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%%Title: C:\Tex_Wall\wall_template2.DVI
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%%CreationDate: 1991 Aug 20 16:35:49
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%%CreationDate: 1992 Feb 19 19:56:16
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
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%%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 3 /asteriskmath put
dup 48 /prime put
dup 62 /latticetop put
readonly def
/FontBBox{21 -944 1448 791}readonly def
/UniqueID 5000815 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: cmmi5
%!PS-AdobeFont-1.1: cmmi5 1.100
%%CreationDate: 1996 Aug 02 08:21:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (cmmi5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /cmmi5 def
/PaintType 0 def
/FontType 1 def
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dup 11 /alpha put
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currentdict end
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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 43 /plus put
dup 49 /one put
readonly def
/FontBBox{-341 -250 1304 965}readonly def
/UniqueID 5000788 def
currentdict end
currentfile eexec
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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 22 /macron put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 55 /seven put
dup 58 /colon put
dup 61 /equal put
dup 94 /circumflex put
dup 126 /tilde put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueID 5000790 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: cmex10
%!PS-AdobeFont-1.1: cmex10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (cmex10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /cmex10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 26 /braceleftbigg put
dup 27 /bracerightbigg put
dup 40 /braceleftBigg put
dup 41 /bracerightBigg put
dup 56 /bracelefttp put
dup 58 /braceleftbt put
dup 60 /braceleftmid put
dup 80 /summationtext put
dup 81 /producttext put
dup 88 /summationdisplay put
dup 110 /braceleftBig put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: cmmi7
%!PS-AdobeFont-1.1: cmmi7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (cmmi7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /cmmi7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /alpha put
dup 23 /nu put
dup 26 /rho put
dup 59 /comma put
dup 60 /less put
dup 62 /greater put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 76 /L put
dup 79 /O put
dup 80 /P put
dup 86 /V put
dup 87 /W put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 101 /e 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
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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%!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 0 /minus put
dup 1 /periodcentered put
dup 2 /multiply put
dup 3 /asteriskmath put
dup 20 /lessequal put
dup 48 /prime put
dup 49 /infinity put
dup 50 /element put
dup 62 /latticetop put
dup 107 /bardbl put
readonly def
/FontBBox{-15 -951 1252 782}readonly def
/UniqueID 5000817 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: cmmi10
%!PS-AdobeFont-1.1: cmmi10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (cmmi10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /cmmi10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /Gamma put
dup 1 /Delta put
dup 11 /alpha put
dup 12 /beta put
dup 13 /gamma put
dup 14 /delta put
dup 18 /theta put
dup 21 /lambda put
dup 22 /mu put
dup 23 /nu put
dup 25 /pi put
dup 26 /rho put
dup 27 /sigma put
dup 28 /tau put
dup 30 /phi put
dup 32 /psi put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater 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 73 /I put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 86 /V put
dup 87 /W put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 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
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: cmmi6
%!PS-AdobeFont-1.1: cmmi6 1.100
%%CreationDate: 1996 Jul 23 07:53:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (cmmi6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /cmmi6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 63 /star put
readonly def
/FontBBox{11 -250 1241 750}readonly def
/UniqueID 5087381 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: cmti8
%!PS-AdobeFont-1.1: cmti8 1.0
%%CreationDate: 1991 Aug 18 21:07:42
% 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 (cmti8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /cmti8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 40 /parenleft put
dup 41 /parenright put
dup 45 /hyphen put
dup 46 /period put
dup 49 /one put
dup 57 /nine put
dup 58 /colon put
dup 65 /A put
dup 67 /C put
dup 73 /I put
dup 74 /J put
dup 77 /M put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 97 /a put
dup 98 /b put
dup 99 /c 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 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 121 /y put
readonly def
/FontBBox{-35 -250 1190 750}readonly def
/UniqueID 5000826 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: cmr6
%!PS-AdobeFont-1.1: cmr6 1.0
%%CreationDate: 1991 Aug 20 16:39:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (cmr6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
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end readonly def
/FontName /cmr6 def
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/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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0 1 255 {1 index exch /.notdef put} for
dup 50 /two put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
/UniqueID 5000789 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: cmmi8
%!PS-AdobeFont-1.1: cmmi8 1.100
%%CreationDate: 1996 Jul 23 07:53:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (cmmi8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /cmmi8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 76 /L put
dup 79 /O put
dup 109 /m put
dup 110 /n put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: cmbx8
%!PS-AdobeFont-1.1: cmbx8 1.0
%%CreationDate: 1991 Aug 20 16:36:07
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (cmbx8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /cmbx8 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 44 /comma put
dup 46 /period 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 56 /eight put
dup 57 /nine put
dup 65 /A put
dup 97 /a put
dup 98 /b put
dup 99 /c put
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dup 115 /s put
dup 116 /t put
readonly def
/FontBBox{-59 -250 1235 750}readonly def
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currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: cmr8
%!PS-AdobeFont-1.1: cmr8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (cmr8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /cmr8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 13 /fl put
dup 14 /ffi put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 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 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 89 /Y put
dup 90 /Z put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 121 /y put
dup 122 /z put
dup 127 /dieresis put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 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 (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (cmmib10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
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/FontName /cmmib10 def
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/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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readonly def
/FontBBox{-15 -250 1216 750}readonly def
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currentdict end
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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
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/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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dup 67 /C put
dup 70 /F put
dup 71 /G put
dup 73 /I put
dup 77 /M put
dup 78 /N put
dup 80 /P put
dup 97 /a put
dup 98 /b put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 104 /h put
dup 105 /i put
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dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
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readonly def
/FontBBox{-53 -251 1139 750}readonly def
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currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: cmsy10
%!PS-AdobeFont-1.1: cmsy10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (cmsy10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /cmsy10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 1 /periodcentered put
dup 17 /equivalence put
dup 18 /reflexsubset put
dup 20 /lessequal put
dup 21 /greaterequal put
dup 32 /arrowleft put
dup 33 /arrowright put
dup 40 /arrowdblleft put
dup 41 /arrowdblright put
dup 49 /infinity put
dup 50 /element put
dup 54 /negationslash put
dup 56 /universal put
dup 59 /emptyset put
dup 88 /X put
dup 91 /union put
dup 92 /intersection put
dup 102 /braceleft put
dup 103 /braceright put
dup 106 /bar put
dup 107 /bardbl put
dup 110 /backslash put
dup 114 /nabla put
dup 116 /unionsq put
dup 117 /intersectionsq put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: cmr10
%!PS-AdobeFont-1.1: cmr10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (cmr10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /cmr10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 22 /macron put
dup 34 /quotedblright put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 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 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 92 /quotedblleft put
dup 93 /bracketright put
dup 94 /circumflex put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 126 /tilde put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: cmbx10
%!PS-AdobeFont-1.1: cmbx10 1.00B
%%CreationDate: 1992 Feb 19 19:54:06
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (cmbx10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /cmbx10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 13 /fl put
dup 46 /period 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 58 /colon put
dup 59 /semicolon put
dup 65 /A put
dup 67 /C put
dup 71 /G put
dup 73 /I put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 80 /P put
dup 82 /R put
dup 84 /T put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueID 5000768 def
currentdict end
currentfile eexec
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%%Page: 14 14
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%%EndDocument
@endspecial
125 2401 a(Supp)r(ose)41 b(no)n(w)f(that)i Fj(\031)894
2371 y Fh(l)891 2422 y(u)980 2401 y Fj(<)j(\031)1140
2371 y Fh(h)1137 2422 y(u)1225 2401 y Ft(for)c(all)f(no)r(des)h
Fj(u)p Ft(.)g(The)g(only)g(direction)g(that)g(w)n(e)0
2501 y(ha)n(v)n(e)24 b(not)i(considered)e(is)h(a)h(zero-cost)d(unit)j
(gain)f(cycle.)g(Without)h(loss)f(of)g(generalit)n(y)-7
b(,)24 b(w)n(e)0 2600 y(assume)j(that)h Fj(G)g Ft(is)f(connected.)g
(Since)h(0)23 b Fj(<)f(x)i(<)e(u)p Ft(,)28 b(there)f(is)g(a)g(directed)
h(path)g(from)f(an)n(y)0 2700 y(no)r(de)34 b Fj(u)f Ft(to)h(an)n(y)f
(other)g(no)r(de)h Fj(v)j Ft(in)d Fj(G)1234 2712 y Fh(x)1276
2700 y Ft(.)g(Th)n(us)f(if)h(there)g(is)g(a)f(\015o)n(w-generating)e
(cycle)j(in)0 2800 y Fj(G)65 2812 y Fh(x)107 2800 y Ft(,)e(then)g
Fj(\031)405 2769 y Fh(l)402 2820 y(u)476 2800 y Fs(6)p
Ft(=)e Fs(\0001)i Ft(for)f(eac)n(h)g(no)r(de)h Fj(u)f
Ft(since)h(there)g(is)f(at)h(least)g(one)f(path)h(from)g(that)0
2899 y(\015o)n(w-generating)26 b(cycle)j(to)f(ev)n(ery)g(no)r(de.)g
(Similarly)-7 b(,)29 b(if)g(there)f(is)h(a)f(\015o)n(w-absorbing)e
(cycle)0 2999 y(in)k Fj(G)164 3011 y Fh(x)206 2999 y
Ft(,)g(then)h Fj(\031)501 2969 y Fh(h)498 3019 y(u)571
2999 y Fs(6)p Ft(=)26 b Fs(1)k Ft(for)f(eac)n(h)g(no)r(de)h
Fj(u)p Ft(,)g(since)f(there)h(is)g(at)f(least)h(one)f(path)h(from)g(an)
n(y)0 3098 y(no)r(de)25 b(to)g(that)g(\015o)n(w-absorbing)d(cycle.)j(A)
n(t)g(this)g(p)r(oin)n(t)g(in)h(our)e(step)h(direction)f(searc)n(h)g
(it)h(is)0 3198 y(not)k(p)r(ossible)f(for)g Fj(\031)637
3210 y Fh(u)681 3198 y Fj(l)r(ow)f Ft(=)e Fs(\0001)j
Ft(and)h Fj(\031)1310 3210 y Fh(u)1353 3198 y Fj(hig)s(h)24
b Ft(=)h Fs(1)k Ft(for)f(all)g(no)r(des)h Fj(u)p Ft(;)f(th)n(us)h
(there)f(is)h(at)0 3298 y(least)e(one)g(\015o)n(w-generating)e(or)i
(one)g(\015o)n(w-absorbing)e(cycle)i(in)h Fj(G)2098 3310
y Fh(x)2140 3298 y Ft(.)125 3397 y(Let)21 b(us)g(assume)f(that)i(there)
f(is)g(at)g(least)g(one)g(\015o)n(w-generating)d(cycle)j(in)h
Fj(G)2460 3409 y Fh(x)2523 3397 y Ft(and)f(hence)0 3497
y(that)35 b Fj(\031)237 3467 y Fh(l)234 3517 y(u)313
3497 y Fj(>)g Fs(\0001)g Ft(for)f(all)h Fj(u)p Ft(.)g(\(The)g(case)f
(when)h(there)g(is)g(at)g(least)f(one)h(\015o)n(w-absorbing)0
3597 y(cycle)c(in)g Fj(G)374 3609 y Fh(x)447 3597 y Ft(is)g(similar.\))
g(Under)g(this)g(assumption,)f(it)i(is)f(easy)f(to)h(see)f(that)i
(there)e(is)h(a)0 3696 y(feasible)36 b(solution)f(to)h(the)g(system)g
Fj(Ax)h Ft(=)g Fj(b;)14 b(x)36 b Fs(\025)h Ft(0)e(for)h(an)n(y)f
Fj(b)h(>)h Ft(0,)e(where)h Fj(A)g Ft(is)g(the)0 3796
y(constrain)n(t)f(matrix)h(in)h(problem)f(\(2\).)g(Th)n(us)g(matrix)g
Fj(A)h Ft(is)f(a)g(Leon)n(tief)g(matrix)g(and)h(it)0
3895 y(follo)n(ws)27 b(from)h(results)f(in)h(Adler)g(and)g(Cosares)e
(\([1]\))i(that)h(there)f(is)f(a)h(maximal)f(solution)0
3995 y(to)33 b(the)g(system)f Fj(A)597 3965 y Fi(>)653
3995 y Fj(y)j Fs(\024)d Ft(^)-43 b Fj(c)32 b Ft(if)h(the)g(system)g(is)
f(feasible.)h(Moreo)n(v)n(er,)d(since)i Fj(\031)j Ft(=)c
Fs(\000)p Fj(y)k Ft(\(the)0 4095 y(constrain)n(t)c(matrix)h(of)h
(problem)f(\(3\))h(is)f Fs(\000)p Fj(A)1452 4065 y Fi(>)1508
4095 y Ft(\))h(and)f Fj(\031)1789 4065 y Fh(l)1786 4115
y(u)1861 4095 y Fj(<)f(\031)2007 4065 y Fh(h)2004 4115
y(u)2083 4095 y Ft(for)h(eac)n(h)g(v)-5 b(ariable,)32
b(this)0 4194 y(system)38 b(is)h(feasible)f(and)h Fj(\031)908
4164 y Fh(l)975 4194 y Ft(=)i(\()p Fj(\031)1163 4164
y Fh(l)1160 4215 y Ff(1)1198 4194 y Fj(;)14 b(:)g(:)g(:)f(;)h(\031)1432
4164 y Fh(l)1429 4215 y(n)1475 4194 y Ft(\))1507 4164
y Fi(>)1602 4194 y Ft(is)38 b(a)g(feasible)h(solution)f(to)g(the)h
(TVPI)0 4294 y(system)27 b Fj(S)h Ft(=)23 b Fs(f)p Fj(\031)j
Ft(:)d Fj(\031)650 4306 y Fh(u)712 4294 y Fs(\000)18
b Fj(\015)838 4306 y Fh(uv)917 4294 y Fj(\031)964 4306
y Fh(v)1026 4294 y Fs(\024)25 b Ft(^)-44 b Fj(c)1150
4306 y Fh(uv)1229 4294 y Fj(;)14 b Ft(\()p Fj(u;)g(v)s
Ft(\))23 b Fs(2)g Fj(E)1620 4306 y Fh(x)1662 4294 y Fs(g)28
b Ft(that)f(w)n(e)h(are)e(considering.)125 4394 y(Let)293
4373 y(\026)274 4394 y Fj(E)j Ft(=)23 b Fs(f)p Ft(\()p
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%%Trailer
end
userdict /end-hook known{end-hook}if
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**