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Edit File: extDyn.ps

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dup 0 /.notdef put
readonly def
/FontBBox{-5 -232 545 699}readonly def
/UniqueID 5000830 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMTI8
%!PS-AdobeFont-1.1: CMTI8 1.0
%%CreationDate: 1991 Aug 18 21:07:42
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-35 -250 1190 750}readonly def
/UniqueID 5000826 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
dup 54 /lessorequalslant put
dup 62 /greaterorequalslant put
readonly def
/FontBBox{8 -463 1331 1003}readonly def
/UniqueID 5031981 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 0 /.notdef put
readonly def
/FontBBox{-163 -250 1146 969}readonly def
/UniqueID 5000828 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: LINE10
%!PS-AdobeFont-1.1: LINE10 1.001
%%CreationDate: 1992 Oct 23 20:22:05
%%RevisionDate: 2001 Jun 05 20:22:05
% Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.001) readonly def
/Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def
/FullName (LINE10) readonly def
/FamilyName (LaTeX) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /LINE10 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 8 /a8 put
dup 72 /a72 put
readonly def
/FontBBox{-150 -150 1020 1020}readonly def
/UniqueID 5011940 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: LCIRCLE10
%!PS-AdobeFont-1.1: LCIRCLE10 1.001
%%CreationDate: 1992 Oct 23 20:21:59
%%RevisionDate: 2001 Jun 05 20:21:59
% Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.001) readonly def
/Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def
/FullName (LCIRCLE10) readonly def
/FamilyName (LaTeX) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /LCIRCLE10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 113 /a113 put
dup 115 /a115 put
readonly def
/FontBBox{-2000 -2000 2040 2040}readonly def
/UniqueID 5011942 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 8 /braceleftbig put
dup 9 /bracerightbig put
dup 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 26 /braceleftbigg put
dup 27 /bracerightbigg put
dup 80 /summationtext put
dup 88 /summationdisplay put
dup 110 /braceleftBig put
dup 111 /bracerightBig put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR5
%!PS-AdobeFont-1.1: CMR5 1.00B
%%CreationDate: 1992 Feb 19 19:55:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-341 -250 1304 965}readonly def
/UniqueID 5000788 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY7
%!PS-AdobeFont-1.1: CMSY7 1.0
%%CreationDate: 1991 Aug 15 07:21:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-15 -951 1252 782}readonly def
/UniqueID 5000817 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 63 /emptyset put
dup 67 /C put
dup 78 /N put
dup 82 /R put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
/UniqueID 5031982 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI5
%!PS-AdobeFont-1.1: CMMI5 1.100
%%CreationDate: 1996 Aug 02 08:21:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{37 -250 1349 750}readonly def
/UniqueID 5087380 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueID 5000790 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 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 0 /.notdef put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMCSC10
%!PS-AdobeFont-1.1: CMCSC10 1.0
%%CreationDate: 1991 Aug 18 17:46:49
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMCSC10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMCSC10 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 /.notdef put
readonly def
/FontBBox{14 -250 1077 750}readonly def
/UniqueID 5000772 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR6
%!PS-AdobeFont-1.1: CMR6 1.0
%%CreationDate: 1991 Aug 20 16:39:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR6 def
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/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 /.notdef put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
/UniqueID 5000789 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI8
%!PS-AdobeFont-1.1: CMMI8 1.100
%%CreationDate: 1996 Jul 23 07:53:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 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 /.notdef put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueID 5000818 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 0 /.notdef put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 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 /.notdef put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 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 0 /.notdef put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueID 5000768 def
currentdict end
currentfile eexec
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%%Page: 2 2
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%%Page: 3 3
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y Fl(~)402 1675 y Fm(E)451 1683 y Fh(8)487 1650 y Fo(\()p
Fn(\037)p Fo(\))23 b(=)724 1594 y(1)p 724 1631 V 724
1707 a(6)775 1650 y(\()p Fn(\013)860 1607 y Fl(\(1\))860
1672 y(1)969 1650 y Fo(+)18 b Fn(\013)1105 1607 y Fl(\(1\))1105
1672 y(2)1213 1650 y Fo(+)g Fn(\013)1349 1607 y Fl(\(1\))1349
1672 y(3)1457 1650 y Fo(+)g Fn(\013)1593 1607 y Fl(\(1\))1593
1672 y(4)1701 1650 y Fo(+)g Fn(\013)1837 1607 y Fl(\(1\))1837
1672 y(5)1945 1650 y Fo(+)g(2)p Fn(\013)2123 1607 y Fl(\(2\))2123
1672 y(1)2230 1650 y Fo(+)g(2)p Fn(\013)2408 1607 y Fl(\(2\))2408
1672 y(2)2516 1650 y Fo(+)g(3)p Fn(\013)2694 1607 y Fl(\(3\))2694
1672 y(1)2783 1650 y Fo(\))p Fn(:)100 1945 y Fo(Recall)32
b(that)i(in)f(case)f(when)i Fn(\015)i Fo(=)c Fn(!)1275
1957 y Fl(\000)1320 1945 y Fo(\()p Fn(\037)p Fo(\))i(the)f(algebras)e
Fv(P)2005 1960 y Fl(\000)p Fm(;\037;!)2169 1968 y Fh(\000)2207
1960 y Fl(\()p Fm(\037)p Fl(\))2338 1945 y Fo(are)h(PI-algebra)f(\(see)
i([)p Fw(?)p Fo(]\))0 2045 y(and)23 b(irreducible)g(represen)n(tations)
f(are)g(of)i(dimension)f(not)h(greater)d(that)j(2,3,4)f(and)g(6)g(resp)
r(ectiv)n(ely)0 2146 y(for)146 2125 y(~)127 2146 y Fn(D)196
2158 y Fl(4)233 2146 y Fo(,)303 2125 y(~)284 2146 y Fn(E)345
2158 y Fl(6)382 2146 y Fo(,)452 2125 y(~)433 2146 y Fn(E)494
2158 y Fl(7)532 2146 y Fo(,)k(and)763 2125 y(~)744 2146
y Fn(E)805 2158 y Fl(8)870 2146 y Fo(graphs.)100 2245
y(Usign)39 b(these)g(functionals)g(it)h(has)f(b)r(een)h(sho)n(wn)e
(that)i(an)f(action)g(of)g(\010)2475 2215 y Fl(+)2569
2245 y Fo(functor)h(could)f(b)r(e)0 2345 y(written)28
b(in)g(the)g(follo)n(wing)e(w)n(a)n(y:)0 2499 y Fw(Theorem)j(1.)40
b Fd(\(se)l(e)28 b Fo([)p Fw(?)p Fo(])p Fd(\))g(L)l(et)g
Fo(\000)g Fd(b)l(e)g(an)g(extende)l(d)g(Dynkin)g(gr)l(aph)i(then)e(fol)
t(lowing)i(formulae)g(holds)0 2642 y Fo(\(1\))534 b(\(\010)732
2608 y Fl(+)788 2642 y Fo(\))820 2608 y Fm(n)865 2642
y Fo(\()p Fn(\037)p Fo(;)14 b Fn(\015)5 b Fo(\))23 b(=)g(\()p
Fn(v)s Fo(\()p Fn(t;)14 b(\037)p Fo(\))19 b Fv(\000)f
Fn(u)p Fo(\()p Fn(t;)c(n)p Fo(\))p Fn(\025)p Fo(;)g Fn(w)1910
2654 y Fl(1)1948 2642 y Fo(\()p Fn(t;)g(\037)p Fo(\))19
b Fv(\000)f Fn(w)2292 2654 y Fl(2)2330 2642 y Fo(\()p
Fn(n)p Fo(\))p Fn(\025)p Fo(\))p Fn(;)100 2785 y Fd(wher)l(e)31
b Fn(\025)24 b Fo(=)g Fn(!)548 2797 y Fl(\000)593 2785
y Fo(\()p Fn(\037)p Fo(\))19 b Fv(\000)g Fn(\015)5 b
Fd(,)30 b Fn(t)24 b Fo(=)g([)1107 2752 y Fm(n)p 1091
2766 74 4 v 1091 2813 a(k)1126 2821 y Fh(\000)1175 2785
y Fo(])p Fd(,)31 b Fn(k)1312 2795 y Fl(~)1297 2810 y
Fm(D)1351 2818 y Fh(4)1412 2785 y Fo(=)24 b(2)p Fn(;)14
b(k)1637 2795 y Fl(~)1623 2810 y Fm(E)1672 2818 y Fh(6)1732
2785 y Fo(=)23 b(6)p Fn(;)14 b(k)1957 2795 y Fl(~)1942
2810 y Fm(E)1991 2818 y Fh(7)2052 2785 y Fo(=)23 b(12)p
Fn(;)14 b(k)2318 2795 y Fl(~)2304 2810 y Fm(E)2353 2818
y Fh(8)2413 2785 y Fo(=)23 b(30)p Fd(.)40 b(Notic)l(e)31
b(that)f(the)0 2892 y(ve)l(ctor)g Fn(v)s Fo(\()p Fn(t;)14
b(n)p Fo(\))31 b Fd(\(as)f(wel)t(l)h(as)f(numb)l(ers)f
Fn(w)1305 2904 y Fl(1)1343 2892 y Fo(\()p Fn(t;)14 b(n)p
Fo(\))p Fd(\))30 b(dep)l(ends)h(on)f Fn(\037)g Fd(and)g(indep)l(endent)
h(on)f Fn(\025)g Fd(and)h(the)0 2992 y(c)l(omp)l(onents)f(of)g(the)g
(ve)l(ctor)g Fn(u)p Fo(\()p Fn(t;)14 b(n)p Fo(\))30 b
Fd(ar)l(e)g(strictly)g(incr)l(e)l(asing)g(with)h(n.)0
3162 y Fw(Lemma)37 b(1.)44 b Fd(L)l(et)34 b Fn(u)659
3119 y Fl(\()p Fm(s)p Fl(1\))659 3184 y Fm(p)p Fl(1)779
3162 y Fo(\()p Fn(t;)14 b(n)p Fo(\))35 b Fd(and)g Fn(u)1209
3119 y Fl(\()p Fm(s)p Fl(1\))1209 3184 y Fm(p)p Fl(2)1329
3162 y Fo(\()p Fn(t;)14 b(n)p Fo(\))35 b Fd(b)l(e)f(the)h(c)l(omp)l
(onents)f(of)i(the)e(ve)l(ctor)h Fn(u)p Fo(\()p Fn(t;)14
b(n)p Fo(\))35 b Fd(\(her)l(e)0 3291 y(by)d(c)l(omp)l(onent)g
Fn(u)574 3248 y Fl(\()p Fm(j)s Fl(\))574 3314 y Fm(i)661
3291 y Fo(\()p Fn(t;)14 b(n)p Fo(\))32 b Fd(we)g(me)l(an)g(a)h(c)l(omp)
l(onent)f(that)g(c)l(orr)l(esp)l(onds)g(to)g Fn(\013)2489
3248 y Fl(\()p Fm(j)s Fl(\))2489 3314 y Fm(i)2609 3291
y Fd(in)g(the)g(char)l(acter)0 3409 y Fn(\037)p Fd(\))e(then)f
Fn(u)348 3366 y Fl(\()p Fm(s)p Fl(1\))348 3431 y Fm(p)p
Fl(1)468 3409 y Fo(\()p Fn(t;)14 b(n)p Fo(\))24 b(=)e
Fn(u)808 3366 y Fl(\()p Fm(s)p Fl(2\))808 3431 y Fm(p)p
Fl(2)928 3409 y Fo(\()p Fn(t;)14 b(n)p Fo(\))30 b Fd(i\013)g
Fn(p)p Fo(1)23 b(=)f Fn(p)p Fo(2)29 b Fd(and)h Fn(u)1761
3366 y Fl(\()p Fm(s)p Fl(1\))1761 3431 y Fm(p)p Fl(1)1881
3409 y Fo(\()p Fn(t;)14 b(n)p Fo(\))24 b Fn(<)e(u)2221
3366 y Fl(\()p Fm(s)p Fl(2\))2221 3431 y Fm(p)p Fl(2)2341
3409 y Fo(\()p Fn(t;)14 b(n)p Fo(\))30 b Fd(i\013)g Fn(p)p
Fo(1)23 b Fn(<)f(p)p Fo(2)p Fd(.)0 3563 y(Pr)l(o)l(of.)43
b Fo(Direct)28 b(calculations.)2161 b Fc(\003)100 3725
y Fo(Using)27 b(the)i(result)f(of)g(the)g(Theorem)f(1)h(w)n(e)g(can)g
(describ)r(e)f(the)i(sets)f(\006)2332 3737 y Fl(\000)p
Fm(;\037)2438 3725 y Fo(.)38 b(Indeed,)29 b(one)e(can)h(\014x)0
3824 y Fn(\015)35 b Fo(and)30 b(apply)f(functor)h(\010)823
3794 y Fl(+)908 3824 y Fo(un)n(til)h(w)n(e)f(can)f(easily)g(c)n(hec)n
(k)h(are)f(there)g(represen)n(tations)f(of)i(obtained)0
3924 y(algebra.)i(This)19 b(requires)f(the)i(kno)n(wledge)e(of)h
(structure)f(of)h(the)h(set)f(\006)2172 3934 y Fl(~)2168
3949 y(\000)p Fm(;\037)2274 3924 y Fo(.)34 b(Set)20 b(\006)2541
3934 y Fl(~)2526 3949 y Fm(D)2580 3957 y Fh(4)2613 3949
y Fm(;\037)2697 3924 y Fo(w)n(as)e(describ)r(ed)0 4031
y(using)24 b(this)h(tec)n(hnique)f(\(see)g(next)h(c)n(hapter\),)g(and)f
(the)h(follo)n(wing)e(complete)h(description)g(of)g(the)h(set)0
4130 y(\006)60 4142 y Fm(D)114 4150 y Fh(4)147 4142 y
Fm(;\037)240 4130 y Fo(\(see)i([)p Fw(?)p Fo(]\))0 4373
y(\(2\))280 b(\006)446 4388 y Fm(D)500 4396 y Fh(4)532
4388 y Fm(;)p Fl(\()p Fm(\013)621 4396 y Fh(1)654 4388
y Fm(;\013)717 4396 y Fh(2)749 4388 y Fm(;\013)812 4396
y Fh(3)844 4388 y Fl(\))897 4373 y Fo(=)23 b Fv(f)p Fo(0)p
Fv(g)17 b([)i(f)1244 4294 y Fg(X)1249 4472 y Fm(i)p Fi(2)p
Fm(J)1377 4373 y Fn(\013)1430 4385 y Fm(i)1458 4373 y
Fn(;)14 b(J)31 b Fv(\032)22 b(f)p Fo(1)p Fn(;)14 b Fo(2)p
Fn(;)g Fo(3)p Fv(gg)i([)j(f)p Fo(\()p Fn(\013)2202 4385
y Fl(1)2257 4373 y Fo(+)f Fn(\013)2393 4385 y Fl(2)2449
4373 y Fo(+)g Fn(\013)2585 4385 y Fl(3)2622 4373 y Fo(\))p
Fn(=)p Fo(2)p Fv(g)p Fn(;)0 4594 y Fo(but)24 b(for)e(other)h(graphs)f
(this)h(task)g(app)r(ears)f(to)h(b)r(e)h(com)n(binatory)d(hard)i(and)g
(just)g(one)g(in\014nite)h(series)0 4694 y(w)n(as)j(found.)0
4848 y Fw(Lemma)33 b(2.)42 b Fd(L)l(et)31 b Fv(A)668
4860 y Fm(n)745 4848 y Fd(b)l(e)g(an)g(algebr)l(a)i(gener)l(ate)l(d)e
(by)h(n-tuples)e(of)i(pr)l(oje)l(ctions)h Fn(p)2607 4818
y Fl(2)2607 4870 y Fm(i)2670 4848 y Fo(=)25 b Fn(p)2802
4818 y Fi(\003)2802 4870 y Fm(i)2866 4848 y Fo(=)g Fn(p)2998
4860 y Fm(i)3057 4848 y Fd(and)0 4948 y(with)30 b(the)g(r)l(elation)996
5056 y Fn(\013)1049 5068 y Fl(1)1086 5056 y Fn(p)1128
5068 y Fl(1)1184 5056 y Fo(+)18 b Fn(\013)1320 5068 y
Fl(2)1357 5056 y Fn(p)1399 5068 y Fl(2)1455 5056 y Fo(+)g
Fv(\001)c(\001)g(\001)k Fo(+)g Fn(\013)1789 5068 y Fm(n)1834
5056 y Fn(p)1876 5068 y Fm(n)1944 5056 y Fo(=)23 b Fn(\013)2085
5068 y Fm(n)2130 5056 y Fn(e;)0 5181 y Fd(\()p Fn(\013)87
5193 y Fm(i)141 5181 y Fd(ar)l(e)28 b(p)l(ositive)g(r)l(e)l(al)f(numb)l
(ers)f(and)h Fn(e)g Fd(is)g(unit)f(element)h(in)g Fv(A)2009
5193 y Fm(n)2054 5181 y Fd(\),)h(then)e(such)h(algebr)l(a)i(has)e(at)g
(le)l(ast)0 5281 y(one)j(r)l(epr)l(esentation.)p eop
end
%%Page: 4 4
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b(ANTYN)23 b(YUSENK)n(O)0 249 y Fd(Pr)l(o)l(of.)43 b
Fo(It)28 b(is)f(easily)g(pro)n(v)n(ed)f(that)i(the)f(collection)g(of)h
(the)g(pro)5 b(jections)26 b Fn(P)2341 261 y Fm(i)2392
249 y Fo(=)c(0)p Fn(;)14 b(i)23 b Fv(6)p Fo(=)f Fn(n)28
b Fo(and)f Fn(P)2989 261 y Fm(n)3057 249 y Fo(=)c Fn(I)0
349 y Fo(form)k(the)h(represen)n(tation)e(of)i Fv(A)1043
361 y Fm(n)1088 349 y Fo(.)2012 b Fc(\003)933 563 y Fo(2.)41
b Fp(Description)32 b(of)g(the)f(set)h Fo(\006)2118 573
y Fl(~)2103 588 y Fm(D)2157 596 y Fh(4)2190 588 y Fm(;\037)100
734 y Fo(Denote)27 b(the)g(c)n(haracter)e Fn(\037)i Fo(on)1100
713 y(~)1081 734 y Fn(D)1150 746 y Fl(4)1214 734 y Fo(b)n(y)f
Fn(\037)d Fo(=)g(\()p Fn(\013)1576 746 y Fl(1)1614 734
y Fo(;)14 b Fn(\013)1704 746 y Fl(2)1741 734 y Fo(;)g
Fn(\013)1831 746 y Fl(3)1868 734 y Fo(;)g Fn(\013)1958
746 y Fl(4)1996 734 y Fo(\))27 b(and)f Fn(\013)e Fo(=)e
Fn(\013)2432 746 y Fl(1)2487 734 y Fo(+)16 b Fn(\013)2621
746 y Fl(2)2675 734 y Fo(+)h Fn(\013)2810 746 y Fl(3)2864
734 y Fo(+)g Fn(\013)2999 746 y Fl(4)3036 734 y Fo(.)37
b(A)n(t)0 833 y(\014rst)27 b(w)n(e)h(state)f(some)g(c)n(haracteristics)
e(of)j(the)g(set)f(\006)1690 843 y Fl(~)1675 858 y Fm(D)1729
866 y Fh(4)1762 858 y Fm(;\037)1827 833 y Fo(.)0 999
y Fw(Lemma)32 b(3.)40 b Fd(\()p Fo([)p Fw(?)p Fo(])p
Fd(\))141 1124 y Fo(\(1\))i(\006)364 1134 y Fl(~)349
1149 y Fm(D)403 1157 y Fh(4)435 1149 y Fm(;\037)524 1124
y Fv(\032)22 b Fo([0)p Fn(;)14 b(\013)p Fo(];)141 1231
y(\(2\))42 b(\006)364 1241 y Fl(~)349 1256 y Fm(D)403
1264 y Fh(4)435 1256 y Fm(;\037)524 1231 y Fv(3)602 1169
y Fg(P)690 1256 y Fm(i)p Fi(2)p Fm(J)818 1231 y Fn(\013)871
1243 y Fm(i)899 1231 y Fn(;)14 b(J)31 b Fv(\032)23 b(f)p
Fo(0)p Fn(;)14 b Fo(1)p Fn(;)g Fo(2)p Fn(;)g Fo(3)p Fn(;)g
Fo(4)p Fv(g)p Fo(;)141 1338 y(\(3\))42 b Fn(\034)32 b
Fv(2)24 b Fo(\006)511 1348 y Fl(~)496 1363 y Fm(D)550
1371 y Fh(4)583 1363 y Fm(;\037)671 1338 y Fv(\()-14
b(\))23 b Fn(\013)c Fv(\000)f Fn(\034)33 b Fv(2)23 b
Fo(\006)1223 1348 y Fl(~)1208 1363 y Fm(D)1262 1371 y
Fh(4)1295 1363 y Fm(;\037)1360 1338 y Fo(;)100 1504 y(Since)k(\006)391
1514 y Fl(~)376 1529 y Fm(D)430 1537 y Fh(4)463 1529
y Fm(;\037)556 1504 y Fo(is)h(symmetric)f(around)1335
1471 y Fm(\013)p 1335 1485 44 4 v 1340 1532 a Fl(2)1416
1504 y Fo(w)n(e)g(study)h(the)g(set)g(\006)2115 1514
y Fl(~)2100 1529 y Fm(D)2154 1537 y Fh(4)2186 1529 y
Fm(;\037)2270 1504 y Fv(\\)19 b Fo([0)p Fn(;)2455 1471
y Fm(\013)p 2455 1485 V 2460 1532 a Fl(2)2509 1504 y
Fo(\).)100 1606 y(Notice)26 b(that)h(all)f(comp)r(onen)n(ts)f(of)i(the)
g(c)n(haracter)d Fn(\037)i Fo(are)g(required)f(to)h(b)r(e)h(less)f
(than)2810 1574 y Fm(\013)p 2810 1588 V 2815 1635 a Fl(2)2863
1606 y Fo(.)37 b(Indeed,)0 1706 y(if)32 b(some)f(co)r(e\016cien)n(t)g
(is)g(equal)g(or)f(greater)g(than)1591 1673 y Fm(\013)p
1591 1687 V 1596 1734 a Fl(2)1676 1706 y Fo(then)i(corresp)r(onding)d
(pro)5 b(jection)30 b(is)h(equal)g(to)0 1819 y(0)d(or)g
Fn(I)35 b Fo(in)29 b(the)f(represen)n(tation)f(and)h(problem)g
(simpli\014es)h(since)f(instead)g(of)2483 1798 y(~)2464
1819 y Fn(D)2533 1831 y Fl(4)2598 1819 y Fo(graph)f(w)n(e)h(obtain)0
1919 y Fn(D)69 1931 y Fl(4)134 1919 y Fo(graph)e(where)h(solution)g(is)
h(kno)n(wn.)100 2018 y(Ha)n(ving)39 b(written)i(the)h(action)e(of)g
(\(\010)1318 1988 y Fl(+)1374 2018 y Fo(\))1406 1988
y Fm(n)1492 2018 y Fo(functor)h(on)f(pair)g(\()p Fn(\037)p
Fo(;)14 b Fn(\015)5 b Fo(\))41 b(\(and)g(applied)g(\()p
Fw(??)p Fo(\))g(and)0 2118 y(Lem.)p Fw(??)p Fo(\))28
b(w)n(e)f(build)i(the)f(follo)n(wing)e(series)h(in)g(\006)1554
2128 y Fl(~)1538 2143 y Fm(D)1592 2151 y Fh(4)1625 2143
y Fm(;\037)1690 2118 y Fo(.)0 2279 y Fw(Lemma)39 b(4.)45
b Fd(The)37 b(set)f Fo(\006)853 2289 y Fl(~)838 2304
y Fm(D)892 2312 y Fh(4)925 2305 y Fm(;\037)1026 2279
y Fd(c)l(ontains)g(the)g(in\014nity)g(series)h Fo(\006)2101
2291 y Fi(1)2207 2279 y Fd(with)f(limit)h(p)l(oint)2823
2247 y Fm(\013)p 2823 2261 V 2828 2308 a Fl(2)2912 2279
y Fd(and)g(the)0 2382 y(\014nite)29 b(series)i Fo(\006)509
2394 y Fl(0)546 2382 y Fd(.)39 b(This)31 b(two)e(series)i(ar)l(e)f
(describ)l(e)l(d)h(by)f(the)g(fol)t(lowing)j(rule:)141
2507 y Fo(\(1\))42 b Fd(when)30 b Fn(\013)554 2519 y
Fl(2)610 2507 y Fo(+)18 b Fn(\013)746 2519 y Fl(3)806
2507 y Fn(>)23 b(\013)947 2519 y Fl(1)1003 2507 y Fo(+)18
b Fn(\013)1139 2519 y Fl(4)1206 2507 y Fd(then)29 b Fo(\006)1450
2519 y Fi(1)1544 2507 y Fo(=)1631 2439 y Fg(\010)1690
2474 y Fm(\013)p 1690 2488 V 1695 2535 a Fl(2)1761 2507
y Fv(\000)1854 2473 y Fm(\013)1897 2481 y Fh(1)p 1854
2488 76 4 v 1855 2535 a Fl(2)p Fm(n)1940 2507 y Fv(j)p
Fn(n)23 b Fv(2)g Fj(N)2174 2439 y Fg(\011)2252 2507 y
Fd(and)289 2639 y Fo(\006)349 2651 y Fl(0)409 2639 y
Fo(=)497 2547 y Fg(n)562 2607 y Fm(\013)p 562 2621 44
4 v 567 2668 a Fl(2)634 2639 y Fv(\000)747 2605 y Fm(\013)p
Fi(\000)p Fl(2)p Fm(\013)918 2613 y Fh(4)p 727 2620 245
4 v 727 2668 a Fl(2\(2)p Fm(n)p Fi(\000)p Fl(1\))981
2639 y Fv(j)p Fn(n)g(<)1386 2607 y Fl(1)p 1174 2621 457
4 v 1174 2668 a Fm(\013)1217 2676 y Fh(2)1250 2668 y
Fl(+)p Fm(\013)1344 2676 y Fh(3)1376 2668 y Fi(\000)p
Fm(\013)1471 2676 y Fh(1)1504 2668 y Fi(\000)p Fm(\013)1599
2676 y Fh(4)1641 2639 y Fn(;)14 b(n)23 b Fv(2)g Fj(N)1889
2547 y Fg(o)141 2797 y Fo(\(2\))42 b Fd(when)30 b Fn(\013)554
2809 y Fl(2)610 2797 y Fo(+)18 b Fn(\013)746 2809 y Fl(3)806
2797 y Fn(<)23 b(\013)947 2809 y Fl(1)1003 2797 y Fo(+)18
b Fn(\013)1139 2809 y Fl(4)1206 2797 y Fd(then)29 b Fo(\006)1450
2809 y Fi(1)1544 2797 y Fo(=)1631 2705 y Fg(n)1697 2765
y Fm(\013)p 1697 2779 44 4 v 1702 2826 a Fl(2)1768 2797
y Fv(\000)1881 2763 y Fm(\013)p Fi(\000)p Fl(2)p Fm(\013)2052
2771 y Fh(4)p 1861 2778 245 4 v 1861 2826 a Fl(2\(2)p
Fm(n)p Fi(\000)p Fl(1\))2115 2797 y Fv(j)p Fn(n)23 b
Fv(2)h Fj(N)2350 2705 y Fg(o)2435 2797 y Fd(and)289 2955
y Fo(\006)349 2967 y Fl(0)409 2955 y Fo(=)497 2863 y
Fg(n)562 2922 y Fm(\013)p 562 2936 44 4 v 567 2984 a
Fl(2)634 2955 y Fv(\000)727 2921 y Fm(\013)770 2929 y
Fh(1)p 727 2936 76 4 v 728 2984 a Fl(2)p Fm(n)812 2955
y Fv(j)p Fn(n)f(<)1218 2922 y Fl(1)p 1006 2936 457 4
v 1006 2984 a Fm(\013)1049 2992 y Fh(1)1081 2984 y Fl(+)p
Fm(\013)1175 2992 y Fh(4)1208 2984 y Fi(\000)p Fm(\013)1303
2992 y Fh(2)1335 2984 y Fi(\000)p Fm(\013)1430 2992 y
Fh(3)1473 2955 y Fn(;)14 b(n)22 b Fv(2)i Fj(N)1721 2863
y Fg(o)141 3088 y Fo(\(3\))42 b Fd(when)30 b Fn(\013)554
3100 y Fl(2)610 3088 y Fo(+)18 b Fn(\013)746 3100 y Fl(3)806
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%%Page: 5 5
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