Content-Type: multipart/mixed; boundary="-------------0012210616900" This is a multi-part message in MIME format. ---------------0012210616900 Content-Type: text/plain; name="00-507.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="00-507.keywords" Quantum dynamics, Fractal, intermittency, Renyi dimensions ---------------0012210616900 Content-Type: application/postscript; name="DUKEfin.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="DUKEfin.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: DUKEfin.dvi %%Pages: 27 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips DUKEfin.dvi -o %DVIPSParameters: dpi=1200, compressed %DVIPSSource: TeX output 2000.12.07:1240 %%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 1200 1200 (DUKEfin.dvi) @start %DVIPSBitmapFont: Fa cmbx8 8 1 /Fa 1 83 df82 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb cmsy6 6 1 /Fb 1 1 df<007FBA12F0BB12F8A46C19F04506739B60>0 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc msam10 10.95 1 /Fc 1 4 df<003FC012FE488BC21280A690D2127FB3B3B3B3B3B390C1FCA66C20006C67 797D76FC8E>3 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd cmr6 6 8 /Fd 8 81 df40 D<127012F8127C7E6C7E6C7E6C7E7F12036C7E6C7E7F137F7F806D7EA26D7EA26D7EA26D 7EA26D7EA2801300A280A2801580A3143F15C0A6EC1FE0B2EC3FC0A61580147FA315005C A25CA213015CA2495AA2495AA2495AA2495AA2495A91C7FC5B13FE5B485A485A12075B48 5A485A003EC8FC5A5A12701B6479CA30>I43 D48 DII72 D80 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe cmbx10 10.95 47 /Fe 47 122 df<0603B5FC0503B612F0057F15FC0407B8FC043F17C093B97E030384030F 84033F9126FE001F7F92B600C001017F4A4AC86C7E020702F04AB5FC4A02C04A804A4A5C 4A49C848804A5B4C5D91B5488449605E5B5EA25B5EA2745CA2745C7491C7FCA2745B0800 13F8F33FE098C9FCAA98381FFFF0073FB6FCBEFCAAD8000702C0C8120386B3B3B3A6007F B700FE013FB8FCA9DAF83FEFFE0F687F7BFE74>12 D[50 181 109 263 81 40 D[<127EB4FC13C07F6C7EEA 3FFC6C7E6C7E6C7F6C7F6C7F6C7F806D7E6D7E6D7E817F6D7F816D7F6D7FA26D7F81147F 816E7F8082A26E7F8280828082A26E7FA28280A2838183A26F7FA38381A283A281A283A3 6F7FA583A281A31880A781A218C0B3A51880A25DA71800A35DA25FA54B5BA35FA25DA25F A25D5FA34B5BA25F92B5FC94C7FCA25C5EA24A5BA25E5C5E5C5E4A5BA25E5C4A90C8FC5D 14FF5D495BA2495B495B5D495B5B92C9FC495A495A495A5C485B485B485B4890CAFC485A 485AEA7FF0485A5B90CBFC127E>50 181 117 263 81 I46 D<933807FFE04BB67E030F15F0037F15FE4AB87E0207 17E0021F17F84A834A02008049B500F0010F6D7E4902C0010380494A6D804991C88003FC 153F498549496F7F49496F7F4B8190B584A2484A6F1480A2481BC0A2484A6F14E0A3481B F0A3481BF8A34891CA14FCA5481BFEA9B619FFB3AB6C1BFEA86C1BFCA26F5DA26C1BF8A4 6C1BF0A36C1BE06F5DA26C1BC0A26C6E4B1480A26C1B006D6D4B5B6F5D6D616D6D4B5B6F 5D6D6D92B55A6D6E495C6D02E001075C6D02F8011F5C6D02FF90B6C7FC023F91B612FC6E 5F020717E0020117806E6C4BC8FC030F15F003011580DB000F01F0C9FC587978F669>48 D<173FEFFF804C7F16075E163F4BB5FC1507153F0203B6FC147F48B8FCB9FCA615DFECFC 1F148048C7FCC8FCB3B3B3B3AF003FBB12E0A9EEE03F4B7771F669>I<4BB5FC033F14F8 0203B77E021F16F0027F16FC49B97E010718E0011F844918FC498490B5D8F003814891C7 003F15C04801FC0207814801F06E814801C014004801F06F8002FC6F80486D6F806E8148 6E6E80846F1880B6816F18C0841CE085A31CF085A26C5CA26C5CA26C91C9FC6C5B6C5B00 0113F038003F8090CB4814E0A496B612C0A21C80601C00606363604E5C634E5C634E5C4E 91C7FC95B55A624D5C4D5C4D14C04D5C97C8FC4D13FC4D5B4D5B94B512C04C5C4C91C9FC 4C13FC4C5B4C13E04C5B4C49EC3FF04C48C8FC4B5B4B49ED7FE04B5B4B13C04B5B4B90C9 FC4B5ADBFFF816FF4A4917C04A5B4A13804A90C95A4A5A4A485EEC7FF04A48043F138049 90BAFC5B5B5B5B5B491A0090BCFC5A5A5A5A5A48625ABCFCA563A4547776F669>I<9338 7FFFC0030FB6FC037F15F00203B712FE020F707E023F17E04A17F849B912FE49DAC00F80 4901FCC7814901E0023F804901806E804990C86C80D97FFC6F806E8490B56C8003E08348 806F834883811C804880A481A25DA36C4D15005D7E5D6C626D495C6D495F010F1380D903 FEC8485C90CAFC4E5C634E5C634E91C7FC95B55A4D5C4D5C050F5C053F14C0041FB65A03 1FB648C8FC4B15F819E096C9FCA219F019FF6F16C092C7000F14F0050114FC716C13FF72 807214E07280728072808772801C80A27215C01CE0A21CF0851CF8EB0F80EBFFF8487F00 0701FF19FC488048804880A24880A3B67EA31CF8A496B612F05D6C1BE0A24B18C06C4A5C 1C806C4A5C4AC816006C494B5C02F05D6C6D606C01FE033F5C6C6D6C4A5C6C02F049B65A 6D9026FF800F15806D91B8C7FC010F18FC0103606D18E06D6C1780020F04FCC8FC020116 E0DA003F4AC9FC03001480567977F669>II<013819E0017FF007F002E0173F02FEEE03FFDAFFE0153FDBFFC001 1FB5FC93B8FC6363A26398C7FC62626262626297C8FC616119F019C096C9FC18FC18F018 C005FCCAFC17C09126F00380CBFC92CDFCAF93381FFFC00303B6FC031F15E0037F15FC02 F1B8FC02F717C091B97E1AF8DCF003804BC76C13FF03F06E8003C0020F8092C86C804A6F 8014F84A6F804A844A84013F826DCA8090CBFC1C80A2851CC0A31CE0A41CF0131E3801FF C04813F0000F7F487F487F805A81B6FCA2811CE0A44B18C096B6FCA26C91C91580A24A19 006C5B4A4B5C14E06C01804B5C49C95D6C6C5E6C6D4B5C02E0606C6D033F5C6C01FC4B5C 6C01FF4AB6C7FC6D01E001075C6D01FE017F5C6D90B812F06D60010318806D4DC8FC6D6C 16F8021F16C002034BC9FCDA007F14E0030701F8CAFC547976F669>I<943803FFF8057F EBFF800407B612F0043F15FC93B77E0303707E030F83033F8392B6D8C01F7F4A9126FC00 037F020702E013004A0280EC3FFC4A49C8127F4A494A487E4A49140791B5484A7F494A5C 495C494A4A14804991C8FC61495B5B5D5B90B55AA25A731400485C735B5A735B4B6F5B48 060113E09638007F8097C8FC5AA35A5D17064CB57E48030714F8041F14FF4C15C093B712 F003C18203C316FE03C782B627CFFE001F8004F8010780DBDFE0010180DBFFC06D804C6E 7F8793C86C7F4B83854B18801CC05D1CE0855D1CF0A25D1CF8A41CFC6C5CA87EA57EA36C 6E18F8A37E1CF0A27E1CE06C606F18C07E1C806D7F4F14006D6D5F6D5F6D6D5F6F92B55A 6D6E495C6D02E0495C6D6E010F5C6D02FE90B65A6E90B8C7FC021F17FC6E5F020317E002 001780033F4BC8FC030F15F8030115C0DB000F01F0C9FC567977F669>I<48B47EA2487F 8014F891B512C093BA1280A45AA41D00A264486364646464A2644898C7FC636363636302 C0C91207D83FFCCA485B63494D90C8FC4F5A494D5A4F5A60007F4D5B49604E5B4E5B4E90 C9FC4E5A187F48484C5A614D5BCA485B4D5BA24D5B4D90CAFC5F604D5A17FF605E5E605E 605E5E605EA25E6093B5FCA25D95CBFC5DA35DA24B5BA35DA35DA35DA25FA292B5FCA55C A65CAE6E5CA26E5CA26F5B6F5B030F90CCFCED03FC597D74FA69>I<93381FFFF00303B6 12C0031F15FC92B8FC020317C0020F17F0023F17FC4A17FF91B526F0007F804949C70007 804901F00200804901C0033F7F4990C96C7F4948824948707F854948707F01FF834A8448 85A21C805A8680A2487FA2808015C08103F84C130015FE6F7E7092B5FC04F05E04FC5C6C 03FF5E715B05E0495B05F8495B6C04FE5B716C485B6C71485B06F1B55A6D93B6C7FC1AFC 6D606D18E0626D95C8FC6D846D846D18F06D18FC6E83021F836E18C06E84021F844A8491 BA7E1303498549496C8249D9F83F1780017FEBF00F90B5D8E00317C048EC800092C7003F 16E048824849020716F0484914014A6E7E487115F84A150F4817034A030015FC193F4849 82190785B517004A8386A28686A37413F8A3806C1BF0A36E4D13E07E6E19C0626C6D1980 6E5F6C6D19006C6D4D5A6FED01FF6C6E4B5B6C02F0030F5B6C02FC033F5B6DD9FF8049B5 5A6D02F8013F5C6D91B8C7FC0107606D18F8010060023F17C002074CC8FC020016F8031F 1580DB003F01E0C9FC567977F669>I<93383FFFE00307B6FC033F15E04AB712F8020716 FE021F707E4A8391B912F0494AC6804902E0013F7F010F0280010F7F4991C76C7F49496E 8049496E8090B5486E804B6F7F5A48727F485C8748727FA24886A2485C1C80A2481BC0A2 851CE0B6FCA31CF0A51CF8A71CFC617EA47E61A27E616C80A26C95B6FCA26C5F816C5F6C 6E5C7F6D6D5C6D6DEC1FEF6D6D6CEB7FCF6D9138E001FF6D91B6008F14F86D170F6D6C15 FE6E15FC020F15F0020315E0DA007F14800307D9FE0015F0923800018093C8FC611CE0A4 D907F819C0EB1FFE90387FFF8090B56C1880486E5D1C00488063486E5D63A26396B5FC63 60634B4A5C6C4D5C5D4E91C7FC4B4A5B6C4A4A5B4AC8B55A6C01F84A5C6E02075C6DB46C 011F5C6DD9F801B6C8FC6D90B75A6D17F86D5F6D17C0010094C9FC023F15F8020F15E002 014ACAFCDA001F13C0567977F669>II65 DI< 0703B517F84EB600FCED01FC063FDBFF8014030503B800F01407051F05FC140F94BA141F 040307C0137F040F07F013FF043FF1FC0193BB6C5A03039326FC001FEBFF87030F4BC814 CF4B03E0033F90B5FC037F92C9120792B600FC1601020303F0824A03C0173F4A92CB7E4A 4A844A02F8844A4A8491B64884494B84494B854992CD7E4C86495C494A8649895E49895E 90B64886A2488A5E5A93CF127F5AA2481F3F5DA25AA24B1C1F5AA3F80FF8489CC7FCA35D A3B6FCB17EA381A37EA2F807F8F80FFC7E81A27EA2816C1F1F21F87E826C1F3F826C20F0 207F6D80701CE06D1EFF705013C07F6D6E5013806D6E62701C006D6F616D6F4F5A6D6F4F 5A6E6E4F5A6E6E19FF6E02FE4E5B6E6E06075B6E03C04D5B6E03F0053F5B020003FC4D90 C7FC6FDAFF804B485A031F03F0030F5B6F03FF037F13F0030304FC010FB55A030093B85A 043F97C8FC040F19FC040319F0040019C0051F95C9FC050317F8DD003F16C006014BCAFC DE000314807E8174FE97>II72 D<031FB6D8F80FB512F896B7FCA992C8000F02FCC7FCB3B3B3B3A8EB3FE03801FF FC487F000F6D7E4880A24880A24880A2B67EA44E5CA3634B5C6C62A26C4A4A5C95B65A6C 4A5B4B94C8FC6C91C700075C6C01FC4A5C02FF4A5C0001DAF801B612E06C91B85A6D95C9 FC011F17FC010717F0010117C0D9003F4BCAFC020715E0DA001F01F8CBFC5D7F7EFC6C> 74 D76 D80 D82 D<000FC112F8A6488CA493C7001F02FCC77E 03E01A0392C8F0007F02FC1C1F4A8802E01C034A884849767F91C91A7FA2491E3FA2491E 1FA2491E0FA3491E07007F8CA4498AA700FF2180498AA5CB97C8FCB3B3B3AE4ABD12C0A9 F1F007817B78FA92>84 D86 D<0307B512C04AB612FE021FEDFFE091B812FC010317FF4918C0011F18F04984499026FC 000714FE03E001008090B56C023F804871806F020780A2486E6E8072808487A2737FA36C 4A6F7FA26C5C6D5B6D5B6D5B6D90C9FCEB01F890CBFCA40607B6FC94B8FC163F0307B9FC 157F0203BAFC141F027FEDF83F49B6EAFC00010715C0011F02FCC7FC017F14E090B61280 484AC8FC485C4814F0485C485C5D5A92C9FC5A5CA2B55AA561A28096B6FC6C5F806C5F6F 5C6C6EDA0FF7806F023F15F86C02F8DAFFE7ECFFF86C6E010301C715FC6C9126FF803F01 8315FE6C92B612036C6CEEFC016D4C7E010F04E07F01030480131FD9007F4AC7000714FC 020F02F0DA007F13F8DA003F90CCFC5F547AD266>97 DI<933807FFFE4BB612F8 030F15FF037F16E04AB812F8020783021F17FF027F188091BA12C049ED8003499126F800 0114E0010F02E016F04902805B4991C7FC4B4A14F8495B90B55A5A5D485C5AA2484A6E14 F0A2487114E04B6E14C073138048721300735AF103F04895C8FC92CCFCA4B6FCAF7E81A3 7EA3817EA26C6EEE03FCF207FE6C801A0F6C6E17FC6F161F7E6C6EEE3FF86FEE7FF06D6E 15FF6D02E04A13E06D6E5C6D02FC4A13C06DDAFF80013F13806DDBF801B51200010092B6 5A6E5F021F17F002075F020117806E6C4BC7FC030F15F003011580DB000701F0C8FC4F54 79D25D>II<93380FFFF04BB67E030F15F8037F15FE4AB87E020717E0021F17F8027F8391B6 C66C7F010302F8010F7F4902E00103804902800100804991C86C7F49496F7F49498190B5 486F7F4B834884484A8385484A83855A4B18805A851CC05AA292CAFC4885A21CE0A3B6FC A292BAFCA51CC01C8092CDFCA57EA3817EA37EA2816CF21F80F33FC06C6EEF7FE0A26C6E 17FF1CC06C6E5E6C6E4C13806F5E6D6D4C13006D6E5D6D6E4B5A6D02F04B5A6D02FCEC01 FF6DDAFF80010F5B6D03F890B55A6D6C91B712C0021F606E95C7FC020317FC020017F003 1F16C003074BC8FCDB007F14F0040149C9FC53547AD260>I<943807FFF04CB512FE041F 6E7E93B712E0030382030F82033F824B824AB5D8FE077F4AECF00F4A02C015804AEC001F 4A5B4A494914C04A5B5E91B5FC495CA25E49701480A3494A6D1400725B725B725B953800 7FE0070FC7FC96C8FCB1B912FCAAD8000702C0CAFCB3B3B3A7007FB812C0A9ECF83F4A7F 79FE40>III<147F903803FFE0010F13F8497F497F497F90B67EA24881A34881A76C 5DA36C5DA26D91C7FC6D5B6D5B6D5B010313E0D9007FC8FC91C9FCB0ED7F8090B6FCB7FC AAC67E131F7FB3B3B3A4B812F0A9ECF07F2C7F78FE3A>I107 DII<03FFEDFFFE90B6020FEBFFF0B702 3F14FC4DB7FC050716C04D82053F824D829426FFFE01804C9026E0007F7F4C01806D7F4C 48C77EC66CDA0FF883011F4A5A6D4A48804D834C5A4CC8FC4C814C84A25EA25EA25EA45E B3B3A7B800FE90B812FEA9DAF87FEFFC3F675278D174>I<933803FFFC93B612F0030715 FE033FEDFFC092B812F0020717FE4A83023F18C04ADA801F8049B526F8000114F84902E0 6D6C7F490280021F7F4949C800077F49496F8049496F8049496F8090B5854B824887484A 707FA248874B824887A2481C80A292CA7E481CC0A3481CE0A5B61AF0AE6C1CE0A56C6E4C 14C0A36C1C80A26C1C006F5E6C63A26C6E4C5BA26C6E93B55A6C636F5D6D6D4B5C6D6D4B 5C6D6D6C021F5C6D02E0027F91C7FC6D02F849B55A6D9126FF801F5C010092B712F06E60 021F188002074DC8FC020117F86E6C16E0030F93C9FC030015F0040301FCCAFC5C547AD2 69>II114 D<92B500C0137C021F9138FC01FE91B71287010716FF131F5B90B9FC48EC C0014801FCC7121F4801E0140348498091C9FC48177F49163F003F171F49160F127FA218 0712FF7FA27F806E6F5A02F092C8FC14FEECFFC015FE6CECFFF8EEFFE017FC6CEEFF8018 E06C17F818FE6C717E6C846C846C846C846D83011F836D83130301001880141F020317C0 EC001FDB007F15E01603EE001F050314F01700D87F8082486C8284846D82A2847FA26D18 E0A27FA26D4C13C07F6E4B1380806E4B130002F85D6EEDFFFEDAFF8001075B03F8017F5B 92B75A61198001F094C7FCD9E03F15FCD9800F15E026FE000192C8FC007CD9001F13E044 5479D253>III 119 D<267FFFE0B500F8913A0FFFF1FFF091B694B5FCA9D8000702F0C9000FEB80007590 C7FC6D6E4C5AA26D6E4C5AA26D6E4C5AA26E6D4C5AA26E6E4B5AA36E6E4A5BA26E6E4A5B A26E6E4A90C8FCA26E6E4A5AA26E6E4A5AA36E6E4A5AA26F6D4A5AA26F6E495AA26F6E48 5BA26F6E485BA36F6E4890C9FCA26F6E485AA26F6E485AA26F6E485AA2706D485AA3704A 5AA2705DA2705DA27092CAFCA2705CA3705CA2705CA2715BA2715BA2715BA3715BA27190 CBFCA24D5AA24D5AA260173FA2D801FE4B5A3807FF80001F01E04A5A487F4C5B487F4C5B B57E4C90CCFCA24C5A161F4C5A4C5A4A495A6C5C4B5BDAF00F5B273FFDE03F5B261FFF41 B5CDFC91B55A6C15F86C5D6C5D6C15806C6C49CEFC011F13F0010390CFFC64757CD06E> 121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff msbm10 10.95 3 /Ff 3 91 df<003FB700E00403B712C048704C16E0B86C5E836C70826C7516C000030180 C7007FDC000390387FE000C66C6C6E6C9326007FFFC7FC6D6C6F715AD90FF0021F725A6D 6C6E6C170F6D6C6E7E010170606D6C020318076E6E7E6F6D7E846F806F6E7E6F6E7E856F 140F6F6E7E6F6E7E6F816F6E7E6F6C13006F6C147F706E7E030F826F6C141F6F6C6E7E70 6E7E6F6C8103001503047F6E7E706C6D7E7180041F81706C6E7E706C6E7E7181706C140F 04016F7E706C6E7E057F81721301053F6E7E716C147F716C81726E7E716C141F05036F7E 716C6E7E716C81721403726E7E726C6D7E726C807380726CEC3F800607ED1FC0726C15E0 726C140F73EC07F00600ED03F8077F15FC736C130174EB00FE736C147F070F1687736C14 3F736CEC1FC774EC0FE7070116F7736CEC07FF087F80757F746C7F1A1F746C147F746C14 3F75141F1A03746C140F746C1407751403757E093F1401757E757E881B07757E757E8875 7E88F43F80F41FC01DE01C0FF407F0F403F81DFCF401FE1C001D7FF53F811EC11D1FF50F E1496DF107F11EF9F503FD496D19016FF100FF010F6D1A7F90387FE7FE003FB7193F4870 181FB8190FA26C1D076C93CC1203D112011E001F707B807CFC5C>78 D<003FBBFC481AFEBD12E01CFC6C1BFF6C1CE026001FF0C7263FF00115F8D903F89226C0 001F14FE01014BC73903FE3FFF6E027E912600FF0713C0010003FEDB7F017F4D92393F80 3FF098391FC00FF8777E98390FE001FE09076D7E787E766D7E0903141F787E766D7E1B01 787E1E01A2768009001400A38B1F7EAA1FFE67A31B01521301671E03671E0709034A5A64 545A0907EC7F805213FF090F4990C8FC9938C007FE091FEB1FFC98397F80FFF0E1FF875B 080790B55A083F92C9FC073FB612FC94B912F01D800AFCCAFC1C8099CBFC9738003F8094 26FC07F06D7E727E757E726C6D7E1800736D7E077F130188736C6C7E737E1C7F736C6D7E 737E767E736C6D7E737E767E736C6D7E1A7F767E746C6C7E746C7F89746C6D7E746C6D7E A2746C6D7E746C6D7E8A746C1303097F6D7E777E756C7F756C7F787E756C6D7E756C801E 0F756C6D7E756C6D7E8B756C6D7E0A7F6D7E797E766C6D7E766C6D7E01016F737E4A027E 706C6D7E0103037F706C6D7ED91FF0DA3FE072B4FC003FB900F86EB712F048726E16F8BA FC886C886C4E6F15F07D7D7DFC60>82 D<011FBEFC491D805BA31F0090267E007F01FCC7 D803F0C75AD9FE01B5C81207494801F04B48495A020F018061DA1FFCC948481303DA3FF0 4D495ADAFFC0163F01FD494CC7485AD9FFFECA5E4A05FE141F4A4D4A5A4801E016014A4C 484AC7FC1D7E4A4C4814FE91CA4848495A5B4F48495A494E5C073F1407494DC7485A1203 07FE4A5A4F5D490401153F4E484AC8FCA200014D4814FE6C484D5C90CA000F14014E4849 5AA24E48495A96C7485A6006FE4A5A644D48143F4E4AC9FC17034D4814FE634D4813014E 495A171F4D48495A634DC7120F05FE4A5AA24C484A5A4D92CAFC04035D4C4814FEA24C48 495A4D5C041F14034C48495AA24CC7485A047E5D04FE141F4B484A5AA24B484ACBFC4C14 FE15074B48495A614B4813034C495A153F4BC7485A6103FE141F4B4A48173802011C7C4A 484ACB12FC187E4A4814FE4A4849481701A24A48494818F84B5C023F020718034AC7485A A202FE4A4817074A5D0101033F180F49484ACB13F01E1F494814FE4A4A183F010F020119 7F4948495A1EFF494849484D13E091C748485F496301FE4A48EF0FF74DEF1FE74848023F F03FC7494ACBEAFF8F000351EB0FC0484802FEEF07FE4CEF0FFC48480101F03FF8494948 933801FFE0001F080713C048484948047F13004C92260FFFFE131F48BF1280A2C0FCA27E 6C1E006E7D7BFC68>90 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg cmr8 8 27 /Fg 27 127 df<933807FFF04BB612C0030F15F8037F15FF4AB812C002079026FE003F13 F0021F01E0010313FC4A018001007FDAFFFEC8383FFF804901F8030F7F4901E003037F49 496F7F49496F7F4990CA6C7E4948717E4948717E01FF864849717FA24849717F48874A83 4887A24849717FA44849717FAB6C636E5FA36C63A26E5F6C63A36C6D4D5BA26C636E5F6C 63017F97C7FC6E5F013F61A26D6C4D5A010F61A26D6C4D5A6D61A26D6D4C5A6D616F5D02 7F95C8FCA26E6C4B5A021F5F00F8F30F806E6C4B5A007CF31F0002075F6F150F02035FA2 6C01014D133E6F151F02005F003F1B7E6C1B7C01C0017C93380001FC90B500FC93B5FC6F 5DA26C63A56C634B81595E7ADD66>10 D40 D<127812FC127E7E6C7E7F6C7E6C7E6C7E6C7E6C7E7F7F6D7E806D7E130F806D7EA2 6D7EA26D7EA26D7EA281147F81143F81A2141F81A2140F81A36E7EA4811403A481A380A5 1680B3A41600A55CA35DA414075DA44A5AA35D141FA25D143FA25D147F5D14FF92C7FCA2 495AA2495AA2495AA2495A5C131F495A5C49C8FC5B5B485A485A485A485A485A5B48C9FC 127E5A1278218678E337>I43 D48 D<157815FC14011407140F147FEB01FF131F001FB5FCB6FC14BFEBFE3F13E0EAE000C7FC B3B3B3AD4A7EA20103B512C0007FB8FCA5305974D847>I<91380FFF80027F13F80103B6 FC4915C0011F8190263FF00F13F89026FF80017F4848C76C7ED803F8EC1FFF496E138048 486E13C048486E13E0484816F090C87E4817F8003E6F13FC127E007C167FD87FE016FE48 7E7FEF3FFF7FA66C5A6C5A6C5AEA0780CA13FE177FA3EFFFFCA218F85E18F04C13E0A24C 13C04C138018004C5A4C5A5F4C5A4C5A4B5B4B5B4B90C7FC5EED0FF84B5A4B5A4B5A4B5A 4A48C8FC4A5A4A5A4A5A4A48141F4A5A4A5A4AC8123E5C495A495A495AD90FC0157E4948 157C49C9FC017E16FC49150148B8FC5A5A4817F85A5A5AB9FCA218F0A3385979D847>I< 913803FFE0023F13FE91B612C0010315F090260FFE017F903A1FF0003FFED93F80EB0FFF 49C76C7F01FC6E7F48488248486E7F5BD807FE826D80486D81A280A66C5B6C90C85B6C5A D800785C90C8FC605E60A24C5B604C90C7FC4C5A4C5A4C5A4C5A03035B037F5B027FB5C8 FC16FC16F016FEEEFFC0DA000113F09238003FFCEE0FFE706C7E707F707F707F84717EA2 84717EA21980A28319C0A2EA07C0EA1FF0487E487EA2487EA319805FA24917006C5A495D 495E6CC95B17FF6C6C5E6C6C4A5B01F04A5BD807FC4A5B6CB44A5BC601C0013F90C7FC90 3A7FFE01FFFE6DB612F8010F15E001031580D9007F01FCC8FC020713C03A5C7AD847>I< 171F4D7E177F17FFA25E5EA25E5EA25E5EA25E93B5FC5D16FBED03F3150716E3ED0FC3ED 1F83A2ED3F03157EA215FCEC01F8140315F0EC07E0140F15C0EC1F80EC3F00A2147E5CA2 495A495A13075C495A131F5C49C7FC137EA25B485AA2485A485A120F5B485A123F90C8FC 127E5ABA12FCA5C90007EB8000B04C7F043F13F04AB712FCA53E5A7CD947>I<913801FF E0020F13FE027F6D7E91B612E001039038807FF8903A07F8000FFCD90FE0EB03FE494890 3800FF8049C8127F017E6F7E496F7E00018349150F0003831707485A841703120FA37FA2 7F17076D5E7F6E140F6C01E05D6E141F02FC4A5A6C6D5D6E6C495A6C02E049C7FC6C9138 F003FE9238FC07FC6D9038FF0FF86DECBFF06DECFFE06D15806D4AC8FC0101806D81023F 14E017F891B67E010315FF49486C8090261FF83F8090263FF00F8090267FC007809026FF 8001804890C76C7F4848804848020F7F48481403496E7F48486E7E003F70138049150F00 7F82496F13C0838348CAFC187FA3183FA319807F127F187F6D1700123F6D16FE121F6D4B 5A6C6C4B5A6C6C4B5A6C6C4B5A6C6C6CEC3FC06C01E0ECFF80D97FF8010390C7FC6DB4EB 3FFE010F90B55A6D15F0010015C0023F49C8FC020113E03A5C7AD847>56 D58 D<007FBD12F0BE12F8A4003F1CF0D1FCB3A6003FBD12F0BE12F8A46C1CF05D2478B26E> 61 D72 D76 D80 D82 D91 D93 D100 D105 D109 D111 DI<903A01FFF001C0011FEBFF07017F14CF48B7FC5A48EB 001FD80FF81303D81FE013004848147F49143F007F151F90C8120F5AA21607A27F7F7F6D 91C7FC13FC387FFFC014FE6CEBFFF015FF6C15C06C15F06C816C15FEC6816D1580131F01 0315C0D9003F14E01400030F13F015019238007FF80078153F00F8151F160F7E1607A27E A26C16F0A26D140F6D15E06D141F6DEC3FC06D147F01FE903801FF809026FFC00F130048 6CB55A486C14F8D8F80F14E0D8F003148027E0007FF8C7FC2D3C7BBA38>115 D117 D<007FB500F8013FB512C0A5C66C01E06D EBF800011F01806D13C06D6F90C7FC6D16FC6D6D5C6D5E6F495A6D6D495A6E6C5C6E6C49 C8FC021F147E6F13FE6E6C485A6EEB83F86EEBC3F06EEBC7E0EEEFC06E13FF6F5B6F90C9 FC6F5AA26F7E6F7F835D834B7F4B6C7E4B6C7EEDFE1FDA01FC7F4B6C7E4A486C7F4A486C 7F020F7FDA1FC0804B6C7F4AC76C7E027E6E7E02FE141F49488101036F7E010F6F7F011F 83017F4B7F2607FFFE4A13F8B66C017FEBFFF8A545397EB84A>120 D126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh cmmi6 6 23 /Fh 23 122 df11 D<933801FFC0040F13F8043F13FE93 B6FC030301801380923A07F8003FC0DB0FE0EB0FE0DB1F8014F04BC71207037E15F85DDA 01F0140314034A4815FC4A4814075D021F16F84AC8FC143E027E150F027C16F002FC151F 4A16E0183F010117C04AED7F80F0FF000103903903FFE1FEDAE01FEBFFFC4B5C18E00107 8202C0816F800307EBC1FE010F90C712014A6E7E841980131F91C913C0183FA25B133EA3 017E167F137CA301FC16FF19805B5F00011800A24D5A6D4B5A12034D5A6D4B5A6D4B5A48 6DECFFC0D9DFC04990C7FCD9CFE0EB07FED9C7FCEB3FFCD80FC3B612F0018015C0023F49 C8FC020F13F0001FD90010C9FC90CCFCA35A123EA3127E127CA312FC5AA45A3E597CC546 >II21 D<147802FC1578496CEC01FC01034B7EA201071507A24A5DA2010F150FA24A5DA201 1F151FA24A5DA2013F153FA24A5DA2017F157FA24A5DA201FF15FFA24A5D1978484B147C 19FCF000F85E485DF001F0EE0FFE161F486D013FEB03E093B5FC9126E001FDEB07C09126 FC0FF8138F4890B539E07FFF804C6C130001F99138001FFE9026F81FF8EB03F8001F90CB FCA25BA2123FA25BA2127FA25BA212FFA25BA390CCFC5A123C3E417AAB4B>II<18F04D7E60A3 170360A3170760A3170F60A3171F95C8FCA35F173EA3D91FE0027EEB03C0D97FF8027CEB 07F0496C160F486DEE1FF82603F0FF02FCEB3FFC48486D5B380FC07FEA1F80D900FF0101 141F484C130F003E1807007E1803D87C010203140103005BD8FC0318F800F85B00780307 1400D800074B13014A17F0130F4A130F4D1303011F18E05C041F140794C7EA0FC0013F18 804A161F4C1500043E5C197E61047E495A6E017C495A011F4C5A4E5A6D6C01FCEB3F806D 6C4901FFC7FC02FFEC03FE6D01C0EB0FF8010001FDEB7FF06EB612C0021F92C8FC020314 F8DA001F13C0DB03E0C9FCA315075EA3150F5EA3151F93CAFCA35D153EA2151E46597AC4 52>32 D<913801FFE0021F13FE91B61280010315E0010F15F04915F8137F9039FFFC007F 480180EB0FF049C7EA03E0D803F8EC0080D807E015005BA59038E07FF83903F7FFFC6CB5 7E7EA200035C485CD80FE013E0D81F80C9FC48CAFCA2127E127CA212FC5AA26C1506160F 7E007F153F01C014FED83FF8EB07FC6CB65A6C5D6C5D6C5D6C92C7FCD8003F13F8010713 802D2F7AAC3A>34 D<4DB4FC011E030F13C0013E033F13F0017E4B7F494AB57E48484A80 48485C494A80000792381FFE0749DBF0001380000FDB3FC0133F494AC7121F001F03FE15 C090C848140F484A5A003E4A5A5E1507007E4B1580007C140F5E4BC8121F00FC19006115 3E197E5D007C60007E4D5A007F02FC1403F00FF06C6C494A5A01E0EE7FC0261FF8014A48 5AD80FFE030790C7FCD9FFE1EC3FFE6C903AFFF007FFFC6C91B65AC617E06D5E6D93C8FC 010F15FC010115F0D9003F1480020F01F8C9FCDA1FE0CAFCA25D143FA44A5AA314FFA349 90CBFCA45C5C6D5A424178AB51>39 D59 D<177017F81601A2160317F0160717E0A2160F17C016 1F1780163F1700A25E167E16FE5EA215015E15035E15075EA2150F5E151F5EA2153F93C7 FC5D157E15FE5DA214015D14035DA214075D140F5D141F5DA2143F92C8FC5C147EA214FE 5C13015CA213035C13075C130F5CA2131F5C133F91C9FCA25B137E13FE5B12015BA21203 5B12075BA2120F5B121F5B123F90CAFCA25A127E12FE5AA25A12782D6477CA40>61 D65 D<91267FFFFC031FB512 F091B56C5DA2821DE0DA007F6D0200EBF800F33FE071ED1F8099C7FC03FD6D5D1B3E03F8 7FA202016D6C157E1B7C4B6C7EA202036D6C15FC634B6C7EA202076D6D1301634B6C7F84 020F6D1503725C4B7E84021F027F1407725C92C7123F844A021F140F725C023E80711380 027E171F7101C090C8FC147C7113E002FC5F71EBF03E5CF07FF80101187E95383FFC7C5C F01FFE0103EFFFFC725B5C841307725B5C84130F725B5C011F177FD97FC0163F2601FFF0 5F007FD9FFC0151FB6FC190F624B15075C4478C360>78 D<027FB712E091B812FEF1FFC0 1AF01AFC9126007FF8C713FF070F7F4C02037F07007F03FF707EA24C6F7EA25C875EA25C 505A5EA24A4D5AA293C8485B634A4C5B4F90C7FC4B4B5AF13FF8021F4C5A953803FFC04B 023F90C8FC92B712FC4A16E061859226F8000113F8027F9138003FFC727E4BEC07FFA202 FF6F7FA25D84495EA25DA2495EA25DA2494C90C8FCA292C8FCA249F107801B0F5C1B1F01 1F1A00013F61007FB66E143EB7EE80FC7213C172EBFFF84B6E6C13E0CC6C5B070390C7FC 514678C35C>82 D100 D106 D<14FF90B57E5AA292C9FCA2EA 0003A25CA313075CA3130F5CA3131F5CA3133F5CEE03F8EE0FFE017FEC3FFF4A90B51280 923801FE1FDB07F013C001FF90380FC03F9139801F807F92383E00FF4B5A4814F8DA03F0 14804A486C13004A485B4849C7127CD9FE7E91C7FC6D5A5C485BECFF8015F015FCD80FFC 7F9038F80FFF02037F6E7F001F7F49137FEF0780EF0FC0003F17805BA2171F007F17005B 173EA200FF5E49013F13FC92381FE1F86FB45A90C76C5B486E5B003C020090C7FC324677 C442>I<017FEC0FFC2601FFC090387FFF8048D9F001B57E48D9F807803C0FC7FC0FF03F F0018390393FC00FF83C1F03FE7F0007FC15FC003E6D4813035D007E4A80007C5C5D00FC 1607484890C75B5C1278000049140F010F5E5CA2171F011F5E5C173F60133F4A147FF0C0 1E05FF133F017FEE803E5C5EF0007C13FF4A16FC4C4813F80401EB01F048170391C7EC07 E0933900FF1FC094387FFF80496F130049ED1FFCD80078ED07F0402D7AAB4D>110 D112 DI116 D<49B4EB03FC010F9038C00F FF49D9F03F13C0017F6D4813E0903BFF07FCFE0FF03B01FC01FFF803D803F09138F007F8 48486CEBE00F4848151F49ECC03F48C7FC48038013F0003EEE1FE04A15C0007E9238000F 80007C93C7FC123CC75A5DA314075DA3140F5DA2EF01E0021FEC03F0000F17E0D83F805B D87FC01507023F15C000FF160F1880027F141F0180ED3F00D900FF14FE48486D485A3B7F 07F3FE0FF8263FFFE1B512E06C01C05C6CD9003F90C7FCD803FCEB07F8352D79AB46> 120 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fi cmex10 10.95 24 /Fi 24 91 df<170FEF1F80173FEFFF004C5A4C5A4C5A4C5A161F4C5A4C5A5F4CC7FC5D 4B5A4B5A4B5A151F5E4B5A157F4B5AA24A5B4A90C8FCA24A5A140F5D141F5D143F5D147F 4A5AA25B5D5B5DA25B92C9FC5BA2495AA3495AA2137F5CA213FF5CA25AA25C5AA4485BA4 5A5CA45A91CAFCA45AA45BA3127FA85BA212FFB3AB127FA27FA8123FA37FA47EA4807EA4 807EA46C7FA47E80A27EA280137FA280133FA26D7EA36D7EA27F817FA2817F817FA26E7E 143F81141F81140F8114076E7EA26E7F6E7FA26F7E153F6F7E82150F6F7E6F7E6F7E8170 7E83707E707E160F707E707E707E707EEF3F80171FEF0F0031D9658653>0 D<127812FC7EEA7F806C7E6C7E6C7E6C7E7F6C7E6C7E7E6D7E806D7E6D7E6D7E8013076D 7E806D7FA26D7F6E7EA26E7E81141F81140F811407816E7FA282808280A282157F82A26F 7EA36F7EA28281A28381A283A28183A46F7FA48381A483167FA483A4163FA383A882A218 80B3AB1800A25EA85FA3167FA45FA416FF5FA45D5FA44B5BA45F5DA25FA25D94C7FCA25D 5EA24B5AA34B5AA25E15FF5EA25C5E5C5EA24A90C8FC5D140F5D141F5D143F5D4A5AA24A 5A495BA24990C9FC5C495A130F5C495A495A495A5C49CAFC5A485A485A5B485A485A485A 485A00FECBFC5A127831D97A8653>III<1208123E127FEAFF80B3B3B3B3B3B3A5EA7F00123E1208097766843D>12 D<00081610003E167C007F16FE486CEC01FFB3B3B3B3B3B3A56CC912FE003E167C000816 103077668465>I[69 326 95 134 109 16 D[<127EB4FC7F6C7E6C7E6C7E6C7E6C7E6C7E6C7E806C7F6D7E6D 7E6D7E6D7E806D7E6D7F7F816D7F6E7E6E7EA26E7E6E7E81806E7F8280826E7F157F826F 7EA26F7E150F826F7FA26F7FA26F7FA26F7FA2707EA283163F83161F838284A2707FA282 84A2707FA28482A284177FA284173FA28483A28583A285A28385A3717FA4717FA48583A4 85187FA385A284A41A80A284A41AC0A484A31AE0A684A21AF0AC841AF8B3B3A21AF060AC 1AE0A260A61AC0A360A41A80A460A21A00A460A261A318FF61A45F61A44D5BA44D5BA361 5FA261A25F96C7FCA25F60A2177F60A217FF60A25E60A24C5BA2605EA24C5BA295C8FC5E 5F163F5F167F5FA24C5AA24B5BA24B5BA24B5BA24B90C9FC5E151F4B5AA24B5A5E15FF4A 5B5E5C5E4A90CAFC5C5D4A5A4A5AA24A5A4A5A495B5D5B4990CBFC495A5C495A495A495A 495A485B91CCFC485A485A485A485A485A485A485A90CDFC127E>69 326 122 134 109 I[90 435 90 134 134 I[<127F487E7F6C7E6C7E6C7E6C7E6CB4FC6C7F6C7F6C7F6D7E133F6D 7E806D7E6D7E6D7F6D7F6D7F816E7E6E7E141F6E7E816E7F6E7F80826E7F6F7EA26F7E6F 7E6F7EA26F7F6F7FA26F7F836F7F167F83163F83707E8284707FA2707FA2707F707FA271 7EA2717EA2717EA2717FA2717FA285838583858385187F85A2727EA28486A2727FA2727F A3727FA28684A28684A286197FA2868587A285A28785A287A28587A28587A38587A38587 A4747EA4747FA48886A488A286A388A286A488A386A388A486A388A686A288A987A21D80 AE871DC0B3B3A71D8063AE1D00A298B5FCA964A262A664A362A464A362A364A462A264A3 62A264A46264A45090C7FCA4505AA46361A36361A36361A26361A263A26163A261A298C8 FC6162A219FF62A26062A26062A24E5BA34E5BA24E5BA297C9FC60A24E5AA26118FF615F 615F615F61A24D5BA24D90CAFCA24D5AA24D5AA24D5AA24C5B4C5BA24C5BA24C5B95CBFC 5E4C5A5F167F5F16FF4B5B5F4B5BA24B5B4B90CCFCA24B5A4B5A4B5AA24B5A4A5B5E5C4A 5B4A90CDFC5D4A5A143F4A5A4A5A5D495B495B4990CEFC495A495A5C495A137F495A485B 485B4890CFFCEA0FFC485A485A485A485A5B6CD0FC>90 435 123 134 134 I[87 435 104 134 136 26 D[87 435 104 134 136 I[95 545 85 134 144 32 D[<127F487E7F6C7E6C7E7F6C7E6C7E12076C7E806C7F6C7F6D7E 6D7EA26D7E6D7E806D7F7F6D7F816D7F147F816E7E6E7EA26E7E6E7F8280826E7F80826F 7E153F826F7EA26F7F83816F7FA26F7F838183167F83163F83707FA2707FA2707FA2707F A2707FA2707FA2717EA284838583858385A2717FA2717FA3717FA2717FA28584A2868486 84A2868486A28486A28486A28486A28684A28785A28785A38785A287A28587A38587A373 7FA4737FA47380A48886A48886A388A286A388A386A288A486A288A5747FA7741480A71D C086A61DE0A387A61DF0A587A51DF8A987A41DFCB187A21DFEB3B3B3A31DFCA263B11DF8 A463A91DF0A563A51DE0A698B5FCA31DC0A6621D80A7501400A7505BA564A262A464A262 A364A362A264A36264A497B5FC64A44F91C7FCA44F5BA44F5BA36361A36361A263A26163 A36163A296B5FC98C8FCA26062A26260A26260A26260A2626062A260626097C9FCA295B5 FC61A24D5BA24D5BA34D5BA24D5BA2615F615F96CAFC5F60A24D5AA24C5BA24C5BA24C5B A24C5BA24C5BA24C90CBFC5F167F5F16FF5F5D5F4B5BA24B5B5D5F4B90CCFCA24B5A5E15 7F4B5A5E5C4A5B5E5C5E4A90CDFC4A5AA24A5A4A5A5D14FF495B5D495B5B4990CEFC5C49 5A495AA2495A495A485B485B91CFFC485A120F485A485A5B485A485A5B6CD0FC>95 545 123 134 144 I[94 545 102 134 147 40 D[94 545 102 134 147 I[100 328 75 133 159 48 D[ 100 328 123 133 159 I[<387FFFF0B57EB3B27EA380B3A27EA680AA7EA680A67EA781 A37EA8817EA87E81A77E81A67FA281A47FA381A37FA4817FA5817FA56D80A47F82A47F82 A380A282A380A282A280A282A280A36E7FA46E7FA46E80A38083A28183A38183A281A283 81A28381A28381A36F7FA36F80A28284A28284A282848284A2828482A28482A2707FA271 7FA3717FA2717FA283858385838583A2858385848684A2727F8486848684868486848619 7F737EA2737FA2737FA2737F8587737FA2737F1A7F871A3F747EA2747F747FA2747F8688 747F1B7F881B3F757E8887757F757FA2757F757FA2767E767E1C1F767E89887613807613 C07613E0A2F57FF01D3FF51FE0>100 328 75 136 159 64 D[<99B512E05114F0B3B21E E0A363B3A21EC0A663AA1E80A663A61E00A763A365A86365A86563A76598B5FCA665A262 A465A362A365A4629AC7FCA56264A5505BA46462A46462A364A297B5FCA364A261A264A2 61A299C8FCA34F5BA44F5BA44F5BA36361A26361A36396B5FCA263A26098C9FCA26062A2 6062A34E5BA34E5BA26260A26260A26295B5FC97CAFC5FA2615F61A25F61A24D5BA24D5B A34D5BA24D5BA296CBFC94B5FC605E605E60A25E605E605E60A24C5B95CCFC5E5F16FF5F 5D5F5D5F5D5F4B5BA24B5BA24B90CDFCA24B5A5E15FF4A5BA24A5B5E5C5E4A5BA24A90CE FC4A5AA24A5A5D14FF495B5D5B5D495B5B92CFFC495A495AA2495A495AA2485B485B5C48 90D0FC5A5B485A485A485AA2485A5B6C5A>100 328 123 136 159 I<007FC512E0C5B47EA3A17FA36CA17E02F8CF7E6C6DE2001F826C6DF5003F6C20036EE4 003F806C6E1E076C21006C6E0D3F806F1F0F6C6E0D03806D21006D6D8C6F0E1F7F6D6D8C 6D22036F7A7F6D6E8B6D237F6D6E7A7E70201F6D6E7A7E6E22076E6D2003707A7E6E7F6E 220070217F6E806E6EF83F806E231F836E6EF80FC0816F7F71F807E06F6D9DC7FC816F7F 846F8081846F8082707F84707F82707F85708082857080717F8385717F83717F86718083 718086727F8486727F727F8487728084728087737F8587737F737F8588857391D1FC735B A2745A745A63505AA2505A4F5B4F90D2FC4F5AA24F5A4F5A4F5A4F5A6219FF4E5B4E90D3 FC4E5A4E5AA24E5A4E5A4E5A4E5AA24D5B4D90D4FC4D5A4D5AA24D5A4D5A4D5A4D5AA24C 5B4C90D5FC4C5A4C5A5F041FF907E04C48F80FC04C5A4C5A4B49F81F80A24B90D4123F4B 4822004B48694B4869A15C4B4820014B4820034B48565A4A49200FA24A90D4485A4A4821 3F4A48217F4A4856485AA15A4A48684A48565B4A48203F49499DB55A92D35A4921074948 0E1F5C4948207F49480D03B6FC49480D1F92C7FC57B7FC49481E1F49480B07B75A48490A 3FB8FC4890C4FCA15B5A5A48A15A5AA248A15AC5B4FCA26CA15AABB6767FC0>80 D82 D[<007FC5BB12F0C5BC7EA2A1 87A3A187A26CA18604C0D212076CA0C7001F856C6FF9000F6C6FFA003F701101836CA1ED 001F6C6FA10001826C6FA1EA003F70A10107816CA117016D6FA1EA003F71A1010F806D6F A113036DA10500806D6FA1143F71A1020F7F6DA1846D6FA114016D6FA16E7F71A1153F6D A1737F6E6FA1806E6FA16E7F72A1806EA118006E6FA16F7E72A1153F6EA1737E6E816E6F A16F7E72A115076EA119036F6FA16E7E6F8173A16E7E6FA1197E6F6FA1157F73A181816F 6FA1ED1F806F8173A1ED0FC06FA196C7FC70817081868270818670818270818682718171 818783718171818783718187837281728188847281728188847281888473817381898573 817381898573818973828674818A86748174818A86748174818B8775818B87758175818B 87758175818C8876818C76818876818C887681768168775C775CA2775C775C775C687791 D6FC775B8967535B67535B535B535B655390D7FC535A66535A525B525B64525B665290D7 C6FC525A525A1CFF515B515B65515B515B5190D7C7FC63515A515A64505B505B505B6250 5B5090D7C8FC63505A505A4F5B614F5B634F5B4F90D7C9FC4F5A197F4F5A4E5B624E5B4E 5B4E5B604E90D7CAFC4E5A614E48A1ED0FC04D49A1ED1F804D5B5F4D49A1ED3F004D5B96 D7C95A4D48A116FE4D5A4D48A14B5A4CA117034C5B4C49A14B5A4EA1150F4C49A1151F4C 90D7C9485A4CA1177F4C48A15F4C48A1ED01FF4DA15D4B49A14B5B4B49A15D4B49A15D4B A1057F5B4B49A192B5FC4B90D7C84891C7FC4CA115074B48A1151F4B48A14B5B4A49A192 B5FC4AA116034A49A1020F5C4A49A1147F4CA149B6FC4A90D7C7000F5D4A48A1147F4A48 A10107B75A02FFA1147F4949A1000FB8FC49491103B95A4B1007BAFC494956BCFC4990C5 BA5A5B49A1625BA290C5BCC8FC5A5A48A1625A48A162A25A48A162C5BCFCA26CA162> 242 255 118 127 263 88 D[161 404 118 127 101 90 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj msbm8 8 3 /Fj 3 91 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmsy8 8 17 /Fk 17 111 df<007FBC12F0BD12F8A46C1BF0550674A36E>0 D<0038F001C0007CF003 E000FC18076C180F007F181F6DEF3FC06C6CEF7F806C6CEFFF006C6C4C5A6C6C4C5A6C6C 4C5A6C6C4C5A6C6C4C5A6D6C4B5A6D6C4B5A6D6C4BC7FC6D6C4A5A6D6C4A5A6D6C4A5A6D 6C4A5A6D6C4A5A6E6C495A6E6C495A6E6C49C8FC6E6C485A6E6C485A6E6C485A6E6C485A 6E6C485A92387FBFC06FB45A6F90C9FC6F5A6F5AA24B7E4B7E4B7F92387FBFC09238FF1F E04A486C7E4A486C7E4A486C7E4A486C7E4A486C7E4A486D7E4A486D7E4AC76C7E49486E 7E49486E7E49486E7E49486E7E49486E7E49486F7E49486F7E49C96C7E4848707E484870 7E4848707E4848707E4848707E4848EF7F804848EF3FC090CBEA1FE000FE180F48180700 7C18030038F001C043446BC26E>2 D<15F04A7E4A7EA2815DA7003EEE07C0007FEE0FE0 9026C001F8133FD8FFE0ED7FF001F015FF01FC1403D87FFE4A13E0D9FF81131F001F01C1 491380000701F19038FFFE000001D9F9F913F827003FFDFB13C0010FB6C7FC010314FC01 0014F0021F1380DA07FEC8FC91381FFF8091B512F0010314FC010F14FF90263FFDFB13C0 2701FFF9F913F80007D9F1F813FE001F01C190383FFF80007F01816D13E0D9FE011307D8 FFFC6E13F001F0140001E0157FD87FC0ED3FE090260003FC130F003EEE07C0C792C7FCA7 815DA26E5A6E5A343977BD47>I<17074D7E84B3B3A6007FBD12F0BE12F8A46C1CF0CAD8 0FC0CAFCB3B3A2007FBD12F0BE12F8A46C1CF05D5E78DB6E>6 D<1CF0F303F81B0F1B3F 1BFF080313F0080F138097383FFE00F2FFF8070313E0070F1380DF3FFEC7FCF1FFF80603 13E0060F1380DE3FFEC8FCF0FFF8050313E0050F1380DD3FFEC9FCEFFFF8040313E0040F 1380DC3FFECAFCEEFFF8030313E0030F1380DB3FFECBFCEDFFF8020313E0020F1380DA3F FECCFCECFFF8010313E0010F1380D93FFECDFCEBFFF8000313E0000F1380D83FFECEFCEA FFF813E0A213F8EA7FFE380FFF80000313E0C613F8EB3FFE90380FFF80010313E0010013 F8EC3FFE91380FFF80020313E0020013F8ED3FFE92380FFF80030313E0030013F8EE3FFE 93380FFF80040313E0040013F8EF3FFE94380FFF80050313E0050013F8F03FFE95380FFF 80060313E0060013F8F13FFE96380FFF80070313E0070013F8F23FFE97380FFF80080313 E0080013F81B3F1B0F1B03F300F01C00B3A6003FBC12E0481BF0BD12F8A36C1BF0557274 D86E>20 D<127812FE6C7E13E013F8EA7FFE380FFF80000313E0C613F8EB3FFE90380FFF 80010313E0010013F8EC3FFE91380FFF80020313E0020013F8ED3FFE92380FFF80030313 E0030013F8EE3FFE93380FFF80040313E0040013F8EF3FFE94380FFF80050313E0050013 F8F03FFE95380FFF80060313E0060013F8F13FFE96380FFF80070313E0070013F8F23FFE 97380FFF80080313F0080013F81B3FA21BFF080313F0080F138097383FFE00F2FFF80703 13E0070F1380DF3FFEC7FCF1FFF8060313E0060F1380DE3FFEC8FCF0FFF8050313E0050F 1380DD3FFEC9FCEFFFF8040313E0040F1380DC3FFECAFCEEFFF8030313E0030F1380DB3F FECBFCEDFFF8020313E0020F1380DA3FFECCFCECFFF8010313E0010F1380D93FFECDFCEB FFF8000313E0000F1380D83FFECEFCEA7FF8EAFFE0138048CFFC1278D0FCB3A6003FBC12 E0481BF0BD12F8A36C1BF0557274D86E>I<1D781DFCA3891D7EA21D7FA2898A1D1F8A1D 0F8A1D078A777EA2777E777E8A787E787E787E787E787EF603FE787E7813C0F77FF0F71F FC003FC112804820E0C212F0A26C20E06C2080D2381FFC00F77FF0F7FFC05490C7FC545A F607F8545A545A545A545A54C8FC66535A535AA2535A661D0F661D1F661D3F9BC9FC65A2 1D7EA21DFE65A31D787C4678C38D>33 D48 D<912603FFC0F01FFC021F01FC4DB512C091B66C040F14F0010303F0043F 14FC4903FC93B67E496F03036F7E013F6F6C4AD9FC037F49704A9039C0007FE090B5003F 02F0023F90C7EA0FF048D9E0016EDA7FF86E7E4890C7003F6D4A48EC01FC49020F6D4901 C01400D807F86E6D4949157E484802016E4848C97E496E6E485A48486F6D4848EE1F8049 6F6D4848160F003F706D484817C090C96C4B1607003E706D485A007E7090B5CA13E0711A 03007C705C724918F000FC715B481F01725B727F727F8486727F72804E806C1F034E6E17 E0007C4D804E6E1607007E86003EDD1FF36D17C0DE3FE16D160F003F057F6F151F6CDDFF C06E16806D4B496C6D153F6C6C4B496C6DED7F004D486D6D5D6C6CDB1FFC6D01FE4A5A6C 6C4B486D6DEC07FC6DDBFFF06D02C0130FD801FE4A496D02F8EB7FF86C6C020F496D9139 FFCFFFF0D97FE0013F90C8003F91B55A90283FFC03FFFE6F5E6DB648030793C7FC010703 F06F5D6D03C003005D010092CA001F14F0023F01F805031480020301809426003FFCC8FC 7C3B78B98D>I<041FB612F04BB712F8151F157F4AB8FC020717F0021F01F0C9FC4A90CA FCECFFF04913C04990CBFCEB07FC495AEB1FE0495A495A49CCFC5B485A485AA2485A5B12 0F5B121F5B123F90CDFCA25A127EA412FE5AA3BB12F01AF8A41AF000FCCDFCA37E127EA4 127F7EA27F121F7F120F7F12077F6C7EA26C7E6C7E7F6D7E6D7E6D7EEB0FF86D7E6DB4FC 6D13C06D13F8EC3FFF6E13F0020790B712F0020117F86E7E150F1501DB001F15F0455474 CA5E>I72 D<923801FFFC037FEBFFF00203B612FE021FEDFFC0027F16F049B812FC0107DA 000713FF4901C0D9001F7FD93FFEC8000313E0D97FF09238007FF0D9FFC0EE1FF84890CA EA07FC4848717ED807F8EF00FF4848F07F8049183F4848F01FC049180F003F1AE090CC12 07481AF0007E1903A200FE1AF8481901B3B3B3A3007C190000381A704D5378CF5E>92 D102 DI<127812FCB3B3B3B3B3B3B3A51278068570E327>106 D<007015E000F8EC01F06C1403B3B3B3B3B3B3B3A44814010070EC00E024866FE347>I< 127812F87EA27E127E127F7EA27F121FA27F120F7F1207A27F1203A27F12017F1200A27F 137EA2137F7F80131FA280130FA2801307801303A2801301A280130080147EA2147F8081 141FA281140FA2811407811403A2811401A281140081157EA2157F81A282151F82150FA2 821507A2821503821501A282150082167EA2167F82A283161F83160FA2831607A2831603 831601A2831600A283177E177F83A21880171FA218C0170F18E01707A218F01703A218F8 170118FC1700A2187C1838368578E347>110 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmmi8 8 43 /Fl 43 123 df11 DII21 DII31 D<190F61A461193EA3197E197CA319FC61A3180161A3180361A3180761A3180F61A3181F D901FE93C7121F902607FFC0EF7FC0011F6DEFFFE0496D4A5B496D023E15F09026FF0FFC 5E2701FC07FE18F8D803F0167ED807E0167CA2D80FC084018004FC7F001F010F4B147F01 00193F481A1F003E011F020116F0007E4A4A140F007C1A07143F00FC4A1303027F4B15E0 C7491703A202FF020715074B4A15C0A25B4B010F150F4E15805B4B171F051F16004993C8 5A92C7163E1B7E4D157C49033E15FC4A4D5A63057E1403057C4A5A505A505A6D6C02FC14 3F4D4AC7FC1AFE6F4B5A6D0201EC07F803C049495A6D01E0ED3FE06D01F0ED7F8091267F FC03D903FFC8FC913B3FFF83E00FFE6E01FBEBFFF8020790B612E002015E6E6C4AC9FC03 0F14F8DB003F1380DC0FC0CAFC5FA3161F94CBFCA35E163EA3167E167CA316FC5EA31501 5EA315036F5A55777DDB5C>I<923803FFE0033F13FC4AB61280020F15E0023F15F091B7 12FC4916FE130749EBF0004948C7121FD93FF0EC07FCD97FC0EC01F891C9127001FE1600 EA01F8A25BA21203A312017F913803FFF02600FC3F13FC90B67E7F7FA25B90B65A48486C 13F02603F80713C04848CAFCEA0FC0485AA248CBFC123E127E127CA212FC5AA317076CEE 0F80A26C161F007EEE3F00D87F80157E6C6CEC01FE01F8EC0FFC6CB46CEBFFF86C90B65A 6C5E6C5E6C93C7FC6C5D013F14F0010F14C0010001F8C8FC373F7CBB41>34 D39 D59 D<1CF0F303F81B0F1B3F1BFF080313F0080F138097383FFE00 F2FFF8070313E0070F1380DF3FFEC7FCF1FFF8060313E0060F1380DE3FFEC8FCF0FFF805 0313E0050F1380DD3FFEC9FCEFFFF8040313E0040F1380DC3FFECAFCEEFFF8030313E003 0F1380DB3FFECBFCEDFFF8020313E0020F1380DA3FFECCFCECFFF8010313E0010F1380D9 3FFECDFCEBFFF8000313E0000F1380D87FFECEFCEAFFF813E0A213F8EA7FFE380FFF8000 0313E0C613F8EB3FFE90380FFF80010313E0010013F8EC3FFE91380FFF80020313E00200 13F8ED3FFE92380FFF80030313E0030013F8EE3FFE93380FFF80040313E0040013F8EF3F FE94380FFF80050313E0050013F8F03FFE95380FFF80060313E0060013F8F13FFE96380F FF80070313E0070013F8F23FFE97380FFF80080313F0080013F81B3F1B0F1B03F300F055 5474CA6E>I<1838187C18FCA2170118F8170318F0A2170718E0A2170F18C0171F1880A2 173F1800A25F177E17FE5FA216015FA216035F16075FA2160F5FA2161F5F163F94C7FCA2 5E167EA216FE5E15015EA215035E15075EA2150F5EA2151F5E153F93C8FCA25D157EA215 FE5D14015DA214035DA214075D140F5DA2141F5DA2143F92C9FC5C147EA214FE5C13015C A213035CA213075C130F5CA2131F5CA2133F91CAFC5B137EA213FE5BA212015B12035BA2 12075BA2120F5B121F5BA2123F90CBFCA25A127E12FE5AA25A1278368578E347>I<1278 12FE6C7E13E013F8EA3FFE380FFF80000313E0C613F8EB3FFE90380FFF80010313E00100 13F8EC3FFE91380FFF80020313E0020013F8ED3FFE92380FFF80030313E0030013F8EE3F FE93380FFF80040313E0040013F8EF3FFE94380FFF80050313E0050013F8F03FFE95380F FF80060313E0060013F8F13FFE96380FFF80070313E0070013F8F23FFE97380FFF800803 13F0080013F81B3FA21BFF080313F0080F138097383FFE00F2FFF8070313E0070F1380DF 3FFEC7FCF1FFF8060313E0060F1380DE3FFEC8FCF0FFF8050313E0050F1380DD3FFEC9FC EFFFF8040313E0040F1380DC3FFECAFCEEFFF8030313E0030F1380DB3FFECBFCEDFFF802 0313E0020F1380DA3FFECCFCECFFF8010313E0010F1380D93FFECDFCEBFFF8000313E000 0F1380D83FFECEFCEAFFF813E0138048CFFC1278555474CA6E>I64 DI<4AB912FE4AF0FFF01CFCF4FF806E8691C749C8000F13F0DC3FFC03037F09007F04 7F717E767E4D82761380A204FF7113C05FA34B7213E05FA25213C05D5FA2644B1A805F52 1300644B6194CA485A525A515B4B4D5B4C4C5B515B093F90C7FC033FEF7FFC4C4B485A08 0F13E0087F13804BB848C8FC1BF01BC01BFC92BAFC04F0C8001F13C0080313F008007F4A 727E4C707E757E757F5C4C707FA2757F5C5E89A25C93CAFCA34A625D63A2023F624B5F65 63027F4E90C7FC4B601B7F515A02FF4D5B4B4C5B505B505B49063F5B4B93B5C8FC070313 FC49050F5B011F94B512E0003FBB1280484FC9FCBB12F01A806C06F0CAFC635B7ADA6A> I<4AB912FE4AF0FFF01CFCF4FF806E8691C791C8003F13F0DC3FFE03037F9838007FFE04 7F717E0A0F7F4D707F1C018A04FF717F4D177F777E8A4B191F4D841D0FA24B865F891F80 5D5FA35D4D19C0A35D94CBFCA34B615E1F80A2157F5E65A203FF1B005E65A24A635E1D7F 665C4C4E5AA34A4F5B5E525B664A614C61649BC7FC4A4F5A93CBFC525A525A4A624B4E5A 515B63027F4E5B4B4D90C8FC515AF33FF802FF4E5A4B4C485A505B080F90C9FC49F03FFE 4BEEFFFC070313F049051F13C0011F0403B5CAFC007FBA12FCBB12F01A8007FCCBFC6C18 806A5B7ADA74>68 D<4AB700F80107B712E04A704916F0A24F18E06E4C6D16C091C702C0 C8000391C7FC043F90CA13FC4D60047F5FA24D60A26416FF4D60A2645D4D60A2645D4D60 A2645D4D95C8FCA2645D4D5FA21C7F5D94CA5BA21CFF5D4C60A2634BBAFC65A392BBFC04 F8C900035BA2635C4C60A2635C4C60A2635C4C95C9FCA2635C4C5FA21B7F5C93CA5BA21B FF5C4B60A262147F4B60A26214FF4B60A2625B4B60A24960011F6D047F7F007FB600FE49 B712F8B84982A36C4B6D5E745B7ADA74>72 D<4AB712F84A16FC5CA26E16F891C7ECE000 043F90C7FC5F167FA25FA316FF5FA35D5FA35D5FA35D5FA35D5FA35D94C8FCA35D5EA315 7F5EA315FF5EA35C5EA35C5EA35C5EA35C5EA35C93C9FCA35C5DA3147F5DA314FF5DA35B 5DA25B011F13FC007FB612FEB8FCA36C5D3E5B7ADA3D>I<0403B712F04C16F8A37016F0 93C7003FEBF00006075B6260A262A26097C7FCA36061A3187F61A318FF61A35F61A35F61 A35F61A35F61A35F96C8FCA35F60A3177F60A317FF60A35E60A35E60A301F05CD807F85E 487E487E486C5C605A5E95C9FC48485C5F494A5A5B494A5A6C48495B007EC7485B4B5B6C 4A5BD81FC04990CAFC01F0EB7FFE3A0FFE03FFF86CB65A000115C06C92CBFC013F13F801 0713804D5E77DA4D>I<4AB60407B612E04A6F4B15F0A27219E06E7315C091C76CDD001F EBF000706D040713807748C7FC72705A4C61047D7F66047C6D160316FC4C6C6C5FA2716C 160715014C6C608571170F0303814C6C60851D1F03076D7F04C096C8FC717F65030F6D7F 4C183E187F73157E031F143F93C76D157C847414FC5D033E6E6D5CA2726D1301157E037C 6E6D5CA272150303FC824B6E5E86077F14070201834B61737E1C0F02037013804B617313 C01C1F02077013E04B96C9FC85755A020F824BEFF83EA273EBFC7E141F92CA387FFE7CA2 97383FFFFC5C023E715BA286147E027C715BA302FC834A6186130186010362496C187FEB 1FFE90B56C173F007F02FE60B7171FA36C4A71CAFC745B7ADA70>78 D<4AB912FC4AF0FFC01CF81CFE6E737E91C791C86C7FDC3FFE03077F090113F8047FEE00 7F767E4D707E8904FF831E805F884B1AC0A25FA24B60A25FA25D5213805FA24B1A00644D 5F1C7F4B61525A94CAFC515B4B4D5B654C4C5B091F90C7FC037F4D5AF3FFF84C03035B08 0F13C003FF4BB5C8FC93B812FC1BF01BC04A05FCC9FC1A8004F0CDFCA25CA25EA25CA25E A25CA25EA25CA293CEFCA25CA25DA2147FA25DA214FFA25DA25BA25DA25B011F7F003FB6 12FE4881B8FCA26C5D625B7ADA59>80 D<4AB97E4A18FCF3FFC01CF06E19FC91C791C700 0313FFDC3FFEDA003F7F090713E0047F04017F757F4D707E1C3F8904FF717E5FA2761380 5D5FA2645D5FA34B4E13005F651C7F4B614D16FF65515B4B4D5B94C95C515B5190C7FC4B EF3FFE4C4C5A973801FFF0080713C0037F043F5B4C912607FFFEC8FC93B812F01BC092B8 48C9FC861BC004F8C7003F7F4A04077F4C02017F736C7E747E4A717E5E86885C5EA35C5E A2625C93C9FC99C8FC625C5DA262027F605DA21EE002FFF201F04B16FFA274481303491C E04B19077514C0491B0F011F6D043FEC1F80007FB600FEF03F00B86F6C5B74EB81FE74EB FFFC6C4B6F5CCE14E0093F5BE103FEC7FC645E7ADA6A>82 D<011FBC12FC491BFEA25BA2 92268000079038E00001D9FFF8C74A9038001FFC02E04A1607480180190349C85C491A01 00035E5B4994C813F81207495DA248485EA249157F001F1CF090C95B5A003E16FFA2007E 5F127C4C170300FC1CE0485F0070F301C0C94894C7FCA260A25EA260A25EA260A25EA295 CBFCA25EA25FA2167FA25FA216FFA25FA25DA25FA25DA25FA25DA25FA25DA25FA25DA294 CCFCA25DA25E157F15FF0207EBFFC048B812FE4883A36C5F5F5A7DD952>84 D<001FB76C027FB512FE487091B7FCA24D17FE6C93C86C14FCD8000F01FCC90001140001 0301F09338007FF84BEF3FE049735A645D99C7FC4961A24B173EA249197E1B7C92CBFCA2 4919FC635CA2017F1801635CA201FF1803635CA2481907635CA248190F635CA248191F98 C8FC5CA248611A3E5CA248197E1A7C91CBFCA24819FC625BA2007F1801625BA2190300FF 615BA219076249170F62191F97C9FC61193E197E6161007F17014E5A6D4C5A003F4D5A4E 5A6C6C4CCAFC000F177E6D4B5A00074C5A6C6CED0FF06C6DEC3FE06C01E0ECFFC0D97FF8 010790CBFC6DB4EB7FFE010F90B512F86D15E001011580D9003F01FCCCFC020313C0605E 77DA5F>I98 DII104 DI< 18F8EF03FCEF07FEEF0FFFA25FA318FEA2EF0FFC18F8EF03E094C7FCB2EE7FC0923803FF F04B13FC031F7F4B7FDB7FC11380DBFE0113C04A487EDA03F014E04A5A4A5A5D141F4AC7 FC143E027E5B147C02FC15C05C01015CA290C81480A35E1800A25EA25FA2161FA25FA216 3FA25FA2167FA25FA216FFA25FA25DA25FA25DA25FA25DA294C7FCA25DA25EA2151FA25E A2153FD807C05CD81FF0137F003F5D486C13FF00FF5D4A5B5C5ED9F00F90C8FC4A5A9038 E03FF89038C1FFF06CB55A6C14806C49C9FC6C13F800011380387482D839>II110 D112 D III<153E157F4B7E4A7FA24A5B A45C93C7FCA35C5DA3141F5DA3143F5DA3147F003FB712C04816E0A2B8FC6C16C0C701E0 C7FCA25B5DA35B5DA35B92C8FCA35B5CA3131F5CA3133F5CA3137F5CA313FF4AEB0380EE 07C0160F4816804A131F17005E48153E4A137E167C16FC4B5A4B5A6C4A5A4B5A6CEBC03F DAE1FFC7FC6DB45A6D5B6D5B010713E0010090C8FC2B547DD233>I119 DII<03FFEC01E0020301C013 03020F6D1307023F01F8EB0FC04A7F91B56CEB1F80496EEB3F0049EDC0FE17FF495E495E DAF8015C90271FC000075B4A9038000FC091C8485A4DC7FC010E157E90C95A4C5A4C5A4C 5A4C5A4C5A047FC8FC16FE4B5AED03F04B5A4B5AED3F804BC9FC15FEEC01F84A5AEC0FE0 4A5A4A5A027EC8120E4A151F49485D4948153E4948157E495A49485D49C81201017EED07 F890B500C0131F4802FEEBFFF04891B65A5A60260FF00F5D261FE00392C7FC263F80015C 90C75C007E6E13F048021F5B486E13800078DA03FCC8FC3B3B7BB942>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmsy10 10.95 29 /Fm 29 113 df<003FBF12F8481EFCC012FEA46C1EFC6C1EF86F0871B08E>0 DI<003C1B78007E1BFCB4F201FE6D19036D19076D190F6C6CF1 1FFC6C6CF13FF86C6CF17FF06C6CF1FFE06C6C4E13C06C6D4D13806C6D4D13006C6D4D5A 6D6C4D5A6D6C4D5A6D6C4D5A6D6C4D5A6D6C4C5B6D6D4B5B6D6D4B90C7FC6D6D4B5A6E6C 4B5A6E6C4B5A6E6C4B5A6E6C4B5A6E6C4A5B6E6D495B6E6D4990C8FC6E6D495A6F6C495A 6F6C495A6F6C495A6F6C495A6F6C485B6F01835B6F01C790C9FC6FEBEFFE70B45A705B70 5B705B705B705BA24C7F4C7F4C7F4C7F4C7F9338FFEFFE4BEBC7FF4B01837F4B01017F4B 486C7F4B486D7E4B486D7E4B486D7E4B486D7E4A496D7E4A496D7F4A90C76C7F4A486E7F 4A486F7E4A486F7E4A486F7E4A486F7E49496F7E49496F7F4990C96C7F4948707F494871 7E4948717E4948717E4948717E4849717E48497113804890CB6C13C048487213E04848F1 7FF04848F13FF84848F11FFC4848F10FFE49190749190390CD1201007EF200FC003C1B78 575865D88E>I<191E193F6186B3B3B2003FC012FE488BC21280A46C20006C67CCD87F80 CCFCB3B3AD003FC012FE488BC21280A46C20006C67797A76F88E>6 D<95380FFFF84DB612C0051F15FC94B87E040717F0041F17FC047F9026F8000F13FF4BB5 C86C13C04B01F003077F030F0180030013F8DB3FFCCAEA1FFEDB7FF0EF07FFDBFFC00501 7F0203497113E04A48CCEA3FF0DA0FF8F10FF84A48737E4A48737EDA7F80F100FF4ACE6C 7E4989496D507E496D4F7F6F6190260FEFF0963807FBF890261FC7F896380FF1FC90263F C3FC96381FE1FEDA81FEF13FC049C66C96387F807F017E6D6C4E487E01FE6D6C4D488048 486D6C4D486D7E6F6C4D5A48486D6C4D486D7E496D6C4D48130700076E6C4D4880496D6C 4D481303706C4CC7FC000F6F6C4B4881496E6C4B481401001F6F6C4B4881496E6C4B4814 00706C4B5A003F6F6C4B488190C96C4B48157E716C4AC9FC716C495A48706C4948167F00 7E706C494882716C495A716C495A716C495A716C495A00FE716C48CA13804894263FC1FE 171F95381FE3FC95380FF7F872B45A725B725B725BA24E7F4E7F4E7F95380FF7F895381F E3FC95383FC1FE6C94267F80FF173F007E4D486C6C17004D486D7E4D486D7E4D486D7E4D 486D7E007F4C486D6C5E6C4C486D6C167E4D486D7E4DC86C7E6D4A486F6C15FE001F4B48 6F6C5D4C486F7E6D4A486F6C1401000F4B486F6C5D6D4A486F6C140300074B486F6C5D4C CA6C7E6D4948716C130700034A48716C5C6D4948716C130F6C6C4948716C495A4B48717E 6C6C4948716C495A017E4948716C91C7FC017F49CC6C6C5A90263F81FE96383FC0FEDAC3 FCF11FE190261FC7F896380FF1FC90260FEFF0963807FBF86DB44873B45A4B856D49735B 6D90CE6C5A6D656E6C50C8FCDA3FE0F103FE6E6C4F5A6E6C4F5ADA07FEF13FF06E6C6CF0 FFE002006D4D1380DB7FF0050790C9FCDB3FFCEF1FFE92260FFF80EEFFF8030301F00307 13E06F01FF037F5B6F6C01F8010FB5CAFC041F90B712FC040717F004001780051F03FCCB FC050115C0DD000F01F8CCFC797A76E98E>10 D<003FC012FE488BC21280A46C20006C67 D5FCB3AA003FC012FE488BC21280A46C20006C67D5FCB3AA003FC012FE488BC21280A46C 20006C67795076D48E>17 D<1F78F601FCF607FE1E1F1E7FF503FF0B0F13FC0B3F13F89A B512E00A0314800A0FEBFE000A3F13F899B512C0090391C7FC090F13FC097F13F050B512 C0080791C8FC081F13FC087F13F04FB512C0070791C9FC071F13F8077F13E04EB5128006 0F49CAFC063F13F895B512E005031480050F49CBFC053F13F894B512E0040391CCFC040F 13FC043F13F04BB512C0030791CDFC031F13FC037F13F04AB512C0020791CEFC021F13FC 027F13E049B51280010749CFFC013F13F890B512E000031480000F49D0FC003F13F84813 E0B5128001FCD1FCA2EBFF806C13E06C13F8000F13FE00036D7EC614E0013F13F8010713 FE01016D7E6D6C13E0021F13FC020713FF020114C06E6C13F0031F13FC030713FF030114 C0DB003F13F0040F13FC040313FF040014E0053F13F8050F13FE05036D7E050014E0063F 13F8060F13FE06016D7E726C13E0071F13F8070713FF070114C0736C13F0081F13FC0807 13FF080114C0746C13F0090F13FC090313FF090014C00A3F13F80A0F13FE0A03EBFF800A 0014E00B3F13F80B0F13FC0B0313FEF5007F1E1F1E07F601FCF600781F00B3AA003FBF12 F8481EFCC012FEA46C1EFC6C1EF86F8E71F38E>20 D<123C127FEAFFC013F013FCEBFF80 6C13E06C13F8000F13FE00036D7EC614E0013F13F8010713FE01016D7E6D6C13E0021F13 FC020713FF020114C06E6C13F0031F13FC030713FF030114C0DB003F13F0040F13FC0403 13FF040014E0053F13F8050F13FE05036D7E050014E0063F13F8060F13FE06016D7E726C 13E0071F13F8070713FF070114C0736C13F0081F13FC080713FF080114C0746C13F0090F 13FC090313FF090014C00A3F13F80A0F13FE0A03EBFF800A0014E00B3F13F80B0F13FC0B 0313FEF5007FA2F503FF0B0F13FC0B3F13F89AB512E00A0314800A0FEBFE000A3F13F899 B512C0090391C7FC090F13FC097F13F050B512C0080791C8FC081F13FC087F13F04FB512 C0070791C9FC071F13F8077F13E04EB51280060F49CAFC063F13F895B512E00503148005 0F49CBFC053F13F894B512E0040391CCFC040F13FC043F13F04BB512C0030791CDFC031F 13FC037F13F04AB512C0020791CEFC021F13FC027F13E049B51280010749CFFC013F13F8 90B512E000031480000F49D0FC003F13F84813E0B5128001FCD1FC13F013C06CD2FC123C D3FCB3AA003FBF12F8481EFCC012FEA46C1EFC6C1EF86F8E71F38E>I24 D<4DBA12F8053F19FC0403BB12FE161F167F0303BCFC030F1BFC4B1BF8037F91CDFC4AB5 12E04A49CEFC4A13F8021F13C04A90CFFC4A5AECFFF84913E0495B495B4948D0FC495A5C 495A495A5C495A5A91D1FC485A12075B485AA25B121FA2485AA25BA2127FA25BA312FFA2 90D2FCAC7FA2127FA37FA2123FA27FA26C7EA2120F7FA26C7E7F12036C7E807E6D7E806D 7E6D7E806D7E6D6C7E6D7F6D7F6D13F8EC7FFE6E7E6E13C0020713F86E13FE6EEBFFE06E 6C13FF031F91BA12F86F1BFC03031BFEED007F161F1603DC003F19FC050119F86F6A71E1 8E>26 D<003FBAFC4819F8BC7E1BF01BFCF3FF806C1BE06C87CC000114FCDF000F13FF08 0080093F7F090713F009017F757FF43FFEF40FFF767F767F0A007F777E1D3F777E777E1D 07777E8A897713801FC01E7FF63FE0A21E1F1FF0A2F60FF8A21E07A21FFCA21E03A31FFE A21E01AC1E03A21FFCA31E07A21FF8A21E0FA2F61FF0A21FE01E3FA2F67FC01EFF1F8053 13006566535A1D0F535A535A1D7F535A0A035B525B5290C7FCF43FFEF4FFFC515B09075B 093F13C098B55A080F91C8FC4FB512FC003FBC12F04863BD128009FCC9FC1BF01B806C07 F8CAFC6C96CBFC6F6A71E18E>I33 D<123C127EB4FC7F7F7F6C7E6C7E6C7E6C 7E6C7E6C7F6C7F6C7F6D7E6D7E6D7E6D7E6D7E6D7F6D7F6D7F6E7E6E7E6E7E6E7E6E7E6E 7F6E7F6E7F6F7E6F7E6F7E6F7E6F7E6F7F6F7F6F7F707E707E707E707E707E707F707F70 7F717E717E717E717E717E717F717F717F727E727E727E727E727E727F727F727F737E73 7E737E737E737E737F737F737F747E747E747E747E747E747F747F747F757E757E757E75 7E757E757F757F757F767E767E767E767E767E767F767F767F777E776C19C0776CF001E0 776C19F0776CF003F8776DEF07FC777F776DEF0FF8787E786CEF1FF0786CEF3FE0787E78 6C18C0786D167F786D1780786D16FF796C1700796C5D797E796C5E796C1503796D5D797F 797F7A6C14077A6C5D7A7E7A7E7A7E7A6D495A7A7F7A7F7B7E7B7E7B7E7B7E7B6C5C7B13 807B13C07B13E0FA7FF0FA3FF8FA1FFCE80FFE7FFA07FF7C138F7C13CF7C13EFFB7FFF8F 8F7D7F8F8F0F1FB6FC0E03B77E203F55B8FC0D07831F1F9CB9FC54DBC07F7F0C0702E0C7 7E0C1F49C8000713805401E015009BB50080161F5301FCCAEA07000DF094C7FC7713C078 CDFC1E3E1E18A6A676FDB6>38 D<922607FFC0F3FFF0037F01FE081F13FF4AB600C096B6 12E0020703F0060315F8021F03FE060F81027F6F063F15FF91B800C094B87E4905F04CDA 80037F4971040701FCC76C7E4905FE4C01E0EC1FF049D9E0076E4C0180EC07F84948C76C 6E4B48C8EA01FCD93FF8021F6EDB7FF86F7ED97FE0020702F0DBFFE0167F494802016E4A 49707E91C96E4A49707E4848706D4A90CA120F4848041F6DDA0FFC717E49706E495A4848 706E4948717E724C4817014848706E49488449706E48491700001F7201F88749716D4890 CC127C5248197E48CB6C6D485A7301FF1B3E003E72EC9FF8007E72DAFFF0193F5385007C 84735D8600FC521A80487391CD120F86867480A2748074807480A2757F89896C97B6191F 007C4F1D008A50817860007E61003EDF0FFC6E183E50486C6D187E003F757F50486C6D60 6CF17FE06D4E486C6D1701000F756E5F6D4D496C6E160300074E496C6E4C5A6D4D48826C 6C4D486D6E4C5A4F486E6D161F6C6CDD7FF06E01FF4C5A6D4D486E6E4B5A6C6C4C496E6E EC01FF017F4C496E02F04A90C7FC6D6C030F90C8000102FCEC0FFE6D6CDB3FFE6F02FFEC 3FFCD90FF0DBFFFC709139F003FFF8D907FC0203497091B65A6DB4021F49040F5F6D01E0 90B500C0705F6D90B74804015F6E4BCB6C93C8FC021F03F87215FC6E03E0060715F00203 0380060115C0DA007F01FCCD003F91C9FC03070180080113F0A15276CFB6>49 D<4DB8FC053F17800403B912C0161F167F0303BAFC030F1980033F19004B91CBFC4AB512 E04A49CCFC4A13F8021F13C04A90CDFCEC7FFC4A5A4913E0495B495B4948CEFC495A5C49 5A495A5C495A5A91CFFC485AA2485AA2485AA2485AA25B123FA25B127FA25BA312FFA290 D0FCA290BDFC1D801DC0A41D801D0090D0FCA27FA2127FA37FA2123F7FA2121F7FA26C7E A26C7EA26C7EA26C7E807E6D7E806D7E6D7E806D7E6D6C7E6D7F6D7F6D13F86E7E6EB4FC 6E13C0020713F86E13FE6EEBFFE06E6C13FF6F91B8FC030F1980030319C0ED007F161F16 03DC003F1780050117005A6A71E179>I[91 170 103 257 0 54 D<191E193F4F7EB3B3B3B3B3B3 A4003FC1FC482080C212C0A46C20806C20007A7A76F98F>63 D<942601FFF0F207C0053F 01FCF23FE00403B61A7F041F6F953801FFC093B76C60030365030F704E1380033F6592B8 6C4E13005C0207664AD9FC0364023FEB8000DA7FFCC76C1AFFDAFFF06E63010301C06449 49804990C84A61494865494867495A49486548695C48494B61484F614A655A4890C96449 66123FD87FF84E96C7FC494C61EAFFC0496700FCCA1AFFCBFC97CB5B95B55FA269676169 4D61A261555BA25F555B61A24D636761A25590C8FC4D5BA2555AA24D5B047FBCFC4BBD5A 1507151F5D4B6492BEFC5CA24A656E1BE791C849CA1207664C4961A34E5F4C63A34C495F 68A24C5B66A24E96C9FC5E9BB5FC605EA295CB5B4C60A25F16FFA24D614B61A25F5DA25F 4B614D61FA01FC4B1E074D1C1F223F4BF67FF84DF301FF4B4F17F094CB4C13E0795B4B1F C04C741580796CB5120003FF99B55A4C1DF84A49654C654C7216804A4952C7FC93CC6C15 F84B1DE003F87392C8FC91CF6C13F8E41FFEC9FC8E857DFB9A>72 D<07F8ED3FFFDE07FC0203B512F0060F031F14FCDE3FF891B7FCDEFFF0010316C04D4901 0F16F0050749013F824D49498294273FFE0001B87EDD7FF849834D48010F84040301C049 EB803F4C4990273FFC0003814C90C7D8FFF0010081DC1FFC4949143FDC7FF84949020F80 4C484949804B494990C86C804B494948814B4949486F804B90C74848824B4814FF4B484B 707F4B484949824B48495B4A4949844A4D844C49844A494990CAFC4A90C75B4A48023F84 023F4B481A805D4A484A5A02FF884B495B495D49495D4B5B49894949495B614990C75A96 CCFC494B5A49485D18F04948EC7FC071CDFC4893CE14005CA25A5C5AA24A525B5AA35A4A 66A24866A269A25C48545BA36967A2B5676769A25590C7FCA2681F7F681FFF6E65666854 5BA2545B6E65666C9CC8FC545A6E1B3F67545A6E515A6C525B6E62676E505B6C5290C9FC 6E505A535A6C6E4F5A6F4F5A6C515B6F4E5B6C6E4E5B6F4E48CAFC6C6EF03FFC6F4E5A6C 6E4D485A04C04C13C06D6E040F5B6D02F8DC3FFECBFC04FEEEFFFC6D6E6C020713F06D03 F0023F5B6D9226FF800FB512806D93B7CCFC6D19FC6D19F0023F18C06E95CDFC020717FC 020117E06E6C93CEFC031F15F003031580DB001F01E0CFFC818475FF91>79 D<003CF403C0007EF407E0B4F40FF0B3B3B3B3A46D1B1FA2007F1DE0A26D1B3FA2003F1D C06D1B7FA26C6CF3FF806D62000F1D006C6C505A6D1A076C6C505A6C6D4F5A6E193F6C01 F0F1FFF06D6C4E5BD93FFE06075B6D6C4E5B6D01C0053F90C7FC6D01F0EFFFFE6D01FE04 075B01006D6C031F13F06E01F84AB55A021FD9FFE0017F14806E91B8C8FC020318FC0200 18F0031F178003074CC9FC030016F0040F92CAFCDC003F13C0647176EC79>91 D<94383FFFC0040FB6FC93B712F0030716FE031F707E92B912F0020318FC020F18FF4A91 26E0007F80027F01F8C7000114E091B50080DA001F7F010349C9000713FC4901F004007F 4901C0EF3FFF4990CB000F7F4948727FD97FF806017F4948727F4801C0F13FF84A191F48 90CD6C7E4848747E491A034848747E001F1D8049864848F37FC0A2491B3F007F1DE0A249 1B1FA200FF1DF0A290CF120FB3B3B3B3A4007EF407E0003CF403C0647176EC79>I[<9538 01FF80067F13C00503B5FC171F057F14804CB5EAE000040749C7FC4C13F04C13C04C90C8 FC4C5A4C5A4B13F05D4B5B5F5D5FA25D94C9FCB3B3B05D5EA2157F5E15FF5E4A5B4A5B4A 5B4A5B023F90CAFCECFFFE01035B011F13F048B55A007F1480B500FCCBFC14E014FC6CEB FF80000114E0D8001F7F010313FC01007FEC3FFF020F7F6E7F6E7F6E7F6E7F82157F8215 3FA28281B3B3B08381A28381836F7F816F13FC707E707E7013C07013F07013FE0401EBFF E0706CEBFF80051F14C01703EF007F06011380>66 181 116 263 91 102 D[66 181 116 263 91 I[<161E163FEE7F80A216FFA217005DA25E1503A24B5AA25E150FA25E151FA24B5AA2 5E157FA24B5AA293C7FC5CA25D1403A24A5AA25D140FA25D141FA24A5AA25D147FA24A5A A292C8FC5BA25C1303A2495AA25C130FA25C131FA2495AA25C137FA25C13FFA24890C9FC A25B1203A2485AA25B120FA25B121FA2485AA25B127FA25B12FFA4127F7FA2123F7FA26C 7EA2120F7FA212077FA26C7EA212017FA26C7FA2137F80A2133F80A26D7EA2130F80A213 0780A26D7EA2130180A27F81A26E7EA2143F81A26E7EA2140F81A2140781A26E7EA21401 81A28082A26F7EA2153F82A26F7EA2150F82A2150782A26F7EA2150182A2811780A2167F A2EE3F00161E>41 182 109 263 71 I[<123C127EB4FCA27FA2127F7FA2123F7FA26C7E A2120F7FA212077FA26C7EA212017FA26C7FA2137F80A2133F80A26D7EA2130F80A21307 80A26D7EA2130180A26D7FA2147F81A2143F81A26E7EA2140F81A2140781A26E7EA21401 81A28082A26F7EA2153F82A26F7EA2150F82A2150782A26F7EA2150182A2811780A41700 5DA25E1503A24B5AA25E150FA25E151FA24B5AA25E157FA24B5AA293C7FC5CA25D1403A2 4A5AA25D140FA25D141FA24A5AA25D147FA25D14FFA24990C8FCA25C1303A2495AA25C13 0FA25C131FA2495AA25C137FA25C13FFA24890C9FCA25B1203A2485AA25B120FA25B121F A2485AA25B127FA25B12FFA290CAFCA2127E123C>41 182 118 263 71 I[<123C127E12FFB3B3B3B3B3B3B3B3B3AF127E123C>8 181 107 263 51 I[<003CED03C0007EED07E0B4ED0FF0B3B3B3B3B3B3B3B3B3B0007EED07E0 003CED03C0>44 182 105 263 91 I[<123C127EB4FCA27FA2127F7FA2123F7FA2121F7F A2120F7FA26C7EA212037FA212017FA27E80A2137F80A26D7EA2131F80A2130F80A21307 80A26D7EA2130180A27F81A2147F81A2143F81A26E7EA2140F81A2140781A2140381A214 0181A26E7FA2157F82A2153F82A2151F82A2150F82A26F7EA2150382A2150182A28183A2 707EA2163F83A2161F83A2160F83A2160783A2707EA2160183A28284A2177F84A2173F84 A2717EA2170F84A2170784A2170384A2170184A2717FA2187F85A2183F85A2181F85A272 7EA2180785A2180385A2180185A2841A80A2F17FC0A2193F1AE0A2191F1AF0A2190F1AF8 A219071AFCA21903A2F101F8F100F0>70 181 118 263 91 110 D<233C237E23FFA26AA2FA03FEA2FA07FCA2FA0FF8A2FA1FF0A2FA3FE0A2FA7FC0A2FAFF 80A2571300A26A2103A2575AA2575AA2575AA2575AA2575AA2575AA25690C7FCA2565AA2 565AA2565AA2565AA2565AA2565AA2565AA25590C8FCA2555AA2681F07A2555AA2555AA2 555AA2555AA2555AA25490C9FCA2545AA2545AA2545AA2545AA2545AA2545AA2545AA253 90CAFCA2535A814A6C4F5AEC07E0020F634A6C190F147F4A6C4F5A5B0107515A497F4951 5A017F7F90B5505A4880D803F85090CBFCD80FF08048486C4F5AD83F808048486C4F5A12 FE486F4D5A00707FC76E4D5A80704D5A80704D5A80525A826E4E90CCFC826E4E5A836F4D 5A836F4D5A836F601B1F836F4D5A836F4D5A836F4D5A836F4C90CDFC836F4C5AA272495A 8272495A8272495A8272495A8272495A82505A84704A90CEFC18FE704A5A18FF704A5A19 8771EB8FF8A2F1DFF083F1FFE083A2715CA2715CA27191CFFCA26183618361187F61183F 61181F61725A90B7748798>112 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn cmmi10 10.95 60 /Fn 60 123 df11 D<973807FF80087F13F80703B512FE070F6E7E073F15E09626FFFC037F4E 9039C0003FF84E48C7EA0FFCDE0FF86E7EDE1FE06E7E4E486E13804EC913C018FE4D48EE 7FE04D5A4D4817F04D48163F4D5A4D4817F895CAFC177E17FE4C5A5F16035F4C5A040F18 7F5F161F4D18F0043F18FF94CBFC5E047E4D13E016FE4C19C00301604C19806403031A00 4C5F6503074E5A4C4D5A65030F187F4C4D5A515B031F4D5B95280FFFF00FFEC7FC4C90B6 485A4DEDFFF8033F495E4C4816C09526F8007F90C8FC95B77E4B84037E6D82719138FE3F F0DD003F9038E01FF803FE91C86C7E4B717E88870201864B8389870203865DA289020719 7F5DA289140F5DA3141F5D1CFFA2143F92CCFCA34A4E5B147EA302FE605C65A201016165 A24A4E5B13035190C7FCA264496C183F64515A1BFF010F626E4D5B505B64496C4D90C8FC 02BF4D5A6F4C5A029F4D5A013F6D4C5ADA0FE04B485A4F5BDA07F8030F5B496C6CDB3FFE C9FC90267E01FEEDFFFC6E6C6C010313F0DB7FF0013F13C001FE6DB7CAFC49010F15FC03 0315F0030015800001031F01F8CBFC49DA0030CCFC94CDFCA212035BA312075BA3120F5B A3121F5BA3123F90D1FCA35A127EA312FE5AA4127865A37DFF67>I<923803FF80033F13 F092B500FC173C020302FF177E020F6F16FE4A6F16FC027F6F150191B76C16F849824970 1503497016F0491A07497016E04971140F49D9C00018C04948C7001F6D141F4801F80207 178002E002016D143F4801806E17004848C9D83FF05C49041F157E48481AFE49706C5C48 480407140149706C5C485A0601140348CA6D5C06001407007E6300FE067E130F48067F5C 1B1F735C1278CCEB803F99C7FC071F5B1B7EA2F2C0FE63F10FC163A21AC3631AE7631907 1AEF631AFF63A398C8FCA362A362A362A362190FA262A362A2191FA34F5AA4197FA297C9 FC61A44E5AA44E5AA3180761A44E5AA44E5AA461183FA261A296CAFCA2181E180C5F777D CF5E>I[<18F094381FFFE094B6FC4C15F0040715FF4C16804C16C0DC3FF015E093387F00 0F047E13034C7F4B486D7E854C020F13C003036F138007011300F1007E97C7FCA282A382 A282A26F7EA283A26F7F83A2707E83A2707E83161F8384707FA2707F84707F848284707F 855E040F80047F804BB6FC0307814B138F92263FFE0F7F92387FF807912601FFE0804AEB 80034A0100804A487FDA3FFC81EC7FF04A487F5B49496E7F5D4990C8FC4982495A494883 84495A13FF5C48835C5A485BA3485BA24890C95CA35A5BA3007F96C7FC5BA34E5A5B12FF A24E5AA361187F6C5A6118FF6D5FA24D5B123F4D5BA26C6C94C8FC4D5A120F6D4B5A0007 4C5A7F6C4C5A6C6D4A5A6C6D4A5A6D6C5D6D6C010390C9FCD91FFC495A6DB4EB1FFC6D90 B512F001015D6D1580021F49CAFC020313F8DA0006CBFC>75 133 122 257 81 I21 DI<03FFEF01F8010FB56CEE03FC0007B6EF07FE4892CA120FF31F FF5AF33FFE5D7ED80003197F01001AFC6E5A1BFF02FF19F8A24B5E1CF05B624B18E06249 1AC0A24B4C1380A2494E1300A24B4C5AA2494E5A634B16FF4F5B49616192C9485B63495F 4F90C7FC4A5F4F5A017F177F624A4C5A4E5B01FF4C5B4E5B4A4B90C8FC61484D5A4E5A4A 4B5A4E5A484C5B4D5B4A4A90C9FCEF1FFE484C5AEF7FF04A4A5A04035B484B5B4C48CAFC 4AEB3FFCEE7FF0484A485A030713809126001FFECBFCED7FFC48903801FFF0020713C0D9 FE1F90CCFCECFFFC48B512F015804ACDFC14F0B5128001FCCEFCEA7FC0585078CF5A>I< 18E04D7E1703A3170760A9943903F7FFFE95B612C0050F15E0057F15F04CB712F80407EC 000F041F91B512F0167F93B5001F14E00303D9FC0F14804BD9F803EBFC004B01E0C9FC4B 5B037F5B92B5CAFC5E4A5B5C4A5B4A5B5C5E5C5E5C5E91B5FC93CBFCA25BA25DAB7FA26E 7EA28082806E9039C07FFFE06E01E7B512FC6E90B67E6E82806FEBC00094B6FC92B75A02 035E912607FE3F5C91260FFC011480DA1FF0CBFCEC7FE0ECFF804990CCFC495A495A495A 5C495A495A137F495A91CDFC5A485AA2485AA2485AA2485AA3485AA3127F5BA27F12FFA4 7FA27F6C7E7F7F806C13E014F86C13FE6E7E6C14F06C14FC6CECFF806C15E06C15FC6DEC FF806D15E06D15FC6D15FF010316E0010016F8023F15FF020F16C0020182DA003F81030F 810301816F6C80040F801603EE007F050F801703EF007F181F8484A27290C7FCA361A203 1C4A5A153EDB7F80495ADB3FE05CDB1FFC495A923A0FFFC07FC0030390B55A030092C8FC 043F5B040F13F8040013C04DA47CFE50>I31 DI34 D39 D58 DI<1F78F601FCF607FE1E1F1E7FF503FF0B0F13FC0B3F13 F89AB512E00A0314800A0FEBFE000A3F13F899B512C0090391C7FC090F13FC097F13F050 B512C0080791C8FC081F13FC087F13F04FB512C0070791C9FC071F13F8077F13E04EB512 80060F49CAFC063F13F895B512E005031480050F49CBFC053F13F894B512E0040391CCFC 040F13FC043F13F04BB512C0030791CDFC031F13FC037F13F04AB512C0020791CEFC021F 13FC027F13E049B51280010749CFFC013F13F890B512E000031480000F49D0FC003F13F8 4813E0B5128001FCD1FCA2EBFF806C13E06C13F8000F13FE00036D7EC614E0013F13F801 0713FE01016D7E6D6C13E0021F13FC020713FF020114C06E6C13F0031F13FC030713FF03 0114C0DB003F13F0040F13FC040313FF040014E0053F13F8050F13FE05036D7E050014E0 063F13F8060F13FE06016D7E726C13E0071F13F8070713FF070114C0736C13F0081F13FC 080713FF080114C0746C13F0090F13FC090313FF090014C00A3F13F80A0F13FE0A03EBFF 800A0014E00B3F13F80B0F13FC0B0313FEF5007F1E1F1E07F601FCF600786F6A71E18E> I[<1AF0F101F8F103FCA21907A21AF8190FA21AF0191FA21AE0193FA21AC0197FA2F1FF 80A21A0060A2611803A2611807A261180FA24E5AA261183FA261187FA26118FFA24D90C7 FCA2601703A2601707A260170FA260171FA24D5AA260177FA26017FFA295C8FC5EA25F16 03A24C5AA25F160FA25F161FA25F163FA25F167FA24C5AA294C9FC5DA25E1503A25E1507 A24B5AA25E151FA25E153FA25E157FA25E15FFA24A90CAFCA25D1403A25D1407A25D140F A25D141FA24A5AA25D147FA25D14FFA292CBFC5BA25C1303A2495AA25C130FA25C131FA2 5C133FA2495AA25C13FFA291CCFC5AA25B1203A25B1207A2485AA25B121FA25B123FA25B 127FA25B12FFA290CDFCA2127E123C>70 181 118 263 91 I<123C127FEAFFC013F013 FCEBFF806C13E06C13F8000F13FE00036D7EC614E0013F13F8010713FE01016D7E6D6C13 E0021F13FC020713FF020114C06E6C13F0031F13FC030713FF030114C0DB003F13F0040F 13FC040313FF040014E0053F13F8050F13FE05036D7E050014E0063F13F8060F13FE0601 6D7E726C13E0071F13F8070713FF070114C0736C13F0081F13FC080713FF080114C0746C 13F0090F13FC090313FF090014C00A3F13F80A0F13FE0A03EBFF800A0014E00B3F13F80B 0F13FC0B0313FEF5007FA2F503FF0B0F13FC0B3F13F89AB512E00A0314800A0FEBFE000A 3F13F899B512C0090391C7FC090F13FC097F13F050B512C0080791C8FC081F13FC087F13 F04FB512C0070791C9FC071F13F8077F13E04EB51280060F49CAFC063F13F895B512E005 031480050F49CBFC053F13F894B512E0040391CCFC040F13FC043F13F04BB512C0030791 CDFC031F13FC037F13F04AB512C0020791CEFC021F13FC027F13E049B51280010749CFFC 013F13F890B512E000031480000F49D0FC003F13F84813E0B5128001FCD1FC13F013C06C D2FC123C6F6A71E18E>I[124 130 122 257 136 65 D<4BBCFC4B1BF81FFF20E04B1CF88C6F1CFF92C7001F91C9001F 80050301FC0403800C00800D3F7F4F717F797F797F5F4F717FA27914805F618B22C05F61 A35F61A34D4F148096CBFCA2220094B56060555BA24C505B4E6267555B4C644E4E5B9CB5 5A5491C7FC4C4F5B4E4D5B545B545B4C077F13C04E94B55A0B0349C8FC0B0F13F84C063F 5B4E4BB512800A1F49C9FC95B912F04C1980A21EF81EFE4C0180C9EBFFC095CA001F13F0 0B077F7713FE93B505007F4D727F787F8C4B747F5F787FA24B747F5F8C8A5D4D86A35D5F A35D5F66A24B645F66685D94CC5A686692B5634C619BB55A684A624C4E5C5391C8FC535B 4A505B4C4E5B659AB512E04A4F5C4C05075C5291C9FC4A073F5B51B512F84A4904075C49 B56C047F14C0003FBECAFC481CFC1DF0BE12C052CBFC1CE06C08FCCCFC827C79FB8A>I< E17FFF1607081FB500F0ED0F804FB600FEED1F00070F6F6C5C077F04E05C4EB800F85C06 0771495A063FDAF8006D130395B6C7D80FFF13074D02F00201EB800F050702806E6C6C48 5A051F49C9383FE03F4D01F893380FF07F94B500E0933807F8FF4C0280DC03FD5B040749 CA6CB5FC4C13F84C4983047F01C0725B93B55A4B91CC7E4B5B4B01F8735B4B5B4B49854B 5B4B496392B5CD7E5C4A5B4A49644A5B4A4986A24A4999C7FC4A5B91B5FC5E49664991CE FC5D5B494964A2495BA24949645B5D90B51C07A2484A755A9CC9FC5D5AA24891D3FCA348 5BA35A5CA35A5CA35A5CA55CA3B5FCA3F601E0547E5C1E076C66A21E0F67A21E1F676E1B 3F6C9BC9FC661E7E1EFE6C651D016E505A7E535A6E505A7E535A6C6D505A53CAFC6C6D1A FE6C1B016E4F5A6D6D4E5A6D505A6F4E5A6D6DF07FC06D6D4E5A6D6D4D90CBFC6D6DEF07 FC6D6DEF1FF86D6D6C4C5A6E01E0EEFFE06E01F8030713806E01FE031F90CCFC0207D9FF C0903801FFFC6E02FE011F13F0020091B75A033F1780030F04FCCDFC030316F0DB007F15 80040F02FCCEFCDC007F1380818477FF82>I<4BBCFC4B1BF01FFF20C04B1CF020FC6F1C FF92C7001F91C96C80050301FC0407800C0014F00D3F7F4F050F7F797F0D017F4D854F72 7F7A7F7A7F4D864F868C7A7F5F4F727FA28E4D864F86A28D5F96CD1480A394B5FC4E1CC0 A35E60A35E60A35E60A34C99B5FC60A35E4E61A223805E6068A24C1E0095CDFC68A293B5 645F686A5D4D626AA24B525B5FA2565B5D4D649DB5FC6A4B634D99C7FC69674B654D6155 5B694B634D63555B555B5D94CDB5C8FC545B545B92B5634C4F5B545B545B4A515B4C4F90 C9FC545A0B035B4A505B4C4E5B0B3F5B5313804A4FB5CAFC4C05075B0A1F13F84A077F13 E00903B55A4A49041F91CBFC49B56C0303B512FC003FBD12F0481CC09ACCFCBD12F81CC0 09FCCDFC6C1A808A7C79FB97>I<4BBF12C04B1EE0A25DA38192C7001F0280C9FC050349 CA1203E5007F13C04F181F20074D868C618C5FF97F8061A25F213F61A25FA24F1A00A25F A261A294B5FC6996CD127E1D1F4C4E7E9BC8FC60A24C600B7E153C4E97C7FCA24C18FE65 4E1501A24C1703654E15071C0F4C171FF47FF04EEC01FF1B1F4C90B8FC65A35E65A20680 C7123F93B51503755B95C9FC1C7F5D9ACBFC5FA25D1C7E5FF807C04B06FE4B7E525E5F20 1F4B05015F52153F4D98C7FC755A4B95C95A207E4D1AFE684B1B01A24D4F5AA24B515AA2 4D190F6892B51A1F6894CD123F555A5C1FFF4C4F90C8FCA24A515A1E074C190F545A4A1B 7F545A4C18031D0F4A083F5B52B5FC4A49050F5C49B56C0403B6FC003FBFFC4866A2C05A A36C9BC9FC837B79FA86>I<98263FFF80ED0380080FB500F8ED07C097B7ED0F80070704 C0141F073F04F0143F4EB86C147F060705FEECFF00061F9127F8007FFF5B067F91C70007 6D5A4DB500F802016D5A050702C06E6C6C485A051F49C9381FF01F4D01F893380FF83F94 B500E0933803FC7F4C0280706C485A040749CA90B5FC4C49834C01F0844C49725B93B512 804B91CC7E4B5B4B49735B4B13F04B5B4B49854B496392B5FC4A91CD7E4A5B4A49644A5B 8B4A5B4A49644A5B91B5FC5E499CC7FC4991CEFC5D5B494964A2495BA24949645B5D90B5 1C03A2484A755A9CC9FC5D5AA24891D3FCA3485BA35A5CA35A5CA35A5CA55CA298B600E0 B512C0B54E92B67EA269A374606C49DE000192C8FCE2001F13F8775BA265A26E64A2656C 66A3656C6680A26C99B5FC806C9BC9FCA26E617E6C6D63A26C6D61666D6D606D6D60816D 505B6D6D606D01FC606D6D4DB5FC6D6D4D486C5A6D02C0EE0FFC6E01F093383FF83F6E01 FCEEFFF0020F01FF0307496C5A6E02F0023FEB800F6E02FF0107B5EA0007020092B600FC 1303033F05F01301030F05C06D5A03034CCDFCDB007F15F0040792CEFCDC003F13C08284 77FF8F>71 D<4BB5D8FC1FB500C0010FB500E0B512FE4B91B76C4991B7FCA34B4E4917FE A26F4E6D17FC92C7001F02F0CAED8000050391CB001F01F8C7FC4F62A24F62A2685F4F62 A2685F4F62A29DB5FC5F4F97C8FCA2675F4F61A2675F4F61A26794B5FC96CB5CA2675E4E 62A2675E4E62A2675E4E62A2675E4E62A29CB5FC5E4E97C9FC95BCFCA25E68A35E0680CA 00035BA26693B5FC95CB5CA2665D4D62A2665D4D62A2665D4D62A2665D4D62A29BB5FC5D 4D97CAFCA2655D4D61A2655D4D61A26592B5FC94CB5CA2655C4C62A2655C4C62A2655C4C 62A24A62A24A97B5FC49B6050F14F8003FB800F849B912C048714984A2B9484960A36C02 074A6DDAF83F5C987C79FB97>I<4BB5D8FE0FB512F04B91B712F8A21CF0A36F18E092C7 000F02F8C7FC0501148097C8FCA261A35F61A35F61A35F61A35F61A35F61A35F61A394B5 FC96C9FCA35E60A35E60A35E60A35E60A35E60A35E60A35E60A393B5FC95CAFCA35D5FA3 5D5FA35D5FA35D5FA35D5FA35D5FA35D5FA392B5FC94CBFCA35C5EA35C5EA25CA25C91B6 7E003FB812FC4883A3B9FCA26C02835C557C7AFB50>I<063FB539FC1FFFF84E91B612FC A57217F895C7003FECE000080191C7FC64A264A262A264A262A264A262A264A262A264A2 62A264A262A299C8FCA297B5FCA263A261A263A261A263A261A263A261A263A261A263A2 61A263A261A298C9FCA296B5FCA262A260A262A260A262A260A262A260A262A260A262A2 013C5E48B47E00076D5F487F486D5D4896CAFCA25A95B5FCB55F5F61A24A4A5B5C4D5B4A 4A5B91C85C01FC5D494B5B90C991CBFC6C4C5A6D4B5A003F4B5B6D4A5B6C6C020F5B6C6C 4A1380D807FC027F90CCFC6CB4903801FFFC6CD9F00F5B6C90B612E0013F15806D02FCCD FC010314E09026003FFECEFC668074FB65>I<4BB5D8FC1FB500C0031FB538C3FFC04B91 B76C4B91B512E0A2A113C05D646F4E6F168092C7001F02F0CA0001EDE000050391CC6C01 FCC7FC4F1BE023804F50C8FC22F8F9FFE04D5013804F4E90C9FCF807FC565A4DF21FE04F 4E5A0EFFCAFC555A4D4F5A4FEF0FF0555A555A4D4F5A4FDC01FECBFC545A545A4DF01FE0 4F4C5A545A54CCFC94B5EE03FC96C9485A535AF53FC04C4E5A4E4CCDFC525AF407F84C4D 5A4E4B5AF47F8052CEFC4C4C5A4E4A5AF30FF81B1F4C4C7E4E14FF62507F4C5D4E011F7F 6250804CEC01FE4E485A4F486C7FF10FF04CDA3FC0804E48487EDFFF0080DE83FC7F93B5 EA87F84E486D7F4E5ADE7F80814B4AC77E4E8206F880604B4A824E8095C8814D814B5B4D 707FA28A4B844D8488A24B727F5F8A884B864D82A28A4B844D8588A292B5727F94CBFC8B 894A884C84A2777F5C4C86898B4A865E8B4A5080A24A5014E049B6067F14FC003FB800F8 033FB712FC48714B82A2B9FC4E92B8FCA26C02074A6F02075B9B7C79FB9B>I<4BB5D8FC 0FB512FE4B91B8FCA2645DA26F6092C7001F02FCCAFC050314804FCBFCA261A35F61A35F 61A35F61A35F61A35F61A394B5FC96CCFCA35E60A35E60A35E60A35E60A35E60A35E60A3 5E60A393B5FC95CDFCA35D5FA35D5F1F7C1FFE4B1BFC5F1E011FF85D4D18031FF01E075D 4D19E01E0F1FC04B1A1F5FF63F80A24B1A7F4D190066A292B54E5A94CBFC535A1D074A1A 0F4C611D1F1D3F4A505A4C18FF640A075B4A614C053F5B99B5FC4A1803091F5C4A4993B6 FC49B56C151F003FBEC7FC5AA2BE5AA36C646F7C79FB7C>I<4BB70507B5380FFFFE4B70 4C91B6FCA2864B5116FE866F7516FC92C70007DF000FECFC0005016E050114C07A6C90C7 FC4D6EF03FFC7B5A6A74615F06F36D61A2213FDD0FF17F06E16306E080217F171F4E6C6D 95C8FCA2736D5F173F068062737F2001057F6D7F060062A2736D16035F4D6D6D5FA22007 04016E7F4D637380200F16034D6E6D5EA2746D151F16074D63747F203F040F6F7F4D63A2 746D157F161F4D6E6D93C9FCA268043F6F7F4D6274801F01167F94C96C6D5CA2756D1303 5E4C63757F1F070301717F4C63A2756D130F15034C706D5CA21F1F0307717F4C63751480 1F3F150F4C7101C05BA276EBE07F151F4C98CAFC7613F067033F727F4C62A27613FD157F 93CB6CEBFFFCA34B844B6388A214014B735BA28914034B6389140789020F64141F4A6C85 ECFFFE01036D6C725B013F14F0003FB712F04870839CCBFCB84883A36C01F04A187E987C 79FB92>78 D<4BBB12FC4BF2FFE01FFC1FFF4B1CC020F06F1CFC92C7001F91C800018005 0301FCDB000F7F0C03800C00804F053F7F797F797F4D854F85797FA24D737F61A34D1C80 61A35F61A2675F96CBFCA394B54E140060A2694C626069674C6460555B694C624E629CB5 5A5491C7FC4C634E4D5B545B545B4C4F5B4E057F5B9BB5C8FC0B035B4C060F5B4E043F13 F052B512C00A3F91C9FC4C90B912FC1EF01E800BFCCAFC93BA12E00AF8CBFC95D0FCA25D 5FA35D5FA35D5FA35D5FA35D5FA35D5FA35D5FA392B5FC94D1FCA35C5EA35C5EA35C5EA2 5CA25C49B6FC003FB812F84883A2B9FC60A26C02075C817C79FB75>80 D<4BBA12FE4BF1FFF8F6FF801FF04B1BFC1FFF6F1CC092C7001F91C8001F14F0050301FC 0300800C1F7F0C077F4F04016D7E8A797F4D737F4F717F8B8D5F4F717FA28D5F61A35F61 A34D6196CBFCA394B54E5B60A2555B5E4E62555BA24C97B55A4E625491C7FC664C634E4D 5B5413F0545B4C4F5B4E4D5B534848C8FC535B4C060F13F04E043F13C052B5C9FC0A0F13 FC4C0403B512F095B912800BFCCAFC1DE04C18801DE095C8000F13F809017F93B56F6C7E 4DEE1FFF767F767F4B864D707F767FA24B864D82A28A5D5FA28A5D5FA2645D4D60A2645D 5FA2645D94CAFCA26492B5FC5EA34A614C61A2210F4AF61F805EA2213F4A1F005E694A1E 7E7616FE4A6649B500FE73495A003FB800F06F150348716F4B5A69B9706DEB1FC04E6F4B 5A77D9C1FFC7FC6CD9FE0F4A041FEBFFFED06C5C0B035CE3007F13E00C071380818079FB 8A>82 D<962607FFE015E0077F01FEEC01F00603B600C01303061F03F0EB07E0067F03FC 130F4DB76C131F4D9027FC007FFF133F050F01E001079038807FC04D90C8EBC0FFDD7FFC ED3FE1DDFFF0ED1FF14C49DB07FB13804C01806FB5FC4C90C97E4C5A4C487014004C4883 4C5A4C48834D605D4B49171FA24B90CB5B5D4C180F151F4C61153FA34B4861A315FF66A3 5C66821D1FA270725A9AC8FC82A2836E8017F017FC17FF6F14F018FF19E06F15FEF1FFE0 6F16FE6FEEFFC01BF06F17FC6F836F717E6F847083041F8370831603040083051F821701 DD001F811801DE001F811903F1003F080F801A031A0087A287757FA387A3010F735B497E 133F91CCFCA34963A2137E6301FE98C8FCA3515A1201641B3F6D62481A7F64515A80484F 5B505B806E4D90C9FC484F5A6E4D5A6E4D5A6E4D5A486D4D5A6E04035B01FD01C04B5B01 F801F0031F90CAFC003FD97FFEED7FFE9027F03FFFC0903803FFFCD9E00F01FE011F13F0 496C90B75A48486C178090C74CCBFC007E023F15F8007C020715E048020092CCFC007003 0713F06C8477FF70>I<0107C012E0491FF0A35BA3490280C7003F01F8C7000314E003F0 C802E0EC003F03801B0F4948C94A150302F81C004A5ED9FFC0F57FC04A60A24890CAB517 3F5B98CAFC48481F80605B0007615B4E1A00485A625B001F4D61A2494E177E123F90CA5A A24861007E1FFE4E6112FE4861A26000781F78CB4A94C7FCA260A262A295B5FCA297CDFC A25FA261A25FA261A25FA261A25FA261A25FA261A25FA261A25FA261A294B5FCA296CEFC A25EA260A25EA260A25EA260A25EA260A25EA260A25EA260A25EA260A293B5FC5D4B8092 B612FC0003BBFC4886A35AA26CDBE07F92CCFC7C7B7CFA6A>I<000FB500E0B500FE923B 3FFFF87FFFF04891B74B90B612F8A3484D92B812F0A26C4D6F16E0C70380CA6CECE00002 1F01F8CB000F49C7FC4C060313F87713E04C725B674A99C8FCA24C61A24A1A01665EA291 B519036693CCFCA2491B07665DA2491B0F665DA2491B1F665DA2491B3F665DA2491B7F9B C9FC5DA24963655DA2491A01655DA290B519036592CCFCA2481B07655CA2481B0F655CA2 481B1F655CA2481B3F655CA2481B7F9ACAFC5CA24863645CA2481A01645CA21B03B56291 CCFC1B0764A21B0F49621B1F641B3F641B7F99CBFC1BFE007F1901631A03505A6C6C4E5A 63505A6C193F6E4D5A6C4FCCFC4F5A6C6DEE07FC6E4C5A6C4E5A6C6DEE7FE06C6D4B485A 6E03075B6DB4DB1FFECDFC6D6DEC7FFC6D01F0903803FFF8010701FE017F13E06D90B75A 6D94CEFC6D6C15FC021F15F002071580020002FCCFFC030F13C07D8074FB7C>I<293FFF F07FFFFE0203B5000FB500E00203B538C3FFE04890B74A91B66C4A91B512F0B95C6BA268 6C4C6E4D6E16E0D8001F02F8C900010380C9001FECF800010702C0706C01F8CA00031480 6D91CB6C01E0050049C7FC4BF97FF85461A16D5AA15CA1495A7896C8FC6D237EA113FEA1 5B761901A15B524F5AA2524F5AA1120F99B561511A1F6F695150C9FCA2516E177E6D22FE E10FDF61091F19010A8F61093F4F5A1C0F097F4F5A097E190F09FC62231FE001F8627003 0350CAFC1BF008071A7E09E06E16FE6EDD0FC0612201E01F8061083F6D1703090061504F 5A1A7E504F5A221F4F486207031A3F704B97CBFC07071A7E624F486F5D6E1E014F486107 3F190397C76C5F4F4F5A197E07FE4F5A4F191F4E4862213F4E4897CCFC7001071A7E6106 0F624F7013016E4B486120034EC85F4E6F1507067E6206FE4F5A604D484F5A203F4D4897 CDFC05076204F049197E050F62604D4871485A6E1C034DC95E4D1907057E705D05FE4F5A 5F04F1505A4D193FDCF3F097CEFC67DCF7E0197E04FF625F675F6E91CB5CA24C62894C62 675E4C97CFFCA24C61A24C61665E93CC5B804B62A24B735A665D6E4897D0FCB48077FBAC >87 D<93277FFFF87FB5923B3FFFFE1FFFF093B96C4A90B612F8A34B98B812F0A26F95C8 6C16E0DC000F03C00303EDF00005014ACA4AC7FC7102F87113F072491980507148C8FC72 6D60F87FF0726D60565A7297C9FC744C5A555A726D4C5A1F0F726D4C5A555A555A726E4B 5A9DCAFC726E4A5A545A545A736D4A5A545A736D4A5A1E7F734C5A754990CBFC535A736D 495A66736D495A535A535A736D495A53CCFC73EC81FE1C83F487FC73ECCFF8F4DFF074EB FFE065745C9ACDFC64745B64747FA3747FA2747FA35080625080626297B67E4F7F4F486C 7FF107FC4F486C7F1AF0F11FE04F486C7FF17F804F486C7F4E5A4E5A06076E7F4E5A4E48 6D804E5A4E487F4F824EC8FC4D486F7F4D5A4D486F7F4D5A4D5A053F707F4D5A4D486F7F 4C90C9FC4C5A4D707F4C5A4C48707F4C5A4C48824C48854CCAFC4B72804B5A4B48727F4B 5A4B5A033F737FEDFFE04A747F1407141F027F6D067F7F0103B56C4DB57E017F02FE050F ECFFE0007FB700E04BB812FCB86C4B8363A34D636C01874A6FDAF83F5B957C7BFB97>I< 197F953803FFC0060F13E04E13F04E13F895387FC1FCF0FF004D48137C4D48137E4D5A17 0F4D5A4E133E173F4D48137E17FF605E95C7FC5E4C5A1AFE4C4814FCA24C5A043F14011A F84C5AA24C4813031AF05D5F4B15071AE04D130F4B16C0A24B90C7121F1A804B153F4C15 0061033F157E4C14FE157F4E5A5E03FF4A5A6118074A495C180F4E5AA24A49495A4EC7FC A24A15FE4C485AA24D5A4A4A5A16804D5A4D5A4A4A5A16004DC8FC17FE4A495A4B485AA2 4C5A4C5A4A48485A4C5A4CC9FC5EEDF9FE5E9138FFFBF8EDFFF05E5E5E93CAFC5D5D5DA2 5D5DA45B5B5B5B5B5B5B90B5FC485AEA03F83807F07FEA0FE0EA1FC0EA3F80D87F00EF03 8000FE013F160748F00FC00078183F00306D6CED7F80C7EFFF004E5A020F4B5A6F4A5A02 07ED1FF04E5A6E6CECFF804D90C7FC6E6CEB07FE913A00FF803FF86FB55A6F14C06F91C8 FC6F13FC030313E0DB0008C9FC47837FFF4C>96 D<4CB47E041F13F0047F13FC0303B57E 4B6E133F031F01806D487E923C7FFC003FC0FFC04B48EB0FE14A01E0D907F37F020749EB 03FB4A90C76CB55A4A5A4A4880147F4A486F5B495B4949815B4B94C7FC495B5B4990C9FC 62495A13FF197F48495FA2485B19FF48615C5A6062485BA26048615CA26048615CA26062 B5C9FCA26097C8FC5BF301F04EEC03F8611CF0A2187F007F4E1307491AE0A206FF140F4D 16C06C6C5F5F4DED1F80001F5E5F6C6C4BED3F00EF7F7F6C04FE5D6C6DD901FC157E9326 03F83F14FE6C6DD90FF05D6C6D903B3FE01FFC01F86D6C9026FFC00F130390263FFE0790 3A8007FE0FF06DB548486CB55A010702F86D5C6D4A6D5CD9007F0180DA3FFEC7FCDA0FFC C8EA07F855527ACF60>IIIIIIIII<1A7E4FB4FC4F13804F13C04F13E06161A41BC0A21B8073130062735AF103F096C8FC B3A6EF03FF051F13E0057F7F4CB512FC4C80933907FE07FF93261FF0037F93263FC0017F EE7F80DCFE00804B487F4B48815E4B5A150F4B5A5E033F5C4BC7FC157E15FE4B5C14014B 5E14034B5C14074B5EA26E485C91C9FC62A260A297C7FCA260A261A2187FA261A218FFA2 61A25FA261A25FA261A25FA261A25FA261A25FA296C8FCA25FA260A2177FA260A217FFA2 60A25EA260A25EA260A25E60A35ED801FC5ED807FE5C486C93C9FC486D5B485E486D495A A24C5AB5485C4B5B4B5B4A485B4B90CAFC49495A6C48495A01F0EBFFF8263FE0035BD9F0 1F13C06CB6CBFC6C14FC000314F0C614C0D91FF8CCFC4B9E82F84B>II<49B4EE3FFE010701E00203B512C0496D020F14F04901FC023F14FC496D91 B67E90267F87FF499038E01FFFD9FE0390288007FE00037F48486C9026C00FF86D7FD803 F8DB1FE08101F09126E03F806D7F00076D4AC8FC49DAF0FC6F7E000FEDF1F849ECF3F0DC F7E082001FEDFFC0495D5C003F93C9FC01005CA24A5B485D127E5E00FE4918FF484B5F5E A20078495FC7625EA24A5F6493C9FCA24A5F645D62027F61A24B5E99C8FC14FF624B5FA2 49187F635D08FFEC03E0494FEB07F0614B4D14E0A2494D150F5114C05D4F151F494F1480 A24B4BED3F006349631D7E92C991C712FE6549505A1C034A705D525A017F1A0F734A5A4A 709038807F8073D9C1FFC7FC74B45A4A7113F86D48715B6D487113C0D90F80050190C8FC 64527CCF6D>110 D112 D<4CB46C1470041F01F014F8047F01FC13010303B56CEB07F04B6E130F031F0180EB801F 923B7FFC003FC03F4B4890390FE07FE04A01E0903807F0FF020749EB03F94A90C712014A 4892B512C04A4880147F4A4881494917804949815B5D494917005B4990C97E6149485F13 FFA24849167F62485BA24818FF4A5F5AA26048495FA3485F4A5FA3485F4A5FA360B5C95C A3604995C7FCA36061A3007F177F495FA218FF5F6C6C5F5F5F001F5E4D5B6C6C5D5F6C93 B5FC6C6D495CEE03FB6C6DEB0FF36C6DEB3FE76D6CD9FFC75B90263FFE0713876DB5EAFE 070107ECF80F6D02F05CD9007F138091380FFC0091C85A96C8FCA35F60A3177F60A317FF 60A35E60A35E60A25E5E047F13F84AB8FC4A835C97C7FCA36E020F5B4D737ACF51>I<49 B4ED03FF010701E0023F13C0496D91B512F04901FC010380496D498090267F87FF90391F FE03FED9FE03903A803FF000FF48486C9039C07F800101F89226FF0007138048486CD9E1 FC5B0007DBE3F85B49DAF7F05BDCFFE04913C048484B15804D90B5FC121F4992C7FC4A5B 003F1A0001004A5D4C6E5A4A705A484B6E5A007EF00FC04C91C8FC00FE5B5A5EA200785B C7FC5EA25CA293CBFCA25CA25DA2147FA25DA214FFA25DA25BA25DA25BA25DA25BA25DA2 5BA25DA25BA292CCFCA25BA25CA2137FA25CA35C6D5A6D5AEB0F804A527CCF52>I<9338 01FFF0043F13FE93B612C0030381030F15F8033F9038003FFCDB7FF8EB07FEDBFFC0EB00 FF4A49EC7F804A48C8123F4A48ED1FC0020F160F4B153F4A48EDFFE0023F5D4B5C027F5D A202FF4B13C05DA21A805B6F6E1300725A6FEC01F895C8FC8115FEEDFFC016FCEEFFE06D 15FEEFFFC06E15F0846E15FE6E816E826E826E82806E6C81031F811501DB001F80160017 1F1707170183187F01FC163FEA03FE487E486D151F487F5A4860A34E5AB55A6191C9127F 495F4916FF6C485F01E04B90C7FC90C95A6C5F6DED0FFC6C6C4B5AD80FF0ED7FF0D807FC 913801FFC06CB46C01075B6C01F890B5C8FC6C90B612FC013F15F0010F15C001014AC9FC D9001F13C0435277CF55>I<163E16FF4B7F4B7F5DA45D5FA35D94C7FCA35D5EA3157F5E A315FF5EA35C5EA35C5EA3003FB812FE4817FFA2BAFC18FEA26C17FCC7000F0180C7FC5C 93C8FCA35C5DA3147F5DA314FF5DA35B5DA35B5DA35B5DA35B5DA35B92C9FCA35B5CA313 7F5C18F8EF01FC13FF4A15F8170318F04816074A15E0170F18C048161F4A1580173FEF7F 00177E5F16016C4B5A4C5A4C5A6C4B5A4C5A6D6C01FFC7FC013FEB03FE90391FF81FFC6D B55A6D14E06D1480010049C8FCEC1FF038747CF142>IIIIIII E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo cmbx12 14.4 41 /Fo 41 123 df[<50B512F00703B7FC96B812E0060F17F8067F17FE0503BA7E051F8505 7F854CBB12F80407DC800180041F03E0C7001F7F047F4AC800037F93B600F01500030303 C0844B92C90003804B02FC5E4B4A4C804B02E05E4B4A4C8092B65A4A92CA4880A24A4A94 B6FC4A5CA24A5CA24A4A4C81765DA25C5FA2775CA2775C775C775C7791C8FC775B775B9A 38003FE09BCAFCB2090FB712FCC1FCABC7003F02F0CA7E1D1FA289B3B3B3B3A9003FB900 F0010FB912FCAA02FCC796C7123F>134 167 122 294 149 12 D[<50B500E095383FFF FE0703B7057FB612E096B800E0031FB712FC060F05F84AB9FC067F05FE020F18C00503BA 6C017F18F0051FDFC003BA7E057FDFE00F854CBBD8F83F19FF0407DC00016EB726F0003F 80041F03E0D9001F90B700FCC7000380047F4AC8000305C0DA007F7F93B600F003004CC9 121F030303C008F8844B92C9000304E0047F7F4B02FC4C048093B5FC4B4A4C93C948804B 02E04C03FC5E4B4A4C4B4C8092B6484C5D4A92CA4C4C809AB7FC4A4A515E4A4A63A24A4A 4C93CAFCA24A4A504D81A16E92C8FCA24A854D62A277745CA277745CA16E5C77745C7774 5C77755BA16F5BA1DB07FCC9FCA192CBFCB2A10003B87EC5B9FCABC7003F02F0CA00074A CA120FA11403A2A180B3B3B3B3A9007FB900F8010FBA0103BA12C0AA02FCC7962680001F 9538E00007>210 167 122 294 224 14 D[<19FEF001FF60180F60F03FFCF07FF8F0FF F0050313E05F4D13C04D13804D13004D5A4D5A4C5B5E4C5B4C5B4C5B5E604C90C7FC4C5A 5D4B5B4B5BA24B5B5D5F5D4B5B92B55AA24A91C8FCA24A5B5C5E5C5E5C5C5E5C5E91B5FC A2495CA2495CA25B93C9FCA25BA2495BA3495BA25B5DA290B5FCA25D5AA35A5DA35AA25D A25AA4485CA65AA292CAFCA45AA75CA2B5FCB3AA7EA280A77EA481A27EA66C80A47EA281 A27EA3817EA37E81A27FA2817FA26D7FA36D7FA27FA2827FA26D80A26D80A28082808280 80828082806E7FA26E80A26F7F6F7F8183816F7FA26F7F6F7F81707E707F8482707F707F 707F82707F717E717E7113807113C07113E083050013F0F07FF8F03FFEF01FFF84180384 F000FE>64 238 103 306 105 40 D[<123F487E487E13F06C7E6C7E6C7E6C7E6C13C080 6C7F6C7F6C7F6D7E6D7E6D7F816D7F6D7F6D7F817F6D7F6E7E826E7F6E7FA26E7F828082 6E7F6E7FA26E80A26F7F83818381838381838183A26F80A26F80A28481A284A2707FA370 7FA28482A284A2821980A319C082A319E0A282A219F0A47014F8A619FCA282A419FEA783 A219FFB3AA19FEA294B5FCA719FCA45EA219F8A64C14F0A419E0A25EA219C0A35E1980A3 19005EA260A25E60A24C5BA393B55AA260A25D60A24B5CA24B91C7FCA25F5D5F5D5F5F5D 5F5D5F92B55AA24A91C8FCA24A5B4A5B5E5C5E4A5BA24A5B4A5B93C9FC4A5A495B5B5D49 5B495B495B5D4990CAFC495A495A485B485B485B5C4890CBFC485A485A485A485A13C06C 5A6CCCFC>64 238 113 306 105 I46 D[96 157 109 284 134 49 D[<94387FFFE0041FB612 C04BB712FC030FEEFF80033F17F04AB912FE0207727E4A19E0023F19F891BB7E491AFF49 9126FC003F82010F02800103824901FCC86C15F04901F0031F814901C06F8190B5C90003 81484970814A70824801F0718148498374814801FE7181486D6C7081814802F07081816F 70815A6F7081A26F711580B7FC821FC087A41FE087A26C92CAFCA36C5CA26C5C6C5C6C5C 6C5C6C5C6C6C90CBFCD91FFC4E15C090CDFCA31F8063A21F0098B7FC66A2505DA2505DA2 66505DA2505D665092C7FC505C65505C97B6FC654F5D4F15809AC8FC4F5C4F5C4F5C644F 5C4F148096B6C9FC4E5C634E14F04E5C4E5C4E91CAFC4E5B4E5B95B512F04D5C4D5C97CB FC4D5B4D5B4D13F04D5B4D49EEFFE094B55A4C91CAFC4C13FC4C494C13C04C5B4C5B4C5B 4C90CAFC4C5A4B495F4B4919804B5B4B13C04B495F4B90CBFC4B5A4B5A4A01F0604C1A00 4A49604A49604A90CB000FB5FC4A90BCFC5C5C91BD5A5B5B5B5B5B5B496490BEFC5A5A5A 5A5A5A4865A2BFFCA566A4>107 157 115 284 134 I[<050FB5FC4CB612FE041FEDFFE0 93B812FC0307EFFF80031F18E0037F18F892BA12FE0203737E4A9126FC007F15E0021F02 800107814A01F8C70001814A01E06E6C8091B5C96C804901FC7080494970814901E07081 4B70814949864913F803FE7081496D7E70854980706F8190B6FC827085A25A82A96C4B61 A26D4A5DA26D4A61A26D5C6D4A4B5D010391C9FC6D49629026007FF85E91CB5EA2505D66 629BC7FC505C65505C97B65A4F5D654F5D070F92C8FC4F14FC4F5C96B612E0060F5D051F B7C9FC043FB712FC4C16F01BC050CAFCA2F2FFE01BFEF3FFC07017F093C86C14FC070714 FF070115C0736C14F074807414FE74807481748174818A74818A75808A751580A21FC0A2 7515E0A21FF0A21FF887A21FFCA3EB0FFE90267FFFC01BFE90B57E000314F84880488048 80A24881A24881A2B77EA21FFCA41FF863A21FF05E7E4C1AE06393CA16C07E4B4D15806C 5C4B1B006C4A94B65A15C06C91CA485D6C01F84D5D6C01FE4D5D6E636C02C04C5D6D01F8 043F5D6D01FE4C92C7FC010FD9FFC04AB65A6D02FC020715F86DDAFFF0017F5D010092B9 12C06E62021F4FC8FC020719F8020119E0DA003F95C9FC030717F8030017C0040F03FCCA FCDC001F49CBFC>111 160 117 284 134 I[119 157 121 284 134 I[<52B47E527F527F527FA2527FA3527FA2527FA399B6FCA25181A35181A25181A35181 A25181A35181A25181A398B8FCA25083A35083A25083A35001BF81A250013F81881BFE08 3F8388E07FFC82881BF808FF83884F01F083881BE04F85884F498389634F85894F90C782 8962073F85894F4884896207FF85894E498589624E87894E49858A624E878A4E90C9828A 61063F878A4E48868A6106FF878A4D49878A614D898A4D49878BA24D49878B4D90CB828B A24D48888B4DBE7EA394C0FCA24C8BA34C8BA24C8B06C0CC7EA24C49898C4C90CD828CA2 4C488A8C4C488A8CA24C488A8C4B498B8CA24B498B8C4B498B8DA24B498B8D4B90CF828D A24B488C8D4B488C8DA24B488C4A6D88027FD9FFF88CBA00C094BDFCAA9126C0000F0BF8 C71203>184 167 119 294 203 65 D[166 164 119 291 191 I[<99263FFFFEF007C0093FB600F8 EF0FE0080FB86C161F97B900F0163F070F06FE16FF077F726C5C0603BB00E05C060F08F8 5C067F08FE5C4DBD6C5B05070AE05B051F9426C0003F6E5B057F04E0C7000102FC90B5FC 4CB748C9003F6D5A4C04E004076D5A040F93CB14C74C03FC063F13EF047F03E07290B6FC 93B70080180703034BCC12014B4B854B03F0864B4B1A1F4B0380864B92CE7E92B648874A 4B874A03F0874A4B885C4A4B884A4B884A92D07E5F91B68A494B89495D8F494B89495DA1 7E495DA17E5B5F498E94D2FC90B78BA2485DA17E5AA25E488FA25A5EA2A17E5AA25E5AA1 6C13C0A190C7FCA35AA35EA4B7FCB3A27EA482A37EA57E70F87FC0A1EBFFE07EA3827EA2 7E7067A26CA113C0A26C81A15A7F7120807F71666DA11200836D6A71676D221F6D6F67A1 123F6D6F545A6D816E575A71656E6F666E6F646E6F525B6E6F525B6E6F646E6F5290C7FC 6E6F525A6F6E525A6F6F505B6F03E0505B6F6F505B6F03FC081F5B6F6F505B03006F6C96 B5C8FC7003E006035B041F03FC060F5B7003FF063F5B040304E04CB512E07004FE040F5C 706CDBFFF092B65A051FDCFFC0011F4AC9FC050794B812F8050164716C1BC0060F98CAFC 06031AFCDE007F19E0070F1980070006FCCBFC080F17C0E0003F03FCCCFCE1003F91CDFC >163 170 113 294 194 I[181 164 119 291 206 I[191 164 119 291 210 72 D[87 164 122 291 100 I[190 167 119 291 201 82 D[<94261FFFF8177C0407B600E016FE047F03FE15010303B800C0 1403030F05F81407033F05FE140F92BA6C131F020307E0133F020F07F8137F4A7313FF02 7F9126F8001FECFF0191B60080D9007F14834902FCC8000714C74902F0030091B5FC4902 C0163F4991CA1207494983494917004949844B181F90B585484A844B8448874B84488889 4891CDFC894888A24A864888A2895A89A31E7FB5FC801E3FA281A21E1F8181A2816F1A0F A28115FF6C8170735A04F096C8FC8216FF6C16E017FEEFFFE06C17FF19F06CF0FF801AF8 F2FFC06C1AFCF3FFC06C1BF86C1BFE767E6C1CE06D1BF8896D1BFF6D886D1CE06D886D88 6D886D886E876E886E88020788800200886F87031F871507030087163F040386EE003F05 011A80EF001F060019C0190FDF007F17E01A07F2003F090716F01B01757E0A1F15F88888 88887615FC89D83FC087487E00FF8889A289A389A27FA289A220F87FA37F20F0A27FA26D 5114E0A2806E1DC0A26E501480806E626E1D00806E505B6F4F5B15E06F4F5B03FC96B55A 6F606F6C4D5C04F04D5C04FC051F5CDCFF804C91C7FC05F84BB55A02CFDAFF8002075C02 83DBFF8090B65A020193B85A496C6C1AC049011F624901074FC8FC49010119F849D9003F 6049020F18804902014DC9FC90C9001F16F048040093CAFC007C050114E0>118 170 113 294 149 I[<0007C5B41280A648A113C0A50580C7001F03F0C7120304E0C8F1 001F93C91A0303F8F6007F03E01F1F4B8B4891CA090314E04A8C4A8C4A8D4A8D4A8DA17E 5C4A8DA291CB88A248A113F0498EA3498EA449237FA3007FA113F8A349233FA84848FB1F FCA6CD9AC7FCB3B3B3B3B3A44BC0FCAA08E0C8120F>166 162 118 289 187 I<4CB512FE93B712FC031FEEFFC092B912F8020318FF020F19C0023F19F04A19 FC91BB7E4992C7003F6E7E4902C0020781496E020015F0496E033F80706F80497280706F 8086496E6F817481A275808A878AA2876D4A85A26D5C75806D5C6D5C6D5C6D5CDA3FFECA FCEC07F091CCFCA90703B7FC060FB8FC0507B9FC94BAFC160F93BBFC1507153F92B8EAC0 0F0207EEF000021F4BC7FC027F15F091B71280010303FCC8FC4915F0011F15C04992C9FC 4914FC90B65A485D485D485D5E4892CAFC5A5D485CA25A5DA3B65AA463A463816C62A26F 94B6FC6C616F5E6C6EEE07FD6C6F030F8170DB1FF9816C6FDB7FF115E06C6F912601FFE1 15FF6C03FC020701C0EEFF806CDBFF80013F4917C06DDBF003B5486C16E0011F92B65A6D 4E7F010306F07F010006C07F023F4D1303020704FCC8FC020004F0033F15C0030F038003 011580DB001F01F0CEFC7B6D79EB83>97 D[<923801FFC0013FB6FCB8FCABEA001F1303 7FA27FB3B3A697380FFFF84FB612E0071F15FE96B812C0060317F0060F17FE063F717E95 BA7E05C319F005C7DAE00115FC05DF49C7001F8094B500F002078007800201814EC96C14 E006F870804E708006C070804E8295CA6C804D71804D71814D874D844D878A8D8D8A8DA3 7880A28DA32280A28AA222C0A522E0B122C0A6228066A22200A369A26669A26966696669 71637195B6FC535D7198C7FC714D5C715F724C5C724C5C724C5C04FD01F84C5C04FC6D4B B612804C6CB44B92C8FC4C6C01C0021F5CDCE00F01F891B65A4C6C9026FF800F15F04C6C 91B85A0500198093C76C4DC9FC4B021F17F84B020717C04B020194CAFC4BDA003F15F84B 030792CBFC91CB003F13C0>131 167 120 293 149 I<95387FFFFE051FB612FC4CB812 E0041F17FC047F17FF0303BA12C0030F19F0033F854B854ABB7E4A03F8C780020F038002 1F14804A4AC84814C04A02F85D4A02E018E091B64892B6FC4992C9FC494A4B15F05B495C 495C495CA2495C90B6FC5E487315E05E487414C0A24892CA6C148075140048745B755B48 4A050113F09838003F8099C8FC5AA4485CA6B6FCB07EA381A37EA36C80A37E82A26CF407 FC70F00FFE7EA26C6F181F1EFC6C6F183F6D6E19F81D7F6D6EF0FFF06D806D6E4D13E071 5E6D6F4C13C06D6F4C13806D03F84C13006D6FEE7FFE6E02FFED01FF021F03C002075B6E 03F8023F13F06E9226FFC003B55A020193B75A6E62033F4EC7FC030F60030318F0030018 C0041F4CC8FC040316F0DC003F1580DD007F01E0C9FC676D77EB78>I[131 167 119 293 149 I<95387FFFE0053FB67E0403B712F8041F 16FF047F17C00303B912F0030F18FC033F18FF92BB12C04ADBF801810207922680001F80 4A02FCC7000714FC023F02F00201804A4A6E8091B600806F804992C9121F494A7080494A 85494A708049854C7080495C4973805E90B6727F485D8A488793CB15805A885A4B1BC0A2 5A7614E0A25AA25DA25A1FF0A388B6FC92BDFCA61FE01FC003FCCFFCA77EA5817EA37EA2 817EA27E70F11FC0F63FE06CF57FF0826C1DFF6C1EE070606D805313C06D6E606D6E1A80 6D6E4E130070606D6F4D5A6D6F177F6D6F4C485A6D03F84C5B6E6E040F5B021F02FF043F 5B6E03E092B55A6E03FC02075C0201DBFFF090B6C7FC6E93B712FC033F61030F19E00303 198003004EC8FC041F17F8040717C0DC007F4BC9FC050715F0DD000F01FCCAFC6C6D79EB 7B>I[<96383FFFC0060FB512FC95B7FC050F16C0053F16F04CB87E0407834C83043F8393 B6D8F80714804BDBC00F14C04B4AC64814E04B02F85B4B4A16F04B4A5B4B5C4B4A90B612 F892B6C7FC4A5CA24A5CA24A5CA25C4D6E14F05C7414E0A24D6E14C04A71148074140074 5B080013F8F33FE098C8FCB3A8BB12FCABC7003F02F0CBFCB3B3B3B3AC003FBAFCAA02FC C77E>93 167 120 294 82 II[<923801FFC0013FB6FCB8FCABEA001F13037FA27FB3B3A698387FFFC0 080FB512FE087FECFFC04FB712F0070716FC071F16FF077F834EB912E04E844E49C6814E 01E0131F063F90C76C80DE7FFC6E80DEFFF06E8019C005C1496E8105C390C8FCDDC7FE85 DDCFF881A2DDDFF085EFFFE0604E82A295CA81A25F5FA35FA35FA55FB3B3B3A3BA00E001 7FB912F0AA9126F0000106F8C7FC>132 166 118 293 149 I[57 167 118 294 75 I[<923801FFC0013FB6FCB8FCABEA001F13037FA27FB3B3B3B3B3B3B3ACBA12C0AA9138 F00003>58 166 118 293 75 108 DI<4BB46C92387FFFC0013FB6030FB512FE B8037FECFFC04FB712F0070716FC071F16FF077F834EB912E04E844E49C6814E01E0131F 063F90C76C80DE7FFC6E80D8001FDCFFF06E80010317C06D0381496E81058390C8FC6DDB 87FE85DD8FF881A2DD9FF085EFBFE060DDFF8082A295CA81A25F5FA35FA35FA55FB3B3B3 A3BA00E0017FB912F0AA9126F0000106F8C7FC846B76EA95>I<95383FFFF8050FB612E0 94B712FE040FEEFFE0043F17F84BBAFC030719C0031F19F0037F19FC92B626F8003F8002 03038001036E7E4A02FCC86C80021F02F0031F14F04A02C00307804A4A6F8091B6C96C80 4902FC706C7F494A71804989494A7180494A7180A2494A718049894C8390B6874892CB6C 80A2481F80A2484A7215C0A2481FE0A3481FF0A24B85481FF8A4481FFCA6B61DFEB06C1F FCA56C1FF86F96B6FCA36C1FF0A36C1FE06F606C1FC0A26C1F80705F6C1F00A26C6F4D5C A26D6E4D5C6D656D6E4D5C705F6D6E4D5C6D6E94B65A6D6E4C5D6D6F4B92C7FC6D03E003 0F5C6E6E4B5C021F02FC037F14F06EDAFF800103B65A6E03F8013F5D020192B9C8FC6E6C 19FC6F61030F19E003031980DB007F05FCC9FC040F17E0040194CAFCDC000F15E0DD003F 01F8CBFC776D79EB86>I<922601FFC0913807FFFC013FB692B612F0B8020F15FF077F16 C04EB812F8060F17FE063F717E95BA12E005C119F805C78505CFDAE0038194B548C76C6E 7E07E0020F81D8001F05806E8101034CC80001816D04F86F8106E070806D4C70804E7080 4DCA7E4D71814D874D834D877781898DA27880A27880A38D8AA22280A28AA222C0A48A22 E0B122C066A52280A2662200A3545CA3545CA2699BB6FC696569714D5DA2714D5D714D92 C7FC7162715F724C5C724C5C7293B65A06F84B5D7203075D06FF4B92C8FC07C0023F5C05 EF01F849B65A05E79026FF801F15F005E391B85A05E01980724DC9FC061F17F8060717C0 060194CAFCDE003F15F807071580DF003F01C0CBFC97CEFCB3B0BA12E0AA9138F0000183 9978EA95>I114 D<93B500F0143E033FDAFF8013FF0203B7EAF003020FEEFE0F027F EEFFBF49BBFC13075B499138C0003F017F01F8C7120390B500C0EC007F4891C9121F02FC 160748498248491600485B4A83488586485BA2865AA286B5FC80A28080A202FC715A6E94 C8FC6E7E15E015FCEDFFC06C15FF17F8EFFFE06C17FF19E06C18FCF1FF806C19E0866C19 FC6C19FF6C866C866D19F06D856D856D850103857F6D6C1980021F19C01407020019E003 1F18F01503DB001F17F8EE007F1701DD000F15FC1800193F070F14FE1903D83FC0170048 6C8400FF85866D84A286A27F867F1CFCA27FA26D1AF86E5FA26E19F0806E4D13E0806E4D 13C06E5F6E4D138003C093B512006F03035B03FC030F5BDBFF80027F5B04F8010FB55A93 B85A02BF60D9FE1F95C7FCD9FC075FD9F00117F8496C6C16C00180011F93C8FC90C70001 15F0007CDA000F01FCC9FC576D77EB6A>I[84 153 123 279 105 IIII<267FFFE00107B56C 91267FFFE0EB3FFF91B894B7FCAAC7001F92C9000103C0C7FC6E6FDB001F01E0C8FC6E6F 606E6F4C5B5390C9FC6E6F5F6E6F4C5A6F6E4B5B6F6E4B5B646F6E4B5B6F6F4A5B6F6F4A 5B6F6F93CAFC734A5A6F4E5A6F6F5B706E495B706E495B706E495B65706F485B706F4890 CBFC706F5A706F485A08F15B7003FB5B7191B55A715E715E64837193CCFC715D715D6383 7280728072807281A27281728172814E81604E814E81884E826095B87E4D834D01F9814D 01F0814D5B4F6C804D496C804D496C804D6E814D48834C497F4C496D814E6D814C496D81 4C496E805E4C496E804C90C86C804C486F814D6F814B5B4B496F814B496F814B71814B49 70804B5B94CA6C804B4871804B4871814A49718102076D8749B66C82B800FE0307B912F8 AA9026FE00079738C0001F856A7CE98E>I<267FFFE0010FB56C923B3FFF8003FFC091B8 95B6FCAAC703F8CB6C49C7FC6E090713E071725B6E515B836E5190C8FC836E515AA27217 3F6E64846E515A846E515A846E505B846F4F5BA2725E6F63846F4F90C9FC846F4F5A856F 4F5A856F4F5AA27315FF6F62856F4E5B85704D5B85704D5B85704D90CAFC856470608670 4D5A86704D5A86704D5A86704C5B1AF8714B5BA2745A715F1AFE714B90CBFC1AFF714B5A 1B9F71EDBFFC1BFF715EA3715EA2715EA2725DA2725DA27292CCFCA3725CA2725CA2725C A2725CA2725CA3735BA2735BA27390CDFCA262A24F5AA24F5AA219FF62A24E5BA24E5BEB 3F802601FFF04B5B000713FC486D4B90CEFC487F486E5C6148804E5A187FB66C5D18FF61 4D5B5F4D5B615F6C4A4990CFFCEF7FFE4B495A6C4B5BDB00075B6C017E011F5B02DC017F 5B6CD9F803B55A6C90B7D0FC6C5E6C16F86C5E6D15C0011F92D1FC010714FC010014E0DA 1FFED2FC82997BE98E>I<48BE12C01EE01EF0A55A1EE04CC8001F15C004804B158003FC C95A03F093B7120003C0614B4B5D92C95A4A4C5D4A624A4C5D4A5E4F5D4849624F92C7FC 4A93B7FC4E5D644A4B5D604E5D91C95E4E5D604E5D99C8FC95B65A485E494B5D634D5D5F 4D5D63CA485D5F94B7C9FC624C5D5E4C5D624C5D5E4C5D624C92CAFC93B7FC4B5D4FED3F F84B5D5D4B5D614B5D4BF17FF04B5D96C9FC92B65A5C4A5D604A4B16FF5C4A5D604A5D4A 4F13E091B7C9FC5F494B5E5B495D4D5E495D4962494B5E5F4992CA5A90B75F484B94B512 C04C5E484B16074862484B163F4C4BB6FC484B150F480603B7FC4892BBFCA2BFFCA21E80 A47E7E656A79E978>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmr10 10.95 86 /Fp 86 128 df<95B512C0051F14FE4CB712E0040F16FC047FEEFF804BB5D8F00314E003 0749C7001F13F8031F01F0020313FE037F01C002006D7E4AB5C9003F13E04A01FC040F7F 4A49707F021F497013FE4A01C004007F4A49717F91B5CB6C7F4949727F49884949727F49 49727F4949727F49884B84498990B5487280A2484A737F488AA24891CD6C7FA3488A4A86 A2488AA34A86488AAD6C666E62A46C66A26E626C66A36C666F616C66A36C6E96B55AA26D 656F606D9AC7FC6D64A26D6D4E5BA26D646D6D4E5BA26D646F606D64027F636F60023F98 C8FC021F626F183F6E626E6270177F6E626E627017FF6E62A26F6C4C5B00FC023F96C7EA 0FC0A26F6C4C5A007EF61F80030F60701607030760007F1E3F6C02034E150070160F0301 60A26D01004E5C001F1E7E70161F6D027E4D14FE6D1C0101FC1C0F6CB600FE94B65AA270 5EA36C66A56C66A24C82728078FF83>10 D<942603FFF0ED7FE0057FD9FF80903807FFFC 0407B600E0013F13FF041F03F890B612C093B76C4815E003039127003FFF079038E07FF0 4B01F00103018F9038003FF8031F01809027007FDFFC137F4B48C8B548EBFFFCDBFFF84A 4A5A4A494A4A4813FE4A01C04A14C04A4917804A90C85A4A4818005D023F604A487313FC 7713F84A486F49EC7FF0F63FE049496FEE1FC07393C7FC735B4949167FB3A8BF12C0A7D8 000301E0C9D87FFCC9FCB3B3B3A7496D4C7E87013F01FE030714E0B8D8801FB8FCA602C1 EFF83F6F807CFF6A>I<943801FFF0057F13FF0403B612C0041F15F0047F15FC4BB53800 3FFE030701F0EB03FF031F018001007F4B48C8EA3FC0DB7FF86F7E4A48484B7E4A01C015 FF4A494A7F4A90C85A4A485D874A485D4A5AA24A5AA2495B735BA249496F5B735B735B08 3FC8FC97C9FCB3A2F201FCF13FFFBCFCA7D8000301E0C8120F19031900A21A7FB3B3B3A3 496D4C7EA2013F01FE0307EBFFC0B8D8801FB712F0A602C1EFF83F5C807CFF65>I<9438 03FFFC057FEBFFE00407B6EAF81C041FEDFFFC93B8FC0303EC000F4B01F01300031F0180 5B4B48C75ADBFFF85C4A5B4A13C04A5B4A90C85A4A48815D143F4A5A854A488185494916 7FA3495BB3A8BCFCA7D8000301E0C9127FB3B3B3A7496D4C7EA2013F01FE0307EBFFC0B8 D8801FB712F0A602C1EFF83F5C807CFF65>I<942601FFF0EE7FFE053F01FF030FB512C0 0403B600C091B612F8041F03F0010381047F6F011F15FF4BB526803FFE017FD9E0077F03 079027F00003FF4948C77F4B01C00100018301F0EC3FE04B90C8D83FC701C0EC0FF0DB7F FCDB1FDF90C8EA03F8DBFFF092267FFFFEED0FFC4A494AB500F8153F4A494A4A4B7E4A49 4A4A15FF4A90C84B5C4A484B4A82674A4895C8FC614A485F854A485F795B8549494D6F5B 73725A73725ADF007FEF0FC09DC9FCB3A2217F0D0FB5FCC3FCA7D8000101F0C9D87FFCC8 12071F00203FA38CB3B3B3A2496D4C6C4C7FA2011F01FF0307D9FFC04AB512F0007FB7D8 C01FB7D8F007B712FCA602E0DDF83FEEFE0F8E807CFF98>I18 D<15F0EC01FCEC07FFA24A13805C4A13C0A25C91B512805B1600495B495B495B5D495B49 13804990C7FC5C495A485B4813E0485B5C4890C8FC485AEA3FF85B485A485A90C9FC127E 121C120822235BFE5B>I34 D39 D[43 182 111 263 71 I[<127012F812FE127F6C7E6C7E6C7E6C7E6C7E6C7E7F6C7E6D7E6D7EA26D7E6D7E80 6D7E1303806D7EA26D7F6E7EA26E7EA26E7E81140F81A26E7EA26E7EA28280A2828082A2 157F82A2153F82A36F7EA46F7EA48281A31780A481A217C0A88117E0B3A817C05DA81780 A25DA41700A35D5EA44B5AA44B5AA35E157FA25E15FFA25E5C5EA25C93C7FCA24A5AA24A 5AA25D141F5D4A5AA24A5AA24A5A4990C8FCA2495A5C1307495A5C495A495AA2495A49C9 FC485A5B485A485A485A485A485A48CAFC12FE12F81270>43 182 118 263 71 I<191E193F4F7EB3B3B3003FC012FE488BC21280A46C20006C67CCD87F80 CCFCB3B3B373CDFC191E797A76E98E>43 DIII[<1AF0F101F8 F103FCA21907A21AF8190FA21AF0191FA21AE0193FA21AC0197FA2F1FF80A21A0060A261 1803A2611807A261180FA24E5AA261183FA261187FA26118FFA24D90C7FCA2601703A260 1707A260170FA260171FA24D5AA260177FA26017FFA295C8FC5EA25F1603A24C5AA25F16 0FA25F161FA25F163FA25F167FA24C5AA294C9FC5DA25E1503A25E1507A24B5AA25E151F A25E153FA25E157FA25E15FFA24A90CAFCA25D1403A25D1407A25D140FA25D141FA24A5A A25D147FA25D14FFA292CBFC5BA25C1303A2495AA25C130FA25C131FA25C133FA2495AA2 5C13FFA291CCFC5AA25B1203A25B1207A2485AA25B121FA25B123FA25B127FA25B12FFA2 90CDFCA2127E123C>70 181 118 263 91 II<16F04B7E15031507151F153F15FF1403141F91B5FC130F0007B6FCB7FC A214FD14E1140113F0EAF800C7FCB3B3B3B3B3A24A7F4A7F027FEBFFE0007FB912F0A6ED E07F3C796FF85B>I<92381FFF804AB512FC0207ECFF80023F15E04A15F849B712FE4982 010FD9C01F14C090271FFE000180D93FF86D6C7FD97FE0021F7FD9FF8002077F4890C86C 7F496F7F48486F1480484818C04982000F7113E0484818F04982003F19F849821AFCEA7F F801FE826D6C17FE80B5FC6E816E17FFA86C5B6C5BA26C5BD807FEC9FCD801F818FECBFC 60A21AFCA2601AF8A24E13F0A24E13E0A24E13C01A8095B5FC1A004D5B614D5B4D5BA24D 5B4D5B614D90C7FC4D5A4D5A604C5B4C13C04C5B4C90C8FC5F4C5A4C5A4C5A4C5A4B1380 4B90C9FC4B5A5E4B5A4B5A4B5A4B5A4B48153F4A90C9FC4A5A4A48167E5D4A5A4A5A4A5A 4A5A4ACA12FE494817FCEB03F8495A4A1601495A495A49CAEA03F8017E171F90BAFC5A5A 5A5A1AF05A5A5ABBFCA31AE0A3487977F85B>I<923803FFF0033FEBFF804AB612F0020F 15FC4A15FF027F16C0494848C66C13F04901E0010F7F4990C700037FD90FFC6E7FD91FF0 6E6C7ED93FC08349486F7F91C96C7F01FE84485AD9FFE06F7F487F6E836E81487F6E83A4 8192C8FCA37E5C6C495F6C5B6D485DEB1FE090CA5CA24E5BA2626062A24E5B97C7FC4E5A 614D5B4D5B4D5B4D5B4D5BDD7FFEC8FC933803FFFC4BB512F092B612C04A92C9FC8418F0 6E15FE92C76C6C7E051F7F050713F005017F7113FE727E727F727F86727F86727F868486 A2721480A21BC0A21BE084A31BF0A2EA01FCEA07FF487F487F487F487FA2B57EA21BE0A3 601BC05CA26C4918804A5D4A18006C90C9FC01FC4C5BEA1FE04E5B6C6C606C6C4C5B6D60 6C6C4C5B6C6C6C4B5B6C01E092B5C7FCD97FF84A5BD93FFE02075B90260FFFC0011F5B6D 01FE017F13E0010190B75A6D6C93C8FC021F15FC020715F0DA007F91C9FC030313F04C7D 79F85B>I<19FC8518011803A21807180FA2181F183FA2187F18FFA25F5FA25F5FA25F5F 187F177E17FE17FCEE01F8160317F0EE07E0160F17C0EE1F80163F1700167E16FE5E4B5A 15035E4B5A150F5E4B5A153F93C7FC157E15FE5D4A5A14035D4A5A140F5D4A5A143F92C8 FC147E14FE5C495A13035C495A130F5C495A133F91C9FC137E13FE5B485A12035B485A12 0F5B485A123F90CAFC127E12FEBDFCA7CB49C7FCB3A34D7F4D80051F14E00303B9FCA6F0 F83F507B7BFA5B>I<0170170701FCEF1F80D9FF80167F02F0ED07FF02FF033F130003F8 90380FFFFE92B7FC6161616161614EC7FC606018E018804DC8FC17F86E14C0020701FCC9 FC91CCFCB3A5923801FFE0031F13FE037FEBFFC04AB612F0020781021F9038007FFEDA3F F0EB0FFFDA7FC06D13C04AC700017F02FC6E7F4A6F7E02E0824A6F7E4A151F8591C96C13 805B1AC0017C7013E090CAFC1AF0841AF8A31AFCA2841AFEA51AFFA4EA03F8EA0FFE487E 487F487FA2B57EA31AFEA44A5D1AFC5C6C90C9FC4918F801F85E90CA14F07E6D18E0606C 6C18C0606C6C18806D4C13000007606C6C167F6D4C5A6C6C4B5B6C6C4B5BD97FC04A5B6D 6C4A5BD91FF8023F90C7FC6DB4ECFFFE6DD9F00F5B010190B612F06D5E023F1580020F02 FCC8FC020314E09126003FFEC9FC487D77F85B>IIIIIII<003FC012FE488BC21280A46C2000 6C67D5FCB3AA003FC012FE488BC21280A46C20006C67792C76C28E>61 D[ 123 130 122 257 136 65 DI<952601FFFC1638067FD9FFC0157C0503B6 00F815FC051F15FF94B800C01301040305F01303040F711307043FDAF00113FE93B548C7 D81FFF130F4B02E00203EB801F03070280020013E04B49C9383FF03F033F01F893381FF8 7F4B01E0933807FCFF92B50080707E4A91CA6CB5FC4A49834A01F8844A49844A49844A49 844A498491B5CCFC4987494985495B4B855B49491A7FA249491A3F5B4B1A1F90B5FC5D48 1D0FA24891CEFC1E075A5C481D03A25C5AA21E015A5CA348F500F81F00A35CA2B5FCB27E A280A47E1F781FFC807EA37E801E016C1EF8807EA26C6E1A031FF07E6F1A077F6F1BE06D 1C0F6D6D1BC01E1F6D7F6D6DF23F80A26D6DF27F006D6D1A7E6D1CFE6E6D4E5A6E6D4E5A 6E7F6E6D4E5A6E6D4E5A6E01FE4E5A6E6DF07F806E6E4DC7FC6F01E04C5A6F01F8EE07FC 030F01FEEE1FF86F6D6CED7FF0030102F04A485A6F02FE020F5B043FD9FFF090B5C8FC04 0F91B65A040317F8040017E0051F1680050303FCC9FCDD007F14E0060101FCCAFC6E8476 FF83>II< BF12FCA48AA3D8000702F8C9121F01004AEE007F6E49170F6E1901F4007F1D3F777E8989 8989A289A2F67F80A31E3FA31E1FA21FC0A21E0FA4F203F0A3F607E0A49BC7FCA21A07A4 1A0FA21A1FA21A3F1AFF1903193F93B8FCA704E0C7123F190319001A3F1A1FA21A0FA21A 07A40803163FA31F7EA697CAFC1FFCA41E01A31FF81E03A41E07A2F60FF0A21E1FA21E3F A21E7FF6FFE0656565651D3F9AB5FC4A070314C091B56C173F01076E040FB6FCC0FCA41F 80A3707B7AFA7C>II<952601FFFC161C063FD9FFE0153E0503B600FC157E051FEDFF8094B800E0 14FE0403711301040F05FC1303043FDAF00013FF93B548C7000FEB80074B02F00203EBC0 0F030702809138007FE04B49C9381FF01F4B01F893380FF83F037F01E0933803FC7F92B5 48EE01FE4A91CBB5FC4A49844A49844A01F0844A49844A49844A498491B5FC4991CC7E49 49855D491C7F495B49491A3FA249491A1F5B4B1A0F90B5FC5D481D07A24891CEFC1E035A 5C481D01A25C5AA3481D005CA3481E7C9CC8FCA35CA2B5FCB27E80A250B639E07FFFF09B B6FCA27EA3806C96C8EDC0000B0F91C7FC775B6C6D86A37E807EA26C80A26C80A27F817F 6D7F817F6D7F6D7FA26D7F6D806E6D606E7F6E7F6E6D606E7F6E6D606E6D6C5F6E6E5F6F 01F0EFFF9F031F01FC4C131F6F01FF933807FE0F6F02C092381FFC07030102F892387FF8 036F02FF913903FFF001043F02F8017FEBE000040F91B70080137E040395C7121E040005 FC140C051F04E091C8FC05031680DD003F02F8CBFC060191CCFC7C8476FF8F>III<92B639F83FFFFC95B6FCA692C7003FECF00005031480837191C7FCB3B3 B3B3ABEA01FCEA07FF487F487F487F487FA2B57EA3615FA34A5E6C5E4A5E5C6C494A5B91 C8FCD81FF84B5B01E04B5B6C6C5F6C6C4B90C8FC6D4B5A6C6C4B5A6C6C6C495B6C01E049 5BD93FF8010F5B90271FFF807F13806D90B6C9FC010315FC010015F0021F1480020101F0 CAFC4E807AFB5E>IIIII<953807FFF095B67E050F15F8057F15FF4CB812C0040F17F8043F 9026FE003F13FE4C01E001037F4BB5C86C13C0030701FC031F13F04B01F003077F4B01C0 03017F037F496F13FF4B48CA003F7F4A49717F4A49717F4A49717F4A49717F4A49717F4A 49717F4A90CC6C7E4A48737F49894949737F4B8549894949737F49894B8549894B854989 90B5487380A24891CE6C7FA2488B4A87A2488BA24849757FA3488BA24A87A2488BA4488B 4A87A5B51F80B16C20006E63A56C67A26E63A26C67A36E636C67A26C676E63A26C676F97 B5FC6C67A26C6E4F5CA26D6D4F91C7FCA26D656D6D4F5B6F616D656D6D4F5BA26D6D4F5B 6D6D4F5B6D656E6D95B5C8FC705F6E6D4D5B6E6D4D5B6E6D4D5B6E6D4D5B02016D4D13C0 6E6D4D5B6F6D93B5C9FC6F01E003035B030F6D4B13F86F01FC031F5B030101FF037F13C0 6F02E00103B55A043F01FE013F49CAFC040F90B712F8040117C0706C93CBFC050F15F805 001580060701F0CCFC798476FF8E>II<9538 07FFF095B67E050F15F8057F15FF4CB812C0040F17F8043F9026FE003F13FE4C01E00103 7F4BB5C86C13C0030701FC031F13F04B01F003077F4B01C003017F037F496F13FF4B48CA 003F7F4A49717F4A49717F4A49717F4A49717F4A49717F4A49717F4A90CC6C7E4A48737F 49894949737F4B8549894949737F4949737FA24949737FA24949737F90B589A24891CE6C 7FA24849757FA34849757FA2488BA24A87488BA44849757FA4488BA34A87A3B51F80B16C 2000A36E63A36C67A46C6D515BA46C676E636C67A26E636C67A26C6D515BA26C676F97B5 FC6D9BC7FC6FDBFF805C6D040301F05E6D6D020F01FC4A5B4E7F6D6D4A6D4A5B6DDC7F80 6D5D6F9127FE001FC05B6D6DD901F8D907E0495B6D4C6D6C5D6D6D010302014A5B6E6C4A 6D6C4990C8FCDC80076F90B5FC6E01C049DA7C015B6E01E070485B6E01F04D5B6E01F8DC 3F0F5B020101FC704813C06E01FE05BF5B92277FFF87E092B5C9FC6F01C36F5B030F01F3 17F86FD9FFF04A5B03016E027F13C06F6E0103B55A043F01FF013F49CAFC040F91B600F8 ED01800401F303C0707E050FEDFBFC0500158306079026F003FE150795C8FC8875160F89 77141F218077143F756D14FF775B0BFE13079A26FFC03F13009BB6FC88A26888A2688868 8868765D8868765D7692C7FC775B0B1F13F87713E00B0113807AA376FF8E>II<922607FFC0EC01C0037F01FEEC03E00203B600C01307020F 15F0023F03FC130F91B8131F4949C66C13804901E00103EBE03F4901800100EBF07FD91F FEC8EA1FF84948923807FCFFD97FF06FB5FC4A150001FF83484982484982488491CAFC48 488385121F4983003F84A25B007F197FA21A3FA212FF1A1FA31A0F7FA37F1A07A27FA26C 7F6EEF03C097C7FC806C7F14FC806C6D7E15E06C14FCEDFFC06C15FC6CEDFFE017FE6CEE FFE06C17FC6DEEFF806D17E06D17F86D17FE6D836D18C06D846D6C836E83020F83020383 DA007F821507DB007F1680040716C0EE007F050715E0DD007F14F01807060114F8727E85 7313FC85857313FEA285851BFF00788512FCA286A4867EA56C1AFEA37FF23FFC7FA26D19 F81A7F7F1BF06D18FF6D19E06D4D13C06D5F6E188002E04C13006E5E02FC4C5A02FF4C5A 01E701C0EDFFF801C101F84A5B01C001FF020F5B496C01FC017F5BD9001F90B7C7FC6E5E 48010316F848D9007F5D030F15C04802014AC8FC0070DA000713E0508476FF65>I<001F C012E0A74802C0C76C01FCC7000F14F002F8C86C49EC007F02C06F49150F4A1B0349C984 4988491D7F491D3F491D1FA2491D0FA2491D07A2007F1FF890CA1903A5007E1E01A800FE 1FFC481E00A6CB1A00B3B3B3B14E7F4E7F050FB612E0037FBA12FCA61901767B7AFA83> IIII89 D[27 181 108 263 51 91 D<02C01518496C153C0103167C010716FC49484A5A49484A5A49C8 485A017E4B5AA2494B5A48484BC7FC49153E0003167E48485DA248484A5AA2495D001F15 0390C85B481507003E5EA3007E150F007C5EA300FC151FA24893C8FCA501FFED1FE000F9 6D4A7EB500E0ECFFFC6E81A26E81A26C6D6D1480A46C81A24A16006C816C496D5B6C816C 496E5A6C0180EC3FF06C6CC8EA0FE0393765FD5B>I[27 181 125 263 51 I<15C04A7E4A7E4A7E4A7E4A7E4A7E4A7F91B57E 4980498049EB3FF849486C7E49486C7E90393FF003FF49486C7F49486C7F48496D7E4890 C76C7E48486E7E48486E7ED81FF0EC03FE48486E7E48486E13804848ED7FC06CC9EA3F80 003EEE1F00001C160E321C6CFD5B>I<92B5FC021F14F091B612FE01036F7E010F16E049 D9C00713F8D97FF8C77FD9FFC0EC3FFE6E6E6C7E486D6E7F486D6E7F6E8048707F6E6E7F 85187F85A2727E6C5BA26C496F7F6C5B6D5AEB1F8090CAFCA84CB6FC93B7FC150F157F02 03B8FC021FECE01F027FEBFC0049B512E0010791C7FC4913F84913E0017F5B90B5C8FC48 5B4813F85A5C485B485BA2485BA24890C9ED0FC0A3B5FC5BA260A4607F6C94B5FCA26E5C 6CDC03F79038C01F806E15E36C16076C6DDA1FC39038E03F006C6DDA3F816D5A6C01FCDA FF01EBFFFE6C01FF902603FE005C6C6C9026E01FFC6D5B6D90B500F06D5B010F4B6D5B01 03038001071380D9007F49C7D801FCC7FC020301E091C9FC525379D05B>97 DIII< 923801FFF0031F13FF037F14E00203B612F84A15FE021F9038C07FFF91277FFE000F13C0 DAFFF801037F4901E001007F49496E7E49496E7E4990C86C7E495A49486F7E017F701380 495A4A6F13C05A484917E0844819F05C48831AF85A5C5AA2197F4819FC91CAFCA4BBFCA4 1AF891CCFCA97EA280A37EA36C7FA26C19786E17FCA26C18016C6D17F8A26C6D16036C19 F06E16076D6CEE0FE0013F18C06D6C161F6D6DED3F806D01E0ED7F006D6D15FE6D01FCEC 03FC6D01FFEC0FF86E01C0EB3FF0021F9039FC01FFE06E90B65A020393C7FC020015FC03 3F14F0030714C09226003FFCC8FC46537BD051>I<933803FF80043F13F093B512FC0303 80030FECFF80033F010113C092267FF80013E04B485A4AD9C00313F04A495A4A494813F8 4A5A141F5D4A5A147F5D02FF6E13F07113E049496D13C0711380F07F0095C7FC495BB3A9 B9FCA7D8000301E0C9FCB3B3B3A7497F81013F13FFB812F8A614C13D807BFF38>IIII<163FEEFFC04B13E04B13F04B13F84B13FCA24B13FEA66F13FCA26F13F86F13F06F13 E06F13C0EE3F0093C7FCB3A517FEED3FFF021FB5FCA7EC000F150181167FA2163FB3B3B3 B3A7EA07F8487E486C15FC486C147F487FB57E17F8A2EEFFF0A217E05D028014C06C4A13 80020014006C48495A6C48495A6C48495A6CB46CB45A6C90B55A6C5D6C6C91C7FC011F13 F8010113C02FA089FA38>III< DA0FE0DAFFF8EE1FFF48B5020FD9FF804AB512F0B6023F02E0020714FC94B600F8021F14 FF040303FE027F15C0040F01006D902701FFE01F7FDC1FF8011F6D48D900037FDC3FC06D 9026C007F86D7F4CC76C9026E00FE06D7FC603FE6E4A48147F011FD9E1F86E6D48C86C7E 0107D9E3F0DCF87E82DBE7E05F4C6E4A816D01EF05FD84DBFF80EEFFF093C95C74834B4E 83A24B60A34B95C9FCA44B5FB3B3A7496D93B54C7FA2013F01FF030702E092B512FCB8D8 C01FB7D8F803B8FCA602E1DDFC3F178790507BCF99>IIIIII<912607FFF0131C027F01FF 133E0103B6EAC07E010FEDF1FE903A3FFE003FFBD97FE0EB03FF2601FF8013004848C812 3FD807F8151F000F160F49150748481503123F1701485A1700A312FF187E7FA27FA27F6D 163C01FF93C7FC6C13C014F014FE6CEBFFF0EDFF806C15FC6CEDFF8017F06C826C16FE6C 826C17C0013F826D820107820101826D7E020781DA003F801501DB000F14801601706C13 C0830078160F00FC7013E083837E83A36C177FA37F19C07FA26D16FF19807F4D13007F6D 4B5A6D5E6D15076EEC1FF802E04A5AD9CFF849B45A902787FF801F1380010390B6C7FC48 C615FC486D14F048010F14800070010101F8C8FC3B537AD048>IIII<2B FFFE1FFFFC0FFFC7B5903A0FFFF8FFF090B692B692B5FCA6C66C91C7000F02800100ECFE 00011F01F8020349C8001F13F06D496E496F13C06D70496F5B7890C7FC6D057F5F741501 6F636D053F5F741503816D716C5E616F1A07027F725D4F160F6E6C63877091B5151F6E64 877049173F6E04F994C8FC877001035F6E04F0167E8770010717FE6EDCE07F5D8770010F 16016E4C6C6C5C181F70DA801F14036E725C063F16076F6C4A6C5D1C807049160F6F027E 6D5D1CC0DD80FE161F6F4A6D5D1CE005C1173F6F4A6D92C9FC1CF005E35F6F4A6D147E1C F805F717FE6F4A6E6C5A17FF4EEC3FFD6FF0FFF8A26F4A6E5BA37090C86C5BA370486F5B A370486F5BA370486F90CAFCA370486F5A7048167C7C507DCD83>I<287FFF87FFFE903A 03FFFE3FFF91B593B6FCA6D8000F02F001001580010102C0023F01F8C7FC6D4A16C06E70 90C8FC6E5F6E6D15F86E5F705D6E6D4A5A6E6D5D6E4CC9FC705C6E6D495A6F6C5C6F4A5A EF80076F6D485A6F6D485A616F6D485A6FEBF87F6F6D48CAFC606FEBFFFC82705B60705B 82707FA2707F707F845E4C7F854C805EDC3FCF7F05877FDC7F037F16FF4B486C7F4C6C7F 4B486D7E15074B486D7F4B486D7F4C7F4B4881037F6E7F4BC76C7F4B804A488202036F7F 4A486F7E020F82021F84027F707F02FF8401036D83011F4D7F48B692B6FCB700C00107ED FFE0A6D9FC7FEFFE1F5B4E7ECD60>II<000FBA12C01AE0A492C8003F13C002E04B1380028092B512004848C9 FC494B5B494B5B494B5BA2494B5B4D5B494B5BA24D5B4992B5C7FCA24C5B4C5B4C5B123F 90C8485B4C5B4C5BA24C5B93B5C8FCC8485BA24B5B4B5BA24B5B4B5B4B5BA24B5B92B5C9 FC4A5BA24A49EC03F04A5B5C5E4A5B4A4914071AE04A5B91B5C8FC495BA2495B4949150F 495BA2495B4949151F1AC0495B90B5C9123F485B197F484916FF48495D48495D60484915 1F4849157F4849020FB5FC91B91280BBFCA47E444E7BCD51>II< 02FE1680902607FFC0EC01C04901F0EC03E0013F01FCEC07F04901FFEC0FE090B66CEB3F C04803F0EB7F80489239FC01FF004892B6FC485FD9F8035D261FE0005D4848011F5C48C7 6C5C00FE02035C007C020091C7FC0038ED3FFE0010ED07F03C1271F95B>126 D I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq cmti10 10.95 68 /Fq 68 128 df11 D<98380FFFFE50B612F0 080F15FE087FEDFF804FB812E04F9026FE000713F0070F01E09038007FF84F90C8EA0FFC DF3FFCED03FE4F5ADFFFE0ED0FFF4E495D4E5F4E495DA24E90C9B5FCA24E5A063F18FEA2 4F17FC067F18F8F67FF04E48EE3FE0F61F809BC7FCA24D5BA35F61A45F61A45F61A55F96 CCFCA3031FBB12FC4B86A25D66A28192C7D87FFCC9FC66A305FF5E4E5FA3644C6160A264 665EA24E5D66A34C5F4E94C7FCA3644C6060A21C7F655E95C9FC1CFF65A25E4D5D65A304 7F5E4D5FA21FFC51EC01FE1DC004FF1AFC5F5114030B8013F85DA24D18075115F01D005D F60FE05F1E1F1FC04B715A4DF03F80A2756CEB7F00A24B7114FE4D170175EB87FC75EBFF F84B725B94CA6C5B0A0F1380E201FEC7FC99C9FC4B5AA44B5AA35EA215FF5EEA01F8EA07 FC486C5C486C5A4801815B5A5E1483B591CFFC14035DEBFE0701FC5B49485AD87FF05BEB C01F003F495A9038F07FC06CB55A6C91D0FC000313FC6C5B38003FC070A584FF66>I19 D<14FE903803FF804913C04913E0 5B4913F05BA290B512F8A86D13F07FEB1FFDEB07F390380003E0A3140715C0140FA21580 141F15005C143E147E147C14FC495A5C1303495A5C130F495A49C7FC137E5B1201485A48 5A485A485A485A48C8FC12FE127812301D3759FD38>39 D[67 182 101 263 74 I[66 182 125 263 74 I<14FEEB03FF010F13804913C04913 E05B15F090B5FCA25AA67EA27F90383FFBE0EB0FE3EB0003140715C0A2140F1580A2141F 15005C143E147E147C14FC495AA2495A5C1307495A495A49C7FCA2137E5B485A485A485A 485AEA3F8048C8FC12FE5A127812301C37739338>44 D<001FB712F84816FC5AA217F8A2 B8FCA217F0A217E06C16C02E0C70AC41>I<137F3801FF804813C0000F13E04813F0A248 13F85AA3B5FC14F0A214E06C13C0A26C1380381FFE006C5AEA07F015146C9338>I<191C 193E197EA219FC18011803180719F8180F181F183FF07FF0EF01FF5F5F4D13E0173F94B5 FC5E040F14C0163F4BB6FC92B7FC4A02CF13804A148F4C5A16F84A01C01400913803FE00 91C85AA260A2177FA260A217FFA260A25EA260A25EA260A25EA260A25EA260A25EA295C7 FCA25EA25FA2167FA25FA216FFA25FA25DA25FA25DA25FA25DA25FA25DA25FA25DA294C8 FCA25DA25EA2157FA25EA215FFA25EA25CA25EA25CA2140F91B6FC007FB812FCB97EA460 6C02075C3F796BF85D>49 DIII<046017E004F8EE03F0DB01FE161F706C15FF05F8020F13 E09426FFC001B512C04B91B71280F3FE0063634B5F631B8098C7FC4B16FC1AF01AC097C8 FC4B15F804C714C09326C01FF0C9FC94CBFC153F5EA3157F93CCFCA35D5DA314015DA314 035DA314075DA2EF3FF8020F0103B5FCDBE01F14C0047F14F003E1B67EDA1FE79038C03F FC923ACFFC000FFEDBDFF0EB03FFDBFFC0814A90C76C7F03FC6E7F5D4B82DA7FC0157F4B 8292C9FC027E83A2143C91CA7FA786A396B5FCA262A260A46001FE60EA03FF487F486D5D 4861487FA24E5B485BA24E5B5C62B5C95A496013F8494C90C8FC48CA5B18FF616C4C5B6C 5E614D5B4D5B6D5F003F4C90C9FC6D4B5A4D5A6C6C4B5A6C6C4A5B04075B6C6C4A1380D8 03FE023F90CAFC6C6C6C48B45A6CD9F00F13F86DB612E06D5D6D92CBFC010714F8010114 C09026003FFCCCFC547D6DF85D>I56 DI<15FCEC07FF4A13804A13C05C4A13E0 91B5FCA25BA416C0A216806D14005D6E5A6E5AEC0FC091C8FCB3B3A2137F48487E487F00 0F7F487FA2487F5AA3B5FC5CA25C6C5BA26C5B6C48C8FC6C5AEA07F0234E6CCD38>I[115 130 117 257 135 65 D<4BBB12E01EFE4BF2FFC01FF01FFC 1FFF6F8892C7001F49C8000380050701F8DB007F7F0C1F7F787F4F707F787FA24D727F61 781480A25F4F8321C0A25F61A35F96CBFCA394B595B5128060A34C4F140060545BA24C4F 5B60545B684C4F5B4E5F545B684C96B5C7FC4E4C5B535B0B0F5B4C4E13E04E4C5B9AB5C8 FC525B4C050713F84E033F13E00903B5128095B800FCC9FC4C18E0A21DFE777E93B5C900 1F13E04D040313F8767F766CB4FC4B737F4D717F8B777F4B854D85A2777F5D4D8589A24B 875FA35D5FA35D5F65A24B6394CBFC656792B5FC4C6067654A644C6067654A97B55A4C62 5291C8FC644A4F5B4C4D5B525B525B4A4F5B4C4CB55A515C4A060F49C9FC093F5B4A494B B55A0103B56C030F14E0003FBD12804899CAFC1CFC1CE01C80BC00F8CBFC6C97CCFC7A7C 75FB80>I<972607FFE0150797B500FEED0F80070FDAFFC0EC1F00077F03F05C0603B76C 5C060F04FE5C063F70495A95B6D8801FEB800305039126F00001EBC007050F0280903900 7FE00F4D01FCC8D81FF05B057F01F092380FF81F94B50080923803FC3F040391C9000113 7F4C01FC71485A4C01F070B5FC043F49834C138093B5CB6C5B4B5B4B01F8844B5B4B4972 5B4B5B4B5B4B90CC7E4B48635C4A5B4A49854A4963A24A5B4A5B4A9AC7FC5E91B5CDFC5B 494963A2495BA24949635B5D5B4B635B5D90B51B07A2484A745A9BC9FC4891D2FCA3485B A3485BA35A5CA35A5CA35A5CA55CB5FCA5F503E04A507EA21D0F66A31D1F6C651D3F66A2 1D7F9BC9FC6C646E621C01525A6C641C076E626C1B0F525A6E4F5A6C641C7F6C6D4FCAFC 515A6C6D4E5A515A6C6D4E5A6D6C4E5A6D4F5A6F4D5A6D6D4C48CBFC6D6D4C5A6D6D4C5A 6D01FCEE1FF86D6DEE7FF06D6D6C913801FFC06E01E002075B6E01FC023F90CCFC020F90 3AFFC007FFFC6E91B612F002015F6E6C1680031F03FCCDFC030715F0DB007F91CEFC0407 13F0798465FF82>I<4BBB7E4B1AFC4BF2FF801FE01FF81FFE6F8792C7003F01FCC8001F 80050F01F0030114E0776C7F0C1F7F4F04077F8A0C007F4D737E4F717FA2797F4D737F4F 838D8B5F96CB808B8D94B5FC4E848DA25E607A7EA25E60A35E602280A25E4E96B5FCA35E 60A222004C6260A35E95CCFC676993B5FC5F67A24B655F67A24B655F67695D4D6169A25D 4D4F5BA2694B98B5FC4D98C7FC66685D4D4E5BA2545B5D94CC485B686692B5634C4F5BA2 5490C8FC4A515A4C6265535B4A505B4C62535B535B4A5090C9FC4C4E5A535A525B4A0707 5B4C4D5B525B0A7F5B4A96B5CAFC4C040313FC090F5B4A063F13E050B55A4A49030F91CB FC0107B56C92B55A007FBC12F8BD12E099CCFC1BFC1BE098CDFC6C19E0817C74FB89>I< 0303BE12C04B1DE0A58192C76C49C97E050F01F8040314C0F6007F4F171F1F075F8B4F83 21805F8B61A25F210061A294B5FCA296CCFCA24C63A260A25EA24E1801E20FC05C4C4D7E 6560A24C173F536D5A4E96C7FCA24C177F9ACAFC4E5DA25E515A4E1403A24C1607F31FFC 4E147FF207FF93B9FC64A35D64A24DC7120F4B1601746C5A4D153FA25D645FA25D645F1F 3F4B057F4B7E99C890C7FC5F674B4D5D5114014D611B7C4B94C81203674D18076792B519 0FA294CC485AA24A641E3F4C197F674A1BFF9CC8FC4C60664A1A031D074C611D0F4A505A 1D3F5E535A4AF101FF525B4C170F1C3F4A96B55A1B034A49043F5C0107B56C030FB6FC00 7FBEFCBFC9FCA265A36C647B7B74FA7B>I<4BBEFC4B1D80A35DA28192C7003F91C9FC05 0701FC16070C0014004F173F8B4D858B618B5F68611F015FA261A25FA24F60A294B5FCA2 96CBFCA25E1F034E61A25EF407C04E4B7EA24C171F536D5A4E95C8FCA24C173F65601C7F 5E9ACAFC4E5D635E515A4E14071B0F4C167F973807FFFC95B7FCA293B9FC64A35D95C700 0F5B4D14001B7F4B173F644D151FA25D645F1B3F5D645FA24B177F99CBFC5FA25D1B3E4D 92CCFCA25DA25FA292B5FCA294D0FCA25CA25EA25CA25EA25CA25EA25CA25EA25CA25C01 03B6FC003FB812FE4883A260B9FCA26CD9FE0F5C797B75FA77>I<972607FFE0150797B5 00FEED0F80070FDAFFC0EC1F00077F03F05C0603B76C5C060F04FE5C063F70495A95B6D8 801FEB800305039126F00001EBC007050F02809039007FE00F4D01FCC8D81FF05B057F01 F092380FF81F94B50080923803FC3F040391C90001137F4C01FC71485A4C01F070B5FC04 3F49834C138093B5CB6C5B4B5B4B01F8844B5B4B49725B4B5B4B5B4B90CC7E4B48635C4A 5B4A49854A4963A24A5B4A5B4A9AC7FC5E91B5CDFC5B494963A2495BA24949635B5D5B4B 635B5D90B51B07A2484A745A9BC9FC4891D2FCA3485BA3485BA35A5CA35A5CA35A5CA55C B5FC087FB500E1B5FC97B97EA29DC7FC615C735FE0000102FCC8FCE1003F13F0765BA264 7E66A26466A26C7F99B5FC9BC9FCA27E63806C64A26E607E6E627E6E606C646E606C626D 7E6D6D4D5B6F5F6D6D94B5FC6D6D5E6D6DDC07FC5B6D6D4C5A6D01FF93383FF07F6D02C0 EDFFE06E01F00203496C5A6E01FE021FEB801F020F903CFFE001FFFE000F6E91B6481307 020105F013036E6C04C06D5A031F93CDFC030715F8DB007F1480040701F0CEFC798465FF 8D>I<4BB527F87FFFFC91B539FC3FFFFE4B91B66C4991B7FC4B61A46F4D6D17FE92C700 3F02C0C9001FECE000050F01FCCA000749C7FC4F61A24F61A2675F4F61A2675F4F61A267 5F4F61A26794B5FC96CB5CA29CB5FC5E4E97C8FCA2665E4E61A2665E4E61A2665E4E61A2 665E4E61A2665E4E61A2665E4E6195BBFCA293BDFC68A35D4DCB91C9FCA2655D4D61A265 5D4D61A2655D4D61A2655D4D61A2655D4D61A2655D4D61A26592B5FC94CB5CA29AB5FC5C 4C97CAFCA2645C4C61A2645C4C61A2645C4C61A2645C4C61A24A61A24A610107B500F804 03B512FC007FB86C013FB812C0B96C4983A44E616CD9FC3F91C76CD9FE1F5C907C75FB87 >I<4BB5D8F83FB5FC4B91B71280A34B1800A26F5F92C7003F02E0C7FC050749C8FC61A2 61A35F61A35F61A35F61A35F61A394B5FC96C9FCA35E60A35E60A35E60A35E60A35E60A3 5E60A35E60A393B5FC95CAFCA35D5FA35D5FA35D5FA35D5FA35D5FA35D5FA35D5FA392B5 FC94CBFCA35C5EA35C5EA35C5EA35C5EA25CA25C0103B512FE003FB812E04883A2B95AA3 6CD9FE0F5C517C76FB46>I<95B600E1B5FC4D92B61280A5711800DE000102FCC7FCDF00 1F13F064A264A262A264A262A299C8FCA297B5FCA263A261A263A261A263A261A263A261 A263A261A263A261A263A261A298C9FCA296B5FCA262A260A262A260A262A260A262A260 A262A260A262A260A262A260A297CAFCA295B5FCA261A25FA261A25F13FE2603FF805E00 0F7F485E486D5EA25A5FB55FA24D5BA24A4A5B5C4D90CBFC91C85B01FC15FF494A5B01E0 5E48C8485B6C4B5B6C4B5B6D4A5B003F4B90CCFC6D4A5A6C6C4A5AD80FF8010313F0D807 FE010F5B2703FFC07F13806C90B6CDFC6C6C14FC6D14E0010791CEFC010013F0618070FB 60>I<4BB5D8F83FB512E04B91B77E5D64A36F6092C7003F02E0C9FC050F49CAFC19F8A2 61A35F61A35F61A35F61A394B5FC96CBFCA35E60A35E60A35E60A35E60A35E60A35E60A3 5E60A393B5FC95CCFCA35D5FA35D5FA35D5FA35D5FF501F8F503FC4B1AF85F1D071EF05D 4D170F1EE0A24B191F4D18C0A21D3F92B5198094CB127FA2F5FF005C4C5F651C035C4C4D 5AA21C0F4A4F5A5E1C3F525A4A19FF4C5E515B634A181F4C4C5B98B5FC4A1703080F5C4A 4992B6FC0107B56C140F007FBDC7FCBEFCA264A36C63667C74FB72>76 D<4BB750B612FE4B704F15FF5D6A6AA26F704F15FE92C7003FF7E000050F5249C7FC585B A210FD5BA2575A4DF303F306EF65F907E306E76D19E7053FF30FC706C765F91F87575A17 7F0687087E5CA2575A05FFF201F8060765726DEF03F06A4CF307E005FEE00FC091C8FCA2 56485A160305FCE03F005BA20E7E13FF0407634D6C6D62555A69040FF203F005F0DF07E0 5CA255485A161F05E0DF1F805CF73F0069043F1A7E4D6C6D626769047F4F5A4D4E485DA2 54485B16FF94C74D485D545A694B6F6C4BC7FC4C9BC9FC1E7E545C15034C4E485DA25348 14FF03074F5A4C65535A736C5F030F4F5A4C6553C7FC0B7E5C151F4C4E5EA252485C033F 4E5A4C65525A7301805E037F4E5A4C4D485EA252C85A15FF93C8037E5FA2525D4AF081F8 4B9BCAFC73EBC3F0680203F0C7E04BDDCFC05EA2E1DF8015FF14074B05FFC95B6367020F 604B6F6163021F6463023F4E5F147F4A6C4D5D1303010F01FE4D5D90B600C093C9B512FC 007FDBFF80050FB812C0B86C6D484A83A262624D656C01C391C76C486E020F5CA87C73FB A3>I<4BB600FC94B538C3FFFE4B6F4C91B6FC4B62A285A26F706F16FE92C7001FDE0003 15000507DF007F13F074051F13C04D99C7FC7A5A7460695F746018EF74171F173F06C762 86203FEF7FC306836D60A20681197F05FF80060162847516FF4C804D6F94C8FCA2735F04 03824D628575150316074D6D60871F07040F804D6F5E8575150F161F4D6D60871F1F043F 804D705DA274163F047F834D628676147F04FF8194C86E5DA27416FF4B844C98C9FC8676 5B15034C6F5E8874150315074C715C86F58007150F4C705D1DC01E0F031F834C06E05BA2 75141F033F19F04C705D1DF81E3F037F834C06FC5BA275147F03FF19FE93CA5E879AB5FC 5C4B7192CAFCA28814034B6288A214074B725BA3020F854B62A2021F85A2023F735B147F 4A7E010386010F01FE6290B612C0007FDBFF8082B87E661D7FA25F6C01C391CB6C5A907C 75FB87>I<97380FFFC04FB512FC071FECFFC096B712F0060316FC061F16FF067FD9F001 804DB5C7003F13E04D01F802077F050F01E06E7F053F0180020013FE4D48C96C7E932601 FFF8707F4C4982040F01C0707F4C49707F4C90CA6C7F4C4883DCFFF8854B49717F03075B 4B49727E4B5B4B747E4B90CCFC4C1B804B48854A491BC05C4A5B4A49854A491BE0A24A5B 4A1DF093CDFC4A5A5B5D5B495B20F8495BA2495B5BA2495BA290B55AA34891CE5AA2481F F05C5A665C5AA220E0484963A4484998B512C0A4485214805CA2531400A34A505BB5FC67 65A2535BA2674A626765679AB5FC67A25291C7FC525B7E525B666E6166525B6C6366525B 6C98B5C8FC6E62636C505B515B6E4E5B6C646E4E5B6C505B5190C9FC6C6D4E5A6C6D4D5B 5013F06D6C050F5B6D6D4C5B505B6D6D4C48CAFC6D6D4B485A6D6D03075B6D01FC4B13E0 6D6D033F13806D6C6C6C49B5CBFC6E01E0010713FC6E01FC017F13F0020790B712C00201 4CCCFC6E6C15F8031F15C0030102FCCDFCDB001F1380758465FF8C>I<4BBA12FE4BF1FF F04B1AFE787E1FE01FF86F8792C7003F01FCC86C7F050F01F003077F0B0014807813C04F 041F13E07813F07813F85F4F7013FCA27813FE5F61A220FF5F96CAFCA394B5FC60A34C61 60A34C4F13FE60A220FC4C616020F8664C1BF0605413E020C04C614E19809BB51200674C 604E4C5B535B535B4C4E5B95CA4813805390C7FC52485A93B504075B4D041F13F099B512 C0090F5C4B90B948C8FC1DF81DC052C9FC4B18F051CAFC05FCCEFCA25D5FA35D5FA35D5F A35D5FA35D5FA392B5FC94CFFCA35C5EA35C5EA35C5EA35C5EA35C5EA25CA25C0107B512 F8007FB87EB97EA4606CD9FC3F91CEFC787C74FB7B>I<97380FFFC04FB512FC071FECFF C096B712F0060316FC061F16FF067FD9F001804DB5C7003F13E04D01F802077F050F01E0 6E7F053F0180020013FE4D48C96C7E932601FFF8707F4C4982040F01C0707F4C49707F4C 90CA6C7F4C4883DCFFF8854B49717F03075B4B49727E4B5B4B90CC6C7E5D4C7313804B5A 4A491BC04A5B4A874A5B4A491BE0A24A5B4A90CD14F08A4A5A495BA2495B5B4B1CF85B5D 5B495BA25B5D90B56392CEFCA25A5C481FF0A2485B66A2485BA220E0484963A448495113 C0A4484998B51280A3531400A25C535BB5FC6765A26791CE5A67A2535BA2535BA2535BA2 9AB5C7FC666C6366525BA2525B525B6C7F525BDD07FC4B5B6CDC1FFF94C8FC057F6D4A5A 6E91B500E014FF6C4B6E495B932603FC074A5B6E902707F001F85D6C92270FC0007C495B 4C484B5B6C6D49C7003C495B043E023E4990C9FC6C6D017E021E495A6C037C4C5A6E01FC DA1F0113F06D6C4903075B6D6C4D5B505B6D0180DC7FFECAFC6D01C14C5A6D01F15F6D01 F817E06D01FC4B13809026007FFF92B5CBFC6E6D010713FC6E6D017F13F0020790B700C0 156002014D15F06E7E031F03DF15010301DAFC3F5EDB001F138093C8160386535A1D0FA2 744A5A077F153F53C8FC745C6474EB07FE74131F9739FF80FFFC98B5FC65A26565A26573 5D9AC9FCA2735C64735C735C7314C0735C7349CAFCF21FF075A365FF8C>I<4BBA12E04B 19FF1EF01EFC1EFF1FC06F1BF092C7001F49C7000180050701F8DA001F7F0B0313FF0B00 804F707F8A787F4D727F4F828C8A4D86618CA25F61A34D8696CAFC68A294B55F60A34C4F 5B60A2545B5E4E6166684C634E5F9BB55A9DC7FC4C4E5B4E60535B535B4C4E5B4E4C1380 0B7F90C8FC535A4C050313F84E030F5B0A3F13C051B5C9FC4C043F13FC95B812E01D800A F8CAFC93B9FC884DC813FF091F7F4B717F4D03037F757F894B717F4D707EA2894B844D84 A35D4D84A35D5FA2645D4D60A299B5FC5D94CAFCA26392B5FC4C96C9FCA2635C5EA34A60 4C60A2201F4AF53F805EA2207F4A1E005E684A651F014A725E0103B500F8505A003FB86C 8048714E5A754B5A766C131FB9704A5A769038C0FF806CD9FC1F4A6F90B5C7FCCF000314 FC765CE2003F13E00B031380798075FB85>I I<0107BF1280491EC0A35BA349912680000791C7000F148003F0C702FC140003801A3F49 48C84A150F4A8702F04B8349481D004A4D815C485F91C9FC4960000366495EA2484860A2 4E60485A625B001F94B51603A24995C95B123F495DA2007F6090C919074D615A4860A25F 007C775ACA4A93C8FCA25FA261A25FA261A25FA261A25FA261A294B5FCA296CDFCA25EA2 60A25EA260A25EA260A25EA260A25EA260A25EA260A25EA260A293B5FCA295CEFCA25DA2 5FA25DA25FA25DA25FA25DA25FA25DA2157F020FB67E001FBA7E4885A35AA26CDAFC0F5D 727B60FA82>I<0003B500F0B500F892B53887FFFC4891B66C4A91B512FE4862A46C4D6E 16FCC76C0280C90003ECFE00021F01F8CB6C13E04C061F138054C7FC4C725A664A63A24C 61A24A1A1F665EA291B5193F6693CCFCA2491B7F9BC8FC5DA24963655DA2491A01655DA2 491A03655DA2491A07655DA2491A0F655DA2491A1F655DA290B5193F6592CCFCA2481B7F 9AC9FC5CA24863645CA2481A01645CA2481A03645CA2481A07645CA2481A0F645CA2481A 1F645CA21B3FB56291CCFC1B7F99CAFCA26349611A01631A03631A07631A0F505A007F62 1A3F505A98CBFC003F616D4D5A4F5A6C4E5A4F5A6C6D4C5A4F5A6C6D4C5A4E48CCFC6C6D 4B5A6C6DED0FFC6C6DED3FF86D6CEDFFF06DB402035B6D01C0011F13806DD9FC01B5CDFC 6D90B612FC6D5E010016E0023F1580020F02FCCEFC020114F09126001FFECFFC77805CFB 87>I<263FFFF0B500F8933A0FFFFC7FFC4890B66C4C90B512FEB85FA46C4C7015FCD800 1F02F0CA0001150001070280DD003F13F06D49CC6C13C07790C7FC4B626F626666535A66 6D1B3F6653C8FC65651C016F611C0365525A6D1A0F651C1F65525A1C7F9AC9FC705F6451 5A1B036E611B0764515A1B1F641B3F705F51CAFC63636E1701631A0363505A1A0F637015 1F63505A1A7F6E95CBFC62624F5A1903621907705D4F5A191F626E163F624FCCFC616118 01705C1803614E5A6E150F61181F614E5A187F96CDFC705B604D5A17036E5D1707604D5A 171F60173F04FE5B4DCEFC5F5F6E13FF5FA25F5FA25FA25F5FA26E91CFFCA25E5EA25EA2 5E5EA25E157F5E93D0FC77805AFB87>I<267FFFE1B500F049B5000FB500C0913A3FFFF8 7FFCB86C4991B66C4A90B512FE4F97B7FC5518FCA36C4C6D4D6E15F8D8003F02E0C80001 0380C80003ECFE00010F91CA6C01F8CA6C13F003FC7101E0051F13C06D499EC7FC53715A A15AA15AA15AA2595AA15A233FA15A237F7795C8FC6B6B585A636F545A98B5FC585A6D4E 190F6B50191F6B50193F6B504FC9FC6209DF18FE1A3F099F4D5A087F1803091F6008FE18 076ADF01FC6E150F6ADF03F8181F07076D6008F04E5A6F150F08E04ECAFC191F08C018FE 6DDD3F80170169DF7F0017036907FE18070601624F4E5A18034F4E5A18074F4E5A060F19 7F4F96CBFC4E4860775C4E481701067F6196C76C4B5A604E4E5A6F13014E4E5A0503191F 6D4C614D48183F684D48187F9DCCFC4D4860053F614E4D5A177F95C84B5A5F4D4E5A4C48 180F674C48EFFC1F674C48183F040F624D6F4ACDFC161FDC9FC018FE16BF4DEFFDFC6E01 FF18FF94C95D5E665E664C61A24C61A24C96CEFCA24C605E6593CAFC655D755B4B61A24B 61A24B616E5A9ACFFC5D644B715AA7805AFBB6>I[<0507B512F84D14FCA21AF8A25FA21A F006E0C7FC173FA260A2177FA260A217FFA295C8FCA25EA25FA21603A25FA21607A25FA2 160FA25FA2161FA25FA2163FA25FA2167FA25FA216FFA294C9FCA25DA25EA21503A25EA2 1507A25EA2150FA25EA2151FA25EA2153FA25EA2157FA25EA215FFA293CAFCA25CA25DA2 1403A25DA21407A25DA2140FA25DA2141FA25DA2143FA25DA2147FA25DA214FFA292CBFC A25BA25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2133FA25CA2137FA25CA213 FFA291CCFCA25AA25BA21203A25BA21207A25BA2120FA25BA2121FA25BA2123FA25BA248 B57E81A3B6FCA25D6C91CBFC>70 181 116 263 56 91 D[<0507B512F84D14FCA21AF8 A25FA27114F094C7120FA2191F1AE0A3193F1AC0A3197F1A80A319FF1A00A36061A31803 61A3180761A3180F61A3181F61A3183F61A3187F61A318FF96C7FCA35F60A3170360A317 0760A3170F60A3171F60A3173F60A3177F60A317FF95C8FCA35E5FA316035FA316075FA3 160F5FA3161F5FA3163F5FA3167F5FA316FF94C9FCA35D5EA315035EA315075EA3150F5E A3151F5EA3153F5EA3157F5EA315FF93CAFCA35C5DA314035DA314075DA3140F5DA3141F 5DA2003FB5FC5A5DA2B6FCA25D6C91CBFC>70 181 131 263 56 93 D97 DIIIIIIII III<49B4922601FF C0ED07FF010701C0021F01F8037F13E04901F091B500FE0203B512F8496D01036E6C010F 14FE496D496F498090267F87FE011F01016D90267FFC077F9026FE03FF90283FF0007FF0 9026FFC0017FD801FC9126807FC06D6C4890C77F6E4AC79026FC03FC81D803F8DAC1FE02 1F4948147F0007DBC3F89226FE0FE08101F0DAE7F04C5ADCEFE04C5AD80FE0DAFFC06F48 C87F4D6E01FE153F121F01C092C85C4A495F123F01804A4B49157F4C5F5C007F4B5F1300 4C5F4849494B90C912FF48684C5EA2007C49057F5EC76793C95BA24A05FF5E694B5FA202 7F4C5F694B5F6702FF4C61A24B4D5D9EC8FC495F674B4D5EA2494D177F684B5F0DFFEC0F C0494D4EEB1FE0A24B94C84816C068494D4C153F5614804B5E54157F49057F4E1400A292 C9496154495B4917FF575A4A5F56485A017F4C637814074A4D4E5A6A01FF4C1A1F784A5A 4A4D6F02FFC7FCF883FE78EBFFFC4A4D705B6D486F497013E06D486F90CA000F5B6DCA00 7CDD03FEC8FC8B5271CF95>I<49B4923803FF80010701C0023F13F84901F091B512FE49 6D010380496D010F8190267F87FE90261FFE037F9026FE03FF90263FF0007F00016D9026 80FFC06D7E01FC02C190C77FD803F8DAC3FE143FDCC7F881D807F0ECEFF0EEFFE0D80FE0 4B6E7E5F121F01C092C8FC4A5B003F5D0180183F5E5C007F5D01005CA24A49157F486248 5DA2007C4917FFC76193C9FCA24A5E635DA2027F5E635D6102FF60A24B5D635B614B94C8 FCA2495F625D077FEC07E0494EEB0FF0A24B03FF15E062494C151F5014C05D4E153F494E 1480A292C8EE7F004E5B5B1CFE5C50485A017F627214034A4E5A6401FF190F724A5A4A6F EC7F80E0C1FFC7FC73B45A4A705B6D487013F06D48040713C06DCA000190C8FC5C5271CF 66>IIII<49B4ED1FF8010701C049B57E4901F0010714E0496D4914F8496D013F8090 267F87FE90397FF01FFE9026FE03FF9039FF8003FF48486CD981FEC7FCDC83FC01031380 D803F8DAC7F05B0007DBCFE05B01F0DAFFC04913C061D80FE05D94C7481380001F5D13C0 4A491600003F5D0180715A4C5D4A705A007F4BEC07E0010094C8FC5E5C12FE5EA2007C5B C7FC93CBFCA25CA25DA2147FA25DA214FFA25DA25BA25DA25BA25DA25BA25DA25BA25DA2 5BA292CCFCA25BA25CA2137FA25CA213FFA25CA35C6D5A6D5A6DCDFC4A5271CF4D>II<167CED01FE4B7E4B7F5DA45D94C7FCA35D5EA3157F5EA315FF5EA35C5EA35C5EA35C 5EA3003FB812C04817E0A2B9FC18C0A26C1780C7001F90C8FC5C5DA3147F5DA314FF5DA3 5B5DA35B5DA35B5DA35B5DA35B92C9FCA35B5CA3137F5CA313FF5C173FEF7F805A4A1500 5F5F5A4A495AA21603485E4A13075F4C5AA24C5A4A495A7E4CC7FC16FE4B5A6C6D485A6C 4A5AED1FE090397FE07FC06DB55A6D91C8FC6D13FC010313F09038007FC0337470F13C> IIII< DB0FFC4AB4FC92267FFF80010F13E04AB56C4913F84A02F0017F13FE020F6E90B6FC9128 1FF81FFC0101031380913E3FE007FE03FC007FC091297F8003FF07F0133F9126FE0001D9 8FE0EBFFE0494892389FC001494803FF5B49486D4A4813F049484C5A131F4A4B4913E049 5A017F5E91C817C05B494C6D138000011B00494A6F5A4EEB01F8000396C8FC5B5E00075F 5BA26C485CC95CA35E60A35E95CAFCA35E5FA3167F5FA316FF5FA21BFC4B4C7EA24D5DA2 4B160363D801F85DD807FC4E5A486C5B486C180F4862484A161F4D5DB54E5A4B167F7192 C7FC494916FE4F5A49D97F7F14034901FE6D495A6C48023F4A5A9028C003FC1FF8EB3FE0 003F49486C6CEBFFC02A1FF81FF007FF0390C8FC6CB5486CEBFFFE6C4A6C5C6C91C714F0 C649023F13C0D91FF0DA07FEC9FC545276CF54>II<04FF153F030301C0EC7F80030F6D150003 3F6D5C4B6D5C92B56C13014A6E5C4A6E13034A4C5A4A03805B4AEDC00F72485A4A9238F8 3FC0DBFE0390B55A91397FF0007F03C0010F91C7FC4A4801015B92C8EA3FFC494815034E 5A4A4B5A4E5A6D484B5A91C9485A4EC8FC6017014D5A4D5A4D5A4D5A4D5A4D5A4DC9FC4C 5A4C5A4C5A4C5A4C5A4C5A4C5A4CCAFC4B5A4B5A4B5A4B5A4B5A4B5A4B5A4BCBFC4A5A4A 5A4A48ED07E04A484B7E4A485E4A5A4A48151F4AC9FC49484C5A495A49484C5A5C010F17 FF49484B90C7FC90263FFFC05C4901F8EC0FFE03FF4A5A90B600E0137F489239FC03FFF8 48018190B65A49C67E48486D5D48486D5D496D5D484894C8FC48486D5C496D5C007F6E5C 90C814E0486F1380486F48C9FC007CED0FF0495275CF4A>I<01FE157ED803FF913801FF 80486D010713C0486D5B486D4913E0484B13F05A5EB5FC93B5FC18E0A24A15C04A7F6C17 8091C76C13006C486E5AD81FF86E5AD807E0EC07E034134FFA5D>127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmmi5 5 1 /Fr 1 33 df<171E173E173CA3177C1778A317F85FA316015FA316035FA3D93F80010714 F0D9FFE091388003F84801F8ED07FC00077FD80FC3020FEB0FFE261F81FE14001301003E 1707003C4B1303D87C03021E13010078491500D8F807177C00F049133E163CEA000F4A16 78011F147C4A137819F8013F17F04A01F813014C14E01803017FEE07C0EC80014CEB0F80 02C0ED1F00013F163E030314FC02E049485AD91FF04A5A02F8EC0FE090260FFE07EB3F80 902803FFE783FFC7FC6D90B512FC6D6C14F0020F14809126007FFCC8FC030FC9FCA25D15 1EA3153E153CA3157C1578A315F85D3F4B78B94D>32 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmmi7 7 5 /Fs 5 117 df22 D32 D<021FB600FC010FB612FEA24A5FA26E4B6D15FCDA000F01F0C80007 EBF8006F01C06F13E04D5F4B5F6594C9FCA24B5F9AC7FC5EA2033F5F645EA2037F173F64 5EA203FF177F645EA24A18FF645EA24A5F645E93B9FC5C64A34A0180C812076493C9FCA2 4A5F99C8FC5DA2023F5F635DA2027F173F635DA202FF177F635DA24918FF635DA2495F63 5DA2495F635DA2495F013F6D031F7F007FB600E0013FB612F0B76C49814C5FA3674F78CE 6D>72 D<157CEC01FE4A7E5CA25CA35D6E5A6E5A6E5A91C8FCAFEB07F8EB1FFEEB7FFF90 B57E3901FC3FC0D803F07FEA07E001C07FEA0F80121F13005A003E137F007E5C007C13FF 5DA2EAFC0100785C12005B92C7FC5B5CA2130F5C131F5CA2133F5CA2017FEB07C014E013 FFECC00F16805AEC801F16005DEC003E157E5D5D6CEB03F0EC8FE06DB45A6D5B010F90C7 FCEB03F8224F7BCD2F>105 D116 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft cmsy7 7 2 /Ft 2 7 df<007FBB12F0BC12F8A46C1AF04D06739F68>0 D<177017F883B3B3A2007FBC 12F0BD12F8A46C1BF0CA00FCCAFCB3B0007FBC12F0BD12F8A46C1BF0555677D268>6 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu cmmi10 10 7 /Fu 7 117 df22 D32 D<191C193E197FA219FF19FEA2180119FCA218 0319F8A2180719F0A2180F19E0181F19C0A2183F1980A2187F1900A26060A21701601703 60A2170760A2170F60A2171F60A2173F60A2177F95C7FC5F5FA216015FA216035FA21607 5FA2160F5F161F5FA2163F5FA2167F94C8FCA25E5EA215015E15035EA215075EA2150F5E A2151F5EA2153F5E157F93C9FCA25D5DA214015DA214035DA214075D140F5DA2141F5DA2 143F5DA2147F92CAFCA25C5C13015CA213035CA213075CA2130F5CA2131F5CA2133F5C13 7F91CBFCA25B5BA212015BA212035BA212075B120F5BA2121F5BA2123F5BA2127F90CCFC A25A5AA2127C123840A777FC53>61 D<030FBA12FE4BF1FFF01EFE4B747E1FE06F1BF8DB 000102E0C86C7FDC003F49030713FF4F0300800C3F7F4D060F7F787F96CA6C7F787F94B5 717F1F7F4E727E7913805E7913C04E8421E05E7913F060A24C7413F8A260A24C1CFCA24E 84A25E21FE60A25EA24E60A25EA295CCFCA293B5FCA24D6121FC5DA25F675D21F85F675D 21F05F674B1DE0A24D6121C05D674D1B80A24B98B51200A24D62664B646694CC5C6692B5 63545B5E545B4A65664C4F90C7FC674A515A535B5E535B4A505B535B4C4E5B5390C8FC4A 505A535A4C4D5B0A0713E04A4F5B0A3F5B4C4D48C9FC51485A4A06075B091F13E04C93B5 12804A050791CAFC0107B593B512FC007FBC12F0BD128051CBFC1BF098CCFC6C19E07F71 7AF089>68 D100 D112 D116 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fv cmbx10 10 7 /Fv 7 117 df65 D<92381FFFFC0207B612F0027F15FE49B812C0 010717F04917FC013F83499026F0007F6D7E038001078090B56C0101804870806F6E7F72 7F486E8086727FA27280A36C4A6E80A26C5CA26D5B6D90C8FCEB0FFC90CAFCA44DB6FC04 0FB7FC0303B8FC153F0203B9FC141F91BAFC0103EDF803010F1500013F14F049148090B5 48C7FC000314F84814E05D485C4891C8FC485B5C5A5CA2B5FC5CA460A2806C5F606E5D6C 7F95B67E6C6D6C496D13FC6C6ED907FEECFFFC6C02F0D91FFC15FE6C913AFE01FFF83F6C 91B612F06C6C4C7E6DEE800F010F9238FE0003010103F81300D9003F02C0021F13FC0200 01FCCBFC574D7BCB5D>97 D<903801FFFCB6FCA9C6FC133F7FB3AA943801FFF8053FEBFF C04CB612F8040715FF041F16C0047F16F003FDB87E92B548C614FE05E0011F7F94C70007 8004FC0201804C6E8004E06F7F4C6F7F4C6F7F93C96C7F5D747FA21D80A27414C0A21DE0 A37414F0A51DF8AE1DF0A41DE062A21DC0A3501480A21D00505B81704B5B704B5B6204F0 5F704AB55A704A5CDBEFFF020F5C03E701C0013F49C7FC03C3D9F803B55A038090B712F0 4B6C5E4A011F16804A01074BC8FC4A010115F04A6D6C148090C9000701E0C9FC5D747AF2 6A>I<93387FFFE0030FB6FC037F15F04AB712FC020F16FF023F834A17E049B97E499138 F8003F4902C06D7F4991C7804901FC5C495B49494A7F90B55A5A485C5D5AA24891C86C5B A248715B5C48715B725B060113804894C9FC5CA4B5FCAE7E80A37EA2807EA21A7F6C6EEE FF80A26C6E5D6C6E1700616C6E5E6C6E15076F4B5A6D6D151F6D6D6C4A5A6D6EECFFF06D 02F801035B01039126FF803F5B6D92B65A6D95C7FC023F5E020F16F8020316E0DA007F15 80030F02FCC8FCDB007F1380494D7ACB55>I<902603FFF0EB0FFCB691387FFF804CB512 E0040714F84C804C804C80DC7FF81480DCFFC114C003F11301C64B4814E0013FEBF3FC6D 14F8EDF7F0A2EDFFE0A216C07114C0168071148072130093C76C5AF00FF895C8FC5DA65D B3B1B812F0A9434B7ACA4F>114 D<912603FFFC131F027F9039FFC03F800103B6EAF8FF 010F92B5FC133F90B9FC48EC000F4801F01301480180EB003F4890C87E4848814981003F 825B007F82A300FF82A27F7F7F6EED7F0002E092C7FC14F8ECFF8015FE6CECFFF8EEFF80 6C16F017FC6C16FF18C06C17F06C836C836C836C836D1780011F17C0010717E013016D6C 16F01407DA003F15F81501ED0007040014FC173F007F160F486C8183836D81A2187F7FA2 6D17F8A27FF0FFF07F7F6D4B13E06E5C6E4A13C002F04A138002FC023F1300913AFFC003 FFFE92B65A6001F316E001C15ED9803F4AC7FC26FE000F14F0007C010091C8FC3E4D7ACB 4B>II E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fw cmr10 10 49 /Fw 49 123 df<94260FFF80EC3FF00403B500F8903803FFFE041F02FE011FEBFF8093B7 D8807F14C0030370B612E0030FD9F80101E39038F03FF0033F902780001FF7EB807F4B48 C76CB53800FFF8912601FFF84A5B4A01E04A494813FC4A494A13F84A4991B512F04A90C8 FC4A4817E04A5A4A484D6C13F8A249496F49EB7FF0F53FE049496FED07007392C7FC98C9 FC495BB3A6007FBD12C0A6D8000701C0C8001F90C9FCB3B3B3A2496D4B7F87013F01F892 B512F0B7D8FE03B8FCA666757DF461>11 D<163E167E16FEED01FCED03F8ED07F0ED0FE0 ED1FC0ED3F80ED7F0015FE14014A5A5D14074A5A4A5AA24A5A147F5D4AC7FC5B5C13035C 1307495AA2131F5CA2495AA2137F5C13FFA25C5AA291C8FC5AA3485AA3120F5BA3121FA2 5BA3123FA35BA2127FA85B12FFB3A7127F7FA8123FA27FA3121FA37FA2120FA37F1207A3 6C7EA37E80A27E80A2137F80133FA26D7EA280130FA26D7E1303801301807F6E7E81143F 6E7EA26E7E6E7E1403816E7E1400157FED3F80ED1FC0ED0FE0ED07F0ED03F8ED01FCED00 FE167E163E27A770FC41>40 D<127812FC127E127F6C7E6C7E6C7E6C7E6C7E6C7E6C7E7F 6D7E133F806D7E6D7EA26D7E8013036D7E807F81147F816E7EA281141FA26E7EA2811407 81A2140381A2801680A36E13C0A316E0157FA316F0A2153FA316F8A3151FA216FCA8150F 16FEB3A716FC151FA816F8A2153FA316F0A3157FA216E0A315FF16C0A34A1380A316005C A25D1407A25D140F5DA24A5AA2143F5DA24A5A5D14FF92C7FC5B5C495A13075C495AA249 5A495A5C137F49C8FC5B485A485A485A485A485A485A48C9FC127E5A127827A777FC41> I43 DIII<923807FF80037F13F84AB512FE02076E7E021F15E09126 7FFE0113F8913AFFF0003FFC4901C0EB0FFE49496D7E4990C76C7FD90FFC02007F011F83 49486F7E4A153F49486F7E01FF834A150F4884A248496F7EA2481980A34890C96C13C0A3 4819E0A44819F0A24982A2007F19F8A900FF19FCB3AA007F19F8A86C6C4C13F0A56C19E0 A46C19C06E5DA26C1980A26C19006E5D6C60A26C6D4B5AA26D6C4B5AA26D6C4B5A6D6C4B 5A6D6C4A5B6D6C4A5B6D6D4990C7FC6D6D495A6D01F0EB3FFC913A7FFE01FFF8021FB612 E00207158002014AC8FC6E6C13F80307138046737AEE53>48 DII57 DI<003FBF12F0481EF8C012FCA36C1EF86C1EF0D3FCB3A9 003FBF12F0481EF8C012FCA36C1EF86C1EF06E2977BD81>61 D64 D66 D69 D72 D<020FB812FEA691C7000FECF8000400 14E083715BB3B3B3B3A4EA07FC487E487E487F487FA2B57EA3615FA34A93C7FC6C4991B5 FC91C85B5B6C484A5B01F05ED81FC05C4C5B6C6C5ED807F84A5B6C6C4A5B6CB44A90C8FC 6C01C0EBFFFE90267FFC0713F8011FB65A6D15C0010392C9FCD9007F13F8020713804775 7AF055>74 D77 D79 DI83 D<001FBFFCA64849C7000F91C7 000F148002E06E49140091C86C49151F01FC1B07498749874987491C7F491C3FA21E1F90 C9FCA2481EC0007E1D0FA4007C1D07A848F503E0A6CA96C7FCB3B3B3AB4D7F4D7F94B612 F00203BA12FCA66B707AEF78>I87 D<913803FFF8027FEBFF800103B612F0010F15FC013F15FF90277FFC003F7FD9FF800107 13E0486D01017F486D6D7F6E6E7E48707E6E6E7E717FA2717FA2717F6C5BA26C496E7F6C 5B013FC8FC90C9FCA8173F047FB5FC031FB6FC92B7FC140F023F140191B512E00103EBFE 00010F13F8013F13C04990C7FC495A4813F8485B485B485B5A5C4890C8FCA24848F003E0 A312FF5BA25FA35FA26D5D127F6D5D6C043E9038F807C06EEC7E7F6C6D02FCEBFC0F6C6D 902601F83F14806C6DD907F090B5FC6C01FC90261FE01F14006C9027FF80FFC05C6C91B5 486C5B013F9126FE00035B010F02F86D13E0010102E06D6CC7FCD9001F90CBFC4B4C7AC9 53>97 DI<923803 FFF8033FEBFFC04AB612F8020715FE021FEDFF80027FD9000713C0DAFFF89038003FE049 01E0EC7FF04949ECFFF8010F495B4948C714FC013F5D5C495A495A5A485B7113F8485B71 13F048EF7FE04AED1F804894C7FCA24890CBFCA35AA35BA212FFAD127F7FA47E807E193E 807E197E6C6D167C6C18FC6E16F87E6C6D15016EED03F06D6C16E0013F16076D6C6CEC0F C06D6DEC1F806D6DEC3F006D01F814FE010001FEEB03FC913A7FFFC01FF8021F90B55A02 0715C0020192C7FCDA003F13FC030313C03F4C7BC94A>I<1AFCF01FFF050FB5FCA6EF00 0F180184A2197FB3AC923803FFC0033F13FC4AB6FC020715C0021F15F0027F9038C03FF8 913AFFFC0007FC010301F0EB00FF4901C0EC7FFF4949141F4948C87E494881017F824948 814A81485B48187F485BA25A5C5AA291CAFC5AA25AA25BA312FFAD127FA47F7EA37E807E A26C7F19FF7E6E5D6C7F6C5F6D6C5D6D6C4B7F6D6C5D6D6C92387F7FFF6D6D02FE14E06D 01E0D903FCECFFE06D01F8EB0FF86D01FFEBFFF0023F90B512C0020F1500020314FC0200 02F0EDF000030F90C7007EC8FC53757BF25C>IIIIII107 DIII<923803FFC0033F13FC4AB67E020715E0021F15F84A01007FDAFFF0 EB0FFF4901C001037F49496D7FD90FFEC8EA7FF049486F7E49486F7E4A150F017F834948 6F7E48496F1380A248496F13C04819E0A24890CA13F0A24819F8A34848EF7FFCA3007F19 FEA400FF19FFAD007F19FEA56C6CEFFFFCA36C19F8A26C6D4B13F0A26C19E06E5D6C19C0 6C6D4B1380A26C6D4B13006D6C4B5A013F5F6D6C4B5A6DB4EDFFF06D6D495B6D6D495B01 0001F0010F90C7FC6EB4EBFFFE021F90B512F8020715E002011580DA003F01FCC8FC0303 13C0484C7BC953>II<92 2603FF8014F8037F01F013014AB512FC020702FF1303021F15C0027F9039C07FE007913A FFFE000FF0010301F8EB03F84901E0903800FC0F4949147E4949EC3F1F4990C8121F4948 16BF4948ED0FFF84485B4849815A4A815A4A815AA2485BA34890CAFCA5485AAD6C7EA57E 80A27E807EA26C6D5DA26C6D5DA26C6D5D6C6D5D017F5E6D6C5D6E157E6D6D14FE6D6D49 5A010301F0EB07F86D6DEB1FE06D01FFEBFFC0023F90B55A6E4A5A020314F8020014E0DB 0FFEC7FC92C9FCB3A34E7FA2060713FF051FB712C0A652697AC858>I<91391F8001FF00 03B5010F13E0B6497F047F13FC93B57E0381130F923983FC1FFF922687F03F1380C615C0 011FEB8F806D139F16006D13BEA203FC6D1300715A4B6D5A715A94C8FC5DA35DA55DB3B3 497F81013F13FCB812C0A639497DC841>I<913A1FFF8001C049B5EAF807010FECFE0F01 3FECFF1F4915FF3901FFF800480180131F4848C712074848140148488049157F4848153F A2007F161F5B170F12FFA217077FA27FA27F01FE92C7FC7F6C13C014FC6CEBFFE015FF6C 15F016FE6C6F7E6C16E06C826C826C82013F816D8101071680010016C0021F15E0140003 0714F0ED003F040F13F8160300788100F86F13FC177F6C163FA2171FA26C160FA37E18F8 7FA26D151F18F07F6DED3FE06D157F6D16C06D913801FF806D6C491300D9BFE0EB0FFED9 1FFCEBFFFC486CB65AD8FC0315E0486C158026F0003F01FCC7FC48010713C0364C7BC941 >IIIII<007FB600F0017FB6FCA6D8003F0280010F14C0 010791C76C01FCC7FC0101496E13F06D4916C097C8FC6E6C5D6E6C5D6E6D5C4E5A6E6D5C 6E6D495A6E4B5A70133F6E6D49C9FC6E6D137E037F5C70485A92383FFF036FEB83F06FEB 87E0EFCFC06F13FF6F5C6F91CAFC5F6F5B707E163F83707F707F5E844C7F4C7F93B5FCDB 01FC7F4C6C7E4B486C7EED07E0030F6D7F4C6C7F4B486C7FED3F004B6D7F03FE6D7F4B6D 7F4A5A4A486E7E02076F7E4B6E7F4A5A021F6F7F027F6F7F02FF6F7F1303496D4A7F013F 4C13FE0003B500F84AEBFFC0B600FE91B712E0A653477EC658>II<000FB912F019 F8A402F8C7000713F002804A13E04848C84813C013F8494B1380494B1300604915FF4C5B 494A5BA24C5B90C8485B4C5BA24C5B484B90C7FC003E5E16FF4B5B4B5B5F5DC8485B4B5B A24B5B4B90C8FC5E15FF4A5B4A5B5E5C4A4914F84A5BA24A5B4A90C8FC4BEC01F014FF49 5B495B5D5B49491403495BA2495B4990C81207494816E0A24849150F485B4A151F48173F 4849157F484915FF17034849140F4890C8B5FCBA12C0A47E3D477BC64A>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fx cmti10 10 49 /Fx 49 121 df18 D<153FED7F80EDFFC04A13E05C5C5C4A13C016804A13004A5A4A5A495B4913E0495B 495B4990C7FCEB3FFC495A495A4813C0485B4890C8FCEA0FFC485A485A485AEAFF8090C9 FC5A12781230232048F255>I 39 D44 D<001FB712804816C05AA21780A2B8FCA217007E6C5D2A0B72A83B>I<13FE3803FF8048 13C04813E05A5A4813F0A3B512E0A314C0A26C138014006C5AEA1FF8EA07E014136E9233 >I48 DI<943801FFC0051F13F8057F13FF4CB612C00407814C01017F933A3FF000 3FFCDC7FC0EB0FFE4CC76C7E4B4880DB03F86E13804B4816C04B486E13E04B5A4B48ED7F F04BC9FC157E4B17F814014A48163F9226F0038015FC020713074B487E140FEDC007DA1F 807F023F0103157F1500A25C147E14FE4A010715FF5F13015C040F5C01034B15F84A131F 94C7FC6101074A16F04A133E047E5C4C16E04C4A13C015014B484A13804B5A902703F01F C04A1300DB7F804A5A91B5C85B6D494B5A6D494A5BDA7FF04A5BDA3FC04A5B91C95C4E90 C7FC4E5A4E5AF0FFF84D5B4D13C04D5BDD1FFEC8FC4D5AEF7FF04C485A4C1380040F90C9 FCEE3FFCEE7FF04B485A030713804B48CAFCED1FF8ED7FF0EDFFC04A90CBFC4A5AEC0FF8 4A5A4A5ADA7F80EE1F804ACA123F494818005C49485F495A4948177E011F18FE4A160149 485F49CA120301FE4D5AA248484D5AD9FFE0161F48D9FFC0ED7FE003FE15FF48DAFFF001 035B9338FF801FD80FFC92B65AD9F00F94C7FC261FE0015E496C7E48486D5D030F5D90C7 6C5D4802015D007E6E5D043F91C8FC705B00FE030313F8007C9238007FC04E7373EE55> II<1AF8F103FCF107FE190FA2 191FA3193F1AFCA3197F1AF8A3F1FFF0A3601AE0A34E13C0A21A8060A21A0060A261181F 61183FA261187F61A24E5AA25F61A24D5BA24D90C7FCA24D5AA24D5AA24D5A60177F6017 FF605E604C90C8FCA24C5A5F160F5F161F4C5A5F4C5A04FFEB01F094388007F84B49487E 4B4A7E5E4B48133F4B485CA24B5A4B48137F4B485C5E15FF4A90C712FF4A485D4A5A5D4A 485B4A485D4A5A4A5A4AC75A49485E495A495A49485C49485E495A90387FFFF890B65B00 0303E091C7FC000F15FC4815FF4893B5FC277FF8001F5CD8FF800101163890C8003FEC03 FC48030F90B512FE007815030030ED007FCA6C14F84D14C0F1FC0006F8C7FCA217FF60A3 5E60A35E60A35E60A35E95C8FCA35EA25FA2705A705AEE03E0478F79EE55>I<030617E0 DB0F80150304F0153FDB1FFEEC01FFDCFFF0017F13C094B712801B004B5E62621AE04B5E 97C7FC19FC19F092B712C04EC8FC03FD14F09226FC0FFEC9FC020190CBFC5DA314035DA3 14075DA3140F5DA3141F5DA3143F92CCFCEE07FE93387FFFC0DA7F03B512F0DA7E0F14FC 4B8092397FF807FF9127FEFFC0017F6E48C77F03F86E7E03E0814949143F4B814AC8121F 4A82495AA24A826D5A90CAFCA385A660A44E5AA418FFD803F85FEA0FFC487E003F5E6D5F 5AA2494B5B12FF61495D495F495D01C05F00FCC9FC4D90C8FC60173F4D5A606C16FF4C5B 60007F4B5B4C5B6D4A90C9FC003F4B5A6DEC7FFC6C6C4A5A6C6C010313E001FC010F5B27 07FF807F90CAFC6C90B55A6C15F86C15E0013F1480010F01FCCBFC010113C04B736EEE55 >II<023ED907F8ED0F80023FD97FFC151F4A48486C153FDA7E076D1600DAFE 1F6E5CDAFC7F17FE010190B64A5A14F9D903FB6F495A91B74A5A49180F63494E5ADCE03F 143FDC001FECFF804901F8010F5B03E06D6C4890C7FC490180ED0FFE92C73803F07FD97F FC6EB55A5C49486E5C4A8148018092381FCFF09538000FE04890CA121F494D5A485A494D 5A485A4FC8FC495E48485F180348484C5A90CAFC484D5A127E00FE4D5A48173F61CB127F 6118FF615F5F96C9FC5F60170F60171FA24D5AA24D5A17FFA24C5BA24C5BA25E605E95CA FCA25E5F163FA24C5AA216FF5F5DA25F5DA24B5BA34B5BA25DA25F5DA294CBFC5DA25E15 FFA34A5BA44A5BA35C5EA35EA25E6E5B6E90CCFCEC00FC517369EE55>II<943801FFC0051F13F894B512FE04036E7E040F814C01007FDC7FF8 EB3FF0DCFFE06D7E0303496D7E4B90C712074B48814B4814034B48814B5A4B486E13805C 4A5B4A5B4A18C093C8FC5C4A5A147FA24A5A4F13E05B5D5BA2495B61A25B5D4F13C0A25B 5DA2615B5D4F1380A392C9FC61A296B512005CA2606260A26062011F5E60A2010F4C5B60 010716FB6E4A5A6D03035C6FEB07E76DDB0FC75B6D6DEB3F8FDA7FF0EBFF0F91273FFC07 FE5C6EB5EAF81F6E14F06E02C05C020114009126003FF84990C7FC92C8FC61187F6118FF 61A24D5B615F614D5BA24D90C8FCD803F05ED80FF8151F486C4B5A003F5F486C4B5A4D5A 12FF4C5B494A5B4C90C9FC494A5A494A5A494A5A01804A5A48C748485A6C4A13806C6C01 0F90CAFC01E0EB3FFE3A3FFC01FFF86CB65A6C15C06C92CBFC6C14FCC614E0010F90CCFC 4B736FEE55>I65 D<030FBA12C04B19FCF5FF80 1EE01EF86F86DB000391C800037F9326007FFE0300EBFF804E043F13C08905FF7113E01F F04E821FF84C841FFC60894C1AFEA260A25EA260A24C601FFC60A24C601FF895CAFC5313 F05E5313E04D19C065047F4E13801F004D4D5A6404FF4D5B5213F04D4C5B525B4B067F5B 5248C7FC4D03035B090F13F04B053F13C00803B5C8FC94B812F81CC04B18F01CFEF4FFC0 05C0C8000F7F4B050313F809007F4D707E767E4B727F8A94CA6C7FA24B727F8A5E88037F 86A25EA215FFA25EA25CA25E645C665E644A63644C61644A63644C6199B5FC4A4E91C7FC 515B93CA5C515B4A60515B4B057F13C098B55A027F4D91C8FC08075B4B041F5B02FF057F 13F0010F0507B512C0007FBC5ABC48C9FC1BF81BC050CAFC6C19C06F7176F075>I<9626 01FFF8151C073FD9FF80141E4EB600E0143E060F03F8147C067F03FE14FC4DB813010507 DAE007EB8003051F01FCC79038C007F8057F01E091381FE00F4CB5C8380FF01F4C01FC92 3803F83F040F01F0923901FC7FF04C01C0030013FF4C4993B5FCDCFFFECA7E4B497113E0 4B5B4B01E0834B5B033F497113C04B90CBFC4B5A4A49844A491A805E4A5B4A864A491A00 4A5B4A90CCFC91B5FC4B62495B5B4B19014964495B1D03495B49645D5B5D90B56392CDFC 5AA24849639AC8FCA2485BA25A5CA25A5CA35A5CA35A5CA45CB5FCA591D1FCF401F01C03 A21C0765A21C0F65A26C1B1F651C3F9AC8FC641C7E6C1BFE6E611B016C505A646E18076C 505A646C6D181F515A6C6D4EC9FC1BFE6C6D4D5A6C4F5A6E4D5A6D6C4D5A6D6C4D5A6D6D EE7F806D6D4CCAFC6D6DED03FE6D01F84B5A6D6DED1FF06D01FFEDFFE06E01E001035B02 1F01FE013F90CBFC6E90B612FC020316F0020016C0033F92CCFC030714F0DB003F90CDFC 6F7968F477>I<030FBC12FE4B1BFFA31FFE81DB00030280C87EDC007F90C912034E1600 1E3F05FF181F1E0F4EEF07FCA24C1903A260A25E1FF8601E014C1903A260A25E1FF060A2 5EA260A24CDC07801307516C14E095C8FCF603C04C041F91C7FC645FA204FF163F99C9FC 5F635D1BFE4D14011A034B1607F21FFC4DEB01FF94B7FC5DA263A25D9426E000015B4DEB 003F1A1F4B160F635FA25D6394C8FCA24B161F635EA203FF163F98CAFC5E1A1E4A94CBFC A25EA25CA25EA25CA25EA25CA25EA25CA25EA25CA293CFFCA25CA391B5FC010F14E0007F B8FCB97EA46C94CDFC707177F06C>70 D<030FB700FE91B812E04B704917F0A46F4C6D17 E0DB000302F0C9003F91C7FCDC007F90CA000713F0A24E6105FF60A24E61A24C616860A2 4C619DC8FC60A24C616760A24C19FF6760A24C606760A24C606795CAFCA24C60675FA204 FF60675FA24B61675FA24B6194BBC9FCA35D66A205E0CA127F4B19FF665FA24B60665FA2 4B606694CAFCA24B60665EA203FF60665EA24A61665EA24A619BCAFC5EA24A61655EA24A 19FF655EA24A60655EA24A606593CAFCA24A60A24B6191B54D7F010F02C093B512FC007F B700F80107B87EB86C4983A24D61A26C4C6D94C9FC847177F07B>72 D<030FB812E04B83A46F5FDB000302F8C9FCDC007F138096CAFC6017FFA260A25EA260A2 5EA260A25EA260A25EA260A25EA260A25EA295CBFCA25EA25FA216FFA25FA25DA25FA25D A25FA25DA25FA25DA25FA25DA25FA25DA294CCFC1D384B197C1DFC5E1C0103FF19F8A24C 17031DF05C1C074C18E01C0F5C1DC04C171FA24AF13F80A24C177F1D004A61634C5F1B03 4A4E5AA24C160F515A4A183F1B7F93C948485A624A170F083F5B4B93B5FC02FF1607010F 94B65A007FBCFCBDFC64A36C98C7FC5E7177F068>76 D<030FB600C00703B612E04B0B0F 15F0A27361A26F5315E0DB00035291C7FCDC007F1DF09EB5FC6B94B561F803F705FD6505 FC6DF007E704011CEFE60FCF5B4DF21F8FA20403515AA0C8FC4D1A7E20FC040764726CDD 01F85B17E0F703F0040F973807E07F6A05C0F10FC0A2041F97381F80FF55485B1780726C 177E043F630DFC5C0500F001F8A24C4F485A6A047EF107E0F60FC004FE63726CDC1F805C 5EF63F000301087E5B6A4C61A203034F485B534892C9FC5E726C4B5A03076453485C4C4E 5AA2030F4FC7127F694C187E65031F1CFF726D49485D5E525A033F4E485B6993C74C5AA2 4B4E485B52C75C157E726D137E03FE63525E4B4D5AA202014E485C694B4D5A515A020364 726D484893CAFC5D51C8FC0207067E5D684B5FA2020FDDE1F8157FE0E3F05E5D72EBF7E0 021F1CFFE0FFC05E4B5FA2023F95C85A68027F5F6202FF6349715A496D64011F6D4C4B7F 90B500FC4C037F13FC007FDAFFF80503B87EB76C4B4983A24C4B6197C7FC6C4B023E6E94 C9FC9C7176F095>I<030FB694B712E04B6F4B16F0A285A26F7316E092C76E0403ECF000 71DE007F1380737148C7FCF71FF894B56173715AA205FD6204016E171F17FC4D6D60A204 03017F183F7395C8FC17F08404076F5E72187E05E080A2040F6D18FE745E17C084041F6F 15017260178086043F6D1703745E1700844C6F1507077F5F167E8604FE6E160F755D5E85 030171141F735F5E8703036F163F7592C9FC5E850307715C73167E5E87030F6F16FE755C 5E1A7F031F711301745D5E1C80033F7014030AC05B93C9FC864BF0E007745D157E1CF003 FE70140F0AF85B5D860201F1FC1F745D5D1CFE0203067F133F0AFF90CAFC5D8702071AFF 755B5DA2020F84655D87141F755B5DA2023F8465147F8714FF49745A497F011F7F90B500 FC183F007FDAFFF860B77E1C1F5EA26C4B715A847177F07B>I<963803FFE0077F13FE06 07B612C0063F15F095B712FC0503D9FC0013FF050F01C0011F7FDD3FFEC7000713E0DDFF F802017F4C01E06E7F040749ED3FFC4C90C96C7EDC3FFE707EDC7FF8844C48707F030349 824B49844B49707F4B90CAFC4B48717F4B5A4B48727E4A5B4A49854A1A3F4A5B4C855C4A 90CCFC4A481B8002FF865D495B5B4B1BC05B495BA2495BA25B5D5B90B5CD5AA3485BA25A 5C4864A25C5A1F804A97B5FC5AA348494F1400A448494F5BA3525BA25CB5505BA3525BA2 6691CD5A666466A299B5C7FCA2515BA2515B65636C64515B636E62515B6C629AC8FC515A 6C6D4D5B505B646C4F5B6E4D5B6C616E4D90C9FC6C4F5A6E4D5A6C4E5B6C6D4C5B6E4C5B 017F051F5B6D6C4C90CAFC6D6DEDFFFE6D6D4A13F86D01F002075B6D6D021F13C06D01FF 91B55A6D6CD9E00F49CBFC6E90B612F8020F16C0020393CCFC020015F8031F14C0030001 F8CDFC6A7968F47F>I<030FBAFC4B19F01DFE777E1EE06F1AF8DB00030280C7003F7FDC 007F90C800037F4E03007F0B3F138005FF7113C0894E7013E01FF04C841FF860A24C1AFC A260A25EA260A25E6560A25E5313F860A24C1AF06595CAFC1FE04C601FC04D19806504FF 1A00535A4D60644B4E5B525B4D4C5B525B4B4E90C7FCF4FFFE4D4B5B090713F04B053F5B 0803B5128094B848C8FC1CF84B18C099C9FC1BF005C0CDFC5DA25FA25DA294CEFCA25DA2 5EA215FFA25EA25CA25EA25CA25EA25CA25EA25CA25EA25CA25EA25CA293CFFCA25CA25D 91B5FC010F14C0007FB712F8B87EA25FA26C5E6E7176F071>I<030FB912E04B18FF1DF0 1DFC1DFF6F1AC0DB0003912680000180DC007F90C8000F13F84E03037F0A007F05FF717E 7713804E7013C0894C1AE0894E18F0A24C1AF8A260A25EA260A25E6560A25E5313F060A2 4C4E13E0A295CA14C05313805E9AB512004D606404FF61525B4D4C5B525B4B4E13805290 C7FC4D4C5A983801FFF84B05075B091F13C04D92B5C8FC081F13FC4B90B812F01C8009FC C9FC1BF04B17FC05E0C76C7E4DEC0FFF08037F4B707F747F4D82757E5D757E94C9FC885D A25EA203FF84A25EA24A60A25EA24A95B5FC645EA24A5FA25EA24A5FA25EA25C50163C4C 1A7EA24A1CFE1FFC93C9FC1E014A1CF8864BF203F091B51A07010F02C06F16E0007FB700 F870130FB86C6EED1FC075EC3F804D6F9038807F0075EBC1FE6C4C6FEBFFFCCE6C5C0901 5C756C13C00A0790C7FC6F7577F079>82 D<952603FFC01470063F01FC14784DB614F805 079238C001F0051FEDE0034DEDF0079426FFFE00EBF80F4C01E090391FFC1FE004070180 EB03FE4C48C73801FF3F4C486E13FFDC3FF06F13C04C48814C48814B5B4B90C96C13805E 4B4882150F4C18004B4882153F5E037F605E15FFA24A615EA34A61A4645CA21B07705F1B 037093C8FCA2826E7F8282707E17F86E14FF18F06E15FEF0FFE06F15FC6FEDFF801AE06F 826F826F826F82030082043F82040F821601DC001F811703DD003F801807060080191F19 0785858785A21A7FA21A3FA2133E133F4961A2137EA213FE63A34848187F63A263486C18 FFA24F5BA2000797C8FC4F5A6D17076248180F6E4C5A626E4C5A486D4C5A4F5A6E4B90C9 FC6EED07FE263FF7FE4B5AD9F3FF4B5A01E101C0EC7FF001C001F8903803FFE0297F807F FF801F5BD9001F90B6CAFC007E6D15FC007C01035D00FC010015E048021F91CBFC007002 0113F05D7975F45D>I<0107BE1280491DC05B1F805BA203FCC7003F9038C000034901C0 4CEB003F4AC891C8120F02F84B701300D9FFE0864A4C815C4890C9834916FF4F5E485AA2 495D0007605B6648485D615B001F1C015F494D5E123F90C9FC5F4860007E1C036600FE5E 4860A20078765ACA4894C8FC96CCFCA35F60A317FF60A35E60A35E60A35E60A35E60A35E 60A35E95CDFCA35E5FA316FF5FA35D5FA35D5FA35D5FA35D5FA35D5FA25DA25D92B5FC02 1F14F8000FB912F04884A25AA26C606A7064EF77>I<0007B8037FB612F0487191B712F8 A46C94C86C15F0D8000102F8C90001ECF800D9003F0180DC003F13C07690C7FC93CBEA0F FC4A62765A5D6502FF190FA24B61A2491A1F655DA2491A3F9AC8FC5DA249621C7E5DA249 1AFE645DA2491901645DA24919036492CBFCA2491907645CA201FF190F645CA2481A1F64 5CA2481A3F99C9FC5CA248621B7E5CA2481AFE635CA2481901A24A60A2481903A291CB5B A2481907A24961A21A0F63485A1A1F63A250CAFCA249601A7E1AFE624F5A1903007F6119 074F5A6D60003F4E5A193F4FCBFC6C6C17FE4E5A000F4D5A6D4C5A6CEF1FE06C6D4B5A6E EDFF806C6D4A90CCFC6C6DEC07FED97FFCEC1FFC6DB4ECFFF06DD9E00F5B010790B61280 6D4BCDFC010015F8023F14E0020F91CEFC020013F06D7560F07B>I<003FB76C030FB612 F048704B15F8B8FCA21FF06C4C6F15E0D8003F0280CAECFC00010F01FCCB001F13E06D01 F01A807648C7FC4B611DF08165525A6D631C3F9AC8FC1C7EA2641B01646F170364515A6D 190F641B1F6451C9FC631B7E1BFE6F5F505A1A036D611A0763505AA2505A1A3F98CAFC6F 167EA262027F1601621903624F5A190F62191F6F5E4FCBFC616E167E19FE614E5A180361 1807705C4E5AA24E5A6E153F96CCFC60187E60170160EEC003604D5A170F6E5D171F604D CDFC5F177E17FE705AEEE1F8A2EEE3F06E13E75FEEEFC0A2EEFF80A294CEFCA25E5EA26E 5BA25E5EA25EA25E93CFFCA26E5AA25D5D6D755EF07B>I97 D99 DII104 D<16FC4B7E4B7E4B13805D5DA417005E6F5A6F5A ED03E092C8FCB3A5EC7FC0903801FFF001077F4913FE497FEB3FC1D97F017FEBFE004848 805B485A4848805CEA0FC0A2EA1F804A5B123F13005C007E5DA25C00FE92C7FC485B5DA2 C7123F5DA2147F5DA214FF5D5B5DA25B5DA25B5D5B92C8FCA25B5CEE0FC0133F4A131F17 80137F5C01FF143F4A1400A2167E485B16FE5E150102C05B4B5AA26C4A5A4B5A151F017F 495ADAE1FFC7FC6DB45A6D5B6D13F001035B010090C8FC2A7073ED33>I108 DIIIIIIIIII120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fy cmbx12 12 25 /Fy 25 121 df<023FB57EA417FCEFFF8018E018F88484DA007F8003071580030015C082 041F14E0A28219F082A45E19E05E5E93B612C003031580033F1500023FB65AB95A18F060 95C7FC17F8178004E0C8FC0380C9FC3C26667D64>24 D45 D[ 138 137 120 264 159 66 D[123 136 120 263 141 70 D[<97261FFFFE173E070FB600F0167F4EB85E061F05C05C95B900F85C050706FE 5C053F726C5B94BB00E05B040308F85B040F745B043F9326E0003F01FF90B5FC93B700F8 C700031481030393C96C13C34B03F8040F13F7031F03C0040390B6FC4B92CBFC4B02FC84 92B600F0181F020303C0844A4B844A92CC7E4A02FC854A4A854A4A8691B64886494B864D 864992CE7E495C498A4C87495C498A5E498B5E90B6895E488C5E5A8D4892D0FCA28D5A5D 5AA28DA2485CA27B5A9EC9FC5AA35DA3B6FCB37EA281A20A7FBA12FEA27EA46C80A46C98 C8000792C7FC817EA2827EA26C81A27E827F827F826D807F826D807F6D81836D816E806E 806E02FE616E806E6F606E15E0020003F8606F6E606F02FF95B7FC6F03E01603030703FC 5E6FDBFF80033F13DF030004F84AB512CF043FDBFFF0011F1487040F93B7EAFE01040350 7E040050133F053F07E0130F05070780130305004EC8FC061F05F8153F060105C0150EDE 000F03FCCCFCDF001F91CDFC>151 141 116 266 176 I[<030FBB1280AA92C800010380 C7FCB3B3B3B3B2EB7FF03801FFFC487F487F488048804880A24880A2B67EA399C8FC60A3 634B5C6C62A24B4A5C7E4B4A5C6C4A4A5C6C91C85D02FC4B5C6C01F04AB6C9FC6C01FC4A 5C6CD9FF80010F5C6C02FC017F5C6D90B812E0011F60010795CAFC010117FC6D6C16E002 0F93CBFC020115F0DA000F01FCCCFC>97 139 123 264 116 74 D[ 196 137 120 264 213 77 D[<93260FFFF0ED01F00303B600C081031F03F8140392B814 07020305E0130F020F05F8131F023F71133F91BA137F49F1C0FF499126FC001F14E1010F 02C0010014F34949C8000F90B5FC4901F815034901E0ED007F4B8290B548160F4891CA7E 484917014A8348864A8448864A845A8748865C875A87A21C7FA2B5FC6E193FA36E191FA3 806E190F80A215C0816C6E725A03FC95C8FC81EDFFC06C15F8EEFF8017FC6CEEFFC018FE 6CEFFFF019FF6C19F01AFE6CF1FFC01BF06C1AFC6C1AFF6D866D1AE0886D866D86010386 6D866D876E86021F8602078614016E6C85031F851503DB003F841603DC001F831701DD00 0F17801800070716C0F1007F1A1F080715E01A018687877514F087007F86487E8787A387 A36D86A31EE07FA37F1EC07F99B5FC6D1C807F636D1C00806E4E5B8002F84E5B6E6002FF 4E5B6F4D5B03E04D5B03FC94B5FC03FF04035C04F04B5C04FF033F91C7FC496C02FE0103 B55A496C91B85AD9F80F19F0D9F0036149C6198049013F95C8FC49010F17FC90C7000117 E048DA001F168048030103F8C9FC007CDB000391CAFC>100 141 116 266 125 83 D[<000FC212FEA6488DA40480C703E0C7123F03F0C818010380F3003F 4AC9190F02F81D034A894A894A8A484978138091CA86498BA2498BA2498BA2498BA4498B 007F22C0A449207FA84848F83FE0A6CC98C7FCB3B3B3B3A4033FBD7EAA>139 135 120 262 156 I<93B512F8037FECFFE00207B712FE023F707E91B912F0010318FC49 18FF49854991C715E04901F0021F80496D0207806F02018090B56F806F6F7F4872806F6F 8085888588A27380A26C5CA26D496F806D5BA26D5B010713C0010190C9FC90CBFCA796B6 FC050FB7FC0407B8FC93B9FC150F157F0203BAFC021F1681027FEDC00149B6EAF8000107 15C0494AC7FC013F14F84914C090B65A484AC8FC485C485C485C485C5D5A5D5A92C9FCA2 B6FC5CA461A36E5E7E616F5D7E6F5D6C6EDBFFBF7F6F4A013F7F6C6EDA03FE15F06C02FE DA0FFCEDFFF86C6E6C017F6D15FC6C9239F007FFF06C92B6487E013F17C0010FEF000701 034C1301010004F87F021F03C0141F020392C8000314F8DA000F01E092C9FC665C7ADA6D >97 D[ 111 139 122 265 125 I<94B512E0041FECFF804BB712F8030F16FF033F17C092B97E02 0318F8020F844A84027F9126F0000F7F91B600806D14804902FCC75A494A17C04902E05C 494A17E0494A5C4991C8FC495B90B55AA2485C5A5D487214C0A2484A6F14807314005A4B 6F5B070013F848F13FE097C8FCA3485CA5B6FCAF7EA281A37EA2817EA36C80F303F86CF2 07FC816C1A0F6F18F86C6E171FA26C6EEF3FF06D6E167F6D6E17E070EEFFC06D6E5D6D02 FC030713806D02FF4B13006D03C0EC3FFE010003F8ECFFFC6E9126FF800F5B6E92B65A02 0F60020318806E95C7FCDA003F16FC030F16F003011680DB001F02FCC8FC04001480565C 79DA64>I<4CB5FC043F14F80303B7FC030F16E0037F16F84AB812FE0207717E4A84023F DAE00F804ADA000114F891B500F8D9003F7F01034A6E7F4902C080494A02037F4991C881 49496F804B81498690B548707F48854B845A4B824887A248737F5D5AA2884885A25D5AA2 1D80A3B6FCA292BBFCA61D000380CDFCA67EA4817EA47E817E1C7F6C6EF0FF80A27E6F5F 6C1C006F5F6C6E4D5A7F6D6D4D5A70161F6D02E04C5A6D6E4C5A6D6E4B485A6D02FE4B5B 6DDAFFC0020F5B6D6C02F8027F90C7FC6E913AFF8007FFFE6E92B65A020760020118E06E 6C1780031F4CC8FC030716F8030016E0040F4AC9FCDC003F13C0595C7ADA66>101 D103 D[112 138 120 265 125 I[48 139 120 266 63 I109 DI<94387FFFC0040FB512FE93B712E0030716FC033FEEFF8092B9 12E0020318F8020F18FE4ADAF001804A91C7001F8091B500FC020714E04902F002018049 02C06E6C7F494A6F7F4991C96C7F4949707F4949708049497080A290B548708048884B82 4888A2484A717FA24888A24888A24B83481D80A3481DC0A6B61BE0AE6C1DC0A56C1D806F 5FA36C1D00A26C646F94B5FCA26C646F5E6C646C646F5E6C646D6D4C5C6F5E6D6D4C5C6D 6E4B91C7FC6D6E4B5B6D02F04AB55A6D02FC02075C010002FF021F14E06EDAF001B65A6E 91B85A020F4EC8FC020318F86E60DA003F1780030F4CC9FC030116F0DB001F92CAFCDC00 7F13C0635C7ADA70>I114 D<92263FFFF0EB07C00207B66C487E023FEDF03F49B7EAFCFF010793B5FC131F5B90B538 F0003F4891C712034801F8EC007F4801E0151F4A81484981488391C97E48835B007F187F A3193F12FF7FA280806E705A6E93C8FC14FCECFF8015F06CECFF8016FEEEFFF06CEEFF80 18F018FC6C17FF6C18C019F06C846C846C18FF6C856D84011F847F010384010084143F02 0F831401DA000F82ED007F040181EE000F1701DD003F148084007F1707486C8284847F85 A26D83A36D1900A27F7F4F5A7F6D606E16FF6E5F6E5D6E4B5B02FC150F02FF4B5B03E091 B55A03FE010F5C92B8C7FC19FC01F85FD9E03F16E0D9C00F1680D900034BC8FC48D9007F 14E0007C020701FCC9FC495C79DA58>IIII<007FB8 020FB712E0AAC76C0280DA003F01E0C7FC6E6E030F90C8FC714B5A6E6E4B5A6E6E4B5A6E 4E5A6E6E5E715C6E6E4A5B6E6F495B6F4C90C9FC6F6E495A72495A6F6E5C6F6E137F6F4C 5A6F6E485B72485B6F6E485B6F038790CAFC70EC8FFE19DF70ECFFFC705D705D705D6282 705D7092CBFC7180867180718083718086864D805F874D814D8194B77E4C13EF4C01C780 0687804C0103804C6D804C487E4C48824C486D804C486D804D6D804B814B49824B496D80 4B90C76C804B48804B486E804C84037F70804B486F804A49814A496F804A49844A90C96C 804B708091B56C81B892B812FEAA6F597DD876>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fz cmr17 17.28 21 /Fz 21 122 df[174 196 114 323 203 68 D[148 196 114 323 173 70 D[68 196 116 323 94 73 D[151 196 114 323 180 80 D[<99387FFFC0093FB67E0803B712F8 081F16FF97B912E0070718FC073F9126C0007FEBFF8096B500F8C7000314E0060302C0DA 007F13F8060F49C9000F13FE063F01F804036D7E4E01E00400804DB50080053F13F00507 49CB000F13FC4D01F806037F053F49726D7E4D01C0726C7F94B548737F040391CD6C13F8 4C01FC08077F4C49747F4C49747F4C4974804C49757F93B548757F4B91CF6C7F4B49767F 4B49767F4B49767F4B8C4B4976804B49768092B548777FA24A4A777F4A91D16C7F4A8E4C 8A4A49787F4A8E4A497880A24A497880A291B548788049A17E4C8B49A17E4C8B49A17E93 D37E49A17E4B8C49A17EA249497A80A249A17F4B8C90B5A17EA24B8C48A180A3484A7A80 A348A1804B8DA248A180A34B8D48A180A448A1158092D57EA448A115C0A64A8EA2B5A114 E0B3A46CA115C0A36E6AA56CA11580A56F696CA11500A46CA15C6F69A36CA15CA26F9EB5 FC6CA15CA36C6E565CA36C6E565CA26DA15B6F68A26DA15B6F686DA190C7FCA26D6D565B A26D6E555BA26DA15A6D6EDD07FE4E5B99383FFFE06D6E94B500F894B55A090314FE6E6D 4C6E4C5C6E4E6F607093261FFC016D5D6E6D93283FE0003FE04B91C8FC6EDE7F80D907F0 5F704CC76C6C5D6E4EDA00FC5F6E6D4B48037E4B5B6E6E4A486F4B5B8B6E6E4B6F6C4A5B 6F6D020797B55A6F6D4B6F6C495C6F9EC9FC6F6D020F706C495B6F6D4B4E5B71736C5B6F 6D525B6F6E726C495B6F6E515B043F6D98B51280706DDF7C0191CAFC706D505B706D505B 706D6EDC7E0F5B04009026FF8007DD3E3F13E07101C04F5B7101F06D043FB55A050FD9F8 034FCBFC7101FE6D60050101FF7213F071DAC1FC047F5B063FD9F8FE0303B51280060FD9 FEFF030F49CCFC060390B56C027F13F8060003E00103B512E0073F02FC017F4A18600707 91B86C18F01901DF003F178F0803EEF80FE0003F03807FE1007FEBC00099C912077B1701 A38DA2A115037A6C18E0A2A115078DA27C160FA27C161F7A19C07C163FA1157F8E7C16FF 7A5F7C4B13807C5D7C5D11C0143F7B6D91B5120011FC1303A038FF801FA1B65A8DA15DA2 8DA15D8DA15D8DA15D7B5FA27B5F7B94C7FC7C5D7C5D7C5D7C5D7C5D100115807C92C8FC 111F13F8110313C0>180 257 115 328 207 I<933801FFFC043FEBFFE04BB612FE030F EDFFC0033F16F092B812FC4ADA001F13FF020701F00101804A01806D6C13E0DA1FFCC800 0F7FDA7FF06F7FDAFFC0030113FE4990CA7F4948717F4A717F4948717F4948834948717F 4A854948717F8649CB8002FC717F90B5FC6F717F816F717F4880A26F717FA48987A36C5C A26D5B6D5B6D5B6D90CBFCEB01F890CDFCAA0703B6FC0603B7FC95B8FC170F94B9FC040F EDFC0F043FECFC004BB6C7FC030714F0033F148092B500FCC8FC020314F04A1480021F49 C9FC4A13F891B55A4914C0495C4949CAFC495B495B495B495B90B55A485CA24891CBFC48 5BA2485BA248491D3FA2485BA3485BA4B54860A563A363A26E95B5FC7E621BF76E17036C DF07E36D147E806CF10FC36EDD1F836D14FE6C6DDD3F0116FC6C6D057F6E13016C07FE17 F86C6E922603FC006D13036C02E04B486D90388007F06D6DDB1FF09238C00FE06D01FCDB 7FC06DEBF03F6D01FF4A48486D90B512C06D02C0010F90C71680010302FCD9FFFC6E1500 010091B6486E5C023F04E0020114F8020F04806E5C020103FCC9003F1380DA001F02E0DC 07FCC7FC030049CEFC788175FE84>97 D99 D[128 201 119 326 147 I<943801FFFC053FEBFFE04CB612FE0407EDFFC0043F16F093B812FC 4BDA801F13FF03079026FC000180031F01E0D9003F13E04B0180020F7F4B48C86C7F4B48 03017F020301F06F7F4A49707E4A49041F7F4A49844A90CA6C7F4A48717F02FF727F5D49 49717F49498549854949858849491A8049864B1AC0498692CCFC90B51BE08848491BF0A2 5A4A85481DF8A2485BA27613FC5AA25CA25AA21EFEA24887A25CA391BDFCBFFCA41EFC02 E0CFFCAD7EA380A37EA56C7FA37E80A27E1E3C6C6D1B7EA26C1DFE6E1BFC7E6F19016D1C F8A26D6D19036D1CF06F19076D6D1AE06D1B0F6FF11FC06D1C806D6D193F6D6DF17F006E 6C197E6E6D18FE6E6D4D5A6E6D4D5A6E6D4D5A6E6D4D5A6E6DEF3FC06E01FF4D5A6F6D4B 48C7FC6F01E04B5A030F01F8ED0FFC6F01FEED7FF00301D9FFC0903803FFE06F6C01FE01 3F1380041F90B7C8FC040716FC040116F0DC003F1580050702FCC9FCDD003F1380678179 FE75>I[85 201 123 328 79 I[129 199 119 326 147 104 D[52 189 119 316 72 I[54 199 119 326 72 108 DII<95381FFF80 0503B512FC053FECFFC04CB712F8040716FE041F707E047FD9F00014E04BB5C7000F13F8 030701F8020113FE4B01E06E6C7E4B0180031F7FDB7FFEC9000713E04B48707F4A01F004 007F4A49717E4A49717E4A49717E4A90CB6C7F4A48727F4A48727F4A48727F4988494972 7F4949737EA24949737E4949737FA2498992CD7E49894948747FA2488A4A86488AA24A86 488AA2488AA24A86481F80A3481FC0A34A87A2481FE0A6B51EF0B16C1FE0A36E98B5FCA3 6C1FC0A46C1F806E62A26C1F00A36C6D505BA36C666E626C66A26C6D505BA26D6D4F5B6D 656F616D656D6D4F90C7FCA26D6D4F5A6D646D6D4E5B6F606D6D4E5B027F636E6C4E5B6E 6D4D5B6E6D4D90C8FC6E6D4D5A6E01F84C485A6E6D4C5B6E6CB4040F13E06F6D4B5B030F 01E0037F90C9FC6F01F84A485A030101FF020F13F86F02F090B55A043F90B712C004074C CAFC040116F8DC003F15C0050302FCCBFCDD001F1380748179FE84>I114 D<93263FFFE0140F030FB500FE5C92B712C0020704F05B 021F04FC5B027F04FF5B49B526C0007F1381010701F8C7000713C14901C0020013E34948 C9EA3FF7D93FF8040FB5FC494882D9FFC016014849824890CB7E484884A2484884498412 1F86485A86127F4984A286A212FFA287A27FA36D85A27FA27F6C7E80806C13F06E95C7FC 14FE6C6D7E15E06C14FC6CECFF8016FC6CEDFFE06C16FF6C17F06DEEFF806D17F06D17FC 6DEFFF806D18E00101846D18FC023F83020F83020318C0020084031F83030183DB000F82 DC007F81050781EF003F06031580DE007F14C0190F070314E085736C13F0007C8500FC07 0F13F886866C1BFC86861B7F1CFE6C1A3FA31B1F7FA21B0F7FA37FA21CFC7FA27F1B1F6D 1AF8A27FF33FF07FF37FE0806EF0FFC0805013806E4D13006E5FD9FBFC4D5AD9F1FF4D5A 01E06D4C5A6E6CEEFFF09026C03FF003035B9026801FFC031F5B6EB46C91B5C7FCD90003 01FC011F5B486D90B712F86E6C16E048021F168048020703FCC8FC030015C048030F01F8 C9FC578179FE67>I[<163FAA5EA75EA55DA45DA35DA25DA35DA25DA25D92B5FCA25C5C5C A25C5C5C91B6FC5B1307131F017F92B8FC0007BCFCBDFCA6C891CBFCB3B3B3AAF303F0B3 A7F307E06F7FA4F30FC06F7FA21B1F6F1880836FEF3F00836F177E836F5F7114016F6D5D 6F6D4A5A706D1307706DEB1FE07001F0EB7FC0709039FE01FF807090B6C7FC04015D706C 14F8051F5C050314809426003FFCC8FC>84 178 125 303 102 II121 D E %EndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 1200dpi TeXDict begin %%PaperSize: A4 %%EndSetup %%Page: 1 1 1 0 bop 14 1887 a Fz(F)-22 b(ractal)83 b(dimensions)h(and)h(the)g (Phenomenon)f(of)i(In)-7 b(termittency)82 b(in)2328 2253 y(Quan)-7 b(tum)83 b(Dynamics)2375 2758 y Fy(Jean-Marie)73 b(Barbaroux)1773 2990 y Fx(UMR)60 b(6629)f(du)g(CNRS,)h(UFR)g(de)g (Math)l(\023)-81 b(ematiques,)536 3223 y(Universit)l(\023)g(e)61 b(de)f(Nantes,)g(2)g(rue)f(de)h(la)g(Houssini)l(\022)-81 b(er)-8 b(e,)60 b(F-44072)f(Nantes)i(C)l(\023)-81 b(edex)60 b(03,)f(F)-13 b(r)-8 b(anc)g(e)1593 3455 y Fw(E-mail:)75 b(Jean-Marie.Barbaroux@math.univ-nan)-5 b(tes.fr)2576 3785 y Fy(F)-19 b(ran\030)-100 b(cois)73 b(Germinet)1773 4018 y Fx(UMR)60 b(8524)f(du)g(CNRS,)h(UFR)g(de)g(Math)l(\023)-81 b(ematiques,)1174 4250 y(Universit)l(\023)g(e)61 b(de)f(Lil)8 b(le)61 b(1,)e(F-59655)g(Vil)8 b(leneuve)64 b(d'Asc)-8 b(q)59 b(C)l(\023)-81 b(edex,)60 b(F)-13 b(r)-8 b(anc)g(e)2223 4483 y Fw(E-mail:)75 b(germinet@gat.univ-lille1.fr)2238 4813 y Fy(Serguei)e(Tc)-6 b(heremc)g(han)g(tsev)2643 5045 y Fx(UMR)60 b(6628)f(-)g(MAPMO,)1111 5278 y(Universit)l(\023)-81 b(e)62 b(d'Orl)l(\023)-81 b(eans,)60 b(B.P.)f(6759,)f(F-45067)i(Orl)l (\023)-81 b(eans)61 b(C)l(\023)-81 b(edex,)59 b(F)-13 b(r)-8 b(anc)g(e)1669 5510 y Fw(E-mail:)75 b(serguei.tc)-5 b(herem@lab)5 b(omath.univ-orleans.fr)1808 5893 y(Octob)g(er)55 b(1999,)g(revised)h(v)-5 b(ersion)56 b(Septem)-5 b(b)5 b(er)55 b(2000)3119 6503 y Fv(Abstract)503 6744 y Fw(W)-14 b(e)67 b(exhibit)g(an)g(in)-5 b(termittency)67 b(phenomenon)h(in)g (quan)-5 b(tum)68 b(dynamics.)111 b(More)67 b(precisely)h(w)-5 b(e)254 6944 y(deriv)g(e)47 b(new)g(lo)-5 b(w)g(er)47 b(b)5 b(ounds)48 b(for)f(the)g(momen)-5 b(ts)48 b(of)f(order)g Fx(p)g Fw(asso)5 b(ciated)47 b(to)f(the)h(state)f Fu( )6 b Fw(\()p Fu(t)p Fw(\))46 b(=)g(e)6274 6883 y Ft(\000)p Fs(itH)6601 6944 y Fu( )254 7143 y Fw(and)72 b(a)-5 b(v)g(eraged)73 b(in)f(time)g(b)5 b(et)-5 b(w)g(een)72 b(0)g(and)h Fx(T)p Fw(.)f(These)g(lo)-5 b(w)g(er)73 b(b)5 b(ounds)73 b(are)f(expressed)h (in)g(terms)f(of)254 7342 y(generalized)55 b(fractal)f(dimensions)j Fu(D)2625 7282 y Ft(\006)2620 7383 y Fs(\026)2701 7401 y Fr( )2798 7342 y Fw(\(1)p Fu(=)p Fw(\(1)35 b(+)h Fu(p=d)p Fw(\)\))54 b(of)h(the)f(measure)i Fu(\026)5035 7367 y Fs( )5190 7342 y Fw(\(where)f Fx(d)f Fw(is)i(the)e(space)254 7558 y(dimension\).)88 b(This)60 b(impro)-5 b(v)g(es)61 b(previous)f(results,)i(obtained)e(in)g(terms)g(of)f(Hausdor\013)h(and) g(P)-5 b(ac)g(king)254 7757 y(dimension.)81 8102 y Fq(1991)65 b(Mathematics)g(Subje)-9 b(ct)64 b(Classi\014c)-9 b(ation.)80 b Fp(Primary:)f(81Q10,)59 b(28A80;)i(Secondary:)79 b(35J10.)-201 8665 y Fo(1)270 b(In)-7 b(tro)7 b(duction)-201 9229 y Fp(A)51 b(b)-5 b(y)49 b(no)-5 b(w)51 b(wide)f(n)-5 b(um)g(b)5 b(er)49 b(of)g(articles)h(deals)g(with)h(the)e(links)i(b)5 b(et)-5 b(w)g(een)49 b(the)h(quan)-5 b(tum)48 b(dynamics)g(of)h(w)-5 b(a)g(v)g(e)-201 9455 y(pac)g(k)g(et)76 b(solutions)h(of)g(the)f(Sc)-5 b(hr\177)-91 b(odinger)77 b(equation,)k(and)76 b(the)h(sp)5 b(ectral)77 b(prop)5 b(erties)76 b(of)h(the)f(asso)5 b(ciated)-201 9680 y(Hamiltonian)65 b Fn(H)15 b Fp(.)92 b(Actually)-15 b(,)65 b(during)h(the)e(last)g(decade,)h(an)f(analysis)h (originated)g(b)-5 b(y)64 b(Guarneri)h(in)g([14])-201 9906 y(and)h(re\014ned)f(b)-5 b(y)66 b(others)e([5,)h(7,)g(22,)g(15,)g (25])g(established)g(that)g(the)g(fractal)g(prop)5 b(erties)65 b(of)g(the)h(sp)5 b(ectral)-201 10132 y(measures)65 b(w)-5 b(ere)68 b(relev)-10 b(an)-5 b(t)67 b(for)g(the)g(study)f(of)h(the)g (spreading)h(of)e(w)-5 b(a)g(v)g(e)68 b(pac)-5 b(k)g(et.)99 b(Consider)68 b(a)f(separable)-201 10358 y(Hilb)5 b(ert)80 b(space)d Fm(H)r Fp(,)k(an)e(orthonormal)e(basis)h Fm(f)p Fn(e)3205 10385 y Fl(n)3298 10358 y Fm(g)3389 10387 y Fl(n)p Fk(2)p Fj(N)3673 10358 y Fp(,)k(and)c(a)h(self-adjoin)-5 b(t)76 b(op)5 b(erator)78 b Fn(H)94 b Fp(on)78 b Fm(H)r Fp(.)132 b(Let)-201 10584 y Fn( )-82 10611 y Fl(t)27 10584 y Fp(=)50 b(e)300 10518 y Fk(\000)p Fl(itH)643 10584 y Fn( )67 b Fp(b)5 b(e)60 b(the)h(solution)f(of)h(the)f(Sc)-5 b(hr\177)-91 b(odinger)61 b(equation)2736 10780 y Fi(\032)2955 10931 y Fn(i)3038 10849 y Fl(@)8 b( )3212 10866 y Fh(t)p 3037 10889 231 8 v 3086 10994 a Fl(@)g(t)3479 10931 y Fp(=)165 b Fn(H)15 b( )4071 10958 y Fl(t)2955 11157 y Fn( )3074 11184 y Fl(t)p Fg(=0)3479 11157 y Fp(=)165 b Fn( )3439 11631 y Fp(1)p eop %%Page: 2 2 2 1 bop -201 1158 a Fp(F)-15 b(or)61 b Fn(X)j Fp(=)533 1022 y Fi(P)725 1212 y Fl(n)880 1158 y Fn(n)p Fm(h)p Fn(:)90 b(e)1286 1185 y Fl(n)1380 1158 y Fm(i)30 b Fn(e)1566 1185 y Fl(n)1720 1158 y Fp(b)5 b(eing)61 b(the)f(\\p)5 b(osition)61 b(op)5 b(erator",)60 b(w)-5 b(e)61 b(de\014ne)f(the)h (time)e(a)-5 b(v)g(eraged)60 b(momen)-5 b(ts)-201 1384 y(of)60 b(order)h Fn(p)f Fp(for)g Fn( )67 b Fp(as)673 1869 y Fm(hhj)p Fn(X)14 b Fm(j)1082 1794 y Fl(p)1160 1869 y Fm(ii)1302 1899 y Fl( )5 b(;T)1598 1869 y Fp(:=)1881 1746 y(1)p 1861 1827 132 8 v 1861 1993 a Fn(T)2042 1621 y Fi(Z)2224 1674 y Fl(T)2143 2033 y Fg(0)2365 1659 y Fi(\015)2365 1769 y(\015)2365 1878 y(\015)2466 1869 y Fm(j)p Fn(X)14 b Fm(j)2733 1794 y Fl(p=)p Fg(2)2952 1869 y Fp(e)3033 1794 y Fk(\000)p Fl(itH)3376 1869 y Fn( )3502 1659 y Fi(\015)3502 1769 y(\015)3502 1878 y(\015)3602 1712 y Fg(2)3602 1995 y Fk(H)3761 1869 y Fp(d)p Fn(t)50 b Fp(=)4210 1746 y(1)p 4190 1827 V 4190 1993 a Fn(T)4372 1621 y Fi(Z)4553 1674 y Fl(T)4473 2033 y Fg(0)4700 1696 y Fi(X)4694 2090 y Fl(n)p Fk(2)p Fj(N)5000 1869 y Fm(j)p Fn(n)p Fm(j)5211 1794 y Fl(p)5289 1869 y Fm(jh)p Fn( )5530 1896 y Fl(t)5588 1869 y Fn(;)60 b(e)5784 1896 y Fl(n)5878 1869 y Fm(ij)6000 1794 y Fg(2)6078 1869 y Fp(d)p Fn(t:)500 b Fp(\(1.1\))-201 2438 y(In)80 b(the)h(sp)5 b(eci\014c)80 b(case)g Fm(H)85 b Fp(=)e Fn(`)1977 2373 y Fg(2)2055 2438 y Fp(\()p Ff(Z)2238 2373 y Fl(d)2328 2438 y Fp(\),)i(more)79 b(relev)-10 b(an)-5 b(t)80 b(from)f(a)i(ph)-5 b(ysical)81 b(p)5 b(oin)-5 b(t)80 b(of)g(view,)86 b Fm(f)p Fn(e)6449 2465 y Fl(n)6543 2438 y Fm(g)80 b Fp(is)h(the)-201 2685 y(canonical)64 b(basis)g Fm(f)p Fn(\016)1222 2712 y Fl(n)1316 2685 y Fm(g)1407 2730 y Fl(n)p Fk(2)p Fj(Z)1674 2692 y Fh(d)1819 2685 y Fp(and)g Fm(hhj)p Fn(X)14 b Fm(j)2585 2619 y Fl(p)2663 2685 y Fm(ii)2805 2715 y Fl( )5 b(;T)3107 2685 y Fp(=)3339 2614 y Fg(1)p 3324 2644 102 8 v 3324 2748 a Fl(T)3476 2539 y Fi(R)3597 2591 y Fl(T)3562 2749 y Fg(0)3737 2549 y Fi(P)3929 2739 y Fl(n)p Fk(2)p Fj(Z)4196 2701 y Fh(d)4309 2685 y Fm(j)p Fn(n)p Fm(j)4520 2619 y Fl(p)4598 2685 y Fm(j)p Fn( )4768 2712 y Fl(t)4826 2685 y Fp(\()p Fn(n)p Fp(\))p Fm(j)5128 2619 y Fg(2)5206 2685 y Fp(d)p Fn(t)p Fp(.)90 b(It)63 b(is)h(no)-5 b(w)64 b(w)-5 b(ell)65 b(kno)-5 b(wn)-201 2911 y(from)57 b(a)h(series)g(of)g (results)g([1)o(],[6)o(],[7)n(],[14)n(],[25)o(],)g(in)g(the)g(case)g Fm(H)52 b Fp(=)e Fn(`)4472 2845 y Fg(2)4550 2911 y Fp(\()p Ff(Z)4733 2845 y Fl(d)4823 2911 y Fp(\))58 b(\(extendable)g(to)g Fm(H)52 b Fp(=)d(L)6666 2845 y Fg(2)6745 2911 y Fp(\()p Ff(R)6938 2845 y Fl(d)7028 2911 y Fp(\)\))-201 3137 y(that)60 b(if)h(dim)664 3165 y Fg(H)777 3137 y Fp(\()p Fn(\026)958 3167 y Fl( )1062 3137 y Fp(\))g(is)g(the)f(Hausdor\013)h(dimension)e (of)h(the)g(sp)5 b(ectral)61 b(measure)d Fn(\026)5401 3167 y Fl( )5506 3137 y Fp(,)i(then)1346 3618 y Fn(\013)1463 3543 y Fk(\000)1582 3618 y Fp(\()p Fn( )7 b(;)30 b(p;)g(d)p Fp(\))47 b(:=)j(lim)30 b(inf)2549 3739 y Fl(T)20 b Fk(!1)3043 3492 y Fp(log)s Fm(hhj)p Fn(X)14 b Fm(j)3687 3426 y Fl(p)3764 3492 y Fm(ii)3906 3522 y Fl( )5 b(;T)p 3043 3577 1110 8 v 3399 3743 a Fp(log)33 b Fn(T)4222 3618 y Fm(\025)50 b Fp(dim)4718 3646 y Fg(H)4831 3618 y Fp(\()p Fn(\026)5012 3648 y Fl( )5117 3618 y Fp(\))30 b(p)p Fn(=)p Fp(d)61 b Fn(:)1173 b Fp(\(1.2\))-201 4078 y(More)55 b(recen)-5 b(tly)-15 b(,)55 b(in)g([15)o(])g(a)f(lo)-5 b(w)g(er)56 b(b)5 b(ound)55 b(has)f(b)5 b(een)54 b(pro)-5 b(v)g(en)55 b(for)f(the)h(upp)5 b(er)55 b(oscillations)g(of)f Fm(hhj)p Fn(X)14 b Fm(j)6653 4012 y Fl(p)6731 4078 y Fm(ii)6873 4108 y Fl( )5 b(;T)7119 4078 y Fp(,)-201 4304 y(namely)1325 4619 y Fn(\013)1442 4544 y Fg(+)1560 4619 y Fp(\()p Fn( )i(;)30 b(p;)g(d)p Fp(\))48 b(:=)h(lim)30 b(sup)2553 4775 y Fl(T)20 b Fk(!1)3074 4492 y Fp(log)s Fm(hhj)p Fn(X)14 b Fm(j)3718 4426 y Fl(p)3795 4492 y Fm(ii)3937 4522 y Fl( )5 b(;T)p 3074 4577 V 3430 4743 a Fp(log)33 b Fn(T)4254 4619 y Fm(\025)50 b Fp(dim)4750 4647 y Fg(P)4853 4619 y Fp(\()p Fn(\026)5034 4649 y Fl( )5138 4619 y Fp(\))30 b(p)p Fn(=)p Fp(d)61 b Fn(;)1152 b Fp(\(1.3\))-201 5036 y(where)61 b(dim)629 5064 y Fg(P)732 5036 y Fp(\()p Fn(\026)913 5066 y Fl( )1018 5036 y Fp(\))f(is)h(the)f(\\pac)-5 b(king")61 b(dimension)e(of)h Fn(\026)3670 5066 y Fl( )3775 5036 y Fp(.)81 5262 y(Ho)-5 b(w)g(ev)g(er)59 b(those)f(results)h(are)f (certainly)i(not)e(optimal.)79 b(Some)57 b(one-dimensional)g(quan)-5 b(tum)57 b(systems)-201 5488 y(with)52 b(pure)g(p)5 b(oin)-5 b(t)52 b(sp)5 b(ectrum)49 b(can)j(giv)-5 b(e)51 b(rise)h(to)g(an)f (almost)f(ballistic)j(motion)d([11)o(],)j(that)e(is)h Fn(\013)6250 5422 y Fg(+)6368 5488 y Fp(\()p Fn( )7 b(;)30 b Fp(2)p Fn(;)g Fp(1\))48 b(=)-201 5714 y(2,)57 b(mean)-5 b(while)56 b(dim)1192 5742 y Fg(P)1295 5714 y Fp(\()p Fn(\026)1476 5744 y Fl( )1581 5714 y Fp(\))50 b(=)g(dim)2198 5742 y Fg(H)2311 5714 y Fp(\()p Fn(\026)2492 5744 y Fl( )2597 5714 y Fp(\))g(=)g(0)56 b(for)h(pure)f(p)5 b(oin)-5 b(t)57 b(measures.)77 b(A)57 b(similar)f(phenomenon)f(has)-201 5939 y(b)5 b(een)68 b(argued)f(to)g(hold)h(for)g(the)f(random)f(dimer)g (mo)5 b(del)67 b([12)o(])g([10].)100 b(In)68 b(quasi-p)5 b(erio)g(dic)68 b(mo)5 b(dels)66 b(almost)-201 6165 y(ballistic)e (motion)e(\()p Fn(\013)1286 6099 y Fg(+)1404 6165 y Fp(\()p Fn( )7 b(;)30 b Fp(2)p Fn(;)g Fp(1\))52 b(=)i(2\))63 b(turns)f(out)h(to)f(b)5 b(e)63 b(a)g(common)d(phenomenon,)h(actually)i (a)g(generic)-201 6391 y(phenomenon)84 b([9],)91 b(ev)-5 b(en)86 b(in)h(presence)e(of)h(purely)g(zero)g(Hausdor\013)h (dimensionalit)-5 b(y)85 b(of)h(the)g(sp)5 b(ectral)-201 6617 y(measures)77 b([25)o(,)i(9].)135 b(These)79 b(examples)e(sho)-5 b(w)79 b(ho)-5 b(w)79 b(far)g(w)-5 b(e)79 b(are)g(from)f(a)h(complete)e (understanding)i(of)-201 6843 y(\\What)61 b(determines)d(the)j (spreading)g(of)f(a)h(w)-5 b(a)g(v)g(e)61 b(pac)-5 b(k)g(et")60 b([21)o(].)81 b(In)60 b(this)h(pap)5 b(er,)60 b(w)-5 b(e)61 b(try)g(to)g(go)f(one)h(step)-201 7068 y(further)75 b(in)h(this)f(undertanding,)k(and)c(also)h(supply)f(\(App)5 b(endix)76 b(B\))f(a)g(new)h(enligh)-5 b(tmen)g(t)73 b(concerning)-201 7294 y(the)60 b(main)g(tec)-5 b(hnique)60 b(used)g(in)h(this)g(\014eld)g(for)f(the)g(past)g(ten)g(y)-5 b(ears.)81 7520 y(W)-15 b(e)64 b(obtain)g(new)f(lo)-5 b(w)g(er)65 b(b)5 b(ounds)63 b(for)h(the)f(gro)-5 b(wth)64 b(exp)5 b(onen)-5 b(ts)62 b(of)h Fm(hhj)p Fn(X)14 b Fm(j)5146 7454 y Fl(p)5224 7520 y Fm(ii)5366 7550 y Fl( )5 b(;T)5612 7520 y Fp(,)64 b(namely)e(\(1.4\)-\(1.5\))-201 7746 y(b)5 b(elo)-5 b(w.)164 b(As)89 b(in)f(\(1.2\)-\(1.3\))e(these)h(b)5 b(ounds)88 b(only)h(rely)g(on)f(the)g(fractal)g(prop)5 b(erties)88 b(of)g(the)g(sp)5 b(ectral)-201 7972 y(measure)64 b Fn(\026)623 8002 y Fl( )728 7972 y Fp(.)97 b(W)-15 b(e)65 b(p)5 b(oin)-5 b(t)66 b(out)g(righ)-5 b(t)66 b(no)-5 b(w)67 b(that)e(unlik)-5 b(e)67 b(the)e(existing)h(results,)h(the)e(b)5 b(ounds)66 b(\(1.4\)-\(1.5\))-201 8198 y(w)-5 b(e)88 b(get)g(can)g(b)5 b(e)88 b(non)g(trivial)i(in)e(the)g(presence)g(of)f (zero)h(dimensionalit)-5 b(y)88 b(of)g(the)f(sp)5 b(ectral)88 b(measure)-201 8423 y(\(dim)174 8451 y Fg(P)277 8423 y Fp(\()p Fn(\026)458 8453 y Fl( )563 8423 y Fp(\))81 b(=)g(dim)1242 8451 y Fg(H)1355 8423 y Fp(\()p Fn(\026)1536 8453 y Fl( )1640 8423 y Fp(\))g(=)g(0\),)i(ev)-5 b(en)79 b(in)g(the)g(case)f(of)h(pure)g(p)5 b(oin)-5 b(t)79 b(sp)5 b(ectrum)77 b(\(see)h(App)5 b(endix)80 b(D\).)-201 8649 y(Moreo)-5 b(v)g(er)59 b(in)h(App)5 b(endix)60 b(D,)f(Theorem)e(D.1,)i (w)-5 b(e)59 b(sho)-5 b(w)59 b(that)g(there)g(is)g(no)h(hop)5 b(e)59 b(to)g(impro)-5 b(v)g(e)58 b(our)h(result)-201 8875 y(b)-5 b(y)86 b(only)h(taking)f(in)-5 b(to)86 b(accoun)-5 b(t)86 b(the)f(fractal)h(prop)5 b(erties)86 b(of)g(the)g(sp)5 b(ectral)86 b(measure)e(enco)5 b(ded)86 b(in)g(its)-201 9101 y(generalized)61 b(fractal)f(dimensions)g Fn(D)2398 9035 y Fk(\006)2393 9146 y Fl(\026)2478 9169 y Fh( )2579 9101 y Fp(\()p Fn(q)7 b Fp(\).)81 9327 y(Our)52 b(result)f(also)h(pro) -5 b(vides)51 b(a)g(precise)h(statemen)-5 b(t)48 b(of)j(a)g(phenomenon) f(disco)-5 b(v)g(ered)51 b(b)-5 b(y)51 b(recen)-5 b(t)51 b(n)-5 b(umer-)-201 9553 y(ical)75 b(computations)d(in)j(some)d(quan)-5 b(tum)72 b(mo)5 b(dels)73 b(for)h(quasicrystals)g([26)o(,)g(29,)f(32];) 80 b(this)74 b(phenomenon)-201 9778 y(has)53 b(b)5 b(een)53 b(called)h(\\In)-5 b(termittency".)75 b(Namely)-15 b(,)54 b(it)f(has)g(b)5 b(een)53 b(suggested)f(b)-5 b(y)54 b(ph)-5 b(ysicists)53 b(that)f(the)h(gro)-5 b(wth)-201 10004 y(exp)5 b(onen)-5 b(ts)63 b Fn(\013)774 9938 y Fk(\006)892 10004 y Fp(\()p Fn( )7 b(;)30 b(p;)g(d)p Fp(\))60 b(should)k(gro)-5 b(w)64 b(faster)e(than)h(linearly)i(in)f Fn(p=d)e Fp(as)h(prop)5 b(osed)64 b(in)f(\(1.2\))g(and)g(\(1.3\);)-201 10230 y(one)j(should)g(observ)-5 b(e)65 b(a)h(more)e(complex)g(la)-5 b(w)67 b(for)e(the)g(b)5 b(eha)-5 b(viour)66 b(of)g Fn(\013)4821 10164 y Fk(\006)4939 10230 y Fp(\()p Fn( )7 b(;)30 b(p;)g(d)p Fp(\))63 b(in)j(the)f(v)-10 b(ariable)67 b Fn(p=d)p Fp(:)-201 10456 y Fn(\013)-84 10390 y Fk(\006)34 10456 y Fp(\()p Fn( )7 b(;)30 b(p;)g(d)p Fp(\))67 b(=)j Fn(\014)1043 10390 y Fk(\006)1160 10456 y Fp(\()p Fn( )7 b(;)30 b(p=d)p Fp(\))p Fn(p=d)p Fp(,)71 b(where)h Fn(\014)2837 10390 y Fk(\006)2955 10456 y Fp(\()p Fn( )7 b(;)30 b(p=d)p Fp(\))69 b(are)j(non)h(decreasing)f(functions)f(of)h Fn(p=d)f Fp(\(and)h(of)-201 10682 y(course)60 b(non)h(smaller)f(than)g (dim)2066 10710 y Fg(H)2239 10682 y Fp(and)h(dim)2897 10710 y Fg(P)3000 10682 y Fp(\).)81 10907 y(These)70 b(recen)-5 b(t)69 b(n)-5 b(umerical)69 b(in)-5 b(v)g(estigations)70 b(emphasized,)g(in)h(this)e(phenomenon)f(of)i(in)-5 b(termittency)-15 b(,)-201 11133 y(the)59 b(role)h(of)f(more)f(re\014ned)i(fractal)f (quan)-5 b(tities,)59 b(the)g(so-called)g(\\)p Fn(q)7 b Fp(-th)59 b(generalized)h(fractal)f(dimensions")3439 11631 y(2)p eop %%Page: 3 3 3 2 bop -201 1158 a Fn(D)-45 1092 y Fk(\006)-50 1203 y Fl(\026)35 1226 y Fh( )136 1158 y Fp(\()p Fn(q)7 b Fp(\).)80 b(The)60 b(lo)-5 b(w)g(er)61 b(b)5 b(ounds)60 b(\(1.4\)-\(1.5\))d(that)j(w)-5 b(e)60 b(establish)g(for)g Fm(hhj)p Fn(X)14 b Fm(j)4942 1092 y Fl(p)5020 1158 y Fm(ii)5162 1188 y Fl( )5 b(;T)5468 1158 y Fp(actually)60 b(app)5 b(ear)61 b(to)e(b)5 b(e)-201 1384 y(\\in)-5 b(termitten)g(t")61 b(lo)-5 b(w)g(er)64 b(b)5 b(ounds,)63 b(pro)-5 b(viding)64 b(th)-5 b(us)63 b(a)g(rigourous)h(statemen)-5 b(t)60 b(concerning)j(in)-5 b(termittency)-201 1610 y(in)59 b(quan)-5 b(tum)57 b(dynamics.)78 b(More)58 b(precisely)-15 b(,)58 b(when)h Fn(D)3523 1544 y Fk(\006)3518 1655 y Fl(\026)3641 1610 y Fp(\()p Fn(q)7 b Fp(\))57 b(is)i(non)f(constan)-5 b(t)58 b(for)g Fn(q)f Fm(2)51 b Fp(\(0)p Fn(;)30 b Fp(1\),)57 b(these)h(lo)-5 b(w)g(er)-201 1836 y(b)5 b(ounds)79 b(gro)-5 b(w)78 b(faster)g(than)g(linearly)i(in)f Fn(p=d)p Fp(.)133 b(After)79 b(Theorem)e(2.1)h(w)-5 b(e)78 b(discuss)g(the)g(application) i(of)-201 2062 y(our)58 b(result)f(to)g(an)g(Hamiltonian)g(constructed) f(with)i(Julia)f(matrices)f(with)h(self-similar)g(sp)5 b(ectra)56 b([4)o(][16)o(].)-201 2288 y(F)-15 b(or)55 b(\\real")h(Sc)-5 b(hr\177)-91 b(odinger)56 b(op)5 b(erators,)55 b(go)5 b(o)g(d)56 b(candidates)f(w)-5 b(ould)56 b(b)5 b(e)55 b(op)5 b(erators)55 b(on)h Fn(`)5719 2222 y Fg(2)5797 2288 y Fp(\()p Ff(N)30 b Fp(\))64 b(or)56 b Fn(`)6419 2222 y Fg(2)6498 2288 y Fp(\()p Ff(Z)8 b Fp(\))64 b(with)-201 2513 y(sparse)73 b(or)g(quasip)5 b(erio)g(dic)75 b(\()p Fq(e.g.)117 b Fp(generated)72 b(b)-5 b(y)74 b(substitution)e (sequences\))g(p)5 b(oten)-5 b(tial.)118 b(But)73 b(a)g(careful)-201 2739 y(analysis)e(of)f(the)g(links)h(b)5 b(et)-5 b(w)g(een)70 b(sp)5 b(ectral)71 b(prop)5 b(erties)70 b(and)h(b)5 b(eha)-5 b(viour)71 b(of)f(the)g(eigenfunctions)g(w)-5 b(ould)-201 2965 y(then)60 b(b)5 b(e)61 b(required;)f(an)h(analysis)g(that)f(go)5 b(es,)59 b(for)i(instance,)e(b)5 b(ey)-5 b(ond)60 b(the)h(scop)5 b(e)59 b(of)i([20)o(])f(.)81 3191 y(Our)g(main)g(result)g(\(Theorem)e (2.1\))i(holds)g(for)g(an)-5 b(y)60 b(self-adjoin)-5 b(t)59 b(op)5 b(erators)60 b Fn(H)15 b Fp(,)59 b(and)i(for)f(an)-5 b(y)60 b(initial)-201 3417 y(state)g Fn( )66 b Fp(suc)-5 b(h)60 b(that)g(the)g(asso)5 b(ciated)60 b(sp)5 b(ectral)60 b(measure)f(d)p Fn(\026)4016 3447 y Fl( )4181 3417 y Fp(satis\014es)1922 3771 y(\()p Fe(H)p Fp(\))181 b Fn(D)2565 3696 y Fk(\006)2560 3816 y Fl(\026)2645 3839 y Fh( )2746 3771 y Fp(\()p Fn(s)p Fp(\))51 b Fn(<)f Fp(+)p Fm(1)120 b Fp(for)60 b(an)-5 b(y)63 b Fn(s)51 b Fm(2)g Fp(\(0)p Fn(;)30 b Fp(1\))p Fn(:)-201 4125 y Fp(The)61 b(result)g(reads)f(then)g (as)g(follo)-5 b(ws:)2137 4534 y Fn(\013)2254 4459 y Fk(\000)2372 4534 y Fp(\()p Fn( )7 b(;)30 b(p;)g(d)p Fp(\))48 b Fm(\025)i Fn(D)3385 4459 y Fk(\000)3380 4579 y Fl(\026)3465 4602 y Fh( )3596 4277 y Fi(\022)4000 4411 y Fp(1)p 3750 4492 591 8 v 3750 4659 a(1)40 b(+)g Fn(p=d)4360 4277 y Fi(\023)4554 4534 y Fn(p=d)1964 b Fp(\(1.4\))-201 4978 y(and)2112 5258 y Fn(\013)2229 5183 y Fg(+)2347 5258 y Fp(\()p Fn( )7 b(;)30 b(p;)g(d)p Fp(\))47 b Fm(\025)j Fn(D)3359 5183 y Fg(+)3354 5303 y Fl(\026)3439 5326 y Fh( )3571 5002 y Fi(\022)3974 5135 y Fp(1)p 3725 5216 V 3725 5383 a(1)40 b(+)g Fn(p=d)4335 5002 y Fi(\023)4529 5258 y Fn(p=d:)1938 b Fp(\(1.5\))-201 5675 y(where)58 b Fn(D)478 5609 y Fk(\000)473 5719 y Fl(\026)558 5742 y Fh( )659 5675 y Fp(\()p Fn(q)7 b Fp(\))57 b(and)h Fn(D)1453 5609 y Fg(+)1448 5719 y Fl(\026)1533 5742 y Fh( )1634 5675 y Fp(\()p Fn(q)7 b Fp(\))57 b(are)g(the)g(lo)-5 b(w)g(er)59 b(and)e(upp)5 b(er)58 b(\\)p Fn(q)7 b Fp(-th)57 b(generalized)h(fractal)f(dimensions")f(\(see)-201 5900 y(De\014nition)74 b(2.2\).)117 b(In)73 b(App)5 b(endix)73 b(C)h(w)-5 b(e)73 b(discuss)g(the)f(v)-10 b(alidit)-5 b(y)74 b(of)f(Hyp)5 b(othesis)73 b(\()p Fe(H)p Fp(\),)f(whic)-5 b(h,)76 b(w)-5 b(e)73 b(note,)-201 6126 y(holds)64 b(for)f(compactly)f (supp)5 b(orted)63 b(measures.)87 b(In)64 b(particular)g(Theorem)e(2.1) h(applies)i(to)e(the)g(examples)-201 6352 y(where)e(the)f(in)-5 b(termittency)59 b(phenomenon)g(has)h(b)5 b(een)60 b(argued)h(to)f (hold.)81 6578 y(T)-15 b(o)57 b(ac)-5 b(hiev)g(e)55 b(this)h(w)-5 b(e)56 b(\014rst)g(deriv)-5 b(e)56 b(a)g Fn(p=d)p Fp(-dep)5 b(enden)-5 b(t)54 b(lo)-5 b(w)g(er)57 b(b)5 b(ound)56 b Fn(L)4996 6608 y Fl( )5101 6578 y Fp(\()p Fn(T)25 b Fp(\))56 b(for)g Fm(hhj)p Fn(X)14 b Fm(j)6113 6512 y Fl(p)6190 6578 y Fm(ii)6332 6608 y Fl( )5 b(;T)6634 6578 y Fp(\(Theo-)-201 6804 y(rem)51 b(3.1\).)77 b(Then)52 b(w)-5 b(e)52 b(establish)g Fq(via)109 b Fp(Theorem)51 b(4.2)g(the)h(connection)g(b)5 b(et)-5 b(w)g(een)51 b Fn(L)5462 6834 y Fl( )5568 6804 y Fp(\()p Fn(T)25 b Fp(\))52 b(and)g(the)g(general-)-201 7029 y(ized)k(fractal)f(dimensions,)g(b)-5 b(y)55 b(adjusting)g(for)g(eac)-5 b(h)55 b(single)h Fn(T)82 b Fp(the)55 b(\\thin")g(part)h(of)f Fn(\026)5684 7059 y Fl( )5844 7029 y Fp(that)g(supplies)h(the)-201 7255 y(faster)j(dynamical)h(tra)-5 b(v)g(el.)80 b(Concerning)60 b(the)g(connection)g(b)5 b(et)-5 b(w)g(een)59 b Fn(L)4761 7285 y Fl( )4866 7255 y Fp(\()p Fn(T)25 b Fp(\))60 b(and)g Fn(D)5708 7189 y Fk(\006)5703 7300 y Fl(\026)5788 7323 y Fh( )5890 7255 y Fp(\()p Fn(q)7 b Fp(\))59 b(w)-5 b(e)60 b(moreo)-5 b(v)g(er)-201 7481 y(obtain)64 b(a)f(kind)h(of)f(optimalit) -5 b(y)-15 b(,)63 b(in)h(the)f(sense)f(that)h(this)g(quan)-5 b(tit)g(y)64 b Fn(L)4671 7511 y Fl( )4776 7481 y Fp(\()p Fn(T)25 b Fp(\))63 b(that)g(minors)f Fm(hhj)p Fn(X)14 b Fm(j)6518 7415 y Fl(p)6596 7481 y Fm(ii)6738 7511 y Fl( )5 b(;T)7047 7481 y Fp(is)-201 7707 y(sho)-5 b(wn)61 b(to)f(ha)-5 b(v)g(e)60 b(its)h(gro)-5 b(wth)60 b(exp)5 b(onen)-5 b(ts)60 b(exactly)g(equal)h(to)f Fn(D)4196 7641 y Fk(\006)4191 7752 y Fl(\026)4276 7775 y Fh( )4377 7707 y Fp(\(1)p Fn(=)p Fp(\(1)40 b(+)g Fn(p=d)p Fp(\)\))30 b Fn(p=d)p Fp(.)81 7957 y(W)-15 b(e)61 b(p)5 b(oin)-5 b(t)62 b(out)f(that)f Fn(D)1745 7891 y Fk(\006)1740 8002 y Fl(\026)1825 8025 y Fh( )1927 7957 y Fp(\(1)p Fn(=)p Fp(\(1)40 b(+)g Fn(p=d)p Fp(\)\))60 b(are)h(increasing)h(functions)e (of)h Fn(p=d)p Fp(,)f(and)h(are)g(resp)5 b(ectiv)-5 b(ely)-201 8183 y(not)60 b(smaller)f(than)g(dim)1476 8211 y Fg(H)1589 8183 y Fp(\()p Fn(\026)1770 8213 y Fl( )1875 8183 y Fp(\))h(and)f(dim) 2662 8211 y Fg(P)2766 8183 y Fp(\()p Fn(\026)2947 8213 y Fl( )3051 8183 y Fp(\))h(\(for)f(all)i Fn(p=d)50 b(>)f Fp(0\).)80 b(Therefore)60 b(\(1.4\)-\(1.5\))d(do)i(impro)-5 b(v)g(e)-201 8409 y(the)60 b(b)5 b(ounds)61 b(\(1.2\))e(and)i(\(1.3\))e (ab)5 b(o)-5 b(v)g(e.)81 8635 y(These)94 b(new)h(b)5 b(ounds)93 b(are)h(a)g(consequence)f(of)h(a)g(double)g(impro)-5 b(v)g(emen)g(t)91 b(of)j(the)f(approac)-5 b(hes)94 b(of)-201 8861 y(Guarneri-Com)-5 b(b)5 b(es-Last)80 b(\(G-C-L\))i([7)o(,)h(25])g (and)h(of)e(Barbaroux-Tc)-5 b(heremc)g(han)g(tsev)81 b(\(BT\))h([5].)148 b(The)-201 9087 y(\014rst)65 b(impro)-5 b(v)g(emen)g(t)61 b(is)k(due,)g(after)f(a)g(decomp)5 b(ostion)63 b Fn( )g Fp(=)57 b Fn(')43 b Fp(+)f Fn(\037)p Fp(,)65 b Fn(')58 b Fm(?)d Fn(\037)p Fp(,)65 b(to)f(a)h(b)5 b(etter)64 b(con)-5 b(trol)65 b(of)f(the)-201 9312 y(k)-5 b(ey)60 b(quan)-5 b(tit)g(y)527 9745 y Fn(B)665 9775 y Fl( )771 9745 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))105 b(:=)1723 9622 y(1)p 1703 9703 132 8 v 1703 9870 a Fn(T)1885 9497 y Fi(Z)2066 9550 y Fk(1)1986 9910 y Fg(0)2315 9572 y Fi(X)2246 9975 y Fk(j)p Fl(n)p Fk(j\024)p Fl(N)2676 9745 y Fm(jh)p Fp(e)2879 9670 y Fk(\000)p Fl(itH)3222 9745 y Fn( )7 b(;)30 b(e)3514 9772 y Fl(n)3606 9745 y Fm(ij)3728 9670 y Fg(2)3806 9745 y Fn(h)p Fp(\()p Fn(t=T)25 b Fp(\)d)p Fn(t)1411 10345 y Fm(\024)130 b Fn(B)1821 10372 y Fl(\037)1917 10345 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))40 b(+)2689 10222 y(2)p 2668 10303 V 2668 10469 a Fn(T)2850 10345 y Fp(Re)3065 10097 y Fi(Z)3247 10150 y Fk(1)3166 10510 y Fg(0)3465 10172 y Fi(X)3396 10575 y Fk(j)p Fl(n)p Fk(j\024)p Fl(N)3796 10345 y Fm(h)p Fp(e)3948 10270 y Fk(\000)p Fl(itH)4291 10345 y Fn(';)30 b(e)4576 10372 y Fl(n)4669 10345 y Fm(i)p 4740 10180 950 8 v(h)p Fp(e)4892 10292 y Fk(\000)p Fl(itH)5235 10345 y Fn( )7 b(;)30 b(e)5527 10372 y Fl(n)5619 10345 y Fm(i)p Fn(h)p Fp(\()p Fn(t=T)25 b Fp(\)d)p Fn(t;)353 b Fp(\(1.6\))-201 10907 y(and)53 b(more)e(particulary)i(of)g(the)f(last)g(term)f(\(the)h (crossed)g(term\).)76 b(W)-15 b(e)52 b(stress)f(righ)-5 b(t)53 b(no)-5 b(w)53 b(that)f(this)h(b)5 b(etter)-201 11133 y(con)-5 b(trol)79 b(of)f(the)g(crossed)g(term)f(is)h(essen)-5 b(tial,)83 b(meaning)77 b(that)h(using)h(the)f(former)e(a)-5 b(v)-10 b(ailable)80 b(estimates)3439 11631 y(3)p eop %%Page: 4 4 4 3 bop -201 1158 a Fp([25,)40 b(5])h(will)j(not)d(lead)g(to)g(the)g (righ)-5 b(t)42 b(fractal)f(dimensions)f Fn(D)3837 1092 y Fk(\006)3832 1203 y Fl(\026)3917 1226 y Fh( )4018 1158 y Fp(\(1)p Fn(=)p Fp(\(1)r(+)r Fn(\014)10 b Fp(\)\),)43 b(as)e(illustrated)h(in)g(App)5 b(endix)42 b(B.)-201 1442 y(Here)61 b Fn(h)p Fp(\()p Fn(z)8 b Fp(\))59 b(is)i(some)e(p)5 b(ositiv)-5 b(e)60 b(function)h(in)g Fn(C)3007 1376 y Fk(1)2994 1491 y Fg(0)3156 1442 y Fp(\([0)p Fn(;)30 b Fp(1]\))59 b(suc)-5 b(h)60 b(that)4526 1296 y Fi(R)4647 1348 y Fg(1)4612 1506 y(0)4756 1442 y Fn(h)p Fp(\()p Fn(z)8 b Fp(\)d)p Fn(z)57 b Fp(=)50 b(1.)81 1668 y(Afterw)-5 b(ards,)58 b(and)g(this)g(is)g(Theorem)f(3.1,)g(one)h(is)g(able)g(to)g (obtain)g(a)g(constan)-5 b(t)56 b Fn(C)13 b Fp(\()p Fn( )7 b(;)30 b(p;)g(h)p Fp(\))48 b Fn(>)i Fp(0,)58 b(suc)-5 b(h)-201 1894 y(that)60 b(for)g(all)i Fn(T)76 b(>)50 b Fp(0,)459 2447 y Fm(hhj)p Fn(X)14 b Fm(j)868 2372 y Fl(p)945 2447 y Fm(ii)1087 2477 y Fl( )5 b(;T)1384 2447 y Fm(\025)49 b Fn(C)13 b Fp(\()p Fn( )7 b(;)30 b(p;)g(h)p Fp(\))p Fn(L)2469 2477 y Fl( )2572 2447 y Fp(\()p Fn(T)25 b Fp(\))p Fn(;)211 b Fp(with)183 b Fn(L)3767 2477 y Fl( )3872 2447 y Fp(\()p Fn(T)25 b Fp(\))50 b(=)113 b(sup)4387 2603 y Fl(')p Fk(2H)4693 2626 y Fh( )4817 2136 y Fi(\()5167 2324 y Fm(jh)p Fn(';)30 b( )7 b Fm(ij)5737 2258 y Fg(2+2)p Fl(\014)p 4983 2405 1280 8 v 4983 2603 a Fm(k)p Fn(')p Fm(k)5284 2550 y Fg(2)5393 2603 y Fp(\()p Fn(U)5588 2633 y Fl('; )5825 2603 y Fp(\()p Fn(T)25 b Fp(\)\))6168 2519 y Fl(\014)6283 2136 y Fi(\))6459 2447 y Fn(;)-201 2999 y Fp(where)61 b Fm(H)479 3029 y Fl( )644 2999 y Fp(is)g(the)f(cyclic)h (subspace)f(spanned)g(b)-5 b(y)61 b Fn( )66 b Fp(and)61 b Fn(H)15 b Fp(,)1826 3502 y Fn(U)1950 3532 y Fl('; )2187 3502 y Fp(\()p Fn(T)25 b Fp(\))50 b(=)2702 3254 y Fi(Z)2803 3667 y Fj(R)2890 3629 y Fd(2)3007 3502 y Fp(d)p Fn(\026)3218 3532 y Fl( )3323 3502 y Fp(\()p Fn(x)p Fp(\)d)p Fn(\026)3780 3529 y Fl(')3879 3502 y Fp(\()p Fn(y)7 b Fp(\))p Fn(R)q Fp(\()p Fn(T)25 b Fp(\()p Fn(x)40 b Fm(\000)g Fn(y)7 b Fp(\)\))p Fn(;)-201 4002 y Fp(and)55 b Fn(R)i Fp(is)e(some)f(b)5 b(ounded)55 b(fast)f(deca)-5 b(ying)55 b(function)f(de\014ned)h(b)-5 b(y)55 b(\(3.5\))f(in)i(Section)f(3)g(\(one)g(should)g(think)-201 4228 y(to)68 b Fn(R)q Fp(\()p Fn(w)5 b Fp(\))69 b(as)f(to)g(the)g (gaussian)g Fn(e)2118 4162 y Fk(\000)p Fl(w)2333 4115 y Fd(2)2401 4162 y Fl(=)p Fg(4)2551 4228 y Fp(\).)103 b(Th)-5 b(us,)70 b(as)e(in)h([5)o(,)f(15],)h(one)g(can)f(\\c)-5 b(ho)5 b(ose",)69 b(for)f(eac)-5 b(h)67 b Fn(T)25 b Fp(,)71 b(a)d Fn(T)25 b Fp(-)-201 4454 y(dep)5 b(enden)-5 b(t)44 b(v)-5 b(ector)45 b Fn(')f Fp(in)i(the)e(decomp)5 b(osition)44 b Fn( )56 b Fp(=)50 b Fn(')9 b Fp(+)g Fn(\037)p Fp(,)47 b(that)d(con)-5 b(tains)44 b(enough)h(sp)5 b(ectral)45 b(information)-201 4680 y(to)66 b(appro)-5 b(ximate)65 b(the)g(suprem)-5 b(um)63 b(in)k Fn(L)2635 4710 y Fl( )2740 4680 y Fp(\()p Fn(T)25 b Fp(\).)97 b(The)66 b(second)g(impro)-5 b(v)g(emen)g(t)63 b(then)j(consists)f(in)h(the)g(w)-5 b(a)g(y)-201 4905 y(one)61 b(c)-5 b(ho)5 b(oses)60 b(this)h(particular) g(v)-5 b(ector)61 b Fn(')p Fp(.)81 b(W)-15 b(e)61 b(sho)-5 b(w)60 b(\(Theorem)g(4.1\))g(that)g(a)h(judicious)g(c)-5 b(hoice)61 b(enables)-201 5131 y(one)g(to)f(connect,)f(up)i(to)f(a)g (logarithmic)g(factor,)g(the)g(quan)-5 b(tit)g(y)60 b Fn(L)4404 5161 y Fl( )4509 5131 y Fp(\()p Fn(T)25 b Fp(\))61 b(to)f(the)g(in)-5 b(tegral)921 5650 y Fn(I)1001 5677 y Fl(\026)1086 5700 y Fh( )1218 5393 y Fi(\022)1622 5527 y Fp(1)p 1372 5608 591 8 v 1372 5774 a(1)40 b(+)g Fn(p=d)1982 5650 y(;)30 b(T)2194 5575 y Fk(\000)p Fg(1)2383 5393 y Fi(\023)2568 5650 y Fp(=)2759 5402 y Fi(Z)2860 5814 y Fj(R)2995 5650 y Fp(d)p Fn(\026)3206 5680 y Fl( )3311 5650 y Fp(\()p Fn(x)p Fp(\))50 b Fn(\026)3717 5680 y Fl( )3852 5502 y Fi(\000\002)4011 5650 y Fn(x)40 b Fm(\000)g Fn(T)4468 5575 y Fk(\000)p Fg(1)4657 5650 y Fn(;)30 b(x)40 b Fp(+)g Fn(T)5195 5575 y Fk(\000)p Fg(1)5384 5502 y Fi(\003\001)5543 5542 y Fk(\000)5750 5474 y Fh(p=d)p 5673 5511 346 6 v 5673 5594 a Fd(1+)p Fh(p=d)-201 6168 y Fp(that)60 b(de\014nes)g(the)g(generalized)h(fractal)f(exp)5 b(onen)-5 b(ts)60 b Fn(D)3625 6102 y Fk(\006)3620 6213 y Fl(\026)3705 6236 y Fh( )3806 6168 y Fp(\(1)p Fn(=)p Fp(\(1)40 b(+)g Fn(p=d)p Fp(\)\).)81 6493 y(Our)53 b(metho)5 b(d)51 b(also)i(applies)h(to)e(the)h(previous)g(approac)-5 b(hes)52 b(\(G-C-L\))f(and)i(\(BT\),)f(where)i(the)e(crossed)-201 6719 y(term)60 b(in)j(\(1.6\))d(w)-5 b(asn't)61 b(treated)g(w)-5 b(ell.)86 b(It)61 b(resp)5 b(ectiv)-5 b(ely)62 b(yields,)g(as)f(stated) g(in)h(App)5 b(endix)63 b(B,)e(the)h(fractal)-201 6945 y(dimensions)50 b Fn(D)877 6879 y Fk(\006)872 6990 y Fl(\026)957 7013 y Fh( )1058 6945 y Fp(\(\(1)21 b(+)g Fn(\014)10 b Fp(\))p Fn(=)p Fp(\(1)21 b(+)g(2)p Fn(\014)10 b Fp(\)\))46 b(and)51 b Fn(D)2988 6879 y Fk(\006)2983 6990 y Fl(\026)3068 7013 y Fh( )3169 6945 y Fp(\(\(1)21 b(+)g(2)p Fn(\014)10 b Fp(\))p Fn(=)p Fp(\(1)21 b(+)g(3)p Fn(\014)10 b Fp(\)\).)72 b(Since)51 b(the)f(functions)g Fn(D)6465 6879 y Fk(\006)6460 6990 y Fl(\026)6545 7013 y Fh( )6646 6945 y Fp(\()p Fn(q)7 b Fp(\))50 b(are)-201 7171 y(non)63 b(increasing)h(functions)e(of)h Fn(q)7 b Fp(,)62 b(our)i(Theorem)d(2.1)i(giv)-5 b(es)63 b(a)g(b)5 b(etter)62 b(lo)-5 b(w)g(er)64 b(b)5 b(ound.)87 b(This)64 b(means)d(that)-201 7397 y(a)g(b)5 b(etter)60 b(estimate)e(of)i(the)g (crossed)g(term)f(in)i(\(1.6\))e(do)5 b(es)60 b(pro)-5 b(vide)61 b(an)g(impro)-5 b(v)g(emen)g(t)57 b(\(Theorem)i(B.3\).)81 7722 y(Finally)-15 b(,)61 b(using)f(extra)f(assumptions)e(on)j(the)f (deca)-5 b(y)59 b(of)h(the)f(generalized)h(eigenfunctions)f Fn(u)p Fp(\()p Fn(n;)30 b(x)p Fp(\))59 b(of)-201 7948 y Fn(H)65 b Fp(\(in)49 b(the)g(spirit)h(of)f([21)o(])g([23)o(]\),)i(it) e(is)h(p)5 b(ossible)50 b(to)f(impro)-5 b(v)g(e)48 b(the)h(ab)5 b(o)-5 b(v)g(e)49 b(b)5 b(ounds.)76 b(In)49 b(particular,)j(supp)5 b(ose)-201 8174 y(that)69 b(there)g(exists)h(a)f(constan)-5 b(t)69 b Fn(C)82 b Fp(suc)-5 b(h)69 b(that)g(for)h Fn(\026)3523 8204 y Fl( )3697 8174 y Fp(a.e.)p Fn(x)p Fp(,)4196 8037 y Fi(P)4388 8227 y Fk(j)p Fl(n)p Fk(j)p Fl()g Fp(0)p Fq(,)65 b Fn(I)4740 11160 y Fl(\026)4898 11133 y Fq(takes)g(the)g(value)e Fp(+)p Fm(1)p Fq(.)3439 11631 y Fp(5)p eop %%Page: 6 6 6 5 bop -201 1158 a Fe(Remark)69 b(2.2.)-201 1384 y Fp(i\))62 b(F)-15 b(or)60 b(our)i(purp)5 b(ose,)60 b(it)h(is)h(su\016cien)-5 b(t)60 b(to)h(discuss)f(the)h(case)f Fn(q)e Fm(2)52 b Fp(\()p Fm(\0001)p Fn(;)30 b Fp(1\))59 b(\(see)i(e.g.)81 b([8)o(])61 b(for)f(the)h(general)-201 1610 y(case\).)-201 1836 y(ii\))79 b(There)g(exists)f(actually)h(a)f(wide)h(n)-5 b(um)g(b)5 b(er)77 b(of)h(\\generalized)h(fractal)f(dimensions".)132 b(F)-15 b(or)78 b(example,)-201 2062 y(they)66 b(can)g(b)5 b(e)66 b(de\014ned)f(with)i(the)f(help)g(of)g(the)f(so-called)h (\\singularit)-5 b(y)67 b(sp)5 b(ectrum)64 b(function")i Fn(f)6545 2089 y Fl(\026)6704 2062 y Fp(of)g(the)-201 2288 y(measure)d Fn(\026)i Fp(\([18)o(],)g([27]\),)g(or)g(as)g(a)g (solution)g(of)g(an)g(implicit)g(equation)g(\([18)o(,)h(F)-15 b(orm)-5 b(ula)64 b(2.8],)h([27)o(]\).)93 b(The)-201 2513 y(resulting)68 b(dimensions)e(coincide)i(with)g(eac)-5 b(h)67 b(other)g(in)h(certain)f(v)-5 b(ery)68 b(sp)5 b(eci\014c)67 b(cases,)h(lik)-5 b(e)68 b(e.g.)100 b(Co)5 b(okie)-201 2739 y(Cutter)61 b(measures)d(in)j Ff(R)96 b Fp([27)o(].)81 3090 y(In)53 b(order)g(to)g(state)f(our)h(results)g(w) -5 b(e)53 b(also)g(de\014ne)g(the)f(follo)-5 b(wing)55 b(in)-5 b(tegrals)53 b(that)f(could)i(b)5 b(e)52 b(considered)-201 3316 y(as)58 b(appro)-5 b(ximations)56 b(of)h(the)g(quan)-5 b(tities)58 b Fn(I)2732 3343 y Fl(\026)2825 3316 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\).)78 b(The)58 b(function)f Fn(R)i Fp(is)f(a)g(b)5 b(ounded)57 b(ev)-5 b(en)58 b(function)f(with)-201 3542 y(fast)j(deca)-5 b(y)60 b(prop)5 b(erties)60 b(at)h Fm(\0061)p Fp(,)e(and)h(will)j(b)5 b(e)60 b(precisely)h(de\014ned)g(in) g(\(3.5\))e(b)5 b(elo)-5 b(w.)1387 4054 y Fn(K)1542 4081 y Fl(\026)1635 4054 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))49 b(=)2272 3807 y Fi(Z)2373 4219 y Fg(supp)q Fl(\026)2787 4054 y Fp(d)p Fn(\026)p Fp(\()p Fn(x)p Fp(\))3274 3798 y Fi(\022)3407 3807 y(Z)3508 4219 y Fj(R)3643 4054 y Fp(d)p Fn(\026)p Fp(\()p Fn(y)7 b Fp(\))p Fn(R)q Fp(\(\()p Fn(x)39 b Fm(\000)h Fn(y)7 b Fp(\))p Fn(=")p Fp(\))5112 3798 y Fi(\023)5244 3843 y Fl(q)e Fk(\000)p Fg(1)5531 4054 y Fn(;)-201 4552 y Fp(In)43 b(Lemma)c(4.3)j(w)-5 b(e)43 b(shall)g(pro)-5 b(v)g(e)43 b(that)f(for)h(an)-5 b(y)42 b(measure)f Fn(\026)h Fp(v)-5 b(erifying)44 b(the)e(condition)h (\(H\))g(of)f(our)h(theorem,)-201 4777 y(taking)59 b Fn(K)513 4804 y Fl(\026)605 4777 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))57 b(in)i(\(2.2\))f(instead)g(of)g Fn(I)2611 4804 y Fl(\026)2704 4777 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))57 b(leads)h(to)g(the)g(same)f(v)-10 b(alues)58 b(for)g(the)g(generalized)h(fractal)-201 5003 y(dimensions.)81 5319 y(W)-15 b(e)60 b(review)h(b)5 b(elo)-5 b(w)61 b(some)e(prop)5 b(erties)60 b(of)g(the)g(fractal)g(dimension)g(n)-5 b(um)g(b)5 b(ers)58 b Fn(D)5631 5253 y Fk(\006)5626 5364 y Fl(\026)5749 5319 y Fp(\()p Fn(q)7 b Fp(\))59 b(that)h(will)j(b)5 b(e)60 b(of)-201 5545 y(in)-5 b(terest)60 b(for)h(us.)-201 5896 y Fe(Prop)6 b(osition)69 b(2.1.)90 b Fq(L)-9 b(et)65 b Fn(\026)f Fq(b)-9 b(e)64 b(a)h(Bor)-9 b(el)64 b(pr)-9 b(ob)g(ability)63 b(me)-9 b(asur)g(e.)-201 6122 y(i\))65 b Fn(D)150 6056 y Fk(\000)145 6167 y Fl(\026)268 6122 y Fp(\()p Fn(q)7 b Fp(\))64 b Fq(and)h Fn(D)1071 6056 y Fg(+)1066 6167 y Fl(\026)1189 6122 y Fp(\()p Fn(q)7 b Fp(\))64 b Fq(ar)-9 b(e)64 b(non)i(incr)-9 b(e)g(asing)63 b(functions)i(of)f Fn(q)58 b Fm(2)50 b Fp(\()p Fm(\0001)p Fn(;)30 b Fp(1\))p Fq(.)-201 6348 y(ii\))65 b(F)-14 b(or)65 b(al)9 b(l)64 b Fn(q)57 b Fm(2)51 b Fp(\()p Fm(\0001)p Fn(;)30 b Fp(1\))p Fq(,)63 b Fn(D)1873 6282 y Fk(\000)1868 6392 y Fl(\026)1990 6348 y Fp(\()p Fn(q)7 b Fp(\))50 b Fm(\025)g Fp(dim)2766 6376 y Fg(H)2879 6348 y Fp(\()p Fn(\026)p Fp(\))64 b Fq(.)-201 6573 y(iii\))h(F)-14 b(or)64 b(al)9 b(l)64 b Fn(q)58 b Fm(2)50 b Fp(\()p Fm(\0001)p Fn(;)30 b Fp(1\))p Fq(,)64 b Fn(D)1929 6507 y Fg(+)1924 6618 y Fl(\026)2046 6573 y Fp(\()p Fn(q)7 b Fp(\))50 b Fm(\025)g Fp(dim)2822 6601 y Fg(P)2925 6573 y Fp(\()p Fn(\026)p Fp(\))p Fq(.)-201 6799 y(iv\))65 b(If)g Fn(\026)g Fq(has)g(a)g(b)-9 b(ounde)g(d)63 b(supp)-9 b(ort,)64 b(then)i(for)e(al)9 b(l)64 b Fn(q)57 b Fm(2)51 b Fp(\(0)p Fn(;)30 b Fp(1\))p Fq(,)64 b Fp(0)50 b Fm(\024)g Fn(D)4597 6733 y Fk(\000)4592 6844 y Fl(\026)4715 6799 y Fp(\()p Fn(q)7 b Fp(\))50 b Fm(\024)f Fn(D)5342 6733 y Fg(+)5337 6844 y Fl(\026)5460 6799 y Fp(\()p Fn(q)7 b Fp(\))50 b Fm(\024)g Fp(1)-201 7150 y Fe(Pro)6 b(of)69 b(of)g(Prop)6 b(osition)68 b(2.1.)-201 7376 y Fp(Statemen)-5 b(t)64 b(i\))j(is)g(already)g(kno)-5 b(wn)67 b(\(see)f Fq(e.g.)98 b Fp([8)o(]\).)g(This)67 b(a)g(straigh)-5 b(tforw)g(ard)67 b(consequence)e(of)h(conca)-5 b(v)g(e)-201 7602 y(and)67 b(con)-5 b(v)g(ex)66 b(Jensen)g(inequalities.)100 b(F)-15 b(or)66 b(the)h(pro)5 b(of)66 b(of)g(ii\),)j(iii\))f(see)e(App)5 b(endix)68 b(A.)e(The)h(statemen)-5 b(t)64 b(iv\))-201 7828 y(follo)-5 b(ws)52 b(from)e(Corollary)j(C.1.)77 b(Note)52 b(that)f(iv\))h(do)5 b(es)51 b(not)h(necessarily)f(hold)h(an) -5 b(y)52 b(more)e(if)i(one)f(lets)h Fn(q)58 b Fp(v)-10 b(ary)-201 8054 y(in)61 b(\()p Fm(\0001)p Fn(;)30 b Fp(1\))59 b(-)i(See)f(App)5 b(endix)61 b(D.)4852 b Fc(\003)81 8369 y Fp(F)-15 b(rom)46 b(no)-5 b(w)48 b(on,)i(eac)-5 b(h)48 b(time)e(w)-5 b(e)48 b(will)h(refer)f(to)f(the)h(exp)5 b(onen)-5 b(t)47 b Fn(\014)57 b Fp(it)48 b(should)g(b)5 b(e)48 b(understo)5 b(o)g(d)47 b(that)g Fn(\014)60 b Fp(=)50 b Fn(p)-201 8595 y Fp(if)59 b Fm(H)h Fp(is)f(a)g(general)g (separable)f(Hilb)5 b(ert)60 b(space)e(with)h(basis)g Fm(f)p Fn(e)4073 8622 y Fl(n)4166 8595 y Fm(g)4257 8624 y Fl(n)p Fk(2)p Fj(N)4541 8595 y Fp(,)g(and)f Fn(\014)i Fp(=)50 b Fn(p=d)58 b Fp(in)h(the)g(sp)5 b(eci\014c)58 b(case)-201 8821 y Fm(H)52 b Fp(=)e Fn(`)273 8755 y Fg(2)352 8821 y Fp(\()p Ff(Z)534 8755 y Fl(d)624 8821 y Fp(\))61 b(equipp)5 b(ed)61 b(with)g(its)f(canonical)h(basis)g Fm(f)p Fn(\016)3618 8848 y Fl(n)3711 8821 y Fm(g)3802 8865 y Fl(n)p Fk(2)p Fj(Z)4069 8828 y Fh(d)4151 8821 y Fp(.)81 9137 y(Our)g(main)e(result)i(is)g(the)f(follo)-5 b(wing)61 b(one:)-201 9578 y Fe(Theorem)68 b(2.1.)90 b Fq(L)-9 b(et)64 b Fn(H)79 b Fq(b)-9 b(e)63 b(a)h(self-adjoint)f(op)-9 b(er)g(ator)63 b(on)h(a)g(sep)-9 b(ar)g(able)62 b(Hilb)-9 b(ert)62 b(sp)-9 b(ac)g(e)63 b Fm(H)r Fq(,)h(and)g(let)f Fn( )70 b Fq(b)-9 b(e)-201 9804 y(a)65 b(ve)-9 b(ctor)64 b(in)h Fm(H)r Fq(,)f Fm(k)p Fn( )7 b Fm(k)1301 9832 y Fk(H)1479 9804 y Fp(=)50 b(1)p Fq(.)83 b(Assume)65 b(that)h(the)f(sp)-9 b(e)g(ctr)g(al)63 b(me)-9 b(asur)g(e)63 b Fn(\026)4716 9834 y Fl( )4886 9804 y Fq(asso)-9 b(ciate)g(d)64 b(to)h Fn( )71 b Fq(is)65 b(such)g(that)1953 10183 y Fp(\(H\))130 b Fn(D)2517 10108 y Fk(\006)2512 10228 y Fl(\026)2597 10251 y Fh( )2698 10183 y Fp(\()p Fn(s)p Fp(\))50 b Fn(<)g Fp(+)p Fm(1)129 b Fp(for)65 b(an)-5 b(y)68 b Fn(s)50 b Fm(2)h Fp(\(0)p Fn(;)30 b Fp(1\))p Fn(:)-201 10563 y Fq(Then)65 b(for)f Fm(hhj)p Fn(X)14 b Fm(j)972 10497 y Fl(p)1050 10563 y Fm(ii)1192 10593 y Fl( )5 b(;T)1503 10563 y Fq(de\014ne)-9 b(d)64 b(by)h(\(1.1\))g(and)g(with)g Fn(\014)75 b Fq(as)65 b(describ)-9 b(e)g(d)62 b(just)k(ab)-9 b(ove,)63 b(the)i(fol)9 b(lowing)63 b(holds:)1874 11052 y Fp(lim)30 b(inf)1934 11173 y Fl(T)20 b Fk(!1)2429 10925 y Fp(log)r Fm(hhj)p Fn(X)14 b Fm(j)3072 10860 y Fl(p)3150 10925 y Fm(ii)3292 10955 y Fl( )5 b(;T)p 2429 11010 1110 8 v 2785 11177 a Fp(log)33 b Fn(T)3608 11052 y Fm(\025)50 b Fn(\014)10 b(D)4069 10977 y Fk(\000)4064 11097 y Fl(\026)4149 11120 y Fh( )4280 10795 y Fi(\022)4601 10929 y Fp(1)p 4434 11010 426 8 v 4434 11177 a(1)40 b(+)g Fn(\014)4879 10795 y Fi(\023)5044 11052 y Fn(;)3439 11631 y Fp(6)p eop %%Page: 7 7 7 6 bop -201 1158 a Fq(and)1848 1439 y Fp(lim)30 b(sup)1934 1595 y Fl(T)20 b Fk(!1)2455 1312 y Fp(log)s Fm(hhj)p Fn(X)14 b Fm(j)3099 1246 y Fl(p)3176 1312 y Fm(ii)3318 1342 y Fl( )5 b(;T)p 2455 1397 1110 8 v 2811 1563 a Fp(log)33 b Fn(T)3635 1439 y Fm(\025)49 b Fn(\014)10 b(D)4095 1364 y Fg(+)4090 1484 y Fl(\026)4175 1507 y Fh( )4306 1182 y Fi(\022)4628 1316 y Fp(1)p 4460 1397 426 8 v 4460 1563 a(1)41 b(+)e Fn(\014)4906 1182 y Fi(\023)5070 1439 y Fn(:)-201 1906 y Fe(Remark)69 b(2.3.)-201 2131 y Fp(i\))85 b(As)f(a)g(consequence)f(of)h(i\)-iii\))i(of)d(Prop)5 b(osition)85 b(2.1,)k(this)84 b(result)h(do)5 b(es)84 b(impro)-5 b(v)g(e)83 b(previous)h(kno)-5 b(wn)-201 2357 y(b)5 b(ounds)61 b(of)f([25)o(],)g([1)o(],[15)n(].)-201 2583 y(ii\))55 b(As)e(w)-5 b(e)54 b(sho)-5 b(w)54 b(in)g(App)5 b(endix)54 b(D,)f(Theorem)f(D.1,)i(for)g(an)-5 b(y)53 b Fn(\014)60 b Fp(=)50 b Fn(p=d)g(>)f Fp(0)54 b(and)g(an)-5 b(y)53 b Fn(\016)k(>)50 b Fp(0)k(there)f(exist)g(a)-201 2809 y(b)5 b(ounded)61 b(self-adjoin)-5 b(t)60 b(op)5 b(erator)61 b Fn(H)76 b Fp(and)61 b(a)f(v)-5 b(ector)61 b Fn( )67 b Fp(suc)-5 b(h)60 b(that)h(lim)4734 2837 y Fl(T)20 b Fk(!1)5157 2809 y Fp(log)s Fm(hhj)p Fn(X)14 b Fm(j)5801 2743 y Fl(p)5878 2809 y Fm(ii)6020 2839 y Fl( )5 b(;T)6266 2809 y Fn(=)30 b Fp(log)k Fn(T)76 b Fp(=)51 b(0,)-201 3090 y(but)72 b(at)g(the)g(same)e(time)h Fn(D)1752 3024 y Fk(\006)1747 3135 y Fl(\026)1832 3158 y Fh( )1964 2888 y Fi(\020)2190 3018 y Fg(1)p 2092 3048 267 8 v 2092 3153 a(1+)p Fl(\014)2419 3090 y Fm(\000)40 b Fn(\016)2689 2888 y Fi(\021)2867 3090 y Fn(>)69 b Fp(0.)116 b(Therefore,)74 b(one)e(cannot)g(hop)5 b(e)72 b(to)g(obtain)g(a)g (general)-201 3361 y(\()p Fq(i.e.)83 b Fp(without)62 b(additional)g(assumptions)e(on)h Fn(\026)3140 3391 y Fl( )3307 3361 y Fp(or)h(on)f(generalized)h(eigenfunctions\))f(lo)-5 b(w)g(er)62 b(b)5 b(ound)62 b(of)-201 3587 y(the)e(form)f Fn(\014)10 b(D)811 3521 y Fk(\006)806 3632 y Fl(\026)891 3655 y Fh( )992 3587 y Fp(\()p Fn(q)d Fp(\()p Fn(\014)j Fp(\)\))58 b(with)k(some)c Fn(q)7 b Fp(\()p Fn(\014)j Fp(\))49 b Fn(<)3107 3515 y Fg(1)p 3009 3545 V 3009 3650 a(1+)p Fl(\014)3295 3587 y Fp(,)60 b Fq(e.g.)80 b Fp(lik)-5 b(e)61 b Fn(D)4255 3521 y Fk(\006)4250 3632 y Fl(\026)4335 3655 y Fh( )4437 3587 y Fp(\(1)40 b Fm(\000)f Fn(\014)10 b Fp(\).)-201 3962 y Fe(Pro)c(of)69 b(of)g(Theorem)f(2.1.)-201 4188 y Fp(The)79 b(pro)5 b(of)79 b(of)f(Theorem)g(2.1)g(is)h(the)g(com) -5 b(bination)78 b(of)g(Theorem)g(3.1)g(and)h(Theorem)e(4.2)i(whic)-5 b(h)79 b(are)-201 4414 y(pro)-5 b(v)g(ed)61 b(resp)5 b(ectiv)-5 b(ely)60 b(in)h(Sections)f(3)h(and)f(4.)4079 b Fc(\003)81 4739 y Fp(W)-15 b(e)71 b(no)-5 b(w)72 b(discuss)f(a)h(mo)5 b(del)70 b(of)h(Jacobi)g(matrices,)h(the)f(Julia)h(matrices.)111 b(In)71 b(this)g(case,)i(the)e(upp)5 b(er)-201 4965 y(b)g(ound)70 b(deriv)-5 b(ed)70 b(in)h([4)o(])f(together)f(with)h(Theorem)e(2.1)i (ab)5 b(o)-5 b(v)g(e)69 b(enable)h(one)g(to)f(pro)-5 b(v)g(e)70 b(for)g(small)f Fn(p)g Fp(that)-201 5191 y(the)58 b(increasing)i(exp)5 b(onen)-5 b(ts)57 b(of)i(the)f(momen)-5 b(ts)55 b(of)j(order)h Fn(p)f Fp(are)h(en)-5 b(tirely)59 b(con)-5 b(trolled)59 b(b)-5 b(y)59 b(the)f(generalized)-201 5417 y(fractal)i(dimensions.)-201 5742 y Fe(Julia)i(matrices:)77 b Fp(There)54 b(exists)f(a)h(class)g(of)f(mo)5 b(dels)53 b(for)g(whic)-5 b(h)55 b(non)f(trivial)h(\(i.e.)e(non)h(ballistic\))h (upp)5 b(er)-201 5968 y(b)g(ounds)54 b(for)g(the)f(momen)-5 b(ts)51 b(of)i(order)i Fn(p)e Fp(are)h(deriv)-5 b(ed)55 b(in)f(terms)e(of)i(generalized)g(fractal)g(dimensions:)76 b(the)-201 6194 y(Julia)66 b(matrices.)95 b(They)66 b(are)g (constructed)e(b)-5 b(y)66 b(considering)g(p)5 b(olynomials,)66 b(disjoin)-5 b(t)66 b(Iterated)f(F)-15 b(unction)-201 6420 y(Systems)74 b(\(IFS\),)g(giving)j(rise)f(to)g(a)g(real)g(h)-5 b(yp)5 b(erb)g(olic)77 b(Julia)f(set)g Fn(J)93 b Fp(\(see)75 b Fq(e.g.)126 b Fp([4)o(])76 b([16)o(])g(and)g(references)-201 6646 y(therein)61 b(for)f(details\).)81 6871 y(Giv)-5 b(en)64 b(suc)-5 b(h)64 b(an)g(IFS,)f(one)h(considers)f(the)h(balanced) g(measure)e Fn(\026)i Fp(of)f(maximal)f(en)-5 b(trop)g(y)64 b(on)g Fn(J)17 b Fp(,)64 b(and)-201 7097 y(then)g(constructs)f(an)h (Hamiltonian)g Fn(H)79 b Fp(\()p Fn(H)f Fp(corresp)5 b(onds)64 b(to)g(the)f(Jacobi)h(matrix)f(asso)5 b(ciated)63 b(to)h Fn(\026)p Fp(\))f(on)-201 7323 y Fn(`)-125 7257 y Fg(2)-46 7323 y Fp(\()p Ff(N)30 b Fp(\))69 b(as)60 b(follo)-5 b(ws.)81 7549 y(Let)68 b Fn(P)532 7576 y Fl(n)626 7549 y Fp(,)i Fn(n)64 b Fm(\025)f Fp(0,)70 b(denote)e(the)g(orthogonal) g(and)h(normalized)f(p)5 b(olynomials)68 b(asso)5 b(ciated)67 b(to)h Fn(\026)p Fp(.)104 b(The)-201 7775 y(family)48 b(\()p Fn(P)531 7802 y Fl(n)624 7775 y Fp(\))695 7804 y Fl(n)p Fk(2)p Fj(N)1027 7775 y Fp(forms)e(a)j(Hilb)5 b(ert)49 b(basis)g(in)g(L)3019 7709 y Fg(2)3097 7775 y Fp(\()p Ff(R)26 b Fn(;)k(\026)p Fp(\))57 b(and)48 b(satis\014es)g(a)g (three)g(terms)f(recurrence)h(relation)-201 8000 y Fn(E)10 b(P)60 8027 y Fl(n)155 8000 y Fp(\()p Fn(E)g Fp(\))50 b(=)g Fn(t)749 8027 y Fl(n)p Fg(+1)1023 8000 y Fn(P)1140 8027 y Fl(n)p Fg(+1)1414 8000 y Fp(\()p Fn(E)10 b Fp(\))17 b(+)g Fn(v)1964 8027 y Fl(n)2058 8000 y Fn(P)2175 8027 y Fl(n)2269 8000 y Fp(\()p Fn(E)10 b Fp(\))17 b(+)g Fn(t)2797 8027 y Fl(n)2890 8000 y Fn(P)3007 8027 y Fl(n)p Fk(\000)p Fg(1)3281 8000 y Fp(\()p Fn(E)10 b Fp(\),)51 b Fn(n)f Fm(\025)g Fp(0,)h(where)e Fn(v)4815 8027 y Fl(n)4960 8000 y Fm(2)i Ff(R)84 b Fp(and)49 b Fn(t)5720 8027 y Fl(n)5864 8000 y Fm(\025)h Fp(0)f(are)f(b)5 b(ounded)-201 8226 y(sequences,)69 b(and)f Fn(P)1163 8253 y Fk(\000)p Fg(1)1415 8226 y Fp(=)63 b(0.)104 b(Therefore)68 b(the)g(isomorphism)e (of)i(L)4419 8160 y Fg(2)4498 8226 y Fp(\()p Ff(R)26 b Fn(;)k(\026)p Fp(\))76 b(on)-5 b(to)68 b Fn(`)5522 8160 y Fg(2)5601 8226 y Fp(\()p Ff(N)30 b Fp(\))77 b(asso)5 b(ciated)68 b(with)-201 8452 y(the)58 b(basis)h(\()p Fn(P)743 8479 y Fl(n)836 8452 y Fp(\))907 8481 y Fl(n)p Fk(2)p Fj(N)1250 8452 y Fp(carries)g(the)f(op)5 b(erator)58 b(of)g(m)-5 b(ultiplication)59 b(b)-5 b(y)59 b Fn(E)69 b Fp(in)59 b(L)5016 8386 y Fg(2)5095 8452 y Fp(\()p Ff(R)26 b Fn(;)k(\026)p Fp(\))67 b(in)-5 b(to)58 b(the)h(self-adjoin)-5 b(t)-201 8678 y(\014nite)61 b(di\013erence)f(op)5 b(erator)61 b Fn(H)75 b Fp(de\014ned)61 b(on)f Fn(`)2992 8612 y Fg(2)3071 8678 y Fp(\()p Ff(N)30 b Fp(\))69 b(b)-5 b(y)1187 9192 y Fn(H)15 b( )7 b Fp(\()p Fn(n)p Fp(\))49 b(=)1971 8935 y Fi(\032)2191 9078 y Fn(t)2257 9105 y Fl(n)p Fg(+1)2531 9078 y Fn( )7 b Fp(\()p Fn(n)39 b Fp(+)h(1\))g(+)g Fn(t)3508 9105 y Fl(n)3601 9078 y Fn( )7 b Fp(\()p Fn(n)39 b Fm(\000)h Fp(1\))g(+)g Fn(v)4600 9105 y Fl(n)4694 9078 y Fn( )7 b Fp(\()p Fn(n)p Fp(\))165 b Fn(n)50 b Fm(\025)g Fp(1)2191 9304 y Fn(t)2257 9331 y Fg(1)2335 9304 y Fn( )7 b Fp(\(1\))39 b(+)h Fn(v)3003 9331 y Fg(0)3082 9304 y Fn( )7 b Fp(\(0\))1795 b Fn(n)50 b Fp(=)g(0)6796 9192 y(\(2.3\))81 9623 y(Then)63 b Fn(\026)f Fp(is)h(the)f(sp)5 b(ectral)62 b(measure)f(of)h Fn(H)77 b Fp(asso)5 b(ciated)62 b(to)g(the)g(state)f Fn(\016)4998 9650 y Fg(0)5139 9623 y Fp(lo)5 b(cated)62 b(at)h(the)f(origin.)87 b(F)-15 b(or)-201 9849 y(this)44 b(mo)5 b(del,)46 b(the)e(upp)5 b(er)44 b(and)g(lo)-5 b(w)g(er)45 b(fractal)e(dimensions)g Fn(D)3937 9783 y Fk(\006)3932 9894 y Fl(\026)4055 9849 y Fp(\()p Fn(q)7 b Fp(\))43 b(are)h(equal)h(\(:=)p Fn(D)5494 9876 y Fl(\026)5585 9849 y Fp(\()p Fn(q)7 b Fp(\)\),)46 b(and)e(con)-5 b(tin)g(uous)-201 10074 y(for)55 b Fn(q)i Fm(2)51 b Fp(\(0)p Fn(;)30 b Fp(1\);)55 b(furthermore,)f(w)-5 b(e)55 b(ha)-5 b(v)g(e)55 b Fn(D)2773 10101 y Fl(\026)2866 10074 y Fp(\(1)p Fn(=)p Fp(\(1)29 b(+)g Fn(p)p Fp(\)\))49 b(=)g Fn(D)4106 10101 y Fl(\026)4199 10074 y Fp(\(1)29 b Fm(\000)g Fn(p)p Fp(\))g(+)g Fm(O)5 b Fp(\()p Fn(p)5237 10008 y Fg(2)5314 10074 y Fp(\))55 b(\(see)f([4])g(and)i(references)-201 10300 y(therein\).)81 10526 y(It)k(is)h(established)g(in)g([4)o(])f(that)g (there)g(exists)g(a)h(critical)g(v)-10 b(alue)61 b Fn(p)4538 10553 y Fl(c)4658 10526 y Fm(\025)49 b Fp(2)61 b(suc)-5 b(h)60 b(that)g(for)g(all)i Fn(p)50 b Fm(2)h Fp(\(0)p Fn(;)30 b(p)6985 10553 y Fl(c)7053 10526 y Fp(\))2528 10934 y Fn(\013)2645 10859 y Fg(+)2763 10934 y Fp(\()p Fn(\016)2915 10961 y Fg(0)2994 10934 y Fn(;)g(p;)g Fp(1\))49 b Fm(\024)h Fn(D)3802 10961 y Fl(\026)3894 10934 y Fp(\(1)40 b Fm(\000)g Fn(p)p Fp(\))3439 11631 y(7)p eop %%Page: 8 8 8 7 bop 81 1158 a Fp(Therefore,)60 b(putting)g(together)g(Theorem)f (2.1)h(and)g(Theorem)f(1)i(of)e([4],)g(w)-5 b(e)61 b(get,)e(for)h(the)g (exp)5 b(onen)-5 b(ts)-201 1384 y(of)60 b(an)-5 b(y)61 b(momen)-5 b(ts)56 b(of)61 b(order)f Fn(p)50 b Fm(2)h Fp(\(0)p Fn(;)30 b(p)2455 1411 y Fl(c)2523 1384 y Fp(\))61 b(and)f(for)g(the)h(initial)h(state)d Fn(\016)4651 1411 y Fg(0)4730 1384 y Fp(,)h(that)1858 1855 y Fn(D)2009 1882 y Fl(\026)2132 1599 y Fi(\022)2443 1732 y Fp(1)p 2286 1813 405 8 v 2286 1980 a(1)40 b(+)g Fn(p)2711 1599 y Fi(\023)2895 1855 y Fm(\024)50 b Fn(\013)3204 1780 y Fk(\006)3322 1855 y Fp(\()p Fn(\016)3474 1882 y Fg(0)3552 1855 y Fn(;)30 b(p;)g Fp(1\))49 b Fm(\024)h Fn(D)4360 1882 y Fl(\026)4453 1855 y Fp(\(1)40 b Fm(\000)g Fn(p)p Fp(\))60 b Fn(:)-201 2315 y Fp(and)h(th)-5 b(us)60 b(for)g(small)g Fn(p)50 b(>)g Fp(0,)1615 2686 y Fn(D)1766 2713 y Fl(\026)1858 2686 y Fp(\(1)40 b Fm(\000)g Fn(p)p Fp(\))g(+)g Fm(O)5 b Fp(\()p Fn(p)2940 2611 y Fg(2)3017 2686 y Fp(\))51 b Fm(\024)f Fn(\013)3448 2611 y Fk(\006)3566 2686 y Fp(\()p Fn(\016)3718 2713 y Fg(0)3796 2686 y Fn(;)30 b(p;)g Fp(1\))49 b Fm(\024)h Fn(D)4604 2713 y Fl(\026)4697 2686 y Fp(\(1)40 b Fm(\000)g Fn(p)p Fp(\))59 b Fn(:)-201 3057 y Fp(This)k(is)f(the)g (\014rst)g(mo)5 b(del)61 b(of)h(Sc)-5 b(hr\177)-91 b(odinger-lik)-5 b(e)63 b(op)5 b(erator)62 b(treated)f(rigorously)i(for)f(whic)-5 b(h)63 b(suc)-5 b(h)62 b(b)5 b(ounds)-201 3283 y(are)61 b(deriv)-5 b(ed.)81 3509 y(If)67 b Fn(D)421 3536 y Fl(\026)514 3509 y Fp(\()p Fn(q)7 b Fp(\))66 b(w)-5 b(ould)68 b(b)5 b(e)68 b(kno)-5 b(wn)67 b(to)g(b)5 b(e)68 b(strictly)f(decreasing)g(in) h(some)d(in)-5 b(terv)-10 b(al)68 b(\(0)p Fn(;)30 b(\016)7 b Fp(\),)68 b(one)f(w)-5 b(ould)68 b(get)-201 3734 y(in)-5 b(termittency)47 b(for)h Fm(hhj)p Fn(X)14 b Fm(j)1594 3668 y Fl(p)1672 3734 y Fm(ii)1814 3764 y Fl( )1919 3734 y Fp(\()p Fn(T)25 b Fp(\),)50 b(with)f(small)f Fn(p)p Fp(.)76 b(Ho)-5 b(w)g(ev)g(er,)50 b(to)f(our)f(b)5 b(est)48 b(kno)-5 b(wledge,)51 b(this)e(fact)e(is)i(only)-201 3960 y(emphasized)j(b)-5 b(y)53 b(n)-5 b(umerics)52 b(on)h(the)g (generalized)h(fractal)f(dimension)f(\(see)g Fq(e.g.)77 b Fp([26]\),)53 b(and)h(no)f(rigourous)-201 4186 y(results)60 b(are)h(pro)-5 b(vided.)7028 4412 y Fc(\003)-201 5066 y Fo(3)270 b(A)89 b(general)h(lo)-7 b(w)g(er)89 b(b)7 b(ound)-201 5472 y Fp(This)51 b(section)g(can)f(b)5 b(e)51 b(regarded)f(as)g(the)h(\014rst)f(part)h(of)f(the)g(pro)5 b(of)50 b(of)g(our)h(main)f(result)h(Theorem)e(2.1.)76 b(Let)-201 5697 y Fn(H)71 b Fp(b)5 b(e)56 b(a)h(self-adjoin)-5 b(t)55 b(op)5 b(erator)55 b(in)i(Hilb)5 b(ert)58 b(space)d Fm(H)r Fp(,)h(and)g Fm(f)p Fn(e)4171 5724 y Fl(n)4265 5697 y Fm(g)g Fp(an)g(orthonormal)f(basis)h(in)h Fm(H)g Fp(lab)5 b(elled)-201 5923 y(b)-5 b(y)63 b Fn(n)56 b Fm(2)f Ff(N)103 b Fp(or)63 b(b)-5 b(y)63 b Fn(n)55 b Fm(2)h Ff(Z)1523 5857 y Fl(d)1613 5923 y Fp(.)88 b(Let)63 b Fn( )69 b Fp(b)5 b(e)63 b(some)f(v)-5 b(ector)62 b(in)i Fm(H)h Fp(suc)-5 b(h)63 b(that)f Fm(k)p Fn( )7 b Fm(k)54 b Fp(=)h(1.)88 b(W)-15 b(e)63 b(are)g(in)-5 b(terested)63 b(in)-201 6149 y(lo)-5 b(w)g(er)60 b(b)5 b(ounds)59 b(for)h(the)f (momen)-5 b(ts)55 b(of)k(the)g(abstract)g(p)5 b(osition)59 b(op)5 b(erator)59 b(asso)5 b(ciated)59 b(to)g(the)g(basis)g Fm(f)p Fn(e)6934 6176 y Fl(n)7028 6149 y Fm(g)p Fp(,)-201 6375 y(de\014ned)h(as)2193 6601 y Fm(j)p Fn(X)14 b Fm(j)2460 6512 y Fl(p)2460 6659 y( )2564 6601 y Fp(\()p Fn(t)p Fp(\))49 b(=)3013 6428 y Fi(X)3102 6810 y Fl(n)3306 6601 y Fm(j)p Fn(n)p Fm(j)3517 6526 y Fl(p)3596 6601 y Fm(jh)p Fp(e)3799 6526 y Fk(\000)p Fl(itH)4141 6601 y Fn( )7 b(;)30 b(e)4433 6628 y Fl(n)4525 6601 y Fm(ij)4647 6526 y Fg(2)4725 6601 y Fn(:)2020 b Fp(\(3.1\))-201 7092 y(In)78 b(particular,)k(if)c Fm(H)j Fp(=)e Fn(`)1671 7026 y Fg(2)1750 7092 y Fp(\()p Ff(Z)1932 7026 y Fl(d)2022 7092 y Fp(\),)j(one)c(can)f (tak)-5 b(e)78 b(the)f(canonical)h(basis)g Fn(e)5033 7119 y Fl(n)5127 7092 y Fp(\()p Fn(k)6 b Fp(\))78 b(=)h Fn(\016)5750 7122 y Fl(nk)5921 7092 y Fn(;)185 b(n;)30 b(k)85 b Fm(2)80 b Ff(Z)6840 7026 y Fl(d)7008 7092 y Fp(to)-201 7318 y(obtain)66 b(the)e(momen)-5 b(ts)62 b(of)i(the)h(usual)h(p)5 b(osition)65 b(op)5 b(erator.)94 b(Our)65 b(results)g(can)g(also)g(b)5 b(e)66 b(extended)e(to)h(the)-201 7544 y(case)60 b Fm(H)52 b Fp(=)e(L)696 7478 y Fg(2)774 7544 y Fp(\()p Ff(R)967 7478 y Fl(d)1057 7544 y Fp(\))61 b([3)o(])f(and)1326 7998 y Fm(j)p Fn(X)14 b Fm(j)1593 7910 y Fl(p)1593 8057 y( )1697 7998 y Fp(\()p Fn(t)p Fp(\))50 b(=)2147 7751 y Fi(Z)2248 8163 y Fj(R)2335 8125 y Fh(d)2455 7998 y Fm(j)p Fn(x)p Fm(j)2661 7923 y Fl(p)2739 7998 y Fm(j)p Fn( )7 b Fp(\()p Fn(t;)30 b(x)p Fp(\))p Fm(j)3360 7923 y Fg(2)3436 7998 y Fn(dx;)211 b( )7 b Fp(\()p Fn(t;)30 b(x)p Fp(\))48 b(=)i(\(e)4808 7923 y Fk(\000)p Fl(itH)5151 7998 y Fn( )7 b Fp(\)\()p Fn(x)p Fp(\))p Fn(:)-201 8461 y Fp(It)73 b(can)g(b)5 b(e)73 b(done)g(using)g(the)g(Theorem)f(3.2)h(in)g(the)g(same)e(manner)h(as)h (in)h([5)o(])f(\(see)f(Corollary)j(2.4)d(and)-201 8687 y(Theorem)53 b(2.5)h(of)h([5)o(],)g(see)f(also)h([25)o(]\).)77 b(Ho)-5 b(w)g(ev)g(er,)56 b(for)e(the)g(sak)-5 b(e)54 b(of)h(simplicit)-5 b(y)-15 b(,)54 b(w)-5 b(e)55 b(shall)h(consider)e (in)h(this)-201 8912 y(pap)5 b(er)61 b(only)g Fm(j)p Fn(X)14 b Fm(j)976 8846 y Fl(p)1115 8912 y Fp(giv)-5 b(en)60 b(b)-5 b(y)61 b(\(3.1\).)81 9138 y(W)-15 b(e)67 b(deriv)-5 b(e)67 b(a)f(lo)-5 b(w)g(er)68 b(b)5 b(ound)67 b(for)f(the)g(time)g(a)-5 b(v)g(eraged)66 b(momen)-5 b(ts)63 b(of)j(p)5 b(osition)67 b(op)5 b(erator)67 b(in)g(term)e(of) -201 9364 y(an)c(abstract)e(quan)-5 b(tit)g(y)61 b(in)g(the)f(spirit)h (of)f([5],)f(namely)268 9852 y Fn(L)392 9882 y Fl( )497 9852 y Fp(\()p Fn(T)25 b Fp(\))50 b(=)g(sup)30 b Fm(f)p Fn(L)1531 9882 y Fl( )1636 9852 y Fp(\()p Fn(';)g(T)25 b Fp(\))p Fn(;)90 b(')51 b Fm(2)f(H)2745 9882 y Fl( )2850 9852 y Fn(;)151 b Fm(h)p Fn( )7 b(;)30 b(')p Fm(i)49 b(6)p Fp(=)h(0)p Fm(g)30 b Fn(;)212 b(L)4360 9882 y Fl( )4465 9852 y Fp(\()p Fn(';)30 b(T)25 b Fp(\))50 b(=)5297 9729 y Fm(jh)p Fn(';)30 b( )7 b Fm(ij)5867 9663 y Fg(2+2)p Fl(\014)p 5200 9810 1108 8 v 5200 9977 a Fm(k)p Fn(')p Fm(k)5501 9925 y Fg(2)5579 9977 y Fn(U)5703 10007 y Fl('; )5940 9977 y Fp(\()p Fn(T)25 b Fp(\))6213 9925 y Fl(\014)6796 9852 y Fp(\(3.2\))-201 10320 y(where)74 b Fm(H)492 10350 y Fl( )671 10320 y Fp(is)g(the)f(cyclic)h(subspace)f(spanned)h(b)-5 b(y)73 b Fn( )80 b Fp(and)74 b Fn(H)15 b Fp(.)120 b(The)74 b(exp)5 b(onen)-5 b(t)73 b Fn(\014)82 b Fp(=)72 b Fn(p)h Fp(if)h Fn(n)e Fm(2)h Ff(N)113 b Fp(and)-201 10546 y Fn(\014)60 b Fp(=)50 b Fn(p=d)j Fp(if)h Fn(n)d Fm(2)g Ff(Z)1089 10480 y Fl(d)1179 10546 y Fp(.)78 b(Notice)54 b(that)f(if)h Fn(')d Fp(=)f Fn(\037)2895 10574 y Fg(\012)3005 10546 y Fp(\()p Fn(H)15 b Fp(\))p Fn( )7 b Fp(,)53 b(where)h(\012)g(is) h(a)e(Borel)i(set,)f(then)f Fn(L)5905 10576 y Fl( )6010 10546 y Fp(\()p Fn(';)30 b(T)25 b Fp(\))54 b(reads)g(as)2603 11044 y Fn(L)2727 11074 y Fl( )2832 11044 y Fp(\()p Fn(';)30 b(T)25 b Fp(\))50 b(=)3608 10921 y Fm(k)p Fn(')p Fm(k)3909 10855 y Fg(2+4)p Fl(\014)p 3567 11003 728 8 v 3567 11169 a Fn(U)3691 11199 y Fl('; )3928 11169 y Fp(\()p Fn(T)25 b Fp(\))4201 11117 y Fl(\014)4315 11044 y Fn(:)2430 b Fp(\(3.3\))3439 11631 y(8)p eop %%Page: 9 9 9 8 bop -201 1158 a Fp(The)61 b(quan)-5 b(tit)g(y)60 b Fn(U)1024 1188 y Fl('; )1261 1158 y Fp(\()p Fn(T)25 b Fp(\))60 b(is)h(de\014ned)f(as)h(follo)-5 b(ws.)1743 1661 y Fn(U)1867 1691 y Fl('; )2104 1661 y Fp(\()p Fn(T)25 b Fp(\))50 b(=)2619 1413 y Fi(Z)2720 1825 y Fj(R)2855 1413 y Fi(Z)2956 1825 y Fj(R)3090 1661 y Fp(d)p Fn(\026)3301 1688 y Fl(')3401 1661 y Fp(\()p Fn(x)p Fp(\)d)p Fn(\026)3858 1691 y Fl( )3962 1661 y Fp(\()p Fn(y)7 b Fp(\))p Fn(R)q Fp(\(\()p Fn(x)39 b Fm(\000)h Fn(y)7 b Fp(\))p Fn(T)25 b Fp(\))p Fn(;)1570 b Fp(\(3.4\))-201 2161 y(where)56 b Fn(R)q Fp(\()p Fn(w)5 b Fp(\))56 b(is)h(a)e(b)5 b(ounded)56 b(and)g(fast)f(deca)-5 b(ying)56 b(function)g(de\014ned)f(in)i(\(3.5\)) d(b)5 b(elo)-5 b(w.)80 b(In)55 b(the)h(sequel,)g(w)-5 b(e)-201 2387 y(shall)61 b(note)g(\()p Fn(")f Fp(pla)-5 b(ying)61 b(the)f(role)h(of)f(1)p Fn(=T)25 b Fp(\),)2066 2895 y Fn(b)2144 2820 y Fg(\()p Fl(R)q Fg(\))2369 2895 y Fp(\()p Fn(x;)30 b(")p Fp(\))50 b(:=)3073 2648 y Fi(Z)3174 3060 y Fj(R)3309 2895 y Fp(d)p Fn(\026)3520 2925 y Fl( )3625 2895 y Fp(\()p Fn(y)7 b Fp(\))p Fn(R)4032 2639 y Fi(\022)4185 2772 y Fn(x)41 b Fm(\000)e Fn(y)p 4185 2853 422 8 v 4354 3020 a(")4627 2639 y Fi(\023)4852 2895 y Fn(:)-201 3433 y Fp(So)82 b(that)e Fn(U)611 3463 y Fl('; )848 3433 y Fp(\()p Fn(T)25 b Fp(\))85 b(=)1433 3286 y Fi(R)1519 3497 y Fj(R)1654 3433 y Fp(d)p Fn(\026)1865 3460 y Fl(')1964 3433 y Fp(\()p Fn(x)p Fp(\))p Fn(b)2288 3367 y Fg(\()p Fl(R)q Fg(\))2513 3433 y Fp(\()p Fn(x;)30 b Fp(1)p Fn(=T)25 b Fp(\).)142 b(The)82 b(quan)-5 b(tit)g(y)81 b Fn(U)4613 3463 y Fl('; )4850 3433 y Fp(\()p Fn(T)25 b Fp(\))81 b(is)h(crucial)g(since)g(one)f(ma)-5 b(y)-201 3659 y(consider)69 b(that)f(it)h(co)5 b(des)68 b(the)g(determinating)f(part)i(of)f(the)g (sp)5 b(ectral)69 b(informations)e(that)h(are)h(in)-5 b(v)g(olv)g(ed)-201 3884 y(in)62 b(the)f(dynamical)f(b)5 b(eha)-5 b(viour)62 b(of)f(the)g(considered)g(quan)-5 b(tum)60 b(system.)80 b(The)61 b(quan)-5 b(tit)g(y)61 b(in)h(\(3.4\))e(should)-201 4110 y(b)5 b(e)61 b(compared)d(to)j(other) f(quan)-5 b(tities)60 b(suc)-5 b(h)60 b(as)897 4345 y Fi(Z)998 4757 y Fk(j)p Fl(x)p Fk(\000)p Fl(y)5 b Fk(j\024)p Fg(1)p Fl(=T)1731 4592 y Fp(d)p Fn(\026)1942 4622 y Fl( )2047 4592 y Fp(\()p Fn(x)p Fp(\)d)p Fn(\026)2504 4622 y Fl( )2608 4592 y Fp(\()p Fn(y)i Fp(\))p Fn(;)211 b Fp(or)3482 4345 y Fi(Z)3583 4757 y Fj(R)3718 4345 y Fi(Z)3819 4757 y Fj(R)3953 4592 y Fp(d)p Fn(\026)4164 4622 y Fl( )4269 4592 y Fp(\()p Fn(x)p Fp(\)d)p Fn(\026)4726 4622 y Fl( )4830 4592 y Fp(\()p Fn(y)7 b Fp(\)e)5149 4517 y Fk(\000)p Fg(\()p Fl(x)p Fk(\000)p Fl(y)e Fg(\))5633 4470 y Fd(2)5701 4517 y Fl(T)5803 4470 y Fd(2)5872 4517 y Fl(=)p Fg(4)6021 4592 y Fn(;)-201 5141 y Fp(whic)-5 b(h)76 b(already)f(app)5 b(ear,)78 b(in)d(the)f(limit)h Fn(")f Fp(=)g Fn(T)3168 5075 y Fk(\000)p Fg(1)3431 5141 y Fm(!)g Fp(0,)k(as)c(k)-5 b(ey)75 b(quan)-5 b(tities)75 b(in)g(order)g(to)f(discuss)h(the)-201 5367 y(nature)60 b(of)h(the)f(sp)5 b(ectrum)58 b([24)o(],[25)o(],[11)n (],[5)o(].)81 5693 y(The)j(main)f(result)g(of)g(this)h(section)f(is)h (the)f(follo)-5 b(wing.)-201 6167 y Fe(Theorem)68 b(3.1.)90 b Fq(L)-9 b(et)70 b Fn(H)84 b Fq(b)-9 b(e)69 b(a)g(self-adjoint)g(op)-9 b(er)g(ator)68 b(on)i Fm(H)g Fq(and)g(let)f Fn( )76 b Fq(b)-9 b(e)68 b(a)i(ve)-9 b(ctor)68 b(in)h Fm(H)r Fq(,)h Fm(k)p Fn( )7 b Fm(k)58 b Fp(=)g(1)p Fq(.)-201 6393 y(L)-9 b(et)65 b Fm(f)p Fn(e)289 6420 y Fl(n)383 6393 y Fm(g)g Fq(b)-9 b(e)64 b(some)g(orthonormal)g(b)-9 b(asis)65 b(in)g Fm(H)h Fq(and)1693 6924 y Fm(hhj)p Fn(X)14 b Fm(j)2102 6849 y Fl(p)2180 6924 y Fm(ii)2322 6954 y Fl( )2427 6924 y Fp(\()p Fn(T)25 b Fp(\))50 b(=)2982 6801 y(1)p 2962 6882 132 8 v 2962 7048 a Fn(T)3144 6676 y Fi(Z)3325 6729 y Fl(T)3245 7089 y Fg(0)3466 6751 y Fi(X)3554 7133 y Fl(n)3759 6924 y Fm(j)p Fn(n)p Fm(j)3970 6849 y Fl(p)4048 6924 y Fm(jh)p Fp(e)4251 6849 y Fk(\000)p Fl(itH)4594 6924 y Fn(;)30 b(e)4760 6951 y Fl(n)4853 6924 y Fm(ij)4975 6849 y Fg(2)5053 6924 y Fp(dt)p Fn(:)-201 7530 y Fq(L)-9 b(et)65 b Fn(h)50 b Fm(2)h Fn(C)583 7464 y Fk(1)570 7578 y Fg(0)732 7530 y Fp(\([0)p Fn(;)30 b Fp(1]\))64 b Fq(b)-9 b(e)64 b(any)h(p)-9 b(ositive)64 b(function)h(such)f(that)4030 7383 y Fi(R)4151 7436 y Fg(1)4116 7594 y(0)4260 7530 y Fn(h)p Fp(\()p Fn(z)8 b Fp(\))p Fn(dz)57 b Fp(=)50 b(1)65 b Fq(and)g(de\014ne)2195 8072 y Fn(R)q Fp(\()p Fn(w)5 b Fp(\))51 b(=)2854 7816 y Fi(\032)3073 7951 y Fp(1)701 b(if)79 b Fm(j)p Fn(w)5 b Fm(j)50 b(\024)g Fp(1)3073 8193 y Fm(j)3126 8145 y Fp(^)3124 8193 y Fn(h)o Fp(\()p Fn(w)5 b Fp(\))p Fm(j)3556 8127 y Fg(2)3865 8193 y Fp(if)79 b Fm(j)p Fn(w)5 b Fm(j)50 b Fn(>)g Fp(1)p Fn(;)6796 8072 y Fp(\(3.5\))-201 8634 y Fq(wher)-9 b(e)310 8586 y Fp(^)308 8634 y Fn(h)61 b Fq(stands)g(for)f(the)h(F)-14 b(ourier)58 b(tr)-9 b(ansform)60 b(of)h Fn(h)p Fq(.)81 b(Then,)62 b(for)d(al)9 b(l)60 b Fn(p)50 b(>)g Fp(0)61 b Fq(and)f(with)h Fn(L)5964 8664 y Fl( )6069 8634 y Fp(\()p Fn(T)25 b Fp(\))60 b Fq(de\014ne)-9 b(d)60 b(in)-201 8860 y(\(3.2\),)65 b(ther)-9 b(e)64 b(exists)i(a)f(c)-9 b(onstant)66 b Fn(C)13 b Fp(\()p Fn( )7 b(;)30 b(p;)g(h)p Fp(\))62 b Fq(such)j(that)h(for)e (al)9 b(l)64 b Fn(T)76 b(>)50 b Fp(0)2168 9268 y Fm(hhj)p Fn(X)14 b Fm(j)2577 9193 y Fl(p)2654 9268 y Fm(ii)2796 9298 y Fl( )2901 9268 y Fp(\()p Fn(T)25 b Fp(\))50 b Fm(\025)g Fn(C)13 b Fp(\()p Fn( )7 b(;)30 b(p;)g(h)p Fp(\))p Fn(L)4310 9298 y Fl( )4413 9268 y Fp(\()p Fn(T)25 b Fp(\))64 b Fn(:)-201 9677 y Fe(Remark)69 b(3.1.)90 b Fp(W)-15 b(e)86 b(p)5 b(oin)-5 b(t)87 b(out)f(that)g Fn(h)g Fp(seems)e(to)i(b)5 b(e)87 b(the)f(necessary)f(tric)-5 b(k)87 b(to)f(tak)-5 b(e)86 b(in)-5 b(to)86 b(accoun)-5 b(t)-201 9903 y(a)g(v)g(eraging)72 b(on)f(time)f(b)5 b(et)-5 b(w)g(een)71 b([0)p Fn(;)30 b(T)25 b Fp(])71 b(only)-15 b(,)74 b(instead)e(of)f([)p Fm(\000)p Fn(T)15 b(;)30 b(T)25 b Fp(].)112 b(This)72 b(tric)-5 b(k)72 b(actually)g(allo)-5 b(ws)72 b(one)g(to)-201 10128 y(deal)86 b(with)g(the)f(crossed)g(term)e(in)j(\(1.6\))e(and)i(to)f(reco)-5 b(v)g(er)85 b(a)g(function)g Fn(R)i Fp(with)f(fast)f(deca)-5 b(y)84 b(at)i Fm(\0061)p Fp(.)-201 10354 y(Replacing)73 b Fn(h)e Fp(b)-5 b(y)72 b(the)g(usual)g(gaussian)g Fn(e)2730 10288 y Fk(\000)p Fl(z)2912 10241 y Fd(2)2979 10288 y Fl(=)p Fg(4)3201 10354 y Fp(in)g(\(3.15\))f(b)5 b(elo)-5 b(w)73 b(and)e(th)-5 b(us)72 b(in)g(\(3.6\))f(will)j(lead)e(to)g(the) -201 10580 y(same)59 b(result)h(but)h(with)g Fm(j)p Fn(X)14 b Fm(j)1776 10492 y Fl(p)1776 10639 y( )1880 10580 y Fp(\()p Fn(t)p Fp(\))60 b(a)-5 b(v)g(eraged)60 b(o)-5 b(v)g(er)60 b([)p Fm(\000)p Fn(T)15 b(;)30 b(T)25 b Fp(].)3439 11631 y(9)p eop %%Page: 10 10 10 9 bop 81 1158 a Fp(As)92 b(it)g(is)g(no)-5 b(w)92 b(w)-5 b(ell-kno)g(wn)93 b([14)o(],)99 b([7)o(],)g([25)o(],)g(a)91 b(k)-5 b(ey)92 b(p)5 b(oin)-5 b(t)92 b(in)g(the)f(pro)5 b(of)92 b(of)f(lo)-5 b(w)g(er)92 b(b)5 b(ounds)92 b(for)-201 1384 y Fm(hhj)p Fn(X)14 b Fm(j)208 1318 y Fl(p)286 1384 y Fm(ii)428 1414 y Fl( )533 1384 y Fp(\()p Fn(T)25 b Fp(\))76 b(is)h(a)f(go)5 b(o)g(d)76 b(con)-5 b(trol)77 b(on)f(the)g(b)5 b(eha)-5 b(viour)77 b(of)f(the)g(w)-5 b(a)g(v)g(e)76 b(pac)-5 b(k)g(et)75 b(inside)i(a)g(ball)g(of)f(radius) -201 1610 y Fn(N)20 b Fp(,)60 b(namely)1549 1914 y Fn(B)1687 1944 y Fl( )1793 1914 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))50 b(=)2585 1791 y(1)p 2564 1872 132 8 v 2564 2039 a Fn(T)2746 1667 y Fi(Z)2928 1719 y Fk(1)2847 2079 y Fg(0)3176 1741 y Fi(X)3108 2144 y Fk(j)p Fl(n)p Fk(j\024)p Fl(N)3538 1914 y Fm(jh)p Fp(e)3741 1839 y Fk(\000)p Fl(itH)4083 1914 y Fn( )7 b(;)30 b(e)4375 1941 y Fl(n)4468 1914 y Fm(ij)4590 1839 y Fg(2)4668 1914 y Fn(h)p Fp(\()p Fn(t=T)25 b Fp(\)d)p Fn(t:)1375 b Fp(\(3.6\))-201 2441 y(T)-15 b(o)69 b(that)f(end,)i(w)-5 b(e)69 b(shall)g(need)g(Theorem)e(3.2)h(b)5 b(elo)-5 b(w,)71 b(whic)-5 b(h)69 b(is)g(a)g(generalization)g(of)f (Theorem)g(2.1)g(in)-201 2667 y([5].)79 b(In)59 b(order)g(to)g(state)f (it)i(w)-5 b(e)59 b(\014rst)g(recall)h(w)-5 b(ell-kno)g(wn)60 b(facts)e(in)-5 b(v)g(olving)60 b(the)f(sp)5 b(ectral)59 b(theorem)e(for)i(the)-201 2892 y(self-adjoin)-5 b(t)60 b(op)5 b(erator)60 b Fn(H)75 b Fp(and)61 b(the)f(c)-5 b(ho)5 b(osen)60 b(v)-5 b(ector)60 b Fn( )7 b Fp(.)79 b(\(see)60 b Fq(e.g.)79 b Fp([30])60 b(and)g(ref.)80 b(therein\).)-201 3118 y(Namely)-15 b(,)49 b(there)f(exists)f(a)h (unitary)h(map)d Fn(W)2765 3148 y Fl( )2918 3118 y Fp(from)g(the)i (cyclic)g(subspace)f Fm(H)5024 3148 y Fl( )5177 3118 y Fp(in)-5 b(to)48 b(the)g(space)f(L)6421 3052 y Fg(2)6500 3118 y Fp(\()p Ff(R)26 b Fn(;)k Fp(d)p Fn(\026)6985 3148 y Fl( )7099 3118 y Fp(\))-201 3344 y(suc)-5 b(h)88 b(that)f Fn(W)830 3374 y Fl( )935 3344 y Fp(\()p Fn( )7 b Fp(\))94 b(=)h(1)88 b(and)g Fn(W)2266 3374 y Fl( )2371 3344 y Fp(\(e)2523 3278 y Fk(\000)p Fl(itH)2865 3344 y Fn( )7 b Fp(\))95 b(=)g(e)3475 3278 y Fk(\000)p Fl(itx)3772 3344 y Fp(.)162 b(W)-15 b(e)87 b(shall)h(denote)f(b)-5 b(y)88 b Fn(P)5787 3374 y Fl( )5980 3344 y Fp(the)f(orthogonal)-201 3570 y(pro)10 b(jection)74 b(on)f Fm(H)1096 3600 y Fl( )1201 3570 y Fp(.)120 b(The)74 b(map)e Fn(W)2348 3600 y Fl( )2527 3570 y Fp(has)h(a)h(k)-5 b(ernel)74 b Fn(u)p Fp(\()p Fn(n;)30 b(x)p Fp(\))73 b(de\014ned)g(b)-5 b(y)74 b Fn(u)p Fp(\()p Fn(n;)30 b Fm(\001)p Fp(\))71 b(=)h Fn(W)6040 3600 y Fl( )6145 3570 y Fp(\()p Fn(P)6333 3600 y Fl( )6438 3570 y Fn(e)6523 3597 y Fl(n)6616 3570 y Fp(\)\()p Fm(\001)p Fp(\),)k(so)-201 3796 y(that)2014 4060 y Fm(h)p Fn(e)2170 3985 y Fk(\000)p Fl(iH)10 b(t)2513 4060 y Fn( )d(;)30 b(e)2805 4087 y Fl(n)2897 4060 y Fm(i)50 b Fp(=)3210 3812 y Fi(Z)3422 4060 y Fn(e)3507 3985 y Fk(\000)p Fl(ixt)p 3803 3902 540 8 v 3803 4060 a Fn(u)p Fp(\()p Fn(n;)30 b(x)p Fp(\)d)p Fn(\026)4554 4090 y Fl( )4659 4060 y Fp(\()p Fn(x)p Fp(\))p Fn(;)1840 b Fp(\(3.7\))-201 4462 y(and)61 b(more)e(generally)-15 b(,)60 b(for)h(an)-5 b(y)60 b(v)-5 b(ector)60 b Fn(\030)e Fm(2)51 b(H)r Fp(,)60 b(one)g(has)1809 4933 y Fm(h)p Fn(P)1997 4963 y Fl( )2102 4933 y Fn(\030)8 b(;)30 b(e)2356 4960 y Fl(n)2449 4933 y Fm(i)50 b Fp(=)2762 4685 y Fi(Z)2974 4933 y Fn(W)3146 4963 y Fl( )3282 4933 y Fp(\()o Fn(P)3469 4963 y Fl( )3574 4933 y Fn(\030)8 b Fp(\))30 b(\()p Fn(x)p Fp(\))p 4009 4774 V Fn(u)p Fp(\()p Fn(n;)g(x)p Fp(\))o(d)p Fn(\026)4759 4963 y Fl( )4864 4933 y Fp(\()p Fn(x)p Fp(\))p Fn(:)1635 b Fp(\(3.8\))-201 5436 y(In)56 b(the)f(case)g Fm(H)d Fp(=)e Fn(`)1184 5370 y Fg(2)1262 5436 y Fp(\()p Ff(Z)1445 5370 y Fl(d)1535 5436 y Fp(\))56 b(and)g Fn(e)2096 5463 y Fl(n)2189 5436 y Fp(\()p Fn(k)6 b Fp(\))50 b(=)f Fn(\016)2754 5466 y Fl(nk)2925 5436 y Fp(,)57 b(for)e(eac)-5 b(h)55 b(\014xed)h Fn(x)50 b Fm(2)h Ff(R)91 b Fp(the)56 b(v)-5 b(ector)55 b(\()p Fn(u)p Fp(\()p Fn(n;)30 b(x)p Fp(\))6119 5480 y Fl(n)p Fk(2)p Fj(Z)6386 5442 y Fh(d)6467 5436 y Fp(\))55 b(ma)-5 b(y)54 b(b)5 b(e)-201 5662 y(seen)66 b(as)g(a)g(generalized)g (eigenfunction)g(of)f Fn(H)82 b Fp(\()p Fq(i.e.)96 b Fp(in)66 b(a)g(distributional)i(sense\).)96 b(This)66 b(observ)-10 b(ation)66 b(is)-201 5887 y(of)60 b(in)-5 b(terest)60 b(for)h(some)d(applications)j(\([24)o(])f(and)h(Theorem)e (4.3)h(b)5 b(elo)-5 b(w\))81 6113 y(The)70 b(expansions)f (\(3.7\)-\(3.8\))d(are)k(of)f(course)f(also)i(p)5 b(ossible)69 b(with)h(an)-5 b(y)70 b(v)-5 b(ector)68 b Fn(')d Fm(2)h(H)k Fp(and)g(corre-)-201 6339 y(sp)5 b(onding)70 b(k)-5 b(ernel)71 b Fn(v)7 b Fp(\()p Fn(n;)30 b(y)7 b Fp(\))65 b(=)h Fn(W)2096 6366 y Fl(')2196 6339 y Fp(\()p Fn(P)2384 6366 y Fl(')2483 6339 y Fn(e)2568 6366 y Fl(n)2662 6339 y Fp(\)\()p Fn(y)7 b Fp(\))69 b(\(actually)h(if)g Fn(')c Fp(=)g Fn(f)20 b Fp(\()p Fn(H)15 b Fp(\))p Fn( )7 b Fp(,)70 b(with)g Fn(f)86 b Fm(2)67 b Fp(L)5945 6273 y Fg(2)6023 6339 y Fp(\()p Ff(R)26 b Fn(;)k Fp(d)p Fn(\026)6508 6369 y Fl( )6622 6339 y Fp(\),)72 b(then)-201 6565 y(one)61 b(c)-5 b(hec)g(ks)59 b(that)h Fn(v)7 b Fp(\()p Fn(n;)30 b(y)7 b Fp(\))49 b(=)h Fn(f)20 b Fp(\()p Fn(y)7 b Fp(\))p Fn(u)p Fp(\()p Fn(n;)30 b(y)7 b Fp(\)\).)-201 6791 y(W)-15 b(e)60 b(are)h(no)-5 b(w)61 b(ready)f(to)g(form)-5 b(ulate)59 b(Theorem)g(3.2.)-201 7253 y Fe(Theorem)68 b(3.2.)90 b Fq(L)-9 b(et)75 b Fn(h)p Fp(\()p Fn(z)8 b Fp(\))73 b Fq(b)-9 b(e)74 b(some)h(function)f(in)h Fp(L)3620 7187 y Fg(1)3698 7253 y Fp(\()p Ff(R)26 b Fp(\))p Fq(,)86 b Fn(H)k Fq(a)74 b(self-adjoint)g(op)-9 b(er)g(ator)74 b(acting)g(on)h Fm(H)-201 7478 y Fq(and)k Fn(A)h Fq(a)f(Hilb)-9 b(ert-Schmidt)77 b(op)-9 b(er)g(ator)78 b(in)h Fm(H)r Fq(.)125 b(F)-14 b(or)78 b(any)i(c)-9 b(ouple)77 b(of)h(ve)-9 b(ctors)78 b Fn( )7 b(;)30 b(')78 b Fq(fr)-9 b(om)78 b Fm(H)j Fq(de\014ne)d(the)-201 7704 y(quantity)1608 8031 y Fn(D)1764 7936 y Fg(\()p Fl(h)p Fg(\))1759 8090 y Fl('; )1995 8031 y Fp(\()p Fn(T)25 b Fp(\))51 b(=)2551 7908 y(1)p 2530 7990 132 8 v 2530 8156 a Fn(T)2712 7784 y Fi(Z)2894 7836 y Fg(+)p Fk(1)2813 8196 y(\0001)3153 8031 y Fm(h)p Fn(A)p Fp(e)3441 7956 y Fk(\000)p Fl(itH)3784 8031 y Fn(';)30 b Fp(e)4065 7956 y Fk(\000)p Fl(itH)4408 8031 y Fn( )7 b Fm(i)p Fn(h)p Fp(\()p Fn(t=T)25 b Fp(\)dt)n Fn(:)-201 8453 y Fq(L)-9 b(et)1671 8717 y Fn(U)1815 8622 y Fg(\()p Fl(h)p Fg(\))1795 8776 y Fl('; )2031 8717 y Fp(\()p Fn(T)25 b Fp(\))51 b(=)2546 8470 y Fi(Z)2647 8882 y Fj(R)2782 8470 y Fi(Z)2883 8882 y Fj(R)3018 8717 y Fp(d)p Fn(\026)3229 8744 y Fl(')3328 8717 y Fp(\()p Fn(x)p Fp(\)d)p Fn(\026)3785 8747 y Fl( )3890 8717 y Fp(\()p Fn(y)7 b Fp(\))p Fm(j)4181 8669 y Fp(^)4179 8717 y Fn(h)n Fp(\(\()p Fn(x)40 b Fm(\000)g Fn(y)7 b Fp(\))p Fn(T)25 b Fp(\))p Fm(j)5170 8642 y Fg(2)5247 8717 y Fn(:)81 9128 y Fq(The)65 b(fol)9 b(lowing)64 b(estimate)g(holds:)2249 9626 y Fm(j)p Fn(D)2456 9530 y Fg(\()p Fl(h)p Fg(\))2451 9685 y Fl('; )2686 9626 y Fp(\()p Fn(T)25 b Fp(\))p Fm(j)50 b(\024)g(k)p Fn(A)p Fm(k)3570 9653 y Fg(2)3679 9424 y Fi(\020)3788 9626 y Fn(U)3932 9530 y Fg(\()p Fl(h)p Fg(\))3912 9685 y Fl('; )4149 9626 y Fp(\()p Fn(T)25 b Fp(\))4422 9424 y Fi(\021)4550 9415 y Fd(1)p 4550 9439 61 6 v 4550 9522 a(2)4669 9626 y Fn(;)-201 10069 y Fq(wher)-9 b(e)64 b Fm(k)p Fn(A)p Fm(k)631 10096 y Fg(2)775 10069 y Fq(is)h(the)g(Hilb)-9 b(ert-Schmidt)63 b(norm)i(of)f Fn(A)p Fq(.)81 10295 y(In)i(the)f(sp)-9 b(e)g(cial)63 b(c)-9 b(ase)64 b Fn(A)51 b Fp(=)1966 10158 y Fi(P)2158 10349 y Fk(j)p Fl(n)p Fk(j\024)p Fl(N)2566 10295 y Fm(h\001)p Fn(;)30 b(e)2854 10322 y Fl(n)2947 10295 y Fm(i)p Fn(e)3103 10322 y Fl(n)3196 10295 y Fq(,)65 b(one)g(has)g Fm(k)p Fn(A)p Fm(k)4304 10322 y Fg(2)4434 10295 y Fm(\024)50 b Fn(C)13 b(N)4935 10229 y Fl(d=)p Fg(2)5157 10295 y Fq(,)64 b(and)h(ther)-9 b(efor)g(e)48 10943 y Fm(j)p Fn(D)255 10847 y Fg(\()p Fl(h)p Fg(\))250 11001 y Fl('; )485 10943 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))p Fm(j)50 b Fp(=)1288 10570 y Fi(\014)1288 10679 y(\014)1288 10788 y(\014)1288 10897 y(\014)1288 11006 y(\014)1288 11115 y(\014)1389 10820 y Fp(1)p 1368 10901 132 8 v 1368 11067 a Fn(T)1550 10695 y Fi(Z)1732 10748 y Fg(+)p Fk(1)1651 11108 y(\0001)2090 10770 y Fi(X)2021 11173 y Fk(j)p Fl(n)p Fk(j\024)p Fl(N)2421 10943 y Fm(h)p Fp(e)2573 10868 y Fk(\000)p Fl(itH)2916 10943 y Fn(';)30 b(e)3201 10970 y Fl(n)3294 10943 y Fm(ih)p Fn(e)3521 10970 y Fl(n)3614 10943 y Fn(;)g Fp(e)3776 10868 y Fk(\000)p Fl(itH)4119 10943 y Fn( )7 b Fm(i)p Fn(h)p Fp(\()p Fn(t=T)25 b Fp(\)d)p Fn(t)5018 10570 y Fi(\014)5018 10679 y(\014)5018 10788 y(\014)5018 10897 y(\014)5018 11006 y(\014)5018 11115 y(\014)5127 10943 y Fm(\024)50 b Fn(C)13 b(N)5628 10868 y Fl(d=)p Fg(2)5880 10741 y Fi(\020)5989 10943 y Fn(U)6133 10847 y Fg(\()p Fl(h)p Fg(\))6113 11001 y Fl('; )6349 10943 y Fp(\()p Fn(T)25 b Fp(\))6622 10741 y Fi(\021)6751 10732 y Fd(1)p 6751 10756 61 6 v 6751 10838 a(2)6870 10943 y Fn(:)3393 11631 y Fp(10)p eop %%Page: 11 11 11 10 bop -201 1158 a Fq(Her)-9 b(e)51 b Fn(d)f Fp(=)g(1)i Fq(if)g(one)g(c)-9 b(onsiders)51 b(the)h(abstr)-9 b(act)52 b(p)-9 b(osition)52 b(op)-9 b(er)g(ator)50 b(asso)-9 b(ciate)g(d)52 b(with)g(the)g(b)-9 b(ase)51 b Fm(f)p Fn(e)6366 1185 y Fl(n)6459 1158 y Fm(g)h Fq(lab)-9 b(el)9 b(le)-9 b(d)-201 1384 y(by)65 b Fn(n)51 b Fm(2)g Ff(N)30 b Fq(,)74 b(and)65 b Fn(d)50 b Fm(\025)g Fp(1)65 b Fq(in)g(the)g(c)-9 b(ase)64 b Fm(H)52 b Fp(=)e Fn(`)2855 1318 y Fg(2)2933 1384 y Fp(\()p Ff(Z)3116 1318 y Fl(d)3206 1384 y Fp(\))65 b Fq(e)-9 b(quipp)g(e)g(d)62 b(with)j(the)g(c)-9 b(anonic)g(al)63 b(b)-9 b(asis)65 b Fn(e)6080 1411 y Fl(n)6224 1384 y Fp(=)50 b Fn(\016)6497 1411 y Fl(n)6591 1384 y Fq(.)-201 1859 y Fe(Pro)6 b(of)69 b(of)g(Theorem)f(3.2.)-201 2085 y Fp(Since)52 b Fn(A)h Fp(is)f(Hilb)5 b(ert-Sc)-5 b(hmidt,)53 b(there)f(exist)g(t)-5 b(w)g(o)51 b(orthonormal)g(bases)h Fm(f)p Fn(f)4906 2112 y Fl(n)5000 2085 y Fm(g)5091 2114 y Fl(n)p Fk(2)p Fj(N)5427 2085 y Fp(and)g Fm(f)p Fn(g)5950 2112 y Fl(n)6043 2085 y Fm(g)6134 2114 y Fl(n)p Fk(2)p Fj(N)6470 2085 y Fp(of)g Fm(H)h Fp(and)-201 2410 y(a)63 b(monotonely)d(decreasing)i(sequence)g Fm(f)p Fn(E)2802 2437 y Fl(n)2896 2410 y Fm(g)2987 2439 y Fl(n)p Fk(2)p Fj(N)3271 2410 y Fp(,)g Fn(E)3518 2437 y Fl(n)3665 2410 y Fm(\025)53 b Fp(0,)63 b(suc)-5 b(h)62 b(that)4872 2274 y Fi(P)5064 2327 y Fk(1)5064 2464 y Fl(n)p Fg(=1)5369 2410 y Fn(E)5513 2344 y Fg(2)5503 2455 y Fl(n)5650 2410 y Fp(=)53 b Fm(k)p Fn(A)p Fm(k)6163 2344 y Fg(2)6163 2459 y(2)6296 2410 y Fn(<)g Fp(+)p Fm(1)61 b Fp(and)-201 2636 y Fn(A)51 b Fp(=)178 2500 y Fi(P)370 2552 y Fk(1)370 2690 y Fl(n)p Fg(=1)675 2636 y Fn(E)809 2663 y Fl(n)903 2636 y Fm(h\001)p Fn(;)30 b(f)1195 2663 y Fl(n)1288 2636 y Fm(i)p Fn(g)1446 2663 y Fl(n)1539 2636 y Fp(.)80 b(Therefore,)1109 3192 y Fn(D)1265 3096 y Fg(\()p Fl(h)p Fg(\))1260 3251 y Fl('; )1496 3192 y Fp(\()p Fn(T)25 b Fp(\))50 b(=)2051 3069 y(1)p 2031 3150 132 8 v 2031 3317 a Fn(T)2213 2944 y Fi(Z)2394 2997 y Fg(+)p Fk(1)2314 3357 y(\0001)2746 2965 y(1)2686 3019 y Fi(X)2684 3408 y Fl(n)p Fg(=1)2980 3192 y Fn(E)3114 3219 y Fl(n)3208 3192 y Fm(h)p Fp(e)3360 3117 y Fk(\000)p Fl(itH)3703 3192 y Fn(';)30 b(f)3992 3219 y Fl(n)4086 3192 y Fm(ih)p Fn(g)4315 3219 y Fl(n)4408 3192 y Fn(;)g Fp(e)4570 3117 y Fk(\000)p Fl(itH)4913 3192 y Fn( )7 b Fm(i)p Fn(h)p Fp(\()p Fn(t=T)25 b Fp(\)d)p Fn(t:)933 b Fp(\(3.9\))-201 3762 y(Then)61 b(\(3.7\))e(reads)i(as)1979 4071 y Fm(h)p Fp(e)2131 3996 y Fk(\000)p Fl(itH)2474 4071 y Fn(';)30 b(f)2763 4098 y Fl(n)2857 4071 y Fm(i)50 b Fp(=)3170 3824 y Fi(Z)3271 4236 y Fj(R)3405 4071 y Fp(d)p Fn(\026)3616 4098 y Fl(')3716 4071 y Fp(\()p Fn(x)p Fp(\)e)4043 3996 y Fk(\000)p Fl(itx)p 4339 3913 540 8 v 4339 4071 a Fn(u)p Fp(\()p Fn(n;)30 b(x)p Fp(\))60 b Fn(;)1715 b Fp(\(3.10\))-201 4512 y(where)97 b Fn(u)p Fp(\()p Fn(n)p Fp(\))110 b(=)g Fn(W)1250 4539 y Fl(')1350 4512 y Fp(\()p Fn(P)1538 4539 y Fl(')1637 4512 y Fn(f)1726 4539 y Fl(n)1820 4512 y Fp(\))g Fm(2)h Fp(L)2347 4446 y Fg(2)2425 4512 y Fp(\()p Ff(R)26 b Fn(;)k Fp(d)p Fn(\026)2910 4539 y Fl(')3019 4512 y Fp(\).)188 b(The)96 b(similar)h(form)-5 b(ula)95 b(holds)i(for)f Fn( )102 b Fp(with)97 b Fn(v)7 b Fp(\()p Fn(n)p Fp(\))110 b(=)-201 4738 y Fn(W)-29 4768 y Fl( )76 4738 y Fp(\()p Fn(P)264 4768 y Fl( )369 4738 y Fn(g)456 4765 y Fl(n)550 4738 y Fp(\))50 b Fm(2)h Fp(L)957 4672 y Fg(2)1035 4738 y Fp(\()p Ff(R)26 b Fn(;)k Fp(d)p Fn(\026)1520 4768 y Fl( )1634 4738 y Fp(\).)80 b(One)60 b(obtains)g(from)f(\(3.9\))g(-\(3.10\))g(that)1475 5240 y Fn(D)1631 5144 y Fg(\()p Fl(h)p Fg(\))1626 5299 y Fl('; )1862 5240 y Fp(\()p Fn(T)25 b Fp(\))51 b(=)2378 4993 y Fi(Z)2479 5405 y Fj(R)2613 4993 y Fi(Z)2714 5405 y Fj(R)2849 5240 y Fp(d)p Fn(\026)3060 5267 y Fl(')3160 5240 y Fp(\()p Fn(x)p Fp(\)d)p Fn(\026)3617 5270 y Fl( )3721 5240 y Fp(\()p Fn(y)7 b Fp(\))3961 5192 y(^)3959 5240 y Fn(h)o Fp(\(\()p Fn(x)39 b Fm(\000)h Fn(y)7 b Fp(\))p Fn(T)25 b Fp(\))p Fn(S)10 b Fp(\()p Fn(x;)30 b(y)7 b Fp(\))p Fn(;)1210 b Fp(\(3.11\))-201 5730 y(where)2273 6050 y Fn(S)10 b Fp(\()p Fn(x;)30 b(y)7 b Fp(\))49 b(=)3122 5822 y Fk(1)3061 5877 y Fi(X)3059 6266 y Fl(n)p Fg(=1)3356 6050 y Fn(E)3490 6077 y Fl(n)p 3584 5892 V 3584 6050 a Fn(u)p Fp(\()p Fn(n;)30 b(x)p Fp(\))o Fn(v)7 b Fp(\()p Fn(n;)30 b(y)7 b Fp(\))p Fn(:)-201 6560 y Fp(The)72 b(sum)e(con)-5 b(v)g(erges)70 b(in)i(L)1742 6494 y Fg(2)1821 6560 y Fp(\()p Ff(R)2014 6494 y Fg(2)2102 6560 y Fn(;)30 b(\026)2293 6587 y Fl(')2440 6560 y Fm(\002)47 b Fn(\026)2739 6590 y Fl( )2844 6560 y Fp(\).)113 b(Applying)73 b(the)e(Cauc)-5 b(h)g(y-Sc)g(h)g(w)g(arz)71 b(inequalit)-5 b(y)72 b(to)f(\(3.11\),)-201 6786 y(one)61 b(gets)1900 7033 y Fm(j)p Fn(D)2107 6937 y Fg(\()p Fl(h)p Fg(\))2102 7092 y Fl('; )2337 7033 y Fp(\()p Fn(T)25 b Fp(\))p Fm(j)2661 6958 y Fg(2)2790 7033 y Fm(\024)50 b Fn(U)3126 6937 y Fg(\()p Fl(h)p Fg(\))3106 7092 y Fl('; )3343 7033 y Fp(\()p Fn(T)25 b Fp(\))p Fm(k)p Fn(S)10 b Fm(k)3920 6958 y Fg(2)3920 7089 y(L)4008 7051 y Fd(2)4077 7089 y Fg(\()p Fj(R)4219 7051 y Fd(2)4297 7089 y Fl(;)p Fg(d)p Fl(\026)4499 7106 y Fh(')4588 7089 y Fk(\002)p Fg(d)p Fl(\026)4861 7112 y Fh( )4955 7089 y Fg(\))5018 7033 y Fn(:)1636 b Fp(\(3.12\))-201 7367 y(One)60 b(can)g(easily)h(see)f(that)1948 7904 y Fm(k)p Fn(S)10 b Fm(k)2252 7829 y Fg(2)2252 7960 y(L)2340 7922 y Fd(2)2409 7960 y Fg(\()p Fj(R)2551 7922 y Fd(2)2629 7960 y Fl(;)p Fg(d)p Fl(\026)2831 7977 y Fh(')2921 7960 y Fk(\002)p Fg(d)p Fl(\026)3194 7983 y Fh( )3288 7960 y Fg(\))3401 7904 y Fp(=)3714 7677 y Fk(1)3653 7731 y Fi(X)3593 8127 y Fl(n;k)t Fg(=1)4006 7904 y Fn(E)4140 7931 y Fl(n)4234 7904 y Fn(E)4368 7934 y Fl(k)4454 7904 y Fn(a)4550 7934 y Fl(nk)p 4721 7756 249 8 v 4721 7904 a Fn(b)4799 7934 y Fl(nk)4970 7904 y Fn(;)-201 8496 y Fp(where)54 8943 y Fn(a)150 8973 y Fl(nk)372 8943 y Fp(=)564 8696 y Fi(Z)665 9108 y Fj(R)799 8943 y Fp(d)p Fn(\026)1010 8970 y Fl(')1110 8943 y Fp(\()p Fn(x)p Fp(\))p Fn(u)p Fp(\()p Fn(k)c(;)30 b(x)p Fp(\))p 1888 8785 540 8 v Fn(u)p Fp(\()p Fn(n;)g(x)p Fp(\))48 b(=)i Fm(h)p Fn(W)2911 8970 y Fl(')3010 8943 y Fp(\()p Fn(P)3198 8970 y Fl(')3298 8943 y Fn(f)3387 8973 y Fl(k)3472 8943 y Fp(\))p Fn(;)30 b(W)3796 8970 y Fl(')3896 8943 y Fp(\()p Fn(P)4084 8970 y Fl(')4184 8943 y Fn(f)4273 8970 y Fl(n)4367 8943 y Fp(\))p Fm(i)4509 8982 y Fg(L)4597 8945 y Fd(2)4665 8982 y Fg(\()p Fj(R)8 b Fl(;)p Fg(d)q Fl(\026)5010 8999 y Fh(')5108 8982 y Fg(\))5222 8943 y Fp(=)50 b Fm(h)p Fn(P)5602 8970 y Fl(')5701 8943 y Fn(f)5790 8973 y Fl(k)5876 8943 y Fn(;)30 b(f)6046 8970 y Fl(n)6139 8943 y Fm(i)6210 8971 y Fk(H)6399 8943 y Fn(;)255 b Fp(\(3.13\))-201 9443 y(where)61 b(w)-5 b(e)61 b(used)f(an)g(analog)h(of)f(\(3.8\),)f(and)i (in)g(the)f(same)e(manner)2056 9852 y Fn(b)2134 9882 y Fl(nk)2355 9852 y Fp(=)50 b Fm(h)p Fn(P)2735 9882 y Fl( )2840 9852 y Fn(g)2927 9882 y Fl(k)3012 9852 y Fn(;)30 b(P)3210 9882 y Fl( )3315 9852 y Fn(g)3402 9879 y Fl(n)3495 9852 y Fm(i)3566 9880 y Fk(H)3745 9852 y Fp(=)50 b Fm(h)p Fn(g)4095 9882 y Fl(k)4180 9852 y Fn(;)30 b(P)4378 9882 y Fl( )4483 9852 y Fn(g)4570 9879 y Fl(n)4663 9852 y Fm(i)4734 9880 y Fk(H)4862 9852 y Fn(:)-201 10260 y Fp(W)-15 b(e)77 b(ha)-5 b(v)g(e)77 b(also)g(used)g(the)g(fact)f(that)h(b)5 b(oth)77 b Fn(P)3057 10287 y Fl(')3234 10260 y Fp(and)g Fn(P)3721 10290 y Fl( )3904 10260 y Fp(are)g(orthogonal)g(pro)10 b(jections.)130 b(By)77 b(P)-5 b(arsev)-10 b(al)-201 10486 y(equalit)-5 b(y)-15 b(,)1788 10614 y Fk(1)1727 10668 y Fi(X)1725 11057 y Fl(n)p Fg(=1)2022 10841 y Fm(j)p Fn(a)2169 10871 y Fl(nk)2339 10841 y Fm(j)2390 10766 y Fg(2)2519 10841 y Fp(=)50 b Fm(k)p Fn(P)2919 10868 y Fl(')3019 10841 y Fn(f)3108 10871 y Fl(k)3193 10841 y Fm(k)3284 10766 y Fg(2)3363 10841 y Fn(;)3626 10614 y Fk(1)3565 10668 y Fi(X)3568 11063 y Fl(k)t Fg(=1)3858 10841 y Fm(j)p Fn(b)3987 10871 y Fl(nk)4157 10841 y Fm(j)4208 10766 y Fg(2)4337 10841 y Fp(=)g Fm(k)p Fn(P)4737 10871 y Fl( )4842 10841 y Fn(g)4929 10868 y Fl(n)5023 10841 y Fm(k)5114 10766 y Fg(2)5193 10841 y Fn(:)3393 11631 y Fp(11)p eop %%Page: 12 12 12 11 bop -201 1158 a Fp(Therefore,)60 b(as)g Fm(k)p Fn(f)1077 1188 y Fl(k)1162 1158 y Fm(k)51 b Fp(=)f Fm(k)p Fn(g)1674 1185 y Fl(n)1767 1158 y Fm(k)h Fp(=)f(1)60 b(for)g(all)i Fn(k)6 b(;)30 b(n)p Fp(,)324 1726 y Fm(k)p Fn(S)10 b Fm(k)628 1651 y Fg(4)628 1782 y(L)716 1745 y Fd(2)785 1782 y Fg(\()p Fj(R)927 1745 y Fd(2)1005 1782 y Fl(;)p Fg(d)p Fl(\026)1207 1799 y Fh(')1297 1782 y Fk(\002)p Fg(d)p Fl(\026)1570 1805 y Fh( )1664 1782 y Fg(\))1777 1726 y Fm(\024)2030 1499 y Fk(1)1969 1554 y Fi(X)1972 1949 y Fl(k)t Fg(=1)2262 1726 y Fn(E)2406 1651 y Fg(2)2396 1773 y Fl(k)2486 1726 y Fm(k)p Fn(P)2694 1753 y Fl(')2794 1726 y Fn(f)2883 1756 y Fl(k)2968 1726 y Fm(k)3059 1651 y Fg(2)3231 1499 y Fk(1)3170 1554 y Fi(X)3168 1942 y Fl(n)p Fg(=1)3464 1726 y Fn(E)3608 1651 y Fg(2)3598 1771 y Fl(n)3693 1726 y Fm(k)p Fn(P)3901 1756 y Fl( )4006 1726 y Fn(g)4093 1753 y Fl(n)4186 1726 y Fm(k)4277 1651 y Fg(2)4406 1726 y Fm(\024)4598 1415 y Fi( )4805 1499 y Fk(1)4744 1554 y Fi(X)4742 1942 y Fl(n)p Fg(=1)5039 1726 y Fn(E)5183 1651 y Fg(2)5173 1771 y Fl(n)5267 1415 y Fi(!)5411 1461 y Fg(2)5540 1726 y Fp(=)50 b Fm(k)p Fn(A)p Fm(k)6050 1651 y Fg(4)6050 1771 y(2)6129 1726 y Fn(:)525 b Fp(\(3.14\))-201 2275 y(The)66 b(\014rst)g(statemen)-5 b(t)63 b(of)i(the)h(Theorem)e(follo)-5 b(ws)67 b(from)d(\(3.12\))g(and)i(\(3.14\).)95 b(The)66 b(pro)5 b(of)66 b(of)g(the)f(second)-201 2501 y(part)e(is)f(essen)-5 b(tially)63 b(the)f(same.)84 b(The)62 b(only)h(di\013erence)g(is)g (that)e(in)i(the)f(case)g Fm(H)55 b Fp(=)e Fn(`)5668 2435 y Fg(2)5747 2501 y Fp(\()p Ff(Z)5930 2435 y Fl(d)6020 2501 y Fp(\))62 b(the)g(sums)e(are)-201 2726 y(tak)-5 b(en)60 b(o)-5 b(v)g(er)61 b Fn(n)50 b Fm(2)h Ff(Z)1127 2660 y Fl(d)1268 2726 y Fp(:)110 b Fm(j)p Fn(n)p Fm(j)50 b(\024)g Fn(N)20 b Fp(.)80 b(In)60 b(particular,)h(the)f(estimate)f (\(3.14\))g(reads)h(as)1174 3134 y Fm(k)p Fn(S)10 b Fm(k)1478 3059 y Fg(4)1478 3190 y(L)1566 3152 y Fd(2)1635 3190 y Fg(\()p Fj(R)1777 3152 y Fd(2)1855 3190 y Fl(;)p Fg(d)p Fl(\026)2057 3207 y Fh(')2147 3190 y Fk(\002)p Fg(d)p Fl(\026)2420 3213 y Fh( )2514 3190 y Fg(\))2627 3134 y Fm(\024)2884 2961 y Fi(X)2819 3364 y Fk(j)p Fl(k)t Fk(j\024)p Fl(N)3241 3134 y Fm(k)p Fn(P)3449 3161 y Fl(')3549 3134 y Fn(e)3634 3164 y Fl(k)3719 3134 y Fm(k)3810 3059 y Fg(2)3988 2961 y Fi(X)3919 3364 y Fk(j)p Fl(n)p Fk(j\024)p Fl(N)4349 3134 y Fm(k)p Fn(P)4557 3164 y Fl( )4662 3134 y Fn(e)4747 3161 y Fl(n)4841 3134 y Fm(k)4932 3059 y Fg(2)5061 3134 y Fm(\024)50 b Fn(C)43 b(N)5592 3059 y Fg(2)p Fl(d)5744 3134 y Fn(:)-201 3713 y Fp(This)61 b(ends)g(the)f(pro) 5 b(of.)5619 b Fc(\003)81 4029 y Fp(One)40 b(should)h(stress)e(that)h (the)g(pro)5 b(of)40 b(w)-5 b(e)41 b(presen)-5 b(ted)40 b(here)g(is)h(simpler)e(than)i(the)f(one)g(of)g(Theorem)f(2.1)h(in)-201 4255 y([5],)49 b(b)5 b(ecause)47 b(w)-5 b(e)48 b(do)g(not)g(use)f(the)h (pro)5 b(duct)47 b(space)h Fm(H)17 b(\012)e(H)r Fp(.)74 b(In)47 b(the)h(case)f Fn( )57 b Fp(=)50 b Fn(')d Fp(and)h Fn(h)p Fp(\()p Fn(z)8 b Fp(\))50 b(=)f(exp\()p Fm(\000)p Fn(z)6839 4189 y Fg(2)6917 4255 y Fn(=)p Fp(4\))-201 4481 y(the)60 b(result)h(of)f(Theorem)f(3.2)h(is)h(equiv)-10 b(alen)-5 b(t)61 b(to)f(that)g(of)g(Theorem)f(2.1)h(in)h([5)o(].)-201 4797 y Fe(Pro)6 b(of)63 b(of)h(Theorem)e(3.1.)79 b Fp(Pic)-5 b(k)55 b(a)h(p)5 b(ositiv)-5 b(e)56 b(function)f Fn(h)p Fp(\()p Fn(z)8 b Fp(\))49 b Fm(2)i Fn(C)4518 4731 y Fk(1)4505 4845 y Fg(0)4668 4797 y Fp(\([0)p Fn(;)30 b Fp(1]\))53 b(suc)-5 b(h)56 b(that)6023 4650 y Fi(R)6144 4703 y Fg(1)6109 4861 y(0)6253 4797 y Fn(h)p Fp(\()p Fn(z)8 b Fp(\)d)p Fn(z)57 b Fp(=)50 b(1.)-201 5051 y(The)70 b(role)h(of)f Fn(h)g Fp(is)g(to)g(supply)g(a)g(fast)f(deca)-5 b(ying)70 b(function)g Fm(j)4005 5003 y Fp(^)4003 5051 y Fn(h)o Fp(\()p Fn(w)5 b Fp(\))p Fm(j)4435 4985 y Fg(2)4513 5051 y Fp(.)109 b(Note)70 b(that)f(one)h(trivially)i(has,)g(for)-201 5277 y(an)-5 b(y)61 b Fn(z)d Fm(2)50 b Fp([0)p Fn(;)30 b Fp(1],)59 b Fn(h)p Fp(\()p Fn(z)8 b Fp(\))49 b Fm(\024)h(k)p Fn(h)p Fm(k)1800 5304 y Fk(1)1949 5277 y Fn(\037)2063 5314 y Fg([0)p Fl(;)p Fg(1])2330 5277 y Fp(\()p Fn(z)8 b Fp(\).)79 b(Then)61 b(one)g(v)-5 b(eri\014es)60 b(that)41 5837 y Fm(hh)p Fn(X)348 5762 y Fl(p)427 5837 y Fm(ii)569 5867 y Fl( )674 5837 y Fp(\()p Fn(T)25 b Fp(\))50 b Fm(\025)1382 5714 y Fp(1)p 1209 5795 437 8 v 1209 5962 a Fm(k)p Fn(h)p Fm(k)1496 5989 y Fk(1)1695 5589 y Fi(Z)1877 5642 y Fk(1)1796 6002 y Fg(0)2057 5664 y Fi(X)2145 6046 y Fl(n)2350 5837 y Fm(j)p Fn(n)p Fm(j)2561 5762 y Fl(p)2639 5837 y Fm(jh)p Fp(e)2842 5762 y Fk(\000)p Fl(itH)3185 5837 y Fn( )7 b(;)30 b(e)3477 5864 y Fl(n)3569 5837 y Fm(ij)3691 5762 y Fg(2)3769 5837 y Fn(h)p Fp(\()p Fn(t=T)25 b Fp(\))4324 5714 y(d)p Fn(t)p 4324 5795 167 8 v 4342 5962 a(T)4560 5837 y Fm(\025)4868 5714 y Fn(N)5034 5648 y Fl(p)p 4772 5795 437 8 v 4772 5962 a Fm(k)p Fn(h)p Fm(k)5059 5989 y Fk(1)5228 5526 y Fi( )5372 5837 y Fm(k)p Fn( )7 b Fm(k)5680 5762 y Fg(2)5798 5837 y Fm(\000)40 b Fn(B)6118 5867 y Fl( )6223 5837 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))6733 5526 y Fi(!)6877 5837 y Fn(;)6705 6217 y Fp(\(3.15\))-201 6443 y(with)76 b Fn(B)366 6473 y Fl( )471 6443 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))75 b(de\014ned)g(line)h(\(3.6\).)123 b(As)76 b(usual,)i(one)d(needs)g(a)g(con)-5 b(trol)76 b(of)e(this)i(quan)-5 b(tit)g(y)75 b Fn(B)6555 6473 y Fl( )6660 6443 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))-201 6669 y(whic)-5 b(h)81 b(represen)-5 b(ts)78 b(the)i(b)5 b(eha)-5 b(viour)80 b(of)f(the)h(w)-5 b(a)g(v)g(e)79 b(pac)-5 b(k)g(et)79 b(in)i(a)e(ball)i(of)e(radius)i Fn(N)20 b Fp(.)138 b(Decomp)5 b(ose)77 b(the)-201 6895 y(v)-5 b(ector)60 b Fn( )67 b Fp(as)60 b Fn(')40 b Fp(+)g Fn(\037)p Fp(,)60 b(with)h Fm(h)p Fn(';)30 b(\037)p Fm(i)50 b Fp(=)f(0)61 b(and)g Fn(')50 b Fm(6)p Fp(=)g(0)60 b(\(one)g(should)h (think)g(to)f Fn(')51 b Fp(=)f Fn(\037)5608 6923 y Fg(\012)5718 6895 y Fp(\()p Fn(H)15 b Fp(\))p Fn( )7 b Fp(\).)78 b(Th)-5 b(us)-94 7363 y Fn(B)44 7393 y Fl( )149 7363 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))166 b(=)f Fn(B)1270 7390 y Fl(')1370 7363 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))40 b(+)g Fn(B)2240 7390 y Fl(\037)2336 7363 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))40 b(+)3108 7240 y(2)p 3088 7322 132 8 v 3088 7488 a Fn(T)3269 7363 y Fp(Re)3514 7116 y Fi(Z)3696 7169 y Fk(1)3615 7528 y Fg(0)3945 7191 y Fi(X)3876 7593 y Fk(j)p Fl(n)p Fk(j\024)p Fl(N)4276 7363 y Fm(h)p Fp(e)4428 7288 y Fk(\000)p Fl(itH)4771 7363 y Fn(';)30 b(e)5056 7390 y Fl(n)5149 7363 y Fm(i)p 5220 7198 939 8 v(h)p Fp(e)5372 7311 y Fk(\000)p Fl(itH)5715 7363 y Fn(\037;)g(e)5995 7390 y Fl(n)6088 7363 y Fm(i)o Fn(h)p Fp(\()p Fn(t=T)25 b Fp(\)d)p Fn(t;)825 7963 y Fp(=)165 b Fm(\000)p Fn(B)1412 7990 y Fl(')1512 7963 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))40 b(+)g Fn(B)2382 7990 y Fl(\037)2477 7963 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))40 b(+)3249 7840 y(2)p 3229 7922 132 8 v 3229 8088 a Fn(T)3411 7963 y Fp(Re)3656 7716 y Fi(Z)3838 7768 y Fk(1)3757 8128 y Fg(0)4086 7791 y Fi(X)4017 8193 y Fk(j)p Fl(n)p Fk(j\024)p Fl(N)4417 7963 y Fm(h)p Fp(e)4569 7888 y Fk(\000)p Fl(itH)4912 7963 y Fn(';)30 b(e)5197 7990 y Fl(n)5291 7963 y Fm(i)p 5362 7798 950 8 v(h)p Fp(e)5514 7911 y Fk(\000)p Fl(itH)5856 7963 y Fn( )7 b(;)30 b(e)6148 7990 y Fl(n)6240 7963 y Fm(i)p Fn(h)p Fp(\()p Fn(t=T)25 b Fp(\)d)p Fn(t:)-201 8567 y Fp(Then,)83 b(taking)c(in)-5 b(to)80 b(accoun)-5 b(t)78 b(that)g(1)p Fn(=T)2760 8421 y Fi(R)2881 8473 y Fk(1)2845 8631 y Fg(0)3061 8567 y Fn(h)p Fp(\()p Fn(t=T)25 b Fp(\)dt)80 b(=)g(1)f(and)g Fn(h)p Fp(\()p Fn(z)8 b Fp(\))80 b Fm(\025)h Fp(0,)i(w)-5 b(e)79 b(ha)-5 b(v)g(e)78 b Fn(B)6341 8594 y Fl(\037)6437 8567 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))81 b Fm(\024)-201 8793 y(k)p Fn(\037)p Fm(k)95 8727 y Fg(2)224 8793 y Fp(=)50 b Fm(k)p Fn( )7 b Fm(k)724 8727 y Fg(2)842 8793 y Fm(\000)40 b(k)p Fn(')p Fm(k)1325 8727 y Fg(2)1404 8793 y Fp(.)80 b(Let)60 b Fn(A)51 b Fp(=)2239 8656 y Fi(P)2431 8847 y Fk(j)p Fl(n)p Fk(j\024)p Fl(N)2840 8793 y Fm(h\001)p Fn(;)30 b(e)3128 8820 y Fl(n)3220 8793 y Fm(i)p Fn(e)3376 8820 y Fl(n)3470 8793 y Fp(.)80 b(Then)1755 9247 y Fn(B)1893 9277 y Fl( )1999 9247 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))50 b Fm(\024)g(k)p Fn( )7 b Fm(k)3059 9171 y Fg(2)3177 9247 y Fm(\000)40 b(k)p Fn(')p Fm(k)3660 9171 y Fg(2)3779 9247 y Fp(+)f(2Re)p Fn(D)4422 9151 y Fg(\()p Fl(h)p Fg(\))4417 9305 y Fl('; )4653 9247 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))p Fn(;)-201 9698 y Fp(where)73 b Fn(D)493 9602 y Fg(\()p Fl(h)p Fg(\))488 9757 y Fl('; )724 9698 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))72 b(w)-5 b(as)73 b(de\014ned)f(in)h(the)f(Theorem)f(3.2.)116 b(The)73 b(second)f(statemen)-5 b(t)69 b(of)j(this)h(Theorem)-201 9924 y(giv)-5 b(es)61 b(immediately)1636 10251 y Fn(B)1774 10281 y Fl( )1879 10251 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))50 b Fm(\024)g(k)p Fn( )7 b Fm(k)2939 10176 y Fg(2)3057 10251 y Fm(\000)40 b(k)p Fn(')p Fm(k)3540 10176 y Fg(2)3659 10251 y Fp(+)g Fn(C)13 b(N)4170 10121 y Fh(d)p 4170 10145 65 6 v 4172 10228 a Fd(2)4292 10049 y Fi(\020)4401 10251 y Fn(U)4545 10155 y Fg(\()p Fl(h)p Fg(\))4525 10309 y Fl('; )4761 10251 y Fp(\()p Fn(T)25 b Fp(\))5034 10049 y Fi(\021)5163 10040 y Fd(1)p 5163 10064 61 6 v 5163 10146 a(2)5282 10251 y Fn(;)1372 b Fp(\(3.16\))-201 10606 y(where,)60 b(as)h(in)g(Theorem)e(3.2,)1671 11060 y Fn(U)1815 10964 y Fg(\()p Fl(h)p Fg(\))1795 11118 y Fl('; )2031 11060 y Fp(\()p Fn(T)25 b Fp(\))51 b(=)2546 10812 y Fi(Z)2647 11225 y Fj(R)2782 10812 y Fi(Z)2883 11225 y Fj(R)3018 11060 y Fp(d)p Fn(\026)3229 11087 y Fl(')3328 11060 y Fp(\()p Fn(x)p Fp(\)d)p Fn(\026)3785 11090 y Fl( )3890 11060 y Fp(\()p Fn(y)7 b Fp(\))p Fm(j)4181 11012 y Fp(^)4179 11060 y Fn(h)n Fp(\(\()p Fn(x)40 b Fm(\000)g Fn(y)7 b Fp(\))p Fn(T)25 b Fp(\))p Fm(j)5170 10985 y Fg(2)5247 11060 y Fn(:)3393 11631 y Fp(12)p eop %%Page: 13 13 13 12 bop -201 1158 a Fp(As)57 b Fm(j)117 1110 y Fp(^)115 1158 y Fn(h)o Fp(\()p Fn(w)5 b Fp(\))p Fm(j)49 b(\024)h Fp(1)57 b(for)e(all)j Fn(w)j Fp(and)56 b(b)-5 b(y)57 b(de\014nition)f(\(3.5\))f(of)h Fn(R)q Fp(,)h(w)-5 b(e)57 b(clearly)g(ha)-5 b(v)g(e)56 b Fn(R)q Fp(\()p Fn(w)5 b Fp(\))50 b Fm(\025)g(j)5897 1110 y Fp(^)5895 1158 y Fn(h)o Fp(\()p Fn(w)5 b Fp(\))p Fm(j)6327 1092 y Fg(2)6461 1158 y Fp(for)56 b(all)i Fn(w)5 b Fp(.)-201 1416 y(Therefore)58 b Fn(U)765 1320 y Fg(\()p Fl(h)p Fg(\))745 1475 y Fl('; )982 1416 y Fp(\()p Fn(T)25 b Fp(\))50 b Fm(\024)g Fn(U)1621 1446 y Fl('; )1858 1416 y Fp(\()p Fn(T)25 b Fp(\),)58 b(and)g(the)g(estimate)d(\(3.16\))i(is)i(v)-10 b(alid)59 b(with)f Fn(U)5303 1446 y Fl('; )5540 1416 y Fp(\()p Fn(T)25 b Fp(\))58 b(de\014ned)g(b)-5 b(y)58 b(\(3.4\),)-201 1691 y(that)i(is)h(with)g(the)f(function)g Fn(R)i Fp(instead)f(of)f Fm(j)2903 1643 y Fp(^)2901 1691 y Fn(h)o Fm(j)3056 1625 y Fg(2)3134 1691 y Fp(.)81 1917 y(W)-15 b(e)53 b(are)g(no)-5 b(w)54 b(in)g(p)5 b(osition)53 b(to)g(\014nish)h(the)e(pro)5 b(of)53 b(of)g(Theorem)f(3.1.)77 b(The)53 b(basic)h(strategy)e(is)h (standard:)-201 2143 y(let)61 b Fn(N)80 b Fp(b)5 b(e)61 b(the)f(largest)g(in)-5 b(teger)61 b(suc)-5 b(h)60 b(that)g Fn(C)13 b(N)3151 2077 y Fl(d=)p Fg(2)3373 2143 y Fn(U)3497 2173 y Fl('; )3733 2143 y Fp(\()p Fn(T)25 b Fp(\))4026 2017 y Fd(1)p 4026 2041 61 6 v 4026 2123 a(2)4166 2143 y Fm(\024)50 b(k)p Fn(')p Fm(k)4659 2077 y Fg(2)4737 2143 y Fn(=)p Fp(2,)60 b(it)h(yields:)2448 2605 y Fn(B)2586 2635 y Fl( )2691 2605 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))50 b Fm(\024)g(k)p Fn( )7 b Fm(k)3751 2530 y Fg(2)3869 2605 y Fm(\000)4071 2482 y(k)p Fn(')p Fm(k)4372 2416 y Fg(2)p 4071 2564 380 8 v 4215 2730 a Fp(2)4470 2605 y Fn(:)2184 b Fp(\(3.17\))-201 2999 y(The)61 b(inequalities)h (\(3.17\))d(and)h(\(3.15\))g(yield)h(with)g(some)e(p)5 b(ositiv)-5 b(e)60 b(constan)-5 b(t)60 b Fn(C)13 b Fp(\()p Fn( )7 b(;)30 b(p;)g(h)p Fp(\):)902 3458 y Fm(hhj)p Fn(X)14 b Fm(j)1311 3383 y Fl(p)1388 3458 y Fm(ii)1530 3488 y Fl( )5 b(;T)1826 3458 y Fm(\025)50 b Fn(C)13 b Fp(\()p Fn( )7 b(;)30 b(p;)g(h)p Fp(\))2846 3335 y Fm(k)p Fn(')p Fm(k)3147 3269 y Fg(2+4)p Fl(\014)p 2808 3416 728 8 v 2808 3582 a Fn(U)2932 3612 y Fl('; )3166 3582 y Fp(\()p Fn(T)25 b Fp(\))3439 3530 y Fl(\014)3604 3458 y Fp(=)50 b Fn(C)13 b Fp(\()p Fn( )7 b(;)30 b(p;)g(h)p Fp(\))p Fn(L)4690 3488 y Fl( )4792 3458 y Fp(\()p Fn(';)g(T)25 b Fp(\))p Fn(;)211 b(\014)60 b Fp(=)5904 3335 y Fn(p)p 5902 3416 95 8 v 5902 3582 a(d)6016 3458 y(:)638 b Fp(\(3.18\))-201 3907 y(One)65 b(reco)-5 b(v)g(ers)66 b Fn(L)1012 3937 y Fl( )1117 3907 y Fp(\()p Fn(';)30 b(T)25 b Fp(\))66 b(as)f(giv)-5 b(en)66 b(Line)g(\(3.3\).)96 b(It)65 b(is)h(this)g (latter)g(lo)-5 b(w)g(er)67 b(b)5 b(ound)66 b(that)f(will)j(b)5 b(e)66 b(used)g(in)-201 4132 y(the)e(pro)5 b(of)65 b(of)f(the)g(lo)-5 b(w)g(er)66 b(b)5 b(ound)64 b(in)h(Theorem)f(4.1.)92 b(Ho)-5 b(w)g(ev)g(er,)65 b(in)g(the)g(more)e(general)i(case)f(where)g Fn(')h Fp(is)-201 4358 y(an)-5 b(y)61 b(function)f(of)g Fm(H)i Fp(with)f Fm(h)p Fn( )7 b(;)30 b(')p Fm(i)49 b(6)p Fp(=)g(0,)60 b(one)h(gets)f(the)g(b)5 b(ound)60 b(with)2388 4817 y Fn(L)2512 4847 y Fl( )2617 4817 y Fp(\()p Fn(';)30 b(T)25 b Fp(\))50 b(:=)3500 4694 y Fm(jh)p Fn(';)30 b( )7 b Fm(ij)4070 4628 y Fg(2+2)p Fl(\014)p 3403 4775 1108 8 v 3403 4942 a Fm(k)p Fn(')p Fm(k)3704 4889 y Fg(2)3782 4942 y Fn(U)3906 4972 y Fl('; )4143 4942 y Fp(\()p Fn(T)25 b Fp(\))4416 4889 y Fl(\014)4530 4817 y Fn(:)2124 b Fp(\(3.19\))-201 5281 y(Indeed)67 b(tak)-5 b(e)66 b(suc)-5 b(h)66 b(a)h Fn(')p Fp(,)i(and)e(then)f(de\014ne)h(as)g(in)g([5)o(])96 b(~)-120 b Fn(')61 b Fp(=)g(\()p Fm(h)p Fn(';)30 b( )7 b Fm(ik)p Fn(')p Fm(k)4852 5215 y Fk(\000)p Fg(2)5038 5281 y Fp(\))p Fn(')p Fp(;)70 b(one)c(th)-5 b(us)67 b(c)-5 b(hec)g(ks)66 b(that)g(if)-201 5507 y Fn(\037)53 b Fp(=)g Fn( )47 b Fm(\000)70 b Fp(~)-120 b Fn(')p Fp(,)62 b(then)g Fm(h)29 b Fp(~)-120 b Fn(')o(;)30 b(\037)p Fm(i)53 b Fp(=)f(0)63 b(and)f(one)g(is)g(able)g(to)g(apply)h(the)f(result)g(line) h(\(3.3\))e(to)h Fn( )68 b Fp(and)91 b(~)-120 b Fn(')p Fp(.)85 b(T)-15 b(aking)-201 5733 y(in)-5 b(to)65 b(accoun)-5 b(t)64 b(that)g Fm(k)29 b Fp(~)-120 b Fn(')p Fm(k)58 b Fp(=)f Fm(jh)p Fn(';)30 b( )7 b Fm(ijk)p Fn(')p Fm(k)2675 5667 y Fk(\000)p Fg(1)2925 5733 y Fp(and)65 b(that)f Fn(U)3827 5763 y Fg(~)-93 b Fl('; )4042 5733 y Fp(\()p Fn(T)25 b Fp(\))57 b(=)h Fm(jh)p Fn(';)30 b( )7 b Fm(ij)5142 5667 y Fg(2)5218 5733 y Fm(k)p Fn(')p Fm(k)5519 5667 y Fk(\000)p Fg(4)5707 5733 y Fn(U)5831 5763 y Fl('; )6068 5733 y Fp(\()p Fn(T)25 b Fp(\),)65 b(one)g(\014nds)-201 5959 y(the)52 b(announced)f(expression)h(\(3.19\).)76 b(T)-15 b(o)52 b(optimize)e(the)i(lo)-5 b(w)g(er)53 b(b)5 b(ound,)53 b(w)-5 b(e)52 b(should)g(tak)-5 b(e)51 b(the)h(suprem)-5 b(um)-201 6185 y(of)72 b Fn(L)142 6215 y Fl( )247 6185 y Fp(\()p Fn(';)30 b(T)25 b Fp(\))72 b(for)g(a)g(giv)-5 b(en)72 b Fn(T)98 b Fp(o)-5 b(v)g(er)72 b(all)h(p)5 b(ossible)73 b Fn(')p Fp(.)115 b(One)72 b(can)g(sho)-5 b(w)72 b(in)g(the)g(same)e (manner)h(as)h(in)h([5)o(],)-201 6410 y(Lemma)c(3.1,)75 b(that)d(it)h(is)g(su\016cien)-5 b(t)72 b(to)g(tak)-5 b(e)73 b Fn(')f Fp(only)i(from)d(the)h(cyclic)h(subspace)f Fm(H)5839 6440 y Fl( )5944 6410 y Fp(.)117 b(This)73 b(giv)-5 b(es)73 b(us)-201 6636 y Fn(L)-77 6666 y Fl( )28 6636 y Fp(\()p Fn(T)25 b Fp(\))61 b(de\014ned)f(line)h(\(3.2\).)5271 b Fc(\003)-201 7276 y Fo(4)270 b(T)-22 b(o)-7 b(w)g(ards)89 b(the)g(fractal)g(dimensions)-201 7682 y Fp(This)74 b(section)g(deals)f (with)i(the)e(connection)g(b)5 b(et)-5 b(w)g(een)73 b(the)h(dynamic)e (quan)-5 b(tit)g(y)73 b Fn(L)5643 7712 y Fl( )5748 7682 y Fp(\()p Fn(T)25 b Fp(\))74 b(in)-5 b(tro)5 b(duced)74 b(in)-201 7908 y(the)69 b(previous)h(section,)h(and)f(the)f(fractal)g (dimensions)f(de\014ned)i(in)g(Section)f(2,)j(called)e(the)f (generalized)-201 8133 y(fractal)60 b(dimensions.)-201 8437 y(W)-15 b(e)60 b(shall)i(pro)-5 b(v)g(e)-201 8756 y Fe(Theorem)68 b(4.1.)90 b Fq(L)-9 b(et)59 b Fn(H)74 b Fq(b)-9 b(e)58 b(a)h(self-adjoint)f(op)-9 b(er)g(ator)57 b(on)i Fm(H)r Fq(,)h(and)f(let)f Fn( )65 b Fq(b)-9 b(e)58 b(a)h(ve)-9 b(ctor)58 b(in)h Fm(H)r Fq(,)g Fm(k)p Fn( )7 b Fm(k)6653 8784 y Fk(H)6831 8756 y Fp(=)50 b(1)p Fq(.)-201 8982 y(Assume)65 b Fe(\(H\))p Fq(,)g(namely)f(the)h(sp)-9 b(e)g(ctr)g(al)64 b(me)-9 b(asur)g(e)62 b Fn(\026)3316 9012 y Fl( )3486 8982 y Fq(asso)-9 b(ciate)g(d)65 b(to)g Fn( )71 b Fq(is)65 b(such)g(that)2157 9323 y Fn(D)2313 9248 y Fk(\006)2308 9368 y Fl(\026)2393 9391 y Fh( )2494 9323 y Fp(\()p Fn(s)p Fp(\))50 b Fn(<)g Fp(+)p Fm(1)130 b Fp(for)64 b(an)-5 b(y)68 b Fn(s)50 b Fm(2)h Fp(\(0)p Fn(;)30 b Fp(1\))p Fn(:)-201 9665 y Fq(Then,)65 b(for)f(al)9 b(l)65 b Fn(\014)59 b(>)50 b Fp(0)p Fq(,)65 b(ther)-9 b(e)64 b(exists)i(a)f(c)-9 b(onstant)66 b Fn(C)3410 9692 y Fg(1)3539 9665 y Fn(>)50 b Fp(0)65 b Fq(such)g(that,)g(for)f(al)9 b(l)65 b Fn(")50 b(>)g Fp(0)p Fq(:)1323 10013 y Fn(C)1453 10040 y Fg(1)p 1050 10094 756 8 v 1050 10261 a Fm(j)30 b Fp(log)j Fn(")p Fm(j)1532 10208 y Fg(1+)p Fl(\014)1825 10136 y Fn(K)1980 10163 y Fl(\026)2065 10186 y Fh( )2197 9880 y Fi(\022)2518 10013 y Fp(1)p 2351 10094 426 8 v 2351 10261 a(1)40 b(+)g Fn(\014)2796 10136 y(;)30 b(")2962 9880 y Fi(\023)3096 9925 y Fg(1+)p Fl(\014)3421 10136 y Fm(\024)50 b Fn(L)3737 10166 y Fl( )3842 10136 y Fp(\()p Fn(")3998 10061 y Fk(\000)p Fg(1)4186 10136 y Fp(\))g Fm(\024)g Fn(K)4654 10163 y Fl(\026)4739 10186 y Fh( )4870 9880 y Fi(\022)5192 10013 y Fp(1)p 5024 10094 V 5024 10261 a(1)41 b(+)e Fn(\014)5470 10136 y(;)30 b(")5636 9880 y Fi(\023)5769 9925 y Fg(1+)p Fl(\014)6074 10136 y Fn(;)671 b Fp(\(4.1\))-201 10567 y Fq(wher)-9 b(e)917 10926 y Fn(K)1072 10953 y Fl(\026)1157 10976 y Fh( )1289 10669 y Fi(\022)1610 10803 y Fp(1)p 1443 10884 V 1443 11050 a(1)40 b(+)g Fn(\014)1888 10926 y(;)30 b(")2054 10669 y Fi(\023)2238 10926 y Fp(=)2430 10678 y Fi(Z)2531 11090 y Fg(supp)q Fl(\026)2907 11113 y Fh( )3039 10926 y Fp(d)p Fn(\026)3250 10956 y Fl( )3355 10926 y Fp(\()p Fn(x)p Fp(\))3631 10669 y Fi(\022)3764 10678 y(Z)3865 11090 y Fj(R)4000 10926 y Fp(d)p Fn(\026)4211 10956 y Fl( )4316 10926 y Fp(\(y\)R\(\(x)39 b Fm(\000)h Fp(y\))p Fn(=")p Fp(\))5561 10669 y Fi(\023)5742 10653 y Fb(\000)p Fh(\014)p 5713 10684 229 6 v 5713 10767 a Fd(1+)p Fh(\014)6001 10926 y Fn(:)3393 11631 y Fp(13)p eop %%Page: 14 14 14 13 bop -201 1158 a Fp(This)61 b(will)i(actually)e(imply)-201 1480 y Fe(Theorem)68 b(4.2.)90 b Fq(Under)65 b(the)g(same)g(hyp)-9 b(othesis)65 b Fp(\(H\))g Fq(as)g(pr)-9 b(eviously,)63 b(one)i(has)472 1923 y Fp(lim)30 b(inf)532 2044 y Fl(T)20 b Fk(!1)1027 1797 y Fp(log)33 b Fn(L)1416 1827 y Fl( )1521 1797 y Fp(\()p Fn(T)25 b Fp(\))p 1027 1881 768 8 v 1212 2048 a(log)33 b Fn(T)1864 1923 y Fp(=)50 b Fn(\014)10 b(D)2325 1848 y Fk(\000)2320 1968 y Fl(\026)2405 1991 y Fh( )2536 1667 y Fi(\022)2857 1800 y Fp(1)p 2690 1881 426 8 v 2690 2048 a(1)40 b(+)g Fn(\014)3135 1667 y Fi(\023)3299 1923 y Fn(;)216 b Fp(lim)30 b(sup)3652 2080 y Fl(T)20 b Fk(!1)4173 1797 y Fp(log)33 b Fn(L)4562 1827 y Fl( )4667 1797 y Fp(\()p Fn(T)25 b Fp(\))p 4173 1881 768 8 v 4358 2048 a(log)33 b Fn(T)5010 1923 y Fp(=)50 b Fn(\014)10 b(D)5471 1848 y Fg(+)5466 1968 y Fl(\026)5551 1991 y Fh( )5682 1667 y Fi(\022)6003 1800 y Fp(1)p 5836 1881 426 8 v 5836 2048 a(1)40 b(+)g Fn(\014)6282 1667 y Fi(\023)6446 1923 y Fn(:)-201 2369 y Fe(Remark)69 b(4.1.)90 b Fp(i\))69 b(W)-15 b(e)69 b(p)5 b(oin)-5 b(t)69 b(out)f(that)g(the)h(\014rst)f (inequalit)-5 b(y)70 b(in)f(\(4.1\),)g(that)g(is)g(the)f(lo)-5 b(w)g(er)70 b(b)5 b(ound)68 b(on)-201 2594 y Fn(L)-77 2624 y Fl( )28 2594 y Fp(\()p Fn(")184 2528 y Fk(\000)p Fg(1)372 2594 y Fp(\),)c(is)h(su\016cien)-5 b(t)63 b(to)g(pro)-5 b(v)g(e)64 b(our)g(main)f(result)h(Theorem)e(2.1.)90 b(Ho)-5 b(w)g(ev)g(er)64 b(the)f(righ)-5 b(t)65 b(side)f(of)f(\(4.1\),) -201 2820 y(that)73 b(is)h(the)f(upp)5 b(er)74 b(b)5 b(ound,)76 b(is)e(of)g(in)-5 b(terest)73 b(to)5 b(o.)119 b(In)73 b(particular)h(it)g(sa)-5 b(ys)73 b(that)g(once)g(one)h(deriv) -5 b(ed)74 b(the)-201 3046 y(lo)-5 b(w)g(er)70 b(b)5 b(ound)69 b Fn(L)976 3076 y Fl( )1081 3046 y Fp(\()p Fn(T)25 b Fp(\),)71 b(one)e(cannot)f(hop)5 b(e)69 b(a)g(b)5 b(etter)69 b(result)g(than)f(the)h(one)g(w)-5 b(e)69 b(stated.)105 b(W)-15 b(e)68 b(shall)i(also)-201 3272 y(tak)-5 b(e)60 b(adv)-10 b(an)-5 b(tage)60 b(of)g(the)g(righ)-5 b(t)61 b(part)f(in)h(\(4.1\))f(in)h(App)5 b(endix)61 b(B,)f(Theorem)f(B.3.)-201 3498 y(ii\))65 b(Note)e(that)g(the)h(pro)5 b(of)63 b(of)g(the)h(righ)-5 b(t-hand-side)63 b(inequalit)-5 b(y)65 b(in)f(\(4.1\),)f(that)g(is)h(the)f(upp)5 b(er)64 b(b)5 b(ound,)64 b(is)-201 3723 y(true)d(for)f(an)-5 b(y)60 b(measures)f Fn(\026)1696 3753 y Fl( )1800 3723 y Fp(.)-201 3949 y(iii\))j(In)e(App)5 b(endix)62 b(C)f(w)-5 b(e)60 b(sho)-5 b(w)61 b(that)f(\(H\))g(holds)h(for)f(all)i(measures)c (v)-5 b(erifying)61 b(the)f(condition)2038 4129 y Fi(Z)2139 4541 y Fj(R)2273 4377 y Fm(j)p Fn(x)p Fm(j)2479 4302 y Fl(\025)2569 4377 y Fp(d)p Fn(\026)2780 4407 y Fl( )2885 4377 y Fp(\()p Fn(x)p Fp(\))49 b Fn(<)h Fp(+)p Fm(1)121 b Fp(for)60 b(an)-5 b(y)63 b Fn(\025)51 b(>)e Fp(0)p Fn(:)1865 b Fp(\(4.2\))-201 4822 y(This)68 b(is)g(true,)g(in)g (particular,)h(if)f Fn(\026)2255 4852 y Fl( )2427 4822 y Fp(has)f(a)h(compact)d(supp)5 b(ort.)100 b(Moreo)-5 b(v)g(er,)68 b(if)f(\(4.2\))g(holds,)h Fn(D)6578 4756 y Fk(\006)6573 4867 y Fl(\026)6658 4890 y Fh( )6760 4822 y Fp(\()p Fn(s)p Fp(\))61 b Fm(2)-201 5048 y Fp([0)p Fn(;)30 b Fp(1])59 b(for)i(an)-5 b(y)60 b Fn(s)51 b Fm(2)g Fp(\(0)p Fn(;)30 b Fp(1\).)81 5369 y(W)-15 b(e)80 b(start)g(b)-5 b(y)80 b(pro)-5 b(viding)82 b(a)e(pro)5 b(of)80 b(for)g(Theorem)f(4.1.) 139 b(Throughout)81 b(this)f(section,)k(in)-5 b(tegrations)-201 5595 y(m)g(ust)59 b(b)5 b(e)60 b(systematically)f(understo)5 b(o)g(d)60 b(on)h(the)f(supp)5 b(ort)60 b(of)g(the)g(measure)f Fn(\026)5210 5625 y Fl( )5375 5595 y Fp(or)i Fn(\026)5708 5622 y Fl(')5868 5595 y Fp(w)-5 b(e)61 b(consider.)-201 5899 y Fe(Pro)6 b(of)69 b(of)g(the)h(upp)6 b(er)70 b(b)6 b(ound)69 b(in)h(Theorem)e(4.1.)81 6203 y Fp(The)86 b(upp)5 b(er)86 b(b)5 b(ound)85 b(of)g(\(4.1\))g(in)h(Theorem)e(4.1)h(will)i(b) 5 b(e)86 b(pro)-5 b(v)g(ed,)91 b(if)85 b(taking)h(an)-5 b(y)85 b(function)g Fn(f)112 b Fm(2)-201 6428 y Fp(L)-87 6362 y Fg(2)-8 6428 y Fp(\()p Ff(R)26 b Fn(;)k Fp(d)p Fn(\026)477 6458 y Fl( )590 6428 y Fp(\),)60 b(one)h(sho)-5 b(ws)641 6922 y Fn(L)765 6952 y Fl( )870 6922 y Fp(\()p Fn(f)20 b Fp(\()p Fn(H)15 b Fp(\))p Fn( )7 b(;)30 b(")1650 6847 y Fk(\000)p Fg(1)1836 6922 y Fp(\))50 b Fm(\024)g Fn(K)2304 6949 y Fl(\026)2389 6972 y Fh( )2520 6665 y Fi(\022)2842 6799 y Fp(1)p 2674 6880 V 2674 7046 a(1)41 b(+)e Fn(\014)3120 6922 y(;)30 b(")3286 6665 y Fi(\023)3419 6711 y Fg(1+)p Fl(\014)3744 6922 y Fp(=)3936 6665 y Fi(\022)4070 6674 y(Z)4282 6922 y Fp(d)p Fn(\026)4493 6952 y Fl( )4598 6922 y Fp(\(x\)b)4937 6847 y Fg(\(R\))5158 6922 y Fp(\(x)p Fn(;)g(")p Fp(\))5610 6769 y Fb(\000)p Fh(\014)p 5581 6800 229 6 v 5581 6883 a Fd(1+)p Fh(\014)5838 6665 y Fi(\023)5972 6711 y Fg(1+)p Fl(\014)6277 6922 y Fn(;)468 b Fp(\(4.3\))-201 7394 y(where)76 b Fn(b)418 7328 y Fg(\()p Fl(R)q Fg(\))643 7394 y Fp(\()p Fn(x;)30 b(")p Fp(\))74 b(=)1345 7248 y Fi(R)1496 7394 y Fp(d)p Fn(\026)1707 7424 y Fl( )1812 7394 y Fp(\()p Fn(y)7 b Fp(\))p Fn(R)q Fp(\(\()p Fn(x)49 b Fm(\000)h Fn(y)7 b Fp(\))p Fn(=")p Fp(\))p Fn(:)73 b Fp(This)j(result)f(will)i(follo)-5 b(w)76 b(from)e(Cauc)-5 b(h)g(y-Sc)g(h)g(w)g(arz)74 b(and)-201 7620 y(H\177)-91 b(older)62 b(Inequalities.)80 b(Pic)-5 b(k)61 b Fn(')50 b Fp(=)g Fn(f)20 b Fp(\()p Fn(H)15 b Fp(\))p Fn( )7 b Fp(,)58 b(with)j Fn(f)70 b Fm(2)51 b Fp(L)3711 7554 y Fg(2)3789 7620 y Fp(\()p Ff(R)26 b Fn(;)k Fp(d)p Fn(\026)4274 7650 y Fl( )4388 7620 y Fp(\).)80 b(Therefore)1387 8057 y(d)p Fn(\026)1598 8084 y Fl(')1698 8057 y Fp(\()p Fn(x)p Fp(\))50 b(=)g Fm(j)p Fn(f)20 b Fp(\()p Fn(x)p Fp(\))p Fm(j)2643 7982 y Fg(2)2720 8057 y Fp(d)p Fn(\026)2931 8087 y Fl( )3036 8057 y Fp(\()p Fn(x)p Fp(\))59 b(and)i Fm(h)p Fn(';)30 b( )7 b Fm(i)49 b Fp(=)4404 7810 y Fi(Z)4616 8057 y Fp(d)p Fn(\026)4827 8087 y Fl( )4932 8057 y Fp(\()p Fn(x)p Fp(\))p Fn(f)20 b Fp(\()p Fn(x)p Fp(\))p Fn(:)-201 8514 y Fp(Remem)-5 b(b)5 b(er)48 b(also)j(that)f Fn(U)1565 8544 y Fl('; )1802 8514 y Fp(\()p Fn(T)25 b Fp(\))50 b(=)2317 8368 y Fi(R)2469 8514 y Fp(d)p Fn(\026)2680 8541 y Fl(')2780 8514 y Fp(\()p Fn(x)p Fp(\))p Fn(b)3104 8448 y Fg(\()p Fl(R)q Fg(\))3328 8514 y Fp(\()p Fn(x;)30 b(")p Fp(\).)76 b(Then,)53 b(rewriting)f Fn(L)5278 8544 y Fl( )5383 8514 y Fp(\(\()p Fn(f)20 b Fp(\()p Fn(H)15 b Fp(\))p Fn( )7 b(;)30 b(")6234 8448 y Fk(\000)p Fg(1)6420 8514 y Fp(\))50 b(as)h(giv)-5 b(en)-201 8740 y(in)61 b(\(3.2\))f(one)g(gets)g(:)916 9248 y Fn(L)1040 9278 y Fl( )1145 9248 y Fp(\()p Fn(f)20 b Fp(\()p Fn(H)15 b Fp(\))p Fn( )7 b(;)30 b(")1925 9173 y Fk(\000)p Fg(1)2110 9248 y Fp(\))51 b(=)3481 8959 y Fi(\014)3481 9068 y(\014)3542 8967 y(R)3693 9114 y Fp(d)p Fn(\026)3904 9144 y Fl( )4009 9114 y Fp(\(x\)f\(x\))4541 8959 y Fi(\014)4541 9068 y(\014)4600 9012 y Fg(2+2)p Fl(\014)p 2443 9207 3540 8 v 2443 9275 a Fi(\000)2527 9276 y(R)2678 9423 y Fp(d)p Fn(\026)2889 9453 y Fl( )2994 9423 y Fp(\(x\))p Fm(j)p Fp(f\(x\))p Fm(j)3628 9370 y Fg(2)3704 9275 y Fi(\001)31 b(\000)3901 9276 y(R)4053 9423 y Fp(d)p Fn(\026)4264 9453 y Fl( )4369 9423 y Fp(\(x\))p Fm(j)p Fp(f\(x\))p Fm(j)5003 9370 y Fg(2)5079 9423 y Fp(b)5180 9370 y Fg(\(R\))5402 9423 y Fp(\(x)p Fn(;)f(")p Fp(\))5806 9275 y Fi(\001)5888 9321 y Fl(\014)6002 9248 y Fn(:)743 b Fp(\(4.4\))-201 9747 y(One)60 b(starts)f(with)i(a)f(Cauc)-5 b(h)g(y-Sc)g(h)g(w)g(arz)60 b(inequalit)-5 b(y)61 b(applied)g(to)f(the)g(n)-5 b(umerator,)58 b(and)i(to)g(the)g(functions)-201 10026 y Fn(b)-123 9960 y Fg(\()p Fl(R)q Fg(\))102 10026 y Fp(\()p Fn(x;)30 b(")p Fp(\))641 9868 y Fb(\000)p Fh(\014)p 533 9899 386 6 v 533 9982 a Fd(2\(1+)p Fh(\014)5 b Fd(\))1008 10026 y Fp(and)60 b Fn(f)20 b Fp(\()p Fn(x)p Fp(\))p Fn(b)1794 9960 y Fg(\()p Fl(R)q Fg(\))2018 10026 y Fp(\()p Fn(x;)30 b(")p Fp(\))2605 9868 y Fh(\014)p 2449 9899 V 2449 9982 a Fd(2\(1+)p Fh(\014)5 b Fd(\))2863 10026 y Fp(.)80 b(It)60 b(yields:)-16 10246 y Fi(\014)-16 10355 y(\014)-16 10464 y(\014)-16 10573 y(\014)44 10262 y(Z)256 10509 y Fp(d)p Fn(\026)467 10539 y Fl( )572 10509 y Fp(\(x\)f\(x\))1104 10246 y Fi(\014)1104 10355 y(\014)1104 10464 y(\014)1104 10573 y(\014)1163 10298 y Fg(2+2)p Fl(\014)1614 10509 y Fm(\024)1861 10253 y Fi(\022)1995 10262 y(Z)2207 10509 y Fp(d)p Fn(\026)2418 10539 y Fl( )2523 10509 y Fp(\(x\)b)2862 10434 y Fg(\(R\))3083 10509 y Fp(\(x)p Fn(;)30 b(")p Fp(\))3535 10357 y Fb(\000)p Fh(\014)p 3506 10388 229 6 v 3506 10470 a Fd(1+)p Fh(\014)3763 10253 y Fi(\023)3897 10298 y Fg(1+)p Fl(\014)4171 10253 y Fi(\022)4305 10262 y(Z)4517 10509 y Fp(d)p Fn(\026)4728 10539 y Fl( )4833 10509 y Fp(\(x\)b)5172 10434 y Fg(\(R\))5393 10509 y Fp(\(x)p Fn(;)g(")p Fp(\))5893 10357 y Fh(\014)p 5816 10388 V 5816 10470 a Fd(1+)p Fh(\014)6073 10509 y Fm(j)p Fp(f\(x\))p Fm(j)6469 10434 y Fg(2)6546 10253 y Fi(\023)6680 10298 y Fg(1+)p Fl(\014)6796 10509 y Fp(\(4.5\))1614 11052 y(=)105 b Fn(K)2016 11079 y Fl(\026)2101 11102 y Fh( )2232 10795 y Fi(\022)2553 10929 y Fp(1)p 2386 11010 426 8 v 2386 11177 a(1)40 b(+)g Fn(\014)2831 11052 y(;)30 b(")2997 10795 y Fi(\023)3131 10841 y Fg(1+)p Fl(\014)3436 10795 y Fi(\022)3570 10804 y(Z)3782 11052 y Fp(d)p Fn(\026)3993 11082 y Fl( )4098 11052 y Fp(\(x\)b)4437 10977 y Fg(\(R\))4658 11052 y Fp(\(x)p Fn(;)g(")p Fp(\))5158 10899 y Fh(\014)p 5081 10931 229 6 v 5081 11013 a Fd(1+)p Fh(\014)5338 11052 y Fm(j)p Fp(f\(x\))p Fm(j)5734 10977 y Fg(2)5811 10795 y Fi(\023)5944 10841 y Fg(1+)p Fl(\014)6249 11052 y Fn(:)3393 11631 y Fp(14)p eop %%Page: 15 15 15 14 bop -201 1158 a Fp(An)90 b(H\177)-91 b(older)91 b(inequalit)-5 b(y)90 b(applied)h(to)e(the)g(last)h(term,)95 b(and)89 b(with)i(the)e(co)5 b(e\016cien)-5 b(ts)88 b Fn(p)99 b Fp(=)f(1)60 b(+)f Fn(\014)99 b Fp(and)-201 1384 y Fn(p)-109 1318 y Fk(0)-12 1384 y Fp(=)50 b(\(1)40 b(+)g Fn(\014)10 b Fp(\))p Fn(=\014)g Fp(,)58 b(leads)j(to:)1271 1676 y Fi(\022)1405 1685 y(Z)1617 1932 y Fp(d)p Fn(\026)1828 1962 y Fl( )1933 1932 y Fp(\(x\)b)2272 1857 y Fg(\(R\))2494 1932 y Fp(\(x)p Fn(;)30 b(")p Fp(\))2993 1780 y Fh(\014)p 2916 1811 229 6 v 2916 1893 a Fd(1+)p Fh(\014)3173 1932 y Fm(j)p Fp(f\(x\))p Fm(j)3569 1857 y Fg(2)3646 1676 y Fi(\023)3780 1721 y Fg(1+)p Fl(\014)1437 2498 y Fp(=)1745 2242 y Fi(\022)1879 2251 y(Z)2091 2498 y Fp(d)p Fn(\026)2302 2528 y Fl( )2407 2498 y Fp(\(x\)\()p Fm(j)p Fp(f\(x\))p Fm(j)3112 2423 y Fg(2)3188 2498 y Fp(\))3362 2353 y Fd(1)p 3278 2377 V 3278 2459 a(1+)p Fh(\014)3566 2296 y Fi(\020)3674 2498 y Fm(j)p Fp(f\(x\))p Fm(j)4070 2423 y Fg(2)4147 2498 y Fp(b)4248 2423 y Fg(\(R\))4470 2498 y Fp(\(x)p Fn(;)g(")p Fp(\))4874 2296 y Fi(\021)5078 2280 y Fh(\014)p 5001 2312 V 5001 2394 a Fd(1+)p Fh(\014)5258 2242 y Fi(\023)5392 2264 y Fg(1+)p Fl(\014)1437 3041 y Fm(\024)1745 2784 y Fi(\022)1879 2793 y(Z)2091 3041 y Fp(d)p Fn(\026)2302 3071 y Fl( )2407 3041 y Fp(\(x\))p Fm(j)p Fp(f\(x\))p Fm(j)3041 2966 y Fg(2)3117 2784 y Fi(\023)g(\022)3415 2793 y(Z)3627 3041 y Fp(d)p Fn(\026)3838 3071 y Fl( )3943 3041 y Fp(\(x\))p Fm(j)p Fp(f\(x\))p Fm(j)4577 2966 y Fg(2)4653 3041 y Fp(b)4754 2966 y Fg(\(R\))4976 3041 y Fp(\(x)p Fn(;)g(")p Fp(\))5380 2784 y Fi(\023)5513 2830 y Fl(\014)5637 3041 y Fn(:)1108 b Fp(\(4.6\))-201 3549 y(One)60 b(th)-5 b(us)60 b(reco)-5 b(v)g(ers)60 b(exactly)g(the)g(denominator)f(term,)g(and)h(\(4.3\))g(holds.)2011 b Fc(\003)-201 4024 y Fe(Remark)69 b(4.2.)-201 4250 y Fp(W)-15 b(e)46 b(stress)g(the)g(v)-5 b(ery)47 b(strong)f(link)i(that)e (comes)e(out)i(b)5 b(et)-5 b(w)g(een)47 b Fn(L)4180 4280 y Fl( )4285 4250 y Fp(\()p Fn(")4441 4184 y Fk(\000)p Fg(1)4629 4250 y Fp(\))f(and)h(the)f(in)-5 b(tegral)47 b Fn(K)6188 4277 y Fl(\026)6273 4300 y Fh( )6374 4250 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))46 b(with)-201 4476 y(the)68 b(particular)i(v)-10 b(alue)69 b Fn(q)h Fp(=)64 b(1)p Fn(=)p Fp(\(1)45 b(+)g Fn(\014)10 b Fp(\).)104 b(The)69 b(same)e(app)5 b(ears)68 b(to)g(hold)h(with)h(the)e(other)g (lo)-5 b(w)g(er)70 b(b)5 b(ounds)-201 4701 y Fn(L)-77 4728 y Fg(1)2 4701 y Fp(\()p Fn(T)25 b Fp(\))81 b(and)f Fn(L)853 4728 y Fg(2)932 4701 y Fp(\()p Fn(T)25 b Fp(\))81 b(de\014ned)f(in)i(App)5 b(endix)81 b(B)g(and)g(coming)e(from)g(the)i (former)e(approac)-5 b(hes)80 b(\(G-C-L)-201 4927 y(and)57 b(BT\).)g(This)g(sho)-5 b(ws)57 b(ho)-5 b(w)57 b(relev)-10 b(an)-5 b(t)57 b(are)g(the)g(fractal)f(dimensions)g Fn(D)4838 4861 y Fk(\006)4833 4972 y Fl(\026)4956 4927 y Fp(\()p Fn(q)7 b Fp(\))56 b(with)i(regards)e(to)h(the)g(time)-201 5153 y(b)5 b(eha)-5 b(viour)61 b(of)f(the)g(quan)-5 b(tities)61 b(that)f(ha)-5 b(v)g(e)60 b(b)5 b(een)60 b(studied)h(for)f(man)-5 b(y)59 b(y)-5 b(ears)60 b(in)h(quan)-5 b(tum)59 b(dynamics.)81 5628 y(W)-15 b(e)63 b(no)-5 b(w)62 b(turn)h(to)f(the)g(second)g(and)g (main)g(part)g(of)g(Theorem)g(4.1,)f(that)h(is)h(the)f(lo)-5 b(w)g(er)63 b(b)5 b(ound.)87 b(Our)-201 5854 y(basic)62 b(strategy)g(to)g(get)f(the)h(lo)-5 b(w)g(er)63 b(b)5 b(ound)62 b(in)h(\(4.1\))e(is)i(to)f(estimate)e(the)h(quan)-5 b(tit)g(y)62 b Fn(L)5800 5884 y Fl( )5905 5854 y Fp(\()p Fn(';)30 b(T)25 b Fp(\))62 b(in)h(\(3.19\),)-201 6080 y(with)86 b(a)f(v)-5 b(ector)85 b Fn(')92 b Fp(=)f Fn(\037)1543 6117 y Fg(\012\()p Fl(r)t Fg(\))1830 6080 y Fp(\()p Fn(H)15 b Fp(\))p Fn( )7 b Fp(.)153 b(And)86 b(\012\()p Fn(r)5 b Fp(\))85 b(will)i(b)5 b(e)85 b(a)h(\\thin")f(set)g(of)f(the)h(form)f (\012\()p Fn(r)5 b Fp(\))91 b(=)h Fm(f)p Fn(x)f Fm(2)-201 6332 y Fp(supp)p Fn(\026)284 6362 y Fl( )451 6332 y Fm(j)61 b Fn(")648 6266 y Fl(r)t Fg(+)p Fl(A=)-8 b(N)1181 6332 y Fn(<)52 b(b)1453 6266 y Fg(\()p Fl(R)q Fg(\))1678 6332 y Fp(\()p Fn(x;)30 b(")p Fp(\))51 b Fm(\024)h Fn(")2420 6266 y Fl(r)2496 6332 y Fm(g)p Fp(,)62 b(but)f(whic)-5 b(h)63 b(supp)5 b(orts,)61 b(roughly)h(sp)5 b(eaking,)62 b(a)g(signi\014can)-5 b(t)61 b(part)-201 6558 y(of)51 b(the)h(mass)d(of)j(the)f(in)-5 b(tegral)52 b Fn(K)2050 6585 y Fl(\026)2135 6608 y Fh( )2236 6558 y Fp(\(1)p Fn(=)p Fp(\(1)23 b(+)g Fn(\014)10 b Fp(\))p Fn(;)30 b(")p Fp(\).)74 b(The)52 b(constan)-5 b(t)51 b Fn(A)p Fp(\()p Fn(q)7 b Fp(\))51 b(is)h(\014xed)f(b)-5 b(y)52 b(Lemma)c(4.1)j(b)5 b(elo)-5 b(w.)-201 6784 y(The)79 b(in)-5 b(teger)79 b Fn(N)99 b Fp(will)81 b(stand)e(for)g(the)f(in)-5 b(teger)79 b(part)g(of)g(log)33 b Fn(T)25 b Fp(.)136 b(Before)78 b(going)i(on)f(with)g(the)g(pro)5 b(of)79 b(of)-201 7010 y(Theorem)59 b(4.1,)h(w)-5 b(e)61 b(need)f(the)g(t)-5 b(w)g(o)60 b(follo)-5 b(wing)62 b(lemmas:)-201 7385 y Fe(Lemma)68 b(4.1.)90 b Fq(L)-9 b(et)67 b Fn(q)61 b Fm(2)54 b Fp(\(0)p Fn(;)30 b Fp(1\))p Fq(,)66 b(and)i(supp)-9 b(ose)66 b(that)i Fp(\(H\))f Fq(holds)g(for)f Fn(\026)4727 7415 y Fl( )4832 7385 y Fq(,)h(i.e.)179 b Fn(D)5542 7308 y Fk(\006)5537 7443 y Fl(\026 )5727 7385 y Fp(\()p Fn(s)p Fp(\))53 b Fn(<)h Fp(+)p Fm(1)66 b Fq(for)h(any)-201 7637 y Fn(s)72 b Fm(2)f Fp(\(0)p Fn(;)30 b Fp(1\))p Fq(.)117 b(De\014ne)77 b Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))70 b(=)2085 7491 y Fi(R)2236 7637 y Fp(d)p Fn(\026)2447 7667 y Fl( )2552 7637 y Fp(\()p Fn(x)p Fp(\))p Fn(g)7 b Fp(\(\()p Fn(x)47 b Fm(\000)h Fn(y)7 b Fp(\))p Fn(")3627 7572 y Fk(\000)p Fg(1)3815 7637 y Fp(\))p Fq(,)79 b(with)d Fn(g)7 b Fp(\()p Fn(w)e Fp(\))70 b(=)h Fn(\037)5195 7674 y Fg([)p Fk(\000)p Fg(1)p Fl(;)p Fg(1])5571 7637 y Fp(\()p Fn(w)5 b Fp(\))76 b Fq(or)h Fn(R)q Fp(\()p Fn(w)5 b Fp(\))p Fq(.)117 b(Then)-201 7863 y(ther)-9 b(e)64 b(exist)i Fn(A)51 b Fp(=)f Fn(A)p Fp(\()p Fn(q)7 b Fp(\))64 b Fq(and)h Fn(")1923 7890 y Fg(0)2002 7863 y Fp(\()p Fn(q)7 b Fp(\))49 b Fn(>)h Fp(0)65 b Fq(such)g(that)h(for)e(al)9 b(l)64 b Fn(")50 b Fm(2)h Fp(\(0)p Fn(;)60 b(")4630 7890 y Fg(0)4709 7863 y Fp(\))1828 8108 y Fi(Z)1929 8520 y Fk(f)p Fl(x)p Fk(2)p Fg(supp)q Fl(\026)65 b Fk(j)g Fl(b)p Fg(\()p Fl(x;")p Fg(\))p Fk(\024)p Fl(")3246 8483 y Fh(A)3347 8520 y Fk(g)3456 8355 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))3946 8280 y Fl(q)5 b Fk(\000)p Fg(1)4202 8355 y Fp(d)p Fn(\026)4413 8385 y Fl( )4518 8355 y Fp(\()p Fn(x)p Fp(\))50 b Fm(\024)f Fn(":)1655 b Fp(\(4.7\))-201 8889 y Fe(Lemma)68 b(4.2.)90 b Fq(L)-9 b(et)89 b Fn(\026)1405 8919 y Fl( )1510 8889 y Fn(;)120 b(q)96 b Fq(and)90 b Fn(A)95 b Fp(=)g Fn(A)p Fp(\()p Fn(q)7 b Fp(\))89 b Fq(b)-9 b(e)89 b(as)h(in)f(the)h(pr)-9 b(evious)88 b(lemma.)156 b(L)-9 b(et)89 b Fn(N)115 b(>)95 b Fp(0)89 b Fq(b)-9 b(e)89 b(an)-201 9115 y(inte)-9 b(ger.)82 b(Then,)63 b(for)f Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))62 b Fq(de\014ne)-9 b(d)63 b(as)g(in)g(L)-9 b(emma)62 b(4.1,)h(ther)-9 b(e)62 b(exists)i(an)f Fn(r)5196 9142 y Fg(0)5338 9115 y Fq(and)g(a)g(set)h Fp(\012\()p Fn(r)6411 9142 y Fg(0)6490 9115 y Fp(\))50 b(=)g Fm(f)p Fn(x)g Fm(2)-201 9341 y Fp(supp)p Fn(\026)284 9371 y Fl( )454 9341 y Fm(j)64 b Fn(")654 9275 y Fl(r)718 9293 y Fd(0)787 9275 y Fg(+)p Fl(A=)-8 b(N)1250 9341 y Fn(<)50 b(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))50 b Fm(\024)g Fn(")2259 9275 y Fl(r)2323 9293 y Fd(0)2400 9341 y Fm(g)65 b Fq(such)f(that,)i(for)e(al)9 b(l)64 b Fn(")h Fq(smal)9 b(l)64 b(enough)1520 9596 y Fi(Z)1621 10008 y Fg(\012\()p Fl(r)1842 10026 y Fd(0)1910 10008 y Fg(\))2004 9843 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))2494 9768 y Fl(q)5 b Fk(\000)p Fg(1)2749 9843 y Fp(d)p Fn(\026)2960 9873 y Fl( )3065 9843 y Fp(\()p Fn(x)p Fp(\))50 b Fm(\025)3656 9720 y Fp(1)p 3573 9801 257 8 v 3573 9968 a(2)p Fn(N)3880 9596 y Fi(Z)4092 9843 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))4582 9768 y Fl(q)5 b Fk(\000)p Fg(1)4837 9843 y Fp(d)p Fn(\026)5048 9873 y Fl( )5153 9843 y Fp(\()p Fn(x)p Fp(\))p Fn(:)81 10367 y Fp(Lemma)58 b(4.2)j(is)h(the)e(k)-5 b(ey)61 b(lemma)e(to)i(get)g(Theorem)f(4.1,)g (since)h(it)h(is)g(this)f(lemma)d(that)j(supplies)h(the)-201 10592 y(set)c(\012\()p Fn(r)5 b Fp(\),)57 b(and)h(so)g(the)g(v)-5 b(ector)57 b Fn(')51 b Fp(=)f Fn(\037)2451 10629 y Fg(\012\()p Fl(r)t Fg(\))2738 10592 y Fp(\()p Fn(H)15 b Fp(\))p Fn( )7 b Fp(,)56 b(that)i(is)g(needed)f(to)h(pro)-5 b(v)g(e)58 b(Theorem)f(4.1.)79 b(Lemma)54 b(4.1)-201 10818 y(will)64 b(not)e(en)-5 b(ter)61 b(explicitely)i(in)g(the)f(pro)5 b(of)61 b(of)h(Theorem)e(4.1)i(but)g(is)g(an)g(imp)5 b(ortan)-5 b(t)60 b(ingredien)-5 b(t)63 b(that)e(w)-5 b(e)-201 11044 y(shall)61 b(use)g(t)-5 b(wice:)80 b(once)60 b(while)i(pro)-5 b(ving)61 b(Lemma)c(4.2)j(and)g(then)h(in)g(Lemma)c (4.3.)3393 11631 y(15)p eop %%Page: 16 16 16 15 bop -201 1158 a Fe(Pro)6 b(of)69 b(of)g(the)h(lo)-6 b(w)g(er)70 b(b)6 b(ound)69 b(in)h(Theorem)e(4.1.)81 1481 y Fp(Let)73 b Fn(N)93 b Fp(b)5 b(e)74 b(the)f(in)-5 b(teger)73 b(part)g(of)g Fm(\000)30 b Fp(log)j Fn(")p Fp(.)118 b(F)-15 b(or)73 b(a)h(sak)-5 b(e)72 b(of)h(simplicit)-5 b(y)73 b(w)-5 b(e)74 b(shall)g(use)f Fn(N)91 b Fp(=)72 b Fm(\000)30 b Fp(log)j Fn(")-201 1706 y Fp(\(rather)57 b(than)g(the)f(in)-5 b(teger)57 b(part\).)79 b(T)-15 b(ak)-5 b(e)57 b Fn(A)h Fp(as)e(in)i(Lemma)c(4.1)i(and)h(Lemma)d(4.2.) 78 b(Here)58 b Fn(q)f Fp(=)50 b(1)p Fn(=)p Fp(\(1)33 b(+)g Fn(\014)10 b Fp(\),)-201 1932 y(and)82 b(th)-5 b(us)81 b Fn(q)61 b Fm(\000)54 b Fp(1)86 b(=)g Fm(\000)p Fn(\014)10 b(=)p Fp(\(1)53 b(+)h Fn(\014)10 b Fp(\).)143 b(F)-15 b(or)81 b(\014xed)h Fn(")p Fp(,)k(w)-5 b(e)82 b(c)-5 b(ho)5 b(ose)81 b Fn(')86 b Fp(=)f Fn(\037)4936 1969 y Fg(\012\()p Fl(r)5157 1987 y Fd(0)5226 1969 y Fg(\))5289 1932 y Fp(\()p Fn(H)15 b Fp(\))p Fn( )87 b Fp(with)c Fn(r)6321 1959 y Fg(0)6481 1932 y Fp(giv)-5 b(en)82 b(b)-5 b(y)-201 2158 y(Lemma)57 b(4.2.)80 b(Th)-5 b(us,)60 b(from)f(the)h(de\014nition)h(of)f(\012\()p Fn(r)3365 2185 y Fg(0)3444 2158 y Fp(\))g(w)-5 b(e)61 b(obtain)1411 2641 y Fn(U)1535 2671 y Fl('; )1771 2641 y Fp(\()p Fn(")1927 2566 y Fk(\000)p Fg(1)2116 2641 y Fp(\))50 b(=)2429 2393 y Fi(Z)2530 2806 y Fg(\012\()p Fl(r)2751 2824 y Fd(0)2819 2806 y Fg(\))2913 2641 y Fn(b)2991 2566 y Fg(\()p Fl(R)q Fg(\))3216 2641 y Fp(\()p Fn(x;)30 b(")p Fp(\)d)p Fn(\026)3839 2671 y Fl( )3943 2641 y Fp(\()p Fn(x)p Fp(\))50 b Fm(\024)g Fn(")4516 2566 y Fl(r)4580 2584 y Fd(0)4657 2641 y Fn(\026)4767 2671 y Fl( )4872 2641 y Fp(\(\012\()p Fn(r)5227 2668 y Fg(0)5305 2641 y Fp(\)\))60 b Fn(;)-201 3180 y Fp(Therefore,)g(using)h(the)f (expression)g(\(4.4\))f(of)i Fn(L)3105 3210 y Fl( )3210 3180 y Fp(\()p Fn(f)20 b Fp(\()p Fn(H)15 b Fp(\))p Fn( )7 b(;)30 b(")3990 3114 y Fk(\000)p Fg(1)4175 3180 y Fp(\))61 b(with)g Fn(f)70 b Fp(=)50 b Fn(\037)5186 3217 y Fg(\012\()p Fl(r)5407 3235 y Fd(0)5475 3217 y Fg(\))5539 3180 y Fp(,)60 b(one)g(has)-64 3798 y Fn(L)60 3828 y Fl( )165 3798 y Fp(\()p Fn(")321 3723 y Fk(\000)p Fg(1)510 3798 y Fp(\))165 b Fm(\025)1104 3671 y Fn(\026)1214 3701 y Fl( )1319 3671 y Fp(\(\012\()p Fn(r)1674 3698 y Fg(0)1753 3671 y Fp(\)\))1895 3605 y Fg(1+2)p Fl(\014)p 1074 3756 1197 8 v 1074 3922 a Fn(")1159 3870 y Fl(r)1223 3888 y Fd(0)1291 3870 y Fl(\014)1386 3922 y Fn(\026)1496 3952 y Fl( )1601 3922 y Fp(\(\012\()p Fn(r)1956 3949 y Fg(0)2034 3922 y Fp(\)\))2176 3870 y Fl(\014)2340 3798 y Fm(\025)50 b Fn(")2637 3661 y Fh(A\014)p 2637 3692 167 6 v 2667 3775 a(N)2862 3487 y Fi( )3006 3550 y(Z)3107 3962 y Fg(\012\()p Fl(r)3328 3980 y Fd(0)3397 3962 y Fg(\))3490 3798 y Fn(b)3568 3723 y Fg(\()p Fl(R)q Fg(\))3794 3798 y Fp(\()p Fn(x;)30 b(")p Fp(\))4253 3645 y Fb(\000)p Fh(\014)p 4224 3676 229 6 v 4224 3759 a Fd(1+)p Fh(\014)4481 3798 y Fp(d)p Fn(\026)4692 3828 y Fl( )4797 3798 y Fp(\()p Fn(x)p Fp(\))5043 3487 y Fi(!)5187 3532 y Fg(1+)p Fl(\014)6796 3798 y Fp(\(4.8\))746 4395 y Fm(\025)1391 4272 y Fn(e)1476 4206 y Fk(\000)p Fl(A\014)p 1074 4353 1029 8 v 1074 4519 a Fp(\()p Fm(\000)p Fp(2)g(log)i Fn(")p Fp(\))1828 4467 y Fg(1+)p Fl(\014)2153 4138 y Fi(\022)2286 4147 y(Z)2499 4395 y Fn(b)2577 4319 y Fg(\()p Fl(R)q Fg(\))2802 4395 y Fp(\()p Fn(x;)e(")p Fp(\))3262 4242 y Fb(\000)p Fh(\014)p 3233 4273 229 6 v 3233 4356 a Fd(1+)p Fh(\014)3490 4395 y Fp(d)p Fn(\026)3701 4425 y Fl( )3805 4395 y Fp(\()p Fn(x)p Fp(\))4051 4138 y Fi(\023)4185 4184 y Fg(1+)p Fl(\014)4510 4395 y Fp(=)4995 4272 y Fn(C)5125 4299 y Fg(1)p 4722 4353 756 8 v 4722 4519 a Fm(j)g Fp(log)j Fn(")p Fm(j)5204 4467 y Fg(1+)p Fl(\014)5497 4395 y Fn(K)5652 4422 y Fl(\026)5737 4445 y Fh( )5869 4138 y Fi(\022)6190 4272 y Fp(1)p 6023 4353 426 8 v 6023 4519 a(1)40 b(+)g Fn(\014)6468 4395 y(;)30 b(")6634 4138 y Fi(\023)6768 4184 y Fg(1+)p Fl(\014)6982 4395 y Fn(;)-201 4883 y Fp(where)79 b(in)g(the)f(last)g(inequalit)-5 b(y)79 b(w)-5 b(e)79 b(used)f(Lemma)c(4.2)k(and)g Fn(N)100 b Fp(=)80 b Fm(\000)30 b Fp(log)j Fn(")p Fp(.)133 b(This)79 b(holds)g(for)f Fn(")g Fp(small)-201 5109 y(enough.)6612 b Fc(\003)81 5335 y Fp(Remark)75 b(that)g(the)g(fact)g(that)g Fn(r)2384 5362 y Fg(0)2539 5335 y Fp(disapp)5 b(ears)76 b(in)g(the)g(relation)g(\(4.8\))f(is)h(crucial.)127 b(It)75 b(is)h(of)g(course)-201 5561 y(related)53 b(to)g(the)g(particular)h(v) -10 b(alue)53 b Fn(q)k Fp(=)50 b(1)p Fn(=)p Fp(\(1)25 b(+)g Fn(\014)10 b Fp(\))52 b(of)g(the)h(fractal)g(dimension)f(that)g (en)-5 b(ters)52 b(in)-5 b(to)54 b(accoun)-5 b(t.)-201 5786 y(This)61 b(is)g(the)f(place)h(where)g(the)f(deep)g(link)i(b)5 b(et)-5 b(w)g(een)60 b Fn(L)3623 5816 y Fl( )3728 5786 y Fp(\()p Fn(T)25 b Fp(\))60 b(and)h Fn(D)4571 5720 y Fk(\006)4566 5831 y Fl(\026)4651 5854 y Fh( )4752 5786 y Fp(\(1)p Fn(=)p Fp(\(1)40 b(+)f Fn(\014)10 b Fp(\)\))60 b(sho)-5 b(ws)60 b(up.)81 6109 y(W)-15 b(e)61 b(are)f(left)g(with)h (the)g(pro)5 b(ofs)60 b(of)g(Lemmas)c(4.1)k(and)h(4.2.)-201 6431 y Fe(Pro)6 b(of)69 b(of)g(Lemma)e(4.1.)-201 6657 y Fp(F)-15 b(or)60 b(an)-5 b(y)61 b Fn(A)51 b(>)f Fp(0)p Fn(;)30 b(")50 b(>)g Fp(0)60 b(de\014ne)1996 7056 y Fn(B)9 b Fp(\()p Fn(A;)30 b(")p Fp(\))49 b(=)h Fm(f)p Fn(x)h Fm(2)f Fp(supp)p Fn(\026)60 b Fm(j)g Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))50 b Fm(\024)g Fn(")4718 6980 y Fl(A)4832 7056 y Fm(g)p Fn(:)-201 7454 y Fp(Let)60 b(0)50 b Fn(<)g(s)h(<)f(q)57 b(<)50 b Fp(1.)80 b(As)61 b Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))49 b Fm(\025)h Fn(\026)p Fp(\([)p Fn(x)39 b Fm(\000)h Fn(";)30 b(x)40 b Fp(+)g Fn(")p Fp(]\))60 b(whatev)-5 b(er)60 b(is)h Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\),)59 b(w)-5 b(e)60 b(can)h(estimate:)809 7689 y Fi(Z)910 8102 y Fl(B)7 b Fg(\()p Fl(A;")p Fg(\))1382 7937 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))1872 7862 y Fl(q)5 b Fk(\000)p Fg(1)2127 7937 y Fp(d)p Fn(\026)p Fp(\(x\))165 b(=)3049 7689 y Fi(Z)3150 8102 y Fl(B)7 b Fg(\()p Fl(A;")p Fg(\))3621 7937 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))4111 7862 y Fl(q)5 b Fk(\000)p Fl(s)4361 7937 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))4851 7862 y Fl(s)p Fk(\000)p Fg(1)5104 7937 y Fp(d)p Fn(\026)p Fp(\(x\))2741 8449 y Fm(\024)166 b Fn(")3134 8374 y Fl(A)p Fg(\()p Fl(q)5 b Fk(\000)p Fl(s)p Fg(\))3630 8201 y Fi(Z)3731 8614 y Fl(B)i Fg(\()p Fl(A;")p Fg(\))4203 8449 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))4693 8374 y Fl(s)p Fk(\000)p Fg(1)4946 8449 y Fp(d)p Fn(\026)p Fp(\(x\))2741 8961 y Fm(\024)166 b Fn(")3134 8886 y Fl(A)p Fg(\()p Fl(q)5 b Fk(\000)p Fl(s)p Fg(\))3630 8713 y Fi(Z)3731 9126 y Fl(B)i Fg(\()p Fl(A;")p Fg(\))4203 8961 y Fn(\026)p Fp(\([)p Fn(x)39 b Fm(\000)h Fn(";)30 b(x)40 b Fp(+)f Fn(")p Fp(]\))5458 8886 y Fl(s)p Fk(\000)p Fg(1)5711 8961 y Fp(d)p Fn(\026)p Fp(\(x\))2741 9400 y Fm(\024)166 b Fn(")3134 9325 y Fl(A)p Fg(\()p Fl(q)5 b Fk(\000)p Fl(s)p Fg(\))3600 9400 y Fn(I)3680 9427 y Fl(\026)3773 9400 y Fp(\()p Fn(s;)30 b(")p Fp(\))p Fn(:)2579 b Fp(\(4.9\))-201 9799 y(Let)55 b(us)h(tak)-5 b(e,)55 b(for)g(example,)g Fn(s)c Fp(=)f Fn(q)7 b(=)p Fp(2.)78 b(As)56 b Fn(D)2968 9733 y Fg(+)2963 9844 y Fl(\026)3085 9799 y Fp(\()p Fn(s)p Fp(\))51 b Fn(<)e Fp(+)p Fm(1)55 b Fp(for)h(an)-5 b(y)55 b Fn(s)c(>)f Fp(0,)56 b(for)f Fn(")h Fp(small)f(enough)g(one)h(has)2316 10394 y Fn(I)2396 10421 y Fl(\026)2489 10394 y Fp(\()p Fn(s;)30 b(")p Fp(\))50 b Fm(\024)3124 10137 y Fi(\022)3277 10271 y Fp(1)p 3277 10352 91 8 v 3280 10518 a Fn(")3388 10137 y Fi(\023)3522 10182 y Fg(\()p Fl(D)3697 10123 y Fd(+)3693 10204 y Fh(\026)3798 10182 y Fg(\()p Fl(s)p Fg(\)+1\)\(1)p Fk(\000)p Fl(s)p Fg(\))4602 10394 y Fn(:)-201 10907 y Fp(T)-15 b(aking)61 b(in)g(\(4.9\))f Fn(A)51 b Fp(=)f(\()p Fn(q)c Fm(\000)40 b Fn(s)p Fp(\))1967 10841 y Fk(\000)p Fg(1)2156 10907 y Fp(\(\()p Fn(D)2454 10841 y Fg(+)2449 10952 y Fl(\026)2571 10907 y Fp(\()p Fn(s)p Fp(\))g(+)g(1\)\(1)f Fm(\000)h Fn(s)p Fp(\))g(+)g(1\),)60 b(w)-5 b(e)61 b(obtain)f(the)g(result)h(of)f (the)g(Lemma.)7028 11133 y Fc(\003)3393 11631 y Fp(16)p eop %%Page: 17 17 17 16 bop -201 1158 a Fe(Pro)6 b(of)69 b(of)g(Lemma)e(4.2.)81 1477 y Fp(T)-15 b(o)61 b(alleviate)h(the)e(notations,)g(denote)g Fn(B)2959 1505 y Fl(A)3124 1477 y Fp(=)51 b Fm(f)p Fn(x)f Fm(2)h Fp(supp)p Fn(\026)4219 1507 y Fl( )4385 1477 y Fm(j)60 b Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))50 b Fm(\024)h Fn(")5314 1411 y Fl(A)5427 1477 y Fm(g)61 b Fp(and)g(also)g Fn(B)6445 1411 y Fl(A)6610 1477 y Fp(=)50 b Fm(f)p Fn(x)h Fm(2)-201 1703 y Fp(supp)p Fn(\026)284 1733 y Fl( )449 1703 y Fm(j)61 b Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))49 b Fn(>)h(")1377 1637 y Fl(A)1491 1703 y Fm(g)p Fp(.)80 b(Then,)60 b(using)h(the)f(b)5 b(ound)61 b(of)f(Lemma)d(4.1,)i(one)i (has)f(for)g Fn(")g Fp(small)g(enough)721 1936 y Fi(Z)933 2184 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))1423 2109 y Fl(q)5 b Fk(\000)p Fg(1)1678 2184 y Fp(d)p Fn(\026)1889 2214 y Fl( )1994 2184 y Fp(\()p Fn(x)p Fp(\))165 b(=)2713 1936 y Fi(Z)2814 2349 y Fl(B)2927 2311 y Fh(A)3066 2184 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))3556 2109 y Fl(q)5 b Fk(\000)p Fg(1)3811 2184 y Fp(d)p Fn(\026)4022 2214 y Fl( )4127 2184 y Fp(\()p Fn(x)p Fp(\))40 b(+)4595 1936 y Fi(Z)4696 2349 y Fl(B)4802 2371 y Fh(A)4941 2184 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))5431 2109 y Fl(q)5 b Fk(\000)p Fg(1)5687 2184 y Fp(d)p Fn(\026)5898 2214 y Fl( )6002 2184 y Fp(\()p Fn(x)p Fp(\))2405 2685 y Fm(\024)2713 2438 y Fi(Z)2814 2850 y Fl(B)2927 2812 y Fh(A)3066 2685 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))3556 2610 y Fl(q)5 b Fk(\000)p Fg(1)3811 2685 y Fp(d)p Fn(\026)4022 2715 y Fl( )4127 2685 y Fp(\()p Fn(x)p Fp(\))40 b(+)g Fn(":)-201 3164 y Fp(Remark)54 b(that)g(one)h(alw)-5 b(a)g(ys)55 b(has)g Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))49 b Fm(\024)h Fp(1)55 b(\(since)g Fn(R)q Fp(\()p Fn(w)5 b Fp(\))50 b Fm(\024)g Fp(1\).)79 b(Th)-5 b(us)55 b(one)f(can)h(divide)h(the)f (remaining)-201 3390 y(set)74 b Fn(B)244 3324 y Fl(A)433 3390 y Fp(in)-5 b(to)74 b Fn(N)95 b Fp(parts:)108 b(\012\()p Fn(k)6 b(A=)-10 b(N)20 b Fp(\))73 b(=)g Fm(f)p Fn(x)h Fm(2)g Fp(supp)p Fn(\026)3615 3420 y Fl( )3794 3390 y Fm(j)g Fn(")4004 3324 y Fg(\()p Fl(k)t Fg(+1\))p Fl(A=)-8 b(N)4748 3390 y Fn(<)73 b(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))73 b Fm(\024)g Fn(")5826 3324 y Fl(k)t(A=)-8 b(N)6206 3390 y Fm(g)p Fp(,)78 b(with)d Fn(k)k Fp(=)-201 3616 y(0)p Fn(;)30 b Fp(1)p Fn(;)g Fm(\001)g(\001)g(\001)f Fn(;)h(N)66 b Fm(\000)47 b Fp(1.)108 b(A)-5 b(t)70 b(least)g(one)g(of)f (these)g Fn(N)90 b Fp(sets)69 b(\012\()p Fn(k)6 b(A=)-10 b(N)20 b Fp(\))70 b(giv)-5 b(es)70 b(rise)g(to)g(an)g(in)-5 b(tegral)70 b(bigger)h(than)-201 3842 y(1)p Fn(=)-10 b(N)84 b Fp(times)63 b(the)h(in)-5 b(tegral)65 b(o)-5 b(v)g(er)64 b(the)g(whole)g(set)g Fn(B)3337 3776 y Fl(A)3451 3842 y Fp(.)92 b(And)64 b(so)g(are)h(pic)-5 b(k)g(ed)64 b Fn(k)5190 3869 y Fg(0)5269 3842 y Fp(,)g Fn(r)5466 3869 y Fg(0)5602 3842 y Fp(=)56 b Fn(Ak)6031 3869 y Fg(0)6110 3842 y Fn(=)-10 b(N)20 b Fp(,)65 b(and)f(th)-5 b(us)-201 4068 y(the)60 b(set)g(\012\()p Fn(r)680 4095 y Fg(0)759 4068 y Fp(\))g(of)g(the)h(Lemma.)81 4294 y(T)-15 b(o)53 b(end)f(the)f(pro)5 b(of,)53 b(remark)e(that)2499 4147 y Fi(R)2650 4294 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))3140 4228 y Fl(q)5 b Fk(\000)p Fg(1)3396 4294 y Fp(d)p Fn(\026)3607 4324 y Fl( )3711 4294 y Fp(\()p Fn(x)p Fp(\))50 b Fm(\025)g Fp(1,)j(since)f Fn(q)58 b(<)50 b Fp(1.)77 b(Therefore,)53 b(for)f Fn(")e Fm(\024)g Fp(1)p Fn(=)p Fp(2,)-201 4519 y(one)61 b(gets)1172 4749 y Fi(Z)1273 5162 y Fg(\012\()p Fl(r)1494 5180 y Fd(0)1563 5162 y Fg(\))1656 4997 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))2146 4922 y Fl(q)5 b Fk(\000)p Fg(1)2402 4997 y Fp(d)p Fn(\026)2613 5027 y Fl( )2718 4997 y Fp(\()p Fn(x)p Fp(\))165 b Fm(\025)3494 4874 y Fp(1)p 3456 4955 166 8 v 3456 5121 a Fn(N)3673 4740 y Fi(\022)3806 4749 y(Z)4019 4997 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))4509 4922 y Fl(q)5 b Fk(\000)p Fg(1)4764 4997 y Fp(d)p Fn(\026)4975 5027 y Fl( )5080 4997 y Fp(\()p Fn(x)p Fp(\))40 b Fm(\000)f Fn(")5632 4740 y Fi(\023)3129 5509 y Fm(\025)3539 5386 y Fp(1)p 3456 5467 257 8 v 3456 5633 a(2)p Fn(N)3763 5261 y Fi(Z)3976 5509 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))4466 5434 y Fl(q)5 b Fk(\000)p Fg(1)4721 5509 y Fp(d)p Fn(\026)4932 5539 y Fl( )5037 5509 y Fp(\()p Fn(x)p Fp(\))p Fn(:)7028 5966 y Fc(\003)81 6285 y Fp(W)-15 b(e)50 b(no)-5 b(w)50 b(turn)g(to)g(the)f(pro)5 b(of)50 b(of)f(Theorem)99 b(4.2,)51 b(whic)-5 b(h)50 b(is)g(actually)h(a)e (consequence)g(of)g(Theorem)g(4.1)-201 6510 y(and)64 b(of)f(the)g(follo)-5 b(wing)65 b(Lemma)59 b(4.3)k(that)g(relates)h (the)f(in)-5 b(tegrals)63 b Fn(K)4585 6537 y Fl(\026)4670 6560 y Fh( )4772 6510 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))62 b(to)h(the)g(in)-5 b(tegrals)64 b Fn(I)6588 6537 y Fl(\026)6673 6560 y Fh( )6775 6510 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))-201 6736 y(that)70 b(en)-5 b(ter)69 b(in)-5 b(to)71 b(accoun)-5 b(t)69 b(in)i(the)f(de\014nition)g(of)g(the)g(generalized)g(fractal)g (dimension)f Fn(D)6189 6670 y Fk(\006)6184 6781 y Fl(\026)6269 6804 y Fh( )6370 6736 y Fp(\()p Fn(q)7 b Fp(\).)109 b(More)-201 6962 y(precisely)-15 b(,)69 b(Lemma)63 b(4.3)k(sa)-5 b(ys)66 b(that,)i(under)f(Assumption)e Fe(\(H\))j Fp(on)f Fn(\026)4685 6992 y Fl( )4790 6962 y Fp(,)h(b)5 b(oth)67 b Fn(K)5500 6989 y Fl(\026)5585 7012 y Fh( )5686 6962 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))66 b(and)h Fn(I)6588 6989 y Fl(\026)6673 7012 y Fh( )6775 6962 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))-201 7188 y(ha)-5 b(v)g(e)47 b(the)h(same)d(gro)-5 b(wth)48 b(exp)5 b(onen)-5 b(ts)46 b Fn(D)2544 7122 y Fk(\006)2539 7233 y Fl(\026)2624 7256 y Fh( )2726 7188 y Fp(\()p Fn(q)7 b Fp(\).)75 b(This)48 b(is)g(of)f(course)g(b)5 b(ecause)47 b(of)g(the)g(fast)f(deca)-5 b(y)47 b(prop)5 b(erties)-201 7414 y(of)60 b(the)g(function)h Fn(R)h Fp(w)-5 b(e)60 b(ha)-5 b(v)g(e)60 b(c)-5 b(hosen)60 b(\()p Fq(via)g Fp(the)g(c)-5 b(hoice)60 b(of)h Fn(h)50 b Fm(2)h Fn(C)4395 7348 y Fk(1)4382 7462 y Fg(0)4544 7414 y Fp(\([0)p Fn(;)30 b Fp(1]\)\).)-201 7864 y Fe(Lemma)68 b(4.3.)90 b Fq(L)-9 b(et)65 b Fn(q)57 b Fm(2)51 b Fp(\(0)p Fn(;)30 b Fp(1\))p Fq(.)82 b(Supp)-9 b(ose)64 b(that)i Fp(\(H\))f Fq(holds)f(for)h Fn(\026)4396 7894 y Fl( )4501 7864 y Fq(.)83 b(Then)65 b(for)f(al)9 b(l)65 b Fn(\027)d Fm(2)50 b Fp(\(0)p Fn(;)30 b Fp(1\))2009 8215 y(1)p 1880 8296 348 8 v 1880 8463 a(2)1971 8410 y Fg(2)p Fk(\000)p Fl(q)2248 8338 y Fn(I)2328 8365 y Fl(\026)2413 8388 y Fh( )2514 8338 y Fp(\()p Fn(q)7 b(;)30 b(")2839 8263 y Fg(1)p Fk(\000)p Fl(\027)3105 8338 y Fp(\))50 b Fm(\024)g Fn(K)3573 8365 y Fl(\026)3658 8388 y Fh( )3759 8338 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))49 b Fm(\024)h Fn(I)4476 8365 y Fl(\026)4561 8388 y Fh( )4663 8338 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))p Fn(;)1595 b Fp(\(4.10\))-201 8777 y Fq(wher)-9 b(e)64 b(the)h(left)f(ine)-9 b(quality)63 b(holds)i(for)f Fn(")h Fq(smal)9 b(l)64 b(enough)g(\()p Fn(")51 b Fm(\024)f Fn(")p Fp(\()p Fn(\027)12 b Fp(\))p Fq(\).)82 b(As)66 b(a)f(c)-9 b(onse)g(quenc)g(e)188 9156 y Fp(1)p 33 9237 401 8 v 33 9403 a(1)40 b Fm(\000)g Fn(q)484 9279 y Fp(lim)30 b(inf)598 9394 y Fl(")p Fk(!)p Fg(0)1038 9138 y Fp(log)k Fn(K)1459 9165 y Fl(\026)1544 9188 y Fh( )1645 9138 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))p 1038 9237 1001 8 v 1278 9403 a Fm(\000)g Fp(log)j Fn(")2110 9279 y Fp(=)50 b Fn(D)2458 9203 y Fk(\000)2453 9323 y Fl(\026)2538 9346 y Fh( )2639 9279 y Fp(\()p Fn(q)7 b Fp(\))185 b(and)3708 9156 y(1)p 3553 9237 401 8 v 3553 9403 a(1)40 b Fm(\000)g Fn(q)4004 9279 y Fp(lim)30 b(sup)4144 9430 y Fl(")p Fk(!)p Fg(0)4611 9138 y Fp(log)j Fn(K)5031 9165 y Fl(\026)5116 9188 y Fh( )5217 9138 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))p 4611 9237 1001 8 v 4850 9403 a Fm(\000)g Fp(log)j Fn(")5682 9279 y Fp(=)50 b Fn(D)6030 9203 y Fg(+)6025 9323 y Fl(\026)6110 9346 y Fh( )6211 9279 y Fp(\()p Fn(q)7 b Fp(\))p Fn(:)213 b Fp(\(4.11\))-201 9763 y Fe(Remark)69 b(4.3.)90 b Fp(W)-15 b(e)60 b(strongly)h(b)5 b(eliev)-5 b(e)61 b(that)f(\(4.11\))f(holds)i (in)g(full)g(generalit)-5 b(y)61 b(for)f(an)-5 b(y)61 b Fn(\026)6124 9793 y Fl( )6228 9763 y Fp(.)