Content-Type: multipart/mixed; boundary="-------------0501141029522" This is a multi-part message in MIME format. ---------------0501141029522 Content-Type: text/plain; name="05-20.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="05-20.keywords" Molchanov-Vainberg Laplacian, discrete Laplacian, Green function, scattering theory ---------------0501141029522 Content-Type: application/postscript; name="art1.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="art1.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: art1.dvi %%Pages: 12 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o art1.ps art1.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2004.12.11:1816 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true 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/IEn 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 IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/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 A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A 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/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 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/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/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{SS restore}B end %%EndProcSet TeXDict begin 40258431 52099146 1000 600 600 (art1.dvi) @start %DVIPSBitmapFont: Fa cmti9 9 41 /Fa 41 123 df<1560EC01E0EC03C0EC0700140E5C143C5C5C495A495A13075C49C7FC5B 131E5B137C137813F85B12015B12035B1207A25B120FA290C8FC5AA2121E123EA3123C12 7CA31278A212F8A35AAF12701278A21238A2123C121CA27EA27E6C7E12011B4A75B71F> 40 D<14301438A28080A2140F801580A2140315C0A4140115E0A81403A415C0A31407A3 1580140FA315005CA3141E143EA2143C147CA25CA25C13015C13035C13075C130F91C7FC 131E133E133C5B5B485AA2485A485A48C8FC121E5A12705A5A1B4A7EB71F>I44 DI49 D57 D<1370EA01FC1203A413F8EA00E01300B0121C127F5AA45A12380E20779F18>I<161C16 3CA2167C16FCA21501821503A2ED077E150F150E151CA21538A2157015F015E0EC01C0A2 913803807F82EC0700A2140E141E141C5CA25CA25C49B6FCA25B913880003F49C7EA1F80 A2130E131E131C133C13385B13F05B12011203D80FF0EC3FC0D8FFFE903807FFFEA32F36 7BB539>65 D67 D<0107B712F05B18E0903A003F80001F1707170392C7FC17015C18C0147EA214FEA24A13 0EA20101EC1E03041C13804A91C7FC163C13035E9138F001F891B5FC5B5EECE001150013 0F5E5C1707011F01015BEEC00E0280141E92C7121C133F173C91C812381778495DA2017E 14014C5A01FE14074C5A49141F00014AB45A007FB7FCB8FC94C7FC34337CB234>69 D<0107B548B512C0495CA2903C003FC0000FF0004B5CA292C75BA24A141F60147EA202FE 143F95C7FC5CA201015D177E5CA2010315FE5F5C91B6FC5B5F9138E00001A2010F14035F 5CA2011F14075F5CA2013F140F5F91C7FCA249141F5F137EA201FE143F94C8FC5B00015D 3B7FFFF01FFFFCB55BA23A337BB239>72 D<010FB51280A216009038003FC05DA292C7FC A25CA2147EA214FEA25CA21301A25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2 133FA291C8FCA25BA2137EA213FEA25B1201B512F8A25C21337BB21E>I<0107B512C05B A29026003FC0C7FC5DA292C8FCA25CA2147EA214FEA25CA21301A25CA21303A25CA21307 A25CA2130FA25C17E0011F140117C05C1603013F1580160791C7FCEE0F005B5E017E143E A201FE5CED01FC4913030001EC1FF8007FB6FCB7FC5E2B337CB230>76 D<902607FFC0ED7FFC4917FF81D9003F4B1300611803023BED077CA2027BED0EFC610273 151C1838DAF1F01439F071F014E118E10101ED01C36102C1EC0383EF070301031607050E 5BEC80F8171C0107ED380F6102001470A249EDE01FDC01C090C7FC130EEE0380011E017C 5C933807003E011C140EA2013C4A137E187C01385C5E017816FC6F485B1370ED3FC001F0 EC80016000011500D807F81503277FFF803E90B512C0B5EB3C01151C46337BB245>I<01 07B612C04915F883903A003F8001FEEE003FEF1F8092C713C0170F5C18E0147EA214FEEF 1FC05CA201011680173F4A1500177E010315FE5F4AEB03F8EE07E00107EC3FC091B6C7FC 16F802E0C9FC130FA25CA2131FA25CA2133FA291CAFCA25BA2137EA213FEA25B1201387F FFF0B5FCA233337CB234>80 D<913901FC018091380FFF03023F13C791387E07EF903A01 F801FF0049487E4A7F495A4948133E131F91C7FC5B013E143CA3137E1638A293C7FC137F A26D7E14E014FE90381FFFC06D13F86D7F01017F6D6C7E020F7F1400153F6F7E150FA412 0EA2001E5D121CA2151F003C92C7FCA2003E143E5D127E007F5C6D485A9038C007E039F3 F80FC000F0B5C8FC38E03FFC38C00FF029377AB42B>83 D87 D97 D<137EEA0FFE121F5B1200A35BA21201A25BA21203A25BA21207A2EBC3E0 EBCFF8380FDC3EEBF81F497E01E01380EA1FC0138015C013005AA2123EA2007E131F1580 127CA2143F00FC14005AA2147EA25CA2387801F85C495A6C485A495A6C48C7FCEA0FFCEA 03F01A3578B323>I<14FCEB07FF90381F078090383E03C0EBFC013801F8033803F00738 07E00F13C0120F391F80070091C7FC48C8FCA35A127EA312FE5AA4007C14C0EC01E0A2EC 03C06CEB0F80EC1F006C137C380F81F03803FFC0C648C7FC1B2278A023>III<151FED7FC0EDF0E0020113F0EC03E3A2 EC07C316E0EDC1C091380FC0005DA4141F92C7FCA45C143E90381FFFFEA3D9007EC7FC14 7CA414FC5CA513015CA413035CA413075CA3130FA25CA3131F91C8FCA35B133E1238EA7E 3CA2EAFE7812FC485AEA78E0EA3FC0000FC9FC244582B418>I<143FECFF80903803E1E6 903807C0FF90380F807FEB1F00133E017E133F49133EA24848137EA24848137CA215FC12 074913F8A21401A2D80FC013F0A21403120715E01407140F141F3903E03FC00001137FEB F0FF38007FCF90381F0F801300141FA21500A25C143E1238007E137E5C00FE5B48485A38 7803E0387C0F80D81FFFC7FCEA07F820317CA023>III<133FEA07FF5A13FEEA007EA3137CA213FCA213F8A21201A213F0A21203A213E0 A21207A213C0A2120FA21380A2121FA21300A25AA2123EA2127EA2127C1318EAFC1C133C EAF838A21378137012F013F0EAF8E01279EA3FC0EA0F00103579B314>108 D<2703C003F8137F3C0FF00FFE01FFC03C1E783C1F07C1E03C1C7CF00F8F01F03B3C3DE0 079E0026383FC001FC7FD97F805B007001005B5E137ED8F0FC90380FC00100E05FD860F8 148012000001021F130360491400A200034A13076049013E130FF081800007027EEC83C0 051F138049017C1403A2000F02FC1407053E130049495CEF1E0E001F01015D183C010049 EB0FF0000E6D48EB03E03A227AA03F>I<3903C007F0390FF01FFC391E787C1E391C7CF0 1F393C3DE00F26383FC01380EB7F8000781300EA707EA2D8F0FC131F00E01500EA60F812 0000015C153E5BA20003147E157C4913FCEDF8180007153C0201133801C013F0A2000F15 78EDE070018014F016E0001FECE1C015E390C7EAFF00000E143E26227AA02B>I<14FCEB 07FF90381F07C090383E03E09038FC01F0EA01F83903F000F8485A5B120F484813FCA248 C7FCA214014814F8127EA2140300FE14F05AA2EC07E0A2007CEB0FC01580141FEC3F006C 137E5C381F01F0380F83E03803FF80D800FCC7FC1E2278A027>I<011E137C90387F81FF 9039F3C387C09039E3EF03E03901E1FE01D9C1FC13F0EBC3F8000313F0018314F814E0EA 07871307000313C01200010F130316F01480A2011F130716E01400A249EB0FC0A2013EEB 1F80A2017EEB3F00017F133E5D5D9038FF81F09038FDC3E09038F8FF80027EC7FC000190 C8FCA25BA21203A25BA21207A25BB5FCA325307FA027>I<903803F01890380FF8389038 3E1C7890387C0EF89038F807F0EA01F0EA03E000071303D80FC013E0A2EA1F801407D83F 0013C0A348130F007E1480A300FE131F481400A35C143E147E127C14FE495AEA3C03EA3E 07EA1F0E3807FCF8EA01F0C7FC13015CA313035CA21307A25C48B5FCA25C1D3078A023> I<3903C00FC0390FF03FF0391E78F078391C7DE03C393C3FC0FC00381380EB7F00007814 F8D8707E13701500EAF0FC12E0EA60F812001201A25BA21203A25BA21207A25BA2120FA2 5BA2121FA290C8FC120E1E227AA020>II<1303EB0F80A3131FA21400A25BA2133EA2137EA2137C387FFFF8A2B5FC38 00F800A21201A25BA21203A25BA21207A25BA2120FA25B1460001F13F014E01300130114 C01303001E1380EB07005BEA0F1EEA07F8EA01E015307AAE19>I I<01F01338D803FC13FCEA0F1E120E121C123C0038147CEA783E0070143CA2137ED8F07C 1338EA60FCC65A1578000114705BA215F0000314E05BA2EC01C0A2EBC003158014071500 EBE00EA26C6C5A3800F878EB7FE0EB1F801E227AA023>II<011F137C90387FC1FF3A01E1E787803A03C0F7 03C0903880FE0FEA07004813FC000E1580001E9038F80700001C91C7FC1301003C5B1218 120013035CA31307A25C1506010F130F150E14800038141ED87C1F131C00FC143C153801 3F5B39F07FC0E03970F3C3C0393FE1FF80260F807EC7FC22227CA023>I<13F0D803FC13 07D80F1E130F000E141F121C123C0038143FD8783E133E1270A2017E137ED8F07C137CEA 60FCC65A15FC000114F85BA21401000314F013E0A2140315E0EA07C0A20003130715C0EB E00F141F0001133F9038F07F8038007FEFEB1F8FEB001F1500A25C003E133E007E137E14 7C5C007C5BEA7001495A38380780D83C1FC7FCEA0FFCEA07F020317AA025>I<90380780 1C90381FE03C90383FF038017F13789038FFF8F03901F07CE0EBE01F3903C003C0903880 0780EC0F00C7121E141C143C5C5C495AEB07C0495A011EC7FC5B5B4913704913F0000114 E0485A38078001390FC003C0381FF80790383E0F80393C1FFF00127838700FFE38F007F8 38E001E01E227CA01F>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb msam10 10 1 /Fb 1 4 df<007FB812F8B912FCA300F0CA123CB3B3ACB912FCA36C17F836387BB741>3 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmbx12 12 29 /Fc 29 123 df46 D49 DII<163FA25E5E 5D5DA25D5D5D5DA25D92B5FCEC01F7EC03E7140715C7EC0F87EC1F07143E147E147C14F8 EB01F0EB03E0130714C0EB0F80EB1F00133E5BA25B485A485A485A120F5B48C7FC123E5A 12FCB91280A5C8000F90C7FCAC027FB61280A531417DC038>I65 D67 D71 D80 D82 D<903801FFE0011F13FE017F6D7E48B612E03A03FE007FF84848EB1FFC6D6D7E486C6D7E A26F7FA36F7F6C5A6C5AEA00F090C7FCA40203B5FC91B6FC1307013F13F19038FFFC0100 0313E0000F1380381FFE00485A5B127F5B12FF5BA35DA26D5B6C6C5B4B13F0D83FFE013E EBFFC03A1FFF80FC7F0007EBFFF86CECE01FC66CEB8007D90FFCC9FC322F7DAD36>97 D99 DII103 D<137C48B4FC4813804813C0A24813E0A56C13C0A26C1380 6C1300EA007C90C7FCAAEB7FC0EA7FFFA512037EB3AFB6FCA518467CC520>105 D108 D<90277F8007FEEC0FFC B590263FFFC090387FFF8092B5D8F001B512E002816E4880913D87F01FFC0FE03FF8913D 8FC00FFE1F801FFC0003D99F009026FF3E007F6C019E6D013C130F02BC5D02F86D496D7E A24A5D4A5DA34A5DB3A7B60081B60003B512FEA5572D7CAC5E>I<90397F8007FEB59038 3FFF8092B512E0028114F8913987F03FFC91388F801F000390399F000FFE6C139E14BC02 F86D7E5CA25CA35CB3A7B60083B512FEA5372D7CAC3E>II<90397FC00FF8B590B57E02C314E002CF14F89139DFC03F FC9139FF001FFE000301FCEB07FF6C496D13804A15C04A6D13E05C7013F0A2EF7FF8A4EF 3FFCACEF7FF8A318F017FFA24C13E06E15C06E5B6E4913806E4913006E495A9139DFC07F FC02CFB512F002C314C002C091C7FCED1FF092C9FCADB67EA536407DAC3E>I<90387F80 7FB53881FFE0028313F0028F13F8ED8FFC91389F1FFE000313BE6C13BC14F8A214F0ED0F FC9138E007F8ED01E092C7FCA35CB3A5B612E0A5272D7DAC2E>114 D<90391FFC038090B51287000314FF120F381FF003383FC00049133F48C7121F127E00FE 140FA215077EA27F01E090C7FC13FE387FFFF014FF6C14C015F06C14FC6C800003806C15 806C7E010F14C0EB003F020313E0140000F0143FA26C141F150FA27EA26C15C06C141FA2 6DEB3F8001E0EB7F009038F803FE90B55A00FC5CD8F03F13E026E007FEC7FC232F7CAD2C >IIII120 DI<001FB71280A4 9026FC001F130001E0495A5B49495A90C7485A48495B123E4A5B4A5B003C495BA24A90C7 FC4A5A4A5AC7FC4A5A495B495BA2495B499038800780491300A2495A4948130F49481400 A2485B48495B485BA248495B4890C75A48485C15034848EB1FFEB7FCA4292C7DAB32>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd cmr12 14.4 1 /Fd 1 9 df<023FB612FEA4DA000701F0C8FC030113C06F5BAA030713E092B6FC020F15 F0DA3FFCEBBFFC902601FF80903881FF80902607FE009038807FE0D90FF8ED1FF0D93FE0 ED07FC49486F7E49486F7E4890C76E13804848EF7FC04848EF3FE0000F19F04848EF1FF8 A24848EF0FFCA2007F19FE491707A200FF19FFA8007F19FEA26D170F003F19FCA26C6CEF 1FF8A26C6CEF3FF0000719E06C6CEF7FC06C6CEFFF806C6D4B13006D6C4B5A6D6C4B5AD9 0FF8ED1FF0D907FEED7FE0902601FF80903881FF809026003FFCD9BFFCC7FC020FB612F0 020092C8FC030713E003001380AA4B7F030713F0023FB612FEA448527AD155>8 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe msbm6 6 1 /Fe 1 91 df<003FB512F0A23933C03060393F0070E0003CEB60C04813E1397001C380EC 830038600387EB07063800060EEB0E1CEB0C18EB1C38495AEB3060EB70E0EB60C013E148 485A0183C7FCD8038713181306EA070ED80E1C1338EA0C18D81C381378EA1830D8387013 F03870E0013960C003B000E1EB0F30B612F0A21D227EA150>90 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff cmex8 8 1 /Ff 1 81 df80 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg cmbx10 10 32 /Fg 32 122 df<49B4FC010F13E0017F13FC9038FF83FE4848C67E4848EB7F804848EB3F C04848EB1FE0A2001F15F0A24848EB0FF8A3007F15FCA500FF15FEB3007F15FCA4003F15 F8A26D131F001F15F0A2000F15E06D133F000715C06C6CEB7F806C6CEBFF003900FF83FE 6DB45A011F13F0010190C7FC27387CB630>48 D<141E143E14FE1307133FB5FCA313CFEA 000FB3B3A6007FB61280A4213779B630>IIII<001C15C0D81F80130701F8137F90B61280A216005D5D15F05D15 804AC7FC14F090C9FCA8EB07FE90383FFFE090B512F89038FC07FC9038E003FFD9800113 8090C713C0120EC813E0157F16F0A216F8A21206EA3F80EA7FE012FF7FA44914F0A26C48 13FF90C713E0007C15C06C5B6C491380D9C0071300390FF01FFE6CB512F8000114E06C6C 1380D90FF8C7FC25387BB630>II<12 3C123EEA3FE090B71280A41700485D5E5E5EA25E007CC7EA0FC000784A5A4BC7FC00F814 7E48147C15FC4A5A4A5AC7485A5D140F4A5A143F92C8FC5C147E14FE1301A2495AA31307 A2130F5CA2131FA5133FA96D5A6D5A6D5A293A7BB830>I<49B47E010F13F0013F13FC90 38FE01FF3A01F8007F804848EB3FC04848EB1FE0150F485AED07F0121FA27FA27F7F01FE EB0FE0EBFF809138E01FC06CEBF03F02FC13809138FF7F006C14FC6C5C7E6C14FE6D7F6D 14C04914E048B612F0EA07F848486C13F8261FE01F13FC383FC007EB8001007F6D13FE90 C7123F48140F48140715031501A21500A216FC7E6C14016D14F86C6CEB03F06D13076C6C EB0FE0D80FFEEB7FC00003B61200C614FC013F13F00103138027387CB630>III67 D70 D76 D80 D82 D<003FB91280A4D9F800EBF003D87FC09238007FC049161F007EC7150FA2007C1707A200 781703A400F818E0481701A4C892C7FCB3AE010FB7FCA43B387DB742>84 D97 D<903803FF80011F13F0017F13FC3901FF83FE3A03FE007F804848133F 484814C0001FEC1FE05B003FEC0FF0A2485A16F8150712FFA290B6FCA301E0C8FCA4127F A36C7E1678121F6C6C14F86D14F000071403D801FFEB0FE06C9038C07FC06DB51200010F 13FC010113E025257DA42C>101 DI<13FFB5FCA412077EAFED7FC0913803FFF8020F13FE91381F03 FFDA3C01138014784A7E4A14C05CA25CA291C7FCB3A3B5D8FC3F13FFA4303A7DB935> 104 DI<13FFB5FCA412077EAF92380FFFE0A4923803FC0016F0ED0FE0 ED1F804BC7FC157E5DEC03F8EC07E04A5A141FEC7FE04A7E8181A2ECCFFEEC0FFF496C7F 806E7F6E7F82157F6F7E6F7E82150F82B5D8F83F13F8A42D3A7EB932>107 D<13FFB5FCA412077EB3B3ACB512FCA4163A7DB91B>I<01FED97FE0EB0FFC00FF902601 FFFC90383FFF80020701FF90B512E0DA1F81903983F03FF0DA3C00903887801F000749DA CF007F00034914DE6D48D97FFC6D7E4A5CA24A5CA291C75BB3A3B5D8FC1FB50083B512F0 A44C257DA451>I<01FEEB7FC000FF903803FFF8020F13FE91381F03FFDA3C0113800007 13780003497E6D4814C05CA25CA291C7FCB3A3B5D8FC3F13FFA430257DA435>I<903801 FFC0010F13F8017F13FFD9FF807F3A03FE003FE048486D7E48486D7E48486D7EA2003F81 491303007F81A300FF1680A9007F1600A3003F5D6D1307001F5DA26C6C495A6C6C495A6C 6C495A6C6C6CB45A6C6CB5C7FC011F13FC010113C029257DA430>I<9039FF01FF80B500 0F13F0023F13FC9138FE07FFDAF00113800007496C13C06C0180EB7FE091C713F0EE3FF8 A2EE1FFCA3EE0FFEAA17FC161FA217F8163F17F06E137F6E14E06EEBFFC0DAF003138091 39FC07FE0091383FFFF8020F13E0020390C7FC91C9FCACB512FCA42F357EA435>I<9038 FE03F000FFEB0FFEEC3FFF91387C7F809138F8FFC000075B6C6C5A5CA29138807F80ED3F 00150C92C7FC91C8FCB3A2B512FEA422257EA427>114 D<90383FF0383903FFFEF8000F 13FF381FC00F383F0003007E1301007C130012FC15787E7E6D130013FCEBFFE06C13FCEC FF806C14C06C14F06C14F81203C614FC131F9038007FFE140700F0130114007E157E7E15 7C6C14FC6C14F8EB80019038F007F090B512C000F8140038E01FF81F257DA426>I<130F A55BA45BA25B5BA25A1207001FEBFFE0B6FCA3000390C7FCB21578A815F86CEB80F01481 6CEBC3E090383FFFC06D1380903803FE001D357EB425>I121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh msbm7 7 2 /Fh 2 85 df82 D84 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fi msbm8 8 3 /Fi 3 91 df82 D84 D<001FB612FCA23A183E00701801F0EB6038D81BC0EBE030001FC7EAC070003E01 0113E0003C90380380C01501003801071380EC0603003090380E0700EC1C06EC180EC7EA 380CEC301CEC7038ECE030ECC07001015B4A5AEB03819038070180EB0603D90E07C7FCEB 0C06EB1C0EEB380CEB301CD970381303EBE030EBC070000101601307EB80E0260381C013 0626070180130ED80603141E000E90C7FCD80C07143ED81C0E1476D8380C14E6D8301CEB 01CED87018EB078CD86038EB3E0CB712FCA2282E7EAD38>90 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj cmmi8 8 7 /Fj 7 121 df<90B612F812035A4815F03A1E0380C000003C130000701301130700E05C EAC00638000E03A3131CA2133C140713381378A201F07FA21201A2D803E07FA200071303 13C0A26C486C5A251E7E9C29>25 D<1506A3150E150CA3151C1518A315381530A31570D8 01E0EB6007D807F8EC1F80EA0E3CD81C3E01E013C0003814C00030150F0070150726607E 011480D8E07CEB800312C013FC3880F803000002001300120113F04A5B00030106130601 E0140E160C020E131C020C131801C0143801E05C021C5B91381801C0D801F0495A030FC7 FC3900FC381C90383F30F890380FFFE0010190C8FCEB00701460A314E05CA313015CA42A 3C7EAD2E>32 D<90383FFFFEA2010090C8FC5C5CA21301A25CA21303A25CA21307A25CA2 130FA25CA2131FA25CA2133FA291C7EA0180A24914031700017E5C160601FE140EA2495C 163C12015E49EB01F84B5A0003141FB7FC5E292D7DAC30>76 D101 D<137CEA0FFCA21200A213F8A21201A213 F0A21203A213E0A21207A213C0A2120FA21380A2121FA21300A25AA2123EA2127EA2127C A2EAFC08131812F8A21338133012F01370EAF860EA78E0EA3FC0EA0F000E2F7DAD15> 108 D<3907C007E0391FE03FF83918F8783E393879E01E39307B801F38707F00126013FE EAE0FC12C05B00815C0001143E5BA20003147E157C5B15FC0007ECF8081618EBC00115F0 000F1538913803E0300180147016E0001F010113C015E390C7EAFF00000E143E251F7E9D 2B>110 D<013F137C9038FFC1FF3A01C1E383803A0380F703C0390700F60F000E13FE48 13FC12180038EC0700003049C7FCA2EA200100005BA313035CA301075B5D14C000385CD8 7C0F130600FC140E011F130C011B131C39F03BE038D8707113F0393FE0FFC0260F803FC7 FC221F7E9D28>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmti8 8 9 /Fk 9 119 df97 D101 D<130E131FEB3F80A2EB1F 00130E90C7FCA9EA03E0EA0FF0EA1E78EA1C7C12381278127013FCEAF0F812E012E1EAC1 F0120112035B12075BA2120F13831387121F13075BEA3F0E123EEA1E1C133C1338EA0FF0 EA03C0112E7AAC16>105 D<137CEA0FFCA21200A213F8A21201A213F0A21203A213E0A2 1207A213C0A2120FA21380A2121FA21300A25AA2123EA2127EA2127CA2EAFC30137012F8 A213F013E012F012F113C012FBEA7F80EA1E000E2F7AAD12>108 D<3907801FC0391FE07FF0393DF1E0F83938F3C0783978FF007CEA70FEA2EAF1FCEAE1F8 A25B00C314FC00035C5BA2000713015D13C01403000FECE0C015E1EB800715C1001F14C3 020F13800100138391380787005A158E003EEB03FC001CEB00F0221F7A9D28>110 D<903807C06090381FF0E0EB7C39EBF81FEA01F03903E00FC0EA07C0120FEA1F801580EA 3F00A248131F007E1400A300FE5B48133EA3147E48137CA214FCEA7801387C03F8A2EA3C 0FEA1E1F380FF9F0EA03E1EA000113035CA313075CA2130FA23801FFFCA21B2B799D21> 113 D<131C133EA2137EA2137CA213FCA25BA21201A2B512E0A23803F000A25BA21207A2 5BA2120FA25BA2121FA290C7FCA24813C01301123E130314801307003C1300130E131E6C 5AEA0FF0EA07C0132B7AA918>116 DI<3903C001C0390FF003E0391E7807F0EA1C7C12380078 13030070130113FCD8F0F813E012E000E1130038C1F001000114C0120313E01403000714 8013C0A2EC0700120F1380140EA25C12076D5A00035B6D5AC6B45A013FC7FC1C1F7A9D21 >I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmti10 10 53 /Fl 53 122 df<04FFEB03F003039038E00FFC923A0FC0F01F1E923A3F00783E0F923A7E 01F87C3FDB7C03EBFC7F03FC14F8DA01F813F905F1137EDC01E1133C913B03F00003F000 A314074B130760A3140F4B130F60A3010FB812C0A3903C001F80001F8000A3023F143F92 C790C7FCA44A5C027E147EA402FE14FE4A5CA413014A13015FA313034A13035FA313074A 495AA44948495AA44948495AA3001CD9038090C8FC007E90380FC03F013E143E00FE011F 5B133C017C5C3AF8780F01E0D878F0EB07C0273FE003FFC9FC390F8000FC404C82BA33> 11 DI< EA01E0EA07F0120F13F8121FA3120FEA07B0EA0030A21370136013E013C0120113801203 EA0700120E5A5A5A5A5A0D196EB919>39 D<150C151C153815F0EC01E0EC03C0EC0780EC 0F00141E5C147C5C5C495A1303495A5C130F49C7FCA2133EA25BA25BA2485AA212035B12 075BA2120F5BA2121FA290C8FCA25AA2123EA2127EA2127CA412FC5AAD1278A57EA3121C 121EA2120E7EA26C7E6C7EA212001E5274BD22>I<140C140E80EC0380A2EC01C015E0A2 140015F0A21578A4157C153CAB157CA715FCA215F8A21401A215F0A21403A215E0A21407 A215C0140F1580A2141F1500A2143EA25CA25CA2495AA2495A5C1307495A91C7FC5B133E 133C5B5B485A12035B48C8FC120E5A12785A12C01E527FBD22>I44 D<387FFFF8A2B5FCA214F0150579941E>I<120EEA3F80127F12FFA313 00127E123C0909778819>I<15181538157815F0140114031407EC0FE0141F147FEB03FF 90383FEFC0148FEB1C1F13001580A2143FA21500A25CA2147EA214FEA25CA21301A25CA2 1303A25CA21307A25CA2130FA25CA2131FA25CA2133FA291C7FC497EB61280A31D3877B7 2A>49 DII<133C137E13FF5AA313FE13FCEA00701300 B2120EEA3F80127F12FFA31300127E123C102477A319>58 D<0007B812FE4817FFA26C17 FECCFCAE007FB812C0B912E0A26C17C03816779F40>61 D67 D<0107B8FCA3903A000FF000034B EB007F183E141F181E5DA2143FA25D181C147FA29238000380A24A130718004A91C7FC5E 13015E4A133E167E49B512FEA25EECF8000107147C163C4A1338A2010F147818E04A1370 1701011F16C016004A14031880013F150718004A5CA2017F151E173E91C8123C177C4915 FC4C5A4914070001ED7FF0B8FCA25F38397BB838>69 D<0107B712FEA3903A000FF00007 4B1300187C021F153CA25DA2143FA25D1838147FA292C8FCEE03804A130718004A91C7FC A201015CA24A131E163E010314FE91B5FC5EA2903807F800167C4A1378A2130FA24A1370 A2011F14F0A24A90C8FCA2133FA25CA2137FA291CAFCA25BA25B487EB6FCA337397BB836 >II<0103B512F8A390390007F8005DA2140FA25DA2141FA25DA2143FA25DA2147F A292C7FCA25CA25CA21301A25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2133F A25CA2137FA291C8FC497EB6FCA25C25397CB820>73 D<0107B512FCA25E9026000FF8C7 FC5D5D141FA25DA2143FA25DA2147FA292C8FCA25CA25CA21301A25CA21303A25CA21307 A25CA2130F170C4A141CA2011F153C17384A1478A2013F157017F04A14E01601017F1403 17C091C71207160F49EC1F80163F4914FF000102071300B8FCA25E2E397BB834>76 D<902607FFF8923807FFF0614F13E0D9000FEFF0004F5AA2021F167FF1EFC0141DDA1CFC EC01CF023C16DF9538039F800238ED071FA20278ED0E3F97C7FC0270151CA202F04B5AF0 707E14E0037E14E0010117FE4D485A02C0EC0380A20103ED0701610280140EA20107ED1C 0305385B14006F137049160705E05B010EEC01C0A2011E913803800F61011CEC0700A201 3C020E131F4C5C1338ED1FB80178163F04F091C8FC01705CA201F04A5B187E00015DD807 F816FEB500C09039007FFFFC151E150E4C397AB84A>I79 D<0107B612F817FF1880903B000FF0 003FE04BEB0FF0EF03F8141FEF01FC5DA2023F15FEA25DA2147FEF03FC92C7FCA24A15F8 17074A15F0EF0FE01301EF1FC04AEC3F80EFFE0001034A5AEE0FF091B612C04CC7FCD907 F8C9FCA25CA2130FA25CA2131FA25CA2133FA25CA2137FA291CAFCA25BA25B1201B512FC A337397BB838>I<0103B612F017FEEFFF80903B0007F8003FC04BEB0FF01707020FEC03 F8EF01FC5DA2021F15FEA25DA2143FEF03FC5DA2027FEC07F818F092C7120F18E04AEC1F C0EF3F004A14FEEE01F80101EC0FE091B6128004FCC7FC9138FC003F0103EC0F80834A6D 7E8301071403A25C83010F14075F5CA2011F140FA25CA2133F161F4AECE007A2017F160F 180E91C7FC49020F131C007F01FE153CB5913807F078040313F0CAEAFFE0EF3F80383B7C B83D>82 D<92383FC00E913901FFF01C020713FC91391FC07E3C91393F001F7C027CEB0F F84A130749481303495A4948EB01F0A2495AA2011F15E091C7FCA34915C0A36E90C7FCA2 806D7E14FCECFF806D13F015FE6D6D7E6D14E0010080023F7F14079138007FFC150F1503 1501A21500A2167C120EA3001E15FC5EA3003E4A5AA24B5AA2007F4A5A4B5A6D49C7FC6D 133ED8F9F013FC39F8FC03F839F07FFFE0D8E01F138026C003FCC8FC2F3D7ABA2F>I<00 07B812E0A25AD9F800EB001F01C049EB07C0485AD900011403121E001C5C003C17801403 123800785C00701607140700F01700485CA2140FC792C7FC5DA2141FA25DA2143FA25DA2 147FA292C9FCA25CA25CA21301A25CA21303A25CA21307A25CA2130FA25CEB3FF0007FB5 12F8B6FCA2333971B83B>I<003FB539800FFFFEA326007F80C7EA7F8091C8EA3F00173E 49153CA2491538A20001167817705BA2000316F05F5BA2000715015F5BA2000F15035F5B A2001F150794C7FC5BA2003F5D160E5BA2007F151E161C90C8FCA2163C4815385A167816 70A216F04B5A5E1503007E4A5A4BC8FC150E6C143E6C6C5B15F0390FC003E03907F01FC0 0001B5C9FC38007FFCEB1FE0373B70B83E>II91 D93 D<14F8EB07FE90381F871C90383E03FE137CEBF8011201 48486C5A485A120FEBC001001F5CA2EA3F801403007F5C1300A21407485C5AA2140F5D48 ECC1C0A2141F15831680143F1587007C017F1300ECFF076C485B9038038F8E391F0F079E 3907FE03FC3901F000F0222677A42A>97 D<133FEA1FFFA3C67E137EA313FE5BA312015B A312035BA31207EBE0F8EBE7FE9038EF0F80390FFC07C013F89038F003E013E0D81FC013 F0A21380A2123F1300A214075A127EA2140F12FE4814E0A2141F15C05AEC3F80A215005C 147E5C387801F8007C5B383C03E0383E07C0381E1F80D80FFEC7FCEA01F01C3B77B926> I<147F903803FFC090380FC1E090381F0070017E13784913383901F801F83803F0031207 13E0120FD81FC013F091C7FC485AA2127F90C8FCA35A5AA45AA3153015381578007C14F0 007EEB01E0003EEB03C0EC0F806CEB3E00380F81F83803FFE0C690C7FC1D2677A426>I< ED01F815FFA3150316F0A21507A216E0A2150FA216C0A2151FA21680A2153FA202F81300 EB07FE90381F877F90383E03FF017C5BEBF80112013803F00048485B120FEBC001121F5D EA3F801403127F01005BA214075A485CA2140FA248ECC1C0A2141F15C3ED8380143F1587 007C017F1300ECFF076C485B9038038F8E391F0F079E3907FE03FC3901F000F0253B77B9 2A>I<147F903803FFC090380FC1E090383F00F0017E13785B485A485A485A120F4913F8 001F14F0383F8001EC07E0EC1F80397F81FF00EBFFF891C7FC90C8FC5A5AA55AA2153000 7C14381578007E14F0003EEB01E0EC03C06CEB0F806CEB3E00380781F83803FFE0C690C7 FC1D2677A426>IIIII107 DI< D801E001FEEB07F03C07F803FF801FFC3C0E3C0F07C0783E3C1E3E3C03E1E01F261C1F78 D9F3C013803C383FF001F7800F02E01400007801C013FE007018C002805B4A4848EB1F80 EAF07FD8E07E5CA200000207143F01FE1700495CA2030F5C0001177E495C18FE031F5C12 0349DA8001131C18F8033F153C00070403133849020013F0A24B1570000F17E049017E15 F019E003FEECE1C0001FEE01E34949903800FF000007C70038143C3E2679A444>II<147F903803FFC090380FC1F090381F00F801 7E137C5B4848137E4848133E0007143F5B120F485AA2485A157F127F90C7FCA215FF5A48 14FEA2140115FC5AEC03F8A2EC07F015E0140F007C14C0007EEB1F80003EEB3F00147E6C 13F8380F83F03803FFC0C648C7FC202677A42A>I<9039078007C090391FE03FF090393C F0787C903938F8E03E9038787FC00170497EECFF00D9F0FE148013E05CEA01E113C15CA2 D80003143FA25CA20107147FA24A1400A2010F5C5E5C4B5A131F5EEC80035E013F495A6E 485A5E6E48C7FC017F133EEC70FC90387E3FF0EC0F8001FEC9FCA25BA21201A25BA21203 A25B1207B512C0A3293580A42A>II<3903 C003F0390FF01FFC391E783C0F381C7C703A3C3EE03F8038383FC0EB7F80007815000070 1300151CD8F07E90C7FCEAE0FE5BA2120012015BA312035BA312075BA3120F5BA3121F5B A3123F90C9FC120E212679A423>I<14FE903807FF8090380F83C090383E00E04913F001 78137001F813F00001130313F0A215E00003EB01C06DC7FC7FEBFFC06C13F814FE6C7F6D 13807F010F13C01300143F141F140F123E127E00FE1480A348EB1F0012E06C133E00705B 6C5B381E03E06CB45AD801FEC7FC1C267AA422>II<13F8D803FEEB01C0D8078FEB03E0390E0F8007121E121C0038 140F131F007815C01270013F131F00F0130000E015805BD8007E133FA201FE14005B5D12 0149137EA215FE120349EBFC0EA20201131E161C15F813E0163CD9F003133814070001EC F07091381EF8F03A00F83C78E090393FF03FC090390FC00F00272679A42D>I<01F0130E D803FC133FD8071EEB7F80EA0E1F121C123C0038143F49131F0070140FA25BD8F07E1400 00E08013FEC6485B150E12015B151E0003141C5BA2153C000714385B5DA35DA24A5A1403 00035C6D48C7FC0001130E3800F83CEB7FF8EB0FC0212679A426>I<01F01507D803FC90 3903801F80D8071E903907C03FC0D80E1F130F121C123C0038021F131F49EC800F007016 07A249133FD8F07E168000E0ED000313FEC64849130718000001147E5B03FE5B0003160E 495BA2171E00070101141C01E05B173C1738A217781770020314F05F0003010713016D48 6C485A000190391E7C07802800FC3C3E0FC7FC90393FF81FFE90390FE003F0322679A437 >I<903907E007C090391FF81FF89039787C383C9038F03E703A01E01EE0FE3803C01F01 8013C0D8070014FC481480000E1570023F1300001E91C7FC121CA2C75AA2147EA214FEA2 5CA21301A24A1370A2010314F016E0001C5B007E1401010714C000FEEC0380010F130701 0EEB0F0039781CF81E9038387C3C393FF03FF03907C00FC027267CA427>I<13F0D803FC EB01C0D8071EEB03E0D80E1F1307121C123C0038140F4914C01270A249131FD8F07E1480 12E013FEC648133F160012015B5D0003147E5BA215FE00075C5BA214015DA314035D1407 0003130FEBF01F3901F87FE038007FF7EB1FC7EB000F5DA2141F003F5C48133F92C7FC14 7E147C007E13FC387001F8EB03E06C485A383C1F80D80FFEC8FCEA03F0233679A428>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmr7 7 13 /Fm 13 117 df0 D<90383FFFFCA2010090C7FC147EA5903803FF80013F13 F89038FC7E7ED803E0EB0F80D80FC0EB07E0D81F00EB01F04815F8007EEC00FCA248157E A6007E15FCA26CEC01F86C15F0D80FC0EB07E0D803E0EB0F80D800FCEB7E0090383FFFF8 01031380D9007EC7FCA514FF013F13FCA227287DA72F>8 D<1306130C13181330136013 E0EA01C0EA0380A2EA07005A120E121EA2121C123CA35AA512F85AAB7E1278A57EA3121C 121EA2120E120F7EEA0380A2EA01C0EA00E0136013301318130C13060F3B7AAB1A>40 D<12C012607E7E7E120E7EEA0380A2EA01C013E0120013F0A213701378A3133CA5133E13 1EAB133E133CA51378A3137013F0A213E0120113C0EA0380A2EA0700120E120C5A5A5A5A 0F3B7DAB1A>I<140EB3A2B812E0A3C7000EC8FCB3A22B2B7DA333>43 D48 D<13381378EA01F8121F12FE12E01200B3AB487EB512F8A215267BA521 >I<13FF000313E0380E03F0381800F848137C48137E00787F12FC6CEB1F80A4127CC7FC 15005C143E147E147C5C495A495A5C495A010EC7FC5B5B903870018013E0EA0180390300 030012065A001FB5FC5A485BB5FCA219267DA521>I<13FF000313E0380F01F8381C007C 0030137E003C133E007E133FA4123CC7123E147E147C5C495AEB07E03801FF8091C7FC38 0001E06D7E147C80143F801580A21238127C12FEA21500485B0078133E00705B6C5B381F 01F03807FFC0C690C7FC19277DA521>I61 D<91387FC002903903FFF80690390FE01E0E90383F0007017CEB019ED801F0EB00FE4848 147E4848143E5B000F151E48C8FC48150E123EA2007E1506A2127C00FC1500A8127C007E 1506A2123EA2003F150C7E6C7E000715186D14386C6C14306C6C1460D8007CEB01C0013F EB038090390FE01E00903803FFF89038007FC0272A7DA82F>67 DI<13C0A412 01A312031207120F121FB512E0A23807C000AC1430A73803E060A23801F0C03800FF80EB 3F0014257FA31A>116 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn cmsy7 7 13 /Fn 13 115 df0 D<1238127C12FEA3127C123807077A9114>I< 160E163E16FEED03F8ED0FE0ED3F80EDFE00EC03F8EC0FE0EC3F8002FEC7FCEB03F8EB0F E0EB3F8001FEC8FCEA03F8EA0FE0EA3F8000FEC9FC12F812FEEA3F80EA0FE0EA03F8EA00 FEEB3F80EB0FE0EB03F8EB00FEEC3F80EC0FE0EC03F8EC00FEED3F80ED0FE0ED03F8ED00 FE163E160E1600AB007FB612FCB712FEA227357AA734>20 D<13E0EA01F0EA03F8A3EA07 F0A313E0A2120F13C0A3EA1F80A21300A25A123EA35AA3127812F8A25A12100D1E7D9F13 >48 D<017F157F2601FFE0903803FFC0000701F890380FF1F0260F83FC90381F0038261E 00FF013C7F001890263F8078130C4890261FC0E07F007090260FE1C07F0060EB07E39138 03F780486DB4C7EA01806E5A157E157F81824B7E0060DAF7E0EB0300913801E3F0DBC3F8 5B6C90260381FC13066C90260F00FE5B001C011E90387F803C6C017C90381FE0F82607C7 F86DB45A2601FFE0010313C06C6CC86CC7FC391B7C9942>I<49B5FC130F133F01FFC7FC EA01F8EA03E0EA078048C8FC121E121C123C123812781270A212F05AA2B7FCA300E0C8FC A27E1270A212781238123C121C121E7E6C7EEA03E0EA01F86CB4FC013FB5FC130F130120 277AA12D>I<1406140EB3B2007FB712E0B8FC7E2B287CA734>63 D<0103B512C0013F14FC90B712802703F0780713E03B0F80F8007FF0D81E00EC0FF848ED 03FC007C15010078ED00FE00F8167E00E0167FC748143F1301171FA35C1303A2171E173E 5C0107153C177C4A1478010F15F0160191C713E049EC03C0EE0780011EEC0F00013E141C 1678013C495A017CEB07C00178013FC7FC9038F803FC48B512E04891C8FC4813F030287E A734>68 D72 D<12E0B3B3B3A5033B78AB14>106 D<38C00180EAE003B3B3B3A3EAC00111 3B78AB22>I<186018E0170118C0170318801707EF0F00170E171E171C173C1738177817 7017F05F16014C5A5F160794C7FC5E160E161E161C163C1638486C147800075DD81FC05C 003F1401D8F7E05C00C31403D803F05C000114076D91C8FC00005C6D130E017C131E017E 5B013E1338013F13786D1370EC80F0010F5B14C101075B14E301035B14F76DB4C9FC5C13 005C147C14781438333A7B8237>112 D114 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo cmex10 10 16 /Fo 16 114 df2 DI<12F0B3B3B2043674811C>12 D<1678A316F816F0A2150116E0A2150316C015071680A2150F1600A25D151EA2153E153C A2157C1578A215F85DA214015D14035DA214075DA2140F92C7FCA25C141EA2143E143CA2 147C147814F85CA213015CA213035CA213075CA2130F91C8FCA25B131EA2133E133C137C 1378A213F85BA212015BA212035BA212075BA2120F90C9FCA25A121E123E123CA2127C12 78A212F85AA325627B8230>14 D<160F161F163E167C16F8ED01F0ED03E0ED07C0150FED 1F801600153E157E5D4A5A5D14034A5A5D140F4A5AA24AC7FC143E147E5CA2495AA2495A A2495AA2130F5CA2495AA2133F91C8FCA25B137E13FEA25B1201A25B1203A35B1207A35B 120FA35BA2121FA45B123FA690C9FC5AAA12FEB3AC127FAA7E7FA6121F7FA4120FA27FA3 12077FA312037FA312017FA212007FA2137E137F7FA280131FA26D7EA2801307A26D7EA2 6D7EA26D7EA2147E143E143F6E7EA26E7E1407816E7E1401816E7E157E153E811680ED0F C01507ED03E0ED01F0ED00F8167C163E161F160F28C66E823D>18 D<12F07E127C7E7E6C7E6C7E6C7E7F6C7E1200137C137E7F6D7E130F806D7E1303806D7E A26D7E147C147E80A26E7EA26E7EA26E7EA2811403A26E7EA2811400A281157E157FA281 1680A2151F16C0A3150F16E0A3150716F0A31503A216F8A4150116FCA6150016FEAA167F B3AC16FEAA16FC1501A616F81503A416F0A21507A316E0150FA316C0151FA31680153FA2 16005DA2157E15FE5DA214015DA24A5AA214075DA24A5AA24A5AA24AC7FCA2147E147C14 FC495AA2495A5C1307495A5C131F49C8FC137E137C5B1201485A5B485A485A48C9FC123E 5A5A5A28C67E823D>I<161E167EED01FE1507ED0FF8ED3FE0ED7FC0EDFF80913801FE00 4A5A4A5A5D140F4A5A5D143F5D147F92C7FCA25C5CB3B3B3A313015CA3495AA213075C49 5AA2495A495A137F49C8FC485A485AEA07F0EA1FE0485AB4C9FC12FCA2B4FCEA3FC06C7E EA07F0EA03FC6C7E6C7E6D7E133F6D7E6D7EA26D7E801303A26D7EA3801300B3B3B3A380 80A281143F81141F816E7E1407816E7E6E7E913800FF80ED7FC0ED3FE0ED0FF8ED07FE15 01ED007E161E27C675823E>26 D80 DI<167F923801FFC0923803C0F0923807803892380F007892381F01FC151E153EA2 157E92387C0070170015FCA44A5AA81403A45DA41407A94A5AAA4A5AA95DA4143FA492C8 FCA7143E147EA4147C123800FE13FC5CA2495A5CEA7803387007C0383C0F80D80FFEC9FC EA03F82E5C7C7F27>I<0078EF078000FCEF0FC0B3B3B3A46C171F007E1880A2007F173F 6C1800A26D5E001F177E6D16FE6C6C4B5A6D15036C6C4B5A6C6C4B5A6C6C4B5A6C6C6CEC 7FC06D6C4A5AD93FF8010790C7FC6DB4EB3FFE6D90B55A010315F06D5D6D6C1480020F01 FCC8FC020113E03A537B7F45>I88 DII<197C9538 07FFC0067F13FC0507B612C0057F15FC040FB50083EBFFE093B526F0001F13FE030F01FC C8387FFFE092B50080030313FE020F01F0CA381FFFE0DAFFFCCCEA7FFE011F0180963803 FFF02601FFF0CEEA1FFFD81FFED013F0D8FF80F503FE00F0D2121E771080BF78>100 D<1B301B78A21BF8A21BF01A01A21BE01A03A21BC01A07A21B801A0FA21B0062A21A1E1A 3EA21A3C1A7CA21A781AF8A262A21901A2621903A2621907A262190FA297C7FC61A2191E 193EA2193C197CA2197819F8A2611801A2611803A261A21807A261180FA296C8FC60A218 1E183EA2183C187C131001301678017016F813F860000116011203486C5E000F1603121D D838FE5E00701607126000C05FEA407F0000160FA26D6C92C9FC5FA2171E6D6C143EA217 3C6D6C147CA2177817F86D7E5F16016D7E5F1603A26D6C5C1607A26D6C5C160FA294CAFC 027F5BA2161EEC3F80163EA2163C91381FC07CA2167891380FE0F8A25E15E1EC07F15E15 F3EC03FB5E15FFA26E5BA36E90CBFCA35D157EA2157C153C15384D96788353>113 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmti7 7 2 /Fp 2 117 df115 D<1338137CA25BA4485AA4485AB512C0A2 3803E000485AA4485AA448C7FCA4123EEB0380A2EB0700127C130E130CEA3C1C5BEA1FE0 EA07C012267AA417>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq cmsy10 10 30 /Fq 30 115 df<007FB81280B912C0A26C17803204799641>0 D<121C127FEAFF80A5EA 7F00121C0909799917>I<0060150600F8150F6C151F007E153F6C157E6C6C14FC6C6CEB 01F86C6CEB03F06C6CEB07E06C6CEB0FC06C6CEB1F80017EEB3F006D137E6D6C5A90380F C1F8903807E3F0903803F7E06DB45A6D5B6EC7FCA24A7E497F903803F7E0903807E3F090 380FC1F890381F80FC90383F007E017E7F49EB1F804848EB0FC04848EB07E04848EB03F0 4848EB01F84848EB00FC48C8127E007E153F48151F48150F00601506282874A841>I<15 301578B3A6007FB812F8B912FCA26C17F8C80078C8FCB3A3007FB812F8B912FCA26C17F8 36367BB641>6 D14 D<020FB6128091B712C01303010F1680D91FF8C9FCEB7F8001FECAFCEA01F8485A485A48 5A5B48CBFCA2123EA25AA2127812F8A25AA87EA21278127CA27EA27EA26C7E7F6C7E6C7E 6C7EEA00FEEB7F80EB1FF86DB71280010316C01300020F158091CAFCAE001FB812804817 C0A26C1780324479B441>18 D20 D<126012F812FEEA7F80EA3FE0EA0FF8EA03FEC6 6C7EEB3FE0EB0FF8EB03FE903800FF80EC3FE0EC0FF8EC03FE913800FF80ED3FE0ED0FF8 ED03FE923800FF80EE3FE0EE0FF8EE03FE933800FF80EF3FC0171FEF7F80933801FF00EE 07FCEE1FF0EE7FC04B48C7FCED07FCED1FF0ED7FC04A48C8FCEC07FCEC1FF0EC7FC04948 C9FCEB07FCEB1FF0EB7FC04848CAFCEA07FCEA1FF0EA7FC048CBFC12FC1270CCFCAE007F B81280B912C0A26C1780324479B441>I24 D<020FB6128091B712C01303010F1680D91FF8C9FCEB7F8001FECAFCEA01F8 485A485A485A5B48CBFCA2123EA25AA2127812F8A25AA87EA21278127CA27EA27EA26C7E 7F6C7E6C7E6C7EEA00FEEB7F80EB1FF86DB71280010316C01300020F1580323279AD41> 26 D<181EA4181F84A285180785727EA2727E727E85197E85F11F80F10FC0F107F0007F BA12FCBCFCA26C19FCCCEA07F0F10FC0F11F80F13F00197E61614E5A4E5AA24E5A61180F 96C7FCA260181EA4482C7BAA53>33 D 49 D<91381FFFFE91B6FC1303010F14FED91FF0C7FCEB7F8001FEC8FCEA01F8485A485A 485A5B48C9FCA2123EA25AA2127812F8A25AA2B712FE16FFA216FE00F0C9FCA27EA21278 127CA27EA27EA26C7E7F6C7E6C7E6C7EEA00FEEB7F80EB1FF06DB512FE010314FF130002 1F13FE283279AD37>I<387FFFF8B6FC15C06C14F0C7EA0FF8EC01FEEC007FED1F80ED0F C0ED07E0ED03F01501ED00F8A2167CA2163EA2161E161FA2160FA2007FB7FCB8FCA27EC9 120FA2161FA2161E163EA2167CA216F8A2ED01F01503ED07E0ED0FC0ED1F80ED7F00EC01 FEEC0FF8007FB55AB612C092C7FC6C13F8283279AD37>I54 D<126012F0AD12FCA412F0AD126006207BA400>I<15301578B3B3AD007FB8 12F8B912FCA26C17F836367BB541>63 D<0203B512F0027F14FF49B712E0010F16F89027 3FC3F00713FED978039038007FFF2601E007020F1380D803C0030313C0D80780030013E0 000F177FD81F00EE3FF048EF1FF8003E4A140F5A0078EF07FC00C0010F1503C7FCA24B14 01A3141F5DA3023F16F8A292C8FCF003F0A25C027EED07E0A219C04A150F1980F01F0049 5A183E6049481578604D5A49484A5A4D5A050EC7FC4948143C5FEE01E04948EB07C0043F C8FC91380001FC49EB3FF049B5128048B500FCC9FC4814E04801FCCAFC3E397FB840>68 D72 D<0203B512FE027FECFFF049B712FC010F16FF90273FC3F00080D9780302077F2601E007 1401D803C06F6C7ED80780163F000F171FEA1F00484A140F123E5A0078010F5E12C0C7FC 4B4A5AA296C7FC021F5D183E4B5C187860023F4A5A4D5A92C7000FC8FC173EEE03F84AEB FFE0DA7E0313804B48C9FC4B7EECFC036F7F6F7F0101147F4A80163F707E495A707EA249 481307830403151049486E14F0F101E04A6D6CEB03C0011F933880078070EC0F0049C8EB C01E716C5A013E92383FF0F0017EEEFFE0017C6F1380496F48C7FC01E0ED07F0443B7FB8 46>82 DI<1A801907F10F00023FB712FE49B85A01 0F17F0013F17C0494CC7FC2801E00003F0C9FC48481307485A120F48C7485A5A5AA200FE 4A5A5A12F01280C8485AA44BCAFCA415FEA44A5AA44A5AA44A5AA4140F5DA35D141FA25D 143FA292CBFC5CA2147E14FE5CA2495A5C495A5C0102CCFC41427DBB2D>I<0060161800 F0163CB3B26C167CA2007C16F8A26CED01F0003F15036C6CEC07E06C6CEC0FC0D807F0EC 3F80D803FE903801FF003A00FFC00FFC6DB55A011F14E0010391C7FC9038007FF82E347C B137>91 DI<14034A7E4A7EA24A7EA34A7EA2EC7CF8A2ECF87CA2ECF0 3C0101133EA249487EA249486C7EA249486C7EA2EC00034980A2013E6D7EA2496D7EA201 78147801F8147CA2484880A2484880A24848EC0F80A2491407000F16C0A248C8EA03E0A2 003EED01F0A2003C1500007C16F8A248167CA248163C006016182E347CB137>94 D102 D<12FCEAFFC0EA07F0EA01FCEA007E7F80131F 80130FB3A7801307806D7E6D7EEB007EEC1FF0EC07F8EC1FF0EC7E00495A495A495A5C13 0F5CB3A7131F5C133F91C7FC137E485AEA07F0EAFFC000FCC8FC1D537ABD2A>I<126012 F0B3B3B3B3A91260045377BD17>106 D<0070131C00F0131EB3B3B3B3A80070131C1752 77BD2A>I114 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmmi10 10 56 /Fr 56 123 df13 D<1403EC3FF891387FFF80D901E313C014800103133F9138001F80ED070092C7FC80A280 A2808013018080130080147F81143F8149B47E130790380F8FF0EB3E0F496C7E13F83801 F003D803E07F1207380FC0011380121FEA3F0014005A127EA212FE5D481301A35DA24813 035D6C13075D127C4A5A6C91C7FC5C6C133E6C6C5A3807C0F03801FFE0D8003FC8FC223D 7DBB25>I<1406A6913807FFC04A13E091383F80609138FDFFE0903903F87F804948C7FC 495A495A495A137F91C8FC5B5B1201A25BA512007F137E90383F3FF090381FFFFC90380F C01C90381FFFF890383C7FE001F0C8FC485A485A485AA248C9FC121EA25AA2127C1278A3 12F87EA2127E127F7FEA3FE013FC6CB4FC6C13E06C13F8000113FF6C6C13C0010F13F001 037FEB007F140F14031400A4010C5BEB0E0190380783E0903801FF80D9007EC7FC234B7E B924>24 D<013FB612E090B712F05A120717E0270F807006C7FC391E00600E48140C0038 13E04813C048141CEAC0011200148001035BA213071400A25B1578011E137CA3133E133C 137C157E13FC5B1201157F1203497FA3D801C0131C2C257EA32F>I<027FB512C00103B6 12E0130F5B017F15C09026FF81FEC7FC3901FC007E48487F485A497F484880485AA248C7 FCA2127EA2153F00FE92C7FC5AA25D157E5A5DA24A5AA24A5A007C495A5D003C495A003E 013FC8FC6C137C380F81F83803FFE0C66CC9FC2B257DA32F>27 D<013FB512FE90B7FC5A 5A4815FE260F801CC7FCEA1E005A00385B5A5A481378C7FC147014F0A4495AA31303A349 5AA3130FA25C131FA3133FA291C8FC131E28257EA324>I<01F8141CD803FE143FD8070F 5C000E6D1480121C12180038153F0030151FD8701F140F12601607D8E03F150000C090C7 FC5BEA007E160613FE5B160E0001150C5B161C1618000315384914301670166016E04B5A 5E15036C6C49C7FC150E6C6C5B017E137890383F01E090380FFFC0D901FEC8FC29267EA4 2D>I<1503A35DA21506A2150EA2150CA2151CA21518A21538A21530A21570A2EC07FE91 383FFFC0903901FCE3F0903907E0E0F890391F80C03ED93E007FEB7C01D801F8EC0F80D8 03F0018013C0D807E014071403D80FC015E0D81F801300A248485AA2007E1306A2020E13 0F12FE48010C14C0A2021CEB1F80A20218EB3F00A20238137E007C5D1430007E4A5A003E 90387003F06CEC07C09138600F80D80F80013FC7FC3903E0E0FC3901F8E7F039007FFF80 D90FFCC8FCEB01C0A25CA21303A291C9FCA25BA21306A2130EA2130CA22B4B7CB931>I< EA01FCD807FF1506260E1FC0140E000C6D141CD81C0F1538261807F01470000016E06D6C EB01C0EE03806E140001015C160E6D6C5B5E5E027F5B4B5A4B5ADA3F83C7FC1587158EEC 1F9C15F85D5D6E5A81A214074A7E141F143F1473ECE3F8EB01C3148390380381FCEB0701 130E496C7E5B5B49137F485A49800003143F48C7FC000E6E7E4816304891380FE07048ED F06048020713E048913801FFC0C9EA7F002F367EA434>I<160C161C1618A316381630A3 16701660A316E05EA315015EA301F80103130FD803FE9138001F80D8070F153F000E0180 15C0001C5C001814060038161F0030160FD8701F010E13070060140C1703D8E03F168000 C0EB001C491318EA007E180001FE13384913305F000116064913700360130E5F00031618 4901E013384B133017705F0201495AD801F849485A4CC7FC160E2600FC035B017EEB0078 013FEB01E090390FE30F80902603FFFEC8FC9038003FF00206C9FCA2140E140CA3141C14 18A314381430A314701460324B7EB936>I<0140151E01E0153F00015E484816805B1207 90C9123F000E161F170F5A1707481700A2003014C014010070010314061260A2170E00E0 4948130C5A171C92C7FC5FA26C495C4A14F04A7E6C017F495A4A6C485A3AF801F7E00F3B FE0FF3F83F80267FFFE3B5FC02C191C7FC6C01815B02005BD80FFCEB7FF0D803F0EB0FC0 31267FA434>II39 D<121C127FEAFF80A5EA7F00121C0909798817>58 D<121C127FEAFF80A213C0A3127F12 1C1200A412011380A2120313005A1206120E5A5A5A12600A19798817>II<150C151E153EA2153C157CA21578 15F8A215F01401A215E01403A215C01407A21580140FA215005CA2141E143EA2143C147C A2147814F8A25C1301A25C1303A2495AA25C130FA291C7FC5BA2131E133EA2133C137CA2 137813F8A25B1201A25B1203A25B1207A25B120FA290C8FC5AA2121E123EA2123C127CA2 127812F8A25A12601F537BBD2A>I<126012FCB4FCEA7FC0EA1FF0EA07FCEA01FF38007F C0EB1FF0EB07FCEB01FF9038007FC0EC1FF0EC07FCEC01FF9138007FC0ED1FF0ED07FCED 01FF9238007FC0EE1FF0EE07FCEE01FF9338007F80EF1FC0A2EF7F80933801FF00EE07FC EE1FF0EE7FC04B48C7FCED07FCED1FF0ED7FC04A48C8FCEC07FCEC1FF0EC7FC04948C9FC EB07FCEB1FF0EB7FC04848CAFCEA07FCEA3FF0EA7FC048CBFC12FC1270323279AD41>I< EC03FC91381FFF80027F7F903901F807F0903903C001F890390780007C91C7127E010E80 4980011F1580D93FC0130F17C01607A24A14E0A2011EC7FC90C8FCA5EC0FF0ECFFFC9038 03F00E903907C0078F90381F8001D93E0013CF491300484814FF0003ED7FC05B485A120F 48481580A2485AA2007F160090C8FC167E16FE5A485D15015E1503485D15075E4B5AA200 7E4A5A4BC7FC003E147E003F5C6C6C485A390FC007F03907F01FC06CB5C8FCC613FCEB1F E02B3E7DBB2C>64 D<9339FF8001C0030F13E0037F9038F80380913A01FF807E07913A07 F8000F0FDA1FE0EB079FDA3F80903803BF0002FFC76CB4FCD901FC80495A4948157E495A 495A4948153E017F163C49C9FC5B1201484816385B1207485A1830121F4993C7FCA2485A A3127F5BA312FF90CCFCA41703A25F1706A26C160E170C171C5F6C7E5F001F5E6D4A5A6C 6C4A5A16076C6C020EC8FC6C6C143C6C6C5C6CB4495A90393FE00FC0010FB5C9FC010313 FC9038007FC03A3D7CBA3B>67 D<0103B7FC4916E018F8903B0007F80007FE4BEB00FFF0 3F80020FED1FC0180F4B15E0F007F0021F1503A24B15F81801143F19FC5DA2147FA292C8 FCA25C18035CA2130119F84A1507A2130319F04A150FA2010717E0181F4A16C0A2010FEE 3F80A24AED7F00187E011F16FE4D5A4A5D4D5A013F4B5A4D5A4A4A5A057FC7FC017F15FE EE03FC91C7EA0FF049EC7FC0B8C8FC16FC16C03E397DB845>I<0103B812F05BA2902600 07F8C7123F4B1407F003E0020F150118005DA2141FA25D19C0143FA24B1330A2027F1470 190092C7126017E05C16014A495A160F49B6FCA25F9138FC000F01031407A24A6DC8FCA2 01075C18034A130660010F160693C7FC4A150E180C011F161C18184A1538A2013F5E18F0 4A4A5AA2017F15074D5A91C8123F49913803FF80B9FCA295C7FC3C397DB83D>I71 D<0103B5D8F803B512F8495DA290260007F8C73807F800 4B5DA2020F150F615DA2021F151F615DA2023F153F615DA2027F157F96C7FC92C8FCA24A 5D605CA249B7FC60A202FCC7120101031503605CA201071507605CA2010F150F605CA201 1F151F605CA2013F153F605CA2017F157F95C8FC91C8FC496C4A7EB690B6FCA345397DB8 45>I<0107B512FCA216F890390007F8005DA2140FA25DA2141FA25DA2143FA25DA2147F A292C7FCA25CA25CA21301A25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2133F A25CA2137FA291C8FC497EB6FCA326397DB824>I<0103B500F8903807FFFC5BA2902600 07F8C813804BEDFC0019F0020F4B5AF003804B4AC7FC180E021F1538604B5CEF0380023F 4AC8FC170E4B133C1770027F5C4C5ADB0007C9FC160E4A5B167E4A13FE4B7E01015B9238 0E7F80ECFC1CED383F010301E07FECFDC04A486C7EECFF00D907FC6D7E5C4A130783130F 707E5C1601011F81A24A6D7EA2013F6F7EA24A143F84137F717E91C8123F496C81B60107 B512C0A26146397DB847>75 D<0103B6FC5B5E90260007FCC8FC5D5D140FA25DA2141FA2 5DA2143FA25DA2147FA292C9FCA25CA25CA21301A25CA21303A25CA2130718404A15C0A2 010F150118804A1403A2011F16005F4A1406170E013F151E171C4A143C177C017F5D1603 91C7120F49EC7FF0B8FCA25F32397DB839>I<902603FFF893383FFF80496081D9000794 38FF80000206DC01BFC7FCA2020E4C5A1A7E020C1606190CDA1C7E16FE4F5A02181630A2 0238166162023016C1F00181DA703F158395380303F002601506A202E0ED0C076202C015 18183001016D6C140F06605B028015C0A20103923801801FDD03005B140092380FC00649 173F4D91C8FC01065DA2010E4B5B4D137E130C6F6C5A011C17FEDCE1805B011802E3C7FC A2013802E6130104EC5C1330ED03F8017016034C5C01F05CD807FC4C7EB500E0D9C007B5 12F01680150151397CB851>I<902603FFF891381FFFF8496D5CA2D90007030113006FEC 007C02061678DA0EFF157081020C6D1460A2DA1C3F15E0705CEC181F82023815016F6C5C 1430150702706D1303030392C7FC02607FA2DAE0015C701306ECC0008201016E130EEF80 0C5C163F0103EDC01C041F131891C713E0160F49EDF03818300106140717F8010E020313 70EFFC60130CEE01FE011C16E004005B011815FF177F1338600130153FA20170151F95C8 FC01F081EA07FCB512E01706A245397DB843>I<4BB4FC031F13F09238FE01FC913903F0 007EDA07C0EB1F80DA1F80EB0FC0023EC7EA07E002FCEC03F0495A4948EC01F8495A4948 EC00FC495A49C912FE49167E13FE49167F1201485AA2485AA2120F5B001F17FFA2485AA3 4848ED01FEA400FFEE03FC90C9FCA2EF07F8A2EF0FF0A218E0171F18C0EF3F806C167F18 0017FE4C5A6C6C5D1603001F4B5A6D4A5A000FED1F806C6C4AC7FC6D147E0003EC01F8D8 01FC495AD8007EEB0FC090263F807FC8FC903807FFF801001380383D7CBA3F>I<4BB4FC 031F13F09238FE01FC913903F0007EDA07C0EB1F80DA1F80EB0FC0023EC7EA07E002FCEC 03F0495A4948EC01F8495A4948EC00FC495A013F16FE49C9FC13FE187F485A12035B1207 5B120F4916FF121FA2485AA34848ED01FEA448C9EA03FCA3EF07F8A218F0170F18E0171F 18C0EF3F807EEF7F0017FEDA07C05B6C90391FF001F8903980383803001F496C485A9139 E00C0FE0260FC0C0EB1F80D807E1D90E3FC7FC0280137ED803F1EB07F8D801F95C3A007F C00FC0903A3FE07F0003903807FFFE0100018F5BDA000F1306170E171E705A177CEEC1F8 16FF5FA25F5F6F5B6F48C7FCED00F8384B7CBA42>81 D<0103B612F849EDFF8018E0903B 0007F8001FF84BEB03FCEF00FE020F157FA24BEC3F80A2021F16C0A25DA2143FF07F805D A2027FEDFF006092C7485A4D5A4A4A5A4D5A4AEC1F80057FC7FC0101EC07F891B612E094 C8FC9139FC000FC00103EC03F0707E4A6D7E831307177E5C177F010F5D5F5CA2011F1401 A25CA2133F16034A4A1360A2017F17E019C091C71401496C01011480B61503933900FE07 00EF7E0ECAEA1FFCEF07F03B3B7DB83F>I<0003B812FEA25A903AF8003FC00101C09138 80007E4848163C90C7007F141C121E001C92C7FCA2485CA200305C007017180060130112 E0485CA21403C716005DA21407A25DA2140FA25DA2141FA25DA2143FA25DA2147FA292C9 FCA25CA25CA21301A25CA21303A25CEB0FFC003FB6FC5AA237397EB831>84 D<003FB56C48B51280485DA226007F80C7381FF00091C8EA07C0604993C7FCA2491506A2 0001160E170C5BA20003161C17185BA20007163817305BA2000F167017605BA2001F16E0 5F5BA2003F15015F5BA2007F150394C8FC90C8FCA25E4815065A160E160C161C16181638 5E127E5E4B5A6C4A5A4BC9FC6C6C131E6C6C5B6C6C13F83903F807E06CB55A6C6C48CAFC EB0FF0393B7BB839>I<267FFFFC91383FFFC0B55DA2000390C83807FC006C48ED03E060 60000094C7FC5F17065FA25F6D5DA26D5D17E05F4C5AA24CC8FC6E1306A2013F5C161C16 185EA25E6E5BA2011F495A150393C9FC1506A25D6E5AA2010F5B157015605DA2ECE18002 E3CAFC14F3EB07F614FE5C5CA25C5CA26D5AA25C91CBFC3A3B7CB830>I<147E903803FF 8090390FC1C38090391F00EFC0017E137F49133F485A4848EB1F8012075B000F143F4848 1400A2485A5D007F147E90C7FCA215FE485C5AA214015D48150CA21403EDF01C16181407 007C1538007E010F1330003E131F027B13706C01E113E03A0F83C0F9C03A03FF007F80D8 00FCEB1F0026267DA42C>97 D<133FEA1FFFA3C67E137EA313FE5BA312015BA312035BA3 1207EBE0FCEBE3FF9038E707C0390FFE03E09038F801F001F013F8EBE000485A15FC5BA2 123F90C7FCA214015A127EA2140312FE4814F8A2140715F05AEC0FE0A215C0EC1F80143F 00781400007C137E5C383C01F86C485A380F07C06CB4C7FCEA01FC1E3B7CB924>I<163F ED1FFFA3ED007F167EA216FEA216FCA21501A216F8A21503A216F0A21507A2027E13E090 3803FF8790380FC1CF90381F00EF017EEB7FC049133F485A4848131F000715805B000F14 3F485A1600485A5D127F90C7127EA215FE5A485CA21401A248ECF80CA21403161CEDF018 1407007C1538007E010F1330003E131F027B13706C01E113E03A0F83C0F9C03A03FF007F 80D800FCEB1F00283B7DB92B>100 DI<16F8ED03FEED0F8792381F0F80ED3E3F 167F157CA215FC1700161C4A48C7FCA414035DA414075DA20107B512F0A39026000FE0C7 FC5DA4141F5DA4143F92C8FCA45C147EA514FE5CA413015CA4495AA45C1307A25C121E12 3F387F8F80A200FF90C9FC131E12FEEA7C3CEA7878EA1FF0EA07C0294C7CBA29>III<14E0EB03F8A21307A314F0EB01C090C7FCAB13F8EA03 FEEA070F000E1380121C121812381230EA701F1260133F00E0130012C05BEA007EA213FE 5B1201A25B12035BA20007131813E01438000F133013C01470EB806014E014C01381EB83 8038078700EA03FEEA00F815397EB71D>I<150FED3F80A2157FA31600151C92C7FCABEC 0F80EC3FE0ECF0F0903801C0F849487E14005B130E130C131CEB1801133801305BA2EB00 03A25DA21407A25DA2140FA25DA2141FA25DA2143FA292C7FCA25CA2147EA214FEA25CA2 1301001E5B123F387F83F0A238FF87E0495A00FE5BD87C1FC8FCEA707EEA3FF8EA0FC021 4981B722>IIIII<3903E001F83907F807FE390E3C1E07391C3E381F3A183F703F800038EB E07F0030EBC0FF00705B00601500EC007E153CD8E07F90C7FCEAC07EA2120013FE5BA312 015BA312035BA312075BA3120F5BA3121F5B0007C9FC21267EA425>114 D<14FF010313C090380F80F090383E00380178131C153C4913FC0001130113E0A33903F0 00F06D13007F3801FFE014FC14FF6C14806D13C0011F13E013039038003FF01407140300 1E1301127FA24814E0A348EB03C012F800E0EB07800070EB0F006C133E001E13F83807FF E0000190C7FC1E267CA427>II<13F8D803FE1438D8070F147C000E6D13FC121C1218003814011230D8701F5C1260 1503EAE03F00C001005B5BD8007E1307A201FE5C5B150F1201495CA2151F120349EC80C0 A2153F1681EE0180A2ED7F0303FF130012014A5B3A00F8079F0E90397C0E0F1C90393FFC 07F8903907F001F02A267EA430>I<01F8EB03C0D803FEEB07E0D8070F130F000E018013 F0121C12180038140700301403D8701F130112601500D8E03F14E000C090C7FC5BEA007E 16C013FE5B1501000115805B150316001203495B1506150E150C151C151815385D00015C 6D485A6C6C485AD97E0FC7FCEB1FFEEB07F024267EA428>I<903907E001F090391FF807 FC9039783E0E0F9039E01F1C1FD801C09038383F803A03800FF07F0100EBE0FF5A000E4A 1300000C157E021F133C001C4AC7FC1218A2C7123FA292C8FCA25CA2147EA214FEA24A13 0CA20101141C001E1518003F5BD87F81143801835C00FF1560010714E03AFE0E7C01C0D8 7C1C495A2778383E0FC7FC391FF00FFC3907C003F029267EA42F>120 D<13F8D803FE1470D8070F14F8000EEB8001121C121800381403003015F0EA701F126001 3F130700E0010013E012C05BD8007E130F16C013FE5B151F000115805BA2153F00031500 5BA25D157EA315FE5D1401000113033800F80790387C1FF8EB3FF9EB0FE1EB00035DA200 0E1307D83F805B007F495AA24A5A92C7FCEB003E007C5B00705B6C485A381E07C06CB4C8 FCEA01FC25367EA429>II E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmmi7 7 27 /Fs 27 123 df14 D<48B61280000715C0481580481500263C0C06C7FC127012C0EB1C0EEA0018A21338 A2EB701EA313F013E01201141F120313C0000780A2380F800FA26C486CC7FC221A7D9827 >25 D<010FB5FC013F148049140048B6FC2603F07EC7FC3807C01FEA0F80497E5A123EA2 003C5B127CA30078133E12F8143C0078137C14785C6C485A495A381E0F80D80FFEC8FCEA 03F8211A7D9826>27 D29 D<16E00003140148EC03F0120E000C 1401001C14005A003015701660481330147014F04815C0A25C0101EB018014C015031600 D8E0035B903807E00E39F01FF03E39FFFEFFFC6C486C5AD83FF85B391FE03FE0390F800F 80241B7E992A>33 DI<157E000349B4FC0006491380484913C048EB0F0391 381C01E048EB18005C4A13605A5CA248484813C0A291C7FC49EB018000E01403ED0700D8 7006130E5D003C143CD83F0E13F8391FEE07E06CB55A00035CC649C7FCEB1FF0013CC8FC A35BA313F8A35B5B23267C992C>39 D<1238127C12FE12FFA2127F123B1203A31206A312 0C121812381270122008127A8614>59 D<160E163E16FEED03F8ED0FE0ED3F80EDFE00EC 03F8EC0FE0EC3F8002FEC7FCEB03F8EB0FE0EB3F8001FEC8FCEA03F8EA0FE0EA3F8000FE C9FC12F812FEEA3F80EA0FE0EA03F8EA00FEEB3F80EB0FE0EB03F8EB00FEEC3F80EC0FE0 EC03F8EC00FEED3F80ED0FE0ED03F8ED00FE163E160E27277AA134>I<4AB41308020FEB E01891397F80F038903A01F8001870D903E0EB0CF0D90F80130749C71203013E15E05B49 1401485A484815C0485A120F5B001F168090C8FC4892C7FCA2127EA4127C12FCA2160600 7C5DA35E007E5D123E5E6C5D6C6C495A00074AC7FCD803E0130E6C6C13383900FE01F090 383FFFC0D907FCC8FC2D2A7DA830>67 D<013FB512FC16FF903A01FC001FC04AEB03E0EE 01F801031400177C4A80A2010781A25CA2130F18805CA2011F1600A24A5CA2133F173E91 C8127E177C4915FC5F017E14015F01FE4A5AA2494A5A4C5A00014BC7FC167C495CED03E0 0003EC1FC0B600FEC8FC15F031287DA736>I<013FB612FCA2903901FC00014AEB007C17 3C0103153817185CA21307A24A13C0A2010F010113005E14C01503011F130F91B5C7FCA2 EC800F013F7F15061400A249010E13E0030C13C0017E90C7FC160101FEEC0380A249EC07 00A20001150E161E495C16FC0003EC07F8B7FC5E2E287DA731>I<000FB712E05A903980 0FE007D81E009038C001C05A0038011F1300123000705C00601501023F148012E0481400 A2C74890C7FCA2147EA214FEA25CA21301A25CA21303A25CA21307A25CA2130FA25CA213 1F001FB57EA22B287DA727>84 D<15F8141FA2EC01F0A21403A215E0A21407A215C0A214 0FEB1F8F90387FCF80EBF0EF3803C03FEA0780390F001F00A2001E5B123E003C133E127C 147E5A147CA214FC5AECF830A3903801F060A2EA7803010E13C0393C1CF980381FF07F39 07C01E001D297CA723>100 D<133EEA07FEA2EA007CA213FCA25BA21201A25BA2120314 FCEBE3FF9038EF0780D807FC13C0EBF00313E0A2EA0FC014071380A2121FEC0F801300A2 48EB1F00A2003E1406143E127EEC7C0C127C151800FCEB3C30157048EB1FE00070EB0F80 1F297CA727>104 D<130E131F5BA2133E131C90C7FCA7EA03E0487EEA0C78EA187C1230 A212605B12C0A2EA01F0A3485AA2485AA2EBC180EA0F81A2381F0300A213066C5A131CEA 07F06C5A11287DA617>I<1407EC0F80141FA21500140E91C7FCA7EB03E0EB07F8EB0C3C 1318EB303E136013C0A248485AA2C7FCA25CA4495AA4495AA4495AA4495AA21238D87C1F C7FC12FC133E485AEA70F8EA7FE0EA1F80193380A61B>I<133EEA07FEA2EA007CA213FC A25BA21201A25BA21203EC07809038E01FC0EC38600007EB61E014C3EBC187EBC307D80F C613C09038CC038001B8C7FC13E0487E13FEEB3F80EB0FC0486C7E1303003E1460A2127E ECC0C0127CECC18012FC903801E30038F800FE0070137C1B297CA723>I<137CEA0FFCA2 EA00F8A21201A213F0A21203A213E0A21207A213C0A2120FA21380A2121FA21300A25AA2 123EA2127EA2EA7C18A3EAF830A21320EA786013C0EA3F80EA0F000E297EA715>I<3B07 801FC007E03B0FE07FF01FF83B18F0E0F8783C3B30F1807CE03E903AFB007D801ED860FE EB3F005B49133E00C14A133E5B1201A24848495BA35F4848485A1830EE01F0A23C0F8003 E003E060A218C0933801E180271F0007C013E3933800FF00000E6D48137C341B7D993B> I<3907801FC0390FE07FF03918F0E0F83930F1807CEBFB00D860FE133C5B5B00C1147C5B 1201A248485BA34A5AEA07C01660EC03E0A23A0F8007C0C0A2EDC180913803C300D81F00 13C7EC01FE000EEB00F8231B7D9929>I<3807803E390FE0FF803818F3C13930F703C0EB FE073860FC0F13F8158039C1F0070091C7FC1201A2485AA4485AA4485AA448C8FCA2120E 1A1B7D991F>114 DI<131C133EA25BA45BA4485AB512 E0A23801F000485AA4485AA4485AA448C7FC1460A214C0123EEB0180EB0300EA1E06EA1F 1CEA0FF8EA03E013267EA419>II<90387C03C03901FF0FF03907 079C30390E03B078000CEBF0F8001813E1123015F0396007C0E015001200A2495AA449C7 FC15301238007C1460EAFC3E15C0EAF87E39F06F03803970C70700383F83FE381F01F81D 1B7D9926>120 D<013E13C0137F9038FF818048EBC3004813FF380701FE3806000C0004 5BC75A5C5CEB03800106C7FC5B5B5B5B9038C00180EA038039060003005C380FF81E381F FFFE38383FFC38601FF86D5A38C007C01A1B7D9920>122 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft msbm10 10 5 /Ft 5 91 df67 D<007FB8FCB9FC7E3B03C038007F8700010178EB0FC70270EB 03E7EE00F7177F8383A28316C0707EA494C7FC1501A315031507A2151F157EEC7FFC15F0 15F815FCEC703E150F150715031501A31500A2186018F04C13E093C7FC1701A217031707 EF0FC0171F173D17F9EE03F10278EB0FE30003013890387F8380007FB8FCB9FC7E34397F B829>69 D<007FB612E0B712FE6C6F7E2703C01E0313E0000190393C00F3F00238EB70F8 EE783CEE381E83EE3C07161C18801703A617071800EE3C0FEE380E173EEE78FCEEF7F892 380FFFE0023FB5128004FCC7FC16B8913838F03CED701CED781EED380EED3C0FED1C0703 1E7FED0E03030F7FED0701EE81E0ED0380707E030113701778EEE0380300133C707EEE70 0EEE780F9338380780EE3C03041C13C093381E01E00003013C90380E00F0007FB539F00F FFFEB67F6C8137397DB836>82 D<007FB812C0B9FCA23BE1FE38071FE1D8E3F0EC03F1D8 E7C0EC00F9D8EF00153D00FE161F48160F481607A2481603A2481601A400601600C71600 B3B102F813C0011FB6FC5B7F32397DB838>84 D<0007B712FC5AA23B0E1FF003C038903A 3F0007807801FC4A5AD80FF0495B49EB0E01D81F80011E5BED3C0390C738380780001E02 7890C7FCED700FEDF00E001C903801E01E4B5A02031338C7EB80780207137091380F00F0 91380E01E0021E5BEC1C03023C5BEC3807027890C8FC4A5AECE01E0101131CECC03C0103 133890380780784A5A495BEB0E01011E49EB0180D93C0314039038380780017890C7FCD9 700F1407EBF00E3801E01E4948EC0F0000031338D980785C00071370D900F05C48495CD8 1E0115F7261C03C0EB01E7003C49495AD83807EC0F8E007890C7EA3F0E4848EB01FEB812 FEA331397DB83E>90 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu cmbx12 14.4 24 /Fu 24 122 df<157815FC14031407141F14FF130F0007B5FCB6FCA2147F13F0EAF800C7 FCB3B3B3A6007FB712FEA52F4E76CD43>49 DI<9138 0FFFC091B512FC0107ECFF80011F15E090263FF8077F9026FF800113FC4848C76C7ED803 F86E7E491680D807FC8048B416C080486D15E0A4805CA36C17C06C5B6C90C75AD801FC16 80C9FC4C13005FA24C5A4B5B4B5B4B13C04B5BDBFFFEC7FC91B512F816E016FCEEFF80DA 000713E0030113F89238007FFE707E7013807013C018E07013F0A218F8A27013FCA218FE A2EA03E0EA0FF8487E487E487EB57EA318FCA25E18F891C7FC6C17F0495C6C4816E001F0 4A13C06C484A1380D80FF84A13006CB44A5A6CD9F0075BC690B612F06D5D011F15800103 02FCC7FCD9001F1380374F7ACD43>I68 D 73 D76 D82 D<91260FFF80130791B5 00F85B010702FF5B011FEDC03F49EDF07F9026FFFC006D5A4801E0EB0FFD4801800101B5 FC4848C87E48488149150F001F824981123F4981007F82A28412FF84A27FA26D82A27F7F 6D93C7FC14C06C13F014FF15F86CECFF8016FC6CEDFFC017F06C16FC6C16FF6C17C06C83 6C836D826D82010F821303010082021F16801400030F15C0ED007F040714E01600173F05 0F13F08383A200788200F882A3187FA27EA219E07EA26CEFFFC0A27F6D4B13806D17006D 5D01FC4B5A01FF4B5A02C04A5A02F8EC7FF0903B1FFFC003FFE0486C90B65AD8FC0393C7 FC48C66C14FC48010F14F048D9007F90C8FC3C5479D24B>I97 D<913801FFF8021FEBFF8091B612F00103 15FC010F9038C00FFE903A1FFE0001FFD97FFC491380D9FFF05B4817C048495B5C5A485B A2486F138091C7FC486F1300705A4892C8FC5BA312FFAD127F7FA27EA2EF03E06C7F1707 6C6D15C07E6E140F6CEE1F806C6DEC3F006C6D147ED97FFE5C6D6CEB03F8010F9038E01F F0010390B55A01001580023F49C7FC020113E033387CB63C>99 D<4DB47E0407B5FCA5EE 001F1707B3A4913801FFE0021F13FC91B6FC010315C7010F9038E03FE74990380007F7D9 7FFC0101B5FC49487F4849143F484980485B83485B5A91C8FC5AA3485AA412FFAC127FA3 6C7EA37EA26C7F5F6C6D5C7E6C6D5C6C6D49B5FC6D6C4914E0D93FFED90FEFEBFF80903A 0FFFC07FCF6D90B5128F0101ECFE0FD9003F13F8020301C049C7FC41547CD24B>I<9138 03FFC0023F13FC49B6FC010715C04901817F903A3FFC007FF849486D7E49486D7E484913 0F48496D7E48178048497F18C0488191C7FC4817E0A248815B18F0A212FFA490B8FCA318 E049CAFCA6127FA27F7EA218E06CEE01F06E14037E6C6DEC07E0A26C6DEC0FC06C6D141F 6C6DEC3F806D6CECFF00D91FFEEB03FE903A0FFFC03FF8010390B55A010015C0021F49C7 FC020113F034387CB63D>II 104 D<137F497E000313E0487FA2487FA76C5BA26C5BC613806DC7FC90C8FCADEB3FF0B5 FCA512017EB3B3A6B612E0A51B547BD325>I108 D110 D<913801FFE0021F13FE91B612C0010315F0010F90 38807FFC903A1FFC000FFED97FF86D6C7E49486D7F48496D7F48496D7F4A147F48834890 C86C7EA24883A248486F7EA3007F1880A400FF18C0AC007F1880A3003F18006D5DA26C5F A26C5F6E147F6C5F6C6D4A5A6C6D495B6C6D495B6D6C495BD93FFE011F90C7FC903A0FFF 807FFC6D90B55A010015C0023F91C8FC020113E03A387CB643>I<90397FE003FEB59038 0FFF80033F13E04B13F09238FE1FF89139E1F83FFC0003D9E3E013FEC6ECC07FECE78014 EF150014EE02FEEB3FFC5CEE1FF8EE0FF04A90C7FCA55CB3AAB612FCA52F367CB537> 114 D<903903FFF00F013FEBFE1F90B7FC120348EB003FD80FF81307D81FE0130148487F 4980127F90C87EA24881A27FA27F01F091C7FC13FCEBFFC06C13FF15F86C14FF16C06C15 F06C816C816C81C681013F1580010F15C01300020714E0EC003F030713F015010078EC00 7F00F8153F161F7E160FA27E17E07E6D141F17C07F6DEC3F8001F8EC7F0001FEEB01FE90 39FFC00FFC6DB55AD8FC1F14E0D8F807148048C601F8C7FC2C387CB635>I<143EA6147E A414FEA21301A313031307A2130F131F133F13FF5A000F90B6FCB8FCA426003FFEC8FCB3 A9EE07C0AB011FEC0F8080A26DEC1F0015806DEBC03E6DEBF0FC6DEBFFF86D6C5B021F5B 020313802A4D7ECB34>III121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fv cmr10 10 83 /Fv 83 128 df0 D<1506150FA24B7EA24B7EA24B 7EA2EDDFF0A29138018FF8A291380307FCA291380603FEA291380E01FF140CDA1C007F14 1802386D7E143002706D7E146002E06D7E5C01016E7E5C01036E7E91C7FC496E7E130601 0E6E7E130C011C6E7F131801386F7E133001706F7E136001E06F7E5B170F484882170748 C97F17030006831701488383481880001FB9FC4818C0A24818E0A2BA12F0A23C3C7CBB45 >I7 D<011FB512FEA39026001FFEC8FCEC07F8A8EC3FFE0103B512E0D91FF713 FC90397F07F87F01FCEC1F80D803F8EC0FE0D807F06E7ED80FE06E7E001F82D83FC06E7E A2007F8201808000FF1780A7007F170001C05C003F5EA2D81FE04A5A000F5ED807F04A5A D803F84A5AD800FCEC1F80017F027FC7FC90391FF7FFFC0103B512E09026003FFEC8FCEC 07F8A8EC1FFE011FB512FEA331397BB83C>I10 DII14 D<133C137EA213FE1201EA03FC13F0EA07E0EA0FC0EA1F80EA1E005A5A5A12C00F0F 6FB92A>19 D<6C130800E0133800F813F8383E03E0381F07C0380FDF803803FE006C5A6C 5A1320150A76B42A>I<121C127FEAFF80A8EA7F00AB123EAB121CABC7FCA8121C127FEA FF80A5EA7F00121C093C79BB17>33 D<030C1303031E497EA2033E130FA2033C91C7FCA2 037C5BA20378131EA303F8133EA24B133CA20201147CA24B1378A2020314F8A24B5BA302 071301007FB91280BA12C0A26C1880C7271F0007C0C7FC021E5CA3023E130FA2023C91C8 FCA2027C5BA20278131EA302F8133E007FB91280BA12C0A26C1880280003E000F8C8FC4A 5BA301071301A202805BA2010F1303A202005BA2491307A2011E5CA3013E130FA2013C91 C9FCA2017C5BA20178131EA20130130C3A4A7BB945>35 D<121C127FEAFF80A213C0A312 7F121C1200A412011380A2120313005A1206120E5A5A5A12600A1979B917>39 D<146014E0EB01C0EB0380EB0700130E131E5B5BA25B485AA2485AA212075B120F90C7FC A25A121EA2123EA35AA65AB2127CA67EA3121EA2121F7EA27F12077F1203A26C7EA26C7E 1378A27F7F130E7FEB0380EB01C0EB00E01460135278BD20>I<12C07E12707E7E7E120F 6C7E6C7EA26C7E6C7EA21378A2137C133C133E131EA2131F7FA21480A3EB07C0A6EB03E0 B2EB07C0A6EB0F80A31400A25B131EA2133E133C137C1378A25BA2485A485AA2485A48C7 FC120E5A5A5A5A5A13527CBD20>I<15301578B3A6007FB812F8B912FCA26C17F8C80078 C8FCB3A6153036367BAF41>43 D<121C127FEAFF80A213C0A3127F121C1200A412011380 A2120313005A1206120E5A5A5A12600A19798817>II<121C127F EAFF80A5EA7F00121C0909798817>I48 DIII<1538A2157815F8A2140114031407A2140F141F141B1433147314 6314C313011483EB030313071306130C131C131813301370136013C01201EA038013005A 120E120C5A123812305A12E0B712F8A3C73803F800AB4A7E0103B512F8A325397EB82A> I<0006140CD80780133C9038F003F890B5FC5D5D158092C7FC14FC38067FE090C9FCABEB 07F8EB3FFE9038780F803907E007E090388003F0496C7E12066E7EC87EA28181A21680A4 123E127F487EA490C71300485C12E000605C12700030495A00385C6C1303001E495A6C6C 485A3907E03F800001B5C7FC38007FFCEB1FE0213A7CB72A>II<12301238123E003FB612E0A316C05A168016000070C712060060140E5D1518 00E01438485C5D5DC712014A5A92C7FC5C140E140C141C5CA25CA214F0495AA21303A25C 1307A2130FA3495AA3133FA5137FA96DC8FC131E233B7BB82A>III<121C127FEAFF80A5EA7F00121CC7FCB2121C127FEAFF 80A5EA7F00121C092479A317>I<121C127FEAFF80A5EA7F00121CC7FCB2121C127F5A13 80A4127F121D1201A412031300A25A1206A2120E5A121812385A1260093479A317>I<00 7FB812F8B912FCA26C17F8CCFCAE007FB812F8B912FCA26C17F836167B9F41>61 D<1538A3157CA315FEA34A7EA34A6C7EA202077FEC063FA2020E7FEC0C1FA2021C7FEC18 0FA202387FEC3007A202707FEC6003A202C07F1501A2D901807F81A249C77F167FA20106 810107B6FCA24981010CC7121FA2496E7EA3496E7EA3496E7EA213E0707E1201486C81D8 0FFC02071380B56C90B512FEA3373C7DBB3E>65 DI<913A01FF8001 80020FEBE003027F13F8903A01FF807E07903A03FC000F0FD90FF0EB039F4948EB01DFD9 3F80EB00FF49C8127F01FE153F12014848151F4848150FA248481507A2485A1703123F5B 007F1601A35B00FF93C7FCAD127F6DED0180A3123F7F001F160318006C7E5F6C7E17066C 6C150E6C6C5D00001618017F15386D6C5CD91FE05C6D6CEB03C0D903FCEB0F80902701FF 803FC7FC9039007FFFFC020F13F002011380313D7BBA3C>IIIIIII<013FB512E0A39039001FFC00EC07 F8B3B3A3123FEA7F80EAFFC0A44A5A1380D87F005B0070131F6C5C6C495A6C49C7FC3807 81FC3801FFF038007F80233B7DB82B>IIIIIII82 DI<003FB812E0A3D9C003EB001F273E0001 FE130348EE01F00078160000701770A300601730A400E01738481718A4C71600B3B09138 07FF80011FB612E0A335397DB83C>I III91 D93 D97 DIIII<147E903803FF8090380FC1E0EB1F8790 383F0FF0137EA213FCA23901F803C091C7FCADB512FCA3D801F8C7FCB3AB487E387FFFF8 A31C3B7FBA19>IIII< EB01C0EB07F0EB0FF8A5EB07F0EB01C090C7FCAAEB01F813FFA313071301B3B3A2123C12 7E00FF13F01303A214E038FE07C0127C383C0F00EA0FFEEA03F8154984B719>III<2703F00FF0EB1FE000FFD93FFCEB7FF8913AF03F01E0 7E903BF1C01F83803F3D0FF3800FC7001F802603F70013CE01FE14DC49D907F8EB0FC0A2 495CA3495CB3A3486C496CEB1FE0B500C1B50083B5FCA340257EA445>I<3903F00FF000 FFEB3FFCECF03F9039F1C01F803A0FF3800FC03803F70013FE496D7EA25BA35BB3A3486C 497EB500C1B51280A329257EA42E>II<3903F01FE000FFEB7FF89038 F1E07E9039F3801F803A0FF7000FC0D803FEEB07E049EB03F04914F849130116FC150016 FEA3167FAA16FEA3ED01FCA26DEB03F816F06D13076DEB0FE001F614C09039F7803F0090 38F1E07E9038F0FFF8EC1FC091C8FCAB487EB512C0A328357EA42E>II<3807E01F00 FFEB7FC09038E1E3E09038E387F0380FE707EA03E613EE9038EC03E09038FC0080491300 A45BB3A2487EB512F0A31C257EA421>II<1318A51338A31378A313F8120112031207001FB5FCB6FC A2D801F8C7FCB215C0A93800FC011580EB7C03017E13006D5AEB0FFEEB01F81A347FB220 >IIIIII<003FB512FCA2EB8003D83E0013F8003CEB07F00038EB0FE012300070EB1FC0 EC3F800060137F150014FE495AA2C6485A495AA2495A495A495AA290387F000613FEA248 5A485A0007140E5B4848130C4848131CA24848133C48C7127C48EB03FC90B5FCA21F247E A325>I<001C131C007F137F39FF80FF80A5397F007F00001C131C190978B72A>127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fw cmr8 8 41 /Fw 41 122 df<156015F0A24A7E4A7EA24A7E1406EC0E7F140C91381C3F8014184A6C7E 150F02607F150702C07F1503D901807F1501D903007F496D7E1306010E147F130C011C6E 7E131801386E7E1330496E7E160749811603484881160148C87F486F7E1206000E167F12 0C001CEE3F801218003FB812C0A24817E0A2B912F0342F7DAE3B>1 D<013FB5FCA29038007F806EC8FCA6903801FFE0011F13FE90397F3F3F80D801F8EB07E0 D807E0EB01F8D80FC06D7ED81F80147ED83F0080481680A2007E151F00FE16C0A5007E16 80007F153FA26C1600D81F80147ED80FC05CD807E0495AD801F8EB07E0D8007FEB3F8090 261FFFFEC7FC010113E0D9003FC8FCA64A7E013FB5FCA22A2D7CAC33>8 D<123C127EB4FCA21380A2127F123D1201A312031300A25A1206120E5A5A5A126009157A AD14>39 D<13031307130E131C1338137013F0EA01E013C01203EA0780A2EA0F00A2121E A35AA45AA512F8A25AAB7EA21278A57EA47EA37EA2EA0780A2EA03C0120113E0EA00F013 701338131C130E1307130310437AB11B>I<12C07E12707E7E7E120FEA0780120313C0EA 01E0A2EA00F0A21378A3133CA4131EA5131FA2130FAB131FA2131EA5133CA41378A313F0 A2EA01E0A2EA03C013801207EA0F00120E5A5A5A5A5A10437CB11B>I<123C127EB4FCA2 1380A2127F123D1201A312031300A25A1206120E5A5A5A126009157A8714>44 D<123C127E12FFA4127E123C08087A8714>46 D50 D61 D66 DI69 DI73 D76 D78 D82 D<90383F80303901FFF0703807C07C390F000EF0 001E13074813034813011400127000F01470A315307EA26C1400127E127FEA3FE013FE38 1FFFE06C13FC6C13FF00011480D8003F13E013039038003FF0EC07F81401140015FC157C 12C0153CA37EA215787E6C14706C14F06CEB01E039F78003C039E3F00F0038E07FFE38C0 0FF01E2F7CAD27>I<007FB712F8A29039000FC003007C150000701638A200601618A200 E0161CA248160CA5C71500B3A94A7E011FB512E0A22E2D7EAC33>I<13FF000713C0380F 01F0381C00F8003F137C80A2143F001E7FC7FCA4EB07FF137F3801FE1FEA07F0EA1FC0EA 3F80EA7F00127E00FE14065AA3143F7E007E137F007FEBEF8C391F83C7FC390FFF03F839 01FC01E01F207D9E23>97 DII<15F8141FA214011400ACEB0FE0EB7FF83801F81E3803E0073807C003380F 8001EA1F00481300123E127EA25AA9127C127EA2003E13017EEB8003000F13073903E00E FC3A01F03CFFC038007FF090391FC0F800222F7EAD27>III<013F13F89038FFC3FE3903E1FF1E3807807C 000F140C391F003E00A2003E7FA76C133EA26C6C5A00071378380FE1F0380CFFC0D81C3F C7FC90C8FCA3121E121F380FFFF814FF6C14C04814F0391E0007F848130048147C12F848 143CA46C147C007C14F86CEB01F06CEB03E03907E01F803901FFFE0038003FF01F2D7E9D 23>III107 DI<2607 C07FEB07F03BFFC3FFC03FFC903AC783F0783F3C0FCE01F8E01F803B07DC00F9C00F01F8 D9FF8013C04990387F000749137EA249137CB2486C01FEEB0FE03CFFFE0FFFE0FFFEA237 1E7E9D3C>I<3807C0FE39FFC3FF809038C703E0390FDE01F0EA07F8496C7EA25BA25BB2 486C487E3AFFFE1FFFC0A2221E7E9D27>II<3807C0 FE39FFC7FF809038CF03E0390FDC01F03907F800FC49137E49133E49133FED1F80A3ED0F C0A8151F1680A2ED3F00A26D137E6D137C5D9038FC01F09038CE07E09038C7FF80D9C1FC C7FC01C0C8FCA9487EEAFFFEA2222B7E9D27>I<380781F838FF87FEEB8E3FEA0F9CEA07 B813B0EBF01EEBE000A45BB0487EB5FCA2181E7E9D1C>114 D<3801FE183807FFB8381E 01F8EA3C00481378481338A21418A27E7EB41300EA7FF06CB4FC6C13C06C13F0000113F8 38001FFC130138C0007E143EA26C131EA27EA26C133CA26C137838FF01F038E3FFC000C0 130017207E9E1C>I<1360A413E0A312011203A21207121FB512F0A23803E000AF1418A7 14383801F03014703800F860EB3FE0EB0F80152A7FA81B>II<3AFFFC01FFC0A23A0FE0007E000007147C15380003143015706C6C1360 A26C6C5BA390387C0180A26D48C7FCA2EB3F07EB1F06A2EB0F8CA214DCEB07D8A2EB03F0 A36D5AA26D5A221E7F9C25>I<3BFFFC3FFE07FFA23B0FE003F001F801C09038E000F000 07010114E0812603E00314C0A2913807F8012701F006781380A29039F80E7C030000D90C 3C1300A290397C181E06A2151F6D486C5AA2168C90391F600798A216D890390FC003F0A3 6D486C5AA36DC75A301E7F9C33>I<3AFFFC01FFC0A23A0FE0007E000007147C15380003 14306D137000011460A26C6C5BA2EBFC01017C5BEB7E03013E90C7FCA2EB1F06A2148EEB 0F8CA2EB07D8A2EB03F0A36D5AA26D5AA2495AA2130391C8FC1278EAFC06A25B131CEA78 38EA7070EA3FE0EA0F80222B7F9C25>121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fx cmr5 5 3 /Fx 3 51 df<14E0B0B712C0A3C700E0C7FCB022237C9B2B>43 D<1360EA01E0120F12FF 12F11201B3A3387FFF80A2111C7B9B1C>49 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fy cmsy5 5 1 /Fy 1 1 df0 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fz cmmi5 5 6 /Fz 6 110 df<137F3803FFC04813E0EA0F010018C7FC5AA2EA39F8EA1FFC5BEA33F000 60C7FCA25AA26C13C038700380383FFF006C5AEA07F813147D921C>34 D100 D106 D II<3A0F01F807E03A3F87FE1FF83A33CE1F387C3A63D80F603CD8C3F013C001E0 1380D803C01300A22607801E5BA3EEF04048484814C0ED01E0EEE18016E3001E90397800 FF00000C0130137C2A127D9133>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FA cmsy9 9 3 /FA 3 107 df<007FB712FCB812FEA26C16FC2F047A943C>0 D<127012FCB4FCEA7FC0EA 1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB01FF9038007FC0EC1FF0EC07FCEC01FF91 38007FC0ED1FF0ED07FCED01FF9238007FC0EE1FF0EE07FCEE01FEA2EE07FCEE1FF0EE7F C0923801FF00ED07FCED1FF0ED7FC04A48C7FCEC07FCEC1FF0EC7FC04948C8FCEB07FCEB 1FF0EB7FC04848C9FCEA07FCEA1FF0EA7FC048CAFC12FC1270CBFCAC007FB712FCB812FE A26C16FC2F3E7AB03C>21 D<126012F0B3B3B3B31260044B78B715>106 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FB msbm9 9 1 /FB 1 91 df<0007B712F05AA2000E9039800701E0271FF8000F13C001E0EB0E03018001 1E138090C7EA3C07001E9138380F0048EC780EEDF01E00384A5A020113380018903803C0 78C7495A02075B1501020F5BEC1E0391381C0780023C90C7FC4A5AEC701EECF01C903801 E03CECC038010313784A5A01075BEB0F0190380E03C0011E5BEB3C07D9380FC8FCD9780E 140CD9701E141CEBF01C2601E03C143C495A000301701438260780F01478D901E014F800 0F5BD81E031403261C07801307003C90C7121FD8380FEC7E70D8780EEB03FCB812F0A27E 2E337EB23B>90 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FC cmmi6 6 5 /FC 5 121 df100 D<1338137CA213781370 1300A7EA0780EA1FC0EA38E01230EA60F0EAC1E0A3EA03C0A3EA0780A2EA0F0013041306 EA1E0CA21318121CEA1E70EA0FE0EA07800F237DA116>105 D<000F017E13FC3A1F81FF 83FF3B31C383C707803A61EE03CC039026EC01F813C0D8C1F813F013F001E013E0000390 3903C0078013C0A2EE0F003907800780A2EE1E041706270F000F00130C163C1718A2001E 011EEB1C70EE1FE0000C010CEB07802F177D9536>109 D<000F13FC381FC3FF3931C707 803861EC0301F813C0EAC1F0A213E03903C00780A3EC0F00EA0780A2EC1E041506D80F00 130C143C15181538001EEB1C70EC1FE0000CEB07801F177D9526>I<3801F01E3907FC7F 80390E1CE1C038180F8100301383007013071260EC0380D8001EC7FCA45BA21580003014 C0397878018012F8EC030038F0FC0638E19C1C387F0FF8381E03E01A177D9523>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FD cmex9 9 2 /FD 2 89 df80 D88 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FE cmr6 6 4 /FE 4 62 df<13FF000313C0380781E0380F00F0001E137848133CA248131EA400F8131F AD0078131EA2007C133E003C133CA26C13786C13F0380781E03803FFC0C6130018227DA0 1E>48 D<13E01201120712FF12F91201B3A7487EB512C0A212217AA01E>II61 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FF cmsy6 6 6 /FF 6 113 df0 D<127812FCA4127806067A8F13>I<13601370 1360A20040132000E0137038F861F0387E67E0381FFF803807FE00EA00F0EA07FE381FFF 80387E67E038F861F038E060700040132000001300A21370136014157B9620>3 D<903807FFF0133F5BD801FCC7FCEA03E0485A48C8FC121E121C123C5A1270A212F05AA2 B612F0A300E0C8FCA27E1270A212787E121C121E7E6C7EEA03E0EA01FC6CB512F0133F13 071C237A9D2A>50 D<12E0B3B3AD033179A413>106 D<170C171C173C1738177817F017 E0160117C0160317801607EE0F00160E161E161C163C163816785E5E15015E15034B5AD8 038091C7FC00075CD81FC0130E003F141ED8F3E0131C0043143CD801F05B15706C6C13F0 5DEB7C015DEB3E034A5A011F90C8FC5CEB0F8E149EEB07DC14FC6D5A5C13015C13002E32 7C8232>112 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FG cmmi9 9 13 /FG 13 111 df14 D<1660A216E05EA315015EA3150393C7FCA35D1506A3150E01F0010C1370D803FC15F8D8 071EEC01FCD80E1F131C001C14180038018013000030167C013F0138133C0070EB003000 60161C5BD8E07E0170131800401460EA00FE491538000102E01330495B17701760000313 0101F04913E0EE01C01780020313039238000700160E5E6C6C485B02065BD800FC495A01 7EEB038090261FCE1FC7FC903807FFFC9038007FE0020CC8FC141C1418A314381430A314 701460A314E05C2E447EB332>32 D<123C127EB4FCA21380A2127F123D1201A412031300 A25A1206120E120C121C5A5A126009177A8715>59 D<171C177EEE01FEEE07FCEE1FF0EE 7FC0923801FF00ED07FCED1FF0ED7FC04A48C7FCEC07FCEC1FF0EC7FC04948C8FCEB07FC EB1FF0EB7FC04848C9FCEA07FCEA1FF0EA7FC048CAFCA2EA7FC0EA1FF0EA07FCEA01FF38 007FC0EB1FF0EB07FCEB01FF9038007FC0EC1FF0EC07FCEC01FF9138007FC0ED1FF0ED07 FCED01FF9238007FC0EE1FF0EE07FCEE01FEEE007E171C2F2E7AA93C>I<1530157815F8 A215F01401A215E01403A215C01407A21580140FA215005CA2143EA2143C147CA2147814 F8A25C1301A25C1303A25C1307A2495AA291C7FC5BA2131E133EA2133C137CA2137813F8 A25B1201A25B1203A2485AA25B120FA290C8FC5AA2121E123EA2123C127CA2127812F8A2 5A12601D4B7CB726>I<127012FCB4FCEA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB 07FCEB01FF9038007FC0EC1FF0EC07FCEC01FF9138007FC0ED1FF0ED07FCED01FF923800 7FC0EE1FF0EE07FCEE01FEA2EE07FCEE1FF0EE7FC0923801FF00ED07FCED1FF0ED7FC04A 48C7FCEC07FCEC1FF0EC7FC04948C8FCEB07FCEB1FF0EB7FC04848C9FCEA07FCEA1FF0EA 7FC048CAFC12FC12702F2E7AA93C>I<010FB712FEA218FC903A003FC000031700187C4B 143CA2027F151C181892C8FCA25CA24A1303A201014A1338040613304A1500160E13035E 4A137C91B512FC5B5EECF0001638130F16305C1860011F027013E0046013C04A14010400 1380133F17034A15005F017F150EA291C8121E5F49157C5F4914030001ED1FF0B8FCA25F 37337DB239>69 D79 D100 D105 D108 DII E %EndDVIPSBitmapFont %DVIPSBitmapFont: FH cmti7 6 2 /FH 2 117 df<133EEBFF803801C1C0EA0381EA0703A2EB010013E013FC13FF6C13807E 38000FC01303127000F01380A238E00700EA701EEA3FFCEA0FE012157C9418>115 D<13E01201A4EA03C0A4EA0780EAFFFEA2EA0780EA0F00A4121EA45AA213041306EA780C 13181338EA3870EA3FC0EA0F800F1F7B9E14>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FI cmr9 9 75 /FI 75 128 df<1538A2157CA215FEA24A7EA24A6C7E153F02067F151F020C7F150F0218 7F150702307F150302607F150102C07F150049487F8249C77F163F010681161F4981160F 498101386E7E133001706E7E136001E06E7E5B00016F7E5B0003EE7F8090C9FC48EE3FC0 1206000EEE1FE0120C001CEE0FF012180038EE07F8003FB8FC4817FCA2B912FEA337367C B540>1 D<91393FE00FE0903A01FFF83FF8903A07E01EF83C903A1F800FF07E903A3F00 1FE0FE017E133F4914C0485A1738484890381F8000ACB812C0A33B03F0001F8000B3A748 6C497EB50083B5FCA32F357FB42D>11 D<137813FCA212011203EA07F813E0EA0FC0EA1F 801300123C5A5A12400E0E71B326>19 D<6C132000E013E0EAF803383E0F80381F1F00EA 0FFE6C5AEA01F06C5A1340130A77AF26>I<123C127E12FFA8127EAB123E123CAB1218A6 1200A7123C127E12FFA4127E123C08367AB515>33 D<14C01301EB0380EB0F00130E5B13 3C5B5BA2485A485AA212075B120F90C7FC5AA2121E123EA3123C127CA55AB0127CA5123C 123EA3121E121FA27E7F12077F1203A26C7E6C7EA213787F131C7F130FEB0380EB01C013 00124A79B71E>40 D<12C07E1270123C121C7E120F6C7E6C7EA26C7E6C7EA27F1378137C 133C133EA2131E131FA37F1480A5EB07C0B0EB0F80A514005BA3131E133EA2133C137C13 7813F85BA2485A485AA2485A48C7FC120E5A123C12705A5A124A7CB71E>I<123C127EB4 FCA21380A2127F123D1201A412031300A25A1206120E120C121C5A5A126009177A8715> 44 DI<123C127E12FFA4127E123C08087A8715>I<1530157815 F8A215F01401A215E01403A215C01407A21580140FA215005CA2143EA2143C147CA21478 14F8A25C1301A25C1303A25C1307A2495AA291C7FC5BA2131E133EA2133C137CA2137813 F8A25B1201A25B1203A2485AA25B120FA290C8FC5AA2121E123EA2123C127CA2127812F8 A25A12601D4B7CB726>I I<13075B5B137FEA07FFB5FC13BFEAF83F1200B3B3A2497E007FB51280A319327AB126> IIII<000C14C0380FC00F90B5128015005C5C14F014C0D80C18C7FC90C8FCA9 EB0FC0EB7FF8EBF07C380FC03F9038001F80EC0FC0120E000CEB07E0A2C713F01403A215 F8A41218127E12FEA315F0140712F8006014E01270EC0FC06C131F003C14806CEB7F0038 