Content-Type: multipart/mixed; boundary="-------------0302110418899" This is a multi-part message in MIME format. ---------------0302110418899 Content-Type: text/plain; name="03-47.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-47.keywords" Gibbs Fields, Semi--invariants, Cluster expansion, Disordered systems ---------------0302110418899 Content-Type: application/postscript; name="bcoalbero_preprint.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="bcoalbero_preprint.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: bcoalbero_preprint.dvi %%Pages: 18 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips bcoalbero_preprint -o %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.02.11:1058 %%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 %%BeginProcSet: color.pro %! TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop setrgbcolor}{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll }repeat setrgbcolor pop}ifelse}B}ifelse/TeXcolorcmyk{setcmykcolor}def /TeXcolorrgb{setrgbcolor}def/TeXcolorgrey{setgray}def/TeXcolorgray{ setgray}def/TeXcolorhsb{sethsbcolor}def/currentcmykcolor where{pop}{ /currentcmykcolor{currentrgbcolor 10}B}ifelse/DC{exch dup userdict exch known{pop pop}{X}ifelse}B/GreenYellow{0.15 0 0.69 0 setcmykcolor}DC /Yellow{0 0 1 0 setcmykcolor}DC/Goldenrod{0 0.10 0.84 0 setcmykcolor}DC /Dandelion{0 0.29 0.84 0 setcmykcolor}DC/Apricot{0 0.32 0.52 0 setcmykcolor}DC/Peach{0 0.50 0.70 0 setcmykcolor}DC/Melon{0 0.46 0.50 0 setcmykcolor}DC/YellowOrange{0 0.42 1 0 setcmykcolor}DC/Orange{0 0.61 0.87 0 setcmykcolor}DC/BurntOrange{0 0.51 1 0 setcmykcolor}DC /Bittersweet{0 0.75 1 0.24 setcmykcolor}DC/RedOrange{0 0.77 0.87 0 setcmykcolor}DC/Mahogany{0 0.85 0.87 0.35 setcmykcolor}DC/Maroon{0 0.87 0.68 0.32 setcmykcolor}DC/BrickRed{0 0.89 0.94 0.28 setcmykcolor}DC/Red{ 0 1 1 0 setcmykcolor}DC/OrangeRed{0 1 0.50 0 setcmykcolor}DC/RubineRed{ 0 1 0.13 0 setcmykcolor}DC/WildStrawberry{0 0.96 0.39 0 setcmykcolor}DC /Salmon{0 0.53 0.38 0 setcmykcolor}DC/CarnationPink{0 0.63 0 0 setcmykcolor}DC/Magenta{0 1 0 0 setcmykcolor}DC/VioletRed{0 0.81 0 0 setcmykcolor}DC/Rhodamine{0 0.82 0 0 setcmykcolor}DC/Mulberry{0.34 0.90 0 0.02 setcmykcolor}DC/RedViolet{0.07 0.90 0 0.34 setcmykcolor}DC /Fuchsia{0.47 0.91 0 0.08 setcmykcolor}DC/Lavender{0 0.48 0 0 setcmykcolor}DC/Thistle{0.12 0.59 0 0 setcmykcolor}DC/Orchid{0.32 0.64 0 0 setcmykcolor}DC/DarkOrchid{0.40 0.80 0.20 0 setcmykcolor}DC/Purple{ 0.45 0.86 0 0 setcmykcolor}DC/Plum{0.50 1 0 0 setcmykcolor}DC/Violet{ 0.79 0.88 0 0 setcmykcolor}DC/RoyalPurple{0.75 0.90 0 0 setcmykcolor}DC /BlueViolet{0.86 0.91 0 0.04 setcmykcolor}DC/Periwinkle{0.57 0.55 0 0 setcmykcolor}DC/CadetBlue{0.62 0.57 0.23 0 setcmykcolor}DC /CornflowerBlue{0.65 0.13 0 0 setcmykcolor}DC/MidnightBlue{0.98 0.13 0 0.43 setcmykcolor}DC/NavyBlue{0.94 0.54 0 0 setcmykcolor}DC/RoyalBlue{1 0.50 0 0 setcmykcolor}DC/Blue{1 1 0 0 setcmykcolor}DC/Cerulean{0.94 0.11 0 0 setcmykcolor}DC/Cyan{1 0 0 0 setcmykcolor}DC/ProcessBlue{0.96 0 0 0 setcmykcolor}DC/SkyBlue{0.62 0 0.12 0 setcmykcolor}DC/Turquoise{0.85 0 0.20 0 setcmykcolor}DC/TealBlue{0.86 0 0.34 0.02 setcmykcolor}DC /Aquamarine{0.82 0 0.30 0 setcmykcolor}DC/BlueGreen{0.85 0 0.33 0 setcmykcolor}DC/Emerald{1 0 0.50 0 setcmykcolor}DC/JungleGreen{0.99 0 0.52 0 setcmykcolor}DC/SeaGreen{0.69 0 0.50 0 setcmykcolor}DC/Green{1 0 1 0 setcmykcolor}DC/ForestGreen{0.91 0 0.88 0.12 setcmykcolor}DC /PineGreen{0.92 0 0.59 0.25 setcmykcolor}DC/LimeGreen{0.50 0 1 0 setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{ 0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor} DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70 setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0 setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1 setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end %%EndProcSet TeXDict begin 39158280 55380996 1000 600 600 (bcoalbero_preprint.dvi) @start %DVIPSBitmapFont: Fa cmmi10 10.95 1 /Fa 1 69 df<49B712F818FF19C0D9000190C7EA3FF0F00FF84BEC03FCF000FE197F0203 EE3F805DF11FC0A20207EE0FE05D1AF0A2020F16075DA21AF8141F5DA2190F143F5DA21A F0147F4B151FA302FF17E092C9123FA21AC049177F5C1A8019FF010318005C4E5A610107 16034A5E4E5A180F010F4C5A4A5E4E5A4EC7FC011F16FE4A4A5AEF07F8013FED0FE0EF3F C04A49B4C8FC017FEC0FFCB812F017C004FCC9FC453E7DBD4B>68 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb cmsl10 10.95 25 /Fb 25 122 df19 D<121EEA3F80EA7FC012FFA41380EA7F0012 3C0A0A788919>46 D<17E016011603831607A2160FA2161F83163FA2167F167716F7EEE7 FCED01E316C3150316831507EE03FEED0F01150E151E151C153C03387FED7800157015F0 5D4A4880177F4A5AA24AC7FCA2020E81173F5C021FB6FC5CA20270C7EA3FE0171F5CA249 5AA2494881170F49C8FCA2130EA24982013C1507A2137CD801FE4B7E2607FF80EC3FFEB5 00F00107B512FC19F85E3E417DC044>65 D67 D<013FB7FC18E018F8903B007FF0000FFE6E48EB01FF9438007FC04B6E7E180F 85727E727E147F4B6E7EA2727EA302FF178092C9FCA54918C05CA41A8013034A5DA41A00 13074A5DA261A24E5A130F4A5E180F61181F61011F4C5A5C4E5A4EC7FC4D5A4D5A013F4B 5A4A4A5AEF3FE0EF7F80017F4A48C8FC01FFEC1FFCB812F0178004FCC9FC423E7DBD45> I<013FB5D8F807B6FC04F015FEA29026007FF0C7380FFE006E486E5AA24B5DA4180F147F 4B5DA4181F14FF92C85BA4183F5B4A5EA491B8FC5B6102FCC8127FA318FF13074A93C7FC A45F130F4A5DA41703131F4A5DA41707133F4A5DA3017F150F496C4A7EB6D8E01FB512FC 6115C0483E7DBD44>72 D<011FB512FC5BA29039003FF8006E5AA25DA5143F5DA5147F5D A514FF92C7FCA55B5CA513035CA513075CA5130F5CA5131F5CA3133F497E007FB512F0A2 B6FC263E7EBD21>I<021FB512FCA3DA000713006F5AA25EA41507A25EA4150FA25EA415 1FA25EA4153FA25EA4157FA25EA415FFA293C7FCA45C121FD87F805BEAFFC0A214035D13 804A5AEAFE0000F8495A48495A00705C6C495A6C01FEC8FC380F81FC3803FFE0C690C9FC 2E407ABD2F>I<90263FFFF093381FFFF85013F0629026007FF8EFF000023F4D5AA2023B 933801DFC0A2DA39FCED039FA2F1073F14790271040E5BEC70FE191C19381A7F02F01670 DAE07F94C7FC19E0A2F001C06201016D6C495A02C05FF00700A2180E6F6C14010103161C 028003385BA218706F7EF0E00313070200DA01C05BA2923907F00380A294380700075B01 0E902603F80E5C5FA25F190F011E6D6C5A011C605FA2EEFDC0DB00FF141F013C5D013860 013C92C7FC017C5C01FE027E143F2607FF80017C4A7EB500FC037FB512E004785E4A1338 553E7CBD53>77 D<013FB612FEEFFFE018F8903B007FF0000FFC6E48EB01FF7113804BEC 7FC0183F19E0F01FF0A2147F5D19F8A402FFED3FF092C8FCA219E0A2F07FC05B4AEDFF80 19004D5A4D5AEF0FF80103ED3FE04A903801FF8091B648C7FC17F002FCCAFCA213075CA5 130F5CA5131F5CA5133F5CA3137F497EB612E0A25D3D3E7DBD3E>80 D<9238FF80070207EBE00F021FEBF81E91387F00FE02FCEB1F3ED903F0EB0FFE49481307 494813034AEB01FC49C7FC491400133E137E177C491578A57F1770A26D1500808080EB7F FEECFFE06D13FEEDFFC06D14F06D14FC010380010080143F02031480DA003F13C0150315 00EE7FE0163F161FA2160F121CA31607160F003C16C0A31780003E151F1700007E5D007F 153E6D5C16FC01E0495AD87DF0495AD8FCFCEB0FC03AF87F803F8027F01FFFFEC7FCD8E0 0713F839C0007FC030427BBF33>83 D97 DIIII<147FEB3FFFA313 017FA25CA513015CA513035CA4ED07F80107EB1FFF9139F0781FC09138F1E00F9139F380 07E0ECF70002FE14F0495A5CA25CA24A130F131F4A14E0A4161F133F4A14C0A4163F137F 91C71380A4167F5B491500A300015D486C491380B5D8F87F13FCA32E3F7DBE33>104 D<1478EB01FE130314FFA25B14FE130314FCEB00F01400ACEB03F8EA01FF14F0A2EA001F 130FA314E0A5131F14C0A5133F1480A5137F1400A55B5BA4EA03FF007F13F0A2B5FC183E 7DBD1A>I<902707F007F8EB03FCD803FFD91FFF90380FFF80913CE0781FC03C0FE09126 E1E00FEBF0073E001FE38007E1C003F090260FE700EBE38002EEDAF70013F802FC14FE02 D85C14F84A5CA24A5C011F020F14074A4A14F0A5013F021F140F4A4A14E0A5017F023F14 1F91C74914C0A549027F143F4992C71380A300014B147F486C496DEBFFC0B5D8F87FD9FC 3F13FEA347287DA74C>109 D<903907F007F8D803FFEB1FFF9139E0781FC09138E1E00F 3B001FE38007E090380FE70002EE14F014FC14D814F85CA24A130F131F4A14E0A4161F13 3F4A14C0A4163F137F91C71380A4167F5B491500A300015D486C491380B5D8F87F13FCA3 2E287DA733>II<903907F01F80D803FFEB7FE09138E1E1F091 38E387F839001FE707EB0FE614EE02FC13F002D813E09138F801804AC7FCA25C131FA25C A4133F5CA5137F91C8FCA55B5BA31201487EB512FEA325287EA724>114 D<9138FF81C0010713E390381F807F90397C003F8049131F4848130F5B00031407A24848 1400A27FA27F6D90C7FCEBFF8014FC6C13FF6C14C015F06C6C7F011F7F13079038007FFE 1403140100381300157EA2123C153E157E007C147CA2007E147815F8007F495A4A5A486C 485A26F9E01FC7FC38E0FFFC38C01FE0222A7DA824>II<90B539E007FFF05E18E0902707FE000313006D48EB01FC705A5F 01014A5A5F16036E5C0100140794C7FC160E805E805E1678ED8070023F13F05EED81C015 C191381FC38015C793C8FC15EF15EEEC0FFCA25DA26E5AA25DA26E5A5DA24AC9FC5C140E 141E141C5C121C003F5B5A485B495A130300FE5B4848CAFCEA701EEA783CEA3FF0EA0FC0 343A80A630>121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmbx12 17.28 7 /Fc 7 116 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fd line10 10 5 /Fd 5 83 df<1C0C1C1E1C3E1C7E1CFCF301F8F303F0F307E0F30FC0F31F80F33F001B7E 63505A505A505A505A505A50C7FC1A7E624F5A4F5A4F5A4F5A4F5A4FC8FC197E614E5A4E 5A4E5A4E5A4E5A4EC9FC187E604D5A4D5A4D5A4D5A4D5A4DCAFC177E5F4C5A4C5A4C5A4C 5A4C5A4CCBFC167E5E4B5A4B5A4B5A4B5A4B5A4BCCFC157E5D4A5A4A5A4A5A4A5A4A5A4A CDFC147E5C495A495A495A495A495A49CEFC137E5B485A485A485A485A485A48CFFC127E 5A5A1260575782D453>0 D<15011502150C153C15F81403EC0FF0143FECFFE01303011F 13C0137F0003B51280121FB612007E6C5B7E6C5B7E7E6C5B7E6D5A133F131F6D5A130713 036D5A1300144020204DD253>18 D<126012F87E127E7E6C7E6C7E6C7E6C7E6C7E6C7E13 7E7F6D7E6D7E6D7E6D7E6D7E6D7E147E806E7E6E7E6E7E6E7E6E7E6E7E157E816F7E6F7E 6F7E6F7E6F7E6F7E167E82707E707E707E707E707E707E177E83717E717E717E717E717E 717E187E84727E727E727E727E727E727E197E85737E737E737E737E737E737E1A7E8674 7E747E747E747E747E747E1B7E87F31F80F30FC0F307E0F303F0F301F8F300FC1C7E1C3E 1C1E1C0C575782D453>64 D<7E12401230123C121F13C0EA0FF013FC6CB4FC14C06C13F8 14FE6CEBFFC015F86C14FF15FE6D13FC15F86D13F015E015C06D138015006D5A5C5C6D5A 5C5C6D5A91C7FC1302202080D253>73 D<144014C01301497E1307130F497E133F137F49 7E5A487F5A5A487F5A487FB6FC001F14801203C66C13C0131F010313E01300EC3FF0140F EC03F81400153C150C1502150120204D9F53>82 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe lcircle10 10 1 /Fe 1 116 df115 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff msbm6 6 1 /Ff 1 77 df76 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg cmex8 8 1 /Fg 1 102 df<017F14082601FFC0131C000701F01378489038FC01F0D83E00B512C000 78013F138000E090380FFE000040EB03F8260880AF27>101 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh cmex7 6 2 /Fh 2 102 df<0060150C00F0151EB3B06C153EA20078153C007C157CA26C15F8003F14 016C6CEB03F06C6CEB07E0D807F0EB1FC03A03FF01FF80C69038FFFE006D5B011F13F001 0190C7FC27327C7F30>83 D101 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fi cmsy6 6 15 /Fi 15 111 df0 D20 D<12E012F812FEEA3F80EA0FE0EA03F8EA00FEEB3F80EB0FC0EB03F0EB00FC147FEC1FC0 EC07F0EC01FCEC007FED1FC01507151FED7F00EC01FCEC07F0EC1FC0027FC7FC14FCEB03 F0EB0FC0EB3F8001FEC8FCEA03F8EA0FE0EA3F80007EC9FC12F812E0CAFCA9007FB61280 B712C0A2222F7AA230>I<0107B512C0133F90B6FCD801FCC8FCEA03E0EA078048C9FC12 1E121C123C5A1270A212F05AA77E1270A212787E121C121E7E6C7EEA03E0EA01FC6CB612 C0133F130722237A9D30>26 D<387FFFF8B6FC6C14C0C7EA0FE0EC01F0EC00788181150E 150FED07801503A216C01501A715031680A21507ED0F00150E151E5D5D4A5AEC0FE0007F B55AB6C7FC6C13F822237A9D30>I48 D<903807FFF0133F5BD8 01FCC7FCEA03E0485A48C8FC121E121C123C5A1270A212F05AA2B612F0A300E0C8FCA27E 1270A212787E121C121E7E6C7EEA03E0EA01FC6CB512F0133F13071C237A9D2A>50 D<1570A215F015E01401EC03C01580140715005C140E141E5C14381478147014F05C1301 495A5C130791C7FC5B130E131E131C133C5B137013F05B12015B1203485A90C8FC5A120E 121E121C123C5A127012F05A12601C2F77A300>54 D<0060140600E0140E6C141E007014 1CA20078143C00381438003C1478001C1470001E14F0000E14E0A2000FB5FC6C14C0A239 03800380EBC00700011400A26D5A0000130EEBF01EEB701CEB783CEB3838A2EB3C78EB1C 70EB1EF0EB0EE0130F6D5AA36D5AA21F247FA223>56 D<146014E013FCEA03FF380787C0 EA0E01381C03E0003813F0A2387807F800701338A2130F38F00E3CA2131E131CA2133C13 3813781370A213F013E0A212F113C0007113381273387B8078A2003F1370EB00F06C13E0 380F01C0EB8780EBFF00EA1EFC001CC7FCA3162A7CA520>59 D92 D102 D<12FCB47EEA0FC0EA01E06C7EB0 1378A2133EEB0FF01303130FEB3E001378A25BB0485AEA0FC0B45A00FCC7FC14317BA420 >I<12E0B3B3AD033179A413>106 D<12E0A27E1270A212781238123C121C121E120EA212 0F7E7F1203A27F12017F1200A27F137013781338133C131CA2131E130E130F7FA2148013 0314C01301A214E0130014F0147014781438A2143C141C140C16317CA420>110 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj cmr6 6 10 /Fj 10 100 df0 D<14E0A3497EA2497EA3EB06FC147CA2EB0C7E143EEB1C3FEB181F A201307F140FA201607F140701E07FEBC003A2D801807F1401A2D803007F140048800006 147CA2000E147E121F3AFFE007FFE0A223247DA329>3 D<130C1338137013E0EA01C0EA 038013005A120EA25AA25AA312781270A312F0AB1270A312781238A37EA27EA27E7E1380 EA01C0EA00E013701338130C0E317AA418>40 D<12C012707E7E7E7E7E1380EA01C0A2EA 00E0A21370A313781338A3133CAB1338A313781370A313E0A2EA01C0A2EA038013005A12 0E5A5A5A12C00E317CA418>I<13FF000313C0380781E0380F00F0001E137848133CA248 131EA400F8131FAD0078131EA2007C133E003C133CA26C13786C13F0380781E03803FFC0 C6130018227DA01E>48 D<13E01201120712FF12F91201B3A7487EB512C0A212217AA01E >II<127812FCA412781200A9127812FCA412 7806157A9412>58 D61 D<137F3803FFE03807C0F0380F0078001E13F85AA2007C13700078130012F8A7127C1418 123C6C13306C13603807C0E03803FF8038007E0015187D961B>99 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmti12 12 55 /Fk 55 124 df12 D14 D<13F0EA03F8EA07FC120FA6EA03CCEA001C1318A213381330A2137013E013C012 0113801203EA0700120E5A5A5A5A5A0E1D6BC41E>39 D<167016E0ED01C0ED0380ED0700 150E153C5D15F85D4A5A4A5A4A5A140F4AC7FC141E143E5C147814F8495A5C1303495AA2 495AA249C8FCA25B133E137E137CA25BA212015BA212035BA212075BA2120FA25BA2121F A290C9FCA25AA2123EA3127EA2127CA65AAB1278A6127C123CA47EA2120E120FA27E6C7E A26C7EA26C7E1360246472CA28>I<1560A2157081A281151E150E150FA2811680A3ED03 C0A516E0A21501A71503A91507A216C0A4150FA21680A2151FA21600A25DA2153EA2157E A2157C15FCA25D1401A25D14035DA214075D140F5DA24AC7FCA2143EA25C147814F8495A A2495A5C1307495A91C8FC131E133E5B13785B485A485A485A48C9FC121E5A5A12E05A23 647FCA28>I<13F0EA03FC1207A2EA0FFEA4EA07FCEA03CCEA000C131C1318A213381330 1370136013E0EA01C013801203EA0700120E5A5A5A5A5A0F1D7A891E>44 D<120FEA3FC0127FA212FFA31380EA7F00123C0A0A76891E>46 DII<16C01501A215031507 ED0F80151F153F157F913801FF005C140F147F903807FCFEEB0FF0EB0700EB00015DA314 035DA314075DA3140F5DA3141F5DA3143F5DA3147F92C7FCA35C5CA313015CA313035CA3 13075CA2130FA2131F133FB612FCA25D224276C132>IIII<026014300278EB01F091397F801FE0 91B612C01780170016FC4914F016C0DACFFEC7FC02C0C8FC13035CA3130791C9FCA35B13 0EA3131E90381C07F8EC3FFE9138F80F8090393DC007C0D93F807F90383E0003013C8049 6D7E1370A290C7FC82A41503A415075E120E123F486C130F00FF5DA390C7485A5A00F84A 5A12E04B5A93C7FC15FE14016C5C0070495A0078495A6CEB1FC0003E495A261F80FEC8FC 6CB45A000313E0C66CC9FC2C4476C132>II56 D<130FEB1FC0133FEB7FE013FFA214C0EB7F801400131E90C7FCB3A5120FEA3FC0127FA2 12FFA35B6CC7FC123C132B76AA1E>58 D65 D67 D<91B712F818FF19C00201903980003FF06E90C7 EA0FF84AED03FCF000FE4B157FA2F13F800203EE1FC05DF10FE0A214074B16F01907A214 0F5D1AF8A2141F5DA2190F143F5D1AF0A2147F4B151FA302FF17E092C9123FA34918C04A 167F1A80A2010317FF4A1700A24E5A13074A4B5A611807010F5F4A4B5A181F61011F4C5A 4A4BC7FC18FE4D5A013F4B5A4A4A5A4D5A017FED3FC005FFC8FC4AEB03FE01FFEC1FF8B8 12E094C9FC16F845447AC34A>I<91B912C0A30201902680000313806E90C8127F4A163F 191F4B150FA30203EE07005DA314074B5D190EA2140F4B1307A25F021F020E90C7FC5DA2 171E023F141C4B133C177C17FC027FEB03F892B5FCA39139FF8003F0ED00011600A2495D 5CA2160101034B13705C19F061010791C8FC4A1501611803010F5F4A150796C7FC60131F 4A151E183E183C013F167C4A15FC4D5A017F1503EF0FF04A143F01FF913803FFE0B9FCA2 6042447AC342>I<91B91280A30201902680000713006E90C8FC4A163FA24B81A3020316 0E5DA314074B151E191CA2140F5D17075F021F020E90C7FC5DA2171E023F141C4B133CA2 177C027F5CED800392B5FCA291B65AED00071601A2496E5A5CA2160101035D5CA2160301 075D4A90CAFCA3130F5CA3131F5CA3133F5CA2137FA313FFB612E0A341447AC340>II<91B6D8 803FB512E0A302010180C7387FE0006E90C86C5A4A167FA24B5EA219FF14034B93C7FCA2 6014074B5DA21803140F4B5DA21807141F4B5DA2180F143F4B5DA2181F147F92B75AA3DA FF80C7123F92C85BA2187F5B4A5EA218FF13034A93C8FCA25F13074A5DA21703130F4A5D A21707131F4A5DA2170F133F4A5DA2017F151FA24A5D496C4A7EB6D8803FB512E0A34B44 7AC348>I<027FB512E091B6FCA20200EBE000ED7F8015FFA293C7FCA35C5DA314035DA3 14075DA3140F5DA3141F5DA3143F5DA3147F5DA314FF92C8FCA35B5CA313035CA313075C A3130F5CA3131F5CA2133FA25CEBFFE0B612E0A25D2B447BC326>I<91B612F0A25F0201 01C0C7FC6E5B4A90C8FCA25DA314035DA314075DA3140F5DA3141F5DA3143F5DA3147F5D A314FF92C9FCA35B5CA3010316104A1538A21878010716705C18F018E0010F15015C18C0 1703011F15074A1580170FA2013FED1F004A5C5F017F15FE16034A130F01FFEC7FFCB8FC A25F35447AC33D>76 D<91B56C93387FFFC08298B5FC02014DEBC0006E614A5FA203DF4C 6CC7FC1A0E63912603CFE05D038F5F1A381A711407030FEEE1FCA2F101C3020FEE038302 0E60F107036F6C1507021E160E021C60191CF1380F143C023804705BA2F1E01F0278ED01 C091267003F85EF003801A3F02F0ED070002E0030E5CA24E137F130102C04B91C8FC6062 01036D6C5B02805F4D5A943803800113070200DA07005BA2050E1303495D010E606F6C5A 1907011E5D011C4B5CA27048130F133C01384B5C017892C7FC191F01F85C486C027E5DD8 07FE027C4A7EB500F00178013FB512C0A216705A447AC357>I<91B712F018FEF0FF8002 01903980007FE06E90C7EA1FF04AED07F818034B15FCF001FE1403A24B15FFA21407A25D A2140FF003FE5DA2021F16FC18074B15F8180F023F16F0F01FE04B15C0F03F80027FED7F 0018FE4BEB03FCEF0FF002FFEC7FC092B6C7FC17F892CAFC5BA25CA21303A25CA21307A2 5CA2130FA25CA2131FA25CA2133FA25CA2137FA25C497EB67EA340447AC342>80 D<91B77E18F818FE020190398001FF806E90C7EA3FC04AED1FE0F00FF04BEC07F8180319 FC14034B15FEA314075DA3020FED07FC5DA2F00FF8141F4B15F0F01FE0F03FC0023F1680 4BEC7F0018FEEF03F8027F4A5A4BEB1FC04CB4C7FC92B512F891B612E092380003F8EE00 FE177F496F7E4A6E7EA28413034A140FA2171F13075CA2173F130F5CA24D5A131F5CA301 3F170E5CA2017FEE801E191C4A163C496C1638B66C90383FC070051F13F094380FE1E0CA 3803FF80943800FE003F467AC347>82 DI<48B912F85AA2913B0007FC001FF0D807F84A130701E0010F14034916014848 5C90C71500A2001E021F15E05E121C123C0038143F4C1301007818C0127000F0147F485D A3C800FF91C7FC93C9FCA35C5DA314035DA314075DA3140F5DA3141F5DA3143F5DA3147F 5DA314FF92CAFCA35B5CA21303A21307497E007FB612C0A25E3D446FC346>I97 DIIIII<15FCEC03FF91390F8383809139 3E01CFC091387C00EF4A13FF4948137F010315804948133F495A131F4A1400133F91C75A 5B167E13FE16FE1201495CA215011203495CA21503A2495CA21507A25EA2150F151F5E00 01143F157F6C6C13FF913801DF8090387C039F90383E0F3FEB0FFCD903F090C7FC90C7FC 5DA2157EA215FEA25DA2001C495A127F48495A14074A5A485C023FC8FC00F8137E387C01 F8381FFFE0000390C9FC2A407BAB2D>I<14FE137FA3EB01FC13001301A25CA21303A25C A21307A25CA2130FA25CA2131FA25C157F90393F83FFC091388F81F091381E00F802387F 4948137C5C4A137EA2495A91C7FCA25B484814FE5E5BA2000314015E5BA2000714035E5B 1507000F5DA249130F5E001F1678031F1370491480A2003F023F13F0EE00E090C7FC1601 48023E13C01603007E1680EE070000FEEC1E0FED1F1E48EC0FF80038EC03E02D467AC432 >I<143C147E14FE1301A3EB00FC14701400AE137C48B4FC3803C780380703C0000F13E0 120E121C13071238A21278EA700F14C0131F00F0138012E0EA003F1400A25B137EA213FE 5B12015BA212035B141E0007131C13E0A2000F133CEBC038A21478EB807014F014E0EB81 C0EA0783EBC7803803FE00EA00F8174378C11E>I108 DIIII114 DI<1470EB01F8A313 035CA313075CA3130F5CA3131F5CA2007FB512E0B6FC15C0D8003FC7FCA25B137EA313FE 5BA312015BA312035BA312075BA3120F5BA2EC0780001F140013805C140E003F131EEB00 1C143C14385C6C13F0495A6C485AEB8780D807FEC7FCEA01F81B3F78BD20>I<137C48B4 14072603C780EB1F80380703C0000F7F000E153F121C0107150012385E1278D8700F147E 5C011F14FE00F05B00E05DEA003FEC0001A2495C137E150313FE495CA215071201495CA2 030F13380003167849ECC070A3031F13F0EE80E0153F00011581037F13C06DEBEF830000 0101148090397C03C787903A3E0F07C70090391FFE01FE903903F000782D2D78AB34>I< 017C143848B414FC3A03C78001FE380703C0000F13E0120E001C14000107147E1238163E 1278D8700F141E5C131F00F049131C12E0EA003F91C7123C16385B137E167801FE14705B A216F0000115E05B150116C0A24848EB0380A2ED0700A2150E12015D6D5B000014786D5B 90387C01E090383F0780D90FFFC7FCEB03F8272D78AB2D>I<017CEE038048B4020EEB0F C02603C780013FEB1FE0380703C0000E7F5E001C037E130F01071607123804FE13030078 5DEA700F4A1501011F130100F001804914C012E0EA003FDA000314034C14805B137E0307 140701FE1700495CA2030F5C0001170E495CA260A24848495A60A2601201033F5C7F4B6C 485A000002F713036D9039E7E0078090267E01C349C7FC903A1F0781F81E903A0FFF007F F8D901FCEB0FE03B2D78AB41>I<02F8133FD907FEEBFFE0903A0F0F83C0F0903A1C07C7 80F890393803CF03017013EE01E0EBFC07120101C013F8000316F00180EC01C000074AC7 FC13001407485C120EC7FC140F5DA3141F5DA3143F92C8FCA34AEB03C01780147EA202FE EB0700121E003F5D267F81FC130E6E5BD8FF83143CD903BE5B26FE079E5B3A7C0F1F01E0 3A3C1E0F83C0271FF803FFC7FC3907E000FC2D2D7CAB2D>I<137C48B414072603C780EB 1F80380703C0000F7F000E153F001C1600130712385E0078157EEA700F5C011F14FE00F0 495B12E0EA003FEC00015E5B137E150301FE5C5BA2150700015D5BA2150F00035D5BA215 1F5EA2153F12014BC7FC6D5B00005BEB7C0390383E0F7EEB1FFEEB03F090C712FE5DA214 015D121F397F8003F0A24A5A4848485A5D48131F00F049C8FC0070137E007813F8383801 F0381E07C06CB4C9FCEA01FC294078AB2F>I<027C130749B4130F49EB800E010F141E49 EBC03CEDE03890393F03F07890397C00FDF00178EB3FE00170EB03C001F0148049130790 C7EA0F00151E5D5D5D4A5A4A5A4A5A4AC7FC141E5C5C5C495A495A495A49C8FC011E14F0 4914E05B491301485A4848EB03C0D807B0130701FEEB0F80390FCF801F3A1F07E07F0039 3E03FFFED83C015B486C5B00705C00F0EB7FC048011FC7FC282D7BAB28>II E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmmi6 6 27 /Fl 27 111 df<13F8D803FE1318487E48EB803048EBC060EA3C03397000E0C000601360 48EB71801431C7FCEC3300141B141EA2141CA31418A31438A214301470A45CA35CA21D21 7E9520>13 D<0003B512FC120F5A4814F8397818180000E01338EAC03000001330A21370 1360EBE070A21478EA01C0A21203EB807C0007133C143E380F003C000613181E167D9424 >25 D<127812FCA4127806067A8513>58 D<127812FCA212FEA2127E1206A3120CA2121C 121812301260124007107A8513>II<90B6FC16E0903907C003F8ED00FC4948133E161E161F EE0F8049C7FCA317C0133EA4491580161FA21700495CA2163E5E485A5E4B5A4B5A484849 5A4B5A033EC7FC0007EB01F8B612E092C8FC2A227CA132>68 D<90B612FCA2903807C000 163C4948131CA2160CA249C7FCA21530A2013EEB6000A215E0140190387FFFC0A2EB7C03 140101F85BA44848C8FCA4485AA31207B57EA226227CA127>70 D<903AFFFE07FFF0A290 3A07C0003E00A249485BA449C75AA4013E495AA3013FB5FC495C90387C0003A349495AA4 4848495AA4484849C7FCA300075C3AFFFE07FFF0A22C227CA132>72 DI<903801FFFCA290380007C0A2EC0F80A4EC1F00A4143EA45CA45CA4495A 1218123C127E48485AA248485A38600F80D8783EC7FCEA3FFCEA0FE01E237CA122>II78 D86 D 88 D<14E0EB01F0EB03181307130E130CEB1C30133C1338137814601370EBF0C0A2EBE1 801201EBE30013E6EA03C613CC13D813F05B12075B5BA2120F121F1237126700C3131000 03133014E0380181C0EBFF006C5A15257FA31A>96 D98 DII<140FEC3FC0EC71E014E3A2010113C0ECE180ECE00049 5AA5495AA2EBFFFEA2EB0780A249C7FCA5131EA65BA55BA31370A2EA38F0EA78E012F8EA F9C0EA7180007FC8FC121E1B2F7CA31E>102 DI<13F8EA0FF0A21200A2485AA4485AA4380787E0EB9FF8EBB83CEBE01C380FC01E1380 A21300001E5BA35C5AA2ECF0201530481460EB01E015C0A239F000E380ECFF000060133C 1C247CA224>I<1338137CA2137813701300A7EA0780EA1FC0EA38E01230EA60F0EAC1E0 A3EA03C0A3EA0780A2EA0F0013041306EA1E0CA21318121CEA1E70EA0FE0EA07800F237D A116>I<1418143C147CA214381400A7EB0780EB1FE01338EB60F013C0A2EA0180A23800 01E0A4EB03C0A4EB0780A4EB0F00A4131EA21238EA783CEAF8381378EA70F0EA7FC0001F C7FC162D81A119>I<13F8EA0FF0A21200A2485AA4485AA43807801E147FEB81C3EB8387 380F060F495A1318EB700E4848C7FCA213FCEA1E7EEA3C0F80EB0781158039780F0300A2 1402EB070600F0138CEB03F8386000F019247CA221>II<000F017E13FC3A1F81FF83FF3B31C383C707803A61EE03CC039026EC01F813 C0D8C1F813F013F001E013E00003903903C0078013C0A2EE0F003907800780A2EE1E0417 06270F000F00130C163C1718A2001E011EEB1C70EE1FE0000C010CEB07802F177D9536> I<000F13FC381FC3FF3931C707803861EC0301F813C0EAC1F0A213E03903C00780A3EC0F 00EA0780A2EC1E041506D80F00130C143C15181538001EEB1C70EC1FE0000CEB07801F17 7D9526>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm msbm8 8 2 /Fm 2 91 df76 D<001FB612FCA23A183E00 701801F0EB6038D81BC0EBE030001FC7EAC070003E010113E0003C90380380C015010038 01071380EC0603003090380E0700EC1C06EC180EC7EA380CEC301CEC7038ECE030ECC070 01015B4A5AEB03819038070180EB0603D90E07C7FCEB0C06EB1C0EEB380CEB301CD97038 1303EBE030EBC070000101601307EB80E0260381C0130626070180130ED80603141E000E 90C7FCD80C07143ED81C0E1476D8380C14E6D8301CEB01CED87018EB078CD86038EB3E0C B712FCA2282E7EAD38>90 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn cmsy8 8 23 /Fn 23 111 df0 D<123C127E12FFA4127E123C08087A9414>I< EE01C01607161FEE7F00ED01FCED07F0ED1FC0037FC7FCEC01FCEC07F0EC0FC0023FC8FC 14FCEB03F8EB0FE0EB3F8001FEC9FCEA03F8EA0FE0EA3F8000FECAFC12F812FEEA3F80EA 0FE0EA03F8EA00FEEB3F80EB0FE0EB03F8EB00FC143FEC0FC0EC07F0EC01FCEC007FED1F C0ED07F0ED01FCED007FEE1FC01607160193C7FCAD007FB71280B812C0A22A3B7AAB37> 20 D<12E012F812FEEA3F80EA0FE0EA03F8EA00FEEB3F80EB0FE0EB03F8EB00FC143FEC 0FC0EC07F0EC01FCEC007FED1FC0ED07F0ED01FCED007FEE1FC01607161FEE7F00ED01FC ED07F0ED1FC0037FC7FCEC01FCEC07F0EC0FC0023FC8FC14FCEB03F8EB0FE0EB3F8001FE C9FCEA03F8EA0FE0EA3F80007ECAFC12F812E0CBFCAD007FB71280B812C0A22A3B7AAB37 >I<91B612C01307131FD97F80C8FC01FCC9FCEA01F0EA03C0485A48CAFC121E121C123C 123812781270A212F05AA97E1270A212781238123C121C121E7E6C7E6C7EEA01F0EA00FC EB7F80011FB612C0130713002A2B7AA537>26 D<137813FE1201A3120313FCA3EA07F8A3 13F0A2EA0FE0A313C0121F1380A3EA3F00A3123E127E127CA35AA35A0F227EA413>48 DI<91B512C01307131FD97F80C7FC01FCC8FCEA01F0EA03 C0485A48C9FC120E121E5A123812781270A212F05AA3B712C0A300E0C9FCA37E1270A212 781238123C7E120E120F6C7E6C7EEA01F0EA00FCEB7F80011FB512C013071300222B7AA5 2F>I<387FFFC0B512F86C13FEC7EA7F80EC0FC0EC03E0EC00F0157881151C151E818116 801503A216C01501A3B7FCA3C81201A315031680A2150716005D151E151C153C5D5DEC03 E0EC0FC0EC7F80267FFFFEC7FCB512F86C13C0222B7AA52F>I54 D<1406140EA2141EEB1F9CEBFFFC3801E07C3803803C3807003E48133F001EEB7F80001C 1373003C14C014F314E3007C14E0007813E1130114C100F814F013031481A313071401A2 130F130EA3131E131CA3133C1338007814E013781370007C1303003C14C013F013E0001E EB0780121F390FC00F000007131E143E3803E078EBFFF0EB9F80D80780C7FC90C8FCA31C 387DB223>59 D67 D<91383FFFF00107B6FC 011F15E0017F812701F83E0313FCD803C09038003FFED80F00EC07FF001E017E6D138048 1500007CEE7FC00078163F48EE1FE048137CC7150FA202FC1407A25CA3010116C05CA2EF 0F8013034A15005F171E49485C177C177849485C4C5A4C5A49C7485A040EC7FC163C013E 14F0ED03E0013CEB0F80017C01FEC8FC90387FFFF848B512E04849C9FC4813E0332D7EAC 37>I<023FB512F80107B6FC011F15E0017F15C09026F8001EC7FCD803C05B4848137C00 0F147890C712F8121E0018495AC7FCA24A5AA34A5AA3140F5DA3141F92C8FCA35C143EA3 5CA2147814F85C010114064A131C0103143C4A5B49485B000FB612C0003F5D484AC7FCB6 12F02D2D81AC27>73 D83 D<181C183C0107B712F8011F16F0 90B812C0481700270780007CC8FC48C712FC121E123E007E495A127C12FC12F048495AC7 FCA34A5AA44A5AA44A5AA4143F92C9FCA4147EA3147C14FCA25C1301A25C13035CA2495A 5C49CAFC130836347DAE27>I<0060150C00E0151CB3AA6C153C00701538A2007815786C 15F06CEC01E06C6CEB07C0D807E0EB1F803A03FE01FF00C6B512FC013F13F0010390C7FC 26297CA72F>91 DI<00E0150C161C6C153C007015380078157800381570003C15F0001C15E0A2001E1401 000E15C0000F14036C15806D1307000315006D5B0001140E6D131E0000141C6D133C0170 1338A20178137801381370013C13F0011C5BEB1E01010E5BEB0F0301075B1487010390C7 FC14CFEB01CEA214FE6D5AA21478A2143026297CA72F>95 D<141F14FFEB03F0EB0FC0EB 1F8014005B133EB3A2137E137C13FC485A485AEA7FC048C7FCEA7FC0EA03F06C7E6C7E13 7C137E133EB3A2133F7F1480EB0FC0EB03F0EB00FF141F18437BB123>102 D<12FCB47EEA0FE0EA01F0EA00FC137C137E133EB3A37F1480130FEB07E0EB01FEEB007F EB01FEEB07E0EB0F80131F1400133EB3A3137E137C13FCEA01F0EA0FE0EAFF8000FCC7FC 18437BB123>I<12E0B3B3B3AD034378B114>106 D<12E0A27E1270A212781238A2123C12 1CA2121E120EA2120F7E7F1203A27F1201A27F1200A27F137013781338A2133C131CA213 1E130EA2130F7FA2801303801301A2801300A2801470A214781438143C141CA2141E140E A2140F80A215801403A215C0140114001A437CB123>110 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo cmex10 12 30 /Fo 30 112 df0 D<12E07E12787E7E7E7F6C7E6C7E7F12016C7E7F137C137E7FA26D7EA26D7EA26D7EA36D 7EA2801301A2801300A280A2147EA2147FA4801580A7EC1FC0B3A5EC3F80A715005CA414 7EA214FEA25CA213015CA213035CA2495AA3495AA2495AA249C7FCA2137E137C13FC5B48 5A12035B485A485A90C8FC121E5A5A5A5A1A777C832E>II I8 D<12F012FEEAFFC0EA3FF0EA07FCEA01FE6C6C7EEB3FC06D7E130F801307801303B3B080 1301A26D7E806E7E6E7E6E7EEC07F8EC01FC9138007F80ED1FE01503151FED7F80913801 FC00EC07F8EC1FE04A5A4A5A4AC7FC5C495AA213035CB3B013075C130F5C131F495AEBFF 804848C8FCEA07FCEA3FF0EAFFC048C9FC12F0237775833A>I<12F0B3B3B3AA04407281 21>12 D<00F0EB03C0B3B3B3AA1A40728137>I<16F01501ED03E0ED07C0ED0F80ED1F00 5D157E5D5D14014A5A4A5A4A5AA24A5A143F92C7FC147EA25C13015C13035C13075C130F 5C131FA2495AA349C8FCA213FEA312015BA212035BA21207A25BA2120FA25BA2121FA45B A2123FA55B127FA990C9FC5AB3AA7E7FA9123F7FA5121FA27FA4120FA27FA21207A27FA2 1203A27F1201A27F1200A3137FA26D7EA36D7EA2130F801307801303801301801300147E A28081141F6E7EA26E7E6E7E6E7E140081157E8181ED0F80ED07C0ED03E0ED01F0150024 B26E833B>16 D<12F07E127C7E7E6C7E7F6C7E6C7E12017F6C7E137E7FA26D7E80130F6D 7EA26D7E80130180130080147E147F8081A26E7EA36E7EA26E7EA3811403A2811401A281 A21400A281A281A21680A4153FA216C0A5151F16E0A9150F16F0B3AA16E0151FA916C015 3FA51680A2157FA41600A25DA25DA21401A25DA214035DA214075DA34A5AA24A5AA34A5A A292C7FC5C147E14FE5C13015C13035C495AA2495A131F5C49C8FCA2137E5B485A5B1203 485A485A5B48C9FC123E5A5A5A24B27C833B>I<171E173E177C17F8EE01F0EE03E0EE07 C0160FEE1F80EE3F00167E167C16FC4B5A4B5A15075E4B5A4B5A153F93C7FC5D15FE5D14 015D14034A5AA24A5AA24A5AA24A5AA24AC8FCA214FEA213015C13035C1307A25C130F5C 131FA25C133FA3495AA349C9FCA35A5BA312035BA31207A25BA2120FA35BA3121FA35BA3 123FA55BA2127FAB485AB3B06C7EAB123FA27FA5121FA37FA3120FA37FA31207A27FA212 03A37F1201A37F7EA36D7EA36D7EA3131F80A2130F80130780A21303801301801300A214 7FA26E7EA26E7EA26E7EA26E7EA26E7E140181140081157F8182151F6F7E6F7E8215036F 7E6F7E167C167E82EE1F80EE0FC01607EE03E0EE01F0EE00F8177C173E171E2FEE6B8349 >I<12F07E127C7E7E6C7E6C7E7F6C7E6C7E6C7E137C137E7F6D7E80130F6D7E6D7E8013 01806D7E147E147F80816E7EA26E7EA26E7EA26E7EA26E7EA26E7EA2818182153F82A215 1F82150F82A2150782A36F7EA36F7EA38281A31780167FA317C0A2163FA217E0A3161FA3 17F0A3160FA317F8A51607A217FCABEE03FEB3B0EE07FCAB17F8A2160FA517F0A3161FA3 17E0A3163FA317C0A2167FA21780A316FF1700A35D5EA34B5AA34B5AA35E150FA25E151F 5E153FA25E157F93C7FC5D5DA24A5AA24A5AA24A5AA24A5AA24A5AA24A5A92C8FC5C147E 14FE495A5C13035C495A495A131F5C49C9FC137E137C13FC485A485A485A5B485A48CAFC 123E5A5A5A2FEE7C8349>II I<170F173F17FF1603EE0FFCEE1FF0EE7FE0EEFF804B13004B5A4B5A4B5A4B5A4B5A4B5A 15FF5E5C93C7FC5C5D14075DA3140F5DB3B3B3AE4A5AA3143F5DA24A5AA24A5AA24990C8 FC495AA2495A495A495A495A495A49C9FC485AEA07FCEA0FF0EA3FC0B4CAFC12FCA2B4FC EA3FC0EA0FF0EA07FCEA01FE6C7EEB7FC06D7E6D7E6D7E6D7E6D7EA26D7E6D7FA26E7EA2 6E7EA281141FA36E7EB3B3B3AE811407A38114038180828082157F6F7E6F7E6F7E6F7E6F 7E6F7E6F1380EE7FE0EE1FF0EE0FFCEE03FF1600173F170F30EE73834B>26 D<12F012FE6C7E7FEA3FF0EA0FFC6C7E3801FF806C7F6D7EEB1FF06D7E6D7E806D7E7F6D 7F81147F81143F81141FA381140FB3B3B3AE6E7EA46E7EA26E7EA26E7FA26F7EA26F7E6F 7E6F7E15076F7E6F7E923800FF80EE7FC0EE1FE0EE0FF8EE03FCEE00FF173FA217FFEE03 FCEE0FF8EE1FE0EE7FC0EEFF80923801FE004B5A4B5A150F4B5A4B5A4B5AA24B5AA24A90 C7FCA24A5AA24A5AA44A5AB3B3B3AE141F5DA3143F5D147F5D14FF5D4990C8FC5B495A5C 495A495AEB7FE0495A485BD807FEC9FC485AEA3FF0EAFFC05B48CAFC12F030EE73834B> I[29 298 101 131 58 34 D[29 298 127 131 58 I[51 298 114 131 80 40 D80 DI<007C193EA200FE197FB3B3B3AE6C19FFA26C19 FEA26D1701A26C6CEF03FCA2001F19F86D17076D170F000F19F06C6CEF1FE06D173F6C6C EF7FC06C6CEFFF806E5D6C01E0030713006D6C4B5AD93FFCED3FFC6DB4EDFFF86D01E001 075B6D01FE017F5B010190B712806D94C7FC023F15FC020F15F002011580DA003F01FCC8 FC030313C048647B7F53>83 D88 DI<003EF407C0007FF40FE0486CF31FF0B3B3B3B3B3A5 6D1B3F007F1DE0A46D1B7F003F1DC0A26D1BFF001F1D806D62A26C6C501300A26C6C505A 6D1A0F6C6D4F5AA26C6D4F5A6E197F6C6D4F5A6D6C4E5B6D6C4E5B6E606D6C4E5B6D01C0 053F90C7FC6D6D4D5A6D01F84C485A6D01FE04075B6D6D6C031F5B6E01E0037F5B021F01 FE0207B512806ED9FFF090B6C8FC020391B712FC6E606E6C17E0031F178003074CC9FC03 0116F8DB003F15C0040302FCCAFCDC001F1380648B7B7F6F>91 D101 D104 DI110 D<12F012FE6C7E13E0EA 3FF8EA0FFCEA03FFC67F6D7E6D7E6D7E6D7E6D7E6D7EA26D7E7FA281147FB3B3AF81143F A281141F81140F8114076E7E6E7E6E7E6F7E6F7EED1FF0ED07F8ED01FE923800FF80163F A216FF923801FE00ED07F8ED1FF0ED3FC04B5A4BC7FC4A5A4A5A4A5A140F5D141F5D143F 5DA2147F5DB3B3AF14FF92C8FCA25B495AA2495A495A495A495A495A495A000390C9FCEA 0FFCEA3FF8EAFFE0138048CAFC12F029B2748342>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmmi8 8 41 /Fp 41 122 df<131FD9FFC013304801F0137000076D13604815E0D9807C13C0391E003C 0148011E13800038EB0E03480107130000605CEC030612E0C7138EEC018C159C159815B8 15B0A215F05DA35DA25DA21403A44AC7FCA4140EA45CA31418242C7F9D24>13 DI<147C49B4FC903803C78090380783C090381F03E0EB 1E01133E017C13F013F8A2EA01F0120313E01207A2EA0FC01403A2EA1F80A21407003F14 E0130090B5FCA2397F000FC0127EA2141F1580127C00FC14005CA2147EA248137C14FC00 785B495AA2387C03E0383C07C0495A001C90C7FCEA1E3EEA0FF8EA03E01C307DAE21>18 D<90B612F812035A4815F03A1E0380C000003C130000701301130700E05CEAC00638000E 03A3131CA2133C140713381378A201F07FA21201A2D803E07FA20007130313C0A26C486C 5A251E7E9C29>25 D<0103B512F0131F137F90B612E03A01FC1F80003903F00FC03807C0 0748486C7E121F1300123EA25AA2140700FC5C5AA2140F5D141F92C7FC143E0078133C14 7C007C5B383C01E0381F07C0D807FFC8FCEA01F8241E7D9C28>27 D<90B6128012035A481500261E00E0C7FC5A00705B130112E012C0EA0003A25CA21307A3 49C8FCA35BA2131E133EA45BA21338211E7E9C1F>I<123C127E12FFA4127E123C08087A 8714>58 D<123C127EB4FCA21380A2127F123D1201A312031300A25A1206120E5A5A5A12 6009157A8714>I<013FB512FEEEFFC0903A00FE0007F0EE01F84AEB007E830101811880 4A140F18C00103150718E05CA21307A25CA2130FA24A140FA2131F18C04A141FA2013F16 80173F91C81300A249157EA2017E5D5F01FE14014C5A494A5A4C5A00014BC7FC163E4914 FCED03F00003EC1FC0B7C8FC15F8332D7CAC3A>68 D<013FB7FCA2D900FEC7127F171F4A 140FA20101150717065CA21303A25C16300107147017004A136016E0130F15019138C007 C091B5FC5BECC0074A6C5AA2133FA2020090C7FCA25B92C8FC137EA213FEA25BA21201A2 5BA21203B512F0A2302D7DAC2D>70 D<90273FFFFC0FB5FCA2D900FEC7EA3F80A24A1500 A201015D177E5CA2010315FE5F5CA2010714015F5CA2010F14035F5C91B6FC5B9139C000 07E05CA2013F140F5F91C7FCA249141F5F137EA201FE143F94C7FC5BA200015D167E5BA2 000315FEB539E03FFFF8A2382D7CAC3A>72 D<90383FFFFCA2903800FE00A25CA21301A2 5CA21303A25CA21307A25CA2130FA25CA2131FA25CA2133FA291C7FCA25BA2137EA213FE A25BA21201A25BA21203B512E0A21E2D7DAC1F>I<91383FFFF8A29138007F00A2157EA2 15FE5DA314015DA314035DA314075DA3140F5DA3141F5DA3143FA292C7FCA2003C5B127E 00FE137E14FE5CEAFC0100F05B48485A386007E038781F80D81FFEC8FCEA07F0252E7BAC 27>I<90263FFFFC90381FFF80A2D900FEC73803F80018E04AEC07804DC7FC0101151C5F 4A14E04C5A01034A5A040EC8FC4A5B5E010714E04B5A9138E00780030EC9FC010F131F15 7F4A487E14C190391FC71FC014CEEC9C0F02F07F90383FE00702C07FEC0003825B6F7E13 7E6F7E13FE167F5B707E1201161F4981831203B539E001FFFEA2392D7CAC3C>I<90383F FFFEA2010090C8FC5C5CA21301A25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2 133FA291C7EA0180A24914031700017E5C160601FE140EA2495C163C12015E49EB01F84B 5A0003141FB7FC5E292D7DAC30>III<000FB8FCA23B1FC003F8003F0100151F001C4A130E123C003801 071406123000704A130EA20060010F140C12E0485CA2141FC715005DA2143FA292C8FCA2 5CA2147EA214FEA25CA21301A25CA21303A25CA21307A25C130F131F001FB512F0A2302D 7FAC29>84 D<3B7FFFF801FFFEA2D801FCC7EA0FC0178049EC070016060003150E160C5B A20007151C16185BA2000F153816305BA2001F157016605BA2003F15E05E90C8FCA24814 015E127EA2150300FE92C7FC5A5D1506150E007C5C151815386C5C5D6CEB03C0260F800F C8FC3803E03C3801FFF038003FC02F2E7BAC30>II<90260FFFFCEB7FFFA29026007FC0EB0FF06E481480 18006E6C131E1718020F5C6F5B02075C6F485A020349C7FCEDF8065E6E6C5A5E6E6C5A5E ED7F8093C8FC6F7EA26F7E153F156FEDCFE0EC018791380307F0EC0703020E7F141C4A6C 7E14704A6C7E495A4948137F49C7FC010E6E7E5B496E7E5BD801F081D807F8143FD8FFFE 0103B5FCA2382D7EAC3A>88 D96 DI<13F8121FA21201A25BA21203A25BA21207 A25BA2120FEBC7E0EB9FF8EBB83C381FF01EEBE01F13C09038800F80EA3F00A2123EA200 7E131FA2127CA2143F00FC14005AA2147EA2147C14FC5C387801F01303495A383C0F806C 48C7FCEA0FFCEA03F0192F7DAD1E>II<151FEC03FF A2EC003FA2153EA2157EA2157CA215FCA215F8A21401EB07E190381FF9F0EB7C1DEBF80F EA01F03903E007E0EA07C0120FEA1F8015C0EA3F00140F5A007E1480A2141F12FE481400 A2EC3F021506143E5AEC7E0E007CEBFE0C14FC0101131C393E07BE18391F0E1E38390FFC 0FF03903F003C0202F7DAD24>I<157C4AB4FC913807C380EC0F87150FEC1F1FA391383E 0E0092C7FCA3147E147CA414FC90383FFFF8A2D900F8C7FCA313015CA413035CA413075C A5130F5CA4131F91C8FCA4133EA3EA383C12FC5BA25B12F0EAE1E0EA7FC0001FC9FC213D 7CAE22>102 D<14FCEB03FF90380F839C90381F01BC013E13FCEB7C005B1201485A15F8 485A1401120F01C013F0A21403121F018013E0A21407A215C0A2000F130F141F0007EB3F 80EBC07F3803E1FF3800FF9F90383E1F0013005CA2143EA2147E0038137C00FC13FC5C49 5A38F807E038F00F80D87FFEC7FCEA1FF81E2C7E9D22>I<131FEA03FFA2EA003FA2133E A2137EA2137CA213FCA25BA21201143F9038F1FFC09038F3C1F03803FF0001FC7F5BA248 5A5BA25B000F13015D1380A2001F13035D1300140748ECC04016C0003E130F1580007E14 8191381F0180007C1403ED070000FCEB0F06151E48EB07F80070EB01E0222F7DAD29>I< 1307EB0F80EB1FC0A2EB0F80EB070090C7FCA9EA01E0EA07F8EA0E3CEA1C3E1238123012 70EA607EEAE07C12C013FC485A120012015B12035BA21207EBC04014C0120F1380138138 1F01801303EB0700EA0F06131EEA07F8EA01F0122E7EAC18>I<15E0EC01F01403A3EC01 C091C7FCA9147CEB03FE9038078F80EB0E07131C013813C01330EB700F0160138013E013 C0EB801F13001500A25CA2143EA2147EA2147CA214FCA25CA21301A25CA21303A25CA213 0700385BEAFC0F5C49C7FCEAF83EEAF0F8EA7FF0EA1F801C3B81AC1D>I<131FEA03FFA2 EA003FA2133EA2137EA2137CA213FCA25BA2120115F89038F003FCEC0F0E0003EB1C1EEC 387EEBE07014E03807E1C09038E3803849C7FC13CEEA0FDC13F8A2EBFF80381F9FE0EB83 F0EB01F81300481404150C123EA2007E141C1518007CEBF038ECF83000FC1470EC78E048 EB3FC00070EB0F801F2F7DAD25>I<137CEA0FFCA21200A213F8A21201A213F0A21203A2 13E0A21207A213C0A2120FA21380A2121FA21300A25AA2123EA2127EA2127CA2EAFC0813 1812F8A21338133012F01370EAF860EA78E0EA3FC0EA0F000E2F7DAD15>I<27078007F0 137E3C1FE01FFC03FF803C18F0781F0783E03B3878E00F1E01263079C001B87F26707F80 13B00060010013F001FE14E000E015C0485A4914800081021F130300015F491400A20003 4A13076049133E170F0007027EEC8080188149017C131F1801000F02FCEB3F03053E1300 49495C180E001F0101EC1E0C183C010049EB0FF0000E6D48EB03E0391F7E9D3E>I<3907 C007E0391FE03FF83918F8783E393879E01E39307B801F38707F00126013FEEAE0FC12C0 5B00815C0001143E5BA20003147E157C5B15FC0007ECF8081618EBC00115F0000F153891 3803E0300180147016E0001F010113C015E390C7EAFF00000E143E251F7E9D2B>I<9038 07E03090381FF87090387C1CF0EBF80D3801F00F3903E007E0EA07C0000F1303381F8007 15C0EA3F00A248130F007E1480A300FE131F481400A35C143E5A147E007C13FE5C1301EA 3E07EA1F0E380FFCF8EA03F0C7FC13015CA313035CA21307A2EBFFFEA21C2B7D9D20> 113 D<3807C01F390FF07FC0391CF8E0E0383879C138307B8738707F07EA607E13FC00E0 EB03804848C7FCA2128112015BA21203A25BA21207A25BA2120FA25BA2121FA290C8FC12 0E1B1F7E9D20>I<130E131FA25BA2133EA2137EA2137CA213FCA2B512F8A23801F800A2 5BA21203A25BA21207A25BA2120FA25BA2001F1310143013001470146014E0381E01C0EB 0380381F0700EA0F0EEA07FCEA01F0152B7EA919>116 DI<013F137C9038FF C1FF3A01C1E383803A0380F703C0390700F60F000E13FE4813FC12180038EC0700003049 C7FCA2EA200100005BA313035CA301075B5D14C000385CD87C0F130600FC140E011F130C 011B131C39F03BE038D8707113F0393FE0FFC0260F803FC7FC221F7E9D28>120 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq msbm10 12 8 /Fq 8 91 df<007FB91280BA12C0A27E2800F803E00113C3913A07C0001FE30178ED07F3 4BEB01FBEF00FF187F183F181F180FA29338018007EE03C01803A4F00180040790C7FCA3 160FA2161F163F167FED81FFED8FFBEDFFF316C316E316F3ED87FF1580163F161F160FA2 1607A31603A21918193CA27048137C93C8FC19FC19F81801A218031807180FF03FF0187F EF01FC6FEB07F801F8ED1FF1913A03E001FFC1007FB912E0BAFCA26C18C03E447FC330> 69 D<007FB9FCBA1280A27E2800F803E0011387913A07C0003FC70178ED07F74BEB03FF 1700187FA2183F181FA2933801800FEE03C01807A40407EB030095C7FCA3160FA2161F16 3F167FED81FFED8FFBEDFFF316C316E316F3ED87FF1580163F161FA2160FA21607A21603 A5705A93C9FCAC01F87F81007FB612E0B77EA26C5D39447FC331>I<007FB6FCB77EA26C 92C9FC3900F807C0A201785BB3B3A21918193CA2197CA319F8A2180118031807A2180FF0 1FF0187F18FEEF01F86FEB07F001F8ED3FE1913A03E001FF81007FB912E0BAFCA26C18C0 3E447FC337>76 D<007FB54AB512C0B66C4914E0816C6E6D14C02707F003F09039000FF8 002601F801ED03F000006D7E017C6D6E5A017E137E017F133E8102807FECC00F6E6C7E01 7B80903979F003F0ECF801903978FC00F8027C7F6E137E023F133E6E6C7E020F14809139 07C00FC0EDE007913903F003E0020114F0913900F801F8EDFC00037E137C033E137E6F13 3EEE801FDB0FC013810307EB0FC1923803E0079338F003E1DB01F813F1923900FC01F9EE 7C0070137D043F137F93381F803F040F131F933807C00F17E0933803F007040113039338 00F80117FC177E173E171F1881EF0FC11707EF03E118F1EF01F91700187D01FC167F183F D803FF161F007F01F8150FB57E18076C491503CB1201725A43467DC339>78 D<007FB712C0B812FCEFFF806C17E02800F807F00F13F8DBC00113FE017890398000FCFF 94387C3F8094383E0FC0727E94381E03F0EF1F011800717FA21978A519F8A24D5B1801EF 1E034E5A94383E0FC094387E3F80DDFDFFC7FC933807FFFE92B612F818E095C8FC17F0ED 87C1EEC0F8923883E0FC177C923881F03EA2923880F81F84EE7C0F717E163E93383F03E0 041F7FEE0F81EF80F8EE07C0187C933803E07E183E706C7E85706C6C7E180794387C03E0 057E7F94383E01F8716C7E197C01F86D6D6C7EF13F80007FB66C6CB512E0B700C015F083 6C4B6C14E044447EC33D>82 D<007FB912E0BA12F0A33CF07FE3C03C7FE026F1FE03EC07 F8D8F3F8ED01FCD8F7E0ED007ED8FFC0163F0180161F0100160F481707A2481703481701 A3481700A400601860C71700B3B3A40207133E020F133F0107B612FE4981A26D5D3C447D C33F>84 D<007FB691387FFFFCB76C90B512FEA26C92C76C13FC270FC007F091380F8FE0 D807E001C0913807DF8000034A1600D801F0EE03DE19FED800F87F61EB7C0361013E7F18 07D91E015E011F7F6190380F80F8180F902607C0785D157CD903E04B5A81EB01F0031E92 C7FC0100011F5C02F8153E6F7E027C157E0307147C023E7F606E6C7EA26E6C6C485A1581 0380495A913807C0F8A2913A03E07C07C0A26E6C6C485AA2913800F81F4DC8FCED780F03 7C139E17BE92383E07FE5FED1F035FED0F81A2923807C1F0A203035B16E3A2923801F7C0 A26FB45AA2167F94C9FC82163EA2161C474680C341>86 D<0003B812FE4883A301879039 000F803ED98FF0011F137ED9BFC0EC007C01FFC7003E5B13FC48484A485A49ECFC034902 F85B4B48485A5B494948485A0307131F04C090C7FC90C7380F803EA24B485A00064A13FC C8003E5B4B485AA24B485A0201130703F05B4A48485AA24A4848C8FC5E91380F803E021F 5B1500023E5B1501027C5B9138FC03E014F84948485AA24948485A0107011F156002C090 C812F090380F803EA249484814014913FC013E5B494848EC03E0A2494848140700011307 01F049140F48484848141FA2484848C8EA3FC0000F49157FD9803E15FF484848EC01FBEF 07F3003E49EC0FE7D87E01ED7F87007C49903903FF0780BAFCA36C18003C447DC345>90 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmsy10 12 33 /Fr 33 121 df<007FB912E0BA12F0A26C18E03C04789A4D>0 D<121FEA3F80EA7FC0EA FFE0A5EA7FC0EA3F80EA1F000B0B789E1C>I<0060160600F8160F6C161F007E163F6C16 7E6C6C15FC6C6CEC01F86C6CEC03F06C6CEC07E06C6CEC0FC06C6CEC1F80017EEC3F006D 147E6D6C5B6D6C485A6D6C485A6D6C485A6D6C485A6D6C485ADA7E3FC7FCEC3F7E6E5A6E 5A6E5AA24A7E4A7EEC3F7EEC7E3F4A6C7E49486C7E49486C7E49486C7E49486C7E49486C 7E49C7127E017E8049EC1F804848EC0FC04848EC07E04848EC03F04848EC01F84848EC00 FC48C9127E007E163F48161F48160F00601606303072B04D>I<007FBA1280BB12C0A26C 1980CEFCB0007FBA1280BB12C0A26C1980CEFCB0007FBA1280BB12C0A26C1980422C7BAE 4D>17 D<19E0F003F0180FF03FE0F0FF80943803FE00EF0FF8EF3FE0EFFF80DC03FEC7FC EE0FF8EE3FE0EEFF80DB03FEC8FCED1FF8ED7FE0913801FF80DA07FEC9FCEC1FF0EC7FC0 4948CAFCEB07FCEB1FF0EB7FC04848CBFCEA07FCEA1FF0EA7FC048CCFCA2EA7FC0EA1FF0 EA07FCEA01FF38007FC0EB1FF0EB07FCEB01FF9038007FC0EC1FF0EC07FC913801FF8091 38007FE0ED1FF8ED07FE923800FF80EE3FE0EE0FF8EE03FE933800FF80EF3FE0EF0FF8EF 03FE943800FF80F03FE0F00FF01803F000E01900B0007FB912E0BA12F0A26C18E03C4E78 BE4D>20 D<127012FCB4FCEA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB01FF 9038007FC0EC1FF0EC07FC913801FF809138007FE0ED1FF8ED07FE923800FF80EE3FE0EE 0FF8EE03FE933800FF80EF3FE0EF0FF8EF03FE943800FF80F03FE0F00FF0A2F03FE0F0FF 80943803FE00EF0FF8EF3FE0EFFF80DC03FEC7FCEE0FF8EE3FE0EEFF80DB03FEC8FCED1F F8ED7FE0913801FF80DA07FEC9FCEC1FF0EC7FC04948CAFCEB07FCEB1FF0EB7FC04848CB FCEA07FCEA1FF0EA7FC048CCFC12FC1270CDFCB0007FB912E0BA12F0A26C18E03C4E78BE 4D>I<037FB612E00207B712F0143F91B812E0010301C0C9FCD907FCCAFCEB0FE0EB3F80 49CBFC13FC485A485A485A5B485A121F90CCFC123EA2123C127CA2127812F8A25AA87EA2 1278127CA2123C123EA27E7F120F6C7E7F6C7E6C7E6C7E137E6D7EEB1FE0EB07FC6DB47E 010090B712E0023F16F01407020016E03C3A78B54D>26 D<007FB612F0B712FEEEFFC06C 16F0C9EA1FFCEE03FE9338007F80EF1FC0EF07E0717E717E717E187E183E841980180FF0 07C0A2180319E0A2180119F0A21800A81801A219E01803A219C01807A2F00F80181F1900 183E187E604D5A4D5AEF0FE04D5A057FC7FCEE03FEEE3FFC007FB712F0B812C04CC8FC6C 15E03C3A78B54D>I<1AF0A3861A78A21A7C1A3CA21A3E1A1E1A1F747EA2747E747E8774 7E747E1B7E87757EF30FE0F303F8007FBC12FEBE1280A26CF3FE00CEEA03F8F30FE0F31F 8051C7FC1B7E63505A505A63505A505AA250C8FC1A1E1A3E1A3CA21A7C1A78A21AF862A3 59347BB264>33 D<18034E7E85180385180185727E1978197C8585737E86737E737E007F BA7EBB7E866C85CDEA0FC0747EF203F8F200FEF37F80F31FE0F307FC983801FF80A29838 07FC00F31FE0F37F8009FEC7FCF203F8F207E0505A007FBBC8FCBB5A626C61CCEA03F04F 5A4F5A624FC9FC193E61197819F84E5A6118036118076172CAFC59387BB464>41 D<49B4EF3FC0010F01E0923803FFF8013F01FC030F13FE4901FF92383FE01F48B66C9139 7E0007C02603F80301E0D901F8EB01E02807E0007FF049486D7E01806D6CD907C0147048 C76C6C494880001EDA07FE49C87E001C6E6C013E150C486E6D48150E71481506486E01E0 160793387FF1F0006092263FF3E08193381FFBC000E004FF1780486F4915017090C9FC82 707F8482717E844D7E6C4B6D1503006004EF1700933803E7FE0070922607C7FF5DDC0F83 7F003004816D140E00384BC6FC0018033E6D6C5C001C4B6D6C143C6C4BD91FFC5C6C4A48 6D6C5C6DD907E06D6C13036C6C49486D9038E00FE0D801F0013FC890B55A27007C03FE6F 91C7FC90263FFFF8031F5B010F01E0030313F8D901FECAEA7FC0592D7BAB64>49 D<92B6FC02071580143F91B7120001030180C8FCD907FCC9FCEB1FE0EB3F80017ECAFC5B 485A485A485A5B485A121F90CBFC123EA2123C127CA2127812F8A25AA2B9FC1880A21800 00F0CBFCA27EA21278127CA2123C123EA27E7F120F6C7E7F6C7E6C7E6C7E137E6D7EEB1F E0EB07FC6DB47E010090B6FC023F1580140702001500313A78B542>I<007FB57EB612F0 15FE6C6E7EC813E0ED1FF0ED03FCED00FE163F707E707E707E707E1601707E83177C83A2 171E171FA2831880A21707A2007FB8FCB9FCA27ECA1207A2170FA218005FA2171E173EA2 5F17FC5F4C5A16034C5A4C5A4C5A4CC7FC16FEED03FCED1FF0EDFFE0007FB61280B648C8 FC15F06C1480313A78B542>I<1706170F171FA2173EA2177CA217F8A2EE01F0A2EE03E0 A2EE07C0A2EE0F80A2EE1F00A2163EA25EA25EA24B5AA24B5AA24B5AA24B5AA24BC7FCA2 153EA25DA25DA24A5AA24A5AA24A5AA24A5AA24AC8FCA2143EA25CA25CA2495AA2495AA2 495AA2495AA249C9FCA2133EA25BA25BA2485AA2485AA2485AA2485AA248CAFCA2123EA2 5AA25AA25A1260305C72C600>54 D<0060171800F0173C6C177CA200781778007C17F8A2 003C17F0003E1601A26CEE03E0A26C17C06D1507A2000717806D150FA26C6CED1F00A200 01161E6D153EA20000163C90B712FCA26D5DA2013CC85A013E1401A2011E5D011F1403A2 6D5D6E1307A26D6C495AA2010392C7FC6E5BA20101141E6E133EA26D6C5BA20278137802 7C13F8A2023C5BEC3E01A26E485AA2020F5B1587A202075B15CFA26EB4C8FCA26E5AA36E 5AA315781530364780C437>56 D<007FB712E0B812F0A27ECAFCB3AA001FB7FC127FA3CA FCB3AB007FB7FCB8FCA26C16E02C457BC437>I<4B7E4B7EA21507A25EECFF8F010313EF 90260F80FFC7FC90383E003F497F49804848804848497E5B0007EC3DF049133C000FEC7C F8A248C7EA787C15F848157E15F0A2140148157F007E4A7E1403A215C0A200FE01071480 A21580140FA21500A25CA2141E143EA2143CA2147CA21478A214F8A25C1301A2007E4914 00A21303A2007F495B1307003F157E5CA2130F001F157C018FC712FCD80F9F5CA201DE13 0100075DD803FE495AA26C48495A00004A5A017C49C7FC017E133E90387F80F89038FBFF E001F8138049C9FC1201A25BA26C5A29557CCC32>59 D67 D<031FB512C00203B7FC021F16 E091B812F8010317FE010F717E90283FE07FC03F80D9FE00020080D801F8041F7FD803E0 4A01077F48481601000F716C7E4848717E003F02FF151F007F180F90C7707E00FE92C8FC 488400F01A80008084C75AA24B81A414035DA21B00A24A5AA24F5AA24A5A621903624A5A 4F5AA24B4B5A023F5F191F4B5E027F4CC7FC197E92C9127C4A5E4E5A4A4B5A01014C5AF0 1F804A033EC8FC01035E4A4A5AEF07E00107ED1FC04A02FFC9FC010FEC07FC4AEBFFF091 B612C0017F4ACAFC90B612F04815804802F8CBFC4891CCFC49447EC34D>I<0403B712F8 043F16FE4BB9FC1507151F157F912601FC0090C7EA07FE912603F001ED01FCDA07C04915 F0DA0F80EE0080021F1800EC3F004A495A5C5C495A4A495A5C495A6DC7FC90C8485AA35F 161FA34C5AA35F167F94B612C0A293B7FC624B93C7FC19FC04FCC71270030392C8FC5EA2 4B5AA2150F5E151F5EA24B5AA24BCBFCA215FEA24A5AA24A5AEA0180000F495AEA1FC048 6C485AD87FF05B39FFFC1F80D87FFF90CCFC14FE6C5B6C13F06C5B00031380D800FCCDFC 50477EC348>70 D<0303B712C092B8FC020F1780023F170049B812FC4917F0D90FFCC700 FCC8FCD91F80495A49C71203017E4A5A13FE00014B5A5B48484A5A13E049143FC95B167F A294C9FC5EA34B5AA35E1503A34B5AA44B5AA44B5AA44B5AA35E157FA293CAFC5DA25D14 015DA24A4814074B141F02075D4B147E4A485C4A48495A92C75B48B85A000F17804894C8 FC4816FC4816E0B8C9FC424483C336>73 D83 D<1B3C1B7CF201F8021FB912F091BA12E001031980010FF0FE00013F18F84918C001F8C7 D807F0C9FCD803F0140F4848141F120F48485D003F153FA2127F5F4848147F90C8FC5A00 F85E00E015FFC9FCA294CAFC5DA35E1503A35E1507A35E150FA35E151FA35E153FA35E15 7FA35E15FFA293CBFCA25CA25D1403A25DA24A5AA34A5AA24A5AA25D143F5D027ECCFC14 7C14604E4E7CC636>I<0060170C00F0171EB3B3A66C173EA20078173C007C177C007E17 FC003E17F86CEE01F06D15036C6CED07E06C6CED0FC0D803F8ED3F80D801FEEDFF002600 7FC0EB07FCD93FFCEB7FF8010FB612E001031580D9007F01FCC7FC020713C0373D7BBA42 >91 D<913807FFC0027F13FC0103B67E010F15E0903A3FFC007FF8D97FC0EB07FCD801FE C8B4FCD803F8ED3F80D807E0ED0FC04848ED07E04848ED03F090C91201003EEE00F8007E 17FC007C177C0078173C00F8173EA248171EB3B3A60060170C373D7BBA42>I<1538157C A215FEA24A7EA215EF02037FA2913807C7C0A291380F83E0A291381F01F0A2EC1E00023E 7FA24A137CA24A7FA249487FA24A7F010381A249486D7EA249486D7EA249C76C7EA2011E 1400013E81A249157CA24981A2484881A24848ED0F80A2491507000717C0A24848ED03E0 A248C9EA01F0A2003EEE00F8A2003C1778007C177CA248173EA248171E0060170C373D7B BA42>94 D<0060170C00F0171E6C173EA2007C177CA2003C1778003E17F8A26CEE01F0A2 6C6CED03E0A26C6CED07C0A2000317806D150FA26C6CED1F00A26C6C153EA2017C5DA26D 5DA2011E5D011F1401A26D6C495AA26D6C495AA26D6C495AA2010192C7FC6E5BA26D6C13 3EA2027C5BA26E5BA2021E5BEC1F01A291380F83E0A2913807C7C0A2913803EF80A20201 90C8FC15FFA26E5AA2157CA21538373D7BBA42>I102 D<12FEEAFFE0EA07F8EA00FEEB7F806D7E6D7E 130F6D7EA26D7EB3AD6D7EA26D7E806E7E6E7EEC0FE0EC03FC913800FFE0A2913803FC00 EC0FE0EC3FC04A5A4AC7FC5C495AA2495AB3AD495AA2495A131F495A495A01FEC8FCEA07 F8EAFFE048C9FC236479CA32>I<126012F0B3B3B3B3B3A81260046474CA1C>106 D<0070130700F01480B3B3B3B3B3A800701400196474CA32>I<126012F07EA21278127C A2123C123EA2121E121FA26C7EA212077FA212037FA212017FA26C7EA21378137CA2133C 133EA2131E131FA26D7EA2130780A2130380A2130180A26D7EA21478147CA2143C143EA2 80A28081A2140781A2140381A26E7EA2140081A21578157CA2153C153EA281A2811680A2 150716C0A2150316E0A2ED01F0A2150016F8A21678167CA2163C163EA2161E160C27647B CA32>110 D120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmr8 8 22 /Fs 22 101 df0 D<1406140FA34A7EA34A7EA3EC6FE01467A2EC C7F014C3A290380183F8148101037F1400A2497F0106137EA249137F81A24980151FA249 80150FA249801507A249801503000181491301A2000381A2487ED81FE0497ED8FFF89038 3FFFF0A22C2F7EAE31>3 D5 D22 D<13031307130E131C13381370 13F0EA01E013C01203EA0780A2EA0F00A2121EA35AA45AA512F8A25AAB7EA21278A57EA4 7EA37EA2EA0780A2EA03C0120113E0EA00F013701338131C130E1307130310437AB11B> 40 D<12C07E12707E7E7E120FEA0780120313C0EA01E0A2EA00F0A21378A3133CA4131E A5131FA2130FAB131FA2131EA5133CA41378A313F0A2EA01E0A2EA03C013801207EA0F00 120E5A5A5A5A5A10437CB11B>I 43 D48 D<130C133C137CEA03FC12FFEAFC7C1200B3B113FE 387FFFFEA2172C7AAB23>III<140EA2141E14 3EA2147E14FEA2EB01BE1303143E1306130E130C131813381330136013E013C0EA018012 0313001206120E120C5A123812305A12E0B612FCA2C7EA3E00A9147F90381FFFFCA21E2D 7EAC23>I<000CEB0180380FC01F90B512005C5C14F014C0D80C7EC7FC90C8FCA8EB1FC0 EB7FF8380DE07C380F801F01001380000E130F000CEB07C0C713E0A2140315F0A4127812 FCA448EB07E012E0006014C00070130F6C14806CEB1F006C133E380780F83801FFE03800 7F801C2D7DAB23>II<1230123C003FB5 12F8A215F05A15E039700001C000601480140348EB0700140E140CC7121C5C143014705C 495AA2495AA249C7FCA25B130E131EA2133EA3133C137CA413FCA913781D2E7CAC23>I< EB1FC0EBFFF03803E07C3807801E48487E001EEB0780A248EB03C0A4123E1407003F1480 381FC00F01E01300EBF81E6C6C5A3807FFF86C13E0C6FCEB3FF8EBFFFC3803C7FFD80783 1380D81F0013C0001E133F48EB1FE0007C13070078EB03F012F84813011400A46C14E000 781301007C14C0003C13036CEB0780390F800F003807E03C3801FFF038003FC01C2D7DAB 23>II<123C127E12FFA4127E123C1200AD123C127E 12FFA4127E123C081D7A9C14>I<123C127E12FFA4127E123C1200AD123C127E12FE12FF A3127F123F1203A312071206A2120E120C121C1218123812701260082A7A9C14>I61 D99 D<15F8141FA214011400ACEB0FE0EB7FF83801F81E3803E0073807C003380F8001EA1F00 481300123E127EA25AA9127C127EA2003E13017EEB8003000F13073903E00EFC3A01F03C FFC038007FF090391FC0F800222F7EAD27>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft cmmi12 12 61 /Ft 61 122 df13 D<1578913807FFE0021F13FC91383C7FFEEC7007EC6003 ECE0004A13381600A280A380A280147CA2147E143E143F816E7EA26E7E81140781EC3FFC 14FF903803E1FEEB07C190381F00FF133E49EB7F805B0001143F485A484814C049131F12 0F485AA248C7FC150F5A127EA300FEEC1F805AA316005A5DA2153E157E157CA26C5C127C 4A5A6C495AA26C495A6C6C485A6C6C48C7FC3803E07C3800FFF0EB1FC027487CC62B>I< 1530A7ED33FF033F13C0ED7C0092B5FCDA03C31300DA0780C7FC4AC8FC141C14785C495A 5C495A130749C9FC131E131C133C5B5BA2485AA2485AA2485AA248CAFCA25A121EA2123E 123CA3127C1278A412F8A67EA2127C127EA2127F6C7E7F6C7E13F8EA0FFE3807FFC06C13 F86C13FF6C6C13E0011F7F010313FC9038007FFEEC1FFF14039138007F80153F151FA215 0FA393C7FCA20102131E13076D6C5A903801E0789038007FE0EC1F802A597CC42B>16 D<157E913801FF80913807C3E091381F01F0EC3E004A13F814FC4948137C495A5C010714 7E495A131F5C133F49C7127FA213FEA212015B12034914FF1207A25B000F15FE1501A248 5AA21503003F15FC5B90B6FCA24815F89038800007A2150F00FF15F090C7FCA2ED1FE0A2 5AED3FC0A21680157F16005A15FEA24A5AA25D14035D4A5A007C495AA24A5A007E49C7FC 003E133E5C001E5B6C485A380783C06CB4C8FCEA00FC28477CC52D>18 D21 D<147002F8140E0101153FA301035DA24A147EA2010715FEA24A5CA2010F1401A2 4A5CA2011F1403A24A5CA2013F1407A291C75BA249140FA2017E5DA201FE021F13181838 49ED8030A20001033F13701860EE7F005E486C16E0DB01DF13C09238039F016DD9071F13 80489039801E0F83903BF7C078078700903AE1FFE003FE903AE07F8000F8000F90CAFCA2 5BA2121FA25BA2123FA290CBFCA25AA2127EA212FEA25A123835417DAB3B>I<010FB712 E0013F16F05B48B812E04817C02807E0060030C7FCEB800EEA0F00001E010C13705A0038 011C13605A0060011813E000E013381240C7FC5C4B5AA214F014E01301150314C01303A3 EB078082130FA2EB1F00A34980133E137EA24980A2000114015BA26C48EB00E0342C7EAA 37>25 D<0203B612E0021F15F091B7FC4916E0010716C090270FF80FF8C7FC90381FC003 49486C7E017EC7FC49147E485A4848143E0007153F5B485AA2485AA2123F90C8FC5E4815 7E127EA216FE00FE5D5A15015EA24B5A007C5D15074B5A5E6C4AC8FC153E6C5C5D390F80 03F03907C007C02601F03FC9FC38007FFCEB1FE0342C7DAA37>27 D<010FB612FC013F15FE5B48B712FC4816F82707E001C0C7FC01805B380F0003121E121C 5A4849C8FC126012E000405BC7FC140E141EA45CA3147CA2147814F8A4495AA31303A25C 1307A3130FA25C6D5A2F2C7EAA2A>I<161CA21618A21638A21630A21670A21660A216E0 A25EA21501A25EA21503A293C8FCA25DED7FE0913807FFFE91391FC63F809139FE0E07C0 D901F8EB03F0903A07E00C00F8D91FC08090263F001C137E017E814913184848ED1F8000 031438485A4848013014C0A248481370A248481360A248C712E0A24B133F481780481301 A24B137F180014034816FE92C7FC4C5A6C49495AA2007E0106495A4C5A6C010E495A4C5A 261F800C49C7FC000F15FC3A07C01C01F8D803E0EB07E03A01F8181F80D8007E01FEC8FC 90381FFFF801011380D90030C9FCA21470A21460A214E0A25CA21301A25CA21303A291CA FCA332597BC43A>30 D<1730A317701760A317E05FA316015FA3160394C8FCA35E1606A3 160E160C013E1607D9FF80ED1F802603C3C0011CEB3FC0260703E01318260601F0157F00 0E173F001C1538D818030230131F0038170F0030170700701570D86007026013035CA2D8 E00F02E0148000C049491301EA001F4A150303011500013F5C1400604901031406017E91 C7FC180E180C01FE49141C4901061418183860030E1460030C14E04D5A4D5A031C49C7FC 0318130E017E5D5F6D01385B90261F80305BD90FC0EB03C0D907F0010FC8FC903901FE70 7C9039003FFFF002031380DA0060C9FC15E05DA314015DA3140392CAFCA35C1406A3140E 140C3A597DC43F>32 D 34 D<15FE913803FFC091380F83E091383E01F89138F800FC4948137C4948137E49487F 130F495A91C713805B137EA25BA2485A167F12035BA216FF000716005BA25D000F5D5B5E 1503001F5D15075E150F003F5D00374A5A00335D6D49C7FC157ED871F05B0060495A9038 7803E090383C0FC0D91FFFC8FC38E003F890CAFCA25AA47EA312F812FE007FB512C015F0 001F800007801201C8121CA2293F78AB32>37 D<177F0130913803FFC00170020F13E049 4A13F048484A13F84848EC7F0190C838F8007C484A48133C00064A48131C000E4B131E00 0C4A48130E001C92C7FC0018140E150C0038021C1406003014185D180E00704A140C1260 154003C0141C00E017184A5A4817386C17304AC8127018E01260007049EC01C0EF038000 78010614070038EE0F00003C010E141E6C167CD81F805D6C6C48EB03F0D807F0EC0FE0D8 03FEEC3FC02801FFFC03FFC7FC6C6CB55A6D14F8010F14E0010114809026007FF8C8FC02 F8C9FCA25CA21301A3495AA31307A25C130FA4131F5C6DCAFC37417BAB40>39 D<121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A0A78891B>58 D<121EEA7F8012FF13C0A2 13E0A3127FEA1E601200A413E013C0A312011380120313005A1206120E5A5A5A12600B1D 78891B>II<1618163C167CA2167816F8A216F01501 A216E01503A216C01507A21680150FA2ED1F00A2151E153EA2153C157CA2157815F8A25D 1401A24A5AA25D1407A25D140FA292C7FC5CA2141E143EA2143C147CA25CA25C1301A25C 1303A25C1307A25C130FA291C8FC5BA2133EA2133C137CA2137813F8A25B1201A25B1203 A2485AA25B120FA290C9FC5AA2121E123EA2123C127CA2127812F8A25A126026647BCA31 >I<127012FCB4FCEA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FE903801FF8090 38007FE0EC1FF8EC03FE913800FF80ED3FE0ED0FF8ED03FF030013C0EE3FF0EE0FFCEE01 FF9338007FC0EF1FF0EF07FCEF01FF9438007FC0F01FE0A2F07FC0943801FF00EF07FCEF 1FF0EF7FC04C48C7FCEE0FFCEE3FF0EEFFC0030390C8FCED0FF8ED3FE0EDFF80DA03FEC9 FCEC1FF8EC7FE0903801FF80D907FECAFCEB1FF0EB7FC04848CBFCEA07FCEA1FF0EA7FC0 48CCFC12FC12703B3878B44C>I64 D<1830187018F0A217011703A24D7EA2170F171FA21737A217 6717E717C793380187FCA2EE0307EE07031606160CA216181638163004607FA216C00301 13011680ED0300A21506150E150C5D845D03707F15605DA24A5A4AB7FCA25C0206C87F5C 021C157F14185CA25C14E05C495A8549C9FC49163F1306130E5B133C137C01FE4C7ED807 FFED01FF007F01F0027FEBFFC0B5FC5C42477DC649>I<4CB46C1318043F01F013384BB5 12FC0307D9007E1378DB1FF090380F80F0DB7F80EB03C1DA01FEC7EA01C34A48EC00E7DA 0FF0ED7FE04A48153F4A5A02FFC9121F494817C04948160F495A130F4A17804948160749 5A137F4948170091CAFC5A485A1906485AA2485A96C7FC121F5BA2123F5BA3127F5BA448 5AA419C0A2180161127F180396C7FC6018066C6C160E601818001F17386D5E000F5F6D4B 5A6C6C4B5A00034CC8FC6C6C150E6C6C153C017F5DD93FC0EB01E0D91FF0EB0FC0D907FE 017FC9FC0101B512FCD9003F13E0020790CAFC45487CC546>67 D<91B87E19F019FC0200 9039C00007FF6F489038007FC003FFED1FE0737E93C86C7E737E19014A707E5D1A7FA202 03EF3F805DA21BC014075DA3140F4B17E0A3141F4B17C0A3143F4B167FA3027F18804B16 FFA302FF180092C95A62A24917034A5F19076201034D5A5C4F5A620107173F4A5F4FC7FC 19FE010F4C5A4A15034E5AF00FE0011F4C5A4A4B5A06FFC8FC013FED01FCEF0FF84AEC3F E001FF913803FF80B848C9FC17F094CAFC4B447CC351>I<91B912FCA3020001C0C7123F 6F48EC03F803FF1501190093C91278A21A385C5DA3020317305DA314074B1460A218E002 0F4B13005DA21701021F5D4B13031707170F023F027FC8FC92B6FCA391397FC0007E4B13 1EA2170E02FF140C92C7FCA2171C49031813035C611906010392C7FC4A160E190C191C01 0717184A163819301970130F4A5E180161011F16034A15074E5A013F163F4EC7FC4AEC03 FF01FFED3FFEB9FCA26046447CC348>I<91B912F8A3020001C0C7123F6F48EC07F003FF 1503190193C9FCA21A705C5DA3020317605DA314075D18C01701020F4B13005DA2170302 1F92C8FC4B5BA25F023F141E4B13FE92B5FCA24A5CED8000173CA202FF141892C7FCA217 384915305CA21770010315604A91C9FCA313075CA3130F5CA3131F5CA2133FA313FFB612 F8A345447CC33F>I<91B6D8E003B61280A3020001E0C70003EB8000DB7F806E48C7FC03 FF1503A293C85BA219075C4B5EA2190F14034B5EA2191F14074B5EA2193F140F4B5EA219 7F141F4B5EA219FF143F92B8C8FCA3DA7FC0C712014B5DA2180314FF92C85BA218075B4A 5EA2180F13034A5EA2181F13074A5EA2183F130F4A5EA2187F131F4A5EA2013F16FFA24A 93C9FCD9FFE002037FB6D8E003B67EA351447CC351>72 D<027FB512F8A217F09139007F F000ED3FC0157FA25EA315FF93C7FCA35C5DA314035DA314075DA3140F5DA3141F5DA314 3F5DA3147F5DA314FF92C8FCA35B5CA313035CA313075CA3130F5CA2131FA25CEB7FF000 7FB512F0B6FCA22D447DC32B>I<031FB512FC5D18F89239000FFE00705AA35FA2160FA2 5FA2161FA25FA2163FA25FA2167FA25FA216FFA294C7FCA25DA25EA21503A25EA21507A2 5EA2150FA25EA2151FA25EA2153FA25EEA0F80D83FE0137F5E127FA24BC8FC485A4A5A13 00006C495A0060495A0070495A0030495A0038EB3F806C49C9FC380F81FC3803FFF03800 7F80364679C336>I<91B600E049B512C0A3020001E0C8383FF800DB7F80ED1FE003FF94 C7FC1A3E93C9127862F101C04A4C5A4B4BC8FC191C6102035E4B5DF003804EC9FC020715 0E4B14386060020F4A5A4B0107CAFC170E5F021F14784B13F84C7E1603023F130F4B487E 163BEEE1FF91387FC1C1DB83807FED8700159CDAFFB86D7E5D03C06D7E5D4990C7FC4A6E 7EA2717E13034A811707A201076F7E5C717EA2130F4A6E7FA2727E131F5C727E133F854A 82D9FFE04B7EB600E0010FB512E05FA252447CC353>I<91B612F8A3020001E0C8FC6F5A 4B5AA293C9FCA35C5DA314035DA314075DA3140F5DA3141F5DA3143F5DA3147F5DA314FF 92CAFCA35B4A16C0A21801010317804A15031900A201075E4A1506180E181E010F161C4A 153C18381878011F16F84A4A5A1703013F150F4D5A4A14FF01FF02075BB9FCA2603A447C C342>I<91B500C0933803FFFE63630200F1FE00DB6FE0EE1BF803EF171F1B3703CFEF67 F0A21BCF0201EF018F038F60DB87F0ED030F1B1F020317060307040C5BA2F2183F020717 300206616F6C15601B7F020E17C0020CDC018090C7FCA24F485A021C16060218606F6C5C 1A0102381618023004305BA2F16003027016C00260606F6CEB01801A0702E0ED03004A03 065CA24E130F01015E4A60047F5B1A1F01035E91C74A5CA24D48133F494BC7FC010661EE 3F861A7F010E158C010C039892C8FCA205B05C011C15E001186001386E5A190101785D01 FC92C75BD803FFEF07FEB500F8011E0107B512FE161C160C5F447BC35E>I<91B500C002 0FB5128082A2DA007F9239007FE00070ED1F8074C7FCDBEFF8150E15CF03C7160C70151C 1401DB83FE1518A2DB81FF1538140303001630831A704A6D7E02061760163F7114E0140E 020C6D6C5CA2706C1301141C021801075D83190302386D7E023094C8FC1601715B147002 606DEB8006A294387FC00E14E04A023F130C18E0191C0101ED1FF04A1618170FF0F83813 0391C83807FC30A2943803FE705B01060301136018FF19E0010E81010C5F187FA2131C01 18705A1338181F137801FC70C9FCEA03FFB512F884180651447CC34E>I81 D<91B712F018FF19E002009039C0003FF86F48EB07FC03FF EC01FEF0007F93C8EA3F801AC0F11FE05C5D1AF0A214035DA30207EE3FE05DA2F17FC002 0F17804B15FF1A004E5A021F4B5A4B4A5AF00FE04E5A023F037FC7FC4BEB03FCEF1FF092 B612804A4AC8FC923980007F80EF0FC0EF07F002FF6E7E92C77F1701845B4A1400A21701 13035CA2170313075CA24D5A130F5CA3011F18185CA2013F4C13381A304A6F1370D9FFE0 020314E0B600E0ED01C00501EB0380943900FE0F00CBEA3FFEF007F045467CC34A>I<48 BA12C05AA291C7D980001380D807F092C7121F4949150F0180170748C75B1903120E4802 0316005E12181238003014074C5C00701806126000E0140F485DA3C8001F92C7FC5EA315 3F5EA3157F5EA315FF93CAFCA35C5DA314035DA314075DA3140F5DA3141F5DA3143F5DA2 147FA214FF01037F001FB612FCA25E42447EC339>84 D<003FB500F80103B512E0A32600 3FF8C8381FF800D91FE0ED07E0013F705A615C96C7FC60017F16065CA2180E01FF160C91 C9FCA2181C4817185BA21838000317305BA21870000717605BA218E0120F495EA2170112 1F495EA21703123F4993C8FCA25F127F491506A2170E00FF160C90C9FC171CA217181738 17304816705F6C5E6C15014C5A4CC9FC6C150E6D141E001F5D6D5C6C6CEB01E06C6C495A 6C6CEB1F80C6B401FECAFC90387FFFF8011F13E0010190CBFC43467AC342>I<007FB56C 91381FFFF8B65DA2000101E0C8000313006C0180ED01FCF000F0614E5AA2017F4C5A96C7 FC1806A2606E5DA2013F5E1870186060A24D5A6E4AC8FCA2011F1506170E170C5FA26E5C 5FA2010F5D16015F4CC9FCA26E13065EA201075C5EA25E16E06E5B4B5A13034BCAFC1506 A25D151CECFE185D13015D5DA26E5AA292CBFC5C13005C5CA25CA25C45467BC339>I<02 3FB500E0011FB5FCA39126007FFEC7000313E0DB3FF8913801FE006F486E5A1AF06F6C4A 5A626F6C4A5A0706C7FC190E6F6C5C616F6C5C6171485A6F5D4EC8FC93387FC00660706C 5A6060706C5A17F193380FFB8005FFC9FC5F705AA2707EA3707E5E04067F5E93381C7FC0 163816704C6C7EED01C04B486C7E160015064B6D7E5D4B6D7E5D5D4A486D7E14034AC76C 7E140E5C4A6E7F143002E06F7E495A0103707E495A131F496C4B7E2603FFE04A487E007F 01FC021FEBFFF0B5FCA250447EC351>88 DI<020FB812C05C1A 809326800001130003F8C7FCDA3FE04A5A03804A5A92C8485A027E4B5A027C4B5A02784B 5A4A4B5AA24A4A90C7FC4A4A5A01014B5A4D5A4A4A5A01034B5A91C8485A4D5AA290C848 90C8FC4C5A4C5A4C5A4C5A4C5A4C5A4C5AA24B90C9FC4B5A4B5A4B5A4B5A4B5A4B5AA24B 5A4A90CAFC4A5A4A4814064A5A4A5A4A48140E4A48140CA24A48141C4990C81218494815 38495A49485D495A494815F049485D1701494814034890C8485A4848150F4848151F4848 4B5A484815FF48481403043F90C8FC48B8FCB9FC5F42447BC343>I96 DIIIIII<157E913803FF8091390FC1E0E091391F0073F0027E13334A 133F4948131F010315E04948130F495AA2494814C0133F4A131F137F91C713805B163F5A 491500A25E120349147EA216FEA2495CA21501A25EA21503150700015D150F0000141F6D 133F017CEB77E090383E01E790381F078F903807FE0FD901F85B90C7FC151FA25EA2153F A293C7FCA2001C147E007F14FE485C4A5A140348495AEC0FC000F8495A007C01FEC8FC38 1FFFF8000313C02C407EAB2F>I<14FE137FA3EB01FC13001301A25CA21303A25CA21307 A25CA2130FA25CA2131FA25CED3FC090393F81FFF0913887C0FC91380E007E023C133ED9 7F70133F4A7F4A14805C13FF91C7FC5BA24848143F17005BA200035D167E5BA2000715FE 5E5B1501000F5DA24913035E001F1607030713064914E0150F003FEDC00E170C90C7141C EE80184816381730007E167017E000FE91380781C0EEC38048913801FF000038EC007C30 467BC438>I<141E143F5C5CA3147E143891C7FCAE133EEBFF803801C3C0380781E03806 01F0120E121CEA180312381230A2EA700700605BA2EAE00F00C05BEA001F5CA2133F91C7 FCA25B137E13FE5BA212015BEC03800003140013F01207495A1406140E140CEBC01C1418 14385C00035BEBE1C0C6B45A013EC7FC19437DC121>I<163C16FEA21501A316FCED0070 1600AE15FCEC03FF91380F0780021C13C091383803E0147014E014C01301EC8007130314 005B0106130F130E010C14C090C7FC151FA21680A2153FA21600A25DA2157EA215FEA25D A21401A25DA21403A25DA21407A25DA2140FA25DA2141F5DA2143F001C91C7FC127F4813 7E5CA248485AEB03E038F807C038781F80D83FFEC8FCEA07F0275681C128>I<14FE137F A3EB01FC13001301A25CA21303A25CA21307A25CA2130FA25CA2131FA25C163F013FECFF C0923803C0E09138000703ED1E0F491338ED701F017E13E0EC01C001FE018013C00203EB 07004948C8FC140E00015B5C495A5C3803FBC001FFC9FC8014F83807F1FE9038F03F8090 38E00FE06E7E000F130381EBC001A2001FED01C017801380A2003F15031700010013F05E 481506160E007E150C161C00FE01005BED787048EC3FE00038EC0F802B467BC433>I<01 F8D903FCEC7F80D803FED91FFF903803FFE0D8071F903B7C0FC00F81F83E0E0F80E007E0 1C00FC001C9026C3C0030178137C271807C700D9F0E0137E02CE902601F1C0133E003801 DCDAFB80133F003001D892C7FCD90FF814FF0070495C0060495CA200E04949485CD8C01F 187E4A5C1200040715FE013F6091C75BA2040F14014960017E5D1903041F5D13FE494B13 0762043F160E0001060F130C4992C713C0191F4CED801C00031A1849027E1638F2003004 FE167000071A60494A16E0F201C0030192380F0380000FF18700494AEC03FED80380D900 70EC00F84F2D7DAB55>109 D<01F8EB03FCD803FEEB1FFFD8071F90387C0FC03B0E0F80 E007E03A0C07C3C003001CD9C7007F001801CE1301003801DC80003013D8EB0FF800705B 00605BA200E0491303D8C01F5D5C12001607013F5D91C7FCA2160F495D137E161F5F13FE 49143F94C7FC187000014B136049147E16FE4C13E0000317C049150104F8138017030007 1700495D170EEE781C000FED7C3849EC1FF0D80380EC07C0342D7DAB3A>I<91380FC003 91383FF0079138F83C0F903903E00E1E90390FC0063E90381F800790393F00037E4914FC 01FE1301485AA2484814F812075B000F140316F0485AA2003F14074914E0A3007F140F49 14C0A3151F90C713805AA2153F6C1500A2127E5D007F14FE6C1301A214036C6C485A000F 131E3807C0383803E0F13901FFC1F838003F01130014035DA314075DA3140F5DA2141FA2 143F011FB51280A21600283F7DAB2B>113 D<01F8EB0FC0D803FEEB7FF0D8070FEBF038 000E903883C07C3A0C07C701FC001C13CE0018EBDC03003813D8003013F8D90FF013F800 709038E000E0006015005C12E0EAC01F5C1200A2133F91C8FCA35B137EA313FE5BA31201 5BA312035BA312075BA3120F5BEA0380262D7DAB2C>I<141C147EA314FE5CA313015CA3 13035CA313075CA2007FB512FCB6FC15F839000FC000A2131F5CA3133F91C7FCA35B137E A313FE5BA312015BA312035BA21570000714605B15E015C0000F130101C013801403EC07 0000071306140E5C6C6C5A000113F03800FFC0013FC7FC1E3F7EBD23>116 D<133ED9FF8014E02603C3C0EB03F0380703E0380601F0000E1507121CD818035D123800 30150FA2D870075D00605B161FEAE00F00C0495CEA001F4A133FA2013F92C7FC91C7FC5E 5B017E147EA216FE13FE495CA20301EB01801703484802F81300A25F0303130616F00000 1407030F130E6D010D130C017C011D131C033913186D9038F0F838903A1F03C07870903A 07FF803FE0903A01FC000F80312D7DAB38>I<013E140ED9FF80EB3F802603C3C0137F38 0703E0380601F0120E121CD81803143F0038151F0030150FA2D87007140700605BA2D8E0 0F150000C0497FEA001F4A5B1606133F91C7FC160E49140C137EA2161C01FE14185B1638 163016704848146016E05E150100005D15036D49C7FC1506017C130E017E5B6D13789038 0F81E06DB45AD900FEC8FC292D7DAB2F>I<02FCEB07E0903A03FF801FFC903A0F07C078 1E903A1C03E0E01F903A3801F1C07FD9700013804901FB13FF4848EBFF00495B000316FE 90C71438484A130012061401000E5C120CC7FC14035DA314075DA3140F5DA3021F143817 305D1770023F1460121E003F16E0267F807FEB01C0026F148000FF01EF1303D901CFEB07 0000FE903887C00E267C03835B3A3C0F01E0783A1FFC00FFE0D803F0EB3F80302D7EAB37 >120 D<133ED9FF8014E02603C3C0EB03F0380703E0380601F0000E1507001C16E0EA18 0312380030150F007016C0EA60075C161FD8E00F158000C05BEA001F4A133F1700133F91 C7FC5E49147E137EA216FE01FE5C5BA215015E485AA215035EA200001407150F6D5C017C 131F153F6D13FF90391F03CFC0903807FF8F903801FC0F90C7121F5EA2153F93C7FCD807 C05BD81FE0137E5DA24848485A4A5A01805B39380007C00018495A001C49C8FC6C137C38 0781F83803FFE0C66CC9FC2C407DAB30>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu cmr12 12 82 /Fu 82 124 df0 D<1507A34B7EA34B7EA34B7EA34B7E156FA2EDEFF815C7A202017F1587158302037F1503 150102077F140681020E80140C167FA24A80163FA24A80161FA24A80160FA24A801607A2 4948801603A249C77F1601A201068182A24982177FA24982173FA24982171FA201708213 6001E0150F6D821201486C82D80FFEED3FFEB500C00107B512F8A33D477DC644>3 D5 D<9239FFC001FC020F9038F80FFF913B3F803E3F03C0913BFC00 077E07E0D903F890390FFC0FF0494890383FF81F4948EB7FF0495A494814E049C7FCF00F E04991393FC0038049021F90C7FCAFB912F0A3C648C7D81FC0C7FCB3B2486CEC3FF0007F D9FC0FB512E0A33C467EC539>11 D<4AB4FC020F13E091387F80F8903901FC001C49487F D907E0130F4948137F011FECFF80495A49C7FCA25B49EC7F00163E93C7FCACEE3F80B8FC A3C648C7FC167F163FB3B0486CEC7FC0007FD9FC1FB5FCA330467EC536>I14 D<131F1480133F137FA2EBFF00485A485A5B485A485A138048C7 FC123E123C5A12E0124011126CC431>19 D22 D<121EEA7F80EAFFC0A9EA7F80ACEA3F00AB121EAC120CA5C7FCAA121EEA7F80A2EAFFC0 A4EA7F80A2EA1E000A4778C61B>33 D<001EEB03C0397F800FF000FF131F01C013F8A201 E013FCA3007F130F391E6003CC0000EB000CA401E0131C491318A3000114384913300003 147090C712604814E0000614C0000E130148EB038048EB070048130E0060130C1E1D7DC4 31>I<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A312011380120313 005A1206120E5A5A5A12600B1D78C41B>39 D<140C141C1438147014E0EB01C01303EB07 80EB0F00A2131E5BA25B13F85B12015B1203A2485AA3485AA348C7FCA35AA2123EA2127E A4127CA312FCB3A2127CA3127EA4123EA2123FA27EA36C7EA36C7EA36C7EA212017F1200 7F13787FA27F7FA2EB0780EB03C01301EB00E014701438141C140C166476CA26>I<12C0 7E12707E7E7E120F6C7E6C7EA26C7E6C7EA21378137C133C133E131E131FA2EB0F80A3EB 07C0A3EB03E0A314F0A21301A214F8A41300A314FCB3A214F8A31301A414F0A21303A214 E0A3EB07C0A3EB0F80A3EB1F00A2131E133E133C137C13785BA2485A485AA2485A48C7FC 120E5A5A5A5A5A16647BCA26>I<16C04B7EB3AB007FBAFCBB1280A26C1900C8D801E0C9 FCB3AB6F5A41407BB84C>43 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E0 13C0A312011380120313005A1206120E5A5A5A12600B1D78891B>II<121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A0A78891B>I<1618163C167CA2167816 F8A216F01501A216E01503A216C01507A21680150FA2ED1F00A2151E153EA2153C157CA2 157815F8A25D1401A24A5AA25D1407A25D140FA292C7FC5CA2141E143EA2143C147CA25C A25C1301A25C1303A25C1307A25C130FA291C8FC5BA2133EA2133C137CA2137813F8A25B 1201A25B1203A2485AA25B120FA290C9FC5AA2121E123EA2123C127CA2127812F8A25A12 6026647BCA31>I<14FF010713E090381F81F890383E007C01FC133F4848EB1F8049130F 4848EB07C04848EB03E0A2000F15F0491301001F15F8A2003F15FCA390C8FC4815FEA548 15FFB3A46C15FEA56D1301003F15FCA3001F15F8A26C6CEB03F0A36C6CEB07E0000315C0 6D130F6C6CEB1F806C6CEB3F00013E137C90381F81F8903807FFE0010090C7FC28447CC1 31>I<143014F013011303131F13FFB5FC13E713071200B3B3B0497E497E007FB6FCA320 4278C131>II<49B4FC010F13E0013F 13FC9038FE01FE3A01F0007F80D803C0EB3FC048C7EA1FE0120EED0FF0EA0FE0486C14F8 A215077F5BA26C48130FEA03C0C813F0A3ED1FE0A2ED3FC01680ED7F0015FE4A5AEC03F0 EC1FC0D90FFFC7FC15F090380001FCEC007FED3F80ED1FC0ED0FE016F0ED07F816FC1503 16FEA2150116FFA3121EEA7F80487EA416FE491303A2007EC713FC00701407003015F800 38140F6C15F06CEC1FE06C6CEB3FC0D803E0EB7F803A01FE01FE0039007FFFF8010F13E0 010190C7FC28447CC131>II<000615C0D807C0130701FCEB7F8090B612005D 5D5D15E0158026063FFCC7FC90C9FCAE14FF010713C090381F01F090383800FC01F0137E D807C07F49EB1F8016C090C7120F000615E0C8EA07F0A316F81503A216FCA5123E127F48 7EA416F890C712075A006015F0A20070140F003015E00038EC1FC07E001EEC3F806CEC7F 006C6C13FE6C6C485A3901F807F039007FFFE0011F90C7FCEB07F826447BC131>II<121CA2EA1F8090B712C0A3481680A217005E0038C8120C 0030151C00705D0060153016705E5E4814014B5A4BC7FCC81206150E5D151815385D1560 15E04A5AA24A5A140792C8FC5CA25C141E143EA2147E147CA214FCA21301A3495AA41307 A6130FAA6D5AEB01C02A457BC231>I<14FF010713E0011F13F890387F00FE01FC133FD8 01F0EB1F804848EB0FC049EB07E00007EC03F048481301A290C713F8481400A47FA26D13 0116F07F6C6CEB03E013FC6C6CEB07C09039FF800F806C9038C01F006CEBF03EECF87839 007FFEF090383FFFC07F01077F6D13F8497F90381E7FFFD97C1F1380496C13C02601E003 13E048486C13F000079038007FF84848EB3FFC48C7120F003EEC07FE150148140016FF16 7F48153FA2161FA56C151E007C153EA2007E153C003E157C6C15F86DEB01F06C6CEB03E0 6C6CEB07C0D803F8EB1F80C6B4EBFF0090383FFFFC010F13F00101138028447CC131>I< 14FF010713E0011F13F890387F80FC9038FC007E48487F4848EB1F804848EB0FC0000FEC 07E0485AED03F0485A16F8007F140190C713FCA25AA216FE1500A516FFA46C5CA36C7E5D 121F7F000F5C6C6C130E150C6C6C131C6C6C5BD8007C5B90383F01E090390FFF80FE9038 01FE0090C8FC150116FCA4ED03F8A216F0D80F801307486C14E0486C130F16C0ED1F80A2 49EB3F0049137E001EC75A001C495A000F495A3907E01FE06CB51280C649C7FCEB1FF028 447CC131>I<121EEA7F80A2EAFFC0A4EA7F80A2EA1E00C7FCB3A5121EEA7F80A2EAFFC0 A4EA7F80A2EA1E000A2B78AA1B>I<121EEA7F80A2EAFFC0A4EA7F80A2EA1E00C7FCB3A5 121E127FEAFF80A213C0A4127F121E1200A512011380A3120313005A1206120E120C121C 5A5A12600A3E78AA1B>I<007FBAFCBB1280A26C1900CEFCB0007FBAFCBB1280A26C1900 41187BA44C>61 D<16C04B7EA34B7EA34B7EA34B7EA3ED19FEA3ED30FFA203707FED607F A203E07FEDC03FA2020180ED801FA2DA03007F160FA20206801607A24A6D7EA34A6D7EA3 4A6D7EA20270810260147FA202E08191B7FCA249820280C7121FA249C87F170FA2010682 1707A2496F7EA3496F7EA3496F7EA201788313F8486C83D80FFF03037FB500E0027FEBFF C0A342477DC649>65 DIIIIIIII75 DIIIII82 D<49B41303010FEBE007013F13F89039FE00FE0FD801F8 131FD807E0EB079F49EB03DF48486DB4FC48C8FC4881003E81127E82127C00FC81A282A3 7E82A27EA26C6C91C7FC7F7FEA3FF813FE381FFFE06C13FE6CEBFFE06C14FC6C14FF6C15 C0013F14F0010F80010180D9001F7F14019138001FFF03031380816F13C0167F163F161F 17E000C0150FA31607A37EA36C16C0160F7E17806C151F6C16006C5D6D147ED8FBC05CD8 F9F0495AD8F07C495A90393FC00FE0D8E00FB51280010149C7FC39C0003FF02B487BC536 >I<003FB912F8A3903BF0001FF8001F01806D481303003EC7150048187C0078183CA200 70181CA30060180CA5481806A5C81600B3B3A54B7EED7FFE49B77EA33F447DC346>IIII91 D<01C01318000114384848137048C712E0 000EEB01C0000C1480001C13030018140000385B003013060070130E0060130CA300E013 1C481318A400CFEB19E039FFC01FF801E013FCA3007F130FA2003F130701C013F8390F00 01E01E1D71C431>II97 DII<167FED3FFFA315018182B3EC7F80903803FFF090380FC07C 90383F000E017E1307496D5AD803F87F48487F5B000F81485AA2485AA2127FA290C8FC5A AB7E7FA2123FA26C7EA2000F5D7F6C6C5B00035C6C6C9038077F806C6C010E13C0013F01 1C13FE90380FC0F8903803FFE09026007F0013002F467DC436>III III<143C14FFA2491380A46D1300A2143C91C7FCADEC7F80EB 3FFFA31300147F143FB3B3AA123E127F39FF807F00A2147EA25C6C485A383C01F06C485A 3807FF80D801FEC7FC195785C21E>IIII<3901FC01FE00FF903807FFC091381E07F091383801F800070170 7F0003EBE0002601FDC07F5C01FF147F91C7FCA25BA35BB3A8486CECFF80B5D8F83F13FE A32F2C7DAB36>II<3901FC03FC00FF9038 0FFF8091383C07E091387001F83A07FDE000FE00030180137FD801FFEC3F8091C7EA1FC0 4915E049140F17F0160717F8160317FCA3EE01FEABEE03FCA3EE07F8A217F0160F6D15E0 EE1FC06D143F17806EEB7E00D9FDC05B9039FCF003F891383C0FE091381FFF80DA03FCC7 FC91C9FCAE487EB512F8A32F3F7DAB36>I<91387F8003903903FFE00790380FE0789039 3F801C0F90387E000E496D5AD803F8EB039F0007EC01BF4914FF48487F121F5B003F81A2 485AA348C8FCAB6C7EA3123F7F121F6D5C120F6D5B12076C6C5B6C6C497E6C6C130E013F 131C90380FC0F8903803FFE09038007F0091C7FCAEEEFF80033F13FEA32F3F7DAB33>I< 3903F803F000FFEB1FFCEC3C3EEC707F0007EBE0FF3803F9C000015B13FBEC007E153C01 FF13005BA45BB3A748B4FCB512FEA3202C7DAB26>I<90383FE0183901FFFC383907E01F 78390F0003F8001E1301481300007C1478127800F81438A21518A27EA27E6C6C13006C7E 13FC383FFFE06C13FC6C13FF6C14C06C14E0C614F0011F13F81300EC0FFC140300C0EB01 FE1400157E7E153EA27EA36C143C6C147C15786C14F86CEB01F039F38003E039F1F00F80 39E07FFE0038C00FF01F2E7DAC26>I<1306A5130EA4131EA3133E137EA213FE12011207 001FB512F0B6FCA2C648C7FCB3A4150CAA017E131C017F1318A26D133890381F8030ECC0 70903807E0E0903801FFC09038007F001E3E7EBC26>IIIIII<003FB612E0A29038C0003F90C713C0003CEC7F800038EC FF00A20030495A0070495AA24A5A0060495AA24A5A4A5AA2C7485A4AC7FC5B5C495A1307 5C495A131F4A1360495A495AA249C712C0485AA2485A485A1501485A48481303A24848EB 07804848131F00FF14FF90B6FCA2232B7DAA2B>II E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fv cmbx12 12 40 /Fv 40 122 df46 D48 DII< ECFFF0010713FF011F14C0017F14F049C66C7ED803F8EB3FFED807E06D7E81D80FF86D13 8013FE001F16C07FA66C5A6C4815806C485BC814005D5E4B5A4B5A4B5A4A5B020F138090 2607FFFEC7FC15F815FF16C090C713F0ED3FFCED0FFEEEFF80816F13C017E0A26F13F0A2 17F8A3EA0FC0EA3FF0487EA2487EA217F0A25D17E06C5A494913C05BD83F80491380D81F F0491300D80FFEEBFFFE6CB612F800015D6C6C14C0011F49C7FC010113E02D427BC038> I<163FA25E5E5D5DA25D5D5D5DA25D92B5FCEC01F7EC03E7140715C7EC0F87EC1F07143E 147E147C14F8EB01F0EB03E0130714C0EB0F80EB1F00133E5BA25B485A485A485A120F5B 48C7FC123E5A12FCB91280A5C8000F90C7FCAC027FB61280A531417DC038>I<00071503 01E0143F01FFEB07FF91B6FC5E5E5E5E5E16804BC7FC5D15E092C8FC01C0C9FCAAEC3FF0 01C1B5FC01C714C001DF14F09039FFE03FFC9138000FFE01FC6D7E01F06D13804915C049 7F6C4815E0C8FC6F13F0A317F8A4EA0F80EA3FE0487E12FF7FA317F05B5D6C4815E05B00 7EC74813C0123E003F4A1380D81FC0491300D80FF0495AD807FEEBFFFC6CB612F0C65D01 3F1480010F01FCC7FC010113C02D427BC038>I58 D65 D67 D73 D75 DIII80 D82 DI<003FBA12E0A59026FE000FEB8003D87FE09338003FF04917 1F90C71607A2007E1803007C1801A300781800A400F819F8481978A5C81700B3B3A20107 B8FCA545437CC24E>I<903801FFE0011F13FE017F6D7E48B612E03A03FE007FF84848EB 1FFC6D6D7E486C6D7EA26F7FA36F7F6C5A6C5AEA00F090C7FCA40203B5FC91B6FC130701 3F13F19038FFFC01000313E0000F1380381FFE00485A5B127F5B12FF5BA35DA26D5B6C6C 5B4B13F0D83FFE013EEBFFC03A1FFF80FC7F0007EBFFF86CECE01FC66CEB8007D90FFCC9 FC322F7DAD36>97 DII IIIII<137C48B4FC4813804813C0A24813E0A56C13C0A26C13806C1300EA007C90C7 FCAAEB7FC0EA7FFFA512037EB3AFB6FCA518467CC520>I107 DI<90277F8007FEEC0FFCB590263FFFC090387FFF8092B5D8F0 01B512E002816E4880913D87F01FFC0FE03FF8913D8FC00FFE1F801FFC0003D99F009026 FF3E007F6C019E6D013C130F02BC5D02F86D496D7EA24A5D4A5DA34A5DB3A7B60081B600 03B512FEA5572D7CAC5E>I<90397F8007FEB590383FFF8092B512E0028114F8913987F0 3FFC91388F801F000390399F000FFE6C139E14BC02F86D7E5CA25CA35CB3A7B60083B512 FEA5372D7CAC3E>II<9039 7FC00FF8B590B57E02C314E002CF14F89139DFC03FFC9139FF001FFE000301FCEB07FF6C 496D13804A15C04A6D13E05C7013F0A2EF7FF8A4EF3FFCACEF7FF8A318F017FFA24C13E0 6E15C06E5B6E4913806E4913006E495A9139DFC07FFC02CFB512F002C314C002C091C7FC ED1FF092C9FCADB67EA536407DAC3E>I<90387F807FB53881FFE0028313F0028F13F8ED 8FFC91389F1FFE000313BE6C13BC14F8A214F0ED0FFC9138E007F8ED01E092C7FCA35CB3 A5B612E0A5272D7DAC2E>114 D<90391FFC038090B51287000314FF120F381FF003383F C00049133F48C7121F127E00FE140FA215077EA27F01E090C7FC13FE387FFFF014FF6C14 C015F06C14FC6C800003806C15806C7E010F14C0EB003F020313E0140000F0143FA26C14 1F150FA27EA26C15C06C141FA26DEB3F8001E0EB7F009038F803FE90B55A00FC5CD8F03F 13E026E007FEC7FC232F7CAD2C>III119 D121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fw cmtt10 10.95 18 /Fw 18 119 df<120FEA3FC0EA7FE0A2EAFFF0A4EA7FE0A2EA3FC0EA0F000C0C6E8B30> 46 D49 DI64 D97 DII<913801FFE04A7F5CA28080EC0007AAEB03FE90381FFF8749 13E790B6FC5A5A481303380FFC00D81FF0133F49131F485A150F4848130790C7FCA25AA2 5AA87E6C140FA27F003F141F6D133F6C7E6D137F390FF801FF2607FE07EBFFC06CB712E0 6C16F06C14F76D01C713E0011F010313C0D907FCC8FC2C397DB730>I<49B4FC010713E0 011F13F8017F7F90B57E488048018113803A07FC007FC04848133FD81FE0EB1FE0150F48 4814F0491307127F90C7FCED03F85A5AB7FCA516F048C9FC7E7EA27F003FEC01F06DEB03 F86C7E6C7E6D1307D807FEEB1FF03A03FFC07FE06C90B5FC6C15C0013F14806DEBFE0001 0713F8010013C0252A7CA830>I<14E0EB03F8A2497EA36D5AA2EB00E091C8FCA9381FFF F8487F5AA27E7EEA0001B3A9003FB612C04815E0B7FCA27E6C15C023397AB830>105 D<387FFFF8B57EA47EEA0001B3B3A8007FB612F0B712F8A46C15F025387BB730>108 D<02FC137E3B7FC3FF01FF80D8FFEF01877F90B500CF7F15DF92B57E6C010F13872607FE 07EB03F801FC13FE9039F803FC01A201F013F8A301E013F0B3A23C7FFE0FFF07FF80B548 018F13C0A46C486C01071380322881A730>II<49B4 FC010F13E0013F13F8497F90B57E0003ECFF8014013A07FC007FC04848EB3FE0D81FE0EB 0FF0A24848EB07F8491303007F15FC90C71201A300FEEC00FEA86C14016C15FCA26D1303 003F15F86D13076D130F6C6CEB1FF06C6CEB3FE06D137F3A07FF01FFC06C90B512806C15 006C6C13FC6D5B010F13E0010190C7FC272A7CA830>I114 D116 DI<3B3FFFC07FFF80486DB512C0B515E0A26C16C06C496C13 803B01F80003F000A26D130700005DA26D130F017E5CA2017F131F6D5CA2EC803F011F91 C7FCA26E5A010F137EA2ECE0FE01075BA214F101035BA3903801FBF0A314FF6D5BA36E5A 6E5A2B277EA630>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fx cmr10 10.95 79 /Fx 79 128 df<4AB4EB0FE0021F9038E03FFC913A7F00F8FC1ED901FC90383FF03FD907 F090397FE07F80494801FF13FF4948485BD93F805C137F0200ED7F00EF003E01FE6D91C7 FC82ADB97EA3C648C76CC8FCB3AE486C4A7E007FD9FC3FEBFF80A339407FBF35>11 DIII<133E133F137F13FFA2EA01FEEA03FCEA07 F813F0EA0FE0EA1FC01380EA3E005A5A1270122010116EBE2D>19 D<001E130F397F803FC000FF137F01C013E0A201E013F0A3007F133F391E600F30000013 00A401E01370491360A3000114E04913C00003130101001380481303000EEB070048130E 0018130C0038131C003013181C1C7DBE2D>34 D<121EEA7F8012FF13C0A213E0A3127FEA 1E601200A413E013C0A312011380120313005A120E5A1218123812300B1C79BE19>39 D<1430147014E0EB01C0EB03801307EB0F00131E133E133C5B13F85B12015B1203A2485A A2120F5BA2121F90C7FCA25AA3123E127EA6127C12FCB2127C127EA6123E123FA37EA27F 120FA27F1207A26C7EA212017F12007F13787F133E131E7FEB07801303EB01C0EB00E014 701430145A77C323>I<12C07E12707E7E121E7E6C7E7F12036C7E7F12007F1378137CA2 7FA2133F7FA21480130FA214C0A3130714E0A6130314F0B214E01307A614C0130FA31480 A2131F1400A25B133EA25BA2137813F85B12015B485A12075B48C7FC121E121C5A5A5A5A 145A7BC323>I<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A3120113 80120313005A120E5A1218123812300B1C798919>44 DI<121E EA7F80A2EAFFC0A4EA7F80A2EA1E000A0A798919>I 48 DIII<15 0E151E153EA2157EA215FE1401A21403EC077E1406140E141CA214381470A214E0EB01C0 A2EB0380EB0700A2130E5BA25B5BA25B5B1201485A90C7FC5A120E120C121C5AA25A5AB8 FCA3C8EAFE00AC4A7E49B6FCA3283E7EBD2D>I<00061403D80780131F01F813FE90B5FC 5D5D5D15C092C7FC14FCEB3FE090C9FCACEB01FE90380FFF8090383E03E090387001F849 6C7E49137E497F90C713800006141FC813C0A216E0150FA316F0A3120C127F7F12FFA416 E090C7121F12FC007015C012780038EC3F80123C6CEC7F00001F14FE6C6C485A6C6C485A 3903F80FE0C6B55A013F90C7FCEB07F8243F7CBC2D>II<1238123C123F90B612FCA316F85A16F016E00078C712010070EC03 C0ED078016005D48141E151C153C5DC8127015F04A5A5D14034A5A92C7FC5C141EA25CA2 147C147814F8A213015C1303A31307A3130F5CA2131FA6133FAA6D5A0107C8FC26407BBD 2D>III<121EEA7F80A2EAFFC0A4EA7F80A2EA1E00C7FCB3 121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A2779A619>I<15074B7EA34B7EA34B7EA34B 7EA34B7E15E7A2913801C7FC15C3A291380381FEA34AC67EA3020E6D7EA34A6D7EA34A6D 7EA34A6D7EA34A6D7EA349486D7E91B6FCA249819138800001A249C87EA24982010E157F A2011E82011C153FA2013C820138151FA2017882170F13FC00034C7ED80FFF4B7EB500F0 010FB512F8A33D417DC044>65 DIIIIIIII<011FB512FCA3D90007 13006E5A1401B3B3A6123FEA7F80EAFFC0A44A5A1380D87F005B007C130700385C003C49 5A6C495A6C495A2603E07EC7FC3800FFF8EB3FC026407CBD2F>IIIIIIIIII<003FB91280A3903AF0 007FE001018090393FC0003F48C7ED1FC0007E1707127C00781703A300701701A548EF00 E0A5C81600B3B14B7E4B7E0107B612FEA33B3D7DBC42>IIII89 D<003FB712F8A391C7EA1FF013F801E0 EC3FE00180EC7FC090C8FC003EEDFF80A2003C4A1300007C4A5A12784B5A4B5AA200704A 5AA24B5A4B5AA2C8485A4A90C7FCA24A5A4A5AA24A5AA24A5A4A5AA24A5A4A5AA24990C8 FCA2495A4948141CA2495A495AA2495A495A173C495AA24890C8FC485A1778485A484815 F8A24848140116034848140F4848143FED01FFB8FCA32E3E7BBD38>II<486C13C00003130101001380481303000EEB0700 48130E0018130C0038131C003013180070133800601330A300E01370481360A400CFEB67 8039FFC07FE001E013F0A3007F133FA2003F131F01C013E0390F0007801C1C73BE2D>I< EAFFFCA4EA003CB3B3B3B3ABEAFFFCA40E5B7FC319>I97 DI<49B4FC010F13E090383F00F801 7C131E4848131F4848137F0007ECFF80485A5B121FA24848EB7F00151C007F91C7FCA290 C9FC5AAB6C7EA3003FEC01C07F001F140316806C6C13076C6C14000003140E6C6C131E6C 6C137890383F01F090380FFFC0D901FEC7FC222A7DA828>IIII< 167C903903F801FF903A1FFF078F8090397E0FDE1F9038F803F83803F001A23B07E000FC 0600000F6EC7FC49137E001F147FA8000F147E6D13FE00075C6C6C485AA23901F803E039 03FE0FC026071FFFC8FCEB03F80006CAFC120EA3120FA27F7F6CB512E015FE6C6E7E6C15 E06C810003813A0FC0001FFC48C7EA01FE003E140048157E825A82A46C5D007C153E007E 157E6C5D6C6C495A6C6C495AD803F0EB0FC0D800FE017FC7FC90383FFFFC010313C0293D 7EA82D>III<1478EB01FEA2EB03FFA4EB01FEA2EB00781400AC 147FEB7FFFA313017F147FB3B3A5123E127F38FF807E14FEA214FCEB81F8EA7F01387C03 F0381E07C0380FFF803801FC00185185BD1C>III<2701F801FE14FF00FF902707FFC00313E0913B1E07E00F03F0913B 7803F03C01F80007903BE001F87000FC2603F9C06D487F000101805C01FBD900FF147F91 C75B13FF4992C7FCA2495CB3A6486C496CECFF80B5D8F87FD9FC3F13FEA347287DA74C> I<3901F801FE00FF903807FFC091381E07E091387803F000079038E001F82603F9C07F00 01138001FB6D7E91C7FC13FF5BA25BB3A6486C497EB5D8F87F13FCA32E287DA733>I<14 FF010713E090381F81F890387E007E01F8131F4848EB0F804848EB07C04848EB03E0000F 15F04848EB01F8A2003F15FCA248C812FEA44815FFA96C15FEA36C6CEB01FCA3001F15F8 6C6CEB03F0A26C6CEB07E06C6CEB0FC06C6CEB1F80D8007EEB7E0090383F81FC90380FFF F0010090C7FC282A7EA82D>I<3901FC03FC00FF90381FFF8091387C0FE09039FDE003F0 3A07FFC001FC6C496C7E6C90C7127F49EC3F805BEE1FC017E0A2EE0FF0A3EE07F8AAEE0F F0A4EE1FE0A2EE3FC06D1580EE7F007F6E13FE9138C001F89039FDE007F09039FC780FC0 DA3FFFC7FCEC07F891C9FCAD487EB512F8A32D3A7EA733>I<02FF131C0107EBC03C9038 1F80F090397F00387C01FC131CD803F8130E4848EB0FFC150748481303121F485A150148 5AA448C7FCAA6C7EA36C7EA2001F14036C7E15076C6C130F6C7E6C6C133DD8007E137990 383F81F190380FFFC1903801FE0190C7FCAD4B7E92B512F8A32D3A7DA730>I<3901F807 E000FFEB1FF8EC787CECE1FE3807F9C100031381EA01FB1401EC00FC01FF1330491300A3 5BB3A5487EB512FEA31F287EA724>I<90383FC0603901FFF8E03807C03F381F000F003E 1307003C1303127C0078130112F81400A27E7E7E6D1300EA7FF8EBFFC06C13F86C13FE6C 7F6C1480000114C0D8003F13E0010313F0EB001FEC0FF800E01303A214017E1400A27E15 F07E14016C14E06CEB03C0903880078039F3E01F0038E0FFFC38C01FE01D2A7DA824>I< 131CA6133CA4137CA213FCA2120112031207001FB512C0B6FCA2D801FCC7FCB3A215E0A9 12009038FE01C0A2EB7F03013F138090381F8700EB07FEEB01F81B397EB723>IIII< B539F01FFFE0A30003D9C00F1300C690388007F8D97F0013E002805BD93FC05B011F49C7 FC90380FE00EECF01E6D6C5A01035B6D6C5A6E5AEB00FF6E5A6E5A81141F814A7E81147B ECF1FC903801E1FEECC0FF01037F49486C7ED90F007F011E6D7E013E130F496D7E01FC80 486C80000F4A7EB539803FFFF8A32D277FA630>II<001FB61280A2EBE0000180140049485A001E 495A121C4A5A003C495A141F00385C4A5A147F5D4AC7FCC6485AA2495A495A130F5C495A 90393FC00380A2EB7F80EBFF005A5B484813071207491400485A48485BA248485B484813 7F00FF495A90B6FCA221277EA628>II<001C130E007FEB3F8039 FF807FC0A5397F003F80001CEB0E001A0977BD2D>127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fy cmti10 10.95 26 /Fy 26 123 df<123812FCA27EA2127FA2EA3F80121F120F13C01207EA03E0120113F012 0013600C1166BE2E>18 D44 D<120FEA3FC0127FA212FFA31380EA7F00123C0A0A77891C>46 D<49B712C018F818FE90 3B0003FE0003FF9438007F804BEC1FC0F00FE0F007F014074BEC03F8F001FCA2140F4BEC 00FEA3141F4B15FFA3143F5DA3027F5D5DA219FE14FF92C81203A34917FC4A1507A219F8 13034A150F19F0A20107EE1FE05CF03FC0A2010FEE7F804A16006060011F4B5A4A4A5A4D 5AA2013F4B5A4AEC3FC04DC7FC017F15FEEE03FC4AEB0FF001FFEC7FE0B8128004FCC8FC 16E0403E7BBD45>68 D<49B612C0A25FD9000390C8FC5D5DA314075DA3140F5DA3141F5D A3143F5DA3147F5DA314FF92C9FCA35B5CA313035C18C0EF01E0010716C05C1703188013 0F4A140718005F131F4A141EA2173E013F5D4A14FC1601017F4A5A16074A131F01FFECFF F0B8FCA25F333E7BBD39>76 D<49B5933807FFFC496062D90003F0FC00505ADBBF805E1A 771AEF1407033F923801CFE0A2F1039F020FEE071F020E606F6C140E1A3F021E161C021C 04385BA2F1707F143C023804E090C7FCF001C0629126780FE0495A02705FF00700F00E01 14F002E0031C5BA2F03803010116704A6C6C5D18E019070103ED01C00280DA03805BA294 3807000F13070200020E5C5FDB03F8141F495D010E4B5CA24D133F131E011CDAF9C05CEE FB80197F013C6DB4C7FC013895C8FC5E01784A5C13F8486C4A5CD807FE4C7EB500F04948 B512FE16E01500563E7BBD52>I<49B612FCEFFF8018F0903B0003FE000FF8EF03FE4BEB 00FF8419800207ED3FC05DA219E0140F5DA3021FED7FC05DA2F0FF80143F4B15004D5A60 027F4A5A4B495A4D5AEF3F8002FF02FEC7FC92380007F892B512E01780499038000FE04A 6D7E707E707E0103814A130083A213075CA25E130F5C5F1603131F5CA3013F020714404A 16E05F017F160119C04A01031303496C1680B6D8800113079438FE0F009338007E1ECAEA 3FFCEF07F03B407BBD42>82 D<92391FE00380ED7FFC913A01FFFE0700913907F01F8F91 390FC007DF4AC66CB4FC023E6D5A4A130014FC495A4948147CA2495AA2010F15785CA301 1F1570A46E91C7FCA2808014FE90380FFFE015FC6DEBFF8016E06D806D806D6C7F141F02 037FEC003FED07FF1501A281A282A212075A167E120EA2001E15FE5EA25E003E14015E00 3F14034B5A486C5C150F6D495A6D49C8FCD8F9F0137C39F8FE01F839F03FFFF0D8E00F13 C026C001FEC9FC314279BF33>I<48B9FCA25A903AFE001FF00101F89138E0007FD807E0 163E49013F141E5B48C75BA2001E147FA2001C4B131C123C003814FFA2007892C7FC1270 4A153C00F01738485CC716001403A25DA21407A25DA2140FA25DA2141FA25DA2143FA25D A2147FA25DA214FFA292C9FCA25BA25CA21303A25CEB0FFE003FB67E5AA2383D71BC41> I<001FB500F090B512F0485DA226003FF0C7380FFC004AEC03F04A5D715A017F1503A24A 5DA201FF150795C7FC91C8FCA2485E170E5BA20003161E171C5BA20007163C17385BA200 0F167817705BA2001F16F05F5BA2003F1501A2495DA2007F1503A2495DA2160794C8FC48 C8FC5E160E161E6C151C163C5E5E5E6C6C13014B5A001F4A5A6C6C011FC9FC6D133E6C6C 13F83903FC07F0C6B512C0013F90CAFCEB07F83C406FBD44>II<147E49B47E903907C1C38090391F80EFC090383F 00FF017E137F4914804848133F485AA248481400120F5B001F5C157E485AA215FE007F5C 90C7FCA21401485C5AA21403EDF0385AA21407EDE078020F1370127C021F13F0007E013F 13E0003E137FECF3E1261F01E313C03A0F8781E3803A03FF00FF00D800FC133E252977A7 2E>97 D99 DII103 D<1478EB01FCA21303A314F8EB00E01400AD137C48B4FC38038F80EA0707000E13C0121E 121CEA3C0F1238A2EA781F00701380A2EAF03F140012005B137E13FE5BA212015BA21203 5B1438120713E0000F1378EBC070A214F0EB80E0A2EB81C01383148038078700EA03FEEA 00F8163E79BC1C>105 D109 DII<903903E001F890390FF807FE903A1E 7C1E0F80903A1C3E3C07C0013C137801389038E003E0EB783F017001C013F0ED80019038 F07F0001E015F8147E1603000113FEA2C75AA20101140717F05CA20103140F17E05CA201 07EC1FC0A24A1480163F010F15005E167E5E131F4B5A6E485A4B5A90393FB80F80DA9C1F C7FCEC0FFCEC03E049C9FCA2137EA213FEA25BA21201A25BA21203A2387FFFE0B5FCA22D 3A80A72E>I114 DII<017CEB01C048B4EB07 F038038F80EA0707000E01C013F8121E001C1403EA3C0F0038EC01F0A2D8781F13000070 5BA2EAF03F91C712E012005B017E130116C013FE5B1503000115805BA2ED07001203495B 150EA25DA25D1578000114706D5B0000495A6D485AD97E0FC7FCEB1FFEEB03F0252979A7 2A>118 D122 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fz cmbx10 10.95 10 /Fz 10 58 df48 D<140F143F5C495A130F48B5 FCB6FCA313F7EAFE071200B3B3A8007FB612F0A5243C78BB34>I<903803FF80013F13F8 90B512FE00036E7E4881260FF80F7F261FC0037F4848C67F486C6D7E6D6D7E487E6D6D7E A26F1380A46C5A6C5A6C5A0007C7FCC8FC4B1300A25E153F5E4B5AA24B5A5E4A5B4A5B4A 48C7FC5D4A5AEC1FE04A5A4A5A9139FF000F80EB01FC495A4948EB1F00495AEB1F8049C7 FC017E5C5B48B7FC485D5A5A5A5A5AB7FC5EA4293C7BBB34>I<903801FFE0010F13FE01 3F6D7E90B612E04801817F3A03FC007FF8D807F06D7E82D80FFC131F6D80121F7FA56C5A 5E6C48133FD801F05CC8FC4B5A5E4B5A4A5B020F5B902607FFFEC7FC15F815FEEDFFC0D9 000113F06E6C7E6F7E6F7E6F7E1780A26F13C0A217E0EA0FC0487E487E487E487EA317C0 A25D491580127F49491300D83FC0495A6C6C495A3A0FFE01FFF86CB65A6C5DC61580013F 49C7FC010313E02B3D7CBB34>II<00071538D80FE0EB01F801FE133F90B6FC5E5E5E5E93C7FC5D15F85D15C04AC8 FC0180C9FCA9ECFFC0018713FC019F13FF90B67E020113E09039F8007FF0496D7E01C06D 7E5B6CC77FC8120F82A31780A21207EA1FC0487E487E12FF7FA21700A25B4B5A6C5A0180 5C6CC7123F6D495AD81FE0495A260FFC075B6CB65A6C92C7FCC614FC013F13F0010790C8 FC293D7BBB34>II<121F7F13 F890B712F0A45A17E017C0178017005E5E5A007EC7EA01F84B5A007C4A5A4B5A4B5A93C7 FC485C157E5DC7485A4A5AA24A5A140F5D141F143F5D147FA214FF92C8FC5BA25BA3495A A3130FA5131FAA6D5A6D5A6D5A2C3F7ABD34>II<903801FF E0010F13FC013F13FF90B612C04801E07F489038003FF048486D7E000F6E7E485A6F7E12 3F48488081178012FFA217C0A517E0A4007F5CA4003F5C6C7E5D6C7E00075C3903FF80FB 6C13FF6C6C13F36D13C3010F018313C090380008031400A24B1380EA03F0487E486C1500 487E4B5AA25E151F4B5A495C6C48EBFFE049485B2607FC0F5B6CB6C7FC6C14FC6C14F06D 13C0D90FFEC8FC2B3D7CBB34>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FA cmr10 10 3 /FA 3 52 df49 DII E %EndDVIPSBitmapFont %DVIPSBitmapFont: FB cmr12 14.4 18 /FB 18 123 df<120FEA3FC0EA7FE0EAFFF0A6EA7FE0EA3FC0EA0F000C0C768B21>46 D66 DI69 D76 D III101 D<1378EA01FE487E487FA66C90C7 FC6C5AEA007890C8FCB0EB7F80B5FCA41203C6FC137FB3B3A43801FFE0B61280A419507C CF21>105 D 108 D<01FFD907FEEC03FFB590261FFFC0010F13E0037F01F0013F13F8912701F80FFC90 38FC07FE913D03C003FE01E001FF000390260700019038038000C6010E6D6C48C76C7E6D 48DA7F8E6E7E4A159CA24ADA3FF86E7E02605D14E04A5DA34A5DB3AD2601FFE0DAFFF0EC 7FF8B6D8C07F9026FFE03FB512F0A45C347CB363>I<01FFEB07FCB590383FFF8092B512 E0913901F00FF8913903C007FC000349C66C7EC6010E13016D486D7E5C143002706E7E14 6014E05CA35CB3AD2601FFE0903801FFE0B600C0B612C0A43A347CB341>II<01FFEB1F80B5EB7FF0913801FFF8913803E1FC91380783FE0003EB0F 07C6131EEB7F1C1438143091387003FC91386000F0160014E05CA45CB3AA8048487EB612 F0A427347DB32E>114 D116 D118 D<001FB712E0A301FCC7EA7FC001E014FF018049138090C714004B5A001E14074B5A485D 4B5A153F4B5A00385D15FF4A5B93C7FC4A5A1407C7485A5D4A5A143F4A5A5D14FF495B92 C8FC494814E01307495A5C495A013FEC01C0495A5C13FF485B91C71203485A1207484814 0749140F485A003FED3F80484814FF491307B8FCA32B337DB234>122 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FC cmr17 20.74 19 /FC 19 124 df65 D<913803FF80021F13F891B512FE903A03FC01FF80903A07E0003FE0D91F 80EB0FF8013EC76C7E496E7E01F06E7E48486E7F717E4848153F4982D807A06F7E13FC48 7E6D6F7E80A2717EA46C90C8FC6C5A6C5ACAFCA6EE07FF0303B5FC157F913903FFFE0702 1F138091387FF800903801FFC0010790C7FCEB1FFCEB3FF0EBFFE0485B485B4890C8FC5B 485A485AA2485A1A0E485AA312FF5B170FA4171FA26D153F007F163B177B6DDBF1FE131C 003F16E16C6C14016C6C912603C0FF13386C6CEC0F806C6C6C903A1F007F80706C6D017C ECE1E028007FF803F8EB3FFF011FB500E06D1380010391C7000713009026003FF8EC01FC 474D79CB4F>97 D<14F8EA03FFB5FCA5C6FC133F131FA2130FB3B04CB47E041F13F8047F 13FE923A01FC01FF80923A07E0003FE0031FC7EA0FF0033EEC07FC0378EC01FE4B6E7EDA F9E06F7EDAFBC06F7EDAFF808292C96C7E737E5C4A707E864A160386851B80A37313C0A3 1BE0A31A7FA21BF0AE1BE0A21AFFA31BC0A2611B80A21B0061626E1607626E160F626E4C 5A02F75FDAE7804B5ADAE3C0157FDAC1E04B5ADAC0F04A48C7FC03784A5A4A6CEC0FF803 1F4A5A4A6C6CEB7FC0922703F803FFC8FC0300B512FC010E023F13E090C8D807FEC9FC4C 797BF758>II<191FF07FFF051FB5FCA5EF001F180784A284B3B0ED07FE92387FFFC00203B512 F091390FFC01FC91393FE0001FDAFF80EB07814990C7EA03E1D903FCEC01F14948EC0079 D91FF0153D4948151D4A151F49488101FF824890C9FC48835B0007835B120F5B121FA212 3F5BA2127FA35BA212FFAE127FA27FA3123FA36C7EA36C7EA200075F7F00035F6C7E606C 6D5D6D6C153D013F16396D6C03797F6D6C15F16D6CDA03E17FD903FEDA078113F0D900FF DA1F01EBFFF0DA7FC0137E91391FF803F80207B512E0020114809127001FF800EC80004C 797AF758>II< EE7FC0923803FFF8030F7F92383FC07F9239FF000F804A48EB3FC04A48137F4A48EBFFE0 4A485AEC1FE0143F15C0147F158002FF6D13C0EF7F804990C7EA0C0094C7FCA3495AB3A9 B812C0A5260003FEC9FCB3B3B3A7805B011F13E0001FB612F8A533797DF82F>I<131EEB 7F80497E487F487FA66C5B6C5B6D5A011EC7FC90C8FCB3A7EB01F0EA07FFB5FCA51201EA 007F133FA2131FB3B3B3A3497EEBFFFEB612FCA51E727AF12A>105 D108 DIII<02F849B47ED803 FF021F13F8B5027F13FE923A01FC01FF80923A07E0003FE0031FC76C7E033EEC0FFCC602 78EC03FE013F496E7E90261FF9E06E7FDAFBC0826DB4486F7E92C96C7E737E5C4A707E86 4A160786851B80A2851BC0A2851BE0A5F27FF0AEF2FFE0A54F13C0A34F1380A21B006162 6E160F626E161F626E4C5A4F5A6F5EDAFBC015FFDAF9E04A5BDAF8F04A48C7FC03784A5A 6F4A5A031FEC3FF06F6CEBFFC0922603F80790C8FC0300B512FC043F13E0DC07FEC9FC93 CBFCB3A7497EEB7FFFB77EA54C6C7BCA58>I114 DI<1407A85CA65CA35CA35CA25CA25BA25B5B5B5B5B5B48B712FE120FB8FCA3D800 0190C9FCB3B3A2EF01C0B0EF03806D7FA3027FEC0700815F6E6C130E021F141E6F131C6E 6C5B6E6C13F8913901FF01F09139007FFFC0031F5BDB03FCC7FC326B7EE93D>I118 D121 D123 D E %EndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: A4 %%EndSetup %%Page: 1 1 1 0 bop Black Black Black Black 20 427 a FC(A)52 b(com)l(binatorial)i (pro)t(of)e(of)h(tree)f(deca)l(y)g(of)g(semi{in)l(v)-9 b(arian)l(ts)487 850 y FB(Lorenzo)38 b(Bertini)1287 800 y FA(1)1435 850 y FB(Emilio)d(N.M.)j(Cirillo)2425 799 y FA(2)2573 850 y FB(Enzo)g(Olivieri)3248 799 y FA(3)560 1097 y Fz(1)100 b Fy(Dip)-5 b(artimento)34 b(di)f(Matematic)-5 b(a,)34 b(Universit\022)-46 b(a)33 b(di)g(R)-5 b(oma)34 b(L)-5 b(a)34 b(Sapienza)712 1233 y Fx(Piazzale)c(Aldo)g(Moro)h(2,)g (00185)i(Roma,)e(Italy)712 1368 y(E{mail:)39 b Fw (bertini@mat.uniroma1.it)560 1639 y Fz(2)100 b Fy(Dip)-5 b(artimento)34 b(Me.)e(Mo.)g(Mat.,)h(Universit\022)-46 b(a)33 b(di)f(R)-5 b(oma)35 b(L)-5 b(a)33 b(Sapienza)712 1775 y Fx(Via)d(A.)h(Scarpa)f(16,)h(00161)i(Roma,)e(Italy)712 1910 y(E{mail:)39 b Fw(cirillo@dmmm.uniroma1.it)560 2181 y Fz(3)100 b Fy(Dip)-5 b(artimento)34 b(di)f(Matematic)-5 b(a,)34 b(Universit\022)-46 b(a)33 b(di)g(R)-5 b(oma)34 b(T)-7 b(or)34 b(V)-7 b(er)i(gata)712 2317 y Fx(Via)30 b(della)f(Ricerca)i(Scien)m(ti\014ca,)f(00133)i(Roma,)f(Italy)712 2452 y(E{mail:)39 b Fw(olivieri@mat.uniroma2.it)1676 2875 y Fv(Abstract)146 3045 y Fu(W)-8 b(e)34 b(consider)f(\014nite)f (range)h(Gibbs)f(\014elds)h(and)g(pro)m(vide)g(a)g(purely)g(com)m (binatorial)c(pro)s(of)j(of)h(the)0 3189 y(exp)s(onen)m(tial)i(tree)h (deca)m(y)i(of)d(semi{in)m(v)-5 b(arian)m(ts,)35 b(supp)s(osing)g(that) h(the)g(logarithm)d(of)i(the)h(partition)0 3334 y(function)28 b(can)g(b)s(e)g(expressed)j(as)d(a)g(sum)g(of)f(suitable)h(lo)s(cal)d (functions)j(of)g(the)g(b)s(oundary)h(conditions.)0 3478 y(This)e(h)m(yp)s(othesis)g(holds)f(for)g(completely)g(analytical)d (Gibbs)j(\014elds;)j(in)d(this)g(con)m(text)i(the)f(tree)g(deca)m(y)0 3623 y(of)h(semi{in)m(v)-5 b(arian)m(ts)26 b(has)j(b)s(een)g(pro)m(v)m (en)h(via)d(analyticit)m(y)g(argumen)m(ts.)42 b(Ho)m(w)m(ev)m(er)31 b(the)d(com)m(binatorial)0 3767 y(pro)s(of)33 b(giv)m(en)h(here)h(can)f (b)s(e)g(applied)f(also)g(to)g(the)i(more)e(complicated)f(case)j(of)e (disordered)i(systems)0 3911 y(in)d(the)h(so)g(called)e(Gri\016ths')h (phase)i(when)f(analyticit)m(y)e(argumen)m(ts)i(fail.)0 4585 y Fv(MSC2000:)44 b Fu(82B20,)32 b(60G60)0 4807 y Fv(Keyw)m(ords:)h Fu(Gibbs)f(Fields,)f(Semi{in)m(v)-5 b(arian)m(ts,)31 b(Cluster)i(expansion,)g(Disordered)f(systems)p 0 5004 1512 4 v 0 5186 a Fx(L.B.)37 b(and)f(E.O.)h(are)g(partially)d (supp)s(orted)h(b)m(y)i(Co\014nanziamen)m(to)f(MURST.)h(E.C.)f(thanks)g (the)h(Istituto)0 5322 y(Nazionale)31 b(di)e(Alta)h(Matematica)j({)e (GNFM)g(for)f(\014nancial)f(supp)s(ort.)p Black Black eop %%Page: 1 2 1 1 bop Black Black 0 407 a Fv(1.)38 b(In)m(tro)s(duction)0 575 y Fu(In)31 b(this)g(note)g(w)m(e)h(presen)m(t)h(a)e(purely)g(com)m (binatorial)d(pro)s(of)i(of)h(the)g(tree)h(deca)m(y)g(of)f(semi{in)m(v) -5 b(arian)m(ts,)0 720 y(also)30 b(called)g(truncated)h(correlations,)f (Ursell)g(functions,)h(or)g(cum)m(ulan)m(ts,)g(for)f(a)h(\014nite)g (range)f(Gibb-)0 864 y(sian)24 b(\014eld)g(under)i(the)f(condition)e (that)h(the)h(logarithm)c(of)j(the)h(partition)e(function)h(can)g(b)s (e)h(expressed)0 1009 y(as)33 b(the)g(sum)f(of)g(suitable)g(lo)s(cal)e (functions)j(of)f(the)h(b)s(oundary)g(condition.)146 1153 y(Let)j Ft(Z)391 1168 y Fs(\003)443 1153 y Fu(\()p Ft(\034)11 b Fu(\))36 b(b)s(e)f(the)h(partition)c(function)j(in)f(the)i (\014nite)f(v)m(olume)f(\003)e Fr(\032)g Fq(Z)2862 1117 y Fp(d)2935 1153 y Fu(with)j(b)s(oundary)g(con-)0 1298 y(dition)c Ft(\034)44 b Fu(outside)32 b(\003;)h(w)m(e)g(assume)g(that) 1204 1535 y(log)17 b Ft(Z)1414 1550 y Fs(\003)1467 1535 y Fu(\()p Ft(\034)11 b Fu(\))44 b(=)1928 1441 y Fo(X)1761 1660 y Fp(X)5 b Fn(\032)p Fm(Z)1929 1641 y Fl(d)1959 1660 y Fs(:)12 b Fp(X)5 b Fn(\\)p Fs(\003)p Fn(6)p Fs(=)p Fn(;)2257 1535 y Ft(\036)2315 1550 y Fp(X)q(;)p Fs(\003)2446 1535 y Fu(\()p Ft(\034)11 b Fu(\))1004 b(\(1.1\))0 1854 y(where)34 b(the)f(\\e\013ectiv)m(e)g(p)s(oten)m(tials")e Ft(\036)1432 1869 y Fp(X)q(;)p Fs(\003)1597 1854 y Fu(are)h(suc)m(h)i (that:)p Black 92 2076 a(\(i\))p Black 48 w(giv)m(en)42 b Ft(X)50 b Fr(\032)44 b Fq(Z)829 2040 y Fp(d)866 2076 y Fu(,)g(the)e(functions)g Ft(\036)1602 2091 y Fp(X)q(;)p Fs(\003)1775 2076 y Fu(are)f(constan)m(t)i(w.r.t.)f(\003)f(for)g(the)h (\003's)f(with)h(a)f(giv)m(en)244 2220 y(in)m(tersection)32 b(with)h Ft(X)8 b Fu(;)p Black 65 2446 a(\(ii\))p Black 47 w(ha)m(v)m(e)34 b(a)e(suitable)g(deca)m(y)i(prop)s(ert)m(y)f(with)f (the)h(size)g(of)f Ft(X)8 b Fu(,)33 b(uniformly)d(in)i(\003.)146 2668 y(The)e(expression)g(\(1.1\))f(can)g(b)s(e)g(obtained)f(via)g (cluster)h(expansion)h(in)e(the)h(w)m(eak)h(coupling)e(\(high)0 2812 y(temp)s(erature)k(and/or)g(small)e(activit)m(y\))i(region)g(but)g (it)g(holds)g(in)f(more)h(general)g(situations.)42 b(It)33 b(can)0 2957 y(also)k(b)s(e)i(obtained)f(in)g(the)g(framew)m(ork)h(of)f (Dobrushin{Shlosman)f(complete)g(analyticit)m(y)g(as)i(w)m(ell)0 3101 y(as)29 b(in)g(the)g(framew)m(ork)g(of)g(the)h(so{called)e Fk(sc)-5 b(ale{adapte)g(d)30 b(cluster)i(exp)-5 b(ansion)p Fu(,)28 b(see)i([3],)g(pro)m(vided)g(the)0 3246 y(v)m(olume)g(\003)f (is)h(a)g(disjoin)m(t)f(union)g(of)h(cub)s(es)h(whose)g(side)g(length)e (equals)i(the)f(scale)g(of)g(the)g(expansion.)0 3390 y(W)-8 b(e)44 b(refer)f(to)g([3])g(for)g(a)g(more)f(exhaustiv)m(e)j (discussion;)k(here)44 b(w)m(e)g(only)f(sa)m(y)h(that)f(scale{adapted)0 3535 y(cluster)d(expansions)h(ha)m(v)m(e)h(b)s(een)e(in)m(tro)s(duced)h (in)e([17,)17 b(18])40 b(in)f(order)h(to)g(p)s(erturbativ)m(ely)g (treat)g(the)0 3679 y(whole)35 b(uniqueness)j(region)c(of)i(lattice)e (spin)h(systems,)j(arbitrarily)33 b(close)i(to)g(the)h(co)s(existence)h (line.)0 3824 y(Moreo)m(v)m(er,)30 b(as)d(w)m(e)h(shall)e(see)j(in)d ([5],)i(a)f(v)-5 b(arian)m(t)26 b(of)h(\(1.1\))g(holds)g(in)f(the)i (con)m(text)g(of)f(disordered)g(lattice)0 3968 y(systems,)41 b(also)d(in)f(the)i(delicate)e(situation)g(of)h(Gri\016ths')f (singularit)m(y)g(that)h(mak)m(es)h(necessary)i(the)0 4113 y(use)34 b(of)e(a)g Fk(gr)-5 b(ade)g(d)34 b(cluster)h(exp)-5 b(ansion)p Fu(,)31 b(see)j([3].)146 4257 y(In)22 b(the)h(framew)m(ork)e (of)h(the)g(renormalization)c(group)k(maps)f(one)h(often)g(encoun)m (ters)i(an)e(expression)0 4402 y(lik)m(e)28 b(\(1.1\))h(for)g(the)g (renormalized)e(partition)g(function.)42 b(In)30 b(that)f(case)h(the)f (family)e Fr(f)p Ft(\036)3210 4417 y Fp(X)q(;)p Fs(\003)3341 4402 y Ft(;)34 b(X)h Fr(\032)28 b Fq(Z)3692 4365 y Fp(d)3730 4402 y Fr(g)0 4546 y Fu(represen)m(ts)47 b(the)e(\\\014nite{v)m(olume)e (renormalized)g(p)s(oten)m(tial".)77 b(Both)45 b(in)e(the)i(case)g(of)f (disordered)0 4690 y(systems)32 b(and)f(of)f(renormalization)d(group)k (maps)f(the)h(deca)m(y)h(prop)s(erties)f(of)f Ft(\036)2941 4705 y Fp(X)q(;)p Fs(\003)3104 4690 y Fu(are)g(w)m(eak)m(er)j(than)0 4835 y(the)g(corresp)s(onding)f(ones)i(of)e(the)h(case)g(of)f(w)m (eakly)i(coupled)f(short)f(range)h(Gibbs)f(\014elds)146 4979 y(The)k(tree)f(deca)m(y)h(of)e(semi{in)m(v)-5 b(arian)m(ts)33 b(is)h(often)h(deduced)h(from)e(analyticit)m(y)f(prop)s(erties)h(of)h (the)0 5124 y(pressure,)d(see)f([8{11,)10 b(19];)29 b(ho)m(w)m(ev)m (er,)k(there)d(are)g(ph)m(ysically)f(in)m(teresting)g(situations)g(in)g (whic)m(h)h(these)0 5268 y(analyticit)m(y)39 b(prop)s(erties)i(do)f (not)g(hold)g(but)h(nev)m(ertheless)i(w)m(e)f(exp)s(ect)g(the)e(exp)s (onen)m(tial)g(deca)m(y)i(of)0 5413 y(semi{in)m(v)-5 b(arian)m(ts.)55 b(The)38 b(main)e(example)g(is)h(giv)m(en)g(b)m(y)h (the)f(already)g(quoted)h(case)g(of)f(a)f(disordered)0 5557 y(lattice)30 b(spin)h(system,)i(lik)m(e)d(a)h(spin)h(glass)e(or)h (a)g(ferromagnetic)f(system)j(sub)5 b(ject)33 b(to)e(a)g(random)f (\014eld,)p Black 1866 5806 a(1)p Black eop %%Page: 2 3 2 2 bop Black Black 0 407 a Fu(in)43 b(presence)j(of)e(the)g(so{called) f(\\Gri\016ths')g(singularit)m(y".)76 b(Consider,)47 b(for)d(example,)i(a)e(random)0 551 y(coupling)31 b(Ising)h(spin)h (system)g(in)f Fq(Z)1339 515 y Fp(d)1410 551 y Fu(describ)s(ed)h(b)m(y) h(the)f(formal)d(Hamiltonian:)1113 795 y Ft(H)8 b Fu(\()p Ft(\033)t Fu(\))27 b(=)1584 701 y Fo(X)1468 917 y Fp(x;y)r Fs(:)p Fn(j)p Fp(x)p Fn(\000)p Fp(y)r Fn(j)p Fs(=1)1862 795 y Ft(J)1916 810 y Fp(x;y)2016 795 y Ft(\033)2071 810 y Fp(x)2116 795 y Ft(\033)2171 810 y Fp(y)2235 795 y Fr(\000)22 b Ft(h)2407 701 y Fo(X)2459 910 y Fp(x)2568 795 y Ft(\033)2623 810 y Fp(x)3579 795 y Fu(\(1.2\))0 1126 y(where)38 b Ft(\033)341 1141 y Fp(x)419 1126 y Fr(2)d(f\000)p Fu(1)p Ft(;)17 b Fu(+1)p Fr(g)p Fu(,)37 b Ft(h)d Fr(2)h Fq(R)48 b Fu(is)36 b(\014xed)h(and)g Ft(J)1868 1141 y Fp(x;y)2005 1126 y Fu(are)f(i.i.d.)g(Gaussian)g (random)f(v)-5 b(ariables)35 b(with)0 1270 y(mean)i(zero)g(and)g(v)-5 b(ariance)37 b(one.)57 b(A)m(t)38 b(high)e(temp)s(erature)h(w)m(e)h (exp)s(ect)g(an)f(exp)s(onen)m(tial)g(tree)h(deca)m(y)0 1415 y(of)31 b(semi{in)m(v)-5 b(arian)m(ts)30 b(with)i(a)g (deterministic)e(rate)i(\(this)f(has)i(actually)d(b)s(een)j(pro)m(v)m (ed)g(long)e(time)g(ago)0 1559 y(in)43 b([12]\))h(but)g(w)m(e)i(do)e (not)g(exp)s(ect)h(analyticit)m(y)e(of)g(thermo)s(dynamic)g(functions.) 78 b(This)44 b(b)s(eha)m(vior)0 1704 y(is)38 b(a)g(consequence)j(of)d (the)h(fact)f(that,)h(ev)m(en)h(though)e(in)g(a)m(v)m(erage)h(the)g (system)g(is)f(w)m(eakly)h(coupled)0 1848 y(nonetheless,)44 b(with)d(a)f(p)s(ositiv)m(e)h(probabilit)m(y)-8 b(,)40 b(arbitrarily)e(large)i(regions)h(with)f(strong)h(ferromag-)0 1993 y(netic)e(couplings)g(can)h(app)s(ear)f(inducing,)h(lo)s(cally)-8 b(,)39 b(long{range)f(order,)j(as)f(a)f(consequence)k(of)c(the)0 2137 y(un)m(b)s(oundedness)d(of)c(the)h(random)e(couplings.)146 2281 y(The)k(starting)e(p)s(oin)m(t)g(of)g(our)h(com)m(binatorial)c (computation)i(can)i(b)s(e)g(illustrated)e(in)h(the)h(simple)0 2426 y(case)25 b(of)f(the)g(semi{in)m(v)-5 b(arian)m(t)22 b(of)i(order)g(t)m(w)m(o)h(namely)-8 b(,)25 b(the)g(co)m(v)-5 b(ariance)24 b(b)s(et)m(w)m(een)i(t)m(w)m(o)f(lo)s(cal)d(functions,)0 2570 y(see)29 b([1].)42 b(F)-8 b(or)27 b(instance,)i(consider)g(a)e (lattice)g(spin)h(system)h(with)e(\014nite)h(state)g(space)h(and)f (\014nite)g(range)0 2715 y(in)m(teraction,)37 b(sa)m(y)h Ft(r)f Fr(2)e Fu([0)p Ft(;)17 b Fr(1)p Fu(\),)37 b(whose)h (Hamiltonian,)c(in)i(a)h(\014nite)f(b)s(o)m(x)h(\003)g(for)f(a)h (con\014guration)e Ft(\033)3726 2730 y Fs(\003)0 2859 y Fu(in)g(\003)g(and)h(a)g(b)s(oundary)g(condition)e Ft(\034)1413 2874 y Fs(\003)1462 2855 y Fl(c)1535 2859 y Fu(is)h(denoted)i(b)m(y)f Ft(H)2227 2874 y Fs(\003)2280 2859 y Fu(\()p Ft(\033)2373 2874 y Fs(\003)2427 2859 y Ft(\034)2469 2874 y Fs(\003)2518 2855 y Fl(c)2554 2859 y Fu(\).)53 b(More)37 b(detailed)d(and)i(precise)0 3004 y(de\014nitions)44 b(will)f(b)s(e)i(giv)m(en)h(later)e(on;)51 b(here)46 b(w)m(e)g(only)e(sa)m(y)i(that)f Ft(H)2607 3019 y Fs(\003)2660 3004 y Fu(\()p Ft(\033)2753 3019 y Fs(\003)2807 3004 y Ft(\034)2849 3019 y Fs(\003)2898 3000 y Fl(c)2934 3004 y Fu(\))g(con)m(tains)g(the)g(self{)0 3148 y(in)m(teraction)25 b(of)g Ft(\033)643 3163 y Fs(\003)723 3148 y Fu(in)g(\003)h(and)g(the)g(m)m(utual)f(in)m(teraction)g(b)s(et)m (w)m(een)j Ft(\033)2504 3163 y Fs(\003)2583 3148 y Fu(and)f Ft(\034)2809 3163 y Fs(\003)2858 3144 y Fl(c)2894 3148 y Fu(.)41 b(The)27 b(Gibbs)f(measure)0 3293 y(is)41 b Ft(\026)166 3256 y Fp(\034)166 3318 y Fs(\003)218 3293 y Fu(\()p Ft(\033)311 3308 y Fs(\003)365 3293 y Fu(\))h(=)g(exp)728 3212 y Fo(\010)786 3293 y Ft(H)867 3308 y Fs(\003)920 3293 y Fu(\()p Ft(\033)1013 3308 y Fs(\003)1067 3293 y Ft(\034)1109 3308 y Fs(\003)1158 3289 y Fl(c)1194 3293 y Fu(\))1232 3212 y Fo(\011)1290 3293 y Ft(=)-5 b(Z)1401 3308 y Fs(\003)1454 3293 y Fu(\()p Ft(\034)1534 3308 y Fs(\003)1583 3289 y Fl(c)1619 3293 y Fu(\))41 b(where)h Ft(Z)2055 3308 y Fs(\003)2108 3293 y Fu(\()p Ft(\034)2188 3308 y Fs(\003)2237 3289 y Fl(c)2273 3293 y Fu(\))g(=)2471 3218 y Fo(P)2576 3322 y Fp(\033)2616 3333 y Fj(\003)2683 3293 y Fu(exp)2849 3212 y Fo(\010)2907 3293 y Ft(H)2988 3308 y Fs(\003)3041 3293 y Fu(\()p Ft(\033)3134 3308 y Fs(\003)3187 3293 y Ft(\034)3229 3308 y Fs(\003)3278 3289 y Fl(c)3315 3293 y Fu(\))3353 3212 y Fo(\011)3411 3293 y Fu(.)68 b(Notice)0 3437 y(that)35 b(w)m(e)i(ha)m(v)m(e)g (included)e(the)h(in)m(v)m(erse)h(temp)s(erature)e(in)g Ft(H)2235 3452 y Fs(\003)2323 3437 y Fu(and)h(c)m(hanged)h(the)f(usual) f(con)m(v)m(en)m(tion)0 3582 y(on)d(the)h(sign)g(in)e(the)i(exp)s(onen) m(t.)146 3726 y(Let)j Ft(f)5 b(;)17 b(g)39 b Fu(b)s(e)d(lo)s(cal)e (functions)h(with)h(supp)s(orts)g(\003)1996 3741 y Fp(f)2041 3726 y Ft(;)17 b Fu(\003)2153 3741 y Fp(g)2226 3726 y Fr(\032)34 b Fu(\003)h(suc)m(h)i(that)f(dist)o(\(\003)3141 3741 y Fp(f)3186 3726 y Ft(;)17 b Fu(\003)3298 3741 y Fp(g)3338 3726 y Fu(\))33 b Ft(>)g(r)s Fu(.)53 b(W)-8 b(e)0 3870 y(ma)m(y)32 b(write)209 4172 y Ft(\026)268 4136 y Fp(\034)268 4197 y Fs(\003)320 4172 y Fu(\()p Ft(f)11 b Fu(;)17 b Ft(g)t Fu(\))82 b(=)h Ft(\026)850 4136 y Fp(\034)850 4197 y Fs(\003)903 4172 y Fu(\()p Ft(f)11 b(g)t Fu(\))21 b Fr(\000)h Ft(\026)1268 4136 y Fp(\034)1268 4197 y Fs(\003)1321 4172 y Fu(\()p Ft(f)11 b Fu(\))17 b Ft(\026)1532 4136 y Fp(\034)1532 4197 y Fs(\003)1584 4172 y Fu(\()p Ft(g)t Fu(\))632 4401 y(=)853 4307 y Fo(X)791 4516 y Fp(\033)831 4527 y Fj(\003)872 4544 y Fl(f)917 4516 y Fp(;\033)977 4527 y Fj(\003)1018 4535 y Fl(g)1075 4401 y Ft(f)11 b Fu(\()p Ft(\033)1227 4416 y Fs(\003)1276 4428 y Fl(f)1320 4401 y Fu(\))p Ft(g)t Fu(\()p Ft(\033)1502 4416 y Fs(\003)1551 4424 y Fl(g)1591 4401 y Fu(\))17 b Ft(e)1691 4352 y Fp(H)1749 4363 y Fj(\003)1790 4381 y Fl(f)1834 4352 y Fs(\()p Fp(\033)1901 4363 y Fj(\003)1942 4381 y Fl(f)1987 4352 y Fp(\034)2018 4365 y Fj(\003)2059 4351 y Fl(c)2096 4352 y Fs(\))2127 4401 y Ft(e)2172 4360 y Fp(H)2230 4371 y Fj(\003)2271 4379 y Fl(g)2312 4360 y Fs(\()p Fp(\033)2379 4371 y Fj(\003)2420 4379 y Fl(g)2462 4360 y Fp(\034)2493 4373 y Fj(\003)2534 4359 y Fl(c)2571 4360 y Fs(\))902 4715 y Fr(\002)979 4604 y Fo(\020)1049 4639 y Ft(Z)1116 4654 y Fs(\003)p Fn(n)p Fs(\(\003)1276 4666 y Fl(f)1316 4654 y Fn([)p Fs(\003)1412 4662 y Fl(g)1448 4654 y Fs(\))1479 4639 y Fu(\()p Ft(\033)1572 4654 y Fs(\003)1621 4666 y Fl(f)1666 4639 y Ft(\033)1721 4654 y Fs(\003)1770 4662 y Fl(g)1810 4639 y Ft(\034)1852 4654 y Fs(\003)1901 4635 y Fl(c)1938 4639 y Fu(\))p 1049 4692 928 4 v 1351 4783 a Ft(Z)1418 4798 y Fs(\003)1470 4783 y Fu(\()p Ft(\034)1550 4798 y Fs(\003)1599 4779 y Fl(c)1636 4783 y Fu(\))2008 4715 y Fr(\000)2118 4639 y Ft(Z)2185 4654 y Fs(\003)p Fn(n)p Fs(\003)2318 4666 y Fl(f)2361 4639 y Fu(\()p Ft(\033)2454 4654 y Fs(\003)2503 4666 y Fl(f)2548 4639 y Ft(\034)2590 4654 y Fs(\003)2639 4635 y Fl(c)2675 4639 y Fu(\))p Ft(Z)2780 4654 y Fs(\003)p Fn(n)p Fs(\003)2913 4662 y Fl(g)2953 4639 y Fu(\()p Ft(\033)3046 4654 y Fs(\003)3095 4662 y Fl(g)3136 4639 y Ft(\034)3178 4654 y Fs(\003)3227 4635 y Fl(c)3263 4639 y Fu(\))p 2118 4692 1184 4 v 2548 4783 a Ft(Z)2622 4749 y Fs(2)2615 4810 y(\003)2668 4783 y Fu(\()p Ft(\034)2748 4798 y Fs(\003)2797 4779 y Fl(c)2833 4783 y Fu(\))3311 4604 y Fo(\021)3579 4429 y Fu(\(1.3\))0 4993 y(It)31 b(is)g(clear)f(that)h(the)g(exp)s (onen)m(tial)g(deca)m(y)h(of)f Ft(\026)1768 4956 y Fp(\034)1768 5018 y Fs(\003)1820 4993 y Fu(\()p Ft(f)11 b Fu(;)17 b Ft(g)t Fu(\))30 b(with)h(dist)o(\(\003)2564 5008 y Fp(f)2609 4993 y Ft(;)17 b Fu(\003)2721 5008 y Fp(g)2761 4993 y Fu(\))31 b(easily)f(follo)m(ws)g(from)g(the)0 5137 y(analogous)h(prop)s(ert)m(y)j(of)e(the)h(quan)m(tit)m(y)1055 5415 y(sup)930 5494 y Fp(\033)970 5505 y Fj(\003)1011 5523 y Fl(f)1056 5494 y Fp(;\033)1116 5505 y Fj(\003)1157 5513 y Fl(g)1197 5494 y Fp(;\034)1248 5507 y Fj(\003)1289 5493 y Fl(c)1343 5270 y Fo(\014)1343 5330 y(\014)1343 5390 y(\014)1343 5450 y(\014)1386 5339 y Ft(Z)1453 5355 y Fs(\003)p Fn(n)p Fs(\(\003)1613 5367 y Fl(f)1653 5355 y Fn([)p Fs(\003)1749 5363 y Fl(g)1785 5355 y Fs(\))1817 5339 y Fu(\()p Ft(\033)1910 5354 y Fs(\003)1959 5366 y Fl(f)2003 5339 y Ft(\033)2058 5354 y Fs(\003)2107 5362 y Fl(g)2148 5339 y Ft(\034)2190 5354 y Fs(\003)2239 5335 y Fl(c)2275 5339 y Fu(\))p Ft(Z)2380 5354 y Fs(\003)2433 5339 y Fu(\()p Ft(\034)2513 5354 y Fs(\003)2562 5335 y Fl(c)2598 5339 y Fu(\))p 1386 5392 1251 4 v 1419 5483 a Ft(Z)1486 5499 y Fs(\003)p Fn(n)p Fs(\003)1619 5511 y Fl(f)1663 5483 y Fu(\()p Ft(\033)1756 5498 y Fs(\003)1805 5510 y Fl(f)1849 5483 y Ft(\034)1891 5498 y Fs(\003)1940 5479 y Fl(c)1977 5483 y Fu(\))p Ft(Z)2082 5499 y Fs(\003)p Fn(n)p Fs(\003)2215 5507 y Fl(g)2255 5483 y Fu(\()p Ft(\033)2348 5498 y Fs(\003)2397 5506 y Fl(g)2438 5483 y Ft(\034)2480 5498 y Fs(\003)2529 5479 y Fl(c)2565 5483 y Fu(\))2668 5415 y Fr(\000)23 b Fu(1)2817 5270 y Fo(\014)2817 5330 y(\014)2817 5390 y(\014)2817 5450 y(\014)3579 5415 y Fu(\(1.4\))p Black 1866 5806 a(2)p Black eop %%Page: 3 4 3 3 bop Black Black 0 407 a Fu(This,)31 b(in)e(turn,)i(is)e(easily)h (seen)h(to)f(follo)m(w)e(from)h(\(1.1\))g(and)h(suitable)g(deca)m(y)h (prop)s(erties)f(of)g Ft(\036)3466 422 y Fp(X)q(;)p Fs(\003)3597 407 y Fu(,)h(see)0 551 y(\(2.11\))j(b)s(elo)m(w.)50 b(Indeed)37 b(b)m(y)e(plugging)e(\(1.1\))i(in)m(to)f(\(1.4\))g(and)h(using)g(\(i\)) e(ab)s(o)m(v)m(e)j(w)m(e)g(easily)e(see)i(that,)0 696 y(in)c(the)h(resulting)e(expression,)j Ft(\036)1238 711 y Fp(X)q(;)p Fs(\003)1403 696 y Fu(cancels)f(out)f(unless)h Ft(X)41 b Fu(in)m(tersects)34 b(b)s(oth)e(\003)3047 711 y Fp(f)3125 696 y Fu(and)g(\003)3382 711 y Fp(g)3422 696 y Fu(.)146 840 y(The)38 b(case)g(of)e(a)h(generic)g(semi{in)m(v)-5 b(arian)m(t)34 b(of)i(order)h Ft(n)g Fu(is)g(m)m(uc)m(h)g(more)f (subtle)h(and)g(some)g(more)0 985 y(e\013orts)47 b(are)g(required)g(to) f(disclose)h(the)g(cancellation)e(mec)m(hanism.)85 b(The)48 b(crucial)d(p)s(oin)m(t)h(in)g(our)0 1129 y(pro)s(of)32 b(is)h(the)g(com)m(binatorial)d(result)j(in)f(Lemma)g(3.1)g(whic)m(h)i (generalizes)f(\(1.3\))f(and)h(expresses)k(the)0 1274 y(semi{in)m(v)-5 b(arian)m(t)30 b(in)i(terms)g(of)h(ratios)e(of)h (partition)f(functions.)146 1418 y(The)39 b(pap)s(er)e(is)g(organized)f (as)i(follo)m(ws.)56 b(In)38 b(Section)f(2)g(w)m(e)h(giv)m(e)f(the)h (notation)e(and)h(a)g(theorem)0 1562 y(stating)c(our)h(main)e(result,)j (with)f(some)g(commen)m(ts)g(and)g(exempla.)47 b(The)35 b(pro)s(of)e(of)h(the)h(theorem)e(is)0 1707 y(\014nally)e(giv)m(en)i (in)f(Section)g(3.)0 2051 y Fv(2.)38 b(Notation)e(and)i(result)0 2220 y Fu(In)d(this)f(Section)g(w)m(e)h(recall)e(the)i(general)e (framew)m(ork)i(of)f(Gibbs)f(states)j(for)d(lattice)g(systems,)k(state) 0 2364 y(our)32 b(main)f(results,)i(and)g(discuss)h(some)e(p)s(ossible) g(applications.)0 2609 y Fk(2.1.)79 b(The)34 b(lattic)-5 b(e)0 2778 y Fu(F)d(or)32 b Ft(a;)17 b(b)29 b Fr(2)g Fq(R)44 b Fu(w)m(e)34 b(set)g Ft(a)23 b Fr(^)g Ft(b)29 b Fu(:=)f(min)o Fr(f)p Ft(a;)17 b(b)p Fr(g)33 b Fu(and)g Ft(a)23 b Fr(_)g Ft(b)29 b Fu(:=)f(max)p Fr(f)p Ft(a;)17 b(b)p Fr(g)p Fu(.)45 b(F)-8 b(or)32 b Ft(x)d Fu(=)g(\()p Ft(x)3134 2793 y Fs(1)3173 2778 y Ft(;)17 b Fr(\001)g(\001)g(\001)32 b Ft(;)17 b(x)3466 2793 y Fp(d)3506 2778 y Fu(\))29 b Fr(2)g Fq(R)3734 2742 y Fp(d)0 2922 y Fu(w)m(e)50 b(set)f Fr(j)p Ft(x)p Fr(j)55 b Fu(:=)g(sup)799 2946 y Fp(k)r Fs(=)p Fp(i;)p Fn(\001\001\001)10 b Fp(;d)1083 2922 y Fr(j)p Ft(x)1166 2937 y Fp(i)1194 2922 y Fr(j)p Fu(.)92 b(The)50 b(spatial)d(structure)i(is)g(mo)s(deled)e(b)m(y)j(the)f Ft(d)p Fu({dimensional)0 3067 y(cubic)38 b(lattice)e Fq(L)47 b Fu(:=)36 b Fq(Z)873 3031 y Fp(d)911 3067 y Fu(.)58 b(W)-8 b(e)38 b(shall)e(denote)j(b)m(y)f Ft(x;)17 b(y)t(;)g Fr(\001)g(\001)g(\001)51 b Fu(the)38 b(p)s(oin)m(ts)g(in)e Fq(L)6 b Fu(,)44 b(called)37 b Fk(sites)p Fu(,)h(and)g(b)m(y)0 3211 y(\003)p Ft(;)17 b(V)5 b(;)17 b(X)r(;)g(:)g(:)g(:)45 b Fu(the)30 b(subsets)h(of)e Fq(L)6 b Fu(.)48 b(W)-8 b(e)30 b(use)g(\003)1646 3175 y Fs(c)1709 3211 y Fu(:=)e Fq(L)21 b Fr(n)16 b Fu(\003)34 b(to)29 b(denote)h(the)g(complemen)m(t)f (of)g(\003.)42 b(F)-8 b(or)28 b(\003)h(a)0 3356 y(\014nite)j(subset)i (of)f Fq(L)5 b Fu(,)39 b(w)m(e)33 b(use)h(\003)27 b Fr(\032\032)i Fq(L)44 b Fu(to)32 b(indicate)f(that)i(\003)f(is)g(\014nite,)g Fr(j)p Fu(\003)p Fr(j)g Fu(denotes)i(the)f(cardinalit)m(y)0 3500 y(of)f(\003.)43 b(W)-8 b(e)33 b(consider)g Fq(L)44 b Fu(endo)m(w)m(ed)35 b(with)d(the)h(distance)g(d\()p Ft(x;)17 b(y)t Fu(\))27 b(=)g Fr(j)p Ft(x)22 b Fr(\000)h Ft(y)t Fr(j)p Fu(.)42 b(As)33 b(usual)f(for)g Ft(X)r(;)17 b(Y)49 b Fr(\032)29 b Fq(L)0 3645 y Fu(w)m(e)34 b(set)f(d\()p Ft(X)r(;)17 b(Y)k Fu(\))28 b(:=)g(inf)6 b Fr(f)p Fu(d\()p Ft(x;)17 b(y)t Fu(\))p Ft(;)43 b(x)28 b Fr(2)g Ft(X)r(;)45 b(y)31 b Fr(2)d Ft(Y)21 b Fr(g)p Fu(,)33 b(diam)n(\()p Ft(X)8 b Fu(\))27 b(:=)h(sup)q Fr(f)p Fu(d\()p Ft(x;)17 b(x)2979 3609 y Fn(0)3003 3645 y Fu(\))p Ft(;)44 b(x;)17 b(x)3266 3609 y Fn(0)3318 3645 y Fr(2)28 b Ft(X)8 b Fr(g)p Fu(.)146 3789 y(F)-8 b(or)37 b Ft(x)f Fr(2)h Fq(L)48 b Fu(and)38 b Ft(m)g Fu(a)f(p)s(ositiv)m(e)g(in)m(teger)g(w)m(e)h(let)f Ft(Q)2091 3804 y Fp(m)2158 3789 y Fu(\()p Ft(x)p Fu(\))f(:=)g Fr(f)p Ft(y)j Fr(2)d Fq(L)48 b Fu(:)k Ft(x)2940 3804 y Fp(i)3005 3789 y Fr(\024)36 b Ft(y)3166 3804 y Fp(i)3230 3789 y Fr(\024)g Ft(x)3398 3804 y Fp(i)3452 3789 y Fu(+)26 b(\()p Ft(m)g Fr(\000)0 3934 y Fu(1\))17 b Ft(;)43 b(i)d Fu(=)g(1)p Ft(;)17 b(:)g(:)g(:)f(;)h(d)p Fr(g)38 b Fu(b)s(e)i(the)h (cub)s(e)f(of)f(side)h Ft(m)g Fu(with)g Ft(x)g Fu(the)g(site)f(with)h (smallest)e(co)s(ordinates.)65 b(W)-8 b(e)0 4078 y(denote)38 b(b)m(y)g Fq(F)48 b Fu(:=)36 b Fr(f)p Ft(X)43 b Fr(\032\032)37 b Fq(L)6 b Fr(g)43 b Fu(the)38 b(collection)d(of)i(all)e(\014nite)i (subsets)j(of)c Fq(L)6 b Fu(.)64 b(Let)37 b Ft(L)h Fu(b)s(e)f(a)h(p)s (ositiv)m(e)0 4222 y(in)m(teger,)e(w)m(e)g(denote)g(b)m(y)g Fq(F)1009 4237 y Fp(L)1103 4222 y Fu(the)f(collection)e(of)i(sets)i(in) d Fq(F)47 b Fu(whic)m(h)36 b(can)f(b)s(e)h(written)f(as)g(the)h (disjoin)m(t)0 4367 y(union)f(of)h(cub)s(es)h(of)e(side)h Ft(L)p Fu(,)h(more)f(precisely)g Ft(X)41 b Fr(2)34 b Fq(F)2030 4382 y Fp(L)2124 4367 y Fu(i\013)h(there)i(exist)f Ft(x)2786 4382 y Fs(1)2826 4367 y Ft(;)17 b(:)g(:)g(:)f(;)h(x)3100 4382 y Fp(k)3176 4367 y Fr(2)34 b Fq(L)47 b Fu(suc)m(h)37 b(that)0 4511 y Ft(X)e Fu(=)220 4437 y Fo(S)303 4463 y Fp(k)303 4540 y(h)p Fs(=1)455 4511 y Ft(Q)532 4526 y Fp(L)584 4511 y Fu(\()p Ft(Lx)743 4526 y Fp(h)789 4511 y Fu(\).)146 4656 y(Let)46 b Fq(E)67 b Fu(:=)601 4575 y Fo(\010)659 4656 y Fr(f)p Ft(x;)17 b(y)t Fr(g)p Ft(;)33 b(x;)17 b(y)52 b Fr(2)d Fq(L)61 b Fu(:)66 b(d\()p Ft(x;)17 b(y)t Fu(\))48 b(=)h(1)1996 4575 y Fo(\011)2099 4656 y Fu(b)s(e)c(the)h(collection)d(of)i Fk(e)-5 b(dges)61 b Fu(in)44 b Fq(L)6 b Fu(.)87 b(Note)0 4800 y(that,)32 b(according)f(to)g(our)g(de\014nitions,)h(the)g(edges)g(can)g(b)s(e)g (also)f(diagonal.)41 b(W)-8 b(e)32 b(sa)m(y)g(that)g(t)m(w)m(o)g(edges) 0 4945 y Ft(e;)17 b(e)134 4909 y Fn(0)186 4945 y Fr(2)30 b Fq(E)51 b Fu(are)34 b(connected)g(i\013)f Ft(e)23 b Fr(\\)g Ft(e)1320 4909 y Fn(0)1372 4945 y Fr(6)p Fu(=)29 b Fr(;)p Fu(.)45 b(A)33 b(subset)i(\()p Ft(V)5 b(;)17 b(E)6 b Fu(\))29 b Fr(\032)g Fu(\()p Fq(L)6 b Ft(;)17 b Fq(E)h Fu(\))39 b(is)33 b(said)g(to)g(b)s(e)g(connected)i(i\013)0 5089 y(for)g(eac)m(h)h(pair)e Ft(x;)17 b(y)35 b Fr(2)e Ft(V)21 b Fu(,)36 b Ft(x)d Fr(6)p Fu(=)f Ft(y)t Fu(,)j(there)h(exists)g (in)e Ft(E)41 b Fu(a)35 b(path)g(of)g(connected)i(edges)f(joining)d (them.)0 5234 y(F)-8 b(or)32 b Ft(X)j Fr(\032\032)29 b Fq(L)44 b Fu(w)m(e)33 b(then)h(set)718 5478 y Fq(T)p Fu(\()p Ft(X)8 b Fu(\))30 b(:=)e(inf)23 b Fr(fj)p Ft(E)6 b Fr(j)17 b Ft(;)48 b Fu(\()p Ft(V)5 b(;)17 b(E)6 b Fu(\))27 b Fr(\032)h Fu(\()p Fq(L)6 b Ft(;)17 b Fq(E)h Fu(\))28 b(connected)h(:)50 b Ft(V)g Fr(\033)28 b Ft(X)8 b Fr(g)516 b Fu(\(2.1\))p Black 1866 5806 a(3)p Black eop %%Page: 4 5 4 4 bop Black Black 0 407 a Fu(and)28 b(remark)g(that)g(the)g(in\014m)m (um)f(is)g(attained)g(\(not)h(necessary)i(uniquely\))e(for)g(a)g(graph) f(\()p Ft(V)3386 422 y Fp(X)3454 407 y Ft(;)17 b(E)3570 422 y Fp(X)3637 407 y Fu(\))28 b Fr(\032)0 551 y Fu(\()p Fq(L)5 b Ft(;)17 b Fq(E)h Fu(\))42 b(whic)m(h)36 b(is)g(a)f(tree,)i (i.e.)e(a)h(connected)h(and)f(lo)s(op{free)e(graph.)53 b(W)-8 b(e)36 b(agree)g(that)g Fq(T)p Fu(\()p Ft(X)8 b Fu(\))36 b(=)d(0)i(if)0 696 y Fr(j)p Ft(X)8 b Fr(j)27 b Fu(=)g(1)33 b(and)f(note)h(that)f(for)h Ft(x;)17 b(y)30 b Fr(2)f Fq(L)43 b Fu(w)m(e)34 b(ha)m(v)m(e)g Fq(T)p Fu(\()p Fr(f)p Ft(x;)17 b(y)t Fr(g)p Fu(\))30 b(=)d(d\()p Ft(x;)17 b(y)t Fu(\).)0 929 y Fk(2.2.)79 b(The)34 b(c)-5 b(on\014gur)g(ation)34 b(sp)-5 b(ac)g(e)0 1096 y Fu(The)33 b Fk(single)h(spin)g(sp)-5 b(ac)g(e)48 b Fu(is)32 b(giv)m(en)g(b)m(y)h (a)g(\014nite)f(set)h Fr(S)1981 1111 y Fs(0)2048 1096 y Fr(\032)28 b Fq(R)43 b Fu(whic)m(h)33 b(w)m(e)h(consider)e(endo)m(w)m (ed)j(with)c(its)0 1241 y(discrete)k Ft(\033)t Fu({algebra)d Fr(F)882 1256 y Fs(0)921 1241 y Fu(.)48 b(The)34 b(con\014guration)f (space)i(in)f(\003)29 b Fr(\032)i Fq(L)45 b Fu(is)33 b Fr(S)2631 1256 y Fs(\003)2715 1241 y Fu(:=)d Fr(S)2915 1204 y Fs(\003)2908 1265 y(0)3002 1241 y Fu(equipp)s(ed)35 b(with)f(the)0 1385 y(pro)s(duct)h Ft(\033)t Fu({algebra)e Fr(F)891 1400 y Fs(\003)974 1385 y Fu(=)e Fr(F)1163 1349 y Fs(\003)1153 1410 y(0)1216 1385 y Fu(;)k(w)m(e)g(denote)h Fr(S)1807 1349 y Fm(L)1800 1410 y Fs(0)1890 1385 y Fu(and)f Fr(F)2164 1349 y Fm(L)2154 1410 y Fs(0)2246 1385 y Fu(simply)e(b)m(y)i Fr(S)42 b Fu(and)35 b Fr(F)10 b Fu(.)48 b(Elemen)m(ts)35 b(of)f Fr(S)7 b Fu(,)0 1529 y(called)33 b Fk(c)-5 b(on\014gur)g(ations) 15 b Fu(,)35 b(are)f(denoted)g(b)m(y)h Ft(\033)n(;)17 b(\034)6 b(;)17 b(:)g(:)g(:)f Fu(.)48 b(In)34 b(other)g(w)m(ords)h(a)f (con\014guration)f Ft(\033)h Fr(2)c(S)42 b Fu(is)33 b(a)0 1674 y(function)d Ft(\033)h Fu(:)d Fq(L)39 b Fr(!)28 b(S)803 1689 y Fs(0)842 1674 y Fu(;)j(for)f(\003)d Fr(\032)h Fq(L)42 b Fu(w)m(e)31 b(denote)g(b)m(y)g Ft(\033)1985 1689 y Fs(\003)2069 1674 y Fu(the)f(restriction)f(of)h Ft(\033)k Fu(to)c(\003.)42 b(Let)31 b(\003)3391 1689 y Fs(1)3430 1674 y Ft(;)17 b Fu(\003)3542 1689 y Fs(2)3608 1674 y Fr(\032)29 b Fq(L)0 1818 y Fu(b)s(e)42 b(disjoin)m(t)f(subsets)k (of)c Fq(L)6 b Fu(;)53 b(if)41 b Ft(\033)1262 1833 y Fp(i)1335 1818 y Fr(2)j(S)1505 1833 y Fs(\003)1554 1843 y Fl(i)1585 1818 y Fu(,)g Ft(i)h Fu(=)f(1)p Ft(;)17 b Fu(2,)44 b(w)m(e)f(denote)g(b)m(y)g Ft(\033)2744 1833 y Fs(1)2784 1818 y Ft(\033)2839 1833 y Fs(2)2921 1818 y Fu(the)f(con\014guration)g(in)0 1963 y Fr(S)60 1978 y Fs(\003)109 1987 y Fj(1)144 1978 y Fn([)p Fs(\003)240 1987 y Fj(2)311 1963 y Fu(giv)m(en)33 b(b)m(y)g Ft(\033)756 1978 y Fs(1)796 1963 y Ft(\033)851 1978 y Fs(2)891 1963 y Fu(\()p Ft(x)p Fu(\))28 b(:=)1181 1888 y Fo(P)1286 1914 y Fs(2)1286 1992 y Fp(i)p Fs(=1)1421 1963 y Fu(1)-28 b(I)1477 1978 y Fn(f)p Fp(x)p Fn(2)p Fs(\003)1648 1988 y Fl(i)1674 1978 y Fn(g)1714 1963 y Ft(\033)1769 1978 y Fp(i)1797 1963 y Fu(\()p Ft(x)p Fu(\))33 b(for)f(an)m(y)i Ft(x)28 b Fr(2)g Fu(\003)2540 1978 y Fs(1)2601 1963 y Fr([)23 b Fu(\003)2758 1978 y Fs(2)2797 1963 y Fu(.)146 2107 y(A)32 b(measurable)f(function)h Ft(f)38 b Fu(:)28 b Fr(S)35 b(!)27 b Fq(R)43 b Fu(is)31 b(called)g(a)g Fk(lo)-5 b(c)g(al)34 b(function)48 b Fu(i\013)30 b(there)j(exists)f (\003)c Fr(2)g Fq(F)43 b Fu(suc)m(h)0 2252 y(that)31 b Ft(f)38 b Fr(2)28 b(F)462 2267 y Fs(\003)515 2252 y Fu(,)j(namely)g Ft(f)42 b Fu(is)30 b Fr(F)1169 2267 y Fs(\003)1222 2252 y Fu({measurable)g(for)h(some)g(\003)c Fr(2)h Fq(F)6 b Fu(.)49 b(F)-8 b(or)30 b Ft(f)42 b Fu(a)31 b(lo)s(cal)e(function)h(w)m(e)i(shall)0 2396 y(denote)38 b(b)m(y)g(supp)q(\()p Ft(f)11 b Fu(\),)38 b(the)g(so)f(called)f Fk(supp)-5 b(ort)54 b Fu(of)37 b Ft(f)11 b Fu(,)38 b(the)f(smallest)f (\003)f Fr(\032\032)i Fq(L)48 b Fu(suc)m(h)39 b(that)e Ft(f)46 b Fr(2)36 b(F)3700 2411 y Fs(\003)3753 2396 y Fu(.)0 2541 y(If)g Ft(f)45 b Fr(2)34 b(F)366 2556 y Fs(\003)455 2541 y Fu(w)m(e)j(shall)e(sometimes)g(abuse)i(the)f(notation)f(b)m(y)i (writing)e Ft(f)11 b Fu(\()p Ft(\033)2781 2556 y Fs(\003)2834 2541 y Fu(\))36 b(instead)g(of)g Ft(f)11 b Fu(\()p Ft(\033)t Fu(\).)54 b(F)-8 b(or)0 2685 y Ft(f)38 b Fr(2)28 b(F)43 b Fu(w)m(e)33 b(let)f Fr(k)p Ft(f)11 b Fr(k)738 2700 y Fn(1)840 2685 y Fu(:=)27 b(sup)1117 2709 y Fp(\033)r Fn(2S)1275 2685 y Fr(j)p Ft(f)11 b Fu(\()p Ft(\033)t Fu(\))p Fr(j)32 b Fu(b)s(e)h(the)g(sup)g(norm)f(of)g Ft(f)11 b Fu(.)0 2919 y Fk(2.3.)79 b(The)34 b(Gibbs)h(state)0 3085 y Fu(A)43 b Fk(p)-5 b(otential)58 b Ft(U)53 b Fu(is)42 b(a)h(collection)d(of)i(lo)s(cal)e(functions)j Ft(U)2158 3100 y Fp(X)2270 3085 y Fu(:)i Fr(S)52 b(!)44 b Fq(R)5 b Fu(,)51 b Fr(F)2814 3100 y Fp(X)2881 3085 y Fu({measurable,)44 b(lab)s(eled)0 3230 y(b)m(y)c(\014nite)e(subsets)j(of)d Fq(L)5 b Fu(,)47 b(namely)38 b Ft(U)48 b Fu(:=)38 b Fr(f)p Ft(U)1708 3245 y Fp(X)1814 3230 y Fr(2)g(F)1990 3245 y Fp(X)2057 3230 y Ft(;)c(X)46 b Fr(2)38 b Fq(F)6 b Fr(g)p Fu(.)68 b(W)-8 b(e)39 b(shall)e(consider)i(only)f Fk(\014nite)0 3374 y(r)-5 b(ange)42 b Fu(p)s(oten)m(tial)25 b(namely)-8 b(,)27 b(p)s(oten)m(tials)e Ft(U)37 b Fu(for)26 b(whic)m(h)h(there)g (exists)h(an)e(in)m(teger)g Ft(r)s Fu(,)i(called)d Fk(r)-5 b(ange)42 b Fu(suc)m(h)0 3519 y(that)37 b Ft(U)282 3534 y Fp(X)385 3519 y Fu(=)e(0)i(if)f(diam)n(\()p Ft(X)8 b Fu(\))35 b Ft(>)g(r)s Fu(.)57 b(W)-8 b(e)37 b(remark)g(that)g(w)m(e)h (do)f(not)g(require)g(the)h(p)s(oten)m(tial)d Ft(U)48 b Fu(to)37 b(b)s(e)0 3663 y(translationally)29 b(in)m(v)-5 b(arian)m(t.)146 3808 y(F)d(or)32 b(\003)27 b Fr(\032\032)i Fq(L)44 b Fu(and)33 b Ft(\033)e Fr(2)e(S)40 b Fu(w)m(e)33 b(de\014ne)h(the)f Fk(Hamiltonian)f Fu(as)1409 4033 y Ft(H)1490 4048 y Fs(\003)1543 4033 y Fu(\()p Ft(\033)t Fu(\))c(:=)1889 3939 y Fo(X)1836 4155 y Fp(X)5 b Fn(\\)p Fs(\003)p Fn(6)p Fs(=)p Fn(;)2102 4033 y Ft(U)2168 4048 y Fp(X)2236 4033 y Fu(\()p Ft(\033)t Fu(\))1208 b(\(2.2\))0 4336 y(In)34 b(this)g(pap)s(er)g(w)m(e)h(shall)d(consider)i(only)g (\014nite)f(v)m(olume)g(Gibbs)h(measures)g(de\014ned)i(as)e(follo)m (ws:)45 b(let)0 4481 y Ft(\034)39 b Fr(2)28 b(S)7 b Fu(,)31 b(the)e(\014nite)g(v)m(olume)f(Gibbs)h(measure)g Ft(\026)1757 4445 y Fp(\034)1757 4506 y Fs(\003)1810 4481 y Fu(,)g(with)g(b)s (oundary)g(condition)f Ft(\034)11 b Fu(,)30 b(is)f(the)g(probabilit)m (y)0 4625 y(measure)k(on)f Fr(S)575 4640 y Fs(\003)661 4625 y Fu(giv)m(en)h(b)m(y)1362 4784 y Ft(\026)1421 4743 y Fp(\034)1421 4809 y Fs(\003)1474 4784 y Fu(\()p Ft(\033)t Fu(\))28 b(:=)1878 4717 y(1)p 1777 4762 250 4 v 1777 4853 a Ft(Z)1844 4868 y Fs(\003)1897 4853 y Fu(\()p Ft(\034)11 b Fu(\))2059 4784 y Ft(e)2104 4743 y Fp(H)2162 4754 y Fj(\003)2208 4743 y Fs(\()p Fp(\033)r(\034)2308 4756 y Fj(\003)2349 4742 y(c)2386 4743 y Fs(\))3579 4784 y Fu(\(2.3\))0 5007 y(where)27 b Ft(\033)32 b Fr(2)c(S)516 5022 y Fs(\003)595 5007 y Fu(and)e Ft(Z)845 5022 y Fs(\003)897 5007 y Fu(\()p Ft(\034)11 b Fu(\),)28 b(called)c(the)j Fk(p)-5 b(artition)28 b(function)p Fu(,)f(is)e(the)h(normalization)c (constan)m(t)27 b(giv)m(en)0 5151 y(b)m(y)1410 5296 y Ft(Z)1477 5311 y Fs(\003)1529 5296 y Fu(\()p Ft(\034)11 b Fu(\))28 b(:=)1834 5201 y Fo(X)1817 5412 y Fp(\033)r Fn(2S)1949 5423 y Fj(\003)2012 5296 y Ft(e)2057 5255 y Fp(H)2115 5266 y Fj(\003)2160 5255 y Fs(\()p Fp(\033)r(\034)2260 5268 y Fj(\003)2301 5254 y(c)2339 5255 y Fs(\))3579 5296 y Fu(\(2.4\))0 5557 y(w)m(e)34 b(remark)e(that,)g(since)h(the)g(p)s (oten)m(tial)e Ft(U)43 b Fu(has)33 b(range)g Ft(r)s Fu(,)f(w)m(e)i(ha)m (v)m(e)g Ft(Z)2625 5572 y Fs(\003)2705 5557 y Fr(2)28 b(F)2871 5573 y Fn(f)p Fp(x)p Fn(2)p Fs(\003)3042 5554 y Fj(c)3085 5573 y Fs(:)11 b(d\()p Fp(x;)p Fs(\003\))p Fn(\024)p Fp(r)r Fn(g)3447 5557 y Fu(.)p Black 1866 5806 a(4)p Black eop %%Page: 5 6 5 5 bop Black Black 146 407 a Fu(F)-8 b(or)43 b Ft(V)68 b Fr(\032)47 b Fu(\003)f Fr(\032\032)i Fq(L)55 b Fu(w)m(e)44 b(shall)f(denote)h(b)m(y)g Ft(\026)1931 371 y Fp(\034)1931 432 y Fs(\003)p Fp(;V)2104 407 y Fu(the)g(pro)5 b(jection)44 b(\(marginal\))c(of)j Ft(\026)3432 371 y Fp(\034)3432 432 y Fs(\003)3528 407 y Fu(to)h Fr(S)3719 422 y Fp(V)0 551 y Fu(namely)-8 b(,)32 b(the)h(probabilit)m(y)d(measure)j(on)g Fr(S)1600 566 y Fp(V)1693 551 y Fu(giv)m(en)g(b)m(y)h Ft(\026)2143 515 y Fp(\034)2143 576 y Fs(\003)p Fp(;V)2272 551 y Fu(\()p Ft(A)p Fu(\))27 b(=)h Ft(\026)2611 515 y Fp(\034)2611 576 y Fs(\003)2664 551 y Fu(\()p Ft(A)p Fu(\),)k Ft(A)c Fr(2)g(F)3139 566 y Fp(V)3200 551 y Fu(.)0 784 y Fk(2.4.)79 b(Semi{invariants)0 950 y Fu(Let)25 b(\003)j Fr(2)g Fq(F)5 b Fu(,)33 b Ft(n)28 b Fr(\025)g Fu(2)d(an)g(in)m(teger,)h Ft(f)1255 965 y Fp(i)1283 950 y Fu(,)h(with)d Ft(i)k Fu(=)g(1)p Ft(;)17 b(:)g(:)g(:)e(;)i(n)p Fu(,)27 b(lo)s(cal)c(functions)h(with)h(\003)3013 965 y Fp(i)3069 950 y Fu(:=)i(supp)q(\()p Ft(f)3486 965 y Fp(i)3514 950 y Fu(\))h Fr(\032)g Fu(\003,)0 1095 y Ft(t)35 1110 y Fp(i)91 1095 y Fr(2)g Fq(R)5 b Fu(,)39 b(with)32 b Ft(i)c Fu(=)f(1)p Ft(;)17 b(:)g(:)g(:)f(;)h(n)p Fu(,)33 b(and)f Ft(\034)39 b Fr(2)28 b(S)7 b Fu(;)34 b(w)m(e)g(de\014ne)1024 1365 y Ft(Z)1091 1380 y Fs(\003)1144 1284 y Fo(\000)1189 1365 y Ft(\034)11 b Fu(;)17 b Ft(t)1321 1380 y Fs(1)1361 1365 y Ft(;)g(:)g(:)g(:)f(;)h(t)1615 1380 y Fp(n)1662 1284 y Fo(\001)1735 1365 y Fu(:=)28 b Ft(\026)1925 1324 y Fp(\034)1925 1390 y Fs(\003)1978 1224 y Fo(\022)2068 1365 y Fu(exp)2233 1254 y Fo(n)2367 1240 y Fp(n)2316 1270 y Fo(X)2331 1480 y Fp(i)p Fs(=1)2477 1365 y Ft(t)2512 1380 y Fp(i)2540 1365 y Ft(f)2588 1380 y Fp(i)2616 1254 y Fo(o)2683 1224 y(\023)3579 1365 y Fu(\(2.5\))0 1647 y(The)h(semi{in)m(v)-5 b(arian)m(t)26 b(of)h Ft(f)994 1662 y Fs(1)1034 1647 y Ft(;)17 b(:)g(:)g(:)f(;)h(f)1301 1662 y Fp(n)1376 1647 y Fu(w.r.t.)28 b(the)h(\014nite)f(v)m(olume)f (Gibbs)h(measure)g Ft(\026)3084 1611 y Fp(\034)3084 1672 y Fs(\003)3165 1647 y Fu(is)g(then)h(de\014ned)0 1791 y(b)m(y)808 1994 y Ft(\026)867 1952 y Fp(\034)867 2018 y Fs(\003)920 1913 y Fo(\000)965 1994 y Ft(f)1013 2009 y Fs(1)1053 1994 y Fu(;)17 b Fr(\001)g(\001)g(\001)31 b Fu(;)17 b Ft(f)1338 2009 y Fp(n)1385 1913 y Fo(\001)1458 1994 y Fu(:=)1599 1920 y Ft(@)1655 1884 y Fp(n)1719 1920 y Fu(log)g Ft(Z)1929 1935 y Fs(\003)1982 1839 y Fo(\000)2027 1920 y Ft(\034)11 b Fu(;)17 b Ft(t)2159 1935 y Fs(1)2199 1920 y Ft(;)g(:)g(:)g(:)f(;)h(t)2453 1935 y Fp(n)2500 1920 y Fu(\))p 1599 1971 940 4 v 1858 2062 a Ft(@)5 b(t)1949 2077 y Fs(1)2006 2062 y Fr(\001)17 b(\001)g(\001)e Ft(@)5 b(t)2230 2077 y Fp(n)2548 1819 y Fo(\014)2548 1879 y(\014)2548 1939 y(\014)2548 1998 y(\014)2548 2058 y(\014)2581 2122 y Fp(t)2606 2131 y Fj(1)2641 2122 y Fs(=)p Fn(\001\001\001)o Fs(=)p Fp(t)2835 2130 y Fl(n)2878 2122 y Fs(=0)3579 1994 y Fu(\(2.6\))0 2270 y(note)27 b(that)g(for)g Ft(n)h Fu(=)g(2)e(w)m(e)j (ha)m(v)m(e)f Ft(\026)1243 2234 y Fp(\034)1243 2295 y Fs(\003)1296 2189 y Fo(\000)1342 2270 y Ft(f)1390 2285 y Fs(1)1429 2270 y Fu(;)17 b Ft(f)1521 2285 y Fs(2)1560 2189 y Fo(\001)1634 2270 y Fu(=)27 b Ft(\026)1796 2234 y Fp(\034)1796 2295 y Fs(\003)1849 2189 y Fo(\000)1895 2270 y Ft(f)1943 2285 y Fs(1)1999 2270 y Ft(f)2047 2285 y Fs(2)2086 2189 y Fo(\001)2143 2270 y Fr(\000)11 b Ft(\026)2290 2234 y Fp(\034)2290 2295 y Fs(\003)2344 2189 y Fo(\000)2389 2270 y Ft(f)2437 2285 y Fs(1)2477 2270 y Fu(\))p Ft(\026)2574 2234 y Fp(\034)2574 2295 y Fs(\003)2627 2189 y Fo(\000)2672 2270 y Ft(f)2720 2285 y Fs(2)2760 2270 y Fu(\))27 b(namely)-8 b(,)27 b(the)h(co)m(v)-5 b(ariance)0 2414 y(b)s(et)m(w)m(een)35 b Ft(f)425 2429 y Fs(1)497 2414 y Fu(and)d Ft(f)734 2429 y Fs(2)774 2414 y Fu(.)146 2559 y(It)g(is)f(p)s(ossible)f(to)h(express) j(the)e(semi{in)m(v)-5 b(arian)m(t)28 b(in)j(terms)g(of)g(the)h(momen)m (ts)f(of)g Ft(f)3215 2574 y Fs(1)3254 2559 y Ft(;)17 b(:)g(:)g(:)f(;)h(f)3521 2574 y Fp(n)3568 2559 y Fu(.)43 b(F)-8 b(or)0 2703 y(notation)34 b(compactness)i(let)e(us)h(set)h Ft(N)42 b Fu(:=)32 b Fr(f)p Fu(1)p Ft(;)17 b(:)g(:)g(:)e(;)i(n)p Fr(g)35 b Fu(and)g(denote)g(b)m(y)h Fr(D)2826 2667 y Fp(`)2823 2728 y(N)2925 2703 y Fu(the)f(collection)e(of)i(the)0 2848 y(partitions)c(of)h Ft(N)43 b Fu(in)m(to)32 b Ft(`)g Fu(atoms)g(namely)-8 b(,)50 3135 y Fr(D)130 3094 y Fp(`)127 3160 y(N)222 3135 y Fu(:=)352 3025 y Fo(n)419 3135 y Ft(D)p 419 3151 84 4 v 30 w Fr(\021)635 3055 y Fo(\010)693 3135 y Ft(D)774 3150 y Fs(1)814 3135 y Ft(;)17 b(:)g(:)g(:)f(;)h(D)1114 3150 y Fp(`)1146 3055 y Fo(\011)1232 3135 y Fu(:)28 b Ft(D)1368 3150 y Fp(i)1424 3135 y Fr(\032)g Ft(N)5 b(;)38 b(D)1758 3150 y Fp(i)1814 3135 y Fr(6)p Fu(=)28 b Fr(;)p Ft(;)38 b(D)2114 3150 y Fp(i)2164 3135 y Fr(\\)23 b Ft(D)2334 3150 y Fp(j)2398 3135 y Fu(=)28 b Fr(;)k Fu(for)g Ft(i)c Fr(6)p Fu(=)f Ft(j;)3046 3011 y Fp(`)3005 3041 y Fo([)3004 3251 y Fp(i)p Fs(=1)3134 3135 y Ft(D)3215 3150 y Fp(i)3271 3135 y Fu(=)h Ft(N)3463 3025 y Fo(o)3579 3135 y Fu(\(2.7\))0 3423 y(W)-8 b(e)33 b(then)g(ha)m(v)m(e,)h(see)g(e.g.)f([21,)f(I)s(I,)h Fr(x)p Fu(12.8])652 3716 y Ft(\026)711 3675 y Fp(\034)711 3741 y Fs(\003)764 3635 y Fo(\000)810 3716 y Ft(f)858 3731 y Fs(1)897 3716 y Fu(;)17 b Fr(\001)g(\001)g(\001)31 b Fu(;)17 b Ft(f)1182 3731 y Fp(n)1229 3635 y Fo(\001)1302 3716 y Fu(=)1456 3592 y Fp(n)1406 3621 y Fo(X)1418 3834 y Fp(`)p Fs(=1)1550 3716 y Fu(\()p Fr(\000)p Fu(1\))1752 3675 y Fp(`)p Fn(\000)p Fs(1)1875 3716 y Fu(\()p Ft(`)22 b Fr(\000)h Fu(1\)!)2244 3621 y Fo(X)2207 3845 y Fp(D)p 2206 3857 60 3 v 1 w Fn(2D)2370 3822 y Fl(`)2368 3868 y(N)2509 3592 y Fp(`)2459 3621 y Fo(Y)2459 3834 y Fp(k)r Fs(=1)2620 3716 y Ft(\026)2679 3675 y Fp(\034)2679 3741 y Fs(\003)2732 3606 y Fo(\020)2828 3621 y(Y)2808 3833 y Fp(i)p Fn(2)p Fp(D)2937 3845 y Fl(k)2992 3716 y Ft(f)3040 3731 y Fp(i)3068 3606 y Fo(\021)3579 3716 y Fu(\(2.8\))0 4123 y Fk(2.5.)79 b(T)-7 b(r)i(e)g(e)34 b(de)-5 b(c)g(ay)35 b(of)f(semi{invariants)0 4289 y Fu(W)-8 b(e)41 b(ma)m(y)f(no)m(w)h (state)g(our)f(main)f(result.)67 b(Let)41 b Ft(f)1850 4304 y Fs(1)1890 4289 y Ft(;)17 b(:)g(:)g(:)e(;)i(f)2156 4304 y Fp(n)2244 4289 y Fu(b)s(e)40 b(lo)s(cal)e(functions,)43 b Ft(n)e Fr(\025)h Fu(2.)67 b(Giv)m(en)40 b(a)0 4434 y(p)s(ositiv)m(e)c(in)m(teger)h Ft(L)p Fu(,)h(b)m(y)g(enlarging)d(\003) 1458 4449 y Fp(i)1521 4434 y Fu(:=)g(supp)q(\()p Ft(f)1946 4449 y Fp(i)1974 4434 y Fu(\),)j(w)m(e)g(ma)m(y)f(\(and)g(do\))f (assume)i(that)f(\003)3476 4449 y Fp(i)3538 4434 y Fr(2)f Fq(F)3695 4449 y Fp(L)3753 4434 y Fu(;)0 4578 y(w)m(e)k(shall)d (further)i(assume)h(that)e(for)g Ft(i)h Fr(6)p Fu(=)f Ft(j)44 b Fr(2)39 b Ft(N)49 b Fu(w)m(e)40 b(ha)m(v)m(e)g(d\(\003)2477 4593 y Fp(i)2505 4578 y Ft(;)17 b Fu(\003)2617 4593 y Fp(j)2653 4578 y Fu(\))38 b Ft(>)h(r)s Fu(.)61 b(W)-8 b(e)40 b(stress)g(that)f(the)0 4723 y(supp)s(orts)33 b(\003)467 4738 y Fp(i)528 4723 y Fu(can)g(b)s(e)f(arbitrarily)e (large,)i(p)s(ossibly)g(div)m(erging)g(with)g(\003.)146 4867 y(Let)41 b(us)h(denote)g(b)m(y)f(\()p Fq(V)1033 4882 y Fp(N)1107 4867 y Ft(;)17 b Fq(E)1211 4882 y Fp(N)1284 4867 y Fu(\))41 b(the)g(graph)g(obtained)f(from)g(\()p Fq(L)5 b Ft(;)17 b Fq(E)h Fu(\))47 b(b)m(y)42 b(con)m(tracting)e(eac)m (h)i(\003)3725 4882 y Fp(i)3753 4867 y Fu(,)0 5012 y Ft(i)28 b Fr(2)g Ft(N)10 b Fu(,)29 b(to)d(a)h(single)f(p)s(oin)m(t,)h (in)g(other)g(w)m(ords)h(w)m(e)g(de\014ne)g Fq(V)2143 5027 y Fp(N)2244 5012 y Fu(:=)g Fr(f)p Ft(x)44 b Fu(:)39 b Ft(x)28 b Fr(2)g Fq(L)16 b Fr(n)2899 4937 y Fo(S)2987 4963 y Fp(n)2987 5041 y(i)p Fs(=1)3122 5012 y Fu(\003)3190 5027 y Fp(i)3218 5012 y Fr(g)11 b([)3356 4937 y Fo(S)3439 4963 y Fp(n)3439 5041 y(i)p Fs(=1)3557 5012 y Fr(f)p Fu(\003)3675 5027 y Fp(i)3703 5012 y Fr(g)p Fu(,)0 5156 y Fq(E)60 5171 y Fp(N)161 5156 y Fu(:=)28 b Fr(ff)p Ft(v)t(;)17 b(v)538 5120 y Fn(0)560 5156 y Fr(g)p Ft(;)33 b(v)t(;)17 b(v)816 5120 y Fn(0)866 5156 y Fr(2)28 b Fq(V)1026 5171 y Fp(N)1144 5156 y Fu(:)60 b(d\()p Ft(v)t(;)17 b(v)1469 5120 y Fn(0)1492 5156 y Fu(\))27 b(=)h(1)p Fr(g)p Fu(,)k(and)250 5432 y Fr(T)329 5351 y Fo(\000)375 5432 y Ft(f)423 5447 y Fs(1)463 5432 y Fu(;)17 b Ft(:)g(:)g(:)e Fu(;)i Ft(f)729 5447 y Fp(n)776 5351 y Fo(\001)850 5432 y Fu(:=)27 b(inf)1115 5321 y Fo(n)1181 5432 y Fr(j)p Ft(E)6 b Fr(j)17 b Ft(;)48 b Fu(\()p Ft(V)5 b(;)17 b(E)6 b Fu(\))28 b Fr(\032)g Fu(\()p Fq(V)1904 5447 y Fp(N)1977 5432 y Ft(;)17 b Fq(E)2081 5447 y Fp(N)2155 5432 y Fu(\))22 b(connected)29 b(:)50 b Ft(V)f Fr(\033)2989 5307 y Fp(n)2955 5337 y Fo([)2953 5547 y Fp(i)p Fs(=1)3068 5432 y Fr(f)p Fu(\003)3186 5447 y Fp(i)3213 5432 y Fr(g)3263 5321 y Fo(o)3579 5432 y Fu(\(2.9\))p Black 1866 5806 a(5)p Black eop %%Page: 6 7 6 6 bop Black Black Black 0 407 a Fv(Theorem)31 b(2.1.)p Black 38 w Fk(L)-5 b(et)30 b Ft(L)e Fr(2)g Fq(N)9 b Fk(,)37 b(assume)29 b(that)i(for)e(e)-5 b(ach)30 b Fu(\003)d Fr(2)h Fq(F)2305 422 y Fp(L)2393 407 y Fk(and)i Ft(\034)39 b Fr(2)28 b(S)38 b Fk(we)29 b(have)h(the)g(exp)-5 b(ansion)1336 620 y Fu(log)17 b Ft(Z)1546 635 y Fs(\003)1598 620 y Fu(\()p Ft(\034)11 b Fu(\))28 b(=)1912 526 y Fo(X)1859 741 y Fp(X)5 b Fn(\\)p Fs(\003)p Fn(6)p Fs(=)p Fn(;)2125 620 y Ft(\036)2183 635 y Fp(X)q(;)p Fs(\003)2315 620 y Fu(\()p Ft(\034)11 b Fu(\))1087 b(\(2.10\))0 915 y Fk(for)39 b(some)g(lo)-5 b(c)g(al)39 b(functions)g Ft(\036)1124 930 y Fp(X)q(;)p Fs(\003)1292 915 y Fr(2)e(F)1467 930 y Fs(\003)1516 911 y Fj(c)1551 915 y Fk(,)k Ft(X)j Fr(2)37 b Fq(F)6 b Fk(,)46 b(such)40 b(that)g(given)e Fu(\003)p Ft(;)17 b Fu(\003)2850 879 y Fn(0)2909 915 y Fr(\032\032)38 b Fq(L)5 b Fk(,)47 b(we)39 b(have)g(that)0 1059 y Ft(X)31 b Fr(\\)24 b Fu(\003)30 b(=)g Ft(X)h Fr(\\)24 b Fu(\003)676 1023 y Fn(0)735 1059 y Fk(implies)36 b Ft(\036)1129 1074 y Fp(X)q(;)p Fs(\003)1291 1059 y Fu(=)30 b Ft(\036)1455 1074 y Fp(X)q(;)p Fs(\003)1583 1055 y Fi(0)1609 1059 y Fk(.)50 b(If)35 b(ther)-5 b(e)37 b(exist)f(r)-5 b(e)g(als)36 b Ft(a;)17 b(b)31 b Fr(\025)g Fu(0)36 b Fk(and)g Ft(C)h(<)30 b Fr(1)36 b Fk(such)h(that)0 1204 y(for)e(any)f Fu(\003)28 b Fr(2)g Fq(F)587 1219 y Fp(L)871 1348 y Fu(sup)878 1430 y Fp(x)p Fn(2)p Fm(L)1054 1253 y Fo(X)1051 1465 y Fp(X)5 b Fn(3)p Fp(x)1217 1348 y Fu(exp)q Fr(f)p Ft(a)p Fq(T)p Fu(\()p Ft(X)j Fu(\))25 b(+)d Ft(b)17 b Fu(diam)o(\()p Ft(X)8 b Fu(\))p Fr(g)33 b(k)o Ft(\036)2443 1363 y Fp(X)q(;)p Fs(\003)2575 1348 y Fr(k)2625 1380 y Fn(1)2727 1348 y Fr(\024)c Ft(C)628 b Fu(\(2.11\))0 1603 y Fk(then)35 b(for)f(e)-5 b(ach)35 b Ft(n)27 b Fr(\025)i Fu(2)34 b Fk(ther)-5 b(e)35 b(exists)g(a)f(r)-5 b(e)g(al)35 b Ft(K)1729 1618 y Fp(n)1803 1603 y Fu(=)28 b Ft(K)1990 1618 y Fp(n)2037 1603 y Fu(\()p Ft(C)7 b Fu(;)17 b Fr(j)p Fu(\003)2292 1618 y Fs(1)2330 1603 y Fr(j)p Ft(;)g(:)g(:)g(:)f(;)h Fr(j)p Fu(\003)2673 1618 y Fp(n)2719 1603 y Fr(j)p Fu(\))34 b Fk(such)h(that)282 1783 y Fo(\014)282 1843 y(\014)316 1868 y Ft(\026)375 1827 y Fp(\034)375 1893 y Fs(\003)427 1868 y Fu(\()p Ft(f)513 1883 y Fs(1)553 1868 y Fu(;)17 b Ft(:)g(:)g(:)f Fu(;)h Ft(f)820 1883 y Fp(n)866 1868 y Fu(\))904 1783 y Fo(\014)904 1843 y(\014)965 1868 y Fr(\024)28 b Ft(K)1153 1883 y Fp(n)1239 1868 y Fu(exp)1405 1758 y Fo(n)1493 1868 y Fr(\000)1593 1758 y Fo(h)1640 1868 y Ft(a)22 b Fu(+)1915 1801 y Ft(b)p 1821 1845 229 4 v 1821 1936 a(n)h Fr(\000)f Fu(1)2060 1758 y Fo(i)2124 1868 y Fr(T)j Fu(\()p Ft(f)2289 1883 y Fs(1)2329 1868 y Fu(;)17 b Ft(:)g(:)g(:)e Fu(;)i Ft(f)2595 1883 y Fp(n)2642 1868 y Fu(\))2680 1758 y Fo(o)2827 1744 y Fp(n)2785 1773 y Fo(Y)2792 1983 y Fp(i)p Fs(=1)2929 1868 y Ft(\026)2988 1827 y Fp(\034)2988 1893 y Fs(\003)3041 1868 y Fu(\()p Fr(j)p Ft(f)3155 1883 y Fp(i)3183 1868 y Fr(j)p Fu(\))282 b(\(2.12\))0 2140 y Fk(for)35 b(any)f Fu(\003)28 b Fr(2)g Fq(F)587 2155 y Fp(L)680 2140 y Fk(and)34 b Ft(\034)39 b Fr(2)28 b(S)7 b Fk(.)0 2284 y(F)-7 b(urthermor)i(e,)50 b(if)e(\(2.11\))f(is)h(satis\014e)-5 b(d)48 b(with)f Ft(a)53 b(>)f Fu(0)c Fk(and)f Fu(\003)2350 2299 y Fs(1)2389 2284 y Ft(;)17 b(:)g(:)g(:)f(;)h Fu(\003)2676 2299 y Fp(n)2771 2284 y Fk(ar)-5 b(e)48 b(such)f(that)i(for)f(some)0 2429 y Ft(\016)32 b Fr(2)c Fu(\(0)p Ft(;)17 b Fu(1\))329 2663 y Ft(\025)27 b Fu(:=)h(sup)550 2744 y Fp(i)p Fn(2)p Fp(N)707 2568 y Fo(X)724 2780 y Fp(j)t Fn(6)p Fs(=)p Fp(i)868 2582 y Fo(\000)913 2663 y Fr(j)p Fu(\003)1009 2678 y Fp(i)1037 2663 y Fr(j)22 b(^)g(j)p Fu(\003)1271 2678 y Fp(j)1307 2663 y Fr(j)1335 2582 y Fo(\001)1414 2663 y Fu(exp)1579 2552 y Fo(n)1668 2663 y Fr(\000)1778 2595 y Fu(1)p 1778 2640 49 4 v 1778 2731 a(2)1853 2663 y Ft(a)17 b(\016)j Fu(d\(\003)2144 2678 y Fp(i)2172 2663 y Ft(;)d Fu(\003)2284 2678 y Fp(j)2320 2663 y Fu(\))2358 2552 y Fo(o)2452 2663 y Fr(\024)2855 2595 y Fu(1)p 2567 2640 625 4 v 2567 2731 a(6)g Ft(e)g Fu(\(1)k(+)h(18)17 b Ft(C)23 b(e)p Fu(\))3531 2663 y(\(2.13\))0 2949 y Fk(then)568 3036 y Fo(\014)568 3096 y(\014)601 3121 y Ft(\026)660 3080 y Fp(\034)660 3145 y Fs(\003)713 3121 y Fu(\()p Ft(f)799 3136 y Fs(1)838 3121 y Fu(;)17 b Ft(:)g(:)g(:)f Fu(;)h Ft(f)1105 3136 y Fp(n)1152 3121 y Fu(\))1190 3036 y Fo(\014)1190 3096 y(\014)1251 3121 y Fr(\024)28 b Fu(exp)1521 3010 y Fo(n)1610 3121 y Fr(\000)23 b Ft(a)17 b Fu(\(1)k Fr(\000)i Ft(\016)t Fu(\))17 b Fr(T)25 b Fu(\()p Ft(f)2253 3136 y Fs(1)2292 3121 y Fu(;)17 b Ft(:)g(:)g(:)f Fu(;)h Ft(f)2559 3136 y Fp(n)2606 3121 y Fu(\))2644 3010 y Fo(o)2791 2996 y Fp(n)2749 3026 y Fo(Y)2756 3236 y Fp(i)p Fs(=1)2893 3121 y Ft(\026)2952 3080 y Fp(\034)2952 3145 y Fs(\003)3005 3121 y Fu(\()p Fr(j)p Ft(f)3119 3136 y Fp(i)3147 3121 y Fr(j)p Fu(\))318 b(\(2.14\))0 3364 y Fk(for)35 b(any)f Fu(\003)28 b Fr(2)g Fq(F)587 3379 y Fp(L)645 3364 y Fk(,)35 b Ft(\034)k Fr(2)28 b(S)7 b Fk(,)36 b(and)e Ft(n)28 b Fr(\025)g Fu(2)p Fk(.)146 3566 y Fu(Note)38 b(that)f(the)h(h)m(yp)s (otheses)i(\(2.10\))c(and)i(\(2.11\))e(with)h Ft(a)26 b Fu(+)f Ft(b)36 b(>)g Fu(0)h(imply)f([8,)h(Condition)f(IV)-8 b(a])0 3710 y(whic)m(h)49 b(is)f(one)h(of)f(the)h(Dobrushin{Shlosman)e (complete)h(analyticit)m(y)f(conditions.)90 b(Indeed)50 b(b)m(y)0 3855 y(setting)1283 4014 y Ft(g)t Fu(\()p Ft(x;)17 b Fu(\003)p Ft(;)g(\034)11 b Fu(\))26 b(:=)1834 3919 y Fo(X)1831 4131 y Fp(X)5 b Fn(3)p Fp(x)2055 3946 y Fu(1)p 2008 3991 145 4 v 2008 4082 a Fr(j)p Ft(X)j Fr(j)2178 4014 y Ft(\036)2236 4029 y Fp(X)q(;)p Fs(\003)2368 4014 y Fu(\()p Ft(\034)j Fu(\))1034 b(\(2.15\))0 4269 y(for)32 b(all)f Ft(\034)39 b Fr(2)28 b(S)7 b Fu(,)33 b(\003)28 b Fr(\032\032)g Fq(L)6 b Fu(,)38 b(and)33 b Ft(x)28 b Fr(2)g Fu(\003,)k(w)m(e)i(ha)m(v)m(e)g(that)e(\(i\))g(e)h(\(ii\))d(of)i ([8,)h(Condition)e(IV)-8 b(a])33 b(hold.)p Black 0 4470 a Fv(Remark)k(2.2.)p Black 42 w Fu(Instead)c(of)g(\(2.10\))e(w)m(e)j (can)f(assume)g(an)f(expansion)h(of)g(the)g(form)1072 4683 y(log)17 b Ft(Z)1282 4698 y Fs(\003)1334 4683 y Fu(\()p Ft(\034)11 b Fu(\))28 b(=)1648 4589 y Fo(X)1595 4804 y Fp(X)5 b Fn(\\)p Fs(\003)p Fn(6)p Fs(=)p Fn(;)1861 4603 y Fo(\002)1903 4683 y Ft( )1966 4698 y Fp(X)q(;)p Fs(\003)2098 4683 y Fu(\()p Ft(\034)11 b Fu(\))22 b(+)g Ft(\036)2405 4698 y Fp(X)q(;)p Fs(\003)2537 4683 y Fu(\()p Ft(\034)11 b Fu(\))2666 4603 y Fo(\003)3531 4683 y Fu(\(2.16\))0 4979 y(where)33 b Ft(\036)339 4994 y Fp(X)q(;)p Fs(\003)501 4979 y Fu(satis\014es)f(the)g(b)s(ound)g(\(2.11\))e(whereas)j Ft( )2037 4994 y Fp(X)q(;)p Fs(\003)2201 4979 y Fu(satisfy)e(the)h (same)f(measurabilit)m(y)e(condi-)0 5124 y(tion)f(namely)-8 b(,)29 b(that)g Ft( )823 5139 y Fp(X)q(;)p Fs(\003)983 5124 y Fr(2)g(F)1150 5139 y Fs(\003)1199 5120 y Fj(c)1263 5124 y Fu(and)g Ft(X)23 b Fr(\\)15 b Fu(\003)29 b(=)e Ft(X)c Fr(\\)15 b Fu(\003)2087 5088 y Fn(0)2141 5124 y Fu(implies)26 b Ft( )2531 5139 y Fp(X)q(;)p Fs(\003)2691 5124 y Fu(=)i Ft( )2858 5139 y Fp(X)q(;)p Fs(\003)2986 5120 y Fi(0)3013 5124 y Fu(,)i Ft(X)35 b Fr(2)28 b Fq(F)6 b Fu(,)36 b(and)30 b Ft( )3648 5139 y Fp(X)q(;)p Fs(\003)0 5268 y Fu(are)36 b(of)f(\014nite)g(range,)h(i.e.)g(for)f(some)g(in)m (teger)40 b(\026)-54 b Ft(r)39 b Fu(w)m(e)d(ha)m(v)m(e)h Ft( )2233 5283 y Fp(X)q(;)p Fs(\003)2398 5268 y Fu(=)c(0)i(for)g(diam)o (\()p Ft(X)8 b Fu(\))32 b Ft(>)37 b Fu(\026)-53 b Ft(r)r Fu(.)53 b(Then)37 b(the)0 5413 y(thesis)d(of)f(Theorem)h(2.1)g(still)d (holds)j(pro)m(vided)g(d\(\003)1967 5428 y Fp(i)1995 5413 y Ft(;)17 b Fu(\003)2107 5428 y Fp(j)2143 5413 y Fu(\))29 b Ft(>)34 b Fu(\026)-53 b Ft(r)r Fu(,)34 b Ft(i)c Fr(6)p Fu(=)g Ft(j)35 b Fr(2)30 b Ft(N)10 b Fu(.)48 b(Note)34 b(that)f(no)h(b)s(ound)0 5557 y(on)e(the)h(norm)f(of)g(the)h(family)d Fr(f)p Ft( )1248 5572 y Fp(X)q(;)p Fs(\003)1381 5557 y Ft(;)j(X)i Fr(2)28 b Fq(F)6 b Fr(g)39 b Fu(is)32 b(required.)p Black 1866 5806 a(6)p Black eop %%Page: 7 8 7 7 bop Black Black 0 407 a Fk(A)-5 b(ddenda:)p Black 21 551 a Fu({)p Black 48 w(One)29 b(ma)m(y)g(w)m(onder)h(ho)m(w)f(w)m (e)h(can)f(b)s(ound)g(the)h(semi{in)m(v)-5 b(arian)m(t)26 b(of)i Ft(n)h Fu(functions)g(in)f(terms)h(of)f(their)118 696 y Ft(L)184 660 y Fs(1)256 696 y Fu(\(rather)33 b(than)g Ft(L)881 660 y Fp(n)928 696 y Fu(\))f(norm.)43 b(This)33 b(is)f(p)s(ossible)g(b)s(ecause)i Ft(f)2388 711 y Fp(i)2449 696 y Fu(ha)m(v)m(e)f(disjoin)m(t)f(supp)s(orts.)p Black 21 851 a({)p Black 48 w(By)26 b(the)g(metho)s(ds)g(in)e([17,)6 b(18],)27 b(it)e(is)g(p)s(ossible)f(to)i(pro)m(v)m(e)g(the)g(follo)m (wing)d(con)m(v)m(erse)28 b(to)d(Theorem)h(2.1.)118 995 y(If)34 b(the)g(b)s(ound)g(\(2.12\))f(holds)g(for)g Ft(n)d Fu(=)g(2)j(then)h(there)h(are)e(an)h(in)m(teger)g Ft(L)2817 959 y Fn(0)2870 995 y Ft(>)29 b Fu(0)34 b(and)f(a)h(real)f Ft(a)3573 959 y Fn(0)3626 995 y Ft(>)c Fu(0)118 1140 y(suc)m(h)34 b(that)e(\(2.10\))g(and)h(\(2.11\))f(hold)g(for)g(an)m(y)h (\003)27 b Fr(2)h Fq(F)2097 1155 y Fp(L)2145 1136 y Fi(0)2178 1140 y Fu(.)p Black 21 1295 a({)p Black 48 w(If)33 b(there)h(exists)g (a)f(unique)g(in\014nite)f(v)m(olume)h(Gibbs)f(state)i Ft(\026)p Fu(,)f(as)g(it)f(is)h(t)m(ypically)f(the)h(case)h(under)118 1439 y(conditions)41 b(implying)e(the)k(v)-5 b(alidit)m(y)40 b(of)h(\(2.10\){\(2.11\),)i(then)f(the)h(b)s(ounds)f(\(2.12\))g(and)g (\(2.14\))118 1584 y(holds)32 b(also)g(for)g Ft(\026)p Fu(.)p Black 21 1739 a({)p Black 48 w(If)42 b(the)g(supp)s(orts)g(\003) 878 1754 y Fp(i)948 1739 y Fu(are)g(at)f(distance)h(large)f(enough)h (\(dep)s(ending)g(on)f Fr(j)p Fu(\003)2986 1754 y Fp(i)3014 1739 y Fr(j)p Fu(,)j Ft(a)e Fu(and)f Ft(C)7 b Fu(\),)44 b(then)118 1883 y(the)f(condition)d(\(2.13\))i(is)f(satis\014ed.)72 b(Note)43 b(also)e(that)h Fk(one)58 b Fu(of)41 b(the)i(functions)f Ft(f)3229 1898 y Fp(i)3299 1883 y Fu(migh)m(t)f(ha)m(v)m(e)118 2028 y(arbitrarily)30 b(large)h(supp)s(ort.)p Black 21 2183 a({)p Black 48 w(In)j([22,)f(Corollary)f(I)s(I.12.8])h(it)g(is)g (sho)m(wn)i(ho)m(w,)g(in)d(a)i(general)f(setting,)g(it)g(is)g(p)s (ossible)g(to)g(deduce)118 2327 y(some)g(deca)m(y)g(of)g(semi{in)m(v)-5 b(arian)m(ts)30 b(from)i(suitable)f(deca)m(y)j(prop)s(erties)f(of)f(co) m(v)-5 b(ariances.)0 2543 y Fk(2.6.)79 b(Exempla)0 2705 y Fu(In)41 b(order)g(to)g(clarify)e(ho)m(w)j(\(2.10\))e(and)h(\(2.11\)) f(can)i(b)s(e)f(sho)m(wn)h(to)f(hold)f(assuming)g(a)h(con)m(v)m(ergen)m (t)0 2849 y(cluster)35 b(expansion,)g(w)m(e)h(discuss)f(the)g(standard) g(Ising)f(mo)s(del)f(at)h(high)f(temp)s(erature;)j(m)m(uc)m(h)f(more)0 2994 y(general)30 b(mo)s(dels)e(can)j(b)s(e)f(analyzed)g(along)f(the)i (same)f(lines.)41 b(The)32 b(single)d(spin)h(con\014guration)f(space)0 3138 y(is)j Fr(S)158 3153 y Fs(0)226 3138 y Fu(=)27 b Fr(f\000)p Fu(1)p Ft(;)17 b Fu(+1)p Fr(g)32 b Fu(and)h(the)g(p)s(oten)m (tial)d Ft(U)44 b Fu(is)32 b(then)h(giv)m(en)g(b)m(y)617 3395 y Ft(U)683 3410 y Fp(X)751 3395 y Fu(\()p Ft(\033)t Fu(\))27 b(:=)1044 3224 y Fo(\()1166 3327 y Ft(J)9 b(\033)t Fu(\()p Ft(x)p Fu(\))p Ft(\033)t Fu(\()p Ft(y)t Fu(\))221 b(if)31 b Ft(X)36 b Fu(=)27 b Fr(f)p Ft(x;)17 b(y)t Fr(g)32 b Fu(and)g Fr(j)p Ft(x)22 b Fr(\000)h Ft(y)t Fr(j)2893 3342 y Fs(2)2959 3327 y Fu(=)28 b(1)1166 3471 y(0)612 b(otherwise)0 3659 y(where)35 b Ft(J)k Fr(2)31 b Fq(R)44 b Fu(and)34 b Fr(j)p Ft(x)p Fr(j)880 3674 y Fs(2)953 3659 y Fu(is)g(the)g(Euclidean)g(norm)f(of)g Ft(x)e Fr(2)f Fq(Z)2294 3623 y Fp(d)2332 3659 y Fu(.)47 b(The)35 b(partition)d (function)h(\(2.4\))h(can)0 3803 y(b)s(e)f(written)f(as)916 3975 y Ft(Z)983 3990 y Fs(\003)1036 3975 y Fu(\()p Ft(\034)11 b Fu(\))28 b(=)f(2)1345 3934 y Fn(j)p Fs(\003)p Fn(j)1437 3834 y Fo(\024)1490 3975 y Fu(1)22 b(+)1659 3880 y Fo(X)1664 4091 y Fp(n)p Fn(\025)p Fs(1)2037 3880 y Fo(X)1920 4080 y Fl(\015)1952 4095 y Fj(1)1987 4080 y Fl(;:::;\015)2114 4088 y(n)2156 4080 y Fi(2)p Fj(\000)2236 4097 y(\003)2281 4080 y(:)1831 4143 y Fh(e)-34 b Fl(\015)1861 4159 y(i)1888 4143 y Fi(\\)r Fh(e)g Fl(\015)1962 4159 y(j)1995 4143 y Fj(=)p Fi(;)52 b Fj(1)p Fi(\024)p Fl(i)h Fu(0.)146 1687 y(Without)i(en)m(tering)h(in)m(to)e(the)i(details,)f(w)m (e)h(discuss)h(here)f(some)f(mo)s(dels)g(to)g(whic)m(h)h(Theorem)f(2.1) 0 1832 y(migh)m(t)h(b)s(e)i(applied)e(on)i(the)g(basis)f(of)g(a)h(con)m (v)m(ergen)m(t)h(cluster)f(expansion.)p Black 21 2072 a({)p Black 48 w Fk(High)i(temp)-5 b(er)g(atur)g(e)35 b(/)g(low)f(activity)h(exp)-5 b(ansions.)118 2216 y Fu(The)44 b(con)m(v)m(ergence)j(of)42 b(the)i(cluster)g(expansion)g(for)f(an)m(y) h(\003)i Fr(2)g Fq(F)55 b Fu(and)44 b(the)g(tree)g(deca)m(y)h(of)e(the) 118 2361 y(semi{in)m(v)-5 b(arian)m(ts)34 b(for)i Ft(f)1009 2376 y Fp(i)1037 2361 y Fu(\()p Ft(\033)t Fu(\))d(=)h Ft(\033)t Fu(\()p Ft(x)1467 2376 y Fp(i)1495 2361 y Fu(\),)j Ft(x)1652 2376 y Fp(i)1714 2361 y Fr(2)d Fq(L)48 b Fu(is)35 b(a)h(classical)e(topic)i(in)f(equilibrium)e(statistical)118 2505 y(mec)m(hanics,)j(see)h(e.g.)e([13,)g Fr(x)p Fu(20.4],)g([22,)g (Theorem)g(V.7.13],)h(and)f([9{11].)50 b(Ho)m(w)m(ev)m(er)38 b(w)m(e)e(are)f(not)118 2650 y(a)m(w)m(are)40 b(of)f(an)m(y)g (reference)i(where)f(the)g(case)g(of)e(lo)s(cal)f(functions)i Ft(f)2630 2665 y Fp(i)2697 2650 y Fu(with)g(arbitrary)f(supp)s(ort)h (is)118 2794 y(discussed)34 b(in)e(detail.)p Black 21 3004 a({)p Black 48 w Fk(Str)-5 b(ong)35 b(Mixing)f(\(SM\))h(p)-5 b(otentials.)118 3148 y Fu(The)40 b(tree)g(deca)m(y)h(of)e(the)g (semi{in)m(v)-5 b(arian)m(ts)38 b(uniform)f(in)i(the)h(b)s(oundary)f (con\014guration)g(is)g(one,)118 3293 y(called)h(condition)g(I)s(Ic,)k (of)d(the)h(equiv)-5 b(alen)m(t)41 b(conditions)f(of)h(the)h (Dobrushin{Shlosman's)e(com-)118 3437 y(pletely)i(analytical)f(in)m (teractions)h([7,)19 b(8].)73 b(It)43 b(is)g(stated)g(in)f(a)g (somewhat)h(di\013eren)m(t)g(form)f(than)118 3582 y(the)g(one)f(giv)m (en)h(here:)62 b(there)42 b(is)e(no)i(restriction)e(on)h(d\(\003)2301 3597 y Fp(i)2329 3582 y Ft(;)17 b Fu(\003)2441 3597 y Fp(j)2477 3582 y Fu(\),)43 b(but)f(the)g(supp)s(orts)g(\003)3426 3597 y Fp(i)3495 3582 y Fu(are)f(re-)118 3726 y(quired)e(to)g(ha)m(v)m (e)i(diam)n(\(\003)1100 3741 y Fp(i)1128 3726 y Fu(\))e Fr(\024)g Ft(r)s Fu(.)63 b(W)-8 b(e)40 b(men)m(tion)e(that)h(the)g (equiv)-5 b(alence)40 b(of)f(the)g(tree)h(deca)m(y)g(of)118 3870 y(the)d(semi{in)m(v)-5 b(arian)m(ts)35 b(with)h(the)h(other)g (conditions)f(is)g(pro)m(v)m(en,)j(via)d(a)h(v)m(ery)h(elegan)m(t)e (analytical)118 4015 y(function)44 b(argumen)m(t,)k(under)d(the)g (additional)d(assumption)i(that)g(the)h(p)s(oten)m(tial)e Ft(U)56 b Fu(is)44 b(in)g(the)118 4159 y(same)39 b(connected)h(comp)s (onen)m(t)f(\(among)e(the)i(in)m(teractions)f(satisfying)g(the)h (conditions\))e(of)i(the)118 4304 y(zero)33 b(p)s(oten)m(tial,)e(see)j ([7,)e(Commen)m(t)g(2.1].)118 4490 y(In)e(the)g(original)d (Dobrushin{Shlosman's)h(setting)i(the)g(exp)s(onen)m(tial)f(deca)m(y)i (\(2.12\))e(is)g(supp)s(osed)118 4634 y(to)41 b(hold)g(for)g(all)e (\003)j Fr(2)h Fq(F)6 b Fu(;)52 b(ho)m(w)m(ev)m(er,)46 b(as)c(discussed)h(in)d([15],)k(there)e(are)f(examples)g(in)g(whic)m(h) h(it)118 4779 y(holds)36 b(only)g(for)f(\003)f Fr(2)g Fq(F)1004 4794 y Fp(L)1099 4779 y Fu(with)i Ft(L)g Fu(large)f(enough.) 55 b(This)37 b(has)f(lead)g(to)g(the)g(so{called)f(restricted)118 4923 y(completely)22 b(analytical)f(\(or)h(Strong)h(Mixing\))f (scenario,)j(see)f([15,)t(16,)t(20],)g(in)e(whic)m(h)i(one)f(considers) 118 5068 y(only)35 b(the)g(\\regular")f(v)m(olumes)h(\003)d Fr(2)g Fq(F)1566 5083 y Fp(L)1624 5068 y Fu(.)51 b(The)37 b(usual)d(argumen)m(t)h(to)g(get)g(the)h(tree)f(deca)m(y)i(of)e(the)118 5212 y(semi{in)m(v)-5 b(arian)m(ts)34 b(for)i(SM)h(p)s(oten)m(tials)e (is)h(the)g(follo)m(wing.)52 b(Consider)37 b(a)f(rescaled)h(system)g (whose)118 5357 y(new)32 b(single)d(spin)i(v)-5 b(ariables)29 b(are)i(the)g(old)e(spin)i(con\014gurations)f(in)g(the)h(blo)s(c)m(ks)g Ft(Q)3161 5372 y Fp(L)3213 5357 y Fu(\()p Ft(Lx)p Fu(\),)h Ft(x)c Fr(2)g Fq(Z)3715 5320 y Fp(d)3753 5357 y Fu(;)118 5501 y(w)m(e)47 b(can)g(then)g(apply)f(Dobrushin{Shlosman's)f(results)h ([7,)21 b(8])46 b(to)g(this)g(rescaled)h(system)g(and)p Black 1866 5806 a(8)p Black eop %%Page: 9 10 9 9 bop Black Black 118 407 a Fu(get)36 b(all)d(their)i(equiv)-5 b(alen)m(t)35 b(mixing)e(and)j(analyticit)m(y)e(prop)s(erties)h(of)g (the)h(Gibbs)e(state)i(for)f(ev)m(ery)118 551 y(\003)27 b Fr(2)i Fq(F)362 566 y Fp(L)421 551 y Fu(.)118 735 y(Theorem)d(2.1)f (allo)m(ws)g(a)h(direct)f(pro)s(of)g(of)g(the)h(tree)h(deca)m(y)g(of)e (semi{in)m(v)-5 b(arian)m(ts)24 b(for)h(SM)h(p)s(oten)m(tials)118 880 y(\(without)i(the)g(h)m(yp)s(otheses)j(that)d Ft(U)39 b Fu(is)27 b(in)h(the)g(same)g(connected)i(comp)s(onen)m(t)e(of)g(the)h (zero)f(p)s(oten-)118 1024 y(tial\))36 b(according)h(to)g(the)h(follo)m (wing)d(route.)58 b(SM)39 b(p)s(oten)m(tials)d(satisfy)i(the)g Fk(\014nite)h(size)53 b Fu(condition)118 1169 y(in)m(tro)s(duced)31 b(in)g([17,)11 b(18])31 b(whic)m(h)g(yields)g(a)g(con)m(v)m(ergen)m(t)i (cluster)f(expansion)f(for)g(whic)m(h)g(\(2.10\))g(and)118 1313 y(\(2.11\))39 b(hold)g(for)g(some)h Ft(a)g(>)g Fu(0)f(and)h(some)g (in)m(teger)g Ft(L)p Fu(.)65 b(As)40 b(a)g(matter)f(of)g(fact)h(in)f ([17,)16 b(18])40 b(it)e(is)118 1458 y(considered)30 b(only)f(the)h(case)g(when)g(\003)f(is)g(a)g(torus,)h(but)g(it)e(is)h (not)g(to)s(o)f(di\016cult,)h(see)i([2,)10 b(4])28 b(for)h(some)118 1602 y(details,)g(to)g(extend)h(it)e(to)h(an)m(y)h(\003)d Fr(2)h Fq(F)1516 1617 y Fp(L)1603 1602 y Fu(and)h Ft(\034)39 b Fr(2)28 b(S)7 b Fu(.)44 b(Then)30 b(Theorem)f(2.1)g(yields)f(the)i (tree)g(deca)m(y)118 1746 y(of)i(the)h(semi{in)m(v)-5 b(arian)m(ts)31 b(in)h(the)h(sense)h(giv)m(en)f(b)m(y)g(\(2.14\).)p Black 21 1954 a({)p Black 48 w Fk(Continuous)i(systems.)44 b(High)35 b(temp)-5 b(er)g(atur)g(e)35 b(/)g(low)f(activity)h(exp)-5 b(ansions.)118 2099 y Fu(W)d(e)43 b(ha)m(v)m(e)g(describ)s(ed)g(only)f (lattice)e(mo)s(dels,)k(but)e(it)f(is)h(p)s(ossible)g(to)f(extend)j (Theorem)f(2.1)e(to)118 2243 y(con)m(tin)m(uous)e(mo)s(dels.)58 b(F)-8 b(or)37 b(the)h(in\014nite)f(v)m(olume)h(state,)h(absolute)f(in) m(tegrabilit)m(y)d(of)j(the)g(Ursell)118 2388 y(functions)30 b(is)f(pro)m(v)m(en)i(in)d([19,)i(Thm.)42 b(4.4.8].)g(F)-8 b(or)29 b(a)g(p)s(ositiv)m(e)g(pairwise)g(in)m(teraction,)g(the)h(con)m (v)m(er-)118 2532 y(gence)h(of)f(the)h(cluster)g(expansion)f(uniform)f (in)h(the)g(b)s(oundary)h(condition)e(is)h(pro)m(v)m(en)i(in)d([23],)i (see)118 2676 y(also)h([1])g(for)g(the)h(exp)s(onen)m(tial)f(deca)m(y)i (of)e(the)h(co)m(v)-5 b(ariance)33 b(b)s(et)m(w)m(een)h(lo)s(cal)d (functions.)p Black 21 2884 a({)p Black 48 w Fk(Disor)-5 b(der)g(e)g(d)29 b(systems)i(in)f(the)h(Gri\016ths')g(phase.)42 b(High)31 b(temp)-5 b(er)g(atur)g(e)30 b(/)h(low)f(activity)h(exp)-5 b(ansions.)118 3029 y Fu(The)26 b(con)m(v)m(ergence)i(of)d(an)g (appropriate)f(m)m(ulti{scale)f(cluster)i(expansion)h(in)e(suc)m(h)j(a) e(situation)f(has)118 3173 y(b)s(een)39 b(obtained)f(in)g([12])g(where) i(the)f(tree)g(deca)m(y)h(of)e(the)h(semi{in)m(v)-5 b(arian)m(ts)37 b(is)h(pro)m(v)m(en)i(in)e(detail)118 3317 y(only)j(for)g Ft(f)547 3332 y Fp(i)575 3317 y Fu(\()p Ft(\033)t Fu(\))i(=)g Ft(\033)t Fu(\()p Ft(x)1024 3332 y Fp(i)1052 3317 y Fu(\).)70 b(W)-8 b(e)42 b(are)f(in)g(a)g(situation)f(lik)m(e)h(the)h(one)f (describ)s(ed)i(in)d(Remark)h(2.2)118 3462 y(with)h(the)g(additional)d (complication)g(that,)44 b(dep)s(ending)e(on)g(the)g(disorder)g (con\014guration,)i(the)118 3606 y(functions)36 b Ft( )605 3621 y Fp(X)q(;)p Fs(\003)773 3606 y Fu(can)f(ha)m(v)m(e)i(arbitrary)e (large)f(supp)s(orts.)54 b(One)35 b(then)i(obtains)e(some)g(probabilit) m(y)118 3751 y(estimates)d(on)h(the)g(disorder)f(whic)m(h)h(lead)f(to)h (a)f(tree)h(deca)m(y)h(in)e(a)g(set)h(of)f(full)f(measure.)p Black 21 3958 a({)p Black 48 w Fk(Disor)-5 b(der)g(e)g(d)34 b(systems)g(in)h(the)g(Gri\016ths')g(phase.)44 b(Smal)5 b(l)34 b(p)-5 b(erturb)g(ation)35 b(of)f(SM)h(p)-5 b(otentials.)118 4103 y Fu(The)41 b(con)m(v)m(ergence)i(of)d(an)g(appropriate)g(m)m (ulti{scale)e(cluster)i(expansion)h(in)f(suc)m(h)h(a)g(situation)118 4247 y(will)32 b(b)s(e)j(pro)m(v)m(en)g(in)f([5].)48 b(W)-8 b(e)35 b(stress)h(that,)e(due)h(to)f(the)h(presence)h(of)e (arbitrary)f(large)h(regions)f(of)118 4392 y(strong)h(in)m(teraction,)g (the)g(b)s(ound)h(\(2.11\))e(holds)h(with)g Ft(b)d(>)f Fu(0)k(but)g Ft(a)d Fu(=)f(0.)48 b(W)-8 b(e)34 b(refer)h(to)f([3])g (for)f(a)118 4536 y(more)f(detailed)g(discussion.)0 4956 y Fv(3.)38 b(Pro)s(of)f(of)g(the)h(tree)f(deca)m(y)0 5124 y Fu(The)c(usual)e(pro)s(ofs)h(of)f(tree)h(deca)m(y)h(of)f(the)g (semi{in)m(v)-5 b(arian)m(ts)30 b(from)g(the)j(con)m(v)m(ergence)h(of)d (the)i(cluster)0 5268 y(expansion,)i(see)h(e.g.)e([13,)g Fr(x)p Fu(20.4])g(or)g([22,)g Fr(x)p Fu(V.7],)h(are)f(based)h(on)f(the) h(expansion)g(of)f(the)g(p)s(erturb)s(ed)0 5413 y(partition)26 b(function)h(\(2.5\))g(and)h(then)h(in)e(the)h(estimates)g(of)f(the)h (deriv)-5 b(ativ)m(es)28 b(in)f(\(2.6\).)42 b(If)27 b(one)h(is)g(will-) 0 5557 y(ing)k(to)h(consider)h(functions)f Ft(f)1133 5572 y Fp(i)1194 5557 y Fu(with)g(arbitrary)g(supp)s(orts)h(\003)2301 5572 y Fp(i)2362 5557 y Fu(there)g(are)f(some)g(di\016culties)f (related)p Black 1866 5806 a(9)p Black eop %%Page: 10 11 10 10 bop Black Black 0 407 a Fu(in)41 b(the)h(need)h(of)f(cluster)g (expand)h(the)f(p)s(erturb)s(ed)g(measure)h(also)d(inside)i(\003)2920 422 y Fp(i)2989 407 y Fu(where)h(the)g(in)m(terac-)0 551 y(tion)33 b(is)g(not)h(necessary)i(w)m(eak.)49 b(The)35 b(com)m(binatorial)30 b(pro)s(of)j(w)m(e)i(presen)m(t)g(here)g(is)e (instead)h(based)h(on)0 696 y(the)f(iden)m(tit)m(y)f(\(2.8\))g(and)g (will)e(in)m(v)m(olv)m(e)j(\(2.10\))e(and)h(\(2.11\),)g(whic)m(h)h (abstract)g(the)f(con)m(v)m(ergence)j(of)d(a)0 840 y(cluster)g (expansion,)f(only)g(outside)g(the)h(supp)s(orts)g(\003)1979 855 y Fp(i)2039 840 y Fu(namely)-8 b(,)32 b(for)f(the)i(unp)s(erturb)s (ed)g(system.)45 b(F)-8 b(or)0 985 y(simplicit)m(y)27 b(w)m(e)k(ha)m(v)m(e)g(required)f(that)f(the)h(supp)s(orts)h(of)e(the)h (functions)g Ft(f)2693 1000 y Fp(i)2751 985 y Fu(are)f(at)h(a)f (distance)h(greater)0 1129 y(than)j(the)g(range)f(of)g(the)h(p)s(oten)m (tial.)146 1292 y(Let)d(us)f(start)g(b)m(y)h(a)f(purely)g(com)m (binatorial)c(lemma)i(whic)m(h)j(reduces)g(the)g(estimate)e(of)h(the)g (semi{)0 1437 y(in)m(v)-5 b(arian)m(t)39 b(to)h(ratios)f(of)h (partition)e(functions.)67 b(F)-8 b(or)40 b(\003)g Fr(2)h Fq(F)2291 1452 y Fp(L)2390 1437 y Fu(and)f Ft(I)49 b Fr(\032)41 b Ft(N)52 b Fu(=)40 b Fr(f)p Fu(1)p Ft(;)17 b(:)g(:)g(:)f(;)h(n)p Fr(g)40 b Fu(w)m(e)h(set)0 1581 y(\003)68 1596 y Fp(I)140 1581 y Fu(:=)275 1506 y Fo(S)358 1610 y Fp(i)p Fn(2)p Fp(I)486 1581 y Fu(\003)554 1596 y Fp(i)614 1581 y Fr(\032)33 b Fu(\003)i(and)g Ft(V)1076 1596 y Fp(I)1148 1581 y Fu(:=)e(\003)23 b Fr(n)h Fu(\003)1517 1596 y Fp(I)1557 1581 y Fu(;)36 b(note)g(that)f(since)h(w)m(e)g(ha)m(v) m(e)h(assumed)f(\003)3132 1596 y Fp(i)3192 1581 y Fr(2)d Ft(F)3354 1596 y Fp(L)3441 1581 y Fu(w)m(e)k(ha)m(v)m(e)0 1726 y(also)32 b Ft(V)253 1741 y Fp(I)320 1726 y Fr(2)c Ft(F)477 1741 y Fp(L)529 1726 y Fu(.)44 b(F)-8 b(or)32 b Ft(\033)f Fr(2)d(S)41 b Fu(let)32 b(also)f Ft(R)1466 1741 y Fp(I)1534 1726 y Fu(=)d Ft(R)1712 1741 y Fp(I)1752 1726 y Fu(\()p Ft(\033)t Fu(\))k(b)s(e)h(de\014ned)h(b)m(y)f Ft(R)2597 1741 y Fn(;)2665 1726 y Fu(=)27 b Ft(R)2842 1741 y Fn(f)p Fp(i)p Fn(g)2969 1726 y Fu(=)g(1)33 b(and)f(for)g Fr(j)p Ft(I)8 b Fr(j)27 b(\025)h Fu(2)0 1870 y(b)m(y)1243 2014 y(log)17 b Ft(R)1460 2029 y Fp(I)1528 2014 y Fu(:=)1659 1920 y Fo(X)1663 2131 y Fp(J)6 b Fn(\032)p Fp(I)1802 2014 y Fu(\()p Fr(\000)p Fu(1\))2004 1973 y Fn(j)p Fp(I)f Fn(j\000j)p Fp(J)h Fn(j)2239 2014 y Fu(log)17 b Ft(Z)2449 2029 y Fp(V)2490 2040 y Fl(J)3579 2014 y Fu(\(3.1\))0 2264 y(note)30 b(that)g Ft(R)497 2279 y Fp(I)564 2264 y Fr(2)f(F)731 2279 y Fp(V)787 2256 y Fj(c)772 2302 y Fl(I)852 2264 y Fu(and)h Ft(V)1118 2227 y Fs(c)1096 2289 y Fp(I)1181 2264 y Fu(=)d(\003)1352 2227 y Fs(c)1404 2264 y Fr([)16 b Fu(\003)1554 2279 y Fp(I)1595 2264 y Fu(.)42 b(W)-8 b(e)30 b(p)s(oin)m(t)f(out)h(the)g(analogy)f(b)s(et)m(w) m(een)j(de\014nition)c(\(3.1\))0 2408 y(and)k(the)g(com)m(binatorial)d (set)j(up)g(of)g(Kotec)m(k)q(\023)-50 b(y{Preiss)33 b([14,)f(Eq.)h (\(3\)].)42 b(W)-8 b(e)33 b(set)f(\014nally)f Ft(\045)3300 2423 y Fp(I)3368 2408 y Fu(:=)c Ft(R)3572 2423 y Fp(I)3633 2408 y Fr(\000)21 b Fu(1)0 2552 y(and)33 b(de\014ne)g Ft(\045)521 2516 y Fs(\(\003\))657 2552 y Fr(2)c(F)824 2567 y Fs(\003)873 2578 y Fl(N)930 2567 y Fn([)p Fs(\003)1026 2548 y Fj(c)1094 2552 y Fu(as)1281 2753 y Ft(\045)1331 2711 y Fs(\(\003\))1439 2753 y Fu(\()p Ft(\033)t Fu(\))f(:=)1732 2658 y Fo(X)1740 2870 y Fp(k)r Fn(\025)p Fs(1)1923 2658 y Fo(X)1915 2869 y Fp(I)p 1915 2881 36 3 v 5 w Fn(2I)2037 2881 y Fl(k)2114 2658 y Fo(Y)2118 2869 y Fp(I)5 b Fn(2)p Fp(I)p 2201 2881 V 2274 2753 a Ft(\045)2324 2768 y Fp(I)2364 2753 y Fu(\()p Ft(\033)t Fu(\))1080 b(\(3.2\))0 3027 y(in)32 b(whic)m(h)76 3272 y Fr(I)130 3287 y Fp(k)200 3272 y Fu(:=)331 3131 y Fo(\032)406 3272 y Ft(I)p 406 3288 51 4 v 35 w Fr(\021)589 3191 y Fo(\010)648 3272 y Ft(I)691 3287 y Fs(1)730 3272 y Ft(;)17 b(:)g(:)g(:)f(;)h(I)992 3287 y Fp(k)1034 3191 y Fo(\011)1137 3272 y Fu(:)50 b Ft(I)1257 3287 y Fp(h)1329 3272 y Fr(\032)28 b Ft(N)f(;)39 b(h)28 b Fr(6)p Fu(=)g Ft(h)1849 3231 y Fn(0)1900 3272 y Fr(\))f Ft(I)2070 3287 y Fp(h)2142 3272 y Fr(6)p Fu(=)h Ft(I)2289 3287 y Fp(h)2330 3268 y Fi(0)2373 3272 y Ft(;)2485 3147 y Fp(k)2449 3177 y Fo([)2439 3389 y Fp(h)p Fs(=1)2586 3272 y Ft(I)2629 3287 y Fp(h)2702 3272 y Fu(=)f Ft(N)g(;)39 b(I)p 2976 3288 V 57 w Fu(is)32 b(connected)3629 3131 y Fo(\033)3579 3482 y Fu(\(3.3\))0 3627 y(where)44 b Ft(I)p 292 3643 V 50 w Fu(connected)h(means)e(that)f(for)g(eac)m(h)i (pair)d Ft(I)8 b(;)17 b(I)2126 3591 y Fn(0)2192 3627 y Fu(in)42 b Ft(I)p 2316 3643 V 50 w Fu(there)i(exists)f(a)f(sequence)k Ft(J)3508 3642 y Fp(q)3591 3627 y Fr(2)f Ft(I)p 3702 3643 V 8 w Fu(,)0 3771 y Ft(q)35 b Fu(=)30 b(0)p Ft(;)17 b(:)g(:)g(:)f(;)h(m)p Fu(,)35 b(suc)m(h)h(that)e Ft(I)39 b Fu(=)30 b Ft(J)1276 3786 y Fs(0)1316 3771 y Fu(,)35 b Ft(J)1432 3786 y Fp(m)1529 3771 y Fu(=)c Ft(I)1687 3735 y Fn(0)1710 3771 y Fu(,)k(and)f Ft(J)2017 3786 y Fp(q)r Fn(\000)p Fs(1)2169 3771 y Fr(\\)24 b Ft(J)2313 3786 y Fp(q)2381 3771 y Fr(6)p Fu(=)31 b Fr(;)p Fu(,)k Ft(q)f Fu(=)d(1)p Ft(;)17 b(:)g(:)g(:)f(;)h(m)p Fu(.)49 b(W)-8 b(e)35 b(note)f(that)0 3916 y(for)e Ft(k)f(>)c Fu(2)383 3880 y Fp(n)463 3916 y Fu(w)m(e)33 b(ha)m(v)m(e)h Fr(I)885 3931 y Fp(k)956 3916 y Fu(=)27 b Fr(;)p Fu(.)p Black 0 4106 a Fv(Lemma)37 b(3.1.)p Black 42 w Fk(If)d Fu(d\(\003)875 4121 y Fp(i)903 4106 y Ft(;)17 b Fu(\003)1015 4121 y Fp(j)1051 4106 y Fu(\))28 b Ft(>)f(r)38 b Fk(for)d(any)f Ft(i)28 b Fr(6)p Fu(=)g Ft(j)34 b Fr(2)28 b Ft(N)45 b Fk(then)35 b(for)f(e)-5 b(ach)35 b Ft(\034)k Fr(2)28 b(S)2927 4121 y Fs(\003)2976 4102 y Fj(c)3046 4106 y Fk(we)35 b(have)733 4306 y Ft(\026)792 4265 y Fp(\034)792 4330 y Fs(\003)845 4225 y Fo(\000)891 4306 y Ft(f)939 4321 y Fs(1)978 4306 y Fu(;)17 b Fr(\001)g(\001)g(\001)32 b Fu(;)17 b Ft(f)1264 4321 y Fp(n)1310 4225 y Fo(\001)1384 4306 y Fu(=)1533 4211 y Fo(X)1487 4423 y Fp(\033)r Fn(2S)1619 4434 y Fj(\003)1660 4451 y Fl(N)1743 4211 y Fo(Y)1740 4423 y Fp(i)p Fn(2)p Fp(N)1890 4225 y Fo(\002)1932 4306 y Ft(\026)1991 4265 y Fp(\034)1991 4330 y Fs(\003;\003)2109 4340 y Fl(i)2138 4306 y Fu(\()p Ft(\033)2231 4321 y Fs(\003)2280 4331 y Fl(i)2311 4306 y Fu(\))p Ft(f)2397 4321 y Fp(i)2425 4306 y Fu(\()p Ft(\033)2518 4321 y Fs(\003)2567 4331 y Fl(i)2598 4306 y Fu(\))2636 4225 y Fo(\003)2700 4306 y Ft(\045)2750 4265 y Fs(\(\003\))2858 4306 y Fu(\()p Ft(\033)t(\034)11 b Fu(\))533 b(\(3.4\))0 4594 y Fk(In)34 b(p)-5 b(articular)1051 4670 y Fo(\014)1051 4730 y(\014)1051 4789 y(\014)1085 4784 y Ft(\026)1144 4743 y Fp(\034)1144 4809 y Fs(\003)1196 4704 y Fo(\000)1242 4784 y Ft(f)1290 4799 y Fs(1)1330 4784 y Fu(;)17 b Fr(\001)g(\001)g(\001)31 b Fu(;)17 b Ft(f)1615 4799 y Fp(n)1661 4704 y Fo(\001)1707 4670 y(\014)1707 4730 y(\014)1707 4789 y(\014)1768 4784 y Fr(\024)1873 4700 y Fo(\015)1873 4760 y(\015)1928 4784 y Ft(\045)1978 4743 y Fs(\(\003\))2087 4700 y Fo(\015)2087 4760 y(\015)2142 4823 y Fn(1)2292 4660 y Fp(n)2250 4690 y Fo(Y)2257 4900 y Fp(i)p Fs(=1)2394 4784 y Ft(\026)2453 4743 y Fp(\034)2453 4809 y Fs(\003)2506 4704 y Fo(\000)2551 4784 y Fr(j)p Ft(f)2627 4799 y Fp(i)2655 4784 y Fr(j)2683 4704 y Fo(\001)3579 4784 y Fu(\(3.5\))0 5038 y Fk(Pr)-5 b(o)g(of.)35 b Fu(F)-8 b(or)35 b(\003)e Fr(2)h Fq(F)6 b Fu(,)43 b Ft(F)k Fr(2)33 b(F)1077 5053 y Fs(\003)1126 5064 y Fl(F)1181 5038 y Fu(,)k(with)e(\003)1538 5053 y Fp(F)1630 5038 y Fr(\032)e Fu(\003,)k(and)f Ft(\034)45 b Fr(2)33 b(S)2311 5053 y Fs(\003)2360 5034 y Fj(c)2396 5038 y Fu(,)k(b)m(y)f(using)g(the)g(de\014nition)f(\(2.3\))g(of)0 5183 y(the)e(Gibbs)f(state,)h(w)m(e)h(get)724 5412 y Ft(\026)783 5370 y Fp(\034)783 5436 y Fs(\003)835 5412 y Fu(\()p Ft(F)14 b Fu(\))28 b(=)1162 5317 y Fo(X)1119 5528 y Fp(\033)r Fn(2S)1251 5539 y Fj(\003)1292 5556 y Fl(F)1375 5341 y Ft(Z)1442 5356 y Fs(\003)p Fn(n)p Fs(\003)1575 5367 y Fl(F)1630 5341 y Fu(\()p Ft(\033)t(\034)11 b Fu(\))p 1375 5389 444 4 v 1472 5480 a Ft(Z)1539 5495 y Fs(\003)1592 5480 y Fu(\()p Ft(\034)g Fu(\))1861 5412 y(exp)2027 5271 y Fo(\032)2195 5317 y(X)2134 5520 y Fl(X)t Fi(\\)p Fj(\003)2271 5537 y Fl(F)2321 5520 y Fi(6)p Fj(=)p Fi(;)2128 5580 y Fl(X)t Fi(\\)p Fj(\003)p Fi(\032)p Fj(\003)2354 5597 y Fl(F)2431 5412 y Ft(U)2497 5427 y Fp(X)2565 5412 y Fu(\()p Ft(\033)t(\034)g Fu(\))2753 5271 y Fo(\033)2845 5412 y Ft(F)j Fu(\()p Ft(\033)t Fu(\))p Black 1841 5806 a(10)p Black eop %%Page: 11 12 11 11 bop Black Black 0 407 a Fu(By)30 b(using)f(\(2.8\),)h(the)g(h)m (yp)s(otheses)h(d\(\003)1478 422 y Fp(i)1507 407 y Ft(;)17 b Fu(\003)1619 422 y Fp(j)1654 407 y Fu(\))28 b Ft(>)g(r)s Fu(,)h(and)h(that)f Ft(D)p 2322 423 84 4 v 32 w Fu(is)g(a)g(partition)f (of)h Ft(N)10 b Fu(,)30 b(w)m(e)h(th)m(us)f(\014nd)191 700 y Ft(\026)250 659 y Fp(\034)250 725 y Fs(\003)303 619 y Fo(\000)349 700 y Ft(f)397 715 y Fs(1)436 700 y Fu(;)17 b Fr(\001)g(\001)g(\001)31 b Fu(;)17 b Ft(f)721 715 y Fp(n)768 619 y Fo(\001)841 700 y Fu(=)1063 605 y Fo(X)1017 817 y Fp(\033)r Fn(2S)1149 828 y Fj(\003)1190 845 y Fl(N)1312 575 y Fp(n)1269 605 y Fo(Y)1276 815 y Fp(i)p Fs(=1)1413 559 y Fo(\024)1476 619 y Ft(Z)1543 634 y Fp(V)1584 648 y Fi(f)p Fl(i)p Fi(g)1678 619 y Fu(\()p Ft(\033)t(\034)11 b Fu(\))p 1476 677 391 4 v 1546 768 a Ft(Z)1613 783 y Fs(\003)1666 768 y Fu(\()p Ft(\034)g Fu(\))1893 700 y(exp)2058 559 y Fo(\032)2214 605 y(X)2165 809 y Fl(X)t Fi(\\)p Fj(\003)2302 825 y Fl(i)2328 809 y Fi(6)p Fj(=)p Fi(;)2160 868 y Fl(X)t Fi(\\)p Fj(\003)p Fi(\032)p Fj(\003)2386 883 y Fl(i)2439 700 y Ft(U)2505 715 y Fp(X)2572 700 y Fu(\()p Ft(\033)t(\034)g Fu(\))2760 559 y Fo(\033)2852 700 y Ft(f)2900 715 y Fp(i)2928 700 y Fu(\()p Ft(\033)t Fu(\))3063 559 y Fo(\025)1133 1084 y Fr(\002)1283 959 y Fp(n)1233 989 y Fo(X)1245 1201 y Fp(`)p Fs(=1)1377 1084 y Fu(\()p Fr(\000)p Fu(1\))1579 1043 y Fp(`)p Fn(\000)p Fs(1)1702 1084 y Fu(\()p Ft(`)22 b Fr(\000)h Fu(1\)!)2071 989 y Fo(X)2034 1213 y Fp(D)p 2033 1225 60 3 v 1 w Fn(2D)2197 1190 y Fl(`)2195 1236 y(N)2319 959 y Fp(`)2270 989 y Fo(Y)2269 1201 y Fp(k)r Fs(=1)2424 1002 y Ft(Z)2491 1017 y Fp(V)2532 1028 y Fl(D)2582 1045 y(k)2628 1002 y Fu(\()p Ft(\033)t(\034)11 b Fu(\))2816 921 y Fo(\002)2858 1002 y Ft(Z)2925 1017 y Fs(\003)2978 1002 y Fu(\()p Ft(\034)g Fu(\))3107 921 y Fo(\003)3149 943 y Fn(j)p Fp(D)3227 955 y Fl(k)3264 943 y Fn(j\000)p Fs(1)p 2424 1061 955 4 v 2565 1078 a Fo(Q)2659 1181 y Fp(i)p Fn(2)p Fp(D)2788 1193 y Fl(k)2847 1152 y Ft(Z)2914 1167 y Fp(V)2955 1181 y Fi(f)p Fl(i)p Fi(g)3049 1152 y Fu(\()p Ft(\033)t(\034)g Fu(\))3579 911 y(\(3.6\))146 1406 y(W)-8 b(e)33 b(therefore)g(need)h(to)e(sho)m(w)i(that)891 1680 y Ft(\045)941 1639 y Fs(\(\003\))1077 1680 y Fu(=)1231 1555 y Fp(n)1180 1585 y Fo(X)1193 1797 y Fp(`)p Fs(=1)1324 1680 y Fu(\()p Fr(\000)p Fu(1\))1526 1639 y Fp(`)p Fn(\000)p Fs(1)1650 1680 y Fu(\()p Ft(`)22 b Fr(\000)g Fu(1\)!)2018 1585 y Fo(X)1981 1809 y Fp(D)p 1981 1821 60 3 v 2 w Fn(2D)2145 1786 y Fl(`)2143 1832 y(N)2266 1555 y Fp(`)2217 1585 y Fo(Y)2216 1797 y Fp(k)r Fs(=1)2372 1598 y Ft(Z)2439 1613 y Fp(V)2480 1624 y Fl(D)2530 1641 y(k)2576 1598 y Ft(Z)2650 1547 y Fn(j)p Fp(D)2728 1559 y Fl(k)2765 1547 y Fn(j\000)p Fs(1)2643 1625 y(\003)p 2372 1657 508 4 v 2383 1674 a Fo(Q)2478 1777 y Fp(i)p Fn(2)p Fp(D)2607 1789 y Fl(k)2665 1748 y Ft(Z)2732 1763 y Fp(V)2773 1777 y Fi(f)p Fl(i)p Fi(g)3579 1680 y Fu(\(3.7\))0 2008 y(Let)33 b Ft(I)i Fr(\032)28 b Ft(N)10 b Fu(,)34 b Fr(j)p Ft(I)8 b Fr(j)26 b(\025)j Fu(2,)j(b)m(y)h(\(3.1\))g(w)m(e)g(ha)m(v)m(e)h(the)f (follo)m(wing)d(c)m(hain)i(of)g(iden)m(tities)186 2203 y Fo(X)191 2414 y Fp(J)6 b Fn(\032)p Fp(I)347 2298 y Fu(log)16 b Ft(R)563 2313 y Fp(J)696 2298 y Fu(=)887 2203 y Fo(X)900 2403 y Fl(J)5 b Fi(\032)p Fl(I)881 2460 y Fi(j)p Fl(J)g Fi(j\025)p Fj(2)1073 2203 y Fo(X)1063 2414 y Fp(K)g Fn(\032)p Fp(J)1226 2298 y Fu(\()p Fr(\000)p Fu(1\))1428 2257 y Fn(j)p Fp(J)h Fn(j\000j)p Fp(K)f Fn(j)1692 2298 y Fu(log)16 b Ft(Z)1901 2313 y Fp(V)1942 2324 y Fl(K)2033 2298 y Fu(=)2142 2203 y Fo(X)2136 2414 y Fp(K)5 b Fn(\032)p Fp(I)2389 2203 y Fo(X)2318 2403 y Fl(J)g Fj(:)k Fl(I)t Fi(\033)p Fl(J)c Fi(\033)p Fl(K)2384 2460 y Fi(j)p Fl(J)g Fi(j\025)p Fj(2)2615 2298 y Fu(\()p Fr(\000)p Fu(1\))2817 2257 y Fn(j)p Fp(J)h Fn(j\000j)p Fp(K)f Fn(j)3080 2298 y Fu(log)16 b Ft(Z)3289 2313 y Fp(V)3330 2324 y Fl(K)696 2708 y Fu(=)906 2576 y Fn(j)p Fp(I)5 b Fn(j)871 2614 y Fo(X)879 2826 y Fp(k)r Fs(=0)1056 2614 y Fo(X)1061 2814 y Fl(K)s Fi(\032)p Fl(I)1042 2870 y Fi(j)p Fl(K)s Fi(j)p Fj(=)p Fl(k)1258 2708 y Fu(log)16 b Ft(Z)1467 2723 y Fp(V)1508 2734 y Fl(K)1654 2576 y Fn(j)p Fp(I)5 b Fn(j)1620 2614 y Fo(X)1588 2826 y Fp(j)t Fs(=2)p Fn(_)p Fp(k)1796 2708 y Fu(\()p Fr(\000)p Fu(1\))1998 2667 y Fp(j)t Fn(\000)p Fp(k)2128 2568 y Fo(\022)2201 2641 y Fr(j)p Ft(I)j Fr(j)21 b(\000)i Ft(k)2231 2777 y(j)28 b Fr(\000)23 b Ft(k)2483 2568 y Fo(\023)696 3037 y Fu(=)99 b(log)17 b Ft(Z)1081 3052 y Fp(V)1122 3063 y Fl(I)1183 3037 y Fu(+)22 b(\()p Fr(j)p Ft(I)8 b Fr(j)22 b(\000)g Fu(1\))17 b(log)f Ft(Z)1860 3052 y Fs(\003)1935 3037 y Fr(\000)2035 2942 y Fo(X)2053 3154 y Fp(i)p Fn(2)p Fp(I)2195 3037 y Fu(log)h Ft(Z)2405 3052 y Fp(V)2446 3066 y Fi(f)p Fl(i)p Fi(g)3579 2671 y Fu(\(3.8\))0 3341 y(Therefore,)34 b(giv)m(en)e Ft(D)p 723 3357 84 4 v 31 w Fr(2)c(D)1009 3305 y Fp(`)1006 3366 y(N)1106 3341 y Fu(and)k Ft(k)f Fr(2)d(f)p Fu(1)p Ft(;)17 b(:)g(:)g(:)e(;)i(`)p Fr(g)32 b Fu(w)m(e)i(ha)m(v)m(e)1083 3546 y Fo(Y)1049 3757 y Fp(J)6 b Fn(\032)p Fp(D)1207 3769 y Fl(k)1245 3640 y Fu(\(1)22 b(+)g Ft(\045)1502 3655 y Fp(J)1551 3640 y Fu(\))28 b(=)1754 3546 y Fo(Y)1720 3757 y Fp(J)6 b Fn(\032)p Fp(D)1878 3769 y Fl(k)1932 3640 y Ft(R)2006 3655 y Fp(J)2083 3640 y Fu(=)2197 3558 y Ft(Z)2264 3573 y Fp(V)2305 3584 y Fl(D)2355 3602 y(k)2417 3558 y Ft(Z)2491 3507 y Fn(j)p Fp(D)2569 3519 y Fl(k)2607 3507 y Fn(j\000)p Fs(1)2484 3585 y(\003)p 2197 3618 525 4 v 2217 3634 a Fo(Q)2311 3738 y Fp(i)p Fn(2)p Fp(D)2440 3750 y Fl(k)2499 3709 y Ft(Z)2566 3724 y Fp(V)2607 3738 y Fi(f)p Fl(i)p Fi(g)3579 3640 y Fu(\(3.9\))0 3945 y(Hence,)34 b(form)m(ula)d(\(3.7\))h (follo)m(ws)f(from)g(\(3.9\))h(and)h(the)g(follo)m(wing)d(iden)m(tit)m (y)868 4241 y Ft(\045)918 4200 y Fs(\(\003\))1054 4241 y Fu(=)1208 4116 y Fp(n)1158 4146 y Fo(X)1170 4358 y Fp(`)p Fs(=1)1302 4241 y Fu(\()p Fr(\000)p Fu(1\))1504 4200 y Fp(`)p Fn(\000)p Fs(1)1627 4241 y Fu(\()p Ft(`)22 b Fr(\000)g Fu(1\)!)1996 4146 y Fo(X)1958 4370 y Fp(D)p 1958 4382 60 3 v 2 w Fn(2D)2122 4347 y Fl(`)2120 4393 y(N)2260 4116 y Fp(`)2211 4146 y Fo(Y)2210 4358 y Fp(k)r Fs(=1)2406 4146 y Fo(Y)2372 4358 y Fp(J)6 b Fn(\032)p Fp(D)2530 4370 y Fl(k)2568 4241 y Fu(\(1)22 b(+)g Ft(\045)2825 4256 y Fp(J)2874 4241 y Fu(\))619 b(\(3.10\))0 4568 y(where)34 b Ft(\045)332 4584 y Fn(;)399 4568 y Fu(=)28 b(0)k(\(w)m(e)i(also)d(ha) m(v)m(e)j Ft(\045)1236 4584 y Fn(f)p Fp(i)p Fn(g)1363 4568 y Fu(=)27 b(0)33 b(but)g(this)f(will)e(not)i(b)s(e)h(used)h(in)e (the)h(pro)s(of)f(of)g(\(3.10\)\).)146 4713 y(T)-8 b(o)33 b(pro)m(v)m(e)h(\(3.10\),)e(w)m(e)h(de\014ne)724 4915 y Fo(e)718 4940 y Fr(I)772 4955 y Fp(k)843 4940 y Fu(:=)973 4829 y Fo(n)1040 4940 y Ft(I)p 1040 4956 51 4 v 35 w Fr(\021)1223 4859 y Fo(\010)1281 4940 y Ft(I)1324 4955 y Fs(1)1364 4940 y Ft(;)17 b(:)g(:)g(:)f(;)h(I)1626 4955 y Fp(k)1668 4859 y Fo(\011)1770 4940 y Fu(:)56 b Ft(I)1896 4955 y Fp(h)1968 4940 y Fr(\032)29 b Ft(N)e(;)39 b(h)27 b Fr(6)p Fu(=)h Ft(h)2488 4899 y Fn(0)2539 4940 y Fr(\))f Ft(I)2709 4955 y Fp(h)2782 4940 y Fr(6)p Fu(=)g Ft(I)2928 4955 y Fp(h)2969 4936 y Fi(0)2996 4829 y Fo(o)0 5167 y Fu(b)m(y)33 b(expanding)g(the)g(pro)s(ducts)h(on)e(the)h(righ)m(t)f (hand)h(side)f(of)g(\(3.10\))g(w)m(e)i(get)e(that)h(it)e(is)h(equal)h (to)992 5321 y Fp(n)942 5351 y Fo(X)954 5563 y Fp(`)p Fs(=1)1086 5446 y Fu(\()p Fr(\000)p Fu(1\))1288 5405 y Fp(`)p Fn(\000)p Fs(1)1411 5446 y Fu(\()p Ft(`)22 b Fr(\000)h Fu(1\)!)1726 5361 y Fo(\014)1726 5421 y(\014)1759 5446 y Fr(D)1839 5405 y Fp(`)1836 5471 y(N)1903 5361 y Fo(\014)1903 5421 y(\014)1958 5446 y Fu(+)2056 5351 y Fo(X)2064 5563 y Fp(k)r Fn(\025)p Fs(1)2224 5351 y Fo(X)2217 5582 y Fp(I)p 2217 5594 36 3 v 4 w Fn(2)2303 5565 y Fg(e)2299 5582 y Fn(I)2338 5594 y Fl(k)2393 5446 y Ft(a)p Fu(\()p Ft(I)p 2482 5462 51 4 v 8 w Fu(\))2604 5351 y Fo(Y)2608 5563 y Fp(I)5 b Fn(2)p Fp(I)p 2691 5575 36 3 v 2748 5446 a Ft(\045)2798 5461 y Fp(I)3531 5446 y Fu(\(3.11\))p Black 1841 5806 a(11)p Black eop %%Page: 12 13 12 12 bop Black Black 0 407 a Fu(for)38 b(appropriate)g(co)s(e\016cien) m(ts)i Ft(a)p Fu(\()p Ft(I)p 1276 423 51 4 v 8 w Fu(\))f(whic)m(h)g (can)g(b)s(e)g(computed)g(as)g(follo)m(ws.)61 b(Let)39 b Ft(d)3204 371 y Fp(`)3204 431 y(n)3289 407 y Fu(:=)3430 322 y Fo(\014)3430 382 y(\014)3464 407 y Fr(D)3544 371 y Fp(`)3541 432 y(N)3608 322 y Fo(\014)3608 382 y(\014)3680 407 y Fu(b)s(e)0 551 y(the)i(n)m(um)m(b)s(er)h(of)e(partitions)g(in)m (to)g Ft(`)h Fu(atoms)f(of)g Ft(N)10 b Fu(;)46 b(w)m(e)c(understand)g (that)f Ft(d)2918 515 y Fp(`)2918 576 y(n)3007 551 y Fu(=)h(0)e(if)g Ft(`)i Fr(\025)g Ft(n)28 b Fu(+)g(1.)0 696 y(Giv)m(en)j Ft(I)p 281 712 V 36 w Fr(2)460 671 y Fo(e)454 696 y Fr(I)508 711 y Fp(k)582 696 y Fu(let)g(us)h(decomp)s (ose)g(it)e(in)m(to)h(maximal)d(connected)33 b(comp)s(onen)m(ts)f Fr(C)3068 711 y Fs(1)3108 696 y Ft(;)17 b(:)g(:)g(:)f(;)h Fr(C)3379 711 y Fp(h)3455 696 y Fu(namely)-8 b(,)0 840 y Ft(I)p 0 856 V 36 w Fu(=)182 765 y Fo(S)265 792 y Fp(h)265 869 y(m)p Fs(=1)439 840 y Fr(C)491 855 y Fp(m)590 840 y Fu(where)34 b(eac)m(h)g Fr(C)1144 855 y Fp(m)1244 840 y Fu(is)e(connected)i(and)f(for)f(an)m(y)h(pair)f Ft(I)k Fr(2)28 b(C)2746 855 y Fp(m)2813 840 y Fu(,)33 b Ft(J)k Fr(2)28 b(C)3110 855 y Fp(m)3172 836 y Fi(0)3232 840 y Fu(with)k Ft(m)d Fr(6)p Fu(=)e Ft(m)3756 804 y Fn(0)0 985 y Fu(w)m(e)34 b(ha)m(v)m(e)g Ft(I)c Fr(\\)22 b Ft(J)37 b Fu(=)27 b Fr(;)p Fu(;)33 b(let)f(also)1186 959 y Fo(e)1170 985 y Fr(C)1222 1000 y Fp(m)1317 985 y Fu(:=)1448 910 y Fo(S)1531 1014 y Fp(I)5 b Fn(2C)1651 1022 y Fl(m)1730 985 y Ft(I)36 b Fr(\032)28 b Ft(N)43 b Fu(and)33 b Ft(c)2267 1000 y Fp(m)2361 985 y Fu(:=)2492 900 y Fo(\014)2492 960 y(\014)2540 959 y(e)2525 985 y Fr(C)2577 1000 y Fp(m)2644 900 y Fo(\014)2644 960 y(\014)2677 985 y Fu(.)44 b(Then)55 1231 y Ft(a)p Fu(\()p Ft(I)p 144 1247 V 8 w Fu(\))83 b(=)g Ft(a)p Fu(\()p Fr(C)616 1246 y Fs(1)656 1231 y Ft(;)17 b(:)g(:)g(:)e(;)i Fr(C)926 1246 y Fp(h)971 1231 y Fu(\))316 1437 y(=)542 1313 y Fp(n)491 1343 y Fo(X)504 1555 y Fp(`)p Fs(=1)635 1437 y Fu(\()p Fr(\000)p Fu(1\))837 1396 y Fp(`)p Fn(\000)p Fs(1)960 1437 y Fu(\()p Ft(`)22 b Fr(\000)h Fu(1\)!)1292 1293 y Fo(\014)1292 1353 y(\014)1292 1413 y(\014)1292 1472 y(\014)1325 1327 y(n)1391 1437 y Ft(D)p 1391 1453 84 4 v 30 w Fr(2)29 b(D)1677 1396 y Fp(`)1674 1462 y(N)1785 1437 y Fu(:)55 b Fr(8)p Ft(m)29 b Fu(=)e(1)p Ft(;)17 b(:)g(:)g(:)f(;)h(h)55 b Fr(9)p Ft(j)c Fr(2)28 b(f)p Fu(1)p Ft(;)17 b(:)g(:)g(:)e(;)i(`)p Fr(g)27 b Fu(:)45 b Ft(D)3346 1452 y Fp(j)3410 1437 y Fr(\033)3530 1412 y Fo(e)3515 1437 y Fr(C)3567 1452 y Fp(m)3634 1357 y Fo(\011)3692 1293 y(\014)3692 1353 y(\014)3692 1413 y(\014)3692 1472 y(\014)316 1728 y Fu(=)542 1604 y Fp(n)491 1633 y Fo(X)504 1846 y Fp(`)p Fs(=1)635 1728 y Fu(\()p Fr(\000)p Fu(1\))837 1687 y Fp(`)p Fn(\000)p Fs(1)960 1728 y Fu(\()p Ft(`)22 b Fr(\000)h Fu(1\)!)17 b Ft(d)1343 1687 y Fp(`)1343 1753 y(n)p Fs(+)p Fp(h)p Fn(\000)p Fs(\()p Fp(c)1595 1762 y Fj(1)1628 1753 y Fs(+)p Fn(\001\001\001)o Fs(+)p Fp(c)1828 1765 y Fl(h)1867 1753 y Fs(\))0 2051 y Fu(W)-8 b(e)39 b(note)g(that)g(the)g(recursion)h (relation)d Ft(d)1629 2015 y Fs(1)1629 2075 y(1)1706 2051 y Fu(=)i(1)f(and)h Ft(d)2155 2015 y Fp(`)2155 2075 y(i)p Fs(+1)2312 2051 y Fu(=)f Ft(d)2477 2010 y Fp(`)p Fn(\000)p Fs(1)2477 2076 y Fp(i)2626 2051 y Fu(+)27 b Ft(`)17 b(d)2838 2015 y Fp(`)2838 2075 y(i)2870 2051 y Fu(,)41 b(with)d Ft(i;)17 b(`)39 b Fu(=)f(1)p Ft(;)17 b Fu(2)p Ft(;)g(:)g(:)g(:)e Fu(,)0 2195 y(holds.)69 b(Suc)m(h)42 b(relation)d(implies)g(that)h(the)i(\014rst)f(term)g(in)f(\(3.11\))g(v) -5 b(anishes)42 b(\(recall)e(that)g Ft(n)j Fr(\025)f Fu(2\).)0 2340 y(Moreo)m(v)m(er,)i(for)c(the)h(same)f(reason,)j(w)m(e)e (ha)m(v)m(e)h(that)e Ft(a)p Fu(\()p Ft(I)p 2083 2356 51 4 v 8 w Fu(\))h(=)g(1)g(if)e Ft(h)i Fu(=)g(1)f(and)h Ft(c)3060 2355 y Fs(1)3140 2340 y Fu(=)g Ft(n)g Fu(namely)-8 b(,)41 b(if)0 2484 y Ft(I)p 0 2500 V 49 w Fr(2)g(I)253 2499 y Fp(k)296 2484 y Fu(,)h(and)e Ft(a)p Fu(\()p Ft(I)p 651 2500 V 8 w Fu(\))h(=)g(0)f(otherwise.)67 b(Recalling)38 b(\(3.2\),)j(w)m(e)h(ha)m(v)m(e)f(th)m(us)h(completed)d(the)i(pro)s(of) e(of)0 2629 y(\(3.10\).)p 3709 2629 4 66 v 3713 2566 59 4 v 3713 2629 V 3771 2629 4 66 v 146 2823 a(The)23 b(next)h(Lemma)c(states)j(that)f(eac)m(h)i Ft(\045)1611 2838 y Fp(I)1673 2823 y Fu(has)f(an)f(exp)s(onen)m(tial)f(deca)m(y)j (with)e(the)g(tree)h(in)m(tersecting)0 2967 y(eac)m(h)33 b(\003)287 2982 y Fp(i)315 2967 y Fu(,)g Ft(i)28 b Fr(2)g Ft(I)8 b Fu(.)43 b(Giv)m(en)33 b Ft(I)i Fu(=)28 b Fr(f)p Ft(h)1222 2982 y Fs(1)1261 2967 y Ft(;)17 b(:)g(:)g(:)f(;)h(h)1536 2983 y Fn(j)p Fp(I)5 b Fn(j)1615 2967 y Fr(g)28 b(\032)g Ft(N)10 b Fu(,)33 b(w)m(e)g(de\014ne)613 3222 y Ft(T)14 b Fu(\()p Ft(I)8 b Fu(\))28 b(:=)f(inf)1104 3111 y Fo(n)1170 3222 y Fq(T)1233 3141 y Fo(\000)1282 3222 y Fr(f)p Ft(x)1387 3237 y Fs(1)1427 3222 y Ft(;)17 b(:)g(:)g(:)f(;)h(x)1701 3237 y Fn(j)p Fp(I)5 b Fn(j)1780 3222 y Fr(g)1830 3141 y Fo(\001)1876 3222 y Ft(;)33 b(x)1991 3237 y Fp(j)2056 3222 y Fr(2)28 b Fu(\003)2218 3237 y Fp(h)2259 3247 y Fl(j)2327 3222 y Fu(with)k Ft(j)i Fu(=)28 b(1)p Ft(;)17 b(:)g(:)g(:)e(;)i Fr(j)p Ft(I)8 b Fr(j)3101 3111 y Fo(o)3531 3222 y Fu(\(3.12\))0 3466 y(and)33 b(note)f(that)h Ft(T)14 b Fu(\()p Ft(N)c Fu(\))28 b Fr(\025)g(T)d Fu(\()p Ft(f)1151 3481 y Fs(1)1191 3466 y Fu(;)17 b Ft(:)g(:)g(:)f Fu(;)h Ft(f)1458 3481 y Fp(n)1504 3466 y Fu(\).)p Black 0 3694 a Fv(Lemma)38 b(3.2.)p Black 42 w Fk(L)-5 b(et)35 b Ft(L)29 b Fr(2)g Fq(N)9 b Fk(,)41 b(assume)35 b(that)g(for)g(e)-5 b(ach)35 b Fu(\003)28 b Fr(2)h Fq(F)2272 3709 y Fp(L)2365 3694 y Fk(and)35 b Ft(\034)40 b Fr(2)29 b(S)43 b Fk(we)35 b(have)f(the)i(exp)-5 b(ansion)0 3838 y(\(2.10\))34 b(as)g(in)h(The)-5 b(or)g(em)34 b(2.1)g(and)g(the)h(b)-5 b(ound)35 b(\(2.11\))f(holds.)44 b(Set)34 b Ft(\022)2534 3854 y Fn(;)2602 3838 y Fu(:=)28 b Ft(\022)2778 3854 y Fn(f)p Fp(i)p Fn(g)2905 3838 y Fu(:=)f(0)35 b Fk(and)875 4123 y Ft(\022)920 4138 y Fp(I)988 4123 y Fu(:=)27 b Ft(C)j Fu(2)1267 4081 y Fn(j)p Fp(I)5 b Fn(j)1384 4123 y Fu(inf)1390 4184 y Fp(i)p Fn(2)p Fp(I)1519 4123 y Fr(j)p Fu(\003)1615 4138 y Fp(i)1642 4123 y Fr(j)39 b Fu(exp)1874 3982 y Fo(\032)1971 4123 y Fr(\000)2071 4012 y Fo(h)2118 4123 y Ft(a)22 b Fu(+)2417 4055 y Ft(b)p 2299 4100 277 4 v 2299 4191 a Fr(j)p Ft(I)8 b Fr(j)22 b(\000)g Fu(1)2586 4012 y Fo(i)2633 4123 y Ft(T)14 b Fu(\()p Ft(I)8 b Fu(\))2831 3982 y Fo(\033)3531 4123 y Fu(\(3.13\))0 4400 y Fk(for)35 b Fr(j)p Ft(I)8 b Fr(j)27 b(\025)h Fu(2)p Fk(.)44 b(Then,)34 b(r)-5 b(e)g(c)g(al)5 b(ling)34 b Ft(\045)1237 4415 y Fp(I)1312 4400 y Fk(has)g(b)-5 b(e)g(en)35 b(de\014ne)-5 b(d)33 b(b)-5 b(elow)34 b(\(3.1\),)g(for)h (any)g Ft(I)g Fr(\032)29 b Ft(N)45 b Fk(we)34 b(have)1570 4559 y Fo(\015)1570 4619 y(\015)1626 4644 y Ft(\045)1676 4659 y Fp(I)1716 4559 y Fo(\015)1716 4619 y(\015)1771 4683 y Fn(1)1874 4644 y Fr(\024)28 b Ft(\022)2024 4659 y Fp(I)2092 4644 y Ft(e)2137 4603 y Fp(\022)2170 4614 y Fl(I)3531 4644 y Fu(\(3.14\))0 4888 y Fk(Pr)-5 b(o)g(of.)44 b Fu(By)h(plugging)e(\(2.10\))h(in)m(to)f(de\014nition)h(\(3.1\))g(and) h(understanding)g Ft(\036)2980 4903 y Fp(X)q(;V)3167 4888 y Fu(=)j(0)c(whenev)m(er)p Black 1841 5806 a(12)p Black eop %%Page: 13 14 13 13 bop Black Black 0 407 a Ft(X)30 b Fr(\\)22 b Ft(V)50 b Fu(=)27 b Fr(;)p Fu(,)33 b(w)m(e)g(get)195 715 y(log)16 b Ft(R)411 730 y Fp(I)535 715 y Fu(=)83 b(\()p Fr(\000)p Fu(1\))896 674 y Fn(j)p Fp(I)5 b Fn(j)1026 583 y(j)p Fp(I)g Fn(j)991 621 y Fo(X)1002 831 y Fp(j)t Fs(=0)1135 715 y Fu(\()p Fr(\000)p Fu(1\))1337 674 y Fp(j)1404 621 y Fo(X)1417 821 y Fl(J)g Fi(\032)p Fl(I)1401 877 y Fi(j)p Fl(J)g Fi(j)p Fj(=)p Fl(j)1643 621 y Fo(X)1624 821 y Fl(X)t Fi(\032\032)p Ff(L)1589 877 y Fl(X)t Fi(\\)p Fl(V)1721 894 y(J)1763 877 y Fi(6)p Fj(=)p Fi(;)1868 715 y Ft(\036)1926 730 y Fp(X)q(;V)2046 741 y Fl(J)2120 715 y Fu(=)28 b(\()p Fr(\000)p Fu(1\))2426 674 y Fn(j)p Fp(I)5 b Fn(j)2556 583 y(j)p Fp(I)g Fn(j)2522 621 y Fo(X)2532 831 y Fp(j)t Fs(=0)2666 715 y Fu(\()p Fr(\000)p Fu(1\))2868 674 y Fp(j)2966 621 y Fo(X)2938 821 y Fl(X)t Fi(\032\032)p Ff(L)-13 b Fj(:)2931 877 y Fl(X)t Fi(\\)p Fj(\003)p Fi(6)p Fj(=)p Fi(;)3186 621 y Fo(X)3199 821 y Fl(J)5 b Fi(\032)p Fl(I)3182 877 y Fi(j)p Fl(J)g Fi(j)p Fj(=)p Fl(j)3360 715 y Ft(\036)3418 730 y Fp(X)q(;V)3538 741 y Fl(J)535 1096 y Fu(=)83 b(\()p Fr(\000)p Fu(1\))896 1055 y Fn(j)p Fp(I)5 b Fn(j)997 1002 y Fo(X)991 1213 y Fp(K)g Fn(\032)p Fp(I)1419 1002 y Fo(X)1201 1205 y Fl(X)t Fi(\\)p Fj(\003)p Fi(6)p Fj(=)p Fi(;)p Fl(;)k(X)t Fi(\\)p Fj(\003)1582 1225 y Fl(I)t Fi(n)p Fl(K)1703 1205 y Fj(=)p Fi(;)1277 1284 y Fl(X)t Fi(\\)p Fj(\003)1414 1302 y Fl(k)1452 1284 y Fi(6)p Fj(=)p Fi(;)h(8)p Fl(k)q Fi(2)p Fl(K)1871 964 y Fn(j)p Fp(I)5 b Fn(j)1836 1002 y Fo(X)1847 1212 y Fp(j)t Fs(=0)1980 1096 y Fu(\()p Fr(\000)p Fu(1\))2182 1055 y Fp(j)2249 1002 y Fo(X)2262 1202 y Fl(J)g Fi(\032)p Fl(I)2245 1258 y Fi(j)p Fl(J)g Fi(j)p Fj(=)p Fl(j)2423 1096 y Ft(\036)2481 1111 y Fp(X)q(;V)2601 1122 y Fl(J)535 1504 y Fu(=)83 b(\()p Fr(\000)p Fu(1\))896 1462 y Fn(j)p Fp(I)5 b Fn(j)997 1409 y Fo(X)991 1620 y Fp(K)g Fn(\032)p Fp(I)1419 1409 y Fo(X)1201 1612 y Fl(X)t Fi(\\)p Fj(\003)p Fi(6)p Fj(=)p Fi(;)p Fl(;)k(X)t Fi(\\)p Fj(\003)1582 1633 y Fl(I)t Fi(n)p Fl(K)1703 1612 y Fj(=)p Fi(;)1277 1691 y Fl(X)t Fi(\\)p Fj(\003)1414 1709 y Fl(k)1452 1691 y Fi(6)p Fj(=)p Fi(;)h(8)p Fl(k)q Fi(2)p Fl(K)1871 1371 y Fn(j)p Fp(I)5 b Fn(j)1836 1409 y Fo(X)1847 1619 y Fp(j)t Fs(=0)1980 1504 y Fu(\()p Fr(\000)p Fu(1\))2182 1462 y Fp(j)2254 1409 y Fo(X)2235 1620 y Fp(H)g Fn(\032)p Fp(K)2578 1409 y Fo(X)2591 1609 y Fl(J)g Fi(\032)p Fl(I)2444 1665 y Fi(j)p Fl(J)g Fi(j)p Fj(=)p Fl(j;)10 b(J)5 b Fi(\\)p Fl(K)s Fj(=)p Fl(H)2883 1504 y Ft(\036)2941 1519 y Fp(X)q(;V)3061 1530 y Fl(J)0 1891 y Fu(W)-8 b(e)28 b(no)m(w)h(note)g(that)e(the)i(h)m (yp)s(otheses)h(on)e Ft(\036)1626 1906 y Fp(X)q(;V)1794 1891 y Fu(imply)e(that)i Ft(\036)2328 1906 y Fp(X)q(;V)2495 1891 y Fu(=)g Ft(\036)2657 1906 y Fp(X)q(;V)2792 1887 y Fi(0)2847 1891 y Fu(if)f Ft(X)21 b Fr(\\)13 b Ft(V)3192 1854 y Fs(c)3255 1891 y Fu(=)27 b Ft(X)21 b Fr(\\)13 b Fu(\()p Ft(V)3656 1854 y Fn(0)3679 1891 y Fu(\))3717 1854 y Fs(c)3753 1891 y Fu(.)0 2035 y(Hence)267 2324 y(log)k Ft(R)484 2339 y Fp(I)607 2324 y Fu(=)83 b(\()p Fr(\000)p Fu(1\))968 2283 y Fn(j)p Fp(I)5 b Fn(j)1069 2230 y Fo(X)1064 2441 y Fp(K)g Fn(\032)p Fp(I)1492 2230 y Fo(X)1273 2433 y Fl(X)t Fi(\\)p Fj(\003)p Fi(6)p Fj(=)p Fi(;)p Fl(;)10 b(X)t Fi(\\)p Fj(\003)1655 2453 y Fl(I)t Fi(n)p Fl(K)1776 2433 y Fj(=)p Fi(;)1349 2512 y Fl(X)t Fi(\\)p Fj(\003)1486 2529 y Fl(k)1524 2512 y Fi(6)p Fj(=)p Fi(;)g(8)p Fl(k)q Fi(2)p Fl(K)1928 2230 y Fo(X)1909 2441 y Fp(H)5 b Fn(\032)p Fp(K)2107 2324 y Ft(\036)2165 2339 y Fp(X)q(;V)2285 2350 y Fl(H)2398 2192 y Fn(j)p Fp(I)g Fn(j)2363 2230 y Fo(X)2374 2440 y Fp(j)t Fs(=0)2507 2324 y Fu(\()p Fr(\000)p Fu(1\))2709 2283 y Fp(j)2907 2230 y Fo(X)2911 2430 y Fl(J)g Fi(\032)p Fl(I)t Fj(:)2773 2486 y Fi(j)p Fl(J)g Fi(j)p Fj(=)p Fl(j;)k(J)c Fi(\\)p Fl(K)s Fj(=)p Fl(H)3212 2324 y Fu(1)607 2731 y(=)83 b(\()p Fr(\000)p Fu(1\))968 2690 y Fn(j)p Fp(I)5 b Fn(j)1069 2637 y Fo(X)1064 2848 y Fp(K)g Fn(\032)p Fp(I)1492 2637 y Fo(X)1273 2840 y Fl(X)t Fi(\\)p Fj(\003)p Fi(6)p Fj(=)p Fi(;)p Fl(;)10 b(X)t Fi(\\)p Fj(\003)1655 2860 y Fl(I)t Fi(n)p Fl(K)1776 2840 y Fj(=)p Fi(;)1349 2919 y Fl(X)t Fi(\\)p Fj(\003)1486 2937 y Fl(k)1524 2919 y Fi(6)p Fj(=)p Fi(;)g(8)p Fl(k)q Fi(2)p Fl(K)1928 2637 y Fo(X)1909 2848 y Fp(H)5 b Fn(\032)p Fp(K)2107 2731 y Ft(\036)2165 2746 y Fp(X)q(;V)2285 2757 y Fl(H)2363 2599 y Fn(j)p Fp(I)g Fn(j\000j)p Fp(K)g Fn(j)p Fs(+)p Fn(j)p Fp(H)g Fn(j)2487 2637 y Fo(X)2464 2853 y Fp(j)t Fs(=)p Fn(j)p Fp(H)g Fn(j)2754 2731 y Fu(\()p Fr(\000)p Fu(1\))2956 2690 y Fp(j)2993 2591 y Fo(\022)3066 2664 y Fr(j)p Ft(I)j Fr(j)21 b(\000)i(j)p Ft(K)7 b Fr(j)3097 2800 y Ft(j)28 b Fr(\000)23 b(j)p Ft(H)8 b Fr(j)3439 2591 y Fo(\023)607 3091 y Fu(=)912 2996 y Fo(X)876 3200 y Fl(X)t Fi(\\)p Fj(\003)p Fi(6)p Fj(=)p Fi(;)793 3256 y Fl(X)t Fi(\\)p Fj(\003)930 3272 y Fl(i)956 3256 y Fi(6)p Fj(=)p Fi(;)i(8)p Fl(i)p Fi(2)p Fl(I)1206 2996 y Fo(X)1201 3208 y Fp(H)5 b Fn(\032)p Fp(I)1355 3091 y Fu(\()p Fr(\000)p Fu(1\))1557 3050 y Fn(j)p Fp(I)g Fn(j\000j)p Fp(H)g Fn(j)1793 3091 y Ft(\036)1851 3106 y Fp(X)q(;V)1971 3117 y Fl(H)0 3465 y Fu(where)33 b(w)m(e)g(used)h(that)d(the)i(sum)f(on)g Ft(j)38 b Fu(on)32 b(the)g(second)h(line)e(equals)h(\()p Fr(\000)p Fu(1)22 b(+)f(1\))2909 3429 y Fn(j)p Fp(I)5 b Fn(j\000j)p Fp(K)g Fn(j)3173 3465 y Fu(=)28 b(0)k(for)f Ft(K)k Fr(\032)28 b Ft(I)0 3610 y Fu(and)33 b Ft(K)i Fr(6)p Fu(=)27 b Ft(I)8 b Fu(.)146 3754 y(No)m(w,)39 b(b)m(y)f(using)f(the)h(b)s(ound)f (\(2.11\))g(and)g(the)h(remark)f(that)g(if)f Ft(X)d Fr(\\)26 b Fu(\003)2855 3769 y Fp(i)2918 3754 y Fr(6)p Fu(=)35 b Fr(;)i Fu(for)g(all)e Ft(i)h Fr(2)g Ft(I)45 b Fu(w)m(e)0 3898 y(ha)m(v)m(e)34 b Ft(T)14 b Fu(\()p Ft(I)8 b Fu(\))27 b Fr(\024)h Fu(\()p Fr(j)p Ft(I)8 b Fr(j)21 b(\000)i Fu(1\))33 b(diam)n(\()p Ft(X)8 b Fu(\))33 b(and)f Ft(T)14 b Fu(\()p Ft(I)8 b Fu(\))27 b Fr(\024)i Fq(T)p Fu(\()p Ft(X)8 b Fu(\),)35 b(w)m(e)f(get)688 4080 y Fo(\015)688 4140 y(\015)760 4165 y Fu(log)17 b Ft(R)977 4180 y Fp(I)1017 4080 y Fo(\015)1017 4140 y(\015)1072 4204 y Fn(1)1175 4165 y Fr(\024)28 b Ft(C)h Fu(2)1428 4124 y Fn(j)p Fp(I)5 b Fn(j)1546 4165 y Fu(inf)1551 4227 y Fp(i)p Fn(2)p Fp(I)1680 4165 y Fr(j)p Fu(\003)1776 4180 y Fp(i)1804 4165 y Fr(j)38 b Fu(exp)2036 4024 y Fo(\032)2133 4165 y Fr(\000)2232 4054 y Fo(\020)2292 4165 y Ft(a)22 b Fu(+)2591 4098 y Ft(b)p 2473 4142 277 4 v 2473 4233 a Fr(j)p Ft(I)8 b Fr(j)22 b(\000)g Fu(1)2760 4054 y Fo(\021)2819 4165 y Ft(T)14 b Fu(\()p Ft(I)8 b Fu(\))3017 4024 y Fo(\033)3531 4165 y Fu(\(3.15\))0 4443 y(whic)m(h,)33 b(b)m(y)h(using)e(the)h (inequalit)m(y)e Fr(j)p Ft(e)1390 4407 y Fp(u)1457 4443 y Fr(\000)23 b Fu(1)p Fr(j)k(\024)h Ft(e)1811 4407 y Fn(j)p Fp(u)p Fn(j)1912 4443 y Fr(j)p Ft(u)p Fr(j)p Fu(,)k(implies)e (the)j(b)s(ound)g(\(3.14\).)p 3709 4443 4 66 v 3713 4380 59 4 v 3713 4443 V 3771 4443 4 66 v 146 4587 a(W)-8 b(e)49 b(remark)f(that)f(it)h(is)f(not)h(di\016cult)f(to)h(c)m(hec)m(k)i(that) e(Lemma)f(3.2)h(holds)f(also)h(under)h(the)0 4732 y(condition)31 b(in)h(Remark)g(2.2.)146 4899 y(W)-8 b(e)33 b(can)g(no)m(w)g(pro)m(v)m (e)h(the)f(\014rst)g(part)g(of)f(Theorem)h(2.1.)0 5067 y Fk(Pr)-5 b(o)g(of)36 b(of)f(the)i(b)-5 b(ound)35 b(\(2.12\).)e Fu(Recalling)e Fr(I)1626 5082 y Fp(k)1703 5067 y Fu(has)j(b)s(een)h (de\014ned)g(in)e(\(3.3\),)h(it)e(is)i(easy)h(to)e(sho)m(w)i(that)0 5212 y(for)d(eac)m(h)i Ft(k)c Fr(\025)e Fu(1)33 b(and)f Ft(I)p 826 5228 51 4 v 36 w Fr(2)c(I)1053 5227 y Fp(k)1128 5212 y Fu(w)m(e)34 b(ha)m(v)m(e)787 5371 y Fo(X)799 5582 y Fp(I)5 b Fn(2)p Fp(I)p 882 5594 36 3 v 947 5355 a Fo(\020)1007 5465 y Ft(a)22 b Fu(+)1306 5398 y Ft(b)p 1188 5442 277 4 v 1188 5534 a Fr(j)p Ft(I)8 b Fr(j)21 b(\000)i Fu(1)1475 5355 y Fo(\021)1551 5465 y Ft(T)14 b Fu(\()p Ft(I)8 b Fu(\))27 b Fr(\025)1881 5355 y Fo(\020)1941 5465 y Ft(a)22 b Fu(+)2216 5398 y Ft(b)p 2122 5442 229 4 v 2122 5534 a(n)g Fr(\000)h Fu(1)2361 5355 y Fo(\021)2437 5465 y Fr(T)i Fu(\()p Ft(f)2602 5480 y Fs(1)2642 5465 y Fu(;)17 b Ft(:)g(:)g(:)f Fu(;)h Ft(f)2909 5480 y Fp(n)2955 5465 y Fu(\))538 b(\(3.16\))p Black 1841 5806 a(13)p Black eop %%Page: 14 15 14 14 bop Black Black 0 407 a Fu(Hence)34 b(\(2.12\))e(follo)m(ws)f (from)g(Lemmata)g(3.1)h(and)h(3.2)f(pro)m(vided)h(w)m(e)h(de\014ne)g Ft(K)2971 422 y Fp(n)3050 407 y Fu(as)240 674 y Ft(K)323 689 y Fp(n)370 674 y Fu(\()p Ft(C)7 b Fu(;)17 b Fr(j)p Fu(\003)625 689 y Fs(1)663 674 y Fr(j)p Ft(;)g(:)g(:)g(:)f(;)h Fr(j)p Fu(\003)1006 689 y Fp(n)1052 674 y Fr(j)p Fu(\))27 b(:=)1276 580 y Fo(X)1283 792 y Fp(k)r Fn(\025)p Fs(1)1461 580 y Fo(X)1453 791 y Fp(I)p 1453 803 36 3 v 4 w Fn(2I)1574 803 y Fl(k)1646 580 y Fo(Y)1650 791 y Fp(I)5 b Fn(2)p Fp(I)p 1733 803 V 1790 534 a Fo(\024)1842 674 y Ft(C)24 b Fu(2)1985 633 y Fn(j)p Fp(I)5 b Fn(j)2097 674 y Fu(inf)2102 736 y Fp(i)p Fn(2)p Fp(I)2232 674 y Fr(j)p Fu(\003)2328 689 y Fp(i)2355 674 y Fr(j)33 b Fu(exp)2582 594 y Fo(\010)2640 674 y Ft(C)23 b Fu(2)2782 633 y Fn(j)p Fp(I)5 b Fn(j)2894 674 y Fu(inf)2900 736 y Fp(i)p Fn(2)p Fp(I)3029 674 y Fr(j)p Fu(\003)3125 689 y Fp(i)3153 674 y Fr(j)3181 594 y Fo(\011)3238 534 y(\025)3531 674 y Fu(\(3.17\))0 984 y(whic)m(h)33 b(is)f(\014nite)g(since)h(it)f(is)g(the)h(sum)g(of)f(a)g (\014nite)g(n)m(um)m(b)s(er)h(of)f(terms.)p 3709 984 4 66 v 3713 921 59 4 v 3713 984 V 3771 984 4 66 v 146 1175 a(The)24 b(constan)m(t)f Ft(K)803 1190 y Fp(n)873 1175 y Fu(in)f(\(3.17\))g(is)g(highly)f(non{optimal.)37 b(If)23 b Ft(a)28 b(>)f Fu(0)c(w)m(e)g(can)g(impro)m(v)m(e)f(the)h (estimates)0 1320 y(and)33 b(get)f(\(2.14\).)p Black 0 1539 a Fv(Prop)s(osition)41 b(3.3.)p Black 44 w Fk(Assume)e(c)-5 b(ondition)39 b(\(2.13\))f(holds)g(for)h(some)g Ft(a)d(>)f Fu(0)p Fk(,)40 b Ft(\016)g Fr(2)c Fu(\(0)p Ft(;)17 b Fu(1\))p Fk(.)57 b(R)-5 b(e)g(c)g(al)5 b(ling)0 1683 y Ft(\022)45 1698 y Fp(I)120 1683 y Fk(has)35 b(b)-5 b(e)g(en)34 b(de\014ne)-5 b(d)34 b(in)g(\(3.13\),)g(set)1296 1891 y Fu(\026)1289 1918 y Ft(\022)1334 1933 y Fp(I)1402 1918 y Fu(:=)27 b(exp)1698 1837 y Fo(\010)1756 1918 y Ft(a)17 b Fu(\(1)22 b Fr(\000)g Ft(\016)t Fu(\))17 b Ft(T)d Fu(\()p Ft(I)8 b Fu(\))2332 1837 y Fo(\011)2406 1918 y Ft(\022)2451 1933 y Fp(I)3531 1918 y Fu(\(3.18\))0 2152 y Fk(then,)35 b(r)-5 b(e)g(c)g(al)5 b(ling)33 b Fr(I)685 2167 y Fp(k)763 2152 y Fk(has)i(b)-5 b(e)g(en)34 b(de\014ne)-5 b(d)33 b(in)i(\(3.3\),)1424 2292 y Fo(X)1432 2504 y Fp(k)r Fn(\025)p Fs(1)1609 2292 y Fo(X)1601 2503 y Fp(I)p 1601 2515 36 3 v 5 w Fn(2I)1723 2515 y Fl(k)1794 2292 y Fo(Y)1799 2503 y Fp(I)5 b Fn(2)p Fp(I)p 1882 2515 V 1963 2360 a Fu(\026)1955 2387 y Ft(\022)2000 2402 y Fp(I)2057 2387 y Ft(e)2102 2346 y Fp(\022)2135 2357 y Fl(I)2202 2387 y Fr(\024)28 b Fu(1)1175 b(\(3.19\))146 2696 y(T)-8 b(o)43 b(pro)m(v)m(e)h(Prop)s(osition)d(3.3)i(w)m(e)g (start)g(b)m(y)h(a)e(general)h(result)f(on)h(trees)h(whic)m(h)f(giv)m (es)g(a)g(lo)m(w)m(er)0 2840 y(b)s(ound)33 b(on)f(the)h(n)m(um)m(b)s (er)g(of)f(edges)i(in)e(term)g(of)g(a)g(path)h(connecting)g(all)d(the)j (v)m(ertices.)p Black 0 3059 a Fv(Lemma)46 b(3.4.)p Black 46 w Fk(L)-5 b(et)42 b Ft(I)48 b Fr(\032)41 b Ft(N)52 b Fk(with)42 b Fu(2)e Fr(\024)h(j)p Ft(I)8 b Fr(j)40 b Fu(=)h Ft(k)30 b Fu(+)d(1)42 b Fk(b)-5 b(e)41 b(given)g(by)h Ft(I)49 b Fu(=)40 b Fr(f)p Ft(i)2917 3074 y Fs(0)2956 3059 y Ft(;)17 b(i)3033 3074 y Fs(1)3073 3059 y Ft(;)g(:)g(:)g(:)f(;)h (i)3325 3074 y Fp(k)3367 3059 y Fr(g)p Fk(.)66 b(L)-5 b(et)42 b(us)0 3204 y(denote)37 b(by)h Fu(\005)517 3219 y Fs(0)557 3204 y Fu(\()p Ft(k)s Fu(\))f Fk(the)h(set)g(of)f(p)-5 b(ermutations)38 b Ft(\031)j Fk(of)d Fr(f)p Fu(0)p Ft(;)17 b Fu(1)p Ft(;)g(:)g(:)g(:)e(;)i(k)s Fr(g)37 b Fk(such)h(that)g Ft(\031)t Fu(\(0\))32 b(=)h(0)p Fk(.)53 b(R)-5 b(e)g(c)g(al)5 b(ling)0 3348 y Ft(T)14 b Fu(\()p Ft(I)8 b Fu(\))34 b Fk(has)h(b)-5 b(e)g(en)34 b(de\014ne)-5 b(d)34 b(in)g(\(3.12\),)g(we)g (then)h(have)1118 3652 y Ft(T)14 b Fu(\()p Ft(I)8 b Fu(\))28 b Fr(\025)1459 3585 y Fu(1)p 1459 3629 49 4 v 1459 3721 a(2)1610 3652 y(inf)1534 3719 y Fp(\031)r Fn(2)p Fs(\005)1677 3728 y Fj(0)1711 3719 y Fs(\()p Fp(k)r Fs(\))1874 3528 y Fp(k)1821 3558 y Fo(X)1837 3770 y Fp(l)q Fs(=1)1982 3652 y Fu(d)2036 3572 y Fo(\000)2082 3652 y Fu(\003)2150 3667 y Fp(i)2174 3681 y Fl(\031)r Fj(\()p Fl(l)p Fi(\000)p Fj(1\))2366 3652 y Ft(;)17 b Fu(\003)2478 3667 y Fp(i)2502 3681 y Fl(\031)r Fj(\()p Fl(l)p Fj(\))2616 3572 y Fo(\001)3531 3652 y Fu(\(3.20\))0 3953 y Fk(Pr)-5 b(o)g(of.)29 b Fu(Let)g Ft(X)36 b Fu(=)27 b Fr(f)6 b Fu(\026)-55 b Ft(x)782 3968 y Fp(i)806 3977 y Fj(0)845 3953 y Ft(;)23 b Fu(\026)-55 b Ft(x)944 3968 y Fp(i)968 3977 y Fj(1)1007 3953 y Ft(;)17 b(:)g(:)g(:)f(;)23 b Fu(\026)-55 b Ft(x)1281 3968 y Fp(i)1305 3980 y Fl(k)1348 3953 y Fr(g)p Fu(,)35 b(\026)-55 b Ft(x)1509 3968 y Fp(i)1533 3980 y Fl(h)1606 3953 y Fr(2)28 b Fu(\003)1768 3968 y Fp(i)1792 3980 y Fl(h)1865 3953 y Fu(b)s(e)i(a)f(minimizer)d (for)j(\(3.12\))f(and,)i(for)f(suc)m(h)i Ft(X)8 b Fu(,)30 b(let)0 4097 y Ft(T)57 4112 y Fp(X)152 4097 y Fu(=)e(\()p Ft(V)351 4112 y Fp(X)418 4097 y Ft(;)17 b(E)534 4112 y Fp(X)601 4097 y Fu(\))28 b Fr(\032)g Fu(\()p Fq(L)5 b Ft(;)17 b Fq(E)h Fu(\))35 b(with)28 b Ft(V)1328 4112 y Fp(X)1423 4097 y Fr(\033)g Ft(X)36 b Fu(b)s(e)29 b(a)f(tree)h(in)e (whic)m(h)i(the)g(in\014m)m(um)e(in)h(\(2.1\))g(is)g(attained.)0 4242 y(The)34 b(Lemma)d(is)h(implied)e(b)m(y)1132 4540 y Fr(j)p Ft(E)1232 4555 y Fp(X)1299 4540 y Fr(j)e(\025)1470 4473 y Fu(1)p 1470 4517 V 1470 4608 a(2)1621 4540 y(inf)1545 4606 y Fp(\031)r Fn(2)p Fs(\005)1688 4615 y Fj(0)1722 4606 y Fs(\()p Fp(k)r Fs(\))1885 4415 y Fp(k)1832 4445 y Fo(X)1848 4657 y Fp(l)q Fs(=1)1993 4540 y Fu(d)2047 4459 y Fo(\000)2099 4540 y Fu(\026)-55 b Ft(x)2148 4555 y Fp(i)2172 4569 y Fl(\031)r Fj(\()p Fl(l)p Fi(\000)p Fj(1\))2365 4540 y Ft(;)23 b Fu(\026)-55 b Ft(x)2464 4555 y Fp(i)2488 4569 y Fl(\031)r Fj(\()p Fl(l)p Fj(\))2602 4459 y Fo(\001)3531 4540 y Fu(\(3.21\))0 4835 y(whic)m(h)31 b(is)f(pro)m(v)m(en)h(as)g(follo)m(ws.)41 b(By)31 b(induction)e(on)i (the)f(n)m(um)m(b)s(er)h(of)f(edges)h(in)f Ft(T)2932 4850 y Fp(X)3029 4835 y Fu(it)g(is)f(easy)j(to)e(pro)m(v)m(e)0 4979 y(that)24 b(there)i(exists)f(a)f(path)h(\(see)g(Fig.)f(1\))g Fr(f)p Ft(`)1580 4994 y Fs(0)1619 4979 y Ft(;)17 b(:)g(:)g(:)f(;)h(`) 1879 4994 y Fp(M)7 b Fn(\000)p Fs(1)2048 4979 y Fr(g)p Fu(,)26 b(with)e Ft(`)2406 4994 y Fp(m)2500 4979 y Fr(2)k Ft(E)2666 4994 y Fp(X)2758 4979 y Fu(for)c(all)f Ft(m)28 b Fu(=)f(0)p Ft(;)17 b(:)g(:)g(:)f(;)h(M)f Fr(\000)6 b Fu(1,)0 5124 y(satisfying)33 b(the)i(follo)m(wing)d(prop)s(erties:)46 b Ft(`)1560 5139 y Fp(m)p Fn(\000)p Fs(1)1740 5124 y Fr(\\)24 b Ft(`)1871 5139 y Fp(m)1968 5124 y Fr(6)p Fu(=)31 b Fr(;)j Fu(for)f(all)g Ft(m)e Fu(=)f(1)p Ft(;)17 b(:)g(:)g(:)f(;)h(M) 33 b Fr(\000)24 b Fu(1,)41 b(\026)-55 b Ft(x)3331 5139 y Fp(i)3355 5148 y Fj(0)3424 5124 y Fr(2)31 b Ft(`)3562 5139 y Fs(0)3602 5124 y Fu(,)j(for)0 5268 y(eac)m(h)k Ft(v)h Fr(2)d Ft(V)469 5283 y Fp(X)574 5268 y Fu(there)i(exists)g Ft(m)e Fr(2)g(f)p Fu(0)p Ft(;)17 b(:)g(:)g(:)e(;)i(M)36 b Fr(\000)26 b Fu(1)p Fr(g)36 b Fu(suc)m(h)j(that)e Ft(`)2492 5283 y Fp(m)2594 5268 y Fr(3)f Ft(v)t Fu(,)i(and)g(eac)m(h)g(edge)g Ft(e)d Fr(2)h Ft(E)3712 5283 y Fp(X)0 5413 y Fu(app)s(ears)f(in)g(the)g (path)g(at)g(most)g(t)m(wice.)51 b(Recalling)33 b(that)i(d\()p Ft(x;)17 b(y)t Fu(\))31 b(=)h Fq(T)p Fu(\()p Fr(f)p Ft(x;)17 b(y)t Fr(g)p Fu(\),)38 b(the)d(b)s(ound)h(\(3.21\))0 5557 y(follo)m(ws.)p 3709 5557 4 66 v 3713 5495 59 4 v 3713 5557 V 3771 5557 4 66 v Black 1841 5806 a(14)p Black eop %%Page: 15 16 15 15 bop Black Black Black 1079 631 a Fe(s)1295 415 y(s)1295 847 y(s)1511 199 y(s)1511 631 y(s)1727 415 y(s)1727 847 y(s)2374 415 y(s)2590 199 y(s)2590 631 y(s)-1544 b Fd(\000)1162 548 y(\000)1212 498 y(\000)1079 714 y(@)1162 797 y(@)1212 847 y(@)1295 415 y(\000)1378 332 y(\000)1428 282 y(\000)1295 498 y(@)1378 581 y(@)1428 631 y(@)1511 714 y(@)1594 797 y(@)1644 847 y(@)1511 282 y(@)1594 365 y(@)1644 415 y(@)647 b(\000)2457 332 y(\000)2507 282 y(\000)2374 498 y(@)2457 581 y(@)2507 631 y(@)p 1079 633 4 4 v 1079 634 V 1079 636 V 1079 638 V 1079 639 V 1079 641 V 1079 642 V 1079 644 V 1079 646 V 1080 647 V 1080 649 V 1080 651 V 1080 652 V 1080 654 V 1080 655 V 1080 657 V 1080 658 V 1080 660 V 1080 661 V 1080 663 V 1081 665 V 1081 666 V 1081 668 V 1081 669 V 1081 671 V 1081 672 V 1081 674 V 1082 675 V 1082 677 V 1082 678 V 1082 680 V 1082 681 V 1083 682 V 1083 684 V 1083 685 V 1083 687 V 1083 688 V 1084 690 V 1084 691 V 1084 693 V 1084 694 V 1085 695 V 1085 697 V 1085 698 V 1085 700 V 1086 701 V 1086 702 V 1086 704 V 1087 705 V 1087 706 V 1087 708 V 1088 709 V 1088 710 V 1088 712 V 1089 713 V 1089 714 V 1089 716 V 1090 717 V 1090 718 V 1090 719 V 1091 721 V 1091 722 V 1092 723 V 1092 725 V 1092 726 V 1093 727 V 1093 728 V 1094 730 V 1094 731 V 1094 732 V 1095 733 V 1095 734 V 1096 736 V 1096 737 V 1097 738 V 1097 739 V 1098 740 V 1098 742 V 1099 743 V 1099 744 V 1100 745 V 1100 746 V 1101 747 V 1101 748 V 1102 750 V 1102 751 V 1103 752 V 1103 753 V 1104 754 V 1105 755 V 1105 756 V 1106 757 V 1106 758 V 1107 759 V 1107 760 V 1108 762 V 1109 763 V 1109 764 V 1110 765 V 1111 766 V 1111 767 V 1112 768 V 1112 769 V 1113 770 V 1114 771 V 1114 772 V 1115 773 V 1116 774 V 1117 775 V 1117 776 V 1118 777 V 1119 778 V 1119 779 V 1120 779 V 1121 780 V 1122 781 V 1122 782 V 1123 783 V 1124 784 V 1124 785 V 1125 786 V 1126 787 V 1127 788 V 1128 789 V 1128 789 V 1129 790 V 1130 791 V 1131 792 V 1132 793 V 1132 794 V 1133 795 V 1134 795 V 1135 796 V 1136 797 V 1137 798 V 1137 799 V 1138 799 V 1139 800 V 1140 801 V 1141 802 V 1142 802 V 1143 803 V 1144 804 V 1145 805 V 1145 806 V 1146 806 V 1147 807 V 1148 808 V 1149 808 V 1150 809 V 1151 810 V 1152 811 V 1153 811 V 1154 812 V 1155 813 V 1156 813 V 1157 814 V 1158 815 V 1159 815 V 1160 816 V 1161 817 V 1162 817 V 1163 818 V 1164 818 V 1165 819 V 1166 820 V 1167 820 V 1168 821 V 1169 821 V 1170 822 V 1172 823 V 1173 823 V 1174 824 V 1175 824 V 1176 825 V 1177 825 V 1178 826 V 1179 826 V 1180 827 V 1182 828 V 1183 828 V 1184 829 V 1185 829 V 1186 830 V 1187 830 V 1189 831 V 1190 831 V 1191 831 V 1192 832 V 1193 832 V 1195 833 V 1196 833 V 1197 834 V 1198 834 V 1199 835 V 1201 835 V 1202 835 V 1203 836 V 1204 836 V 1206 837 V 1207 837 V 1208 837 V 1210 838 V 1211 838 V 1212 838 V 1213 839 V 1215 839 V 1216 840 V 1217 840 V 1219 840 V 1220 841 V 1221 841 V 1223 841 V 1224 841 V 1225 842 V 1227 842 V 1228 842 V 1230 843 V 1231 843 V 1232 843 V 1234 843 V 1235 844 V 1237 844 V 1238 844 V 1239 844 V 1241 845 V 1242 845 V 1244 845 V 1245 845 V 1247 845 V 1248 846 V 1250 846 V 1251 846 V 1253 846 V 1254 846 V 1256 846 V 1257 847 V 1259 847 V 1260 847 V 1262 847 V 1263 847 V 1265 847 V 1266 847 V 1268 848 V 1269 848 V 1271 848 V 1273 848 V 1274 848 V 1276 848 V 1277 848 V 1279 848 V 1280 848 V 1282 848 V 1284 848 V 1285 848 V 1287 848 V 1289 848 V 1290 848 V 1292 848 V 1293 848 V 1295 848 V 1061 804 a(R)p 1079 633 V 1081 633 V 1083 633 V 1084 633 V 1086 633 V 1088 633 V 1089 633 V 1091 633 V 1092 633 V 1094 633 V 1096 633 V 1097 633 V 1099 633 V 1100 633 V 1102 633 V 1103 633 V 1105 633 V 1107 634 V 1108 634 V 1110 634 V 1111 634 V 1113 634 V 1114 634 V 1116 634 V 1117 634 V 1119 635 V 1120 635 V 1122 635 V 1123 635 V 1125 635 V 1126 636 V 1128 636 V 1129 636 V 1131 636 V 1132 636 V 1133 637 V 1135 637 V 1136 637 V 1138 637 V 1139 637 V 1141 638 V 1142 638 V 1143 638 V 1145 639 V 1146 639 V 1148 639 V 1149 639 V 1150 640 V 1152 640 V 1153 640 V 1154 641 V 1156 641 V 1157 641 V 1158 642 V 1160 642 V 1161 642 V 1162 643 V 1164 643 V 1165 643 V 1166 644 V 1167 644 V 1169 645 V 1170 645 V 1171 645 V 1172 646 V 1174 646 V 1175 647 V 1176 647 V 1177 647 V 1179 648 V 1180 648 V 1181 649 V 1182 649 V 1183 650 V 1185 650 V 1186 651 V 1187 651 V 1188 652 V 1189 652 V 1191 653 V 1192 653 V 1193 654 V 1194 654 V 1195 655 V 1196 655 V 1197 656 V 1198 656 V 1200 657 V 1201 657 V 1202 658 V 1203 658 V 1204 659 V 1205 660 V 1206 660 V 1207 661 V 1208 661 V 1209 662 V 1210 663 V 1211 663 V 1212 664 V 1213 665 V 1214 665 V 1215 666 V 1216 666 V 1217 667 V 1218 668 V 1219 668 V 1220 669 V 1221 670 V 1222 671 V 1223 671 V 1224 672 V 1225 673 V 1226 673 V 1227 674 V 1228 675 V 1229 676 V 1230 676 V 1231 677 V 1232 678 V 1233 679 V 1233 679 V 1234 680 V 1235 681 V 1236 682 V 1237 683 V 1238 683 V 1239 684 V 1240 685 V 1240 686 V 1241 687 V 1242 687 V 1243 688 V 1244 689 V 1244 690 V 1245 691 V 1246 692 V 1247 693 V 1248 693 V 1248 694 V 1249 695 V 1250 696 V 1251 697 V 1251 698 V 1252 699 V 1253 700 V 1254 701 V 1254 702 V 1255 703 V 1256 704 V 1257 704 V 1257 705 V 1258 706 V 1259 707 V 1259 708 V 1260 709 V 1261 710 V 1261 711 V 1262 712 V 1263 713 V 1263 714 V 1264 715 V 1264 716 V 1265 717 V 1266 718 V 1266 720 V 1267 721 V 1268 722 V 1268 723 V 1269 724 V 1269 725 V 1270 726 V 1270 727 V 1271 728 V 1272 729 V 1272 730 V 1273 732 V 1273 733 V 1274 734 V 1274 735 V 1275 736 V 1275 737 V 1276 738 V 1276 740 V 1277 741 V 1277 742 V 1278 743 V 1278 744 V 1279 745 V 1279 747 V 1279 748 V 1280 749 V 1280 750 V 1281 752 V 1281 753 V 1282 754 V 1282 755 V 1282 757 V 1283 758 V 1283 759 V 1284 760 V 1284 762 V 1284 763 V 1285 764 V 1285 765 V 1285 767 V 1286 768 V 1286 769 V 1287 771 V 1287 772 V 1287 773 V 1287 775 V 1288 776 V 1288 777 V 1288 779 V 1289 780 V 1289 782 V 1289 783 V 1290 784 V 1290 786 V 1290 787 V 1290 789 V 1291 790 V 1291 791 V 1291 793 V 1291 794 V 1291 796 V 1292 797 V 1292 799 V 1292 800 V 1292 802 V 1292 803 V 1293 804 V 1293 806 V 1293 807 V 1293 809 V 1293 810 V 1293 812 V 1294 813 V 1294 815 V 1294 817 V 1294 818 V 1294 820 V 1294 821 V 1294 823 V 1294 824 V 1295 826 V 1295 827 V 1295 829 V 1295 831 V 1295 832 V 1295 834 V 1295 835 V 1295 837 V 1295 839 V 1295 840 V 1295 842 V 1295 844 V 1295 845 V 1295 847 V 1295 848 V 1230 757 a(I)p 1079 633 V 1079 631 V 1079 629 V 1079 628 V 1079 626 V 1079 624 V 1079 623 V 1079 621 V 1079 620 V 1080 618 V 1080 616 V 1080 615 V 1080 613 V 1080 612 V 1080 610 V 1080 608 V 1080 607 V 1080 605 V 1080 604 V 1080 602 V 1081 601 V 1081 599 V 1081 598 V 1081 596 V 1081 595 V 1081 593 V 1081 592 V 1082 590 V 1082 589 V 1082 587 V 1082 586 V 1082 584 V 1083 583 V 1083 581 V 1083 580 V 1083 578 V 1083 577 V 1084 576 V 1084 574 V 1084 573 V 1084 571 V 1085 570 V 1085 569 V 1085 567 V 1085 566 V 1086 564 V 1086 563 V 1086 562 V 1087 560 V 1087 559 V 1087 558 V 1088 556 V 1088 555 V 1088 554 V 1089 552 V 1089 551 V 1089 550 V 1090 548 V 1090 547 V 1090 546 V 1091 544 V 1091 543 V 1092 542 V 1092 541 V 1092 539 V 1093 538 V 1093 537 V 1094 536 V 1094 534 V 1094 533 V 1095 532 V 1095 531 V 1096 530 V 1096 528 V 1097 527 V 1097 526 V 1098 525 V 1098 524 V 1099 523 V 1099 521 V 1100 520 V 1100 519 V 1101 518 V 1101 517 V 1102 516 V 1102 515 V 1103 513 V 1103 512 V 1104 511 V 1105 510 V 1105 509 V 1106 508 V 1106 507 V 1107 506 V 1107 505 V 1108 504 V 1109 503 V 1109 502 V 1110 501 V 1111 500 V 1111 499 V 1112 498 V 1112 496 V 1113 495 V 1114 494 V 1114 493 V 1115 493 V 1116 492 V 1117 491 V 1117 490 V 1118 489 V 1119 488 V 1119 487 V 1120 486 V 1121 485 V 1122 484 V 1122 483 V 1123 482 V 1124 481 V 1124 480 V 1125 479 V 1126 478 V 1127 478 V 1128 477 V 1128 476 V 1129 475 V 1130 474 V 1131 473 V 1132 472 V 1132 472 V 1133 471 V 1134 470 V 1135 469 V 1136 468 V 1137 467 V 1137 467 V 1138 466 V 1139 465 V 1140 464 V 1141 464 V 1142 463 V 1143 462 V 1144 461 V 1145 460 V 1145 460 V 1146 459 V 1147 458 V 1148 458 V 1149 457 V 1150 456 V 1151 455 V 1152 455 V 1153 454 V 1154 453 V 1155 453 V 1156 452 V 1157 451 V 1158 451 V 1159 450 V 1160 449 V 1161 449 V 1162 448 V 1163 447 V 1164 447 V 1165 446 V 1166 446 V 1167 445 V 1168 444 V 1169 444 V 1170 443 V 1172 443 V 1173 442 V 1174 441 V 1175 441 V 1176 440 V 1177 440 V 1178 439 V 1179 439 V 1180 438 V 1182 438 V 1183 437 V 1184 437 V 1185 436 V 1186 436 V 1187 435 V 1189 435 V 1190 434 V 1191 434 V 1192 433 V 1193 433 V 1195 432 V 1196 432 V 1197 432 V 1198 431 V 1199 431 V 1201 430 V 1202 430 V 1203 429 V 1204 429 V 1206 429 V 1207 428 V 1208 428 V 1210 428 V 1211 427 V 1212 427 V 1213 426 V 1215 426 V 1216 426 V 1217 425 V 1219 425 V 1220 425 V 1221 424 V 1223 424 V 1224 424 V 1225 424 V 1227 423 V 1228 423 V 1230 423 V 1231 422 V 1232 422 V 1234 422 V 1235 422 V 1237 421 V 1238 421 V 1239 421 V 1241 421 V 1242 420 V 1244 420 V 1245 420 V 1247 420 V 1248 420 V 1250 419 V 1251 419 V 1253 419 V 1254 419 V 1256 419 V 1257 419 V 1259 418 V 1260 418 V 1262 418 V 1263 418 V 1265 418 V 1266 418 V 1268 418 V 1269 418 V 1271 417 V 1273 417 V 1274 417 V 1276 417 V 1277 417 V 1279 417 V 1280 417 V 1282 417 V 1284 417 V 1285 417 V 1287 417 V 1289 417 V 1290 417 V 1292 417 V 1293 417 V 1295 417 V 1061 541 a(\022)p 1295 417 V 1295 418 V 1295 420 V 1295 422 V 1295 423 V 1295 425 V 1295 427 V 1295 428 V 1295 430 V 1295 431 V 1295 433 V 1296 435 V 1296 436 V 1296 438 V 1296 439 V 1296 441 V 1296 443 V 1296 444 V 1296 446 V 1296 447 V 1296 449 V 1297 450 V 1297 452 V 1297 453 V 1297 455 V 1297 456 V 1297 458 V 1297 459 V 1298 461 V 1298 462 V 1298 464 V 1298 465 V 1298 467 V 1299 468 V 1299 470 V 1299 471 V 1299 472 V 1300 474 V 1300 475 V 1300 477 V 1300 478 V 1301 479 V 1301 481 V 1301 482 V 1301 484 V 1302 485 V 1302 486 V 1302 488 V 1302 489 V 1303 490 V 1303 492 V 1303 493 V 1304 494 V 1304 496 V 1304 497 V 1305 498 V 1305 500 V 1306 501 V 1306 502 V 1306 504 V 1307 505 V 1307 506 V 1307 507 V 1308 509 V 1308 510 V 1309 511 V 1309 512 V 1309 514 V 1310 515 V 1310 516 V 1311 517 V 1311 519 V 1312 520 V 1312 521 V 1313 522 V 1313 523 V 1314 525 V 1314 526 V 1315 527 V 1315 528 V 1316 529 V 1316 530 V 1317 531 V 1317 533 V 1318 534 V 1318 535 V 1319 536 V 1319 537 V 1320 538 V 1320 539 V 1321 540 V 1322 541 V 1322 543 V 1323 544 V 1323 545 V 1324 546 V 1325 547 V 1325 548 V 1326 549 V 1326 550 V 1327 551 V 1328 552 V 1328 553 V 1329 554 V 1330 555 V 1330 556 V 1331 557 V 1332 558 V 1332 559 V 1333 560 V 1334 561 V 1334 562 V 1335 563 V 1336 564 V 1337 565 V 1337 565 V 1338 566 V 1339 567 V 1340 568 V 1340 569 V 1341 570 V 1342 571 V 1343 572 V 1343 573 V 1344 574 V 1345 574 V 1346 575 V 1347 576 V 1347 577 V 1348 578 V 1349 579 V 1350 579 V 1351 580 V 1352 581 V 1352 582 V 1353 583 V 1354 584 V 1355 584 V 1356 585 V 1357 586 V 1358 587 V 1359 587 V 1360 588 V 1360 589 V 1361 590 V 1362 590 V 1363 591 V 1364 592 V 1365 593 V 1366 593 V 1367 594 V 1368 595 V 1369 595 V 1370 596 V 1371 597 V 1372 597 V 1373 598 V 1374 599 V 1375 599 V 1376 600 V 1377 601 V 1378 601 V 1379 602 V 1380 603 V 1381 603 V 1382 604 V 1383 604 V 1384 605 V 1385 606 V 1386 606 V 1387 607 V 1388 607 V 1390 608 V 1391 608 V 1392 609 V 1393 610 V 1394 610 V 1395 611 V 1396 611 V 1397 612 V 1399 612 V 1400 613 V 1401 613 V 1402 614 V 1403 614 V 1404 615 V 1406 615 V 1407 616 V 1408 616 V 1409 617 V 1410 617 V 1412 617 V 1413 618 V 1414 618 V 1415 619 V 1417 619 V 1418 620 V 1419 620 V 1420 620 V 1422 621 V 1423 621 V 1424 622 V 1425 622 V 1427 622 V 1428 623 V 1429 623 V 1431 623 V 1432 624 V 1433 624 V 1435 624 V 1436 625 V 1437 625 V 1439 625 V 1440 626 V 1441 626 V 1443 626 V 1444 626 V 1445 627 V 1447 627 V 1448 627 V 1450 628 V 1451 628 V 1452 628 V 1454 628 V 1455 628 V 1457 629 V 1458 629 V 1460 629 V 1461 629 V 1463 630 V 1464 630 V 1466 630 V 1467 630 V 1468 630 V 1470 630 V 1471 631 V 1473 631 V 1474 631 V 1476 631 V 1478 631 V 1479 631 V 1481 631 V 1482 632 V 1484 632 V 1485 632 V 1487 632 V 1488 632 V 1490 632 V 1492 632 V 1493 632 V 1495 632 V 1496 632 V 1498 632 V 1499 632 V 1501 633 V 1503 633 V 1504 633 V 1506 633 V 1508 633 V 1509 633 V 1511 633 V 1277 588 a(R)p 1511 633 V 1511 634 V 1511 636 V 1511 638 V 1511 639 V 1511 641 V 1511 642 V 1511 644 V 1511 646 V 1511 647 V 1511 649 V 1511 651 V 1511 652 V 1512 654 V 1512 655 V 1512 657 V 1512 658 V 1512 660 V 1512 661 V 1512 663 V 1512 665 V 1512 666 V 1513 668 V 1513 669 V 1513 671 V 1513 672 V 1513 674 V 1513 675 V 1514 677 V 1514 678 V 1514 680 V 1514 681 V 1514 682 V 1514 684 V 1515 685 V 1515 687 V 1515 688 V 1515 690 V 1516 691 V 1516 693 V 1516 694 V 1516 695 V 1517 697 V 1517 698 V 1517 700 V 1517 701 V 1518 702 V 1518 704 V 1518 705 V 1519 706 V 1519 708 V 1519 709 V 1520 710 V 1520 712 V 1520 713 V 1521 714 V 1521 716 V 1521 717 V 1522 718 V 1522 719 V 1522 721 V 1523 722 V 1523 723 V 1524 725 V 1524 726 V 1524 727 V 1525 728 V 1525 730 V 1526 731 V 1526 732 V 1527 733 V 1527 734 V 1528 736 V 1528 737 V 1528 738 V 1529 739 V 1529 740 V 1530 742 V 1530 743 V 1531 744 V 1531 745 V 1532 746 V 1532 747 V 1533 748 V 1534 750 V 1534 751 V 1535 752 V 1535 753 V 1536 754 V 1536 755 V 1537 756 V 1537 757 V 1538 758 V 1539 759 V 1539 760 V 1540 762 V 1540 763 V 1541 764 V 1542 765 V 1542 766 V 1543 767 V 1544 768 V 1544 769 V 1545 770 V 1546 771 V 1546 772 V 1547 773 V 1548 774 V 1548 775 V 1549 776 V 1550 777 V 1550 778 V 1551 779 V 1552 779 V 1552 780 V 1553 781 V 1554 782 V 1555 783 V 1555 784 V 1556 785 V 1557 786 V 1558 787 V 1559 788 V 1559 789 V 1560 789 V 1561 790 V 1562 791 V 1562 792 V 1563 793 V 1564 794 V 1565 795 V 1566 795 V 1567 796 V 1567 797 V 1568 798 V 1569 799 V 1570 799 V 1571 800 V 1572 801 V 1573 802 V 1574 802 V 1574 803 V 1575 804 V 1576 805 V 1577 806 V 1578 806 V 1579 807 V 1580 808 V 1581 808 V 1582 809 V 1583 810 V 1584 811 V 1585 811 V 1586 812 V 1587 813 V 1588 813 V 1589 814 V 1590 815 V 1591 815 V 1592 816 V 1593 817 V 1594 817 V 1595 818 V 1596 818 V 1597 819 V 1598 820 V 1599 820 V 1600 821 V 1601 821 V 1602 822 V 1603 823 V 1604 823 V 1605 824 V 1607 824 V 1608 825 V 1609 825 V 1610 826 V 1611 826 V 1612 827 V 1613 828 V 1614 828 V 1616 829 V 1617 829 V 1618 830 V 1619 830 V 1620 831 V 1621 831 V 1623 831 V 1624 832 V 1625 832 V 1626 833 V 1627 833 V 1629 834 V 1630 834 V 1631 835 V 1632 835 V 1634 835 V 1635 836 V 1636 836 V 1637 837 V 1639 837 V 1640 837 V 1641 838 V 1643 838 V 1644 838 V 1645 839 V 1646 839 V 1648 840 V 1649 840 V 1650 840 V 1652 841 V 1653 841 V 1654 841 V 1656 841 V 1657 842 V 1659 842 V 1660 842 V 1661 843 V 1663 843 V 1664 843 V 1666 843 V 1667 844 V 1668 844 V 1670 844 V 1671 844 V 1673 845 V 1674 845 V 1676 845 V 1677 845 V 1678 845 V 1680 846 V 1681 846 V 1683 846 V 1684 846 V 1686 846 V 1687 846 V 1689 847 V 1690 847 V 1692 847 V 1693 847 V 1695 847 V 1696 847 V 1698 847 V 1700 848 V 1701 848 V 1703 848 V 1704 848 V 1706 848 V 1707 848 V 1709 848 V 1711 848 V 1712 848 V 1714 848 V 1715 848 V 1717 848 V 1719 848 V 1720 848 V 1722 848 V 1724 848 V 1725 848 V 1727 848 V 1493 804 a(R)p 1727 848 V 1727 847 V 1727 845 V 1727 844 V 1727 842 V 1727 840 V 1727 839 V 1727 837 V 1727 835 V 1727 834 V 1727 832 V 1726 831 V 1726 829 V 1726 827 V 1726 826 V 1726 824 V 1726 823 V 1726 821 V 1726 820 V 1726 818 V 1726 817 V 1725 815 V 1725 814 V 1725 812 V 1725 810 V 1725 809 V 1725 807 V 1725 806 V 1724 804 V 1724 803 V 1724 802 V 1724 800 V 1724 799 V 1723 797 V 1723 796 V 1723 794 V 1723 793 V 1722 791 V 1722 790 V 1722 789 V 1722 787 V 1721 786 V 1721 784 V 1721 783 V 1721 782 V 1720 780 V 1720 779 V 1720 778 V 1720 776 V 1719 775 V 1719 773 V 1719 772 V 1718 771 V 1718 769 V 1718 768 V 1717 767 V 1717 766 V 1716 764 V 1716 763 V 1716 762 V 1715 760 V 1715 759 V 1715 758 V 1714 757 V 1714 755 V 1713 754 V 1713 753 V 1713 752 V 1712 750 V 1712 749 V 1711 748 V 1711 747 V 1710 745 V 1710 744 V 1709 743 V 1709 742 V 1708 741 V 1708 740 V 1707 738 V 1707 737 V 1706 736 V 1706 735 V 1705 734 V 1705 733 V 1704 732 V 1704 730 V 1703 729 V 1703 728 V 1702 727 V 1702 726 V 1701 725 V 1700 724 V 1700 723 V 1699 722 V 1699 721 V 1698 720 V 1697 719 V 1697 717 V 1696 716 V 1696 715 V 1695 714 V 1694 713 V 1694 712 V 1693 711 V 1692 710 V 1692 709 V 1691 708 V 1690 707 V 1690 706 V 1689 705 V 1688 704 V 1688 704 V 1687 703 V 1686 702 V 1685 701 V 1685 700 V 1684 699 V 1683 698 V 1682 697 V 1682 696 V 1681 695 V 1680 694 V 1679 693 V 1679 693 V 1678 692 V 1677 691 V 1676 690 V 1675 689 V 1675 688 V 1674 687 V 1673 687 V 1672 686 V 1671 685 V 1670 684 V 1670 683 V 1669 683 V 1668 682 V 1667 681 V 1666 680 V 1665 679 V 1664 679 V 1663 678 V 1662 677 V 1662 676 V 1661 676 V 1660 675 V 1659 674 V 1658 673 V 1657 673 V 1656 672 V 1655 671 V 1654 671 V 1653 670 V 1652 669 V 1651 669 V 1650 668 V 1649 667 V 1648 667 V 1647 666 V 1646 665 V 1645 665 V 1644 664 V 1643 663 V 1642 663 V 1641 662 V 1640 661 V 1639 661 V 1638 660 V 1637 660 V 1636 659 V 1635 658 V 1634 658 V 1632 657 V 1631 657 V 1630 656 V 1629 656 V 1628 655 V 1627 655 V 1626 654 V 1625 654 V 1623 653 V 1622 653 V 1621 652 V 1620 652 V 1619 651 V 1618 651 V 1616 650 V 1615 650 V 1614 649 V 1613 649 V 1612 648 V 1610 648 V 1609 647 V 1608 647 V 1607 647 V 1605 646 V 1604 646 V 1603 645 V 1602 645 V 1600 645 V 1599 644 V 1598 644 V 1597 643 V 1595 643 V 1594 643 V 1593 642 V 1591 642 V 1590 642 V 1589 641 V 1587 641 V 1586 641 V 1585 640 V 1583 640 V 1582 640 V 1581 639 V 1579 639 V 1578 639 V 1577 639 V 1575 638 V 1574 638 V 1572 638 V 1571 637 V 1570 637 V 1568 637 V 1567 637 V 1565 637 V 1564 636 V 1562 636 V 1561 636 V 1559 636 V 1558 635 V 1556 635 V 1555 635 V 1554 635 V 1552 635 V 1551 635 V 1549 634 V 1548 634 V 1546 634 V 1545 634 V 1543 634 V 1541 634 V 1540 634 V 1538 634 V 1537 633 V 1535 633 V 1534 633 V 1532 633 V 1531 633 V 1529 633 V 1527 633 V 1526 633 V 1524 633 V 1523 633 V 1521 633 V 1519 633 V 1518 633 V 1516 633 V 1514 633 V 1513 633 V 1511 633 V 1662 757 a(I)p 1511 633 V 1511 631 V 1511 629 V 1511 628 V 1511 626 V 1511 624 V 1511 623 V 1511 621 V 1511 620 V 1511 618 V 1511 616 V 1511 615 V 1511 613 V 1510 612 V 1510 610 V 1510 608 V 1510 607 V 1510 605 V 1510 604 V 1510 602 V 1510 601 V 1510 599 V 1509 598 V 1509 596 V 1509 595 V 1509 593 V 1509 592 V 1509 590 V 1509 589 V 1508 587 V 1508 586 V 1508 584 V 1508 583 V 1508 581 V 1507 580 V 1507 578 V 1507 577 V 1507 576 V 1506 574 V 1506 573 V 1506 571 V 1506 570 V 1505 569 V 1505 567 V 1505 566 V 1505 564 V 1504 563 V 1504 562 V 1504 560 V 1503 559 V 1503 558 V 1503 556 V 1502 555 V 1502 554 V 1502 552 V 1501 551 V 1501 550 V 1501 548 V 1500 547 V 1500 546 V 1500 544 V 1499 543 V 1499 542 V 1498 541 V 1498 539 V 1498 538 V 1497 537 V 1497 536 V 1496 534 V 1496 533 V 1495 532 V 1495 531 V 1494 530 V 1494 528 V 1494 527 V 1493 526 V 1493 525 V 1492 524 V 1492 523 V 1491 521 V 1491 520 V 1490 519 V 1490 518 V 1489 517 V 1488 516 V 1488 515 V 1487 513 V 1487 512 V 1486 511 V 1486 510 V 1485 509 V 1485 508 V 1484 507 V 1483 506 V 1483 505 V 1482 504 V 1482 503 V 1481 502 V 1480 501 V 1480 500 V 1479 499 V 1478 498 V 1478 496 V 1477 495 V 1476 494 V 1476 493 V 1475 493 V 1474 492 V 1474 491 V 1473 490 V 1472 489 V 1472 488 V 1471 487 V 1470 486 V 1470 485 V 1469 484 V 1468 483 V 1467 482 V 1467 481 V 1466 480 V 1465 479 V 1464 478 V 1463 478 V 1463 477 V 1462 476 V 1461 475 V 1460 474 V 1460 473 V 1459 472 V 1458 472 V 1457 471 V 1456 470 V 1455 469 V 1455 468 V 1454 467 V 1453 467 V 1452 466 V 1451 465 V 1450 464 V 1449 464 V 1448 463 V 1448 462 V 1447 461 V 1446 460 V 1445 460 V 1444 459 V 1443 458 V 1442 458 V 1441 457 V 1440 456 V 1439 455 V 1438 455 V 1437 454 V 1436 453 V 1435 453 V 1434 452 V 1433 451 V 1432 451 V 1431 450 V 1430 449 V 1429 449 V 1428 448 V 1427 447 V 1426 447 V 1425 446 V 1424 446 V 1423 445 V 1422 444 V 1421 444 V 1420 443 V 1419 443 V 1418 442 V 1417 441 V 1415 441 V 1414 440 V 1413 440 V 1412 439 V 1411 439 V 1410 438 V 1409 438 V 1408 437 V 1406 437 V 1405 436 V 1404 436 V 1403 435 V 1402 435 V 1401 434 V 1399 434 V 1398 433 V 1397 433 V 1396 432 V 1395 432 V 1393 432 V 1392 431 V 1391 431 V 1390 430 V 1388 430 V 1387 429 V 1386 429 V 1385 429 V 1383 428 V 1382 428 V 1381 428 V 1379 427 V 1378 427 V 1377 426 V 1376 426 V 1374 426 V 1373 425 V 1372 425 V 1370 425 V 1369 424 V 1368 424 V 1366 424 V 1365 424 V 1363 423 V 1362 423 V 1361 423 V 1359 422 V 1358 422 V 1356 422 V 1355 422 V 1354 421 V 1352 421 V 1351 421 V 1349 421 V 1348 420 V 1346 420 V 1345 420 V 1344 420 V 1342 420 V 1341 419 V 1339 419 V 1338 419 V 1336 419 V 1335 419 V 1333 419 V 1332 418 V 1330 418 V 1329 418 V 1327 418 V 1326 418 V 1324 418 V 1322 418 V 1321 418 V 1319 417 V 1318 417 V 1316 417 V 1315 417 V 1313 417 V 1311 417 V 1310 417 V 1308 417 V 1307 417 V 1305 417 V 1303 417 V 1302 417 V 1300 417 V 1298 417 V 1297 417 V 1295 417 V 1446 541 a(I)p 1295 417 V 1295 415 V 1295 413 V 1295 412 V 1295 410 V 1295 409 V 1295 407 V 1295 405 V 1295 404 V 1295 402 V 1295 400 V 1296 399 V 1296 397 V 1296 396 V 1296 394 V 1296 393 V 1296 391 V 1296 389 V 1296 388 V 1296 386 V 1296 385 V 1297 383 V 1297 382 V 1297 380 V 1297 379 V 1297 377 V 1297 376 V 1297 374 V 1298 373 V 1298 371 V 1298 370 V 1298 368 V 1298 367 V 1299 365 V 1299 364 V 1299 363 V 1299 361 V 1300 360 V 1300 358 V 1300 357 V 1300 355 V 1301 354 V 1301 353 V 1301 351 V 1301 350 V 1302 349 V 1302 347 V 1302 346 V 1302 344 V 1303 343 V 1303 342 V 1303 340 V 1304 339 V 1304 338 V 1304 336 V 1305 335 V 1305 334 V 1306 333 V 1306 331 V 1306 330 V 1307 329 V 1307 327 V 1307 326 V 1308 325 V 1308 324 V 1309 322 V 1309 321 V 1309 320 V 1310 319 V 1310 317 V 1311 316 V 1311 315 V 1312 314 V 1312 313 V 1313 311 V 1313 310 V 1314 309 V 1314 308 V 1315 307 V 1315 306 V 1316 304 V 1316 303 V 1317 302 V 1317 301 V 1318 300 V 1318 299 V 1319 298 V 1319 296 V 1320 295 V 1320 294 V 1321 293 V 1322 292 V 1322 291 V 1323 290 V 1323 289 V 1324 288 V 1325 287 V 1325 286 V 1326 285 V 1326 284 V 1327 283 V 1328 282 V 1328 281 V 1329 280 V 1330 279 V 1330 278 V 1331 277 V 1332 276 V 1332 275 V 1333 274 V 1334 273 V 1334 272 V 1335 271 V 1336 270 V 1337 269 V 1337 268 V 1338 267 V 1339 266 V 1340 265 V 1340 264 V 1341 264 V 1342 263 V 1343 262 V 1343 261 V 1344 260 V 1345 259 V 1346 258 V 1347 257 V 1347 257 V 1348 256 V 1349 255 V 1350 254 V 1351 253 V 1352 252 V 1352 252 V 1353 251 V 1354 250 V 1355 249 V 1356 248 V 1357 248 V 1358 247 V 1359 246 V 1360 245 V 1360 245 V 1361 244 V 1362 243 V 1363 242 V 1364 242 V 1365 241 V 1366 240 V 1367 240 V 1368 239 V 1369 238 V 1370 237 V 1371 237 V 1372 236 V 1373 235 V 1374 235 V 1375 234 V 1376 233 V 1377 233 V 1378 232 V 1379 232 V 1380 231 V 1381 230 V 1382 230 V 1383 229 V 1384 229 V 1385 228 V 1386 227 V 1387 227 V 1388 226 V 1390 226 V 1391 225 V 1392 225 V 1393 224 V 1394 223 V 1395 223 V 1396 222 V 1397 222 V 1399 221 V 1400 221 V 1401 220 V 1402 220 V 1403 219 V 1404 219 V 1406 218 V 1407 218 V 1408 217 V 1409 217 V 1410 217 V 1412 216 V 1413 216 V 1414 215 V 1415 215 V 1417 214 V 1418 214 V 1419 214 V 1420 213 V 1422 213 V 1423 212 V 1424 212 V 1425 212 V 1427 211 V 1428 211 V 1429 211 V 1431 210 V 1432 210 V 1433 210 V 1435 209 V 1436 209 V 1437 209 V 1439 208 V 1440 208 V 1441 208 V 1443 207 V 1444 207 V 1445 207 V 1447 207 V 1448 206 V 1450 206 V 1451 206 V 1452 206 V 1454 205 V 1455 205 V 1457 205 V 1458 205 V 1460 204 V 1461 204 V 1463 204 V 1464 204 V 1466 204 V 1467 203 V 1468 203 V 1470 203 V 1471 203 V 1473 203 V 1474 203 V 1476 202 V 1478 202 V 1479 202 V 1481 202 V 1482 202 V 1484 202 V 1485 202 V 1487 202 V 1488 202 V 1490 201 V 1492 201 V 1493 201 V 1495 201 V 1496 201 V 1498 201 V 1499 201 V 1501 201 V 1503 201 V 1504 201 V 1506 201 V 1508 201 V 1509 201 V 1511 201 V 1277 325 a(\022)p 1511 201 V 1513 201 V 1514 201 V 1516 201 V 1518 201 V 1519 201 V 1521 201 V 1522 201 V 1524 201 V 1526 201 V 1527 201 V 1529 201 V 1530 201 V 1532 201 V 1534 202 V 1535 202 V 1537 202 V 1538 202 V 1540 202 V 1541 202 V 1543 202 V 1544 202 V 1546 202 V 1548 203 V 1549 203 V 1551 203 V 1552 203 V 1554 203 V 1555 203 V 1556 204 V 1558 204 V 1559 204 V 1561 204 V 1562 204 V 1564 205 V 1565 205 V 1567 205 V 1568 205 V 1569 206 V 1571 206 V 1572 206 V 1574 206 V 1575 207 V 1576 207 V 1578 207 V 1579 207 V 1581 208 V 1582 208 V 1583 208 V 1585 209 V 1586 209 V 1587 209 V 1589 210 V 1590 210 V 1591 210 V 1593 211 V 1594 211 V 1595 211 V 1597 212 V 1598 212 V 1599 212 V 1600 213 V 1602 213 V 1603 214 V 1604 214 V 1605 214 V 1607 215 V 1608 215 V 1609 216 V 1610 216 V 1612 217 V 1613 217 V 1614 217 V 1615 218 V 1616 218 V 1618 219 V 1619 219 V 1620 220 V 1621 220 V 1622 221 V 1623 221 V 1625 222 V 1626 222 V 1627 223 V 1628 223 V 1629 224 V 1630 225 V 1631 225 V 1632 226 V 1633 226 V 1635 227 V 1636 227 V 1637 228 V 1638 229 V 1639 229 V 1640 230 V 1641 230 V 1642 231 V 1643 232 V 1644 232 V 1645 233 V 1646 233 V 1647 234 V 1648 235 V 1649 235 V 1650 236 V 1651 237 V 1652 237 V 1653 238 V 1654 239 V 1655 240 V 1656 240 V 1657 241 V 1658 242 V 1659 242 V 1660 243 V 1661 244 V 1662 245 V 1662 245 V 1663 246 V 1664 247 V 1665 248 V 1666 248 V 1667 249 V 1668 250 V 1669 251 V 1670 252 V 1670 252 V 1671 253 V 1672 254 V 1673 255 V 1674 256 V 1675 257 V 1675 257 V 1676 258 V 1677 259 V 1678 260 V 1679 261 V 1679 262 V 1680 263 V 1681 263 V 1682 264 V 1682 265 V 1683 266 V 1684 267 V 1685 268 V 1685 269 V 1686 270 V 1687 271 V 1688 272 V 1688 273 V 1689 274 V 1690 275 V 1690 276 V 1691 277 V 1692 278 V 1692 279 V 1693 280 V 1694 281 V 1694 282 V 1695 283 V 1696 284 V 1696 285 V 1697 286 V 1697 287 V 1698 288 V 1699 289 V 1699 290 V 1700 291 V 1700 292 V 1701 293 V 1702 294 V 1702 295 V 1703 296 V 1703 298 V 1704 299 V 1704 300 V 1705 301 V 1705 302 V 1706 303 V 1706 304 V 1707 305 V 1707 307 V 1708 308 V 1708 309 V 1709 310 V 1709 311 V 1710 313 V 1710 314 V 1711 315 V 1711 316 V 1712 317 V 1712 319 V 1713 320 V 1713 321 V 1713 322 V 1714 324 V 1714 325 V 1715 326 V 1715 327 V 1715 329 V 1716 330 V 1716 331 V 1716 332 V 1717 334 V 1717 335 V 1718 336 V 1718 338 V 1718 339 V 1719 340 V 1719 342 V 1719 343 V 1720 344 V 1720 346 V 1720 347 V 1720 348 V 1721 350 V 1721 351 V 1721 353 V 1721 354 V 1722 355 V 1722 357 V 1722 358 V 1722 360 V 1723 361 V 1723 363 V 1723 364 V 1723 365 V 1724 367 V 1724 368 V 1724 370 V 1724 371 V 1724 373 V 1725 374 V 1725 376 V 1725 377 V 1725 379 V 1725 380 V 1725 382 V 1725 383 V 1726 385 V 1726 386 V 1726 388 V 1726 389 V 1726 391 V 1726 393 V 1726 394 V 1726 396 V 1726 397 V 1726 399 V 1727 400 V 1727 402 V 1727 404 V 1727 405 V 1727 407 V 1727 408 V 1727 410 V 1727 412 V 1727 413 V 1727 415 V 1727 417 V 1601 264 a(R)p 1727 417 V 1728 396 V 1731 378 V 1737 362 V 1744 348 V 1754 336 V 1766 326 V 1780 319 V 1796 313 V 1814 310 V 1835 309 V 1835 417 V 1856 417 V 1878 417 V 1900 417 V 1921 417 V 1943 417 V 1964 417 V 1986 417 V 2007 417 V 2029 417 V 2051 417 V 2072 417 V 2094 417 V 2115 417 V 2137 417 V 2159 417 V 2180 417 V 2202 417 V 2223 417 V 2245 417 V 2267 417 V 2267 309 V 2287 310 V 2305 313 V 2322 319 V 2336 326 V 2347 336 V 2357 348 V 2365 362 V 2370 378 V 2373 396 V 2374 417 V 2374 417 V 2374 418 V 2374 420 V 2374 422 V 2374 423 V 2375 425 V 2375 427 V 2375 428 V 2375 430 V 2375 431 V 2375 433 V 2375 435 V 2375 436 V 2375 438 V 2375 439 V 2375 441 V 2375 443 V 2375 444 V 2375 446 V 2376 447 V 2376 449 V 2376 450 V 2376 452 V 2376 453 V 2376 455 V 2376 456 V 2377 458 V 2377 459 V 2377 461 V 2377 462 V 2377 464 V 2378 465 V 2378 467 V 2378 468 V 2378 470 V 2378 471 V 2379 472 V 2379 474 V 2379 475 V 2379 477 V 2380 478 V 2380 479 V 2380 481 V 2380 482 V 2381 484 V 2381 485 V 2381 486 V 2381 488 V 2382 489 V 2382 490 V 2382 492 V 2383 493 V 2383 494 V 2383 496 V 2384 497 V 2384 498 V 2384 500 V 2385 501 V 2385 502 V 2386 504 V 2386 505 V 2386 506 V 2387 507 V 2387 509 V 2388 510 V 2388 511 V 2388 512 V 2389 514 V 2389 515 V 2390 516 V 2390 517 V 2391 519 V 2391 520 V 2391 521 V 2392 522 V 2392 523 V 2393 525 V 2393 526 V 2394 527 V 2394 528 V 2395 529 V 2395 530 V 2396 531 V 2396 533 V 2397 534 V 2397 535 V 2398 536 V 2399 537 V 2399 538 V 2400 539 V 2400 540 V 2401 541 V 2401 543 V 2402 544 V 2403 545 V 2403 546 V 2404 547 V 2404 548 V 2405 549 V 2406 550 V 2406 551 V 2407 552 V 2408 553 V 2408 554 V 2409 555 V 2410 556 V 2410 557 V 2411 558 V 2412 559 V 2412 560 V 2413 561 V 2414 562 V 2414 563 V 2415 564 V 2416 565 V 2417 565 V 2417 566 V 2418 567 V 2419 568 V 2420 569 V 2420 570 V 2421 571 V 2422 572 V 2423 573 V 2424 574 V 2424 574 V 2425 575 V 2426 576 V 2427 577 V 2428 578 V 2428 579 V 2429 579 V 2430 580 V 2431 581 V 2432 582 V 2433 583 V 2433 584 V 2434 584 V 2435 585 V 2436 586 V 2437 587 V 2438 587 V 2439 588 V 2440 589 V 2441 590 V 2442 590 V 2442 591 V 2443 592 V 2444 593 V 2445 593 V 2446 594 V 2447 595 V 2448 595 V 2449 596 V 2450 597 V 2451 597 V 2452 598 V 2453 599 V 2454 599 V 2455 600 V 2456 601 V 2457 601 V 2458 602 V 2459 603 V 2460 603 V 2461 604 V 2462 604 V 2463 605 V 2465 606 V 2466 606 V 2467 607 V 2468 607 V 2469 608 V 2470 608 V 2471 609 V 2472 610 V 2473 610 V 2474 611 V 2476 611 V 2477 612 V 2478 612 V 2479 613 V 2480 613 V 2481 614 V 2483 614 V 2484 615 V 2485 615 V 2486 616 V 2487 616 V 2488 617 V 2490 617 V 2491 617 V 2492 618 V 2493 618 V 2495 619 V 2496 619 V 2497 620 V 2498 620 V 2500 620 V 2501 621 V 2502 621 V 2503 622 V 2505 622 V 2506 622 V 2507 623 V 2509 623 V 2510 623 V 2511 624 V 2513 624 V 2514 624 V 2515 625 V 2517 625 V 2518 625 V 2519 626 V 2521 626 V 2522 626 V 2523 626 V 2525 627 V 2526 627 V 2528 627 V 2529 628 V 2530 628 V 2532 628 V 2533 628 V 2535 628 V 2536 629 V 2538 629 V 2539 629 V 2540 629 V 2542 630 V 2543 630 V 2545 630 V 2546 630 V 2548 630 V 2549 630 V 2551 631 V 2552 631 V 2554 631 V 2555 631 V 2557 631 V 2558 631 V 2560 631 V 2561 632 V 2563 632 V 2565 632 V 2566 632 V 2568 632 V 2569 632 V 2571 632 V 2572 632 V 2574 632 V 2576 632 V 2577 632 V 2579 632 V 2580 633 V 2582 633 V 2584 633 V 2585 633 V 2587 633 V 2589 633 V 2590 633 V 2356 588 a(R)p 2590 633 V 2590 631 V 2590 629 V 2590 628 V 2590 626 V 2590 624 V 2590 623 V 2590 621 V 2590 620 V 2590 618 V 2590 616 V 2590 615 V 2590 613 V 2590 612 V 2590 610 V 2590 608 V 2589 607 V 2589 605 V 2589 604 V 2589 602 V 2589 601 V 2589 599 V 2589 598 V 2589 596 V 2588 595 V 2588 593 V 2588 592 V 2588 590 V 2588 589 V 2588 587 V 2587 586 V 2587 584 V 2587 583 V 2587 581 V 2587 580 V 2586 578 V 2586 577 V 2586 576 V 2586 574 V 2585 573 V 2585 571 V 2585 570 V 2585 569 V 2584 567 V 2584 566 V 2584 564 V 2584 563 V 2583 562 V 2583 560 V 2583 559 V 2582 558 V 2582 556 V 2582 555 V 2581 554 V 2581 552 V 2581 551 V 2580 550 V 2580 548 V 2580 547 V 2579 546 V 2579 544 V 2578 543 V 2578 542 V 2578 541 V 2577 539 V 2577 538 V 2576 537 V 2576 536 V 2576 534 V 2575 533 V 2575 532 V 2574 531 V 2574 530 V 2573 528 V 2573 527 V 2572 526 V 2572 525 V 2571 524 V 2571 523 V 2570 521 V 2570 520 V 2569 519 V 2569 518 V 2568 517 V 2568 516 V 2567 515 V 2567 513 V 2566 512 V 2566 511 V 2565 510 V 2564 509 V 2564 508 V 2563 507 V 2563 506 V 2562 505 V 2561 504 V 2561 503 V 2560 502 V 2560 501 V 2559 500 V 2558 499 V 2558 498 V 2557 496 V 2556 495 V 2556 494 V 2555 493 V 2554 493 V 2554 492 V 2553 491 V 2552 490 V 2552 489 V 2551 488 V 2550 487 V 2550 486 V 2549 485 V 2548 484 V 2547 483 V 2547 482 V 2546 481 V 2545 480 V 2544 479 V 2544 478 V 2543 478 V 2542 477 V 2541 476 V 2540 475 V 2540 474 V 2539 473 V 2538 472 V 2537 472 V 2536 471 V 2536 470 V 2535 469 V 2534 468 V 2533 467 V 2532 467 V 2531 466 V 2530 465 V 2529 464 V 2529 464 V 2528 463 V 2527 462 V 2526 461 V 2525 460 V 2524 460 V 2523 459 V 2522 458 V 2521 458 V 2520 457 V 2519 456 V 2518 455 V 2518 455 V 2517 454 V 2516 453 V 2515 453 V 2514 452 V 2513 451 V 2512 451 V 2511 450 V 2510 449 V 2509 449 V 2508 448 V 2506 447 V 2505 447 V 2504 446 V 2503 446 V 2502 445 V 2501 444 V 2500 444 V 2499 443 V 2498 443 V 2497 442 V 2496 441 V 2495 441 V 2494 440 V 2493 440 V 2491 439 V 2490 439 V 2489 438 V 2488 438 V 2487 437 V 2486 437 V 2485 436 V 2483 436 V 2482 435 V 2481 435 V 2480 434 V 2479 434 V 2477 433 V 2476 433 V 2475 432 V 2474 432 V 2473 432 V 2471 431 V 2470 431 V 2469 430 V 2468 430 V 2466 429 V 2465 429 V 2464 429 V 2463 428 V 2461 428 V 2460 428 V 2459 427 V 2457 427 V 2456 426 V 2455 426 V 2453 426 V 2452 425 V 2451 425 V 2450 425 V 2448 424 V 2447 424 V 2445 424 V 2444 424 V 2443 423 V 2441 423 V 2440 423 V 2439 422 V 2437 422 V 2436 422 V 2434 422 V 2433 421 V 2432 421 V 2430 421 V 2429 421 V 2427 420 V 2426 420 V 2424 420 V 2423 420 V 2421 420 V 2420 419 V 2418 419 V 2417 419 V 2415 419 V 2414 419 V 2412 419 V 2411 418 V 2409 418 V 2408 418 V 2406 418 V 2405 418 V 2403 418 V 2402 418 V 2400 418 V 2399 417 V 2397 417 V 2396 417 V 2394 417 V 2392 417 V 2391 417 V 2389 417 V 2388 417 V 2386 417 V 2384 417 V 2383 417 V 2381 417 V 2379 417 V 2378 417 V 2376 417 V 2374 417 V 2526 541 a(I)p 2374 417 V 2374 415 V 2374 413 V 2374 412 V 2374 410 V 2375 409 V 2375 407 V 2375 405 V 2375 404 V 2375 402 V 2375 400 V 2375 399 V 2375 397 V 2375 396 V 2375 394 V 2375 393 V 2375 391 V 2375 389 V 2375 388 V 2376 386 V 2376 385 V 2376 383 V 2376 382 V 2376 380 V 2376 379 V 2376 377 V 2377 376 V 2377 374 V 2377 373 V 2377 371 V 2377 370 V 2378 368 V 2378 367 V 2378 365 V 2378 364 V 2378 363 V 2379 361 V 2379 360 V 2379 358 V 2379 357 V 2380 355 V 2380 354 V 2380 353 V 2380 351 V 2381 350 V 2381 349 V 2381 347 V 2381 346 V 2382 344 V 2382 343 V 2382 342 V 2383 340 V 2383 339 V 2383 338 V 2384 336 V 2384 335 V 2384 334 V 2385 333 V 2385 331 V 2386 330 V 2386 329 V 2386 327 V 2387 326 V 2387 325 V 2388 324 V 2388 322 V 2388 321 V 2389 320 V 2389 319 V 2390 317 V 2390 316 V 2391 315 V 2391 314 V 2391 313 V 2392 311 V 2392 310 V 2393 309 V 2393 308 V 2394 307 V 2394 306 V 2395 304 V 2395 303 V 2396 302 V 2396 301 V 2397 300 V 2397 299 V 2398 298 V 2399 296 V 2399 295 V 2400 294 V 2400 293 V 2401 292 V 2401 291 V 2402 290 V 2403 289 V 2403 288 V 2404 287 V 2404 286 V 2405 285 V 2406 284 V 2406 283 V 2407 282 V 2408 281 V 2408 280 V 2409 279 V 2410 278 V 2410 277 V 2411 276 V 2412 275 V 2412 274 V 2413 273 V 2414 272 V 2414 271 V 2415 270 V 2416 269 V 2417 268 V 2417 267 V 2418 266 V 2419 265 V 2420 264 V 2420 264 V 2421 263 V 2422 262 V 2423 261 V 2424 260 V 2424 259 V 2425 258 V 2426 257 V 2427 257 V 2428 256 V 2428 255 V 2429 254 V 2430 253 V 2431 252 V 2432 252 V 2433 251 V 2433 250 V 2434 249 V 2435 248 V 2436 248 V 2437 247 V 2438 246 V 2439 245 V 2440 245 V 2441 244 V 2442 243 V 2442 242 V 2443 242 V 2444 241 V 2445 240 V 2446 240 V 2447 239 V 2448 238 V 2449 237 V 2450 237 V 2451 236 V 2452 235 V 2453 235 V 2454 234 V 2455 233 V 2456 233 V 2457 232 V 2458 232 V 2459 231 V 2460 230 V 2461 230 V 2462 229 V 2463 229 V 2465 228 V 2466 227 V 2467 227 V 2468 226 V 2469 226 V 2470 225 V 2471 225 V 2472 224 V 2473 223 V 2474 223 V 2476 222 V 2477 222 V 2478 221 V 2479 221 V 2480 220 V 2481 220 V 2483 219 V 2484 219 V 2485 218 V 2486 218 V 2487 217 V 2488 217 V 2490 217 V 2491 216 V 2492 216 V 2493 215 V 2495 215 V 2496 214 V 2497 214 V 2498 214 V 2500 213 V 2501 213 V 2502 212 V 2503 212 V 2505 212 V 2506 211 V 2507 211 V 2509 211 V 2510 210 V 2511 210 V 2513 210 V 2514 209 V 2515 209 V 2517 209 V 2518 208 V 2519 208 V 2521 208 V 2522 207 V 2523 207 V 2525 207 V 2526 207 V 2528 206 V 2529 206 V 2530 206 V 2532 206 V 2533 205 V 2535 205 V 2536 205 V 2538 205 V 2539 204 V 2540 204 V 2542 204 V 2543 204 V 2545 204 V 2546 203 V 2548 203 V 2549 203 V 2551 203 V 2552 203 V 2554 203 V 2555 202 V 2557 202 V 2558 202 V 2560 202 V 2561 202 V 2563 202 V 2565 202 V 2566 202 V 2568 202 V 2569 201 V 2571 201 V 2572 201 V 2574 201 V 2576 201 V 2577 201 V 2579 201 V 2580 201 V 2582 201 V 2584 201 V 2585 201 V 2587 201 V 2589 201 V 2590 201 V 2356 325 a(\022)939 631 y Fu(\026)-55 b Ft(x)988 646 y Fp(i)1012 655 y Fj(0)1058 836 y Ft(`)1099 851 y Fs(0)1295 717 y Ft(`)1336 732 y Fs(1)1058 447 y Ft(`)1099 462 y Fs(2)1274 620 y Ft(`)1315 635 y Fs(3)1489 836 y Ft(`)1530 851 y Fs(4)1727 717 y Ft(`)1768 732 y Fs(5)1511 501 y Ft(`)1552 516 y Fs(6)1274 232 y Ft(`)1315 247 y Fs(7)1727 286 y Ft(`)1768 301 y Fs(8)1856 350 y Ft(`)1897 365 y Fs(9)2105 350 y Ft(`)2146 365 y Fp(M)7 b Fn(\000)p Fs(4)2353 674 y Ft(`)2394 689 y Fp(M)g Fn(\000)p Fs(3)2590 501 y Ft(`)2631 516 y Fp(M)g Fn(\000)p Fs(2)2342 178 y Ft(`)2383 193 y Fp(M)g Fn(\000)p Fs(1)p Black 252 1260 a Fu(Figure)31 b(1:)44 b(The)33 b(path)g Ft(`)27 b Fu(=)h Fr(f)p Ft(`)1370 1275 y Fs(0)1409 1260 y Ft(;)17 b(:)g(:)g(:)f(;)h(`)1669 1275 y Fp(M)7 b Fn(\000)p Fs(1)1838 1260 y Fr(g)32 b Fu(in)m(tro)s(duced)h(in)f(the)h (pro)s(of)e(of)h(Lemma)g(3.4)p Black Black Black 0 1550 a Fv(Lemma)42 b(3.5.)p Black 44 w Fk(Assume)d(c)-5 b(ondition)38 b(\(2.13\))g(is)h(satis\014e)-5 b(d)38 b(then,)i(r)-5 b(e)g(c)g(al)5 b(ling)2849 1524 y Fu(\026)2841 1550 y Ft(\022)2886 1565 y Fp(I)2966 1550 y Fk(has)38 b(b)-5 b(e)g(en)38 b(de\014ne)-5 b(d)38 b(in)0 1695 y(\(3.18\),)1278 1834 y Fo(e)1255 1859 y Ft(K)d Fu(:=)28 b(sup)1510 1941 y Fp(i)p Fn(2)p Fp(N)1739 1765 y Fo(X)1667 1976 y Fp(I)5 b Fn(\032)p Fp(N)s(;)12 b(I)5 b Fn(3)p Fp(i)1955 1859 y Fu(\(3)17 b Ft(e)p Fu(\))2142 1818 y Fn(j)p Fp(I)5 b Fn(j)2245 1833 y Fu(\026)2238 1859 y Ft(\022)2283 1874 y Fp(I)2351 1859 y Fr(\024)2466 1792 y Fu(1)p 2466 1837 49 4 v 2466 1928 a(3)3531 1859 y(\(3.22\))0 2160 y Fk(Pr)-5 b(o)g(of.)32 b Fu(By)h(using)f(Lemma)g(3.4)g(and)h(recalling)d(that)i Ft(\022)2039 2175 y Fn(f)p Fp(i)p Fn(g)2166 2160 y Fu(=)27 b(0)33 b(for)f(all)e Ft(i)e Fr(2)g Ft(N)10 b Fu(,)33 b(w)m(e)h(get)103 2414 y(sup)109 2496 y Fp(i)p Fn(2)p Fp(N)338 2320 y Fo(X)266 2531 y Fp(I)5 b Fn(\032)p Fp(N)s(;)11 b(I)5 b Fn(3)p Fp(i)554 2414 y Fu(\(3)17 b Ft(e)p Fu(\))741 2373 y Fn(j)p Fp(I)5 b Fn(j)844 2388 y Fu(\026)836 2414 y Ft(\022)881 2429 y Fp(I)977 2414 y Fr(\024)56 b Fu(6)17 b Ft(C)23 b(e)33 b Fu(sup)1354 2496 y Fp(i)p Fn(2)p Fp(N)1511 2320 y Fo(X)1518 2532 y Fp(k)r Fn(\025)p Fs(1)1734 2320 y Fo(X)1681 2523 y Fl(I)t Fi(\032)p Fl(N)5 b Fi(nf)p Fl(i)p Fi(g)1732 2582 y(j)p Fl(I)t Fi(j)p Fj(=)p Fl(k)1942 2414 y Fu(\(6)17 b Ft(e)p Fu(\))2129 2373 y Fp(k)2171 2304 y Fo(\020)2247 2414 y Fu(inf)2248 2476 y Fp(j)t Fn(2)p Fp(I)2381 2414 y Fr(j)p Fu(\003)2477 2429 y Fp(j)2513 2414 y Fr(j)2541 2304 y Fo(\021)2623 2414 y Ft(e)2668 2373 y Fn(\000)p Fp(a)12 b(\016)i(T)c Fs(\()p Fp(I)5 b Fs(\))298 2754 y Fr(\024)56 b Fu(6)17 b Ft(C)23 b(e)44 b Fu(sup)668 2835 y Fp(i)692 2844 y Fj(0)727 2835 y Fn(2)p Fp(N)853 2659 y Fo(X)861 2871 y Fp(k)r Fn(\025)p Fs(1)1024 2686 y Fu(\(6)17 b Ft(e)p Fu(\))1211 2650 y Fp(k)p 1024 2731 230 4 v 1098 2822 a Ft(k)s Fu(!)624 3073 y Fr(\002)918 2979 y Fo(X)761 3182 y Fl(i)783 3197 y Fj(1)818 3182 y Fl(;:::)o(;i)934 3199 y(k)973 3182 y Fi(2)p Fl(N)5 b Fi(nf)p Fl(i)1154 3197 y Fj(0)1188 3182 y Fi(g)801 3250 y Fl(i)823 3268 y(h)863 3250 y Fi(6)p Fj(=)p Fl(i)932 3275 y(h)968 3261 y Fi(0)1006 3250 y Fl(;)14 b(h)p Fi(6)p Fj(=)p Fl(h)1158 3236 y Fi(0)1246 2963 y Fo(\020)1397 3073 y Fu(inf)1323 3136 y Fp(h)p Fs(=0)p Fp(;:::)n(;k)1607 3073 y Fr(j)p Fu(\003)1703 3088 y Fp(i)1727 3100 y Fl(h)1770 3073 y Fr(j)1798 2963 y Fo(\021)1896 3073 y Fu(exp)2062 2963 y Fo(n)2150 3073 y Fr(\000)23 b Ft(a)17 b(\016)2391 3006 y Fu(1)p 2391 3050 49 4 v 2391 3142 a(2)2560 3073 y(inf)2483 3140 y Fp(\031)r Fn(2)p Fs(\005)2626 3149 y Fj(0)2661 3140 y Fs(\()p Fp(k)r Fs(\))2823 2949 y Fp(k)2771 2979 y Fo(X)2787 3191 y Fp(l)q Fs(=1)2931 3073 y Fu(d)2985 2992 y Fo(\000)3031 3073 y Fu(\003)3099 3088 y Fp(i)3123 3102 y Fl(\031)r Fj(\()p Fl(l)p Fi(\000)p Fj(1\))3316 3073 y Ft(;)g Fu(\003)3428 3088 y Fp(i)3452 3102 y Fl(\031)r Fj(\()p Fl(l)p Fj(\))3565 2992 y Fo(\001)3611 2963 y(o)298 3466 y Fr(\024)56 b Fu(6)17 b Ft(C)23 b(e)44 b Fu(sup)668 3547 y Fp(i)692 3556 y Fj(0)727 3547 y Fn(2)p Fp(N)853 3371 y Fo(X)861 3583 y Fp(k)r Fn(\025)p Fs(1)1024 3398 y Fu(\(6)17 b Ft(e)p Fu(\))1211 3362 y Fp(k)p 1024 3443 230 4 v 1098 3534 a Ft(k)s Fu(!)1447 3371 y Fo(X)1289 3574 y Fl(i)1311 3589 y Fj(1)1346 3574 y Fl(;:::;i)1463 3592 y(k)1501 3574 y Fi(2)p Fl(N)5 b Fi(nf)p Fl(i)1682 3589 y Fj(0)1717 3574 y Fi(g)1329 3643 y Fl(i)1351 3660 y(h)1392 3643 y Fi(6)p Fj(=)p Fl(i)1461 3668 y(h)1497 3654 y Fi(0)1534 3643 y Fl(;)14 b(h)p Fi(6)p Fj(=)p Fl(h)1686 3629 y Fi(0)1838 3371 y Fo(X)1775 3587 y Fp(\031)r Fn(2)p Fs(\005)1918 3596 y Fj(0)1952 3587 y Fs(\()p Fp(k)r Fs(\))2062 3355 y Fo(\020)2213 3466 y Fu(inf)2138 3528 y Fp(h)p Fs(=0)p Fp(;:::)o(;k)2422 3466 y Fr(j)p Fu(\003)2518 3481 y Fp(i)2542 3493 y Fl(h)2586 3466 y Fr(j)2614 3355 y Fo(\021)2734 3341 y Fp(k)2690 3371 y Fo(Y)2698 3583 y Fp(l)q Fs(=1)2834 3466 y Ft(e)2879 3412 y Fn(\000)p Fp(a)e(\016)3039 3385 y Fj(1)p 3039 3397 31 3 v 3039 3438 a(2)3091 3412 y Fs(d\(\003)3206 3422 y Fl(i)3228 3443 y(\031)r Fj(\()p Fl(l)p Fi(\000)p Fj(1\))3421 3412 y Fp(;)p Fs(\003)3490 3422 y Fl(i)3512 3443 y(\031)r Fj(\()p Fl(l)p Fj(\))3626 3412 y Fs(\))298 3842 y Fr(\024)56 b Fu(6)17 b Ft(C)23 b(e)705 3717 y Fn(1)668 3747 y Fo(X)676 3959 y Fp(k)r Fs(=1)812 3842 y Fu(\(6)17 b Ft(e)p Fu(\))999 3801 y Fp(k)1041 3701 y Fo(\022)1131 3842 y Fu(sup)1151 3923 y Fp(i)p Fn(2)p Fp(I)1345 3747 y Fo(X)1294 3963 y Fp(j)t Fn(2)p Fp(I)5 b Fn(nf)p Fp(i)p Fn(g)1556 3842 y Fr(j)p Fu(\003)1652 3857 y Fp(i)1680 3842 y Fr(j)21 b(^)i(j)p Fu(\003)1914 3857 y Fp(j)1950 3842 y Fr(j)f Ft(e)2045 3801 y Fn(\000)p Fp(a)12 b(\016)2204 3774 y Fj(1)p 2204 3786 V 2204 3827 a(2)2257 3801 y Fs(d\(\003)2372 3811 y Fl(j)2405 3801 y Fp(;)p Fs(\003)2474 3811 y Fl(i)2500 3801 y Fs(\))2531 3701 y Fo(\023)2605 3724 y Fp(k)298 4153 y Fr(\024)56 b Fu(6)17 b Ft(C)23 b(e)747 4086 y Fu(6)17 b Ft(e)g(\025)p 661 4130 355 4 v 661 4222 a Fu(1)22 b Fr(\000)h Fu(6)17 b Ft(e)g(\025)1081 4153 y Fr(\024)1224 4086 y Fu(1)p 1224 4130 49 4 v 1224 4222 a(3)0 4431 y(where,)34 b(in)e(the)h(last)f(line,)f(w)m(e)i(used)h(\(2.13\).)p 3709 4431 4 66 v 3713 4368 59 4 v 3713 4431 V 3771 4431 4 66 v 0 4575 a Fk(Pr)-5 b(o)g(of)41 b(of)f(Pr)-5 b(op)g(osition)40 b(3.3.)e Fu(W)-8 b(e)40 b(note)f(that)g(from)f(the)h(b)s(ound)g (\(3.22\))f(it)g(follo)m(ws)g Ft(e)3208 4539 y Fp(\022)3241 4550 y Fl(I)3319 4575 y Fr(\024)h Ft(e)3486 4521 y Fs(\026)3480 4539 y Fp(\022)3513 4550 y Fl(I)3592 4575 y Fr(\024)g Ft(e)p Fu(.)0 4719 y(By)c(letting)e Ft(")e Fu(:=)g(1)p Ft(=)p Fu(3)j(and)1054 4693 y Fo(e)1049 4719 y Ft(\022)1094 4734 y Fp(I)1166 4719 y Fu(:=)d(\(3)p Ft(e)p Fu(\))1470 4683 y Fn(j)p Fp(I)5 b Fn(j)1557 4693 y Fu(\026)1549 4719 y Ft(\022)1594 4734 y Fp(I)1669 4719 y Fu(and)35 b(using)f(Lemma)f(3.5,)i(w)m(e)h(can)e(apply)h(the)g(estimate)0 4864 y(in)d([6,)g(App)s(endix)h(B])g(and)g(get)316 5076 y Fo(X)323 5289 y Fp(k)r Fn(\025)p Fs(1)501 5076 y Fo(X)493 5288 y Fp(I)p 493 5300 36 3 v 5 w Fn(2I)615 5300 y Fl(k)686 5076 y Fo(Y)690 5288 y Fp(I)5 b Fn(2)p Fp(I)p 773 5300 V 854 5145 a Fu(\026)846 5171 y Ft(\022)891 5186 y Fp(I)948 5171 y Ft(e)993 5130 y Fp(\022)1026 5141 y Fl(I)1094 5171 y Fr(\024)1199 5076 y Fo(X)1206 5289 y Fp(k)r Fn(\025)p Fs(1)1384 5076 y Fo(X)1376 5288 y Fp(I)p 1376 5300 V 5 w Fn(2I)1498 5300 y Fl(k)1569 5076 y Fo(Y)1573 5288 y Fp(I)g Fn(2)p Fp(I)p 1656 5300 V 1713 5171 a Ft(")1759 5130 y Fn(j)p Fp(I)g Fn(j)1859 5145 y Fo(e)1854 5171 y Ft(\022)1899 5186 y Fp(I)1967 5171 y Fr(\024)28 b Ft(")2141 5146 y Fo(e)2118 5171 y Ft(K)2225 5001 y Fo(")2283 5171 y Fu(1)22 b(+)2668 5104 y Ft(e)2729 5051 y Fg(e)2713 5068 y Fp(K)2804 5104 y Fr(\000)h Fu(1)p 2462 5148 698 4 v 2462 5254 a(1)f(+)g Ft(")2677 5225 y Fs(2)2716 5254 y Ft(e)2777 5208 y Fg(e)2761 5225 y Fp(K)2852 5254 y Fr(\000)g Fu(2)p Ft("e)3107 5208 y Fg(e)3091 5225 y Fp(K)3169 5001 y Fo(#)3283 5171 y Fr(\024)55 b Fu(1)0 5518 y(since)33 b Ft(")27 b Fr(\024)h Fu(1)p Ft(=)p Fu(3)k(and)809 5493 y Fo(e)786 5518 y Ft(K)j Fr(\024)28 b Fu(1)p Ft(=)p Fu(3.)p 3709 5518 4 66 v 3713 5455 59 4 v 3713 5518 V 3771 5518 4 66 v Black 1841 5806 a(15)p Black eop %%Page: 16 17 16 16 bop Black Black 146 407 a Fu(It)33 b(is)f(no)m(w)h(straigh)m (tforw)m(ard)f(to)h(conclude)g(the)g(pro)s(of)e(of)h(Theorem)h(2.1.)0 576 y Fk(Pr)-5 b(o)g(of)35 b(of)f(the)h(b)-5 b(ound)35 b(\(2.14\).)c Fu(F)-8 b(or)32 b Ft(I)p 1316 592 51 4 v 35 w Fr(2)c(I)1542 591 y Fp(k)1618 576 y Fu(w)m(e)33 b(ha)m(v)m(e,)h(recalling)d(\(3.16\))596 726 y Fo(Y)600 937 y Fp(I)5 b Fn(2)p Fp(I)p 683 949 36 3 v 740 820 a Ft(\022)785 835 y Fp(I)842 820 y Ft(e)887 779 y Fp(\022)920 790 y Fl(I)987 820 y Fu(=)1091 726 y Fo(Y)1095 937 y Fp(I)g Fn(2)p Fp(I)p 1178 949 V 1235 820 a Ft(e)1280 779 y Fn(\000)p Fp(a)12 b Fs(\(1)p Fn(\000)p Fp(\016)r Fs(\))i Fp(T)c Fs(\()p Fp(I)5 b Fs(\))1745 794 y Fu(\026)1737 820 y Ft(\022)1782 835 y Fp(I)1839 820 y Ft(e)1884 779 y Fp(\022)1917 790 y Fl(I)1984 820 y Fr(\024)28 b Ft(e)2134 779 y Fn(\000)p Fp(a)13 b Fs(\(1)p Fn(\000)p Fp(\016)r Fs(\))g Fn(T)k Fs(\()p Fp(f)2546 788 y Fj(1)2581 779 y Fs(;)p Fp(:::)o Fs(;)p Fp(f)2714 787 y Fl(n)2756 779 y Fs(\))2820 726 y Fo(Y)2825 937 y Fp(I)5 b Fn(2)p Fp(I)p 2908 949 V 2972 794 a Fu(\026)2964 820 y Ft(\022)3009 835 y Fp(I)3066 820 y Ft(e)3111 779 y Fp(\022)3144 790 y Fl(I)0 1145 y Fu(and)33 b(the)g(b)s(ound)f(\(2.14\))g(follo)m(ws)g (from)f(Lemmata)g(3.1,)h(3.2)g(and)h(Prop)s(osition)e(3.3.)p 3709 1145 4 66 v 3713 1082 59 4 v 3713 1145 V 3771 1145 4 66 v 0 1389 a Fv(Ac)m(kno)m(wledgmen)m(ts)0 1533 y Fx(It)f(is)g(a)h(pleasure)e(to)i(express)f(our)g(thanks)g(to)h(B.)g (Scopp)s(ola)e(for)h(useful)f(discussions)f(and)h(commen)m(ts.)0 1902 y Fc(References)p Black 56 2137 a Fx([1])p Black 50 w(L.)43 b(Bertini,)j(N.)e(Cancrini,)g(F.)g(Cesi,)i(\\The)e(sp)s (ectral)f(gap)g(for)h(a)g(Glaub)s(er{t)m(yp)s(e)e(dynamics)g(in)h(a)201 2272 y(con)m(tin)m(uous)30 b(gas.")h Fb(Ann.)f(Inst.)g(H.)h(P)m(oincar) m(\023)-43 b(e)32 b(Probab.)e(Statist.)g Fz(32)p Fx(,)h(91{108)i (\(2001\).)p Black 56 2491 a([2])p Black 50 w(L.)48 b(Bertini,)j (E.N.M.)f(Cirillo,)f(E.)f(Olivieri,)i(\\Renormalization)d(group)h (transformations)f(under)201 2626 y(strong)d(mixing)e(conditions:)67 b(Gibbsianness)42 b(and)i(con)m(v)m(ergence)i(of)f(renormalized)d(in)m (teractions.")201 2762 y Fb(J.)30 b(Statist.)g(Ph)m(ys.)h Fz(97)p Fx(,)g(831{915)i(\(1999\).)p Black 56 2980 a([3])p Black 50 w(L.)44 b(Bertini,)i(E.N.M.)g(Cirillo,)e(E.)h(Olivieri,)f (\\Graded)h(cluster)e(expansion)h(for)g(lattice)g(systems.")201 3116 y(Preprin)m(t)28 b(2003.)p Black 56 3334 a([4])p Black 50 w(L.)36 b(Bertini,)g(E.N.M.)i(Cirillo,)c(E.)i(Olivieri,)f (\\Renormalization)g(group)h(in)f(the)h(uniqueness)e(region:)201 3470 y(w)m(eak)d(Gibbsianit)m(y)d(and)i(con)m(v)m(ergence.")j(Preprin)m (t)c(2003.)p Black 56 3688 a([5])p Black 50 w(L.)f(Bertini,)f(E.N.M.)j (Cirillo,)25 b(E.)j(Olivieri,)e(\\Randomly)h(p)s(erturb)s(ed)f(strong)i (mixing)f(systems:)39 b(b)s(eat-)201 3824 y(ing)29 b(Gri\016ths')g (singularit)m(y)g(ab)s(o)m(v)m(e)i(the)g(critical)e(temp)s(erature.")i (In)e(preparation.)p Black 56 4042 a([6])p Black 50 w(M.)39 b(Cassandro,)i(E.)e(Olivieri,)f(\\Renormalization)g(group)g(and)h (analyticit)m(y)f(in)g(one)h(dimension:)56 b(a)201 4178 y(pro)s(of)29 b(of)i(Dobrushin's)d(theorem.")j Fb(Comm.)f(Math.)i(Ph)m (ys.)e Fz(80)p Fx(,)h(255{269)i(\(1981\).)p Black 56 4396 a([7])p Black 50 w(R.L.)i(Dobrushin,)f(S.B.)h(Shlosman,)g (\\Completely)f(analytical)h(Gibbs)e(\014elds.")h Fb(Statist.)i(Ph)m (ys.)f(and)201 4532 y(Dyn.)30 b(Syst.)p Fx(,)h(Birkhauser,)e(371{403)k (\(1985\).)p Black 56 4750 a([8])p Black 50 w(R.L.)f(Dobrushin,)f(S.B.) i(Shlosman,)e(\\Completely)h(analytical)g(in)m(teractions)g (constructiv)m(e)h(descrip-)201 4886 y(tion.")d Fb(J.)g(Statist.)h(Ph)m (ys.)f Fz(46)p Fx(,)h(983{1014)j(\(1987\).)p Black 56 5104 a([9])p Black 50 w(M.)45 b(Duneau,)j(D.)d(Iagolnitzer,)j(B.)d (Souillard,)g(\\Decrease)i(prop)s(erties)c(of)i(truncated)f (correlation)201 5240 y(functions)29 b(and)g(analyticit)m(y)i(prop)s (erties)d(for)j(classical)e(lattices)i(and)f(con)m(tin)m(uous)g (systems.")h Fb(Comm.)201 5375 y(Math.)g(Ph)m(ys.)f Fz(31)p Fx(,)h(191{208)j(\(1973\).)p Black 1841 5806 a Fu(16)p Black eop %%Page: 17 18 17 17 bop Black Black Black 10 407 a Fx([10])p Black 51 w(M.)38 b(Duneau,)i(D.)f(Iagolnitzer,)h(B.)f(Souillard,)e(\\Strong)h (cluster)f(prop)s(erties)g(for)h(classical)f(systems)201 542 y(with)29 b(\014nite)g(range)i(in)m(teraction.")g Fb(Comm.)f(Math.)h(Ph)m(ys.)f Fz(35)p Fx(,)h(307{320)j(\(1974\).)p Black 10 761 a([11])p Black 51 w(M.)h(Duneau,)g(B.)g(Souillard,)e (\\Cluster)g(prop)s(erties)g(of)i(lattice)g(and)f(con)m(tin)m(uous)g (systems.")h Fb(Comm.)201 896 y(Math.)c(Ph)m(ys.)f Fz(47)p Fx(,)h(155{166)j(\(1977\).)p Black 10 1115 a([12])p Black 51 w(J.)24 b(F)-8 b(r\177)-45 b(ohlic)m(h,)26 b(J.Z.)e(Im)m(brie,)h (\\Impro)m(v)m(ed)g(p)s(erturbation)e(expansion)h(for)h(disordered)e (systems:)38 b(b)s(eating)201 1250 y(Gri\016ths')29 b(singularities.")f Fb(Comm.)i(Math.)h(Ph)m(ys.)f Fz(96)p Fx(,)h(145{180)j(\(1984\).)p Black 10 1469 a([13])p Black 51 w(J.)23 b(Glimm,)g(A.)g(Ja\013e,)i (\\Quan)m(tum)e(ph)m(ysics.)f(A)i(functional)d(in)m(tegral)i(p)s(oin)m (t)f(of)h(view.")g(Second)g(edition.)201 1604 y(Springer{V)-8 b(erlag,)29 b(New)i(Y)-8 b(ork,)31 b(1987.)p Black 10 1823 a([14])p Black 51 w(R.)38 b(Kotec)m(k)q(\023)-47 b(y,)43 b(D.)c(Preiss,)h(\\Cluster)d(expansion)g(for)h(abstract)h(p)s (olymer)e(mo)s(dels.")h Fb(Comm.)g(Math.)201 1958 y(Ph)m(ys.)30 b Fz(103)p Fx(,)h(491{498)j(\(1986\).)p Black 10 2177 a([15])p Black 51 w(F.)29 b(Martinelli,)f(E.)h(Olivieri,)d(\\Approac)m (h)k(to)g(equilibrium)24 b(of)30 b(Glaub)s(er)e(dynamics)f(in)h(the)i (one)f(phase)201 2312 y(region)g(I.)i(The)f(attractiv)m(e)i(case.")g Fb(Comm.)e(Math.)i(Ph)m(ys.)e Fz(161)p Fx(,)h(447{486)j(\(1994\).)p Black 10 2531 a([16])p Black 51 w(F.)22 b(Martinelli,)f(E.)h(Olivieri,) e(R.)i(Sc)m(honmann,)h(\\F)-8 b(or)22 b(2{)p Fa(D)k Fx(lattice)c(spin)e (systems)h(w)m(eak)i(mixing)d(implies)201 2666 y(strong)30 b(mixing.")f Fb(Comm.)h(Math.)i(Ph)m(ys.)e Fz(165)p Fx(,)h(33{47)i (\(1994\).)p Black 10 2885 a([17])p Black 51 w(E.)d(Olivieri,)d(\\On)i (a)i(cluster)e(expansion)g(for)h(lattice)g(spin)e(systems:)41 b(a)30 b(\014nite)f(size)h(condition)f(for)h(the)201 3020 y(con)m(v)m(ergence.")j Fb(J.)d(Statist.)h(Ph)m(ys.)f Fz(50)p Fx(,)h(1179{1200)k(\(1988\).)p Black 10 3239 a([18])p Black 51 w(E.)c(Olivieri,)d(P)-8 b(.)32 b(Picco,)g(\\Cluster)f (expansion)f(for)h Fa(D)s Fx({dimensional)e(lattice)i(systems)h(and)e (\014nite)h(v)m(ol-)201 3374 y(ume)e(factorization)j(prop)s(erties.")d Fb(J.)h(Statist.)h(Ph)m(ys.)f Fz(59)p Fx(,)h(221{256)j(\(1990\).)p Black 10 3593 a([19])p Black 51 w(D.)43 b(Ruelle,)h(\\Statistical)f (mec)m(hanics:)65 b(Rigorous)42 b(results.")g(W.A.)i(Benjamin,)h(Inc.,) h(New)d(Y)-8 b(ork{)201 3728 y(Amsterdam)30 b(1969.)p Black 10 3947 a([20])p Black 51 w(R.H.)i(Sc)m(honmann,)g(S.B.)g (Shlosman,)f(\\Complete)h(analyticit)m(y)f(for)h(2D)h(Ising)e (completed.")h Fb(Comm.)201 4082 y(Math.)f(Ph)m(ys.)f Fz(170)p Fx(,)h(453{482)j(\(1995\).)p Black 10 4301 a([21])p Black 51 w(A.N.)d(Shiry)m(aev,)e(\\Probabilit)m(y)-8 b(.")30 b(Springer{V)-8 b(erlag,)30 b(New)g(Y)-8 b(ork,)32 b(1996.)p Black 10 4519 a([22])p Black 51 w(B.)h(Simon,)f(\\The)g (statistical)h(mec)m(hanics)f(of)h(lattice)g(gases.")h(V)-8 b(ol.)34 b(I.)e(Princeton)g(Univ)m(ersit)m(y)g(Press,)201 4655 y(Princeton,)d(NJ,)i(USA,)f(1993.)p Black 10 4873 a([23])p Black 51 w(H.)42 b(Sp)s(ohn,)g(\\Equilibrium)37 b(\015uctuations)k(for)g(in)m(teracting)h(Bro)m(wnian)f(particles.")h Fb(Comm.)f(Math.)201 5009 y(Ph)m(ys.)30 b Fz(103)p Fx(,)h(1{33)h (\(1986\).)p Black 1841 5806 a Fu(17)p Black eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0302110418899--