Content-Type: multipart/mixed; boundary="-------------0503240816311" This is a multi-part message in MIME format. ---------------0503240816311 Content-Type: text/plain; name="05-116.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="05-116.keywords" 2D Euler equation, Navier-Stokes, 2D turbulence, stationary measure, white noise, vorticity ---------------0503240816311 Content-Type: application/postscript; name="new.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="new.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.94a Copyright 2003 Radical Eye Software %%Title: new.dvi %%Pages: 12 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMR17 CMR12 CMBX9 CMR9 CMMI9 CMSY9 MSBM10 CMMI6 CMSY6 %%+ CMR6 CMBX12 CMR10 CMR7 CMMI10 CMSY10 CMEX10 CMMI7 CMSY7 MSBM7 CMR5 %%+ CMBX10 CMR8 CMSY8 CMMI8 CMTI10 CMMI5 EUFM10 CMSY5 CMTT10 %%DocumentPaperSizes: A4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o 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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 (CMTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT10 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /arrowup put dup 175 /arrowdown put dup 176 /quotesingle put dup 177 /exclamdown put dup 178 /questiondown put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /visiblespace put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /arrowup put dup 12 /arrowdown put dup 13 /quotesingle put dup 14 /exclamdown put dup 15 /questiondown put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /visiblespace put dup 33 /exclam put dup 34 /quotedbl put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /less put dup 61 /equal put dup 62 /greater put dup 63 /question put dup 64 /at 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /backslash put dup 93 /bracketright put dup 94 /asciicircum put dup 95 /underscore put dup 96 /quoteleft 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 123 /braceleft put dup 124 /bar put dup 125 /braceright put dup 126 /asciitilde put dup 127 /dieresis put dup 128 /visiblespace put dup 160 /space put readonly def /FontBBox{-4 -235 731 800}readonly def /UniqueID 5000832 def currentdict end currentfile eexec 8053514D28EC28DA1630165FAB262882D3FCA78881823C5537FE6C3DDA8EE5B897E17CB027F5 C73FDBB56B0A7C25FC3512B55FE8F3ACFBFFCC7F4A382D8299CC8FD37D3CEA49DABDCA92847A F0560B404EF71134B0F3D99934FC9D0B4E602011B9CFB856C23F958F3C5A2FBE0EF8587D1F57 74879C324E51FCB22888B74F241550D7401EB990D4F3A7AF635198422283CAC1B6CD446DDBCB D915DB9BFF88844E784C6BF7389803D9450B0C21756A017306462C563D51ECEFAACD079732F1 2C29315E4B9623A5752C6F1D8145869E120D910B2644887CEA7E30B15676A92537C29D3AA80D C30082ABA94B40990B82FB1A877E805E0C8C48F61E9F2EDAC05B944EE4D8084EC1D5CC517AAE 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /minus put dup 162 /periodcentered put dup 163 /multiply put dup 164 /asteriskmath put dup 165 /divide put dup 166 /diamondmath put dup 167 /plusminus put dup 168 /minusplus put dup 169 /circleplus put dup 170 /circleminus put dup 173 /circlemultiply put dup 174 /circledivide put dup 175 /circledot put dup 176 /circlecopyrt put dup 177 /openbullet put dup 178 /bullet put dup 179 /equivasymptotic put dup 180 /equivalence put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 183 /lessequal put dup 184 /greaterequal put dup 185 /precedesequal put dup 186 /followsequal put dup 187 /similar put dup 188 /approxequal put dup 189 /propersubset put dup 190 /propersuperset put dup 191 /lessmuch put dup 192 /greatermuch put dup 193 /precedes put dup 194 /follows put dup 195 /arrowleft put dup 196 /spade put dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 4 /divide put dup 5 /diamondmath put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 9 /circleminus put dup 10 /circlemultiply put dup 11 /circledivide put dup 12 /circledot put dup 13 /circlecopyrt put dup 14 /openbullet put dup 15 /bullet put dup 16 /equivasymptotic put dup 17 /equivalence put dup 18 /reflexsubset put dup 19 /reflexsuperset put dup 20 /lessequal put dup 21 /greaterequal put dup 22 /precedesequal put dup 23 /followsequal put dup 24 /similar put dup 25 /approxequal put dup 26 /propersubset put dup 27 /propersuperset put dup 28 /lessmuch put dup 29 /greatermuch put dup 30 /precedes put dup 31 /follows put dup 32 /arrowleft put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 36 /arrowboth put dup 37 /arrownortheast put dup 38 /arrowsoutheast put dup 39 /similarequal put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 42 /arrowdblup put dup 43 /arrowdbldown put dup 44 /arrowdblboth put dup 45 /arrownorthwest put dup 46 /arrowsouthwest put dup 47 /proportional put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 52 /triangle put dup 53 /triangleinv put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 57 /existential put dup 58 /logicalnot put dup 59 /emptyset put dup 60 /Rfractur put dup 61 /Ifractur put dup 62 /latticetop put dup 63 /perpendicular put dup 64 /aleph 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 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%%BeginFont: EUFM10 %!PS-AdobeFont-1.1: EUFM10 2.1 %%CreationDate: 1992 Nov 20 17:36:20 % Euler fonts were designed by Hermann Zapf. % 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 (EUFM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /EUFM10 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 161 /dnos put dup 162 /dalt put dup 163 /fnos put dup 164 /falt put dup 165 /galt put dup 166 /kalt put dup 167 /talt put dup 168 /ualt put dup 181 /quoteleft put dup 182 /quoteright put dup 195 /space put dup 196 /onealt put dup 0 /dnos put dup 1 /dalt put dup 2 /fnos put dup 3 /falt put dup 4 /galt put dup 5 /kalt put dup 6 /talt put dup 7 /ualt put dup 18 /quoteleft put dup 19 /quoteright put dup 32 /space put dup 33 /exclam put dup 38 /ampersand put dup 39 /quotesingle put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /minus 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 94 /asciicircum 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 125 /quotedbl put dup 127 /onealt put dup 128 /space put dup 160 /space put readonly def /FontBBox{-26 -224 1055 741}readonly def /UniqueID 5031986 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % 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 (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon 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 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at 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 88 /X 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 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACDD6500ABDA5ED9835F6A016CFC8F00B6C052ED76A 87856B50F4D80DFAEB508C97F8281F3F88B17E4D3B90C0F65EC379791AACDC162A66CBBC5BE2 F53AAD8DE72DD113B55A022FBFEE658CB95F5BB32BA0357B5E050FDDF264A07470BEF1C52119 B6FBD5C77EBED964AC5A2BBEC9D8B3E48AE5BB003A63D545774B922B9D5FF6B0066ECE43645A 131879B032137D6D823385FE55F3402D557FD3B4486BE79011D1F5BFAE5C1F476EE6F05EB1D2 CAEB269958B194521197B312FCCED4867F3C8FBD030BD715D8FFDA1DCD454B174E7A1A97B59F E770E67702519D9D9B23D61AC08424D555242A8CA08C49AEF300945D99B999A79CE74804AE6B FDE623F4463371442F6523A5F6CE19C839A708C025132E22C696C8CCADE45680E5197189D0F9 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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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 194 /chi put dup 195 /psi put dup 196 /tie put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 19 /iota 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 27 /sigma put dup 28 /tau put dup 29 /upsilon put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 35 /theta1 put dup 36 /pi1 put dup 37 /rho1 put dup 38 /sigma1 put dup 39 /phi1 put dup 40 /arrowlefttophalf put dup 41 /arrowleftbothalf put dup 42 /arrowrighttophalf put dup 43 /arrowrightbothalf put dup 44 /arrowhookleft put dup 45 /arrowhookright put dup 46 /triangleright put dup 47 /triangleleft put dup 48 /zerooldstyle put dup 49 /oneoldstyle put dup 50 /twooldstyle put dup 51 /threeoldstyle put dup 52 /fouroldstyle put dup 53 /fiveoldstyle put dup 54 /sixoldstyle put dup 55 /sevenoldstyle put dup 56 /eightoldstyle put dup 57 /nineoldstyle put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 63 /star put dup 64 /partialdiff 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /flat put dup 92 /natural put dup 93 /sharp put dup 94 /slurbelow put dup 95 /slurabove put dup 96 /lscript 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 123 /dotlessi put dup 124 /dotlessj put dup 125 /weierstrass put dup 126 /vector put dup 127 /tie put dup 128 /psi put dup 160 /space put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueID 5087380 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon 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 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /sterling put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 194 /chi put dup 195 /psi put dup 196 /tie put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 19 /iota 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 27 /sigma put dup 28 /tau put dup 29 /upsilon put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 35 /theta1 put dup 36 /pi1 put dup 37 /rho1 put dup 38 /sigma1 put dup 39 /phi1 put dup 40 /arrowlefttophalf put dup 41 /arrowleftbothalf put dup 42 /arrowrighttophalf put dup 43 /arrowrightbothalf put dup 44 /arrowhookleft put dup 45 /arrowhookright put dup 46 /triangleright put dup 47 /triangleleft put dup 48 /zerooldstyle put dup 49 /oneoldstyle put dup 50 /twooldstyle put dup 51 /threeoldstyle put dup 52 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%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 161 /minus put dup 162 /periodcentered put dup 163 /multiply put dup 164 /asteriskmath put dup 165 /divide put dup 166 /diamondmath put dup 167 /plusminus put dup 168 /minusplus put dup 169 /circleplus put dup 170 /circleminus put dup 173 /circlemultiply put dup 174 /circledivide put dup 175 /circledot put dup 176 /circlecopyrt put dup 177 /openbullet put dup 178 /bullet put dup 179 /equivasymptotic put dup 180 /equivalence put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 183 /lessequal put dup 184 /greaterequal put dup 185 /precedesequal put dup 186 /followsequal put dup 187 /similar put dup 188 /approxequal put dup 189 /propersubset put dup 190 /propersuperset put dup 191 /lessmuch put dup 192 /greatermuch put dup 193 /precedes put dup 194 /follows put dup 195 /arrowleft put dup 196 /spade put dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 4 /divide put dup 5 /diamondmath put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 9 /circleminus put dup 10 /circlemultiply put dup 11 /circledivide put dup 12 /circledot put dup 13 /circlecopyrt put dup 14 /openbullet put dup 15 /bullet put dup 16 /equivasymptotic put dup 17 /equivalence put dup 18 /reflexsubset put dup 19 /reflexsuperset put dup 20 /lessequal put dup 21 /greaterequal put dup 22 /precedesequal put dup 23 /followsequal put dup 24 /similar put dup 25 /approxequal put dup 26 /propersubset put dup 27 /propersuperset put dup 28 /lessmuch put dup 29 /greatermuch put dup 30 /precedes put dup 31 /follows put dup 32 /arrowleft put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 36 /arrowboth put dup 37 /arrownortheast put dup 38 /arrowsoutheast put dup 39 /similarequal put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 42 /arrowdblup put dup 43 /arrowdbldown put dup 44 /arrowdblboth put dup 45 /arrownorthwest put dup 46 /arrowsouthwest put dup 47 /proportional put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 52 /triangle put dup 53 /triangleinv put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 57 /existential put dup 58 /logicalnot put dup 59 /emptyset put dup 60 /Rfractur put dup 61 /Ifractur put dup 62 /latticetop put dup 63 /perpendicular put dup 64 /aleph 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /union put dup 92 /intersection put dup 93 /unionmulti put dup 94 /logicaland put dup 95 /logicalor put dup 96 /turnstileleft put dup 97 /turnstileright put dup 98 /floorleft put dup 99 /floorright put dup 100 /ceilingleft put dup 101 /ceilingright put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 108 /arrowbothv put dup 109 /arrowdblbothv put dup 110 /backslash put dup 111 /wreathproduct put dup 112 /radical put dup 113 /coproduct put dup 114 /nabla put dup 115 /integral put dup 116 /unionsq put dup 117 /intersectionsq put dup 118 /subsetsqequal put dup 119 /supersetsqequal put dup 120 /section put dup 121 /dagger put dup 122 /daggerdbl put dup 123 /paragraph put dup 124 /club put dup 125 /diamond put dup 126 /heart put dup 127 /spade put dup 128 /arrowleft put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon 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 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at 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 88 /X 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 95 /dotaccent put dup 96 /quoteleft 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 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon 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 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 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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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /arrowup put dup 175 /arrowdown put dup 176 /quotesingle put dup 177 /exclamdown put dup 178 /questiondown put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /arrowup put dup 12 /arrowdown put dup 13 /quotesingle put dup 14 /exclamdown put dup 15 /questiondown put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /less put dup 61 /equal put dup 62 /greater put dup 63 /question put dup 64 /at 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 88 /X 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 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 def currentdict end currentfile eexec 8053514D28EC28DA1630165FAB262882D3FCA78881823C5537FE6C3DDA8EE5B897E17CB027F5 C73FDBB56B0A7C25FC3512B55FE8F3ACFBFFCC7F4A382D8299CC8FD37D3CEA49DABDCA92847A F0560B404EF71134B0F3D99934FC9D0B4E602011B9CFB856C23F958F3C5A2FBE0EF8587D1F57 74879C324E51FCB22888B74F241550D7401EB990D4F3A7AF635198422283CAC1B6CD446DDBCB D915DB9BFF88844E784C6BF7389803D9450B0C21756A017306457C7E62C1D269F306BD3402E2 66DEFC3B5E7D8A8D2F5BF0FE6DDD40D07391DF4FAD4A6018DCE29A2B8F692B29F2023A7C0E66 DE8ED85C14F1F8492167357F51A7E84CC5D92E0FEE4A71813D2FFB26445026F89B4787516ECD 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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 161 /lessornotequal put dup 162 /greaterornotequal put dup 163 /notlessequal put dup 164 /notgreaterequal put dup 165 /notless put dup 166 /notgreater put dup 167 /notprecedes put dup 168 /notfollows put dup 169 /lessornotdbleql put dup 170 /greaterornotdbleql put dup 173 /notlessorslnteql put dup 174 /notgreaterorslnteql put dup 175 /lessnotequal put dup 176 /greaternotequal put dup 177 /notprecedesoreql put dup 178 /notfollowsoreql put dup 179 /precedeornoteqvlnt put dup 180 /followornoteqvlnt put dup 181 /lessornotsimilar put dup 182 /greaterornotsimilar put dup 183 /notlessdblequal put dup 184 /notgreaterdblequal put dup 185 /precedenotslnteql put dup 186 /follownotslnteql put dup 187 /precedenotdbleqv put dup 188 /follownotdbleqv put dup 189 /lessnotdblequal put dup 190 /greaternotdblequal put dup 191 /notsimilar put dup 192 /notapproxequal put dup 193 /upslope put dup 194 /downslope put dup 195 /notsubsetoreql put dup 196 /epsiloninv put dup 0 /lessornotequal put dup 1 /greaterornotequal put dup 2 /notlessequal put dup 3 /notgreaterequal put dup 4 /notless put dup 5 /notgreater put dup 6 /notprecedes put dup 7 /notfollows put dup 8 /lessornotdbleql put dup 9 /greaterornotdbleql put dup 10 /notlessorslnteql put dup 11 /notgreaterorslnteql put dup 12 /lessnotequal put dup 13 /greaternotequal put dup 14 /notprecedesoreql put dup 15 /notfollowsoreql put dup 16 /precedeornoteqvlnt put dup 17 /followornoteqvlnt put dup 18 /lessornotsimilar put dup 19 /greaterornotsimilar put dup 20 /notlessdblequal put dup 21 /notgreaterdblequal put dup 22 /precedenotslnteql put dup 23 /follownotslnteql put dup 24 /precedenotdbleqv put dup 25 /follownotdbleqv put dup 26 /lessnotdblequal put dup 27 /greaternotdblequal put dup 28 /notsimilar put dup 29 /notapproxequal put dup 30 /upslope put dup 31 /downslope put dup 32 /notsubsetoreql put dup 33 /notsupersetoreql put dup 34 /notsubsetordbleql put dup 35 /notsupersetordbleql put dup 36 /subsetornotdbleql put dup 37 /supersetornotdbleql put dup 38 /subsetornoteql put dup 39 /supersetornoteql put dup 40 /subsetnoteql put dup 41 /supersetnoteql put dup 42 /notsubseteql put dup 43 /notsuperseteql put dup 44 /notparallel put dup 45 /notbar put dup 46 /notshortbar put dup 47 /notshortparallel put dup 48 /notturnstile put dup 49 /notforces put dup 50 /notsatisfies put dup 51 /notforcesextra put dup 52 /nottriangeqlright put dup 53 /nottriangeqlleft put dup 54 /nottriangleleft put dup 55 /nottriangleright put dup 56 /notarrowleft put dup 57 /notarrowright put dup 58 /notdblarrowleft put dup 59 /notdblarrowright put dup 60 /notdblarrowboth put dup 61 /notarrowboth put dup 62 /dividemultiply put dup 63 /emptyset put dup 64 /notexistential 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /hatwide put dup 92 /hatwider put dup 93 /tildewide put dup 94 /tildewider put dup 96 /Finv put dup 97 /Gmir put dup 102 /Omegainv put dup 103 /eth put dup 104 /equalorsimilar put dup 105 /beth put dup 106 /gimel put dup 107 /daleth put dup 108 /lessdot put dup 109 /greaterdot put dup 110 /multicloseleft put dup 111 /multicloseright put dup 112 /barshort put dup 113 /parallelshort put dup 114 /integerdivide put dup 115 /similar put dup 116 /approxequal put dup 117 /approxorequal put dup 118 /followsorequal put dup 119 /precedesorequal put dup 120 /archleftdown put dup 121 /archrightdown put dup 122 /Digamma put dup 123 /kappa put dup 124 /k put dup 125 /planckover2pi put dup 126 /planckover2pi1 put dup 127 /epsiloninv put dup 128 /notsubsetoreql put dup 160 /space put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueID 5032014 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%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 161 /minus put dup 162 /periodcentered put dup 163 /multiply put dup 164 /asteriskmath put dup 165 /divide put dup 166 /diamondmath put dup 167 /plusminus put dup 168 /minusplus put dup 169 /circleplus put dup 170 /circleminus put dup 173 /circlemultiply put dup 174 /circledivide put dup 175 /circledot put dup 176 /circlecopyrt put dup 177 /openbullet put dup 178 /bullet put dup 179 /equivasymptotic put dup 180 /equivalence put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 183 /lessequal put dup 184 /greaterequal put dup 185 /precedesequal put dup 186 /followsequal put dup 187 /similar put dup 188 /approxequal put dup 189 /propersubset put dup 190 /propersuperset put dup 191 /lessmuch put dup 192 /greatermuch put dup 193 /precedes put dup 194 /follows put dup 195 /arrowleft put dup 196 /spade put dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 4 /divide put dup 5 /diamondmath put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 9 /circleminus put dup 10 /circlemultiply put dup 11 /circledivide put dup 12 /circledot put dup 13 /circlecopyrt put dup 14 /openbullet put dup 15 /bullet put dup 16 /equivasymptotic put dup 17 /equivalence put dup 18 /reflexsubset put dup 19 /reflexsuperset put dup 20 /lessequal put dup 21 /greaterequal put dup 22 /precedesequal put dup 23 /followsequal put dup 24 /similar put dup 25 /approxequal put dup 26 /propersubset put dup 27 /propersuperset put dup 28 /lessmuch put dup 29 /greatermuch put dup 30 /precedes put dup 31 /follows put dup 32 /arrowleft put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 36 /arrowboth put dup 37 /arrownortheast put dup 38 /arrowsoutheast put dup 39 /similarequal put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 42 /arrowdblup put dup 43 /arrowdbldown put dup 44 /arrowdblboth put dup 45 /arrownorthwest put dup 46 /arrowsouthwest put dup 47 /proportional put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 52 /triangle put dup 53 /triangleinv put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 57 /existential put dup 58 /logicalnot put dup 59 /emptyset put dup 60 /Rfractur put dup 61 /Ifractur put dup 62 /latticetop put dup 63 /perpendicular put dup 64 /aleph 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 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 194 /chi put dup 195 /psi put dup 196 /tie put dup 0 /Gamma put dup 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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 161 /parenleftbig put dup 162 /parenrightbig put dup 163 /bracketleftbig put dup 164 /bracketrightbig put dup 165 /floorleftbig put dup 166 /floorrightbig put dup 167 /ceilingleftbig put dup 168 /ceilingrightbig put dup 169 /braceleftbig put dup 170 /bracerightbig put dup 173 /angbracketleftbig put dup 174 /angbracketrightbig put dup 175 /vextendsingle put dup 176 /vextenddouble put dup 177 /slashbig put dup 178 /backslashbig put dup 179 /parenleftBig put dup 180 /parenrightBig put dup 181 /parenleftbigg put dup 182 /parenrightbigg put dup 183 /bracketleftbigg put dup 184 /bracketrightbigg put dup 185 /floorleftbigg put dup 186 /floorrightbigg put dup 187 /ceilingleftbigg put dup 188 /ceilingrightbigg put dup 189 /braceleftbigg put dup 190 /bracerightbigg put dup 191 /angbracketleftbigg put dup 192 /angbracketrightbigg put dup 193 /slashbigg put dup 194 /backslashbigg put dup 195 /parenleftBigg put dup 196 /arrowdblbt put dup 0 /parenleftbig put dup 1 /parenrightbig put dup 2 /bracketleftbig put dup 3 /bracketrightbig put dup 4 /floorleftbig put dup 5 /floorrightbig put dup 6 /ceilingleftbig put dup 7 /ceilingrightbig put dup 8 /braceleftbig put dup 9 /bracerightbig put dup 10 /angbracketleftbig put dup 11 /angbracketrightbig put dup 12 /vextendsingle put dup 13 /vextenddouble put dup 14 /slashbig put dup 15 /backslashbig put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 22 /floorleftbigg put dup 23 /floorrightbigg put dup 24 /ceilingleftbigg put dup 25 /ceilingrightbigg put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 28 /angbracketleftbigg put dup 29 /angbracketrightbigg put dup 30 /slashbigg put dup 31 /backslashbigg put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 34 /bracketleftBigg put dup 35 /bracketrightBigg put dup 36 /floorleftBigg put dup 37 /floorrightBigg put dup 38 /ceilingleftBigg put dup 39 /ceilingrightBigg put dup 40 /braceleftBigg put dup 41 /bracerightBigg put dup 42 /angbracketleftBigg put dup 43 /angbracketrightBigg put dup 44 /slashBigg put dup 45 /backslashBigg put dup 46 /slashBig put dup 47 /backslashBig put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 50 /bracketlefttp put dup 51 /bracketrighttp put dup 52 /bracketleftbt put dup 53 /bracketrightbt put dup 54 /bracketleftex put dup 55 /bracketrightex 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 63 /arrowvertex put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 66 /parenleftex put dup 67 /parenrightex put dup 68 /angbracketleftBig put dup 69 /angbracketrightBig put dup 70 /unionsqtext put dup 71 /unionsqdisplay put dup 72 /contintegraltext put dup 73 /contintegraldisplay put dup 74 /circledottext put dup 75 /circledotdisplay put dup 76 /circleplustext put dup 77 /circleplusdisplay put dup 78 /circlemultiplytext put dup 79 /circlemultiplydisplay put dup 80 /summationtext put dup 81 /producttext put dup 82 /integraltext put dup 83 /uniontext put dup 84 /intersectiontext put dup 85 /unionmultitext put dup 86 /logicalandtext put dup 87 /logicalortext put dup 88 /summationdisplay put dup 89 /productdisplay put dup 90 /integraldisplay put dup 91 /uniondisplay put dup 92 /intersectiondisplay put dup 93 /unionmultidisplay put dup 94 /logicalanddisplay put dup 95 /logicalordisplay put dup 96 /coproducttext put dup 97 /coproductdisplay put dup 98 /hatwide put dup 99 /hatwider put dup 100 /hatwidest put dup 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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 161 /minus put dup 162 /periodcentered put dup 163 /multiply put dup 164 /asteriskmath put dup 165 /divide put dup 166 /diamondmath put dup 167 /plusminus put dup 168 /minusplus put dup 169 /circleplus put dup 170 /circleminus put dup 173 /circlemultiply put dup 174 /circledivide put dup 175 /circledot put dup 176 /circlecopyrt put dup 177 /openbullet put dup 178 /bullet put dup 179 /equivasymptotic put dup 180 /equivalence put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 183 /lessequal put dup 184 /greaterequal put dup 185 /precedesequal put dup 186 /followsequal put dup 187 /similar put dup 188 /approxequal put dup 189 /propersubset put dup 190 /propersuperset put dup 191 /lessmuch put dup 192 /greatermuch put dup 193 /precedes put dup 194 /follows put dup 195 /arrowleft put dup 196 /spade put dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 4 /divide put dup 5 /diamondmath put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 9 /circleminus put dup 10 /circlemultiply put dup 11 /circledivide put dup 12 /circledot put dup 13 /circlecopyrt put dup 14 /openbullet put dup 15 /bullet put dup 16 /equivasymptotic put dup 17 /equivalence put dup 18 /reflexsubset put dup 19 /reflexsuperset put dup 20 /lessequal put dup 21 /greaterequal put dup 22 /precedesequal put dup 23 /followsequal put dup 24 /similar put dup 25 /approxequal put dup 26 /propersubset put dup 27 /propersuperset put dup 28 /lessmuch put dup 29 /greatermuch put dup 30 /precedes put dup 31 /follows put dup 32 /arrowleft put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 36 /arrowboth put dup 37 /arrownortheast put dup 38 /arrowsoutheast put dup 39 /similarequal put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 42 /arrowdblup put dup 43 /arrowdbldown put dup 44 /arrowdblboth put dup 45 /arrownorthwest put dup 46 /arrowsouthwest put dup 47 /proportional put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 52 /triangle put dup 53 /triangleinv put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 57 /existential put dup 58 /logicalnot put dup 59 /emptyset put dup 60 /Rfractur put dup 61 /Ifractur put dup 62 /latticetop put dup 63 /perpendicular put dup 64 /aleph 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /union put dup 92 /intersection put dup 93 /unionmulti put dup 94 /logicaland put dup 95 /logicalor put dup 96 /turnstileleft put dup 97 /turnstileright put dup 98 /floorleft put dup 99 /floorright put dup 100 /ceilingleft put dup 101 /ceilingright put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 108 /arrowbothv put dup 109 /arrowdblbothv put dup 110 /backslash put dup 111 /wreathproduct put dup 112 /radical put dup 113 /coproduct put dup 114 /nabla put dup 115 /integral put dup 116 /unionsq put dup 117 /intersectionsq put dup 118 /subsetsqequal put dup 119 /supersetsqequal put dup 120 /section put dup 121 /dagger put dup 122 /daggerdbl put dup 123 /paragraph put dup 124 /club put dup 125 /diamond put dup 126 /heart put dup 127 /spade put dup 128 /arrowleft put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 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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 (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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 194 /chi put dup 195 /psi put dup 196 /tie put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 19 /iota 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 27 /sigma put dup 28 /tau put dup 29 /upsilon put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 35 /theta1 put dup 36 /pi1 put dup 37 /rho1 put dup 38 /sigma1 put dup 39 /phi1 put dup 40 /arrowlefttophalf put dup 41 /arrowleftbothalf put dup 42 /arrowrighttophalf put dup 43 /arrowrightbothalf put dup 44 /arrowhookleft put dup 45 /arrowhookright put dup 46 /triangleright put dup 47 /triangleleft put dup 48 /zerooldstyle put dup 49 /oneoldstyle put dup 50 /twooldstyle put dup 51 /threeoldstyle put dup 52 /fouroldstyle put dup 53 /fiveoldstyle put dup 54 /sixoldstyle put dup 55 /sevenoldstyle put dup 56 /eightoldstyle put dup 57 /nineoldstyle put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 63 /star put dup 64 /partialdiff 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /flat put dup 92 /natural put dup 93 /sharp put dup 94 /slurbelow put dup 95 /slurabove put dup 96 /lscript 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 123 /dotlessi put dup 124 /dotlessj put dup 125 /weierstrass put dup 126 /vector put dup 127 /tie put dup 128 /psi put dup 160 /space put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec 80347982AB3942D930E069A70D0D48311D725E830D1C76FBA12E12486E989C9874C2B527F092 5722787027F44470D484262C360CDFDDDF3657533A57BB16F73048BFBBFCB73A650484015441 FDC837ADD94AC8FBD2022E3EC8F115D4B4BB7B7F15388F22CC6198EFE768BD9FCEB3446EE4A8 DC27D6CD152485384EF5F59381FFDA43F2D20C8FB08AA27AB2015B774DB10DACFDCD33E60F17 8C461553146AB427BDD7DA12534BA078AD3D780414930DA4F8D58ABEFD45DB119B10EB409DD8 97923C6E705479464A4B310B58348C4B42393988FEF4925CF984423AAF65FEA9F0E64629953B CF50B919D968D99BD185F83112B2759CC411764E9BDE677F57C5EE5AC555448D5F81A16259DE 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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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon 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 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at 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 88 /X 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 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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B5FBF780CF8754FA7422C3F57E62CCEEAD9AA3470000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /lessornotequal put dup 162 /greaterornotequal put dup 163 /notlessequal put dup 164 /notgreaterequal put dup 165 /notless put dup 166 /notgreater put dup 167 /notprecedes put dup 168 /notfollows put dup 169 /lessornotdbleql put dup 170 /greaterornotdbleql put dup 173 /notlessorslnteql put dup 174 /notgreaterorslnteql put dup 175 /lessnotequal put dup 176 /greaternotequal put dup 177 /notprecedesoreql put dup 178 /notfollowsoreql put dup 179 /precedeornoteqvlnt put dup 180 /followornoteqvlnt put dup 181 /lessornotsimilar put dup 182 /greaterornotsimilar put dup 183 /notlessdblequal put dup 184 /notgreaterdblequal put dup 185 /precedenotslnteql put dup 186 /follownotslnteql put dup 187 /precedenotdbleqv put dup 188 /follownotdbleqv put dup 189 /lessnotdblequal put dup 190 /greaternotdblequal put dup 191 /notsimilar put dup 192 /notapproxequal put dup 193 /upslope put dup 194 /downslope put dup 195 /notsubsetoreql put dup 196 /epsiloninv put dup 0 /lessornotequal put dup 1 /greaterornotequal put dup 2 /notlessequal put dup 3 /notgreaterequal put dup 4 /notless put dup 5 /notgreater put dup 6 /notprecedes put dup 7 /notfollows put dup 8 /lessornotdbleql put dup 9 /greaterornotdbleql put dup 10 /notlessorslnteql put dup 11 /notgreaterorslnteql put dup 12 /lessnotequal put dup 13 /greaternotequal put dup 14 /notprecedesoreql put dup 15 /notfollowsoreql put dup 16 /precedeornoteqvlnt put dup 17 /followornoteqvlnt put dup 18 /lessornotsimilar put dup 19 /greaterornotsimilar put dup 20 /notlessdblequal put dup 21 /notgreaterdblequal put dup 22 /precedenotslnteql put dup 23 /follownotslnteql put dup 24 /precedenotdbleqv put dup 25 /follownotdbleqv put dup 26 /lessnotdblequal put dup 27 /greaternotdblequal put dup 28 /notsimilar put dup 29 /notapproxequal put dup 30 /upslope put dup 31 /downslope put dup 32 /notsubsetoreql put dup 33 /notsupersetoreql put dup 34 /notsubsetordbleql put dup 35 /notsupersetordbleql put dup 36 /subsetornotdbleql put dup 37 /supersetornotdbleql put dup 38 /subsetornoteql put dup 39 /supersetornoteql put dup 40 /subsetnoteql put dup 41 /supersetnoteql put dup 42 /notsubseteql put dup 43 /notsuperseteql put dup 44 /notparallel put dup 45 /notbar put dup 46 /notshortbar put dup 47 /notshortparallel put dup 48 /notturnstile put dup 49 /notforces put dup 50 /notsatisfies put dup 51 /notforcesextra put dup 52 /nottriangeqlright put dup 53 /nottriangeqlleft put dup 54 /nottriangleleft put dup 55 /nottriangleright put dup 56 /notarrowleft put dup 57 /notarrowright put dup 58 /notdblarrowleft put dup 59 /notdblarrowright put dup 60 /notdblarrowboth put dup 61 /notarrowboth put dup 62 /dividemultiply put dup 63 /emptyset put dup 64 /notexistential 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /hatwide put dup 92 /hatwider put dup 93 /tildewide put dup 94 /tildewider put dup 96 /Finv put dup 97 /Gmir put dup 102 /Omegainv put dup 103 /eth put dup 104 /equalorsimilar put dup 105 /beth put dup 106 /gimel put dup 107 /daleth put dup 108 /lessdot put dup 109 /greaterdot put dup 110 /multicloseleft put dup 111 /multicloseright put dup 112 /barshort put dup 113 /parallelshort put dup 114 /integerdivide put dup 115 /similar put dup 116 /approxequal put dup 117 /approxorequal put dup 118 /followsorequal put dup 119 /precedesorequal put dup 120 /archleftdown put dup 121 /archrightdown put dup 122 /Digamma put dup 123 /kappa put dup 124 /k put dup 125 /planckover2pi put dup 126 /planckover2pi1 put dup 127 /epsiloninv put dup 128 /notsubsetoreql put dup 160 /space put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon 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 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at 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 88 /X 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 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec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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. 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon 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 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at 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 88 /X 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 95 /dotaccent put dup 96 /quoteleft 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 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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 161 /minus put dup 162 /periodcentered put dup 163 /multiply put dup 164 /asteriskmath put dup 165 /divide put dup 166 /diamondmath put dup 167 /plusminus put dup 168 /minusplus put dup 169 /circleplus put dup 170 /circleminus put dup 173 /circlemultiply put dup 174 /circledivide put dup 175 /circledot put dup 176 /circlecopyrt put dup 177 /openbullet put dup 178 /bullet put dup 179 /equivasymptotic put dup 180 /equivalence put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 183 /lessequal put dup 184 /greaterequal put dup 185 /precedesequal put dup 186 /followsequal put dup 187 /similar put dup 188 /approxequal put dup 189 /propersubset put dup 190 /propersuperset put dup 191 /lessmuch put dup 192 /greatermuch put dup 193 /precedes put dup 194 /follows put dup 195 /arrowleft put dup 196 /spade put dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 4 /divide put dup 5 /diamondmath put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 9 /circleminus put dup 10 /circlemultiply put dup 11 /circledivide put dup 12 /circledot put dup 13 /circlecopyrt put dup 14 /openbullet put dup 15 /bullet put dup 16 /equivasymptotic put dup 17 /equivalence put dup 18 /reflexsubset put dup 19 /reflexsuperset put dup 20 /lessequal put dup 21 /greaterequal put dup 22 /precedesequal put dup 23 /followsequal put dup 24 /similar put dup 25 /approxequal put dup 26 /propersubset put dup 27 /propersuperset put dup 28 /lessmuch put dup 29 /greatermuch put dup 30 /precedes put dup 31 /follows put dup 32 /arrowleft put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 36 /arrowboth put dup 37 /arrownortheast put dup 38 /arrowsoutheast put dup 39 /similarequal put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 42 /arrowdblup put dup 43 /arrowdbldown put dup 44 /arrowdblboth put dup 45 /arrownorthwest put dup 46 /arrowsouthwest put dup 47 /proportional put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 52 /triangle put dup 53 /triangleinv put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 57 /existential put dup 58 /logicalnot put dup 59 /emptyset put dup 60 /Rfractur put dup 61 /Ifractur put dup 62 /latticetop put dup 63 /perpendicular put dup 64 /aleph 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 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 194 /chi put dup 195 /psi put dup 196 /tie put dup 0 /Gamma put dup 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cleartomark %%EndFont %%BeginFont: CMSY9 %!PS-AdobeFont-1.1: CMSY9 1.0 %%CreationDate: 1991 Aug 15 07:22:27 % 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 (CMSY9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY9 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 161 /minus put dup 162 /periodcentered put dup 163 /multiply put dup 164 /asteriskmath put dup 165 /divide put dup 166 /diamondmath put dup 167 /plusminus put dup 168 /minusplus put dup 169 /circleplus put dup 170 /circleminus put dup 173 /circlemultiply put dup 174 /circledivide put dup 175 /circledot put dup 176 /circlecopyrt put dup 177 /openbullet put dup 178 /bullet put dup 179 /equivasymptotic put dup 180 /equivalence put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 183 /lessequal put dup 184 /greaterequal put dup 185 /precedesequal put dup 186 /followsequal put dup 187 /similar put dup 188 /approxequal put dup 189 /propersubset put dup 190 /propersuperset put dup 191 /lessmuch put dup 192 /greatermuch put dup 193 /precedes put dup 194 /follows put dup 195 /arrowleft put dup 196 /spade put dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 4 /divide put dup 5 /diamondmath put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 9 /circleminus put dup 10 /circlemultiply put dup 11 /circledivide put dup 12 /circledot put dup 13 /circlecopyrt put dup 14 /openbullet put dup 15 /bullet put dup 16 /equivasymptotic put dup 17 /equivalence put dup 18 /reflexsubset put dup 19 /reflexsuperset put dup 20 /lessequal put dup 21 /greaterequal put dup 22 /precedesequal put dup 23 /followsequal put dup 24 /similar put dup 25 /approxequal put dup 26 /propersubset put dup 27 /propersuperset put dup 28 /lessmuch put dup 29 /greatermuch put dup 30 /precedes put dup 31 /follows put dup 32 /arrowleft put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 36 /arrowboth put dup 37 /arrownortheast put dup 38 /arrowsoutheast put dup 39 /similarequal put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 42 /arrowdblup put dup 43 /arrowdbldown put dup 44 /arrowdblboth put dup 45 /arrownorthwest put dup 46 /arrowsouthwest put dup 47 /proportional put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 52 /triangle put dup 53 /triangleinv put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 57 /existential put dup 58 /logicalnot put dup 59 /emptyset put dup 60 /Rfractur put dup 61 /Ifractur put dup 62 /latticetop put dup 63 /perpendicular put dup 64 /aleph 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /union put dup 92 /intersection put dup 93 /unionmulti put dup 94 /logicaland put dup 95 /logicalor put dup 96 /turnstileleft put dup 97 /turnstileright put dup 98 /floorleft put dup 99 /floorright put dup 100 /ceilingleft put dup 101 /ceilingright put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 108 /arrowbothv put dup 109 /arrowdblbothv put dup 110 /backslash put dup 111 /wreathproduct put dup 112 /radical put dup 113 /coproduct put dup 114 /nabla put dup 115 /integral put dup 116 /unionsq put dup 117 /intersectionsq put dup 118 /subsetsqequal put dup 119 /supersetsqequal put dup 120 /section put dup 121 /dagger put dup 122 /daggerdbl put dup 123 /paragraph put dup 124 /club put dup 125 /diamond put dup 126 /heart put dup 127 /spade put dup 128 /arrowleft put readonly def /FontBBox{-30 -958 1146 777}readonly def /UniqueID 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % 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 (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 194 /chi put dup 195 /psi put dup 196 /tie put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 19 /iota 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 27 /sigma put dup 28 /tau put dup 29 /upsilon put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 35 /theta1 put dup 36 /pi1 put dup 37 /rho1 put dup 38 /sigma1 put dup 39 /phi1 put dup 40 /arrowlefttophalf put dup 41 /arrowleftbothalf put dup 42 /arrowrighttophalf put dup 43 /arrowrightbothalf put dup 44 /arrowhookleft put dup 45 /arrowhookright put dup 46 /triangleright put dup 47 /triangleleft put dup 48 /zerooldstyle put dup 49 /oneoldstyle put dup 50 /twooldstyle put dup 51 /threeoldstyle put dup 52 /fouroldstyle put dup 53 /fiveoldstyle put dup 54 /sixoldstyle put dup 55 /sevenoldstyle put dup 56 /eightoldstyle put dup 57 /nineoldstyle put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 63 /star put dup 64 /partialdiff 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /flat put dup 92 /natural put dup 93 /sharp put dup 94 /slurbelow put dup 95 /slurabove put dup 96 /lscript 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 123 /dotlessi put dup 124 /dotlessj put dup 125 /weierstrass put dup 126 /vector put dup 127 /tie put dup 128 /psi put dup 160 /space put readonly def /FontBBox{-29 -250 1075 750}readonly def /UniqueID 5087384 def currentdict end currentfile eexec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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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon 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 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at 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 88 /X 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 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict end currentfile eexec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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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon 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 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at 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 88 /X 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 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-58 -250 1195 750}readonly def /UniqueID 5000767 def currentdict end currentfile eexec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271DB64DA625559B31C7D422EEF1ED5A35CBF1F37958EA0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon 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 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at 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 88 /X 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 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR17 %!PS-AdobeFont-1.1: CMR17 1.0 %%CreationDate: 1991 Aug 20 16:38:24 % 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 (CMR17) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR17 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon 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 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at 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 88 /X 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 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-33 -250 945 749}readonly def /UniqueID 5000795 def currentdict end currentfile eexec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Ft(\(1.3\))515 1101 y(Here)31 b Fq(Z)778 1070 y Fr(2)772 1121 y(0)844 1101 y Ft(=)e Fs(Z)993 1070 y Fr(2)1051 1101 y Fp(n)21 b(f)p Ft(0)p Fp(g)p Ft(,)31 b Fp(f)p Fq(\014)1383 1113 y Fn(s)1417 1101 y Ft(\()p Fq(t)p Ft(\))f(=)f Fq(\014)1686 1070 y Fn(!)1682 1121 y(s)1735 1101 y Ft(\()p Fq(t)p Ft(\))p Fp(g)i Ft(is)g(a)g(set)g(of)h(indep)r(enden)n(t)g(standard)e(Wiener)515 1200 y(pro)r(cesses,)25 b(de\014ned)h(on)g(a)f(complete)h(probabilit)n (y)f(space)h(\(\012)p Fq(;)14 b Fp(F)8 b Fq(;)14 b Fj(P)p Ft(\),)27 b(satisfying)e Fq(\014)3150 1212 y Fn(s)3185 1200 y Ft(\(0\))e(=)515 1300 y(0.)36 b(The)28 b(real)f(co)r(e\016cien)n (ts)g Fq(b)1405 1312 y Fn(s)1468 1300 y Ft(are)f(suc)n(h)h(that)h Fq(M)2054 1312 y Fr(1)2114 1300 y Fq(<)23 b Fp(1)p Ft(,)k(where)1448 1485 y Fq(M)1529 1497 y Fn(n)1597 1485 y Ft(=)1698 1406 y Fo(X)1685 1591 y Fn(s)p Fm(2)p Fl(Z)1800 1571 y Fk(2)1800 1609 y(0)1846 1485 y Fp(j)p Fq(s)p Fp(j)1931 1451 y Fr(2)p Fn(n)2009 1485 y Fq(b)2045 1451 y Fr(2)2045 1506 y Fn(s)2096 1485 y Fq(;)97 b(n)23 b Fp(2)g Fs(Z)p Fq(;)515 1767 y Ft(and)k(\()p Fq(e)747 1779 y Fn(s)783 1767 y Fq(;)14 b(s)22 b Fp(2)i Fs(Z)1015 1737 y Fr(2)1015 1788 y(0)1052 1767 y Ft(\))k(is)g(the)g(standard)f(trigonometric)f(basis)g(of)i Fq(H)7 b Ft(:)1115 1990 y Fq(e)1154 2002 y Fn(s)1189 1990 y Ft(\()p Fq(x)p Ft(\))24 b(=)1422 1934 y(sin\()p Fq(s)18 b Fp(\001)h Fq(x)p Ft(\))p 1422 1971 313 4 v 1455 1988 a Fp(p)p 1524 1988 42 4 v 69 x Ft(2)p Fq(\031)s Fp(j)p Fq(s)p Fp(j)1758 1873 y Fo(\024)1802 1940 y Fp(\000)p Fq(s)1906 1952 y Fr(2)1835 2039 y Fq(s)1874 2051 y Fr(1)1943 1873 y Fo(\025)2084 1990 y Ft(if)83 b Fq(s)2254 2002 y Fr(1)2310 1990 y Ft(+)18 b Fq(s)2432 2002 y Fr(2)2469 1990 y Fq(\016)2506 2002 y Fn(s)2537 2010 y Fk(1)2570 2002 y Fn(;)p Fr(0)2650 1990 y Fq(>)k Ft(0)1099 2280 y Fq(e)1138 2292 y Fn(s)1173 2280 y Ft(\()p Fq(x)p Ft(\))i(=)1406 2224 y(cos)o(\()p Fq(s)18 b Fp(\001)h Fq(x)p Ft(\))p 1406 2261 323 4 v 1444 2277 a Fp(p)p 1513 2277 42 4 v 69 x Ft(2)o Fq(\031)s Fp(j)p Fq(s)p 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Ft(\).)639 2786 y(It)h(is)f(w)n(ell)f(kno)n(wn)h(\(see)g([VF88)o (,)g(DZ92,)g(Fla94)o(]\))g(that)g(for)g(an)n(y)f(random)g(initial)i (data)515 2885 y Fq(u)563 2897 y Fr(0)600 2885 y Ft(,)33 b(indep)r(enden)n(t)g(of)e Fq(\021)s Ft(\()p Fp(\001)p Ft(\),)k(and)c(suc)n(h)h(that)g Fj(E)p Fp(k)p Fq(u)2112 2897 y Fr(0)2148 2885 y Fp(k)2190 2855 y Fr(2)2257 2885 y Fq(<)e Fp(1)p Ft(,)k(the)e(equation)f(\(1.2\))h(has)f(a)515 2985 y(unique)e(solution)f Fq(u)p Ft(\()p Fq(t)p Ft(\),)i(b)r(elonging) e(to)h Fq(C)6 b Ft(\([0)p Fq(;)14 b Fp(1)p Ft(\))p Fq(;)g(H)7 b Ft(\))29 b(almost)g(sure.)40 b(This)29 b(solution)g(is)f(a)515 3084 y(Mark)n(o)n(v)d(pro)r(cess)h(in)i Fq(H)7 b Ft(.)37 b(W)-7 b(e)28 b(shall)f(denote)h(it)g(as)f Fq(u)22 b Ft(=)h Fq(u)p Ft(\()p Fq(t)p Ft(;)14 b Fq(u)2482 3096 y Fr(0)2518 3084 y Ft(\).)38 b(If)1751 3258 y Fq(b)1787 3270 y Fn(s)1845 3258 y Fp(6)p Ft(=)23 b(0)83 b Fp(8)p Fq(s)1065 b Ft(\(1.4\))515 3431 y(then)22 b(the)h(Mark)n(o)n(v)d(pro)r 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5006 y Fh(j)p Fg(s)p Fh(j)18 b(\024)i Fg(N)7 b Fi(,)23 b(where)h Fg(N)i Fi(=)20 b Fg(N)7 b Fi(\()p Fg(\027)t Fi(\))21 b Fg(<)e Fh(1)k Fi(is)g(su\016cien)n(tly)h(large\).)1926 5255 y Ft(2)p eop end %%Page: 3 3 TeXDict begin 3 2 bop 515 523 a Ft(Then)19 b(the)g(random)g(\014eld)g Fq(\020)6 b Ft(\()p Fq(t;)14 b(x)p Ft(\))20 b(is)f(translationary)e(in) n(v)-5 b(arian)n(t.)33 b(That)19 b(is,)i(its)e(distribution)515 623 y(is)33 b(in)n(v)-5 b(arian)n(t)33 b(under)g(the)h(translation)f Fq(T)1825 635 y Fn(h)1901 623 y Ft(of)h(the)g(torus)f Fs(T)2425 593 y Fr(2)2462 623 y Ft(,)j Fq(T)2570 635 y Fn(h)2612 623 y Fq(x)e Ft(=)f Fq(x)23 b Ft(+)f Fq(h)33 b Ft(\()p Fq(h)h Fp(2)f Fs(T)3286 593 y Fr(2)3324 623 y Ft(\).)515 722 y(Due)38 b(to)f(the)i(uniqueness,)h(this)d(implies)h (that)g(the)g(stationary)e(measure)h Fq(\026)3013 734 y Fn(\027)3092 722 y Ft(and)h(the)515 822 y(stationary)26 b(pro)r(cess)g Fq(u)1247 834 y Fn(\027)1288 822 y Ft(\()p Fq(t;)14 b(x)p Ft(\))29 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1421 y Fr(2)2187 1472 y Fn(\027)p 2090 1488 138 4 v 2092 1564 a Fq(@)g(x)2188 1576 y Fr(1)2256 1508 y Fp(\000)2349 1451 y Fq(@)g(u)2446 1421 y Fr(1)2446 1472 y Fn(\027)p 2349 1488 V 2351 1564 a Fq(@)g(x)2447 1576 y Fr(2)2510 1508 y Fq(:)515 1694 y Ft(The)23 b(measure)g Fq(m)1074 1706 y Fn(\027)1138 1694 y Ft(=)g Fp(D)r Fq(\030)1328 1706 y Fn(\027)1370 1694 y Ft(\()p Fq(t)p Ft(\))h(is)f(time)h(indep)r (enden)n(t,)h(and)f(is)f(the)h(image)f(of)g(the)h(measure)515 1794 y Fq(\026)565 1806 y Fn(\027)634 1794 y Ft(under)j(the)h(map)g Fq(u)22 b Fp(!)h Ft(curl)14 b Fq(u)p Ft(.)36 b(Moreo)n(v)n(er,)25 b(since)1145 2031 y Fq(u)1193 2043 y Fn(\027)1257 2031 y Ft(=)e Fq(D)r(\030)1452 2043 y Fn(\027)1494 2031 y Fq(;)180 b(D)25 b Ft(=)1878 1914 y Fo(\022)1992 1975 y Fq(@)p 1949 2012 134 4 v 1949 2088 a(@)5 b(x)2045 2100 y Fr(2)2093 2031 y Fq(;)14 b Fp(\000)2246 1975 y Fq(@)p 2205 2012 V 2205 2088 a(@)5 b(x)2301 2100 y Fr(1)2347 1914 y Fo(\023)2409 1931 y Fn(t)2438 2031 y Ft(\()p Fp(\000)p Ft(\001\))2636 1997 y Fm(\000)p Fr(1)2725 2031 y Fq(;)460 b Ft(\(1.6\))515 2264 y(where)31 b Fp(\000)p Ft(\(\001\))957 2233 y Fm(\000)p Fr(1)1079 2264 y Ft(is)h(the)g(in)n(v)n(erse)f(of)h (the)g(min)n(us-Laplacian,)g(de\014ned)h(on)e(the)i(functions)515 2363 y(on)28 b Fs(T)686 2333 y Fr(2)752 2363 y Ft(with)h(zero)e(mean-v) -5 b(alue,)28 b(then)g Fq(\026)1817 2375 y Fn(\027)1887 2363 y Ft(is)g(the)h(image)e(of)i Fq(m)2524 2375 y Fn(\027)2593 2363 y Ft(under)f(the)h(map)f Fq(D)r Ft(.)39 b(So)515 2463 y(a)29 b(study)g(of)h(the)g(pro)r(cess)e Fq(\030)1385 2475 y Fn(\027)1456 2463 y Ft(and)h(the)h(measure)f Fq(m)2163 2475 y Fn(\027)2233 2463 y Ft(is)h(equiv)-5 b(alen)n(t)29 b(to)g(the)h(study)g(of)f Fq(u)3338 2475 y Fn(\027)515 2562 y Ft(and)e Fq(\026)726 2574 y Fn(\027)768 2562 y Ft(.)639 2662 y(The)h(balance)f(relations)f(reed)h(as)g(follo)n(ws:) 1110 2839 y Fj(E)1173 2747 y Fo(\020)1222 2839 y Fq(g)s Ft(\()p Fq(\030)1333 2851 y Fn(\027)1375 2839 y Ft(\()p Fq(t;)14 b(x)p Ft(\)\))24 b 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Ft(are)c(some)g (\014xed)g(constan)n(ts.)36 b(Equiv)-5 b(alen)n(tly)e(,)1395 3426 y Fj(E)p Ft(\()p Fp(jr)p Fq(\030)1618 3438 y Fn(\027)1659 3426 y Ft(\()p Fq(t;)14 b(x)p Ft(\))p Fp(j)1860 3391 y Fr(2)1922 3426 y Fp(j)23 b(F)2028 3441 y Fn(\030)2058 3449 y Fe(\027)2094 3441 y Fr(\()p Fn(t;x)p Fr(\))2233 3426 y Ft(\))g(=)g Fq(B)2439 3438 y Fr(1)2476 3426 y Fq(;)515 3603 y Ft(where)35 b Fj(E)p Ft(\()p Fp(\001)i(j)g(F)1038 3618 y Fn(\030)1068 3626 y Fe(\027)1104 3618 y Fr(\()p Fn(t;x)p Fr(\))1243 3603 y Ft(\))f(denotes)g(the)g(conditional)f(exp)r (ectation)h(with)g(resp)r(ect)g(to)g(the)515 3702 y Fq(\033)s Ft(-algebra,)26 b(generated)g(b)n(y)h(the)h(random)f(v)-5 b(ariable)27 b Fq(\030)2196 3714 y Fn(\027)2237 3702 y Ft(\()p Fq(t;)14 b(x)p Ft(\).)639 3802 y(It)34 b(is)g(kno)n(wn)e (\(e.g.,)j(see)e([VF88,)h(Fla94)n(,)g(KS03)o(]\))g(that)f(if)h Fq(M)2617 3814 y Fn(k)2691 3802 y Fq(<)e Fp(1)i Ft(\()p Fq(k)i Fp(\025)c Ft(1\),)j(and)515 3902 y Fq(u)563 3914 y Fr(0)630 3902 y Fp(2)30 b Fq(H)39 b Ft(is)32 b(a)f(non-random)g(v)n (ector,)g(then)i(for)e(an)n(y)g Fq(T)42 b Fp(\025)29 b Ft(2)j(the)g(solution)g Fq(u)d Ft(=)h Fq(u)p Ft(\()p Fq(t)p Ft(;)14 b Fq(u)3310 3914 y Fr(0)3347 3902 y Ft(\))515 4001 y(satis\014es)862 4178 y Fq(u)23 b Fp(2)g Fq(C)6 b Ft(\([1)p Fq(;)14 b(T)e Ft(])p Fq(;)i(H)1407 4144 y Fn(k)1447 4178 y Ft(\))83 b(and)g Fq(u)18 b Fp(\000)1928 4115 y(p)p 1997 4115 47 4 v 63 x Fq(\027)h(\020)30 b Fp(2)23 b Fq(C)2266 4144 y Fr(1)2304 4178 y Ft(\([1)p Fq(;)14 b(T)e Ft(])p Fq(;)i(H)2635 4144 y Fn(k)q Fm(\000)p Fr(2)2759 4178 y Ft(\))83 b(a.s.)14 b Fq(:)176 b Ft(\(1.8\))515 4356 y(The)32 b(stationary)f(solutions)g Fq(u)1489 4368 y Fn(\027)1530 4356 y Ft(\()p Fq(t;)14 b(x)p Ft(\))33 b(also)e(satisfy)i(\(1.8\).)51 b(Moreo)n(v)n(er,)30 b(in)j(this)f(case) g(the)515 4455 y(relations)26 b(hold)i(with)g([1)p Fq(;)14 b(T)e Ft(])26 b(replaced)h(b)n(y)g(an)n(y)g(\014nite)h(segmen)n(t)f([)p Fq(T)2643 4467 y Fr(1)2680 4455 y Fq(;)14 b(T)2766 4467 y Fr(2)2802 4455 y Ft(],)28 b 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Fq(\030)t Ft(\()p Fq(t;)g(x)p Ft(;)g Fq(u)1856 4984 y Fr(0)1894 4972 y Ft(\))p Fp(j)1949 4938 y Fr(2)2001 4972 y Fq(dt)23 b Fp(!)g Fj(E)2266 4905 y Fo(\000)2304 4972 y Fq(g)s Ft(\()p Fq(\030)2415 4984 y Fn(\027)2456 4972 y Ft(\()p Fq(x)p Ft(\))p Fp(jr)p Fq(\030)2695 4984 y Fn(\027)2738 4972 y Ft(\()p Fq(x)p Ft(\))p Fp(j)2872 4938 y Fr(2)2911 4905 y Fo(\001)3032 4972 y Ft(a.s.)o Fq(;)1926 5255 y Ft(3)p eop end %%Page: 4 4 TeXDict begin 4 3 bop 515 523 a Ft(b)n(y)27 b(the)h(Strong)f(La)n(w)g (of)g(Large)f(Num)n(b)r(ers)i(\(see)f([Kuk02)o(,)g(Shi05]\),)h(if)1074 694 y Fq(M)1155 706 y Fr(5)1215 694 y Fq(<)22 b Fp(1)p Fq(;)97 b Fj(E)p Fp(j)p Fq(u)1639 706 y Fr(0)1676 694 y Fp(j)1699 660 y Fr(2)1759 694 y Fq(<)23 b Fp(1)p Fq(;)97 b(g)s Ft(\()p Fq(\030)t Ft(\))46 b(is)28 b(a)f(p)r(olynomial)o Fq(:)388 b Ft(\(1.9\))515 865 y(Similar)30 b(result)g(holds)g(for)f (the)i(functional)g Fq(\030)g Fp(!)d Fq(g)s Ft(\()p Fq(\030)t Ft(\()p Fq(t;)14 b(x)p Ft(\)\),)32 b(so)e Ff(the)i(e)l(quality)40 b 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b(us)f(\014x)g(an)n(y)g Fq(t)f Fp(\025)h Ft(0,)h(abbreviate)e Fq(\030)1901 2729 y Fn(\027)1943 2717 y Ft(\()p Fq(t;)14 b(x)p Ft(\))33 b(=)f Fq(\030)t Ft(\()p Fq(x)p Ft(\))j(and)e(in)n(tegrate)f(the)i(balance)515 2816 y(relation)26 b(o)n(v)n(er)g Fs(T)1052 2786 y Fr(2)1090 2816 y Ft(:)1093 3009 y Fj(E)1170 2896 y Fo(Z)1215 3085 y Fl(T)1254 3068 y Fk(2)1291 3009 y Ft(\()p Fq(g)s Ft(\()p Fq(\030)t Ft(\()p Fq(x)p Ft(\))p Fp(jr)p Fq(\030)t Ft(\()p Fq(x)p Ft(\))p Fp(j)1815 2975 y Fr(2)1855 3009 y Ft(\))14 b Fq(dx)24 b Ft(=)e Fq(B)2165 3021 y Fr(1)2202 3009 y Fj(E)2279 2896 y Fo(Z)2325 3085 y Fl(T)2364 3068 y Fk(2)2414 3009 y Fq(g)s Ft(\()p Fq(\030)t Ft(\()p Fq(x)p Ft(\)\))14 b Fq(dx:)409 b Ft(\(2.3\))515 3227 y(F)-7 b(or)27 b(a)g(con)n(tin)n (uous)f(function)j Fq(g)h Ft(suc)n(h)d(that)h Fp(j)p Fq(g)s Fp(j)23 b(\024)f Ft(1,)28 b(w)n(e)f(denote)934 3440 y Fq(I)970 3452 y Fr(1)1031 3440 y Ft(=)c Fj(E)1196 3327 y Fo(Z)1241 3516 y Fl(T)1280 3499 y Fk(2)1330 3373 y Fo(\000)1368 3440 y Fq(g)s 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4972 y Ft(\()p Fq(x;)14 b(!)s Ft(\))g Fq(dxP)e Ft(\()p Fq(d!)s Ft(\))p Fq(:)1926 5255 y Ft(4)p eop end %%Page: 5 5 TeXDict begin 5 4 bop 515 523 a Ft(Since)30 b(the)h(in)n(tegrand)f(con) n(v)n(erges)e(to)i Fq(I)1770 538 y Fm(fr)p Fn(\030)r Fr(=0)p Fm(g)2045 523 y Ft(when)h Fq(")c Fp(!)h Ft(0,)j(then)g(b)n(y)g (Lemma)f(2.1)f(w)n(e)515 623 y(ha)n(v)n(e)1563 722 y Fq(I)1606 688 y Fn(")1599 743 y Fr(2)1664 722 y Fp(!)24 b Fq(I)1807 734 y Fr(2)1927 722 y Ft(as)83 b Fq(")22 b Fp(!)h Ft(0)14 b Fq(:)639 872 y Ft(Let)35 b(us)f(denote)g Fq(K)1253 884 y Fn(")1288 872 y Ft(\()p Fq(!)s Ft(\))g(=)g Fp(f)p Fq(x)g Fp(j)h Ft(\()p Fq(x;)14 b(!)s Ft(\))34 b Fp(2)h Fq(K)2119 884 y Fn(")2154 872 y Fp(g)p Ft(.)56 b(Then)35 b(b)n(y)f(the)g(implicit)h(function)515 971 y(theorem,)27 b(for)g(ev)n(ery)f Fq(!)s Ft(,)i(ev)n(ery)e Fq(\034)33 b Fp(2)23 b Fs(R)28 b Ft(and)f(an)n(y)g Fq(")c(>)f Ft(0,)28 b(the)g(set)1332 1154 y(\000)1384 1166 y Fn(")1419 1154 y Ft(\()p Fq(\034)5 b(;)14 b(!)s Ft(\))23 b(=)g Fp(f)p 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Fq(;)515 1885 y Ft(w)n(e)27 b(ha)n(v)n(e)f Fq(d\034)e(d\015)k Ft(=)23 b Fp(jr)p Fq(\030)t Fp(j)14 b Fq(dx)1392 1897 y Fr(1)1444 1885 y Fq(dx)1534 1897 y Fr(2)1572 1885 y Ft(.)37 b(So)1334 2110 y Fq(I)1377 2075 y Fn(")1370 2130 y Fr(1)1436 2110 y Ft(=)23 b Fj(E)1601 1997 y Fo(Z)1646 2185 y Fl(R)1706 2110 y Fq(g)s Ft(\()p Fq(\034)9 b Ft(\))1872 1997 y Fo(Z)1919 2185 y Fr(\000)1960 2193 y Fe(e)1992 2185 y Fr(\()p Fn(\034)s(;!)r Fr(\))2160 2110 y Fp(jr)p Fq(\030)t Fp(j)14 b Fq(d\015)19 b(d\034)k(;)515 2349 y Ft(and)1290 2470 y Fq(I)1333 2436 y Fn(")1326 2491 y Fr(2)1391 2470 y Ft(=)g Fj(E)1556 2357 y Fo(Z)1602 2546 y Fl(R)1662 2470 y Fq(g)s Ft(\()p Fq(\034)9 b Ft(\))1828 2357 y Fo(Z)1875 2546 y Fr(\000)1916 2554 y Fe(")1948 2546 y Fr(\()p Fn(\034)s(;!)r Fr(\))2115 2470 y Fp(jr)p Fq(\030)t Fp(j)2270 2436 y Fm(\000)p Fr(1)2373 2470 y Fq(d\015)19 b(d\034)24 b(:)639 2686 y Ft(Since)k(the)g(map)g Fq(\030)k Ft(is)27 b Fq(C)1400 2656 y Fr(3)1438 2686 y Ft(-smo)r(oth,)g(then)h(the)g(Sard)f(lemma)h(applies,)f(so)g(for)g (ev)n(ery)f Fq(!)515 2786 y Ft(and)h(almost)g(ev)n(ery)f Fq(\034)33 b Fp(2)24 b Fs(R)j Ft(the)h(lev)n(el-set)1416 2968 y(\000\()p Fq(\034)5 b(;)14 b(!)s Ft(\))23 b(=)g Fp(f)p Fq(x)g Fp(2)g Fs(T)2021 2934 y Fr(2)2082 2968 y Fp(j)g Fq(\030)t Ft(\()p Fq(x)p Ft(\))h(=)f Fq(\034)9 b Fp(g)730 b Ft(\(2.5\))515 3151 y(is)27 b(a)g Fq(C)732 3121 y Fr(3)770 3151 y Ft(-smo)r(oth)g(manifold.)37 b(So)1048 3242 y Fo(Z)1095 3431 y Fr(\000)1136 3439 y Fe(e)1168 3431 y Fr(\()p Fn(\034)s(;!)r Fr(\))1335 3355 y Fp(jr)p Fq(\030)t Fp(j)14 b Fq(d\015)28 b Fp(\045)1724 3242 y Fo(Z)1770 3431 y Fr(\000\()p Fn(\034)s(;!)r Fr(\))1979 3355 y Fp(jr)p Fq(\030)t Fp(j)14 b Fq(d\015)28 b(<)23 b Fp(1)46 b Ft(as)f Fq(")23 b Fp(!)g Ft(0)14 b Fq(;)362 b Ft(\(2.6\))515 3594 y(for)27 b(ev)n(ery)f Fq(!)k Ft(and)e(a.e.)36 b Fq(\034)9 b Ft(.)38 b(Hence,)1153 3815 y Fq(I)1196 3781 y Fn(")1189 3835 y Fr(1)1255 3815 y Fp(!)23 b Fj(E)1438 3702 y Fo(Z)1484 3891 y Fl(R)1544 3815 y Fq(g)s Ft(\()p Fq(\034)9 b Ft(\))1710 3702 y Fo(Z)1756 3891 y Fr(\000\()p Fn(\034)s(;!)r Fr(\))1965 3815 y Fp(jr)p Fq(\030)t Fp(j)14 b Fq(d\015)19 b(d\034)56 b Ft(as)45 b Fq(")23 b Fp(!)g Ft(0)14 b Fq(;)515 4054 y Ft(b)n(y)27 b(the)h(monotone)f(con)n(v)n (ergence)e(theorem.)639 4154 y(Similar,)959 4261 y Fo(Z)1005 4450 y Fr(\000)1046 4458 y Fe(e)1079 4450 y Fr(\()p Fn(\034)s(;!)r Fr(\))1246 4374 y Fp(jr)p Fq(\030)t Fp(j)1401 4340 y Fm(\000)p Fr(1)1504 4374 y Fq(d\015)j Fp(\045)1724 4261 y Fo(Z)1770 4450 y Fr(\000\()p Fn(\034)s(;!)r Fr(\))1979 4374 y Fp(jr)p Fq(\030)t Fp(j)2134 4340 y Fm(\000)p Fr(1)2237 4374 y Fq(d\015)g Fp(\024)23 b(1)46 b Ft(as)f Fq(")23 b Fp(!)g Ft(0)14 b Fq(;)515 4623 y Ft(for)28 b(ev)n(ery)f Fq(!)32 b Ft(and)d(a.e.)39 b Fq(\034)9 b Ft(,)30 b(where)f(w)n(e)f (accept)g(the)i(follo)n(wing)d(agreemen)n(t:)38 b(0)2968 4593 y Fm(\000)p Fr(1)3082 4623 y Ft(=)24 b(0.)40 b(By)515 4723 y(this)28 b(con)n(v)n(ergence,)1109 4943 y Fq(I)1152 4909 y Fn(")1145 4964 y Fr(2)1210 4943 y Fp(!)23 b Fj(E)1393 4830 y Fo(Z)1439 5019 y Fl(R)1499 4943 y Fq(g)s Ft(\()p Fq(\034)9 b Ft(\))1665 4830 y Fo(Z)1712 5019 y Fr(\000\()p Fn(\034)s(;!)r Fr(\))1920 4943 y Fp(jr)p Fq(\030)t Fp(j)2075 4909 y Fm(\000)p Fr(1)2179 4943 y Fq(d\015)18 b(d\034)56 b Ft(as)46 b Fq(")22 b Fp(!)i Ft(0)14 b Fq(:)1926 5255 y Ft(5)p eop end %%Page: 6 6 TeXDict begin 6 5 bop 639 523 a Ft(F)-7 b(rom)30 b(the)h(other)e(hand,) i(w)n(e)f(kno)n(w)g(that)g Fq(I)2029 493 y Fn(")2022 544 y Fr(1)2092 523 y Fp(!)e Fq(I)2239 535 y Fr(1)2307 523 y Ft(and)i Fq(I)2514 493 y Fn(")2507 544 y Fr(2)2577 523 y Fp(!)e Fq(I)2724 535 y Fr(2)2761 523 y Ft(.)45 b(Therefore)29 b(\(2.4\))515 623 y(implies)f(that)720 843 y Fj(E)797 730 y Fo(Z)842 919 y Fl(R)902 843 y Fq(g)s Ft(\()p Fq(\034)9 b Ft(\))1068 730 y Fo(Z)1115 919 y Fr(\000\()p Fn(\034)s(;!)r Fr(\))1323 843 y Fp(jr)p Fq(\030)t Fp(j)14 b Fq(d\015)19 b(d\034)33 b Ft(=)23 b Fq(B)1860 855 y Fr(1)1911 843 y Fj(E)1988 730 y Fo(Z)2034 919 y Fl(R)2094 843 y Fq(g)s Ft(\()p Fq(\034)9 b Ft(\))2260 730 y Fo(Z)2306 919 y Fr(\000\()p Fn(\034)s(;!)r Fr(\))2515 843 y Fp(jr)p Fq(\030)t Fp(j)2670 809 y Fm(\000)p Fr(1)2773 843 y Fq(d\015)19 b(d\034)k(;)205 b Ft(\(2.7\))515 1082 y(where)29 b(the)i(in)n(tegral)e(in)i(the)f(r.h.s.)45 b(is)30 b(\014nite)h(and)f(equals)f Fq(B)2461 1094 y Fr(1)2498 1082 y Fq(I)2534 1094 y Fr(2)2572 1082 y Ft(.)45 b(Since)31 b(for)e(eac)n(h)h Fq(!)j Ft(the)515 1182 y(set)d(of)g (critical)g(v)-5 b(alues)30 b Fq(\034)40 b Ft(of)30 b Fq(\030)k Ft(has)c(zero)f(measure,)h(then)h(w)n(e)f(can)f(arbitrarily)g (re-de\014ne)515 1282 y Fp(jr)p Fq(\030)t Fp(j)670 1251 y Fm(\000)p Fr(1)786 1282 y Ft(in)d(critical)f(p)r(oin)n(ts)i(of)f Fq(\030)t Ft(,)g(without)h(c)n(hanging)e(the)h(in)n(tegral)f(in)h(the)h (r.h.s..)36 b(Belo)n(w)515 1381 y(w)n(e)27 b(adopt)g(the)h(follo)n (wing)f(natural)g(agreemen)n(t:)1033 1489 y Fo(Z)1079 1677 y Fr(\000\()p Fn(\034)s(;!)r Fr(\))1288 1602 y Fp(jr)p Fq(\030)t Fp(j)1443 1567 y Fm(\000)p Fr(1)1546 1602 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Fq(\030)2815 3001 y Fn(\027)2856 2989 y Ft(\()p Fq(t;)14 b(x)p Ft(\))p Ff(\),)31 b(and)g(we)515 3088 y(assume)36 b Ft(\(2.8\))o Ff(.)639 3254 y Ft(In)26 b(other)f(w)n(ords,)f(the)i (l.h.s.)37 b(and)25 b(the)h(r.h.s.)36 b(of)31 b(\(2.9\))26 b(de\014ne)f(the)h(same)f Fq(L)3017 3266 y Fr(1)3054 3254 y Ft(-function)515 3354 y(of)31 b Fq(\034)9 b Ft(.)50 b(Cho)r(osing)31 b(in)h(\(2.7\))f Fq(g)i Ft(=)c(1)i(w)n(e)h(see)f(that) h(the)g(in)n(tegral)e(of)i(this)g(function)g(o)n(v)n(er)e Fs(R)515 3454 y Ft(equals)d(\(2)p Fq(\031)s Ft(\))923 3424 y Fr(2)960 3454 y Ft(.)639 3553 y(If)d Fq(\034)33 b Ft(is)23 b(a)g(regular)e(v)-5 b(alue)23 b(of)g Fq(\030)1544 3565 y Fn(\027)1609 3553 y Ft(as)g(a)g(function)g(of)h Fq(x)p Ft(,)g(then)g(\000\()p Fq(\034)5 b(;)14 b(!)s Ft(\))23 b(is)g(a)g(\014nite)h(union)f(of)515 3653 y(smo)r(oth)k(curv)n (es,)f(and)i(in)f(an)n(y)g(p)r(oin)n(t)h Fq(x)23 b Fp(2)h Ft(\000\()p Fq(\034)5 b(;)14 b(!)s Ft(\))27 b(w)n(e)g(ha)n(v)n(e)g Fp(r)p Fq(\030)2561 3665 y Fn(\027)2625 3653 y Ft(=)c Fp(\006)2808 3620 y Fn(@)p 2788 3634 81 4 v 2788 3682 a(@)t(n)2878 3653 y Fq(\030)2914 3665 y Fn(\027)2955 3653 y Ft(,)28 b(where)f Fq(n)g Ft(is)515 3763 y(a)e(unit)h(normal)f (to)h(the)g(curv)n(e.)35 b(Hence,)26 b(in)g(\(2.9\))g Fp(jr)p Fq(\030)2217 3775 y Fn(\027)2259 3763 y Fp(j)g Ft(can)f(b)r(e)h(replaced)f(b)n(y)g Fp(j)3062 3730 y Fn(@)p 3041 3744 V 3041 3792 a(@)t(n)3131 3763 y Fq(\030)3167 3775 y Fn(\027)3209 3763 y Fp(j)p Ft(.)36 b(So)515 3863 y(the)30 b(in)n(tegral)965 3796 y Fo(R)1034 3863 y Fp(jr)p Fq(\030)1162 3875 y Fn(\027)1204 3863 y Fp(j)14 b Fq(d\015)35 b Ft(is)30 b(a)g(sum)g(of)g(the)h(mo)r(duli)f(of)g(the)h(\015o)n(ws)e (of)h Fp(r)p Fq(\030)2875 3875 y Fn(\027)2947 3863 y Ft(through)g(the)515 3962 y(curv)n(es,)24 b(forming)h(the)h(set)g (\000.)36 b(The)25 b(in)n(tegral)1943 3895 y Fo(R)2013 3962 y Fp(jr)p Fq(\030)2141 3974 y Fn(\027)2183 3962 y Fp(j)2206 3932 y Fm(\000)p Fr(1)2309 3962 y Fq(d\015)30 b Ft(can)25 b(b)r(e)h(in)n(terpreted)f(similar.)515 4386 y Fu(3)134 b(Bounds)44 b(for)h(some)h(exp)t(onen)l(tial)g(momen)l(ts) 515 4568 y Ft(As)30 b(b)r(efore,)f(w)n(e)h(abbreviate)e Fq(\030)1485 4580 y Fn(\027)1527 4568 y Ft(\()p Fq(t;)14 b(x)p Ft(\))27 b(=)f Fq(\030)t Ft(\()p Fq(x)p Ft(\).)45 b(Cho)r(osing)28 b(in)i(\(2.3\))g Fq(g)s Ft(\()p Fq(v)s Ft(\))d(=)f Fq(v)3017 4538 y Fr(2)p Fn(m)3113 4568 y Ft(,)31 b(where)515 4668 y Fq(m)c Ft(is)h(a)f(natural)g(n)n(um)n(b)r (er,)g(and)h(denoting)f Fq(\030)t Ft(\()p Fq(x)p Ft(\))2038 4638 y Fn(m)p Fr(+1)2209 4668 y Ft(=)c Fq(w)r Ft(\()p Fq(x)p Ft(\),)29 b(w)n(e)f(get:)1002 4893 y Fj(E)1079 4780 y Fo(Z)1124 4968 y Fl(T)1163 4952 y Fk(2)1214 4893 y Fp(jr)p Fq(w)r Ft(\()p Fq(x)p Ft(\))p Fp(j)1501 4858 y Fr(2)1554 4893 y Fq(dx)23 b Ft(=)g Fq(B)1818 4905 y Fr(1)1855 4893 y Ft(\()p Fq(m)c Ft(+)f(1\))2136 4858 y Fr(2)2187 4893 y Fj(E)2264 4780 y Fo(Z)2309 4968 y Fl(T)2348 4952 y Fk(2)2399 4893 y Fp(j)p Fq(w)r Ft(\()p Fq(x)p Ft(\))p Fp(j)2650 4835 y Fk(2)p Fe(m)p 2628 4844 122 3 v 2628 4877 a(m)p Fk(+1)2778 4893 y Fq(dx:)317 b Ft(\(3.1\))1926 5255 y(6)p eop end %%Page: 7 7 TeXDict begin 7 6 bop 515 523 a Ft(By)27 b(the)h(H\177)-42 b(older)27 b(inequalit)n(y)-7 b(,)1098 652 y Fo(Z)1195 765 y Fp(j)p Fq(w)r Ft(\()p Fq(x)p Ft(\))p Fp(j)1446 707 y Fk(2)p Fe(m)p 1425 716 122 3 v 1425 749 a(m)p Fk(+1)1575 765 y Fq(dx)23 b Fp(\024)g Ft(\(2)p Fq(\031)s Ft(\))1989 707 y Fk(2)p 1942 716 V 1942 749 a Fe(m)p Fk(+1)2078 648 y Fo(\022)2153 652 y(Z)2250 765 y Fq(w)r Ft(\()p Fq(x)p Ft(\))2422 731 y Fr(2)2475 765 y Fq(dx)2565 648 y Fo(\023)2672 643 y Fe(m)p 2637 652 V 2637 685 a(m)p Fk(+1)2773 765 y Fq(:)412 b Ft(\(3.2\))515 998 y(By)32 b(\(2.1\),)h Fq(w)r Ft(\()p Fq(x)p Ft(\))e Fp(2)f Fq(C)1230 968 y Fr(1)1268 998 y Ft(\()p Fs(T)1355 968 y Fr(2)1393 998 y Ft(\))i(for)f(all)g Fq(!)s Ft(.)49 b(W)-7 b(e)32 b(wish)f(to)h(estimate)f(the)h(in)n(tegral)e(of)i Fq(w)r Ft(\()p Fq(x)p Ft(\))3340 968 y Fr(2)515 1097 y Ft(in)d(the)h(r.h.s.)40 b(of)c(\(3.2\))29 b(b)n(y)f(its)i(in)n(tegral)e(Diric)n(hlet.)41 b(If)29 b Fq(m)g Ft(w)n(as)g(zero,)f(then)i Fq(w)r Ft(\()p Fq(x)p Ft(\))d(=)e Fq(\030)t Ft(\()p Fq(x)p Ft(\))515 1197 y(w)n(ould)j(b)r(e)i(a)e Fq(C)1008 1167 y Fr(1)1046 1197 y Ft(-smo)r(oth)g(function)i(with)g(zero)d(mean-v)-5 b(alue,)29 b(and)g(the)h(estimate)f(w)n(ould)515 1297 y(follo)n(w)34 b(from)h(the)g(P)n(oincar)n(\023)-39 b(e)32 b(inequalit)n(y)-7 b(.)59 b(Since)35 b Fq(m)g Fp(\025)g Ft(1,)i(then)e(what)g(w)n(e)g(need)g(is)g(the)515 1396 y(`nonlinear)i(P)n(oincar)n(\023)-39 b(e)35 b(inequalit)n(y',)40 b(giv)n(en)e(b)r(elo)n(w.)68 b(A)38 b(short)g(and)g(nice)g(pro)r(of)g (of)g(this)515 1496 y(result,)27 b(suggested)g(b)n(y)g(M.)h(Stru)n(w)n (e)f(and)g(S.)h(Brandle,)f(is)g(giv)n(en)g(in)h(App)r(endix.)515 1658 y Fj(Lemma)34 b(3.1.)41 b Ff(Ther)l(e)33 b(exists)e(a)i(c)l (onstant)e Fq(C)i Fp(\025)26 b Ft(1)31 b Ff(such)h(that)g(for)h(any)f Fq(k)d Fp(2)f Fs(N)j Ff(and)i(any)515 1757 y Fq(C)580 1727 y Fr(1)617 1757 y Ff(-smo)l(oth)d(function)g Fq(u)p Ft(\()p Fq(x)p Ft(\))g Ff(on)g Fs(T)1619 1727 y Fr(2)1686 1757 y Ff(with)h(zer)l(o)f(me)l(an-value)g(we)g(have)1426 1864 y Fo(Z)1522 1977 y Fq(u)1570 1943 y Fr(2)p Fn(k)1658 1977 y Fq(dx)23 b Fp(\024)g Fq(C)1938 1864 y Fo(Z)2035 1977 y Fp(jr)p Ft(\()p Fq(u)2207 1943 y Fn(k)2248 1977 y Ft(\))p Fp(j)2303 1943 y Fr(2)2354 1977 y Fq(dx:)741 b Ft(\(3.3\))639 2197 y(Com)n(bining)28 b(\(3.1\){\(3.3\))f(w)n(e)g (get:)805 2444 y Fj(E)882 2331 y Fo(Z)978 2444 y Fp(jr)p Fq(w)r Ft(\()p Fq(x)p Ft(\))p Fp(j)1265 2409 y Fr(2)1318 2444 y Fq(dx)d Fp(\024)f Fq(B)1583 2456 y Fr(1)1620 2444 y Ft(\()p Fq(m)c Ft(+)f(1\))1901 2409 y Fr(2)1938 2444 y Ft(\(2)p Fq(\031)s Ft(\))2151 2385 y Fk(2)p 2104 2394 V 2104 2428 a Fe(m)p Fk(+1)2240 2444 y Fq(C)6 b Fj(E)2368 2326 y Fo(\022)2443 2331 y(Z)2540 2444 y Fp(jr)p Fq(w)r Fp(j)2716 2409 y Fr(2)2768 2444 y Fq(dx)2858 2326 y Fo(\023)2965 2321 y Fe(m)p 2930 2330 V 2930 2364 a(m)p Fk(+1)3066 2444 y Fq(:)515 2666 y Ft(Therefore,)1215 2804 y Fj(E)1292 2691 y Fo(Z)1389 2804 y Fp(jr)p Fq(w)r Ft(\()p Fq(x)p Ft(\))p Fp(j)1676 2769 y Fr(2)1729 2804 y Fq(dx)24 b Fp(\024)e Fq(C)1995 2768 y Fn(m)p Fr(+1)1989 2826 y(1)2143 2804 y Ft(\()p Fq(m)c Ft(+)g(1\))2423 2769 y Fr(2\()p Fn(m)p Fr(+1\))2655 2804 y Fq(:)515 2992 y Ft(Using)28 b(\(3.3\))g(\(with)g Fq(k)e Ft(=)d Fq(m)18 b Ft(+)g(1\))27 b(once)g(again)g(w)n(e)g(see)g(that)1186 3212 y Fj(E)1263 3099 y Fo(Z)1360 3212 y Fq(\030)t Ft(\()p Fq(x)p Ft(\))1511 3178 y Fr(2\()p Fn(m)p Fr(+1\))1758 3212 y Fq(dx)d Fp(\024)e Fq(C)2024 3176 y Fn(m)p Fr(+1)2018 3234 y(2)2172 3212 y Ft(\()p Fq(m)c Ft(+)g(1\))2452 3178 y Fr(2\()p Fn(m)p Fr(+1\))2684 3212 y Fq(:)501 b Ft(\(3.4\))515 3443 y(Since)23 b Fq(\030)28 b Ft(is)23 b(a)g(homogeneous)e(random)h(\014eld,)j(then)f (the)f(l.h.s.)36 b(equals)22 b(\(2)p Fq(\031)s Ft(\))2871 3413 y Fr(2)2909 3443 y Fj(E)p Fq(\030)t Ft(\()p Fq(x)p Ft(\))3123 3413 y Fr(2\()p Fn(m)p Fr(+1\))3356 3443 y Fq(:)515 3543 y Ft(Th)n(us,)27 b(w)n(e)g(ha)n(v)n(e)g(pro)n(v)n(ed)f (that)1579 3671 y Fo(\022)1640 3788 y Fj(E)p Fp(j)p Fq(\030)t Ft(\()p Fq(x)p Ft(\))p Fp(j)1900 3754 y Fn(j)1936 3671 y Fo(\023)1997 3689 y Fr(1)p Fn(=j)2123 3788 y Fp(\024)c Fq(C)6 b(j)899 b Ft(\(3.5\))515 4011 y(for)27 b Fq(j)h Ft(=)22 b(2)p Fq(r)r Ft(,)28 b Fq(r)e Ft(=)d(2)p Fq(;)14 b Ft(3)p Fq(;)g(:)g(:)g(:)e Ft(.)37 b(Since)28 b(for)f(an)n(y)g(random) g(v)-5 b(ariable)26 b Fq(\021)31 b Ft(the)d(function)1426 4188 y(\(0)p Fq(;)14 b Ft(1])22 b Fp(3)i Fq(t)f Fp(!)g Ft(ln\()p Fj(E)p Fp(j)p Fq(\021)s Fp(j)2116 4154 y Fr(1)p Fn(=t)2213 4188 y Ft(\))2245 4154 y Fn(t)2297 4188 y Fp(\024)g(1)515 4366 y Ft(is)k(con)n(v)n(ex)f(b)n(y)i(the)g(H\177)-42 b(older)27 b(inequalit)n(y)-7 b(,)27 b(then)h(\(3.5\))f(holds)h(for)f (all)g Fq(j)h Fp(2)23 b Fs(N)p Ft(.)639 4465 y(F)-7 b(or)28 b Fq(\033)h(>)24 b Ft(0)29 b(w)n(e)f(ha)n(v)n(e)57 b Fj(E)p Fq(e)1472 4435 y Fn(\033)r Fm(j)p Fn(\030)r Fr(\()p Fn(x)p Fr(\))p Fm(j)1702 4465 y Ft(=)1791 4403 y Fo(P)1879 4490 y Fn(m)1956 4465 y Ft(\()p Fq(\033)2038 4435 y Fn(m)2102 4465 y Fq(=m)p Ft(!)o(\))p Fj(E)p 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Fp(\024)23 b Fq(C)q(:)971 b Ft(\(3.6\))639 938 y Fj(Remark)45 b(1.)68 b Ft(The)39 b(op)r(erator)d Fq(D)41 b Ft(\(see)d(\(1.6\)\),)k (de\014ned)c(on)g(functions)h(with)g(zero)515 1038 y(mean-v)-5 b(alue,)35 b(is)f(b)r(ounded)h(as)e(a)h(linear)g(op)r(erator)e(in)j Fq(L)2342 1050 y Fr(2)2378 1038 y Ft(\()p Fs(T)2465 1008 y Fr(2)2503 1038 y Ft(\))g(and)f(as)f(an)h(op)r(erator)f(in)515 1137 y Fq(L)572 1149 y Fm(1)642 1137 y Ft(\()p Fq(T)735 1107 y Fr(2)771 1137 y Ft(\).)i(Hence,)21 b(b)n(y)f(the)g(in)n(terp)r (olation)f(theorem)h(its)g(norm)f(as)g(an)h(op)r(erator)e(in)i Fq(L)3161 1149 y Fn(p)3199 1137 y Ft(\()p Fs(T)3286 1107 y Fr(2)3324 1137 y Ft(\),)515 1237 y(2)i Fp(\024)h Fq(p)g Fp(\024)f(1)p Ft(,)g(is)e(b)r(ounded)g(b)n(y)g(a)f Fq(p)p Ft(-indep)r(enden)n(t)h(constan)n(t)f Fq(C)2447 1207 y Fm(0)2471 1237 y Ft(.)34 b(Due)21 b(to)e(this)h(observ)-5 b(ation,)515 1337 y(\(1.6\))27 b(and)g(\(3.4\),)968 1562 y Fj(E)1045 1449 y Fo(Z)1142 1562 y Fq(u)1190 1574 y Fn(\027)1231 1562 y Ft(\()p Fq(t;)14 b(x)p Ft(\))1409 1527 y Fr(2\()p Fn(m)p Fr(+1\))1655 1562 y Fq(dx)24 b Fp(\024)f Fq(C)1922 1527 y Fm(0)1945 1516 y Fr(2\()p Fn(m)p Fr(+1\))2177 1562 y Fq(C)2242 1526 y Fn(m)p Fr(+1)2236 1584 y(2)2390 1562 y Ft(\()p Fq(m)18 b Ft(+)g(1\))2670 1527 y Fr(2\()p Fn(m)p Fr(+1\))2902 1562 y Fq(:)515 1782 y Ft(Therefore)1630 1882 y Fj(E)p Fq(e)1732 1848 y Fn(\033)1770 1856 y Fk(1)1802 1848 y Fm(j)p Fn(u)1861 1856 y Fe(\027)1898 1848 y Fr(\()p Fn(t;x)p Fr(\))p Fm(j)2079 1882 y Fp(\024)23 b Fq(C)2226 1894 y Fr(1)3208 1882 y Ft(\(3.7\))515 2031 y(for)k(some)g Fq(\033)897 2043 y Fr(1)935 2031 y Fq(;)14 b(C)1031 2043 y Fr(1)1091 2031 y Fq(>)23 b Ft(0.)639 2131 y Fj(Remark)i(2.)34 b Ft(Let)22 b(us)f(abbreviate)g Fq(u)1798 2143 y Fn(\027)1839 2131 y Ft(\()p Fq(t;)14 b(x)p Ft(\))24 b(=)e Fq(u)p Ft(\()p Fq(x)p Ft(\).)36 b(Due)22 b(to)f(\(1.6\),)i Fp(r)p Fq(u)f Ft(=)h Fp(r)p Fq(D)r(\030)t Ft(.)35 b(So)515 2231 y Fp(r)p Fq(u)p Ft(\()p Fq(x)p Ft(\))e(is)e(obtained)h(from)g Fq(\030)t Ft(\()p Fq(x)p Ft(\))h(b)n(y)f(applying)f(a)h(singular)f(in)n(tegral)f(op)r (erator.)49 b(Hence,)515 2330 y Fp(jr)p Fq(u)p Fp(j)678 2342 y Fn(L)724 2350 y Fe(p)802 2330 y Fp(\024)39 b Fq(C)965 2342 y Fn(p)1004 2330 y Fp(j)p Fq(\030)t Fp(j)1090 2342 y Fn(L)1136 2350 y Fe(p)1212 2330 y Ft(for)e(1)j Fq(<)f(p)g(<)h Fp(1)d Ft(b)n(y)h(the)g(Calder\023)-42 b(on{Zydm)n(und)35 b(theorem.)67 b(F)-7 b(or)515 2430 y(2)30 b Fp(\024)f Fq(p)h(<)g Fp(1)i Ft(the)h(constan)n(t)e Fq(C)1509 2442 y Fn(p)1580 2430 y Ft(can)g(b)r(e)i(c)n(hosen)e Fq(C)2183 2442 y Fn(p)2252 2430 y Ft(=)e Fq(C)6 b(p)p Ft(,)34 b(e.g.,)e(see)g ([Ste70)o(],)h(section)515 2529 y(I)r(I.6.)k(Due)28 b(to)f(this)h (estimate)g(with)g Fq(p)23 b Ft(=)f(2\()p Fq(m)c Ft(+)g(1\))28 b(and)f(\(3.4\))h(w)n(e)f(ha)n(v)n(e)1125 2754 y Fj(E)1202 2641 y Fo(Z)1298 2754 y Fp(jr)p Fq(u)p Ft(\()p Fq(x)p Ft(\))p Fp(j)1572 2720 y Fr(2\()p Fn(m)p Fr(+1\))1819 2754 y Fq(dx)d Fp(\024)f Fq(C)2086 2719 y Fn(m)p Fr(+1)2080 2777 y(3)2233 2754 y Ft(\()p Fq(m)c Ft(+)f(1\))2514 2720 y Fr(4\()p Fn(m)p Fr(+1\))2746 2754 y Fq(:)515 2991 y Ft(As)28 b(b)r(efore,)g(this)g(inequalit)n(y)g(implies)g(that)g(\()p Fj(E)p Fp(jr)p Fq(u)p Ft(\()p Fq(x)p Ft(\))p Fp(j)2290 2961 y Fn(j)s(=)p Fr(2)2393 2991 y Ft(\))2425 2961 y Fr(1)p Fn(=j)2551 2991 y Fp(\024)c Fq(C)6 b(j)33 b Ft(for)28 b(all)f Fq(j)i Fp(2)24 b Fs(N)k Ft(and)515 3091 y(all)f Fq(x)p Ft(.)37 b(Therefore,)1600 3206 y Fj(E)p Fq(e)1702 3171 y Fn(\033)r Fm(j)p Fn(u)1801 3179 y Fe(\027)1837 3171 y Fr(\()p Fn(t;x)p Fr(\))p Fm(j)1992 3146 y Fk(1)p Fe(=)p Fk(2)2110 3206 y Fp(\024)22 b Fq(C)2256 3218 y Fr(2)3208 3206 y Ft(\(3.8\))515 3355 y(for)27 b(an)n(y)g Fq(t;)14 b(x)p Ft(,)28 b(with)g(some)f Fq(\033)1408 3367 y Fr(2)1445 3355 y Fq(;)14 b(C)1541 3367 y Fr(2)1602 3355 y Fq(>)23 b Ft(0.)639 3455 y Fj(Remark)35 b(3.)43 b Ft(It)31 b(is)e(sho)n(wn)h(in)g([Kuk04)n(])h(that,)f(along)f (sequences)g Fq(\027)2818 3467 y Fn(j)2881 3455 y Fp(!)e Ft(0,)j(the)g(pro-)515 3554 y(cesses)25 b Fq(u)798 3566 y Fn(\027)831 3574 y Fe(j)866 3554 y Ft(\()p Fq(t;)14 b(x)p Ft(\))27 b(con)n(v)n(erge)d(in)j(distribution)f(to)g(limiting)h (stationary)e(pro)r(cesses)f Fq(u)3163 3566 y Fr(0)3200 3554 y Ft(\()p Fq(t;)14 b(x)p Ft(\))515 3654 y(suc)n(h)35 b(that)g(a.a.)59 b(their)35 b(tra)5 b(jectories)34 b(satisfy)g(the)i (Euler)e(equation.)60 b(Using)35 b(the)g(F)-7 b(atou)515 3754 y(lemma)31 b(it)h(is)f(easy)f(to)h(c)n(hec)n(k)f(that)i Fq(u)1710 3766 y Fr(0)1747 3754 y Ft(\()p Fq(t;)14 b(x)p Ft(\))32 b(and)f Fq(\030)2158 3766 y Fr(0)2195 3754 y Ft(\()p Fq(t;)14 b(x)p Ft(\))30 b(=)f(curl)13 b Fq(u)2697 3766 y Fr(0)2734 3754 y Ft(\()p Fq(t;)h(x)p Ft(\))32 b(satisfy)g(\(3.5\))515 3853 y(and)21 b(\(3.6\))h(\(as)g(b)r(efore,)g (\014rst)g(one)g(has)f(to)h(establish)f(analogies)f(of)i(the)g (inequalities)g(\(3.4\)\).)515 3953 y(Similar,)27 b Fq(u)872 3965 y Fr(0)936 3953 y Ft(satisfy)i(\(3.7\))e(and)h(\(3.8\))o(.)515 4227 y Fu(4)134 b(App)t(endix.)515 4426 y Fd(4.1)112 b(Pro)s(of)37 b(of)h(Lemma)h(2.1.)515 4579 y Ft(Let)28 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1782 y Fo(R)1414 1879 y Fr(\012)1479 1732 y Fo(\022)1554 1782 y(R)1610 1803 y Fr(1)1594 1879 y(0)1661 1849 y Fq(I)1697 1864 y Fn(Q)p Fr(\()p Fn(x)1813 1872 y Fk(0)1846 1864 y Fn(;!)r Fr(\))1953 1849 y Fq(dt)2026 1732 y Fo(\023)2101 1849 y Fq(d)p Fj(P)g Ft(=)e(\()p Fq(L)2409 1861 y Fn(t)2457 1849 y Fp(\002)c Fj(P)p Ft(\))p Fq(Q)p Ft(\()p Fq(x)2782 1861 y Fr(0)2820 1849 y Ft(\))23 b(=)g Fq(p:)515 2079 y Ft(In)28 b(particular,)e(there)h(exists)g Fq(t)1496 2091 y Fr(0)1557 2079 y Fq(<)22 b Ft(1)28 b(suc)n(h)f(that)h Fq(\031)s Ft(\()p Fq(t)2193 2091 y Fr(0)2231 2079 y Ft(\))23 b Fq(>)g Ft(0.)515 2243 y Fj(Lemma)33 b(4.1.)41 b Ff(In)30 b Ft([0)p Fq(;)14 b Ft(1])30 b Ff(ther)l(e)h(exists)g(a)g(c)l(onver)l (ging)g(se)l(quenc)l(e)g Fq(t)2640 2255 y Fn(n)2710 2243 y Fp(&)25 b Fq(t)2848 2255 y Fr(0)2917 2243 y Ff(\()p Fq(n)f Fp(\025)h Ft(1\))31 b Ff(such)515 2343 y(that)1309 2443 y Fj(P)p Fp(f)p Fq(!)26 b Fp(j)d Ft(\()p Fq(t)1602 2455 y Fn(n)1647 2443 y Fq(;)14 b(x)1731 2455 y Fr(0)1769 2443 y 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y Fm(0)953 2713 y Fn(n)p Fr(+1)1083 2692 y Ft(\),)i(satisfying)d Fp(j)p Fq(\014)t Ft(\()p Fq(t)1684 2662 y Fm(0)1684 2713 y Fn(n)p Fr(+1)1814 2692 y Ft(\))23 b Fp(\000)e Fq(\014)2002 2704 y Fn(t)2027 2712 y Fk(0)2064 2692 y Fp(j)32 b(\024)2216 2626 y Fo(p)p 2299 2626 328 4 v 66 x Fq(t)2329 2663 y Fm(0)2329 2714 y Fn(n)p Fr(+1)2477 2692 y Fp(\000)18 b Fq(t)2590 2704 y Fr(0)2641 2692 y Ft(.)54 b(No)n(w,)34 b(c)n(ho)r(osing)e(for)515 2792 y Fp(f)p Fq(t)587 2761 y Fm(0)587 2812 y Fn(n)631 2792 y Fp(g)23 b Ft(a)g(subsequnce,)g(con)n(v)n(erging)e(to)i Fq(t)1748 2804 y Fr(0)1808 2792 y Ft(fast)h(enough)e(and)h(using)g(the) g(Mark)n(o)n(v)e(prop)r(ert)n(y)-7 b(,)515 2891 y(w)n(e)28 b(see)g(that)h(\(4.5\))g Fp(\024)24 b Fq(c)1279 2861 y Fn(K)t Fm(\000)p Fn(k)q Fr(+1)1516 2891 y Ft(.)40 b(Since)29 b Fq(c)c(<)f Ft(1)k(and)h Fq(K)34 b Ft(is)28 b(an)n(y)g(n)n(um)n(b)r (er)h Fq(>)24 b(k)s Ft(,)29 b(then)g(\(4.4\))515 2991 y(follo)n(ws.)515 3222 y Fd(4.2)112 b(Pro)s(of)37 b(of)h(Lemma)h(3.1.) 515 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