0F80FE3807FFF8000113E038003F801D347CB126>I<14FE903807FF80011F13E090383F 00F0017C13703901F801F8EBF003EA03E01207EA0FC0EC01F04848C7FCA248C8FCA35A12 7EEB07F0EB1FFC38FE381F9038700F809038E007C039FFC003E0018013F0EC01F8130015 FC1400A24814FEA5127EA4127F6C14FCA26C1301018013F8000F14F0EBC0030007EB07E0 3903E00FC03901F81F806CB51200EB3FFCEB0FE01F347DB126>I<1230123C003FB6FCA3 4814FEA215FC0070C7123800601430157015E04814C01401EC0380C7EA07001406140E5C 141814385CA25CA2495A1303A3495AA2130FA3131F91C7FCA25BA55BA9131C20347CB126 >III<123C127E12FFA4127E123C1200B0123C127E12FFA4127E123C08207A9F15>I<007FB8 12C0B912E0A26C17C0CCFCAC007FB812C0B912E0A26C17C033147C9C3C>61 D<15E0A34A7EA24A7EA34A7EA3EC0DFE140CA2EC187FA34A6C7EA202707FEC601FA202E0 7FECC00FA2D901807F1507A249486C7EA301066D7EA2010E80010FB5FCA249800118C77E A24981163FA2496E7EA3496E7EA20001821607487ED81FF04A7ED8FFFE49B512E0A33336 7DB53A>65 DIIIIIIII<017FB5FCA3 9038003FE0EC1FC0B3B1127EB4FCA4EC3F805A0060140000705B6C13FE6C485A380F03F0 3803FFC0C690C7FC20357DB227>IIIIIII82 D<90381FE00390387FFC0748B5FC3907F01FCF390F8003FF 48C7FC003E80814880A200788000F880A46C80A27E92C7FC127F13C0EA3FF013FF6C13F0 6C13FF6C14C06C14F0C680013F7F01037F9038003FFF140302001380157F153FED1FC015 0F12C0A21507A37EA26CEC0F80A26C15006C5C6C143E6C147E01C05B39F1FC03F800E0B5 12E0011F138026C003FEC7FC22377CB42B>I<007FB712FEA390398007F001D87C00EC00 3E0078161E0070160EA20060160600E01607A3481603A6C71500B3AB4A7E011FB512FCA3 30337DB237>IIII89 D91 D93 D97 DII<153FEC0FFFA3EC007F81AEEB07F0EB3FFCEBFC0F3901F003 BF3907E001FF48487E48487F8148C7FCA25A127E12FEAA127E127FA27E6C6C5BA26C6C5B 6C6C4813803A03F007BFFC3900F81E3FEB3FFCD90FE0130026357DB32B>III<151F90391FC07F809039FFF8E3C03901F07FC73907E03F033A0FC01F 83809039800F8000001F80EB00074880A66C5CEB800F000F5CEBC01F6C6C48C7FCEBF07C 380EFFF8380C1FC0001CC9FCA3121EA2121F380FFFFEECFFC06C14F06C14FC4880381F00 01003EEB007F4880ED1F8048140FA56C141F007C15006C143E6C5C390FC001F83903F007 E0C6B51280D91FFCC7FC22337EA126>IIIIII<2703F01FE013FF00FF90267FF80313C0903BF1E07C0F 03E0903BF3803E1C01F02807F7003F387FD803FE1470496D486C7EA2495CA2495CB3486C 496C487EB53BC7FFFE3FFFF0A33C217EA041>I<3903F01FC000FFEB7FF09038F1E0FC90 38F3807C3907F7007EEA03FE497FA25BA25BB3486CEB7F80B538C7FFFCA326217EA02B> II<3903F03F8000FFEBFFE0 9038F3C0F89038F7007ED807FE7F6C48EB1F804914C049130F16E0ED07F0A3ED03F8A915 0716F0A216E0150F16C06D131F6DEB3F80160001FF13FC9038F381F89038F1FFE0D9F07F C7FC91C8FCAA487EB512C0A325307EA02B>I<903807F00390383FFC07EBFC0F3901F803 8F3807E001000F14DF48486CB4FC497F123F90C77E5AA25A5AA9127FA36C6C5B121F6D5B 000F5B3907E003BF3903F0073F3800F81EEB3FF8EB0FE090C7FCAAED7F8091380FFFFCA3 26307DA029>I<3803E07C38FFE1FF9038E38F809038E71FC0EA07EEEA03ECA29038FC0F 8049C7FCA35BB2487EB512E0A31A217FA01E>II<1330A51370A313F0A21201A212031207381FFFFEB5FCA23803F000AF 1403A814073801F806A23800FC0EEB7E1CEB1FF8EB07E0182F7FAD1E>III II<3A7FFF807FF8A33A07F8001FC00003EC0F800001EC070015066C6C5BA26D131C 017E1318A26D5BA2EC8070011F1360ECC0E0010F5BA2903807E180A214F3010390C7FC14 FBEB01FEA26D5AA31478A21430A25CA214E05CA2495A1278D8FC03C8FCA21306130EEA70 1CEA7838EA1FF0EA0FC025307F9F29>I123 D<001C1370387F01FC00FF13FEA4007F13FC381C0070170879B226>127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FJ cmbx9 9 15 /FJ 15 117 df48 D<147814F81303131FEA03FFB5FCA3EAFC1F1200B3B2007FB5 12FEA41F317AB02C>II<151F5D5DA25D5C5C5C5CA2 5C143D147D14F9EB01F114E1EB03C1EB0781130FEB1F01133E133C137813F01201EA03E0 EA07C01380EA0F00121E123E5A5AB712FEA4C700031300A80103B512FEA427317EB02C> 52 D54 D<123C123F90B612F8A44815F016E016C0168016005D007CC7127E00785C4A5A00F8495A 48495A4A5A4A5AC7FC4AC7FC147E14FE5C13015C1303A2495AA2130FA2131FA25C133FA4 137FA96D5AA2010FC8FC25337BB12C>III65 D97 DI<90 3807FF80013F13F090B512FC3903FE01FE4848487EEA0FF8EA1FF0EA3FE0A2007F6D5A49 6C5A153000FF91C7FCA9127F7FA2003FEC07807F6C6C130F000FEC1F00D807FE133E3903 FF80FCC6EBFFF8013F13E0010790C7FC21217DA027>I<3901F81F8000FFEB7FF0ECFFF8 9038F9E3FC9038FBC7FE380FFF876C1307A213FEEC03FCEC01F8EC0060491300B1B512F0 A41F217EA024>114 D<9038FFE1C0000713FF5A383F803F387E000F14075A14037EA26C 6CC7FC13FCEBFFE06C13FC806CEBFF80000F14C06C14E0C6FC010F13F0EB007F140F00F0 130714037EA26C14E06C13076CEB0FC09038C01F8090B5120000F913FC38E03FE01C217D A023>I<133CA5137CA313FCA21201A212031207001FB51280B6FCA3D807FCC7FCB0EC03 C0A79038FE078012033901FF0F006C13FEEB3FFCEB0FF01A2F7EAE22>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FK cmsy8 8 4 /FK 4 71 df<130C131EA50060EB01800078130739FC0C0FC0007FEB3F80393F8C7F0038 07CCF83801FFE038007F80011EC7FCEB7F803801FFE03807CCF8383F8C7F397F0C3F8000 FCEB0FC039781E078000601301000090C7FCA5130C1A1D7C9E23>3 D<170EA3170F8384170384170184717E1878187C84180FF007C0BA12F819FC19F8CBEA07 C0F00F00183E601878604D5A60170360170795C7FC5F170EA33E237CA147>33 D<91B512C01307131FD97F80C7FC01FCC8FCEA01F0EA03C0485A48C9FC120E121E5A1238 12781270A212F05AA3B712C0A300E0C9FCA37E1270A212781238123C7E120E120F6C7E6C 7EEA01F0EA00FCEB7F80011FB512C013071300222B7AA52F>50 D<033FB512FE0203B7FC 140F143F913A780F80007E902601E01F1438D903C01520D9078090C8FCEB0F005B011E5B 5B0138133E90C7FCA25DA35DA34AB512FCA25F4A5C9238E000C04B90C7FC1407A24A5AA2 92C9FC5C141E143E143C147C147814F8001E5BEA3F01387F81E038FFE3C06CB45A6C48CA FC6C5AEA07E0382F7FAC32>70 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FL cmr12 12 43 /FL 43 122 df<131F1480133F137FA2EBFF00485A485A5B485A485A138048C7FC123E12 3C5A12E0124011126CC431>19 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413 E013C0A312011380120313005A1206120E5A5A5A12600B1D78891B>44 DI<14FF010713E090381F81F890383E007C01FC133F4848EB1F 8049130F4848EB07C04848EB03E0A2000F15F0491301001F15F8A2003F15FCA390C8FC48 15FEA54815FFB3A46C15FEA56D1301003F15FCA3001F15F8A26C6CEB03F0A36C6CEB07E0 000315C06D130F6C6CEB1F806C6CEB3F00013E137C90381F81F8903807FFE0010090C7FC 28447CC131>48 D<143014F013011303131F13FFB5FC13E713071200B3B3B0497E497E00 7FB6FCA3204278C131>II<49B4FC01 0F13E0013F13FC9038FE01FE3A01F0007F80D803C0EB3FC048C7EA1FE0120EED0FF0EA0F E0486C14F8A215077F5BA26C48130FEA03C0C813F0A3ED1FE0A2ED3FC01680ED7F0015FE 4A5AEC03F0EC1FC0D90FFFC7FC15F090380001FCEC007FED3F80ED1FC0ED0FE016F0ED07 F816FC150316FEA2150116FFA3121EEA7F80487EA416FE491303A2007EC713FC00701407 003015F80038140F6C15F06CEC1FE06C6CEB3FC0D803E0EB7F803A01FE01FE0039007FFF F8010F13E0010190C7FC28447CC131>II<000615C0D807C0130701FCEB7F80 90B612005D5D5D15E0158026063FFCC7FC90C9FCAE14FF010713C090381F01F090383800 FC01F0137ED807C07F49EB1F8016C090C7120F000615E0C8EA07F0A316F81503A216FCA5 123E127F487EA416F890C712075A006015F0A20070140F003015E00038EC1FC07E001EEC 3F806CEC7F006C6C13FE6C6C485A3901F807F039007FFFE0011F90C7FCEB07F826447BC1 31>II<14FF010713E0011F13F890387F00FE01FC13 3FD801F0EB1F804848EB0FC049EB07E00007EC03F048481301A290C713F8481400A47FA2 6D130116F07F6C6CEB03E013FC6C6CEB07C09039FF800F806C9038C01F006CEBF03EECF8 7839007FFEF090383FFFC07F01077F6D13F8497F90381E7FFFD97C1F1380496C13C02601 E00313E048486C13F000079038007FF84848EB3FFC48C7120F003EEC07FE150148140016 FF167F48153FA2161FA56C151E007C153EA2007E153C003E157C6C15F86DEB01F06C6CEB 03E06C6CEB07C0D803F8EB1F80C6B4EBFF0090383FFFFC010F13F00101138028447CC131 >56 D<16C04B7EA34B7EA34B7EA34B7EA3ED19FEA3ED30FFA203707FED607FA203E07FED C03FA2020180ED801FA2DA03007F160FA20206801607A24A6D7EA34A6D7EA34A6D7EA202 70810260147FA202E08191B7FCA249820280C7121FA249C87F170FA20106821707A2496F 7EA3496F7EA3496F7EA201788313F8486C83D80FFF03037FB500E0027FEBFFC0A342477D C649>65 D67 DI71 DI75 D77 D79 DII<49B41303010FEBE007013F13 F89039FE00FE0FD801F8131FD807E0EB079F49EB03DF48486DB4FC48C8FC4881003E8112 7E82127C00FC81A282A37E82A27EA26C6C91C7FC7F7FEA3FF813FE381FFFE06C13FE6CEB FFE06C14FC6C14FF6C15C0013F14F0010F80010180D9001F7F14019138001FFF03031380 816F13C0167F163F161F17E000C0150FA31607A37EA36C16C0160F7E17806C151F6C1600 6C5D6D147ED8FBC05CD8F9F0495AD8F07C495A90393FC00FE0D8E00FB51280010149C7FC 39C0003FF02B487BC536>83 D85 D97 DII<167FED3FFFA315018182B3EC7F80 903803FFF090380FC07C90383F000E017E1307496D5AD803F87F48487F5B000F81485AA2 485AA2127FA290C8FC5AAB7E7FA2123FA26C7EA2000F5D7F6C6C5B00035C6C6C9038077F 806C6C010E13C0013F011C13FE90380FC0F8903803FFE09026007F0013002F467DC436> III104 DI107 DII<3901FC01FE00FF90 3807FFC091381E07F091383801F8000701707F0003EBE0002601FDC07F5C01FF147F91C7 FCA25BA35BB3A8486CECFF80B5D8F83F13FEA32F2C7DAB36>II<3901FC03FC00FF90380FFF8091383C07E091387001F83A07FDE000 FE00030180137FD801FFEC3F8091C7EA1FC04915E049140F17F0160717F8160317FCA3EE 01FEABEE03FCA3EE07F8A217F0160F6D15E0EE1FC06D143F17806EEB7E00D9FDC05B9039 FCF003F891383C0FE091381FFF80DA03FCC7FC91C9FCAE487EB512F8A32F3F7DAB36>I< 3903F803F000FFEB1FFCEC3C3EEC707F0007EBE0FF3803F9C000015B13FBEC007E153C01 FF13005BA45BB3A748B4FCB512FEA3202C7DAB26>114 D<90383FE0183901FFFC383907 E01F78390F0003F8001E1301481300007C1478127800F81438A21518A27EA27E6C6C1300 6C7E13FC383FFFE06C13FC6C13FF6C14C06C14E0C614F0011F13F81300EC0FFC140300C0 EB01FE1400157E7E153EA27EA36C143C6C147C15786C14F86CEB01F039F38003E039F1F0 0F8039E07FFE0038C00FF01F2E7DAC26>I<1306A5130EA4131EA3133E137EA213FE1201 1207001FB512F0B6FCA2C648C7FCB3A4150CAA017E131C017F1318A26D133890381F8030 ECC070903807E0E0903801FFC09038007F001E3E7EBC26>III121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FM cmr17 17.28 18 /FM 18 124 df76 DI<003FBC12F8A49126C000039038C0000301FCC7 6C49EB007F01F0190F01C019074848F103FC90C81701007E1A00007C1B7CA300781B3CA4 00701B1CA600F01B1E481B0EA7C91800B3B3B3A54C7FA2041F13F84AB87EA457627CE160 >84 D86 D97 DI<4AB47E020F13F8023F13FE9139FF007F80D903FCEB07E0D907F0EB01F0D91FE0EB00 7849488049488049C87E48485D4915FF00034B138048485CA2485AA2485AA2003F6F1300 49EC007C94C7FC127FA35B12FFAD127F7FA4123F7FA2001FEE01C07F000F16036D168012 076C6C15076D160000015E6C6C151E6D6C5C6D6C5C6D6C5CD90FF8495AD903FCEB07C090 3A00FF803F8091263FFFFEC7FC020F13F80201138032417CBF3A>I101 D103 DI<133C13FF487F487FA66C5B6C90C7FC133C90C8FCB3A2EB03C0EA07FF127F A41201EA007FA2133FB3B3AC497E497EB612E0A41B5F7DDE23>I108 D110 DII<9039078003F8D807FFEB0FFFB5013F13 C092387C0FE0913881F01F9238E03FF00001EB838039007F8700148FEB3F8E029CEB1FE0 EE0FC00298EB030002B890C7FCA214B014F0A25CA55CB3B0497EEBFFF8B612FCA42C3F7C BE33>114 D118 D123 D E %EndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%EndSetup %%Page: 1 1 1 0 bop 912 872 a FM(The)44 b(Molc)l(hano)l(v{V)-11 b(ain)l(b)t(erg)45 b(Laplacian)1615 1112 y FL(Philipp)s(e)31 b(P)m(oulin)2280 1076 y FK(\003)1038 1345 y FL(Departmen)m(t)h(of)g(Mathematics)g(and)h (Statistics)1567 1461 y(McGill)d(Univ)m(ersit)m(y)1382 1577 y(805,)i(rue)h(Sherbro)s(ok)m(e)g(Ouest)1144 1694 y(Mon)m(tr)m(\023)-46 b(eal,)32 b(Qu)m(\023)-46 b(eb)s(ec,)34 b(H3A-2K6,)d(Canada)1544 1889 y(Decem)m(b)s(er)i(11,)f(2004)1778 2271 y FJ(Abstract)837 2401 y FI(It)18 b(is)h(w)n(ell)g(kno)n(wn)f (that)g(the)g(Green)h(function)f(of)h(the)f(standard)g(discrete)h (Lapla-)722 2492 y(cian)29 b(\001)951 2500 y FH(st)1004 2492 y FG( )s FI(\()p FG(n)p FI(\))c(=)g(\(2)p FG(d)p FI(\))1411 2461 y FF(\000)p FE(1)1506 2436 y FD(P)1587 2515 y FF(j)p FC(n)p FF(\000)p FC(m)q FF(j)p FE(=1)1860 2492 y FG( )s FI(\()p FG(m)p FI(\))i(on)h FG(l)2201 2461 y FE(2)2235 2492 y FI(\()p FB(Z)2321 2461 y FC(d)2351 2492 y FI(\))g(exhibits)g(a)g(pathological)722 2584 y(b)r(eha)n(vior)e (in)g(dimension)f FG(d)c FA(\025)g FI(3.)35 b(In)25 b(particular,)i (the)e(estimate)1250 2765 y FG(<)34 b(\016)1378 2773 y FE(0)1413 2765 y FA(j)p FI(\(\001)1528 2773 y FH(st)1598 2765 y FA(\000)17 b FG(E)k FA(\000)16 b FG(i)p FI(0\))1923 2729 y FF(\000)p FE(1)2007 2765 y FG(\016)2041 2773 y FC(n)2117 2765 y FG(>)p FI(=)21 b FG(O)r FI(\()p FA(j)p FG(n)p FA(j)2436 2729 y FF(\000)2495 2706 y Fz(d)p Fy(\000)p Fx(1)p 2495 2718 104 3 v 2533 2750 a(2)2613 2765 y FI(\))722 2927 y(fails)31 b(for)e(0)d FG(<)g FA(j)p FG(E)t FA(j)h FG(<)f FI(1)19 b FA(\000)g FI(2)p FG(=d)p FI(.)43 b(This)30 b(fact)f(complicates)g(the)f(study)g(of)h(the)f(scat-)722 3018 y(tering)d(theory)f(of)h(discrete)f(Sc)n(hr\177)-38 b(odinger)25 b(op)r(erators.)35 b(Molc)n(hano)n(v)25 b(and)f(V)-6 b(ain)n(b)r(erg)722 3109 y(suggested)27 b(the)e(follo)n(wing)j(alternativ)n(e)f(to)e(the)h(standard)f(discrete) h(Laplacian,)1425 3281 y(\001)p FG( )s FI(\()p FG(n)p FI(\))c(=)f(2)1789 3245 y FF(\000)p FC(d)1873 3281 y FG(d)p FI(!)2045 3210 y FD(X)1947 3382 y FF(j)p FC(n)p FF(\000)p FC(m)q FF(j)p FE(=)2173 3340 y FF(p)p 2222 3340 33 3 v 2222 3382 a FC(d)2267 3281 y FG( )s FI(\()p FG(m)p FI(\))p FG(;)722 3534 y FI(and)26 b(conjectured)g(that)f(the)g (estimate)1277 3715 y FG(<)34 b(\016)1405 3723 y FE(0)1439 3715 y FA(j)p FI(\(\001)18 b FA(\000)e FG(E)21 b FA(\000)c FG(i)p FI(0\))1897 3679 y FF(\000)p FE(1)1980 3715 y FG(\016)2014 3723 y FC(n)2091 3715 y FG(>)p FI(=)k FG(O)r FI(\()p FA(j)p FG(n)p FA(j)2410 3679 y FF(\000)2469 3656 y Fz(d)p Fy(\000)p Fx(1)p 2469 3668 104 3 v 2507 3700 a(2)2587 3715 y FI(\))722 3877 y(holds)26 b(for)h(all)f(0)c FG(<)f FA(j)p FG(E)t FA(j)h FG(<)f FI(1.)35 b(In)25 b(this)h(pap)r(er)f (w)n(e)h(pro)n(v)n(e)f(this)h(conjecture.)p 515 4929 1146 4 v 606 4983 a FF(\003)642 5006 y Fw(This)d(researc)n(h)h(w)n(as)g (supp)r(orted)g(in)g(part)g(b)n(y)g(NSER)n(C.)1926 5255 y Fv(1)p eop %%Page: 1 2 1 1 bop 515 523 a Fu(1)134 b(In)l(tro)t(duction)515 705 y Fv(In)25 b(the)h(recen)n(t)f(y)n(ears)f(there)h(has)g(b)r(een)h (considerable)f(in)n(terest)g(in)g(the)h(scattering)f(theory)515 805 y(of)31 b(discrete)f(random)h(Sc)n(hr\177)-42 b(odinger)29 b(op)r(erators)g(on)i(the)g(lattice)g Ft(Z)2643 774 y Fs(d)2707 805 y Fv([B)o(,)h(BBP)o(,)f(CK,)g(CS,)515 904 y(HK,)f(JL1)o(,)g(JL2)o(,)g(JM,)g(JMP)o(,)g(K,)g(MV1,)g(MV2,)g(RS,)g (SV)q(].)44 b(T)n(ypical)29 b(mo)r(dels)h(considered)515 1004 y(in)e(the)g(literature)e(ha)n(v)n(e)h(the)h(general)e(form)1261 1196 y Fr(H)1330 1208 y Fs(!)1401 1196 y Fv(=)d Fq(\000)p Fv(\001)1623 1208 y Fp(st)1702 1196 y Fv(+)1788 1117 y Fo(X)1785 1295 y Fs(n)p Fn(2)p Fm(\000)1926 1196 y Fr(V)1974 1208 y Fs(!)2022 1196 y Fv(\()p Fr(n)p Fv(\))h Fr(<)36 b(\016)2298 1208 y Fs(n)2343 1196 y Fq(j)14 b(\001)37 b Fr(>)23 b(\016)2565 1208 y Fs(n)2610 1196 y Fr(;)640 b Fv(\(1\))515 1467 y(where)28 b Fr(\016)k Fv(is)d(the)g(Kronec)n(k)n (er)c(delta)k(on)f Ft(Z)1835 1437 y Fs(d)1897 1467 y Fv(and)g Fr(V)2107 1479 y Fs(!)2156 1467 y Fv(\()p Fr(n)p Fv(\))h(are)e(indep)r(enden)n(t)i(random)f(v)-5 b(ari-)515 1567 y(ables)27 b(indexed)g(b)n(y)h Fr(n)23 b Fq(2)g Fv(\000)g Fq(\022)g Ft(Z)1520 1537 y Fs(d)1553 1567 y Fv(.)37 b(\001)1682 1579 y Fp(st)1770 1567 y Fv(is)28 b(the)g Fl(standar)l(d)37 b Fv(discrete)27 b(Laplacian,)1428 1782 y(\001)1497 1794 y Fp(st)1558 1782 y Fr( )s Fv(\()p Fr(n)p Fv(\))d(=)1872 1725 y(1)p 1850 1763 85 4 v 1850 1839 a(2)p Fr(d)2037 1703 y Fo(X)1959 1885 y Fn(j)p Fs(n)p Fn(\000)p Fs(m)o Fn(j)p Fm(=1)2248 1782 y Fr( )s Fv(\()p Fr(m)p Fv(\))p Fr(;)515 2093 y Fv(where)38 b Fr( )44 b Fq(2)e Fr(l)988 2063 y Fm(2)1025 2093 y Fv(\()p Ft(Z)1118 2063 y Fs(d)1151 2093 y Fv(\))d(and)f Fq(j)p Fr(n)p Fq(j)k Fv(=)1638 2003 y Fo(q)p 1721 2003 224 4 v 28 x(P)1808 2118 y Fs(j)1857 2093 y Fr(n)1907 2065 y Fm(2)1907 2116 y Fs(j)1944 2093 y Fv(.)70 b(The)39 b(sym)n(b)r(ol)f(of)h(\001)2689 2105 y Fp(st)2788 2093 y Fv(is)2893 2060 y Fm(1)p 2893 2074 35 4 v 2893 2122 a Fs(d)2951 2031 y Fo(P)3039 2051 y Fs(d)3039 2118 y(j)s Fm(=1)3172 2093 y Fv(cos)13 b Fr(x)3344 2105 y Fs(j)515 2220 y Fv(and)27 b(its)i(sp)r(ectrum)f(is)f (absolutely)h(con)n(tin)n(uous)e(and)i(equal)g(to)f([)p Fq(\000)p Fv(1)p Fr(;)14 b Fv(1])o(.)38 b(Concerning)27 b(the)515 2319 y(random)36 b(p)r(oten)n(tial)h Fr(V)1237 2331 y Fs(!)1323 2319 y Fv(in)g(\(1\),)j(the)e(follo)n(wing)e(t)n(w)n (o)h(cases)f(are)g(distinguished)h(in)h(the)515 2419 y(literature:)e(sparse)26 b(random)h(p)r(oten)n(tials,)g(for)g(whic)n (h)1432 2599 y(#)p Fq(f)p Fr(n)c Fq(2)g Fv(\000)g(;)37 b Fq(j)p Fr(n)p Fq(j)23 b(\024)g Fr(R)p Fq(g)2141 2532 y Fo(\016)2189 2599 y Fr(R)2253 2565 y Fs(d)2314 2599 y Fq(!)g Fv(0)515 2780 y(as)36 b Fr(R)k Fq(!)g(1)p Fv(,)f(and)f(deca)n (ying)e(random)g(p)r(oten)n(tials,)j(for)e(whic)n(h)g Ft(E)23 b Fv(\()p Fq(j)p Fr(V)2803 2792 y Fs(!)2857 2780 y Fv(\()p Fr(n)p Fv(\))p Fq(j)2994 2749 y Fm(2)3032 2780 y Fv(\))40 b Fq(!)f Fv(0)e(as)515 2879 y Fq(j)p Fr(n)p Fq(j)23 b(!)g(1)p Fv(.)639 2979 y(Practically)37 b(all)h(recen)n(t)g(w) n(orks)f(on)h(the)h(scattering)f(theory)f(of)i(Hamiltonians)f(\(1\))515 3078 y(mak)n(e)32 b(use)h(of)g(the)h(stationary)e(scattering)g(theory) -7 b(.)53 b(An)34 b(imp)r(ortan)n(t)f(ingredien)n(t)f(of)i(the)515 3178 y(stationary)26 b(metho)r(ds)i(is)f(an)g Fl(a)k(priori)38 b Fv(estimate)27 b(on)g(the)h(Green)g(function)1271 3358 y Fr(G)1336 3370 y Fs(E)1392 3358 y Fv(\()p Fr(n)p Fv(\))c(:=)p Fr(<)36 b(\016)1756 3370 y Fm(0)1793 3358 y Fq(j)p Fv(\(\001)1917 3370 y Fp(st)1997 3358 y Fq(\000)18 b Fr(E)24 b Fq(\000)18 b Fr(i)p Fv(0\))2351 3324 y Fn(\000)p Fm(1)2439 3358 y Fr(\016)2476 3370 y Fs(n)2558 3358 y Fr(>)515 3538 y Fv(for)29 b(energies)g Fr(E)35 b Fv(in)c(the)f(sp)r(ectrum)h(of)f (\001)1834 3550 y Fp(st)1895 3538 y Fv(.)44 b(In)31 b(con)n(trast)d(to) i(the)h(standard)e(con)n(tin)n(uous)515 3648 y(Laplacian)g(on)i Fr(L)1073 3617 y Fm(2)1110 3648 y Fv(\()p Ft(R)1196 3617 y Fs(d)1241 3648 y Fv(\),)h(the)f(Green)g(function)g Fr(G)2116 3660 y Fs(E)2173 3648 y Fv(\()p Fr(n)p Fv(\))g(is)g(not)g (necessarily)e Fr(O)r Fv(\()p Fq(j)p Fr(n)p Fq(j)3166 3617 y Fn(\000)3229 3592 y Fz(d)p Fy(\000)p Fx(1)p 3229 3605 104 3 v 3267 3637 a(2)3347 3648 y Fv(\))515 3747 y(for)e Fr(d)c Fq(\025)g Fv(3.)36 b(The)28 b(reason)e(for)h(this)h(is)f (that)h(the)g(constan)n(t)f(energy)f(surfaces)1445 4005 y Fq(f)p Fr(x)d Fq(2)g Ft(T)1691 3970 y Fs(d)1752 4005 y Fv(;)1823 3949 y(1)p 1822 3986 44 4 v 1822 4062 a Fr(d)1932 3901 y Fs(d)1889 3926 y Fo(X)1892 4103 y Fs(j)s Fm(=1)2023 4005 y Fv(cos)13 b Fr(x)2195 4017 y Fs(j)2254 4005 y Fv(=)22 b Fr(E)5 b Fq(g)515 4281 y Fv(are)36 b(not)i(con)n(v)n(ex)d (for)i Fq(j)p Fr(E)5 b Fq(j)40 b Fr(<)f Fv(1)24 b Fq(\000)1662 4249 y Fm(2)p 1661 4263 35 4 v 1661 4310 a Fs(d)1706 4281 y Fv(.)66 b(Hence,)40 b(while)e(the)f(exp)r(ected)h(deca)n(y)f (holds)g(for)515 4381 y(1)9 b Fq(\000)649 4348 y Fm(2)p 648 4362 V 648 4410 a Fs(d)716 4381 y Fr(<)22 b Fq(j)p Fr(E)5 b Fq(j)24 b Fr(<)e Fv(1,)h(it)h(fails)e(otherwise)g([SV].)36 b(This)22 b(prop)r(ert)n(y)g(of)h(the)g(standard)e(Laplacian)515 4481 y(is)27 b(an)h(unfortunate)f(obstacle)g(in)h(the)g(dev)n(elopmen)n (t)f(of)g(the)h(scattering)f(theory)f(of)i(\(1\).)639 4580 y(On)36 b(ph)n(ysical)g(grounds)f(the)i(c)n(hoice)f(of)g(the)h (standard)e(discrete)h(Laplacian)f(is)i(pri-)515 4680 y(marily)26 b(dictated)i(b)n(y)f(custom)g(and)h(con)n(v)n(enience,)e (due)i(to)f(its)g(relation)g(to)g(the)h(standard)515 4779 y(random)j(w)n(alk)h(on)h Ft(Z)1205 4749 y Fs(d)1238 4779 y Fv(.)52 b(Indeed,)34 b(equiv)-5 b(alen)n(t)32 b(c)n(hoices)g(are)g(p)r(ossible.)2748 4749 y Fm(1)2837 4779 y Fv(Since)g(\001)3127 4791 y Fp(st)3221 4779 y Fv(is)h(ill)p 515 4848 1146 4 v 607 4904 a FE(1)642 4927 y Fw(By)26 b Fk(e)l(quivalent)p Fw(,)f(w)n(e)h(mean)g(that)h(b)n(y)f (taking)h(the)f(scaling)g(limit,)e Fj(l)2448 4904 y FE(2)2482 4927 y Fw(\()p Fi(Z)2560 4904 y FC(d)2590 4927 y Fw(\))g FK(!)f Fj(L)2783 4904 y FE(2)2817 4927 y Fw(\()p Fi(R)2892 4904 y FC(d)2929 4927 y Fw(\),)j(one)g(reco)n(v)n(ers)515 5006 y(the)e(con)n(tin)n(uous)i(Laplacian.)1926 5255 y Fv(1)p eop %%Page: 2 3 2 2 bop 515 523 a Fv(suited)33 b(for)g(the)h(study)f(of)h(the)f (scattering)g(theory)-7 b(,)34 b(Molc)n(hano)n(v)d(and)i(V)-7 b(ain)n(b)r(erg)33 b([MV1])515 623 y(suggested)28 b(the)i(follo)n(wing) e(alternativ)n(e,)h(whic)n(h)g(w)n(e)g(will)h(call)f(the)h Fl(Molchanov-V)-6 b(ainb)l(er)l(g)515 722 y(L)l(aplacian)6 b Fv(:)1384 834 y(\001)p Fr( )s Fv(\()p Fr(n)p Fv(\))23 b(=)g(2)1777 800 y Fn(\000)p Fs(d)1867 834 y Fr(d)p Fv(!)2053 755 y Fo(X)1947 949 y Fn(j)p Fs(m)p Fn(\000)p Fs(n)p Fn(j)p Fm(=)2190 899 y Fn(p)p 2244 899 35 3 v 2244 949 a Fs(d)2292 834 y Fr( )s Fv(\()p Fr(m)p Fv(\))p Fr(:)515 1077 y Fv(In)31 b(other)f(w)n(ords,)h(\001)p Fr( )s Fv(\()p Fr(n)p Fv(\))g(is)g(equal)f(to)h(a)g(constan)n(t)f(times)h(the)g(sum)g (of)g(the)g Fr( )s Fv(\()p Fr(m)p Fv(\)'s)h(for)515 1177 y Fr(m)j Fv(v)-5 b(arying)34 b(o)n(v)n(er)g(the)h(v)n(ertices)g(of)g (the)h(h)n(yp)r(ercub)r(e)f(of)g(side)g(2)g(cen)n(tered)g(at)g Fr(n)p Fv(.)60 b(These)515 1277 y(v)n(ertices)26 b(are)h(the)h(neigh)n (b)r(ours)e(of)i Fr(n)f Fv(along)g(the)h(full)g(diagonals.)35 b(The)28 b(sym)n(b)r(ol)f(of)g(\001)h(is)1624 1512 y(\010\()p Fr(x)p Fv(\):)14 b(=)1951 1409 y Fs(d)1915 1434 y Fo(Y)1911 1610 y Fs(j)s Fm(=1)2040 1512 y Fv(cos)f Fr(x)2212 1524 y Fs(j)2247 1512 y Fr(;)515 1765 y Fv(as)25 b(the)i(reader)e(ma)n(y)g (easily)g(v)n(erify)-7 b(.)1635 1735 y Fm(2)1708 1765 y Fv(Consequen)n(tly)g(,)26 b(the)h(sp)r(ectrum)f(of)g(\001)h(is)f (absolutely)515 1864 y(con)n(tin)n(uous)37 b(and)h(equal)f(to)h([)p Fq(\000)p Fv(1)o Fr(;)14 b Fv(1].)68 b(Since)39 b(the)f(F)-7 b(ourier)37 b(transform)g(is)h(unitary)-7 b(,)41 b(the)515 1964 y(Green)27 b(function)h(of)g(\001)g(for)f Fr(z)35 b(=)-51 b Fq(2)23 b Ft(R)34 b Fv(is)923 2159 y Fr(G)988 2171 y Fs(z)1026 2159 y Fv(\()p Fr(n)p Fv(\):)15 b(=)22 b Fr(<)37 b(\016)1404 2171 y Fm(0)1441 2159 y Fq(j)p Fv(\(\001)19 b Fq(\000)f Fr(z)t Fv(\))1742 2125 y Fn(\000)p Fm(1)1831 2159 y Fr(\016)1868 2171 y Fs(n)1950 2159 y Fr(>)p Fv(=)k(\(2)p Fr(\031)s Fv(\))2258 2125 y Fn(\000)p Fs(d)2363 2046 y Fo(Z)2409 2235 y Fh(T)2453 2218 y Fz(d)2586 2103 y Fr(e)2625 2073 y Fs(in)p Fn(\001)p Fs(x)p 2510 2140 316 4 v 2510 2216 a Fv(\010\()p Fr(x)p Fv(\))e Fq(\000)e Fr(z)2854 2159 y Fv(d)p Fr(x:)515 2366 y Fv(Molc)n(hano)n(v)28 b(and)j(V)-7 b(ain)n(b)r(erg)29 b([MV1])i(conjectured)f(that)g(the)h (constan)n(t)f(energy)f(surfaces)515 2466 y(of)e(\001,)1332 2643 y(\000\()p Fr(E)5 b Fv(\):)15 b(=)o Fq(f)p Fr(x)23 b Fq(2)h Ft(T)1863 2609 y Fs(d)1924 2643 y Fv(;)2024 2539 y Fs(d)1988 2564 y Fo(Y)1984 2741 y Fs(j)s Fm(=1)2113 2643 y Fv(cos)13 b Fr(x)2285 2655 y Fs(j)2343 2643 y Fv(=)23 b Fr(E)5 b Fq(g)p Fr(;)515 2889 y Fv(are)30 b(strictly)h(con)n (v)n(ex)e(and)i(that)h(the)f(b)r(ound)h Fr(G)2040 2901 y Fs(E)s Fm(+)p Fs(i)p Fm(0)2203 2889 y Fv(\()p Fr(n)p Fv(\))e(=)e Fr(O)r Fv(\()p Fq(j)p Fr(n)p Fq(j)2633 2859 y Fn(\000)2696 2833 y Fz(d)p Fy(\000)p Fx(1)p 2696 2846 104 3 v 2734 2879 a(2)2814 2889 y Fv(\))j(holds.)48 b(In)31 b(this)515 2988 y(pap)r(er)c(w)n(e)g(pro)n(v)n(e)f(this)i(conjecture.) 639 3088 y(Let)j Fr(D)860 3100 y Fs(")922 3088 y Fv(=)c Ft(C)1068 3100 y Fm(+)1149 3088 y Fq([)21 b Fv([)p Fq(\000)p Fv(1)c(+)h Fr(";)c Fq(\000)p Fr(")o Fv(])20 b Fq([)h Fv([)p Fr(";)14 b Fv(1)j Fq(\000)h Fr(")p Fv(],)31 b(where)f(0)d Fr(<)f(")h(<)2681 3055 y Fm(1)p 2681 3069 34 4 v 2681 3117 a(2)2724 3088 y Fv(.)45 b(Our)29 b(main)h(result)515 3188 y(is:)515 3346 y Fg(Theorem)g(1)41 b Fv(\(1\))30 b Fl(F)-6 b(or)30 b Fv(0)23 b Fr(<)f Fq(j)p Fr(E)5 b Fq(j)24 b Fr(<)e Fv(1)29 b Fl(the)h(surfac)l(e)h Fv(\000\()p Fr(E)5 b Fv(\))30 b Fl(is)g(strictly)g(c)l(onvex.)515 3446 y Fv(\(2\))g Fl(The)g(function)g Ft(C)1201 3458 y Fm(+)1285 3446 y Fq(3)24 b Fr(z)i Fq(7!)d Fr(G)1600 3458 y Fs(z)1638 3446 y Fv(\()p Fr(n)p Fv(\))31 b Fl(extends)e(c)l (ontinuously)g(to)h Fr(D)2726 3458 y Fs(")2791 3446 y Fl(and)g(satis\014es)1484 3623 y Fv(sup)1455 3692 y Fs(E)s Fn(2)p Fs(D)1606 3700 y Fz(")1652 3623 y Fq(j)p Fr(G)1740 3635 y Fs(E)1797 3623 y Fv(\()p Fr(n)p Fv(\))p Fq(j)23 b(\024)g Fr(C)2104 3635 y Fs(")2140 3623 y Fq(j)p Fr(n)p Fq(j)2236 3588 y Fn(\000)2297 3563 y Fz(d)p Fy(\000)p Fx(1)p 2297 3576 104 3 v 2335 3608 a(2)2415 3623 y Fr(:)515 3881 y Fg(Remark:)59 b Fl(One)24 b(may)h(derive)h(the)f(c)l(omplete)h (asymptotic)f(exp)l(ansion)h(of)f Fr(G)2940 3893 y Fs(E)2996 3881 y Fv(\()p Fr(n)p Fv(\))h Fl(on)e Fr(D)3318 3893 y Fs(")3354 3881 y Fl(,)515 3980 y(se)l(e)30 b(R)l(emark)f(at)h(the)g (end)g(of)g(Se)l(ction)g(3.)639 4180 y Fv(Applications)g(of)h(Theorem)e (1)h(to)h(the)f(scattering)g(theory)f(of)h(random)g(Sc)n(hr\177)-42 b(odinger)515 4279 y(op)r(erators)39 b(with)j(sparse)e(random)g(p)r (oten)n(tials)h(will)g(b)r(e)h(discussed)f(in)g(a)g(forthcoming)515 4379 y(article)27 b([JP)o(].)639 4479 y(I)37 b(w)n(ould)g(lik)n(e)g(to) g(thank)g(E.)g(Kritc)n(hevski,)h(P)-7 b(.)37 b(Ko)r(osis,)h(M.)f (Merkli,)j(S.)d(Starr)f(and)515 4578 y(esp)r(ecially)23 b(B.)g(V)-7 b(ain)n(b)r(erg)22 b(for)h(useful)h(discussion)e(and)h (commen)n(ts,)h(and)f(V.)h(Jak)l(\024)-37 b(si)n(\023)e(c)20 b(for)j(his)515 4678 y(help)28 b(and)f(w)n(onderful)g(teac)n(hing.)p 515 4737 1146 4 v 607 4812 a FE(2)642 4836 y Fw(In)k(other)g(w)n(ords)g FK(F)7 b Fw(\001)p FK(F)1311 4812 y FF(\000)p FE(1)1425 4836 y Fw(=)31 b(\010,)h(where)f(\()p FK(F)7 b Fj( )r Fw(\)\()p Fj(x)p Fw(\))33 b(=)e(\(2)p Fj(\031)r Fw(\))2329 4807 y FF(\000)2388 4788 y Fz(d)p 2388 4796 31 3 v 2389 4829 a Fx(2)2445 4786 y Ff(P)2520 4857 y FC(n)p FF(2)p Fe(Z)2639 4843 y Fz(d)2683 4836 y Fj(e)2716 4812 y FC(in)p FF(\001)p FC(x)2834 4836 y Fj( )r Fw(\()p Fj(n)p Fw(\))h(is)e(the)i (usual)515 4927 y(F)-6 b(ourier)25 b(transform)f(acting)j(on)f Fj( )g FK(2)d Fj(l)1565 4904 y FE(2)1599 4927 y Fw(\()p Fi(Z)1677 4904 y FC(d)1707 4927 y Fw(\))j(and)g(\010)g(denotes)h(the)g (op)r(erator)f(of)g(m)n(ultiplication)f(b)n(y)h(the)515 5006 y(function)e(\010\()p Fj(x)p Fw(\))g(on)g Fj(L)1106 4983 y FE(2)1141 5006 y Fw(\()p Fi(T)1218 4983 y FC(d)1249 5006 y Fw(\).)31 b(This)23 b(result)h(follo)n(ws)e(from)g(Euler's)h (form)n(ula)f(for)g(the)j(cosine.)1926 5255 y Fv(2)p eop %%Page: 3 4 3 3 bop 515 523 a Fu(2)134 b(Lev)l(el)46 b(Surfaces)f(of)h Fd(\010)515 721 y Fc(2.1)112 b(Connected)38 b(Comp)s(onen)m(ts)515 892 y Fv(Consider)26 b(\014rst)i(the)g(co)n(v)n(ering)1514 865 y Fo(d)1501 892 y Fv(\000\()p Fr(t)p Fv(\))q(:)13 b(=)p Fq(f)p Fr(x)23 b Fq(2)g Ft(R)1993 861 y Fs(d)2061 892 y Fv(;)37 b(\010\()p Fr(x)p Fv(\))24 b(=)f Fr(t)p Fq(g)k Fv(of)h(\000\()p Fr(t)p Fv(\).)639 1009 y(If)36 b Fr(t)g Fv(=)g(0,)1013 983 y Fo(d)999 1009 y Fv(\000\()p Fr(t)p Fv(\))g(consists)f(of)h(the)g(h)n(yp)r(erplanes)e Fr(x)2263 1021 y Fs(j)2335 1009 y Fv(=)i(\(2)p Fr(n)23 b Fv(+)g(1\))2755 977 y Fs(\031)p 2755 991 41 4 v 2759 1038 a Fm(2)2842 1009 y Fv(for)35 b Fr(n)h Fq(2)g Ft(Z)29 b Fv(and)515 1109 y Fr(j)k Fv(=)28 b(1)p Fr(;)14 b Fq(\001)g(\001)g (\001)27 b Fr(;)14 b(d)p Fv(.)47 b(These)31 b(h)n(yp)r(erplanes)f (divide)h(the)g(space)f(in)n(to)h(op)r(en)g(h)n(yp)r(ercub)r(es)f(whic) n(h)515 1209 y(are)38 b(called)g Fl(c)l(el)t(ls)p Fv(.)72 b(The)39 b(cells)g(admit)g(a)g(go)r(o)r(d)f(bicoloration)f(in)i(the)h (follo)n(wing)e(sense:)515 1308 y(starting)26 b(from)h(a)h(set)f(of)g (t)n(w)n(o)g(colours,)f(sa)n(y)g(red)i(and)f(blue,)h(it)g(is)f(p)r (ossible)g(to)h(pain)n(t)f(eac)n(h)515 1408 y(cell)d(in)g(suc)n(h)g(a)g (w)n(a)n(y)f(that)h(the)g(2)p Fr(d)g Fv(neigh)n(b)r(ours)f(of)h(an)n(y) g(red)f(cell)h(are)g(blue)g(and)g Fl(vic)l(e)j(versa)p Fv(.)515 1508 y(Let)g(us)h(accomplish)f(this,)h(the)g(cell)f(con)n (taining)g Fr(O)j Fv(b)r(eing)e(pain)n(ted)f(red.)639 1607 y(When)d Fr(x)f Fv(v)-5 b(aries)22 b(con)n(tin)n(uously)-7 b(,)23 b(\010\()p Fr(x)p Fv(\))h(c)n(hanges)d(sign)h(eac)n(h)g(time)i (one)e(of)h(the)g(previous)515 1725 y(h)n(yp)r(erplanes)33 b(is)i(crossed.)57 b(It)35 b(follo)n(ws)e(that)i(the)g(connected)g (comp)r(onen)n(ts)f(of)3100 1698 y Fo(d)3087 1725 y Fv(\000\()p Fr(t)p Fv(\))h(are)515 1825 y(enclosed)c(in)i(the)f(red)g(cells)g(when) g Fr(t)e(>)h Fv(0,)h(eac)n(h)g(red)f(cell)h(con)n(taining)g(one)f(comp) r(onen)n(t.)515 1924 y(Moreo)n(v)n(er,)h(these)i(comp)r(onen)n(ts)f (are)f(all)h(congruen)n(t.)54 b(The)33 b(situation)h(is)f(similar)g (when)515 2024 y Fr(t)23 b(<)f Fv(0,)28 b(but)g(with)g(the)g(blue)g (cells.)639 2137 y(Finally)-7 b(,)46 b(\000\()p Fr(t)p Fv(\))d(is)f(obtained)g(from)1823 2111 y Fo(d)1810 2137 y Fv(\000\()p Fr(t)p Fv(\))h(b)n(y)f(restricting)f(it)i(to)f(the)g (torus,)k(where)515 2237 y(0)38 b Fr(<)g Fq(j)p Fr(t)p Fq(j)g Fr(<)g Fv(1)f(is)f(\014xed.)65 b(One)36 b(easily)g(concludes)h (that)g(\000\()p Fr(t)p Fv(\))g(consists)f(of)h(2)2986 2207 y Fs(d)p Fn(\000)p Fm(1)3146 2237 y Fv(iden)n(ti-)515 2336 y(cal)27 b(connected)g(comp)r(onen)n(ts.)515 2661 y Fc(2.2)112 b(Regularit)m(y)36 b(and)i(Con)m(v)m(exit)m(y)515 2815 y Fv(\000\()p Fr(t)p Fv(\))28 b(is)f(a)h(regular)d(smo)r(oth)j (surface)e(for)h(0)c Fr(<)g Fq(j)p Fr(t)p Fq(j)g Fr(<)f Fv(1,)28 b(since)f(for)g(all)h Fr(x)23 b Fq(2)g Fv(\000\()p Fr(t)p Fv(\))1387 3038 y Fq(kr)t Fv(\010\()p Fr(x)p Fv(\))p Fq(k)1715 3003 y Fm(2)1776 3038 y Fv(=)f Fr(t)1893 3003 y Fm(2)1987 2934 y Fs(d)1944 2959 y Fo(X)1947 3135 y Fs(j)s Fm(=1)2078 3038 y Fv(tan)2198 3003 y Fm(2)2249 3038 y Fr(x)2296 3050 y Fs(j)2355 3038 y Fq(6)p Fv(=)g(0)p Fr(:)639 3267 y Fv(Assuming)43 b(\014rst)f(that)h(0)k Fr(<)h(t)f(<)h Fv(1,)e(one)c(pro)n(v)n(es)e(that)j(an)n(y)f(comp)r (onen)n(t,)k Fq(R)p Fv(\()p Fr(t)p Fv(\),)515 3367 y(of)36 b(the)h(region)e Fq(f)p Fr(x)23 b Fq(2)h Ft(R)1273 3337 y Fs(d)1355 3367 y Fv(;)52 b(\010\()p Fr(x)p Fv(\))24 b Fq(\025)f Fr(t)p Fq(g)36 b Fv(is)g(con)n(v)n(ex.)63 b(Giv)n(en)36 b(an)g(arbitrarily)f(\014xed)h Fr(\030)42 b Fv(=)515 3466 y(\()p Fr(\030)583 3478 y Fm(1)621 3466 y Fr(;)14 b Fq(\001)g(\001)g(\001)27 b Fr(;)14 b(\030)855 3478 y Fs(d)894 3466 y Fv(\))23 b Fq(2)h(R)p Fv(\()p Fr(t)p Fv(\),)k(one)g(de\014nes)f(for)g Fr(j)h Fv(=)23 b(1)p Fr(;)14 b Fq(\001)g(\001)g(\001)27 b Fr(;)14 b(d)p Fv(,)714 3658 y Fr(f)755 3670 y Fs(j)790 3658 y Fv(\()p Fr(u)p Fv(\))23 b(=)1013 3541 y Fo(\032)1117 3608 y Fv(cos)o(\()p Fr(u)p Fv(\))161 b(if)28 b(cos)o(\()p Fr(\030)1756 3620 y Fs(j)1792 3608 y Fv(\))23 b Fr(>)g Fv(0,)k(with)h(dom)14 b Fr(f)2428 3620 y Fs(j)2486 3608 y Fv(=)2573 3540 y Fo(\003)2608 3608 y Fq(\000)2683 3575 y Fs(\031)p 2683 3589 V 2687 3636 a Fm(2)2733 3608 y Fr(;)2780 3575 y Fs(\031)p 2780 3589 V 2784 3636 a Fm(2)2831 3540 y Fo(\002)2884 3608 y Fv(+)k(2)p Fr(k)s(\031)s(;)1117 3708 y Fq(\000)c Fv(cos)n(\()p Fr(u)p Fv(\))83 b(if)28 b(cos)o(\()p Fr(\030)1756 3720 y Fs(j)1792 3708 y Fv(\))23 b Fr(<)g Fv(0,)k(with)h(dom)14 b Fr(f)2428 3720 y Fs(j)2486 3708 y Fv(=)2573 3641 y Fo(\003)2618 3675 y Fs(\031)p 2618 3689 V 2622 3737 a Fm(2)2669 3708 y Fr(;)2716 3675 y Fm(3)p Fs(\031)p 2716 3689 75 4 v 2736 3737 a Fm(2)2800 3641 y Fo(\002)2853 3708 y Fv(+)k(2)p Fr(l)r(\031)s(;)515 3845 y Fv(where)33 b(the)h(c)n(hoice)f(of)g Fr(k)k Fv(or)c Fr(l)i Fv(is)e(determined)h(b)n (y)f Fr(\030)2197 3857 y Fs(j)2266 3845 y Fq(2)g Fv(dom)14 b Fr(f)2566 3857 y Fs(j)2601 3845 y Fv(.)55 b(This)33 b(last)h(de\014nition)515 3945 y(do)r(es)27 b(not)h(dep)r(end)g(on)f Fr(\030)g Fq(2)d(R)p Fv(\()p Fr(t)p Fv(\).)639 4045 y(Since)32 b(\010\()p Fr(\030)t Fv(\))e(=)g(cos)13 b Fr(\030)1310 4057 y Fm(1)1361 4045 y Fr(:)h(:)g(:)g Fv(cos)f Fr(\030)1633 4057 y Fs(d)1701 4045 y Fq(\025)30 b Fr(t)f(>)g Fv(0,)k(cos)13 b Fr(\030)2208 4057 y Fs(j)2275 4045 y Fv(is)31 b(negativ)n(e)f(an)i (ev)n(en)f(n)n(um)n(b)r(er)g(of)515 4144 y(times,)38 b(whic)n(h)e(implies)g(that)g(\010\()p Fr(x)p Fv(\))h(=)g Fr(f)1845 4156 y Fm(1)1882 4144 y Fv(\()p Fr(x)1961 4156 y Fm(1)1999 4144 y Fv(\))14 b Fr(:)g(:)g(:)f(f)2196 4156 y Fs(d)2235 4144 y Fv(\()p Fr(x)2314 4156 y Fs(d)2353 4144 y Fv(\))36 b(on)g Fq(R)p Fv(\()p Fr(t)p Fv(\).)62 b(Note)36 b(that)g Fr(f)3232 4156 y Fs(j)3267 4144 y Fv(\()p Fr(u)p Fv(\))515 4244 y(is)c(strictly)f(p)r(ositiv)n(e,)i (conca)n(v)n(e,)e(and)h(hence)g(logarithmically)e(conca)n(v)n(e)h(on)g (its)h(domain.)515 4343 y(Consequen)n(tly)-7 b(,)515 4485 y Fg(Lemma)29 b(2)42 b Fq(R)p Fv(\()p Fr(t)p Fv(\))30 b Fl(is)g(c)l(onvex.)515 4626 y Fg(Pro)s(of:)52 b Fv(Let)19 b Fr(r)n(;)14 b(s)23 b Fq(2)h Fv([0)p Fr(;)14 b Fv(1])k(suc)n(h)i(that) f Fr(r)5 b Fv(+)r Fr(s)23 b Fv(=)g(1)c(and)g Fr(x;)14 b(y)27 b Fq(2)c(R)p Fv(\()p Fr(t)p Fv(\).)35 b(Then,)22 b Fr(r)r(x)r Fv(+)r Fr(sy)27 b Fq(2)c(R)p Fv(\()p Fr(t)p Fv(\))515 4725 y(since)967 4867 y(\010\()p Fr(r)r(x)d Fv(+)e Fr(sy)s Fv(\))83 b(=)f Fr(f)1634 4879 y Fm(1)1671 4867 y Fv(\()p Fr(r)r(x)1789 4879 y Fm(1)1846 4867 y Fv(+)18 b Fr(sy)2009 4879 y Fm(1)2046 4867 y Fv(\))c Fr(:)g(:)g(:)g(f)2244 4879 y Fs(d)2282 4867 y Fv(\()p Fr(r)r(x)2400 4879 y Fs(d)2459 4867 y Fv(+)k Fr(sy)2622 4879 y Fs(d)2660 4867 y Fv(\))1446 4991 y Fq(\025)82 b Fr(f)1634 5003 y Fm(1)1671 4991 y Fv(\()p Fr(x)1750 5003 y Fm(1)1788 4991 y Fv(\))1820 4957 y Fs(r)1857 4991 y Fr(f)1898 5003 y Fm(1)1935 4991 y Fv(\()p Fr(y)2008 5003 y Fm(1)2045 4991 y Fv(\))2077 4957 y Fs(s)2127 4991 y Fr(:)14 b(:)g(:)g(f)2279 5003 y Fs(d)2317 4991 y Fv(\()p Fr(x)2396 5003 y Fs(d)2435 4991 y Fv(\))2467 4957 y Fs(r)2504 4991 y Fr(f)2545 5003 y Fs(d)2584 4991 y Fv(\()p Fr(y)2657 5003 y Fs(d)2695 4991 y Fv(\))2727 4957 y Fs(s)2786 4991 y Fq(\025)23 b Fr(t:)3314 5132 y Fb(\003)1926 5255 y Fv(3)p eop %%Page: 4 5 4 4 bop 515 523 a Fv(The)27 b(case)g Fr(t)c(<)g Fv(0)k(is)g(similar,)g (starting)g(from)g(\()p Fq(\000)14 b Fv(cos)f Fr(x)2239 535 y Fm(1)2277 523 y Fv(\))h(cos)f Fr(x)2495 535 y Fm(2)2546 523 y Fr(:)h(:)g(:)g Fv(cos)f Fr(x)2829 535 y Fs(d)2891 523 y Fq(\025)23 b(\000)p Fr(t)p Fv(.)639 722 y(Let)28 b Fq(D)r Fv(\()p Fr(t)p Fv(\))c(=)f Fr(@)5 b Fq(R)p Fv(\()p Fr(t)p Fv(\))28 b(b)r(e)g(a)f(comp)r(onen)n(t)g(of)h(\000\()p Fr(t)p Fv(\))g(and)g Fr(N)9 b Fv(\()p Fr(x)p Fv(\))23 b(=)2680 682 y Fn(r)t Fm(\010\()p Fs(x)p Fm(\))p 2646 703 265 4 v 2646 751 a Fn(kr)t Fm(\010\()p Fs(x)p Fm(\))p Fn(k)2920 722 y Fv(.)515 927 y Fg(Theorem)30 b(3)41 b Fl(F)-6 b(or)27 b(any)g Fr(!)e Fq(2)f Fv(S)1519 897 y Fs(d)p Fn(\000)p Fm(1)1669 927 y Fl(ther)l(e)i(exists)g(exactly)h(one)f (p)l(oint)h Fr(x)c Fv(=)g(x\()p Fr(!)s(;)14 b(t)p Fv(\))23 b Fq(2)g(D)r Fv(\()p Fr(t)p Fv(\))515 1027 y Fl(such)31 b(that)h Fr(N)9 b Fv(\()p Fr(x)p Fv(\))27 b(=)e Fr(!)s Fl(.)44 b(Mor)l(e)l(over,)33 b Fv(x\()p Fr(!)s(;)14 b(t)p Fv(\))32 b Fl(extends)f(to)g(a)h(holomorphic)j(function)c(in)h(a)515 1127 y(neighb)l(ourho)l(o)l(d)g(of)e Fv(S)1196 1096 y Fs(d)p Fn(\000)p Fm(1)1338 1127 y Fq(\002)18 b(f)p Fr(t)p Fq(g)p Fl(.)515 1309 y Fg(Pro)s(of:)64 b Fr(N)9 b Fv(\()p Fr(x)p Fv(\))24 b(=)e Fr(!)31 b Fv(i\013)d Fr(x)g Fv(satis\014es)f (under)g(the)h(constrain)n(t)e(\010\()p Fr(x)p Fv(\))f(=)d Fr(t)28 b Fv(the)g(relations)1405 1492 y Fq(\000)p Fr(t)14 b Fv(tan)f Fr(x)1694 1504 y Fs(j)1752 1492 y Fv(=)23 b Fr(C)6 b(!)1957 1504 y Fs(j)1992 1492 y Fr(;)41 b(j)28 b Fv(=)23 b(1)p Fr(;)14 b Fq(\001)g(\001)g(\001)27 b Fr(;)14 b(d)515 1689 y Fv(for)23 b(a)h(scalar)f Fr(C)29 b(>)23 b Fv(0.)35 b(Then,)25 b Fr(x)1497 1701 y Fs(j)1556 1689 y Fv(=)d(arctan)1898 1647 y Fn(\000)p Fs(C)t(!)2044 1655 y Fz(j)p 1898 1670 177 4 v 1974 1717 a Fs(t)2084 1689 y Fv(,)j(where)f(the)g(branc)n(h)g(of)g(arctan)f(is)h(\014xed)515 1807 y(b)n(y)h(the)h(c)n(hoice)f(of)h Fq(D)r Fv(\()p Fr(t)p Fv(\).)37 b(Moreo)n(v)n(er,)23 b(sec)1820 1777 y Fm(2)1871 1807 y Fr(x)1918 1819 y Fs(j)1977 1807 y Fv(=)f(1)14 b(+)h(\()2242 1765 y Fs(C)t(!)2336 1773 y Fz(j)p 2242 1788 125 4 v 2292 1836 a Fs(t)2376 1807 y Fv(\))2408 1777 y Fm(2)2446 1807 y Fv(,)26 b(so)f(the)h(constrain)n(t)f (implies)1277 2051 y Fr(t)1307 2017 y Fm(2)1358 1934 y Fo(\022)1419 2051 y Fv(1)18 b(+)1572 1995 y Fr(C)1637 1965 y Fm(2)1675 1995 y Fr(!)1730 1965 y Fm(2)1727 2016 y(1)p 1572 2032 195 4 v 1636 2108 a Fr(t)1666 2084 y Fm(2)1776 1934 y Fo(\023)1851 2051 y Fr(:)c(:)g(:)1962 1934 y Fo(\022)2023 2051 y Fv(1)k(+)2176 1995 y Fr(C)2241 1965 y Fm(2)2279 1995 y Fr(!)2334 1965 y Fm(2)2331 2019 y Fs(d)p 2176 2032 V 2240 2108 a Fr(t)2270 2084 y Fm(2)2380 1934 y Fo(\023)2465 2051 y Fv(=)k(1)p Fr(:)656 b Fv(\(2\))515 2284 y(This)34 b(equation)f(has)g(a)h(unique)g(p)r(ositiv)n(e)f(ro)r (ot)g Fr(C)40 b Fv(=)33 b(C\()p Fr(!)s(;)14 b(t)p Fv(\).)56 b(The)34 b(desired)f Fr(x)i Fv(is)f(then)515 2398 y(giv)n(en)22 b(b)n(y)g Fr(x)884 2410 y Fs(j)943 2398 y Fv(=)g(arctan)1285 2356 y Fn(\000)p Fm(C\()p Fs(!)r(;t)p Fm(\))p Fs(!)1567 2364 y Fz(j)p 1285 2379 313 4 v 1429 2427 a Fs(t)1608 2398 y Fv(.)35 b(Finally)-7 b(,)24 b(x\()p Fr(!)s(;)14 b(t)p Fv(\))23 b(is)f(holomorphic)g(since)g(the)i(left)f(side)515 2498 y(of)k(\(2\))h(has)f(a)g(non)h(v)-5 b(anishing)27 b(deriv)-5 b(ativ)n(e)27 b(in)g Fr(C)6 b Fv(.)1260 b Fb(\003)639 2697 y Fv(Note)32 b(that)h(the)f(in)n(v)n(erse,)g(\()p Fr(N)t(;)14 b Fv(\010\),)34 b(of)e(x)g(also)f(extends)h(to)g(a)g (holomorphic)e(function)515 2797 y(in)e(a)f(neigh)n(b)r(ourho)r(o)r(d)f (of)i Fq(D)r Fv(\()p Fr(t)p Fv(\).)515 3029 y Fc(2.3)112 b(Gaussian)39 b(Curv)-6 b(ature)515 3183 y Fv(In)28 b(this)f(section)h (w)n(e)f(pro)n(v)n(e)f(P)n(art)g(\(1\))i(of)f(Theorem)g(1.)639 3282 y(A)19 b(regular)e(smo)r(oth)h(surface)g Fq(S)25 b Fv(ma)n(y)18 b(b)r(e)h(expressed)e(lo)r(cally)h(as)g(the)g(graph)g (of)g(a)g(smo)r(oth)515 3382 y(function)28 b Fr(h)37 b Fv(:)g Fr(U)32 b Fq(\022)22 b Ft(R)1215 3352 y Fs(d)p Fn(\000)p Fm(1)1368 3382 y Fq(!)h Ft(R)p Fv(.)44 b(The)27 b(Gaussian)g(curv)-5 b(ature)27 b(of)h Fq(S)34 b Fv(in)28 b(a)f(neigh)n(b)r(ourho)r(o)r(d)515 3481 y(of)g(a)g(p)r(oin)n(t)h(\()p Fr(u;)14 b(h)p Fv(\()p Fr(u)p Fv(\)\))28 b(is)f(then)h(giv)n(en)f(b)n (y)1740 3661 y(det)15 b(D)1933 3631 y Fm(2)1970 3661 y Fr(h)p Fv(\()p Fr(u)p Fv(\))p 1636 3698 599 4 v 1636 3774 a(\(1)j(+)g Fq(kr)t