(original) (raw)

%!PS-Adobe-2.0 %%Creator: dvips 5.511 Copyright 1986, 1993 Radical Eye Software %%Title: All.dvi %%CreationDate: Fri Oct 16 15:52:21 1998 %%Pages: 6 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSCommandLine: dvips -pp 35-40 All.dvi -o /net/blagny/algo/web/seminars/sem97-98/bradley.ps %DVIPSSource: TeX output 1998.10.05:1746 %%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 /@rigin{isls{[0 -1 1 0 0 0] concat}if 72 Resolution div 72 VResolution div neg scale isls{Resolution hsize -72 div mul 0 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 %%BeginProcSet: special.pro TeXDict begin /SDict 200 dict N SDict begin /@SpecialDefaults{/hs 612 N /vs 792 N /ho 0 N /vo 0 N /hsc 1 N /vsc 1 N /ang 0 N /CLIP 0 N /rwiSeen false N /rhiSeen false N /letter{}N /note{}N /a4{}N /legal{}N}B /@scaleunit 100 N /@hscale{@scaleunit div /hsc X}B /@vscale{@scaleunit div /vsc X}B /@hsize{/hs X /CLIP 1 N}B /@vsize{/vs X /CLIP 1 N}B /@clip{/CLIP 2 N}B /@hoffset{/ho X}B /@voffset{/vo X}B /@angle{/ang X}B /@rwi{10 div /rwi X /rwiSeen true N}B /@rhi {10 div /rhi X /rhiSeen true N}B /@llx{/llx X}B /@lly{/lly X}B /@urx{/urx X}B /@ury{/ury X}B /magscale true def end /@MacSetUp{userdict /md known{userdict /md get type /dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N /note{}N /legal{ }N /od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{closepath}}pathforall newpath counttomark array astore /gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}N /txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N /cp{pop pop showpage pm restore}N end}if}if}N /normalscale{Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale}if 0 setgray}N /psfts{S 65781.76 div N}N /startTexFig{/psf$SavedState save N userdict maxlength dict begin /magscale false def normalscale currentpoint TR /psf$ury psfts /psf$urx psfts /psf$lly psfts /psf$llx psfts /psf$y psfts /psf$x psfts currentpoint /psf$cy X /psf$cx X /psf$sx psf$x psf$urx psf$llx sub div N /psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR /showpage{}N /erasepage{}N /copypage{}N /p 3 def @MacSetUp}N /doclip{psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N /endTexFig{end psf$SavedState restore}N /@beginspecial{ SDict begin /SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count /ocount X /dcount countdictstack N}N /@setspecial{CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{ rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if /showpage{}N /erasepage{}N /copypage{}N newpath}N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end}repeat grestore SpecialSave restore end}N /@defspecial{SDict begin}N /@fedspecial{end}B /li{lineto}B /rl{ rlineto}B /rc{rcurveto}B /np{/SaveX currentpoint /SaveY X N 1 setlinecap newpath}N /st{stroke SaveX SaveY moveto}N /fil{fill SaveX SaveY moveto}N /ellipse{/endangle X /startangle X /yrad X /xrad X /savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet TeXDict begin 39158280 55380996 1000 300 300 (/a/home/pommard/algo/salvy/Tex/Sem/Sem97-98/All.dvi) @start /Fa 6 118 df<07801FE0387070706038E038FFF8FFF8E0006000703838381FF007C00D0E7E8D 12>101 D<007E00FF01C70382038003807FFEFFFE038003800380038003800380038003800380 03803FF83FF81014809312>I108 D<1FF03FF06070C070E0007F003FE00FF0 00786018E018F030FFE0DFC00D0E7E8D12>115 D<06000E000E000E007FF8FFF80E000E000E00 0E000E000E000E000E380E380E3807F003C00D127F9112>II E /Fb 11 118 df<00700000F80000F80000 D80000D80001DC0001DC0001DC00018C00038E00038E00038E00038E0003060007070007070007 07000707000FFF800FFF800FFF800E03800E03801C01C01C01C07F07F0FF8FF87F07F0151C7F9B 18>65 D<7FFF00FFFF807FFF0001C00001C00001C00001C00001C00001C00001C00001C00001C0 0001C00001C00001C00001C00001C00001C00001C00001C00001C00001C00001C00001C00001C0 007FFF00FFFF807FFF00111C7D9B18>73 D77 D<0FF8003FFE007FFF00780F00700700F00780E00380E00380E00380E00380E00380E00380E003 80E00380E00380E00380E00380E00380E00380E00380E00380E00380F00780700700780F007FFF 003FFE000FF800111C7D9B18>79 D<7F8FE07F9FE07F8FE00E07000F0700070E00078E00039C00 03DC0001F80001F80000F00000F00000700000F00000F80001F80001DC00039E00038E00070F00 0707000E07800E03801E03C07F07F0FF8FF87F07F0151C7F9B18>88 D<01F00007FC001FFE003E 0F00380780700380700380E001C0E001C0FFFFC0FFFFC0FFFFC0E000007000007001C03801C03E 03C01FFF8007FF0001FC0012147D9318>101 D<001F80007FC000FFE000E1E001C0C001C00001 C00001C0007FFFC0FFFFC0FFFFC001C00001C00001C00001C00001C00001C00001C00001C00001 C00001C00001C00001C00001C00001C0007FFF007FFF007FFF00131C7F9B18>I<7FE000FFE000 7FE00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E000 00E00000E00000E00000E00000E00000E00000E00000E00000E00000E0007FFFC0FFFFE07FFFC0 131C7E9B18>108 D<07F7003FFF007FFF00780F00E00700E00700E007007C00007FE0001FFC00 03FE00001F00600780E00380E00380F00380F80F00FFFF00FFFC00E7F00011147D9318>115 D<0180000380000380000380000380007FFFC0FFFFC0FFFFC00380000380000380000380000380 000380000380000380000380000380400380E00380E00380E001C1C001FFC000FF80003E001319 7F9818>I<7E07E0FE0FE07E07E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E 00E00E00E00E00E00E00E00E01E00F03E007FFFC03FFFE01FCFC1714809318>I E /Fc 9 108 df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d 2 4 df0 D<0C000C008C40EDC07F800C007F80EDC08C400C000C000A0B7D8B10>3 D E /Fe 8 115 df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f 14 113 df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g 8 107 df0 D<60F0F06004047D890A>I21 D<0F8007C019E01C202070301040184008C00C8004800780048007000480038004800780048004 C00C400860082030381010E01E600F8007C01E0E7E8D23>49 D<01FF8007FF800E000018000030 0000600000600000600000C00000C00000FFFF80FFFF80C00000C0000060000060000060000030 00001800000E000007FF8001FF8011167D9218>I<007800C00180030003000300030003000300 0300030003000300030006000C00F0000C00060003000300030003000300030003000300030003 000300018000C000780D217E9812>102 DI106 D E /Fh 27 91 df<000180000300000600000C0000180000 380000300000600000E00000C0000180000380000300000700000700000600000E00000C00001C 00001C0000180000380000380000380000380000700000700000700000700000700000700000E0 0000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E0 0000E00000E00000E00000E00000E0000070000070000070000070000070000070000038000038 00003800003800001800001C00001C00000C00000E000006000007000007000003000003800001 800000C00000E000006000003000003800001800000C00000600000300000180115178811B>16 DI<00000C0000180000300000600000C00001C000038000 0700000600000E00001C00001C0000380000700000700000E00000E00001E00001C00003C00003 80000380000780000700000700000F00000E00000E00001E00001E00001C00003C00003C00003C 00003C0000380000780000780000780000780000780000780000780000700000F00000F00000F0 0000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F0 0000F00000F00000F00000F0000070000078000078000078000078000078000078000078000038 00003C00003C00003C00003C00001C00001E00001E00000E00000E00000F000007000007000007 800003800003800003C00001C00001E00000E00000E000007000007000003800001C00001C0000 0E000006000007000003800001C00000C000006000003000001800000C166C778121>II34 DI<00000C00003C00007800 01E00003C0000380000700000F00001E00001E00003C00003C00003C0000780000780000780000 780000780000780000780000780000780000780000780000780000780000780000780000780000 780000780000780000780000780000780000780000780000780000780000780000780000780000 780000780000780000780000780000780000780000780000780000780000780000780000780000 F00000F00000F00000E00001E00001C00003C0000780000700000E00001C0000780000E00000E0 00007800001C00000E000007000007800003C00001C00001E00000E00000F00000F00000F00000 780000780000780000780000780000780000780000780000780000780000780000780000780000 780000780000780000780000780000780000780000780000780000780000780000780000780000 780000780000780000780000780000780000780000780000780000780000780000780000780000 7800007800007800003C00003C00003C00001E00001E00000F000007000003800003C00001E000 007800003C00000C1688798125>40 D<0000018000000300000007000000060000000C0000001C 000000380000003000000070000000E0000000E0000001C0000001C00000038000000780000007 0000000F0000000E0000001E0000001C0000003C0000003C000000380000007800000078000000 F0000000F0000000F0000001E0000001E0000001E0000003C0000003C0000003C0000007C00000 0780000007800000078000000F8000000F0000000F0000000F0000001F0000001F0000001F0000 001E0000001E0000001E0000003E0000003E0000003E0000003E0000003C0000003C0000007C00 00007C0000007C0000007C0000007C0000007C0000007C0000007C0000007C0000007800000078 000000F8000000F8000000F8000000F8000000F8000000F8000000F8000000F8000000F8000000 F8000000F8000000F8000000F8000000F8000000F8000000F8000000F80000001952738028>48 DIIII<001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C 001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C 001C001C001C001C001C001C001C001C001C001C001C001CFFFCFFFCFFFC0E5180811E>I<000C 003C007800F001E003C007C00F801F001F003F003E007E007E007E007C00FC00FC00FC00FC00FC 00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00 FC000E296F7E28>56 DII<007E007E007E00 7E007E007E007E007E007E007E007E007E007E007E007E007E007E007E007E007E007E007E007E 007E007E007C00FC00FC00F800F801F001F003E003E007C00F801F003E007800F000C0000F2978 8028>I<007E007E007E007E007E007E007E007E007E007E007E007E007E007E007E007E007E00 7E007E007E007E007E007E007E007E007E007C00FC00FC00F800F801F001F003E003E007C00780 0F001E003C007800E000E00078003C001E000F00078007C003E003E001F001F000F800F800FC00 FC007C007E007E007E007E007E007E007E007E007E007E007E007E007E007E007E007E007E007E 007E007E007E007E007E007E007E007E0F54788028>II64 D<00000F8000000F8000000F80 00000F8000000F8000000F8000000F8000000F8000000F8000000F8000000F8000000F8000000F 8000000F8000000F8000000F8000000F8000000F0000000F0000001F0000001F0000001F000000 1F0000001F0000001F0000001F0000001F0000001F0000001E0000001E0000003E0000003E0000 003E0000003E0000003C0000003C0000003C0000007C0000007C0000007C000000780000007800 000078000000F8000000F0000000F0000000F0000001F0000001E0000001E0000001E0000003C0 000003C0000003C000000780000007800000078000000F0000000F0000000E0000001E0000001E 0000001C0000003C000000380000007800000070000000F0000000E0000001C0000001C0000003 8000000380000007000000060000000E0000001C00000018000000300000007000000060000000 C000000019527F8228>I80 DI<0000F800018400030E00031E00071E00070C00060000060000 0E00000E00000E00000E00000E00000E00001E00001E00001E00001E00001E00001C00001C0000 3C00003C00003C00003C00003C00003C00003C00003C00003C0000380000380000780000780000 780000780000780000700000700000700000700000700000700000600000600060E000F0C000F0 C000E180004300003E000017337D7F15>I88 DI<00000000F000000001880000 00039C000000033C000000073C000000071800000006000000000E000000000E000000000E0000 00001E000000001C000000001C000000003C000000003C00000000380000000038000000007800 000000780000000078000000007000000000F000000000F000000000F000000000F000000001F0 00000001E000000001E000000001E000000001E000000003E000000003C000000003C000000003 C000000007C000000007C000000007C000000007800000000F800000000F800000000F80000000 0F800000000F800000001F000000001F000000001F000000001F000000001F000000003E000000 003E000000003E000000003E000000003E000000007C000000007C000000007C000000007C0000 00007C00000000F800000000F800000000F800000000F800000000F800000000F000000001F000 000001F000000001F000000001E000000001E000000001E000000003E000000003C000000003C0 00000003C000000003C000000007C0000000078000000007800000000780000000078000000007 000000000F000000000F000000000F000000000E000000000E000000001E000000001E00000000 1C000000001C000000003C00000000380000000038000000007000000000700000006060000000 F0E0000000F0C0000000E18000000043000000003E0000000026657D7F19>I E /Fi 22 127 df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j 12 122 df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k 1 83 df82 D E /Fl 38 127 df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m 21 120 df<70F8F8F8700505798414>46 D<0006000E000E001C001C003800380070007000E000 E001C001C0038003800380070007000E000E001C001C003800380070007000E000E000C0000F1D 7E9914>I<0300030007000F003F00F70047000700070007000700070007000700070007000700 07000700070007007FF07FF00C177C9614>49 D<0FE03FF8783C701CE00EE00EE00EE00E701C1E F003801FF03838701CE00EE00EE00EE00EF01E701C38381FF007C00F177E9614>56 D<07C01FE038307038601CE01CE00CE00EE00E601E701E383E1FEE07CE000E001C001C001C7038 707070E03FC01F000F177E9614>I<70F8F8F87000000000000070F8F8F8700510798F14>I<1FC0 007FF000707800201800001C00001C0007FC001FFC003C1C00701C00E01C00E01C00E01C00707C 003FFF800F8F8011107E8F14>97 D<03F80FFC1C1C380870006000E000E000E000E00060007000 380E1C1E0FFC03F00F107E8F14>99 D<07E00FF01C38301C700CE00EE00EFFFEFFFEE000600070 00380E1C1E0FFC03F00F107E8F14>101 D<007C00FE01CE03840380038003807FFEFFFE038003 8003800380038003800380038003800380038003807FFC7FFC0F177F9614>I104 D<030007800780030000000000000000007F807F80038003800380038003800380038003800380 038003800380FFFCFFFC0E187D9714>I108 DII112 D114 D<0FD83FF86038C038C038F0007F803FF007F8001C 6006E006F006F81CFFF8CFE00F107E8F14>I<030007000700070007007FFCFFFC070007000700 07000700070007000700070E070E070E070C03FC00F00F157F9414>II119 D E /Fn 4 51 df<0204081030206040 40C0C0C0C0C0C0C0C0404060203010080402071A7F920C>40 D<8040201018080C040406060606 0606060604040C081810204080071A7E920C>I<0C003C00CC000C000C000C000C000C000C000C 000C000C000C000C000C00FF8009107E8F0F>49 D<1F00618040C08060C0600060006000C00180 030006000C00102020207FC0FFC00B107F8F0F>I E /Fo 37 123 df<00003F80FF380000E1C3 83B8000183C607F0000383CE07F00003819C03700007001C00700007001C00E00007003800E000 07003800E0000E003800E0000E003801C0000E003801C000FFFFFFFFC0000E007001C0001C0070 0380001C00700380001C00700380001C00700380001C00E00700001C00E00700003800E0070000 3800E00700003800E00E00003801C00E00003801C00E00007001C00E20007001C01C40007001C0 1C40007003801C40007003801C4000E003800C8000E00380070000E00300000000E00700000000 C00700000001C00600000031860E000000798F0C000000F31E18000000620C300000003C07C000 00002D29829F29>15 D<1C3C3C3C3C040408081020204080060E7D840E>44 D<70F8F8F0E005057B840E>46 D<000200020006000E003C00DC031C001C003800380038003800 7000700070007000E000E000E000E001C001C001C001C003800380038003800780FFF80F1E7B9D 17>49 D<01FFFFFE001E001C001E000C001E0004001E0004003C0004003C0004003C0004003C00 040078080800780800007808000078180000F0300000FFF00000F0300000F0300001E0200001E0 200001E0200001E0001003C0002003C0002003C0004003C0004007800080078001800780010007 8007000F001F00FFFFFE001F1F7D9E1F>69 D<01FFFFFC001E0038001E0018001E0008001E0008 003C0008003C0008003C0008003C00080078001000780800007808000078080000F0100000F030 0000FFF00000F0300001E0200001E0200001E0200001E0200003C0000003C0000003C0000003C0 0000078000000780000007800000078000000F800000FFF800001E1F7D9E1E>I<01FFF0001F00 001E00001E00001E00003C00003C00003C00003C0000780000780000780000780000F00000F000 00F00000F00001E00001E00001E00001E00003C00003C00003C00003C000078000078000078000 0780000F8000FFF800141F7D9E12>73 D<01FFF800001F0000001E0000001E0000001E0000003C 0000003C0000003C0000003C00000078000000780000007800000078000000F0000000F0000000 F0000000F0000001E0000001E0000001E0000001E0008003C0010003C0010003C0030003C00200 078006000780060007800C0007801C000F007800FFFFF800191F7D9E1D>76 D<01FE00007FC0001E0000FC00001E0000F80000170001780000170001780000270002F0000027 0004F00000270004F00000270008F00000470009E00000470011E00000470021E00000470021E0 0000870043C00000838043C00000838083C00000838083C0000103810780000103820780000103 820780000103840780000203840F00000203880F00000203900F00000203900F00000401E01E00 000401E01E00000401C01E00000C01801E00001C01803E0000FF8103FFC0002A1F7D9E29>I<01 FFFF00001E03C0001E00E0001E0070001E0078003C0078003C0078003C0078003C0078007800F0 007800F0007801E0007801C000F0070000F01E0000FFF00000F0380001E01C0001E01E0001E00E 0001E00F0003C01E0003C01E0003C01E0003C01E0007803C0007803C0807803C0807803C100F80 1C10FFF00C20000007C01D207D9E21>82 D<0FFFFFF01E0780E018078020100780202007802020 0F0020600F0020400F0020400F0020801E0040001E0000001E0000001E0000003C0000003C0000 003C0000003C00000078000000780000007800000078000000F0000000F0000000F0000000F000 0001E0000001E0000001E0000001E0000003E00000FFFF00001C1F789E21>84 D86 D<007FFFF800FC00F000E001E000C003C0008007 800180078001000F0001001E0001003C00020078000000F8000000F0000001E0000003C0000007 8000000F0000000F0000001E0000003C00000078010000F0010001F0020001E0020003C0060007 8004000F000C001E0008003E0018003C0038007801F000FFFFF0001D1F7D9E1C>90 D<00F1800389C00707800E03801C03803C0380380700780700780700780700F00E00F00E00F00E 00F00E20F01C40F01C40703C40705C40308C800F070013147C9317>97 D<07803F800700070007 0007000E000E000E000E001C001C001CF01D0C3A0E3C0E380F380F700F700F700F700FE01EE01E E01EE01CE03CE038607060E031C01F0010207B9F15>I<007E0001C1000300800E07801E07801C 07003C0200780000780000780000F00000F00000F00000F00000F0000070010070020030040018 380007C00011147C9315>I<0000780003F80000700000700000700000700000E00000E00000E0 0000E00001C00001C000F1C00389C00707800E03801C03803C0380380700780700780700780700 F00E00F00E00F00E00F00E20F01C40F01C40703C40705C40308C800F070015207C9F17>I<007C 01C207010E011C013C013802780C7BF07C00F000F000F000F0007000700170023804183807C010 147C9315>I<00007800019C00033C00033C000718000700000700000E00000E00000E00000E00 000E0001FFE0001C00001C00001C00001C00003800003800003800003800003800007000007000 00700000700000700000700000E00000E00000E00000E00000C00001C00001C000018000318000 7B0000F300006600003C00001629829F0E>I<003C6000E27001C1E00380E00700E00F00E00E01 C01E01C01E01C01E01C03C03803C03803C03803C03803C07003C07001C0F001C17000C2E0003CE 00000E00000E00001C00001C00301C00783800F0700060E0003F8000141D7E9315>I<01E0000F E00001C00001C00001C00001C000038000038000038000038000070000070000071E000763000E 81800F01C00E01C00E01C01C03801C03801C03801C0380380700380700380700380E10700E2070 0C20701C20700C40E00CC060070014207D9F17>I<00C001E001E001C000000000000000000000 000000000E003300230043804300470087000E000E000E001C001C001C00384038803080708031 0033001C000B1F7C9E0E>I<03C01FC0038003800380038007000700070007000E000E000E000E 001C001C001C001C0038003800380038007000700070007100E200E200E200E200640038000A20 7C9F0C>108 D<1C0F80F0002630C318004740640C004780680E004700700E004700700E008E00 E01C000E00E01C000E00E01C000E00E01C001C01C038001C01C038001C01C038001C01C0708038 038071003803806100380380E10038038062007007006600300300380021147C9325>I<1C0F80 2630C04740604780604700704700708E00E00E00E00E00E00E00E01C01C01C01C01C01C01C0384 3803883803083807083803107003303001C016147C931A>I<007C0001C3000301800E01C01E01 C01C01E03C01E07801E07801E07801E0F003C0F003C0F003C0F00780F00700700F00700E003018 0018700007C00013147C9317>I<01C1E002621804741C04781C04701E04701E08E01E00E01E00 E01E00E01E01C03C01C03C01C03C01C0380380780380700380E003C1C0072380071E0007000007 00000E00000E00000E00000E00001C00001C0000FFC000171D809317>I<00F0400388C0070580 0E03801C03803C0380380700780700780700780700F00E00F00E00F00E00F00E00F01C00F01C00 703C00705C0030B8000F380000380000380000700000700000700000700000E00000E0000FFE00 121D7C9315>I<1C1E002661004783804787804707804703008E00000E00000E00000E00001C00 001C00001C00001C000038000038000038000038000070000030000011147C9313>I<00FC0302 06010C030C070C060C000F800FF007F803FC003E000E700EF00CF00CE008401020601F8010147D 9313>I<018001C0038003800380038007000700FFF007000E000E000E000E001C001C001C001C 003800380038003820704070407080708031001E000C1C7C9B0F>I<0E00C03300E02301C04381 C04301C04701C08703800E03800E03800E03801C07001C07001C07001C07101C0E20180E20180E 201C1E200C264007C38014147C9318>I<0E03803307802307C04383C04301C04700C08700800E 00800E00800E00801C01001C01001C01001C02001C02001C04001C04001C08000E300003C00012 147C9315>I<0E00C1C03300E3C02301C3E04381C1E04301C0E04701C060870380400E0380400E 0380400E0380401C0700801C0700801C0700801C0701001C0701001C0602001C0F02000C0F0400 0E13080003E1F0001B147C931E>I<0383800CC4401068E01071E02071E02070C040E00000E000 00E00000E00001C00001C00001C00001C040638080F38080F38100E5810084C60078780013147D 9315>I<0E00C03300E02301C04381C04301C04701C08703800E03800E03800E03801C07001C07 001C07001C07001C0E00180E00180E001C1E000C3C0007DC00001C00001C00003800F03800F070 00E06000C0C0004380003E0000131D7C9316>I<01C04003E08007F1800C1F0008020000040000 08000010000020000040000080000100000200000401000802001002003E0C0063FC0041F80080 E00012147D9313>I E /Fp 18 121 df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q 11 122 df66 D<0FF8001C1E003E0F803E07803E07C01C07C00007C0007FC007E7C0 1F07C03C07C07C07C0F807C0F807C0F807C0780BC03E13F80FE1F815127F9117>97 DI<03F8F00E0F381E0F381C07303C07803C07803C07803C 07801C07001E0F000E0E001BF8001000001800001800001FFF001FFFC00FFFE01FFFF07801F8F0 0078F00078F000787000707800F01E03C007FF00151B7F9118>103 DI<1E003F003F003F003F001E00000000000000000000000000FF00FF001F001F001F 001F001F001F001F001F001F001F001F001F001F001F00FFE0FFE00B1E7F9D0E>I108 D<01FC000F07801C01C03C01E07800F078 00F0F800F8F800F8F800F8F800F8F800F8F800F87800F07800F03C01E01E03C00F078001FC0015 127F9118>111 DI114 D121 D E /Fr 35 122 df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s 38 124 df<000FE000007FF80000F81C0001E07C0003E07C0007C07C0007C07C0007C0380007C0 000007C0000007C0000007C1FE00FFFFFE00FFFFFE0007C03E0007C03E0007C03E0007C03E0007 C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E00 07C03E0007C03E003FF9FFC03FF9FFC01A20809F1D>12 D<387CFEFEFE7C3807077C860F>46 D<00E00001E0000FE000FFE000F3E00003E00003E00003E00003E00003E00003E00003E00003E0 0003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E0 0003E000FFFF80FFFF80111D7C9C1A>49 D<07F0001FFE00383F007C1F80FE0FC0FE0FC0FE0FE0 FE07E07C07E03807E0000FE0000FC0000FC0001F80001F00003E0000780000F00000E00001C000 0380600700600E00601C00E01FFFC03FFFC07FFFC0FFFFC0FFFFC0131D7D9C1A>I<01FC0007FF 000E0F801E0FC03F07E03F07E03F07E03F07E01E0FC0000FC0000F80001F0001FC0001FC00000F 800007C00003E00003F00003F83803F87C03F8FE03F8FE03F8FE03F0FC03F07807E03C0FC01FFF 8003FC00151D7E9C1A>I<0001C00003C00007C00007C0000FC0001FC0003BC00073C00063C000 C3C00183C00383C00703C00E03C00C03C01803C03803C07003C0E003C0FFFFFEFFFFFE0007C000 07C00007C00007C00007C00007C000FFFE00FFFE171D7F9C1A>I<3803803FFF803FFF003FFE00 3FFC003FF0003F800030000030000030000030000033F80037FE003C1F00380F801007C00007C0 0007E00007E07807E0FC07E0FC07E0FC07E0FC07C0780FC0600F80381F001FFC0007F000131D7D 9C1A>I<003F0001FFC007E0E00F81E01F03F01E03F03E03F07C03F07C01E07C0000FC1000FCFF 00FDFFC0FD03E0FE01F0FE01F0FC01F8FC01F8FC01F8FC01F87C01F87C01F87C01F83C01F03E01 F01E03E00F07C007FF8001FE00151D7E9C1A>I<6000007FFFF87FFFF87FFFF07FFFE07FFFC0E0 0180C00300C00300C00600000C0000180000380000380000780000700000F00000F00001F00001 F00001F00001F00003F00003F00003F00003F00003F00003F00001E00000C000151E7D9D1A>I< 01FC0007FF000F07801E03C01C01E03C01E03C01E03E01E03F01E03FC3C01FE3801FFF000FFE00 07FF8007FFC01FFFE03C3FF0780FF07803F8F001F8F000F8F00078F00078F000707800707C00E0 3E03C00FFF8003FC00151D7E9C1A>I<0007FC02003FFF0E00FE03DE03F000FE07E0003E0FC000 1E1F80001E3F00000E3F00000E7F0000067E0000067E000006FE000000FE000000FE000000FE00 0000FE000000FE000000FE0000007E0000007E0000067F0000063F0000063F00000C1F80000C0F C0001807E0003803F0007000FE01C0003FFF800007FC001F1F7D9E26>67 DI73 D77 D80 D82 D<03FC080FFF381E03F83800F870007870 0038F00038F00018F00018F80000FC00007FC0007FFE003FFF801FFFE00FFFF007FFF000FFF800 07F80000FC00007C00003CC0003CC0003CC0003CE00038E00078F80070FE01E0E7FFC081FF0016 1F7D9E1D>I<7FFFFFFC7FFFFFFC7C07E07C7007E01C6007E00C6007E00CE007E00EC007E006C0 07E006C007E006C007E0060007E0000007E0000007E0000007E0000007E0000007E0000007E000 0007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0 0003FFFFC003FFFFC01F1E7E9D24>I86 D<07FC001FFF003F0F803F07C03F03E03F 03E00C03E00003E0007FE007FBE01F03E03C03E07C03E0F803E0F803E0F803E0FC05E07E0DE03F F8FE0FE07E17147F9319>97 D<01FE0007FF801F0FC03E0FC03E0FC07C0FC07C0300FC0000FC00 00FC0000FC0000FC0000FC00007C00007E00003E00603F00C01F81C007FF0001FC0013147E9317 >99 D<0007F80007F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F8 01F8F80FFEF81F83F83E01F87E00F87C00F87C00F8FC00F8FC00F8FC00F8FC00F8FC00F8FC00F8 7C00F87C00F87E00F83E01F81F07F80FFEFF03F8FF18207E9F1D>I<01FE0007FF800F83C01E01 E03E00F07C00F07C00F8FC00F8FFFFF8FFFFF8FC0000FC0000FC00007C00007C00003E00181E00 180F807007FFE000FF8015147F9318>I<001F8000FFC001F3E003E7E003C7E007C7E007C3C007 C00007C00007C00007C00007C000FFFC00FFFC0007C00007C00007C00007C00007C00007C00007 C00007C00007C00007C00007C00007C00007C00007C00007C00007C0003FFC003FFC0013207F9F 10>I<01FC3C07FFFE0F079E1E03DE3E03E03E03E03E03E03E03E03E03E01E03C00F07800FFF00 09FC001800001800001C00001FFF800FFFF007FFF81FFFFC3C007C70003EF0001EF0001EF0001E 78003C78003C3F01F80FFFE001FF00171E7F931A>II<1C003E007F007F007F003E001C00000000000000000000000000FF00FF001F 001F001F001F001F001F001F001F001F001F001F001F001F001F001F001F00FFE0FFE00B217EA0 0E>I<0038007C00FE00FE00FE007C003800000000000000000000000001FE01FE003E003E003E 003E003E003E003E003E003E003E003E003E003E003E003E003E003E003E003E003E303E783EFC 3CFC7C78783FF01FC00F2A83A010>I108 DII<01FF0007FFC01F83F03E 00F83E00F87C007C7C007CFC007EFC007EFC007EFC007EFC007EFC007E7C007C7C007C3E00F83E 00F81F83F007FFC001FF0017147F931A>II114 D<0FE63FFE701E600EE006E006F800 FFC07FF83FFC1FFE03FE001FC007C007E007F006F81EFFFCC7F010147E9315>I<018001800180 03800380038007800F803F80FFFCFFFC0F800F800F800F800F800F800F800F800F800F800F860F 860F860F860F8607CC03F801F00F1D7F9C14>II123 D E /Ft 79 128 df0 D<003FC00000E0700003801C00 07000E000F000F001E0007803E0007C03C0003C07C0003E07C0003E07C0003E07C0003E07C0003 E07C0003E07C0003E03C0003C03E0007C01E0007801E0007800E0007000F000F0007000E000300 0C0003801C0001801800818018108080101040C03020404020207FC03FE03FC03FC03FC03FC01C 207E9F21>10 D<003F0000E0C001C0C00381E00701E00701E00700000700000700000700000700 00070000FFFFE00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700 E00700E00700E00700E00700E00700E00700E00700E07FC3FE1720809F19>12 D<001F81F80000F04F040001C07C06000380F80F000300F00F000700F00F000700700000070070 00000700700000070070000007007000000700700000FFFFFFFF00070070070007007007000700 700700070070070007007007000700700700070070070007007007000700700700070070070007 007007000700700700070070070007007007000700700700070070070007007007000700700700 7FE3FE3FF02420809F26>14 D<001F81FF0000F06F070001C07C0F000380F80F000300F0070007 00700700070070070007007007000700700700070070070007007007000700700700FFFFFFFF00 070070070007007007000700700700070070070007007007000700700700070070070007007007 000700700700070070070007007007000700700700070070070007007007000700700700070070 0700070070070007007007007FE3FE3FF02420809F26>I<70F8F8F8F8F8F8F870707070707070 7070702020202020000000000070F8F8F87005217CA00D>33 D<7038F87CFC7EFC7E743A040204 0204020804080410081008201040200F0E7E9F17>I<000300C0000300C0000300C0000300C000 06018000060180000601800006018000060180000C0300000C0300000C0300000C0300000C0300 001806007FFFFFFCFFFFFFFE00300C0000300C0000300C0000300C000060180000601800006018 0000601800FFFFFFFE7FFFFFFC00C0300001806000018060000180600001806000018060000300 C0000300C0000300C0000300C0000300C0000601800006018000060180001F297D9F26>I<70F8 FCFC74040404080810102040060E7C9F0D>39 D<0020004000800100020006000C000C00180018 003000300030007000600060006000E000E000E000E000E000E000E000E000E000E000E000E000 6000600060007000300030003000180018000C000C000600020001000080004000200B2E7DA112 >I<800040002000100008000C00060006000300030001800180018001C000C000C000C000E000 E000E000E000E000E000E000E000E000E000E000E000C000C000C001C001800180018003000300 060006000C00080010002000400080000B2E7DA112>I<00060000000600000006000000060000 000600000006000000060000000600000006000000060000000600000006000000060000000600 0000060000FFFFFFF0FFFFFFF00006000000060000000600000006000000060000000600000006 000000060000000600000006000000060000000600000006000000060000000600001C207D9A23 >43 D<70F8FCFC74040404080810102040060E7C840D>II<70F8F8F870 05057C840D>I<03F0000E1C001C0E00180600380700700380700380700380700380F003C0F003 C0F003C0F003C0F003C0F003C0F003C0F003C0F003C0F003C0F003C0F003C0F003C07003807003 807003807807803807001806001C0E000E1C0003F000121F7E9D17>48 D<018003800F80F38003 800380038003800380038003800380038003800380038003800380038003800380038003800380 038003800380038007C0FFFE0F1E7C9D17>I<03F0000C1C00100E00200700400780800780F007 C0F803C0F803C0F803C02007C00007C0000780000780000F00000E00001C000038000070000060 0000C0000180000300000600400C00401800401000803FFF807FFF80FFFF80121E7E9D17>I<03 F0000C1C00100E00200F00780F80780780780780380F80000F80000F00000F00000E00001C0000 380003F000003C00000E00000F000007800007800007C02007C0F807C0F807C0F807C0F0078040 0780400F00200E001C3C0003F000121F7E9D17>I<000600000600000E00000E00001E00002E00 002E00004E00008E00008E00010E00020E00020E00040E00080E00080E00100E00200E00200E00 400E00C00E00FFFFF0000E00000E00000E00000E00000E00000E00000E0000FFE0141E7F9D17> I<1803001FFE001FFC001FF8001FE00010000010000010000010000010000010000011F000161C 00180E001007001007800003800003800003C00003C00003C07003C0F003C0F003C0E003804003 80400700200600100E000C380003E000121F7E9D17>I<007C000182000701000E03800C07801C 0780380300380000780000700000700000F1F000F21C00F40600F80700F80380F80380F003C0F0 03C0F003C0F003C0F003C07003C07003C07003803803803807001807000C0E00061C0001F00012 1F7E9D17>I<03F0000C0C001006003003002001806001806001806001807001807803003E0300 3F06001FC8000FF00003F80007FC000C7E00103F00300F806003804001C0C001C0C000C0C000C0 C000C0C000806001802001001002000C0C0003F000121F7E9D17>56 D<03F0000E18001C0C0038 0600380700700700700380F00380F00380F003C0F003C0F003C0F003C0F003C07007C07007C038 07C0180BC00E13C003E3C0000380000380000380000700300700780600780E00700C0020180010 70000FC000121F7E9D17>I<70F8F8F8700000000000000000000070F8F8F87005147C930D>I<70 F8F8F8700000000000000000000070F0F8F878080808101010202040051D7C930D>I<7FFFFFE0 FFFFFFF00000000000000000000000000000000000000000000000000000000000000000FFFFFF F07FFFFFE01C0C7D9023>61 D<000100000003800000038000000380000007C0000007C0000007 C0000009E0000009E0000009E0000010F0000010F0000010F00000207800002078000020780000 403C0000403C0000403C0000801E0000801E0000FFFE0001000F0001000F0001000F0002000780 0200078002000780040003C00E0003C01F0007E0FFC03FFE1F207F9F22>65 DI<000FC040007030C001C009C0038005C0070003C00E0001C0 1E0000C01C0000C03C0000C07C0000407C00004078000040F8000000F8000000F8000000F80000 00F8000000F8000000F8000000F8000000F8000000780000007C0000407C0000403C0000401C00 00401E0000800E000080070001000380020001C0040000703800000FC0001A217D9F21>IIII<000FE0200078186000E004E0038002E0070001E00F0000E01E0000601E0000603C0000603C00 00207C00002078000020F8000000F8000000F8000000F8000000F8000000F8000000F8000000F8 007FFCF80003E0780001E07C0001E03C0001E03C0001E01E0001E01E0001E00F0001E0070001E0 038002E000E0046000781820000FE0001E217D9F24>III<0FFFC0007C00003C00003C 00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C 00003C00003C00003C00003C00003C00003C00203C00F83C00F83C00F83C00F038004078004070 0030E0000F800012207E9E17>I76 DII<001F800000F0F00001C0380007801E000F00 0F000E0007001E0007803C0003C03C0003C07C0003E0780001E0780001E0F80001F0F80001F0F8 0001F0F80001F0F80001F0F80001F0F80001F0F80001F0F80001F0780001E07C0003E07C0003E0 3C0003C03C0003C01E0007800E0007000F000F0007801E0001C0380000F0F000001F80001C217D 9F23>II82 D<07E0800C1980100780300380600180600180E00180E00080E00080E00080F00000F000007800 007F00003FF0001FFC000FFE0003FF00001F800007800003C00003C00001C08001C08001C08001 C08001C0C00180C00380E00300F00600CE0C0081F80012217D9F19>I<7FFFFFE0780F01E0600F 0060400F0020400F0020C00F0030800F0010800F0010800F0010800F0010000F0000000F000000 0F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000 000F0000000F0000000F0000000F0000000F0000000F0000000F0000001F800007FFFE001C1F7E 9E21>IIII<7FFFF87C00F87000F06001E04001E0C003C0C003C0800780800F80800F00001E0000 1E00003C00003C0000780000F80000F00001E00001E00003C00403C0040780040F80040F000C1E 000C1E00083C00183C0018780038F801F8FFFFF8161F7D9E1C>90 DI<080410082010201040204020804080408040B85CFC7EFC7E7C3E381C0F0E7B9F17>II<1FE000303000781800781C00300E00000E00000E00000E0000FE00078E 001E0E00380E00780E00F00E10F00E10F00E10F01E10781E103867200F83C014147E9317>97 D<0E0000FE00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E3E 000EC3800F01C00F00E00E00E00E00700E00700E00780E00780E00780E00780E00780E00780E00 700E00700E00E00F00E00D01C00CC300083E0015207F9F19>I<03F80E0C1C1E381E380C700070 00F000F000F000F000F000F00070007000380138011C020E0C03F010147E9314>I<000380003F 8000038000038000038000038000038000038000038000038000038000038003E380061B801C07 80380380380380700380700380F00380F00380F00380F00380F00380F003807003807003803803 803807801C07800E1B8003E3F815207E9F19>I<03F0000E1C001C0E0038070038070070070070 0380F00380F00380FFFF80F00000F00000F000007000007000003800801800800C010007060001 F80011147F9314>I<007C00C6018F038F07060700070007000700070007000700FFF007000700 07000700070007000700070007000700070007000700070007000700070007007FF01020809F0E >I<0000E003E3300E3C301C1C30380E00780F00780F00780F00780F00780F00380E001C1C001E 380033E0002000002000003000003000003FFE001FFF800FFFC03001E0600070C00030C00030C0 0030C000306000603000C01C038003FC00141F7F9417>I<0E0000FE00000E00000E00000E0000 0E00000E00000E00000E00000E00000E00000E00000E3E000E43000E81800F01C00F01C00E01C0 0E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C0 FFE7FC16207F9F19>I<1C003E003E003E001C000000000000000000000000000E007E000E000E 000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFC00A1F809E0C> I<00E001F001F001F000E0000000000000000000000000007007F000F000700070007000700070 00700070007000700070007000700070007000700070007000700070007000706070F060F0C061 803F000C28829E0E>I<0E0000FE00000E00000E00000E00000E00000E00000E00000E00000E00 000E00000E00000E0FF00E03C00E03000E02000E04000E08000E10000E30000E70000EF8000F38 000E1C000E1E000E0E000E07000E07800E03800E03C00E03E0FFCFF815207F9F18>I<0E00FE00 0E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E 000E000E000E000E000E000E000E000E000E00FFE00B20809F0C>I<0E1F01F000FE618618000E 81C81C000F00F00E000F00F00E000E00E00E000E00E00E000E00E00E000E00E00E000E00E00E00 0E00E00E000E00E00E000E00E00E000E00E00E000E00E00E000E00E00E000E00E00E000E00E00E 000E00E00E00FFE7FE7FE023147F9326>I<0E3E00FE43000E81800F01C00F01C00E01C00E01C0 0E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C0FFE7FC 16147F9319>I<01F800070E001C03803801C03801C07000E07000E0F000F0F000F0F000F0F000 F0F000F0F000F07000E07000E03801C03801C01C0380070E0001F80014147F9317>I<0E3E00FE C3800F01C00F00E00E00E00E00F00E00700E00780E00780E00780E00780E00780E00780E00700E 00F00E00E00F01E00F01C00EC3000E3E000E00000E00000E00000E00000E00000E00000E00000E 0000FFE000151D7F9319>I<03E0800619801C05803C0780380380780380700380F00380F00380 F00380F00380F00380F003807003807803803803803807801C0B800E138003E380000380000380 000380000380000380000380000380000380003FF8151D7E9318>I<0E78FE8C0F1E0F1E0F0C0E 000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00F147F9312>I<1F9030 704030C010C010C010E00078007F803FE00FF00070803880188018C018C018E030D0608F800D14 7E9312>I<020002000200060006000E000E003E00FFF80E000E000E000E000E000E000E000E00 0E000E000E000E080E080E080E080E080610031001E00D1C7F9B12>I<0E01C0FE1FC00E01C00E 01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E 03C00603C0030DC001F1FC16147F9319>III<7FC3FC0F01E00701C007018003810001C20000E40000EC 00007800003800003C00007C00004E000087000107000303800201C00601E01E01E0FF07FE1714 809318>II<3FFF380E200E201C40384078407000E001E0 01C00380078007010E011E011C0338027006700EFFFE10147F9314>I<30307878F87C78783030 0E057C9E17>127 D E /Fu 67 128 df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v 17 122 df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end %%EndProlog %%BeginSetup %%Feature: *Resolution 300dpi TeXDict begin %%PaperSize: A4 %%EndSetup %%Page: 35 1 35 0 bop 568 269 a Fv(Multidimensional)15 b(P)n(olylogarithms)783 396 y Fj(Da)o(vid)h(M.)g(Bradley)681 463 y Ft(Dalhousie)g(Univ)o(ersit)o(y)l (,)g(Canada)854 563 y(July)g(6,)f(1998)650 662 y([summary)f(b)o(y)h(Hoang)g (Ngo)q(c)g(Minh])800 794 y(1.)26 b Fs(In)o(tro)q(duction)50 875 y Ft(Recen)o(tly)l(,)e(sev)o(eral)d(extensions)h(of)e(p)q(olylogarithms,) j(Euler)f(sums)f(\(or)g(m)o(ultiple)i(harmonic)e(sums\))g(and)0 929 y(Riemann)d(zeta)f(functions)h(ha)o(v)o(e)f(b)q(een)h(in)o(tro)q(duced.) 27 b(These)17 b(ha)o(v)o(e)g(arisen)g(in)h(n)o(um)o(b)q(er)g(theory)l(,)f (knot)g(theory)l(,)0 983 y(high-energy)f(ph)o(ysics,)g(analysis)g(of)e (quadtrees,)h(con)o(trol)g(theory)l(,)f Fl(:)8 b(:)g(:)21 b Ft(In)15 b(this)h(talk,)e(the)h(author)g(presen)o(ts)g(the)0 1037 y(m)o(ultidimensional)k(p)q(olylogarithms)d(and)g(their)g(sp)q(ecial)h (v)m(alues)g([1,)e(2)o(].)21 b(After)16 b(de\014nitions)h(related)f(to)f(m)o (ulti-)0 1091 y(dimensional)j(p)q(olylogarithms)e(\(Section)g(2\),)f (results,)h(conjectures)g(and)g(com)o(binatorial)g(asp)q(ects)g(concerning)0 1145 y(unit)i(Euler)h(sums)e(and)h(unsigned)h(Euler)f(sums)g(are)f(discussed) i(\(Section)f(3\).)26 b(In)o(tegral)18 b(represen)o(tations)f(are)0 1198 y(also)e(p)q(oin)o(ted)h(out)f(to)g(understand)g(m)o(ultidimensional)j (p)q(olylogarithms)e(\(Section)g(4\).)821 1290 y(2.)25 b Fs(De\014nitions)0 1371 y(De\014nition)19 b(1.)j Ft(The)16 b Fo(multidimensional)f(p)n(olylo)n (garithms)k Ft(\(MDPs\))14 b(are)h(de\014ned)h(as)f(follo)o(ws)554 1490 y Fl(\025)589 1426 y Fh(\022)621 1462 y Fl(s)642 1469 y Fp(1)662 1462 y Fl(;)8 b(:)g(:)g(:)d(;)j(s)785 1469 y Fi(k)623 1516 y Fl(b)643 1523 y Fp(1)662 1516 y Fl(;)g(:)g(:)g(:)d(;)j(b)784 1523 y Fi(k)806 1426 y Fh(\023)852 1490 y Ft(=)921 1433 y Fi(k)902 1447 y Fh(Y)900 1545 y Fi(j)r Fp(=1)975 1447 y Fh(X)969 1545 y Fi(\027)986 1550 y Fe(j)1002 1545 y Fg(\025)p Fp(1)1178 1452 y Fl(b)1198 1427 y Fg(\000)p Fi(\027)1242 1432 y Fe(j)1198 1466 y Fi(j)p 1060 1480 319 2 v 1060 1521 a Ft(\()p Fl(\027)1100 1528 y Fi(j)1129 1521 y Ft(+)i Ff(\001)e(\001)g(\001)g Ft(+)j Fl(\027)1305 1528 y Fi(k)1326 1521 y Ft(\))1344 1506 y Fi(s)1360 1511 y Fe(j)1384 1490 y Fl(:)0 1648 y(k)16 b Ft(is)g(the)f Fo(depth)20 b Ft(and)15 b Fl(s)e Ft(=)g Fl(s)480 1655 y Fp(1)510 1648 y Ft(+)d Ff(\001)e(\001)g(\001)h Ft(+)h Fl(s)685 1655 y Fi(k)722 1648 y Ft(is)16 b(the)f Fo(weight)20 b Ft(of)14 b Fl(\025)1076 1584 y Fh(\022)1109 1621 y Fl(s)1130 1628 y Fp(1)1150 1621 y Fl(;)8 b(:)g(:)g(:)d(;)j(s)1273 1628 y Fi(k)1111 1675 y Fl(b)1131 1682 y Fp(1)1150 1675 y Fl(;)g(:)g(:)g(:)d(;)j(b)1272 1682 y Fi(k)1294 1584 y Fh(\023)1327 1648 y Ft(.)59 1753 y Fs({)21 b Ft(When)15 b Fl(k)f Ft(=)f(0,)i(b)o(y)g(con)o(v)o(en)o(tion)g Fl(\025)p Ft(\()p Ff(fg)p Ft(\))c(=)i(1;)59 1807 y Fs({)21 b Ft(When)15 b Fl(k)f Ft(=)f(1,)i Fl(s)g Ft(is)h(a)f(p)q(ositiv)o(e)h(in)o (teger)f(and)h Ff(j)p Fl(b)p Ff(j)11 b(\025)i Ft(1,)i(one)g(get)g(the)g (usual)h Fo(p)n(olylo)n(garithm)691 1909 y Fl(\025)726 1844 y Fh(\022)759 1881 y Fl(s)760 1935 y(b)780 1844 y Fh(\023)826 1909 y Ft(=)874 1865 y Fh(X)875 1963 y Fi(\027)r Fg(\025)p Fp(1)952 1878 y Fl(b)972 1861 y Fg(\000)p Fi(\027)p 952 1898 69 2 v 965 1940 a Fl(\027)990 1927 y Fi(s)1038 1909 y Ft(=)d(Li)1127 1916 y Fi(s)1146 1909 y Ft(\(1)p Fl(=b)p Ft(\))p Fl(:)106 2028 y Ft(The)i(classical)i Fo(R)o(iemann)f(zeta)g(function)i Ft(is)e(obtained)g (in)g(the)f(sp)q(ecial)i(case)e(where)h Fl(b)c Ft(=)h(1.)59 2085 y Fs({)21 b Ft(When)15 b Fl(k)f(>)f Ft(1,)i(let)g Fl(n)467 2092 y Fi(j)499 2085 y Ft(=)547 2051 y Fh(P)594 2064 y Fi(k)594 2099 y(i)p Fp(=)p Fi(j)660 2085 y Fl(\027)682 2092 y Fi(i)711 2085 y Ft(and)h Fl(b)820 2092 y Fi(j)850 2085 y Ft(=)898 2051 y Fh(Q)941 2063 y Fi(j)941 2099 y(i)p Fp(=1)1008 2085 y Fl(a)1032 2092 y Fi(i)1046 2085 y Ft(.)k(Then)555 2202 y Fl(\025)590 2138 y Fh(\022)623 2174 y Fl(s)644 2181 y Fp(1)664 2174 y Fl(;)8 b(:)g(:)g(:)d(;)j(s)787 2181 y Fi(k)625 2228 y Fl(b)645 2235 y Fp(1)664 2228 y Fl(;)g(:)g(:)g(:)d(;)j(b)786 2235 y Fi(k)808 2138 y Fh(\023)854 2202 y Ft(=)973 2159 y Fh(X)902 2256 y Fi(n)923 2261 y Fn(1)940 2256 y Fi(>)p Fg(\001\001\001)p Fi(>n)1045 2262 y Fe(k)1065 2256 y Fi(>)p Fp(0)1123 2170 y Fl(a)1147 2149 y Fg(\000)p Fi(n)1195 2154 y Fn(1)1147 2183 y Fp(1)1222 2170 y Ff(\001)g(\001)g(\001)e Fl(a)1307 2148 y Fg(\000)p Fi(n)1355 2154 y Fe(k)1307 2184 y Fi(k)p 1123 2192 255 2 v 1152 2233 a Fl(n)1179 2213 y Fi(s)1195 2218 y Fn(1)1179 2246 y Fp(1)1222 2233 y Ff(\001)i(\001)g(\001)e Fl(n)1310 2212 y Fi(s)1326 2218 y Fe(k)1310 2248 y Fi(k)1382 2202 y Fl(:)143 2321 y Ff(\003)21 b Ft(If)15 b(eac)o(h)h Fl(a)359 2328 y Fi(j)390 2321 y Ft(=)d(1)h(then)i (these)f(sums)h(are)e(called)j Fo(Euler)f(sums)p Ft(;)143 2375 y Ff(\003)21 b Ft(If)15 b(eac)o(h)h Fl(a)359 2382 y Fi(j)390 2375 y Ft(=)d Ff(\006)p Ft(1)i(then)g(they)h(are)e(called)j Fo(alternating)f(Euler)g(sums)p Ft(.)0 2452 y Fs(De\014nition)j(2.)j Ft(The)16 b Fo(unit)g(Euler)g(sum)j Ft(is)d(de\014ned)g(as)f(follo)o(ws)421 2560 y Fl(\026)p Ft(\()p Fl(b)486 2567 y Fp(1)505 2560 y Fl(;)8 b(:)g(:)g(:)d(;)j(b)627 2567 y Fi(k)647 2560 y Ft(\))k(=)h Fl(\025)760 2496 y Fh(\022)810 2532 y Ft(1)p Fl(;)8 b(:)g(:)g(:)t(;)g Ft(1)793 2586 y Fl(b)813 2593 y Fp(1)832 2586 y Fl(;)g(:)g(:)g(:)d(;)j(b)954 2593 y Fi(k)974 2496 y Fh(\023)1020 2560 y Ft(=)1089 2503 y Fi(k)1069 2516 y Fh(Y)1068 2614 y Fi(j)r Fp(=1)1143 2516 y Fh(X)1137 2614 y Fi(\027)1154 2619 y Fe(j)1170 2614 y Fg(\025)p Fp(1)1328 2522 y Fl(b)1348 2496 y Fg(\000)p Fi(\027)1392 2501 y Fe(j)1348 2535 y Fi(j)p 1228 2549 284 2 v 1228 2591 a Ft(\()p Fl(\027)1268 2598 y Fi(j)1296 2591 y Ft(+)j Ff(\001)d(\001)g(\001)g Ft(+)i Fl(\027)1472 2598 y Fi(k)1494 2591 y Ft(\))1517 2560 y Fl(:)957 2679 y Fp(35)p eop %%Page: 36 2 36 1 bop 0 22 a Fp(36)0 120 y Fs(De\014nition)19 b(3.)j Ft(The)16 b Fo(unsigne)n(d)f(Euler)h(sum)j Ft(is)d(de\014ned)g(as)f(follo)o(ws)392 243 y Fl(\025)419 250 y Fi(b)435 243 y Ft(\()p Fl(s)474 250 y Fp(1)494 243 y Fl(;)8 b(:)g(:)g(:)d(;)j(s)617 250 y Fi(k)638 243 y Ft(\))k(=)h Fl(\025)751 179 y Fh(\022)783 216 y Fl(s)804 223 y Fp(1)824 216 y Fl(;)8 b(:)g(:)g(:)d(;)j(s)947 223 y Fi(k)806 270 y Fl(b;)g(:)g(:)g(:)t(;)g(b)968 179 y Fh(\023)1014 243 y Ft(=)1083 187 y Fi(k)1064 200 y Fh(Y)1062 298 y Fi(j)r Fp(=1)1137 200 y Fh(X)1131 298 y Fi(\027)1148 303 y Fe(j)1165 298 y Fg(\025)p Fp(1)1340 213 y Fl(b)1360 196 y Fg(\000)p Fi(\027)1404 201 y Fe(j)p 1222 233 319 2 v 1222 275 a Ft(\()p Fl(\027)1262 282 y Fi(j)1291 275 y Ft(+)i Ff(\001)e(\001)g(\001)g Ft(+)j Fl(\027)1467 282 y Fi(k)1489 275 y Ft(\))1507 260 y Fi(s)1523 265 y Fe(j)1546 243 y Fl(:)59 382 y Fs({)21 b Ft(When)15 b Fl(b)e Ft(=)g(1,)h Fl(\025)396 389 y Fp(1)431 382 y Ft(is)h(often)g(called)i(the)e(unsigned)i (Euler)f(sum)f(or)g Fo(multiple)h(zeta)g(value)j Ft(\(MZV\))442 483 y Fl(\025)469 490 y Fp(1)489 483 y Ft(\()p Fl(s)528 490 y Fp(1)547 483 y Fl(;)8 b(:)g(:)g(:)d(;)j(s)670 490 y Fi(k)691 483 y Ft(\))k(=)h Fl(\020)s Ft(\()p Fl(s)831 490 y Fp(1)851 483 y Fl(;)8 b(:)g(:)g(:)d(;)j(s)974 490 y Fi(k)995 483 y Ft(\))k(=)1145 440 y Fh(X)1073 537 y Fi(n)1094 542 y Fn(1)1112 537 y Fi(>)p Fg(\001\001\001)p Fi(>n)1217 543 y Fe(k)1237 537 y Fi(>)p Fp(0)1381 452 y Ft(1)p 1294 472 196 2 v 1294 514 a Fl(n)1321 494 y Fi(s)1337 499 y Fn(1)1321 527 y Fp(1)1365 514 y Ff(\001)c(\001)g(\001)d Fl(n)1452 493 y Fi(s)1468 499 y Fe(k)1452 529 y Fi(k)1495 483 y Fl(:)59 611 y Fs({)21 b Ft(When)13 b Fl(b)f Ft(=)h(2,)f Fl(\025)391 618 y Fp(2)423 611 y Ft(represen)o(ts)g(an)h(iterated)f(sum)h(extension)g(of) f(the)g(p)q(olylogarithm)i(with)f(argumen)o(t)e(1)p Fl(=)p Ft(2,)106 665 y(and)k(pla)o(ys)h(a)f(crucial)h(role)g(in)g(computing)f(the)h (MZVs.)669 776 y(3.)26 b Fs(Sp)q(ecial)19 b(V)l(alues)e(of)h(MDPs)0 857 y(Theorem)f(1.)22 b Fo(L)n(et)c Fl(p)g Fo(and)h Fl(q)h Fo(satisfy)e Ft(1)p Fl(=p)11 b Ft(+)h(1)p Fl(=q)18 b Ft(=)f(1)p Fo(.)27 b(If)18 b(in)g(addition,)h Fl(p)d(>)h Ft(1)p Fo(,)i(or)g Fl(p)d Ff(\024)h(\000)p Ft(1)p Fo(,)i(then)f(for)h(any)0 911 y(nonne)n(gative)c(inte)n(ger)g Fl(k)q Fo(,)785 1020 y Fl(\026)p Ft(\()p Ff(f)p Fl(p)p Ff(g)899 1001 y Fi(k)919 1020 y Ft(\))e(=)1003 989 y(\(log)8 b Fl(q)r Ft(\))1127 973 y Fi(k)p 1003 1010 145 2 v 1056 1051 a Fl(k)q Ft(!)1153 1020 y Fl(:)0 1126 y Ft(The)15 b(pro)q(of)g(is)h(done)g(b)o(y)f(co)q(e\016cien)o(t)h(extraction)f(in)h(the)f (generating)g(function)1390 1092 y Fh(P)1438 1139 y Fi(k)q Fg(\025)p Fp(0)1511 1126 y Fl(x)1537 1109 y Fi(k)1559 1126 y Fl(\026)p Ft(\()p Ff(f)p Fl(p)p Ff(g)1673 1109 y Fi(k)1694 1126 y Ft(\))p Fl(:)0 1214 y Fs(Theorem)i(2.)22 b Fo(L)n(et)16 b Fl(A)398 1221 y Fi(r)430 1214 y Ft(=)c(Li)519 1221 y Fi(r)537 1214 y Ft(\(1)p Fl(=)p Ft(2\))p Fl(;)c(P)692 1221 y Fi(r)722 1214 y Ft(=)13 b(\(log)8 b(2\))895 1197 y Fi(r)913 1214 y Fl(=r)q Ft(!)o Fl(;)g(Z)1022 1221 y Fi(r)1053 1214 y Ft(=)13 b(\()p Ff(\000)p Ft(1\))1195 1197 y Fi(r)1214 1214 y Fl(\020)s Ft(\()p Fl(r)q Ft(\))p Fl(:)i Fo(Then,)g(for)i Fl(m)c Ff(\025)f Ft(1)p Fl(;)c(n)k Ff(\025)h Ft(0)30 1331 y Fl(\026)p Ft(\()p Ff(f\000)p Ft(1)p Ff(g)179 1312 y Fi(m)212 1331 y Fl(;)8 b Ft(1)p Fl(;)g Ff(f\000)p Ft(1)p Ff(g)381 1312 y Fi(n)402 1331 y Ft(\))k(=)h(\()p Ff(\000)p Ft(1\))574 1312 y Fi(m)p Fp(+1)677 1274 y Fi(m)660 1287 y Fh(X)660 1386 y Fi(k)q Fp(=0)733 1267 y Fh(\022)766 1300 y Fl(n)e Ft(+)f Fl(k)808 1362 y(k)874 1267 y Fh(\023)908 1331 y Fl(A)942 1338 y Fi(k)q Fp(+)p Fi(n)p Fp(+1)1057 1331 y Fl(P)1086 1338 y Fi(m)p Fg(\000)p Fi(k)1176 1331 y Ft(+)h(\()p Ff(\000)p Ft(1\))1316 1312 y Fi(n)p Fp(+1)1413 1274 y Fi(n)1391 1287 y Fh(X)1392 1386 y Fi(k)q Fp(=0)1465 1267 y Fh(\022)1498 1300 y Fl(m)f Ft(+)g Fl(k)1538 1362 y(m)1619 1267 y Fh(\023)1652 1331 y Fl(Z)1683 1338 y Fi(k)q Fp(+)p Fi(m)p Fp(+1)1808 1331 y Fl(P)1837 1338 y Fi(n)p Fg(\000)p Fi(k)1908 1331 y Fl(:)0 1460 y Ft(The)15 b(pro)q(of)g(of)g(this)h(theorem)f(can)g(b)q(e)h(done)f(via) h(the)f Fo(duality)i(principle)h Ft(\(see)d(Section)h(4\).)50 1514 y(F)l(or)f(an)o(y)g(nonnegativ)o(e)g(in)o(teger)h Fl(k)q Ft(,)f(the)h(follo)o(wing)g(iden)o(tities)h(pro)o(vide)f(nested)g(sum)f (extensions)i(of)e(Euler's)0 1568 y Fl(\020)s Ft(\(2\))p Fl(;)8 b(\020)s Ft(\(4\))p Fl(;)g(\020)s Ft(\(6\))k(and)j Fl(\020)s Ft(\(8\))f(ev)m(aluations,)i(resp)q(ectiv)o(ely)411 1685 y Fl(\020)s Ft(\()p Ff(f)p Ft(2)p Ff(g)521 1666 y Fi(k)541 1685 y Ft(\))c(=)638 1654 y(2\(2)p Fl(\031)r Ft(\))748 1638 y Fp(2)p Fi(k)p 624 1674 175 2 v 624 1716 a Ft(\(2)p Fl(k)f Ft(+)f(1\)!)811 1621 y Fh(\022)849 1654 y Ft(1)p 849 1674 23 2 v 849 1716 a(2)877 1621 y Fh(\023)911 1632 y Fp(2)p Fi(k)q Fp(+1)1002 1685 y Fl(;)411 1821 y(\020)s Ft(\()p Ff(f)p Ft(4)p Ff(g)521 1803 y Fi(k)541 1821 y Ft(\))i(=)638 1791 y(4\(2)p Fl(\031)r Ft(\))748 1774 y Fp(4)p Fi(k)p 624 1811 175 2 v 624 1853 a Ft(\(4)p Fl(k)f Ft(+)f(2\)!)811 1757 y Fh(\022)849 1791 y Ft(1)p 849 1811 23 2 v 849 1853 a(2)877 1757 y Fh(\023)911 1769 y Fp(2)p Fi(k)q Fp(+1)1002 1821 y Fl(;)411 1953 y(\020)s Ft(\()p Ff(f)p Ft(6)p Ff(g)521 1934 y Fi(k)541 1953 y Ft(\))i(=)638 1922 y(6\(2)p Fl(\031)r Ft(\))748 1905 y Fp(6)p Fi(k)p 624 1942 175 2 v 624 1984 a Ft(\(6)p Fl(k)f Ft(+)f(3\)!)803 1953 y Fl(;)411 2092 y(\020)s Ft(\()p Ff(f)p Ft(8)p Ff(g)521 2074 y Fi(k)541 2092 y Ft(\))i(=)638 2062 y(8\(2)p Fl(\031)r Ft(\))748 2045 y Fp(8)p Fi(k)p 624 2082 V 624 2123 a Ft(\(8)p Fl(k)f Ft(+)f(4\)!)811 2015 y Fh(")837 2028 y(\022)871 2092 y Ft(1)g(+)973 2062 y(1)p 954 2082 61 2 v 954 2091 a Ff(p)p 992 2091 23 2 v 38 x Ft(2)1020 2028 y Fh(\023)1053 2040 y Fp(4)p Fi(k)q Fp(+2)1147 2092 y Ft(+)1193 2028 y Fh(\022)1226 2092 y Ft(1)g Ff(\000)1329 2062 y Ft(1)p 1310 2082 61 2 v 1310 2091 a Ff(p)p 1347 2091 23 2 v 1347 2129 a Ft(2)1375 2028 y Fh(\023)1409 2040 y Fp(4)p Fi(k)q Fp(+2)1493 2015 y Fh(#)1527 2092 y Fl(:)0 2220 y Ft(In)16 b(general,)f(for)g (an)o(y)g(p)q(ositiv)o(e)h(in)o(teger)f Fl(n)p Ft(,)g Fl(")e Ft(=)g(e)857 2204 y Fi(i\031)q(=n)932 2220 y Ft(,)i(one)g(has)583 2298 y Fh(X)584 2397 y Fi(k)q Fg(\025)p Fp(0)649 2342 y Ft(\()p Ff(\000)p Ft(1\))743 2323 y Fi(k)764 2342 y Fl(x)790 2323 y Fp(2)p Fi(k)q(n)850 2342 y Fl(\020)s Ft(\()p Ff(f)p Ft(2)p Fl(n)p Ff(g)987 2323 y Fi(k)1008 2342 y Ft(\))d(=)1086 2285 y Fi(n)p Fg(\000)p Fp(1)1090 2298 y Fh(Y)1089 2396 y Fi(j)r Fp(=0)1165 2311 y Ft(sin)q(\()p Fl(\031)r(x")1314 2294 y Fi(j)1332 2311 y Ft(\))p 1165 2331 185 2 v 1211 2373 a Fl(\031)r(x")1286 2360 y Fi(j)1354 2342 y Fl(:)0 2477 y Fs(Theorem)17 b(3)h Ft(\(Zagier's)c (conjecture)h([6]\))p Fs(.)606 2586 y Fl(\020)s Ft(\()p Ff(f)p Ft(3)p Fl(;)8 b Ft(1)p Ff(g)760 2568 y Fi(n)782 2586 y Ft(\))k(=)h(4)883 2568 y Fg(\000)p Fi(n)934 2586 y Fl(\020)s Ft(\()p Ff(f)p Ft(4)p Ff(g)1044 2568 y Fi(n)1066 2586 y Ft(\))g(=)1192 2556 y(2)p Fl(\031)1243 2539 y Fp(4)p Fi(n)p 1150 2576 177 2 v 1150 2618 a Ft(\(4)p Fl(n)c Ft(+)i(2\)!)1331 2586 y Fl(:)p eop %%Page: 37 3 37 2 bop 1915 22 a Fp(37)0 120 y Fs(Conjecture)17 b(1.)67 253 y Fl(\020)s Ft(\(2)p Fl(;)8 b Ff(f)p Ft(3)p Fl(;)g Ft(1)p Ff(g)265 235 y Fi(n)285 253 y Ft(\))13 b(=)g(4)387 235 y Fg(\000)p Fi(n)467 197 y(n)445 210 y Fh(X)445 309 y Fi(k)q Fp(=0)510 253 y Ft(\()p Ff(\000)p Ft(1\))604 235 y Fi(k)625 253 y Fl(\020)s Ft(\()p Ff(f)p Ft(4)p Ff(g)735 235 y Fi(n)p Fg(\000)p Fi(k)804 253 y Ft(\))830 162 y Fh(2)830 244 y(4)860 253 y Ft(\(4)p Fl(k)e Ft(+)f(1\))p Fl(\020)s Ft(\(4)p Fl(n)g Ft(+)g(2\))f Ff(\000)i Ft(4)1317 197 y Fi(k)1294 210 y Fh(X)1296 308 y Fi(j)r Fp(=1)1367 253 y Fl(\020)s Ft(\(4)p Fl(j)i Ff(\000)d Ft(1\))p Fl(\020)s Ft(\(4)p Fl(k)g Ff(\000)h Ft(4)p Fl(j)h Ft(+)e(3\))1833 162 y Fh(3)1833 244 y(5)1871 253 y Fl(:)50 391 y Ft(In)20 b(practice,)g(one)f(w)o (ould)h(lik)o(e)g(to)f(kno)o(w)f(whic)o(h)i(unsigned)h(Euler)f(sums)f(can)g (b)q(e)h(expressed)g(in)g(terms)e(of)0 445 y(lo)o(w)o(er)d(depth)h(sums.)k (When)c(the)f(sum)g(can)h(b)q(e)g(expressed,)f(it)h(is)g(said)g(to)e (\\reduce".)21 b(Hoang)14 b(Ngo)q(c)i(Minh)g(and)0 499 y(Mic)o(hel)e(P)o (etitot)e(ha)o(v)o(e)g(implemen)o(ted)j(in)f Fb(AXIOM)e Ft(an)g(algorithm)h (to)f(reduce)i(the)f(MZVs)f(via)h(a)g(table)g(of)f(Gr\177)-23 b(obner)0 553 y(basis)16 b(of)e(these)i(sums)f(at)f(\014xed)i(w)o(eigh)o(t)f ([5].)k(Here,)c(the)g(authors)g(also)g(get)g(the)g(follo)o(wing)0 639 y Fs(Theorem)i(4.)22 b Fo(F)m(or)16 b(any)g(p)n(ositive)g(inte)n(ger)g Fl(k)q Fo(,)647 720 y Fl(\020)s Ft(\()p Fl(s)709 727 y Fp(1)729 720 y Fl(;)8 b(:)g(:)g(:)t(;)g(s)851 727 y Fi(k)872 720 y Ft(\))i(+)g(\()p Ff(\000)p Ft(1\))1039 701 y Fi(k)1060 720 y Fl(\020)s Ft(\()p Fl(s)1122 727 y Fi(k)1144 720 y Fl(;)e(:)g(:)g(:)d(;)j(s)1267 727 y Fp(1)1286 720 y Ft(\))0 801 y Fo(r)n(e)n(duc)n(es)15 b(to)i(lower)f(depth)h(MZVs.)50 887 y Ft(The)h(follo)o(wing)g(theorem)f(giv)o (es)h(Crandall's)f(recurrence)i(for)e(unsigned)i(Euler)f(sums)f Fl(\020)s Ft(\()p Ff(f)p Fl(s)p Ff(g)1687 870 y Fi(k)1708 887 y Ft(\))g(and)h(it)g(can)0 942 y(b)q(e)e(pro)o(v)o(ed)f(b)o(y)g(co)q (e\016cien)o(t)h(extraction)f(in)h(the)f(generating)h(function)1233 908 y Fh(P)1281 955 y Fi(k)q Fg(\025)p Fp(0)1355 942 y Fl(k)q(x)1406 925 y Fi(k)1427 942 y Fl(\020)s Ft(\()p Ff(f)p Fl(s)p Ff(g)1535 925 y Fi(k)1556 942 y Ft(\))p Fl(:)0 1031 y Fs(Theorem)h(5)h Ft(\(Crandall's)d(recurrence\))p Fs(.)23 b Fo(F)m(or)15 b(any)i(nonne)n (gative)d(inte)n(ger)i Fl(k)h Fo(and)f Ff(<)p Ft(\()p Fl(s)p Ft(\))d Fl(>)f Ft(0)p Fo(,)596 1157 y Fl(k)q(\020)s Ft(\()p Ff(f)p Fl(s)p Ff(g)729 1139 y Fi(k)750 1157 y Ft(\))g(=)851 1101 y Fi(k)828 1114 y Fh(X)830 1212 y Fi(j)r Fp(=1)894 1157 y Ft(\()p Ff(\000)p Ft(1\))988 1139 y Fi(j)r Fp(+1)1050 1157 y Fl(\020)s Ft(\()p Fl(j)s(s)p Ft(\))p Fl(\020)s Ft(\()p Ff(f)p Fl(s)p Ff(g)1260 1139 y Fi(k)q Fg(\000)p Fi(j)1324 1157 y Ft(\))p Fl(:)50 1290 y Ft(F)l(or)i(example)590 1371 y Fl(\020)s Ft(\()p Ff(f)p Fl(s)p Ff(g)p Ft(\))e(=)h Fl(\020)s Ft(\()p Fl(s)p Ft(\))p Fl(;)548 1467 y(\020)s Ft(\()p Ff(f)p Fl(s;)8 b(s)p Ff(g)p Ft(\))k(=)781 1436 y(1)p 781 1456 23 2 v 781 1498 a(2)809 1467 y Fl(\020)832 1448 y Fp(2)852 1467 y Ft(\()p Fl(s)p Ft(\))d Ff(\000)969 1436 y Ft(1)p 969 1456 V 969 1498 a(2)996 1467 y Fl(\020)s Ft(\(2)p Fl(s)p Ft(\))p Fl(;)507 1576 y(\020)s Ft(\()p Ff(f)p Fl(s;)f(s;)g(s)p Ff(g)p Ft(\))j(=)781 1545 y(1)p 781 1565 V 781 1607 a(6)809 1576 y Fl(\020)832 1557 y Fp(3)852 1576 y Ft(\()p Fl(s)p Ft(\))e Ff(\000)969 1545 y Ft(1)p 969 1565 V 969 1607 a(2)996 1576 y Fl(\020)s Ft(\()p Fl(s)p Ft(\))p Fl(\020)s Ft(\(2)p Fl(s)p Ft(\))h(+)1240 1545 y(1)p 1240 1565 V 1240 1607 a(3)1267 1576 y Fl(\020)s Ft(\(3)p Fl(s)p Ft(\))p Fl(;)e(:)g(:)g(:)0 1670 y Ft(Crandall's)16 b(recurrence)g(is)f(also)g(a)g(sp) q(ecial)i(case)f(of)e(Newton's)h(form)o(ula)643 1794 y Fl(k)q(e)689 1801 y Fi(k)723 1794 y Ft(=)794 1737 y Fi(k)771 1751 y Fh(X)773 1848 y Fi(j)r Fp(=1)837 1794 y Ft(\()p Ff(\000)p Ft(1\))931 1775 y Fi(j)r Fp(+1)993 1794 y Fl(p)1016 1801 y Fi(j)1034 1794 y Fl(e)1055 1801 y Fi(k)q Fg(\000)p Fi(j)1121 1794 y Fl(;)52 b(k)14 b Ff(\025)f Ft(0)p Fl(;)0 1922 y Ft(relating)h(the)g(Elemen)o(tary)g (Symmetric)g(F)l(unctions)g Fl(e)938 1929 y Fi(k)973 1922 y Ft(and)g(and)g(the)g(P)o(o)o(w)o(er-Sum)f(Symmetric)h(F)l(unctions)h Fl(p)1919 1929 y Fi(r)1937 1922 y Ft(,)580 2010 y Fl(e)601 2017 y Fi(k)635 2010 y Ft(=)724 1966 y Fh(X)683 2064 y Fi(j)697 2069 y Fn(1)715 2064 y Fi(>)p Fg(\001\001\001)p Fi(>j)813 2068 y Fe(r)838 2010 y Fl(x)864 2017 y Fi(j)878 2022 y Fn(1)905 2010 y Ff(\001)8 b(\001)g(\001)e Fl(x)992 2017 y Fi(j)1006 2021 y Fe(r)1026 2010 y Fl(;)98 b(p)1160 2017 y Fi(r)1191 2010 y Ft(=)1239 1966 y Fh(X)1241 2064 y Fi(r)q(>)p Fp(0)1312 2010 y Fl(x)1338 1991 y Fi(r)1338 2021 y(j)1357 2010 y Fl(;)0 2140 y Ft(with)16 b(indeterminates)g Fl(x)438 2147 y Fi(j)469 2140 y Ft(=)d(1)p Fl(=j)585 2124 y Fi(s)602 2140 y Ft(,)i Fl(e)651 2147 y Fi(r)683 2140 y Ft(=)e Fl(\020)s Ft(\()p Ff(f)p Fl(s)p Ff(g)839 2124 y Fi(r)857 2140 y Ft(\))i(and)g Fl(p)1001 2147 y Fi(r)1033 2140 y Ft(=)e Fl(\020)s Ft(\()p Fl(r)q(s)p Ft(\).)0 2230 y Fs(De\014nition)19 b(4.)j Ft(Let)14 b Fl(~)-21 b(s)13 b Ft(=)g(\()p Fl(s)510 2237 y Fp(1)530 2230 y Fl(;)8 b(:)g(:)g(:)t(;)g(s)652 2237 y Fi(k)673 2230 y Ft(\),)716 2222 y Fl(~)719 2230 y(t)13 b Ft(=)g(\()p Fl(t)830 2237 y Fp(1)849 2230 y Fl(;)8 b(:)g(:)g(:)d(;)j(t)967 2237 y Fi(r)986 2230 y Ft(\).)19 b(The)d(set)f Fb(stuffle)o Ft(\()n Fl(~)-21 b(s)p Ff(j)1417 2222 y Fl(~)1420 2230 y(t)p Ft(\))15 b(is)g(de\014ned)i(as)e(follo)o(ws)48 2300 y(1.)22 b(\()p Fl(s)145 2307 y Fp(1)165 2300 y Fl(;)8 b(:)g(:)g(:)t(;)g(s)287 2307 y Fi(k)308 2300 y Fl(;)g(t)345 2307 y Fp(1)365 2300 y Fl(;)g(:)g(:)g(:)t(;)g(t)482 2307 y Fi(r)501 2300 y Ft(\))k Ff(2)h Fb(stuffle)o Ft(\()n Fl(~)-21 b(s)p Ff(j)790 2291 y Fl(~)793 2300 y(t)p Ft(\).)48 2356 y(2.)22 b(If)15 b(\()p Fl(U;)8 b(s)242 2363 y Fi(n)265 2356 y Fl(;)g(t)302 2363 y Fi(m)335 2356 y Fl(;)g(V)h Ft(\))15 b(is)g(in)h Fb(stuffle)o Ft(\()n Fl(~)-21 b(s)p Ff(j)739 2348 y Fl(~)742 2356 y(t)p Ft(\))15 b(then)h(also)f(are)g(\()p Fl(U;)8 b(t)1148 2363 y Fi(m)1180 2356 y Fl(;)g(s)1222 2363 y Fi(n)1245 2356 y Fl(;)g(V)h Ft(\))15 b(and)g(\()p Fl(U;)8 b(s)1514 2363 y Fi(n)1547 2356 y Ft(+)i Fl(t)1608 2363 y Fi(m)1642 2356 y Fl(;)e(V)h Ft(\).)50 2442 y(One)16 b(also)f(has)413 2563 y(#)p Fb(stuffle)o Ft(\()n Fl(~)-21 b(s)p Ff(j)667 2555 y Fl(~)670 2563 y(t)p Ft(\))12 b(=)789 2507 y Fi(r)764 2520 y Fh(X)767 2618 y Fi(j)r Fp(=0)838 2499 y Fh(\022)871 2533 y Fl(k)f Ft(+)g Fl(j)911 2595 y(r)973 2499 y Fh(\023)q(\022)1040 2533 y Fl(r)1040 2595 y(j)1062 2499 y Fh(\023)1108 2563 y Ft(=)1156 2502 y Fp(max)o(\()p Fi(k)q(;r)q Fp(\))1193 2520 y Fh(X)1195 2618 y Fi(j)r Fp(=0)1302 2499 y Fh(\022)1336 2533 y Fl(k)1338 2595 y(r)1361 2499 y Fh(\023)q(\022)1428 2533 y Fl(r)1428 2595 y(j)1450 2499 y Fh(\023)1483 2563 y Ft(2)1506 2545 y Fi(j)1524 2563 y Fl(:)p eop %%Page: 38 4 38 3 bop 0 22 a Fp(38)0 120 y Fs(Theorem)17 b(6)h Ft(\(Stu\017e)d(Iden)o (tities)h([4]\))p Fs(.)698 210 y Fl(\020)s Ft(\()n Fl(~)-21 b(s)p Ft(\))p Fl(\020)s Ft(\()816 202 y Fl(~)819 210 y(t)p Ft(\))12 b(=)998 167 y Fh(X)913 273 y Fi(~)-18 b(u)q Fg(2)p Fa(stuffle)m Fp(\()o Fi(~)h(s)p Fg(j)1119 267 y Fi(~)1121 273 y(t)p Fp(\))1155 210 y Fl(\020)s Ft(\()o Fl(~)-22 b(u)p Ft(\))p Fl(:)50 353 y Ft(F)l(or)14 b(example)304 434 y Fl(\020)s Ft(\()p Fl(r)o(;)8 b(s)p Ft(\))p Fl(\020)s Ft(\()p Fl(t)p Ft(\))j(=)i Fl(\020)s Ft(\()p Fl(r)o(;)8 b(s;)g(t)p Ft(\))g(+)i Fl(\020)s Ft(\()p Fl(r)o(;)e(s)h Ft(+)h Fl(t)p Ft(\))g(+)h Fl(\020)s Ft(\()p Fl(r)o(;)d(t;)g(s)p Ft(\))g(+)i Fl(\020)s Ft(\()p Fl(r)h Ft(+)g Fl(t;)d(s)p Ft(\))h(+)i Fl(\020)s Ft(\()p Fl(t;)d(r)o(;)g(s)p Ft(\))p Fl(:)541 548 y Ft(4.)25 b Fs(In)o(tegral)18 b(Represen)o(tations)f (for)g(MDPs)50 629 y Ft(Let)e Fl(R)166 636 y Fp(1)185 629 y Fl(;)8 b(:)g(:)g(:)d(;)j(R)322 636 y Fi(k)357 629 y Ft(b)q(e)16 b(disjoin)o(t)g(sets)f(of)g(partitions)g(of)g Ff(f)p Ft(1)p Fl(;)8 b(:)g(:)g(:)t(;)g(k)q Ff(g)p Ft(.)19 b(F)l(or)c(eac)o(h)g(1)d Ff(\024)h Fl(m)g Ff(\024)g Fl(n)p Ft(,)i(let)637 719 y Fl(r)658 726 y Fi(m)704 719 y Ft(=)764 676 y Fh(X)752 775 y Fi(i)p Fg(2)p Fi(R)815 779 y Fe(m)851 719 y Fl(s)872 726 y Fi(i)931 719 y Ft(and)46 b Fl(d)1074 726 y Fi(m)1120 719 y Ft(=)1184 676 y Fh(Y)1168 775 y Fi(i)p Fg(2)p Fi(R)1231 779 y Fe(m)1267 719 y Fl(b)1287 726 y Fi(i)1300 719 y Fl(:)0 846 y Ft(F)l(rom)14 b(the)i(gamma)e(function)i(iden)o(tit)o(y)537 949 y Fl(r)559 930 y Fg(\000)p Fi(s)604 949 y Ft(\000\()p Fl(s)p Ft(\))d(=)750 887 y Fh(Z)795 900 y Fg(1)775 990 y Fp(1)833 949 y Ft(\(log)8 b Fl(x)p Ft(\))961 930 y Fi(s)p Fg(\000)p Fp(1)1024 949 y Fl(x)1050 930 y Fg(\000)p Fi(r)q Fg(\000)p Fp(1)1141 949 y Fl(dx;)53 b(r)o(;)8 b(s)j(>)i Ft(0)p Fl(:)0 1049 y Ft(one)i(gets)0 1134 y Fs(Prop)q(osition)k(1.)234 1276 y Fl(\025)269 1212 y Fh(\022)304 1248 y Fl(r)325 1255 y Fp(1)345 1248 y Fl(;)8 b(:)g(:)g(:)t(;)g(r)467 1255 y Fi(n)301 1302 y Fl(d)325 1309 y Fp(1)345 1302 y Fl(;)g(:)g(:)g(:)t(;)g (d)470 1309 y Fi(n)493 1212 y Fh(\023)539 1276 y Ft(=)587 1182 y Fh(8)587 1223 y(<)587 1305 y(:)648 1219 y Fi(k)629 1232 y Fh(Y)627 1330 y Fi(j)r Fp(=1)696 1214 y Fh(Z)742 1227 y Fg(1)721 1317 y Fp(1)791 1245 y Ft(\(log)g Fl(x)901 1252 y Fi(j)920 1245 y Ft(\))938 1228 y Fi(s)954 1233 y Fe(j)970 1228 y Fg(\000)p Fp(1)p 791 1265 226 2 v 853 1307 a Ft(\000\()p Fl(s)920 1314 y Fi(j)938 1307 y Ft(\))1027 1245 y Fl(dx)1077 1252 y Fi(j)p 1027 1265 68 2 v 1039 1307 a Fl(x)1065 1314 y Fi(j)1100 1182 y Fh(9)1100 1223 y(=)1100 1305 y(;)1175 1219 y Fi(n)1157 1232 y Fh(Y)1148 1330 y Fi(m)p Fp(=1)1232 1184 y Fh(0)1232 1266 y(@)1272 1276 y Fl(d)1296 1283 y Fi(m)1351 1219 y(m)1338 1232 y Fh(Y)1336 1330 y Fi(j)r Fp(=1)1415 1232 y Fh(Y)1405 1331 y Fi(i)p Fg(2)p Fi(R)1468 1336 y Fe(j)1491 1276 y Fl(x)1517 1283 y Fi(i)1541 1276 y Ff(\000)i Ft(1)1609 1184 y Fh(1)1609 1266 y(A)1649 1196 y Fg(\000)p Fp(1)1704 1276 y Fl(:)50 1416 y Ft(F)l(or)15 b(example,)i(giv)o(en)f(a)g(rational)g(function)h(on)f Fl(x)f Ft(and)i Fl(y)r Ft(,)e Fl(R)p Ft(\()p Fl(x;)8 b(y)r Ft(\).)21 b(Let)16 b Fl(I)t Ft(\()p Fl(R)p Ft(\))e(b)q(e)j(the)f(follo)o (wing)h Fo(p)n(artition)0 1470 y(inte)n(gr)n(als)508 1559 y Fl(I)t Ft(\()p Fl(R)p Ft(\))11 b(=)662 1498 y Fh(Z)708 1511 y Fg(1)687 1601 y Fp(1)753 1498 y Fh(Z)798 1511 y Fg(1)778 1601 y Fp(1)848 1529 y Ft(\(log)d Fl(x)p Ft(\))976 1512 y Fi(s)p Fg(\000)p Fp(1)1039 1529 y Ft(\(log)g Fl(y)r Ft(\))1165 1512 y Fi(t)p Fg(\000)p Fp(1)p 848 1549 377 2 v 954 1591 a Ft(\000\()p Fl(s)p Ft(\)\000\()p Fl(t)p Ft(\))1281 1529 y Fl(dxdy)p 1234 1549 191 2 v 1234 1591 a(xy)r(R)p Ft(\()p Fl(x;)g(y)r Ft(\))1430 1559 y Fl(:)0 1655 y Ft(It)15 b(follo)o(ws)g(that)657 1752 y Fl(\025)692 1688 y Fh(\022)725 1724 y Fl(s)10 b Ft(+)h Fl(t)750 1778 y(ab)818 1688 y Fh(\023)864 1752 y Ft(=)i Fl(I)t Ft(\()p Fl(abxy)e Ff(\000)f Ft(1\))p Fl(;)663 1879 y(\025)698 1815 y Fh(\022)745 1851 y Fl(s;)e(t)730 1905 y(a;)g(ab)818 1815 y Fh(\023)864 1879 y Ft(=)13 b Fl(I)t Ft([\()p Fl(ax)c Ff(\000)h Ft(1\)\()p Fl(abxy)h Ff(\000)f Ft(1\)])p Fl(;)667 2005 y(\025)702 1941 y Fh(\022)747 1978 y Fl(t;)e(s)735 2032 y(b;)g(ab)818 1941 y Fh(\023)864 2005 y Ft(=)13 b Fl(I)t Ft([\()p Fl(by)d Ff(\000)h Ft(1\)\()p Fl(abxy)f Ff(\000)h Ft(1\)])p Fl(;)598 2132 y(\025)633 2068 y Fh(\022)667 2105 y Fl(s)666 2159 y(a)690 2068 y Fh(\023)731 2132 y Fl(\025)766 2068 y Fh(\022)800 2105 y Fl(t)798 2159 y(b)818 2068 y Fh(\023)864 2132 y Ft(=)i Fl(I)t Ft([\()p Fl(ax)c Ff(\000)h Ft(1\)\()p Fl(by)h Ff(\000)f Ft(1\)])p Fl(:)0 2238 y Ft(F)l(rom)k(the)i(rational)f(iden)o(tit)o(y)593 2313 y(1)p 444 2333 321 2 v 444 2375 a(\()p Fl(ax)10 b Ff(\000)h Ft(1\)\()p Fl(by)f Ff(\000)h Ft(1\))783 2344 y(=)910 2313 y(1)p 836 2333 172 2 v 836 2375 a Fl(abxy)g Ff(\000)g Ft(1)1020 2280 y Fh(\022)1111 2313 y Ft(1)p 1058 2333 129 2 v 1058 2375 a Fl(ax)f Ff(\000)h Ft(1)1202 2344 y(+)1302 2313 y(1)p 1252 2333 122 2 v 1252 2375 a Fl(by)h Ff(\000)e Ft(1)1389 2344 y(+)g(1)1457 2280 y Fh(\023)1498 2344 y Fl(;)0 2446 y Ft(one)15 b(gets)469 2533 y Fl(\025)504 2468 y Fh(\022)538 2505 y Fl(s)536 2559 y(a)560 2468 y Fh(\023)601 2533 y Fl(\025)636 2468 y Fh(\022)671 2505 y Fl(t)669 2559 y(b)688 2468 y Fh(\023)735 2533 y Ft(=)e Fl(\025)818 2468 y Fh(\022)865 2505 y Fl(s;)8 b(t)850 2559 y(a;)g(ab)938 2468 y Fh(\023)981 2533 y Ft(+)j Fl(\025)1062 2468 y Fh(\022)1107 2505 y Fl(t;)d(s)1094 2559 y(b;)g(ab)1178 2468 y Fh(\023)1221 2533 y Ft(+)j Fl(\025)1302 2468 y Fh(\022)1334 2505 y Fl(s)g Ft(+)f Fl(t)1359 2559 y(ab)1428 2468 y Fh(\023)1469 2533 y Fl(:)0 2629 y Ft(One)16 b(can)f(sa)o(y)g(that)f Fo(stu\017e)i (identities)g(ar)n(e)g(e)n(quivalent)f(to)i(r)n(ational)f(identities)f(via)i (p)n(artition)f(inte)n(gr)n(als)p Ft(.)p eop %%Page: 39 5 39 4 bop 1915 22 a Fp(39)0 120 y Fs(De\014nition)19 b(5.)j Ft(Giv)o(en)15 b(functions)g Fl(f)655 127 y Fi(j)686 120 y Ft(:)e([)p Fl(a;)8 b(c)p Ft(])i Ff(!)j Fk(R)c Ft(and)15 b(the)f(1-forms)f (\012)1278 127 y Fi(j)1309 120 y Ft(=)g Fl(f)1379 127 y Fi(j)1398 120 y Ft(\()p Fl(y)1438 127 y Fi(j)1456 120 y Ft(\))p Fl(dy)1520 127 y Fi(j)1538 120 y Fl(;)h Ft(the)g Fo(iter)n(ate)n(d)h(inte)n(gr)n(al)0 174 y Ft(o)o(v)o(er)f(\012)130 181 y Fi(j)164 174 y Ft(are)g(de\014ned)j(as)e (follo)o(ws)449 232 y Fh(Z)494 245 y Fi(c)474 335 y(a)519 294 y Ft(\012)552 301 y Fp(1)579 294 y Ff(\001)8 b(\001)g(\001)e Ft(\012)673 301 y Fi(n)709 294 y Ft(=)757 216 y Fh(\()794 263 y Ft(1)514 b(if)16 b Fl(n)d Ft(=)g(0)p Fl(;)794 291 y Fh(R)824 304 y Fi(c)815 344 y(a)849 328 y Fl(f)5 b Ft(\()p Fl(y)916 335 y Fp(1)936 328 y Ft(\))962 291 y Fh(R)991 304 y Fi(y)1008 309 y Fn(1)982 344 y Fi(a)1036 328 y Ft(\012)1069 335 y Fp(2)1096 328 y Ff(\001)j(\001)g(\001)d Ft(\012)1189 335 y Fi(n)1220 328 y Fl(dy)1266 335 y Fp(1)1331 328 y Ft(if)16 b Fl(n)d(>)g Ft(0.)50 415 y(It)k(turns)h(out)f(that)g(MDPs)g(ha)o(v)o(e)g(a)g(con)o(v)o (enien)o(t)h(iterated)g(in)o(tegral)g(represen)o(tation)f(in)i(terms)e(of)g (1-forms)0 469 y Fl(!)28 476 y Fi(b)58 469 y Ft(=)c Fl(dy)r(=)p Ft(\()p Fl(y)e Ff(\000)g Fl(b)o Ft(\))p Fl(;)j Ft(i.e.)489 558 y Fl(\025)524 494 y Fh(\022)556 531 y Fl(s)577 538 y Fp(1)597 531 y Fl(;)8 b(:)g(:)g(:)d(;)j(s)720 538 y Fi(k)558 585 y Fl(b)578 592 y Fp(1)597 585 y Fl(;)g(:)g(:)g(:)d(;)j(b)719 592 y Fi(k)741 494 y Fh(\023)787 558 y Ft(=)13 b(\()p Ff(\000)p Ft(1\))929 540 y Fi(k)957 497 y Fh(Z)1003 510 y Fp(1)983 600 y(0)1030 558 y Fl(!)1060 538 y Fi(s)1076 543 y Fn(1)1094 538 y Fg(\000)p Fp(1)1058 571 y(0)1141 558 y Fl(!)1169 565 y Fi(b)1184 570 y Fn(1)1211 558 y Ff(\001)8 b(\001)g(\001)e Fl(!)1302 537 y Fi(s)1318 543 y Fe(k)1337 537 y Fg(\000)p Fp(1)1300 571 y(0)1384 558 y Fl(!)1412 565 y Fi(b)1427 571 y Fe(k)1449 558 y Fl(:)0 650 y Ft(By)16 b(the)f(iterated)h(in)o(tegral)g(represen)o(tation,)f(Broadh)o (urst)g(has)g(generalized)i(the)f(notion)g(of)f(dualit)o(y)h(principle)0 704 y(for)d(MZVs)h(to)f(include)k(the)d(relations)h(b)q(et)o(w)o(een)f (iterated)g(in)o(tegrals)h(in)o(v)o(olving)g(the)f(sixth)h(ro)q(ot)e(of)h (unit)o(y)g(using)0 758 y(the)21 b(c)o(hange)g(of)g(v)m(ariable)i Fl(y)h Ff(7!)f Ft(1)14 b Ff(\000)h Fl(y)23 b Ft(at)d(eac)o(h)h(lev)o(el)i(of) e(in)o(tegration)g([3)o(].)37 b(This)22 b(principle)i(generates)d(an)0 812 y(in)o(v)o(olution)16 b Fl(!)241 819 y Fi(b)271 812 y Ff(7!)e Fl(!)358 819 y Fp(1)p Fg(\000)p Fi(b)435 812 y Ft(holding)j(for)d(an)o(y)h (complex)h(v)m(alue)h Fl(b)p Ft(.)i(F)l(or)c(example)469 920 y Fl(\025)504 856 y Fh(\022)554 892 y Ft(2)p Fl(;)8 b Ft(1)537 946 y(1)p Fl(;)g Ff(\000)p Ft(1)638 856 y Fh(\023)684 920 y Ft(=)732 858 y Fh(Z)777 871 y Fp(1)757 961 y(0)805 920 y Fl(!)833 927 y Fp(0)853 920 y Fl(!)881 927 y Fp(1)901 920 y Fl(!)929 927 y Fg(\000)p Fp(1)989 920 y Ft(=)1037 858 y Fh(Z)1082 871 y Fp(1)1062 961 y(0)1109 920 y Fl(!)1137 927 y Fp(2)1157 920 y Fl(!)1185 927 y Fp(0)1205 920 y Fl(!)1233 927 y Fp(1)1266 920 y Ft(=)13 b Fl(\025)1349 856 y Fh(\022)1382 892 y Ft(1)p Fl(;)8 b Ft(2)1382 946 y(2)p Fl(;)g Ft(1)1447 856 y Fh(\023)0 1021 y Ft(whic)o(h)16 b(is)566 1068 y Fh(X)566 1166 y Fi(n)p Fg(\025)p Fp(1)657 1081 y Ft(1)p 645 1101 48 2 v 645 1143 a Fl(n)672 1130 y Fp(2)704 1034 y Fh(")731 1055 y Fi(n)p Fg(\000)p Fp(1)731 1068 y Fh(X)732 1167 y Fi(k)q Fp(=1)810 1081 y Ft(\()p Ff(\000)p Ft(1\))904 1064 y Fi(k)p 810 1101 115 2 v 855 1143 a Fl(k)930 1034 y Fh(#)969 1112 y Ft(=)1017 1068 y Fh(X)1017 1166 y Fi(n)p Fg(\025)p Fp(1)1121 1081 y Ft(1)p 1096 1101 74 2 v 1096 1143 a Fl(n)p Ft(2)1146 1130 y Fi(n)1182 1034 y Fh(")1209 1055 y Fi(n)p Fg(\000)p Fp(1)1209 1068 y Fh(X)1210 1167 y Fi(k)q Fp(=1)1288 1081 y Ft(2)1311 1064 y Fi(k)p 1288 1101 45 2 v 1288 1143 a Fl(k)1313 1130 y Fp(2)1337 1034 y Fh(#)1371 1112 y Fl(:)0 1225 y Ft(Sev)o(eral)f(results)g(can)f(b)q(e)h(similarly)h(pro)o(v)o (ed)e(b)o(y)h(using)g(other)f(transformations)f(of)h(v)m(ariables)i(in)f (their)g(in)o(tegral)0 1279 y(represen)o(tations.)20 b(Here,)15 b(the)g(authors)g(get)0 1362 y Fs(Theorem)i(7)h Ft(\(Cyclotomic\))p Fs(.)k Fo(L)n(et)12 b Fl(n)h Fo(b)n(e)g(a)g(p)n(ositive)f(inte)n(ger.)19 b(L)n(et)13 b Fl(b)1190 1369 y Fp(1)1209 1362 y Fl(;)8 b(:)g(:)g(:)d(;)j(b) 1331 1369 y Fi(k)1364 1362 y Fo(b)n(e)k(arbitr)n(ary)i(c)n(omplex)f(numb)n (ers,)0 1416 y(and)j(let)g Fl(s)173 1423 y Fp(1)193 1416 y Fl(;)8 b(:)g(:)g(:)d(;)j(s)316 1423 y Fi(k)353 1416 y Fo(b)n(e)16 b(p)n(ositive)g(inte)n(gers.)j(Then)294 1518 y Fl(\025)329 1453 y Fh(\022)362 1490 y Fl(s)383 1497 y Fp(1)403 1490 y Fl(;)8 b(:)g(:)g(:)d(;)j(s)526 1497 y Fi(k)361 1544 y Fl(b)381 1527 y Fi(n)381 1556 y Fp(1)404 1544 y Fl(;)g(:)g(:)g(:)d(;)j(b)526 1527 y Fi(n)526 1558 y(k)548 1453 y Fh(\023)594 1518 y Ft(=)13 b Fl(n)669 1499 y Fi(s)p Fg(\000)p Fi(k)970 1474 y Fh(X)742 1579 y Fi(")758 1584 y Fn(1)776 1579 y Fi(;:::)o(;")841 1585 y Fe(k)860 1579 y Fg(2f)p Fp(1)p Fi(;)p Fp(e)946 1569 y Fn(2)p Fe(\031)q(i=n)1027 1579 y Fi(;:::)o(;)p Fp(e)1092 1569 y Fn(2)p Fe(\031)q Fn(\()p Fe(n)p Fd(\000)p Fn(1\))p Fe(=n)1245 1579 y Fg(g)1271 1518 y Fl(\025)1306 1453 y Fh(\022)1378 1490 y Fl(s)1399 1497 y Fp(1)1419 1490 y Fl(;)8 b(:)g(:)g(:)d(;)j(s)1542 1497 y Fi(k)1338 1544 y Fl(")1359 1551 y Fp(1)1379 1544 y Fl(b)1399 1551 y Fp(1)1418 1544 y Fl(;)g(:)g(:)g(:)d(;)j(")1541 1551 y Fi(k)1562 1544 y Fl(b)1582 1551 y Fi(k)1603 1453 y Fh(\023)1644 1518 y Fl(:)0 1656 y Fs(Theorem)17 b(8.)22 b Fo(L)n(et)16 b Fl(s)385 1663 y Fp(1)405 1656 y Fl(;)8 b(:)g(:)g(:)d(;)j(s)528 1663 y Fi(k)565 1656 y Fo(b)n(e)16 b(nonne)n(gative)e(inte)n(gers.)239 1776 y Fl(\025)274 1712 y Fh(\022)307 1748 y Ft(1)c(+)g Fl(s)406 1755 y Fp(1)426 1748 y Fl(;)e(:)g(:)g(:)d(;)j Ft(1)h(+)h Fl(s)626 1755 y Fi(k)369 1802 y Ff(\000)p Ft(1)p Fl(;)e(:)g(:)g(:)d(;)j Ff(\000)p Ft(1)648 1712 y Fh(\023)694 1776 y Ft(=)742 1733 y Fh(X)815 1776 y Fl(\026)850 1726 y Fh(\020)877 1776 y Ft(Cat)951 1757 y Fi(k)951 1787 y(j)r Fp(=1)1014 1776 y Ff(f\000)p Ft(1)p Ff(g)g Ft(Cat)1198 1750 y Fi(s)1214 1755 y Fe(j)1198 1790 y Fi(i)p Fp(=1)1257 1776 y Ff(f)p Fl(")1301 1783 y Fi(i;j)1341 1776 y Ff(g)1364 1726 y Fh(\021)1420 1719 y Fi(k)1400 1733 y Fh(Y)1399 1831 y Fi(j)r Fp(=1)1460 1776 y Ff(f\000)p Ft(1)p Ff(g)1584 1713 y Fi(s)1600 1718 y Fe(j)1571 1733 y Fh(Y)1572 1831 y Fi(i)p Fp(=1)1637 1776 y Fl(")1658 1783 y Fi(i;j)1698 1776 y Fl(;)0 1902 y Fo(wher)n(e)16 b(the)h(sum)f(is)g(over)g(al)r(l)g Ft(2)537 1886 y Fi(s)571 1902 y Fo(se)n(quenc)n(es)e(of)j(signs)e Ft(\()p Fl(")981 1909 y Fi(i;j)1021 1902 y Ft(\))g Fo(with)i(e)n(ach)f Fl(")1276 1909 y Fi(i;j)1329 1902 y Ff(2)d(f)p Ft(1)p Fl(;)8 b Ff(\000)p Ft(1)p Ff(g)15 b Fo(for)h(al)r(l)g(1)p Ff(\024)d Fl(i)g Ff(\024)g Fl(s)1841 1909 y Fi(j)1859 1902 y Fl(;)8 b Ft(1)k Ff(\024)0 1956 y Fl(j)j Ff(\024)e Fl(k)q Fo(,)j(and)h Ft(Cat)e Fo(denotes)h(string)f(c)n(onc)n(atenation.)841 2054 y Fq(Bibliograp)o(h)o(y)0 2127 y Fu([1])k(Borw)o(ein)d(\(Jonathan)h(M.\),)e (Bradley)i(\(Da)o(vid)g(M.\),)e(and)i(Broadh)o(urst)g(\(Da)o(vid)g(J.\).)d({) h(Ev)n(aluations)k(of)c Fc(k)q Fu(-fold)h(Euler/Zagier)60 2172 y(sums:)f(a)9 b(comp)q(endium)j(of)d(results)h(for)f(arbitrary)h Fc(k)q Fu(.)f Fr(Ele)n(ctr)n(onic)f(Journal)h(of)g(Combinatorics)p Fu(,)e(v)o(ol.)j(4,)f(n)1572 2175 y(\027)1602 2172 y(2,)g Fc(1997)q Fu(,)h(pp.)f(Researc)o(h)60 2218 y(P)o(ap)q(er)k(5,)g(21)g(pp.)g({)g(The)g (Wilf)i(F)m(estsc)o(hrift)e(\(Philadelp)q(hi)q(a,)i(P)m(A,)d(1996\).)0 2264 y([2])19 b(Borw)o(ein)24 b(\(Jonathan)h(M.\),)h(Bradley)f(\(Da)o(vid)h (M.\),)f(Broadh)o(urst)h(\(Da)o(vid)f(J.\),)g(and)g(P)o(etr)e(\(Lison)o(\024) -18 b(ek\).)25 b({)f Fr(Sp)n(e)n(cial)d(val-)60 2309 y(ues)h(of)g (multidimensiona)o(l)e(p)n(olylo)n(garithms)p Fu(.)f({)k(Researc)o(h)h(rep)q (ort)f(n)1122 2312 y(\027)1152 2309 y(98-106,)j(CECM,)c Fc(1998)q Fu(.)g(Av)n(ailable)k(at)d(the)g(URL)60 2355 y Fm(http://ww)o(w.)o(cec)o(m.s) o(fu)o(.ca)o(/p)o(rep)o(rin)o(ts)o(/19)o(98)o(pp.)o(htm)o(l)p Fu(.)0 2401 y([3])c(Broadh)o(urst)13 b(\(D.)f(J.\).)f({)h Fr(Massive)f(3-lo)n (op)f(F)m(eynman)i(Diagr)n(ams)f(R)n(e)n(ducible)f(to)j Fc(S)r(C)1290 2385 y Fd(\003)1321 2401 y Fr(primitives)e(of)h(algebr)n(as)f(of)h(the)g (sixth)f(r)n(o)n(ot)60 2446 y(of)i(unity)p Fu(.)e({)i(T)m(ec)o(hnical)h(Rep)q (ort)g(n)557 2449 y(\027)586 2446 y(OUT-4102-72,)f(hep-th/9803091,)i(Op)q(en) e(Univ)o(ersit)o(y)m(,)i Fc(1998)q Fu(.)0 2492 y([4])k(Ho\013man)11 b(\(Mic)o(hael)i(E.\).)e({)g(The)f(algebra)j(of)e(m)o(ultiple)i(harmonic)g (series.)e Fr(Journal)g(of)g(A)o(lgebr)n(a)p Fu(,)e(v)o(ol.)i(194,)h(n)1640 2495 y(\027)1669 2492 y(2,)f Fc(1997)q Fu(,)g(pp.)g(477{)60 2538 y(495.)0 2583 y([5])19 b(Minh)13 b(\(Hoang)g(Ngo)q(c\))f(and)h(P)o (etitot)g(\(M.\).)e({)h(Lyndon)i(w)o(ords,)e(p)q(olylogarith)q(mic)j (functions)f(and)f(the)f(Riemann)i Fc(\020)h Fu(function.)e({)60 2629 y(Preprin)o(t.)p eop %%Page: 40 6 40 5 bop 0 22 a Fp(40)0 120 y Fu([6])19 b(Zagier)c(\(Don\).)e({)h(V)m(alues)g (of)f(zeta)h(functions)h(and)f(their)g(application)q(s.)i(In)d Fr(et)h(al.)e Fu(\(A.)h(Joseph\))h(\(editor\),)g Fr(Pr)n(o)n(c)n(e)n(e)n (dings)d(of)j(the)60 166 y(First)i(Eur)n(op)n(e)n(an)g(Congr)n(ess)g(of)g (Mathematics,)g(Paris)p Fu(.)g(v)o(ol.)h(I)q(I,)f(pp.)h(497{512.)h({)f (Birkh\177)-19 b(auser)19 b(V)m(erlag,)f Fc(1994)q Fu(.)e(\(Progress)i(in)60 212 y(Mathematics,)c(v)o(olume)g(120.\).)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF