Content-Type: multipart/mixed; boundary="-------------0006010817843" This is a multi-part message in MIME format. ---------------0006010817843 Content-Type: text/plain; name="00-253.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="00-253.keywords" ergodic theory; expanding maps; multi-dimensional dynamics; absolutely continuous invariant probability measure; existence; uniqueness; smoothness ---------------0006010817843 Content-Type: application/postscript; name="modtsj.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="modtsj.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.85 Copyright 1999 Radical Eye Software %%Title: modtsj.dvi %%Pages: 6 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips modtsj %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2000.06.01:1500 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]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/IEn 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 IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/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 A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A 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/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 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 A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 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/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/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$SavedState save N userdict maxlength dict begin/magscale true def normalscale currentpoint TR/psf$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 600 600 (modtsj.dvi) @start %DVIPSBitmapFont: Fa cmtt8 8 20 /Fa 20 123 df<121C127FA2EAFF80A3EA7F00A2121C0909738823>46 D64 D97 DII101 D<143E903801FF804913C0010F13E0A2EB1F8F90383F07C090383E0380 91C7FCA4007FB51280B612C0A36C1480D8003EC7FCB3383FFFFE487FA36C5B1B297EA823 >I104 D<133013FCA2487EA26C5AA2133090C7FCA5EA7FFC7F12FF127FA2EA003EB3387FFFFEB6 FCA36C13FE182A7AA923>I108 D<397F0F80F89038BFC3FCB5EAE7FE6C90B5FCA2D80FF1EB1F809038 E0FE0FEBC0FCA2EB80F8AF267FF0FF13F001F1131FD8FFF9EB9FF8D87FF1EB1FF001F013 0F251D819C23>I<387F81F838FFC7FE9038DFFF8090B5FC6C14C03807FC079038F803E0 13F013E0A213C0AE397FFC1FFE39FFFE3FFFA3397FFC1FFE201D7F9C23>I<133F3801FF E0487F487F487F381FC0FE383F807F383E001F007E1480007C130F00FC14C0481307A66C 130FA2007C1480007E131F6CEB3F006D5A381FE1FE6CB45A6C5B6C5B6C5BD8003FC7FC1A 1D7C9C23>I<387F81FC38FFC7FF01DF138090B512C06C14E03907FE07F09038F803F8EB F0004913FC157C5B153EA76D137CA215FC9038F001F8EBF8039038FC0FF090B512E015C0 01DF13809038C7FE00EBC1F801C0C7FCAAEA7FFC487EA36C5A1F2C7F9C23>I<90381F81 C09038FFE3E04813FB000713FF5A381FE03FEB801F383F000F007E1307127CA2481303A7 007C1307A2007E130F7EEB801F381FE07F6CB5FC7E6C13FBC613E3EB3F83EB0003AAEC7F FFA291B512806E1300A2212C7E9C23>I<397FF00FC09038F83FF000FFEBFFF8D87FFB13 FC90B5FCC613F1ECC0F8148091C7FC5B5BA35BAB387FFFFCA2B57E6C5BA21E1D7E9C23> I<137013F8A7007FB51280B612C0A36C1480D800F8C7FCACEC01C0EC03E0A49038FC07C0 EB7E0F90387FFF806D13006D5A6D5AEB03F01B257EA423>116 D<397F803FC039FFC07F E0A3007F133F00071303B11407EBE01F6CB512FE15FF7E6C13FB90383FC1FE201D7F9C23 >I<397FF03FF839FFF87FFCA3397FF03FF83907C007C0EC0F8013E01203EC1F0013F012 015CEBF83E1200A2EB7C7CA3EB3C78EB3EF8A2EB1EF0A2131F6D5AA21307A25CA2130F5C A2131F003E90C7FCEA7F3F133EEA7CFEEA7FFC5B6C5A6C5AEA0F801E2C7E9C23>121 D<003FB512F04814F8A315F0397C0007E0EC0FC0EC1F800038EB3F00C712FE495A495A49 5A495A495A495A49C7FC13FE485A48481370D807E013F8485A485A48C7FC48B5FCB6FCA3 6C14F01D1D7E9C23>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb cmti8 8 31 /Fb 31 122 df<387FFFC0A3B512806C130012057A901A>45 D<121C123E127F12FFA212 FE127C12380808788716>I65 D<010FB612FE5BA2903900FC0001EE007E173E173C4948141CA4495A 16E0A3903A07E001C01817001503A290390FC00F8091B5FCA390261F800FC7FCA490263F 000E136017E0A292380C01C0017E1300EE0380A2EE07005B5E161E163E48485CED01FCED 0FF8007FB6FCB75A7E2F2D7CAC30>69 D77 D<4AB4FC020F13C091383F 03F09138F800FCD903E0137E49487FD91F807F49C7EA0F80137E4915C0484814074915E0 1203485AA2485A121F5B123FA290C8120F5AA300FEED1FC0A3EE3F80A217005E48157E16 FE6C5D15015E007E4A5A4B5A6C4A5A4B5A6C4AC7FC6C6C137E6D13F83903E003F03901F8 0FC026007FFFC8FCEB0FF02B2F75AD37>79 D<010FB512FC49ECFF8017C0903A00FC000F F0EE03F8160117FC49481300A449481301A317F84948130317F0EE07E0160F4948EB1F80 EE3F00ED01FE91B512F84914C00280C8FCA349C9FCA4137EA45BA4485AA3387FFFC0B5FC 7E2E2D7CAC30>I97 D<13F8121FA3EA01F0A4485AA4485AA4380F87C0EB9FF0EBB878EBE03C381FC03EEB801E 141F1300123EA448133FA448137EA3147C14FC14F8EAF00100F813F0387803E014C0EB07 8038380F00EA1C3EEA0FF8EA03E0182F78AD21>II<153E EC07FEA3EC007CA415F8A4EC01F0A4903807C3E0EB1FF3EB7C3BEBF01F3901E00FC01203 EA07C0EA0F801580EA1F00A25A003EEB1F00127EA348133EA31518EC7C385AA214FC0078 EBF870EA7C01EA3C0390380778E0391E1E38C0380FF81F3903E00F001F2F79AD24>III<14F8EB03FE90380F873090381E03F8EB3C01137813F8EA01F015F0 EA03E01207A29038C003E0120FA3391F8007C0A4EC0F80A2120F141FEC3F0000075B0003 5BEBC3DF3800FFBEEB7E3E1300A25CA400385B007C5BEAFC01495A48485AD8F01FC7FCEA 7FFEEA1FF01D2C7C9D21>I<131FEA03FFA3EA003EA45BA45BA43801F07EEBF1FF9038F7 83809038FE03C0D803FC13E013F813F0A2EA07E013C0A3390F8007C0A3EC0F80EA1F00A2 EC1F001506003E140E143EA2150C48EB3C1C147CEC3C38153048EB1C60EC0FC00070EB07 801F2F7BAD24>I<1306131F1480EB3F007F130C90C7FCA9EA03E0487EEA0C781218EA38 7C12301270A2485AA2EAE1F012411201485AA3485AA3EA0F831387EA1F07A21306EA1E0E 123EEA1E1C1318EA0E30EA0FE0EA03C0112E7AAC16>I<131FEA03FFA3EA003EA45BA45B A43901F001E0EC07F0EC0E38EC18783903E030F8146114C19038E181F03907C300E001C6 130013CC13D8EA0FF0A213FFEB9F80381F07C06D7E6D7E1530003E1470A4007CEBE0E0A2 15C014E139F800F380EC7F000070131E1D2F7BAD21>107 D<137CEA07FC120FA2EA00F8 A4EA01F0A4EA03E0A4EA07C0A4EA0F80A4EA1F00A4123EA45AA31330EAF870A4EAF0E0A3 EAF1C0EA7180EA3F00121E0E2F7AAD12>I<3B07801FC007F03B0FC07FE01FF83B18E1E0 F0783C3B38F38078E01E3B30F7007DC01FD870FEEB7F80491400A2D8E1F8137EA249137C 1241D803E049133EA35F4848485AA25F1830484848481470EE01F0A218603C1F0007C003 E0E0A2933801E1C01880003E903A0F8000E300177E001C6DC7123C341F7A9D3A>I<3907 801FC0390FC07FE03918E1E0F03938F380783930F7007CEA70FE5BA2EAE1F8A25B1241D8 03E05BA34A5AEA07C0A24A5A16C0D80F8013E1EC07C1A21680D81F001383140F91380787 001586003EEB038CEC01F8001C6D5A221F7A9D28>II<90383C01F090387E07FC9038C70E1E0001EB980F02B01380390387E00716C014 C038070F80A3120239001F000FA4013EEB1F80A31600495B153E157E157C01FC5B5D6D48 5A4A5A3901F30F80D9F1FEC7FCEBF0F891C8FC485AA4485AA4EA7FFC12FF127F222B7F9D 24>I<903807C02090381FF0E0EB7C39EBF01D3901E00FC01203EA07C0EA0F801580EA1F 00A25A003EEB1F00127EA348133EA45C5AA214FC00785BEA7C01EA3C031307381E1FF0EA 0FF9EA03E1EA0001495AA4495AA43801FFFCA31B2B799D21>I<3807803E390FC0FF8039 18E1C1C03938F301E0EBF6033870FE0713FC01F813C000E1EB038049C7FCA21241EA03E0 A4485AA4485AA448C8FCA4123EA2121C1B1F7A9D1E>II<131C133EA35BA45BA4485A387FFFE0B5FC14C03803E000A4485A A4485AA448C7FCA314C0EA3E01A3EB0380003C13005B130E5BEA1C38EA0FF0EA07C0132B 7AA918>II<3903C001C03907F003E0 380C7807001814F038387C0312300070130115E0EAE0F81400EAE1F000411301000114C0 EA03E0A33907C00380A3EC0700EA0F80A2140EA200075B1418EBC038000313303801E0E0 6CB45A013FC7FC1C1F7A9D21>II<90383E01F09038FF07F8 3901C38E1C390303DC1E390701F83E000EEBF07E120C001C147C903803E03800381400A2 1210C6485AA4495AA3151890381F0038A21238007C1470EAFC3F15E0484813C039F06F01 803970E78700383FC3FE381F00F81F1F7C9D21>II E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmsy5 5 1 /Fc 1 1 df0 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd cmr5 5 3 /Fd 3 50 df<14E0B0B712C0A3C700E0C7FCB022237C9B2B>43 D48 D<1360EA01E0120F12FF12F11201B3A3387FFF80 A2111C7B9B1C>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe msam10 10 1 /Fe 1 4 df<007FB812F8B912FCA300F0CA123CB3B3ACB912FCA36C17F836387BB741>3 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff cmr6 6 3 /Ff 3 50 df<130C1338137013E0EA01C0EA0380A2EA07005A120E121E121C123CA21238 1278A412F85AA97E1278A41238123CA2121C121E120E120F7EEA0380A2EA01C0EA00E013 701338130C0E317AA418>40 D<12C012707E7E7E7EA2EA038013C0120113E0120013F0A2 13701378A4137C133CA9137C1378A4137013F0A213E0120113C012031380EA0700A2120E 5A5A5A12C00E317CA418>I<137013F0120712FF12F91201B3A7487EB512E0A213217AA0 1E>49 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg cmti10 10 30 /Fg 30 122 df12 D44 D<120E123FEA7F80A212FFA21300127E 123C0909778819>46 D<151015381570A215F01401EC03E0140F141F147F903803FFC0EB 1FEFEB3F8FEB1C0F9038001F80A4EC3F00A4147EA45CA4495AA4495AA4495AA4495AA449 5AA449C7FCA25B007FB5FCB6128015001D3877B72A>49 DI<133C13 7E13FF5AA213FEA2EA00FC13701300B2120E123FEA7F80A212FFA21300127E123C102477 A319>58 D<0103B712FE5B7F903A000FF000074B1300187C183C4A5AA44A5A1838A34AC8 FCA21603EF803002FE49C7FCA35E4948130E161EA216FE49B55AA3ECF80049481378A449 481370A44948136093C8FCA3495AA449CAFCA413FEA2487EB6FCA25C37397BB836>70 D<0103B612E04915FC17FF903B000FF0007F804BEB1FE0170FEF07F04A48EB03F8A318FC 4A5AA44AC7EA07F8A3EF0FF002FE15E0171F18C0EF3F804948EC7E004C5AEE03F0EE1FC0 49B6C7FC16F89138F8007E161F49486D7E83160783495AA283A24948495AA44948131FA4 49C7485A180EA301FE161C161F00011738B500FC010F1330EFE060933807E1C0C93801FF 809338007F00373B7BB83D>82 D<14F8EB07FE90380F071C90383E03BE90387C01FE13F8 EA01F000036D5A5B1207485A4A5AEA1F80123FA249485A5AA300FE495AA448495AEDC1C0 A391381F8380A3007C133F91387F8700ECFF07393C01CF06391E038F0E390F0F078C3907 FC03F83901F000F0222677A42A>97 D<147F903803FFC0903807C1E090381F0070013E13 385B4913F83801F0013803E0031207D80FC013F0EC01E04848C7FCA2123F90C8FC5AA312 FEA55AA315101538007C147015F0EC01E06CEB03C0001EEB0F006C133E380781F83803FF E0C690C7FC1D2677A426>99 DI<147F903803FFC090380FC1E090381F00F0017C13785B485A1203485AA2484813F012 1F90388001E0003FEB07C0EC1F80397F01FE00EBFFF891C7FC90C8FC12FEA55AA3007C14 1015381570007E14F0003EEB01E0001EEB03C0EC0F006C133E380781F83803FFE0C690C7 FC1D2677A426>III II107 DIII<147F903803FFC0903807C1E090381F00F0013E137849137C4913 3E485A485A0007143F485AA2485AA2123F90C7127F5AA300FE14FEA315FC48130115F8A2 EC03F0A2EC07E0007C14C0EC0F80EC1F006C133E001E5B6C5B380783E06CB45AC648C7FC 202677A42A>I<9039078007C090390FE01FF0903918F0787890393878E03C90393079C0 1E9039707F801FECFF00495A4A1480A33801C1F8A3EA00014948133FA44948EB7F00A316 7E494813FEA25E4B5AEB1F804B5A5E1507D93FC05B4B5A4BC7FCECE03E90387E7078EC3F F0EC0F8091C9FC5BA4485AA4485AA3387FFFC0B5FC6C5B293580A42A>II<3903C003F03907F00FFC390C783C0E391C7C700F3A183CE01F803938 3FC03FEB7F80007001001300153E017E131C92C7FC485AA31200485AA4485AA4485AA448 5AA4485AA448C9FC7E120E212679A423>I<14FE903807FF8090380F83C090381E00E049 13705B01F813F0EBF00100011303A215E00003EB01C06DC7FC7F3801FFC014F8806C7F6D 7E6D1380130F010013C0141F140FA2123C127E00FE1480A2481400485B00E0131E00605B 12706C13F0381E03E06CB45AD801FEC7FC1C267AA422>I<1307EB0F80131FA4EB3F00A4 137EA45BA2B512FC14FE14FC3801F800A3485AA4485AA4485AA4485AA448C7FC1438A214 70127E146014E014C01301387C0380003C1300EA3E06EA1E1CEA0FF8EA03E0173578B31C >I<13F8D801FEEB01C0D8038FEB03E039060F8007120C121C1238ED0FC0EA301F1270A2 3AE03F001F80A3EA007EED3F005BA34848137EA448485B160EA3913801F81CA213E01638 140301F013F00001010613700000EB0CF89039783878E090393FF03FC090390FC00F0027 2679A42D>I<01F01507D803FC903903800F80D8071E903807C01FD80C1F010FEB3FC012 1C0018161F0038160FED1F8048481507A21880D8E07E90383F0003A3C6481507037E1400 485AA3484849130EA4484848485BA35FA21730177002031460000316E002075C00010106 495A9039F00E7C032800FC3C3E0FC7FC90393FF00FFC90390FE003F0322679A437>119 D<903907E007C090391FF01FF09039383838389039603C703C9039C01EE07E3A01801FC0 FE1203D8070014FCED80F8000E157016004849C7FCA3C7FC147EA45CA4495A1670A34948 13E0121C003EEC01C0EA7E0700FEEC03801600D8FC0E130639781C780C3938383838391F F01FF03907C00FC027267CA427>I<13F0D803FCEB01C0D8071EEB03E0D80E1F1307121C 12181238ED0FC0485AA3D8E07EEB1F80A3C65AED3F00485AA34848137EA448485BA44A5A A213C013E04A5A00031307A20001131F3900F07FE0EB7FF7EB1FC7EB00074A5AA25D001E 131F003F91C7FC485B143E007E5B007C5B00705B495A383807C0D81C1FC8FCEA0FFEEA03 F0233679A428>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh msbm10 10 1 /Fh 1 83 df<007FB612E0B712FC6CEDFF802703801E0313E03B01C03800F3F0EE707870 7E83170E707EA2EF0380A7EF0700A25FEE380E173CEE707CEEF3F0923807FFE0023FB512 8004FCC7FC1638EC38E0ED701CA26F7EA26F7EA26F6C7EA26F6C7EA292380380E0839238 01C07083ED00E083167083EE380FEF0780EE1C03EF01C0040E13E048486CEC00F0007FB5 39F007FFFEB6FC6C8137397DB836>82 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fi cmsy8 8 4 /Fi 4 84 df0 D<17101770EE01F016031607A2160FA2161BA2 1633A21663A216C3A2ED01831503EE03F81507150EED0C01151C151815301570156015E0 EC01C01580020380EC0700140E92B5FC141D143F5C0270C77E5C495AD82003157E387007 80D8780FC8127FEAFE3ED8FFFE160449ED3F9C6C4816F84916E06C48ED1FC06C48ED0E00 0007CBFC36337EAF38>65 D<0338172003F81760020118E01A011BC06F16031A071A0F1A 1FDA037C163F037EEE7F80A21AFFDA073E5DDA063FED03DFF1079FF10F1F4A6C031E1300 70143E197C4F5A4A6C6C14F0F001E0F003C0DA3007EC078070EB0F00181E02604B133E6F 6C137C02C05D4D48137E6F6C485AD901804A5A70485A49C749C7FCEEFE3EEE7EFC0106EC 7FF8705A495DD8301C6E5AD83C384B147FD87FF86EC8130849020C16F04991C9EA3FE000 FF1AC06C48F01E006C4895C7FC000FCEFC4D317FAD54>77 D83 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj cmmi5 5 2 /Fj 2 110 df107 D<3A0F01F807E03A3F87FE1FF83A33CE1F387C3A63D80F603CD8C3F0 13C001E01380D803C01300A22607801E5BA3EEF04048484814C0ED01E0EEE18016E3001E 90397800FF00000C0130137C2A127D9133>109 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmex10 10 3 /Fk 3 89 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmsy7 7 5 /Fl 5 91 df0 D<1238127C12FEA3127C123807077A9114>I<13 E0EA01F0EA03F8A3EA07F0A313E0A2120F13C0A3EA1F80A21300A25A123EA35AA3127812 F8A25A12100D1E7D9F13>48 D<49B5FC130F133F01FEC7FCEA01F0EA03C0485A48C8FC12 1E121C5AA25AA35AA3B7FCA300E0C8FCA31270A37EA27E121E7E6C7E6C7EEA01F0EA00FE 013FB5FC130F130120277AA12D>50 D<913903FF8030021FEBFFE0027F14C091B6128090 3803803F49C7EA0F0049141E011E5C491438495C01605C90C7485A4B5A4BC7FC150E5D5D 91387FFF8091B57E5B9026000383C7FC4AC8FC140E14385C5C495A4948148049C7120301 0E140F49EC1F0001705C49143E4848143C48485C2607FFFC1370001F90B55A4815804892 C7FCD8C00113F82C287CA730>90 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmsy10 10 12 /Fm 12 111 df<007FB81280B912C0A26C17803204799641>0 D<0060150600F0150F6C 151F007C153E6C157C6C15F86C6CEB01F06C6CEB03E06C6CEB07C06C6CEB0F806C6CEB1F 00017C133E6D5B6D5B90380F81F0903807C3E0903803E7C06DB45A6D90C7FC147EA214FF 497F903803E7C0903807C3E090380F81F049C67E013E137C497F497F4848EB0F804848EB 07C04848EB03E04848EB01F048C812F8003E157C48153E48151F48150F00601506282874 A841>2 D20 D<126012F812FEEA7F80EA1FE0EA07F8EA01FE38007F 80EB1FE0EB07F8EB01FE9038007F80EC1FE0EC07F8EC01FE9138007F80ED1FE0ED07F8ED 01FE9238007F80EE1FE0EE07F8EE01FE9338007F80EF1FC0A2EF7F80933801FE00EE07F8 EE1FE0EE7F80DB01FEC7FCED07F8ED1FE0ED7F80DA01FEC8FCEC07F8EC1FE0EC7F80D901 FEC9FCEB07F8EB1FE0EB7F80D801FECAFCEA07F8EA1FE0EA7F8000FECBFC12F81260CCFC AE007FB81280B912C0A26C1780324479B441>I<020FB6128091B712C01303010F1680D9 1FF0C9FC017FCAFC13FC485AEA03E0485A5B48CBFC5A121E5AA25AA45AAA1278A47EA27E 121F7E6C7E7F6C7EEA01F86C7E137FEB1FF06DB71280010316C01300020F1580323279AD 41>26 D<181C181EA384A3727EA2727EA2727E85180019788585F11F80F107C0F103F000 7FBA12FCBCFCA26C19FCCCEA03F0F107C0F11F80F11E006161611801614E5AA24E5AA24E C7FCA3181EA3181C482C7BAA53>33 D49 D<91380FFFFE91B6FC1303010F14FED93FF0C7FC49C8FC13FCEA01F0485A485A5B48C9FC 5A121E5AA25AA45AA3B712FE16FFA216FE00F0C9FCA31278A47EA27E121F7E6C7E7F6C7E 6C7EEA00FC137FEB3FF0010FB512FE010314FF1300020F13FE283279AD37>I<922601FF C01320031F01FF13E0037FECFFC04AB712800207160091260F003F5B023C010013BE4AEC 007C02F85D01015E49484A5A4A4A5A49484A5A91C848C7FC01045D90C9123E5F17785F4C 5A4C5A4C5A4CC8FC161E4AB512E04A14F84A8091390001E3F8923803C0F04B485A4BC9FC 151E5D5D5D4A5A4A5A4A5A020ECAFC5C0278150C4A153C49485D4948EC01F849485D49C8 1203011E5E49150701705E494B5A2603DFFF92C7FC48B6EAC01E48EDFFF8485E4816C0D8 700092C8FC00C09038003FFC3B397DB83C>90 D<126012F0B3B3B3B3A91260045377BD17 >106 D<0060130C0070131C00F0131EB3B3B3B3A60070131C0060130C175277BD2A>I<12 6012F0A21278A37EA37EA37EA36C7EA36C7EA36C7EA36C7EA31378A37FA37FA37FA36D7E A36D7EA26D7EA36D7EA31478A380A380A380A3EC0780A3EC03C0A3EC01E0A3EC00F0A315 78A3153CA3151EA2150C1F537BBD2A>110 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn cmr7 7 10 /Fn 10 112 df<1306130C13181330136013E0EA01C0EA0380A2EA07005A120E121EA212 1C123CA35AA512F85AAB7E1278A57EA3121C121EA2120E120F7EEA0380A2EA01C0EA00E0 136013301318130C13060F3B7AAB1A>40 D<12C012607E7E7E120E7EEA0380A2EA01C013 E0120013F0A213701378A3133CA5133E131EAB133E133CA51378A3137013F0A213E01201 13C0EA0380A2EA0700120E120C5A5A5A5A0F3B7DAB1A>I<140EB3A2B812E0A3C7000EC8 FCB3A22B2B7DA333>43 D48 D<13381378EA01F8121F12FE12E01200B3AB48 7EB512F8A215267BA521>I<13FF000313E0380E03F0381801F8486C7E48137E00787F12 FC6C1480A2141FA2127CC7123F1500A2147EA25C5C495A495A495A49C7FC131E131C5B90 3860018013C0EA0180390300030012065A001FB5FC5A485BB5FCA219267DA521>I61 D<90387E03E03901FF9FF03807C3FC 380F00F048EBF800001E1378003E137CA6001E1378001F13F86C5BEBC3E0380DFF80D81C 7EC7FC90C8FCA3121E380FFFF014FC6C13FF001F1480393E001FC000781307EC03E04813 01A40078EB03C0007C13076CEB0F80390FC07E003803FFF838007FC01C277E9921>103 D108 D111 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo cmbx8 8 22 /Fo 22 122 df12 D<121FEA3F80EA7FC0EAFFE0A5EA7FC0EA3F80EA1F000B0B7A8A17>46 D48 DII54 D56 D97 D99 DII 103 D105 D108 D<2707E00FF8EB1FF000FFD97FFEEBFFFC01E1B500037F903BE3E07F87C0FF903CE7803F CF007F80280FEE001FDC133F01FC02F814C0495CA3495CB0B53B01FFFE03FFFCA43E1E7C 9D45>I<3907E01FF000FFEB7FFC9038E1FFFE9038E3E0FF9039E7007F80D80FEE133F01 FC14C05BA35BB0B53803FFFCA4261E7C9D2D>II<3903F03FE039FFF1FFFC01F77F9039FFC0FF809039FE003FC0D80FF8 EB1FE05BED0FF016F8A2150716FCA816F8150FA216F06DEB1FE06DEB3FC06DEB7F809039 FF81FF009038F7FFFE01F113F89038F07FC091C8FCA9B5FCA4262B7D9D2D>I<3807E07E 39FFE1FF8001E313C09038E78FE09038EF1FF0EA0FEE13FCA29038F80FE0EC07C091C7FC 5BAFB57EA41C1E7D9D22>114 D<133CA4137CA313FCA2120112031207001FB5FCB6FCA3 D803FCC7FCAEEC03C0A73901FE07803900FF0F00EB7FFE6D5AEB0FF01A2A7FA920>116 D118 D121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmmi6 6 3 /Fp 3 115 df<14E0EB01F0EB03181307130E130CEB1C30133C1338137814601370EBF0 C0A2EBE1801201EBE30013E6EA03C613CC13D813F05B12075B5BA2120F121F1237126700 C313100003133014E0380181C0EBFF006C5A15257FA31A>96 D<000F017E13FC3A1F81FF 83FF3B31C383C707803A61EE03CC039026EC01F813C0D8C1F813F013F001E013E0000390 3903C0078013C0A2EE0F003907800780A2EE1E041706270F000F00130C163C1718A2001E 011EEB1C70EE1FE0000C010CEB07802F177D9536>109 D<380F01F0381FC7F83831CE1C EA61F8EBF03C00C1137C13E014383803C000A4485AA448C7FCA4121EA2120C16177D951D >114 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq cmmi8 8 7 /Fq 7 110 df<133ED9FF80136000037F486D13C0487F3A1F00F80180003C1338007090 381C03000060130C00E014064813065D5AC76C5AA25DA35DA25DA35DA392C7FCA35CA214 06140EA45CA45CA31410232C7E9D24>13 D<123C127EB4FCA21380A2127F123D1201A3EA 0300A31206A25AA25A5A122009157A8714>59 D<12C012F012FC123FEA0FC0EA03F0EA00 FC133FEB0FC0EB03F0EB00FC143FEC0FC0EC03F0EC00FC153FED0FC0ED03F0ED00FC163F EE0FC01603160FEE3F0016FCED03F0ED0FC0033FC7FC15FCEC03F0EC0FC0023FC8FC14FC EB03F0EB0FC0013FC9FC13FCEA03F0EA0FC0003FCAFC12FC12F012C02A2B7AA537>62 D<92387FC001913903FFF803021FEBFC0791397FE01F0F903A01FE00079ED903F8EB01BE D90FE0EB00FE4948147E49C8127C017E153C5B485A000316385B485A120F491530001F16 1048481500A348CAFCA312FEA65E1780EE0300127E1606A26C5D5E6C6C14385E6C6C5C6C 6CEB03C0D803F8010FC7FCC6B4137E90387FFFF8011F13E0010390C8FC302F7CAD32>67 D<011FB512F04914FF6D15C0903A00FC001FE0EE07F0EE01F88349481300A449481301A3 4C5A49485C1607EE0FC04C5A4948017FC7FCED03FC91B512E093C8FC90391F8007C06F7E 6F7E8249C7FCA282A2017E495AA4491303A3EF01804848ED0300A21706B5D8E0015B9238 00FC384AEB7FF0C9EA0FC0312E7CAC35>82 D<140FEC3F80EC70C014E0A2EB01C01303EB 0780A290380F0180A2131EA290383E0300133CEB7C06A2EB780C13F85CA248485A5CA25C 3803E18001E3C7FC13E613EC5BA2EA07F05B5BA3120F121F1233126300C3148000831301 0001EB0300140E6C6C5AEB60F0EB3FE06DC7FC1A307FAE1D>96 D<27078007F0137E3C0F E01FFC01FF803C18F0381E0783C03C3078E00F0E01E0D979C001987F26607F0013B016E0 017E14C0485A16805B120048484948485AA34D5A4848133EA24D5A19804848491481EF1F 01A2F00300484849133E1806171E6048484848EB0E18EF07F0000E6D486D5A391F7E9D3E >109 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmr8 8 74 /Fr 74 124 df<14FF010713C090381F80F090383E0038017813F801F87F3801F001A2EA 03E06E5A152092C7FCA6157CB612FCA33803E000157CB3A43A7FFF0FFFE0A3232F7FAE27 >12 D<13E0EA01F01203A2EA07E0EA0FC0EA1F00121E5A5A12E012400C0C72AD23>19 D38 D<123C127EB4FCA21380A2127F123D1201A3EA0300A31206A25AA25A5A122009157AAD14 >I<13031307130C131C1338137013E0A2EA01C0EA0380A2EA0700A25A120E121EA2121C 123CA35AA512F8A25AAB7EA21278A57EA3121C121EA2120E120F7EA2EA0380A2EA01C0EA 00E0A213701338131C130C1307130310437AB11B>I<7E7E126012707E7E7EA27EEA0380 A2EA01C0A213E0120013F0A213701378A3133CA5133EA2131EAB133EA2133CA51378A313 7013F0A213E0120113C0A2EA0380A2EA0700120EA25A5A5A12605A5A0F437BB11B>I<12 3C127EB4FCA21380A2127F123D1201A3EA0300A31206A25AA25A5A122009157A8714>44 DI<123C127E12FFA4127E123C08087A8714>I<15C01401A2EC03 80A3EC0700A2140EA35CA35CA35CA35CA2495AA3495AA349C7FCA3130EA25BA35BA35BA3 5BA3485AA2485AA348C8FCA3120EA35AA35AA25AA35AA25A1A437CB123>II<130E131E137EEA01FE12FFA2EAFE7E1200B3AF13FF007F13FFA3182C7B AB23>III<14075CA2 5C5CA25C5C5B14BFEB033F13071306130C131C13381330136013E013C0EA01801203EA07 0012065A121C12185A12705AB612FCA3C7EA3F00A8EC7F8090381FFFFCA31E2D7EAC23> I<000CEB0180380FC01F90B512005C5C14F014C0D80C7EC7FC90C8FCA8EB1FC0EB7FF038 0DE07C380F801E380E001F000CEB0F80000814C0C7FCEC07E0A215F0A31238127C12FE7E A24814E05A0078EB0FC012606CEB1F80003814006C133E380F80FC6CB45A000113E06C6C C7FC1C2D7DAB23>II<1230123C 003FB512F8A34814F015E015C00070C7FC0060EB0180EC0300481306A25CC75A5CA25C5C 13015C1303A249C7FCA25BA25BA2133EA3137EA513FEA7137C13381D2E7CAC23>I II<123C127E12FFA4127E123C1200AD123C127E12FFA4 127E123C081D7A9C14>I<123C127E12FFA4127E123C1200AD1238127C12FE12FFA3127F 123F1203A41206A3120CA212181230A21220082A7A9C14>I<4A7E4A7EA34A7EA24A7EA3 4A7E141BA2EC31FCA2EC71FE1460A24A7E81A249486C7EA2010380EC001FA2010680150F A2496D7EA2011FB57EA39039300003FC1501A2496D7EA201E0804980A20001ED3F801203 D80FE0EC7FC0D8FFFC0107B5FCA3302F7EAE35>65 DIIIII< DA1FF013C0ECFFFE0103EBFF8190390FF807C390393FC000E749C7123701FC141F484814 0F48481407485A48481403A248481401123F90C9FCA25AA2007E160012FEA892383FFFFE 127E127F9238003FC06C151FA27F121F6C7EA26C7E6C7E6C7E6C6C143F137FD93FC013E7 90390FF803C30103B512810100EBFE00DA1FF013002F2F7CAD37>III<90383FFFFCA390 38007F80143FB3AB121C127FA2EAFF80A21500495A6C137E007C5B383801F8381E03F038 07FFC0D801FEC7FC1E2E7FAC24>I76 DIIII82 D<90383F80303801FFF048EBFC70390FC07EF0381F000F 001E1303481301007C1300127800F81470A21530A27EA26C1400127F7FEA3FF8EBFF806C 13F86C13FE6C7F6C14C0C614E0130F010013F0EC0FF814031401EC00FCA20040147C12C0 A46C1478A26C14F07E6CEB01E0B4EB03C039F7F00F8000E1B5120038C07FFEEB0FF01E2F 7CAD27>I<007FB712F8A39039000FE003007C150000701638A20060161800E0161CA348 160CA5C71500B3A74A7E011FB512F0A32E2D7EAC33>II87 D<3B7FFFF007FFF8A30001D9800013006C90C7127C6D6C13701660 6D6C13E06D6C485A5E6D6C48C7FC6D6C5A903803FC065D903801FE1C6D6C5A1530EC7FE0 143F5D6E7E6E7EA26E7E4A7EEC1DFE1439EC30FF4A6C7E14E04A6C7E49486C7E13034948 6C7E01066D7E496D7E131C496D7E01306D7E137001F0EC7F80D807F8ECFFC0B5010713FF A3302D7EAC35>II<003FB612C0A39039E0003F800180EB7F00003EC75A003C5C0038495A0078 130300705C4A5A140F00605C141F5D4A5AC7127F92C7FC14FE13015C495A13075C495A13 1F5C49481360137F91C7FC13FE12014914E012035B485A000FEC01C05B48481303003F14 0749131F48C712FFB7FCA3232D7CAC2B>II93 D<13C0487E487E487EEA0F3C EA1E1E487E3870038038E001C0EAC000120A78AD23>I<13FF000713C0381F01E0383C00 F8003E137C007F133C143E141E003E131F121CC7FCA3EB07FF137F3801FE1FEA07F0EA0F C0EA1F00123E127E007C140612FCA3143FA2007E136F003EEBCF8C391F8387FC390FFF03 F83901FC01E01F207D9E23>97 DII<15F8141FA314011400ABEB0FE0EB7FF8EBF81C3803E006380780 03000F130148C7FC123EA2127E127CA212FCA7127CA2127E123EA26C13016C1303D80780 7F3A03C00EFFC03801F03C38007FF090391FC0F800222F7EAD27>III<013F13F89038FFC3 FC3903E1FF1E3807807C390F003C0C48EB3E00001E131EA2003E131FA5001E131EA2001F 133E6C133C6C6C5AEBE1F0380CFFC0D81C3FC7FC90C8FCA47E380FFFF86C13FF6C14C000 0F14E0391E0007F048EB00F84814780070143C12F0A400781478A26C14F0001FEB03E039 07E01F803901FFFE0038003FF01F2D7E9D23>I III< EA07C012FFA3120F1207ACEC1FFEA3EC0FE0EC0780020EC7FC5C5C14605CEBC180EBC3C0 13CFEBDDE0EBF1F0EBE0F8EBC07880143E80806E7E816E7E81813AFFFE07FF80A3212E7E AD25>II<2607C07FEB07F03BFF C1FFC01FFC903AC781E0781E903ACE00F0E00FD80FD8D9F9801380D807F090387B000703 7F14C049137EA249137CB23CFFFE0FFFE0FFFEA3371E7E9D3C>I<3807C0FE39FFC3FF80 9038C703C09038CC01E0D80FD87F3807F000497FA35BB23AFFFE1FFFC0A3221E7E9D27> II<3807C0FE39FFC7FF809038CF03E09038D801F039 07F000F849137C8149133F811680A2150F16C0A71680151FA216005D6D133E5D6D5B9038 D801F09038CE07C09038C7FF80D9C1FCC7FC01C0C8FCA9EAFFFEA3222B7E9D27>I<3807 81F838FF83FCEB861EEB8C3FEA0F98EA07B0141EEBE000A35BB07FB5FCA3181E7E9D1C> 114 D<3801FE183807FFB8381E01F83838007800781338127012F01418A27E7E007F1300 13F06CB4FC6C13C0000713E0000113F038001FF8EB01FC3840007C00C0133EA26C131EA3 6C131CA26C13386C137838E701E038C3FFC000C0130017207E9E1C>I<1360A413E0A312 01A21203A2120F381FFFF0B5FCA23803E000AE1418A71201EBF0301200EB7860EB3FC0EB 0F80152A7FA81B>II<3AFFFC01FFC0A33A07E0 007E00153800031430A26C6C5BA26C6C5BA390387C0180A26D48C7FCA2EB3F07EB1F06A2 EB0F8CA214DCEB07D8A2EB03F0A36D5AA26D5A221E7F9C25>I<3BFFFC3FFE07FFA33B0F E003F001F83B07C001E000E0812603E00314C0A2913807F8012701F006781380A29039F8 0E7C030000D90C3C1300A290397C181E06A2151F6D486C5AA2168C90391F600798A216D8 90390FC003F0A36D486C5AA36DC75A301E7F9C33>I<3AFFFC07FF80A33A03F003F80000 01EB01C001F85B000049C7FCEB7C06EB3E0E6D5A14B8EB0FB0EB07E013036D7E497E1307 EB067C497EEB1C1F01387FEB700F90386007C0496C7E00036D7E390FE003F83AFFF007FF C0A3221D7F9C25>I<3AFFFC01FFC0A33A07E0007E000003143815306D137000011460A2 6C6C5BA2EBFC01017C5BEB7E03013E90C7FCA2EB1F06A2148EEB0F8CA2EB07D8A2EB03F0 A36D5AA26D5AA2495AA2130391C8FC1278EAFC06A25B131CEA7838EA7070EA3FE0EA0F80 222B7F9C25>I<003FB51280A29038001F00003C133E0038137E0030137C00705B386001 F013035C495AC6485A131F91C7FC133E5B9038FC018013F8EA01F0EA03E00007130313C0 D80F801300EA1F00485B003E5B48133FB6FCA2191D7E9C1F>II E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmcsc8 8 30 /Fs 30 122 df<123C127E12FFA4127E123C0808798716>46 D<15181538A21570A215E0 A3EC01C0A2EC0380A3EC0700A2140EA35CA25CA25CA35CA2495AA3495AA249C7FCA3130E A25BA35BA25BA35BA2485AA2485AA348C8FCA2120EA35AA25AA35AA25AA25A1D437BB127 >I<13075B133F48B4FCB5FCA2EAFE3F1200B3AF497E007FB51280A3192C79AB27>49 DI56 DI65 D67 D69 DI77 D80 D<007FB712FCA39039000FE001007CED007C0070161CA20060160C00E0160EA34816 06A5C71500B3A74A7E011FB512F0A32F2D7CAC37>84 D<14E0A2497EA3497EA3EB067CA2 EB0E3E130CA2497EA201387FEB300FA2496C7EA3496C7E90B5FC4880EB8001A248C77EA2 48800006147C120E157E003F147F3AFFC003FFE0A223237DA22A>97 DI<903803FC03EB1FFF90387E03C79038F800EFD801E0 133F4848131F485A48C7120F5A003E1407A2007E1403A2127C12FC1500A7007C1403127E A2123E15067E7E6C6C130C6C6C13186C6C1330D800F8136090387E03C090381FFF809038 03FC0020247CA229>III<3AFFF80FFF80A23A1FC001FC006C486C5AAC90B5FCA2EB8000AE486C487E3AFFF80F FF80A221227CA12A>104 D I 108 D110 DI113 DI<3801FC0CEA07FF 380E03DC381800FC48133C12700060131C12E0140CA36C13001278127CEA3FC0EA1FFC38 0FFF806C13E0000113F038003FF81301EB007C143C141E140E124012C0A36C130C141C6C 131800FC133000EF13E038C3FFC000C0130017247CA220>I<007FB61280A2397C01F00F 0070140300601401A200E015C000C01400A400001500B3A2497E90387FFFC0A222227DA1 29>I<3AFFF801FF80A23A1FC0007E006C48133C1518B3A400075C7F00035C7F00015C6C 6C485AD93C0FC7FCEB1FFEEB03F021237CA12A>I<3AFFF803FF80A23A0FF001FC003907 E000F06C6C5B00015C6D485A3800FC03D97C07C7FCEB3E06EB3F0CEB1F9CEB0F98EB07F0 A21303130180497EEB077CEB063EEB0C3F90381C1F80EB380F01307F496C7E9038E003F0 3801C00101807F00036D7E0007147C001F14FF26FFE00113E0A223227DA12A>120 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft cmr10 10 73 /Ft 73 125 df11 DI14 D<133C137EA213FE1201 EA03FC13F0EA07E0EA0FC0EA1F80EA1E005A5A5A12C00F0F6FB92A>19 D<001C131C007E137E007F137F39FF80FF80A26D13C0007F137FA2001C131C00001300A4 3901800180A33903000300A300061306485BA2485B485B002013201A197DB92A>34 D<121C127E127FEAFF80A213C0127FA2121C1200A4EA0180A3EA0300A312065AA25A5A12 200A1979B917>39 D<146014E0EB01C0EB0380EB0700130E5B133C13385B13F05B120148 5AA2485AA348C7FCA25A121EA2123EA2123CA2127CA5127812F8B01278127CA5123CA212 3EA2121EA2121F7EA26C7EA36C7EA26C7E12007F13707F133C131C7F7FEB0380EB01C0EB 00E01460135278BD20>I<7E7E7E12707E7E7E120F7E6C7E7F12017F6C7EA21378A37FA2 133E131EA2131FA27FA21480A5130714C0B01480130FA51400A25BA2131EA2133E133CA2 5BA35BA2485A5B12035B48C7FC5A120E5A5A5A5A5A5A12527BBD20>I<15301578B3A600 7FB812F8B912FCA26C17F8C80078C8FCB3A6153036367BAF41>43 D<121C127E127FEAFF80A213C0127FA2121C1200A4EA0180A3EA0300A312065AA25A5A12 200A19798817>II<121C123E127FEAFF80A3EA7F00123E121C09 09798817>I<150C151EA2153CA31578A315F0A3EC01E0A3EC03C0A3EC0780A3EC0F00A3 141EA35CA35CA35CA3495AA3495AA2495AA349C7FCA3131EA35BA35BA35BA3485AA3485A A3485AA348C8FCA3121EA35AA35AA35AA212601F537BBD2A>IIIII<1538A2157815F8A2140114031407A2140F141F 141B14331473146314C313011483EB030313071306130C131C131813301370136013C012 01EA038013005A120E120C5A123812305A12E0B712F8A3C73803F800AB4A7E0103B512F8 A325397EB82A>I<0006140CD80780133C9038F003F890B55A5D5D5D92C7FC14FC38067F E090C9FCABEB07F8EB3FFE9038780F809038C007C039078003E0496C7E00068000046D7E C8FC81157E157FA31680A3123E127F5A7FA290C7FC16005A00605C5D00705C0030130100 385C6C495A6C495A6C6C485A3903E03F806CB5C7FC38007FFCEB1FE0213A7CB72A>II<12301238123E003FB612E0A316C0481580A2160000 70C7120600605CA25D00E05C5A5D5DC7485AA24AC7FC1406A25C141C141814385CA25CA2 1301A2495AA21307A2130FA3495AA4133FA4137FA96DC8FC131E233B7BB82A>II<121C123E127F EAFF80A3EA7F00123E121CC7FCB2121C123E127FEAFF80A3EA7F00123E121C092479A317 >58 D<007FB812F8B912FCA26C17F8CCFCAE007FB812F8B912FCA26C17F836167B9F41> 61 D63 D<1538A3157CA315FEA34A7EA34A6C7EA202077FEC063FA2020E7FEC0C1FA2021C7F EC180FA202387FEC3007A202707FEC6003A202C07F1501A2D901807F81A249C77F167FA2 0106810107B6FCA24981010CC7121FA2496E7EA3496E7EA3496E7EA301E06E7E1201486C 81D80FFC02071380B56C90B512FEA3373C7DBB3E>65 DI<913A01FF 800180020F13E0027FEBF803903A01FF807E07903A03FC000F0FD90FF0EB038FD91FC0EB 01DF4948EB00FF49C8127F01FE153F4848151F485A170F485A000F16075B001F1603A248 5AA21701127FA25B94C7FC12FFAB127FA26DED0180A2123FA36C7EEF0300120F7F000716 066C7E6D5D12016C6C5D017F5D6D6C14706D6C5CD90FF0EB03C0D903FCEB0F80902701FF 803EC7FC9039007FFFFC020F13F002011380313D7BBA3C>IIII72 DI<013FB5 12E0A39039001FFC00EC07F8B3B3A3123FEA7F80EAFFC0A35D140F1380D87F005B006049 5A6C5C6C49C7FC000E137E380781FC3801FFF038007F80233B7DB82B>I76 DIIII82 DI< 003FB812E0A3D9C003EB001F273E0001FE130348EE01F00078160000701770A300601730 A400E01738481718A4C71600B3B0913807FF80011FB612E0A335397DB83C>I87 D89 D91 D93 D97 DIIII<147E903803FF8090 3807C1C090380F07E0011E13F0EB3E0F137C13FCEC07E09038F803C0000190C7FCADB512 FCA3D801F8C7FCB3AB487E387FFFF8A31C3B7FBA19>IIIIIII<2703F00FF0EB1FE000FFD93FFCEB7FF8913AF03E01E07C903BF1C01F03803E 3C0FF3000F86001FD803F602CC14800307140F01FC02F814C0495CA3495CB3A4486C496C EB1FE0B500C1B50083B5FCA340257EA445>I<3903F00FF000FFEB3FFCECF03E9038F1C0 1F3A0FF3000F80D803F680150701FC805BA35BB3A4486C497EB500C1B51280A329257EA4 2E>II<3903F01FE000FFEB7FF89038F1E07E9038F3801F3A07F6000F 80D803FCEB07C049EB03E016F049EB01F816FC150016FEA3167E167FA8167E16FEA216FC A2ED01F8A26DEB03F016E06DEB07C001F6EB0F8001F3EB1F009038F1E07E9038F0FFF8EC 1FC091C8FCAB487EB512C0A328357EA42E>II<3807E03F00FFEBFF809038E1C3 E0EBE307390FE60FF0120313ECEC07E09038F803C0EC018091C7FCA25BB3A3487EB512F0 A31C257EA421>II<1318A51338A31378A313F8120112031207001FB5FCB6FCA2D801F8C7FC B215C0A90000EB018013FC137C90383E0300EB1F06EB0FFCEB01F81A347FB220>IIIIII<003FB512FCA290388001 F8393E0003F0003C1307003814E00030EB0FC00070131F15800060EB3F005C14FE5C495A EA00035C495A130F495A5C49C7FC491306137E5B1201485A49130E485A000F140C49131C 485A003F143C90C7127C007EEB03FCB6FCA21F247EA325>I124 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu cmcsc10 10 32 /Fu 32 123 df<133C137EA213FE1201EA03FC13F0EA07E0EA0FC0EA1F80EA1E005A5A5A 12C00F0F6DB92E>19 D<121C127E127FEAFF80A213C0127FA2121C1200A4EA0180A3EA03 00A21206A25A5AA25A12200A1977B91B>39 D45 D<121C123E127FEAFF80A3EA7F00123E121C090977881B>I66 DI69 D73 D<011FB512F0A39039000FFE00EC03FCB3B3A3123FEA7F80EAFFC0A35D14071380D87F00 5B0060495A6C5C6C495A000E49C7FC3807C0FE3801FFF838003FC0243B7CB82F>I78 D82 D<003FB812FCA3D9C001EB800390C790C7FC007C173E 0078171E0070170EA300601706A400E01707481703A4C81500B3B0020313C0010FB612F0 A338397CB841>84 D<13101338137C13FE487E3803C780380783C0380F01E0381E00F048 13780070131C48130E00401304170D75B92E>94 D<1407A24A7EA34A7EA3EC37E0A2EC77 F01463A2ECC1F8A201017F1480A2903803007EA301067FA2010E80010C131FA2496D7EA2 013FB57EA29038300007496D7EA3496D7EA2000181491300120382487ED81FE0497ED8FF F8010F13F8A22D2C7DAB33>97 D<91383FC006903801FFF8903907E03E0E90391F00071E 017EEB01BE01F8EB00FE0001157E4848143E485A000F151E5B001F150E485AA21606127F 90C8FCA2481500A97E16067F123FA36C6C140C120F6D141812076C6C14306C7E00001560 017EEB01C0011FEB0780903907E01E00903801FFF89038003FE0272D7BAB31>99 DIII105 D<90B512C0A2903801FE006D5AB3AB1210127C12FEA348485A127800605B6C485A381E0F C06CB4C7FCEA01FC1A2C7CAA23>I108 DIIII114 D<017F13603801FFE0390780F8E0380E001D48130748130314015A1400 12F01560A37E1500127C127F13C0EA3FFE381FFFE06C13F86C13FE6C7FC61480010F13C0 1300EC0FE01407EC03F01401A20040130012C0A46C14E014016C14C07E6CEB038000F7EB 070038E3E01E38C0FFF8EB1FE01C2D7BAB26>I<007FB712C0A23A7E003FC00F00789038 1F8003007015011600126000E016E0A2481660A5C71500B3A8EC7FE0011FB57EA22B2B7D AA31>II<3B7F FF800FFFC0A2000790390003FE00D801FEEB01F84914E06C6C5C017F5C6D13036E48C7FC 90381FC0066D6C5A151C6D6C5A903803F83001015BECFCE06D6C5AEC7F80A2143F6E7E14 0F4A7E4A7E1433EC63F8ECE1FCECC0FE903801807E0103137F49486C7E0106131F498001 1C6D7E496D7E01301303498001E06D7E1201486C80001F913803FF80D8FFFC4913F8A22D 2B7DAA33>120 DI<00 3FB6FCA29038E0007E90C712FE003E5C003C495A00381303485C4A5AA20060495A141F5D 4AC7FCC75A147E5C13015C495AA2495A495AA2495A133F91C8FC017EEB018013FE5B485A 1203491303485AA24848EB0700121F495B48C75A485C007E49B4FCB7FCA2212B7BAA2A> I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fv cmmi7 7 15 /Fv 15 121 df<137E48B4EB0180000713C0489038E00300481406383E01F0393800700C 4813380060EB181848131CEC0C305AC75B14065DA3EC0780A292C7FCA31406A3140EA214 0C141CA45CA31430A2142021267E9923>13 D15 D61 D<017FB612C017E0903903F0000F1601A2EE00C0495AA4495AA2 15020303130090381F8006A3150E90383F003CECFFFCA2EC003C017E1318A4495B151092 C8FCA2485AA4485AA31207B512C0A22B287CA72A>70 D77 D<010FB612C0A2903A1FE0003F8091C7EA7F00011E14FE49495A 0138495A01305C49495A4B5A4B5A4949C7FC157E90C75A4A5A4A5A4A5A140F4A5A4A5A4A C8FC14FE495A5C494813204948133049485B495A49C7FC017E5C5B4848130148485C0007 140348481307484849C7FC4848133F484848B4FCB65AA22A287CA72D>90 D<143C147E14E6EB01C3EB038313071402EB0F06130E131EA2EB3E0C133CEB7C18A2EB78 3013F8146014E03801F0C0EBF180EBF30013F7EA03E613EC13F85B5B5BA31207120F121B 123300E313040043130E0001131C14383800E0E0EBF7C0EB7F00182A7FA81C>96 D<1578EC0FFC15F81400A3EC01F0A4EC03E0A490380FC7C0EB3FE7EBF8773801E03F3907 C01F80EB800FEA0F005A48EB1F00123E127EA248133EA4485B1518A3ECF8301278130139 3C077860391E1E7CC0380FF83F3903E00F001E297DA723>100 D<130E131F5BA2133E13 1C90C7FCA7EA03E0487EEA0C78EA187C1230A212605B12C0A2EA01F0A3485AA2485AA2EB C180EA0F81A2381F0300A213066C5A131CEA07F06C5A11287DA617>105 D<133CEA07FE5BEA007CA35BA4485AA43903E00780EC1FC0EC3860EC61E03807C0C3EBC1 87EBC30701C613C0390F8C038001B8C7FC13E07FEA1FFEEB3F80EB0FC06D7EEA3E031560 A3007CEBC0C0A2ECC180A239F801E300EB00FE0070137C1B297CA723>107 D<3B07801FC007E03B0FE07FF01FF83B18F0E0F8783C3B30F1807CE03E903AFB007D801E D860FEEB3F005B49133E00C14A133E5B1201A24848495BA35F4848485A1830EE01F0A23C 0F8003E003E060A218C0933801E180271F0007C013E3933800FF00000E6D48137C341B7D 993B>109 D<3907801FC0390FE07FF03918F0E0F83930F1807CEBFB00D860FE133C5B5B 00C1147C5B1201A248485BA34A5AEA07C01660EC03E0A23A0F8007C0C0A2EDC180913803 C300D81F0013C7EC01FE000EEB00F8231B7D9929>I<9038F007E03901FC1FF039031E38 7C0006EBE03E90381FC01E000CEB801F1400A2D8183E1480A212001600495BA3153E4913 7EA2157C5D485A6D485A4A5A6D485A2603EE0FC7FCEBE7FEEBE1F001E0C8FC485AA4485A A3EAFFF8A22125809922>112 D<3807803E390FE0FF803818F3C13930F703C0EBFE0738 60FC0F13F8158039C1F0070091C7FC1201A2485AA4485AA4485AA448C8FCA2120E1A1B7D 991F>114 D<90387C03C03901FF0FF03907079C30390E03B078000CEBF0F8001813E112 3015F0396007C0E015001200A2495AA449C7FC15301238007C1460EAFC3E15C0EAF87E39 F06F03803970C70700383F83FE381F01F81D1B7D9926>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fw cmmi10 10 36 /Fw 36 122 df13 D<1403EC3FF891387FFF8002E313C0EB0180903803003FED1F80ED 070092C7FC80A38080A26D7E8013008080147E147F6E7E81EB01FF903807EFE090380F8F F0EB3E07137C01F87F3801F003EA03E048486C7EA2EA0F80121F90C7FC5AA2127EA3485C A21401A25DA24813035DA2007C495A5D140F003C91C7FC6C131E000E5B000F5B3803C0F0 6CB45AD8003FC8FC223D7DBB25>II 17 D<131F14C0EB07E06D7E6D7E80A2130080A2147E147F80A281141F81A2140F81A214 0781A2140381A2140181A214008114011403EC077F140E4A7E023C13801478ECF01FD901 E013C0EB03C00107130FD90F8013E0EB1F00013E13074914F0491303000115F8485A4848 1301484814FC485A003F140048C812FE12FE48157E48153F0070151F283B7CB930>21 DI<121C123E127FEAFF80A3EA7F00123E121C0909798817>58 D<121C127E127FEAFF80A213C0127FA2121C1200A4EA0180A3EA0300A312065AA25A5A12 200A19798817>I I<150C151EA2153CA31578A315F0A3EC01E0A3EC03C0A3EC0780A3EC0F00A3141EA35CA3 5CA35CA3495AA3495AA2495AA349C7FCA3131EA35BA35BA35BA3485AA3485AA3485AA348 C8FCA3121EA35AA35AA35AA212601F537BBD2A>I<126012F812FEEA7F80EA1FE0EA07F8 EA01FE38007F80EB1FE0EB07F8EB01FE9038007F80EC1FE0EC07F8EC01FE9138007F80ED 1FE0ED07F8ED01FE9238007F80EE1FE0EE07F8EE01FE9338007F80EF1FC0A2EF7F809338 01FE00EE07F8EE1FE0EE7F80DB01FEC7FCED07F8ED1FE0ED7F80DA01FEC8FCEC07F8EC1F E0EC7F80D901FEC9FCEB07F8EB1FE0EB7F80D801FECAFCEA07F8EA1FE0EA7F8000FECBFC 12F81260323279AD41>I67 D<0103B812F05B7F90260007F8C7123F4B1407F001E0A24A481400A4 4A5A19C0A34A5A1730A219804AC7481300A317E002FE5C1601160F91B6FC495DA29138FC 000F160749486DC8FCA4494801065B60A204041306494890C7FC60A2181C494815181838 18301870495A6017014D5A49C8120F173F49913803FF80007F90B7FCB9C7FCA23C397DB8 3D>69 D<0103B812E0A390260007F8C7123F4B1407F003C0A24A481401A44A5A1980A34A 5AA21740056013004AC748C7FCA3160102FE5C16031607161F49B6C8FCA39138FC001F49 48130EA44948130CA44948130893C9FCA3495AA4495AA449CBFCA2497E007FEBFF80B67E 5D3B397DB835>I<0103B5D8F803B512F8495D6D8190260007F8C73807F8004B5DA34A48 4A5AA44A484A5AA44A484A5AA44AC848C7FCA402FE15FEA391B7FC495EA202FCC71201A2 49484A5AA449484A5AA449484A5AA449484A5AA449484A5AA449C848C8FCA2495D007F01 FE017F13FEB690B6FC4A5D45397DB845>72 D<4AB512FC5CA2DA000113006F5AA34B5AA4 4B5AA44B5AA44B5AA44B5AA44B5AA44BC7FCA415FEA44A5AA4000F495AEA3F80127F13C0 4848485AA249485A485C48495A0060133F92C8FC6C137C383801F8381E07F03807FFC0D8 01FEC9FC2E3B7AB82E>74 D<902603FFF893383FFF8049606D7FD900069438FF8000DF01 BFC7FCA2F1033F020C177E1906190C157E02184C5A1930A219600230EE61F819C1F00181 8102604B485A1806A2180C02C04C5A181818306F7ED901804B485A18C0A2EF0180D90300 4A48485AA292380FC006A201064B49C8FC5FA25F494B137EA26F6C5AA249DAE1805B04E3 C7FCA216E64902EC495AA2ED03F813704C495A01F05CD807FC1607267FFFC0D9C003B512 E0B500E0494880DAC0015E51397CB851>77 D<0103B612F849EDFF806D16E0903B0007F8 001FF84BEB03FCEF00FE187F4A5AF03F80A219C04A5AA44A48EC7F80A3F0FF004AC85A4D 5A4D5A4D5A02FE4A5AEF1F80057FC7FCEE07F849B612E094C8FC9139FC000FC0EE03F049 486D7E707EA2177E495AA2177FA2494814FEA449481301A44948495A1960A349C715C016 0149EE0180007F01FE0100EB0300B6ECFE064AEC7E0CCAEA1FF8EF07F03B3B7DB83F>82 D<92381FE0019238FFFC030203EBFE0791390FE01F0F91391F00078F023CEB01DE4AEB00 FE4A147E495A4948143C13075C130F91C812385BA3491530A36E1400A26D7E14F014FE90 380FFFE015FE6DEBFFC06D14F06D806D6C7F021F7F14039138003FFF150303001380163F A2161FA30004150F120CA3001CED1F00A2161E163E003C153C167C003E15785E007F4A5A 6D495AD87DC0495AD878F0011FC7FCD8F07E13FE39E03FFFF8D8C00F13E0D8800190C8FC 303D7CBA33>I<91B500F890387FFFE05B5ED90003018090380FFC006E48C7EA07E01980 0606C7FC6E6C5C606F1438705B606F6C485A4D5A031F91C8FCEEE0065F6F6C5A5F03075B 705A16F96FB45A94C9FC6F5AA36F7EA34B7FED037F9238063FC0150E4B6C7E1538ED700F 03E07F15C04A486C7EEC0300020613034A805C4A6D7E14704A1300494880495A49C86C7E 130E011E153F017E82D803FFEDFFE0007F01E0010FEBFF80B55C6C8143397EB845>88 DI<027FB612FC91B7FC18F8 499039E00007F04AC7120F02F8EC1FE0D903E015C04AEC3F804AEC7F00010715FE91C748 5A01061403010E4A5A010C4A5A5F4C5A494A5A4CC7FC011014FE90C712014B5A5E4B5A4B 5A4B5A4B5A157F4BC8FC4A5A5D4A5A4A5A4A5A4A5A143F4A48130492C7120C14FE49485C 495A495A49481438011F1530495A4A147049C8126001FE15E04848140148485D00071503 4848140749141F4848EC7F804848EB07FF48B7FCB8C7FCA236397BB839>I<1578EC01FC EC0386EC0706EC0E03141E143CA2EC780614F814F0130114E00103130CA2EB07C0151813 0F14801530131FEC00605B15C0A290387E0180EC0300A21406495AA25C5C48485A5CA2EB F98001FBC7FC13F613FC5B485AA45B1207120D12191231EA61F000C1140C000014181530 01701360EC01C0903838078090381C1E00EB0FF8EB07E0203C7FBA23>96 D101 D<16F8ED03FEED070792380E0F80ED1E1FED3E3FED7C7FA203FC1300163E 161C4A48C7FCA54A5AA54A5AA20103B512F05B5E9026000FC0C7FCA54A5AA64AC8FCA514 7EA55CA5495AA55C1303A35CA213075C121E003F5BEA7F8F91C9FCEAFF0F131EEA7E1CEA 7C38EA3870EA1FE0EA07C0294C7CBA29>I104 D<14E0EB01F0EB03F81307A214F0EB03E0EB01C090C7FCAB13F8EA01FEEA070F1206000C 138012181230A2EA601FA338C03F00A3EA007EA25BA3485AA3485AA23807E018A3380FC0 30A3EB8060A214C0EB8180380783001387EA03FCC65A15397EB71D>I107 D109 DI<90390F8003F090391FE00FFC903930F03C1E903960F8 700F9238C007809026C0FD8013C09139FF0003E048485A5C17F0A2380301F8A312004948 1307A44948EB0FE0A317C04948131F1780A2EE3F00495A167E167C5E496C485A5E913860 03C0ED0F8090267E383FC7FCEC1FFCEC07E091C9FC5BA4485AA4485AA3387FFFC0B5FC7E 2C3583A42A>112 D<3903E001F83907F807FC390C3C1E0639183E381FEC603FD8303FEB 7F8014C0913880FF0000605B157E153CD8C07E90C7FCA312005BA4485AA4485AA4485AA4 485AA4485A120F6CC9FC21267EA425>114 D<01F8EB0380D801FEEB07C0D8070FEB0FE0 000E15F0000C13801218003014071503D8601F1301150016E04848C7FCA3EA007E16C05B A34848EB0180A3ED0300485A1506A35DA25D5D12015D6C6C5B9038780380D93E0FC7FCEB 1FFCEB07F024267EA428>118 D<01F816E0D801FE9138E001F0D8070F903901F003F800 0E020314FC000C1380121800301601923807E000D8601F167C183C1838484848485AA3EA 007E4B4813305BA3484849C71260A318C04848137EA2EF0180A3EF0300A21706000102FE 5BA22700F8019F5B902678030F5B903A3E0E07C0E0903A1FFC03FFC0902703F0007FC7FC 36267EA43B>I<903907E001F090391FF807FC9039383C0E0E9039601E181F496C485AD8 0180EC7F80D8030013E00006EDFF005D48157E163C484948C7FCA3C7FC4AC8FCA4147EA4 5C160CA3261E01F85B123FD87F815C1383D8FF035CD906785B007E4A5A277C0C3C03C7FC 3938381E0E391FF00FFC3907C003F029267EA42F>I<13F8D801FE1470D8070F14F8000E 1401000C138012181230ED03F0EA601FA33AC03F0007E0A3EA007EED0FC05BA34848EB1F 80A44848EB3F00A4157EA45D0001130114033800F80690387C1DF8EB3FF9EB0FE1EB0001 4A5AA2000E5C001F1307D83F805B007F130F5D4948C7FC007E133E007C5B00305B495A38 1E07C06CB4C8FCEA01FC25367EA429>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fx cmbx10 10 45 /Fx 45 123 df<913803FFC0027F13F00103B57E010FEB00FED91FF8133ED93FE0137F49 48EBFF8049485A5A481300A46F1300167E93C7FCA592383FFFC0B8FCA4000390C7FCB3AB B5D8FC3F13FFA4303A7EB935>12 D44 DII58 D 65 D67 DIIIIII76 DI< B500FC0203B512F0A28080C66C6D90390003F0006F6E5A81137B01797F8101787F6E7E6E 7E6E7F806E7F826E7F6E7F6E7F6F7E153F6F7E17806F13C06F13E06F13F06F13F88117FC EE7FFEEE3FFF7013817013C1827013E118F17013F97013FDEF7FFF838383A28383838318 7F183FA2181F01FC160FB500FC150718031801A244397DB84B>IIIIII<003FB91280A4D9F800EBF003D87FC09238007FC049161F007EC7150FA2007C1707A2 00781703A400F818E0481701A4C892C7FCB3AE010FB7FCA43B387DB742>I87 D<007FB5D8F803B512F8A4C6 6C48C7D80FF0C7FC6D6C5D6D5E6F495A6D6D49C8FC7F6D6D137E6F5B6DEBF8016D5D6F48 5A6E6C485A023F130FDA1FFF5BEE9F806E01FFC9FC805E6E5B6E5B80826F7E153F826F7F 5D4B7F92B57EA2DA01F97FDA03F17F03F07F913807E07FDA0FC07F021F6D7E4B7E4A486C 7F027E8102FE6D7F4A7F49488149486D7F0107804A6E7E49488149486E7E013F81017F83 B60107B61280A441397DB848>II97 D<13FFB5FCA412077EAF4AB47E020F 13F0023F13FC9138FE03FE9139F000FF8002C0EB7FC04AEB3FE091C7EA1FF0A217F8160F 17FCA317FEA917FCA3EE1FF8A217F0EE3FE06E14C06EEB7F80D9FDF0EBFF009039F8FC07 FE9039F03FFFF8D9E00F13E0D9C00390C7FC2F3A7EB935>I<903801FFC0010F13FC017F 7F9038FF807F3A01FE00FF802607FC0113C0EA0FF8A2EA1FF0003F6D1380A24848EB7F00 151C92C7FC12FFA9127FA27F123FED01E06C7E000FEC03C07F6C6CEB0780D801FFEB0F00 6CEBC07E6DB45A010F13F00101138023257DA42A>II<49B47E011F13F0017F13FC9038FF81FE3A03FE007F 804848133F4848EB1FC0484814E0150F003F15F05B127FED07F8A212FFA290B6FCA301E0 C8FCA4127FA36C7E1678121F6C6C14F816F06C6CEB03E0D801FF13076C9038C03F80013F B51200010F13FC010013C025257DA42C>II<13FFB5FCA412077EAFED7FC0913803FFF84A7F91381F03 FE91383C01FF027014804A7E4A14C0A25CA391C7FCB3A3B5D8FC3F13FFA4303A7DB935> 104 DI<13FFB5FCA412077EB3B3ACB512FCA4163A7DB91B>108 D<01FED97FE0EB0FFC00FF902601FFFC90383FFF8002076D90B57E913C1F81FF03F03FE0 DA3C00903987801FF0000749DACF007F000301E0D97FDC130F01FF03FC804A5C4A5CA391 C75BB3A3B5D8FC1FB50083B512F0A44C257DA451>I<01FEEB7FC000FF903803FFF84A7F 91381F03FE91383C01FF0007017014800003497E6D4814C0A25CA391C7FCB3A3B5D8FC3F 13FFA430257DA435>I<903801FFC0010F13F8017F13FFD9FF807F3A03FE003FE048486D 7E48486D7E48486D7EA2003F81491303007F81A300FF1680A9007F1600A3003F5D6D1307 001F5DA26C6C495A6C6C495A6C6C495A6C6C6CB45A6C6CB5C7FC011F13FC010113C02925 7DA430>I<9039FF01FF80B5000F13F0023F13FC9138FE07FE9139F001FF800003D9C000 13C04AEB7FE091C7EA3FF0A2EE1FF8A217FCA2160F17FEA917FC161FA217F8163F17F017 E06EEB7FC06EEBFF80DAF00113009138FC07FE91383FFFF8020F13E0020390C7FC91C9FC ACB512FCA42F357EA435>I<9038FE07F000FFEB1FFC4A7EEC787F9138E0FF80000701E1 13C03803FFC1A2148102801380A2ED7F00EC001C92C7FCB3A2B512FEA422257EA427> 114 D<90383FF0383903FFFEF84813FF381FC00F383E000314005A157812FCA27E6C6C13 0013FCEBFFE06C13FC6CEBFF8015C06C14E06C14F0000314F8C614FC131F9038007FFE14 070070130100F01300157E7EA26C147C7E6C14F890388001F09038F007E090B512C000F0 140038E01FF81F257DA426>I<130FA55BA45BA25B5BA25A1207001FEBFFE0B6FCA30003 90C7FCB21578A86C1470EC80F06C14E0EB7FC190383FFFC06D1300EB03FE1D357EB425> I<01FFEC3FC0B5EB3FFFA4000714016C80B3A35DA36C5C5D6CD9800E13E090267FC03C13 FF90383FFFF86D5B0103138030257DA435>II121 D<003FB612C0A3D9F0031380D9800713001300003E495A003C495A007C133F 5D0078495A14FF5D495B495B12004990C7FC495A131F5C495A90397FF003C0A2EBFFE048 13C05AEC80074813005A49EB0F80485A4848131F153F397FF001FFB7FCA322257DA42A> I E %EndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: a4 %%BeginPaperSize: a4 /setpagedevice where { pop 1 dict dup /PageSize [ 595 842 ] put setpagedevice } { statusdict /a4tray known { statusdict begin a4tray end /a4 where { pop a4 } if } { /a4 where { pop a4 } { statusdict /setpage known { statusdict begin 595 842 0 setpage end } if } ifelse } ifelse } ifelse %%EndPaperSize %%EndSetup %%Page: 1 1 1 0 bop 230 556 a Fx(NO)45 b(OR)g(INFINITEL)-8 b(Y)46 b(MANY)f(A.C.I.P)-8 b(.)44 b(F)m(OR)h(PIECEWISE)320 686 y(EXP)-8 b(ANDING)48 b Fw(C)1031 656 y Fv(r)1114 686 y Fx(MAPS)f(IN)g(HIGHER)f(DIMENSIONS)1215 1018 y Fu(J)1262 1011 y(\023)1262 1018 y(er)1361 1011 y(^)1358 1018 y(ome)31 b(Buzzi)374 1188 y Ft(Cen)n(tre)c(de)h(Math)n(\023)-39 b(ematique)26 b(de)i(l'Ecole)f(P)n(olytec)n(hnique)f(/)h(C.N.R.S.)558 1384 y(Created:)36 b(Ma)n(y)27 b(23,)g(2000)f(|)h(Mo)r(di\014ed:)38 b(June)27 b(1st,)g(2000)199 1613 y Fs(Abstra)o(ct.)38 b Fr(W)-6 b(e)27 b(mo)r(dify)e(Tsujii's)g(example)h([8])f(to)i(sho)n(w) g(that)h(in)e(con)n(trast)h(with)g(the)g(one-)199 1696 y(dimensional)c(case,)h(piecewise)g(uniformly)d(expanding)26 b(and)e Fq(C)1916 1672 y Fp(r)1974 1696 y Fr(maps)f(of)g(the)i(plane)f (ma)n(y:)342 1804 y(\(1\))36 b(either)20 b(ha)n(v)n(e)h Fo(no)f Fr(absolutely)h(con)n(tin)n(uous)h(in)n(v)l(arian)n(t)e (probabilit)n(y)g(measures)f(\(a.c.i.p.)467 1887 y(for)j(short\))h(and) g(b)r(e)g(suc)n(h)g(that)h Fo(ev)n(ery)h(p)r(oin)n(t)d Fr(is)g(statistically)h(attracted)i(to)e(a)g(\014xed)467 1970 y(rep)r(elling)g(p)r(oin)n(t;)342 2053 y(\(2\))36 b(or)23 b(ha)n(v)n(e)i Fo(in\014nitely)h(man)n(y)g(ergo)r(dic)g (a.c.i.p.)1212 2459 y Fu(Intr)n(oduction)100 2610 y Ft(A)k(piecewise)g (expanding)f Fw(C)1021 2580 y Fn(2)1089 2610 y Ft(map)h(on)g(the)g(in)n (terv)-5 b(al)30 b(is)g(a)g(map)g Fw(F)39 b Ft(:)27 b([0)p Fw(;)14 b Ft(1])27 b Fm(!)g Ft([0)p Fw(;)14 b Ft(1])29 b(suc)n(h)0 2710 y(that)19 b([0)p Fw(;)14 b Ft(1])j(is)i(the)g(union)f (of)h(\014nitely)g(man)n(y)f(in)n(terv)-5 b(als)17 b(on)i(eac)n(h)e(of) i(whic)n(h)f Fw(F)31 b Ft(is)18 b Fw(C)2502 2680 y Fn(2)2558 2710 y Ft(and)h(satis\014es)0 2810 y(inf)i Fm(j)p Fw(F)203 2779 y Fl(0)226 2810 y Fm(j)27 b Fw(>)f Ft(1.)42 b(It)30 b(is)g(w)n(ell-kno)n(wn)e(\(Lasota-Y)-7 b(ork)n(e)27 b([4]\))j(that)g(suc)n(h)f(a)g(map)h(admits)g(a)f Fx(\014nite,)0 2909 y(non-zero)24 b(n)m(um)m(b)s(er)g(of)g(a.c.i.p.)34 b Ft(\(ergo)r(dic)20 b(absolutely)h(con)n(tin)n(uous)f(in)n(v)-5 b(arian)n(t)20 b(probabilit)n(y)0 3009 y(measures\))27 b Fw(\026)439 3021 y Fn(1)476 3009 y Fw(;)14 b(:)g(:)g(:)f(;)h(\026)710 3021 y Fv(r)747 3009 y Ft(,)28 b(suc)n(h)f(that)h(for)f(Leb)r(esgue)g (almost)g(ev)n(ery)f(p)r(oin)n(t)i Fw(x)c Fm(2)f Ft([0)p Fw(;)14 b Ft(1],)1187 3223 y(1)p 1183 3260 50 4 v 1183 3336 a Fw(n)1296 3175 y Fv(n)1257 3200 y Fk(X)1257 3379 y Fv(k)q Fn(=0)1391 3279 y Fw(\016)1428 3296 y Fv(F)1479 3279 y Fj(k)1515 3296 y Fn(\()p Fv(x)p Fn(\))1632 3279 y Fm(!)23 b Fw(\026)1788 3291 y Fv(i)0 3562 y Ft(in)g(the)g(w)n(eak)e (star)h(top)r(ology)-7 b(,)22 b(for)g(some)g Fw(i)g Ft(dep)r(ending)h (on)f Fw(x)h Ft(\(one)f(sa)n(ys)f(that)i Fw(x)g Ft(is)f(statistically)0 3662 y(attracted)27 b(to)g Fw(\026)511 3674 y Fv(i)539 3662 y Ft(\).)100 3763 y(On)i(the)i(in)n(terv)-5 b(al,)30 b(v)n(ery)f(little)h(smo)r(othness)f(is)h(required)f(\(sa)n(y)g Fw(C)2198 3733 y Fn(1)2266 3763 y Ft(plus)h(summabilit)n(y)g(of)0 3862 y(the)37 b(mo)r(dulus)h(of)e(con)n(tin)n(uit)n(y)h(of)g Fw(F)1171 3832 y Fl(0)1231 3862 y Ft(\(see)g([6,1]\)\).)65 b(In)37 b(dimension)g(2,)h(the)g(corresp)r(onding)0 3962 y(result)27 b([2,7])g(requires)f Fx(real-analyticit)m(y)p Ft(.)100 4063 y(M.)k(Tsujii)h([8])f(pro)n(v)n(ed)f(that,)j(at)e(an)n(y) g(rate,)g(\014nite)h(di\013eren)n(tiabilit)n(y)g(is)f(not)g(enough:)42 b(for)0 4163 y(arbitrary)29 b Fw(r)j(<)d Fm(1)p Ft(,)j(there)f(exist)g (piecewise)g Fw(C)1503 4133 y Fv(r)1571 4163 y Ft(and)g(expanding)g (maps)f(of)i(the)f(plane)g(suc)n(h)0 4262 y(that)24 b(for)g(a)g(set)g (of)g(p)r(oin)n(ts)g Fw(x)g Ft(with)h(p)r(ositiv)n(e)f(measure,)1747 4230 y Fn(1)p 1743 4244 42 4 v 1743 4291 a Fv(n)1808 4200 y Fk(P)1896 4221 y Fv(n)1896 4287 y(k)q Fn(=0)2035 4262 y Fw(\016)2072 4279 y Fv(F)2123 4263 y Fj(k)2159 4279 y Fn(\()p Fv(x)p Fn(\))2276 4262 y Fm(!)f Fw(\016)2419 4274 y Fv(p)2481 4262 y Ft(as)g Fw(n)g Fm(!)g(1)p Ft(,)i(for)0 4362 y(some)k Fw(p)e Fm(2)g Fw(X)36 b Ft(indep)r(enden)n(t)31 b(of)f Fw(x)p Ft(.)44 b(Th)n(us)30 b(there)f(is)h(a)g(large)e(set)i(of) g(p)r(oin)n(ts)g(not)f(statistically)0 4462 y(attracted)23 b(to)g(an)g(a.c.i.p.,)h(in)f(con)n(trast)f(with)i(the)f(Lasota-Y)-7 b(ork)n(e)21 b(situtation)i(recalled)f(ab)r(o)n(v)n(e.)100 4616 y Fx(Question:)47 b Ft(Can)33 b(one)h(arrange)d(this)j(example)f (so)g(as)g(to)h(ha)n(v)n(e)f(no)g(a.c.i.p.?)55 b(in\014nitely)0 4715 y(man)n(y)27 b(a.c.i.p.?)100 4869 y(In)g(this)h(note,)g(w)n(e)f (answ)n(er)f(this)i(question)f(p)r(ositiv)n(ely)-7 b(.)2305 5031 y Fr(T)n(yp)r(eset)24 b(b)n(y)g Fi(A)2715 5045 y(M)2791 5031 y(S)p Fr(-T)2897 5045 y(E)2936 5031 y(X)1477 5131 y(1)p eop %%Page: 2 2 2 1 bop 0 42 a Fr(2)1170 b(J)1247 25 y(\023)1241 42 y(ER)1351 25 y(^)1341 42 y(OME)30 b(BUZZI)0 241 y Fx(Results.)100 368 y Ft(Let)d(us)h(recall)f(that)g(a)h(piecewise)f Fw(C)1251 338 y Fv(r)1316 368 y Ft(map)g(is)h(\()p Fw(X)r(;)14 b Fm(Z)7 b Fw(;)14 b(F)e Ft(\))27 b(suc)n(h)g(that:)126 520 y(\(1\))42 b Fw(X)34 b Ft(is)27 b(a)h(compact)f(subset)g(of)h Fh(R)1265 490 y Fv(d)1310 520 y Ft(,)126 620 y(\(2\))42 b Fm(Z)34 b Ft(is)27 b(a)g Fx(\014nite)g Ft(collection)f(of)i(pairwise) e(disjoin)n(t)h(op)r(en)g(subsets)g(of)g Fw(X)7 b Ft(,)27 b(the)h(union)f(of)274 720 y(whic)n(h)f(is)h(dense)f(in)h Fw(X)7 b Ft(.)36 b(Moreo)n(v)n(er)24 b(the)j(subsets)f(in)h Fm(Z)33 b Ft(ha)n(v)n(e)26 b Fw(C)2286 689 y Fv(r)2354 720 y Fx(b)s(oundaries)p Ft(,)g(i.e.,)274 819 y(the)19 b(b)r(oundaries)e(are)h(\014nite)h(unions)f(of)g(compact)g(subsets)h (of)f(op)r(en)g Fw(C)2436 789 y Fv(r)2492 819 y Ft(submanifolds,)126 919 y(\(3\))42 b Fw(F)h Ft(restricted)30 b(to)g(eac)n(h)g(subset)h(in)g Fm(Z)38 b Ft(extends)31 b(to)f(a)h Fw(C)2041 889 y Fv(r)2109 919 y Ft(di\013eomorphism)f(b)r(et)n(w)n(een)274 1018 y(a)d(neigh)n(b)r(orho)r(o)r(d)g(of)g(the)h(closure)f(of)g(the)h (subset)g(and)f(some)g(op)r(en)h(set)f(in)h Fh(R)2722 988 y Fv(d)2767 1018 y Ft(.)0 1171 y Fw(F)39 b Ft(is)26 b(expanding)g(if)h Fm(k)p Fw(F)754 1141 y Fl(0)777 1171 y Ft(\()p Fw(x)p Ft(\))p Fw(:v)s Fm(k)d(\025)e Fw(\025)p Fm(k)p Fw(v)s Fm(k)27 b Ft(for)f(all)g Fw(x)d Fm(2)1698 1108 y Fk(S)1767 1196 y Fv(Z)t Fl(2Z)1932 1171 y Fw(Z)6 b Ft(,)26 b Fw(v)g Fm(2)e Fh(R)2243 1141 y Fv(d)2314 1171 y Ft(and)j(some)f(constan)n(t)0 1270 y Fw(\025)d(>)g Ft(1.)0 1503 y Fx(Theorem.)100 1630 y Fg(1.)38 b(F)-6 b(or)28 b(any)g Fw(r)e(<)c Fm(1)p Fg(,)29 b(ther)l(e)f(exists)f(a)h (pie)l(c)l(ewise)i Fw(C)1722 1600 y Fv(r)1786 1630 y Fg(exp)l(anding)f(map)f(of)h(the)e(squar)l(e)h(with)0 1730 y(no)i(a.c.i.p.)100 1857 y(2.)38 b(F)-6 b(or)28 b(any)g Fw(r)e(<)c Fm(1)p Fg(,)29 b(ther)l(e)f(exists)f(a)h(pie)l(c)l (ewise)i Fw(C)1722 1827 y Fv(r)1786 1857 y Fg(exp)l(anding)f(map)f(of)h (the)e(squar)l(e)h(with)0 1957 y(in\014nitely)i(many)g(a.c.i.p.)0 2189 y(R)l(emark.)43 b Ft(It)26 b(w)n(as)f(already)f(kno)n(wn)h([3])g (that)i(one)e(can)g(ha)n(v)n(e)g(an)n(y)g(\(\014nite,)i(non-zero\))d(n) n(um)n(b)r(er)0 2289 y(of)k(ergo)r(dic)e(a.c.i.p.)37 b(for)27 b(maps)g(with)h(10)f(pieces)g(\(i.e.,)h(elemen)n(ts)g(of)f (the)h(partition)f Fm(Z)7 b Ft(\).)947 2627 y Fu(Tsuji)r(i's)31 b(Counter-Example)100 2804 y Ft(W)-7 b(e)29 b(recall)f(the)i(basic)f (structure)f(of)h(Tsujii's)h(construction)e(for)h(the)g(con)n(v)n (enience)f(of)h(the)0 2904 y(reader.)100 3031 y(Cho)r(ose)f(the)i (di\013eren)n(tiabilit)n(y)f Fw(r)f(<)e Fm(1)p Ft(.)42 b(It)30 b(\014xes)f Fw(\015)h Ft(:=)c Fw(r)c Ft(+)d(1,)29 b Fw(\017)d(>)g Ft(0)i(small)h(enough)g(and)0 3131 y Fw(M)36 b Ft(large)26 b(enough.)100 3258 y(The)e(map)g Fw(F)35 b Ft(is)24 b(de\014ned)h(on)e([0)p Fw(;)14 b Ft(1])d Fm(\002)g Ft([)p Fm(\000)p Ft(1)p Fw(;)j Ft(1].)34 b(It)24 b(is)g(made)g(of)g(8)f(nearly)g(rectangular)f(pieces)0 3358 y(\(see)28 b(Figure)g(1\),)g(only)f(three)h(of)g(whic)n(h)g(b)r (eing)h(imp)r(ortan)n(t)e(\(they)i(are)e(lab)r(elled)h(A,)h(B)f(and)g (C)0 3457 y(on)h(the)h(\014gure\).)42 b(Observ)n(e)27 b(the)j(role)f(of)g(the)h(functions)f Fw(f)38 b Ft(\(de\014ning)30 b(the)g(discon)n(tin)n(uit)n(y)f(line)0 3557 y(near)e Fw(y)e Ft(=)e(0\))28 b(and)f Fw(\021)k Ft(\(de\014ning)d(the)g(do)n(wn) n(w)n(ard)d(push)j(in)g(piece)g(B\).)100 3684 y(The)21 b(k)n(ey)f(prop)r(ert)n(y)g(of)h Fw(F)33 b Ft(is)21 b(the)h(existence)f (of)g(a)g(coun)n(table)f(collection)h(of)g(disjoin)n(t)g(rectan-)0 3784 y(gles)26 b Fw(R)q Ft(\()p Fw(k)s(;)14 b(m)p Ft(\),)27 b(for)g Fw(m)22 b(>)h(M)36 b Ft(and)26 b(0)d Fm(\024)g Fw(k)i(<)e(\015)1439 3754 y Fv(m)1502 3784 y Ft(.)36 b(Eac)n(h)26 b(rectangle)g(is)h(mapp)r(ed)g(in)n(to)f(the)i(next)0 3883 y(one:)35 b Fw(F)12 b Ft(\()p Fw(R)q Ft(\()p Fw(k)s(;)i(m)p Ft(\)\))24 b(=)e Fw(R)q Ft(\()p Fw(k)17 b Ft(+)d(1)p Fw(;)g(m)p Ft(\))23 b(if)j Fw(k)g(<)d(\015)1428 3853 y Fv(m)1504 3883 y Fm(\000)14 b Ft(1,)24 b(and)h Fw(F)12 b Ft(\()p Fw(R)q Ft(\()p Fw(\015)2072 3853 y Fv(m)2148 3883 y Fm(\000)i Ft(1)p Fw(;)g(m)p Ft(\)\))22 b(=)h Fw(R)q Ft(\(0)p Fw(;)14 b(m)g Ft(+)g(1\).)100 4011 y(The)30 b(rectangles)g(are)g(organized)f(in)n(to)h(lines)h Fw(R)q Ft(\(0)p Fw(;)14 b(m)p Ft(\))p Fw(;)g(R)q Ft(\(1)p Fw(;)g(m)p Ft(\))p Fw(;)g(:)g(:)g(:)e(;)i(R)q Ft(\()p Fw(\015)2472 3981 y Fv(m)2555 4011 y Fm(\000)21 b Ft(1)p Fw(;)14 b(m)p Ft(\))30 b(and)0 4114 y(in)n(to)25 b(columns:)36 b Fw(R)q Ft(\()p Fw(k)s(;)14 b(m)p Ft(\))23 b Fm(\032)g Fw(J)962 4126 y Fv(\015)1001 4109 y Fj(m)1055 4126 y Fl(\000)p Fv(k)1163 4114 y Fm(\002)14 b Ft([0)p Fw(;)g Ft(1])25 b(with)h Fw(J)1667 4126 y Fv(`)1722 4114 y Ft(=)d([)p Fw(e)1872 4083 y Fl(\000)p Fv(\017`)1983 4114 y Fw(;)14 b(e)2059 4083 y Fl(\000)p Fv(\017`)2185 4114 y Ft(+)g(\()p Fw(e)2335 4083 y Fl(\000)p Fv(\017)p Fn(\()p Fv(`)p Fl(\000)p Fn(1\))2598 4114 y Fm(\000)g Fw(e)2716 4083 y Fl(\000)p Fv(\017`)2827 4114 y Ft(\))p Fw(=)p Ft(6].)100 4241 y(T)-7 b(o)24 b(eac)n(h)f(column)i Fw(J)736 4253 y Fv(`)780 4241 y Fm(\002)12 b Ft([0)p Fw(;)i Ft(1])24 b(with)h Fw(`)d(>)h(M)9 b Ft(,)25 b(corresp)r(onds)d(a)j("bump")f(in)g(the)h (functions)g Fw(f)0 4341 y Ft(and)k Fw(\021)s Ft(.)40 b(These)29 b(functions)g(are)f(constan)n(t)g(on)g Fw(J)1509 4353 y Fv(`)1570 4341 y Ft(with)h(v)-5 b(alues)29 b(suc)n(h)f(that)h (the)g(discon)n(tin)n(uit)n(y)0 4440 y(line)34 b(cuts)h(in)f(the)g (middle)h(the)g(highest)e(rectangle)g(in)i(the)f(column)2197 4410 y Fn(1)2269 4440 y Ft(\(i.e.,)i Fw(f)43 b Ft(on)33 b Fw(J)2717 4452 y Fv(`)2783 4440 y Ft(is)h(the)0 4540 y Fw(y)s Ft(-co)r(ordinate)h(of)i(the)h(middle)f(of)g(the)h (rectangle\))e(and)h Fw(F)49 b Ft(maps)36 b(the)i(higher)e(half)h(of)g (the)0 4639 y(rectangle)27 b(to)h(the)g(same)g(place)g(as)f(the)i(lo)n (w)n(er)d(half)i(\(i.e.,)h Fw(\021)j Ft(on)c Fw(J)2075 4651 y Fv(`)2135 4639 y Ft(is)g(half)g(the)g(heigh)n(t)g(of)g(the)0 4739 y(rectangle\).)p 0 4940 499 4 v 100 5008 a Ff(1)134 5031 y Fr(the)d(highest)f(rectangle)h(is)e Fq(R)p Fr(\()p Fq(\015)992 5008 y Fp(m)p Ff(\()p Fp(`)p Ff(\))1142 5031 y Fi(\000)15 b Fq(`;)c(m)p Fr(\()p Fq(`)p Fr(\)\))25 b(with)f Fq(m)p Fr(\()p Fq(`)p Fr(\))h(minim)n(um)19 b(with)24 b Fq(\015)2316 5008 y Fp(m)2395 5031 y Fq(>)19 b(`)p Fr(.)p eop %%Page: 3 3 3 2 bop 139 42 a Fr(UNIF)n(ORML)-6 b(Y)30 b(EXP)-6 b(ANDING)31 b Fq(C)1129 18 y Fp(r)1194 42 y Fr(MAP)f(WITH)h(NO)g(OR)f(INFINITEL)-6 b(Y)32 b(MANY)d(A.C.I.P)-6 b(.)103 b(3)0 158 y 27970197 23774657 723599 263127 33088225 27891466 startTexFig 0 158 a %%BeginDocument: tsujii.epsf %!PS-Adobe-2.0 EPSF-1.2 %%Title: tsujii.epsf %%Creator: Canvas 3.0 %%For: Salle Info 3ième %%CreationDate: Mar 30 mai 2000 15:59 %%BoundingBox:11 4 503 424 %%DocumentProcSets: CanvasDict %%DocumentSuppliedProcSets: CanvasDict %%Copyright ©1988-91 Deneba Systems, Inc. - All Rights Reserved Worldwide %%DocumentFonts: Helvetica %%+ Symbol %%DocumentNeededFonts: Helvetica %%+ Symbol %%EndComments %%BeginProcSet:CanvasDict /CanvasDict where not{/CanvasDict 250 dict def}{pop}ifelse CanvasDict begin systemdict/setpacking known{/origpack currentpacking def true setpacking}if /bdf{bind def}bind def /xdf{exch bind def}bdf /min{2 copy gt{exch}if pop}bdf /edf{exch def}bdf /max{2 copy lt{exch}if pop}bdf /cvmtx matrix def /tpmx matrix def /currot 0 def /rotmtx matrix def /origmtx matrix def /cvangle{360 exch sub 90 add 360 mod}bdf /setrot{/currot edf rotmtx currentmatrix pop 2 copy translate currot rotate neg exch neg exch translate}bdf /endrot{rotmtx setmatrix}bdf /i systemdict/image get def/T true def/F false def/dbg F def /ncolors 0 def/st0 ()def/st1 ()def/proc0 {}def /penh 1 def/penv 1 def/penv2 0 def/penh2 0 def/samplesize 0 def/width 0 def/height 0 def /setcmykcolor where not{/setcmykcolor{/b edf 3{b add 1.0 exch sub 0.0 max 1.0 min 3 1 roll}repeat systemdict begin setrgbcolor end}bdf}{pop}ifelse /doeoclip{closepath{eoclip}stopped{currentflat dup 2 mul setflat eoclip setflat}if}bdf /SpaceExtra 0 def/LetterSpace 0 def/StringLength 0 def/NumSpaces 0 def/JustOffset 0 def /f0/fill load def /s0{1 setlinewidth cvmtx currentmatrix pop penh penv scale stroke cvmtx setmatrix}bdf /f1{_bp _fp impat}def /s1{cvmtx currentmatrix pop 1 setlinewidth penh penv scale {strokepath}stopped{currentflat dup 2 mul setflat strokepath setflat}if _bp cvmtx setmatrix _fp impat}def /filltype 0 def /stroketype 0 def /f{filltype 0 eq{f0}{f1}ifelse}bdf /s{stroketype 0 eq{s0}{s1}ifelse}bdf /_fp{}def /_bp{}def /_fg 1 def /_pg 0 def /_bkg 1 def /_frg 0 def /_frgb 3 array def /_frrgb [0 0 0] def /_fcmyk 4 array def /_frcmyk [0 0 0 1] def /_prgb 3 array def /_pcmyk 4 array def /_bkrgb [1 1 1] def /_bkcmyk [0 0 0 0] def /fg{/_fg exch def /filltype 0 def/fills{_fg setgray}def}def /frgb{_frgb astore pop /filltype 0 def/fills{_frgb aload pop setrgbcolor}def}def /fcmyk{_fcmyk astore pop /filltype 0 def/fills{_fcmyk aload pop setcmykcolor}def}def /pg{/_pg exch def /stroketype 0 def/pens{_pg setgray}def}def /prgb{_prgb astore pop /stroketype 0 def/pens{_prgb aload pop setrgbcolor}def}def /pcmyk{_pcmyk astore pop /stroketype 0 def/pens{_pcmyk aload pop setcmykcolor}def}def /fpat{/fstr edf/filltype 1 def/fills{/patstr fstr def}bdf}bdf /ppat{/sstr edf/stroketype 1 def/pens{/patstr sstr def}bdf}bdf /bkg{ /_bkg exch def /_bp{gsave _bkg setgray fill grestore}def}def /bkrgb{_bkrgb astore pop/_bp{gsave _bkrgb aload pop setrgbcolor fill grestore}def}def /bkcmyk{_bkcmyk astore pop/_bp{gsave _bkcmyk aload pop setcmykcolor fill grestore}def}def /frg{ /_frg exch def /_fp{_frg setgray}def}def /frrgb{_frrgb astore pop/_fp{_frrgb aload pop setrgbcolor}def}def /frcmyk{_frcmyk astore pop/_fp{_frcmyk aload pop setcmykcolor}def}def /icomp{/ncolors edf ncolors 1 gt{/proc0 edf dup dup 0 get ncolors div cvi exch 0 3 -1 roll put 4 -1 roll ncolors div cvi 4 1 roll{proc0 dup/st0 edf 0 exch ncolors exch length dup ncolors sub exch ncolors div cvi string/st1 edf {dup 0 exch dup 1 exch 2 add{st0 exch get add}bind for 3 div ncolors 4 eq{exch dup 3 1 roll 3 add st0 exch get add 255 exch sub dup 0 lt{pop 0}if}if cvi dup 255 gt{pop 255}if exch ncolors div cvi exch st1 3 1 roll put}bind for st1}}if i}bdf /ci {/colorimage where {pop false exch colorimage} {icomp} ifelse}bdf /impat {/cnt 0 def /MySave save def currot 0 ne{currot neg rotate}if clip flattenpath pathbbox 3 -1 roll 8 div floor 8 mul dup/starty edf sub abs 8 div ceiling 8 mul cvi/height edf exch 8 div floor 8 mul dup/startx edf sub abs 8 div ceiling 8 mul cvi/width edf startx starty translate width height scale /height height 8 mul def /st0 width string def width height T [width 0 0 height neg 0 height] {patstr cnt 8 mod get/st1 edf 0 1 st0 length 1 sub dup 0 le{pop 1}if {st0 exch st1 put}bind for/cnt cnt 1 add def st0}bind imagemask MySave restore newpath}bdf /cm{/ncolors edf translate scale/height edf/colorimage where {pop} {ncolors mul}ifelse/width edf /tbitstr width string def width height 8 [width 0 0 height neg 0 height] {currentfile tbitstr readhexstring pop}bind ncolors dup 3 eq {ci}{icomp}ifelse}bdf /im{translate scale /height edf /width edf /tbitstr width 7 add 8 div cvi string def width height 1 [width 0 0 height neg 0 height] {currentfile tbitstr readhexstring pop}bind i}bdf /imk{/invFlag edf translate scale /height edf /width edf /tbitstr width 7 add 8 div cvi string def width height invFlag [width 0 0 height neg 0 height] {currentfile tbitstr readhexstring pop}bind imagemask}bdf /BeginEPSF {/MySave save def /dict_count countdictstack def /op_count count 1 sub def userdict begin /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath /languagelevel where {pop languagelevel 1 ne{false setstrokeadjust false setoverprint}if}if }bdf /EndEPSF {count op_count sub {pop}repeat countdictstack dict_count sub {end}repeat MySave restore}bdf /rectpath {/cv_r edf/cv_b edf/cv_l edf/cv_t edf cv_l cv_t moveto cv_r cv_t lineto cv_r cv_b lineto cv_l cv_b lineto cv_l cv_t lineto closepath}bdf /setpen{/penh edf/penv edf/penv2 penv 2 div def/penh2 penh 2 div def}bdf /dostroke{not pens 1.0 currentgray ne or {s}{newpath}ifelse}bdf /dodashfill{not fills 1.0 currentgray ne or {gsave f grestore gsave [] 0 setdash stroketype/stroketype filltype def s/stroketype edf grestore}{newpath}ifelse}bdf /dofill{not fills 1.0 currentgray ne or {f}{newpath}ifelse}bdf /dofillsave{not fills 1.0 currentgray ne or {gsave f grestore}if}bdf /doline{not pens 1.0 currentgray ne or {filltype/filltype stroketype def f/filltype edf}{newpath}ifelse}bdf /spx{SpaceExtra 0 32 4 -1 roll widthshow}bdf /lsx{SpaceExtra 0 32 LetterSpace 0 6 -1 roll awidthshow}bdf /Rjust{stringwidth pop JustOffset exch sub /JustOffset edf}bdf /Cjust{stringwidth pop 2 div JustOffset exch sub /JustOffset edf}bdf /adjfit{stringwidth pop LetterSpace StringLength 1 sub mul add SpaceExtra NumSpaces mul add dup /pw edf JustOffset exch sub dup /wdif edf StringLength div dup abs 1.0 gt{pop 0}if LetterSpace add /LetterSpace edf}bdf /ulb{currentpoint pop /underlinpt edf}bdf /ule{gsave currentpoint newpath moveto currentfont dup /ft1 known{dup /ft1 get begin /FontMatrix get FontMatrix tpmx concatmatrix pop} {begin FontMatrix tpmx copy pop}ifelse FontInfo begin UnderlinePosition UnderlineThickness end end dup tpmx dtransform pop setlinewidth dup tpmx dtransform pop 0 exch rmoveto underlinpt currentpoint pop sub 0 rlineto stroke grestore}bdf /fittext{ /SpaceExtra edf /LetterSpace edf /StringLength edf /NumSpaces edf /JustOffset edf not 1 currentgray ne or {dup {ulb}if exch dup adjfit lsx {ule}if}{pop pop}ifelse}bdf /cvRecFont{/encod edf FontDirectory 2 index known{cleartomark}{findfont dup length 1 add dict begin {1 index/FID ne{def}{pop pop}ifelse}forall encod{/Encoding CVvec def}if currentdict end definefont cleartomark}ifelse}bdf /wrk1 ( ) def/wdict 16 dict def /Work75 75 string def /Nmk{Work75 cvs dup}bdf /Npt{put cvn}bdf /dhOdh{Nmk 2 79 Npt}bdf /dhodh{Nmk 2 111 Npt}bdf /dhSdh{Nmk 2 83 Npt}bdf /sfWidth{gsave 0 0 moveto 0 0 lineto 0 0 lineto 0 0 lineto closepath clip stringwidth grestore}bdf /MakOF{dup dhodh FontDirectory 1 index known{exch pop}{exch findfont dup length 1 add dict begin {1 index/FID ne 2 index /UniqueID ne and{def}{pop pop}ifelse}forall /PaintType 2 def /StrokeWidth .24 1000 mul ftSize div dup 12 lt{pop 12}if def dup currentdict end definefont pop}ifelse}bdf /fts{dup/ftSize edf}def /mkFT{/tempFT 11 dict def tempFT begin /FontMatrix [1 0 0 1 0 0] def/FontType 3 def FontDirectory 3 index get /Encoding get/Encoding exch def /proc2 edf/ft2 exch findfont def/ft1 exch findfont def/FontBBox [0 0 1 1] def /BuildChar{wdict begin/chr edf/ftdt edf/chrst wrk1 dup 0 chr put def ftdt/proc2 get exec end}def end tempFT definefont pop}bdf /OLFt{dup dhOdh FontDirectory 1 index known{exch pop} {dup 3 -1 roll dup MakOF {outproc} mkFT}ifelse}bdf /mshw{moveto show}bdf /outproc{ftdt/ft1 get setfont gsave chrst sfWidth grestore setcharwidth dblsh}bdf /dblsh{currentgray 1 setgray chrst 0 0 mshw setgray ftdt/ft2 get setfont chrst 0 0 mshw}bdf /ShadChar{ftdt/ft1 get setfont gsave chrst sfWidth 1 index 0 ne{exch .05 add exch}if grestore setcharwidth chrst .06 0 mshw 0 .05 translate dblsh}bdf /ShFt{dup dhSdh FontDirectory 1 index known{exch pop} {dup 3 -1 roll dup MakOF {ShadChar} mkFT}ifelse}bdf /LswUnits{72 75 div dup scale}bdf /erasefill{_bp}def /CVvec 256 array def /NUL/SOH/STX/ETX/EOT/ENQ/ACK/BEL/BS/HT/LF/VT/FF/CR/SO/SI/DLE/DC1/DC2/DC3/DC4/NAK/SYN/ETB/CAN/EM/SUB/ESC/FS/GS/RS/US CVvec 0 32 getinterval astore pop CVvec 32/Times-Roman findfont/Encoding get 32 96 getinterval putinterval CVvec dup 39/quotesingle put 96/grave put /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/blank/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand/Acircumflex/Ecircumflex/Aacute /Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex /apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron CVvec 128 128 getinterval astore pop end %%EndProcSet %%BeginSetup CanvasDict begin 0 setlinecap 0 setlinejoin 4 setmiterlimit /currot 0 def origmtx currentmatrix pop [] 0 setdash 1 1 setpen 1 fg 0 pg 0 frg 1 bkg newpath /dbg F def %%EndSetup % ---- Object #1:147 Obj Type: 10 0 setlinecap 354.7749 255.7054 moveto 310.8908 271.7647 262.0763 271.1065 217.2698 282.0142 curveto 172.1391 293.0007 114.5913 312.8309 72.0728 290.7542 curveto 42.8140 275.5623 9.7518 232.2234 35.7910 204.9934 curveto F dofillsave F dostroke gsave newpath 26.2073 212.2152 moveto 26.3347 212.3812 lineto 26.5982 212.7066 lineto 26.8730 213.0227 lineto 27.1585 213.3289 lineto 27.4551 213.6255 lineto 27.7613 213.9111 lineto 28.0774 214.1858 lineto 28.4028 214.4494 lineto 28.7372 214.7014 lineto 29.0802 214.9416 lineto 29.4318 215.1699 lineto 29.7908 215.3856 lineto 30.1570 215.5886 lineto 30.5301 215.7787 lineto 30.9097 215.9558 lineto 31.2957 216.1196 lineto 31.6866 216.2697 lineto 32.0826 216.4060 lineto 32.4830 216.5285 lineto 32.8875 216.6369 lineto 33.0912 216.6858 lineto 35.7910 204.9934 lineto 26.2073 212.2152 lineto closepath F doline grestore % ---- Object #2:149 Obj Type: 10 0 setlinecap 351.3693 277.2189 moveto 279.8742 308.4673 184.6089 329.9763 111.9267 290.7662 curveto 84.7314 276.0950 47.4641 253.3098 55.8367 219.5153 curveto F dofillsave F dostroke gsave newpath 51.5361 230.7183 moveto 51.7323 230.7916 lineto 52.1282 230.9280 lineto 52.5287 231.0504 lineto 52.9331 231.1588 lineto 53.3412 231.2530 lineto 53.7527 231.3330 lineto 54.1665 231.3986 lineto 54.5821 231.4496 lineto 54.9993 231.4861 lineto 55.4174 231.5080 lineto 55.8367 231.5153 lineto 56.2559 231.5080 lineto 56.6740 231.4861 lineto 57.0912 231.4496 lineto 57.5068 231.3986 lineto 57.9206 231.3330 lineto 58.3321 231.2530 lineto 58.7402 231.1588 lineto 59.1446 231.0504 lineto 59.5451 230.9280 lineto 59.7437 230.8615 lineto 55.8367 219.5153 lineto 51.5361 230.7183 lineto closepath F doline grestore % ---- Object #3:148 Obj Type: 10 0 setlinecap 350.4961 305.9864 moveto 266.4422 349.6652 116.1189 335.0945 86.2600 231.6327 curveto F dofillsave F dostroke gsave newpath 86.4700 243.6308 moveto 86.6792 243.6253 lineto 87.0974 243.6034 lineto 87.5145 243.5669 lineto 87.9301 243.5159 lineto 88.3439 243.4503 lineto 88.7555 243.3703 lineto 89.1635 243.2761 lineto 89.5680 243.1677 lineto 89.9684 243.0453 lineto 90.3643 242.9089 lineto 90.7553 242.7589 lineto 91.1412 242.5950 lineto 91.5209 242.4180 lineto 91.8940 242.2279 lineto 92.2602 242.0248 lineto 92.6191 241.8092 lineto 92.9708 241.5808 lineto 93.3138 241.3406 lineto 93.6482 241.0886 lineto 93.9736 240.8250 lineto 94.1329 240.6890 lineto 86.2600 231.6327 lineto 86.4700 243.6308 lineto closepath F doline grestore % ---- Object #4:146 Obj Type: 10 0 setlinecap 349.1630 339.0964 moveto 287.8729 377.4886 174.8328 338.8558 153.5382 268.3265 curveto F dofillsave F dostroke gsave newpath 153.7483 280.3247 moveto 153.9575 280.3192 lineto 154.3756 280.2973 lineto 154.7928 280.2608 lineto 155.2084 280.2097 lineto 155.6222 280.1442 lineto 156.0337 280.0642 lineto 156.4418 279.9700 lineto 156.8462 279.8616 lineto 157.2467 279.7391 lineto 157.6426 279.6028 lineto 158.0335 279.4527 lineto 158.4195 279.2889 lineto 158.7992 279.1118 lineto 159.1723 278.9217 lineto 159.5385 278.7187 lineto 159.8974 278.5030 lineto 160.2490 278.2746 lineto 160.5920 278.0345 lineto 160.9264 277.7824 lineto 161.2519 277.5189 lineto 161.4111 277.3829 lineto 153.5382 268.3265 lineto 153.7483 280.3247 lineto closepath F doline grestore % ---- Object #5:5 Obj Type: 4 0 setlinecap 289.3333 234.3333 283.3333 239.3333 rectpath F dofillsave F dostroke % ---- Object #6:7 Obj Type: 4 0 setlinecap 295.0025 248.5066 289.0025 253.5066 rectpath F dofillsave F dostroke % ---- Object #7:8 Obj Type: 4 0 setlinecap 300.6717 262.6798 294.6717 267.6798 rectpath F dofillsave F dostroke % ---- Object #8:9 Obj Type: 4 0 setlinecap 306.3410 276.8530 300.3410 281.8530 rectpath F dofillsave F dostroke % ---- Object #9:10 Obj Type: 4 0 setlinecap 312.0102 291.0263 306.0102 296.0263 rectpath F dofillsave F dostroke % ---- Object #10:11 Obj Type: 4 0 setlinecap 317.6794 305.1995 311.6794 310.1995 rectpath F dofillsave F dostroke % ---- Object #11:12 Obj Type: 4 0 setlinecap 323.3486 319.3727 317.3486 324.3727 rectpath F dofillsave F dostroke % ---- Object #12:13 Obj Type: 4 0 setlinecap 329.0178 333.5460 323.0178 338.5460 rectpath F dofillsave F dostroke % ---- Object #13:14 Obj Type: 4 0 setlinecap 334.6870 347.7192 328.6870 352.7192 rectpath F dofillsave F dostroke % ---- Object #14:29 Obj Type: 4 0 setlinecap 303.5707 349.1207 297.5707 353.1207 rectpath F dofillsave F dostroke % ---- Object #15:30 Obj Type: 4 0 setlinecap 299.3189 334.9475 293.3189 338.9475 rectpath F dofillsave F dostroke % ---- Object #16:31 Obj Type: 4 0 setlinecap 295.0671 320.7742 289.0671 324.7742 rectpath F dofillsave F dostroke % ---- Object #17:32 Obj Type: 4 0 setlinecap 290.8153 306.6010 284.8153 310.6010 rectpath F dofillsave F dostroke % ---- Object #18:33 Obj Type: 4 0 setlinecap 286.5635 292.4278 280.5635 296.4278 rectpath F dofillsave F dostroke % ---- Object #19:34 Obj Type: 4 0 setlinecap 282.3117 278.2545 276.3117 282.2545 rectpath F dofillsave F dostroke % ---- Object #20:35 Obj Type: 4 0 setlinecap 278.0599 264.0813 272.0599 268.0813 rectpath F dofillsave F dostroke % ---- Object #21:36 Obj Type: 4 0 setlinecap 273.8081 249.9081 267.8081 253.9081 rectpath F dofillsave F dostroke % ---- Object #22:6 Obj Type: 99 % ---- Object #23:37 Obj Type: 4 0 setlinecap 269.5563 235.4015 263.2230 239.7348 rectpath F dofillsave F dostroke % ---- Object #24:58 Obj Type: 4 0 setlinecap 249.8110 236.7348 244.8110 238.7348 rectpath F dofillsave F dostroke % ---- Object #25:70 Obj Type: 3 2 setlinecap gsave newpath 232.3333 286.3333 moveto 241.6667 286 lineto F dostroke grestore % ---- Object #26:69 Obj Type: 3 2 setlinecap gsave newpath 231.8333 286.3333 moveto 231.8333 199.8333 lineto F dostroke grestore % ---- Object #27:71 Obj Type: 3 2 setlinecap gsave newpath 241.6666 286 moveto 241.6666 200 lineto F dostroke grestore % ---- Object #28:38 Obj Type: 4 0 setlinecap 265.3045 221.5616 259.3045 225.5616 rectpath F dofillsave F dostroke % ---- Object #29:39 Obj Type: 4 0 setlinecap 261.0527 207.3884 255.0527 211.3884 rectpath F dofillsave F dostroke % ---- Object #30:40 Obj Type: 4 0 setlinecap 256.8009 193.2151 250.8009 197.2151 rectpath F dofillsave F dostroke % ---- Object #31:41 Obj Type: 4 0 setlinecap 252.5491 179.0419 246.5491 183.0419 rectpath F dofillsave F dostroke % ---- Object #32:42 Obj Type: 4 0 setlinecap 248.2973 164.8687 242.2973 168.8687 rectpath F dofillsave F dostroke % ---- Object #33:50 Obj Type: 4 0 setlinecap 272.4896 350.1207 267.4896 352.1207 rectpath F dofillsave F dostroke % ---- Object #34:51 Obj Type: 4 0 setlinecap 269.6548 335.9475 264.6548 337.9475 rectpath F dofillsave F dostroke % ---- Object #35:52 Obj Type: 4 0 setlinecap 266.8199 321.7742 261.8199 323.7742 rectpath F dofillsave F dostroke % ---- Object #36:53 Obj Type: 4 0 setlinecap 263.9851 307.6010 258.9851 309.6010 rectpath F dofillsave F dostroke % ---- Object #37:54 Obj Type: 4 0 setlinecap 261.1503 293.4278 256.1503 295.4278 rectpath F dofillsave F dostroke % ---- Object #38:55 Obj Type: 4 0 setlinecap 258.3155 279.2545 253.3155 281.2545 rectpath F dofillsave F dostroke % ---- Object #39:56 Obj Type: 4 0 setlinecap 255.4806 265.0813 250.4806 267.0813 rectpath F dofillsave F dostroke % ---- Object #40:57 Obj Type: 4 0 setlinecap 252.6458 250.9081 247.6458 252.9081 rectpath F dofillsave F dostroke % ---- Object #41:59 Obj Type: 4 0 setlinecap 246.9762 222.5616 241.9762 224.5616 rectpath F dofillsave F dostroke % ---- Object #42:60 Obj Type: 4 0 setlinecap 244.1413 208.3884 239.1413 210.3884 rectpath F dofillsave F dostroke % ---- Object #43:61 Obj Type: 4 0 setlinecap 241.3065 194.2151 236.3065 196.2151 rectpath F dofillsave F dostroke % ---- Object #44:62 Obj Type: 4 0 setlinecap 238.4717 180.0419 233.4717 182.0419 rectpath F dofillsave F dostroke % ---- Object #45:63 Obj Type: 4 0 setlinecap 235.6369 165.8687 230.6369 167.8687 rectpath F dofillsave F dostroke % ---- Object #46:64 Obj Type: 4 0 setlinecap 232.8020 151.6954 227.8020 153.6954 rectpath F dofillsave F dostroke % ---- Object #47:65 Obj Type: 4 0 setlinecap 229.9672 137.5222 224.9672 139.5222 rectpath F dofillsave F dostroke % ---- Object #48:66 Obj Type: 4 0 setlinecap 227.1324 123.3490 222.1324 125.3490 rectpath F dofillsave F dostroke % ---- Object #49:67 Obj Type: 4 0 setlinecap 224.2976 109.1757 219.2976 111.1757 rectpath F dofillsave F dostroke % ---- Object #50:68 Obj Type: 4 0 setlinecap 221.4627 95.0025 216.4627 97.0025 rectpath F dofillsave F dostroke % ---- Object #51:76 Obj Type: 3 2 setlinecap gsave newpath 246.8418 293 moveto 256 293.3333 lineto F dostroke grestore % ---- Object #52:77 Obj Type: 3 2 setlinecap gsave newpath 246.3333 293 moveto 246.2500 199.7500 lineto F dostroke grestore % ---- Object #53:78 Obj Type: 3 2 setlinecap gsave newpath 256 293.3333 moveto 256 199.5000 lineto F dostroke grestore % ---- Object #54:79 Obj Type: 3 2 setlinecap gsave newpath 260.6667 298.3333 moveto 270 298 lineto F dostroke grestore % ---- Object #55:80 Obj Type: 3 2 setlinecap gsave newpath 260.3333 298 moveto 260.3333 199.6667 lineto F dostroke grestore % ---- Object #56:81 Obj Type: 3 2 setlinecap gsave newpath 270 298 moveto 270 199.6667 lineto F dostroke grestore % ---- Object #57:73 Obj Type: 3 2 setlinecap gsave newpath 274.3333 303.6667 moveto 274.3333 199.6667 lineto F dostroke grestore % ---- Object #58:74 Obj Type: 3 2 setlinecap gsave newpath 274.3333 304.3333 moveto 284.6667 304 lineto F dostroke grestore % ---- Object #59:75 Obj Type: 3 2 setlinecap gsave newpath 284.6667 304.3333 moveto 284.6667 199.6667 lineto F dostroke grestore % ---- Object #60:82 Obj Type: 3 2 setlinecap gsave newpath 364 199.5000 moveto 284.5000 199.5000 lineto F dostroke grestore % ---- Object #61:83 Obj Type: 3 2 setlinecap gsave newpath 219.3333 262.3333 moveto 228.3333 262.3333 lineto F dostroke grestore % ---- Object #62:84 Obj Type: 3 2 setlinecap gsave newpath 218.3333 262.3333 moveto 218.3333 199.3333 lineto F dostroke grestore % ---- Object #63:85 Obj Type: 3 2 setlinecap gsave newpath 228.3333 262.3333 moveto 228.2500 199.7500 lineto F dostroke grestore % ---- Object #64:86 Obj Type: 3 2 setlinecap gsave newpath 213.6667 258.3333 moveto 213.6667 199.3333 lineto F dostroke grestore % ---- Object #65:87 Obj Type: 3 2 setlinecap gsave newpath 213.3333 258.3333 moveto 204.6667 258.3333 lineto F dostroke grestore % ---- Object #66:88 Obj Type: 3 2 setlinecap gsave newpath 204.3333 258.3333 moveto 204.2500 199.5000 lineto F dostroke grestore % ---- Object #67:89 Obj Type: 3 2 setlinecap gsave newpath 191.3333 254.3333 moveto 198.6667 254 lineto F dostroke grestore % ---- Object #68:90 Obj Type: 3 2 setlinecap gsave newpath 190.6667 254.3333 moveto 190.7500 200.2500 lineto F dostroke grestore % ---- Object #69:91 Obj Type: 3 2 setlinecap gsave newpath 199.6667 254.3333 moveto 199.6667 199.3333 lineto F dostroke grestore % ---- Object #70:92 Obj Type: 3 2 setlinecap gsave newpath 176.6667 250.3333 moveto 185.3333 250 lineto F dostroke grestore % ---- Object #71:93 Obj Type: 3 2 setlinecap gsave newpath 176.3333 250 moveto 176.2500 199.7500 lineto F dostroke grestore % ---- Object #72:94 Obj Type: 3 2 setlinecap gsave newpath 185.3333 250.3333 moveto 185.2500 200 lineto F dostroke grestore % ---- Object #73:95 Obj Type: 3 2 setlinecap gsave newpath 162.3333 246.3333 moveto 170 246.2500 lineto F dostroke grestore % ---- Object #74:96 Obj Type: 3 2 setlinecap gsave newpath 170.3333 246.3333 moveto 170.2500 200.7500 lineto F dostroke grestore % ---- Object #75:97 Obj Type: 3 2 setlinecap gsave newpath 162.3333 246.3333 moveto 162.2500 200.5000 lineto F dostroke grestore % ---- Object #76:98 Obj Type: 3 2 setlinecap gsave newpath 156.3333 231 moveto 149.3333 231.3333 lineto F dostroke grestore % ---- Object #77:99 Obj Type: 3 2 setlinecap gsave newpath 149.3333 231.3333 moveto 149.2500 199.7500 lineto F dostroke grestore % ---- Object #78:100 Obj Type: 3 2 setlinecap gsave newpath 156.3333 199.6667 moveto 156.2500 231.2500 lineto F dostroke grestore % ---- Object #79:101 Obj Type: 3 2 setlinecap gsave newpath 141.3333 228.3333 moveto 135.3333 228.3333 lineto F dostroke grestore % ---- Object #80:102 Obj Type: 3 2 setlinecap gsave newpath 141.3333 228.3333 moveto 141.2500 200 lineto F dostroke grestore % ---- Object #81:103 Obj Type: 3 2 setlinecap gsave newpath 134.6667 228 moveto 134.7500 199.7500 lineto F dostroke grestore % ---- Object #82:16 Obj Type: 4 0 setlinecap 252.6472 350.1207 248.3972 351.8206 rectpath F dofillsave F dostroke % ---- Object #83:17 Obj Type: 4 0 setlinecap 250.3794 335.9475 246.1294 337.6474 rectpath F dofillsave F dostroke % ---- Object #84:18 Obj Type: 4 0 setlinecap 248.1116 321.7742 243.8617 323.4742 rectpath F dofillsave F dostroke % ---- Object #85:19 Obj Type: 4 0 setlinecap 245.8439 307.6010 241.5939 309.3009 rectpath F dofillsave F dostroke % ---- Object #86:20 Obj Type: 4 0 setlinecap 243.5761 293.4278 239.3262 295.1277 rectpath F dofillsave F dostroke % ---- Object #87:21 Obj Type: 4 0 setlinecap 241.3083 279.2545 237.0584 280.9545 rectpath F dofillsave F dostroke % ---- Object #88:22 Obj Type: 4 0 setlinecap 239.0406 265.0813 234.7906 266.7812 rectpath F dofillsave F dostroke % ---- Object #89:23 Obj Type: 4 0 setlinecap 236.7728 250.9081 232.5229 252.6080 rectpath F dofillsave F dostroke % ---- Object #90:24 Obj Type: 4 0 setlinecap 234.5051 236.7348 230.2551 238.4348 rectpath F dofillsave F dostroke % ---- Object #91:25 Obj Type: 4 0 setlinecap 232.2373 222.5616 227.9873 224.2615 rectpath F dofillsave F dostroke % ---- Object #92:26 Obj Type: 4 0 setlinecap 229.9695 208.3884 225.7196 210.0883 rectpath F dofillsave F dostroke % ---- Object #93:27 Obj Type: 4 0 setlinecap 227.7018 194.2151 223.4518 195.9151 rectpath F dofillsave F dostroke % ---- Object #94:28 Obj Type: 4 0 setlinecap 225.4340 180.0419 221.1841 181.7418 rectpath F dofillsave F dostroke % ---- Object #95:43 Obj Type: 4 0 setlinecap 223.1663 165.8687 218.9163 167.5686 rectpath F dofillsave F dostroke % ---- Object #96:44 Obj Type: 4 0 setlinecap 220.8985 151.6954 216.6485 153.3954 rectpath F dofillsave F dostroke % ---- Object #97:45 Obj Type: 4 0 setlinecap 218.6307 137.5222 214.3808 139.2221 rectpath F dofillsave F dostroke % ---- Object #98:46 Obj Type: 4 0 setlinecap 216.3630 123.3490 212.1130 125.0489 rectpath F dofillsave F dostroke % ---- Object #99:47 Obj Type: 4 0 setlinecap 214.0952 109.1757 209.8453 110.8757 rectpath F dofillsave F dostroke % ---- Object #100:48 Obj Type: 4 0 setlinecap 211.8274 95.0025 207.5775 96.7024 rectpath F dofillsave F dostroke % ---- Object #101:49 Obj Type: 4 0 setlinecap 209.5597 80.8293 205.3097 82.5292 rectpath F dofillsave F dostroke % ---- Object #102:72 Obj Type: 4 0 setlinecap 207.2919 66.6560 203.0420 68.3560 rectpath F dofillsave F dostroke % ---- Object #103:104 Obj Type: 4 0 setlinecap 233 350.5000 232 351.5000 rectpath F dofillsave F dostroke % ---- Object #104:105 Obj Type: 4 0 setlinecap 231.4411 336.3268 230.4411 337.3268 rectpath F dofillsave F dostroke % ---- Object #105:106 Obj Type: 4 0 setlinecap 229.8823 322.1535 228.8823 323.1535 rectpath F dofillsave F dostroke % ---- Object #106:107 Obj Type: 4 0 setlinecap 228.3234 307.9803 227.3234 308.9803 rectpath F dofillsave F dostroke % ---- Object #107:108 Obj Type: 4 0 setlinecap 226.7646 293.8071 225.7646 294.8071 rectpath F dofillsave F dostroke % ---- Object #108:109 Obj Type: 4 0 setlinecap 225.2057 279.6338 224.2057 280.6338 rectpath F dofillsave F dostroke % ---- Object #109:110 Obj Type: 4 0 setlinecap 223.6469 265.4606 222.6469 266.4606 rectpath F dofillsave F dostroke % ---- Object #110:111 Obj Type: 4 0 setlinecap 222.0880 251.2874 221.0880 252.2874 rectpath F dofillsave F dostroke % ---- Object #111:112 Obj Type: 4 0 setlinecap 220.5292 237.1141 219.5292 238.1141 rectpath F dofillsave F dostroke % ---- Object #112:113 Obj Type: 4 0 setlinecap 218.9703 222.9409 217.9703 223.9409 rectpath F dofillsave F dostroke % ---- Object #113:114 Obj Type: 4 0 setlinecap 217.4115 208.7677 216.4115 209.7677 rectpath F dofillsave F dostroke % ---- Object #114:115 Obj Type: 4 0 setlinecap 215.8526 194.5944 214.8526 195.5944 rectpath F dofillsave F dostroke % ---- Object #115:116 Obj Type: 4 0 setlinecap 214.2938 180.4212 213.2938 181.4212 rectpath F dofillsave F dostroke % ---- Object #116:117 Obj Type: 4 0 setlinecap 212.7349 166.2480 211.7349 167.2480 rectpath F dofillsave F dostroke % ---- Object #117:118 Obj Type: 4 0 setlinecap 211.1761 152.0747 210.1761 153.0747 rectpath F dofillsave F dostroke % ---- Object #118:119 Obj Type: 4 0 setlinecap 209.6172 137.9015 208.6172 138.9015 rectpath F dofillsave F dostroke % ---- Object #119:120 Obj Type: 4 0 setlinecap 208.0583 123.7283 207.0583 124.7283 rectpath F dofillsave F dostroke % ---- Object #120:121 Obj Type: 4 0 setlinecap 206.4995 109.5550 205.4995 110.5550 rectpath F dofillsave F dostroke % ---- Object #121:122 Obj Type: 4 0 setlinecap 204.9406 95.3818 203.9406 96.3818 rectpath F dofillsave F dostroke % ---- Object #122:123 Obj Type: 4 0 setlinecap 203.3818 81.2086 202.3818 82.2086 rectpath F dofillsave F dostroke % ---- Object #123:124 Obj Type: 4 0 setlinecap 201.8229 67.0353 200.8229 68.0353 rectpath F dofillsave F dostroke % ---- Object #124:125 Obj Type: 3 2 setlinecap gsave newpath 127.5000 225 moveto 121.2500 225 lineto F dostroke grestore % ---- Object #125:126 Obj Type: 3 2 setlinecap gsave newpath 121 225 moveto 121 199.5000 lineto F dostroke grestore % ---- Object #126:127 Obj Type: 3 2 setlinecap gsave newpath 127.5000 225 moveto 127.5000 199.7500 lineto F dostroke grestore % ---- Object #127:128 Obj Type: 3 2 setlinecap gsave newpath 107.7500 222 moveto 113 222 lineto F dostroke grestore % ---- Object #128:129 Obj Type: 3 2 setlinecap gsave newpath 107.5000 222 moveto 107.5000 200 lineto F dostroke grestore % ---- Object #129:130 Obj Type: 3 2 setlinecap gsave newpath 113.5000 222 moveto 113.5000 199.5000 lineto F dostroke grestore % ---- Object #130:131 Obj Type: 3 2 setlinecap gsave newpath 93 219.2500 moveto 99.2500 219.2500 lineto F dostroke grestore % ---- Object #131:132 Obj Type: 3 2 setlinecap gsave newpath 92 219.2500 moveto 92 199.5000 lineto F dostroke grestore % ---- Object #132:133 Obj Type: 3 2 setlinecap gsave newpath 99.7500 219.5000 moveto 99.7500 200 lineto F dostroke grestore % ---- Object #133:134 Obj Type: 4 0 setlinecap 201.2500 55.2500 200.7500 56 rectpath F dofillsave F dostroke % ---- Object #134:135 Obj Type: 3 2 setlinecap gsave newpath 83.7500 207.2500 moveto 78.3750 207.1250 lineto F dostroke grestore % ---- Object #135:136 Obj Type: 3 2 setlinecap gsave newpath 84 207 moveto 84 199.7500 lineto F dostroke grestore % ---- Object #136:137 Obj Type: 3 2 setlinecap gsave newpath 78.2500 200 moveto 78.2500 206.5000 lineto F dostroke grestore % ---- Object #137:138 Obj Type: 3 2 setlinecap gsave newpath 63.7500 205 moveto 71 204.8750 lineto F dostroke grestore % ---- Object #138:139 Obj Type: 3 2 setlinecap gsave newpath 71.2500 204.5000 moveto 71.2500 200 lineto F dostroke grestore % ---- Object #139:140 Obj Type: 3 2 setlinecap gsave newpath 63.5000 204.7500 moveto 63.5000 200 lineto F dostroke grestore % ---- Object #140:141 Obj Type: 3 2 setlinecap gsave newpath 354.2238 344.8159 moveto 354.0823 344.9703 lineto 353.8076 345.2864 lineto 353.5441 345.6118 lineto 353.2921 345.9462 lineto 353.0519 346.2892 lineto 352.8235 346.6408 lineto 352.6078 346.9998 lineto 352.4048 347.3660 lineto 352.2147 347.7391 lineto 352.0376 348.1188 lineto 351.8738 348.5047 lineto 351.7237 348.8956 lineto 351.5874 349.2916 lineto 351.4649 349.6920 lineto 351.3566 350.0965 lineto 351.2623 350.5045 lineto 351.1823 350.9161 lineto 351.1168 351.3298 lineto 351.0658 351.7455 lineto 351.0292 352.1626 lineto 351.0165 352.3715 lineto 363 353 lineto 354.2238 344.8159 lineto closepath F doline grestore gsave newpath 229 295 moveto 352.2168 348.3326 lineto F dostroke grestore % ---- Object #141:142 Obj Type: 3 2 setlinecap gsave newpath 345.5441 309.6118 moveto 345.4167 309.7778 lineto 345.1705 310.1166 lineto 344.9359 310.4643 lineto 344.7140 310.8194 lineto 344.5047 311.1821 lineto 344.3081 311.5518 lineto 344.1245 311.9282 lineto 343.9542 312.3107 lineto 343.7971 312.6994 lineto 343.6539 313.0929 lineto 343.5245 313.4912 lineto 343.4090 313.8939 lineto 343.3077 314.3002 lineto 343.2205 314.7103 lineto 343.1477 315.1227 lineto 343.0895 315.5373 lineto 343.0457 315.9538 lineto 343.0165 316.3715 lineto 343.0018 316.7900 lineto 343.0018 317.2095 lineto 343.0073 317.4187 lineto 355 317 lineto 345.5441 309.6118 lineto closepath F doline grestore gsave newpath 161 255 moveto 343.8077 313.4231 lineto F dostroke grestore % ---- Object #142:143 Obj Type: 3 2 setlinecap gsave newpath 347.8235 276.6408 moveto 347.7140 276.8194 lineto 347.5047 277.1821 lineto 347.3081 277.5518 lineto 347.1245 277.9282 lineto 346.9542 278.3107 lineto 346.7971 278.6994 lineto 346.6539 279.0929 lineto 346.5245 279.4912 lineto 346.4090 279.8939 lineto 346.3077 280.3002 lineto 346.2205 280.7103 lineto 346.1477 281.1227 lineto 346.0895 281.5373 lineto 346.0457 281.9538 lineto 346.0165 282.3715 lineto 346.0018 282.7900 lineto 346.0018 283.2095 lineto 346.0164 283.6279 lineto 346.0456 284.0457 lineto 346.0894 284.4621 lineto 346.1167 284.6696 lineto 358 283 lineto 347.8235 276.6408 lineto closepath F doline grestore gsave newpath 94 225 moveto 346.5237 280.4787 lineto F dostroke grestore % ---- Object #143:144 Obj Type: 3 2 setlinecap gsave newpath 347.5047 253.1821 moveto 347.4048 253.3660 lineto 347.2147 253.7391 lineto 347.0376 254.1188 lineto 346.8738 254.5047 lineto 346.7237 254.8956 lineto 346.5874 255.2916 lineto 346.4649 255.6920 lineto 346.3566 256.0965 lineto 346.2623 256.5045 lineto 346.1823 256.9161 lineto 346.1168 257.3298 lineto 346.0658 257.7455 lineto 346.0292 258.1626 lineto 346.0073 258.5808 lineto 346 259 lineto 346.0073 259.4187 lineto 346.0292 259.8368 lineto 346.0657 260.2540 lineto 346.1167 260.6696 lineto 346.1822 261.0832 lineto 346.2204 261.2891 lineto 358 259 lineto 347.5047 253.1821 lineto closepath F doline grestore gsave newpath 65 211 moveto 346.4046 257.1004 lineto F dostroke grestore % ---- Object #144:145 Obj Type: 3 2 setlinecap gsave newpath 343.3081 232.5518 moveto 343.2147 232.7391 lineto 343.0376 233.1188 lineto 342.8738 233.5047 lineto 342.7237 233.8956 lineto 342.5874 234.2916 lineto 342.4649 234.6920 lineto 342.3566 235.0965 lineto 342.2623 235.5045 lineto 342.1823 235.9161 lineto 342.1168 236.3298 lineto 342.0658 236.7455 lineto 342.0292 237.1626 lineto 342.0073 237.5808 lineto 342 238 lineto 342.0073 238.4187 lineto 342.0292 238.8368 lineto 342.0657 239.2540 lineto 342.1167 239.6696 lineto 342.1822 240.0832 lineto 342.2622 240.4950 lineto 342.3075 240.6993 lineto 354 238 lineto 343.3081 232.5518 lineto closepath F doline grestore gsave newpath 54 203 moveto 342.3292 236.6384 lineto F dostroke grestore % ---- Object #145:150 Obj Type: 3 2 setlinecap gsave newpath 49.5000 420.5000 moveto 49.5000 30.5000 lineto F dostroke grestore % ---- Object #146:151 Obj Type: 3 2 setlinecap gsave newpath 49 420.5000 moveto 364.5000 420.5000 lineto F dostroke grestore % ---- Object #147:152 Obj Type: 3 2 setlinecap gsave newpath 364 420.5000 moveto 364 31.5000 lineto F dostroke grestore % ---- Object #148:153 Obj Type: 3 2 setlinecap gsave newpath 49 31 moveto 363 31 lineto F dostroke grestore % ---- Object #149:154 Obj Type: 3 2 setlinecap gsave newpath 343.5000 419.5000 moveto 343.5000 31 lineto F dostroke grestore % ---- Object #150:155 Obj Type: 3 2 setlinecap gsave newpath 49.5000 402.5000 moveto 363.5000 402.5000 lineto F dostroke grestore % ---- Object #151:156 Obj Type: 3 2 setlinecap gsave newpath 50 54.5000 moveto 364 54.5000 lineto F dostroke grestore % ---- Object #152:157 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 10 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 102 136 moveto (A: F\(x,y\)=\() F F 59 1 11 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 10 fts /|___Symbol findfont exch scalefont setfont 0 setgray 161 136 moveto (l) show 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 10 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 166 136 moveto (x,) F F 10 0 2 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 10 fts /|___Symbol findfont exch scalefont setfont 0 setgray 176 136 moveto (l) show 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 10 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 181 136 moveto (y\)) F F 12 0 2 0 0 fittext restore % ---- Object #153:158 Obj Type: 2 save 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 10 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 102 363 moveto (B: F\(x,y\)=\() F F 60 1 11 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 10 fts /|___Symbol findfont exch scalefont setfont 0 setgray 162 363 moveto (l) show 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 10 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 167 363 moveto (x,) F F 10 0 2 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 10 fts /|___Symbol findfont exch scalefont setfont 0 setgray 177 363 moveto (l\() F F 8.8184 0 2 0 0 fittext 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 10 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 185 363 moveto (y-) F F 13 0 2 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 10 fts /|___Symbol findfont exch scalefont setfont 0 setgray 198 363 moveto (h) show 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 10 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 204 363 moveto (\(x\)\)\)) F F 30 0 5 0 0 fittext restore % ---- Object #154:159 Obj Type: 2 save 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 10 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 400 312 moveto (C: F\(x,y\)=\() F F 59 1 11 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 10 fts /|___Symbol findfont exch scalefont setfont 0 setgray 459 312 moveto (l) show 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 10 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 464 312 moveto (y,) F F 10 0 2 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 10 fts /|___Symbol findfont exch scalefont setfont 0 setgray 474 312 moveto (l) show 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 10 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 479 312 moveto (x) show 0 setgray mark /|___Symbol /Symbol F cvRecFont 10 fts /|___Symbol findfont exch scalefont setfont 0 setgray 485 312 moveto (-1) F F 10.4883 0 2 0 0 fittext 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 10 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 495 312 moveto (\)) show restore % ---- Object #155:15 Obj Type: 3 1 1 setpen 2 setlinecap gsave newpath 421 307 moveto 357 214.5000 lineto F dostroke grestore % ---- Object #156:161 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 12 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 383 392 moveto (e) show 0 setgray mark /|___Symbol /Symbol F cvRecFont 12 fts /|___Symbol findfont exch scalefont setfont 0 setgray 389 396 moveto (-e) F F 11.8535 0 2 0 0 fittext restore % ---- Object #157:162 Obj Type: 2 save 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 12 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 331 9 moveto (e) show 0 setgray mark /|___Symbol /Symbol F cvRecFont 12 fts /|___Symbol findfont exch scalefont setfont 0 setgray 337 13 moveto (-e) F F 11.8535 0 2 0 0 fittext restore % ---- Object #158:160 Obj Type: 2 save 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 12 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 44 10 moveto (0) show restore % ---- Object #159:163 Obj Type: 2 save 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 12 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 362 9 moveto (1) show restore % ---- Object #160:165 Obj Type: 2 save 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 12 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 384 192 moveto (0) show restore % ---- Object #161:164 Obj Type: 2 save 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 12 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 384 411 moveto (1) show restore % ---- Object #162:167 Obj Type: 2 save 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 12 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 381 28 moveto (-1) F F 12.5449 0 2 0 0 fittext restore % ---- Object #163:169 Obj Type: 2 save 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 12 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 380 54 moveto (-e) F F 11.4551 0 2 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 12 fts /|___Symbol findfont exch scalefont setfont 0 setgray 391 58 moveto (-e) F F 11.8535 0 2 0 0 fittext restore % ---- Object #164:168 Obj Type: 3 1 1 setpen 2 setlinecap gsave newpath 274 199.5000 moveto 270 199.5000 lineto F dostroke grestore % ---- Object #165:170 Obj Type: 3 2 setlinecap gsave newpath 260 199.7500 moveto 256 199.7500 lineto F dostroke grestore % ---- Object #166:171 Obj Type: 3 2 setlinecap gsave newpath 246 199.7500 moveto 241.7500 199.7500 lineto F dostroke grestore % ---- Object #167:172 Obj Type: 3 2 setlinecap gsave newpath 231.5000 199.5000 moveto 228 199.5000 lineto F dostroke grestore % ---- Object #168:173 Obj Type: 3 2 setlinecap gsave newpath 217.7500 199.2500 moveto 214 199.2500 lineto F dostroke grestore % ---- Object #169:174 Obj Type: 3 2 setlinecap gsave newpath 203.7500 199.5000 moveto 200 199.5000 lineto F dostroke grestore % ---- Object #170:175 Obj Type: 3 2 setlinecap gsave newpath 190.5000 200 moveto 185.5000 200 lineto F dostroke grestore % ---- Object #171:176 Obj Type: 3 2 setlinecap gsave newpath 176 199.7500 moveto 170.2500 199.7500 lineto F dostroke grestore % ---- Object #172:177 Obj Type: 3 2 setlinecap gsave newpath 162.2500 199.5000 moveto 156.2500 199.5000 lineto F dostroke grestore % ---- Object #173:178 Obj Type: 3 2 setlinecap gsave newpath 148.7500 199.7500 moveto 141.5000 199.7500 lineto F dostroke grestore % ---- Object #174:179 Obj Type: 3 2 setlinecap gsave newpath 134.2500 199.7500 moveto 127.5000 199.7500 lineto F dostroke grestore % ---- Object #175:181 Obj Type: 3 2 setlinecap gsave newpath 120.5000 199.5000 moveto 114 199.5000 lineto F dostroke grestore % ---- Object #176:180 Obj Type: 3 2 setlinecap gsave newpath 106.5000 200 moveto 99.7500 200 lineto F dostroke grestore % ---- Object #177:182 Obj Type: 3 2 setlinecap gsave newpath 84 199.2500 moveto 91.7500 199.2500 lineto F dostroke grestore % ---- Object #178:183 Obj Type: 3 2 setlinecap gsave newpath 77.2500 200 moveto 71 200 lineto F dostroke grestore % ---- Object #179:184 Obj Type: 3 2 setlinecap gsave newpath 63 199.5000 moveto 49.7500 199.5000 lineto F dostroke grestore % ---- Object #180:166 Obj Type: 3 2 setlinecap gsave newpath 311 196.5000 moveto 417.5000 140.5000 lineto F dostroke grestore % ---- Object #181:186 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 12 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 425 122 moveto (y=f\(x\)) F F 36.6269 0 6 0 0 fittext restore origmtx setmatrix systemdict /setpacking known {origpack setpacking} if end showpage %%EndDocument: %%EndDocument endTexFig 1331 3269 a Ft(Figure)27 b(1.)100 3376 y Fg(R)l(emarks:)37 b Ft(1.)g Fw(\025)24 b Ft(=)f Fw(e)775 3346 y Fv(\017)807 3376 y Ft(.)37 b(2.)g(The)28 b(smo)r(oth)g(bumps)g(in)g(the)g(discon)n (tin)n(uit)n(y)f(lines)h(are)f(dra)n(wn)0 3475 y(as)g(rectangles.)1280 3709 y Fu(No)j(a.c.i.p.)100 3865 y Ft(W)-7 b(e)33 b(start)g(with)g (Tsujii's)h(map)f Fw(F)44 b Ft(:)33 b([0)p Fw(;)14 b Ft(1])21 b Fm(\002)h Ft([)p Fm(\000)p Ft(1)p Fw(;)14 b Ft(1])31 b Fm(!)h Ft([0)p Fw(;)14 b Ft(1])21 b Fm(\002)h Ft([)p Fm(\000)p Ft(1)p Fw(;)14 b Ft(1])32 b(and)h(mo)r(dify)g(it)0 3965 y(b)n(y)26 b(carving)f(some)h(new)g(pieces.)37 b(The)26 b(idea)g(is)g(to)h(capture)e(in)i(these)g(new)f(pieces)g(ev)n(ery)f (orbit)0 4064 y(whic)n(h)j(w)n(ould)g(not)g(ev)n(en)n(tually)f(en)n (ter)g(some)h(rectangle)e Fw(R)q Ft(\()p Fw(k)s(;)14 b(m)p Ft(\))28 b(under)g(the)h(iteration)e(of)h Fw(F)0 4164 y Ft(so)j(that)h(the)h(mo)r(di\014cation)f(of)f Fw(F)44 b Ft(can)32 b(send)g(it)g(in)n(to)g(some)f(rectangle.)49 b(T)-7 b(o)31 b(do)h(this)g(w)n(e)g(are)0 4263 y(going)e(to)h(sp)r (ecify)g(a)g(subset)g Fw(E)k Fm(\032)28 b Ft([0)p Fw(;)14 b Ft(1])20 b Fm(\002)g Ft([)p Fm(\000)p Ft(1)p Fw(;)14 b Ft(1])30 b(with)i Fw(C)1920 4233 y Fv(r)1993 4263 y Fx(b)s(oundary)g Ft(suc)n(h)f(that)g(ev)n(ery)0 4363 y Fw(F)12 b Ft(-orbit)29 b(whic)n(h)g(do)r(es)g(not)g(ev)n(en)n(tually) g(en)n(ter)g(some)f(rectangle)g(ev)n(en)n(tually)h(en)n(ters)g Fw(E)5 b Ft(.)42 b(This)0 4463 y(will)37 b(solv)n(e)e(our)h(problem:)55 b(w)n(e)36 b(shall)g(de\014ne)h Fw(F)1557 4433 y Fl(0)1617 4463 y Ft(on)f([0)p Fw(;)14 b Ft(1])24 b Fm(\002)g Ft([)p Fm(\000)p Ft(1)p Fw(;)14 b Ft(1])35 b(to)h(coincide)h(with)g Fw(F)0 4562 y Ft(outside)f(of)g Fw(E)41 b Ft(and)35 b(to)h(b)r(e)h(a)e (piecewise)h(a\016ne)f(and)h(expanding)f(map)h(on)g Fw(E)41 b Ft(with)36 b(v)-5 b(alues)0 4662 y(inside)26 b Fw(R)q Ft(\(0)p Fw(;)14 b(M)23 b Ft(+)14 b(1\).)37 b(Th)n(us,)26 b Fx(ev)m(ery)h Ft(orbit)e(of)h Fw(F)1568 4632 y Fl(0)1617 4662 y Ft(will)g(en)n(ter)f(the)i(rectangles)d(and)i(therefore)0 4762 y(b)r(e)33 b(statistically)e(attracted)h(to)g Fw(p)f Ft(=)g(\(0)p Fw(;)14 b Ft(0\),)33 b(excluding)f(the)h(existence)f(of)g (an)n(y)g(a.c.i.p.)50 b(\(or)0 4861 y(an)n(y)27 b(in)n(v)-5 b(arian)n(t)26 b(probabilit)n(y)h(measure)f(indeed\).)100 5031 y(Let)h Fw(E)309 5043 y Fn(0)370 5031 y Ft(=)c([0)p Fw(;)14 b Ft(1])j Fm(\002)h Ft([)p Fm(\000)p Ft(1)p Fw(;)c Ft(1])j Fm(n)h Ft(\([0)p Fw(;)c(e)1207 5001 y Fl(\000)p Fv(\017)1290 5031 y Ft(])19 b Fm(\002)f Ft([0)p Fw(;)c(e)1556 5001 y Fl(\000)p Fv(\017)1639 5031 y Ft(]\).)p eop %%Page: 4 4 4 3 bop 0 42 a Fr(4)1170 b(J)1247 25 y(\023)1241 42 y(ER)1351 25 y(^)1341 42 y(OME)30 b(BUZZI)100 241 y Ft(Consider)22 b(the)i(pre-images)d(in)j([)p Fw(e)1147 211 y Fl(\000)p Fv(\017)1230 241 y Fw(;)14 b Ft(1])c Fm(\002)g Ft([0)p Fw(;)k(e)1558 211 y Fl(\000)p Fv(\017)1640 241 y Ft(])24 b(of)f(the)h(higher)e(rectangles.)34 b(Mak)n(e)23 b(these)0 340 y(rectangles)h(in)n(to)h(a)f(strip)h Fw(S)5 b Ft(,)26 b(as)e(pictured)i(in)f(\014gure)f(2)h(taking)g(v)n(ertically)f(some)g (margin)g(\(i.e.,)0 443 y(enlarge)g(the)i(rectangles)e(b)n(y)h (replacing)f(the)i(horizon)n(tal)d(side)j(of)f Fw(R)q Ft(\()p Fw(\015)2206 413 y Fv(m)p Fn(\()p Fv(`)p Fn(\))2362 443 y Fm(\000)14 b Fw(`;)g(m)p Ft(\()p Fw(`)p Ft(\)\))25 b(b)n(y)g Fw(J)2901 455 y Fv(`)2933 443 y Ft(\).)0 543 y(Eac)n(h)k(of)i(the)g(t)n(w)n(o)e(lateral)h(b)r(oundaries)f(of)i(the)g (strip)f(can)g(b)r(e)h(assumed)f(to)g(b)r(e)h(a)f Fw(C)2704 513 y Fv(r)2772 543 y Ft(curv)n(e:)0 642 y(it)e(has)f(essen)n(tially)g (the)h(same)f(shap)r(e)g(as)g(the)h(discon)n(tin)n(uit)n(y)f(line)h Fw(y)e Ft(=)c Fw(f)9 b Ft(\()p Fw(x)p Ft(\).)100 742 y(De\014ne)37 b Fw(E)42 b Ft(to)37 b(b)r(e)g Fw(E)763 754 y Fn(0)838 742 y Ft(min)n(us)g(the)g(strip)g Fw(S)5 b Ft(.)64 b(The)37 b(b)r(oundary)f(of)h Fw(E)42 b Ft(is)37 b Fw(C)2517 712 y Fv(r)2554 742 y Ft(.)65 b(The)37 b(strip)0 842 y(con)n(taining)28 b(all)h(the)g(rectangles)f(in)h Fw(E)1215 854 y Fn(0)1281 842 y Ft(\(i.e.,)h Fw(R)q Ft(\()p Fw(\015)1616 812 y Fv(m)1698 842 y Fm(\000)19 b Ft(1)p Fw(;)14 b(m)p Ft(\),)29 b Fw(m)c(>)g(M)9 b Ft(\),)30 b Fw(E)k Ft(do)r(es)29 b(not)g(meet)0 941 y(an)n(y)e(rectangle.)35 b(It)28 b(remains)f(to)h(see)f(that)h(an)n(y)f(orbit)g(of)g Fw(F)40 b Ft(ev)n(en)n(tually)27 b(en)n(ters)f Fw(E)5 b Ft(.)100 1041 y(First,)31 b(observ)n(e)e(that)i(on)f(the)h(complemen) n(t)g(of)f Fw(E)1700 1053 y Fn(0)1738 1041 y Ft(,)i Fw(F)42 b Ft(m)n(ultiplies)31 b(the)g Fw(y)s Ft(-co)r(ordinate)e(b)n(y)0 1141 y Fw(e)39 1110 y Fv(\017)70 1141 y Ft(.)37 b(Th)n(us,)28 b(an)n(y)f(p)r(oin)n(t)g(ev)n(en)n(tually)g(en)n(ters)g Fw(E)1438 1153 y Fn(0)1475 1141 y Ft(.)100 1240 y(Consider)j(a)h(p)r (oin)n(t,)h(whic)n(h)f(nev)n(er)f(en)n(ters)g(the)i(rectangles.)46 b(W)-7 b(e)31 b(ha)n(v)n(e)f(just)i(seen)f(that)g(it)0 1340 y(en)n(ters)i Fw(E)310 1352 y Fn(0)348 1340 y Ft(.)55 b(If)34 b(it)g(do)r(es)g(not)f(en)n(ter)h Fw(E)5 b Ft(,)35 b(this)f(means)g(that)g(it)g(en)n(ters)f(the)h(strip)f Fw(S)5 b Ft(.)56 b(A)n(t)34 b(this)0 1439 y(time,)28 b(the)g(p)r(oin)n(t)g(m)n(ust)g(b)r(e)g(in)g(the)f(strip)h(b)r(et)n(w)n (een)f(t)n(w)n(o)g(higher)g(rectangles.)100 1539 y(If)c(it)g(is)g(far)f (from)h(either)f(rectangles,)h(in)g(the)g(sense)g(that)g(it)g(do)r(es)f (not)h(b)r(elong)g(to)f(a)h(column)0 1639 y(of)h(the)g(form)g Fw(J)469 1651 y Fv(`)513 1639 y Fm(\002)11 b Ft([0)p Fw(;)j Ft(1],)23 b(then)i(it)f(will)h(ev)n(en)n(tually)e(b)r(e)h(mapp)r (ed)h(in)n(to)f([)p Fw(e)2263 1609 y Fl(\000)p Fv(\017)2346 1639 y Fw(;)14 b Ft(1])d Fm(\002)g Ft([)p Fm(\000)p Ft(1)p Fw(;)j Ft(1])d Fm(n)g Fw(J)2877 1651 y Fn(1)2924 1639 y Fm(\002)0 1738 y Ft([)p Fm(\000)p Ft(1)p Fw(;)j Ft(1].)36 b(But)27 b(this)h(is)g(a)f(subset)h(of)f Fw(E)5 b Ft(.)0 1853 y 14917438 16260004 394690 1118289 25457541 28680847 startTexFig 0 1853 a %%BeginDocument: strip.epsf %!PS-Adobe-2.0 EPSF-1.2 %%Title: strip.epsf %%Creator: Canvas 3.0 %%For: Salle Info 3ième %%CreationDate: Mar 30 mai 2000 17:09 %%BoundingBox:6 17 387 436 %%DocumentProcSets: CanvasDict %%DocumentSuppliedProcSets: CanvasDict %%Copyright ©1988-91 Deneba Systems, Inc. - All Rights Reserved Worldwide %%DocumentFonts: Helvetica %%+ Symbol %%+ BrushScriptMT %%DocumentNeededFonts: Helvetica %%+ Symbol %%+ BrushScriptMT %%EndComments %%BeginProcSet:CanvasDict /CanvasDict where not{/CanvasDict 250 dict def}{pop}ifelse CanvasDict begin systemdict/setpacking known{/origpack currentpacking def true setpacking}if /bdf{bind def}bind def /xdf{exch bind def}bdf /min{2 copy gt{exch}if pop}bdf /edf{exch def}bdf /max{2 copy lt{exch}if pop}bdf /cvmtx matrix def /tpmx matrix def /currot 0 def /rotmtx matrix def /origmtx matrix def /cvangle{360 exch sub 90 add 360 mod}bdf /setrot{/currot edf rotmtx currentmatrix pop 2 copy translate currot rotate neg exch neg exch translate}bdf /endrot{rotmtx setmatrix}bdf /i systemdict/image get def/T true def/F false def/dbg F def /ncolors 0 def/st0 ()def/st1 ()def/proc0 {}def /penh 1 def/penv 1 def/penv2 0 def/penh2 0 def/samplesize 0 def/width 0 def/height 0 def /setcmykcolor where not{/setcmykcolor{/b edf 3{b add 1.0 exch sub 0.0 max 1.0 min 3 1 roll}repeat systemdict begin setrgbcolor end}bdf}{pop}ifelse /doeoclip{closepath{eoclip}stopped{currentflat dup 2 mul setflat eoclip setflat}if}bdf /SpaceExtra 0 def/LetterSpace 0 def/StringLength 0 def/NumSpaces 0 def/JustOffset 0 def /f0/fill load def /s0{1 setlinewidth cvmtx currentmatrix pop penh penv scale stroke cvmtx setmatrix}bdf /f1{_bp _fp impat}def /s1{cvmtx currentmatrix pop 1 setlinewidth penh penv scale {strokepath}stopped{currentflat dup 2 mul setflat strokepath setflat}if _bp cvmtx setmatrix _fp impat}def /filltype 0 def /stroketype 0 def /f{filltype 0 eq{f0}{f1}ifelse}bdf /s{stroketype 0 eq{s0}{s1}ifelse}bdf /_fp{}def /_bp{}def /_fg 1 def /_pg 0 def /_bkg 1 def /_frg 0 def /_frgb 3 array def /_frrgb [0 0 0] def /_fcmyk 4 array def /_frcmyk [0 0 0 1] def /_prgb 3 array def /_pcmyk 4 array def /_bkrgb [1 1 1] def /_bkcmyk [0 0 0 0] def /fg{/_fg exch def /filltype 0 def/fills{_fg setgray}def}def /frgb{_frgb astore pop /filltype 0 def/fills{_frgb aload pop setrgbcolor}def}def /fcmyk{_fcmyk astore pop /filltype 0 def/fills{_fcmyk aload pop setcmykcolor}def}def /pg{/_pg exch def /stroketype 0 def/pens{_pg setgray}def}def /prgb{_prgb astore pop /stroketype 0 def/pens{_prgb aload pop setrgbcolor}def}def /pcmyk{_pcmyk astore pop /stroketype 0 def/pens{_pcmyk aload pop setcmykcolor}def}def /fpat{/fstr edf/filltype 1 def/fills{/patstr fstr def}bdf}bdf /ppat{/sstr edf/stroketype 1 def/pens{/patstr sstr def}bdf}bdf /bkg{ /_bkg exch def /_bp{gsave _bkg setgray fill grestore}def}def /bkrgb{_bkrgb astore pop/_bp{gsave _bkrgb aload pop setrgbcolor fill grestore}def}def /bkcmyk{_bkcmyk astore pop/_bp{gsave _bkcmyk aload pop setcmykcolor fill grestore}def}def /frg{ /_frg exch def /_fp{_frg setgray}def}def /frrgb{_frrgb astore pop/_fp{_frrgb aload pop setrgbcolor}def}def /frcmyk{_frcmyk astore pop/_fp{_frcmyk aload pop setcmykcolor}def}def /icomp{/ncolors edf ncolors 1 gt{/proc0 edf dup dup 0 get ncolors div cvi exch 0 3 -1 roll put 4 -1 roll ncolors div cvi 4 1 roll{proc0 dup/st0 edf 0 exch ncolors exch length dup ncolors sub exch ncolors div cvi string/st1 edf {dup 0 exch dup 1 exch 2 add{st0 exch get add}bind for 3 div ncolors 4 eq{exch dup 3 1 roll 3 add st0 exch get add 255 exch sub dup 0 lt{pop 0}if}if cvi dup 255 gt{pop 255}if exch ncolors div cvi exch st1 3 1 roll put}bind for st1}}if i}bdf /ci {/colorimage where {pop false exch colorimage} {icomp} ifelse}bdf /impat {/cnt 0 def /MySave save def currot 0 ne{currot neg rotate}if clip flattenpath pathbbox 3 -1 roll 8 div floor 8 mul dup/starty edf sub abs 8 div ceiling 8 mul cvi/height edf exch 8 div floor 8 mul dup/startx edf sub abs 8 div ceiling 8 mul cvi/width edf startx starty translate width height scale /height height 8 mul def /st0 width string def width height T [width 0 0 height neg 0 height] {patstr cnt 8 mod get/st1 edf 0 1 st0 length 1 sub dup 0 le{pop 1}if {st0 exch st1 put}bind for/cnt cnt 1 add def st0}bind imagemask MySave restore newpath}bdf /cm{/ncolors edf translate scale/height edf/colorimage where {pop} {ncolors mul}ifelse/width edf /tbitstr width string def width height 8 [width 0 0 height neg 0 height] {currentfile tbitstr readhexstring pop}bind ncolors dup 3 eq {ci}{icomp}ifelse}bdf /im{translate scale /height edf /width edf /tbitstr width 7 add 8 div cvi string def width height 1 [width 0 0 height neg 0 height] {currentfile tbitstr readhexstring pop}bind i}bdf /imk{/invFlag edf translate scale /height edf /width edf /tbitstr width 7 add 8 div cvi string def width height invFlag [width 0 0 height neg 0 height] {currentfile tbitstr readhexstring pop}bind imagemask}bdf /BeginEPSF {/MySave save def /dict_count countdictstack def /op_count count 1 sub def userdict begin /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath /languagelevel where {pop languagelevel 1 ne{false setstrokeadjust false setoverprint}if}if }bdf /EndEPSF {count op_count sub {pop}repeat countdictstack dict_count sub {end}repeat MySave restore}bdf /rectpath {/cv_r edf/cv_b edf/cv_l edf/cv_t edf cv_l cv_t moveto cv_r cv_t lineto cv_r cv_b lineto cv_l cv_b lineto cv_l cv_t lineto closepath}bdf /setpen{/penh edf/penv edf/penv2 penv 2 div def/penh2 penh 2 div def}bdf /dostroke{not pens 1.0 currentgray ne or {s}{newpath}ifelse}bdf /dodashfill{not fills 1.0 currentgray ne or {gsave f grestore gsave [] 0 setdash stroketype/stroketype filltype def s/stroketype edf grestore}{newpath}ifelse}bdf /dofill{not fills 1.0 currentgray ne or {f}{newpath}ifelse}bdf /dofillsave{not fills 1.0 currentgray ne or {gsave f grestore}if}bdf /doline{not pens 1.0 currentgray ne or {filltype/filltype stroketype def f/filltype edf}{newpath}ifelse}bdf /spx{SpaceExtra 0 32 4 -1 roll widthshow}bdf /lsx{SpaceExtra 0 32 LetterSpace 0 6 -1 roll awidthshow}bdf /Rjust{stringwidth pop JustOffset exch sub /JustOffset edf}bdf /Cjust{stringwidth pop 2 div JustOffset exch sub /JustOffset edf}bdf /adjfit{stringwidth pop LetterSpace StringLength 1 sub mul add SpaceExtra NumSpaces mul add dup /pw edf JustOffset exch sub dup /wdif edf StringLength div dup abs 1.0 gt{pop 0}if LetterSpace add /LetterSpace edf}bdf /ulb{currentpoint pop /underlinpt edf}bdf /ule{gsave currentpoint newpath moveto currentfont dup /ft1 known{dup /ft1 get begin /FontMatrix get FontMatrix tpmx concatmatrix pop} {begin FontMatrix tpmx copy pop}ifelse FontInfo begin UnderlinePosition UnderlineThickness end end dup tpmx dtransform pop setlinewidth dup tpmx dtransform pop 0 exch rmoveto underlinpt currentpoint pop sub 0 rlineto stroke grestore}bdf /fittext{ /SpaceExtra edf /LetterSpace edf /StringLength edf /NumSpaces edf /JustOffset edf not 1 currentgray ne or {dup {ulb}if exch dup adjfit lsx {ule}if}{pop pop}ifelse}bdf /cvRecFont{/encod edf FontDirectory 2 index known{cleartomark}{findfont dup length 1 add dict begin {1 index/FID ne{def}{pop pop}ifelse}forall encod{/Encoding CVvec def}if currentdict end definefont cleartomark}ifelse}bdf /wrk1 ( ) def/wdict 16 dict def /Work75 75 string def /Nmk{Work75 cvs dup}bdf /Npt{put cvn}bdf /dhOdh{Nmk 2 79 Npt}bdf /dhodh{Nmk 2 111 Npt}bdf /dhSdh{Nmk 2 83 Npt}bdf /sfWidth{gsave 0 0 moveto 0 0 lineto 0 0 lineto 0 0 lineto closepath clip stringwidth grestore}bdf /MakOF{dup dhodh FontDirectory 1 index known{exch pop}{exch findfont dup length 1 add dict begin {1 index/FID ne 2 index /UniqueID ne and{def}{pop pop}ifelse}forall /PaintType 2 def /StrokeWidth .24 1000 mul ftSize div dup 12 lt{pop 12}if def dup currentdict end definefont pop}ifelse}bdf /fts{dup/ftSize edf}def /mkFT{/tempFT 11 dict def tempFT begin /FontMatrix [1 0 0 1 0 0] def/FontType 3 def FontDirectory 3 index get /Encoding get/Encoding exch def /proc2 edf/ft2 exch findfont def/ft1 exch findfont def/FontBBox [0 0 1 1] def /BuildChar{wdict begin/chr edf/ftdt edf/chrst wrk1 dup 0 chr put def ftdt/proc2 get exec end}def end tempFT definefont pop}bdf /OLFt{dup dhOdh FontDirectory 1 index known{exch pop} {dup 3 -1 roll dup MakOF {outproc} mkFT}ifelse}bdf /mshw{moveto show}bdf /outproc{ftdt/ft1 get setfont gsave chrst sfWidth grestore setcharwidth dblsh}bdf /dblsh{currentgray 1 setgray chrst 0 0 mshw setgray ftdt/ft2 get setfont chrst 0 0 mshw}bdf /ShadChar{ftdt/ft1 get setfont gsave chrst sfWidth 1 index 0 ne{exch .05 add exch}if grestore setcharwidth chrst .06 0 mshw 0 .05 translate dblsh}bdf /ShFt{dup dhSdh FontDirectory 1 index known{exch pop} {dup 3 -1 roll dup MakOF {ShadChar} mkFT}ifelse}bdf /LswUnits{72 75 div dup scale}bdf /erasefill{_bp}def /CVvec 256 array def /NUL/SOH/STX/ETX/EOT/ENQ/ACK/BEL/BS/HT/LF/VT/FF/CR/SO/SI/DLE/DC1/DC2/DC3/DC4/NAK/SYN/ETB/CAN/EM/SUB/ESC/FS/GS/RS/US CVvec 0 32 getinterval astore pop CVvec 32/Times-Roman findfont/Encoding get 32 96 getinterval putinterval CVvec dup 39/quotesingle put 96/grave put /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/blank/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand/Acircumflex/Ecircumflex/Aacute /Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex /apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron CVvec 128 128 getinterval astore pop end %%EndProcSet %%BeginSetup CanvasDict begin 0 setlinecap 0 setlinejoin 4 setmiterlimit /currot 0 def origmtx currentmatrix pop [] 0 setdash 1 1 setpen 1 fg 0 pg 0 frg 1 bkg newpath /dbg F def %%EndSetup % ---- Object #1:5 Obj Type: 3 2 setlinecap gsave newpath 30 434 moveto 30 18.5000 lineto F dostroke grestore % ---- Object #2:7 Obj Type: 4 0 setlinecap 410 56 386 95 rectpath F dofillsave F dostroke % ---- Object #3:8 Obj Type: 4 0 setlinecap 353 58 339 87 rectpath F dofillsave F dostroke % ---- Object #4:9 Obj Type: 4 0 setlinecap 304 50 293 68 rectpath F dofillsave F dostroke % ---- Object #5:10 Obj Type: 4 0 setlinecap 265 47 254 58 rectpath F dofillsave F dostroke % ---- Object #6:11 Obj Type: 4 0 setlinecap 227 43 219 51 rectpath F dofillsave F dostroke % ---- Object #7:12 Obj Type: 4 0 setlinecap 200 39 192 44 rectpath F dofillsave F dostroke % ---- Object #8:13 Obj Type: 4 0 setlinecap 177 36 173 41 rectpath F dofillsave F dostroke % ---- Object #9:14 Obj Type: 4 0 setlinecap 161 35 157 37 rectpath F dofillsave F dostroke % ---- Object #10:16 Obj Type: 10 0 setlinecap 56 386 moveto 57 369.5000 57 369.5000 58 353 curveto F dofillsave F dostroke % ---- Object #11:17 Obj Type: 10 0 setlinecap 95 387 moveto 91 370.5000 91 370.5000 87 354 curveto F dofillsave F dostroke % ---- Object #12:18 Obj Type: 10 0 setlinecap 58 339 moveto 54 320.5000 54 320.5000 50 302 curveto F dofillsave F dostroke % ---- Object #13:19 Obj Type: 3 2 setlinecap gsave newpath 69 304 moveto 86.5000 339 lineto F dostroke grestore % ---- Object #14:20 Obj Type: 3 2 setlinecap gsave newpath 50 293.5000 moveto 47 265 lineto F dostroke grestore % ---- Object #15:21 Obj Type: 3 2 setlinecap gsave newpath 68 293 moveto 59 265 lineto F dostroke grestore % ---- Object #16:22 Obj Type: 3 2 setlinecap gsave newpath 47 255 moveto 44 227 lineto F dostroke grestore % ---- Object #17:23 Obj Type: 3 2 setlinecap gsave newpath 51 227 moveto 57.5000 253.5000 lineto F dostroke grestore % ---- Object #18:24 Obj Type: 3 2 setlinecap gsave newpath 43 219 moveto 39 200 lineto F dostroke grestore % ---- Object #19:25 Obj Type: 3 2 setlinecap gsave newpath 50.5000 219 moveto 43.5000 200 lineto F dostroke grestore % ---- Object #20:26 Obj Type: 3 2 setlinecap gsave newpath 38.5000 192 moveto 36 177 lineto F dostroke grestore % ---- Object #21:27 Obj Type: 3 2 setlinecap gsave newpath 44 192 moveto 40.5000 177 lineto F dostroke grestore % ---- Object #22:28 Obj Type: 3 2 setlinecap gsave newpath 35.5000 172.5000 moveto 35.5000 161.5000 lineto F dostroke grestore % ---- Object #23:29 Obj Type: 3 2 setlinecap gsave newpath 41 173 moveto 37 160.5000 lineto F dostroke grestore % ---- Object #24:30 Obj Type: 3 2 setlinecap gsave newpath 35.5000 156 moveto 34.5000 142.5000 lineto F dostroke grestore % ---- Object #25:15 Obj Type: 3 2 setlinecap gsave newpath 34 142 moveto 33 127.5000 lineto F dostroke grestore % ---- Object #26:31 Obj Type: 3 2 setlinecap gsave newpath 32 126.5000 moveto 32 110 lineto F dostroke grestore % ---- Object #27:32 Obj Type: 3 2 setlinecap gsave newpath 31.5000 109.5000 moveto 31.5000 88 lineto F dostroke grestore % ---- Object #28:33 Obj Type: 3 2 setlinecap gsave newpath 31.5000 87.5000 moveto 30.5000 72 lineto F dostroke grestore % ---- Object #29:34 Obj Type: 3 2 setlinecap gsave newpath 141.5000 435 moveto 141.5000 42 lineto F dostroke grestore % ---- Object #30:35 Obj Type: 3 2 setlinecap gsave newpath 8.5000 70.5000 moveto 141 70.5000 lineto F dostroke grestore % ---- Object #31:36 Obj Type: 3 2 setlinecap gsave newpath 56 402 moveto 95.5000 402 lineto F dostroke grestore % ---- Object #32:37 Obj Type: 3 2 setlinecap gsave newpath 58 349.5000 moveto 87 349.5000 lineto F dostroke grestore % ---- Object #33:38 Obj Type: 3 2 setlinecap gsave newpath 50 300.5000 moveto 68 300.5000 lineto F dostroke grestore % ---- Object #34:39 Obj Type: 3 2 setlinecap gsave newpath 47 262 moveto 58 262 lineto F dostroke grestore % ---- Object #35:40 Obj Type: 3 2 setlinecap gsave newpath 43.5000 224 moveto 50 224 lineto F dostroke grestore % ---- Object #36:41 Obj Type: 3 2 setlinecap gsave newpath 39 197.5000 moveto 44 197.5000 lineto F dostroke grestore % ---- Object #37:42 Obj Type: 3 2 setlinecap gsave newpath 36.1250 175.5000 moveto 40.8750 175.5000 lineto F dostroke grestore % ---- Object #38:43 Obj Type: 3 2 setlinecap gsave newpath 37 159 moveto 35 159 lineto F dostroke grestore % ---- Object #39:44 Obj Type: 3 2 setlinecap gsave newpath 81.0955 304.1333 moveto 81.1922 303.9477 lineto 81.3757 303.5713 lineto 81.5460 303.1888 lineto 81.7031 302.8000 lineto 81.8464 302.4064 lineto 81.9757 302.0081 lineto 82.0912 301.6056 lineto 82.1925 301.1993 lineto 82.2796 300.7891 lineto 82.3523 300.3768 lineto 82.4106 299.9621 lineto 82.4544 299.5457 lineto 82.4836 299.1279 lineto 82.4982 298.7095 lineto 82.4982 298.2905 lineto 82.4836 297.8721 lineto 82.4544 297.4543 lineto 82.4106 297.0379 lineto 82.3523 296.6232 lineto 82.2796 296.2108 lineto 82.2378 296.0050 lineto 70.5000 298.5000 lineto 81.0955 304.1333 lineto closepath F doline grestore gsave newpath 278 327 moveto 82.1407 300.0988 lineto F dostroke grestore % ---- Object #40:46 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 12 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 285 323 moveto (F) show 0 setgray 0 setgray 291 327 moveto (-1) F F 12.5449 0 2 0 0 fittext 0 setgray 0 setgray 303 323 moveto (R\() F F 12.6328 0 2 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 12 fts /|___Symbol findfont exch scalefont setfont 0 setgray 315 323 moveto (g) show 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 12 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 319 327 moveto (m\() F F 16.0898 0 2 0 0 fittext 0 setgray mark /|___BrushScriptMT /BrushScriptMT T cvRecFont 12 fts /|___BrushScriptMT findfont exch scalefont setfont 0 setgray 335 327 moveto (l) show 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 12 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 337 327 moveto (\)) show 0 setgray 0 setgray 342 323 moveto (-l,m\() F F 27.0937 0 5 0 0 fittext 0 setgray mark /|___BrushScriptMT /BrushScriptMT T cvRecFont 12 fts /|___BrushScriptMT findfont exch scalefont setfont 0 setgray 369 323 moveto (l) show 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 12 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 371 323 moveto (\)\)) F F 10.7227 0 2 0 0 fittext restore % ---- Object #41:45 Obj Type: 3 1 1 setpen 2 setlinecap gsave newpath 56 393.5000 moveto 94.5000 393.5000 lineto F dostroke grestore % ---- Object #42:48 Obj Type: 3 2 setlinecap gsave newpath 58 343 moveto 87.5000 343 lineto F dostroke grestore % ---- Object #43:47 Obj Type: 3 2 setlinecap gsave newpath 50 296.5000 moveto 68 296.5000 lineto F dostroke grestore % ---- Object #44:49 Obj Type: 3 2 setlinecap gsave newpath 47 257.5000 moveto 58 257.5000 lineto F dostroke grestore % ---- Object #45:50 Obj Type: 3 2 setlinecap gsave newpath 43 221 moveto 50.7500 221 lineto F dostroke grestore % ---- Object #46:51 Obj Type: 3 2 setlinecap gsave newpath 39.2500 195 moveto 44 195 lineto F dostroke grestore % ---- Object #47:52 Obj Type: 3 2 setlinecap gsave newpath 36.2500 174.2500 moveto 40.5000 174.2500 lineto F dostroke grestore % ---- Object #48:53 Obj Type: 3 2 setlinecap gsave newpath 35.5000 158.2500 moveto 36.7500 158.2500 lineto F dostroke grestore % ---- Object #49:54 Obj Type: 3 2 setlinecap gsave newpath 49.5000 304 moveto 24 304 lineto F dostroke grestore % ---- Object #50:55 Obj Type: 3 2 setlinecap gsave newpath 50 293 moveto 24.5000 293 lineto F dostroke grestore % ---- Object #51:56 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Helvetica /Helvetica T cvRecFont 12 fts /|___Helvetica findfont exch scalefont setfont 0 setgray 12 295 moveto (J) show 0 setgray mark /|___BrushScriptMT /BrushScriptMT T cvRecFont 12 fts /|___BrushScriptMT findfont exch scalefont setfont 0 setgray 17 291 moveto (l) show restore origmtx setmatrix systemdict /setpacking known {origpack setpacking} if end showpage %%EndDocument: %%EndDocument endTexFig 1331 4013 a Ft(Figure)27 b(2.)100 4198 y(Otherwise)32 b(the)h(p)r(oin)n(t)h(is)f(near)f(the)i(highest)f(rectangle)f Fw(R)q Ft(\()p Fw(\015)2094 4168 y Fv(m)2178 4198 y Fm(\000)22 b Fw(`;)14 b(m)p Ft(\))33 b(in)g(the)h(column)0 4298 y Fw(J)46 4310 y Fv(`)98 4298 y Fm(\002)20 b Ft([0)p Fw(;)14 b Ft(1].)44 b(It)31 b(is)f(then)h(easy)e(to)h(see)g(that,)i (under)e(iteration)f(of)i Fw(F)12 b Ft(,)31 b(the)f(p)r(oin)n(t)h(will) f(remain)0 4397 y(on)g(the)g(side)g(of)g(the)g(rectangle.)42 b(Hence,)31 b(when)f(it)h(will)f(come)f(bac)n(k)g(to)h(column)g Fw(J)2658 4409 y Fn(1)2715 4397 y Fm(\002)20 b Ft([0)p Fw(;)14 b Ft(1],)0 4497 y(it)28 b(will)g(b)r(e)g(outside)f(the)h(strip) g Fw(S)k Ft(and)27 b(therefore)g(in)h Fw(E)5 b Ft(.)100 4597 y(W)-7 b(e)32 b(ha)n(v)n(e)f(seen)h(that)g(all)g(p)r(oin)n(ts)f (not)h(en)n(tering)g(the)g(rectangles)f(are)g(ev)n(en)n(tually)g(caugh) n(t)0 4696 y(in)d Fw(E)5 b Ft(.)37 b(This)27 b(concludes)h(the)g (construction)e(of)i(the)g(map)f(with)h(no)g(a.c.i.p.)83 b Fe(\003)1011 4882 y Fu(Infinitel)-6 b(y)31 b(many)f(a.c.i.p.)100 5031 y Ft(W)-7 b(e)24 b(start)f(againg)f(from)h(Tsujii's)h(map)f Fw(F)35 b Ft(:)23 b([0)p Fw(;)14 b Ft(1])d Fm(\002)g Ft([)p Fm(\000)p Ft(1)p Fw(;)j Ft(1])20 b Fm(!)j Ft([0)p Fw(;)14 b Ft(1])d Fm(\002)g Ft([)p Fm(\000)p Ft(1)p Fw(;)j Ft(1].)32 b(This)23 b(time)p eop %%Page: 5 5 5 4 bop 139 42 a Fr(UNIF)n(ORML)-6 b(Y)30 b(EXP)-6 b(ANDING)31 b Fq(C)1129 18 y Fp(r)1194 42 y Fr(MAP)f(WITH)h(NO)g(OR)f(INFINITEL)-6 b(Y)32 b(MANY)d(A.C.I.P)-6 b(.)103 b(5)0 241 y Ft(w)n(e)30 b(mo)r(dify)h(the)g(cutting)f(\(i.e.,)i(functions)e Fw(f)39 b Ft(and)31 b Fw(\021)s Ft(\))g(so)e(that,)j(instead)e(of)g(ha)n(ving)f (a)h(single)0 340 y(sequence)35 b(of)g(rectangles,)h(one)e(mapp)r(ed)i (in)n(to)f(the)h(next,)h(w)n(e)e(shall)g(ha)n(v)n(e)f(in\014nitely)h (man)n(y)0 440 y(cycles)27 b(of)h(rectangles,)e(eac)n(h)h(supp)r (orting)g(an)g(a.c.i.p.)100 540 y(Fix)g Fw(\015)h Ft(=)23 b(2)p Fw(r)r Ft(,)28 b(0)22 b Fw(<)h(\017)g(<)f Ft(\(1)d Fm(\000)f Fw(\015)1059 510 y Fl(\000)p Fn(1)1147 540 y Ft(\))c(log)g(2)p Fw(=)p Ft(\(1)k(+)g Fw(\015)5 b Ft(\).)37 b(Set)28 b Fw(M)36 b Ft(so)27 b(large)f(that)i Fw(\017\015)2540 510 y Fv(M)2636 540 y Fw(>)23 b Ft(1000.)100 639 y(F)-7 b(or)28 b(eac)n(h)g(ev)n(en)h(in)n(teger)f Fw(m)d Fm(\025)g Fw(M)9 b Ft(,)29 b(w)n(e)g(shall)f(ha)n(v)n(e)g(the)i(follo)n(wing)e (cycle:)39 b(the)29 b(rectangles)0 739 y Fw(R)q Ft(\(0)p Fw(;)14 b(m)p Ft(\))p Fw(;)g(R)q Ft(\(1)p Fw(;)g(m)p Ft(\))p Fw(;)g(:)g(:)g(:)f(;)h(R)q Ft(\()p Fw(\015)925 709 y Fv(m)1008 739 y Fm(\000)21 b Ft(1)p Fw(;)14 b(m)p Ft(\))p Fw(;)g(R)q Ft(\(0)p Fw(;)g(m)20 b Ft(+)g(1\))p Fw(;)14 b(:)g(:)g(:)g(;)g(R)q Ft(\()p Fw(\015)2071 709 y Fv(m)p Fn(+1)2238 739 y Fm(\000)21 b Ft(1)p Fw(;)14 b(m)20 b Ft(+)h(1\))31 b(are)g(eac)n(h)0 839 y(mapp)r(ed)d(in)n(to)f (the)h(next)g(one)f(\(the)i(last)e(one)g(b)r(eing)h(mapp)r(ed)g(in)n (to)f(the)h(\014rst)f(one\).)100 938 y(This)j(is)g(represen)n(ted)g(in) g(Figure)g(3,)h(together)f(with)h(the)f(necessary)f(cutting.)46 b(The)31 b(rect-)0 1038 y(angles)42 b Fw(R)q Ft(\()p Fw(k)s(;)14 b(m)p Ft(\))43 b(for)g(0)48 b Fm(\024)g Fw(k)k(<)d(\015) 1195 1008 y Fv(m)1286 1038 y Fm(\000)28 b Ft(2)p Fw(\015)1469 1008 y Fv(m)p Fl(\000)p Fn(2)1660 1038 y Ft(and)43 b(the)g(rectangles)f Fw(R)q Ft(\()p Fw(k)s(;)14 b(m)28 b Ft(+)g(1\))43 b(for)0 1137 y Fw(\015)48 1107 y Fv(m)p Fn(+1)220 1137 y Fm(\000)24 b Ft(2)p Fw(\015)399 1107 y Fv(m)500 1137 y Fm(\024)39 b Fw(k)j(<)d(\015)841 1107 y Fv(m)p Fn(+1)1013 1137 y Fm(\000)24 b Fw(\015)1150 1107 y Fv(m)1250 1137 y Ft(are)36 b(cut)i(in)g(the)f(middle)h(b)n(y)f(a)g(horizon)n(tal)e(segmen)n(t)0 1237 y(whic)n(h)c(is)g(part)g(of)g(the)h(discon)n(tin)n(uit)n(y)e(line) i Fw(y)f Ft(=)e Fw(f)9 b Ft(\()p Fw(x)p Ft(\).)48 b(What)32 b(is)f(ab)r(o)n(v)n(e)f(the)h(discon)n(tin)n(uit)n(y)0 1337 y(line)24 b(is)g(pushed)h(do)n(wn)e(b)n(y)h(half)h(the)f(heigh)n (t)g(of)g(the)h(rectangle.)34 b(In)25 b(this)f(w)n(a)n(y)f(b)r(oth)i (upp)r(er)f(and)0 1436 y(lo)n(w)n(er)31 b(halv)n(es)g(of)h(the)h (rectangle)e(ha)n(v)n(e)g(the)h(same)g(image.)50 b(Observ)n(e)30 b(that)j(in)f(eac)n(h)g(column)0 1536 y Fw(J)46 1548 y Fv(`)96 1536 y Fm(\002)18 b Ft([0)p Fw(;)c Ft(1])27 b(w)n(e)g(do)h(this)g(at)f(most)g(once.)100 1636 y(W)-7 b(e)27 b(realize)e(this)i(cutting)g(in)g(the)g(same)f(w)n(a)n(y)f(as)h (Tsujii)h(b)n(y)g(making)f(bumps)h(in)g(the)g(func-)0 1735 y(tions)f Fw(f)35 b Ft(and)27 b Fw(\021)s Ft(.)36 b(T)-7 b(o)27 b(ensure)e(that)i(w)n(e)f(get)h(globally)e Fw(C)1734 1705 y Fv(r)1797 1735 y Ft(functions)i(it)g(is)f(enough)g(to) g(see)h(that)0 1835 y(the)h(heigh)n(t)f Fw(h)h Ft(and)f(the)h(width)h Fw(w)h Ft(of)d(these)h(bumps)g(satisfy:)37 b Fw(h=w)2117 1805 y Fv(r)2176 1835 y Fm(!)23 b Ft(0)28 b(as)f Fw(m)c Fm(!)g(1)p Ft(.)0 1952 y 22376157 10516787 328908 -328908 49138974 22694707 startTexFig 0 1952 a %%BeginDocument: cycle.epsf %!PS-Adobe-2.0 EPSF-1.2 %%Title: cycle.epsf %%Creator: Canvas 3.0 %%For: Salle Info 3ième %%CreationDate: Jeu 01 juin 2000 12:20 %%BoundingBox:5 -5 747 345 %%DocumentProcSets: CanvasDict %%DocumentSuppliedProcSets: CanvasDict %%Copyright ©1988-91 Deneba Systems, Inc. - All Rights Reserved Worldwide %%DocumentFonts: TimesNewRomanPSMT %%+ Times-Roman %%+ Symbol %%+ CourierNewPSMT %%DocumentNeededFonts: TimesNewRomanPSMT %%+ Times-Roman %%+ Symbol %%+ CourierNewPSMT %%EndComments %%BeginProcSet:CanvasDict /CanvasDict where not{/CanvasDict 250 dict def}{pop}ifelse CanvasDict begin systemdict/setpacking known{/origpack currentpacking def true setpacking}if /bdf{bind def}bind def /xdf{exch bind def}bdf /min{2 copy gt{exch}if pop}bdf /edf{exch def}bdf /max{2 copy lt{exch}if pop}bdf /cvmtx matrix def /tpmx matrix def /currot 0 def /rotmtx matrix def /origmtx matrix def /cvangle{360 exch sub 90 add 360 mod}bdf /setrot{/currot edf rotmtx currentmatrix pop 2 copy translate currot rotate neg exch neg exch translate}bdf /endrot{rotmtx setmatrix}bdf /i systemdict/image get def/T true def/F false def/dbg F def /ncolors 0 def/st0 ()def/st1 ()def/proc0 {}def /penh 1 def/penv 1 def/penv2 0 def/penh2 0 def/samplesize 0 def/width 0 def/height 0 def /setcmykcolor where not{/setcmykcolor{/b edf 3{b add 1.0 exch sub 0.0 max 1.0 min 3 1 roll}repeat systemdict begin setrgbcolor end}bdf}{pop}ifelse /doeoclip{closepath{eoclip}stopped{currentflat dup 2 mul setflat eoclip setflat}if}bdf /SpaceExtra 0 def/LetterSpace 0 def/StringLength 0 def/NumSpaces 0 def/JustOffset 0 def /f0/fill load def /s0{1 setlinewidth cvmtx currentmatrix pop penh penv scale stroke cvmtx setmatrix}bdf /f1{_bp _fp impat}def /s1{cvmtx currentmatrix pop 1 setlinewidth penh penv scale {strokepath}stopped{currentflat dup 2 mul setflat strokepath setflat}if _bp cvmtx setmatrix _fp impat}def /filltype 0 def /stroketype 0 def /f{filltype 0 eq{f0}{f1}ifelse}bdf /s{stroketype 0 eq{s0}{s1}ifelse}bdf /_fp{}def /_bp{}def /_fg 1 def /_pg 0 def /_bkg 1 def /_frg 0 def /_frgb 3 array def /_frrgb [0 0 0] def /_fcmyk 4 array def /_frcmyk [0 0 0 1] def /_prgb 3 array def /_pcmyk 4 array def /_bkrgb [1 1 1] def /_bkcmyk [0 0 0 0] def /fg{/_fg exch def /filltype 0 def/fills{_fg setgray}def}def /frgb{_frgb astore pop /filltype 0 def/fills{_frgb aload pop setrgbcolor}def}def /fcmyk{_fcmyk astore pop /filltype 0 def/fills{_fcmyk aload pop setcmykcolor}def}def /pg{/_pg exch def /stroketype 0 def/pens{_pg setgray}def}def /prgb{_prgb astore pop /stroketype 0 def/pens{_prgb aload pop setrgbcolor}def}def /pcmyk{_pcmyk astore pop /stroketype 0 def/pens{_pcmyk aload pop setcmykcolor}def}def /fpat{/fstr edf/filltype 1 def/fills{/patstr fstr def}bdf}bdf /ppat{/sstr edf/stroketype 1 def/pens{/patstr sstr def}bdf}bdf /bkg{ /_bkg exch def /_bp{gsave _bkg setgray fill grestore}def}def /bkrgb{_bkrgb astore pop/_bp{gsave _bkrgb aload pop setrgbcolor fill grestore}def}def /bkcmyk{_bkcmyk astore pop/_bp{gsave _bkcmyk aload pop setcmykcolor fill grestore}def}def /frg{ /_frg exch def /_fp{_frg setgray}def}def /frrgb{_frrgb astore pop/_fp{_frrgb aload pop setrgbcolor}def}def /frcmyk{_frcmyk astore pop/_fp{_frcmyk aload pop setcmykcolor}def}def /icomp{/ncolors edf ncolors 1 gt{/proc0 edf dup dup 0 get ncolors div cvi exch 0 3 -1 roll put 4 -1 roll ncolors div cvi 4 1 roll{proc0 dup/st0 edf 0 exch ncolors exch length dup ncolors sub exch ncolors div cvi string/st1 edf {dup 0 exch dup 1 exch 2 add{st0 exch get add}bind for 3 div ncolors 4 eq{exch dup 3 1 roll 3 add st0 exch get add 255 exch sub dup 0 lt{pop 0}if}if cvi dup 255 gt{pop 255}if exch ncolors div cvi exch st1 3 1 roll put}bind for st1}}if i}bdf /ci {/colorimage where {pop false exch colorimage} {icomp} ifelse}bdf /impat {/cnt 0 def /MySave save def currot 0 ne{currot neg rotate}if clip flattenpath pathbbox 3 -1 roll 8 div floor 8 mul dup/starty edf sub abs 8 div ceiling 8 mul cvi/height edf exch 8 div floor 8 mul dup/startx edf sub abs 8 div ceiling 8 mul cvi/width edf startx starty translate width height scale /height height 8 mul def /st0 width string def width height T [width 0 0 height neg 0 height] {patstr cnt 8 mod get/st1 edf 0 1 st0 length 1 sub dup 0 le{pop 1}if {st0 exch st1 put}bind for/cnt cnt 1 add def st0}bind imagemask MySave restore newpath}bdf /cm{/ncolors edf translate scale/height edf/colorimage where {pop} {ncolors mul}ifelse/width edf /tbitstr width string def width height 8 [width 0 0 height neg 0 height] {currentfile tbitstr readhexstring pop}bind ncolors dup 3 eq {ci}{icomp}ifelse}bdf /im{translate scale /height edf /width edf /tbitstr width 7 add 8 div cvi string def width height 1 [width 0 0 height neg 0 height] {currentfile tbitstr readhexstring pop}bind i}bdf /imk{/invFlag edf translate scale /height edf /width edf /tbitstr width 7 add 8 div cvi string def width height invFlag [width 0 0 height neg 0 height] {currentfile tbitstr readhexstring pop}bind imagemask}bdf /BeginEPSF {/MySave save def /dict_count countdictstack def /op_count count 1 sub def userdict begin /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath /languagelevel where {pop languagelevel 1 ne{false setstrokeadjust false setoverprint}if}if }bdf /EndEPSF {count op_count sub {pop}repeat countdictstack dict_count sub {end}repeat MySave restore}bdf /rectpath {/cv_r edf/cv_b edf/cv_l edf/cv_t edf cv_l cv_t moveto cv_r cv_t lineto cv_r cv_b lineto cv_l cv_b lineto cv_l cv_t lineto closepath}bdf /setpen{/penh edf/penv edf/penv2 penv 2 div def/penh2 penh 2 div def}bdf /dostroke{not pens 1.0 currentgray ne or {s}{newpath}ifelse}bdf /dodashfill{not fills 1.0 currentgray ne or {gsave f grestore gsave [] 0 setdash stroketype/stroketype filltype def s/stroketype edf grestore}{newpath}ifelse}bdf /dofill{not fills 1.0 currentgray ne or {f}{newpath}ifelse}bdf /dofillsave{not fills 1.0 currentgray ne or {gsave f grestore}if}bdf /doline{not pens 1.0 currentgray ne or {filltype/filltype stroketype def f/filltype edf}{newpath}ifelse}bdf /spx{SpaceExtra 0 32 4 -1 roll widthshow}bdf /lsx{SpaceExtra 0 32 LetterSpace 0 6 -1 roll awidthshow}bdf /Rjust{stringwidth pop JustOffset exch sub /JustOffset edf}bdf /Cjust{stringwidth pop 2 div JustOffset exch sub /JustOffset edf}bdf /adjfit{stringwidth pop LetterSpace StringLength 1 sub mul add SpaceExtra NumSpaces mul add dup /pw edf JustOffset exch sub dup /wdif edf StringLength div dup abs 1.0 gt{pop 0}if LetterSpace add /LetterSpace edf}bdf /ulb{currentpoint pop /underlinpt edf}bdf /ule{gsave currentpoint newpath moveto currentfont dup /ft1 known{dup /ft1 get begin /FontMatrix get FontMatrix tpmx concatmatrix pop} {begin FontMatrix tpmx copy pop}ifelse FontInfo begin UnderlinePosition UnderlineThickness end end dup tpmx dtransform pop setlinewidth dup tpmx dtransform pop 0 exch rmoveto underlinpt currentpoint pop sub 0 rlineto stroke grestore}bdf /fittext{ /SpaceExtra edf /LetterSpace edf /StringLength edf /NumSpaces edf /JustOffset edf not 1 currentgray ne or {dup {ulb}if exch dup adjfit lsx {ule}if}{pop pop}ifelse}bdf /cvRecFont{/encod edf FontDirectory 2 index known{cleartomark}{findfont dup length 1 add dict begin {1 index/FID ne{def}{pop pop}ifelse}forall encod{/Encoding CVvec def}if currentdict end definefont cleartomark}ifelse}bdf /wrk1 ( ) def/wdict 16 dict def /Work75 75 string def /Nmk{Work75 cvs dup}bdf /Npt{put cvn}bdf /dhOdh{Nmk 2 79 Npt}bdf /dhodh{Nmk 2 111 Npt}bdf /dhSdh{Nmk 2 83 Npt}bdf /sfWidth{gsave 0 0 moveto 0 0 lineto 0 0 lineto 0 0 lineto closepath clip stringwidth grestore}bdf /MakOF{dup dhodh FontDirectory 1 index known{exch pop}{exch findfont dup length 1 add dict begin {1 index/FID ne 2 index /UniqueID ne and{def}{pop pop}ifelse}forall /PaintType 2 def /StrokeWidth .24 1000 mul ftSize div dup 12 lt{pop 12}if def dup currentdict end definefont pop}ifelse}bdf /fts{dup/ftSize edf}def /mkFT{/tempFT 11 dict def tempFT begin /FontMatrix [1 0 0 1 0 0] def/FontType 3 def FontDirectory 3 index get /Encoding get/Encoding exch def /proc2 edf/ft2 exch findfont def/ft1 exch findfont def/FontBBox [0 0 1 1] def /BuildChar{wdict begin/chr edf/ftdt edf/chrst wrk1 dup 0 chr put def ftdt/proc2 get exec end}def end tempFT definefont pop}bdf /OLFt{dup dhOdh FontDirectory 1 index known{exch pop} {dup 3 -1 roll dup MakOF {outproc} mkFT}ifelse}bdf /mshw{moveto show}bdf /outproc{ftdt/ft1 get setfont gsave chrst sfWidth grestore setcharwidth dblsh}bdf /dblsh{currentgray 1 setgray chrst 0 0 mshw setgray ftdt/ft2 get setfont chrst 0 0 mshw}bdf /ShadChar{ftdt/ft1 get setfont gsave chrst sfWidth 1 index 0 ne{exch .05 add exch}if grestore setcharwidth chrst .06 0 mshw 0 .05 translate dblsh}bdf /ShFt{dup dhSdh FontDirectory 1 index known{exch pop} {dup 3 -1 roll dup MakOF {ShadChar} mkFT}ifelse}bdf /LswUnits{72 75 div dup scale}bdf /erasefill{_bp}def /CVvec 256 array def /NUL/SOH/STX/ETX/EOT/ENQ/ACK/BEL/BS/HT/LF/VT/FF/CR/SO/SI/DLE/DC1/DC2/DC3/DC4/NAK/SYN/ETB/CAN/EM/SUB/ESC/FS/GS/RS/US CVvec 0 32 getinterval astore pop CVvec 32/Times-Roman findfont/Encoding get 32 96 getinterval putinterval CVvec dup 39/quotesingle put 96/grave put /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/blank/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand/Acircumflex/Ecircumflex/Aacute /Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex /apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron CVvec 128 128 getinterval astore pop end %%EndProcSet %%BeginSetup CanvasDict begin 0 setlinecap 0 setlinejoin 4 setmiterlimit /currot 0 def origmtx currentmatrix pop [] 0 setdash 1 1 setpen 1 fg 0 pg 0 frg 1 bkg newpath /dbg F def %%EndSetup % ---- Object #1:58 Obj Type: 10 0 setlinecap 616.7019 269.2447 moveto 532.4936 366.3385 366.8647 352.9488 256.1825 315.5115 curveto 211.8957 300.5318 172.1508 280.9126 156.0983 246.8009 curveto 142.9600 218.8821 147.7499 191.2683 181.5656 193.1831 curveto F dofillsave F dostroke gsave newpath 169.9222 190.2796 moveto 169.8733 190.4833 lineto 169.7861 190.8934 lineto 169.7134 191.3058 lineto 169.6551 191.7204 lineto 169.6113 192.1369 lineto 169.5821 192.5546 lineto 169.5674 192.9731 lineto 169.5674 193.3926 lineto 169.5820 193.8110 lineto 169.6112 194.2288 lineto 169.6550 194.6452 lineto 169.7133 195.0599 lineto 169.7860 195.4723 lineto 169.8731 195.8824 lineto 169.9744 196.2887 lineto 170.0899 196.6912 lineto 170.2192 197.0895 lineto 170.3625 197.4832 lineto 170.5196 197.8719 lineto 170.6899 198.2545 lineto 170.7800 198.4434 lineto 181.5656 193.1831 lineto 169.9222 190.2796 lineto closepath F doline grestore % ---- Object #2:21 Obj Type: 4 0 setlinecap 104 27 97 34 rectpath F dofillsave F dostroke % ---- Object #3:6 Obj Type: 4 0 setlinecap 112.5040 55.3464 105.1540 62.6965 rectpath F dofillsave F dostroke % ---- Object #4:7 Obj Type: 4 0 setlinecap 121.0081 83.6929 113.3080 91.3930 rectpath F dofillsave F dostroke % ---- Object #5:8 Obj Type: 4 0 setlinecap 129.5121 112.0393 121.4620 120.0895 rectpath F dofillsave F dostroke % ---- Object #6:9 Obj Type: 4 0 setlinecap 138.0161 140.3858 129.6160 148.7859 rectpath F dofillsave F dostroke % ---- Object #7:10 Obj Type: 4 0 setlinecap 146.5201 168.7322 137.7700 177.4824 rectpath F dofillsave F dostroke % ---- Object #8:11 Obj Type: 4 0 setlinecap 155.0242 197.0787 145.9239 206.1789 rectpath F dofillsave F dostroke % ---- Object #9:12 Obj Type: 4 0 setlinecap 163.5282 227.4252 154.0779 236.8754 rectpath F dofillsave F dostroke % ---- Object #10:13 Obj Type: 4 0 setlinecap 172.0322 255.7716 162.2319 265.5719 rectpath F dofillsave F dostroke % ---- Object #11:14 Obj Type: 4 0 setlinecap 180.5363 284.1181 170.3859 294.2684 rectpath F dofillsave F dostroke % ---- Object #12:15 Obj Type: 4 0 setlinecap 189.0403 310.4645 178.5399 320.9649 rectpath F dofillsave F dostroke % ---- Object #13:16 Obj Type: 4 0 setlinecap 197.5443 338.8110 186.6939 349.6614 rectpath F dofillsave F dostroke % ---- Object #14:17 Obj Type: 4 0 setlinecap 206.0483 367.1574 194.8479 378.3578 rectpath F dofillsave F dostroke % ---- Object #15:18 Obj Type: 4 0 setlinecap 214.5524 395.5039 203.0019 407.0543 rectpath F dofillsave F dostroke % ---- Object #16:19 Obj Type: 4 0 setlinecap 223.0564 423.8503 211.1559 435.7508 rectpath F dofillsave F dostroke % ---- Object #17:20 Obj Type: 4 0 setlinecap 231.5604 452.1968 219.3099 464.4473 rectpath F dofillsave F dostroke % ---- Object #18:22 Obj Type: 4 0 setlinecap 240.0644 480.5432 227.4639 493.1438 rectpath F dofillsave F dostroke % ---- Object #19:23 Obj Type: 4 0 setlinecap 248.5685 508.8897 235.6179 521.8403 rectpath F dofillsave F dostroke % ---- Object #20:24 Obj Type: 4 0 setlinecap 257.0725 537.2361 243.7718 550.5368 rectpath F dofillsave F dostroke % ---- Object #21:25 Obj Type: 4 0 setlinecap 265.5765 565.5826 251.9258 579.2333 rectpath F dofillsave F dostroke % ---- Object #22:26 Obj Type: 4 0 setlinecap 274.0806 593.9290 260.0798 607.9297 rectpath F dofillsave F dostroke % ---- Object #23:29 Obj Type: 4 0 setlinecap 205.7642 195.0787 196.2090 204.6339 rectpath F dofillsave F dostroke % ---- Object #24:30 Obj Type: 4 0 setlinecap 214.6935 227.8425 204.7707 237.7652 rectpath F dofillsave F dostroke % ---- Object #25:31 Obj Type: 4 0 setlinecap 223.6227 256.6062 213.3324 266.8966 rectpath F dofillsave F dostroke % ---- Object #26:32 Obj Type: 4 0 setlinecap 232.5519 284.3700 221.8941 295.0279 rectpath F dofillsave F dostroke % ---- Object #27:33 Obj Type: 4 0 setlinecap 241.4812 313.1338 230.4558 324.1592 rectpath F dofillsave F dostroke % ---- Object #28:34 Obj Type: 4 0 setlinecap 249.4104 341.8976 238.0175 353.2905 rectpath F dofillsave F dostroke % ---- Object #29:35 Obj Type: 4 0 setlinecap 260.3396 369.6613 248.5792 381.4218 rectpath F dofillsave F dostroke % ---- Object #30:36 Obj Type: 4 0 setlinecap 269.2688 398.4251 257.1408 410.5531 rectpath F dofillsave F dostroke % ---- Object #31:37 Obj Type: 4 0 setlinecap 277.1981 426.1889 264.7025 438.6844 rectpath F dofillsave F dostroke % ---- Object #32:38 Obj Type: 4 0 setlinecap 287.1273 455.9526 274.2642 468.8157 rectpath F dofillsave F dostroke % ---- Object #33:39 Obj Type: 4 0 setlinecap 295.0565 483.7164 281.8259 496.9470 rectpath F dofillsave F dostroke % ---- Object #34:40 Obj Type: 4 0 setlinecap 303.9858 511.4802 290.3876 525.0783 rectpath F dofillsave F dostroke % ---- Object #35:41 Obj Type: 4 0 setlinecap 312.9150 538.2440 298.9493 552.2097 rectpath F dofillsave F dostroke % ---- Object #36:42 Obj Type: 4 0 setlinecap 317.8442 564.0077 303.5110 578.3410 rectpath F dofillsave F dostroke % ---- Object #37:43 Obj Type: 4 0 setlinecap 325.7735 591.7715 311.0727 606.4723 rectpath F dofillsave F dostroke % ---- Object #38:27 Obj Type: 3 2 setlinecap gsave newpath 183 142 moveto 162 142 lineto F dostroke grestore % ---- Object #39:28 Obj Type: 3 2 setlinecap gsave newpath 154 135 moveto 133 135 lineto F dostroke grestore % ---- Object #40:44 Obj Type: 3 2 setlinecap gsave newpath 107 126 moveto 126 126 lineto F dostroke grestore % ---- Object #41:45 Obj Type: 3 2 setlinecap gsave newpath 212 202 moveto 191 201 lineto F dostroke grestore % ---- Object #42:46 Obj Type: 3 2 setlinecap gsave newpath 221 210 moveto 242 210 lineto F dostroke grestore % ---- Object #43:47 Obj Type: 3 2 setlinecap gsave newpath 251 218 moveto 275 218 lineto F dostroke grestore % ---- Object #44:48 Obj Type: 3 2 setlinecap gsave newpath 78 118 moveto 96 118 lineto F dostroke grestore % ---- Object #45:5 Obj Type: 3 2 setlinecap gsave newpath 180.6076 214.9998 moveto 180.7138 215.1801 lineto 180.9356 215.5352 lineto 181.1701 215.8828 lineto 181.4163 216.2217 lineto 181.6741 216.5517 lineto 181.9433 216.8725 lineto 182.2235 217.1837 lineto 182.5147 217.4853 lineto 182.8159 217.7761 lineto 183.1271 218.0563 lineto 183.4479 218.3255 lineto 183.7778 218.5833 lineto 184.1166 218.8295 lineto 184.4643 219.0641 lineto 184.8194 219.2859 lineto 185.1821 219.4953 lineto 185.5518 219.6919 lineto 185.9282 219.8755 lineto 186.3107 220.0458 lineto 186.6994 220.2029 lineto 186.8956 220.2763 lineto 191 209 lineto 180.6076 214.9998 lineto closepath F doline grestore gsave newpath 141 269 moveto 183.4778 218.0266 lineto F dostroke grestore % ---- Object #46:50 Obj Type: 2 0 0 setpen save 0 setgray mark /|___TimesNewRomanPSMT /TimesNewRomanPSMT T cvRecFont 12 fts /|___TimesNewRomanPSMT findfont exch scalefont setfont 0 setgray 106 277 moveto (R\(0,m\)) F F 34.3301 0 6 0 0 fittext restore % ---- Object #47:49 Obj Type: 3 1 1 setpen 2 setlinecap gsave newpath 276.9356 246.5352 moveto 277.0516 246.7103 lineto 277.2917 247.0533 lineto 277.5437 247.3878 lineto 277.8073 247.7132 lineto 278.0820 248.0292 lineto 278.3675 248.3355 lineto 278.6641 248.6321 lineto 278.9703 248.9177 lineto 279.2864 249.1924 lineto 279.6118 249.4559 lineto 279.9462 249.7079 lineto 280.2892 249.9481 lineto 280.6408 250.1765 lineto 280.9998 250.3922 lineto 281.3660 250.5952 lineto 281.7391 250.7853 lineto 282.1188 250.9624 lineto 282.5047 251.1262 lineto 282.8956 251.2763 lineto 283.2916 251.4126 lineto 283.4912 251.4755 lineto 287 240 lineto 276.9356 246.5352 lineto closepath F doline grestore gsave newpath 279.9500 249.4000 moveto 230 316 lineto F dostroke grestore % ---- Object #48:52 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Times-Roman /Times-Roman T cvRecFont 12 fts /|___Times-Roman findfont exch scalefont setfont 0 setgray 148 311 moveto (R\() F F 12 0 2 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 12 fts /|___Symbol findfont exch scalefont setfont 0 setgray 160 311 moveto (g) show 0 setgray mark /|___TimesNewRomanPSMT /TimesNewRomanPSMT T cvRecFont 12 fts /|___TimesNewRomanPSMT findfont exch scalefont setfont 0 setgray 164 314 moveto (m) show 0 setgray mark /|___CourierNewPSMT /CourierNewPSMT T cvRecFont 12 fts /|___CourierNewPSMT findfont exch scalefont setfont 0 setgray 173 311 moveto (-2) F F 14.4023 0 2 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 12 fts /|___Symbol findfont exch scalefont setfont 0 setgray 187 311 moveto (g) show 0 setgray mark /|___TimesNewRomanPSMT /TimesNewRomanPSMT T cvRecFont 12 fts /|___TimesNewRomanPSMT findfont exch scalefont setfont 0 setgray 191 315 moveto (m-2) F F 19.3301 0 3 0 0 fittext 0 setgray 0 setgray 210 311 moveto (,m\)) F F 16.3301 0 3 0 0 fittext restore % ---- Object #49:51 Obj Type: 3 1 1 setpen 2 setlinecap gsave newpath 47.4956 85.1826 moveto 47.3924 85.0002 lineto 47.1768 84.6413 lineto 46.9484 84.2897 lineto 46.7082 83.9467 lineto 46.4562 83.6122 lineto 46.1927 83.2868 lineto 45.9180 82.9708 lineto 45.6325 82.6645 lineto 45.3359 82.3679 lineto 45.0296 82.0823 lineto 44.7136 81.8076 lineto 44.3882 81.5441 lineto 44.0538 81.2921 lineto 43.7108 81.0519 lineto 43.3592 80.8235 lineto 43.0002 80.6078 lineto 42.6340 80.4048 lineto 42.2609 80.2147 lineto 41.8812 80.0376 lineto 41.4953 79.8738 lineto 41.3005 79.7971 lineto 37 91 lineto 47.4956 85.1826 lineto closepath F doline grestore gsave newpath 106 12 moveto 44.7295 82.1503 lineto F dostroke grestore % ---- Object #50:54 Obj Type: 2 0 0 setpen save 0 setgray mark /|___TimesNewRomanPSMT /TimesNewRomanPSMT T cvRecFont 12 fts /|___TimesNewRomanPSMT findfont exch scalefont setfont 0 setgray 121 0 moveto (R\(0,m+1\)) F F 47.0977 0 8 0 0 fittext restore % ---- Object #51:56 Obj Type: 3 1 1 setpen 2 setlinecap gsave newpath 99.4956 101.1826 moveto 99.3924 101.0002 lineto 99.1768 100.6413 lineto 98.9484 100.2897 lineto 98.7082 99.9467 lineto 98.4562 99.6122 lineto 98.1927 99.2868 lineto 97.9180 98.9708 lineto 97.6325 98.6645 lineto 97.3359 98.3679 lineto 97.0296 98.0823 lineto 96.7136 97.8076 lineto 96.3882 97.5441 lineto 96.0538 97.2921 lineto 95.7108 97.0519 lineto 95.3592 96.8235 lineto 95.0002 96.6078 lineto 94.6340 96.4048 lineto 94.2609 96.2147 lineto 93.8812 96.0376 lineto 93.4953 95.8738 lineto 93.3005 95.7971 lineto 89 107 lineto 99.4956 101.1826 lineto closepath F doline grestore gsave newpath 133 56 moveto 96.6755 98.1034 lineto F dostroke grestore % ---- Object #52:55 Obj Type: 2 0 0 setpen save 0 setgray mark /|___TimesNewRomanPSMT /TimesNewRomanPSMT T cvRecFont 12 fts /|___TimesNewRomanPSMT findfont exch scalefont setfont 0 setgray 147 41 moveto (R\() F F 12 0 2 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 12 fts /|___Symbol findfont exch scalefont setfont 0 setgray 159 41 moveto (g) show 0 setgray mark /|___TimesNewRomanPSMT /TimesNewRomanPSMT T cvRecFont 12 fts /|___TimesNewRomanPSMT findfont exch scalefont setfont 0 setgray 163 44 moveto (m+1) F F 22.1016 0 3 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 12 fts /|___Symbol findfont exch scalefont setfont 0 setgray 185 41 moveto (-2g) F F 17.5195 0 3 0 0 fittext 0 setgray mark /|___TimesNewRomanPSMT /TimesNewRomanPSMT T cvRecFont 12 fts /|___TimesNewRomanPSMT findfont exch scalefont setfont 0 setgray 202 44 moveto (m) show 0 setgray 0 setgray 211 41 moveto (,m+1\)) F F 29.0977 0 5 0 0 fittext restore % ---- Object #53:53 Obj Type: 3 1 1 setpen 2 setlinecap gsave newpath 189.9927 136.4187 moveto 189.9982 136.2095 lineto 189.9982 135.7905 lineto 189.9836 135.3721 lineto 189.9544 134.9543 lineto 189.9106 134.5379 lineto 189.8523 134.1232 lineto 189.7796 133.7108 lineto 189.6925 133.3007 lineto 189.5912 132.8944 lineto 189.4757 132.4919 lineto 189.3464 132.0936 lineto 189.2031 131.6999 lineto 189.0460 131.3112 lineto 188.8757 130.9286 lineto 188.6922 130.5523 lineto 188.4956 130.1826 lineto 188.2862 129.8199 lineto 188.0643 129.4648 lineto 187.8299 129.1172 lineto 187.5837 128.7783 lineto 187.4562 128.6122 lineto 178 136 lineto 189.9927 136.4187 lineto closepath F doline grestore gsave newpath 189.1666 132.3437 moveto 291 99 lineto F dostroke grestore % ---- Object #54:57 Obj Type: 2 0 0 setpen save 0 setgray mark /|___TimesNewRomanPSMT /TimesNewRomanPSMT T cvRecFont 12 fts /|___TimesNewRomanPSMT findfont exch scalefont setfont 0 setgray 294 93 moveto (R\() F F 12 0 2 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 12 fts /|___Symbol findfont exch scalefont setfont 0 setgray 306 93 moveto (g) show 0 setgray mark /|___TimesNewRomanPSMT /TimesNewRomanPSMT T cvRecFont 12 fts /|___TimesNewRomanPSMT findfont exch scalefont setfont 0 setgray 310 96 moveto (m+1) F F 22.1016 0 3 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 12 fts /|___Symbol findfont exch scalefont setfont 0 setgray 332 93 moveto (-g) F F 11.5195 0 2 0 0 fittext 0 setgray mark /|___TimesNewRomanPSMT /TimesNewRomanPSMT T cvRecFont 12 fts /|___TimesNewRomanPSMT findfont exch scalefont setfont 0 setgray 343 96 moveto (m) show 0 setgray 0 setgray 352 93 moveto (,m+1\)) F F 29.0977 0 5 0 0 fittext restore % ---- Object #55:61 Obj Type: 3 1 1 setpen 2 setlinecap gsave newpath 42.3259 116.5517 moveto 42.4562 116.3878 lineto 42.7082 116.0533 lineto 42.9484 115.7103 lineto 43.1768 115.3587 lineto 43.3924 114.9998 lineto 43.5955 114.6333 lineto 43.7856 114.2602 lineto 43.9626 113.8807 lineto 44.1264 113.4948 lineto 44.2765 113.1038 lineto 44.4128 112.7079 lineto 44.5352 112.3074 lineto 44.6436 111.9030 lineto 44.7378 111.4950 lineto 44.8178 111.0832 lineto 44.8833 110.6696 lineto 44.9343 110.2540 lineto 44.9708 109.8368 lineto 44.9927 109.4187 lineto 45 109 lineto 44.9982 108.7905 lineto 33 109 lineto 42.3259 116.5517 lineto closepath F doline grestore gsave newpath 598 307 moveto 44.0888 112.8860 lineto F dostroke grestore % ---- Object #56:60 Obj Type: 3 2 setlinecap gsave newpath 77 118 moveto 77 62 lineto F dostroke grestore % ---- Object #57:63 Obj Type: 3 2 setlinecap gsave newpath 98 118 moveto 98 63 lineto F dostroke grestore % ---- Object #58:62 Obj Type: 3 2 setlinecap gsave newpath 105 126 moveto 105 63 lineto F dostroke grestore % ---- Object #59:64 Obj Type: 3 2 setlinecap gsave newpath 128 126 moveto 128 63 lineto F dostroke grestore % ---- Object #60:65 Obj Type: 3 2 setlinecap gsave newpath 133 135 moveto 133 63 lineto F dostroke grestore % ---- Object #61:66 Obj Type: 3 2 setlinecap gsave newpath 155 135 moveto 155 62 lineto F dostroke grestore % ---- Object #62:67 Obj Type: 3 2 setlinecap gsave newpath 274 62 moveto 618 62 lineto F dostroke grestore % ---- Object #63:68 Obj Type: 3 2 setlinecap gsave newpath 162 142 moveto 162 62 lineto F dostroke grestore % ---- Object #64:69 Obj Type: 3 2 setlinecap gsave newpath 184 142 moveto 184 62 lineto F dostroke grestore % ---- Object #65:70 Obj Type: 3 2 setlinecap gsave newpath 191 62 moveto 191 202 lineto F dostroke grestore % ---- Object #66:71 Obj Type: 3 2 setlinecap gsave newpath 212 202 moveto 212 62 lineto F dostroke grestore % ---- Object #67:72 Obj Type: 3 2 setlinecap gsave newpath 221 210 moveto 221 62 lineto F dostroke grestore % ---- Object #68:73 Obj Type: 3 2 setlinecap gsave newpath 242 210 moveto 242 62 lineto F dostroke grestore % ---- Object #69:74 Obj Type: 3 2 setlinecap gsave newpath 250 218 moveto 250 62 lineto F dostroke grestore % ---- Object #70:75 Obj Type: 3 2 setlinecap gsave newpath 274 218 moveto 274 62 lineto F dostroke grestore % ---- Object #71:78 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Times-Roman /Times-Roman T cvRecFont 12 fts /|___Times-Roman findfont exch scalefont setfont 0 setgray 664 309 moveto (R\() F F 12 0 2 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 12 fts /|___Symbol findfont exch scalefont setfont 0 setgray 676 309 moveto (g) show 0 setgray mark /|___TimesNewRomanPSMT /TimesNewRomanPSMT T cvRecFont 12 fts /|___TimesNewRomanPSMT findfont exch scalefont setfont 0 setgray 680 312 moveto (m) show 0 setgray mark /|___CourierNewPSMT /CourierNewPSMT T cvRecFont 12 fts /|___CourierNewPSMT findfont exch scalefont setfont 0 setgray 689 309 moveto (-1) F F 14.4023 0 2 0 0 fittext 0 setgray mark /|___TimesNewRomanPSMT /TimesNewRomanPSMT T cvRecFont 12 fts /|___TimesNewRomanPSMT findfont exch scalefont setfont 0 setgray 703 309 moveto (,m\)) F F 16.3301 0 3 0 0 fittext restore % ---- Object #72:79 Obj Type: 2 save 0 setgray mark /|___TimesNewRomanPSMT /TimesNewRomanPSMT T cvRecFont 12 fts /|___TimesNewRomanPSMT findfont exch scalefont setfont 0 setgray 666 266 moveto (R\() F F 12 0 2 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 12 fts /|___Symbol findfont exch scalefont setfont 0 setgray 678 266 moveto (g) show 0 setgray mark /|___TimesNewRomanPSMT /TimesNewRomanPSMT T cvRecFont 12 fts /|___TimesNewRomanPSMT findfont exch scalefont setfont 0 setgray 682 269 moveto (m+1) F F 22.1016 0 3 0 0 fittext 0 setgray mark /|___Symbol /Symbol F cvRecFont 12 fts /|___Symbol findfont exch scalefont setfont 0 setgray 704 266 moveto (-1) F F 12.5859 0 2 0 0 fittext 0 setgray mark /|___TimesNewRomanPSMT /TimesNewRomanPSMT T cvRecFont 12 fts /|___TimesNewRomanPSMT findfont exch scalefont setfont 0 setgray 716 266 moveto (,m+1\)) F F 29.0977 0 5 0 0 fittext restore % ---- Object #73:76 Obj Type: 3 1 1 setpen 2 setlinecap gsave newpath 622.7796 320.2891 moveto 622.8178 320.0832 lineto 622.8833 319.6696 lineto 622.9343 319.2540 lineto 622.9708 318.8368 lineto 622.9927 318.4187 lineto 623 318 lineto 622.9927 317.5813 lineto 622.9708 317.1632 lineto 622.9343 316.7460 lineto 622.8833 316.3304 lineto 622.8178 315.9168 lineto 622.7378 315.5050 lineto 622.6436 315.0970 lineto 622.5352 314.6925 lineto 622.4128 314.2921 lineto 622.2765 313.8962 lineto 622.1264 313.5052 lineto 621.9626 313.1193 lineto 621.7856 312.7397 lineto 621.5955 312.3666 lineto 621.4956 312.1826 lineto 611 318 lineto 622.7796 320.2891 lineto closepath F doline grestore gsave newpath 655 311 moveto 622.6041 316.1539 lineto F dostroke grestore % ---- Object #74:77 Obj Type: 3 2 setlinecap gsave newpath 624.7378 275.4950 moveto 624.7796 275.2891 lineto 624.8523 274.8768 lineto 624.9106 274.4621 lineto 624.9544 274.0457 lineto 624.9836 273.6279 lineto 624.9982 273.2095 lineto 624.9982 272.7905 lineto 624.9836 272.3721 lineto 624.9544 271.9543 lineto 624.9106 271.5379 lineto 624.8523 271.1232 lineto 624.7796 270.7108 lineto 624.6925 270.3007 lineto 624.5912 269.8944 lineto 624.4757 269.4919 lineto 624.3464 269.0936 lineto 624.2031 268.6999 lineto 624.0460 268.3112 lineto 623.8757 267.9286 lineto 623.6922 267.5523 lineto 623.5955 267.3666 lineto 613 273 lineto 624.7378 275.4950 lineto closepath F doline grestore gsave newpath 656 267 moveto 624.6372 271.3762 lineto F dostroke grestore % ---- Object #75:80 Obj Type: 3 2 setlinecap gsave newpath 250 62 moveto 242 62 lineto F dostroke grestore % ---- Object #76:81 Obj Type: 3 2 setlinecap gsave newpath 212 61.5000 moveto 221 61.5000 lineto F dostroke grestore % ---- Object #77:82 Obj Type: 3 2 setlinecap gsave newpath 191 62 moveto 184 62 lineto F dostroke grestore % ---- Object #78:83 Obj Type: 3 2 setlinecap gsave newpath 162 62 moveto 155 62 lineto F dostroke grestore % ---- Object #79:84 Obj Type: 3 2 setlinecap gsave newpath 127.5000 62.5000 moveto 133 62.5000 lineto F dostroke grestore % ---- Object #80:85 Obj Type: 3 2 setlinecap gsave newpath 104.5000 63 moveto 97.5000 63 lineto F dostroke grestore % ---- Object #81:86 Obj Type: 3 2 setlinecap gsave newpath 76.5000 61.5000 moveto 7 61.5000 lineto F dostroke grestore origmtx setmatrix systemdict /setpacking known {origpack setpacking} if end showpage %%EndDocument: %%EndDocument endTexFig 1331 3383 a Ft(Figure)k(3.)100 3483 y Fg(R)l(emark:)37 b Ft(The)28 b(smo)r(oth)f(bumps)h(are)f(represen)n(ted)f(as)h(large,)f (v)n(ertical)h(rectangles.)100 3670 y(W)-7 b(e)29 b(compute)h(the)g(p)r (osition)f(of)h(the)f(b)r(ottom)h(left)g(corner)e(\()p Fw(x;)14 b(y)s Ft(\))31 b(of)e Fw(R)q Ft(\(0)p Fw(;)14 b(m)p Ft(\))29 b(b)n(y)g(writing)0 3770 y(that)f(it)g(comes)f(bac)n(k)g (to)g(itself)h(under)g(iteration)e(of)i Fw(F)12 b Ft(:)540 3942 y Fw(x)23 b Ft(=)g Fw(e)737 3908 y Fv(\017\015)804 3883 y Fj(m)858 3908 y Fn(+)p Fv(\017\015)976 3883 y Fj(m)p Fd(+1)1105 3942 y Fw(x)c Fm(\000)f Fw(e)1293 3908 y Fv(\017\015)1360 3883 y Fj(m)p Fd(+1)1516 3942 y Ft(and)28 b Fw(y)e Ft(=)c Fw(e)1871 3908 y Fv(\017\015)1938 3883 y Fj(m)1992 3908 y Fn(+)p Fv(\017\015)2110 3883 y Fj(m)p Fd(+1)2239 3942 y Fw(y)g Fm(\000)c Ft(1)p Fw(:)0 4115 y Ft(Th)n(us:)661 4233 y Fw(x)23 b Ft(=)1084 4177 y(1)p 829 4214 553 4 v 829 4292 a Fw(e)868 4268 y Fv(\017\015)935 4251 y Fj(m)1011 4292 y Fm(\000)18 b Fw(e)1133 4268 y Fl(\000)p Fv(\017\015)1252 4251 y Fj(m)p Fd(+1)1419 4233 y Ft(and)27 b Fw(y)f Ft(=)1999 4177 y(1)p 1745 4214 551 4 v 1745 4292 a Fw(e)1784 4268 y Fv(\017\015)1851 4251 y Fj(m)1905 4268 y Fn(+)p Fv(\017\015)2023 4251 y Fj(m)p Fd(+1)2170 4292 y Fm(\000)18 b Ft(1)2305 4233 y Fw(:)0 4436 y Ft(W)-7 b(e)23 b(de\014ne)g(the)g(heigh)n(t)g(and)g(width)g(of)g Fw(R)q Ft(\(0)p Fw(;)14 b(m)p Ft(\))22 b(to)h(b)r(e)g Fw(e)1781 4406 y Fl(\000)p Fv(\017\015)1900 4381 y Fj(m)p Fd(+10)2080 4436 y Ft(\(an)n(y)f(small)h(n)n(um)n(b)r(er)f(w)n(ould)0 4536 y(do\).)58 b(One)34 b(c)n(hec)n(ks)g(easily)f(that)i(the)g (rectangles)f(so)f(de\014ned)i(remain)f(inside)h(the)g(columns)0 4635 y Fw(J)46 4647 y Fv(`)96 4635 y Fm(\002)18 b Ft([0)p Fw(;)c Ft(1].)100 4747 y(Observ)n(e)34 b(that)i Fw(F)680 4717 y Fv(\015)719 4692 y Fj(m)773 4717 y Fn(+)p Fv(\015)863 4692 y Fj(m)p Fd(+1)993 4747 y Ft(\()p Fw(R)q Ft(\(0)p Fw(;)14 b(m)p Ft(\)\))36 b Fm(\032)g Fw(R)q Ft(\(0)p Fw(;)14 b(m)p Ft(\))35 b(b)r(ecause)h(the)g(heigh)n(t)f(of)h Fw(R)q Ft(\(0)p Fw(;)14 b(m)p Ft(\))35 b(is)0 4847 y(m)n(ultiplied)28 b(b)n(y:)523 5031 y Fw(e)562 4997 y Fv(\017)p Fn(\()p Fv(\015)655 4972 y Fj(m)709 4997 y Fn(+)p Fv(\015)799 4972 y Fj(m)p Fd(+1)924 4997 y Fn(\))954 5031 y Fw(=)p Ft(2)1038 4997 y Fv(\015)1077 4972 y Fj(m)1131 4997 y Fl(\000)p Fv(\015)1222 4972 y Fj(m)p Fc(\000)p Fd(1)1377 5031 y Ft(=)22 b Fw(e)1503 4997 y Fv(\015)1542 4972 y Fj(m)1597 4997 y Fn(\()p Fv(\017)p Fn(\(1+)p Fv(\015)t Fn(\))p Fl(\000)p Fn(\(1)p Fl(\000)p Fn(1)p Fv(=\015)t Fn(\))9 b(log)j(2\))2314 5031 y Fw(<)22 b Ft(1)p Fw(;)p eop %%Page: 6 6 6 5 bop 0 42 a Fr(6)1170 b(J)1247 25 y(\023)1241 42 y(ER)1351 25 y(^)1341 42 y(OME)30 b(BUZZI)0 241 y Ft(and)d(its)h(width)g(b)n(y:) 759 452 y Fw(e)798 418 y Fv(\017)p Fn(\()p Fv(\015)891 393 y Fj(m)945 418 y Fn(+)p Fv(\015)1035 393 y Fj(m)p Fd(+1)1160 418 y Fn(\))1190 452 y Fw(=)p Ft(2)1274 418 y Fv(\015)1313 393 y Fj(m)1394 452 y Ft(=)23 b Fw(e)1521 418 y Fv(\015)1560 393 y Fj(m)1614 418 y Fn(\()p Fv(\017)p Fn(\(1+)p Fv(\015)t Fn(\))p Fl(\000)p Fn(log)11 b(2\))2078 452 y Fw(<)22 b Ft(1)p Fw(:)100 651 y Ft(Finally)38 b(w)n(e)g(c)n(hec)n (k)f(the)i(condition)f(for)g Fw(C)1492 621 y Fv(r)1568 651 y Ft(smo)r(othness.)68 b(Observ)n(e)37 b(that)i(the)f(bumps)0 751 y(asso)r(ciated)29 b(to)i(rectangles)e Fw(R)q Ft(\()p Fw(k)s(;)14 b(m)p Ft(\),)31 b(resp.)46 b Fw(R)q Ft(\()p Fw(k)s(;)14 b(m)20 b Ft(+)g(1\),)31 b(are)f(magni\014ed)g(v)n(ersions)f (of)h(the)0 850 y(one)22 b(asso)r(ciated)g(to)g Fw(R)q Ft(\(0)p Fw(;)14 b(m)p Ft(\),)24 b(resp.)34 b Fw(R)q Ft(\()p Fw(\015)1311 820 y Fv(m)p Fn(+1)1467 850 y Fm(\000)9 b Ft(2)p Fw(\015)1631 820 y Fv(m)1692 850 y Fw(;)14 b(m)9 b Ft(+)g(1\).)34 b(Hence)23 b(it)g(is)g(enough)f(to)h(c)n(hec)n(k)0 950 y(the)28 b(condition)f(for)g(these)h(t)n(w)n(o)f(rectangles.)100 1050 y(The)j(width)h(of)f(the)h(bump)g(asso)r(ciated)e(to)h Fw(R)q Ft(\(0)p Fw(;)14 b(m)p Ft(\))27 b Fm(\032)g Fw(J)1939 1062 y Fv(m)2023 1050 y Fm(\002)20 b Ft([0)p Fw(;)14 b Ft(1])29 b(is)h(ab)r(out)h Fw(e)2670 1019 y Fl(\000)p Fv(\017\015)2789 994 y Fj(m)2847 1050 y Ft(,)g(its)0 1162 y(heigh)n(t)e(is)g Fw(y)i Ft(whic)n(h)e(is)g(appro)n(ximately)e Fw(e)1321 1131 y Fl(\000)p Fv(\017\015)1440 1106 y Fj(m)1494 1131 y Fl(\000)p Fv(\017\015)1613 1106 y Fj(m)p Fd(+1)1742 1162 y Ft(,)j(the)f(relev)-5 b(an)n(t)28 b(quotien)n(t)h(is)g (therefore)0 1261 y Fw(e)39 1231 y Fl(\000)p Fv(\017\015)158 1206 y Fj(m)212 1231 y Fn(\()p Fv(\015)t Fn(+1)p Fl(\000)p Fv(r)r Fn(\))475 1261 y Ft(.)37 b(As)27 b Fw(\015)h(>)23 b(r)e Fm(\000)d Ft(1,)27 b(this)h(go)r(es)f(to)g(zero)g(and)g(it)h(is)g (ok.)100 1361 y(F)-7 b(or)36 b(the)i(second)e(bump,)41 b(the)c(relev)-5 b(an)n(t)37 b(quotien)n(t)g(is)g(similarly)f(\()p Fw(e)2285 1331 y Fv(\017\015)2352 1306 y Fj(m)2410 1361 y Fw(x)26 b Fm(\000)e Ft(1\))p Fw(=e)2727 1331 y Fl(\000)p Fn(2)p Fv(\017\015)2879 1306 y Fj(m)2932 1331 y Fl(\001)p Fv(r)0 1464 y Ft(whic)n(h)k(is)f(equiv)-5 b(alen)n(t)27 b(to)h Fw(e)856 1433 y Fl(\000)p Fv(\017\015)975 1408 y Fj(m)1029 1433 y Fn(\()p Fv(\015)t Fn(+1)p Fl(\000)p Fn(2)p Fv(r)r Fn(\))1325 1464 y Ft(.)37 b(This)27 b(is)h(also)e(ok)h (as)g Fw(\015)h(>)23 b Ft(2)p Fw(r)d Fm(\000)e Ft(1.)100 1571 y Fw(H)36 b Ft(:=)29 b Fw(F)387 1541 y Fv(\015)426 1516 y Fj(m)480 1541 y Fn(+)p Fv(\015)570 1516 y Fj(m)p Fd(+1)729 1571 y Ft(:)h Fw(R)q Ft(\(0)p Fw(;)14 b(m)p Ft(\))29 b Fm(!)g Fw(R)q Ft(\(0)p Fw(;)14 b(m)p Ft(\))31 b(is)h(a)f(piecewise)g(expanding)g(and)g(a\016ne)g(map)0 1670 y(preserving)k(the)h(t)n(w)n(o)g(axis)f(directions)h(together)f (and)i(made)f(of)g(rectangular)e(pieces)i(with)0 1770 y(sides)30 b(aligned)f(with)h(the)g(axis.)43 b(It)30 b(is)g(w)n(ell-kno)n(wn)f(that)h(suc)n(h)f(a)h(map)g(has)f(an)g (a.c.i.p.)44 b(\(see,)0 1870 y(for)24 b(instance)h([5],)h(using)e(that) i(an)n(y)e(iterate)g(is)h(piecewise)g(a\016ne)g(on)f(rectangles)g (aligned)g(with)0 1969 y(the)j(axis)f(and)h(therefore)e(at)i(most)f(4)h (rectangles)e(can)h(touc)n(h)h(a)f(giv)n(en)g(p)r(oin)n(t:)36 b Fw(Y)19 b Ft(\()p Fw(H)2663 1939 y Fv(n)2708 1969 y Ft(\))24 b Fm(\024)e Ft(4)27 b(in)0 2069 y(the)h(language)e(of)h(that)h (pap)r(er\).)100 2169 y(W)-7 b(e)25 b(therefore)f(ha)n(v)n(e)g(built)h (a)g(piecewise)f(expanding)h(and)g Fw(C)2015 2138 y Fv(r)2077 2169 y Ft(map)f(with)i(in\014nitely)f(man)n(y)0 2268 y(a.c.i.p.)83 b Fe(\003)1252 2467 y Fu(References)0 2600 y Fr([1])50 b(J.)28 b(Buzzi,)h Fb(a.c.i.m.)h(as)g(e)l(quilibrium)g (states)f(for)h(pie)l(c)l(ewise)h(invertible)d(dynamic)l(al)j(systems)p Fr(,)e(preprin)n(t)125 2683 y(I.M.L.)23 b(\(1998\).)0 2766 y([2])50 b(J.)35 b(Buzzi,)i Fb(a.c.i.m.)e(for)h(arbitr)l(ary)g (pie)l(c)l(ewise)g(exp)l(anding)g(and)h(r)l(e)l(al-analytic)f(maps)h (on)f(the)f(plane)p Fr(,)125 2849 y(Ergo)r(d.)24 b(Th.)f(&)h(Dynam.)e (Syst.)i(\(to)h(app)r(ear\).)0 2932 y([3])50 b(P)-6 b(.)16 b(G\023)-35 b(ora;)18 b(A.)d(Bo)n(y)n(arsky;)k(H.)c(Propp)r(e,)i Fb(On)h(the)g(numb)l(er)h(of)g(invariant)f(me)l(asur)l(es)i(for)f (higher-dimensional)125 3015 y(chaotic)26 b(tr)l(ansformations)p Fr(,)g(J.)d(Statist.)h(Ph)n(ys.)g Fo(62)f Fr(\(1991\),)i(709{728.)0 3098 y([4])50 b(Jim)18 b(Y)-6 b(ork)n(e)20 b(and)g(Alexander)g(Lasota,) h Fb(On)g(the)h(existenc)l(e)f(of)h(invariant)g(me)l(asur)l(es)h(for)f (pie)l(c)l(ewise)g(mono-)125 3181 y(tonic)k(tr)l(ansformations)p Fr(,)f(T)-6 b(rans.)23 b(Amer.)f(Math.)h(So)r(c.)h Fo(186)f Fr(\(1973\),)i(481{488.)0 3264 y([5])50 b(Benoit)31 b(Saussol,)g Fb(A)n(bsolutely)h(c)l(ontinuous)h(invariant)e(me)l(asur)l(es)i(for)f (multidimensional)h(exp)l(andings)125 3348 y(maps)p Fr(,)25 b(Israel)e(J.)h(Math.)f Fo(116)g Fr(\(2000\),)i(pp.)f(223-248.)0 3431 y([6])50 b(Bernard)26 b(Sc)n(hmitt,)f Fb(Er)l(go)l(dic)j(the)l (ory)g(and)g(thermo)l(dynamic)g(of)g(one-dimensional)g(Markov)g(exp)l (anding)125 3514 y(endomorphisms)p Fr(,)g(Dynamical)d(systems)f(\(T)-6 b(em)n(uco,)25 b(1991/1992\),)j(T)-6 b(ra)n(v)l(aux)26 b(en)g(Cours,)e(52,)i(Hermann,)125 3597 y(P)n(aris,)d(1996.)0 3680 y([7])50 b(Masato)18 b(Tsujii,)f Fb(A)n(bsolutely)j(c)l(ontinuous) h(invariant)f(me)l(asur)l(es)h(for)f(pie)l(c)l(ewise)g(r)l(e)l (al-analytic)h(exp)l(anding)125 3763 y(maps)27 b(on)f(the)g(plane)p Fr(,)e(Comm.)d(Math.)j(Ph)n(ys.)f Fo(208)g Fr(\(2000\),)i(605{622.)0 3846 y([8])50 b(Masato)18 b(Tsujii,)e Fb(Pie)l(c)l(ewise)k(exp)l (anding)g(maps)h(on)f(the)f(plane)h(with)g(singular)g(er)l(go)l(dic)g (pr)l(op)l(erties)p Fr(,)f(Ergo)r(d.)125 3929 y(Th.)24 b(&)f(Dynam.)g(Syst.)h(\(to)g(app)r(ear\).)100 4111 y Fs(CMA)-6 b(T)26 b(/)g(Ecole)g(Pol)l(ytechnique)h(/)e(91128)f(P)-6 b(alaisea)o(u)26 b(cedex)h(/)e(France)100 4194 y Fb(E-mail)h(addr)l (ess)5 b Fr(:)37 b Fa(buzzi@math.polytechnique)q(.fr)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0006010817843--