Fr(h)p Fv(\()p Fr(u)p Fv(\))p Fq(k)2128 3750 y Fm(2)2165 3774 y Fv(\))2197 3750 y Fm(2)2244 3717 y Fr(;)515 3949 y Fv(where)31 b Fr(u)e Fq(2)g Fr(U)9 b Fv(.)49 b(F)-7 b(or)31 b Fq(S)k Fv(=)30 b(\000\()p Fr(t)p Fv(\),)i(w)n(e)g(will)f(pro)n(v)n(e)f(that)i(this)f(curv)-5 b(ature)31 b(nev)n(er)g(v)-5 b(anishes.)515 4048 y(This)27 b(computation)h(together)e(with)i(Lemma)g(2)f(giv)n(es)f(the)i(follo)n (wing:)515 4231 y Fg(Theorem)i(4)41 b Fl(F)-6 b(or)30 b Fv(0)23 b Fr(<)g Fq(j)p Fr(t)p Fq(j)g Fr(<)f Fv(1)30 b Fl(any)g(c)l(omp)l(onent)f(of)i Fv(\000\()p Fr(t)p Fv(\))f Fl(is)g(strictly)g(c)l(onvex.)515 4413 y Fg(Pro)s(of:)62 b Fv(W)-7 b(e)28 b(treat)e(the)h(case)f(0)d Fr(<)f(t)h(<)g Fv(1,)j(the)i(other)e(case)g(b)r(eing)h(similar.)35 b(W.l.o.g.)i(the) 515 4528 y(comp)r(onen)n(t)c(under)g(consideration)e(is)j(giv)n(en)e(b) n(y)h Fq(f)p Fr(x)23 b Fq(2)2322 4461 y Fo(\003)2357 4528 y Fq(\000)2432 4496 y Fs(\031)p 2431 4510 41 4 v 2435 4557 a Fm(2)2482 4528 y Fr(;)2529 4496 y Fs(\031)p 2529 4510 V 2533 4557 a Fm(2)2580 4461 y Fo(\002)2615 4478 y Fs(d)2686 4528 y Fv(;)2755 4466 y Fo(Q)2833 4487 y Fs(d)2833 4553 y(j)s Fm(=1)2966 4528 y Fv(cos)13 b Fr(x)3138 4540 y Fs(j)3197 4528 y Fv(=)22 b Fr(t)p Fq(g)p Fr(:)515 4628 y Fv(Let)38 b Fr(m)i Fv(=)f Fr(d)26 b Fq(\000)f Fv(1,)40 b Fr(u)f Fv(=)h(\()p Fr(x)1426 4640 y Fm(1)1464 4628 y Fr(;)14 b Fq(\001)g(\001)g(\001)27 b Fr(;)14 b(x)1709 4640 y Fs(m)1773 4628 y Fv(\),)41 b(and)c Fr(h)j Fv(=)g Fr(x)2280 4640 y Fs(d)2319 4628 y Fv(.)68 b(The)38 b(equation)f (de\014ning)h(the)515 4728 y(previous)f(comp)r(onen)n(t)g(b)r(ecomes)h (cos)13 b Fr(x)1803 4740 y Fm(1)1854 4728 y Fr(:)h(:)g(:)g Fv(cos)f Fr(x)2137 4740 y Fs(m)2214 4728 y Fv(cos)g Fr(h)40 b Fv(=)g Fr(t)e Fv(or,)i(eac)n(h)d(factor)g(b)r(eing)515 4827 y(p)r(ositiv)n(e,)1118 4927 y(ln)14 b(cos)f Fr(x)1373 4939 y Fm(1)1429 4927 y Fv(+)18 b Fq(\001)c(\001)g(\001)k Fv(+)g(ln)c(cos)f Fr(x)1965 4939 y Fs(m)2047 4927 y Fv(+)18 b(ln)c(cos)f Fr(h)19 b Fq(\000)f Fv(ln)c Fr(t)23 b Fv(=)f(0)p Fr(:)497 b Fv(\(3\))1926 5255 y(4)p eop %%Page: 5 6 5 5 bop 639 523 a Fv(Since)32 b(the)g(comp)r(onen)n(t)g(is)g(symmetric) f(with)h(resp)r(ect)g(to)f(the)i(h)n(yp)r(erplanes)d Fr(x)3177 535 y Fs(j)3243 523 y Fv(=)f(0)515 623 y(and)i Fr(x)727 635 y Fs(j)791 623 y Fv(=)d Fr(x)931 635 y Fs(l)957 623 y Fv(,)k(where)f Fr(j)5 b Fv(,)32 b Fr(l)e Fq(2)f(f)p Fv(1)p Fr(;)14 b(:)g(:)g(:)f(;)h(d)p Fq(g)31 b Fv(are)f(distinct,)j(it) e(su\016ces)g(to)g(sho)n(w)f(the)h(result)515 722 y(for)37 b(the)i(fundamen)n(tal)f(domain)f Fr(h)j Fq(\024)g Fr(x)1841 734 y Fm(1)1919 722 y Fq(\024)g(\001)14 b(\001)g(\001)40 b(\024)g Fr(x)2313 734 y Fs(m)2417 722 y Fq(\024)g Fv(0.)68 b(There,)40 b Fr(h)g Fq(6)p Fv(=)g(0)d(since)515 822 y Fr(t)26 b Fq(6)p Fv(=)g(1.)42 b(The)29 b(deriv)-5 b(ativ)n(e)29 b(with)h(resp)r(ect)f(to)g Fr(h)h Fv(of)f(the)h(left)g(side)g(of)f (\(3\))h(is)f Fq(\000)14 b Fv(tan)f Fr(h)p Fv(,)30 b(whic)n(h)515 922 y(do)r(es)i(not)h(v)-5 b(anish.)53 b(Consequen)n(tly)-7 b(,)33 b(an)g(implicit)h(function)f Fr(h)f Fv(=)g(h\()p Fr(u;)14 b(t)p Fv(\))33 b(satisfying)f(\(3\))515 1021 y(in)e(a)g(neigh)n(b)r(ourho)r(o)r(d)f(of)h(an)f(arbitrary)f(p)r(oin)n (t)j(of)f(the)g(fundamen)n(tal)g(domain)g(exists,)g(is)515 1121 y(analytic,)d(and)g(induces)h(a)f(lo)r(cal)g(parametrization)f(of) h(the)h(previous)f(comp)r(onen)n(t.)639 1220 y(W)-7 b(e)27 b(th)n(us)f(ha)n(v)n(e)f(to)h(sho)n(w)g(that)g(the)h(Hessian)e(D)2141 1190 y Fm(2)2141 1241 y Fs(u)2185 1220 y Fv(h\()p Fr(u;)14 b(t)p Fv(\))26 b(is)h(not)f(singular.)35 b(Di\013eren)n(ti-)515 1320 y(ating)27 b(\(3\))h(with)g(resp)r(ect)f(to)h Fr(x)1483 1332 y Fs(j)1546 1320 y Fv(giv)n(es)1456 1475 y Fq(\000)14 b Fv(tan)f Fr(x)1715 1487 y Fs(j)1769 1475 y Fq(\000)18 b Fv(\(tan)c Fr(h)p Fv(\))p Fr(@)2142 1487 y Fs(x)2180 1495 y Fz(j)2215 1475 y Fr(h)23 b Fv(=)f(0)p Fr(;)515 1630 y Fv(where)27 b Fr(h)c Fv(=)f(h\()p Fr(u;)14 b(t)p Fv(\).)37 b(Di\013eren)n(tiating)28 b(this)g(last)f(equation)g(with)h (resp)r(ect)g(to)f Fr(x)3031 1642 y Fs(l)3085 1630 y Fv(giv)n(es)898 1785 y Fq(\000)14 b Fv(sec)1083 1755 y Fm(2)1134 1785 y Fr(x)1181 1797 y Fs(j)1235 1785 y Fq(\000)k Fv(\(sec)1457 1755 y Fm(2)1508 1785 y Fr(h)p Fv(\)\()p Fr(@)1664 1797 y Fs(x)1702 1805 y Fz(j)1738 1785 y Fr(h)p Fv(\))1818 1755 y Fm(2)1873 1785 y Fq(\000)g Fv(\(tan)c Fr(h)p Fv(\))p Fr(@)2251 1755 y Fm(2)2246 1805 y Fs(x)2284 1813 y Fz(j)2319 1785 y Fr(h)23 b Fv(=)g(0)110 b(if)28 b Fr(l)d Fv(=)d Fr(j)5 b Fv(,)898 1891 y Fq(\000)p Fv(\(sec)1102 1861 y Fm(2)1153 1891 y Fr(h)p Fv(\))p Fr(@)1277 1903 y Fs(x)1315 1911 y Fz(j)1350 1891 y Fr(h)14 b(@)1456 1903 y Fs(x)1494 1912 y Fz(l)1522 1891 y Fr(h)k Fq(\000)g Fv(\(tan)c Fr(h)p Fv(\))p Fr(@)1961 1903 y Fs(x)1999 1911 y Fz(j)2034 1891 y Fr(@)2078 1903 y Fs(x)2116 1912 y Fz(l)2144 1891 y Fr(h)23 b Fv(=)f(0)286 b(otherwise.)515 2048 y(Let)24 b Fr(a)704 2060 y Fs(j)s(l)783 2048 y Fv(=)f Fq(\000)p Fv(\(tan)13 b Fr(h)p Fv(\))p Fr(@)1225 2060 y Fs(x)1263 2068 y Fz(j)1298 2048 y Fr(@)1342 2060 y Fs(x)1380 2069 y Fz(l)1408 2048 y Fr(h)p Fv(.)36 b(Since)24 b(tan)13 b Fr(h)23 b Fq(6)p Fv(=)g(0,)h(it)g(su\016ces)g(to)f(sho)n(w)g (that)h(det[)p Fr(a)3124 2060 y Fs(j)s(l)3181 2048 y Fv(])f Fq(6)p Fv(=)f(0.)515 2147 y(By)27 b(the)h(ab)r(o)n(v)n(e,)1087 2348 y Fr(a)1131 2360 y Fs(j)s(l)1210 2348 y Fv(=)1298 2231 y Fo(\032)1402 2297 y Fv(sec)1508 2267 y Fm(2)1559 2297 y Fr(x)1606 2309 y Fs(j)1660 2297 y Fv(+)18 b(\(sec)1882 2267 y Fm(2)1933 2297 y Fr(h)p Fv(\)\()p Fr(@)2089 2309 y Fs(x)2127 2317 y Fz(j)2162 2297 y Fr(h)p Fv(\))2242 2267 y Fm(2)2390 2297 y Fv(if)28 b Fr(l)d Fv(=)e Fr(j)5 b Fv(,)1402 2397 y(\(sec)1540 2366 y Fm(2)1591 2397 y Fr(h)p Fv(\))p Fr(@)1715 2409 y Fs(x)1753 2417 y Fz(j)1788 2397 y Fr(h)14 b(@)1894 2409 y Fs(x)1932 2418 y Fz(l)1960 2397 y Fr(h)382 b Fv(otherwise.)639 2561 y(Let)28 b Fr(C)847 2573 y Fs(l)901 2561 y Fv(b)r(e)g(the)f Fr(l)1183 2531 y Fs(th)1279 2561 y Fv(column)g(of)h([)p Fr(a)1731 2573 y Fs(j)s(l)1787 2561 y Fv(].)37 b(Explicitly)-7 b(,)916 2726 y Fr(C)975 2738 y Fm(1)1096 2726 y Fv(=)82 b(sec)1350 2692 y Fm(2)1401 2726 y Fr(x)1448 2738 y Fm(1)1486 2726 y Fv([1)27 b(0)14 b Fr(:)g(:)g(:)f Fv(0])1808 2684 y Fm(t)1857 2726 y Fv(+)18 b(\(sec)2079 2692 y Fm(2)2130 2726 y Fr(h)p Fv(\))p Fr(@)2254 2738 y Fs(x)2292 2746 y Fx(1)2328 2726 y Fr(h)p Fv([)p Fr(@)2443 2738 y Fs(x)2481 2746 y Fx(1)2518 2726 y Fr(h)c(:)g(:)g(:)f(@)2734 2738 y Fs(x)2772 2746 y Fz(m)2831 2726 y Fr(h)p Fv(])2902 2684 y Fm(t)2932 2726 y Fr(;)916 2850 y(C)975 2862 y Fm(2)1096 2850 y Fv(=)82 b(sec)1350 2816 y Fm(2)1401 2850 y Fr(x)1448 2862 y Fm(2)1486 2850 y Fv([0)27 b(1)14 b Fr(:)g(:)g(:)f Fv(0])1808 2809 y Fm(t)1857 2850 y Fv(+)18 b(\(sec)2079 2816 y Fm(2)2130 2850 y Fr(h)p Fv(\))p Fr(@)2254 2862 y Fs(x)2292 2870 y Fx(2)2328 2850 y Fr(h)p Fv([)p Fr(@)2443 2862 y Fs(x)2481 2870 y Fx(1)2518 2850 y Fr(h)c(:)g(:)g(:)f (@)2734 2862 y Fs(x)2772 2870 y Fz(m)2831 2850 y Fr(h)p Fv(])2902 2809 y Fm(t)2932 2850 y Fr(;)916 2975 y(:)h(:)g(:)890 3100 y(C)949 3112 y Fs(m)1096 3100 y Fv(=)82 b(sec)1350 3065 y Fm(2)1401 3100 y Fr(x)1448 3112 y Fs(m)1511 3100 y Fv([0)28 b(0)14 b Fr(:)g(:)g(:)f Fv(1])1834 3058 y Fm(t)1883 3100 y Fv(+)18 b(\(sec)2105 3065 y Fm(2)2156 3100 y Fr(h)p Fv(\))p Fr(@)2280 3112 y Fs(x)2318 3120 y Fz(m)2377 3100 y Fr(h)p Fv([)p Fr(@)2492 3112 y Fs(x)2530 3120 y Fx(1)2566 3100 y Fr(h)c(:)g(:)g(:)f(@)2782 3112 y Fs(x)2820 3120 y Fz(m)2879 3100 y Fr(h)p Fv(])2950 3058 y Fm(t)2980 3100 y Fr(:)639 3255 y Fv(Since)24 b Fq(^)g Fv(is)f(alternate,)h(the)g(only)f(non)g(v)-5 b(anishing)24 b(terms)f(in)h(det[)p Fr(a)2721 3267 y Fs(j)s(l)2777 3255 y Fv(])f(=)g Fr(C)2970 3267 y Fm(1)3018 3255 y Fq(^)10 b(\001)k(\001)g(\001)d(^)f Fr(C)3315 3267 y Fs(m)515 3354 y Fv(are)32 b(sec)765 3324 y Fm(2)816 3354 y Fr(x)863 3366 y Fm(1)915 3354 y Fr(:)14 b(:)g(:)f Fv(sec)1132 3324 y Fm(2)1183 3354 y Fr(x)1230 3366 y Fs(m)1326 3354 y Fv(and)33 b Fr(m)g Fv(terms)f(similar)g(to)h(\()p Fr(@)2296 3366 y Fs(x)2334 3374 y Fx(1)2370 3354 y Fr(h)p Fv(\))2450 3324 y Fm(2)2502 3354 y Fv(sec)2608 3324 y Fm(2)2659 3354 y Fr(h)14 b Fv(sec)2827 3324 y Fm(2)2879 3354 y Fr(x)2926 3366 y Fm(2)2977 3354 y Fr(:)g(:)g(:)g Fv(sec)3194 3324 y Fm(2)3245 3354 y Fr(x)3292 3366 y Fs(m)3356 3354 y Fv(,)515 3454 y(where)34 b(the)h(index)h(v)-5 b(aries)33 b(in)j(the)f(ob)n(vious)f(w)n(a)n(y)-7 b(.)57 b(All)36 b(these)f(terms)f(are)g(non)h(negativ)n(e)515 3554 y(and)e(the)h (\014rst)f(one)g(is)h(strictly)f(p)r(ositiv)n(e.)54 b(Th)n(us,)35 b(the)f(Gaussian)e(curv)-5 b(ature)33 b(is)g(strictly)515 3653 y(p)r(ositiv)n(e)27 b(on)g(the)h(c)n(hosen)f(fundamen)n(tal)h (domain)f(and)g(the)h(result)f(follo)n(ws.)389 b Fb(\003)515 3981 y Fc(2.4)112 b(Analytic)36 b(P)m(arametrization)515 4152 y Fv(In)25 b(this)g(section)f(w)n(e)h(limit)g(our)f (considerations)f(to)i(a)f(sp)r(eci\014c)h(cell)g(in)g Ft(R)2791 4122 y Fs(d)2836 4152 y Fv(,)g(sa)n(y)3025 4085 y Fo(\003)3059 4152 y Fq(\000)3134 4120 y Fs(\031)p 3134 4134 41 4 v 3138 4181 a Fm(2)3185 4152 y Fr(;)3232 4120 y Fs(\031)p 3232 4134 V 3236 4181 a Fm(2)3283 4085 y Fo(\002)3317 4102 y Fs(d)3356 4152 y Fv(.)515 4252 y(Exactly)i(one)i(comp)r(onen)n(t,)f Fq(D)r Fv(\()p Fr(t)p Fv(\),)i(of)f(\000\()p Fr(t)p Fv(\))g(is)g(enclosed)f(in)h(this)g(cell) g(for)f(0)c Fr(<)h(t)f(<)h Fv(1.)40 b(W)-7 b(e)515 4352 y(sho)n(w)24 b(that)h Fq(D)r Fv(\()p Fr(t)p Fv(\))h(inherits)f(the)g Fr(C)1584 4321 y Fs(!)1633 4352 y Fv(-structure)f(of)h(the)g(sphere.)36 b(This)25 b(last)f(is)h(sp)r(eci\014ed)g(b)n(y)515 4451 y(the)k(follo)n(wing)f(system)h(of)g(lo)r(cal)f(parametrizations:)37 b(eac)n(h)28 b(h)n(yp)r(erplane)h(of)f(co)r(ordinates)515 4551 y(divides)23 b(S)836 4521 y Fs(d)p Fn(\000)p Fm(1)984 4551 y Fv(in)n(to)g(t)n(w)n(o)g(hemispheres,)h(whose)f(pro)5 b(jections)23 b(on)g(D)2627 4521 y Fs(d)p Fn(\000)p Fm(1)2775 4551 y Fv(are)f(denoted)i Fr(\015)3267 4515 y Fn(\000)p Fm(1)3262 4574 y Fs(j)3356 4551 y Fv(;)515 4664 y(one)j(then)h (constitutes)g Fq(f)p Fr(\015)1362 4676 y Fs(j)1433 4664 y Fv(:)37 b(D)1556 4634 y Fs(d)p Fn(\000)p Fm(1)1703 4664 y Fq(!)23 b Fv(S)1855 4634 y Fs(d)p Fn(\000)p Fm(1)1979 4664 y Fq(g)2021 4634 y Fm(2)p Fs(d)2021 4686 y(j)s Fm(=1)2140 4664 y Fv(.)639 4764 y(By)28 b(Theorem)e(3)i(the)g(follo)n(wing)e (system)h(then)i(yields)e(a)g Fr(C)2515 4733 y Fs(!)2563 4764 y Fv(-structure)g(on)g Fq(D)r Fv(\()p Fr(t)p Fv(\):)1035 4919 y Fq(f)p Fr(\033)1124 4931 y Fs(j)1159 4919 y Fv(\()p Fq(\001)p Fr(;)14 b(t)p Fv(\))37 b(:)g(D)1473 4885 y Fs(d)p Fn(\000)p Fm(1)1620 4919 y Fq(!)23 b(D)r Fv(\()p Fr(t)p Fv(\))q Fr(;)28 b(\033)1985 4931 y Fs(j)2020 4919 y Fv(\()p Fr(u;)14 b(t)p Fv(\))23 b(=)g(x\()p Fr(\015)2429 4931 y Fs(j)2464 4919 y Fv(\()p Fr(u)p Fv(\))p Fr(;)14 b(t)p Fv(\))p Fq(g)2717 4885 y Fm(2)p Fs(d)2717 4939 y(j)s Fm(=1)2836 4919 y Fr(:)1926 5255 y Fv(5)p eop %%Page: 6 7 6 6 bop 639 523 a Fv(Th)n(us,)515 706 y Fg(Corollary)31 b(5)42 b Fl(Each)31 b(c)l(omp)l(onent)f Fq(D)r Fv(\()p Fr(t)p Fv(\))g Fl(of)h Fv(\000\()p Fr(t)p Fv(\))f Fl(is)g Fr(C)2270 676 y Fs(!)2318 706 y Fl(-di\013e)l(omorphic)j(to)c Fv(S)3012 676 y Fs(d)p Fn(\000)p Fm(1)3136 706 y Fl(.)639 888 y Fv(Let)i(us)g(compute)g(the)g(elemen)n(t)g(of)g(surface.)46 b(T)-7 b(o)31 b(this)g(end)g(w)n(e)f(consider)g(the)i(deter-)515 999 y(minan)n(ts)j Fr(M)929 956 y Fm(\()p Fs(l)p Fm(\))920 1023 y Fs(j)1006 999 y Fv(\()p Fr(u;)14 b(t)p Fv(\))36 b(of)f(the)h(submatrices)f(of)g(format)g Fr(d)24 b Fq(\000)f Fv(1)h Fq(\002)f Fr(d)h Fq(\000)f Fv(1)35 b(obtained)g(from)515 1129 y([)p Fr(@)582 1141 y Fs(u)621 1150 y Fz(k)662 1129 y Fr(\033)712 1086 y Fm(\()p Fs(l)p Fm(\))709 1152 y Fs(j)789 1129 y Fv(\()p Fr(u;)14 b(t)p Fv(\)])991 1152 y Fs(k)q(;l)1101 1129 y Fv(b)n(y)27 b(remo)n(ving)f(its)i Fr(l)1719 1099 y Fs(th)1814 1129 y Fv(column,)g(where)f Fr(\033)2415 1141 y Fs(j)2473 1129 y Fv(=)c(\()p Fr(\033)2643 1086 y Fm(\(1\))2640 1152 y Fs(j)2733 1129 y Fr(;)14 b Fq(\001)g(\001)g(\001)27 b Fr(;)14 b(\033)2981 1086 y Fm(\()p Fs(d)p Fm(\))2978 1152 y Fs(j)3072 1129 y Fv(\).)37 b(Let)872 1342 y Fr(D)941 1354 y Fs(j)976 1342 y Fv(\()p Fr(u;)14 b(t)p Fv(\))23 b(=)f(\()p Fr(M)1387 1299 y Fm(\(1\))1378 1365 y Fs(j)1476 1342 y Fv(\()p Fr(u;)14 b(t)p Fv(\))p Fr(;)g Fq(\000)p Fr(M)1847 1299 y Fm(\(2\))1838 1365 y Fs(j)1936 1342 y Fv(\()p Fr(u;)g(t)p Fv(\))p Fr(;)g Fq(\001)g(\001)g(\001)27 b Fr(;)14 b Fv(\()p Fq(\000)p Fv(1\))2484 1308 y Fs(d)p Fn(\000)p Fm(1)2607 1342 y Fr(M)2697 1299 y Fm(\()p Fs(d)p Fm(\))2688 1365 y Fs(j)2787 1342 y Fv(\()p Fr(u;)g(t)p Fv(\)\))p Fr(:)515 1524 y Fv(By)27 b(de\014nition)h(the)g(elemen)n(t)g(of)f(surface)g(is)h Fq(k)p Fr(D)2033 1536 y Fs(j)2067 1524 y Fv(\()p Fr(u;)14 b(t)p Fv(\))p Fq(k)k Fv(d)p Fr(u)p Fv(.)515 1707 y Fg(Lemma)29 b(6)42 b Fq(k)p Fr(D)1054 1719 y Fs(j)1088 1707 y Fv(\()p Fr(u;)14 b(t)p Fv(\))p Fq(k)23 b Fv(=)h Fq(kr)t Fv(\010\()p Fr(\033)1675 1719 y Fs(j)1711 1707 y Fv(\()p Fr(u;)14 b(t)p Fv(\)\))p Fq(k)k(j)c Fv(det)g(D)t Fr(\033)2262 1719 y Fs(j)2298 1707 y Fv(\()p Fr(u;)g(t)p Fv(\))p Fq(j)p Fl(,)31 b(wher)l(e)g(the)g(derivative)h(of)515 1807 y Fr(\033)562 1819 y Fs(j)627 1807 y Fl(is)e(taken)g(with)g(r)l(esp)l(e)l (ct)g(to)f Fv(\()p Fr(u;)14 b(t)p Fv(\))p Fl(.)515 1989 y Fg(Pro)s(of:)64 b Fv(The)27 b(c)n(hain)g(rule)h(applied)f(to)h (\010\()p Fr(\033)1925 2001 y Fs(j)1960 1989 y Fv(\()p Fr(u;)14 b(t)p Fv(\)\))24 b(=)e Fr(t)28 b Fv(giv)n(es)1288 2172 y Fq(r)t Fv(\010\()p Fr(\033)1500 2184 y Fs(j)1536 2172 y Fv(\()p Fr(u;)14 b(t)p Fv(\)\))k(D)t Fr(\033)1879 2184 y Fs(j)1915 2172 y Fv(\()p Fr(u;)c(t)p Fv(\))23 b(=)g([0)41 b Fq(\001)14 b(\001)g(\001)41 b Fv(0)28 b(1])p Fr(;)515 2355 y Fv(whic)n(h)c(w)n(e)f(abbreviate)g Fq(r)t Fv(\010)11 b(D)t Fr(\033)1530 2367 y Fs(j)1589 2355 y Fv(=)23 b Fr(e)1716 2367 y Fs(d)1754 2325 y Fm(t)1784 2355 y Fr(:)h Fv(Since)g(\()p Fr(u;)14 b(t)p Fv(\))24 b Fq(7!)f Fr(\033)2400 2367 y Fs(j)2435 2355 y Fv(\()p Fr(u;)14 b(t)p Fv(\))24 b(is)g(bijectiv)n(e,)h(analytic,)515 2454 y(and)i(has)g(an)h(analytic)e(in)n(v)n(erse,)h(D)t Fr(\033)1668 2466 y Fs(j)1731 2454 y Fv(is)h(in)n(v)n(ertible.)36 b(Th)n(us,)1185 2679 y Fq(r)t Fv(\010)24 b(=)e Fr(e)1468 2691 y Fs(d)1507 2645 y Fm(t)1537 2679 y Fv(\(D)t Fr(\033)1683 2691 y Fs(j)1719 2679 y Fv(\))1751 2645 y Fn(\000)p Fm(1)1864 2679 y Fv(=)2080 2623 y(1)p 1961 2660 280 4 v 1961 2736 a(det)14 b(D)t Fr(\033)2204 2748 y Fs(j)2250 2679 y Fr(e)2289 2691 y Fs(d)2328 2645 y Fm(t)2358 2679 y Fv(\(adjD)t Fr(\033)2617 2691 y Fs(j)2653 2679 y Fv(\))p Fr(;)515 2917 y Fv(where)20 b(adj)h(stands)f(for)g(the)h(classical)e(adjoin)n (t.)34 b(The)21 b(result)f(follo)n(ws)g(from)g Fr(e)2895 2929 y Fs(d)2934 2887 y Fm(t)2964 2917 y Fv(\(adjD)t Fr(\033)3223 2929 y Fs(j)3259 2917 y Fv(\))j(=)515 3017 y(\()p Fq(\000)p Fv(1\))686 2986 y Fs(d)p Fn(\000)p Fm(1)809 3017 y Fr(D)878 3029 y Fs(j)913 3017 y Fv(\()p Fr(u;)14 b(t)p Fv(\).)2199 b Fb(\003)639 3216 y Fv(The)40 b(whole)f Fq(D)r Fv(\()p Fr(t)p Fv(\))i(except)e(a)g(set)h(of)f(measure)g(zero)f (ma)n(y)h(b)r(e)h(co)n(v)n(ered)e(using)h(t)n(w)n(o)515 3315 y(parametrizations,)30 b Fr(\033)1227 3327 y Fs(j)1295 3315 y Fv(and)h Fr(\033)1507 3327 y Fs(k)1548 3315 y Fv(,)i(asso)r(ciated)e(with)h(opp)r(osite)f(hemispheres,)h Fr(\015)3069 3327 y Fs(j)3104 3315 y Fv(\(D)3199 3285 y Fs(d)p Fn(\000)p Fm(1)3324 3315 y Fv(\),)515 3415 y Fr(\015)558 3427 y Fs(k)599 3415 y Fv(\(D)694 3385 y Fs(d)p Fn(\000)p Fm(1)818 3415 y Fv(\))23 b Fq(\032)g Fv(S)1007 3385 y Fs(d)p Fn(\000)p Fm(1)1131 3415 y Fv(,)d(and)e (admitting)h(holomorphic)e(extensions.)33 b(Using)18 b(suc)n(h)g(parametriza-)515 3515 y(tions)27 b(for)g(eac)n(h)g(comp)r (onen)n(t)g(of)h(\000\()p Fr(t)p Fv(\),)g(one)f(obtains:)515 3697 y Fg(Corollary)k(7)42 b Fl(F)-6 b(or)23 b(a)g(\014xe)l(d)f Fv(0)h Fr(<)g Fq(j)p Fr(t)p Fq(j)g Fr(<)f Fv(1)p Fl(,)i(let)f Fr(f)9 b Fv(\()p Fr(x)p Fv(\))24 b Fl(b)l(e)f(holomorphic)j(in)d(a)g (neighb)l(ourho)l(o)l(d)515 3797 y(of)30 b Fv(\000\()p Fr(t)p Fv(\))p Fl(.)39 b(Then,)31 b(the)f(F)-6 b(ourier)30 b(tr)l(ansform)1400 4022 y Fv(\()p Fg(F)p Fr(f)9 b Fv(\)\()p Fr(n;)14 b(t)p Fv(\))p Fl(:)h(=)1873 3909 y Fo(Z)1919 4098 y Fm(\000\()p Fs(t)p Fm(\))2055 4022 y Fr(e)2094 3988 y Fs(in)p Fn(\001)p Fs(x)2220 4022 y Fr(f)9 b Fv(\()p Fr(x)p Fv(\))19 b(d)p Fr(x)515 4274 y Fl(is)30 b(holomorphic)j(at)d Fr(t)p Fl(,)g(wher)l(e)g Fr(n)23 b Fq(2)h Ft(Z)1708 4244 y Fs(d)1770 4274 y Fl(and)49 b Fv(d)p Fr(x)30 b Fl(denotes)g(the)g (element)g(of)h(surfac)l(e.)639 4457 y Fv(W)-7 b(e)31 b(close)e(this)i(section)f(b)n(y)g(presen)n(ting)f(a)h(lo)r(cal)g (parametrization)e(of)i Fq(D)r Fv(\()p Fr(t)p Fv(\))i(used)e(in)515 4556 y(the)e(sequel.)639 4656 y(Let)g Fq(R)p Fv(\()p Fr(t)p Fv(\))h(b)r(e)e(the)h(in)n(terior)f(of)g Fq(D)r Fv(\()p Fr(t)p Fv(\).)38 b(F)-7 b(or)27 b(an)g(arbitrarily)f(\014xed)i Fr(!)d Fq(2)f Fv(S)2912 4626 y Fs(d)p Fn(\000)p Fm(1)3035 4656 y Fv(,)k(let)g(\012)g(b)r(e)515 4756 y(a)k(p)r(oin)n(t)i(in)f Fq(R)p Fv(\()p Fr(t)p Fv(\))h(inciden)n(t)f(to)g(the)h(line)f(through)f (x\()p Fr(!)s(;)14 b(t)p Fv(\))33 b(and)g(parallel)f(to)h Fr(!)s Fv(,)h(and)f(let)515 4855 y Fr(!)570 4825 y Fn(?)650 4855 y Fv(b)r(e)24 b(the)h(h)n(yp)r(erplane)f(p)r(erp)r(endicular)g(to) g Fr(!)j Fv(through)c(\012.)36 b(Let)24 b Fr(R)h Fv(b)r(e)g(the)g (rigid)e(motion)515 4955 y(sending)k Fr(e)854 4967 y Fs(d)920 4955 y Fv(to)h Fr(!)i Fv(and)d Fr(O)k Fv(to)c(\012.)37 b(Finally)-7 b(,)28 b(let)g Fr(V)41 b Fv(=)23 b Fr(!)2231 4925 y Fn(?)2305 4955 y Fq(\\)c(R)p Fv(\()p Fr(t)p Fv(\).)1926 5255 y(6)p eop %%Page: 7 8 7 7 bop 639 523 a Fv(By)33 b(con)n(v)n(exit)n(y)f(of)h Fq(D)r Fv(\()p Fr(t)p Fv(\))h(the)g(ra)n(y)e(parallel)g(to)h Fr(!)j Fv(emanating)c(from)h(a)g(giv)n(en)g Fr(v)i Fq(2)e Fr(V)515 623 y Fv(in)n(tersects)28 b Fq(D)r Fv(\()p Fr(t)p Fv(\))i(at)e(exactly)g(one)h(p)r(oin)n(t,)g Fr(Q)p Fv(\()p Fr(v)s Fv(\),)h(whose)e(normal)g(is)g(not)h(parallel)f(to)g Fr(!)3300 593 y Fn(?)3356 623 y Fv(.)515 722 y(Using)j(the)h(natural)e (em)n(b)r(edding)i Ft(R)1671 692 y Fs(d)p Fn(\000)p Fm(1)1830 722 y Fq(\032)d Ft(R)1978 692 y Fs(d)2023 722 y Fv(,)j(the)g(comp)r (osition)f Fr(Q)21 b Fq(\016)f Fr(R)32 b Fv(then)g(giv)n(es)e(a)515 822 y(parametrization)j Fr(\034)60 b Fv(:)50 b(\007)23 b Fq(\032)f Ft(R)1525 792 y Fs(d)p Fn(\000)p Fm(1)1691 822 y Fq(!)36 b(D)r Fv(\()p Fr(t)p Fv(\))h(compatible)e(with)h(the)f Fr(C)2851 792 y Fs(!)2900 822 y Fv(-structure)f(on)515 922 y Fq(D)r Fv(\()p Fr(t)p Fv(\).)639 1021 y(Note)k(that)g(\007)i Fq(!)g Fr(R)1332 991 y Fn(\000)p Fm(1)1421 1021 y Fq(D)r Fv(\()p Fr(t)p Fv(\))p Fr(;)29 b(\035)43 b Fq(7!)d Fv(\()p Fr(\035)s(;)14 b(!)28 b Fq(\001)d Fr(\034)9 b Fv(\()p Fr(\035)s Fv(\))q(\))39 b(is)e(a)h(lo)r(cal)f(parametrization)f(of)515 1121 y Fr(R)579 1091 y Fn(\000)p Fm(1)668 1121 y Fq(D)r Fv(\()p Fr(t)p Fv(\).)49 b(Since)31 b(the)h(curv)-5 b(ature)31 b(is)g(in)n(v)-5 b(arian)n(t)30 b(under)i(rotation,)f(it)h(follo)n(ws)e (from)h(Sec-)515 1220 y(tion)c(2.3)g(that)1573 1320 y(det)14 b(D)1765 1286 y Fm(2)1765 1341 y Fs(\035)1808 1320 y Fv(\()p Fr(!)22 b Fq(\001)c Fr(\034)9 b Fv(\()p Fr(\035)s Fv(\))q(\))24 b Fr(>)e Fv(0)p Fr(:)952 b Fv(\(4\))515 1595 y Fu(3)134 b(Deca)l(y)46 b(of)f(the)h(Resolv)l(en)l(t)515 1776 y Fv(In)32 b(this)g(section)f(w)n(e)h(pro)n(v)n(e)e(P)n(art)g (\(2\))i(of)g(Theorem)f(1.)49 b(Our)31 b(pro)r(of,)h(based)f(on)h(the)g (sta-)515 1876 y(tionary)26 b(phase)h(metho)r(d,)h(uses)g(of)f(the)h (follo)n(wing)f(classical)f(result)h(\()p Fl(cf)p Fv(.)38 b([P,)27 b(S)q(]\):)515 2059 y Fg(Prop)s(osition)j(8)41 b Fl(L)l(et)31 b Fr(I)7 b Fv(\()p Fr(r)n(;)14 b(t)p Fv(\))28 b(=)1593 1992 y Fo(R)1632 2088 y Fh(R)1679 2072 y Fz(d)1727 2059 y Fr(e)1766 2029 y Fs(ir)r(')p Fm(\()p Fs(x;t)p Fm(\))2004 2059 y Fr(f)9 b Fv(\()p Fr(x;)14 b(t)p Fv(\))20 b(d)p Fr(x)p Fl(,)34 b(wher)l(e)e Fr(r)e(>)c Fv(0)p Fl(,)32 b Fr(t)27 b Fq(2)g Fr(T)12 b Fl(,)32 b Fr(T)42 b Fl(is)33 b(a)515 2167 y(c)l(omp)l(act)i(set)f(in)h Ft(R)1135 2137 y Fs(m)1204 2167 y Fl(,)h Fr(m)e Fl(is)h(arbitr)l(ary,)i Fr(')e Fl(and)g Fr(f)43 b Fl(ar)l(e)35 b(smo)l(oth)g(on)g Ft(R)2794 2137 y Fs(d)2860 2167 y Fq(\002)22 b Fr(T)12 b Fl(,)35 b Fr(')g Fl(is)g(r)l(e)l(al)515 2267 y(value)l(d,)c(and)f Fr(f)9 b Fv(\()p Fr(x;)14 b(t)p Fv(\))23 b(=)g(0)29 b Fl(when)h Fr(x)h Fl(is)f(outside)g(a)g(c)l(omp)l(act)h(subset)e Fr(K)f Fq(\022)23 b Ft(R)2907 2237 y Fs(d)2951 2267 y Fl(.)613 2433 y(1.)42 b(If)30 b Fq(r)878 2445 y Fs(x)920 2433 y Fr(')p Fv(\()p Fr(x;)14 b(t)p Fv(\))25 b Fq(6)p Fv(=)d(0)30 b Fl(for)g(al)t(l)h Fr(t)23 b Fq(2)g Fr(T)41 b Fl(and)30 b Fr(x)24 b Fq(2)f Fr(K)6 b Fl(,)30 b(then)g Fr(I)7 b Fv(\()p Fr(r)n(;)14 b(t)p Fv(\))23 b(=)g Fr(O)r Fv(\()p Fr(r)2891 2403 y Fn(\0001)3015 2433 y Fv(\))p Fl(.)613 2599 y(2.)42 b(If,)31 b(for)h(al)t(l)f Fr(t)24 b Fq(2)g Fr(T)12 b Fl(,)30 b Fr(')p Fv(\()p Fr(x;)14 b(t)p Fv(\))31 b Fl(admits)g(exactly)f(one)h(critic)l(al)g(p)l(oint)g Fr(x)2841 2611 y Fm(0)2902 2599 y Fv(=)24 b Fr(x)3038 2611 y Fm(0)3076 2599 y Fv(\()p Fr(t)p Fv(\))30 b Fl(in)h Fr(K)722 2698 y Fl(\(i.e.)51 b Fq(r)989 2710 y Fs(x)1031 2698 y Fr(')p Fv(\()p Fr(x)1164 2710 y Fm(0)1202 2698 y Fr(;)14 b(t)p Fv(\))30 b(=)g(0)p Fl(\),)k(which)h(is)f(not)f(de)l (gener)l(ate)h(\(i.e.)51 b Fv(det)14 b(D)2841 2668 y Fm(2)2841 2719 y Fs(x)2883 2698 y Fr(')p Fv(\()p Fr(x)3016 2710 y Fm(0)3055 2698 y Fr(;)g(t)p Fv(\))30 b Fq(6)p Fv(=)f(0)p Fl(\),)722 2809 y(then)h Fr(I)7 b Fv(\()p Fr(r)n(;)14 b(t)p Fv(\))24 b(=)e Fr(O)r Fv(\()p Fr(r)1363 2779 y Fn(\000)1427 2756 y Fz(d)p 1427 2765 31 3 v 1428 2799 a Fx(2)1472 2809 y Fv(\))p Fl(.)515 2975 y(These)27 b(estimates)g(hold)h(when)f Fr(r)f Fq(!)d(1)j Fl(and)h(ar)l(e)g (uniform)g(in)g Fr(t)c Fq(2)g Fr(T)12 b Fl(.)37 b(Mor)l(e)l(over,)29 b(1)e(holds)515 3074 y(for)33 b Fr(I)7 b Fv(\()p Fr(r)n(;)14 b(t)p Fv(\))33 b Fl(over)g Ft(T)1134 3044 y Fs(d)1204 3074 y Fl(under)f(the)h(same)f(assumptions)h(exc)l(ept)f(that)g(the)g (c)l(omp)l(actness)h(of)515 3174 y Fv(supp)16 b Fr(f)38 b Fl(is)30 b(r)l(eplac)l(e)l(d)h(with)g(the)e(p)l(erio)l(dicity)k(of)d Fr(f)9 b Fl(.)639 3357 y Fv(In)31 b(the)f(sequel)g Fr(r)r(!)k Fv(stands)c(for)g(the)h(p)r(olar)e(form)h(of)g Fr(n)e Fq(2)g Ft(Z)2539 3327 y Fs(d)2572 3357 y Fv(.)45 b(F)-7 b(or)30 b(a)g(\014xed)g(non)g(zero)515 3456 y Fq(\000)p Fv(1)22 b Fr(<)h(E)28 b(<)22 b Fv(1,)28 b(let)f Fr(\037)h Fv(b)r(e)g(a)f(smo)r(oth)h(compactly)f(supp)r(orted)g(function)h(on)f Ft(T)2961 3426 y Fs(d)3027 3456 y Fv(satisfying)1340 3686 y Fr(\037)p Fv(\()p Fr(x)p Fv(\))d(=)1615 3569 y Fo(\032)1719 3637 y Fv(1)110 b(if)28 b Fq(j)p Fv(\010\()p Fr(x)p Fv(\))20 b Fq(\000)e Fr(E)5 b Fq(j)23 b Fr(<)2454 3604 y Fs(\016)p 2453 3618 34 4 v 2453 3665 a Fm(2)1719 3736 y Fv(0)110 b(if)28 b Fq(j)p Fv(\010\()p Fr(x)p Fv(\))20 b Fq(\000)e Fr(E)5 b Fq(j)23 b Fr(>)f(\016)o(;)515 3928 y Fv(where)27 b(0)22 b Fr(<)h(\016)j(<)d Fv(dist\()p Fr(E)5 b(;)14 b Fq(f\000)p Fv(1)p Fr(;)g Fv(0)p Fr(;)g Fv(1)p Fq(g)p Fv(\).)34 b(Finally)-7 b(,)28 b(let)g Fr(\036)23 b Fv(=)2423 3895 y Fm(1)p 2354 3909 171 4 v 2354 3956 a Fn(kr)p Fm(\010)p Fn(k)2535 3928 y Fv(.)37 b(Then,)515 4133 y Fg(Theorem)30 b(9)41 b Fr(G)1074 4145 y Fs(E)s Fm(+)p Fs(i)p Fm(0)1238 4133 y Fv(\()p Fr(n)p Fv(\))30 b Fl(exists)g(and)g(is)g(e)l(qual)g(to)g Fv(\(2)p Fr(\031)s Fv(\))2326 4103 y Fn(\000)p Fs(d)2447 4133 y Fl(times)969 4363 y Fr(\031)s(i)p Fv(\()p Fg(F)p Fr(\036)p Fv(\)\()p Fr(n;)14 b(E)5 b Fv(\))20 b(+)e(p)p Fr(:)p Fv(v)q Fr(:)1692 4250 y Fo(Z)1738 4439 y Fn(j)p Fs(t)p Fn(\000)p Fs(E)s Fn(j\024)p Fs(\016)2019 4307 y Fv(\()p Fg(F)p Fr(\037\036)q Fv(\)\()p Fr(n;)c(t)p Fv(\))p 2019 4344 408 4 v 2124 4420 a Fr(t)k Fq(\000)g Fr(E)2455 4363 y Fv(d)p Fr(t)g Fv(+)g Fr(O)r Fv(\()p Fr(r)2768 4329 y Fn(\0001)2892 4363 y Fv(\))515 4612 y Fl(when)26 b Fr(r)g Fq(!)d(1)p Fl(,)k(uniformly)g(in)f Fr(!)i Fl(and)e(uniformly)h(in)f Fr(E)31 b Fl(on)26 b(e)l(ach)g(c)l(omp)l(act,)i(wher)l(e)f Fv(p)p Fr(:)p Fv(v)q Fr(:)3324 4545 y Fo(R)515 4711 y Fl(stands)i(for)i(the)f(Cauchy)h(princip)l(al)h(value.)1926 5255 y Fv(7)p eop %%Page: 8 9 8 8 bop 515 523 a Fg(Pro)s(of:)120 b Fv(Consider)46 b(the)h(second)f (term)g(in)h(the)g(follo)n(wing)e(decomp)r(osition,)51 b(where)515 623 y Fr(z)j Fq(2)d Ft(C)768 635 y Fm(+)829 623 y Fv(:)921 856 y(\(2)p Fr(\031)s Fv(\))1077 821 y Fs(d)1116 856 y Fr(G)1181 868 y Fs(z)1219 856 y Fv(\()p Fr(n)p Fv(\))24 b(=)1444 743 y Fo(Z)1490 931 y Fh(T)1535 915 y Fz(d)1592 800 y Fr(\037)p Fv(\()p Fr(x)p Fv(\))p Fr(e)1794 769 y Fs(in)p Fn(\001)p Fs(x)p 1592 837 329 4 v 1598 913 a Fv(\010\()p Fr(x)p Fv(\))c Fq(\000)e Fr(z)1949 856 y Fv(d)p Fr(x)h Fv(+)2144 743 y Fo(Z)2190 931 y Fh(T)2235 915 y Fz(d)2292 800 y Fv(\(1)f Fq(\000)g Fr(\037)p Fv(\()p Fr(x)p Fv(\)\))p Fr(e)2701 769 y Fs(in)p Fn(\001)p Fs(x)p 2292 837 537 4 v 2402 913 a Fv(\010\()p Fr(x)p Fv(\))i Fq(\000)e Fr(z)2856 856 y Fv(d)p Fr(x:)515 1080 y Fv(By)25 b(the)h(dominated)f(con)n(v)n(ergence)e(theorem)i(its)h(limit)g(exists) f(when)h Fr(z)g Fq(!)d Fr(E)5 b Fv(.)37 b(Moreo)n(v)n(er,)515 1180 y(in)n(tegration)26 b(b)n(y)h(parts)g(sho)n(ws)g(that)h(this)f (limit)i(is)e Fr(O)r Fv(\()p Fq(j)p Fr(n)p Fq(j)2320 1149 y Fn(\0001)2443 1180 y Fv(\))h(\()p Fl(cf)p Fv(.)38 b(Prop)r(osition)26 b(8\).)639 1279 y(It)c(then)f(su\016ces)g(to)g (analyze)f(the)i(\014rst)f(term.)35 b(One)20 b(ma)n(y)h(express)f(it)i (as)e(a)h(sum)g(of)g(in)n(te-)515 1379 y(grals)d(o)n(v)n(er)g(the)i(op) r(en)g(cells)f(of)h Ft(T)1519 1349 y Fs(d)1577 1379 y Fv(and)f(then)h(break)f(eac)n(h)g(cell)h(in)n(to)f(t)n(w)n(o)g(halv)n (es)g(co)n(v)n(ered)e(b)n(y)515 1478 y(surfaces)26 b(of)h(the)h(form)f Fq(D)r Fv(\()p Fr(t)p Fv(\))1420 1448 y Fm(+)1499 1478 y Fv(=)22 b Fr(\033)1633 1490 y Fs(j)1669 1478 y Fv(\(D)1764 1448 y Fs(d)p Fn(\000)p Fm(1)1888 1478 y Fr(;)14 b(t)p Fv(\))28 b(and)f Fq(D)r Fv(\()p Fr(t)p Fv(\))2336 1448 y Fn(\000)2416 1478 y Fv(=)c Fr(\033)2551 1490 y Fs(k)2592 1478 y Fv(\(D)2687 1448 y Fs(d)p Fn(\000)p Fm(1)2811 1478 y Fr(;)14 b(t)p Fv(\))28 b(resp)r(ectiv)n(ely)-7 b(,)515 1578 y(where)24 b Fr(\015)795 1590 y Fs(j)855 1578 y Fv(and)g Fr(\015)1056 1590 y Fs(k)1122 1578 y Fv(parametrize)f(opp)r(osite)i(hemispheres)f(\(see)g(Section)h(2.4\).) 36 b(F)-7 b(or)24 b(one)g(of)515 1678 y(these)g(halv)n(es,)g(sa)n(y)f Fq(H)1205 1648 y Fm(+)1283 1678 y Fv(=)1371 1615 y Fo(S)1440 1703 y Fm(0)p Fs()e Fv(0,)515 2559 y(as)27 b(desired.)639 2659 y(Prop)r(osition)f (8)h(then)h(completes)g(the)g(pro)r(of.)1230 b Fb(\003)639 2858 y Fv(The)27 b(previous)e(theorem)h(tak)n(es)f(care)g(of)i(the)g (\014rst)f(term)g(in)h(the)f(decomp)r(osition)g(pro-)515 2958 y(vided)33 b(b)n(y)g(Theorem)g(9,)h(taking)f Fr(f)41 b Fv(=)32 b Fr(\036)i Fv(and)g Fr(t)e Fv(=)g Fr(E)5 b Fv(.)55 b(In)33 b(order)f(to)h(study)h(the)g(second)515 3057 y(term,)k(let)f Fr(E)k Fv(v)-5 b(ary)35 b(in)i(an)e(arbitrary)g (in)n(terv)-5 b(al)35 b([)p Fr(a;)14 b(b)p Fv(])37 b Fq(\032)g Fv(])p Fq(\000)p Fv(1)o Fr(;)14 b Fv(1[)36 b(not)g(con)n(taining)f(zero.)515 3157 y(One)30 b(ma)n(y)g(assume)f (that)i Fr(\016)j Fv(is)c(less)g(than)g(the)h(distance)f(b)r(et)n(w)n (een)h([)p Fr(a;)14 b(b)p Fv(])30 b(and)g Fq(f\000)p Fv(1)p Fr(;)14 b Fv(0)p Fr(;)g Fv(1)p Fq(g)p Fv(,)515 3257 y(and)31 b(apply)g(the)h(previous)e(pro)r(of)g(to)h Fr(T)41 b Fv(=)29 b([)p Fr(a)18 b Fq(\000)g Fr(\016)s(;)c(b)k Fv(+)g Fr(\016)s Fv(].)48 b(The)31 b(next)h(result)f(is)g(an)g(easy)515 3356 y(consequence)26 b(of)i(this)g(pro)r(of.)515 3539 y Fg(Lemma)h(11)41 b Fl(Supp)l(ose)58 b Fr(f)9 b Fv(\()p Fr(x)p Fv(\))58 b Fl(is)f(smo)l(oth)h(in)f(the)h(neighb)l(ourho)l(o)l (d)h(of)f Fq(S)6 b Fl(.)122 b(Then,)515 3653 y Fr(@)559 3665 y Fs(t)588 3653 y Fv(\()p Fg(F)p Fr(f)9 b Fv(\)\()p Fr(n;)14 b(t)p Fv(\))24 b(=)e Fr(O)r Fv(\()p Fr(r)1190 3623 y Fn(\000)1254 3597 y Fz(d)p Fy(\000)p Fx(1)p 1254 3610 104 3 v 1292 3643 a(2)1372 3653 y Fv(\))30 b Fl(uniformly)h(in)e Fr(!)d Fq(2)e Fv(S)2117 3623 y Fs(d)p Fn(\000)p Fm(1)2270 3653 y Fl(and)30 b Fr(t)23 b Fq(2)h Fr(T)40 b Fl(when)31 b Fr(r)25 b Fq(!)f(1)p Fl(.)515 3835 y Fg(Pro)s(of:)64 b Fv(F)-7 b(rom)27 b(\(5\),)h(setting)f Fr(g)1525 3847 y Fs(j)1560 3835 y Fv(\()p Fr(u;)14 b(t)p Fv(\))23 b(=)g Fr(\037)1902 3847 y Fs(j)1936 3835 y Fv(\()p Fr(\033)2015 3847 y Fs(j)2051 3835 y Fv(\()p Fr(u;)14 b(t)p Fv(\)\))p Fr(f)9 b Fv(\()p Fr(\033)2391 3847 y Fs(j)2427 3835 y Fv(\()p Fr(u;)14 b(t)p Fv(\)\))p Fq(k)p Fr(D)2749 3847 y Fs(j)2783 3835 y Fv(\()p Fr(u;)g(t)p Fv(\))p Fq(k)p Fv(,)523 4063 y Fr(@)567 4075 y Fs(t)597 4063 y Fv(\()p Fg(F)p Fr(f)9 b Fv(\)\()p Fr(n;)14 b(t)p Fv(\))83 b(=)1183 3985 y Fo(X)1227 4161 y Fs(j)1316 3950 y Fo(Z)1363 4139 y Fm(D)1413 4122 y Fz(d)p Fy(\000)p Fx(1)1539 4063 y Fr(@)1583 4075 y Fs(t)1612 4063 y Fv(\()p Fr(e)1683 4029 y Fs(ir)r(!)r Fn(\001)p Fs(\033)1841 4037 y Fz(j)1872 4029 y Fm(\()p Fs(u;t)p Fm(\))2012 4063 y Fr(g)2052 4075 y Fs(j)2087 4063 y Fv(\()p Fr(u;)14 b(t)p Fv(\)\))k(d)p Fr(u)1035 4327 y Fv(=)1183 4248 y Fo(X)1227 4425 y Fs(j)1316 4214 y Fo(Z)1363 4403 y Fm(D)1413 4386 y Fz(d)p Fy(\000)p Fx(1)1539 4327 y Fr(e)1578 4293 y Fs(ir)r(!)q Fn(\001)p Fs(\033)1735 4301 y Fz(j)1767 4293 y Fm(\()p Fs(u;t)p Fm(\))1907 4327 y Fv(\(\()p Fr(ir)r(!)k Fq(\001)c Fr(@)2198 4339 y Fs(t)2227 4327 y Fr(\033)2274 4339 y Fs(j)2310 4327 y Fv(\()p Fr(u;)c(t)p Fv(\)\))p Fr(g)2561 4339 y Fs(j)2596 4327 y Fv(\()p Fr(u;)g(t)p Fv(\))k(+)g Fr(@)2920 4339 y Fs(t)2949 4327 y Fr(g)2989 4339 y Fs(j)3024 4327 y Fv(\()p Fr(u;)c(t)p Fv(\)\))19 b(d)p Fr(u;)515 4594 y Fv(where)29 b(in)n(terc)n(hange)f(of)i(the)h(order)d(of)i(di\013eren) n(tiation)g(and)f(in)n(tegration)g(is)h(justi\014ed)g(b)n(y)515 4693 y(the)e(dominated)f(con)n(v)n(ergence)e(theorem.)37 b(Prop)r(osition)26 b(8)h(completes)g(the)h(pro)r(of.)176 b Fb(\003)1926 5255 y Fv(9)p eop %%Page: 10 11 10 10 bop 515 523 a Fg(Theorem)30 b(12)41 b Fl(Supp)l(ose)30 b Fr(f)9 b Fv(\()p Fr(x)p Fv(\))31 b Fl(is)f(smo)l(oth)g(in)g(the)g (neighb)l(ourho)l(o)l(d)h(of)g Fq(S)6 b Fl(.)39 b(Then,)1248 754 y Fv(p)p Fr(:)p Fv(v)q Fr(:)1399 641 y Fo(Z)1445 829 y Fn(j)p Fs(t)p Fn(\000)p Fs(E)s Fn(j\024)p Fs(\016)1725 697 y Fv(\()p Fg(F)p Fr(f)9 b Fv(\)\()p Fr(n;)14 b(t)p Fv(\))p 1725 734 356 4 v 1804 810 a Fr(t)19 b Fq(\000)f Fr(E)2109 754 y Fv(d)p Fr(t)23 b Fv(=)g Fr(O)r Fv(\()p Fr(r)2432 719 y Fn(\000)2496 694 y Fz(d)p Fy(\000)p Fx(1)p 2496 707 104 3 v 2533 739 a(2)2614 754 y Fv(\))515 1006 y Fl(uniformly)30 b(in)g Fr(!)c Fq(2)d Fv(S)1197 975 y Fs(d)p Fn(\000)p Fm(1)1351 1006 y Fl(and)30 b Fr(E)e Fq(2)c Fv([)p Fr(a;)14 b(b)p Fv(])29 b Fl(when)h Fr(r)c Fq(!)d(1)p Fl(.)515 1188 y Fg(Pro)s(of:)64 b Fv(The)27 b(result)h(follo)n(ws)e(from)i(the)g(lemma)f(and)g(the)h(estimate)1178 1280 y Fo(\014)1178 1329 y(\014)1178 1379 y(\014)1178 1429 y(\014)1178 1479 y(\014)1206 1425 y Fv(p)p Fr(:)p Fv(v)q Fr(:)1357 1312 y Fo(Z)1403 1500 y Fn(j)p Fs(t)p Fn(\000)p Fs(E)s Fn(j\024)p Fs(\016)1714 1369 y Fr(g)s Fv(\()p Fr(t)p Fv(\))p 1684 1406 198 4 v 1684 1482 a Fr(t)18 b Fq(\000)g Fr(E)1910 1425 y Fv(d)p Fr(t)1986 1280 y Fo(\014)1986 1329 y(\014)1986 1379 y(\014)1986 1429 y(\014)1986 1479 y(\014)2036 1425 y Fq(\024)23 b Fv(2)p Fr(\016)65 b Fv(max)2219 1482 y Fn(j)p Fs(t)p Fn(\000)p Fs(E)s Fn(j\024)p Fs(\016)2486 1425 y Fq(j)p Fr(g)2552 1391 y Fn(0)2575 1425 y Fv(\()p Fr(t)p Fv(\))p Fq(j)p Fr(;)515 1678 y Fv(whic)n(h)27 b(holds)h(for)f(an)n(y)f(con)n (tin)n(uously)h(di\013eren)n(tiable)g Fr(g)s Fv(.)1014 b Fb(\003)639 1877 y Fv(Joining)27 b(Theorems)g(4,)g(9,)g(10,)g(and)g (12,)g(w)n(e)g(ha)n(v)n(e)g(pro)n(v)n(en)f(Theorem)g(1.)515 2076 y Fg(Remark:)75 b Fl(Using)33 b(the)g(same)g(te)l(chnique)g(one)g (may)g(derive)h(the)f(c)l(omplete)h(asymptotic)515 2185 y(exp)l(ansion)27 b(of)g(the)g(Gr)l(e)l(en)g(function,)h Fr(G)1779 2197 y Fs(E)s Fm(+)p Fs(i)p Fm(0)1943 2185 y Fv(\()p Fr(r)r(!)s Fv(\))c Fq(\030)e Fr(r)2251 2155 y Fn(\000)2314 2129 y Fz(d)p Fy(\000)p Fx(1)p 2314 2142 104 3 v 2352 2175 a(2)2446 2123 y Fo(P)2533 2143 y Fn(1)2533 2210 y Fs(k)q Fm(=0)2672 2185 y Fv(a)2714 2197 y Fs(k)2754 2185 y Fv(\()p Fr(E)5 b(;)14 b(!)s Fv(\))p Fr(r)3015 2155 y Fn(\000)3078 2133 y Fz(k)p 3078 2142 33 3 v 3080 2175 a Fx(2)3125 2185 y Fr(;)26 b Fl(wher)l(e)515 2285 y(the)k Fv(a)695 2297 y Fs(k)735 2285 y Fl('s)g(ar)l(e)g(smo)l(oth)g (and)h(the)f(estimates)f(ar)l(e)i(uniform)f(in)g Fr(!)i Fl(and)e Fr(E)5 b Fl(,)30 b(se)l(e)g([P)q(].)515 2646 y Fu(References)515 2812 y FI([B])154 b(Bourgain,)27 b(J.:)35 b(On)24 b(random)g(Sc)n(hr\177)-38 b(odinger)25 b(op)r(erators)i(on)e FB(Z)2563 2780 y FE(2)2592 2812 y FI(.)g(Discrete)h(and)f(Con)n(tin)n(u-)765 2903 y(ous)h(Dynamical)f (Systems)g FJ(8)p FI(,)h(1)g(\(2002\))515 3028 y([BBP])48 b(Ben)n(tosela,)34 b(F.,)f(Briet,)g(Ph.,)f(P)n(astur,)h(L.:)45 b(On)30 b(the)g(sp)r(ectral)i(and)e(w)n(a)n(v)n(e)h(propagation)765 3119 y(prop)r(erties)k(of)f(the)g(surface)g(Maryland)g(mo)r(del.)g(J.)h (Math.)f(Ph)n(ys.)f(44)i(\(2003\),)i(no.)d(1,)765 3210 y(1{35.)515 3335 y([CK])93 b(Christ,)38 b(M.,)g(Kiselev,)f(A.:)53 b(Scattering)35 b(and)f(w)n(a)n(v)n(e)h(op)r(erators)h(for)f (one-dimensional)765 3426 y(Sc)n(hr\177)-38 b(odinger)46 b(op)r(erators)i(with)e(slo)n(wly)h(deca)n(ying)f(nonsmo)r(oth)g(p)r (oten)n(tials.)h(Geom.)765 3517 y(F)-6 b(unct.)25 b(Anal.)h(12)h (\(2002\),)g(no.)f(6,)g(1174{1234.)515 3642 y([CS])110 b(Chahrour,)46 b(A.,)g(Sah)n(bani,)f(J.:)68 b(On)40 b(the)i(sp)r (ectral)g(and)f(scattering)i(theory)e(of)h(the)765 3733 y(Sc)n(hr\177)-38 b(odinger)26 b(op)r(erator)g(with)g(surface)g(p)r (oten)n(tial.)h(Rev.)e(Math.)h(Ph)n(ys.)f FJ(12)p FI(,)h(561)h (\(2000\))515 3858 y([HK])90 b(Hundertmark,)20 b(D.,)i(Kirsc)n(h,)h (W.:)32 b(Sp)r(ectral)22 b(theory)e(of)i(sparse)g(p)r(oten)n(tials.)g (In)f Fa(Sto)l(chas-)765 3949 y(tic)34 b(pr)l(o)l(c)l(esses,)j(physics) e(and)f(ge)l(ometry:)48 b(new)34 b(interplays,)h(I)e(\(L)l(eipzig,)i (1999\))p FI(,)g(CMS)765 4040 y(Conf.)27 b(Pro)r(c.)g FJ(28)p FI(,)f(213)h(\(2000\))515 4165 y([JL1])83 b(Jak)l(\024)-34 b(si)n(\023)e(c,)25 b(V.,)f(Last,)h(Y.:)33 b(Corrugated)24 b(surfaces)h(and)e(a.c.)h(sp)r(ectrum.)f(Rev.)f(Math.)i(Ph)n(ys.)765 4256 y FJ(12)p FI(,)j(1465)g(\(2000\))515 4381 y([JL2])83 b(Jak)l(\024)-34 b(si)n(\023)e(c,)31 b(V.,)e(Last,)h(Y.:)41 b(Surface)29 b(states)g(and)f(sp)r(ectra.)i(Comm)n(un.)c(Math.)k(Ph)n (ys.)e FJ(218)p FI(,)765 4472 y(459)f(\(2001\))515 4597 y([JM])99 b(Jak)l(\024)-34 b(si)n(\023)e(c,)27 b(V.,)e(Molc)n(hano)n (v,)h(S.:)34 b(W)-6 b(a)n(v)n(e)24 b(op)r(erators)i(for)g(the)e (surface)i(Maryland)f(mo)r(del.)g(J.)765 4688 y(Math.)i(Ph)n(ys.)e FJ(41)p FI(,)h(4452)i(\(2000\))515 4813 y([JMP])47 b(Jak)l(\024)-34 b(si)n(\023)e(c,)23 b(V.,)f(Molc)n(hano)n(v,)h(S.,)f(P)n(astur,)h(L.:) 32 b(On)20 b(the)h(propagation)h(prop)r(erties)f(of)h(surface)765 4904 y(w)n(a)n(v)n(es.)g(In)f Fa(Wave)j(Pr)l(op)l(agation)h(in)e (Complex)h(Me)l(dia)p FI(,)f(IMA)e(V)-6 b(ol.)21 b(Math.)h(Appl.)f FJ(96)p FI(,)i(143)765 4995 y(\(1998\))1905 5255 y Fv(10)p eop %%Page: 11 12 11 11 bop 515 523 a FI([JP])117 b(Jak)l(\024)-34 b(si)n(\023)e(c,)27 b(V.,)f(P)n(oulin,)h(P)-6 b(.:)34 b(In)25 b(preparation.)515 648 y([K])148 b(Krishna,)46 b(M.:)67 b(Anderson)41 b(mo)r(del)h(with)g (deca)n(ying)f(randomness-extended)f(states.)765 739 y(Pro)r(c.)27 b(Indian)e(Acad.)h(Sci.)g(\(MathSci.\))g FJ(100)p FI(,)h(285)f(\(1990\))515 863 y([MV1])42 b(Molc)n(hano)n(v,)33 b(S.,)f(V)-6 b(ain)n(b)r(erg,)31 b(B.:)45 b(Scattering)31 b(on)f(the)g(system)g(of)h(the)f(sparse)h(bumps:)765 955 y(m)n(ultidimensional)25 b(case.)i(Appl.)e(Anal.)h FJ(71)p FI(,)g(167)h(\(1999\))515 1079 y([MV2])42 b(Molc)n(hano)n(v,)25 b(S.,)g(V)-6 b(ain)n(b)r(erg,)24 b(B.:)34 b(Sp)r(ectrum)23 b(of)h(m)n(ultidimensional)f(Sc)n(hr\177)-38 b(odinger)24 b(op)r(er-)765 1171 y(ators)29 b(with)f(sparse)g(p)r(oten)n(tials.)h (Analytic)f(and)f(computational)h(metho)r(ds)f(in)h(scatter-)765 1262 y(ing)d(and)g(applied)f(mathematics)g(Chapman)g(Hall/CR)n(C)i (Res.)f(Notes)g(Math.)g FJ(417)p FI(,)h(231)765 1353 y(\(2000\))515 1478 y([P])156 b(P)n(oulin,)27 b(P)-6 b(.:)34 b(Ph.D.)26 b(Thesis,)h(McGill)h(Univ)n(ersit)n(y)-6 b(.)24 b(In)h(preparation.)515 1602 y([RS])108 b(Ro)r(dnianski,)22 b(I.,)f(Sc)n(hlag,)i(W.:)32 b(Classical)23 b(and)d(quan)n(tum)d (scattering)22 b(for)f(a)g(class)g(of)g(long)765 1694 y(range)27 b(random)d(p)r(oten)n(tials.)j(In)n(t.)e(Math.)h(Res.)g (Not.)g(2003,)i(no.)e(5,)g(243{300.)515 1818 y([S])165 b(Stein,)28 b(E.:)39 b Fa(Harmonic)30 b(analysis:)39 b(r)l(e)l(al-variable)31 b(metho)l(ds,)g(ortho)l(gonality,)h(and)e (oscil-)765 1910 y(latory)f(inte)l(gr)l(als)p FI(.)e(Princeton)f(Univ)n (ersit)n(y)f(Press,)i(Princeton)f(1993.)515 2034 y([SV])107 b(Shaban,)24 b(W.,)h(V)-6 b(ain)n(b)r(erg,)24 b(B.:)34 b(Radiation)24 b(conditions)g(for)h(the)e(di\013erence)h(Sc)n(hr\177) -38 b(odinger)765 2125 y(op)r(erators.)28 b(Appl.)d(Anal.)h(80)g (\(2001\),)h(no.)f(3-4,)h(525{556.)515 2250 y([V])150 b(V)-6 b(ain)n(b)r(erg,)22 b(B.:)33 b Fa(Asymptotic)24 b(Metho)l(ds)h(in)d(Equations)i(of)f(Mathematic)l(al)h(Physics)p FI(.)e(Gor-)765 2341 y(don)k(and)f(Breac)n(h)h(Science)g(Publishers,)h (New-Y)-6 b(ork)24 b(1982.)1905 5255 y Fv(11)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0501141029522--