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%%Title: web_version.dvi
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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 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 65 /A put
dup 66 /B put
dup 67 /C put
dup 73 /I put
dup 77 /M put
dup 80 /P put
dup 82 /R 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 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{-53 -251 1139 750}readonly def
/UniqueID 5000769 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: MSAM10
%!PS-AdobeFont-1.1: MSAM10 2.1
%%CreationDate: 1993 Sep 17 09:05:00
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSAM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSAM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 3 /square put
readonly def
/FontBBox{8 -463 1331 1003}readonly def
/UniqueID 5031981 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 15 /epsilon1 put
dup 79 /O put
dup 84 /T 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 116 /t put
dup 120 /x put
dup 121 /y put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 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 103 /g put
dup 108 /l put
dup 111 /o put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 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 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one 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 64 /at put
dup 66 /B put
dup 71 /G put
dup 73 /I put
dup 78 /N put
dup 83 /S put
dup 85 /U 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 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 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{-39 -250 1036 750}readonly def
/UniqueID 5000792 def
currentdict end
currentfile eexec
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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 3 /asteriskmath put
dup 121 /dagger put
dup 122 /daggerdbl put
readonly def
/FontBBox{-4 -948 1329 786}readonly def
/UniqueID 5000816 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 40 /parenleft put
dup 41 /parenright put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 65 /A put
dup 67 /C put
dup 68 /D put
dup 76 /L put
dup 77 /M put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 84 /T put
dup 87 /W put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueID 5000768 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 15 /epsilon1 put
dup 24 /xi put
dup 25 /pi put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 64 /partialdiff put
dup 65 /A put
dup 67 /C put
dup 69 /E 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 81 /Q 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 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 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 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 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen 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 55 /seven put
dup 65 /A 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 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 124 /emdash put
readonly def
/FontBBox{-163 -250 1146 969}readonly def
/UniqueID 5000828 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 1 /periodcentered put
dup 15 /bullet put
dup 18 /reflexsubset put
dup 19 /reflexsuperset put
dup 21 /greaterequal put
dup 26 /propersubset put
dup 50 /element put
dup 54 /negationslash put
dup 59 /emptyset put
dup 68 /D put
dup 71 /G put
dup 83 /S put
dup 85 /U put
dup 86 /V put
dup 91 /union put
dup 92 /intersection put
dup 98 /floorleft put
dup 99 /floorright put
dup 102 /braceleft put
dup 103 /braceright put
dup 106 /bar 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 14 /ffi put
dup 19 /acute put
dup 34 /quotedblright put
dup 35 /numbersign 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 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 92 /quotedblleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 124 /emdash put
dup 127 /dieresis put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 def
currentdict end
currentfile eexec
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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 3 /asteriskmath put
dup 48 /prime put
dup 121 /dagger put
dup 122 /daggerdbl put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueID 5000818 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 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 50 /two put
dup 52 /four put
dup 54 /six put
dup 66 /B put
dup 74 /J put
dup 75 /K put
dup 77 /M put
dup 83 /S put
dup 97 /a put
dup 99 /c put
dup 101 /e put
dup 104 /h put
dup 105 /i put
dup 108 /l put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 119 /w put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-34 -251 988 750}readonly def
/UniqueID 5000794 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR17
%!PS-AdobeFont-1.1: CMR17 1.0
%%CreationDate: 1991 Aug 20 16:38:24
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR17) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR17 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 45 /hyphen put
dup 65 /A put
dup 67 /C put
dup 70 /F put
dup 71 /G put
dup 79 /O 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 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 120 /x put
readonly def
/FontBBox{-33 -250 945 749}readonly def
/UniqueID 5000795 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
TeXDict begin 39158280 55380996 1000 600 600 (web_version.dvi)
@start /Fa 212[71 43[{}1 90.9091 /MSBM10 rf /Fb 133[40
48 48 66 48 51 35 36 36 1[51 45 51 76 25 1[28 25 51 45
28 40 51 40 51 45 12[66 7[57 2[33 2[59 2[66 16[45 45
2[25 30 25 2[35 35 27[51 12[{}37 90.9091 /CMSL10 rf /Fc
134[59 4[44 44 46 1[62 56 62 4[31 62 2[51 62 50 1[54
12[78 16[81 14[56 56 56 56 56 1[31 46[{}21 99.6264 /CMBX12
rf /Fd 252[71 3[{}1 90.9091 /MSAM10 rf /Fe 134[35 40
3[25 1[32 1[36 34 43 62 21 37 29 24 20[41 4[54 63[29
15[{}15 66.4176 /CMMI8 rf /Ff 144[35 2[20 4[35 50[35
35 35 35 35 4[55 1[27 27 40[{}11 66.4176 /CMR8 rf /Fg
134[41 2[41 43 30 30 30 2[38 43 64 21 41 23 21 43 38
1[34 43 34 43 38 7[58 3[58 1[43 4[58 4[28 1[60 4[54 1[60
6[38 38 38 38 38 38 38 1[38 38 1[21 26 21 44[{}40 74.7198
/CMR9 rf /Fh 133[29 29 117[32 3[{}3 49.8132 /CMSY6 rf
/Fi 137[55 58 41 41 43 1[58 52 58 87 29 55 1[29 58 52
32 48 58 46 58 51 9[108 2[73 1[78 1[71 79 1[99 63 7[80
76 1[79 6[29 52 52 52 52 52 52 52 52 52 52 1[29 35 3[41
41 27[58 12[{}46 90.9091 /CMBX10 rf /Fj 134[45 52 65
44 52 2[41 41 46 1[55 80 27 47 37 31 1[43 2[47 39 39
48 10[53 62 53 56 69 72 58 69 73 88 62 2[40 76 71 1[67
1[65 1[68 48 1[71 45 71 25 25 32[52 40 8[37 15[{}45 90.9091
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68 65 51 2[62 70 68 82 57 2[35 68 70 59 62 69 65 1[68
9[46 1[46 46 46 46 46 2[28 33 28 2[37 37 40[{}55 90.9091
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1[55 11[54 2[70 8[45 4[0 3[61 23[71 4[71 1[71 71 2[45
13[25 71{}22 90.9091 /CMSY10 rf /Fm 128[45 2[91 45 40
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51 67 1[62 71 68 83 57 71 47 33 68 71 59 62 69 66 64
68 3[71 1[25 25 45 45 45 45 45 45 45 45 45 45 45 25 30
25 71 1[35 35 25 3[76 45 14[45 4[76 51 51 53 11[{}85
90.9091 /CMR10 rf /Fn 134[71 3[75 52 53 55 2[67 75 112
37 2[37 75 67 41 61 75 60 1[65 12[94 1[100 1[92 2[128
3[50 5[97 96 102 11[67 67 67 67 67 3[45 45[{}31 119.552
/CMBX12 rf /Fo 176[63 79[{}1 83.022 /CMMI10 rf /Fp 134[44
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32 27[46 12[{}33 83.022 /CMR10 rf /Fq 139[37 38 39 14[42
53 46 31[72 65[{}7 83.022 /CMBX10 rf /Fr 133[31 31 72[19
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372.321 37.6206 m
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401.055 72.152 401.726 72.8235 401.726 73.652 c
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401.726 73.652 m
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Q
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362.519 54.5768 m
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361.847 53.0768 362.519 53.7484 362.519 54.5768 c
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362.519 54.5768 m
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h
S
Q
q
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Q
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h
f*
1076.4 99.1653 m
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@endspecial 983 676 a Fm(Figure)30 b(1:)42 b(The)29
b(o)m(v)m(erall)k(structure)d(of)h(the)f(algorithm.)141
937 y(Let)40 b Fj(T)379 904 y Fr(00)462 937 y Fm(=)g([)p
Fj(u;)15 b(v)s Fm(])41 b(b)s(e)e(a)g(subterrain)g(of)h
Fj(T)1644 904 y Fr(0)1667 937 y Fm(.)68 b(W)-8 b(e)40
b(sa)m(y)h(that)f Fj(T)2364 904 y Fr(00)2445 937 y Fk(r)-5
b(e)g(quir)g(es)42 b(a)g(lo)-5 b(c)g(al)42 b(guar)-5
b(d)41 b Fm(if)f(there)f(exists)0 1050 y(a)44 b(v)m(ertex)g
Fj(w)i Fm(in)d(the)g(in)m(terior)h(of)g Fj(T)1293 1017
y Fr(00)1378 1050 y Fm(that)g(is)f(not)h(seen)f(from)g(\()p
Fj(T)2406 1017 y Fr(0)2458 1050 y Fl(\000)29 b Fj(T)2624
1017 y Fr(00)2666 1050 y Fm(\))g Fl([)g(f)p Fj(u;)15
b(v)s Fl(g)p Fm(,)48 b(or,)f(in)c(other)g(w)m(ords,)0
1163 y Fj(u)25 b(<)g(L)p Fm(\()p Fj(w)r Fm(\))i Fj(<)e(R)q
Fm(\()p Fj(w)r Fm(\))h Fj(<)f(v)s Fm(.)141 1275 y(Let)k
Fj(T)368 1242 y Fr(0)420 1275 y Fm(b)s(e)f(one)i(of)f(the)g
(subterrains)e(obtained)j(from)e(the)h(\014rst)f(stage.)42
b(In)28 b(the)h(second)g(stage)h(w)m(e)f(partition)0
1388 y Fj(T)66 1355 y Fr(0)113 1388 y Fm(in)m(to)c(subterrains)e(suc)m
(h)h(that)g(eac)m(h)h(of)g(them)f(do)s(es)f(not)i(require)e(a)i(lo)s
(cal)g(guard.)38 b(W)-8 b(e)25 b(do)f(this)g(as)g(follo)m(ws.)40
b(F)-8 b(or)0 1501 y(eac)m(h)31 b(in)m(ternal)f(v)m(ertex)h
Fj(v)i Fm(of)d Fj(T)1060 1468 y Fr(0)1083 1501 y Fm(,)g(w)m(e)g
(compute)g(the)g(p)s(oin)m(ts)g(\(v)m(ertices\))i Fj(L)p
Fm(\()p Fj(v)s Fm(\))e(and)g Fj(R)q Fm(\()p Fj(v)s Fm(\).)41
b(Let)30 b Fj(T)13 b Fm(\()p Fj(v)s Fm(\))30 b(denote)h(the)0
1614 y(subterrain)f([)p Fj(L)p Fm(\()p Fj(v)s Fm(\))p
Fj(;)15 b(R)q Fm(\()p Fj(v)s Fm(\)].)43 b(Viewing)32
b(the)e(subterrains)g Fj(T)13 b Fm(\()p Fj(v)s Fm(\))31
b(as)g(op)s(en)f(horizon)m(tal)i(in)m(terv)-5 b(als)32
b(and)e(considering)0 1727 y(only)22 b Fk(minimal)i Fm(in)m(terv)-5
b(als)23 b(\(i.e.,)i(in)m(terv)-5 b(als)23 b(that)g(do)f(not)h(con)m
(tain)g(other)f(in)m(terv)-5 b(als\),)26 b(w)m(e)c(compute)h(a)f
(maximal)h(set)0 1840 y Fl(S)32 b Fm(of)26 b(disjoin)m(t)g
(subterrains.)38 b(Let)26 b Fl(S)1230 1807 y Fr(0)1279
1840 y Fm(b)s(e)e(the)i(complimen)m(tary)h(set)f(of)g(subterrains;)g
(th)m(us,)g(an)m(y)g(t)m(w)m(o)h(consecutiv)m(e)0 1953
y(subterrains)i(in)h Fl(S)37 b Fm(de\014ne)30 b(at)h(most)g(one)g
(subterrain)e(in)h Fl(S)2036 1920 y Fr(0)2059 1953 y
Fm(.)0 2144 y Fi(Claim)k(3.1)46 b Fk(L)-5 b(et)33 b Fj(T)708
2111 y Fr(00)783 2144 y Fk(b)-5 b(e)33 b(a)g(subterr)-5
b(ain)33 b(in)g Fl(S)27 b([)20 b(S)1740 2111 y Fr(0)1763
2144 y Fk(.)42 b(Then)33 b Fj(T)2136 2111 y Fr(00)2210
2144 y Fk(do)-5 b(es)34 b(not)f(r)-5 b(e)g(quir)g(e)34
b(a)f(lo)-5 b(c)g(al)34 b(guar)-5 b(d.)141 2335 y Fi(Pro)s(of:)82
b Fm(F)-8 b(ollo)m(ws)32 b(immediately)g(from)e(the)h(construction.)
1567 b Fd(\003)141 2582 y Fm(W)-8 b(e)25 b(place)h(guards)d(at)i(the)f
(end)g(v)m(ertices)h(of)g(the)f(subterrains)f(in)h Fl(S)7
b Fm(.)38 b(In)24 b(addition,)h(for)f(eac)m(h)i Fj(T)3370
2549 y Fr(00)3437 2582 y Fl(2)f(S)15 b([)8 b(S)3724 2549
y Fr(0)3746 2582 y Fm(,)25 b(w)m(e)0 2695 y(place)30
b(guards)e(at)h(the)g(at)h(most)f(4)g(v)m(ertices)h Fj(R)q
Fm(\()p Fj(a)1672 2710 y Fe(l)1698 2695 y Fm(\))p Fj(;)15
b(R)q Fm(\()p Fj(a)1926 2709 y Fe(r)1965 2695 y Fm(\))p
Fj(;)g(L)p Fm(\()p Fj(b)2176 2710 y Fe(l)2203 2695 y
Fm(\))p Fj(;)g(L)p Fm(\()p Fj(b)2414 2709 y Fe(r)2453
2695 y Fm(\),)30 b(where)e Fj(a)2852 2710 y Fe(l)2907
2695 y Fm(\(resp.,)h Fj(a)3232 2709 y Fe(r)3270 2695
y Fm(\))g(is)g(the)g(leftmost)0 2808 y(\(resp.,)35 b(righ)m(tmost\))g
(in)m(ternal)f(v)m(ertex)h(of)f Fj(T)1525 2775 y Fr(00)1600
2808 y Fm(that)h(is)e(seen)h(from)f(the)h(righ)m(t)g(of)g
Fj(T)2870 2775 y Fr(00)2912 2808 y Fm(,)h(and)e Fj(b)3191
2823 y Fe(l)3251 2808 y Fm(\(resp.,)h Fj(b)3572 2822
y Fe(r)3610 2808 y Fm(\))g(is)g(the)0 2921 y(leftmost)39
b(\(resp.,)h(righ)m(tmost\))f(in)m(ternal)f(v)m(ertex)h(of)f
Fj(T)1905 2888 y Fr(00)1985 2921 y Fm(that)h(is)e(seen)h(from)g(the)g
(left)g(of)g Fj(T)3223 2888 y Fr(00)3265 2921 y Fm(.)63
b(Since)38 b Fl(jS)7 b(j)p Fj(=)p Fm(2)39 b(is)0 3034
y(clearly)c(a)f(lo)m(w)m(er)g(b)s(ound)e(on)h(the)h(n)m(um)m(b)s(er)e
(of)h(guards)g(needed)g(to)h(guard)f Fj(T)2670 3001 y
Fr(0)2693 3034 y Fm(,)i(w)m(e)f(only)f(increase)i(the)e(n)m(um)m(b)s
(er)0 3147 y(of)e(v)m(ertices)h(b)m(y)e(a)h(constan)m(t)g(factor.)141
3260 y(W)-8 b(e)23 b(no)m(w)f(\\solv)m(e")i(eac)m(h)f(of)f(the)g
(subterrains)f(in)g Fl(S)10 b([)s(S)1965 3227 y Fr(0)2009
3260 y Fk(sep)-5 b(ar)g(ately)p Fm(.)41 b(Eac)m(h)22
b(suc)m(h)g(subterrain)f(is)h(considered)f(to)0 3373
y(b)s(e)j(a)h Fk(b)-5 b(ase)28 b(c)-5 b(ase)p Fm(,)27
b(in)d(that)i(it)f(do)s(es)g(not)g(require)f(a)h(lo)s(cal)h(guard,)g
(and)e(is)h(solv)m(ed)g(using)g(the)g(base-case)h(algorithms)0
3486 y(detailed)35 b(in)e(Section)h(4.)51 b(The)33 b
Fk(indep)-5 b(endenc)g(e)36 b(pr)-5 b(op)g(erty)37 b
Fm(\(based)c(on)h(Claims)f(3.2-3.3\))k(sho)m(wn)c(b)s(elo)m(w)g
(justi\014es)0 3599 y(this)k(approac)m(h,)j(i.e.,)h(that)d(the)g
(subterrains)e(in)h Fl(S)32 b([)25 b(S)1985 3566 y Fr(0)2045
3599 y Fm(ma)m(y)38 b(b)s(e)f(solv)m(ed)h(separately)h(without)f(h)m
(urting)f(the)0 3711 y(appro)m(ximation)31 b(b)s(ound.)141
3824 y(The)f(o)m(v)m(erall)j(structure)d(of)g(the)h(algorithm)g(is)f
(th)m(us)g(as)h(follo)m(ws.)136 3994 y Fl(\017)46 b Fm(Giv)m(en)29
b(a)f(terrain)g Fj(T)41 b Fm(compute)28 b(its)g(\(upp)s(er\))e(con)m(v)
m(ex)k(h)m(ull,)e(place)h(guards)e(at)i(the)f(v)m(ertices)h(of)f(the)g
(con)m(v)m(ex)227 4107 y(h)m(ull,)j(and)f(solv)m(e)h(eac)m(h)h
(subterrain)d Fj(T)1537 4074 y Fr(0)1591 4107 y Fm(separately)-8
b(.)136 4288 y Fl(\017)46 b Fm(Giv)m(en)26 b(a)e(subterrain)g
Fj(T)1050 4255 y Fr(0)1097 4288 y Fm(partition)h(it)g(in)m(to)g
(subterrains)e Fl(S)15 b([)8 b(S)2399 4255 y Fr(0)2422
4288 y Fm(,)26 b(as)f(describ)s(ed)e(ab)s(o)m(v)m(e.)40
b(F)-8 b(or)25 b(eac)m(h)g(subter-)227 4401 y(rain)20
b Fj(T)470 4368 y Fr(00)538 4401 y Fl(2)25 b(S)7 b([S)809
4368 y Fr(0)831 4401 y Fm(,)23 b(place)e(guards)f(at)h(the)f(end)g(v)m
(ertices)i(of)e Fj(T)2272 4368 y Fr(00)2334 4401 y Fm(and)g(at)h(the)g
(v)m(ertices)g Fj(R)q Fm(\()p Fj(a)3220 4416 y Fe(l)3247
4401 y Fm(\))p Fj(;)15 b(R)q Fm(\()p Fj(a)3475 4415 y
Fe(r)3513 4401 y Fm(\))p Fj(;)g(L)p Fm(\()p Fj(b)3724
4416 y Fe(l)3751 4401 y Fm(\))p Fj(;)g(L)p Fm(\()p Fj(b)3962
4415 y Fe(r)4001 4401 y Fm(\),)227 4513 y(and)23 b(solv)m(e)i(the)f
(remaining)g(unguarded)e(fragmen)m(ts)i(of)g Fj(T)2200
4480 y Fr(00)2266 4513 y Fm(separately)-8 b(,)27 b(using)c(the)h
(base-case)h(algorithms)227 4626 y(detailed)32 b(in)e(Section)h(4.)0
4866 y Fc(The)38 b(indep)s(endence)h(prop)s(ert)m(y)0
5038 y Fm(Let)34 b Fj(T)47 b Fm(b)s(e)33 b(a)h(terrain,)i(and)d(let)i
Fj(T)1169 5052 y Ff(1)1208 5038 y Fj(;)15 b(:)g(:)g(:)i(;)e(T)1463
5053 y Fe(k)1540 5038 y Fm(b)s(e)33 b Fj(k)k Fm(disjoin)m(t)d
(subterrains)f(of)h Fj(T)13 b Fm(.)51 b(\(Tw)m(o)35 b(subterrains)d(ma)
m(y)j(ha)m(v)m(e)0 5151 y(a)c(common)g(end)f(v)m(ertex.\))42
b(Assume)30 b(that)h(the)g(size)h Fj(l)g Fm(of)f(an)f(optimal)i
(solution)f(for)f Fj(T)2981 5165 y Ff(1)3041 5151 y Fl([)20
b(\001)15 b(\001)g(\001)21 b([)f Fj(T)3382 5166 y Fe(k)3455
5151 y Fm(\(b)m(y)31 b(placing)1927 5400 y(4)p eop end
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cleartomark
%%EndResource
/F5_0 /ISDIZV+CMMI12 1 1
[ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font VFIHJN+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 /VFIHJN+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 40 /parenleft put
dup 41 /parenright put
readonly def
/FontBBox{-34 -251 988 750}readonly def
/UniqueID 5000794 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F8_0 /VFIHJN+CMR12 1 1
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font BKTNZK+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 /BKTNZK+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 49 /one put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F11_0 /BKTNZK+CMR8 1 1
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font TTDGGW+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 /TTDGGW+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 3 /asteriskmath put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueID 5000818 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F14_0 /TTDGGW+CMSY8 1 1
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@endspecial 0 2199 a(Figure)44 b(3:)68 b(W)-8 b(e)44
b(can)g(reduce)f(the)h(problem)f Fj(A)h Fm(to)g(the)g(Case)g(1a)g
(problem)f Fj(A)2831 2213 y Ff(1)2918 2199 y Fm(=)k([)p
Fj(a)3109 2213 y Ff(1)3149 2199 y Fj(;)15 b(b)3228 2213
y Ff(1)3268 2199 y Fm(])47 b(=)g([)p Fj(c;)15 b(d)p Fm(],)49
b(since)0 2312 y Fj(A)68 2279 y Fr(0)112 2312 y Fl(\000)20
b Fj(A)271 2279 y Fr(\003)335 2312 y Fl(\022)25 b Fj(V)c
Fm(\()p Fj(A)608 2279 y Fr(0)631 2312 y Fj(;)15 b(L)p
Fm(\()p Fj(d)p Fm(\)\))22 b Fl([)e Fj(V)g Fm(\()p Fj(A)1164
2279 y Fr(0)1188 2312 y Fj(;)15 b(d)p Fm(\).)141 2525
y(W)-8 b(e)34 b(no)m(w)e(consider)g(the)g(case)i(where)d
Fj(V)20 b Fm(\()p Fj(A)1640 2492 y Fr(0)1664 2525 y Fj(;)15
b(L)p Fm(\()p Fj(d)p Fm(\)\))23 b Fl([)e Fj(V)g Fm(\()p
Fj(A)2200 2492 y Fr(0)2223 2525 y Fj(;)15 b(d)p Fm(\))30
b Fl(\023)e Fj(A)2542 2492 y Fr(0)2587 2525 y Fl(\000)21
b Fj(A)2747 2492 y Fr(\003)2819 2525 y Fm(\(see)33 b(Figure)f(3\).)47
b(In)32 b(this)g(case)0 2637 y(w)m(e)42 b(sa)m(y)f(that)h
Fj(A)g Fm(is)f Fk(r)-5 b(e)g(ducible)p Fm(,)44 b(and)d(reduce)g
Fj(A)1698 2651 y Ff(0)1781 2637 y Fm(=)i Fj(A)e Fm(to)h(the)f(Case)h
(1a)g(problem)e Fj(A)3086 2651 y Ff(1)3169 2637 y Fm(=)j([)p
Fj(a)3356 2651 y Ff(1)3396 2637 y Fj(;)15 b(b)3475 2651
y Ff(1)3515 2637 y Fm(])43 b(=)g([)p Fj(c;)15 b(d)p Fm(].)0
2750 y(No)m(w,)38 b(if)e Fj(A)396 2764 y Ff(1)471 2750
y Fm(is)g(also)h(reducible,)g(that)f(is,)i(if)d Fj(A)1659
2764 y Ff(1)1735 2750 y Fm(is)h(a)g(single-p)s(o)s(c)m(k)m(et)i(case)e
(with)g(p)s(o)s(c)m(k)m(et)h Fj(A)3236 2717 y Fr(\003)3236
2775 y Ff(1)3310 2750 y Fm(=)d(\()p Fj(c)3489 2764 y
Ff(1)3529 2750 y Fj(;)15 b(d)3616 2764 y Ff(1)3656 2750
y Fm(\),)38 b(and)0 2863 y Fj(V)20 b Fm(\()p Fj(A)176
2830 y Fr(0)200 2863 y Fj(;)15 b(L)p Fm(\()p Fj(d)384
2877 y Ff(1)424 2863 y Fm(\)\))21 b Fl([)f Fj(V)g Fm(\()p
Fj(A)772 2830 y Fr(0)796 2863 y Fj(;)15 b(d)883 2877
y Ff(1)923 2863 y Fm(\))26 b Fl(\023)f Fj(A)1148 2830
y Fr(0)1191 2863 y Fl(\000)20 b Fj(A)1350 2830 y Fr(\003)1350
2888 y Ff(1)1389 2863 y Fm(,)31 b(where)f Fj(A)1776 2830
y Fr(0)1829 2863 y Fm(is)h(the)f Fk(original)h Fj(A)2478
2830 y Fr(0)2502 2863 y Fm(,)f(then)g(w)m(e)h(reduce)f
Fj(A)3254 2877 y Ff(1)3324 2863 y Fm(to)h(the)g(Case)f(1a)0
2976 y(problem)24 b Fj(A)416 2990 y Ff(2)481 2976 y Fm(=)h([)p
Fj(a)650 2990 y Ff(2)690 2976 y Fj(;)15 b(b)769 2990
y Ff(2)809 2976 y Fm(])25 b(=)g([)p Fj(c)1019 2990 y
Ff(1)1059 2976 y Fj(;)15 b(d)1146 2990 y Ff(1)1186 2976
y Fm(].)39 b(This)25 b(pro)s(cess)f(con)m(tin)m(ues)i(un)m(til)f(w)m(e)
g(reac)m(h)h(a)f(problem)g Fj(A)3242 2990 y Fe(i)3295
2976 y Fm(=)g([)p Fj(a)3464 2990 y Fe(i)3493 2976 y Fj(;)15
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cc aload pop setrgbcolor
cm setmatrix
end
} bind def
/PATDict 3 dict def
/PATsp {
true PATredef
PATDict begin
/CurrentPattern exch def
% If it's an uncolored pattern, save the color
CurrentPattern /PaintType get 2 eq {
/PColor exch def
} if
/CColor [ currentrgbcolor ] def
end
} bind def
% PATstroke - stroke with the current pattern
/PATstroke {
countdictstack
save
mark
{
currentpoint strokepath moveto
PATpcalc % proc nw nh px py
clip newpath PATfill
} stopped {
(*** PATstroke Warning: Path is too complex, stroking
with gray) =
cleartomark
restore
countdictstack exch sub dup 0 gt
{ { end } repeat } { pop } ifelse
gsave 0.5 setgray oldstroke grestore
} { pop restore pop } ifelse
newpath
} bind def
/PATtcalc { % modmtx tilingtype PATtcalc tilematrix
% Note: tiling types 2 and 3 are not supported
gsave
exch concat % tilingtype
matrix currentmatrix exch % cmtx tilingtype
% Tiling type 1 and 3: constant spacing
2 ne {
% Distort the pattern so that it occupies
% an integral number of device pixels
dup 4 get exch dup 5 get exch % tx ty cmtx
XStep 0 dtransform
round exch round exch % tx ty cmtx dx.x dx.y
XStep div exch XStep div exch % tx ty cmtx a b
0 YStep dtransform
round exch round exch % tx ty cmtx a b dy.x dy.y
YStep div exch YStep div exch % tx ty cmtx a b c d
7 -3 roll astore % { a b c d tx ty }
} if
grestore
} bind def
/PATusp {
false PATredef
PATDict begin
CColor PATsc
end
} bind def
% this is the pattern fill program from the Second edition Reference Manual
% with changes to call the above pattern fill
% left30
11 dict begin
/PaintType 1 def
/PatternType 1 def
/TilingType 1 def
/BBox [0 0 1 1] def
/XStep 1 def
/YStep 1 def
/PatWidth 1 def
/PatHeight 1 def
/Multi 2 def
/PaintData [
{ clippath } bind
{ 32 16 true [ 32 0 0 -16 0 16 ]
{}
imagemask } bind
] def
/PaintProc {
pop
exec fill
} def
currentdict
end
/P1 exch def
/cp {closepath} bind def
/ef {eofill} bind def
/gr {grestore} bind def
/gs {gsave} bind def
/sa {save} bind def
/rs {restore} bind def
/l {lineto} bind def
/m {moveto} bind def
/rm {rmoveto} bind def
/n {newpath} bind def
/s {stroke} bind def
/sh {show} bind def
/slc {setlinecap} bind def
/slj {setlinejoin} bind def
/slw {setlinewidth} bind def
/srgb {setrgbcolor} bind def
/rot {rotate} bind def
/sc {scale} bind def
/sd {setdash} bind def
/ff {findfont} bind def
/sf {setfont} bind def
/scf {scalefont} bind def
/sw {stringwidth} bind def
/tr {translate} bind def
/tnt {dup dup currentrgbcolor
4 -2 roll dup 1 exch sub 3 -1 roll mul add
4 -2 roll dup 1 exch sub 3 -1 roll mul add
4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb}
bind def
/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul
4 -2 roll mul srgb} bind def
/DrawEllipse {
/endangle exch def
/startangle exch def
/yrad exch def
/xrad exch def
/y exch def
/x exch def
/savematrix mtrx currentmatrix def
x y tr xrad yrad sc 0 0 1 startangle endangle arc
closepath
savematrix setmatrix
} def
/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def
/$F2psEnd {$F2psEnteredState restore end} def
$F2psBegin
10 setmiterlimit
0 slj 0 slc
0.06000 0.06000 sc
%
% Fig objects follow
%
%
% here starts figure with depth 100
/Times-Roman ff 300.00 scf sf
9600 11025 m
gs 1 -1 sc (b) col0 sh gr
% Ellipse
7.500 slw
n 1612 10500 84 84 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def
15.00 15.00 sc P1 [16 0 0 -8 101.87 694.40] PATmp PATsp ef gr PATusp gs col0 s gr
% Ellipse
n 6487 11400 84 84 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def
15.00 15.00 sc P1 [16 0 0 -8 426.87 754.40] PATmp PATsp ef gr PATusp gs col0 s gr
% Ellipse
n 3450 11250 84 84 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def
15.00 15.00 sc P1 [16 0 0 -8 224.40 744.40] PATmp PATsp ef gr PATusp gs col0 s gr
% Ellipse
n 9600 11175 84 84 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def
15.00 15.00 sc P1 [16 0 0 -8 634.40 739.40] PATmp PATsp ef gr PATusp gs col0 s gr
% Polyline
[60] 0 sd
n 1650 10500 m 6525 11400 l
11400 10500 l gs col0 s gr [] 0 sd
% Polyline
2 slj
n 3525 10200 m 3525 10199 l 3526 10196 l 3528 10191 l 3530 10183 l 3535 10173 l
3540 10160 l 3547 10145 l 3556 10128 l 3567 10110 l 3579 10091 l
3593 10072 l 3609 10054 l 3626 10036 l 3646 10020 l 3666 10005 l
3689 9991 l 3714 9979 l 3741 9968 l 3770 9958 l 3802 9950 l
3837 9943 l 3875 9937 l 3917 9932 l 3963 9928 l 4013 9925 l
4044 9924 l 4076 9922 l 4110 9921 l 4145 9921 l 4182 9920 l
4220 9920 l 4260 9920 l 4301 9920 l 4344 9920 l 4387 9920 l
4432 9921 l 4479 9922 l 4526 9922 l 4575 9923 l 4624 9924 l
4675 9924 l 4726 9925 l 4778 9926 l 4831 9927 l 4884 9928 l
4937 9928 l 4991 9929 l 5045 9929 l 5098 9930 l 5151 9930 l
5204 9930 l 5257 9930 l 5308 9930 l 5359 9929 l 5410 9928 l
5459 9927 l 5507 9926 l 5554 9925 l 5600 9923 l 5645 9921 l
5688 9919 l 5731 9916 l 5771 9913 l 5811 9910 l 5849 9906 l
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6089 9866 l 6135 9854 l 6179 9841 l 6220 9826 l 6258 9811 l
6294 9794 l 6328 9777 l 6359 9760 l 6388 9742 l 6414 9723 l
6439 9705 l 6461 9687 l 6481 9670 l 6499 9653 l 6515 9636 l
6529 9621 l 6541 9607 l 6552 9594 l 6561 9583 l 6569 9573 l
6577 9565 l 6583 9559 l 6589 9554 l 6595 9551 l 6600 9550 l
6605 9551 l 6611 9554 l 6617 9559 l 6623 9565 l 6630 9573 l
6639 9583 l 6648 9595 l 6659 9607 l 6671 9622 l 6685 9637 l
6700 9654 l 6718 9671 l 6737 9689 l 6759 9707 l 6783 9726 l
6809 9745 l 6837 9763 l 6868 9782 l 6901 9800 l 6936 9817 l
6973 9833 l 7013 9849 l 7056 9863 l 7101 9877 l 7149 9889 l
7200 9900 l 7233 9906 l 7268 9912 l 7305 9918 l 7342 9923 l
7381 9928 l 7422 9932 l 7464 9936 l 7508 9940 l 7553 9943 l
7599 9947 l 7646 9949 l 7695 9952 l 7745 9954 l 7796 9957 l
7848 9959 l 7901 9960 l 7954 9962 l 8008 9963 l 8062 9964 l
8117 9965 l 8172 9966 l 8226 9967 l 8281 9968 l 8335 9968 l
8388 9969 l 8441 9970 l 8494 9970 l 8545 9971 l 8595 9971 l
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9060 9983 l 9093 9985 l 9125 9988 l 9173 9992 l 9218 9997 l
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9416 10049 l 9440 10062 l 9462 10076 l 9483 10092 l 9501 10109 l
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9578 10219 l 9585 10235 l 9591 10248 l 9595 10258 l 9597 10266 l
9599 10271 l 9600 10274 l
9600 10275 l gs col0 s gr
% Polyline
n 3450 10800 m 3450 10798 l 3451 10795 l 3453 10789 l 3456 10780 l 3460 10769 l
3466 10756 l 3473 10742 l 3481 10727 l 3491 10713 l 3502 10699 l
3515 10687 l 3529 10676 l 3544 10667 l 3562 10659 l 3582 10652 l
3604 10647 l 3629 10643 l 3656 10640 l 3688 10638 l 3710 10637 l
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3876 10637 l 3909 10637 l 3942 10638 l 3978 10639 l 4014 10640 l
4050 10641 l 4088 10642 l 4126 10642 l 4164 10643 l 4203 10644 l
4241 10644 l 4278 10644 l 4316 10643 l 4352 10643 l 4388 10642 l
4422 10640 l 4455 10639 l 4487 10636 l 4518 10634 l 4547 10631 l
4575 10627 l 4601 10623 l 4626 10618 l 4650 10613 l 4686 10602 l
4720 10590 l 4750 10576 l 4778 10561 l 4803 10544 l 4826 10526 l
4847 10508 l 4865 10489 l 4881 10471 l 4895 10453 l 4907 10437 l
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5413 10657 l 5445 10661 l 5478 10665 l 5512 10668 l 5548 10671 l
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5774 10684 l 5812 10686 l 5850 10687 l 5886 10689 l 5922 10690 l
5958 10692 l 5991 10694 l 6024 10695 l 6055 10697 l 6085 10699 l
6114 10701 l 6141 10704 l 6166 10706 l 6190 10709 l 6213 10713 l
6241 10718 l 6267 10723 l 6290 10730 l 6311 10738 l 6329 10747 l
6346 10757 l 6361 10769 l 6375 10782 l 6388 10797 l 6399 10813 l
6409 10830 l 6418 10848 l 6426 10866 l 6433 10884 l 6438 10901 l
6442 10916 l 6446 10929 l 6448 10938 l 6449 10945 l 6450 10948 l
6450 10950 l gs col0 s gr
% Polyline
n 6450 10950 m 6450 10948 l 6451 10945 l 6453 10938 l 6455 10929 l 6459 10916 l
6464 10901 l 6470 10884 l 6478 10866 l 6487 10848 l 6497 10830 l
6509 10813 l 6522 10797 l 6537 10782 l 6553 10769 l 6570 10757 l
6590 10747 l 6611 10738 l 6636 10730 l 6662 10723 l 6692 10718 l
6725 10713 l 6749 10709 l 6775 10707 l 6803 10704 l 6831 10702 l
6862 10700 l 6894 10698 l 6927 10696 l 6962 10694 l 6998 10693 l
7035 10691 l 7074 10690 l 7113 10688 l 7153 10687 l 7194 10686 l
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7441 10674 l 7481 10672 l 7520 10669 l 7557 10666 l 7594 10663 l
7629 10660 l 7663 10656 l 7696 10652 l 7727 10647 l 7757 10642 l
7785 10637 l 7812 10631 l 7838 10625 l 7875 10614 l 7910 10602 l
7942 10588 l 7972 10574 l 7999 10558 l 8024 10542 l 8047 10525 l
8067 10507 l 8085 10490 l 8101 10473 l 8115 10456 l 8127 10441 l
8137 10426 l 8146 10413 l 8153 10402 l 8159 10393 l 8164 10385 l
8168 10380 l 8172 10376 l 8175 10375 l 8179 10376 l 8183 10381 l
8188 10387 l 8193 10396 l 8200 10408 l 8208 10421 l 8217 10437 l
8229 10453 l 8242 10471 l 8257 10489 l 8275 10508 l 8295 10526 l
8316 10544 l 8341 10561 l 8367 10576 l 8396 10590 l 8428 10602 l
8463 10613 l 8485 10618 l 8509 10623 l 8534 10627 l 8560 10631 l
8588 10634 l 8617 10636 l 8647 10639 l 8679 10640 l 8712 10642 l
8745 10643 l 8780 10643 l 8815 10644 l 8851 10644 l 8887 10644 l
8923 10643 l 8960 10642 l 8996 10642 l 9031 10641 l 9066 10640 l
9100 10639 l 9133 10638 l 9166 10637 l 9196 10637 l 9226 10636 l
9254 10636 l 9281 10636 l 9307 10636 l 9331 10636 l 9354 10637 l
9375 10638 l 9404 10640 l 9431 10643 l 9454 10647 l 9475 10652 l
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9561 10713 l 9571 10727 l 9579 10742 l 9585 10756 l 9590 10769 l
9594 10780 l 9597 10789 l 9599 10795 l 9600 10798 l
9600 10800 l gs col0 s gr
/Times-Roman ff 300.00 scf sf
1275 10350 m
gs 1 -1 sc (L\(m\)) col0 sh gr
/Times-Roman ff 300.00 scf sf
6375 11250 m
gs 1 -1 sc (m) col0 sh gr
/Times-Roman ff 300.00 scf sf
11250 10350 m
gs 1 -1 sc (R\(m\)) col0 sh gr
/Times-Roman ff 300.00 scf sf
3375 11100 m
gs 1 -1 sc (a) col0 sh gr
/Times-Roman ff 300.00 scf sf
6525 9450 m
gs 1 -1 sc (A) col0 sh gr
/Times-Roman ff 300.00 scf sf
4875 10275 m
gs 1 -1 sc (A) col0 sh gr
/Times-Roman ff 300.00 scf sf
8100 10275 m
gs 1 -1 sc (A) col0 sh gr
/Times-Roman ff 225.00 scf sf
5175 10350 m
gs 1 -1 sc (l) col0 sh gr
/Times-Roman ff 225.00 scf sf
8400 10350 m
gs 1 -1 sc (r) col0 sh gr
% Ellipse
n 11437 10500 84 84 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def
15.00 15.00 sc P1 [16 0 0 -8 756.87 694.40] PATmp PATsp ef gr PATusp gs col0 s gr
% here ends figure;
$F2psEnd
rs
end
showpage
%%EndDocument
@endspecial 0 796 a Fm(Figure)38 b(4:)54 b(The)36 b(t)m(w)m(o)j
(subterrains)d(de\014ned)g(b)m(y)g(a)i(shared)e(v)m(ertex)i(that)g
(implies)f(a)h(non-trivial)g(division)f(are)0 909 y(guard)30
b(indep)s(enden)m(t.)141 1184 y Fi(Pro)s(of:)103 b Fm(An)m(y)36
b(guard)f(that)i(can)f(see)g(a)g(v)m(ertex)h(in)f Fj(A)2058
1151 y Fr(0)2058 1212 y Fe(l)2084 1184 y Fm(\()p Fj(m)p
Fm(\))g(m)m(ust)g(lie)g(either)g(b)s(et)m(w)m(een)h Fj(L)p
Fm(\()p Fj(m)p Fm(\))f(and)f Fj(m)p Fm(,)i(or)0 1297
y(to)31 b(the)g(righ)m(t)h(of)e Fj(R)q Fm(\()p Fj(m)p
Fm(\),)i(while)e(an)m(y)h(guard)g(that)g(can)g(see)g(a)g(v)m(ertex)h
(in)e Fj(A)2574 1264 y Fr(0)2574 1319 y Fe(r)2613 1297
y Fm(\()p Fj(m)p Fm(\))h(m)m(ust)f(lie)i(either)f(to)g(the)g(left)h(of)
0 1410 y Fj(L)p Fm(\()p Fj(m)p Fm(\),)f(or)f(b)s(et)m(w)m(een)h
Fj(m)f Fm(and)g Fj(R)q Fm(\()p Fj(m)p Fm(\).)41 b(See)31
b(Figure)g(4.)1977 b Fd(\003)0 1760 y Fi(Claim)34 b(4.13)47
b Fk(Ther)-5 b(e)33 b(is)g(at)g(le)-5 b(ast)34 b(one)e(shar)-5
b(e)g(d)35 b(vertex)e(in)g Fj(A)25 b Fm(=)g([)p Fj(a;)15
b(b)p Fm(])p Fk(.)141 1973 y Fi(Pro)s(of:)91 b Fj(a)33
b Fm(is)g(surely)f(seen)h(from)f(the)h(left)g(of)g Fj(A)g
Fm(\(e.g.,)i(b)m(y)e(the)g(v)m(ertex)h(immediately)g(to)f(its)g
(left\),)i(and)d Fj(b)0 2086 y Fm(is)f(surely)g(seen)g(from)g(the)h
(righ)m(t)g(of)f Fj(A)p Fm(.)44 b(Let)31 b Fj(c)h Fm(b)s(e)f(the)g
(righ)m(tmost)h(v)m(ertex)h(in)e Fj(A)g Fm(that)h(is)f(seen)h(from)e
(the)i(left)g(of)0 2198 y Fj(A)p Fm(.)48 b(\(If)33 b
Fj(c)d Fm(=)f Fj(b)p Fm(,)k(then)g(let)h Fj(c)f Fm(b)s(e)f(the)h
(previous)f(v)m(ertex)i(in)f Fj(A)g Fm(that)g(is)g(seen)g(from)f(the)h
(left)h(of)f Fj(A)p Fm(.\))48 b(Let)33 b Fj(d)h Fm(b)s(e)e(the)0
2311 y(v)m(ertex)j(immediately)g(to)f(the)g(righ)m(t)h(of)f
Fj(c)p Fm(.)51 b(Then)33 b Fj(d)h Fm(is)f(necessarily)i(seen)f(from)f
(the)h(righ)m(t)g(of)g Fj(A)p Fm(.)51 b(W)-8 b(e)35 b(observ)m(e)0
2424 y(that)d(either)f Fj(L)p Fm(\()p Fj(c)p Fm(\))h(or)f
Fj(R)q Fm(\()p Fj(d)p Fm(\))g(m)m(ust)g(lie)h(ab)s(o)m(v)m(e)g(the)g
(line)f(through)f Fj(c)h Fm(and)g Fj(d)p Fm(.)43 b(\(Otherwise,)31
b Fj(c)g Fm(and)g Fj(d)g Fm(are)g(v)m(ertices)0 2537
y(of)36 b(the)g(con)m(v)m(ex)h(h)m(ull)e(of)h(the)g(original)h(terrain)
e(|)h(imp)s(ossible,)h(see)f(assumptions)f(and)g(observ)-5
b(ation)36 b(ab)s(o)m(v)m(e.\))0 2650 y(Therefore)31
b(either)g Fj(c)g Fm(or)g Fj(d)g Fm(is)f(a)i(shared)e(v)m(ertex.)43
b(E.g.,)32 b(if)e Fj(L)p Fm(\()p Fj(c)p Fm(\))i(lies)f(ab)s(o)m(v)m(e)h
(the)f(line)g(through)g Fj(c)g Fm(and)f Fj(d)h Fm(it)g(m)m(ust)0
2763 y(also)g(see)g Fj(d)p Fm(,)g(so)g Fj(d)f Fm(is)h(a)g(shared)e(v)m
(ertex)j(in)e(this)g(case.)1977 b Fd(\003)141 3014 y
Fm(Let)35 b Fj(M)44 b Fm(b)s(e)34 b(the)g(set)h(of)f(all)h(shared)f(v)m
(ertices)i(in)d Fj(A)p Fm(.)53 b(According)35 b(to)g(the)f(claim)h(ab)s
(o)m(v)m(e)h Fj(M)41 b Fl(6)p Fm(=)32 b Fl(;)p Fm(.)52
b(W)-8 b(e)36 b(next)0 3127 y(sho)m(w)e(that)i(an)m(y)f(subterrain)e
(of)i Fj(A)g Fm(without)f(shared)g(v)m(ertices)i(\(i.e.,)i(v)m(ertices)
e(of)f Fj(M)10 b Fm(\))34 b(can)h(b)s(e)f(nicely)i(divided)0
3240 y(in)m(to)31 b(t)m(w)m(o)h(subterrains.)0 3452 y
Fi(Claim)i(4.14)47 b Fk(L)-5 b(et)32 b Fj(A)762 3419
y Fr(\003)827 3452 y Fm(=)24 b([)p Fj(l)r(;)15 b(r)s
Fm(])26 b Fl(\032)f Fj(A)32 b Fk(b)-5 b(e)31 b(a)h(subterr)-5
b(ain)33 b(such)f(that)h Fj(A)2383 3419 y Fr(\003)2441
3452 y Fl(\\)17 b Fj(M)36 b Fm(=)25 b Fl(;)p Fk(.)42
b(L)-5 b(et)32 b Fj(u)f Fk(b)-5 b(e)32 b(a)g(vertex)g(in)f
Fj(A)3728 3419 y Fr(\003)3768 3452 y Fk(.)41 b(If)0 3565
y Fj(u)33 b Fk(c)-5 b(an)34 b(b)-5 b(e)33 b(se)-5 b(en)34
b(fr)-5 b(om)34 b(the)g(left)f(of)h Fj(A)p Fk(,)f(then)h(any)g(vertex)g
(in)f Fj(A)2154 3532 y Fr(\003)2227 3565 y Fk(to)g(the)h(right)g(of)g
Fj(u)f Fk(c)-5 b(an)34 b(also)g(b)-5 b(e)33 b(se)-5 b(en)34
b(fr)-5 b(om)35 b(the)0 3678 y(left)e(of)g Fj(A)f Fk(\(and)i(ther)-5
b(efor)g(e)34 b(c)-5 b(annot)34 b(b)-5 b(e)33 b(se)-5
b(en)33 b(fr)-5 b(om)34 b(the)f(right)g(of)g Fj(A)p Fk(\).)141
3890 y Fi(Pro)s(of:)88 b Fm(Since)32 b Fj(A)h Fm(do)s(es)e(not)i
(require)e(a)i(lo)s(cal)g(guard,)f(an)m(y)g(v)m(ertex)i(in)d
Fj(A)2733 3857 y Fr(\003)2805 3890 y Fm(can)h(b)s(e)g(seen)g(either)g
(from)g(the)0 4003 y(left)e(of)g Fj(A)g Fm(or)f(from)h(the)f(righ)m(t)i
(of)e Fj(A)p Fm(,)h(but)f(since)h Fj(A)1740 3970 y Fr(\003)1799
4003 y Fl(\\)18 b Fj(M)35 b Fm(=)25 b Fl(;)p Fm(,)31
b(it)f(can)g(b)s(e)f(seen)g(from)g(only)h(one)g(of)g(these)g(sides.)0
4116 y(Assume)i(there)h(is)g(a)g(v)m(ertex)h(to)g(the)f(righ)m(t)g(of)g
Fj(u)g Fm(that)g(is)g(seen)g(from)f(the)h(righ)m(t)g(of)g
Fj(A)p Fm(.)48 b(Let)34 b Fj(v)i Fm(b)s(e)c(the)h(leftmost)0
4229 y(suc)m(h)i(v)m(ertex,)i(and)d(let)i Fj(u)885 4196
y Fr(0)943 4229 y Fm(b)s(e)f(the)g(v)m(ertex)h(immediately)g(to)g(the)f
(left)h(of)f Fj(v)s Fm(.)54 b(Then)34 b Fj(u)3004 4196
y Fr(0)3063 4229 y Fm(\(whic)m(h)h(is)g(p)s(ossibly)f
Fj(u)p Fm(\))0 4342 y(is)i(seen)g(from)g(the)g(left)h(of)f
Fj(A)p Fm(.)58 b(Observ)m(e)36 b(that)h(either)g Fj(L)p
Fm(\()p Fj(u)2079 4309 y Fr(0)2102 4342 y Fm(\))f(or)h
Fj(R)q Fm(\()p Fj(v)s Fm(\))f(m)m(ust)g(lie)h(ab)s(o)m(v)m(e)h(the)e
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/J { setlinecap } def
/M { setmiterlimit } def
/w { setlinewidth } def
% color operators
/g { dup 1 array astore /pdfFill exch def setgray
/pdfLastFill true def /pdfLastStroke false def } def
/G { dup 1 array astore /pdfStroke exch def setgray
/pdfLastStroke true def /pdfLastFill false def } def
/rg { 3 copy 3 array astore /pdfFill exch def setrgbcolor
/pdfLastFill true def /pdfLastStroke false def } def
/RG { 3 copy 3 array astore /pdfStroke exch def setrgbcolor
/pdfLastStroke true def /pdfLastFill false def } def
/k { 4 copy 4 array astore /pdfFill exch def setcmykcolor
/pdfLastFill true def /pdfLastStroke false def } def
/K { 4 copy 4 array astore /pdfStroke exch def setcmykcolor
/pdfLastStroke true def /pdfLastFill false def } def
/ck { 6 copy 6 array astore /pdfFill exch def
findcmykcustomcolor exch setcustomcolor
/pdfLastFill true def /pdfLastStroke false def } def
/CK { 6 copy 6 array astore /pdfStroke exch def
findcmykcustomcolor exch setcustomcolor
/pdfLastStroke true def /pdfLastFill false def } def
% path segment operators
/m { moveto } def
/l { lineto } def
/c { curveto } def
/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
neg 0 rlineto closepath } def
/h { closepath } def
% path painting operators
/S { sCol stroke } def
/Sf { fCol stroke } def
/f { fCol fill } def
/f* { fCol eofill } def
% clipping operators
/W { clip newpath } def
/W* { eoclip newpath } def
% text state operators
/Tc { /pdfCharSpacing exch def } def
/Tf { dup /pdfFontSize exch def
dup pdfHorizScaling mul exch matrix scale
pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put
exch findfont exch makefont setfont } def
/Tr { /pdfTextRender exch def } def
/Ts { /pdfTextRise exch def } def
/Tw { /pdfWordSpacing exch def } def
/Tz { /pdfHorizScaling exch def } def
% text positioning operators
/Td { pdfTextMat transform moveto } def
/Tm { /pdfTextMat exch def } def
% text string operators
/awcp { % awidthcharpath
exch {
1 string dup 0 3 index put 2 index charpath
3 index 3 index rmoveto
4 index eq { 5 index 5 index rmoveto } if
} forall
6 {pop} repeat
} def
/Tj { fCol
0 pdfTextRise pdfTextMat dtransform rmoveto
1 index stringwidth pdfTextMat idtransform pop
sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse
pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32
4 3 roll pdfCharSpacing pdfHorizScaling mul add 0
pdfTextMat dtransform
6 5 roll
currentpoint 8 2 roll
pdfTextRender 1 and 0 eq {
6 copy awidthshow
} if
pdfTextRender 3 and dup 1 eq exch 2 eq or {
8 6 roll moveto
currentfont /FontType get 3 eq { fCol } { sCol } ifelse
false awcp currentpoint stroke moveto
} {
8 {pop} repeat
} ifelse
0 pdfTextRise neg pdfTextMat dtransform rmoveto } def
/Tj16 { pdfTextRender 1 and 0 eq { fCol } { sCol } ifelse
0 pdfTextRise pdfTextMat dtransform rmoveto
2 index stringwidth pdfTextMat idtransform pop
sub exch div
pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32
4 3 roll pdfCharSpacing pdfHorizScaling mul add 0
pdfTextMat dtransform
6 5 roll awidthshow
0 pdfTextRise neg pdfTextMat dtransform rmoveto } def
/Tj16V { pdfTextRender 1 and 0 eq { fCol } { sCol } ifelse
0 pdfTextRise pdfTextMat dtransform rmoveto
2 index stringwidth pdfTextMat idtransform exch pop
sub exch div
0 pdfWordSpacing pdfTextMat dtransform 32
4 3 roll pdfCharSpacing add 0 exch
pdfTextMat dtransform
6 5 roll awidthshow
0 pdfTextRise neg pdfTextMat dtransform rmoveto } def
/TJm { pdfFontSize 0.001 mul mul neg 0
pdfTextMat dtransform rmoveto } def
/TJmV { pdfFontSize 0.001 mul mul neg 0 exch
pdfTextMat dtransform rmoveto } def
% Level 1 image operators
/pdfIm1 {
/pdfImBuf1 4 index string def
{ currentfile pdfImBuf1 readhexstring pop } image
} def
/pdfIm1Sep {
/pdfImBuf1 4 index string def
/pdfImBuf2 4 index string def
/pdfImBuf3 4 index string def
/pdfImBuf4 4 index string def
{ currentfile pdfImBuf1 readhexstring pop }
{ currentfile pdfImBuf2 readhexstring pop }
{ currentfile pdfImBuf3 readhexstring pop }
{ currentfile pdfImBuf4 readhexstring pop }
true 4 colorimage
} def
/pdfImM1 {
/pdfImBuf1 4 index 7 add 8 idiv string def
{ currentfile pdfImBuf1 readhexstring pop } imagemask
} def
% Level 2 image operators
/pdfImBuf 100 string def
/pdfIm {
image
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
/pdfImSep {
findcmykcustomcolor exch
dup /Width get /pdfImBuf1 exch string def
begin Width Height BitsPerComponent ImageMatrix DataSource end
/pdfImData exch def
{ pdfImData pdfImBuf1 readstring pop
0 1 2 index length 1 sub {
1 index exch 2 copy get 255 exch sub put
} for }
6 5 roll customcolorimage
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
/pdfImM {
fCol imagemask
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
end
%%EndResource
%%EndProlog
%%BeginSetup
xpdf begin
%%BeginResource: font FQDZSO+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 /FQDZSO+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 65 /A put
dup 76 /L put
dup 82 /R put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 109 /m put
readonly def
/FontBBox{-30 -250 1026 750}readonly def
/UniqueID 5087386 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F5_0 /FQDZSO+CMMI12 1 1
[ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/A/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/L/.notdef/.notdef/.notdef
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/.notdef/a/b/c/d/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/m/.notdef/.notdef
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font XABZQM+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 /XABZQM+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 40 /parenleft put
dup 41 /parenright put
readonly def
/FontBBox{-34 -251 988 750}readonly def
/UniqueID 5000794 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F8_0 /XABZQM+CMR12 1 1
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font FRTEPB+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 /FRTEPB+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 49 /one put
dup 50 /two put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F11_0 /FRTEPB+CMR8 1 1
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font WGZFLG+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 /WGZFLG+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 3 /asteriskmath put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueID 5000818 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F14_0 /WGZFLG+CMSY8 1 1
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font CMAWQN+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 /CMAWQN+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 108 /l put
dup 114 /r put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec
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%
%
%
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%
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%
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%
%
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%396.76 226.72
%269.23 226.72
%255.06 240.89 s
%
%
%382.59 141.7 m
%382.59 170.04
%368.42 170.04
%269.23 170.04
%255.06 184.21 s
%
%
%141.7 141.7 m
%141.7 170.04
%155.87 170.04
%240.89 170.04
%255.06 184.21 s
%
%
%141.7 113.36 m
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%
%
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%184.21 141.7
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%
%
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%
%
%382.59 113.36 m
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%
%
%$A$
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%
%224.72 56.21 m
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%
%
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%433.27 88.55 l
%
%
%
%
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%
%
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%
%
%
pdfStartPage
[] 0 d
0 i
0 j
0 J
10 M
1 w
0 g
0 G
18.34 40.8 514.345 157.284 re
W
q
q
1 w
24.84 102.72 m
24.84 104.101 23.7207 105.22 22.34 105.22 c
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19.84 101.339 20.9593 100.22 22.34 100.22 c
23.7207 100.22 24.84 101.339 24.84 102.72 c
h
f*
24.84 102.72 m
24.84 104.101 23.7207 105.22 22.34 105.22 c
20.9593 105.22 19.84 104.101 19.84 102.72 c
19.84 101.339 20.9593 100.22 22.34 100.22 c
23.7207 100.22 24.84 101.339 24.84 102.72 c
h
S
Q
q
1 w
506.62 102.72 m
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502.739 105.22 501.62 104.101 501.62 102.72 c
501.62 101.339 502.739 100.22 504.12 100.22 c
505.501 100.22 506.62 101.339 506.62 102.72 c
h
f*
506.62 102.72 m
506.62 104.101 505.501 105.22 504.12 105.22 c
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505.501 100.22 506.62 101.339 506.62 102.72 c
h
S
Q
q
1 w
81.52 88.55 m
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h
f*
81.52 88.55 m
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h
S
Q
q
1 w
225.62 53.01 m
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224.501 50.51 225.62 51.6293 225.62 53.01 c
h
f*
225.62 53.01 m
225.62 54.3907 224.501 55.51 223.12 55.51 c
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h
S
Q
q
1 w
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h
f*
296.47 53.01 m
296.47 54.3907 295.351 55.51 293.97 55.51 c
292.589 55.51 291.47 54.3907 291.47 53.01 c
291.47 51.6293 292.589 50.51 293.97 50.51 c
295.351 50.51 296.47 51.6293 296.47 53.01 c
h
S
Q
q
1 w
435.77 88.55 m
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h
f*
435.77 88.55 m
435.77 89.9307 434.651 91.05 433.27 91.05 c
431.889 91.05 430.77 89.9307 430.77 88.55 c
430.77 87.1693 431.889 86.05 433.27 86.05 c
434.651 86.05 435.77 87.1693 435.77 88.55 c
h
S
Q
q
1 w
416.43 78.38 m
416.43 79.7607 415.311 80.88 413.93 80.88 c
412.549 80.88 411.43 79.7607 411.43 78.38 c
411.43 76.9993 412.549 75.88 413.93 75.88 c
415.311 75.88 416.43 76.9993 416.43 78.38 c
h
f*
416.43 78.38 m
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114.5 76 m
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223.12 53.01 m
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139.354 76.9849 m
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387.493 78.9324 m
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387.493 78.9324 m
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407 y(The)g(ory)34 b(Appl.)p Fm(,)d(7:173{185,)k(1997.)45
595 y([2])47 b(H.)f(Br\177)-45 b(onnimann)44 b(and)g(M.)i(T.)f(Go)s(o)s
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5400 y(15)p eop end
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userdict /end-hook known{end-hook}if
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