(original) (raw)

%!PS-Adobe-2.0 %%Creator: dvips 5.511 Copyright 1986, 1993 Radical Eye Software %%Title: All.dvi %%CreationDate: Mon Aug 12 14:38:38 1996 %%Pages: 5 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSCommandLine: dvips -pp 117-121 All.dvi -o /home/blagny/lib/algo/seminars/sem91-92/lafforgue.ps %DVIPSSource: TeX output 1996.08.08:1909 %%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/blagny/algo2/zimmermann/Adm/Semin/All.dvi) @start /Fa 1 51 df<7FFFFFFF80FFFFFFFF80FFFFFFFF80E000000380E000000380E000000380E00000 0380E000000380E000000380E000000380E000000380E000000380E000000380E000000380E000 000380E000000380E000000380E000000380E000000380E000000380E000000380E000000380E0 00000380E000000380E000000380E000000380E000000380E000000380E000000380E000000380 FFFFFFFF80FFFFFFFF807FFFFFFF8021217BA42D>50 D E /Fb 3 111 df<004000C001800180 01800300030003000600060006000C000C000C00180018001800300030003000600060006000C0 00C0000A197D9210>61 D<007800180018003000300030073018E0306060606060C0C0C0C0C0C8 41C862D03C700D117E9010>100 D<71F09A189C18981818183030303030323062606460380F0B 7E8A13>110 D E /Fc 1 101 df<0007E00000E00000E00001C00001C00001C00001C000038000 038000038000038001E7000717000C0F00180F00380E00300E00700E00700E00E01C00E01C00E0 1C00E01C00E03880E03880E038806078803199001E0E00131D7E9C16>100 D E /Fd 39 122 df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e 27 122 df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f 4 77 df0 D<00000100000000800000008000 00004000000020FFFFFFFCFFFFFFFC00000020000000400000008000000080000001001E0C7E8D 23>33 D<0F8007C019E01C202070301040184008C00C8004800780048007000480038004800780 048004C00C400860082030381010E01E600F8007C01E0E7E8D23>49 D<0007C0001FC00021E000 41E000C0C00180000180000300000300000700000600000600000E00000E00000C00000C000018 00001800103000303F80607FF04043FF80807E0014177E9618>76 D E /Fg 13 115 df2 DI<0000180000300000600000E00000C0000180000380000700000600000E00000C00001C000038 0000380000700000700000E00000E00001E00001C00001C0000380000380000380000780000700 000700000F00000E00000E00001E00001E00001E00001C00001C00003C00003C00003C00003C00 00380000780000780000780000780000780000780000780000780000700000F00000F00000F000 00F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F000 00F00000F00000F00000F00000F00000F00000F00000F00000F00000F000007000007800007800 007800007800007800007800007800007800003800003C00003C00003C00003C00001C00001C00 001E00001E00001E00000E00000E00000F000007000007000007800003800003800003800001C0 0001C00001E00000E00000E000007000007000003800003800001C00000C00000E000006000007 000003800001800000C00000E0000060000030000018157C768121>32 DIII<0018007800F001E003C007800F001F001E 003E003C007C007C007800F800F800F800F800F800F800F800F800F800F800F800F800F800F800 F800F800F800F800F800F800F800F800F8000D25707E25>56 D58 D<007C007C007C007C00 7C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C 00F800F800F800F001F001E003E003C0078007000E001C003800F000C000F00038001C000E0007 00078003C003E001E001F000F000F800F800F8007C007C007C007C007C007C007C007C007C007C 007C007C007C007C007C007C007C007C007C007C007C007C007C007C0E4D798025>60 D62 D88 D<000000038000000006600000000C700000000CF00000000CF00000001C6000 000018000000003800000000380000000038000000007000000000700000000070000000007000 000000F000000000E000000000E000000000E000000001E000000001E000000001C000000001C0 00000003C000000003C000000003C000000003C000000007800000000780000000078000000007 800000000F800000000F800000000F000000000F000000001F000000001F000000001F00000000 1F000000001E000000003E000000003E000000003E000000003E000000003C000000007C000000 007C000000007C000000007C000000007800000000F800000000F800000000F800000000F80000 0000F000000001F000000001F000000001F000000001F000000001E000000001E000000003E000 000003E000000003C000000003C000000003C000000003C0000000078000000007800000000780 0000000780000000070000000007000000000F000000000F000000000E000000000E000000000E 000000001E000000001C000000001C000000001C00000000180000000038000000003800000000 3000000000700000006060000000F060000000F0C0000000E18000000063000000001E00000000 245C7E7F17>90 D<000000000200000000060000000006000000000C000000000C000000000C00 0000000C0000000018000000001800000000180000000018000000003000000000300000000030 0000000030000000006000000000600000000060000000006000000000C000000000C000000000 C000000000C0000000018000000001800000000180000000018000000001800000000300000000 03000000000300000000030000000006000000000600000000060000000006000000000C000000 000C000000000C000000000C000000001800000000180000000018000000001800000000300000 000030000000003000000000300000000060000000006000000000600008000060001C0000C000 1C0000C0003C0000C0005C0000C0005C000180008E000180000E000180000E000180000E000300 00070003000007000300000700030000070006000007000600000380060000038006000003800C 000003800C000001C00C000001C00C000001C018000001C018000001C018000000E018000000E0 18000000E030000000E030000000E0300000007030000000706000000070600000007060000000 386000000038C000000038C000000038C000000038C00000001D800000001D800000001D800000 001D800000000F000000000F000000000F000000000F000000000E000000000600000000060000 0027647C812A>114 D E /Fh 1 51 df<0007FE0000007FFFE00001FFFFF80003FFFFFE0007F0 1FFF000F8007FF801F0001FFC03E0000FFE07F8000FFF07FC0007FF0FFE0007FF8FFF0003FF8FF F0003FFCFFF0003FFCFFF0003FFCFFF0003FFC7FE0003FFC3FC0003FFC1F80003FFC0000003FFC 0000003FF80000007FF80000007FF00000007FF0000000FFE0000000FFC0000001FF80000001FF 00000003FE00000007FC00000007F80000000FF00000001FC00000003F800000007F00000000FC 00000001F800000001F0003C0003E0003C0007C0003C000F000078001E000078003C0000780078 0000F800F00000F801FFFFFFF803FFFFFFF007FFFFFFF00FFFFFFFF01FFFFFFFF03FFFFFFFF07F FFFFFFF0FFFFFFFFF0FFFFFFFFE0FFFFFFFFE0FFFFFFFFE026387BB731>50 D E /Fi 14 113 df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j 16 123 df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k 31 123 df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l 3 55 df<0C003C00CC000C000C000C000C000C000C000C000C000C000C000C000C00FF 8009107E8F0F>49 D<1F00618040C08060C0600060006000C00180030006000C00102020207FC0 FFC00B107F8F0F>I<0780184030C060C06000C000CF00F080E040C060C060C060406060C03080 1F000B107F8F0F>54 D E /Fm 34 123 df<00003F03E00000C386700001878CF00003879CF000 03031860000700380000070038000007003800000E003800000E007000000E007000000E007000 00FFFFFF80001C007000001C00E000001C00E000001C00E000001C00E000003800E000003801C0 00003801C000003801C000003801C000007001C000007003800000700380000070038000007003 8000006003800000E007000000E007000000E007000000E007000000C006000001C00E000001C0 0E000031860C0000798F180000F31E100000620C6000003C07C000002429829F1C>11 D<00003FE00000E01000018038000380780003007800070030000700000007000000070000000E 0000000E0000000E000000FFFFE0000E00E0001C01C0001C01C0001C01C0001C01C0001C038000 38038000380380003803800038070000380700007007000070071000700E2000700E2000700E20 00E00E2000E0064000E0038000E0000000C0000001C0000001C000003180000079800000F30000 00620000003C0000001D29829F1A>I<000100020004000800100020006000C001800180030007 0006000E000C001C0018003800380030007000700060006000E000E000C000C000C000C000C000 C000C000C000C000C000C000C000C0004000600060002000100010000800102E79A113>40 D<0010000008000004000006000002000003000003000003000001000001800001800001800001 800001800001800001800003800003800003800003000003000003000007000007000006000006 00000E00000C00000C00001C0000180000380000300000700000600000E00000C0000180000100 000300000600000C0000180000300000600000800000112E80A113>I<1C3C3C3C3C0404080810 20204080060E7D840E>44 D<7FF0FFE07FE00C037D8A10>I<70F8F8F0E005057B840E>I<070F1F 1F0E0000000000000000000070F8F8F0E008147B930E>58 D<0000FC040007030C001C00980030 007800E0007801C000380380003003800030070000300E0000301E0000201E0000203C0000003C 00000078000000780000007800000078000000F0000000F000FFF0F0000780F0000780F0000F00 70000F0070000F0070000F0070001E0038001E0018003E001C002E000E00CC000383040000FC00 001E217A9F23>71 D<0FFFFFF01E0780E0180780201007802020078020200F0020600F0020400F 0020400F0020801E0040001E0000001E0000001E0000003C0000003C0000003C0000003C000000 78000000780000007800000078000000F0000000F0000000F0000000F0000001E0000001E00000 01E0000001E0000003E00000FFFF00001C1F789E21>84 D<00F1800389C00707800E03801C0380 3C0380380700780700780700780700F00E00F00E00F00E00F00E20F01C40F01C40703C40705C40 308C800F070013147C9317>97 D<07803F8007000700070007000E000E000E000E001C001C001C F01D0C3A0E3C0E380F380F700F700F700F700FE01EE01EE01EE01CE03CE038607060E031C01F00 10207B9F15>I<007E0001C1000300800E07801E07801C07003C0200780000780000780000F000 00F00000F00000F00000F0000070010070020030040018380007C00011147C9315>I<00007800 03F80000700000700000700000700000E00000E00000E00000E00001C00001C000F1C00389C007 07800E03801C03803C0380380700780700780700780700F00E00F00E00F00E00F00E20F01C40F0 1C40703C40705C40308C800F070015207C9F17>I<007C01C207010E011C013C013802780C7BF0 7C00F000F000F000F0007000700170023804183807C010147C9315>I<00007800019C00033C00 033C000718000700000700000E00000E00000E00000E00000E0001FFE0001C00001C00001C0000 1C0000380000380000380000380000380000700000700000700000700000700000700000E00000 E00000E00000E00000C00001C00001C0000180003180007B0000F300006600003C00001629829F 0E>I<003C6000E27001C1E00380E00700E00F00E00E01C01E01C01E01C01E01C03C03803C0380 3C03803C03803C07003C07001C0F001C17000C2E0003CE00000E00000E00001C00001C00301C00 783800F0700060E0003F8000141D7E9315>I<01E0000FE00001C00001C00001C00001C0000380 00038000038000038000070000070000071E000763000E81800F01C00E01C00E01C01C03801C03 801C03801C0380380700380700380700380E10700E20700C20701C20700C40E00CC06007001420 7D9F17>I<00C001E001E001C000000000000000000000000000000E0033002300438043004700 87000E000E000E001C001C001C003840388030807080310033001C000B1F7C9E0E>I<01E0000F E00001C00001C00001C00001C0000380000380000380000380000700000700000703C00704200E 08E00E11E00E21E00E40C01C80001D00001E00001FC00038E00038700038700038384070708070 7080707080703100E03100601E0013207D9F15>107 D<03C01FC0038003800380038007000700 070007000E000E000E000E001C001C001C001C0038003800380038007000700070007100E200E2 00E200E200640038000A207C9F0C>I<1C0F80F0002630C318004740640C004780680E00470070 0E004700700E008E00E01C000E00E01C000E00E01C000E00E01C001C01C038001C01C038001C01 C038001C01C0708038038071003803806100380380E10038038062007007006600300300380021 147C9325>I<1C0F802630C04740604780604700704700708E00E00E00E00E00E00E00E01C01C0 1C01C01C01C01C03843803883803083807083803107003303001C016147C931A>I<007C0001C3 000301800E01C01E01C01C01E03C01E07801E07801E07801E0F003C0F003C0F003C0F00780F007 00700F00700E0030180018700007C00013147C9317>I<01C1E002621804741C04781C04701E04 701E08E01E00E01E00E01E00E01E01C03C01C03C01C03C01C0380380780380700380E003C1C007 2380071E000700000700000E00000E00000E00000E00001C00001C0000FFC000171D809317>I< 00F0400388C00705800E03801C03803C0380380700780700780700780700F00E00F00E00F00E00 F00E00F01C00F01C00703C00705C0030B8000F3800003800003800007000007000007000007000 00E00000E0000FFE00121D7C9315>I<1C1E002661004783804787804707804703008E00000E00 000E00000E00001C00001C00001C00001C00003800003800003800003800007000003000001114 7C9313>I<00FC030206010C030C070C060C000F800FF007F803FC003E000E700EF00CF00CE008 401020601F8010147D9313>I<018001C0038003800380038007000700FFF007000E000E000E00 0E001C001C001C001C003800380038003820704070407080708031001E000C1C7C9B0F>I<0E00 C03300E02301C04381C04301C04701C08703800E03800E03800E03801C07001C07001C07001C07 101C0E20180E20180E201C1E200C264007C38014147C9318>I<0E03803307802307C04383C043 01C04700C08700800E00800E00800E00801C01001C01001C01001C02001C02001C04001C04001C 08000E300003C00012147C9315>I<0E00C1C03300E3C02301C3E04381C1E04301C0E04701C060 870380400E0380400E0380400E0380401C0700801C0700801C0700801C0701001C0701001C0602 001C0F02000C0F04000E13080003E1F0001B147C931E>I<0E00C03300E02301C04381C04301C0 4701C08703800E03800E03800E03801C07001C07001C07001C07001C0E00180E00180E001C1E00 0C3C0007DC00001C00001C00003800F03800F07000E06000C0C0004380003E0000131D7C9316> 121 D<01C04003E08007F1800C1F00080200000400000800001000002000004000008000010000 0200000401000802001002003E0C0063FC0041F80080E00012147D9313>I E /Fn 8 62 df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o 27 122 df<0018007000E001C00380038007000E 000E001E001C003C003C007800780078007800F800F000F000F000F000F000F000F000F000F000 F80078007800780078003C003C001C001E000E000E0007000380038001C000E0007000180D2D7D A114>40 DI<387CFEFFFF7F3B030306060E0C1870 2008107C860F>44 D<387CFEFEFE7C3807077C860F>46 D<00E00001E0000FE000FFE000F3E000 03E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E000 03E00003E00003E00003E00003E00003E00003E00003E00003E000FFFF80FFFF80111D7C9C1A> 49 D<07F0001FFE00383F007C1F80FE0FC0FE0FC0FE0FE0FE07E07C07E03807E0000FE0000FC0 000FC0001F80001F00003E0000780000F00000E00001C0000380600700600E00601C00E01FFFC0 3FFFC07FFFC0FFFFC0FFFFC0131D7D9C1A>I<01FC0007FF000E0F801E0FC03F07E03F07E03F07 E03F07E01E0FC0000FC0000F80001F0001FC0001FC00000F800007C00003E00003F00003F83803 F87C03F8FE03F8FE03F8FE03F0FC03F07807E03C0FC01FFF8003FC00151D7E9C1A>I69 D72 DI<03FFFC03FFFC000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0 000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0100FC0 7C0FC0FE0FC0FE0FC0FE0F80FC1F80783F003FFE000FF000161F7F9E1B>I76 D80 D<7FFFFFFC7FFFFFFC7C07E07C7007E01C60 07E00C6007E00CE007E00EC007E006C007E006C007E006C007E0060007E0000007E0000007E000 0007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0 000007E0000007E0000007E0000007E00003FFFFC003FFFFC01F1E7E9D24>84 D<07FC001FFF003F0F803F07C03F03E03F03E00C03E00003E0007FE007FBE01F03E03C03E07C03 E0F803E0F803E0F803E0FC05E07E0DE03FF8FE0FE07E17147F9319>97 DI<01FE0007FF801F0FC03E0FC03E0FC07C0FC07C0300FC00 00FC0000FC0000FC0000FC0000FC00007C00007E00003E00603F00C01F81C007FF0001FC001314 7E9317>I<0007F80007F80000F80000F80000F80000F80000F80000F80000F80000F80000F800 00F801F8F80FFEF81F83F83E01F87E00F87C00F87C00F8FC00F8FC00F8FC00F8FC00F8FC00F8FC 00F87C00F87C00F87E00F83E01F81F07F80FFEFF03F8FF18207E9F1D>I<01FE0007FF800F83C0 1E01E03E00F07C00F07C00F8FC00F8FFFFF8FFFFF8FC0000FC0000FC00007C00007C00003E0018 1E00180F807007FFE000FF8015147F9318>I<001F8000FFC001F3E003E7E003C7E007C7E007C3 C007C00007C00007C00007C00007C000FFFC00FFFC0007C00007C00007C00007C00007C00007C0 0007C00007C00007C00007C00007C00007C00007C00007C00007C00007C0003FFC003FFC001320 7F9F10>I104 D<1C003E007F007F007F003E001C00000000000000000000000000FF00FF001F001F001F001F00 1F001F001F001F001F001F001F001F001F001F001F001F00FFE0FFE00B217EA00E>I109 DI<01FF0007FFC01F83F03E00F83E00F87C007C7C007CFC00 7EFC007EFC007EFC007EFC007EFC007E7C007C7C007C3E00F83E00F81F83F007FFC001FF001714 7F931A>I114 D121 D E /Fp 15 118 df68 D76 D<00000FFE0000000000FFFFE000000007FFFFFC0000001FFC07FF0000003FE000 FF800000FFC0007FE00001FF00001FF00003FE00000FF80007FE00000FFC0007FC000007FC000F F8000003FE001FF8000003FF001FF8000003FF003FF0000001FF803FF0000001FF803FF0000001 FF807FF0000001FFC07FE0000000FFC07FE0000000FFC0FFE0000000FFE0FFE0000000FFE0FFE0 000000FFE0FFE0000000FFE0FFE0000000FFE0FFE0000000FFE0FFE0000000FFE0FFE0000000FF E0FFE0000000FFE0FFE0000000FFE0FFE0000000FFE07FE0000000FFC07FE0000000FFC07FF000 0001FFC07FF0000001FFC03FF0000001FF803FF0000001FF801FF8000003FF001FF8000003FF00 0FF803F003FE000FFC0FFC07FE0007FE1FFE0FFC0003FE1C0F0FF80001FF38079FF00000FFF807 FFE000003FF803FF8000001FFC07FF00000007FFFFFC00000000FFFFF0004000000FFFF800E000 000001FC00E000000001FC01E000000001FF03E000000000FFFFE000000000FFFFE000000000FF FFC0000000007FFFC0000000007FFFC0000000003FFF80000000003FFF80000000001FFF000000 00000FFE000000000007FC000000000001F000333F7BB03E>81 D<007FF8000003FFFF000007FF FFC0000FE01FE0001FF007F0001FF003F8001FF003FC001FF001FE000FE001FE0007C001FE0001 0001FE00000001FE00000001FE000001FFFE00003FFFFE0001FFF1FE0007FE01FE000FF001FE00 1FC001FE003F8001FE007F8001FE00FF0001FE00FF0001FE00FF0001FE00FF0001FE00FF0003FE 007F8003FE007FC00EFE003FF03CFF000FFFF87FF807FFF03FF800FF800FF825207E9F28>97 D<01F8000000FFF8000000FFF8000000FFF80000000FF800000007F800000007F800000007F800 000007F800000007F800000007F800000007F800000007F800000007F800000007F800000007F8 00000007F800000007F800000007F80FF00007F87FFE0007F9FFFF8007FFE03FC007FF000FE007 FE0007F007F80003F807F80003FC07F80003FC07F80001FE07F80001FE07F80001FE07F80001FF 07F80001FF07F80001FF07F80001FF07F80001FF07F80001FF07F80001FF07F80001FF07F80001 FE07F80001FE07F80001FE07F80003FC07F80003FC07FC0007F807FE0007F007F7001FE007E3E0 7FC007C1FFFF0007807FFE0007001FE00028327EB12E>I<00000007E0000003FFE0000003FFE0 000003FFE00000003FE00000001FE00000001FE00000001FE00000001FE00000001FE00000001F E00000001FE00000001FE00000001FE00000001FE00000001FE00000001FE00000001FE0000FF8 1FE0007FFF1FE001FFFFDFE003FE03FFE007F800FFE00FE0003FE01FE0001FE03FC0001FE03FC0 001FE07F80001FE07F80001FE07F80001FE0FF80001FE0FF80001FE0FF80001FE0FF80001FE0FF 80001FE0FF80001FE0FF80001FE0FF80001FE07F80001FE07F80001FE07F80001FE03FC0001FE0 3FC0001FE01FC0003FE00FE0007FE007F001FFE003FC07DFF001FFFF9FFF007FFE1FFF000FF01F FF28327DB12E>100 D<0007FC0000003FFF800000FFFFE00003FC07F00007F801F8000FE000FC 001FE0007E003FC0007E003FC0003F007FC0003F007F80003F007F80003F80FF80003F80FF8000 3F80FFFFFFFF80FFFFFFFF80FFFFFFFF80FF80000000FF80000000FF800000007F800000007F80 0000003FC00000003FC00003801FC00003801FE00007800FF0000F0007F8001E0003FE00FC0000 FFFFF800003FFFE0000003FF000021207E9F26>I<01C00007F0000FF8000FF8001FFC001FFC00 1FFC000FF8000FF80007F00001C000000000000000000000000000000000000000000000000000 01F800FFF800FFF800FFF8000FF80007F80007F80007F80007F80007F80007F80007F80007F800 07F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F800 07F80007F80007F800FFFF80FFFF80FFFF8011337DB217>105 D<03F007F8000FF000FFF03FFF 007FFE00FFF07FFF80FFFF00FFF0F03FC1E07F800FF1C01FE3803FC007F3000FE6001FC007F600 0FFC001FE007FE000FFC001FE007FC000FF8001FE007FC000FF8001FE007F8000FF0001FE007F8 000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007 F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE0 07F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001F E007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE0FFFFC1FFFF83FFFFFFFFC1FFFF83 FFFFFFFFC1FFFF83FFFF40207D9F45>109 D<03F007F80000FFF03FFF0000FFF07FFF8000FFF0 F03FC0000FF1C01FE00007F3000FE00007F6000FF00007FE000FF00007FC000FF00007FC000FF0 0007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8 000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF0 0007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF000FFFF C1FFFF80FFFFC1FFFF80FFFFC1FFFF8029207D9F2E>I<0007FE0000003FFFC00000FFFFF00003 FC03FC0007F000FE000FE0007F001FC0003F803FC0003FC03FC0003FC07F80001FE07F80001FE0 7F80001FE0FF80001FF0FF80001FF0FF80001FF0FF80001FF0FF80001FF0FF80001FF0FF80001F F0FF80001FF07F80001FE07F80001FE07F80001FE03FC0003FC03FC0003FC01FE0007F800FE000 7F0007F801FE0003FE07FC0001FFFFF800003FFFC0000007FE000024207E9F29>I<03F03F00FF F07FC0FFF1FFE0FFF3C7F00FF38FF807F70FF807F60FF807FE0FF807FC07F007FC03E007FC0080 07F8000007F8000007F8000007F8000007F8000007F8000007F8000007F8000007F8000007F800 0007F8000007F8000007F8000007F8000007F8000007F8000007F8000007F80000FFFFE000FFFF E000FFFFE0001D207E9F22>114 D<00FF870007FFEF001FFFFF003F007F003C001F0078000F00 F8000700F8000700F8000700FC000700FF000000FFF800007FFFC0003FFFF0003FFFFC000FFFFE 0007FFFF0001FFFF80001FFF800000FFC000001FC060000FC0E00007C0E00007C0F00007C0F800 0780F8000F80FE000F00FF803E00FFFFFC00F3FFF800C07FC0001A207D9F21>I<003800003800 00380000380000380000780000780000780000F80000F80001F80003F80007F8001FF800FFFFFE FFFFFEFFFFFE07F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F800 07F80007F80007F80007F80007F80007F80707F80707F80707F80707F80707F80707F80703F80E 03FC0E01FE1C00FFF8007FF0000FE0182E7EAD20>I<01F80003F000FFF801FFF000FFF801FFF0 00FFF801FFF0000FF8001FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8 000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF0 0007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8 000FF00007F8000FF00007F8001FF00007F8001FF00003F8003FF00003F8006FF00001FE03CFF8 0000FFFF8FFF80007FFF0FFF80000FFC0FFF8029207D9F2E>I E /Fq 76 125 df0 D<07FFF800003F0000001E0000 001E0000001E0000001E0000007F800003DEF0000F1E3C001E1E1E003C1E0F007C1E0F80781E07 80F81E07C0F81E07C0F81E07C0F81E07C0F81E07C0781E07807C1E0F803C1E0F001E1E1E000F1E 3C0003DEF000007F8000001E0000001E0000001E0000001E0000003F000007FFF8001A1F7D9E21 >8 D<001F83E000F06E3001C078780380F8780300F03007007000070070000700700007007000 070070000700700007007000FFFFFF800700700007007000070070000700700007007000070070 000700700007007000070070000700700007007000070070000700700007007000070070000700 700007007000070070007FE3FF001D20809F1B>11 D<003F0000E0C001C0C00381E00701E00701 E0070000070000070000070000070000070000FFFFE00700E00700E00700E00700E00700E00700 E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E07FC3 FE1720809F19>I<003FE000E0E001C1E00381E00700E00700E00700E00700E00700E00700E007 00E00700E0FFFFE00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E007 00E00700E00700E00700E00700E00700E00700E00700E07FE7FE1720809F19>I<001F81F80000 F04F040001C07C06000380F80F000300F00F000700F00F00070070000007007000000700700000 070070000007007000000700700000FFFFFFFF0007007007000700700700070070070007007007 000700700700070070070007007007000700700700070070070007007007000700700700070070 07000700700700070070070007007007000700700700070070070007007007007FE3FE3FF02420 809F26>I<07070F1C383060C00808779F17>19 D<70F8F8F8F8F8F8F870707070707070707070 2020202020000000000070F8F8F87005217CA00D>33 D<7038F87CFC7EFC7E743A040204020402 0804080410081008201040200F0E7E9F17>I<70F8FCFC74040404080810102040060E7C9F0D> 39 D<0020004000800100020006000C000C00180018003000300030007000600060006000E000 E000E000E000E000E000E000E000E000E000E000E0006000600060007000300030003000180018 000C000C000600020001000080004000200B2E7DA112>I<800040002000100008000C00060006 000300030001800180018001C000C000C000C000E000E000E000E000E000E000E000E000E000E0 00E000E000C000C000C001C001800180018003000300060006000C00080010002000400080000B 2E7DA112>I<000600000006000000060000000600000006000000060000000600000006000000 060000000600000006000000060000000600000006000000060000FFFFFFF0FFFFFFF000060000 000600000006000000060000000600000006000000060000000600000006000000060000000600 00000600000006000000060000000600001C207D9A23>43 D<70F8FCFC74040404080810102040 060E7C840D>II<70F8F8F87005057C840D>I<03F0000E1C001C0E0018 0600380700700380700380700380700380F003C0F003C0F003C0F003C0F003C0F003C0F003C0F0 03C0F003C0F003C0F003C0F003C0F003C07003807003807003807807803807001806001C0E000E 1C0003F000121F7E9D17>48 D<018003800F80F380038003800380038003800380038003800380 03800380038003800380038003800380038003800380038003800380038007C0FFFE0F1E7C9D17 >I<03F0000C1C00100E00200700400780800780F007C0F803C0F803C0F803C02007C00007C000 0780000780000F00000E00001C0000380000700000600000C0000180000300000600400C004018 00401000803FFF807FFF80FFFF80121E7E9D17>I<03F0000C1C00100E00200F00780F80780780 780780380F80000F80000F00000F00000E00001C0000380003F000003C00000E00000F00000780 0007800007C02007C0F807C0F807C0F807C0F00780400780400F00200E001C3C0003F000121F7E 9D17>I<000600000600000E00000E00001E00002E00002E00004E00008E00008E00010E00020E 00020E00040E00080E00080E00100E00200E00200E00400E00C00E00FFFFF0000E00000E00000E 00000E00000E00000E00000E0000FFE0141E7F9D17>I<1803001FFE001FFC001FF8001FE00010 000010000010000010000010000010000011F000161C00180E0010070010078000038000038000 03C00003C00003C07003C0F003C0F003C0E00380400380400700200600100E000C380003E00012 1F7E9D17>I<007C000182000701000E03800C07801C0780380300380000780000700000700000 F1F000F21C00F40600F80700F80380F80380F003C0F003C0F003C0F003C0F003C07003C07003C0 7003803803803807001807000C0E00061C0001F000121F7E9D17>I<4000007FFFC07FFF807FFF 8040010080020080020080040000080000080000100000200000200000400000400000C00000C0 0001C0000180000380000380000380000380000780000780000780000780000780000780000780 00030000121F7D9D17>I<03F0000C0C0010060030030020018060018060018060018070018078 03003E03003F06001FC8000FF00003F80007FC000C7E00103F00300F806003804001C0C001C0C0 00C0C000C0C000C0C000806001802001001002000C0C0003F000121F7E9D17>I<03F0000E1800 1C0C00380600380700700700700380F00380F00380F003C0F003C0F003C0F003C0F003C07007C0 7007C03807C0180BC00E13C003E3C0000380000380000380000700300700780600780E00700C00 2018001070000FC000121F7E9D17>I<70F8F8F8700000000000000000000070F8F8F87005147C 930D>I<70F8F8F8700000000000000000000070F0F8F878080808101010202040051D7C930D>I< 7FFFFFE0FFFFFFF000000000000000000000000000000000000000000000000000000000000000 00FFFFFFF07FFFFFE01C0C7D9023>61 D<000100000003800000038000000380000007C0000007 C0000007C0000009E0000009E0000009E0000010F0000010F0000010F000002078000020780000 20780000403C0000403C0000403C0000801E0000801E0000FFFE0001000F0001000F0001000F00 020007800200078002000780040003C00E0003C01F0007E0FFC03FFE1F207F9F22>65 DI68 DII<000FE0200078186000E004E0038002E0070001E0 0F0000E01E0000601E0000603C0000603C0000207C00002078000020F8000000F8000000F80000 00F8000000F8000000F8000000F8000000F8007FFCF80003E0780001E07C0001E03C0001E03C00 01E01E0001E01E0001E00F0001E0070001E0038002E000E0046000781820000FE0001E217D9F24 >III76 D80 D<001F800000F0F00001C0380007801E000F000F000E0007001E0007803C0003C03C 0003C07C0003E07C0003E0780001E0F80001F0F80001F0F80001F0F80001F0F80001F0F80001F0 F80001F0F80001F0F80001F0780001E0780001E07C0003E03C0003C03C0F03C01E1087800E20C7 000F20CF0007A0FE0001E0F80000F0F010001FF01000007010000078300000387000003FF00000 3FE000001FE000000FC0000007801C297D9F23>II< 07E0800C1980100780300380600180600180E00180E00080E00080E00080F00000F00000780000 7F00003FF0001FFC000FFE0003FF00001F800007800003C00003C00001C08001C08001C08001C0 8001C0C00180C00380E00300F00600CE0C0081F80012217D9F19>I<7FFFFFE0780F01E0600F00 60400F0020400F0020C00F0030800F0010800F0010800F0010800F0010000F0000000F0000000F 0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F000000 0F0000000F0000000F0000000F0000000F0000000F0000000F0000001F800007FFFE001C1F7E9E 21>I87 D91 D<0804100820102010402040208040804080 40B85CFC7EFC7E7C3E381C0F0E7B9F17>II<0C001E0033006180 C0C080400A067A9E17>I<1FE000303000781800781C00300E00000E00000E00000E0000FE0007 8E001E0E00380E00780E00F00E10F00E10F00E10F01E10781E103867200F83C014147E9317>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>III E /Fr 69 124 df<007E1F0001C1B1800303E3C00703C3C00E03C1 800E01C0000E01C0000E01C0000E01C0000E01C0000E01C000FFFFFC000E01C0000E01C0000E01 C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E 01C0000E01C0000E01C0000E01C0007F87FC001A1D809C18>11 D<1C1C3C3870C0800607779C15 >19 D<60F0F8680808081010204080050C7C9C0C>39 D<004000800100020006000C000C001800 1800300030007000600060006000E000E000E000E000E000E000E000E000E000E000E000E00060 0060006000700030003000180018000C000C00060002000100008000400A2A7D9E10>I<800040 002000100018000C000C000600060003000300038001800180018001C001C001C001C001C001C0 01C001C001C001C001C001C0018001800180038003000300060006000C000C0018001000200040 0080000A2A7E9E10>I<60F0F0701010101020204080040C7C830C>44 DI<60F0F06004047C830C>I<03C00C301818300C300C700E60066006E007E007E007E007E007E0 07E007E007E007E007E007E007E00760066006700E300C300C18180C3007E0101D7E9B15>48 D<030007003F00C700070007000700070007000700070007000700070007000700070007000700 07000700070007000700070007000F80FFF80D1C7C9B15>I<07C01830201C400C400EF00FF80F F807F8077007000F000E000E001C001C00380070006000C00180030006010C01180110023FFE7F FEFFFE101C7E9B15>I<07E01830201C201C781E780E781E381E001C001C00180030006007E000 30001C001C000E000F000F700FF80FF80FF80FF00E401C201C183007E0101D7E9B15>I<000C00 000C00001C00003C00003C00005C0000DC00009C00011C00031C00021C00041C000C1C00081C00 101C00301C00201C00401C00C01C00FFFFC0001C00001C00001C00001C00001C00001C00001C00 01FFC0121C7F9B15>I<300C3FF83FF03FC020002000200020002000200023E024302818301C20 0E000E000F000F000F600FF00FF00FF00F800E401E401C2038187007C0101D7E9B15>I<00F003 0C06040C0E181E301E300C700070006000E3E0E430E818F00CF00EE006E007E007E007E007E007 600760077006300E300C18180C3003E0101D7E9B15>I<4000007FFF807FFF007FFF0040020080 040080040080080000100000100000200000600000400000C00000C00001C00001800001800003 8000038000038000038000078000078000078000078000078000078000030000111D7E9B15>I< 03E00C301008200C20066006600660067006780C3E083FB01FE007F007F818FC307E601E600FC0 07C003C003C003C00360026004300C1C1007E0101D7E9B15>I<03C00C301818300C700C600EE0 06E006E007E007E007E007E0076007700F300F18170C2707C700060006000E300C780C78187010 203030C00F80101D7E9B15>I<60F0F0600000000000000000000060F0F06004127C910C>I<0006 00000006000000060000000F0000000F0000000F00000017800000178000001780000023C00000 23C0000023C0000041E0000041E0000041E0000080F0000080F0000180F8000100780001FFF800 03007C0002003C0002003C0006003E0004001E0004001E000C001F001E001F00FF80FFF01C1D7F 9C1F>65 DI<001F808000E0618001801980070007800E0003801C 0003801C00018038000180780000807800008070000080F0000000F0000000F0000000F0000000 F0000000F0000000F0000000F0000000700000807800008078000080380000801C0001001C0001 000E000200070004000180080000E03000001FC000191E7E9C1E>IIII<001F808000E0618001801980070007800E0003801C00 03801C00018038000180780000807800008070000080F0000000F0000000F0000000F0000000F0 000000F0000000F000FFF0F0000F80700007807800078078000780380007801C0007801C000780 0E00078007000B800180118000E06080001F80001C1E7E9C21>III<1FFF00F8007800780078007800780078007800780078007800 78007800780078007800780078007800787078F878F878F878F0F040E021C01F00101D7F9B15> I76 DII80 D<003F800000E0E0000380380007001C000E 000E001C0007003C00078038000380780003C0780003C0700001C0F00001E0F00001E0F00001E0 F00001E0F00001E0F00001E0F00001E0F00001E0700001C0780003C0780003C0380003803C0E07 801C1107000E208E000720DC0003A0F80000F0E020003FE0200000602000007060000078E00000 3FC000003FC000001F8000000F001B257E9C20>II<07E0801C1980300580700380 600180E00180E00080E00080E00080F00000F800007C00007FC0003FF8001FFE0007FF0000FF80 000F800007C00003C00001C08001C08001C08001C0C00180C00180E00300D00200CC0C0083F800 121E7E9C17>I<7FFFFFC0700F01C0600F00C0400F0040400F0040C00F0020800F0020800F0020 800F0020000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F00 00000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000001F800003FF FC001B1C7F9B1E>II87 D89 D91 D93 D<1FC000307000783800781C00301C00001C00001C0001FC000F1C00381C00701C00601C00E01C 40E01C40E01C40603C40304E801F870012127E9115>97 DI<07E00C301878307870306000E000E000E000E000E000E00060007004300418080C3007C00E12 7E9112>I<003F0000070000070000070000070000070000070000070000070000070000070003 E7000C1700180F00300700700700600700E00700E00700E00700E00700E00700E0070060070070 0700300700180F000C370007C7E0131D7E9C17>I<03E00C301818300C700E6006E006FFFEE000 E000E000E00060007002300218040C1803E00F127F9112>I<00F8018C071E061E0E0C0E000E00 0E000E000E000E00FFE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E 000E007FE00F1D809C0D>I<00038003C4C00C38C01C3880181800381C00381C00381C00381C00 1818001C38000C300013C0001000003000001800001FF8001FFF001FFF803003806001C0C000C0 C000C0C000C06001803003001C0E0007F800121C7F9215>II<18003C003C0018000000000000000000000000000000FC001C001C001C001C001C001C001C 001C001C001C001C001C001C001C001C001C00FF80091D7F9C0C>I<00C001E001E000C0000000 00000000000000000000000FE000E000E000E000E000E000E000E000E000E000E000E000E000E0 00E000E000E000E000E000E000E060E0F0C0F1C061803E000B25839C0D>IIIII<03F000 0E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180700380 3003001806000E1C0003F00012127F9115>II<03C1000C3300180B00300F0070 0700700700E00700E00700E00700E00700E00700E00700600700700700300F00180F000C370007 C700000700000700000700000700000700000700000700003FE0131A7E9116>II<1F90 30704030C010C010E010F8007F803FE00FF000F880388018C018C018E010D0608FC00D127F9110 >I<04000400040004000C000C001C003C00FFE01C001C001C001C001C001C001C001C001C001C 101C101C101C101C100C100E2003C00C1A7F9910>IIII<7F8FF00F03800F03000702 0003840001C80001D80000F00000700000780000F800009C00010E00020E000607000403801E07 C0FF0FF81512809116>II<7FFC70386038407040F040E041C003C0038007000F 040E041C043C0C380870087038FFF80E127F9112>II E /Fs 30 122 df<000E00001E00007E0007FE00FFFE00FFFE00F8FE0000FE0000FE0000FE0000 FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000 FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE007F FFFE7FFFFE7FFFFE17277BA622>49 D<00FF800003FFF0000FFFFC001F03FE003800FF007C007F 80FE003FC0FF003FC0FF003FE0FF001FE0FF001FE07E001FE03C003FE000003FE000003FC00000 3FC000007F8000007F000000FE000000FC000001F8000003F0000003E00000078000000F000000 1E0000003C00E0007000E000E000E001C001C0038001C0070001C00FFFFFC01FFFFFC03FFFFFC0 7FFFFFC0FFFFFF80FFFFFF80FFFFFF801B277DA622>I<007F800003FFF00007FFFC000F81FE00 1F00FF003F80FF003F807F803F807F803F807F801F807F800F007F800000FF000000FF000000FE 000001FC000001F8000007F00000FFC00000FFF0000001FC0000007E0000007F0000007F800000 3FC000003FC000003FE000003FE03C003FE07E003FE0FF003FE0FF003FE0FF003FC0FF007FC07E 007F807C007F003F01FE001FFFFC0007FFF00000FF80001B277DA622>I<00000E0000001E0000 003E0000007E000000FE000000FE000001FE000003FE0000077E00000E7E00000E7E00001C7E00 00387E0000707E0000E07E0000E07E0001C07E0003807E0007007E000E007E000E007E001C007E 0038007E0070007E00E0007E00FFFFFFF8FFFFFFF8FFFFFFF80000FE000000FE000000FE000000 FE000000FE000000FE000000FE000000FE00007FFFF8007FFFF8007FFFF81D277EA622>I66 D73 D76 D82 D<7FFFFFFFFFC07FFFFFFFFFC07FFFFFFFFFC07F803FC03FC07E003FC007C078003FC003C07800 3FC003C070003FC001C0F0003FC001E0F0003FC001E0E0003FC000E0E0003FC000E0E0003FC000 E0E0003FC000E0E0003FC000E000003FC0000000003FC0000000003FC0000000003FC000000000 3FC0000000003FC0000000003FC0000000003FC0000000003FC0000000003FC0000000003FC000 0000003FC0000000003FC0000000003FC0000000003FC0000000003FC0000000003FC000000000 3FC0000000003FC0000000003FC0000000003FC0000000003FC00000007FFFFFE000007FFFFFE0 00007FFFFFE0002B287EA730>84 D<01FF800007FFF0000F81F8001FC07E001FC07E001FC03F00 0F803F8007003F8000003F8000003F8000003F80000FFF8000FFFF8007FC3F800FE03F803F803F 803F003F807F003F80FE003F80FE003F80FE003F80FE003F807E007F807F00DF803F839FFC0FFF 0FFC01FC03FC1E1B7E9A21>97 DI<001FF8 0000FFFE0003F01F0007E03F800FC03F801F803F803F801F007F800E007F0000007F000000FF00 0000FF000000FF000000FF000000FF000000FF000000FF0000007F0000007F0000007F8000003F 8001C01F8001C00FC0038007E0070003F01E0000FFFC00001FE0001A1B7E9A1F>I<00003FF800 00003FF80000003FF800000003F800000003F800000003F800000003F800000003F800000003F8 00000003F800000003F800000003F800000003F800000003F800000003F800001FE3F80000FFFB F80003F03FF80007E00FF8000FC007F8001F8003F8003F8003F8007F0003F8007F0003F8007F00 03F800FF0003F800FF0003F800FF0003F800FF0003F800FF0003F800FF0003F800FF0003F8007F 0003F8007F0003F8007F0003F8003F8003F8001F8003F8000F8007F80007C00FF80003F03BFF80 00FFF3FF80003FC3FF80212A7EA926>I<003FE00001FFF80003F07E0007C01F000F801F801F80 0F803F800FC07F000FC07F0007C07F0007E0FF0007E0FF0007E0FFFFFFE0FFFFFFE0FF000000FF 000000FF0000007F0000007F0000007F0000003F8000E01F8000E00FC001C007E0038003F81F00 00FFFE00001FF0001B1B7E9A20>I<0007F0003FFC00FE3E01F87F03F87F03F07F07F07F07F03E 07F00007F00007F00007F00007F00007F00007F000FFFFC0FFFFC0FFFFC007F00007F00007F000 07F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007F000 07F00007F00007F00007F00007F0007FFF807FFF807FFF80182A7EA915>I<00FF81F003FFE7F8 0FC1FE7C1F80FC7C1F007C383F007E107F007F007F007F007F007F007F007F007F007F007F007F 003F007E001F007C001F80FC000FC1F8001FFFE00018FF800038000000380000003C0000003E00 00003FFFF8001FFFFF001FFFFF800FFFFFC007FFFFE01FFFFFF03E0007F07C0001F8F80000F8F8 0000F8F80000F8F80000F87C0001F03C0001E01F0007C00FC01F8003FFFE00007FF0001E287E9A 22>II<07000F801FC03FE03FE03FE01FC0 0F8007000000000000000000000000000000FFE0FFE0FFE00FE00FE00FE00FE00FE00FE00FE00F E00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE0FFFEFFFEFFFE0F2B7DAA14> I108 DII<003FE00001FFFC0003F07E000FC01F801F800FC03F800FE03F0007E07F0007F07F0007F0 7F0007F0FF0007F8FF0007F8FF0007F8FF0007F8FF0007F8FF0007F8FF0007F8FF0007F87F0007 F07F0007F03F800FE03F800FE01F800FC00FC01F8007F07F0001FFFC00003FE0001D1B7E9A22> II<001FC0380000FFF0780003F838F80007E00DF8000FC007F8001FC007F8003F 8003F8007F8003F8007F8003F8007F0003F800FF0003F800FF0003F800FF0003F800FF0003F800 FF0003F800FF0003F800FF0003F8007F0003F8007F0003F8007F8003F8003F8003F8001F8007F8 000FC007F80007E01FF80003F07BF80000FFF3F800003FC3F800000003F800000003F800000003 F800000003F800000003F800000003F800000003F800000003F800000003F80000003FFF800000 3FFF8000003FFF8021277E9A24>II<03FE300FFFF01E03F03800F07000 70F00070F00070F80070FC0000FFE0007FFE007FFF803FFFE01FFFF007FFF800FFF80003FC0000 FC60007CE0003CF0003CF00038F80038FC0070FF01E0F7FFC0C1FF00161B7E9A1B>I<00700000 700000700000700000F00000F00000F00001F00003F00003F00007F0001FFFF0FFFFF0FFFFF007 F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007 F03807F03807F03807F03807F03807F03803F03803F87001F86000FFC0001F8015267FA51B>I< FFE03FF800FFE03FF800FFE03FF8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8 000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003 F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE007F80007E007F80007E0 0FF80003F03BFF8001FFF3FF80003FC3FF80211B7D9A26>I119 D121 D E /Ft 17 122 df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u 28 121 df<00FC7C0183C607078E0607040E07000E07000E07000E07000E07000E 0700FFFFF00E07000E07000E07000E07000E07000E07000E07000E07000E07000E07000E07000E 07000E07000E07007F0FF0171A809916>11 D<60F0F07010101020204080040B7D830B>44 D<60F0F06004047D830B>46 D<03000700FF000700070007000700070007000700070007000700 0700070007000700070007000700070007000700FFF00C187D9713>49 D<0F8010602030403880 3CC01CE01C401C003C003800380070006000C001800100020004040804100430083FF87FF8FFF8 0E187E9713>I87 D91 D93 D<3F8070C070E020700070007007F01C7030707070E070E071E071E0F171FB1E3C 10107E8F13>97 DI<07F80C1C381C30087000E000E000E000E000E000E0007000 300438080C1807E00E107F8F11>I<007E00000E00000E00000E00000E00000E00000E00000E00 000E00000E0003CE000C3E00380E00300E00700E00E00E00E00E00E00E00E00E00E00E00E00E00 600E00700E00381E001C2E0007CFC0121A7F9915>I<07C01C3030187018600CE00CFFFCE000E0 00E000E0006000300438080C1807E00E107F8F11>I<01F0031807380E100E000E000E000E000E 000E00FFC00E000E000E000E000E000E000E000E000E000E000E000E000E000E007FE00D1A8099 0C>I104 D<18003C003C001800000000000000000000000000FC001C001C001C 001C001C001C001C001C001C001C001C001C001C001C00FF80091A80990A>I107 DIII<07E01C38300C70 0E6006E007E007E007E007E007E0076006700E381C1C3807E010107F8F13>II<03C2000C2600381E00 300E00700E00E00E00E00E00E00E00E00E00E00E00E00E00700E00700E00381E001C2E0007CE00 000E00000E00000E00000E00000E00000E00007FC012177F8F14>II<1F2060E04020C020C020F0 007F003FC01FE000F080708030C030C020F0408F800C107F8F0F>I<0400040004000C000C001C 003C00FFC01C001C001C001C001C001C001C001C001C201C201C201C201C200E4003800B177F96 0F>II120 D E end %%EndProlog %%BeginSetup %%Feature: *Resolution 300dpi TeXDict begin %%PaperSize: A4 %%EndSetup %%Page: 117 1 117 0 bop 855 292 a Fh(22)326 438 y Fp(Limit)27 b(Distributions)g(in)g (Quadtrees)727 605 y Ft(Thomas)17 b(La\013orgue)802 663 y(LRI,)e(Orsa)o(y)623 774 y Fq([r)o(\023)-21 b(esum)o(\023)g(e)13 b(par)i(Philipp)q(e)j(Fla)s (jolet])-54 885 y(Quadtrees)d(constitute)g(a)f(classical)i(data)e(structure)h (for)f(storing)g(and)h(accessing)g(m)o(ultidimensional)j(data.)h(It)-54 942 y(is)e(pro)o(v)o(ed)e(here)i(that,)e(in)i(all)g(dimensions,)h(the)e(cost) g(of)f(a)h(random)g(searc)o(h)g(in)h(a)e(randomly)i(gro)o(wn)e(quadtree)-54 998 y(has)i(logarithmic)h(mean)g(and)f(v)m(ariance)h(and)g(that)e(it)i(is)f (asymptotically)h(distributed)h(as)e(a)g(normal)g(v)m(ariate.)-54 1055 y(The)e(limit)i(distribution)g(prop)q(ert)o(y)e(extends)g(to)g (quadtrees)g(a)g(result)g(only)h(kno)o(wn)f(so)g(far)f(to)h(hold)h(for)e (binary)-54 1111 y(searc)o(h)h(trees.)-54 1169 y(The)c(analysis)h(is)f(based) h(on)e(a)h(tec)o(hnique)h(of)f(singularit)o(y)h(p)q(erturbation)f(analysis)h (applied)g(to)f(linear)h(di\013eren)o(tial)-54 1225 y(equations)k (satis\014ed)f(b)o(y)g(in)o(terv)o(ening)i(biv)m(ariate)f(generating)f (functions.)-54 1282 y(The)g(w)o(ork)g(describ)q(ed)i(is)f(based)f(on)g(a)g (join)o(t)g(pap)q(er)h(of)f(La\013orgue)f(and)h(Fla)s(jolet)g([4].)-54 1431 y Fs(1)69 b(In)n(tro)r(duction)-54 1535 y Fq(Quadtrees)15 b(are)g(a)g(w)o(ell)h(kno)o(wn)f(data)f(structure)h(disco)o(v)o(ered)h(b)o(y) f(Fink)o(el)h(and)f(Ben)o(tley)h(whic)o(h)g(is)g(discussed)g(in)-54 1591 y(classical)g(treatises)f(on)f(algorithms)h([5)o(,)f(11])g(and)h (examined)h(in)f(great)f(detail)i(in)f(Samet's)f(reference)h(b)q(o)q(oks)g ([9)o(,)-54 1647 y(10)o(].)20 b(Their)c(analysis)g(has)f(made)g(visible)i (progress)e(o)o(v)o(er)f(recen)o(t)i(y)o(ears)e([2)o(,)h(3,)g(6)o(,)g(7,)g(8) o(].)-54 1705 y(The)21 b(probabilistic)i(mo)q(del)f(considered)g(tak)o(es)e (all)i(data)e(uniformly)h(from)f(the)h Fk(d)p Fq({dimensional)h(h)o(yp)q (ercub)q(e)-54 1761 y Fi(Q)16 b Fq(=)g([0)p Fk(;)8 b Fq(1])143 1745 y Fj(d)161 1761 y Fq(.)25 b(The)17 b(searc)o(h)g(cost)f Fk(D)567 1768 y Fj(n)607 1761 y Fq(is)i(de\014ned)g(as)f(the)g(cost|measured) g(in)h(in)o(ternal)f(no)q(des)h(tra)o(v)o(ersed|of)-54 1818 y(searc)o(hing)d(a)e(random)h(p)q(oin)o(t)h(in)g(a)e(randomly)i(gro)o(wn)e (quadtree)h(of)g(size)h Fk(n)8 b Fi(\000)g Fq(1;)14 b(it)g(is)h(also)f (called)i(the)e(insertion)-54 1874 y(depth)i(of)f(the)g Fk(n)p Fq(th)g(no)q(de)h(and)f(is)h(a)f(random)g(v)m(ariable)h(de\014ned)h(on)e(the) g(space)h Fi(Q)1366 1858 y Fj(n)p Ff(\000)p Fn(1)1445 1874 y Fi(\002)10 b(Q)1540 1862 y(\030)1540 1876 y Fq(=)1588 1874 y Fi(Q)1625 1858 y Fj(n)1648 1874 y Fq(.)-54 1932 y(The)21 b(main)g(result)g(rep)q(orted)g(is)h(that)e Fk(D)679 1939 y Fj(n)722 1932 y Fm(c)n(onver)n(ges)g(in)h(distribution)h(to)f(a)h(Gaussian)f (variate)k Fq(when)c(the)-54 1988 y(size)g Fk(n)13 b Fi(\000)h Fq(1)20 b(of)f(the)h(tree)g(structure)g(b)q(ecomes)g(large.)35 b(Figure)20 b(1)f(illustrates)i(the)g(clear)f(o)q(ccurrence)h(of)f(this)-54 2045 y(phenomenon)c(already)g(for)e(lo)o(w)h(v)m(alues)i(of)d Fk(n)p Fq(.)-54 2157 y Fo(Theorem)j(1)23 b Fm(\(i\).)k(The)18 b(me)n(an)h Fk(\026)556 2164 y Fj(n)598 2157 y Fm(and)g(standar)n(d)f (deviation)h Fk(\033)1101 2164 y Fj(n)1143 2157 y Fm(of)g(the)g(c)n(ost)f Fk(D)1409 2164 y Fj(n)1451 2157 y Fm(of)h(a)g(r)n(andom)f(se)n(ar)n(ch)h(in) -54 2213 y(r)n(andom)e(quadtr)n(e)n(e)f(of)g(size)g Fk(n)10 b Fi(\000)h Fq(1)16 b Fm(in)f(dimension)h Fk(d)c Fi(\025)h Fq(1)j Fm(satisfy)g(asymptotic)n(al)r(ly)510 2345 y Fk(\026)537 2352 y Fj(n)573 2345 y Fi(\030)627 2314 y Fq(2)p 626 2334 24 2 v 626 2376 a Fk(d)662 2345 y Fq(log)9 b Fk(n)93 b Fm(and)g Fk(\033)1040 2352 y Fj(n)1076 2345 y Fi(\030)1124 2278 y Fg(r)p 1165 2278 155 2 v 1181 2314 a Fq(2)p 1170 2334 44 2 v 1170 2376 a Fk(d)1194 2363 y Fn(2)1226 2345 y Fq(log)9 b Fk(n:)505 b Fq(\(1\))-54 2464 y Fm(\(ii\).)20 b(The)c(distribution)g(of)h Fk(D)474 2471 y Fj(n)513 2464 y Fm(c)n(onver)n(ges)e(in)g(distribution)i(to)f (a)h(normal)f(variate:)22 b(for)16 b(al)r(l)g(r)n(e)n(al)g Fk(\013;)8 b(\014)r Fm(,)280 2595 y Fq(Pr)p Fi(f)p Fk(\013)k Fi(\024)446 2564 y Fk(D)484 2571 y Fj(n)518 2564 y Fi(\000)e Fk(\026)590 2571 y Fj(n)p 446 2585 168 2 v 505 2626 a Fk(\033)531 2633 y Fj(n)632 2595 y Fi(\024)j Fk(\014)r Fi(g)28 b(!)871 2564 y Fq(1)p 839 2585 89 2 v 839 2593 a Fi(p)p 876 2593 51 2 v 876 2631 a Fq(2)p Fk(\031)939 2538 y Fg(Z)981 2551 y Fj(\014)962 2632 y(\013)1012 2595 y Fk(e)1033 2576 y Ff(\000)p Fj(x)1080 2565 y Fl(2)1098 2576 y Fj(=)p Fn(2)1143 2595 y Fk(dx)185 b Fq(\()p Fk(n)13 b Fi(!)g(1)p Fq(\))p Fk(:)268 b Fq(\(2\))-54 2730 y(The)20 b(mean)f(w)o(as)g(determined)h(b)o(y)g(Devro)o(y)o(e)e(and)i (Laforest)e([2])h(and)g(indep)q(enden)o(tly)k(b)o(y)c(Fla)s(jolet,)h(Gonnet,) -54 2786 y(Puec)o(h,)15 b(and)h(Robson)f([3].)887 3022 y(117)p eop %%Page: 118 2 118 1 bop -54 98 a Fq(118)823 b Fe(P)o(art)14 b(IV.)h(Analysis)h(of)f (Algorithms)h(and)f(Data)f(Structures)p -54 118 1950 2 v 446 236 a 14992019 11188078 0 0 41442508 30917427 startTexFig 446 236 a %%BeginDocument: dens100.ps gsave /m {stroke moveto} def /l {lineto} def /lthick 3 def % line thickness /athick 7 def % axis thickness /tthick 1 def % tickmark thickness /Helvetica findfont 60 scalefont setfont 0.19 0.19 scale 1 setlinejoin 1 setlinecap newpath [] 0 setdash lthick setlinewidth 1 1 m athick setlinewidth [] 0 setdash 3299 1 l 1 1 m athick setlinewidth 1 2449 l stroke lthick setlinewidth 1 6 m 1 6 l 8 6 l 15 7 l 22 7 l 30 8 l 37 9 l 44 10 l 51 11 l 58 11 l 65 13 l 72 14 l 80 15 l 87 16 l 87 16 m 87 16 l 94 18 l 100 19 l 107 21 l 113 23 l 120 25 l 127 27 l 133 29 l 140 32 l 147 34 l 153 37 l 160 40 l 166 43 l 173 46 l 173 46 m 173 46 l 178 49 l 183 51 l 189 54 l 194 57 l 199 60 l 204 64 l 210 68 l 215 72 l 220 76 l 226 80 l 231 85 l 236 90 l 242 96 l 247 102 l 253 109 l 259 115 l 259 115 m 259 115 l 262 120 l 266 125 l 270 130 l 274 136 l 278 141 l 282 147 l 286 153 l 290 159 l 293 165 l 297 171 l 301 177 l 305 183 l 308 189 l 312 196 l 316 202 l 319 208 l 323 214 l 326 221 l 329 227 l 333 233 l 336 239 l 339 245 l 342 251 l 345 257 l 345 257 m 345 257 l 348 264 l 352 272 l 355 280 l 358 287 l 361 294 l 364 301 l 367 307 l 369 313 l 371 320 l 374 326 l 376 332 l 378 338 l 380 343 l 382 349 l 384 354 l 386 359 l 387 365 l 387 365 m 387 365 l 389 369 l 391 373 l 392 378 l 394 382 l 395 387 l 397 392 l 399 397 l 401 402 l 403 408 l 405 414 l 407 420 l 409 427 l 411 434 l 413 442 l 416 450 l 418 459 l 421 469 l 424 479 l 427 490 l 430 502 l 430 502 m 430 502 l 432 507 l 433 512 l 434 517 l 436 522 l 437 527 l 439 533 l 440 539 l 442 544 l 443 550 l 445 556 l 446 562 l 448 568 l 449 574 l 451 581 l 453 587 l 454 594 l 456 600 l 458 607 l 459 614 l 461 621 l 463 628 l 464 635 l 466 642 l 468 649 l 470 656 l 471 664 l 473 671 l 475 678 l 477 686 l 478 693 l 480 701 l 482 709 l 484 717 l 486 724 l 487 732 l 489 740 l 491 748 l 493 756 l 495 764 l 497 772 l 498 780 l 500 788 l 502 796 l 504 804 l 506 812 l 507 821 l 509 829 l 511 837 l 513 845 l 515 853 l 516 862 l 516 862 m 516 862 l 518 869 l 519 876 l 521 883 l 522 890 l 524 897 l 525 904 l 527 911 l 528 918 l 530 925 l 531 932 l 532 939 l 534 946 l 535 953 l 537 960 l 538 967 l 540 974 l 541 981 l 542 989 l 544 996 l 545 1003 l 547 1010 l 548 1017 l 549 1024 l 551 1031 l 552 1039 l 554 1046 l 555 1053 l 556 1060 l 558 1067 l 559 1075 l 561 1082 l 562 1089 l 563 1096 l 565 1104 l 566 1111 l 568 1118 l 569 1126 l 570 1133 l 572 1140 l 573 1148 l 575 1155 l 576 1162 l 578 1170 l 579 1177 l 580 1185 l 582 1192 l 583 1200 l 585 1207 l 586 1215 l 588 1222 l 589 1230 l 590 1237 l 592 1245 l 593 1252 l 595 1260 l 596 1268 l 598 1275 l 599 1283 l 601 1291 l 602 1298 l 602 1298 m 602 1298 l 604 1306 l 605 1314 l 607 1322 l 608 1330 l 610 1338 l 612 1346 l 613 1354 l 615 1362 l 616 1371 l 618 1379 l 620 1387 l 621 1395 l 623 1403 l 624 1411 l 626 1419 l 627 1427 l 629 1435 l 631 1443 l 632 1451 l 634 1459 l 635 1467 l 637 1474 l 639 1482 l 640 1490 l 642 1498 l 643 1506 l 645 1513 l 646 1521 l 648 1528 l 650 1536 l 651 1543 l 653 1551 l 654 1558 l 656 1565 l 657 1573 l 659 1580 l 660 1587 l 662 1594 l 663 1601 l 665 1608 l 666 1615 l 667 1621 l 669 1628 l 670 1634 l 672 1641 l 673 1647 l 674 1654 l 676 1660 l 677 1666 l 678 1672 l 680 1678 l 681 1683 l 682 1689 l 683 1695 l 685 1700 l 686 1705 l 687 1711 l 688 1716 l 688 1716 m 688 1716 l 691 1728 l 694 1740 l 696 1751 l 699 1761 l 701 1770 l 703 1779 l 705 1788 l 708 1796 l 710 1803 l 711 1810 l 713 1816 l 715 1823 l 717 1829 l 718 1834 l 720 1840 l 721 1845 l 723 1850 l 724 1854 l 726 1859 l 727 1864 l 728 1869 l 730 1873 l 731 1878 l 731 1878 m 731 1878 l 733 1884 l 735 1891 l 736 1898 l 738 1905 l 740 1912 l 742 1919 l 744 1926 l 746 1933 l 748 1939 l 751 1946 l 754 1953 l 756 1959 l 759 1966 l 763 1972 l 766 1978 l 770 1984 l 774 1989 l 774 1989 m 774 1989 l 780 1996 l 786 2002 l 792 2007 l 799 2012 l 806 2016 l 813 2020 l 821 2023 l 828 2025 l 835 2026 l 841 2026 l 848 2026 l 854 2025 l 860 2022 l 860 2022 m 860 2022 l 865 2019 l 870 2015 l 874 2010 l 878 2005 l 882 1999 l 885 1992 l 888 1986 l 891 1978 l 893 1971 l 896 1964 l 898 1956 l 900 1949 l 903 1941 l 903 1941 m 903 1941 l 904 1937 l 906 1933 l 907 1928 l 909 1924 l 911 1919 l 912 1914 l 914 1909 l 916 1904 l 918 1899 l 920 1893 l 922 1887 l 924 1880 l 926 1873 l 929 1865 l 931 1857 l 934 1848 l 937 1838 l 940 1827 l 943 1816 l 946 1804 l 946 1804 m 946 1804 l 947 1799 l 948 1794 l 949 1789 l 951 1784 l 952 1779 l 953 1774 l 954 1768 l 956 1763 l 957 1757 l 958 1751 l 960 1746 l 961 1740 l 963 1734 l 964 1728 l 966 1721 l 967 1715 l 968 1709 l 970 1702 l 971 1695 l 973 1689 l 974 1682 l 976 1675 l 978 1668 l 979 1661 l 981 1654 l 982 1647 l 984 1639 l 985 1632 l 987 1625 l 989 1617 l 990 1609 l 992 1602 l 994 1594 l 995 1586 l 997 1578 l 999 1571 l 1000 1563 l 1002 1555 l 1004 1547 l 1005 1538 l 1007 1530 l 1009 1522 l 1011 1514 l 1012 1505 l 1014 1497 l 1016 1488 l 1018 1480 l 1019 1471 l 1021 1463 l 1023 1454 l 1025 1446 l 1026 1437 l 1028 1428 l 1030 1420 l 1032 1411 l 1032 1411 m 1032 1411 l 1033 1403 l 1035 1395 l 1036 1387 l 1038 1379 l 1040 1371 l 1041 1363 l 1043 1355 l 1044 1347 l 1046 1339 l 1047 1331 l 1049 1323 l 1051 1315 l 1052 1307 l 1054 1299 l 1055 1291 l 1057 1283 l 1058 1275 l 1060 1267 l 1062 1259 l 1063 1251 l 1065 1243 l 1066 1236 l 1068 1228 l 1069 1220 l 1071 1212 l 1072 1204 l 1074 1197 l 1075 1189 l 1077 1181 l 1078 1174 l 1080 1166 l 1081 1158 l 1082 1151 l 1084 1144 l 1085 1136 l 1087 1129 l 1088 1121 l 1089 1114 l 1091 1107 l 1092 1100 l 1094 1093 l 1095 1086 l 1096 1079 l 1097 1072 l 1099 1065 l 1100 1059 l 1101 1052 l 1103 1045 l 1104 1039 l 1105 1033 l 1106 1026 l 1107 1020 l 1109 1014 l 1110 1008 l 1111 1002 l 1112 996 l 1113 990 l 1114 985 l 1115 979 l 1116 973 l 1118 968 l 1118 968 m 1118 968 l 1120 957 l 1122 947 l 1124 937 l 1126 927 l 1127 918 l 1129 909 l 1131 900 l 1133 892 l 1134 884 l 1136 877 l 1137 869 l 1139 862 l 1140 856 l 1142 849 l 1143 843 l 1144 836 l 1146 830 l 1147 824 l 1148 819 l 1149 813 l 1151 807 l 1152 802 l 1153 796 l 1154 791 l 1155 786 l 1157 780 l 1158 775 l 1159 769 l 1160 764 l 1160 764 m 1160 764 l 1162 757 l 1163 751 l 1165 744 l 1166 738 l 1168 731 l 1169 724 l 1171 717 l 1173 710 l 1174 703 l 1176 696 l 1177 689 l 1179 682 l 1181 675 l 1183 668 l 1184 661 l 1186 653 l 1188 646 l 1189 639 l 1191 632 l 1193 625 l 1195 618 l 1196 611 l 1198 604 l 1200 597 l 1202 590 l 1203 583 l 1203 583 m 1203 583 l 1205 575 l 1208 567 l 1210 559 l 1212 551 l 1214 544 l 1216 536 l 1218 529 l 1220 521 l 1222 514 l 1224 507 l 1226 500 l 1228 493 l 1230 486 l 1232 480 l 1234 473 l 1236 467 l 1238 460 l 1239 454 l 1241 448 l 1243 442 l 1245 436 l 1246 431 l 1246 431 m 1246 431 l 1248 424 l 1250 418 l 1252 412 l 1254 406 l 1256 400 l 1258 394 l 1259 388 l 1261 382 l 1263 376 l 1265 370 l 1268 363 l 1270 357 l 1272 351 l 1275 344 l 1277 337 l 1280 330 l 1283 323 l 1286 316 l 1289 308 l 1289 308 m 1289 308 l 1292 302 l 1294 297 l 1297 291 l 1300 285 l 1302 278 l 1305 272 l 1308 266 l 1311 260 l 1314 253 l 1317 247 l 1320 240 l 1324 234 l 1327 227 l 1330 221 l 1334 214 l 1337 208 l 1340 201 l 1344 195 l 1347 189 l 1351 183 l 1354 176 l 1358 171 l 1361 165 l 1365 159 l 1368 154 l 1372 148 l 1375 143 l 1375 143 m 1375 143 l 1381 135 l 1386 128 l 1391 121 l 1397 115 l 1402 108 l 1407 103 l 1412 97 l 1417 92 l 1422 88 l 1427 83 l 1432 79 l 1437 75 l 1442 72 l 1447 68 l 1452 65 l 1456 62 l 1461 59 l 1461 59 m 1461 59 l 1467 55 l 1472 52 l 1478 49 l 1483 46 l 1489 43 l 1495 40 l 1501 37 l 1507 35 l 1513 32 l 1519 30 l 1526 28 l 1532 26 l 1540 23 l 1547 22 l 1547 22 m 1547 22 l 1552 20 l 1556 19 l 1561 18 l 1567 17 l 1572 16 l 1578 15 l 1583 14 l 1589 13 l 1596 12 l 1602 11 l 1609 10 l 1616 9 l 1623 9 l 1631 8 l 1639 7 l 1648 6 l 1657 6 l 1666 5 l 1676 5 l 1686 4 l 1696 4 l 1707 3 l 1719 3 l 1719 3 m 1719 3 l 1725 3 l 1731 2 l 1738 2 l 1744 2 l 1751 2 l 1758 2 l 1765 2 l 1772 1 l 1779 1 l 1786 1 l 1793 1 l 1801 1 l 1808 1 l 1816 1 l 2062 1 m 2062 1 l 2070 1 l 2079 1 l 2087 1 l 2095 1 l 2103 1 l 2111 1 l 2119 1 l 2127 1 l 2135 1 l 2143 1 l 2151 1 l 2159 1 l 2167 1 l 2175 1 l 2183 1 l 2191 1 l 2198 1 l 2206 1 l 2214 1 l 2222 1 l 2229 1 l 2237 1 l 2245 1 l 2253 1 l 2260 1 l 2268 1 l 2276 1 l 2283 1 l 2291 1 l 2299 1 l 2306 1 l 2314 1 l 2322 1 l 2329 1 l 2337 1 l 2345 1 l 2352 1 l 2360 1 l 2367 1 l 2375 1 l 2383 1 l 2390 1 l 2398 1 l 2406 1 l 2406 1 m 2406 1 l 2414 1 l 2749 1 m 2749 1 l 2757 1 l 2765 1 l 2773 1 l 2781 1 l 2788 1 l 2796 1 l 2804 1 l 2812 1 l 2820 1 l 2828 1 l 2835 1 l 2843 1 l 2851 1 l 2859 1 l 2867 1 l 2874 1 l 2882 1 l 2890 1 l 2898 1 l 2906 1 l 2914 1 l 2921 1 l 2929 1 l 2937 1 l 2945 1 l 2953 1 l 2960 1 l 2968 1 l 2976 1 l 2984 1 l 2992 1 l 2999 1 l 3007 1 l 3015 1 l 3023 1 l 3030 1 l 3038 1 l 3046 1 l 3054 1 l 3062 1 l 3069 1 l 3077 1 l 3085 1 l 3093 1 l 3093 1 m 3093 1 l 3101 1 l 1 1 m [5 3] 6 setdash 1 1 l 166 1 l 166 1 l 166 1 l 166 13 l 331 13 l 331 1 l 331 1 l 331 186 l 496 186 l 496 1 l 496 1 l 496 831 l 661 831 l 661 1 l 661 1 l 661 1732 l 825 1732 l 825 1 l 825 1 l 825 2027 l 990 2027 l 990 1 l 990 1 l 990 1489 l 1155 1489 l 1155 1 l 1155 1 l 1155 739 l 1320 739 l 1320 1 l 1320 1 l 1320 261 l 1485 261 l 1485 1 l 1485 1 l 1485 69 l 1650 69 l 1650 1 l 1650 1 l 1650 14 l 1815 14 l 1815 1 l 1815 1 l 1815 3 l 1980 3 l 1980 1 l 1980 1 l 1980 1 l 2145 1 l 2145 1 l 2145 1 l 2145 1 l 2310 1 l 2310 1 l 2310 1 l 2310 1 l 2474 1 l 2474 1 l 2474 1 l 2474 1 l 2639 1 l 2639 1 l 2639 1 l 2639 1 l 2804 1 l 2804 1 l 2804 1 l 2804 1 l 2969 1 l 2969 1 l 2969 1 l 2969 1 l 3134 1 l 3134 1 l 3134 1 l 3134 1 l 3299 1 l 3299 1 l 3299 1 l 3299 1 l 1 0 m tthick setlinewidth [] 0 setdash 1 10 m 1 10 l stroke lthick setlinewidth 0 126 m (0) show 1 101 m 825 0 m tthick setlinewidth 825 10 l stroke lthick setlinewidth 780 126 m (5) show 810 101 m 1650 0 m tthick setlinewidth 1650 10 l stroke lthick setlinewidth 1590 126 m (10) show 1620 101 m 2474 0 m tthick setlinewidth 2474 10 l stroke lthick setlinewidth 2414 126 m (15) show 2444 101 m 3299 0 m tthick setlinewidth 3299 10 l stroke lthick setlinewidth 3210 126 m (20) show 3240 101 m 0 1 m tthick setlinewidth 10 1 l stroke lthick setlinewidth 17 26 m (0) show 47 1 m 0 369 m tthick setlinewidth 10 369 l stroke lthick setlinewidth 17 394 m (0.05) show 47 369 m 0 736 m tthick setlinewidth 10 736 l stroke lthick setlinewidth 17 761 m (0.1) show 47 736 m 0 1104 m tthick setlinewidth 10 1104 l stroke lthick setlinewidth 17 1129 m (0.15) show 47 1104 m 0 1472 m tthick setlinewidth 10 1472 l stroke lthick setlinewidth 17 1497 m (0.2) show 47 1472 m 0 1839 m tthick setlinewidth 10 1839 l stroke lthick setlinewidth 17 1864 m (0.25) show 47 1839 m 0 2207 m tthick setlinewidth 10 2207 l stroke lthick setlinewidth 17 2232 m (0.3) show 47 2207 m 3240 226 m (x) show 17 2275 m (y) show stroke grestore %%EndDocument endTexFig -54 1043 a Fq(Figure)i(1:)22 b(The)16 b(histogram)g(of)f(the)i(probabilit)o (y)g(distribution)h(of)d Fk(D)1160 1050 y Fj(n)1200 1043 y Fq(\(for)g(dimension)j Fk(d)13 b Fq(=)i(2)h(and)g Fk(n)f Fq(=)f(100\))-54 1099 y(plotted)i(against)e(a)h(Gaussian)h(densit)o(y)f(function)h(of)f(same)g (mean)g(and)h(v)m(ariance.)-54 1229 y Fs(2)69 b(Basic)22 b(equations)-54 1330 y Fq(Tw)o(o)14 b(in)o(tegral)i(op)q(erators)e(pla)o(y)i(an)f(essen)o (tial)h(r^)-23 b(ole)15 b(here:)406 1445 y Fo(I)8 b Fk(f)d Fq(\()p Fk(z)r Fq(\))12 b(=)580 1388 y Fg(Z)621 1401 y Fj(z)603 1482 y Fn(0)649 1445 y Fk(f)5 b Fq(\()p Fk(t)p Fq(\))767 1415 y Fk(dt)p 740 1435 95 2 v 740 1476 a Fq(1)10 b Fi(\000)g Fk(t)931 1445 y Fo(J)e Fk(f)d Fq(\()p Fk(z)r Fq(\))12 b(=)1112 1388 y Fg(Z)1153 1401 y Fj(z)1135 1482 y Fn(0)1181 1445 y Fk(f)5 b Fq(\()p Fk(t)p Fq(\))1325 1415 y Fk(dt)p 1272 1435 147 2 v 1272 1476 a(t)p Fq(\(1)10 b Fi(\000)g Fk(t)p Fq(\))1423 1445 y Fk(:)-54 1569 y Fo(Lemma)17 b(1)23 b Fm(The)18 b(gener)n(ating)f(functions) h(of)g(the)g(c)n(osts)g(of)g(a)g(r)n(andom)h(se)n(ar)n(ch,)f(suc)n(c)n (essful)e Fq(\()p Fk(C)1617 1576 y Fj(n)1640 1569 y Fq(\))i Fm(and)g(unsuc-)-54 1625 y(c)n(essful)d Fq(\()p Fk(D)145 1632 y Fj(n)168 1625 y Fq(\))p Fm(,)h(in)f(a)i(quadtr)n(e)n(e)f(of)h(size)e Fk(n)i Fm(ar)n(e)f(given)f(by)290 1685 y Fg(8)290 1722 y(>)290 1735 y(>)290 1747 y(>)290 1759 y(<)290 1834 y(>)290 1847 y(>)290 1859 y(>)290 1872 y(:)348 1741 y Fk(\015)372 1748 y Fj(n)395 1741 y Fq(\()p Fk(u)p Fq(\))41 b(:=)587 1700 y Fg(X)608 1793 y Fj(k)655 1741 y Fq(Pr)p Fi(f)p Fk(C)760 1748 y Fj(n)795 1741 y Fq(=)13 b Fk(k)q Fi(g)p Fk(u)917 1722 y Fj(k)951 1741 y Fq(=)1006 1710 y(1)p 1004 1730 28 2 v 1004 1772 a Fk(n)1109 1710 y(u)p 1049 1730 148 2 v 1049 1772 a Fq(2)1072 1759 y Fj(d)1091 1772 y Fk(u)e Fi(\000)f Fq(1)1201 1741 y(\()p Fk(\036)1246 1748 y Fj(n)1269 1741 y Fq(\()p Fk(u)p Fq(\))f Fi(\000)i Fq(1\))348 1857 y Fk(\016)368 1864 y Fj(n)392 1857 y Fq(\()p Fk(u)p Fq(\))44 b(:=)587 1816 y Fg(X)608 1909 y Fj(k)655 1857 y Fq(Pr)p Fi(f)p Fk(D)765 1864 y Fj(n)800 1857 y Fq(=)13 b Fk(k)q Fi(g)p Fk(u)922 1838 y Fj(k)956 1857 y Fq(=)1071 1826 y(1)p 1009 1846 V 1009 1888 a(2)1032 1875 y Fj(d)1052 1888 y Fk(u)d Fi(\000)g Fq(1)1161 1857 y(\()p Fk(\036)1206 1864 y Fj(n)1229 1857 y Fq(\()p Fk(u)p Fq(\))g Fi(\000)g Fk(\036)1373 1864 y Fj(n)p Ff(\000)p Fn(1)1442 1857 y Fq(\()p Fk(u)p Fq(\)\))p Fk(;)1838 1808 y Fq(\(3\))-54 1988 y Fm(wher)n(e)16 b(the)h(bivariate)f(gener)n(ating)g(function)709 2085 y Fq(\010\()p Fk(u;)8 b(z)r Fq(\))j(=)907 2044 y Fg(X)926 2131 y Fj(n)975 2085 y Fk(\036)1002 2092 y Fj(n)1025 2085 y Fq(\()p Fk(u)p Fq(\))p Fk(z)1110 2066 y Fj(n)-54 2213 y Fm(of)16 b(the)h(level)e(p)n(olynomials)h Fk(\036)452 2220 y Fj(n)475 2213 y Fq(\()p Fk(u)p Fq(\))g Fm(is)g(char)n(acterize)n(d)g(by)g(the)g(inte)n (gr)n(al)g(e)n(quation)613 2310 y Fq(\010\()p Fk(u;)8 b(z)r Fq(\))k(=)h(1)c(+)i(2)913 2291 y Fj(d)933 2310 y Fk(u)p Fo(J)986 2291 y Fj(d)p Ff(\000)p Fn(1)1051 2310 y Fo(I)d Fq(\010\()p Fk(u;)g(z)r Fq(\))p Fk(:)607 b Fq(\(4\))-54 2409 y Fo(Pro)q(of.)20 b Fq(A)15 b(quadtree)g(of)g(size)h Fk(n)g Fq(giv)o(es)f(rise)h(to)e(a)h(ro)q (ot)f(subtree)i(of)f(size)h Fk(k)g Fq(with)g(probabilit)o(y)499 2522 y Fk(\031)525 2529 y Fj(n;k)590 2522 y Fq(=)645 2491 y(1)p 643 2511 28 2 v 643 2553 a Fk(n)683 2481 y Fg(X)700 2573 y Ff(L)1029 2491 y Fq(1)p 755 2511 571 2 v 755 2553 a(\()p Fk(`)792 2560 y Fn(1)822 2553 y Fq(+)10 b(1\)\()p Fk(`)945 2560 y Fn(2)974 2553 y Fq(+)g(1\))e Fi(\001)g(\001)g(\001)d Fq(\()p Fk(`)1165 2560 y Fj(d)p Ff(\000)p Fn(1)1240 2553 y Fq(+)10 b(1\))1331 2522 y Fk(;)494 b Fq(\(5\))-54 2653 y(where)14 b(the)g(summation)f(is)h(o)o (v)o(er)f Fk(n)g(>)g(`)633 2660 y Fn(1)665 2653 y Fi(\025)g Fk(`)732 2660 y Fn(2)765 2653 y Fi(\025)g(\001)8 b(\001)g(\001)i(\025)j Fk(`)945 2660 y Fj(d)p Ff(\000)p Fn(1)1023 2653 y Fi(\025)g Fk(k)q Fq(.)20 b(The)13 b(rest)h(relies)h(on)e(simple)i(com)o(binatorial)-54 2709 y(prop)q(erties)k(of)g(the)f(\\lev)o(el)i(p)q(olynomials")g Fk(\036)736 2716 y Fj(n)778 2709 y Fq(and)f(on)g(translating)f(recurrences)i (in)o(to)e(generating)h(function)-54 2766 y(equations.)1704 b Fa(2)p eop %%Page: 119 3 119 2 bop -54 98 a Fe(Limit)16 b(Distributions)h(in)f(Quadtrees)1227 b Fq(119)p -54 118 1950 2 v -54 278 a Fs(3)69 b(Lo)n(w)n(er)23 b(dimensions)-54 379 y Fm(The)e(binary)g(se)n(ar)n(ch)g(tr)n(e)n(e)j Fq(\()p Fk(d)d Fq(=)h(1\))p Fm(.)36 b Fq(The)21 b(main)g(results)g(are)f (originally)i(due)g(to)e(Hibbard)h(for)f(the)h(mean)-54 436 y(and)16 b(Lync)o(h)h(for)f(the)g(whole)h(distribution.)25 b(See)17 b([8)o(].)23 b(Related)17 b(results)f(hold)i(for)d(successful)j (searc)o(hes.)23 b(When)-54 492 y Fk(d)16 b Fq(=)h(1,)g(the)h(in)o(tegral)g (equation)g(satis\014ed)g(b)o(y)f(\010\()p Fk(u;)8 b(z)r Fq(\))16 b(is)i(homogeneous)f(of)g(order)h(1,)f(and)h(th)o(us)f(solv)m(able)i(b)o(y) -54 549 y(quadratures.)g(W)l(e)d(\014nd)207 671 y(\010\()p Fk(u;)8 b(z)r Fq(\))j(=)487 641 y(1)p 410 661 177 2 v 410 703 a(\(1)f Fi(\000)g Fk(z)r Fq(\))547 689 y Fn(2)p Fj(u)683 671 y Fq(and)91 b Fk(\036)874 678 y Fj(n)898 671 y Fq(\()p Fk(u)p Fq(\))12 b(=)1025 641 y(\(2)p Fk(u)p Fq(\))d Fi(\001)h Fq(\(2)p Fk(u)f Fq(+)i(1\))d Fi(\001)g(\001)g(\001)t Fq(\(2)p Fk(u)i Fq(+)g Fk(n)h Fi(\000)f Fq(1\))p 1025 661 593 2 v 1301 703 a Fk(n)p Fq(!)1622 671 y Fk(:)203 b Fq(\(6\))-54 803 y(Th)o(us,)15 b(w)o(e)g(ha)o(v)o(e)g([)p Fk(u)285 786 y Fj(k)306 803 y Fq(])p Fk(\036)346 810 y Fj(n)370 803 y Fq(\()p Fk(u)p Fq(\))d(=)h(2)515 786 y Fj(k)536 768 y Fg(\002)554 782 y Fj(n)555 818 y(k)575 768 y Fg(\003)592 803 y Fk(=n)p Fq(!,)i(whic)o(h)h(in)o(v)o(olv)o(es)g(the)g (Stirling)h(n)o(um)o(b)q(ers)f(of)f(the)g(\014rst)g(kind)i(\(\\cycle")-54 859 y(Stirling)g(n)o(um)o(b)q(ers\).)-54 964 y Fo(Theorem)g(2)h(\(Hibbard,)f (Lync)o(h\))23 b Fm(The)17 b(c)n(ost)g Fk(D)860 971 y Fj(n)901 964 y Fm(of)h(a)f(r)n(andom)h(se)n(ar)n(ch)f(in)g(a)g(binary)h(se)n(ar)n(ch)f (tr)n(e)n(e)f(of)i(size)-54 1021 y Fk(n)10 b Fi(\000)h Fq(1)16 b Fm(has)g(me)n(an)g(and)g(varianc)n(e)g(given)g(by)494 1122 y Fk(\026)521 1129 y Fj(n)558 1122 y Fq(=)d(2\()p Fk(H)685 1129 y Fj(n)717 1122 y Fi(\000)e Fq(1\))92 b Fk(\033)924 1104 y Fn(2)922 1134 y Fj(n)958 1122 y Fq(=)13 b(2)p Fk(H)1067 1129 y Fj(n)1100 1122 y Fi(\000)e Fq(4)p Fk(H)1211 1104 y Fn(\(2\))1207 1134 y Fj(n)1267 1122 y Fq(+)g(2)p Fk(;)-54 1224 y Fm(and)16 b(pr)n(ob)n(ability)g(distribution)658 1310 y Fq(Pr)p Fi(f)p Fk(D)768 1317 y Fj(n)803 1310 y Fq(=)d Fk(k)q Fi(g)g Fq(=)967 1280 y(2)990 1263 y Fj(k)p 965 1300 48 2 v 965 1342 a Fk(n)8 b Fq(!)1017 1238 y Fg(")1041 1280 y Fk(n)j Fi(\000)f Fq(1)1082 1342 y Fk(k)1147 1238 y Fg(#)1171 1310 y Fk(:)-54 1449 y Fm(The)18 b(standar)n(d)h(quadtr)n(e)n(e)f Fq(\()p Fk(d)e Fq(=)h(2\))p Fm(.)27 b Fq(In)18 b(the)g(case)f(of)g(dimension)j Fk(d)c Fq(=)h(2,)g(the)h (analytic)g(mo)q(del)h(of)e(quadtrees)-54 1505 y(can)e(b)q(e)g(solv)o(ed)f (explicitly)j(in)f(terms)d(of)h(h)o(yp)q(ergeometric)h(functions)g(that)f (are)g(otherwise)h(kno)o(wn)f(to)f(o)q(ccur)i(in)-54 1561 y(the)g(a)o(v)o (erage)f(case)i(analysis)f(of)g(partial)h(matc)o(h.)-54 1667 y Fo(Theorem)h(3)23 b Fm(The)14 b(c)n(ost)h Fk(D)437 1674 y Fj(n)475 1667 y Fm(of)g(a)g(r)n(andom)g(se)n(ar)n(ch)g(in)f(a)h(standar)n(d)g (quadtr)n(e)n(e)g(of)g(size)f Fk(n)7 b Fi(\000)g Fq(1)16 b Fm(has)f(a)g(gener)n(ating)-54 1723 y(function)h Fk(\015)149 1730 y Fj(n)172 1723 y Fq(\()p Fk(u)p Fq(\))g Fm(given)f(by)256 1858 y Fk(\015)280 1865 y Fj(n)303 1858 y Fq(\()p Fk(u)347 1839 y Fn(2)366 1858 y Fq(\))e Fi(\021)f Fo(E)q Fi(f)p Fk(u)528 1839 y Fn(2)p Fj(D)575 1843 y Fb(n)597 1858 y Fi(g)h Fq(=)748 1827 y(1)p 686 1847 147 2 v 686 1889 a(4)p Fk(u)735 1876 y Fn(2)764 1889 y Fi(\000)e Fq(1)865 1805 y Fj(n)846 1817 y Fg(X)845 1908 y Fj(j)r Fn(=0)914 1786 y Fg( )947 1827 y Fq(2)p Fk(u)961 1889 y(j)996 1786 y Fg(!)o( )1061 1827 y Fq(2)p Fk(u)f Fi(\000)h Fq(1)1114 1889 y Fk(j)1188 1786 y Fg(! )1254 1827 y Fq(2)p Fk(u)f Fi(\000)g Fq(2)g(+)h Fk(n)f Fi(\000)g Fk(j)1345 1889 y(n)h Fi(\000)f Fk(j)1541 1786 y Fg(!)1574 1858 y Fk(:)-54 2004 y Fq(Th)o(us)22 b(the)g(probabilit)o(y)h(distribution)g(of)e Fk(D)742 2011 y Fj(n)787 2004 y Fq(is)h(expressible)i(as)d(a)h(complicated)h (con)o(v)o(olution)f(of)f(Stirling)-54 2060 y(n)o(um)o(b)q(ers.)-54 2116 y Fo(Pro)q(of.)f Fq(The)15 b(generating)g(function)i(\010)e(of)f(the)i (lev)o(el)g(p)q(olynomials)h(satis\014es)462 2237 y(\010\()p Fk(u;)8 b(z)r Fq(\))j(=)i(1)d(+)g(2)761 2218 y Fn(2)781 2237 y Fk(u)815 2179 y Fg(Z)856 2192 y Fj(z)837 2274 y Fn(0)946 2206 y Fk(dx)p 888 2226 166 2 v 888 2268 a(x)p Fq(\(1)g Fi(\000)g Fk(x)p Fq(\))1066 2179 y Fg(Z)1108 2192 y Fj(x)1089 2274 y Fn(0)1137 2237 y Fq(\010\()p Fk(u;)e(t)p Fq(\))1308 2206 y Fk(dt)p 1281 2226 95 2 v 1281 2268 a Fq(1)i Fi(\000)g Fk(t)-54 2360 y Fq(an)15 b(equation)h(whose)f(solution)h(admits)f(an)g(h)o(yp)q (ergeometric)h(form:)519 2478 y(\010\()p Fk(u)596 2459 y Fn(2)616 2478 y Fq(;)8 b Fk(z)r Fq(\))j(=)819 2447 y(1)p 742 2467 177 2 v 742 2509 a(\(1)f Fi(\000)g Fk(z)r Fq(\))879 2496 y Fn(2)p Fj(u)932 2478 y Fk(F)c Fq([)p Fi(\000)p Fq(2)p Fk(u;)i Fq(1)h Fi(\000)h Fq(2)p Fk(u)p Fq(;)e(1;)g Fk(z)r Fq(])p Fk(:)513 b Fq(\(7\))-54 2601 y(where)333 2674 y Fk(F)19 b Fi(\021)13 b Fk(F)6 b Fq([)p Fk(a;)i(b)p Fq(;)g Fk(c)p Fq(;)g Fk(z)r Fq(])h(=)k(1)d(+) 781 2643 y Fk(a)g Fi(\001)g Fk(b)p 781 2663 77 2 v 809 2705 a(c)873 2643 y(z)p 867 2663 36 2 v 867 2705 a Fq(1!)917 2674 y(+)968 2643 y Fk(a)p Fq(\()p Fk(a)g Fq(+)g(1\))g Fi(\001)f Fk(b)p Fq(\()p Fk(b)g Fq(+)i(1\))p 968 2663 348 2 v 1065 2705 a Fk(c)p Fq(\()p Fk(c)e Fq(+)i(1\))1325 2643 y Fk(z)1348 2627 y Fn(2)p 1325 2663 43 2 v 1329 2705 a Fq(2!)1383 2674 y(+)f Fi(\001)e(\001)g(\001)14 b Fk(:)328 b Fq(\(8\))1851 2774 y Fa(2)p eop %%Page: 120 4 120 3 bop -54 98 a Fq(120)823 b Fe(P)o(art)14 b(IV.)h(Analysis)h(of)f (Algorithms)h(and)f(Data)f(Structures)p -54 118 1950 2 v -54 278 a Fs(4)69 b(The)23 b(singularit)n(y)e(p)r(erturbation)j(metho)r(d)-54 379 y Fq(The)11 b(arc)o(hitecture)h(of)e(the)h(pro)q(of)g(of)g(the)g(main)g (theorem)g(asserting)g(asymptotic)g(normalit)o(y)g(of)f(the)h(distribution) -54 436 y(is)22 b(transparen)o(t)e(although)h(implemen)o(tation)h(of)f(it)g (requires)h(quite)g(some)f(care.)37 b(In)22 b(essence,)h(w)o(e)e(need)h(to) -54 492 y(solv)o(e)d(a)g(double)h(in)o(v)o(ersion)g(problem)g(in)g(order)e (to)h(reco)o(v)o(er)f(the)h(co)q(e\016cien)o(ts)h([)p Fk(z)1379 476 y Fj(n)1402 492 y Fk(u)1428 476 y Fj(k)1450 492 y Fq(]\010\()p Fk(u;)8 b(z)r Fq(\).)29 b(A)19 b(\014rst)g(stage)-54 549 y(consists)f(in)h (extracting)f Fk(\036)418 556 y Fj(n)442 549 y Fq(\()p Fk(u)p Fq(\))e(=)i([)p Fk(z)609 532 y Fj(n)632 549 y Fq(]\010\()p Fk(u;)8 b(z)r Fq(\).)27 b(This)18 b(in)o(v)o(olv)o(es)h(examining)g(the)f (in\015uence)i(of)e(a)g(parameter)-54 605 y(\()p Fk(u)p Fq(\))e(on)h(the)f (singularit)o(y)i(\(at)e Fk(z)h Fq(=)e(1\))h(of)h(a)f(di\013eren)o(tial)i (equation.)25 b(F)l(or)16 b(that)g(reason)g(w)o(e)g(call)i(our)e(metho)q(d)h (a)-54 661 y Fm(singularity)f(p)n(erturb)n(ation)h(metho)n(d)p Fq(.)22 b(It)16 b(is)h(in)o(termediate)f(in)h(di\016cult)o(y)g(b)q(et)o(w)o (een)f(regular)g(p)q(erturbations)g(and)-54 718 y(singular)h(p)q (erturbations,)f(the)g(latter)g(implying)h(reduction)g(of)f(order)1169 701 y Fn(6)1188 718 y Fq(.)22 b(A)16 b(second)h(stage)e(\(from)g Fk(\036)1691 725 y Fj(n)1714 718 y Fq(\()p Fk(u)p Fq(\))h(to)f(its)-54 774 y(co)q(e\016cien)o(ts\))h(relies)g(on)f(con)o(tin)o(uit)o(y)h(theorems)f (of)g(analytic)h(probabilit)o(y)l(.)21 b(W)l(e)15 b(o\013er)g(here)g(a)g (brief)h(outline.)-54 831 y(The)f(starting)g(p)q(oin)o(t)h(is)f(the)h(in)o (tegral)f(equation)h(furnished)g(b)o(y)g(Lemma)f(1,)613 929 y(\010\()p Fk(u;)8 b(z)r Fq(\))k(=)h(1)c(+)i(2)913 910 y Fj(d)933 929 y Fk(u)p Fo(J)986 910 y Fj(d)p Ff(\000)p Fn(1)1051 929 y Fo(I)d Fq(\010\()p Fk(u;)g(z)r Fq(\))p Fk(:)607 b Fq(\(9\))-54 1027 y(That)14 b(equation)h(is)g(itself)g(equiv)m(alen)o(t)h(to)e(a)g(linear) i(di\013eren)o(tial)f(equation)g(with)g(co)q(e\016cien)o(ts)g(that)f(are)g(p) q(olyno-)-54 1084 y(mial)e(in)g(the)f(main)h(v)m(ariable)g Fk(z)h Fq(and)f(the)f(parameter)f Fk(u)p Fq(.)19 b(The)11 b(order)g(of)f(the) i(equation)f(is)h(equal)g(to)e(the)h(dimension)-54 1140 y(of)i(the)h(data)f (space,)h Fk(d)p Fq(.)19 b(The)14 b(standard)f(theory)g(is)i(more)e(con)o(v)o (enien)o(tly)i(dev)o(elop)q(ed)g(from)e Fm(di\013er)n(ential)h(systems)-54 1197 y Fq(rather)h(than)g(equations,)g(and)g(the)h(asso)q(ciated)f(system)g (is)g(also)h(of)e(dimension)j Fk(d)p Fq(.)-54 1253 y(The)d(most)f(common)g (case)h(for)f(linear)h(di\013eren)o(tial)h(equations)f(and)g(systems)f(is)h (the)g(one)g(called)h Fm(r)n(e)n(gular)f(singu-)-54 1310 y(larity)20 b Fq(or)15 b Fm(singularity)i(of)g(the)g(\014rst)f(kind)g Fq([1)o(,)g(12)o (].)22 b(In)16 b(suc)o(h)h(a)e(case,)h(a)f(basis)i(of)e(solutions)i(can)f(b)q (e)g(found)h(that)-54 1366 y(are)e(of)g(the)h(appro)o(ximate)f(form)g Fk(c=)p Fq(\(1)9 b Fi(\000)i Fk(z)r Fq(\))704 1350 y Fj(\013)728 1366 y Fk(:)16 b Fq(The)f(p)q(ossible)j(exp)q(onen)o(ts)e Fk(\013)g Fq(are)f(determined)i(b)o(y)e(substituting)-54 1423 y(in)o(to)g(the)g (equation.)21 b(They)15 b(th)o(us)g(app)q(ear)h(as)e(ro)q(ots)h(of)f(a)h(p)q (olynomial)i(called)g(the)e Fm(indicial)h(p)n(olynomial)p Fq(.)-54 1479 y(In)h(a)f(parameterized)h(case)g(lik)o(e)g(\(9\),)f(w)o(e)g(th)o(us)g (exp)q(ect)h(solutions)g(to)f(in)o(v)o(olv)o(e)h(linear)h(com)o(binations)f (of)f(terms)-54 1536 y(of)f(the)g(form)874 1574 y Fk(c)p Fq(\()p Fk(u)p Fq(\))p 810 1594 210 2 v 810 1637 a(\(1)10 b Fi(\000)g Fk(z)r Fq(\))947 1624 y Fj(\013)p Fn(\()p Fj(u)p Fn(\))1024 1605 y Fk(;)778 b Fq(\(10\))-54 1712 y(as)18 b Fk(z)h Fi(!)f Fq(1.)28 b(In)18 b(the)g(case)g(of)g(\(9\),)f(it)h(is)h(found)f(that)f(the)h (exp)q(onen)o(ts)h(are)e(the)h(algebraic)h(functions)g(that)e(are)-54 1768 y(ro)q(ots)d(of)h(the)g(indicial)j(equation)738 1825 y(\()p Fk(\013)p Fq(\()p Fk(u)p Fq(\)\))865 1806 y Fj(d)894 1825 y Fi(\000)10 b Fq(2)962 1806 y Fj(d)982 1825 y Fk(u)j Fq(=)g(0)p Fk(:)-54 1906 y Fq(F)l(orms)j(b)q(elonging)i(to)f(the)f(general)i(t)o(yp)q(e) f(\(10\))e(w)o(ere)i(already)g(encoun)o(tered)g(when)h Fk(d)c Fq(=)i(1,)h(see)g(Eq.)f(\(6\),)g(and)-54 1963 y(when)g Fk(d)c Fq(=)h(2,)h(see)i(Eq.)f(\(7\).)-54 2019 y(As)e Fk(z)i Fi(!)e Fq(1,)g(the)g(dominan)o(t)h(term)e(in)i(the)g(expansion)g(of)e(\010\()p Fk(u;)c(z)r Fq(\))k(is)i(the)f(one)g(corresp)q(onding)i(to)d(the)h(ro)q(ot)g (2)p Fk(u)1841 2003 y Fn(1)p Fj(=d)-54 2076 y Fq(whic)o(h)i(has)f(maximal)g (real)g(part.)19 b(In)c(particular)f(when)h(the)f(parameter)f Fk(u)h Fq(is)g(close)h(to)e(1,)h(this)g(is)h(the)f(principal)-54 2132 y(determination)h(of)f(2)324 2117 y Fb(d)315 2099 y Fi(p)p 353 2099 27 2 v 33 x Fk(u)p Fq(.)19 b(F)l(rom)14 b(the)g(shap)q(e)h(\(10\))d (of)i(singular)h(elemen)o(ts,)g(w)o(e)f(th)o(us)g(exp)q(ect)g(the)h(singular) g(form)-54 2189 y(of)g(\010)g(to)f(b)q(e)576 2257 y(\010\()p Fk(u;)8 b(z)r Fq(\))j Fi(\031)852 2227 y Fk(c)p Fq(\()p Fk(u)p Fq(\))p 779 2247 227 2 v 779 2294 a(\(1)f Fi(\000)g Fk(z)r Fq(\))916 2280 y Fn(2)p Fj(u)954 2271 y Fl(1)p Fb(=d)1101 2257 y Fq(\()p Fk(z)15 b Fi(!)e Fq(1\))p Fk(;)548 b Fq(\(11\))-54 2366 y(at)15 b(least)g(for)f Fk(u)i Fq(near)f(1.)-54 2422 y(According)21 b(to)f(the)h(usual)g(principles)i(of)d(singularit)o(y)h(analysis,)h(the)f Fm(dominant)g(singular)f(b)n(ehaviour)26 b Fq(of)20 b(\010)-54 2479 y(pro)o(vides)c(the)g(dominan)o(t)g(asymptotic)f(term)g(in)h(its)g(co)q (e\016cien)o(ts)h Fk(\036)1127 2486 y Fj(n)1150 2479 y Fq(\()p Fk(u)p Fq(\))c(=)h([)p Fk(z)1310 2462 y Fj(n)1333 2479 y Fq(]\010\()p Fk(u;)8 b(z)r Fq(\).)19 b(T)l(ranslating)d(\(11\))f(to)-54 2535 y(co)q(e\016cien)o(ts,)h(w)o(e)f(exp)q(ect)h(to)e(get,)h(as)f(an)h (appro)o(ximation)h(of)e Fk(\036)1044 2542 y Fj(n)1068 2535 y Fq(\()p Fk(u)p Fq(\),)695 2670 y Fk(\036)722 2677 y Fj(n)746 2670 y Fq(\()p Fk(u)p Fq(\))e Fi(\031)h Fk(c)p Fq(\()p Fk(u)p Fq(\))964 2639 y Fk(n)991 2623 y Fn(2)p Fj(u)1029 2611 y Fl(1)p Fb(=d)1079 2623 y Ff(\000)p Fn(1)p 961 2660 169 2 v 961 2703 a Fq(\000\(2)p Fk(u)1056 2689 y Fn(1)p Fj(=d)1112 2703 y Fq(\))1134 2670 y Fk(:)668 b Fq(\(12\))p -54 2743 780 2 v -2 2770 a Fl(6)15 2786 y Fu(W)m(e)13 b(refer)g(to)g(standard)h(texts)f(lik)o(e)i([1,)d(12)q(])g (for)h(basics)h(on)f(linear)i(di\013eren)o(tial)h(equations)f(in)f(the)f (complex)i(domain.)p eop %%Page: 121 5 121 4 bop -54 98 a Fe(Limit)16 b(Distributions)h(in)f(Quadtrees)1227 b Fq(121)p -54 118 1950 2 v -54 278 a(Giv)o(en)18 b(the)f(appro)o(ximation)h (\(12\),)e(v)m(alues)i(of)f(the)h(p)q(olynomial)h Fk(\036)1113 285 y Fj(n)1136 278 y Fq(\()p Fk(u)p Fq(\))e(are)g(asymptotically)h(kno)o(wn) f(at)g(least)-54 334 y(for)d Fk(u)g Fq(in)i(a)e(neigh)o(b)q(ourho)q(o)q(d)i (of)e(1.)19 b(An)c(in)o(v)o(ersion)g(problem)g(\(the)f(second)h(one)g(after)f (the)g(phase)h(of)f(singularit)o(y)-54 391 y(analysis)k(ensuring)h(the)f (transition)f(from)g(\(11\))g(to)f(\(12\)\))g(is)i(then)g(to)f(b)q(e)i(solv)o (ed.)27 b(The)18 b(appro)o(ximation)f(\(12\))-54 447 y(p)q(ermits)f(to)e (estimate)g Fk(\036)375 454 y Fj(n)399 447 y Fq(\()p Fk(e)438 431 y Fj(i\022)469 447 y Fq(\),)h(suitably)h(normalized,)f(when)h Fk(\022)g Fq(lies)g(near)f(0.)20 b(The)15 b(F)l(ourier)g(transform)e(of)i (the)-54 504 y(distribution)j(de\014ned)g(b)o(y)f(the)f(co)q(e\016cien)o(ts)i (of)e Fk(\036)809 511 y Fj(n)832 504 y Fq(\()p Fk(u)p Fq(\))g(tends)h(to)f Fk(e)1111 487 y Ff(\000)p Fj(\022)1155 475 y Fl(2)1173 487 y Fj(=)p Fn(2)1211 504 y Fq(,)g(the)h(c)o(haracteristic)f(function)i(of)e (the)-54 560 y(Gaussian)f(distribution:)596 636 y(lim)568 663 y Fj(n)p Ff(!)p Fn(+)p Ff(1)695 636 y Fk(e)716 618 y Ff(\000)p Fj(i\022)q(a)791 622 y Fb(n)813 618 y Fj(=b)846 622 y Fb(n)887 606 y Fk(f)909 613 y Fj(n)933 606 y Fq(\()p Fk(e)972 589 y Fj(i\022)q(=b)1034 593 y Fb(n)1057 606 y Fq(\))p 887 626 188 2 v 929 667 a Fk(f)951 674 y Fj(n)975 667 y Fq(\(1\))1092 636 y(=)e Fk(e)1161 618 y Ff(\000)p Fj(\022)1205 606 y Fl(2)1224 618 y Fj(=)p Fn(2)1261 636 y Fk(;)-54 744 y Fq(for)i(some)h(suitably)h(c)o (hosen)f(cen)o(tering)g(constan)o(ts)f Fk(a)873 751 y Fj(n)897 744 y Fk(;)8 b(b)938 751 y Fj(n)976 744 y Fq(\(that)14 b(ma)o(y)i(b)q(e)g (tak)o(en)g(equal)g(to)f(the)h(mean)g Fk(\026)1783 751 y Fj(n)1823 744 y Fq(and)-54 801 y(v)m(ariance)g Fk(\033)150 808 y Fj(n)189 801 y Fq(of)f(the)g(distribution\).)-54 857 y(Since)g Fk(\036)90 864 y Fj(n)114 857 y Fq(\()p Fk(u)p Fq(\))e(has)g(p)q(ositiv)o(e)i(co)q (e\016cien)o(ts,)g(the)e(con)o(tin)o(uit)o(y)i(theorem)e(for)g(c)o (haracteristic)h(functions)h(\(or)e(equiv)m(a-)-54 913 y(len)o(tly)i(F)l (ourier)f(transforms)f(of)g(measures\))h(of)f(analytic)i(probabilit)o(y)g (theory)f(applies.)21 b(This)14 b(leads)h(to)e(the)h(end)-54 970 y(result,)g(namely)h(the)f(con)o(v)o(ergence)h(in)g(distribution)h(to)d (a)h(normal)g(distribution)i(for)d(the)h(co)q(e\016cien)o(ts)h(of)f Fk(\036)1811 977 y Fj(n)1835 970 y Fq(\()p Fk(u)p Fq(\))-54 1026 y(whic)o(h)i(in)g(turn)f(carries)h(to)e(the)i(distribution)g(of)f Fk(D)846 1033 y Fj(n)884 1026 y Fq(as)g(expressed)h(b)o(y)f(the)h(main)f (theorem.)-54 1083 y(The)10 b(metho)q(d)h(is)g(exp)q(ected)g(to)e(b)q(e)i (instrumen)o(tal)g(for)f(a)f(wide)j(class)e(of)g(recurrences)h(whose)f (generating)g(functions)-54 1139 y(satisfy)15 b(parameterized)h(linear)g (di\013eren)o(tial)g(equations.)-54 1277 y Fs(References)-33 1367 y Fr([1])21 b(E.)14 b(A.)f(Co)q(ddington)h(and)f(M.)h(Levinson.)k Fd(The)n(ory)c(of)h(Or)n(dinary)f(Di\013er)n(ential)h(Equations)p Fr(.)k(McGra)o(w-Hill,)12 b(1955.)-33 1455 y([2])21 b(L.)f(Devro)o(y)o(e)g (and)g(L.)f(Laforest.)37 b(An)20 b(analysis)f(of)g(random)g Fc(d)p Fr({dimensional)e(quad)i(trees.)38 b Fd(SIAM)21 b(Journal)f(on)33 1504 y(Computing)p Fr(,)14 b(19:821{832,)d(1990.)-33 1592 y([3])21 b(Ph.)13 b(Fla)r(jolet,)g(G.)f(Gonnet,)h(C.)g(Puec)o(h,)g(and)h(J.)f(M.)f (Robson.)18 b(Analytic)12 b(v)n(ariations)g(on)i(quadtrees.)19 b Fd(A)o(lgorithmic)n(a)p Fr(,)33 1641 y(1992.)e(24)d(pages,)f(to)h(app)q (ear.)-33 1729 y([4])21 b(Ph.)13 b(Fla)r(jolet)f(and)g(Th.)h(La\013orgue.)k (Searc)o(h)d(costs)g(in)e(quadtrees)i(and)f(singularit)o(y)e(p)q(erturbation) i(asymptotics.)k(In)33 1778 y(preparation,)d(1992.)-33 1866 y([5])21 b(G.)c(H.)g(Gonnet)h(and)f(R.)g(Baeza-Y)m(ates.)30 b Fd(Handb)n(o)n(ok)19 b(of)f(A)o(lgorithms)f(and)i(Data)g(Structur)n(es:)25 b(in)18 b(Pasc)n(al)h(and)g(C)p Fr(.)33 1915 y(Addison{W)m(esley)m(,)13 b(second)i(edition,)e(1991.)-33 2003 y([6])21 b(M.)14 b(Hoshi)f(and)h(Ph.)g (Fla)r(jolet.)j(P)o(age)d(usage)g(in)g(a)f(quadtree)i(index.)j Fd(BIT)p Fr(,)13 b(32:384{402,)e(1992.)-33 2090 y([7])21 b(L.)f(Laforest.)289 2079 y(\023)286 2090 y(Etude)g(des)h(arbres)g(h)o(yp)q(erquaternaires.)37 b(T)m(ec)o(hnical)20 b(Rep)q(ort)g(3,)g(LA)o(CIM,)g(UQAM,)g(Mon)o(treal,)33 2140 y(No)o(v)o(em)o(b)q(er)13 b(1990.)k(\(Author's)e(PhD)f(Thesis)g(at)g (McGill)e(Univ)o(ersit)o(y\).)-33 2227 y([8])21 b(H.)14 b(M.)f(Mahmoud.)k Fd(Evolution)e(of)g(R)n(andom)h(Se)n(ar)n(ch)f(T)m(r)n(e)n(es)p Fr(.)i(John)d(Wiley)m(,)e(1992.)-33 2314 y([9])21 b(H.)14 b(Samet.)j Fd(Applic)n(ations)d(of)h(Sp)n(atial)g(Data)h(Structur)n(es)p Fr(.)h(Addison{W)m(esley)m(,)c(1990.)-54 2401 y([10])21 b(H.)14 b(Samet.)j Fd(The)e(Design)g(and)h(A)o(nalysis)e(of)h(Sp)n(atial)g(Data)g (Structur)n(es)p Fr(.)j(Addison{W)m(esley)m(,)12 b(1990.)-54 2488 y([11])21 b(R.)13 b(Sedgewic)o(k.)19 b Fd(A)o(lgorithms)p Fr(.)d(Addison-W)m(esley)m(,)d(Reading,)g(Mass.,)g(second)i(edition,)e(1988.) -54 2575 y([12])21 b(W.)13 b(W)m(aso)o(w.)k Fd(Asymptotic)d(Exp)n(ansions)i (for)e(Or)n(dinary)g(Di\013er)n(ential)h(Equations)p Fr(.)j(Do)o(v)o(er,)13 b(1987.)k(A)d(reprin)o(t)g(of)f(the)33 2625 y(John)h(Wiley)f(edition,)g (1965.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF