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readonly def
/FontBBox{-5 -232 545 699}readonly def
/UniqueID 5000830 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY5
%!PS-AdobeFont-1.1: CMSY5 1.0
%%CreationDate: 1991 Aug 15 07:21:16
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{21 -944 1448 791}readonly def
/UniqueID 5000815 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: 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: 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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1A08EE7B31EBCA5A369BA18D4446B2CEBE067D2FC627F6B0F42AAD3FBA44B77E
9F00E4568EC82295C97EC14BCD3192F1B4D780B748EF1A6B586033C58C14420B
B9897F7C029E1DE9D32670633A8D33750A57EF7694D92AEDBEAA565A8EB9612F
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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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1D56801ACCF98612DE2C19685E0F4D52369AD642D169AB57DAB10665C6C01538
497544391FABD08A483766E9B5C7ABA9A537C053A8ADC16DEBD8B5C9E1EDEB21
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0B49839C58E426531833D30F153863E92A79516C2878AEE6916F0FA78F94714E
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4A334B4D9B914EA59194239AAD1358BC269B8CBD35A7685ACB29282D46440A38
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0CDBCECDD2DFE4EE609FBBCC258274325227E6D3B23B6E5690A6674832EDC5FA
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53E18A79AEE6882811139DB1284020269452D2BF0D06BB70CF9A6742ADF537DA
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9BDEB6A39A6D5A17625C7743CACCBA84D4034804C752008C7CED6AB3655FFAFE
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B7761B6FE21F67D992BCDC83C8B6B34FB39BCC94DF403D220AFBD1A40329A87A
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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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532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470
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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 2 /bracketleftbig put
dup 3 /bracketrightbig put
dup 16 /parenleftBig put
dup 17 /parenrightBig put
dup 20 /bracketleftbigg put
dup 21 /bracketrightbigg put
dup 26 /braceleftbigg put
dup 27 /bracerightbigg put
dup 34 /bracketleftBigg put
dup 35 /bracketrightBigg put
dup 80 /summationtext put
dup 88 /summationdisplay put
dup 91 /uniondisplay 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
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end readonly def
/FontName /CMMI5 def
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/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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/FontBBox{37 -250 1349 750}readonly def
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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
/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{-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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y(t)n(yp)r(e)i Fo(A)249 976 y Fn(n)294 964 y Fp(,)g Fo(D)414
976 y Fn(n)459 964 y Fp(,)g Fo(E)571 976 y Fm(6)608 964
y Fp(,)g Fo(E)720 976 y Fm(7)757 964 y Fp(,)g(or)f Fo(E)971
976 y Fm(8)1008 964 y Fp(:)598 1172 y Ff(s)299 b(s)50
b(q)66 b(q)g(q)g(s)299 b(s)p 598 1173 333 4 v 1262 1173
V 627 1076 a Fo(A)689 1088 y Fn(n)1926 1338 y Ff(s)1926
1006 y(s)2258 1172 y(s)50 b(q)66 b(q)g(q)g(s)299 b(s)1926
1338 y Fe(\010)2009 1296 y(\010)2092 1255 y(\010)2175
1213 y(\010)1926 1047 y(H)2009 1089 y(H)2092 1130 y(H)2175
1172 y(H)p 2590 1173 V 1886 1192 a Fo(D)1955 1204 y Fn(n)764
1737 y Ff(s)133 b(s)g(s)g(s)g(s)1096 1571 y(s)p 764 1739
167 4 v 930 1739 V 1096 1739 V 1262 1739 V 1094 1737
4 167 v 798 1642 a Fo(E)859 1654 y Fm(6)1926 1737 y Ff(s)g(s)g(s)g(s)g
(s)g(s)2258 1571 y(s)p 1926 1739 167 4 v 2092 1739 V
2258 1739 V 2424 1739 V 2590 1739 V 2257 1737 4 167 v
1960 1642 a Fo(E)2021 1654 y Fm(7)1262 2137 y Ff(s)g(s)g(s)g(s)g(s)g(s)
g(s)1594 1971 y(s)p 1262 2139 167 4 v 1428 2139 V 1594
2139 V 1760 2139 V 1926 2139 V 2092 2139 V 1592 2137
4 167 v 1296 2041 a Fo(E)1357 2053 y Fm(8)0 2339 y Fp(then)19
b Fw(P)238 2351 y Fm(\000)p Fn(;\037;\015)421 2339 y
Fp(is)f(\014nite)h(dimensional,)h(if)e(\000)h(is)f(an)g(extended)h
(Dynkin)g(graph)e(of)h(the)h(t)n(yp)r(e)2759 2318 y(~)2739
2339 y Fo(D)2808 2351 y Fm(4)2845 2339 y Fo(;)2902 2318
y Fp(~)2882 2339 y Fo(E)2943 2351 y Fm(6)2981 2339 y
Fo(;)3037 2318 y Fp(~)3018 2339 y Fo(E)3079 2351 y Fm(7)3116
2339 y Fo(;)3172 2318 y Fp(~)3153 2339 y Fo(E)3214 2351
y Fm(8)847 2713 y Ff(s)216 b(s)g(s)1096 2463 y(s)1096
2962 y(s)p 847 2714 250 4 v 1096 2714 V 1094 2713 4 250
v 1094 2962 V 896 2513 a Fp(~)877 2534 y Fo(D)946 2546
y Fm(4)1677 2796 y Ff(s)133 b(s)g(s)g(s)g(s)2009 2630
y(s)2009 2463 y(s)p 1677 2797 167 4 v 1843 2797 V 2009
2797 V 2175 2797 V 2007 2796 4 167 v 2007 2630 V 1730
2679 a Fp(~)1711 2700 y Fo(E)1772 2712 y Fm(6)515 3278
y Ff(s)g(s)g(s)g(s)g(s)g(s)g(s)1013 3112 y(s)p 515 3280
167 4 v 681 3280 V 1013 3280 V 847 3280 V 1179 3280 V
1345 3280 V 1011 3278 4 167 v 568 3162 a Fp(~)548 3183
y Fo(E)609 3195 y Fm(7)1677 3278 y Ff(s)g(s)g(s)g(s)g(s)g(s)g(s)g(s)
2009 3112 y(s)p 1677 3280 167 4 v 1843 3280 V 2009 3280
V 2175 3280 V 2341 3280 V 2507 3280 V 2673 3280 V 2007
3278 4 167 v 1730 3162 a Fp(~)1711 3183 y Fo(E)1772 3195
y Fm(8)0 3461 y Fp(then)31 b(the)h(algebra)d Fw(P)691
3473 y Fm(\000)p Fn(;\037;\015)886 3461 y Fp(is)i(in\014nite)h
(dimensional)e(and)h(of)g(p)r(olynomial)f(gro)n(wth,)h(and)g(\014nally)
g(if)0 3561 y(\000)36 b(neither)g(a)f(Dynkin)i(graph)e(nor)g(an)h
(extended)g(Dynkin)g(graph)f(then)h Fw(P)2444 3573 y
Fm(\000)p Fn(;\037;\015)2645 3561 y Fp(con)n(tains)f(a)g(free)0
3661 y(algebra)26 b(with)i(t)n(w)n(o)f(generators)e(\(in)j(this)g(case)
f(task)g(\(2\))g(could)h(b)r(e)g(to)r(o)f(complicated\).)100
3760 y(A)n(tten)n(tion)33 b(in)g(this)g(article)g(is)f(concen)n(trated)
g(at)h(studing)g(sets)g(\006)2231 3772 y Fm(\000)p Fn(;\037)2370
3760 y Fp(in)g(the)h(case)e(where)g(\000)h(is)0 3860
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3870 y Fm(~)2862 3885 y Fn(D)2916 3893 y Fi(4)2948 3885
y Fn(;\037)3014 3860 y Fp(,)i(the)0 3962 y(conditions)24
b(under)h(whic)n(h)f(sets)h(\006)1081 3974 y Fm(\000)p
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Fn(;\037;\015)990 4062 y Fp(on)g(sp)r(ecial)f(case)g(where)g
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y Fp(\(see)28 b(section)g(2)f(for)g(the)i(di\014nition)0
4162 y(of)f Fo(!)147 4174 y Fm(\000)191 4162 y Fp(\).)1022
4331 y(1.)41 b Fq(Description)32 b(of)f(set)h Fp(\006)2029
4341 y Fm(~)2014 4356 y Fn(D)2068 4364 y Fi(4)2101 4356
y Fn(;\037)100 4488 y Fp(As)f(it)i(w)n(as)d(sho)n(wn)h(in)i([11)o(])f
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4521 y Fi(4)1423 4513 y Fn(;\037)1520 4488 y Fp(can)g(b)r(e)g(reduced)f
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y(Complete)c(description)f(of)g(set)h(\006)1083 4607
y Fn(D)1137 4615 y Fi(4)1169 4607 y Fn(;\037)1262 4595
y Fp(w)n(as)f(giv)n(en)g(in)h([7)o(]:)437 4749 y(\006)497
4764 y Fn(D)551 4772 y Fi(4)583 4764 y Fn(;)p Fm(\()p
Fn(\013)672 4772 y Fi(1)704 4764 y Fn(;\013)767 4772
y Fi(2)800 4764 y Fn(;\013)863 4772 y Fi(3)895 4764 y
Fm(\))948 4749 y Fp(=)23 b Fw(f)p Fp(0)p Fo(;)14 b Fp(\()p
Fo(\013)1242 4761 y Fm(1)1297 4749 y Fp(+)k Fo(\013)1433
4761 y Fm(2)1489 4749 y Fp(+)g Fo(\013)1625 4761 y Fm(3)1662
4749 y Fp(\))p Fo(=)p Fp(2)p Fw(g)f([)i(f)1953 4671 y
Fh(X)1958 4849 y Fn(i)p Fj(2)p Fn(J)2086 4749 y Fo(\013)2139
4761 y Fn(i)2167 4749 y Fo(;)14 b(J)31 b Fw(\032)23 b(f)p
Fp(1)p Fo(;)14 b Fp(2)p Fo(;)g Fp(3)p Fw(gg)p Fo(;)g(;)0
4962 y Fp(Let)25 b Fo(\013)199 4974 y Fn(i)227 4962 y
Fo(;)14 b(i)23 b Fp(=)f(1)p Fo(;)14 b(:)g(:)g(:)f(;)h
Fp(4)25 b(denote)g(i-th)g(comp)r(onen)n(t)g(of)g(the)g(c)n(haracter)e
Fo(\037)i Fp(and)g Fo(\013)f Fp(=)e Fo(\013)2582 4974
y Fm(1)2633 4962 y Fp(+)13 b Fo(\013)2764 4974 y Fm(2)2815
4962 y Fp(+)g Fo(\013)2946 4974 y Fm(3)2997 4962 y Fp(+)g
Fo(\013)3128 4974 y Fm(4)3165 4962 y Fp(.)0 5062 y(The)28
b(set)f(\006)375 5072 y Fm(~)360 5087 y Fn(D)414 5095
y Fi(4)447 5087 y Fn(;\037)540 5062 y Fp(satisfy)g(the)h(follo)n(wing)f
(prop)r(erties)f(\(see)i([11)o(]\))141 5186 y(\(1\))42
b(\006)364 5196 y Fm(~)349 5211 y Fn(D)403 5219 y Fi(4)435
5212 y Fn(;\037)524 5186 y Fw(\032)22 b Fp([0)p Fo(;)14
b(\013)p Fp(];)141 5294 y(\(2\))42 b(\006)364 5304 y
Fm(~)349 5319 y Fn(D)403 5327 y Fi(4)435 5319 y Fn(;\037)524
5294 y Fw(3)602 5231 y Fh(P)690 5318 y Fn(i)p Fj(2)p
Fn(J)818 5294 y Fo(\013)871 5306 y Fn(i)899 5294 y Fo(;)14
b(J)31 b Fw(\032)23 b(f)p Fp(0)p Fo(;)14 b Fp(1)p Fo(;)g
Fp(2)p Fo(;)g Fp(3)p Fo(;)g Fp(4)p Fw(g)p Fp(;)p eop
end
%%Page: 3 3
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524 y Fn(;\037)230 499 y Fw(\\)19 b Fp([0)p Fo(;)416
466 y Fn(\013)p 416 480 V 421 527 a Fm(2)469 499 y Fp(\).)100
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n(ts)f(of)h(c)n(haracter)e Fo(\037)j Fp(are)e(less)h(than)1850
870 y Fn(\013)p 1850 884 V 1855 932 a Fm(2)1903 903 y
Fp(.)39 b(In)28 b(this)g(case)g(the)g(set)h(\006)2757
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Fn(;\037)2922 903 y Fp(is)f(quite)0 1005 y(di\013eren)n(t)d(from)h
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1105 y(description)j(of)h(the)g(set)f(\006)867 1115 y
Fm(~)852 1130 y Fn(D)906 1138 y Fi(4)939 1130 y Fn(;\037)1032
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y Fi(4)925 1308 y Fn(;\037)1027 1283 y Fc(c)l(ontains)h(the)g
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2823 1265 V 2828 1312 a Fm(2)2912 1283 y Fc(and)g(the)0
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b Fc(if)30 b Fo(\013)422 1537 y Fm(2)478 1525 y Fp(+)18
b Fo(\013)614 1537 y Fm(3)675 1525 y Fo(>)k(\013)815
1537 y Fm(1)871 1525 y Fp(+)c Fo(\013)1007 1537 y Fm(4)1074
1525 y Fc(then)1140 1730 y Fp(\006)1200 1742 y Fj(1)1293
1730 y Fp(=)1381 1638 y Fh(n)1446 1674 y Fo(\013)p 1446
1711 54 4 v 1452 1787 a Fp(2)1528 1730 y Fw(\000)1621
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1787 a Fp(2)p Fo(n)1722 1730 y Fw(j)p Fo(n)23 b Fw(2)g
Fk(N)1956 1638 y Fh(o)2025 1730 y Fo(;)583 2041 y Fp(\006)643
2053 y Fm(0)703 2041 y Fp(=)791 1924 y Fh(\032)863 1985
y Fo(\013)p 863 2022 54 4 v 869 2098 a Fp(2)945 2041
y Fw(\000)1065 1985 y Fo(\013)c Fw(\000)f Fp(2)p Fo(\013)1315
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2098 a Fo(\013)1635 2110 y Fm(2)1691 2098 y Fp(+)18 b
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2110 y Fm(1)2074 2098 y Fw(\000)g Fo(\013)2210 2110 y
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2483 y Fp(\006)1068 2495 y Fj(1)1161 2483 y Fp(=)1249
2366 y Fh(\032)1321 2427 y Fo(\013)p 1321 2464 54 4 v
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54 4 v 286 4990 a Fp(2)362 4933 y Fw(\000)487 4877 y
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Fo(;)14 b Fp(2)p Fo(;)g Fp(3)p Fo(:)0 5153 y Fx(Corollary)32
b(1.)41 b Fc(By)29 b(using)g(the)h(structur)l(e)d(of)j
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(oint)g Fo(!)1800 5270 y Fm(~)1785 5285 y Fn(D)1839 5293
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end
%%Page: 4 4
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%%Page: 5 5
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Fc(.)p eop end
%%Page: 6 6
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