Content-Type: multipart/mixed; boundary="-------------0709210629392" This is a multi-part message in MIME format. ---------------0709210629392 Content-Type: text/plain; name="07-216.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="07-216.keywords" WIBG, Bose-Einstein condensation, Kac distribution, large deviations, equivalence of ensembles. ---------------0709210629392 Content-Type: application/postscript; name="Bru_Zagrebnov-bis.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Bru_Zagrebnov-bis.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.96 Copyright 2007 Radical Eye Software %%Title: Bru_Zagrebnov-bis.dvi %%CreationDate: Fri Sep 21 13:27:10 2007 %%Pages: 15 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: CMCSC10 CMR10 CMBX12 CMMI7 CMTI10 CMBX9 CMR9 CMBX10 %%+ CMMI10 CMSY10 CMSY7 CMR7 CMR5 MSBM10 CMEX10 CMSY5 CMSY6 CMR8 CMMI8 %%+ CMR6 CMMI5 MSBM7 CMMI6 CMSY8 MSAM10 MSBM5 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: DVIPS.EXE -P pdf Bru_Zagrebnov-bis %DVIPSParameters: dpi=8000 %DVIPSSource: TeX output 2007.09.21:1327 %%BeginProcSet: tex.pro 0 0 %! /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/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]{Ci}imagemask restore}B/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: alt-rule.pro 0 0 %! % Patch by TVZ % Makes dvips files draw rules with stroke rather than fill. % Makes narrow rules more predictable at low resolutions % after distilling to PDF. % May have unknown consequences for very thick rules. % Tested only with dvips 5.85(k). 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C147076537A22FB801CBF0A341B3806C4040487E572D 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM5 %!PS-AdobeFont-1.1: MSBM5 2.1 %%CreationDate: 1992 Oct 17 08:36:07 % 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 (MSBM5) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM5 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 readonly def /FontBBox{0 -574 3027 1074}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % 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 (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 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 3 /square put readonly def /FontBBox{8 -463 1331 1003}readonly def currentdict end currentfile eexec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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 3 /bracketrightbig put dup 8 /braceleftbig put dup 9 /bracerightbig put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 28 /angbracketleftbigg put dup 29 /angbracketrightbigg put dup 40 /braceleftBigg put dup 41 /bracerightBigg put dup 56 /bracelefttp put dup 57 /bracerighttp put dup 58 /braceleftbt put dup 59 /bracerightbt put dup 60 /braceleftmid put dup 61 /bracerightmid put dup 62 /braceex put dup 77 /circleplusdisplay put dup 80 /summationtext put dup 82 /integraltext put dup 88 /summationdisplay put dup 89 /productdisplay put dup 90 /integraldisplay put dup 110 /braceleftBig put dup 111 /bracerightBig put dup 112 /radicalbig put readonly def /FontBBox{-24 -2960 1454 772}readonly def currentdict end currentfile eexec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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. 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 33 /arrowright put readonly def /FontBBox{-30 -955 1185 779}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % 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 (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 39 /phi1 put dup 105 /i put dup 107 /k put readonly def /FontBBox{11 -250 1241 750}readonly 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 currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % 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 (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 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 21 /lambda put dup 26 /rho put dup 59 /comma put dup 66 /B put dup 83 /S put dup 86 /V put dup 99 /c put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 121 /y put readonly def /FontBBox{37 -250 1349 750}readonly 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 3 /Lambda put dup 48 /zero put readonly def /FontBBox{-20 -250 1193 750}readonly 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 31 /chi put dup 34 /epsilon put dup 58 /period put dup 97 /a put dup 101 /e put dup 120 /x put readonly def /FontBBox{-24 -250 1110 750}readonly 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 3 /Lambda put dup 40 /parenleft put dup 41 /parenright put dup 48 /zero put dup 61 /equal put dup 67 /C put dup 72 /H put dup 82 /R 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 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 119 /w put dup 120 /x put readonly def /FontBBox{-36 -250 1070 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 3 /asteriskmath put dup 121 /dagger put dup 122 /daggerdbl put readonly def /FontBBox{-4 -948 1329 786}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % 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 (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 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 dup 49 /infinity put dup 54 /negationslash put dup 67 /C put readonly def /FontBBox{21 -944 1448 791}readonly 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 68 /D put dup 75 /K put dup 76 /L put dup 80 /P put dup 82 /R put dup 90 /Z put dup 126 /planckover2pi1 put readonly def /FontBBox{-55 -420 2343 920}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % 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 (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 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 3 /Lambda put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 61 /equal put dup 91 /bracketleft put dup 93 /bracketright put readonly def /FontBBox{-341 -250 1304 965}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % 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 (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 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 3 /Lambda put dup 22 /macron 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 61 /equal put dup 73 /I put dup 82 /R put dup 91 /bracketleft put dup 93 /bracketright put dup 94 /circumflex put dup 100 /d put dup 109 /m put dup 112 /p put dup 115 /s put dup 117 /u put dup 121 /y put dup 126 /tilde put readonly def /FontBBox{-27 -250 1122 750}readonly def currentdict end currentfile eexec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%%CreationDate: 1991 Aug 15 07:21:52 % 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 (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 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 10 /circlemultiply put dup 20 /lessequal put dup 21 /greaterequal put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 63 /perpendicular put dup 65 /A put dup 66 /B put dup 67 /C put dup 70 /F put dup 71 /G put dup 72 /H put dup 88 /X 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 121 /dagger put dup 122 /daggerdbl put readonly def /FontBBox{-15 -951 1252 782}readonly def currentdict end 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%%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 6 /plusminus put dup 10 /circlemultiply put dup 20 /lessequal put dup 21 /greaterequal put dup 25 /approxequal put dup 26 /propersubset put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 65 /A put dup 66 /B put dup 67 /C put dup 70 /F put dup 71 /G put dup 72 /H put dup 77 /M put dup 79 /O put dup 88 /X put dup 91 /union put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 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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 12 /beta put dup 13 /gamma put dup 14 /delta put dup 18 /theta put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 31 /chi put dup 32 /psi put dup 34 /epsilon put dup 39 /phi1 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 69 /E put dup 72 /H put dup 76 /L put dup 77 /M put dup 78 /N put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 97 /a put dup 99 /c put dup 101 /e put dup 102 /f put dup 105 /i put dup 107 /k put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 116 /t put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-32 -250 1048 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 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 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 71 /G put dup 72 /H put dup 75 /K put dup 76 /L put dup 82 /R put dup 83 /S put dup 84 /T 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 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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 12 /fi put dup 13 /fl put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 65 /A put dup 66 /B put dup 71 /G put dup 73 /I put dup 75 /K put dup 84 /T 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 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 121 /y put readonly def /FontBBox{-39 -250 1036 750}readonly def currentdict end currentfile eexec 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX9 %!PS-AdobeFont-1.1: CMBX9 1.0 %%CreationDate: 1991 Aug 20 16:36:25 % 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 (CMBX9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX9 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 65 /A put dup 97 /a put dup 98 /b put dup 99 /c put dup 114 /r put dup 115 /s put dup 116 /t put readonly def /FontBBox{-58 -250 1195 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F0364CD5660F74BEE96790DE35AFA90CCF712 B1805DA88AE375A04D99598EADFC625BDC1F9C315B6CF28C9BD427F32C745C99 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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 37 /percent put dup 40 /parenleft put dup 41 /parenright 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 65 /A put dup 66 /B put dup 67 /C put dup 68 /D 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 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 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 127 /dieresis put readonly def /FontBBox{-163 -250 1146 969}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E3948FFB0B4E70F212EC976D65099D84E0D37A7A771C3101D6AD26A0513378F 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cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % 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 (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 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 12 /beta put dup 13 /gamma put dup 18 /theta put dup 21 /lambda put dup 22 /mu put dup 25 /pi put dup 26 /rho put dup 32 /psi put dup 34 /epsilon put dup 59 /comma put dup 61 /slash put dup 62 /greater put dup 66 /B put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 77 /M put dup 78 /N put dup 83 /S put dup 86 /V put dup 97 /a put dup 98 /b put dup 99 /c put dup 102 /f put dup 105 /i put dup 106 /j 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 116 /t put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{0 -250 1171 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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. 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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 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 19 /acute put dup 22 /macron put dup 33 /exclam put dup 34 /quotedblright 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 47 /slash 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 63 /question 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 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex 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 106 /j 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 126 /tilde put readonly def /FontBBox{-251 -250 1009 969}readonly def currentdict end currentfile eexec 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741 1[785 16[1063 82[{}7 1328.35 /CMCSC10 rf /Fb 188[400 67[{}1 553.48 /MSBM5 rf /Fc 252[861 3[{}1 1106.96 /MSAM10 rf /Fd 173[430 54[668 668 26[{}3 774.872 /CMEX10 rf /Fe 222[941 33[{}1 885.568 /CMSY8 rf /Ff 148[439 1[296 65[539 39[{}3 664.176 /CMMI6 rf /Fg 173[560 14[560 67[{}2 774.872 /MSBM7 rf /Fh 134[404 10[488 680 1[420 326 6[359 12[458 2[474 16[574 6[254 32[402 4[465 21[{}12 553.48 /CMMI5 rf /Fi 207[406 44[552 3[{}2 664.176 /CMR6 rf /Fj 135[530 18[436 3[500 38[261 23[434 2[584 31[{}6 885.568 /CMMI8 rf /Fk 135[497 680 1[523 366 371 367 2[470 523 784 261 2[261 523 470 288 418 523 418 523 470 14[692 9[705 4[680 5[732 12[470 6[366 366 36[653 3[{}27 885.568 /CMR8 rf /Fl 133[381 381 117[424 3[{}3 664.176 /CMSY6 rf /Fm 188[433 12[0 4[753 244 44[407 2[600{}6 553.48 /CMSY5 rf /Fn 143[1107 738 738 19[615 1414 1599 5[523 1[1168 2[1673 14[984 984 984 984 984 984 984 14[892 892 10[830 830 830 830 6[815 815 661 661 6[646 646 4[461 1[507 507{}31 1106.96 /CMEX10 rf /Fo 129[598 35[738 7[799 1[676 3[738 861 6[799 799 67[{}8 1106.96 /MSBM10 rf /Fp 162[223 1[223 29[569 9[377 377 377 377 4[569 39[504 3[{}9 553.48 /CMR5 rf /Fq 129[441 4[465 3[489 1[351 2[489 2[727 8[489 5[441 251 1[251 8[643 8[320 11[680 8[441 441 441 441 441 4[680 1[346 346 17[441 18[606 3[{}23 774.872 /CMR7 rf /Fr 133[406 406 10[454 3[263 358 358 454 454 13[635 15[758 534 634 2[481 584 711 1[692 8[0 3[597 882 255 14[882 11[692 692 9[692 6[454 1[263 692{}27 774.872 /CMSY7 rf /Fs 143[922 1[553 3[307 430 430 553 553 9[738 738 2[790 8[881 1[1329 4[935 658 796 2[583 727 884 10[0 3[738 1107 13[553 553 1107 6[861 861 3[861 861 9[861 3[861 3[861 307 861{}33 1106.96 /CMSY10 rf /Ft 133[515 543 633 3[400 3[557 537 664 972 1[576 1[381 2[542 515 1[479 1[585 8[917 1045 646 756 6[889 1074 753 3[920 2[817 2[840 1[588 1[861 553 861 307 307 18[724 4[516 1[721 693 4[572 631 484 547 667 646 638 1[520 3[492 573 626 708 11[{}46 1106.96 /CMMI10 rf /Fu 133[566 672 672 919 672 707 495 502 524 1[707 636 707 1061 354 672 1[354 707 636 389 583 707 566 707 619 3[354 1[354 6[886 707 955 5[766 998 2[996 1001 2[976 919 906 962 6[354 636 636 636 636 636 636 636 636 636 636 1[354 424 354 2[495 495 27[707 12[{}54 1106.96 /CMBX10 rf /Fv 134[540 1[740 540 569 398 404 401 1[569 512 569 853 284 540 1[284 569 512 313 455 569 455 569 512 9[1052 2[740 8[796 1[370 1[803 4[725 768 18[284 341 284 2[398 398 26[569 569 12[{}36 996.264 /CMR9 rf /Fw 139[458 465 486 14[524 655 573 31[890 65[{}7 996.264 /CMBX9 rf /Fx 128[566 4[453 537 514 736 509 594 368 453 467 509 566 566 622 905 283 509 1[339 566 509 339 509 566 509 509 566 9[1106 823 823 792 622 807 849 751 849 1[993 694 851 581 427 823 856 723 1[836 792 779 823 6[339 566 566 566 566 566 566 566 566 566 566 1[339 396 339 2[453 453 2[905 17[566 6[622 12[{}66 1106.96 /CMTI10 rf /Fy 133[423 449 502 3[334 3[456 437 547 786 280 471 366 313 2[432 2[396 389 480 10[523 2[544 4[701 844 4[725 1[561 650 724 1[669 3[692 454 1[263 24[418 1[586 5[459 518 2[538 525 2[422 4[465 502 575 11[{}38 774.872 /CMMI7 rf /Fz 134[946 2[946 996 697 707 732 1[996 897 996 1494 498 946 1[498 996 897 548 818 1[797 996 872 9[1852 3[996 6[1077 2[668 1[1410 2[1374 1[1275 66[{}27 1594.02 /CMBX12 rf /FA 129[553 3[492 584 584 799 584 615 430 437 434 584 615 553 615 922 307 584 338 307 615 553 338 492 615 492 615 553 2[553 307 553 307 676 830 1[1138 830 830 799 615 815 861 753 861 830 1015 692 861 569 400 830 869 723 753 846 799 784 830 1[523 1[861 1[307 307 553 553 553 553 553 553 553 553 553 553 553 307 369 307 861 1[430 430 307 4[553 307 10[553 2[553 4[922 615 615 646 799 861 799 4[769 861 922 1[{}92 1106.96 /CMR10 rf /FB 133[556 679 679 1[679 679 654 507 667 1[617 704 679 827 568 704 1[335 679 710 593 617 691 654 642 679 6[741 2[1224 901 1[870 676 2[821 3[756 933 627 449 1[942 2[918 1[853 901 6[354 4[612 612 612 612 612 2[354 418 45[{}45 1106.96 /CMCSC10 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 8000dpi TeXDict begin %%PaperSize: A4 end %%EndSetup %%Page: 1 1 TeXDict begin 1 0 bop Black 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b(y)435 b(at)f(the)h(phase)g(transition)g(p)28 b(oin)-28 b(t)1193 24535 y(disapp)28 b(ears)322 b(as)g(a)h(function)f (of)h(the)f(particle)i(densit)-28 b(y)-85 b(.)449 b(Indeed,)327 b(the)c(Bose)g(condensate)g(con)-28 b(tin)g(uously)322 b(starts)g(at)h(the)g(\014rst)1193 25813 y(critical)449 b(particle)g(densit)-28 b(y)449 b(and)f(progressiv)-28 b(ely)449 b(gro)-28 b(ws)446 b(but)i(the)h(free-energy)h(p)28 b(er)448 b(particle)h(sta)-28 b(ys)448 b(constan)-28 b(t)448 b(un)-28 b(til)449 b(the)1193 27092 y(second)388 b(critical)h(densit)-28 b(y)388 b(is)g(reac)-28 b(hed.)595 b(A)-28 b(t)388 b(higher)g(particle)h(densities,)401 b(the)388 b(Bose)h(condensate)f(densit)-28 b(y)389 b(as)f(w)-28 b(ell)388 b(as)g(the)1193 28370 y(free-energy)342 b(p)28 b(er)342 b(particle)g(b)28 b(oth)342 b(increase)g(monotonously.)-1575 32385 y Fu(Keyw)-35 b(ords)370 b FA(:)492 b(WIBG,)368 b(Bose-Einstein)j(condensation,)g(Kac)e(distribution,)i(large)e (deviations,)j(equiv)-61 b(alence)369 b(of)h(ensem)-31 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y(that)6712 15885 y Ft(p)7269 15428 y Fy(S)42 b(B)7269 16159 y Fq(\003)8617 15885 y FA(\()p Ft(\014)58 b(;)184 b(\026)p FA(\))310 b(=)13441 15136 y(1)p 12930 15630 V 12930 16644 a Ft(\014)58 b(V)14824 15885 y FA(ln)16399 15136 y(1)p 16063 15630 1225 45 v 16063 16644 a(2)p Ft(\031)17728 14378 y Fn(Z)18002 17556 y Fg(C)19142 15885 y FA(T)-92 b(r)20283 16078 y Fr(F)20995 15811 y Fm(0)20917 16338 y Fp(\003)21717 15885 y Fs(f)p Ft(W)23315 16051 y Fq(\003)24161 15885 y FA(\()q Ft(c)p FA(\))p Fs(g)185 b FA(d)26854 15428 y Fq(2)27351 15885 y Ft(c)307 b FA(=)29950 15136 y(1)p 29439 15630 1577 45 v 29439 16644 a Ft(\014)58 b(V)31332 15885 y FA(ln)32907 15136 y(1)p 32572 15630 1225 45 v 32572 16644 a(2)p Ft(\031)34237 14378 y Fn(Z)34510 17556 y Fg(C)35651 15885 y Ft(e)36166 15428 y Fy(\014)40 b(V)191 b(p)37878 15094 y Fh(S)28 b(B)37878 15649 y Fp(\003)39035 15428 y Fq(\()p Fy(\014)40 b(;\026;c)p Fq(\))41784 15885 y FA(d)42399 15428 y Fq(2)42895 15885 y Ft(c;)6012 b FA(\(3.3\))-1575 19543 y(where)440 b(d)2312 19141 y Fq(2)2809 19543 y Ft(c)426 b FA(:=)g Ft(V)246 b(\031)6871 19141 y Fr(\000)p Fq(1)8059 19543 y FA(d)p Ft(c)9153 19709 y Fq(1)9650 19543 y FA(d)p Ft(c)10744 19709 y Fq(2)11681 19543 y FA(with)441 b Ft(c)426 b FA(:=)h Ft(c)17252 19709 y Fq(1)18042 19543 y FA(+)293 b Ft(ic)20056 19709 y Fq(2)20553 19543 y FA(,)458 b Ft(W)22363 19709 y Fq(\003)23025 19543 y FA(\()p Ft(c)p FA(\))441 b(results)f(from)h(the)f(Bogoliub)31 b(o)-31 b(v)444 b(appro)-31 b(ximation)444 b(\(3.1\))e(of)f(the)-1575 20938 y(statistical)372 b(op)31 b(erator)370 b Ft(W)8990 21104 y Fq(\003)9652 20938 y Ft(;)f FA(and)16492 22925 y Ft(p)17049 22468 y Fy(S)42 b(B)17049 23199 y Fq(\003)18397 22925 y FA(\()p Ft(\014)58 b(;)184 b(\026;)g(c)p FA(\))311 b(:=)24500 22176 y(1)p 23989 22671 1577 45 v 23989 23685 a Ft(\014)58 b(V)25882 22925 y FA(ln)185 b(T)-92 b(r)28130 23118 y Fr(F)28842 22852 y Fm(0)28764 23378 y Fp(\003)29564 22925 y Fs(f)p Ft(W)31162 23091 y Fq(\003)32008 22925 y FA(\()q Ft(c)p FA(\))p Fs(g)15792 b FA(\(3.4\))-1575 25643 y(is)393 b(the)h(pressure)d(de\014ned)j(b)-31 b(y)393 b(the)h(partial)h(trace.)565 b(F)-92 b(or)393 b(an)-31 b(y)394 b Ft(\032)348 b(>)g FA(0,)400 b(the)393 b(corresp)31 b(onding)394 b(distribution)h Fo(D)43481 25809 y Fq(\003)p Fy(;\026)45337 25643 y FA(related)f(to)g(the)-1575 27038 y(Bose)369 b(condensate)h(n)-31 b(um)g(b)31 b(er)370 b(densit)-31 b(y)-92 b(,)370 b(is)f(no)-31 b(w)370 b(de\014ned)f(on)g (the)h(Borel)f(subsets)g Fs(A)g FA(of)g Fo(C)h FA(b)-31 b(y)13628 30111 y Fo(D)14427 30277 y Fq(\003)p Fy(;\026)16075 30111 y FA([)p Fs(A)p FA(])308 b(:=)g Ft(e)19872 29654 y Fr(\000)p Fy(\014)40 b(V)190 b(p)22275 29319 y Fh(S)28 b(B)22275 29875 y Fp(\003)23433 29654 y Fq(\()p Fy(\014)40 b(;\026)p Fq(\))25991 29362 y FA(1)p 25656 29856 1225 45 v 25656 30870 a(2)p Ft(\031)27320 28604 y Fn(Z)27518 31778 y Fr(A)28735 30111 y Ft(e)29250 29654 y Fy(\014)g(V)190 b(p)30961 29319 y Fh(S)28 b(B)30961 29875 y Fp(\003)32119 29654 y Fq(\()p Fy(\014)40 b(;\026;c)p Fq(\))34867 30111 y FA(d)35482 29654 y Fq(2)35979 30111 y Ft(c:)12928 b FA(\(3.5\))-1575 34069 y(Then,)425 b(at)413 b(\014xed)g(particle)h (densit)-31 b(y)414 b Ft(\032)381 b(>)f FA(0,)425 b(w)-31 b(e)413 b(express)f(a)h(large)h(deviations)h(principle)e(\(Section)i (5.2\))f(for)f(the)h(condensate)-1575 35464 y(distribution)371 b Fo(D)5260 35630 y Fq(\003)p Fy(;\032)6951 35464 y FA(:=)308 b Fo(D)9226 35630 y Fq(\003)p Fy(;\026)10633 35741 y Fp(\003)p Fh(;\032)11904 35464 y FA(.)p Black -1575 38633 a Fu(Theorem)426 b(3.1)f(\(LD)f(principle)g(for)h(the)h(condensate)g (distribution)f(at)f(a)g(\014xed)h(densit)-35 b(y)425 b Ft(\032)p Fu(\))p Black -1575 40028 a Fx(The)396 b(se)-57 b(quenc)g(e)398 b Fs(f)p Fo(D)6538 40194 y Fq(\003)p Fy(;\032)7922 40028 y Fs(g)f Fx(satis\014es)e(a)h(lar)-57 b(ge)397 b(deviation)f(principle)h(with)f(sp)-57 b(e)g(e)g(d)397 b Ft(\014)58 b(V)642 b Fx(and)396 b(r)-57 b(ate)396 b(function)6667 43345 y FA(D)7513 43511 y Fy(\032)8212 43345 y FA(\()p Ft(x)p FA(\))308 b(:=)181 b(inf)11181 44061 y Fy(\013)p Fr(\024)p Fq(0)13198 41784 y Fn(\032)14028 43345 y Ft(p)14585 42888 y Fy(B)14585 43619 y Fq(0)15347 43345 y FA(\()p Ft(\014)58 b(;)184 b(\013)t(;)g(x)18788 43511 y Fy(\032)19305 43345 y FA(\))247 b(+)21221 42596 y(\()p Ft(\026)22318 42762 y Fy(\032)23080 42596 y Fs(\000)e Ft(\013)t FA(\))25328 42194 y Fq(2)p 21221 43090 4605 45 v 22676 44104 a FA(2)p Ft(\025)23875 44270 y Fq(0)25959 41784 y Fn(\033)26973 43345 y Fs(\000)489 b FA(inf)28142 44061 y Fy(\013)p Fr(\024)p Fq(0)30158 41784 y Fn(\032)30988 43345 y Ft(p)31545 42888 y Fy(B)31545 43619 y Fq(0)32307 43345 y FA(\()p Ft(\014)58 b(;)184 b(\013)t(;)g(x)p FA(\))249 b(+)37667 42596 y(\()p Ft(\026)38764 42762 y Fy(\032)39525 42596 y Fs(\000)d Ft(\013)t FA(\))41774 42194 y Fq(2)p 37667 43090 V 39121 44104 a FA(2)p Ft(\025)40320 44270 y Fq(0)42404 41784 y Fn(\033)43419 43345 y Ft(;)-1575 46648 y Fx(for)396 b Ft(x)307 b FA(=)h Fs(j)p Ft(c)p Fs(j)3395 46247 y Fq(2)4200 46648 y Fs(\025)f FA(0)p Fx(,)397 b(cf.)h(\(2.9\)-\(2.10\).)-468 49817 y FA(This)425 b(theorem)f(sho)-31 b(ws)425 b(in)f(particular)h (that)h(the)e(probabilit)-31 b(y)427 b(to)d(observ)-31 b(e)424 b(a)h(densit)-31 b(y)424 b Ft(n)37276 49983 y Fq(0)37774 49817 y Ft(=V)645 b Fs(2)398 b(A)424 b FA(of)h(condensed)f (b)31 b(osons)-1575 51212 y(enclosed)481 b(in)f(\003)g(for)g(a)h (\014xed)f(c)-31 b(hemical)482 b(p)31 b(oten)-31 b(tial)483 b Ft(\026)492 b Fs(2)g Fo(R)481 b FA(decreases)e(exp)31 b(onen)-31 b(tially)483 b(with)f(the)e(v)-31 b(olume)482 b Ft(V)738 b FA(=)493 b Fs(j)p FA(\003)p Fs(j)480 b FA(if)h(the)-1575 52607 y(distance)422 b(b)31 b(et)-31 b(w)g(een)422 b(the)f(Bose)g (condensate)h(densit)-31 b(y)422 b Ft(x)21979 52773 y Fy(\032)22914 52607 y FA(\(2.6\))h(and)e(the)h(set)e Fs(A)394 b(\032)g Fo(R)421 b FA(is)g(strictly)h(p)31 b(ositiv)-31 b(e.)650 b(No)-31 b(w,)436 b(the)421 b(next)-1575 54001 y(step)352 b(is)g(to)h(ev)-61 b(aluate)354 b(the)e(limiting)k (probabilit)-31 b(y)355 b(measure,)g(in)e(particular)g(at)g(the)g (phase)f(transition)i(de\014ned)e(for)g(a)g(c)-31 b(hemical)-1575 55396 y(p)31 b(oten)-31 b(tial)411 b Ft(\032)373 b Fs(2)f FA([)p Ft(\032)6072 55562 y Fr(\000)6820 55396 y Ft(;)184 b(\032)7883 55562 y Fq(+)8619 55396 y FA(].)610 b(Recall)410 b(that)f(the)f(Bose)g(condensate)h(densit)-31 b(y)409 b Ft(x)30469 55562 y Fy(\032)31392 55396 y FA(\(2.6\))h(con)-31 b(v)g(erges)409 b(to)g(0)f(when)h Ft(\032)372 b Fs(")h Ft(\032)46799 55562 y Fr(\000)47955 55396 y FA(but)408 b(to)h(a)-1575 56791 y(strictly)371 b(p)31 b(ositiv)-31 b(e)370 b(v)-61 b(alue)370 b Ft(x)9805 56957 y Fy(\032)10264 57068 y Fp(+)11251 56791 y Ft(>)307 b FA(0)370 b(when)f Ft(\032)308 b Fs(#)g Ft(\032)18545 56957 y Fq(+)19280 56791 y Ft(:)p Black -1575 59960 a Fu(Theorem)426 b(3.2)f(\(The)f (condensate)j(distribution)e(outside)g(the)g(p)35 b(oin)-35 b(t)425 b(of)g(the)g(phase)g(transition\))p Black -1575 61354 a Fx(The)541 b(\(\014nite)g(volume\))f(distribution)h Fo(D)15516 61520 y Fq(\003)p Fy(;\032)17441 61354 y Fx(of)f(the)g(c)-57 b(ondensate)541 b(c)-57 b(onver)g(ges)542 b(we)-57 b(akly)541 b(in)g(the)g(set)f(of)g(pr)-57 b(ob)g(ability)542 b(me)-57 b(asur)g(es)-1575 62749 y Fs(M)-246 62915 y Fq(1)436 62749 y FA(\()p Fo(C)p FA(\))397 b Fx(as)f FA(\003)307 b Fs(")h Fo(R)6643 62347 y Fq(3)7536 62749 y Fx(towar)-57 b(ds)394 b(the)i(singular)g(me)-57 b(asur)g(es)14712 66715 y Fo(D)15511 66881 y Fy(\032)16334 66715 y FA(:=lim)17968 67429 y Fq(\003)19347 66715 y Fo(D)20146 66881 y Fq(\003)p Fy(;\032)21837 66715 y FA(=)23474 65966 y(1)p 23139 66460 1225 45 v 23139 67474 a(2)p Ft(\031)24863 64987 y Fq(2)p Fy(\031)24803 65208 y Fn(Z)25136 68352 y Fq(0)26218 66715 y Ft(\016)26936 65486 y Fn(\020)27597 66715 y Ft(c)246 b Fs(\000)g Ft(x)30062 66258 y Fq(1)p Fy(=)p Fq(2)30062 66988 y Fy(\032)31453 66715 y Ft(e)31968 66258 y Fy(i\022)32783 65486 y Fn(\021)33628 66715 y FA(d)p Ft(\022)31 b(;)-1575 70643 y Fx(for)396 b(any)h Ft(\032)308 b Fs(2)f FA(\(0)p Ft(;)184 b(\032)6286 70809 y Fr(\000)7036 70643 y FA(\))246 b Fs([)g FA(\()p Ft(\032)9698 70809 y Fq(+)10434 70643 y Ft(;)184 b FA(+)p Fs(1)p FA(\))p Ft(:)-468 73812 y FA(F)-92 b(or)403 b Ft(\014)423 b Fs(!)364 b FA(+)p Fs(1)p Ft(;)403 b FA(i.e.)596 b(at)404 b(zero-temp)31 b(erature,)413 b(observ)-31 b(e)403 b(that)i Ft(\032)26131 73978 y Fr(\000)27281 73812 y FA(and)f Ft(\032)30040 73978 y Fq(+)31178 73812 y FA(could)g(b)31 b(oth)404 b(con)-31 b(v)g(erge)404 b(to)g(zero,)412 b(dep)31 b(ending)404 b(on)-1575 75207 y(the)312 b(in)-31 b(teraction)314 b(p)31 b(oten)-31 b(tial.)476 b(But,)324 b(at)313 b(\014nite)f(temp)31 b(erature,)324 b(i.e.)475 b(at)312 b Ft(\014)366 b(>)308 b FA(0)p Ft(;)k FA(one)g(alw)-31 b(a)g(ys)314 b(has)d Ft(\032)38429 75373 y Fq(+)39472 75207 y Ft(>)d(\032)41213 75373 y Fr(\000)42272 75207 y FA(and)j(the)h(con)-31 b(v)g(ergence)-1575 76602 y(of)370 b Fo(D)485 76768 y Fq(\003)p Fy(;\032)2238 76602 y FA(is)f(not)h(solv)-31 b(ed)370 b(for)f Ft(\032)308 b Fs(2)f FA([)p Ft(\032)13144 76768 y Fr(\000)13892 76602 y Ft(;)184 b(\032)14955 76768 y Fq(+)15691 76602 y FA(])p Ft(:)370 b FA(The)g(corresp)31 b(onding)369 b(result)g(is)g(therefore)h(expressed)e(in)h(the)g(next)h (theorem.)p Black Black eop end %%Page: 6 6 TeXDict begin 6 5 bop Black -800 1882 a FA(6)19294 b FB(J.-B.)418 b(Br)-25 b(u)419 b(-)f(V.A.)f(Za)-25 b(grebno)g(v)p Black Black -800 4649 a Fu(Theorem)426 b(3.3)f(\(The)f(condensate)i (distribution)f(at)g(the)g(p)35 b(oin)-35 b(t)425 b(of)f(the)h(phase)h (transition\))p Black -800 6044 a Fx(L)-57 b(et)437 b Ft(\032)1723 6210 y Fq(+)2840 6044 y Ft(>)382 b(\032)4655 6210 y Fr(\000)5402 6044 y Fx(.)632 b(As)437 b FA(\003)381 b Fs(")h Fo(R)10970 5642 y Fq(3)11467 6044 y Ft(;)437 b Fx(the)g(\(\014nite)g(volume\))g(distribution)g Fo(D)28463 6210 y Fq(\003)p Fy(;\032)30284 6044 y Fx(of)g(the)g(c)-57 b(ondensate)437 b(c)-57 b(onver)g(ges)438 b(we)-57 b(akly)438 b(in)f Fs(M)50401 6210 y Fq(1)51083 6044 y FA(\()p Fo(C)p FA(\))-800 7439 y Fx(towar)-57 b(ds)394 b(a)i(c)-57 b(onvex)397 b(c)-57 b(ombination)398 b(of)e(the)g(singular)g(me)-57 b(asur)g(es)12019 11095 y Fo(D)12818 11261 y Fy(\032)13641 11095 y FA(:=lim)15275 11809 y Fq(\003)16654 11095 y Fo(D)17453 11261 y Fq(\003)p Fy(;\032)19145 11095 y FA(=)307 b(\()q(1)246 b Fs(\000)g Ft(\024)23288 11261 y Fy(\032)23802 11095 y FA(\))185 b Ft(\016)227 b FA(\()p Ft(c)p FA(\))247 b(+)27997 10347 y Ft(\024)28635 10513 y Fy(\032)p 27961 10841 1225 45 v 27961 11855 a FA(2)p Ft(\031)29686 9367 y Fq(2)p Fy(\031)29626 9589 y Fn(Z)29959 12733 y Fq(0)31040 11095 y Ft(\016)31759 9867 y Fn(\020)32420 11095 y Ft(c)f Fs(\000)g Ft(x)34885 10638 y Fq(1)p Fy(=)p Fq(2)34885 11369 y Fy(\032)35344 11480 y Fp(+)36276 11095 y Ft(e)36791 10638 y Fy(i\022)37605 9867 y Fn(\021)38451 11095 y FA(d)p Ft(\022)31 b(;)-800 14777 y Fx(for)396 b(any)h Ft(\032)307 b Fs(2)h FA([)p Ft(\032)5894 14943 y Fr(\000)6642 14777 y Ft(;)184 b(\032)7705 14943 y Fq(+)8441 14777 y FA(])397 b Fx(and)f(with)f Ft(\024)14337 14943 y Fy(\032)15159 14777 y FA(:=)308 b(\()p Ft(\032)247 b Fs(\000)f Ft(\032)19563 14943 y Fr(\000)20310 14777 y FA(\))p Ft(=)p FA(\()p Ft(\032)22295 14943 y Fq(+)23278 14777 y Fs(\000)g Ft(\032)24957 14943 y Fr(\000)25704 14777 y FA(\))p Fx(.)307 17526 y FA(Note)336 b(that)h Ft(\024)5951 17692 y Fy(\032)6801 17526 y FA(is)e(a)h(strictly)h(increasing)f(and)g(con)-31 b(tin)g(uous)337 b(function)g(from)f([)p Ft(\032)33058 17692 y Fr(\000)33806 17526 y Ft(;)184 b(\032)34869 17692 y Fq(+)35606 17526 y FA(])335 b(to)i([0)p Ft(;)184 b FA(1])j Ft(:)336 b FA(This)g(result)f(giv)-31 b(es)337 b(a)f(strong)-800 18921 y(evidence)441 b(that,)461 b(at)442 b(the)f(phase)f(transition,)462 b(the)441 b(corresp)31 b(onding)441 b(Gibbs)f(state)i(is)f(not)h(a)f(pure)f(state)i(an)-31 b(ymore)442 b([11)q(])g(but)f(a)-800 20315 y(con)-31 b(v)g(ex)370 b(com)-31 b(bination)373 b(of)d(pure)e(states,)i(see)f (for)g(example)i(Section)f(4)g(in)f([1)q(].)307 22072 y(In)-31 b(tegrating)359 b Fo(D)6816 22238 y Fq(\003)p Fy(;\032)8556 22072 y FA(with)f(the)g(function)g Ft(')p FA(\()p Ft(c)p FA(\))308 b(=)g Fs(j)p Ft(c)p Fs(j)21916 21670 y Fq(2)22413 22072 y FA(,)360 b(w)-31 b(e)357 b(\014nally)i (obtain)f(the)f(Bose)g(condensate)h(densit)-31 b(y)358 b(\(2.6\))h(inside)e(the)-800 23466 y(phase)369 b(transition,)j(i.e.) 493 b(for)369 b Ft(\032)308 b Fs(2)f FA([)p Ft(\032)14045 23632 y Fr(\000)14793 23466 y Ft(;)184 b(\032)15856 23632 y Fq(+)16593 23466 y FA(].)p Black -800 26215 a Fu(Corollary)425 b(3.4)g(\(Deriv)-71 b(ation)425 b(of)g(the)g(Bose)g(condensate)h (densit)-35 b(y)425 b(for)g(an)-35 b(y)424 b(total)g(densit)-35 b(y\))p Black -800 27610 a Fx(The)396 b(Bose)g(c)-57 b(ondensate)396 b(density)h(e)-57 b(quals)12250 31862 y FA(lim)12716 32576 y Fq(\003)14095 30301 y Fn(\034)15058 31113 y Ft(a)15643 30712 y Fr(\003)15643 31388 y Fq(0)16152 31113 y Ft(a)16737 31279 y Fq(0)p 15058 31608 2176 45 v 15700 32622 a Ft(V)17366 30301 y Fn(\035)18197 32969 y Fy(H)18981 32702 y Fh(S)28 b(B)18922 33237 y Fp(\003)19426 33415 y Fh(j)19839 33237 y(;\025)20558 33403 y Fp(0)21408 31862 y FA(=)22577 28929 y Fn(8)22577 29925 y(>)22577 30257 y(>)22577 30589 y(<)22577 32582 y(>)22577 32914 y(>)22577 33246 y(:)24114 29961 y FA(0)6903 b(for)397 b Ft(\032)307 b Fs(\024)h Ft(\032)35912 30127 y Fr(\000)36659 29961 y Ft(:)24615 31025 y(\032)246 b Fs(\000)g Ft(\032)27112 31191 y Fr(\000)p 24247 31519 3980 45 v 24247 32533 a Ft(\032)24819 32699 y Fq(+)25800 32533 y Fs(\000)g Ft(\032)27479 32699 y Fr(\000)28360 31774 y Ft(x)28993 31940 y Fy(\032)29452 32051 y Fp(+)31319 31774 y FA(for)397 b Ft(\032)307 b Fs(2)h FA([)p Ft(\032)35845 31940 y Fr(\000)36593 31774 y Ft(;)184 b(\032)37656 31940 y Fq(+)38392 31774 y FA(])p Ft(:)24114 33768 y(x)24747 33934 y Fy(\032)25569 33768 y Ft(>)308 b FA(0)4356 b(for)397 b Ft(\032)308 b Fs(\025)f Ft(\032)35989 33934 y Fq(+)36724 33768 y Ft(:)-800 36176 y Fx(In)396 b(p)-57 b(articular,)396 b(it)h(is)f(c)-57 b(ontinuous)397 b(as)e(a)h(function)h(of)g Ft(\032)307 b(>)h FA(0)396 b Fx(and)g(line)-57 b(arly)398 b(incr)-57 b(e)g(asing)398 b(for)e Ft(\032)308 b Fs(2)f FA([)p Ft(\032)40832 36342 y Fr(\000)41580 36176 y Ft(;)184 b(\032)42643 36342 y Fq(+)43379 36176 y FA(])p Ft(;)397 b Fx(cf.)511 b(\014gur)-57 b(e)397 b(1.)307 38925 y FA(As)430 b(a)h(function)h(of)f(the)g(densit) -31 b(y)431 b Ft(\032)410 b(>)g FA(0)431 b(in)g(the)g(grand-canonical)i (ensem)-31 b(ble,)447 b(the)431 b(phase)f(transition)j(is)d(of)h(order) f(t)-31 b(w)g(o)433 b(if)-800 40319 y Ft(\032)-228 40485 y Fq(+)815 40319 y Ft(>)307 b(\032)2555 40485 y Fr(\000)3658 40319 y FA(whereas)356 b(it)h(is)f(of)h(order)e(one)i(as)e(a)i (function)g(of)g(the)f(c)-31 b(hemical)358 b(p)31 b(oten)-31 b(tial.)491 b(In)356 b(particular,)k(tak)-31 b(e)357 b Ft(\032)308 b(<)g(\032)47287 40485 y Fr(\000)48034 40319 y Ft(;)357 b FA(then)f(the)-800 41714 y(system)369 b(b)31 b(eha)-31 b(v)g(es)370 b(as)f(the)g(so-called)i(Mean-Field)f (Bose)f(Gas,)g(i.e.)493 b(the)370 b(mo)31 b(del)370 b(de\014ned)f(b)-31 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b(an)-31 b(y)370 b Ft(c)308 b Fs(2)f Fo(C)p FA(,)370 b Ft(\026)308 b Fs(2)f Fo(R)370 b FA(and)f Ft(\014)d(>)308 b FA(0)p Ft(:)p Black Black eop end %%Page: 12 12 TeXDict begin 12 11 bop Black -800 1882 a FA(12)19294 b FB(J.-B.)419 b(Br)-25 b(u)418 b(-)g(V.A.)g(Za)-25 b(grebno)g(v)p Black 307 4649 a FA(T)-92 b(o)296 b(obtain)h(an)f(upp)31 b(er)294 b(b)31 b(ound)296 b(on)g Ft(p)15154 4248 y Fy(S)42 b(B)16501 4649 y FA(\()p Ft(\014)58 b(;)184 b(\026;)g(c)p FA(\),)314 b(w)-31 b(e)296 b(follo)-31 b(w)299 b(the)c(idea)i(of)f([18) q(],)311 b(and)296 b(use)f(the)h(coheren)-31 b(t)296 b(state)g(represen)-31 b(tation)-800 6044 y(of)370 b Fs(f)p Ft(H)2024 5642 y Fy(S)42 b(B)1934 6358 y Fq(\003)p Fy(;\025)3328 6469 y Fp(0)4061 6044 y Fs(\000)246 b Ft(\026N)6724 6210 y Fq(\003)7386 6044 y Fs(g)369 b FA(giv)-31 b(en)371 b(b)-31 b(y)15479 8126 y Ft(H)16489 7669 y Fy(S)42 b(B)16399 8399 y Fq(\003)p Fy(;\025)17793 8510 y Fp(0)18526 8126 y Fs(\000)246 b Ft(\026N)21189 8292 y Fq(\003)22158 8126 y FA(=)23019 6619 y Fn(Z)23293 9797 y Fg(C)24434 8126 y FA(d)25049 7669 y Fq(2)25545 8126 y Ft(c)26208 6897 y Fn(n)27236 7846 y FA(^)26947 8126 y Ft(H)27957 7669 y Fy(S)42 b(B)27867 8399 y Fq(\003)p Fy(;\025)29261 8510 y Fp(0)29932 8126 y FA(\()q Ft(c;)184 b(\026)p FA(\))i Fs(j)p Ft(c)p Fs(i)f(h)q Ft(c)p Fs(j)35234 6897 y Fn(o)36157 8126 y Ft(;)14004 b FA(\(5.5\))-800 11700 y(where)369 b(the)g(Hamiltonian)10962 11421 y(^)10672 11700 y Ft(H)11682 11299 y Fy(S)42 b(B)11592 12014 y Fq(\003)p Fy(;\025)12986 12125 y Fp(0)13658 11700 y FA(\()q Ft(c;)184 b(\026)p FA(\))370 b(is)f(de\014ned)g(on)h Fs(F)23896 11299 y Fr(0)23786 12005 y Fq(\003)24815 11700 y FA(b)-31 b(y)18594 14100 y(^)18304 14380 y Ft(H)19314 13923 y Fy(S)42 b(B)19224 14653 y Fq(\003)p Fy(;\025)20618 14764 y Fp(0)21289 14380 y FA(\()q Ft(c;)184 b(\026)p FA(\))309 b(:=)f Ft(H)26582 13923 y Fy(S)42 b(B)26492 14653 y Fq(\003)p Fy(;\025)27886 14764 y Fp(0)28558 14380 y FA(\()p Ft(c;)184 b(\026)p FA(\))248 b(+)e(\001)p Ft(;)16829 b FA(\(5.6\))-800 16830 y(with)13395 18459 y(\001)308 b(:=)g Ft(\026)246 b Fs(\000)g FA(2)p Ft(\025)19320 18625 y Fq(0)19817 18459 y Fs(j)p Ft(c)p Fs(j)20910 18001 y Fq(2)21653 18459 y FA(+)22893 17710 y Ft(\025)23539 17876 y Fq(0)p 22893 18204 1143 45 v 23018 19218 a Ft(V)24414 18459 y Fs(\000)25823 17710 y FA(1)p 25654 18204 892 45 v 25654 19218 a Ft(V)28165 17407 y Fn(X)26986 19833 y Fy(k)19 b Fr(2)p Fq(\003)28679 19612 y Fm(\003)29141 19833 y Fr(nf)o Fq(0)p Fr(g)31250 18459 y FA(\()p Ft(\025)32326 18625 y Fq(0)33069 18459 y FA(+)246 b Ft(\025)34822 18625 y Fy(k)35366 18459 y FA(\))185 b Ft(a)36566 18001 y Fr(\003)36566 18732 y Fy(k)37111 18459 y Ft(a)37696 18625 y Fy(k)38241 18459 y Ft(:)11920 b FA(\(5.7\))-800 21930 y(Actually)-92 b(,)4249 21650 y(^)3959 21930 y Ft(H)4969 21528 y Fy(S)42 b(B)4879 22244 y Fq(\003)p Fy(;\025)6273 22355 y Fp(0)6945 21930 y FA(\()p Ft(c;)184 b(\026)p FA(\))414 b(is)f(deriv)-31 b(ed)413 b(b)-31 b(y)413 b(replacing)h(the)f(op)31 b(erators)413 b Ft(a)28777 21528 y Fr(\003)28777 22205 y Fq(0)29286 21930 y Ft(a)29871 22096 y Fq(0)30367 21930 y FA(,)424 b Ft(a)31683 22096 y Fq(0)32180 21930 y Ft(a)32765 22096 y Fq(0)33262 21930 y FA(,)g Ft(a)34578 21528 y Fr(\003)34578 22205 y Fq(0)35087 21930 y Ft(a)35672 21528 y Fr(\003)35672 22205 y Fq(0)36181 21930 y FA(,)g(and)413 b Ft(a)39693 21528 y Fr(\003)39693 22205 y Fq(0)40202 21930 y Ft(a)40787 21528 y Fr(\003)40787 22205 y Fq(0)41296 21930 y Ft(a)41881 22096 y Fq(0)42377 21930 y Ft(a)42962 22096 y Fq(0)43872 21930 y FA(in)g Fs(f)p Ft(H)46770 21528 y Fy(S)42 b(B)46680 22244 y Fq(\003)p Fy(;\025)48074 22355 y Fp(0)48836 21930 y Fs(\000)275 b Ft(\026N)51528 22096 y Fq(\003)52190 21930 y Fs(g)-800 23325 y FA(resp)31 b(ectiv)-31 b(ely)517 b(b)-31 b(y)517 b Fs(j)p Ft(V)247 b(c)p Fs(j)9054 22923 y Fq(2)9895 23325 y Fs(\000)344 b FA(1)p Ft(;)518 b(V)245 b(c)13848 22923 y Fq(2)14345 23325 y Ft(;)517 b(V)270 b FA(\026)-577 b Ft(c)16540 22923 y Fq(2)17553 23325 y FA(and)517 b Ft(V)20745 22923 y Fq(2)21241 23325 y Fs(j)p Ft(c)p Fs(j)22334 22923 y Fq(4)23176 23325 y Fs(\000)344 b FA(4)p Ft(V)247 b Fs(j)p Ft(c)p Fs(j)26920 22923 y Fq(2)27761 23325 y FA(+)345 b(2)p Ft(:)517 b FA(Let)g Fs(fh)p Ft( )34219 22923 y Fr(0)34179 23599 y Fy(n)34967 23325 y FA(\()q Ft(c)p FA(\))185 b Fs(jg)37352 22923 y Fr(1)37352 23600 y Fy(n)p Fq(=1)39592 23325 y FA(b)31 b(e)517 b(an)f(othonormal)k(basis)d(of)-800 24720 y(eigen)-31 b(v)g(ectors)371 b(of)6940 24440 y(^)6650 24720 y Ft(H)7660 24318 y Fy(S)42 b(B)7570 25033 y Fq(\003)p Fy(;\025)8964 25144 y Fp(0)9636 24720 y FA(\()q Ft(c;)184 b(\026)p FA(\))i Ft(:)369 b FA(Since)g(for)h(an)-31 b(y)370 b Ft(z)49 b(;)184 b(c)308 b Fs(2)f Fo(C)18798 27461 y Fs(h)q Ft(z)49 b Fs(j)p Ft(c)p Fs(i)308 b FA(=)f Ft(e)23000 27004 y Fr(\000)23825 26707 y Fp(1)p 23825 26830 377 38 v 23825 27271 a(2)24335 27004 y Fr(f)o Fq(\()55 b(\026)-496 b Fy(z)32 b Fr(\000)25 b Fq(\026)-466 b Fy(c)p Fq(\))o(\()p Fy(z)32 b Fr(\000)p Fy(c)p Fq(\))o(+)25 b(\026)-466 b Fy(cz)32 b Fr(\000)54 b Fq(\026)-495 b Fy(z)31 b(c)p Fr(g)32837 27461 y Ft(;)17324 b FA(\(5.8\))-800 29912 y(it)370 b(follo)-31 b(ws)371 b(that)4128 32907 y(T)-92 b(r)5269 33100 y Fr(F)5981 32833 y Fm(0)5903 33360 y Fp(\003)6703 32907 y Fs(f)p Ft(W)8301 33073 y Fq(\003)9147 32907 y FA(\()q Ft(c)p FA(\))p Fs(g)1108 b FA(=)14508 31523 y Fr(1)14150 31855 y Fn(X)14116 34199 y Fy(n)p Fq(=1)16091 32907 y Fs(h)q Ft(c)246 b Fs(\012)g Ft( )19115 32449 y Fr(0)19075 33180 y Fy(n)19862 32907 y FA(\()p Ft(c)p FA(\))q Fs(j)185 b Ft(e)22209 31929 y Fr(\000)p Fy(\014)23443 31305 y Fd(R)23541 32677 y Fb(C)24039 31929 y Fq(d)24528 31595 y Fp(2)24960 31929 y Fy(z)25634 31733 y Fq(^)25415 31929 y Fy(H)26199 31595 y Fh(S)28 b(B)26140 32151 y Fp(\003)p Fh(;\025)27363 32317 y Fp(0)27850 31929 y Fq(\()p Fy(z)k(;\026)p Fq(\))p Fr(j)p Fy(z)g Fr(ih)p Fy(z)g Fr(j)32190 32907 y Fs(j)p Ft(c)246 b Fs(\012)g Ft( )35090 32449 y Fr(0)35050 33180 y Fy(n)35837 32907 y FA(\()q Ft(c)p FA(\))p Fs(i)12148 37022 y FA(=)14508 35638 y Fr(1)14150 35970 y Fn(X)14116 38315 y Fy(n)p Fq(=1)16091 34753 y Fn(8)16091 35749 y(<)16091 37742 y(:)17075 37022 y FA(1+)19309 35638 y Fr(1)18951 35970 y Fn(X)18797 38315 y Fy(m)p Fq(=1)21144 36273 y FA(\()p Fs(\000)p Ft(\014)58 b FA(\))23550 35717 y Fy(m)p 21144 36767 3248 45 v 22128 37781 a Ft(m)p FA(!)24925 35515 y Fn(Z)24831 38694 y Fg(C)25391 38472 y Fh(m)26433 37022 y FA(d)27048 36565 y Fq(2)27545 37022 y Ft(z)28060 37188 y Fq(1)28741 37022 y Fs(\001)184 b(\001)g(\001)j FA(d)30832 36565 y Fq(2)31328 37022 y Ft(z)31843 37188 y Fy(m)32684 37022 y Ft(e)33199 36565 y Fr(\000)34024 36267 y Fh(V)p 34024 36390 612 38 v 34142 36832 a Fp(2)34769 36565 y Fr(f)o Fq(R)35865 36676 y Fh(m)36600 36565 y Fq(\()p Fy(z)37369 36676 y Fp(1)37801 36565 y Fy(;)p Fr(\001\001\001)151 b Fy(;z)39690 36676 y Fh(m)40425 36565 y Fq(\)+)p Fy(i)p Fq(I)42084 36676 y Fh(m)42818 36565 y Fq(\()p Fy(z)43587 36676 y Fp(1)44019 36565 y Fy(;)p Fr(\001\001\001)g Fy(;z)45908 36676 y Fh(m)46643 36565 y Fq(\))p 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b(+)g Ft(i)25517 49848 y Fy(m)25326 50069 y Fn(P)25144 51873 y Fy(j)45 b Fq(=1)26983 50899 y FA(\()67 b(\026)-619 b Ft(z)27929 51065 y Fy(j)28395 50899 y Ft(z)28910 51065 y Fy(j)45 b Fr(\000)p Fq(1)30755 50899 y Fs(\000)313 b FA(\026)-620 b Ft(z)32377 51065 y Fy(j)45 b Fr(\000)p Fq(1)33977 50899 y Ft(z)34492 51065 y Fy(j)34958 50899 y FA(\))246 b(+)g Ft(i)184 b FA(\()26 b(\026)-577 b Ft(cz)38732 51065 y Fy(m)39818 50899 y Fs(\000)313 b FA(\026)-620 b Ft(z)41440 51065 y Fy(m)42281 50899 y Ft(c)p FA(\))185 b Ft(:)49914 49680 y FA(\(5.10\))-800 54131 y(Since)369 b(I)2490 54297 y Fy(m)3515 54131 y FA(\()q Ft(c;)184 b Fs(\001)g(\001)g(\001)372 b Ft(;)184 b(c)p FA(\))309 b(=)f(0)369 b(and)16230 56582 y(inf)13873 57347 y Fq(\()o Fy(z)14641 57458 y Fp(1)15073 57347 y Fy(;)p Fr(\001\001\001)151 b Fy(;z)16962 57458 y Fh(m)17697 57347 y Fq(\))p Fr(2)p Fg(C)19200 57126 y Fh(m)20242 56582 y FA(R)21057 56748 y Fy(m)22082 56582 y FA(\()p Ft(z)23027 56748 y Fq(1)23524 56582 y Ft(;)184 b 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Ft(:)12744 b FA(\(5.12\))-800 65525 y(Justi\014cation)377 b(of)f(the)f(LD)f(tec)-31 b(hnique)376 b(in)g(sums)e(\(5.9\))j(is)e(based)g(on)g(the)h(uniform)g (domination)i(theorem)d(and)h(it)f(follo)-31 b(ws)378 b(the)-800 66920 y(line)331 b(of)h(reasoning)f(dev)-31 b(elop)31 b(ed)332 b(in)f([18)r(].)480 b(Mean)-31 b(while,)340 b(b)-31 b(y)331 b(using)h(the)f(Bogoliub)31 b(o)-31 b(v)333 b(con)-31 b(v)g(exit)g(y)334 b(inequalit)-31 b(y)334 b([14)q(])d(it)h(follo)-31 b(ws)333 b(that)8813 69825 y(T)-92 b(r)9954 70018 y Fr(F)10666 69752 y Fm(0)10588 70278 y Fp(\003)11388 68597 y Fn(n)12126 69825 y Ft(e)12641 69319 y Fr(\000)p Fy(\014)14094 69123 y Fq(^)13875 69319 y Fy(H)14659 68985 y Fh(S)28 b(B)14600 69540 y Fp(\003)p Fh(;\025)15823 69706 y Fp(0)16310 69319 y Fq(\()p Fy(c;\026)p Fq(\))18254 68597 y Fn(o)19300 69825 y Fs(\024)21112 69077 y FA(1)p 20601 69571 V 20601 70585 a Ft(\014)58 b(V)22495 69825 y FA(ln)184 b(T)-92 b(r)24742 70018 y Fr(F)25454 69752 y Fm(0)25376 70278 y Fp(\003)26176 68597 y Fn(n)26914 69825 y Ft(e)27429 69319 y Fr(\000)p Fy(\014)40 b(H)29447 68985 y Fh(S)28 b(B)29388 69540 y Fp(\003)p Fh(;\025)30611 69706 y Fp(0)31098 69319 y Fq(\()p Fy(c;\026)p Fq(\))33042 68597 y Fn(o)34026 69825 y Fs(\000)35435 69077 y FA(1)p 35266 69571 892 45 v 35266 70585 a Ft(V)36475 69825 y Fs(h)p FA(\001)p Fs(i)38478 69982 y Fq(^)38258 70178 y Fy(H)39042 69911 y Fh(S)g(B)38983 70446 y Fp(\003)p Fh(;\025)40206 70612 y Fp(0)40694 70178 y Fq(\()p Fy(c;\026)p Fq(\))42822 69825 y Ft(;)6785 b FA(\(5.13\))-800 72735 y(where)16223 75270 y Fs(h\000i)18164 75427 y Fq(^)17945 75623 y Fy(H)18729 75356 y Fh(S)28 b(B)18670 75891 y Fp(\003)p Fh(;\025)19893 76057 y Fp(0)20380 75623 y Fq(\()p Fy(c;\026)p Fq(\))22632 75270 y FA(:=)24240 74119 y(T)-92 b(r)25381 74312 y Fr(F)26093 74045 y Fm(0)26015 74572 y Fp(\003)26815 72890 y Fn(n)27553 74119 y Fs(\000)p Ft(e)28929 73612 y Fr(\000)p Fy(\014)30382 73416 y Fq(^)30163 73612 y Fy(H)30947 73278 y Fh(S)28 b(B)30888 73834 y Fp(\003)p Fh(;\025)32111 74000 y Fp(0)32598 73612 y Fq(\()p Fy(c;\026)p Fq(\))34542 72890 y Fn(o)p 24240 75016 11040 45 v 24671 76436 a FA(T)-92 b(r)25812 76629 y Fr(F)26524 76362 y Fm(0)26446 76889 y Fp(\003)27245 75207 y Fn(n)27983 76436 y Ft(e)28498 75882 y Fr(\000)p Fy(\014)29951 75686 y Fq(^)29732 75882 y Fy(H)30516 75615 y Fh(S)28 b(B)30457 76150 y Fp(\003)p Fh(;\025)31680 76316 y Fp(0)32168 75882 y Fq(\()p Fy(c;\026)p Fq(\))34112 75207 y Fn(o)35413 75270 y Ft(:)14194 b FA(\(5.14\))p Black Black eop end %%Page: 13 13 TeXDict begin 13 12 bop Black 6447 1882 a FB(Lar)-25 b(ge)419 b(Devia)-74 b(tions)417 b(in)h(the)h(Superst)-74 b(able)420 b(Weakl)-74 b(y)418 b(Imperfect)h(Bose)f(Gas)8023 b FA(13)p Black -1575 4649 a(In)337 b(particular,)345 b(since)337 b(for)g Ft(k)343 b Fs(2)307 b Fo(R)12274 4248 y Fq(3)12771 4649 y Ft(;)338 b FA(0)308 b Fs(\024)f Ft(\025)16091 4815 y Fy(k)16943 4649 y Fs(\024)g Ft(\025)18757 4815 y Fq(0)19591 4649 y FA(b)-31 b(y)337 b(our)g(assumption)i(\(B\))e 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b(y)370 b Ft(\026)308 b Fs(2)f Fo(R)370 b FA(one)f(can)h(c)-31 b(hec)g(k)369 b(that)14195 17786 y(1)p 14026 18280 892 45 v 14026 19294 a Ft(V)16537 17483 y Fn(X)15358 19909 y Fy(k)19 b Fr(2)p Fq(\003)17051 19688 y Fm(\003)17513 19909 y Fr(nf)o Fq(0)p Fr(g)19622 18535 y Fs(h)p Ft(a)20637 18078 y Fr(\003)20637 18808 y Fy(k)21182 18535 y Ft(a)21767 18701 y Fy(k)22312 18535 y Fs(i)22962 18692 y Fq(^)22742 18888 y Fy(H)23526 18621 y Fh(S)28 b(B)23467 19155 y Fp(\003)p Fh(;\025)24690 19321 y Fp(0)25178 18887 y Fq(\()p Fy(c;\026)p Fq(\))27429 18535 y FA(=)308 b Fs(O)215 b FA(\()q(1\))554 b(as)308 b(\003)f Fs(")h Fo(R)35696 18078 y Fq(3)36193 18535 y Ft(:)12640 b FA(\(5.16\))-1575 22212 y(Therefore,)370 b(from)g(\(5.15\))i(together)e(with)g(\(5.3\))i(and)d (\(5.12\))j(one)e(deduces)e(that)13808 25307 y Ft(p)14365 24850 y Fy(S)42 b(B)15713 25307 y FA(\()p Ft(\014)58 b(;)184 b(\026;)g(c)p FA(\))311 b Fs(\024)181 b FA(inf)20557 26022 y Fy(\013)p Fr(\024)p Fq(0)22573 23746 y Fn(\032)23404 25307 y Ft(p)23961 24850 y Fy(B)23961 25580 y Fq(0)24722 25307 y FA(\()p Ft(\014)58 b(;)184 b(\013)t(;)g Fs(j)p Ft(c)p Fs(j)28623 24850 y Fq(2)29124 25307 y FA(\))247 b(+)31040 24558 y(\()p Ft(\026)g Fs(\000)f Ft(\013)t FA(\))34633 24156 y Fq(2)p 31040 25052 4090 45 v 32237 26066 a FA(2)p Ft(\025)33436 26232 y Fq(0)35263 23746 y Fn(\033)36278 25307 y Ft(:)12555 b FA(\(5.17\))-1575 28356 y(T)-92 b(ogether)370 b(with)h(the)e(lo)-31 b(w)g(er)371 b(b)31 b(ound)369 b(\(5.4\),)j(this)d(inequalit)-31 b(y)372 b(pro)-31 b(v)g(es)370 b(the)f(lemma.)495 b Fc(\003)p Black -1575 31181 a Fu(Lemma)424 b(5.2)h(\(The)g(free-energy)i(densit) -35 b(y)425 b Ft(f)19792 30780 y Fy(S)42 b(B)19673 31486 y Fq(\003)21140 31181 y FA(\()p Ft(\014)58 b(;)184 b(y)40 b(;)184 b(c)p FA(\))427 b Fu(in)d(the)h(thermo)35 b(dynamic)426 b(limit\))p Black -1575 32576 a Fx(F)-85 b(or)436 b(any)g Ft(c)381 b Fs(2)f Fo(C)p Fx(,)447 b Ft(y)420 b Fs(\025)380 b FA(0)437 b Fx(and)f Ft(\014)i(>)381 b FA(0)p Fx(,)447 b(the)436 b(thermo)-57 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Ft(e)23579 45097 y Fy(\014)40 b(V)24834 45180 y FA(\()25265 45097 y Fy(\026y)28 b Fr(\000)p Fy(f)27491 44763 y Fh(S)g(B)27404 45319 y Fp(\003)28647 45097 y Fq(\()p Fy(\014)40 b(;y)28 b(;c)p Fq(\))31279 45180 y FA(\))31765 45576 y Ft(\027)32312 45742 y Fq(\003)33157 45576 y FA(\()q(d)p Ft(y)40 b FA(\))246 b(+)g Ft(\026)p Fs(j)p Ft(c)p Fs(j)38329 45119 y Fq(2)38826 45576 y Ft(;)10007 b FA(\(5.18\))-1575 49660 y(with)399 b Ft(\027)1522 49826 y Fq(\003)2183 49660 y FA(\(d)p Ft(y)40 b FA(\))398 b(de\014ned)g(in)g (\(4.3\).)581 b(It)398 b(is)g(then)g(straigh)-31 b(tforw)g(ard)400 b(to)f(c)-31 b(hec)g(k)398 b(that)i(the)e(thermo)31 b(dynamic)400 b(limit)g Ft(p)45656 49259 y Fy(S)42 b(B)47004 49660 y FA(\()p Ft(\014)58 b(;)184 b(\026;)g(c)p FA(\))401 b(of)-1575 51055 y Ft(p)-1018 50653 y Fy(S)42 b(B)-1018 51360 y Fq(\003)330 51055 y FA(\()p Ft(\014)58 b(;)184 b(\026;)g(c)p FA(\))372 b(\(3.4\))g(equals)14037 52450 y Ft(p)14594 51993 y Fy(S)42 b(B)15942 52450 y FA(\()p Ft(\014)58 b(;)184 b(\026;)g(c)p FA(\))311 b(=sup)20814 53381 y Fy(y)28 b Fr(\025)p Fq(0)22760 51553 y Fn(\010)23406 52450 y Ft(\026y)285 b Fs(\000)246 b Ft(f)26669 51993 y Fy(S)42 b(B)28202 52450 y FA(\()p Ft(\014)58 b(;)184 b(y)40 b(;)184 b(c)p FA(\))31793 51553 y Fn(\011)32684 52450 y FA(+)246 b Ft(\026)p Fs(j)p Ft(c)p Fs(j)35551 51993 y Fq(2)36049 52450 y Ft(;)12784 b FA(\(5.19\))-1575 55319 y(with)414 b Ft(f)1651 54917 y Fy(S)42 b(B)2999 55319 y FA(\()p Ft(\014)58 b(;)184 b(y)40 b(;)184 b(c)p FA(\))382 b Ft(<)e Fs(1)412 b FA(for)g Ft(y)419 b Fs(\025)380 b FA(0.)623 b(The)412 b(deriv)-61 b(ativ)-31 b(e)414 b(of)f(the)g(pressure)d Ft(p)30767 54917 y Fy(S)42 b(B)32115 55319 y FA(\()p Ft(\014)58 b(;)184 b(\026;)g(c)p FA(\))416 b(is)c(con)-31 b(tin)g(uous)414 b(as)f(a)f(function)i(of)f Ft(\026)p FA(,)-1575 56713 y(cf.)683 b(Lemma)434 b(5.1)f(and)g (\(4.5\).)685 b(Th)-31 b(us,)449 b(b)-31 b(y)433 b(using)g(the)g Fx(T)-85 b(aub)-57 b(erien)456 b(the)-57 b(or)g(em)518 b FA(pro)-31 b(v)g(en)433 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