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cleartomark
%%EndFont
%%BeginFont: CMTI7
%!PS-AdobeFont-1.1: CMTI7 1.0
%%CreationDate: 1991 Aug 18 21:07:18
% 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 (CMTI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 39 /quoteright 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 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 65 /A put
dup 67 /C put
dup 69 /E put
dup 70 /F put
dup 72 /H 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 83 /S put
dup 84 /T put
dup 87 /W put
dup 97 /a put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 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 119 /w put
dup 121 /y put
readonly def
/FontBBox{-27 -250 1268 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY5
%!PS-AdobeFont-1.1: CMSY5 1.0
%%CreationDate: 1991 Aug 15 07:21:16
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 3 /asteriskmath put
readonly def
/FontBBox{21 -944 1448 791}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMBX7
%!PS-AdobeFont-1.1: CMBX7 1.0
%%CreationDate: 1991 Aug 20 16:35:49
% 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 (CMBX7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 65 /A put
dup 67 /C put
dup 69 /E put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 83 /S put
dup 97 /a put
dup 99 /c put
dup 100 /d 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 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 119 /w put
readonly def
/FontBBox{-55 -250 1289 751}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 78 /N put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR5
%!PS-AdobeFont-1.1: CMR5 1.00B
%%CreationDate: 1992 Feb 19 19:55:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 91 /bracketleft put
dup 93 /bracketright put
readonly def
/FontBBox{-341 -250 1304 965}readonly def
currentdict end
currentfile eexec
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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 56 /bracelefttp put
dup 58 /braceleftbt put
dup 60 /braceleftmid put
dup 62 /braceex put
dup 80 /summationtext put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMMI6
%!PS-AdobeFont-1.1: CMMI6 1.100
%%CreationDate: 1996 Jul 23 07:53:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 59 /comma put
dup 104 /h put
dup 107 /k put
readonly def
/FontBBox{11 -250 1241 750}readonly def
currentdict end
currentfile eexec
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D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5
5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC
4391C9DF440285B8FC159D0E98D4258FC57892DDF0342CA1080743A076089583
6AD6FB2DC4C13F077F17789476E48402796E685107AF60A63FB0DE0266D55CF1
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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 11 /alpha put
dup 58 /period put
dup 59 /comma put
dup 82 /R put
dup 97 /a put
dup 106 /j put
dup 109 /m put
dup 115 /s put
readonly def
/FontBBox{-29 -250 1075 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR6
%!PS-AdobeFont-1.1: CMR6 1.0
%%CreationDate: 1991 Aug 20 16:39:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 40 /parenleft put
dup 41 /parenright 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
readonly def
/FontBBox{-20 -250 1193 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSS10
%!PS-AdobeFont-1.1: CMSS10 1.0
%%CreationDate: 1991 Aug 20 17:33:34
% 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 (CMSS10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMSS10 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 97 /a put
dup 110 /n put
dup 112 /p put
dup 115 /s put
readonly def
/FontBBox{-61 -250 999 759}readonly 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 40 /parenleft put
dup 41 /parenright 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 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 75 /K put
dup 76 /L 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 85 /U put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 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
readonly def
/FontBBox{-301 -250 1164 946}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMMI5
%!PS-AdobeFont-1.1: CMMI5 1.100
%%CreationDate: 1996 Aug 02 08:21:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 27 /sigma put
dup 58 /period put
dup 59 /comma put
dup 67 /C put
dup 68 /D put
dup 73 /I put
dup 75 /K put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 86 /V put
dup 105 /i put
readonly def
/FontBBox{37 -250 1349 750}readonly def
currentdict end
currentfile eexec
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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 0 /minus put
dup 1 /periodcentered put
dup 8 /circleplus put
dup 20 /lessequal put
dup 32 /arrowleft put
readonly def
/FontBBox{-15 -951 1252 782}readonly 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 58 /period put
dup 59 /comma put
dup 60 /less put
dup 67 /C put
dup 73 /I put
dup 82 /R put
dup 86 /V put
dup 102 /f put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 118 /v put
readonly def
/FontBBox{0 -250 1171 750}readonly 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 11 /alpha put
dup 12 /beta put
dup 13 /gamma put
dup 14 /delta put
dup 22 /mu put
dup 27 /sigma put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 67 /C put
dup 68 /D put
dup 73 /I put
dup 75 /K put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 86 /V put
dup 88 /X put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 102 /f put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 118 /v put
readonly def
/FontBBox{-32 -250 1048 750}readonly 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 11 /ff 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 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 89 /Y put
dup 91 /bracketleft put
dup 92 /quotedblleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 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{-27 -250 1122 750}readonly 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 45 /hyphen put
dup 70 /F put
dup 73 /I put
dup 76 /L put
dup 82 /R put
dup 83 /S 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 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{-163 -250 1146 969}readonly 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 2 /multiply put
dup 8 /circleplus put
dup 20 /lessequal put
dup 21 /greaterequal put
dup 33 /arrowright put
dup 50 /element put
dup 55 /mapsto put
dup 102 /braceleft put
dup 103 /braceright put
readonly def
/FontBBox{-29 -960 1116 775}readonly 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 45 /hyphen put
dup 47 /slash put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 65 /A put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 72 /H put
dup 73 /I put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 97 /a put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 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 119 /w put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMTI9
%!PS-AdobeFont-1.1: CMTI9 1.0
%%CreationDate: 1991 Aug 18 21:08:07
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 97 /a put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 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{-35 -250 1148 750}readonly 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 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 58 /colon put
dup 65 /A put
dup 70 /F put
dup 75 /K 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 103 /g put
dup 105 /i put
dup 108 /l put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 119 /w put
dup 121 /y put
readonly def
/FontBBox{-58 -250 1195 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMTT9
%!PS-AdobeFont-1.1: CMTT9 1.0
%%CreationDate: 1991 Aug 20 16:46:24
% 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 (CMTT9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch true def
end readonly def
/FontName /CMTT9 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 64 /at put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 103 /g put
dup 104 /h put
dup 105 /i 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 121 /y put
readonly def
/FontBBox{-6 -233 542 698}readonly def
currentdict end
currentfile eexec
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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 102 /braceleft put
dup 103 /braceright put
readonly def
/FontBBox{-30 -958 1146 777}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR9
%!PS-AdobeFont-1.1: CMR9 1.0
%%CreationDate: 1991 Aug 20 16:39:59
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 14 /ffi put
dup 40 /parenleft put
dup 41 /parenright put
dup 42 /asterisk 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 56 /eight 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 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 87 /W put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 127 /dieresis put
readonly def
/FontBBox{-39 -250 1036 750}readonly 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 14 /ffi put
dup 34 /quotedblright 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 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 88 /X put
dup 89 /Y put
dup 91 /bracketleft put
dup 92 /quotedblleft 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{-251 -250 1009 969}readonly def
currentdict end
currentfile eexec
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%EndPhotoshop
%begin_xml_code
/pdfmark where {pop true} {false} ifelse
/currentdistillerparams where {pop currentdistillerparams
/CoreDistVersion get 5000 ge } {false} ifelse
and not {userdict /pdfmark /cleartomark load put} if
[/NamespacePush pdfmark
[/_objdef {photoshop_metadata_stream} /type /stream /OBJ pdfmark
/MetadataString 5036 string def % exact length of metadata
/TempString 100 string def
/ConsumeMetadata {
currentfile TempString readline pop pop
currentfile MetadataString readstring pop pop
} bind def
ConsumeMetadata
%begin_xml_packet: 5036
Adobe Photoshop Elements for Windows, version 2.0
adobe:docid:photoshop:e3f10417-abc8-11db-b155-e5fe4d93f3bb
%end_xml_packet
[{photoshop_metadata_stream} 2 dict begin /Type /Metadata def /Subtype /XML def currentdict end /PUT pdfmark
[{photoshop_metadata_stream} MetadataString /PUT pdfmark
[/_objdef {nextImage} /NI pdfmark
%end_xml_code
gsave % EPS gsave
/hascolor
/deviceinfo where
{pop deviceinfo /Colors known
{deviceinfo /Colors get exec 1 gt}
{false} ifelse}
{/statusdict where
{pop statusdict /processcolors known
{statusdict /processcolors get exec 1 gt}
{false} ifelse}
{false} ifelse}
ifelse
def
40 dict begin
/_image systemdict /image get def
/_setgray systemdict /setgray get def
/_currentgray systemdict /currentgray get def
/_settransfer systemdict /settransfer get def
/_currenttransfer systemdict /currenttransfer get def
/blank 0 _currenttransfer exec
1 _currenttransfer exec eq def
/negative blank
{0 _currenttransfer exec 0.5 lt}
{0 _currenttransfer exec 1 _currenttransfer exec gt}
ifelse def
/inverted? negative def
/level2 systemdict /languagelevel known
{languagelevel 2 ge} {false} ifelse def
/level3 systemdict /languagelevel known
{languagelevel 3 ge} {false} ifelse def
/foureq {4 index eq 8 1 roll
4 index eq 8 1 roll
4 index eq 8 1 roll
4 index eq 8 1 roll
pop pop pop pop and and and} def
hascolor {/band 0 def} {/band 5 def} ifelse
/setcmykcolor where {pop
1 0 0 0 setcmykcolor _currentgray 1 exch sub
0 1 0 0 setcmykcolor _currentgray 1 exch sub
0 0 1 0 setcmykcolor _currentgray 1 exch sub
0 0 0 1 setcmykcolor _currentgray 1 exch sub
4 {4 copy} repeat
1 0 0 0 foureq {/band 1 store} if
0 1 0 0 foureq {/band 2 store} if
0 0 1 0 foureq {/band 3 store} if
0 0 0 1 foureq {/band 4 store} if
0 0 0 0 foureq {/band 6 store} if} if
blank {/band 6 store} if
gsave % Image Header gsave
/rows 615 def
/cols 1024 def
1024 615 scale
level2 {
band 0 eq {
/DeviceRGB
} {/DeviceGray} ifelse
setcolorspace currentdict /PhotoshopDuotoneColorSpace undef currentdict /PhotoshopDuotoneAltColorSpace undef } if
/picstr1 1024 string def
/picstr2 1024 string def
/picstr3 1024 string def
/picstr4 1024 string def
/_rowpadstr 1024 string def
/rawreaddata {currentfile exch readstring pop} def
/padreaddata { _topPad 0 gt { /_topPad _topPad 1 sub def pop _rowpadstr }
{ _subImageRows 0 gt { /_subImageRows _subImageRows 1 sub def
dup _leftPad _picsubstr rawreaddata putinterval }
{ pop _rowpadstr } ifelse } ifelse } def
/image2 level2 {/image load def} {{begin
Width Height BitsPerComponent ImageMatrix
Decode length 2 eq
{/DataSource load image} if
Decode length 6 eq
{DataSource 0 get DataSource 1 get DataSource 2 get
true 3 colorimage} if
Decode length 8 eq
{DataSource 0 get DataSource 1 get
DataSource 2 get DataSource 3 get
true 4 colorimage} if
end} def} ifelse
/_image2 level2 {/_image load def} {{begin
Width Height BitsPerComponent ImageMatrix
/DataSource load _image end} def} ifelse
/beginimage {
band 0 eq band 4 eq or band 5 eq or
{image2}
{negative {{pop 0}} {{pop 1}} ifelse
_settransfer _image2} ifelse
} def
/readdata /rawreaddata load bind def
12 dict begin
/ImageType 1 def
/Width cols def
/Height rows def
/ImageMatrix [cols 0 0 rows neg 0 rows] def
/BitsPerComponent 8 def
band 0 eq
{/Decode [0 1 0 1 0 1] def
/MultipleDataSources true def
/DataSource [
{picstr1 readdata}
{picstr2 readdata}
{picstr3 readdata picstr4 readdata pop}
] def}
{/Decode [0 1] def
/DataSource {
picstr1 readdata pop
picstr2 readdata pop
picstr3 readdata pop
picstr4 readdata
} def}
ifelse
currentdict end
%%BeginBinary: 2519052
beginimage
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ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ
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@endspecial 1151 2184 a Fv(Fig.)13 b(1.)26 b Fy(Design)g(of)g(A5/2)h
(\(the)e(Figure)h(is)g(due)f(to)h([2)q(]\))523 2545 y
Ft(2)112 b(The)38 b(A5/2)f(Stream)h(Cipher)523 2733 y
Fz(A5/2)25 b(is)h(a)g(sync)n(hronous)e(stream)h(cipher)h(accepting)f(a)
h(64-bit)f(k)n(ey)g Fp(K)k Fz(=)22 b(\()p Fp(k)2958 2745
y Fq(0)2996 2733 y Fp(;)14 b(:)g(:)g(:)g(;)g(k)3224 2745
y Fq(63)3294 2733 y Fz(\))24 b Fs(2)523 2832 y Fz(GF\(2\))748
2802 y Fq(64)850 2832 y Fz(and)32 b(a)f(22-bit)f(initial)i(v)n(ector)e
Fp(I)7 b(V)49 b Fz(=)29 b(\()p Fp(v)2135 2844 y Fq(0)2173
2832 y Fp(;)14 b(:)g(:)g(:)f(;)h(v)2397 2844 y Fq(21)2468
2832 y Fz(\))29 b Fs(2)h Fz(GF)q(\(2\))2840 2802 y Fq(22)2942
2832 y Fz(deriv)n(ed)g(from)523 2932 y(the)j(22-bit)f(frame)g(n)n(um)n
(b)r(er)g(whic)n(h)h(is)f(publicly)h(kno)n(wn.)f(It)h(uses)f(four)g
(linear)g(feedbac)n(k)523 3031 y(shift)j(registers)d(\(LFSRs\))j
Fp(R)q Fz(1,)f Fp(R)q Fz(2,)g Fp(R)q Fz(3)f(and)h Fp(R)q
Fz(4)g(of)g(lengths)g(19,)f(22,)h(23)f(and)h(17)g(bits,)523
3131 y(resp)r(ectiv)n(ely)-7 b(,)37 b(as)h(its)g(main)h(building)f(blo)
r(c)n(ks)f(\(see)i(Figure)e(1\).)h(The)g(taps)g(of)h(the)f(LF-)523
3231 y(SRs)c(corresp)r(ond)e(to)i(primitiv)n(e)f(p)r(olynomials)g(and,)
h(therefore,)f(the)h(registers)e(pro)r(duce)523 3330
y(sequences)d(of)g(maximal)g(p)r(erio)r(ds.)g Fp(R)q
Fz(1,)g Fp(R)q Fz(2)g(and)g Fp(R)q Fz(3)f(are)h(clo)r(c)n(k)n(ed)f
(irregularly)f(based)i(on)523 3430 y(the)f(curren)n(t)f(state)g(of)h
Fp(R)q Fz(4.)648 3530 y(The)22 b(A5/2)f(k)n(eystream)f(generator)g(w)n
(orks)h(as)g(follo)n(ws.)h(First,)g(an)g Fr(initialization)k(phase)523
3629 y Fz(is)33 b(run)f(\(see)h(Figure)f(2\).)h(A)n(t)g(the)g(b)r
(eginning)g(of)g(this)g(phase)f(all)h(registers)e(are)h(set)h(to)f(0.)
523 3729 y(Then)c(the)h Fr(key)i(setup)i Fz(and)28 b(the)g
Fr(IV)i(setup)j Fz(are)27 b(p)r(erformed.)h(Here)g(the)g(k)n(ey)g
(resp.)f(IV)i(bits)523 3828 y(are)i(cyclically)h(added)g(to)g(the)h
(registers)e(mo)r(dulo)h(2.)g(A)n(t)h(the)g(end)f(of)h(the)f
(initialization)523 3928 y(phase)27 b(one)g(bit)h(in)g(eac)n(h)f
(register)f(is)i(set)f(to)h(1.)648 4028 y(Then)d(the)g
Fr(warm-up)i(phase)33 b Fz(is)25 b(p)r(erformed)f(where)g(R4)h(is)g
(clo)r(c)n(k)n(ed)e(99)h(times)h(and)g(and)523 4127 y(the)36
b(output)g(is)g(discarded.)f(Note)h(that)g(already)e(during)h(this)h
(phase)f(and)h(also)e(during)523 4227 y(the)d(stream)f(generation)g
(phase)g(whic)n(h)h(starts)f(afterw)n(ards,)f(the)i(registers)e
Fp(R)q Fz(1,)h Fp(R)q Fz(2)g(and)523 4327 y Fp(R)q Fz(3)23
b(are)f(clo)r(c)n(k)n(ed)h(irregularly)-7 b(.)21 b(More)i(precisely)-7
b(,)23 b(the)h(stop/go)e(clo)r(c)n(king)g(is)i(determined)f(b)n(y)523
4426 y(the)31 b(bits)g Fp(R)q Fz(4[3],)f Fp(R)q Fz(4[7])g(and)g
Fp(R)q Fz(4[10])f(in)i(eac)n(h)f(clo)r(c)n(k)g(cycle)h(as)f(follo)n
(ws:)g(the)h(ma)5 b(jorit)n(y)29 b(of)523 4526 y(the)g(three)f(bits)g
(is)h(computed,)f(where)g(the)h(ma)5 b(jorit)n(y)27 b(of)h(three)g
(bits)h Fp(a;)14 b(b;)g(c)27 b Fz(is)i(de\014ned)f(b)n(y)523
4625 y Fp(maj)5 b Fz(\()p Fp(a;)14 b(b;)g(c)p Fz(\))23
b(=)f Fp(ab)15 b Fs(\010)f Fp(ac)g Fs(\010)h Fp(bc)p
Fz(.)25 b Fp(R)q Fz(1)g(is)h(clo)r(c)n(k)n(ed)e(i\013)j
Fp(R)q Fz(4[10])d(agrees)g(with)i(the)g(ma)5 b(jorit)n(y)-7
b(.)25 b Fp(R)q Fz(2)523 4725 y(is)j(clo)r(c)n(k)n(ed)g(i\013)h
Fp(R)q Fz(4[3])f(agrees)e(with)j(the)g(ma)5 b(jorit)n(y)-7
b(.)28 b Fp(R)q Fz(3)f(is)i(clo)r(c)n(k)n(ed)e(i\013)i
Fp(R)q Fz(4[7])f(agrees)e(with)523 4825 y(the)j(ma)5
b(jorit)n(y)-7 b(.)28 b(In)g(eac)n(h)g(cycle)h(at)f(least)g(t)n(w)n(o)g
(of)h(the)g(three)f(registers)f(are)h(clo)r(c)n(k)n(ed.)g(After)523
4924 y(these)j(clo)r(c)n(kings,)f Fp(R)q Fz(4)g(is)h(\(regularly\))f
(clo)r(c)n(k)n(ed,)g(and)h(an)f(output)i(bit)g(is)e(generated)g(from)p
eop end
%%Page: 5 5
TeXDict begin 5 4 bop 762 491 a Fo(R)p Fq(1)20 b Fn( )f
Fq(0)p Fo(;)33 b(R)p Fq(2)19 b Fn( )h Fq(0)p Fo(;)33
b(R)p Fq(3)19 b Fn( )g Fq(0)p Fo(;)34 b(R)p Fq(4)19 b
Fn( )g Fq(0;)762 557 y(for)j Fo(i)e Fq(=)e(0)p Fo(:::)p
Fq(63)k(do)808 623 y(-Clo)r(c)n(k)g Fo(R)p Fq(1)p Fo(;)12
b(R)p Fq(2)p Fo(;)f(R)p Fq(3)p Fo(;)h(R)p Fq(4;)808 690
y(-)p Fo(R)p Fq(1[0])19 b Fn( )g Fo(R)p Fq(1[0])d Fn(\010)f
Fo(k)1360 698 y Fm(i)1386 690 y Fo(;)c(R)p Fq(2[0])19
b Fn( )g Fo(R)p Fq(2[0])c Fn(\010)g Fo(k)1946 698 y Fm(i)1973
690 y Fo(;)c(R)p Fq(3[0])19 b Fn( )g Fo(R)p Fq(3[0])c
Fn(\010)g Fo(k)2533 698 y Fm(i)2560 690 y Fo(;)c(R)p
Fq(4[0])19 b Fn( )g Fo(R)p Fq(4[0])c Fn(\010)g Fo(k)3120
698 y Fm(i)3147 690 y Fq(;)762 756 y(for)22 b Fo(i)e
Fq(=)e(0)p Fo(:::)p Fq(21)k(do)808 823 y(-Clo)r(c)n(k)g
Fo(R)p Fq(1)p Fo(;)12 b(R)p Fq(2)p Fo(;)f(R)p Fq(3)p
Fo(;)h(R)p Fq(4;)808 889 y(-)p Fo(R)p Fq(1[0])19 b Fn( )g
Fo(R)p Fq(1[0])d Fn(\010)f Fo(v)1358 897 y Fm(i)1384
889 y Fo(;)c(R)p Fq(2[0])19 b Fn( )g Fo(R)p Fq(2[0])c
Fn(\010)g Fo(v)1942 897 y Fm(i)1969 889 y Fo(;)c(R)p
Fq(3[0])19 b Fn( )g Fo(R)p Fq(3[0])c Fn(\010)g Fo(v)2527
897 y Fm(i)2554 889 y Fo(;)c(R)p Fq(4[0])19 b Fn( )g
Fo(R)p Fq(4[0])c Fn(\010)g Fo(v)3112 897 y Fm(i)3139
889 y Fq(;)762 956 y Fo(R)p Fq(1[15])k Fn( )g Fq(1)p
Fo(;)34 b(R)p Fq(2[16])19 b Fn( )g Fq(1)p Fo(;)34 b(R)p
Fq(3[18])19 b Fn( )g Fq(1)p Fo(;)33 b(R)p Fq(4[10])19
b Fn( )g Fq(1;)1371 1111 y Fv(Fig.)13 b(2.)26 b Fy(Initialization)h
(phase)f(of)g(A5/2)523 1497 y Fz(the)31 b(v)-5 b(alues)30
b(of)h Fp(R)q Fz(1,)e Fp(R)q Fz(2,)h(and)h Fp(R)q Fz(3)e(b)n(y)i
(adding)f(their)g(righ)n(tmost)g(bits)h(to)f(three)g(ma)5
b(jorit)n(y)523 1596 y(v)-5 b(alues,)31 b(one)g(for)f(eac)n(h)h
(register)e(\(see)j(Figure)e(1\).)h(After)h(w)n(arm-up)e(A5/2)g(pro)r
(duces)g(228)523 1696 y(output)f(bits,)f(one)g(p)r(er)g(clo)r(c)n(k)f
(cycle.)h(114)f(of)h(them)g(are)f(used)h(to)g(encrypt)g(uplink)g
(tra\016c,)523 1795 y(while)21 b(the)h(remaining)e(bits)i(are)e(used)h
(to)g(decrypt)g(do)n(wnlink)f(tra\016c.)h(In)g(the)h(remainder)e(of)523
1895 y(this)k(pap)r(er)f(w)n(e)g(alw)n(a)n(ys)f(consider)g(only)h(a)g
(\014xed)h(half)f(of)h(this)g(k)n(eystream)d(used)j(to)f(encrypt)523
1995 y(the)28 b(tra\016c)f(in)h(one)f(direction.)523
2291 y Ft(3)112 b(Description)38 b(of)f(the)h(A)m(ttac)m(k)523
2521 y Fz(Our)32 b(general)g(approac)n(h)f(is)i(similar)g(to)g(the)g
(ciphertext-only)g(attac)n(k)f(describ)r(ed)h(in)g([2].)523
2621 y(Ho)n(w)n(ev)n(er,)27 b(no)i(precomputation)g(is)g(required)f
(and)h(the)h(ciphertext)f(frames)f(that)i(can)f(b)r(e)523
2720 y(used)j(to)h(moun)n(t)f(the)h(attac)n(k)f(do)g(not)g(need)h(to)f
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%%Page: 9 9
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1078
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(ultiplying)h(eac)n(h)g(elemen)n(t)g(of)g(one)g(v)n(ector)e(with)j(eac)
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(resulting)g(term)g(for)g(one)g(k)n(ey)g(bit)h Fp(s)2851
859 y Fo(h;k)2976 847 y Fz(is)g(linearized)523 946 y(b)n(y)h(assigning)
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523 1345 y(of)28 b(a)f(sp)r(eci\014c)h(output)g(bit.)648
1446 y(Since)33 b(the)h(domain)f(of)g(eac)n(h)f(instance)h(of)h(the)f
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(linear)g(or)g(quadratic)f(term)i(is)f(represen)n(ted)523
2343 y(b)n(y)27 b(one)h(bit\).)648 2444 y(Eac)n(h)35
b(of)i(the)g(8)g(SGs)g(accepts)f(3)h(con)n(trol)e(signals)h(from)h(the)
g(CLU)g(indicating)g(the)523 2544 y(clo)r(c)n(king)30
b(direction)h(\(forw)n(ard)f(or)h(bac)n(kw)n(ard\),)f(the)h(stop-go)f
(command)h(\(as)g(the)h(v)n(ector)523 2643 y(LFSRs)19
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(c)n(k)n(ed)e(a)g(di\013eren)n(t)i(n)n(um)n(b)r(er)e(of)h(times\),)523
2743 y(and)27 b(the)h(initialization)g(command)f(\(incremen)n(t)h(R4)f
(and)g(p)r(erform)g(w)n(arm-up\).)523 3000 y Fl(Stream)38
b(Com)m(biner)f(\(SC\).)47 b Fz(The)33 b(SC)g(com)n(bines)f(the)g
(results)g(of)h(the)g(SGs)g(with)g(the)523 3099 y(righ)n(t)26
b(ciphertext)h(bits)h(from)e(the)i(CM)f(to)g(pro)r(duce)f(the)i
(equations)e(for)g(the)i(LSE)e(Solv)n(er.)523 3199 y(More)31
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(output)f(of)g(an)f(SG)h(are)f(656)g(signals)f(repre-)523
3298 y(sen)n(ting)24 b(a)h(certain)f(stream)g(bit)h Fp(s)1580
3310 y Fo(h;k)1679 3298 y Fz(.)g(The)g(signal)f(represen)n(ting)f(the)i
(constan)n(t)f(v)-5 b(alue)24 b Fp(c)h Fz(of)523 3398
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(Eq.)f(\(9\))h(and)g(the)g(in)n(v)n(olv)n(ed)f(function)i
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(er,)f(note)i(that)h(sometimes)f(also)g(the)h(curren)n(t)e(and)i(the)
523 3797 y(previous)25 b(result)h(of)g(an)g(SG)h(are)e(required)g(at)i
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(bu\013ered)g(in)g(the)h(SC)f(\(see)g(Figure)g(6\).)g(A)g(signal)g(of)g
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(8)f(previous)g(and)g(8)h(curren)n(t)e(results)i(are)e(X)n(ORed)523
4095 y(together.)i(The)g(resulting)g(equation)g(is)g(no)n(w)g(passed)g
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(GF\(2\).)j(The)g(arc)n(hitecture)e(is)h(describ)r(ed)g(in)g([5])523
2995 y(for)e(LSEs)g(of)g(dimension)h Fp(m)12 b Fs(\002)g
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(erage)c(running)k(time)g(for)e(systems)523 3094 y(of)36
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3393 y(underdetermined)33 b(LSEs)g(\()p Fp(m)f(<)g(n)p
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b(ariable)28 b(n)n(um)n(b)r(er)h(of)g(clo)r(c)n(k)g(cycles)g(for)523
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(1965)g(of)g Fb(LNCS)p Fq(,)h(pages)f(318{327.)h(Springer-V)-5
b(erlag,)19 b(2000.)p eop end
%%Trailer
userdict /end-hook known{end-hook}if
%%EOF