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% @@psencodingfile@{
%   author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry",
%   version = "0.6",
%   date = "1 July 1998",
%   filename = "8r.enc",
%   email = "tex-fonts@@tug.org",
%   docstring = "Encoding for TrueType or Type 1 fonts
%                to be used with TeX."
% @}
% 
% Idea is to have all the characters normally included in Type 1 fonts
% available for typesetting. This is effectively the characters in Adobe
% Standard Encoding + ISO Latin 1 + extra characters from Lucida.
% 
% Character code assignments were made as follows:
% 
% (1) the Windows ANSI characters are almost all in their Windows ANSI
% positions, because some Windows users cannot easily reencode the
% fonts, and it makes no difference on other systems. The only Windows
% ANSI characters not available are those that make no sense for
% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen
% (173). quotesingle and grave are moved just because it's such an
% irritation not having them in TeX positions.
% 
% (2) Remaining characters are assigned arbitrarily to the lower part
% of the range, avoiding 0, 10 and 13 in case we meet dumb software.
% 
% (3) Y&Y Lucida Bright includes some extra text characters; in the
% hopes that other PostScript fonts, perhaps created for public
% consumption, will include them, they are included starting at 0x12.
% 
% (4) Remaining positions left undefined are for use in (hopefully)
% upward-compatible revisions, if someday more characters are generally
% available.
% 
% (5) hyphen appears twice for compatibility with both 
% ASCII and Windows.
% 
/TeXBase1Encoding [
% 0x00 (encoded characters from Adobe Standard not in Windows 3.1)
  /.notdef /dotaccent /fi /fl
  /fraction /hungarumlaut /Lslash /lslash
  /ogonek /ring /.notdef
  /breve /minus /.notdef 
% These are the only two remaining unencoded characters, so may as
% well include them.
  /Zcaron /zcaron 
% 0x10
 /caron /dotlessi 
% (unusual TeX characters available in, e.g., Lucida Bright)
 /dotlessj /ff /ffi /ffl 
 /.notdef /.notdef /.notdef /.notdef
 /.notdef /.notdef /.notdef /.notdef
 % very contentious; it's so painful not having quoteleft and quoteright
 % at 96 and 145 that we move the things normally found there to here.
 /grave /quotesingle 
% 0x20 (ASCII begins)
 /space /exclam /quotedbl /numbersign
 /dollar /percent /ampersand /quoteright
 /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash
% 0x30
 /zero /one /two /three /four /five /six /seven
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% 0x40
 /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O
% 0x50
 /P /Q /R /S /T /U /V /W
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% 0x60
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% 0x70
 /p /q /r /s /t /u /v /w
 /x /y /z /braceleft /bar /braceright /asciitilde
 /.notdef % rubout; ASCII ends
% 0x80
 /.notdef /.notdef /quotesinglbase /florin
 /quotedblbase /ellipsis /dagger /daggerdbl
 /circumflex /perthousand /Scaron /guilsinglleft
 /OE /.notdef /.notdef /.notdef
% 0x90
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 /quotedblright /bullet /endash /emdash
 /tilde /trademark /scaron /guilsinglright
 /oe /.notdef /.notdef /Ydieresis
% 0xA0
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 /logicalnot
 /hyphen % Y&Y (also at 45); Windows' softhyphen
 /registered
 /macron
% 0xD0
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 /cedilla /onesuperior /ordmasculine /guillemotright
 /onequarter /onehalf /threequarters /questiondown
% 0xC0
 /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
 /Egrave /Eacute /Ecircumflex /Edieresis
 /Igrave /Iacute /Icircumflex /Idieresis
% 0xD0
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 /Ocircumflex /Otilde /Odieresis /multiply
 /Oslash /Ugrave /Uacute /Ucircumflex
 /Udieresis /Yacute /Thorn /germandbls
% 0xE0
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 /adieresis /aring /ae /ccedilla
 /egrave /eacute /ecircumflex /edieresis
 /igrave /iacute /icircumflex /idieresis
% 0xF0
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%%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
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/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
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/FontName /CMMI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
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dup 58 /period put
dup 78 /N put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec
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%%BeginFont: CMMI6
%!PS-AdobeFont-1.1: CMMI6 1.100
%%CreationDate: 1996 Jul 23 07:53:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
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readonly def
/FontBBox{11 -250 1241 750}readonly def
/UniqueID 5087381 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR9
%!PS-AdobeFont-1.1: CMR9 1.0
%%CreationDate: 1991 Aug 20 16:39:59
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 53 /five put
dup 61 /equal put
readonly def
/FontBBox{-39 -250 1036 750}readonly def
/UniqueID 5000792 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI9
%!PS-AdobeFont-1.1: CMMI9 1.100
%%CreationDate: 1996 Jul 23 07:53:55
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 21 /lambda put
dup 22 /mu put
dup 28 /tau put
dup 58 /period put
dup 78 /N put
dup 109 /m put
readonly def
/FontBBox{-29 -250 1075 750}readonly def
/UniqueID 5087384 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY7
%!PS-AdobeFont-1.1: CMSY7 1.0
%%CreationDate: 1991 Aug 15 07:21:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 3 /asteriskmath put
dup 33 /arrowright put
dup 48 /prime put
dup 49 /infinity put
readonly def
/FontBBox{-15 -951 1252 782}readonly def
/UniqueID 5000817 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
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dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 77 /M put
dup 100 /d put
dup 101 /e put
dup 108 /l put
dup 111 /o put
dup 120 /x put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueID 5000768 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 40 /parenleft put
dup 41 /parenright put
dup 43 /plus 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 61 /equal put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueID 5000790 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 0 /parenleftbig put
dup 1 /parenrightbig put
dup 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 20 /bracketleftbigg put
dup 21 /bracketrightbigg put
dup 26 /braceleftbigg put
dup 27 /bracerightbigg put
dup 32 /parenleftBigg put
dup 33 /parenrightBigg put
dup 80 /summationtext put
dup 88 /summationdisplay put
dup 114 /radicalbigg put
dup 115 /radicalBigg put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 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 65 /A put
dup 66 /B put
dup 69 /E put
dup 78 /N put
dup 79 /O put
dup 84 /T put
dup 98 /b put
dup 102 /f put
dup 105 /i put
dup 107 /k put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 119 /w put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 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 13 /circlecopyrt put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueID 5000818 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 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 56 /eight put
dup 61 /equal put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 94 /circumflex put
dup 105 /i put
dup 108 /l put
dup 109 /m put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 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 21 /lambda put
dup 22 /mu put
dup 26 /rho put
dup 28 /tau put
dup 58 /period put
dup 60 /less put
dup 61 /slash put
dup 68 /D put
dup 69 /E put
dup 73 /I put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 81 /Q put
dup 84 /T put
dup 87 /W put
dup 88 /X put
dup 98 /b put
dup 102 /f 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 119 /w put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 2 /multiply put
dup 15 /bullet put
dup 17 /equivalence put
dup 20 /lessequal put
dup 39 /similarequal put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964
7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4
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cleartomark
%%EndFont 
%%BeginFont: CMSY9
%!PS-AdobeFont-1.1: CMSY9 1.0
%%CreationDate: 1991 Aug 15 07:22:27
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 13 /circlecopyrt put
readonly def
/FontBBox{-30 -958 1146 777}readonly def
/UniqueID 5000819 def
currentdict end
currentfile eexec
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221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A
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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 49 /one put
dup 50 /two put
dup 51 /three put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
/UniqueID 5000789 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
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D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C
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3645B82392D5CAE11A7CB49D7E2E82DCD485CBA17D1AFFF95F4224CF7ECEE45C
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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 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 53 /five put
dup 61 /equal put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec
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2121 y(contro) n(l) j(mechan) n(ism) h(of) e(TCP) h(and) f(the) h(netw)
o(ork) e(as) j(a) f(feed) n(back) f(system) h(for) f(in) m(v) o(e) n
(stigating) g(the) h(steady) f(state) 191 2221 y(and) i(the) h
(transient) f(state) i(beha) l(viors) f(of) g(TCP) -9
b(.) 31 b(F) o(or) f(modelin) n(g) h(the) g(cong) n(estion) g(contro) n
(l) g(mechanism) f(of) g(TCP) -9 b(,) 191 2320 y(we) 20
b(use) g(four) f(dif) n(fe) n(rent) h(analytic) f(mode) n(ls) i
(presented) e(in) h([13) n(-15].) f(As) h(a) g(netw) o(ork) f(mode) n
(l,) i(we) f(use) g(a) p Fo 20 w(M) t(=) -5 b(M) t(=) p
Fn(1) p Fo(=m) p Fr 191 2420 a(queu) n(eing) 17 b(system,) g(where) g
(the) g(input) g(traf) n(\002c) g(is) h(mixtur) n(e) g(of) f(TCP) h
(traf) n(\002c) f(and) f(backgr) n(ound) g(traf) n(\002c) h(\(i.e.,) g
(non) n(-TCP) 191 2520 y(traf) n(\002c\).) 274 2623 y(In) f([12]) n(,) h
(the) f(autho) n(rs) h(ha) n(v) o(e) f(analyze) n(d) h(the) f(perfo) n
(rmance) f(of) h(TCP) h(by) f(mode) n(ling) g(the) h(netw) o(or) n(k) g
(as) g(a) p Fo 16 w(M) t(=D) r(=) p Fn(1) p Fo(=m) p
Fr 191 2723 a(queu) n(ing) 22 b(system.) g(Ho) n(we) n(v) o(er) -5
b(,) 22 b(the) h(autho) n(rs) g(ha) n(v) o(e) e(focused) g(only) h(on) f
(the) i(steady) e(state) i(beha) n(vio) n(r) g(of) f(TCP;) h(that) f
(is,) 191 2823 y(the) d(transient) f(state) i(beha) n(v) n(ior) f(of) g
(TCP) h(has) f(not) f(been) g(e) n(v) n(aluated) n(.) i(In) e(addition)
n(,) i(their) e(analytic) h(mod) n(el) h(is) f(not) g(TCP) 191
2922 y(Reno) 28 b(b) n(ut) g(TCP) h(T) -7 b(ahoe,) 28
b(which) g(does) g(not) g(ha) n(v) o(e) f(se) n(v) o(eral) h(impor) n
(tant) h(mecha) n(nisms) g(foun) n(d) g(in) f(TCP) h(Reno.) f(F) o(or)
191 3022 y(instance,) 18 b(the) h(ef) n(fect) f(of) h(the) f(f) o(ast) i
(retran) n(smit) g(mecha) n(nism) f(in) g(TCP) h(Reno) e(has) h(not) g
(been) f(in) m(v) o(e) n(stigated.) g(In) h([4,) f(15]) n(,) 191
3122 y(analytic) 26 b(models) h(for) f(TCP) i(Reno) f(and) f(the) h
(RED) h(\(Rando) n(m) f(Early) g(Detection\)) f(rou) n(ter) i(ha) n(v) o
(e) e(been) g(presented) n(,) 191 3221 y(and) k(the) g(perfor) n(mance)
g(of) g(TCP) i(with) e(the) h(RED) g(router) e(has) i(been) f(analyze) n
(d.) h(In) f([4],) g(the) g(primary) f(focus) h(of) 191
3321 y(the) 21 b(analysis) h(is) g(on) f(the) h(steady) f(state) h
(beha) n(vio) n(r) g(of) f(TCP) -9 b(.) 22 b(Only) f(a) h(qua) n
(litati) n(v) o(e) g(discussion) f(on) g(the) g(transient) g(state) 191
3421 y(beha) n(vio) n(r) 16 b(has) g(been) g(presen) n(ted.) g(In) g
([15) n(],) g(a) g(control) f(theoretic) g(appro) n(ach) h(has) g(been)
f(tak) o(en) h(to) g(analyz) n(e) h(the) f(stability) 191
3520 y(and) i(the) g(transient) g(state) h(beha) n(v) n(ior) f(of) g
(TCP) -9 b(,) 19 b(where) f(the) g(RED) h(router) e(is) i(modeled) e
(by) h(a) h(non) n(-linear) f(discrete-tim) n(e) 191
3620 y(system.) i(On) g(the) f(other) g(hand,) g(the) h(main) f
(objecti) n(v) o(e) g(of) g(this) i(pape) n(r) f(is) h(to) f(analyze) f
(the) h(transient) f(state) i(beha) n(v) n(ior) f(of) 191
3719 y(TCP) f(with) g(the) f(Drop-) n(T) -7 b(ail) 19
b(router) -5 b(,) 19 b(since) f(most) h(e) o(xisting) e(router) n(s) j
(in) e(the) g(curren) n(t) h(Interne) n(t) g(are) g(Drop) n(-T) -7
b(ail) 19 b(router) n(s.) 191 3819 y(W) -7 b(e) 21 b(tak) o(e) g(a) f
(dif) n(fer) n(ent) h(appr) n(oach) f(of) g(mod) n(eling) g(the) g
(Drop-) n(T) -7 b(ail) 21 b(router) e(using) h(a) h(queu) n(ing) f
(theor) n(y) -5 b(.) 274 3923 y(In) 17 b([3],) f(the) h(author) n(s) h
(ha) n(v) o(e) f(deri) n(v) m(ed) g(the) g(a) n(v) o(erag) n(e) h
(\002le) g(transfer) e(time) h(without) f(assuming) h(a) g(constant) g
(pack) m(et) h(loss) 191 4022 y(prob) n(ability) g(in) g(the) f(netw) o
(ork.) g(Ho) n(we) n(v) m(er) m(,) g(the) h(stability) g(and) f(the) h
(transient) f(state) i(beha) l(vior) f(of) f(TCP) i(ha) n(v) o(e) e
(not) h(been) 191 4122 y(analyze) n(d.) 27 b(In) f([9],) f(the) i
(autho) n(rs) g(ha) n(v) o(e) f(mode) n(led) h(the) f(interaction) n(s)
i(of) e(a) g(set) i(of) e(TCP) h(\003o) n(ws) g(and) f(A) -5
b(QM) 27 b(\(Acti) n(v) o(e) 191 4222 y(Queue) f(Manage) n(ment\)) g
(gate) n(w) o(ays,) g(and) g(the) o(y) g(ha) n(v) o(e) h(sho) n(wed) e
(a) j(transient) e(state) h(beha) n(vior) f(of) g(TCP) -9
b(.) 27 b(Since) g(their) 191 4321 y(method) n(ology) 21
b(is) h(based) g(on) f(the) h(solution) f(of) g(the) h(dif) n(fere) n
(ntial) g(equation) n(s,) h(the) o(y) e(ha) n(v) o(e) g(not) h(sho) n
(wed) e(the) i(transient) 191 4421 y(state) d(beha) n(vio) n(r) g(of) f
(TCP) -9 b(,) 19 b(rigor) n(ously) -5 b(.) 18 b(In) g([5],) f(the) i
(autho) n(rs) g(ha) n(v) o(e) f(analyzed) f(a) i(comb) n(ined) f(TCP) i
(and) d(A) -5 b(QM) 20 b(\(Acti) n(v) o(e) 191 4521 y(Queue) 27
b(Managem) n(ent\)) h(gate) n(w) o(ays) g(mod) n(el) h(from) f(a) g
(contro) n(l) h(theoretic) f(standp) n(oint.) g(Ho) n(we) n(v) o(e) n
(r) m(,) g(the) o(y) g(ha) n(v) o(e) g(only) 191 4620
y(focu) n(sed) 21 b(on) f(the) g(stability) g(of) g(the) g(queue) f
(length) h(of) g(RED) g(gate) n(w) o(ays.) 274 4724 y(In) j(our) g
(analytic) f(model,) h(both) f(TCP) j(traf) n(\002c) e(and) f(backgr) n
(ound) g(traf) n(\002c) h(are) h(tak) o(en) f(accou) n(nt) h(of.) f(W)
-7 b(e) 24 b(model) f(the) 191 4824 y(interaction) d(between) h(the) g
(cong) n(estion) h(contr) n(ol) g(mechan) n(ism) g(of) f(TCP) h(and) f
(the) h(netw) o(or) n(k) g(as) g(a) g(feedb) n(ack) g(system;) 191
4923 y(that) f(is,) h(both) e(the) i(cong) n(estion) f(contro) n(l) h
(mechan) n(ism) g(of) f(TCP) h(runn) n(ing) f(on) g(a) g(source) g
(host) g(and) g(the) g(netw) o(or) n(k) h(seen) 191 5023
y(by) e(TCP) h(are) f(mod) n(eled) h(by) e(dynam) n(ic) i(systems) g
(\(Fig.) f(1\).) p FD 191 5222 a(Cop) o(yri) r(ght) 497
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      280 240 L
   TGSM
   3 W
   S
   [] 0 SD
   1 W
GR

% POLY/OPEN-SPLINE
0 SG
GS
   [4 12] 0 SD
   NP
      305 240 M
      330 240 L
   TGSM
   3 W
   S
   [] 0 SD
   1 W
GR

% TEXT
NP
0 SG
NP 274 135 M 325 135 L 325 165 L 274 165 L CP 1 SG F
0 SG
   GS
      1 W
      275 160 M
      GS
            0 SG
            /Helvetica FF [25 0 0 -25 0 0] MS
            (TCP) SH
      GR
   GR

% BOX
0 SG
NP 520 185 M 570 185 L 570 220 L 520 220 L CP 1 SG F
   0 SG
GS
   10 SM
   GS
      NP 520 185 M 570 185 L 570 220 L 520 220 L CP
      2 W
      S
   GR
GR

% OVAL
0 SG
NP 582 202 22 22 TGEL
CP 1 SG F
   0 SG
GS
   GS
      NP 582 202 22 22 TGEL
      2 W
      S
   GR
GR

% POLY/OPEN-SPLINE
0 SG
GS
   NP
      530 185 M
      530 220 L
   TGSM
   2 W
   S
   1 W
GR

% POLY/OPEN-SPLINE
0 SG
GS
   NP
      540 185 M
      540 220 L
   TGSM
   2 W
   S
   1 W
GR

% POLY/OPEN-SPLINE
0 SG
GS
   NP
      550 185 M
      550 220 L
   TGSM
   2 W
   S
   1 W
GR

% POLY/OPEN-SPLINE
0 SG
GS
   NP
      560 185 M
      560 220 L
   TGSM
   2 W
   S
   1 W
GR

% TEXT
NP
0 SG
   GS
      1 W
      435 120 M
      GS
            0 SG
            /Helvetica FF [20 0 0 -20 0 0] MS
            (Background Traffic) SH
      GR
   GR

% TEXT
NP
0 SG
   GS
      1 W
      220 415 M
      GS
            0 SG
            /Helvetica FF [14 0 0 -14 0 0] MS
            (TCP1) SH
      GR
   GR

% TEXT
NP
0 SG
   GS
      1 W
      270 350 M
      GS
            0 SG
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            (TCP) SH
            0 SG
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% TEXT
NP
0 SG
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      GS
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@endspecial 361 1631 a(Figure) i(1:) i(Analytic) e(model) h(as) h(a) f
(feedba) n(ck) h(system) f(consisting) f(of) h(TCP) h(connectio) n(ns) g
(and) e(netw) o(ork.) 274 2122 y(The) 35 b(con) n(gestion) g(contr) n
(ol) g(mechan) n(ism) h(of) e(TCP) i(is) g(a) f(windo) n(w-) n(based) g
(\003o) n(w) g(contr) n(ol) g(mechanism,) f(and) g(it) 191
2221 y(dyn) n(amically) 20 b(chan) n(ges) g(the) g(windo) n(w) f(size) h
(accord) n(ing) g(to) f(occurr) n(ence) h(of) f(pack) o(et) g(losses) i
(in) f(the) f(netw) o(ork) n(.) h(Hence,) 191 2321 y(there) h(e) o
(xists) h(a) g(tendenc) m(y) g(that) g(when) f(the) g(pack) o(et) g
(loss) i(pro) n(bability) e(is) i(small,) f(the) f(windo) n(w) g(size) h
(becomes) f(lar) o(ge) n(.) 191 2421 y(On) f(the) h(contra) n(ry) -5
b(,) 20 b(when) g(the) g(pack) o(et) g(loss) i(pro) n(bability) e(is) h
(lar) o(ge,) f(the) g(windo) n(w) g(size) h(tends) f(to) h(beco) n(me) g
(small.) g(W) -7 b(e) 191 2520 y(mode) n(l) 24 b(the) e(cong) n(estion)
h(contr) n(ol) g(mechan) n(ism) g(of) g(TCP) g(as) g(a) g(dyn) n(amic) g
(system,) f(where) g(the) h(inpu) n(t) g(to) g(the) g(system) 191
2620 y(is) d(the) f(pack) o(et) f(loss) i(prob) n(ability) f(in) g(the)
g(netw) o(ork) f(and) h(the) g(outp) n(ut) h(fro) n(m) g(the) f(system)
g(is) h(the) f(windo) n(w) f(size) i(of) e(TCP) -9 b(.) 274
2790 y(On) 19 b(the) f(other) g(hand,) g(the) g(netw) o(ork) g(seen) h
(by) f(TCP) i(beh) n(a) n(v) o(es) f(such) g(that) g(when) f(the) g
(numbe) n(r) h(of) g(pack) o(ets) f(entering) 191 2890
y(the) 24 b(netw) o(ork) f(increases,) h(some) f(pack) o(ets) h(are) g
(w) o(aited) g(at) h(the) f(b) n(uf) n(fe) n(r) h(of) f(the) g(rou) n
(ter) h(destined) e(for) g(the) h(bottleneck) 191 2989
y(link.) f(This) g(sometimes) g(causes) g(b) n(uf) n(fer) f(o) o(v) o
(er) n(\003o) n(w) -5 b(,) 23 b(resulting) f(in) i(a) f(pack) o(et) g
(loss.) h(So) f(the) g(pack) o(et) g(loss) h(prob) n(ability) 191
3089 y(becom) n(es) e(lar) o(g) n(e) g(when) e(the) h(num) n(ber) g(of)
f(pack) o(ets) h(enterin) n(g) g(the) g(netw) o(ork) e(increases.) i
(Thus,) f(the) h(netw) o(or) n(k) g(seen) g(by) 191 3188
y(TCP) j(can) f(be) g(modeled) f(by) h(a) h(dyna) n(mic) g(system,) f
(where) g(the) g(input) g(to) g(the) h(system) f(is) h(the) g(windo) l
(w) g(size) g(and) f(the) 191 3288 y(outpu) n(t) e(from) e(the) h
(system) h(is) g(the) f(pack) o(et) g(loss) h(pro) n(bability) -5
b(.) 274 3458 y(The) 22 b(main) g(contrib) n(utio) n(n) h(of) f(this) h
(paper) f(is) i(to) e(allo) n(w) h(steady) f(state) i(analy) n(sis) g
(of) f(TCP) -9 b(,) 23 b(and) f(mor) n(e) h(importan) n(tly) -5
b(,) 191 3558 y(to) 27 b(analy) n(ze) g(the) g(transient) f(state) h
(beha) n(vio) n(r) g(of) f(TCP) i(using) e(a) h(rigo) n(rous) f(manner)
f(based) i(on) f(contr) n(ol) h(theory) -7 b(.) 27 b(W) -7
b(e) 191 3657 y(deri) n(v) m(e) 20 b(the) g(throu) n(ghput) f(of) g
(each) h(TCP) g(connectio) n(n,) g(the) g(pack) m(et) h(loss) f(proba) n
(bility) g(at) g(the) g(bottlenec) n(k) g(router) m(,) e(and) 191
3757 y(the) 26 b(a) n(v) o(erage) g(que) n(ue) h(length) e(\(i.e.,) h
(the) h(num) n(ber) f(of) h(pack) m(ets) h(a) o(w) o(aited) e(in) g
(the) h(b) n(uf) n(f) n(er\)) g(at) f(the) h(bottlene) n(ck) g(rou) n
(ter) -5 b(.) 191 3857 y(By) 34 b(utilizing) f(the) g(contro) n(l) i
(theor) n(y) -5 b(,) 33 b(which) g(has) h(been) f(de) n(v) m(eloped) g
(in) g(the) h(contr) n(ol) g(engine) n(ering,) f(we) h(analyz) n(e) 191
3956 y(the) 28 b(transien) n(t) h(state) f(beha) n(v) n(ior) g(of) f
(TCP) -9 b(.) 28 b(W) -7 b(e) 29 b(sho) n(w) e(quan) n(titati) n(v) o
(ely) g(ho) n(w) g(the) h(stability) g(and) e(the) i(transient) f
(state) 191 4056 y(beha) n(vio) n(r) 34 b(of) g(TCP) h(are) e(af) n
(fected) g(by) h(se) n(v) o(er) n(al) h(system) f(param) n(eters:) h
(the) f(num) n(ber) g(of) f(TCP) i(conn) n(ections,) f(the) 191
4155 y(prop) n(agation) 19 b(delay) -5 b(,) 19 b(the) h(bottlenec) n(k)
h(link) f(capacity) -7 b(,) 20 b(and) g(the) g(b) n(uf) n(fer) f(size) i
(of) f(the) g(bottlene) n(ck) h(rou) n(ter) -5 b(.) 274
4325 y(Or) o(ga) n(nization) 30 b(of) i(this) f(paper) g(is) h(as) g
(follo) n(ws.) f(In) g(Section) g(2,) g(we) h(describe) e(ho) n(w) h
(the) h(interactio) n(n) g(between) 191 4425 y(TCP) 24
b(and) f(the) g(netw) o(ork) f(can) h(be) g(modeled) f(as) i(a) f
(feedback) f(system.) h(W) -7 b(e) 24 b(then) f(present) g(fou) n(r) h
(analytic) e(models) h(of) 191 4525 y(the) k(cong) n(estion) g(contro) n
(l) h(mechan) n(ism) f(of) g(TCP) -9 b(.) 27 b(In) g(Section) g(3,) f
(compar) n(ing) h(these) g(four) f(analytic) g(models) h(with) 191
4624 y(simulation) d(results,) h(we) g(discuss) g(which) f(analytic) h
(mod) n(el) h(is) f(most) g(suitable) g(for) f(analyzin) n(g) h(the) g
(transient) f(state) 191 4724 y(beha) n(vio) n(r) 17
b(of) g(TCP) -9 b(.) 18 b(In) e(Section) h(4,) g(we) g(deri) n(v) o(e) f
(the) h(TCP) h(throu) n(ghpu) n(t,) g(the) f(pack) o(et) f(loss) i
(prob) n(ability) -5 b(,) 16 b(and) h(the) g(queu) n(e) 191
4824 y(length) e(of) h(the) g(bottleneck) f(router) -7
b(.) 17 b(W) -7 b(e) 18 b(also) e(v) n(alidate) g(our) f(appro) n
(ximate) h(analysis) g(by) g(comp) n(aring) g(analytic) f(results) 191
4923 y(with) 30 b(simulation) f(one) n(s.) i(In) e(Section) g(5,) h(we)
g(analyze) f(the) g(transient) h(state) g(beha) n(vio) n(r) g(of) f
(TCP) i(using) e(a) h(contro) n(l) 191 5023 y(theore) n(tic) 21
b(appro) n(ach.) f(Finally) -5 b(,) 19 b(in) i(Section) f(6,) g(we) g
(conclu) n(de) h(the) f(curr) n(ent) h(pape) n(r) g(and) e(discuss) i
(futur) n(e) g(w) o(orks.) p FD 191 5222 a(Cop) o(yri) r(ght) 497
5220 y(c) p Fm 476 5222 a(\015) p FD 16 w(2005) d(John) f(W) m(ile) o
(y) h(&) f(Sons,) f(Ltd.) p FC 1233 w(Int.) 21 b(J) n(.) c(Commun.) k
(Syst.) p FD 18 w(2005;) p FB 18 w(00) p FD(:1\22618) p
FC 191 5301 a(Pr) n(epar) n(ed) 16 b(using) p FA 18 w(dacauth.cls) p
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b(,) 28 b(and) g(then) g(presen) n(t) h(four) e(analytic) 191
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p Fq 27 w(bottlen) n(ec) n(k) g(r) l(outer) p Fr(.) g(W) -7
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y(are) i(kno) n(w) n(n,) h(the) f(pack) m(et) h(loss) g(prob) n
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(oscillatory) -5 b(,) 15 b(in) i(reality) -5 b(,) 16
b(the) h(netw) o(ork) e(is) j(not) 191 1890 y(stationary) -7
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e(in) h(Section) g(3,) f(the) h(netw) o(ork) f(seen) g(by) h(TCP) g
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Fo 28 w(w) p Fl 1972 2223 a(i) p Fr 2029 2211 a(and) p
Fo 28 w(r) p Fl 2215 2223 a(i) p Fr 2272 2211 a(be) g(the) h(windo) l
(w) g(size) g(and) f(the) h(rou) n(nd-trip) 191 2311
y(time) e(of) p Fo 26 w(i) p Fr(th) g(\() p Fn(1) p Fp
34 w(\024) p Fo 34 w(i) p Fp 35 w(\024) p Fo 34 w(N) p
Fr 9 w(\)) g(TCP) g(connectio) n(n.) g(Assuming) f(that) g(each) h(TCP)
g(conne) n(ction) g(con) n(tinuously) f(sends) 191 2411
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Fo 25 w(i) p Fr(th) g(TCP) g(conne) n(ction) g(can) g(be) f(appro) n
(ximated) g(by) p Fo 26 w(w) p Fl 2986 2423 a(i) p Fo
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(at) g(the) g(bottleneck) f(route) n(r) m(,) p Fo 27
w(\025) p Fr(,) i(is) g(therefo) n(re) f(gi) n(v) o(en) f(by) p
Fk 2487 2459 a(P) p Fl 2574 2480 a(N) 2574 2546 y(i) p
Fj(=1) p Fo 2700 2521 a(w) p Fl 2759 2533 a(i) p Fo 2787
2521 a(=r) p Fl 2866 2533 a(i) p Fn 2917 2521 a(+) p
Fo 23 w(\025) p Fl 3053 2533 a(B) p Fr 3111 2521 a(,) h(where) p
Fo 27 w(\025) p Fl 3438 2533 a(B) p Fr 3523 2521 a(is) 191
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g(the) g(backg) n(roun) n(d) h(traf) n(\002c) e(at) i(the) f(bottlenec)
n(k) h(rou) n(ter) -5 b(.) 24 b(Let) p Fo 23 w(\026) p
Fr 24 w(be) f(the) g(capacity) f(of) h(the) 191 2720
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Fo 29 w(\032) p Fr 29 w(is) g(gi) n(v) o(en) f(by) p
Fo 28 w(\032) p Fn 38 w(=) p Fo 38 w(\025=\026) p Fr(.) h(Depend) n
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(queu) n(ing) g(system,) p Fo 23 w(M) t(=) -5 b(M) t(=) p
Fn(1) p Fo(=m) p Fr(,) 23 b(where) p Fo 23 w(m) p Fr
24 w(represen) n(ts) i(the) f(b) n(uf) n(f) n(er) g(size) g(of) g(the)
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Fo 1553 3479 a(p) p Fn 83 w(=) 1836 3423 y(\(1) p Fp
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Fl 2143 3392 a(m) p 1836 3460 371 4 v Fn 1854 3536 a(1) p
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Fr 3481 3479 a(\(1\)) 191 3728 y(where) p Fo 20 w(\032) p
Fr 20 w(and) p Fo 20 w(r) p Fr 23 w(are) h(gi) n(v) o(en) f(by) p
Fo 1228 4010 a(\032) p Fn 83 w(=) 1516 3954 y(1) p 1511
3991 51 4 v Fo 1511 4067 a(\026) p Fk 1585 3868 a( ) 1661
3891 y(P) p Fl 1749 3911 a(N) 1749 3978 y(i) p Fj(=1) p
Fo 1888 3953 a(w) p Fl 1947 3965 a(i) p 1661 3991 315
4 v Fo 1785 4067 a(r) p Fl 1822 4079 a(i) p Fn 2003 4010
a(+) p Fo 18 w(\025) p Fl 2134 4022 a(B) p Fk 2192 3868
a(!) p Fo 1206 4271 a(r) p Fl 1243 4283 a(i) p Fn 1354
4271 a(=) 82 b(2) p Fo(\034) p Fl 1579 4283 a(i) p Fn
1625 4271 a(+) p Fo 1718 4215 a(\032) p Fn 14 w(\(1) p
Fp 18 w(\000) p Fo 18 w(m) 14 b(\032) p Fl 2080 4185
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4 v Fo 1780 4328 a(\026) p Fn(\(1) p Fp 18 w(\000) p
Fo 18 w(\032) p Fl 2048 4304 a(m) p Fj(+2) p Fn 2195
4328 a(\)) g(\(1) p Fp 19 w(\000) p Fo 18 w(\032) p Fn(\)) p
Fr 191 4525 a(Use) j(of) g(the) f(queuin) n(g) h(mod) n(el) h(to) e
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3956 y(In) d(what) g(follo) n(w) n(s,) h(we) f(describe) g(a) g
(modi\002catio) n(n) h(to) f(the) g(analytic) f(model) g(presented) g
(in) h([15]) f(for) h(analy) n(zing) g(TCP) 191 4056
y(with) g(the) h(Drop) n(-T) -7 b(ail) 21 b(rou) n(ter) -5
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(RED) 191 4255 y(router) 19 b(at) i(slot) p Fo 20 w(k) p
Fr 24 w(as) p 1461 4377 V Fo 1461 4444 a(X) p Fn 6 w(\() p
Fo(k) p Fn 3 w(\)) 83 b(=) 1887 4388 y(1) p Fo(=p) p
Fl 2013 4400 a(b) p Fn 2045 4388 a(\() p Fo(k) p Fn 3
w(\)) 19 b(+) f(1) p 1887 4425 412 4 v 2072 4501 a(2) p
Fr 191 4632 a(where) p Fo 25 w(p) p Fl 462 4644 a(b) p
Fn 495 4632 a(\() p Fo(k) p Fn 3 w(\)) p Fr 27 w(is) 27
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4732 y(prob) n(ability) 20 b(of) g(the) g(Drop-) n(T) -7
b(ail) 21 b(router) m(,) p 1371 4665 76 4 v Fo 19 w(X) p
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@endspecial 557 1631 a(Figure) j(2:) g(Simulation) g(mod) n(el) h(of) f
(10) g(TCP) h(con) n(nections) f(and) g(a) g(single) g(bottleneck) f
(link.) 191 2016 y(Thus,) k(when) h(the) g(pack) m(et) h(loss) g(pro) n
(bability) f(is) p Fo 24 w(p) p Fr(,) g(the) g(windo) n(w) f(size) p
Fo 25 w(w) p Fr 27 w(at) i(the) f(be) o(g) n(inning) f(of) h(slot) p
Fo 24 w(k) p Fr 27 w(is) h(obtained) 191 2115 y(as) c([15]) p
Fo 1056 2367 a(w) p Fn 2 w(\() p Fo(k) p Fn 3 w(\)) 84
b(=) 1468 2311 y(1) p 1468 2348 42 4 v 1468 2424 a(4) p
Fk 1534 2250 a(\032) p Fp 1596 2367 a(\000) p Fn(1) 18
b(+) p Fk 1804 2245 a(r) p 1887 2245 765 4 v Fn 1887
2367 a(\(1) p Fp 18 w(\000) p Fn 18 w(2) p Fo(w) p Fn
2 w(\() p Fo(k) p Fp 22 w(\000) p Fn 18 w(1\)\)) p Fj
2451 2343 a(2) p Fn 2506 2367 a(+) 2600 2311 y(8) p 2599
2348 42 4 v Fo 2599 2424 a(p) p Fk 2651 2250 a(\033) p
Fr 3481 2367 a(\(6\)) 191 2612 y(Note) 24 b(that) g(Eq.) f(\(6\)) g(is)
i(deri) n(v) m(ed) f(by) f(assuming) g(that) h(a) g(pack) o(et) g(loss)
g(prob) n(ability) g(is) h(con) n(stant) g(in) f(a) g(slot.) g(Since) g
(the) 191 2712 y(pack) o(et) c(loss) i(prob) n(ability) f(is,) g(in) g
(reality) -5 b(,) 20 b(increased) g(as) i(the) f(windo) l(w) h(size) f
(increases,) g(this) g(analytic) f(model) g(might) 191
2811 y(o) o(v) o(e) n(restimate) g(the) h(windo) l(w) g(size.) 274
2928 y(W) -7 b(e) 30 b(note) e(that) h(mod) n(els) h(A) f(and) f(A) -9
b(') 28 b(are) h(b) n(uilt) g(based) f(on) g(the) h(windo) l(w) h(size)
f(in) g(steady) f(state.) h(It) g(is) h(theref) n(ore) 191
3028 y(e) o(xpe) n(cted) k(that) f(these) h(mode) n(ls) h(are) e(not) g
(suitable) h(for) e(analyzing) g(the) i(transient) f(state) h(beha) n
(vio) n(r) g(of) f(TCP) -9 b(.) 34 b(On) 191 3128 y(the) 29
b(contrar) n(y) -5 b(,) 29 b(models) g(B) i(and) d(C) j(describ) n(e) f
(the) g(dyn) n(amic) g(beha) l(vior) f(of) h(the) f(windo) n(w) f(size)
j(in) e(the) h(con) n(gestion) 191 3227 y(a) n(v) n(oidan) n(ce) h
(phase.) g(Thu) n(s,) h(it) f(is) h(e) o(xp) n(ected) f(that) g(mod) n
(els) h(B) f(and) g(C) g(are) g(suitable) f(for) h(analy) n(zing) g
(the) f(transient) 191 3327 y(state) 20 b(beha) n(vio) n(r) g(of) f
(TCP) -9 b(.) 20 b(In) f(the) g(ne) o(xt) g(section,) g(we) g(compar) n
(e) h(these) g(fou) n(r) g(analytic) f(mod) n(els) i(using) d(numeric) n
(al) i(and) 191 3426 y(simulation) f(results.) 1267 3812
y(3.) 40 b(Model) 20 b(V) -9 b(alidation) 19 b(with) h(Simulation) p
Fq 191 3977 a(3.1.) 40 b(Simulatio) n(n) 21 b(Model) p
Fr 191 4126 a(The) 30 b(simulation) g(model) g(is) i(sho) n(wn) d(in) i
(Fig.) g(2.) g(In) f(this) h(model,) f(10) g(TCP) h(connectio) n(ns) g
(share) g(the) f(bottleneck) 191 4226 y(link.) c(The) g(prop) n
(agation) g(delay) f(of) p Fo 27 w(i) p Fr(th) h(TCP) h(connectio) n(n)
g(is) p Fn 27 w(5) c(+) p Fo 23 w(i) p Fr 26 w([ms],) j(and) g(the) h
(link) f(capacity) g(from) f(the) p Fo 27 w(i) p Fr(th) 191
4325 y(source) h(host) g(to) g(the) h(rou) n(ter) g(is) p
Fn 27 w(5) c(+) f(0) p Fo(:) p Fn(5) p Fo(i) p Fr 26
w([pack) m(et/ms].) 27 b(W) -7 b(e) 27 b(model) f(the) g(backgr) n
(ound) f(traf) n(\002c) h(as) h(UDP) g(pack) o(ets,) 191
4425 y(where) 20 b(the) h(pack) m(et) h(arri) n(v) n(a) n(l) g(of) e
(UDP) h(pack) o(ets) g(is) g(modeled) f(by) g(a) h(Poisson) g(pro) n
(cess) h(with) f(the) g(a) n(v) o(era) n(ge) g(arri) n(v) n(a) n(l) h
(rate) 191 4525 y(of) p Fo 25 w(\025) p Fl 334 4537 a(B) p
Fn 424 4525 a(=) 33 b(2) p Fr 25 w([pack) o(et/m) n(s].) 26
b(Unless) g(e) o(xplicitly) f(noted) n(,) h(we) g(use) f(the) h(follo) n
(w) n(ing) f(parameter) n(s) i(in) e(all) h(simulations:) 191
4624 y(both) 31 b(TCP) i(and) e(UDP) h(pack) o(et) g(sizes) h(are) e
(\002x) o(ed) h(at) g(1000) f([by) n(te],) h(the) g(capacity) f(of) h
(the) f(bottleneck) g(link) p Fo 31 w(\026) p Fr 33 w(is) 191
4724 y(5) i([pack) m(et/ms],) h(and) e(the) h(prop) n(agation) f(delay)
g(of) h(the) g(bottlenec) n(k) h(link) p Fo 32 w(\034) p
Fr 44 w(is) g(5) f([ms].) f(Note) h(that) g(with) h(these) 191
4824 y(simulation) d(parame) n(ters,) i(1) f([pack) m(et/ms]) g
(correspo) n(nds) g(to) g(about) f(8) h([Mbit/s].) g(Also) g(note) g
(that) g(perf) n(ormanc) n(e) 191 4923 y(e) n(v) n(alua) n(tion) 25
b(for) f(\002x) o(ed) n(-sized) h(TCP) g(pack) o(ets) f(w) o(ould) g
(be) g(suf) n(\002cient) g(since) h(we) g(assume) f(persistent) g(TCP) h
(traf) n(\002c) g(in) 191 5023 y(our) 19 b(analysis.) 41
b(W) -7 b(e) 21 b(run) f(e) n(v) o(er) n(y) h(simulation) e(for) h(30) f
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%%Page: 8 8
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b(HISAMA) -7 b(TSU) 16 b(ET) g(AL.) 1139 1448 y @beginspecial
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(Model A) Rshow
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1.000 UL
LT3
2711 1799 M
(Model B) Rshow
2795 1799 M
399 0 V
1143 2352 M
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13 -30 V
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12 -3 V
12 -2 V
13 -3 V
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12 -2 V
1.000 UL
LT4
2711 1659 M
(Model C) Rshow
2795 1659 M
399 0 V
745 2352 M
84 -229 V
994 1780 L
117 -204 V
91 -140 V
74 -103 V
63 -80 V
55 -64 V
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@endspecial 780 1631 a(Figure) i(4:) i(Compar) n(ison) f(of) g(four) f
(TCP) i(models) f(with) g(simulation) g(results.) 191
2040 y(A) 30 b(and) g(A) -9 b(') 30 b(gi) n(v) o(e) f(close) h
(analytic) f(results) i(with) f(those) f(with) i(the) f(mod) n(el) h
(B,) f(models) g(A) g(and) f(A) -9 b(') 30 b(should) f(not) h(be) 191
2140 y(appr) n(opriate) h(for) g(analyzing) f(the) i(transient) f
(state) i(beha) l(vior) f(of) f(TCP) i(since) f(these) f(models) h(are)
f(based) h(on) f(the) 191 2240 y(steady) d(state) i(analysis) f(of) f
(TCP) -9 b(.) 29 b(In) g(the) g(follo) l(wing) g(sections,) f(with) h
(using) g(the) f(model) g(B,) i(we) f(will) g(deri) n(v) o(e) f(the) 191
2339 y(TCP) 19 b(thro) n(ughp) n(ut,) f(the) g(pack) o(et) f(loss) i
(pro) n(bability) -5 b(,) 17 b(and) g(the) h(queu) n(e) h(length) e(of)
g(the) h(bottlene) n(ck) g(router) -7 b(.) 19 b(W) -7
b(e) 19 b(will) g(also) 191 2439 y(analyze) g(the) h(transient) g
(state) h(beha) n(vio) n(r) g(of) f(TCP) h(using) e(a) i(contr) n(ol) g
(theor) n(etic) g(appro) n(ach.) 1471 2886 y(4.) 40 b(Steady) 20
b(State) h(Analysis) 191 3026 y(In) 29 b(what) g(follo) n(ws,) f(we) i
(present) e(steady) h(state) h(analysis) f(for) g(the) g(comb) n
(ination) g(of) f(the) i(mod) n(el) g(B) g(for) e(TCP) i(and) 191
3126 y(a) p Fo 27 w(M) t(=) -5 b(M) t(=) p Fn(1) p Fo(=m) p
Fr 25 w(queu) n(ing) 26 b(system) h(for) f(the) g(netw) o(ork) n(.) h
(As) g(ha) n(v) o(e) f(been) g(e) o(xp) n(lained) g(in) h(Section) f
(2.2) n(,) h(the) f(model) g(B) 191 3225 y(describes) k(the) g(chang) n
(e) h(of) f(the) g(windo) n(w) g(size) h(e) n(v) o(er) n(y) g(receip) n
(t) g(of) f(an) h(A) m(CK) f(pack) o(et.) g(Hence,) g(in) g(the) g
(follo) n(wing) 191 3325 y(analysis,) 18 b(the) h(dura) n(tion) g
(between) e(tw) o(o) i(succeedin) n(g) g(A) m(CK) g(pack) o(ets) f
(correspo) n(nds) h(to) f(a) h(unit) g(time.) f(In) g(this) h(section,)
191 3425 y(we) f(deri) n(v) m(e) g(the) g(TCP) g(throu) n(ghpu) n(t,) g
(the) g(pack) m(et) h(loss) f(prob) n(ability) -5 b(,) 17
b(and) g(the) g(a) n(v) o(erage) f(queue) h(length) f(in) i(steady) f
(state.) 191 3524 y(W) -7 b(e) 21 b(then) f(v) n(alidate) g(our) f
(appr) n(oximate) h(analysis) g(by) g(comp) n(aring) g(analy) n(tic) h
(results) g(with) f(simulation) f(ones.) 274 3654 y(The) 36
b(congestion) f(contro) n(l) j(mecha) n(nism) f(of) g(TCP) g(is) h(an) e
(AIMD) h(\(Additi) n(v) m(e) g(Increase) f(and) g(Multiplicati) n(v) o
(e) 191 3753 y(Decrease\)) 30 b(based) h(feedba) n(ck) g(control.) f
(When) h(the) g(prop) n(agation) f(delay) g(is) j(non) n(-ne) o(g) n
(ligible,) e(the) g(windo) n(w) f(size) 191 3853 y(oscillates) 19
b(and) e(ne) n(v) o(er) g(con) m(v) m(er) o(ge) n(s) j(to) e(a) h
(constan) n(t) g(v) n(alue.) e(Note) i(that) f(the) g(symbol) p
Fo 17 w(w) p Fn 2 w(\() p Fo(k) p Fn 3 w(\)) p Fr 20
w(represents) g(not) g(the) g(instant) 191 3952 y(v) n(alue) k(of) g
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(e) o(xpected) f(v) n(alue) h(of) g(the) h(TCP) g(windo) n(w) e(size) j
(after) e(a) h(long) 191 4052 y(period) n(.) 274 4181
y(Let) c(equilibr) n(ium) g(v) n(alues) g(of) g(the) g(TCP) g(windo) n
(w) f(size) i(and) e(the) h(pack) o(et) g(loss) h(pro) n(bability) f
(in) g(the) g(netw) o(or) n(k) g(be) p Fo 19 w(w) p Fh
3539 4151 a(\003) p Fr 191 4281 a(and) p Fo 20 w(p) p
Fh 374 4251 a(\003) p Fr 412 4281 a(,) h(respecti) n(v) o(e) n(ly;) h
(i.e.,) p Fo 1542 4506 a(w) p Fh 1603 4472 a(\003) p
Fp 1725 4506 a(\021) p Fn 109 w(lim) p Fl 1872 4561 a(k) p
Fh 1 w(!1) p Fo 2055 4506 a(w) p Fn 2 w(\() p Fo(k) p
Fn 3 w(\)) p Fr 1255 w(\(7\)) p Fo 1562 4664 a(p) p Fh
1604 4630 a(\003) p Fp 1725 4664 a(\021) p Fn 109 w(lim) p
Fl 1872 4719 a(k) p Fh 1 w(!1) p Fo 2055 4664 a(p) p
Fn(\() p Fo(k) p Fn 3 w(\)) p Fr 1274 w(\(8\)) 191 4923
y(These) f(v) n(alue) n(s) h(can) f(be) g(num) n(erically) g(obtaine) n
(d) g(by) g(solving) f(Eqs.) h(\(1\)) f(and) g(\(5\)) h(with) g
(equatin) n(g) p Fo 20 w(w) p Fn 2 w(\() p Fo(k) p Fn
22 w(+) d(1\)) p Fp 23 w(\021) p Fo 22 w(w) p Fn 2 w(\() p
Fo(k) p Fn 3 w(\)) p Fr 191 5023 a(and) p Fo 24 w(p) p
Fn(\() p Fo(k) p Fn 24 w(+) 22 b(1\)) p Fp 31 w(\021) p
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FD 191 5222 a(Cop) o(yri) r(ght) 497 5220 y(c) p Fm 476
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FD 18 w(2005;) p FB 18 w(00) p FD(:1\22618) p FC 191
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dyy eop end
%%Page: 10 10
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@endspecial 499 1439 a(\(a\)) h(TCP) g(throughp) r(ut) 1353
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@endspecial 1536 1439 a(\(b\)) g(P) o(ack) o(e) r(t) g(loss) g(probabi)
r(lity) 2478 1256 y @beginspecial 50 @llx 50 @lly 230
@urx 176 @ury 1300 @rwi 879 @rhi @setspecial
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@endspecial FD 499 2900 a(\(a\)) d(TCP) g(throughp) r(ut) 1353
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%%EndDocument
@endspecial 1536 2900 a(\(b\)) g(P) o(ack) o(e) r(t) g(loss) g(probabi)
r(lity) 2478 2718 y @beginspecial 50 @llx 50 @lly 230
@urx 176 @ury 1300 @rwi 879 @rhi @setspecial
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@endspecial 2676 2900 a(\(c\)) h(A) -5 b(v) o(erage) 18
b(queu) r(e) f(length) p Fr 659 3146 a(Figure) j(6:) g(Analytic) g(and)
f(simulation) h(results) g(for) g(dif) n(fe) n(rent) g(prop) n(agation)
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Fo(k) p Fn 3 w(\)) p Fr(,) g(the) f(transient) g(state) g(beha) n(vior)
f(of) h(TCP) h(can) f(be) 191 3612 y(analyze) n(d.) e(W) -7
b(e) 20 b(ne) o(x) n(t) g(present) f(se) n(v) o(eral) f(numer) n(ical) i
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4517 y(suf) n(fer) n(s) 28 b(less) g(throu) n(ghpu) n(t.) f(One) g(can)
g(also) g(\002nd) f(that) h(the) g(con) m(v) m(er) o(g) n(ence) g
(speed) f(\(i.e.,) g(in) h(this) h(case,) e(the) h(increase) 191
4616 y(rate) c(of) f(the) h(windo) n(w) f(size\)) h(of) g(the) g(windo)
l(w) h(size) f(is) h(indepe) n(ndent) e(of) h(the) g(amou) n(nt) g(of) g
(backg) n(roun) n(d) g(traf) n(\002c.) g(This) 191 4716
y(is) 29 b(because,) f(in) h(the) f(congestio) n(n) h(a) n(v) n(oidanc)
n(e) g(phase,) f(TCP) i(increa) n(ses) g(the) f(windo) l(w) g(size) g
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b(time,) h(which) g(is) h(essentially) g(irrele) n(v) l(ant) f(to) h
(the) f(TCP) h(throu) n(ghpu) n(t.) 274 4923 y(Figure) 40
b(8) h(sho) n(ws) f(the) h(e) n(v) n(olutio) n(n) g(of) f(the) h(windo)
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  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke } def
/TriUE { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke } def
/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath stroke } def
/PentE { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath stroke grestore } def
/CircE { stroke [] 0 setdash 
  hpt 0 360 arc stroke } def
/Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def
/DiaW { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V Opaque stroke } def
/BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V Opaque stroke } def
/TriUW { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V Opaque stroke } def
/TriDW { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V Opaque stroke } def
/PentW { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  Opaque stroke grestore } def
/CircW { stroke [] 0 setdash 
  hpt 0 360 arc Opaque stroke } def
/BoxFill { gsave Rec 1 setgray fill grestore } def
/MFshow {{dup dup 0 get findfont exch 1 get scalefont setfont
     [ currentpoint ] exch dup 2 get 0 exch rmoveto dup dup 5 get exch 4 get
     {show} {stringwidth pop 0 rmoveto}ifelse dup 3 get
     {2 get neg 0 exch rmoveto pop} {pop aload pop moveto}ifelse} forall} bind def
/MFwidth {0 exch {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont
      5 get stringwidth pop add}
    {pop} ifelse} forall} bind def
/MLshow { currentpoint stroke M
  0 exch R MFshow } bind def
/MRshow { currentpoint stroke M
  exch dup MFwidth neg 3 -1 roll R MFshow } def
/MCshow { currentpoint stroke M
  exch dup MFwidth -2 div 3 -1 roll R MFshow } def
end
%%EndProlog
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1.000 UL
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546 420 M
63 0 V
2753 0 R
-63 0 V
 stroke
462 420 M
[ [(Helvetica) 140.0 0.0 true true (0)]
] -46.7 MRshow
546 696 M
63 0 V
2753 0 R
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462 696 M
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546 972 M
63 0 V
2753 0 R
-63 0 V
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462 972 M
[ [(Helvetica) 140.0 0.0 true true (10)]
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546 1248 M
63 0 V
2753 0 R
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462 1248 M
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546 1524 M
63 0 V
2753 0 R
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462 1524 M
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546 1800 M
63 0 V
2753 0 R
-63 0 V
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462 1800 M
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546 2076 M
63 0 V
2753 0 R
-63 0 V
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462 2076 M
[ [(Helvetica) 140.0 0.0 true true (30)]
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546 2352 M
63 0 V
2753 0 R
-63 0 V
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462 2352 M
[ [(Helvetica) 140.0 0.0 true true (35)]
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546 420 M
0 63 V
0 1869 R
0 -63 V
 stroke
546 280 M
[ [(Helvetica) 140.0 0.0 true true (0)]
] -46.7 MCshow
1250 420 M
0 63 V
0 1869 R
0 -63 V
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1250 280 M
[ [(Helvetica) 140.0 0.0 true true (0.5)]
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1954 420 M
0 63 V
0 1869 R
0 -63 V
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1954 280 M
[ [(Helvetica) 140.0 0.0 true true (1)]
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2658 420 M
0 63 V
0 1869 R
0 -63 V
 stroke
2658 280 M
[ [(Helvetica) 140.0 0.0 true true (1.5)]
] -46.7 MCshow
3362 420 M
0 63 V
0 1869 R
0 -63 V
 stroke
3362 280 M
[ [(Helvetica) 140.0 0.0 true true (2)]
] -46.7 MCshow
1.000 UL
LTb
546 420 M
2816 0 V
0 1932 V
-2816 0 V
546 420 L
 stroke
140 1386 M
currentpoint gsave translate 90 rotate 0 0 moveto
[ [(Helvetica) 140.0 0.0 true true (Average Window Size [packet])]
] -46.7 MCshow
grestore
1954 70 M
[ [(Helvetica) 140.0 0.0 true true (Time [s])]
] -46.7 MCshow
1.000 UL
LT0
2711 2219 M
[ [(Symbol) 140.0 0.0 true true (l)]
[(Verbetica-Oblique) 112.0 -42.0 true true (B)]
[(Helvetica) 140.0 0.0 true true (=0.0)]
] -32.7 MRshow
2795 2219 M
399 0 V
546 475 M
21 54 V
18 26 V
15 21 V
13 17 V
12 18 V
12 16 V
10 14 V
10 14 V
10 13 V
9 12 V
8 12 V
8 11 V
8 11 V
8 10 V
7 10 V
8 10 V
7 10 V
6 9 V
7 9 V
7 8 V
6 9 V
6 8 V
6 8 V
6 8 V
6 8 V
6 7 V
5 8 V
6 7 V
5 7 V
6 7 V
5 7 V
5 7 V
5 7 V
5 7 V
5 6 V
5 7 V
5 6 V
5 6 V
4 7 V
5 6 V
5 6 V
4 6 V
5 6 V
4 5 V
4 6 V
5 6 V
4 6 V
4 5 V
5 6 V
4 5 V
4 6 V
4 5 V
4 5 V
4 6 V
4 5 V
4 5 V
4 5 V
4 5 V
4 5 V
4 5 V
3 5 V
4 5 V
4 5 V
3 5 V
4 5 V
4 5 V
3 5 V
4 4 V
4 5 V
3 5 V
4 4 V
3 5 V
4 4 V
3 5 V
4 4 V
3 5 V
3 4 V
4 5 V
3 4 V
3 4 V
4 5 V
3 4 V
3 4 V
3 4 V
4 5 V
3 4 V
3 4 V
3 4 V
3 4 V
4 4 V
3 4 V
3 5 V
3 4 V
3 4 V
3 4 V
3 4 V
3 3 V
3 4 V
3 4 V
3 4 V
3 4 V
3 4 V
3 4 V
3 4 V
3 3 V
3 4 V
3 4 V
3 4 V
2 3 V
3 4 V
3 4 V
3 3 V
3 4 V
3 4 V
2 3 V
3 4 V
3 4 V
3 3 V
2 4 V
3 3 V
3 4 V
3 3 V
2 4 V
3 3 V
3 4 V
2 3 V
3 4 V
3 3 V
2 4 V
3 3 V
3 3 V
2 4 V
3 3 V
2 4 V
3 3 V
3 3 V
2 4 V
3 3 V
2 3 V
3 3 V
2 4 V
3 3 V
3 3 V
2 4 V
3 3 V
2 3 V
3 3 V
2 3 V
3 4 V
2 3 V
2 3 V
3 3 V
2 3 V
3 3 V
2 3 V
3 4 V
2 3 V
3 3 V
2 3 V
2 3 V
3 3 V
2 3 V
3 3 V
2 3 V
2 3 V
3 3 V
2 3 V
3 3 V
2 3 V
2 3 V
3 3 V
2 3 V
2 2 V
3 3 V
2 3 V
3 3 V
2 3 V
2 2 V
3 3 V
2 3 V
2 2 V
3 3 V
2 2 V
3 3 V
2 2 V
2 2 V
3 3 V
2 2 V
3 2 V
2 2 V
2 2 V
3 1 V
2 2 V
3 2 V
2 1 V
3 1 V
2 2 V
3 1 V
3 0 V
2 1 V
3 0 V
2 1 V
3 0 V
3 -1 V
2 0 V
3 -1 V
2 -1 V
3 -1 V
2 -2 V
3 -2 V
2 -2 V
3 -2 V
2 -3 V
3 -3 V
2 -3 V
2 -4 V
3 -3 V
2 -4 V
2 -4 V
3 -4 V
2 -4 V
3 -4 V
2 -4 V
2 -4 V
3 -4 V
2 -3 V
2 -3 V
3 -4 V
2 -2 V
3 -2 V
2 -2 V
2 -2 V
3 -1 V
2 0 V
3 -1 V
2 0 V
2 1 V
3 0 V
2 1 V
2 2 V
3 1 V
2 2 V
3 1 V
2 2 V
2 3 V
3 2 V
2 2 V
3 2 V
2 2 V
2 3 V
3 2 V
2 3 V
2 2 V
3 2 V
2 3 V
2 2 V
3 3 V
2 2 V
3 2 V
2 3 V
2 2 V
3 2 V
2 3 V
2 2 V
3 2 V
2 2 V
3 2 V
2 1 V
2 2 V
3 2 V
2 1 V
3 2 V
2 1 V
3 1 V
2 1 V
3 1 V
2 1 V
3 0 V
3 1 V
2 0 V
3 0 V
2 0 V
3 -1 V
2 -1 V
3 0 V
2 -2 V
3 -1 V
2 -2 V
3 -2 V
2 -2 V
3 -2 V
2 -3 V
2 -3 V
3 -3 V
2 -3 V
2 -4 V
3 -3 V
2 -3 V
3 -4 V
2 -4 V
2 -3 V
3 -4 V
2 -3 V
2 -3 V
3 -3 V
2 -3 V
2 -2 V
3 -2 V
2 -2 V
3 -1 V
2 -1 V
2 -1 V
3 -1 V
2 0 V
3 1 V
2 0 V
2 1 V
3 1 V
2 2 V
2 1 V
3 2 V
2 1 V
3 2 V
2 2 V
2 2 V
3 2 V
2 2 V
2 3 V
3 2 V
2 2 V
3 2 V
2 3 V
2 2 V
3 2 V
2 3 V
2 2 V
3 2 V
2 2 V
2 3 V
3 2 V
2 2 V
3 2 V
2 2 V
2 2 V
3 1 V
2 2 V
3 2 V
2 1 V
3 1 V
2 2 V
3 1 V
2 1 V
3 1 V
2 1 V
3 0 V
2 1 V
3 0 V
2 0 V
3 0 V
2 -1 V
3 0 V
2 -1 V
3 -1 V
2 -2 V
3 -1 V
2 -2 V
3 -2 V
2 -2 V
2 -3 V
3 -3 V
2 -2 V
3 -3 V
2 -4 V
2 -3 V
3 -3 V
2 -4 V
2 -3 V
3 -3 V
2 -4 V
3 -3 V
2 -3 V
2 -3 V
3 -2 V
2 -3 V
2 -2 V
3 -2 V
2 -1 V
3 -1 V
2 -1 V
2 0 V
3 -1 V
2 1 V
2 0 V
3 1 V
2 1 V
3 1 V
2 1 V
currentpoint stroke M
2 2 V
3 1 V
2 2 V
2 2 V
3 2 V
2 2 V
3 2 V
2 2 V
2 2 V
3 3 V
2 2 V
2 2 V
3 2 V
2 3 V
2 2 V
3 2 V
2 2 V
3 2 V
2 3 V
2 2 V
3 2 V
2 2 V
2 2 V
3 1 V
2 2 V
3 2 V
2 1 V
3 2 V
2 1 V
3 1 V
2 2 V
3 1 V
2 0 V
3 1 V
2 1 V
3 0 V
2 0 V
3 0 V
2 0 V
3 0 V
2 -1 V
3 -1 V
2 -1 V
3 -1 V
2 -1 V
3 -2 V
2 -2 V
2 -2 V
3 -3 V
2 -3 V
3 -2 V
2 -3 V
2 -4 V
3 -3 V
2 -3 V
2 -3 V
3 -4 V
2 -3 V
2 -3 V
3 -3 V
2 -3 V
3 -3 V
2 -3 V
2 -2 V
3 -2 V
2 -2 V
2 -2 V
3 -1 V
2 0 V
3 -1 V
2 0 V
2 0 V
3 1 V
2 0 V
3 1 V
2 2 V
2 1 V
3 1 V
2 2 V
2 2 V
3 1 V
2 2 V
3 2 V
2 2 V
2 2 V
3 3 V
2 2 V
2 2 V
3 2 V
2 3 V
2 2 V
3 2 V
2 2 V
3 2 V
2 3 V
2 2 V
3 2 V
2 2 V
2 2 V
3 2 V
2 1 V
3 2 V
2 2 V
3 1 V
2 2 V
2 1 V
3 1 V
2 1 V
3 1 V
2 1 V
3 1 V
2 1 V
3 0 V
2 0 V
3 0 V
2 0 V
3 0 V
2 -1 V
3 -1 V
2 -1 V
3 -1 V
2 -2 V
3 -1 V
2 -2 V
3 -3 V
2 -2 V
2 -3 V
3 -3 V
2 -3 V
3 -3 V
2 -3 V
2 -3 V
3 -3 V
2 -4 V
2 -3 V
3 -3 V
2 -3 V
3 -3 V
2 -3 V
2 -3 V
3 -2 V
2 -2 V
2 -2 V
3 -1 V
2 -1 V
3 -1 V
2 0 V
2 -1 V
3 1 V
2 0 V
2 1 V
3 1 V
2 1 V
3 1 V
2 2 V
2 1 V
3 2 V
2 2 V
2 1 V
3 2 V
2 3 V
3 2 V
2 2 V
2 2 V
3 2 V
2 2 V
2 3 V
3 2 V
2 2 V
2 2 V
3 3 V
2 2 V
3 2 V
2 2 V
2 2 V
3 2 V
2 2 V
3 1 V
2 2 V
2 2 V
3 1 V
2 2 V
3 1 V
2 1 V
3 1 V
2 1 V
3 1 V
2 1 V
3 1 V
2 0 V
3 0 V
2 0 V
3 0 V
2 0 V
3 -1 V
2 -1 V
3 -1 V
2 -1 V
3 -2 V
2 -1 V
3 -3 V
2 -2 V
2 -2 V
3 -3 V
2 -3 V
3 -3 V
2 -3 V
2 -3 V
3 -3 V
2 -3 V
2 -4 V
3 -3 V
2 -3 V
2 -3 V
3 -3 V
2 -3 V
3 -2 V
2 -3 V
2 -2 V
3 -2 V
2 -1 V
2 -1 V
3 -1 V
2 0 V
3 0 V
2 0 V
2 0 V
3 1 V
2 1 V
2 1 V
3 1 V
2 2 V
3 1 V
2 2 V
2 2 V
3 2 V
2 2 V
2 2 V
3 2 V
2 2 V
3 2 V
2 2 V
2 3 V
3 2 V
2 2 V
2 2 V
3 2 V
2 3 V
2 2 V
3 2 V
2 2 V
3 2 V
2 2 V
2 2 V
3 1 V
2 2 V
3 2 V
2 1 V
3 2 V
2 1 V
2 1 V
3 1 V
2 1 V
3 1 V
2 1 V
3 1 V
2 0 V
3 0 V
2 0 V
3 0 V
3 -1 V
2 0 V
3 -1 V
2 -1 V
2 -1 V
3 -2 V
2 -2 V
3 -2 V
2 -2 V
3 -2 V
2 -3 V
2 -3 V
3 -3 V
2 -3 V
3 -3 V
2 -3 V
2 -4 V
3 -3 V
2 -3 V
2 -3 V
3 -3 V
2 -3 V
2 -3 V
3 -3 V
2 -2 V
3 -2 V
2 -2 V
2 -1 V
3 -1 V
2 -1 V
2 0 V
3 0 V
2 0 V
3 0 V
2 1 V
2 1 V
3 1 V
2 2 V
2 1 V
3 2 V
2 1 V
3 2 V
2 2 V
2 2 V
3 2 V
2 2 V
2 2 V
3 2 V
2 3 V
3 2 V
2 2 V
2 2 V
3 2 V
2 3 V
2 2 V
3 2 V
2 2 V
2 2 V
3 2 V
2 2 V
3 2 V
2 2 V
2 1 V
3 2 V
2 1 V
3 2 V
2 1 V
3 1 V
2 1 V
3 1 V
2 1 V
3 1 V
2 1 V
3 0 V
2 0 V
3 0 V
2 0 V
3 -1 V
2 0 V
3 -1 V
2 -1 V
3 -2 V
2 -1 V
3 -2 V
2 -2 V
2 -2 V
3 -3 V
2 -2 V
3 -3 V
2 -3 V
2 -3 V
3 -3 V
2 -4 V
2 -3 V
3 -3 V
2 -3 V
3 -3 V
2 -3 V
2 -3 V
3 -3 V
2 -3 V
2 -2 V
3 -2 V
2 -2 V
3 -1 V
2 -1 V
2 -1 V
3 0 V
2 0 V
2 0 V
3 1 V
2 0 V
3 1 V
2 1 V
2 2 V
3 1 V
2 2 V
2 1 V
3 2 V
2 2 V
3 2 V
2 2 V
2 2 V
3 2 V
2 3 V
2 2 V
3 2 V
2 2 V
3 2 V
2 3 V
currentpoint stroke M
2 2 V
3 2 V
2 2 V
2 2 V
3 2 V
2 2 V
3 2 V
2 2 V
2 2 V
3 1 V
2 2 V
3 2 V
2 1 V
2 1 V
3 1 V
2 2 V
3 1 V
2 0 V
3 1 V
2 1 V
3 0 V
2 0 V
3 0 V
3 0 V
2 -1 V
3 0 V
2 -1 V
3 -1 V
2 -2 V
2 -1 V
3 -2 V
2 -2 V
3 -2 V
2 -3 V
3 -3 V
2 -2 V
2 -3 V
3 -3 V
2 -4 V
2 -3 V
3 -3 V
2 -3 V
2 -3 V
3 -4 V
2 -3 V
3 -3 V
2 -2 V
2 -3 V
3 -2 V
2 -2 V
2 -2 V
3 -1 V
2 -1 V
3 -1 V
2 0 V
2 0 V
3 0 V
2 1 V
2 0 V
3 1 V
2 2 V
3 1 V
2 1 V
2 2 V
3 2 V
2 1 V
2 2 V
3 2 V
2 2 V
3 2 V
2 3 V
2 2 V
3 2 V
2 2 V
2 2 V
3 3 V
2 2 V
2 2 V
3 2 V
2 2 V
3 2 V
2 2 V
2 2 V
3 2 V
2 2 V
3 2 V
2 2 V
2 1 V
3 2 V
2 1 V
3 1 V
2 2 V
3 1 V
2 1 V
3 0 V
2 1 V
3 1 V
2 0 V
3 0 V
2 0 V
3 0 V
2 -1 V
3 0 V
2 -1 V
3 -1 V
2 -2 V
3 -1 V
2 -2 V
3 -2 V
2 -3 V
2 -2 V
3 -3 V
2 -3 V
2 -3 V
3 -3 V
2 -3 V
3 -3 V
2 -3 V
2 -3 V
3 -4 V
2 -3 V
2 -3 V
3 -3 V
2 -2 V
3 -3 V
2 -2 V
2 -2 V
3 -2 V
2 -1 V
2 -1 V
3 -1 V
2 0 V
3 0 V
2 0 V
2 1 V
3 0 V
2 1 V
2 2 V
3 1 V
2 1 V
3 2 V
2 2 V
2 1 V
3 2 V
2 2 V
2 2 V
3 3 V
2 2 V
3 2 V
2 2 V
2 2 V
3 3 V
2 2 V
2 2 V
3 2 V
2 2 V
2 2 V
3 3 V
2 2 V
3 2 V
2 1 V
2 2 V
3 2 V
2 2 V
3 1 V
2 2 V
3 1 V
2 1 V
2 2 V
3 1 V
2 1 V
3 0 V
2 1 V
3 1 V
2 0 V
3 0 V
3 0 V
2 0 V
3 -1 V
2 -1 V
3 0 V
2 -2 V
2 -1 V
3 -1 V
2 -2 V
3 -2 V
2 -3 V
3 -2 V
2 -3 V
2 -3 V
3 -3 V
2 -3 V
2 -3 V
3 -3 V
2 -3 V
3 -4 V
2 -3 V
2 -3 V
3 -3 V
2 -3 V
2 -3 V
3 -2 V
2 -2 V
3 -2 V
2 -2 V
2 -1 V
3 -1 V
2 -1 V
2 0 V
3 0 V
2 0 V
3 1 V
2 1 V
2 1 V
3 1 V
2 1 V
2 2 V
3 1 V
2 2 V
3 2 V
2 2 V
2 2 V
3 2 V
2 2 V
2 2 V
3 2 V
2 2 V
2 3 V
3 2 V
2 2 V
3 2 V
2 2 V
2 3 V
3 2 V
2 2 V
2 2 V
3 2 V
2 2 V
3 1 V
2 2 V
2 2 V
3 1 V
2 2 V
3 1 V
2 1 V
3 2 V
2 1 V
1.000 UL
LT1
2711 2079 M
[ [(Symbol) 140.0 0.0 true true (l)]
[(Verbetica-Oblique) 112.0 -42.0 true true (B)]
[(Helvetica) 140.0 0.0 true true (=2.0)]
] -32.7 MRshow
2795 2079 M
399 0 V
546 475 M
22 54 V
17 26 V
15 21 V
13 17 V
13 18 V
11 16 V
11 14 V
10 14 V
9 13 V
9 12 V
9 12 V
8 11 V
8 11 V
8 10 V
7 10 V
7 10 V
7 10 V
7 9 V
7 9 V
7 8 V
6 9 V
6 8 V
6 8 V
6 8 V
6 8 V
6 7 V
6 8 V
5 7 V
6 7 V
5 7 V
5 7 V
6 7 V
5 7 V
5 7 V
5 6 V
5 7 V
5 6 V
5 6 V
4 7 V
5 6 V
5 6 V
4 6 V
5 6 V
5 5 V
4 6 V
4 6 V
5 6 V
4 5 V
5 6 V
4 5 V
4 6 V
4 5 V
5 5 V
4 6 V
4 5 V
4 5 V
4 5 V
4 5 V
4 5 V
4 5 V
5 5 V
4 4 V
4 5 V
4 4 V
4 5 V
4 4 V
4 4 V
5 5 V
5 3 V
5 4 V
7 4 V
30 3 V
3 3 V
4 3 V
3 2 V
4 2 V
3 2 V
4 1 V
3 0 V
4 1 V
3 0 V
3 -1 V
4 -1 V
3 -2 V
4 -2 V
3 -2 V
4 -3 V
18 -3 V
6 -4 V
6 -4 V
4 -3 V
5 -4 V
4 -4 V
4 -4 V
4 -3 V
5 -4 V
4 -2 V
4 -3 V
4 -1 V
4 -2 V
4 0 V
4 -1 V
4 1 V
4 0 V
4 1 V
4 2 V
5 1 V
4 2 V
4 3 V
4 2 V
4 2 V
4 3 V
5 2 V
4 2 V
4 3 V
5 2 V
5 3 V
5 2 V
5 2 V
7 2 V
8 2 V
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@endspecial 479 1631 a(Figure) j(7:) g(T) m(ransien) n(t) h(state) g
(beha) n(vio) n(r) g(of) f(TCP) h(for) e(dif) n(fere) n(nt) i(amou) n
(nt) g(of) f(back) n(grou) n(nd) g(traf) n(\002c.) 1139
2831 y @beginspecial 50 @llx 50 @lly 230 @urx 176 @ury
1788 @rwi 1209 @rhi @setspecial
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 stroke
462 972 M
[ [(Helvetica) 140.0 0.0 true true (10)]
] -46.7 MRshow
546 1248 M
63 0 V
2753 0 R
-63 0 V
 stroke
462 1248 M
[ [(Helvetica) 140.0 0.0 true true (15)]
] -46.7 MRshow
546 1524 M
63 0 V
2753 0 R
-63 0 V
 stroke
462 1524 M
[ [(Helvetica) 140.0 0.0 true true (20)]
] -46.7 MRshow
546 1800 M
63 0 V
2753 0 R
-63 0 V
 stroke
462 1800 M
[ [(Helvetica) 140.0 0.0 true true (25)]
] -46.7 MRshow
546 2076 M
63 0 V
2753 0 R
-63 0 V
 stroke
462 2076 M
[ [(Helvetica) 140.0 0.0 true true (30)]
] -46.7 MRshow
546 2352 M
63 0 V
2753 0 R
-63 0 V
 stroke
462 2352 M
[ [(Helvetica) 140.0 0.0 true true (35)]
] -46.7 MRshow
546 420 M
0 63 V
0 1869 R
0 -63 V
 stroke
546 280 M
[ [(Helvetica) 140.0 0.0 true true (0)]
] -46.7 MCshow
1250 420 M
0 63 V
0 1869 R
0 -63 V
 stroke
1250 280 M
[ [(Helvetica) 140.0 0.0 true true (0.5)]
] -46.7 MCshow
1954 420 M
0 63 V
0 1869 R
0 -63 V
 stroke
1954 280 M
[ [(Helvetica) 140.0 0.0 true true (1)]
] -46.7 MCshow
2658 420 M
0 63 V
0 1869 R
0 -63 V
 stroke
2658 280 M
[ [(Helvetica) 140.0 0.0 true true (1.5)]
] -46.7 MCshow
3362 420 M
0 63 V
0 1869 R
0 -63 V
 stroke
3362 280 M
[ [(Helvetica) 140.0 0.0 true true (2)]
] -46.7 MCshow
1.000 UL
LTb
546 420 M
2816 0 V
0 1932 V
-2816 0 V
546 420 L
 stroke
140 1386 M
currentpoint gsave translate 90 rotate 0 0 moveto
[ [(Helvetica) 140.0 0.0 true true (Average Window Size [packet])]
] -46.7 MCshow
grestore
1954 70 M
[ [(Helvetica) 140.0 0.0 true true (Time [s])]
] -46.7 MCshow
1.000 UL
LT0
2711 2219 M
[ [(Symbol) 140.0 0.0 true true (t)]
[(Helvetica) 140.0 0.0 true true (=10)]
] -46.7 MRshow
2795 2219 M
399 0 V
546 475 M
7 53 V
6 26 V
5 20 V
5 17 V
4 18 V
4 16 V
4 15 V
3 14 V
4 13 V
3 12 V
3 12 V
3 11 V
3 11 V
3 10 V
3 10 V
4 10 V
3 10 V
2 9 V
2 8 V
2 9 V
2 8 V
2 7 V
2 7 V
3 5 V
2 4 V
1 2 V
2 -1 V
2 -3 V
2 -4 V
3 -7 V
2 -9 V
2 -9 V
2 -10 V
2 -9 V
3 -8 V
4 -6 V
4 -4 V
4 -2 V
4 1 V
4 3 V
6 4 V
3 6 V
2 6 V
2 7 V
2 7 V
3 6 V
2 7 V
2 5 V
2 5 V
2 4 V
2 2 V
2 1 V
2 -1 V
2 -3 V
2 -5 V
2 -5 V
2 -7 V
3 -8 V
2 -8 V
2 -6 V
2 -6 V
22 -4 V
6 -3 V
6 -1 V
7 2 V
3 2 V
2 4 V
2 6 V
2 5 V
3 6 V
2 5 V
2 6 V
2 5 V
2 4 V
2 4 V
2 2 V
2 1 V
2 0 V
2 -2 V
3 -3 V
2 -4 V
2 -6 V
2 -6 V
2 -7 V
2 -6 V
3 -5 V
2 -5 V
2 -2 V
3 -2 V
2 1 V
2 2 V
3 3 V
2 4 V
2 5 V
2 5 V
3 5 V
2 5 V
2 4 V
2 4 V
2 4 V
2 2 V
2 2 V
2 0 V
2 -2 V
2 -2 V
3 -4 V
2 -4 V
2 -6 V
2 -6 V
2 -5 V
3 -5 V
2 -4 V
2 -3 V
2 -2 V
3 0 V
2 1 V
2 3 V
3 3 V
2 4 V
2 5 V
2 4 V
3 5 V
2 4 V
2 4 V
2 3 V
2 3 V
2 1 V
2 1 V
2 -1 V
2 -2 V
2 -3 V
2 -4 V
3 -5 V
2 -5 V
2 -5 V
2 -5 V
3 -4 V
2 -3 V
2 -2 V
3 0 V
2 1 V
2 2 V
2 3 V
3 3 V
2 4 V
2 5 V
2 4 V
2 4 V
3 3 V
2 3 V
2 3 V
2 2 V
2 0 V
2 -1 V
2 -1 V
2 -3 V
2 -3 V
2 -4 V
3 -5 V
2 -5 V
2 -4 V
2 -4 V
3 -3 V
2 -2 V
2 -1 V
3 1 V
2 2 V
2 2 V
2 3 V
3 4 V
2 4 V
2 4 V
2 3 V
2 4 V
2 3 V
3 2 V
2 2 V
2 1 V
2 -1 V
2 -1 V
2 -2 V
2 -3 V
2 -4 V
2 -4 V
3 -5 V
2 -4 V
2 -4 V
2 -3 V
3 -1 V
2 -1 V
2 0 V
3 1 V
2 2 V
2 3 V
2 4 V
3 3 V
2 4 V
2 4 V
2 3 V
2 3 V
2 2 V
2 2 V
2 1 V
3 0 V
2 -2 V
2 -2 V
2 -2 V
2 -4 V
2 -4 V
2 -4 V
3 -4 V
2 -4 V
2 -2 V
2 -2 V
3 -1 V
2 0 V
2 1 V
3 2 V
2 2 V
2 4 V
2 3 V
2 4 V
3 3 V
2 3 V
2 3 V
2 2 V
2 2 V
2 1 V
2 0 V
2 -1 V
3 -2 V
2 -2 V
2 -4 V
2 -3 V
2 -4 V
2 -4 V
3 -4 V
2 -3 V
2 -1 V
3 -2 V
2 0 V
2 1 V
2 2 V
3 3 V
2 2 V
2 4 V
2 3 V
2 3 V
3 3 V
2 3 V
2 2 V
2 2 V
2 1 V
2 0 V
2 -1 V
2 -1 V
2 -3 V
3 -3 V
2 -3 V
2 -4 V
2 -4 V
2 -3 V
3 -3 V
2 -2 V
2 -1 V
3 0 V
2 1 V
2 1 V
2 3 V
3 2 V
2 4 V
2 3 V
2 3 V
2 3 V
2 2 V
3 3 V
2 1 V
2 1 V
2 0 V
2 0 V
2 -2 V
2 -2 V
2 -3 V
3 -3 V
2 -3 V
2 -4 V
2 -3 V
2 -3 V
3 -2 V
2 -1 V
2 0 V
3 0 V
2 2 V
2 2 V
2 2 V
2 3 V
3 3 V
2 3 V
2 3 V
2 3 V
2 2 V
2 2 V
3 1 V
2 0 V
2 -1 V
2 -1 V
2 -2 V
2 -3 V
2 -3 V
3 -3 V
2 -4 V
2 -3 V
2 -2 V
2 -2 V
3 -1 V
2 -1 V
2 1 V
3 1 V
2 2 V
2 2 V
2 3 V
2 3 V
3 3 V
2 3 V
2 2 V
2 2 V
2 2 V
2 1 V
2 0 V
3 0 V
2 -1 V
2 -2 V
2 -3 V
2 -2 V
2 -4 V
2 -3 V
3 -3 V
2 -3 V
2 -2 V
2 -1 V
3 0 V
2 0 V
2 1 V
3 2 V
2 3 V
2 2 V
2 3 V
2 3 V
3 2 V
2 3 V
2 2 V
2 2 V
2 1 V
2 0 V
2 0 V
2 -2 V
3 -1 V
2 -3 V
2 -2 V
2 -4 V
2 -3 V
2 -3 V
3 -2 V
2 -2 V
2 -2 V
3 0 V
2 0 V
2 2 V
2 1 V
2 3 V
3 2 V
2 3 V
2 3 V
2 2 V
2 3 V
3 2 V
2 1 V
2 1 V
2 1 V
2 -1 V
2 -1 V
2 -1 V
2 -3 V
3 -2 V
2 -4 V
2 -3 V
2 -3 V
2 -2 V
3 -2 V
2 -1 V
2 -1 V
3 1 V
2 1 V
2 1 V
2 3 V
2 2 V
3 3 V
currentpoint stroke M
2 2 V
2 3 V
2 2 V
2 2 V
2 2 V
3 1 V
2 0 V
2 0 V
2 -1 V
2 -2 V
2 -2 V
2 -2 V
3 -3 V
2 -4 V
2 -2 V
2 -3 V
2 -2 V
3 -1 V
2 0 V
2 0 V
3 1 V
2 2 V
2 2 V
2 2 V
2 3 V
3 2 V
2 3 V
2 2 V
2 2 V
2 1 V
2 1 V
2 1 V
3 0 V
2 -1 V
2 -2 V
2 -2 V
2 -2 V
2 -3 V
3 -3 V
2 -3 V
2 -2 V
2 -2 V
2 -1 V
3 -1 V
2 0 V
2 1 V
2 2 V
3 2 V
2 2 V
2 3 V
2 2 V
2 2 V
3 2 V
2 2 V
2 2 V
2 1 V
2 0 V
2 0 V
2 -1 V
3 -1 V
2 -2 V
2 -2 V
2 -3 V
2 -3 V
3 -3 V
2 -2 V
2 -2 V
2 -1 V
2 0 V
3 0 V
2 1 V
2 1 V
2 2 V
3 2 V
2 3 V
2 2 V
2 2 V
2 2 V
3 2 V
2 2 V
2 1 V
2 0 V
2 0 V
2 -1 V
2 -1 V
2 -2 V
3 -2 V
2 -3 V
2 -3 V
2 -2 V
2 -3 V
3 -1 V
2 -2 V
2 0 V
2 0 V
3 1 V
2 1 V
2 2 V
2 2 V
3 2 V
2 3 V
2 2 V
2 2 V
2 2 V
2 1 V
3 1 V
2 1 V
2 -1 V
2 0 V
2 -2 V
2 -1 V
2 -2 V
3 -3 V
2 -3 V
2 -2 V
2 -2 V
2 -2 V
3 -1 V
2 -1 V
2 0 V
2 1 V
3 1 V
2 2 V
2 2 V
2 2 V
3 3 V
2 2 V
2 2 V
2 2 V
2 1 V
2 1 V
2 0 V
3 0 V
2 -1 V
2 -1 V
2 -1 V
2 -3 V
2 -2 V
3 -3 V
2 -2 V
2 -2 V
2 -2 V
2 -1 V
3 -1 V
2 1 V
2 0 V
2 2 V
3 1 V
2 2 V
2 2 V
2 3 V
2 2 V
3 2 V
2 1 V
2 2 V
2 1 V
2 0 V
2 0 V
2 -1 V
3 -1 V
2 -2 V
2 -2 V
2 -2 V
2 -3 V
3 -2 V
2 -2 V
2 -2 V
2 -1 V
2 0 V
3 0 V
2 1 V
2 1 V
2 1 V
3 2 V
2 2 V
2 3 V
2 2 V
2 1 V
3 2 V
2 2 V
2 0 V
2 1 V
2 0 V
2 -1 V
2 -1 V
3 -2 V
2 -2 V
2 -2 V
2 -3 V
2 -2 V
3 -2 V
2 -1 V
2 -1 V
2 -1 V
2 0 V
3 1 V
2 1 V
2 2 V
2 1 V
3 2 V
2 3 V
2 2 V
2 1 V
2 2 V
2 1 V
3 1 V
2 1 V
2 -1 V
2 0 V
2 -1 V
2 -2 V
2 -2 V
3 -2 V
2 -3 V
2 -2 V
2 -2 V
3 -1 V
2 -1 V
2 -1 V
2 0 V
2 1 V
3 1 V
2 2 V
2 1 V
2 2 V
3 3 V
2 1 V
2 2 V
2 2 V
2 1 V
2 1 V
2 0 V
3 0 V
2 0 V
2 -1 V
2 -2 V
2 -2 V
2 -2 V
3 -2 V
2 -3 V
2 -2 V
2 -1 V
3 -1 V
2 -1 V
2 0 V
2 1 V
2 1 V
3 2 V
2 2 V
2 2 V
2 2 V
2 1 V
3 2 V
2 2 V
2 1 V
2 1 V
2 0 V
2 0 V
2 -1 V
3 -1 V
2 -1 V
2 -2 V
2 -2 V
2 -2 V
3 -3 V
2 -1 V
2 -2 V
2 -1 V
3 0 V
2 0 V
2 0 V
2 1 V
2 2 V
3 2 V
2 2 V
2 1 V
2 2 V
2 2 V
3 2 V
2 1 V
2 1 V
2 0 V
2 0 V
2 -1 V
2 -1 V
3 -1 V
2 -2 V
2 -2 V
2 -2 V
2 -2 V
3 -2 V
2 -2 V
2 -1 V
2 0 V
2 0 V
3 0 V
2 2 V
2 1 V
2 2 V
3 2 V
2 1 V
2 2 V
2 2 V
2 1 V
2 2 V
3 0 V
2 1 V
2 0 V
2 -1 V
2 -1 V
2 -1 V
2 -2 V
3 -2 V
2 -2 V
2 -2 V
2 -2 V
3 -2 V
2 -1 V
2 0 V
2 0 V
2 1 V
3 1 V
2 1 V
2 2 V
2 2 V
3 1 V
2 2 V
2 2 V
2 1 V
2 1 V
2 1 V
2 0 V
3 0 V
2 0 V
2 -1 V
2 -2 V
2 -1 V
2 -2 V
3 -2 V
2 -2 V
2 -2 V
2 -1 V
3 -1 V
2 -1 V
2 0 V
2 1 V
2 1 V
3 1 V
2 2 V
2 2 V
2 1 V
2 2 V
3 2 V
2 1 V
2 1 V
2 1 V
2 0 V
2 0 V
3 -1 V
2 -1 V
2 -1 V
2 -1 V
2 -2 V
2 -2 V
3 -2 V
2 -2 V
2 -1 V
2 -1 V
3 0 V
2 0 V
2 0 V
2 1 V
2 2 V
3 1 V
2 2 V
2 1 V
2 2 V
2 1 V
3 2 V
2 1 V
2 0 V
2 1 V
2 0 V
2 -1 V
2 -1 V
3 -1 V
2 -2 V
2 -1 V
2 -2 V
2 -2 V
3 -2 V
2 -1 V
2 -1 V
2 0 V
3 0 V
2 1 V
2 1 V
2 1 V
2 1 V
3 2 V
currentpoint stroke M
2 1 V
2 2 V
2 1 V
2 1 V
2 1 V
3 1 V
2 0 V
2 0 V
2 0 V
2 -1 V
2 -1 V
3 -2 V
2 -2 V
2 -1 V
2 -2 V
2 -2 V
3 -1 V
2 0 V
2 -1 V
2 0 V
3 1 V
2 1 V
2 1 V
2 1 V
2 2 V
3 2 V
2 1 V
2 1 V
2 1 V
2 1 V
2 1 V
3 0 V
2 0 V
2 -1 V
2 0 V
2 -2 V
2 -1 V
3 -2 V
2 -2 V
2 -1 V
2 -2 V
2 -1 V
3 0 V
2 -1 V
2 1 V
2 0 V
3 1 V
2 1 V
2 2 V
2 1 V
2 2 V
2 1 V
3 1 V
2 1 V
2 1 V
2 1 V
2 0 V
2 0 V
3 -1 V
2 -1 V
2 -1 V
2 -2 V
2 -1 V
2 -2 V
3 -1 V
2 -1 V
2 -1 V
2 -1 V
3 0 V
2 0 V
2 1 V
2 0 V
2 2 V
3 1 V
2 1 V
2 2 V
2 1 V
2 1 V
3 1 V
2 1 V
2 0 V
2 1 V
2 -1 V
2 0 V
3 -1 V
2 -1 V
2 -2 V
2 -1 V
2 -2 V
2 -1 V
3 -1 V
2 -1 V
2 -1 V
2 0 V
3 0 V
2 1 V
2 1 V
2 1 V
2 1 V
3 2 V
2 1 V
2 1 V
2 1 V
2 1 V
2 1 V
3 0 V
2 0 V
2 0 V
2 -1 V
2 -1 V
2 -1 V
3 -1 V
2 -2 V
2 -1 V
2 -1 V
2 -1 V
3 -1 V
2 -1 V
2 0 V
2 1 V
3 0 V
2 1 V
2 1 V
2 2 V
2 1 V
3 1 V
2 1 V
2 1 V
2 1 V
2 1 V
2 0 V
3 0 V
2 0 V
2 -1 V
2 -1 V
2 -1 V
2 -2 V
3 -1 V
2 -1 V
2 -1 V
2 -1 V
2 -1 V
3 0 V
2 0 V
2 0 V
2 1 V
3 1 V
2 1 V
2 1 V
2 1 V
2 1 V
3 1 V
2 1 V
2 1 V
2 0 V
2 0 V
2 0 V
3 0 V
2 -1 V
2 -1 V
2 -1 V
2 -1 V
2 -1 V
3 -1 V
2 -1 V
2 -1 V
2 -1 V
2 0 V
3 0 V
2 1 V
2 0 V
2 1 V
3 1 V
2 1 V
2 2 V
2 1 V
2 0 V
2 1 V
3 0 V
2 1 V
2 -1 V
2 0 V
2 -1 V
2 0 V
3 -1 V
2 -1 V
2 -1 V
2 -1 V
2 -1 V
3 -1 V
2 0 V
2 0 V
2 0 V
3 0 V
2 1 V
2 1 V
2 1 V
2 1 V
3 1 V
2 0 V
2 1 V
2 1 V
2 0 V
2 0 V
3 0 V
2 -1 V
2 0 V
2 -1 V
2 -1 V
2 -1 V
3 0 V
2 -1 V
2 -1 V
2 0 V
3 0 V
2 0 V
2 0 V
2 0 V
2 1 V
3 0 V
2 1 V
2 1 V
2 1 V
2 0 V
2 1 V
3 0 V
2 0 V
2 0 V
2 0 V
2 0 V
3 -1 V
2 0 V
2 -1 V
2 -1 V
2 0 V
3 -1 V
2 -1 V
2 0 V
2 0 V
2 0 V
3 0 V
2 1 V
2 0 V
2 1 V
2 0 V
3 1 V
2 1 V
2 0 V
2 1 V
2 0 V
2 0 V
3 0 V
2 0 V
2 -1 V
2 0 V
2 -1 V
3 0 V
2 -1 V
2 0 V
2 -1 V
2 0 V
3 0 V
2 -1 V
2 0 V
2 1 V
2 0 V
3 0 V
2 1 V
2 0 V
2 1 V
2 1 V
2 0 V
3 0 V
2 0 V
2 1 V
2 -1 V
2 0 V
3 0 V
2 0 V
2 -1 V
2 0 V
2 -1 V
3 0 V
2 -1 V
2 0 V
2 0 V
2 0 V
3 0 V
2 0 V
2 0 V
2 1 V
2 0 V
3 1 V
2 0 V
2 0 V
2 1 V
2 0 V
2 0 V
3 0 V
2 0 V
2 0 V
2 0 V
2 -1 V
3 0 V
2 0 V
2 -1 V
2 0 V
2 -1 V
3 0 V
2 0 V
2 0 V
2 0 V
2 0 V
3 1 V
2 0 V
2 0 V
2 1 V
2 0 V
3 0 V
2 1 V
2 0 V
2 0 V
2 0 V
2 0 V
3 0 V
2 -1 V
2 0 V
2 0 V
2 -1 V
3 0 V
2 0 V
2 0 V
2 -1 V
2 0 V
3 0 V
2 0 V
2 1 V
2 0 V
2 0 V
3 0 V
2 1 V
2 0 V
2 0 V
2 1 V
2 0 V
3 0 V
2 0 V
2 0 V
2 -1 V
2 0 V
3 0 V
2 0 V
2 -1 V
2 0 V
2 0 V
3 0 V
2 0 V
2 0 V
2 0 V
2 0 V
3 0 V
2 0 V
2 0 V
2 1 V
2 0 V
3 0 V
2 0 V
2 0 V
2 1 V
2 0 V
2 0 V
3 -1 V
2 0 V
2 0 V
2 0 V
2 0 V
3 -1 V
2 0 V
2 0 V
2 0 V
2 0 V
3 0 V
2 0 V
2 0 V
2 0 V
2 0 V
3 0 V
2 1 V
2 0 V
2 0 V
2 0 V
2 0 V
3 0 V
2 0 V
2 0 V
2 0 V
2 0 V
3 0 V
2 0 V
2 0 V
currentpoint stroke M
2 -1 V
2 0 V
3 0 V
2 0 V
2 0 V
2 0 V
2 0 V
3 0 V
2 0 V
2 0 V
2 0 V
2 1 V
3 0 V
2 0 V
2 0 V
2 0 V
2 0 V
2 0 V
3 0 V
2 0 V
2 0 V
2 0 V
2 0 V
3 0 V
2 -1 V
2 0 V
2 0 V
2 0 V
3 0 V
2 0 V
2 0 V
2 0 V
2 0 V
3 0 V
2 1 V
2 0 V
2 0 V
2 0 V
3 0 V
2 0 V
2 0 V
2 0 V
2 0 V
2 0 V
3 0 V
2 0 V
2 0 V
2 0 V
2 -1 V
3 0 V
2 0 V
2 0 V
2 0 V
2 0 V
3 0 V
1.000 UL
LT1
2711 2079 M
[ [(Symbol) 140.0 0.0 true true (t)]
[(Helvetica) 140.0 0.0 true true (=30)]
] -46.7 MRshow
2795 2079 M
399 0 V
546 475 M
22 54 V
17 26 V
15 21 V
13 17 V
13 18 V
11 16 V
11 14 V
10 14 V
9 13 V
9 12 V
9 12 V
8 11 V
8 11 V
8 10 V
7 10 V
7 10 V
7 10 V
7 9 V
7 9 V
7 8 V
6 9 V
6 8 V
6 8 V
6 8 V
6 8 V
6 7 V
6 8 V
5 7 V
6 7 V
5 7 V
5 7 V
6 7 V
5 7 V
5 7 V
5 6 V
5 7 V
5 6 V
5 6 V
4 7 V
5 6 V
5 6 V
4 6 V
5 6 V
5 5 V
4 6 V
4 6 V
5 6 V
4 5 V
5 6 V
4 5 V
4 6 V
4 5 V
5 5 V
4 6 V
4 5 V
4 5 V
4 5 V
4 5 V
4 5 V
4 5 V
5 5 V
4 4 V
4 5 V
4 4 V
4 5 V
4 4 V
4 4 V
5 5 V
5 3 V
5 4 V
7 4 V
30 3 V
3 3 V
4 3 V
3 2 V
4 2 V
3 2 V
4 1 V
3 0 V
4 1 V
3 0 V
3 -1 V
4 -1 V
3 -2 V
4 -2 V
3 -2 V
4 -3 V
18 -3 V
6 -4 V
6 -4 V
4 -3 V
5 -4 V
4 -4 V
4 -4 V
4 -3 V
5 -4 V
4 -2 V
4 -3 V
4 -1 V
4 -2 V
4 0 V
4 -1 V
4 1 V
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2711 1939 M
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@endspecial 362 3014 a(Figure) f(8:) i(T) m(ran) n(sient) g(state) g
(beha) n(vio) n(r) g(of) e(TCP) i(for) f(dif) n(fer) n(ent) h(pro) n
(pagatio) n(n) f(delay) g(of) g(bottlene) n(ck) h(link.) 191
3346 y(prop) n(agation) 26 b(delay) g(increases.) h(This) g(can) g(be) g
(intuiti) n(v) o(e) n(ly) h(und) n(erstood) e(from) g(the) h(increased)
f(bandwid) n(th-delay) 191 3446 y(prod) n(uct.) c(In) f(addition) n(,) i
(as) f(the) g(prop) n(agation) e(delay) i(beco) n(mes) h(lar) o(g) n
(e,) f(one) f(can) h(\002nd) g(that) g(the) f(con) m(v) m(er) o(gen) n
(ce) h(speed) 191 3545 y(of) 27 b(the) g(windo) n(w) g(size) h(becom) n
(es) g(slo) n(w) -5 b(,) 27 b(and) g(that) h(the) f(ramp-) n(up) g
(time) h(of) f(the) g(windo) n(w) g(size) h(becom) n(es) g(short.) f
(In) 191 3645 y(gener) n(al,) d(as) g(the) f(feedba) n(ck) h(delay) e
(becomes) h(lar) o(g) n(e,) h(the) f(transient) g(state) h(beha) n(v) n
(ior) f(is) i(de) o(g) n(raded) e(and) f(the) i(system) 191
3744 y(becom) n(es) 18 b(less) f(stable.) g(Ho) n(we) n(v) m(er) m(,) f
(the) h(contr) n(ary) f(occurs) g(when) g(the) h(pro) n(pagatio) n(n) g
(delay) p Fo 16 w(\034) p Fr 27 w(is) g(small) g(\(e.g.,1) n(0) g
([ms]\)) n(,) 191 3844 y(the) j(windo) l(w) h(size) f(oscillates) g
(for) f(long) g(\(e.g.,) g(more) g(than) g(1.5) g([s]\).) h(This) g(is)
g(because,) f(from) g(a) h(contro) n(l) h(theor) n(etical) 191
3944 y(vie) n(wpo) n(int,) 26 b(the) g(feedba) n(ck) g(gain) f(in) i
(the) f(con) n(gestion) g(a) n(v) n(oidan) n(ce) h(phase) e(of) h(TCP) h
(is) g(chan) n(ged) f(accord) n(ing) g(to) g(the) 191
4043 y(roun) n(d-trip) e(time.) i(Namely) -7 b(,) 26
b(in) f(the) g(congestion) f(a) n(v) n(oidan) n(ce) i(phase) f(of) g
(TCP) -9 b(,) 25 b(the) h(windo) l(w) g(size) g(is) g(increm) n(ented)
191 4143 y(by) 19 b(one) g(pack) m(et) i(for) d(e) n(v) o(ery) g(roun) n
(d-trip) h(time.) g(Thus,) g(increasing) f(the) i(pro) n(pagatio) n(n) g
(delay) e(implies) i(decrea) n(sing) g(the) 191 4243
y(feedb) n(ack) g(gain.) 274 4342 y(W) -7 b(e) 28 b(then) f(analyze) g
(the) g(TCP) h(beha) n(vio) n(r) g(in) f(transient) g(state) h(using) f
(state) h(transition) e(equatio) n(ns.) i(Speci\002cally) -5
b(,) 191 4442 y(by) 28 b(apply) n(ing) g(the) g(contro) n(l) h(theory)
-7 b(,) 28 b(we) h(sho) n(w) f(ho) n(w) f(the) i(TCP) g(windo) l(w) g
(size) g(and) e(the) h(pack) o(et) g(loss) h(prob) n(ability) 191
4541 y(con) m(v) m(er) o(g) n(e) 21 b(to) f(their) g(equilibr) n(ium) g
(points.) 274 4641 y(Let) p Fi 20 w(x) p Fn(\() p Fo(k) p
Fn 3 w(\)) p Fr 22 w(be) g(the) g(dif) n(fere) n(nce) g(between) g(\() p
Fo(w) p Fn 2 w(\() p Fo(k) p Fn 3 w(\)) p Fr(,) p Fo
21 w(p) p Fn(\() p Fo(k) p Fn 3 w(\)) p Fr(\)) h(and) e(\() p
Fo(w) p Fh 2132 4611 a(\003) p Fr 2171 4641 a(,) p Fo
20 w(p) p Fh 2254 4611 a(\003) p Fr 2292 4641 a(\).) p
Fi 1352 4835 a(x) p Fn(\() p Fo(k) p Fn 3 w(\)) p Fp
84 w(\021) p Fk 1744 4718 a(\024) p Fo 1829 4784 a(w) p
Fn 2 w(\() p Fo(k) p Fn 3 w(\)) p Fp 84 w(\000) p Fo
83 w(w) p Fh 2293 4754 a(\003) p Fo 1849 4884 a(p) p
Fn(\() p Fo(k) p Fn 3 w(\)) p Fp 83 w(\000) p Fo 83 w(p) p
Fh 2274 4854 a(\003) p Fk 2373 4718 a(\025) p Fr 191
5023 a(Since) j(Eqs.) f(\(1\)) g(and) g(\(5\)) g(ha) n(v) o(e) g
(non-lin) n(earity) -5 b(,) 21 b(we) h(linearize) f(them) g(aroun) n(d)
h(their) g(equ) n(ilibrium) f(points) h(and) f(write) p
FD 191 5222 a(Cop) o(yri) r(ght) 497 5220 y(c) p Fm 476
5222 a(\015) p FD 16 w(2005) d(John) f(W) m(ile) o(y) h(&) f(Sons,) f
(Ltd.) p FC 1233 w(Int.) 21 b(J) n(.) c(Commun.) k(Syst.) p
FD 18 w(2005;) p FB 18 w(00) p FD(:1\22618) p FC 191
5301 a(Pr) n(epar) n(ed) 16 b(using) p FA 18 w(dacauth.cls) p
dyy eop end
%%Page: 14 14
TeXDict begin 14 13 bop Fr 191 266 a(14) p FD 1269 w(H.) 16
b(HISAMA) -7 b(TSU) 16 b(ET) g(AL.) p Fr 191 523 a(them) k(in) g(a) h
(matrix) e(form) p Fi 1471 708 a(x) p Fn(\() p Fo(k) p
Fn 22 w(+) f(1\)) 23 b(=) p Fi 22 w(A) 14 b(x) p Fn(\() p
Fo(k) p Fn 3 w(\)) p Fr 1309 w(\(11\)) 191 892 y(where) p
Fd 24 w(A) p Fr 25 w(is) 25 b(a) g(state) g(transition) e(matrix.) h
(Eigen) m(v) l(alues) g(of) g(the) h(state) g(transition) f(matrix) f
(determin) n(e) i(the) g(stability) 191 992 y(and) c(the) h(transient) g
(state) g(beha) n(vio) n(r) g(of) g(the) g(feedb) n(ack) g(system) g
(aroun) n(d) g(the) g(equilib) n(rium) g(poin) n(t) h([18]) n(.) f(It) h
(is) f(kno) n(wn) 191 1091 y(that) k(the) h(system) f(is) h(stable) g
(if) f(the) g(maximu) n(m) h(mod) n(ulus) g(is) g(less) g(than) f(one.)
f(It) i(is) g(also) g(kno) l(wn) f(that) h(the) f(smaller) 191
1191 y(the) c(maximu) n(m) h(mod) n(ulus) g(is,) g(the) f(better) g
(the) g(transient) g(state) h(beha) n(v) n(ior) f(becomes.) g(In) f
(the) i(follo) n(w) n(ings,) f(we) h(sho) n(w) 191 1291
y(se) n(v) o(eral) 17 b(num) n(erical) h(e) o(xam) n(ples) g(to) g(re) n
(v) o(e) n(al) g(ho) n(w) f(the) h(stability) f(and) g(the) g(TCP) i
(transient) e(state) h(beha) n(v) n(ior) g(are) f(af) n(fected) 191
1390 y(by) h(se) n(v) o(er) n(al) h(system) f(parameter) n(s) h(\227) g
(the) f(num) n(ber) g(of) g(TCP) h(conn) n(ections,) f(the) g(pro) n
(pagatio) n(n) h(delay) -7 b(,) 18 b(the) g(bottleneck) 191
1490 y(link) i(capacity) -5 b(,) 19 b(and) g(the) h(b) n(uf) n(fer) f
(size) i(of) f(the) g(bottleneck) f(router) -7 b(.) 274
1599 y(Figure) 27 b(9) i(and) e(10) h(sho) n(ws) g(the) g(contou) n(r) h
(plot) f(of) f(the) i(maxim) n(um) f(modu) n(lus) h(of) f(the) g(eigen)
m(v) l(alues.) g(The) g(\002gur) n(e) 191 1698 y(means) 17
b(that) g(the) g(maximu) n(m) h(mod) n(ulus) f(of) g(the) h(eigen) -5
b(v) n(alues) 17 b(becom) n(es) h(lar) o(ge) e(as) i(the) f(\002lled) h
(color) e(becom) n(es) i(dark.) e(A) 191 1798 y(white) i(area) h(is) g
(an) g(area) f(where) g(the) g(maximu) n(m) h(modu) n(lus) g(of) f
(eigen) m(v) l(alues) h(is) g(more) f(than) g(1.0) g(\(i.e.,) g
(unstable) g(area\)) n(.) 191 1898 y(Figure) g(9) h(sho) n(ws) f(the) h
(maximu) n(m) g(modu) n(lus) g(of) g(the) f(eigen) m(v) l(alues) h(for)
f(dif) n(fere) n(nt) h(numb) n(ers) g(of) g(TCP) g(connec) n(tions) g
(of) p Fo 191 1997 a(N) p Fr 33 w(=) 24 b(5,) f(10,) g(and) g(15.) g
(In) g(this) h(\002gure) n(,) g(we) g(plot) f(the) h(maxim) n(um) g
(mod) n(ulus) g(of) f(eigen) m(v) l(alues) g(of) h(the) f(state) h
(transient) 191 2097 y(matrix) p Fd 20 w(A) p Fr 21 w(for) 19
b(dif) n(fere) n(nt) i(bottlenec) n(k) g(link) f(capacities) g(of) p
Fo 20 w(\026) p Fr 21 w(=) h(0\2265) f([pac) n(k) o(et/ms]) h(and) e
(propag) n(ation) h(delay) n(s) i(of) p Fo 20 w(\034) p
Fr 30 w(=) 191 2196 y(0\2265) d([ms].) h(The) g(b) n(uf) n(fer) f(size)
i(of) f(the) h(bottlen) n(eck) f(router) p Fo 20 w(m) p
Fr 20 w(is) i(\002x) o(ed) d(at) p Fn 21 w(50) p Fr 20
w([pack) m(et]) i(and) f(the) g(a) n(v) o(erage) f(arri) n(v) n(al) h
(rate) 191 2296 y(of) g(the) g(backg) n(round) f(traf) n(\002c) p
Fo 20 w(\025) p Fl 1081 2308 a(B) p Fr 1159 2296 a(is) i(\002x) o(ed) f
(at) p Fn 20 w(0) p Fo(:) p Fn(2) p Fr 20 w([pack) o(et/m) n(s].) 274
2405 y(From) 25 b(Fig.) h(9,) g(one) f(can) h(\002nd) f(that) h(the) g
(maximu) n(m) g(modu) n(lus) h(of) e(the) h(eigen) m(v) l(alues) g(is) h
(mostly) e(determin) n(ed) h(by) p Fo 191 2504 a(\026) p
Fp 21 w(\002) p Fo 22 w(\034) p Fr 9 w(.) f(This) f(indicates) g(that) h
(the) f(stability) h(and) e(the) i(transien) n(t) g(state) g(beha) n
(vior) e(of) h(TCP) h(are) g(deter) n(mined) f(by) g(the) 191
2604 y(band) n(width\226d) n(elay) 30 b(prod) n(uct.) g(This) g(is) g
(because) g(the) f(congestion) f(contro) n(l) j(mechan) n(ism) f(of) g
(TCP) g(is) h(a) f(windo) n(w-) 191 2704 y(based) 18
b(mechan) n(ism,) h(and) f(it) h(chang) n(es) g(the) g(windo) l(w) g
(size) g(at) g(e) n(v) o(ery) e(receipt) h(of) g(an) g(A) m(CK) h(pack)
o(et.) f(Pro) o(v) n(ided) g(that) h(the) 191 2803 y(pack) o(et) e
(size) i(is) g(\002x) o(ed,) e(the) h(numb) n(er) g(of) g(A) m(CK) h
(pack) o(ets) f(in) g(the) g(netw) o(or) n(k) h(dur) n(ing) f(a) g
(round) n(-trip) g(time) g(is) h(pro) n(portion) n(al) 191
2903 y(to) k(the) h(ban) n(dwidth\226d) n(elay) f(prod) n(uct.) g(In) g
(the) h(contr) n(ol) g(engin) n(eer') -5 b(s) 24 b(vie) n(w) -5
b(,) 22 b(the) h(increase) g(of) g(the) g(propa) n(gation) f(delay) 191
3003 y(means) i(the) h(decr) n(ease) g(of) g(the) f(feedb) n(ack) h
(gain) e(or) i(the) f(feedb) n(ack) h(delay) -5 b(.) 23
b(Hence,) h(the) g(stability) h(and) f(the) g(transient) 191
3102 y(state) d(beha) n(v) n(ior) f(of) g(TCP) h(are) g(deter) n(mined)
f(by) g(the) g(band) n(width\226d) n(elay) g(produ) n(ct.) 274
3211 y(By) 29 b(compar) n(ing) g(Figs.) g(9\(a\)\226) n(\(c\),) g(one) f
(can) h(\002nd) g(that) g(as) h(the) f(num) n(ber) g(of) f(TCP) i
(conne) n(ctions) f(increases,) g(the) 191 3311 y(stability) e(re) o
(gion) f(becom) n(es) i(lar) o(ge.) e(This) i(is) g(because) f(the) g
(lar) o(ge) n(r) h(the) f(numb) n(er) h(of) f(TCP) h(con) n(nections) f
(becom) n(es,) 191 3410 y(the) j(smaller) g(the) f(bandwid) n
(th\226delay) g(pro) n(duct) h(of) f(each) h(TCP) g(conne) n(ction) g
(becom) n(es.) g(The) g(small) g(bandwid) n(th\226) 191
3510 y(delay) 19 b(prod) n(uct) h(means) f(that) h(a) g(source) f(host)
h(recei) n(v) m(es) h(a) f(small) g(num) n(ber) g(of) f(A) m(CK) h
(pack) o(ets) g(which) f(carry) g(feedb) n(ack) 191 3610
y(infor) n(mation.) k(As) h(a) f(result,) h(the) f(increase) g(of) g
(the) g(numb) n(er) h(of) f(TCP) h(conn) n(ections) f(has) h(the) f
(same) h(ef) n(fec) n(t) g(with) g(the) 191 3709 y(decrease) 19
b(of) h(the) h(feed) n(back) f(delay) g(and) n(/or) g(the) h(feedb) n
(ack) f(gain.) 274 3818 y(Figure) f(10) g(sho) n(ws) g(the) h(maxim) n
(um) f(modu) n(lus) h(of) f(eigen) m(v) l(alues) h(for) f(the) g(numb) n
(er) h(of) f(TCP) h(conne) n(ctions) p Fo 20 w(N) p Fn
32 w(=) i(10) p Fr 191 3918 a(and) 28 b(dif) n(f) n(erent) g(arri) n(v)
n(al) g(rate) g(of) g(the) g(backg) n(round) f(traf) n(\002c,) p
Fo 28 w(\025) p Fl 1990 3930 a(B) p Fr 2076 3918 a(=) i(0,) f(0.2) f
(and) h(0.5) g([pack) m(et/ms].) g(By) h(compar) n(ing) 191
4017 y(Fig.) 19 b(10\(a) n(\)\226\(c\),) f(one) g(can) h(\002nd) f
(that) h(the) g(stability) g(re) o(gio) n(n) g(become) n(s) h(slightly)
f(lar) o(g) n(er) m(,) g(as) p Fo 19 w(\025) p Fl 2839
4029 a(B) p Fr 2916 4017 a(becom) n(es) h(lar) o(ge) n(.) g(This) 191
4117 y(is) e(because) f(the) g(increase) g(of) g(the) g(backg) n(roun) n
(d) h(traf) n(\002c) f(corr) n(espond) n(s) i(to) e(the) g(decrease) g
(of) g(the) g(a) n(v) n(ailable) g(band) n(width) 191
4217 y(to) 26 b(TCP) h(connectio) n(ns.) g(Namely) -5
b(,) 25 b(the) h(decrease) g(of) g(the) g(a) n(v) n(ailable) g(band) n
(width) g(to) h(TCP) g(conn) n(ections) f(results) h(in) 191
4316 y(the) 22 b(smaller) h(band) n(width\226d) n(elay) f(produ) n(ct,)
h(which) f(mean) n(s) i(a) e(little) i(feedb) n(ack) e(gain.) f
(Because) i(the) f(little) i(feedb) n(ack) 191 4416 y(gain) j(mak) o
(es) g(system) h(sensiti) n(vity) g(to) g(the) f(chang) n(es) i(of) e
(the) h(en) m(vir) n(onmen) n(t) h(lo) n(w) -5 b(,) 27
b(the) g(reductio) n(n) h(of) g(the) f(a) n(v) n(ailable) 191
4515 y(band) n(width) 20 b(w) o(ould) g(brin) n(g) h(the) f(lar) o(ge) n
(r) h(stability) f(re) o(gio) n(n.) 274 4624 y(T) -7
b(o) 19 b(v) n(alidate) g(our) g(transient) g(state) h(beha) l(vior) f
(analysis,) h(we) f(ne) o(xt) g(sho) n(w) g(ho) n(w) g(the) g(TCP) h
(transient) f(state) h(beha) n(vior) 191 4724 y(chang) n(es) 29
b(for) e(dif) n(fe) n(rent) h(maxim) n(um) g(mod) n(uli) g(using) g
(simulation) e(e) o(xperim) n(ents.) i(Figure) f(11) g(sho) n(ws) h
(the) g(windo) l(w) 191 4824 y(size) e(and) f(the) g(a) n(v) o(erag) n
(e) h(queu) n(e) g(length) f(obtain) n(ed) g(from) g(our) f(simulation)
h(e) o(xp) n(eriments) g(for) g(dif) n(fe) n(rent) g(bottleneck) 191
4923 y(link) c(capacities) p Fo 22 w(\026) p Fr 22 w(=) h(0.5,) f(2.0,)
g(and) g(5.0) g([pack) m(et/ms].) h(Note) g(that) g(when) f(the) g
(bottleneck) g(link) g(capacity) p Fo 21 w(\026) p Fr
22 w(is) i(0.5) n(,) 191 5023 y(2.0,) i(and) g(5.0,) g(the) h(maximu) n
(m) g(modu) n(lus) h(of) e(eigen) m(v) l(alues) h(of) g(the) g(state) g
(transient) f(matrix) h(is) g(0.619) n(,) g(0.780) n(,) g(and) p
FD 191 5222 a(Cop) o(yri) r(ght) 497 5220 y(c) p Fm 476
5222 a(\015) p FD 16 w(2005) 18 b(John) f(W) m(ile) o(y) h(&) f(Sons,) f
(Ltd.) p FC 1233 w(Int.) 21 b(J) n(.) c(Commun.) k(Syst.) p
FD 18 w(2005;) p FB 18 w(00) p FD(:1\22618) p FC 191
5301 a(Pr) n(epar) n(ed) 16 b(using) p FA 18 w(dacauth.cls) p
dyy eop end
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1256 y @beginspecial 90 @llx 218 @lly 520 @urx 540 @ury
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%%EndImage
%%EndPreview
save
countdictstack
mark
newpath
/showpage {} def
%%EndProlog
%%Page 1 1
% Start of procedure set
userdict /Mathdict 100 dict dup begin put
% The externally visible functions are:
%	MathPictureStart- start page.
%	MathPictureEnd	- finish off page.
%	MathSubStart	- start a sub-page.
%	MathSubEnd	- finish off a sub-page.
%	Mdot		- draw a dot.
%	Mtetra		- draw a filled tetragon.
%	Metetra		- draw a filled tetragon with black edges.
%	Mistroke	- intermediate stroke of multi-stroke line/curve.
%	Mfstroke	- final stroke of multi-stroke line/curve.
%	Msboxa		- compute coordinates of text bounding box.
%	Mshowa		- plot characters.
%	MathScale	- compute scaling info to contain array of points.
%start of ISOLatin1 stuff
/ISOLatin1Encoding dup where
{ pop pop }
{
[
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright
/parenleft /parenright /asterisk /plus /comma /minus /period /slash
/zero /one /two /three /four /five /six /seven
/eight /nine /colon /semicolon /less /equal /greater /question
/at /A /B /C /D /E /F /G
/H /I /J /K /L /M /N /O
/P /Q /R /S /T /U /V /W
/X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore
/quoteleft /a /b /c /d /e /f /g
/h /i /j /k /l /m /n /o
/p /q /r /s /t /u /v /w
/x /y /z /braceleft /bar /braceright /asciitilde /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent
/dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron
/space /exclamdown /cent /sterling /currency /yen /brokenbar /section
/dieresis /copyright /ordfeminine /guillemotleft
/logicalnot /hyphen /registered /macron
/degree /plusminus /twosuperior /threesuperior
/acute /mu /paragraph /periodcentered
/cedilla /onesuperior /ordmasculine /guillemotright
/onequarter /onehalf /threequarters /questiondown
/Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
/Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis
/Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply
/Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls
/agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla
/egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis
/eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide
/oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis
] def
} ifelse
/WindowsANSIEncoding [
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle
/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash
/zero/one/two/three/four/five/six/seven
/eight/nine/colon/semicolon/less/equal/greater/question
/at/A/B/C/D/E/F/G
/H/I/J/K/L/M/N/O
/P/Q/R/S/T/U/V/W
/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore
/grave/a/b/c/d/e/f/g
/h/i/j/k/l/m/n/o
/p/q/r/s/t/u/v/w
/x/y/z/braceleft/bar/braceright/asciitilde/.notdef
/.notdef/.notdef/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl
/circumflex/perthousand/Scaron/guilsinglleft/OE/.notdef/Zcaron/.notdef
/.notdef/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash
/tilde/trademark/scaron/guilsinglright/oe/.notdef/zcaron/Ydieresis
/.notdef/exclamdown/cent/sterling/currency/yen/brokenbar/section
/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron
/degree/plusminus/twosuperior/threesuperior/acute/.notdef/paragraph/dotaccent
/ogonek/onesuperior/ring/guillemotright/onequarter/onehalf/threequarters/questiondown
/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla
/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis
/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply
/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls
/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla
/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis
/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide
/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis
] def
/MacintoshRomanEncoding [
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle
/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash
/zero/one/two/three/four/five/six/seven
/eight/nine/colon/semicolon/less/equal/greater/question
/at/A/B/C/D/E/F/G
/H/I/J/K/L/M/N/O
/P/Q/R/S/T/U/V/W
/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore
/grave/a/b/c/d/e/f/g
/h/i/j/k/l/m/n/o
/p/q/r/s/t/u/v/w
/x/y/z/braceleft/bar/braceright/asciitilde/.notdef
/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute
/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave
/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute
/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis
/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls
/registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash
/.notdef/plusminus/.notdef/.notdef/yen/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/ordfeminine/ring/.notdef/ae/oslash
/questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef/guillemotleft
/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe
/endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/.notdef
/ydieresis/Ydieresis/.notdef/currency/guilsinglleft/guilsinglright/.notdef/.notdef
/daggerdbl/dotaccent/quotesinglbase/quotedblbase/perthousand/Acircumflex/Ecircumflex/Aacute
/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex
/.notdef/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde
/macron/.notdef/.notdef/.notdef/ogonek/.notdef/.notdef/.notdef
] def
/MFontDict 50 dict def
/MStrCat
{
exch
dup length
2 index length add
string
dup 3 1 roll
copy
length
exch dup
4 2 roll exch
putinterval
} bind def
/MCreateEncoding
{
1 index
255 string cvs
(-) MStrCat
1 index MStrCat
cvn exch
(Encoding) MStrCat
cvn dup where
{
exch get
}
{
pop
StandardEncoding
} ifelse
3 1 roll
dup MFontDict exch known not
{
1 index findfont
dup length dict
begin
{1 index /FID ne
{def}
{pop pop}
ifelse} forall
/Encoding 3 index
def
currentdict
end
1 index exch definefont pop
MFontDict 1 index
null put
}
if
exch pop
exch pop
} bind def
/ISOLatin1 { (ISOLatin1) MCreateEncoding } bind def
%end of ISOLatin1 stuff
% Set up for the start of a page.
/MathPictureStart {
/Msaveobj save def
/findresource where
{ pop /WRI-Mathematica-prolog /ProcSet findresource begin }
{ Mathdict begin }
ifelse
userdict begin
/MathPictureStartHook where {
/MathPictureStartHook get exec
} if
Mtransform
Mlmarg
Mbmarg
translate
Mwidth
Mlmarg Mrmarg add
sub
/Mwidth exch def
Mheight
Mbmarg Mtmarg add
sub
/Mheight exch def
/Mtmatrix
matrix currentmatrix
def
/Mgmatrix
matrix currentmatrix
def
/MathDPSFlag where {
pop
clientsync
} if
} def
% Finish off a page.
/MathPictureEnd {
end
end
Msaveobj restore
/MathDPSFlag where { pop } { showpage } ifelse
} def
%MFill fills the drawing area with the current color.
/MFill {
0 0 		moveto
Mwidth 0 	lineto
Mwidth Mheight 	lineto
0 Mheight 	lineto
fill
} def
%New device-specific optimizing operators
/Mfill /.devicefill where
{ pop /.devicefill load def }
{ /fill load def }
ifelse
/Mstroke /.devicestroke where
{ pop /.devicestroke load def }
{ /stroke load def }
ifelse
% xmin xmax ymin ymax MPlotRegion alters the origin, Mwidth and Mheight 
% so that the picture fills the altered region
/MPlotRegion {
3 index
Mwidth mul
2 index
Mheight mul
translate
exch sub
Mheight mul
/Mheight
exch def
exch sub
Mwidth mul
/Mwidth
exch def
} def
% Given a rectangle, set it up as a sub-picture.
/MathSubStart {
Momatrix
Mgmatrix Mtmatrix
Mwidth Mheight
7 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
Mgmatrix setmatrix
9 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
2 copy translate
/Mtmatrix matrix currentmatrix def
3 -1 roll
exch sub
/Mheight exch def
sub
/Mwidth exch def
} def
% Restore the saved state left by the matching MathSubStart.
% Note, we also leave with the new Mgmatrix as the current matrix.
/MathSubEnd {
/Mheight exch def
/Mwidth exch def
/Mtmatrix exch def
dup setmatrix
/Mgmatrix exch def
/Momatrix exch def
} def
% Given a point, draw a dot.
/Mdot {
newpath
currentlinewidth 2 div
0 360
arc fill
} bind def
% Given 4 points, draw the corresponding filled tetragon.
/Mtetra {
moveto
lineto
lineto
lineto
Mfill
} bind def
% Given 4 points, draw the corresponding filled tetragon with black edges.
% Note, this leaves the gray level at 0 (for compatibility with the old
% C code.
/Metetra {
moveto
lineto
lineto
lineto
closepath
gsave
Mfill
grestore
0 setgray
Mstroke
} bind def
% Mistroke is called to stroke intermediate parts of a path.  It makes
% sure to resynchronize the dashing pattern and to leave the current point
% as the final point of the path.
/Mistroke {
flattenpath
0 0 0
{
4 2 roll
pop pop
}
{
4 -1 roll
2 index
sub dup mul
4 -1 roll
2 index
sub dup mul
add sqrt
4 -1 roll
add
3 1 roll
}
{
stop
}
{
stop
}
pathforall
pop pop
currentpoint
Mstroke
moveto
currentdash
3 -1 roll
add
setdash
} bind def
% Mfstroke is called to stroke the final parts of a path.  It resets
% the dashing pattern to compensate for any adjustments made by Mistroke.
/Mfstroke {
Mstroke
currentdash
pop 0
setdash
} bind def
% Mrotsboxa is the same as Msboxa except that it takes an angle 
% from the stack and the box is calculated for text rendered at this  angle.  
% It gsaves in case we are starting a MathSubStart
% save Mrot so that Msboxa can convert bouding box back to the non-rotated
% coordinate system
% call Mrotcheck to alter the offsets into the rotated system
% converts Mtmatrix to render in the rotated system
% the calls Msboxa which does all the work
% at the end  Mtmatrix is restored and Mrot is reset to 0 
/Mrotsboxa {
gsave
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
grestore
Msboxa
3  -1 roll
/Mtmatrix
exch def
/Mrot
0 def
} bind def
% Given an array of strings ([str...]), which represent consecutive lines
% of text, a position in graphics coordinates (gx,gy) and a position in
% the bounding box coordinates (sx,sy), compute the low and high coordinates
% of the resulting text, in the [gx gy tx ty] form, which corresponds to
% the point (gx,gy) (in graphics coordinates) plus the offset (tx,ty) (in
% text coordinates).
% Note, Msboxa assumes that the current matrix is the text matrix.
% Mboxout is called in case we are in Mouter to make the box bigger
% Mboxrot adjusts the box to account for a rotation to convert the box
% into a nonrotated coordinate system
%
/Msboxa {
newpath
5 -1 roll
Mvboxa
pop
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Msboxa1
5 -3 roll
Msboxa1
Mboxrot
[
7 -2 roll
2 copy
[
3 1 roll
10 -1 roll
9 -1 roll
]
6 1 roll
5 -2 roll
]
} bind def
% Msboxa1 is an internal function which, given a bounding box coordinate
% (sz), and the bounding box limits (blz and bhz), computes the actual
% offsets (tlz = (blz-bhz)(sz+1)/2, thz = (blz-bhz)(sz-1)/2).
/Msboxa1 {
sub
2 div
dup
2 index
1 add
mul
3 -1 roll
-1 add
3 -1 roll
mul
} bind def
% Given a (non-empty) array of strings ([str...]) which represent consecutive
% lines of text, compute the total bounding box assuming that we start at
% (0,0) and the array of y offsets to place the lines correctly.
% Note, Mvboxa assumes that the current matrix is the text matrix.
% Note, Mvboxa does not alter the current path.
% The vertical spacing is set so that the bounding boxes of adjacent lines
% are .3 times the width of an `m' apart.
/Mvboxa {
gsave
newpath
[ true
3 -1 roll
{
Mbbox
5 -1 roll
{
0
5 1 roll
}
{
7 -1 roll
exch sub
(m) stringwidth pop
.3 mul
sub
7 1 roll
6 -1 roll
4 -1 roll
Mmin
3 -1 roll
5 index
add
5 -1 roll
4 -1 roll
Mmax
4 -1 roll
}
ifelse
false
}
forall
{ stop } if
counttomark
1 add
4 roll
]
grestore
} bind def
% Given a string, compute the bounding box assuming that we start at (0,0).
% Note, the path is assumed to be empty, and we are assumed to be in text
% coordinates.  Allows for long strings.
/Mbbox {
1 dict begin
0 0 moveto
/temp (T) def
{	gsave
currentpoint newpath moveto
temp 0 3 -1 roll put temp
false charpath flattenpath currentpoint
pathbbox
grestore moveto lineto moveto} forall
pathbbox
newpath
end
} bind def
% Compute the minimum of two numbers.
/Mmin {
2 copy
gt
{ exch } if
pop
} bind def
% Compute the maximum of two numbers.
/Mmax {
2 copy
lt
{ exch } if
pop
} bind def
%
% Mrotwork saves Mrot (not really needed but saved anyway)
% calls Mrotcheck to adjust the offsets into the rotated coordinate system
% converts Mtmatrix to render in the rotated system
%
/Mrotwork {
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
Mgmatrix setmatrix
} def
%
% Mrotshowa is the same as Mshowa except that it takes an angle
% from the stack and the text is rendered at this angle.
% It call Mrotwork to do all the rotation work.
% Then it calls Mshowa which does all the drawing work.
% At the end Mtmatrix is restored and Mrot is reset to zero.
%
/Mrotshowa {
Mrotwork
Mshowa
/Mtmatrix
exch def
/Mrot 0 def
} def
%
% Draws rotated text with a background.
%
/Mrotback {
7 1 roll
dup
8 1 roll
Mrotwork
8 -2 roll
Mshowback
/Mtmatrix
exch def
/Mrot 0 def
} def
%
% Given an array of strings ([str...]), which represent consecutive lines
% of text, a position in graphics coordinates (gx,gy) and a position in
% the bounding box coordinates (sx,sy), display the strings.
% Mboxout is called in case we are in Mouter
%
/Mshowa {
4 -2 roll
moveto
2 index
Mtmatrix setmatrix
Mvboxa
7 1 roll
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Mshowa1
4 1 roll
Mshowa1
rmoveto
currentpoint
Mshowax
pop pop pop pop
Mgmatrix setmatrix
} def
%
% The background box of text is increased by the
% size of an "m"
%
/Madjust	{
(m)
stringwidth
pop
mul
dup
4 -1 roll
add
3 1 roll
add
} def
%
%
%
/Mbuildcoord {
7 index
7 index
4 -1 roll
4 -1 roll
index
exch
index
Mabsadd
} def
%
% If the text is rotated then translate to the drawing point.
% Rotate then translate back.  Do not do this if the angle
% of rotation is 0.
%
/Mrotate {
8 index
0 ne
{
13 copy
4 -2 roll
pop pop
6 -2 roll
pop pop
4 -1 roll
3 -1 roll
sub
6 -1 roll
mul
3 1 roll
sub
4 -1 roll
mul
3 -1 roll
5 1 roll
Mabsadd
2 copy
translate
3 -1 roll
rotate
exch -1 mul
exch -1 mul
translate
} if
9 -1 roll
pop
} def
%
% Draw text but into a box with a certain color.
% Uses Msboxa to build the box.
%
/Mshowback {
gsave
exec
6 copy pop
Msboxa
aload pop
0.5 Madjust
5 -1 roll
aload pop
Mrotate
-0.5
Madjust
4 -1 roll
pop
3 -1 roll
pop
3 4
Mbuildcoord
moveto
3 4
Mbuildcoord
lineto
3 6
Mbuildcoord
lineto
5 6
Mbuildcoord
lineto
5 4
Mbuildcoord
lineto
pop pop pop
pop pop pop
fill		
grestore
Mshowa
} def
% This is used for fixedwidth fonts
% It simply shows each string and advances the y direction by the offset
%
/Mshowax {	
0 1
4 index length
-1 add
{
2 index
4 index
2 index
get
3 index
add
moveto
4 index
exch get
Mfixdash
{
Mfixdashp		
}
if
show
} for
} def
% Fix if all dashes and length > 1
/Mfixdashp {
dup
length
1
gt
1 index
true exch
{
45
eq
and
} forall
and
{
gsave
(--)		
stringwidth pop
(-)
stringwidth pop
sub
2 div
0 rmoveto
dup
length
1 sub
{
(-)
show
}
repeat
grestore
}
if
} bind def	
% Mshowa1 is an internal routine which, given a bounding box coordinate
% (sz), and the bounding box limits if we started drawing at 0 (tlz and thz),
% computes the offset at which to start drawing
% (relz = (sz-1)tlz/2 - (sz+1)thz/2 = sz(tlz-thz)/2-(tlz+thz)/2).
/Mshowa1 {
2 copy
add
4 1 roll
sub
mul
sub
-2 div
} bind def
% Given the x and y scaling to user coordinates and an array of points to
% fit (xbias xscale ybias yscale [pnts]), set up the scaling.  The array
% must contain atleast two points, and the last two must be of the form
% [gxlow gylow 0 0] and [gxhigh gyhigh 0 0].
% Note, MathScale assumes that we are already scaled so that the active area
% is the rectangle [0,Mwidth-Mlmarg-Mrmarg]x[0,Mheight-Mbmarg-Mtmarg].
% also keep bias and scale info for PostScript commands
/MathScale {
Mwidth
Mheight
Mlp
/MathScaleHook where {
/MathScaleHook get exec
} if
translate
scale
pop pop pop pop
pop pop pop pop
/yscale exch def
/ybias exch def
/xscale exch def
/xbias exch def
/Momatrix
xscale yscale matrix scale
xbias ybias matrix translate
matrix concatmatrix def
/Mgmatrix
matrix currentmatrix
def
} def
% Given a non-empty array of points to fit ([p]) and a maximum width (sx)
% and height (sy) find the largest scale (Ax and Ay) and offsets (Bx and By)
% such that the transformation
%	[gx gy tx ty] -> (Ax gx + tx + bx, Ay gy + ty + By)
% maps the points into the rectangle [0,sx]x[0,sy]
/Mlp {
3 copy
Mlpfirst
{
Mnodistort
{
Mmin
dup
} if
4 index
2 index
2 index
Mlprun
16 -8 roll
21 8 roll
11 index
11 -1 roll
10 -4 roll
Mlp1
8 index
9 -5 roll
Mlp1
4 -1 roll
and
{ exit } if
15 -8 roll
pop pop pop pop
pop pop pop pop
3 -1 roll
pop pop
} loop
exch
3 1 roll
7 -3 roll
pop pop pop
} def
% Given an array of points in the [gx gy tx ty] form, with the last two
% being [gxlow gylow 0 0] and [gxhigh gyhigh 0 0], and the width and height
% (sx and sy) in which to fit them, compute the maximum scaling (Ax and Ay).
/Mlpfirst {
3 -1 roll
dup length
2 copy
-2 add
get
aload
pop pop pop
4 -2 roll
-1 add
get
aload
pop pop pop
6 -1 roll
3 -1 roll
5 -1 roll
sub
div
4 1 roll
exch sub
div
} bind def
% Given a non-empty array of points to fit ([pnts]) and scale factors
% for graphics->text (Ax and Ay), compute the limiting points.
/Mlprun {
2 copy
4 index
0 get
dup
4 1 roll
Mlprun1
3 copy
8 -2 roll
9 -1 roll
{
3 copy
Mlprun1
3 copy
11 -3 roll
/gt Mlpminmax
8 3 roll
11 -3 roll
/lt Mlpminmax
8 3 roll
} forall
pop pop pop pop
3 1 roll
pop pop
aload pop
5 -1 roll
aload pop
8 copy
exch
6 -1 roll
Mlprun2
8 2 roll
4 -1 roll
Mlprun2
6 2 roll
3 -1 roll
Mlprun2
4 2 roll
exch
Mlprun2
6 2 roll
} bind def
% Given scale factors for graphics->text (Ax and Ay) and a point in the
% [gx gy tx ty] form, return the text x and y coordinate that results.
/Mlprun1 {
aload pop
exch
6 -1 roll
5 -1 roll
mul add
4 -2 roll
mul
3 -1 roll
add
} bind def
% Given a low and high coordinate, compute the center and width.
/Mlprun2 {
2 copy
add 2 div
3 1 roll
exch sub
} bind def
% Given two points stored as [gx gy tx ty] followed by the scaled
% result (rx, ry), and a comparison function (lt or gt) leave the
% point which is the minimum (or maximum) in each dimension.
/Mlpminmax {
cvx
2 index
6 index
2 index
exec
{
7 -3 roll
4 -1 roll
} if
1 index
5 index
3 -1 roll
exec
{
4 1 roll
pop
5 -1 roll
aload
pop pop
4 -1 roll
aload pop
[
8 -2 roll
pop
5 -2 roll
pop
6 -2 roll
pop
5 -1 roll
]
4 1 roll
pop
}
{
pop pop pop
} ifelse
} bind def
% Given a size (s), graphics->text scale (A), text center (ct), text
% width (wt), graphics center (cg) and graphics width (wg), compute
% a new graphics->text scale (Anew) and offset (B) and whether or not
% we are done.
% Note, the mysterious .99999 is magic juju which is supposed to ward
% off the possibility that floating point errors would cause this
% routine to return the old A and yet claim not-done.
/Mlp1 {
5 index
3 index	sub
5 index
2 index mul
1 index
le
1 index
0 le
or
dup
not
{
1 index
3 index	div
.99999 mul
8 -1 roll
pop
7 1 roll
}
if
8 -1 roll
2 div
7 -2 roll
pop sub
5 index
6 -3 roll
pop pop
mul sub
exch
} bind def
% The following are the workings of the tick, axes and plot labels.
% NOTE a possible source of confusion is that for xticks ie tickmarks on
% the x axis we keep y information and vice versa for yticks
%
%	When Minner is found then
%
% assumes that box starts at zero on the left lower side
%
%		0)	if outflag = 1 then intop = 0, inrht = 0 outflag = 0
%		1)	Save intop 	largest top of box 
%		2)	Save inrht 	largest rht of box
%		3)	set inflag	notifies that inner marks are present
%
%	When Mouter is found then
%
%	if inflag is set then
%		1)	get vecx and vecy off the stack (points in direcn to move)
%		2)	vecx < 1 xadrht = inrht*abs(vecx)
%		3)	vecx > 1 xadlft = inrht*abs(vecx)
%		4)	vecy < 1 yadtop = intop*abs(vecy)
%		5)	vecy > 1 yadbot = intop*abs(vecy)
%		6)	set outflag = 1
%		7)	clear inflag, inrht, intop
%	guaranteed to be zero if no inner is present??
%
%
%	These all have effects in Mrotsboxa and Mrotshowa
%		check inflag and if set
%
%		1) increase top of bbox by yadtop
%		2) decrease bot of bbox by yadbot
%		3) increase rht of bbox by xadrht
%		4) increase lft of bbox by xadlft
%		5) clear outflag, yadtop, yadbot,
%			         xadrht, xadlft
%
% 
% This saves the top right corner of the bounding box as a side effect
% This is to allow the adjustment of text placed with Mouter so that
% it misses the Minner text.  It is assumed that the ang is 0
% in the same way it is assumed that the text of Mouter is 0 or 90
%
/Minner {
outflag
1
eq
{
/outflag 0 def
/intop 0 def
/inrht 0 def
} if		
5 index
gsave
Mtmatrix setmatrix
Mvboxa pop
grestore
3 -1 roll
pop
dup
intop
gt
{
/intop
exch def
}
{ pop }
ifelse
dup
inrht
gt
{
/inrht
exch def
}
{ pop }
ifelse
pop
/inflag
1 def
} def
% This takes two number off the stack and uses them as a vector in graphics
% coordinates which points in the direction in which the Mouter text is to move
% it calculates the bouding box adjustments yadtop yadbot xadrht and xadlft
% these are in Mboxout to adjust the bounding box to compensate.
/Mouter {
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
inflag
1 eq
{
dup
0 lt
{
dup
intop
mul
neg
/yadtop
exch def
} if
dup
0 gt
{
dup
intop
mul
/yadbot
exch def
}
if
pop
dup
0 lt
{
dup
inrht
mul
neg
/xadrht
exch def
} if
dup
0 gt
{
dup
inrht
mul
/xadlft
exch def
} if
pop
/outflag 1 def
}
{ pop pop}
ifelse
/inflag 0 def
/inrht 0 def
/intop 0 def
} def	
%
% This adjusts the bounding box to account for adjacent text
% This allows the two text strings to avoid each other 
% current matrix is the text matrix
/Mboxout {
outflag
1
eq
{
4 -1
roll
xadlft
leadjust
add
sub
4 1 roll
3 -1
roll
yadbot
leadjust
add
sub
3 1
roll
exch
xadrht
leadjust
add
add
exch
yadtop
leadjust
add
add
/outflag 0 def
/xadlft 0 def
/yadbot 0 def
/xadrht 0 def
/yadtop 0 def
} if
} def
/leadjust {
(m) stringwidth pop
.5 mul
} bind def
% The offsets sx and sy refer to the graphics coordinate system 
% thus they must be altered if a rotation has taken place.
% We must also change the bounding box computations for Minner
%
/Mrotcheck {
dup
90
eq
{
%
% Mouter only applies to strings which are either at 0 or 90
% sort out the box adjust factors
%
%	xadrht -> yadbot
%	xadlft -> yadtop
%	yadtop -> xadrht
%	yadbot -> xadlft
yadbot
/yadbot
xadrht
def	
/xadrht
yadtop
def
/yadtop
xadlft
def
/xadlft
exch
def
}
if
dup
cos
1 index
sin
Checkaux
dup
cos
1 index
sin neg
exch
Checkaux
3 1 roll
pop pop
} def
%
% Checkaux is an auxilliary function for Mrotcheck it multiplies a 
% row vector by a column vector
% 
/Checkaux {
4 index
exch
4 index
mul
3 1 roll
mul add
4 1 roll
} bind def
%
% Mboxrot converts the bounding box back from the rotated coordinate
% system to the Mgmatrix system to compensate for a rotation
% It has the opposite functionality of Mrotcheck
% This is not the most neatest or most efficient implementation but it works
%
/Mboxrot {
Mrot
90 eq
{
% old		 tlx  thx  tly  thy
% new		-thy -tly  tlx  thx
%
brotaux
4 2
roll
}
if
Mrot
180 eq
{
% old		 tlx  thx  tly  thy
% new		-thx -tlx -thx -tly
%
4 2
roll
brotaux
4 2
roll
brotaux
}	
if
Mrot
270 eq
{
% old		 tlx  thx  tly  thy
% new		 tly  thy -thx -tlx
%
4 2
roll
brotaux
}
if
} def
%
% auxilliary function negate and reverse
/brotaux {
neg
exch
neg
} bind def
%
% Mabsproc takes a measurement in the default user units and converts
% it to the present units.   This allows absolute thickness and dashing
% to work.  It works by using a {0, x} vector and using the RMS of the result.
/Mabsproc {
0
matrix defaultmatrix
dtransform idtransform
dup mul exch
dup mul
add sqrt
} bind def
%
% Mabswid allows the linewidth to be specified in absolute coordinates
% It does this by recording the graphics transformation matrix at the
% begining of the plot.
% This will break if the scaling in the x and y directions is
% different.  This is the case if Mnodistort is false
%
/Mabswid {
Mabsproc
setlinewidth	
} bind def
% Mabsdash allows the dashing pattern to be specified in absolute coordinates
% It does this by recording the graphics transformation matrix at the
% begining of the plot.
% This will break if the scaling in the x and y directions is
% different.  This is the case if Mnodistort is false
%
/Mabsdash {
exch
[
exch
{
Mabsproc
}
forall
]
exch
setdash
} bind def
%
% Mabs takes a pair of coordinates in points
% and converts them into a pair of coordinates in
% the current drawing scheme
%
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
%
% Mabs takes a pair of numbers in drawing coordinates
% and a pair in points.  It converts the points to
% drawing coordinates and adds them to the first pair.
%
/Mabsadd {
Mabs
3 -1 roll add
3 1 roll add
exch 
} bind def
%
% These two procedures are for using Offset coordinates
% with MathScale computations
%
/Mabsfix1 {
3 -1 roll
/ar exch 
def
ar 2 get
3 -1 roll
add exch
ar 3 get
add
ar 3
3 -1 roll
put
ar 2
3 -1 roll
put
ar
} bind def
/Mabsfix {
2 copy
6 -1 roll
3 1 roll
Mabsfix1
4 1 roll
Mabsfix1
} bind def
%MBeginOrig start coordinates in user coordinates
/MBeginOrig { Momatrix concat} bind def
%MEndOrig start coordinates in user coordinates
/MEndOrig { Mgmatrix setmatrix} bind def
/sampledsound where
{ pop }
{ /MathDPSFlag where
{ pop /sampledsound { clientsync } def }
{ /sampledsound {
exch pop
exch 5 1 roll
mul
4 idiv
mul
2 idiv
exch pop
exch
/Mtempproc exch def
{ Mtempproc pop }
repeat
} def
} ifelse
} ifelse
% Define setrgbcolor for those ancient PostScript devices lacking it
/setrgbcolor dup where
{ pop pop }
{ { .114 mul exch .587 mul add exch .299 mul add setgray } bind def }
ifelse
%
% now simple conversion of cmykcolor to rgbcolor
% subtract k and then take complements
/setcmykcolor where
{ pop}
{ /setcmykcolor {
4 1
roll
[
4 1 
roll
]
{
1 index
sub
1
sub neg
dup
0
lt
{
pop
0
}
if
dup
1
gt
{
pop
1
}
if
exch
} forall
pop
setrgbcolor
} bind def
} ifelse
% Here are the short operators
/g /setgray load def
/k /setcmykcolor load def
/m /moveto load def
/p /gsave load def
/r /setrgbcolor load def
/w /setlinewidth load def
/C /curveto load def
/F /Mfill load def
/L /lineto load def
/P /grestore load def
/s /Mstroke load def
/Mcharproc
{
currentfile
(x)
readhexstring
pop
0 get
exch
div
} bind def
/Mshadeproc
{
dup
3 1
roll
{
dup
Mcharproc
3 1
roll
} repeat
1 eq
{
setgray
}
{
3 eq
{
setrgbcolor
}
{
setcmykcolor
} ifelse
} ifelse
} bind def
/Mrectproc
{
3 index
2 index
moveto
2 index
3 -1
roll
lineto
dup
3 1
roll
lineto
lineto
Mfill
} bind def
/Mcolorimage
{
7 1
roll
pop
pop
matrix
invertmatrix
concat
2 exch exp
1 sub
3 1 roll
1 1
2 index
{
1 1
4 index
{
dup
1 sub
exch
2 index
dup
1 sub
exch
7 index
9 index
Mshadeproc
Mrectproc
} for
pop
} for
pop pop pop pop
} bind def
/Mimage
{
pop
matrix
invertmatrix
concat
2 exch exp
1 sub
3 1 roll
1 1
2 index
{
1 1
4 index
{
dup
1 sub
exch
2 index
dup
1 sub
exch
7 index
Mcharproc
setgray
Mrectproc
} for
pop
} for
pop pop pop
} bind def
% Default values for variables
/Mlmarg		1.0 72 mul def
/Mrmarg		1.0 72 mul def
/Mbmarg		1.0 72 mul def
/Mtmarg		1.0 72 mul def
/Mwidth		8.5 72 mul def
/Mheight	11 72 mul def
/Mtransform	{  } bind def
/Mnodistort	true def	
/Mfixdash	false def	
/Mrot		0	def	
/intop 0 def
/inrht 0 def
/inflag 0 def
/outflag 0 def
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
/defineresource where
{ pop /WRI-Mathematica-prolog currentdict /ProcSet defineresource pop }
if
end
%KLUDGE until Mathematica output uses resources directly
userdict /MathPictureStart {
	/findresource where
	{ pop /WRI-Mathematica-prolog /ProcSet findresource }
	{ Mathdict }
	ifelse
	/MathPictureStart get exec
} put
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% ContourGraphics
/Helvetica findfont 24  scalefont  setfont
% Scaling calculations
-0.000392465 0.196232 -0.000392465 0.0196232 [
[.19584 -0.0125 -7.2 -31.2 ]
[.19584 -0.0125 7.2 0 ]
[.39207 -0.0125 -7.2 -31.2 ]
[.39207 -0.0125 7.2 0 ]
[.5883 -0.0125 -7.2 -31.2 ]
[.5883 -0.0125 7.2 0 ]
[.78454 -0.0125 -7.2 -31.2 ]
[.78454 -0.0125 7.2 0 ]
[.98077 -0.0125 -7.2 -31.2 ]
[.98077 -0.0125 7.2 0 ]
[ 0 0 -0.125 0 ]
[.5 -0.0125 -280.8 -62.4 ]
[.5 -0.0125 280.8 -31.2 ]
[-0.0125 .19584 -28.8 -15.6 ]
[-0.0125 .19584 0 15.6 ]
[-0.0125 .39207 -28.8 -15.6 ]
[-0.0125 .39207 0 15.6 ]
[-0.0125 .5883 -28.8 -15.6 ]
[-0.0125 .5883 0 15.6 ]
[-0.0125 .78454 -28.8 -15.6 ]
[-0.0125 .78454 0 15.6 ]
[-0.0125 .98077 -28.8 -15.6 ]
[-0.0125 .98077 0 15.6 ]
[ 0 0 -0.125 0 ]
[-0.01875 .5 -60 -187.2 ]
[-0.01875 .5 -28.8 187.2 ]
[ 0 1 .125 0 ]
[ 1 0 .125 0 ]
[ 0 0 0 0 ]
[ 1 1 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.19584 0 m
.19584 .00625 L
s
[(1)] .19584 -0.0125 0 1 Mshowa
.39207 0 m
.39207 .00625 L
s
[(2)] .39207 -0.0125 0 1 Mshowa
.5883 0 m
.5883 .00625 L
s
[(3)] .5883 -0.0125 0 1 Mshowa
.78454 0 m
.78454 .00625 L
s
[(4)] .78454 -0.0125 0 1 Mshowa
.98077 0 m
.98077 .00625 L
s
[(5)] .98077 -0.0125 0 1 Mshowa
.125 Mabswid
.03885 0 m
.03885 .00375 L
s
.0781 0 m
.0781 .00375 L
s
.11735 0 m
.11735 .00375 L
s
.15659 0 m
.15659 .00375 L
s
.23509 0 m
.23509 .00375 L
s
.27433 0 m
.27433 .00375 L
s
.31358 0 m
.31358 .00375 L
s
.35283 0 m
.35283 .00375 L
s
.43132 0 m
.43132 .00375 L
s
.47057 0 m
.47057 .00375 L
s
.50981 0 m
.50981 .00375 L
s
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%%EndImage
%%EndPreview
save
countdictstack
mark
newpath
/showpage {} def
%%EndProlog
%%Page 1 1
% Start of procedure set
userdict /Mathdict 100 dict dup begin put
% The externally visible functions are:
%	MathPictureStart- start page.
%	MathPictureEnd	- finish off page.
%	MathSubStart	- start a sub-page.
%	MathSubEnd	- finish off a sub-page.
%	Mdot		- draw a dot.
%	Mtetra		- draw a filled tetragon.
%	Metetra		- draw a filled tetragon with black edges.
%	Mistroke	- intermediate stroke of multi-stroke line/curve.
%	Mfstroke	- final stroke of multi-stroke line/curve.
%	Msboxa		- compute coordinates of text bounding box.
%	Mshowa		- plot characters.
%	MathScale	- compute scaling info to contain array of points.
%start of ISOLatin1 stuff
/ISOLatin1Encoding dup where
{ pop pop }
{
[
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright
/parenleft /parenright /asterisk /plus /comma /minus /period /slash
/zero /one /two /three /four /five /six /seven
/eight /nine /colon /semicolon /less /equal /greater /question
/at /A /B /C /D /E /F /G
/H /I /J /K /L /M /N /O
/P /Q /R /S /T /U /V /W
/X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore
/quoteleft /a /b /c /d /e /f /g
/h /i /j /k /l /m /n /o
/p /q /r /s /t /u /v /w
/x /y /z /braceleft /bar /braceright /asciitilde /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent
/dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron
/space /exclamdown /cent /sterling /currency /yen /brokenbar /section
/dieresis /copyright /ordfeminine /guillemotleft
/logicalnot /hyphen /registered /macron
/degree /plusminus /twosuperior /threesuperior
/acute /mu /paragraph /periodcentered
/cedilla /onesuperior /ordmasculine /guillemotright
/onequarter /onehalf /threequarters /questiondown
/Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
/Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis
/Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply
/Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls
/agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla
/egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis
/eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide
/oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis
] def
} ifelse
/WindowsANSIEncoding [
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle
/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash
/zero/one/two/three/four/five/six/seven
/eight/nine/colon/semicolon/less/equal/greater/question
/at/A/B/C/D/E/F/G
/H/I/J/K/L/M/N/O
/P/Q/R/S/T/U/V/W
/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore
/grave/a/b/c/d/e/f/g
/h/i/j/k/l/m/n/o
/p/q/r/s/t/u/v/w
/x/y/z/braceleft/bar/braceright/asciitilde/.notdef
/.notdef/.notdef/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl
/circumflex/perthousand/Scaron/guilsinglleft/OE/.notdef/Zcaron/.notdef
/.notdef/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash
/tilde/trademark/scaron/guilsinglright/oe/.notdef/zcaron/Ydieresis
/.notdef/exclamdown/cent/sterling/currency/yen/brokenbar/section
/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron
/degree/plusminus/twosuperior/threesuperior/acute/.notdef/paragraph/dotaccent
/ogonek/onesuperior/ring/guillemotright/onequarter/onehalf/threequarters/questiondown
/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla
/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis
/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply
/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls
/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla
/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis
/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide
/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis
] def
/MacintoshRomanEncoding [
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle
/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash
/zero/one/two/three/four/five/six/seven
/eight/nine/colon/semicolon/less/equal/greater/question
/at/A/B/C/D/E/F/G
/H/I/J/K/L/M/N/O
/P/Q/R/S/T/U/V/W
/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore
/grave/a/b/c/d/e/f/g
/h/i/j/k/l/m/n/o
/p/q/r/s/t/u/v/w
/x/y/z/braceleft/bar/braceright/asciitilde/.notdef
/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute
/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave
/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute
/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis
/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls
/registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash
/.notdef/plusminus/.notdef/.notdef/yen/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/ordfeminine/ring/.notdef/ae/oslash
/questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef/guillemotleft
/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe
/endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/.notdef
/ydieresis/Ydieresis/.notdef/currency/guilsinglleft/guilsinglright/.notdef/.notdef
/daggerdbl/dotaccent/quotesinglbase/quotedblbase/perthousand/Acircumflex/Ecircumflex/Aacute
/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex
/.notdef/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde
/macron/.notdef/.notdef/.notdef/ogonek/.notdef/.notdef/.notdef
] def
/MFontDict 50 dict def
/MStrCat
{
exch
dup length
2 index length add
string
dup 3 1 roll
copy
length
exch dup
4 2 roll exch
putinterval
} bind def
/MCreateEncoding
{
1 index
255 string cvs
(-) MStrCat
1 index MStrCat
cvn exch
(Encoding) MStrCat
cvn dup where
{
exch get
}
{
pop
StandardEncoding
} ifelse
3 1 roll
dup MFontDict exch known not
{
1 index findfont
dup length dict
begin
{1 index /FID ne
{def}
{pop pop}
ifelse} forall
/Encoding 3 index
def
currentdict
end
1 index exch definefont pop
MFontDict 1 index
null put
}
if
exch pop
exch pop
} bind def
/ISOLatin1 { (ISOLatin1) MCreateEncoding } bind def
%end of ISOLatin1 stuff
% Set up for the start of a page.
/MathPictureStart {
/Msaveobj save def
/findresource where
{ pop /WRI-Mathematica-prolog /ProcSet findresource begin }
{ Mathdict begin }
ifelse
userdict begin
/MathPictureStartHook where {
/MathPictureStartHook get exec
} if
Mtransform
Mlmarg
Mbmarg
translate
Mwidth
Mlmarg Mrmarg add
sub
/Mwidth exch def
Mheight
Mbmarg Mtmarg add
sub
/Mheight exch def
/Mtmatrix
matrix currentmatrix
def
/Mgmatrix
matrix currentmatrix
def
/MathDPSFlag where {
pop
clientsync
} if
} def
% Finish off a page.
/MathPictureEnd {
end
end
Msaveobj restore
/MathDPSFlag where { pop } { showpage } ifelse
} def
%MFill fills the drawing area with the current color.
/MFill {
0 0 		moveto
Mwidth 0 	lineto
Mwidth Mheight 	lineto
0 Mheight 	lineto
fill
} def
%New device-specific optimizing operators
/Mfill /.devicefill where
{ pop /.devicefill load def }
{ /fill load def }
ifelse
/Mstroke /.devicestroke where
{ pop /.devicestroke load def }
{ /stroke load def }
ifelse
% xmin xmax ymin ymax MPlotRegion alters the origin, Mwidth and Mheight 
% so that the picture fills the altered region
/MPlotRegion {
3 index
Mwidth mul
2 index
Mheight mul
translate
exch sub
Mheight mul
/Mheight
exch def
exch sub
Mwidth mul
/Mwidth
exch def
} def
% Given a rectangle, set it up as a sub-picture.
/MathSubStart {
Momatrix
Mgmatrix Mtmatrix
Mwidth Mheight
7 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
Mgmatrix setmatrix
9 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
2 copy translate
/Mtmatrix matrix currentmatrix def
3 -1 roll
exch sub
/Mheight exch def
sub
/Mwidth exch def
} def
% Restore the saved state left by the matching MathSubStart.
% Note, we also leave with the new Mgmatrix as the current matrix.
/MathSubEnd {
/Mheight exch def
/Mwidth exch def
/Mtmatrix exch def
dup setmatrix
/Mgmatrix exch def
/Momatrix exch def
} def
% Given a point, draw a dot.
/Mdot {
newpath
currentlinewidth 2 div
0 360
arc fill
} bind def
% Given 4 points, draw the corresponding filled tetragon.
/Mtetra {
moveto
lineto
lineto
lineto
Mfill
} bind def
% Given 4 points, draw the corresponding filled tetragon with black edges.
% Note, this leaves the gray level at 0 (for compatibility with the old
% C code.
/Metetra {
moveto
lineto
lineto
lineto
closepath
gsave
Mfill
grestore
0 setgray
Mstroke
} bind def
% Mistroke is called to stroke intermediate parts of a path.  It makes
% sure to resynchronize the dashing pattern and to leave the current point
% as the final point of the path.
/Mistroke {
flattenpath
0 0 0
{
4 2 roll
pop pop
}
{
4 -1 roll
2 index
sub dup mul
4 -1 roll
2 index
sub dup mul
add sqrt
4 -1 roll
add
3 1 roll
}
{
stop
}
{
stop
}
pathforall
pop pop
currentpoint
Mstroke
moveto
currentdash
3 -1 roll
add
setdash
} bind def
% Mfstroke is called to stroke the final parts of a path.  It resets
% the dashing pattern to compensate for any adjustments made by Mistroke.
/Mfstroke {
Mstroke
currentdash
pop 0
setdash
} bind def
% Mrotsboxa is the same as Msboxa except that it takes an angle 
% from the stack and the box is calculated for text rendered at this  angle.  
% It gsaves in case we are starting a MathSubStart
% save Mrot so that Msboxa can convert bouding box back to the non-rotated
% coordinate system
% call Mrotcheck to alter the offsets into the rotated system
% converts Mtmatrix to render in the rotated system
% the calls Msboxa which does all the work
% at the end  Mtmatrix is restored and Mrot is reset to 0 
/Mrotsboxa {
gsave
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
grestore
Msboxa
3  -1 roll
/Mtmatrix
exch def
/Mrot
0 def
} bind def
% Given an array of strings ([str...]), which represent consecutive lines
% of text, a position in graphics coordinates (gx,gy) and a position in
% the bounding box coordinates (sx,sy), compute the low and high coordinates
% of the resulting text, in the [gx gy tx ty] form, which corresponds to
% the point (gx,gy) (in graphics coordinates) plus the offset (tx,ty) (in
% text coordinates).
% Note, Msboxa assumes that the current matrix is the text matrix.
% Mboxout is called in case we are in Mouter to make the box bigger
% Mboxrot adjusts the box to account for a rotation to convert the box
% into a nonrotated coordinate system
%
/Msboxa {
newpath
5 -1 roll
Mvboxa
pop
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Msboxa1
5 -3 roll
Msboxa1
Mboxrot
[
7 -2 roll
2 copy
[
3 1 roll
10 -1 roll
9 -1 roll
]
6 1 roll
5 -2 roll
]
} bind def
% Msboxa1 is an internal function which, given a bounding box coordinate
% (sz), and the bounding box limits (blz and bhz), computes the actual
% offsets (tlz = (blz-bhz)(sz+1)/2, thz = (blz-bhz)(sz-1)/2).
/Msboxa1 {
sub
2 div
dup
2 index
1 add
mul
3 -1 roll
-1 add
3 -1 roll
mul
} bind def
% Given a (non-empty) array of strings ([str...]) which represent consecutive
% lines of text, compute the total bounding box assuming that we start at
% (0,0) and the array of y offsets to place the lines correctly.
% Note, Mvboxa assumes that the current matrix is the text matrix.
% Note, Mvboxa does not alter the current path.
% The vertical spacing is set so that the bounding boxes of adjacent lines
% are .3 times the width of an `m' apart.
/Mvboxa {
gsave
newpath
[ true
3 -1 roll
{
Mbbox
5 -1 roll
{
0
5 1 roll
}
{
7 -1 roll
exch sub
(m) stringwidth pop
.3 mul
sub
7 1 roll
6 -1 roll
4 -1 roll
Mmin
3 -1 roll
5 index
add
5 -1 roll
4 -1 roll
Mmax
4 -1 roll
}
ifelse
false
}
forall
{ stop } if
counttomark
1 add
4 roll
]
grestore
} bind def
% Given a string, compute the bounding box assuming that we start at (0,0).
% Note, the path is assumed to be empty, and we are assumed to be in text
% coordinates.  Allows for long strings.
/Mbbox {
1 dict begin
0 0 moveto
/temp (T) def
{	gsave
currentpoint newpath moveto
temp 0 3 -1 roll put temp
false charpath flattenpath currentpoint
pathbbox
grestore moveto lineto moveto} forall
pathbbox
newpath
end
} bind def
% Compute the minimum of two numbers.
/Mmin {
2 copy
gt
{ exch } if
pop
} bind def
% Compute the maximum of two numbers.
/Mmax {
2 copy
lt
{ exch } if
pop
} bind def
%
% Mrotwork saves Mrot (not really needed but saved anyway)
% calls Mrotcheck to adjust the offsets into the rotated coordinate system
% converts Mtmatrix to render in the rotated system
%
/Mrotwork {
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
Mgmatrix setmatrix
} def
%
% Mrotshowa is the same as Mshowa except that it takes an angle
% from the stack and the text is rendered at this angle.
% It call Mrotwork to do all the rotation work.
% Then it calls Mshowa which does all the drawing work.
% At the end Mtmatrix is restored and Mrot is reset to zero.
%
/Mrotshowa {
Mrotwork
Mshowa
/Mtmatrix
exch def
/Mrot 0 def
} def
%
% Draws rotated text with a background.
%
/Mrotback {
7 1 roll
dup
8 1 roll
Mrotwork
8 -2 roll
Mshowback
/Mtmatrix
exch def
/Mrot 0 def
} def
%
% Given an array of strings ([str...]), which represent consecutive lines
% of text, a position in graphics coordinates (gx,gy) and a position in
% the bounding box coordinates (sx,sy), display the strings.
% Mboxout is called in case we are in Mouter
%
/Mshowa {
4 -2 roll
moveto
2 index
Mtmatrix setmatrix
Mvboxa
7 1 roll
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Mshowa1
4 1 roll
Mshowa1
rmoveto
currentpoint
Mshowax
pop pop pop pop
Mgmatrix setmatrix
} def
%
% The background box of text is increased by the
% size of an "m"
%
/Madjust	{
(m)
stringwidth
pop
mul
dup
4 -1 roll
add
3 1 roll
add
} def
%
%
%
/Mbuildcoord {
7 index
7 index
4 -1 roll
4 -1 roll
index
exch
index
Mabsadd
} def
%
% If the text is rotated then translate to the drawing point.
% Rotate then translate back.  Do not do this if the angle
% of rotation is 0.
%
/Mrotate {
8 index
0 ne
{
13 copy
4 -2 roll
pop pop
6 -2 roll
pop pop
4 -1 roll
3 -1 roll
sub
6 -1 roll
mul
3 1 roll
sub
4 -1 roll
mul
3 -1 roll
5 1 roll
Mabsadd
2 copy
translate
3 -1 roll
rotate
exch -1 mul
exch -1 mul
translate
} if
9 -1 roll
pop
} def
%
% Draw text but into a box with a certain color.
% Uses Msboxa to build the box.
%
/Mshowback {
gsave
exec
6 copy pop
Msboxa
aload pop
0.5 Madjust
5 -1 roll
aload pop
Mrotate
-0.5
Madjust
4 -1 roll
pop
3 -1 roll
pop
3 4
Mbuildcoord
moveto
3 4
Mbuildcoord
lineto
3 6
Mbuildcoord
lineto
5 6
Mbuildcoord
lineto
5 4
Mbuildcoord
lineto
pop pop pop
pop pop pop
fill		
grestore
Mshowa
} def
% This is used for fixedwidth fonts
% It simply shows each string and advances the y direction by the offset
%
/Mshowax {	
0 1
4 index length
-1 add
{
2 index
4 index
2 index
get
3 index
add
moveto
4 index
exch get
Mfixdash
{
Mfixdashp		
}
if
show
} for
} def
% Fix if all dashes and length > 1
/Mfixdashp {
dup
length
1
gt
1 index
true exch
{
45
eq
and
} forall
and
{
gsave
(--)		
stringwidth pop
(-)
stringwidth pop
sub
2 div
0 rmoveto
dup
length
1 sub
{
(-)
show
}
repeat
grestore
}
if
} bind def	
% Mshowa1 is an internal routine which, given a bounding box coordinate
% (sz), and the bounding box limits if we started drawing at 0 (tlz and thz),
% computes the offset at which to start drawing
% (relz = (sz-1)tlz/2 - (sz+1)thz/2 = sz(tlz-thz)/2-(tlz+thz)/2).
/Mshowa1 {
2 copy
add
4 1 roll
sub
mul
sub
-2 div
} bind def
% Given the x and y scaling to user coordinates and an array of points to
% fit (xbias xscale ybias yscale [pnts]), set up the scaling.  The array
% must contain atleast two points, and the last two must be of the form
% [gxlow gylow 0 0] and [gxhigh gyhigh 0 0].
% Note, MathScale assumes that we are already scaled so that the active area
% is the rectangle [0,Mwidth-Mlmarg-Mrmarg]x[0,Mheight-Mbmarg-Mtmarg].
% also keep bias and scale info for PostScript commands
/MathScale {
Mwidth
Mheight
Mlp
/MathScaleHook where {
/MathScaleHook get exec
} if
translate
scale
pop pop pop pop
pop pop pop pop
/yscale exch def
/ybias exch def
/xscale exch def
/xbias exch def
/Momatrix
xscale yscale matrix scale
xbias ybias matrix translate
matrix concatmatrix def
/Mgmatrix
matrix currentmatrix
def
} def
% Given a non-empty array of points to fit ([p]) and a maximum width (sx)
% and height (sy) find the largest scale (Ax and Ay) and offsets (Bx and By)
% such that the transformation
%	[gx gy tx ty] -> (Ax gx + tx + bx, Ay gy + ty + By)
% maps the points into the rectangle [0,sx]x[0,sy]
/Mlp {
3 copy
Mlpfirst
{
Mnodistort
{
Mmin
dup
} if
4 index
2 index
2 index
Mlprun
16 -8 roll
21 8 roll
11 index
11 -1 roll
10 -4 roll
Mlp1
8 index
9 -5 roll
Mlp1
4 -1 roll
and
{ exit } if
15 -8 roll
pop pop pop pop
pop pop pop pop
3 -1 roll
pop pop
} loop
exch
3 1 roll
7 -3 roll
pop pop pop
} def
% Given an array of points in the [gx gy tx ty] form, with the last two
% being [gxlow gylow 0 0] and [gxhigh gyhigh 0 0], and the width and height
% (sx and sy) in which to fit them, compute the maximum scaling (Ax and Ay).
/Mlpfirst {
3 -1 roll
dup length
2 copy
-2 add
get
aload
pop pop pop
4 -2 roll
-1 add
get
aload
pop pop pop
6 -1 roll
3 -1 roll
5 -1 roll
sub
div
4 1 roll
exch sub
div
} bind def
% Given a non-empty array of points to fit ([pnts]) and scale factors
% for graphics->text (Ax and Ay), compute the limiting points.
/Mlprun {
2 copy
4 index
0 get
dup
4 1 roll
Mlprun1
3 copy
8 -2 roll
9 -1 roll
{
3 copy
Mlprun1
3 copy
11 -3 roll
/gt Mlpminmax
8 3 roll
11 -3 roll
/lt Mlpminmax
8 3 roll
} forall
pop pop pop pop
3 1 roll
pop pop
aload pop
5 -1 roll
aload pop
8 copy
exch
6 -1 roll
Mlprun2
8 2 roll
4 -1 roll
Mlprun2
6 2 roll
3 -1 roll
Mlprun2
4 2 roll
exch
Mlprun2
6 2 roll
} bind def
% Given scale factors for graphics->text (Ax and Ay) and a point in the
% [gx gy tx ty] form, return the text x and y coordinate that results.
/Mlprun1 {
aload pop
exch
6 -1 roll
5 -1 roll
mul add
4 -2 roll
mul
3 -1 roll
add
} bind def
% Given a low and high coordinate, compute the center and width.
/Mlprun2 {
2 copy
add 2 div
3 1 roll
exch sub
} bind def
% Given two points stored as [gx gy tx ty] followed by the scaled
% result (rx, ry), and a comparison function (lt or gt) leave the
% point which is the minimum (or maximum) in each dimension.
/Mlpminmax {
cvx
2 index
6 index
2 index
exec
{
7 -3 roll
4 -1 roll
} if
1 index
5 index
3 -1 roll
exec
{
4 1 roll
pop
5 -1 roll
aload
pop pop
4 -1 roll
aload pop
[
8 -2 roll
pop
5 -2 roll
pop
6 -2 roll
pop
5 -1 roll
]
4 1 roll
pop
}
{
pop pop pop
} ifelse
} bind def
% Given a size (s), graphics->text scale (A), text center (ct), text
% width (wt), graphics center (cg) and graphics width (wg), compute
% a new graphics->text scale (Anew) and offset (B) and whether or not
% we are done.
% Note, the mysterious .99999 is magic juju which is supposed to ward
% off the possibility that floating point errors would cause this
% routine to return the old A and yet claim not-done.
/Mlp1 {
5 index
3 index	sub
5 index
2 index mul
1 index
le
1 index
0 le
or
dup
not
{
1 index
3 index	div
.99999 mul
8 -1 roll
pop
7 1 roll
}
if
8 -1 roll
2 div
7 -2 roll
pop sub
5 index
6 -3 roll
pop pop
mul sub
exch
} bind def
% The following are the workings of the tick, axes and plot labels.
% NOTE a possible source of confusion is that for xticks ie tickmarks on
% the x axis we keep y information and vice versa for yticks
%
%	When Minner is found then
%
% assumes that box starts at zero on the left lower side
%
%		0)	if outflag = 1 then intop = 0, inrht = 0 outflag = 0
%		1)	Save intop 	largest top of box 
%		2)	Save inrht 	largest rht of box
%		3)	set inflag	notifies that inner marks are present
%
%	When Mouter is found then
%
%	if inflag is set then
%		1)	get vecx and vecy off the stack (points in direcn to move)
%		2)	vecx < 1 xadrht = inrht*abs(vecx)
%		3)	vecx > 1 xadlft = inrht*abs(vecx)
%		4)	vecy < 1 yadtop = intop*abs(vecy)
%		5)	vecy > 1 yadbot = intop*abs(vecy)
%		6)	set outflag = 1
%		7)	clear inflag, inrht, intop
%	guaranteed to be zero if no inner is present??
%
%
%	These all have effects in Mrotsboxa and Mrotshowa
%		check inflag and if set
%
%		1) increase top of bbox by yadtop
%		2) decrease bot of bbox by yadbot
%		3) increase rht of bbox by xadrht
%		4) increase lft of bbox by xadlft
%		5) clear outflag, yadtop, yadbot,
%			         xadrht, xadlft
%
% 
% This saves the top right corner of the bounding box as a side effect
% This is to allow the adjustment of text placed with Mouter so that
% it misses the Minner text.  It is assumed that the ang is 0
% in the same way it is assumed that the text of Mouter is 0 or 90
%
/Minner {
outflag
1
eq
{
/outflag 0 def
/intop 0 def
/inrht 0 def
} if		
5 index
gsave
Mtmatrix setmatrix
Mvboxa pop
grestore
3 -1 roll
pop
dup
intop
gt
{
/intop
exch def
}
{ pop }
ifelse
dup
inrht
gt
{
/inrht
exch def
}
{ pop }
ifelse
pop
/inflag
1 def
} def
% This takes two number off the stack and uses them as a vector in graphics
% coordinates which points in the direction in which the Mouter text is to move
% it calculates the bouding box adjustments yadtop yadbot xadrht and xadlft
% these are in Mboxout to adjust the bounding box to compensate.
/Mouter {
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
inflag
1 eq
{
dup
0 lt
{
dup
intop
mul
neg
/yadtop
exch def
} if
dup
0 gt
{
dup
intop
mul
/yadbot
exch def
}
if
pop
dup
0 lt
{
dup
inrht
mul
neg
/xadrht
exch def
} if
dup
0 gt
{
dup
inrht
mul
/xadlft
exch def
} if
pop
/outflag 1 def
}
{ pop pop}
ifelse
/inflag 0 def
/inrht 0 def
/intop 0 def
} def	
%
% This adjusts the bounding box to account for adjacent text
% This allows the two text strings to avoid each other 
% current matrix is the text matrix
/Mboxout {
outflag
1
eq
{
4 -1
roll
xadlft
leadjust
add
sub
4 1 roll
3 -1
roll
yadbot
leadjust
add
sub
3 1
roll
exch
xadrht
leadjust
add
add
exch
yadtop
leadjust
add
add
/outflag 0 def
/xadlft 0 def
/yadbot 0 def
/xadrht 0 def
/yadtop 0 def
} if
} def
/leadjust {
(m) stringwidth pop
.5 mul
} bind def
% The offsets sx and sy refer to the graphics coordinate system 
% thus they must be altered if a rotation has taken place.
% We must also change the bounding box computations for Minner
%
/Mrotcheck {
dup
90
eq
{
%
% Mouter only applies to strings which are either at 0 or 90
% sort out the box adjust factors
%
%	xadrht -> yadbot
%	xadlft -> yadtop
%	yadtop -> xadrht
%	yadbot -> xadlft
yadbot
/yadbot
xadrht
def	
/xadrht
yadtop
def
/yadtop
xadlft
def
/xadlft
exch
def
}
if
dup
cos
1 index
sin
Checkaux
dup
cos
1 index
sin neg
exch
Checkaux
3 1 roll
pop pop
} def
%
% Checkaux is an auxilliary function for Mrotcheck it multiplies a 
% row vector by a column vector
% 
/Checkaux {
4 index
exch
4 index
mul
3 1 roll
mul add
4 1 roll
} bind def
%
% Mboxrot converts the bounding box back from the rotated coordinate
% system to the Mgmatrix system to compensate for a rotation
% It has the opposite functionality of Mrotcheck
% This is not the most neatest or most efficient implementation but it works
%
/Mboxrot {
Mrot
90 eq
{
% old		 tlx  thx  tly  thy
% new		-thy -tly  tlx  thx
%
brotaux
4 2
roll
}
if
Mrot
180 eq
{
% old		 tlx  thx  tly  thy
% new		-thx -tlx -thx -tly
%
4 2
roll
brotaux
4 2
roll
brotaux
}	
if
Mrot
270 eq
{
% old		 tlx  thx  tly  thy
% new		 tly  thy -thx -tlx
%
4 2
roll
brotaux
}
if
} def
%
% auxilliary function negate and reverse
/brotaux {
neg
exch
neg
} bind def
%
% Mabsproc takes a measurement in the default user units and converts
% it to the present units.   This allows absolute thickness and dashing
% to work.  It works by using a {0, x} vector and using the RMS of the result.
/Mabsproc {
0
matrix defaultmatrix
dtransform idtransform
dup mul exch
dup mul
add sqrt
} bind def
%
% Mabswid allows the linewidth to be specified in absolute coordinates
% It does this by recording the graphics transformation matrix at the
% begining of the plot.
% This will break if the scaling in the x and y directions is
% different.  This is the case if Mnodistort is false
%
/Mabswid {
Mabsproc
setlinewidth	
} bind def
% Mabsdash allows the dashing pattern to be specified in absolute coordinates
% It does this by recording the graphics transformation matrix at the
% begining of the plot.
% This will break if the scaling in the x and y directions is
% different.  This is the case if Mnodistort is false
%
/Mabsdash {
exch
[
exch
{
Mabsproc
}
forall
]
exch
setdash
} bind def
%
% Mabs takes a pair of coordinates in points
% and converts them into a pair of coordinates in
% the current drawing scheme
%
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
%
% Mabs takes a pair of numbers in drawing coordinates
% and a pair in points.  It converts the points to
% drawing coordinates and adds them to the first pair.
%
/Mabsadd {
Mabs
3 -1 roll add
3 1 roll add
exch 
} bind def
%
% These two procedures are for using Offset coordinates
% with MathScale computations
%
/Mabsfix1 {
3 -1 roll
/ar exch 
def
ar 2 get
3 -1 roll
add exch
ar 3 get
add
ar 3
3 -1 roll
put
ar 2
3 -1 roll
put
ar
} bind def
/Mabsfix {
2 copy
6 -1 roll
3 1 roll
Mabsfix1
4 1 roll
Mabsfix1
} bind def
%MBeginOrig start coordinates in user coordinates
/MBeginOrig { Momatrix concat} bind def
%MEndOrig start coordinates in user coordinates
/MEndOrig { Mgmatrix setmatrix} bind def
/sampledsound where
{ pop }
{ /MathDPSFlag where
{ pop /sampledsound { clientsync } def }
{ /sampledsound {
exch pop
exch 5 1 roll
mul
4 idiv
mul
2 idiv
exch pop
exch
/Mtempproc exch def
{ Mtempproc pop }
repeat
} def
} ifelse
} ifelse
% Define setrgbcolor for those ancient PostScript devices lacking it
/setrgbcolor dup where
{ pop pop }
{ { .114 mul exch .587 mul add exch .299 mul add setgray } bind def }
ifelse
%
% now simple conversion of cmykcolor to rgbcolor
% subtract k and then take complements
/setcmykcolor where
{ pop}
{ /setcmykcolor {
4 1
roll
[
4 1 
roll
]
{
1 index
sub
1
sub neg
dup
0
lt
{
pop
0
}
if
dup
1
gt
{
pop
1
}
if
exch
} forall
pop
setrgbcolor
} bind def
} ifelse
% Here are the short operators
/g /setgray load def
/k /setcmykcolor load def
/m /moveto load def
/p /gsave load def
/r /setrgbcolor load def
/w /setlinewidth load def
/C /curveto load def
/F /Mfill load def
/L /lineto load def
/P /grestore load def
/s /Mstroke load def
/Mcharproc
{
currentfile
(x)
readhexstring
pop
0 get
exch
div
} bind def
/Mshadeproc
{
dup
3 1
roll
{
dup
Mcharproc
3 1
roll
} repeat
1 eq
{
setgray
}
{
3 eq
{
setrgbcolor
}
{
setcmykcolor
} ifelse
} ifelse
} bind def
/Mrectproc
{
3 index
2 index
moveto
2 index
3 -1
roll
lineto
dup
3 1
roll
lineto
lineto
Mfill
} bind def
/Mcolorimage
{
7 1
roll
pop
pop
matrix
invertmatrix
concat
2 exch exp
1 sub
3 1 roll
1 1
2 index
{
1 1
4 index
{
dup
1 sub
exch
2 index
dup
1 sub
exch
7 index
9 index
Mshadeproc
Mrectproc
} for
pop
} for
pop pop pop pop
} bind def
/Mimage
{
pop
matrix
invertmatrix
concat
2 exch exp
1 sub
3 1 roll
1 1
2 index
{
1 1
4 index
{
dup
1 sub
exch
2 index
dup
1 sub
exch
7 index
Mcharproc
setgray
Mrectproc
} for
pop
} for
pop pop pop
} bind def
% Default values for variables
/Mlmarg		1.0 72 mul def
/Mrmarg		1.0 72 mul def
/Mbmarg		1.0 72 mul def
/Mtmarg		1.0 72 mul def
/Mwidth		8.5 72 mul def
/Mheight	11 72 mul def
/Mtransform	{  } bind def
/Mnodistort	true def	
/Mfixdash	false def	
/Mrot		0	def	
/intop 0 def
/inrht 0 def
/inflag 0 def
/outflag 0 def
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
/defineresource where
{ pop /WRI-Mathematica-prolog currentdict /ProcSet defineresource pop }
if
end
%KLUDGE until Mathematica output uses resources directly
userdict /MathPictureStart {
	/findresource where
	{ pop /WRI-Mathematica-prolog /ProcSet findresource }
	{ Mathdict }
	ifelse
	/MathPictureStart get exec
} put
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% ContourGraphics
/Helvetica findfont 24  scalefont  setfont
% Scaling calculations
-0.000392465 0.196232 -0.000392465 0.0196232 [
[.19584 -0.0125 -7.2 -31.2 ]
[.19584 -0.0125 7.2 0 ]
[.39207 -0.0125 -7.2 -31.2 ]
[.39207 -0.0125 7.2 0 ]
[.5883 -0.0125 -7.2 -31.2 ]
[.5883 -0.0125 7.2 0 ]
[.78454 -0.0125 -7.2 -31.2 ]
[.78454 -0.0125 7.2 0 ]
[.98077 -0.0125 -7.2 -31.2 ]
[.98077 -0.0125 7.2 0 ]
[ 0 0 -0.125 0 ]
[.5 -0.0125 -280.8 -62.4 ]
[.5 -0.0125 280.8 -31.2 ]
[-0.0125 .19584 -28.8 -15.6 ]
[-0.0125 .19584 0 15.6 ]
[-0.0125 .39207 -28.8 -15.6 ]
[-0.0125 .39207 0 15.6 ]
[-0.0125 .5883 -28.8 -15.6 ]
[-0.0125 .5883 0 15.6 ]
[-0.0125 .78454 -28.8 -15.6 ]
[-0.0125 .78454 0 15.6 ]
[-0.0125 .98077 -28.8 -15.6 ]
[-0.0125 .98077 0 15.6 ]
[ 0 0 -0.125 0 ]
[-0.01875 .5 -60 -187.2 ]
[-0.01875 .5 -28.8 187.2 ]
[ 0 1 .125 0 ]
[ 1 0 .125 0 ]
[ 0 0 0 0 ]
[ 1 1 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.19584 0 m
.19584 .00625 L
s
[(1)] .19584 -0.0125 0 1 Mshowa
.39207 0 m
.39207 .00625 L
s
[(2)] .39207 -0.0125 0 1 Mshowa
.5883 0 m
.5883 .00625 L
s
[(3)] .5883 -0.0125 0 1 Mshowa
.78454 0 m
.78454 .00625 L
s
[(4)] .78454 -0.0125 0 1 Mshowa
.98077 0 m
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%%EndImage
%%EndPreview
save
countdictstack
mark
newpath
/showpage {} def
%%EndProlog
%%Page 1 1
% Start of procedure set
userdict /Mathdict 100 dict dup begin put
% The externally visible functions are:
%	MathPictureStart- start page.
%	MathPictureEnd	- finish off page.
%	MathSubStart	- start a sub-page.
%	MathSubEnd	- finish off a sub-page.
%	Mdot		- draw a dot.
%	Mtetra		- draw a filled tetragon.
%	Metetra		- draw a filled tetragon with black edges.
%	Mistroke	- intermediate stroke of multi-stroke line/curve.
%	Mfstroke	- final stroke of multi-stroke line/curve.
%	Msboxa		- compute coordinates of text bounding box.
%	Mshowa		- plot characters.
%	MathScale	- compute scaling info to contain array of points.
%start of ISOLatin1 stuff
/ISOLatin1Encoding dup where
{ pop pop }
{
[
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright
/parenleft /parenright /asterisk /plus /comma /minus /period /slash
/zero /one /two /three /four /five /six /seven
/eight /nine /colon /semicolon /less /equal /greater /question
/at /A /B /C /D /E /F /G
/H /I /J /K /L /M /N /O
/P /Q /R /S /T /U /V /W
/X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore
/quoteleft /a /b /c /d /e /f /g
/h /i /j /k /l /m /n /o
/p /q /r /s /t /u /v /w
/x /y /z /braceleft /bar /braceright /asciitilde /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent
/dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron
/space /exclamdown /cent /sterling /currency /yen /brokenbar /section
/dieresis /copyright /ordfeminine /guillemotleft
/logicalnot /hyphen /registered /macron
/degree /plusminus /twosuperior /threesuperior
/acute /mu /paragraph /periodcentered
/cedilla /onesuperior /ordmasculine /guillemotright
/onequarter /onehalf /threequarters /questiondown
/Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
/Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis
/Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply
/Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls
/agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla
/egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis
/eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide
/oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis
] def
} ifelse
/WindowsANSIEncoding [
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle
/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash
/zero/one/two/three/four/five/six/seven
/eight/nine/colon/semicolon/less/equal/greater/question
/at/A/B/C/D/E/F/G
/H/I/J/K/L/M/N/O
/P/Q/R/S/T/U/V/W
/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore
/grave/a/b/c/d/e/f/g
/h/i/j/k/l/m/n/o
/p/q/r/s/t/u/v/w
/x/y/z/braceleft/bar/braceright/asciitilde/.notdef
/.notdef/.notdef/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl
/circumflex/perthousand/Scaron/guilsinglleft/OE/.notdef/Zcaron/.notdef
/.notdef/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash
/tilde/trademark/scaron/guilsinglright/oe/.notdef/zcaron/Ydieresis
/.notdef/exclamdown/cent/sterling/currency/yen/brokenbar/section
/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron
/degree/plusminus/twosuperior/threesuperior/acute/.notdef/paragraph/dotaccent
/ogonek/onesuperior/ring/guillemotright/onequarter/onehalf/threequarters/questiondown
/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla
/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis
/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply
/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls
/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla
/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis
/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide
/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis
] def
/MacintoshRomanEncoding [
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle
/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash
/zero/one/two/three/four/five/six/seven
/eight/nine/colon/semicolon/less/equal/greater/question
/at/A/B/C/D/E/F/G
/H/I/J/K/L/M/N/O
/P/Q/R/S/T/U/V/W
/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore
/grave/a/b/c/d/e/f/g
/h/i/j/k/l/m/n/o
/p/q/r/s/t/u/v/w
/x/y/z/braceleft/bar/braceright/asciitilde/.notdef
/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute
/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave
/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute
/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis
/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls
/registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash
/.notdef/plusminus/.notdef/.notdef/yen/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/ordfeminine/ring/.notdef/ae/oslash
/questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef/guillemotleft
/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe
/endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/.notdef
/ydieresis/Ydieresis/.notdef/currency/guilsinglleft/guilsinglright/.notdef/.notdef
/daggerdbl/dotaccent/quotesinglbase/quotedblbase/perthousand/Acircumflex/Ecircumflex/Aacute
/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex
/.notdef/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde
/macron/.notdef/.notdef/.notdef/ogonek/.notdef/.notdef/.notdef
] def
/MFontDict 50 dict def
/MStrCat
{
exch
dup length
2 index length add
string
dup 3 1 roll
copy
length
exch dup
4 2 roll exch
putinterval
} bind def
/MCreateEncoding
{
1 index
255 string cvs
(-) MStrCat
1 index MStrCat
cvn exch
(Encoding) MStrCat
cvn dup where
{
exch get
}
{
pop
StandardEncoding
} ifelse
3 1 roll
dup MFontDict exch known not
{
1 index findfont
dup length dict
begin
{1 index /FID ne
{def}
{pop pop}
ifelse} forall
/Encoding 3 index
def
currentdict
end
1 index exch definefont pop
MFontDict 1 index
null put
}
if
exch pop
exch pop
} bind def
/ISOLatin1 { (ISOLatin1) MCreateEncoding } bind def
%end of ISOLatin1 stuff
% Set up for the start of a page.
/MathPictureStart {
/Msaveobj save def
/findresource where
{ pop /WRI-Mathematica-prolog /ProcSet findresource begin }
{ Mathdict begin }
ifelse
userdict begin
/MathPictureStartHook where {
/MathPictureStartHook get exec
} if
Mtransform
Mlmarg
Mbmarg
translate
Mwidth
Mlmarg Mrmarg add
sub
/Mwidth exch def
Mheight
Mbmarg Mtmarg add
sub
/Mheight exch def
/Mtmatrix
matrix currentmatrix
def
/Mgmatrix
matrix currentmatrix
def
/MathDPSFlag where {
pop
clientsync
} if
} def
% Finish off a page.
/MathPictureEnd {
end
end
Msaveobj restore
/MathDPSFlag where { pop } { showpage } ifelse
} def
%MFill fills the drawing area with the current color.
/MFill {
0 0 		moveto
Mwidth 0 	lineto
Mwidth Mheight 	lineto
0 Mheight 	lineto
fill
} def
%New device-specific optimizing operators
/Mfill /.devicefill where
{ pop /.devicefill load def }
{ /fill load def }
ifelse
/Mstroke /.devicestroke where
{ pop /.devicestroke load def }
{ /stroke load def }
ifelse
% xmin xmax ymin ymax MPlotRegion alters the origin, Mwidth and Mheight 
% so that the picture fills the altered region
/MPlotRegion {
3 index
Mwidth mul
2 index
Mheight mul
translate
exch sub
Mheight mul
/Mheight
exch def
exch sub
Mwidth mul
/Mwidth
exch def
} def
% Given a rectangle, set it up as a sub-picture.
/MathSubStart {
Momatrix
Mgmatrix Mtmatrix
Mwidth Mheight
7 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
Mgmatrix setmatrix
9 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
2 copy translate
/Mtmatrix matrix currentmatrix def
3 -1 roll
exch sub
/Mheight exch def
sub
/Mwidth exch def
} def
% Restore the saved state left by the matching MathSubStart.
% Note, we also leave with the new Mgmatrix as the current matrix.
/MathSubEnd {
/Mheight exch def
/Mwidth exch def
/Mtmatrix exch def
dup setmatrix
/Mgmatrix exch def
/Momatrix exch def
} def
% Given a point, draw a dot.
/Mdot {
newpath
currentlinewidth 2 div
0 360
arc fill
} bind def
% Given 4 points, draw the corresponding filled tetragon.
/Mtetra {
moveto
lineto
lineto
lineto
Mfill
} bind def
% Given 4 points, draw the corresponding filled tetragon with black edges.
% Note, this leaves the gray level at 0 (for compatibility with the old
% C code.
/Metetra {
moveto
lineto
lineto
lineto
closepath
gsave
Mfill
grestore
0 setgray
Mstroke
} bind def
% Mistroke is called to stroke intermediate parts of a path.  It makes
% sure to resynchronize the dashing pattern and to leave the current point
% as the final point of the path.
/Mistroke {
flattenpath
0 0 0
{
4 2 roll
pop pop
}
{
4 -1 roll
2 index
sub dup mul
4 -1 roll
2 index
sub dup mul
add sqrt
4 -1 roll
add
3 1 roll
}
{
stop
}
{
stop
}
pathforall
pop pop
currentpoint
Mstroke
moveto
currentdash
3 -1 roll
add
setdash
} bind def
% Mfstroke is called to stroke the final parts of a path.  It resets
% the dashing pattern to compensate for any adjustments made by Mistroke.
/Mfstroke {
Mstroke
currentdash
pop 0
setdash
} bind def
% Mrotsboxa is the same as Msboxa except that it takes an angle 
% from the stack and the box is calculated for text rendered at this  angle.  
% It gsaves in case we are starting a MathSubStart
% save Mrot so that Msboxa can convert bouding box back to the non-rotated
% coordinate system
% call Mrotcheck to alter the offsets into the rotated system
% converts Mtmatrix to render in the rotated system
% the calls Msboxa which does all the work
% at the end  Mtmatrix is restored and Mrot is reset to 0 
/Mrotsboxa {
gsave
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
grestore
Msboxa
3  -1 roll
/Mtmatrix
exch def
/Mrot
0 def
} bind def
% Given an array of strings ([str...]), which represent consecutive lines
% of text, a position in graphics coordinates (gx,gy) and a position in
% the bounding box coordinates (sx,sy), compute the low and high coordinates
% of the resulting text, in the [gx gy tx ty] form, which corresponds to
% the point (gx,gy) (in graphics coordinates) plus the offset (tx,ty) (in
% text coordinates).
% Note, Msboxa assumes that the current matrix is the text matrix.
% Mboxout is called in case we are in Mouter to make the box bigger
% Mboxrot adjusts the box to account for a rotation to convert the box
% into a nonrotated coordinate system
%
/Msboxa {
newpath
5 -1 roll
Mvboxa
pop
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Msboxa1
5 -3 roll
Msboxa1
Mboxrot
[
7 -2 roll
2 copy
[
3 1 roll
10 -1 roll
9 -1 roll
]
6 1 roll
5 -2 roll
]
} bind def
% Msboxa1 is an internal function which, given a bounding box coordinate
% (sz), and the bounding box limits (blz and bhz), computes the actual
% offsets (tlz = (blz-bhz)(sz+1)/2, thz = (blz-bhz)(sz-1)/2).
/Msboxa1 {
sub
2 div
dup
2 index
1 add
mul
3 -1 roll
-1 add
3 -1 roll
mul
} bind def
% Given a (non-empty) array of strings ([str...]) which represent consecutive
% lines of text, compute the total bounding box assuming that we start at
% (0,0) and the array of y offsets to place the lines correctly.
% Note, Mvboxa assumes that the current matrix is the text matrix.
% Note, Mvboxa does not alter the current path.
% The vertical spacing is set so that the bounding boxes of adjacent lines
% are .3 times the width of an `m' apart.
/Mvboxa {
gsave
newpath
[ true
3 -1 roll
{
Mbbox
5 -1 roll
{
0
5 1 roll
}
{
7 -1 roll
exch sub
(m) stringwidth pop
.3 mul
sub
7 1 roll
6 -1 roll
4 -1 roll
Mmin
3 -1 roll
5 index
add
5 -1 roll
4 -1 roll
Mmax
4 -1 roll
}
ifelse
false
}
forall
{ stop } if
counttomark
1 add
4 roll
]
grestore
} bind def
% Given a string, compute the bounding box assuming that we start at (0,0).
% Note, the path is assumed to be empty, and we are assumed to be in text
% coordinates.  Allows for long strings.
/Mbbox {
1 dict begin
0 0 moveto
/temp (T) def
{	gsave
currentpoint newpath moveto
temp 0 3 -1 roll put temp
false charpath flattenpath currentpoint
pathbbox
grestore moveto lineto moveto} forall
pathbbox
newpath
end
} bind def
% Compute the minimum of two numbers.
/Mmin {
2 copy
gt
{ exch } if
pop
} bind def
% Compute the maximum of two numbers.
/Mmax {
2 copy
lt
{ exch } if
pop
} bind def
%
% Mrotwork saves Mrot (not really needed but saved anyway)
% calls Mrotcheck to adjust the offsets into the rotated coordinate system
% converts Mtmatrix to render in the rotated system
%
/Mrotwork {
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
Mgmatrix setmatrix
} def
%
% Mrotshowa is the same as Mshowa except that it takes an angle
% from the stack and the text is rendered at this angle.
% It call Mrotwork to do all the rotation work.
% Then it calls Mshowa which does all the drawing work.
% At the end Mtmatrix is restored and Mrot is reset to zero.
%
/Mrotshowa {
Mrotwork
Mshowa
/Mtmatrix
exch def
/Mrot 0 def
} def
%
% Draws rotated text with a background.
%
/Mrotback {
7 1 roll
dup
8 1 roll
Mrotwork
8 -2 roll
Mshowback
/Mtmatrix
exch def
/Mrot 0 def
} def
%
% Given an array of strings ([str...]), which represent consecutive lines
% of text, a position in graphics coordinates (gx,gy) and a position in
% the bounding box coordinates (sx,sy), display the strings.
% Mboxout is called in case we are in Mouter
%
/Mshowa {
4 -2 roll
moveto
2 index
Mtmatrix setmatrix
Mvboxa
7 1 roll
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Mshowa1
4 1 roll
Mshowa1
rmoveto
currentpoint
Mshowax
pop pop pop pop
Mgmatrix setmatrix
} def
%
% The background box of text is increased by the
% size of an "m"
%
/Madjust	{
(m)
stringwidth
pop
mul
dup
4 -1 roll
add
3 1 roll
add
} def
%
%
%
/Mbuildcoord {
7 index
7 index
4 -1 roll
4 -1 roll
index
exch
index
Mabsadd
} def
%
% If the text is rotated then translate to the drawing point.
% Rotate then translate back.  Do not do this if the angle
% of rotation is 0.
%
/Mrotate {
8 index
0 ne
{
13 copy
4 -2 roll
pop pop
6 -2 roll
pop pop
4 -1 roll
3 -1 roll
sub
6 -1 roll
mul
3 1 roll
sub
4 -1 roll
mul
3 -1 roll
5 1 roll
Mabsadd
2 copy
translate
3 -1 roll
rotate
exch -1 mul
exch -1 mul
translate
} if
9 -1 roll
pop
} def
%
% Draw text but into a box with a certain color.
% Uses Msboxa to build the box.
%
/Mshowback {
gsave
exec
6 copy pop
Msboxa
aload pop
0.5 Madjust
5 -1 roll
aload pop
Mrotate
-0.5
Madjust
4 -1 roll
pop
3 -1 roll
pop
3 4
Mbuildcoord
moveto
3 4
Mbuildcoord
lineto
3 6
Mbuildcoord
lineto
5 6
Mbuildcoord
lineto
5 4
Mbuildcoord
lineto
pop pop pop
pop pop pop
fill		
grestore
Mshowa
} def
% This is used for fixedwidth fonts
% It simply shows each string and advances the y direction by the offset
%
/Mshowax {	
0 1
4 index length
-1 add
{
2 index
4 index
2 index
get
3 index
add
moveto
4 index
exch get
Mfixdash
{
Mfixdashp		
}
if
show
} for
} def
% Fix if all dashes and length > 1
/Mfixdashp {
dup
length
1
gt
1 index
true exch
{
45
eq
and
} forall
and
{
gsave
(--)		
stringwidth pop
(-)
stringwidth pop
sub
2 div
0 rmoveto
dup
length
1 sub
{
(-)
show
}
repeat
grestore
}
if
} bind def	
% Mshowa1 is an internal routine which, given a bounding box coordinate
% (sz), and the bounding box limits if we started drawing at 0 (tlz and thz),
% computes the offset at which to start drawing
% (relz = (sz-1)tlz/2 - (sz+1)thz/2 = sz(tlz-thz)/2-(tlz+thz)/2).
/Mshowa1 {
2 copy
add
4 1 roll
sub
mul
sub
-2 div
} bind def
% Given the x and y scaling to user coordinates and an array of points to
% fit (xbias xscale ybias yscale [pnts]), set up the scaling.  The array
% must contain atleast two points, and the last two must be of the form
% [gxlow gylow 0 0] and [gxhigh gyhigh 0 0].
% Note, MathScale assumes that we are already scaled so that the active area
% is the rectangle [0,Mwidth-Mlmarg-Mrmarg]x[0,Mheight-Mbmarg-Mtmarg].
% also keep bias and scale info for PostScript commands
/MathScale {
Mwidth
Mheight
Mlp
/MathScaleHook where {
/MathScaleHook get exec
} if
translate
scale
pop pop pop pop
pop pop pop pop
/yscale exch def
/ybias exch def
/xscale exch def
/xbias exch def
/Momatrix
xscale yscale matrix scale
xbias ybias matrix translate
matrix concatmatrix def
/Mgmatrix
matrix currentmatrix
def
} def
% Given a non-empty array of points to fit ([p]) and a maximum width (sx)
% and height (sy) find the largest scale (Ax and Ay) and offsets (Bx and By)
% such that the transformation
%	[gx gy tx ty] -> (Ax gx + tx + bx, Ay gy + ty + By)
% maps the points into the rectangle [0,sx]x[0,sy]
/Mlp {
3 copy
Mlpfirst
{
Mnodistort
{
Mmin
dup
} if
4 index
2 index
2 index
Mlprun
16 -8 roll
21 8 roll
11 index
11 -1 roll
10 -4 roll
Mlp1
8 index
9 -5 roll
Mlp1
4 -1 roll
and
{ exit } if
15 -8 roll
pop pop pop pop
pop pop pop pop
3 -1 roll
pop pop
} loop
exch
3 1 roll
7 -3 roll
pop pop pop
} def
% Given an array of points in the [gx gy tx ty] form, with the last two
% being [gxlow gylow 0 0] and [gxhigh gyhigh 0 0], and the width and height
% (sx and sy) in which to fit them, compute the maximum scaling (Ax and Ay).
/Mlpfirst {
3 -1 roll
dup length
2 copy
-2 add
get
aload
pop pop pop
4 -2 roll
-1 add
get
aload
pop pop pop
6 -1 roll
3 -1 roll
5 -1 roll
sub
div
4 1 roll
exch sub
div
} bind def
% Given a non-empty array of points to fit ([pnts]) and scale factors
% for graphics->text (Ax and Ay), compute the limiting points.
/Mlprun {
2 copy
4 index
0 get
dup
4 1 roll
Mlprun1
3 copy
8 -2 roll
9 -1 roll
{
3 copy
Mlprun1
3 copy
11 -3 roll
/gt Mlpminmax
8 3 roll
11 -3 roll
/lt Mlpminmax
8 3 roll
} forall
pop pop pop pop
3 1 roll
pop pop
aload pop
5 -1 roll
aload pop
8 copy
exch
6 -1 roll
Mlprun2
8 2 roll
4 -1 roll
Mlprun2
6 2 roll
3 -1 roll
Mlprun2
4 2 roll
exch
Mlprun2
6 2 roll
} bind def
% Given scale factors for graphics->text (Ax and Ay) and a point in the
% [gx gy tx ty] form, return the text x and y coordinate that results.
/Mlprun1 {
aload pop
exch
6 -1 roll
5 -1 roll
mul add
4 -2 roll
mul
3 -1 roll
add
} bind def
% Given a low and high coordinate, compute the center and width.
/Mlprun2 {
2 copy
add 2 div
3 1 roll
exch sub
} bind def
% Given two points stored as [gx gy tx ty] followed by the scaled
% result (rx, ry), and a comparison function (lt or gt) leave the
% point which is the minimum (or maximum) in each dimension.
/Mlpminmax {
cvx
2 index
6 index
2 index
exec
{
7 -3 roll
4 -1 roll
} if
1 index
5 index
3 -1 roll
exec
{
4 1 roll
pop
5 -1 roll
aload
pop pop
4 -1 roll
aload pop
[
8 -2 roll
pop
5 -2 roll
pop
6 -2 roll
pop
5 -1 roll
]
4 1 roll
pop
}
{
pop pop pop
} ifelse
} bind def
% Given a size (s), graphics->text scale (A), text center (ct), text
% width (wt), graphics center (cg) and graphics width (wg), compute
% a new graphics->text scale (Anew) and offset (B) and whether or not
% we are done.
% Note, the mysterious .99999 is magic juju which is supposed to ward
% off the possibility that floating point errors would cause this
% routine to return the old A and yet claim not-done.
/Mlp1 {
5 index
3 index	sub
5 index
2 index mul
1 index
le
1 index
0 le
or
dup
not
{
1 index
3 index	div
.99999 mul
8 -1 roll
pop
7 1 roll
}
if
8 -1 roll
2 div
7 -2 roll
pop sub
5 index
6 -3 roll
pop pop
mul sub
exch
} bind def
% The following are the workings of the tick, axes and plot labels.
% NOTE a possible source of confusion is that for xticks ie tickmarks on
% the x axis we keep y information and vice versa for yticks
%
%	When Minner is found then
%
% assumes that box starts at zero on the left lower side
%
%		0)	if outflag = 1 then intop = 0, inrht = 0 outflag = 0
%		1)	Save intop 	largest top of box 
%		2)	Save inrht 	largest rht of box
%		3)	set inflag	notifies that inner marks are present
%
%	When Mouter is found then
%
%	if inflag is set then
%		1)	get vecx and vecy off the stack (points in direcn to move)
%		2)	vecx < 1 xadrht = inrht*abs(vecx)
%		3)	vecx > 1 xadlft = inrht*abs(vecx)
%		4)	vecy < 1 yadtop = intop*abs(vecy)
%		5)	vecy > 1 yadbot = intop*abs(vecy)
%		6)	set outflag = 1
%		7)	clear inflag, inrht, intop
%	guaranteed to be zero if no inner is present??
%
%
%	These all have effects in Mrotsboxa and Mrotshowa
%		check inflag and if set
%
%		1) increase top of bbox by yadtop
%		2) decrease bot of bbox by yadbot
%		3) increase rht of bbox by xadrht
%		4) increase lft of bbox by xadlft
%		5) clear outflag, yadtop, yadbot,
%			         xadrht, xadlft
%
% 
% This saves the top right corner of the bounding box as a side effect
% This is to allow the adjustment of text placed with Mouter so that
% it misses the Minner text.  It is assumed that the ang is 0
% in the same way it is assumed that the text of Mouter is 0 or 90
%
/Minner {
outflag
1
eq
{
/outflag 0 def
/intop 0 def
/inrht 0 def
} if		
5 index
gsave
Mtmatrix setmatrix
Mvboxa pop
grestore
3 -1 roll
pop
dup
intop
gt
{
/intop
exch def
}
{ pop }
ifelse
dup
inrht
gt
{
/inrht
exch def
}
{ pop }
ifelse
pop
/inflag
1 def
} def
% This takes two number off the stack and uses them as a vector in graphics
% coordinates which points in the direction in which the Mouter text is to move
% it calculates the bouding box adjustments yadtop yadbot xadrht and xadlft
% these are in Mboxout to adjust the bounding box to compensate.
/Mouter {
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
inflag
1 eq
{
dup
0 lt
{
dup
intop
mul
neg
/yadtop
exch def
} if
dup
0 gt
{
dup
intop
mul
/yadbot
exch def
}
if
pop
dup
0 lt
{
dup
inrht
mul
neg
/xadrht
exch def
} if
dup
0 gt
{
dup
inrht
mul
/xadlft
exch def
} if
pop
/outflag 1 def
}
{ pop pop}
ifelse
/inflag 0 def
/inrht 0 def
/intop 0 def
} def	
%
% This adjusts the bounding box to account for adjacent text
% This allows the two text strings to avoid each other 
% current matrix is the text matrix
/Mboxout {
outflag
1
eq
{
4 -1
roll
xadlft
leadjust
add
sub
4 1 roll
3 -1
roll
yadbot
leadjust
add
sub
3 1
roll
exch
xadrht
leadjust
add
add
exch
yadtop
leadjust
add
add
/outflag 0 def
/xadlft 0 def
/yadbot 0 def
/xadrht 0 def
/yadtop 0 def
} if
} def
/leadjust {
(m) stringwidth pop
.5 mul
} bind def
% The offsets sx and sy refer to the graphics coordinate system 
% thus they must be altered if a rotation has taken place.
% We must also change the bounding box computations for Minner
%
/Mrotcheck {
dup
90
eq
{
%
% Mouter only applies to strings which are either at 0 or 90
% sort out the box adjust factors
%
%	xadrht -> yadbot
%	xadlft -> yadtop
%	yadtop -> xadrht
%	yadbot -> xadlft
yadbot
/yadbot
xadrht
def	
/xadrht
yadtop
def
/yadtop
xadlft
def
/xadlft
exch
def
}
if
dup
cos
1 index
sin
Checkaux
dup
cos
1 index
sin neg
exch
Checkaux
3 1 roll
pop pop
} def
%
% Checkaux is an auxilliary function for Mrotcheck it multiplies a 
% row vector by a column vector
% 
/Checkaux {
4 index
exch
4 index
mul
3 1 roll
mul add
4 1 roll
} bind def
%
% Mboxrot converts the bounding box back from the rotated coordinate
% system to the Mgmatrix system to compensate for a rotation
% It has the opposite functionality of Mrotcheck
% This is not the most neatest or most efficient implementation but it works
%
/Mboxrot {
Mrot
90 eq
{
% old		 tlx  thx  tly  thy
% new		-thy -tly  tlx  thx
%
brotaux
4 2
roll
}
if
Mrot
180 eq
{
% old		 tlx  thx  tly  thy
% new		-thx -tlx -thx -tly
%
4 2
roll
brotaux
4 2
roll
brotaux
}	
if
Mrot
270 eq
{
% old		 tlx  thx  tly  thy
% new		 tly  thy -thx -tlx
%
4 2
roll
brotaux
}
if
} def
%
% auxilliary function negate and reverse
/brotaux {
neg
exch
neg
} bind def
%
% Mabsproc takes a measurement in the default user units and converts
% it to the present units.   This allows absolute thickness and dashing
% to work.  It works by using a {0, x} vector and using the RMS of the result.
/Mabsproc {
0
matrix defaultmatrix
dtransform idtransform
dup mul exch
dup mul
add sqrt
} bind def
%
% Mabswid allows the linewidth to be specified in absolute coordinates
% It does this by recording the graphics transformation matrix at the
% begining of the plot.
% This will break if the scaling in the x and y directions is
% different.  This is the case if Mnodistort is false
%
/Mabswid {
Mabsproc
setlinewidth	
} bind def
% Mabsdash allows the dashing pattern to be specified in absolute coordinates
% It does this by recording the graphics transformation matrix at the
% begining of the plot.
% This will break if the scaling in the x and y directions is
% different.  This is the case if Mnodistort is false
%
/Mabsdash {
exch
[
exch
{
Mabsproc
}
forall
]
exch
setdash
} bind def
%
% Mabs takes a pair of coordinates in points
% and converts them into a pair of coordinates in
% the current drawing scheme
%
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
%
% Mabs takes a pair of numbers in drawing coordinates
% and a pair in points.  It converts the points to
% drawing coordinates and adds them to the first pair.
%
/Mabsadd {
Mabs
3 -1 roll add
3 1 roll add
exch 
} bind def
%
% These two procedures are for using Offset coordinates
% with MathScale computations
%
/Mabsfix1 {
3 -1 roll
/ar exch 
def
ar 2 get
3 -1 roll
add exch
ar 3 get
add
ar 3
3 -1 roll
put
ar 2
3 -1 roll
put
ar
} bind def
/Mabsfix {
2 copy
6 -1 roll
3 1 roll
Mabsfix1
4 1 roll
Mabsfix1
} bind def
%MBeginOrig start coordinates in user coordinates
/MBeginOrig { Momatrix concat} bind def
%MEndOrig start coordinates in user coordinates
/MEndOrig { Mgmatrix setmatrix} bind def
/sampledsound where
{ pop }
{ /MathDPSFlag where
{ pop /sampledsound { clientsync } def }
{ /sampledsound {
exch pop
exch 5 1 roll
mul
4 idiv
mul
2 idiv
exch pop
exch
/Mtempproc exch def
{ Mtempproc pop }
repeat
} def
} ifelse
} ifelse
% Define setrgbcolor for those ancient PostScript devices lacking it
/setrgbcolor dup where
{ pop pop }
{ { .114 mul exch .587 mul add exch .299 mul add setgray } bind def }
ifelse
%
% now simple conversion of cmykcolor to rgbcolor
% subtract k and then take complements
/setcmykcolor where
{ pop}
{ /setcmykcolor {
4 1
roll
[
4 1 
roll
]
{
1 index
sub
1
sub neg
dup
0
lt
{
pop
0
}
if
dup
1
gt
{
pop
1
}
if
exch
} forall
pop
setrgbcolor
} bind def
} ifelse
% Here are the short operators
/g /setgray load def
/k /setcmykcolor load def
/m /moveto load def
/p /gsave load def
/r /setrgbcolor load def
/w /setlinewidth load def
/C /curveto load def
/F /Mfill load def
/L /lineto load def
/P /grestore load def
/s /Mstroke load def
/Mcharproc
{
currentfile
(x)
readhexstring
pop
0 get
exch
div
} bind def
/Mshadeproc
{
dup
3 1
roll
{
dup
Mcharproc
3 1
roll
} repeat
1 eq
{
setgray
}
{
3 eq
{
setrgbcolor
}
{
setcmykcolor
} ifelse
} ifelse
} bind def
/Mrectproc
{
3 index
2 index
moveto
2 index
3 -1
roll
lineto
dup
3 1
roll
lineto
lineto
Mfill
} bind def
/Mcolorimage
{
7 1
roll
pop
pop
matrix
invertmatrix
concat
2 exch exp
1 sub
3 1 roll
1 1
2 index
{
1 1
4 index
{
dup
1 sub
exch
2 index
dup
1 sub
exch
7 index
9 index
Mshadeproc
Mrectproc
} for
pop
} for
pop pop pop pop
} bind def
/Mimage
{
pop
matrix
invertmatrix
concat
2 exch exp
1 sub
3 1 roll
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%%EndDocument
@endspecial FD 2851 1439 a(\(c\)) p Fc 17 w(N) p Fx 27
w(=) g(15) p Fr 439 1682 a(Figure) g(9:) g(Maximu) n(m) h(mod) n(ulus) f
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(of) g(TCP) h(conn) n(ections.) 228 2712 y @beginspecial
90 @llx 218 @lly 520 @urx 540 @ury 1300 @rwi 879 @rhi
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%%EndImage
%%EndPreview
save
countdictstack
mark
newpath
/showpage {} def
%%EndProlog
%%Page 1 1
% Start of procedure set
userdict /Mathdict 100 dict dup begin put
% The externally visible functions are:
%	MathPictureStart- start page.
%	MathPictureEnd	- finish off page.
%	MathSubStart	- start a sub-page.
%	MathSubEnd	- finish off a sub-page.
%	Mdot		- draw a dot.
%	Mtetra		- draw a filled tetragon.
%	Metetra		- draw a filled tetragon with black edges.
%	Mistroke	- intermediate stroke of multi-stroke line/curve.
%	Mfstroke	- final stroke of multi-stroke line/curve.
%	Msboxa		- compute coordinates of text bounding box.
%	Mshowa		- plot characters.
%	MathScale	- compute scaling info to contain array of points.
%start of ISOLatin1 stuff
/ISOLatin1Encoding dup where
{ pop pop }
{
[
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright
/parenleft /parenright /asterisk /plus /comma /minus /period /slash
/zero /one /two /three /four /five /six /seven
/eight /nine /colon /semicolon /less /equal /greater /question
/at /A /B /C /D /E /F /G
/H /I /J /K /L /M /N /O
/P /Q /R /S /T /U /V /W
/X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore
/quoteleft /a /b /c /d /e /f /g
/h /i /j /k /l /m /n /o
/p /q /r /s /t /u /v /w
/x /y /z /braceleft /bar /braceright /asciitilde /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent
/dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron
/space /exclamdown /cent /sterling /currency /yen /brokenbar /section
/dieresis /copyright /ordfeminine /guillemotleft
/logicalnot /hyphen /registered /macron
/degree /plusminus /twosuperior /threesuperior
/acute /mu /paragraph /periodcentered
/cedilla /onesuperior /ordmasculine /guillemotright
/onequarter /onehalf /threequarters /questiondown
/Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
/Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis
/Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply
/Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls
/agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla
/egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis
/eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide
/oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis
] def
} ifelse
/WindowsANSIEncoding [
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle
/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash
/zero/one/two/three/four/five/six/seven
/eight/nine/colon/semicolon/less/equal/greater/question
/at/A/B/C/D/E/F/G
/H/I/J/K/L/M/N/O
/P/Q/R/S/T/U/V/W
/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore
/grave/a/b/c/d/e/f/g
/h/i/j/k/l/m/n/o
/p/q/r/s/t/u/v/w
/x/y/z/braceleft/bar/braceright/asciitilde/.notdef
/.notdef/.notdef/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl
/circumflex/perthousand/Scaron/guilsinglleft/OE/.notdef/Zcaron/.notdef
/.notdef/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash
/tilde/trademark/scaron/guilsinglright/oe/.notdef/zcaron/Ydieresis
/.notdef/exclamdown/cent/sterling/currency/yen/brokenbar/section
/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron
/degree/plusminus/twosuperior/threesuperior/acute/.notdef/paragraph/dotaccent
/ogonek/onesuperior/ring/guillemotright/onequarter/onehalf/threequarters/questiondown
/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla
/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis
/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply
/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls
/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla
/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis
/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide
/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis
] def
/MacintoshRomanEncoding [
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle
/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash
/zero/one/two/three/four/five/six/seven
/eight/nine/colon/semicolon/less/equal/greater/question
/at/A/B/C/D/E/F/G
/H/I/J/K/L/M/N/O
/P/Q/R/S/T/U/V/W
/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore
/grave/a/b/c/d/e/f/g
/h/i/j/k/l/m/n/o
/p/q/r/s/t/u/v/w
/x/y/z/braceleft/bar/braceright/asciitilde/.notdef
/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute
/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave
/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute
/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis
/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls
/registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash
/.notdef/plusminus/.notdef/.notdef/yen/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/ordfeminine/ring/.notdef/ae/oslash
/questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef/guillemotleft
/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe
/endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/.notdef
/ydieresis/Ydieresis/.notdef/currency/guilsinglleft/guilsinglright/.notdef/.notdef
/daggerdbl/dotaccent/quotesinglbase/quotedblbase/perthousand/Acircumflex/Ecircumflex/Aacute
/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex
/.notdef/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde
/macron/.notdef/.notdef/.notdef/ogonek/.notdef/.notdef/.notdef
] def
/MFontDict 50 dict def
/MStrCat
{
exch
dup length
2 index length add
string
dup 3 1 roll
copy
length
exch dup
4 2 roll exch
putinterval
} bind def
/MCreateEncoding
{
1 index
255 string cvs
(-) MStrCat
1 index MStrCat
cvn exch
(Encoding) MStrCat
cvn dup where
{
exch get
}
{
pop
StandardEncoding
} ifelse
3 1 roll
dup MFontDict exch known not
{
1 index findfont
dup length dict
begin
{1 index /FID ne
{def}
{pop pop}
ifelse} forall
/Encoding 3 index
def
currentdict
end
1 index exch definefont pop
MFontDict 1 index
null put
}
if
exch pop
exch pop
} bind def
/ISOLatin1 { (ISOLatin1) MCreateEncoding } bind def
%end of ISOLatin1 stuff
% Set up for the start of a page.
/MathPictureStart {
/Msaveobj save def
/findresource where
{ pop /WRI-Mathematica-prolog /ProcSet findresource begin }
{ Mathdict begin }
ifelse
userdict begin
/MathPictureStartHook where {
/MathPictureStartHook get exec
} if
Mtransform
Mlmarg
Mbmarg
translate
Mwidth
Mlmarg Mrmarg add
sub
/Mwidth exch def
Mheight
Mbmarg Mtmarg add
sub
/Mheight exch def
/Mtmatrix
matrix currentmatrix
def
/Mgmatrix
matrix currentmatrix
def
/MathDPSFlag where {
pop
clientsync
} if
} def
% Finish off a page.
/MathPictureEnd {
end
end
Msaveobj restore
/MathDPSFlag where { pop } { showpage } ifelse
} def
%MFill fills the drawing area with the current color.
/MFill {
0 0 		moveto
Mwidth 0 	lineto
Mwidth Mheight 	lineto
0 Mheight 	lineto
fill
} def
%New device-specific optimizing operators
/Mfill /.devicefill where
{ pop /.devicefill load def }
{ /fill load def }
ifelse
/Mstroke /.devicestroke where
{ pop /.devicestroke load def }
{ /stroke load def }
ifelse
% xmin xmax ymin ymax MPlotRegion alters the origin, Mwidth and Mheight 
% so that the picture fills the altered region
/MPlotRegion {
3 index
Mwidth mul
2 index
Mheight mul
translate
exch sub
Mheight mul
/Mheight
exch def
exch sub
Mwidth mul
/Mwidth
exch def
} def
% Given a rectangle, set it up as a sub-picture.
/MathSubStart {
Momatrix
Mgmatrix Mtmatrix
Mwidth Mheight
7 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
Mgmatrix setmatrix
9 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
2 copy translate
/Mtmatrix matrix currentmatrix def
3 -1 roll
exch sub
/Mheight exch def
sub
/Mwidth exch def
} def
% Restore the saved state left by the matching MathSubStart.
% Note, we also leave with the new Mgmatrix as the current matrix.
/MathSubEnd {
/Mheight exch def
/Mwidth exch def
/Mtmatrix exch def
dup setmatrix
/Mgmatrix exch def
/Momatrix exch def
} def
% Given a point, draw a dot.
/Mdot {
newpath
currentlinewidth 2 div
0 360
arc fill
} bind def
% Given 4 points, draw the corresponding filled tetragon.
/Mtetra {
moveto
lineto
lineto
lineto
Mfill
} bind def
% Given 4 points, draw the corresponding filled tetragon with black edges.
% Note, this leaves the gray level at 0 (for compatibility with the old
% C code.
/Metetra {
moveto
lineto
lineto
lineto
closepath
gsave
Mfill
grestore
0 setgray
Mstroke
} bind def
% Mistroke is called to stroke intermediate parts of a path.  It makes
% sure to resynchronize the dashing pattern and to leave the current point
% as the final point of the path.
/Mistroke {
flattenpath
0 0 0
{
4 2 roll
pop pop
}
{
4 -1 roll
2 index
sub dup mul
4 -1 roll
2 index
sub dup mul
add sqrt
4 -1 roll
add
3 1 roll
}
{
stop
}
{
stop
}
pathforall
pop pop
currentpoint
Mstroke
moveto
currentdash
3 -1 roll
add
setdash
} bind def
% Mfstroke is called to stroke the final parts of a path.  It resets
% the dashing pattern to compensate for any adjustments made by Mistroke.
/Mfstroke {
Mstroke
currentdash
pop 0
setdash
} bind def
% Mrotsboxa is the same as Msboxa except that it takes an angle 
% from the stack and the box is calculated for text rendered at this  angle.  
% It gsaves in case we are starting a MathSubStart
% save Mrot so that Msboxa can convert bouding box back to the non-rotated
% coordinate system
% call Mrotcheck to alter the offsets into the rotated system
% converts Mtmatrix to render in the rotated system
% the calls Msboxa which does all the work
% at the end  Mtmatrix is restored and Mrot is reset to 0 
/Mrotsboxa {
gsave
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
grestore
Msboxa
3  -1 roll
/Mtmatrix
exch def
/Mrot
0 def
} bind def
% Given an array of strings ([str...]), which represent consecutive lines
% of text, a position in graphics coordinates (gx,gy) and a position in
% the bounding box coordinates (sx,sy), compute the low and high coordinates
% of the resulting text, in the [gx gy tx ty] form, which corresponds to
% the point (gx,gy) (in graphics coordinates) plus the offset (tx,ty) (in
% text coordinates).
% Note, Msboxa assumes that the current matrix is the text matrix.
% Mboxout is called in case we are in Mouter to make the box bigger
% Mboxrot adjusts the box to account for a rotation to convert the box
% into a nonrotated coordinate system
%
/Msboxa {
newpath
5 -1 roll
Mvboxa
pop
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Msboxa1
5 -3 roll
Msboxa1
Mboxrot
[
7 -2 roll
2 copy
[
3 1 roll
10 -1 roll
9 -1 roll
]
6 1 roll
5 -2 roll
]
} bind def
% Msboxa1 is an internal function which, given a bounding box coordinate
% (sz), and the bounding box limits (blz and bhz), computes the actual
% offsets (tlz = (blz-bhz)(sz+1)/2, thz = (blz-bhz)(sz-1)/2).
/Msboxa1 {
sub
2 div
dup
2 index
1 add
mul
3 -1 roll
-1 add
3 -1 roll
mul
} bind def
% Given a (non-empty) array of strings ([str...]) which represent consecutive
% lines of text, compute the total bounding box assuming that we start at
% (0,0) and the array of y offsets to place the lines correctly.
% Note, Mvboxa assumes that the current matrix is the text matrix.
% Note, Mvboxa does not alter the current path.
% The vertical spacing is set so that the bounding boxes of adjacent lines
% are .3 times the width of an `m' apart.
/Mvboxa {
gsave
newpath
[ true
3 -1 roll
{
Mbbox
5 -1 roll
{
0
5 1 roll
}
{
7 -1 roll
exch sub
(m) stringwidth pop
.3 mul
sub
7 1 roll
6 -1 roll
4 -1 roll
Mmin
3 -1 roll
5 index
add
5 -1 roll
4 -1 roll
Mmax
4 -1 roll
}
ifelse
false
}
forall
{ stop } if
counttomark
1 add
4 roll
]
grestore
} bind def
% Given a string, compute the bounding box assuming that we start at (0,0).
% Note, the path is assumed to be empty, and we are assumed to be in text
% coordinates.  Allows for long strings.
/Mbbox {
1 dict begin
0 0 moveto
/temp (T) def
{	gsave
currentpoint newpath moveto
temp 0 3 -1 roll put temp
false charpath flattenpath currentpoint
pathbbox
grestore moveto lineto moveto} forall
pathbbox
newpath
end
} bind def
% Compute the minimum of two numbers.
/Mmin {
2 copy
gt
{ exch } if
pop
} bind def
% Compute the maximum of two numbers.
/Mmax {
2 copy
lt
{ exch } if
pop
} bind def
%
% Mrotwork saves Mrot (not really needed but saved anyway)
% calls Mrotcheck to adjust the offsets into the rotated coordinate system
% converts Mtmatrix to render in the rotated system
%
/Mrotwork {
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
Mgmatrix setmatrix
} def
%
% Mrotshowa is the same as Mshowa except that it takes an angle
% from the stack and the text is rendered at this angle.
% It call Mrotwork to do all the rotation work.
% Then it calls Mshowa which does all the drawing work.
% At the end Mtmatrix is restored and Mrot is reset to zero.
%
/Mrotshowa {
Mrotwork
Mshowa
/Mtmatrix
exch def
/Mrot 0 def
} def
%
% Draws rotated text with a background.
%
/Mrotback {
7 1 roll
dup
8 1 roll
Mrotwork
8 -2 roll
Mshowback
/Mtmatrix
exch def
/Mrot 0 def
} def
%
% Given an array of strings ([str...]), which represent consecutive lines
% of text, a position in graphics coordinates (gx,gy) and a position in
% the bounding box coordinates (sx,sy), display the strings.
% Mboxout is called in case we are in Mouter
%
/Mshowa {
4 -2 roll
moveto
2 index
Mtmatrix setmatrix
Mvboxa
7 1 roll
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Mshowa1
4 1 roll
Mshowa1
rmoveto
currentpoint
Mshowax
pop pop pop pop
Mgmatrix setmatrix
} def
%
% The background box of text is increased by the
% size of an "m"
%
/Madjust	{
(m)
stringwidth
pop
mul
dup
4 -1 roll
add
3 1 roll
add
} def
%
%
%
/Mbuildcoord {
7 index
7 index
4 -1 roll
4 -1 roll
index
exch
index
Mabsadd
} def
%
% If the text is rotated then translate to the drawing point.
% Rotate then translate back.  Do not do this if the angle
% of rotation is 0.
%
/Mrotate {
8 index
0 ne
{
13 copy
4 -2 roll
pop pop
6 -2 roll
pop pop
4 -1 roll
3 -1 roll
sub
6 -1 roll
mul
3 1 roll
sub
4 -1 roll
mul
3 -1 roll
5 1 roll
Mabsadd
2 copy
translate
3 -1 roll
rotate
exch -1 mul
exch -1 mul
translate
} if
9 -1 roll
pop
} def
%
% Draw text but into a box with a certain color.
% Uses Msboxa to build the box.
%
/Mshowback {
gsave
exec
6 copy pop
Msboxa
aload pop
0.5 Madjust
5 -1 roll
aload pop
Mrotate
-0.5
Madjust
4 -1 roll
pop
3 -1 roll
pop
3 4
Mbuildcoord
moveto
3 4
Mbuildcoord
lineto
3 6
Mbuildcoord
lineto
5 6
Mbuildcoord
lineto
5 4
Mbuildcoord
lineto
pop pop pop
pop pop pop
fill		
grestore
Mshowa
} def
% This is used for fixedwidth fonts
% It simply shows each string and advances the y direction by the offset
%
/Mshowax {	
0 1
4 index length
-1 add
{
2 index
4 index
2 index
get
3 index
add
moveto
4 index
exch get
Mfixdash
{
Mfixdashp		
}
if
show
} for
} def
% Fix if all dashes and length > 1
/Mfixdashp {
dup
length
1
gt
1 index
true exch
{
45
eq
and
} forall
and
{
gsave
(--)		
stringwidth pop
(-)
stringwidth pop
sub
2 div
0 rmoveto
dup
length
1 sub
{
(-)
show
}
repeat
grestore
}
if
} bind def	
% Mshowa1 is an internal routine which, given a bounding box coordinate
% (sz), and the bounding box limits if we started drawing at 0 (tlz and thz),
% computes the offset at which to start drawing
% (relz = (sz-1)tlz/2 - (sz+1)thz/2 = sz(tlz-thz)/2-(tlz+thz)/2).
/Mshowa1 {
2 copy
add
4 1 roll
sub
mul
sub
-2 div
} bind def
% Given the x and y scaling to user coordinates and an array of points to
% fit (xbias xscale ybias yscale [pnts]), set up the scaling.  The array
% must contain atleast two points, and the last two must be of the form
% [gxlow gylow 0 0] and [gxhigh gyhigh 0 0].
% Note, MathScale assumes that we are already scaled so that the active area
% is the rectangle [0,Mwidth-Mlmarg-Mrmarg]x[0,Mheight-Mbmarg-Mtmarg].
% also keep bias and scale info for PostScript commands
/MathScale {
Mwidth
Mheight
Mlp
/MathScaleHook where {
/MathScaleHook get exec
} if
translate
scale
pop pop pop pop
pop pop pop pop
/yscale exch def
/ybias exch def
/xscale exch def
/xbias exch def
/Momatrix
xscale yscale matrix scale
xbias ybias matrix translate
matrix concatmatrix def
/Mgmatrix
matrix currentmatrix
def
} def
% Given a non-empty array of points to fit ([p]) and a maximum width (sx)
% and height (sy) find the largest scale (Ax and Ay) and offsets (Bx and By)
% such that the transformation
%	[gx gy tx ty] -> (Ax gx + tx + bx, Ay gy + ty + By)
% maps the points into the rectangle [0,sx]x[0,sy]
/Mlp {
3 copy
Mlpfirst
{
Mnodistort
{
Mmin
dup
} if
4 index
2 index
2 index
Mlprun
16 -8 roll
21 8 roll
11 index
11 -1 roll
10 -4 roll
Mlp1
8 index
9 -5 roll
Mlp1
4 -1 roll
and
{ exit } if
15 -8 roll
pop pop pop pop
pop pop pop pop
3 -1 roll
pop pop
} loop
exch
3 1 roll
7 -3 roll
pop pop pop
} def
% Given an array of points in the [gx gy tx ty] form, with the last two
% being [gxlow gylow 0 0] and [gxhigh gyhigh 0 0], and the width and height
% (sx and sy) in which to fit them, compute the maximum scaling (Ax and Ay).
/Mlpfirst {
3 -1 roll
dup length
2 copy
-2 add
get
aload
pop pop pop
4 -2 roll
-1 add
get
aload
pop pop pop
6 -1 roll
3 -1 roll
5 -1 roll
sub
div
4 1 roll
exch sub
div
} bind def
% Given a non-empty array of points to fit ([pnts]) and scale factors
% for graphics->text (Ax and Ay), compute the limiting points.
/Mlprun {
2 copy
4 index
0 get
dup
4 1 roll
Mlprun1
3 copy
8 -2 roll
9 -1 roll
{
3 copy
Mlprun1
3 copy
11 -3 roll
/gt Mlpminmax
8 3 roll
11 -3 roll
/lt Mlpminmax
8 3 roll
} forall
pop pop pop pop
3 1 roll
pop pop
aload pop
5 -1 roll
aload pop
8 copy
exch
6 -1 roll
Mlprun2
8 2 roll
4 -1 roll
Mlprun2
6 2 roll
3 -1 roll
Mlprun2
4 2 roll
exch
Mlprun2
6 2 roll
} bind def
% Given scale factors for graphics->text (Ax and Ay) and a point in the
% [gx gy tx ty] form, return the text x and y coordinate that results.
/Mlprun1 {
aload pop
exch
6 -1 roll
5 -1 roll
mul add
4 -2 roll
mul
3 -1 roll
add
} bind def
% Given a low and high coordinate, compute the center and width.
/Mlprun2 {
2 copy
add 2 div
3 1 roll
exch sub
} bind def
% Given two points stored as [gx gy tx ty] followed by the scaled
% result (rx, ry), and a comparison function (lt or gt) leave the
% point which is the minimum (or maximum) in each dimension.
/Mlpminmax {
cvx
2 index
6 index
2 index
exec
{
7 -3 roll
4 -1 roll
} if
1 index
5 index
3 -1 roll
exec
{
4 1 roll
pop
5 -1 roll
aload
pop pop
4 -1 roll
aload pop
[
8 -2 roll
pop
5 -2 roll
pop
6 -2 roll
pop
5 -1 roll
]
4 1 roll
pop
}
{
pop pop pop
} ifelse
} bind def
% Given a size (s), graphics->text scale (A), text center (ct), text
% width (wt), graphics center (cg) and graphics width (wg), compute
% a new graphics->text scale (Anew) and offset (B) and whether or not
% we are done.
% Note, the mysterious .99999 is magic juju which is supposed to ward
% off the possibility that floating point errors would cause this
% routine to return the old A and yet claim not-done.
/Mlp1 {
5 index
3 index	sub
5 index
2 index mul
1 index
le
1 index
0 le
or
dup
not
{
1 index
3 index	div
.99999 mul
8 -1 roll
pop
7 1 roll
}
if
8 -1 roll
2 div
7 -2 roll
pop sub
5 index
6 -3 roll
pop pop
mul sub
exch
} bind def
% The following are the workings of the tick, axes and plot labels.
% NOTE a possible source of confusion is that for xticks ie tickmarks on
% the x axis we keep y information and vice versa for yticks
%
%	When Minner is found then
%
% assumes that box starts at zero on the left lower side
%
%		0)	if outflag = 1 then intop = 0, inrht = 0 outflag = 0
%		1)	Save intop 	largest top of box 
%		2)	Save inrht 	largest rht of box
%		3)	set inflag	notifies that inner marks are present
%
%	When Mouter is found then
%
%	if inflag is set then
%		1)	get vecx and vecy off the stack (points in direcn to move)
%		2)	vecx < 1 xadrht = inrht*abs(vecx)
%		3)	vecx > 1 xadlft = inrht*abs(vecx)
%		4)	vecy < 1 yadtop = intop*abs(vecy)
%		5)	vecy > 1 yadbot = intop*abs(vecy)
%		6)	set outflag = 1
%		7)	clear inflag, inrht, intop
%	guaranteed to be zero if no inner is present??
%
%
%	These all have effects in Mrotsboxa and Mrotshowa
%		check inflag and if set
%
%		1) increase top of bbox by yadtop
%		2) decrease bot of bbox by yadbot
%		3) increase rht of bbox by xadrht
%		4) increase lft of bbox by xadlft
%		5) clear outflag, yadtop, yadbot,
%			         xadrht, xadlft
%
% 
% This saves the top right corner of the bounding box as a side effect
% This is to allow the adjustment of text placed with Mouter so that
% it misses the Minner text.  It is assumed that the ang is 0
% in the same way it is assumed that the text of Mouter is 0 or 90
%
/Minner {
outflag
1
eq
{
/outflag 0 def
/intop 0 def
/inrht 0 def
} if		
5 index
gsave
Mtmatrix setmatrix
Mvboxa pop
grestore
3 -1 roll
pop
dup
intop
gt
{
/intop
exch def
}
{ pop }
ifelse
dup
inrht
gt
{
/inrht
exch def
}
{ pop }
ifelse
pop
/inflag
1 def
} def
% This takes two number off the stack and uses them as a vector in graphics
% coordinates which points in the direction in which the Mouter text is to move
% it calculates the bouding box adjustments yadtop yadbot xadrht and xadlft
% these are in Mboxout to adjust the bounding box to compensate.
/Mouter {
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
inflag
1 eq
{
dup
0 lt
{
dup
intop
mul
neg
/yadtop
exch def
} if
dup
0 gt
{
dup
intop
mul
/yadbot
exch def
}
if
pop
dup
0 lt
{
dup
inrht
mul
neg
/xadrht
exch def
} if
dup
0 gt
{
dup
inrht
mul
/xadlft
exch def
} if
pop
/outflag 1 def
}
{ pop pop}
ifelse
/inflag 0 def
/inrht 0 def
/intop 0 def
} def	
%
% This adjusts the bounding box to account for adjacent text
% This allows the two text strings to avoid each other 
% current matrix is the text matrix
/Mboxout {
outflag
1
eq
{
4 -1
roll
xadlft
leadjust
add
sub
4 1 roll
3 -1
roll
yadbot
leadjust
add
sub
3 1
roll
exch
xadrht
leadjust
add
add
exch
yadtop
leadjust
add
add
/outflag 0 def
/xadlft 0 def
/yadbot 0 def
/xadrht 0 def
/yadtop 0 def
} if
} def
/leadjust {
(m) stringwidth pop
.5 mul
} bind def
% The offsets sx and sy refer to the graphics coordinate system 
% thus they must be altered if a rotation has taken place.
% We must also change the bounding box computations for Minner
%
/Mrotcheck {
dup
90
eq
{
%
% Mouter only applies to strings which are either at 0 or 90
% sort out the box adjust factors
%
%	xadrht -> yadbot
%	xadlft -> yadtop
%	yadtop -> xadrht
%	yadbot -> xadlft
yadbot
/yadbot
xadrht
def	
/xadrht
yadtop
def
/yadtop
xadlft
def
/xadlft
exch
def
}
if
dup
cos
1 index
sin
Checkaux
dup
cos
1 index
sin neg
exch
Checkaux
3 1 roll
pop pop
} def
%
% Checkaux is an auxilliary function for Mrotcheck it multiplies a 
% row vector by a column vector
% 
/Checkaux {
4 index
exch
4 index
mul
3 1 roll
mul add
4 1 roll
} bind def
%
% Mboxrot converts the bounding box back from the rotated coordinate
% system to the Mgmatrix system to compensate for a rotation
% It has the opposite functionality of Mrotcheck
% This is not the most neatest or most efficient implementation but it works
%
/Mboxrot {
Mrot
90 eq
{
% old		 tlx  thx  tly  thy
% new		-thy -tly  tlx  thx
%
brotaux
4 2
roll
}
if
Mrot
180 eq
{
% old		 tlx  thx  tly  thy
% new		-thx -tlx -thx -tly
%
4 2
roll
brotaux
4 2
roll
brotaux
}	
if
Mrot
270 eq
{
% old		 tlx  thx  tly  thy
% new		 tly  thy -thx -tlx
%
4 2
roll
brotaux
}
if
} def
%
% auxilliary function negate and reverse
/brotaux {
neg
exch
neg
} bind def
%
% Mabsproc takes a measurement in the default user units and converts
% it to the present units.   This allows absolute thickness and dashing
% to work.  It works by using a {0, x} vector and using the RMS of the result.
/Mabsproc {
0
matrix defaultmatrix
dtransform idtransform
dup mul exch
dup mul
add sqrt
} bind def
%
% Mabswid allows the linewidth to be specified in absolute coordinates
% It does this by recording the graphics transformation matrix at the
% begining of the plot.
% This will break if the scaling in the x and y directions is
% different.  This is the case if Mnodistort is false
%
/Mabswid {
Mabsproc
setlinewidth	
} bind def
% Mabsdash allows the dashing pattern to be specified in absolute coordinates
% It does this by recording the graphics transformation matrix at the
% begining of the plot.
% This will break if the scaling in the x and y directions is
% different.  This is the case if Mnodistort is false
%
/Mabsdash {
exch
[
exch
{
Mabsproc
}
forall
]
exch
setdash
} bind def
%
% Mabs takes a pair of coordinates in points
% and converts them into a pair of coordinates in
% the current drawing scheme
%
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
%
% Mabs takes a pair of numbers in drawing coordinates
% and a pair in points.  It converts the points to
% drawing coordinates and adds them to the first pair.
%
/Mabsadd {
Mabs
3 -1 roll add
3 1 roll add
exch 
} bind def
%
% These two procedures are for using Offset coordinates
% with MathScale computations
%
/Mabsfix1 {
3 -1 roll
/ar exch 
def
ar 2 get
3 -1 roll
add exch
ar 3 get
add
ar 3
3 -1 roll
put
ar 2
3 -1 roll
put
ar
} bind def
/Mabsfix {
2 copy
6 -1 roll
3 1 roll
Mabsfix1
4 1 roll
Mabsfix1
} bind def
%MBeginOrig start coordinates in user coordinates
/MBeginOrig { Momatrix concat} bind def
%MEndOrig start coordinates in user coordinates
/MEndOrig { Mgmatrix setmatrix} bind def
/sampledsound where
{ pop }
{ /MathDPSFlag where
{ pop /sampledsound { clientsync } def }
{ /sampledsound {
exch pop
exch 5 1 roll
mul
4 idiv
mul
2 idiv
exch pop
exch
/Mtempproc exch def
{ Mtempproc pop }
repeat
} def
} ifelse
} ifelse
% Define setrgbcolor for those ancient PostScript devices lacking it
/setrgbcolor dup where
{ pop pop }
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%%EndImage
%%EndPreview
save
countdictstack
mark
newpath
/showpage {} def
%%EndProlog
%%Page 1 1
% Start of procedure set
userdict /Mathdict 100 dict dup begin put
% The externally visible functions are:
%	MathPictureStart- start page.
%	MathPictureEnd	- finish off page.
%	MathSubStart	- start a sub-page.
%	MathSubEnd	- finish off a sub-page.
%	Mdot		- draw a dot.
%	Mtetra		- draw a filled tetragon.
%	Metetra		- draw a filled tetragon with black edges.
%	Mistroke	- intermediate stroke of multi-stroke line/curve.
%	Mfstroke	- final stroke of multi-stroke line/curve.
%	Msboxa		- compute coordinates of text bounding box.
%	Mshowa		- plot characters.
%	MathScale	- compute scaling info to contain array of points.
%start of ISOLatin1 stuff
/ISOLatin1Encoding dup where
{ pop pop }
{
[
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright
/parenleft /parenright /asterisk /plus /comma /minus /period /slash
/zero /one /two /three /four /five /six /seven
/eight /nine /colon /semicolon /less /equal /greater /question
/at /A /B /C /D /E /F /G
/H /I /J /K /L /M /N /O
/P /Q /R /S /T /U /V /W
/X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore
/quoteleft /a /b /c /d /e /f /g
/h /i /j /k /l /m /n /o
/p /q /r /s /t /u /v /w
/x /y /z /braceleft /bar /braceright /asciitilde /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent
/dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron
/space /exclamdown /cent /sterling /currency /yen /brokenbar /section
/dieresis /copyright /ordfeminine /guillemotleft
/logicalnot /hyphen /registered /macron
/degree /plusminus /twosuperior /threesuperior
/acute /mu /paragraph /periodcentered
/cedilla /onesuperior /ordmasculine /guillemotright
/onequarter /onehalf /threequarters /questiondown
/Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
/Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis
/Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply
/Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls
/agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla
/egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis
/eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide
/oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis
] def
} ifelse
/WindowsANSIEncoding [
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle
/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash
/zero/one/two/three/four/five/six/seven
/eight/nine/colon/semicolon/less/equal/greater/question
/at/A/B/C/D/E/F/G
/H/I/J/K/L/M/N/O
/P/Q/R/S/T/U/V/W
/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore
/grave/a/b/c/d/e/f/g
/h/i/j/k/l/m/n/o
/p/q/r/s/t/u/v/w
/x/y/z/braceleft/bar/braceright/asciitilde/.notdef
/.notdef/.notdef/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl
/circumflex/perthousand/Scaron/guilsinglleft/OE/.notdef/Zcaron/.notdef
/.notdef/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash
/tilde/trademark/scaron/guilsinglright/oe/.notdef/zcaron/Ydieresis
/.notdef/exclamdown/cent/sterling/currency/yen/brokenbar/section
/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron
/degree/plusminus/twosuperior/threesuperior/acute/.notdef/paragraph/dotaccent
/ogonek/onesuperior/ring/guillemotright/onequarter/onehalf/threequarters/questiondown
/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla
/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis
/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply
/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls
/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla
/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis
/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide
/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis
] def
/MacintoshRomanEncoding [
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle
/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash
/zero/one/two/three/four/five/six/seven
/eight/nine/colon/semicolon/less/equal/greater/question
/at/A/B/C/D/E/F/G
/H/I/J/K/L/M/N/O
/P/Q/R/S/T/U/V/W
/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore
/grave/a/b/c/d/e/f/g
/h/i/j/k/l/m/n/o
/p/q/r/s/t/u/v/w
/x/y/z/braceleft/bar/braceright/asciitilde/.notdef
/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute
/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave
/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute
/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis
/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls
/registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash
/.notdef/plusminus/.notdef/.notdef/yen/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/ordfeminine/ring/.notdef/ae/oslash
/questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef/guillemotleft
/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe
/endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/.notdef
/ydieresis/Ydieresis/.notdef/currency/guilsinglleft/guilsinglright/.notdef/.notdef
/daggerdbl/dotaccent/quotesinglbase/quotedblbase/perthousand/Acircumflex/Ecircumflex/Aacute
/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex
/.notdef/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde
/macron/.notdef/.notdef/.notdef/ogonek/.notdef/.notdef/.notdef
] def
/MFontDict 50 dict def
/MStrCat
{
exch
dup length
2 index length add
string
dup 3 1 roll
copy
length
exch dup
4 2 roll exch
putinterval
} bind def
/MCreateEncoding
{
1 index
255 string cvs
(-) MStrCat
1 index MStrCat
cvn exch
(Encoding) MStrCat
cvn dup where
{
exch get
}
{
pop
StandardEncoding
} ifelse
3 1 roll
dup MFontDict exch known not
{
1 index findfont
dup length dict
begin
{1 index /FID ne
{def}
{pop pop}
ifelse} forall
/Encoding 3 index
def
currentdict
end
1 index exch definefont pop
MFontDict 1 index
null put
}
if
exch pop
exch pop
} bind def
/ISOLatin1 { (ISOLatin1) MCreateEncoding } bind def
%end of ISOLatin1 stuff
% Set up for the start of a page.
/MathPictureStart {
/Msaveobj save def
/findresource where
{ pop /WRI-Mathematica-prolog /ProcSet findresource begin }
{ Mathdict begin }
ifelse
userdict begin
/MathPictureStartHook where {
/MathPictureStartHook get exec
} if
Mtransform
Mlmarg
Mbmarg
translate
Mwidth
Mlmarg Mrmarg add
sub
/Mwidth exch def
Mheight
Mbmarg Mtmarg add
sub
/Mheight exch def
/Mtmatrix
matrix currentmatrix
def
/Mgmatrix
matrix currentmatrix
def
/MathDPSFlag where {
pop
clientsync
} if
} def
% Finish off a page.
/MathPictureEnd {
end
end
Msaveobj restore
/MathDPSFlag where { pop } { showpage } ifelse
} def
%MFill fills the drawing area with the current color.
/MFill {
0 0 		moveto
Mwidth 0 	lineto
Mwidth Mheight 	lineto
0 Mheight 	lineto
fill
} def
%New device-specific optimizing operators
/Mfill /.devicefill where
{ pop /.devicefill load def }
{ /fill load def }
ifelse
/Mstroke /.devicestroke where
{ pop /.devicestroke load def }
{ /stroke load def }
ifelse
% xmin xmax ymin ymax MPlotRegion alters the origin, Mwidth and Mheight 
% so that the picture fills the altered region
/MPlotRegion {
3 index
Mwidth mul
2 index
Mheight mul
translate
exch sub
Mheight mul
/Mheight
exch def
exch sub
Mwidth mul
/Mwidth
exch def
} def
% Given a rectangle, set it up as a sub-picture.
/MathSubStart {
Momatrix
Mgmatrix Mtmatrix
Mwidth Mheight
7 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
Mgmatrix setmatrix
9 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
2 copy translate
/Mtmatrix matrix currentmatrix def
3 -1 roll
exch sub
/Mheight exch def
sub
/Mwidth exch def
} def
% Restore the saved state left by the matching MathSubStart.
% Note, we also leave with the new Mgmatrix as the current matrix.
/MathSubEnd {
/Mheight exch def
/Mwidth exch def
/Mtmatrix exch def
dup setmatrix
/Mgmatrix exch def
/Momatrix exch def
} def
% Given a point, draw a dot.
/Mdot {
newpath
currentlinewidth 2 div
0 360
arc fill
} bind def
% Given 4 points, draw the corresponding filled tetragon.
/Mtetra {
moveto
lineto
lineto
lineto
Mfill
} bind def
% Given 4 points, draw the corresponding filled tetragon with black edges.
% Note, this leaves the gray level at 0 (for compatibility with the old
% C code.
/Metetra {
moveto
lineto
lineto
lineto
closepath
gsave
Mfill
grestore
0 setgray
Mstroke
} bind def
% Mistroke is called to stroke intermediate parts of a path.  It makes
% sure to resynchronize the dashing pattern and to leave the current point
% as the final point of the path.
/Mistroke {
flattenpath
0 0 0
{
4 2 roll
pop pop
}
{
4 -1 roll
2 index
sub dup mul
4 -1 roll
2 index
sub dup mul
add sqrt
4 -1 roll
add
3 1 roll
}
{
stop
}
{
stop
}
pathforall
pop pop
currentpoint
Mstroke
moveto
currentdash
3 -1 roll
add
setdash
} bind def
% Mfstroke is called to stroke the final parts of a path.  It resets
% the dashing pattern to compensate for any adjustments made by Mistroke.
/Mfstroke {
Mstroke
currentdash
pop 0
setdash
} bind def
% Mrotsboxa is the same as Msboxa except that it takes an angle 
% from the stack and the box is calculated for text rendered at this  angle.  
% It gsaves in case we are starting a MathSubStart
% save Mrot so that Msboxa can convert bouding box back to the non-rotated
% coordinate system
% call Mrotcheck to alter the offsets into the rotated system
% converts Mtmatrix to render in the rotated system
% the calls Msboxa which does all the work
% at the end  Mtmatrix is restored and Mrot is reset to 0 
/Mrotsboxa {
gsave
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
grestore
Msboxa
3  -1 roll
/Mtmatrix
exch def
/Mrot
0 def
} bind def
% Given an array of strings ([str...]), which represent consecutive lines
% of text, a position in graphics coordinates (gx,gy) and a position in
% the bounding box coordinates (sx,sy), compute the low and high coordinates
% of the resulting text, in the [gx gy tx ty] form, which corresponds to
% the point (gx,gy) (in graphics coordinates) plus the offset (tx,ty) (in
% text coordinates).
% Note, Msboxa assumes that the current matrix is the text matrix.
% Mboxout is called in case we are in Mouter to make the box bigger
% Mboxrot adjusts the box to account for a rotation to convert the box
% into a nonrotated coordinate system
%
/Msboxa {
newpath
5 -1 roll
Mvboxa
pop
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Msboxa1
5 -3 roll
Msboxa1
Mboxrot
[
7 -2 roll
2 copy
[
3 1 roll
10 -1 roll
9 -1 roll
]
6 1 roll
5 -2 roll
]
} bind def
% Msboxa1 is an internal function which, given a bounding box coordinate
% (sz), and the bounding box limits (blz and bhz), computes the actual
% offsets (tlz = (blz-bhz)(sz+1)/2, thz = (blz-bhz)(sz-1)/2).
/Msboxa1 {
sub
2 div
dup
2 index
1 add
mul
3 -1 roll
-1 add
3 -1 roll
mul
} bind def
% Given a (non-empty) array of strings ([str...]) which represent consecutive
% lines of text, compute the total bounding box assuming that we start at
% (0,0) and the array of y offsets to place the lines correctly.
% Note, Mvboxa assumes that the current matrix is the text matrix.
% Note, Mvboxa does not alter the current path.
% The vertical spacing is set so that the bounding boxes of adjacent lines
% are .3 times the width of an `m' apart.
/Mvboxa {
gsave
newpath
[ true
3 -1 roll
{
Mbbox
5 -1 roll
{
0
5 1 roll
}
{
7 -1 roll
exch sub
(m) stringwidth pop
.3 mul
sub
7 1 roll
6 -1 roll
4 -1 roll
Mmin
3 -1 roll
5 index
add
5 -1 roll
4 -1 roll
Mmax
4 -1 roll
}
ifelse
false
}
forall
{ stop } if
counttomark
1 add
4 roll
]
grestore
} bind def
% Given a string, compute the bounding box assuming that we start at (0,0).
% Note, the path is assumed to be empty, and we are assumed to be in text
% coordinates.  Allows for long strings.
/Mbbox {
1 dict begin
0 0 moveto
/temp (T) def
{	gsave
currentpoint newpath moveto
temp 0 3 -1 roll put temp
false charpath flattenpath currentpoint
pathbbox
grestore moveto lineto moveto} forall
pathbbox
newpath
end
} bind def
% Compute the minimum of two numbers.
/Mmin {
2 copy
gt
{ exch } if
pop
} bind def
% Compute the maximum of two numbers.
/Mmax {
2 copy
lt
{ exch } if
pop
} bind def
%
% Mrotwork saves Mrot (not really needed but saved anyway)
% calls Mrotcheck to adjust the offsets into the rotated coordinate system
% converts Mtmatrix to render in the rotated system
%
/Mrotwork {
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
Mgmatrix setmatrix
} def
%
% Mrotshowa is the same as Mshowa except that it takes an angle
% from the stack and the text is rendered at this angle.
% It call Mrotwork to do all the rotation work.
% Then it calls Mshowa which does all the drawing work.
% At the end Mtmatrix is restored and Mrot is reset to zero.
%
/Mrotshowa {
Mrotwork
Mshowa
/Mtmatrix
exch def
/Mrot 0 def
} def
%
% Draws rotated text with a background.
%
/Mrotback {
7 1 roll
dup
8 1 roll
Mrotwork
8 -2 roll
Mshowback
/Mtmatrix
exch def
/Mrot 0 def
} def
%
% Given an array of strings ([str...]), which represent consecutive lines
% of text, a position in graphics coordinates (gx,gy) and a position in
% the bounding box coordinates (sx,sy), display the strings.
% Mboxout is called in case we are in Mouter
%
/Mshowa {
4 -2 roll
moveto
2 index
Mtmatrix setmatrix
Mvboxa
7 1 roll
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Mshowa1
4 1 roll
Mshowa1
rmoveto
currentpoint
Mshowax
pop pop pop pop
Mgmatrix setmatrix
} def
%
% The background box of text is increased by the
% size of an "m"
%
/Madjust	{
(m)
stringwidth
pop
mul
dup
4 -1 roll
add
3 1 roll
add
} def
%
%
%
/Mbuildcoord {
7 index
7 index
4 -1 roll
4 -1 roll
index
exch
index
Mabsadd
} def
%
% If the text is rotated then translate to the drawing point.
% Rotate then translate back.  Do not do this if the angle
% of rotation is 0.
%
/Mrotate {
8 index
0 ne
{
13 copy
4 -2 roll
pop pop
6 -2 roll
pop pop
4 -1 roll
3 -1 roll
sub
6 -1 roll
mul
3 1 roll
sub
4 -1 roll
mul
3 -1 roll
5 1 roll
Mabsadd
2 copy
translate
3 -1 roll
rotate
exch -1 mul
exch -1 mul
translate
} if
9 -1 roll
pop
} def
%
% Draw text but into a box with a certain color.
% Uses Msboxa to build the box.
%
/Mshowback {
gsave
exec
6 copy pop
Msboxa
aload pop
0.5 Madjust
5 -1 roll
aload pop
Mrotate
-0.5
Madjust
4 -1 roll
pop
3 -1 roll
pop
3 4
Mbuildcoord
moveto
3 4
Mbuildcoord
lineto
3 6
Mbuildcoord
lineto
5 6
Mbuildcoord
lineto
5 4
Mbuildcoord
lineto
pop pop pop
pop pop pop
fill		
grestore
Mshowa
} def
% This is used for fixedwidth fonts
% It simply shows each string and advances the y direction by the offset
%
/Mshowax {	
0 1
4 index length
-1 add
{
2 index
4 index
2 index
get
3 index
add
moveto
4 index
exch get
Mfixdash
{
Mfixdashp		
}
if
show
} for
} def
% Fix if all dashes and length > 1
/Mfixdashp {
dup
length
1
gt
1 index
true exch
{
45
eq
and
} forall
and
{
gsave
(--)		
stringwidth pop
(-)
stringwidth pop
sub
2 div
0 rmoveto
dup
length
1 sub
{
(-)
show
}
repeat
grestore
}
if
} bind def	
% Mshowa1 is an internal routine which, given a bounding box coordinate
% (sz), and the bounding box limits if we started drawing at 0 (tlz and thz),
% computes the offset at which to start drawing
% (relz = (sz-1)tlz/2 - (sz+1)thz/2 = sz(tlz-thz)/2-(tlz+thz)/2).
/Mshowa1 {
2 copy
add
4 1 roll
sub
mul
sub
-2 div
} bind def
% Given the x and y scaling to user coordinates and an array of points to
% fit (xbias xscale ybias yscale [pnts]), set up the scaling.  The array
% must contain atleast two points, and the last two must be of the form
% [gxlow gylow 0 0] and [gxhigh gyhigh 0 0].
% Note, MathScale assumes that we are already scaled so that the active area
% is the rectangle [0,Mwidth-Mlmarg-Mrmarg]x[0,Mheight-Mbmarg-Mtmarg].
% also keep bias and scale info for PostScript commands
/MathScale {
Mwidth
Mheight
Mlp
/MathScaleHook where {
/MathScaleHook get exec
} if
translate
scale
pop pop pop pop
pop pop pop pop
/yscale exch def
/ybias exch def
/xscale exch def
/xbias exch def
/Momatrix
xscale yscale matrix scale
xbias ybias matrix translate
matrix concatmatrix def
/Mgmatrix
matrix currentmatrix
def
} def
% Given a non-empty array of points to fit ([p]) and a maximum width (sx)
% and height (sy) find the largest scale (Ax and Ay) and offsets (Bx and By)
% such that the transformation
%	[gx gy tx ty] -> (Ax gx + tx + bx, Ay gy + ty + By)
% maps the points into the rectangle [0,sx]x[0,sy]
/Mlp {
3 copy
Mlpfirst
{
Mnodistort
{
Mmin
dup
} if
4 index
2 index
2 index
Mlprun
16 -8 roll
21 8 roll
11 index
11 -1 roll
10 -4 roll
Mlp1
8 index
9 -5 roll
Mlp1
4 -1 roll
and
{ exit } if
15 -8 roll
pop pop pop pop
pop pop pop pop
3 -1 roll
pop pop
} loop
exch
3 1 roll
7 -3 roll
pop pop pop
} def
% Given an array of points in the [gx gy tx ty] form, with the last two
% being [gxlow gylow 0 0] and [gxhigh gyhigh 0 0], and the width and height
% (sx and sy) in which to fit them, compute the maximum scaling (Ax and Ay).
/Mlpfirst {
3 -1 roll
dup length
2 copy
-2 add
get
aload
pop pop pop
4 -2 roll
-1 add
get
aload
pop pop pop
6 -1 roll
3 -1 roll
5 -1 roll
sub
div
4 1 roll
exch sub
div
} bind def
% Given a non-empty array of points to fit ([pnts]) and scale factors
% for graphics->text (Ax and Ay), compute the limiting points.
/Mlprun {
2 copy
4 index
0 get
dup
4 1 roll
Mlprun1
3 copy
8 -2 roll
9 -1 roll
{
3 copy
Mlprun1
3 copy
11 -3 roll
/gt Mlpminmax
8 3 roll
11 -3 roll
/lt Mlpminmax
8 3 roll
} forall
pop pop pop pop
3 1 roll
pop pop
aload pop
5 -1 roll
aload pop
8 copy
exch
6 -1 roll
Mlprun2
8 2 roll
4 -1 roll
Mlprun2
6 2 roll
3 -1 roll
Mlprun2
4 2 roll
exch
Mlprun2
6 2 roll
} bind def
% Given scale factors for graphics->text (Ax and Ay) and a point in the
% [gx gy tx ty] form, return the text x and y coordinate that results.
/Mlprun1 {
aload pop
exch
6 -1 roll
5 -1 roll
mul add
4 -2 roll
mul
3 -1 roll
add
} bind def
% Given a low and high coordinate, compute the center and width.
/Mlprun2 {
2 copy
add 2 div
3 1 roll
exch sub
} bind def
% Given two points stored as [gx gy tx ty] followed by the scaled
% result (rx, ry), and a comparison function (lt or gt) leave the
% point which is the minimum (or maximum) in each dimension.
/Mlpminmax {
cvx
2 index
6 index
2 index
exec
{
7 -3 roll
4 -1 roll
} if
1 index
5 index
3 -1 roll
exec
{
4 1 roll
pop
5 -1 roll
aload
pop pop
4 -1 roll
aload pop
[
8 -2 roll
pop
5 -2 roll
pop
6 -2 roll
pop
5 -1 roll
]
4 1 roll
pop
}
{
pop pop pop
} ifelse
} bind def
% Given a size (s), graphics->text scale (A), text center (ct), text
% width (wt), graphics center (cg) and graphics width (wg), compute
% a new graphics->text scale (Anew) and offset (B) and whether or not
% we are done.
% Note, the mysterious .99999 is magic juju which is supposed to ward
% off the possibility that floating point errors would cause this
% routine to return the old A and yet claim not-done.
/Mlp1 {
5 index
3 index	sub
5 index
2 index mul
1 index
le
1 index
0 le
or
dup
not
{
1 index
3 index	div
.99999 mul
8 -1 roll
pop
7 1 roll
}
if
8 -1 roll
2 div
7 -2 roll
pop sub
5 index
6 -3 roll
pop pop
mul sub
exch
} bind def
% The following are the workings of the tick, axes and plot labels.
% NOTE a possible source of confusion is that for xticks ie tickmarks on
% the x axis we keep y information and vice versa for yticks
%
%	When Minner is found then
%
% assumes that box starts at zero on the left lower side
%
%		0)	if outflag = 1 then intop = 0, inrht = 0 outflag = 0
%		1)	Save intop 	largest top of box 
%		2)	Save inrht 	largest rht of box
%		3)	set inflag	notifies that inner marks are present
%
%	When Mouter is found then
%
%	if inflag is set then
%		1)	get vecx and vecy off the stack (points in direcn to move)
%		2)	vecx < 1 xadrht = inrht*abs(vecx)
%		3)	vecx > 1 xadlft = inrht*abs(vecx)
%		4)	vecy < 1 yadtop = intop*abs(vecy)
%		5)	vecy > 1 yadbot = intop*abs(vecy)
%		6)	set outflag = 1
%		7)	clear inflag, inrht, intop
%	guaranteed to be zero if no inner is present??
%
%
%	These all have effects in Mrotsboxa and Mrotshowa
%		check inflag and if set
%
%		1) increase top of bbox by yadtop
%		2) decrease bot of bbox by yadbot
%		3) increase rht of bbox by xadrht
%		4) increase lft of bbox by xadlft
%		5) clear outflag, yadtop, yadbot,
%			         xadrht, xadlft
%
% 
% This saves the top right corner of the bounding box as a side effect
% This is to allow the adjustment of text placed with Mouter so that
% it misses the Minner text.  It is assumed that the ang is 0
% in the same way it is assumed that the text of Mouter is 0 or 90
%
/Minner {
outflag
1
eq
{
/outflag 0 def
/intop 0 def
/inrht 0 def
} if		
5 index
gsave
Mtmatrix setmatrix
Mvboxa pop
grestore
3 -1 roll
pop
dup
intop
gt
{
/intop
exch def
}
{ pop }
ifelse
dup
inrht
gt
{
/inrht
exch def
}
{ pop }
ifelse
pop
/inflag
1 def
} def
% This takes two number off the stack and uses them as a vector in graphics
% coordinates which points in the direction in which the Mouter text is to move
% it calculates the bouding box adjustments yadtop yadbot xadrht and xadlft
% these are in Mboxout to adjust the bounding box to compensate.
/Mouter {
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
inflag
1 eq
{
dup
0 lt
{
dup
intop
mul
neg
/yadtop
exch def
} if
dup
0 gt
{
dup
intop
mul
/yadbot
exch def
}
if
pop
dup
0 lt
{
dup
inrht
mul
neg
/xadrht
exch def
} if
dup
0 gt
{
dup
inrht
mul
/xadlft
exch def
} if
pop
/outflag 1 def
}
{ pop pop}
ifelse
/inflag 0 def
/inrht 0 def
/intop 0 def
} def	
%
% This adjusts the bounding box to account for adjacent text
% This allows the two text strings to avoid each other 
% current matrix is the text matrix
/Mboxout {
outflag
1
eq
{
4 -1
roll
xadlft
leadjust
add
sub
4 1 roll
3 -1
roll
yadbot
leadjust
add
sub
3 1
roll
exch
xadrht
leadjust
add
add
exch
yadtop
leadjust
add
add
/outflag 0 def
/xadlft 0 def
/yadbot 0 def
/xadrht 0 def
/yadtop 0 def
} if
} def
/leadjust {
(m) stringwidth pop
.5 mul
} bind def
% The offsets sx and sy refer to the graphics coordinate system 
% thus they must be altered if a rotation has taken place.
% We must also change the bounding box computations for Minner
%
/Mrotcheck {
dup
90
eq
{
%
% Mouter only applies to strings which are either at 0 or 90
% sort out the box adjust factors
%
%	xadrht -> yadbot
%	xadlft -> yadtop
%	yadtop -> xadrht
%	yadbot -> xadlft
yadbot
/yadbot
xadrht
def	
/xadrht
yadtop
def
/yadtop
xadlft
def
/xadlft
exch
def
}
if
dup
cos
1 index
sin
Checkaux
dup
cos
1 index
sin neg
exch
Checkaux
3 1 roll
pop pop
} def
%
% Checkaux is an auxilliary function for Mrotcheck it multiplies a 
% row vector by a column vector
% 
/Checkaux {
4 index
exch
4 index
mul
3 1 roll
mul add
4 1 roll
} bind def
%
% Mboxrot converts the bounding box back from the rotated coordinate
% system to the Mgmatrix system to compensate for a rotation
% It has the opposite functionality of Mrotcheck
% This is not the most neatest or most efficient implementation but it works
%
/Mboxrot {
Mrot
90 eq
{
% old		 tlx  thx  tly  thy
% new		-thy -tly  tlx  thx
%
brotaux
4 2
roll
}
if
Mrot
180 eq
{
% old		 tlx  thx  tly  thy
% new		-thx -tlx -thx -tly
%
4 2
roll
brotaux
4 2
roll
brotaux
}	
if
Mrot
270 eq
{
% old		 tlx  thx  tly  thy
% new		 tly  thy -thx -tlx
%
4 2
roll
brotaux
}
if
} def
%
% auxilliary function negate and reverse
/brotaux {
neg
exch
neg
} bind def
%
% Mabsproc takes a measurement in the default user units and converts
% it to the present units.   This allows absolute thickness and dashing
% to work.  It works by using a {0, x} vector and using the RMS of the result.
/Mabsproc {
0
matrix defaultmatrix
dtransform idtransform
dup mul exch
dup mul
add sqrt
} bind def
%
% Mabswid allows the linewidth to be specified in absolute coordinates
% It does this by recording the graphics transformation matrix at the
% begining of the plot.
% This will break if the scaling in the x and y directions is
% different.  This is the case if Mnodistort is false
%
/Mabswid {
Mabsproc
setlinewidth	
} bind def
% Mabsdash allows the dashing pattern to be specified in absolute coordinates
% It does this by recording the graphics transformation matrix at the
% begining of the plot.
% This will break if the scaling in the x and y directions is
% different.  This is the case if Mnodistort is false
%
/Mabsdash {
exch
[
exch
{
Mabsproc
}
forall
]
exch
setdash
} bind def
%
% Mabs takes a pair of coordinates in points
% and converts them into a pair of coordinates in
% the current drawing scheme
%
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
%
% Mabs takes a pair of numbers in drawing coordinates
% and a pair in points.  It converts the points to
% drawing coordinates and adds them to the first pair.
%
/Mabsadd {
Mabs
3 -1 roll add
3 1 roll add
exch 
} bind def
%
% These two procedures are for using Offset coordinates
% with MathScale computations
%
/Mabsfix1 {
3 -1 roll
/ar exch 
def
ar 2 get
3 -1 roll
add exch
ar 3 get
add
ar 3
3 -1 roll
put
ar 2
3 -1 roll
put
ar
} bind def
/Mabsfix {
2 copy
6 -1 roll
3 1 roll
Mabsfix1
4 1 roll
Mabsfix1
} bind def
%MBeginOrig start coordinates in user coordinates
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save
countdictstack
mark
newpath
/showpage {} def
%%EndProlog
%%Page 1 1
% Start of procedure set
userdict /Mathdict 100 dict dup begin put
% The externally visible functions are:
%	MathPictureStart- start page.
%	MathPictureEnd	- finish off page.
%	MathSubStart	- start a sub-page.
%	MathSubEnd	- finish off a sub-page.
%	Mdot		- draw a dot.
%	Mtetra		- draw a filled tetragon.
%	Metetra		- draw a filled tetragon with black edges.
%	Mistroke	- intermediate stroke of multi-stroke line/curve.
%	Mfstroke	- final stroke of multi-stroke line/curve.
%	Msboxa		- compute coordinates of text bounding box.
%	Mshowa		- plot characters.
%	MathScale	- compute scaling info to contain array of points.
%start of ISOLatin1 stuff
/ISOLatin1Encoding dup where
{ pop pop }
{
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/space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright
/parenleft /parenright /asterisk /plus /comma /minus /period /slash
/zero /one /two /three /four /five /six /seven
/eight /nine /colon /semicolon /less /equal /greater /question
/at /A /B /C /D /E /F /G
/H /I /J /K /L /M /N /O
/P /Q /R /S /T /U /V /W
/X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore
/quoteleft /a /b /c /d /e /f /g
/h /i /j /k /l /m /n /o
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/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent
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/space /exclamdown /cent /sterling /currency /yen /brokenbar /section
/dieresis /copyright /ordfeminine /guillemotleft
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/degree /plusminus /twosuperior /threesuperior
/acute /mu /paragraph /periodcentered
/cedilla /onesuperior /ordmasculine /guillemotright
/onequarter /onehalf /threequarters /questiondown
/Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
/Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis
/Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply
/Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls
/agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla
/egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis
/eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide
/oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis
] def
} ifelse
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/at/A/B/C/D/E/F/G
/H/I/J/K/L/M/N/O
/P/Q/R/S/T/U/V/W
/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore
/grave/a/b/c/d/e/f/g
/h/i/j/k/l/m/n/o
/p/q/r/s/t/u/v/w
/x/y/z/braceleft/bar/braceright/asciitilde/.notdef
/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute
/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave
/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute
/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis
/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls
/registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash
/.notdef/plusminus/.notdef/.notdef/yen/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/ordfeminine/ring/.notdef/ae/oslash
/questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef/guillemotleft
/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe
/endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/.notdef
/ydieresis/Ydieresis/.notdef/currency/guilsinglleft/guilsinglright/.notdef/.notdef
/daggerdbl/dotaccent/quotesinglbase/quotedblbase/perthousand/Acircumflex/Ecircumflex/Aacute
/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex
/.notdef/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde
/macron/.notdef/.notdef/.notdef/ogonek/.notdef/.notdef/.notdef
] def
/MFontDict 50 dict def
/MStrCat
{
exch
dup length
2 index length add
string
dup 3 1 roll
copy
length
exch dup
4 2 roll exch
putinterval
} bind def
/MCreateEncoding
{
1 index
255 string cvs
(-) MStrCat
1 index MStrCat
cvn exch
(Encoding) MStrCat
cvn dup where
{
exch get
}
{
pop
StandardEncoding
} ifelse
3 1 roll
dup MFontDict exch known not
{
1 index findfont
dup length dict
begin
{1 index /FID ne
{def}
{pop pop}
ifelse} forall
/Encoding 3 index
def
currentdict
end
1 index exch definefont pop
MFontDict 1 index
null put
}
if
exch pop
exch pop
} bind def
/ISOLatin1 { (ISOLatin1) MCreateEncoding } bind def
%end of ISOLatin1 stuff
% Set up for the start of a page.
/MathPictureStart {
/Msaveobj save def
/findresource where
{ pop /WRI-Mathematica-prolog /ProcSet findresource begin }
{ Mathdict begin }
ifelse
userdict begin
/MathPictureStartHook where {
/MathPictureStartHook get exec
} if
Mtransform
Mlmarg
Mbmarg
translate
Mwidth
Mlmarg Mrmarg add
sub
/Mwidth exch def
Mheight
Mbmarg Mtmarg add
sub
/Mheight exch def
/Mtmatrix
matrix currentmatrix
def
/Mgmatrix
matrix currentmatrix
def
/MathDPSFlag where {
pop
clientsync
} if
} def
% Finish off a page.
/MathPictureEnd {
end
end
Msaveobj restore
/MathDPSFlag where { pop } { showpage } ifelse
} def
%MFill fills the drawing area with the current color.
/MFill {
0 0 		moveto
Mwidth 0 	lineto
Mwidth Mheight 	lineto
0 Mheight 	lineto
fill
} def
%New device-specific optimizing operators
/Mfill /.devicefill where
{ pop /.devicefill load def }
{ /fill load def }
ifelse
/Mstroke /.devicestroke where
{ pop /.devicestroke load def }
{ /stroke load def }
ifelse
% xmin xmax ymin ymax MPlotRegion alters the origin, Mwidth and Mheight 
% so that the picture fills the altered region
/MPlotRegion {
3 index
Mwidth mul
2 index
Mheight mul
translate
exch sub
Mheight mul
/Mheight
exch def
exch sub
Mwidth mul
/Mwidth
exch def
} def
% Given a rectangle, set it up as a sub-picture.
/MathSubStart {
Momatrix
Mgmatrix Mtmatrix
Mwidth Mheight
7 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
Mgmatrix setmatrix
9 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
2 copy translate
/Mtmatrix matrix currentmatrix def
3 -1 roll
exch sub
/Mheight exch def
sub
/Mwidth exch def
} def
% Restore the saved state left by the matching MathSubStart.
% Note, we also leave with the new Mgmatrix as the current matrix.
/MathSubEnd {
/Mheight exch def
/Mwidth exch def
/Mtmatrix exch def
dup setmatrix
/Mgmatrix exch def
/Momatrix exch def
} def
% Given a point, draw a dot.
/Mdot {
newpath
currentlinewidth 2 div
0 360
arc fill
} bind def
% Given 4 points, draw the corresponding filled tetragon.
/Mtetra {
moveto
lineto
lineto
lineto
Mfill
} bind def
% Given 4 points, draw the corresponding filled tetragon with black edges.
% Note, this leaves the gray level at 0 (for compatibility with the old
% C code.
/Metetra {
moveto
lineto
lineto
lineto
closepath
gsave
Mfill
grestore
0 setgray
Mstroke
} bind def
% Mistroke is called to stroke intermediate parts of a path.  It makes
% sure to resynchronize the dashing pattern and to leave the current point
% as the final point of the path.
/Mistroke {
flattenpath
0 0 0
{
4 2 roll
pop pop
}
{
4 -1 roll
2 index
sub dup mul
4 -1 roll
2 index
sub dup mul
add sqrt
4 -1 roll
add
3 1 roll
}
{
stop
}
{
stop
}
pathforall
pop pop
currentpoint
Mstroke
moveto
currentdash
3 -1 roll
add
setdash
} bind def
% Mfstroke is called to stroke the final parts of a path.  It resets
% the dashing pattern to compensate for any adjustments made by Mistroke.
/Mfstroke {
Mstroke
currentdash
pop 0
setdash
} bind def
% Mrotsboxa is the same as Msboxa except that it takes an angle 
% from the stack and the box is calculated for text rendered at this  angle.  
% It gsaves in case we are starting a MathSubStart
% save Mrot so that Msboxa can convert bouding box back to the non-rotated
% coordinate system
% call Mrotcheck to alter the offsets into the rotated system
% converts Mtmatrix to render in the rotated system
% the calls Msboxa which does all the work
% at the end  Mtmatrix is restored and Mrot is reset to 0 
/Mrotsboxa {
gsave
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
grestore
Msboxa
3  -1 roll
/Mtmatrix
exch def
/Mrot
0 def
} bind def
% Given an array of strings ([str...]), which represent consecutive lines
% of text, a position in graphics coordinates (gx,gy) and a position in
% the bounding box coordinates (sx,sy), compute the low and high coordinates
% of the resulting text, in the [gx gy tx ty] form, which corresponds to
% the point (gx,gy) (in graphics coordinates) plus the offset (tx,ty) (in
% text coordinates).
% Note, Msboxa assumes that the current matrix is the text matrix.
% Mboxout is called in case we are in Mouter to make the box bigger
% Mboxrot adjusts the box to account for a rotation to convert the box
% into a nonrotated coordinate system
%
/Msboxa {
newpath
5 -1 roll
Mvboxa
pop
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Msboxa1
5 -3 roll
Msboxa1
Mboxrot
[
7 -2 roll
2 copy
[
3 1 roll
10 -1 roll
9 -1 roll
]
6 1 roll
5 -2 roll
]
} bind def
% Msboxa1 is an internal function which, given a bounding box coordinate
% (sz), and the bounding box limits (blz and bhz), computes the actual
% offsets (tlz = (blz-bhz)(sz+1)/2, thz = (blz-bhz)(sz-1)/2).
/Msboxa1 {
sub
2 div
dup
2 index
1 add
mul
3 -1 roll
-1 add
3 -1 roll
mul
} bind def
% Given a (non-empty) array of strings ([str...]) which represent consecutive
% lines of text, compute the total bounding box assuming that we start at
% (0,0) and the array of y offsets to place the lines correctly.
% Note, Mvboxa assumes that the current matrix is the text matrix.
% Note, Mvboxa does not alter the current path.
% The vertical spacing is set so that the bounding boxes of adjacent lines
% are .3 times the width of an `m' apart.
/Mvboxa {
gsave
newpath
[ true
3 -1 roll
{
Mbbox
5 -1 roll
{
0
5 1 roll
}
{
7 -1 roll
exch sub
(m) stringwidth pop
.3 mul
sub
7 1 roll
6 -1 roll
4 -1 roll
Mmin
3 -1 roll
5 index
add
5 -1 roll
4 -1 roll
Mmax
4 -1 roll
}
ifelse
false
}
forall
{ stop } if
counttomark
1 add
4 roll
]
grestore
} bind def
% Given a string, compute the bounding box assuming that we start at (0,0).
% Note, the path is assumed to be empty, and we are assumed to be in text
% coordinates.  Allows for long strings.
/Mbbox {
1 dict begin
0 0 moveto
/temp (T) def
{	gsave
currentpoint newpath moveto
temp 0 3 -1 roll put temp
false charpath flattenpath currentpoint
pathbbox
grestore moveto lineto moveto} forall
pathbbox
newpath
end
} bind def
% Compute the minimum of two numbers.
/Mmin {
2 copy
gt
{ exch } if
pop
} bind def
% Compute the maximum of two numbers.
/Mmax {
2 copy
lt
{ exch } if
pop
} bind def
%
% Mrotwork saves Mrot (not really needed but saved anyway)
% calls Mrotcheck to adjust the offsets into the rotated coordinate system
% converts Mtmatrix to render in the rotated system
%
/Mrotwork {
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
Mgmatrix setmatrix
} def
%
% Mrotshowa is the same as Mshowa except that it takes an angle
% from the stack and the text is rendered at this angle.
% It call Mrotwork to do all the rotation work.
% Then it calls Mshowa which does all the drawing work.
% At the end Mtmatrix is restored and Mrot is reset to zero.
%
/Mrotshowa {
Mrotwork
Mshowa
/Mtmatrix
exch def
/Mrot 0 def
} def
%
% Draws rotated text with a background.
%
/Mrotback {
7 1 roll
dup
8 1 roll
Mrotwork
8 -2 roll
Mshowback
/Mtmatrix
exch def
/Mrot 0 def
} def
%
% Given an array of strings ([str...]), which represent consecutive lines
% of text, a position in graphics coordinates (gx,gy) and a position in
% the bounding box coordinates (sx,sy), display the strings.
% Mboxout is called in case we are in Mouter
%
/Mshowa {
4 -2 roll
moveto
2 index
Mtmatrix setmatrix
Mvboxa
7 1 roll
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Mshowa1
4 1 roll
Mshowa1
rmoveto
currentpoint
Mshowax
pop pop pop pop
Mgmatrix setmatrix
} def
%
% The background box of text is increased by the
% size of an "m"
%
/Madjust	{
(m)
stringwidth
pop
mul
dup
4 -1 roll
add
3 1 roll
add
} def
%
%
%
/Mbuildcoord {
7 index
7 index
4 -1 roll
4 -1 roll
index
exch
index
Mabsadd
} def
%
% If the text is rotated then translate to the drawing point.
% Rotate then translate back.  Do not do this if the angle
% of rotation is 0.
%
/Mrotate {
8 index
0 ne
{
13 copy
4 -2 roll
pop pop
6 -2 roll
pop pop
4 -1 roll
3 -1 roll
sub
6 -1 roll
mul
3 1 roll
sub
4 -1 roll
mul
3 -1 roll
5 1 roll
Mabsadd
2 copy
translate
3 -1 roll
rotate
exch -1 mul
exch -1 mul
translate
} if
9 -1 roll
pop
} def
%
% Draw text but into a box with a certain color.
% Uses Msboxa to build the box.
%
/Mshowback {
gsave
exec
6 copy pop
Msboxa
aload pop
0.5 Madjust
5 -1 roll
aload pop
Mrotate
-0.5
Madjust
4 -1 roll
pop
3 -1 roll
pop
3 4
Mbuildcoord
moveto
3 4
Mbuildcoord
lineto
3 6
Mbuildcoord
lineto
5 6
Mbuildcoord
lineto
5 4
Mbuildcoord
lineto
pop pop pop
pop pop pop
fill		
grestore
Mshowa
} def
% This is used for fixedwidth fonts
% It simply shows each string and advances the y direction by the offset
%
/Mshowax {	
0 1
4 index length
-1 add
{
2 index
4 index
2 index
get
3 index
add
moveto
4 index
exch get
Mfixdash
{
Mfixdashp		
}
if
show
} for
} def
% Fix if all dashes and length > 1
/Mfixdashp {
dup
length
1
gt
1 index
true exch
{
45
eq
and
} forall
and
{
gsave
(--)		
stringwidth pop
(-)
stringwidth pop
sub
2 div
0 rmoveto
dup
length
1 sub
{
(-)
show
}
repeat
grestore
}
if
} bind def	
% Mshowa1 is an internal routine which, given a bounding box coordinate
% (sz), and the bounding box limits if we started drawing at 0 (tlz and thz),
% computes the offset at which to start drawing
% (relz = (sz-1)tlz/2 - (sz+1)thz/2 = sz(tlz-thz)/2-(tlz+thz)/2).
/Mshowa1 {
2 copy
add
4 1 roll
sub
mul
sub
-2 div
} bind def
% Given the x and y scaling to user coordinates and an array of points to
% fit (xbias xscale ybias yscale [pnts]), set up the scaling.  The array
% must contain atleast two points, and the last two must be of the form
% [gxlow gylow 0 0] and [gxhigh gyhigh 0 0].
% Note, MathScale assumes that we are already scaled so that the active area
% is the rectangle [0,Mwidth-Mlmarg-Mrmarg]x[0,Mheight-Mbmarg-Mtmarg].
% also keep bias and scale info for PostScript commands
/MathScale {
Mwidth
Mheight
Mlp
/MathScaleHook where {
/MathScaleHook get exec
} if
translate
scale
pop pop pop pop
pop pop pop pop
/yscale exch def
/ybias exch def
/xscale exch def
/xbias exch def
/Momatrix
xscale yscale matrix scale
xbias ybias matrix translate
matrix concatmatrix def
/Mgmatrix
matrix currentmatrix
def
} def
% Given a non-empty array of points to fit ([p]) and a maximum width (sx)
% and height (sy) find the largest scale (Ax and Ay) and offsets (Bx and By)
% such that the transformation
%	[gx gy tx ty] -> (Ax gx + tx + bx, Ay gy + ty + By)
% maps the points into the rectangle [0,sx]x[0,sy]
/Mlp {
3 copy
Mlpfirst
{
Mnodistort
{
Mmin
dup
} if
4 index
2 index
2 index
Mlprun
16 -8 roll
21 8 roll
11 index
11 -1 roll
10 -4 roll
Mlp1
8 index
9 -5 roll
Mlp1
4 -1 roll
and
{ exit } if
15 -8 roll
pop pop pop pop
pop pop pop pop
3 -1 roll
pop pop
} loop
exch
3 1 roll
7 -3 roll
pop pop pop
} def
% Given an array of points in the [gx gy tx ty] form, with the last two
% being [gxlow gylow 0 0] and [gxhigh gyhigh 0 0], and the width and height
% (sx and sy) in which to fit them, compute the maximum scaling (Ax and Ay).
/Mlpfirst {
3 -1 roll
dup length
2 copy
-2 add
get
aload
pop pop pop
4 -2 roll
-1 add
get
aload
pop pop pop
6 -1 roll
3 -1 roll
5 -1 roll
sub
div
4 1 roll
exch sub
div
} bind def
% Given a non-empty array of points to fit ([pnts]) and scale factors
% for graphics->text (Ax and Ay), compute the limiting points.
/Mlprun {
2 copy
4 index
0 get
dup
4 1 roll
Mlprun1
3 copy
8 -2 roll
9 -1 roll
{
3 copy
Mlprun1
3 copy
11 -3 roll
/gt Mlpminmax
8 3 roll
11 -3 roll
/lt Mlpminmax
8 3 roll
} forall
pop pop pop pop
3 1 roll
pop pop
aload pop
5 -1 roll
aload pop
8 copy
exch
6 -1 roll
Mlprun2
8 2 roll
4 -1 roll
Mlprun2
6 2 roll
3 -1 roll
Mlprun2
4 2 roll
exch
Mlprun2
6 2 roll
} bind def
% Given scale factors for graphics->text (Ax and Ay) and a point in the
% [gx gy tx ty] form, return the text x and y coordinate that results.
/Mlprun1 {
aload pop
exch
6 -1 roll
5 -1 roll
mul add
4 -2 roll
mul
3 -1 roll
add
} bind def
% Given a low and high coordinate, compute the center and width.
/Mlprun2 {
2 copy
add 2 div
3 1 roll
exch sub
} bind def
% Given two points stored as [gx gy tx ty] followed by the scaled
% result (rx, ry), and a comparison function (lt or gt) leave the
% point which is the minimum (or maximum) in each dimension.
/Mlpminmax {
cvx
2 index
6 index
2 index
exec
{
7 -3 roll
4 -1 roll
} if
1 index
5 index
3 -1 roll
exec
{
4 1 roll
pop
5 -1 roll
aload
pop pop
4 -1 roll
aload pop
[
8 -2 roll
pop
5 -2 roll
pop
6 -2 roll
pop
5 -1 roll
]
4 1 roll
pop
}
{
pop pop pop
} ifelse
} bind def
% Given a size (s), graphics->text scale (A), text center (ct), text
% width (wt), graphics center (cg) and graphics width (wg), compute
% a new graphics->text scale (Anew) and offset (B) and whether or not
% we are done.
% Note, the mysterious .99999 is magic juju which is supposed to ward
% off the possibility that floating point errors would cause this
% routine to return the old A and yet claim not-done.
/Mlp1 {
5 index
3 index	sub
5 index
2 index mul
1 index
le
1 index
0 le
or
dup
not
{
1 index
3 index	div
.99999 mul
8 -1 roll
pop
7 1 roll
}
if
8 -1 roll
2 div
7 -2 roll
pop sub
5 index
6 -3 roll
pop pop
mul sub
exch
} bind def
% The following are the workings of the tick, axes and plot labels.
% NOTE a possible source of confusion is that for xticks ie tickmarks on
% the x axis we keep y information and vice versa for yticks
%
%	When Minner is found then
%
% assumes that box starts at zero on the left lower side
%
%		0)	if outflag = 1 then intop = 0, inrht = 0 outflag = 0
%		1)	Save intop 	largest top of box 
%		2)	Save inrht 	largest rht of box
%		3)	set inflag	notifies that inner marks are present
%
%	When Mouter is found then
%
%	if inflag is set then
%		1)	get vecx and vecy off the stack (points in direcn to move)
%		2)	vecx < 1 xadrht = inrht*abs(vecx)
%		3)	vecx > 1 xadlft = inrht*abs(vecx)
%		4)	vecy < 1 yadtop = intop*abs(vecy)
%		5)	vecy > 1 yadbot = intop*abs(vecy)
%		6)	set outflag = 1
%		7)	clear inflag, inrht, intop
%	guaranteed to be zero if no inner is present??
%
%
%	These all have effects in Mrotsboxa and Mrotshowa
%		check inflag and if set
%
%		1) increase top of bbox by yadtop
%		2) decrease bot of bbox by yadbot
%		3) increase rht of bbox by xadrht
%		4) increase lft of bbox by xadlft
%		5) clear outflag, yadtop, yadbot,
%			         xadrht, xadlft
%
% 
% This saves the top right corner of the bounding box as a side effect
% This is to allow the adjustment of text placed with Mouter so that
% it misses the Minner text.  It is assumed that the ang is 0
% in the same way it is assumed that the text of Mouter is 0 or 90
%
/Minner {
outflag
1
eq
{
/outflag 0 def
/intop 0 def
/inrht 0 def
} if		
5 index
gsave
Mtmatrix setmatrix
Mvboxa pop
grestore
3 -1 roll
pop
dup
intop
gt
{
/intop
exch def
}
{ pop }
ifelse
dup
inrht
gt
{
/inrht
exch def
}
{ pop }
ifelse
pop
/inflag
1 def
} def
% This takes two number off the stack and uses them as a vector in graphics
% coordinates which points in the direction in which the Mouter text is to move
% it calculates the bouding box adjustments yadtop yadbot xadrht and xadlft
% these are in Mboxout to adjust the bounding box to compensate.
/Mouter {
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
inflag
1 eq
{
dup
0 lt
{
dup
intop
mul
neg
/yadtop
exch def
} if
dup
0 gt
{
dup
intop
mul
/yadbot
exch def
}
if
pop
dup
0 lt
{
dup
inrht
mul
neg
/xadrht
exch def
} if
dup
0 gt
{
dup
inrht
mul
/xadlft
exch def
} if
pop
/outflag 1 def
}
{ pop pop}
ifelse
/inflag 0 def
/inrht 0 def
/intop 0 def
} def	
%
% This adjusts the bounding box to account for adjacent text
% This allows the two text strings to avoid each other 
% current matrix is the text matrix
/Mboxout {
outflag
1
eq
{
4 -1
roll
xadlft
leadjust
add
sub
4 1 roll
3 -1
roll
yadbot
leadjust
add
sub
3 1
roll
exch
xadrht
leadjust
add
add
exch
yadtop
leadjust
add
add
/outflag 0 def
/xadlft 0 def
/yadbot 0 def
/xadrht 0 def
/yadtop 0 def
} if
} def
/leadjust {
(m) stringwidth pop
.5 mul
} bind def
% The offsets sx and sy refer to the graphics coordinate system 
% thus they must be altered if a rotation has taken place.
% We must also change the bounding box computations for Minner
%
/Mrotcheck {
dup
90
eq
{
%
% Mouter only applies to strings which are either at 0 or 90
% sort out the box adjust factors
%
%	xadrht -> yadbot
%	xadlft -> yadtop
%	yadtop -> xadrht
%	yadbot -> xadlft
yadbot
/yadbot
xadrht
def	
/xadrht
yadtop
def
/yadtop
xadlft
def
/xadlft
exch
def
}
if
dup
cos
1 index
sin
Checkaux
dup
cos
1 index
sin neg
exch
Checkaux
3 1 roll
pop pop
} def
%
% Checkaux is an auxilliary function for Mrotcheck it multiplies a 
% row vector by a column vector
% 
/Checkaux {
4 index
exch
4 index
mul
3 1 roll
mul add
4 1 roll
} bind def
%
% Mboxrot converts the bounding box back from the rotated coordinate
% system to the Mgmatrix system to compensate for a rotation
% It has the opposite functionality of Mrotcheck
% This is not the most neatest or most efficient implementation but it works
%
/Mboxrot {
Mrot
90 eq
{
% old		 tlx  thx  tly  thy
% new		-thy -tly  tlx  thx
%
brotaux
4 2
roll
}
if
Mrot
180 eq
{
% old		 tlx  thx  tly  thy
% new		-thx -tlx -thx -tly
%
4 2
roll
brotaux
4 2
roll
brotaux
}	
if
Mrot
270 eq
{
% old		 tlx  thx  tly  thy
% new		 tly  thy -thx -tlx
%
4 2
roll
brotaux
}
if
} def
%
% auxilliary function negate and reverse
/brotaux {
neg
exch
neg
} bind def
%
% Mabsproc takes a measurement in the default user units and converts
% it to the present units.   This allows absolute thickness and dashing
% to work.  It works by using a {0, x} vector and using the RMS of the result.
/Mabsproc {
0
matrix defaultmatrix
dtransform idtransform
dup mul exch
dup mul
add sqrt
} bind def
%
% Mabswid allows the linewidth to be specified in absolute coordinates
% It does this by recording the graphics transformation matrix at the
% begining of the plot.
% This will break if the scaling in the x and y directions is
% different.  This is the case if Mnodistort is false
%
/Mabswid {
Mabsproc
setlinewidth	
} bind def
% Mabsdash allows the dashing pattern to be specified in absolute coordinates
% It does this by recording the graphics transformation matrix at the
% begining of the plot.
% This will break if the scaling in the x and y directions is
% different.  This is the case if Mnodistort is false
%
/Mabsdash {
exch
[
exch
{
Mabsproc
}
forall
]
exch
setdash
} bind def
%
% Mabs takes a pair of coordinates in points
% and converts them into a pair of coordinates in
% the current drawing scheme
%
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
%
% Mabs takes a pair of numbers in drawing coordinates
% and a pair in points.  It converts the points to
% drawing coordinates and adds them to the first pair.
%
/Mabsadd {
Mabs
3 -1 roll add
3 1 roll add
exch 
} bind def
%
% These two procedures are for using Offset coordinates
% with MathScale computations
%
/Mabsfix1 {
3 -1 roll
/ar exch 
def
ar 2 get
3 -1 roll
add exch
ar 3 get
add
ar 3
3 -1 roll
put
ar 2
3 -1 roll
put
ar
} bind def
/Mabsfix {
2 copy
6 -1 roll
3 1 roll
Mabsfix1
4 1 roll
Mabsfix1
} bind def
%MBeginOrig start coordinates in user coordinates
/MBeginOrig { Momatrix concat} bind def
%MEndOrig start coordinates in user coordinates
/MEndOrig { Mgmatrix setmatrix} bind def
/sampledsound where
{ pop }
{ /MathDPSFlag where
{ pop /sampledsound { clientsync } def }
{ /sampledsound {
exch pop
exch 5 1 roll
mul
4 idiv
mul
2 idiv
exch pop
exch
/Mtempproc exch def
{ Mtempproc pop }
repeat
} def
} ifelse
} ifelse
% Define setrgbcolor for those ancient PostScript devices lacking it
/setrgbcolor dup where
{ pop pop }
{ { .114 mul exch .587 mul add exch .299 mul add setgray } bind def }
ifelse
%
% now simple conversion of cmykcolor to rgbcolor
% subtract k and then take complements
/setcmykcolor where
{ pop}
{ /setcmykcolor {
4 1
roll
[
4 1 
roll
]
{
1 index
sub
1
sub neg
dup
0
lt
{
pop
0
}
if
dup
1
gt
{
pop
1
}
if
exch
} forall
pop
setrgbcolor
} bind def
} ifelse
% Here are the short operators
/g /setgray load def
/k /setcmykcolor load def
/m /moveto load def
/p /gsave load def
/r /setrgbcolor load def
/w /setlinewidth load def
/C /curveto load def
/F /Mfill load def
/L /lineto load def
/P /grestore load def
/s /Mstroke load def
/Mcharproc
{
currentfile
(x)
readhexstring
pop
0 get
exch
div
} bind def
/Mshadeproc
{
dup
3 1
roll
{
dup
Mcharproc
3 1
roll
} repeat
1 eq
{
setgray
}
{
3 eq
{
setrgbcolor
}
{
setcmykcolor
} ifelse
} ifelse
} bind def
/Mrectproc
{
3 index
2 index
moveto
2 index
3 -1
roll
lineto
dup
3 1
roll
lineto
lineto
Mfill
} bind def
/Mcolorimage
{
7 1
roll
pop
pop
matrix
invertmatrix
concat
2 exch exp
1 sub
3 1 roll
1 1
2 index
{
1 1
4 index
{
dup
1 sub
exch
2 index
dup
1 sub
exch
7 index
9 index
Mshadeproc
Mrectproc
} for
pop
} for
pop pop pop pop
} bind def
/Mimage
{
pop
matrix
invertmatrix
concat
2 exch exp
1 sub
3 1 roll
1 1
2 index
{
1 1
4 index
{
dup
1 sub
exch
2 index
dup
1 sub
exch
7 index
Mcharproc
setgray
Mrectproc
} for
pop
} for
pop pop pop
} bind def
% Default values for variables
/Mlmarg		1.0 72 mul def
/Mrmarg		1.0 72 mul def
/Mbmarg		1.0 72 mul def
/Mtmarg		1.0 72 mul def
/Mwidth		8.5 72 mul def
/Mheight	11 72 mul def
/Mtransform	{  } bind def
/Mnodistort	true def	
/Mfixdash	false def	
/Mrot		0	def	
/intop 0 def
/inrht 0 def
/inflag 0 def
/outflag 0 def
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
/defineresource where
{ pop /WRI-Mathematica-prolog currentdict /ProcSet defineresource pop }
if
end
%KLUDGE until Mathematica output uses resources directly
userdict /MathPictureStart {
	/findresource where
	{ pop /WRI-Mathematica-prolog /ProcSet findresource }
	{ Mathdict }
	ifelse
	/MathPictureStart get exec
} put
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% ContourGraphics
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[.5883 -0.0125 7.2 0 ]
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[-0.0125 .5883 -28.8 -15.6 ]
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[-0.0125 .78454 -28.8 -15.6 ]
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[-0.0125 .98077 0 15.6 ]
[ 0 0 -0.125 0 ]
[-0.01875 .5 -60 -187.2 ]
[-0.01875 .5 -28.8 187.2 ]
[ 0 1 .125 0 ]
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[ 0 0 0 0 ]
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1 .0781 L
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1 .11735 L
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closepath
clip
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1 g
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F
.8 g
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F
.7 g
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F
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F
.5 g
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F
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F
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F
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F
.5 g
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F
.6 g
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F
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F
1 g
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F
% End of Graphics
MathPictureEnd
%%Trailer
cleartomark
countdictstack exch sub { end } repeat
restore
%%EOF

%%EndDocument
@endspecial 2661 2894 a(\(c\)) p Fc 17 w(\025) p Fe 2792
2905 a(B) p Fx 2865 2894 a(=) f(0) p Fc(:) p Fx(5) p
FD 17 w([pack) q(et/ms]) p Fr 347 3140 a(Figure) g(10:) h(Maximu) n(m) h
(mod) n(ulus) f(of) g(eigen) m(v) l(alues) h(for) e(dif) n(fere) n(nt) i
(arri) n(v) l(al) g(rate) f(of) g(backg) n(round) f(traf) n(\002c.) 191
3503 y(0.92) n(3,) 25 b(respecti) n(v) o(ely) -7 b(.) 25
b(W) -7 b(e) 27 b(use) f(the) f(same) g(v) n(alues) g(with) h(T) -7
b(ab) m(.) 24 b(I) i(for) f(all) h(para) n(meters) g(e) o(xcep) n(t) g
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@endspecial 1549 2633 a(\(b\)) f(A) -5 b(v) o(era) r(ge) 17
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3242 y(length) 25 b(at) h(the) g(bottlene) n(ck) g(router) -7
b(.) 27 b(W) -7 b(e) 27 b(ha) n(v) o(e) e(also) h(analyzed) f(the) h
(TCP) g(transient) f(state) i(beha) n(vio) n(r) f(by) g(using) f(the)
191 3342 y(contro) n(l) k(theory) -7 b(.) 28 b(As) h(a) g(result,) f
(we) g(ha) n(v) o(e) g(foun) n(d) g(that) h(the) f(band) n(width\226d) n
(elay) h(pro) n(duct) f(mostly) g(determ) n(ines) h(the) 191
3441 y(stability) 22 b(and) g(the) h(transient) f(state) h(beha) l
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(found) f(that) i(the) f(netw) o(ork) f(becom) n(es) j(stable) 191
3541 y(as) d(the) f(numb) n(er) g(of) g(TCP) h(connectio) n(ns) g(or) f
(the) g(amou) n(nts) h(of) f(the) g(backg) n(round) f(traf) n(\002c) h
(increases.) g(W) -7 b(e) 21 b(ha) n(v) o(e) f(sho) n(wn) 191
3640 y(that) k(the) g(transient) f(state) i(beha) n(vio) n(r) g(is) f
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g(of) h(the) g(bottlene) n(ck) g(link,) 191 3740 y(b) n(ut) d(is) g
(almost) g(indep) n(endent) f(of) g(the) h(amou) n(nt) g(of) g(back) n
(groun) n(d) g(traf) n(\002c.) f(As) i(futu) n(re) f(w) o(ork,) f(it) h
(w) o(ould) f(be) h(interesting) 191 3840 y(to) 29 b(apply) f(our) f
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(el) h(of) f(a) p Fo 191 4039 a(M) t(=D) r(=) p Fn(1) p
Fo(=m) p Fr 19 w(queu) n(e.) p FD 1676 4372 a(REFERENCES) 252
4575 y(1.) 37 b(V) -9 b(.) 17 b(Jacob) r(son) g(and) i(M.) e(J.) g
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i(A) n(CM) e(SIGCOMM) i('88) p FD(,) f(pp.) f(314\226329) r(,) 339
4649 y(No) o(v) l(.) f(1988.) 252 4724 y(2.) 37 b(B.Sikdar) m(,) h
(S.Kalyana) r(raman,) f(and) h(K.S.V) -7 b(astola,) 37
b(\223) -5 b(Analy) r(tic) 38 b(models) f(and) h(compara) r(ti) n(v) o
(e) h(study) e(of) g(lat) r(enc) o(y) h(and) g(steady-) r(state) 339
4799 y(through) r(put) 17 b(of) g(TCP) f(Tahoe,) i(Reno) f(nad) h(SA) m
(CK,) -5 b(\224) p FC 17 w(IEEE/A) n(CM) 17 b(T) l(r) o(ansacti) r(ons)
f(on) h(Net) r(working) p FD(,) h(v) o(ol.) e(11,) h(pp.) g
(959\226971,) g(Dec.) g(2003.) 252 4873 y(3.) 37 b(E.Alessio,) 21
b(M.Garett) r(o,) g(R.Cigno,) g(M.Meo,) g(and) h(M.Marsan,) g(\223) -5
b(Analyt) r(ical) 23 b(estimat) r(ion) f(of) f(comple) r(tion) h(times)
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FD(,) 339 5023 y(No) o(v) l(.) c(2001.) 191 5222 y(Cop) o(yri) r(ght)
497 5220 y(c) p Fm 476 5222 a(\015) p FD 16 w(2005) i(John) f(W) m(ile)
o(y) h(&) f(Sons,) f(Ltd.) p FC 1233 w(Int.) 21 b(J) n(.) c(Commun.) k
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