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11 dict begin
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cleartomark
%%EndFont 
%%BeginFont: LCIRCLE10
%!PS-AdobeFont-1.1: LCIRCLE10 1.001
%%CreationDate: 1992 Oct 23 20:21:59
%%RevisionDate: 2001 Jun 05 20:21:59
% Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.001) readonly def
/Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def
/FullName (LCIRCLE10) readonly def
/FamilyName (LaTeX) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /LCIRCLE10 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 113 /a113 put
readonly def
/FontBBox{-2000 -2000 2040 2040}readonly def
/UniqueID 5011942 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: MSBM7
%!PS-AdobeFont-1.1: MSBM7 2.1
%%CreationDate: 1992 Oct 17 08:30:50
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM7) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 67 /C put
dup 83 /S put
readonly def
/FontBBox{0 -504 2615 1004}readonly def
/UniqueID 5032014 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 25 /pi put
dup 77 /M put
dup 115 /s put
dup 116 /t put
readonly def
/FontBBox{11 -250 1241 750}readonly def
/UniqueID 5087381 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR6
%!PS-AdobeFont-1.1: CMR6 1.0
%%CreationDate: 1991 Aug 20 16:39:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 49 /one put
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: CMMI12
%!PS-AdobeFont-1.1: CMMI12 1.100
%%CreationDate: 1996 Jul 27 08:57:55
% 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 (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI12 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 14 /delta put
dup 24 /xi put
dup 25 /pi put
dup 27 /sigma put
dup 34 /epsilon put
dup 37 /rho1 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 71 /G 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 80 /P put
dup 83 /S 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 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 120 /x put
readonly def
/FontBBox{-30 -250 1026 750}readonly def
/UniqueID 5087386 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: LASY10
%!PS-AdobeFont-1.1: LASY10 1.001
%%CreationDate: 1992 Oct 23 20:19:17
%%RevisionDate: 2001 Jun 05 20:19:17
% Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.001) readonly def
/Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def
/FullName (LASY10) readonly def
/FamilyName (LaTeX) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /LASY10 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 50 /a50 put
readonly def
/FontBBox{-19 -192 944 683}readonly def
/UniqueID 5011949 def
currentdict end
currentfile eexec
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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
/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 45 /hyphen 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 65 /A put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 71 /G put
dup 73 /I put
dup 76 /L 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 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 121 /y put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
/UniqueID 5000769 def
currentdict end
currentfile eexec
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56B5A2ED3A3FC5C34A8F72CA3232B7694AF44381C117A8D8287C3A86D1E6EAE8
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FC1F54EC2C3E436F0593D5905FB5FAAC15CF0B45FEA94E095B4C14A6D10669DD
1921367C285E09780BED3C41A4EB351B19974EDD6CD6974FC9BA720D9413D179
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3BFB308ACDE16FC291F0AFC6F89933075B7746C362D057803F79F5388FF07990
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cleartomark
%%EndFont 
%%BeginFont: CMSY6
%!PS-AdobeFont-1.1: CMSY6 1.0
%%CreationDate: 1991 Aug 15 07:21:34
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 48 /prime put
dup 101 /ceilingright put
readonly def
/FontBBox{-4 -948 1329 786}readonly def
/UniqueID 5000816 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 40 /subsetnoteql put
dup 67 /C put
dup 83 /S put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
/UniqueID 5031982 def
currentdict end
currentfile eexec
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8CF7E1280B6C9A0AE0A35F74B15B1FDD024A9E8F6367C0C93C751C888523AF9B
231C9052D5C5FB0CC64EAAED511BC528D28B1CD35859F6E3A1AA58B50D374FE6
5B76E70FEDFC301B7388C6BD80DD068AE790FDF3E4E7063E5927607DB5A3A722
6E1AFB589C54FA46F99B60E403F20F10EE56A4274E9B2E17F4087BF65E3CCDF6
19E6953EB6CB346C701AA2114020454C2D3E44A7D178B37FF447C6D9DC4EFE0A
FF565E7742EEF5A3A6B50DE81B0FE5526D363523510CA572DC4AA806181A437C
88C5EFFB15213158BA939211DE8E54CCA0E0A6849C8CE839FE7A7DE79DF5DE84
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1B4067DA2AFB6AE00EB03B79F2C0EF420B42D9FD22AF9FA5DC68BAF29DD90BC1
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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 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 45 /hyphen 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 91 /bracketleft put
dup 93 /bracketright put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
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0FC45FA2A3312E0C46A5FD0466AB097C58FFEEC40601B8395E52775D0AFCD7DB
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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 0 /minus put
dup 48 /prime put
dup 50 /element put
dup 59 /emptyset put
dup 110 /backslash put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueID 5000818 def
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 14 /openbullet put
dup 18 /reflexsubset put
dup 19 /reflexsuperset put
dup 20 /lessequal put
dup 21 /greaterequal put
dup 24 /similar put
dup 40 /arrowdblleft put
dup 41 /arrowdblright put
dup 50 /element put
dup 54 /negationslash put
dup 56 /universal put
dup 59 /emptyset put
dup 63 /perpendicular put
dup 76 /L put
dup 77 /M put
dup 82 /R put
dup 95 /logicalor put
dup 102 /braceleft put
dup 103 /braceright put
dup 104 /angbracketleft put
dup 105 /angbracketright put
dup 106 /bar put
dup 110 /backslash put
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 12 /fi put
dup 20 /caron put
dup 40 /parenleft put
dup 41 /parenright 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 57 /nine put
dup 59 /semicolon put
dup 65 /A put
dup 67 /C put
dup 69 /E 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 82 /R put
dup 83 /S put
dup 84 /T put
dup 86 /V put
dup 89 /Y 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 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{-251 -250 1009 969}readonly def
/UniqueID 5000793 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 49 /one put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueID 5000790 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 25 /pi put
dup 27 /sigma put
dup 34 /epsilon put
dup 37 /rho1 put
dup 59 /comma put
dup 62 /greater put
dup 67 /C put
dup 71 /G 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 83 /S put
dup 84 /T put
dup 99 /c put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 120 /x put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec
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%%EndFont 
%%BeginFont: CMMI10
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%%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
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end readonly def
/FontName /CMMI10 def
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/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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dup 14 /delta put
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dup 102 /f put
