.7185 104.0527 m S 255.8893 98.3302 m S 244.2307 98.3302 m S 250.0601 92.6077 m S 244.2307 98.3302 m S 238.4015 92.6077 m S 244.2307 98.3302 m S 238.4015 104.0527 m S 4 M 238.4015 92.6077 m S 261.7185 92.6077 m S 10 M 267.5478 98.3302 m S 273.3771 92.6077 m S 267.5478 98.3302 m S 273.3771 104.0527 m S 4 M 273.3771 92.6077 m S 10 M 267.5478 98.3302 m S 273.3771 92.6077 m S 267.5478 98.3302 m S 273.3771 104.0527 m S 4 M 273.3771 92.6077 m S 10 M 244.2307 98.3302 m S 4 M 244.2307 98.3302 m S 10 M 244.2307 98.3302 m S 244.2307 98.3302 m S 244.2307 98.3302 m S 4 M 244.2307 98.3302 m S 10 M 244.2307 98.3302 m S 244.2307 98.3302 m S 1 g 0.5 w 4 M 238.2203 98.3302 m 238.2203 95.1084 240.9113 92.4966 244.2307 92.4966 c 246.8835 92.4966 250.2411 95.1084 250.2411 98.3302 c B 250.2411 98.3302 m 250.2411 101.552 247.5501 104.1638 244.2307 104.1638 c 240.9113 104.1638 238.2203 101.552 238.2203 98.3302 c B 3 w 244.2307 98.3302 m S 10 M 244.2307 98.3302 m S 4 M 244.2307 98.3302 m S 10 M 244.2307 98.3302 m S 244.2307 98.3302 m S 267.5478 98.3302 m S 4 M 267.5478 98.3302 m S 10 M 267.5478 98.3302 m S 267.5478 98.3302 m S 267.5478 98.3302 m S 4 M 267.5478 98.3302 m S 10 M 267.5478 98.3302 m S 267.5478 98.3302 m S 1 g 0.5 w 4 M 261.5375 98.3302 m 261.5375 95.1084 264.2285 92.4966 267.5478 92.4966 c 270.8672 92.4966 273.5583 95.1084 273.5583 98.3302 c B 273.5583 98.3302 m 273.5583 101.552 270.8672 104.1638 267.5478 104.1638 c 264.2285 104.1638 261.5375 101.552 261.5375 98.3302 c S 3 w 267.5478 98.3302 m S 10 M 267.5478 98.3302 m S 4 M 267.5478 98.3302 m S 10 M 267.5478 98.3302 m S 267.5478 98.3302 m S 1 g 4 M 226.9242 98.3302 m B 238.2205 98.3302 m B 87.0217 98.3302 m B 98.318 98.3302 m B 0.5 w 104.3283 115.3867 m B 104.3283 104.1638 m B 3 w 127.6454 115.3867 m 127.6454 104.1638 l S 1 g 104.3283 115.3867 m 104.3283 104.1638 l B 150.9626 115.3867 m 150.9626 104.1638 l B 174.2797 115.3867 m 174.2797 104.1638 l B 197.5966 115.3867 m 197.5966 104.1638 l B 220.9138 115.3867 m 220.9138 104.1638 l B 0.3 w 10 M 46.0357 292.8961 m S 34.3772 292.8961 m S 69.3528 281.4511 m S 69.3528 270.006 m S 57.6942 270.006 m S 57.6942 281.4511 m S 63.5235 275.7286 m S 57.6942 292.8961 m S 57.6942 281.4511 m S 46.0357 281.4511 m S 46.0357 292.8961 m S 51.865 287.1736 m S 57.6942 292.8961 m S 46.0357 292.8961 m S 69.3528 292.8961 m S 57.6942 292.8961 m S 69.3528 292.8961 m S 69.3528 281.4511 m S 57.6942 281.4511 m S 57.6942 292.8961 m S 63.5235 287.1736 m S 57.6942 281.4511 m S 57.6942 270.006 m S 46.0357 270.006 m S 46.0357 281.4511 m S 51.865 275.7286 m S 46.0357 281.4511 m S 46.0357 270.006 m S 34.3772 270.006 m S 34.3772 281.4511 m S 40.2064 275.7286 m S 46.0357 292.8961 m S 46.0357 281.4511 m S 34.3772 281.4511 m S 34.3772 292.8961 m S 40.2064 287.1736 m S 0 g 1 w 4 M 40.2064 275.7286 m F 63.5235 275.7286 m F 0 G 0.3 w 10 M 81.0113 292.8961 m S 69.3528 292.8961 m S 104.3284 281.4511 m S 104.3284 270.006 m S 92.6698 270.006 m S 92.6698 281.4511 m S 98.4991 275.7286 m S 92.6698 292.8961 m S 92.6698 281.4511 m S 81.0113 281.4511 m S 81.0113 292.8961 m S 86.8406 287.1736 m S 92.6698 292.8961 m S 81.0113 292.8961 m S 104.3284 292.8961 m S 92.6698 292.8961 m S 104.3284 292.8961 m S 104.3284 281.4511 m S 92.6698 281.4511 m S 92.6698 292.8961 m S 98.4991 287.1736 m S 92.6698 281.4511 m S 92.6698 270.006 m S 81.0113 270.006 m S 81.0113 281.4511 m S 86.8406 275.7286 m S 81.0113 281.4511 m S 81.0113 270.006 m S 69.3528 270.006 m S 69.3528 281.4511 m S 75.182 275.7286 m S 81.0113 292.8961 m S 81.0113 281.4511 m S 69.3528 281.4511 m S 69.3528 292.8961 m S 75.182 287.1736 m S 0 g 1 w 4 M 75.182 275.7286 m F 98.4991 275.7286 m F 0 G 0.3 w 10 M 115.9869 292.8961 m S 104.3284 292.8961 m S 139.304 281.4511 m S 139.304 270.006 m S 127.6455 270.006 m S 127.6455 281.4511 m S 133.4747 275.7286 m S 127.6455 292.8961 m S 127.6455 281.4511 m S 115.9869 281.4511 m S 115.9869 292.8961 m S 121.8162 287.1736 m S 127.6455 292.8961 m S 115.9869 292.8961 m S 139.304 292.8961 m S 127.6455 292.8961 m S 139.304 292.8961 m S 139.304 281.4511 m S 127.6455 281.4511 m S 127.6455 292.8961 m S 133.4747 287.1736 m S 127.6455 281.4511 m S 127.6455 270.006 m S 115.9869 270.006 m S 115.9869 281.4511 m S 121.8162 275.7286 m S 115.9869 281.4511 m S 115.9869 270.006 m S 104.3284 270.006 m S 104.3284 281.4511 m S 110.1576 275.7286 m S 115.9869 292.8961 m S 115.9869 281.4511 m S 104.3284 281.4511 m S 104.3284 292.8961 m S 110.1576 287.1736 m S 0 g 1 w 4 M 110.1576 275.7286 m F 133.4747 275.7286 m F 0 G 0.3 w 10 M 139.304 292.8961 m S 139.304 270.006 m S 139.304 281.4511 m S 139.304 281.4511 m S 139.304 292.8961 m S 46.0357 270.006 m S 34.3772 270.006 m S 57.6942 270.006 m S 46.0357 270.006 m S 69.3528 270.006 m S 57.6942 270.006 m S 81.0113 270.006 m S 69.3528 270.006 m S 92.6698 270.006 m S 81.0113 270.006 m S 104.3284 270.006 m S 92.6698 270.006 m S 115.9869 270.006 m S 104.3284 270.006 m S 127.6455 270.006 m S 115.9869 270.006 m S 139.304 270.006 m S 127.6455 270.006 m S 139.304 270.006 m S 115.9869 292.8961 m S 104.3284 292.8961 m S 139.304 281.4511 m S 139.304 270.006 m S 127.6455 270.006 m S 127.6455 281.4511 m S 133.4747 275.7286 m S 127.6455 292.8961 m S 127.6455 281.4511 m S 115.9869 281.4511 m S 115.9869 292.8961 m S 121.8162 287.1736 m S 127.6455 292.8961 m S 115.9869 292.8961 m S 139.304 292.8961 m S 127.6455 292.8961 m S 139.304 292.8961 m S 139.304 281.4511 m S 127.6455 281.4511 m S 127.6455 292.8961 m S 133.4747 287.1736 m S 127.6455 281.4511 m S 127.6455 270.006 m S 115.9869 270.006 m S 115.9869 281.4511 m S 121.8162 275.7286 m S 115.9869 281.4511 m S 115.9869 270.006 m S 104.3284 270.006 m S 104.3284 281.4511 m S 110.1576 275.7286 m S 115.9869 292.8961 m S 115.9869 281.4511 m S 104.3284 281.4511 m S 104.3284 292.8961 m S 110.1576 287.1736 m S 0 g 1 w 4 M 110.1576 275.7286 m F 133.4747 275.7286 m F 0 G 0.3 w 10 M 150.9626 292.8961 m S 139.304 292.8961 m S 174.2796 281.4511 m S 174.2796 270.006 m S 162.6211 270.006 m S 162.6211 281.4511 m S 168.4504 275.7286 m S 162.6211 292.8961 m S 162.6211 281.4511 m S 150.9626 281.4511 m S 150.9626 292.8961 m S 156.7918 287.1736 m S 162.6211 292.8961 m S 150.9626 292.8961 m S 174.2796 292.8961 m S 162.6211 292.8961 m S 174.2796 292.8961 m S 174.2796 281.4511 m S 162.6211 281.4511 m S 162.6211 292.8961 m S 168.4504 287.1736 m S 162.6211 281.4511 m S 162.6211 270.006 m S 150.9626 270.006 m S 150.9626 281.4511 m S 156.7918 275.7286 m S 150.9626 281.4511 m S 150.9626 270.006 m S 139.304 270.006 m S 139.304 281.4511 m S 145.1333 275.7286 m S 150.9626 292.8961 m S 150.9626 281.4511 m S 139.304 281.4511 m S 139.304 292.8961 m S 145.1333 287.1736 m S 0 g 1 w 4 M 145.1333 275.7286 m F 168.4504 275.7286 m F 0 G 0.3 w 10 M 185.9382 292.8961 m S 174.2796 292.8961 m S 209.2552 281.4511 m S 209.2552 270.006 m S 197.5967 270.006 m S 197.5967 281.4511 m S 203.426 275.7286 m S 197.5967 292.8961 m S 197.5967 281.4511 m S 185.9382 281.4511 m S 185.9382 292.8961 m S 191.7674 287.1736 m S 197.5967 292.8961 m S 185.9382 292.8961 m S 209.2552 292.8961 m S 197.5967 292.8961 m S 209.2552 292.8961 m S 209.2552 281.4511 m S 197.5967 281.4511 m S 197.5967 292.8961 m S 203.426 287.1736 m S 197.5967 281.4511 m S 197.5967 270.006 m S 185.9382 270.006 m S 185.9382 281.4511 m S 191.7674 275.7286 m S 185.9382 281.4511 m S 185.9382 270.006 m S 174.2796 270.006 m S 174.2796 281.4511 m S 180.1089 275.7286 m S 185.9382 292.8961 m S 185.9382 281.4511 m S 174.2796 281.4511 m S 174.2796 292.8961 m S 180.1089 287.1736 m S 0 g 1 w 4 M 180.1089 275.7286 m F 203.426 275.7286 m F 0 G 0.3 w 10 M 209.2552 292.8961 m S 209.2552 270.006 m S 209.2552 281.4511 m S 209.2552 281.4511 m S 209.2552 292.8961 m S 115.9869 270.006 m S 104.3284 270.006 m S 127.6455 270.006 m S 115.9869 270.006 m S 139.304 270.006 m S 127.6455 270.006 m S 150.9626 270.006 m S 139.304 270.006 m S 162.6211 270.006 m S 150.9626 270.006 m S 174.2796 270.006 m S 162.6211 270.006 m S 185.9382 270.006 m S 174.2796 270.006 m S 197.5967 270.006 m S 185.9382 270.006 m S 209.2552 270.006 m S 197.5967 270.006 m S 209.2552 270.006 m S 46.0357 292.8962 m S 34.3772 292.8962 m S 69.3528 281.4511 m S 69.3528 270.006 m S 57.6942 270.006 m S 57.6942 281.4511 m S 63.5235 275.7286 m S 57.6942 292.8962 m S 57.6942 281.4511 m S 46.0357 281.4511 m S 46.0357 292.8962 m S 51.865 287.1737 m S 57.6942 292.8962 m S 46.0357 292.8962 m S 69.3528 292.8962 m S 57.6942 292.8962 m S 69.3528 292.8962 m S 69.3528 281.4511 m S 57.6942 281.4511 m S 57.6942 292.8962 m S 63.5235 287.1737 m S 57.6942 281.4511 m S 57.6942 270.006 m S 46.0357 270.006 m S 46.0357 281.4511 m S 51.865 275.7286 m S 46.0357 281.4511 m S 46.0357 270.006 m S 34.3772 270.006 m S 34.3772 281.4511 m S 40.2064 275.7286 m S 46.0357 292.8962 m S 46.0357 281.4511 m S 34.3772 281.4511 m S 34.3772 292.8962 m S 40.2064 287.1737 m S 0 g 1 w 4 M 40.2064 275.7286 m F 63.5235 275.7286 m F 0 G 0.3 w 10 M 81.0113 292.8962 m S 69.3528 292.8962 m S 104.3284 281.4511 m S 104.3284 270.006 m S 92.6698 270.006 m S 92.6698 281.4511 m S 98.4991 275.7286 m S 92.6698 292.8962 m S 92.6698 281.4511 m S 81.0113 281.4511 m S 81.0113 292.8962 m S 86.8406 287.1737 m S 92.6698 292.8962 m S 81.0113 292.8962 m S 104.3284 292.8962 m S 92.6698 292.8962 m S 104.3284 292.8962 m S 104.3284 281.4511 m S 92.6698 281.4511 m S 92.6698 292.8962 m S 98.4991 287.1737 m S 92.6698 281.4511 m S 92.6698 270.006 m S 81.0113 270.006 m S 81.0113 281.4511 m S 86.8406 275.7286 m S 81.0113 281.4511 m S 81.0113 270.006 m S 69.3528 270.006 m S 69.3528 281.4511 m S 75.182 275.7286 m S 81.0113 292.8962 m S 81.0113 281.4511 m S 69.3528 281.4511 m S 69.3528 292.8962 m S 75.182 287.1737 m S 0 g 1 w 4 M 75.182 275.7286 m F 98.4991 275.7286 m F 0 G 0.3 w 10 M 115.9869 292.8962 m S 104.3284 292.8962 m S 139.304 281.4511 m S 139.304 270.006 m S 127.6455 270.006 m S 127.6455 281.4511 m S 133.4747 275.7286 m S 127.6455 292.8962 m S 127.6455 281.4511 m S 115.9869 281.4511 m S 115.9869 292.8962 m S 121.8162 287.1737 m S 127.6455 292.8962 m S 115.9869 292.8962 m S 139.304 292.8962 m S 127.6455 292.8962 m S 139.304 292.8962 m S 139.304 281.4511 m S 127.6455 281.4511 m S 127.6455 292.8962 m S 133.4747 287.1737 m S 127.6455 281.4511 m S 127.6455 270.006 m S 115.9869 270.006 m S 115.9869 281.4511 m S 121.8162 275.7286 m S 115.9869 281.4511 m S 115.9869 270.006 m S 104.3284 270.006 m S 104.3284 281.4511 m S 110.1576 275.7286 m S 115.9869 292.8962 m S 115.9869 281.4511 m S 104.3284 281.4511 m S 104.3284 292.8962 m S 110.1576 287.1737 m S 0 g 1 w 4 M 110.1576 275.7286 m F 133.4747 275.7286 m F 0 G 0.3 w 10 M 139.304 292.8962 m S 139.304 270.006 m S 139.304 281.4511 m S 139.304 281.4511 m S 139.304 292.8962 m S 46.0357 270.006 m S 46.0357 258.561 m S 34.3772 258.561 m S 34.3772 270.006 m S 40.2064 264.2835 m S 69.3528 247.1159 m S 69.3528 235.6709 m S 57.6942 235.6709 m S 57.6942 247.1159 m S 63.5235 241.3934 m S 57.6942 258.561 m S 57.6942 247.1159 m S 46.0357 247.1159 m S 46.0357 258.561 m S 51.865 252.8385 m S 57.6942 270.006 m S 57.6942 258.561 m S 46.0357 258.561 m S 46.0357 270.006 m S 51.865 264.2835 m S 69.3528 270.006 m S 69.3528 258.561 m S 57.6942 258.561 m S 57.6942 270.006 m S 63.5235 264.2835 m S 69.3528 258.561 m S 69.3528 247.1159 m S 57.6942 247.1159 m S 57.6942 258.561 m S 63.5235 252.8385 m S 57.6942 247.1159 m S 57.6942 235.6709 m S 46.0357 235.6709 m S 46.0357 247.1159 m S 51.865 241.3934 m S 46.0357 247.1159 m S 46.0357 235.6709 m S 34.3772 235.6709 m S 34.3772 247.1159 m S 40.2064 241.3934 m S 46.0357 258.561 m S 46.0357 247.1159 m S 34.3772 247.1159 m S 34.3772 258.561 m S 40.2064 252.8385 m S 0 g 1 w 4 M 40.2064 264.2835 m F 63.5235 264.2835 m F 40.2064 241.3934 m F 63.5235 241.3934 m F 0 G 0.3 w 10 M 81.0113 270.006 m S 81.0113 258.561 m S 69.3528 258.561 m S 69.3528 270.006 m S 75.182 264.2835 m S 104.3284 247.1159 m S 104.3284 235.6709 m S 92.6698 235.6709 m S 92.6698 247.1159 m S 98.4991 241.3934 m S 92.6698 258.561 m S 92.6698 247.1159 m S 81.0113 247.1159 m S 81.0113 258.561 m S 86.8406 252.8385 m S 92.6698 270.006 m S 92.6698 258.561 m S 81.0113 258.561 m S 81.0113 270.006 m S 86.8406 264.2835 m S 104.3284 270.006 m S 104.3284 258.561 m S 92.6698 258.561 m S 92.6698 270.006 m S 98.4991 264.2835 m S 104.3284 258.561 m S 104.3284 247.1159 m S 92.6698 247.1159 m S 92.6698 258.561 m S 98.4991 252.8385 m S 92.6698 247.1159 m S 92.6698 235.6709 m S 81.0113 235.6709 m S 81.0113 247.1159 m S 86.8406 241.3934 m S 81.0113 247.1159 m S 81.0113 235.6709 m S 69.3528 235.6709 m S 69.3528 247.1159 m S 75.182 241.3934 m S 81.0113 258.561 m S 81.0113 247.1159 m S 69.3528 247.1159 m S 69.3528 258.561 m S 75.182 252.8385 m S 0 g 1 w 4 M 75.182 264.2835 m F 98.4991 264.2835 m F 75.182 241.3934 m F 98.4991 241.3934 m F 0 G 0.3 w 10 M 115.9869 270.006 m S 115.9869 258.561 m S 104.3284 258.561 m S 104.3284 270.006 m S 110.1576 264.2835 m S 139.304 247.1159 m S 139.304 235.6709 m S 127.6455 235.6709 m S 127.6455 247.1159 m S 133.4747 241.3934 m S 127.6455 258.561 m S 127.6455 247.1159 m S 115.9869 247.1159 m S 115.9869 258.561 m S 121.8162 252.8385 m S 127.6455 270.006 m S 127.6455 258.561 m S 115.9869 258.561 m S 115.9869 270.006 m S 121.8162 264.2835 m S 139.304 270.006 m S 139.304 258.561 m S 127.6455 258.561 m S 127.6455 270.006 m S 133.4747 264.2835 m S 139.304 258.561 m S 139.304 247.1159 m S 127.6455 247.1159 m S 127.6455 258.561 m S 133.4747 252.8385 m S 127.6455 247.1159 m S 127.6455 235.6709 m S 115.9869 235.6709 m S 115.9869 247.1159 m S 121.8162 241.3934 m S 115.9869 247.1159 m S 115.9869 235.6709 m S 104.3284 235.6709 m S 104.3284 247.1159 m S 110.1576 241.3934 m S 115.9869 258.561 m S 115.9869 247.1159 m S 104.3284 247.1159 m S 104.3284 258.561 m S 110.1576 252.8385 m S 0 g 1 w 4 M 110.1576 264.2835 m F 133.4747 264.2835 m F 110.1576 241.3934 m F 133.4747 241.3934 m F 0 G 0.3 w 10 M 139.304 258.561 m S 139.304 270.006 m S 139.304 235.6709 m S 139.304 247.1159 m S 139.304 247.1159 m S 139.304 258.561 m S 0 g 1 w 4 M 40.2064 229.9484 m F 63.5235 229.9484 m F 75.182 229.9484 m F 98.4991 229.9484 m F 110.1576 229.9484 m F 133.4747 229.9484 m F 0 G 0.3 w 10 M 46.0357 235.6709 m S 34.3772 235.6709 m S 40.2064 229.9484 m S 57.6942 235.6709 m S 46.0357 235.6709 m S 51.865 229.9484 m S 69.3528 235.6709 m S 57.6942 235.6709 m S 63.5235 229.9484 m S 0 g 1 w 4 M 40.2064 229.9484 m F 63.5235 229.9484 m F 0 G 0.3 w 10 M 81.0113 235.6709 m S 69.3528 235.6709 m S 75.182 229.9484 m S 92.6698 235.6709 m S 81.0113 235.6709 m S 86.8406 229.9484 m S 104.3284 235.6709 m S 92.6698 235.6709 m S 98.4991 229.9484 m S 0 g 1 w 4 M 75.182 229.9484 m F 98.4991 229.9484 m F 0 G 0.3 w 10 M 115.9869 235.6709 m S 104.3284 235.6709 m S 110.1576 229.9484 m S 127.6455 235.6709 m S 115.9869 235.6709 m S 121.8162 229.9484 m S 139.304 235.6709 m S 127.6455 235.6709 m S 133.4747 229.9484 m S 0 g 1 w 4 M 110.1576 229.9484 m F 133.4747 229.9484 m F 0 G 0.3 w 10 M 139.304 235.6709 m S 115.9869 292.8962 m S 104.3284 292.8962 m S 139.304 281.4511 m S 139.304 270.006 m S 127.6455 270.006 m S 127.6455 281.4511 m S 133.4747 275.7286 m S 127.6455 292.8962 m S 127.6455 281.4511 m S 115.9869 281.4511 m S 115.9869 292.8962 m S 121.8162 287.1737 m S 127.6455 292.8962 m S 115.9869 292.8962 m S 139.304 292.8962 m S 127.6455 292.8962 m S 139.304 292.8962 m S 139.304 281.4511 m S 127.6455 281.4511 m S 127.6455 292.8962 m S 133.4747 287.1737 m S 127.6455 281.4511 m S 127.6455 270.006 m S 115.9869 270.006 m S 115.9869 281.4511 m S 121.8162 275.7286 m S 115.9869 281.4511 m S 115.9869 270.006 m S 104.3284 270.006 m S 104.3284 281.4511 m S 110.1576 275.7286 m S 115.9869 292.8962 m S 115.9869 281.4511 m S 104.3284 281.4511 m S 104.3284 292.8962 m S 110.1576 287.1737 m S 0 g 1 w 4 M 110.1576 275.7286 m F 133.4747 275.7286 m F 0 G 0.3 w 10 M 150.9626 292.8962 m S 139.304 292.8962 m S 174.2796 281.4511 m S 174.2796 270.006 m S 162.6211 270.006 m S 162.6211 281.4511 m S 168.4504 275.7286 m S 162.6211 292.8962 m S 162.6211 281.4511 m S 150.9626 281.4511 m S 150.9626 292.8962 m S 156.7918 287.1737 m S 162.6211 292.8962 m S 150.9626 292.8962 m S 174.2796 292.8962 m S 162.6211 292.8962 m S 174.2796 292.8962 m S 174.2796 281.4511 m S 162.6211 281.4511 m S 162.6211 292.8962 m S 168.4504 287.1737 m S 162.6211 281.4511 m S 162.6211 270.006 m S 150.9626 270.006 m S 150.9626 281.4511 m S 156.7918 275.7286 m S 150.9626 281.4511 m S 150.9626 270.006 m S 139.304 270.006 m S 139.304 281.4511 m S 145.1333 275.7286 m S 150.9626 292.8962 m S 150.9626 281.4511 m S 139.304 281.4511 m S 139.304 292.8962 m S 145.1333 287.1737 m S 0 g 1 w 4 M 145.1333 275.7286 m F 168.4504 275.7286 m F 0 G 0.3 w 10 M 185.9382 292.8962 m S 174.2796 292.8962 m S 209.2552 281.4511 m S 209.2552 270.006 m S 197.5967 270.006 m S 197.5967 281.4511 m S 203.426 275.7286 m S 197.5967 292.8962 m S 197.5967 281.4511 m S 185.9382 281.4511 m S 185.9382 292.8962 m S 191.7674 287.1737 m S 197.5967 292.8962 m S 185.9382 292.8962 m S 209.2552 292.8962 m S 197.5967 292.8962 m S 209.2552 292.8962 m S 209.2552 281.4511 m S 197.5967 281.4511 m S 197.5967 292.8962 m S 203.426 287.1737 m S 197.5967 281.4511 m S 197.5967 270.006 m S 185.9382 270.006 m S 185.9382 281.4511 m S 191.7674 275.7286 m S 185.9382 281.4511 m S 185.9382 270.006 m S 174.2796 270.006 m S 174.2796 281.4511 m S 180.1089 275.7286 m S 185.9382 292.8962 m S 185.9382 281.4511 m S 174.2796 281.4511 m S 174.2796 292.8962 m S 180.1089 287.1737 m S 0 g 1 w 4 M 180.1089 275.7286 m F 203.426 275.7286 m F 0 G 0.3 w 10 M 209.2552 292.8962 m S 209.2552 270.006 m S 209.2552 281.4511 m S 209.2552 281.4511 m S 209.2552 292.8962 m S 115.9869 270.006 m S 115.9869 258.561 m S 104.3284 258.561 m S 104.3284 270.006 m S 110.1576 264.2835 m S 139.304 247.1159 m S 139.304 235.6709 m S 127.6455 235.6709 m S 127.6455 247.1159 m S 133.4747 241.3934 m S 127.6455 258.561 m S 127.6455 247.1159 m S 115.9869 247.1159 m S 115.9869 258.561 m S 121.8162 252.8385 m S 127.6455 270.006 m S 127.6455 258.561 m S 115.9869 258.561 m S 115.9869 270.006 m S 121.8162 264.2835 m S 139.304 270.006 m S 139.304 258.561 m S 127.6455 258.561 m S 127.6455 270.006 m S 133.4747 264.2835 m S 139.304 258.561 m S 139.304 247.1159 m S 127.6455 247.1159 m S 127.6455 258.561 m S 133.4747 252.8385 m S 127.6455 247.1159 m S 127.6455 235.6709 m S 115.9869 235.6709 m S 115.9869 247.1159 m S 121.8162 241.3934 m S 115.9869 247.1159 m S 115.9869 235.6709 m S 104.3284 235.6709 m S 104.3284 247.1159 m S 110.1576 241.3934 m S 115.9869 258.561 m S 115.9869 247.1159 m S 104.3284 247.1159 m S 104.3284 258.561 m S 110.1576 252.8385 m S 0 g 1 w 4 M 110.1576 264.2835 m F 133.4747 264.2835 m F 110.1576 241.3934 m F 133.4747 241.3934 m F 0 G 0.3 w 10 M 150.9626 270.006 m S 150.9626 258.561 m S 139.304 258.561 m S 139.304 270.006 m S 145.1333 264.2835 m S 174.2796 247.1159 m S 174.2796 235.6709 m S 162.6211 235.6709 m S 162.6211 247.1159 m S 168.4504 241.3934 m S 162.6211 258.561 m S 162.6211 247.1159 m S 150.9626 247.1159 m S 150.9626 258.561 m S 156.7918 252.8385 m S 162.6211 270.006 m S 162.6211 258.561 m S 150.9626 258.561 m S 150.9626 270.006 m S 156.7918 264.2835 m S 174.2796 270.006 m S 174.2796 258.561 m S 162.6211 258.561 m S 162.6211 270.006 m S 168.4504 264.2835 m S 174.2796 258.561 m S 174.2796 247.1159 m S 162.6211 247.1159 m S 162.6211 258.561 m S 168.4504 252.8385 m S 162.6211 247.1159 m S 162.6211 235.6709 m S 150.9626 235.6709 m S 150.9626 247.1159 m S 156.7918 241.3934 m S 150.9626 247.1159 m S 150.9626 235.6709 m S 139.304 235.6709 m S 139.304 247.1159 m S 145.1333 241.3934 m S 150.9626 258.561 m S 150.9626 247.1159 m S 139.304 247.1159 m S 139.304 258.561 m S 145.1333 252.8385 m S 0 g 1 w 4 M 145.1333 264.2835 m F 168.4504 264.2835 m F 145.1333 241.3934 m F 168.4504 241.3934 m F 0 G 0.3 w 10 M 185.9382 270.006 m S 185.9382 258.561 m S 174.2796 258.561 m S 174.2796 270.006 m S 180.1089 264.2835 m S 209.2552 247.1159 m S 209.2552 235.6709 m S 197.5967 235.6709 m S 197.5967 247.1159 m S 203.426 241.3934 m S 197.5967 258.561 m S 197.5967 247.1159 m S 185.9382 247.1159 m S 185.9382 258.561 m S 191.7674 252.8385 m S 197.5967 270.006 m S 197.5967 258.561 m S 185.9382 258.561 m S 185.9382 270.006 m S 191.7674 264.2835 m S 209.2552 270.006 m S 209.2552 258.561 m S 197.5967 258.561 m S 197.5967 270.006 m S 203.426 264.2835 m S 209.2552 258.561 m S 209.2552 247.1159 m S 197.5967 247.1159 m S 197.5967 258.561 m S 203.426 252.8385 m S 197.5967 247.1159 m S 197.5967 235.6709 m S 185.9382 235.6709 m S 185.9382 247.1159 m S 191.7674 241.3934 m S 185.9382 247.1159 m S 185.9382 235.6709 m S 174.2796 235.6709 m S 174.2796 247.1159 m S 180.1089 241.3934 m S 185.9382 258.561 m S 185.9382 247.1159 m S 174.2796 247.1159 m S 174.2796 258.561 m S 180.1089 252.8385 m S 0 g 1 w 4 M 180.1089 264.2835 m F 203.426 264.2835 m F 180.1089 241.3934 m F 203.426 241.3934 m F 0 G 0.3 w 10 M 209.2552 258.561 m S 209.2552 270.006 m S 209.2552 235.6709 m S 209.2552 247.1159 m S 209.2552 247.1159 m S 209.2552 258.561 m S 0 g 1 w 4 M 110.1576 229.9484 m F 133.4747 229.9484 m F 145.1333 229.9484 m F 168.4504 229.9484 m F 180.1089 229.9484 m F 203.426 229.9484 m F 0 G 0.3 w 10 M 115.9869 235.6709 m S 104.3284 235.6709 m S 110.1576 229.9484 m S 127.6455 235.6709 m S 115.9869 235.6709 m S 121.8162 229.9484 m S 139.304 235.6709 m S 127.6455 235.6709 m S 133.4747 229.9484 m S 0 g 1 w 4 M 110.1576 229.9484 m F 133.4747 229.9484 m F 0 G 0.3 w 10 M 150.9626 235.6709 m S 139.304 235.6709 m S 145.1333 229.9484 m S 162.6211 235.6709 m S 150.9626 235.6709 m S 156.7918 229.9484 m S 174.2796 235.6709 m S 162.6211 235.6709 m S 168.4504 229.9484 m S 0 g 1 w 4 M 145.1333 229.9484 m F 168.4504 229.9484 m F 0 G 0.3 w 10 M 185.9382 235.6709 m S 174.2796 235.6709 m S 180.1089 229.9484 m S 197.5967 235.6709 m S 185.9382 235.6709 m S 191.7674 229.9484 m S 209.2552 235.6709 m S 197.5967 235.6709 m S 203.426 229.9484 m S 0 g 1 w 4 M 180.1089 229.9484 m F 203.426 229.9484 m F 0 G 0.3 w 10 M 209.2552 235.6709 m S 220.9137 292.8961 m S 209.2552 292.8961 m S 244.2308 281.4511 m S 244.2308 270.006 m S 232.5722 270.006 m S 232.5722 281.4511 m S 238.4015 275.7286 m S 232.5722 292.8961 m S 232.5722 281.4511 m S 220.9137 281.4511 m S 220.9137 292.8961 m S 226.743 287.1736 m S 232.5722 292.8961 m S 220.9137 292.8961 m S 244.2308 292.8961 m S 232.5722 292.8961 m S 244.2308 292.8961 m S 244.2308 281.4511 m S 232.5722 281.4511 m S 232.5722 292.8961 m S 238.4015 287.1736 m S 232.5722 281.4511 m S 232.5722 270.006 m S 220.9137 270.006 m S 220.9137 281.4511 m S 226.743 275.7286 m S 220.9137 281.4511 m S 220.9137 270.006 m S 209.2552 270.006 m S 209.2552 281.4511 m S 215.0844 275.7286 m S 220.9137 292.8961 m S 220.9137 281.4511 m S 209.2552 281.4511 m S 209.2552 292.8961 m S 215.0844 287.1736 m S 0 g 1 w 4 M 215.0844 275.7286 m F 238.4015 275.7286 m F 0 G 0.3 w 10 M 255.8893 292.8961 m S 244.2308 292.8961 m S 279.2064 281.4511 m S 279.2064 270.006 m S 267.5479 270.006 m S 267.5479 281.4511 m S 273.3771 275.7286 m S 267.5479 292.8961 m S 267.5479 281.4511 m S 255.8893 281.4511 m S 255.8893 292.8961 m S 261.7186 287.1736 m S 267.5479 292.8961 m S 255.8893 292.8961 m S 279.2064 292.8961 m S 267.5479 292.8961 m S 279.2064 292.8961 m S 279.2064 281.4511 m S 267.5479 281.4511 m S 267.5479 292.8961 m S 273.3771 287.1736 m S 267.5479 281.4511 m S 267.5479 270.006 m S 255.8893 270.006 m S 255.8893 281.4511 m S 261.7186 275.7286 m S 255.8893 281.4511 m S 255.8893 270.006 m S 244.2308 270.006 m S 244.2308 281.4511 m S 250.0601 275.7286 m S 255.8893 292.8961 m S 255.8893 281.4511 m S 244.2308 281.4511 m S 244.2308 292.8961 m S 250.0601 287.1736 m S 0 g 1 w 4 M 250.0601 275.7286 m F 273.3771 275.7286 m F 0 G 0.3 w 10 M 290.8649 292.8961 m S 279.2064 292.8961 m S 290.8649 281.4511 m S 290.8649 292.8961 m S 290.8649 292.8961 m S 290.8649 270.006 m S 290.8649 281.4511 m S 290.8649 281.4511 m S 290.8649 270.006 m S 279.2064 270.006 m S 279.2064 281.4511 m S 285.0357 275.7286 m S 290.8649 292.8961 m S 290.8649 281.4511 m S 279.2064 281.4511 m S 279.2064 292.8961 m S 285.0357 287.1736 m S 0 g 1 w 4 M 285.0357 275.7286 m F 0 G 0.3 w 10 M 220.9137 270.006 m S 209.2552 270.006 m S 232.5722 270.006 m S 220.9137 270.006 m S 244.2308 270.006 m S 232.5722 270.006 m S 255.8893 270.006 m S 244.2308 270.006 m S 267.5479 270.006 m S 255.8893 270.006 m S 279.2064 270.006 m S 267.5479 270.006 m S 290.8649 270.006 m S 279.2064 270.006 m S 290.8649 270.006 m S 290.8649 292.8961 m S 279.2064 292.8961 m S 290.8649 281.4511 m S 290.8649 292.8961 m S 290.8649 292.8961 m S 290.8649 270.006 m S 290.8649 281.4511 m S 290.8649 281.4511 m S 290.8649 270.006 m S 279.2064 270.006 m S 279.2064 281.4511 m S 285.0357 275.7286 m S 290.8649 292.8961 m S 290.8649 281.4511 m S 279.2064 281.4511 m S 279.2064 292.8961 m S 285.0357 287.1736 m S 0 g 1 w 4 M 285.0357 275.7286 m F 0 G 0.3 w 10 M 290.8649 270.006 m S 279.2064 270.006 m S 290.8649 270.006 m S 220.9137 292.8962 m S 209.2552 292.8962 m S 244.2308 281.4511 m S 244.2308 270.006 m S 232.5722 270.006 m S 232.5722 281.4511 m S 238.4015 275.7286 m S 232.5722 292.8962 m S 232.5722 281.4511 m S 220.9137 281.4511 m S 220.9137 292.8962 m S 226.743 287.1737 m S 232.5722 292.8962 m S 220.9137 292.8962 m S 244.2308 292.8962 m S 232.5722 292.8962 m S 244.2308 292.8962 m S 244.2308 281.4511 m S 232.5722 281.4511 m S 232.5722 292.8962 m S 238.4015 287.1737 m S 232.5722 281.4511 m S 232.5722 270.006 m S 220.9137 270.006 m S 220.9137 281.4511 m S 226.743 275.7286 m S 220.9137 281.4511 m S 220.9137 270.006 m S 209.2552 270.006 m S 209.2552 281.4511 m S 215.0844 275.7286 m S 220.9137 292.8962 m S 220.9137 281.4511 m S 209.2552 281.4511 m S 209.2552 292.8962 m S 215.0844 287.1737 m S 0 g 1 w 4 M 215.0844 275.7286 m F 238.4015 275.7286 m F 0 G 0.3 w 10 M 255.8893 292.8962 m S 244.2308 292.8962 m S 279.2064 281.4511 m S 279.2064 270.006 m S 267.5479 270.006 m S 267.5479 281.4511 m S 273.3771 275.7286 m S 267.5479 292.8962 m S 267.5479 281.4511 m S 255.8893 281.4511 m S 255.8893 292.8962 m S 261.7186 287.1737 m S 267.5479 292.8962 m S 255.8893 292.8962 m S 279.2064 292.8962 m S 267.5479 292.8962 m S 279.2064 292.8962 m S 279.2064 281.4511 m S 267.5479 281.4511 m S 267.5479 292.8962 m S 273.3771 287.1737 m S 267.5479 281.4511 m S 267.5479 270.006 m S 255.8893 270.006 m S 255.8893 281.4511 m S 261.7186 275.7286 m S 255.8893 281.4511 m S 255.8893 270.006 m S 244.2308 270.006 m S 244.2308 281.4511 m S 250.0601 275.7286 m S 255.8893 292.8962 m S 255.8893 281.4511 m S 244.2308 281.4511 m S 244.2308 292.8962 m S 250.0601 287.1737 m S 0 g 1 w 4 M 250.0601 275.7286 m F 273.3771 275.7286 m F 0 G 0.3 w 10 M 290.8649 292.8962 m S 279.2064 292.8962 m S 290.8649 281.4511 m S 290.8649 292.8962 m S 290.8649 292.8962 m S 290.8649 270.006 m S 290.8649 281.4511 m S 290.8649 281.4511 m S 290.8649 270.006 m S 279.2064 270.006 m S 279.2064 281.4511 m S 285.0357 275.7286 m S 290.8649 292.8962 m S 290.8649 281.4511 m S 279.2064 281.4511 m S 279.2064 292.8962 m S 285.0357 287.1737 m S 0 g 1 w 4 M 285.0357 275.7286 m F 0 G 0.3 w 10 M 220.9137 270.006 m S 220.9137 258.561 m S 209.2552 258.561 m S 209.2552 270.006 m S 215.0844 264.2835 m S 244.2308 247.1159 m S 244.2308 235.6709 m S 232.5722 235.6709 m S 232.5722 247.1159 m S 238.4015 241.3934 m S 232.5722 258.561 m S 232.5722 247.1159 m S 220.9137 247.1159 m S 220.9137 258.561 m S 226.743 252.8385 m S 232.5722 270.006 m S 232.5722 258.561 m S 220.9137 258.561 m S 220.9137 270.006 m S 226.743 264.2835 m S 244.2308 270.006 m S 244.2308 258.561 m S 232.5722 258.561 m S 232.5722 270.006 m S 238.4015 264.2835 m S 244.2308 258.561 m S 244.2308 247.1159 m S 232.5722 247.1159 m S 232.5722 258.561 m S 238.4015 252.8385 m S 232.5722 247.1159 m S 232.5722 235.6709 m S 220.9137 235.6709 m S 220.9137 247.1159 m S 226.743 241.3934 m S 220.9137 247.1159 m S 220.9137 235.6709 m S 209.2552 235.6709 m S 209.2552 247.1159 m S 215.0844 241.3934 m S 220.9137 258.561 m S 220.9137 247.1159 m S 209.2552 247.1159 m S 209.2552 258.561 m S 215.0844 252.8385 m S 0 g 1 w 4 M 215.0844 264.2835 m F 238.4015 264.2835 m F 215.0844 241.3934 m F 238.4015 241.3934 m F 0 G 0.3 w 10 M 255.8893 270.006 m S 255.8893 258.561 m S 244.2308 258.561 m S 244.2308 270.006 m S 250.0601 264.2835 m S 279.2064 247.1159 m S 279.2064 235.6709 m S 267.5479 235.6709 m S 267.5479 247.1159 m S 273.3771 241.3934 m S 267.5479 258.561 m S 267.5479 247.1159 m S 255.8893 247.1159 m S 255.8893 258.561 m S 261.7186 252.8385 m S 267.5479 270.006 m S 267.5479 258.561 m S 255.8893 258.561 m S 255.8893 270.006 m S 261.7186 264.2835 m S 279.2064 270.006 m S 279.2064 258.561 m S 267.5479 258.561 m S 267.5479 270.006 m S 273.3771 264.2835 m S 279.2064 258.561 m S 279.2064 247.1159 m S 267.5479 247.1159 m S 267.5479 258.561 m S 273.3771 252.8385 m S 267.5479 247.1159 m S 267.5479 235.6709 m S 255.8893 235.6709 m S 255.8893 247.1159 m S 261.7186 241.3934 m S 255.8893 247.1159 m S 255.8893 235.6709 m S 244.2308 235.6709 m S 244.2308 247.1159 m S 250.0601 241.3934 m S 255.8893 258.561 m S 255.8893 247.1159 m S 244.2308 247.1159 m S 244.2308 258.561 m S 250.0601 252.8385 m S 0 g 1 w 4 M 250.0601 264.2835 m F 273.3771 264.2835 m F 250.0601 241.3934 m F 273.3771 241.3934 m F 0 G 0.3 w 10 M 290.8649 270.006 m S 290.8649 258.561 m S 279.2064 258.561 m S 279.2064 270.006 m S 285.0357 264.2835 m S 290.8649 247.1159 m S 290.8649 258.561 m S 290.8649 258.561 m S 290.8649 270.006 m S 290.8649 235.6709 m S 290.8649 247.1159 m S 290.8649 247.1159 m S 290.8649 235.6709 m S 279.2064 235.6709 m S 279.2064 247.1159 m S 285.0357 241.3934 m S 290.8649 258.561 m S 290.8649 247.1159 m S 279.2064 247.1159 m S 279.2064 258.561 m S 285.0357 252.8385 m S 0 g 1 w 4 M 285.0357 264.2835 m F 285.0357 241.3934 m F 215.0844 229.9484 m F 238.4015 229.9484 m F 250.0601 229.9484 m F 273.3771 229.9484 m F 285.0357 229.9484 m F 0 G 0.3 w 10 M 220.9137 235.6709 m S 209.2552 235.6709 m S 215.0844 229.9484 m S 232.5722 235.6709 m S 220.9137 235.6709 m S 226.743 229.9484 m S 244.2308 235.6709 m S 232.5722 235.6709 m S 238.4015 229.9484 m S 0 g 1 w 4 M 215.0844 229.9484 m F 238.4015 229.9484 m F 0 G 0.3 w 10 M 255.8893 235.6709 m S 244.2308 235.6709 m S 250.0601 229.9484 m S 267.5479 235.6709 m S 255.8893 235.6709 m S 261.7186 229.9484 m S 279.2064 235.6709 m S 267.5479 235.6709 m S 273.3771 229.9484 m S 0 g 1 w 4 M 250.0601 229.9484 m F 273.3771 229.9484 m F 0 G 0.3 w 10 M 290.8649 235.6709 m S 279.2064 235.6709 m S 285.0357 229.9484 m S 290.8649 235.6709 m S 0 g 1 w 4 M 285.0357 229.9484 m F 0 G 0.3 w 10 M 290.8649 292.8962 m S 279.2064 292.8962 m S 290.8649 281.4511 m S 290.8649 292.8962 m S 290.8649 292.8962 m S 290.8649 270.006 m S 290.8649 281.4511 m S 290.8649 281.4511 m S 290.8649 270.006 m S 279.2064 270.006 m S 279.2064 281.4511 m S 285.0357 275.7286 m S 290.8649 292.8962 m S 290.8649 281.4511 m S 279.2064 281.4511 m S 279.2064 292.8962 m S 285.0357 287.1737 m S 0 g 1 w 4 M 285.0357 275.7286 m F 0 G 0.3 w 10 M 290.8649 270.006 m S 290.8649 258.561 m S 279.2064 258.561 m S 279.2064 270.006 m S 285.0357 264.2835 m S 290.8649 247.1159 m S 290.8649 258.561 m S 290.8649 258.561 m S 290.8649 270.006 m S 290.8649 235.6709 m S 290.8649 247.1159 m S 290.8649 247.1159 m S 290.8649 235.6709 m S 279.2064 235.6709 m S 279.2064 247.1159 m S 285.0357 241.3934 m S 290.8649 258.561 m S 290.8649 247.1159 m S 279.2064 247.1159 m S 279.2064 258.561 m S 285.0357 252.8385 m S 0 g 1 w 4 M 285.0357 264.2835 m F 285.0357 241.3934 m F 285.0357 229.9484 m F 0 G 0.3 w 10 M 290.8649 235.6709 m S 279.2064 235.6709 m S 285.0357 229.9484 m S 290.8649 235.6709 m S 0 g 1 w 4 M 285.0357 229.9484 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 56.6091 282.5193 m 53.0235 282.5304 L 53.0235 280.372 L 56.6091 280.3831 L F 58.7793 280.3831 m 62.3649 280.372 L 62.3649 282.5304 L 58.7793 282.5193 L F 53.0235 282.5304 m 62.3649 282.5304 l 62.3649 280.372 l 53.0235 280.372 l 53.0235 282.5304 l f 0 G 0.3 w 10 M 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 57.6942 281.4511 m S 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 57.6942 281.4511 m S 1 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 57.6942 281.4511 m S 1 g 0.5 w 4 M 57.6942 281.4511 m B 0.3 w 10 M 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 57.6942 281.4511 m S 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 57.6942 281.4511 m S 1 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 57.6942 281.4511 m S 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 57.6942 281.4511 m S 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 57.6942 281.4511 m S 1 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 57.6942 281.4511 m S 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 46.0357 292.8961 m S 69.3528 270.0059 m S 57.6942 281.4511 m S 57.6942 281.4511 m S 46.0357 292.8961 m S 46.0357 292.8961 m S 69.3528 292.8961 m S 69.3528 292.8961 m S 57.6942 281.4511 m S 57.6942 281.4511 m S 46.0357 270.0059 m S 46.0357 270.0059 m S 46.0357 292.8961 m S 69.3528 292.8961 m S 69.3528 270.0059 m S 69.3528 292.8961 m S 46.0357 270.0059 m S 46.0357 270.0059 m S 69.3528 270.0059 m S 69.3528 270.0059 m S 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 57.6942 281.4511 m S 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 57.6942 281.4511 m S 57.6942 281.4511 m S 0 g 1 w 4 M 57.6942 281.4511 m F 0 G 0.3 w 10 M 57.6942 281.4511 m S 57.6942 281.4511 m S 69.3528 270.0059 m S 0 g 1 w 4 M 69.3528 270.0059 m F 0 G 0.3 w 10 M 69.3528 270.0059 m S 69.3528 270.0059 m S 69.3528 270.0059 m S 0 g 1 w 4 M 69.3528 270.0059 m F 0 G 0.3 w 10 M 69.3528 270.0059 m S 69.3528 270.0059 m S 69.3528 270.0059 m S 0 g 1 w 4 M 69.3528 270.0059 m F 0 G 0.3 w 10 M 69.3528 270.0059 m S 69.3528 270.0059 m S 69.3528 270.0059 m S 0 g 1 w 4 M 69.3528 270.0059 m F 0 G 0.3 w 10 M 69.3528 270.0059 m S 69.3528 270.0059 m S 69.3528 270.0059 m S 0 g 1 w 4 M 69.3528 270.0059 m F 0 G 0.3 w 10 M 69.3528 270.0059 m S 69.3528 270.0059 m S 1 g 1 w 4 M 69.3528 270.0059 m F 0 G 0.3 w 10 M 69.3528 270.0059 m S 0 g 1 w 4 M 69.3528 270.0059 m F 0 G 0.3 w 10 M 69.3528 270.0059 m S 69.3528 270.0059 m S 0.5 w 4 M 46.0357 292.8961 m 69.3528 292.8961 l 69.3528 270.0059 l 46.0357 270.0059 l 46.0357 292.8961 l s 0.3 w 10 M 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 196.5116 282.5193 m 192.926 282.5304 L 192.926 280.372 L 196.5116 280.3831 L F 198.6818 280.3831 m 202.2674 280.372 L 202.2674 282.5304 L 198.6818 282.5193 L F 192.926 282.5304 m 202.2674 282.5304 l 202.2674 280.372 l 192.926 280.372 l 192.926 282.5304 l f 0 G 0.3 w 10 M 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 197.5967 281.4511 m S 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 197.5967 281.4511 m S 1 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 197.5967 281.4511 m S 1 g 0.5 w 4 M 197.5967 281.4511 m B 0.3 w 10 M 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 197.5967 281.4511 m S 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 197.5967 281.4511 m S 1 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 197.5967 281.4511 m S 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 197.5967 281.4511 m S 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 197.5967 281.4511 m S 1 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 197.5967 281.4511 m S 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 185.9382 292.8961 m S 209.2553 270.0059 m S 197.5967 281.4511 m S 197.5967 281.4511 m S 185.9382 292.8961 m S 185.9382 292.8961 m S 209.2553 292.8961 m S 209.2553 292.8961 m S 197.5967 281.4511 m S 197.5967 281.4511 m S 185.9382 270.0059 m S 185.9382 270.0059 m S 185.9382 292.8961 m S 209.2553 292.8961 m S 209.2553 270.0059 m S 209.2553 292.8961 m S 185.9382 270.0059 m S 185.9382 270.0059 m S 209.2553 270.0059 m S 209.2553 270.0059 m S 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 197.5967 281.4511 m S 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 197.5967 281.4511 m S 197.5967 281.4511 m S 0 g 1 w 4 M 197.5967 281.4511 m F 0 G 0.3 w 10 M 197.5967 281.4511 m S 197.5967 281.4511 m S 209.2553 270.0059 m S 0 g 1 w 4 M 209.2553 270.0059 m F 0 G 0.3 w 10 M 209.2553 270.0059 m S 209.2553 270.0059 m S 209.2553 270.0059 m S 0 g 1 w 4 M 209.2553 270.0059 m F 0 G 0.3 w 10 M 209.2553 270.0059 m S 209.2553 270.0059 m S 209.2553 270.0059 m S 0 g 1 w 4 M 209.2553 270.0059 m F 0 G 0.3 w 10 M 209.2553 270.0059 m S 209.2553 270.0059 m S 209.2553 270.0059 m S 0 g 1 w 4 M 209.2553 270.0059 m F 0 G 0.3 w 10 M 209.2553 270.0059 m S 209.2553 270.0059 m S 209.2553 270.0059 m S 0 g 1 w 4 M 209.2553 270.0059 m F 0 G 0.3 w 10 M 209.2553 270.0059 m S 209.2553 270.0059 m S 1 g 1 w 4 M 209.2553 270.0059 m F 0 G 0.3 w 10 M 209.2553 270.0059 m S 0 g 1 w 4 M 209.2553 270.0059 m F 0 G 0.3 w 10 M 209.2553 270.0059 m S 209.2553 270.0059 m S 0.5 w 4 M 185.9382 292.8961 m 209.2553 292.8961 l 209.2553 270.0059 l 185.9382 270.0059 l 185.9382 292.8961 l s 0.3 w 10 M 127.6455 281.4511 m S 0 g 1 w 4 M 127.6455 281.4511 m F 0 G 0.3 w 10 M 127.6455 281.4511 m S 127.6455 281.4511 m S 127.6455 281.4511 m S 0 g 1 w 4 M 127.6455 281.4511 m F 0 G 0.3 w 10 M 127.6455 281.4511 m S 127.6455 281.4511 m S 127.6455 281.4511 m S 0 g 1 w 4 M 127.6455 281.4511 m F 0 G 0.3 w 10 M 127.6455 281.4511 m S 127.6455 281.4511 m S 0 g 1 w 4 M 126.5604 280.3832 m 126.5604 276.8061 L 128.7306 276.8061 L 128.7306 280.3832 L 132.3162 280.372 L 132.3162 282.5304 L 128.7306 282.5193 L 128.7306 286.0964 L 126.5604 286.0964 L 126.5604 282.5193 L 122.9748 282.5304 L 122.9748 280.372 L 126.5604 280.3832 L f 0 G 0.3 w 10 M 127.6455 281.4511 m S 0 g 1 w 4 M 127.6455 281.4511 m F 0 G 0.3 w 10 M 127.6455 281.4511 m S 127.6455 281.4511 m S 127.6455 281.4511 m S 0 g 1 w 4 M 127.6455 281.4511 m F 0 G 0.3 w 10 M 127.6455 281.4511 m S 127.6455 281.4511 m S 1 g 1 w 4 M 127.6455 281.4511 m F 0 G 0.3 w 10 M 127.6455 281.4511 m S 0 g 1 w 4 M 127.6455 281.4511 m F 0 G 0.3 w 10 M 127.6455 281.4511 m S 127.6455 281.4511 m S 127.6455 281.4511 m S 0 g 1 w 4 M 127.6455 281.4511 m F 0 G 0.3 w 10 M 127.6455 281.4511 m S 0 g 1 w 4 M 127.6455 281.4511 m F 0 G 0.3 w 10 M 115.9869 292.8961 m S 139.304 270.0059 m S 127.6455 281.4511 m S 127.6455 281.4511 m S 115.9869 292.8961 m S 115.9869 292.8961 m S 139.304 292.8961 m S 139.304 292.8961 m S 127.6455 281.4511 m S 127.6455 281.4511 m S 115.9869 270.0059 m S 115.9869 270.0059 m S 115.9869 292.8961 m S 139.304 292.8961 m S 139.304 270.0059 m S 139.304 292.8961 m S 115.9869 270.0059 m S 115.9869 270.0059 m S 139.304 270.0059 m S 139.304 270.0059 m S 127.6455 281.4511 m S 0 g 1 w 4 M 127.6455 281.4511 m F 0 G 0.3 w 10 M 127.6455 281.4511 m S 127.6455 281.4511 m S 127.6455 281.4511 m S 0 g 1 w 4 M 127.6455 281.4511 m F 0 G 0.3 w 10 M 127.6455 281.4511 m S 127.6455 281.4511 m S 127.6455 281.4511 m S 0 g 1 w 4 M 127.6455 281.4511 m F 0 G 0.3 w 10 M 127.6455 281.4511 m S 127.6455 281.4511 m S 139.304 270.0059 m S 0 g 1 w 4 M 139.304 270.0059 m F 0 G 0.3 w 10 M 139.304 270.0059 m S 139.304 270.0059 m S 139.304 270.0059 m S 0 g 1 w 4 M 139.304 270.0059 m F 0 G 0.3 w 10 M 139.304 270.0059 m S 139.304 270.0059 m S 139.304 270.0059 m S 0 g 1 w 4 M 139.304 270.0059 m F 0 G 0.3 w 10 M 139.304 270.0059 m S 139.304 270.0059 m S 139.304 270.0059 m S 0 g 1 w 4 M 139.304 270.0059 m F 0 G 0.3 w 10 M 139.304 270.0059 m S 139.304 270.0059 m S 139.304 270.0059 m S 0 g 1 w 4 M 139.304 270.0059 m F 0 G 0.3 w 10 M 139.304 270.0059 m S 139.304 270.0059 m S 1 g 1 w 4 M 139.304 270.0059 m F 0 G 0.3 w 10 M 139.304 270.0059 m S 0 g 1 w 4 M 139.304 270.0059 m F 0 G 0.3 w 10 M 139.304 270.0059 m S 139.304 270.0059 m S 0.5 w 4 M 115.9869 292.8961 m 139.304 292.8961 l 139.304 270.0059 l 115.9869 270.0059 l 115.9869 292.8961 l s 0.3 w 10 M 267.5479 281.4511 m S 0 g 1 w 4 M 267.5479 281.4511 m F 0 G 0.3 w 10 M 267.5479 281.4511 m S 267.5479 281.4511 m S 267.5479 281.4511 m S 0 g 1 w 4 M 267.5479 281.4511 m F 0 G 0.3 w 10 M 267.5479 281.4511 m S 267.5479 281.4511 m S 267.5479 281.4511 m S 0 g 1 w 4 M 267.5479 281.4511 m F 0 G 0.3 w 10 M 267.5479 281.4511 m S 267.5479 281.4511 m S 0 g 1 w 4 M 266.4628 280.3832 m 266.4628 276.8061 L 268.633 276.8061 L 268.633 280.3832 L 272.2186 280.372 L 272.2186 282.5304 L 268.633 282.5193 L 268.633 286.0964 L 266.4628 286.0964 L 266.4628 282.5193 L 262.8772 282.5304 L 262.8772 280.372 L 266.4628 280.3832 L f 0 G 0.3 w 10 M 267.5479 281.4511 m S 0 g 1 w 4 M 267.5479 281.4511 m F 0 G 0.3 w 10 M 267.5479 281.4511 m S 267.5479 281.4511 m S 267.5479 281.4511 m S 0 g 1 w 4 M 267.5479 281.4511 m F 0 G 0.3 w 10 M 267.5479 281.4511 m S 267.5479 281.4511 m S 1 g 1 w 4 M 267.5479 281.4511 m F 0 G 0.3 w 10 M 267.5479 281.4511 m S 0 g 1 w 4 M 267.5479 281.4511 m F 0 G 0.3 w 10 M 267.5479 281.4511 m S 267.5479 281.4511 m S 267.5479 281.4511 m S 0 g 1 w 4 M 267.5479 281.4511 m F 0 G 0.3 w 10 M 267.5479 281.4511 m S 0 g 1 w 4 M 267.5479 281.4511 m F 0 G 0.3 w 10 M 255.8893 292.8961 m S 279.2064 270.0059 m S 267.5479 281.4511 m S 267.5479 281.4511 m S 255.8893 292.8961 m S 255.8893 292.8961 m S 279.2064 292.8961 m S 279.2064 292.8961 m S 267.5479 281.4511 m S 267.5479 281.4511 m S 255.8893 270.0059 m S 255.8893 270.0059 m S 255.8893 292.8961 m S 279.2064 292.8961 m S 279.2064 270.0059 m S 279.2064 292.8961 m S 255.8893 270.0059 m S 255.8893 270.0059 m S 279.2064 270.0059 m S 279.2064 270.0059 m S 267.5479 281.4511 m S 0 g 1 w 4 M 267.5479 281.4511 m F 0 G 0.3 w 10 M 267.5479 281.4511 m S 267.5479 281.4511 m S 267.5479 281.4511 m S 0 g 1 w 4 M 267.5479 281.4511 m F 0 G 0.3 w 10 M 267.5479 281.4511 m S 267.5479 281.4511 m S 267.5479 281.4511 m S 0 g 1 w 4 M 267.5479 281.4511 m F 0 G 0.3 w 10 M 267.5479 281.4511 m S 267.5479 281.4511 m S 279.2064 270.0059 m S 0 g 1 w 4 M 279.2064 270.0059 m F 0 G 0.3 w 10 M 279.2064 270.0059 m S 279.2064 270.0059 m S 279.2064 270.0059 m S 0 g 1 w 4 M 279.2064 270.0059 m F 0 G 0.3 w 10 M 279.2064 270.0059 m S 279.2064 270.0059 m S 279.2064 270.0059 m S 0 g 1 w 4 M 279.2064 270.0059 m F 0 G 0.3 w 10 M 279.2064 270.0059 m S 279.2064 270.0059 m S 279.2064 270.0059 m S 0 g 1 w 4 M 279.2064 270.0059 m F 0 G 0.3 w 10 M 279.2064 270.0059 m S 279.2064 270.0059 m S 279.2064 270.0059 m S 0 g 1 w 4 M 279.2064 270.0059 m F 0 G 0.3 w 10 M 279.2064 270.0059 m S 279.2064 270.0059 m S 1 g 1 w 4 M 279.2064 270.0059 m F 0 G 0.3 w 10 M 279.2064 270.0059 m S 0 g 1 w 4 M 279.2064 270.0059 m F 0 G 0.3 w 10 M 279.2064 270.0059 m S 279.2064 270.0059 m S 0.5 w 4 M 255.8893 292.8961 m 279.2064 292.8961 l 279.2064 270.0059 l 255.8893 270.0059 l 255.8893 292.8961 l s 0.3 w 10 M 57.6942 258.561 m S 51.865 252.8385 m S 57.6942 258.561 m S 51.865 264.2835 m S 69.3528 258.561 m S 57.6942 258.561 m S 63.5235 264.2835 m S 69.3528 258.561 m S 57.6942 258.561 m S 63.5235 252.8385 m S 0 g 1 w 4 M 63.5235 264.2835 m F 0 G 0.3 w 10 M 81.0113 258.561 m S 69.3528 258.561 m S 75.182 264.2835 m S 92.6698 258.561 m S 81.0113 258.561 m S 86.8406 252.8385 m S 92.6698 258.561 m S 81.0113 258.561 m S 86.8406 264.2835 m S 104.3284 258.561 m S 92.6698 258.561 m S 98.4991 264.2835 m S 104.3284 258.561 m S 92.6698 258.561 m S 98.4991 252.8385 m S 81.0113 258.561 m S 69.3528 258.561 m S 75.182 252.8385 m S 0 g 1 w 4 M 75.182 264.2835 m F 98.4991 264.2835 m F 0 G 0.3 w 10 M 115.9869 258.561 m S 104.3284 258.561 m S 110.1576 264.2835 m S 127.6455 258.561 m S 115.9869 258.561 m S 121.8162 252.8385 m S 127.6455 258.561 m S 115.9869 258.561 m S 121.8162 264.2835 m S 139.304 258.561 m S 127.6455 258.561 m S 133.4747 264.2835 m S 139.304 258.561 m S 127.6455 258.561 m S 133.4747 252.8385 m S 115.9869 258.561 m S 104.3284 258.561 m S 110.1576 252.8385 m S 0 g 1 w 4 M 110.1576 264.2835 m F 133.4747 264.2835 m F 0 G 0.3 w 10 M 139.304 258.561 m S 139.304 258.561 m S 115.9869 258.561 m S 104.3284 258.561 m S 110.1576 264.2835 m S 127.6454 258.561 m S 115.9869 258.561 m S 121.8162 252.8385 m S 127.6454 258.561 m S 115.9869 258.561 m S 121.8162 264.2835 m S 139.304 258.561 m S 127.6454 258.561 m S 133.4747 264.2835 m S 139.304 258.561 m S 127.6454 258.561 m S 133.4747 252.8385 m S 115.9869 258.561 m S 104.3284 258.561 m S 110.1576 252.8385 m S 0 g 1 w 4 M 110.1576 264.2835 m F 133.4747 264.2835 m F 0 G 0.3 w 10 M 150.9626 258.561 m S 139.304 258.561 m S 145.1332 264.2835 m S 162.6211 258.561 m S 150.9626 258.561 m S 156.7918 252.8385 m S 162.6211 258.561 m S 150.9626 258.561 m S 156.7918 264.2835 m S 174.2796 258.561 m S 162.6211 258.561 m S 168.4504 264.2835 m S 174.2796 258.561 m S 162.6211 258.561 m S 168.4504 252.8385 m S 150.9626 258.561 m S 139.304 258.561 m S 145.1332 252.8385 m S 0 g 1 w 4 M 145.1332 264.2835 m F 168.4504 264.2835 m F 0 G 0.3 w 10 M 185.9382 258.561 m S 174.2796 258.561 m S 180.1088 264.2835 m S 197.5967 258.561 m S 185.9382 258.561 m S 191.7674 252.8385 m S 197.5967 258.561 m S 185.9382 258.561 m S 191.7674 264.2835 m S 209.2552 258.561 m S 197.5967 258.561 m S 203.426 264.2835 m S 209.2552 258.561 m S 197.5967 258.561 m S 203.426 252.8385 m S 185.9382 258.561 m S 174.2796 258.561 m S 180.1088 252.8385 m S 0 g 1 w 4 M 180.1088 264.2835 m F 203.426 264.2835 m F 0 G 0.3 w 10 M 209.2552 258.561 m S 209.2552 258.561 m S 57.6942 258.561 m S 0 g 1 w 4 M 57.6942 258.561 m F 0 G 0.3 w 10 M 57.6942 258.561 m S 57.6942 258.561 m S 57.6942 258.561 m S 0 g 1 w 4 M 57.6942 258.561 m F 0 G 0.3 w 10 M 57.6942 258.561 m S 57.6942 258.561 m S 57.6942 258.561 m S 0 g 1 w 4 M 57.6942 258.561 m F 0 G 0.3 w 10 M 57.6942 258.561 m S 57.6942 258.561 m S 69.3528 258.561 m S 0 g 1 w 4 M 69.3528 258.561 m F 0 G 0.3 w 10 M 69.3528 258.561 m S 69.3528 258.561 m S 69.3528 258.561 m S 0 g 1 w 4 M 69.3528 258.561 m F 0 G 0.3 w 10 M 69.3528 258.561 m S 69.3528 258.561 m S 69.3528 258.561 m S 0 g 1 w 4 M 69.3528 258.561 m F 0 G 0.3 w 10 M 69.3528 258.561 m S 69.3528 258.561 m S 220.9137 258.561 m S 209.2552 258.561 m S 215.0844 264.2835 m S 232.5722 258.561 m S 220.9137 258.561 m S 226.743 252.8385 m S 232.5722 258.561 m S 220.9137 258.561 m S 226.743 264.2835 m S 244.2308 258.561 m S 232.5722 258.561 m S 238.4015 264.2835 m S 244.2308 258.561 m S 232.5722 258.561 m S 238.4015 252.8385 m S 220.9137 258.561 m S 209.2552 258.561 m S 215.0844 252.8385 m S 0 g 1 w 4 M 215.0844 264.2835 m F 238.4015 264.2835 m F 0 G 0.3 w 10 M 255.8893 258.561 m S 244.2308 258.561 m S 250.06 264.2835 m S 267.5478 258.561 m S 255.8893 258.561 m S 261.7186 252.8385 m S 267.5478 258.561 m S 255.8893 258.561 m S 261.7186 264.2835 m S 267.5478 258.561 m S 273.3771 264.2835 m S 267.5478 258.561 m S 273.3771 252.8385 m S 255.8893 258.561 m S 244.2308 258.561 m S 250.06 252.8385 m S 0 g 1 w 4 M 250.06 264.2835 m F 273.3771 264.2835 m F 0 G 0.3 w 10 M 232.5722 258.561 m S 0 g 1 w 4 M 232.5722 258.561 m F 0 G 0.3 w 10 M 232.5722 258.561 m S 232.5722 258.561 m S 232.5722 258.561 m S 0 g 1 w 4 M 232.5722 258.561 m F 0 G 0.3 w 10 M 232.5722 258.561 m S 232.5722 258.561 m S 232.5722 258.561 m S 0 g 1 w 4 M 232.5722 258.561 m F 0 G 0.3 w 10 M 232.5722 258.561 m S 232.5722 258.561 m S 244.2308 258.561 m S 0 g 1 w 4 M 244.2308 258.561 m F 0 G 0.3 w 10 M 244.2308 258.561 m S 244.2308 258.561 m S 244.2308 258.561 m S 0 g 1 w 4 M 244.2308 258.561 m F 0 G 0.3 w 10 M 244.2308 258.561 m S 244.2308 258.561 m S 244.2308 258.561 m S 0 g 1 w 4 M 244.2308 258.561 m F 0 G 0.3 w 10 M 244.2308 258.561 m S 244.2308 258.561 m S 81.0113 258.561 m S 69.3528 258.561 m S 75.182 252.8385 m S 69.3528 258.561 m S 57.6942 258.561 m S 63.5235 264.2835 m S 81.0113 258.561 m S 69.3528 258.561 m S 75.182 264.2835 m S 69.3528 258.561 m S 57.6942 258.561 m S 63.5235 252.8385 m S 57.6942 258.561 m S 51.865 252.8385 m S 57.6942 258.561 m S 51.865 264.2835 m S 0 g 1 w 4 M 51.865 252.8385 m F 75.182 252.8385 m F 0 G 0.3 w 10 M 81.0113 258.561 m S 86.8406 252.8385 m S 81.0113 258.561 m S 86.8406 264.2835 m S 0 g 1 w 4 M 86.8406 252.8385 m F 0 G 0.3 w 10 M 81.0113 258.561 m S 86.8406 252.8385 m S 81.0113 258.561 m S 86.8406 264.2835 m S 0 g 1 w 4 M 86.8406 252.8385 m F 0 G 0.3 w 10 M 57.6942 258.561 m S 0 g 1 w 4 M 57.6942 258.561 m F 0 G 0.3 w 10 M 57.6942 258.561 m S 57.6942 258.561 m S 57.6942 258.561 m S 0 g 1 w 4 M 57.6942 258.561 m F 0 G 0.3 w 10 M 57.6942 258.561 m S 57.6942 258.561 m S 1 g 0.5 w 4 M 51.6838 258.561 m 51.6838 255.3392 54.3748 252.7274 57.6942 252.7274 c 61.0136 252.7274 63.7046 255.3392 63.7046 258.561 c B 63.7046 258.561 m 63.7046 261.7828 61.0136 264.3946 57.6942 264.3946 c 54.3748 264.3946 51.6838 261.7828 51.6838 258.561 c B 57.6942 258.561 m B 0.3 w 10 M 57.6942 258.561 m S 0 g 1 w 4 M 57.6942 258.561 m F 0 G 0.3 w 10 M 57.6942 258.561 m S 57.6942 258.561 m S 81.0113 258.561 m S 0 g 1 w 4 M 81.0113 258.561 m F 0 G 0.3 w 10 M 81.0113 258.561 m S 81.0113 258.561 m S 81.0113 258.561 m S 0 g 1 w 4 M 81.0113 258.561 m F 0 G 0.3 w 10 M 81.0113 258.561 m S 81.0113 258.561 m S 1 g 0.5 w 4 M 75.0009 258.561 m 75.0009 255.3392 77.6919 252.7274 81.0113 252.7274 c 84.3307 252.7274 87.0217 255.3392 87.0217 258.561 c B 87.0217 258.561 m 87.0217 261.7828 84.3307 264.3946 81.0113 264.3946 c 77.6919 264.3946 75.0009 261.7828 75.0009 258.561 c B 81.0113 258.561 m B 0.3 w 10 M 81.0113 258.561 m S 0 g 1 w 4 M 81.0113 258.561 m F 0 G 0.3 w 10 M 81.0113 258.561 m S 81.0113 258.561 m S 127.6454 258.561 m S 115.9869 258.561 m S 121.8161 252.8385 m S 115.9869 258.561 m S 104.3283 258.561 m S 110.1576 264.2835 m S 127.6454 258.561 m S 115.9869 258.561 m S 121.8161 264.2835 m S 115.9869 258.561 m S 104.3283 258.561 m S 110.1576 252.8385 m S 104.3283 258.561 m S 98.4991 252.8385 m S 104.3283 258.561 m S 98.4991 264.2835 m S 0 g 1 w 4 M 98.4991 252.8385 m F 121.8161 252.8385 m F 0 G 0.3 w 10 M 127.6454 258.561 m S 133.4747 252.8385 m S 127.6454 258.561 m S 133.4747 264.2835 m S 0 g 1 w 4 M 133.4747 252.8385 m F 0 G 0.3 w 10 M 127.6454 258.561 m S 133.4747 252.8385 m S 127.6454 258.561 m S 133.4747 264.2835 m S 0 g 1 w 4 M 133.4747 252.8385 m F 0 G 0.3 w 10 M 104.3283 258.561 m S 0 g 1 w 4 M 104.3283 258.561 m F 0 G 0.3 w 10 M 104.3283 258.561 m S 104.3283 258.561 m S 104.3283 258.561 m S 0 g 1 w 4 M 104.3283 258.561 m F 0 G 0.3 w 10 M 104.3283 258.561 m S 104.3283 258.561 m S 1 g 0.5 w 4 M 98.3179 258.561 m 98.3179 255.3392 101.0089 252.7274 104.3283 252.7274 c 107.6477 252.7274 110.3387 255.3392 110.3387 258.561 c B 110.3387 258.561 m 110.3387 261.7828 107.6477 264.3946 104.3283 264.3946 c 101.0089 264.3946 98.3179 261.7828 98.3179 258.561 c B 104.3283 258.561 m B 0.3 w 10 M 104.3283 258.561 m S 0 g 1 w 4 M 104.3283 258.561 m F 0 G 0.3 w 10 M 104.3283 258.561 m S 104.3283 258.561 m S 127.6454 258.561 m S 0 g 1 w 4 M 127.6454 258.561 m F 0 G 0.3 w 10 M 127.6454 258.561 m S 127.6454 258.561 m S 127.6454 258.561 m S 0 g 1 w 4 M 127.6454 258.561 m F 0 G 0.3 w 10 M 127.6454 258.561 m S 127.6454 258.561 m S 1 g 0.5 w 4 M 121.635 258.561 m 121.635 255.3392 124.326 252.7274 127.6454 252.7274 c 130.9648 252.7274 133.6558 255.3392 133.6558 258.561 c B 133.6558 258.561 m 133.6558 261.7828 130.9648 264.3946 127.6454 264.3946 c 124.326 264.3946 121.635 261.7828 121.635 258.561 c B 127.6454 258.561 m B 0.3 w 10 M 127.6454 258.561 m S 0 g 1 w 4 M 127.6454 258.561 m F 0 G 0.3 w 10 M 127.6454 258.561 m S 127.6454 258.561 m S 174.2797 258.561 m S 162.6211 258.561 m S 168.4504 252.8385 m S 162.6211 258.561 m S 150.9626 258.561 m S 156.7919 264.2835 m S 174.2797 258.561 m S 162.6211 258.561 m S 168.4504 264.2835 m S 162.6211 258.561 m S 150.9626 258.561 m S 156.7919 252.8385 m S 150.9626 258.561 m S 145.1333 252.8385 m S 150.9626 258.561 m S 145.1333 264.2835 m S 0 g 1 w 4 M 145.1333 252.8385 m F 168.4504 252.8385 m F 0 G 0.3 w 10 M 174.2797 258.561 m S 180.1089 252.8385 m S 174.2797 258.561 m S 180.1089 264.2835 m S 0 g 1 w 4 M 180.1089 252.8385 m F 0 G 0.3 w 10 M 174.2797 258.561 m S 180.1089 252.8385 m S 174.2797 258.561 m S 180.1089 264.2835 m S 0 g 1 w 4 M 180.1089 252.8385 m F 0 G 0.3 w 10 M 150.9626 258.561 m S 0 g 1 w 4 M 150.9626 258.561 m F 0 G 0.3 w 10 M 150.9626 258.561 m S 150.9626 258.561 m S 150.9626 258.561 m S 0 g 1 w 4 M 150.9626 258.561 m F 0 G 0.3 w 10 M 150.9626 258.561 m S 150.9626 258.561 m S 1 g 0.5 w 4 M 144.9522 258.561 m 144.9522 255.3392 147.6432 252.7274 150.9626 252.7274 c 154.282 252.7274 156.973 255.3392 156.973 258.561 c B 156.973 258.561 m 156.973 261.7828 154.282 264.3946 150.9626 264.3946 c 147.6432 264.3946 144.9522 261.7828 144.9522 258.561 c B 150.9626 258.561 m B 0.3 w 10 M 150.9626 258.561 m S 0 g 1 w 4 M 150.9626 258.561 m F 0 G 0.3 w 10 M 150.9626 258.561 m S 150.9626 258.561 m S 174.2797 258.561 m S 0 g 1 w 4 M 174.2797 258.561 m F 0 G 0.3 w 10 M 174.2797 258.561 m S 174.2797 258.561 m S 174.2797 258.561 m S 0 g 1 w 4 M 174.2797 258.561 m F 0 G 0.3 w 10 M 174.2797 258.561 m S 174.2797 258.561 m S 1 g 0.5 w 4 M 168.2693 258.561 m 168.2693 255.3392 170.9603 252.7274 174.2797 252.7274 c 177.5991 252.7274 180.2901 255.3392 180.2901 258.561 c B 180.2901 258.561 m 180.2901 261.7828 177.5991 264.3946 174.2797 264.3946 c 170.9603 264.3946 168.2693 261.7828 168.2693 258.561 c B 174.2797 258.561 m B 0.3 w 10 M 174.2797 258.561 m S 0 g 1 w 4 M 174.2797 258.561 m F 0 G 0.3 w 10 M 174.2797 258.561 m S 174.2797 258.561 m S 220.9138 258.561 m S 209.2552 258.561 m S 215.0844 252.8385 m S 209.2552 258.561 m S 197.5966 258.561 m S 203.426 264.2835 m S 220.9138 258.561 m S 209.2552 258.561 m S 215.0844 264.2835 m S 209.2552 258.561 m S 197.5966 258.561 m S 203.426 252.8385 m S 197.5966 258.561 m S 191.7674 252.8385 m S 197.5966 258.561 m S 191.7674 264.2835 m S 0 g 1 w 4 M 191.7674 252.8385 m F 215.0844 252.8385 m F 0 G 0.3 w 10 M 220.9138 258.561 m S 226.743 252.8385 m S 220.9138 258.561 m S 226.743 264.2835 m S 0 g 1 w 4 M 226.743 252.8385 m F 0 G 0.3 w 10 M 220.9138 258.561 m S 226.743 252.8385 m S 220.9138 258.561 m S 226.743 264.2835 m S 0 g 1 w 4 M 226.743 252.8385 m F 0 G 0.3 w 10 M 197.5966 258.561 m S 0 g 1 w 4 M 197.5966 258.561 m F 0 G 0.3 w 10 M 197.5966 258.561 m S 197.5966 258.561 m S 197.5966 258.561 m S 0 g 1 w 4 M 197.5966 258.561 m F 0 G 0.3 w 10 M 197.5966 258.561 m S 197.5966 258.561 m S 1 g 0.5 w 4 M 191.5863 258.561 m 191.5863 255.3392 194.2772 252.7274 197.5966 252.7274 c 200.916 252.7274 203.6071 255.3392 203.6071 258.561 c B 203.6071 258.561 m 203.6071 261.7828 200.916 264.3946 197.5966 264.3946 c 194.2772 264.3946 191.5863 261.7828 191.5863 258.561 c B 197.5966 258.561 m B 0.3 w 10 M 197.5966 258.561 m S 0 g 1 w 4 M 197.5966 258.561 m F 0 G 0.3 w 10 M 197.5966 258.561 m S 197.5966 258.561 m S 220.9138 258.561 m S 0 g 1 w 4 M 220.9138 258.561 m F 0 G 0.3 w 10 M 220.9138 258.561 m S 220.9138 258.561 m S 220.9138 258.561 m S 0 g 1 w 4 M 220.9138 258.561 m F 0 G 0.3 w 10 M 220.9138 258.561 m S 220.9138 258.561 m S 1 g 0.5 w 4 M 214.9034 258.561 m 214.9034 255.3392 217.5944 252.7274 220.9138 252.7274 c 224.2332 252.7274 226.9242 255.3392 226.9242 258.561 c B 226.9242 258.561 m 226.9242 261.7828 224.2332 264.3946 220.9138 264.3946 c 217.5944 264.3946 214.9034 261.7828 214.9034 258.561 c B 220.9138 258.561 m B 0.3 w 10 M 220.9138 258.561 m S 0 g 1 w 4 M 220.9138 258.561 m F 0 G 0.3 w 10 M 220.9138 258.561 m S 220.9138 258.561 m S 3 w 267.5478 258.561 m S 255.8893 258.561 m S 261.7185 252.8385 m S 255.8893 258.561 m S 244.2307 258.561 m S 250.0601 264.2835 m S 267.5478 258.561 m S 255.8893 258.561 m S 261.7185 264.2835 m S 255.8893 258.561 m S 244.2307 258.561 m S 250.0601 252.8385 m S 244.2307 258.561 m S 238.4015 252.8385 m S 244.2307 258.561 m S 238.4015 264.2835 m S 4 M 238.4015 252.8385 m S 261.7185 252.8385 m S 10 M 267.5478 258.561 m S 273.3771 252.8385 m S 267.5478 258.561 m S 273.3771 264.2835 m S 4 M 273.3771 252.8385 m S 10 M 267.5478 258.561 m S 273.3771 252.8385 m S 267.5478 258.561 m S 273.3771 264.2835 m S 4 M 273.3771 252.8385 m S 10 M 244.2307 258.561 m S 4 M 244.2307 258.561 m S 10 M 244.2307 258.561 m S 244.2307 258.561 m S 244.2307 258.561 m S 4 M 244.2307 258.561 m S 10 M 244.2307 258.561 m S 244.2307 258.561 m S 1 g 0.5 w 4 M 238.2203 258.561 m 238.2203 255.3392 240.9113 252.7274 244.2307 252.7274 c 246.8835 252.7274 250.2411 255.3392 250.2411 258.561 c B 250.2411 258.561 m 250.2411 261.7828 247.5501 264.3946 244.2307 264.3946 c 240.9113 264.3946 238.2203 261.7828 238.2203 258.561 c B 3 w 244.2307 258.561 m S 10 M 244.2307 258.561 m S 4 M 244.2307 258.561 m S 10 M 244.2307 258.561 m S 244.2307 258.561 m S 267.5478 258.561 m S 4 M 267.5478 258.561 m S 10 M 267.5478 258.561 m S 267.5478 258.561 m S 267.5478 258.561 m S 4 M 267.5478 258.561 m S 10 M 267.5478 258.561 m S 267.5478 258.561 m S 1 g 0.5 w 4 M 261.5375 258.561 m 261.5375 255.3392 264.2285 252.7274 267.5478 252.7274 c 270.8672 252.7274 273.5583 255.3392 273.5583 258.561 c B 273.5583 258.561 m 273.5583 261.7828 270.8672 264.3946 267.5478 264.3946 c 264.2285 264.3946 261.5375 261.7828 261.5375 258.561 c S 3 w 267.5478 258.561 m S 10 M 267.5478 258.561 m S 4 M 267.5478 258.561 m S 10 M 267.5478 258.561 m S 267.5478 258.561 m S 1 g 4 M 226.9242 258.561 m B 238.2205 258.561 m B 87.0217 258.561 m B 98.318 258.561 m B 0.3 w 10 M 57.6942 235.6709 m S 51.865 229.9485 m S 57.6942 235.6709 m S 51.865 241.3934 m S 69.3528 235.6709 m S 57.6942 235.6709 m S 63.5235 241.3934 m S 69.3528 235.6709 m S 57.6942 235.6709 m S 63.5235 229.9485 m S 0 g 1 w 4 M 63.5235 241.3934 m F 0 G 0.3 w 10 M 81.0113 235.6709 m S 69.3528 235.6709 m S 75.182 241.3934 m S 92.6698 235.6709 m S 81.0113 235.6709 m S 86.8406 229.9485 m S 92.6698 235.6709 m S 81.0113 235.6709 m S 86.8406 241.3934 m S 104.3284 235.6709 m S 92.6698 235.6709 m S 98.4991 241.3934 m S 104.3284 235.6709 m S 92.6698 235.6709 m S 98.4991 229.9485 m S 81.0113 235.6709 m S 69.3528 235.6709 m S 75.182 229.9485 m S 0 g 1 w 4 M 75.182 241.3934 m F 98.4991 241.3934 m F 0 G 0.3 w 10 M 115.9869 235.6709 m S 104.3284 235.6709 m S 110.1576 241.3934 m S 127.6455 235.6709 m S 115.9869 235.6709 m S 121.8162 229.9485 m S 127.6455 235.6709 m S 115.9869 235.6709 m S 121.8162 241.3934 m S 139.304 235.6709 m S 127.6455 235.6709 m S 133.4747 241.3934 m S 139.304 235.6709 m S 127.6455 235.6709 m S 133.4747 229.9485 m S 115.9869 235.6709 m S 104.3284 235.6709 m S 110.1576 229.9485 m S 0 g 1 w 4 M 110.1576 241.3934 m F 133.4747 241.3934 m F 0 G 0.3 w 10 M 139.304 235.6709 m S 139.304 235.6709 m S 115.9869 235.6709 m S 104.3284 235.6709 m S 110.1576 241.3934 m S 127.6454 235.6709 m S 115.9869 235.6709 m S 121.8162 229.9485 m S 127.6454 235.6709 m S 115.9869 235.6709 m S 121.8162 241.3934 m S 139.304 235.6709 m S 127.6454 235.6709 m S 133.4747 241.3934 m S 139.304 235.6709 m S 127.6454 235.6709 m S 133.4747 229.9485 m S 115.9869 235.6709 m S 104.3284 235.6709 m S 110.1576 229.9485 m S 0 g 1 w 4 M 110.1576 241.3934 m F 133.4747 241.3934 m F 0 G 0.3 w 10 M 150.9626 235.6709 m S 139.304 235.6709 m S 145.1332 241.3934 m S 162.6211 235.6709 m S 150.9626 235.6709 m S 156.7918 229.9485 m S 162.6211 235.6709 m S 150.9626 235.6709 m S 156.7918 241.3934 m S 174.2796 235.6709 m S 162.6211 235.6709 m S 168.4504 241.3934 m S 174.2796 235.6709 m S 162.6211 235.6709 m S 168.4504 229.9485 m S 150.9626 235.6709 m S 139.304 235.6709 m S 145.1332 229.9485 m S 0 g 1 w 4 M 145.1332 241.3934 m F 168.4504 241.3934 m F 0 G 0.3 w 10 M 185.9382 235.6709 m S 174.2796 235.6709 m S 180.1088 241.3934 m S 197.5967 235.6709 m S 185.9382 235.6709 m S 191.7674 229.9485 m S 197.5967 235.6709 m S 185.9382 235.6709 m S 191.7674 241.3934 m S 209.2552 235.6709 m S 197.5967 235.6709 m S 203.426 241.3934 m S 209.2552 235.6709 m S 197.5967 235.6709 m S 203.426 229.9485 m S 185.9382 235.6709 m S 174.2796 235.6709 m S 180.1088 229.9485 m S 0 g 1 w 4 M 180.1088 241.3934 m F 203.426 241.3934 m F 0 G 0.3 w 10 M 209.2552 235.6709 m S 209.2552 235.6709 m S 57.6942 235.6709 m S 0 g 1 w 4 M 57.6942 235.6709 m F 0 G 0.3 w 10 M 57.6942 235.6709 m S 57.6942 235.6709 m S 57.6942 235.6709 m S 0 g 1 w 4 M 57.6942 235.6709 m F 0 G 0.3 w 10 M 57.6942 235.6709 m S 57.6942 235.6709 m S 57.6942 235.6709 m S 0 g 1 w 4 M 57.6942 235.6709 m F 0 G 0.3 w 10 M 57.6942 235.6709 m S 57.6942 235.6709 m S 69.3528 235.6709 m S 0 g 1 w 4 M 69.3528 235.6709 m F 0 G 0.3 w 10 M 69.3528 235.6709 m S 69.3528 235.6709 m S 69.3528 235.6709 m S 0 g 1 w 4 M 69.3528 235.6709 m F 0 G 0.3 w 10 M 69.3528 235.6709 m S 69.3528 235.6709 m S 69.3528 235.6709 m S 0 g 1 w 4 M 69.3528 235.6709 m F 0 G 0.3 w 10 M 69.3528 235.6709 m S 69.3528 235.6709 m S 220.9137 235.6709 m S 209.2552 235.6709 m S 215.0844 241.3934 m S 232.5722 235.6709 m S 220.9137 235.6709 m S 226.743 229.9485 m S 232.5722 235.6709 m S 220.9137 235.6709 m S 226.743 241.3934 m S 244.2308 235.6709 m S 232.5722 235.6709 m S 238.4015 241.3934 m S 244.2308 235.6709 m S 232.5722 235.6709 m S 238.4015 229.9485 m S 220.9137 235.6709 m S 209.2552 235.6709 m S 215.0844 229.9485 m S 0 g 1 w 4 M 215.0844 241.3934 m F 238.4015 241.3934 m F 0 G 0.3 w 10 M 255.8893 235.6709 m S 244.2308 235.6709 m S 250.06 241.3934 m S 267.5478 235.6709 m S 255.8893 235.6709 m S 261.7186 229.9485 m S 267.5478 235.6709 m S 255.8893 235.6709 m S 261.7186 241.3934 m S 267.5478 235.6709 m S 273.3771 241.3934 m S 267.5478 235.6709 m S 273.3771 229.9485 m S 255.8893 235.6709 m S 244.2308 235.6709 m S 250.06 229.9485 m S 0 g 1 w 4 M 250.06 241.3934 m F 273.3771 241.3934 m F 0 G 0.3 w 10 M 232.5722 235.6709 m S 0 g 1 w 4 M 232.5722 235.6709 m F 0 G 0.3 w 10 M 232.5722 235.6709 m S 232.5722 235.6709 m S 232.5722 235.6709 m S 0 g 1 w 4 M 232.5722 235.6709 m F 0 G 0.3 w 10 M 232.5722 235.6709 m S 232.5722 235.6709 m S 232.5722 235.6709 m S 0 g 1 w 4 M 232.5722 235.6709 m F 0 G 0.3 w 10 M 232.5722 235.6709 m S 232.5722 235.6709 m S 244.2308 235.6709 m S 0 g 1 w 4 M 244.2308 235.6709 m F 0 G 0.3 w 10 M 244.2308 235.6709 m S 244.2308 235.6709 m S 244.2308 235.6709 m S 0 g 1 w 4 M 244.2308 235.6709 m F 0 G 0.3 w 10 M 244.2308 235.6709 m S 244.2308 235.6709 m S 244.2308 235.6709 m S 0 g 1 w 4 M 244.2308 235.6709 m F 0 G 0.3 w 10 M 244.2308 235.6709 m S 244.2308 235.6709 m S 81.0113 235.6709 m S 69.3528 235.6709 m S 75.182 229.9484 m S 69.3528 235.6709 m S 57.6942 235.6709 m S 63.5235 241.3934 m S 81.0113 235.6709 m S 69.3528 235.6709 m S 75.182 241.3934 m S 69.3528 235.6709 m S 57.6942 235.6709 m S 63.5235 229.9484 m S 57.6942 235.6709 m S 51.865 229.9484 m S 57.6942 235.6709 m S 51.865 241.3934 m S 0 g 1 w 4 M 51.865 229.9484 m F 75.182 229.9484 m F 0 G 0.3 w 10 M 81.0113 235.6709 m S 86.8406 229.9484 m S 81.0113 235.6709 m S 86.8406 241.3934 m S 0 g 1 w 4 M 86.8406 229.9484 m F 0 G 0.3 w 10 M 81.0113 235.6709 m S 86.8406 229.9484 m S 81.0113 235.6709 m S 86.8406 241.3934 m S 0 g 1 w 4 M 86.8406 229.9484 m F 0 G 0.3 w 10 M 57.6942 235.6709 m S 0 g 1 w 4 M 57.6942 235.6709 m F 0 G 0.3 w 10 M 57.6942 235.6709 m S 57.6942 235.6709 m S 57.6942 235.6709 m S 0 g 1 w 4 M 57.6942 235.6709 m F 0 G 0.3 w 10 M 57.6942 235.6709 m S 57.6942 235.6709 m S 1 g 0.5 w 4 M 51.6838 235.6709 m 51.6838 232.4491 54.3748 229.8373 57.6942 229.8373 c 61.0136 229.8373 63.7046 232.4491 63.7046 235.6709 c B 63.7046 235.6709 m 63.7046 238.8927 61.0136 241.5045 57.6942 241.5045 c 54.3748 241.5045 51.6838 238.8927 51.6838 235.6709 c B 57.6942 235.6709 m B 0.3 w 10 M 57.6942 235.6709 m S 0 g 1 w 4 M 57.6942 235.6709 m F 0 G 0.3 w 10 M 57.6942 235.6709 m S 57.6942 235.6709 m S 81.0113 235.6709 m S 0 g 1 w 4 M 81.0113 235.6709 m F 0 G 0.3 w 10 M 81.0113 235.6709 m S 81.0113 235.6709 m S 81.0113 235.6709 m S 0 g 1 w 4 M 81.0113 235.6709 m F 0 G 0.3 w 10 M 81.0113 235.6709 m S 81.0113 235.6709 m S 1 g 0.5 w 4 M 75.0009 235.6709 m 75.0009 232.4491 77.6919 229.8373 81.0113 229.8373 c 84.3307 229.8373 87.0217 232.4491 87.0217 235.6709 c B 87.0217 235.6709 m 87.0217 238.8927 84.3307 241.5045 81.0113 241.5045 c 77.6919 241.5045 75.0009 238.8927 75.0009 235.6709 c B 81.0113 235.6709 m B 0.3 w 10 M 81.0113 235.6709 m S 0 g 1 w 4 M 81.0113 235.6709 m F 0 G 0.3 w 10 M 81.0113 235.6709 m S 81.0113 235.6709 m S 127.6454 235.6709 m S 115.9869 235.6709 m S 121.8161 229.9484 m S 115.9869 235.6709 m S 104.3283 235.6709 m S 110.1576 241.3934 m S 127.6454 235.6709 m S 115.9869 235.6709 m S 121.8161 241.3934 m S 115.9869 235.6709 m S 104.3283 235.6709 m S 110.1576 229.9484 m S 104.3283 235.6709 m S 98.4991 229.9484 m S 104.3283 235.6709 m S 98.4991 241.3934 m S 0 g 1 w 4 M 98.4991 229.9484 m F 121.8161 229.9484 m F 0 G 0.3 w 10 M 127.6454 235.6709 m S 133.4747 229.9484 m S 127.6454 235.6709 m S 133.4747 241.3934 m S 0 g 1 w 4 M 133.4747 229.9484 m F 0 G 0.3 w 10 M 127.6454 235.6709 m S 133.4747 229.9484 m S 127.6454 235.6709 m S 133.4747 241.3934 m S 0 g 1 w 4 M 133.4747 229.9484 m F 0 G 0.3 w 10 M 104.3283 235.6709 m S 0 g 1 w 4 M 104.3283 235.6709 m F 0 G 0.3 w 10 M 104.3283 235.6709 m S 104.3283 235.6709 m S 104.3283 235.6709 m S 0 g 1 w 4 M 104.3283 235.6709 m F 0 G 0.3 w 10 M 104.3283 235.6709 m S 104.3283 235.6709 m S 1 g 0.5 w 4 M 98.3179 235.6709 m 98.3179 232.4491 101.0089 229.8373 104.3283 229.8373 c 107.6477 229.8373 110.3387 232.4491 110.3387 235.6709 c B 110.3387 235.6709 m 110.3387 238.8927 107.6477 241.5045 104.3283 241.5045 c 101.0089 241.5045 98.3179 238.8927 98.3179 235.6709 c B 104.3283 235.6709 m B 0.3 w 10 M 104.3283 235.6709 m S 0 g 1 w 4 M 104.3283 235.6709 m F 0 G 0.3 w 10 M 104.3283 235.6709 m S 104.3283 235.6709 m S 127.6454 235.6709 m S 0 g 1 w 4 M 127.6454 235.6709 m F 0 G 0.3 w 10 M 127.6454 235.6709 m S 127.6454 235.6709 m S 127.6454 235.6709 m S 0 g 1 w 4 M 127.6454 235.6709 m F 0 G 0.3 w 10 M 127.6454 235.6709 m S 127.6454 235.6709 m S 1 g 0.5 w 4 M 121.635 235.6709 m 121.635 232.4491 124.326 229.8373 127.6454 229.8373 c 130.9648 229.8373 133.6558 232.4491 133.6558 235.6709 c B 133.6558 235.6709 m 133.6558 238.8927 130.9648 241.5045 127.6454 241.5045 c 124.326 241.5045 121.635 238.8927 121.635 235.6709 c B 127.6454 235.6709 m B 0.3 w 10 M 127.6454 235.6709 m S 0 g 1 w 4 M 127.6454 235.6709 m F 0 G 0.3 w 10 M 127.6454 235.6709 m S 127.6454 235.6709 m S 174.2797 235.6709 m S 162.6211 235.6709 m S 168.4504 229.9484 m S 162.6211 235.6709 m S 150.9626 235.6709 m S 156.7919 241.3934 m S 174.2797 235.6709 m S 162.6211 235.6709 m S 168.4504 241.3934 m S 162.6211 235.6709 m S 150.9626 235.6709 m S 156.7919 229.9484 m S 150.9626 235.6709 m S 145.1333 229.9484 m S 150.9626 235.6709 m S 145.1333 241.3934 m S 0 g 1 w 4 M 145.1333 229.9484 m F 168.4504 229.9484 m F 0 G 0.3 w 10 M 174.2797 235.6709 m S 180.1089 229.9484 m S 174.2797 235.6709 m S 180.1089 241.3934 m S 0 g 1 w 4 M 180.1089 229.9484 m F 0 G 0.3 w 10 M 174.2797 235.6709 m S 180.1089 229.9484 m S 174.2797 235.6709 m S 180.1089 241.3934 m S 0 g 1 w 4 M 180.1089 229.9484 m F 0 G 0.3 w 10 M 150.9626 235.6709 m S 0 g 1 w 4 M 150.9626 235.6709 m F 0 G 0.3 w 10 M 150.9626 235.6709 m S 150.9626 235.6709 m S 150.9626 235.6709 m S 0 g 1 w 4 M 150.9626 235.6709 m F 0 G 0.3 w 10 M 150.9626 235.6709 m S 150.9626 235.6709 m S 1 g 0.5 w 4 M 144.9522 235.6709 m 144.9522 232.4491 147.6432 229.8373 150.9626 229.8373 c 154.282 229.8373 156.973 232.4491 156.973 235.6709 c B 156.973 235.6709 m 156.973 238.8927 154.282 241.5045 150.9626 241.5045 c 147.6432 241.5045 144.9522 238.8927 144.9522 235.6709 c B 150.9626 235.6709 m B 0.3 w 10 M 150.9626 235.6709 m S 0 g 1 w 4 M 150.9626 235.6709 m F 0 G 0.3 w 10 M 150.9626 235.6709 m S 150.9626 235.6709 m S 174.2797 235.6709 m S 0 g 1 w 4 M 174.2797 235.6709 m F 0 G 0.3 w 10 M 174.2797 235.6709 m S 174.2797 235.6709 m S 174.2797 235.6709 m S 0 g 1 w 4 M 174.2797 235.6709 m F 0 G 0.3 w 10 M 174.2797 235.6709 m S 174.2797 235.6709 m S 1 g 0.5 w 4 M 168.2693 235.6709 m 168.2693 232.4491 170.9603 229.8373 174.2797 229.8373 c 177.5991 229.8373 180.2901 232.4491 180.2901 235.6709 c B 180.2901 235.6709 m 180.2901 238.8927 177.5991 241.5045 174.2797 241.5045 c 170.9603 241.5045 168.2693 238.8927 168.2693 235.6709 c B 174.2797 235.6709 m B 0.3 w 10 M 174.2797 235.6709 m S 0 g 1 w 4 M 174.2797 235.6709 m F 0 G 0.3 w 10 M 174.2797 235.6709 m S 174.2797 235.6709 m S 220.9138 235.6709 m S 209.2552 235.6709 m S 215.0844 229.9484 m S 209.2552 235.6709 m S 197.5966 235.6709 m S 203.426 241.3934 m S 220.9138 235.6709 m S 209.2552 235.6709 m S 215.0844 241.3934 m S 209.2552 235.6709 m S 197.5966 235.6709 m S 203.426 229.9484 m S 197.5966 235.6709 m S 191.7674 229.9484 m S 197.5966 235.6709 m S 191.7674 241.3934 m S 0 g 1 w 4 M 191.7674 229.9484 m F 215.0844 229.9484 m F 0 G 0.3 w 10 M 220.9138 235.6709 m S 226.743 229.9484 m S 220.9138 235.6709 m S 226.743 241.3934 m S 0 g 1 w 4 M 226.743 229.9484 m F 0 G 0.3 w 10 M 220.9138 235.6709 m S 226.743 229.9484 m S 220.9138 235.6709 m S 226.743 241.3934 m S 0 g 1 w 4 M 226.743 229.9484 m F 0 G 0.3 w 10 M 197.5966 235.6709 m S 0 g 1 w 4 M 197.5966 235.6709 m F 0 G 0.3 w 10 M 197.5966 235.6709 m S 197.5966 235.6709 m S 197.5966 235.6709 m S 0 g 1 w 4 M 197.5966 235.6709 m F 0 G 0.3 w 10 M 197.5966 235.6709 m S 197.5966 235.6709 m S 1 g 0.5 w 4 M 191.5863 235.6709 m 191.5863 232.4491 194.2772 229.8373 197.5966 229.8373 c 200.916 229.8373 203.6071 232.4491 203.6071 235.6709 c B 203.6071 235.6709 m 203.6071 238.8927 200.916 241.5045 197.5966 241.5045 c 194.2772 241.5045 191.5863 238.8927 191.5863 235.6709 c B 197.5966 235.6709 m B 0.3 w 10 M 197.5966 235.6709 m S 0 g 1 w 4 M 197.5966 235.6709 m F 0 G 0.3 w 10 M 197.5966 235.6709 m S 197.5966 235.6709 m S 220.9138 235.6709 m S 0 g 1 w 4 M 220.9138 235.6709 m F 0 G 0.3 w 10 M 220.9138 235.6709 m S 220.9138 235.6709 m S 220.9138 235.6709 m S 0 g 1 w 4 M 220.9138 235.6709 m F 0 G 0.3 w 10 M 220.9138 235.6709 m S 220.9138 235.6709 m S 1 g 0.5 w 4 M 214.9034 235.6709 m 214.9034 232.4491 217.5944 229.8373 220.9138 229.8373 c 224.2332 229.8373 226.9242 232.4491 226.9242 235.6709 c B 226.9242 235.6709 m 226.9242 238.8927 224.2332 241.5045 220.9138 241.5045 c 217.5944 241.5045 214.9034 238.8927 214.9034 235.6709 c B 220.9138 235.6709 m B 0.3 w 10 M 220.9138 235.6709 m S 0 g 1 w 4 M 220.9138 235.6709 m F 0 G 0.3 w 10 M 220.9138 235.6709 m S 220.9138 235.6709 m S 3 w 267.5478 235.6709 m S 255.8893 235.6709 m S 261.7185 229.9484 m S 255.8893 235.6709 m S 244.2307 235.6709 m S 250.0601 241.3934 m S 267.5478 235.6709 m S 255.8893 235.6709 m S 261.7185 241.3934 m S 255.8893 235.6709 m S 244.2307 235.6709 m S 250.0601 229.9484 m S 244.2307 235.6709 m S 238.4015 229.9484 m S 244.2307 235.6709 m S 238.4015 241.3934 m S 4 M 238.4015 229.9484 m S 261.7185 229.9484 m S 10 M 267.5478 235.6709 m S 273.3771 229.9484 m S 267.5478 235.6709 m S 273.3771 241.3934 m S 4 M 273.3771 229.9484 m S 10 M 267.5478 235.6709 m S 273.3771 229.9484 m S 267.5478 235.6709 m S 273.3771 241.3934 m S 4 M 273.3771 229.9484 m S 10 M 244.2307 235.6709 m S 4 M 244.2307 235.6709 m S 10 M 244.2307 235.6709 m S 244.2307 235.6709 m S 244.2307 235.6709 m S 4 M 244.2307 235.6709 m S 10 M 244.2307 235.6709 m S 244.2307 235.6709 m S 1 g 0.5 w 4 M 238.2203 235.6709 m 238.2203 232.4491 240.9113 229.8373 244.2307 229.8373 c 246.8835 229.8373 250.2411 232.4491 250.2411 235.6709 c B 250.2411 235.6709 m 250.2411 238.8927 247.5501 241.5045 244.2307 241.5045 c 240.9113 241.5045 238.2203 238.8927 238.2203 235.6709 c B 3 w 244.2307 235.6709 m S 10 M 244.2307 235.6709 m S 4 M 244.2307 235.6709 m S 10 M 244.2307 235.6709 m S 244.2307 235.6709 m S 267.5478 235.6709 m S 4 M 267.5478 235.6709 m S 10 M 267.5478 235.6709 m S 267.5478 235.6709 m S 267.5478 235.6709 m S 4 M 267.5478 235.6709 m S 10 M 267.5478 235.6709 m S 267.5478 235.6709 m S 1 g 0.5 w 4 M 261.5375 235.6709 m 261.5375 232.4491 264.2285 229.8373 267.5478 229.8373 c 270.8672 229.8373 273.5583 232.4491 273.5583 235.6709 c B 273.5583 235.6709 m 273.5583 238.8927 270.8672 241.5045 267.5478 241.5045 c 264.2285 241.5045 261.5375 238.8927 261.5375 235.6709 c S 3 w 267.5478 235.6709 m S 10 M 267.5478 235.6709 m S 4 M 267.5478 235.6709 m S 10 M 267.5478 235.6709 m S 267.5478 235.6709 m S 1 g 4 M 226.9242 235.6709 m B 238.2205 235.6709 m B 87.0217 235.6709 m B 98.318 235.6709 m B 0.5 w 104.3283 252.7274 m B 104.3283 241.5045 m B 3 w 127.6454 252.7274 m 127.6454 241.5045 l S 1 g 104.3283 252.7274 m 104.3283 241.5045 l B 150.9626 252.7274 m 150.9626 241.5045 l B 174.2797 252.7274 m 174.2797 241.5045 l B 197.5966 252.7274 m 197.5966 241.5045 l B 220.9138 252.7274 m 220.9138 241.5045 l B 87.0217 235.6709 m 98.318 235.6709 l B 226.9242 235.6709 m 238.2205 235.6709 l B 0.3 w 10 M 174.2796 281.4511 m S 162.6211 281.4511 m S 168.4504 275.7285 m S 162.6211 281.4511 m S 150.9626 281.4511 m S 156.7918 287.1736 m S 174.2796 281.4511 m S 162.6211 281.4511 m S 168.4504 287.1736 m S 162.6211 281.4511 m S 150.9626 281.4511 m S 156.7918 275.7285 m S 150.9626 281.4511 m S 145.1333 275.7285 m S 150.9626 281.4511 m S 145.1333 287.1736 m S 0 g 1 w 4 M 145.1333 275.7285 m F 168.4504 275.7285 m F 0 G 0.3 w 10 M 174.2796 281.4511 m S 180.1089 275.7285 m S 174.2796 281.4511 m S 180.1089 287.1736 m S 0 g 1 w 4 M 180.1089 275.7285 m F 0 G 0.3 w 10 M 174.2797 281.4511 m S 162.6211 281.4511 m S 168.4504 275.7285 m S 162.6211 281.4511 m S 150.9626 281.4511 m S 156.7919 287.1736 m S 174.2797 281.4511 m S 162.6211 281.4511 m S 168.4504 287.1736 m S 162.6211 281.4511 m S 150.9626 281.4511 m S 156.7919 275.7285 m S 150.9626 281.4511 m S 145.1333 275.7285 m S 150.9626 281.4511 m S 145.1333 287.1736 m S 0 g 1 w 4 M 145.1333 275.7285 m F 168.4504 275.7285 m F 0 G 0.3 w 10 M 174.2797 281.4511 m S 180.1089 275.7285 m S 174.2797 281.4511 m S 180.1089 287.1736 m S 0 g 1 w 4 M 180.1089 275.7285 m F 0 G 0.3 w 10 M 174.2797 281.4511 m S 180.1089 275.7285 m S 174.2797 281.4511 m S 180.1089 287.1736 m S 0 g 1 w 4 M 180.1089 275.7285 m F 0 G 0.3 w 10 M 150.9626 281.4511 m S 0 g 1 w 4 M 150.9626 281.4511 m F 0 G 0.3 w 10 M 150.9626 281.4511 m S 150.9626 281.4511 m S 150.9626 281.4511 m S 0 g 1 w 4 M 150.9626 281.4511 m F 0 G 0.3 w 10 M 150.9626 281.4511 m S 150.9626 281.4511 m S 1 g 0.5 w 4 M 144.9522 281.4511 m 144.9522 278.2293 147.6432 275.6175 150.9626 275.6175 c 154.282 275.6175 156.973 278.2293 156.973 281.4511 c B 156.973 281.4511 m 156.973 284.6729 154.282 287.2847 150.9626 287.2847 c 147.6432 287.2847 144.9522 284.6729 144.9522 281.4511 c B 150.9626 281.4511 m B 0.3 w 10 M 150.9626 281.4511 m S 0 g 1 w 4 M 150.9626 281.4511 m F 0 G 0.3 w 10 M 150.9626 281.4511 m S 150.9626 281.4511 m S 174.2797 281.4511 m S 0 g 1 w 4 M 174.2797 281.4511 m F 0 G 0.3 w 10 M 174.2797 281.4511 m S 174.2797 281.4511 m S 174.2797 281.4511 m S 0 g 1 w 4 M 174.2797 281.4511 m F 0 G 0.3 w 10 M 174.2797 281.4511 m S 174.2797 281.4511 m S 1 g 0.5 w 4 M 168.2693 281.4511 m 168.2693 278.2293 170.9603 275.6175 174.2797 275.6175 c 177.5991 275.6175 180.2901 278.2293 180.2901 281.4511 c B 180.2901 281.4511 m 180.2901 284.6729 177.5991 287.2847 174.2797 287.2847 c 170.9603 287.2847 168.2693 284.6729 168.2693 281.4511 c B 174.2797 281.4511 m B 0.3 w 10 M 174.2797 281.4511 m S 0 g 1 w 4 M 174.2797 281.4511 m F 0 G 0.3 w 10 M 174.2797 281.4511 m S 174.2797 281.4511 m S 244.2307 281.4511 m S 232.5722 281.4511 m S 238.4015 275.7285 m S 232.5722 281.4511 m S 220.9137 281.4511 m S 226.7429 287.1736 m S 244.2307 281.4511 m S 232.5722 281.4511 m S 238.4015 287.1736 m S 232.5722 281.4511 m S 220.9137 281.4511 m S 226.7429 275.7285 m S 220.9137 281.4511 m S 215.0844 275.7285 m S 220.9137 281.4511 m S 215.0844 287.1736 m S 0 g 1 w 4 M 215.0844 275.7285 m F 238.4015 275.7285 m F 0 G 0.3 w 10 M 244.2307 281.4511 m S 250.06 275.7285 m S 244.2307 281.4511 m S 250.06 287.1736 m S 0 g 1 w 4 M 250.06 275.7285 m F 0 G 0.3 w 10 M 244.2308 281.4511 m S 232.5722 281.4511 m S 238.4015 275.7285 m S 232.5722 281.4511 m S 220.9137 281.4511 m S 226.743 287.1736 m S 244.2308 281.4511 m S 232.5722 281.4511 m S 238.4015 287.1736 m S 232.5722 281.4511 m S 220.9137 281.4511 m S 226.743 275.7285 m S 220.9137 281.4511 m S 215.0844 275.7285 m S 220.9137 281.4511 m S 215.0844 287.1736 m S 0 g 1 w 4 M 215.0844 275.7285 m F 238.4015 275.7285 m F 0 G 0.3 w 10 M 244.2308 281.4511 m S 250.0601 275.7285 m S 244.2308 281.4511 m S 250.0601 287.1736 m S 0 g 1 w 4 M 250.0601 275.7285 m F 0 G 0.3 w 10 M 244.2308 281.4511 m S 250.0601 275.7285 m S 244.2308 281.4511 m S 250.0601 287.1736 m S 0 g 1 w 4 M 250.0601 275.7285 m F 0 G 0.3 w 10 M 220.9137 281.4511 m S 0 g 1 w 4 M 220.9137 281.4511 m F 0 G 0.3 w 10 M 220.9137 281.4511 m S 220.9137 281.4511 m S 220.9137 281.4511 m S 0 g 1 w 4 M 220.9137 281.4511 m F 0 G 0.3 w 10 M 220.9137 281.4511 m S 220.9137 281.4511 m S 1 g 0.5 w 4 M 214.9033 281.4511 m 214.9033 278.2293 217.5943 275.6175 220.9137 275.6175 c 224.2331 275.6175 226.9241 278.2293 226.9241 281.4511 c B 226.9241 281.4511 m 226.9241 284.6729 224.2331 287.2847 220.9137 287.2847 c 217.5943 287.2847 214.9033 284.6729 214.9033 281.4511 c B 220.9137 281.4511 m B 0.3 w 10 M 220.9137 281.4511 m S 0 g 1 w 4 M 220.9137 281.4511 m F 0 G 0.3 w 10 M 220.9137 281.4511 m S 220.9137 281.4511 m S 244.2308 281.4511 m S 0 g 1 w 4 M 244.2308 281.4511 m F 0 G 0.3 w 10 M 244.2308 281.4511 m S 244.2308 281.4511 m S 244.2308 281.4511 m S 0 g 1 w 4 M 244.2308 281.4511 m F 0 G 0.3 w 10 M 244.2308 281.4511 m S 244.2308 281.4511 m S 1 g 0.5 w 4 M 238.2204 281.4511 m 238.2204 278.2293 240.9114 275.6175 244.2308 275.6175 c 247.5502 275.6175 250.2412 278.2293 250.2412 281.4511 c B 250.2412 281.4511 m 250.2412 284.6729 247.5502 287.2847 244.2308 287.2847 c 240.9114 287.2847 238.2204 284.6729 238.2204 281.4511 c B 244.2308 281.4511 m B 0.3 w 10 M 244.2308 281.4511 m S 0 g 1 w 4 M 244.2308 281.4511 m F 0 G 0.3 w 10 M 244.2308 281.4511 m S 244.2308 281.4511 m S 104.3283 281.4511 m S 92.6698 281.4511 m S 98.4991 275.7285 m S 92.6698 281.4511 m S 81.0113 281.4511 m S 86.8405 287.1736 m S 104.3283 281.4511 m S 92.6698 281.4511 m S 98.4991 287.1736 m S 92.6698 281.4511 m S 81.0113 281.4511 m S 86.8405 275.7285 m S 81.0113 281.4511 m S 75.182 275.7285 m S 81.0113 281.4511 m S 75.182 287.1736 m S 0 g 1 w 4 M 75.182 275.7285 m F 98.4991 275.7285 m F 0 G 0.3 w 10 M 104.3283 281.4511 m S 110.1576 275.7285 m S 104.3283 281.4511 m S 110.1576 287.1736 m S 0 g 1 w 4 M 110.1576 275.7285 m F 0 G 0.3 w 10 M 104.3284 281.4511 m S 92.6698 281.4511 m S 98.4991 275.7285 m S 92.6698 281.4511 m S 81.0113 281.4511 m S 86.8406 287.1736 m S 104.3284 281.4511 m S 92.6698 281.4511 m S 98.4991 287.1736 m S 92.6698 281.4511 m S 81.0113 281.4511 m S 86.8406 275.7285 m S 81.0113 281.4511 m S 75.182 275.7285 m S 81.0113 281.4511 m S 75.182 287.1736 m S 0 g 1 w 4 M 75.182 275.7285 m F 98.4991 275.7285 m F 0 G 0.3 w 10 M 104.3284 281.4511 m S 110.1576 275.7285 m S 104.3284 281.4511 m S 110.1576 287.1736 m S 0 g 1 w 4 M 110.1576 275.7285 m F 0 G 0.3 w 10 M 104.3284 281.4511 m S 110.1576 275.7285 m S 104.3284 281.4511 m S 110.1576 287.1736 m S 0 g 1 w 4 M 110.1576 275.7285 m F 0 G 0.3 w 10 M 81.0113 281.4511 m S 0 g 1 w 4 M 81.0113 281.4511 m F 0 G 0.3 w 10 M 81.0113 281.4511 m S 81.0113 281.4511 m S 81.0113 281.4511 m S 0 g 1 w 4 M 81.0113 281.4511 m F 0 G 0.3 w 10 M 81.0113 281.4511 m S 81.0113 281.4511 m S 1 g 0.5 w 4 M 75.0009 281.4511 m 75.0009 278.2293 77.6919 275.6175 81.0113 275.6175 c 84.3307 275.6175 87.0217 278.2293 87.0217 281.4511 c B 87.0217 281.4511 m 87.0217 284.6729 84.3307 287.2847 81.0113 287.2847 c 77.6919 287.2847 75.0009 284.6729 75.0009 281.4511 c B 81.0113 281.4511 m B 0.3 w 10 M 81.0113 281.4511 m S 0 g 1 w 4 M 81.0113 281.4511 m F 0 G 0.3 w 10 M 81.0113 281.4511 m S 81.0113 281.4511 m S 104.3284 281.4511 m S 0 g 1 w 4 M 104.3284 281.4511 m F 0 G 0.3 w 10 M 104.3284 281.4511 m S 104.3284 281.4511 m S 104.3284 281.4511 m S 0 g 1 w 4 M 104.3284 281.4511 m F 0 G 0.3 w 10 M 104.3284 281.4511 m S 104.3284 281.4511 m S 1 g 0.5 w 4 M 98.318 281.4511 m 98.318 278.2293 101.009 275.6175 104.3284 275.6175 c 107.6478 275.6175 110.3388 278.2293 110.3388 281.4511 c B 110.3388 281.4511 m 110.3388 284.6729 107.6478 287.2847 104.3284 287.2847 c 101.009 287.2847 98.318 284.6729 98.318 281.4511 c B 104.3284 281.4511 m B 0.3 w 10 M 104.3284 281.4511 m S 0 g 1 w 4 M 104.3284 281.4511 m F 0 G 0.3 w 10 M 104.3284 281.4511 m S 104.3284 281.4511 m S 174.2796 144.1104 m S 162.6211 144.1104 m S 168.4504 138.3878 m S 162.6211 144.1104 m S 150.9626 144.1104 m S 156.7918 149.8329 m S 174.2796 144.1104 m S 162.6211 144.1104 m S 168.4504 149.8329 m S 162.6211 144.1104 m S 150.9626 144.1104 m S 156.7918 138.3878 m S 150.9626 144.1104 m S 145.1333 138.3878 m S 150.9626 144.1104 m S 145.1333 149.8329 m S 0 g 1 w 4 M 145.1333 138.3878 m F 168.4504 138.3878 m F 0 G 0.3 w 10 M 174.2796 144.1104 m S 180.1089 138.3878 m S 174.2796 144.1104 m S 180.1089 149.8329 m S 0 g 1 w 4 M 180.1089 138.3878 m F 0 G 0.3 w 10 M 174.2797 144.1104 m S 162.6211 144.1104 m S 168.4504 138.3878 m S 162.6211 144.1104 m S 150.9626 144.1104 m S 156.7919 149.8329 m S 174.2797 144.1104 m S 162.6211 144.1104 m S 168.4504 149.8329 m S 162.6211 144.1104 m S 150.9626 144.1104 m S 156.7919 138.3878 m S 150.9626 144.1104 m S 145.1333 138.3878 m S 150.9626 144.1104 m S 145.1333 149.8329 m S 0 g 1 w 4 M 145.1333 138.3878 m F 168.4504 138.3878 m F 0 G 0.3 w 10 M 174.2797 144.1104 m S 180.1089 138.3878 m S 174.2797 144.1104 m S 180.1089 149.8329 m S 0 g 1 w 4 M 180.1089 138.3878 m F 0 G 0.3 w 10 M 174.2797 144.1104 m S 180.1089 138.3878 m S 174.2797 144.1104 m S 180.1089 149.8329 m S 0 g 1 w 4 M 180.1089 138.3878 m F 0 G 0.3 w 10 M 150.9626 144.1104 m S 0 g 1 w 4 M 150.9626 144.1104 m F 0 G 0.3 w 10 M 150.9626 144.1104 m S 150.9626 144.1104 m S 150.9626 144.1104 m S 0 g 1 w 4 M 150.9626 144.1104 m F 0 G 0.3 w 10 M 150.9626 144.1104 m S 150.9626 144.1104 m S 1 g 0.5 w 4 M 144.9522 144.1104 m 144.9522 140.8886 147.6432 138.2768 150.9626 138.2768 c 154.282 138.2768 156.973 140.8886 156.973 144.1104 c B 156.973 144.1104 m 156.973 147.3322 154.282 149.944 150.9626 149.944 c 147.6432 149.944 144.9522 147.3322 144.9522 144.1104 c B 150.9626 144.1104 m B 0.3 w 10 M 150.9626 144.1104 m S 0 g 1 w 4 M 150.9626 144.1104 m F 0 G 0.3 w 10 M 150.9626 144.1104 m S 150.9626 144.1104 m S 174.2797 144.1104 m S 0 g 1 w 4 M 174.2797 144.1104 m F 0 G 0.3 w 10 M 174.2797 144.1104 m S 174.2797 144.1104 m S 174.2797 144.1104 m S 0 g 1 w 4 M 174.2797 144.1104 m F 0 G 0.3 w 10 M 174.2797 144.1104 m S 174.2797 144.1104 m S 1 g 0.5 w 4 M 168.2693 144.1104 m 168.2693 140.8886 170.9603 138.2768 174.2797 138.2768 c 177.5991 138.2768 180.2901 140.8886 180.2901 144.1104 c B 180.2901 144.1104 m 180.2901 147.3322 177.5991 149.944 174.2797 149.944 c 170.9603 149.944 168.2693 147.3322 168.2693 144.1104 c B 174.2797 144.1104 m B 0.3 w 10 M 174.2797 144.1104 m S 0 g 1 w 4 M 174.2797 144.1104 m F 0 G 0.3 w 10 M 174.2797 144.1104 m S 174.2797 144.1104 m S 174.2796 75.44 m S 162.6211 75.44 m S 168.4504 69.7175 m S 162.6211 75.44 m S 150.9626 75.44 m S 156.7918 81.1625 m S 174.2796 75.44 m S 162.6211 75.44 m S 168.4504 81.1625 m S 162.6211 75.44 m S 150.9626 75.44 m S 156.7918 69.7175 m S 150.9626 75.44 m S 145.1333 69.7175 m S 150.9626 75.44 m S 145.1333 81.1625 m S 0 g 1 w 4 M 145.1333 69.7175 m F 168.4504 69.7175 m F 0 G 0.3 w 10 M 174.2796 75.44 m S 180.1089 69.7175 m S 174.2796 75.44 m S 180.1089 81.1625 m S 0 g 1 w 4 M 180.1089 69.7175 m F 0 G 0.3 w 10 M 174.2797 75.44 m S 162.6211 75.44 m S 168.4504 69.7175 m S 162.6211 75.44 m S 150.9626 75.44 m S 156.7919 81.1625 m S 174.2797 75.44 m S 162.6211 75.44 m S 168.4504 81.1625 m S 162.6211 75.44 m S 150.9626 75.44 m S 156.7919 69.7175 m S 150.9626 75.44 m S 145.1333 69.7175 m S 150.9626 75.44 m S 145.1333 81.1625 m S 0 g 1 w 4 M 145.1333 69.7175 m F 168.4504 69.7175 m F 0 G 0.3 w 10 M 174.2797 75.44 m S 180.1089 69.7175 m S 174.2797 75.44 m S 180.1089 81.1625 m S 0 g 1 w 4 M 180.1089 69.7175 m F 0 G 0.3 w 10 M 174.2797 75.44 m S 180.1089 69.7175 m S 174.2797 75.44 m S 180.1089 81.1625 m S 0 g 1 w 4 M 180.1089 69.7175 m F 0 G 0.3 w 10 M 150.9626 75.44 m S 0 g 1 w 4 M 150.9626 75.44 m F 0 G 0.3 w 10 M 150.9626 75.44 m S 150.9626 75.44 m S 150.9626 75.44 m S 0 g 1 w 4 M 150.9626 75.44 m F 0 G 0.3 w 10 M 150.9626 75.44 m S 150.9626 75.44 m S 1 g 0.5 w 4 M 144.9522 75.44 m 144.9522 72.2182 147.6432 69.6064 150.9626 69.6064 c 154.282 69.6064 156.973 72.2182 156.973 75.44 c B 156.973 75.44 m 156.973 78.6618 154.282 81.2736 150.9626 81.2736 c 147.6432 81.2736 144.9522 78.6618 144.9522 75.44 c B 150.9626 75.44 m B 0.3 w 10 M 150.9626 75.44 m S 0 g 1 w 4 M 150.9626 75.44 m F 0 G 0.3 w 10 M 150.9626 75.44 m S 150.9626 75.44 m S 174.2797 75.44 m S 0 g 1 w 4 M 174.2797 75.44 m F 0 G 0.3 w 10 M 174.2797 75.44 m S 174.2797 75.44 m S 174.2797 75.44 m S 0 g 1 w 4 M 174.2797 75.44 m F 0 G 0.3 w 10 M 174.2797 75.44 m S 174.2797 75.44 m S 1 g 0.5 w 4 M 168.2693 75.44 m 168.2693 72.2182 170.9603 69.6064 174.2797 69.6064 c 177.5991 69.6064 180.2901 72.2182 180.2901 75.44 c B 180.2901 75.44 m 180.2901 78.6618 177.5991 81.2736 174.2797 81.2736 c 170.9603 81.2736 168.2693 78.6618 168.2693 75.44 c B 174.2797 75.44 m B 0.3 w 10 M 174.2797 75.44 m S 0 g 1 w 4 M 174.2797 75.44 m F 0 G 0.3 w 10 M 174.2797 75.44 m S 174.2797 75.44 m S 244.2307 75.44 m S 232.5722 75.44 m S 238.4015 69.7175 m S 232.5722 75.44 m S 220.9137 75.44 m S 226.7429 81.1625 m S 244.2307 75.44 m S 232.5722 75.44 m S 238.4015 81.1625 m S 232.5722 75.44 m S 220.9137 75.44 m S 226.7429 69.7175 m S 220.9137 75.44 m S 215.0844 69.7175 m S 220.9137 75.44 m S 215.0844 81.1625 m S 0 g 1 w 4 M 215.0844 69.7175 m F 238.4015 69.7175 m F 0 G 0.3 w 10 M 244.2307 75.44 m S 250.06 69.7175 m S 244.2307 75.44 m S 250.06 81.1625 m S 0 g 1 w 4 M 250.06 69.7175 m F 0 G 0.3 w 10 M 244.2308 75.44 m S 232.5722 75.44 m S 238.4015 69.7175 m S 232.5722 75.44 m S 220.9137 75.44 m S 226.743 81.1625 m S 244.2308 75.44 m S 232.5722 75.44 m S 238.4015 81.1625 m S 232.5722 75.44 m S 220.9137 75.44 m S 226.743 69.7175 m S 220.9137 75.44 m S 215.0844 69.7175 m S 220.9137 75.44 m S 215.0844 81.1625 m S 0 g 1 w 4 M 215.0844 69.7175 m F 238.4015 69.7175 m F 0 G 0.3 w 10 M 244.2308 75.44 m S 250.0601 69.7175 m S 244.2308 75.44 m S 250.0601 81.1625 m S 0 g 1 w 4 M 250.0601 69.7175 m F 0 G 0.3 w 10 M 244.2308 75.44 m S 250.0601 69.7175 m S 244.2308 75.44 m S 250.0601 81.1625 m S 0 g 1 w 4 M 250.0601 69.7175 m F 0 G 0.3 w 10 M 220.9137 75.44 m S 0 g 1 w 4 M 220.9137 75.44 m F 0 G 0.3 w 10 M 220.9137 75.44 m S 220.9137 75.44 m S 220.9137 75.44 m S 0 g 1 w 4 M 220.9137 75.44 m F 0 G 0.3 w 10 M 220.9137 75.44 m S 220.9137 75.44 m S 1 g 0.5 w 4 M 214.9033 75.44 m 214.9033 72.2182 217.5943 69.6064 220.9137 69.6064 c 224.2331 69.6064 226.9241 72.2182 226.9241 75.44 c B 226.9241 75.44 m 226.9241 78.6618 224.2331 81.2736 220.9137 81.2736 c 217.5943 81.2736 214.9033 78.6618 214.9033 75.44 c B 220.9137 75.44 m B 0.3 w 10 M 220.9137 75.44 m S 0 g 1 w 4 M 220.9137 75.44 m F 0 G 0.3 w 10 M 220.9137 75.44 m S 220.9137 75.44 m S 244.2308 75.44 m S 0 g 1 w 4 M 244.2308 75.44 m F 0 G 0.3 w 10 M 244.2308 75.44 m S 244.2308 75.44 m S 244.2308 75.44 m S 0 g 1 w 4 M 244.2308 75.44 m F 0 G 0.3 w 10 M 244.2308 75.44 m S 244.2308 75.44 m S 1 g 0.5 w 4 M 238.2204 75.44 m 238.2204 72.2182 240.9114 69.6064 244.2308 69.6064 c 247.5502 69.6064 250.2412 72.2182 250.2412 75.44 c B 250.2412 75.44 m 250.2412 78.6618 247.5502 81.2736 244.2308 81.2736 c 240.9114 81.2736 238.2204 78.6618 238.2204 75.44 c B 244.2308 75.44 m B 0.3 w 10 M 244.2308 75.44 m S 0 g 1 w 4 M 244.2308 75.44 m F 0 G 0.3 w 10 M 244.2308 75.44 m S 244.2308 75.44 m S 104.3283 75.44 m S 92.6698 75.44 m S 98.4991 69.7175 m S 92.6698 75.44 m S 81.0113 75.44 m S 86.8405 81.1625 m S 104.3283 75.44 m S 92.6698 75.44 m S 98.4991 81.1625 m S 92.6698 75.44 m S 81.0113 75.44 m S 86.8405 69.7175 m S 81.0113 75.44 m S 75.182 69.7175 m S 81.0113 75.44 m S 75.182 81.1625 m S 0 g 1 w 4 M 75.182 69.7175 m F 98.4991 69.7175 m F 0 G 0.3 w 10 M 104.3283 75.44 m S 110.1576 69.7175 m S 104.3283 75.44 m S 110.1576 81.1625 m S 0 g 1 w 4 M 110.1576 69.7175 m F 0 G 0.3 w 10 M 104.3284 75.44 m S 92.6698 75.44 m S 98.4991 69.7175 m S 92.6698 75.44 m S 81.0113 75.44 m S 86.8406 81.1625 m S 104.3284 75.44 m S 92.6698 75.44 m S 98.4991 81.1625 m S 92.6698 75.44 m S 81.0113 75.44 m S 86.8406 69.7175 m S 81.0113 75.44 m S 75.182 69.7175 m S 81.0113 75.44 m S 75.182 81.1625 m S 0 g 1 w 4 M 75.182 69.7175 m F 98.4991 69.7175 m F 0 G 0.3 w 10 M 104.3284 75.44 m S 110.1576 69.7175 m S 104.3284 75.44 m S 110.1576 81.1625 m S 0 g 1 w 4 M 110.1576 69.7175 m F 0 G 0.3 w 10 M 104.3284 75.44 m S 110.1576 69.7175 m S 104.3284 75.44 m S 110.1576 81.1625 m S 0 g 1 w 4 M 110.1576 69.7175 m F 0 G 0.3 w 10 M 81.0113 75.44 m S 0 g 1 w 4 M 81.0113 75.44 m F 0 G 0.3 w 10 M 81.0113 75.44 m S 81.0113 75.44 m S 81.0113 75.44 m S 0 g 1 w 4 M 81.0113 75.44 m F 0 G 0.3 w 10 M 81.0113 75.44 m S 81.0113 75.44 m S 1 g 0.5 w 4 M 75.0009 75.44 m 75.0009 72.2182 77.6919 69.6064 81.0113 69.6064 c 84.3307 69.6064 87.0217 72.2182 87.0217 75.44 c B 87.0217 75.44 m 87.0217 78.6618 84.3307 81.2736 81.0113 81.2736 c 77.6919 81.2736 75.0009 78.6618 75.0009 75.44 c B 81.0113 75.44 m B 0.3 w 10 M 81.0113 75.44 m S 0 g 1 w 4 M 81.0113 75.44 m F 0 G 0.3 w 10 M 81.0113 75.44 m S 81.0113 75.44 m S 104.3284 75.44 m S 0 g 1 w 4 M 104.3284 75.44 m F 0 G 0.3 w 10 M 104.3284 75.44 m S 104.3284 75.44 m S 104.3284 75.44 m S 0 g 1 w 4 M 104.3284 75.44 m F 0 G 0.3 w 10 M 104.3284 75.44 m S 104.3284 75.44 m S 1 g 0.5 w 4 M 98.318 75.44 m 98.318 72.2182 101.009 69.6064 104.3284 69.6064 c 107.6478 69.6064 110.3388 72.2182 110.3388 75.44 c B 110.3388 75.44 m 110.3388 78.6618 107.6478 81.2736 104.3284 81.2736 c 101.009 81.2736 98.318 78.6618 98.318 75.44 c B 104.3284 75.44 m B 0.3 w 10 M 104.3284 75.44 m S 0 g 1 w 4 M 104.3284 75.44 m F 0 G 0.3 w 10 M 104.3284 75.44 m S 104.3284 75.44 m S 104.4534 144.1107 m S 92.7948 144.1107 m S 98.6241 149.8332 m S 92.7948 144.1107 m S 81.1363 144.1107 m S 86.9656 149.8332 m S 81.1363 144.1107 m S 75.307 149.8332 m S 0 g 1 w 4 M 75.307 149.8332 m F 98.6241 149.8332 m F 0 G 0.3 w 10 M 104.4534 144.1107 m S 110.2826 149.8332 m S 0 g 1 w 4 M 110.2826 149.8332 m F 75.307 138.3882 m F 98.6241 138.3882 m F 110.2826 138.3882 m F 0 G 0.3 w 10 M 81.1363 144.1107 m S 75.307 138.3882 m S 92.7948 144.1107 m S 81.1363 144.1107 m S 86.9656 138.3882 m S 104.4534 144.1107 m S 92.7948 144.1107 m S 98.6241 138.3882 m S 0 g 1 w 4 M 75.307 138.3882 m F 98.6241 138.3882 m F 0 G 0.3 w 10 M 104.4534 144.1107 m S 110.2826 138.3882 m S 0 g 1 w 4 M 110.2826 138.3882 m F 0 G 0.3 w 10 M 104.4534 144.1107 m S 110.2826 149.8332 m S 0 g 1 w 4 M 110.2826 149.8332 m F 110.2826 138.3882 m F 0 G 0.3 w 10 M 104.4534 144.1107 m S 110.2826 138.3882 m S 0 g 1 w 4 M 110.2826 138.3882 m F 0 G 0.3 w 10 M 81.1363 144.1107 m S 75.307 138.3882 m S 92.7948 144.1107 m S 81.1363 144.1107 m S 86.9656 138.3882 m S 104.4534 144.1107 m S 92.7948 144.1107 m S 98.6241 138.3882 m S 0 g 1 w 4 M 75.307 138.3882 m F 98.6241 138.3882 m F 0 G 0.3 w 10 M 104.4534 144.1107 m S 110.2826 138.3882 m S 0 g 1 w 4 M 110.2826 138.3882 m F 0 G 0.3 w 10 M 104.4534 144.1107 m S 110.2826 138.3882 m S 0 g 1 w 4 M 110.2826 138.3882 m F 0 G 0.3 w 10 M 81.1363 144.1107 m S 75.307 149.8332 m S 92.7948 144.1107 m S 81.1363 144.1107 m S 86.9656 138.3883 m S 92.7948 144.1107 m S 81.1363 144.1107 m S 86.9656 149.8332 m S 104.4534 144.1107 m S 92.7948 144.1107 m S 98.6241 149.8332 m S 104.4534 144.1107 m S 92.7948 144.1107 m S 98.6241 138.3883 m S 81.1363 144.1107 m S 75.307 138.3883 m S 0 g 1 w 4 M 75.307 149.8332 m F 98.6241 149.8332 m F 0 G 0.3 w 10 M 104.4534 144.1107 m S 110.2826 149.8332 m S 104.4534 144.1107 m S 110.2826 138.3883 m S 0 g 1 w 4 M 110.2826 149.8332 m F 0 G 0.3 w 10 M 104.4534 144.1107 m S 110.2826 149.8332 m S 104.4534 144.1107 m S 110.2826 138.3883 m S 0 g 1 w 4 M 110.2826 149.8332 m F 0 G 0.3 w 10 M 81.1363 144.1107 m S 75.307 138.3882 m S 81.1363 144.1107 m S 75.307 149.8332 m S 0 g 1 w 4 M 75.307 138.3882 m F 0 G 0.3 w 10 M 81.1363 144.1107 m S 86.9656 138.3882 m S 81.1363 144.1107 m S 86.9656 149.8332 m S 0 g 1 w 4 M 86.9656 138.3882 m F 0 G 0.3 w 10 M 81.1363 144.1107 m S 86.9656 138.3882 m S 81.1363 144.1107 m S 86.9656 149.8332 m S 0 g 1 w 4 M 86.9656 138.3882 m F 0 G 0.3 w 10 M 81.1363 144.1107 m S 0 g 1 w 4 M 81.1363 144.1107 m F 0 G 0.3 w 10 M 81.1363 144.1107 m S 81.1363 144.1107 m S 81.1363 144.1107 m S 0 g 1 w 4 M 81.1363 144.1107 m F 0 G 0.3 w 10 M 81.1363 144.1107 m S 81.1363 144.1107 m S 1 g 0.5 w 4 M 75.1259 144.1107 m 75.1259 140.8889 77.8169 138.2771 81.1363 138.2771 c 84.4557 138.2771 87.1467 140.8889 87.1467 144.1107 c B 87.1467 144.1107 m 87.1467 147.3325 84.4557 149.9443 81.1363 149.9443 c 77.8169 149.9443 75.1259 147.3325 75.1259 144.1107 c B 81.1363 144.1107 m B 0.3 w 10 M 81.1363 144.1107 m S 0 g 1 w 4 M 81.1363 144.1107 m F 0 G 0.3 w 10 M 81.1363 144.1107 m S 81.1363 144.1107 m S 104.4533 144.1107 m S 110.2826 149.8332 m S 104.4533 144.1107 m S 110.2826 138.3882 m S 104.4533 144.1107 m S 98.6241 138.3882 m S 104.4533 144.1107 m S 98.6241 149.8332 m S 0 g 1 w 4 M 98.6241 138.3882 m F 0 G 0.3 w 10 M 104.4533 144.1107 m S 0 g 1 w 4 M 104.4533 144.1107 m F 0 G 0.3 w 10 M 104.4533 144.1107 m S 104.4533 144.1107 m S 104.4533 144.1107 m S 0 g 1 w 4 M 104.4533 144.1107 m F 0 G 0.3 w 10 M 104.4533 144.1107 m S 104.4533 144.1107 m S 1 g 0.5 w 4 M 98.4429 144.1107 m 98.4429 140.8889 101.1339 138.2771 104.4533 138.2771 c 107.7727 138.2771 110.4637 140.8889 110.4637 144.1107 c B 110.4637 144.1107 m 110.4637 147.3325 107.7727 149.9443 104.4533 149.9443 c 101.1339 149.9443 98.4429 147.3325 98.4429 144.1107 c B 104.4533 144.1107 m B 0.3 w 10 M 104.4533 144.1107 m S 0 g 1 w 4 M 104.4533 144.1107 m F 0 G 0.3 w 10 M 104.4533 144.1107 m S 104.4533 144.1107 m S 1 g 3 w 4 M 87.1467 144.1107 m 98.443 144.1107 l B 0.3 w 10 M 244.3558 144.1107 m S 232.6972 144.1107 m S 238.5265 149.8332 m S 232.6972 144.1107 m S 221.0387 144.1107 m S 226.868 149.8332 m S 221.0387 144.1107 m S 215.2094 149.8332 m S 0 g 1 w 4 M 215.2094 149.8332 m F 238.5265 149.8332 m F 0 G 0.3 w 10 M 244.3558 144.1107 m S 250.1851 149.8332 m S 0 g 1 w 4 M 250.1851 149.8332 m F 215.2094 138.3882 m F 238.5265 138.3882 m F 250.1851 138.3882 m F 0 G 0.3 w 10 M 221.0387 144.1107 m S 215.2094 138.3882 m S 232.6972 144.1107 m S 221.0387 144.1107 m S 226.868 138.3882 m S 244.3558 144.1107 m S 232.6972 144.1107 m S 238.5265 138.3882 m S 0 g 1 w 4 M 215.2094 138.3882 m F 238.5265 138.3882 m F 0 G 0.3 w 10 M 244.3558 144.1107 m S 250.1851 138.3882 m S 0 g 1 w 4 M 250.1851 138.3882 m F 0 G 0.3 w 10 M 244.3558 144.1107 m S 250.1851 149.8332 m S 0 g 1 w 4 M 250.1851 149.8332 m F 250.1851 138.3882 m F 0 G 0.3 w 10 M 244.3558 144.1107 m S 250.1851 138.3882 m S 0 g 1 w 4 M 250.1851 138.3882 m F 0 G 0.3 w 10 M 221.0387 144.1107 m S 215.2094 138.3882 m S 232.6972 144.1107 m S 221.0387 144.1107 m S 226.868 138.3882 m S 244.3558 144.1107 m S 232.6972 144.1107 m S 238.5265 138.3882 m S 0 g 1 w 4 M 215.2094 138.3882 m F 238.5265 138.3882 m F 0 G 0.3 w 10 M 244.3558 144.1107 m S 250.1851 138.3882 m S 0 g 1 w 4 M 250.1851 138.3882 m F 0 G 0.3 w 10 M 244.3558 144.1107 m S 250.1851 138.3882 m S 0 g 1 w 4 M 250.1851 138.3882 m F 0 G 0.3 w 10 M 221.0387 144.1107 m S 215.2094 149.8332 m S 232.6972 144.1107 m S 221.0387 144.1107 m S 226.868 138.3883 m S 232.6972 144.1107 m S 221.0387 144.1107 m S 226.868 149.8332 m S 244.3558 144.1107 m S 232.6972 144.1107 m S 238.5265 149.8332 m S 244.3558 144.1107 m S 232.6972 144.1107 m S 238.5265 138.3883 m S 221.0387 144.1107 m S 215.2094 138.3883 m S 0 g 1 w 4 M 215.2094 149.8332 m F 238.5265 149.8332 m F 0 G 0.3 w 10 M 244.3558 144.1107 m S 250.185 149.8332 m S 244.3558 144.1107 m S 250.185 138.3883 m S 0 g 1 w 4 M 250.185 149.8332 m F 0 G 0.3 w 10 M 244.3558 144.1107 m S 250.185 149.8332 m S 244.3558 144.1107 m S 250.185 138.3883 m S 0 g 1 w 4 M 250.185 149.8332 m F 0 G 0.3 w 10 M 221.0387 144.1107 m S 215.2094 138.3882 m S 221.0387 144.1107 m S 215.2094 149.8332 m S 0 g 1 w 4 M 215.2094 138.3882 m F 0 G 0.3 w 10 M 221.0387 144.1107 m S 226.868 138.3882 m S 221.0387 144.1107 m S 226.868 149.8332 m S 0 g 1 w 4 M 226.868 138.3882 m F 0 G 0.3 w 10 M 221.0387 144.1107 m S 226.868 138.3882 m S 221.0387 144.1107 m S 226.868 149.8332 m S 0 g 1 w 4 M 226.868 138.3882 m F 0 G 0.3 w 10 M 221.0387 144.1107 m S 0 g 1 w 4 M 221.0387 144.1107 m F 0 G 0.3 w 10 M 221.0387 144.1107 m S 221.0387 144.1107 m S 221.0387 144.1107 m S 0 g 1 w 4 M 221.0387 144.1107 m F 0 G 0.3 w 10 M 221.0387 144.1107 m S 221.0387 144.1107 m S 1 g 0.5 w 4 M 215.0283 144.1107 m 215.0283 140.8889 217.7193 138.2771 221.0387 138.2771 c 224.3581 138.2771 227.0491 140.8889 227.0491 144.1107 c B 227.0491 144.1107 m 227.0491 147.3325 224.3581 149.9443 221.0387 149.9443 c 217.7193 149.9443 215.0283 147.3325 215.0283 144.1107 c B 221.0387 144.1107 m B 0.3 w 10 M 221.0387 144.1107 m S 0 g 1 w 4 M 221.0387 144.1107 m F 0 G 0.3 w 10 M 221.0387 144.1107 m S 221.0387 144.1107 m S 244.3557 144.1107 m S 250.185 149.8332 m S 244.3557 144.1107 m S 250.185 138.3882 m S 244.3557 144.1107 m S 238.5265 138.3882 m S 244.3557 144.1107 m S 238.5265 149.8332 m S 0 g 1 w 4 M 238.5265 138.3882 m F 0 G 0.3 w 10 M 244.3557 144.1107 m S 0 g 1 w 4 M 244.3557 144.1107 m F 0 G 0.3 w 10 M 244.3557 144.1107 m S 244.3557 144.1107 m S 244.3557 144.1107 m S 0 g 1 w 4 M 244.3557 144.1107 m F 0 G 0.3 w 10 M 244.3557 144.1107 m S 244.3557 144.1107 m S 1 g 0.5 w 4 M 238.3453 144.1107 m 238.3453 140.8889 241.0363 138.2771 244.3557 138.2771 c 247.6751 138.2771 250.3661 140.8889 250.3661 144.1107 c B 250.3661 144.1107 m 250.3661 147.3325 247.6751 149.9443 244.3557 149.9443 c 241.0363 149.9443 238.3453 147.3325 238.3453 144.1107 c B 244.3557 144.1107 m B 0.3 w 10 M 244.3557 144.1107 m S 0 g 1 w 4 M 244.3557 144.1107 m F 0 G 0.3 w 10 M 244.3557 144.1107 m S 244.3557 144.1107 m S 1 g 3 w 4 M 227.0491 144.1107 m 238.3455 144.1107 l B 92.6698 247.1159 m 92.6698 109.7752 l 232.5722 109.7752 l 232.5722 247.1159 l 92.6698 247.1159 l s u u 0 g 1 w /_Times-Roman 12 14.5 0 0 z [1 0 0 1 156.5 35.5]e (\(b\))t T U U showpage _E end %%EndDocument @endspecial 60 2447 a FQ(Figure)17 b(14:)24 b(System)16 b(of)i(in)o(ternal)e (spins)i(\(small)d(circles\))h(under)h(decimation,)f(when)h(the)g(image)60 2508 y(spins)23 b(\(squares\))h(are)f(\014xed)g(in)g(the)g(fully)f (alternating)h(\\+)p FF(=)p FE(\000)p FQ(")h(con\014guration.)43 b(\(a\))24 b(A)e(\\)p FE(\000)p FQ(")60 2568 y(con)o(tour)f(\000)g(\(thic)o (k)e(lines\).)33 b(\(b\))21 b(The)f(fundamen)o(tal)f(b)q(onds)j(\(b)q(ounded) g(b)o(y)e(thic)o(k)f(lines\))h(of)h(an)60 2628 y(equiv)m(alen)o(t)15 b FF(m)p FQ(-p)q(oten)o(tial.)938 2784 y(238)p eop %%Page: 239 239 bop 60 91 a FQ(the)16 b(sublattice)g(of)h(image)e(spins,)i(the)f(energy)g (con)o(tribution)g(of)h(the)f(latter)h(is)f(almost)g(the)g(same)60 152 y(as)g(for)g(the)f(usual)h(Ising)f(mo)q(del.)20 b(This)15 b(pro)q(duces)h(an)g(estimation)e(of)i(the)f(P)o(eierls)f(constan)o(t)h (\(and)60 212 y(hence)j(of)g(the)g(critical)f(temp)q(erature\),)g(with)h(t)o (w)o(o)g(comp)q(eting)g(terms:)23 b(one)c(dep)q(ending)f(on)h(the)60 272 y(decimation)13 b(p)q(erio)q(d)i FF(b)g FQ(\(and)g(tending)g(to)g(0)g(as) h FF(b)e FQ(tends)h(to)h(in\014nit)o(y\),)d(and)i(another)h(indep)q(enden)o (t)60 332 y(of)21 b FF(b)f FQ(and)h(close)f(to)h(the)f(P)o(eierls)f(constan)o (t)i(for)g(the)f(Ising)g(mo)q(del)g(\(the)g(closer)g(the)g(higher)g(the)60 392 y(dimension\).)133 452 y(T)l(o)c(formalize)d(these)i(ideas)h(w)o(e)f(c)o (ho)q(ose)h(one)f(co)q(ordinate)h(axis,)f(sa)o(y)h(the)f(one)h(lab)q(elled)e (1,)h(and)60 513 y(p)q(erform)d(the)g(cancellations)g(b)o(y)h(sw)o(eeping)f (in)g(order)h(along)h(it.)19 b(T)l(o)14 b(abbreviate,)e(let)g(us)h(call)f (\\left")60 573 y(the)17 b(direction)e(in)i Fq(Z)436 552 y FD(d)473 573 y FQ(to)o(w)o(ards)h(smaller)c(1-comp)q(onen)o(ts,)j(and)g (\\righ)o(t")g(the)g(opp)q(osite)g(direction.)60 633 y(Also,)h(w)o(e)g(shall) h(sa)o(y)f(that)h(an)g(image)f(spin)g(is)g(\\in")h(the)g(con)o(tour)f(if)g (it)g(is)h(visited)e(b)o(y)h(it)g(or)h(it)f(is)60 693 y(con)o(tained)g(in)h (its)f(v)o(olume.)26 b(More)19 b(sp)q(eci\014cally)l(,)e(an)i(\\in)o(ternal)f (spin)h(with)g FF(l)g FQ(plaquettes)f(in)g(the)60 753 y(con)o(tour")f(is)e (an)i(in)o(ternal)e(spin)h(suc)o(h)f(that)i(the)f(con)o(tour)g(surrounds)h FF(l)g FQ(of)f(the)g(plaquettes)f(of)h(the)60 814 y(unit)d(cub)q(e)f(cen)o (tered)g(on)h(it)f(\(e.g.)g(in)h(Fig.)f(14\(a\),)i(the)f(in)o(ternal)f(spin)h (at)g FF(a)1404 821 y FH(1)1436 814 y FQ(has)g(1)h(plaquette)e(in)g(the)60 874 y(con)o(tour,)17 b(the)f(one)h(at)g FF(a)512 881 y FH(4)549 874 y FQ(has)g(3,)g(etc.\).)22 b(Note)16 b(that,)h(in)f(suc)o(h)h(a)g(case,)g (the)f(energy)h(con)o(tribution)60 934 y(of)g(the)f(image)e(spin)j(is)812 1044 y(\001)p FF(E)889 1051 y Fy(\000)960 1044 y FQ(=)41 b(2)p FE(j)p FF(J)5 b FE(j)p FF(l)593 b FQ(\(B.72a\))812 1117 y(\001)p FF(E)889 1124 y FH(+)960 1117 y FQ(=)41 b(0)665 b(\(B.72b\))60 1227 y(if)19 b(it)g(is)h(a)f(\\)p FE(\000)p FQ(")i(spin,)f(and)g(the)f(con)o (v)o(erse)f(for)i(a)g(\\+")h(image)d(spin.)31 b(The)20 b(cancellation)e(can)i (b)q(e)60 1287 y(done,)e(for)f(instance,)g(as)h(follo)o(ws:)24 b(F)l(or)17 b(eac)o(h)g(line)f(in)h(the)h(left-righ)o(t)e(direction)g(in)o (tersecting)g(the)60 1347 y(con)o(tour,)i(w)o(e)g(c)o(ho)q(ose)h(the)e(image) g(spin)h(in)g(the)g(con)o(tour)g(further)g(to)h(the)e(left)h(and)g(lo)q(ok)h (for)f(the)60 1407 y(next)c(image)g(spin)g(in)h(the)f(con)o(tour,)h(of)g(opp) q(osite)g(sign)g(and)h(lo)q(cated)f(to)g(the)f(righ)o(t)g(and)i(along)f(the) 60 1467 y(same)j(line.)28 b(If)19 b(the)g(\\+")g(image)f(spin)h(has)h(the)f (same)f(n)o(um)o(b)q(er)f(of)i(plaquettes)g(or)g(more)f(in)g(the)60 1528 y(con)o(tour)f(than)h(the)f(\\)p FE(\000)p FQ(",)g(w)o(e)g(cancel)f(b)q (oth)i(con)o(tributions)f(\(obtaining)g(a)h(lo)o(w)o(er)e(b)q(ound)i(for)f (the)60 1588 y(energy)i(if)g(the)h(n)o(um)o(b)q(er)e(of)i(plaquettes)f(is)g (not)i(the)e(same\).)31 b(Otherwise)19 b(w)o(e)g(do)h(nothing.)32 b(W)l(e)60 1648 y(then)15 b(pro)q(ceed)f(to)h(the)g(next)f(uncancelled)g (image)f(spin)i(along)g(the)g(same)f(line,)f(alw)o(a)o(ys)i(tra)o(v)o(elling) 60 1708 y(to)o(w)o(ards)k(the)f(righ)o(t.)28 b(Once)17 b(all)h(the)g (left-righ)o(t)g(lines)f(ha)o(v)o(e)h(b)q(een)g(scanned,)h(w)o(e)f(obtain)h (a)g(lo)o(w)o(er)60 1768 y(b)q(ound)d(for)e(the)g(energy)g(of)h(the)f(form)f (\(B.71\))h(but)h(where)f(\001)p FF(E)1219 1775 y Fy(\000)1263 1768 y FQ(and)h(\001)p FF(E)1433 1775 y FH(+)1476 1768 y FQ(refer)f(only)g (to)h(a)f(la)o(y)o(er)60 1829 y(of)22 b(image)e(spins)h(in)g(the)h(con)o (tour)f(at)h(a)g(distance)f(not)h(exceeding)e FF(b)14 b FQ(+)h(1)21 b(from)g(it)g(\(remaining)60 1889 y(spins\).)g(The)13 b(energy)g(gain)h(due)g (to)g(these)f(remaining)f(spins)i(can)g(not)g(exceed)e(that)i(of)g(the)g (case)f(in)60 1949 y(whic)o(h)h(there)h(are)g(no)g(\\+")h(image)d(spins)i (left)f(and)i(all)e(the)h(\\)p FE(\000)p FQ(")g(spins)h(ha)o(v)o(e)e(their)g (2)p FF(d)i FQ(plaquettes)60 2009 y(in)g(the)g(con)o(tour.)21 b(W)l(e)16 b(therefore)g(b)q(ound)698 2119 y(\001)p FF(E)775 2126 y Fy(\000)816 2119 y FE(\000)11 b FQ(\001)p FF(E)943 2126 y FH(+)1000 2119 y FE(\024)27 b FQ(2)p FF(dJ)5 b(N)1186 2126 y Fy(\000)1230 2119 y FF(;)511 b FQ(\(B)p FF(:)p FQ(73\))60 2229 y(where)16 b FF(N)240 2236 y Fy(\000)286 2229 y FQ(is)g(the)g(n)o(um)o (b)q(er)e(of)j(\\)p FE(\000)p FQ(")g(image)e(spins)h(inside)f(the)h(ab)q(o)o (v)o(e-men)o(tioned)f(la)o(y)o(er.)133 2289 y(T)l(o)k(complete)d(the)i(P)o (eierls)f(b)q(ound,)j(w)o(e)d(ha)o(v)o(e)h(to)h(relate)e FF(N)1253 2296 y Fy(\000)1301 2289 y FQ(to)i(the)f(con)o(tour)g(area)h FE(j)p FQ(\000)p FE(j)p FQ(.)28 b(A)o(t)60 2350 y(this)18 b(p)q(oin)o(t)f(w)o (e)g(m)o(ust)g(distinguish)g(b)q(et)o(w)o(een)g(con)o(tours)h(with)g FF(N)1269 2357 y Fy(\000)1314 2350 y FE(\025)e FQ(2)i(\(\\wide)g(con)o (tours"\))g(and)60 2410 y(con)o(tours)c(with)f FF(N)401 2417 y Fy(\000)444 2410 y FE(\024)h FQ(1)g(\(\\narro)o(w)g(con)o(tours"\).)21 b(F)l(or)13 b(the)g(wide)g(con)o(tours,)h(the)f(k)o(ey)f(observ)m(ation)60 2470 y(is)g(that)h(eac)o(h)f(t)o(w)o(o)g(\\)p FE(\000)p FQ(")h(image)e(spins) h(m)o(ust)f(b)q(e)i(at)f(least)g(a)h(distance)f(2)p FF(b)h FQ(apart)g(in)f(eac)o(h)f(co)q(ordinate)60 2530 y(direction)f(and)i(the)f (con)o(tour)g(m)o(ust)f(pass)i(at)f(a)h(distance)e FF(b)q FQ(+)q(1)g(or)i (less)f(of)g(eac)o(h)g(of)g(them.)18 b(Therefore,)60 2590 y(the)g(n)o(um)o(b) q(er)e(of)i(remaining)e(\\)p FE(\000)p FQ(")j(image)d(spins)i(for)g(a)h(giv)o (en)e(v)m(alue)g(of)h(\000)h(can)f(not)g(exceed)f(that)60 2650 y(of)h(the)g(case)h(in)e(whic)o(h)h(all)g(of)g(the)g(spins)h(are)f(lo)q (cated)g(so)h(as)g(to)f(form)f(a)i(\\tub)q(e",)g(separated)g(2)p FF(b)938 2784 y FQ(239)p eop %%Page: 240 240 bop 60 91 a FQ(units)16 b(from)f(eac)o(h)h(other,)g(and)h(\000)g(b)q(eing)f (the)g(w)o(all)g(of)g(suc)o(h)g(a)h(\\tub)q(e":)717 222 y FF(N)756 229 y Fy(\000)813 222 y FE(\024)1014 189 y(j)p FQ(\000)p FE(j)p 884 211 317 2 v 884 256 a FQ(2\()p FF(d)12 b FE(\000)f FQ(1\)\()p FF(b)g FE(\000)g FQ(1\))1220 222 y FF(:)521 b FQ(\(B)p FF(:)p FQ(74\))60 356 y(\(Note)11 b(that)g(the)g(b)q(ound)h(con)o(tains)f FF(b)q FE(\000)q FQ(1,)g(rather)g(than)h FF(b)p FQ(,)f(b)q(ecause)h(the)f (plaquettes)f(corresp)q(onding)60 417 y(to)k(\\+")g(image)e(spins)h(are)h (not)g(part)f(of)h(the)f(con)o(tour.\))20 b(F)l(rom)13 b(\(B.71\){\(B.74\),)g (w)o(e)g(conclude)g(that)387 548 y FF(H)t FQ(\()p FF(!)482 527 y FH(\000)506 548 y FE(j)p FF(!)p 520 555 33 2 v 552 527 a FH(\(+\))609 548 y FQ(\))28 b FE(\025)f FQ(2)p FF(J)778 487 y Fx(\024)800 548 y FQ(1)11 b FE(\000)1036 514 y FF(d)p 890 536 317 2 v 890 582 a FQ(2\()p FF(d)h FE(\000)f FQ(1\)\()p FF(b)g FE(\000)g FQ(1\))1212 487 y Fx(\025)1234 548 y FE(j)p FQ(\000)p FE(j)j FQ(;)57 b FF(N)1416 555 y Fy(\000)1459 548 y FE(\025)14 b FQ(2)g FF(:)191 b FQ(\(B)p FF(:)p FQ(75\))60 679 y(This)20 b(b)q(ound)g(is)f(not)h(useful)f(for)h(the)f(limit)e(case)j FF(d)f FQ(=)h(2,)g FF(b)f FQ(=)g(2;)i(but)f(for)f(it)g(w)o(e)h(ha)o(v)o(e)e (already)60 739 y(go)q(o)q(d)g(b)q(ounds)g(for)e(the)g(critical)f(temp)q (erature)g(\(Section)g(4.1.2\).)133 799 y(Let)d(us)f(no)o(w)h(consider)f(the) h(narro)o(w)g(con)o(tours)g(\()p FF(N)1044 806 y Fy(\000)1087 799 y FE(\024)i FQ(1\).)20 b(It)11 b(is)g(not)h(hard)g(to)f(con)o(vince)f (oneself)60 859 y(that)19 b(the)g(w)o(orst)g(case)g(is)f(when)h(the)g(con)o (tour)g(visits)f(only)g(one)h(\\)p FE(\000)p FQ(")g(image)f(spin,)h(whic)o(h) f(has)h FF(l)60 920 y FQ(plaquettes)g(in)h(the)g(con)o(tour.)32 b(The)20 b(con)o(tour)g(m)o(ust)f(then)h(include)f(the)g(opp)q(osite)i FF(l)g FQ(plaquettes)60 980 y(plus)e(the)g(plaquettes)f(needed)h(to)g(join)g (these)g(among)f(themselv)o(es)f(or/and)j(to)f(the)g(cub)q(e)g(so)h(to)60 1040 y(form)f(a)i(closed)e(surface.)33 b(One)20 b(can)g(c)o(hec)o(k)f(that)h (the)g(w)o(orst)h(situation)f(\(smallest)e(ratio)j FF(l)q(=)p FE(j)p FQ(\000)p FE(j)p FQ(\))60 1100 y(is)f(when)h(the)f FF(l)h FQ(plaquettes)f(of)h(the)f(cub)q(e)g(are)h(not)g(consecutiv)o(e,)e(in)h(whic) o(h)g(case)h(the)f(con)o(tour)60 1160 y(includes)15 b(the)g FF(l)i FQ(opp)q(osite)g(plaquettes)e(and)h(the)g(2\()p FF(d)11 b FE(\000)f FQ(1\))p FF(l)17 b FQ(plaquettes)e(needed)g(to)i(join)e(them)g (to)60 1221 y(the)h(cub)q(e.)21 b(Hence,)735 1281 y FE(j)p FQ(\000)p FE(j)28 b(\025)f FF(l)q FQ([2\()p FF(d)11 b FE(\000)g FQ(1\))h(+)f(1])i FF(:)60 1366 y FQ(Therefore,)i(using)i(\(B.72\),)690 1451 y(\001)p FF(E)767 1458 y Fy(\000)807 1451 y FE(\000)11 b FQ(\001)p FF(E)934 1458 y FH(+)991 1451 y FE(\024)1102 1417 y FQ(2)p FF(J)p 1062 1439 136 2 v 1062 1485 a FQ(2)p FF(d)h FE(\000)f FQ(1)1202 1451 y FE(j)p FQ(\000)p FE(j)60 1553 y FQ(and)478 1623 y FF(H)t FQ(\()p FF(!)573 1603 y FH(\000)597 1623 y FE(j)p FF(!)p 611 1630 33 2 v 643 1603 a FH(\(+\))700 1623 y FQ(\))28 b FE(\025)f FQ(2)p FF(J)869 1562 y Fx(\024)891 1623 y FQ(1)11 b FE(\000)1036 1589 y FQ(1)p 981 1611 136 2 v 981 1657 a(2)p FF(d)h FE(\000)f FQ(1)1121 1562 y Fx(\025)1143 1623 y FE(j)p FQ(\000)p FE(j)j FQ(;)57 b FF(N)1325 1630 y Fy(\000)1368 1623 y FE(\024)14 b FQ(1)g FF(:)282 b FQ(\(B)p FF(:)p FQ(76\))60 1728 y(\(Another)13 b(w)o(a)o(y)h(to)g(in)o(terpret)e(this)h(P)o(eierls)f(b)q (ound)j(is)e(b)o(y)h(noting)g(that)g(the)f(narro)o(w)h(con)o(tour)g(with)60 1788 y(the)j(least)g(energy)g(cost)g(is)g(the)g(one)g(pro)q(duced)h(b)o(y)e (a)i(single)e(\015ipp)q(ed)h(in)o(ternal)g(spin)g(adjacen)o(t)g(to)60 1849 y(a)g(\\)p FE(\000)p FQ(")f(image)f(spin.\))133 1909 y(F)l(orm)o(ulas)j (\(B.75\))h(and)i(\(B.76\))e(sho)o(w)h(b)q(oth)g(that)g(the)f (con\014gurations)i FF(!)p 1510 1916 33 2 v 1542 1891 a FH(\(+\))1618 1909 y FQ(and)f FF(!)p 1716 1916 V 1749 1891 a FH(\()p Fy(\000)p FH(\))1825 1909 y FQ(are)60 1969 y(indeed)c(the)h(only)g(p)q(erio)q(dic)g (ground-state)i(con\014gurations)f(and)g(that)g(the)f(P)o(eierls)e(condition) i(is)60 2029 y(satis\014ed)g(for)f(the)g(in)o(ternal-spin)f(system)g(with)h (P)o(eierls)f(constan)o(t)770 2135 y FF(\032)795 2142 y FH(0)829 2135 y FE(\025)e FQ(2)p FF(J)5 b FQ(\(1)12 b FE(\000)e FF(M)1088 2142 y FD(d;b)1134 2135 y FQ(\))k FF(;)574 b FQ(\(B)p FF(:)p FQ(77\))60 2242 y(where)526 2321 y FF(M)573 2328 y FD(d;b)646 2321 y FQ(=)28 b(max)811 2247 y Fx(\()905 2287 y FQ(1)p 849 2309 136 2 v 849 2355 a(2)p FF(d)12 b FE(\000)f FQ(1)998 2321 y FF(;)1179 2287 y(d)p 1033 2309 317 2 v 1033 2355 a FQ(2\()p FF(d)h FE(\000)e FQ(1\)\()p FF(b)h FE(\000)g FQ(1\))1355 2247 y Fx(\))1410 2321 y FF(:)331 b FQ(\(B)p FF(:)p FQ(78\))60 2437 y(This)17 b(v)m(alue)f(of)h FF(\032)379 2444 y FH(0)399 2437 y FQ(,)f(together)h(with)f(the)h(estimates)e(\(B.58\))h(for)h FF(\014)1287 2444 y FH(0)1323 2437 y FQ(and)g(\(B.68\))g(for)f(the)h(en)o (trop)o(y)60 2497 y(factor)g FF(\013)f FQ(of)h(thin)f(con)o(tours,)g(implies) e(there)h(is)h(a)h(phase)g(transition)f(at)h(least)f(for)677 2628 y FF(\014)g FE(\025)778 2595 y FQ(4)8 b(log)r(\(2)p FF(d)k FE(\000)f FQ(1\))g(+)g(1)p FF(=)p FQ(\(2)p FF(e)p FQ(\))p 778 2617 463 2 v 874 2662 a(2)p FF(J)5 b FQ(\(1)11 b FE(\000)g FF(M)1081 2669 y FD(d;b)1126 2662 y FQ(\))1260 2628 y FF(:)481 b FQ(\(B)p FF(:)p FQ(79\))938 2784 y(240)p eop %%Page: 241 241 bop 60 91 a FQ(This)18 b(estimate)d(is)j(probably)g(v)o(ery)e(w)o(eak,)h(but) h(at)g(least)g(it)f(increases)g(with)g FF(d)h FQ(and)g(with)g FF(b)f FQ(as)h(it)60 152 y(should.)27 b(In)18 b(fact,)g(if)f FF(b)h FQ(is)g(large,)g(the)f(alternating)h(\014elds)g(are)g(v)o(ery)f(far)h (apart,)h(and)g(the)e(system)60 212 y(b)q(ecomes)f(almost)h (indistinguishable)f(from)g(a)i(zero-\014eld)f(Ising)g(mo)q(del.)23 b(Therefore)17 b(w)o(e)g(exp)q(ect,)60 272 y(but)24 b(can)f(not)h(pro)o(v)o (e,)g(that)g(this)f(limit)d(temp)q(erature)i(approac)o(hes)i(the)f(Ising-mo)q (del)g(critical)60 332 y(temp)q(erature)15 b(when)h FF(b)g FQ(tends)g(to)h(in\014nit)o(y)l(.)133 392 y(Inequalit)o(y)11 b(\(B.79\))i(determines)e(the)i(range)h(of)f(temp)q(eratures)f(for)i(whic)o (h)e(w)o(e)h(can)g(pro)o(v)o(e)g(that)60 452 y(the)j(decimation)e (transformation)j(has)f(pathologies)h(\(Sections)f(4.2)h(and)g(4.3.2\).)133 533 y(As)d(a)g(w)o(arm-up)g(for)g(the)g(follo)o(wing)f(sections,)h(let)f(us)i (sk)o(etc)o(h)d(ho)o(w)j(the)f(P)o(eierls)e(condition)i(can)60 593 y(b)q(e)21 b(v)o(eri\014ed)f(in)h(the)f(presen)o(t)h(example)e(using)i (the)g(Holszt)o(ynski-Sla)o(wn)o(y)e(criterion)h(\(Theorem)60 653 y(B.21\).)35 b(The)20 b(argumen)o(t)g(dep)q(ends)h(sligh)o(tly)f(on)h (the)g(decimation)e(spacing)i FF(b)p FQ(.)34 b(F)l(or)21 b FF(b)h FQ(=)f(2)g(the)60 714 y(in)o(ternal-spin)e(in)o(teraction)g(is)h (already)g(an)g FF(m)p FQ(-p)q(oten)o(tial)g(b)q(ecause)g(it)f(is)h(just)g(a) h(ferromagnetic)60 774 y(t)o(w)o(o-b)q(o)q(dy)k(in)o(teraction)e(in)g(a)i (\\diluted")e(lattice)g(\(Sections)g(4.2)i(and)f(4.3.1\).)44 b(F)l(or)24 b FF(b)j FE(\025)f FQ(3)f(a)60 834 y(p)q(erio)q(dic)17 b FF(m)p FQ(-p)q(oten)o(tial)g(is)f(obtained)i(b)o(y)e(grouping)i(all)f(the)g (b)q(onds)h(inside)e(cub)q(es)i(con)o(taining)f(at)60 894 y(least)j(one)g(p)q (erio)q(d)g(of)g(the)g(image-spin)f(con\014guration)i([Figure)e(14\(b\)].)32 b(Explicitly)l(,)18 b(if)h(\010)1784 876 y Fr(in)o(ternal)60 954 y FQ(is)f(the)g(in)o(teraction)g(for)g(the)g(in)o(ternal-spin)g(system,)f (the)h(equiv)m(alen)o(t)f(2)p FF(b)p FQ(-p)q(erio)q(dic)h FF(m)p FQ(-p)q(oten)o(tial)60 1015 y(\010)95 997 y Fs(m)p Ft(\000)p Fr(p)q(ot)210 1015 y FQ(has)f(\010)332 993 y Fs(m)p Ft(\000)p Fr(p)q(ot)332 1027 y FD(A)444 1015 y FQ(=)d(0)i(unless)g FF(A)g FQ(is)g(a)h(p)q(erio)q(dic)f(translate,)g(with)g(p)q(erio)q(d)h(2)p FF(b)p FQ(,)f(of)g(the)g(cub)q(e)655 1150 y FF(V)25 b FQ(=)759 1077 y Fx(")784 1150 y FE(\000)831 1077 y Fx($)862 1116 y FF(b)11 b FE(\000)g FQ(1)p 862 1138 107 2 v 903 1184 a(2)973 1077 y Fx(\045)1022 1150 y FF(;)1058 1077 y Fx($)1089 1116 y FQ(3)p FF(b)g FE(\000)g FQ(1)p 1089 1138 131 2 v 1142 1184 a(2)1224 1077 y Fx(\045#)1275 1088 y FD(d)1755 1150 y FQ(\(B)p FF(:)p FQ(80\))60 1275 y(\(here)16 b FE(b)8 b(c)17 b FQ(denotes)g(in)o(teger)f (part\),)g(or)h(of)g(the)f(in)o(ter-cub)q(e)g(b)q(onds)i(formed)d(b)o(y)h (nearest-neigh)o(b)q(or)60 1335 y(pairs)22 b FE(h)p FF(x;)8 b(y)r FE(i)21 b FQ(with,)h(sa)o(y)l(,)g FF(x)f FQ(in)g(the)g(\(in)o(ternal\)) f(b)q(oundary)j(of)e FF(V)12 b FQ(.)36 b(F)l(or)22 b(these)f(pairs)g(\010) 1731 1313 y Fs(m)p Ft(\000)p Fr(p)q(ot)1731 1350 y Fy(f)p FD(xy)q Fy(g)1852 1335 y FQ(=)60 1396 y(\010)95 1403 y Fy(f)p FD(xy)q Fy(g)185 1396 y FQ(=)14 b FE(\000)p FF(J)5 b FQ(,)15 b(and)i(for)f(the)g(cub) q(e)g FF(V)732 1496 y FQ(\010)767 1474 y Fs(m)p Ft(\000)p Fr(p)q(ot)767 1508 y FD(V)893 1496 y FQ(=)970 1454 y Fx(X)959 1546 y FD(A)p Fy(\032)p FD(V)1050 1496 y FQ(\010)1085 1475 y Fr(in)o(ternal)1085 1508 y FD(A)1204 1496 y FF(:)537 b FQ(\(B)p FF(:)p FQ(81\))60 1633 y(It)17 b(is)g(not)i(hard)f(to)g(v)o(erify)d(that)j(the)g (con\014gurations)h FF(!)p 1074 1640 33 2 v 1106 1615 a FH(\(+\))1180 1633 y FQ(and)f FF(!)p 1276 1640 V 1309 1615 a FH(\()p Fy(\000)p FH(\))1383 1633 y FQ(are)g(the)f(only)g(minimi)o(zers)60 1694 y(of)j(the)g(\010)242 1672 y Fs(m)p Ft(\000)p Fr(p)q(ot)242 1706 y FD(V)341 1694 y FQ(,)g(and)h(they)f(ob)o(viously)f(also)i(minim)o(iz)o (e)c(the)j(energy)g(of)g(the)g(in)o(ter-cub)q(e)f(b)q(onds.)60 1754 y(Therefore,)12 b(\010)326 1736 y Fs(m)p Ft(\000)p Fr(p)q(ot)437 1754 y FQ(is)g(an)h FF(m)p FQ(-p)q(oten)o(tial)f(with)g(a)h(\014nite)f(n)o (um)o(b)q(er)f(of)h(ground-state)i(con\014gurations.)60 1814 y(By)j(Theorem)f(B.21,)h(the)g(P)o(eierls)f(condition)h(is)g(satis\014ed.)25 b(No)17 b(estimation)f(of)h FF(\014)1593 1821 y FH(0)1630 1814 y FQ(follo)o(ws)g(from)60 1874 y(this)f(approac)o(h.)60 2002 y FM(B.5.4)55 b(In)n(ternal)18 b(Spins)h(under)g(the)f(Kadano\013)h(T)-5 b(ransformation.)23 b(Uniformit)n(y)60 2094 y FQ(F)l(or)14 b(this)h(case)f(w)o(e)g(ha)o(v)o(e)f(to)i(apply)f(the)g(uniformit)o(y)e (results)i(that)g(w)o(e)g(so)h(carefully)e(stated)i(ab)q(o)o(v)o(e.)60 2154 y(The)h(Hamiltonian)f(\(4.33\))i(can)f(b)q(e)g(decomp)q(osed)g(in)g(the) g(form)797 2249 y FF(H)837 2256 y FH(e\013)906 2249 y FQ(=)28 b FF(H)1012 2256 y FH(0)1043 2249 y FQ(+)1096 2233 y Fx(f)1092 2249 y FF(H)1132 2256 y FD(p)1755 2249 y FQ(\(B)p FF(:)p FQ(82\))60 2348 y(where)14 b FF(H)239 2355 y FH(0)274 2348 y FQ(is)g(the)g(usual)h (Ising)f(Hamiltonian)f(and)1021 2332 y Fx(f)1017 2348 y FF(H)1057 2355 y FD(p)1091 2348 y FQ(corresp)q(onds)j(to)f(the)f(in)o(teraction)1746 2332 y Fx(e)1740 2348 y FQ(\010\()p FF(p;)8 b(\014)s FQ(\))60 2408 y(de\014ned)16 b(b)o(y)125 2579 y(\()150 2563 y Fx(e)144 2579 y FQ(\010)179 2586 y FD(A)208 2579 y FQ(\()p FF(p;)8 b(\014)s FQ(\)\)\()p FF(\033)r FQ(\))27 b(=)502 2467 y Fx(8)502 2504 y(>)502 2517 y(>)502 2529 y(<)502 2604 y(>)502 2616 y(>)502 2629 y(:)560 2499 y FE(\000)p FQ(\()p FF(p=\014)s FQ(\))p FF(\033)746 2480 y Fy(0)744 2511 y FD(x)774 2499 y FF(\033)802 2506 y FD(i)1195 2499 y FQ(if)15 b FF(A)f FQ(=)g FE(f)p FF(i)p FE(g)h FQ(and)i FF(i)d FE(2)g FF(B)1634 2506 y FD(x)560 2579 y FQ(\(1)p FF(=\014)s FQ(\))8 b(log)i(2)e(cosh)882 2518 y Fx(\022)912 2579 y FF(p)944 2546 y Fx(P)989 2589 y FD(i)p Fy(2)p FD(B)1052 2593 y Fs(x)1081 2579 y FF(\033)1109 2586 y FD(i)1123 2518 y Fx(\023)1195 2579 y FQ(if)15 b FF(A)f FQ(=)g FF(B)1379 2586 y FD(x)560 2658 y FQ(0)611 b(otherwise)13 b FF(:)1755 2579 y FQ(\(B)p FF(:)p FQ(83\))938 2784 y(241)p eop %%Page: 242 242 bop 60 91 a FQ(\(W)l(e)18 b(recall)f(that)h(in)g(this)g(app)q(endix)g(w)o(e)f (are)i(\\unabsorbing")h FF(\014)g FQ(whic)o(h)d(in)h(\(4.33\))h(is)f(absorb)q (ed)60 152 y FP(only)f FQ(in)f FF(J)5 b FQ(.\))21 b(W)l(e)16 b(c)o(ho)q(ose)h FF(!)579 133 y Fy(0)577 164 y FH(sp)q(ecial)699 152 y FQ(as)g(some)e(alternating)h(con\014guration|with)h(as)g(man)o(y)e (pluses)60 212 y(as)k(min)o(uses|so)d(that,)j(b)o(y)e(symmetry)l(,)e(the)j (co)q(existence)f(of)h(the)g(\\+")h(and)f(\\)p FE(\000)p FQ(")h(in)o (ternal-spin)60 272 y(Gibbs)j(measures)f(do)q(es)i(not)f(require)e(an)o(y)i (additional)g(\014eld.)38 b(That)22 b(is,)h(as)f(b)q(efore)g(w)o(e)g(forget) 60 332 y(ab)q(out)c(symmet)o(ry-breaking)c(in)o(teractions.)133 392 y(The)k(in)o(teraction)f(\010)517 399 y FH(0)555 392 y FQ(satis\014es)h(the)g(original)g(P)o(eierls)e(condition)i(with)p 1487 366 26 2 v 18 w FF(\032)1512 404 y FH(0)1548 392 y FQ(=)f(2)p FF(J)23 b FQ(\(thin)18 b(con-)60 452 y(tours,)h FE(K)f FQ(=)g FE(f)p FF(!)370 434 y FH(\(+\))427 452 y FF(;)8 b(!)481 434 y FH(\()p Fy(\000)p FH(\))538 452 y FE(g)p FQ(\).)28 b(W)l(e)18 b(can)g(then)h(resort)f(to)h(Corollary)g(B.25)f(to)h(conclude)e(that)i(the)60 513 y(whole)e(in)o(teraction)f(\010)480 520 y FH(0)511 513 y FQ(+)567 496 y Fx(e)561 513 y FQ(\010\()p FF(p;)8 b(\014)s FQ(\))16 b(satis\014es)i(the)e(original)h(P)o(eierls)f(condition.)23 b(Ho)o(w)o(ev)o(er,)15 b(to)i(es-)60 573 y(timate)f(the)i(P)o(eierls)e (constan)o(t)i(w)o(e)g(m)o(ust)e(correct)p 1018 546 V 17 w FF(\032)1043 585 y FH(0)1081 573 y FQ(so)i(as)h(to)f(satisfy)g(\(C1\))g(and)h (\(C2\))f(for)g(the)60 633 y(total)13 b(in)o(teraction.)19 b(F)l(or)13 b(instance)g(\(see)g(remarks)e(at)j(the)e(end)h(of)g(Section)g (B.4.2\),)f(w)o(e)h(can)g(replace)60 693 y(it)j(b)o(y)791 775 y FF(\032)816 782 y FH(0)863 775 y FQ(=)987 742 y(2)p FF(\014)s(J)p 934 764 193 2 v 934 810 a FQ(\(2)p FF(a)11 b FQ(+)g(1\))1106 795 y FD(d)1146 775 y FF(;)60 884 y FQ(with)16 b FF(a)f FQ(equal)g(to)h(half) g(the)g(length)f(of)h(the)g(largest)g(side)f(of)h(the)g(blo)q(c)o(k.)k(W)l(e) c(then)g(conclude)f(that)60 945 y(for)i(eac)o(h)e FF(p)i FQ(there)f(exists)f (a)i(v)m(alue)f FF(\014)739 952 y FH(1)758 945 y FQ(\()p FF(p)p FQ(\))h(de\014ned)f(b)o(y)558 1037 y FF(p)p 547 1059 48 2 v 547 1105 a(\014)575 1112 y FH(1)610 1071 y FQ(+)676 1037 y(1)p 664 1059 V 664 1105 a FF(\014)692 1112 y FH(1)725 1071 y FQ(log)q(\(2)8 b(cosh)h FF(p)f FE(j)p FF(B)s FE(j)p FQ(\))28 b(=)1224 1037 y(2)p FF(cJ)p 1157 1059 211 2 v 1157 1105 a FQ(\(2)p FF(a)11 b FQ(+)g(1\))1329 1091 y FH(2)p FD(d)1386 1071 y FF(;)355 b FQ(\(B)p FF(:)p FQ(84\))60 1201 y(suc)o(h)14 b(that)h(for)g FF(\014)h FE(\025)e FF(\014)470 1208 y FH(1)489 1201 y FQ(\()p FF(p)p FQ(\))h(the)g(e\013ectiv)o(e)d(in)o(ternal-spin)i(in)o(teraction)g (for)h(the)f FF(p)p FQ(-Kadano\013)j(trans-)60 1261 y(formation)f (satis\014es)g(the)g(P)o(eierls)f(condition)h(with)g(constan)o(t)785 1378 y FF(\032)28 b FQ(=)908 1345 y(2)p FF(J)5 b FQ(\(1)12 b FE(\000)e FQ(2)p FF(c)p FQ(\))p 908 1367 225 2 v 924 1412 a(\(2)p FF(a)h FQ(+)g(1\))1096 1398 y FD(d)1152 1378 y FF(:)589 b FQ(\(B)p FF(:)p FQ(85\))60 1508 y(In)17 b(the)g(last)g(t)o(w)o(o)g(form)o (ulas,)f(the)h(constan)o(t)h FF(c)f FQ(is)g(arbitrary)g(as)h(long)f(as)h(0)e FF(<)f(c)h(<)f FQ(1)p FF(=)p FQ(2.)25 b(W)l(e)17 b(shall)60 1569 y(\014nd)g(an)f(optimal)f(c)o(hoice)g(b)q(elo)o(w.)133 1629 y(A)o(t)20 b(this)h(p)q(oin)o(t)g(w)o(e)f(can)h(apply)l(,)g(for)g (instance,)h(Corollary)f(B.29)f(to)h(obtain)h(that)f FP(for)g(e)n(ach)60 1689 y(\014nite)e FF(p)g FP(ther)n(e)f(exists)h(a)f(value)h FF(\014)682 1696 y FH(0)702 1689 y FQ(\()p FF(p)p FQ(\))f FP(such)h(that)f (for)f FF(\014)h FE(\025)c FF(\014)1199 1696 y FH(0)1219 1689 y FQ(\()p FF(p)p FQ(\))k FP(the)h(system)f(of)g(internal)h(spins)60 1749 y(c)n(orr)n(esp)n(onding)g(to)i(a)f FF(p)p FP(-Kadano\013)h(tr)n (ansformation)e(has)h(a)g(nontrivial)h(phase)f(diagr)n(am)g(with)g(a)60 1809 y(\014rst-or)n(der)g(phase)h(tr)n(ansition)g(b)n(etwe)n(en)h(a)f(\\)p FQ(+)p FP(")f(and)h(a)g(\\)p FE(\000)p FP(")f(Gibbs)h(me)n(asur)n(e)t FQ(.)31 b(The)20 b(form)o(ulas)60 1870 y(\(B.66\))c(and)h(\(B.68\))f(imply)e (the)i(estimate)364 2003 y FF(\014)392 2010 y FH(0)425 2003 y FE(\025)e FQ(max)577 1930 y Fx(\()610 2003 y FF(\014)638 2010 y FH(1)657 2003 y FQ(\()p FF(p)p FQ(\))j FF(;)25 b FQ([4)8 b(log)q(\(2)p FF(d)k FE(\000)f FQ(1\))g(+)g(\(2)p FF(e)p FQ(\))1202 1982 y Fy(\000)p FH(1)1249 2003 y FQ(])1294 1969 y(\(2)p FF(a)g FQ(+)g(1\))1466 1951 y FD(d)p 1268 1991 245 2 v 1268 2037 a FQ(2)p FF(J)5 b FQ(\(1)11 b FE(\000)g FQ(2)p FF(c)p FQ(\))1492 2023 y FH(2)1517 1930 y Fx(\))1573 2003 y FF(:)168 b FQ(\(B)p FF(:)p FQ(86\))60 2136 y(F)l(rom)14 b(the)i(p)q(oin)o(t)f(of)h(view)f(of)h (this)g(b)q(ound,)g(the)f(optimal)g(c)o(hoice)f(of)i FF(c)g FQ(is)f(when)h FF(\014)1578 2143 y FH(1)1597 2136 y FQ(\()p FF(p)p FQ(\))g(equals)f(the)60 2196 y(comp)q(eting)g(term)g(in)h(the)g(RHS)f (of)i(\(B.86\).)k(This)16 b(pro)q(duces)h(the)f(rather)g(ugly-lo)q(oking)h(b) q(ound)360 2335 y FF(\014)388 2342 y FH(0)435 2335 y FE(\025)507 2301 y FQ(\(2)p FF(a)11 b FQ(+)g(1\))679 2283 y FH(2)p FD(d)p 507 2323 211 2 v 584 2369 a FQ(2)p FF(J)1062 2295 y FQ(16)p FF(L)1143 2276 y FH(2)1143 2308 y FD(p;)p Fy(j)p FD(B)r Fy(j)p 735 2323 814 2 v 735 2379 a FF(M)782 2386 y FD(d)803 2379 y FQ([4)p FF(L)874 2387 y FD(p;)p Fy(j)p FD(B)r Fy(j)962 2379 y FQ(+)g FF(M)1058 2386 y FD(d)1090 2379 y FE(\000)1140 2331 y Fx(q)p 1181 2331 368 2 v 1181 2379 a FF(M)1228 2386 y FD(d)1249 2379 y FQ(\()p FF(M)1315 2386 y FD(d)1346 2379 y FQ(+)g(8)p FF(L)1452 2387 y FD(p;)p Fy(j)p FD(B)r Fy(j)1530 2379 y FQ(\))1568 2335 y FF(;)173 b FQ(\(B)p FF(:)p FQ(87\))60 2485 y(with)672 2587 y FF(M)719 2594 y FD(d)781 2587 y FQ(=)41 b(4)8 b(log)r(\(2)p FF(d)k FE(\000)f FQ(1\))g(+)g(\(2)p FF(e)p FQ(\))1274 2567 y Fy(\000)p FH(1)629 2660 y FF(L)662 2668 y FD(p;)p Fy(j)p FD(B)r Fy(j)781 2660 y FQ(=)41 b FF(p)12 b FQ(+)f(log)e(2)f(cosh)i FF(p)e FE(j)p FF(B)s FE(j)14 b FF(:)938 2784 y FQ(242)p eop %%Page: 243 243 bop 133 91 a FQ(F)l(orm)o(ula)18 b(\(B.87\))g(giv)o(es)h(a)g(lo)o(w)o(er)f(b) q(ound)i(for)g(the)e(temp)q(erature)g(up)h(to)h(whic)o(h)e(a)h(Kadano\013)60 152 y FF(p)p FQ(-transformation)k(exhibits)d(pathologies)j(\(Section)f (4.3.3\).)38 b(This)22 b(b)q(ound)h(go)q(es)g(to)f(zero)g(if)g FF(p)60 212 y FQ(tends)16 b(to)h(in\014nit)o(y)l(,)d(hence)i(it)g(is)g (useless)g(for)g(ma)s(jorit)o(y-rule)e(transformations.)60 342 y FM(B.5.5)55 b(In)n(ternal)18 b(Spins)h(under)g(Ma)s(jorit)n(y)f(Rule)60 434 y FQ(F)l(or)i(this)g(case,)g(w)o(e)f(use)h(the)f(Holszt)o(ynski-Sla)o(wn) o(y)f(criterion)h(\(Theorem)f(B.21\).)32 b(The)19 b(system)60 494 y(of)g(in)o(ternal)f(spins)h(sub)s(jected)f(to)h(the)g(constrain)o(t)g (of)g(a)g(doubly-alternating)g(7)13 b FE(\002)g FQ(7)19 b(blo)q(c)o(k-spin)60 554 y(con\014guration)12 b(can)g(b)q(e)f(written)g(as)h(a)f(p)q(erio)q(dic)g FF(m)p FQ(-p)q(oten)o(tial)g(with)g(p)q(erio)q(d)h(28.)20 b(The)11 b(fundamen)o(tal)60 615 y(b)q(onds)18 b(of)e(this)h(p)q(oten)o(tial)f(are)g (the)g(squares)h(of)f(size)g(28)c FE(\002)f FQ(28)17 b(depicted)e(in)h (Figure)g(8\(a\),)h(and)g(all)60 675 y(the)23 b(b)q(onds)i(connecting)e (neigh)o(b)q(oring)h(squares.)43 b(It)23 b(is)g(straigh)o(tforw)o(ard)h(to)g (c)o(hec)o(k)d(that)j(the)60 735 y(con\014gurations)h(of)e(Figure)g(8\(b\))h (are)f(the)g(only)g(ones)h(satisfying)f(all)g(the)g(b)q(onds)h(of)g(this)f FF(m)p FQ(-)60 795 y(p)q(oten)o(tial.)36 b(Hence,)20 b(the)h(system)f(has)i (a)g(\014nite)e(n)o(um)o(b)q(er)g(\(t)o(w)o(o\))h(of)g(ground)i(states)e (whic)o(h,)h(b)o(y)60 855 y(Theorem)16 b(B.21)i(and)g(PS)g(theory)l(,)f(giv)o (e)g(rise)g(to)h(di\013eren)o(t)f(and)h(co)q(existing)f(Gibbs)h(measures)f (at)60 915 y(lo)o(w-enough)h(temp)q(erature.)23 b(By)17 b(symmetry)d (considerations)k(this)f(co)q(existence)f(tak)o(es)h(place)g(at)60 976 y(zero)i(v)m(alues)g(of)h(the)f(symmetry)o(-breaking)e(\014eld.)29 b(An)19 b(analogous)i(argumen)o(t)e(can)g(b)q(e)g(used)h(for)60 1036 y(all)c(the)g(other)g(blo)q(c)o(k-sizes)f FF(b)600 1043 y FD(k)638 1036 y FQ(giv)o(en)g(in)h(\(4.35\).)60 1166 y FM(B.5.6)55 b(In)n(ternal)18 b(Spins)h(under)g(Blo)r(c)n(k-Av)n(eraging)e(T)-5 b(ransformations)60 1258 y FQ(Again,)18 b(w)o(e)f(resort)h(to)g(the)g(Holszt) o(ynski-Sla)o(wn)o(y)e(criterion)g(\(Theorem)h(B.21\).)26 b(The)17 b(system)g(of)60 1318 y(in)o(ternal)d(spins)i(sub)s(jected)f(to)h(the)f (constrain)o(t)g(of)h(zero)f(a)o(v)o(erage)g(spin)h(in)f(ev)o(ery)f(2)c FE(\002)f FQ(2)16 b(blo)q(c)o(k)f(can)60 1379 y(again)g(b)q(e)f(written)f(as) i(an)f(m-p)q(oten)o(tial)e(whic)o(h)h(is)h(p)q(erio)q(dic)g(\(with)f(p)q (erio)q(d)i(2\).)21 b(The)13 b(fundamen)o(tal)60 1439 y(b)q(onds)i(are)g(the) e(2)7 b FE(\002)g FQ(2)15 b(squares)f(and)h(the)f(b)q(onds)h(connecting)f (them,)e(and)j(the)f(only)g(four)g(p)q(erio)q(dic)60 1499 y(ground)h(states)g (satisfying)g(ev)o(ery)e(b)q(ond)i(are)g(easily)e(seen)h(to)h(b)q(e)g(the)f (ones)h(depicted)e(in)h(Figure)g(9.)60 1559 y(Th)o(us)g(at)g(su\016cien)o (tly)d(lo)o(w)i(temp)q(erature)f(PS-theory)i(pro)o(vides)f(the)g(phase)h (transition)g(needed)e(in)60 1619 y(Step)j(1.)21 b(Again)16 b(symme)o(try)c(allo)o(ws)k(us)f(to)h(disp)q(ose)g(of)f(an)o(y)g (symmetry-breaki)o(ng)e(\014eld)i(to)g(follo)o(w)60 1679 y(the)h(co)q (existence)f(p)q(oin)o(t.)60 1809 y FM(B.5.7)55 b(In)n(ternal)18 b(Spins)h(when)g FF(h)14 b FE(6)p FQ(=)g(0)p FM(.)25 b(Random)17 b(Field)60 1902 y FQ(The)h(result)g(needed)g(to)h(pro)o(v)o(e)f(the)g (presence)g(of)g(pathologies)i(for)e(non-zero)h(\014eld)f(in)h(the)f(deci-)60 1962 y(mation)f(and)i(Kadano\013)g(examples)d(of)j(Section)e(4.3,)i(is)e(a)i (direct)e(consequence)g(of)h(Zahradn)-5 b(\023)-19 b(\020k's)60 2022 y(Theorem)14 b(B.31.)21 b(W)l(e)14 b(apply)h(this)g(theorem)f(with)h (\010)1040 2029 y FH(0)1075 2022 y FQ(equal)g(to)g(the)g(in)o(teraction)f (for)i(the)e(system)60 2082 y(of)f(in)o(ternal)g(spins)g(with)g(fully)f (alternating)h(image)f(spins,)i(and)g(the)f(symmetr)o(y-breaking)e(p)q (ertur-)60 2142 y(bation)k(\010)245 2149 y FH(1)279 2142 y FQ(tak)o(en)e(to)i(b)q(e)f(a)h(uniform)d(magnetic)h(\014eld.)20 b(The)14 b(random)g(in)o(teraction)f(is)h(the)f(random)60 2203 y(magnetic)k(\014eld)h(induced)g(b)o(y)g(those)h(blo)q(c)o(k)f(spins)g(that)h (w)o(ere)f(\015ipp)q(ed)h(from)e(\\+")i(to)g(\\)p FE(\000)p FQ(")g(with)60 2263 y(probabilit)o(y)c FF(\017=)p FQ(\(2)p FF(J)5 b FQ(\),)15 b(as)i(discussed)f(in)f(Section)g(4.3.6.)22 b(By)15 b(Theorem)g(B.31,)g(the)h(resulting)f(lo)o(w-)60 2323 y(temp)q(erature)c(and)i(lo)o(w-)p FF(\017)f FQ(phase)h(diagram)e(is)i(only)f (a)g(small)f(p)q(erturbation)i(of)g(the)f(phase)h(diagram)60 2383 y(for)19 b(the)f(non-random)h(part,)h(whic)o(h)e(is)g(itself)g(a)h (small)e(p)q(erturbation)i(of)g(its)g(zero-temp)q(erature)60 2443 y(phase)c(diagram.)20 b(In)14 b(particular,)g(the)h(ground-state)h (energy)e(for)h(almost)e(all)h(realizations)g(of)h(the)60 2504 y(Hamiltonian)g(is)i(an)g(almost)g(linear)f(function)h(of)g(the)g(parameters) f FF(h)h FQ(and)g FF(\017)p FQ(.)23 b(F)l(or)17 b FF(\017)g FQ(su\016cien)o(tly)60 2564 y(small,)e(the)i(linearit)o(y)f(is)h(only)g(w)o (eakly)f(violated,)g(and)i(the)f(comp)q(ensating)g(uniform)f(\014eld)h (\(that)938 2784 y(243)p eop %%Page: 244 244 bop 60 91 a FQ(is,)14 b(the)g(v)m(alue)g(of)h FF(h)f FQ(as)h(a)g(function)f (of)g FF(\017)g FQ(needed)g(to)h(k)o(eep)e(the)h(system)f(on)h(a)h(co)q (existence)e(surface\))60 152 y(is)j(an)h(almost)e(linear)h(|)g(hence)f (strictly)g(increasing)h(|)g(function.)60 314 y FG(C)82 b(Solution)27 b(of)h(the)g(Diophan)n(tine)e(Equation)i(\(4.34\))60 424 y FQ(Consider)23 b(the)g(pair)g(of)g(Diophan)o(tine)g(equations)g FF(b)1060 406 y FH(2)1105 424 y FQ(=)i(2)p FF(c)1213 406 y FH(2)1249 424 y FE(\006)15 b FQ(1)24 b(\()p FF(b;)8 b(c)22 b FQ(in)o(tegers)g FE(\025)j FQ(1\).)42 b(The)60 484 y(follo)o(wing)18 b(in)o(tuition)f(w)o(as)i(suggested)g(to)g(us)g(b)o(y)f(Vincen)o(t)e(Riv)m (asseau:)26 b(If)18 b(\()p FF(b;)8 b(c)p FQ(\))18 b(satis\014es)h(either)60 544 y(of)c(these)g(equations,)g(then)f FF(b=c)i FQ(m)o(ust)d(b)q(e)i(an)h (excellen)o(t)c(rational)j(appro)o(ximation)f(to)1672 503 y FE(p)p 1714 503 25 2 v 41 x FQ(2,)h(in)f(the)60 605 y(sense)i(that)568 632 y Fx(\014)568 657 y(\014)568 682 y(\014)p FF(b=c)k FE(\000)726 638 y(p)p 767 638 V 767 682 a FQ(2)792 632 y Fx(\014)792 657 y(\014)792 682 y(\014)27 b FQ(=)904 648 y FE(j)o FF(b)938 630 y FH(2)958 648 y FF(=c)1003 630 y FH(2)1042 648 y FE(\000)20 b FQ(2)p FE(j)p 904 670 236 2 v 917 720 a FF(b=c)f FQ(+)1060 679 y FE(p)p 1101 679 25 2 v 1101 720 a FQ(2)1171 682 y FE(\024)1288 648 y FQ(1)p 1243 670 115 2 v 1243 679 a FE(p)p 1284 679 25 2 v 1284 720 a FQ(2)9 b FF(c)1338 706 y FH(2)1377 682 y FF(:)388 b FQ(\(C)p FF(:)p FQ(1\))60 799 y(\(Note)15 b(that,)g(b)o(y)g(con)o(trast,)h (for)f(\\t)o(ypical")g(in)o(teger)g(denominators)f FF(c)p FQ(,)i(one)f(has)i (inf)1552 829 y FD(b)p Fy(2)p Fl(Z)1620 799 y FE(j)p FF(b=c)10 b FE(\000)1758 758 y(p)p 1799 758 V 1799 799 a FQ(2)q FE(j)j(\030)60 884 y FQ(1)p FF(=c)j FE(\035)g FQ(1)p FF(=c)280 866 y FH(2)300 884 y FQ(.\))25 b(No)o(w,)17 b(the)g(b)q(est)g(rational)h(appro)o(ximations)f (to)1263 843 y FE(p)p 1305 843 V 41 x FQ(2)g(can)h(b)q(e)f(obtained)h(from)e (the)60 944 y(con)o(tin)o(ued)f(fraction)h([234)q(,)g(317)q(])668 1009 y FE(p)p 710 1009 V 44 x FQ(2)11 b FE(\000)g FQ(1)28 b(=)1071 1019 y(1)p 918 1041 332 2 v 918 1125 a(2)11 b(+)1114 1088 y(1)p 1007 1113 238 2 v 1007 1196 a(2)h(+)1156 1160 y(1)p 1097 1185 143 2 v 1097 1231 a(2)f(+)g FE(\001)d(\001)g(\001)1268 1053 y FF(:)497 b FQ(\(C)p FF(:)p FQ(2\))60 1299 y(This)16 b(suggests)i(to)e (consider)g(the)g(recursion)794 1405 y FF(x)822 1412 y FD(n)p FH(+1)918 1405 y FQ(=)1044 1371 y(1)p 988 1394 136 2 v 988 1439 a(2)c(+)f FF(x)1101 1446 y FD(n)1143 1405 y FF(;)622 b FQ(\(C)p FF(:)p FQ(3\))60 1522 y(whic)o(h)24 b(con)o(v)o(erges)f(to)502 1481 y FE(p)p 543 1481 25 2 v 543 1522 a FQ(2)17 b FE(\000)g FQ(1)24 b(as)h FF(n)j FE(!)g(1)c FQ(\(for)g(an)o(y)h FF(x)1195 1529 y FH(0)1242 1522 y FF(>)i FE(\000)p FQ(2\);)h(equiv)m(alen)o(tly)l(,)c (de\014ning)60 1582 y FF(y)84 1589 y FD(n)121 1582 y FQ(=)14 b FF(x)201 1589 y FD(n)235 1582 y FQ(+)d(1,)16 b(w)o(e)g(\014nd)h(the)f (recursion)798 1688 y FF(y)822 1695 y FD(n)p FH(+1)918 1688 y FQ(=)988 1654 y(2)c(+)f FF(y)1097 1661 y FD(n)p 988 1677 132 2 v 988 1722 a FQ(1)h(+)f FF(y)1097 1729 y FD(n)1139 1688 y FF(;)626 b FQ(\(C)p FF(:)p FQ(4\))60 1807 y(whic)o(h)15 b(con)o(v)o(erges)g (to)476 1766 y FE(p)p 518 1766 25 2 v 41 x FQ(2)h(\(for)g(an)o(y)g FF(y)767 1814 y FH(0)800 1807 y FF(>)e FE(\000)p FQ(1\).)21 b(In)15 b(particular,)g(setting)h FF(y)1451 1814 y FD(n)1488 1807 y FQ(=)e FF(b)1561 1814 y FD(n)1584 1807 y FF(=c)1629 1814 y FD(n)1669 1807 y FQ(with)h FF(b)1800 1814 y FD(n)1824 1807 y FF(;)8 b(c)1867 1814 y FD(n)60 1868 y FQ(p)q(ositiv)o(e)15 b(in)o(tegers,)g(w)o(e)h(\014nd)h(the)f(linear)f(recursion)783 1954 y FF(b)804 1961 y FD(n)p FH(+1)914 1954 y FQ(=)42 b FF(b)1015 1961 y FD(n)1049 1954 y FQ(+)11 b(2)p FF(c)1143 1961 y FD(n)1755 1954 y FQ(\(C.5a\))783 2027 y FF(c)804 2034 y FD(n)p FH(+1)914 2027 y FQ(=)42 b FF(b)1015 2034 y FD(n)1049 2027 y FQ(+)11 b FF(c)1119 2034 y FD(n)1752 2027 y FQ(\(C.5b\))60 2113 y(No)o(w)16 b(this)g(recursion)g(has)h(the)f(remark)m(able)f(prop)q(ert)o(y)h(that)657 2199 y FF(b)678 2179 y FH(2)678 2212 y FD(n)p FH(+1)758 2199 y FE(\000)10 b FQ(2)p FF(c)852 2179 y FH(2)852 2212 y FD(n)p FH(+1)949 2199 y FQ(=)28 b FE(\000)p FQ(\()p FF(b)1094 2179 y FH(2)1094 2212 y FD(n)1128 2199 y FE(\000)11 b FQ(2)p FF(c)1223 2179 y FH(2)1223 2212 y FD(n)1246 2199 y FQ(\))j(;)486 b(\(C)p FF(:)p FQ(6\))60 2286 y(in)22 b(particular,)g(if)g FF(b)440 2268 y FH(2)440 2298 y FD(n)487 2286 y FQ(=)h(2)p FF(c)593 2268 y FH(2)593 2298 y FD(n)632 2286 y FE(\006)15 b FQ(1,)24 b(then)d FF(b)885 2268 y FH(2)885 2298 y FD(n)p FH(+1)977 2286 y FQ(=)j(2)p FF(c)1084 2268 y FH(2)1084 2298 y FD(n)p FH(+1)1168 2286 y FE(\007)15 b FQ(1.)39 b(Therefore,)22 b(if)g(w)o(e)g(start)g(from)60 2346 y(\()p FF(b)100 2353 y FH(0)119 2346 y FF(;)8 b(c)162 2353 y FH(0)182 2346 y FQ(\))14 b(=)g(\(1)p FF(;)8 b FQ(1\),)13 b(w)o(e)g(generate)g(pairs)g(\()p FF(b)819 2353 y FD(n)842 2346 y FF(;)8 b(c)885 2353 y FD(n)908 2346 y FQ(\))13 b(whic)o(h)f(satisfy)h FF(b)1246 2328 y FH(2)1246 2358 y FD(n)1284 2346 y FQ(=)g(2)p FF(c)1380 2328 y FH(2)1380 2358 y FD(n)1408 2346 y FE(\000)t FQ(1)h(\(resp.)e FF(b)1642 2328 y FH(2)1642 2358 y FD(n)1679 2346 y FQ(=)i(2)p FF(c)1776 2328 y FH(2)1776 2358 y FD(n)1804 2346 y FQ(+)t(1\))60 2406 y(for)j(ev)o(en)e(\(resp.)g(o)q(dd\))j(v)m(alues)e (of)g FF(n)p FQ(.)22 b(The)16 b(explicit)e(form)o(ula)h(is)531 2515 y FF(b)552 2522 y FD(n)617 2515 y FQ(=)701 2481 y(1)p 701 2503 V 701 2549 a(2)739 2467 y Fx(h)758 2515 y FQ(\(1)d(+)862 2471 y FE(p)p 903 2471 V 903 2515 a FQ(2)q(\))947 2494 y FD(n)p FH(+1)1026 2515 y FQ(+)f(\(1)h FE(\000)1180 2471 y(p)p 1221 2471 V 1221 2515 a FQ(2\))1264 2494 y FD(n)p FH(+1)1333 2467 y Fx(i)1755 2515 y FQ(\(C.7a\))531 2631 y FF(c)552 2638 y FD(n)617 2631 y FQ(=)734 2598 y(1)p 701 2620 91 2 v 701 2670 a(2)725 2629 y FE(p)p 767 2629 25 2 v 41 x FQ(2)805 2583 y Fx(h)824 2631 y FQ(\(1)g(+)928 2588 y FE(p)p 969 2588 V 969 2631 a FQ(2)q(\))1013 2611 y FD(n)p FH(+1)1092 2631 y FE(\000)f FQ(\(1)g FE(\000)1246 2588 y(p)p 1288 2588 V 43 x FQ(2\))1331 2611 y FD(n)p FH(+1)1400 2583 y Fx(i)1752 2631 y FQ(\(C.7b\))938 2784 y(244)p eop %%Page: 245 245 bop 60 91 a FQ(T)l(o)20 b(pro)o(v)o(e)e(that)h(this)g(sequence)f(constitutes) h(the)g FP(c)n(omplete)24 b FQ(set)19 b(of)g(in)o(teger)f(solutions)i(to)f FF(b)1814 73 y FH(2)1852 91 y FQ(=)60 152 y(2)p FF(c)105 133 y FH(2)136 152 y FE(\006)11 b FQ(1,)16 b(w)o(e)g(run)g(the)g(iteration)g (\(C.5\))h(bac)o(kw)o(ards:)k(giv)o(en)15 b(\()p FF(b;)8 b(c)p FQ(\),)16 b(w)o(e)f(de\014ne)816 257 y FF(b)837 237 y Fy(0)890 257 y FQ(=)41 b FE(\000)p FF(b)11 b FQ(+)g(2)p FF(c)621 b FQ(\(C.8a\))816 330 y FF(c)837 309 y Fy(0)890 330 y FQ(=)41 b FF(b)11 b FE(\000)g FF(c)680 b FQ(\(C.8b\))60 436 y(and)15 b(sho)o(w)g(that)g(rep)q(eated)g (application)f(of)h(this)f(map)g(m)o(ust)f(ev)o(en)o(tually)f(lead)i(to)h (the)f(pair)h(\(1)p FF(;)8 b FQ(1\).)60 545 y FM(Lemma)16 b(C.1)24 b FP(L)n(et)19 b FF(b;)8 b(c)17 b FE(\025)g FQ(1)j FP(b)n(e)f(inte)n(gers)i (satisfying)e FF(b)1118 527 y FH(2)1155 545 y FQ(=)e(2)p FF(c)1255 527 y FH(2)1288 545 y FE(\006)12 b FQ(1)p FP(.)28 b(Then)20 b FF(b)1556 527 y Fy(0)1568 545 y FF(;)8 b(c)1611 527 y Fy(0)1642 545 y FP(ar)n(e)18 b(inte)n(gers)60 605 y(satisfying)g FQ(0)c FF(<)g(b)388 587 y Fy(0)413 605 y FE(\024)f FF(b)p FP(,)18 b FQ(0)c FE(\024)f FF(c)630 587 y Fy(0)656 605 y FF(<)h(c)j FP(and)h FF(b)862 587 y Fy(0)873 582 y FH(2)907 605 y FQ(=)13 b(2)p FF(c)1003 587 y Fy(0)1015 582 y FH(2)1046 605 y FE(\007)e FQ(1)p FP(.)60 762 y Fd(Pr)o(oof.)48 b FQ(\(a\))17 b FF(c)f FE(\025)g FQ(1)i(implies)d FF(b)682 744 y FH(2)717 762 y FQ(=)h(2)p FF(c)816 744 y FH(2)848 762 y FE(\006)c FQ(1)k FE(\025)g FQ(2)p FF(c)1039 744 y FH(2)1071 762 y FE(\000)c FQ(1)k FE(\025)g FQ(2)p FF(c)1262 744 y FH(2)1294 762 y FE(\000)c FF(c)1366 744 y FH(2)1401 762 y FQ(=)k FF(c)1476 744 y FH(2)1496 762 y FQ(.)25 b(Hence)16 b FF(b)g FE(\025)g FF(c)h FQ(and)60 822 y FF(c)81 804 y Fy(0)106 822 y FE(\025)d FQ(0.)22 b(Also)16 b FF(b)10 b FE(\000)h FF(b)431 804 y Fy(0)457 822 y FQ(=)i(2\()p FF(b)e FE(\000)g FF(c)p FQ(\))j FE(\025)g FQ(0,)i(so)h FF(b)875 804 y Fy(0)900 822 y FE(\024)d FF(b)p FQ(.)133 882 y(\(b\))j FF(c)d FE(\025)g FQ(1)j(implies)d FF(b)531 864 y FH(2)564 882 y FQ(=)h(2)p FF(c)662 864 y FH(2)693 882 y FE(\006)c FQ(1)k FE(\024)f FQ(2)p FF(c)880 864 y FH(2)911 882 y FQ(+)d(1)k FE(\024)f FQ(2)p FF(c)1097 864 y FH(2)1128 882 y FQ(+)d FF(c)1198 864 y FH(2)1232 882 y FQ(=)j(3)p FF(c)1329 864 y FH(2)1364 882 y FF(<)g FQ(4)p FF(c)1461 864 y FH(2)1481 882 y FQ(.)22 b(Hence)15 b FF(b)f(<)h FQ(2)p FF(c)h FQ(and)60 943 y FF(b)81 925 y Fy(0)106 943 y FF(>)e FQ(0.)22 b(Also)16 b FF(c)11 b FE(\000)f FF(c)430 925 y Fy(0)456 943 y FQ(=)k(2)p FF(c)d FE(\000)g FF(b)j(>)f FQ(0,)k(so)f FF(c)835 925 y Fy(0)861 943 y FF(<)e(c)p FQ(.)133 1003 y(\(c\))i FF(b)230 985 y Fy(0)241 979 y FH(2)272 1003 y FE(\000)11 b FQ(2)p FF(c)367 985 y Fy(0)379 979 y FH(2)413 1003 y FQ(=)i(\(2)p FF(c)f FE(\000)f FF(b)p FQ(\))630 985 y FH(2)660 1003 y FE(\000)g FQ(2\()p FF(b)g FE(\000)g FF(c)p FQ(\))875 985 y FH(2)908 1003 y FQ(=)j FE(\000)p FQ(\()p FF(b)1039 985 y FH(2)1069 1003 y FE(\000)d FQ(2)p FF(c)1164 985 y FH(2)1184 1003 y FQ(\))j(=)g FE(\007)p FQ(1.)p 1485 1007 25 34 v 133 1110 a(Since)f FF(c)h FQ(strictly)f(decreases)g(at)i(eac)o(h)e(iteration)h (of)g(\(C.8\),)g(w)o(e)g(m)o(ust)e(ev)o(en)o(tually)g(reac)o(h)h FF(c)h FQ(=)g(1,)60 1171 y(hence)h FF(b)e FQ(=)h(1.)21 b(Since)15 b(\(C.8\))h(is)f(the)g(in)o(v)o(erse)f(of)i(\(C.5\),)f(the)g(original)g(pair) h(\()p FF(b;)8 b(c)p FQ(\))15 b(m)o(ust)f(b)q(e)i(\()p FF(b)1782 1178 y FD(n)1805 1171 y FF(;)8 b(c)1848 1178 y FD(n)1871 1171 y FQ(\))60 1231 y(for)17 b(some)e FF(n)p FQ(.)21 b(W)l(e)16 b(ha)o(v)o(e)g(therefore)f(pro)o(v)o(en:)60 1329 y FM(Theorem)i(C.2)24 b FP(A)g(p)n(air)f(of)g(inte)n(gers)i FF(b;)8 b(c)25 b FE(\025)g FQ(1)f FP(satis\014es)h(the)f(Diophantine)g(e)n(quation)h FF(b)1807 1311 y FH(2)1852 1329 y FQ(=)60 1389 y(2)p FF(c)105 1371 y FH(2)138 1389 y FE(\000)13 b FQ(1)20 b FP(\(r)n(esp.)g FF(b)396 1371 y FH(2)434 1389 y FQ(=)e(2)p FF(c)535 1371 y FH(2)569 1389 y FQ(+)13 b(1)p FP(\))20 b(if)g(and)g(only)h(if)f FQ(\()p FF(b;)8 b(c)p FQ(\))18 b(=)h(\()p FF(b)1207 1396 y FD(n)1230 1389 y FF(;)8 b(c)1273 1396 y FD(n)1296 1389 y FQ(\))20 b FP(for)g(some)g (even)i(\(r)n(esp.)d(o)n(dd\))60 1449 y(inte)n(ger)f FF(n)c FE(\025)g FQ(0)p FP(.)60 1547 y FQ(In)f(particular,)h(the)f(blo)q(c)o(k)g (sizes)g FF(b)h FQ(for)g(whic)o(h)f(the)g(ma)s(jorit)o(y-rule)e(construction) j(in)g(Section)f(4.3.4)60 1608 y(w)o(orks)j(are)h FF(b)301 1615 y FH(2)320 1608 y FF(;)8 b(b)363 1615 y FH(4)383 1608 y FF(;)g(b)426 1615 y FH(6)445 1608 y FF(;)g(:)g(:)g(:)13 b FQ(=)h(7)p FF(;)8 b FQ(41)p FF(;)g FQ(239)p FF(;)g FQ(1393)p FF(;)g FQ(81)q(19)p FF(;)g(:)g(:)g(:)14 b FQ(.)133 1715 y FM(Remarks.)44 b FQ(1.)i(After)23 b(completing)f(this)j(pro)q(of,)i(w)o(e)d(learned)f(that)i (it)f(w)o(as)h(previously)60 1775 y(published)20 b(b)o(y)f(Theon)i(of)f(Sm)o (yrna)f([344)q(])g(circa)h(130)h(A.D.,)f(and)g(probably)h(go)q(es)g(bac)o(k)f (to)g(the)60 1836 y(Pythagorean)h(sc)o(ho)q(ol)f([301)q(];)h(the)e(iden)o (tit)o(y)f(\(C.6\))i(is)f(pro)o(v)o(en)g(geometrically)e(in)j(Euclid's)f FP(Ele-)60 1896 y(ments)h FQ(\(Bo)q(ok)15 b(I)q(I,)g(Prop)q(osition)h(10\).) 22 b(The)15 b(sp)q(ecial)f(case)h FF(b)f FQ(=)g(7,)h FF(c)f FQ(=)g(5)h(is)g(men)o(tioned)e(in)i(Plato's)60 1956 y FP(R)n(epublic)h FQ(\(546)e(C\),)e(though)h(without)g(the)f(renormalization-group)g (application.)20 b(F)l(or)13 b(a)g(history)l(,)60 2016 y(see)j(Heath)g([191)q (],)f(Dic)o(kson)h([76,)g(Chapter)h(XI)q(I],)d(T)l(annery)i([343)q(])g(and)h (Mugler)e([270)q(].)133 2076 y(2.)33 b(One)20 b(migh)o(t)e(w)o(onder)j(ab)q (out)g(the)f(rational)g(appro)o(ximan)o(ts)f(to)1417 2035 y FE(p)p 1458 2035 25 2 v 1458 2076 a FQ(2)i(obtained)f(b)o(y)g(using)60 2137 y(Newton's)c(metho)q(d)f FF(y)h FE(7!)558 2117 y FH(1)p 558 2125 18 2 v 558 2154 a(2)581 2137 y FQ(\()p FF(y)c FQ(+)f(2)p FF(=y)r FQ(\).)22 b(Setting)16 b FF(y)f FQ(=)f FF(b=c)p FQ(,)i(w)o(e)f (obtain)i(the)f FP(nonline)n(ar)22 b FQ(recursion)60 2206 y(\()p FF(b;)8 b(c)p FQ(\))13 b FE(7!)h FQ(\()p FF(b)279 2188 y FH(2)299 2206 y FQ(+)q(2)p FF(c)383 2188 y FH(2)403 2206 y FF(;)8 b FQ(2)p FF(bc)p FQ(\))14 b FE(\021)f FQ(\()593 2192 y(^)595 2206 y FF(b;)c FQ(^)-25 b FF(c)p FQ(\).)19 b(It)11 b(is)g(straigh)o(tforw)o (ard)h(to)g(pro)o(v)o(e)e(b)o(y)h(induction)f(that)i(if)f(\()p FF(b;)d(c)p FQ(\))13 b(=)60 2266 y(\()p FF(b)100 2273 y FD(n)123 2266 y FF(;)8 b(c)166 2273 y FD(n)190 2266 y FQ(\),)19 b(then)g(\()373 2253 y(^)375 2266 y FF(b;)9 b FQ(^)-25 b FF(c)p FQ(\))18 b(=)h(\()p FF(b)573 2273 y FH(2)p FD(n)p FH(+1)659 2266 y FF(;)8 b(c)702 2273 y FH(2)p FD(n)p FH(+1)788 2266 y FQ(\).)30 b(So)20 b(Newton's)f(metho)q (d)f(generates)h(a)h FP(subse)n(quenc)n(e)25 b FQ(of)60 2326 y(the)16 b(con)o(tin)o(ued-fraction)f(sequence.)133 2434 y(It)k(is)f(natural) h(to)g(ask)h(whether)e(our)h(construction)g(in)g(Section)f(4.3.4)h(can)g(b)q (e)g(extended)f(to)60 2494 y(Ising)e(mo)q(dels)f(in)g(dimension)f FF(d)g FE(\025)g FQ(3.)21 b(Clearly)15 b(this)h(w)o(orks)g(if)g(and)g(only)g (if)f(the)h(blo)q(c)o(k)f(size)g FF(b)g FQ(and)60 2554 y(island)h(size)g FF(c)g FQ(satisfy)g(the)g(Diophan)o(tine)g(equation)819 2660 y(1)c(+)f FF(b)925 2639 y FD(d)972 2660 y FQ(=)28 b(2)p FF(c)1083 2639 y FD(d)1117 2660 y FF(:)648 b FQ(\(C)p FF(:)p FQ(9\))938 2784 y(245)p eop %%Page: 246 246 bop 60 91 a FQ(Unfortunately)l(,)22 b(w)o(e)f(susp)q(ect)i(that)f(for)g FF(d)i FE(\025)f FQ(3)f(there)f(are)h FP(no)j FQ(p)q(ositiv)o(e-in)o(teger)20 b(solutions)j(to)60 152 y(\(C.9\))e(other)f(than)h FF(b)g FQ(=)g FF(c)g FQ(=)g(1.)34 b(The)21 b(b)q(est)g(results)f(w)o(e)g(ha)o(v)o(e)g(b)q (een)g(able)g(to)h(glean)g(from)e(the)60 212 y(mathematical)13 b(literature)i(are)i(summarize)o(d)d(in)i(Theorems)f(C.3)h(and)h(C.4:)60 313 y FM(Theorem)g(C.3)24 b FP(L)n(et)g FF(l)g FP(b)n(e)h(a)f(p)n(ositive)g (inte)n(ger)h(satisfying)f(any)g(one)h(of)f(the)g(fol)r(lowing)j(thr)n(e)n(e) 60 374 y(c)n(onditions:)93 475 y(\(a\))d FF(l)14 b FQ(=)g(3)p FP(;)k(or)95 577 y(\(b\))25 b FF(l)14 b FQ(=)g(4)p FP(;)k(or)95 679 y(\(c\))25 b FF(l)20 b FP(is)f(a)g(r)n(e)n(gular)f(prime)601 661 y FH(78)658 679 y FP(such)h(that)h(the)f(exp)n(onent)i(of)e(2)g(mo)n(d)f FF(l)i FP(is)1438 661 y FH(79)1495 679 y FP(either)f FQ(\()p FF(l)13 b FE(\000)f FQ(1\))p FF(=)p FQ(2)21 b FP(or)182 739 y(even,)e(and)f(such)f(that)h FQ(2)638 721 y FD(l)p Fy(\000)p FH(1)710 739 y FE(6\021)c FQ(1)42 b(\(mo)q(d)16 b FF(l)974 721 y FH(2)993 739 y FQ(\))p FP(.)60 841 y(L)n(et)i FF(d)g FP(b)n(e)g(any)g(multiple)i(of)d FF(l)i FP(\(including)h FF(l)e FP(itself)5 b(\).)25 b(Then)19 b(the)f(only)h(p)n(ositive-inte)n(ger)g (solutions)60 901 y(to)i FF(x)150 883 y FD(d)184 901 y FQ(+)13 b FF(y)261 883 y FD(d)301 901 y FQ(=)20 b(2)p FF(z)408 883 y FD(d)449 901 y FP(ar)n(e)h FF(x)f FQ(=)g FF(y)h FQ(=)g FF(z)r FP(.)32 b(In)21 b(p)n(articular,)g(the)h(only)f(p)n(ositive-inte)n(ger)h (solution)g(to)60 961 y FQ(1)11 b(+)g FF(b)165 943 y FD(d)199 961 y FQ(=)j(2)p FF(c)296 943 y FD(d)334 961 y FP(is)j FF(b)d FQ(=)g FF(c)g FQ(=)f(1)p FP(.)133 1063 y FQ(Theorem)21 b(C.3)h(has)h(a)f (long)g(history)l(.)38 b(Ob)o(viously)l(,)22 b(if)g(the)f(theorem)g(holds)h (for)g(an)o(y)g(giv)o(en)60 1123 y(p)q(o)o(w)o(er)17 b FF(l)q FQ(,)f(it)h(trivially)e(holds)i(also)h(for)f(m)o(ultiples)d(of)j(that)h(p)q (o)o(w)o(er.)23 b(The)17 b(case)g FF(l)f FQ(=)f(3)i(w)o(as)h(pro)o(v)o(en)60 1183 y(b)o(y)d(Euler)g(sometime)e(b)q(efore)j(1770)h([76,)f(p.)f(572];)h(m)o (uc)o(h)e(more)g(general)i(results)f(are)h(no)o(w)g(kno)o(wn)60 1243 y([265)q(,)21 b(pp.)f(126,)i(203,)g(220].)35 b(The)20 b(case)h FF(l)g FQ(=)g(4)g(is)f(a)h(sp)q(ecialization)e(of)i(a)g(theorem)e (pro)o(v)o(en)h(b)o(y)60 1303 y(Sc)o(hopis)g(in)f(1825)i([76)q(,)f(p.)f(618]) i([265,)g(p.)e(18];)i(again,)g(more)e(general)g(results)h(are)g(no)o(w)g(kno) o(wn)60 1364 y([265)q(,)15 b(pp.)g(271,)h(274,)g(276].)21 b(The)16 b(case)f FF(l)f FQ(=)g(5)i(w)o(as)f(pro)o(v)o(en)g(in)g(the)g(mid-nineteen)o (th)d(cen)o(tury)l(,)i(but)60 1424 y(the)j(prop)q(er)h(attribution)f(is)g (unclear.)23 b(D)o(\023)-23 b(enes)17 b([74)q(])f(credits)h(Diric)o(hlet)e ([81],)h(but)i(our)f(reading)h(of)60 1484 y(Diric)o(hlet's)f(pap)q(er)i (indicates)g(that)g(he)g(treated)g(n)o(umerous)f(cases)h(of)g FF(x)1425 1466 y FH(5)1458 1484 y FQ(+)13 b FF(y)1535 1466 y FH(5)1573 1484 y FQ(=)18 b FF(Az)1691 1466 y FH(5)1729 1484 y FQ(but)i FP(not)60 1544 y FF(A)e FQ(=)h(2)h(\(see)e(also)i([76,)g(p.)e (735]\).)31 b(The)19 b(correct)g(attribution)g(seems)e(to)j(b)q(e)f(V.A.)f (Leb)q(esgue)h(in)60 1604 y(1843)e([235)q(])e([76)q(,)g(p.)h(738].)21 b(See)16 b(also)g([76,)g(pp.)f(755{756])j(and)f([265,)f(p.)f(276])i(for)f (generalizations.)133 1665 y(The)23 b(case)g(\(c\))f(w)o(as)i(pro)o(v)o(en)e (b)o(y)g(D)o(\023)-23 b(enes)23 b([74)q(])f(in)h(1952.)42 b(T)l(o)24 b(in)o(terpret)d(it,)j(note)f(that)g(the)60 1725 y(\014rst)f(irregular)e (primes)g(are)h(37)p FF(;)8 b FQ(59)p FF(;)g FQ(67)p FF(;)g FQ(101)p FF(;)g(:)g(:)g(:)25 b FQ(.)36 b(The)22 b(\014rst)f(regular)h(primes) d(for)j(whic)o(h)e(the)60 1785 y(exp)q(onen)o(t)f(condition)g(fails)g(are)g (31)p FF(;)8 b FQ(73)p FF(;)g FQ(89)p FF(;)g FQ(127)p FF(;)g(:)g(:)g(:)21 b FQ(.)29 b(Finally)l(,)18 b(the)h(only)g(primes)e FF(l)j(<)e FQ(6)c FE(\002)f FQ(10)1870 1767 y FH(9)60 1845 y FQ(\(and)22 b(indeed)e(the)h(only)g(ones)h(curren)o(tly)e(kno)o(wn\))h(for)h(whic)o(h)e (2)1293 1827 y FD(l)p Fy(\000)p FH(1)1374 1845 y FE(\021)j FQ(1)41 b(\(mo)q(d)17 b FF(l)1647 1827 y FH(2)1666 1845 y FQ(\))k(are)g(1093) 60 1905 y(and)f(3511)h([308)q(,)e(pp.)g(263{264].)33 b(Th)o(us,)20 b(the)f(\014rst)h(primes)e(for)h(whic)o(h)g(condition)g(\(c\))g(fails)g(are) 60 1966 y(31)p FF(;)8 b FQ(37)p FF(;)g FQ(59)p FF(;)g FQ(67)p FF(;)g FQ(73)p FF(;)g FQ(8)q(9)p FF(;)g FQ(10)q(1)p FF(;)g(:)g(:)g(:)20 b FQ(.)28 b(In)18 b(particular,)g(Theorem)f(C.3)i(holds)g(for)g(all)f(exp)q (onen)o(ts)g FF(d)g FE(\024)60 2026 y FQ(100)f(except)f(p)q(ossibly)g(31)p FF(;)8 b FQ(37)p FF(;)g FQ(59)p FF(;)g FQ(62)p FF(;)g FQ(67)p FF(;)g FQ(7)q(3)p FF(;)g FQ(74)q FF(;)g FQ(89.)1044 2008 y FH(80)60 2140 y FM(Theorem)17 b(C.4)24 b FP(F)l(or)c(arbitr)n(ary)e FF(d)h FE(\025)f FQ(3)p FP(,)j(ther)n(e)f(is)g(at)g(most)g(one)h(p)n (ositive-inte)n(ger)g(solution)g(to)60 2200 y FQ(1)11 b(+)g FF(b)165 2182 y FD(d)199 2200 y FQ(=)j(2)p FF(c)296 2182 y FD(d)334 2200 y FP(other)j(than)h FF(b)c FQ(=)g FF(c)f FQ(=)h(1)p FP(.)p 60 2238 732 2 v 100 2292 a FA(78)135 2307 y Fz(A)d(prime)f Fv(l)j(>)f Fz(3)e(is)h(called)g Fw(r)n(e)n(gular)k Fz(if)10 b(it)h(do)q(es)h(not)f(divide)g(an)o(y)f(of)h(the)h(n)o(umerators)e(of)h(the) h(Bernoulli)e(n)o(um)o(b)q(ers)60 2357 y Fv(B)91 2363 y FA(2)110 2357 y Fv(;)d(B)160 2363 y FA(4)179 2357 y Fv(;)g(:)g(:)g(:)t(;)g(B)302 2363 y Fp(l)p Fo(\000)p FA(3)371 2357 y Fz(expressed)17 b(in)c(lo)o(w)o(est)h (terms.)100 2415 y FA(79)135 2430 y Fz(The)g(exp)q(onen)o(t)h(of)e(2)h(mo)q (d)e Fv(l)j Fz(is)f(the)g(smallest)f(in)o(teger)h Fv(n)e Fu(\025)g Fz(1)h(suc)o(h)i(that)f(2)1331 2415 y Fp(n)1365 2430 y Fu(\021)d Fz(1)35 b(\(mo)q(d)12 b Fv(l)q Fz(\).)100 2488 y FA(80)135 2503 y Fz(D)o(\023)-20 b(enes')15 b(pap)q(er)f([74])f(con)o(tains)h(a)g(list) g(of)g(all)f(primes)g Fv(l)h(<)e Fz(619)i(for)g(whic)o(h)g(condition)f(\(c\)) i(fails.)j(This)c(list)g(has,)60 2553 y(ho)o(w)o(ev)o(er,)e(a)g(few)f(mistak) o(es:)16 b(The)c(primes)f(389)g(and)h(613)f(should)h(b)q(e)g(added)g(to)g (the)g(list)f(of)h(irregular)f(primes)g([247)o(];)60 2602 y(the)16 b(exp)q(onen)o(t)h(of)e(2)h(mo)q(d)e(281)h(\(resp.)h(mo)q(d)f(563\))g(is)h (70)f(\(resp.)h(562\);)g(and)f(the)i(\014nal)e(list)g(in)h(his)f(article)h (should)60 2652 y(read)e(31)p Fv(;)7 b Fz(73)p Fv(;)g Fz(89)p Fv(;)g Fz(127)p Fv(;)f Fz(15)o(1)p Fv(;)h Fz(2)o(23)p Fv(;)f Fz(337)p Fv(;)g Fz(431)o Fv(;)h Fz(43)o(9)p Fv(;)g Fz(6)o(01.)938 2784 y FQ(246)p eop %%Page: 247 247 bop 133 91 a FQ(Theorem)11 b(C.4)h(is)f(a)h(sp)q(ecial)g(case)g(of)g(a)g (result)f(of)h(Domar)g([98],)g(who)g(pro)o(v)o(es)g(that)g(for)g(arbitrary)60 152 y(in)o(tegers)k FF(A;)8 b(B)16 b FE(\025)f FQ(1)i(and)g FF(d)e FE(\025)f FQ(5,)j(the)g(equation)f FE(j)p FF(Ax)1054 133 y FD(d)1085 152 y FE(\000)11 b FF(B)s(y)1201 133 y FD(d)1220 152 y FE(j)k FQ(=)f(1)j(has)h(at)f(most)f(t)o(w)o(o)g(solutions)60 212 y(in)g(p)q(ositiv)o(e)f(in)o(tegers)h FF(x;)8 b(y)r FQ(.)20 b(See)c(also)h([111].)133 322 y(The)k(conjectured)e(unsolv)m(abilit)o(y)g(of) i FF(x)881 304 y FD(d)915 322 y FQ(+)14 b FF(y)993 304 y FD(d)1033 322 y FQ(=)21 b(2)p FF(z)1141 304 y FD(d)1182 322 y FQ(for)f FF(d)i FE(\025)e FQ(3)h(is)f(a)h(sp)q(ecial)f(case)g(of)h(an)60 382 y(\\extended)16 b(F)l(ermat's)e(last)j(theorem")e(whic)o(h)g(migh)o(t)g (conceiv)m(ably)g(b)q(e)h(true)g([142)q(,)g(62]:)60 484 y FM(Conjecture)i (C.5)25 b FP(L)n(et)18 b FF(d)g FP(and)h FF(a)f FP(b)n(e)g(inte)n(gers,)h (with)g FF(d)d FE(\025)f FQ(3)j FP(and)h FQ(1)c FE(\024)g FF(a)g FE(\024)g FF(d)p FP(.)26 b(Then)18 b(ther)n(e)h(ar)n(e)60 544 y(no)i(solutions)g(of)f FF(x)428 526 y FD(d)462 544 y FQ(+)13 b FF(y)539 526 y FD(d)578 544 y FQ(=)19 b FF(az)686 526 y FD(d)726 544 y FP(in)i(nonzer)n(o)g(inte)n(gers,)h(exc)n(ept)f(for)f FF(x)f FQ(=)g FF(y)i FQ(=)f FF(z)i FP(in)f(the)g(c)n(ase)60 604 y FF(a)13 b FQ(=)h(2)p FP(.)60 706 y FQ(W)l(e)i(\014nd)i(it)e(am)o(using) g(that)h(a)g(real)f(problem)f(in)i(ph)o(ysics)f(should)h(b)q(e)g(connected)f (with)h(F)l(ermat's)60 766 y(last)g(theorem,)f(but)h(w)o(e)g(think)g(that)g (this)g(is)g(an)h(artifact)f(of)g(our)h(metho)q(d)e(of)i(pro)q(of)g(and)g FP(not)23 b FQ(an)60 826 y(in)o(trinsic)17 b(fact)i(ab)q(out)g(ma)s(jorit)o (y-rule)e(transformations.)28 b(Indeed,)18 b(w)o(e)g(susp)q(ect)h(that)g (Theorem)60 886 y(4.5)f(holds)f(for)h(all)e(blo)q(c)o(k)h(sizes)f FF(b)g FE(\025)f FQ(2)i(and)h(all)f(dimensions)e FF(d)h FE(\025)f FQ(3,)j(without)f(regard)h(for)f(subtle)60 946 y(n)o(um)o(b)q(er-theoretic)d (prop)q(erties.)21 b(But)16 b(w)o(e)g(could)g(b)q(e)g(wrong.)60 1113 y FG(Ac)n(kno)n(wledgm)o(en)n(ts)60 1222 y FQ(W)l(e)22 b(are)h(v)o(ery)e(grateful)h(to)h(Jean)f(Bricmon)o(t,)f(Anna)i(Hasenfratz,)g (Mic)o(hael)e(Kiessling,)i(Jes)q(\023)-26 b(us)60 1283 y(Salas,)14 b(Dan)g(Stein)f(and)h(Doug)g(T)l(oussain)o(t)g(for)g(man)o(y)d(helpful)i (commen)n(ts)e(on)j(a)f(\014rst)h(draft)g(of)f(this)60 1343 y(pap)q(er.)20 b(In)12 b(addition,)h(w)o(e)e(wish)h(to)g(thank)h(P)o(a)o(v)o (el)d(Bleher,)h(Carlo)i(di)e(Castro,)j(Jo)q(el)e(Cohen,)h(Roland)60 1403 y(Dobrushin,)j(Mic)o(hael)d(Fisher,)i(J)q(\177)-26 b(urg)16 b(F)l(r\177)-24 b(ohlic)o(h,)14 b(Stuart)i(Geman,)e(Hans-Otto)i(Georgii,)e (An)o(tonio)60 1463 y(Gonz\023)-24 b(alez-Arro)o(y)o(o,)17 b(Bob)g(Gri\016ths,)g(Rob)q(ert)h(Israel,)f(T)l(om)g(Kennedy)l(,)f(Roman)h (Kotec)o(k)q(\023)-25 b(y,)16 b(An)o(tti)60 1523 y(Kupiainen,)24 b(Jo)q(el)f(Leb)q(o)o(witz,)h(Christian)f(Maes,)h(F)l(abio)g(Martinelli,)e (Ja)o(\024)-23 b(cek)22 b(Mi\030)-22 b(ekisz,)23 b(Ch)o(uc)o(k)60 1584 y(Newman,)11 b(Enzo)h(Olivieri,)d(Charles)j(Radin,)g(Vincen)o(t)e(Riv)m (asseau,)i(Rob)q(erto)g(Sc)o(honmann,)g(Sen)o(y)o(a)60 1644 y(Shlosman,)i(Bob)g(Sw)o(endsen,)f(Sriniv)m(asa)i(V)l(aradhan,)g(Marin)o(us)f (Winnink)f(and)h(Milo)m(\024)-22 b(s)15 b(Zahradn)-5 b(\023)-19 b(\020k)60 1704 y(for)17 b(helpful)e(con)o(v)o(ersations)h(and)h(corresp)q (ondence.)133 1764 y(Tw)o(o)d(of)h(the)e(authors)i(\(R.F.)e(and)h(A.D.S.\))e (thank)i(the)g(Univ)o(ersit\022)-24 b(a)12 b(di)i(Roma)f(\\T)l(or)h(V)l (ergata")60 1824 y(and)h(the)f(Rijksuniv)o(ersiteit)e(Groningen)j(for)f (hospitalit)o(y)g(while)f(this)i(pap)q(er)g(w)o(as)f(b)q(eing)h(written.)60 1884 y(The)d(other)g(author)h(\(A.C.D.v.E.\))d(thanks)j(the)f(ETH{H\177)-24 b(onggerb)q(erg)13 b(and)g(the)e(EPFL{Lausanne)60 1945 y(for)17 b(hospitalit)o(y)e(during)h(this)h(same)e(p)q(erio)q(d.)133 2005 y(Last)f(but)e(not)h(least,)f(w)o(e)g(wish)g(to)h(thank)g(Jo)q(el)f(Leb) q(o)o(witz)g(for)h(b)q(eing)f(willing)f(ev)o(en)g(to)i FP(c)n(onsider)60 2065 y FQ(a)k(pap)q(er)f(of)h(this)f(length)g(for)h(publication)e(in)h(the)g FP(Journal)i(of)f(Statistic)n(al)h(Physics)t FQ(.)133 2125 y(The)12 b(researc)o(h)g(of)h(the)f(\014rst)g(author)h(\(A.C.D.v.E.\))d(has)j (b)q(een)f(made)f(p)q(ossible)i(b)o(y)e(a)i(fello)o(wship)60 2185 y(of)i(the)g(Ro)o(y)o(al)f(Netherlands)g(Academ)o(y)e(of)j(Arts)g(and)g (Sciences)f(\(KNA)-5 b(W\).)13 b(The)i(researc)o(h)f(of)h(the)60 2246 y(second)21 b(author)g(\(R.F.\))e(w)o(as)i(supp)q(orted)g(in)g(part)f(b) o(y)g(the)g(Sc)o(h)o(w)o(eizer)e(Nationalfonds)k(and)f(b)o(y)60 2306 y(the)d(F)l(onds)h(National)g(Suisse.)28 b(The)18 b(researc)o(h)g(of)h (the)f(third)h(author)g(\(A.D.S.\))e(w)o(as)i(supp)q(orted)60 2366 y(in)14 b(part)h(b)o(y)f(U.S.)g(National)g(Science)f(F)l(oundation)j (gran)o(ts)f(DMS{8705599,)j(DMS{8911273)f(and)60 2426 y(DMS{9200719)i(and)e (b)o(y)f(U.S.)f(Departmen)o(t)g(of)h(Energy)h(con)o(tract)f(DE-F)o (G02-90ER40581)q(.)938 2784 y(247)p eop %%Page: 248 248 bop 60 100 a FG(References)109 209 y FQ([1])24 b(M.)15 b(Aizenman.)j(T)l (ranslation)f(in)o(v)m(ariance)e(and)i(instabilit)o(y)d(of)i(phase)h(co)q (existence)e(in)g(the)185 269 y(t)o(w)o(o)h(dimensional)e(Ising)i(system.)k FP(Commun.)e(Math.)f(Phys.)p FQ(,)e(73:83{94,)j(1980.)109 370 y([2])24 b(M.)16 b(Aizenman.)22 b(Geometric)15 b(analysis)i(of)h FF(')1021 352 y FH(4)1021 382 y(4)1058 370 y FQ(\014elds)f(and)g(Ising)h(mo)q (dels.)d(Parts)j(I)f(and)h(I)q(I.)185 430 y FP(Commun.)f(Math.)g(Phys.)p FQ(,)e(86:1{48,)j(1982.)109 531 y([3])24 b(M.)13 b(Aizenman.)j(The)e(in)o (tersection)e(of)j(Bro)o(wnian)f(paths)h(as)g(a)f(case)h(study)f(of)g(a)h (renormal-)185 591 y(ization)j(group)h(metho)q(d)f(for)g(quan)o(tum)g (\014eld)f(theory)l(.)28 b FP(Commun.)19 b(Math.)g(Phys.)p FQ(,)g(97:91{)185 651 y(110,)e(1985.)109 752 y([4])24 b(M.)17 b(Aizenman,)f(J.)i(T.)g(Cha)o(y)o(es,)g(L.)h(Cha)o(y)o(es,)f(J.)g(F)l(r\177) -24 b(ohlic)o(h,)17 b(and)i(L.)f(Russo.)28 b(On)19 b(a)f(sharp)185 812 y(transition)e(from)e(area)i(la)o(w)g(to)g(p)q(erimeter)d(la)o(w)j(in)f (a)h(system)e(of)i(random)f(surfaces.)21 b FP(Com-)185 872 y(mun.)c(Math.)g(Phys.)p FQ(,)f(92:19{69,)i(1983.)109 972 y([5])24 b(M.)19 b(Aizenman,)f(J.)h(T.)h(Cha)o(y)o(es,)g(L.)f(Cha)o(y)o(es,)h(and)h (C.)e(M.)g(Newman.)31 b(Discon)o(tin)o(uit)o(y)18 b(of)185 1033 y(the)c(magnetization)g(in)g(one-dimensional)g(1)p FF(=)p FE(j)p FF(x)8 b FE(\000)g FF(y)r FE(j)1180 1015 y FH(2)1214 1033 y FQ(Ising)14 b(and)i(Potts)f(mo)q(dels.)j FP(J.)d(Stat.)185 1093 y(Phys.)p FQ(,)g(50:1{40,)j(1988.)109 1193 y([6])24 b(M.)17 b(Aizenman)e(and)k(R.)e(F)l(ern\023)-24 b(andez.)26 b(On)18 b(the)f(critical)g(b)q(eha)o(vior)g(of)i(the)e(magnetization)185 1254 y(in)f(high-dimensional)e(Ising)j(mo)q(dels.)j FP(J.)d(Stat.)h(Phys.)p FQ(,)d(44:393{454,)k(1986.)109 1354 y([7])24 b(M.)17 b(Aizenman)f(and)i(R.)g (Graham.)26 b(On)18 b(the)g(renormalized)d(coupling)j(constan)o(t)h(and)f (the)185 1414 y(susceptibilit)o(y)13 b(in)j FF(')569 1396 y FH(4)569 1427 y(4)604 1414 y FQ(\014eld)f(theory)h(and)g(the)g(Ising)f(mo)q (del)g(in)g(four)h(dimensions.)j FP(Nucle)n(ar)185 1474 y(Physics)p FQ(,)c(B225)i([FS9]:261{288,)h(1983.)109 1575 y([8])24 b(M.)13 b(Aizenman)e(and)j(E.)g(Lieb.)j(The)d(third)f(la)o(w)g(of)i(thermo)q (dynamics)c(and)j(the)g(degeneracy)185 1635 y(of)i(the)g(ground)h(state)g (for)g(lattice)e(systems.)k FP(J.)e(Stat.)h(Phys.)p FQ(,)e(24:279{297,)j (1981.)109 1736 y([9])24 b(M.)12 b(P)l(.)g(Almeida)e(and)j(B.)f(Gidas.)k(A)c (v)m(ariational)h(metho)q(d)f(for)h(estimating)f(the)g(parameters)185 1796 y(of)k(MRF)g(from)f(complete)f(or)j(incomplete)c(data.)22 b(Bro)o(wn)16 b(Univ)o(ersit)o(y)e(preprin)o(t,)h(1990.)84 1897 y([10])25 b(D.)11 b(J.)g(Amit)e(and)j(L.)g(P)o(eliti.)f(On)h(dangerous)h (irrelev)m(an)o(t)d(op)q(erators.)15 b FP(A)o(nn.)e(Phys.)p FQ(,)f(140:207{)185 1957 y(231,)17 b(1982.)84 2057 y([11])25 b(P)l(.)18 b(W.)h(Anderson)g(and)h(G.)f(Y)l(uv)m(al.)29 b(Some)17 b(n)o(umerical)g(results)h(on)i(the)f(Kondo)h(problem)185 2117 y(and)15 b(the)f(in)o(v)o(erse-square)f(one-dimensional)g(Ising)h(mo)q(del.)j FP(J.)e(Phys.)p FQ(,)f(C4:607{620,)j(1971.)84 2218 y([12])25 b(P)l(.)d(W.)g(Anderson,)i(G.)e(Y)l(uv)m(al,)h(and)g(D.)f(R.)g(Hamann.)39 b(Exact)23 b(results)f(in)g(the)g(Kondo)185 2278 y(problem.)15 b(I)q(I.)g(Scaling)i(theory)l(,)g(qualitativ)o(ely)d(correct)i(solution,)h (and)h(some)d(new)i(results)185 2338 y(on)f(one-dimensional)f(classical)g (statistical)g(mo)q(dels.)20 b FP(Phys.)c(R)n(ev.)p FQ(,)f(B1:4464{4473,)k (1970.)84 2439 y([13])25 b(C.)14 b(Arag~)-24 b(ao)16 b(de)f(Carv)m(alho,)g (S.)g(Caracciolo,)f(and)i(J.)e(F)l(r\177)-24 b(ohlic)o(h.)17 b(P)o(olymers)c(and)j FF(g)r(')1719 2421 y FH(4)1753 2439 y FQ(theory)185 2499 y(in)g(four)g(dimensions.)k FP(Nucl.)f(Phys.)p FQ(,)c(B215)i([FS7]:209{248,)g(1983.)84 2600 y([14])25 b(M.)14 b(Asorey)l(,)h(J.)g(G.)g(Estev)o(e,)g(R.)g(F)l(ern\023)-24 b(andez,)14 b(and)i(J.)f(Salas.)21 b(Rigorous)16 b(analysis)g(of)g(renor-)185 2660 y(malization)e(group)j(pathologies)g(in)f(the)g(4-state)h(clo)q(c)o(k)f (mo)q(del.)k(Preprin)o(t,)14 b(1992.)938 2784 y(248)p eop %%Page: 249 249 bop 84 91 a FQ([15])25 b(M.)17 b(B.)g(Av)o(erin)o(tsev.)24 b(Gibbs)18 b(description)f(of)h(random)g(\014elds)g(whose)g(conditional)g (proba-)185 152 y(bilities)c(ma)o(y)h(v)m(anish.)21 b FP(Pr)n(obl.)d(Inform.) e(T)l(r)n(ansmission)p FQ(,)g(11:326{334,)i(1975.)84 253 y([16])25 b(R.)15 b(R.)h(Bahadur.)22 b FP(Some)c(Limit)f(The)n(or)n(ems)f(in)i (Statistics)p FQ(.)k(SIAM,)15 b(Philadelphia,)g(1971.)84 355 y([17])25 b(G.)d(A.)g(Bak)o(er)g(and)i(S.)e(Krinsky)l(.)41 b(Renormalization)21 b(group)j(structure)e(of)h(translation)185 415 y(in)o(v)m(arian)o(t)15 b(ferromagnets.)21 b FP(J.)c(Math.)g(Phys.)p FQ(,)e(18:590{607,)k(1977.)84 517 y([18])25 b(T.)13 b(Balaban.)j(Ultra)o (violet)11 b(stabilit)o(y)h(in)h(\014eld)g(theory)l(.)f(The)h FF(\036)1323 499 y FH(4)1323 529 y(3)1356 517 y FQ(mo)q(del.)i(In)e(J.)g(F)l (r\177)-24 b(ohlic)o(h,)12 b(ed-)185 577 y(itor,)h FP(Sc)n(aling)k(and)e (Self-Similarity)i(in)f(Physics)p FQ(.)d(Birkh\177)-24 b(auser,)13 b(Boston{Basel{Stuttgart,)185 637 y(1983.)84 739 y([19])25 b(T.)c(Balaban.)39 b(Large)23 b(\014eld)e(renormalization.)f(I)q(I.)h(Lo)q (calization,)j(exp)q(onen)o(tiation)d(and)185 799 y(b)q(ounds)c(for)g(the)f FM(R)g FQ(op)q(eration.)22 b FP(Commun.)17 b(Math.)g(Phys.)p FQ(,)f(122:355{392,)j(1989.)84 901 y([20])25 b(R.)c(Balian.)36 b FP(F)l(r)n(om)22 b(Micr)n(ophysics)f(to)h(Macr)n(ophysics:)31 b(Metho)n(ds)22 b(and)g(Applic)n(ations)h(of)185 961 y(Statistic)n(al)18 b(Physics)p FQ(.)j(Springer-V)l(erlag,)15 b(Berlin{New)g(Y)l(ork,)g(1991.)84 1063 y([21])25 b(A.)18 b(G.)g(Basuev.)29 b(Complete)17 b(phase)i(diagrams)g (with)g(resp)q(ect)f(to)h(external)f(\014elds)h(at)g(lo)o(w)185 1123 y(temp)q(eratures)14 b(for)i(mo)q(dels)f(with)h(nearest-neigh)o(b)q(or)g (in)o(teraction)f(in)h(the)f(case)h(of)g(a)h(\014nite)185 1183 y(or)f(coun)o(table)g(n)o(um)o(b)q(er)f(of)h(ground)h(states.)22 b FP(The)n(or.)17 b(Math.)g(Phys.)p FQ(,)e(58:171{182,)k(1984.)84 1285 y([22])25 b(A.)13 b(G.)i(Basuev.)j(Hamiltonian)12 b(of)j(the)f(phase)h (separation)g(b)q(order)g(and)h(phase)f(transitions)185 1345 y(of)h(the)g(\014rst)h(kind.)e(I.)21 b FP(The)n(or.)16 b(Math.)h(Phys.)p FQ(,)f(64:716{734,)j(1985.)84 1447 y([23])25 b(A.)13 b(G.)i(Basuev.)j (Hamiltonian)12 b(of)j(the)f(phase)h(separation)g(b)q(order)g(and)h(phase)f (transitions)185 1507 y(of)f(the)f(\014rst)h(kind.)f(I)q(I.)g(The)h(simplest) d(disordered)j(phases.)k FP(The)n(or.)c(Math.)h(Phys.)p FQ(,)e(72:861{)185 1567 y(871,)k(1987.)84 1669 y([24])25 b(G.)15 b(A.)h(Battle)f(and)h(L.)g (Rosen.)21 b(The)16 b(FK)o(G)g(inequalit)o(y)e(for)i(the)g(Yuk)m(a)o(w)o(a) 1559 1676 y FH(2)1595 1669 y FQ(quan)o(tum)f(\014eld)185 1729 y(theory)l(.)21 b FP(J.)c(Stat.)h(Phys.)p FQ(,)d(22:123{192,)k(1980.)84 1831 y([25])25 b(H.)16 b(Bauer.)25 b FP(Pr)n(ob)n(ability)18 b(The)n(ory)f(and)i(Elements)i(of)d(Me)n(asur)n(e)g(The)n(ory)p FQ(.)23 b(Holt,)17 b(Rinehart)185 1891 y(and)f(Winston,)h(New)e(Y)l(ork,)h (1972.)84 1993 y([26])25 b(R.)16 b(T.)g(Baumel.)k FP(On)e(sp)n(ontane)n (ously)g(br)n(oken)h(symmetry)d(in)j(the)f FF(P)7 b FQ(\()p FF(\036)p FQ(\))1530 2000 y FH(2)1567 1993 y FP(mo)n(del)18 b(quantum)185 2053 y(\014eld)g(the)n(ory)p FQ(.)j(PhD)16 b(thesis,)g (Princeton)g(Univ)o(ersit)o(y)l(,)d(June)j(1979.)84 2154 y([27])25 b(T.)19 b(L.)g(Bell)f(and)i(K.)f(G.)g(Wilson.)30 b(Finite-lattice)17 b(appro)o(ximations)i(to)h(renormalization)185 2215 y(groups.)i FP(Phys.)17 b(R)n(ev.)p FQ(,)f(B11:3431{3444,)j(1975.)84 2316 y([28])25 b(G.)13 b(Benfatto,)g(M.)f(Cassandro,)k(G.)d(Galla)o(v)o(otti,)f (F.)h(Nicol\022)-24 b(o,)13 b(E.)f(Olivieri,)f(E.)i(Presutti,)g(and)185 2377 y(E.)j(Scacciatelli.)j(Ultra)o(violet)14 b(stabilit)o(y)h(in)h (Euclidean)g(scalar)g(\014eld)g(theories.)21 b FP(Commun.)185 2437 y(Math.)c(Phys.)p FQ(,)e(71:95{130,)j(1980.)84 2538 y([29])25 b(P)l(.)16 b(Billingsley)l(.)i FP(Conver)n(genc)n(e)h(of)e(Pr)n(ob)n(ability) g(Me)n(asur)n(es)p FQ(.)k(Wiley)l(,)14 b(New)i(Y)l(ork,)f(1968.)84 2640 y([30])25 b(P)l(.)16 b(Billingsley)l(.)i FP(Pr)n(ob)n(ability)f(and)h (Me)n(asur)n(e)p FQ(.)i(Wiley)l(,)14 b(New)i(Y)l(ork,)f(1979.)938 2784 y(249)p eop %%Page: 250 250 bop 84 91 a FQ([31])25 b(M.)17 b(J.)g(Bissett.)24 b(A)17 b(p)q (erturbation-theoretic)h(deriv)m(ation)f(of)h(Wilson's)f(`incomplete)e(in)o (te-)185 152 y(gration')h(theory)l(.)21 b FP(J.)c(Phys.)g(C)p FQ(,)f(6:3061{3070,)j(1973.)84 253 y([32])25 b(P)l(.)e(M.)g(Bleher)f(and)i(P) l(.)f(Ma)s(jor.)43 b(Critical)22 b(phenomena)h(and)h(univ)o(ersal)f(exp)q (onen)o(ts)g(in)185 313 y(statistical)11 b(ph)o(ysics.)g(On)h(Dyson's)h (Hierarc)o(hical)d(mo)q(del.)j FP(A)o(nn.)h(Pr)n(ob.)p FQ(,)e(15:431{477,)k (1987.)84 415 y([33])25 b(H.)14 b(W.)g(J.)h(Bl\177)-24 b(ote)14 b(and)h(R.)f(H.)g(Sw)o(endsen.)19 b(First-order)c(phase)g(transitions)g(and)h (the)e(three-)185 475 y(state)i(Potts)h(mo)q(del.)j FP(Phys.)d(R)n(ev.)g(L)n (ett.)p FQ(,)f(43:799{802,)j(1979.)84 577 y([34])25 b(E.)17 b(Bolthausen.)24 b(Mark)o(o)o(v)17 b(pro)q(cess)h(large)f(deviations)g(in)g (the)g FF(\034)6 b FQ(-top)q(ology)l(.)25 b FP(Sto)n(ch.)19 b(Pr)n(o)n(c.)185 637 y(Appl.)p FQ(,)d(25:95{108,)i(1987.)84 739 y([35])25 b(C.)15 b(Borgs)i(and)f(J.)f(Z.)h(Im)o(brie.)h(A)f(uni\014ed)f (approac)o(h)i(to)f(phase)g(diagrams)f(in)h(\014eld)f(theory)185 799 y(and)h(statistical)g(mec)o(hanics.)j FP(Commun.)e(Math.)h(Phys.)p FQ(,)d(123:305{328,)k(1989.)84 901 y([36])25 b(C.)18 b(Borgs)h(and)h(R.)e (Kotec)o(k)q(\023)-25 b(y.)27 b(A)19 b(rigorous)g(theory)g(of)g (\014nite-size)f(scaling)g(at)h(\014rst-order)185 961 y(phase)d(transitions.) 22 b FP(J.)17 b(Stat.)h(Phys.)p FQ(,)d(61:79{119,)k(1990.)84 1063 y([37])25 b(H.)19 b(J.)h(Brascamp)f(and)h(E.)g(H.)f(Lieb.)33 b(Some)19 b(inequalities)f(for)i(Gaussian)i(measures.)31 b(In)185 1123 y(A.)13 b(M.)g(Arth)o(urs,)g(editor,)h FP(F)l(unctional)j(Inte)n(gr)n (ation)e(and)h(its)f(Applic)n(ations)p FQ(,)g(Oxford,)f(1975.)185 1183 y(Clarendon)i(Press.)84 1285 y([38])25 b(H.)20 b(J.)i(Brascamp)f(and)h (E.)f(H.)g(Lieb.)37 b(On)22 b(extensions)g(of)g(the)f(Brunn-Mink)o(o)o(wski)f (and)185 1345 y(Pr)o(\023)-23 b(ek)o(opa-Leindler)15 b(theorems,)g(including) g(inequalities)f(for)i(log)h(conca)o(v)o(e)e(functions,)g(and)185 1405 y(with)g(an)g(application)g(to)g(the)g(di\013usion)h(equation.)j FP(J.)d(F)l(unct.)h(A)o(nal.)p FQ(,)f(22:366{389,)i(1976.)84 1507 y([39])25 b(H.)19 b(J.)g(Brascamp,)h(E.)g(H.)f(Lieb,)h(and)h(J.)f(L.)g (Leb)q(o)o(witz.)32 b(The)20 b(statistical)g(mec)o(hanics)e(of)185 1567 y(anharmonic)d(lattices.)20 b FP(Bul)r(l.)g(Internat.)e(Statist.)g (Inst.)p FQ(,)e(46)h(\(Bo)q(ok)g(1\):393{404,)h(1975.)84 1669 y([40])25 b(O.)c(Bratteli)f(and)i(D.)g(W.)f(Robinson.)39 b FP(Op)n(er)n(ator)21 b(A)o(lgebr)n(as)i(and)g(Quantum)g(Statistic)n(al)185 1729 y(Me)n(chanics)18 b(II)p FQ(.)i(Springer-V)l(erlag,)c(New)f(Y)l (ork{Heidelb)q(erg{Berlin,)f(1981.)84 1831 y([41])25 b(J.)17 b(Bricmon)o(t,)f(J.-R.)h(F)l(on)o(taine,)h(and)g(L.)g(J.)g(Landau.)28 b(On)18 b(the)g(uniqueness)g(of)g(the)g(equi-)185 1891 y(librium)13 b(state)k(for)f(plane)g(rotators.)23 b FP(Commun.)17 b(Math.)g(Phys.)p FQ(,)f(56:281{290,)i(1977.)84 1993 y([42])25 b(J.)11 b(Bricmon)o(t,)f(J.)i (R.)g(F)l(on)o(taine,)g(J.)g(L.)g(Leb)q(o)o(witz,)h(and)f(T.)g(Sp)q(encer.)i (Lattice)e(systems)f(with)185 2053 y(a)19 b(con)o(tin)o(uous)f(symmetry)d(I.) j(Perturbation)h(theory)f(for)h(un)o(b)q(ounded)h(spins.)28 b FP(Commun.)185 2113 y(Math.)17 b(Phys.)p FQ(,)e(78:281{302,)k(1980.)84 2215 y([43])25 b(J.)20 b(Bricmon)o(t)e(and)j(A.)f(Kupiainen.)33 b(Lo)o(w)o(er)21 b(critical)d(dimension)h(for)i(the)f(random)h(\014eld)185 2275 y(Ising)16 b(mo)q(del.)k FP(Phys.)d(R)n(ev.)g(L)n(ett.)p FQ(,)e(59:1829{183)q(2,)k(1987.)84 2377 y([44])25 b(J.)20 b(Bricmon)o(t)e (and)j(A.)f(Kupiainen.)34 b(Phase)22 b(transition)e(in)h(the)f(3)p FF(d)i FQ(random)e(\014eld)g(Ising)185 2437 y(mo)q(del.)g FP(Commun.)d(Math.) g(Phys.)p FQ(,)e(116:539{572)q(,)k(1988.)84 2538 y([45])25 b(J.)d(Bricmon)o(t,)g(K.)g(Kuro)q(da,)k(and)d(J.)g(L.)g(Leb)q(o)o(witz.)41 b(The)23 b(structure)f(of)h(Gibbs)h(states)185 2599 y(and)c(phase)g(co)q (existence)e(for)h(non-symmetric)e(con)o(tin)o(uum)g(Widom-Ro)o(wlinson)i(mo) q(del.)185 2659 y FP(Z.Wahrscheinlichkeitsthe)n(orie)f(V)l(erw.)h(Geb.)p FQ(,)d(67:121{138,)j(1984.)938 2784 y(250)p eop %%Page: 251 251 bop 84 91 a FQ([46])25 b(J.)20 b(Bricmon)o(t,)e(K.)i(Kuro)q(da,)i(and)g(J.)e (L.)g(Leb)q(o)o(witz.)34 b(First)20 b(order)g(phase)h(transitions)g(in)185 152 y(lattice)f(and)i(con)o(tin)o(uous)f(systems:)31 b(Extension)21 b(of)h(Pirogo)o(v-Sinai)g(theory)l(.)36 b FP(Commun.)185 212 y(Math.)17 b(Phys.)p FQ(,)e(101:501{538,)k(1985.)84 313 y([47])25 b(J.)17 b(Bricmon)o(t)e(and)j(J.)f(Sla)o(wn)o(y)l(.)24 b(First)17 b(order)h(phase)g(transitions)g(and)g(p)q(erturbation)g(the-)185 374 y(ory)l(.)f(In)c(T.)h(C.)f(Dorlas,)i(N.)d(M.)h(Hugenholtz,)h(and)g(M.)f (Winnink,)g(editors,)g FP(Statistic)n(al)j(Me-)185 434 y(chanics)f(and)g (Field)h(The)n(ory:)k(Mathematic)n(al)15 b(Asp)n(e)n(cts)f(\(Pr)n(o)n(c)n(e)n (e)n(dings,)g(Gr)n(oningen)i(1985\))p FQ(,)185 494 y(Berlin{Heidelb)q (erg{New)i(Y)l(ork,)k(1986.)g(Springer-V)l(erlag)f(\(Lecture)g(Notes)g(in)g (Ph)o(ysics)185 554 y(#257\).)84 656 y([48])k(J.)15 b(Bricmon)o(t)e(and)j(J.) f(Sla)o(wn)o(y)l(.)k(Phase)d(transitions)g(in)g(systems)e(with)h(a)h (\014nite)f(n)o(um)o(b)q(er)f(of)185 716 y(dominan)o(t)h(ground)i(states.)22 b FP(J.)17 b(Stat.)h(Phys.)p FQ(,)d(54:89{161,)j(1989.)84 818 y([49])25 b(D.)14 b(A.)f(Bro)o(wne)h(and)h(P)l(.)f(Kleban.)j(Equilibrium)12 b(statistical)h(mec)o(hanics)f(for)j(kinetic)e(phase)185 878 y(transitions.)21 b FP(Phys.)c(R)n(ev..)p FQ(,)f(A40:1615{1626,)j(1989.)84 980 y([50])25 b(A.)20 b(D.)i(Bruce)e(and)j(A.)d(Aharon)o(y)l(.)37 b(Coupled)22 b(order)g(parameters,)f(symmetry-breaking)185 1040 y(irrelev)m(an)o(t)14 b(scaling)i(\014elds,)g(and)g(tetracritical)f(p)q (oin)o(ts.)21 b FP(Phys.)c(R)n(ev.)p FQ(,)f(B11:478{499,)i(1975.)84 1142 y([51])25 b(W.)16 b(Bryc.)k(On)d(the)f(large)g(deviation)g(principle)e (for)j(stationary)g(w)o(eakly)e(dep)q(enden)o(t)h(ran-)185 1202 y(dom)f(\014elds.)21 b FP(A)o(nn.)d(Pr)n(ob.)p FQ(,)d(20:1004{103)q(0,)k (1992.)84 1303 y([52])25 b(D.)16 b(Brydges)g(and)h(T.)f(Sp)q(encer.)22 b(Self-a)o(v)o(oiding)15 b(w)o(alks)i(in)f(5)h(or)f(more)g(dimensions.)k FP(Com-)185 1364 y(mun.)d(Math.)g(Phys.)p FQ(,)f(97:125{148,)j(1985.)84 1465 y([53])25 b(D.)19 b(Brydges)h(and)g(H.-T.)f(Y)l(au.)32 b(Grad)20 b FF(')g FQ(p)q(erturbations)h(of)f(massless)f(Gaussian)i (\014elds.)185 1526 y FP(Commun.)c(Math.)g(Phys.)p FQ(,)e(129:351{392)q(,)k (1990.)84 1627 y([54])25 b(T.)16 b(W.)h(Burkhardt.)23 b(Random-\014eld)17 b(singularities)f(in)g(p)q(osition-space)i(renormalization-)185 1687 y(group)f(transformations.)k FP(Phys.)c(R)n(ev.)g(L)n(ett.)p FQ(,)f(43:1629{1631)q(,)j(1979.)84 1789 y([55])25 b(T.)13 b(W.)h(Burkhardt)g (and)g(J.)g(M.)f(J.)g(v)m(an)i(Leeu)o(w)o(en.)h(Progress)f(and)g(problems)e (in)g(real-space)185 1849 y(renormalization.)25 b(In)18 b(T.)g(W.)g (Burkhardt)g(and)h(J.)f(M.)f(J.)h(v)m(an)h(Leeu)o(w)o(en,)e(editors,)h FP(R)n(e)n(al-)185 1910 y(Sp)n(ac)n(e)f(R)n(enormalization)p FQ(.)f(Springer-V)l(erlag,)f(Berlin{Heidelb)q(erg{New)f(Y)l(ork,)h(1982.)84 2011 y([56])25 b(C.)16 b(Cammarota.)k(The)c(large)g(blo)q(c)o(k)g(spin)g(in)o (teraction.)k FP(Nuovo)e(Cim.)p FQ(,)e(B96:1{16,)h(1986.)84 2113 y([57])25 b(J.)12 b(L.)h(Cardy)l(.)k(One-dimensional)11 b(mo)q(dels)h(with)h(1)p FF(=r)1159 2095 y FH(2)1192 2113 y FQ(in)o(teractions.)j FP(J.)d(Phys.)p FQ(,)g(A14:1407{)185 2173 y(1415,)k(1981.)84 2275 y([58])25 b(E.)18 b(A.)g(Carlen)h(and)g(A.)f (So\013er.)29 b(En)o(trop)o(y)18 b(pro)q(duction)i(b)o(y)e(blo)q(c)o(k)g (spin)h(summation)d(and)185 2335 y(cen)o(tral)f(limit)e(theorems.)20 b FP(Commun.)e(Math.)f(Phys.)p FQ(,)e(140:339{371,)k(1992.)84 2437 y([59])25 b(M.)c(Cassandro)j(and)f(E.)f(Olivieri.)36 b(Renormalization) 21 b(group)i(and)g(analyticit)o(y)d(in)i(one)185 2497 y(dimension:)d(a)d(pro) q(of)g(of)g(Dobrushin's)g(theorem.)i FP(Commun.)f(Math.)f(Phys.)p FQ(,)e(80:255{269,)185 2557 y(1981.)938 2784 y(251)p eop %%Page: 252 252 bop 84 91 a FQ([60])25 b(M.)f(Cassandro,)k(E.)d(Olivieri,)f(A.)g(P)o (ellegrinotti,)g(and)i(E.)e(Presutti.)47 b(Existence)23 b(and)185 152 y(uniqueness)12 b(of)g(DLR)h(measures)f(for)h(un)o(b)q(ounded)g(spin)f (systems.)i FP(Z.)g(Wahrscheinlichkeit-)185 212 y(sthe)n(orie)j(verw.)h(Geb.) p FQ(,)e(41:313{334,)j(1978.)84 312 y([61])25 b(N.)12 b(N.)316 299 y(\024)310 312 y(Cenco)o(v.)j FP(Statistic)n(al)h(De)n(cision)e(R)o(ules) h(and)f(Optimal)h(Infer)n(enc)n(e)p FQ(.)h(American)11 b(Math-)185 372 y(ematical)21 b(So)q(ciet)o(y)h(\(T)l(ranslations)i(of)f(Mathematical)e (Monographs,)26 b(V)l(ol.)c(53\),)j(Pro)o(vi-)185 432 y(dence,)15 b(R.I.,)f(1982.)84 533 y([62])25 b(S.)18 b(Cho)o(wla)h(and)g(M.)f(Co)o(wles.) 28 b(Remarks)17 b(on)i(equations)g(related)f(to)h(F)l(ermat's)d(last)j(the-) 185 593 y(orem.)i(In)c(N.)f(Koblitz,)g(editor,)g FP(Numb)n(er)i(The)n(ory)f (R)n(elate)n(d)h(to)g(F)l(ermat's)f(L)n(ast)h(The)n(or)n(em)p FQ(,)185 653 y(Boston{Basel{Stuttgart,)f(1982.)g(Birkh\177)-24 b(auser.)84 754 y([63])25 b(F.)15 b(S.)h(Cohen)g(and)h(D.)f(B.)f(Co)q(op)q (er.)22 b(Simple)14 b(parallel)h(hierarc)o(hical)g(and)h(relaxation)g(algo-) 185 814 y(rithms)d(for)h(segmen)o(ting)f(noncausal)i(Mark)o(o)o(vian)f (random)g(\014elds.)k FP(IEEE)d(T)l(r)n(ans.)g(Pattern)185 874 y(A)o(nal.)j(Machine)g(Intel)r(l.)p FQ(,)g(9:195{219,)g(1987.)84 974 y([64])25 b(J.)20 b(E.)h(Cohen,)h(Y.)e(Iw)o(asa,)i(G.)e(Rautu,)j(M.)d(B.) g(Rusk)m(ai,)h(E.)g(Seneta,)g(and)h(G.)f(Zbagan)o(u.)185 1034 y(Relativ)o(e)13 b(en)o(trop)o(y)i(under)h(mappings)f(b)o(y)g(sto)q(c)o (hastic)h(matrices.)i(T)l(o)e(app)q(ear)g(in)g FP(Lin.)g(A)o(lg.)185 1095 y(Appl.)84 1195 y FQ([65])25 b(F.)c(Comets.)39 b(Grandes)23 b(d)o(\023)-23 b(eviations)22 b(p)q(our)i(des)e(c)o(hamps)f(de)h(Gibbs)h(sur) g Fq(Z)1633 1174 y FD(d)1653 1195 y FQ(.)40 b FP(Comptes)185 1255 y(R)n(endus)17 b(A)n(c)n(ad.)g(Sci.)h(Paris)f(S)o(\023)-24 b(erie)18 b(I)p FQ(,)d(303:511{513)q(,)k(1986.)84 1355 y([66])25 b(I.)15 b(P)l(.)i(Cornfeld,)f(S.)g(V.)g(F)l(omin,)e(and)k(Y)l(a.)e(G.)g (Sinai.)22 b FP(Er)n(go)n(dic)17 b(The)n(ory)p FQ(.)k(Springer-V)l(erlag,)185 1416 y(New)15 b(Y)l(ork{Heidelb)q(erg{Berlin,)f(1982.)84 1516 y([67])25 b(I.)17 b(Csisz\023)-24 b(ar.)26 b(Eine)17 b (informationstheoretisc)o(he)f(Ungleic)o(h)o(ung)g(und)i(ihre)f(An)o(w)o (endung)h(auf)185 1576 y(den)f(Bew)o(eis)e(der)i(Ergo)q(dizit\177)-24 b(at)18 b(v)o(on)f(Mark)o(o\013sc)o(hen)f(Ketten.)23 b FP(Magyar)18 b(T)l(ud.)g(A)o(kad.)g(Mat.)185 1636 y(Kutat\023)-25 b(o)18 b(Int.)g(K\177)-25 b(ozl.)p FQ(,)16 b(8:85{108,)i(1963.)23 b([See)15 b(also)i FP(Math.)g(R)n(eviews)k FM(29)p FQ(,)16 b(#1671)h(\(1965\).].)84 1737 y([68])25 b(I.)16 b(Csisz\023)-24 b(ar.)26 b FF(I)t FQ(-div)o(ergence)16 b(geometry)g(of)i(probabilit)o(y)e (distributions)i(and)g(minim)o(ization)185 1797 y(problems.)h FP(A)o(nn.)g(Pr)n(ob.)p FQ(,)c(3:146{158,)j(1975.)84 1897 y([69])25 b(I.)15 b(Csisz\023)-24 b(ar.)23 b(Sano)o(v)17 b(prop)q(ert)o(y)l(,)f (generalized)g FF(I)t FQ(-pro)s(jection)f(and)j(a)f(conditional)f(limit)e (the-)185 1957 y(orem.)19 b FP(A)o(nn.)g(Pr)n(ob.)p FQ(,)c(12:768{793,)k (1984.)84 2058 y([70])25 b(H.)c(A.)f(M.)i(Dani)o(\177)-23 b(els)21 b(and)i(A.)d(C.)i(D.)g(v)m(an)g(En)o(ter.)37 b(Di\013eren)o(tiabilit)o(y)19 b(prop)q(erties)j(of)g(the)185 2118 y(pressure)16 b(in)g(lattice)f(systems.) 20 b FP(Commun.)d(Math.)g(Phys.)p FQ(,)e(71:65{76,)k(1980.)84 2218 y([71])25 b(J.)19 b(de)h(Coninc)o(k)g(and)h(C.)e(M.)h(Newman.)31 b(The)20 b(magnetization-energy)f(scaling)h(limit)d(in)185 2279 y(high)f(dimension.)k FP(J.)d(Stat.)h(Phys.)p FQ(,)d(59:1451{1467)q(,)j (1990.)84 2379 y([72])25 b(K.)20 b(Dec)o(k)o(er,)h(A.)f(Hasenfratz,)j(and)f (P)l(.)f(Hasenfratz.)36 b(Singular)21 b(renormalization)f(group)185 2439 y(transformations)c(and)h(\014rst)f(order)h(phase)f(transitions)h(\(I)q (I\).)e(Mon)o(te)h(Carlo)g(renormaliza-)185 2499 y(tion)g(group)h(results.)k FP(Nucl.)e(Phys.)p FQ(,)c(B295)i([FS21]:21{35,)g(1988.)84 2600 y([73])25 b(C.)e(Dellac)o(herie)e(and)i(P)l(.-A.)g(Mey)o(er.)40 b FP(Pr)n(ob)n(abilities)24 b(and)g(Potential)p FQ(.)44 b(North-Holland,)185 2660 y(Amsterdam{Ne)o(w)14 b(Y)l(ork{Oxford,)i(1978.)938 2784 y(252)p eop %%Page: 253 253 bop 84 95 a FQ([74])25 b(P)l(.)16 b(D)o(\023)-23 b(enes.)414 83 y(\177)408 95 y(Ub)q(er)17 b(die)f(Diophan)o(tisc)o(he)g(Gleic)o(h)o(ung)g FF(x)1184 77 y FD(l)1208 95 y FQ(+)11 b FF(y)1283 77 y FD(l)1311 95 y FQ(=)k FF(cz)1410 77 y FD(l)1423 95 y FQ(.)23 b FP(A)n(cta)18 b(Math.)p FQ(,)e(88:241{)185 156 y(251,)h(1952.)84 256 y([75])25 b(J.-D.)e(Deusc)o(hel)f(and)i(D.)g(W.)f(Stro)q(o)q(c)o(k.)43 b FP(L)n(ar)n(ge)23 b(Deviations)p FQ(.)43 b(Academic)21 b(Press,)k(San)185 316 y(Diego{London,)18 b(1989.)84 416 y([76])25 b(L.)14 b(E.)g(Dic)o(kson.)j FP(History)e(of)g(the)h(The)n(ory)f(of)g(Numb)n(ers)p FQ(,)f(v)o(olume)e(I)q (I.)17 b(Chelsea,)d(New)g(Y)l(ork,)185 476 y(1971.)84 576 y([77])25 b(E.)16 b(L.)g(Dinaburg)h(and)g(A.)e(E.)h(Mazel.)k(Lo)o(w-temp)q(erature)c (phase)h(transitions)f(in)g(ANNNI)185 636 y(mo)q(del.)31 b(In)19 b(M.)h(Mebkhout)f(and)i(R.)e(S)o(\023)-23 b(eneor,)21 b(editors,)f FP(Pr)n(o)n(c)n(e)n(e)n(dings)g(8th)h(International)185 696 y(Congr)n(ess)c(on)h(Mathematic)n(al)f(Physics)p FQ(,)f(Singap)q(ore,)h (1987.)g(W)l(orld)g(Scien)o(ti\014c.)84 797 y([78])25 b(E.)16 b(L.)g(Dinaburg)h(and)g(A.)e(E.)h(Mazel.)k(Analysis)15 b(of)i(lo)o(w-temp)q (erature)d(phase)j(diagram)f(of)185 857 y(the)g(micro)q(em)n(ulsion)d(mo)q (del.)20 b FP(Commun.)e(Math.)f(Phys.)p FQ(,)e(125:25{42,)j(1989.)84 957 y([79])25 b(E.)11 b(L.)g(Dinaburg,)i(A.)e(E.)g(Mazel,)g(and)h(Y)l(a.)f (G.)g(Sinai.)i(ANNNI)c(mo)q(del)h(and)i(con)o(tour)g(mo)q(dels)185 1017 y(with)k(in)o(teractions.)23 b(In)17 b(S.)f(P)l(.)h(No)o(vik)o(o)o(v,)e (editor,)h FP(Mathematic)n(al)j(Physics)f(R)n(eviews,)g(Sov.)185 1077 y(Sci.)g(R)n(eviews)g(Se)n(ct.)g(C,)f(V)l(ol.)i(6)p FQ(.)c(Gordon)j(and) f(Breac)o(h,)d(New)i(Y)l(ork,)f(1986.)84 1177 y([80])25 b(E.)16 b(L.)h(Dinaburg)g(and)g(Y)l(a.)f(G.)g(Sinai.)22 b(An)16 b(analysis)h(of)g (ANNNI)d(mo)q(del)i(b)o(y)g(Peierl's)f([)p FP(sic)s FQ(])185 1237 y(con)o(tour)h(metho)q(d.)21 b FP(Commun.)c(Math.)g(Phys.)p FQ(,)e(98:119{144,)k(1985.)84 1337 y([81])25 b(P)l(.)37 b(G.)h(L.)g(Diric)o (hlet.)84 b(M)o(\023)-23 b(emoire)35 b(sur)k(l'imp)q(ossibilit)n(\023)-23 b(e)35 b(de)j(quelques)e(\023)-23 b(equations)185 1398 y(ind)o(\023)g (etermin)o(\023)g(ee)o(s)18 b(du)j(cinqui)o(\022)-23 b(eme)17 b(degr)o(\023)-23 b(e.)34 b FP(J.)21 b(R)n(eine)g(A)o(ngew.)i(Math.)e(\(Cr)n (el)r(le's)i(Journal\))p FQ(,)185 1458 y(3:354{376,)18 b(1828.)84 1558 y([82])25 b(R.)c(L.)g(Dobrushin.)38 b(Existence)20 b(of)i(a)g(phase)g (transition)g(in)f(the)g(t)o(w)o(o-dimensional)f(and)185 1618 y(three-dimensional)14 b(Ising)i(mo)q(dels.)k FP(Soviet)f(Phys.)e(Doklady)p FQ(,)f(10:111{113,)i(1965.)84 1718 y([83])25 b(R.)c(L.)i(Dobrushin.)39 b(The)23 b(description)e(of)i(a)f(random)g(\014eld)g(b)o(y)f(means)h(of)g (conditional)185 1778 y(probabilities)e(and)j(conditions)e(of)h(its)f (regularit)o(y)l(.)36 b FP(The)n(or.)22 b(Pr)n(ob.)g(Appl.)p FQ(,)g(13:197{224,)185 1838 y(1968.)84 1938 y([84])j(R.)18 b(L.)i(Dobrushin.)31 b(The)19 b(problem)f(of)i(uniqueness)f(of)g(a)h(Gibbs)g (random)f(\014eld)f(and)i(the)185 1999 y(problem)14 b(of)j(phase)g (transitions.)k FP(F)l(unct.)e(A)o(nal.)f(Appl.)p FQ(,)e(2:302{312,)j(1968.) 84 2099 y([85])25 b(R.)f(L.)g(Dobrushin.)46 b(Gibbs)25 b(states)g(describing) f(co)q(existence)f(of)i(phases)g(for)g(a)f(three-)185 2159 y(dimensional)14 b(Ising)i(mo)q(del.)k FP(The)n(or.)d(Pr)n(ob.)g(Appl.)p FQ(,)f(17:582{600,)j(1972.)84 2259 y([86])25 b(R.)20 b(L.)h(Dobrushin.)35 b(Gaussian)22 b(random)f(\014elds)f({)h(Gibbsian)g(p)q(oin)o(t)g(of)g(view.) 34 b(In)21 b(R.)f(L.)185 2319 y(Dobrushin)12 b(and)f(Y)l(a.)g(G.)g(Sinai,)g (editors,)h FP(Multic)n(omp)n(onent)i(R)n(andom)d(Systems)i(\(A)n(dvanc)n(es) 185 2379 y(in)h(Pr)n(ob)n(ability)g(and)g(R)n(elate)n(d)g(T)l(opics,)h(V)l (ol.)g(6\))p FQ(,)e(pages)h(119{152,)h(New)e(Y)l(ork{Basel,)f(1980.)185 2439 y(Marcel)j(Dekk)o(er.)84 2539 y([87])25 b(R.)c(L.)h(Dobrushin,)h(J.)f (Kolafa,)h(and)f(S.)g(B.)f(Shlosman.)37 b(Phase)22 b(diagram)f(of)h(the)g(t)o (w)o(o-)185 2600 y(dimensional)c(Ising)i(an)o(tiferromagnet)f (\(computer-assisted)g(pro)q(of)s(\).)34 b FP(Commun.)20 b(Math.)185 2660 y(Phys.)p FQ(,)15 b(102:89{103,)k(1985.)938 2784 y(253)p eop %%Page: 254 254 bop 84 91 a FQ([88])25 b(R.)15 b(L.)g(Dobrushin)h(and)g(M.R.)e(Martirosy)o (an.)20 b(Non\014nite)15 b(p)q(erturbations)h(of)g(Gibbs)g(\014elds.)185 152 y FP(The)n(or.)g(Math.)h(Phys.)p FQ(,)f(74:10{20,)i(1988.)84 253 y([89])25 b(R.)18 b(L.)h(Dobrushin)h(and)g(M.R.)e(Martirosy)o(an.)30 b(P)o(ossibilit)o(y)17 b(of)i(high-temp)q(erature)g(phase)185 313 y(transitions)14 b(due)f(to)h(the)g(man)o(y-particle)d(nature)j(of)g(the) f(p)q(oten)o(tial.)k FP(The)n(or.)d(Math.)h(Phys.)p FQ(,)185 374 y(75:443{448,)j(1988.)84 475 y([90])25 b(R.)11 b(L.)i(Dobrushin)g(and)g (E.)f(A.)f(P)o(ec)o(herski.)i(Uniqueness)f(condition)g(for)g(\014nitely)g (dep)q(enden)o(t)185 535 y(random)f(\014elds.)i(In)e FP(R)n(andom)h(Fields.)i (Eszter)n(gom)f(\(Hungary\))g(1979,)g(V)l(ol.)h(I)p FQ(,)d(Amsterdam,)185 596 y(1981.)17 b(North-Holland.)84 697 y([91])25 b(R.)14 b(L.)h(Dobrushin)h (and)g(E.)f(A.)f(P)o(ec)o(herski.)j(A)e(criterion)f(for)h(the)g(uniqueness)f (of)i(Gibbsian)185 758 y(\014elds)g(in)g(the)g(non-compact)h(case.)22 b(In)16 b FP(Pr)n(ob.)h(Th.)g(and)h(Math.)g(Statistics)p FQ(,)f(v)o(olume)d (LNM)185 818 y(1021,)j(pages)g(97{110,)h(1983.)84 919 y([92])25 b(R.)15 b(L.)g(Dobrushin)h(and)g(S.)f(B.)g(Shlosman.)k(Nonexistence)14 b(of)i(one-)g(and)g(t)o(w)o(o-dimensional)185 980 y(Gibbs)22 b(\014elds)g(with)g(noncompact)f(group)i(of)g(con)o(tin)o(uous)f(symmetri)o (es.)36 b(In)21 b(R.)h(L.)g(Do-)185 1040 y(brushin)c(and)h(Y)l(a.)f(G.)g (Sinai,)g(editors,)g FP(Multic)n(omp)n(onent)i(R)n(andom)f(Systems)g(\(A)n (dvanc)n(es)185 1100 y(in)14 b(Pr)n(ob)n(ability)g(and)g(R)n(elate)n(d)g(T)l (opics,)h(V)l(ol.)g(6\))p FQ(,)e(pages)h(199{210,)h(New)e(Y)l(ork{Basel,)f (1980.)185 1160 y(Marcel)j(Dekk)o(er.)84 1262 y([93])25 b(R.)20 b(L.)i(Dobrushin)g(and)g(S.)e(B.)h(Shlosman.)35 b(Completely)19 b(analytic)i(random)g(\014elds.)35 b(In)185 1322 y FP(Statistic)n(al)18 b(Me)n(chanics)g(and)g(Dynamic)n(al)f(Systems)p FQ(,)f(Boston)h(etc.,)e (1985.)i(Birkh\177)-24 b(auser.)84 1424 y([94])25 b(R.)17 b(L.)g(Dobrushin)h (and)g(S.)g(B.)e(Shlosman.)24 b(Constructiv)o(e)17 b(criterion)g(for)g(the)g (uniqueness)185 1484 y(of)i(a)h(gibbs)g(\014eld.)31 b(In)19 b FP(Statistic)n(al)i(Me)n(chanics)g(and)g(Dynamic)n(al)f(Systems)p FQ(,)g(Boston)h(etc.,)185 1544 y(1985.)c(Birkh\177)-24 b(auser.)84 1646 y([95])25 b(R.)17 b(L.)h(Dobrushin)h(and)g(S.)e(B.)g(Shlosman.)26 b(The)18 b(problem)f(of)h(translation)h(in)o(v)m(ariance)e(of)185 1706 y(Gibbs)e(states)g(at)g(lo)o(w)f(temp)q(eratures.)k FP(Sov.)e(Sci.)h(R)n (ev.)f(C)f(Math.)h(Phys.)p FQ(,)e(5:53{196,)j(1985.)84 1808 y([96])25 b(R.)18 b(L.)g(Dobrushin)i(and)f(S.)g(B.)e(Shlosman.)28 b(Completely)16 b(analytical)i(in)o(teractions:)26 b(con-)185 1868 y(structiv)o(e)14 b(description.)21 b FP(J.)c(Stat.)h(Phys.)p FQ(,)d(46:983{1014)q(,)j(1987.)84 1970 y([97])25 b(R.)13 b(L.)g(Dobrushin)h (and)g(M.)f(Zahradn)-5 b(\023)-19 b(\020k.)17 b(Phase)d(diagrams)f(for)h(con) o(tin)o(uous)f(spin)h(systems.)185 2030 y(In)22 b(R.)g(L.)g(Dobrushin,)j (editor,)e FP(Mathematic)n(al)g(Pr)n(oblems)h(of)f(Statistic)n(al)h(Physics)f (and)185 2090 y(Dynamics)p FQ(.)15 b(Reidel,)g(1985.)84 2192 y([98])25 b(Y.)11 b(Domar.)j(On)e(the)g(Diophan)o(tine)g(equation)g FE(j)p FF(Ax)1125 2174 y FD(n)1150 2192 y FE(\000)s FF(B)s(y)1258 2174 y FD(n)1280 2192 y FE(j)i FQ(=)g(1.)g FP(Math.)g(Sc)n(and.)p FQ(,)f(2:29{32,)185 2252 y(1954.)84 2354 y([99])25 b(M.)14 b(D.)g(Donsk)o(er)h(and)h(S.)e(R.)g(S.)h(V)l(aradhan.)20 b(Asymptotic)12 b(ev)m(aluation)j(of)h(certain)e(Mark)o(o)o(v)185 2414 y(pro)q(cess)j(exp)q (ectations)f(for)g(large)g(time,)e(I.)21 b FP(Comm.)c(Pur)n(e)g(Appl.)h (Math.)p FQ(,)d(28:1{47,)j(1975.)60 2516 y([100])25 b(M.)14 b(D.)g(Donsk)o(er)h(and)h(S.)e(R.)g(S.)h(V)l(aradhan.)20 b(Asymptotic)12 b(ev)m(aluation)j(of)h(certain)e(Mark)o(o)o(v)185 2576 y(pro)q(cess)20 b(exp)q(ectations)g(for)g(large)f(time,)f(I)q(I.)31 b FP(Comm.)20 b(Pur)n(e)h(Appl.)g(Math.)p FQ(,)e(28:279{301,)185 2636 y(1975.)938 2784 y(254)p eop %%Page: 255 255 bop 60 91 a FQ([101])25 b(M.)14 b(D.)g(Donsk)o(er)h(and)h(S.)e(R.)g(S.)h(V)l (aradhan.)20 b(Asymptotic)12 b(ev)m(aluation)j(of)h(certain)e(Mark)o(o)o(v) 185 152 y(pro)q(cess)k(exp)q(ectations)g(for)h(large)f(time,)e(I)q(I)q(I.)26 b FP(Comm.)19 b(Pur)n(e)g(Appl.)h(Math.)p FQ(,)d(29:389{461,)185 212 y(1976.)60 313 y([102])25 b(M.)14 b(D.)g(Donsk)o(er)h(and)h(S.)e(R.)g(S.) h(V)l(aradhan.)20 b(Asymptotic)12 b(ev)m(aluation)j(of)h(certain)e(Mark)o(o)o (v)185 374 y(pro)q(cess)19 b(exp)q(ectations)f(for)g(large)g(time,)f(IV.)26 b FP(Comm.)19 b(Pur)n(e)g(Appl.)g(Math.)p FQ(,)f(36:183{212,)185 434 y(1983.)60 535 y([103])25 b(T.)11 b(C.)g(Dorlas)h(and)g(A.)f(C.)g(D.)g(v) m(an)h(En)o(ter.)h(Non-Gibbsian)f(limit)d(for)j(large-blo)q(c)o(k)f(ma)s (jorit)o(y-)185 596 y(spin)16 b(transformations.)21 b FP(J.)c(Stat.)h(Phys.)p FQ(,)e(55:171{181,)i(1989.)60 697 y([104])25 b(N.)13 b(Dunford)i(and)g(J.)f (T.)g(Sc)o(h)o(w)o(artz.)i FP(Line)n(ar)f(Op)n(er)n(ators)p FQ(.)i(In)o(terscience,)11 b(New)j(Y)l(ork,)g(1958.)60 799 y([105])25 b(F.)f(Dunlop.)46 b(Correlation)25 b(inequalities)d(for)j(m)o (ulticom)o(p)q(onen)o(t)d(rotators.)47 b FP(Commun.)185 859 y(Math.)17 b(Phys.)p FQ(,)e(49:247{256,)k(1976.)60 961 y([106])25 b(F.)e(Dunlop)i(and)g(C.)f(M.)f(Newman.)44 b(Multicomp)q(onen)o(t)22 b(\014eld)h(theories)h(and)h(classical)185 1021 y(rotators.)d FP(Commun.)17 b(Math.)h(Phys.)p FQ(,)d(44:223{235,)k(1975.)60 1123 y([107])25 b(E.)18 b(B.)g(Dynkin.)28 b(Su\016cien)o(t)18 b(statistics)g(and)i(extreme)c(p)q(oin)o(ts.)29 b FP(A)o(nn.)20 b(Pr)n(ob.)p FQ(,)f(6:705{730,)185 1183 y(1978.)60 1285 y([108])25 b(R.)12 b(E.)h(Edw)o(ards.)k FP(F)l(ourier)d(Series:)21 b(A)15 b(Mo)n(dern)f(Intr)n(o)n(duction)p FQ(,)e(v)o(olume)f(I.)16 b(Holt,)c(Rinehart)185 1345 y(and)k(Winston,)h(New)e(Y)l(ork,)h(1967.)60 1447 y([109])25 b(R.)h(G.)g(Edw)o(ards)i(and)f(A.)f(D.)h(Sok)m(al.)53 b(Generalization)26 b(of)h(the)f(Fortuin-Kasteleyn-)185 1507 y(Sw)o(endsen-Wang)35 b(represen)o(tation)f(and)h(Mon)o(te)f(Carlo)h (algorithm.)75 b FP(Phys.)34 b(R)n(ev.)p FQ(,)185 1567 y(D38:2009{2012)q(,)19 b(1988.)60 1669 y([110])25 b(R.)11 b(S.)h(Ellis.)h FP(Entr)n(opy,)g(L)n(ar)n (ge)g(Deviations)h(and)g(Statistic)n(al)g(Me)n(chanics)p FQ(.)h(Springer-V)l (erlag,)185 1729 y(New)g(Y)l(ork{Heidelb)q(erg{Berlin{T)l(oky)o(o,)f(1985.)60 1831 y([111])25 b(J.)14 b(H.)g(Ev)o(ertse.)k FP(Upp)n(er)e(Bounds)g(for)g (the)h(Numb)n(ers)f(of)g(Solutions)h(of)f(Diophantine)h(Equa-)185 1891 y(tions)p FQ(.)g(Mathematisc)o(h)12 b(Cen)o(trum)g(\(Mathematical)g(Cen) o(tre)h(T)l(racts)i(#168\),)f(Amsterdam,)185 1951 y(1983.)60 2053 y([112])25 b(G.)20 b(F)l(elder)g(and)h(J.)f(F)l(r\177)-24 b(ohlic)o(h.)34 b(In)o(tersection)19 b(prop)q(erties)i(of)g(simple)d(random)i (w)o(alks:)30 b(A)185 2113 y(renormalization)14 b(group)j(approac)o(h.)22 b FP(Commun.)c(Math.)f(Phys.)p FQ(,)e(97:111{124,)k(1985.)60 2215 y([113])25 b(B.)16 b(U.)h(F)l(elderhof.)24 b(Phase)19 b(transitions)f(in)f(one-dimensional)f(cluster-in)o(teraction)g(\015uids.)185 2275 y(I)q(I)q(I.)f(Correlation)h(functions.)22 b FP(A)o(nn.)c(Phys.)p FQ(,)d(58:281{300,)k(1970.)60 2377 y([114])25 b(B.)15 b(U.)h(F)l(elderhof)g (and)h(M.)f(E.)h(Fisher.)k(Phase)d(transitions)f(in)f(one-dimensional)g (cluster-)185 2437 y(in)o(teraction)f(\015uids.)h(I)q(I.)f(Simple)f (logarithmic)g(mo)q(del.)20 b FP(A)o(nn.)e(Phys.)p FQ(,)e(58:268{280,)j (1970.)60 2538 y([115])25 b(R.)12 b(F)l(ern\023)-24 b(andez,)13 b(J.)g(F)l(r\177)-24 b(ohlic)o(h,)12 b(and)i(A.)e(D.)h(Sok)m(al.)k FP(R)n(andom)d(Walks,)h(Critic)n(al)g(Phenomena,)185 2599 y(and)22 b(T)l(riviality)h(in)g(Quantum)g(Field)g(The)n(ory)p FQ(.)36 b(Springer-V)l(erlag,)22 b(Berlin{Heidelb)q(erg{)185 2659 y(New)15 b(Y)l(ork,)h(1992.)938 2784 y(255)p eop %%Page: 256 256 bop 60 91 a FQ([116])25 b(M.)15 b(E.)g(Fisher.)20 b(On)15 b(discon)o(tin)o (uit)o(y)f(of)i(the)f(pressure.)20 b FP(Commun.)d(Math.)g(Phys.)p FQ(,)e(26:6{14,)185 152 y(1972.)60 251 y([117])25 b(M.)17 b(E.)i(Fisher.)27 b(Crosso)o(v)o(er)18 b(e\013ects)h(and)g(op)q(erator)g(expansions.)29 b(In)18 b(J.)g(D.)g(Gun)o(ton)h(and)185 311 y(M.)c(S.)h(Green,)f(editors,)h FP(R)n(enormalization)h(Gr)n(oup)f(in)i(Critic)n(al)f(Phenomena)h(and)g (Quan-)185 372 y(tum)e(Field)g(The)n(ory:)21 b(Pr)n(o)n(c)n(e)n(e)n(dings)15 b(of)h(a)g(Confer)n(enc)n(e)p FQ(,)f(pages)g(65{68.)i(T)l(emple)12 b(Univ)o(ersit)o(y)l(,)185 432 y(Philadelphia,)j(1974.)60 531 y([118])25 b(M.)12 b(E.)i(Fisher.)i(Scaling,)d(univ)o(ersalit)o(y)e(and)j (renormalization)e(group)j(theory)l(.)h(In)d(F.)g(J.)g(W.)185 592 y(Hahne,)18 b(editor,)h FP(Critic)n(al)h(Phenomena)h(\(Stel)r(lenb)n (osch)i(1982\))p FQ(,)18 b(pages)i(1{139.)g(Springer-)185 652 y(V)l(erlag)15 b(\(Lecture)h(Notes)g(in)g(Ph)o(ysics)g(#186\),)g (Berlin{Heidelb)q(erg{New)e(Y)l(ork,)h(1983.)60 752 y([119])25 b(M.)16 b(E.)g(Fisher)g(and)i(A.)e(N.)g(Berk)o(er.)21 b(Scaling)16 b(for)i(\014rst-order)f(phase)g(transitions)h(in)e(ther-)185 812 y(mo)q(dynamic)d(and)k(\014nite)f(systems.)k FP(Phys.)d(R)n(ev.)p FQ(,)e(B26:2507{2513)q(,)k(1982.)60 911 y([120])25 b(M.)16 b(E.)g(Fisher)g(and)h(B.)f(U.)g(F)l(elderhof.)21 b(Phase)d(transitions)f(in)f (one-dimensional)g(cluster-)185 972 y(in)o(teraction)f(\015uids.)h(IA.)f (Thermo)q(dynamics.)k FP(A)o(nn.)f(Phys.)p FQ(,)d(58:176{216,)k(1970.)60 1071 y([121])25 b(M.)16 b(E.)g(Fisher)g(and)h(B.)f(U.)g(F)l(elderhof.)21 b(Phase)d(transitions)f(in)f(one-dimensional)g(cluster-)185 1132 y(in)o(teraction)f(\015uids.)h(IB.)f(Critical)g(b)q(eha)o(vior.)21 b FP(A)o(nn.)d(Phys.)p FQ(,)d(58:217{267,)k(1970.)60 1231 y([122])25 b(H.)15 b(F\177)-24 b(ollmer.)20 b(On)d(en)o(trop)o(y)f(and)h(information)f (gain)h(in)f(random)g(\014elds.)22 b FP(Z.)c(Wahrschein-)185 1291 y(lichkeitsthe)n(orie)h(verw.)f(Geb.)p FQ(,)e(26:207{217,)j(1973.)60 1391 y([123])25 b(H.)c(F\177)-24 b(ollmer.)36 b(Random)21 b(\014elds)h(and)g (di\013usion)h(pro)q(cesses.)39 b(In)22 b(P)l(.)f(Hennequin,)h(editor,)192 1439 y FP(\023)185 1451 y(Ec)n(ole)27 b(d')o(\023)-24 b(et)o(\023)g(e)28 b(de)g(Pr)n(ob)n(abilit)o(\023)-24 b(es)27 b(de)g(Saint-Flour)h(XV{XVII)p FQ(,)f(Berlin{Heidelb)q(erg{New)185 1512 y(Y)l(ork,)15 b(1988.)i(Springer-V)l (erlag)f(\(Lecture)g(Notes)g(in)g(Mathematics)f(#1362\).)60 1611 y([124])25 b(H.)d(F\177)-24 b(ollmer)21 b(and)j(S.)f(Orey)l(.)41 b(Large)25 b(deviations)e(for)g(the)g(empirical)e(\014eld)h(of)i(a)g(Gibbs) 185 1671 y(measure.)c FP(A)o(nn.)e(Pr)n(ob.)p FQ(,)d(16:961{977,)k(1988.)60 1771 y([125])25 b(C.)20 b(M.)f(F)l(ortuin.)33 b(On)20 b(the)g(random)g (cluster)f(mo)q(del.)g(I)q(I)q(I.)g(The)h(simple)e(random)i(cluster)185 1831 y(mo)q(del.)g FP(Physic)n(a)p FQ(,)15 b(59:545{570,)j(1972.)60 1931 y([126])25 b(C.)13 b(M.)g(F)l(ortuin,)g(J.)g(Ginibre,)g(and)h(P)l(.)g (W.)f(Kasteleyn.)j(Correlation)d(inequalities)f(on)i(some)185 1991 y(partially)h(ordered)h(sets.)22 b FP(Commun.)17 b(Math.)g(Phys.)p FQ(,)e(22:89{103,)k(1971.)60 2091 y([127])25 b(C.)11 b(M.)g(F)l(ortuin)h(and) g(P)l(.)f(W.)h(Kasteleyn.)h(On)f(the)f(random)g(cluster)g(mo)q(del.)f(I.)h (In)o(tro)q(duction)185 2151 y(and)16 b(relation)g(to)h(other)f(mo)q(dels.)k FP(Physic)n(a)p FQ(,)c(57:536{564,)i(1972.)60 2251 y([128])25 b(Z.)10 b(F)l(riedman)g(and)i(J.)f(F)l(elsteiner.)g(Kadano\013)j(blo)q(c)o(k) c(transformation)i(b)o(y)f(the)g(Mon)o(te-Carlo)185 2311 y(tec)o(hnique.)19 b FP(Phys.)e(R)n(ev.)g(B)p FQ(,)f(15:5317{531)q(9,)j(1977.)60 2411 y([129])25 b(A.)11 b(F)l(rigessi)g(and)h(M.)f(Piccioni.)i(P)o(arameter)d (estimation)g(for)i(t)o(w)o(o-dimensional)f(Ising)g(\014elds)185 2471 y(corrupted)16 b(b)o(y)g(noise.)21 b FP(Sto)n(ch.)c(Pr)n(o)n(c.)g(Appl.) p FQ(,)f(34:297{311,)j(1990.)60 2571 y([130])25 b(J.)20 b(F)l(r\177)-24 b(ohlic)o(h.)32 b(On)21 b(the)f(trivialit)o(y)e(of)j FF(\025')964 2553 y FH(4)964 2583 y(4)1004 2571 y FQ(theories)f(and)h(the)f(approac)o(h)i (to)e(the)h(critical)185 2631 y(p)q(oin)o(t)16 b(in)g FF(d)23 b(>)408 2664 y FH(\(=\))477 2631 y FQ(4)16 b(dimensions.)k FP(Nucle)n(ar)e(Physics)p FQ(,)e(B200)h([FS4]:281{296,)g(1982.)938 2784 y(256)p eop %%Page: 257 257 bop 60 91 a FQ([131])25 b(J.)13 b(F)l(r\177)-24 b(ohlic)o(h.)15 b(Mathematical)c(asp)q(ects)j(of)f(the)g(ph)o(ysics)g(of)h(disordered)f (systems.)i(In)e(K.)g(Os-)185 152 y(terw)o(alder)18 b(and)i(R.)e(Stora,)j (editors,)e FP(Critic)n(al)h(Phenomena,)i(R)n(andom)d(Systems,)i(Gauge)185 212 y(The)n(ories)c([L)n(es)f(Houches)j(1984],)e(Part)g(II)p FQ(,)f(pages)h(725{893,)h(Amsterdam,)13 b(1986.)18 b(North-)185 272 y(Holland.)60 374 y([132])25 b(J.)15 b(F)l(r\177)-24 b(ohlic)o(h,)13 b(R.)i(B.)g(Israel,)f(E.)h(H.)g(Lieb,)g(and)h(B.)e(Simon.)19 b(Phase)d(transitions)g(and)g(re\015ec-)185 434 y(tion)k(p)q(ositivit)o(y)l (.)e(I)q(I.)h(Lattice)g(systems)g(with)h(short-range)h(and)f(Coulom)o(b)f(in) o(teractions.)185 494 y FP(J.)e(Stat.)h(Phys.)p FQ(,)d(22:297{347,)k(1980.)60 596 y([133])25 b(J.)14 b(F)l(r\177)-24 b(ohlic)o(h)13 b(and)i(C.)f(E.)g (P\014ster.)k(On)d(the)f(absence)g(of)h(sp)q(on)o(taneous)h(symmetry)11 b(breaking)185 656 y(and)18 b(of)f(crystalline)f(ordering)i(in)f(t)o(w)o (o-dimensional)f(systems.)23 b FP(Commun.)c(Math.)f(Phys.)p FQ(,)185 716 y(81:277{298,)g(1981.)60 818 y([134])25 b(J.)14 b(F)l(r\177)-24 b(ohlic)o(h)13 b(and)i(T.)f(Sp)q(encer.)k(The)d (Kosterlitz-Thouless)f(phase)h(transition)g(in)f(the)g(t)o(w)o(o-)185 878 y(dimensional)20 b(plane)j(rotator)g(and)g(Coulom)o(b)f(gas.)41 b FP(Phys.)22 b(R)n(ev.)h(L)n(ett.)p FQ(,)h(46:1006{1009,)185 938 y(1981.)60 1040 y([135])h(J.)34 b(F)l(r\177)-24 b(ohlic)o(h)33 b(and)i(T.)f(Sp)q(encer.)75 b(The)34 b(Kosterlitz-Thouless)g(transition)h(in) f(t)o(w)o(o-)185 1100 y(dimensional)13 b(Ab)q(elian)h(spin)g(systems)g(and)h (the)g(Coulom)o(b)f(gas.)19 b FP(Commun.)d(Math.)g(Phys.)p FQ(,)185 1160 y(81:527{602,)i(1981.)60 1262 y([136])25 b(J.)15 b(F)l(r\177)-24 b(ohlic)o(h)15 b(and)i(T.)f(Sp)q(encer.)k(Phase)d(diagrams)e (and)i(critical)d(prop)q(erties)i(of)h(\(classical\))185 1322 y(Coulom)o(b)h(systems.)31 b(In)19 b FP(R)o(igor)n(ous)g(A)o(tomic)i(and)g (Mole)n(cular)g(Physics)p FQ(,)f(pages)h(327{370,)185 1382 y(New)15 b(Y)l(ork)h(and)h(London,)g(1981.)h(Plen)o(um)c(Press.)60 1484 y([137])25 b(J.)19 b(F)l(r\177)-24 b(ohlic)o(h)18 b(and)i(T.)f(Sp)q (encer.)30 b(The)19 b(phase)h(transition)g(in)f(the)g(one-dimensional)f (Ising)185 1544 y(mo)q(del)d(with)h(1)p FF(=r)512 1526 y FH(2)549 1544 y FQ(in)o(teraction)f(energy)l(.)21 b FP(Commun.)c(Math.)g(Phys.)p FQ(,)e(84:87{101,)k(1982.)60 1646 y([138])25 b(J.)17 b(F)l(r\177)-24 b(ohlic)o(h)16 b(and)i(T.)g(Sp)q(encer.)25 b(Absence)16 b(of)i(di\013usion)g (in)g(the)f(Anderson)h(tigh)o(t)f(binding)185 1706 y(mo)q(del)12 b(for)i(large)g(disorder)g(or)g(lo)o(w)g(energy)l(.)j FP(Commun.)e(Math.)g (Phys.)p FQ(,)e(88:151{184,)k(1983.)60 1808 y([139])25 b(G.)14 b(Galla)o(v)o(otti)f(and)h(S.)g(Miracle-Sole.)i(Statistical)e(mec)o(hanics)d (of)k(lattice)e(systems.)j FP(Com-)185 1868 y(mun.)h(Math.)g(Phys.)p FQ(,)f(5:317{324,)i(1967.)60 1970 y([140])25 b(G.)13 b(Galla)o(v)o(otti)g (and)h(S.)f(Miracle-Sole.)j(Correlation)d(functions)h(of)g(lattice)e (systems.)k FP(Com-)185 2030 y(mun.)h(Math.)g(Phys.)p FQ(,)f(7:274{288,)i (1968.)60 2132 y([141])25 b(G.)17 b(Galla)o(v)o(otti)g(and)i(S.)e (Miracle-Sole.)25 b(Equilibrium)15 b(states)j(of)h(the)e(Ising)h(mo)q(del)f (in)g(the)185 2192 y(t)o(w)o(o-phase)g(region.)k FP(Phys.)c(R)n(ev.)p FQ(,)e(B5:2555{2559,)k(1972.)60 2293 y([142])25 b(J.)18 b(M.)f(Gandhi.)28 b(On)18 b(Fermat's)f(last)i(theorem.)25 b FP(A)o(mer.)19 b(Math.)g(Monthly)p FQ(,)g(71:998{1006,)185 2354 y(1964.)60 2455 y([143])25 b(P)l(.)15 b(G\177)-24 b(anssler.)21 b(Compactness)15 b(and)h(sequen)o(tial)e (compactness)h(in)g(spaces)h(of)g(measures.)j FP(Z.)185 2516 y(Wahrscheinlichkeitsthe)n(orie)g(verw.)f(Geb.)p FQ(,)e(17:124{146,)j(1971.) 938 2784 y(257)p eop %%Page: 258 258 bop 60 91 a FQ([144])25 b(P)l(.)20 b(L.)g(Garrido,)h(A.)e(Labarta,)k(and)e (J.)e(Marro.)34 b(Stationary)20 b(nonequilibrium)e(states)i(in)185 152 y(the)13 b(Ising)g(mo)q(del)g(with)g(lo)q(cally)g(comp)q(eting)f(temp)q (eratures.)j FP(J.)g(Stat.)g(Phys.)p FQ(,)e(49:551{568,)185 212 y(1987.)60 313 y([145])25 b(K.)20 b(Ga)o(w\030)-22 b(edzki.)34 b(Rigorous)22 b(renormalization)d(group)j(at)f(w)o(ork.)35 b FP(Physic)n(a)p FQ(,)21 b(140A:78{84,)185 374 y(1986.)60 475 y([146])k(K.)16 b(Ga)o(w\030)-22 b(edzki,)16 b(R.)h(Kotec)o(k)q(\023)-25 b(y,)16 b(and)h(A.)g(Kupiainen.)23 b(Coarse)18 b(graining)f(approac)o(h)h(to) g(\014rst)185 535 y(order)e(phase)h(transitions.)k FP(J.)c(Stat.)h(Phys.)p FQ(,)e(47:701{724,)j(1987.)60 637 y([147])25 b(K.)d(Ga)o(w)o(edzki)f(and)i (A.)f(Kupiainen.)39 b(A)22 b(rigorous)i(blo)q(c)o(k)e(spin)h(approac)o(h)g (to)g(massless)185 697 y(lattice)15 b(theories.)20 b FP(Commun.)e(Math.)f (Phys.)p FQ(,)e(77:31{64,)j(1980.)60 799 y([148])25 b(K.)14 b(Ga)o(w)o(edzki)g(and)i(A.)e(Kupiainen.)19 b(Blo)q(c)o(k)14 b(spin)h(renormalization)e(group)j(for)f(dip)q(ole)g(gas)185 859 y(and)h(\()p FE(r)p FF(\036)p FQ(\))388 841 y FH(4)408 859 y FQ(.)21 b FP(A)o(nn.)d(Phys.)p FQ(,)d(147:198{243)q(,)j(1983.)60 961 y([149])25 b(K.)15 b(Ga)o(w\030)-22 b(edzki)14 b(and)i(A.)f(Kupiainen.)k (Gross-Nev)o(eu)c(mo)q(del)f(through)j(con)o(v)o(ergen)o(t)d(p)q(ertur-)185 1021 y(bation)i(expansions.)22 b FP(Commun.)17 b(Math.)h(Phys.)p FQ(,)d(102:1{30,)j(1985.)60 1123 y([150])25 b(K.)16 b(Ga)o(w\030)-22 b(edzki)16 b(and)i(A.)e(Kupiainen.)22 b(Massless)17 b(lattice)f FF(\036)1272 1105 y FH(4)1272 1135 y(4)1308 1123 y FQ(theory:)22 b(Rigorous)c(con)o(trol)f(of)185 1183 y(a)e(renormalizable)e(asymptotically)g (free)h(mo)q(del.)19 b FP(Commun.)d(Math.)g(Phys.)p FQ(,)e(99:197{252,)185 1243 y(1985.)60 1345 y([151])25 b(K.)10 b(Ga)o(w\030)-22 b(edzki)10 b(and)i(A.)e(Kupiainen.)i(Asymptotic)d(freedom)g(b)q(ey)o(ond)i(p)q (erturbation)h(theory)l(.)185 1405 y(In)j(K.)g(Osterw)o(alder)g(and)h(R.)f (Stora,)h(editors,)f FP(Critic)n(al)i(Phenomena,)h(R)n(andom)e(Systems,)185 1465 y(Gauge)k(The)n(ories)f([L)n(es)h(Houches)g(1984],)g(Part)g(I)p FQ(,)e(pages)i(185{293,)i(Amsterdam,)16 b(1986.)185 1526 y(North-Holland.)60 1627 y([152])25 b(D.)e(Geman.)40 b(Random)23 b(\014elds)g(and)h(in)o(v)o (erse)d(problems)h(in)g(imaging.)41 b(In)23 b FP(Ec)n(ole)h(d'Et)o(\023)-24 b(e)185 1687 y(de)25 b(Pr)n(ob)n(abilit)o(\023)-24 b(es)25 b(de)g(Saint-Flour)h(XVIII)e({)h(1988)p FQ(,)h(pages)f(116{193.)h(Springer-V) l(erlag)185 1748 y(\(Lecture)15 b(Notes)i(in)e(Mathematics)g(#1427\),)i (Berlin{Heidelb)q(erg{New)c(Y)l(ork,)j(1990.)60 1849 y([153])25 b(S.)16 b(Geman.)k(Hidden)15 b(Mark)o(o)o(v)h(mo)q(dels)f(for)i(image)d (analysis.)22 b(Lecture)16 b(at)g(Istituto)g(p)q(er)h(le)185 1910 y(Applicazioni)d(del)i(Calcolo,)g(Roma)f(\(July)h(1990\).)60 2011 y([154])25 b(S.)c(Geman)g(and)h(D.)f(Geman.)37 b(Sto)q(c)o(hastic)21 b(relaxation,)i(Gibbs)f(distributions)f(and)h(the)185 2071 y(Ba)o(y)o(esian)h(restoration)h(of)g(images.)43 b FP(IEEE)25 b(T)l(r)n(ans.)f(Pattern)h(A)o(nal.)g(Machine)g(Intel)r(l.)p FQ(,)185 2132 y(6:721{741,)18 b(1984.)60 2233 y([155])25 b(H.-O.)16 b(Georgii.)23 b(Large)18 b(deviations)f(and)h(maxim)n(um)13 b(en)o(trop)o(y)j(principle)g(for)h(in)o(teracting)185 2293 y(random)e(\014elds)h(on)h Fq(Z)587 2273 y FD(d)607 2293 y FQ(.)k(T)l(o)c(app)q(ear)g(in)f FP(A)o(nn.)i(Pr)n(ob.)60 2395 y FQ([156])25 b(H.-O.)19 b(Georgii.)32 b(Tw)o(o)21 b(remarks)d(on)j(extremal) d(equilibrium)e(states.)33 b FP(Commun.)21 b(Math.)185 2455 y(Phys.)p FQ(,)15 b(32:107{118,)k(1973.)60 2557 y([157])25 b(H.-O.)18 b(Georgii.)30 b FP(Gibbs)21 b(Me)n(asur)n(es)e(and)i(Phase)g(T)l (r)n(ansitions)p FQ(.)30 b(W)l(alter)19 b(de)g(Gruyter)g(\(de)185 2617 y(Gruyter)d(Studies)g(in)f(Mathematics,)g(V)l(ol.)g(9\),)h(Berlin{New)e (Y)l(ork,)i(1988.)938 2784 y(258)p eop %%Page: 259 259 bop 60 91 a FQ([158])25 b(B.)11 b(Gidas.)j(A)e(renormalization)e(group)j (approac)o(h)g(to)f(image)f(pro)q(cessing)h(problems.)h FP(IEEE)185 152 y(T)l(r)n(ans.)j(Pattern)j(A)o(nal.)f(Mach.)f(Intel)r(l.)p FQ(,)h(11:164{180,)h(1989.)60 253 y([159])25 b(J.)13 b(Glimm)d(and)k(A.)e (Ja\013e.)17 b(P)o(ositivit)o(y)12 b(of)h(the)g FF(')1065 235 y FH(4)1065 266 y(3)1098 253 y FQ(Hamiltonian.)i FP(F)l(ortschritte)g(der)g (Physik)p FQ(,)185 313 y(21:327{376,)j(1973.)60 415 y([160])25 b(J.)15 b(Glimm)e(and)j(A.)f(Ja\013e.)21 b FP(Quantum)d(Physics:)k(A)c(F)l (unctional)h(Inte)n(gr)n(al)e(Point)h(of)f(View)p FQ(.)185 475 y(Springer-V)l(erlag,)e(Berlin{Heidelb)q(erg{New)f(Y)l(ork,)h(1981.)60 577 y([161])25 b(S.)13 b(Goldstein.)18 b(A)13 b(note)i(on)f(sp)q (eci\014cations.)k FP(Z.)d(Wahrscheinlichkeitsthe)n(orie)i(verw.)f(Geb.)p FQ(,)185 637 y(46:45{51,)i(1978.)60 739 y([162])25 b(S.)15 b(Goldstein,)g(R.)f(Kuik,)h(J.)g(L.)g(Leb)q(o)o(witz,)g(and)h(C.)f(Maes.)20 b(F)l(rom)14 b(PCA's)h(to)g(equilibrium)185 799 y(systems)g(and)h(bac)o(k.)21 b FP(Commun.)d(Math.)f(Phys.)p FQ(,)e(125:71{79,)j(1989.)60 901 y([163])25 b(A.)16 b(Gonzalez-Arro)o(y)o(o,)f(M.)h(Ok)m(a)o(w)o(a,)h(and) g(Y.)f(Shimizu.)21 b(Mon)o(te)16 b(Carlo)h(renormalization-)185 961 y(group)h(study)g(of)f(the)h(four-dimensional)e FF(Z)1006 968 y FH(2)1044 961 y FQ(gauge)i(theory)l(.)25 b FP(Phys.)18 b(R)n(ev.)g(L)n(ett.)p FQ(,)f(60:487{)185 1021 y(490,)g(1988.)60 1123 y([164])25 b(A.)12 b(Gonz\023)-24 b(alez-Arro)o(y)o(o)13 b(and)h(J.)f(Salas.)k(Computing)c(the)g(couplings)h(of)g(Ising)f(systems)f (from)185 1183 y(Sc)o(h)o(winger-Dyson)k(equations.)21 b FP(Phys.)c(L)n(ett.) p FQ(,)f(B214:418{424,)j(1988.)60 1285 y([165])25 b(A.)h(Gonz\023)-24 b(alez-Arro)o(y)o(o)27 b(and)h(J.)g(Salas.)55 b(Renormalization)26 b(group)j(\015o)o(w)f(of)g(the)f(t)o(w)o(o-)185 1345 y(dimensional)14 b(Ising)i(mo)q(del)f(at)i FF(T)j(<)14 b(T)906 1352 y FD(c)923 1345 y FQ(.)21 b FP(Phys.)c(L)n(ett.)p FQ(,)f(B261:415{423,)i(1991.)60 1447 y([166])25 b(M.)14 b(G\177)-24 b(opfert)14 b(and)i(G.)e(Mac)o(k.)k(Pro)q (of)e(of)f(con\014nemen)o(t)e(of)h(static)h(quarks)g(in)f(3-dimensional)185 1507 y FF(U)5 b FQ(\(1\))13 b(lattice)f(gauge)i(theory)f(for)h(all)e(v)m (alues)h(of)h(the)e(coupling)h(constan)o(t.)k FP(Commun.)d(Math.)185 1567 y(Phys.)p FQ(,)h(82:545{606,)k(1982.)60 1669 y([167])25 b(F.)11 b(P)l(.)g(Greenleaf.)i FP(Invariant)h(Me)n(ans)f(on)h(T)l(op)n(olo)n (gic)n(al)f(Gr)n(oups)p FQ(.)f(V)l(an)g(Nostrand-Reinhold,)185 1729 y(New)j(Y)l(ork,)h(1969.)60 1831 y([168])25 b(R.)13 b(B.)g(Gri\016ths.)k (P)o(eierls')12 b(pro)q(of)j(of)g(sp)q(on)o(taneous)g(magnetization)e(of)h(a) h(t)o(w)o(o-dimensional)185 1891 y(Ising)h(ferromagnet.)k FP(Phys.)d(R)n(ev.) p FQ(,)f(A136:437{439,)i(1964.)60 1993 y([169])25 b(R.)18 b(B.)g(Gri\016ths.) 28 b(Rigorous)20 b(results)f(and)g(theorems.)28 b(In)18 b(C.)h(Dom)o(b)f(and) h(M.)f(S.)h(Green,)185 2053 y(editors,)25 b FP(Phase)g(T)l(r)n(ansitions)g (and)g(Critic)n(al)f(Phenomena,)k(Vol.)d(1)p FQ(.)f(Academic)d(Press,)185 2113 y(London{New)c(Y)l(ork,)f(1972.)60 2215 y([170])25 b(R.)17 b(B.)g(Gri\016ths.)25 b(Phase)18 b(diagrams)f(and)i(higher-order)f(critical)e (p)q(oin)o(ts.)25 b FP(Phys.)19 b(R)n(ev.)f(B)p FQ(,)185 2275 y(12:345{355,)g(1975.)60 2377 y([171])25 b(R.)19 b(B.)g(Gri\016ths.)32 b(Mathematical)17 b(prop)q(erties)j(of)g(renormalization-group)g(transforma-) 185 2437 y(tions.)h FP(Physic)n(a)p FQ(,)15 b(106A:59{69,)j(1981.)60 2538 y([172])25 b(R.)15 b(B.)g(Gri\016ths)h(and)g(P)l(.)g(A.)e(P)o(earce.)20 b(P)o(osition-space)c(renormalization-group)g(transfor-)185 2599 y(mations:)k(Some)15 b(pro)q(ofs)j(and)f(some)e(problems.)20 b FP(Phys.)d(R)n(ev.)g(L)n(ett.)p FQ(,)e(41:917{920)q(,)j(1978.)938 2784 y(259)p eop %%Page: 260 260 bop 60 91 a FQ([173])25 b(R.)e(B.)g(Gri\016ths)h(and)g(P)l(.)g(A.)f(P)o (earce.)43 b(Mathematical)22 b(prop)q(erties)i(of)g(p)q(osition-space)185 152 y(renormalization-group)15 b(transformations.)22 b FP(J.)17 b(Stat.)h(Phys.)p FQ(,)d(20:499{545,)k(1979.)60 253 y([174])25 b(R.)16 b(B.)g(Gri\016ths)h(and)h(D.)f(Ruelle.)22 b(Strict)16 b(con)o(v)o(exit)o(y)f(\(\\con)o(tin)o(uit)o(y"\))h(of)h(the)g(pressure)g(in) 185 313 y(lattice)e(systems.)20 b FP(Commun.)d(Math.)g(Phys.)p FQ(,)e(23:169{175,)k(1971.)60 415 y([175])25 b(C.)19 b(Grillen)o(b)q(erger)f (and)j(U.)e(Krengel.)31 b(On)19 b(the)h(spatial)g(constan)o(t)g(of)g(sup)q (eradditiv)o(e)f(set)185 475 y(functions)14 b(in)g Fq(R)481 454 y FD(d)502 475 y FQ(.)k(In)c(H.)f(Mic)o(hel,)g(editor,)h FP(Er)n(go)n(dic)g(The)n(ory)h(and)h(R)n(elate)n(d)g(T)l(opics)p FQ(,)e(Berlin,)185 535 y(1982.)j(Ak)m(ademie-V)l(erlag.)60 637 y([176])25 b(P)l(.)15 b(Gro)q(eneb)q(o)q(om,)i(J.)e(Oosterho\013,)i(and)g (F.)e(H.)g(Ruymgaart.)21 b(Large)c(deviation)e(theorems)185 697 y(for)h(empirical)e(probabilit)o(y)h(measures.)20 b FP(A)o(nn.)e(Pr)n (ob.)p FQ(,)d(7:553{586,)k(1979.)60 799 y([177])25 b(L.)13 b(Gross.)18 b(Absence)13 b(of)h(second-order)g(phase)g(transitions)g(in)g (the)f(Dobrushin)h(uniqueness)185 859 y(region.)21 b FP(J.)c(Stat.)h(Phys.)p FQ(,)d(25:57{72,)j(1981.)60 961 y([178])25 b(L.)18 b(Gross.)30 b(Thermo)q(dynamics,)16 b(statistical)i(mec)o(hanics,)f(and)i(random)f (\014elds.)28 b(In)18 b FP(Ec)n(ole)185 1021 y(d'Et)o(\023)-24 b(e)16 b(de)f(Pr)n(ob)n(abilit)o(\023)-24 b(es)16 b(de)g(Saint-Flour)h(X)e({) h(1980)p FQ(.)d(Springer-V)l(erlag)h(\(Lecture)f(Notes)h(in)185 1081 y(Mathematics)g(#929\),)j(Berlin{Heidelb)q(erg{New)c(Y)l(ork,)j(1982.)60 1183 y([179])25 b(C.)18 b(Grub)q(er)h(and)g(A.)f(S)q(\177)-26 b(ut})i(o.)29 b(Phase)20 b(diagrams)e(of)h(lattice)e(systems)g(of)i(residual) f(en)o(trop)o(y)l(.)185 1243 y FP(J.)f(Stat.)h(Phys.)p FQ(,)d(42:113{142,)k (1988.)60 1345 y([180])25 b(P)l(.)12 b(Hall)g(and)h(C.)g(C.)f(Heyde.)i FP(Martingale)h(Limit)f(The)n(ory)f(and)h(its)h(Applic)n(ation)p FQ(.)h(Academic)185 1405 y(Press,)g(New)f(Y)l(ork,)h(1980.)60 1507 y([181])25 b(T.)c(Hara.)36 b(A)20 b(rigorous)i(con)o(trol)f(of)h (logarithmic)d(corrections)i(in)f(four-dimensional)g FF(')1870 1489 y FH(4)185 1567 y FQ(spin)f(systems.)e(I.)h(Tra)s(jectory)h(of)h (e\013ectiv)o(e)d(Hamiltonians.)28 b FP(J.)20 b(Stat.)g(Phys.)p FQ(,)f(47:57{98,)185 1627 y(1987.)60 1729 y([182])25 b(T.)19 b(Hara.)30 b(Mean-\014eld)19 b(critical)f(b)q(eha)o(viour)h(for)g (correlation)g(length)g(for)h(p)q(ercolation)f(in)185 1789 y(high)d(dimensions.)k FP(Pr)n(ob.)d(Th.)g(R)n(el.)g(Fields)p FQ(,)f(86:337{385,)j(1990.)60 1891 y([183])25 b(T.)f(Hara)g(and)h(G.)f (Slade.)44 b(Mean-\014eld)24 b(critical)e(b)q(eha)o(viour)i(for)h(p)q (ercolation)f(in)g(high)185 1951 y(dimensions.)19 b FP(Commun.)f(Math.)f (Phys.)p FQ(,)e(128:333{391)q(,)j(1990.)60 2053 y([184])25 b(T.)13 b(Hara)h(and)g(G.)f(Slade.)k(On)d(the)f(upp)q(er)h(critical)e (dimension)g(of)i(lattice)e(trees)h(and)h(lattice)185 2113 y(animals.)20 b FP(J.)d(Stat.)h(Phys.)p FQ(,)d(59:1469{1510)q(,)k(1990.)60 2215 y([185])25 b(T.)19 b(Hara)g(and)h(G.)f(Slade.)30 b(Critical)18 b(b)q(eha)o(viour)i(of)f(self-a)o(v)o(oiding)g(w)o(alk)f(in)h(\014v)o(e)g(or) g(more)185 2275 y(dimensions.)g FP(Bul)r(l.)h(A)o(mer.)d(Math.)g(So)n(c.)p FQ(,)f(25:417{423,)j(1991.)60 2377 y([186])25 b(T.)16 b(Hara)h(and)g(G.)f (Slade.)22 b(The)16 b(lace)g(expansion)h(for)g(self-a)o(v)o(oiding)f(w)o(alk) g(in)g(\014v)o(e)f(or)i(more)185 2437 y(dimensions.)i FP(R)n(ev.)f(Math.)f (Phys.)p FQ(,)e(4:235{327,)j(1992.)60 2538 y([187])25 b(T.)c(Hara)h(and)h(G.) f(Slade.)37 b(Self-a)o(v)o(oiding)21 b(w)o(alk)h(in)f(\014v)o(e)g(or)h(more)f (dimensions.)f(I.)h(The)185 2599 y(critical)14 b(b)q(eha)o(viour.)21 b FP(Commun.)d(Math.)f(Phys.)p FQ(,)e(147:101{136)q(,)j(1992.)938 2784 y(260)p eop %%Page: 261 261 bop 60 91 a FQ([188])25 b(T.)20 b(Hara)h(and)h(H.)d(T)l(asaki.)35 b(A)21 b(rigorous)g(con)o(trol)g(of)g(logarithmic)e(corrections)h(in)g(four-) 185 152 y(dimensional)10 b FF(')481 133 y FH(4)512 152 y FQ(spin)i(systems.)e (I)q(I.)h(Critical)g(b)q(eha)o(vior)g(of)i(susceptibilit)o(y)c(and)j (correlation)185 212 y(length.)21 b FP(J.)c(Stat.)h(Phys.)p FQ(,)d(47:99{121,)j(1987.)60 313 y([189])25 b(A.)11 b(Hasenfratz)h(and)g(P)l (.)g(Hasenfratz.)i(Singular)e(renormalization)e(group)j(transformations)185 374 y(and)j(\014rst)h(order)f(phase)h(transitions)g(\(I\).)k FP(Nucl.)d(Phys.)p FQ(,)d(B295)i([FS21]:1{20,)g(1988.)60 475 y([190])25 b(A.)16 b(Hasenfratz,)i(P)l(.)f(Hasenfratz,)g(U.)g(Heller,)e(and)j (F.)f(Karsc)o(h.)25 b(Impro)o(v)o(ed)15 b(Mon)o(te)i(Carlo)185 535 y(renormalization)d(group)j(metho)q(ds.)k FP(Phys.)c(L)n(ett.)p FQ(,)f(B140:76{82,)i(1984.)60 637 y([191])25 b(T.)d(Heath.)39 b FP(A)23 b(History)g(of)g(Gr)n(e)n(ek)f(Mathematics)p FQ(,)i(v)o(olume)c(I,) i(pages)h(91{93)h(and)f(380.)185 697 y(Clarendon)16 b(Press,)h(Oxford,)e (1921.)60 799 y([192])25 b(Y.)15 b(Higuc)o(hi.)k(On)d(the)f(absence)h(of)g (non-translationally)h(in)o(v)m(arian)o(t)e(Gibbs)h(states)g(for)g(the)185 859 y(t)o(w)o(o-dimensional)e(Ising)i(system.)k(In)15 b(J.)h(F)l(ritz,)f(J.)g (L.)h(Leb)q(o)o(witz,)g(and)h(D.)f(Szasz,)g(editors,)185 919 y FP(R)n(andom)k(Fields:)31 b(R)o(igor)n(ous)19 b(R)n(esults)j(in)g (Statistic)n(al)g(Me)n(chanics)g(and)f(Quantum)h(Field)185 980 y(The)n(ory)16 b(\(Eszter)n(gom)h(1979\))p FQ(.)e(North-Holland,)h (Amsterdam,)d(1981.)60 1081 y([193])25 b(Y.)19 b(Higuc)o(hi)h(and)h(R.)f (Lang.)36 b(On)21 b(the)f(con)o(v)o(ergence)f(of)i(the)g(Kadano\013)h (transformation)185 1142 y(to)o(w)o(ards)e(trivial)e(\014xed)h(p)q(oin)o(ts.) 31 b FP(Z.)21 b(Wahrscheinlichkeitsthe)n(orie)h(verw.)f(Geb.)p FQ(,)f(58:109{)185 1202 y(123,)d(1981.)60 1303 y([194])25 b(P)l(.)14 b(Holic)o(k)q(\023)-25 b(y,)13 b(R.)h(Kotec)o(k)q(\023)-25 b(y,)14 b(and)i(M.)e(Zahradn)-5 b(\023)-19 b(\020k.)19 b(Rigid)c(in)o (terfaces)f(for)h(lattice)f(mo)q(dels)g(at)185 1364 y(lo)o(w)i(temp)q (eratures.)k FP(J.)d(Stat.)h(Phys.)p FQ(,)d(50:755{812,)k(1988.)60 1465 y([195])25 b(W.)12 b(Holszt)o(ynski)e(and)j(J.)f(Sla)o(wn)o(y)l(.)i(P)o (eierls)d(condition)h(and)h(the)f(n)o(um)o(b)q(er)e(of)j(ground)g(states.)185 1526 y FP(Commun.)k(Math.)g(Phys.)p FQ(,)e(61:177{190,)k(1978.)60 1627 y([196])25 b(P)l(.)16 b(J.)f(Hub)q(er.)21 b(The)c(b)q(eha)o(vior)f(of)g (maxim)o(um)c(lik)o(eliho)q(o)q(d)j(estimates)g(under)h(nonstandard)185 1687 y(conditions.)33 b(In)20 b(L.)g(M.)g(LeCam)g(and)h(J.)f(Neyman,)f (editors,)h FP(Pr)n(o)n(c)n(e)n(e)n(dings)g(of)i(the)f(Fifth)185 1748 y(Berkeley)k(Symp)n(osium)e(on)h(Mathematic)n(al)f(Statistics)i(and)f (Pr)n(ob)n(ability,)h(vol.)f(I)p FQ(,)e(pages)185 1808 y(221{233.)c(Univ)o (ersit)o(y)c(of)i(California)h(Press,)f(Berk)o(eley{Los)f(Angeles,)g(1967.)60 1910 y([197])25 b(O.)11 b(Hud\023)-24 b(ak.)13 b(On)e(the)g(c)o(haracter)g (of)h(p)q(eculiarities)e(in)h(the)g(p)q(osition-space)h(renormalization-)185 1970 y(group)17 b(transformations.)k FP(Phys.)c(L)n(ett.)p FQ(,)f(A73:273{274,)i(1979.)60 2071 y([198])25 b(N.)d(M.)h(Hugenholtz.)43 b(C)675 2053 y Fy(\003)695 2071 y FQ(-algebras)25 b(and)f(statistical)f(mec)o (hanics.)42 b(In)23 b FP(Pr)n(o)n(c)n(e)n(e)n(dings)g(of)185 2132 y(Symp)n(osia)17 b(in)h(Pur)n(e)f(Mathematics,)h(V)l(olume)i(38,)d(Part) h(2)p FQ(,)e(pages)i(407{465,)h(Pro)o(vidence,)185 2192 y(R.I.,)14 b(1982.)j(American)d(Mathematical)g(So)q(ciet)o(y)l(.)60 2293 y([199])25 b(N.)17 b(M.)h(Hugenholtz.)28 b(On)18 b(the)g(in)o(v)o(erse)f (problem)g(in)h(statistical)g(mec)o(hanics.)26 b FP(Commun.)185 2354 y(Math.)17 b(Phys.)p FQ(,)e(85:27{38,)j(1982.)60 2455 y([200])25 b(D.)17 b(Iagolnitzer)g(and)h(B.)f(Souillard.)25 b(Random)17 b(\014elds)g(and)h(limit)d(theorems.)24 b(In)17 b(J.)h(F)l(ritz,)185 2516 y(J.)13 b(L.)i(Leb)q(o)o(witz,)f(and)g(D.)g(Sz\023) -24 b(asz,)14 b(editors,)g FP(R)n(andom)h(Fields)h(\(Eszter)n(gom,)f(1979\),) h(V)l(ol.)g(II)p FQ(,)185 2576 y(pages)h(573{591.)h(North-Holland,)e (Amsterdam,)d(1981.)938 2784 y(261)p eop %%Page: 262 262 bop 60 91 a FQ([201])25 b(I.)20 b(A.)h(Ibragimo)o(v)e(and)j(Y)l(u.)f(V.)f (Linnik.)36 b FP(Indep)n(endent)24 b(and)e(Stationary)g(Se)n(quenc)n(es)i(of) 185 152 y(R)n(andom)16 b(V)l(ariables)p FQ(.)22 b(W)l(olters{No)q(ordho\013,) c(Groningen,)e(1971.)60 253 y([202])25 b(J.)16 b(Z.)g(Im)o(brie.)j(Phase)e (diagrams)f(and)h(cluster)f(expansions)h(for)g(lo)o(w)f(temp)q(erature)f FF(P)7 b FQ(\()p FF(\036)p FQ(\))1870 260 y FH(2)185 313 y FQ(mo)q(dels.)14 b(I.)i(The)g(phase)h(diagram.)j FP(Commun.)e(Math.)f(Phys.)p FQ(,)e(82:261{304,)k(1981.)60 415 y([203])25 b(J.)16 b(Z.)g(Im)o(brie.)j (Phase)e(diagrams)f(and)h(cluster)f(expansions)h(for)g(lo)o(w)f(temp)q (erature)f FF(P)7 b FQ(\()p FF(\036)p FQ(\))1870 422 y FH(2)185 475 y FQ(mo)q(dels.)14 b(I)q(I.)i(The)g(Sc)o(h)o(winger)f(function.)21 b FP(Commun.)d(Math.)f(Phys.)p FQ(,)e(82:305{343,)k(1981.)60 577 y([204])25 b(S.)15 b(N.)f(Isak)o(o)o(v.)19 b(Nonanalytic)c(features)g(of) h(the)f(\014rst)g(order)h(phase)g(transition)f(in)g(the)g(Ising)185 637 y(mo)q(del.)20 b FP(Commun.)d(Math.)g(Phys.)p FQ(,)e(95:427{443,)k(1984.) 60 739 y([205])25 b(R.)14 b(B.)g(Israel.)k(High-temp)q(erature)13 b(analyticit)o(y)g(in)i(classical)f(lattice)f(systems.)18 b FP(Commun.)185 799 y(Math.)f(Phys.)p FQ(,)e(50:245{257,)k(1976.)60 901 y([206])25 b(R.)17 b(B.)h(Israel.)27 b FP(Convexity)20 b(in)g(the)g(The)n(ory)e(of)h(L)n(attic)n(e)g(Gases)p FQ(.)27 b(Princeton)18 b(Univ.)f(Press,)185 961 y(Princeton,)e(N.J.,)g(1979.)60 1063 y([207])25 b(R.)18 b(B.)g(Israel.)28 b(Banac)o(h)18 b(algebras)i(and)f (Kadano\013)h(transformations.)29 b(In)18 b(J.)h(F)l(ritz,)f(J.)g(L.)185 1123 y(Leb)q(o)o(witz,)12 b(and)h(D.)f(Sz\023)-24 b(asz,)12 b(editors,)g FP(R)n(andom)h(Fields)h(\(Eszter)n(gom,)g(1979\),)g(V)l(ol.)g (II)p FQ(,)d(pages)185 1183 y(593{608.)18 b(North-Holland,)e(Amsterdam,)d (1981.)60 1285 y([208])25 b(R.)17 b(B.)h(Israel.)26 b(Generic)17 b(trivialit)o(y)f(of)j(phase)f(diagrams)g(in)g(spaces)h(of)f(long-range)i(in) o(ter-)185 1345 y(actions.)h FP(Commun.)d(Math.)f(Phys.)p FQ(,)e (106:459{466,)k(1986.)60 1447 y([209])25 b(R.)20 b(B.)f(Israel)h(and)h(R.)f (R.)g(Phelps.)34 b(Some)19 b(con)o(v)o(exit)o(y)f(questions)j(arising)f(in)h (statistical)185 1507 y(mec)o(hanics.)e FP(Math.)e(Sc)n(and.)p FQ(,)f(54:133{156,)j(1984.)60 1609 y([210])25 b(L.)13 b(P)l(.)g(Kadano\013)j (and)e(A.)e(Hough)o(ton.)18 b(Numerical)10 b(ev)m(aluations)k(of)g(the)f (critical)f(prop)q(erties)185 1669 y(of)k(the)g(t)o(w)o(o-dimensional)f (Ising)h(mo)q(del.)k FP(Phys.)d(R)n(ev.)p FQ(,)e(B11:377{386,)k(1975.)60 1770 y([211])25 b(J.-P)l(.)e(Kahane.)46 b FP(S)o(\023)-24 b(eries)25 b(de)g(F)l(ourier)g(A)o(bsolument)h(Conver)n(gentes)p FQ(.)47 b(Springer-V)l(erlag,)185 1831 y(Berlin{Heidelb)q(erg{New)13 b(Y)l(ork,)j(1970.)60 1932 y([212])25 b(I.)11 b(A.)h(Kashap)q(o)o(v.)17 b(Justi\014cation)12 b(of)h(the)g(renormalization-group)f(metho)q(d.)i FP(The)n(or.)f(Math.)185 1993 y(Phys.)p FQ(,)i(42:184{186,)k(1980.)60 2094 y([213])25 b(A.)17 b(Katz.)28 b FP(Principles)21 b(of)e(Statistic)n(al)i (Me)n(chanics)p FQ(.)29 b(F)l(reeman,)17 b(San)i(F)l(rancisco{London,)185 2154 y(1967.)60 2256 y([214])25 b(T.)13 b(Kennedy)l(.)j(Some)c(rigorous)j (results)e(on)h(ma)s(jorit)o(y)e(rule)h(renormalization)f(group)i(trans-)185 2316 y(formations)h(near)i(the)f(critical)e(p)q(oin)o(t.)22 b(Univ)o(ersit)o(y)13 b(of)k(Arizona)f(preprin)o(t,)f(1992.)60 2418 y([215])25 b(T.)d(Kennedy)g(and)h(E.)f(H.)f(Lieb.)40 b(An)22 b(itineran)o(t)f(electron)g(mo)q(del)h(with)g(crystalline)f(or)185 2478 y(magnetic)14 b(long-range)k(order.)j FP(Physic)n(a)p FQ(,)15 b(138A:320{358,)k(1986.)60 2580 y([216])25 b(J.)h(C.)h(Kie\013er.)52 b(A)27 b(coun)o(terexample)d(to)j(Perez's)f(generalization)h(of)g(the)f (Shannon-)185 2640 y(McMillan)11 b(theorem.)i FP(A)o(nn.)i(Pr)n(ob.)p FQ(,)e(1:362{364,)i(1973.)i(Correction)c(in)f FM(4)p FQ(:153{154)j(\(1976\).) 938 2784 y(262)p eop %%Page: 263 263 bop 60 91 a FQ([217])25 b(W.)17 b(Klein,)g(D.)h(J.)f(W)l(allace,)g(and)i(R.)e (K.)h(P)l(.)f(Zia.)26 b(Essen)o(tial)18 b(singularities)f(at)h(\014rst-order) 185 152 y(phase)e(transitions.)22 b FP(Phys.)17 b(R)n(ev.)g(L)n(ett.)p FQ(,)f(37:639{642,)j(1976.)60 253 y([218])25 b(H.)c(Ko)q(c)o(h)i(and)g(P)l(.) f(Witt)o(w)o(er.)38 b(A)22 b(non-Gaussian)j(renormalization)20 b(group)k(\014xed)e(p)q(oin)o(t)185 313 y(for)15 b(hierarc)o(hical)f(scalar)h (lattice)f(\014eld)h(theories.)k FP(Commun.)d(Math.)h(Phys.)p FQ(,)d(106:495{532,)185 374 y(1986.)60 475 y([219])25 b(H.)12 b(Ko)q(c)o(h)i(and)f(P)l(.)g(Witt)o(w)o(er.)j(On)d(the)g(renormalization)f (group)i(transformation)f(for)h(scalar)185 535 y(hierarc)o(hical)g(mo)q (dels.)20 b FP(Commun.)e(Math.)f(Phys.)p FQ(,)e(138:537{568,)k(1991.)60 637 y([220])25 b(J.)20 b(M.)g(Kosterlitz.)33 b(The)21 b(critical)e(prop)q (erties)h(of)h(the)g(t)o(w)o(o-dimensional)e FF(xy)j FQ(mo)q(del.)32 b FP(J.)185 697 y(Phys.)17 b(C)p FQ(,)e(7:1046{1060)q(,)j(1974.)60 799 y([221])25 b(F.)11 b(Koukiou,)i(D.)e(P)o(etritis,)h(and)g(M.)g(Zahradn)-5 b(\023)-19 b(\020k.)14 b(Extension)e(of)g(the)g(Pirogo)o(v-Sinai)g(theory)185 859 y(to)23 b(a)g(class)f(of)h(quasip)q(erio)q(dic)f(in)o(teractions.)40 b FP(Commun.)23 b(Math.)g(Phys.)p FQ(,)g(118:365{383,)185 919 y(1988.)60 1021 y([222])i(O.)14 b(K.)g(Kozlo)o(v.)k(Gibbs)d(description)f(of) h(a)g(system)e(of)i(random)f(v)m(ariables.)19 b FP(Pr)n(obl.)d(Inform.)185 1081 y(T)l(r)n(ansmission)p FQ(,)f(10:258{265,)k(1974.)60 1183 y([223])25 b(U.)14 b(Krengel.)k FP(Er)n(go)n(dic)d(The)n(or)n(ems)p FQ(.)j(W)l(alter)c(de)h(Gruyter)f(\(de)h(Gruyter)g(Studies)f(in)h(Math-)185 1243 y(ematics,)f(V)l(ol.)h(6\),)h(Berlin{New)e(Y)l(ork,)i(1985.)60 1345 y([224])25 b(K.)15 b(Kric)o(k)o(eb)q(erg.)20 b FP(Pr)n(ob)n(ability)d (The)n(ory)p FQ(.)j(Addison-W)l(esley)l(,)15 b(Reading,)h(Mass.,)g(1965.)60 1447 y([225])25 b(S.)16 b(Kullbac)o(k.)j FP(Information)f(The)n(ory)e(and)h (Statistics)p FQ(.)23 b(Wiley)l(,)14 b(New)i(Y)l(ork,)f(1959.)60 1548 y([226])25 b(S.)13 b(Kullbac)o(k)f(and)j(R.)e(A.)f(Leibler.)k(On)e (information)f(and)h(su\016ciency)l(.)h FP(A)o(nn.)h(Math.)f(Stat.)p FQ(,)185 1609 y(22:79{86,)j(1951.)60 1710 y([227])25 b(H.)14 b(K)q(\177)-26 b(unsc)o(h.)21 b(Thermo)q(dynamics)13 b(and)j(statistical)f (analysis)h(of)g(Gaussian)h(random)e(\014elds.)185 1770 y FP(Z.)i (Wahrscheinlichkeitsthe)n(orie)i(verw.)f(Geb.)p FQ(,)e(58:407{421,)j(1981.)60 1872 y([228])25 b(H.)18 b(K)q(\177)-26 b(unsc)o(h.)31 b(Deca)o(y)19 b(of)g(correlations)g(under)h(Dobrushin's)g(uniqueness)e(condition)h(and)185 1932 y(its)d(applications.)21 b FP(Commun.)c(Math.)g(Phys.)p FQ(,)f(84:207{222,)i(1982.)60 2034 y([229])25 b(H.)19 b(K)q(\177)-26 b(unsc)o(h.)33 b(Non-rev)o(ersible)18 b(stationary)j(measures)e(for)h (in\014nite)f(in)o(teracting)g(particle)185 2094 y(systems.)h FP(Z.)d(Wahrscheinlichkeitsthe)n(orie)i(verw.)f(Geb.)p FQ(,)e(66:407{424,)j (1984.)60 2196 y([230])25 b(O.)c(E.)h(Lanford)h(I)q(I)q(I.)37 b(En)o(trop)o(y)22 b(and)h(equilibrium)18 b(states)k(in)g(classical)f (statistical)g(me-)185 2256 y(c)o(hanics.)g(In)16 b(A.)f(Lenard,)i(editor,)f FP(Statistic)n(al)i(Me)n(chanics)g(and)g(Mathematic)n(al)g(Pr)n(oblems)185 2316 y(\(Battel)r(le)i(Se)n(attle)f(R)n(enc)n(ontr)n(es)e(1971\))p FQ(,)e(pages)j(1{113.)f(Springer-V)l(erlag)f(\(Lecture)g(Notes)185 2377 y(in)g(Ph)o(ysics)f(#20\),)h(Berlin{Heidelb)q(erg{New)e(Y)l(ork,)h (1973.)60 2478 y([231])25 b(O.)18 b(E.)g(Lanford)i(I)q(I)q(I)e(and)h(D.)g(W.) f(Robinson.)29 b(Statistical)18 b(mec)o(hanics)e(of)j(quan)o(tum)e(spin)185 2538 y(systems.)d(I)q(I)q(I.)21 b FP(Commun.)c(Math.)g(Phys.)p FQ(,)f(9:327{338,)i(1968.)938 2784 y(263)p eop %%Page: 264 264 bop 60 91 a FQ([232])25 b(O.)18 b(E.)g(Lanford)i(I)q(I)q(I)f(and)g(D.)g (Ruelle.)27 b(Observ)m(ables)18 b(at)i(in\014nit)o(y)d(and)i(states)h(with)e (short)185 152 y(range)g(correlations)g(in)g(statistical)g(mec)o(hanics.)24 b FP(Commun.)19 b(Math.)g(Phys.)p FQ(,)e(13:194{215,)185 212 y(1969.)60 313 y([233])25 b(C.)16 b(B.)f(Lang.)22 b(Renormalization)15 b(study)h(of)g(compact)f FF(U)5 b FQ(\(1\))17 b(lattice)e(gauge)i(theory)l(.) k FP(Nucl.)185 374 y(Phys.)p FQ(,)15 b(B280)i([FS18]:255{275,)h(1987.)60 475 y([234])25 b(S.)12 b(Lang.)17 b FP(Intr)n(o)n(duction)c(to)i(Diophantine) g(Appr)n(oximations)p FQ(.)f(Addison-W)l(esley)l(,)e(Reading,)185 535 y(Mass.,)k(1966.)60 637 y([235])25 b(V.)16 b(A.)f(Leb)q(esgue.)24 b(Sur)17 b(l')o(\023)-23 b(equation)15 b(ind)o(\023)-23 b(etermin)o(\023)g (ee)14 b FF(x)1185 619 y FH(5)1216 637 y FQ(+)d FF(y)1291 619 y FH(5)1325 637 y FQ(=)k FF(az)1429 619 y FH(5)1448 637 y FQ(.)22 b FP(J.)c(de)g(Maths.)f(Pur)n(es)185 697 y(Appl.)p FQ(,)f(8:49{70,)i(1843.)60 799 y([236])25 b(J.)d(L.)g(Leb)q(o)o(witz.)40 b(Co)q(existence)22 b(of)h(phases)g(in)f(Ising)g(ferromagnets.)39 b FP(J.)23 b(Stat.)h(Phys.)p FQ(,)185 859 y(16:463{476,)18 b(1977.)60 961 y([237])25 b(J.)31 b(L.)g(Leb)q(o)o(witz.)67 b(Num)o(b)q(er)29 b(of)j(phases)g(in)f(one)h(comp)q (onen)o(t)f(ferromagnets.)65 b(In)185 1021 y(G.)15 b(Dell'An)o(tonio,)e(S.)i (Doplic)o(her,)f(and)i(G.)f(Jona-Lasinio,)h(editors,)f FP(Mathematic)n(al)i (Pr)n(ob-)185 1081 y(lems)24 b(in)g(The)n(or)n(etic)n(al)g(Physics)p FQ(.)e(Springer-V)l(erlag)h(\(Lecture)g(Notes)g(in)f(Ph)o(ysics)h(#80\),)185 1142 y(Berlin{Heidelb)q(erg{New)13 b(Y)l(ork,)j(1978.)60 1243 y([238])25 b(J.)18 b(L.)g(Leb)q(o)o(witz.)28 b(Microscopic)17 b(origin)i(of)f(h)o(ydro)q(dynamic)f(equations:)26 b(Deriv)m(ation)18 b(and)185 1303 y(consequences.)i FP(Physic)n(a)p FQ(,)15 b(140A:232{239,)k (1986.)60 1405 y([239])25 b(J.)d(L.)g(Leb)q(o)o(witz)h(and)g(C.)f(Maes.)40 b(The)22 b(e\013ect)g(of)h(an)g(external)e(\014eld)h(on)h(an)g(in)o(terface,) 185 1465 y(en)o(tropic)15 b(repulsion.)21 b FP(J.)c(Stat.)h(Phys.)p FQ(,)d(46:39{49,)j(1987.)60 1567 y([240])25 b(J.)16 b(L.)g(Leb)q(o)o(witz,)h (C.)f(Maes,)g(and)h(E.)g(R.)f(Sp)q(eer.)22 b(Statistical)16 b(mec)o(hanics)e(of)j(probabilistic)185 1627 y(cellular)d(automata.)22 b FP(J.)17 b(Stat.)h(Phys.)p FQ(,)d(59:117{170,)k(1990.)60 1729 y([241])25 b(J.)11 b(L.)h(Leb)q(o)o(witz)f(and)i(O.)e(P)o(enrose.)j (Rigorous)e(treatmen)o(t)e(of)i(the)f(V)l(an)h(der)g(W)l(aals-Maxw)o(ell)185 1789 y(theory)k(of)g(the)g(liquid-v)m(ap)q(or)h(transition.)k FP(J.)c(Math.)g(Phys.)p FQ(,)e(7:98{113,)j(1966.)60 1891 y([242])25 b(J.)19 b(L.)i(Leb)q(o)o(witz)f(and)g(O.)g(P)o(enrose.)33 b(Analytic)18 b(and)j(clustering)e(prop)q(erties)i(of)f(thermo-)185 1951 y(dynamic)13 b(functions)j(and)g(distribution)f(functions)h(for)g(classical)f (lattice)f(and)i(con)o(tin)o(uous)185 2011 y(systems.)k FP(Commun.)d(Math.)g (Phys.)p FQ(,)e(11:99{124,)k(1968.)60 2113 y([243])25 b(J.)11 b(L.)i(Leb)q(o)o(witz)f(and)h(O.)e(P)o(enrose.)k(Div)o(ergen)o(t)c (susceptibilit)o(y)f(of)i(isotropic)g(ferromagnets.)185 2173 y FP(Phys.)17 b(R)n(ev.)g(L)n(ett.)p FQ(,)e(35:549{551,)k(1975.)60 2275 y([244])25 b(J.)20 b(L.)g(Leb)q(o)o(witz,)h(M.)e(K.)h(Phani,)h(and)g(D.) f(F.)g(St)o(y)o(er.)32 b(Phase)21 b(diagram)e(of)i(Cu-Au-t)o(yp)q(e)185 2335 y(allo)o(ys.)f FP(J.)d(Stat.)h(Phys.)p FQ(,)e(pages)h(413{431,)h(1985.) 60 2437 y([245])25 b(J.)12 b(L.)i(Leb)q(o)o(witz)f(and)h(E.)f(Presutti.)j (Statistical)c(mec)o(hanics)f(of)j(un)o(b)q(ounded)g(spin)f(systems.)185 2497 y FP(Commun.)k(Math.)g(Phys.)p FQ(,)e(50:195{218,)k(1976.)60 2599 y([246])25 b(J.)15 b(L.)h(Leb)q(o)o(witz)g(and)h(R.)e(H.)g(Sc)o (honmann.)20 b(Pseudo-free)d(energies)e(and)h(large)g(deviations)185 2659 y(for)g(non-Gibbsian)i(FK)o(G)d(measures.)21 b FP(Pr)n(ob.)16 b(Th.)i(R)n(el.)f(Fields)p FQ(,)f(77:49{64,)i(1988.)938 2784 y(264)p eop %%Page: 265 265 bop 60 91 a FQ([247])25 b(D.)16 b(H.)f(Lehmer.)20 b(Review)15 b(of)h([74)q(].)k FP(Math.)d(R)n(eviews)p FQ(,)g(16:903,)g(1955.)60 190 y([248])25 b(B.)12 b(G.)i(Leroux.)j(Maxim)o(um-l)o(ik)n(eli)o(ho)q(o)q(d) c(estimation)f(for)i(hidden)f(Mark)o(o)o(v)g(mo)q(dels.)j FP(Sto)n(ch.)185 251 y(Pr)n(o)n(c.)g(Appl.)p FQ(,)g(40:127{143,)j(1992.)60 350 y([249])25 b(A.)12 b(L.)h(Lewis.)j(Lattice)c(renormalization)g(group)h(and)h (thermo)q(dynamic)c(limit.)j FP(Phys.)h(R)n(ev.)185 410 y(B)p FQ(,)i(16:1249{1252)q(,)i(1977.)60 509 y([250])25 b(E.)13 b(H.)h(Lieb)f(and)i (A.)e(D.)h(Sok)m(al.)k(A)c(general)g(Lee-Yang)g(theorem)f(for)h(one-comp)q (onen)o(t)f(and)185 569 y(m)o(ulti-com)o(p)q(onen)o(t)h(ferromagnets.)20 b FP(Commun.)e(Math.)f(Phys.)p FQ(,)e(80:153{179,)k(1981.)60 668 y([251])25 b(T.)15 b(M.)f(Liggett.)20 b FP(Inter)n(acting)e(Particle)f (Systems)p FQ(.)j(Springer-V)l(erlag,)15 b(New)f(Y)l(ork{Berlin{)185 728 y(Heidelb)q(erg{T)l(oky)o(o,)h(1985.)60 827 y([252])25 b(J.)17 b(Lindenstrauss,)i(G.)e(Olsen,)h(and)g(Y.)f(Sternfeld.)24 b(The)18 b(Poulsen)g(simplex.)23 b FP(A)o(nn.)d(Inst.)185 887 y(F)l(ourier)d(\(Gr)n(enoble\))p FQ(,)f(28:91{114,)j(1978.)60 986 y([253])25 b(J.)e(L\177)-24 b(orinczi)22 b(and)i(M.)f(Winnink.)41 b(Some)22 b(remarks)g(on)i(almost)e(Gibbs)i(states.)42 b(T)l(o)24 b(b)q(e)185 1046 y(published)14 b(in)h(the)f(pro)q(ceedings)h(of)g(the)g(NA)l (TO)f(Adv)m(anced)h(Studies)f(Institute)g(w)o(orkshop)185 1107 y(on)g(Cellular)f(Automata)h(and)g(Co)q(op)q(erativ)o(e)h(Systems)e([Les)h (Houc)o(hes)f(1992].)i(N.)e(Bo)q(ccara,)185 1167 y(E.)j(Goles,)g(S.)f (Martinez)h(and)h(P)l(.)f(Picco,)f(editors.)g(Klu)o(w)o(er,)g(Dordrec)o(h)o (t,)g(1993.)60 1266 y([254])25 b(S.)19 b(K.)f(Ma.)31 b FP(Mo)n(dern)19 b(The)n(ory)g(of)i(Critic)n(al)f(Phenomena)p FQ(.)31 b(Benjamin,)18 b(Reading,)h(Mass.,)185 1326 y(1976.)60 1425 y([255])25 b(C.)14 b(Maes)g(and)h(F.)f(Redig.)k(Anisotropic)13 b(p)q(erturbations)j(of)e(the)g (simple)f(symme)o(tric)e(exclu-)185 1485 y(sion)16 b(pro)q(cess:)22 b(long)17 b(range)f(correlations.)22 b FP(J.)16 b(Physique)i(I)p FQ(,)e(1:669{684,)i(1991.)60 1584 y([256])25 b(C.)17 b(Maes)g(and)h(K.)f(v)m (an)h(de)f(V)l(elde.)22 b(De\014ning)c(relativ)o(e)d(energies)i(for)h(the)f (pro)s(jected)f(Ising)185 1644 y(measure.)k(T)l(o)c(app)q(ear)i(in)d FP(Helv.)k(Phys.)e(A)n(cta)p FQ(.)60 1743 y([257])25 b(C.)12 b(Maes)g(and)h(K.)f(v)m(an)h(de)f(V)l(elde.)i(The)e(in)o(teraction)f(p)q (oten)o(tial)h(of)h(the)f(stationary)h(measure)185 1804 y(of)j(a)h (high-noise)f(spin\015ip)g(pro)q(cess.)22 b(Leuv)o(en)16 b(preprin)o(t,)f (1992.)60 1903 y([258])25 b(F.)16 b(Martinelli)f(and)i(E.)g(Olivieri.)j(Priv) m(ate)d(comm)o(unic)o(ation)d(and)k(pap)q(er)f(in)g(preparation,)185 1963 y(1992.)60 2062 y([259])25 b(F.)18 b(Martinelli)g(and)i(E.)f(Scopp)q (ola.)31 b(A)19 b(simple)e(sto)q(c)o(hastic)j(cluster)e(dynamics:)26 b(rigorous)185 2122 y(results.)21 b FP(J.)c(Phys.)f(A)p FQ(,)g(24:3135{315)q (7,)j(1991.)60 2221 y([260])25 b(D.)13 b(G.)g(Martirosy)o(an.)k(Uniqueness)12 b(of)i(Gibbs)g(states)g(in)f(lattice)f(mo)q(dels)h(with)g(one)h(ground)185 2281 y(state.)21 b FP(The)n(or.)c(Mat.)g(Phys.)p FQ(,)e(63:511{518,)k(1985.) 60 2380 y([261])25 b(A.)14 b(E.)g(Mazel)g(and)i(Y)l(u.)e(M.)g(Suho)o(v.)19 b(Random)14 b(surfaces)h(with)g(t)o(w)o(o-sided)g(constrain)o(ts:)21 b(an)185 2440 y(application)16 b(of)g(the)g(theory)g(of)h(dominan)o(t)e (ground)i(states.)22 b(Preprin)o(t,)15 b(1991.)60 2539 y([262])25 b(A.)d(Messager,)i(S.)f(Miracle-Sol)o(\023)-23 b(e,)23 b(and)g(C.-E.)g (P\014ster.)41 b(Correlation)23 b(inequalities)e(and)185 2600 y(uniqueness)e(of)i(the)e(equilibrium)e(state)j(for)h(the)e(plane)h(rotator)h (ferromagnetic)e(mo)q(del.)185 2660 y FP(Commun.)e(Math.)g(Phys.)p FQ(,)e(58:19{30,)j(1978.)938 2784 y(265)p eop %%Page: 266 266 bop 60 91 a FQ([263])25 b(J.)16 b(Mi\030)-22 b(ekisz.)23 b(The)17 b(global)g(minim)o(um)c(of)k(energy)g(is)g(not)h(alw)o(a)o(ys)f(a)g(sum)f(of) i(lo)q(cal)f(minima)185 152 y(|)f(a)g(note)h(on)f(frustration.)22 b(Preprin)o(t,)15 b(1990.)60 253 y([264])25 b(J.)13 b(Mi\030)-22 b(ekisz.)16 b(Classical)e(lattice)f(gas)i(mo)q(del)e(with)h(a)g(unique)f (nondegenerate)i(but)f(unstable)185 313 y(p)q(erio)q(dic)i(ground)h(state)f (con\014guration.)23 b FP(Commun.)17 b(Math.)g(Phys.)p FQ(,)e(111:533{538)q (,)k(1987.)60 415 y([265])25 b(L.)12 b(J.)h(Mordell.)h FP(Diophantine)h (Equations)p FQ(.)i(Academic)10 b(Press,)j(London{New)h(Y)l(ork,)f(1969.)60 517 y([266])25 b(J.)14 b(Moulin-Ollagnier.)k(Th)o(\023)-23 b(eor)o(\022)g(eme)13 b(ergo)q(dique)i(presque)g(sous-additif)g(et)g(con)o(v) o(ergence)e(en)185 577 y(mo)o(y)o(enne)h(de)i(l'information.)j FP(A)o(nn.)f(Inst.)g(Henri)g(Poinc)n(ar)o(\023)-24 b(e)p FQ(,)15 b(B19:257{266,)k(1983.)60 679 y([267])25 b(J.)19 b(Moulin-Ollagnier)f(and)h (D.)h(Pinc)o(hon.)29 b(Mesures)19 b(de)g(Gibbs)h(in)o(v)m(arian)o(tes)f(et)f (mesures)185 739 y(d'equilibre.)g FP(Z.)g(Wahrscheinlichkeitsthe)n(orie)h (verw.)f(Geb.)p FQ(,)e(55:11{23,)i(1981.)60 841 y([268])25 b(J.)16 b(Moulin-Ollagnier)g(and)h(D.)g(Pinc)o(hon.)23 b(Filtre)16 b(mo)o(y)o(ennan)o(t)f(et)h(v)m(aleurs)h(mo)o(y)o(ennes)e(des)185 901 y(capacit)o(\023)-23 b(es)16 b(in)o(v)m(arian)o(tes.)k FP(Bul)r(l.)f(So)n(c.)f(Math.)f(F)l(r)n(anc)n(e)p FQ(,)e(110:259{277)q(,)k (1982.)60 1002 y([269])25 b(J.)20 b(Moussouris.)37 b(Gibbs)21 b(and)h(Mark)o(o)o(v)e(random)h(systems)f(with)h(constrain)o(ts.)36 b FP(J.)21 b(Stat.)185 1063 y(Phys.)p FQ(,)15 b(10:11{33,)j(1974.)60 1164 y([270])25 b(C.)15 b(Mugler.)k FP(Platon)f(et)g(la)f(R)n(e)n(cher)n(che) f(Math)o(\023)-24 b(ematique)18 b(de)f(son)1402 1152 y(\023)1395 1164 y(Ep)n(o)n(que)p FQ(,)e(pages)i(226{236.)185 1225 y(P)l(.H.)e(Heitz,)f (Strasb)q(ourg{Z)q(\177)-26 b(uric)o(h,)18 b(1948.)60 1326 y([271])25 b(D.)19 b(R.)h(Nelson.)31 b(Co)q(existence-curv)o(e)18 b(singularities)h(in)h(isotropic)f(ferromagnets.)32 b FP(Phys.)185 1386 y(R)n(ev.)p FQ(,)15 b(B13:2222{2230)q(,)j(1976.)60 1488 y([272])25 b(J.)20 b(Nev)o(eu.)35 b FP(Bases)22 b(Math)o(\023)-24 b(ematiques)23 b(du)f(Calcul)i(des)e(Pr)n(ob)n(abilit)o(\023)-24 b(es,)23 b FQ(2)1533 1470 y FH(\022)-17 b(eme)1617 1488 y FQ(\023)-23 b(ed.)36 b(Masson,)185 1548 y(P)o(aris,)20 b(1980.)33 b([English)20 b(translation)g(of)g(\014rst)g(edition:)28 b FP(Mathematic)n(al)21 b(F)l(oundations)g(of)185 1609 y(the)d(Calculus)g(of)g(Pr)n(ob)n(ability)i FQ(\(Holden-Da)o(y)l(,)15 b(San)i(F)l(rancisco,)e(1965\).].)60 1710 y([273])25 b(C.)14 b(M.)f(Newman.)k(Normal)12 b(\015uctuations)j(and)g (the)f(FK)o(G)g(inequalities.)i FP(Commun.)f(Math.)185 1770 y(Phys.)p FQ(,)g(74:119{128,)k(1980.)60 1872 y([274])25 b(C.)19 b(M.)g(Newman.)30 b(A)19 b(general)h(cen)o(tral)e(limit)f(theorem)i(for)g(FK) o(G)h(systems.)30 b FP(Commun.)185 1932 y(Math.)17 b(Phys.)p FQ(,)e(91:75{80,)j(1983.)60 2034 y([275])25 b(C.)16 b(M.)f(Newman.)20 b(Priv)m(ate)c(comm)o(unic)o(ation,)e(1984.)60 2136 y([276])25 b(T.)20 b(Niemei)o(jer)d(and)k(J.)f(M.)g(J.)g(v)m(an)h(Leeu)o(w)o(en.)32 b(Wilson)21 b(theory)f(for)g(spin)h(systems)e(on)i(a)185 2196 y(triangular)16 b(lattice.)k FP(Phys.)d(R)n(ev.)g(L)n(ett.)p FQ(,)f(31:1411{1414)q(,)j(1973.)60 2298 y([277])25 b(T.)11 b(Niemeijer)d(and)13 b(J.)e(M.)h(J.)f(v)m(an)i(Leeu)o(w)o(en.)g (Renormalization)d(theory)i(for)g(Ising-lik)o(e)e(spin)185 2358 y(systems.)25 b(In)17 b(C.)h(Dom)o(b)f(and)i(M.)e(S.)h(Green,)f (editors,)h FP(Phase)h(T)l(r)n(ansitions)g(and)g(Critic)n(al)185 2418 y(Phenomena,)f(Vol.)g(6)p FQ(.)e(Academic)d(Press,)k(London{New)g(Y)l (ork{San)g(F)l(rancisco,)f(1976.)60 2520 y([278])25 b(T.)18 b(Niemey)o(e)o(r)e(and)j(J.)g(M.)f(J.)g(v)m(an)h(Leeu)o(w)o(en.)28 b(Wilson)19 b(theory)f(for)h(2-dimensional)f(Ising)185 2580 y(spin)e(systems.)k FP(Physic)n(a)p FQ(,)15 b(71:17{40,)j(1974.)938 2784 y(266)p eop %%Page: 267 267 bop 60 91 a FQ([279])25 b(B.)14 b(Nienh)o(uis,)g(A.)h(N.)g(Berk)o(er,)f(E.)h (K.)g(Riedel,)f(and)i(M.)f(Sc)o(hic)o(k.)k(First-)c(and)h(second-order)185 152 y(phase)i(transitions)h(in)f(Potts)h(mo)q(dels:)24 b (Renormalization-group)18 b(solution.)27 b FP(Phys.)19 b(R)n(ev.)185 212 y(L)n(ett.)p FQ(,)c(43:737{740,)k(1979.)60 313 y([280])25 b(B.)13 b(Nienh)o(uis)f(and)i(M.)f(Nauen)o(b)q(erg.)18 b(First-order)13 b(phase)i(transitions)f(in)f(renormalization-)185 374 y(group)k(theory)l(.)k FP(Phys.)c(R)n(ev.)g(L)n(ett.)p FQ(,)f(35:477{479,)i(1975.)60 475 y([281])25 b(G.)33 b(L.)g(O'Brien.)71 b(Scaling)33 b(transformations)h (for)g FE(f)p FQ(0)p FF(;)8 b FQ(1)p FE(g)p FQ(-v)m(alued)34 b(sequences.)71 b FP(Z.)185 535 y(Wahrscheinlichkeitsthe)n(orie)19 b(verw.)f(Geb.)p FQ(,)e(53:35{49,)i(1980.)60 637 y([282])25 b(S.)11 b(Olla.)i(Large)f(deviations)f(for)h(almost)f(Mark)o(o)o(vian)g(pro)q (cesses.)j FP(Pr)n(ob)n(ab.)e(Th.)h(R)n(el.)g(Fields)p FQ(,)185 697 y(76:395{409,)18 b(1987.)60 799 y([283])25 b(S.)e(Olla.)43 b(Large)24 b(deviations)g(for)f(Gibbs)h(random)g(\014elds.)42 b FP(Pr)n(ob)n(ab.)24 b(Th.)g(R)n(el.)g(Fields)p FQ(,)185 859 y(77:343{357,)18 b(1988.)60 961 y([284])25 b(G.)13 b(H.)f(Olsen.)j(On)e (simplices)e(and)i(the)g(Poulsen)h(simplex.)f(In)g FP(F)l(unctional)j(A)o (nalysis:)21 b(Sur-)185 1021 y(veys)c(and)g(R)n(e)n(c)n(ent)g(R)n(esults)g (II)f([Pr)n(o)n(c)n(e)n(e)n(dings)g(of)g(the)i(c)n(onfer)n(enc)n(e)f(on)g (functional)i(analysis,)185 1081 y(Paderb)n(orn,)d(Germany,)h(1979])p FQ(,)e(pages)i(31{52,)g(Amsterdam{New)c(Y)l(ork{Oxford,)j(1980.)185 1142 y(North-Holland)g(\(North-Holland)g(Mathematics)e(Studies)i(#38\).)60 1243 y([285])25 b(J.)19 b(C.)g(Oxtob)o(y)l(.)30 b FP(Me)n(asur)n(e)19 b(and)i(Cate)n(gory)p FQ(.)30 b(Springer-V)l(erlag,)19 b(New)g(Y)l (ork{Heidelb)q(erg{)185 1303 y(Berlin,)14 b(1971.)60 1405 y([286])25 b(Y.)12 b(M.)h(P)o(ark.)j(Cluster)d(expansion)h(for)f(classical)g(and)h(quan) o(tum)e(lattice)g(systems.)j FP(J.)f(Stat.)185 1465 y(Phys.)p FQ(,)h(27:553{576,)k(1982.)60 1567 y([287])25 b(Y.)19 b(M.)g(P)o(ark.)33 b(Extension)20 b(of)g(Pirogo)o(v-Sinai)g(theory)g(of)g(phase)h(transitions)g (to)f(in\014nite)185 1627 y(range)i(in)o(teractions)g(I.)f(Cluster)h (expansion.)39 b FP(Commun.)23 b(Math.)f(Phys.)p FQ(,)h(114:187{218,)185 1687 y(1988.)60 1789 y([288])i(Y.)19 b(M.)g(P)o(ark.)33 b(Extension)20 b(of)g(Pirogo)o(v-Sinai)g(theory)g(of)g(phase)h(transitions)g(to)f (in\014nite)185 1849 y(range)13 b(in)o(teractions.)e(I)q(I.)g(Phase)i (diagram.)i FP(Commun.)f(Math.)f(Phys.)p FQ(,)g(114:219{241,)j(1988.)60 1951 y([289])25 b(K.)18 b(R.)g(P)o(arthasarath)o(y)l(.)30 b FP(Pr)n(ob)n(ability)20 b(Me)n(asur)n(es)f(on)h(Metric)g(Sp)n(ac)n(es)p FQ(.)29 b(Academic)16 b(Press,)185 2011 y(New)f(Y)l(ork{San)i(F)l (rancisco{London,)h(1967.)60 2113 y([290])25 b(E.)18 b(A.)f(P)o(ec)o(herski.) 25 b(The)18 b(Peierls)f(condition)h(\(GPS)h(condition\))f(is)g(not)g(alw)o(a) o(ys)g(satis\014ed.)185 2173 y FP(Sel.)g(Math.)f(Sov.)p FQ(,)g(3:87{91,)h (1983/84.)60 2275 y([291])25 b(R.)f(P)o(eierls.)46 b(Ising's)25 b(mo)q(del)e(of)j(ferromagnetism.)44 b FP(Pr)n(o)n(c.)25 b(Cambridge)h (Philos.)f(So)n(c.)p FQ(,)185 2335 y(32:477{481,)18 b(1936.)60 2437 y([292])25 b(P)l(.)18 b(Pfeut)o(y)h(and)g(G.)g(T)l(oulouse.)31 b FP(Intr)n(o)n(duction)19 b(to)i(the)f(R)n(enormalization)g(Gr)n(oup)f(and)h (to)185 2497 y(Critic)n(al)d(Phenomena)p FQ(.)22 b(Wiley)l(,)15 b(Chic)o(hester{New)g(Y)l(ork,)g(1977.)60 2599 y([293])25 b(R.)15 b(R.)h(Phelps.)21 b FP(L)n(e)n(ctur)n(es)c(on)g(Cho)n(quet's)h(The)n(or)n(em) p FQ(.)i(V)l(an)c(Nostrand,)h(Princeton,)e(1966.)938 2784 y(267)p eop %%Page: 268 268 bop 60 91 a FQ([294])25 b(R.)17 b(R.)g(Phelps.)25 b(Generic)16 b(Fr)o(\023)-23 b(ec)o(het)16 b(di\013eren)o(tiabilit)o(y)f(of)j(the)f (pressure)h(in)f(certain)g(lattice)185 152 y(systems.)j FP(Commun.)d(Math.)g (Phys.)p FQ(,)e(91:557{562,)k(1983.)60 253 y([295])25 b(S.)c(A.)f(Pirogo)o (v.)36 b(Co)q(existence)21 b(of)g(phases)h(in)f(a)h(m)o(ulticom)o(p)q(onen)o (t)c(lattice)i(liquid)g(with)185 313 y(complex)14 b(thermo)q(dynamic)f (parameters.)20 b FP(The)n(or.)d(Math.)g(Phys.)p FQ(,)e(66:218{221,)k(1986.) 60 415 y([296])25 b(S.)d(A.)g(Pirogo)o(v)h(and)g(Y)l(a.)f(G.)h(Sinai.)40 b(Phase)24 b(diagrams)e(of)h(classical)f(lattice)g(systems.)185 475 y FP(The)n(or.)16 b(Math.)h(Phys.)p FQ(,)f(25:1185{1192,)j(1976.)60 577 y([297])25 b(S.)d(A.)g(Pirogo)o(v)h(and)g(Y)l(a.)f(G.)h(Sinai.)40 b(Phase)24 b(diagrams)e(of)h(classical)f(lattice)g(systems.)185 637 y(Con)o(tin)o(uation.)f FP(The)n(or.)16 b(Math.)i(Phys.)p FQ(,)d(26:39{49,)j(1976.)60 739 y([298])25 b(C.)d(Prak)m(ash.)41 b(High-temp)q(erature)20 b(di\013eren)o(tiabilit)o(y)g(of)j(lattice)e(Gibbs)h (states)h(b)o(y)f(Do-)185 799 y(brushin)16 b(uniqueness)g(tec)o(hniques.)j FP(J.)e(Stat.)h(Phys.)p FQ(,)e(31:169{228,)j(1983.)60 901 y([299])25 b(C.)d(Preston.)41 b FP(R)n(andom)22 b(Fields)p FQ(.)41 b(Springer-V)l(erlag) 22 b(\(Lecture)g(Notes)g(in)h(Mathematics)185 961 y(#534\),)16 b(Berlin{Heidelb)q(erg{New)e(Y)l(ork,)h(1976.)60 1063 y([300])25 b(C.)15 b(Preston.)21 b(Construction)c(of)f(sp)q(eci\014cations.)k(In)c(L.)g (Streit,)e(editor,)i FP(Quantum)i(Fields,)185 1123 y(A)o(lgebr)n(as,)g(Pr)n (o)n(c)n(esses)p FQ(,)c(Wien{New)i(Y)l(ork,)f(1980.)j(Springer-V)l(erlag.)60 1225 y([301])25 b(Pro)q(clus.)34 b FP(Commentair)n(e)21 b(sur)f(la)i(R)o (\023)-24 b(epublique)p FQ(,)23 b(v)o(olume)18 b(I)q(I,)h(pages)j(133{135.)36 b(Librairie)185 1285 y(Philosophique)16 b(J.)f(V)l(rin,)g(P)o(aris,)h(1970.) 23 b(T)l(ranslation)17 b(and)g(notes)f(b)o(y)g(A.)f(J.)h(F)l(estugi)o(\022) -23 b(ere.)60 1386 y([302])25 b(L.)15 b(R.)g(Rabiner.)k(A)c(tutorial)g(on)h (hidden)f(Mark)o(o)o(v)g(mo)q(dels)f(and)i(selected)e(applications)h(in)185 1447 y(sp)q(eec)o(h)g(recognition.)21 b FP(Pr)n(o)n(c.)c(IEEE)p FQ(,)e(77:257{286,)k(1989.)60 1548 y([303])25 b(C.)15 b(Radin.)k(Lo)o(w)d (temp)q(erature)e(and)h(the)g(origin)g(of)h(crystalline)d(symmetry)l(.)j FP(Int.)h(J.)f(Mo)n(d.)185 1609 y(Phys.)h(B)p FQ(,)f(1:1157{1191,)j(1987.)60 1710 y([304])25 b(C.)13 b(Radin.)k(Disordered)d(ground)h(states)f(of)g (classical)f(lattice)f(mo)q(dels.)k FP(R)n(ev.)f(Math.)g(Phys.)p FQ(,)185 1770 y(3:125{135,)j(1991.)60 1872 y([305])25 b(C.)20 b(Rebbi)h(and)g(R.)g(H.)f(Sw)o(endsen.)35 b(Mon)o(te)21 b(Carlo)g (renormalization-group)g(studies)g(of)185 1932 y FF(q)r FQ(-state)16 b(Potts)h(mo)q(dels)e(in)h(t)o(w)o(o)g(dimensions.)k FP(Phys.)d(R)n(ev.)p FQ(,)e(B21:4094{4107)q(,)k(1980.)60 2034 y([306])25 b(M.)15 b(Reed)g(and)i(B.)e(Simon.)20 b FP(Metho)n(ds)d(of)g(Mo)n(dern)f(Mathematic)n (al)i(Physics)f(I:)g(F)l(unctional)185 2094 y(A)o(nalysis)p FQ(.)k(Academic)14 b(Press,)i(New)f(Y)l(ork{London,)j(1972.)60 2196 y([307])25 b(L.)c(E.)h(Reic)o(hl.)35 b FP(A)23 b(Mo)n(dern)f(Course)g (in)h(Statistic)n(al)g(Physics)p FQ(.)37 b(Univ.)20 b(of)i(T)l(exas)g(Press,) 185 2256 y(Austin,)15 b(1980.)60 2358 y([308])25 b(P)l(.)13 b(Rib)q(en)o(b)q(oim.)k FP(The)e(Bo)n(ok)h(of)f(Prime)h(Numb)n(er)f(R)n(e)n (c)n(or)n(ds)p FQ(.)h(Springer-V)l(erlag,)d(New)h(Y)l(ork{)185 2418 y(Berlin{Heidelb)q(erg,)f(second)j(edition,)f(1989.)60 2520 y([309])25 b(H.)15 b(L.)h(Ro)o(yden.)21 b FP(R)n(e)n(al)c(A)o(nalysis)p FQ(.)k(Macmillan,)13 b(New)j(Y)l(ork,)g(second)g(edition,)f(1968.)60 2621 y([310])25 b(W.)16 b(Rudin.)k FP(F)l(unctional)g(A)o(nalysis)p FQ(.)h(McGra)o(w-Hill,)14 b(New)i(Y)l(ork,)f(1973.)938 2784 y(268)p eop %%Page: 269 269 bop 60 91 a FQ([311])25 b(D.)19 b(Ruelle.)31 b(Some)19 b(remarks)f(on)j(the)f (ground)h(state)f(of)g(in\014nite)f(systems)g(in)h(statistical)185 152 y(mec)o(hanics.)f FP(Commun.)e(Math.)g(Phys.)p FQ(,)e(11:339{345,)k (1969.)60 253 y([312])25 b(D.)20 b(Ruelle.)32 b FP(Statistic)n(al)23 b(Me)n(chanics:)30 b(R)o(igor)n(ous)20 b(R)n(esults)p FQ(.)34 b(Benjamin,)19 b(Reading,)i(Mas-)185 313 y(sac)o(h)o(usetts,)15 b(1969.)60 415 y([313])25 b(D.)33 b(Ruelle.)69 b FP(Thermo)n(dynamic)32 b(F)l(ormalism)p FQ(.)71 b(Addison-W)l(esley)l(,)36 b(Reading,)h(Mas-)185 475 y(sac)o(h)o(usetts,)15 b(1978.)60 577 y([314])25 b(J.)16 b(Salas.)21 b(Priv)m(ate)16 b(comm)o(unication.)i(1991.)60 679 y([315])25 b(H.)31 b(H.)g(Sc)o(haefer.)67 b FP(T)l(op)n(olo)n(gic)n(al)31 b(V)l(e)n(ctor)i(Sp)n(ac)n(es)p FQ(.)68 b(Springer-V)l(erlag,)35 b(New)c(Y)l(ork{)185 739 y(Heidelb)q(erg{Berlin,)13 b(1980.)60 841 y([316])25 b(A.)e(G.)i(Sc)o(hlijp)q(er.)44 b(Tiling)24 b(problems)f(and)i(undecidabilit)o(y)e(in)h(the)g(cluster)g(v)m(ariation)185 901 y(metho)q(d.)c FP(J.)d(Stat.)h(Phys.)p FQ(,)d(50:689{714,)k(1988.)60 1002 y([317])25 b(W.)d(Sc)o(hmidt.)38 b FP(Diophantine)23 b(Appr)n(oximation) p FQ(.)40 b(Springer-V)l(erlag)22 b(\(Lecture)g(Notes)g(in)185 1063 y(Mathematics)14 b(#785\),)j(Berlin{Heidelb)q(erg{New)c(Y)l(ork,)j (1980.)60 1164 y([318])25 b(R.)17 b(H.)g(Sc)o(honmann.)24 b(Pro)s(jections)18 b(of)g(Gibbs)g(measures)e(ma)o(y)g(b)q(e)i(non-Gibbsian.)27 b FP(Com-)185 1225 y(mun.)17 b(Math.)g(Phys.)p FQ(,)f(124:1{7,)h(1989.)60 1326 y([319])25 b(R.)13 b(Sc)o(hrader.)k(Ground)e(states)f(in)g(classical)f (lattice)g(systems)g(with)g(hard)i(core.)i FP(Commun.)185 1386 y(Math.)g(Phys.)p FQ(,)e(16:247{264,)k(1970.)60 1488 y([320])25 b(L.)20 b(Sc)o(h)o(w)o(artz.)31 b FP(R)n(adon)21 b(Me)n(asur)n(es)f(on)h(A)o (rbitr)n(ary)e(T)l(op)n(olo)n(gic)n(al)i(Sp)n(ac)n(es)g(and)g(Cylindric)n(al) 185 1548 y(me)n(asur)n(es)p FQ(.)d(T)l(ata)e(Institute)e(of)h(F)l(undamen)o (tal)f(Researc)o(h)g(and)i(Oxford)f(Univ)o(ersit)o(y)d(Press,)185 1609 y(Oxford,)j(1973.)60 1710 y([321])25 b(S.)15 b(H.)g(Shenk)o(er)g(and)h (J.)f(T)l(ob)q(o)q(c)o(hnik.)21 b(Mon)o(te)15 b(Carlo)i (renormalization-group)e(analysis)h(of)185 1770 y(the)j(classical)g(Heisen)o (b)q(erg)f(mo)q(del)g(in)i(t)o(w)o(o)f(dimensions.)29 b FP(Phys.)20 b(R)n(ev.)p FQ(,)g(B22:4462{4472,)185 1831 y(1980.)60 1932 y([322])25 b(S.)c(B.)g(Shlosman.)38 b(Uniqueness)21 b(and)i(half-space)f(non) o(uniqueness)g(of)h(Gibbs)f(states)g(in)185 1993 y(Czec)o(h)15 b(mo)q(dels.)20 b FP(The)n(or.)d(Math.)g(Phys.)p FQ(,)e(66:284{293,)k(1986.) 60 2094 y([323])25 b(S.)12 b(B.)g(Shlosman.)j(Gaussian)f(b)q(eha)o(vior)e(of) h(the)g(critical)e(Ising)h(mo)q(del)g(in)g(dimension)f FF(d)j(>)g FQ(4.)185 2154 y FP(Soviet)k(Phys.)f(Dokl.)p FQ(,)g(33:905{906,)h(1988.)60 2256 y([324])25 b(S.)12 b(B.)g(Shlosman.)j(Relations)e(among)g(the)f(cum)o (ulan)o(ts)f(of)i(random)g(\014elds)f(with)h(attraction.)185 2316 y FP(The)n(ory)j(Pr)n(ob.)h(Appl.)p FQ(,)f(33:645{655,)j(1989.)60 2418 y([325])25 b(S.)16 b(D.)g(Silv)o(ey)l(.)j FP(Statistic)n(al)f(Infer)n (enc)n(e)p FQ(.)k(Chapman)16 b(and)h(Hall,)e(London,)i(1975.)60 2520 y([326])25 b(B.)16 b(Simon)g(and)i(A.)f(D.)g(Sok)m(al.)25 b(Rigorous)19 b(en)o(trop)o(y-energy)d(argumen)o(ts.)24 b FP(J.)18 b(Stat.)h(Phys.)p FQ(,)185 2580 y(25:679{694,)f(1981.)23 b(Addendum)15 b(in)h FM(29)p FQ(:155)h(\(1982\).)938 2784 y(269)p eop %%Page: 270 270 bop 60 91 a FQ([327])25 b(Y)l(a.)17 b(G.)h(Sinai.)26 b(Self-similar)16 b(probabilit)o(y)h(distributions.)26 b FP(The)n(or.)18 b(Pr)n(ob.)h(and)g (its)g(Appl.)p FQ(,)185 152 y(21:64{80,)f(1976.)60 253 y([328])25 b(Y)l(a.)17 b(G.)h(Sinai.)25 b FP(The)n(ory)18 b(of)g(Phase)i(T)l(r)n (ansitions:)25 b(R)o(igor)n(ous)17 b(R)n(esults)p FQ(.)26 b(P)o(ergamon)17 b(Press,)185 313 y(Oxford{New)f(Y)l(ork,)f(1982.)60 415 y([329])25 b(J.)14 b(Sla)o(wn)o(y)l(.)19 b(Lo)o(w-temp)q(erature)c(prop)q(erties)g(of)h (classical)e(lattice)g(systems:)20 b(phase)c(transi-)185 475 y(tions)f(and)h(phase)g(diagrams.)k(In)15 b(C.)g(Dom)o(b)f(and)i(J.)g(L.)f (Leb)q(o)o(witz,)g(editors,)g FP(Phase)i(T)l(r)n(an-)185 535 y(sitions)k(and)h(Critic)n(al)f(Phenomena,)i(Vol.)f(11)p FQ(.)e(Academic)e (Press,)j(London{New)h(Y)l(ork,)185 596 y(1985.)60 697 y([330])j(A.)13 b(D.)i(Sok)m(al.)k(Existence)13 b(of)i(compatible)d(families)g(of)j(prop)q (er)g(regular)g(conditional)f(prob-)185 758 y(abilities.)19 b FP(Z.)f(Wahrscheinlichkeitsthe)n(orie)h(verw.)f(Geb.)p FQ(,)e(56:537{548,)j (1981.)60 859 y([331])25 b(A.)15 b(D.)h(Sok)m(al.)22 b(Unpublished,)15 b(1982.)60 961 y([332])25 b(A.)16 b(D.)i(Sok)m(al.)26 b(More)17 b(surprises)h(in)f(the)h(general)f(theory)h(of)f(lattice)g(systems.)24 b FP(Commun.)185 1021 y(Math.)17 b(Phys.)p FQ(,)e(86:327{336,)k(1982.)60 1123 y([333])25 b(A.)10 b(D.)h(Sok)m(al.)j(Subadditiv)o(e)d(set)g(functions)h (on)f(a)h(discrete)f(amenable)f(group.)k(Unpublished)185 1183 y(man)o(uscript,)g(1984.)60 1285 y([334])25 b(A.)h(Stella.)51 b(Singularities)26 b(in)h(renormalization)e(group)i(transformations.)53 b FP(Physic)n(a)p FQ(,)185 1345 y(108A:211{220,)18 b(1981.)60 1447 y([335])25 b(K.)20 b(Subbarao.)35 b(Renormalization)19 b(group)j(for)e(Ising)h(spins)g(on)g(a)g(\014nite)f(lattice.)33 b FP(Phys.)185 1507 y(R)n(ev.)p FQ(,)15 b(B11:1165{1168)q(,)j(1975.)60 1609 y([336])25 b(W.)14 b(G.)g(Sulliv)m(an.)j(P)o(oten)o(tials)c(for)i (almost)e(Mark)o(o)o(vian)h(random)f(\014elds.)18 b FP(Commun.)d(Math.)185 1669 y(Phys.)p FQ(,)g(33:61{74,)j(1973.)60 1770 y([337])25 b(R.)13 b(H.)h(Sw)o(endsen.)k(Mon)o(te)c(Carlo)g(renormalization.)j(In)d(T.)g (W.)g(Burkhardt)g(and)h(J.)f(M.)f(J.)185 1831 y(v)m(an)g(Leeu)o(w)o(en,)g (editors,)g FP(R)n(e)n(al-Sp)n(ac)n(e)h(R)n(enormalization)p FQ(,)f(pages)g(57{86.)i(Springer-V)l(erlag,)185 1891 y(Berlin{Heidelb)q (erg{New)e(Y)l(ork,)j(1982.)60 1993 y([338])25 b(R.)15 b(H.)g(Sw)o(endsen.)21 b(Mon)o(te-Carlo)16 b(renormalization)e(group.)22 b(In)15 b(M.)g(L)o(\023)-23 b(evy)l(,)16 b(J.-C.)f(LeGuil-)185 2053 y(lou,)k(and)h(J.)e(Zinn-Justin,)i (editors,)f FP(Phase)h(T)l(r)n(ansitions)g(\(Car)n(g)o(\022)-24 b(ese)20 b(1980\))p FQ(,)f(pages)g(395{)185 2113 y(422.)e(Plen)o(um,)c(New)j (Y)l(ork{London,)h(1982.)60 2215 y([339])25 b(R.)16 b(H.)h(Sw)o(endsen.)24 b(Mon)o(te)17 b(Carlo)h(calculation)f(of)g(renormalized)e(coupling)i (parameters.)185 2275 y(I.)e FF(d)f FQ(=)g(2)j(Ising)f(mo)q(del.)k FP(Phys.)d(R)n(ev.)p FQ(,)e(B30:3866{3874)q(,)j(1984.)60 2377 y([340])25 b(R.)13 b(H.)g(Sw)o(endsen)h(and)h(J.-S.)e(W)l(ang.)19 b(Non-univ)o(ersal)13 b(critical)g(dynamics)f(in)i(Mon)o(te)f(Carlo)185 2437 y(sim)o(ulations.)19 b FP(Phys.)e(R)n(ev.)g(L)n(ett.)p FQ(,)f(58:86{88,)i(1987.)60 2538 y([341])25 b(G.)d(S.)g(Sylv)o(ester.)38 b(Inequalities)20 b(for)j(con)o(tin)o(uous)f(spin)h(Ising)f(ferromagnets.)39 b FP(J.)22 b(Stat.)185 2599 y(Phys.)p FQ(,)15 b(15:327{341,)k(1976.)938 2784 y(270)p eop %%Page: 271 271 bop 60 91 a FQ([342])25 b(I.)15 b(Sy)o(ozi.)20 b(T)l(ransformation)c(of)h (Ising)f(mo)q(dels.)k(In)c(C.)g(Dom)o(b)f(and)i(M.)e(S.)h(Green,)g(editors,) 185 152 y FP(Phase)22 b(T)l(r)n(ansitions)f(and)i(Critic)n(al)e(Phenomena,)j (Vol.)f(1)p FQ(.)d(Academic)f(Press,)j(London{)185 212 y(New)15 b(Y)l(ork,)h(1972.)60 313 y([343])25 b(P)l(.)16 b(T)l(annery)l(.)23 b(Review)15 b(of)i(H.)f(Konen,)h(Gesc)o(hic)o(h)o(te)d(der)j(Gleic)o(h)o(ung) e FF(t)1489 295 y FH(2)1520 313 y FE(\000)c FF(D)q(u)1639 295 y FH(2)1674 313 y FQ(=)j(1.)23 b FP(Bul)r(l.)185 374 y(des)17 b(Sci.)h(Math.)p FQ(,)e(27:47{51,)i(1903.)23 b(See)15 b(page)i(51.)60 475 y([344])25 b(Th)o(\023)-23 b(eon)18 b(de)g(Sm)o(yrne.)25 b FP(Exp)n(osition)19 b(des)g(Connaissanc)n(es)h(Math)o(\023)-24 b(ematiques)20 b(Utiles)g(p)n(our)f(la)185 535 y(L)n(e)n(ctur)n(e)d(de)h (Platon)p FQ(,)f(pages)g(71{75.)22 b(Hac)o(hette,)14 b(P)o(aris,)h(1892.)21 b(T)l(ranslated)16 b(b)o(y)f(J.)g(Dupuis.)60 637 y([345])25 b(C.)11 b(J.)g(Thompson.)j FP(Mathematic)n(al)g(Statistic)n(al)g(Me)n (chanics)p FQ(.)g(Princeton)d(Univ)o(ersit)o(y)e(Press,)185 697 y(Princeton,)15 b(NJ,)g(1979.)60 799 y([346])25 b(C.)17 b(J.)g(Thompson.)25 b FP(Classic)n(al)19 b(Equilibrium)h(Statistic)n(al)f(Me) n(chanics)p FQ(.)26 b(Clarendon)18 b(Press,)185 859 y(Oxford,)d(1988.)60 961 y([347])25 b(A.)18 b(L.)g(T)l(o)q(om.)29 b(Stable)19 b(and)g(attractiv)o (e)f(tra)s(jectories)g(in)g(m)o(ulticomp)q(onen)o(t)e(systems.)27 b(In)185 1021 y(R.)22 b(L.)g(Dobrushin)h(and)g(Y)l(a.)f(G.)h(Sinai,)g (editors,)g FP(Multic)n(omp)n(onent)h(R)n(andom)f(Systems)185 1081 y(\(A)n(dvanc)n(es)16 b(in)h(Pr)n(ob)n(ability)f(and)g(R)n(elate)n(d)g (T)l(opics,)h(V)l(ol.)g(6\))p FQ(,)d(pages)i(549{575,)i(New)c(Y)l(ork{)185 1142 y(Basel,)h(1980.)i(Marcel)e(Dekk)o(er.)60 1243 y([348])25 b(H.)13 b(v)m(an)i(Beijeren.)i(In)o(terface)c(sharpness)j(in)e(the)g(Ising)h (system.)i FP(Commun.)e(Math.)h(Phys.)p FQ(,)185 1303 y(40:1{6,)h(1975.)60 1405 y([349])25 b(A.)13 b(C.)i(D.)f(v)m(an)h(En)o(ter.)k(A)14 b(note)h(on)g(the)f(stabilit)o(y)g(of)g(phase)i(diagrams)e(in)g(lattice)g (systems.)185 1465 y FP(Commun.)j(Math.)g(Phys.)p FQ(,)e(79:25{32,)j(1981.)60 1567 y([350])25 b(A.)c(C.)h(D.)h(v)m(an)g(En)o(ter.)39 b(Instabilit)o(y)21 b(of)i(phase)g(diagrams)f(for)h(a)f(class)h(of)g(\\irrelev)m(an)o(t")185 1627 y(p)q(erturbations.)f FP(Phys.)17 b(R)n(ev.)p FQ(,)e(B26:1336{1339)q(,)j (1982.)60 1729 y([351])25 b(A.)10 b(C.)g(D.)h(v)m(an)g(En)o(ter)g(and)g(R.)f (F)l(ern\023)-24 b(andez.)12 b(A)f(remark)e(on)i(di\013eren)o(t)f(norms)g (and)i(analyticit)o(y)185 1789 y(for)k(man)o(y-particle)e(in)o(teractions.)20 b FP(J.)d(Stat.)h(Phys.)p FQ(,)e(56:965{972,)j(1989.)60 1891 y([352])25 b(A.)17 b(C.)h(D.)g(v)m(an)h(En)o(ter,)f(R.)g(F)l(ern\023)-24 b(andez,)18 b(and)h(A.)e(D.)h(Sok)m(al.)28 b(Regularit)o(y)17 b(prop)q(erties)h(and)185 1951 y(pathologies)13 b(of)f(p)q(osition-space)i (renormalization-group)e(transformations.)j FP(Nucl.)g(Phys.)185 2011 y(B)i(\(Pr)n(o)n(c.)g(Suppl.\))p FQ(,)f(20:48{52,)i(1991.)60 2113 y([353])25 b(A.)17 b(C.)h(D.)g(v)m(an)h(En)o(ter,)f(R.)g(F)l(ern\023)-24 b(andez,)17 b(and)i(A.)f(D.)g(Sok)m(al.)27 b(Renormalization)17 b(transfor-)185 2173 y(mations)e(in)g(the)h(vicinit)o(y)d(of)j(\014rst-order) h(phase)f(transitions:)22 b(What)16 b(can)g(and)h(cannot)f(go)185 2233 y(wrong.)22 b FP(Phys.)17 b(R)n(ev.)g(L)n(ett.)p FQ(,)f(66:3253{3256,)j (1991.)60 2335 y([354])25 b(A.)14 b(C.)h(D.)h(v)m(an)g(En)o(ter,)f(R.)f(F)l (ern\023)-24 b(andez,)15 b(and)h(A.)f(D.)g(Sok)m(al.)20 b(Non-Gibbsian)c (states.)21 b(T)l(o)16 b(b)q(e)185 2395 y(published)d(in)g(the)g(pro)q (ceedings)h(of)g(the)f(1992)j(Prague)e(W)l(orkshop)h(on)f(Phase)g(T)l (ransitions.)185 2455 y(R.)h(Kotec)o(k)q(\023)-25 b(y,)15 b(editor.)g(W)l (orld)i(Scien)o(ti\014c,)d(Singap)q(ore,)i(1993.)938 2784 y(271)p eop %%Page: 272 272 bop 60 91 a FQ([355])25 b(A.)20 b(C.)g(D.)h(v)m(an)g(En)o(ter,)g(R.)g(F)l (ern\023)-24 b(andez,)21 b(and)g(A.)f(D.)h(Sok)m(al.)35 b(Non-Gibbsian)21 b(states)h(for)185 152 y(renormalization-group)15 b(transformations)h(and)h (b)q(ey)o(ond.)k(T)l(o)16 b(b)q(e)g(published)g(in)g(the)f(pro-)185 212 y(ceedings)22 b(of)i(the)f(NA)l(TO)f(Adv)m(anced)h(Studies)g(Institute)g (w)o(orkshop)h(on)g(Cellular)e(Au-)185 272 y(tomata)c(and)h(Co)q(op)q(erativ) o(e)g(Systems)e([Les)i(Houc)o(hes)f(1992].)h(N.)f(Bo)q(ccara,)h(E.)f(Goles,)h (S.)185 332 y(Martinez)c(and)i(P)l(.)f(Picco,)f(editors.)h(Klu)o(w)o(er,)e (Dordrec)o(h)o(t,)h(1993.)60 434 y([356])25 b(A.)15 b(C.)h(D.)g(v)m(an)h(En)o (ter)e(and)i(J.)f(Mi\030)-22 b(ekisz.)19 b(Breaking)d(of)g(p)q(erio)q(dicit)o (y)f(at)i(p)q(ositiv)o(e)e(temp)q(era-)185 494 y(tures.)21 b FP(Commun.)c(Math.)g(Phys.)p FQ(,)f(134:647{651,)j(1990.)60 596 y([357])25 b(J.)19 b(M.)g(J.)h(v)m(an)g(Leeu)o(w)o(en.)31 b(Singularities)19 b(in)g(the)h(critical)e(surface)i(and)g(univ)o(ersalit)o (y)e(for)185 656 y(Ising-lik)o(e)c(spin)i(systems.)k FP(Phys.)d(R)n(ev.)h(L)n (ett.)p FQ(,)d(34:1056{105)q(8,)k(1975.)60 758 y([358])25 b(V.)18 b(S.)h(V)l(aradara)s(jan.)32 b(Measures)19 b(on)h(top)q(ological)g(spaces)g ([in)f(Russian].)30 b FP(Mat.)20 b(Sb)n(ornik)185 818 y(\(N.S.\))p FQ(,)e(55\(97\):35{100,)j(1961.)29 b([English)17 b(translation)i(in)f(Amer.)d (Math.)j(So)q(c.)g(T)l(ransla-)185 878 y(tions)e(\(Ser.)g(2\))g FM(48)p FQ(,)g(161{228)j(\(1965\).].)60 980 y([359])25 b(S.)16 b(R.)f(S.)h(V)l(aradhan.)22 b(Priv)m(ate)16 b(comm)o(unication,)d(1984.)60 1081 y([360])25 b(S.)11 b(R.)h(S.)g(V)l(aradhan.)j FP(L)n(ar)n(ge)d (Deviations)j(and)f(Applic)n(ations)p FQ(.)h(SIAM,)10 b(Philadelphia,)i (1984.)60 1183 y([361])25 b(J.)15 b(V)l(oigt.)k(Sto)q(c)o(hastic)c(op)q (erators,)i(information)d(and)i(en)o(trop)o(y)l(.)i FP(Commun.)f(Math.)f (Phys.)p FQ(,)185 1243 y(81:31{38,)i(1981.)60 1345 y([362])25 b(J.-S.)14 b(W)l(ang)h(and)h(J.)e(L.)h(Leb)q(o)o(witz.)j(Phase)e(transitions) f(and)g(univ)o(ersalit)o(y)e(in)h(nonequilib-)185 1405 y(rium)g(steady)j (states)f(of)h(sto)q(c)o(hastic)f(Ising)g(mo)q(dels.)21 b FP(J.)16 b(Stat.)j(Phys.)p FQ(,)c(51:893{906,)k(1988.)60 1507 y([363])25 b(A.)19 b(S.)g(Wigh)o(tman.)31 b(Con)o(v)o(exit)o(y)19 b(and)h(the)g(notion)g (of)g(equilibrium)d(state)j(in)g(thermo)q(dy-)185 1567 y(namics)15 b(and)i(statistical)f(mec)o(hanics.)21 b(In)o(tro)q(duction)16 b(to)h(R.)g(B.)e(Israel,)h FP(Convexity)j(in)f(the)185 1627 y(The)n(ory)e(of)h(L)n(attic)n(e)g(Gases)t FQ(,)f(Princeton)g(Univ)o(ersit)o (y)e(Press,)i(1979.)60 1729 y([364])25 b(K.)17 b(G.)h(Wilson.)28 b(The)18 b(renormalization)e(group:)27 b(Critical)17 b(phenomena)g(and)i(the) f(Kondo)185 1789 y(problem.)h FP(R)n(ev.)e(Mo)n(d.)g(Phys.)p FQ(,)e(47:773{840,)k(1975.)60 1891 y([365])25 b(K.)20 b(G.)h(Wilson)g(and)g (J.)g(Kogut.)36 b(The)21 b(renormalization)e(group)j(and)g(the)e FF(\017)p FQ(-expansion.)185 1951 y FP(Phys.)d(R)n(ep)n(orts)p FQ(,)d(12C:75{200,)19 b(1974.)60 2053 y([366])25 b(M.)19 b(Zahradn)-5 b(\023)-19 b(\020k.)33 b(An)20 b(alternate)g(v)o(ersion)g(of)g(Pirogo)o (v-Sinai)h(theory)l(.)32 b FP(Commun.)21 b(Math.)185 2113 y(Phys.)p FQ(,)15 b(93:559{5581,)k(1984.)60 2215 y([367])25 b(M.)18 b(Zahradn)-5 b(\023)-19 b(\020k.)28 b(Lo)o(w)19 b(temp)q(erature)f(con)o(tin)o(uous)g (spin)h(Gibbs)g(states)g(on)g(a)g(lattice)e(and)185 2275 y(the)f(in)o (terfaces)f(b)q(et)o(w)o(een)h(them)f(|)h(a)h(Pirogo)o(v-Sinai)f(t)o(yp)q(e)g (approac)o(h.)23 b(In)16 b(T.)g(C.)h(Dorlas,)185 2335 y(N.)10 b(M.)h(Hugenholtz,)h(and)g(M.)f(Winnink,)g(editors,)h FP(Statistic)n(al)j(Me) n(chanics)e(and)h(Field)f(The-)185 2395 y(ory:)29 b(Mathematic)n(al)22 b(Asp)n(e)n(cts)g(\(Pr)n(o)n(c)n(e)n(e)n(dings,)f(Gr)n(oningen)h(1985\))p FQ(,)f(Berlin{Heidelb)q(erg{)185 2455 y(New)15 b(Y)l(ork,)h(1986.)h (Springer-V)l(erlag)f(\(Lecture)g(Notes)g(in)g(Ph)o(ysics)f(#257\).)60 2557 y([368])25 b(M.)c(Zahradn)-5 b(\023)-19 b(\020k.)39 b(Analyticit)o(y)20 b(of)i(lo)o(w-temp)q(erature)f(phase)i(diagrams)f(of)g(lattice)f(spin)185 2617 y(mo)q(dels.)f FP(J.)d(Stat.)h(Phys.)p FQ(,)d(47:725{755,)k(1987.)938 2784 y(272)p eop %%Page: 273 273 bop 60 91 a FQ([369])25 b(M.)14 b(Zahradn)-5 b(\023)-19 b(\020k.)20 b(Phase)d(diagrams)e(of)g(lattice)g(spin)g(mo)q(dels.)k(Cours)e(de)e(T)l (roisi)o(\022)-23 b(eme)13 b(Cycle)185 152 y(de)j(la)g(Ph)o(ysique)f(en)h (Suisse)g(Romande)g(\(Lausanne\),)h(Ma)o(y)f(1987.)60 253 y([370])25 b(M.)16 b(Zahradn)-5 b(\023)-19 b(\020k.)23 b(Lo)o(w)18 b(temp)q(erature)d (phase)i(diagrams)g(of)g(lattice)f(mo)q(dels)g(with)g(random)185 313 y(impurities.)i(Preprin)o(t,)d(1988.)60 415 y([371])25 b(M.)15 b(Zahradn)-5 b(\023)-19 b(\020k.)21 b(Priv)m(ate)16 b(comm)o(unication.)i(1990.)938 2784 y(273)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF