%!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: unyex.dvi %%Pages: 12 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips unyex.dvi -o %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2001.01.02:1126 %%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 TeXDict begin 39158280 55380996 1000 600 600 (unyex.dvi) @start %DVIPSBitmapFont: Fa cmsy10 10.95 1 /Fa 1 3 df<0060166000F816F06C1501007E15036CED07E06C6CEC0FC06C6CEC1F806C 6CEC3F006C6C147E6C6C5C6C6C495A017E495A6D495A6D6C485A6D6C485A6D6C48C7FC90 3803F07E6D6C5A903800FDF8EC7FF06E5A6E5AA24A7E4A7EECFDF8903801F8FC903803F0 7E49487E49486C7E49486C7E49486C7E017E6D7E496D7E48486D7E4848147E4848804848 EC1F804848EC0FC048C8EA07E0007EED03F0481501481500006016602C2C73AC47>2 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb msbm10 10.95 1 /Fb 1 83 df<007FB612FCB812C06C16F83B03E007C07FFE0000903A0F001F7F80020E90 38078FC093380383E0EFC0F0040113788484EFE00E1600180F84A760180E0401131EEFC0 1C183C04035BEF81F093380787E093381F7FC04BB5C7FC020FB512FC17C004F7C8FC9139 0E1C078092381E03C0ED0E01030F7FED078003037FEEC078923801E0380300133C707EEE 780EEE380F93383C0780EE1E03040E7F93380F01E093380780F004031370EFC078706C7E 04007F717E943878078094383803C00003D90F8090383C01E0007FB500FE90381FFFFCB6 806C823E3E7EBD39>82 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmbx12 17.28 7 /Fc 7 116 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fd cmsy6 6 3 /Fd 3 49 df0 D<136013701360A20040132000E0137038F861 F0387E67E0381FFF803807FE00EA00F0EA07FE381FFF80387E67E038F861F038E0607000 40132000001300A21370136014157B9620>3 D48 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe cmex10 12 29 /Fe 29 112 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 D[<12F812FE6C7E13E07FEA3FF8EA1FFEEA07FF6C7F6C7F6C7FEB 3FF06D7E806D7E6D7E7F6D7F817F81147F81143F81141FA281140FA3811407B3B3B3B3AD 8180A46E7FA36E7FA36F7EA26F7E151F82150F826F7E6F7E816F7F707E707E707E707E70 7E707E933801FF809338007FC0EF3FE0170FA2173FEF7FC0933801FF80933803FE004C5A 4C5A4C5A4C5A4C5A4C5A4B90C7FC5D4B5A4B5A5E151F5E153F4B5AA24B5AA34A5BA34A90 C8FCA45C5DB3B3B3B3AD140F5DA3141F5DA2143F5D147F5D14FF5D5B5D4990C9FC5B495A 495A5C495AEBFFE0485B485B4890CAFCEA1FFEEA3FF8B45A5B138048CBFC12F8>51 298 114 131 80 I<12F812FE6C7E7F13F06C7EEA1FFC6C7E6C7E6C13C06C7F6C7F137F 6D7E6D7E6D7E807F6D7F817F817F81147F81143F81A2141F81A36E7EA56E1380B3B3B021 5A6F7E59>57 D<913807FF80B3B3B04A1300A54A5AA35D143FA25D147F5D14FF5D5B5D5B 5D4990C7FC5B5C495A495A495A13FF485B485B4890C8FC485A485AEA7FF8485A13C05B48 C9FC12F8215A6F8059>59 D61 D<17FF040313C093380F81F093381E0078043E137C93387C01FC9338 F803FEA2150116F01503EF01FC9338E0007003071400A3150FA45E151FA7153FA74B5AA7 15FFA85C93C8FCA95C5DA85DA74A5AA75DA75D140FA45DA3001C5C007F131FEAFF8092C9 FC5C143EA26C485A007C5B003C5B381F03E03807FF80D801FECAFC376F7B7F2F>82 D<1B3FF3FFC0973803E0F0973807C03897380F801C081F137E97383F01FEF303FF1A7E1A FE1AFC1901A2963903F801FEF300781C004F5AA2190FA262191FA34F5AA44F5AA319FF97 C8FCA360A261A21803A3611807A461180FA44E5AA4183FA261A2187FA361A218FFA44D5B A55F96C9FCA35FA360A2170FA460171FA460173FA54D5AA54D5AA45E60A55E60A44C90CA FCA54C5AA55F161FA45F163FA45FA2167FA35FA316FF5FA54B5BA494CBFCA25DA35EA215 07A25EA44B5AA45E151FA45E153FA35EA2157FA25EA315FF93CCFCA34A5AA44A5AA35D14 075DA2140F5D121E397F801FC0EAFFC05D143F92CDFC5C147E6C485AEA7E00383801F86C 485A380F07C03803FF80D800FCCEFC58DD7B7F37>90 D104 DI110 D<12F012FE6C7E13E0EA3FF8EA0FFCEA03FFC67F6D7E6D7E6D7E6D7E6D 7E6D7EA26D7E7FA281147FB3B3AF81143FA281141F81140F8114076E7E6E7E6E7E6F7E6F 7EED1FF0ED07F8ED01FE923800FF80163FA216FF923801FE00ED07F8ED1FF0ED3FC04B5A 4BC7FC4A5A4A5A4A5A140F5D141F5D143F5DA2147F5DB3B3AF14FF92C8FCA25B495AA249 5A495A495A495A495A495A000390C9FCEA0FFCEA3FF8EAFFE0138048CAFC12F029B27483 42>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff cmr6 6 8 /Ff 8 57 df<14E0A3497EA2497EA3EB06FC147CA2EB0C7E143EEB1C3FEB181FA201307F 140FA201607F140701E07FEBC003A2D801807F1401A2D803007F140048800006147CA200 0E147E121F3AFFE007FFE0A223247DA329>3 D<130C1338137013E0EA01C0EA03801300 5A120EA25AA25AA312781270A312F0AB1270A312781238A37EA27EA27E7E1380EA01C0EA 00E013701338130C0E317AA418>40 D<12C012707E7E7E7E7E1380EA01C0A2EA00E0A213 70A313781338A3133CAB1338A313781370A313E0A2EA01C0A2EA038013005A120E5A5A5A 12C00E317CA418>I<1438B2B712FEA3C70038C7FCB227277C9F2F>43 D<13E01201120712FF12F91201B3A7487EB512C0A212217AA01E>49 DI<14E01301A213031307A2130D131D133913 31136113E113C1EA01811203EA07011206120C121C12181230127012E0B6FCA2380001E0 A6EB03F0EB3FFFA218227DA11E>52 D<137F3803FFC0380781E0380E0070481338001813 1C1238A3123C003F1338381FC078EBE0F0380FF9E03807FF80120114C0000713F0380F0F F8381C03FC383801FE3870007E141F48130F1407A314060070130E0078130C6C1338001F 13F03807FFC0C6130018227DA01E>56 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg msbm8 8 1 /Fg 1 83 df82 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh cmmi6 6 13 /Fh 13 117 df11 D<13F8D803FE1318487E48EB803048EBC060EA3C03 397000E0C00060136048EB71801431C7FCEC3300141B141EA2141CA31418A31438A21430 1470A45CA35CA21D217E9520>13 D37 D<127812FCA212FEA2127E1206A3120CA2121C121812301260124007107A8513>59 D<1308A4131CA500C0EB0180397FBEFF00381FFFFC000713F0000113C06C6CC7FCA2497E 13F73801E3C013C1380380E0EB006000067F00041310487F19197D9820>63 D<903AFFFE07FFF0A2903A07C0003E00A249485BA449C75AA4013E495AA3013FB5FC495C 90387C0003A349495AA44848495AA4484849C7FCA300075C3AFFFE07FFF0A22C227CA132 >72 D<001FB612FCA29039003E007C003C151C00385B12300070151812605C5AA3C64848 1300A4495AA4495AA4495AA449C8FCA35B381FFFFE5C26227DA124>84 D<13F8EA0FF0A21200A2485AA4485AA43807801E147FEB81C3EB8387380F060F495A1318 EB700E4848C7FCA213FCEA1E7EEA3C0F80EB0781158039780F0300A21402EB070600F013 8CEB03F8386000F019247CA221>107 D<000F13FC381FC3FF3931C707803861EC0301F8 13C0EAC1F0A213E03903C00780A3EC0F00EA0780A2EC1E041506D80F00130C143C151815 38001EEB1C70EC1FE0000CEB07801F177D9526>110 D<3801E01F3903F07FC0390639C1 E0390C3F80F0EB3E00001814F8013C137815F8C65AA49038F001F0A3EC03E0D801E013C0 EBF00715809038F80F003803DC3CEBCFF8EBC7E001C0C7FC485AA448C8FCA2EA7FF012FF 1D20809520>112 DI115 D<133013785BA4485AA4485AB51280 A23803C000485AA448C7FCA4121EA25B1480383C03001306A25BEA1C38EA0FF0EA07C011 217D9F18>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fi cmsy8 8 11 /Fi 11 108 df0 D<006015C000E014016C14030078EC07806C EC0F006C141E6C5C6C6C5B6C6C5B6C6C485A6C6C485A90387807806D48C7FCEB1E1E6D5A EB07F86D5A6D5A497E497EEB0F3CEB1E1E497E496C7E496C7E48486C7E48486C7E484813 7848C77E001E80488048EC078048EC03C048140100601400222376A137>2 D<130C131EA50060EB01800078130739FC0C0FC0007FEB3F80393F8C7F003807CCF83801 FFE038007F80011EC7FCEB7F803801FFE03807CCF8383F8C7F397F0C3F8000FCEB0FC039 781E078000601301000090C7FCA5130C1A1D7C9E23>I20 D<137813FE1201A3120313FC A3EA07F8A313F0A2EA0FE0A313C0121F1380A3EA3F00A3123E127E127CA35AA35A0F227E A413>48 DI<91B512C01307131FD97F80C7FC01FCC8FCEA 01F0EA03C0485A48C9FC120E121E5A123812781270A212F05AA3B712C0A300E0C9FCA37E 1270A212781238123C7E120E120F6C7E6C7EEA01F0EA00FCEB7F80011FB512C013071300 222B7AA52F>I54 D<14301478A214FCA2497E14CEA2EB03CF14870107 7F1403010F7FEB0E01011E7FEB1C00013C7F013813700178137801701338A201F0133C49 131C0001141E49130E0003140F497F0007158090C712034815C0000E1401001E15E0001C 1400A2003C15F000381570007815780070153800F0153C48151C160C26297CA72F>94 D<12E0B3B3B3AD034378B114>106 D<0060136000E01370B3B3B3AB00601360144379B1 23>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj cmmi8 8 27 /Fj 27 122 df11 DI<131FD9 FFC013304801F0137000076D13604815E0D9807C13C0391E003C0148011E13800038EB0E 03480107130000605CEC030612E0C7138EEC018C159C159815B815B0A215F05DA35DA25D A21403A44AC7FCA4140EA45CA31418242C7F9D24>I<131C013EEB0380ED07C0017E130F 1680137CA201FC131F16005BA200015C153E5BA20003147E157C5BA20007ECFC08EDF818 5BA2000F0101133816309038E003F002071370001F90380EF8609039F83C78E090397FF0 3FC090391FC00F0048C9FCA2123EA2127EA2127CA212FCA25AA21270252C7E9D2A>22 D<14FC903803FF8090380F87C090381F03E090383C01F013789038F800F8485A485AA248 5A1401120F1380A21403001F14F01300A2EC07E05A15C0140FEC1F80481400006F133E6D 5A00675B3863C1F038E1FFC0D8E07EC7FC48C8FCA47EA212F8B512E06C13F8121F1207C7 12181D2B7B9D24>37 D39 D<123C127E12FFA4127E123C08087A8714>58 D<123C127EB4FCA21380A212 7F123D1201A312031300A25A1206120E5A5A5A126009157A8714>I<15C0140114031580 A214071500A25C140EA2141E141CA2143C143814781470A214F05CA213015CA213035C13 0791C7FCA25B130EA2131E131CA2133C1338A21378137013F05BA212015BA212035BA212 0790C8FC5A120EA2121E121CA2123C1238A212781270A212F05AA21A437CB123>61 D<14C0A5497EA700F0EC03C039FF83F07F003FB61200000F14FC000114E06C6C1380D91F FEC7FCEB07F8497EA2497EEB3F3FEB3E1F496C7EEB7807496C7EA248486C7E48486C7E49 137090C71230222180A023>63 D<92387FC003913903FFF80791391FC03E0F91397E0007 1FD901F8EB03BF4948EB01FED90FC013004948147E49C8FC017E157C49153C485A120348 481538485AA2485A173048481500A2127F90CAFCA35A5AA5EE018016031700A2007E5D16 06160E6C5D5E6C6C5C000F5D6C6C495A6C6CEB0780D801F8011EC7FCD8007E13F890381F FFE0010390C8FC302F7CAD32>67 D<90273FFFFC0FB5FCA2D900FEC7EA3F80A24A1500A2 01015D177E5CA2010315FE5F5CA2010714015F5CA2010F14035F5C91B6FC5B9139C00007 E05CA2013F140F5F91C7FCA249141F5F137EA201FE143F94C7FC5BA200015D167E5BA200 0315FEB539E03FFFF8A2382D7CAC3A>72 D<90263FFFFC90381FFF80A2D900FEC73803F8 0018E04AEC07804DC7FC0101151C5F4A14E04C5A01034A5A040EC8FC4A5B5E010714E04B 5A9138E00780030EC9FC010F131F157F4A487E14C190391FC71FC014CEEC9C0F02F07F90 383FE00702C07FEC0003825B6F7E137E6F7E13FE167F5B707E1201161F4981831203B539 E001FFFEA2392D7CAC3C>75 D<90383FFFFEA2010090C8FC5C5CA21301A25CA21303A25C A21307A25CA2130FA25CA2131FA25CA2133FA291C7EA0180A24914031700017E5C160601 FE140EA2495C163C12015E49EB01F84B5A0003141FB7FC5E292D7DAC30>I<000FB8FCA2 3B1FC003F8003F0100151F001C4A130E123C003801071406123000704A130EA20060010F 140C12E0485CA2141FC715005DA2143FA292C8FCA25CA2147EA214FEA25CA21301A25CA2 1303A25CA21307A25C130F131F001FB512F0A2302D7FAC29>84 D89 D<13F8121FA21201A25BA2 1203A25BA21207A25BA2120FEBC7E0EB9FF8EBB83C381FF01EEBE01F13C09038800F80EA 3F00A2123EA2007E131FA2127CA2143F00FC14005AA2147EA2147C14FC5C387801F01303 495A383C0F806C48C7FCEA0FFCEA03F0192F7DAD1E>98 D<151FEC03FFA2EC003FA2153E A2157EA2157CA215FCA215F8A21401EB07E190381FF9F0EB7C1DEBF80FEA01F03903E007 E0EA07C0120FEA1F8015C0EA3F00140F5A007E1480A2141F12FE481400A2EC3F02150614 3E5AEC7E0E007CEBFE0C14FC0101131C393E07BE18391F0E1E38390FFC0FF03903F003C0 202F7DAD24>100 D<131FEA03FFA2EA003FA2133EA2137EA2137CA213FCA25BA2120115 F89038F003FCEC0F0E0003EB1C1EEC387EEBE07014E03807E1C09038E3803849C7FC13CE EA0FDC13F8A2EBFF80381F9FE0EB83F0EB01F81300481404150C123EA2007E141C151800 7CEBF038ECF83000FC1470EC78E048EB3FC00070EB0F801F2F7DAD25>107 D<3907C007E0391FE03FF83918F8783E393879E01E39307B801F38707F00126013FEEAE0 FC12C05B00815C0001143E5BA20003147E157C5B15FC0007ECF8081618EBC00115F0000F 1538913803E0300180147016E0001F010113C015E390C7EAFF00000E143E251F7E9D2B> 110 D<90387C01F89038FE07FE3901CF8E0F3A03879C0780D907B813C0000713F0000690 38E003E0EB0FC0000E1380120CA2D8081F130712001400A249130F16C0133EA2017EEB1F 80A2017C14005D01FC133E5D15FC6D485A3901FF03E09038FB87C0D9F1FFC7FCEBF0FC00 0390C8FCA25BA21207A25BA2120FA2EAFFFCA2232B829D24>112 D<903807E03090381FF87090387C1CF0EBF80D3801F00F3903E007E0EA07C0000F130338 1F800715C0EA3F00A248130F007E1480A300FE131F481400A35C143E5A147E007C13FE5C 1301EA3E07EA1F0E380FFCF8EA03F0C7FC13015CA313035CA21307A2EBFFFEA21C2B7D9D 20>I115 D<130E131FA25BA2133EA2137EA2137CA213FCA2B512F8A23801F800A25BA21203A25BA2 1207A25BA2120FA25BA2001F1310143013001470146014E0381E01C0EB0380381F0700EA 0F0EEA07FCEA01F0152B7EA919>II<013F137C9038FFC1FF3A01C1E383803A 0380F703C0390700F60F000E13FE4813FC12180038EC0700003049C7FCA2EA200100005B A313035CA301075B5D14C000385CD87C0F130600FC140E011F130C011B131C39F03BE038 D8707113F0393FE0FFC0260F803FC7FC221F7E9D28>120 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmmi12 12 52 /Fk 52 123 df11 DI I<1578913807FFE0021F13FC91383C7FFEEC7007EC6003ECE0004A13381600A280A380A2 80147CA2147E143E143F816E7EA26E7E81140781EC3FFC14FF903803E1FEEB07C190381F 00FF133E49EB7F805B0001143F485A484814C049131F120F485AA248C7FC150F5A127EA3 00FEEC1F805AA316005A5DA2153E157E157CA26C5C127C4A5A6C495AA26C495A6C6C485A 6C6C48C7FC3803E07C3800FFF0EB1FC027487CC62B>I<01F8EB03FCD803FEEB1FFFD807 1F90387C0FC03B0E0F80E007E0001C9038C3C003271807C70013F002CE1301003801DC14 F8003013D8EB0FF800705B00605BA200E0491303D8C01F15F05C12001607133F91C713E0 A2160F5B017E15C0A2161F13FE491580A2163F1201491500A25E120349147EA216FE1207 495CA21501120F495CEA0380C81203A25EA21507A25EA2150FA25EA2151FA25EA2153FA2 93C7FC150E2D417DAB30>17 D21 D<147002F8140E0101153FA301035DA24A147EA201 0715FEA24A5CA2010F1401A24A5CA2011F1403A24A5CA2013F1407A291C75BA249140FA2 017E5DA201FE021F1318183849ED8030A20001033F13701860EE7F005E486C16E0DB01DF 13C09238039F016DD9071F1380489039801E0F83903BF7C078078700903AE1FFE003FE90 3AE07F8000F8000F90CAFCA25BA2121FA25BA2123FA290CBFCA25AA2127EA212FEA25A12 3835417DAB3B>II<010FB712E0013F 16F05B48B812E04817C02807E0060030C7FCEB800EEA0F00001E010C13705A0038011C13 605A0060011813E000E013381240C7FC5C4B5AA214F014E01301150314C01303A3EB0780 82130FA2EB1F00A34980133E137EA24980A2000114015BA26C48EB00E0342C7EAA37>25 D<0203B612E0021F15F091B7FC4916E0010716C090270FF80FF8C7FC90381FC00349486C 7E017EC7FC49147E485A4848143E0007153F5B485AA2485AA2123F90C8FC5E48157E127E A216FE00FE5D5A15015EA24B5A007C5D15074B5A5E6C4AC8FC153E6C5C5D390F8003F039 07C007C02601F03FC9FC38007FFCEB1FE0342C7DAA37>27 D<137E48B46C150626078FE0 150E260607F0151C260E03F81538000C6D1570D81C0116E000006D15C0010015016EEC03 806EEC0700170E6E6C5B5F5F6E6C136017E04C5A6E6C485A4CC7FC0207130E6F5A5E1630 913803F8705EEDF9C06EB45A93C8FC5D6E5A81A2157E15FF5C5C9138073F80140E141C91 38181FC014381470ECE00FD901C07FEB038049486C7E130E130C011C6D7E5B5B496D7E48 5A48488048C8FC000681000E6F137048EE806048033F13E04892381FC0C048ED0FE34892 3803FF00CA12FC37407DAB3D>31 D<15FE913803FFC091380F83E091383E01F89138F800 FC4948137C4948137E49487F130F495A91C713805B137EA25BA2485A167F12035BA216FF 000716005BA25D000F5D5B5E1503001F5D15075E150F003F5D00374A5A00335D6D49C7FC 157ED871F05B0060495A90387803E090383C0FC0D91FFFC8FC38E003F890CAFCA25AA47E A312F812FE007FB512C015F0001F800007801201C8121CA2293F78AB32>37 D<177F0130913803FFC00170020F13E0494A13F048484A13F84848EC7F0190C838F8007C 484A48133C00064A48131C000E4B131E000C4A48130E001C92C7FC0018140E150C003802 1C1406003014185D180E00704A140C1260154003C0141C00E017184A5A4817386C17304A C8127018E01260007049EC01C0EF03800078010614070038EE0F00003C010E141E6C167C D81F805D6C6C48EB03F0D807F0EC0FE0D803FEEC3FC02801FFFC03FFC7FC6C6CB55A6D14 F8010F14E0010114809026007FF8C8FC02F8C9FCA25CA21301A3495AA31307A25C130FA4 131F5C6DCAFC37417BAB40>39 D<121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A0A78891B >58 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A312011380120313 005A1206120E5A5A5A12600B1D78891B>II<161816 3C167CA2167816F8A216F01501A216E01503A216C01507A21680150FA2ED1F00A2151E15 3EA2153C157CA2157815F8A25D1401A24A5AA25D1407A25D140FA292C7FC5CA2141E143E A2143C147CA25CA25C1301A25C1303A25C1307A25C130FA291C8FC5BA2133EA2133C137C A2137813F8A25B1201A25B1203A2485AA25B120FA290C9FC5AA2121E123EA2123C127CA2 127812F8A25A126026647BCA31>I<127012FCB4FCEA7FC0EA1FF0EA07FCEA01FF38007F C0EB1FF0EB07FE903801FF809038007FE0EC1FF8EC03FE913800FF80ED3FE0ED0FF8ED03 FF030013C0EE3FF0EE0FFCEE01FF9338007FC0EF1FF0EF07FCEF01FF9438007FC0F01FE0 A2F07FC0943801FF00EF07FCEF1FF0EF7FC04C48C7FCEE0FFCEE3FF0EEFFC0030390C8FC ED0FF8ED3FE0EDFF80DA03FEC9FCEC1FF8EC7FE0903801FF80D907FECAFCEB1FF0EB7FC0 4848CBFCEA07FCEA1FF0EA7FC048CCFC12FC12703B3878B44C>I64 D<4CB46C1318043F01F01338 4BB512FC0307D9007E1378DB1FF090380F80F0DB7F80EB03C1DA01FEC7EA01C34A48EC00 E7DA0FF0ED7FE04A48153F4A5A02FFC9121F494817C04948160F495A130F4A1780494816 07495A137F4948170091CAFC5A485A1906485AA2485A96C7FC121F5BA2123F5BA3127F5B A4485AA419C0A2180161127F180396C7FC6018066C6C160E601818001F17386D5E000F5F 6D4B5A6C6C4B5A00034CC8FC6C6C150E6C6C153C017F5DD93FC0EB01E0D91FF0EB0FC0D9 07FE017FC9FC0101B512FCD9003F13E0020790CAFC45487CC546>67 D<91B912F8A3020001C0C7123F6F48EC07F003FF1503190193C9FCA21A705C5DA3020317 605DA314075D18C01701020F4B13005DA21703021F92C8FC4B5BA25F023F141E4B13FE92 B5FCA24A5CED8000173CA202FF141892C7FCA217384915305CA21770010315604A91C9FC A313075CA3130F5CA3131F5CA2133FA313FFB612F8A345447CC33F>70 D<4CB46C1318043F01F013384BB512FC0307D9007E1378DB1FF090380F80F0DB7F80EB03 C1DA01FEC7EA01C34A48EC00E7DA0FF0ED7FE04A48153F4A5A02FFC9121F494817C04948 160F495A130F4A178049481607495A137F4948170091CAFC5A485A1906485AA2485A96C7 FC121F5BA2123F5BA3127F5BA4485A4CB612805EA293C7EBE000725AA3007F60A218FF96 C7FCA26C7E5F606C7EA2000F16036D5E6C6C15070003160F6C6C151F6C6CED3DF8D97F80 14786D6CEB01E0D91FF0903807C078D907FE90387F00700101B500FC1330D9003F01F090 C8FC020790CAFC45487CC54D>I<91B6D8E003B61280A3020001E0C70003EB8000DB7F80 6E48C7FC03FF1503A293C85BA219075C4B5EA2190F14034B5EA2191F14074B5EA2193F14 0F4B5EA2197F141F4B5EA219FF143F92B8C8FCA3DA7FC0C712014B5DA2180314FF92C85B A218075B4A5EA2180F13034A5EA2181F13074A5EA2183F130F4A5EA2187F131F4A5EA201 3F16FFA24A93C9FCD9FFE002037FB6D8E003B67EA351447CC351>I<91B612F8A3020001 E0C8FC6F5A4B5AA293C9FCA35C5DA314035DA314075DA3140F5DA3141F5DA3143F5DA314 7F5DA314FF92CAFCA35B4A16C0A21801010317804A15031900A201075E4A1506180E181E 010F161C4A153C18381878011F16F84A4A5A1703013F150F4D5A4A14FF01FF02075BB9FC A2603A447CC342>76 D<91B500C0933803FFFE63630200F1FE00DB6FE0EE1BF803EF171F 1B3703CFEF67F0A21BCF0201EF018F038F60DB87F0ED030F1B1F020317060307040C5BA2 F2183F020717300206616F6C15601B7F020E17C0020CDC018090C7FCA24F485A021C1606 0218606F6C5C1A0102381618023004305BA2F16003027016C00260606F6CEB01801A0702 E0ED03004A03065CA24E130F01015E4A60047F5B1A1F01035E91C74A5CA24D48133F494B C7FC010661EE3F861A7F010E158C010C039892C8FCA205B05C011C15E001186001386E5A 190101785D01FC92C75BD803FFEF07FEB500F8011E0107B512FE161C160C5F447BC35E> I79 D<91B712F018FF19E002009039C0003FF86F48EB07FC03FFEC01FEF0 007F93C8EA3F801AC0F11FE05C5D1AF0A214035DA30207EE3FE05DA2F17FC0020F17804B 15FF1A004E5A021F4B5A4B4A5AF00FE04E5A023F037FC7FC4BEB03FCEF1FF092B612804A 4AC8FC923980007F80EF0FC0EF07F002FF6E7E92C77F1701845B4A1400A2170113035CA2 170313075CA24D5A130F5CA3011F18185CA2013F4C13381A304A6F1370D9FFE0020314E0 B600E0ED01C00501EB0380943900FE0F00CBEA3FFEF007F045467CC34A>82 D<48BA12C05AA291C7D980001380D807F092C7121F4949150F0180170748C75B1903120E 48020316005E12181238003014074C5C00701806126000E0140F485DA3C8001F92C7FC5E A3153F5EA3157F5EA315FF93CAFCA35C5DA314035DA314075DA3140F5DA3141F5DA3143F 5DA2147FA214FF01037F001FB612FCA25E42447EC339>84 D<003FB500F80103B512E0A3 26003FF8C8381FF800D91FE0ED07E0013F705A615C96C7FC60017F16065CA2180E01FF16 0C91C9FCA2181C4817185BA21838000317305BA21870000717605BA218E0120F495EA217 01121F495EA21703123F4993C8FCA25F127F491506A2170E00FF160C90C9FC171CA21718 173817304816705F6C5E6C15014C5A4CC9FC6C150E6D141E001F5D6D5C6C6CEB01E06C6C 495A6C6CEB1F80C6B401FECAFC90387FFFF8011F13E0010190CBFC43467AC342>I<007F B56C91381FFFF8B65DA2000101E0C8000313006C0180ED01FCF000F0614E5AA2017F4C5A 96C7FC1806A2606E5DA2013F5E1870186060A24D5A6E4AC8FCA2011F1506170E170C5FA2 6E5C5FA2010F5D16015F4CC9FCA26E13065EA201075C5EA25E16E06E5B4B5A13034BCAFC 1506A25D151CECFE185D13015D5DA26E5AA292CBFC5C13005C5CA25CA25C45467BC339> I89 D<020FB812C05C1A809326800001130003F8C7FCDA3FE04A 5A03804A5A92C8485A027E4B5A027C4B5A02784B5A4A4B5AA24A4A90C7FC4A4A5A01014B 5A4D5A4A4A5A01034B5A91C8485A4D5AA290C84890C8FC4C5A4C5A4C5A4C5A4C5A4C5A4C 5AA24B90C9FC4B5A4B5A4B5A4B5A4B5A4B5AA24B5A4A90CAFC4A5A4A4814064A5A4A5A4A 48140E4A48140CA24A48141C4990C8121849481538495A49485D495A494815F049485D17 01494814034890C8485A4848150F4848151F48484B5A484815FF48481403043F90C8FC48 B8FCB9FC5F42447BC343>I96 DI III II<157E9138 03FF8091390FC1E0E091391F0073F0027E13334A133F4948131F010315E04948130F495A A2494814C0133F4A131F137F91C713805B163F5A491500A25E120349147EA216FEA2495C A21501A25EA21503150700015D150F0000141F6D133F017CEB77E090383E01E790381F07 8F903807FE0FD901F85B90C7FC151FA25EA2153FA293C7FCA2001C147E007F14FE485C4A 5A140348495AEC0FC000F8495A007C01FEC8FC381FFFF8000313C02C407EAB2F>I<14FE 137FA3EB01FC13001301A25CA21303A25CA21307A25CA2130FA25CA2131FA25CED3FC090 393F81FFF0913887C0FC91380E007E023C133ED97F70133F4A7F4A14805C13FF91C7FC5B A24848143F17005BA200035D167E5BA2000715FE5E5B1501000F5DA24913035E001F1607 030713064914E0150F003FEDC00E170C90C7141CEE80184816381730007E167017E000FE 91380781C0EEC38048913801FF000038EC007C30467BC438>I<14FE137FA3EB01FC1300 1301A25CA21303A25CA21307A25CA2130FA25CA2131FA25C163F013FECFFC0923803C0E0 9138000703ED1E0F491338ED701F017E13E0EC01C001FE018013C00203EB07004948C8FC 140E00015B5C495A5C3803FBC001FFC9FC8014F83807F1FE9038F03F809038E00FE06E7E 000F130381EBC001A2001FED01C017801380A2003F15031700010013F05E481506160E00 7E150C161C00FE01005BED787048EC3FE00038EC0F802B467BC433>107 D<01F8D903FCEC7F80D803FED91FFF903803FFE0D8071F903B7C0FC00F81F83E0E0F80E0 07E01C00FC001C9026C3C0030178137C271807C700D9F0E0137E02CE902601F1C0133E00 3801DCDAFB80133F003001D892C7FCD90FF814FF0070495C0060495CA200E04949485CD8 C01F187E4A5C1200040715FE013F6091C75BA2040F14014960017E5D1903041F5D13FE49 4B130762043F160E0001060F130C4992C713C0191F4CED801C00031A1849027E1638F200 3004FE167000071A60494A16E0F201C0030192380F0380000FF18700494AEC03FED80380 D90070EC00F84F2D7DAB55>109 D<01F8EB03FCD803FEEB1FFFD8071F90387C0FC03B0E 0F80E007E03A0C07C3C003001CD9C7007F001801CE1301003801DC80003013D8EB0FF800 705B00605BA200E0491303D8C01F5D5C12001607013F5D91C7FCA2160F495D137E161F5F 13FE49143F94C7FC187000014B136049147E16FE4C13E0000317C049150104F813801703 00071700495D170EEE781C000FED7C3849EC1FF0D80380EC07C0342D7DAB3A>I 112 D<91380FC00391383FF0079138F83C0F903903E00E1E90390FC0063E90381F800790 393F00037E4914FC01FE1301485AA2484814F812075B000F140316F0485AA2003F140749 14E0A3007F140F4914C0A3151F90C713805AA2153F6C1500A2127E5D007F14FE6C1301A2 14036C6C485A000F131E3807C0383803E0F13901FFC1F838003F01130014035DA314075D A3140F5DA2141FA2143F011FB51280A21600283F7DAB2B>I115 D<141C147EA314FE5CA313015CA313035CA313075CA200 7FB512FCB6FC15F839000FC000A2131F5CA3133F91C7FCA35B137EA313FE5BA312015BA3 12035BA21570000714605B15E015C0000F130101C013801403EC070000071306140E5C6C 6C5A000113F03800FFC0013FC7FC1E3F7EBD23>I<133ED9FF8014E02603C3C0EB03F038 0703E0380601F0000E1507121CD818035D12380030150FA2D870075D00605B161FEAE00F 00C0495CEA001F4A133FA2013F92C7FC91C7FC5E5B017E147EA216FE13FE495CA20301EB 01801703484802F81300A25F0303130616F000001407030F130E6D010D130C017C011D13 1C033913186D9038F0F838903A1F03C07870903A07FF803FE0903A01FC000F80312D7DAB 38>I<02FCEB07E0903A03FF801FFC903A0F07C0781E903A1C03E0E01F903A3801F1C07F D9700013804901FB13FF4848EBFF00495B000316FE90C71438484A130012061401000E5C 120CC7FC14035DA314075DA3140F5DA3021F143817305D1770023F1460121E003F16E026 7F807FEB01C0026F148000FF01EF1303D901CFEB070000FE903887C00E267C03835B3A3C 0F01E0783A1FFC00FFE0D803F0EB3F80302D7EAB37>120 D<133ED9FF8014E02603C3C0 EB03F0380703E0380601F0000E1507001C16E0EA180312380030150F007016C0EA60075C 161FD8E00F158000C05BEA001F4A133F1700133F91C7FC5E49147E137EA216FE01FE5C5B A215015E485AA215035EA200001407150F6D5C017C131F153F6D13FF90391F03CFC09038 07FF8F903801FC0F90C7121F5EA2153F93C7FCD807C05BD81FE0137E5DA24848485A4A5A 01805B39380007C00018495A001C49C8FC6C137C380781F83803FFE0C66CC9FC2C407DAB 30>I<027CEB018049B413034901801300010F6D5A49EBE00E6F5A90393F03F838903978 007EF80170EB1FF00160EB01E001E05C49495A90C748C7FC150E5D5D5D5D4A5A4A5A4AC8 FC140E5C5C5C5CEB03C049C9FC130E49141C4914185B49143848481430491470D8039014 F048B4495A3A0FEFC007C0391E03F01FD81C01B55A486C91C7FC485C00606D5A00E0EB3F F048EB0FC0292D7CAB2D>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmti12 12 46 /Fl 46 124 df12 D<167016E0ED01C0ED0380ED0700150E153C5D15F85D4A5A4A5A4A5A140F4AC7FC141E14 3E5C147814F8495A5C1303495AA2495AA249C8FCA25B133E137E137CA25BA212015BA212 035BA212075BA2120FA25BA2121FA290C9FCA25AA2123EA3127EA2127CA65AAB1278A612 7C123CA47EA2120E120FA27E6C7EA26C7EA26C7E1360246472CA28>40 D<1560A2157081A281151E150E150FA2811680A3ED03C0A516E0A21501A71503A91507A2 16C0A4150FA21680A2151FA21600A25DA2153EA2157EA2157C15FCA25D1401A25D14035D A214075D140F5DA24AC7FCA2143EA25C147814F8495AA2495A5C1307495A91C8FC131E13 3E5B13785B485A485A485A48C9FC121E5A5A12E05A23647FCA28>I<13F0EA03FC1207A2 EA0FFEA4EA07FCEA03CCEA000C131C1318A2133813301370136013E0EA01C013801203EA 0700120E5A5A5A5A5A0F1D7A891E>44 D<120FEA3FC0127FA212FFA31380EA7F00123C0A 0A76891E>46 D<16C01501A215031507ED0F80151F153F157F913801FF005C140F147F90 3807FCFEEB0FF0EB0700EB00015DA314035DA314075DA3140F5DA3141F5DA3143F5DA314 7F92C7FCA35C5CA313015CA313035CA313075CA2130FA2131F133FB612FCA25D224276C1 32>49 DII<026014300278EB01F091397F801FE091B612C01780170016FC4914F016C0 DACFFEC7FC02C0C8FC13035CA3130791C9FCA35B130EA3131E90381C07F8EC3FFE9138F8 0F8090393DC007C0D93F807F90383E0003013C80496D7E1370A290C7FC82A41503A41507 5E120E123F486C130F00FF5DA390C7485A5A00F84A5A12E04B5A93C7FC15FE14016C5C00 70495A0078495A6CEB1FC0003E495A261F80FEC8FC6CB45A000313E0C66CC9FC2C4476C1 32>53 D57 D<14F0EB01FC1303EB07FE130FA214FCEB07F814F0EB01E090C7FCB3A513 F0EA03F8487EA2120FA46C5AEA03D8EA001813381330A21370136013E05B12015B120348 C7FC1206120E5A5A5A5A5A173E7AAA1E>59 D67 D<91B91280A30201902680000713006E90C8FC4A163F A24B81A30203160E5DA314074B151E191CA2140F5D17075F021F020E90C7FC5DA2171E02 3F141C4B133CA2177C027F5CED800392B5FCA291B65AED00071601A2496E5A5CA2160101 035D5CA2160301075D4A90CAFCA3130F5CA3131F5CA3133F5CA2137FA313FFB612E0A341 447AC340>70 D<027FB512E091B6FCA20200EBE000ED7F8015FFA293C7FCA35C5DA31403 5DA314075DA3140F5DA3141F5DA3143F5DA3147F5DA314FF92C8FCA35B5CA313035CA313 075CA3130F5CA3131F5CA2133FA25CEBFFE0B612E0A25D2B447BC326>73 D<91B66C90383FFFF8A302010180C7000F13006E90C8EA07FC4A17F01AC04B4B5A4FC7FC 193C02035E4B5DF003E0F0078002074BC8FC4B141E6018F8020F4A5A4BEB03C04D5A4DC9 FC021F141E4B137C17F04C5A023F495A4B487E161F163F027F497EED80FFED81EF923883 CFF89138FF8F8FED1E07033C7F157849EBF00303E07F15C092380001FF495A5C707FA213 074A6E7EA2173F010F825C171F84131F4A140F84A2013F6F7E5CA2017F6F7EA24A4A7E49 6C4A7FB66C90B512FC5E614D447AC34B>75 D<91B612F0A25F020101C0C7FC6E5B4A90C8 FCA25DA314035DA314075DA3140F5DA3141F5DA3143F5DA3147F5DA314FF92C9FCA35B5C A3010316104A1538A21878010716705C18F018E0010F15015C18C01703011F15074A1580 170FA2013FED1F004A5C5F017F15FE16034A130F01FFEC7FFCB8FCA25F35447AC33D>I< 91B56C93387FFFC08298B5FC02014DEBC0006E614A5FA203DF4C6CC7FC1A0E63912603CF E05D038F5F1A381A711407030FEEE1FCA2F101C3020FEE0383020E60F107036F6C150702 1E160E021C60191CF1380F143C023804705BA2F1E01F0278ED01C091267003F85EF00380 1A3F02F0ED070002E0030E5CA24E137F130102C04B91C8FC606201036D6C5B02805F4D5A 943803800113070200DA07005BA2050E1303495D010E606F6C5A1907011E5D011C4B5CA2 7048130F133C01384B5C017892C7FC191F01F85C486C027E5DD807FE027C4A7EB500F001 78013FB512C0A216705A447AC357>I<91B712F018FEF0FF800201903980007FE06E90C7 EA1FF04AED07F818034B15FCF001FE1403A24B15FFA21407A25DA2140FF003FE5DA2021F 16FC18074B15F8180F023F16F0F01FE04B15C0F03F80027FED7F0018FE4BEB03FCEF0FF0 02FFEC7FC092B6C7FC17F892CAFC5BA25CA21303A25CA21307A25CA2130FA25CA2131FA2 5CA2133FA25CA2137FA25C497EB67EA340447AC342>80 D83 D<48B912F85AA2913B0007FC001FF0D807F84A130701E001 0F140349160148485C90C71500A2001E021F15E05E121C123C0038143F4C1301007818C0 127000F0147F485DA3C800FF91C7FC93C9FCA35C5DA314035DA314075DA3140F5DA3141F 5DA3143F5DA3147F5DA314FF92CAFCA35B5CA21303A21307497E007FB612C0A25E3D446F C346>I97 DIIIII<14FE137FA3EB01FC 13001301A25CA21303A25CA21307A25CA2130FA25CA2131FA25C157F90393F83FFC09138 8F81F091381E00F802387F4948137C5C4A137EA2495A91C7FCA25B484814FE5E5BA20003 14015E5BA2000714035E5B1507000F5DA249130F5E001F1678031F1370491480A2003F02 3F13F0EE00E090C7FC160148023E13C01603007E1680EE070000FEEC1E0FED1F1E48EC0F F80038EC03E02D467AC432>104 D<143C147E14FE1301A3EB00FC14701400AE137C48B4 FC3803C780380703C0000F13E0120E121C13071238A21278EA700F14C0131F00F0138012 E0EA003F1400A25B137EA213FE5B12015BA212035B141E0007131C13E0A2000F133CEBC0 38A21478EB807014F014E0EB81C0EA0783EBC7803803FE00EA00F8174378C11E>I<16F0 ED03F8A21507A316F0ED01C092C7FCAEEC01F0EC07FCEC1E1EEC380F0270138014E01301 14C0EB03800107131F1400A2130E153F131E011C140090C7FC5DA2157EA215FEA25DA214 01A25DA21403A25DA21407A25DA2140FA25DA2141FA25DA2143FA292C7FCA25C147EA214 FE001C5B127F48485A495AA248485A495AD8F81FC8FCEA707EEA3FF8EA0FC0255683C11E >I<14FE137FA3EB01FC13001301A25CA21303A25CA21307A25CA2130FA25CA2131FA25C 167E013F49B4FC92380783C09138000E07ED3C1F491370ED603F017E13E0EC01C09026FE 03801380913907000E00D9FC0E90C7FC5C00015B5C495AEBF9C03803FB8001FFC9FCA214 F03807F3FCEBF07F9038E01FC06E7E000F130781EBC003A2001F150FA20180140EA2003F 151E161C010013E0A2485DA2007E1578167000FE01015B15F1489038007F800038021FC7 FC2A467AC42D>IIIIII<91381F800C91387FE01C903901F0703C9039 07C0387890390F801CF890381F001D013E130F017E14F05B48481307A2484814E012075B 000F140F16C0485AA2003F141F491480A3007F143F90C71300A35D00FE147EA315FE5DA2 007E1301A24A5A1407003E130FA26C495A143B380F80F33807C3E73901FF87E038007E07 1300140F5DA3141F5DA3143F92C7FCA25CA25C017F13FEA25D263F76AB2D>III<1470EB01F8A313035CA313 075CA3130F5CA3131F5CA2007FB512E0B6FC15C0D8003FC7FCA25B137EA313FE5BA31201 5BA312035BA312075BA3120F5BA2EC0780001F140013805C140E003F131EEB001C143C14 385C6C13F0495A6C485AEB8780D807FEC7FCEA01F81B3F78BD20>I<137C48B414072603 C780EB1F80380703C0000F7F000E153F121C0107150012385E1278D8700F147E5C011F14 FE00F05B00E05DEA003FEC0001A2495C137E150313FE495CA215071201495CA2030F1338 0003167849ECC070A3031F13F0EE80E0153F00011581037F13C06DEBEF83000001011480 90397C03C787903A3E0F07C70090391FFE01FE903903F000782D2D78AB34>I<017C1438 48B414FC3A03C78001FE380703C0000F13E0120E001C14000107147E1238163E1278D870 0F141E5C131F00F049131C12E0EA003F91C7123C16385B137E167801FE14705BA216F000 0115E05B150116C0A24848EB0380A2ED0700A2150E12015D6D5B000014786D5B90387C01 E090383F0780D90FFFC7FCEB03F8272D78AB2D>I<017CEE038048B4020EEB0FC02603C7 80013FEB1FE0380703C0000E7F5E001C037E130F01071607123804FE130300785DEA700F 4A1501011F130100F001804914C012E0EA003FDA000314034C14805B137E0307140701FE 1700495CA2030F5C0001170E495CA260A24848495A60A2601201033F5C7F4B6C485A0000 02F713036D9039E7E0078090267E01C349C7FC903A1F0781F81E903A0FFF007FF8D901FC EB0FE03B2D78AB41>I<02F8133FD907FEEBFFE0903A0F0F83C0F0903A1C07C780F89039 3803CF03017013EE01E0EBFC07120101C013F8000316F00180EC01C000074AC7FC130014 07485C120EC7FC140F5DA3141F5DA3143F92C8FCA34AEB03C01780147EA202FEEB070012 1E003F5D267F81FC130E6E5BD8FF83143CD903BE5B26FE079E5B3A7C0F1F01E03A3C1E0F 83C0271FF803FFC7FC3907E000FC2D2D7CAB2D>I<137C48B414072603C780EB1F803807 03C0000F7F000E153F001C1600130712385E0078157EEA700F5C011F14FE00F0495B12E0 EA003FEC00015E5B137E150301FE5C5BA2150700015D5BA2150F00035D5BA2151F5EA215 3F12014BC7FC6D5B00005BEB7C0390383E0F7EEB1FFEEB03F090C712FE5DA214015D121F 397F8003F0A24A5A4848485A5D48131F00F049C8FC0070137E007813F8383801F0381E07 C06CB4C9FCEA01FC294078AB2F>I<027C130749B4130F49EB800E010F141E49EBC03CED E03890393F03F07890397C00FDF00178EB3FE00170EB03C001F0148049130790C7EA0F00 151E5D5D5D4A5A4A5A4A5A4AC7FC141E5C5C5C495A495A495A49C8FC011E14F04914E05B 491301485A4848EB03C0D807B0130701FEEB0F80390FCF801F3A1F07E07F00393E03FFFE D83C015B486C5B00705C00F0EB7FC048011FC7FC282D7BAB28>I I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmsy10 12 19 /Fm 19 115 df<007FB912E0BA12F0A26C18E03C04789A4D>0 D<0060160600F8160F6C 161F007E163F6C167E6C6C15FC6C6CEC01F86C6CEC03F06C6CEC07E06C6CEC0FC06C6CEC 1F80017EEC3F006D147E6D6C5B6D6C485A6D6C485A6D6C485A6D6C485A6D6C485ADA7E3F C7FCEC3F7E6E5A6E5A6E5AA24A7E4A7EEC3F7EEC7E3F4A6C7E49486C7E49486C7E49486C 7E49486C7E49486C7E49C7127E017E8049EC1F804848EC0FC04848EC07E04848EC03F048 48EC01F84848EC00FC48C9127E007E163F48161F48160F00601606303072B04D>2 D<19E0F003F0180FF03FE0F0FF80943803FE00EF0FF8EF3FE0EFFF80DC03FEC7FCEE0FF8 EE3FE0EEFF80DB03FEC8FCED1FF8ED7FE0913801FF80DA07FEC9FCEC1FF0EC7FC04948CA FCEB07FCEB1FF0EB7FC04848CBFCEA07FCEA1FF0EA7FC048CCFCA2EA7FC0EA1FF0EA07FC EA01FF38007FC0EB1FF0EB07FCEB01FF9038007FC0EC1FF0EC07FC913801FF809138007F E0ED1FF8ED07FE923800FF80EE3FE0EE0FF8EE03FE933800FF80EF3FE0EF0FF8EF03FE94 3800FF80F03FE0F00FF01803F000E01900B0007FB912E0BA12F0A26C18E03C4E78BE4D> 20 D<127012FCB4FCEA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB01FF9038 007FC0EC1FF0EC07FC913801FF809138007FE0ED1FF8ED07FE923800FF80EE3FE0EE0FF8 EE03FE933800FF80EF3FE0EF0FF8EF03FE943800FF80F03FE0F00FF0A2F03FE0F0FF8094 3803FE00EF0FF8EF3FE0EFFF80DC03FEC7FCEE0FF8EE3FE0EEFF80DB03FEC8FCED1FF8ED 7FE0913801FF80DA07FEC9FCEC1FF0EC7FC04948CAFCEB07FCEB1FF0EB7FC04848CBFCEA 07FCEA1FF0EA7FC048CCFC12FC1270CDFCB0007FB912E0BA12F0A26C18E03C4E78BE4D> I<037FB612E00207B712F0143F91B812E0010301C0C9FCD907FCCAFCEB0FE0EB3F8049CB FC13FC485A485A485A5B485A121F90CCFC123EA2123C127CA2127812F8A25AA87EA21278 127CA2123C123EA27E7F120F6C7E7F6C7E6C7E6C7E137E6D7EEB1FE0EB07FC6DB47E0100 90B712E0023F16F01407020016E03C3A78B54D>26 D<1AF0A3861A78A21A7C1A3CA21A3E 1A1E1A1F747EA2747E747E87747E747E1B7E87757EF30FE0F303F8007FBC12FEBE1280A2 6CF3FE00CEEA03F8F30FE0F31F8051C7FC1B7E63505A505A63505A505AA250C8FC1A1E1A 3E1A3CA21A7C1A78A21AF862A359347BB264>33 D<1403A34A7EA44A7EA24A7EA24A7E4A 7EA24A7E903801F7BE903803E79F903907C78F80010F8090391F8787E090397F0783F801 FCEB80FCD803F8147FD81FF0EC3FE0D8FFC0EC0FFC0100140300FC150000601618C71500 B3B3B3A56EC8FC2E587EC432>I<49B4EF3FC0010F01E0923803FFF8013F01FC030F13FE 4901FF92383FE01F48B66C91397E0007C02603F80301E0D901F8EB01E02807E0007FF049 486D7E01806D6CD907C0147048C76C6C494880001EDA07FE49C87E001C6E6C013E150C48 6E6D48150E71481506486E01E0160793387FF1F0006092263FF3E08193381FFBC000E004 FF1780486F4915017090C9FC82707F8482717E844D7E6C4B6D1503006004EF1700933803 E7FE0070922607C7FF5DDC0F837F003004816D140E00384BC6FC0018033E6D6C5C001C4B 6D6C143C6C4BD91FFC5C6C4A486D6C5C6DD907E06D6C13036C6C49486D9038E00FE0D801 F0013FC890B55A27007C03FE6F91C7FC90263FFFF8031F5B010F01E0030313F8D901FECA EA7FC0592D7BAB64>49 D<92B6FC02071580143F91B7120001030180C8FCD907FCC9FCEB 1FE0EB3F80017ECAFC5B485A485A485A5B485A121F90CBFC123EA2123C127CA2127812F8 A25AA2B9FC1880A2180000F0CBFCA27EA21278127CA2123C123EA27E7F120F6C7E7F6C7E 6C7E6C7E137E6D7EEB1FE0EB07FC6DB47E010090B6FC023F1580140702001500313A78B5 42>I<126012F0B012FC12FEA212FC12F0B0126007267BAB00>55 D<0403B712F8043F16FE4BB9FC1507151F157F912601FC0090C7EA07FE912603F001ED01 FCDA07C04915F0DA0F80EE0080021F1800EC3F004A495A5C5C495A4A495A5C495A6DC7FC 90C8485AA35F161FA34C5AA35F167F94B612C0A293B7FC624B93C7FC19FC04FCC7127003 0392C8FC5EA24B5AA2150F5E151F5EA24B5AA24BCBFCA215FEA24A5AA24A5AEA0180000F 495AEA1FC0486C485AD87FF05B39FFFC1F80D87FFF90CCFC14FE6C5B6C13F06C5B000313 80D800FCCDFC50477EC348>70 D76 D<1538157CA215FEA24A7EA215EF02037FA2913807C7C0A291380F83E0A291381F01F0A2 EC1E00023E7FA24A137CA24A7FA249487FA24A7F010381A249486D7EA249486D7EA249C7 6C7EA2011E1400013E81A249157CA24981A2484881A24848ED0F80A2491507000717C0A2 4848ED03E0A248C9EA01F0A2003EEE00F8A2003C1778007C177CA248173EA248171E0060 170C373D7BBA42>94 D102 D<12FEEAFFE0EA07F8EA00FEEB7F806D7E6D7E130F6D7EA26D7EB3AD6D7E A26D7E806E7E6E7EEC0FE0EC03FC913800FFE0A2913803FC00EC0FE0EC3FC04A5A4AC7FC 5C495AA2495AB3AD495AA2495A131F495A495A01FEC8FCEA07F8EAFFE048C9FC236479CA 32>I<126012F0B3B3B3B3B3A81260046474CA1C>106 D<0070130700F01480B3B3B3B3B3 A800701400196474CA32>I<1B0C1B1E1B3EA21B7CA21BF8A2F201F0A2F203E0A2F207C0 A2F20F80A2F21F00A21A3EA262A262A24F5AA2621903A24F5AA24F5AA24FC7FCA2193EA2 61A261A24E5AA24E5AA24E5AA24E5AA2010C4CC8FC133C017C163EEA01FE00035F487E00 1E5F00387FD8707F4B5A00E07FD8003F4B5A80011F4B5AA26E4A5A130F6E4AC9FC13076E 143E13036E5C13016E5C7F6F5B027F1301A26F485A143F6F485A141F6F485A140F6F48CA FC1407EDFC3E14035E15FE02015B15FF6E5BA26F5AA26F5AA26F5AA26FCBFC150E4F647A 8353>112 D114 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn cmr8 8 15 /Fn 15 94 df<156015F0A24A7E4A7EA24A7E1406EC0E7F140C91381C3F8014184A6C7E 150F02607F150702C07F1503D901807F1501D903007F496D7E1306010E147F130C011C6E 7E131801386E7E1330496E7E160749811603484881160148C87F486F7E1206000E167F12 0C001CEE3F801218003FB812C0A24817E0A2B912F0342F7DAE3B>1 D<1406140FA34A7EA34A7EA3EC6FE01467A2ECC7F014C3A290380183F8148101037F1400 A2497F0106137EA249137F81A24980151FA24980150FA249801507A24980150300018149 1301A2000381A2487ED81FE0497ED8FFF890383FFFF0A22C2F7EAE31>3 D22 D<13031307130E131C1338137013F0EA01E013C01203EA0780 A2EA0F00A2121EA35AA45AA512F8A25AAB7EA21278A57EA47EA37EA2EA0780A2EA03C012 0113E0EA00F013701338131C130E1307130310437AB11B>40 D<12C07E12707E7E7E120F EA0780120313C0EA01E0A2EA00F0A21378A3133CA4131EA5131FA2130FAB131FA2131EA5 133CA41378A313F0A2EA01E0A2EA03C013801207EA0F00120E5A5A5A5A5A10437CB11B> I43 D48 D<130C133C137CEA03FC12FFEAFC7C1200B3B113FE387FFFFEA2172C7AAB23>III<140EA2141E143EA2147E14FEA2EB01BE130314 3E1306130E130C131813381330136013E013C0EA0180120313001206120E120C5A123812 305A12E0B612FCA2C7EA3E00A9147F90381FFFFCA21E2D7EAC23>I<123C127E12FFA412 7E123C1200AD123C127E12FFA4127E123C081D7A9C14>58 D61 D91 D93 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo msbm10 12 3 /Fo 3 83 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmr12 12 79 /Fp 79 128 df0 D<1618163CA2167EA216FFA24B7FA24B6C7EA29238063FE0A24B6C7EA24B6C7EA2923838 07FC153092387003FE15609238E001FF15C002016D7F5D02036E7E92C7FC4A6E7E140602 0E6E7E140C021C6E7E141802386E7E143002706E7E146002E06E7E5C01016F7F5C010370 7E91C9FC183F010683181F4983180F49831807498318034983A249707EA24848701380A2 48CBEA7FC0A20006F03FE0A248F01FF0A2001FBA12F8A24819FCA24819FEA2BCFC48477C C651>I<1507A34B7EA34B7EA34B7EA34B7E156FA2EDEFF815C7A202017F158715830203 7F1503150102077F140681020E80140C167FA24A80163FA24A80161FA24A80160FA24A80 1607A24948801603A249C77F1601A201068182A24982177FA24982173FA24982171FA201 7082136001E0150F6D821201486C82D80FFEED3FFEB500C00107B512F8A33D477DC644> 3 D<9239FFC001FC020F9038F80FFF913B3F803E3F03C0913BFC00077E07E0D903F89039 0FFC0FF0494890383FF81F4948EB7FF0495A494814E049C7FCF00FE04991393FC0038049 021F90C7FCAFB912F0A3C648C7D81FC0C7FCB3B2486CEC3FF0007FD9FC0FB512E0A33C46 7EC539>11 D<4AB4FC020F13E091387F80F8903901FC001C49487FD907E0130F4948137F 011FECFF80495A49C7FCA25B49EC7F00163E93C7FCACEE3F80B8FCA3C648C7FC167F163F B3B0486CEC7FC0007FD9FC1FB5FCA330467EC536>I<913801FFC0020FEBFB8091387F80 3F903801FC00494813FFEB07E0EB1FC0A2495A49C7FC167F49143F5BAFB8FCA3C648C712 3FB3B2486CEC7FC0007FD9FC1FB5FCA330467EC536>II22 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413 E013C0A312011380120313005A1206120E5A5A5A12600B1D78C41B>39 D<140C141C1438147014E0EB01C01303EB0780EB0F00A2131E5BA25B13F85B12015B1203 A2485AA3485AA348C7FCA35AA2123EA2127EA4127CA312FCB3A2127CA3127EA4123EA212 3FA27EA36C7EA36C7EA36C7EA212017F12007F13787FA27F7FA2EB0780EB03C01301EB00 E014701438141C140C166476CA26>I<12C07E12707E7E7E120F6C7E6C7EA26C7E6C7EA2 1378137C133C133E131E131FA2EB0F80A3EB07C0A3EB03E0A314F0A21301A214F8A41300 A314FCB3A214F8A31301A414F0A21303A214E0A3EB07C0A3EB0F80A3EB1F00A2131E133E 133C137C13785BA2485A485AA2485A48C7FC120E5A5A5A5A5A16647BCA26>I<16C04B7E B3AB007FBAFCBB1280A26C1900C8D801E0C9FCB3AB6F5A41407BB84C>43 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A312011380120313005A 1206120E5A5A5A12600B1D78891B>II<121EEA7F80A2EAFFC0A4 EA7F80A2EA1E000A0A78891B>I<14FF010713E090381F81F890383E007C01FC133F4848 EB1F8049130F4848EB07C04848EB03E0A2000F15F0491301001F15F8A2003F15FCA390C8 FC4815FEA54815FFB3A46C15FEA56D1301003F15FCA3001F15F8A26C6CEB03F0A36C6CEB 07E0000315C06D130F6C6CEB1F806C6CEB3F00013E137C90381F81F8903807FFE0010090 C7FC28447CC131>48 D<143014F013011303131F13FFB5FC13E713071200B3B3B0497E49 7E007FB6FCA3204278C131>II<49B4 FC010F13E0013F13FC9038FE01FE3A01F0007F80D803C0EB3FC048C7EA1FE0120EED0FF0 EA0FE0486C14F8A215077F5BA26C48130FEA03C0C813F0A3ED1FE0A2ED3FC01680ED7F00 15FE4A5AEC03F0EC1FC0D90FFFC7FC15F090380001FCEC007FED3F80ED1FC0ED0FE016F0 ED07F816FC150316FEA2150116FFA3121EEA7F80487EA416FE491303A2007EC713FC0070 1407003015F80038140F6C15F06CEC1FE06C6CEB3FC0D803E0EB7F803A01FE01FE003900 7FFFF8010F13E0010190C7FC28447CC131>II<000615C0D807C0130701FCEB 7F8090B612005D5D5D15E0158026063FFCC7FC90C9FCAE14FF010713C090381F01F09038 3800FC01F0137ED807C07F49EB1F8016C090C7120F000615E0C8EA07F0A316F81503A216 FCA5123E127F487EA416F890C712075A006015F0A20070140F003015E00038EC1FC07E00 1EEC3F806CEC7F006C6C13FE6C6C485A3901F807F039007FFFE0011F90C7FCEB07F82644 7BC131>II<121CA2EA1F8090B712C0A3481680A217 005E0038C8120C0030151C00705D0060153016705E5E4814014B5A4BC7FCC81206150E5D 151815385D156015E04A5AA24A5A140792C8FC5CA25C141E143EA2147E147CA214FCA213 01A3495AA41307A6130FAA6D5AEB01C02A457BC231>I<14FF010713E0011F13F890387F 00FE01FC133FD801F0EB1F804848EB0FC049EB07E00007EC03F048481301A290C713F848 1400A47FA26D130116F07F6C6CEB03E013FC6C6CEB07C09039FF800F806C9038C01F006C EBF03EECF87839007FFEF090383FFFC07F01077F6D13F8497F90381E7FFFD97C1F138049 6C13C02601E00313E048486C13F000079038007FF84848EB3FFC48C7120F003EEC07FE15 0148140016FF167F48153FA2161FA56C151E007C153EA2007E153C003E157C6C15F86DEB 01F06C6CEB03E06C6CEB07C0D803F8EB1F80C6B4EBFF0090383FFFFC010F13F001011380 28447CC131>I<14FF010713E0011F13F890387F80FC9038FC007E48487F4848EB1F8048 48EB0FC0000FEC07E0485AED03F0485A16F8007F140190C713FCA25AA216FE1500A516FF A46C5CA36C7E5D121F7F000F5C6C6C130E150C6C6C131C6C6C5BD8007C5B90383F01E090 390FFF80FE903801FE0090C8FC150116FCA4ED03F8A216F0D80F801307486C14E0486C13 0F16C0ED1F80A249EB3F0049137E001EC75A001C495A000F495A3907E01FE06CB51280C6 49C7FCEB1FF028447CC131>I<121EEA7F80A2EAFFC0A4EA7F80A2EA1E00C7FCB3A5121E EA7F80A2EAFFC0A4EA7F80A2EA1E000A2B78AA1B>I<121EEA7F80A2EAFFC0A4EA7F80A2 EA1E00C7FCB3A5121E127FEAFF80A213C0A4127F121E1200A512011380A3120313005A12 06120E120C121C5A5A12600A3E78AA1B>I<007FBAFCBB1280A26C1900CEFCB0007FBAFC BB1280A26C190041187BA44C>61 D<16C04B7EA34B7EA34B7EA34B7EA3ED19FEA3ED30FF A203707FED607FA203E07FEDC03FA2020180ED801FA2DA03007F160FA20206801607A24A 6D7EA34A6D7EA34A6D7EA20270810260147FA202E08191B7FCA249820280C7121FA249C8 7F170FA20106821707A2496F7EA3496F7EA3496F7EA201788313F8486C83D80FFF03037F B500E0027FEBFFC0A342477DC649>65 DII< B8FC17F017FC00019039C00007FF6C499038007FC0017FED1FE0EF07F0EF03FC717E717E 84727E727E727EA2727E85180385A2180185A38584A31A80AD1A00A36061A36118036118 0761180F614E5A183F614EC7FC18FEEF03FC4D5AEF1FE001FFED7FC0486DD907FFC8FCB8 12FC17F094C9FC41447CC34B>IIIIII 75 DIIIII82 D<49B41303010FEBE007013F13F89039FE00FE0FD8 01F8131FD807E0EB079F49EB03DF48486DB4FC48C8FC4881003E81127E82127C00FC81A2 82A37E82A27EA26C6C91C7FC7F7FEA3FF813FE381FFFE06C13FE6CEBFFE06C14FC6C14FF 6C15C0013F14F0010F80010180D9001F7F14019138001FFF03031380816F13C0167F163F 161F17E000C0150FA31607A37EA36C16C0160F7E17806C151F6C16006C5D6D147ED8FBC0 5CD8F9F0495AD8F07C495A90393FC00FE0D8E00FB51280010149C7FC39C0003FF02B487B C536>I<003FB912F8A3903BF0001FF8001F01806D481303003EC7150048187C0078183C A20070181CA30060180CA5481806A5C81600B3B3A54B7EED7FFE49B77EA33F447DC346> I87 D89 D91 D93 D97 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<01F81302D803 FE13073907FF800E48EBE01C391F1FF8F8393807FFF0D8700113E039E0007FC00040EB1F 00200978C131>126 D<001EEB0780007FEB0FE039FF801FF0EBC03FA4EB801F397F000F E0001EEB07801C0A76C231>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq cmbx12 12 36 /Fq 36 121 df12 D46 D49 DII<163FA25E5E5D5DA25D5D5D5D A25D92B5FCEC01F7EC03E7140715C7EC0F87EC1F07143E147E147C14F8EB01F0EB03E013 0714C0EB0F80EB1F00133E5BA25B485A485A485A120F5B48C7FC123E5A12FCB91280A5C8 000F90C7FCAC027FB61280A531417DC038>I<0007150301E0143F01FFEB07FF91B6FC5E 5E5E5E5E16804BC7FC5D15E092C8FC01C0C9FCAAEC3FF001C1B5FC01C714C001DF14F090 39FFE03FFC9138000FFE01FC6D7E01F06D13804915C0497F6C4815E0C8FC6F13F0A317F8 A4EA0F80EA3FE0487E12FF7FA317F05B5D6C4815E05B007EC74813C0123E003F4A1380D8 1FC0491300D80FF0495AD807FEEBFFFC6CB612F0C65D013F1480010F01FCC7FC010113C0 2D427BC038>I<4AB47E021F13F0027F13FC49B6FC01079038807F8090390FFC001FD93F F014C04948137F4948EBFFE048495A5A1400485A120FA248486D13C0EE7F80EE1E00003F 92C7FCA25B127FA2EC07FC91381FFF8000FF017F13E091B512F89039F9F01FFC9039FBC0 07FE9039FF8003FF17804A6C13C05B6F13E0A24915F0A317F85BA4127FA5123FA217F07F 121FA2000F4A13E0A26C6C15C06D4913806C018014006C6D485A6C9038E01FFC6DB55A01 1F5C010714C0010191C7FC9038003FF02D427BC038>I65 D70 D73 D76 D80 D<003FBA12E0A59026FE000FEB8003D87FE09338003FF049171F90C71607A2007E180300 7C1801A300781800A400F819F8481978A5C81700B3B3A20107B8FCA545437CC24E>84 D<903801FFE0011F13FE017F6D7E48B612E03A03FE007FF84848EB1FFC6D6D7E486C6D7E A26F7FA36F7F6C5A6C5AEA00F090C7FCA40203B5FC91B6FC1307013F13F19038FFFC0100 0313E0000F1380381FFE00485A5B127F5B12FF5BA35DA26D5B6C6C5B4B13F0D83FFE013E EBFFC03A1FFF80FC7F0007EBFFF86CECE01FC66CEB8007D90FFCC9FC322F7DAD36>97 DIIII103 DI< 137C48B4FC4813804813C0A24813E0A56C13C0A26C13806C1300EA007C90C7FCAAEB7FC0 EA7FFFA512037EB3AFB6FCA518467CC520>I107 DI<90277F8007FEEC0FFCB590263FFFC090387FFF8092B5D8F001B512E002 816E4880913D87F01FFC0FE03FF8913D8FC00FFE1F801FFC0003D99F009026FF3E007F6C 019E6D013C130F02BC5D02F86D496D7EA24A5D4A5DA34A5DB3A7B60081B60003B512FEA5 572D7CAC5E>I<90397F8007FEB590383FFF8092B512E0028114F8913987F03FFC91388F 801F000390399F000FFE6C139E14BC02F86D7E5CA25CA35CB3A7B60083B512FEA5372D7C AC3E>II<90397FC00FF8B5 90B57E02C314E002CF14F89139DFC03FFC9139FF001FFE000301FCEB07FF6C496D13804A 15C04A6D13E05C7013F0A2EF7FF8A4EF3FFCACEF7FF8A318F017FFA24C13E06E15C06E5B 6E4913806E4913006E495A9139DFC07FFC02CFB512F002C314C002C091C7FCED1FF092C9 FCADB67EA536407DAC3E>II<90387F807FB53881FFE0028313F0028F13F8ED8FFC91389F1FFE000313BE6C 13BC14F8A214F0ED0FFC9138E007F8ED01E092C7FCA35CB3A5B612E0A5272D7DAC2E>I< 90391FFC038090B51287000314FF120F381FF003383FC00049133F48C7121F127E00FE14 0FA215077EA27F01E090C7FC13FE387FFFF014FF6C14C015F06C14FC6C800003806C1580 6C7E010F14C0EB003F020313E0140000F0143FA26C141F150FA27EA26C15C06C141FA26D EB3F8001E0EB7F009038F803FE90B55A00FC5CD8F03F13E026E007FEC7FC232F7CAD2C> IIII II E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmtt10 10.95 20 /Fr 20 123 df<120FEA3FC0EA7FE0A2EAFFF0A4EA7FE0A2EA3FC0EA0F000C0C6E8B30> 46 D49 DI64 D97 DII<49B4FC010713E0011F13F8017F7F90B57E48804801811380 3A07FC007FC04848133FD81FE0EB1FE0150F484814F0491307127F90C7FCED03F85A5AB7 FCA516F048C9FC7E7EA27F003FEC01F06DEB03F86C7E6C7E6D1307D807FEEB1FF03A03FF C07FE06C90B5FC6C15C0013F14806DEBFE00010713F8010013C0252A7CA830>101 D<14E0EB03F8A2497EA36D5AA2EB00E091C8FCA9381FFFF8487F5AA27E7EEA0001B3A900 3FB612C04815E0B7FCA27E6C15C023397AB830>105 D<387FFFF8B57EA47EEA0001B3B3 A8007FB612F0B712F8A46C15F025387BB730>108 D<02FC137E3B7FC3FF01FF80D8FFEF 01877F90B500CF7F15DF92B57E6C010F13872607FE07EB03F801FC13FE9039F803FC01A2 01F013F8A301E013F0B3A23C7FFE0FFF07FF80B548018F13C0A46C486C01071380322881 A730>II<49B4FC010F13E0013F13F8497F90B57E00 03ECFF8014013A07FC007FC04848EB3FE0D81FE0EB0FF0A24848EB07F8491303007F15FC 90C71201A300FEEC00FEA86C14016C15FCA26D1303003F15F86D13076D130F6C6CEB1FF0 6C6CEB3FE06D137F3A07FF01FFC06C90B512806C15006C6C13FC6D5B010F13E0010190C7 FC272A7CA830>II114 D<90381FFC1E48B5129F000714FF5A5A5A387FF007EB800100FEC7FC4880A46C 143E007F91C7FC13E06CB4FC6C13FC6CEBFF806C14E0000114F86C6C7F01037F9038000F FF02001380007C147F00FEEC1FC0A2150F7EA27F151F6DEB3F806D137F9039FC03FF0090 B6FC5D5D00FC14F0D8F83F13C026780FFEC7FC222A79A830>III< 3B3FFFC07FFF80486DB512C0B515E0A26C16C06C496C13803B01F80003F000A26D130700 005DA26D130F017E5CA2017F131F6D5CA2EC803F011F91C7FCA26E5A010F137EA2ECE0FE 01075BA214F101035BA3903801FBF0A314FF6D5BA36E5A6E5A2B277EA630>I<001FB612 FC4815FE5AA316FC90C7EA0FF8ED1FF0ED3FE0ED7FC0EDFF80003E491300C7485A4A5A4A 5A4A5A4A5A4A5A4A5A4990C7FC495A495A495A495A495A495A4948133E4890C7127F485A 485A485A485A485A48B7FCB8FCA46C15FE28277DA630>122 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmr10 10.95 67 /Fs 67 124 df12 D16 D<127C12FC7E7EA2EA7F80EA3FC0EA1FE0120FEA07F0 EA03F81201EA007C133E131F130E1304101176BE2D>18 D<133E133F137F13FFA2EA01FE EA03FCEA07F813F0EA0FE0EA1FC01380EA3E005A5A1270122010116EBE2D>I<14301470 14E0EB01C0EB03801307EB0F00131E133E133C5B13F85B12015B1203A2485AA2120F5BA2 121F90C7FCA25AA3123E127EA6127C12FCB2127C127EA6123E123FA37EA27F120FA27F12 07A26C7EA212017F12007F13787F133E131E7FEB07801303EB01C0EB00E014701430145A 77C323>40 D<12C07E12707E7E121E7E6C7E7F12036C7E7F12007F1378137CA27FA2133F 7FA21480130FA214C0A3130714E0A6130314F0B214E01307A614C0130FA31480A2131F14 00A25B133EA25BA2137813F85B12015B485A12075B48C7FC121E121C5A5A5A5A145A7BC3 23>I<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A312011380120313 005A120E5A1218123812300B1C798919>44 D<121EEA7F80A2EAFFC0A4EA7F80A2EA1E00 0A0A798919>46 D48 DIII<150E151E153EA2157EA215FE1401A214 03EC077E1406140E141CA214381470A214E0EB01C0A2EB0380EB0700A2130E5BA25B5BA2 5B5B1201485A90C7FC5A120E120C121C5AA25A5AB8FCA3C8EAFE00AC4A7E49B6FCA3283E 7EBD2D>I<00061403D80780131F01F813FE90B5FC5D5D5D15C092C7FC14FCEB3FE090C9 FCACEB01FE90380FFF8090383E03E090387001F8496C7E49137E497F90C713800006141F C813C0A216E0150FA316F0A3120C127F7F12FFA416E090C7121F12FC007015C012780038 EC3F80123C6CEC7F00001F14FE6C6C485A6C6C485A3903F80FE0C6B55A013F90C7FCEB07 F8243F7CBC2D>II<1238123C123F 90B612FCA316F85A16F016E00078C712010070EC03C0ED078016005D48141E151C153C5D C8127015F04A5A5D14034A5A92C7FC5C141EA25CA2147C147814F8A213015C1303A31307 A3130F5CA2131FA6133FAA6D5A0107C8FC26407BBD2D>II I<121EEA7F80A2EAFFC0A4EA7F80A2EA1E00C7FCB3121EEA7F80A2EAFFC0A4EA7F80A2EA 1E000A2779A619>I<15074B7EA34B7EA34B7EA34B7EA34B7E15E7A2913801C7FC15C3A2 91380381FEA34AC67EA3020E6D7EA34A6D7EA34A6D7EA34A6D7EA34A6D7EA349486D7E91 B6FCA249819138800001A249C87EA24982010E157FA2011E82011C153FA2013C82013815 1FA2017882170F13FC00034C7ED80FFF4B7EB500F0010FB512F8A33D417DC044>65 DII IIIIII<011FB512FCA3D9000713006E5A1401B3B3A6123FEA7F 80EAFFC0A44A5A1380D87F005B007C130700385C003C495A6C495A6C495A2603E07EC7FC 3800FFF8EB3FC026407CBD2F>I76 DIIII82 DI<003FB91280 A3903AF0007FE001018090393FC0003F48C7ED1FC0007E1707127C00781703A300701701 A548EF00E0A5C81600B3B14B7E4B7E0107B612FEA33B3D7DBC42>III< B500FE017FB5D88007B5FCA3000301C0010101E0C713F86C90C849EC3FE07148EC0F807E 7215006E143F017F190E84A26D6C60A24D7E6D6C60A2EFE7F86D6C60A2933801C3FC6E18 F001076104037F6E0281140101036104077F17006D6C4D5AA2040EEB7F806D6C4DC7FCA2 4CEB3FC0DA7F80160EA24CEB1FE003C0161E023F171C047814F0DBE070010F133C021F17 3804F014F84C1307DA0FF05EA2DBF1C0EB03FCDA07F95EA2DBFB80EB01FEDA03FF6F5AA2 93C8FCA26E5FA24B157F020094C8FCA24B81037C153EA20378151E0338151C58407EBD5D >I<007FB5D8C003B512E0A3C649C7EBFC00D93FF8EC3FE06D48EC1F806D6C92C7FC171E 6D6C141C6D6C143C5F6D6C14706D6D13F04C5ADA7FC05B023F13036F485ADA1FF090C8FC 020F5BEDF81E913807FC1C163C6E6C5A913801FF7016F06E5B6F5AA26F7E6F7EA2828215 3FED3BFEED71FF15F103E07F913801C07F0203804B6C7EEC07004A6D7E020E6D7E5C023C 6D7E02386D7E14784A6D7E4A6D7F130149486E7E4A6E7E130749C86C7E496F7E497ED9FF C04A7E00076DEC7FFFB500FC0103B512FEA33F3E7EBD44>I91 D93 D97 D I<49B4FC010F13E090383F00F8017C131E4848131F4848137F0007ECFF80485A5B121FA2 4848EB7F00151C007F91C7FCA290C9FC5AAB6C7EA3003FEC01C07F001F140316806C6C13 076C6C14000003140E6C6C131E6C6C137890383F01F090380FFFC0D901FEC7FC222A7DA8 28>IIII<167C903903F801FF903A1FFF078F8090397E0FDE1F90 38F803F83803F001A23B07E000FC0600000F6EC7FC49137E001F147FA8000F147E6D13FE 00075C6C6C485AA23901F803E03903FE0FC026071FFFC8FCEB03F80006CAFC120EA3120F A27F7F6CB512E015FE6C6E7E6C15E06C810003813A0FC0001FFC48C7EA01FE003E140048 157E825A82A46C5D007C153E007E157E6C5D6C6C495A6C6C495AD803F0EB0FC0D800FE01 7FC7FC90383FFFFC010313C0293D7EA82D>III107 DI<2701F801FE14FF 00FF902707FFC00313E0913B1E07E00F03F0913B7803F03C01F80007903BE001F87000FC 2603F9C06D487F000101805C01FBD900FF147F91C75B13FF4992C7FCA2495CB3A6486C49 6CECFF80B5D8F87FD9FC3F13FEA347287DA74C>I<3901F801FE00FF903807FFC091381E 07E091387803F000079038E001F82603F9C07F0001138001FB6D7E91C7FC13FF5BA25BB3 A6486C497EB5D8F87F13FCA32E287DA733>I<14FF010713E090381F81F890387E007E01 F8131F4848EB0F804848EB07C04848EB03E0000F15F04848EB01F8A2003F15FCA248C812 FEA44815FFA96C15FEA36C6CEB01FCA3001F15F86C6CEB03F0A26C6CEB07E06C6CEB0FC0 6C6CEB1F80D8007EEB7E0090383F81FC90380FFFF0010090C7FC282A7EA82D>I<3901FC 03FC00FF90381FFF8091387C0FE09039FDE003F03A07FFC001FC6C496C7E6C90C7127F49 EC3F805BEE1FC017E0A2EE0FF0A3EE07F8AAEE0FF0A4EE1FE0A2EE3FC06D1580EE7F007F 6E13FE9138C001F89039FDE007F09039FC780FC0DA3FFFC7FCEC07F891C9FCAD487EB512 F8A32D3A7EA733>I<3901F807E000FFEB1FF8EC787CECE1FE3807F9C100031381EA01FB 1401EC00FC01FF1330491300A35BB3A5487EB512FEA31F287EA724>114 D<90383FC0603901FFF8E03807C03F381F000F003E1307003C1303127C0078130112F814 00A27E7E7E6D1300EA7FF8EBFFC06C13F86C13FE6C7F6C1480000114C0D8003F13E00103 13F0EB001FEC0FF800E01303A214017E1400A27E15F07E14016C14E06CEB03C090388007 8039F3E01F0038E0FFFC38C01FE01D2A7DA824>I<131CA6133CA4137CA213FCA2120112 031207001FB512C0B6FCA2D801FCC7FCB3A215E0A912009038FE01C0A2EB7F03013F1380 90381F8700EB07FEEB01F81B397EB723>IIII121 D<001FB61280A2EBE0000180140049485A 001E495A121C4A5A003C495A141F00385C4A5A147F5D4AC7FCC6485AA2495A495A130F5C 495A90393FC00380A2EB7F80EBFF005A5B484813071207491400485A48485BA248485B48 48137F00FF495A90B6FCA221277EA628>II E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft cmti10 10.95 46 /Ft 46 124 df11 D<933807FF80043F13E09338FE00F8DB01F0133EDB07E0130E4B48131F4C137F031F14FF 4BC7FCA218FE157E1878180015FE5DA31401A25DA414030103B712F0A218E0903A0003F0 00070207140F4B14C0A3171F020F15805DA2173F1800141F5D5F177EA2143F92C712FE5F A34A1301027EECF81CA3160302FEECF03C4A1538A21878187013014A010113F018E09338 00F1C0EF7F804948EC1F0094C7FCA35C1307A2001E5B127F130F00FF5BA249CAFC12FEEA F81EEA703CEA7878EA1FF0EA07C0385383BF33>II<137C48B4FC38038F80EA0707000E13C0121E121CEA3C0F1238A2EA781F00 701380A2EAF03F140012005B137E13FE5BA212015BA212035B1438120713E0000F1378EB C070A214F0EB80E0A2EB81C01383148038078700EA03FEEA00F8152979A71C>16 D<123812FCA27EA2127FA2EA3F80121F120F13C01207EA03E0120113F0120013600C1166 BE2E>18 DI44 D<120FEA3FC0127FA212FFA31380EA7F00123C0A0A77891C>46 D<131EEB3F80137FEBFF C05AA214806C13005B133C90C7FCB3120FEA3FC0127FA212FFA35B6CC7FC123C122777A6 1C>58 D<9339FF8001C0030F13E0033F9038F803809239FF807E07913A03FC001F0FDA0F F0EB071FDA1FC0ECBF00DA7F806DB4FC4AC77E495AD903F86E5A495A130F4948157E4948 157C495A13FF91C9FC4848167812035B1207491670120FA2485A95C7FC485AA3127F5BA3 12FF5BA490CCFCA2170FA2170EA2171E171C173C173817786C16706D15F04C5A003F5E6D 1403001F4B5A6D4AC8FC000F151E6C6C5C6C6C14F86C6C495A6C6CEB07C090397FC03F80 90261FFFFEC9FC010713F0010013803A4272BF41>67 D<49B712C018F818FE903B0003FE 0003FF9438007F804BEC1FC0F00FE0F007F014074BEC03F8F001FCA2140F4BEC00FEA314 1F4B15FFA3143F5DA3027F5D5DA219FE14FF92C81203A34917FC4A1507A219F813034A15 0F19F0A20107EE1FE05CF03FC0A2010FEE7F804A16006060011F4B5A4A4A5A4D5AA2013F 4B5A4AEC3FC04DC7FC017F15FEEE03FC4AEB0FF001FFEC7FE0B8128004FCC8FC16E0403E 7BBD45>I<49B812F0A390260003FEC7123F180F4B1403A2F001E014075DA3140F5D19C0 A2141F5D1770EFF003023F02E013804B91C7FCA21601027F5CED8003A2160702FFEB1F80 92B5FCA349D9003FC8FC4A7F82A20103140E5CA2161E0107141C5CA293C9FC130F5CA313 1F5CA3133F5CA2137FA25C497EB612E0A33C3E7BBD3B>70 D<49B6FC5BA2D9000313005D 5DA314075DA3140F5DA3141F5DA3143F5DA3147F5DA314FF92C7FCA35B5CA313035CA313 075CA3130F5CA3131F5CA3133F5CA2137FA25C497EB67EA3283E7BBD23>73 D<49B612C0A25FD9000390C8FC5D5DA314075DA3140F5DA3141F5DA3143F5DA3147F5DA3 14FF92C9FCA35B5CA313035C18C0EF01E0010716C05C17031880130F4A140718005F131F 4A141EA2173E013F5D4A14FC1601017F4A5A16074A131F01FFECFFF0B8FCA25F333E7BBD 39>76 D<49B5933807FFFC496062D90003F0FC00505ADBBF805E1A771AEF1407033F9238 01CFE0A2F1039F020FEE071F020E606F6C140E1A3F021E161C021C04385BA2F1707F143C 023804E090C7FCF001C0629126780FE0495A02705FF00700F00E0114F002E0031C5BA2F0 3803010116704A6C6C5D18E019070103ED01C00280DA03805BA2943807000F1307020002 0E5C5FDB03F8141F495D010E4B5CA24D133F131E011CDAF9C05CEEFB80197F013C6DB4C7 FC013895C8FC5E01784A5C13F8486C4A5CD807FE4C7EB500F04948B512FE16E01500563E 7BBD52>I<902601FFFE020FB5FC496D5CA2D900016D010013C04AEE3F00193E70141C19 3CEC07BFDB3FE01438151F1978020F7FDA0E0F15708219F0EC1E07021C6D5CA203031401 023C7FDA38015DA2701303EC7800027002805BA2047F130702F014C04A013F91C7FCA271 5A0101141F4AECF00EA2040F131E010315F84A151C1607EFFC3C0107140391C7143817FE 040113784915FF010E16708218F0131E011C6F5AA2173F133C01385E171F137813F8486C 6F5AEA07FEB500F01407A295C8FC483E7BBD44>I<49B612FCEFFF8018F0903B0003FE00 0FF8EF03FE4BEB00FF8419800207ED3FC05DA219E0140F5DA3021FED7FC05DA2F0FF8014 3F4B15004D5A60027F4A5A4B495A4D5AEF3F8002FF02FEC7FC92380007F892B512E01780 499038000FE04A6D7E707E707E0103814A130083A213075CA25E130F5C5F1603131F5CA3 013F020714404A16E05F017F160119C04A01031303496C1680B6D8800113079438FE0F00 9338007E1ECAEA3FFCEF07F03B407BBD42>82 D<92391FE00380ED7FFC913A01FFFE0700 913907F01F8F91390FC007DF4AC66CB4FC023E6D5A4A130014FC495A4948147CA2495AA2 010F15785CA3011F1570A46E91C7FCA2808014FE90380FFFE015FC6DEBFF8016E06D806D 806D6C7F141F02037FEC003FED07FF1501A281A282A212075A167E120EA2001E15FE5EA2 5E003E14015E003F14034B5A486C5C150F6D495A6D49C8FCD8F9F0137C39F8FE01F839F0 3FFFF0D8E00F13C026C001FEC9FC314279BF33>I<48B9FCA25A903AFE001FF00101F891 38E0007FD807E0163E49013F141E5B48C75BA2001E147FA2001C4B131C123C003814FFA2 007892C7FC12704A153C00F01738485CC716001403A25DA21407A25DA2140FA25DA2141F A25DA2143FA25DA2147FA25DA214FFA292C9FCA25BA25CA21303A25CEB0FFE003FB67E5A A2383D71BC41>I<001FB500F090B512F0485DA226003FF0C7380FFC004AEC03F04A5D71 5A017F1503A24A5DA201FF150795C7FC91C8FCA2485E170E5BA20003161E171C5BA20007 163C17385BA2000F167817705BA2001F16F05F5BA2003F1501A2495DA2007F1503A2495D A2160794C8FC48C8FC5E160E161E6C151C163C5E5E5E6C6C13014B5A001F4A5A6C6C011F C9FC6D133E6C6C13F83903FC07F0C6B512C0013F90CAFCEB07F83C406FBD44>II<147E49B47E903907C1C3809039 1F80EFC090383F00FF017E137F4914804848133F485AA248481400120F5B001F5C157E48 5AA215FE007F5C90C7FCA21401485C5AA21403EDF0385AA21407EDE078020F1370127C02 1F13F0007E013F13E0003E137FECF3E1261F01E313C03A0F8781E3803A03FF00FF00D800 FC133E252977A72E>97 DIIII<167C4BB4FC923807C78092380F83C0ED1F87161FED3F3F A2157EA21780EE0E004BC7FCA414015DA414035DA30103B512F8A390260007E0C7FCA314 0F5DA5141F5DA4143F92C8FCA45C147EA414FE5CA413015CA4495AA4495AA4495A121E12 7F5C12FF49C9FCA2EAFE1EEAF83C1270EA7878EA3FE0EA0F802A5383BF1C>III<1478EB01FCA21303A314 F8EB00E01400AD137C48B4FC38038F80EA0707000E13C0121E121CEA3C0F1238A2EA781F 00701380A2EAF03F140012005B137E13FE5BA212015BA212035B1438120713E0000F1378 EBC070A214F0EB80E0A2EB81C01383148038078700EA03FEEA00F8163E79BC1C>I107 DIIII<903903E001F890390FF807FE903A1E7C1E0F80903A1C3E3C07 C0013C137801389038E003E0EB783F017001C013F0ED80019038F07F0001E015F8147E16 03000113FEA2C75AA20101140717F05CA20103140F17E05CA20107EC1FC0A24A1480163F 010F15005E167E5E131F4B5A6E485A4B5A90393FB80F80DA9C1FC7FCEC0FFCEC03E049C9 FCA2137EA213FEA25BA21201A25BA21203A2387FFFE0B5FCA22D3A80A72E>I<027E1360 903901FF81E0903807C1C390391F80E7C090383F00F7017E137F5B4848EB3F80485AA248 5A000F15005B121F5D4848137EA3007F14FE90C75AA3481301485CA31403485CA314074A 5A127C141F007E133F003E495A14FF381F01EF380F879F3903FF1F80EA00FC1300143F92 C7FCA35C147EA314FE5CA21301130390B512F05AA2233A77A72A>IIII<137C48B4141C26038F80137EEA0707000E7F001E15FE121CD83C 0F5C12381501EA781F007001805BA2D8F03F1303140000005D5B017E1307A201FE5C5B15 0F1201495CA2151F0003EDC1C0491481A2153F1683EE0380A2ED7F07000102FF13005C01 F8EBDF0F00009038079F0E90397C0F0F1C90391FFC07F8903907F001F02A2979A731>I< 017CEB01C048B4EB07F038038F80EA0707000E01C013F8121E001C1403EA3C0F0038EC01 F0A2D8781F130000705BA2EAF03F91C712E012005B017E130116C013FE5B150300011580 5BA2ED07001203495B150EA25DA25D1578000114706D5B0000495A6D485AD97E0FC7FCEB 1FFEEB03F0252979A72A>I<017C167048B491387001FC3A038F8001F8EA0707000E01C0 15FE001E1403001CEDF000EA3C0F0038177C1507D8781F4A133C00701380A2D8F03F130F 020049133812005B017E011F14784C137013FE5B033F14F0000192C712E05BA217010003 4A14C049137E17031880A2EF070015FE170E00010101141E01F86D131C0000D9039F5BD9 FC076D5A903A3E0F07C1E0903A1FFC03FFC0902703F0007FC7FC372979A73C>I<137C48 B4143826038F8013FCEA0707000E7F001E1401001C15F8EA3C0F12381503D8781F14F000 701380A2D8F03F1307020013E012005B017E130F16C013FE5B151F1201491480A2153F00 0315005BA25D157EA315FE5D00011301EBF8030000130790387C1FF8EB3FF9EB07E1EB00 035DA21407000E5CEA3F80007F495AA24A5AD8FF0090C7FC143E007C137E00705B387801 F0383803E0381E0FC06CB4C8FCEA03F8263B79A72C>121 DII E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu cmbx10 10.95 7 /Fu 7 58 df48 D<140F143F5C495A130F48B5FC B6FCA313F7EAFE071200B3B3A8007FB612F0A5243C78BB34>I<903803FF80013F13F890 B512FE00036E7E4881260FF80F7F261FC0037F4848C67F486C6D7E6D6D7E487E6D6D7EA2 6F1380A46C5A6C5A6C5A0007C7FCC8FC4B1300A25E153F5E4B5AA24B5A5E4A5B4A5B4A48 C7FC5D4A5AEC1FE04A5A4A5A9139FF000F80EB01FC495A4948EB1F00495AEB1F8049C7FC 017E5C5B48B7FC485D5A5A5A5A5AB7FC5EA4293C7BBB34>I<903801FFE0010F13FE013F 6D7E90B612E04801817F3A03FC007FF8D807F06D7E82D80FFC131F6D80121F7FA56C5A5E 6C48133FD801F05CC8FC4B5A5E4B5A4A5B020F5B902607FFFEC7FC15F815FEEDFFC0D900 0113F06E6C7E6F7E6F7E6F7E1780A26F13C0A217E0EA0FC0487E487E487E487EA317C0A2 5D491580127F49491300D83FC0495A6C6C495A3A0FFE01FFF86CB65A6C5DC61580013F49 C7FC010313E02B3D7CBB34>II<00071538D80FE0EB01F801FE133F90B6FC5E5E5E5E93C7FC5D15F85D15C04AC8FC 0180C9FCA9ECFFC0018713FC019F13FF90B67E020113E09039F8007FF0496D7E01C06D7E 5B6CC77FC8120F82A31780A21207EA1FC0487E487E12FF7FA21700A25B4B5A6C5A01805C 6CC7123F6D495AD81FE0495A260FFC075B6CB65A6C92C7FCC614FC013F13F0010790C8FC 293D7BBB34>I<903801FFE0010F13FC013F13FF90B612C04801E07F489038003FF04848 6D7E000F6E7E485A6F7E123F48488081178012FFA217C0A517E0A4007F5CA4003F5C6C7E 5D6C7E00075C3903FF80FB6C13FF6C6C13F36D13C3010F018313C090380008031400A24B 1380EA03F0487E486C1500487E4B5AA25E151F4B5A495C6C48EBFFE049485B2607FC0F5B 6CB6C7FC6C14FC6C14F06D13C0D90FFEC8FC2B3D7CBB34>57 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fv cmr10 10 4 /Fv 4 53 df49 DII<15 38A2157815F8A2140114031407A2140F141F141B14331473146314C313011483EB030313 071306130C131C131813301370136013C01201EA038013005A120E120C5A123812305A12 E0B712F8A3C73803F800AB4A7E0103B512F8A325397EB82A>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fw cmr12 14.4 18 /Fw 18 123 df<127C12FE7E7FA27F6C7E6C7E121F6C7E6C7EEA01FE1200137FEB3F80EB 1FC0130FEB07E0EB01F0130014781430151673D23B>18 D66 D69 D76 D80 D83 D97 D99 D101 D<1378EA01FE487E487FA66C90 C7FC6C5AEA007890C8FCB0EB7F80B5FCA41203C6FC137FB3B3A43801FFE0B61280A41950 7CCF21>105 D 108 D<01FFEB07FCB590383FFF8092B512E0913901F00FF8913903C007FC000349C66C7E C6010E13016D486D7E5C143002706E7E146014E05CA35CB3AD2601FFE0903801FFE0B600 C0B612C0A43A347CB341>110 DI<01FFEB1F80B5EB7FF0 913801FFF8913803E1FC91380783FE0003EB0F07C6131EEB7F1C1438143091387003FC91 386000F0160014E05CA45CB3AA8048487EB612F0A427347DB32E>114 DIII<001FB712E0A301FCC7EA7FC0 01E014FF018049138090C714004B5A001E14074B5A485D4B5A153F4B5A00385D15FF4A5B 93C7FC4A5A1407C7485A5D4A5A143F4A5A5D14FF495B92C8FC494814E01307495A5C495A 013FEC01C0495A5C13FF485B91C71203485A12074848140749140F485A003FED3F804848 14FF491307B8FCA32B337DB234>122 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fx cmr17 20.74 18 /Fx 18 121 df12 D58 D83 D<913803FF80021F13F891B512FE903A03FC01FF80903A07E0003FE0D91F80EB0FF8013E C76C7E496E7E01F06E7E48486E7F717E4848153F4982D807A06F7E13FC487E6D6F7E80A2 717EA46C90C8FC6C5A6C5ACAFCA6EE07FF0303B5FC157F913903FFFE07021F138091387F F800903801FFC0010790C7FCEB1FFCEB3FF0EBFFE0485B485B4890C8FC5B485A485AA248 5A1A0E485AA312FF5B170FA4171FA26D153F007F163B177B6DDBF1FE131C003F16E16C6C 14016C6C912603C0FF13386C6CEC0F806C6C6C903A1F007F80706C6D017CECE1E028007F F803F8EB3FFF011FB500E06D1380010391C7000713009026003FF8EC01FC474D79CB4F> 97 D 99 D<191FF07FFF051FB5FCA5EF001F180784A284B3B0ED07FE92387FFFC00203B512F0 91390FFC01FC91393FE0001FDAFF80EB07814990C7EA03E1D903FCEC01F14948EC0079D9 1FF0153D4948151D4A151F49488101FF824890C9FC48835B0007835B120F5B121FA2123F 5BA2127FA35BA212FFAE127FA27FA3123FA36C7EA36C7EA200075F7F00035F6C7E606C6D 5D6D6C153D013F16396D6C03797F6D6C15F16D6CDA03E17FD903FEDA078113F0D900FFDA 1F01EBFFF0DA7FC0137E91391FF803F80207B512E0020114809127001FF800EC80004C79 7AF758>II<14 F8EA03FFB5FCA5C6FC133F131FA2130FB3B0933803FF80041F13F8047F13FE923A01FC03 FF80923A03E0007FE0DB0F80EB1FF0031EC76C7E5D4B6E7E4B6E7E5D14F9DAFBC06E7E5D 14FF92C9FC865CA35CA45CB3B3A8496C4B7FD97FFF030713F0B7D8800FB612F8A54D787A F758>104 D<131EEB7F80497E487F487FA66C5B6C5B6D5A011EC7FC90C8FCB3A7EB01F0 EA07FFB5FCA51201EA007F133FA2131FB3B3B3A3497EEBFFFEB612FCA51E727AF12A>I< EB01F0EA07FFB5FCA51201EA007F133FA2131FB3B3B3B3B3AC497EEBFFFEB612FEA51F78 7AF72A>108 D110 DI<02F849B47ED803FF021F13F8B5027F13FE 923A01FC01FF80923A07E0003FE0031FC76C7E033EEC0FFCC60278EC03FE013F496E7E90 261FF9E06E7FDAFBC0826DB4486F7E92C96C7E737E5C4A707E864A160786851B80A2851B C0A2851BE0A5F27FF0AEF2FFE0A54F13C0A34F1380A21B0061626E160F626E161F626E4C 5A4F5A6F5EDAFBC015FFDAF9E04A5BDAF8F04A48C7FC03784A5A6F4A5A031FEC3FF06F6C EBFFC0922603F80790C8FC0300B512FC043F13E0DC07FEC9FC93CBFCB3A7497EEB7FFFB7 7EA54C6C7BCA58>II115 D<1407A85CA65CA35CA35CA25CA25BA25B5B5B5B5B5B48B712FE120FB8FCA3D8000190C9 FCB3B3A2EF01C0B0EF03806D7FA3027FEC0700815F6E6C130E021F141E6F131C6E6C5B6E 6C13F8913901FF01F09139007FFFC0031F5BDB03FCC7FC326B7EE93D>I<02F8EE0F80D8 03FFEE3FFFB5030FB5FCA5C6EE000F013F1603011F82A2010F82B3B3A660A460A3601307 606E150E0103161E606E4B7F010116706D6C03F07F6FD903E013F86E6C4948EBFFF8DA1F E0EB1F00DA0FFE13FE0203B512F8DA007F13E0030790C7EBC0004D4C7ACA58>I<007FB5 00FC0203B512FEA5C66C01F06E14C0010F496E01FCC7FC010349ED7FF06D18C06D60077E C8FC6E6C157C6E6C5D6E6C5D4E5A6E6C5D6E6C14036E6C4A5A4EC9FC6E6D131E6E7F6F6C 5B033F5C705B6F6C5B92380FFC010307495A70485A6F6C48CAFC6F138E6F139E17FC705A 705A161F83707E707E835E4C7F043C7F4C6C7E16709338F03FF04B486C7E4B486C7E1680 03076D7E4B486C7E031E6D7F5D03386D7F03786E7E4B6E7E4A48141F4A4881727E4A486E 7E4AC81203021E82023E6F7F027E6F7F4A167F010184010784D91FFE83017FEFFFFE0007 B54B6D7EB600C00207ECFFC0A5524A80C953>120 D E %EndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: A4 %%EndSetup %%Page: 1 1 1 0 bop 777 427 a Fx(Sto)t(c)l(hastic)52 b(phase)g(\014eld)h (equations:)1031 755 y(existence)g(and)f(uniqueness)146 1148 y Fw(Lorenzo)37 b(Bertini)946 1098 y Fv(1)1094 1148 y Fw(Stella)g(Brassesco)1907 1097 y Fv(2)2055 1148 y Fw(P)m(aolo)f(Butt\022)-59 b(a)2676 1097 y Fv(3)2824 1148 y Fw(Errico)37 b(Presutti)3589 1098 y Fv(4)155 1370 y Fu(1)100 b Ft(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)307 1483 y Fs(Piazzale)c(Aldo)g(Moro)h(2,)g (00185)i(Roma,)e(Italy)307 1596 y(E{mail:)39 b Fr (lorenzo@carpenter.mat.unir)o(oma)o(1.it)155 1822 y Fu(2)100 b Ft(Dep)-5 b(artamento)35 b(de)e(Matem\023)-46 b(atic)-5 b(as,)34 b(Instituto)f(V)-7 b(enezolano)34 b(de)f(Investigaciones)g (Cient)-9 b(\023)-37 b(\020\014c)-5 b(as)307 1935 y Fs(Apartado)30 b(P)m(ostal)i(21827,)g(Caracas)g(1020{A,)h(V)-8 b(enezuela)307 2048 y(E{mail:)39 b Fr(sbrasses@ivic.ivic.ve)155 2274 y Fu(3)100 b Ft(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)307 2387 y Fs(Piazzale)c(Aldo)g(Moro)h(2,)g (00185)i(Roma,)e(Italy)307 2500 y(E{mail:)39 b Fr (butta@mat.uniroma1.it)155 2725 y Fu(4)100 b Ft(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)307 2838 y Fs(Via)30 b(della)f(Ricerca)i(Scien)m(ti\014ca,)f(00133)i(Roma,) g(Italy)307 2951 y(E{mail:)39 b Fr(presutti@mat.uniroma2.it)1676 3368 y Fq(Abstract)146 3513 y Fp(W)-8 b(e)45 b(consider)g(a)f(conserv) -5 b(ativ)m(e)45 b(system)h(of)d(sto)s(c)m(hastic)i(PDE's,)j(namely)c (a)g(one)g(dimensional)0 3633 y(phase)c(\014eld)e(mo)s(del)f(p)s (erturb)s(ed)j(b)m(y)g(an)e(additiv)m(e)g(space{time)h(white)g(noise.) 62 b(W)-8 b(e)39 b(pro)m(v)m(e)h(a)e(global)0 3754 y(existence)31 b(and)e(uniqueness)i(result)e(in)g(a)g(space)h(of)e(con)m(tin)m(uous)i (functions)f(on)h Fo(R)3008 3769 y Fn(+)3088 3754 y Fm(\002)15 b Fo(R)5 b Fp(.)49 b(This)29 b(result)0 3874 y(is)43 b(obtained)f(b)m(y)j(extending)e(previous)h(results)g(of)f(Do)s(ering)e ([3])i(on)g(the)h(sto)s(c)m(hastic)g(Allen{Cahn)0 3994 y(equation)32 b(to)h(the)g(phase)g(\014eld)f(mo)s(del.)0 4459 y Fl(1991)i(Mathematics)h(Subje)-5 b(ct)34 b(Classi\014c)-5 b(ation.)42 b Fp(Primary)31 b(60H15,)h(60K35;)g(secondary)i(82C24.)0 4657 y Fl(Key)h(wor)-5 b(ds)34 b(and)g(phr)-5 b(ases.)86 b Fp(Sto)s(c)m(hastic)33 b(PDEs,)g(Phase)h(\014eld)e(mo)s(del.)p 0 4854 1512 4 v 0 5037 a Fs(L.B.)f(is)e(partially)g(supp)s(orted)f(b)m (y)j(Co\014nanziamen)m(to)f(MURST)g(1999.)0 5240 y(S.B.)h(is)e (partially)g(supp)s(orted)f(b)m(y)i(agreemen)m(t)i(CONICIT{CNR.)0 5444 y(P)-8 b(.B.)34 b(and)e(E.P)-8 b(.)33 b(are)g(partially)e(supp)s (orted)f(b)m(y)j(Co\014nanziamen)m(to)g(MURST)f(1999)i(and)e(b)m(y)h (NA)-8 b(TO)32 b(Gran)m(t)0 5557 y(PST.CLG.976552.)p eop %%Page: 1 2 1 1 bop 0 407 a Fq(1.)38 b(In)m(tro)s(duction)e(and)i(results)146 550 y Fp(W)-8 b(e)25 b(consider)g(a)g(phase)g(\014eld)g(system)h(with)e (additiv)m(e)g(sto)s(c)m(hastic)h(noise)g(in)e(one)i(space)h (dimension,)0 670 y(whic)m(h)33 b(is)f(formally)e(written)i(as)925 913 y Fk(@)976 928 y Fj(t)1006 913 y Fk(m)p Fp(\()p Fk(t)p Fp(\))c(=)1344 846 y(1)p 1344 890 49 4 v 1344 981 a(2)1403 913 y(\001)p Fk(m)p Fp(\()p Fk(t)p Fp(\))23 b Fm(\000)f Fk(V)1881 872 y Fi(0)1904 913 y Fp(\()p Fk(m)p Fp(\()p Fk(t)p Fp(\)\))g(+)g Fk(\025h)p Fp(\()p Fk(t)p Fp(\))h(+)f Fk(a\021)t Fp(\()p Fk(t)p Fp(\))925 1233 y Fk(@)976 1248 y Fj(t)1023 1233 y Fp([)p Fk(h)p Fp(\()p Fk(t)p Fp(\))g(+)g Fk(m)p Fp(\()p Fk(t)p Fp(\)])29 b(=)1702 1166 y(1)p 1702 1210 V 1702 1302 a(2)1761 1233 y(\001)p Fk(h)p Fp(\()p Fk(t)p Fp(\))3579 1066 y(\(1.1\))0 1468 y(where)43 b(\()p Fk(t;)17 b(x)p Fp(\))42 b Fm(2)h Fo(R)718 1483 y Fn(+)811 1468 y Fm(\002)29 b Fo(R)5 b Fp(,)49 b Fk(m)p Fp(\()p Fk(t)p Fp(\))43 b(=)g Fk(m)p Fp(\()p Fk(t;)17 b(x)p Fp(\),)44 b Fk(h)p Fp(\()p Fk(t)p Fp(\))f(=)f Fk(h)p Fp(\()p Fk(t;)17 b(x)p Fp(\))42 b(are)f(t)m(w)m(o)h(scalar)f(random)f(\014elds,)k Fk(\025)0 1588 y Fp(is)g(a)h(p)s(ositiv)m(e)f(parameter,)j(\001)e(is)g (the)g(Laplacian)e(on)h Fo(R)5 b Fp(,)54 b Fk(V)22 b Fp(\()p Fk(m)p Fp(\))48 b(=)h Fk(m)2752 1552 y Fn(4)2791 1588 y Fk(=)p Fp(4)30 b Fm(\000)h Fk(m)3112 1552 y Fn(2)3152 1588 y Fk(=)p Fp(2)44 b(is)h(a)f(double)0 1709 y(w)m(ell)35 b(p)s(oten)m(tial,)g Fk(a)f Fp(=)f Fk(a)p Fp(\()p Fk(x)p Fp(\))g Fm(2)h Fk(C)1223 1724 y Fj(b)1257 1709 y Fp(\()p Fo(R)5 b Fp(\),)43 b(i.e.)35 b(a)h(b)s(ounded)g(con)m(tin)m(uous)h (function,)f(and)g Fk(\021)t Fp(\()p Fk(t)p Fp(\))d(=)g Fk(\021)t Fp(\()p Fk(t;)17 b(x)p Fp(\))0 1829 y(is)43 b(a)g(space{time)g(white)g(noise,)j(i.e.)d Fo(E)29 b Fp(\()6 b Fk(\021)t Fp(\()p Fk(t;)17 b(x)p Fp(\))g Fk(\021)t Fp(\()p Fk(s;)g(y)t Fp(\)\))43 b(=)j Fk(\016)t Fp(\()p Fk(t)29 b Fm(\000)h Fk(s)p Fp(\))17 b Fk(\016)t Fp(\()p Fk(x)30 b Fm(\000)g Fk(y)t Fp(\).)74 b(In)44 b(particular)d(a)0 1950 y(translationally)29 b(co)m(v)-5 b(arian)m(t)32 b(noise)h(is)f(obtained)g(for)g Fk(a)c Fp(=)f(1.)146 2093 y(The)42 b(deterministic)d(system)j(obtained)e(b)m(y)i(setting)e Fk(a)i Fp(=)g(0)e(in)g(\(1.1\),)j(usually)d(referred)h(to)g(as)0 2213 y Fl(phase)33 b(\014eld)e Fp(equations,)h(describ)s(es)h(the)f (kinetic)f(of)g(phase)h(segregation)f(when)i(the)f(presence)h(of)f(the) 0 2333 y Fl(latent)44 b(he)-5 b(at)42 b Fp(is)f(tak)m(en)i(in)m(to)e (accoun)m(t.)73 b(The)43 b(\014rst)g(equation)e(describ)s(es)j(in)d (fact)h(the)g(ev)m(olution)f(of)0 2454 y(the)g(order)f(parameter)f Fk(m)i Fp(whic)m(h)f(is)g(coupled)g(to)g(the)g(external)g(\014eld)g Fk(h)h Fp(\(whic)m(h)f(can)g(b)s(e)h(though)m(t)0 2574 y(as)e(the)g(excess)i(temp)s(erature)e(measured)g(from)e(the)i(melting) e(temp)s(erature\);)k Fk(h)e Fp(is)f(ho)m(w)m(ev)m(er)j(itself)0 2694 y(a)34 b(dynamic)g(v)-5 b(ariable)33 b(whic)m(h)i(di\013uses)h (and,)f(via)f(the)h(coupling)e Fk(\025)p Fp(,)i(in)m(tro)s(duces)g(a)f (feedbac)m(k)j(in)m(to)d Fk(m)0 2815 y Fp(whose)40 b(e\013ect)h(is)d (to)h(slo)m(w)h(do)m(wn)g(the)f(phase)i(segregation)d(pro)s(cess.)65 b(W)-8 b(e)40 b(stress)g(that)f Fk(q)k Fp(=)c Fk(m)27 b Fp(+)g Fk(h)0 2935 y Fp(is)38 b(lo)s(cally)d(conserv)m(ed)40 b(as)f(apparen)m(t)f(from)f(the)h(second)i(equation)d(in)h(\(1.1\).)59 b(Scaling)36 b(limit)f(of)j(the)0 3056 y(deterministic)31 b(phase)i(\014eld)g(equations)g(as)f Fk(\025)c Fm(!)f Fp(0)32 b(ha)m(v)m(e)i(b)s(een)g(considered)f(in)f([2])g(and)h([6].)146 3176 y(Due)d(to)g(the)g(phenomenological)d(c)m(haracter)k(of)e(the)i (phase)f(\014eld)g(mo)s(del,)f(the)h(in)m(tro)s(duction)f(of)g(a)0 3296 y(random)i(forcing)h(term)f(app)s(ears)i(natural)e(and)i(mak)m(es) g(p)s(ossible)e(to)h(discuss)i(statistical)c(prop)s(erties)0 3417 y(of)45 b(solutions.)82 b(W)-8 b(e)46 b(also)f(men)m(tion)f(that)i (the)g(sto)s(c)m(hastic)g(system)g(\(1.1\))g(is)f(v)m(ery)i(similar)42 b(to)k(the)0 3537 y(so{called,)c(in)e(the)h(ph)m(ysical)f(literature)g (on)g(critical)f(phenomena,)k(mo)s(del)c(C)i(of)f(Hohen)m(b)s(erg)i (and)0 3658 y(Halp)s(erin)g([5].)78 b(The)45 b(sp)s(eci\014c)g(c)m (hoice)f(of)g(an)f(additiv)m(e)h(white)g(noise)g(only)f(in)g(the)i (\014rst)f(equation)0 3778 y(has)34 b(b)s(een)f(done)h(to)f(k)m(eep)i (the)e(mo)s(del)f(as)h(simple)f(as)h(p)s(ossible:)44 b(the)34 b(random)e(forcing)g(term)g(is)h(non{)0 3898 y(conserv)-5 b(ativ)m(e,)29 b(whereas)g(the)f(conserv)-5 b(ation)27 b(la)m(w)f(is)h(still)e(linear)g(and)i(not)g(p)s(erturb)s (ed.)43 b(Moreo)m(v)m(er,)29 b(for)0 4019 y Fk(\025)d Fp(small,)f Fk(m)h Fp(and)g Fk(h)g Fp(are)g(w)m(eakly)h(coupled)f(so)g (that)f(w)m(e)i(ma)m(y)f(refer)g(to)g(\(1.1\))f(as)h(a)g Fl(we)-5 b(akly)28 b(c)-5 b(onservative)0 4139 y(system.)40 b Fp(This)24 b(simplifying)c(feature)k(migh)m(t)e(help)i(in)f(dev)m (eloping)g(a)g(mathematical)e(theory)j(for)f(phase)0 4259 y(segregation)k(in)f(conserv)-5 b(ativ)m(e)28 b(mo)s(dels.)41 b(Indeed,)30 b(in)c(the)i(companion)d(pap)s(er)j([1)o(],)h(fron)m(t)e (\015uctuations)0 4380 y(for)43 b(\(1.1\))h(are)g(analyzed)g(in)f(a)g (suitable)g(scaling)g(limit)d(as)45 b Fk(\025)h Fm(!)h Fp(0)d(and)g Fk(a)j Fp(=)g Fk(O)s Fp(\()p Fk(\025)p Fp(\).)76 b(The)45 b(need)0 4500 y(of)40 b(an)g(existence)i(and)e(uniqueness)i (result)e(for)g(the)g(sto)s(c)m(hastic)h(system)g(\(1.1\))f(in)f([1])h (is)g(the)h(main)0 4621 y(motiv)-5 b(ation)29 b(for)j(the)h(presen)m(t) i(pap)s(er.)146 4786 y(Referring)22 b(to)h([1])f(for)h(a)f(more)g (exhaustiv)m(e)i(discussion)f(on)g(the)g(sto)s(c)m(hastic)g(phase)h (\014eld)f(equations,)0 4907 y(w)m(e)37 b(next)g(state)f(precisely)h (our)f(results.)54 b(F)-8 b(or)35 b Fk(\013)f(>)g Fp(0)h(and)h Fk(\015)j Fm(2)34 b Fp(\(0)p Fk(;)17 b Fp(1],)36 b(let)f(us)i(de\014ne) g(the)g(follo)m(wing)0 5027 y(norms)32 b(on)h Fk(C)7 b Fp(\()p Fo(R)e Fp(\):)742 5231 y Fm(k)p Fk(')p Fm(k)906 5246 y Fj(C)956 5254 y Fh(\013)1000 5246 y Fn(\()p Fg(R)p Fn(\))1190 5231 y Fp(:=)83 b(sup)1382 5313 y Fj(x)p Fi(2)p Fg(R)1539 5231 y Fk(e)1584 5190 y Fi(\000)p Fj(\013)p Fi(j)p Fj(x)p Fi(j)1784 5231 y Fm(j)p Fk(')p Fp(\()p Fk(x)p Fp(\))p Fm(j)741 5502 y(k)p Fk(')p Fm(k)905 5522 y Fj(C)960 5489 y Fh(\015)955 5532 y(\013)1000 5522 y Fn(\()p Fg(R)p Fn(\))1190 5502 y Fp(:=)g Fm(k)p Fk(')p Fm(k)1540 5518 y Fj(C)1590 5526 y Fh(\013)1634 5518 y Fn(\()p Fg(R)p Fn(\))1763 5502 y Fp(+)22 b(sup)1868 5584 y Fj(x)p Fi(6)p Fn(=)p Fj(y)2024 5502 y Fk(e)2069 5461 y Fi(\000)p Fj(\013)p Fn(\()p Fi(j)p Fj(x)p Fi(j)p Fn(+)p Fi(j)p Fj(y)r Fi(j)p Fn(\))2466 5435 y Fm(j)p Fk(')p Fp(\()p Fk(x)p Fp(\))g Fm(\000)g Fk(')p Fp(\()p Fk(y)t Fp(\))p Fm(j)p 2466 5479 564 4 v 2583 5570 a(j)p Fk(x)g Fm(\000)h Fk(y)t Fm(j)2868 5542 y Fj(\015)1866 5806 y Fp(1)p eop %%Page: 2 3 2 2 bop 0 407 a Fp(and)33 b(also)e(the)i(follo)m(wing)d(ones)k(on)e Fk(C)7 b Fp(\()p Fo(R)1499 422 y Fn(+)1586 407 y Fm(\002)23 b Fo(R)5 b Fp(\))1021 629 y Fm(k)p Fk(f)11 b Fm(k)1180 644 y Fj(C)1230 652 y Fh(\013)1274 644 y Fn(\()p Fg(R)1349 653 y Ff(+)1400 644 y Fi(\002)p Fg(R)p Fn(\))1617 629 y Fp(:=)96 b(sup)1803 710 y Fj(t)p Fi(2)p Fg(R)1923 719 y Ff(+)1991 629 y Fk(e)2036 587 y Fi(\000)p Fj(\013)2136 564 y Ff(2)2171 587 y Fj(t=)p Fn(2)2288 629 y Fm(k)p Fk(f)11 b Fp(\()p Fk(t)p Fp(\))p Fm(k)2558 644 y Fj(C)2608 652 y Fh(\013)2652 644 y Fn(\()p Fg(R)p Fn(\))1021 866 y Fm(k)p Fk(f)g Fm(k)1180 886 y Fj(C)1235 853 y Fh(\015)1230 896 y(\013)1274 886 y Fn(\()p Fg(R)1349 895 y Ff(+)1400 886 y Fi(\002)p Fg(R)p Fn(\))1617 866 y Fp(:=)96 b(sup)1803 948 y Fj(t)p Fi(2)p Fg(R)1923 957 y Ff(+)1991 866 y Fk(e)2036 825 y Fi(\000)p Fj(\013)2136 801 y Ff(2)2171 825 y Fj(t=)p Fn(2)2288 866 y Fm(k)p Fk(f)11 b Fp(\()p Fk(t)p Fp(\))p Fm(k)2558 886 y Fj(C)2613 853 y Fh(\015)2608 896 y(\013)2652 886 y Fn(\()p Fg(R)p Fn(\))0 1148 y Fp(w)m(e)34 b(shall)d(denote)i(b)m (y)h Fk(C)892 1163 y Fj(\013)941 1148 y Fp(\()p Fo(R)5 b Fp(\))p Fk(;)17 b(:)g(:)g(:)k(;)33 b Fp(the)g(corresp)s(onding)g (Banac)m(h)g(spaces.)146 1269 y(Let)51 b Fk(p)388 1284 y Fj(t)477 1269 y Fp(=)59 b Fk(e)657 1233 y Fj(t)p Fn(\001)p Fj(=)p Fn(2)867 1269 y Fp(b)s(e)51 b(the)h(heat)f(semigroup,)k(namely) 50 b(the)h(in)m(tegral)e(op)s(erator)i(with)f(k)m(ernel)0 1389 y Fk(p)49 1404 y Fj(t)79 1389 y Fp(\()p Fk(x;)17 b(y)t Fp(\))26 b(=)i(\(2)p Fk(\031)t(t)p Fp(\))655 1341 y Fi(\000)p Fn(1)p Fj(=)p Fn(2)836 1389 y Fp(exp)q Fm(f\000)p Fp(\()p Fk(x)16 b Fm(\000)g Fk(y)t Fp(\))1404 1353 y Fn(2)1445 1389 y Fk(=)p Fp(2)p Fk(t)p Fm(g)p Fp(.)42 b(W)-8 b(e)30 b(in)m(tro)s(duce)g(the)g(pro)s(cess)h Fk(Z)7 b Fp(\()p Fk(t)p Fp(\))28 b(=)f Fk(Z)7 b Fp(\()p Fk(t;)17 b(x)p Fp(\))30 b(giv)m(en)g(b)m(y)0 1510 y Fk(Z)7 b Fp(\()p Fk(t)p Fp(\))28 b(=)316 1429 y Fe(R)383 1456 y Fj(t)363 1544 y Fn(0)412 1510 y Fk(ds)17 b(p)575 1525 y Fj(t)p Fi(\000)p Fj(s)692 1510 y Fp([)p Fk(a\021)t Fp(\()p Fk(s)p Fp(\)].)43 b(Then)34 b Fk(Z)39 b Fp(is)32 b(the)h(mean)f(zero)h(Gaussian)f(pro)s(cess)i(with)e(co)m(v)-5 b(ariance)189 1794 y Fo(E)30 b Fp(\()5 b Fk(Z)i Fp(\()p Fk(t;)17 b(x)p Fp(\))p Fk(Z)7 b Fp(\()p Fk(s;)17 b(y)t Fp(\)\))27 b(=)g(\000\()p Fk(t;)17 b(s)p Fp(;)g Fk(x;)g(y)t Fp(\))27 b(:=)1668 1659 y Fe(Z)1768 1685 y Fj(t)p Fi(^)p Fj(s)1724 1884 y Fn(0)1877 1794 y Fk(du)2001 1659 y Fe(Z)2100 1794 y Fk(dz)21 b(p)2266 1809 y Fj(t)p Fi(\000)p Fj(u)2391 1794 y Fp(\()p Fk(x)i Fm(\000)f Fk(z)t Fp(\))p Fk(p)2742 1809 y Fj(s)p Fi(\000)p Fj(u)2875 1794 y Fp(\()p Fk(y)k Fm(\000)c Fk(z)t Fp(\))p Fk(a)p Fp(\()p Fk(z)t Fp(\))3349 1753 y Fn(2)3579 1794 y Fp(\(1.2\))0 2059 y(where)35 b Fk(t)23 b Fm(^)g Fk(s)30 b Fp(:=)g(min)n Fm(f)p Fk(t;)17 b(s)p Fm(g)p Fp(.)47 b(In)34 b(the)g(next)g(lemma)e(w)m(e)j(state)f (some)f(prop)s(erties)h(of)f(the)h(paths)h(of)e Fk(Z)7 b Fp(,)0 2180 y(whic)m(h)36 b(follo)m(w,)e(b)m(y)i(standard)g(Gaussian) e(argumen)m(ts,)j(from)d(the)h(prop)s(erties)g(of)g(the)h(co)m(v)-5 b(ariance)35 b(\000,)0 2300 y(see)f(e.g.)f([3)o(])g(and)g(references)h (therein.)0 2497 y Fq(Lemma)j(1.1.)42 b Fl(F)-7 b(or)34 b(e)-5 b(ach)34 b Fk(\013)28 b(>)g Fp(0)35 b Fl(and)f Fk(\015)f Fm(2)28 b Fp(\(0)p Fk(;)17 b Fp(1\))34 b Fl(we)g(have)g(that) i Fk(Z)e Fm(2)28 b Fk(C)2751 2460 y Fj(\015)2744 2521 y(\013)2796 2497 y Fp(\()p Fo(R)2900 2512 y Fn(+)2987 2497 y Fm(\002)22 b Fo(R)5 b Fp(\))p Fl(,)41 b Fo(P)p Fl({a.s.)146 2693 y Fp(W)-8 b(e)35 b(shall)e(denote)i(b)m(y)h Fm(F)1072 2708 y Fj(t)1135 2693 y Fp(the)f(\014ltration)e(giv)m(en)h(b) m(y)i Fm(F)2180 2708 y Fj(t)2240 2693 y Fp(:=)30 b Fk(\033)t Fm(f)p Fk(Z)7 b Fp(\()p Fk(s;)17 b(x)p Fp(\);)33 b(\()p Fk(s;)17 b(x)p Fp(\))31 b Fm(2)h Fp([0)p Fk(;)17 b(t)p Fp(])23 b Fm(\002)h Fo(R)5 b Fm(g)p Fp(.)55 b(In)0 2814 y(the)33 b(follo)m(wing)d(w)m(e)j(consider)g(a)g(\014xed)g(realization) d(of)i Fk(Z)j Fm(2)28 b Fk(C)2281 2778 y Fj(\015)2274 2838 y(\013)2325 2814 y Fp(\()p Fo(R)2429 2829 y Fn(+)2517 2814 y Fm(\002)22 b Fo(R)5 b Fp(\).)146 2958 y(Let)41 b Fk(q)j Fp(:=)d Fk(m)27 b Fp(+)g Fk(h)41 b Fp(and)f Fk(U)1145 2922 y Fi(0)1169 2958 y Fp(\()p Fk(m)p Fp(\))h(:=)f Fk(V)1593 2922 y Fi(0)1616 2958 y Fp(\()p Fk(m)p Fp(\))27 b Fm(\000)h Fk(\025m)p Fp(;)44 b(w)m(e)e(form)m(ulate)c(the)j(problem)e (\(1.1\))g(in)h(the)0 3078 y(in)m(tegral)31 b(form)726 3348 y Fk(m)p Fp(\()p Fk(t)p Fp(\))e(=)e Fk(p)1103 3363 y Fj(t)1133 3348 y Fk(m)p Fp(\(0\))22 b(+)1463 3212 y Fe(Z)1562 3239 y Fj(t)1518 3438 y Fn(0)1592 3348 y Fk(ds)17 b(p)1755 3363 y Fj(t)p Fi(\000)p Fj(s)1888 3348 y Fp([)p Fm(\000)p Fk(U)2068 3307 y Fi(0)2093 3348 y Fp(\()p Fk(m)p Fp(\()p Fk(s)p Fp(\)\))22 b(+)g Fk(\025q)t Fp(\()p Fk(s)p Fp(\)])g(+)g Fk(Z)7 b Fp(\()p Fk(t)p Fp(\))726 3708 y Fk(q)t Fp(\()p Fk(t)p Fp(\))28 b(=)g Fk(p)1065 3723 y Fj(t)1094 3708 y Fk(q)t Fp(\(0\))22 b Fm(\000)1397 3641 y Fp(1)p 1397 3686 49 4 v 1397 3777 a(2)1473 3573 y Fe(Z)1572 3599 y Fj(t)1528 3798 y Fn(0)1602 3708 y Fk(ds)17 b Fp(\001)p Fk(p)1846 3723 y Fj(t)p Fi(\000)p Fj(s)1963 3708 y Fk(m)p Fp(\()p Fk(s)p Fp(\))3579 3523 y(\(1.3\))0 3973 y(note)35 b(that)f(the)h(in)m(tegral)e(on)h(the)h(r.h.s.)g(of)f(the)h(second)h (equation)e(is)g(w)m(ell)g(de\014ned)i(\(the)f(result)f(is)g(a)0 4094 y(con)m(tin)m(uous)f(function\))f(pro)m(vided)h Fk(x)28 b Fm(7!)g Fk(m)p Fp(\()p Fk(s;)17 b(x)p Fp(\))33 b(is)f(H\177)-49 b(older)32 b(con)m(tin)m(uous.)146 4214 y(Our)j(main)e(result)i(is)g(the)g(follo)m(wing)d(existence)37 b(and)e(uniqueness)i(result)e(for)f(the)i(system)f(\(1.3\))0 4334 y(on)d(the)h(space)h(of)e(H\177)-49 b(older)32 b(con)m(tin)m(uous) i(functions.)0 4531 y Fq(Theorem)40 b(1.2.)k Fl(L)-5 b(et)37 b Fk(m)p Fp(\(0\))p Fk(;)17 b(q)t Fp(\(0\))32 b Fm(2)h Fk(C)1500 4495 y Fj(\015)1493 4556 y(\013)1544 4531 y Fp(\()p Fo(R)5 b Fp(\))44 b Fl(for)37 b(any)g Fk(\013)d(>)e Fp(0)37 b Fl(and)g Fk(\015)h Fm(2)33 b Fp(\(0)p Fk(;)17 b Fp(1\))p Fl(.)51 b(Then)37 b(ther)-5 b(e)37 b(exists)0 4651 y(a)45 b(unique)f Fm(F)490 4666 y Fj(t)519 4651 y Fl({adapte)-5 b(d)44 b(pr)-5 b(o)g(c)g(ess)44 b Fp(\()p Fk(m;)17 b(q)t Fp(\))46 b Fm(2)g Fk(C)1762 4615 y Fj(\015)1755 4676 y(\013)1807 4651 y Fp(\()p Fo(R)1910 4666 y Fn(+)2005 4651 y Fm(\002)30 b Fo(R)5 b Fp(\))35 b Fm(\002)30 b Fk(C)2435 4615 y Fj(\015)2428 4676 y(\013)2480 4651 y Fp(\()p Fo(R)2583 4666 y Fn(+)2678 4651 y Fm(\002)g Fo(R)5 b Fp(\))50 b Fl(for)45 b(any)g Fk(\013)h(>)g Fp(0)f Fl(and)0 4772 y Fk(\015)33 b Fm(2)28 b Fp(\(0)p Fk(;)17 b Fp(1\))34 b Fl(which)g(solves)g(\(1.3\).)146 4969 y Fp(W)-8 b(e)33 b(in)m(tro)s(duce)g(the)g(linear)e(op)s(erators)h Fk(G)p Fp(,)1777 4943 y(~)1755 4969 y Fk(G)g Fp(on)h Fk(C)2070 4984 y Fj(\013)2119 4969 y Fp(\()p Fo(R)2223 4984 y Fn(+)2310 4969 y Fm(\002)23 b Fo(R)5 b Fp(\))38 b(giv)m(en)33 b(b)m(y)1208 5244 y Fk(G)p Fp([)p Fk(F)14 b Fp(])j(\()p Fk(t)p Fp(\))27 b(:=)1702 5108 y Fe(Z)1802 5134 y Fj(t)1757 5334 y Fn(0)1831 5244 y Fk(ds)17 b(p)1994 5259 y Fj(t)p Fi(\000)p Fj(s)2111 5244 y Fk(F)d Fp(\()p Fk(s)p Fp(\))1230 5492 y(~)1208 5517 y Fk(G)p Fp([)p Fk(F)g Fp(])j(\()p Fk(t)p Fp(\))27 b(:=)1702 5381 y Fe(Z)1802 5408 y Fj(t)1757 5607 y Fn(0)1831 5517 y Fk(ds)17 b Fp(\()p Fk(t)22 b Fm(\000)g Fk(s)p Fp(\))2233 5450 y(1)p 2233 5494 V 2233 5585 a(2)2292 5517 y(\001)p Fk(p)2422 5532 y Fj(t)p Fi(\000)p Fj(s)2539 5517 y Fk(F)14 b Fp(\()p Fk(s)p Fp(\))841 b(\(1.4\))1866 5806 y(2)p eop %%Page: 3 4 3 3 bop 0 407 a Fp(and)33 b(set)h Fk(R)q Fp(\()p Fk(t)p Fp(\))29 b(:=)f Fk(p)738 422 y Fj(t)768 407 y Fk(m)p Fp(\(0\))22 b(+)g Fk(\025t)17 b(p)1256 422 y Fj(t)1286 407 y Fk(q)t Fp(\(0\))22 b(+)g Fk(Z)7 b Fp(\()p Fk(t)p Fp(\).)45 b(By)33 b(plugging)e(the)j(second)g(equation)f(in)f(\(1.3\))h (in)m(to)0 527 y(the)g(\014rst)g(one)g(w)m(e)h(get)e(that)g Fk(m)h Fp(solv)m(es)h(the)f(problem)1281 727 y Fk(m)28 b Fp(=)g Fk(R)23 b Fm(\000)g Fk(G)p Fp([)p Fk(U)1875 685 y Fi(0)1899 727 y Fp(\()p Fk(m)p Fp(\)])f Fm(\000)h Fk(\025)2304 701 y Fp(~)2283 727 y Fk(G)o Fp([)p Fk(m)p Fp(])1081 b(\(1.5\))146 926 y(By)33 b(standard)g(estimates)f(on)g(the)h (heat)g(k)m(ernel,)g(it)e(is)h(easy)i(to)e(v)m(erify)h(that)f(for)g (eac)m(h)h Fk(\013)28 b(>)g Fp(0)k(and)0 1046 y Fk(\015)h Fm(2)28 b Fp(\(0)p Fk(;)17 b Fp(1])32 b(there)h(exists)g Fk(\013)998 1010 y Fi(0)1049 1046 y Fk(>)27 b Fp(0)33 b(and)f(a)h(constan)m(t)g Fk(C)i Fp(=)27 b Fk(C)7 b Fp(\()p Fk(\013)q(;)17 b(\015)5 b Fp(\))32 b(suc)m(h)i(that)1305 1246 y Fm(k)p Fk(Gf)11 b Fm(k)1541 1265 y Fj(C)1596 1233 y Fh(\015)1591 1276 y(\013)1635 1265 y Fn(\()p Fg(R)1710 1274 y Ff(+)1761 1265 y Fi(\002)p Fg(R)p Fn(\))1923 1246 y Fm(\024)28 b Fk(C)7 b Fm(k)p Fk(f)k Fm(k)2264 1261 y Fj(C)2314 1280 y Fh(\013)2354 1266 y Fd(0)2381 1261 y Fn(\()p Fg(R)2456 1270 y Ff(+)2507 1261 y Fi(\002)p Fg(R)p Fn(\))1305 1407 y Fm(k)1377 1381 y Fp(~)1355 1407 y Fk(Gf)g Fm(k)1541 1426 y Fj(C)1596 1394 y Fh(\015)1591 1437 y(\013)1635 1426 y Fn(\()p Fg(R)1710 1435 y Ff(+)1761 1426 y Fi(\002)p Fg(R)p Fn(\))1923 1407 y Fm(\024)28 b Fk(C)7 b Fm(k)p Fk(f)k Fm(k)2264 1422 y Fj(C)2314 1441 y Fh(\013)2354 1427 y Fd(0)2381 1422 y Fn(\()p Fg(R)2456 1431 y Ff(+)2507 1422 y Fi(\002)p Fg(R)p Fn(\))0 1606 y Fp(F)-8 b(urthermore,)30 b(for)g(eac)m(h)h Fk(\013)d(>)g Fp(0)i(and)g Fk(\015)j Fm(2)28 b Fp(\(0)p Fk(;)17 b Fp(1\),)30 b(there)h(exists)g Fk(\013)2444 1570 y Fi(0)2494 1606 y Fk(>)d Fp(0,)i Fk(\015)2760 1570 y Fi(0)2811 1606 y Fm(2)f Fp(\(0)p Fk(;)17 b Fp(1\))29 b(and)h(a)g(constan)m(t)0 1726 y Fk(C)35 b Fp(=)27 b Fk(C)7 b Fp(\()p Fk(\013)q(;)17 b(\015)5 b Fp(\))32 b(suc)m(h)i(that)949 1844 y Fe(\015)949 1904 y(\015)949 1964 y(\015)949 2024 y(\015)1004 1853 y(Z)1104 1879 y Fj(t)1059 2079 y Fn(0)1133 1989 y Fk(ds)17 b Fp(\001)p Fk(p)1377 2004 y Fj(t)p Fi(\000)p Fj(s)1494 1989 y Fk(f)11 b Fp(\()p Fk(s)p Fp(\))1675 1844 y Fe(\015)1675 1904 y(\015)1675 1964 y(\015)1675 2024 y(\015)1730 2088 y Fj(C)1785 2055 y Fh(\015)1780 2098 y(\013)1825 2088 y Fn(\()p Fg(R)1900 2097 y Ff(+)1951 2088 y Fi(\002)p Fg(R)p Fn(\))2113 1989 y Fm(\024)28 b Fk(C)7 b Fm(k)p Fk(f)k Fm(k)2454 2029 y Fj(C)2509 1996 y Fh(\015)2544 1982 y Fd(0)2504 2060 y Fh(\013)2544 2046 y Fd(0)2571 2029 y Fn(\()p Fg(R)2646 2038 y Ff(+)2697 2029 y Fi(\002)p Fg(R)p Fn(\))0 2261 y Fp(Therefore)28 b(Theorem)g(1.2)f(can)g(b)s(e)g (easily)g(deduced)i(from)d(the)h(follo)m(wing)e(existence)k(and)e (uniqueness)0 2381 y(result)33 b(for)f(the)h(problem)e(\(1.5\))h(on)g (the)h(space)h(of)e(con)m(tin)m(uous)h(functions.)0 2567 y Fq(Theorem)43 b(1.3.)h Fl(L)-5 b(et)40 b Fk(m)p Fp(\(0\))p Fk(;)17 b(q)t Fp(\(0\))36 b Fm(2)g Fk(C)1506 2582 y Fj(\013)1556 2567 y Fp(\()p Fo(R)5 b Fp(\))45 b Fl(for)39 b(any)h Fk(\013)d(>)f Fp(0)p Fl(.)59 b(Then)38 b(ther)-5 b(e)40 b(exists)f(a)g(unique)h Fm(F)3701 2582 y Fj(t)3730 2567 y Fl({)0 2687 y(adapte)-5 b(d)34 b(pr)-5 b(o)g(c)g(ess)34 b Fk(m)28 b Fm(2)g Fk(C)963 2702 y Fj(\013)1013 2687 y Fp(\()p Fo(R)1116 2702 y Fn(+)1204 2687 y Fm(\002)22 b Fo(R)5 b Fp(\))41 b Fl(for)35 b(any)f Fk(\013)29 b(>)e Fp(0)35 b Fl(which)f(solves)g(\(1.5\).)146 2873 y Fp(In)26 b(the)h(rest)f(of)g(the)g(pap)s(er)g(w)m(e)h(pro)m(v)m(e)g(Theorem)f (1.3)f(b)m(y)i(adapting)e(the)h(tec)m(hniques)i(dev)m(elop)s(ed)e(to)0 2993 y(treat)34 b(the)h(\(one)f(space)i(dimensional\))31 b(sto)s(c)m(hastic)k(Allen{Cahn)e(equation,)i(i.e.)f(the)g(\014rst)h (equation)0 3114 y(in)45 b(\(1.1\))h(with)g Fk(\025)k Fp(=)h(0.)84 b(W)-8 b(e)47 b(shall)d(follo)m(w)h(closely)g(the)i(pro)s (of)e(in)h([3)o(])h(referring)e(to)h(that)g(pap)s(er)0 3234 y(for)36 b(some)g(tec)m(hnical)g(Lemmata;)g(see)h(also)f([4)o(])h (for)e(the)i(analogous)e(result)h(in)g(a)g(b)s(ounded)h(domain.)0 3354 y(The)k(main)e(di\016culties)h(of)g(the)g(phase)i(\014eld)e(mo)s (del)f(are)h(due)h(to)g(the)f(non)h(lo)s(cal)d(term)i(\(although)0 3475 y(linear\))30 b Fk(\025h)i Fp(in)e(\(1.1\).)43 b(Since)32 b(w)m(e)g(cannot)g(estimate)f(the)h Fk(L)2174 3439 y Fj(p)2246 3475 y Fp(norm)e(of)i Fk(h)f Fp(b)m(y)i(the)f Fk(L)3065 3439 y Fj(p)3136 3475 y Fp(norm)f(of)g Fk(m)p Fp(,)i(the)0 3595 y(necessary)39 b Fl(a)f(priori)e Fp(b)s(ounds)h (\(needed)h(b)s(oth)e(for)g(the)g(existence)i(and)f(the)f(uniqueness\)) j(are)d(not)g(a)0 3716 y(straigh)m(tforw)m(ard)e(extension)i(of)e(the)h (analogous)f(ones)h(for)f(the)h(sto)s(c)m(hastic)g(Allen{Cahn)f (equation.)0 3836 y(T)-8 b(o)34 b(o)m(v)m(ercame)h(this)f(problem)f(w)m (e)j(shall)d(b)s(ound)h(an)g(appropriate)g(negativ)m(e)g(Sob)s(olev)g (norm)g(of)f Fk(h)i Fp(in)0 3956 y(terms)e(of)f(the)h Fk(L)617 3920 y Fj(p)689 3956 y Fp(norm)f(of)g Fk(m)p Fp(,)h(see)h(Lemmata)d(2.4)h(and)g(2.5)h(b)s(elo)m(w.)146 4077 y(W)-8 b(e)37 b(\014nally)f(remark)g(that)h(the)g(quartic)f (double)h(w)m(ell)f(p)s(oten)m(tial,)g Fk(V)21 b Fp(\()p Fk(m)p Fp(\))35 b(=)g Fk(m)3115 4041 y Fn(4)3155 4077 y Fk(=)p Fp(4)24 b Fm(\000)i Fk(m)3465 4041 y Fn(2)3504 4077 y Fk(=)p Fp(2)37 b(has)0 4197 y(b)s(een)46 b(c)m(hosen)h(only)e (for)g(notation)f(simplicit)m(y;)50 b(the)c(pro)s(of)e(w)m(orks)j(for)e (an)m(y)h(p)s(olynomial)c(of)j(ev)m(en)0 4317 y(degree)33 b(with)g(p)s(ositiv)m(e)f(leading)f(co)s(e\016cien)m(t.)146 4438 y(Since)g(the)g(parameter)g Fk(\025)f Fp(will)f(b)s(e)i(k)m(ept)h (\014xed)g(throughout)e(all)f(the)i(pap)s(er)g(w)m(e)h(omit)d(to)h (indicate)0 4558 y(the)j(dep)s(endence)h(on)e(it.)42 b(W)-8 b(e)33 b(shall)e(denote)i(b)m(y)g Fk(C)39 b Fp(a)31 b(generic)i(p)s(ositiv)m(e)e(constan)m(t)i(whose)g(n)m(umerical)0 4679 y(v)-5 b(alue)32 b(ma)m(y)g(c)m(hange)i(from)d(line)g(to)i(line.)0 4975 y Fq(2.)38 b(Finite)e(v)m(olume)g(appro)m(ximations)146 5117 y Fp(Let)e Fk(C)399 5081 y Fi(1)392 5142 y Fj(K)473 5117 y Fp(\()p Fo(R)5 b Fp(\))39 b(b)s(e)34 b(the)f(space)h(of)f (in\014nitely)f(di\013eren)m(tiable)g(functions)h(on)g Fo(R)44 b Fp(with)33 b(compact)g(sup-)0 5237 y(p)s(ort)43 b(and)g(in)m(tro)s(duce)h Fm(L)i Fp(=)g Fm(f)p Fp(\003)f Fm(2)i Fk(C)1460 5201 y Fi(1)1453 5263 y Fj(K)1534 5237 y Fp(\()p Fo(R)5 b Fp(\))69 b(:)63 b(0)46 b Fm(\024)g Fp(\003)g Fm(\024)g Fp(1)p Fm(g)p Fp(.)76 b(F)-8 b(or)43 b(\003)i Fm(2)i(L)p Fp(,)f(w)m(e)e(in)m(tro)s(duce)g(the)0 5358 y(follo)m(wing)30 b(\014nite)i(v)m(olume)g(appro)m(ximations)f(of) h(the)h(problem)e(\(1.5\))1100 5557 y Fk(m)1185 5572 y Fn(\003)1266 5557 y Fp(=)d(\003)p Fk(R)23 b Fm(\000)f Fk(G)p Fp([\003)p Fk(U)1882 5516 y Fi(0)1906 5557 y Fp(\()p Fk(m)2029 5572 y Fn(\003)2082 5557 y Fp(\)])h Fm(\000)f Fk(\025)2365 5532 y Fp(~)2343 5557 y Fk(G)p Fp([\003)p Fk(m)2600 5572 y Fn(\003)2653 5557 y Fp(])899 b(\(2.1\))1866 5806 y(3)p eop %%Page: 4 5 4 4 bop 146 407 a Fp(In)48 b(this)f(section)h(w)m(e)g(establish)g(a)f (global)e(existence)k(result)e(for)g(\(2.1\))g(together)h(with)f(some)0 527 y(b)s(ounds)33 b(uniform)e(for)h(\003)27 b Fm(2)i(L)p Fp(.)43 b(T)-8 b(o)32 b(this)h(end)g(w)m(e)g(need)h(to)e(in)m(tro)s (duce)h(some)f(more)g(notation.)146 648 y(F)-8 b(or)39 b Fk(\013)g(>)g Fp(0,)h(let)e Fk(\045)p Fp(\()p Fk(x)p Fp(\))i(:=)f Fk(e)1215 611 y Fi(\000)p Fj(\013)p Fi(j)p Fj(x)p Fi(j)1398 648 y Fp(.)63 b(W)-8 b(e)39 b(shall)f(denote)i(b)m(y)g Fk(\045)f Fp(also)f(the)i(measure)f Fk(\045)p Fp(\()p Fk(x)p Fp(\))p Fk(dx)h Fp(on)f Fo(R)5 b Fp(.)0 768 y(W)-8 b(e)30 b(in)m(tro)s(duce)f(the)g(follo)m(wing)e(\014nite)i(measures)h (on)f Fo(R)2027 783 y Fn(+)2107 768 y Fm(\002)15 b Fo(R)6 b Fp(,)36 b(omitting)26 b(the)k(dep)s(endence)h(on)e Fk(\013)g(>)e Fp(0)0 888 y(from)k(the)i(notation)1168 1090 y Fk(\026)p Fp(\()p Fk(dt;)17 b(dx)p Fp(\))83 b(:=)g Fk(e)1853 1049 y Fi(\000)p Fj(\013)1953 1026 y Ff(2)1988 1049 y Fj(t=)p Fn(2)2088 1090 y Fk(\045)p Fp(\()p Fk(x)p Fp(\))17 b Fk(dx)g(dt)1113 1236 y(\026)1172 1251 y Fj(T)1227 1236 y Fp(\()p Fk(dt;)g(dx)p Fp(\))83 b(:=)g Fk(\037)1869 1251 y Fn([0)p Fj(;T)10 b Fn(])2018 1236 y Fp(\()p Fk(t)p Fp(\))17 b Fk(\026)p Fp(\()p Fk(dt;)g(dx)p Fp(\))1115 1381 y Fk(\026)1174 1396 y Fn(\003)1227 1381 y Fp(\()p Fk(dt;)g(dx)p Fp(\))83 b(:=)g(\003\()p Fk(x)p Fp(\))17 b Fk(\026)p Fp(\()p Fk(dt;)g(dx)p Fp(\))1049 1526 y Fk(\026)1108 1541 y Fj(T)6 b(;)p Fn(\003)1227 1526 y Fp(\()p Fk(dt;)17 b(dx)p Fp(\))83 b(:=)g Fk(\037)1869 1542 y Fn([0)p Fj(;T)10 b Fn(])2018 1526 y Fp(\()p Fk(t)p Fp(\))17 b(\003\()p Fk(x)p Fp(\))g Fk(\026)p Fp(\()p Fk(dt;)g(dx)p Fp(\))0 1728 y(where)28 b Fk(\037)337 1744 y Fn([0)p Fj(;T)10 b Fn(])513 1728 y Fp(denotes)29 b(the)e(c)m(haracteristic)g(function)f (of)h([0)p Fk(;)17 b(T)d Fp(].)41 b(F)-8 b(or)26 b Fk(\027)33 b Fp(a)27 b(measure)g(and)g Fk(f)38 b Fp(a)26 b(function)0 1848 y(use)34 b(the)f(notation)e Fk(\027)6 b Fp(\()p Fk(f)11 b Fp(\))27 b(=)1047 1768 y Fe(R)1113 1848 y Fk(d\027)c(f)11 b Fp(.)146 1969 y(F)-8 b(or)29 b Fk(p)f Fm(2)g Fp(\(1)p Fk(;)17 b Fm(1)p Fp(\),)29 b(w)m(e)i(in)m(tro)s(duce)f(the)g(Sob)s (olev)g(space)h Fk(H)2259 1922 y Fj(p)2251 1993 y Fn(1)2298 1969 y Fp(\()p Fk(\045)p Fp(\))f(obtained)f(b)m(y)i(completing)d Fk(C)3558 1933 y Fi(1)3551 1994 y Fj(K)3632 1969 y Fp(\()p Fo(R)5 b Fp(\))0 2089 y(with)32 b(resp)s(ect)i(to)e(the)h(norm)1187 2291 y Fm(k)p Fk(')p Fm(k)1351 2244 y Fj(p)1351 2327 y(H)1414 2294 y Fh(p)1409 2348 y Ff(1)1450 2327 y Fn(\()p Fj(\045)p Fn(\))1573 2291 y Fp(:=)28 b Fm(kr)p Fk(')p Fm(k)1951 2244 y Fj(p)1951 2323 y(L)1999 2304 y Fh(p)2034 2323 y Fn(\()p Fj(\045)p Fn(\))2152 2291 y Fp(+)22 b Fm(k)p Fk(')p Fm(k)2414 2244 y Fj(p)2414 2323 y(L)2462 2304 y Fh(p)2497 2323 y Fn(\()p Fj(\045)p Fn(\))0 2514 y Fp(where)35 b Fm(r)f Fp(denotes)h(the)g(deriv)-5 b(ativ)m(e)33 b(with)h(resp)s(ect)h(to)f Fk(x)p Fp(.)48 b(Since)34 b Fk(H)2527 2466 y Fj(p)2519 2538 y Fn(1)2566 2514 y Fp(\()p Fk(\045)p Fp(\))c Fm(\032)h Fk(L)2896 2478 y Fj(p)2936 2514 y Fp(\()p Fk(\045)p Fp(\))j(for)f Fk(p;)17 b(q)34 b Fm(2)c Fp(\(1)p Fk(;)17 b Fm(1)p Fp(\))0 2634 y(suc)m(h)39 b(that)f Fk(p)491 2598 y Fi(\000)p Fn(1)611 2634 y Fp(+)26 b Fk(q)760 2598 y Fi(\000)p Fn(1)890 2634 y Fp(=)37 b(1)g(w)m(e)i(in)m(tro)s(duce)f(the)g(dual)f(space)i Fk(H)2427 2587 y Fj(q)2419 2659 y Fi(\000)p Fn(1)2513 2634 y Fp(\()p Fk(\045)p Fp(\))f(b)m(y)h(completing)d Fk(L)3388 2598 y Fj(q)3426 2634 y Fp(\()p Fk(\045)p Fp(\))i(with)0 2754 y(resp)s(ect)c(to)e(the)h(norm)1248 2875 y Fm(k)p Fk(`)p Fm(k)1389 2895 y Fj(H)1452 2862 y Fh(q)1447 2916 y Fd(\000)p Ff(1)1529 2895 y Fn(\()p Fj(\045)p Fn(\))1651 2875 y Fp(:=)189 b(sup)1782 2961 y Fj(')12 b Fn(:)f Fi(k)p Fj(')p Fi(k)1987 2986 y Fh(H)2041 2959 y(p)2037 3011 y Ff(1)2078 2986 y(\()p Fh(\045)p Ff(\))2161 2961 y Fi(\024)p Fn(1)2285 2875 y Fk(\045)p Fp(\()p Fk(`)17 b(')p Fp(\))0 3150 y(F)-8 b(or)32 b Fk(f)38 b Fp(=)28 b Fk(f)11 b Fp(\()p Fk(t;)17 b(x)p Fp(\))32 b(w)m(e)i(shall)d(use)i(the)g(notation)1057 3419 y Fm(k)p Fk(f)11 b Fm(k)1216 3372 y Fj(p)1216 3455 y(H)1279 3422 y Fh(p)1274 3476 y Fd(\000)p Ff(1)1356 3455 y Fn(\()p Fj(\026)1425 3466 y Fh(T)1474 3455 y Fn(\))1533 3419 y Fp(:=)1664 3284 y Fe(Z)1764 3310 y Fj(T)1719 3509 y Fn(0)1819 3419 y Fk(dt)17 b(e)1967 3378 y Fi(\000)p Fj(\013)2067 3355 y Ff(2)2101 3378 y Fj(t=)p Fn(2)2218 3419 y Fm(k)p Fk(f)11 b Fp(\()p Fk(t)p Fp(\))p Fm(k)2488 3372 y Fj(p)2488 3455 y(H)2551 3422 y Fh(p)2546 3476 y Fd(\000)p Ff(1)2628 3455 y Fn(\()p Fj(\045)p Fn(\))0 3668 y Fp(omitting)30 b(to)i(write)g Fk(T)46 b Fp(on)33 b(the)g(l.h.s.)f(if)g Fk(T)41 b Fp(=)28 b Fm(1)p Fp(.)146 3833 y(F)-8 b(rom)36 b(Lemma)h(1.1)g(it)g(follo)m(ws)f(that)h(for)g (eac)m(h)i Fk(\013)e(>)f Fp(0)h(and)h Fk(p)e Fm(2)h Fp([1)p Fk(;)17 b Fm(1)p Fp(\))37 b(w)m(e)h(ha)m(v)m(e)h Fk(Z)44 b Fm(2)36 b Fk(L)3578 3797 y Fj(p)3618 3833 y Fp(\()p Fk(\026)p Fp(\).)0 3954 y(F)-8 b(urthermore)44 b(for)f(eac)m(h)j Fk(T)61 b(>)48 b Fp(0)c(and)g(\003)j Fm(2)i(L)43 b Fp(w)m(e)j(ha)m(v)m (e)f(sup)2386 3977 y Fj(t)p Fi(2)p Fn([0)p Fj(;T)10 b Fn(])2641 3954 y Fp(sup)2788 3977 y Fj(x)p Fi(2)p Fg(R)2944 3954 y Fm(j)p Fp(\003\()p Fk(x)p Fp(\))p Fk(Z)d Fp(\()p Fk(t;)17 b(x)p Fp(\))p Fm(j)47 b Fk(<)g Fm(1)p Fp(.)0 4074 y(Moreo)m(v)m(er,)c(b)m(y)d(the)g(assumptions)f(on)g(the)h (initial)35 b(data,)41 b(the)f(same)f(holds)g(for)g Fk(R)q Fp(\()p Fk(t)p Fp(\))g(=)g Fk(p)3438 4089 y Fj(t)3467 4074 y Fk(m)p Fp(\(0\))27 b(+)0 4195 y Fk(\025t)17 b(p)158 4210 y Fj(t)187 4195 y Fk(q)t Fp(\(0\))22 b(+)g Fk(Z)7 b Fp(\()p Fk(t)p Fp(\).)146 4315 y(W)-8 b(e)43 b(next)g(state)g(a)f(lo) s(cal)f(existence)j(result)e(for)g(the)h(problem)e(\(2.1\).)72 b(Since)3153 4290 y(~)3131 4315 y Fk(G)42 b Fp(has)h(a)f(k)m(ernel)0 4435 y(whic)m(h)36 b(can)g(b)s(e)g(estimated)f(as)h(the)g(one)g(of)g Fk(G)p Fp(,)g(the)g(pro)s(of)f(of)g(the)i(next)f(result,)h(whic)m(h)f (is)f(based)i(on)0 4556 y(Picard)32 b(iterations,)f(is)i(the)g(same)f (as)h([3,)f(Prop.)44 b(1])32 b(and)h(w)m(e)h(omit)c(it.)0 4744 y Fq(Lemma)42 b(2.1.)i Fl(F)-7 b(or)38 b(e)-5 b(ach)38 b Fp(\003)c Fm(2)h(L)j Fl(and)g(e)-5 b(ach)38 b(r)-5 b(e)g(alization)38 b(of)h Fk(Z)45 b Fl(in)39 b Fk(C)2656 4759 y Fj(\013)2705 4744 y Fp(\()p Fo(R)2809 4759 y Fn(+)2899 4744 y Fm(\002)25 b Fo(R)5 b Fp(\))45 b Fl(ther)-5 b(e)38 b(is)h(a)f(time)0 4864 y Fk(T)57 4879 y Fn(0)140 4864 y Fk(>)43 b Fp(0)g Fl(such)h(that)f(ther)-5 b(e)44 b(exists)f(a)g (unique)g Fm(F)1803 4879 y Fj(t)1832 4864 y Fl({adapte)-5 b(d)43 b(c)-5 b(ontinuous)43 b(and)g(b)-5 b(ounde)g(d)42 b(solution)h(of)0 4984 y(\(2.1\))34 b(on)h Fp([0)p Fk(;)17 b(T)561 4999 y Fn(0)600 4984 y Fp(])22 b Fm(\002)h Fo(R)5 b Fl(.)146 5172 y Fp(T)-8 b(o)27 b(sho)m(w)h(the)f(existence)h(of)e(a)h (global)d(solution,)j(w)m(e)g(pro)m(v)m(e)h(that)f(if)e Fk(m)2713 5187 y Fn(\003)2793 5172 y Fp(is)i(a)f(con)m(tin)m(uous)h (solution)0 5293 y(of)32 b(\(2.1\))g(on)h([0)p Fk(;)17 b(T)671 5257 y Fi(\003)709 5293 y Fp(\))22 b Fm(\002)h Fo(R)44 b Fp(then)1409 5495 y(sup)1352 5580 y Fj(t)p Fi(2)p Fn([0)p Fj(;T)1550 5562 y Fd(\003)1586 5580 y Fn(\))1630 5495 y Fp(sup)1636 5576 y Fj(x)p Fi(2)p Fg(R)1793 5495 y Fm(j)p Fk(m)1906 5510 y Fn(\003)1959 5495 y Fp(\()p Fk(t;)17 b(x)p Fp(\))p Fm(j)28 b Fk(<)f Fm(1)1151 b Fp(\(2.2\))1866 5806 y(4)p eop %%Page: 5 6 5 5 bop 0 407 a Fp(A)37 b(standard)g(argumen)m(t)f(p)s(ermits)g(then)h (to)f(conclude.)56 b(The)38 b(k)m(ey)g(ingredien)m(t)e(for)g(pro)m (ving)g(\(2.2\))g(is)0 527 y(the)d(follo)m(wing)d Fl(a)35 b(priori)42 b Fp(b)s(ound)32 b(on)h(the)g Fk(L)1619 491 y Fj(p)1659 527 y Fp(\()p Fk(\026)1756 542 y Fj(T)1807 523 y Fd(\003)1842 542 y Fj(;)p Fn(\003)1915 527 y Fp(\))g(norm)e(of)h (solutions.)0 731 y Fq(Prop)s(osition)47 b(2.2.)g Fl(L)-5 b(et)45 b Fk(m)1101 746 y Fn(\003)1199 731 y Fl(b)-5 b(e)44 b(a)g(c)-5 b(ontinuous)44 b(solution)g(of)g(\(2.1\))f(on)h Fp([0)p Fk(;)17 b(T)3017 694 y Fi(\003)3056 731 y Fp(\))29 b Fm(\002)g Fo(R)5 b Fl(.)79 b(F)-7 b(or)44 b(e)-5 b(ach)0 851 y Fk(\013)28 b(>)g Fp(0)35 b Fl(and)f Fk(p)27 b Fm(2)h Fp([1)p Fk(;)17 b Fm(1)p Fp(\))34 b Fl(ther)-5 b(e)35 b(exists)g(a)f(c)-5 b(onstant)35 b Fk(C)f Fp(=)28 b Fk(C)2214 770 y Fe(\000)2259 851 y Fk(\013)q(;)17 b(p;)g Fm(k)p Fk(R)q Fm(k)2634 866 y Fj(L)2682 848 y Fh(p)2717 866 y Fn(\()p Fj(\026)p Fn(\))2819 770 y Fe(\001)2892 851 y Fk(<)28 b Fm(1)p Fl(,)34 b(indep)-5 b(endent)33 b(of)0 971 y Fk(T)71 935 y Fi(\003)138 971 y Fk(>)27 b Fp(0)35 b Fl(and)f Fp(\003)28 b Fm(2)g(L)p Fl(,)34 b(such)h(that)1501 1092 y Fm(k)p Fk(m)1636 1107 y Fn(\003)1689 1092 y Fm(k)1739 1107 y Fj(L)1787 1088 y Fh(p)1823 1107 y Fn(\()p Fj(\026)1892 1122 y Fh(T)1936 1108 y Fd(\003)1973 1122 y Fh(;)p Ff(\003)2038 1107 y Fn(\))2097 1092 y Fm(\024)28 b Fk(C)1307 b Fp(\(2.3\))146 1295 y(The)30 b(pro)s(of)d(of)h(the)h(prop)s(osition)d(is)i(split)f(in) h(sev)m(eral)h(Lemmata,)f(the)g(\014rst)h(one,)h(whic)m(h)f(is)e(pro)m (v)m(en)0 1416 y(in)m(tegrating)k(b)m(y)i(parts,)g(is)f([3,)h(Lemma)e (7].)0 1619 y Fq(Lemma)37 b(2.3.)k Fl(If)34 b(b)-5 b(oth)35 b Fk(f)11 b Fp(\()p Fk(t;)17 b(x)p Fp(\))34 b Fl(and)g Fp(\()p Fk(@)1502 1634 y Fj(t)1554 1619 y Fm(\000)1679 1580 y Fn(1)p 1679 1596 36 4 v 1679 1653 a(2)1724 1619 y Fp(\001\))p Fk(f)46 b Fl(ar)-5 b(e)34 b(c)-5 b(ontinuous)35 b(on)f Fp(\(0)p Fk(;)17 b(T)d Fp(\))20 b Fm(\002)i Fo(R)5 b Fl(,)41 b Fk(f)11 b Fp(\(0\))27 b(=)g(0)35 b Fl(and)0 1739 y Fm(j)p Fk(f)11 b Fm(j)115 1703 y Fn(2)p Fj(n)p Fn(+2)321 1739 y Fl(and)35 b Fm(jr)p Fk(f)11 b Fm(j)709 1703 y Fn(2)p Fj(n)p Fn(+2)915 1739 y Fl(ar)-5 b(e)35 b(in)f Fk(L)1266 1703 y Fn(1)1306 1739 y Fp(\()p Fk(\026)1403 1754 y Fj(T)1458 1739 y Fp(\))p Fl(,)g(then,)h(for)g(any)f Fk(n)28 b Fp(=)g(0)p Fk(;)17 b Fp(1)p Fk(;)g(:)g(:)g(:)e Fl(,)843 2017 y Fk(\026)902 2032 y Fj(T)973 1876 y Fe(\022)1046 2017 y Fk(f)1105 1975 y Fn(2)p Fj(n)p Fn(+1)1277 1936 y Fe(\000)1323 2017 y Fk(@)1374 2032 y Fj(t)1426 2017 y Fm(\000)1536 1949 y Fp(1)p 1536 1994 49 4 v 1536 2085 a(2)1595 2017 y(\001)1676 1936 y Fe(\001)1722 2017 y Fk(f)1781 1876 y Fe(\023)1881 2017 y Fm(\025)28 b Fp(\(2)p Fk(n)23 b Fp(+)f(1\))p Fk(\026)2398 2032 y Fj(T)2469 1936 y Fe(\000)2514 2017 y Fk(f)2573 1975 y Fn(2)p Fj(n)2655 2017 y Fm(jr)p Fk(f)11 b Fm(j)2853 1975 y Fn(2)2892 1936 y Fe(\001)3579 2017 y Fp(\(2.4\))146 2294 y(Let)33 b Fk(m)406 2309 y Fn(\003)492 2294 y Fp(b)s(e)g(a)f(con)m(tin)m(uous)h (solution)e(of)i(\(2.1\).)43 b(W)-8 b(e)32 b(de\014ne)869 2558 y Fk(u)925 2573 y Fn(\003)1005 2558 y Fp(:=)c Fk(m)1221 2573 y Fn(\003)1296 2558 y Fm(\000)23 b Fp(\003)p Fk(R)q(;)309 b(q)1918 2573 y Fn(\003)1999 2558 y Fp(:=)2130 2478 y Fe(\000)2175 2558 y Fk(@)2226 2573 y Fj(t)2279 2558 y Fm(\000)2388 2491 y Fp(1)p 2388 2535 V 2388 2627 a(2)2447 2558 y(\001)2528 2478 y Fe(\001)2596 2533 y Fp(~)2574 2558 y Fk(G)p Fp([\003)p Fk(m)2831 2573 y Fn(\003)2884 2558 y Fp(])668 b(\(2.5\))0 2809 y(F)-8 b(rom)29 b(\(2.1\),)i(if)e Fk(m)685 2824 y Fn(\003)769 2809 y Fp(is)h(con)m(tin)m(uous)h(and)g(b)s (ounded)g(on)g([0)p Fk(;)17 b(T)d Fp(])j Fm(\002)i Fo(R)5 b Fp(,)37 b(then)31 b Fk(u)2806 2824 y Fn(\003)2886 2809 y Fm(2)d Fk(C)3057 2773 y Fi(1)3149 2809 y Fp(\(\(0)p Fk(;)17 b(T)d Fp(])21 b Fm(\002)i Fo(R)5 b Fp(\))36 b(b)m(y)0 2930 y(the)h(regularizing)c(prop)s(erties)j(of)g Fk(G)g Fp(and)1611 2905 y(~)1589 2930 y Fk(G)p Fp(.)54 b(Moreo)m(v)m(er,)38 b(for)e Fk(t)e Fm(2)g Fp([0)p Fk(;)17 b(T)d Fp(],)36 b Fk(u)2865 2945 y Fn(\003)2918 2930 y Fp(\()p Fk(t;)17 b(x)p Fp(\))36 b(\(together)g(with)0 3050 y(its)c(deriv)-5 b(ativ)m(e\))32 b(is)g(exp)s(onen)m(tially)g(deca)m(ying)h(as)g Fk(x)28 b Fm(!)f(1)p Fp(.)0 3253 y Fq(Lemma)51 b(2.4.)e Fl(L)-5 b(et)46 b Fk(m)898 3268 y Fn(\003)998 3253 y Fl(b)-5 b(e)46 b(a)g(c)-5 b(ontinuous)46 b(solution)h(of)f(\(2.1\))f (on)h Fp([0)p Fk(;)17 b(T)2831 3217 y Fi(\003)2870 3253 y Fp(\))30 b Fm(\002)h Fo(R)5 b Fl(;)58 b(then)47 b(for)f(e)-5 b(ach)0 3374 y Fk(n)33 b Fp(=)f(0)p Fk(;)17 b Fp(1)p Fk(;)g(:)g(:)g(:)53 b Fl(and)37 b Fk(\014)h(>)33 b Fp(0)k Fl(ther)-5 b(e)37 b(exists)h(a)f(c)-5 b(onstant)37 b Fk(C)j Fp(=)32 b Fk(C)7 b Fp(\()p Fk(n;)17 b(\014)6 b Fp(\))p Fl(,)38 b(indep)-5 b(endent)36 b(of)h Fk(T)3359 3338 y Fi(\003)3431 3374 y Fk(>)32 b Fp(0)38 b Fl(and)0 3494 y Fp(\003)27 b Fm(2)h(L)p Fl(,)35 b(such)g(that)769 3714 y Fk(\026)828 3729 y Fj(T)879 3710 y Fd(\003)915 3729 y Fj(;)p Fn(\003)1004 3634 y Fe(\000)1050 3714 y Fk(e)1095 3673 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)1445 3714 y Fk(u)1501 3673 y Fn(2)p Fj(n)p Fn(+1)1501 3741 y(\003)1673 3714 y Fk(U)1749 3673 y Fi(0)1773 3714 y Fp(\()p Fk(m)1896 3729 y Fn(\003)1950 3714 y Fp(\))1988 3634 y Fe(\001)2061 3714 y Fm(\024)28 b Fk(C)7 b Fm(k)p Fk(e)2338 3673 y Fi(\000)p Fj(\014)s(t)2466 3714 y Fk(q)2509 3729 y Fn(\003)2562 3714 y Fm(k)2612 3673 y Fn(2)p Fj(n)p Fn(+2)2612 3758 y Fj(H)2675 3728 y Ff(2)p Fh(n)p Ff(+2)2670 3779 y Fd(\000)p Ff(1)2825 3758 y Fn(\()p Fj(\026)2894 3773 y Fh(T)2938 3759 y Fd(\003)2979 3758 y Fn(\))3579 3714 y Fp(\(2.6\))0 3976 y Fl(Pr)-5 b(o)g(of.)68 b Fp(W)-8 b(e)35 b(apply)f(Lemma)f(2.3)h(with)g Fk(f)41 b Fp(=)31 b Fk(e)1739 3940 y Fi(\000)p Fj(\014)s(t)1866 3976 y Fk(u)1922 3991 y Fn(\003)2009 3976 y Fp(and)k Fk(T)44 b(<)31 b(T)2480 3940 y Fi(\003)2519 3976 y Fp(.)49 b(By)34 b(using)g(equation)h(\(2.1\),)f(w)m(e)0 4096 y(get)742 4175 y Fe(\000)787 4256 y Fk(@)838 4271 y Fj(t)890 4256 y Fm(\000)1000 4188 y Fp(1)p 1000 4233 V 1000 4324 a(2)1059 4256 y(\001)1140 4175 y Fe(\001)1186 4256 y Fk(e)1231 4215 y Fi(\000)p Fj(\014)s(t)1359 4256 y Fk(u)1415 4271 y Fn(\003)1495 4256 y Fp(=)27 b Fm(\000)p Fk(\014)6 b(e)1781 4215 y Fi(\000)p Fj(\014)s(t)1909 4256 y Fk(u)1965 4271 y Fn(\003)2040 4256 y Fm(\000)23 b Fk(e)2185 4215 y Fi(\000)p Fj(\014)s(t)2329 4256 y Fp([\003)p Fk(U)2500 4215 y Fi(0)2524 4256 y Fp(\()p Fk(m)2647 4271 y Fn(\003)2700 4256 y Fp(\))f(+)g Fk(\025q)2958 4271 y Fn(\003)3011 4256 y Fp(])0 4461 y(hence,)34 b(b)m(y)g(\(2.4\))638 4681 y Fk(\026)697 4696 y Fj(T)769 4600 y Fe(\000)814 4681 y Fk(e)859 4640 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)1227 4600 y Fe(\002)1269 4681 y Fp(\(2)p Fk(n)22 b Fp(+)g(1\))p Fk(u)1677 4640 y Fn(2)p Fj(n)1677 4706 y Fn(\003)1758 4681 y Fp(\()p Fm(r)p Fk(u)1935 4696 y Fn(\003)1988 4681 y Fp(\))2026 4640 y Fn(2)2087 4681 y Fp(+)g Fk(\014)6 b(u)2302 4640 y Fn(2)p Fj(n)p Fn(+2)2302 4708 y(\003)2496 4681 y Fp(+)22 b Fk(u)2650 4640 y Fn(2)p Fj(n)p Fn(+1)2650 4708 y(\003)2822 4681 y Fp(\003)p Fk(U)2966 4640 y Fi(0)2989 4681 y Fp(\()p Fk(m)3112 4696 y Fn(\003)3166 4681 y Fp(\))3204 4600 y Fe(\003)o(\001)945 4840 y Fm(\024)28 b(\000)p Fk(\025\026)1243 4855 y Fj(T)1315 4759 y Fe(\000)1361 4840 y Fk(e)1406 4799 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)1757 4840 y Fk(u)1813 4799 y Fn(2)p Fj(n)p Fn(+1)1813 4867 y(\003)1985 4840 y Fk(q)2028 4855 y Fn(\003)2081 4759 y Fe(\001)3579 4840 y Fp(\(2.7\))146 5060 y(Let)33 b Fk(p;)17 b(q)31 b Fm(2)e Fp(\(1)p Fk(;)17 b Fm(1)p Fp(\))31 b(suc)m(h)j(that)f Fk(p)1364 5024 y Fi(\000)p Fn(1)1480 5060 y Fp(+)22 b Fk(q)1625 5024 y Fi(\000)p Fn(1)1747 5060 y Fp(=)28 b(1;)k(then)i(for)e(eac)m(h)h Fk(\015)g(>)28 b Fp(0)k(there)h(exists)h(a)e(constan)m(t)0 5180 y Fk(C)j Fp(=)27 b Fk(C)7 b Fp(\()p Fk(\015)e(;)17 b(p)p Fp(\))32 b(suc)m(h)i(that)f(for)f(an)m(y)h Fk(a;)17 b(b)28 b Fm(2)g Fo(R)1474 5401 y Fm(j)p Fk(a)17 b(b)p Fm(j)27 b(\024)i Fk(\015)5 b Fm(j)p Fk(a)p Fm(j)1935 5359 y Fj(p)1996 5401 y Fp(+)22 b Fk(C)7 b Fm(j)p Fk(b)p Fm(j)2268 5359 y Fj(q)3579 5401 y Fp(\(2.8\))1866 5806 y(5)p eop %%Page: 6 7 6 6 bop 0 407 a Fp(therefore,)33 b(b)m(y)h(the)f(dualit)m(y)e(b)s(et)m (w)m(een)k Fk(H)1536 360 y Fj(p)1528 431 y Fn(1)1575 407 y Fp(\()p Fk(\045)p Fp(\))e(and)g Fk(H)2013 360 y Fj(q)2005 431 y Fi(\000)p Fn(1)2099 407 y Fp(\()p Fk(\045)p Fp(\),)g(w)m(e)g(ha)m(v)m(e)1183 627 y Fm(j)o Fk(\045)p Fp(\()p Fk(f)11 b(g)t Fp(\))p Fm(j)27 b(\024)h Fk(\015)5 b Fm(k)p Fk(f)11 b Fm(k)1821 580 y Fj(p)1821 662 y(H)1884 630 y Fh(p)1879 684 y Ff(1)1920 662 y Fn(\()p Fj(\045)p Fn(\))2037 627 y Fp(+)22 b Fk(C)7 b Fm(k)p Fk(g)t Fm(k)2363 580 y Fj(q)2363 662 y(H)2426 630 y Fh(q)2421 684 y Fd(\000)p Ff(1)2502 662 y Fn(\()p Fj(\045)p Fn(\))3579 627 y Fp(\(2.9\))146 873 y(By)33 b(applying)f(\(2.9\))g(w)m(e)h(get)93 1076 y Fe(\014)93 1136 y(\014)127 1161 y Fk(\026)186 1176 y Fj(T)257 1080 y Fe(\000)303 1161 y Fk(e)348 1120 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)699 1161 y Fk(u)755 1119 y Fn(2)p Fj(n)p Fn(+1)755 1188 y(\003)926 1161 y Fk(q)969 1176 y Fn(\003)1023 1080 y Fe(\001)1068 1076 y(\014)1068 1136 y(\014)1129 1161 y Fm(\024)1235 1025 y Fe(Z)1334 1051 y Fj(T)1290 1251 y Fn(0)1389 1161 y Fk(dt)17 b(e)1537 1120 y Fi(\000)p Fj(\013)1637 1096 y Ff(2)1672 1120 y Fj(t=)p Fn(2)p Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)2135 1076 y Fe(\014)2135 1136 y(\014)2168 1161 y Fk(\045)2235 1080 y Fe(\000)2281 1161 y Fk(u)2337 1119 y Fn(2)p Fj(n)p Fn(+1)2337 1188 y(\003)2509 1161 y Fp(\()p Fk(t)p Fp(\))p Fk(q)2663 1176 y Fn(\003)2716 1161 y Fp(\()p Fk(t)p Fp(\))2827 1080 y Fe(\001)2873 1076 y(\014)2873 1136 y(\014)243 1439 y Fm(\024)348 1303 y Fe(Z)448 1329 y Fj(T)403 1529 y Fn(0)503 1439 y Fk(dt)g(e)651 1397 y Fi(\000)p Fj(\013)751 1374 y Ff(2)785 1397 y Fj(t=)p Fn(2)p Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)1249 1328 y Fe(h)1296 1439 y Fk(\015)5 b Fp(\(2)p Fk(n)22 b Fp(+)g(1\))1714 1367 y Ff(2)p Fh(n)p Ff(+2)p 1713 1380 146 3 v 1713 1421 a(2)p Fh(n)p Ff(+1)1873 1439 y Fk(\045)1940 1328 y Fe(\020)2000 1439 y Fk(u)2056 1454 y Fn(\003)2108 1439 y Fp(\()p Fk(t)p Fp(\))2219 1395 y Fn(2)p Fj(n)2307 1367 y Ff(2)p Fh(n)p Ff(+2)p 2308 1380 V 2308 1421 a(2)p Fh(n)p Ff(+1)2484 1439 y Fp(\()p Fm(r)p Fk(u)2661 1454 y Fn(\003)2714 1439 y Fp(\()p Fk(t)p Fp(\)\))2873 1362 y Ff(2)p Fh(n)p Ff(+2)p 2873 1375 V 2873 1416 a(2)p Fh(n)p Ff(+1)3033 1328 y Fe(\021)1259 1716 y Fp(+)p Fk(\015)5 b(\045)1458 1636 y Fe(\000)1503 1716 y Fk(u)1559 1675 y Fn(2)p Fj(n)p Fn(+2)1559 1743 y(\003)1731 1716 y Fp(\()p Fk(t)p Fp(\))1842 1636 y Fe(\001)1910 1716 y Fp(+)22 b Fk(C)7 b Fm(k)p Fk(q)2178 1731 y Fn(\003)2231 1716 y Fp(\()p Fk(t)p Fp(\))p Fm(k)2392 1675 y Fn(2)p Fj(n)p Fn(+2)2392 1760 y Fj(H)2455 1730 y Ff(2)p Fh(n)p Ff(+2)2450 1781 y Fd(\000)p Ff(1)2605 1760 y Fn(\()p Fj(\045)p Fn(\))2700 1606 y Fe(i)243 1994 y Fm(\024)348 1859 y Fe(Z)448 1885 y Fj(T)403 2084 y Fn(0)503 1994 y Fk(dt)17 b(e)651 1953 y Fi(\000)p Fj(\013)751 1930 y Ff(2)785 1953 y Fj(t=)p Fn(2)p Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)1249 1884 y Fe(h)1296 1994 y Fk(\015)5 b Fp(\(2)p Fk(n)22 b Fp(+)g(1\))1714 1923 y Ff(2)p Fh(n)p Ff(+2)p 1713 1936 V 1713 1977 a(2)p Fh(n)p Ff(+1)1873 1994 y Fk(c)1915 2009 y Fn(1)1955 1994 y Fp(\()p Fk(n)p Fp(\))p Fk(\045)2156 1914 y Fe(\000)2201 1994 y Fk(u)2257 2009 y Fn(\003)2310 1994 y Fp(\()p Fk(t)p Fp(\))2421 1953 y Fn(2)p Fj(n)2520 1994 y Fp(\()p Fm(r)p Fk(u)2697 2009 y Fn(\003)2750 1994 y Fp(\()p Fk(t)p Fp(\)\))2899 1946 y Fn(2)2960 1994 y Fp(+)g Fk(u)3114 2009 y Fn(\003)3167 1994 y Fp(\()p Fk(t)p Fp(\))3278 1953 y Fn(2)p Fj(n)p Fn(+2)3450 1914 y Fe(\001)1259 2272 y Fp(+)p Fk(\015)5 b(\045)1458 2191 y Fe(\000)1503 2272 y Fk(u)1559 2231 y Fn(2)p Fj(n)p Fn(+2)1559 2299 y(\003)1731 2272 y Fp(\()p Fk(t)p Fp(\))1842 2191 y Fe(\001)1910 2272 y Fp(+)22 b Fk(C)7 b Fm(k)p Fk(q)2178 2287 y Fn(\003)2231 2272 y Fp(\()p Fk(t)p Fp(\))p Fm(k)2392 2231 y Fn(2)p Fj(n)p Fn(+2)2392 2316 y Fj(H)2455 2286 y Ff(2)p Fh(n)p Ff(+2)2450 2337 y Fd(\000)p Ff(1)2605 2316 y Fn(\()p Fj(\045)p Fn(\))2700 2162 y Fe(i)243 2499 y Fp(=)27 b Fk(\015)5 b Fp(\(2)p Fk(n)22 b Fp(+)h(1\))765 2427 y Ff(2)p Fh(n)p Ff(+2)p 764 2440 V 764 2481 a(2)p Fh(n)p Ff(+1)924 2499 y Fk(c)966 2514 y Fn(1)1006 2499 y Fp(\()p Fk(n)p Fp(\))p Fk(\026)1199 2514 y Fj(T)1270 2418 y Fe(\000)1316 2499 y Fk(e)1361 2458 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)1712 2499 y Fk(u)1768 2458 y Fn(2)p Fj(n)1768 2524 y Fn(\003)1866 2499 y Fp(\()p Fm(r)p Fk(u)2043 2514 y Fn(\003)2095 2499 y Fp(\))2133 2451 y Fn(2)2173 2418 y Fe(\001)341 2682 y Fp(+)f Fk(\015)511 2571 y Fe(h)559 2682 y Fp(\(2)p Fk(n)g Fp(+)g(1\))921 2610 y Ff(2)p Fh(n)p Ff(+2)p 920 2623 V 920 2664 a(2)p Fh(n)p Ff(+1)1080 2682 y Fk(c)1122 2697 y Fn(1)1162 2682 y Fp(\()p Fk(n)p Fp(\))g(+)g(1)1465 2571 y Fe(i)1528 2682 y Fk(\026)1587 2697 y Fj(T)1659 2601 y Fe(\000)1704 2682 y Fk(e)1749 2641 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)2100 2682 y Fk(u)2156 2640 y Fn(2)p Fj(n)p Fn(+2)2156 2709 y(\003)2328 2601 y Fe(\001)2396 2682 y Fp(+)g Fk(C)7 b Fm(k)p Fk(e)2666 2641 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)3017 2682 y Fk(q)3060 2697 y Fn(\003)3113 2682 y Fm(k)3163 2640 y Fn(2)p Fj(n)p Fn(+2)3163 2725 y Fj(H)3226 2695 y Ff(2)p Fh(n)p Ff(+2)3221 2746 y Fd(\000)p Ff(1)3376 2725 y Fn(\()p Fj(\026)3445 2736 y Fh(T)3494 2725 y Fn(\))3531 2682 y Fp(\(2.10\))0 2936 y(where)34 b(w)m(e)f(used,)h(in)e(the)h (third)f(step,)i(H\177)-49 b(older)32 b(inequalit)m(y)f(in)h(the)h (form)e(\(as)i(follo)m(ws)e(from)h(\(2.8\)\))1017 3183 y Fk(\045)p Fp(\()p Fk(f)11 b(g)t Fp(\))27 b Fm(\024)h Fk(c)1427 3198 y Fn(1)1467 3183 y Fp(\()p Fk(n)p Fp(\))1618 3073 y Fe(h)1664 3183 y Fk(\045)1731 3073 y Fe(\020)1791 3183 y Fm(j)p Fk(f)11 b Fm(j)1916 3112 y Ff(2)p Fh(n)p Ff(+1)p 1915 3125 V 1930 3166 a Fh(n)p Ff(+1)2075 3073 y Fe(\021)2156 3183 y Fp(+)22 b Fk(\045)2321 3073 y Fe(\020)2381 3183 y Fm(j)p Fk(g)t Fm(j)2498 3114 y Ff(2)p Fh(n)p Ff(+1)p 2496 3127 V 2550 3168 a Fh(n)2656 3073 y Fe(\021)q(i)0 3460 y Fp(with)32 b Fk(f)39 b Fp(=)27 b([)p Fk(u)495 3475 y Fn(\003)548 3460 y Fp(\()p Fk(t)p Fp(\))659 3424 y Fj(n)706 3460 y Fm(r)p Fk(u)845 3475 y Fn(\003)898 3460 y Fp(\()p Fk(t)p Fp(\)])1046 3388 y Ff(2)p Fh(n)p Ff(+2)p 1046 3401 V 1046 3442 a(2)p Fh(n)p Ff(+1)1238 3460 y Fp(and)33 b Fk(g)e Fp(=)c Fk(u)1665 3475 y Fn(\003)1718 3460 y Fp(\()p Fk(t)p Fp(\))1829 3416 y Fj(n)1882 3388 y Ff(2)p Fh(n)p Ff(+2)p 1882 3401 V 1882 3442 a(2)p Fh(n)p Ff(+1)2042 3460 y Fp(.)146 3580 y(Cho)s(osing)k Fk(\015)i Fp(=)28 b Fk(\015)5 b Fp(\()p Fk(n;)17 b(\025;)g(\014)6 b Fp(\))30 b(small)f(enough)j(and)g(taking)f Fk(T)41 b Fm(")28 b Fk(T)2510 3544 y Fi(\003)2580 3580 y Fp(the)k(lemma)e(no)m (w)i(follo)m(ws)e(from)0 3701 y(\(2.7\))i(and)h(\(2.10\).)p 3709 3701 4 66 v 3713 3638 59 4 v 3713 3701 V 3771 3701 4 66 v 0 3904 a Fq(Lemma)44 b(2.5.)g Fl(F)-7 b(or)40 b(e)-5 b(ach)39 b Fk(p)e Fm(2)h Fp(\(1)p Fk(;)17 b Fm(1)p Fp(\))39 b Fl(ther)-5 b(e)40 b(exists)g(a)g(c)-5 b(onstant)39 b Fk(C)45 b Fp(=)37 b Fk(C)7 b Fp(\()p Fk(p)p Fp(\))40 b Fl(such)g(that,)h(for)f(any)0 4024 y Fk(\013)q(;)17 b(\014)6 b(;)17 b(T)40 b(>)28 b Fp(0)34 b Fl(and)h Fk(F)41 b Fm(2)28 b Fk(L)950 3988 y Fj(p)990 4024 y Fp(\()p Fk(\026)1087 4039 y Fj(T)1142 4024 y Fp(\))p Fl(,)659 4157 y Fe(\015)659 4217 y(\015)659 4277 y(\015)659 4337 y(\015)714 4302 y Fk(e)759 4261 y Fi(\000)p Fj(\014)s(t)887 4221 y Fe(\000)933 4302 y Fk(@)984 4317 y Fj(t)1036 4302 y Fm(\000)1146 4234 y Fp(1)p 1146 4279 49 4 v 1146 4370 a(2)1204 4302 y(\001)1285 4221 y Fe(\001)1354 4277 y Fp(~)1331 4302 y Fk(G)p Fp([)p Fk(F)14 b Fp(])1539 4157 y Fe(\015)1539 4217 y(\015)1539 4277 y(\015)1539 4337 y(\015)1595 4401 y Fj(H)1658 4368 y Fh(p)1653 4422 y Fd(\000)p Ff(1)1735 4401 y Fn(\()p Fj(\026)1804 4412 y Fh(T)1854 4401 y Fn(\))1913 4302 y Fm(\024)28 b Fk(C)2112 4161 y Fe(\022)2185 4302 y Fp(1)22 b(+)2371 4234 y(1)p 2364 4279 63 4 v 2364 4370 a Fk(\013)2437 4161 y Fe(\023)2526 4217 y(\015)2526 4277 y(\015)2582 4302 y Fk(e)2627 4261 y Fi(\000)p Fj(\014)s(t)2755 4302 y Fk(F)2832 4217 y Fe(\015)2832 4277 y(\015)2887 4341 y Fj(L)2935 4322 y Fh(p)2971 4341 y Fn(\()p Fj(\026)3040 4352 y Fh(T)3089 4341 y Fn(\))3531 4302 y Fp(\(2.11\))0 4606 y Fl(Pr)-5 b(o)g(of.)65 b Fp(W)-8 b(e)33 b(can)f(write)1054 4858 y(~)1032 4883 y Fk(G)p Fp([)p Fk(F)14 b Fp(]\()p Fk(t)p Fp(\))28 b(=)1482 4748 y Fe(Z)1582 4774 y Fj(t)1538 4973 y Fn(0)1612 4883 y Fk(ds)17 b(p)1775 4898 y Fj(t)p Fi(\000)p Fj(s)1907 4748 y Fe(Z)2007 4774 y Fj(s)1963 4973 y Fn(0)2044 4883 y Fk(ds)2141 4842 y Fi(0)2190 4816 y Fp(1)p 2190 4860 49 4 v 2190 4952 a(2)2249 4883 y(\001)p Fk(p)2379 4898 y Fj(s)p Fi(\000)p Fj(s)2500 4879 y Fd(0)2526 4883 y Fk(F)d Fp(\()p Fk(s)2687 4842 y Fi(0)2710 4883 y Fp(\))783 b(\(2.12\))0 5156 y(so)33 b(that)f(\(in)g(distribution)f (sense\))1056 5358 y Fe(\000)1102 5439 y Fk(@)1153 5454 y Fj(t)1205 5439 y Fm(\000)1314 5371 y Fp(1)p 1314 5416 V 1314 5507 a(2)1373 5439 y(\001)1454 5358 y Fe(\001)1522 5414 y Fp(~)1500 5439 y Fk(G)p Fp([)p Fk(F)14 b Fp(])j(\()p Fk(t)p Fp(\))27 b(=)1967 5303 y Fe(Z)2067 5329 y Fj(t)2022 5529 y Fn(0)2096 5439 y Fk(ds)2219 5371 y Fp(1)p 2219 5416 V 2219 5507 a(2)2278 5439 y(\001)p Fk(p)2408 5454 y Fj(t)p Fi(\000)p Fj(s)2526 5439 y Fk(F)14 b Fp(\()p Fk(s)p Fp(\))806 b(\(2.13\))1866 5806 y(6)p eop %%Page: 7 8 7 7 bop 0 407 a Fp(W)-8 b(e)33 b(th)m(us)h(get)698 537 y Fe(\015)698 596 y(\015)698 656 y(\015)698 716 y(\015)753 600 y(\000)799 681 y Fk(@)850 696 y Fj(t)902 681 y Fm(\000)1012 614 y Fp(1)p 1012 658 49 4 v 1012 749 a(2)1070 681 y(\001)1151 600 y Fe(\001)1219 656 y Fp(~)1197 681 y Fk(G)p Fp([)p Fk(F)14 b Fp(])j(\()p Fk(t)p Fp(\))1533 537 y Fe(\015)1533 596 y(\015)1533 656 y(\015)1533 716 y(\015)1588 780 y Fj(H)1651 747 y Fh(p)1646 801 y Fd(\000)p Ff(1)1729 780 y Fn(\()p Fj(\045)p Fn(\))1851 681 y Fm(\024)1967 614 y Fp(1)p 1967 658 V 1967 749 a(2)2042 545 y Fe(Z)2142 572 y Fj(t)2097 771 y Fn(0)2171 681 y Fk(ds)33 b Fm(k)p Fp(\001)p Fk(p)2481 696 y Fj(t)p Fi(\000)p Fj(s)2598 681 y Fk(F)14 b Fp(\()p Fk(s)p Fp(\))p Fm(k)2847 710 y Fj(H)2910 678 y Fh(p)2905 731 y Fd(\000)p Ff(1)2987 710 y Fn(\()p Fj(\045)p Fn(\))3531 681 y Fp(\(2.14\))146 992 y(F)-8 b(or)32 b Fk(q)368 955 y Fi(\000)p Fn(1)484 992 y Fp(+)22 b Fk(p)631 955 y Fi(\000)p Fn(1)753 992 y Fp(=)28 b(1)k(and)h Fk(')27 b Fm(2)i Fk(C)1391 955 y Fi(1)1384 1017 y Fj(K)1465 992 y Fp(\()p Fo(R)5 b Fp(\))39 b(w)m(e)33 b(no)m(w)g(ha)m(v)m(e)140 1208 y(\()p Fk(';)17 b Fp(\001)p Fk(p)416 1223 y Fj(t)p Fi(\000)p Fj(s)533 1208 y Fk(F)d Fp(\()p Fk(s)p Fp(\)\))769 1237 y Fj(\045)894 1208 y Fp(=)83 b(\()p Fk(\045';)17 b Fp(\001)p Fk(p)1379 1223 y Fj(t)p Fi(\000)p Fj(s)1496 1208 y Fk(F)d Fp(\()p Fk(s)p Fp(\)\))1733 1237 y Fj(L)1781 1218 y Ff(2)1816 1237 y Fn(\()p Fj(dx)p Fn(\))894 1432 y Fp(=)83 b Fm(\000)1147 1291 y Fe(\022)1221 1432 y Fk(\045)1288 1291 y Fe(\024)1340 1432 y Fm(r)p Fk(')22 b Fp(+)1617 1364 y Fm(r)p Fk(\045)p 1617 1409 134 4 v 1659 1500 a(\045)1760 1291 y Fe(\025)1830 1432 y Fk(;)17 b Fm(r)p Fk(p)2006 1447 y Fj(t)p Fi(\000)p Fj(s)2123 1432 y Fk(F)d Fp(\()p Fk(s)p Fp(\))2322 1291 y Fe(\023)2394 1530 y Fj(L)2442 1512 y Ff(2)2477 1530 y Fn(\()p Fj(dx)p Fn(\))893 1725 y Fm(\024)1053 1584 y Fe(\024)1106 1725 y Fm(kr)p Fk(')p Fm(k)1353 1740 y Fj(L)1401 1721 y Fh(q)1435 1740 y Fn(\()p Fj(\045)p Fn(\))1552 1725 y Fp(+)22 b Fm(k)p Fk(')p Fm(k)1814 1740 y Fj(L)1862 1721 y Fh(q)1896 1740 y Fn(\()p Fj(\045)p Fn(\))2008 1725 y Fp(sup)2014 1806 y Fj(x)p Fi(2)p Fg(R)2171 1725 y Fm(jr)17 b Fp(log)f Fk(\045)p Fp(\()p Fk(x)p Fp(\))p Fm(j)2650 1584 y Fe(\025)2720 1725 y Fm(k)o(r)p Fk(p)2901 1740 y Fj(t)p Fi(\000)p Fj(s)3019 1725 y Fk(F)e Fp(\()p Fk(s)p Fp(\))p Fm(k)3267 1754 y Fj(L)3315 1735 y Fh(p)3351 1754 y Fn(\()p Fj(\045)p Fn(\))3531 1725 y Fp(\(2.15\))0 2000 y(since)33 b(sup)386 2024 y Fj(x)p Fi(2)p Fg(R)541 2000 y Fm(jr)17 b Fp(log)f Fk(\045)p Fp(\()p Fk(x)p Fp(\))p Fm(j)28 b Fp(=)g Fk(\013)33 b Fp(w)m(e)h(conclude)908 2217 y Fm(k)o Fp(\001)p Fk(p)1087 2232 y Fj(t)p Fi(\000)p Fj(s)1205 2217 y Fk(F)14 b Fp(\()p Fk(s)p Fp(\))p Fm(k)1453 2246 y Fj(H)1516 2213 y Fh(p)1511 2267 y Fd(\000)p Ff(1)1594 2246 y Fn(\()p Fj(\045)p Fn(\))1717 2217 y Fm(\024)28 b Fp(\(1)22 b(+)g Fk(\013)q Fp(\))17 b Fm(k)o(r)p Fk(p)2328 2232 y Fj(t)p Fi(\000)p Fj(s)2445 2217 y Fk(F)d Fp(\()p Fk(s)p Fp(\))p Fm(k)2693 2246 y Fj(L)2741 2227 y Fh(p)2777 2246 y Fn(\()p Fj(\045)p Fn(\))3531 2217 y Fp(\(2.16\))146 2453 y(As)33 b(exp)q Fm(f\000)p Fk(\013)q Fm(j)p Fk(x)p Fm(jg)28 b(\024)g Fp(exp)q Fm(f\000)p Fk(\013)q Fm(j)p Fk(y)t Fm(jg)17 b Fp(exp)o Fm(f)p Fk(\013)q Fm(j)p Fk(x)22 b Fm(\000)g Fk(y)t Fm(jg)p Fp(,)281 2719 y Fm(jr)p Fk(p)441 2734 y Fj(t)p Fi(\000)p Fj(s)558 2719 y Fk(F)14 b Fp(\()p Fk(s)p Fp(\))j(\()p Fk(x)p Fp(\))p Fm(j)e Fk(e)993 2677 y Fi(\000)p Fj(\013)p Fi(j)p Fj(x)p Fi(j)p Fj(=p)1275 2719 y Fm(\024)1381 2583 y Fe(Z)1480 2719 y Fk(dy)20 b(e)1644 2677 y Fi(\000)p Fj(\013)p Fi(j)p Fj(y)r Fi(j)p Fj(=p)1896 2719 y Fm(j)p Fk(F)14 b Fp(\()p Fk(s;)j(y)t Fp(\))p Fm(j)g(j)l(r)p Fk(p)2420 2734 y Fj(t)p Fi(\000)p Fj(s)2538 2719 y Fp(\()p Fk(x)22 b Fm(\000)h Fk(y)t Fp(\))p Fm(j)15 b Fk(e)2931 2677 y Fj(\013)p Fi(j)p Fj(x)p Fi(\000)p Fj(y)r Fi(j)p Fj(=p)3223 2719 y Fk(;)281 b Fp(\(2.17\))0 2978 y(b)m(y)33 b(applying)f(Y)-8 b(oung's)33 b(inequalit)m(y)e(for)h (con)m(v)m(olutions)h(w)m(e)g(then)h(obtain)745 3238 y Fm(kr)p Fk(p)927 3253 y Fj(t)p Fi(\000)p Fj(s)1044 3238 y Fk(F)14 b Fp(\()p Fk(s)p Fp(\))p Fm(k)1293 3267 y Fj(L)1341 3248 y Fh(p)1377 3267 y Fn(\()p Fj(\045)p Fn(\))1500 3238 y Fm(\024)28 b(k)p Fk(F)14 b Fp(\()p Fk(s)p Fp(\))p Fm(k)1903 3267 y Fj(L)1951 3248 y Fh(p)1987 3267 y Fn(\()p Fj(\045)p Fn(\))2099 3102 y Fe(Z)2198 3238 y Fk(dx)34 b Fm(jr)p Fk(p)2498 3253 y Fj(t)p Fi(\000)p Fj(s)2615 3238 y Fp(\()p Fk(x)p Fp(\))p Fm(j)16 b Fk(e)2835 3197 y Fj(\013)p Fi(j)p Fj(x)p Fi(j)p Fj(=p)3531 3238 y Fp(\(2.18\))146 3498 y(W)-8 b(e)33 b(de\014ne)666 3749 y Fk(h)722 3764 y Fj(\013;p)827 3749 y Fp(\()p Fk(t)p Fp(\))28 b(:=)1096 3613 y Fe(Z)1196 3749 y Fk(dx)33 b Fm(jr)p Fk(p)1495 3764 y Fj(t)1525 3749 y Fp(\()p Fk(x)p Fp(\))p Fm(j)g Fk(e)1762 3707 y Fj(\013)p Fi(j)p Fj(x)p Fi(j)p Fj(=p)1989 3749 y Fm(\024)2209 3681 y Fp(2)p 2104 3726 260 4 v 2104 3746 a Fm(p)p 2187 3746 177 4 v 82 x Fp(2)17 b Fk(\031)j(t)2395 3749 y Fp(+)2503 3681 y(2)p Fk(\013)p 2503 3726 112 4 v 2535 3817 a(p)2641 3749 y Fp(exp)2807 3608 y Fe(\032)2892 3681 y Fk(\013)2955 3645 y Fn(2)2994 3681 y Fk(t)p 2892 3726 138 4 v 2892 3817 a Fp(2)p Fk(p)2990 3788 y Fn(2)3039 3608 y Fe(\033)3531 3749 y Fp(\(2.19\))0 4023 y(Then,)34 b(from)d(\(2.14\),)h(\(2.16\))g (and)h(\(2.18\),)152 4297 y Fk(\037)213 4312 y Fn([0)p Fj(;T)10 b Fn(])362 4297 y Fp(\()p Fk(t)p Fp(\))17 b Fk(e)535 4250 y Fi(\000)600 4223 y Fh(\013)640 4202 y Ff(2)675 4223 y Fh(t)p 600 4235 99 3 v 618 4276 a Ff(2)p Fh(p)709 4250 y Fi(\000)p Fj(\014)s(t)853 4152 y Fe(\015)853 4212 y(\015)853 4272 y(\015)853 4332 y(\015)908 4216 y(\000)954 4297 y Fk(@)1005 4312 y Fj(t)1057 4297 y Fm(\000)1167 4229 y Fp(1)p 1167 4274 49 4 v 1167 4365 a(2)1225 4297 y(\001)1306 4216 y Fe(\001)1374 4272 y Fp(~)1352 4297 y Fk(G)p Fp([)p Fk(F)d Fp(])j(\()p Fk(t)p Fp(\))1688 4152 y Fe(\015)1688 4212 y(\015)1688 4272 y(\015)1688 4332 y(\015)1743 4396 y Fj(H)1806 4363 y Fh(p)1801 4417 y Fd(\000)p Ff(1)1884 4396 y Fn(\()p Fj(\045)p Fn(\))365 4592 y Fm(\024)480 4525 y Fp(1)22 b(+)g Fk(\013)p 480 4570 232 4 v 571 4661 a Fp(2)738 4457 y Fe(Z)838 4592 y Fk(ds)17 b(\037)1013 4608 y Fn([0)p Fj(;T)10 b Fn(])1161 4592 y Fp(\()p Fk(s)p Fp(\))p Fk(e)1328 4546 y Fi(\000)1393 4519 y Fh(\013)1433 4498 y Ff(2)1468 4519 y Fh(s)p 1393 4531 104 3 v 1414 4572 a Ff(2)p Fh(p)1507 4546 y Fi(\000)p Fj(\014)s(s)1658 4592 y Fm(k)p Fk(F)k Fp(\()p Fk(s)p Fp(\))p Fm(k)1956 4621 y Fj(L)2004 4603 y Fh(p)2040 4621 y Fn(\()p Fj(\045)p Fn(\))2152 4592 y Fk(\037)2213 4608 y Fn([0)p Fj(;T)c Fn(])2362 4592 y Fp(\()p Fk(t)23 b Fm(\000)f Fk(s)p Fp(\))p Fk(e)2686 4546 y Fi(\000)2751 4512 y Fh(\013)2791 4492 y Ff(2)2826 4512 y(\()p Fh(t)p Fd(\000)p Fh(s)p Ff(\))p 2751 4531 224 3 v 2832 4572 a(2)p Fh(p)2985 4546 y Fi(\000)p Fj(\014)s Fn(\()p Fj(t)p Fi(\000)p Fj(s)p Fn(\))3255 4592 y Fk(h)3311 4607 y Fj(\013;p)3415 4592 y Fp(\()p Fk(t)h Fm(\000)f Fk(s)p Fp(\))0 4852 y(Again)31 b(b)m(y)j(Y)-8 b(oung's)33 b(inequalit)m(y)f(for)g(con)m(v)m(olutions)g (w)m(e)i(get)177 5030 y Fe(\015)177 5089 y(\015)177 5149 y(\015)177 5209 y(\015)232 5174 y Fk(e)277 5133 y Fi(\000)p Fj(\014)s(t)405 5093 y Fe(\000)451 5174 y Fk(@)502 5189 y Fj(t)554 5174 y Fm(\000)664 5107 y Fp(1)p 664 5151 49 4 v 664 5242 a(2)722 5174 y(\001)803 5093 y Fe(\001)871 5149 y Fp(~)849 5174 y Fk(G)p Fp([)p Fk(F)14 b Fp(])1057 5030 y Fe(\015)1057 5089 y(\015)1057 5149 y(\015)1057 5209 y(\015)1112 5273 y Fj(H)1175 5240 y Fh(p)1170 5294 y Fd(\000)p Ff(1)1253 5273 y Fn(\()p Fj(\026)1322 5284 y Fh(T)1371 5273 y Fn(\))1431 5174 y Fp(=)1534 5004 y Fe(\()1615 5038 y(Z)1714 5065 y Fj(T)1670 5264 y Fn(0)1769 5174 y Fk(dt)j(e)1917 5133 y Fi(\000)1982 5106 y Fh(\013)2022 5085 y Ff(2)2056 5106 y Fh(t)p 1982 5118 99 3 v 2016 5159 a Ff(2)2090 5133 y Fi(\000)p Fj(\014)s(pt)2270 5030 y Fe(\015)2270 5089 y(\015)2270 5149 y(\015)2270 5209 y(\015)2325 5093 y(\000)2371 5174 y Fk(@)2422 5189 y Fj(t)2474 5174 y Fm(\000)2584 5107 y Fp(1)p 2584 5151 49 4 v 2584 5242 a(2)2642 5174 y(\001)2723 5093 y Fe(\001)2792 5149 y Fp(~)2769 5174 y Fk(G)p Fp([)p Fk(F)d Fp(])j(\()p Fk(t)p Fp(\))3105 5030 y Fe(\015)3105 5089 y(\015)3105 5149 y(\015)3105 5209 y(\015)3160 5056 y Fj(p)3160 5273 y(H)3223 5240 y Fh(p)3218 5294 y Fd(\000)p Ff(1)3301 5273 y Fn(\()p Fj(\045)p Fn(\))3396 5004 y Fe(\))3476 5026 y Fn(1)p Fj(=p)456 5512 y Fm(\024)571 5445 y Fp(1)22 b(+)g Fk(\013)p 571 5489 232 4 v 662 5581 a Fp(2)829 5372 y Fe(\032)904 5377 y(Z)1004 5403 y Fj(T)959 5602 y Fn(0)1059 5512 y Fk(dt)17 b(e)1207 5466 y Fi(\000)1272 5439 y Fh(\013)1312 5418 y Ff(2)1346 5439 y Fh(t)p 1271 5451 99 3 v 1289 5492 a Ff(2)p Fh(p)1384 5512 y Fk(h)1440 5527 y Fj(\013;p)1545 5512 y Fp(\()p Fk(t)p Fp(\))1656 5372 y Fe(\033)f(\032)1822 5377 y(Z)1921 5403 y Fj(T)1877 5602 y Fn(0)1976 5512 y Fk(dt)h(e)2124 5471 y Fi(\000)2189 5444 y Fh(\013)2229 5423 y Ff(2)2264 5444 y Fh(t)p 2189 5456 V 2223 5497 a Ff(2)2297 5471 y Fi(\000)p Fj(\014)s(pt)2477 5512 y Fm(k)p Fk(F)d Fp(\()p Fk(t)p Fp(\))p Fm(k)2764 5464 y Fj(p)2764 5543 y(L)2812 5524 y Fh(p)2849 5543 y Fn(\()p Fj(\045)p Fn(\))2944 5372 y Fe(\033)3018 5384 y Fn(1)p Fj(=p)1866 5806 y Fp(7)p eop %%Page: 8 9 8 8 bop 0 407 a Fp(By)32 b(using)g(the)g(estimate)f(in)g(\(2.19\))g (and)h(recalling)e Fk(p)e(>)f Fp(1,)32 b(it)f(is)g(easy)i(to)f(sho)m(w) h(there)f(is)f(a)h(constan)m(t)0 527 y Fk(C)j Fp(=)27 b Fk(C)7 b Fp(\()p Fk(p)p Fp(\))28 b Fk(>)f Fp(0)32 b(so)h(that)1078 699 y(1)22 b(+)g Fk(\013)p 1078 743 232 4 v 1169 834 a Fp(2)1336 630 y Fe(Z)1436 657 y Fj(T)1391 856 y Fn(0)1491 766 y Fk(dt)17 b(e)1639 719 y Fi(\000)1704 692 y Fh(\013)1744 671 y Ff(2)1778 692 y Fh(t)p 1703 704 99 3 v 1721 746 a Ff(2)p Fh(p)1816 766 y Fk(h)1872 781 y Fj(\013;p)1976 766 y Fp(\()p Fk(t)p Fp(\))28 b Fm(\024)g Fk(C)2314 625 y Fe(\022)2387 766 y Fp(1)22 b(+)2573 699 y(1)p 2566 743 63 4 v 2566 834 a Fk(\013)2639 625 y Fe(\023)0 989 y Fp(The)34 b(lemma)c(is)i(pro)m(v)m(ed.)p 3709 989 4 66 v 3713 926 59 4 v 3713 989 V 3771 989 4 66 v 0 1145 a Fl(Pr)-5 b(o)g(of)25 b(of)g(Pr)-5 b(op)g(osition)25 b(2.2.)d Fp(Recalling)e(\(2.5\))i(and)g(that)g Fk(U)2141 1109 y Fi(0)2165 1145 y Fp(\()p Fk(m)p Fp(\))28 b(=)g Fk(m)2543 1109 y Fn(3)2584 1145 y Fm(\000)q Fp(\(1)q Fm(\000)q Fk(\025)p Fp(\))p Fk(m)p Fp(,)e(b)m(y)d(expanding)g(the)0 1266 y(l.h.s.)i(of)g(\(2.6\),)h(using)f(Lemma)f(2.5,)i(and)f(\003)1601 1229 y Fn(2)1668 1266 y Fm(\024)j Fp(\003,)f(w)m(e)f(get)f(there)h (exists)g(a)f(constan)m(t)h Fk(C)35 b Fp(=)27 b Fk(C)7 b Fp(\()p Fk(\013)q(;)17 b(n;)g(\014)6 b Fp(\))0 1386 y(suc)m(h)34 b(that)40 1557 y Fk(\026)99 1572 y Fj(T)150 1553 y Fd(\003)185 1572 y Fj(;)p Fn(\003)274 1476 y Fe(\000)320 1557 y Fk(e)365 1516 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)716 1557 y Fk(u)772 1516 y Fn(2)p Fj(n)p Fn(+4)772 1584 y(\003)944 1476 y Fe(\001)1073 1557 y Fm(\024)83 b Fk(C)7 b(\026)1369 1572 y Fj(T)1420 1553 y Fd(\003)1456 1572 y Fj(;)p Fn(\003)1545 1476 y Fe(\000)1591 1557 y Fk(e)1636 1516 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)2003 1476 y Fe(\010)2061 1557 y Fm(j)p Fk(u)2145 1572 y Fn(\003)2198 1557 y Fm(j)2226 1516 y Fn(2)p Fj(n)p Fn(+1)2414 1476 y Fe(\002)2456 1557 y Fk(u)2512 1516 y Fn(2)2512 1582 y(\003)2564 1557 y Fm(j)p Fp(\003)p Fk(R)q Fm(j)22 b Fp(+)g Fm(j)p Fk(u)2967 1572 y Fn(\003)3019 1557 y Fm(j)p Fp(\(\003)p Fk(R)q Fp(\))3266 1516 y Fn(2)3327 1557 y Fp(+)g Fm(j)p Fp(\003)p Fk(R)q Fm(j)3624 1516 y Fn(3)3662 1476 y Fe(\003)1629 1702 y Fp(+)p Fk(u)1761 1661 y Fn(2)p Fj(n)p Fn(+2)1761 1729 y(\003)1955 1702 y Fp(+)g Fm(j)p Fk(u)2137 1717 y Fn(\003)2190 1702 y Fm(j)2218 1661 y Fn(2)p Fj(n)p Fn(+1)2390 1702 y Fm(j)p Fp(\003)p Fk(R)q Fm(j)f Fp(+)h Fm(j)p Fp(\003)p Fk(R)q Fm(j)2907 1661 y Fn(2)p Fj(n)p Fn(+2)3079 1622 y Fe(\011\001)3531 1702 y Fp(\(2.20\))146 1874 y(Let)1089 1994 y Fk(M)38 b Fp(:=)1352 1913 y Fe(\000)1398 1994 y Fk(\026)1457 2009 y Fj(T)1508 1990 y Fd(\003)1543 2009 y Fj(;)p Fn(\003)1632 1913 y Fe(\000)1678 1994 y Fk(e)1723 1953 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)2074 1994 y Fk(u)2130 1953 y Fn(2)p Fj(n)p Fn(+4)2130 2021 y(\003)2302 1913 y Fe(\001\001)2393 1929 y Fn(1)p Fj(=)p Fn(\(2)p Fj(n)p Fn(+4\))0 2147 y Fp(b)m(y)33 b(using)g(rep)s(eatedly)g(H\177)-49 b(older)32 b(inequalit)m(y)f(in)h(\(2.20\))g(w)m(e)h(get)323 2346 y Fk(M)427 2305 y Fn(2)p Fj(n)p Fn(+4)683 2346 y Fm(\024)84 b Fk(C)937 2235 y Fe(n)1004 2346 y Fk(M)1108 2305 y Fn(2)p Fj(n)p Fn(+3)1281 2346 y Fm(k)p Fp(\003)p Fk(R)q Fm(k)1524 2363 y Fj(L)1572 2344 y Ff(2)p Fh(n)p Ff(+4)1721 2363 y Fn(\()p Fj(\026)p Fn(\))1845 2346 y Fp(+)22 b Fk(M)2047 2305 y Fn(2)p Fj(n)p Fn(+2)2220 2265 y Fe(\002)2261 2346 y Fp(1)g(+)g Fm(k)p Fp(\003)p Fk(R)q Fm(k)2673 2305 y Fn(2)2673 2372 y Fj(L)2721 2353 y Ff(2)p Fh(n)p Ff(+4)2871 2372 y Fn(\()p Fj(\026)p Fn(\))2972 2265 y Fe(\003)1023 2559 y Fp(+)17 b Fk(M)1220 2517 y Fn(2)p Fj(n)p Fn(+1)1393 2559 y Fm(k)p Fp(\003)p Fk(R)q Fm(k)1636 2575 y Fj(L)1684 2556 y Ff(2)p Fh(n)p Ff(+4)1833 2575 y Fn(\()p Fj(\026)p Fn(\))1935 2478 y Fe(\002)1976 2559 y Fp(1)22 b(+)g Fm(k)p Fp(\003)p Fk(R)q Fm(k)2388 2517 y Fn(2)2388 2584 y Fj(L)2436 2565 y Ff(2)p Fh(n)p Ff(+4)2586 2584 y Fn(\()p Fj(\026)p Fn(\))2687 2478 y Fe(\003)2751 2559 y Fp(+)g Fm(k)p Fp(\003)p Fk(R)q Fm(k)3092 2517 y Fn(2)p Fj(n)p Fn(+2)3092 2591 y Fj(L)3140 2572 y Ff(2)p Fh(n)p Ff(+4)3289 2591 y Fn(\()p Fj(\026)p Fn(\))3391 2448 y Fe(o)0 2767 y Fp(w)m(e)34 b(then)f(conclude)g(that)f Fk(M)44 b Fp(is)32 b(b)s(ounded)h(b)m(y)g(some)g(constan)m(t)g Fk(C)i Fp(=)27 b Fk(C)2687 2686 y Fe(\000)2733 2767 y Fk(\013)q(;)17 b(n;)g(\014)6 b(;)17 b Fm(k)p Fp(\003)p Fk(R)q Fm(k)3290 2784 y Fj(L)3338 2765 y Ff(2)p Fh(n)p Ff(+4)3486 2784 y Fn(\()p Fj(\026)p Fn(\))3587 2686 y Fe(\001)3633 2767 y Fp(.)146 2887 y(Recalling)34 b Fk(m)659 2902 y Fn(\003)745 2887 y Fp(=)f Fk(u)910 2902 y Fn(\003)987 2887 y Fp(+)24 b(\003)p Fk(R)q Fp(,)36 b(b)m(y)h(using)e(triangular)f (and)i(Cauc)m(h)m(y{Sc)m(h)m(w)m(artz)j(inequalities,)c(w)m(e)0 3008 y(ha)m(v)m(e)524 3128 y Fm(k)p Fk(m)659 3143 y Fn(\003)712 3128 y Fm(k)762 3144 y Fj(L)810 3125 y Fh(p)846 3144 y Fn(\()p Fj(\026)915 3159 y Ff(\003)p Fh(;T)1019 3145 y Fd(\003)1061 3144 y Fn(\))1120 3128 y Fm(\024)29 b(k)p Fp(\003)p Fk(R)q Fm(k)1469 3144 y Fj(L)1517 3125 y Fh(p)1552 3144 y Fn(\()p Fj(\026)1621 3159 y Ff(\003)p Fh(;T)1725 3145 y Fd(\003)1767 3144 y Fn(\))1821 3128 y Fp(+)22 b Fm(k)p Fk(e)2014 3087 y Fj(\014)s(t)2086 3128 y Fm(k)2136 3145 y Fj(L)2184 3126 y Ff(2)p Fh(p)2251 3145 y Fn(\()p Fj(\026)2320 3160 y Ff(\003)p Fh(;T)2424 3146 y Fd(\003)2466 3145 y Fn(\))2514 3128 y Fm(k)p Fk(e)2609 3087 y Fi(\000)p Fj(\014)s(t)2736 3128 y Fk(u)2792 3143 y Fn(\003)2845 3128 y Fm(k)2895 3145 y Fj(L)2943 3126 y Ff(2)p Fh(p)3009 3145 y Fn(\()p Fj(\026)3078 3160 y Ff(\003)p Fh(;T)3182 3146 y Fd(\003)3224 3145 y Fn(\))0 3282 y Fp(Since,)34 b(for)e(eac)m(h)j Fk(p)28 b Fm(2)i Fp([1)p Fk(;)17 b Fm(1)p Fp(\),)32 b Fm(k)p Fp(\003)p Fk(R)q Fm(k)1386 3297 y Fj(L)1434 3278 y Fh(p)1470 3297 y Fn(\()p Fj(\026)1539 3312 y Ff(\003)p Fh(;T)1643 3298 y Fd(\003)1685 3297 y Fn(\))1745 3282 y Fm(\024)d(k)p Fk(R)q Fm(k)2026 3297 y Fj(L)2074 3278 y Fh(p)2110 3297 y Fn(\()p Fj(\026)p Fn(\))2240 3282 y Fk(<)g Fm(1)p Fp(,)k(b)m(y)h(c)m(ho)s(osing)f Fk(\014)i Fp(=)28 b Fk(\014)6 b Fp(\()p Fk(\013)q(;)17 b(p)p Fp(\))32 b(small)0 3402 y(enough)h(and)g Fk(n)28 b Fp(=)f Fk(n)p Fp(\()p Fk(p)p Fp(\))33 b(large)e(enough,)i(the)g(prop) s(osition)e(follo)m(ws.)p 3709 3402 V 3713 3340 59 4 v 3713 3402 V 3771 3402 4 66 v 0 3558 a Fl(Pr)-5 b(o)g(of)29 b(of)f(\(2.2\).)40 b Fp(Let)27 b Fk(Y)891 3522 y Fj(?)958 3558 y Fp(:=)h(sup)q Fm(fj)p Fk(x)p Fm(j)f Fp(:)h(\003\()p Fk(x)p Fp(\))f Fk(>)h Fp(0)p Fm(g)p Fp(;)g(writing)c(explicitly)g(the)j (k)m(ernels)g(in)e(the)i(in)m(tegral)0 3679 y(equation)32 b(\(2.1\))g(w)m(e)i(ha)m(v)m(e,)g(for)e Fk(t)c(<)f(T)1413 3643 y Fi(\003)1453 3679 y Fp(,)95 3884 y Fm(j)p Fk(m)208 3899 y Fn(\003)261 3884 y Fp(\()p Fk(t;)17 b(x)p Fp(\))p Fm(j)28 b(\024)g(j)p Fp(\003\()p Fk(x)p Fp(\))17 b Fk(R)q Fp(\()p Fk(t;)g(x)p Fp(\))p Fm(j)22 b Fp(+)g Fk(e)1364 3816 y Fh(\013)1404 3795 y Ff(2)p 1364 3828 75 3 v 1386 3869 a(4)1448 3843 y Fj(T)1499 3819 y Fd(\003)1535 3843 y Fn(+)1600 3816 y Fh(\013)p 1600 3828 41 3 v 1605 3869 a Ff(2)1650 3843 y Fj(Y)1707 3819 y Fh(?)248 4087 y Fm(\002)348 3946 y Fe(\032)422 3951 y(Z)522 4087 y Fk(ds)636 3951 y Fe(Z)718 4087 y Fk(dy)e(\037)898 4102 y Fn([0)p Fj(;T)1024 4083 y Fd(\003)1059 4102 y Fn(\))1091 4087 y Fp(\()p Fk(t)i Fm(\000)h Fk(s)p Fp(\))17 b Fk(p)1436 4102 y Fj(t)p Fi(\000)p Fj(s)1552 4087 y Fp(\()p Fk(x)23 b Fm(\000)f Fk(y)t Fp(\))p Fk(\037)1918 4102 y Fn([0)p Fj(;T)2044 4083 y Fd(\003)2079 4102 y Fn(\))2110 4087 y Fp(\()p Fk(s)p Fp(\))17 b Fm(j)p Fk(U)2353 4045 y Fi(0)2377 4087 y Fp(\()p Fk(m)2500 4102 y Fn(\003)2553 4087 y Fp(\()p Fk(s;)g(y)t Fp(\)\))p Fm(j)e Fp(\003\()p Fk(y)t Fp(\))p Fk(e)3093 4045 y Fi(\000)3158 4018 y Fh(\013)3198 3997 y Ff(2)p 3157 4030 75 3 v 3179 4071 a(4)3241 4045 y Fj(s)p Fi(\000)3339 4018 y Fh(\013)p 3339 4030 41 3 v 3344 4071 a Ff(2)3389 4045 y Fi(j)p Fj(y)r Fi(j)434 4359 y Fp(+)p Fk(\025)584 4223 y Fe(Z)683 4359 y Fk(ds)797 4223 y Fe(Z)879 4359 y Fk(dy)20 b(\037)1059 4374 y Fn([0)p Fj(;T)1185 4355 y Fd(\003)1220 4374 y Fn(\))1252 4359 y Fp(\()p Fk(t)i Fm(\000)h Fk(s)p Fp(\))1557 4291 y(1)p 1557 4336 49 4 v 1557 4427 a(2)1632 4359 y Fm(j)p Fp(\001)p Fk(p)1790 4374 y Fj(t)p Fi(\000)p Fj(s)1907 4359 y Fp(\()p Fk(x)g Fm(\000)g Fk(y)t Fp(\))p Fm(j)15 b Fk(\037)2317 4374 y Fn([0)p Fj(;T)2443 4355 y Fd(\003)2478 4374 y Fn(\))2510 4359 y Fp(\()p Fk(s)p Fp(\)\003\()p Fk(y)t Fp(\))i Fm(j)n Fk(m)2956 4374 y Fn(\003)3009 4359 y Fp(\()p Fk(s;)g(y)t Fp(\))p Fm(j)e Fk(e)3315 4318 y Fi(\000)3380 4291 y Fh(\013)3420 4270 y Ff(2)p 3380 4303 75 3 v 3402 4344 a(4)3465 4318 y Fj(s)p Fi(\000)3563 4291 y Fh(\013)p 3562 4303 41 3 v 3567 4344 a Ff(2)3612 4318 y Fi(j)p Fj(y)r Fi(j)3693 4218 y Fe(\033)146 4582 y Fp(Then,)34 b(from)d(Y)-8 b(oung's)33 b(inequalities)e(for)h(con)m(v)m(olutions,)309 4753 y(sup)252 4839 y Fj(t)p Fi(2)p Fn([0)p Fj(:T)450 4820 y Fd(\003)486 4839 y Fn(\))530 4753 y Fp(sup)536 4835 y Fj(x)p Fi(2)p Fg(R)693 4753 y Fm(j)p Fk(m)806 4768 y Fn(\003)859 4753 y Fp(\()p Fk(t;)17 b(x)p Fp(\))p Fm(j)28 b(\024)85 b Fp(sup)1230 4839 y Fj(t)p Fi(2)p Fn([0)p Fj(;T)1428 4820 y Fd(\003)1464 4839 y Fn(\))1508 4753 y Fp(sup)1514 4835 y Fj(x)p Fi(2)p Fg(R)1671 4753 y Fm(j)p Fp(\003\()p Fk(x)p Fp(\))p Fk(R)q Fp(\()p Fk(t;)17 b(x)p Fp(\))p Fm(j)426 5088 y Fp(+)22 b Fk(e)579 5019 y Fh(\013)619 4998 y Ff(2)p 579 5031 75 3 v 601 5072 a(4)663 5046 y Fj(T)714 5023 y Fd(\003)750 5046 y Fn(+)815 5019 y Fh(\013)p 815 5031 41 3 v 820 5072 a Ff(2)865 5046 y Fj(Y)922 5023 y Fh(?)984 5088 y Fm(\002)1084 4917 y Fe(\()1164 4947 y(\024)1216 4952 y(Z)1316 4978 y Fj(T)1367 4955 y Fd(\003)1272 5177 y Fn(0)1407 5088 y Fk(dt)1493 4952 y Fe(Z)1593 5088 y Fk(dz)f(p)1759 5103 y Fj(t)1788 5088 y Fp(\()p Fk(z)t Fp(\))1913 5046 y Fn(2)1953 4947 y Fe(\025)2016 4931 y Ff(1)p 2016 4943 31 3 v 2016 4984 a(2)2077 4947 y Fe(\024)2130 4952 y(Z)2229 5088 y Fk(\026)2288 5103 y Fj(T)2339 5084 y Fd(\003)2375 5103 y Fj(;)p Fn(\003)2447 5088 y Fp(\()p Fk(dt;)c(dx)p Fp(\))g Fk(U)2852 5046 y Fi(0)2892 5088 y Fp(\()p Fk(m)3015 5103 y Fn(\003)3069 5088 y Fp(\()p Fk(t;)g(y)t Fp(\)\))3312 5039 y Fn(2)3352 4947 y Fe(\025)3414 4942 y Ff(1)p 3414 4954 V 3414 4995 a(2)573 5453 y Fp(+)p Fk(\025)723 5282 y Fe(")780 5317 y(Z)880 5343 y Fj(T)931 5320 y Fd(\003)835 5543 y Fn(0)971 5453 y Fk(dt)1057 5317 y Fe(Z)1156 5453 y Fk(dz)k(p)1322 5468 y Fj(t)1352 5453 y Fp(\()p Fk(z)t Fp(\))1477 5411 y Fn(2)1534 5312 y Fe(\024)1596 5385 y Fk(z)1645 5349 y Fn(2)p 1596 5430 90 4 v 1599 5521 a Fp(2)p Fk(t)1717 5453 y Fp(+)1825 5385 y(1)p 1825 5430 49 4 v 1825 5521 a(2)1884 5312 y Fe(\025)1937 5333 y Fn(2)1976 5282 y Fe(#)2044 5277 y Ff(1)p 2044 5289 31 3 v 2044 5331 a(2)2105 5312 y Fe(\024)2158 5317 y(Z)2258 5453 y Fk(\026)2317 5468 y Fj(T)2368 5449 y Fd(\003)2403 5468 y Fj(;)p Fn(\003)2476 5453 y Fp(\()p Fk(dt;)c(dx)p Fp(\))g Fk(m)2890 5468 y Fn(\003)2942 5453 y Fp(\()p Fk(t;)g(y)t Fp(\))3149 5411 y Fn(2)3188 5312 y Fe(\025)3250 5307 y Ff(1)p 3250 5319 V 3250 5360 a(2)3295 5248 y Fe(9)3295 5338 y(=)3295 5517 y(;)3531 5453 y Fp(\(2.21\))1866 5806 y(8)p eop %%Page: 9 10 9 9 bop 0 407 a Fp(where)34 b(w)m(e)g(used)g(also)e(that)h(\003)1125 371 y Fn(2)1192 407 y Fm(\024)c Fp(\003.)44 b(By)33 b(using)g(that,)g (as)g(follo)m(ws)e(from)h(Prop)s(osition)f(2.2,)i Fk(U)3542 371 y Fi(0)3566 407 y Fp(\()p Fk(m)3689 422 y Fn(\003)3742 407 y Fp(\))0 527 y(is)j(in)g Fk(L)286 491 y Fn(2)326 527 y Fp(\()p Fk(\026)423 542 y Fj(T)474 523 y Fd(\003)509 542 y Fj(;)p Fn(\003)582 527 y Fp(\),)h(and)g(the)g(prop)s(erties)g(of) f(the)h(heat)f(k)m(ernel,)j(it)c(is)h(easy)i(to)e(see)i(that)e(the)h (r.h.s.)56 b(of)0 648 y(\(2.21\))32 b(is)g(b)s(ounded.)p 3709 648 4 66 v 3713 585 59 4 v 3713 648 V 3771 648 4 66 v 146 818 a(The)c(follo)m(wing)c(lemma)g(states)j(an)f Fl(a)k(priori)36 b Fp(uniform)24 b(b)s(ound)j(for)f(the)h(solutions)e (of)h(\(2.1\),)h(whic)m(h)0 938 y(b)m(y)33 b(\(2.2\))g(are)f(de\014ned) i(for)e(an)m(y)h Fk(t)28 b Fm(\025)g Fp(0.)0 1142 y Fq(Lemma)35 b(2.6.)40 b Fl(L)-5 b(et)33 b Fk(m)860 1157 y Fn(\003)946 1142 y Fl(b)-5 b(e)33 b(a)g(c)-5 b(ontinuous)32 b(solution)h(of)g (\(2.1\))f(on)g Fo(R)2560 1157 y Fn(+)2643 1142 y Fm(\002)18 b Fo(R)5 b Fl(.)50 b(Then)33 b(for)f(e)-5 b(ach)32 b Fk(\013)d(>)e Fp(0)p Fl(,)0 1262 y Fk(p)h Fm(2)g Fp([1)p Fk(;)17 b Fm(1)p Fp(\))32 b Fl(ther)-5 b(e)32 b(exists)h(a)g(c)-5 b(onstant)32 b Fk(C)j Fp(=)27 b Fk(C)1737 1181 y Fe(\000)1782 1262 y Fk(\013)q(;)17 b(p;)g Fm(k)p Fk(R)q Fm(k)2157 1277 y Fj(L)2205 1259 y Fh(p)2240 1277 y Fn(\()p Fj(\026)p Fn(\))2342 1181 y Fe(\001)2415 1262 y Fk(<)28 b Fm(1)k Fl(indep)-5 b(endent)32 b(of)g Fp(\003)c Fm(2)g(L)k Fl(such)0 1382 y(that)j Fm(k)p Fk(m)334 1397 y Fn(\003)387 1382 y Fm(k)437 1398 y Fj(L)485 1379 y Fh(p)521 1398 y Fn(\()p Fj(\026)p Fn(\))651 1382 y Fm(\024)28 b Fk(C)7 b Fl(.)0 1586 y(Pr)-5 b(o)g(of.)48 b Fp(Since)25 b(the)g(con)m(tin)m(uous)g (solution)e(of)h(equation)g(\(2.1\))g(exist)h(globally)d(in)h(time,)i (the)g(inequalit)m(y)0 1706 y(\(2.3\))32 b(ma)m(y)g(b)s(e)h(extended)i (for)d Fk(T)1212 1670 y Fi(\003)1279 1706 y Fm(")27 b(1)p Fp(;)32 b(w)m(e)i(get)1123 1926 y Fm(k)p Fp(\003)p Fk(m)1326 1941 y Fn(\003)1379 1926 y Fm(k)1429 1955 y Fj(L)1477 1936 y Fh(p)1513 1955 y Fn(\()p Fj(\026)p Fn(\))1642 1926 y Fm(\024)28 b(k)p Fk(m)1882 1941 y Fn(\003)1935 1926 y Fm(k)1985 1955 y Fj(L)2033 1936 y Fh(p)2069 1955 y Fn(\()p Fj(\026)2138 1966 y Ff(\003)2185 1955 y Fn(\))2244 1926 y Fm(\024)g Fk(C)35 b(<)27 b Fm(1)874 b Fp(\(2.22\))146 2171 y(Note)33 b(that)g(for)f Fk(p)c(>)g Fp(1)k(b)s(oth)g Fk(G)h Fp(and)1557 2146 y(~)1535 2171 y Fk(G)f Fp(are)h(b)s(ounded)h (op)s(erators)e(in)g Fk(L)2817 2135 y Fj(p)2857 2171 y Fp(\()p Fk(\026)p Fp(\))g(\(see)i([3,)f(Lemma)e(9])0 2291 y(for)g Fk(G)g Fp(and)h(the)g(same)f(pro)s(of)g(also)g(w)m(orks)h (for)1750 2266 y(~)1727 2291 y Fk(G)p Fp(\).)43 b(F)-8 b(rom)30 b(the)i(in)m(tegral)e(equation)i(\(2.1\),)f(the)h(b)s(ound)0 2412 y(\(2.22\),)g(and)h Fk(R)28 b Fm(2)g Fk(L)761 2376 y Fj(p)801 2412 y Fp(\()p Fk(\026)p Fp(\))33 b(the)g(lemma)d(follo)m (ws.)p 3709 2412 V 3713 2349 59 4 v 3713 2412 V 3771 2412 4 66 v 0 2731 a Fq(3.)38 b(In\014nite)e(v)m(olume)h(equation)146 2877 y Fp(In)31 b(this)f(section)g(w)m(e)h(conclude)g(the)f(pro)s(of)g (of)f(Theorem)i(1.3)e(b)m(y)j(remo)m(ving)d(the)h(truncation)g(\003)g (in)0 2997 y(\(2.1\);)f(follo)m(wing)c([3],)j(w)m(e)h(pro)m(v)m(e)g (\014rst)f(that,)g(pro)m(vided)g Fk(\014)33 b Fp(is)27 b(c)m(hosen)i(large)e(enough,)i(exp)17 b(\()p Fm(\000)p Fk(\014)6 b(t)p Fp(\))17 b(\003)g Fk(m)3727 3012 y Fn(\003)0 3117 y Fp(con)m(v)m(erges)35 b(in)d Fk(L)617 3081 y Fj(p)657 3117 y Fp(\()p Fk(\026)p Fp(\).)0 3321 y Fq(Lemma)42 b(3.1.)i Fl(L)-5 b(et)39 b Fk(m)877 3336 y Fn(\003)969 3321 y Fl(b)-5 b(e)39 b(a)f(solution)h(of)f(\(2.1\).)56 b(F)-7 b(or)38 b(e)-5 b(ach)38 b Fk(p)d Fm(2)g Fp([1)p Fk(;)17 b Fm(1)p Fp(\))38 b Fl(ther)-5 b(e)39 b(exists)f(a)h(p)-5 b(ositive)0 3441 y(c)g(onstant)29 b Fk(k)434 3456 y Fj(p)501 3441 y Fk(<)e Fm(1)i Fl(such)g(that,)i(for)d(any)h Fk(\013)g(>)e Fp(0)i Fl(and)g Fk(\014)k Fm(\025)28 b Fk(k)2204 3456 y Fj(p)2244 3441 y Fp(\(1)9 b(+)g Fk(\013)2488 3405 y Fi(\000)p Fj(p)2582 3441 y Fp(\))p Fl(,)30 b Fm(f)p Fp(exp)18 b(\()p Fm(\000)p Fk(\014)6 b(t)p Fp(\))16 b(\003)h Fk(m)3331 3456 y Fn(\003)3401 3441 y Fk(;)44 b Fp(\003)27 b Fm(2)h(Lg)0 3562 y Fl(is)35 b(Cauchy)f(in)h Fk(L)639 3525 y Fj(p)679 3562 y Fp(\()p Fk(\026)p Fp(\))f Fl(as)h Fp(\003)27 b Fm(")h Fp(1)p Fl(.)0 3765 y(Pr)-5 b(o)g(of.)77 b Fp(Recall)38 b(that)g Fk(u)908 3780 y Fn(\003)1000 3765 y Fp(and)h Fk(q)1239 3780 y Fn(\003)1331 3765 y Fp(ha)m(v)m(e)i(b)s(een)e (de\014ned)i(in)d(\(2.5\).)62 b(W)-8 b(e)39 b(apply)g(Lemma)e(2.3)i(to) g(the)0 3885 y(function)32 b Fk(f)38 b Fp(=)28 b Fk(e)617 3849 y Fi(\000)p Fj(\014)s(t)745 3885 y Fp([)p Fk(u)828 3900 y Fn(\003)903 3885 y Fm(\000)22 b Fk(u)1065 3889 y Fn(\026)1058 3906 y(\003)1111 3885 y Fp(].)43 b(W)-8 b(e)33 b(ha)m(v)m(e)466 4069 y Fe(\000)512 4150 y Fk(@)563 4165 y Fj(t)615 4150 y Fm(\000)725 4082 y Fp(1)p 725 4127 49 4 v 725 4218 a(2)784 4150 y(\001)865 4069 y Fe(\001)911 4150 y Fk(f)38 b Fp(=)27 b Fm(\000)p Fk(\014)6 b(f)33 b Fm(\000)23 b Fk(e)1464 4109 y Fi(\000)p Fj(\014)s(t)1608 4069 y Fe(\002)1650 4150 y Fp(\003)p Fk(U)1794 4109 y Fi(0)1818 4150 y Fp(\()p Fk(m)1941 4165 y Fn(\003)1994 4150 y Fp(\))f Fm(\000)2163 4125 y Fp(\026)2154 4150 y(\003)o Fk(U)2297 4109 y Fi(0)2321 4150 y Fp(\()p Fk(m)2451 4154 y Fn(\026)2444 4170 y(\003)2498 4150 y Fp(\))2536 4069 y Fe(\003)2599 4150 y Fm(\000)h Fk(\025e)2801 4109 y Fi(\000)p Fj(\014)s(t)2945 4150 y Fp([)p Fk(q)3015 4165 y Fn(\003)3091 4150 y Fm(\000)f Fk(q)3240 4154 y Fn(\026)3233 4170 y(\003)3287 4150 y Fp(])0 4401 y(Therefore,)38 b(b)m(y)f(the)g(same)f(computations)f(as)h(in)g(Lemma)e(2.4)i(\(see)h (equations)g(\(2.7\))e(and)i(\(2.10\)\),)0 4521 y(but)29 b(no)m(w)g(c)m(ho)s(osing)f Fk(\015)33 b Fp(=)27 b Fk(\015)5 b Fp(\()p Fk(n;)17 b(\025)p Fp(\))28 b(indep)s(enden)m(t)i(of)e Fk(\014)34 b Fp(and)29 b(taking)e Fk(T)42 b Fm(")27 b(1)p Fp(,)i(there)h(exists)f(a)f(constan)m(t)0 4642 y Fk(c)42 4657 y Fn(1)109 4642 y Fp(=)g Fk(c)255 4657 y Fn(1)294 4642 y Fp(\()p Fk(n)p Fp(\))33 b(indep)s(enden)m(t)g(of)g Fk(\013)q(;)17 b(\014)37 b Fp(suc)m(h)d(that)320 4862 y Fk(\026)396 4781 y Fe(\000)441 4862 y Fk(e)486 4820 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)854 4862 y Fp([)p Fk(u)937 4877 y Fn(\003)1011 4862 y Fm(\000)23 b Fk(u)1174 4866 y Fn(\026)1167 4882 y(\003)1220 4862 y Fp(])1247 4813 y Fn(2)p Fj(n)p Fn(+1)1436 4781 y Fe(\002)1477 4862 y Fp(\003)p Fk(U)1621 4820 y Fi(0)1645 4862 y Fp(\()p Fk(m)1768 4877 y Fn(\003)1821 4862 y Fp(\))f Fm(\000)1990 4836 y Fp(\026)1981 4862 y(\003)p Fk(U)2125 4820 y Fi(0)2149 4862 y Fp(\()p Fk(m)2279 4866 y Fn(\026)2272 4882 y(\003)2325 4862 y Fp(\))2363 4781 y Fe(\003)o(\001)523 5021 y Fp(+)g(\()p Fk(\014)27 b Fm(\000)c Fp(1\))p Fk(\026)1004 4940 y Fe(\000)1049 5021 y Fk(e)1094 4980 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)1461 5021 y Fp([)p Fk(u)1544 5036 y Fn(\003)1619 5021 y Fm(\000)g Fk(u)1782 5025 y Fn(\026)1775 5041 y(\003)1827 5021 y Fp(])1854 4972 y Fn(2)p Fj(n)p Fn(+2)2027 4940 y Fe(\001)2100 5021 y Fm(\024)28 b Fk(c)2247 5036 y Fn(1)2287 5021 y Fm(k)p Fk(e)2382 4980 y Fi(\000)p Fj(\014)s(t)2526 5021 y Fp(\()p Fk(q)2607 5036 y Fn(\003)2682 5021 y Fm(\000)23 b Fk(q)2832 5025 y Fn(\026)2825 5041 y(\003)2878 5021 y Fp(\))17 b Fm(k)2983 4980 y Fn(2)p Fj(n)p Fn(+2)2983 5064 y Fj(H)3046 5035 y Ff(2)p Fh(n)p Ff(+2)3041 5086 y Fd(\000)p Ff(1)3196 5064 y Fn(\()p Fj(\026)p Fn(\))3579 5021 y Fp(\(3.1\))0 5275 y(By)33 b(using)f(Lemma)g(2.5)g(there)h(is)f (a)g(constan)m(t)i Fk(c)1778 5290 y Fn(2)1845 5275 y Fp(=)27 b Fk(c)1990 5290 y Fn(2)2030 5275 y Fp(\()p Fk(n)p Fp(\))32 b(suc)m(h)j(that)160 5523 y Fm(k)p Fk(e)255 5481 y Fi(\000)p Fj(\014)s(t)399 5523 y Fp(\()p Fk(q)480 5538 y Fn(\003)556 5523 y Fm(\000)22 b Fk(q)705 5527 y Fn(\026)698 5543 y(\003)752 5523 y Fp(\))16 b Fm(k)856 5481 y Fn(2)p Fj(n)p Fn(+2)856 5566 y Fj(H)919 5536 y Ff(2)p Fh(n)p Ff(+2)914 5587 y Fd(\000)p Ff(1)1069 5566 y Fn(\()p Fj(\026)p Fn(\))1198 5523 y Fm(\024)28 b Fk(c)1345 5538 y Fn(2)1401 5442 y Fe(\000)1447 5523 y Fp(1)22 b(+)g Fk(\013)1679 5481 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))1961 5442 y Fe(\001)2023 5523 y Fk(\026)2099 5412 y Fe(\020)2158 5523 y Fk(e)2203 5481 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)2570 5442 y Fe(\002)2612 5523 y Fp(\003)p Fk(m)2765 5538 y Fn(\003)2840 5523 y Fm(\000)2949 5497 y Fp(\026)2940 5523 y(\003)p Fk(m)3100 5527 y Fn(\026)3093 5543 y(\003)3146 5442 y Fe(\003)3187 5464 y Fn(2)p Fj(n)p Fn(+2)3360 5412 y Fe(\021)3579 5523 y Fp(\(3.2\))1866 5806 y(9)p eop %%Page: 10 11 10 10 bop 0 407 a Fp(On)38 b(the)h(other)f(hand,)i(since)e(for)g(an)m (y)h Fk(a;)17 b(b)37 b Fm(2)h Fo(R)49 b Fp(w)m(e)39 b(ha)m(v)m(e)g(\()p Fk(a)2324 371 y Fn(3)2390 407 y Fm(\000)26 b Fk(b)2534 371 y Fn(3)2574 407 y Fp(\)\()p Fk(a)g Fm(\000)h Fk(b)p Fp(\))37 b Fm(\025)h Fp(\()p Fk(a)26 b Fm(\000)g Fk(b)p Fp(\))3359 371 y Fn(4)3399 407 y Fk(=)p Fp(4,)39 b(there)0 527 y(exists)33 b(a)g(constan)m(t)g Fk(c)786 542 y Fn(3)853 527 y Fp(=)28 b Fk(c)999 542 y Fn(3)1038 527 y Fp(\()p Fk(\025)p Fp(\))k(suc)m(h)i(that)250 747 y(\()p Fk(u)344 762 y Fn(\003)418 747 y Fm(\000)23 b Fk(u)581 751 y Fn(\026)574 768 y(\003)627 747 y Fp(\))681 666 y Fe(\002)723 747 y Fp(\003)p Fk(U)867 706 y Fi(0)890 747 y Fp(\()p Fk(m)1013 762 y Fn(\003)1067 747 y Fp(\))f Fm(\000)1236 722 y Fp(\026)1226 747 y(\003)p Fk(U)1370 706 y Fi(0)1394 747 y Fp(\()p Fk(m)1524 751 y Fn(\026)1517 768 y(\003)1571 747 y Fp(\))1609 666 y Fe(\003)333 892 y Fp(=)436 812 y Fe(\000)482 892 y Fk(m)567 907 y Fn(\003)643 892 y Fm(\000)g Fk(m)834 896 y Fn(\026)827 913 y(\003)903 892 y Fm(\000)g Fp(\(\003)g Fm(\000)1239 867 y Fp(\026)1230 892 y(\003\))p Fk(R)1411 812 y Fe(\001)16 b(\000)1518 892 y Fp(\003)p Fk(m)1671 851 y Fn(3)1671 917 y(\003)1747 892 y Fm(\000)1856 867 y Fp(\026)1846 892 y(\003)p Fk(m)1999 851 y Fn(3)2006 905 y(\026)1999 922 y(\003)2052 812 y Fe(\001)2120 892 y Fm(\000)23 b Fp(\(1)f Fm(\000)g Fk(\025)p Fp(\))17 b(\()p Fk(u)2634 907 y Fn(\003)2708 892 y Fm(\000)23 b Fk(u)2871 896 y Fn(\026)2864 913 y(\003)2917 892 y Fp(\))2971 812 y Fe(\000)3017 892 y Fp(\003)p Fk(m)3170 907 y Fn(\003)3245 892 y Fm(\000)3354 867 y Fp(\026)3345 892 y(\003)p Fk(m)3505 896 y Fn(\026)3498 913 y(\003)3551 812 y Fe(\001)333 1092 y Fm(\025)448 1025 y Fp(1)p 448 1069 49 4 v 448 1161 a(4)523 1011 y Fe(\000)569 1092 y Fp(\003)p Fk(m)722 1107 y Fn(\003)797 1092 y Fm(\000)906 1067 y Fp(\026)897 1092 y(\003)p Fk(m)1057 1096 y Fn(\026)1050 1113 y(\003)1103 1011 y Fe(\001)1149 1034 y Fn(4)1210 1092 y Fm(\000)g Fk(c)1352 1107 y Fn(3)1391 1092 y Fp(\()p Fk(u)1485 1107 y Fn(\003)1560 1092 y Fm(\000)g Fk(u)1723 1096 y Fn(\026)1716 1113 y(\003)1768 1092 y Fp(\))1806 1051 y Fn(2)432 1278 y Fm(\000)g Fk(c)574 1293 y Fn(3)630 1198 y Fe(\000)676 1278 y Fm(j)p Fp(1)e Fm(\000)i Fp(\003)p Fm(j)f Fp(+)g Fm(j)p Fp(1)f Fm(\000)1297 1253 y Fp(\026)1288 1278 y(\003)o Fm(j)1383 1198 y Fe(\001)16 b(\002)1487 1278 y Fk(m)1572 1237 y Fn(2)1572 1303 y(\003)1625 1278 y Fp(\(1)22 b(+)g Fk(m)1917 1237 y Fn(2)1917 1303 y(\003)1971 1278 y Fp(\))g(+)g Fk(m)2214 1237 y Fn(2)2221 1291 y(\026)2214 1308 y(\003)2267 1278 y Fp(\(1)g(+)g Fk(m)2559 1237 y Fn(2)2566 1291 y(\026)2559 1308 y(\003)2612 1278 y Fp(\))g(+)g Fk(R)2845 1237 y Fn(2)2885 1278 y Fp(\(1)g(+)g Fk(R)3167 1237 y Fn(2)3206 1278 y Fp(\))3244 1198 y Fe(\003)3579 1278 y Fp(\(3.3\))146 1498 y(By)30 b(plugging)d(the)i(b)s(ounds)h (\(3.2\))f(and)g(\(3.3\))f(in)m(to)h(\(3.1\))f(and)h(using)g(H\177)-49 b(older)29 b(inequalit)m(y)-8 b(,)28 b(w)m(e)i(\014nd)0 1619 y(there)j(exists)h Fk(c)561 1634 y Fn(4)628 1619 y Fp(=)27 b Fk(c)773 1634 y Fn(4)813 1619 y Fp(\()p Fk(n;)17 b(\013)q(;)g(\025)p Fp(\))31 b(suc)m(h)j(that)142 1816 y(1)p 142 1860 V 142 1952 a(4)200 1883 y Fk(\026)276 1773 y Fe(\020)335 1883 y Fk(e)380 1842 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)748 1803 y Fe(\000)793 1883 y Fp(\003)p Fk(m)946 1898 y Fn(\003)1022 1883 y Fm(\000)1131 1858 y Fp(\026)1121 1883 y(\003)p Fk(m)1281 1887 y Fn(\026)1274 1904 y(\003)1327 1803 y Fe(\001)1373 1825 y Fn(2)p Fj(n)p Fn(+4)1546 1773 y Fe(\021)632 2076 y Fp(+)730 1995 y Fe(\000)775 2076 y Fk(\014)28 b Fm(\000)23 b Fp(1)f Fm(\000)g Fk(c)1170 2091 y Fn(3)1232 2076 y Fm(\000)h Fk(c)1374 2091 y Fn(1)1413 2076 y Fk(c)1455 2091 y Fn(2)1511 1995 y Fe(\000)1557 2076 y Fp(1)f(+)g Fk(\013)1789 2035 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))2070 1995 y Fe(\001\001)2178 2076 y Fk(\026)2254 1995 y Fe(\000)2299 2076 y Fk(e)2344 2035 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))p Fj(\014)s(t)2712 2076 y Fp(\()p Fk(u)2806 2091 y Fn(\003)2880 2076 y Fm(\000)h Fk(u)3043 2080 y Fn(\026)3036 2097 y(\003)3089 2076 y Fp(\))3127 2028 y Fn(2)p Fj(n)p Fn(+2)3299 1995 y Fe(\001)148 2259 y Fm(\024)29 b Fk(c)296 2274 y Fn(4)352 2178 y Fe(\000)397 2259 y Fm(k)p Fp(1)22 b Fm(\000)h Fp(\003)p Fm(k)736 2275 y Fj(L)784 2256 y Ff(2)818 2275 y Fn(\()p Fj(\026)p Fn(\))941 2259 y Fp(+)f Fm(k)p Fp(1)g Fm(\000)1269 2233 y Fp(\026)1260 2259 y(\003)o Fm(k)1377 2275 y Fj(L)1425 2256 y Ff(2)1460 2275 y Fn(\()p Fj(\026)p Fn(\))1561 2178 y Fe(\001)1624 2148 y(n)1690 2259 y Fp(1)g(+)g Fm(k)p Fk(m)1994 2274 y Fn(\003)2047 2259 y Fm(k)2097 2210 y Fn(2)p Fj(n)p Fn(+4)2097 2288 y Fj(L)2145 2269 y Ff(4)p Fh(n)p Ff(+8)2295 2288 y Fn(\()p Fj(\026)p Fn(\))2418 2259 y Fp(+)g Fm(k)p Fk(m)2658 2263 y Fn(\026)2651 2279 y(\003)2705 2259 y Fm(k)2755 2210 y Fn(2)p Fj(n)p Fn(+4)2755 2288 y Fj(L)2803 2269 y Ff(4)p Fh(n)p Ff(+8)2952 2288 y Fn(\()p Fj(\026)p Fn(\))3076 2259 y Fp(+)g Fm(k)p Fk(R)q Fm(k)3349 2210 y Fn(2)p Fj(n)p Fn(+4)3349 2288 y Fj(L)3397 2269 y Ff(4)p Fh(n)p Ff(+8)3547 2288 y Fn(\()p Fj(\026)p Fn(\))3648 2148 y Fe(o)0 2517 y Fp(Giv)m(en)40 b Fk(p)g Fm(\025)g Fp(2,)i(let)d Fk(n)h Fp(=)g Fk(n)p Fp(\()p Fk(p)p Fp(\))h(=)e([)p Fk(p=)p Fp(2])27 b Fm(\000)h Fp(1)39 b(and)h Fk(k)1984 2532 y Fj(p)2064 2517 y Fp(suc)m(h)h(that)f(1)27 b(+)f Fk(c)2730 2532 y Fn(3)2797 2517 y Fp(+)h Fk(c)2942 2532 y Fn(1)2981 2517 y Fk(c)3023 2532 y Fn(2)3063 2517 y Fp(\(1)g(+)g Fk(\013)3343 2481 y Fi(\000)p Fn(\(2)p Fj(n)p Fn(+2\))3624 2517 y Fp(\))41 b Fm(\024)0 2638 y Fk(k)51 2653 y Fj(p)90 2638 y Fp(\(1)24 b(+)g Fk(\013)364 2602 y Fi(\000)p Fj(p)458 2638 y Fp(\))35 b(for)f(an)m(y)i Fk(\013)d(>)f Fp(0.)51 b(The)36 b(lemma)c(no)m(w)k(follo)m(ws)e(from)g (Lemma)g(2.6)g(and)h Fk(R)e Fm(2)g Fk(L)3454 2602 y Fj(p)3494 2638 y Fp(\()p Fk(\026)p Fp(\))h(for)0 2758 y(an)m(y)f Fk(p)28 b Fm(2)g Fp([1)p Fk(;)17 b Fm(1)p Fp(\).)p 3709 2758 4 66 v 3713 2696 59 4 v 3713 2758 V 3771 2758 4 66 v 146 2928 a(The)42 b(pro)s(of)d(of)h(Theorem)g(1.3)g(can)h(no)m(w)g (b)s(e)f(completed)g(as)g(in)g([3],)i(w)m(e)f(shall)e(just)i(sk)m(etc)m (h)i(the)0 3049 y(argumen)m(t.)0 3194 y Fl(Pr)-5 b(o)g(of)37 b(of)g(The)-5 b(or)g(em)35 b(1.3.)g Fp(T)-8 b(o)35 b(pro)m(v)m(e)h (existence)g(of)f(a)g(con)m(tin)m(uous)g(solution)f(of)g(\(1.5\),)h(w)m (e)h(\014rst)g(note)0 3314 y(that,)g(for)g(eac)m(h)g Fk(p)d Fm(2)h Fp([1)p Fk(;)17 b Fm(1)p Fp(\))35 b(and)h Fk(\013)g Fp(so)g(large)f(that)g Fk(\013)2025 3278 y Fn(2)2098 3314 y Fk(>)e(k)2258 3329 y Fj(p)2297 3314 y Fp(\(1)24 b(+)g Fk(\013)2571 3278 y Fi(\000)p Fj(p)2666 3314 y Fp(\),)36 b Fk(m)2852 3329 y Fn(\003)2941 3314 y Fp(is)g(Cauc)m(h)m(y)h(in)e Fk(L)3578 3278 y Fj(p)3618 3314 y Fp(\()p Fk(\026)p Fp(\).)0 3435 y(This)29 b(follo)m(ws)e(from)g (Lemmata)g(2.6,)i(3.1,)h(and)e(H\177)-49 b(older)28 b(inequalit)m(y;)h (moreo)m(v)m(er)g(the)g(limit)c Fk(m)k Fp(satis\014es)0 3555 y(equation)35 b(\(1.5\).)50 b(Since)36 b Fk(G)f Fp(and)1263 3530 y(~)1241 3555 y Fk(G)g Fp(map)f Fk(L)1638 3519 y Fn(2)1678 3555 y Fp(\()p Fk(\026)p Fp(\))g(in)m(to)h Fk(C)2118 3570 y Fj(\013)2167 3555 y Fp(\()p Fo(R)2271 3570 y Fn(+)2360 3555 y Fm(\002)24 b Fo(R)5 b Fp(\),)42 b(see)36 b([3,)g(Lemma)d(12],)j(w)m(e)g(also)0 3675 y(ha)m(v)m(e)e Fk(m)28 b Fm(2)g Fk(C)502 3690 y Fj(\013)551 3675 y Fp(\()p Fo(R)655 3690 y Fn(+)742 3675 y Fm(\002)23 b Fo(R)5 b Fp(\).)146 3796 y(In)46 b(order)f(to)f(sho)m(w)i Fk(m)j Fm(2)g Fk(C)1252 3811 y Fj(\013)1301 3796 y Fp(\()p Fo(R)1405 3811 y Fn(+)1501 3796 y Fm(\002)31 b Fo(R)5 b Fp(\))51 b(for)44 b(an)m(y)i Fk(\013)j(>)f Fp(0,)g(w)m(e)e(note)f(that,)j(b)m(y) e(Lemma)d(2.6,)0 3916 y Fk(m)85 3931 y Fn(\003)179 3916 y Fp(is)e(uniformly)d(b)s(ounded)k(in)e Fk(L)1333 3880 y Fj(p)1373 3916 y Fp(\()p Fk(\026)p Fp(\);)45 b(w)m(e)d(can)f(th)m(us) h(\014nd)f(a)g(w)m(eakly)g(con)m(v)m(ergen)m(t)i(subsequence)0 4037 y Fk(m)85 4052 y Fn(\003)134 4064 y Fh(k)212 4037 y Fm(!)36 b Fk(m)433 4000 y Fi(0)456 4037 y Fp(.)58 b(On)37 b(the)h(other)f(hand,)i(b)m(y)f(Lemma)e(3.1,)j Fk(e)2146 4000 y Fi(\000)p Fj(\014)s(t)2273 4037 y Fp(\003)2341 4052 y Fj(k)2384 4037 y Fk(m)2469 4052 y Fn(\003)2518 4064 y Fh(k)2597 4037 y Fp(con)m(v)m(erges)h(strongly)d(in)f Fk(L)3605 4000 y Fj(p)3645 4037 y Fp(\()p Fk(\026)p Fp(\))0 4157 y(for)29 b Fk(\014)k Fm(\025)28 b Fk(k)390 4172 y Fj(p)430 4157 y Fp(\(1)15 b(+)g Fk(\013)686 4121 y Fi(\000)p Fj(p)780 4157 y Fp(\),)30 b(hence)h Fk(m)d Fp(=)f Fk(m)1444 4121 y Fi(0)1497 4157 y Fk(\026)p Fp({a.s.)42 b(Since)30 b Fk(m)2125 4121 y Fi(0)2176 4157 y Fm(2)e Fk(L)2336 4121 y Fj(p)2376 4157 y Fp(\()p Fk(\026)p Fp(\))h(for)g(an)m (y)h Fk(\013)e(>)g Fp(0)h(and)g Fk(p)f Fm(2)g Fp([1)p Fk(;)17 b Fm(1)p Fp(\),)0 4277 y(b)m(y)33 b(the)g(same)g(argumen)m(t)f (as)h(ab)s(o)m(v)m(e,)g(w)m(e)h(get)f Fk(m)1799 4241 y Fi(0)1850 4277 y Fm(2)28 b Fk(C)2014 4292 y Fj(\013)2063 4277 y Fp(\()p Fo(R)2167 4292 y Fn(+)2254 4277 y Fm(\002)23 b Fo(R)5 b Fp(\))38 b(and)33 b Fk(m)28 b Fp(=)g Fk(m)2988 4241 y Fi(0)3011 4277 y Fp(.)146 4398 y(T)-8 b(o)29 b(pro)m(v)m(e)h (uniqueness,)i(let)c Fk(m)1283 4413 y Fn(1)1351 4398 y Fp(and)h Fk(m)1622 4413 y Fn(2)1690 4398 y Fp(b)s(e)g(t)m(w)m(o)h (con)m(tin)m(uous)f(solutions)f(of)g(\(1.5\).)42 b(By)29 b(applying)0 4518 y(Lemma)35 b(2.3)h(to)f(the)i(function)f Fk(f)44 b Fp(=)34 b Fk(e)1440 4482 y Fi(\000)p Fj(\014)s(t)1568 4518 y Fp([)p Fk(m)1680 4533 y Fn(1)1744 4518 y Fm(\000)25 b Fk(m)1931 4533 y Fn(2)1971 4518 y Fp(])36 b(and)h(rep)s(eating)e(the) i(same)f(computations)f(as)0 4639 y(in)d(Lemma)f(3.1)h(it)g(is)g(easy)h (to)g(sho)m(w)g Fk(m)1475 4654 y Fn(1)1543 4639 y Fp(=)27 b Fk(m)1731 4654 y Fn(2)1771 4639 y Fp(.)p 3709 4639 V 3713 4576 59 4 v 3713 4639 V 3771 4639 4 66 v 0 4958 a Fq(Ac)m(kno)m(wledgmen)m(ts)146 5103 y Fs(L.)c(Bertini)e(ac)m(kno)m (wledges)i(the)f(v)m(ery)h(kind)e(hospitalit)m(y)f(of)j(Departamen)m (to)h(de)e(Matem\023)-45 b(aticas,)27 b(Instituto)0 5224 y(V)-8 b(enezolano)32 b(de)e(In)m(v)m(estigaciones)h(Cien)m(t)-10 b(\023)-35 b(\020\014cas.)1841 5806 y Fp(10)p eop %%Page: 11 12 11 11 bop 0 407 a Fc(References)56 618 y Fs([1])50 b(L.)39 b(Bertini,)h(S.)f(Brassesco,)j(P)-8 b(.)40 b(Butt\022)-45 b(a,)43 b(E.)c(Presutti)f(:)97 b Ft(F)-7 b(r)i(ont)43 b(\015uctuations)f(in)e(one)h(dimensional)201 731 y(sto)-5 b(chastic)34 b(phase)g(\014eld)f(e)-5 b(quations)p Fs(.)62 b(Preprin)m(t)29 b(2000.)56 927 y([2])50 b(G.)30 b(Caginalp,)e(X.)i (Chen)e(:)70 b Ft(Conver)-5 b(genc)g(e)33 b(of)f(the)g(phase)h(\014eld) f(mo)-5 b(del)34 b(to)e(its)g(sharp)i(interfac)-5 b(e)32 b(limits.)201 1040 y Fs(Europ)s(ean)d(J.)h(Appl.)f(Math.)i Fu(9)g Fs(\(1998\),)i(417{445.)56 1236 y([3])50 b(C.R.)34 b(Do)s(ering)g(:)82 b Ft(Nonline)-5 b(ar)38 b(p)-5 b(ar)g(ab)g(olic)39 b(sto)-5 b(chastic)38 b(di\013er)-5 b(ential)37 b(e)-5 b(quations)37 b(with)g(additive)g(c)-5 b(olor)g(e)g(d)201 1349 y(noise)36 b(on)h Fb(R)634 1316 y Fj(d)704 1349 y Fa(\002)22 b Fb(R)857 1363 y Fn(+)922 1349 y Ft(:)49 b(a)37 b(r)-5 b(e)g(gulate)g(d)38 b(sto)-5 b(chastic)38 b(quantization.)70 b Fs(Comm.)34 b(Math.)h(Ph)m(ys.)f Fu(109)h Fs(\(1987\),)201 1462 y(537{561.)56 1658 y([4])50 b(W.G.)28 b(F)-8 b(aris,)27 b(G.)h(Jona{Lasinio)d(:)66 b Ft(L)-5 b(ar)g(ge)30 b(\015uctuations)h(for)f(a)g(nonline)-5 b(ar)31 b(he)-5 b(at)30 b(e)-5 b(quation)30 b(with)h(noise.)201 1771 y Fs(J.)f(Ph)m(ys.)g(A)h Fu(15)f Fs(\(1982\),)j(3025{3055.)56 1967 y([5])50 b(P)-8 b(.C.)27 b(Hohen)m(b)s(erg,)h(B.I.)g(Halp)s(erin)d (:)66 b Ft(The)-5 b(ory)31 b(of)f(dynamic)h(critic)-5 b(al)31 b(phenomena.)56 b Fs(Rev.)28 b(Mo)s(d.)f(Ph)m(ys.)201 2080 y Fu(49)j Fs(\(1977\),)j(435{479.)56 2275 y([6])50 b(H.M.)39 b(Soner)g(:)97 b Ft(Conver)-5 b(genc)g(e)41 b(of)g(the)g(phase{\014eld)i(e)-5 b(quations)41 b(to)g(the)g(Mul)5 b(lins{Sekerka)41 b(pr)-5 b(oblem)201 2388 y(with)33 b(kinetic)f(under)-5 b(c)g(o)g(oling.)63 b Fs(Arc)m(h.)31 b(Rational)f(Mec)m(h.)h(Anal.)f Fu(131)h Fs(\(1995\),)i(139{197.)1841 5806 y Fp(11)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF