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%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
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% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
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%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMMI6.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
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%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name MSAM10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/MSAM10 known{/MSAM10 findfont dup/UniqueID known{dup
/UniqueID get 5031981 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /MSAM10 def
/FontBBox {8 -463 1331 1003 }readonly def
/UniqueID 5031981 def
/PaintType 0 def
/FontInfo 7 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name MSAM10.) readonly def
/FullName (MSAM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 3 /square put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMR6
%!PS-AdobeFont-1.0: CMR6 003.002
%%Title: CMR6
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR6.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMR6 known{/CMR6 findfont dup/UniqueID known{dup
/UniqueID get 5000789 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMR6 def
/FontBBox {-20 -250 1193 750 }readonly def
/UniqueID 5000789 def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR6.) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 43 /plus put
dup 48 /zero put
dup 49 /one put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMBX12
%!PS-AdobeFont-1.0: CMBX12 003.002
%%Title: CMBX12
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMBX12.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMBX12 known{/CMBX12 findfont dup/UniqueID known{dup
/UniqueID get 5000769 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMBX12 def
/FontBBox {-53 -251 1139 750 }readonly def
/UniqueID 5000769 def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMBX12.) readonly def
/FullName (CMBX12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 40 /parenleft put
dup 41 /parenright 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 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine 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 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 84 /T put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 120 /x put
dup 121 /y put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMSY8
%!PS-AdobeFont-1.0: CMSY8 003.002
%%Title: CMSY8
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMSY8.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMSY8 known{/CMSY8 findfont dup/UniqueID known{dup
/UniqueID get 5096649 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMSY8 def
/FontBBox {-30 -955 1185 779 }readonly def
/UniqueID 5096649 def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMSY8.) readonly def
/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end 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 49 /infinity put
dup 50 /element put
dup 102 /braceleft put
dup 103 /braceright put
dup 106 /bar put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMEX10
%!PS-AdobeFont-1.0: CMEX10 003.002
%%Title: CMEX10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMEX10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMEX10 known{/CMEX10 findfont dup/UniqueID known{dup
/UniqueID get 5092766 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMEX10 def
/FontBBox {-24 -2960 1454 772 }readonly def
/UniqueID 5092766 def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMEX10.) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 2 /bracketleftbig put
dup 3 /bracketrightbig put
dup 12 /vextendsingle put
dup 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 26 /braceleftbigg put
dup 27 /bracerightbigg put
dup 88 /summationdisplay put
dup 101 /tildewide put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: EUFM10
%!PS-AdobeFont-1.0: EUFM10 003.003
%%Title: EUFM10
%Version: 003.003
%%CreationDate: Mon Jun 13 12:00:00 2011
%%Creator: American Mathematical Society
%Copyright: Copyright (c) 1997, 2009, 2011 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name EUFM10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
%%VMusage: 120000 150000
11 dict begin
/FontInfo 15 dict dup begin
/version (003.003) readonly def
/Notice (Copyright \050c\051 1997, 2009, 2011 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name EUFM10.) readonly def
/FullName (EUFM10) readonly def
/FamilyName (Euler) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Weight (Medium) readonly def
end readonly def
/FontName /EUFM10 def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 103 /g put
dup 108 /l put
readonly def
/PaintType 0 def
/FontType 1 def
/FontMatrix [ 0.001 0 0 0.001 0 0 ] readonly def
/FontBBox {-28 -257 1055 741} readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR8
%!PS-AdobeFont-1.0: CMR8 003.002
%%Title: CMR8
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR8.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMR8 known{/CMR8 findfont dup/UniqueID known{dup
/UniqueID get 5000791 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMR8 def
/FontBBox {-36 -250 1070 750 }readonly def
/UniqueID 5000791 def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR8.) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 10 /Omega put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMSY10
%!PS-AdobeFont-1.0: CMSY10 003.002
%%Title: CMSY10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMSY10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMSY10 known{/CMSY10 findfont dup/UniqueID known{dup
/UniqueID get 5096651 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMSY10 def
/FontBBox {-29 -960 1116 775 }readonly def
/UniqueID 5096651 def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMSY10.) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 1 /periodcentered put
dup 2 /multiply put
dup 6 /plusminus put
dup 8 /circleplus put
dup 18 /reflexsubset put
dup 20 /lessequal put
dup 21 /greaterequal put
dup 26 /propersubset put
dup 28 /lessmuch put
dup 29 /greatermuch put
dup 33 /arrowright put
dup 37 /arrownortheast put
dup 49 /infinity put
dup 50 /element put
dup 54 /negationslash put
dup 55 /mapsto put
dup 71 /G put
dup 79 /O put
dup 82 /R put
dup 92 /intersection put
dup 102 /braceleft put
dup 103 /braceright put
dup 104 /angbracketleft put
dup 105 /angbracketright put
dup 106 /bar put
dup 107 /bardbl put
dup 110 /backslash put
readonly def
currentdict end
currentfile eexec
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%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name MSBM10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/MSBM10 known{/MSBM10 findfont dup/UniqueID known{dup
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/FontInfo 7 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name MSBM10.) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
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/isFixedPitch false def
end readonly def
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dup 80 /P put
dup 82 /R put
dup 83 /S put
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readonly def
currentdict end
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMMI8
%!PS-AdobeFont-1.0: CMMI8 003.002
%%Title: CMMI8
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMMI8.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMMI8 known{/CMMI8 findfont dup/UniqueID known{dup
/UniqueID get 5087383 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMMI8 def
/FontBBox {-24 -250 1110 750 }readonly def
/UniqueID 5087383 def
/PaintType 0 def
/FontInfo 10 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI8.) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/ascent 750 def
end 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 21 /lambda put
dup 22 /mu put
dup 23 /nu put
dup 28 /tau put
dup 33 /omega put
dup 59 /comma put
dup 61 /slash put
dup 62 /greater put
dup 71 /G put
dup 75 /K put
dup 78 /N put
dup 82 /R put
dup 84 /T put
dup 96 /lscript put
dup 97 /a put
dup 99 /c put
dup 100 /d put
dup 105 /i put
dup 107 /k put
dup 109 /m put
dup 110 /n 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
dup 122 /z put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMMI12
%!PS-AdobeFont-1.0: CMMI12 003.002
%%Title: CMMI12
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMMI12.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMMI12 known{/CMMI12 findfont dup/UniqueID known{dup
/UniqueID get 5087386 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMMI12 def
/FontBBox {-31 -250 1026 750 }readonly def
/UniqueID 5087386 def
/PaintType 0 def
/FontInfo 10 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI12.) readonly def
/FullName (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/ascent 750 def
end 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 16 /zeta put
dup 17 /eta put
dup 21 /lambda put
dup 22 /mu put
dup 23 /nu put
dup 24 /xi put
dup 27 /sigma put
dup 28 /tau put
dup 33 /omega put
dup 34 /epsilon put
dup 39 /phi1 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 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 84 /T put
dup 86 /V put
dup 88 /X put
dup 96 /lscript put
dup 97 /a put
dup 99 /c put
dup 100 /d put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 107 /k put
dup 109 /m put
dup 110 /n put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 122 /z put
readonly def
currentdict end
currentfile eexec
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%%EndFont 
%%BeginFont: CMCSC10
%!PS-AdobeFont-1.0: CMCSC10 003.002
%%Title: CMCSC10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMCSC10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMCSC10 known{/CMCSC10 findfont dup/UniqueID known{dup
/UniqueID get 5087402 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMCSC10 def
/FontBBox {14 -250 1077 750 }readonly def
/UniqueID 5087402 def
/PaintType 0 def
/FontInfo 10 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMCSC10.) readonly def
/FullName (CMCSC10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/ascent 750 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 97 /a put
dup 107 /k put
dup 109 /m put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMTI12
%!PS-AdobeFont-1.0: CMTI12 003.002
%%Title: CMTI12
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMTI12.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMTI12 known{/CMTI12 findfont dup/UniqueID known{dup
/UniqueID get 5000829 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMTI12 def
/FontBBox {-36 -251 1103 750 }readonly def
/UniqueID 5000829 def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMTI12.) readonly def
/FullName (CMTI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end 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 38 /ampersand put
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 58 /colon put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 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 86 /V put
dup 87 /W put
dup 90 /Z put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 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 123 /endash put
dup 124 /emdash put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMR10
%!PS-AdobeFont-1.0: CMR10 003.002
%%Title: CMR10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup
/UniqueID get 5000793 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMR10 def
/FontBBox {-40 -250 1009 750 }readonly def
/UniqueID 5000793 def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR10.) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 49 /one put
dup 68 /D put
dup 70 /F put
dup 73 /I put
dup 78 /N put
dup 84 /T put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j 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 123 /endash put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMBX10
%!PS-AdobeFont-1.0: CMBX10 003.002
%%Title: CMBX10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMBX10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMBX10 known{/CMBX10 findfont dup/UniqueID known{dup
/UniqueID get 5000768 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMBX10 def
/FontBBox {-56 -250 1164 750 }readonly def
/UniqueID 5000768 def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMBX10.) readonly def
/FullName (CMBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 65 /A put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 114 /r put
dup 115 /s put
dup 116 /t put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMTI10
%!PS-AdobeFont-1.0: CMTI10 003.002
%%Title: CMTI10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMTI10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMTI10 known{/CMTI10 findfont dup/UniqueID known{dup
/UniqueID get 5000828 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMTI10 def
/FontBBox {-35 -250 1124 750 }readonly def
/UniqueID 5000828 def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMTI10.) readonly def
/FullName (CMTI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end 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 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 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 73 /I put
dup 74 /J put
dup 77 /M put
dup 78 /N put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 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 121 /y put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMR12
%!PS-AdobeFont-1.0: CMR12 003.002
%%Title: CMR12
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR12.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMR12 known{/CMR12 findfont dup/UniqueID known{dup
/UniqueID get 5000794 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMR12 def
/FontBBox {-34 -251 988 750 }readonly def
/UniqueID 5000794 def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR12.) readonly def
/FullName (CMR12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /Gamma put
dup 1 /Delta put
dup 8 /Phi put
dup 10 /Omega put
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 19 /acute put
dup 22 /macron put
dup 24 /cedilla put
dup 25 /germandbls put
dup 33 /exclam 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 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 93 /bracketright put
dup 95 /dotaccent put
dup 96 /quoteleft put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 124 /emdash put
dup 127 /dieresis put
readonly def
currentdict end
currentfile eexec
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%%EndFont 
%%BeginFont: CMR17
%!PS-AdobeFont-1.0: CMR17 003.002
%%Title: CMR17
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR17.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMR17 known{/CMR17 findfont dup/UniqueID known{dup
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/FontName /CMR17 def
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/UniqueID 5000795 def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR17.) readonly def
/FullName (CMR17) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 72 /H put
dup 78 /N put
dup 80 /P put
dup 84 /T put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 101 /e put
dup 102 /f put
dup 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 121 /y put
readonly def
currentdict end
currentfile eexec
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476.131 91.491 L
476.341 88.075 L
476.55 84.55 L
476.76 80.927 L
476.969 81.361 L
477.179 84.972 L
477.389 88.486 L
477.598 91.888 L
477.808 95.167 L
478.017 98.308 L
478.227 101.298 L
478.436 104.123 L
478.646 106.768 L
478.855 109.221 L
479.065 111.47 L
479.274 113.503 L
479.484 115.312 L
479.693 116.892 L
479.903 118.24 L
480.112 119.36 L
480.322 120.26 L
480.532 120.953 L
480.741 121.461 L
480.951 121.81 L
481.16 122.029 L
481.37 122.153 L
481.579 122.214 L
481.789 122.238 L
481.998 122.245 L
482.208 122.246 L
482.417 122.246 L
482.627 122.246 L
482.836 122.246 L
483.046 122.246 L
483.255 122.246 L
483.465 122.246 L
483.674 122.246 L
483.884 122.246 L
484.303 122.246 L
484.513 122.246 L
484.722 122.246 L
485.141 122.246 L
485.979 122.246 L
486.189 122.246 L
486.398 122.246 L
486.608 122.246 L
486.817 122.246 L
487.656 122.246 L
489.332 122.246 L
489.559 122.246 L
489.787 122.246 L
490.241 122.246 L
491.151 122.246 L
492.97 122.246 L
496.608 122.246 L
503.883 122.246 L
504.095 122.246 L
504.307 122.246 L
504.732 122.246 L
505.58 122.246 L
507.277 122.246 L
510.671 122.246 L
510.884 122.246 L
511.096 122.246 L
511.52 122.246 L
512.369 122.246 L
514.066 122.246 L
514.278 122.246 L
514.49 122.246 L
514.914 122.246 L
515.126 122.246 L
515.338 122.246 L
515.551 122.246 L
515.763 122.246 L
515.975 122.246 L
516.187 122.246 L
516.399 122.244 L
516.611 122.237 L
516.823 122.21 L
517.036 122.145 L
517.248 122.011 L
517.46 121.775 L
517.69 121.547 L
517.92 121.889 L
518.15 122.089 L
518.38 122.19 L
518.61 122.231 L
518.84 122.243 L
519.07 122.246 L
519.3 122.246 L
519.529 122.246 L
519.759 122.246 L
519.989 122.246 L
520.219 122.246 L
520.449 122.246 L
520.679 122.246 L
521.139 122.246 L
521.369 122.246 L
521.599 122.246 L
522.059 122.246 L
522.979 122.246 L
524.819 122.246 L
525.049 122.246 L
525.279 122.246 L
525.739 122.246 L
526.658 122.246 L
528.498 122.246 L
532.178 122.246 L
532.392 122.246 L
532.607 122.246 L
532.822 122.246 L
533.037 122.246 L
533.251 122.246 L
533.466 122.246 L
533.681 122.246 L
533.895 122.246 L
535.613 122.246 L
535.828 122.246 L
536.043 122.246 L
536.472 122.246 L
537.331 122.246 L
537.546 122.246 L
537.761 122.246 L
538.19 122.246 L
538.405 122.246 L
538.62 122.246 L
538.834 122.246 L
539.049 122.246 L
539.264 122.246 L
539.479 122.246 L
539.693 122.246 L
539.908 122.244 L
540.123 122.235 L
540.338 122.204 L
540.552 122.129 L
540.767 121.979 L
540.982 121.718 L
541.196 121.312 L
541.411 120.729 L
541.626 119.943 L
541.841 118.934 L
542.055 117.689 L
542.27 116.202 L
542.485 114.473 L
542.7 112.505 L
542.914 111.53 L
543.129 113.604 L
543.344 115.443 L
543.559 117.041 L
543.773 118.396 L
543.988 119.511 L
544.203 120.397 L
544.418 121.07 L
544.632 121.553 L
544.847 121.876 L
545.062 122.072 L
545.276 122.177 L
545.491 122.224 L
545.706 122.241 L
545.921 122.245 L
546.131 122.246 L
546.342 122.246 L
546.552 122.246 L
546.763 122.246 L
546.973 122.246 L
547.184 122.246 L
547.605 122.246 L
547.815 122.246 L
548.026 122.246 L
548.447 122.246 L
549.289 122.246 L
549.5 122.246 L
549.71 122.246 L
550.131 122.246 L
550.973 122.246 L
552.658 122.246 L
552.868 122.246 L
553.079 122.246 L
553.5 122.246 L
554.342 122.246 L
556.026 122.246 L
559.394 122.246 L
559.623 122.246 L
559.851 122.246 L
560.308 122.246 L
561.221 122.246 L
563.048 122.246 L
566.702 122.246 L
566.93 122.246 L
567.159 122.246 L
567.387 122.246 L
567.615 122.246 L
567.844 122.246 L
568.072 122.246 L
568.3 122.246 L
568.529 122.246 L
568.757 122.246 L
568.985 122.246 L
569.214 122.246 L
569.442 122.246 L
569.67 122.246 L
569.899 122.246 L
570.356 122.246 L
570.584 122.246 L
570.812 122.246 L
571.269 122.246 L
572.182 122.246 L
572.411 122.246 L
572.639 122.246 L
573.096 122.246 L
573.324 122.246 L
573.553 122.246 L
573.781 122.246 L
574.009 122.246 L
574.222 122.246 L
574.436 122.246 L
574.649 122.246 L
574.862 122.246 L
575.075 122.246 L
575.288 122.246 L
575.714 122.246 L
575.927 122.246 L
576.141 122.246 L
576.567 122.246 L
577.419 122.246 L
577.632 122.246 L
577.846 122.246 L
578.059 122.246 L
578.272 122.246 L
578.485 122.245 L
578.698 122.238 L
578.911 122.216 L
579.124 122.156 L
579.337 122.032 L
579.551 121.809 L
579.764 121.453 L
579.977 120.932 L
580.19 120.217 L
580.403 119.289 L
580.616 118.132 L
580.829 116.738 L
581.042 115.104 L
581.256 113.234 L
581.469 111.133 L
581.682 108.811 L
581.895 106.279 L
582.108 103.551 L
582.534 97.562 L
582.748 94.33 L
582.961 90.96 L
583.174 87.466 L
583.387 83.861 L
583.6 80.158 L
583.813 82.186 L
584.026 85.837 L
584.239 89.384 L
584.453 92.812 L
584.666 96.109 L
584.879 99.258 L
585.092 102.247 L
585.305 105.06 L
585.518 107.683 L
585.731 110.103 L
585.944 112.305 L
586.158 114.282 L
586.371 116.024 L
586.584 117.527 L
586.797 118.791 L
587.01 119.822 L
587.223 120.632 L
587.436 121.238 L
587.649 121.666 L
587.88 121.962 L
588.111 122.128 L
588.342 122.207 L
588.573 122.237 L
588.804 122.245 L
589.035 122.246 L
589.266 122.246 L
589.497 122.246 L
589.728 122.246 L
589.959 122.246 L
590.19 122.246 L
590.421 122.246 L
590.652 122.246 L
590.883 122.246 L
591.345 122.246 L
591.576 122.246 L
591.807 122.246 L
592.269 122.246 L
592.5 122.246 L
592.731 122.246 L
592.962 122.246 L
593.192 122.246 L
593.423 122.246 L
593.654 122.246 L
593.885 122.246 L
594.116 122.246 L
594.347 122.246 L
594.578 122.246 L
595.04 122.246 L
595.271 122.246 L
595.502 122.246 L
595.964 122.246 L
596.888 122.246 L
598.736 122.246 L
602.431 122.246 L
602.658 122.246 L
602.884 122.246 L
603.338 122.246 L
604.245 122.246 L
606.059 122.246 L
606.286 122.246 L
606.512 122.246 L
606.966 122.246 L
607.193 122.246 L
607.419 122.246 L
607.646 122.246 L
607.873 122.246 L
608.1 122.243 L
608.326 122.231 L
608.553 122.191 L
608.78 122.094 L
609.007 122.13 L
609.233 122.207 L
609.46 122.237 L
609.687 122.245 L
609.914 122.246 L
610.14 122.246 L
610.367 122.246 L
610.594 122.246 L
610.821 122.246 L
611.047 122.246 L
611.501 122.246 L
611.728 122.246 L
611.954 122.246 L
612.408 122.246 L
613.315 122.246 L
613.542 122.246 L
613.768 122.246 L
614.222 122.246 L
615.129 122.246 L
616.943 122.246 L
630.48 122.246 L
645.159 122.246 L
658.862 122.246 L
672.297 122.246 L
686.872 122.246 L
700.473 122.246 L
700.711 122.246 L
700.948 122.246 L
701.422 122.246 L
702.371 122.246 L
704.269 122.246 L
708.065 122.246 L
708.302 122.246 L
708.539 122.246 L
709.014 122.246 L
709.962 122.246 L
711.86 122.246 L
712.098 122.246 L
712.335 122.246 L
712.809 122.246 L
713.046 122.246 L
713.284 122.246 L
713.521 122.246 L
713.758 122.245 L
713.995 122.235 L
714.233 122.2 L
714.47 122.109 L
714.707 121.918 L
714.944 121.581 L
715.182 121.051 L
715.419 120.288 L
cp
false upath dup ufill ustroke
P
0.247 0.24 0.6 r
1 1 1 r
0.5 w
[ ] 0 setdash
3.25 setmiterlimit
24.456 122.246 m
24.668 122.246 L
24.88 122.246 L
25.304 122.246 L
26.152 122.246 L
27.848 122.246 L
31.24 122.246 L
38.023 122.246 L
52.732 122.246 L
52.946 122.246 L
53.161 122.246 L
53.59 122.246 L
54.449 122.246 L
54.663 122.246 L
54.878 122.246 L
55.307 122.246 L
55.522 122.246 L
55.736 122.246 L
55.951 122.246 L
56.165 122.246 L
56.38 122.245 L
56.594 122.241 L
56.809 122.224 L
57.024 122.176 L
57.238 122.069 L
57.453 121.918 L
57.667 122.096 L
57.882 122.189 L
58.097 122.229 L
58.311 122.243 L
58.526 122.246 L
58.74 122.246 L
58.955 122.246 L
59.17 122.246 L
59.384 122.246 L
59.599 122.246 L
59.813 122.246 L
60.028 122.246 L
60.457 122.246 L
61.315 122.246 L
63.032 122.246 L
63.247 122.246 L
63.461 122.246 L
63.676 122.246 L
63.891 122.246 L
64.105 122.242 L
64.32 122.227 L
64.534 122.184 L
64.749 122.086 L
64.964 121.901 L
65.178 121.593 L
65.393 121.715 L
65.607 121.977 L
65.822 122.128 L
66.036 122.203 L
66.251 122.234 L
66.466 122.244 L
66.676 122.246 L
66.886 122.246 L
67.097 122.246 L
67.307 122.246 L
67.518 122.246 L
67.728 122.246 L
67.938 122.246 L
68.149 122.246 L
68.359 122.246 L
68.569 122.246 L
68.99 122.246 L
69.832 122.246 L
70.042 122.246 L
70.253 122.246 L
70.673 122.246 L
71.515 122.246 L
73.198 122.246 L
73.408 122.246 L
73.619 122.246 L
74.039 122.246 L
74.25 122.246 L
74.46 122.246 L
74.671 122.246 L
74.881 122.246 L
75.091 122.246 L
75.302 122.246 L
75.512 122.242 L
75.722 122.228 L
75.933 122.188 L
76.143 122.097 L
76.354 121.925 L
76.564 121.638 L
76.774 121.205 L
76.985 120.595 L
77.195 119.786 L
77.406 118.761 L
77.616 117.508 L
77.826 116.281 L
78.037 117.728 L
78.247 118.943 L
78.457 119.932 L
78.668 120.707 L
78.878 121.286 L
79.089 121.694 L
79.299 121.96 L
79.509 122.116 L
79.72 122.197 L
79.93 122.232 L
80.158 122.244 L
80.387 122.246 L
80.615 122.246 L
80.843 122.246 L
81.071 122.246 L
81.299 122.246 L
81.528 122.246 L
81.756 122.246 L
81.984 122.246 L
82.212 122.246 L
82.669 122.246 L
83.581 122.246 L
83.81 122.246 L
84.038 122.246 L
84.494 122.246 L
85.407 122.246 L
85.635 122.246 L
85.864 122.246 L
86.32 122.246 L
86.548 122.246 L
86.776 122.246 L
87.005 122.246 L
87.233 122.246 L
87.461 122.245 L
87.689 122.237 L
87.918 122.209 L
88.146 122.134 L
88.374 121.976 L
88.602 121.692 L
88.83 121.242 L
89.059 120.587 L
89.287 119.697 L
89.515 118.551 L
89.743 117.136 L
89.971 115.447 L
90.2 113.485 L
90.428 111.258 L
90.656 112.89 L
90.884 114.926 L
91.113 116.692 L
91.341 118.184 L
91.569 119.404 L
91.797 120.363 L
92.025 121.081 L
92.254 121.585 L
92.482 121.911 L
92.71 122.1 L
92.938 122.194 L
93.166 122.232 L
93.395 122.244 L
93.623 122.246 L
93.851 122.246 L
94.079 122.246 L
94.307 122.246 L
94.536 122.246 L
94.749 122.246 L
94.962 122.246 L
95.388 122.246 L
96.24 122.246 L
96.453 122.246 L
96.666 122.246 L
97.092 122.246 L
97.304 122.246 L
97.517 122.246 L
97.73 122.246 L
97.943 122.246 L
98.156 122.246 L
98.369 122.246 L
98.582 122.246 L
98.795 122.246 L
99.008 122.246 L
99.221 122.246 L
99.647 122.246 L
99.86 122.246 L
100.073 122.246 L
100.286 122.246 L
100.499 122.246 L
101.351 122.246 L
101.564 122.246 L
101.777 122.246 L
102.203 122.246 L
103.055 122.246 L
104.759 122.246 L
104.972 122.246 L
105.185 122.246 L
105.398 122.246 L
105.611 122.246 L
105.824 122.242 L
106.037 122.227 L
106.25 122.185 L
106.463 122.09 L
106.676 121.909 L
106.889 121.609 L
107.102 121.155 L
107.315 120.519 L
107.528 119.677 L
107.741 118.61 L
107.954 117.31 L
108.167 115.771 L
108.397 113.835 L
108.628 111.625 L
108.859 109.154 L
109.09 106.434 L
109.321 103.483 L
109.552 100.319 L
110.013 93.424 L
110.244 89.73 L
110.475 85.896 L
110.706 81.94 L
110.936 80.718 L
111.167 84.708 L
111.398 88.581 L
111.86 95.904 L
112.09 99.319 L
112.321 102.545 L
112.552 105.562 L
112.783 108.354 L
113.014 110.903 L
113.245 113.193 L
113.475 115.213 L
113.706 116.955 L
113.937 118.417 L
114.168 119.602 L
114.399 120.524 L
114.629 121.203 L
114.86 121.671 L
115.091 121.965 L
115.322 122.13 L
115.553 122.208 L
115.783 122.237 L
116.014 122.245 L
116.245 122.246 L
116.476 122.246 L
116.707 122.246 L
116.938 122.246 L
117.168 122.246 L
117.399 122.246 L
117.63 122.246 L
117.861 122.246 L
118.322 122.246 L
119.246 122.246 L
119.477 122.246 L
119.707 122.246 L
120.169 122.246 L
121.092 122.246 L
122.939 122.246 L
123.165 122.246 L
123.392 122.246 L
123.619 122.246 L
123.845 122.246 L
124.752 122.246 L
124.978 122.246 L
125.205 122.246 L
125.431 122.246 L
125.658 122.246 L
125.885 122.246 L
126.111 122.245 L
126.338 122.236 L
126.564 122.206 L
126.791 122.128 L
127.018 121.965 L
127.244 121.677 L
127.471 121.223 L
127.697 120.565 L
127.924 119.676 L
128.151 118.534 L
128.377 117.126 L
128.604 115.448 L
128.83 113.501 L
129.057 111.292 L
129.284 108.833 L
129.51 106.136 L
129.737 103.218 L
130.19 96.787 L
130.417 93.309 L
130.643 89.68 L
130.87 85.915 L
131.097 82.033 L
131.323 80.551 L
131.55 84.474 L
131.776 88.284 L
132.003 91.966 L
132.23 95.503 L
132.456 98.877 L
132.683 102.071 L
132.909 105.068 L
133.136 107.849 L
133.363 110.4 L
133.589 112.704 L
133.816 114.75 L
134.042 116.529 L
134.269 118.038 L
134.496 119.279 L
134.722 120.261 L
134.949 121.002 L
135.175 121.528 L
135.402 121.874 L
135.629 122.079 L
135.855 122.184 L
136.082 122.229 L
136.308 122.243 L
136.535 122.246 L
136.762 122.246 L
136.988 122.246 L
137.215 122.246 L
137.441 122.246 L
137.653 122.246 L
137.864 122.246 L
138.287 122.246 L
139.132 122.246 L
139.344 122.246 L
139.555 122.246 L
139.978 122.246 L
140.189 122.246 L
140.401 122.246 L
140.612 122.246 L
140.823 122.246 L
141.035 122.246 L
141.246 122.246 L
141.458 122.246 L
141.669 122.246 L
141.88 122.246 L
142.092 122.246 L
142.514 122.246 L
142.726 122.246 L
142.937 122.246 L
143.149 122.246 L
143.36 122.246 L
143.571 122.245 L
143.783 122.238 L
143.994 122.241 L
144.205 122.245 L
144.417 122.246 L
144.628 122.246 L
144.84 122.246 L
145.051 122.246 L
145.262 122.246 L
145.474 122.246 L
145.896 122.246 L
146.108 122.246 L
146.319 122.246 L
146.531 122.246 L
146.742 122.246 L
146.953 122.246 L
147.165 122.246 L
147.376 122.246 L
147.587 122.246 L
147.799 122.246 L
148.01 122.246 L
148.433 122.246 L
149.278 122.246 L
150.969 122.246 L
151.199 122.246 L
151.428 122.246 L
151.657 122.246 L
151.886 122.246 L
152.116 122.246 L
152.345 122.246 L
152.574 122.246 L
152.803 122.246 L
154.637 122.246 L
154.866 122.246 L
155.095 122.246 L
155.324 122.246 L
155.554 122.246 L
155.783 122.241 L
156.012 122.221 L
156.241 122.163 L
156.47 122.033 L
156.7 121.79 L
156.929 121.39 L
157.158 120.794 L
157.387 119.969 L
157.616 118.89 L
157.846 117.543 L
158.075 115.92 L
158.304 114.021 L
158.533 111.852 L
158.763 109.423 L
158.992 106.748 L
159.221 103.843 L
159.45 100.725 L
159.679 97.413 L
160.138 90.278 L
160.367 86.491 L
160.596 82.58 L
161.055 74.449 L
161.971 57.336 L
162.201 52.948 L
162.43 48.537 L
162.888 39.674 L
163.117 35.236 L
163.347 30.804 L
163.576 26.381 L
163.805 21.973 L
164.034 17.584 L
164.263 19.458 L
164.493 23.855 L
164.722 28.27 L
164.951 32.698 L
165.18 37.134 L
165.639 46.004 L
165.853 50.132 L
166.067 54.244 L
166.495 62.391 L
167.351 78.137 L
167.564 81.902 L
167.778 85.575 L
168.206 92.594 L
168.42 95.912 L
168.634 99.083 L
169.062 104.927 L
169.276 107.57 L
169.49 110.008 L
169.704 112.228 L
169.918 114.22 L
170.132 115.976 L
170.346 117.492 L
170.56 118.767 L
170.774 119.807 L
170.988 120.623 L
171.202 121.233 L
171.416 121.664 L
171.63 121.944 L
171.844 122.11 L
172.058 122.195 L
172.272 122.231 L
172.486 122.243 L
172.7 122.246 L
172.914 122.246 L
173.128 122.246 L
173.342 122.246 L
173.556 122.246 L
173.77 122.246 L
173.984 122.246 L
174.198 122.246 L
174.412 122.246 L
174.626 122.246 L
175.054 122.246 L
175.91 122.246 L
176.124 122.246 L
176.338 122.246 L
176.552 122.246 L
176.765 122.246 L
176.979 122.246 L
177.193 122.246 L
177.407 122.246 L
177.621 122.246 L
179.333 122.246 L
179.543 122.246 L
179.753 122.246 L
180.172 122.246 L
181.011 122.246 L
182.689 122.246 L
182.899 122.246 L
183.109 122.246 L
183.529 122.246 L
183.738 122.246 L
183.948 122.246 L
184.158 122.246 L
184.368 122.246 L
184.577 122.246 L
184.787 122.246 L
184.997 122.243 L
185.207 122.23 L
185.416 122.193 L
185.626 122.108 L
185.836 121.945 L
186.046 121.672 L
186.256 121.255 L
186.465 120.666 L
186.675 119.881 L
186.885 118.883 L
187.095 117.659 L
187.304 116.204 L
187.514 114.518 L
187.724 112.604 L
187.934 110.468 L
188.143 108.122 L
188.563 102.844 L
188.773 99.938 L
188.983 96.873 L
189.402 90.321 L
189.612 86.861 L
189.822 83.297 L
190.241 75.901 L
191.08 60.345 L
192.758 28.009 L
192.986 23.626 L
193.214 19.26 L
193.669 10.597 L
194.579 -6.376 L
194.807 -10.531 L
195.034 -14.647 L
195.49 -22.759 L
195.717 -26.752 L
195.945 -30.702 L
196.4 -38.471 L
196.627 -42.289 L
196.855 -46.062 L
197.083 -48.397 L
197.31 -44.652 L
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cp
false upath dup ufill ustroke
P
0.247 0.24 0.6 r
1 1 1 r
[ ] 0 setdash
24.456 122.246 m
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s
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0 g
p
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np 29.579 -495.788 m
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31.748 -495.788 L
cp
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P
p
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np 32.745 -495.788 m
32.745 740.28 L
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33.469 -495.788 L
cp
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P
p
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np 34.703 -495.788 m
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36.252 -495.788 L
cp
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P
p
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np 37.872 -495.788 m
37.872 740.28 L
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39.04 -495.788 L
cp
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P
p
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np 41.034 -495.788 m
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41.653 -495.788 L
cp
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P
p
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np 42.1 -495.788 m
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43.556 -495.788 L
cp
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P
p
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np 46.148 -495.788 m
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48.047 -495.788 L
cp
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P
p
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np 51.287 -495.788 m
51.287 740.28 L
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52.283 -495.788 L
cp
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P
p
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np 53.003 -495.788 m
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55.12 -495.788 L
cp
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P
p
0.1 w
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np 59.744 -495.788 m
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60.225 -495.788 L
cp
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P
p
0.1 w
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np 60.643 -495.788 m
60.643 740.28 L
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62.003 -495.788 L
cp
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P
p
0.1 w
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np 62.543 -495.788 m
62.543 740.28 L
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62.657 -495.788 L
cp
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P
p
0.1 w
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np 67.841 -495.788 m
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69.474 -495.788 L
cp
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P
p
0.1 w
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np 70.653 -495.788 m
70.653 740.28 L
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72.757 -495.788 L
cp
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P
p
0.1 w
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np 73.321 -495.788 m
73.321 740.28 L
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74.068 -495.788 L
cp
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P
p
0.1 w
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np 81.55 -495.788 m
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82.328 -495.788 L
cp
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P
p
0.1 w
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np 83.01 -495.788 m
83.01 740.28 L
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85.213 -495.788 L
cp
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P
p
0.1 w
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np 86.077 -495.788 m
86.077 740.28 L
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86.14 -495.788 L
cp
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P
p
0.1 w
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np 94.78 -495.788 m
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95.035 -495.788 L
cp
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P
p
0.1 w
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np 95.515 -495.788 m
95.515 740.28 L
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95.993 -495.788 L
cp
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P
p
0.1 w
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np 96.829 -495.788 m
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97.325 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 99.176 -495.788 m
99.176 740.28 L
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99.55 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 100.63 -495.788 m
100.63 740.28 L
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102.602 -495.788 L
cp
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P
p
0.1 w
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np 103.528 -495.788 m
103.528 740.28 L
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104.376 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 117.336 -495.788 m
117.336 740.28 L
118.107 740.28 L
118.107 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 119.187 -495.788 m
119.187 740.28 L
121.059 740.28 L
121.059 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 122.186 -495.788 m
122.186 740.28 L
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122.742 -495.788 L
cp
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P
p
0.1 w
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np 124.182 -495.788 m
124.182 740.28 L
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124.772 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 137.732 -495.788 m
137.732 740.28 L
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138.662 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 139.424 -495.788 m
139.424 740.28 L
140.2 740.28 L
140.2 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 141.564 -495.788 m
141.564 740.28 L
142.238 740.28 L
142.238 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 145.478 -495.788 m
145.478 740.28 L
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145.97 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 147.698 -495.788 m
147.698 740.28 L
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148.414 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 148.932 -495.788 m
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150.929 740.28 L
150.929 -495.788 L
cp
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P
p
0.1 w
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np 152.369 -495.788 m
152.369 740.28 L
154.303 740.28 L
154.303 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 173.896 -495.788 m
173.896 740.28 L
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175.934 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 177.785 -495.788 m
177.785 740.28 L
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179.596 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 180.076 -495.788 m
180.076 740.28 L
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180.749 -495.788 L
cp
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P
p
0.1 w
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np 182.6 -495.788 m
182.6 740.28 L
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183.57 -495.788 L
cp
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P
p
0.1 w
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np 210.51 -495.788 m
210.51 740.28 L
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211.757 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 213.917 -495.788 m
213.917 740.28 L
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214.467 -495.788 L
cp
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P
p
0.1 w
2 setlinejoin
np 214.886 -495.788 m
214.886 740.28 L
215.492 740.28 L
215.492 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
2 setlinejoin
np 219.812 -495.788 m
219.812 740.28 L
221.027 740.28 L
221.027 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
2 setlinejoin
np 223.907 -495.788 m
223.907 740.28 L
225.038 740.28 L
225.038 -495.788 L
cp
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P
p
0.1 w
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np 225.848 -495.788 m
225.848 740.28 L
227.9 740.28 L
227.9 -495.788 L
cp
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P
p
0.1 w
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np 228.937 -495.788 m
228.937 740.28 L
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228.962 -495.788 L
cp
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P
p
0.1 w
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np 231.554 -495.788 m
231.554 740.28 L
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231.665 -495.788 L
cp
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P
p
0.1 w
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np 232.529 -495.788 m
232.529 740.28 L
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233.01 -495.788 L
cp
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P
p
0.1 w
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np 233.457 -495.788 m
233.457 740.28 L
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234.809 -495.788 L
cp
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P
p
0.1 w
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241.289 740.28 L
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242.365 -495.788 L
cp
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P
p
0.1 w
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243.362 740.28 L
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245.531 -495.788 L
cp
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P
p
0.1 w
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246.148 740.28 L
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246.916 -495.788 L
cp
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P
p
0.1 w
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np 254.392 -495.788 m
254.392 740.28 L
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255.16 -495.788 L
cp
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P
p
0.1 w
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255.778 740.28 L
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257.946 -495.788 L
cp
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P
p
0.1 w
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260.02 -495.788 L
cp
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P
p
0.1 w
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np 266.5 -495.788 m
266.5 740.28 L
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267.851 -495.788 L
cp
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P
p
0.1 w
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np 268.298 -495.788 m
268.298 740.28 L
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268.779 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 269.643 -495.788 m
269.643 740.28 L
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269.754 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 272.346 -495.788 m
272.346 740.28 L
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272.371 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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273.408 740.28 L
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275.46 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
2 setlinejoin
np 276.27 -495.788 m
276.27 740.28 L
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277.401 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 280.281 -495.788 m
280.281 740.28 L
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281.496 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 285.816 -495.788 m
285.816 740.28 L
286.423 740.28 L
286.423 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
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np 286.841 -495.788 m
286.841 740.28 L
287.391 740.28 L
287.391 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
2 setlinejoin
np 289.551 -495.788 m
289.551 740.28 L
290.799 740.28 L
290.799 -495.788 L
cp
false upath dup ufill ustroke
P
p
0.1 w
2 setlinejoin
np 317.738 -495.788 m
317.738 740.28 L
318.708 740.28 L
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%%EndDocument
  @endspecial 3767 1337 a Fn(\013)230 366 y(\014)109 2496
y Fw(Figure)29 b(1:)42 b(P)m(arameter)30 b(sets)g(with)g(p)s(ersisten)m
(t)i(in)m(v)-5 b(arian)m(t)29 b(tori)g(and)h(the)g(subset)h(of)d(p)s
(ersisten)m(t)k(quasi-)109 2616 y(p)s(erio)s(dic)38 b(in)m(v)-5
b(arian)m(t)38 b(tori.)58 b(The)38 b(latter)g(set)g(is)g(the)g(pro)s
(duct)g(of)f(a)g(Can)m(tor)h(set)g(in)g(the)g Fn(\013)q
Fw({direction)109 2736 y(and)c(the)g(real)h(line)f(in)h(the)f
Fn(\014)6 b Fw({direction:)47 b(it)34 b(is)h(no)m(where)g(dense.)50
b(The)35 b(complemen)m(t)h(of)e(the)g(former)109 2857
y(set)k(\(whic)m(h)i(includes)g(the)e(resonance)i(set)e(on)g(the)h
Fn(\014)6 b Fw({axis\))38 b(is)g(a)g(set)h(of)e(ignorance,)i(in)f
(particular)109 2977 y(p)s(ersisten)m(t)f(in)m(v)-5 b(arian)m(t)36
b(tori)f(ma)m(y)h(exist)h(there)f(as)g(w)m(ell.)53 b(A)m(t)36
b(the)f(fra)m(y)m(ed)i(b)s(oundary)f(around)f(the)h Fn(\014)6
b Fw({)109 3097 y(axis)37 b(the)f(\014gure)h(is)g(self-similar:)51
b(it)37 b(rep)s(eats)g(itself)g(when)g(zo)s(omed)f(in)m(to)h(\(outside)
g(of)f(a)g(resonance)109 3218 y(bubble\).)p 0 TeXcolorgray
109 3508 a(b)s(oundary)g(b)s(et)m(w)m(een)i(the)e(parametrisations)h
(of)f(attracting)f(and)h(rep)s(elling)h Fn(n)p Fw({tori;)g(see)g
(Figure)f(1.)109 3629 y(Rep)s(elling)c Fn(n)p Fw({tori)f(p)s(erturb)s
(ed)h(from)f Fl(T)1579 3593 y Fm(n)1646 3629 y Fk(\002)21
b(f)p Fw(0)p Fk(g)30 b Fw(with)i Fn(\014)i(>)27 b Fw(0)k(also)h(ha)m(v)
m(e)h(resonance)g(strips)f(b)s(et)m(w)m(een)109 3749
y(the)41 b(p)s(ersisten)m(t)h(Diophan)m(tine)g(tori)e(with)i(their)f
(normally)g(h)m(yp)s(erb)s(olic)h(fattening,)h(\014nitely)f(man)m(y)109
3870 y(for)33 b(an)m(y)h(\014xed)g Fn(\014)h(>)29 b Fw(0,)k(and)h
(those)g(are)f(one)h(b)m(y)g(one)g(closed)g(as)g Fn(\014)39
b Fw(increases)c(un)m(til)f(none)g(are)f(left)h(as)109
3990 y Fn(\014)j Fk(\035)31 b Fw(0)j(|)h(a)f(pro)s(cess)i(whic)m(h)g
(is)g(the)f(rev)m(erse)i(to)d(the)h(one)g(as)g Fn(\014)41
b Fw(increases)36 b(from)f Fn(\014)i Fk(\034)31 b Fw(0)k(to)f
Fn(\014)j Fw(=)31 b(0,)109 4110 y(again)h(go)m(v)m(erned)i(b)m(y)h
(\(19\))o(.)109 4256 y(F)-8 b(or)44 b Fn(\014)54 b(>)49
b Fw(0)44 b(there)i(are)f(furthermore)g(attracting)g(\()p
Fn(n)30 b Fw(+)h(1\){tori)44 b(that)h(are)f(p)s(erturb)s(ed)i(from)f
(the)109 4376 y(\()p Fn(n)27 b Fw(+)g(1\){tori)40 b Fl(T)729
4340 y Fm(n)803 4376 y Fk(\002)28 b Fl(S)963 4340 y Fj(1)1043
4376 y Fw(of)39 b(the)i(unp)s(erturb)s(ed)g(dynamics)h(that)e(ha)m(v)m
(e)i(b)s(een)e(created)h(in)g(the)f(Hopf)109 4496 y(bifurcation.)73
b(Starting)42 b(with)h Fn(\014)51 b Fk(\035)44 b Fw(0)e(the)h
(situation)g(is)g(similar)g(to)f(that)g(of)g(the)h(attracting)f
Fn(n)p Fw({)109 4617 y(tori.)h(Where)32 b(the)g(normal)f(attraction)h
(is)g(su\016cien)m(tly)i(strong)d(all)h(orbits,)g(except)h(for)e(those)
h(on)g(the)109 4737 y(rep)s(elling)j Fn(n)p Fw({torus,)i(are)e
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b(As)33 b Fn(\014)39 b Fw(decreases)c(to)m(w)m(ards)g(0,)e(more)g(and)g
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b(alues)34 b(of)e(the)h(constan)m(ts)h Fn(E)k Fw(and)33
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b(of)f(a)h(single)h(parameter)f(and)109 979 y(it)44 b(is)i(instructiv)m
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1099 y(parameter)38 b Fn(\026)f Fk(2)h Fw(\000)f Fk(\022)h
Fl(R)p Fw(.)61 b(T)-8 b(o)38 b(a)m(v)m(oid)h(that)f(the)h(bifurcation)f
(itself)h(disapp)s(ears)g(in)m(to)g(a)f(resonance)109
1219 y(gap)43 b(w)m(e)h(follo)m(w)f([5])h(and)f(assume)i(that)e(the)g
(bifurcation)h(v)-5 b(alue)44 b Fn(\026)h Fw(=)h Fn(\026)2900
1183 y Fg(\003)2982 1219 y Fw(is)e(an)f(elemen)m(t)i(of)e
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b(f)p Fw(0)p Fk(g)39 b Fw(has)g(Diophan)m(tine)h(frequencies)i(and)e
(th)m(us)h(p)s(ersists)g(as)e(an)109 1460 y(in)m(v)-5
b(arian)m(t)40 b Fn(n)p Fw({torus)f Fn(V)945 1475 y Fm(\026)987
1456 y Fa(\003)1028 1460 y Fw(.)63 b(F)-8 b(urthermore)40
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b Fw(\()p Fn(\026)p Fw(\)\))37 b(crosses)109 1581 y(the)31
b(fra)m(y)m(ed)i(b)s(oundary)e(transv)m(ersely)j(|)d(this)h(is)g(ac)m
(hiev)m(ed)i(through)d(the)g(condition)h Fn(\014)3371
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1581 y Fw(\))c Fk(6)p Fw(=)f(0;)32 b(in)109 1701 y(fact)37
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g Fn(n)p Fw({tori)g(and)h(for)e(the)i(\()p Fn(n)17 b
Fw(+)g(1\){tori)30 b(the)g(path)109 1942 y(sta)m(ys)41
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(path)f(an)h(attracting)f Fn(n)p Fw({torus,)j(not)109
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(\015o)m(w,)i(b)s(ecomes)g(rep)s(elling,)f(with)g(an)e(attracting)109
2182 y(\()p Fn(n)17 b Fw(+)g(1\){torus,)30 b(again)g(not)f(necessarily)
k(but)d(`often')g(with)h(a)f(quasi-p)s(erio)s(dic)h(\015o)m(w,)g
(bifurcating)f(o\013.)109 2303 y(One)j(also)f(sp)s(eaks)i(of)e(a)h
(Hopf{Landau)f(bifurcation)h([5].)109 2447 y(Out)23 b(of)h(all)f(paths)
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b(,)25 b(only)g(the)f(ones)g(passing)h(through)109 2568
y(some)46 b Fn(\026)425 2531 y Fg(\003)513 2568 y Fk(2)k(G)688
2583 y Fm(\034)t(;\015)832 2568 y Fw(undergo)c(the)g(ab)s(o)m(v)m(e)g
(Hopf{Landau)f(bifurcation,)k(but)c(since)i Fk(G)3351
2583 y Fm(\034)t(;\015)3496 2568 y Fw(has)e(large)109
2688 y(relativ)m(e)d(measure)h(this)f(happ)s(ens)h(with)f(high)f
(probabilit)m(y)-8 b(.)71 b(F)-8 b(or)41 b(a)g(giv)m(en)i(path)e(that)h
(passes)h(the)109 2808 y(fra)m(y)m(ed)j(b)s(oundary)g(through)g(a)f
(resonance)i(bubble,)k(in)46 b(the)g(complemen)m(t)h(of)f(the)g(disks)h
(\(16\))o(,)i(a)109 2929 y(further)30 b(analysis)h(of)e(the)h(dynamics)
i(inside)f(that)f(resonance)h(bubble)g(is)f(needed)i(to)d(clarify)h
(the)g(\014ne)109 3049 y(details)j(of)f(the)h(bifurcation)g(along)f
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(bifurcation.)74 b(F)-8 b(or)41 b(a)109 3338 y(treatmen)m(t)33
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(tre-saddle)g(bifurcation)109 3811 y Fw(In)f(an)g(in)m(tegrable)h
(Hamiltonian)g(system)h(the)e(necessary)j(parameters)e(to)e(con)m(trol)
i(the)f(in)m(ternal)109 3931 y(frequencies)36 b(of)e(an)g(in)m(v)-5
b(arian)m(t)34 b(torus)h(are)f(built-in)g(in)m(to)g(the)h(system)h(as)e
(tori)g(are)g(parametrised)h(b)m(y)109 4051 y(the)29
b(actions)h(conjugate)f(to)f(the)i(toral)e(angles.)43
b(W)-8 b(e)30 b(restrict)g(to)e(the)i(case)g Fn(n)e Fw(=)f(2)i(of)f(in)
m(v)-5 b(arian)m(t)30 b(2{tori)109 4172 y(in)j(3)f(degrees)i(of)f
(freedom.)45 b(Using)33 b(Kolmogoro)m(v's)g(non-degeneracy)i(condition)
e(on)g(the)g(frequency)109 4292 y(mapping)46 b(w)m(e)g(ma)m(y)g(simply)
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Fl(R)1057 4376 y Fj(2)1131 4413 y Fw(the)f(Diophan)m(tine)g(conditions)
h(\(6\))e(yield)i(one)f(discon)m(tin)m(uous)i(direction)109
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f(the)h(half)f(lines,)k(putting)d(us)f(e\013ectiv)m(ely)j(in)m(to)e
(the)109 4653 y(situation)33 b(of)f(a)g(1{dimensional)i(parameter)f
Fn(\026)p Fw(.)109 4822 y(During)38 b(a)h(cen)m(tre-saddle)i
(bifurcation)f(a)f(cen)m(tre)h(and)f(a)g(saddle)h(meet)h(under)e(v)-5
b(ariation)39 b(of)g(a)g(pa-)109 4942 y(rameter)d(at)g(a)g(parab)s
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4967 y(0)3782 4906 y Fm(a)3782 4967 y Fj(0)3823 4942
y Fw(\),)109 5062 y Fn(a)f Fk(6)p Fw(=)g(0)i(|)g(and)g(v)-5
b(anish.)58 b(In)37 b(the)h(quasi-p)s(erio)s(dic)g(v)m(ersion)g(of)f
(this)h(bifurcation)f(the)h(equilibria)g(are)109 5183
y(replaced)d(b)m(y)g(in)m(v)-5 b(arian)m(t)34 b(tori)g(and)g(using)g
(the)g(parametrisation)h(b)m(y)f(the)h(actions)f(conjugate)g(to)g(the)
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b(alues)33 b(approac)m(h-)109 5424 y(ing)e(0)f(|)h(where)h(the)g(tori)e
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(y)h(the)e(absolute)109 329 y(v)-5 b(alue,)33 b(or)f(the)h(p)s(ositiv)m
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b(alues.)109 466 y(Suc)m(h)37 b(a)g(quasi-p)s(erio)s(dic)g(cen)m
(tre-saddle)i(bifurcation)e(p)s(ersists)h(a)e(su\016cien)m(tly)k(small)
d(p)s(erturbation)109 587 y(from)h(the)i(in)m(tegrable)g(Hamiltonian)f
(system)i(to)e(a)g(non-in)m(tegrable)g(one,)i(see)f([12,)f(13,)g(4)o
(].)63 b(Again)109 707 y(Diophan)m(tine)36 b(conditions)g(are)g(needed)
h(to)e(ac)m(hiev)m(e)j(this)e(p)s(ersistence)i(result.)54
b(The)36 b(parab)s(olic)f(tori)109 828 y(are)d(de\014ned)i(b)m(y)g(the)
f(additional)f(equation)1769 995 y(det)18 b(\012)55 b(=)h(0)109
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b(.)45 b(V)-8 b(ariation)31 b(of)h(the)g(frequency)i(ratio)e(is)g
(needed)i(along)109 1283 y(this)46 b(1{parameter)g(family)g(of)f(parab)
s(olic)h(2{tori)f(to)g(ensure)j(that)d(the)h(whole)h(family)f(do)s(es)g
(not)109 1403 y(disapp)s(ear)31 b(in)g(a)f(resonance)i(gap.)43
b(Under)31 b(this)h(requiremen)m(t)h(the)e(con)m(tin)m(uous)h(half)f
(lines)g(in)g(the)g(set)109 1524 y(of)39 b(Diophan)m(tine)i
(frequencies)h(are)e(transv)m(erse)i(to)e(the)g(1{dimensional)h(subset)
h(of)d(frequencies)k(of)109 1644 y(parab)s(olic)32 b(tori.)109
1799 y(On)f(the)g(h)m(yp)s(erb)s(olic)i(side)f(the)g(situation)f(is)h
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(bifurca-)109 1920 y(tion)36 b(|)f(next)j(to)d(Theorem)j(2.1)e(w)m(e)h
(can)f(again)g(apply)h(Theorem)h(2.2)d(to)h(\014ll)h(the)f(resonance)i
(gaps)109 2040 y(b)s(et)m(w)m(een)33 b(the)f(half)f(lines)i(emanating)f
(from)f(the)h(p)s(ersisten)m(t)h(parab)s(olic)e(tori.)43
b(Su\016cien)m(tly)34 b(far)d(a)m(w)m(a)m(y)109 2160
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(erturb)s(ed)i(h)m(yp)s(erb)s(olic)g(tori)e(forms)g(a)h(normally)109
2281 y(h)m(yp)s(erb)s(olic)26 b(in)m(v)-5 b(arian)m(t)25
b(manifold)g(that)f(p)s(ersists)j(the)e(small)g(p)s(erturbation)g(a)m
(w)m(a)m(y)h(from)f(in)m(tegrabilit)m(y)-8 b(,)109 2401
y(see)39 b([10)o(].)60 b(Note,)40 b(ho)m(w)m(ev)m(er,)i(that)c(the)g
(actions)h(conjugate)f(to)g(the)g(toral)f(angles)i(are)f(not)g
(external)109 2522 y(parameters,)i(but)f(phase)g(space)g(v)-5
b(ariables)39 b(to)f(whic)m(h)i(the)f(non-in)m(tegrable)g(p)s
(erturbation)f(assigns)109 2642 y(a)i(slo)m(w)i(drift.)69
b(The)41 b(individual)i(unp)s(erturb)s(ed)f(2{tori)e(do)g
Fq(not)h Fw(constitute)h(normally)g(h)m(yp)s(erb)s(olic)109
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(union)g(to)f(whic)m(h)i(Theorem)g(2.2)e(can)h(b)s(e)g(applied.)109
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i(to)d(parab)s(olic)h(tori)g(less)i(transparan)m(t.)63
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