200 Pages

hw5

Course: MATH 504, Fall 2009
School: Rutgers
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Word Count: 166224

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%%Creator: %!PS-Adobe-2.0 dvips 5.528 Copyright 1986, 1994 Radical Eye Software %%Title: hw5.dvi %%CreationDate: Mon Feb 21 11:22:53 2000 %%Pages: 1 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: CMSL10 CMR7 CMBX10 CMR10 MSBM10 CMSY7 CMSY10 CMMI7 %%+ CMMI10 CMTI10 CMMI5 CMR5 CMEX10 CMTT10 %%EndComments %DVIPSCommandLine: dvips hw5.dvi -o hw5.ps %DVIPSParameters: dpi=300, comments removed...

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%%Creator: %!PS-Adobe-2.0 dvips 5.528 Copyright 1986, 1994 Radical Eye Software %%Title: hw5.dvi %%CreationDate: Mon Feb 21 11:22:53 2000 %%Pages: 1 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: CMSL10 CMR7 CMBX10 CMR10 MSBM10 CMSY7 CMSY10 CMMI7 %%+ CMMI10 CMTI10 CMMI5 CMR5 CMEX10 CMTT10 %%EndComments %DVIPSCommandLine: dvips hw5.dvi -o hw5.ps %DVIPSParameters: dpi=300, comments removed %DVIPSSource: TeX output 2000.02.21:1122 %%BeginProcSet: tex.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR matrix currentmatrix dup dup 4 get round 4 exch put dup dup 5 get round 5 exch put setmatrix}N /@landscape{/isls true N}B /@manualfeed{ statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{/nn 8 dict N nn begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N string /base X array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{/sf 1 N /fntrx FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0]N df-tail}B /E{ pop nn dup definefont setfont}B /ch-width{ch-data dup length 5 sub get} B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup type /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N /rc 0 N /gp 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 add]{ ch-image}imagemask restore}B /D{/cc X dup type /stringtype ne{]}if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1 sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{cc 1 add D }B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin 0 0 moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore showpage userdict /eop-hook known{eop-hook}if}N /@start{userdict /start-hook known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for 65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0 0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V {}B /RV statusdict begin /product where{pop product dup length 7 ge{0 7 getinterval dup(Display)eq exch 0 4 getinterval(NeXT)eq or}{pop false} ifelse}{false}ifelse end{{gsave TR -.1 -.1 TR 1 1 scale rulex ruley false RMat{BDot}imagemask grestore}}{{gsave TR -.1 -.1 TR rulex ruley scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave transform round exch round exch itransform moveto rulex 0 rlineto 0 ruley neg rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta 0 N /tail{dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail} B /c{-4 M}B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{ 3 M}B /k{4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p -1 w}B /q{p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{ 3 2 roll p a}B /bos{/SS save N}B /eos{SS restore}B end %%EndProcSet %%BeginFont: CMSL10 %!PS-AdobeFont-1.1: CMSL10 1.0 %%CreationDate: 1991 Aug 20 16:40:20 % 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 (CMSL10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -9.46 def /isFixedPitch false def end readonly def /FontName /CMSL10 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup 0 /Gamma put 1 /Delta put 2 /Theta put 3 /Lambda put 4 /Xi put 5 /Pi put 6 /Sigma put 7 /Upsilon put 8 /Phi put 9 /Psi put 10 /Omega put 11 /ff put 12 /fi put 13 /fl put 14 /ffi put 15 /ffl put 16 /dotlessi put 17 /dotlessj put 18 /grave put 19 /acute put 20 /caron put 21 /breve put 22 /macron put 23 /ring put 24 /cedilla put 25 /germandbls put 26 /ae put 27 /oe put 28 /oslash put 29 /AE put 30 /OE put 31 /Oslash put 32 /suppress put 33 /exclam put 34 /quotedblright put 35 /numbersign put 36 /dollar put 37 /percent put 38 /ampersand put 39 /quoteright put 40 /parenleft put 41 /parenright put 42 /asterisk put 43 /plus put 44 /comma put 45 /hyphen put 46 /period put 47 /slash put 48 /zero put 49 /one put 50 /two put 51 /three put 52 /four put 53 /five put 54 /six put 55 /seven put 56 /eight put 57 /nine put 58 /colon put dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup 59 /semicolon put 60 /exclamdown put 61 /equal put 62 /questiondown put 63 /question put 64 /at put 65 /A put 66 /B put 67 /C put 68 /D put 69 /E put 70 /F put 71 /G put 72 /H put 73 /I put 74 /J put 75 /K put 76 /L put 77 /M put 78 /N put 79 /O put 80 /P put 81 /Q put 82 /R put 83 /S put 84 /T put 85 /U put 86 /V put 87 /W put 88 /X put 89 /Y put 90 /Z put 91 /bracketleft put 92 /quotedblleft put 93 /bracketright put 94 /circumflex put 95 /dotaccent put 96 /quoteleft put 97 /a put 98 /b put 99 /c put 100 /d put 101 /e put 102 /f put 103 /g put 104 /h put 105 /i put 106 /j put 107 /k put 108 /l put 109 /m put 110 /n put 111 /o put 112 /p put 113 /q put 114 /r put 115 /s put 116 /t put 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-62 -250 1123 750}readonly def /UniqueID 5000798 def currentdict end currentfile eexec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Society. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def All Rights Reserved. /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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 /ff put /fi put /fl put /ffi put /ffl put /dotlessi put /dotlessj put /grave put /acute put /caron put /breve put /macron put /ring put /cedilla put /germandbls put /ae put /oe put /oslash put /AE put /OE put /Oslash put /suppress put /exclam put /quotedblright put /numbersign put /dollar put /percent put /ampersand put /quoteright put /parenleft put /parenright put /asterisk put /plus put /comma put /hyphen put /period put /slash put /zero put /one put /two put /three put /four put /five put /six put /seven put /eight put /nine put /colon put /semicolon put /exclamdown put /equal put /questiondown put /question put /at put /A put /B put /C put /D put /E put dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup 70 /F put 71 /G put 72 /H put 73 /I put 74 /J put 75 /K put 76 /L put 77 /M put 78 /N put 79 /O put 80 /P put 81 /Q put 82 /R put 83 /S put 84 /T put 85 /U put 86 /V put 87 /W put 88 /X put 89 /Y put 90 /Z put 91 /bracketleft put 92 /quotedblleft put 93 /bracketright put 94 /circumflex put 95 /dotaccent put 96 /quoteleft put 97 /a put 98 /b put 99 /c put 100 /d put 101 /e put 102 /f put 103 /g put 104 /h put 105 /i put 106 /j put 107 /k put 108 /l put 109 /m put 110 /n put 111 /o put 112 /p put 113 /q put 114 /r put 115 /s put 116 /t put 117 /u put 118 /v put 119 /w put 120 /x put 121 /y put 122 /z put 123 /endash put 124 /emdash put 125 /hungarumlaut put 126 /tilde put 127 /dieresis put 128 /suppress put dup 160 /space put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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B5FBF780CF8754FA7422C3F57E62CCEEAD9AA3470000000000000000000000000000000000000000000 000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 /grave put /acute put /caron put /breve put /macron put /ring put /cedilla put /germandbls put /ae put /oe put /oslash put /AE put /OE put /Oslash put /suppress put /exclam put /quotedblright put /numbersign put /dollar put /percent put /ampersand put /quoteright put /parenleft put /parenright put /asterisk put /plus put /comma put /hyphen put /period put /slash put /zero put /one put /two put /three put /four put /five put /six put /seven put /eight put /nine put /colon put /semicolon put /exclamdown put /equal put /questiondown put /question put /at put /A put /B put /C put /D put /E put /F put /G put /H put /I put /J put /K put /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec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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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup 191 /oslash put 192 /AE put 193 /OE put 194 /Oslash put 195 /suppress put 196 /dieresis put 0 /Gamma put 1 /Delta put 2 /Theta put 3 /Lambda put 4 /Xi put 5 /Pi put 6 /Sigma put 7 /Upsilon put 8 /Phi put 9 /Psi put 10 /Omega put 11 /ff put 12 /fi put 13 /fl put 14 /ffi put 15 /ffl put 16 /dotlessi put 17 /dotlessj put 18 /grave put 19 /acute put 20 /caron put 21 /breve put 22 /macron put 23 /ring put 24 /cedilla put 25 /germandbls put 26 /ae put 27 /oe put 28 /oslash put 29 /AE put 30 /OE put 31 /Oslash put 32 /suppress put 33 /exclam put 34 /quotedblright put 35 /numbersign put 36 /dollar put 37 /percent put 38 /ampersand put 39 /quoteright put 40 /parenleft put 41 /parenright put 42 /asterisk put 43 /plus put 44 /comma put 45 /hyphen put 46 /period put 47 /slash put 48 /zero put 49 /one put 50 /two put 51 /three put 52 /four put dup dup dup dup dup dup dup dup dup dup 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11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /lessornotequal put dup 162 /greaterornotequal put dup 163 /notlessequal put dup 164 /notgreaterequal put dup 165 /notless put dup 166 /notgreater put dup 167 /notprecedes put dup 168 /notfollows put dup 169 /lessornotdbleql put dup 170 /greaterornotdbleql put dup 173 /notlessorslnteql put dup 174 /notgreaterorslnteql put dup 175 /lessnotequal put dup 176 /greaternotequal put dup 177 /notprecedesoreql put dup 178 /notfollowsoreql put dup 179 /precedeornoteqvlnt put dup 180 /followornoteqvlnt put dup 181 /lessornotsimilar put dup 182 /greaterornotsimilar put dup 183 /notlessdblequal put dup 184 /notgreaterdblequal put dup 185 /precedenotslnteql put dup 186 /follownotslnteql put dup 187 /precedenotdbleqv put dup 188 /follownotdbleqv put dup 189 /lessnotdblequal put dup 190 /greaternotdblequal put dup 191 /notsimilar put dup 192 /notapproxequal put dup 193 /upslope put dup 194 /downslope put dup 195 /notsubsetoreql put dup 196 /epsiloninv put dup 0 /lessornotequal put dup 1 /greaterornotequal put dup 2 /notlessequal put dup 3 /notgreaterequal put dup 4 /notless put dup 5 /notgreater put dup 6 /notprecedes put dup 7 /notfollows put dup 8 /lessornotdbleql put dup 9 /greaterornotdbleql put dup 10 /notlessorslnteql put dup 11 /notgreaterorslnteql put dup 12 /lessnotequal put dup 13 /greaternotequal put dup 14 /notprecedesoreql put dup 15 /notfollowsoreql put dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 /precedeornoteqvlnt put /followornoteqvlnt put /lessornotsimilar put /greaterornotsimilar put /notlessdblequal put /notgreaterdblequal put /precedenotslnteql put /follownotslnteql put /precedenotdbleqv put /follownotdbleqv put /lessnotdblequal put /greaternotdblequal put /notsimilar put /notapproxequal put /upslope put /downslope put /notsubsetoreql put /notsupersetoreql put /notsubsetordbleql put /notsupersetordbleql put /subsetornotdbleql put /supersetornotdbleql put /subsetornoteql put /supersetornoteql put /subsetnoteql put /supersetnoteql put /notsubseteql put /notsuperseteql put /notparallel put /notbar put /notshortbar put /notshortparallel put /notturnstile put /notforces put /notsatisfies put /notforcesextra put /nottriangeqlright put /nottriangeqlleft put /nottriangleleft put /nottriangleright put /notarrowleft put /notarrowright put /notdblarrowleft put /notdblarrowright put /notdblarrowboth put /notarrowboth put /dividemultiply put /emptyset put /notexistential put /A put /B put /C put /D put /E put /F put /G put /H put /I put /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /hatwide put dup 92 /hatwider put dup 93 /tildewide put dup 94 /tildewider put dup 96 /Finv put dup 97 /Gmir put dup 102 /Omegainv put dup 103 /eth put dup 104 /equalorsimilar put dup 105 /beth put dup 106 /gimel put dup 107 /daleth put dup 108 /lessdot put dup 109 /greaterdot put dup 110 /multicloseleft put dup 111 /multicloseright put dup 112 /barshort put dup 113 /parallelshort put dup 114 /integerdivide put dup 115 /similar put dup 116 /approxequal put dup 117 /approxorequal put dup 118 /followsorequal put dup 119 /precedesorequal put dup 120 /archleftdown put dup 121 /archrightdown put dup 122 /Digamma put dup 123 /kappa put dup 124 /k put dup 125 /planckover2pi put dup 126 /planckover2pi1 put dup 127 /epsiloninv put dup 128 /notsubsetoreql put dup 160 /space put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 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 161 /minus put dup 162 /periodcentered put dup 163 /multiply put dup 164 /asteriskmath put dup 165 /divide put dup 166 /diamondmath put dup 167 /plusminus put dup 168 /minusplus put dup 169 /circleplus put dup 170 /circleminus put dup 173 /circlemultiply put dup 174 /circledivide put dup 175 /circledot put dup 176 /circlecopyrt put dup 177 /openbullet put dup 178 /bullet put dup 179 /equivasymptotic put dup 180 /equivalence put dup 181 /reflexsubset put dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup 182 /reflexsuperset put 183 /lessequal put 184 /greaterequal put 185 /precedesequal put 186 /followsequal put 187 /similar put 188 /approxequal put 189 /propersubset put 190 /propersuperset put 191 /lessmuch put 192 /greatermuch put 193 /precedes put 194 /follows put 195 /arrowleft put 196 /spade put 0 /minus put 1 /periodcentered put 2 /multiply put 3 /asteriskmath put 4 /divide put 5 /diamondmath put 6 /plusminus put 7 /minusplus put 8 /circleplus put 9 /circleminus put 10 /circlemultiply put 11 /circledivide put 12 /circledot put 13 /circlecopyrt put 14 /openbullet put 15 /bullet put 16 /equivasymptotic put 17 /equivalence put 18 /reflexsubset put 19 /reflexsuperset put 20 /lessequal put 21 /greaterequal put 22 /precedesequal put 23 /followsequal put 24 /similar put 25 /approxequal put 26 /propersubset put 27 /propersuperset put 28 /lessmuch put 29 /greatermuch put 30 /precedes put 31 /follows put 32 /arrowleft put 33 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /minus put dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup 162 /periodcentered put 163 /multiply put 164 /asteriskmath put 165 /divide put 166 /diamondmath put 167 /plusminus put 168 /minusplus put 169 /circleplus put 170 /circleminus put 173 /circlemultiply put 174 /circledivide put 175 /circledot put 176 /circlecopyrt put 177 /openbullet put 178 /bullet put 179 /equivasymptotic put 180 /equivalence put 181 /reflexsubset put 182 /reflexsuperset put 183 /lessequal put 184 /greaterequal put 185 /precedesequal put 186 /followsequal put 187 /similar put 188 /approxequal put 189 /propersubset put 190 /propersuperset put 191 /lessmuch put 192 /greatermuch put 193 /precedes put 194 /follows put 195 /arrowleft put 196 /spade put 0 /minus put 1 /periodcentered put 2 /multiply put 3 /asteriskmath put 4 /divide put 5 /diamondmath put 6 /plusminus put 7 /minusplus put 8 /circleplus put 9 /circleminus put 10 /circlemultiply put 11 /circledivide put 12 /circledot put 13 /circlecopyrt put 14 /openbullet put 15 /bullet put 16 /equivasymptotic put 17 /equivalence put 18 /reflexsubset put 19 /reflexsuperset put 20 /lessequal put 21 /greaterequal put 22 /precedesequal put 23 /followsequal put 24 /similar put 25 /approxequal put dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 /propersubset put /propersuperset put /lessmuch put /greatermuch put /precedes put /follows put /arrowleft put /arrowright put /arrowup put /arrowdown put /arrowboth put /arrownortheast put /arrowsoutheast put /similarequal put /arrowdblleft put /arrowdblright put /arrowdblup put /arrowdbldown put /arrowdblboth put /arrownorthwest put /arrowsouthwest put /proportional put /prime put /infinity put /element put /owner put /triangle put /triangleinv put /negationslash put /mapsto put /universal put /existential put /logicalnot put /emptyset put /Rfractur put /Ifractur put /latticetop put /perpendicular put /aleph put /A put /B put /C put /D put /E put /F put /G put /H put /I put /J put /K put /L put /M put /N put /O put /P put /Q put /R put /S put /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /union put dup 92 /intersection put dup 93 /unionmulti put dup 94 /logicaland put dup 95 /logicalor put dup 96 /turnstileleft put dup 97 /turnstileright put dup 98 /floorleft put dup 99 /floorright put dup 100 /ceilingleft put dup 101 /ceilingright put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 108 /arrowbothv put dup 109 /arrowdblbothv put dup 110 /backslash put dup 111 /wreathproduct put dup 112 /radical put dup 113 /coproduct put dup 114 /nabla put dup 115 /integral put dup 116 /unionsq put dup 117 /intersectionsq put dup 118 /subsetsqequal put dup 119 /supersetsqequal put dup 120 /section put dup 121 /dagger put dup 122 /daggerdbl put dup 123 /paragraph put dup 124 /club put dup 125 /diamond put dup 126 /heart put dup 127 /spade put dup 128 /arrowleft put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 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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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 194 /chi put dup 195 /psi put dup 196 /tie put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 /zeta put /eta put /theta put /iota put /kappa put /lambda put /mu put /nu put /xi put /pi put /rho put /sigma put /tau put /upsilon put /phi put /chi put /psi put /omega put /epsilon put /theta1 put /pi1 put /rho1 put /sigma1 put /phi1 put /arrowlefttophalf put /arrowleftbothalf put /arrowrighttophalf put /arrowrightbothalf put /arrowhookleft put /arrowhookright put /triangleright put /triangleleft put /zerooldstyle put /oneoldstyle put /twooldstyle put /threeoldstyle put /fouroldstyle put /fiveoldstyle put /sixoldstyle put /sevenoldstyle put /eightoldstyle put /nineoldstyle put /period put /comma put /less put /slash put /greater put /star put /partialdiff put /A put /B put /C put /D put /E put /F put /G put /H put /I put /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 put /S dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /flat put dup 92 /natural put dup 93 /sharp put dup 94 /slurbelow put dup 95 /slurabove put dup 96 /lscript put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /dotlessi put dup 124 /dotlessj put dup 125 /weierstrass put dup 126 /vector put dup 127 /tie put dup 128 /psi put dup 160 /space put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec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4D23942EE66E911426C4EB4422CD6B5F519CB91E969D3F475C80668D4AE5CEAB15DFE7F64029 8178AC464AAE2C8198E1C12A2369D81E2CD1EFE2FB3E8C499D1F45BB2C1859F44DF0776EC3C5 6E6D31E587E6DA50CA97AAD5D8AC1E9EA7E5E7460000000000000000000000000000000000000000000 000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup 194 /chi put 195 /psi put 196 /tie put 0 /Gamma put 1 /Delta put 2 /Theta put 3 /Lambda put 4 /Xi put 5 /Pi put 6 /Sigma put 7 /Upsilon put 8 /Phi put 9 /Psi put 10 /Omega put 11 /alpha put 12 /beta put 13 /gamma put 14 /delta put 15 /epsilon1 put 16 /zeta put 17 /eta put 18 /theta put 19 /iota put 20 /kappa put 21 /lambda put 22 /mu put 23 /nu put 24 /xi put 25 /pi put 26 /rho put 27 /sigma put 28 /tau put 29 /upsilon put 30 /phi put 31 /chi put 32 /psi put 33 /omega put 34 /epsilon put 35 /theta1 put 36 /pi1 put 37 /rho1 put 38 /sigma1 put 39 /phi1 put 40 /arrowlefttophalf put 41 /arrowleftbothalf put 42 /arrowrighttophalf put 43 /arrowrightbothalf put 44 /arrowhookleft put 45 /arrowhookright put 46 /triangleright put 47 /triangleleft put 48 /zerooldstyle put 49 /oneoldstyle put 50 /twooldstyle put 51 /threeoldstyle 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cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup 188 /germandbls put 189 /ae put 190 /oe put 191 /oslash put 192 /AE put 193 /OE put 194 /Oslash put 195 /suppress put 196 /dieresis put 0 /Gamma put 1 /Delta put 2 /Theta put 3 /Lambda put 4 /Xi put 5 /Pi put 6 /Sigma put 7 /Upsilon put 8 /Phi put 9 /Psi put 10 /Omega put 11 /ff put 12 /fi put 13 /fl put 14 /ffi put 15 /ffl put 16 /dotlessi put 17 /dotlessj put 18 /grave put 19 /acute put 20 /caron put 21 /breve put 22 /macron put 23 /ring put 24 /cedilla put 25 /germandbls put 26 /ae put 27 /oe put 28 /oslash put 29 /AE put 30 /OE put 31 /Oslash put 32 /suppress put 33 /exclam put 34 /quotedblright put 35 /numbersign put 36 /sterling put 37 /percent put 38 /ampersand put 39 /quoteright put 40 /parenleft put 41 /parenright put 42 /asterisk put 43 /plus put 44 /comma put 45 /hyphen put 46 /period put 47 /slash put 48 /zero put 49 /one put dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup 50 /two put 51 /three put 52 /four put 53 /five put 54 /six put 55 /seven put 56 /eight put 57 /nine put 58 /colon put 59 /semicolon put 60 /exclamdown put 61 /equal put 62 /questiondown put 63 /question put 64 /at put 65 /A put 66 /B put 67 /C put 68 /D put 69 /E put 70 /F put 71 /G put 72 /H put 73 /I put 74 /J put 75 /K put 76 /L put 77 /M put 78 /N put 79 /O put 80 /P put 81 /Q put 82 /R put 83 /S put 84 /T put 85 /U put 86 /V put 87 /W put 88 /X put 89 /Y put 90 /Z put 91 /bracketleft put 92 /quotedblleft put 93 /bracketright put 94 /circumflex put 95 /dotaccent put 96 /quoteleft put 97 /a put 98 /b put 99 /c put 100 /d put 101 /e put 102 /f put 103 /g put 104 /h put 105 /i put 106 /j put 107 /k put 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 194 /chi put dup 195 /psi put dup 196 /tie put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 19 /iota put dup 20 /kappa put dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup dup 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 /lambda put /mu put /nu put /xi put /pi put /rho put /sigma put /tau put /upsilon put /phi put /chi put /psi put /omega put /epsilon put /theta1 put /pi1 put /rho1 put /sigma1 put /phi1 put /arrowlefttophalf put /arrowleftbothalf put 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East Los Angeles College - MATHS - 3830
MATH 3830 Handout 2 Page 1Math 3830 Handout 2Analyzing shapes in R1. I have prepared a set of routines to facilitate the analysis of shapes in R. These routines use some of the datasets collected in the library "shapes" created by Ian Drdyen. 2.
Rutgers - MATH - 504
East Los Angeles College - MATHS - 3830
MATH 3830 Handout 3 Page 1MATH 3830 Handout 3 Dependence of shape on sizeOverviewThis handout studies the dependence of shape on size for the Globorotalia data. The following R program computes the centroid size for each configuration and labels
Rutgers - MATH - 504
%!PS-Adobe-2.0 %Creator: dvips(k) 5.83 Copyright 1998 Radical Eye Software %Title: hw6.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 596 842 %DocumentFonts: CMR7 CMBX10 CMR10 CMSY10 CMMI10 CMMI7 CMSY7 MSBM7 %+ CMSL10 MSBM10 CMEX10 %EndComments %
East Los Angeles College - MATHS - 5835
MATH 5835 Solution Practical 1 Page 1Solution Practical 11. A needle of length a is dropped "at random" on the plane containing a grid of horizontal lines separated by one unit. The position and orientation of the needle can be described by the co
Rutgers - MATH - 504
Rutgers - MATH - 504
%!PS-Adobe-2.0 %Creator: dvips(k) 5.83 Copyright 1998 Radical Eye Software %Title: hw7.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 596 842 %DocumentFonts: CMR7 CMBX10 CMR10 CMMI10 CMSY10 CMMI7 CMR5 CMTI10 %+ MSBM10 %EndComments %DVIPSWebPage:
Rutgers - MATH - 504
Rutgers - MATH - 504
%!PS-Adobe-2.0 %Creator: dvips(k) 5.83 Copyright 1998 Radical Eye Software %Title: hw8.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 596 842 %DocumentFonts: CMR7 CMBX10 CMR10 CMSY10 CMMI10 CMMI7 CMSY7 MSBM7 CMMI5 %+ CMTI10 MSBM10 CMR5 CMEX10 CMS
Rutgers - MATH - 504
East Los Angeles College - MATHS - 1917
University of Leeds MATH1915/7 MATH1915/1917 Basic Use of Computers for MathematicsPractical 5Calculus Using MapleRecall how to : Open Maple: Start - Programs - Miscellaneous Type Ctrl M every time you want to type a new calculation. To delete
Rutgers - MATH - 504
%!PS-Adobe-2.0 %Creator: dvips(k) 5.83 Copyright 1998 Radical Eye Software %Title: hw9.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 596 842 %DocumentFonts: CMR7 CMBX10 CMMI10 CMR10 MSBM10 CMSL10 CMSY10 CMMI7 %+ CMEX10 CMSY7 CMTI10 %EndComments
Rutgers - MATH - 504
Rutgers - MATH - 504
%!PS-Adobe-2.0 %Creator: dvips(k) 5.83 Copyright 1998 Radical Eye Software %Title: hw10.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 596 842 %DocumentFonts: CMR7 CMBX10 CMR10 CMMI7 CMR5 CMSY10 MSBM10 CMMI10 %+ CMTI10 CMEX10 CMSY7 CMMI5 CMSL10 M
Rutgers - MATH - 504
Rutgers - MATH - 403
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Rutgers - MATH - 403
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Rutgers - MATH - 403
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Rutgers - MATH - 403
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Rutgers - MATH - 403
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Rutgers - MATH - 403
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Rutgers - MATH - 403
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Rutgers - MATH - 403
Math 403:02Student informationPlease print! Name Major(s) E-mail addressA Rutgers address is best.I'd like to post this information on a web page connected with the course. I hope this will help students get in touch with each other and work to
Rutgers - MATH - 403
Math 403, section 2Entrance "exam"Due at the beginning of class, Thursday, January 20, 200221. (4) Compute1dx and simplify. 1 - 2x22. (8) If u(x, y) = ey x , what are5u 2u and ? x5 y 2 v v = x + y and = x - y. x y3. (10) Find all func
Rutgers - MATH - 151
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Rutgers - MATH - 151
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Rutgers - MATH - 151
#9Problems for 151:070911/7/20071. Suppose 5x3 y - 3xy 2 + y 3 = 6 . (1, 2) is a point on this curve. Is the curve concave up or concave down at (1, 2)? dy implicitly and Explicit way to go y can be solved as a Implicit way to go Find dx functi
Rutgers - MATH - 151
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East Los Angeles College - MATHS - 3830
xb=bk.coords(glob.dat,baseline=c(1,3)y=t(xb[2,]) # 20 x 2 matrixya=xb[2,drop=FALSE] # 1 x 2 x 20 array (for just landmark 2)sz=size.configs(glob.dat)szszr=round(sz/10)szrmod1=lm(y~sz)summary(mod1)anova(mod1)cc=coef(mod1)[2,]ccslope=cc[2
Maryland - ENDEAVORS - 0812
FOR ALUMNI AND FRIENDS OF THE COLLEGE OF EDUCATION, UNIVERSITY OF MARYLANDDECEMBERYE AR -E NDEndeavors2008 |VOLUME 11IS SU E| ISSUE 20College Welcomes New Members to Alumni Board of Directors~ Toni Ungaretti, Ph.D. ('92),Alumni Chapter
Rutgers - MATH - 151
Math 151:7-91111 0000 1111 0000 1111 0000 1111 00001111 0000 1111 0000 1111 0000 1111 0000 1111 0000 111 000 111 000 111 000 111 000 111 000 1111111111111 0000000000000 1111111111111 0000000000000 1111111111111 0000000000000 1111111111111 0000000
Rutgers - MATH - 151
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Rutgers - MATH - 151
Math 151:7-9 Name FindTest on derivativesSection10/17/2007dy in each case. Please do not simplify your answers. For example, you may (and dx should!) write the derivative of 37x46 as (46)37x45 .1. y = 174x + ln x3 - 7x2 + 44 Answer 174x ln(1
Rutgers - MATH - 151
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Rutgers - MATH - 151
640:151:0709Answers to version A of the First Exam10/14/2006Here are answers that would earn full credit. Other methods may also be valid. (12) 1. Compute the derivatives of the functions shown. In this problem, you may write only the answers a
Rutgers - MATH - 151
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Rutgers - MATH - 151
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Rutgers - MATH - 151
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Rutgers - MATH - 151
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Rutgers - MATH - 151
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Rutgers - MATH - 151
Rutgers - MATH - 151
#2Problems for 151:07099/12/20071. A surveyor stands on flat ground at an unknown distance from a tall building. She measures the angle from the horizontal ground to the top of the building; this angle is /3. Next she paces 40 feet further away
Rutgers - MATH - 151
#1Problems for 151:07099/5/20071. Suppose f (x) = x - |x - 3| . f (x) is defined for all real numbers. a) Find the graph of y = f (x) in the window -5 x 5 and 0 y 10. b) Give a piecewise definition (on all of its domain) of f (x) without us
East Los Angeles College - LEEDS - 3772
MATH 3772, November 2008.Summary of module evaluation formsOut of thirty three people enrolled on this module, twenty five took the time to fill in an return a module evaluation form - thank you very much to those people. The results are given in
Rutgers - MATH - 151
Math 151:07-08-09 (Please circle your section number!)Section 7's recitation meets Wednesday 1 (8:40-10:00 AM in ARC 203). Section 8's recitation meets Wednesday 2 (10:20-11:40 AM in SEC 218). Section 9's recitation meets Wednesday 3 (12:00-1:20 AM
East Los Angeles College - DOCS - 2735
MATH 2735 handout 14Multiple comparisonsProblems with multiple comparisonsIf a one-way fixed effects ANOVA has said that there are differences among the t treatments, we would like to be able to say which treatments are significantly different to
East Los Angeles College - DOCS - 2735
MATH 2735 exercises 3Handed out in lecture 7. Hand in your answers to all questions in lecture 11. Your work will be marked out of five and one mark will be deducted for each day that your work is late.1 Recall the sugar fermentation data from ex
East Los Angeles College - DOCS - 2735
MATH 2735 handout 12Estimating components of varianceComponents of variance for dyestuff dataRecall the dyestuff data from handout 11. We had n = 6 observations on each of t = 6 groups, so N = 36, and the mean squares were MSA = 83.095 and MSE =
East Los Angeles College - DOCS - 2735
MATH 2735 solutions 11 The required percentage points are Percentage point table value (a) F4,6 (5%) 4.534 (b) F6,4 (5%) 6.613 (c) F12,2 (5%) 19.413 (d) F3,3 (5%) 9.277 (e) F3,10 (5%) 3.708 (f) F3,20 (5%) 3.098 (g) F3,5 (5%) 5.409 (h) F12,5 (5%) 4.
East Los Angeles College - LEEDS - 3772
1MATH 3772 module survey results, 2004.Summary of module evaluation formsNineteen people filled in a module evaluation form - thank you very much to those people. The raw scores are tabulated below and shown in these bar plots. As a reminder, th
Rutgers - MATH - 421
1(18) 1. Here is a graph of the piecewise linear function f (t). f (t) is defined for t 0. The graph connects the points (0, 2) and (1, 0). f (t) = 0 for all t 1. a) Use the definition of the Laplace transform to find the Laplace transform F (s) o
Delaware - IR - 0506
Rutgers - MATH - 421
Math 421Some two-dimensional problemsDecember 5, 2005The last two lectures will discuss some aspects of solutions of the heat and wave equations for two-dimensional regions. Sections 13.5 and 13.8 of the text contain some relevant material. In
Rutgers - MATH - 421
Math 421An example of two-dimensional heat flowDecember 5u=0 here u=0 here u=1 here0.5 1 1.5 2 2.5 3 yI want steady-state solutions for the two-dimensional heat equation, utt = uxx + uyy , in one the square which has sides parallel to the coo
Rutgers - MATH - 421
Math 421:01Some vibration examplesDecember 1, 2005I defined a small triangular initial condition for Maple as an initial position: >F:=x->piecewise(x<Pi/3,0,x<Pi/3+Pi/12,x-(Pi/3),x<Pi/2,Pi/3+Pi/6-x,0); Here is a picture of the initial perturbat
Rutgers - MATH - 421
Math 421:01One heat flow exampleNovember 21, 2005The Maple command which follows defines a function piecewise. In the language of Laplace transforms, F (x) = U(x - ) - U(x - ). It is a block of height 1 in the interval , and is 0 otherwise.
Rutgers - MATH - 421
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Rutgers - MATH - 421
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Rutgers - MATH - 421
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Rutgers - MATH - 421
Math 421 Some Fourier series examplesSuppose we define a function F (x) in Maple. Below are some Maple commands which compute Fourier coefficients and partial sums of the Fourier series. The responses have generally not been given (they are mostly e
Maryville MO - NYSGIH - 182002