Content-Type: multipart/mixed; boundary="-------------0411290302410" This is a multi-part message in MIME format. ---------------0411290302410 Content-Type: text/plain; name="04-399.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-399.keywords" mountain pass, adiabatic reactions ---------------0411290302410 Content-Type: application/postscript; name="atom.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="atom.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.90a Copyright 2002 Radical Eye Software %%Title: C:\LATEX\these\reaction\atom.dvi %%CreationDate: Mon Nov 29 09:58:50 2004 %%Pages: 13 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMR12 CMSY8 CMBX10 CMR10 CMSY6 CMR9 CMTI9 CMMI10 %%+ CMSY10 CMR8 MSBM10 CMMI8 LINE10 LINEW10 CMEX10 CMMI6 CMTI10 CMR6 %%+ MSBM7 CMTT10 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips C:\LATEX\these\reaction\atom.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2004.11.29:0945 %%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 %%BeginProcSet: texps.pro %! 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cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 58 /colon put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 76 /L put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 82 /R put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueID 5032014 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 43 /plus put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 54 /six put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 19 /acute put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 78 /N put dup 105 /i put dup 106 /j put dup 110 /n put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 8 /braceleftbig put dup 9 /bracerightbig put dup 12 /vextendsingle put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 26 /braceleftbigg put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 82 /integraltext put dup 88 /summationdisplay put dup 89 /productdisplay put dup 90 /integraldisplay put dup 112 /radicalbig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end 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3B5232CEE98CA124E869EAA65755E5CB20003B39911FE76491C5435D8BFF1EBE 87AC6B36CF21F8608D292FE1C1D606234808C72DA0B89284206942F790B64666 74933E85688CC71E745D04EB522781B9EFABE735F2645F21FC6DBB1D29AB4917 F1B279CBB0EF6985CD4EE341680452A3B84EA481CDB4A3C7C8C2C92A6B5715F8 B7AC6A5F4BAE94604AB2D42A38D92AF022C255D90E20F3391B285563A6113B25 9F544B42BDB44B2EBC8BA1CC6B686342D0E7AC8D5CB363CD2B30EA6F4837E195 B2FA668818F6929C2214453A2999300C9D304FD928915748BAB5322BF8EC101A DAE0C825C348125F1CA0821A7EA0AEFFE3A11E85F5F66A5D93B6E0FEC2A9243A 2B565731843B49240FB48BAAE0F245C7A7EDDD3ED4662CF69D64035B624058E2 5ADB49ECA5289B1636AA5FE2727AF229071C32604D9C82DECEC4E8E08F081BD1 B5B9E543C6663A4852B6F6F32937E13D788E766D49EFF4E0FFE6666A20B2021A FE5B4BC07C2F9B0B2CF75AC89A076F91FE5BB223D8D789109E6650BC9AD9D182 2F2F7826BD3FFB7494522493504D5292B8FBBCF8B2B93C9EEB0330A951555D9D 93B2510445CD0D79239EC76C071BB180F705CEE6D0B49B6893FBB976D87E2BC9 8503B73F66F96BAA2A917D1E562332A2FAE327A69DCAB711A23F956C8533A7A8 03CC9529BE2BB374D4DA4D4A12DCDF0580516DF1827BA7018B4217338AF2BF5F A7D5D1FD6930779853C1D3CF371830456444F26F347EB88EE32DABE5A402B7F5 A40DE2AA3DF72674759D5EB7611A7132AD3E82D5F5FC83B7EA89962224286427 015927673C242228B9BC9B70639A933DB6F3C19908999E25B8441942CA619AE1 041D7BBFAFD5B599E75BC2A890F17A4F3C6A91EE623A6396DD7AAA3E45703B4D 346D97739EE4CD7176576F15840E7CC292E1543165EB629C9E8B42FC097E5AA2 BBECD765ADD468BF09FDEB1EBBCEF3D761CF01B1BCBC54E8FC1F7F48F0B4BCBA 8DF5EE2E158A29DA9BDD3F6977561A58BB24E82FED6FF0D1C525AFE52F2AFD81 F70C48065FA55005A3585E3AA7AE4D074C17F46DA4685E40E2CA09AA68FA1858 6C96BFD533FFB32E148D19A80FA922C7C7558089941DCD144F90A20444C1CEF8 0D4831DC176F4EFA3B2E41E55BAA69FC756B6D0A0A79B575E6F0AB7D41C636A1 237983F25CC9136B9EA0AEC970A0ECDF70700892B27BDCFA647E87CB2A8B19E3 3196050E2F2E245C7004B7CC7AD532470C35A64FC0496570BCD2935BEFBE4988 4037389B74DE246C9A648CAB6B4F42CFE709E90E779B11A2BED1292761DE7FDE EABEFA9049800CE37F78A420157142097F237303A68C4772172B3B1B2D0E94D2 939AC07A338387F11608E195C029CC06F09276E619D5516D21720F21B776CEAB 5DF7D9DAE529665DD39527CF21893E8E60E388A8C849E3B0AF2B122CA8A2C4A2 5A837CC7719EBACF40091DBCBD9901F0491888F276AF084759CE91DAD29832F4 E25AF57EE16D59D475351506DE72AC5B98BC7F31E4F8DB8CE3F0657A9AEEF8B2 0F300641B110C94D8CA58F09DBD118560E13F7F72AFA9A0B5849BF2F743AF72D D38B313878F68E18B925837F122ADFD3C4F4936810656550F27D545B5678C39E 9ABD17AB018D5D275040CDB2C30F06D2100B612086317AC4642F637CA3883FCB C70D88BD913EB996A9DFB2A04564ACA23CADB0AAD6A7439BE5862C3F9C131685 4D497BA4509005CADF3AAFFBB237FC94D5CB6ABBC8AF593AAF8560EFD455E640 5392D34B3E23DCB2052928683762877223F653B72A39C4F0DC41E31644437A2B 9C3A7DDFFA896BFEE4087E152BE8B33F3107BE02DC768DDC9984585A4E0B9AFB 7E383EBD0C7EA564D9594C736994FABE480D392DC856AAB0AAA3B85696BAD0EC 7559BECAA125A5120C1611EF6F9CFE3A85D55FA3C5EE6671BDFE40E27990D653 65355060202C2DA0DEF739E31268312F0A7FD702B6AB0C7E066673338E5C540E 198C11033A1EEB6E61456EDE984FB9B22556887270552142FC8F95 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: LINEW10 %!PS-AdobeFont-1.1: LINEW10 1.001 %%CreationDate: 1992 Oct 23 20:22:06 %%RevisionDate: 2001 Jun 05 20:22:06 % Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.001) readonly def /Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def /FullName (LINEW10) readonly def /FamilyName (LaTeX) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /LINEW10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 45 /a45 put readonly def /FontBBox{-220 -220 1040 1040}readonly def /UniqueID 5011941 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: LINE10 %!PS-AdobeFont-1.1: LINE10 1.001 %%CreationDate: 1992 Oct 23 20:22:05 %%RevisionDate: 2001 Jun 05 20:22:05 % Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.001) readonly def /Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def /FullName (LINE10) readonly def /FamilyName (LaTeX) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /LINE10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 42 /a42 put dup 45 /a45 put dup 94 /a94 put dup 113 /a113 put dup 126 /a126 put readonly def /FontBBox{-150 -150 1020 1020}readonly def /UniqueID 5011940 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 13 /gamma put dup 15 /epsilon1 put dup 26 /rho put dup 27 /sigma put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 82 /R put dup 83 /S put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 101 /e put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 112 /p put dup 113 /q put dup 114 /r put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put dup 122 /z put dup 126 /vector put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 9 /Psi put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 54 /six put dup 55 /seven put dup 59 /semicolon put dup 61 /equal put dup 91 /bracketleft put dup 93 /bracketright put dup 126 /tilde put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec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2C0CC4D39A26CD3DCD771B51C890698CC61F55732008B36AE9E16835DFE7E846 B9934360E01F44D252571633AE88B92FDD2DDCB8B138E4A283D55AC925A5E10B 0D069B5BB91CC93E690A06CA81CD0AFEE3F898D1B458B57F397AF362F472C270 85075532C147F8BFB7AB183FDB3A45DA84C8CEAD77BB001AC4A121AF8017B944 2E06C0938B35CE85F3288293B40673BFF2AED8308EB54471E26242D543E1A7E0 B87A3AA42346154E7655B8F26981A6E4B4E7B05109864DE84DD1120CBF2C9BBF A73AEEB57214236389ACAF53F50E442D570A705E2F41EB49D46EEB853E687ABA 2B0B2895A0EA73209B142B8BE2F1FAF4A83AE10433C502A2682B7BDA91DE8852 D903495F07E94B1875A7AF3E49F0C0A671CE084656C6A0EA89CF1464D7624549 7D547EDAEA22093BBE57DA03600115079ED75432E1E8CA2F6C6953C889AF0EF2 09FD1A43799424BC39941D900ED711175A6F741BC0E22E6E70012AD1F5E9FEA3 06A2321A6A336E32DAF195CD0162ADD0522DCA31C8BE0BDE29FC457B3818232D 0BED31D3947C267953F9192665BF41237F0EF56B65D44DC1C093233A32D24592 644495428B6D521FD680E241BE83054BFC193945393F76BA14EC03D9D59B5F20 3EFA5160548400444FF81986AB4BE5D30DDD3182BF1EA629669B062F63B0C709 88E2B12B2CBAFC20BAD9B646951B90FBF0F0EF02F8243CCEB938745DB7FD3EA8 763F26D8EF45663FAFD8AC261A9D5429616203847FC3110113CDC3AF22F0426F E8EC44DB50A27CA5357E1CF14239B752462BD9A6B3C8C381B652F7EC66F291D2 41FCCF04B2CB42A46ED3CA43ABB6AAFA04679A610419E9EA8F601437E56EA3DD F7FABDDB6C3F850CD880CD27AFC38737A14A7C5BF9F187CE2ACDCC64B25A0B38 E801DA5F476BD7D2A2612D032366F51CB97ED3D8DA9234558CDC2E6F45169AF4 F495CA9BC7A6993E6155F992801A45868370741EBD58151EB7A069DE880DD3AB 69963F37B221FFA02F5724F3423446000881B71027939554AB3A 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 10 /circlemultiply put dup 15 /bullet put dup 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 33 /arrowright put dup 39 /similarequal put dup 41 /arrowdblright put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 67 /C put dup 68 /D put dup 69 /E put dup 81 /Q put dup 91 /union put dup 92 /intersection put dup 94 /logicaland put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 110 /backslash put dup 114 /nabla put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 21 /lambda put dup 22 /mu put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 34 /epsilon put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 66 /B put dup 67 /C put dup 69 /E put dup 72 /H put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 112 /p put dup 113 /q put dup 114 /r put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put dup 122 /z put dup 126 /vector put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI9 %!PS-AdobeFont-1.1: CMTI9 1.0 %%CreationDate: 1991 Aug 18 21:08:07 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 38 /ampersand put dup 65 /A put dup 81 /Q put dup 97 /a put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 115 /s put dup 116 /t put dup 117 /u put dup 121 /y put readonly def /FontBBox{-35 -250 1148 750}readonly def /UniqueID 5000827 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 19 /acute put dup 39 /quoteright put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 50 /two put dup 55 /seven put dup 67 /C put dup 69 /E put dup 72 /H put dup 73 /I put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict 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cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 48 /prime put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 1 /Delta put dup 9 /Psi put dup 11 /ff put dup 12 /fi put dup 14 /ffi put dup 19 /acute put dup 22 /macron put dup 31 /Oslash put dup 33 /exclam put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 126 /tilde put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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%%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 3 /asteriskmath put dup 20 /lessequal put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 63 /perpendicular put dup 106 /bar put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 69 /E put dup 73 /I put dup 76 /L put dup 77 /M put dup 78 /N put dup 87 /W put dup 97 /a put dup 101 /e put dup 104 /h put dup 105 /i put dup 116 /t put dup 117 /u put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 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3334 y Fj(n)1259 3320 y Fr(\()p Fn(t)1327 3283 y Fj(k)1370 3320 y Fr(\))p Fn(;)g Fr(\011)1516 3283 y Fj(k)1559 3320 y Fr(\))26 b Fm(\024)f Fn(\025)1769 3283 y Fc(R)1769 3343 y Fl(2)1821 3320 y Fr(\()p Fn(a)1904 3334 y Fj(n)1951 3320 y Fn(;)15 b(v)2035 3334 y Fj(n)2083 3320 y Fr(\()p Fn(t)2151 3283 y Fj(k)2193 3320 y Fr(\)\))21 b(+)f Fn(\017)2412 3335 y Fj(k)2455 3320 y Fn(;)183 3518 y Fr(where)25 b Fn(\025)494 3485 y Fc(R)494 3542 y Fl(2)546 3518 y Fr(\()p Fn(a)629 3532 y Fj(n)677 3518 y Fn(;)15 b(v)761 3532 y Fj(n)808 3518 y Fr(\()p Fn(t)876 3485 y Fj(k)919 3518 y Fr(\)\))27 b(is)f(the)g(second)g(eigen)m(v)-5 b(alue)28 b(of)e Fn(H)2156 3485 y Fj(N)2223 3518 y Fr(\()p Fn(R)q Fr(\()p Fn(a)2411 3532 y Fj(n)2459 3518 y Fn(;)15 b(v)2543 3532 y Fj(n)2590 3518 y Fr(\()p Fn(t)2658 3485 y Fj(k)2701 3518 y Fr(\)\))p Fn(;)g(Z)7 b Fr(\),)28 b(as)e(an)183 3631 y(op)s(erator)j(acting)i(on)e Fn(L)1007 3598 y Fl(2)1007 3654 y Fj(a)1049 3631 y Fr(\(\()p Fk(R)1185 3598 y Fl(3)1225 3631 y Fr(\))1260 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(Theorem)f(2.)1654 5652 y(7)p eop end %%Page: 8 8 TeXDict begin 8 7 bop 581 548 a Fb(Pro)s(of)31 b(of)g(Theorem)f(2.)40 b Fr(Since)26 b(the)h(function)f Fn(v)j Fm(7!)c Fn(E)5 b Fr(\()p Fn(\013;)15 b(v)s Fr(\))29 b(is)d(con)m(tin)m(uous)h(on)g (the)581 661 y(compact)38 b(set)g Fn(S)5 b(O)1230 675 y Fl(3)1270 661 y Fr(\()p Fk(R)p Fr(\),)39 b(there)e(exists)g(a)h Fn(u)2101 675 y Fj(\013)2186 661 y Fm(2)e Fn(S)5 b(O)2413 675 y Fl(3)2453 661 y Fr(\()p Fk(R)p Fr(\))37 b(\(dep)s(ending)f(on)h Fn(\013)p Fr(\),)i(suc)m(h)581 774 y(that)31 b Fn(E)5 b Fr(\()p Fn(\013;)15 b(u)1035 788 y Fj(\013)1086 774 y Fr(\))26 b(=)f(max)1412 792 y Fj(v)r Fv(2)p Fj(S)t(O)1596 801 y Fd(3)1631 792 y Fl(\()p Fc(R)p Fl(\))1753 774 y Fn(E)5 b Fr(\()p Fn(\013;)15 b(v)s Fr(\).)722 899 y(W)-8 b(e)45 b(no)m(w)f(use)f(ideas)h(from)f([7].)81 b(Namely)-8 b(,)48 b(w)m(e)c(consider)f(real-v)-5 b(alued)45 b(ground)581 1012 y(states)38 b Fn(\036)900 1026 y Fl(1)977 1012 y Fr(and)e Fn(\036)1214 1026 y Fl(2)1291 1012 y Fr(of)h 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Fj(z)1617 1680 y Fq(0)1645 1684 y Fr(\))26 b(:=)f Fn(k)1877 1646 y Fj(\013)1874 1706 y Fl(1)1927 1684 y Fn(\036)1981 1698 y Fl(1)2020 1684 y Fr(\()p Fn(x)2107 1698 y Fl(1)2147 1684 y Fn(;)15 b(:::;)g(x)2354 1699 y Fj(z)2390 1680 y Fq(0)2418 1684 y Fr(\))2497 1570 y Fj(z)2533 1547 y Fq(0)2468 1597 y Fg(Y)2469 1793 y Fj(i)p Fl(=1)2599 1684 y Fn(\037)p Fr(\(5)p Fm(j)p Fn(x)2813 1698 y Fj(i)2843 1684 y Fm(j)p Fn(=\013)p Fr(\))1127 2156 y Fn(\036)1181 2119 y Fj(\013)1181 2179 y Fl(2)1231 2156 y Fr(\()p Fn(x)1318 2170 y Fl(1)1358 2156 y Fn(;)g(:::;)g(x)1565 2175 y Fv(j)p Fj(z)s Fv(j)1645 2156 y Fr(\))26 b(:=)f Fn(k)1877 2119 y Fj(\013)1874 2179 y Fl(2)1927 2156 y Fn(\036)1981 2170 y Fl(2)2020 2156 y Fr(\()p Fn(x)2107 2170 y Fl(1)2147 2156 y Fn(;)15 b(:::;)g(x)2354 2175 y Fv(j)p Fj(z)s Fv(j)2434 2156 y Fr(\))2506 2034 y Fv(j)p Fj(z)s Fv(j)2485 2070 y Fg(Y)2486 2265 y Fj(i)p Fl(=1)2616 2156 y Fn(\037)p Fr(\(5)p Fm(j)p Fn(x)2830 2170 y Fj(i)2859 2156 y Fm(j)p Fn(=\013)p Fr(\))581 2448 y(where)30 b Fn(k)894 2415 y Fj(\013)891 2473 y(i)974 2448 y Fr(are)h(real)g(n)m(um) m(b)s(ers)e(suc)m(h)h(that)h Fm(j)-15 b(j)p Fn(\036)2161 2415 y Fj(\013)2161 2473 y(i)2211 2448 y Fm(j)g(j)2246 2468 y Fj(L)2294 2449 y Fd(2)2358 2448 y Fr(=)25 b(1)31 b(for)f Fn(i)25 b Fr(=)g(1)p Fn(;)15 b Fr(2.)722 2573 y(Lik)m(e)32 b(in)e([7],)h(w)m(e)g(tak)m(e)h(a)f(trial)g(function)f(of) g(the)h(form)906 2814 y(\011)977 2777 y Fj(p;q)r(;u)977 2837 y(\017)1155 2814 y Fr(=)25 b Fn(\034)1291 2830 y Fj(\013)n(~)-33 b(v)1377 2814 y Fn(u\036)1483 2777 y Fj(\013)1483 2837 y Fl(1)1553 2814 y Fm(^)20 b Fn(u)1686 2828 y Fj(\013)1735 2814 y Fn(\036)1789 2777 y Fj(\013)1789 2837 y Fl(2)1859 2814 y Fr(+)g Fn(\017)15 b Fr([)q(\()p Fn(p)20 b Fm(\001)g(r)p Fr(\))p Fn(\034)2325 2830 y Fj(\013)n(~)-33 b(v)2411 2814 y Fn(u\036)2517 2777 y Fj(\013)2517 2837 y Fl(1)2567 2814 y Fr(])20 b Fm(^)g Fr([)q(\()p Fn(q)j Fm(\001)d(r)p Fr(\))p Fn(u)3026 2828 y Fj(\013)3076 2814 y Fn(\036)3130 2777 y Fj(\013)3130 2837 y Fl(2)3180 2814 y Fr(])15 b Fn(;)209 b Fr(\(5\))581 3055 y(where)30 b(w)m(e)h(ha)m(v)m (e)g(used)f(the)h(notations)1342 3296 y Fn(u )s Fr(\()p Fn(x)1543 3310 y Fl(1)1583 3296 y Fn(;)15 b(:::;)g(x)1790 3310 y Fj(N)1859 3296 y Fr(\))26 b(=)f Fn( )s Fr(\()p Fn(u)2165 3259 y Fv(\000)p Fl(1)2260 3296 y Fn(x)2312 3310 y Fl(1)2351 3296 y Fn(;)15 b(:::;)g(u)2558 3259 y Fv(\000)p Fl(1)2654 3296 y Fn(x)2706 3310 y Fj(N)2774 3296 y Fr(\))1310 3574 y Fn(\034)1350 3588 y Fj(e)1387 3574 y Fn( )s Fr(\()p Fn(x)1536 3588 y Fl(1)1576 3574 y Fn(;)g(:::;)g(x)1783 3588 y Fj(N)1852 3574 y Fr(\))25 b(=)g Fn( )s Fr(\()p Fn(x)2157 3588 y Fl(1)2218 3574 y Fm(\000)20 b Fn(e;)15 b(:::;)g(x)2558 3588 y Fj(N)2647 3574 y Fm(\000)20 b Fn(e)p Fr(\))p Fn(;)1594 3907 y Fr(\()p Fn(p)g Fm(\001)h(r)p Fr(\))p Fn( )28 b Fr(=)2070 3794 y Fj(N)2035 3821 y Fg(X)2044 4016 y Fj(i)p Fl(=1)2167 3907 y Fr(\()p Fn(p)20 b Fm(\001)g(r)p Fr(\))2424 3921 y Fj(x)2464 3931 y Ff(i)2495 3907 y Fn( )581 4194 y Fr(for)37 b(an)m(y)g Fn(N)10 b Fr(-b)s(o)s(dy)35 b(w)m(a)m(v)m(efunction)j Fn( )s Fr(,)h(and)d(where)h Fm(^)f Fr(denotes)h(the)g(usual)f(an)m (tisym-)581 4307 y(metric)h(tensor)f(pro)s(duct.)55 b(It)36 b(is)g(de\014ned)f(for)g Fn( )j Fm(2)c Fn(L)2459 4274 y Fl(2)2459 4329 y Fj(a)2501 4307 y Fr(\()p Fk(R)2602 4274 y Fl(3)p Fj(N)2693 4283 y Fd(1)2732 4307 y Fr(\))i(and)f Fn( )3047 4274 y Fv(0)3105 4307 y Fm(2)f Fn(L)3262 4274 y Fl(2)3262 4329 y Fj(a)3304 4307 y Fr(\()p Fk(R)3405 4274 y Fl(3)p Fj(N)3496 4283 y Fd(2)3535 4307 y Fr(\))581 4420 y(b)m(y)646 4694 y Fn( )23 b Fm(^)d Fn( )871 4656 y Fv(0)895 4694 y Fr(\()p Fn(x)982 4708 y Fl(1)1022 4694 y Fn(;)15 b(:::;)g(x)1229 4708 y Fj(N)1285 4717 y Fd(1)1321 4708 y Fl(+)p Fj(N)1432 4717 y Fd(2)1470 4694 y Fr(\))26 b(=)2013 4633 y(1)p 1637 4673 799 4 v 1637 4691 a Fg(p)p 1728 4691 708 4 v 78 x Fr(\()p Fn(N)1836 4783 y Fl(1)1896 4769 y Fr(+)20 b Fn(N)2060 4783 y Fl(2)2099 4769 y Fr(\)!)p Fn(N)2232 4783 y Fl(1)2272 4769 y Fr(!)p Fn(N)2370 4783 y Fl(2)2410 4769 y Fr(!)2569 4608 y Fg(X)2460 4805 y Fj(\033)r Fv(2)p Fj(S)2592 4816 y Ff(N)2640 4831 y Fd(1)2676 4816 y(+)p Ff(N)2771 4831 y Fd(2)2825 4694 y Fn(")p Fr(\()p Fn(\033)s Fr(\))p Fn( )s Fr(\()p Fn(x)3141 4656 y Fl(1)3141 4717 y Fj(\033)3190 4694 y Fr(\))p Fn( )3287 4656 y Fv(0)3311 4694 y Fr(\()p Fn(x)3398 4656 y Fl(2)3398 4717 y Fj(\033)3445 4694 y Fr(\))p Fn(:)581 5052 y Fr(where)39 b Fn(x)905 5019 y Fl(1)905 5075 y Fj(\033)992 5052 y Fr(:=)h(\()p Fn(x)1215 5071 y Fj(\033)r Fl(\(1\))1352 5052 y Fn(;)15 b(:::;)g(x)1559 5071 y Fj(\033)r Fl(\()p Fj(N)1684 5080 y Fd(1)1721 5071 y Fl(\))1753 5052 y Fr(\))39 b(and)g Fn(x)2065 5019 y Fl(2)2065 5075 y Fj(\033)2152 5052 y Fr(=)g(\()p Fn(x)2349 5071 y Fj(\033)r Fl(\()p Fj(N)2474 5080 y Fd(1)2510 5071 y Fl(+1\))2632 5052 y Fn(;)15 b(:::;)g(x)2839 5071 y Fj(\033)r Fl(\()p Fj(N)2964 5080 y Fd(1)3001 5071 y Fl(+)p Fj(N)3112 5080 y Fd(2)3147 5071 y Fl(\))3179 5052 y Fr(\).)67 b(In)39 b(\(5\))q(,)581 5165 y Fn(u)26 b Fm(2)g Fn(S)5 b(O)876 5179 y Fl(3)916 5165 y Fr(\()p Fk(R)p Fr(\),)31 b Fn(p)26 b Fm(2)f Fn(S)1327 5132 y Fl(2)1367 5165 y Fr(,)31 b Fn(q)e Fm(2)c Fn(S)1640 5132 y Fl(2)1710 5165 y Fr(\()p Fn(S)1806 5132 y Fl(2)1877 5165 y Fr(b)s(eing)30 b(the)h(sphere)f(of)h Fk(R)2733 5132 y Fl(3)2772 5165 y Fr(\))h(and)e Fn(\017)c Fm(2)f Fr([)p Fm(\000)p Fr(1;)15 b(1])32 b(are)581 5278 y(parameters)f(that)g (will)g(b)s(e)e(c)m(hosen)i(later)h(on.)722 5403 y(The)h(energy)h(of)f (the)h(trial)g(function)f(\011)2102 5359 y Fj(p;q)r(;u)2102 5415 y(\017)2289 5403 y Fr(can)h(b)s(e)f(computed)g(to)h(get)h (\(details)2053 5652 y(8)p eop end %%Page: 9 9 TeXDict begin 9 8 bop 183 548 a Fr(can)30 b(b)s(e)g(found)f(in)h([7)q (]\))183 746 y Fm(E)239 708 y Fj(N)306 746 y Fr(\()p Fn(\013;)15 b(u)491 760 y Fj(\013)542 746 y Fn(;)g Fr(\011)653 708 y Fj(p;q)r(;u)653 768 y(\017)807 746 y Fr(\))83 b(=)g(\()p Fn(E)1186 708 y Fj(z)1222 685 y Fq(0)1248 746 y Fr(\(0)p Fn(;)15 b(z)1414 708 y Fv(0)1439 746 y Fr(\))21 b(+)f Fn(E)1658 708 y Fv(j)p Fj(z)s Fv(j)1737 746 y Fr(\()p Fn(r)m(;)15 b(z)t Fr(\)\))p Fm(j)-15 b(j)p Fr(\011)2072 708 y Fj(p;q)r(;u)2072 768 y(\017)2228 746 y Fm(j)g(j)2263 708 y Fl(2)2263 774 y Fj(L)2311 755 y Fd(2)3251 746 y Fr(\(6\))1170 944 y(+)1251 883 y Fn(\017)1288 850 y Fl(2)p 1251 924 77 4 v 1266 1007 a Fr(2)1352 871 y Fg(\000)1393 944 y Fm(Q)1467 958 y Fl(1)1507 944 y Fr(\()p Fn(up)p Fr(\))p Fm(j)g(j)p Fr(\()p Fn(q)24 b Fm(\001)d(r)p Fr(\))p Fn(\036)2021 958 y Fl(2)2060 944 y Fm(j)-15 b(j)2095 907 y Fl(2)2095 973 y Fj(L)2143 954 y Fd(2)2203 944 y Fr(+)20 b Fm(Q)2368 958 y Fl(2)2407 944 y Fr(\()p Fn(u)2494 958 y Fj(\013)2544 944 y Fn(q)s Fr(\))p Fm(j)-15 b(j)p Fr(\()p Fn(p)21 b Fm(\001)f(r)p Fr(\))p Fn(\036)2970 958 y Fl(1)3010 944 y Fm(j)-15 b(j)3045 907 y Fl(2)3045 973 y Fj(L)3093 954 y Fd(2)3132 871 y Fg(\001)1351 1170 y Fr(+)1437 1046 y Fg(Z)10 b(Z)1548 1252 y Fc(R)1596 1233 y Fd(6)1660 1108 y Fn(u)e Fr(~)-53 b Fn(\032)1759 1075 y Fj(\013)1759 1133 y Fl(1)1809 1108 y Fr(\()p Fn(x)p Fr(\))p Fn(u)1983 1122 y Fj(\013)2041 1108 y Fr(~)g Fn(\032)2080 1075 y Fj(\013)2080 1133 y Fl(2)2129 1108 y Fr(\()p Fn(y)s Fr(\))p 1660 1149 588 4 v 1715 1232 a Fm(j)p Fn(x)20 b Fm(\000)g Fn(y)j Fr(+)d Fn(\013)m(~)-42 b(v)t Fm(j)2258 1170 y Fn(dx)15 b(dy)1079 1418 y Fr(+)1164 1357 y Fn(\017)p 1160 1397 46 4 v 1160 1481 a Fr(2)1230 1294 y Fg(Z)9 b(Z)1341 1501 y Fc(R)1389 1482 y Fd(6)1453 1356 y Fr(\()p Fn(p)20 b Fm(\001)h(r)p Fr(\))1711 1370 y Fj(x)1755 1356 y Fn(u\032)1854 1323 y Fj(\013)1854 1381 y Fl(1)1903 1356 y Fr(\()p Fn(x)p Fr(\)\()p Fn(q)j Fm(\001)d(r)p Fr(\))2282 1370 y Fj(y)2323 1356 y Fn(u)2375 1370 y Fj(\013)2425 1356 y Fn(\032)2472 1323 y Fj(\013)2472 1381 y Fl(2)2521 1356 y Fr(\()p Fn(y)s Fr(\))p 1453 1397 1187 4 v 1807 1481 a Fm(j)p Fn(x)f Fm(\000)g Fn(y)j Fr(+)d Fn(\013)m(~)-42 b(v)t Fm(j)2650 1418 y Fn(dx)15 b(dy)1260 1674 y Fr(+)p Fn(\017)1368 1636 y Fl(2)1423 1550 y Fg(Z)9 b(Z)1534 1756 y Fc(R)1582 1737 y Fd(6)1646 1612 y Fn(T)1699 1626 y Fl(1)1738 1612 y Fr(\()p Fn(up;)15 b(u)1963 1579 y Fv(\000)p Fl(1)2058 1612 y Fn(x)p Fr(\))p Fn(T)2198 1626 y Fl(2)2238 1612 y Fr(\()p Fn(u)2325 1626 y Fj(\013)2375 1612 y Fn(q)s(;)g(u)2511 1579 y Fv(\000)p Fl(1)2511 1635 y Fj(\013)2605 1612 y Fn(y)s Fr(\))p 1646 1653 1044 4 v 1928 1736 a Fm(j)p Fn(x)20 b Fm(\000)g Fn(y)j Fr(+)d Fn(\013)m(~)-42 b(v)t Fm(j)2699 1674 y Fn(dx)15 b(dy)23 b Fr(+)d Fn(O)3106 1600 y Fg(\000)3148 1674 y Fn(e)3190 1636 y Fv(\000)p Fj(c\013)3325 1600 y Fg(\001)183 1915 y Fr(where)30 b Fn(\032)493 1882 y Fj(\013)493 1940 y Fl(1)572 1915 y Fr(and)g Fn(\032)796 1882 y Fj(\013)796 1940 y Fl(2)876 1915 y Fr(are)h(the)f(c)m(harge)i(densities)e(of)h Fn(\036)1997 1882 y Fj(\013)1997 1940 y Fl(1)2077 1915 y Fr(and)f Fn(\036)2308 1882 y Fj(\013)2308 1940 y Fl(2)2388 1915 y Fr(de\014ned)f(b)m(y)720 2157 y Fn(\032)767 2119 y Fj(\013)767 2179 y Fl(1)817 2157 y Fr(\()p Fn(x)p Fr(\))d(=)f Fn(z)1107 2119 y Fv(0)1145 2033 y Fg(Z)1251 2157 y Fm(\001)15 b(\001)g(\001)1373 2033 y Fg(Z)1479 2157 y Fm(j)p Fn(\036)1558 2119 y Fj(\013)1558 2179 y Fl(1)1608 2157 y Fr(\()p Fn(x;)g(x)1787 2171 y Fl(2)1827 2157 y Fn(;)g(:::;)g(x)2034 2172 y Fj(z)2070 2153 y Fq(0)2097 2157 y Fr(\))p Fm(j)2157 2119 y Fl(2)2197 2157 y Fn(dx)2296 2171 y Fl(2)2351 2157 y Fm(\001)g(\001)g(\001)h Fn(dx)2571 2172 y Fj(z)2607 2153 y Fq(0)677 2452 y Fn(\032)724 2415 y Fj(\013)724 2475 y Fl(2)774 2452 y Fr(\()p Fn(x)p Fr(\))26 b(=)f Fm(j)p Fn(z)t Fm(j)1129 2329 y Fg(Z)1236 2452 y Fm(\001)15 b(\001)g(\001)1357 2329 y Fg(Z)1463 2452 y Fm(j)p Fn(\036)1542 2415 y Fj(\013)1542 2475 y Fl(2)1592 2452 y Fr(\()p Fn(x;)g(x)1771 2466 y Fl(2)1811 2452 y Fn(;)g(:::;)g(x)2018 2471 y Fv(j)p Fj(z)s Fv(j)2098 2452 y Fr(\))p Fm(j)2158 2415 y Fl(2)2198 2452 y Fn(dx)2297 2466 y Fl(2)2352 2452 y Fm(\001)g(\001)g(\001)h Fn(dx)2572 2471 y Fv(j)p Fj(z)s Fv(j)2652 2452 y Fn(;)895 2741 y Fr(~)-54 b Fn(\032)933 2704 y Fj(\013)933 2764 y Fl(1)1008 2741 y Fr(=)25 b Fn(\032)1151 2704 y Fj(\013)1151 2764 y Fl(1)1221 2741 y Fm(\000)20 b Fn(z)1358 2704 y Fv(0)1381 2741 y Fn(\016)1421 2755 y Fl(0)1461 2741 y Fn(;)205 b Fr(~)-53 b Fn(\032)1730 2704 y Fj(\013)1730 2764 y Fl(2)1805 2741 y Fr(=)25 b Fn(\032)1948 2704 y Fj(\013)1948 2764 y Fl(2)2018 2741 y Fm(\000)2143 2628 y Fj(m)2108 2655 y Fg(X)2113 2850 y Fj(j)t Fl(=1)2255 2741 y Fn(z)2297 2755 y Fj(j)2334 2741 y Fn(\016)2374 2755 y Fj(r)2406 2765 y Ff(j)2443 2741 y Fn(;)183 2995 y Fm(Q)257 3009 y Fl(1)327 2995 y Fr(and)k Fm(Q)577 3009 y Fl(2)647 2995 y Fr(are)i(the)g(quadratic)g(forms)1011 3237 y Fm(Q)1085 3251 y Fl(1)1124 3237 y Fr(\()p Fn(p)p Fr(\))26 b(=)f Fm(\000)1448 3113 y Fg(Z)1498 3319 y Fc(R)1546 3301 y Fd(3)1627 3176 y Fn(z)1673 3143 y Fv(0)p 1610 3216 103 4 v 1610 3299 a Fm(j)p Fn(x)p Fm(j)1723 3237 y Fr(\()p Fn(p)20 b Fm(\001)g(r)p Fr(\))1980 3199 y Fl(2)2020 3237 y Fn(\032)2067 3251 y Fl(1)2106 3237 y Fr(\()p Fn(x)p Fr(\))15 b Fn(dx)757 3575 y Fm(Q)831 3589 y Fl(2)871 3575 y Fr(\()p Fn(q)s Fr(\))25 b(=)g Fm(\000)1192 3451 y Fg(Z)1243 3657 y Fc(R)1291 3638 y Fd(3)1345 3419 y Fg( )1451 3461 y Fj(m)1417 3488 y Fg(X)1425 3684 y Fj(i)p Fl(=1)1679 3513 y Fn(z)1721 3527 y Fj(i)p 1573 3554 283 4 v 1573 3637 a Fm(j)p Fn(x)20 b Fm(\000)g Fn(r)1802 3651 y Fj(i)1831 3637 y Fm(j)1866 3419 y Fg(!)1953 3575 y Fr(\()p Fn(q)j Fm(\001)e(r)p Fr(\))2209 3537 y Fl(2)2248 3575 y Fn(\032)2295 3589 y Fl(2)2335 3575 y Fr(\()p Fn(x)p Fr(\))15 b Fn(dx;)183 3815 y(\032)230 3829 y Fj(i)288 3815 y Fr(b)s(eing)30 b(the)h(densit)m(y)f(of)h(c)m(harge)g(asso)s (ciated)h(with)e Fn(\036)2086 3829 y Fj(i)2115 3815 y Fr(,)g(and)g(where)g(\014nally)505 4055 y(~)488 4077 y Fn(T)541 4091 y Fj(i)569 4077 y Fr(\()p Fn(p;)15 b(x)p Fr(\))26 b(=)f Fn(T)952 4091 y Fj(i)980 4077 y Fr(\()p Fn(p;)15 b(x)p Fr(\))21 b Fm(\000)f Fn(z)1346 4040 y Fv(0)1370 4077 y Fn(\016)1410 4091 y Fl(0)1450 4077 y Fn(;)1690 4055 y Fr(~)1672 4077 y Fn(T)1725 4091 y Fl(2)1764 4077 y Fr(\()p Fn(p;)15 b(x)p Fr(\))27 b(=)d Fn(T)2147 4091 y Fl(2)2187 4077 y Fr(\()p Fn(p;)15 b(x)p Fr(\))21 b Fm(\000)2541 3964 y Fj(m)2507 3991 y Fg(X)2511 4187 y Fj(j)t Fl(=1)2653 4077 y Fn(z)2695 4091 y Fj(j)2732 4077 y Fn(\016)2772 4091 y Fj(r)2804 4101 y Ff(j)2841 4077 y Fn(;)183 4370 y(T)236 4384 y Fj(i)264 4370 y Fr(\()p Fn(p;)15 b(x)p Fr(\))31 b(b)s(eing)f(the)h(densit)m(y)f(of)h(c)m(harge) g(of)g(\()p Fn(p)20 b Fm(\001)h(r)p Fr(\))p Fn(\036)2023 4384 y Fj(i)2051 4370 y Fr(.)324 4483 y(Notice)36 b(that)f(in)f(\(6\))q (,)i(w)m(e)f(ha)m(v)m(e)g(used)f(the)g(fact)h(that)g(if)g Fn(\036)f Fr(is)g(a)h(ground)f(state)h(of)183 4596 y Fn(H)266 4563 y Fj(N)333 4596 y Fr(\()p Fn(R)q(;)15 b(Z)7 b Fr(\),)29 b(then)e Fn(u\036)h Fr(is)g(a)g(ground)e(state)k(of)d Fn(H)1845 4563 y Fj(N)1913 4596 y Fr(\()p Fn(u)15 b Fm(\001)g Fn(R)q(;)g(Z)7 b Fr(\).)40 b(In)27 b(particular,)i Fn(u)2940 4610 y Fj(\013)2989 4596 y Fn(\036)3043 4610 y Fl(2)3110 4596 y Fr(is)183 4709 y(a)h(ground)f(state)j(of)e Fn(H)975 4676 y Fv(j)p Fj(z)s Fv(j)1054 4709 y Fr(\()p Fn(u)1141 4723 y Fj(\013)1191 4709 y Fn(r)m(;)15 b(z)t Fr(\))32 b(and)d Fn(u\036)1664 4723 y Fl(1)1734 4709 y Fr(is)h(a)h(ground)e (state)j(of)e Fn(H)2618 4676 y Fj(z)2654 4652 y Fq(0)2680 4709 y Fr(\(0)p Fn(;)15 b(z)2846 4676 y Fv(0)2871 4709 y Fr(\))31 b(for)e(all)183 4822 y Fn(u)j Fm(2)g Fn(S)5 b(O)490 4836 y Fl(3)530 4822 y Fr(\()p Fk(R)p Fr(\).)53 b(This)34 b(last)i(prop)s(ert)m(y)e(of)g(the)h(ground)f(states)i(of)e (atoms)i(is)f(a)g(crucial)183 4935 y(p)s(oin)m(t)30 b(in)g(the)h(pro)s (of.)324 5048 y(In)c([7],)i(the)f(form)m(ula)g(\(6\))h(is)e(in)m (tegrated)j(o)m(v)m(er)f(all)f(the)g(rotations)h(of)f(eac)m(h)h (subsys-)183 5177 y(tem)e(to)g(kill)h(the)f(term)985 5104 y Fg(R)s(R)1074 5209 y Fc(R)1122 5190 y Fd(6)1186 5128 y Fj(u)6 b Fl(~)-41 b Fj(\032)1263 5105 y Ff(\013)1263 5149 y Fd(1)1307 5128 y Fl(\()p Fj(x)p Fl(\))p Fj(u)1442 5136 y Ff(\013)1493 5128 y Fl(~)g Fj(\032)1523 5105 y Ff(\013)1523 5149 y Fd(2)1567 5128 y Fl(\()p Fj(y)r Fl(\))p 1186 5156 474 4 v 1268 5210 a Fv(j)p Fj(x)p Fv(\000)p Fj(y)r Fl(+)p Fj(\013)n(~)-33 b(v)s Fv(j)1669 5177 y Fn(dx)15 b(dy)30 b Fr(and)c(simplify)h(the)g(computation)g(of)183 5290 y(the)k(energy)-8 b(.)43 b(In)30 b(the)h(case)h(where)e(one)h (subsystem)f(is)h(an)g(atom,)h(this)e(in)m(tegration)j(is)183 5403 y(not)d(necessary)h(since)g(w)m(e)g(can)f(pro)m(v)m(e)h(the)1654 5652 y(9)p eop end %%Page: 10 10 TeXDict begin 10 9 bop 581 548 a Fb(Lemma)35 b(1.)42 b Fe(F)-7 b(or)33 b(any)h Fn(\013)p Fe(,)f(ther)-5 b(e)33 b(exists)g(a)g(r)-5 b(otation)35 b Fn(v)2481 562 y Fj(\013)2556 548 y Fm(2)25 b Fn(S)5 b(O)2772 562 y Fl(3)2811 548 y Fr(\()p Fk(R)p Fr(\))33 b Fe(such)g(that)1444 684 y Fg(Z)9 b(Z)1555 890 y Fc(R)1603 871 y Fd(6)1667 746 y Fn(v)1711 760 y Fj(\013)1769 746 y Fr(~)-54 b Fn(\032)1807 713 y Fj(\013)1807 771 y Fl(1)1857 746 y Fr(\()p Fn(x)p Fr(\))p Fn(u)2031 760 y Fj(\013)2089 746 y Fr(~)h Fn(\032)2128 713 y Fj(\013)2128 771 y Fl(2)2177 746 y Fr(\()p Fn(y)s Fr(\))p 1667 787 630 4 v 1742 870 a Fm(j)p Fn(x)21 b Fm(\000)e Fn(y)k Fr(+)d Fn(\013)m(~)-42 b(v)t Fm(j)2306 808 y Fn(dx)15 b(dy)29 b Fr(=)c(0)p Fn(:)747 b Fr(\(7\))581 1066 y Fe(Pr)-5 b(o)g(of.)47 b Fr(W)-8 b(e)32 b(ha)m(v)m(e)1271 1197 y Fg(Z)1321 1403 y Fj(S)t(O)1422 1412 y Fd(3)1456 1403 y Fl(\()p Fc(R)p Fl(\))1578 1321 y Fn(dv)1688 1197 y Fg(Z)10 b(Z)1799 1403 y Fc(R)1847 1384 y Fd(6)1911 1259 y Fn(v)i Fr(~)-54 b Fn(\032)2005 1226 y Fj(\013)2005 1283 y Fl(1)2055 1259 y Fr(\()p Fn(x)p Fr(\))p Fn(u)2229 1273 y Fj(\013)2287 1259 y Fr(~)h Fn(\032)2326 1226 y Fj(\013)2326 1283 y Fl(2)2375 1259 y Fr(\()p Fn(y)s Fr(\))p 1911 1300 584 4 v 1963 1383 a Fm(j)p Fn(x)21 b Fm(\000)f Fn(y)j Fr(+)d Fn(\013)m(~)-42 b(v)s Fm(j)2504 1321 y Fn(dx)15 b(dy)29 b Fr(=)c(0)581 1600 y(since)31 b Fn(\026)859 1567 y Fj(\013)859 1625 y Fl(1)908 1600 y Fr(\()p Fn(x)p Fr(\))26 b(=)1152 1527 y Fg(R)1195 1632 y Fj(S)t(O)1296 1641 y Fd(3)1330 1632 y Fl(\()p Fc(R)p Fl(\))1452 1600 y Fn(v)12 b Fr(~)-54 b Fn(\032)1546 1567 y Fj(\013)1546 1625 y Fl(1)1596 1600 y Fr(\()p Fn(x)p Fr(\))15 b Fn(dv)34 b Fr(is)d(a)g(radial)f(function)g(and)1712 1762 y Fg(Z)1763 1968 y Fc(R)1811 1949 y Fd(3)1905 1824 y Fn(\026)1960 1791 y Fj(\013)1960 1849 y Fl(1)2010 1824 y Fr(\()p Fn(x)p Fr(\))p 1874 1865 289 4 v 1874 1948 a Fm(j)p Fn(x)21 b Fm(\000)f Fn(x)2115 1922 y Fv(0)2138 1948 y Fm(j)2173 1886 y Fn(dx)26 b Fr(=)f(0)581 2154 y(when)e Fn(x)864 2121 y Fv(0)913 2154 y Fm(2)i Fk(R)1065 2121 y Fl(3)1112 2154 y Fm(n)8 b Fn(B)d Fr(\(0)p Fn(;)15 b Fr(2)p Fn(\013=)p Fr(5\),)29 b(due)24 b(to)h(Newton's)g(theorem.)39 b(Therefore,)26 b(there)e(exists)581 2267 y(a)31 b Fn(v)701 2281 y Fj(\013)776 2267 y Fm(2)25 b Fn(S)5 b(O)992 2281 y Fl(3)1031 2267 y Fr(\()p Fk(R)p Fr(\))31 b(suc)m(h)f(that)h(\(7\))g(holds.)p 3504 2267 4 62 v 3508 2209 55 4 v 3508 2267 V 3562 2267 4 62 v 722 2475 a(In)36 b(the)i(follo)m(wing,)i(w)m(e)d(therefore)h(c)m (ho)s(ose)g Fn(u)e Fr(=)g Fn(v)2486 2489 y Fj(\013)2535 2475 y Fr(,)j(giv)m(en)f(b)m(y)f(Lemma)g(1.)60 b(Let)581 2588 y(us)29 b(no)m(w)g(explain)h(ho)m(w)f Fn(q)j Fr(is)d(c)m(hosen.)41 b(Indeed,)29 b(the)g(trace)i(of)e(the)h(quadratic)f(form)g Fm(Q)3530 2602 y Fl(2)581 2701 y Fr(can)i(b)s(e)f(easily)h(computed)f (since,)h(follo)m(wing)h([7)q(,)e(page)h(44],)656 3017 y(tr\()p Fm(Q)836 3031 y Fl(2)876 3017 y Fr(\))25 b(=)g Fm(\000)1166 2904 y Fl(3)1118 2931 y Fg(X)1127 3127 y Fj(i)p Fl(=1)1264 2894 y Fg(Z)1315 3100 y Fc(R)1363 3081 y Fd(3)1417 2835 y Fg(0)1417 2998 y(@)1531 2904 y Fj(m)1496 2931 y Fg(X)1501 3127 y Fj(j)t Fl(=1)1759 2955 y Fn(z)1801 2969 y Fj(j)p 1653 2997 292 4 v 1653 3080 a Fm(j)p Fn(x)20 b Fm(\000)g Fn(r)1882 3094 y Fj(j)1919 3080 y Fm(j)1954 2835 y Fg(1)1954 2998 y(A)2049 3017 y Fn(@)2102 2980 y Fl(2)2097 3040 y Fj(x)2137 3050 y Ff(i)2167 3017 y Fn(\032)2214 3031 y Fl(2)2254 3017 y Fr(\()p Fn(x)p Fr(\))15 b Fn(dx)26 b Fr(=)f(4)p Fn(\031)2776 2904 y Fl(3)2727 2931 y Fg(X)2732 3127 y Fj(j)t Fl(=1)2874 3017 y Fn(z)2916 3031 y Fj(j)2953 3017 y Fn(\032)3000 3031 y Fl(2)3039 3017 y Fr(\()p Fn(r)3115 3031 y Fj(j)3152 3017 y Fr(\))h Fm(\025)f Fr(0)p Fn(:)75 b Fr(\(8\))581 3329 y(Therefore,)42 b Fm(Q)1104 3343 y Fl(2)1183 3329 y Fr(p)s(ossesses)d(an)h(eigen)m(v)m (ector)j Fn(e)2241 3343 y Fl(2)2320 3329 y Fr(with)c(a)h(non-negativ)m (e)i(eigen)m(v)-5 b(alue)581 3442 y Fn(\025)634 3456 y Fl(2)699 3442 y Fr(=)25 b Fm(Q)869 3456 y Fl(2)909 3442 y Fr(\()p Fn(e)986 3456 y Fl(2)1026 3442 y Fr(\))g Fm(\025)g Fr(0.)41 b(W)-8 b(e)32 b(c)m(ho)s(ose)1866 3654 y Fn(q)c Fr(=)d Fn(u)2083 3616 y Fv(\000)p Fl(1)2083 3676 y Fj(\013)2178 3654 y Fn(e)2220 3668 y Fl(2)2260 3654 y Fn(:)581 3866 y Fr(T)-8 b(o)29 b(\014nish)e(the)i(pro)s(of,)f (it)h(remains)f(to)h(c)m(ho)s(ose)g Fn(p)f Fr(and)g Fn(\017)g Fr(appropriately)-8 b(.)41 b(T)-8 b(o)29 b(this)f(end,)581 3979 y(w)m(e)j(use)f([6)q(,)g(Lemma)h(9])g(whic)m(h)f(pro)m(vides)g(a)h (uniform)e(constan)m(t)j Fn(K)37 b Fr(suc)m(h)30 b(that)855 4114 y Fg(\014)855 4169 y(\014)855 4223 y(\014)855 4278 y(\014)1014 4185 y Fr(1)p 895 4225 284 4 v 895 4308 a Fm(j)p Fn(R)21 b Fr(+)f Fn(h)p Fm(j)1209 4246 y(\000)1300 4118 y Fg(\022)1414 4185 y Fr(1)p 1377 4225 121 4 v 1377 4308 a Fm(j)p Fn(R)q Fm(j)1527 4246 y(\000)1628 4185 y Fn(e)1670 4199 y Fj(R)1748 4185 y Fm(\001)h Fn(h)p 1628 4225 219 4 v 1657 4308 a Fm(j)p Fn(R)q Fm(j)1777 4282 y Fl(2)1876 4246 y Fr(+)1977 4185 y(3\()p Fn(e)2099 4199 y Fj(R)2178 4185 y Fm(\001)g Fn(h)p Fr(\))2311 4152 y Fl(2)2371 4185 y Fm(\000)f(j)p Fn(h)p Fm(j)2564 4152 y Fl(2)p 1977 4225 628 4 v 2188 4308 a Fr(2)p Fm(j)p Fn(R)q Fm(j)2353 4282 y Fl(3)2614 4118 y Fg(\023)2681 4114 y(\014)2681 4169 y(\014)2681 4223 y(\014)2681 4278 y(\014)2737 4246 y Fm(\024)2944 4185 y Fn(K)i Fm(j)p Fn(h)p Fm(j)3145 4152 y Fl(3)p 2843 4225 444 4 v 2843 4308 a Fm(j)p Fn(R)q Fm(j)2963 4282 y Fl(3)3002 4308 y Fm(j)p Fn(R)g Fr(+)e Fn(h)p Fm(j)3454 4246 y Fr(\(9\))581 4516 y(for)28 b(an)m(y)g Fn(R)h Fr(and)e Fn(h)f Fm(2)f Fk(R)1389 4483 y Fl(3)1456 4516 y Fr(with)i Fn(R)16 b Fr(+)f Fn(h)26 b Fm(6)p Fr(=)f(0,)k(and)e(where)h(w)m(e)g(ha)m(v)m(e)h (used)e(the)i(notation)581 4628 y Fn(e)623 4642 y Fj(R)706 4628 y Fr(=)c Fn(R)q(=)p Fm(j)p Fn(R)q Fm(j)p Fr(.)41 b(Using)31 b(the)g(prop)s(erties)1087 4882 y Fm(8)p Fn(p)1184 4845 y Fv(0)1207 4882 y Fn(;)15 b(q)1291 4845 y Fv(0)1340 4882 y Fm(2)24 b Fn(S)1486 4845 y Fl(2)1526 4882 y Fn(;)1748 4759 y Fg(Z)1799 4965 y Fc(R)1847 4946 y Fd(3)1885 4882 y Fr(\()p Fn(p)1966 4845 y Fv(0)2010 4882 y Fm(\001)c(r)p Fr(\))p Fn(\032)2213 4845 y Fj(\013)2213 4905 y Fl(1)2288 4882 y Fr(=)2384 4759 y Fg(Z)2435 4965 y Fc(R)2483 4946 y Fd(3)2521 4882 y Fr(\()p Fn(q)2600 4845 y Fv(0)2644 4882 y Fm(\001)h(r)p Fr(\))p Fn(\032)2848 4845 y Fj(\013)2848 4905 y Fl(2)2922 4882 y Fr(=)k(0)581 5135 y(and)818 5366 y Fm(8)p Fn(p)915 5329 y Fv(0)963 5366 y Fm(2)g Fn(S)1110 5329 y Fl(2)1150 5366 y Fn(;)45 b(i)26 b Fr(=)f(1)p Fn(;)15 b Fr(2)p Fn(;)1726 5243 y Fg(Z)1777 5449 y Fc(R)1825 5430 y Fd(3)1879 5366 y Fn(x)p Fr(\()p Fn(p)2012 5329 y Fv(0)2055 5366 y Fm(\001)21 b(r)p Fr(\))p Fn(\032)2259 5329 y Fj(\013)2259 5389 y(i)2308 5366 y Fr(\()p Fn(x)p Fr(\))15 b Fn(dx)27 b Fr(=)e Fm(\000)p Fn(p)2784 5329 y Fv(0)2821 5243 y Fg(Z)2872 5449 y Fc(R)2920 5430 y Fd(3)2974 5366 y Fn(\032)3021 5329 y Fj(\013)3021 5389 y(i)3070 5366 y Fr(\()p Fn(x)p Fr(\))15 b Fn(dx;)2030 5652 y Fr(10)p eop end %%Page: 11 11 TeXDict begin 11 10 bop 183 548 a Fr(w)m(e)30 b(obtain)281 684 y Fg(\014)281 739 y(\014)281 794 y(\014)281 848 y(\014)311 693 y(Z)10 b(Z)422 899 y Fc(R)470 880 y Fd(6)534 754 y Fr(\()p Fn(p)20 b Fm(\001)h(r)p Fr(\))792 768 y Fj(x)836 754 y Fn(v)880 768 y Fj(\013)929 754 y Fn(\032)976 721 y Fj(\013)976 779 y Fl(1)1026 754 y Fr(\()p Fn(x)p Fr(\)\()p Fn(u)1235 721 y Fv(\000)p Fl(1)1235 777 y Fj(\013)1330 754 y Fn(e)1372 768 y Fl(2)1432 754 y Fm(\001)g(r)p Fr(\))1589 768 y Fj(y)1630 754 y Fn(u)1682 768 y Fj(\013)1732 754 y Fn(\032)1779 721 y Fj(\013)1779 779 y Fl(2)1828 754 y Fr(\()p Fn(y)s Fr(\))p 534 795 1413 4 v 1001 879 a Fm(j)p Fn(x)g Fm(\000)f Fn(y)j Fr(+)c Fn(\013)m(~)-42 b(v)t Fm(j)1957 816 y Fn(dx)15 b(dy)23 b Fm(\000)2287 755 y Fn(z)2333 722 y Fv(0)2357 755 y Fm(j)p Fn(z)t Fm(jD)s Fr(\()p Fn(up;)15 b(e)2741 769 y Fl(2)2782 755 y Fr(\))p 2287 795 530 4 v 2503 879 a Fn(\013)2561 852 y Fl(3)2827 684 y Fg(\014)2827 739 y(\014)2827 794 y(\014)2827 848 y(\014)472 1074 y Fm(\024)585 1012 y Fn(K)p 578 1053 98 4 v 578 1136 a(\013)636 1110 y Fl(3)701 950 y Fg(Z)10 b(Z)812 1156 y Fc(R)860 1137 y Fd(6)924 1012 y Fm(j)p Fn(x)20 b Fm(\000)g Fn(y)s Fm(j)1185 979 y Fl(3)1225 1012 y Fm(j)p Fr(\()p Fn(p)g Fm(\001)h(r)p Fr(\))1508 1026 y Fj(x)1552 1012 y Fn(v)1596 1026 y Fj(\013)1645 1012 y Fn(\032)1692 979 y Fj(\013)1692 1036 y Fl(1)1742 1012 y Fr(\()p Fn(x)p Fr(\)\()p Fn(u)1951 979 y Fv(\000)p Fl(1)1951 1034 y Fj(\013)2046 1012 y Fn(e)2088 1026 y Fl(2)2148 1012 y Fm(\001)g(r)p Fr(\))2305 1026 y Fj(y)2346 1012 y Fn(u)2398 1026 y Fj(\013)2448 1012 y Fn(\032)2495 979 y Fj(\013)2495 1036 y Fl(2)2544 1012 y Fr(\()p Fn(y)s Fr(\))p Fm(j)p 924 1053 1764 4 v 1567 1136 a(j)p Fn(x)f Fm(\000)g Fn(y)j Fr(+)d Fn(\013)m(~)-42 b(v)t Fm(j)2698 1074 y Fn(dx)15 b(dy)208 1324 y Fm(\024)314 1262 y Fr(5)p Fn(K)p 314 1303 130 4 v 329 1386 a(\013)387 1360 y Fl(4)468 1200 y Fg(Z)10 b(Z)579 1406 y Fc(R)627 1387 y Fd(6)681 1324 y Fm(j)p Fn(x)j Fm(\000)g Fn(y)s Fm(j)928 1286 y Fl(3)968 1324 y Fm(j)p Fr(\()p Fn(p)g Fm(\001)g(r)p Fr(\))1236 1338 y Fj(x)1281 1324 y Fn(v)1325 1338 y Fj(\013)1375 1324 y Fn(\032)1422 1286 y Fj(\013)1422 1346 y Fl(1)1471 1324 y Fr(\()p Fn(x)p Fr(\)\()p Fn(u)1680 1286 y Fv(\000)p Fl(1)1680 1346 y Fj(\013)1776 1324 y Fn(e)1818 1338 y Fl(2)1871 1324 y Fm(\001)g(r)p Fr(\))2020 1338 y Fj(y)2062 1324 y Fn(u)2114 1338 y Fj(\013)2164 1324 y Fn(\032)2211 1286 y Fj(\013)2211 1346 y Fl(2)2260 1324 y Fr(\()p Fn(y)s Fr(\))p Fm(j)i Fn(dx)g(dy)30 b Fr(=)25 b Fn(O)2837 1196 y Fg(\022)2940 1262 y Fr(1)p 2914 1303 98 4 v 2914 1386 a Fn(\013)2972 1360 y Fl(4)3021 1196 y Fg(\023)183 1579 y Fr(where)30 b Fm(D)i Fr(is)f(the)f(dip)s(ole-dip)s(ole)h(in)m (teraction)693 1789 y Fm(D)s Fr(\()p Fn(p;)15 b(q)s Fr(\))26 b(=)f Fn(p)20 b Fm(\001)g Fn(q)j Fm(\000)d Fr(3\()p Fn(p)h Fm(\001)c Fn(~)-41 b(v)s Fr(\)\()p Fn(q)24 b Fm(\001)17 b Fn(~)-42 b(v)s Fr(\))26 b(=)f Fn(p)20 b Fm(\001)g Fr(\()p Fn(q)k Fm(\000)c Fr(3\()p Fn(q)k Fm(\001)16 b Fn(~)-41 b(v)s Fr(\))l Fn(~)g(v)t Fr(\))p Fn(;)183 1999 y Fr(and)43 b(where)h(our)g Fn(O)913 1926 y Fg(\000)987 1964 y Fl(1)p 964 1979 80 4 v 964 2033 a Fj(\013)1009 2014 y Fd(4)1054 1926 y Fg(\001)1140 1999 y Fr(is)g(uniform)f(in)h Fn(p)p Fr(,)j Fn(u)1890 2013 y Fj(\013)1984 1999 y Fr(and)d Fn(v)2219 2013 y Fj(\013)2268 1999 y Fr(.)82 b(Using)44 b(also)i(\(9\))f(or)f(a)183 2112 y(simpli\014ed)29 b(v)m(ersion)i(for)f (the)h(last)g(term)f(in)g Fn(\017)1729 2079 y Fl(2)1769 2112 y Fr(,)g(w)m(e)h(no)m(w)g(arriv)m(e)g(at)183 2335 y Fm(E)239 2298 y Fj(N)306 2335 y Fr(\()p Fn(\013;)15 b(u)491 2349 y Fj(\013)542 2335 y Fn(;)g Fr(\011)653 2298 y Fj(p;u)750 2268 y Fq(\000)p Fd(1)750 2308 y Ff(\013)831 2298 y Fj(e)864 2307 y Fd(2)899 2298 y Fj(;v)953 2306 y Ff(\013)653 2358 y Fj(\017)1001 2335 y Fr(\))83 b(=)g(\()p Fn(E)1380 2298 y Fj(z)1416 2274 y Fq(0)1443 2335 y Fr(\(0)p Fn(;)15 b(z)1609 2298 y Fv(0)1634 2335 y Fr(\))20 b(+)g Fn(E)1852 2298 y Fv(j)p Fj(z)s Fv(j)1932 2335 y Fr(\()p Fn(r)m(;)15 b(z)t Fr(\)\))p Fm(j)-15 b(j)p Fr(\011)2267 2298 y Fj(p;u)2364 2268 y Fq(\000)p Fd(1)2364 2308 y Ff(\013)2447 2298 y Fj(e)2480 2307 y Fd(2)2515 2298 y Fj(;v)2569 2306 y Ff(\013)2267 2358 y Fj(\017)2617 2335 y Fm(j)g(j)2652 2298 y Fl(2)2652 2363 y Fj(L)2700 2344 y Fd(2)3064 2335 y Fr(\(10\))1364 2534 y(+)1445 2472 y Fn(\017)1482 2439 y Fl(2)p 1445 2513 77 4 v 1460 2596 a Fr(2)1546 2460 y Fg(\000)1588 2534 y Fm(Q)1662 2548 y Fl(1)1702 2534 y Fr(\()p Fn(v)1781 2548 y Fj(\013)1830 2534 y Fn(p)p Fr(\))p Fm(j)g(j)p Fr(\()p Fn(e)2023 2548 y Fl(2)2084 2534 y Fm(\001)21 b(r)p Fr(\))p Fn(\036)2295 2548 y Fl(2)2334 2534 y Fm(j)-15 b(j)2369 2496 y Fl(2)2369 2562 y Fj(L)2417 2543 y Fd(2)2477 2534 y Fr(+)20 b Fn(\025)2621 2548 y Fl(2)2660 2534 y Fm(j)-15 b(j)p Fr(\()p Fn(p)21 b Fm(\001)f(r)p Fr(\))p Fn(\036)3007 2548 y Fl(1)3047 2534 y Fm(j)-15 b(j)3082 2496 y Fl(2)3082 2562 y Fj(L)3130 2543 y Fd(2)3169 2460 y Fg(\001)1455 2767 y Fr(+)p Fn(\017)1573 2705 y(z)1619 2672 y Fv(0)1642 2705 y Fm(j)p Fn(z)t Fm(jD)s Fr(\()p Fn(v)1890 2719 y Fj(\013)1940 2705 y Fn(p;)15 b(e)2068 2719 y Fl(2)2108 2705 y Fr(\))p 1573 2746 572 4 v 1786 2829 a(2)p Fn(\013)1889 2803 y Fl(3)2174 2767 y Fr(+)20 b Fn(O)2352 2666 y Fg(\020)2447 2705 y Fn(\017)p 2416 2746 98 4 v 2416 2829 a(\013)2474 2803 y Fl(4)2524 2666 y Fg(\021)2598 2767 y Fr(+)g Fn(O)2776 2638 y Fg(\022)2853 2705 y Fn(\017)2890 2672 y Fl(2)p 2853 2746 77 4 v 2862 2829 a Fn(\013)2940 2638 y Fg(\023)3022 2767 y Fn(:)183 3022 y Fr(Let)31 b(us)e(explain)i(ho)m(w)f(w)m(e)h(c)m(ho)s(ose)g Fn(p)p Fr(.)183 3217 y Fb(Lemma)23 b(2.)33 b Fe(Ther)-5 b(e)24 b(exists)g(a)g(ve)-5 b(ctor)24 b Fn(e)1519 3231 y Fl(1)1584 3217 y Fm(2)h Fn(S)1731 3184 y Fl(2)1793 3217 y Fe(such)f(that)g Fm(Q)p Fr(\()p Fn(e)2318 3231 y Fl(1)2359 3217 y Fr(\))h Fm(\025)g Fr(0)f Fe(and)g Fm(D)s Fr(\()p Fn(e)2901 3231 y Fl(1)2941 3217 y Fn(;)15 b(e)3023 3231 y Fl(2)3063 3217 y Fr(\))26 b Fm(6)p Fr(=)183 3330 y(0)p Fe(.)183 3526 y(Pr)-5 b(o)g(of.)46 b Fr(Notice)26 b(that)f Fn(e)979 3540 y Fl(2)1026 3526 y Fm(\000)7 b Fr(3\()p Fn(e)1226 3540 y Fl(2)1273 3526 y Fm(\001)t Fn(~)-42 b(v)t Fr(\))l Fn(~)h(v)28 b Fm(6)p Fr(=)d(0)g(since)20 b Fn(~)-41 b(v)28 b Fm(2)d Fn(S)2061 3493 y Fl(2)2101 3526 y Fr(.)38 b(By)24 b(the)g(same)g(computation)183 3639 y(as)43 b(\(8\))r(,)k(w)m(e)d(\014nd)e(that)i(tr\()p Fm(Q)1228 3653 y Fl(1)1268 3639 y Fr(\))j Fm(\025)g Fr(0.)81 b(If)43 b Fm(Q)1797 3653 y Fl(1)1884 3639 y Fr(=)k(0,)g(it)e(su\016ces) e(to)h(c)m(ho)s(ose)h Fn(e)3014 3653 y Fl(1)3101 3639 y Fr(=)220 3720 y Fj(e)253 3729 y Fd(2)287 3720 y Fv(\000)p Fl(3\()p Fj(e)437 3729 y Fd(2)472 3720 y Fv(\001)n Fj(~)-33 b(v)s Fl(\))n Fj(~)g(v)p 193 3744 428 4 v 193 3797 a Fv(j)-12 b(j)p Fj(e)254 3806 y Fd(2)287 3797 y Fv(\000)p Fl(3\()p Fj(e)437 3806 y Fd(2)472 3797 y Fv(\001)n Fj(~)-33 b(v)s Fl(\))n Fj(~)g(v)s Fv(j)-12 b(j)630 3765 y Fr(.)69 b(If)39 b Fm(Q)898 3779 y Fl(1)979 3765 y Fm(6)p Fr(=)h(0,)j(it)d(p)s (ossesses)f(a)h(p)s(ositiv)m(e)h(eigen)m(v)-5 b(alue)42 b Fn(\025)2629 3779 y Fl(1)2708 3765 y Fr(and)d(the)h(set)183 3898 y Fm(f)p Fn(x)c Fm(2)f Fn(S)473 3865 y Fl(2)549 3898 y Fm(j)i(Q)685 3912 y Fl(1)724 3898 y Fr(\()p Fn(x)p Fr(\))g Fn(>)e Fr(0)p Fm(g)i Fr(is)g(a)g(non-empt)m(y)g(op)s(en)f(set)h (of)g Fn(S)2302 3865 y Fl(2)2341 3898 y Fr(.)59 b(Since)37 b(on)f(the)h(other)183 4011 y(hand)25 b Fm(f)p Fn(x)h Fm(2)f Fn(S)676 3978 y Fl(2)741 4011 y Fm(j)i(D)s Fr(\()p Fn(x;)15 b(e)1035 4025 y Fl(2)1075 4011 y Fr(\))26 b(=)f(0)p Fm(g)h Fr(=)f Fm(f)p Fn(e)1531 4025 y Fl(2)1583 4011 y Fm(\000)12 b Fr(3\()p Fn(e)1788 4025 y Fl(2)1842 4011 y Fm(\001)d Fn(~)-42 b(v)t Fr(\))l Fn(~)h(v)s Fm(g)2054 3978 y Fv(?)2126 4011 y Fm(\\)12 b Fn(S)2260 3978 y Fl(2)2326 4011 y Fr(has)26 b(an)h(empt)m(y)g(in)m(terior)183 4124 y(in)j Fn(S)350 4091 y Fl(2)389 4124 y Fr(,)h(it)g(exists)g(a)f Fn(e)904 4138 y Fl(1)969 4124 y Fm(2)25 b Fn(S)1116 4091 y Fl(2)1186 4124 y Fr(suc)m(h)30 b(that)h Fm(Q)1662 4138 y Fl(1)1702 4124 y Fr(\()p Fn(e)1779 4138 y Fl(1)1819 4124 y Fr(\))25 b Fn(>)g Fr(0)31 b(and)f Fm(D)s Fr(\()p Fn(e)2378 4138 y Fl(1)2418 4124 y Fn(;)15 b(e)2500 4138 y Fl(2)2540 4124 y Fr(\))25 b Fm(6)p Fr(=)g(0.)p 3105 4124 4 62 v 3109 4066 55 4 v 3109 4124 V 3163 4124 4 62 v 324 4327 a(Cho)s(osing)30 b(no)m(w)g Fn(p)25 b Fr(=)g Fn(v)1124 4294 y Fv(\000)p Fl(1)1121 4350 y Fj(\013)1219 4327 y Fn(e)1261 4341 y Fl(1)1301 4327 y Fr(,)30 b(w)m(e)h(obtain)266 4580 y Fm(E)322 4542 y Fj(N)389 4580 y Fr(\()p Fn(\013;)15 b(u)574 4594 y Fj(\013)625 4580 y Fn(;)g Fr(\011)736 4542 y Fj(v)772 4512 y Fq(\000)p Fd(1)770 4553 y Ff(\013)855 4542 y Fj(e)888 4551 y Fd(1)923 4542 y Fj(;u)984 4512 y Fq(\000)p Fd(1)984 4553 y Ff(\013)1066 4542 y Fj(e)1099 4551 y Fd(2)1133 4542 y Fj(;v)1187 4550 y Ff(\013)736 4602 y Fj(\017)1235 4580 y Fr(\))26 b(=)f(\()p Fn(E)1499 4542 y Fj(z)1535 4519 y Fq(0)1562 4580 y Fr(\(0)p Fn(;)15 b(z)1728 4542 y Fv(0)1752 4580 y Fr(\))21 b(+)f Fn(E)1971 4542 y Fv(j)p Fj(z)s Fv(j)2050 4580 y Fr(\()p Fn(r)m(;)15 b(z)t Fr(\)\))p Fm(j)-15 b(j)p Fr(\011)2385 4542 y Fj(v)2421 4512 y Fq(\000)p Fd(1)2419 4553 y Ff(\013)2507 4542 y Fj(e)2540 4551 y Fd(1)2574 4542 y Fj(;u)2635 4512 y Fq(\000)p Fd(1)2635 4553 y Ff(\013)2717 4542 y Fj(e)2750 4551 y Fd(2)2784 4542 y Fj(;v)2838 4550 y Ff(\013)2385 4602 y Fj(\017)2887 4580 y Fm(j)g(j)2922 4542 y Fl(2)2922 4608 y Fj(L)2970 4589 y Fd(2)1740 4784 y Fr(+)1841 4723 y Fn(\017)1878 4690 y Fl(2)1917 4723 y Fn(b)p 1841 4763 116 4 v 1876 4847 a Fr(2)1986 4784 y(+)2094 4723 y Fn(\017a)p 2087 4763 98 4 v 2087 4847 a(\013)2145 4820 y Fl(3)2215 4784 y Fr(+)20 b Fn(O)2393 4683 y Fg(\020)2488 4723 y Fn(\017)p 2458 4763 V 2458 4847 a(\013)2516 4820 y Fl(4)2565 4683 y Fg(\021)2640 4784 y Fr(+)g Fn(O)2818 4656 y Fg(\022)2895 4723 y Fn(\017)2932 4690 y Fl(2)p 2895 4763 77 4 v 2904 4847 a Fn(\013)2981 4656 y Fg(\023)3063 4784 y Fn(:)183 5039 y Fr(where)1230 5185 y Fn(a)25 b Fr(=)1409 5124 y Fn(z)1455 5091 y Fv(0)1478 5124 y Fm(j)p Fn(z)t Fm(jD)s Fr(\()p Fn(e)1724 5138 y Fl(1)1765 5124 y Fn(;)15 b(e)1847 5138 y Fl(2)1887 5124 y Fr(\))p 1409 5164 514 4 v 1643 5247 a(2)1958 5185 y Fm(6)p Fr(=)25 b(0)p Fn(;)721 5403 y(b)g Fr(=)g Fm(Q)955 5417 y Fl(1)995 5403 y Fr(\()p Fn(e)1072 5417 y Fl(1)1112 5403 y Fr(\))p Fm(j)-15 b(j)p Fr(\()p Fn(e)1259 5417 y Fl(2)1320 5403 y Fm(\001)21 b(r)p Fr(\))p Fn(\036)1531 5417 y Fl(2)1570 5403 y Fm(j)-15 b(j)1605 5366 y Fl(2)1605 5431 y Fj(L)1653 5412 y Fd(2)1713 5403 y Fr(+)20 b Fn(\025)1857 5417 y Fl(2)1896 5403 y Fm(j)-15 b(j)p Fr(\()p Fn(e)2008 5417 y Fl(1)2069 5403 y Fm(\001)20 b(r)p Fr(\))p Fn(\036)2279 5417 y Fl(1)2319 5403 y Fm(j)-15 b(j)2354 5366 y Fl(2)2354 5431 y Fj(L)2402 5412 y Fd(2)2466 5403 y Fm(\025)25 b Fr(0)p Fn(;)1632 5652 y Fr(11)p eop end %%Page: 12 12 TeXDict begin 12 11 bop 581 548 a Fr(whic)m(h)26 b(are)h(indep)s(enden) m(t)f(on)g Fn(u)1671 562 y Fj(\013)1747 548 y Fr(and)g Fn(v)1964 562 y Fj(\013)2014 548 y Fr(.)39 b(If)26 b Fn(b)f(>)g Fr(0,)j(w)m(e)f(optimize)h(the)f(real)g(function)581 661 y Fn(\017)e Fm(7!)769 625 y Fj(\017)798 602 y Fd(2)833 625 y Fj(b)p 769 640 94 4 v 798 692 a Fl(2)893 661 y Fr(+)1001 625 y Fj(\017a)p 994 640 80 4 v 994 695 a(\013)1039 676 y Fd(3)1114 661 y Fr(and)30 b(c)m(ho)s(ose,)h(for)g Fn(\013)f Fr(large)i(enough,)e Fn(\017)25 b Fr(=)g Fm(\000)2668 625 y Fj(a)p 2632 640 111 4 v 2632 695 a(b\013)2707 676 y Fd(3)2782 661 y Fr(to)31 b(obtain)646 899 y Fm(E)702 862 y Fj(N)770 899 y Fr(\()p Fn(\013;)15 b(u)955 913 y Fj(\013)1005 899 y Fn(;)g Fr(\011)1116 855 y Fj(v)1152 825 y Fq(\000)p Fd(1)1150 866 y Ff(\013)1236 855 y Fj(e)1269 864 y Fd(1)1303 855 y Fj(;u)1364 825 y Fq(\000)p Fd(1)1364 866 y Ff(\013)1446 855 y Fj(e)1479 864 y Fd(2)1513 855 y Fj(;v)1567 863 y Ff(\013)1116 934 y Fv(\000)p Fj(a=)p Fl(\()p Fj(b\013)1345 915 y Fd(3)1382 934 y Fl(\))1616 899 y Fr(\))83 b(=)g(\()p Fn(E)1995 862 y Fj(z)2031 838 y Fq(0)2058 899 y Fr(\(0)p Fn(;)15 b(z)2224 862 y Fv(0)2248 899 y Fr(\))21 b(+)f Fn(E)2467 862 y Fv(j)p Fj(z)s Fv(j)2546 899 y Fr(\()p Fn(r)m(;)15 b(z)t Fr(\)\))p Fm(j)-15 b(j)p Fr(\011)2881 855 y Fj(v)2917 825 y Fq(\000)p Fd(1)2915 866 y Ff(\013)3003 855 y Fj(e)3036 864 y Fd(1)3070 855 y Fj(;u)3131 825 y Fq(\000)p Fd(1)3131 866 y Ff(\013)3213 855 y Fj(e)3246 864 y Fd(2)3281 855 y Fj(;v)3335 863 y Ff(\013)2881 934 y Fv(\000)p Fj(a=)p Fl(\()p Fj(b\013)3110 915 y Fd(3)3149 934 y Fl(\))3383 899 y Fm(j)g(j)3418 862 y Fl(2)3418 927 y Fj(L)3466 909 y Fd(2)1979 1121 y Fm(\000)2107 1059 y Fn(a)2155 1026 y Fl(2)p 2060 1100 183 4 v 2060 1183 a Fr(2)p Fn(b\013)2202 1157 y Fl(6)2272 1121 y Fr(+)20 b Fn(O)2450 993 y Fg(\022)2553 1059 y Fr(1)p 2527 1100 98 4 v 2527 1183 a Fn(\013)2585 1157 y Fl(7)2635 993 y Fg(\023)2717 1121 y Fn(:)581 1382 y Fr(If)38 b Fn(b)g Fr(=)g(0,)j(w)m(e)e(c)m(ho)s(ose)g(for)f(instance)h Fn(\017)f Fr(=)h Fm(\000)p Fn(a=\013)2331 1349 y Fl(3)2409 1382 y Fr(and)e(obtain)i(the)g(same)f(t)m(yp)s(e)h(of)581 1495 y(result.)i(This)29 b(ends)h(the)h(pro)s(of)e(of)i(Theorem)f(2)h (since)990 1710 y Fm(j)-15 b(j)p Fr(\011)1096 1673 y Fj(v)1132 1643 y Fq(\000)p Fd(1)1130 1683 y Ff(\013)1215 1673 y Fj(e)1248 1682 y Fd(1)1283 1673 y Fj(;u)1344 1643 y Fq(\000)p Fd(1)1344 1683 y Ff(\013)1426 1673 y Fj(e)1459 1682 y Fd(2)1493 1673 y Fj(;v)1547 1681 y Ff(\013)1096 1733 y Fj(\017)1595 1710 y Fm(j)g(j)1630 1673 y Fl(2)1630 1738 y Fj(L)1678 1720 y Fd(2)1743 1710 y Fr(=)25 b(1)20 b(+)g Fn(\017)2032 1673 y Fl(2)2071 1710 y Fm(j)-15 b(j)p Fr(\()p Fn(e)2183 1724 y Fl(1)2244 1710 y Fm(\001)21 b(r)p Fr(\))p Fn(\036)2455 1724 y Fl(1)2494 1710 y Fm(j)-15 b(j)2529 1673 y Fl(2)2529 1738 y Fj(L)2577 1720 y Fd(2)2616 1710 y Fm(j)g(j)p Fr(\()p Fn(e)2728 1724 y Fl(2)2789 1710 y Fm(\001)20 b(r)p Fr(\))p Fn(\036)2999 1724 y Fl(2)3039 1710 y Fm(j)-15 b(j)3074 1673 y Fl(2)3074 1738 y Fj(L)3122 1720 y Fd(2)581 1914 y Fr(and)30 b(therefore)631 2180 y Fm(E)687 2143 y Fj(N)769 2025 y Fg( )841 2180 y Fn(\013;)15 b(u)991 2194 y Fj(\013)1042 2180 y Fn(;)1171 2119 y Fr(\011)1242 2074 y Fj(v)1278 2045 y Fq(\000)p Fd(1)1276 2085 y Ff(\013)1361 2074 y Fj(e)1394 2083 y Fd(1)1428 2074 y Fj(;u)1489 2045 y Fq(\000)p Fd(1)1489 2085 y Ff(\013)1571 2074 y Fj(e)1604 2083 y Fd(2)1638 2074 y Fj(;v)1692 2082 y Ff(\013)1242 2130 y Fj(\017)p 1092 2159 728 4 v 1092 2276 a Fm(j)-15 b(j)p Fr(\011)1198 2232 y Fj(v)1234 2202 y Fq(\000)p Fd(1)1232 2243 y Ff(\013)1317 2232 y Fj(e)1350 2241 y Fd(1)1385 2232 y Fj(;u)1446 2202 y Fq(\000)p Fd(1)1446 2243 y Ff(\013)1528 2232 y Fj(e)1561 2241 y Fd(2)1595 2232 y Fj(;v)1649 2240 y Ff(\013)1198 2288 y Fj(\017)1697 2276 y Fm(j)g(j)1732 2296 y Fj(L)1780 2277 y Fd(2)1829 2025 y Fg(!)1927 2180 y Fr(=)25 b Fn(E)2095 2143 y Fj(z)2131 2119 y Fq(0)2157 2180 y Fr(\(0)p Fn(;)15 b(z)2323 2143 y Fv(0)2348 2180 y Fr(\))20 b(+)g Fn(E)2566 2143 y Fv(j)p Fj(z)s Fv(j)2646 2180 y Fr(\()p Fn(r)m(;)15 b(z)t Fr(\))22 b Fm(\000)2976 2119 y Fn(C)p 2963 2159 98 4 v 2963 2242 a(\013)3021 2216 y Fl(6)3091 2180 y Fr(+)e Fn(O)3269 2052 y Fg(\022)3372 2119 y Fr(1)p 3346 2159 V 3346 2242 a Fn(\013)3404 2216 y Fl(7)3453 2052 y Fg(\023)581 2473 y Fr(with)30 b Fn(C)i Fr(=)25 b Fn(a)1029 2440 y Fl(2)1068 2473 y Fn(=)p Fr(\(2)p Fn(b)p Fr(\))i Fn(>)e Fr(0)31 b(if)f Fn(b)c(>)f Fr(0)30 b(and)g Fn(C)i Fr(=)25 b Fn(a)2203 2440 y Fl(2)2268 2473 y Fn(>)f Fr(0)31 b(if)g Fn(b)25 b Fr(=)g(0.)p 3504 2473 4 62 v 3508 2415 55 4 v 3508 2473 V 3562 2473 4 62 v 581 2760 a Fs(References)627 2963 y Fr([1])46 b(A.)g(Am)m(brosetti,)k(P)-8 b(.H.)46 b(Rabino)m(witz.)h(Dual)e(v)-5 b(ariation)47 b(metho)s(ds)d(in)h (critical)768 3076 y(p)s(oin)m(t)30 b(theory)h(and)f(applications.)i Fe(J.)g(F)-7 b(unct.)32 b(A)n(nal.)p Fr(,)f(14:)41 b(349{381,)34 b(1973.)627 3263 y([2])46 b(A.)27 b(Bahri.)g Fe(Critic)-5 b(al)30 b(Points)f(at)h(In\014nity)g(in)e(some)i(V)-7 b(ariational)31 b(Pr)-5 b(oblems)p Fr(.)28 b(Pit-)768 3376 y(man)40 b(Researc)m(h)h(Notes)g(in)f(Mathematics)i(Series,)g (182.)g(Longman)e(Scien)m(ti\014c)768 3489 y(and)30 b(T)-8 b(ec)m(hnical)32 b(Ed.,)e(1989.)627 3676 y([3])46 b(G.)40 b(F)-8 b(ang,)43 b(N.)d(Ghoussoub.)f(Morse-t)m(yp)s(e)h(information)g (on)g(P)m(alais-Smale)h(se-)768 3789 y(quences)31 b(obtained)h(b)m(y)f (min-max)g(principles.)g Fe(Manuscripta)k(Math.)p Fr(,)d(75)g(:)43 b(81{)768 3902 y(95,)31 b(1992.)627 4089 y([4])46 b(J.)31 b(B.)h(F)-8 b(oresman,)33 b(A.)f(F)-8 b(risc)m(h.)33 b Fe(Exploring)h(Chemistry)h(with)g(Ele)-5 b(ctr)g(onic)34 b(Struc-)768 4202 y(tur)-5 b(e)33 b(Metho)-5 b(ds)p Fr(,)32 b(Gaussian)f(Inc,)f(1996.)i(Chapter)e(3)h(and)f(references)g(therein.) 627 4389 y([5])46 b(N.)34 b(Ghoussoub.)f Fe(Duality)j(and)h(p)-5 b(erturb)g(ation)38 b(metho)-5 b(ds)38 b(in)d(critic)-5 b(al)37 b(p)-5 b(oint)37 b(the-)768 4502 y(ory.)31 b Fr(Cam)m(bridge)g(Univ)m(ersit)m(y)g(Press,)f(1993.)627 4690 y([6])46 b(M.)57 b(Lewin.)f(A)h(Moun)m(tain)g(P)m(ass)g(for)g (Reacting)h(Molecules.)g Fe(A)n(nn.)e(Henri)768 4803 y(Poinc)-5 b(ar)n(\023)-44 b(e)p Fr(,)31 b(5:)42 b(477{521,)33 b(2004.)627 4990 y([7])46 b(E.)29 b(H.)h(Lieb,)f(W.)h(E.)f(Thirring.)f (Univ)m(ersal)i(Nature)f(of)h(V)-8 b(an)29 b(Der)h(W)-8 b(aals)30 b(F)-8 b(orces)768 5103 y(for)30 b(Coulom)m(b)h(Systems.)f Fe(Phys.)j(R)-5 b(ev.)32 b(A)p Fr(,)e(34)i(:)40 b(40{46,)33 b(1986.)627 5290 y([8])46 b(A.)21 b(J.)g(O'Connor.)f(Exp)s(onen)m(tial) h(deca)m(y)h(of)f(b)s(ound)d(state)23 b(w)m(a)m(v)m(e)f(functions,)h Fe(Com-)768 5403 y(mun.)33 b(Math.)g(Phys.)p Fr(,)e(32:)41 b(319{340,)34 b(1973.)2030 5652 y(12)p eop end %%Page: 13 13 TeXDict begin 13 12 bop 228 548 a Fr([9])47 b(P)-8 b(.K.)29 b(P)m(earson,)h(H.F.)g(Sc)m(haefer)f(I)s(I)s(I,)e(U.)j(W)-8 b(ahlgren.)30 b(P)m(oten)m(tial)h(energy)e(surface)370 661 y(for)39 b(the)i(mo)s(del)f(unimolecular)g(reaction)i(HNC)e Fm(!)g Fr(HCN.)h Fe(J.)g(Chem.)h(Phys.)p Fr(:)370 774 y(62\(2\),)32 b(350{354,)i(1975.)183 961 y([10])47 b(H.)32 b(B.)h(Sc)m(hlegel.)i(In)c 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