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readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 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 12 /fi put
dup 46 /period put
dup 65 /A put
dup 75 /K put
dup 77 /M put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 104 /h put
dup 105 /i put
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dup 108 /l put
dup 109 /m put
dup 110 /n put
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dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 119 /w put
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readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueID 5000768 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMTT12
%!PS-AdobeFont-1.1: CMTT12 1.0
%%CreationDate: 1991 Aug 20 16:45:46
% 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 (CMTT12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch true def
end readonly def
/FontName /CMTT12 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 46 /period put
dup 64 /at put
dup 97 /a put
dup 99 /c put
dup 101 /e put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 114 /r put
dup 122 /z put
readonly def
/FontBBox{-1 -234 524 695}readonly def
/UniqueID 5000833 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR12
%!PS-AdobeFont-1.1: CMR12 1.0
%%CreationDate: 1991 Aug 20 16:38:05
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /ff put
dup 12 /fi put
dup 14 /ffi put
dup 19 /acute put
dup 20 /caron put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 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 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 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
readonly def
/FontBBox{-34 -251 988 750}readonly def
/UniqueID 5000794 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMTI12
%!PS-AdobeFont-1.1: CMTI12 1.0
%%CreationDate: 1991 Aug 18 21:06:53
% 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 (CMTI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI12 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 16 /dotlessi put
dup 19 /acute put
dup 20 /caron put
dup 38 /ampersand put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G 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 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 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
readonly def
/FontBBox{-36 -251 1103 750}readonly def
/UniqueID 5000829 def
currentdict end
currentfile eexec
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47[48{}3 49.8132 /CMSY6 rf /Fk 172[55 15[72 26[77 40[{}3
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35 35 35 35 35 2[24 1[55 1[27 27 40[{}16 66.4176 /CMR8
rf /Fm 150[47 47 15[144 6[94 13[87 87 87 87 3[89 1[89
1[89 6[87 87 36[47 47 10[{}15 99.6264 /CMEX10 rf /Fn
145[35 50[35 8[47 1[19 47[55{}5 66.4176 /CMSY8 rf /Fo
145[50 3[28 39 39 50 50 6[66 12[84 4[120 69 12[77 3[50
2[55 1[0 3[66 8[100 100 15[77 2[77 77 77 77 3[50 13[77{}24
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Fo(L)g Fy(for)f(all)h Fp(K)45 b Fo(\022)38 b Fp(N)10
b Fo(n)p Fp(ij;)39 b Fy(the)0 4289 y(circles)32 b Fp(i)e
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(while)f(if)f(it)g(is)h(not)f(in)g Fo(L)g Fy(for)f(an)m(y)i(suc)m(h)h
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b(that)f(\()p Fp(ij)6 b Fo(j)p Fp(K)h Fy(\))28 b Fo(2)g(L)p
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b(the)g(lists.)45 b(Th)m(us,)34 b(for)e(example,)i(the)f(diagram)g(in)f
(Figure)h(1)f(represen)m(ts)j(the)e(relation)628 4860
y Fo(f)p Fy(\(12)p Fo(j)p Fy(3\))p Fp(;)17 b Fy(\(14)p
Fo(j;)p Fy(\))p Fp(;)g Fy(\(23)p Fo(j)p Fy(1\))p Fp(;)g
Fy(\(23)p Fo(j)p Fy(14\))p Fp(;)g Fy(\(34)p Fo(j)o(;)p
Fy(\))p Fp(;)g Fy(\(3)o(4)p Fo(j)p Fy(1\))p Fp(;)f Fy(\(34)p
Fo(j)p Fy(2)o(\))p Fp(;)h Fy(\(34)o Fo(j)p Fy(12\))p
Fo(g)0 5070 y Fy(o)m(v)m(er)34 b Fp(N)k Fy(=)27 b Fo(f)p
Fy(1)p Fp(;)17 b Fy(2)p Fp(;)g Fy(3)p Fp(;)g Fy(4)p Fo(g)p
Fp(:)146 5190 y Fy(By)42 b(a)f(distribution)h(o)m(v)m(er)g
Fp(N)52 b Fy(w)m(e)42 b(mean)g(the)f(distribution)h Fp(P)55
b Fy(of)41 b(a)f(random)i(v)m(ector)g Fp(\030)j Fy(whose)0
5310 y(comp)s(onen)m(ts)31 b(are)e(indexed)i(b)m(y)f
Fp(N)5 b(:)30 b Fy(If)f Fp(I)36 b Fo(\022)28 b Fp(N)5
b(;)29 b Fy(the)h(sub)m(v)m(ector)i(\()p Fp(\030)2419
5325 y Ft(i)2446 5310 y Fy(\))2484 5325 y Ft(i)p Fn(2)p
Ft(I)2624 5310 y Fy(is)e(written)g(as)g Fp(\030)3217
5325 y Ft(I)3256 5310 y Fp(;)g Fy(whereas)h Fp(\030)3722
5326 y Fn(;)0 5431 y Fy(is)h(assumed)i(to)d(b)s(e)h(constan)m(t.)44
b(W)-8 b(e)33 b(use)f(the)h(notation)e Fp(I)8 b Fo(?)-66
b(?)p Fp(J)9 b Fo(j)p Fp(K)39 b Fy([)p Fp(P)14 b Fy(])32
b(to)f(abbreviate)i(the)f(statemen)m(t)0 5551 y(')p Fp(\030)70
5566 y Ft(I)138 5551 y Fy(and)c Fp(\030)366 5566 y Ft(J)443
5551 y Fy(are)h(conditionally)g(indep)s(enden)m(t)i(giv)m(en)e
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Fp(I)8 b(;)17 b(J)n(;)g(K)42 b Fo(\022)35 b Fp(N)48 b
Fy(the)37 b(follo)m(wing)g(equiv)-5 b(alence)39 b(holds,)g(cf.)e([10,)0
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b Fo(j)p Fp(K)40 b Fy([)p Fp(P)14 b Fy(])27 b Fo(\()-50
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b Fp(J)9 b Fy(\)\()p Fo(8)p Fp(L)29 b Fo(\023)f Fp(K)7
b Fy(\))32 b Fp(L)c Fo(\022)h Fp(I)8 b(J)h(K)e Fo(n)p
Fp(ij)34 b Fy(=)-66 b Fo(\))26 b Fp(i)p Fo(?)-66 b(?)p
Fp(j)6 b Fo(j)p Fp(L)34 b Fy([)p Fp(P)14 b Fy(])3345
353 y Fm(i)3383 463 y Fp(:)226 b Fy(\(1\))0 707 y(As)32
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(conditional)g(indep)s(endences)j Fp(i)p Fo(?)-66 b(?)p
Fp(j)6 b Fo(j)p Fp(K)39 b Fy([)p Fp(P)14 b Fy(])0 827
y(where)34 b Fp(i;)17 b(j)35 b Fo(2)29 b Fp(N)43 b Fy(are)33
b(distinct)h(and)g Fp(K)h Fo(\022)29 b Fp(N)10 b Fo(n)p
Fp(ij:)34 b Fy(W)-8 b(e)34 b(sa)m(y)g(that)f(a)f(relation)i
Fo(L)e Fy(o)m(v)m(er)i Fp(N)44 b Fy(is)33 b Fp(g)3420
842 y Ft(>)3479 827 y Fz(-r)-5 b(epr)g(e-)0 947 y(sentable)32
b Fy(if)g(there)h(exists)i(a)d(regular)h(Gaussian)g(distribution)g
Fp(P)46 b Fy(o)m(v)m(er)34 b Fp(N)43 b Fy(suc)m(h)34
b(that)1322 1163 y(\()p Fp(ij)6 b Fo(j)p Fp(K)h Fy(\))27
b Fo(2)i(L)e(\()-50 b(\))27 b Fp(i)p Fo(?)-66 b(?)p Fp(j)6
b Fo(j)p Fp(K)40 b Fy([)p Fp(P)14 b Fy(])0 1378 y(for)32
b(all)h(\()p Fp(ij)6 b Fo(j)p Fp(K)h Fy(\))27 b Fo(2)h(R)p
Fy(\()p Fp(N)10 b Fy(\))p Fp(:)146 1499 y Fy(Let)j Fp(P)32
b Fy(b)s(e)22 b(a)f(Gaussian)h(distribution)h(with)g(p)s(ositiv)m(e)g
(de\014nite)g(co)m(v)-5 b(ariance)22 b(matrix)c Fp(A)11
b Fy(=)g(\()p Fp(a)3437 1514 y Ft(i;j)3518 1499 y Fy(\))3556
1514 y Ft(i;j)t Fn(2)p Ft(N)3734 1499 y Fp(:)0 1619 y
Fy(F)-8 b(or)45 b(nonempt)m(y)i(subsets)g Fp(I)8 b(;)17
b(J)54 b Fy(of)45 b Fp(N)10 b Fy(,)50 b(denote)c(b)m(y)g
Fp(A)2046 1634 y Ft(I)5 b(;J)2196 1619 y Fy(the)46 b(submatrix)h(\()p
Fp(a)2943 1634 y Ft(i;j)3023 1619 y Fy(\))3061 1634 y
Ft(i)p Fn(2)p Ft(I)5 b(;j)t Fn(2)p Ft(J)3361 1619 y Fy(of)45
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b(2)49 b Fz(Up)37 b(to)h(isomorphisms,)d(ther)-5 b(e)38
b(ar)-5 b(e)37 b(exactly)g(58)g(gaussoids)f(over)h(a)g(set)g(of)g(c)-5
b(ar)g(dinal-)0 2909 y(ity)45 b(4.)71 b(A)n(ny)44 b(gaussoid)f(over)h
(such)f(a)h(set)g(which)f(is)h(not)g(a)g(sep)-5 b(ar)g(ation)43
b(gr)-5 b(aphoid)42 b(is)i(isomorphic)0 3030 y(either)33
b(to)f(one)h(of)f(the)h(r)-5 b(elations)32 b Fo(L)1309
3045 y Fl(1)1348 3030 y Fz({)p Fo(L)1467 3045 y Fl(31)1574
3030 y Fz(in)g(Figur)-5 b(e)33 b(3)f(or)h(to)g(one)f(of)g(the)h(duals)
3020 2949 y Fm(\012)3067 3046 y Fc(q)3067 2963 y(q)3150
3046 y(q)3150 2963 y(q)p 3067 2965 84 4 v 3066 3046 4
84 v 3150 2949 a Fm(\013)3197 2971 y Fj(e)3218 3030 y
Fp(;)3278 2949 y Fm(\012)3325 3046 y Fc(q)3325 2963 y(q)3408
3046 y(q)3408 2963 y(q)p 3325 2965 84 4 v 3323 3046 4
84 v 3325 3046 a Fb(@)3408 2949 y Fm(\013)3455 2971 y
Fj(e)3476 3030 y Fp(;)3536 2949 y Fm(\012)3583 3046 y
Fc(q)3583 2963 y(q)3666 3046 y(q)3666 2963 y(q)p 3583
2965 84 4 v 3581 3046 4 84 v 3664 3046 V 3666 2949 a
Fm(\013)3713 2971 y Fj(e)3734 3030 y Fp(;)0 3088 y Fm(\012)47
3185 y Fc(q)47 3102 y(q)130 3185 y(q)130 3102 y(q)p 47
3104 84 4 v 45 3185 4 84 v 47 3185 a Fb(@)p 128 3185
V -97 x Fm(\013)177 3110 y Fj(e)198 3168 y Fp(;)260 3088
y Fm(\012)307 3185 y Fc(q)307 3102 y(q)390 3185 y(q)390
3102 y(q)p 307 3104 84 4 v 305 3185 4 84 v 388 3185 V
307 3187 84 4 v 390 3088 a Fm(\013)437 3110 y Fj(e)458
3168 y Fp(;)520 3088 y Fm(\012)567 3185 y Fc(q)567 3102
y(q)650 3185 y(q)650 3102 y(q)p 567 3104 V 565 3185 4
84 v 567 3185 a Fb(@)p 648 3185 V 567 3187 84 4 v -97
x Fm(\013)697 3110 y Fj(e)718 3168 y Fp(;)i Fo(L)849
3183 y Fl(2)888 3127 y Fj(e)909 3168 y Fz({)p Fo(L)1028
3183 y Fl(4)1067 3127 y Fj(e)1087 3168 y Fp(;)g Fo(L)1218
3183 y Fl(6)1258 3127 y Fj(e)1278 3168 y Fp(;)g Fo(L)1409
3183 y Fl(8)1448 3127 y Fj(e)1469 3168 y Fz({)p Fo(L)1588
3183 y Fl(12)1663 3127 y Fj(e)1683 3168 y Fp(;)g Fo(L)1814
3183 y Fl(18)1889 3127 y Fj(e)1910 3168 y Fp(:)0 3397
y Fz(Pr)-5 b(o)g(of.)64 b Fy(Let)40 b Fp(N)50 b Fy(=)40
b Fo(f)p Fy(1)p Fp(;)17 b Fy(2)p Fp(;)g Fy(3)p Fp(;)g
Fy(4)p Fo(g)37 b Fy(and)j Fo(L)g(\022)g(R)p Fy(\()p Fp(N)10
b Fy(\))40 b(b)s(e)g(a)g(gaussoid.)65 b(F)-8 b(or)39
b(purp)s(oses)i(of)e(this)h(pro)s(of,)0 3517 y(isomorphic)26
b(relations)g(o)m(v)m(er)g Fp(N)35 b Fy(are)25 b(iden)m(ti\014ed)i(and)
e(a)g(couple)h(\()p Fp(ij)6 b Fo(j)p Fp(K)h Fy(\))27
b Fo(2)h(R)p Fy(\()p Fp(N)10 b Fy(\))26 b(is)g(called)g(a)e
Fp(p)p Fz(-c)-5 b(ouple)0 3638 y Fy(if)25 b Fp(p)j Fy(=)f(card)q(\()p
Fp(K)7 b Fy(\))p Fp(:)25 b Fy(By)h(Lemma)g(2,)h(it)e(su\016ces)j(to)d
(assume)h(that)g(the)f(n)m(um)m(b)s(er)i(of)32 b(2-couples)26
b(con)m(tained)0 3758 y(in)35 b Fo(L)f Fy(is)h(not)f(less)i(than)f(the)
g(n)m(um)m(b)s(er)h(of)e(its)h(0-couples,)h(an)m(y)f(other)g(gaussoid)g
(o)m(v)m(er)g Fp(N)45 b Fy(is)35 b(the)g(dual)0 3878
y(of)30 b(some)h(gaussoid)h(of)e(this)h(kind.)44 b(W)-8
b(e)31 b(shall)g(sho)m(w)g(that)g(if)f Fo(L)g Fy(is)h(not)g(a)f
(separation)h(graphoid,)g(then)0 3999 y(it)i(is)g(either)g(one)g(of)f
(the)h(relations)g Fo(L)1395 4014 y Fl(1)1434 3999 y
Fy({)p Fo(L)1552 4014 y Fl(31)1659 3999 y Fy(or)f(the)h(dual)g
Fo(L)2232 4014 y Fl(18)2306 3957 y Fj(e)2327 3999 y Fp(:)146
4119 y Fy(Let)k Fo(L)394 4134 y Fl(0)469 4119 y Fy(b)s(e)f(the)h(set)g
(of)e(all)h(2-couples)h(included)h(in)e Fo(L)p Fp(:)g
Fy(According)h(to)f(Corollary)h(4,)f(the)h(least)0 4239
y(gaussoid)30 b(con)m(taining)f Fo(L)927 4254 y Fl(0)966
4239 y Fp(;)g Fy(sa)m(y)p 1187 4159 69 4 v 30 w Fo(L)1256
4254 y Fl(0)1295 4239 y Fp(;)g Fy(is)h(the)f(separation)h(graphoid)e
(whose)j(set)e(of)g(2-couples)g(is)h(equal)0 4360 y(to)i
Fo(L)188 4375 y Fl(0)227 4360 y Fp(:)h Fy(F)-8 b(rom)32
b(no)m(w)h(on,)g(supp)s(ose)h(that)p 1487 4280 V 32 w
Fo(L)1556 4375 y Fl(0)1623 4360 y Fk(\()28 b Fo(L)p Fp(:)k
Fy(With)h(regard)g(to)f(\(2\){\(4\),)p 2889 4280 V 32
w Fo(L)2958 4375 y Fl(0)3029 4360 y Fy(is)i(none)f(of)1032
4499 y Fm(\012)1079 4596 y Fc(q)1079 4513 y(q)1162 4596
y(q)1162 4513 y(q)1162 4499 y Fm(\013)1209 4580 y Fp(;)1285
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y(q)1415 4513 y(q)p 1332 4515 84 4 v 1415 4499 a Fm(\013)1462
4580 y Fp(;)1538 4499 y Fm(\012)1585 4596 y Fc(q)1585
4513 y(q)1668 4596 y(q)1668 4513 y(q)p 1585 4515 V 1584
4596 4 84 v 1668 4499 a Fm(\013)1716 4580 y Fp(;)1792
4499 y Fm(\012)1839 4596 y Fc(q)1839 4513 y(q)1922 4596
y(q)1922 4513 y(q)p 1839 4515 84 4 v 1839 4598 V 1922
4499 a Fm(\013)1969 4580 y Fp(;)2045 4499 y Fm(\012)2092
4596 y Fc(q)2092 4513 y(q)2175 4596 y(q)2175 4513 y(q)p
2092 4515 V 2090 4596 4 84 v 2092 4596 a Fb(@)2175 4499
y Fm(\013)2222 4580 y Fp(;)2298 4499 y Fm(\012)2345 4596
y Fc(q)2345 4513 y(q)2428 4596 y(q)2428 4513 y(q)p 2345
4515 84 4 v 2344 4596 4 84 v 2345 4596 a Fb(\000)2428
4499 y Fm(\013)2476 4580 y Fp(;)2552 4499 y Fm(\012)2599
4596 y Fc(q)2599 4513 y(q)2682 4596 y(q)2682 4513 y(q)p
2599 4515 84 4 v 2597 4596 4 84 v 2680 4596 V 2682 4499
a Fm(\013)0 4800 y Fy(under)54 b(this)f(assumption)h(since)g(an)m(y)g
(gaussoid)f(strictly)h(including)g(an)m(y)g(of)e(these)i(separation)0
4920 y(graphoids)33 b(in)m(v)m(olv)m(es)i(either)f(another)e(2-couple)h
(or)f(more)h(0-couples)h(than)e(2-couples.)146 5041 y(F)-8
b(or)30 b(similar)h(reasons,)g(in)g(the)f(case)p 1486
4961 69 4 v 32 w Fo(L)1554 5056 y Fl(0)1621 5041 y Fy(=)1725
4960 y Fm(\012)1772 5057 y Fc(q)1772 4974 y(q)1855 5057
y(q)1855 4974 y(q)p 1772 4976 84 4 v 1770 5057 4 84 v
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y Fp(;)g Fy(if)g Fo(L)g Fy(in)m(v)m(olv)m(es)j(a)d(1-couple)g(whic)m(h)
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y Fl(0)3734 5041 y Fp(;)0 5161 y Fy(it)k(is)h(either)h
Fo(L)547 5176 y Fl(1)620 5161 y Fy(or)e Fo(L)810 5176
y Fl(2)850 5161 y Fp(:)g Fy(On)h(the)g(other)f(hand,)i(supp)s(osing)f
(that)f(there)h(is)g(no)g(other)g(1-couple)f(in)h Fo(L)0
5281 y Fy(but)e(some)g(0-couples,)h(the)f(only)g(p)s(ossibilit)m(y)h
(for)e Fo(L)g Fy(is)h Fo(L)2137 5296 y Fl(3)2177 5281
y Fp(:)146 5402 y Fy(F)-8 b(urther,)32 b(if)p 615 5322
V 32 w Fo(L)684 5417 y Fl(0)751 5402 y Fy(=)854 5321
y Fm(\012)901 5418 y Fc(q)901 5335 y(q)984 5418 y(q)984
5335 y(q)p 901 5337 84 4 v 900 5418 4 84 v 983 5418 V
901 5420 84 4 v 984 5321 a Fm(\013)1031 5402 y Fp(;)g
Fy(then)h(there)f(is)g(no)g(1-couple)g(in)g Fo(L)p Fp(:)f
Fy(All)h(p)s(ossibilities)i(ho)m(w)f(to)e(add)h(t)m(w)m(o)0
5533 y(0-couples)h(at)f(most)h(to)p 901 5453 69 4 v 33
w Fo(L)969 5548 y Fl(0)1041 5533 y Fy(without)g(yielding)h(a)f
(1-couple)f(are)h(co)m(v)m(ered)h(b)m(y)g Fo(L)2953 5548
y Fl(4)2992 5533 y Fp(;)f Fo(L)3121 5548 y Fl(5)3160
5533 y Fp(;)g Fo(L)3289 5548 y Fl(6)3328 5533 y Fp(;)f
Fy(and)h Fo(L)3646 5548 y Fl(7)3685 5533 y Fp(:)1856
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1 1 s 
gs
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p
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gr
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pc
gs
pum
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gr
gs
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51 -101 l  55 -101 l  56 -101 57 -101 58 -101 ct 71 -101 80 -103 87 -108 ct 
94 -112 97 -119 97 -128 ct 97 -136 95 -142 90 -146 ct 85 -150 78 -152 69 -152 ct 
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125 -69 129 -59 129 -48 ct 129 -33 123 -21 111 -11 ct 100 -1 86 3 69 4 ct 49 3 34 0 24 -9 ct 
14 -18 9 -30 9 -43 ct p ef
pom
gr
gs
pum
3430 12766 t
26 -144 m  44 -153 58 -163 69 -172 ct 95 -172 l  95 0 l  66 0 l  66 -141 l 
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gs
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pom
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gs
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p ef
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pc
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p ef
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pc
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p ef
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pc
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p ef
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pc
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124 -112 118 -98 106 -83 ct 95 -70 83 -57 72 -46 ct 43 -21 l  41 -24 l  124 -24 l 
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gr
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14 -18 9 -30 9 -43 ct p ef
pom
gr
gs
pum
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57 -132 43 -124 26 -117 ct p ef
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gr
gs
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176 -287 l  132 -227 l  205 -234 l  205 -204 l  132 -211 l  176 -152 l 
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p ef
pom
gr
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p
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263 -101 l  267 -101 l  268 -101 269 -101 270 -101 ct 283 -101 292 -103 299 -108 ct 
306 -112 309 -119 309 -128 ct 309 -136 307 -142 302 -146 ct 297 -150 290 -152 281 -152 ct 
274 -152 268 -150 262 -146 ct 257 -143 254 -136 253 -127 ct 224 -127 l  224 -142 229 -154 239 -163 ct 
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226 -18 221 -30 221 -43 ct p ef
pom
gr
gs
pum
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pom
gr
gs
pum
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176 -287 l  132 -227 l  205 -234 l  205 -204 l  132 -211 l  176 -152 l 
149 -135 l  119 -202 l  120 -202 l  91 -135 l  62 -151 l  106 -211 l  33 -204 l 
p ef
pom
gr
tm setmatrix
0 0 t 
1 1 s 
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pom
count op_count sub {pop} repeat countdictstack dict_count sub {end} repeat b4_inc_state restore
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%%EndDocument
 @endspecial 1548 71 a Fo(L)1617 86 y Fl(2)1700 543 y
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 @endspecial 2680 667 a Fo(L)2749 682 y Fl(7)2833 1069
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 @endspecial 2754 1281 a Fo(L)2823 1296 y Fl(13)2930
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 @endspecial 2404 1891 a Fo(L)2473 1906 y Fl(14)2577
2294 y @beginspecial 0 @llx 0 @lly 56 @urx 56 @ury 560
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16218 21608 t
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14631 21608 t
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16218 23169 t
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15795 22534 t
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 @endspecial 3106 1891 a Fo(L)3175 1906 y Fl(15)3280
2294 y @beginspecial 0 @llx 0 @lly 56 @urx 56 @ury 560
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p ef
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gr
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17047 21502 t
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18211 22428 t
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p
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 @endspecial 2175 5025 a Fo(L)2244 5040 y Fl(30)2348
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 @endspecial 2877 5025 a Fo(L)2946 5040 y Fl(31)3050
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%%Page: 12 12
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f(to)f(F)-8 b(ran)m(ti)j(\024)-44 b(sek)34 b(Mat)s(\023)-51
b(u)-5 b(\024)-44 b(s)32 b(for)g(simplifying)h(the)g(pro)s(of)f(of)f
(Theo-)0 5551 y(rem)i(1)f(and)h(for)f(man)m(y)i(other)e(v)-5
b(aluable)33 b(suggestions)h(for)f(impro)m(v)m(emen)m(ts.)1832
5800 y(12)p eop end
%%Page: 13 13
TeXDict begin 13 12 bop 0 100 a Fs(References)49 319
y Fy([1])49 b(D.)43 b(Co)m(x,)48 b(J.)c(Little,)j(D.)c(O'Shea:)67
b Fz(Ide)-5 b(als,)47 b(V)-7 b(arieties,)47 b(and)e(A)n(lgorithms.)f(A)
n(n)h(Intr)-5 b(o)g(duction)201 439 y(to)44 b(Computational)g(A)n
(lgebr)-5 b(aic)43 b(Ge)-5 b(ometry)45 b(and)f(Commutative)g(A)n(lgebr)
-5 b(a.)44 b(Se)-5 b(c)g(ond)43 b(Edition.)201 559 y
Fy(Springer-V)-8 b(erlag,)32 b(New)i(Y)-8 b(ork,)33 b(USA,)g(1997.)49
751 y([2])49 b(A.)32 b(P)-8 b(.)33 b(Dempster:)45 b(Co)m(v)-5
b(ariance)33 b(Selection.)h Fz(Biometrics)e Fi(28)g Fy(\(1972\))g
(157{175.)49 942 y([3])49 b(M.)30 b(F)-8 b(ryden)m(b)s(erg:)42
b(Marginalization)30 b(and)g(Collapsibilit)m(y)i(in)d(Graphical)h(In)m
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y([4])49 b(S.)c(L.)h(Lauritzen:)71 b Fz(Gr)-5 b(aphic)g(al)46
b(Mo)-5 b(dels.)45 b Fy(Oxford)h(Statistical)g(Science)h(Series,)k
Fi(17)p Fy(.)46 b(Oxford)201 1374 y(Univ)m(ersit)m(y)35
b(Press,)f(New)f(Y)-8 b(ork,)33 b(1996.)49 1565 y([5])49
b(F.)26 b(Mat)s(\023)-51 b(u)-5 b(\024)-44 b(s:)41 b(Ascending)29
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Fz(Infor-)201 1685 y(mation)k(The)-5 b(ory,)34 b(Statistic)-5
b(al)33 b(De)-5 b(cision)32 b(F)-7 b(unctions)32 b(and)h(R)-5
b(andom)33 b(Pr)-5 b(o)g(c)g(esses.)32 b(T)-7 b(r)i(ansactions)201
1805 y(of)40 b(the)h(11th)f(Pr)-5 b(ague)41 b(Confer)-5
b(enc)g(e,)40 b(V)-7 b(ol.)41 b(B)f(\(S.)g(Kub)-10 b(\023)-40
b(\020k,)42 b(J.)2530 1780 y(\023)2512 1805 y(A.)f(V)-10
b(\023)-40 b(\020)-5 b(\024)-45 b(sek)41 b(e)-5 b(ds.\).)38
b Fy(Klu)m(w)m(er,)k(Dor-)201 1926 y(drec)m(h)m(t)34
b({)e(Boston)h({)f(London)h(\(also)f(Academia,)i(Prague\))f(1992,)e
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b(\024)-44 b(s:)63 b(Conditional)43 b(Indep)s(endence)i(Structures)f
(Examined)h(via)d(Minors.)i Fz(A)n(nnals)f(of)201 2237
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b(e)31 b Fi(21)h Fy(\(1997\))g(99{128.)49 2429 y([7])49
b(F.)33 b(Mat)s(\023)-51 b(u)-5 b(\024)-44 b(s:)45 b(Conditional)35
b(Indep)s(endences)i(among)c(F)-8 b(our)33 b(Random)h(V)-8
b(ariables)34 b(I)s(I.)g Fz(Combina-)201 2549 y(torics,)g(Pr)-5
b(ob)g(ability)35 b(&)g(Computing)c Fi(4)i Fy(\(1995\))e(407{417.)49
2740 y([8])49 b(F.)24 b(Mat)s(\023)-51 b(u)-5 b(\024)-44
b(s:)40 b(Conditional)25 b(Indep)s(endences)j(among)d(F)-8
b(our)24 b(Random)h(V)-8 b(ariables)26 b(I)s(I)s(I:)f(Final)g(Con-)201
2860 y(clusion.)33 b Fz(Combinatorics,)h(Pr)-5 b(ob)g(ability)34
b(&)h(Computing)d Fi(8)g Fy(\(1999\))g(269{276.)49 3052
y([9])49 b(F.)23 b(Mat)s(\023)-51 b(u)-5 b(\024)-44 b(s:)39
b(Conditional)25 b(Indep)s(endences)i(in)d(Gaussian)g(V)-8
b(ectors)25 b(and)f(Rings)g(of)g(P)m(olynomials.)201
3172 y(In)36 b Fz(Pr)-5 b(o)g(c)g(e)g(e)g(dings)36 b(of)i
(Conditionals,)f(Information,)g(and)g(Infer)-5 b(enc)g(e,)35
b Fy(Hagen,)i(German)m(y)-8 b(,)38 b(Ma)m(y)201 3292
y(13-15,)31 b(2002.)0 3483 y([10])49 b(F.)37 b(Mat)s(\023)-51
b(u)-5 b(\024)-44 b(s:)54 b(On)37 b(Equiv)-5 b(alence)40
b(of)e(Mark)m(o)m(v)h(Prop)s(erties)g(o)m(v)m(er)f(Undirected)i
(Graphs.)e Fz(Journal)201 3604 y(of)c(Applie)-5 b(d)34
b(Pr)-5 b(ob)g(ability)33 b Fi(29)f Fy(\(1992\))g(745{749.)0
3795 y([11])49 b(F.)54 b(Mat)s(\023)-51 b(u)-5 b(\024)-44
b(s:)89 b(T)-8 b(o)m(w)m(ards)56 b(Classi\014cation)h(of)d
(Semigraphoids.)j Fz(Discr)-5 b(ete)55 b(Mathematics)g
Fi(277)201 3915 y Fy(\(2004\))31 b(115{145.)0 4107 y([12])49
b(F.)25 b(Mat)s(\023)-51 b(u)-5 b(\024)-44 b(s,)27 b(M.)f(Studen)q
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b(our)25 b(Random)h(V)-8 b(ariables)26 b(I.)201 4227
y Fz(Combinatorics,)33 b(Pr)-5 b(ob)g(ability)34 b(&)h(Computing)d
Fi(4)g Fy(\(1995\))g(269{278.)0 4418 y([13])49 b(J.)38
b(P)m(earl:)55 b Fz(Pr)-5 b(ob)g(abilistic)40 b(R)-5
b(e)g(asoning)38 b(in)i(Intel)5 b(ligent)39 b(Systems:)55
b(Networks)40 b(of)g(Plausible)f(In-)201 4538 y(fer)-5
b(enc)g(e.)31 b Fy(Morgan)h(Kaufmann,)h(San)g(Mateo,)g(California,)f
(1988.)0 4730 y([14])49 b(V.)29 b(V.)g(Prasolo)m(v:)42
b Fz(Pr)-5 b(oblems)31 b(and)g(The)-5 b(or)g(ems)30 b(in)h(Line)-5
b(ar)31 b(A)n(lgebr)-5 b(a.)28 b Fy(American)i(Mathematical)201
4850 y(So)s(ciet)m(y)-8 b(,)33 b(USA,)g(1996.)0 5041
y([15])49 b(M.)41 b(Studen)q(\023)-50 b(y:)63 b(Structural)42
b(Semigraphoids.)h Fz(International)f(Journal)h(of)g(Gener)-5
b(al)43 b(Systems)201 5161 y Fi(22)32 b Fy(\(1994\))g(207{217.)0
5353 y([16])49 b(J.)30 b(Whittak)m(er:)43 b Fz(Gr)-5
b(aphic)g(al)32 b(Mo)-5 b(dels)32 b(in)g(Applie)-5 b(d)31
b(Multivariate)i(Statistics.)d Fy(John)g(Wiley)-8 b(,)32
b(New)201 5473 y(Y)-8 b(ork,)32 b(1990.)1832 5800 y(13)p
eop end
%%Trailer

userdict /end-hook known{end-hook}if
%%EOF