-201 10213 y Fe(Pro)6 b(of)69 b(of)g(Lemma)e(4.3.)81 10531 y Fp(Throughout)61 b(this)g(pro)5 b(of)60 b(w)-5 b(e)61 b(shall)g(denote)f Fn(B)9 b Fp(\()p Fn(x;)30 b(")p Fp(\))49 b(=)h([)p Fn(x)40 b Fm(\000)g Fn(";)30 b(x)40 b Fp(+)f Fn(")p Fp(].)80 b(One)60 b(has)42 11052 y Fn(I)122 11079 y Fl(\026)207 11102 y Fh( )309 11052 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))49 b(=)946 10804 y Fi(Z)1158 11052 y Fn(\026)1268 11082 y Fl( )1373 11052 y Fp(\()p Fn(B)9 b Fp(\()p Fn(x;)30 b(")p Fp(\)\))2074 10977 y Fl(q)5 b Fk(\000)p Fg(1)2328 11052 y Fp(d)p Fn(\026)2539 11082 y Fl( )2644 11052 y Fp(\()p Fn(x)p Fp(\))50 b(=)3132 10804 y Fi(Z)3344 11052 y Fp(d)p Fn(\026)3555 11082 y Fl( )3660 11052 y Fp(\()p Fn(x)p Fp(\))3936 10795 y Fi(\022)4070 10804 y(Z)4282 11052 y Fn(\037)4396 11089 y Fg([)p Fk(\000)p Fg(1)p Fl(;)p Fg(1])4803 10795 y Fi(\022)4956 10929 y Fn(x)41 b Fm(\000)e Fn(y)p 4956 11010 422 8 v 5125 11177 a(")5398 10795 y Fi(\023)5562 11052 y Fp(d)p Fn(\026)5773 11082 y Fl( )5878 11052 y Fp(\()p Fn(x)p Fp(\))6124 10795 y Fi(\023)6257 10841 y Fl(q)5 b Fk(\000)p Fg(1)6544 11052 y Fn(:)3393 11631 y Fp(17)p eop %%Page: 18 18 18 17 bop -201 1158 a Fp(Since,)63 b(b)-5 b(y)63 b(\(3.5\),)f Fn(\037)1184 1195 y Fg([)p Fk(\000)p Fg(1)p Fl(;)p Fg(1])1561 1158 y Fp(\()p Fn(w)5 b Fp(\))54 b Fm(\024)f Fn(R)q Fp(\()p Fn(w)5 b Fp(\),)63 b(and)g Fn(q)49 b Fm(\000)41 b Fp(1)55 b Fn(<)f Fp(0,)63 b(one)f(has)h Fn(K)4650 1185 y Fl(\026)4735 1208 y Fh( )4836 1158 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))53 b Fm(\024)h Fn(I)5561 1185 y Fl(\026)5646 1208 y Fh( )5748 1158 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\).)86 b(So)63 b(w)-5 b(e)63 b(need)-201 1384 y(to)d(get)g(the)h(lo)-5 b(w)g(er)61 b(b)5 b(ound)60 b(of)h(\(4.10\).)78 b(First)61 b(notice)f(that)452 1893 y Fn(b)530 1818 y Fg(\()p Fl(R)q Fg(\))755 1893 y Fp(\()p Fn(x;)30 b(")p Fp(\))165 b(=)1639 1645 y Fi(Z)1851 1893 y Fp(d)p Fn(\026)2062 1923 y Fl( )2167 1893 y Fp(\()p Fn(y)7 b Fp(\))p Fn(R)2574 1636 y Fi(\022)2728 1770 y Fn(x)40 b Fm(\000)g Fn(y)p 2728 1851 422 8 v 2896 2017 a(")3170 1636 y Fi(\023)1332 2395 y Fp(=)1639 2148 y Fi(Z)1740 2572 y Fm(j)1811 2499 y Fh(x)p Fb(\000)p Fh(y)p 1811 2530 233 6 v 1898 2612 a(")2063 2572 y Fm(j)2113 2560 y Fl(<")2288 2522 y Fb(\000)p Fh(\027)2500 2395 y Fp(d)p Fn(\026)2711 2425 y Fl( )2816 2395 y Fp(\()p Fn(y)7 b Fp(\))p Fn(R)3222 2139 y Fi(\022)3376 2272 y Fn(x)41 b Fm(\000)e Fn(y)p 3376 2354 422 8 v 3545 2520 a(")3818 2139 y Fi(\023)3992 2395 y Fp(+)4174 2148 y Fi(Z)4275 2572 y Fm(j)4345 2499 y Fh(x)p Fb(\000)p Fh(y)p 4345 2530 233 6 v 4432 2612 a(")4598 2572 y Fm(j)4648 2560 y Fk(\025)p Fl(")4823 2522 y Fb(\000)p Fh(\027)5035 2395 y Fp(d)p Fn(\026)5246 2425 y Fl( )5350 2395 y Fp(\()p Fn(y)7 b Fp(\))p Fn(R)5757 2139 y Fi(\022)5911 2272 y Fn(x)40 b Fm(\000)g Fn(y)p 5911 2354 422 8 v 6080 2520 a(")6353 2139 y Fi(\023)1332 2845 y Fm(\024)165 b Fn(\026)1749 2875 y Fl( )1854 2845 y Fp(\()p Fn(B)9 b Fp(\()p Fn(x;)30 b(")2413 2770 y Fg(1)p Fk(\000)p Fl(\027)2679 2845 y Fp(\)\))40 b(+)168 b(sup)3042 3012 y Fk(j)p Fl(w)t Fk(j\025)p Fl(")3400 2974 y Fb(\000)p Fh(\027)3604 2845 y Fn(R)q Fp(\()p Fn(w)5 b Fp(\))p Fn(;)-201 3423 y Fp(where)61 b(w)-5 b(e)61 b(used)f Fn(R)q Fp(\()p Fn(w)5 b Fp(\))50 b Fm(\024)g Fp(1.)80 b(Let)p 2214 3277 140 8 v 60 w Fn(R)r Fp(\()p Fn(z)8 b Fp(\))49 b(=)h(sup)3104 3467 y Fk(j)p Fl(w)t Fk(j\025)p Fl(z)3507 3423 y Fn(R)q Fp(\()p Fn(w)5 b Fp(\).)80 b(De\014ne)60 b(also)-38 3913 y Fn(A)98 3838 y Fg(\()p Fl(R)q Fg(\))98 3958 y Fl(\027)323 3913 y Fp(\()p Fn(")p Fp(\))50 b(=)g Fm(f)p Fn(x)g Fm(2)h Fp(supp)o Fn(\026)1693 3943 y Fl( )1859 3913 y Fm(j)60 b Fn(\026)2080 3943 y Fl( )2185 3913 y Fp(\()p Fn(B)9 b Fp(\()p Fn(x;)30 b(")2744 3838 y Fg(1)p Fk(\000)p Fl(\027)3010 3913 y Fp(\)\))50 b Fm(\025)p 3393 3767 V 49 w Fn(R)r Fp(\()p Fn(")3689 3838 y Fk(\000)p Fl(\027)3885 3913 y Fp(\))p Fm(g)60 b Fp(and)4508 3867 y(~)4460 3913 y Fn(A)4596 3838 y Fg(\()p Fl(R)q Fg(\))4596 3958 y Fl(\027)4822 3913 y Fp(\()p Fn(")p Fp(\))50 b(=)5290 3711 y Fi(\020)5399 3913 y Fn(A)5535 3838 y Fg(\()p Fl(R)q Fg(\))5535 3958 y Fl(\027)5761 3913 y Fp(\()p Fn(")p Fp(\))5988 3711 y Fi(\021)6095 3757 y Fl(c)6205 3913 y Fm(\\)41 b Fp(supp)p Fn(\026)6852 3943 y Fl( )6956 3913 y Fn(:)-201 4426 y Fp(It)60 b(is)h(clear)g(that)f(for)g(an)-5 b(y)61 b Fn(x)50 b Fm(2)h Fn(A)2092 4330 y Fg(\()p Fl(R)q Fg(\))2092 4450 y Fl(\027)2317 4426 y Fp(\()p Fn(")p Fp(\))p Fn(;)90 b(b)2763 4360 y Fg(\()p Fl(R)q Fg(\))2988 4426 y Fp(\()p Fn(x;)30 b(")p Fp(\))49 b Fm(\024)h Fp(2)p Fn(\026)3842 4456 y Fl( )3947 4426 y Fp(\()p Fn(B)9 b Fp(\()p Fn(x;)30 b(")4506 4360 y Fg(1)p Fk(\000)p Fl(\027)4772 4426 y Fp(\)\).)81 4652 y(Th)-5 b(us,)61 b(with)g(these)e(notations,)h(one)g (has)634 5134 y Fn(K)789 5161 y Fl(\026)874 5184 y Fh( )975 5134 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))165 b(=)1843 4887 y Fi(Z)2055 5134 y Fp(d)p Fn(\026)2266 5164 y Fl( )2371 5134 y Fp(\()p Fn(x)p Fp(\))p Fn(b)2695 5059 y Fg(\()p Fl(R)q Fg(\))2920 5134 y Fp(\()p Fn(x;)30 b(")p Fp(\))3332 5059 y Fl(q)5 b Fk(\000)p Fg(1)3638 5134 y Fm(\025)3830 4887 y Fi(Z)3931 5299 y Fl(A)4037 5228 y Fd(\()p Fh(R)p Fd(\))4037 5320 y Fh(\027)4233 5299 y Fg(\()p Fl(")p Fg(\))4446 5134 y Fp(d)p Fn(\026)4657 5164 y Fl( )4762 5134 y Fp(\()p Fn(x)p Fp(\))p Fn(b)5086 5059 y Fg(\()p Fl(R)q Fg(\))5311 5134 y Fp(\()p Fn(x;)30 b(")p Fp(\))5723 5059 y Fl(q)5 b Fk(\000)p Fg(1)1536 5646 y Fm(\025)1843 5399 y Fi(Z)1944 5811 y Fl(A)2050 5740 y Fd(\()p Fh(R)p Fd(\))2050 5832 y Fh(\027)2247 5811 y Fg(\()p Fl(")p Fg(\))2460 5646 y Fp(d)p Fn(\026)2671 5676 y Fl( )2776 5646 y Fp(\()p Fn(x)p Fp(\))3022 5444 y Fi(\020)3130 5646 y Fp(2)p Fn(\026)3331 5676 y Fl( )3436 5646 y Fp(\()p Fn(B)k Fp(\()p Fn(x;)30 b(")3995 5571 y Fg(1)p Fk(\000)p Fl(\027)4260 5646 y Fp(\)\))4402 5444 y Fi(\021)4510 5490 y Fl(q)5 b Fk(\000)p Fg(1)1536 6229 y Fp(=)1991 6106 y(1)p 1863 6187 348 8 v 1863 6353 a(2)1954 6301 y Fg(1)p Fk(\000)p Fl(q)2231 5918 y Fi( )2374 6229 y Fn(I)2454 6256 y Fl(\026)2539 6279 y Fh( )2641 6229 y Fp(\()p Fn(q)i(;)30 b(")2966 6154 y Fg(1)p Fk(\000)p Fl(\027)3232 6229 y Fp(\))40 b Fm(\000)3525 5981 y Fi(Z)3663 6360 y Fg(~)3626 6394 y Fl(A)3732 6323 y Fd(\()p Fh(R)p Fd(\))3732 6415 y Fh(\027)3928 6394 y Fg(\()p Fl(")p Fg(\))4141 6229 y Fp(d)p Fn(\026)4352 6259 y Fl( )4457 6229 y Fp(\()p Fn(x)p Fp(\))p Fn(\026)4813 6259 y Fl( )4918 6229 y Fp(\()p Fn(B)9 b Fp(\()p Fn(x;)30 b(")5477 6154 y Fg(1)p Fk(\000)p Fl(\027)5742 6229 y Fp(\)\))5884 6154 y Fl(q)5 b Fk(\000)p Fg(1)6140 5918 y Fi(!)6284 6229 y Fn(:)-201 6792 y Fp(Since)56 b Fn(R)q Fp(\()p Fn(w)5 b Fp(\))56 b(deca)-5 b(ys)55 b(at)g(+)p Fm(1)g Fp(faster)g(than)g(an)-5 b(y)56 b(in)-5 b(v)g(erse)56 b(p)5 b(o)-5 b(w)g(er,)56 b(for)f Fn(")h Fp(small)f(enough,)h(that)f(is)h Fn(")50 b Fm(\024)g Fn(")p Fp(\()p Fn(\027)12 b Fp(\),)-201 7017 y(one)61 b(has)p 457 6871 140 8 v 60 w Fn(R)q Fp(\()p Fn(")752 6951 y Fk(\000)p Fl(\027)948 7017 y Fp(\))50 b Fm(\024)g Fn(")1346 6951 y Fl(A)1460 7017 y Fp(,)60 b(where)h Fn(A)g Fp(is)f(the)h(n)-5 b(um)g(b)5 b(er)59 b(from)g(Lemma)e(4.1.)81 7243 y(Hence,)j(with)1135 7197 y(~)1087 7243 y Fn(A)1223 7270 y Fl(\027)1309 7243 y Fp(\()p Fn(")p Fp(\))50 b(=)g Fm(f)p Fn(x)g Fm(2)h Fp(supp)p Fn(\026)2680 7273 y Fl( )2845 7243 y Fm(j)60 b Fn(\026)3066 7273 y Fl( )3171 7243 y Fp(\()p Fn(B)9 b Fp(\()p Fn(x;)30 b(")3730 7177 y Fg(1)p Fk(\000)p Fl(\027)3996 7243 y Fp(\)\))50 b Fm(\024)g Fn(")4465 7177 y Fl(A)4578 7243 y Fm(g)p Fp(,)883 7745 y(2)974 7670 y Fg(1)p Fk(\000)p Fl(q)1230 7745 y Fn(K)1385 7772 y Fl(\026)1470 7795 y Fh( )1571 7745 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))165 b Fm(\025)h Fn(I)2520 7772 y Fl(\026)2605 7795 y Fh( )2706 7745 y Fp(\()p Fn(q)7 b(;)30 b(")3031 7670 y Fg(1)p Fk(\000)p Fl(\027)3297 7745 y Fp(\))40 b Fm(\000)3590 7498 y Fi(Z)3728 7877 y Fg(~)3691 7910 y Fl(A)3797 7927 y Fh(\027)3874 7910 y Fg(\()p Fl(")p Fg(\))4087 7745 y Fp(d)p Fn(\026)4298 7775 y Fl( )4403 7745 y Fp(\()p Fn(x)p Fp(\))p Fn(\026)4759 7775 y Fl( )4863 7745 y Fp(\()p Fn(B)9 b Fp(\()p Fn(x;)30 b(")5422 7670 y Fg(1)p Fk(\000)p Fl(\027)5688 7745 y Fp(\)\))5830 7670 y Fl(q)5 b Fk(\000)p Fg(1)6705 7745 y Fp(\(4.12\))2132 8250 y Fm(\025)166 b Fn(I)2520 8277 y Fl(\026)2605 8300 y Fh( )2706 8250 y Fp(\()p Fn(q)7 b(;)30 b(")3031 8175 y Fg(1)p Fk(\000)p Fl(\027)3297 8250 y Fp(\))40 b Fm(\000)g Fn(")3675 8175 y Fg(1)p Fk(\000)p Fl(\027)3992 8250 y Fm(\025)4204 8127 y Fp(1)p 4204 8208 91 8 v 4204 8375 a(2)4314 8250 y Fn(I)4394 8277 y Fl(\026)4479 8300 y Fh( )4581 8250 y Fp(\()p Fn(q)7 b(;)30 b(")4906 8175 y Fg(1)p Fk(\000)p Fl(\027)5172 8250 y Fp(\))p Fn(;)1411 b Fp(\(4.13\))-201 8726 y(if)67 b(in)g(addition)f Fn(")997 8660 y Fg(1)p Fk(\000)p Fl(\027)1324 8726 y Fm(\024)60 b Fp(1)p Fn(=)p Fp(2)66 b(\(since)g Fn(I)2467 8753 y Fl(\026)2552 8776 y Fh( )2653 8726 y Fp(\()p Fn(q)7 b(;)30 b(")2978 8660 y Fg(1)p Fk(\000)p Fl(\027)3244 8726 y Fp(\))60 b Fm(\025)f Fp(1\).)98 b(W)-15 b(e)66 b(ha)-5 b(v)g(e)65 b(used)h(Lemma)d(4.1)j(with)h Fn(")6510 8660 y Fk(0)6616 8726 y Fp(=)60 b Fn(")6903 8660 y Fg(1)p Fk(\000)p Fl(\027)-201 8951 y Fp(and)52 b(with)h(the)f(function)g Fn(g)7 b Fp(\()p Fn(w)e Fp(\))49 b(=)h Fn(\037)2285 8988 y Fg([)p Fk(\000)p Fg(1)p Fl(;)p Fg(1])2662 8951 y Fp(\()p Fn(w)5 b Fp(\).)77 b(This)52 b(ends)g(the)g(pro)5 b(of)52 b(of)g(the)f(\014rst)h(part.)78 b(The)52 b(conclusion)-201 9177 y(of)60 b(the)g(lemma)e(then)i(follo)-5 b(ws:)81 b(\(4.13\))59 b(yields)1686 9577 y(log)33 b Fn(K)2106 9604 y Fl(\026)2191 9627 y Fh( )2292 9577 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))p 1686 9676 1001 8 v 1925 9842 a Fm(\000)g Fp(log)j Fn(")2757 9718 y Fm(\025)2969 9577 y Fp(log)3234 9429 y Fi(\000)3318 9577 y Fp(2)3409 9511 y Fl(q)5 b Fk(\000)p Fg(2)3665 9577 y Fn(I)3745 9604 y Fl(\026)3830 9627 y Fh( )3932 9577 y Fp(\()p Fn(q)i(;)30 b(")4257 9511 y Fg(1)p Fk(\000)p Fl(\027)4522 9577 y Fp(\))4593 9429 y Fi(\001)p 2969 9676 1708 8 v 3428 9842 a Fm(\000)g Fp(log)j Fn(")3950 9790 y Fg(1)p Fk(\000)p Fl(\027)4696 9718 y Fp(\(1)40 b Fm(\000)g Fn(\027)12 b Fp(\))p Fn(;)-201 10203 y Fp(for)62 b Fn(")g Fp(small)f(enough.)84 b(Then)62 b(tak)-5 b(e)61 b(resp)5 b(ectiv)-5 b(ely)62 b(the)f(lim)30 b(inf)76 b(and)62 b(lim)30 b(sup)62 b(and)g(notice)g(that)f(the)g (result)-201 10429 y(is)g(v)-10 b(alid)61 b(for)g(all)g Fn(\027)h(>)50 b Fp(0)61 b(as)f(small)g(as)g(one)g(w)-5 b(an)g(ts.)3818 b Fc(\003)-201 10754 y Fe(Pro)6 b(of)69 b(of)g(Theorem)137 b(4.2.)-201 10980 y Fp(Theorem)120 b(4.2)60 b(is)h(a)f(direct)h(consequence)e(of)h(Theorem)f(4.1)h(and)h (of)f(Lemma)d(4.3.)1469 b Fc(\003)3393 11631 y Fp(18)p eop %%Page: 19 19 19 18 bop 81 1158 a Fp(As)67 b(already)g(men)-5 b(tioned)66 b(at)g(the)g(end)h(of)f(Section)h(2,)g(our)g(main)f(Theorem,)h(namely)e (Theorem)g(2.1,)-201 1384 y(is)c(a)g(direct)f(consequence)f(of)i (Theorem)e(3.1)h(\(Section)g(3\))g(and)g(of)h(Theorem)e(4.2.)81 1710 y(W)-15 b(e)65 b(end)f(this)h(section)f(with)h(a)g(few)f(w)-5 b(ords)65 b(concerning)g(the)f(case)g(where,)h(as)f(in)h([21])f(and)h ([23)o(],)g(one)-201 1936 y(assumes)59 b(some)h(further)h(prop)5 b(erties)62 b(on)f(the)h(spatial)g(b)5 b(eha)-5 b(viour)62 b(of)f(the)g(k)-5 b(ernel)62 b Fn(u)p Fp(\()p Fn(n;)30 b(x)p Fp(\).)83 b(Assume)60 b(that)-201 2161 y(for)e(some)f(constan)-5 b(t)57 b Fn(C)13 b Fp(,)58 b(indep)5 b(enden)-5 b(t)58 b(of)g(the)g(energy)g Fn(x)p Fp(,)g(and)g(for)g Fn(\015)j Fm(\024)50 b Fn(d)58 b Fp(one)g(kno)-5 b(ws)58 b(that)g(for)g Fn(\026)6628 2191 y Fl( )6784 2161 y Fn(a:e)49 b(x)1738 2434 y Fi(X)1669 2837 y Fk(j)p Fl(n)p Fk(j\024)p Fl(N)2100 2607 y Fm(j)p Fn(u)p Fp(\()p Fn(n;)30 b(x)p Fp(\))p Fm(j)2742 2532 y Fg(2)2869 2607 y Fm(\024)50 b Fn(C)13 b(N)3370 2532 y Fl(\015)3519 2607 y Fn(;)273 b Fp(\(Hyp)5 b(othesis)60 b(\(HS\)\))-201 3224 y(then)f(one)f(can)h(not)f(only)i(get)e(a)h(b)5 b(etter)58 b(result)h(taking)g Fn(\014)h Fp(=)49 b Fn(p=\015)69 b Fp(instead)58 b(of)h Fn(\014)h Fp(=)50 b Fn(p=d)p Fp(,)57 b(but)i(it)g(turns)g(out)-201 3450 y(that)53 b(one)g(can)h(push)f(one)g (step)g(further)g(our)h(approac)-5 b(h)53 b(to)g(reac)-5 b(h)53 b(the)g(dimension)g(n)-5 b(um)g(b)5 b(ers)52 b Fn(D)6399 3384 y Fk(\006)6394 3495 y Fl(\026)6479 3518 y Fh( )6580 3450 y Fp(\(1)26 b Fm(\000)g Fn(\014)10 b Fp(\).)-201 3676 y(The)61 b(gain)g(tak)-5 b(es)59 b(place)i(in)g (Inequalit)-5 b(y)61 b(\(3.12\),)d(where)j(a)g(direct)f(estimate)e(is)j (made)e(p)5 b(ossible)61 b(thanks)f(to)-201 3901 y(Hyp)5 b(othesis)69 b(\(HS\).)f(This)h(thereb)-5 b(y)68 b(enables)g(us)h(to)f (a)-5 b(v)g(oid)69 b(the)f(Cauc)-5 b(h)g(y-Sc)g(h)g(w)g(arz)68 b(inequalit)-5 b(y)69 b(w)-5 b(e)69 b(made)-201 4127 y(in)f(order)g(to)f(split)g(the)g(in)-5 b(tegral)68 b(in)-5 b(to)68 b(a)f(spatial)h(part)f(and)g(a)g(sp)5 b(ectral)68 b(part.)100 b(This)68 b(therefore)e(leads)i(to)-201 4385 y(the)61 b(lo)-5 b(w)g(er)62 b(b)5 b(ound)61 b Fm(hhj)p Fn(X)14 b Fm(j)1559 4319 y Fl(p)1637 4385 y Fm(ii)1779 4415 y Fl( )5 b(;T)2076 4385 y Fm(\025)51 b Fn(C)13 b(L)2536 4319 y Fk(0)2536 4440 y Fl( )2641 4385 y Fp(\()p Fn(T)i(;)30 b(')p Fp(\))51 b(:=)f Fn(C)3597 4295 y Fk(k)p Fl(')p Fk(k)3831 4248 y Fd(2+2)p Fh(\014)p 3561 4343 603 8 v 3561 4457 a Fl(U)3656 4480 y Fh('; )3869 4457 y Fg(\()p Fl(T)20 b Fg(\))4081 4419 y Fh(\014)4183 4385 y Fn(:)61 b Fp(Then)g(the)g(same)e(tec)-5 b(hnique)61 b(as)g(the)g(one)-201 4643 y(used)f(to)h(pro)-5 b(v)g(e)60 b(Theorem)f(4.1)h(supplies)h(the)f (follo)-5 b(wing)62 b(result.)-201 5018 y Fe(Theorem)68 b(4.3.)90 b Fq(Supp)-9 b(ose)55 b(in)h(addition)g(to)g(the)f(hyp)-9 b(otheses)56 b(of)g(The)-9 b(or)g(em)53 b(2.1)j(that)g(the)g(sp)-9 b(atial)55 b(Hyp)-9 b(oth-)-201 5244 y(esis)65 b(\(HS\))h(ab)-9 b(ove)64 b(holds)h(for)f(some)h Fn(\015)75 b Fq(and)65 b(c)-9 b(onstant)66 b Fn(C)13 b Fq(.)83 b(Then,)65 b(if)g Fn(\014)59 b Fp(=)50 b Fn(p=\015)61 b(<)49 b Fp(1)p Fq(,)65 b(one)g(has)1196 5781 y Fp(lim)30 b(inf)1256 5902 y Fl(T)20 b Fk(!1)1750 5654 y Fp(log)s Fm(hhj)p Fn(X)14 b Fm(j)2394 5588 y Fl(p)2472 5654 y Fm(ii)2614 5684 y Fl( )5 b(;T)p 1750 5739 1110 8 v 2106 5905 a Fp(log)34 b Fn(T)2930 5781 y Fm(\025)50 b Fp(lim)30 b(inf)3182 5902 y Fl(T)20 b Fk(!1)3676 5628 y Fp(log)33 b Fn(L)4065 5562 y Fk(0)4065 5684 y Fl( )4170 5628 y Fp(\()p Fn(T)25 b Fp(\))p 3676 5739 768 8 v 3861 5905 a(log)33 b Fn(T)4514 5781 y Fp(=)49 b Fn(\014)10 b(D)4974 5705 y Fk(\000)4969 5825 y Fl(\026)5054 5848 y Fh( )5155 5781 y Fp(\(1)40 b Fm(\000)g Fn(\014)10 b Fp(\))p Fn(;)-201 6266 y Fq(and)1143 6575 y Fp(lim)30 b(sup)1230 6731 y Fl(T)20 b Fk(!1)1750 6448 y Fp(log)s Fm(hhj)p Fn(X)14 b Fm(j)2394 6382 y Fl(p)2472 6448 y Fm(ii)2614 6478 y Fl( )5 b(;T)p 1750 6533 1110 8 v 2106 6699 a Fp(log)34 b Fn(T)2930 6575 y Fm(\025)50 b Fp(lim)30 b(sup)3208 6731 y Fl(T)20 b Fk(!1)3729 6423 y Fp(log)33 b Fn(L)4118 6357 y Fk(0)4118 6478 y Fl( )4223 6423 y Fp(\()p Fn(T)25 b Fp(\))p 3729 6533 768 8 v 3914 6699 a(log)33 b Fn(T)4566 6575 y Fp(=)50 b Fn(\014)10 b(D)5027 6500 y Fg(+)5022 6620 y Fl(\026)5107 6643 y Fh( )5208 6575 y Fp(\(1)40 b Fm(\000)g Fn(\014)10 b Fp(\))p Fn(:)-201 7281 y Fo(App)d(endices)-201 7853 y(A)269 b(Complemen)-7 b(t)90 b(of)h(Section)e(2)-201 8359 y Fp(F)-15 b(or)50 b(the)f(reader's)h(con)-5 b(v)g(enience,)50 b(w)-5 b(e)51 b(pro)-5 b(vide)50 b(the)f(pro)5 b(of)50 b(of)f(statemen)-5 b(ts)47 b(ii\))k(and)f(iii\))h(of)e(Prop)5 b(osition)50 b(2.1.)-201 8684 y Fe(Pro)6 b(of)62 b(of)g(ii\))h(of)g(Prop)6 b(osition)61 b(2.1.)78 b Fp(W)-15 b(e)54 b(\014rst)h(note)f(that)g (from)f(the)h(con)-5 b(v)g(ex)54 b(Jensen)f(Inequalit)-5 b(y)-15 b(,)55 b(and)-201 8910 y(since)61 b Fn(q)47 b Fm(\000)40 b Fp(1)50 b Fn(<)g Fp(0,)60 b(w)-5 b(e)61 b(ha)-5 b(v)g(e,)59 b(for)i(an)-5 b(y)60 b(set)g Fn(A)51 b Fm(\032)f Ff(R)821 9474 y Fn(I)901 9501 y Fl(\026)994 9474 y Fp(\()p Fn(q)7 b(;)30 b("=)p Fp(2\))1669 9329 y Fd(1)p 1591 9353 218 6 v 1591 9435 a Fh(q)t Fb(\000)p Fd(1)1887 9474 y Fp(=)2079 9218 y Fi(\022)2212 9227 y(Z)2313 9639 y Fj(R)2448 9474 y Fn(\026)p Fp(\()p Fn(x)40 b Fm(\000)f Fn("=)p Fp(2)p Fn(;)30 b(x)40 b Fp(+)g Fn("=)p Fp(2\))3966 9399 y Fl(q)5 b Fk(\000)p Fg(1)4222 9474 y Fp(d)p Fn(\026)p Fp(\()p Fn(x)p Fp(\))4679 9218 y Fi(\023)4910 9209 y Fd(1)p 4831 9233 V 4831 9315 a Fh(q)t Fb(\000)p Fd(1)987 10043 y Fm(\024)1295 9787 y Fi(\022)1428 9796 y(Z)1529 10208 y Fl(A)1674 10043 y Fn(\026)p Fp(\()p Fn(x)39 b Fm(\000)h Fn(";)30 b(x)40 b Fp(+)g Fn(")p Fp(\))2828 9968 y Fl(q)5 b Fk(\000)p Fg(1)3084 10043 y Fp(d)p Fn(\026)p Fp(\()p Fn(x)p Fp(\))3541 9787 y Fi(\023)3772 9778 y Fd(1)p 3694 9802 V 3694 9884 a Fh(q)t Fb(\000)p Fd(1)3989 10043 y Fm(\024)4181 9796 y Fi(Z)4282 10208 y Fl(A)4427 10043 y Fn(\026)p Fp(\()p Fn(x)39 b Fm(\000)h Fn(";)30 b(x)40 b Fp(+)g Fn(")p Fp(\)d)p Fn(\026)p Fp(\()p Fn(x)p Fp(\))59 b Fn(:)602 b Fp(\(A.1\))81 10551 y(Consider)62 b(no)-5 b(w,)60 b(for)g(all)i Fn(\027)g Fm(2)50 b Fp(\(0)p Fn(;)30 b Fp(1\),)59 b(the)i(set)1496 10960 y Fn(A)1632 10885 y Fg(\()p Fl(H)10 b Fg(\))1632 11005 y Fl(\027)1877 10960 y Fp(\()p Fn(")p Fp(\))50 b Fm(\021)g(f)p Fn(x)g Fm(2)h Ff(R)96 b Fm(j)60 b Fn(\026)p Fp(\()p Fn(x)39 b Fm(\000)h Fn(";)30 b(x)40 b Fp(+)g Fn(")p Fp(\))50 b Fn(<)g(")4547 10885 y Fg(dim)4783 10907 y Fd(H)4879 10885 y Fg(\()p Fl(\026)p Fg(\))p Fk(\000)p Fl(\027)5270 10960 y Fm(g)61 b Fn(:)3393 11631 y Fp(19)p eop %%Page: 20 20 20 19 bop -201 1158 a Fp(W)-15 b(e)60 b(ha)-5 b(v)g(e)1174 1384 y Fn(A)1310 1309 y Fg(\()p Fl(H)10 b Fg(\))1310 1429 y Fl(\027)1605 1384 y Fp(:=)50 b(lim)30 b(inf)1961 1500 y Fl(")p Fk(!)p Fg(0)2382 1384 y Fn(A)2518 1309 y Fg(\()p Fl(H)10 b Fg(\))2518 1429 y Fl(\027)2763 1384 y Fp(\()p Fn(")p Fp(\))49 b Fm(\033)h(f)p Fn(x)h Fm(2)f Ff(R)96 b Fm(j)60 b Fn(\015)4055 1309 y Fk(\000)4045 1429 y Fl(\026)4174 1384 y Fp(\()p Fn(x)p Fp(\))49 b Fn(>)h Fp(dim)4965 1412 y Fg(H)5078 1384 y Fp(\()p Fn(\026)p Fp(\))40 b Fm(\000)g Fn(\027)12 b Fm(g)p Fn(:)-201 1788 y Fp(By)60 b(the)g(de\014nition)h(of)e(dim)1715 1816 y Fg(H)1828 1788 y Fp(\()p Fn(\026)p Fp(\))h(giv)-5 b(en)60 b(Line)g(\(2.1\))f(w)-5 b(e)60 b(get)g Fn(\026)p Fp(\()p Fm(f)p Fn(x)50 b Fm(2)g Ff(R)96 b Fm(j)60 b Fn(\015)5028 1722 y Fk(\000)5018 1833 y Fl(\026)5146 1788 y Fp(\()p Fn(x)p Fp(\))50 b Fn(>)g Fp(dim)5938 1816 y Fg(H)6051 1788 y Fp(\()p Fn(\026)p Fp(\))38 b Fm(\000)h Fn(\027)12 b Fm(g)p Fp(\))50 b Fn(>)g Fp(0.)-201 2071 y(F)-15 b(urthermore,)77 b(lim)30 b(inf)1427 2098 y Fl(")p Fk(!)p Fg(0)1743 2071 y Fn(\026)p Fp(\()p Fn(A)2060 1975 y Fg(\()p Fl(H)10 b Fg(\))2060 2094 y Fl(\027)2304 2071 y Fp(\)\()p Fn(")p Fp(\))75 b Fm(\025)g Fn(\026)p Fp(\()p Fn(A)3211 1975 y Fg(\()p Fl(H)10 b Fg(\))3211 2094 y Fl(\027)3455 2071 y Fp(\))75 b Fm(\025)h Fn(\026)p Fp(\()p Fm(f)p Fn(x)f Fm(2)h Ff(R)111 b Fm(j)75 b Fn(\015)4904 2005 y Fk(\000)4894 2115 y Fl(\026)5023 2071 y Fp(\()p Fn(x)p Fp(\))g Fn(>)g Fp(dim)5865 2099 y Fg(H)5978 2071 y Fp(\()p Fn(\026)p Fp(\))50 b Fm(\000)g Fn(\027)12 b Fm(g)p Fp(\))75 b Fn(>)g Fp(0.)-201 2353 y(Th)-5 b(us,)60 b(letting)h Fn(A)51 b Fp(=)f Fn(A)1401 2258 y Fg(\()p Fl(H)10 b Fg(\))1401 2377 y Fl(\027)1645 2353 y Fp(\()p Fn(")p Fp(\))60 b(in)h(\(A.1\),)f(w) -5 b(e)60 b(obtain)2089 2929 y Fn(D)2245 2854 y Fk(\000)2240 2974 y Fl(\026)2362 2929 y Fp(\()p Fn(q)7 b Fp(\))50 b(=)g(lim)30 b(inf)2947 3045 y Fl(")p Fk(!)p Fg(0)3388 2805 y Fp(log)j Fn(I)3733 2832 y Fl(\026)3826 2805 y Fp(\()p Fn(q)7 b(;)30 b("=)p Fp(2\))4501 2660 y Fd(1)p 4423 2684 218 6 v 4423 2766 a Fh(q)t Fb(\000)p Fd(1)p 3388 2888 1281 8 v 3707 3054 a Fp(log)r(\()p Fn("=)p Fp(2\))4739 2929 y Fm(\025)1450 3621 y Fp(lim)g(inf)1564 3737 y Fl(")p Fk(!)p Fg(0)2005 3432 y Fp(log)2270 3230 y Fi(\020)2378 3432 y Fn(\026)p Fp(\()p Fn(A)2695 3336 y Fg(\()p Fl(H)10 b Fg(\))2695 3455 y Fl(\027)2939 3432 y Fp(\()p Fn(")p Fp(\)\))p Fn(")3322 3366 y Fg(dim)3558 3388 y Fd(H)3654 3366 y Fg(\()p Fl(\026)p Fg(\))p Fk(\000)p Fl(\027)4045 3230 y Fi(\021)p 2005 3579 2149 8 v 2757 3746 a Fp(log)s(\()p Fn("=)p Fp(2\))4224 3621 y(=)49 b(dim)4719 3649 y Fg(H)4833 3621 y Fp(\()p Fn(\026)p Fp(\))39 b Fm(\000)h Fn(\027)72 b(:)-201 4051 y Fp(Since)61 b(the)f(ab)5 b(o)-5 b(v)g(e)60 b(inequalit)-5 b(y)62 b(is)f(v)-10 b(alid)61 b(for)f(all)i Fn(\027)g Fm(2)50 b Fp(\(0)p Fn(;)30 b Fp(1\),)59 b(ii\))j(of)e(Prop)5 b(osition)61 b(2.1)f(is)g(pro)-5 b(v)g(en.)-201 4375 y Fe(Pro)6 b(of)69 b(of)g(iii\))h(of)f(Prop)6 b(osition)69 b(2.1.)80 b Fp(W)-15 b(e)60 b(de\014ne,)g(for)g Fn(")3967 4405 y Fl(k)4103 4375 y Fp(=)49 b(e)4375 4309 y Fk(\000)p Fl(k)1356 4812 y Fn(A)1492 4737 y Fg(\()p Fl(P)20 b Fg(\))1492 4857 y Fl(\027)1719 4812 y Fp(\()p Fn(")1875 4842 y Fl(k)1960 4812 y Fp(\))50 b(:=)g Fm(f)p Fn(x)g Fm(2)h Ff(R)95 b Fm(j)61 b Fn(\026)p Fp(\()p Fn(x)39 b Fm(\000)h Fn(")3635 4842 y Fl(k)3720 4812 y Fn(;)30 b(x)40 b Fp(+)g Fn(")4212 4842 y Fl(k)4297 4812 y Fp(\))50 b Fn(<)g(")4695 4717 y Fg(dim)4931 4739 y Fd(P)5020 4717 y Fg(\()p Fl(\026)p Fg(\))p Fk(\000)p Fl(\027)4695 4871 y(k)5411 4812 y Fm(g)60 b Fn(:)81 5218 y Fp(Since)92 b(lim)840 5248 y Fl(k)t Fk(!1)1237 5218 y Fp(log)34 b Fn(")1588 5248 y Fl(k)1673 5218 y Fn(=)c Fp(log)j Fn(")2144 5248 y Fl(k)t Fg(+1)2511 5218 y Fp(=)102 b(1,)c(w)-5 b(e)92 b(ha)-5 b(v)g(e)91 b(lim)30 b(sup)4300 5262 y Fl(k)t Fk(!1)4698 5218 y Fp(log)j Fn(\026)p Fp(\()p Fn(x)60 b Fm(\000)h Fn(")5596 5248 y Fl(k)5681 5218 y Fn(;)30 b(x)60 b Fp(+)h Fn(")6214 5248 y Fl(k)6299 5218 y Fp(\))p Fn(=)30 b Fp(log)j Fn(")6841 5248 y Fl(k)7028 5218 y Fp(=)-201 5444 y(lim)d(sup)356 5487 y Fl(")p Fk(!)p Fg(0)671 5444 y Fp(log)j Fn(\026)p Fp(\()p Fn(x)40 b Fm(\000)g Fn(";)30 b(x)40 b Fp(+)g Fn(")p Fp(\))p Fn(=)30 b Fp(log)i Fn(")p Fp(.)80 b(Th)-5 b(us)61 b(w)-5 b(e)61 b(get)1032 6075 y Fn(A)1168 6000 y Fg(\()p Fl(P)20 b Fg(\))1168 6120 y Fl(\027)1562 6075 y Fp(:=)165 b(lim)30 b(sup)2018 6233 y Fl(k)t Fk(!1)2507 6075 y Fn(A)2643 6000 y Fg(\()p Fl(P)20 b Fg(\))2643 6120 y Fl(\027)2870 6075 y Fp(\()p Fn(")3026 6105 y Fl(k)3111 6075 y Fp(\))1587 6577 y Fm(\033)191 b(f)p Fn(x)50 b Fm(2)h Ff(R)96 b Fm(j)90 b Fp(lim)30 b(sup)2769 6735 y Fl(k)t Fk(!1)3277 6454 y Fn(\026)p Fp(\()p Fn(x)39 b Fm(\000)h Fn(")3868 6484 y Fl(k)3953 6454 y Fn(;)30 b(x)41 b Fp(+)e Fn(")4445 6484 y Fl(k)4530 6454 y Fp(\))p 3277 6535 1325 8 v 3721 6702 a(log)34 b Fn(")4072 6732 y Fl(k)4672 6577 y Fn(>)50 b Fp(dim)5168 6605 y Fg(P)5271 6577 y Fp(\()p Fn(\026)p Fp(\))39 b Fm(\000)h Fn(\027)12 b Fm(g)1587 6975 y Fp(=)191 b Fm(f)p Fn(x)50 b Fm(2)h Ff(R)96 b Fm(j)60 b Fn(\015)2744 6900 y Fg(+)2734 7020 y Fl(\026)2862 6975 y Fp(\()p Fn(x)p Fp(\))50 b Fn(>)g Fp(dim)3654 7003 y Fg(P)3757 6975 y Fp(\()p Fn(\026)p Fp(\))40 b Fm(\000)f Fn(\027)12 b Fm(g)p Fn(:)-201 7381 y Fp(Therefore,)71 b(from)d(the)h(de\014nition)h(of)f(dim)2783 7409 y Fg(P)2886 7381 y Fp(\()p Fn(\026)p Fp(\))g(giv)-5 b(en)70 b(Line)f(\(2.1\))g(and)g(the)g(ab)5 b(o)-5 b(v)g(e)69 b(inclusions,)j(w)-5 b(e)70 b(get)-201 7638 y Fn(\026)p Fp(\()p Fn(A)116 7542 y Fg(\()p Fl(P)20 b Fg(\))116 7662 y Fl(\027)343 7638 y Fp(\))50 b Fn(>)g Fp(0.)78 b(Using)55 b(the)e(Borel)h(Can)-5 b(telli)56 b(lemma)51 b(\(as)i(done)h(in)g ([15]\))f(implies)g(that)5744 7502 y Fi(P)5936 7692 y Fl(k)6051 7638 y Fn(\026)p Fp(\()p Fn(A)6368 7542 y Fg(\()p Fl(P)20 b Fg(\))6368 7662 y Fl(\027)6595 7638 y Fp(\()p Fn(")6751 7668 y Fl(k)6836 7638 y Fp(\)\))50 b(=)-201 7904 y Fm(1)63 b Fp(and)f(th)-5 b(us,)62 b(there)g(exists)g(a)h (subsequence)e Fn(")3091 7941 y Fl(k)t Fg(\()p Fl(n)p Fg(\))3425 7904 y Fm(&)54 b Fp(0)62 b(of)g Fn(")4108 7934 y Fl(k)4256 7904 y Fp(suc)-5 b(h)62 b(that)g Fn(\026)p Fp(\()p Fn(A)5381 7808 y Fg(\()p Fl(P)20 b Fg(\))5381 7928 y Fl(\027)5608 7904 y Fp(\()p Fn(")5764 7941 y Fl(k)t Fg(\()p Fl(n)p Fg(\))6044 7904 y Fp(\)\))53 b Fm(\025)h Fn(k)6 b Fp(\()p Fn(n)p Fp(\))6787 7838 y Fk(\000)p Fg(2)7028 7904 y Fp(=)-201 8186 y(\(log)33 b Fn(")220 8223 y Fl(k)t Fg(\()p Fl(n)p Fg(\))501 8186 y Fp(\))572 8120 y Fk(\000)p Fg(2)760 8186 y Fp(.)80 b(Th)-5 b(us,)60 b(letting)h Fn(A)51 b Fp(=)f Fn(A)2493 8090 y Fg(\()p Fl(P)20 b Fg(\))2493 8210 y Fl(\027)2720 8186 y Fp(\()p Fn(")2876 8223 y Fl(k)t Fg(\()p Fl(n)p Fg(\))3157 8186 y Fp(\))60 b(in)h(\(A.1\),)e(w)-5 b(e)61 b(obtain)-128 8851 y Fn(D)28 8776 y Fg(+)23 8896 y Fl(\026)147 8851 y Fp(\()p Fn(q)7 b Fp(\))49 b(=)h(lim)30 b(sup)758 9002 y Fl(")p Fk(!)p Fg(0)1225 8727 y Fp(log)j Fn(I)1570 8754 y Fl(\026)1663 8727 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))2156 8582 y Fd(1)p 2078 8606 218 6 v 2078 8688 a Fh(q)t Fb(\000)p Fd(1)p 1225 8809 1099 8 v 1599 8976 a Fp(log)j Fn(")2394 8851 y Fm(\025)107 b Fp(lim)2586 8960 y Fl(n)p Fk(!1)3004 8662 y Fp(log)3269 8460 y Fi(\020)3377 8662 y Fn(\026)p Fp(\()p Fn(A)3694 8566 y Fg(\()p Fl(P)20 b Fg(\))3694 8686 y Fl(\027)3921 8662 y Fp(\()p Fn(")4077 8699 y Fl(k)t Fg(\()p Fl(n)p Fg(\))4357 8662 y Fp(\)\))p Fn(")4584 8566 y Fg(dim)4820 8588 y Fd(P)4909 8566 y Fg(\()p Fl(\026)p Fg(\))p Fk(\000)p Fl(\027)4584 8728 y(k)t Fg(\()p Fl(n)p Fg(\))5300 8460 y Fi(\021)p 3004 8809 2405 8 v 3891 8976 a Fp(log)33 b Fn(")4241 9013 y Fl(k)t Fg(\()p Fl(n)p Fg(\))5479 8851 y Fp(=)50 b(dim)5975 8879 y Fg(P)6078 8851 y Fp(\()p Fn(\026)p Fp(\))39 b Fm(\000)h Fn(\027)72 b(:)-201 9379 y Fp(Again,)61 b(since)f(the)g (result)g(is)g(true)g(for)g(all)i Fn(\027)f Fm(2)51 b Fp(\(0)p Fn(;)30 b Fp(1\),)59 b(statemen)-5 b(t)57 b(iii\))62 b(of)d(Prop)5 b(osition)61 b(2.1)e(is)i(pro)-5 b(v)g(en.)80 b Fc(\003)-201 9951 y Fo(B)269 b(Relation)89 b(to)h(other)g(lo)-7 b(w)g(er)89 b(b)7 b(ounds)-201 10456 y Fp(Getting)60 b(a)h(gro)-5 b(wth)61 b(exp)5 b(onen)-5 b(t)60 b(in)h(terms)e(of)h (fractal)g(dimensions)g Fn(D)4599 10390 y Fk(\006)4594 10501 y Fl(\026)4679 10524 y Fh( )4780 10456 y Fp(\()p Fn(q)7 b Fp(\))60 b(is)h(not)f(sp)5 b(eci\014c)60 b(to)h(our)g(lo)-5 b(w)g(er)-201 10682 y(b)5 b(ound)68 b Fn(L)491 10712 y Fl( )596 10682 y Fp(\()p Fn(T)25 b Fp(\))68 b(\(3.2\).)100 b(It)67 b(is)h(also)g(p)5 b(ossible)68 b(to)f(get)g(suc)-5 b(h)68 b(relations)g(from)e(the)h(lo)-5 b(w)g(er)68 b(b)5 b(ounds)68 b(formerly)-201 10907 y(deriv)-5 b(ed,)59 b(either)h(directly)f(\(Barbaroux-Tc)-5 b(heremc)g(han)g(tsev's)55 b(lo)-5 b(w)g(er)60 b(b)5 b(ound)59 b Fn(L)5347 10934 y Fg(2)5425 10907 y Fp(\()p Fn(T)25 b Fp(\))59 b(b)5 b(elo)-5 b(w\),)60 b(either)f(im-)-201 11133 y(pro)-5 b(ving)74 b(them)d(\(Guarneri-Com)-5 b(b)5 b(es-Last's)69 b(lo)-5 b(w)g(er)73 b(b)5 b(ound,)76 b(impro)-5 b(v)g(ed)72 b(b)-5 b(y)73 b(optimizing)f(in)i Fn(')f Fp(for)g(eac)-5 b(h)3393 11631 y(20)p eop %%Page: 21 21 21 20 bop -201 1158 a Fp(single)73 b Fn(T)25 b Fp(,)75 b(see)c Fn(L)1003 1185 y Fg(1)1082 1158 y Fp(\()p Fn(T)25 b Fp(\))72 b(b)5 b(elo)-5 b(w\).)115 b(W)-15 b(e)71 b(shall)i (brie\015y)f(explain)h(this)f(p)5 b(oin)-5 b(t)72 b(in)h(this)f (section,)i(and)e(thereb)-5 b(y)-201 1384 y(prop)5 b(ose)56 b(to)h(the)f(reader)h(a)f(link)i(b)5 b(et)-5 b(w)g(een)56 b(the)g(presen)-5 b(t)56 b(w)-5 b(ork)57 b(and)f(the)h(former)d(metho)5 b(ds.)77 b(In)57 b(particular)-201 1610 y(this)52 b(app)5 b(endix)51 b(illustrates)h(ho)-5 b(w)51 b(actually)h(deeply)g (connected)e(are)h(the)g(generalized)h(fractal)f(dimensions)-201 1836 y Fn(D)-45 1770 y Fk(\006)-50 1881 y Fl(\026)35 1904 y Fh( )136 1836 y Fp(\()p Fn(q)7 b Fp(\))46 b(to)g(the)f(lo)-5 b(w)g(er)47 b(b)5 b(ounds)46 b(of)g Fm(hhj)p Fn(X)14 b Fm(j)2599 1770 y Fl(p)2677 1836 y Fm(ii)2819 1866 y Fl( )5 b(;T)3111 1836 y Fp(studied)46 b(for)g(the)f(past)h(ten)g(y)-5 b(ears,)48 b(that)d(is)i(since)f(Guarneri)-201 2062 y([14].)81 2288 y(Since)j(w)-5 b(e)48 b(shall)h(fo)5 b(cus)48 b(on)g(the)g (relation)g(b)5 b(et)-5 b(w)g(een)48 b(those)g(lo)-5 b(w)g(er)49 b(b)5 b(ounds)48 b(and)g(the)g(fractal)g(dimensions)-201 2513 y Fn(D)-45 2447 y Fk(\006)-50 2558 y Fl(\026)35 2581 y Fh( )136 2513 y Fp(\()p Fn(q)7 b Fp(\),)78 b(and)d(for)f(a)h (sak)-5 b(e)75 b(of)f(simplicit)-5 b(y)-15 b(,)78 b(w)-5 b(e)75 b(shall)h(only)f(consider)g(v)-5 b(ectors)75 b Fn(')g Fp(of)f(the)h(form)e Fn(\037)6627 2541 y Fg(\012)6737 2513 y Fp(\()p Fn(H)15 b Fp(\))p Fn( )-201 2739 y Fp(instead)60 b(of)h(general)f Fn(')51 b Fm(2)f(H)1755 2769 y Fl( )1921 2739 y Fp(as)60 b(in)h(\(3.2\).)81 2965 y(W)-15 b(e)65 b(\014rst)f(consider)g(the)g(lo)-5 b(w)g(er)65 b(b)5 b(ound)65 b(that)f(app)5 b(ears)64 b(in)h([5)o(].)92 b(F)-15 b(or)64 b(some)f(constan)-5 b(t)63 b Fn(C)13 b Fp(\()p Fn( )7 b(;)30 b(p)p Fp(\))55 b Fn(>)h Fp(0,)65 b(it)-201 3191 y(is)c(sho)-5 b(wn)61 b(that)e(for)i(all)g Fn(T)76 b(>)50 b Fp(0,)-91 3704 y Fm(hhj)p Fn(X)14 b Fm(j)318 3629 y Fl(p)396 3704 y Fm(ii)538 3734 y Fl( )5 b(;T)834 3704 y Fm(\025)50 b Fn(C)13 b Fp(\()p Fn( )7 b(;)30 b(p)p Fp(\))p Fn(L)1734 3731 y Fg(2)1810 3704 y Fp(\()p Fn(T)25 b Fp(\))p Fn(;)212 b Fp(with)182 b Fn(L)3005 3731 y Fg(2)3084 3704 y Fp(\()p Fn(T)25 b Fp(\))50 b(=)g(sup)3903 3448 y Fi(\032)4039 3704 y Fn(L)4163 3731 y Fg(2)4242 3704 y Fp(\()p Fn(';)30 b(T)25 b Fp(\))50 b(:=)5027 3581 y Fm(k)p Fn(')p Fm(k)5328 3515 y Fg(2+8)p Fl(\014)p 5027 3662 646 8 v 5061 3829 a Fn(S)5173 3856 y Fl(')5273 3829 y Fp(\()p Fn(T)25 b Fp(\))5546 3776 y Fl(\014)5693 3704 y Fn(;)81 b(')50 b Fp(=)g Fn(\037)6300 3732 y Fg(\012)6410 3704 y Fp(\()p Fn(H)15 b Fp(\))p Fn( )6844 3448 y Fi(\033)7009 3704 y Fn(;)-201 4205 y Fp(where)1903 4469 y Fn(S)2015 4496 y Fl(')2115 4469 y Fp(\()p Fn(T)25 b Fp(\))50 b(=)2630 4222 y Fi(Z)2731 4634 y Fj(R)2818 4596 y Fd(2)2935 4469 y Fp(d)p Fn(\026)3146 4496 y Fl(')3246 4469 y Fp(\()p Fn(x)p Fp(\)d)p Fn(\026)3703 4496 y Fl(')3802 4469 y Fp(\()p Fn(y)7 b Fp(\))p Fn(R)q Fp(\()p Fn(T)25 b Fp(\()p Fn(x)40 b Fm(\000)g Fn(y)7 b Fp(\)\))p Fn(:)-201 4934 y Fp(Here)52 b Fn(R)q Fp(\()p Fn(w)5 b Fp(\))52 b(can)f(b)5 b(e)52 b(c)-5 b(hosen)51 b(as)g(the)g(usual)h(gaussian)f Fn(e)3614 4868 y Fk(\000)p Fl(w)3829 4822 y Fd(2)3898 4868 y Fl(=)p Fg(4)4047 4934 y Fp(.)78 b(Then)51 b(one)h(can)f(mimic)f(the)h(pro)5 b(of)51 b(of)h(The-)-201 5160 y(orem)46 b(3.1,)j(and)e(relate)g(the)g (quan)-5 b(tit)g(y)47 b Fn(L)2544 5187 y Fg(2)2623 5160 y Fp(\()p Fn(';)30 b(T)25 b Fp(\))50 b(=)g Fm(k)p Fn(')p Fm(k)3639 5094 y Fg(2+8)p Fl(\014)3984 5160 y Fn(=S)4187 5187 y Fl(')4286 5160 y Fp(\()p Fn(T)25 b Fp(\))4559 5094 y Fl(\014)4701 5160 y Fp(to)47 b(the)g(in)-5 b(tegral)47 b Fn(K)6013 5187 y Fl(\026)6098 5210 y Fh( )6200 5160 y Fp(\()6291 5078 y Fg(1+2)p Fl(\014)p 6291 5118 337 8 v 6291 5223 a Fg(1+3)p Fl(\014)6647 5160 y Fn(;)30 b(T)6859 5094 y Fk(\000)p Fg(1)7048 5160 y Fp(\).)-201 5386 y(More)54 b(precisely)-15 b(,)55 b(the)e(same)f(kind)i(of)g(H\177) -91 b(older)54 b(Inequalities)g(as)g(in)g(\(4.5\)-\(4.6\))d(supplies)j (an)g(upp)5 b(er)54 b(b)5 b(ound)-201 5612 y(for)60 b Fn(L)201 5639 y Fg(2)279 5612 y Fp(\()p Fn(T)25 b Fp(\))60 b(and)g(using)f(a)h(set)f(\012\()p Fn(r)5 b Fp(\))60 b(in)g(the)f(same)f(spirit)i(as)f(previously)i(yields)f(the)f(lo)-5 b(w)g(er)61 b(b)5 b(ound,)59 b(again)-201 5838 y(up)i(to)f(a)h (logarithmic)f(factor.)79 b(The)61 b(follo)-5 b(wing)62 b(theorem)c(then)i(holds:)-201 6211 y Fe(Theorem)68 b(B.1.)90 b Fq(Under)65 b(the)g(same)g(hyp)-9 b(otheses)65 b(as)g(in)g(The)-9 b(or)g(em)63 b(2.1,)i(one)g(has)153 6707 y Fp(lim)30 b(inf)213 6828 y Fl(T)20 b Fk(!1)708 6584 y Fp(log)33 b Fn(L)1097 6611 y Fg(2)1175 6584 y Fp(\()p Fn(T)25 b Fp(\))p 708 6665 741 8 v 880 6831 a(log)33 b Fn(T)1519 6707 y Fp(=)50 b Fn(\014)10 b(D)1980 6632 y Fk(\000)1975 6752 y Fl(\026)2060 6775 y Fh( )2191 6450 y Fi(\022)2344 6584 y Fp(1)41 b(+)e(2)p Fn(\014)p 2344 6665 517 8 v 2344 6831 a Fp(1)i(+)e(3)p Fn(\014)2881 6450 y Fi(\023)3045 6707 y Fn(;)216 b Fp(and)g(lim)30 b(sup)3907 6863 y Fl(T)20 b Fk(!1)4427 6584 y Fp(log)34 b Fn(L)4817 6611 y Fg(2)4895 6584 y Fp(\()p Fn(T)25 b Fp(\))p 4427 6665 741 8 v 4599 6831 a(log)34 b Fn(T)5239 6707 y Fp(=)49 b Fn(\014)10 b(D)5699 6632 y Fg(+)5694 6752 y Fl(\026)5779 6775 y Fh( )5910 6450 y Fi(\022)6064 6584 y Fp(1)41 b(+)e(2)p Fn(\014)p 6064 6665 517 8 v 6064 6831 a Fp(1)i(+)e(3)p Fn(\014)6601 6450 y Fi(\023)6765 6707 y Fn(:)81 7215 y Fp(The)j(second)f(lo)-5 b(w)g(er)42 b(b)5 b(ound)42 b(w)-5 b(e)41 b(w)-5 b(an)g(t)42 b(to)f(discuss)g(in)h(this)f(section)g (is)h(the)f(impro)-5 b(v)g(ed)40 b(v)-5 b(ersion,)45 b(using)d([5)o(],)-201 7440 y(of)j(the)g(\014rst)f(kind)i(of)f(quan)-5 b(tit)g(y)44 b(that)h(has)g(b)5 b(een)45 b(considered)f(in)i(order)f (to)g(b)5 b(ound)45 b(from)f(b)5 b(elo)-5 b(w)45 b Fm(hhj)p Fn(X)14 b Fm(j)6653 7374 y Fl(p)6731 7440 y Fm(ii)6873 7470 y Fl( )5 b(;T)7119 7440 y Fp(,)-201 7666 y(and)51 b(that)f(comes)f(from)g(Guarneri-Com)-5 b(b)5 b(es-Last)48 b([14)o(,)i(7,)g(25].)77 b(Roughly)-15 b(,)52 b(the)f(basic)f(idea)h (is)h(to)e(tak)-5 b(e)50 b(in)-5 b(to)-201 7892 y(accoun)g(t)60 b(the)g(function)g Fn(G)1639 7919 y Fl(')1739 7892 y Fp(\()p Fn(T)25 b Fp(\))50 b(:=)g Fn(\026)2415 7919 y Fl(')2554 7892 y Fm(\000)40 b Fp(ess)29 b(sup)3294 7746 y Fi(R)3446 7892 y Fp(d)p Fn(\026)3657 7919 y Fl(')3757 7892 y Fp(\()p Fn(y)7 b Fp(\))p Fn(R)q Fp(\()p Fn(T)25 b Fp(\()p Fn(x)39 b Fm(\000)h Fn(y)7 b Fp(\)\))59 b(where)i Fn(R)q Fp(\()p Fn(w)5 b Fp(\))50 b(=)g(exp\()p Fm(\000)p Fn(w)6839 7826 y Fg(2)6917 7892 y Fn(=)p Fp(4\))-201 8118 y(\(notice)74 b(that)g Fn(G)970 8145 y Fl(')1070 8118 y Fp(\()p Fn(T)25 b Fp(\))74 b(will)i(b)5 b(e)74 b(smaller)g(than)g Fn(C)13 b(T)3389 8052 y Fk(\000)p Fl(\013)3672 8118 y Fp(if)74 b Fn(\026)3962 8145 y Fl(')4137 8118 y Fp(is)g(uniformly)g Fn(\013)q Fp(-H\177)-91 b(older)74 b(con)-5 b(tin)g(uous,)77 b(see)-201 8344 y(\(3.10\))h(in)i([25]\).)136 b(One)78 b(then)h(uses)g Fn(G)2499 8371 y Fl(')2599 8344 y Fp(\()p Fn(T)25 b Fp(\))80 b(in)g(order)f(to)g(b)5 b(ound)80 b Fn(B)4636 8371 y Fl(')4736 8344 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))79 b(de\014ned)g(as)g(in)h(\(3.6\))f(but) -201 8598 y(with)56 b(1)p Fn(=T)552 8452 y Fi(R)673 8504 y Fl(T)638 8662 y Fg(0)839 8598 y Fp(rather)f(than)g(1)p Fn(=T)2142 8452 y Fi(R)2264 8504 y Fg(+)p Fk(1)2228 8662 y Fg(0)2553 8598 y Fn(h)p Fp(\()p Fn(t=T)25 b Fp(\).)78 b(Using,)57 b(for)e(instance,)g(2)p Fm(j)p Fn(v)7 b Fp(\()p Fn(n;)30 b(x)p Fp(\))p Fn(v)7 b Fp(\()p Fn(n;)30 b(y)7 b Fp(\))p Fm(j)47 b(\024)j(j)p Fn(v)7 b Fp(\()p Fn(n;)30 b(x)p Fp(\))p Fm(j)6921 8532 y Fg(2)7028 8598 y Fp(+)-201 8824 y Fm(j)p Fn(v)7 b Fp(\()p Fn(n;)30 b(y)7 b Fp(\))p Fm(j)424 8758 y Fg(2)501 8824 y Fp(,)705 9314 y Fn(B)843 9341 y Fl(')943 9314 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))166 b Fm(\024)f Fn(C)2099 9066 y Fi(Z)2201 9478 y Fj(R)2335 9066 y Fi(Z)2436 9478 y Fj(R)2571 9314 y Fp(d)p Fn(\026)2782 9341 y Fl(')2881 9314 y Fp(\()p Fn(x)p Fp(\)d)p Fn(\026)3338 9341 y Fl(')3438 9314 y Fp(\()p Fn(y)7 b Fp(\))p Fn(R)q Fp(\(\()p Fn(x)39 b Fm(\000)h Fn(y)7 b Fp(\))p Fn(T)25 b Fp(\))4749 9141 y Fi(X)4681 9543 y Fk(j)p Fl(n)p Fk(j\024)p Fl(N)5111 9314 y Fm(j)p Fn(v)7 b Fp(\()p Fn(n;)30 b(x)p Fp(\))p Fn(v)7 b Fp(\()p Fn(n;)30 b(y)7 b Fp(\))p Fm(j)1619 9909 y(\024)165 b Fn(C)13 b(G)2212 9936 y Fl(')2312 9909 y Fp(\()p Fn(T)25 b Fp(\))2615 9661 y Fi(Z)2717 10074 y Fj(R)2851 9909 y Fp(d)p Fn(\026)3062 9936 y Fl(')3162 9909 y Fp(\()p Fn(x)p Fp(\))3506 9736 y Fi(X)3438 10139 y Fk(j)p Fl(n)p Fk(j\024)p Fl(N)3868 9909 y Fm(j)p Fn(v)7 b Fp(\()p Fn(n;)30 b(x)p Fp(\))p Fm(j)4501 9834 y Fg(2)4628 9909 y Fm(\024)50 b Fn(C)4963 9834 y Fk(0)5010 9909 y Fn(G)5153 9936 y Fl(')5253 9909 y Fp(\()p Fn(T)25 b Fp(\))p Fn(N)5692 9834 y Fl(d)5803 9909 y Fn(:)-201 10523 y Fp(F)-15 b(ollo)-5 b(wing)62 b([25)o(,)e(5],)g(this)g(leads)h(to)f(the)g(lo)-5 b(w)g(er)62 b(b)5 b(ound)-91 11047 y Fm(hhj)p Fn(X)14 b Fm(j)318 10972 y Fl(p)396 11047 y Fm(ii)538 11077 y Fl( )5 b(;T)834 11047 y Fm(\025)50 b Fn(C)13 b Fp(\()p Fn( )7 b(;)30 b(p)p Fp(\))p Fn(L)1734 11074 y Fg(1)1810 11047 y Fp(\()p Fn(T)25 b Fp(\))p Fn(;)212 b Fp(with)182 b Fn(L)3005 11074 y Fg(1)3084 11047 y Fp(\()p Fn(T)25 b Fp(\))50 b(=)g(sup)3903 10790 y Fi(\032)4039 11047 y Fn(L)4163 11074 y Fg(1)4242 11047 y Fp(\()p Fn(';)30 b(T)25 b Fp(\))50 b(:=)5027 10924 y Fm(k)p Fn(')p Fm(k)5328 10858 y Fg(2+4)p Fl(\014)p 5027 11005 646 8 v 5045 11171 a Fn(G)5188 11198 y Fl(')5288 11171 y Fp(\()p Fn(T)25 b Fp(\))5561 11119 y Fl(\014)5693 11047 y Fn(;)81 b(')50 b Fp(=)g Fn(\037)6300 11075 y Fg(\012)6410 11047 y Fp(\()p Fn(H)15 b Fp(\))p Fn( )6844 10790 y Fi(\033)7009 11047 y Fn(:)3393 11631 y Fp(21)p eop %%Page: 22 22 22 21 bop -201 1158 a Fp(One)60 b(should)h(compare)e(the)h(obtained)g (lo)-5 b(w)g(er)61 b(b)5 b(ound)61 b Fn(L)3708 1185 y Fg(1)3787 1158 y Fp(\()p Fn(T)25 b Fp(\))60 b(to)g(the)h(expression)f (\(6.10\))f(in)i([25].)81 1384 y(Then)55 b(one)f(can)g(again)g(mimic)e (the)i(pro)5 b(of)54 b(of)f(Theorem)g(4.1,)h(and)h(relate)f(the)f(quan) -5 b(tit)g(y)54 b Fn(L)6295 1411 y Fg(1)6374 1384 y Fp(\()p Fn(T)25 b Fp(\))54 b(to)g(the)-201 1610 y(in)-5 b(tegral)61 b Fn(K)616 1637 y Fl(\026)701 1660 y Fh( )802 1610 y Fp(\()928 1528 y Fg(1+)p Fl(\014)p 893 1568 337 8 v 893 1673 a Fg(1+2)p Fl(\014)1250 1610 y Fn(;)30 b(T)1462 1544 y Fk(\000)p Fg(1)1651 1610 y Fp(\).)80 b(This)61 b(leads)g(to)f(the)g(follo)-5 b(wing)62 b(theorem:)-201 1930 y Fe(Theorem)68 b(B.2.)90 b Fq(Under)65 b(the)g(same)g(hyp)-9 b(otheses)65 b(as)g(in)g(The)-9 b(or)g(em)63 b(2.1,)i(one)g(has)153 2361 y Fp(lim)30 b(inf)213 2482 y Fl(T)20 b Fk(!1)708 2238 y Fp(log)33 b Fn(L)1097 2265 y Fg(1)1175 2238 y Fp(\()p Fn(T)25 b Fp(\))p 708 2319 741 8 v 880 2486 a(log)33 b Fn(T)1519 2361 y Fp(=)50 b Fn(\014)10 b(D)1980 2286 y Fk(\000)1975 2406 y Fl(\026)2060 2429 y Fh( )2191 2105 y Fi(\022)2390 2238 y Fp(1)40 b(+)g Fn(\014)p 2344 2319 517 8 v 2344 2486 a Fp(1)h(+)e(2)p Fn(\014)2881 2105 y Fi(\023)3045 2361 y Fn(;)216 b Fp(and)g(lim)30 b(sup)3907 2517 y Fl(T)20 b Fk(!1)4427 2238 y Fp(log)34 b Fn(L)4817 2265 y Fg(1)4895 2238 y Fp(\()p Fn(T)25 b Fp(\))p 4427 2319 741 8 v 4599 2486 a(log)34 b Fn(T)5239 2361 y Fp(=)49 b Fn(\014)10 b(D)5699 2286 y Fg(+)5694 2406 y Fl(\026)5779 2429 y Fh( )5910 2105 y Fi(\022)6110 2238 y Fp(1)40 b(+)g Fn(\014)p 6064 2319 517 8 v 6064 2486 a Fp(1)h(+)e(2)p Fn(\014)6601 2105 y Fi(\023)6765 2361 y Fn(:)81 2882 y Fp(One)67 b(should)g(also)g(compare)f(the)g(expression)h(of)g Fn(L)3701 2909 y Fg(1)3780 2882 y Fp(\()p Fn(T)25 b Fp(\))67 b(and)g Fn(L)4604 2909 y Fg(2)4682 2882 y Fp(\()p Fn(T)25 b Fp(\))67 b(to)g(the)g(expression)g(of)f Fn(L)6791 2912 y Fl( )6896 2882 y Fp(\()p Fn(T)25 b Fp(\))-201 3107 y(giv)-5 b(en)70 b(Line)f(\(3.3\),)h(that)e(is)i(where)f(as)g(ab)5 b(o)-5 b(v)g(e)69 b(the)g(suprem)-5 b(um)66 b(is)k(tak)-5 b(en)68 b(o)-5 b(v)g(er)69 b(the)g(set)g(of)g(v)-5 b(ectors)68 b Fn(')d Fp(=)-201 3333 y Fn(\037)-87 3361 y Fg(\012)23 3333 y Fp(\()p Fn(H)15 b Fp(\))p Fn( )7 b Fp(,)78 b(namely)e(the)g (suprem)-5 b(um)73 b(of)j Fm(k)p Fn(')p Fm(k)2988 3267 y Fg(2+4)p Fl(\014)3333 3333 y Fn(=U)3548 3363 y Fl('; )3784 3333 y Fp(\()p Fn(T)25 b Fp(\))4057 3267 y Fl(\014)4152 3333 y Fp(.)128 b(One)75 b(ma)-5 b(y)75 b(ha)-5 b(v)g(e)76 b(the)g(righ)-5 b(t)77 b(to)f(w)-5 b(onder)-201 3559 y(whether)62 b(there)f(are)g(some)e(links)k(b)5 b(et)-5 b(w)g(een)60 b(these)h(quan)-5 b(tities,)61 b(and)g(also)h(whether)f Fn(L)5758 3589 y Fl( )5863 3559 y Fp(\()p Fn(T)25 b Fp(\))62 b(is)f(e\013ectiv)-5 b(ely)-201 3785 y(a)58 b(b)5 b(etter)57 b(lo)-5 b(w)g(er)58 b(b)5 b(ound)57 b(than)h Fn(L)2061 3812 y Fg(1)2139 3785 y Fp(\()p Fn(T)25 b Fp(\))58 b(and)f Fn(L)2944 3812 y Fg(2)3023 3785 y Fp(\()p Fn(T)25 b Fp(\).)79 b(Theorem)56 b(B.3)h(b)5 b(elo)-5 b(w)58 b(answ)-5 b(ers)58 b(to)f(these)f(questions.)-201 4011 y(This)44 b(theorem)c(is)j (actually)g(a)g(consequence)f(of)g(Theorems)f(4.1,)k(B.2)d(and)h(B.1,)i (and)e(of)f(the)g(non)h(increasing)-201 4237 y(prop)5 b(ert)-5 b(y)61 b(of)f(the)g(functions)g Fn(D)2003 4171 y Fk(\006)1998 4282 y Fl(\026)2083 4305 y Fh( )2184 4237 y Fp(\()p Fn(q)7 b Fp(\))60 b(\(p)5 b(oin)-5 b(t)60 b(i\))h(of)f(Prop)5 b(osition)61 b(2.1\).)-201 4556 y Fe(Theorem)68 b(B.3.)90 b Fq(Under)65 b(the)g(same)g(hyp)-9 b(otheses)65 b(as)g(pr)-9 b(eviously,)63 b(one)i(has)1231 4987 y Fp(lim)30 b(inf)1291 5108 y Fl(T)20 b Fk(!1)1785 4860 y Fp(log)33 b Fn(L)2174 4890 y Fl( )2280 4860 y Fp(\()p Fn(T)25 b Fp(\))p 1785 4945 768 8 v 1971 5111 a(log)33 b Fn(T)2623 4987 y Fm(\025)50 b Fp(lim)30 b(inf)2875 5108 y Fl(T)20 b Fk(!1)3369 4864 y Fp(log)33 b Fn(L)3758 4891 y Fg(1)3837 4864 y Fp(\()p Fn(T)25 b Fp(\))p 3369 4945 741 8 v 3541 5111 a(log)33 b Fn(T)4180 4987 y Fm(\025)50 b Fp(lim)30 b(inf)4432 5108 y Fl(T)20 b Fk(!1)4926 4864 y Fp(log)33 b Fn(L)5315 4891 y Fg(2)5394 4864 y Fp(\()p Fn(T)25 b Fp(\))p 4926 4945 V 5098 5111 a(log)34 b Fn(T)5687 4987 y(;)-201 5405 y Fq(and)1152 5685 y Fp(lim)c(sup)1239 5841 y Fl(T)20 b Fk(!1)1759 5558 y Fp(log)33 b Fn(L)2148 5588 y Fl( )2253 5558 y Fp(\()p Fn(T)25 b Fp(\))p 1759 5643 768 8 v 1944 5809 a(log)33 b Fn(T)2597 5685 y Fm(\025)50 b Fp(lim)30 b(sup)2875 5841 y Fl(T)20 b Fk(!1)3395 5562 y Fp(log)33 b Fn(L)3784 5589 y Fg(1)3863 5562 y Fp(\()p Fn(T)25 b Fp(\))p 3395 5643 741 8 v 3567 5809 a(log)33 b Fn(T)4206 5685 y Fm(\025)50 b Fp(lim)30 b(sup)4485 5841 y Fl(T)20 b Fk(!1)5005 5562 y Fp(log)33 b Fn(L)5394 5589 y Fg(2)5473 5562 y Fp(\()p Fn(T)25 b Fp(\))p 5005 5643 V 5177 5809 a(log)33 b Fn(T)5766 5685 y(:)-201 6200 y Fe(Remark)69 b(B.1.)196 b Fp(i\))53 b(It)g(is)g(w)-5 b(orth)53 b(to)f(p)5 b(oin)-5 b(t)53 b(out)g(that)f(suc)-5 b(h)53 b(a)f(comparison)g(is)h (made)e(p)5 b(ossible)53 b(thanks)g(to)-201 6425 y(the)62 b(upp)5 b(er)63 b(b)5 b(ounds)63 b(obtained)f(for)g Fn(L)2425 6455 y Fl( )2530 6425 y Fp(\()p Fn(T)25 b Fp(\),)63 b Fn(L)3041 6452 y Fg(1)3120 6425 y Fp(\()p Fn(T)25 b Fp(\))62 b(and)h Fn(L)3935 6452 y Fg(2)4013 6425 y Fp(\()p Fn(T)25 b Fp(\);)63 b(upp)5 b(er)63 b(b)5 b(ounds)63 b(that)f(are)g(for)g(the)h (\014rst)-201 6651 y(time)c(deriv)-5 b(ed)61 b(for)g(suc)-5 b(h)60 b(quan)-5 b(tities.)-201 6877 y(ii\))52 b(Theorem)e(B.3)h(tells) h(us)f(that)f(it)i(is)g(w)-5 b(orth)51 b(to)g(deal)h(with)g(the)f (crossed)f(term)g(in)i(\(1.6\))e(while)j(one)e(dev)-5 b(el-)-201 7103 y(opps)58 b Fn(B)360 7133 y Fl( )465 7103 y Fp(\()p Fn(T)15 b(;)30 b(N)20 b Fp(\))58 b(with)g Fn( )f Fp(=)50 b Fn(')35 b Fp(+)g Fn(\037)p Fp(.)79 b(Dealing)59 b(with)f(the)g(crossed)f(term)f(do)5 b(es)58 b(lead)g(to)g(an)g(impro) -5 b(v)g(emen)g(t,)-201 7329 y(with)52 b(regards)f(to)f(the)h(former)e (approac)-5 b(hes)50 b(\(G-C-L\))g(and)g(\(BT\))h(where)g(this)g(term)e (w)-5 b(asn't)51 b(treated)f(w)-5 b(ell.)-201 7555 y(iii\))76 b(One)f(can)f(sho)-5 b(w)75 b(that)f Fn(L)1839 7585 y Fl( )1944 7555 y Fp(\()p Fn(';)30 b(T)25 b Fp(\))74 b Fm(\025)g Fn(c)2786 7582 y Fg(1)2865 7555 y Fn(L)2989 7582 y Fg(1)3067 7555 y Fp(\()p Fn(';)30 b(T)25 b Fp(\))75 b(with)g(some)e(constan)-5 b(t)74 b Fn(c)5340 7582 y Fg(1)5493 7555 y Fn(>)g Fp(0)h(uniform)e(in)j Fn(T)15 b(;)30 b(')p Fp(.)-201 7780 y(The)70 b(latter)f(is)h(not)f(true)g(as)g (one)g(compares)f Fn(L)3110 7810 y Fl( )3215 7780 y Fp(\()p Fn(';)30 b(T)25 b Fp(\))69 b(and)g Fn(L)4243 7807 y Fg(2)4322 7780 y Fp(\()p Fn(';)30 b(T)25 b Fp(\))69 b(for)g(some)e Fn(')p Fp(.)107 b(W)-15 b(e)69 b(confess)f(that)-201 8006 y(the)77 b(inequalities)g(in)-5 b(v)g(olving)78 b Fn(L)2018 8033 y Fg(2)2097 8006 y Fp(\()p Fn(T)25 b Fp(\))77 b(in)g(Theorem)f(B.3)g(are)g(quite)h(a)g(surprise)g(for)f(us,) 81 b(since)76 b(w)-5 b(e)77 b(w)-5 b(ere)-201 8232 y(exp)5 b(ecting)60 b(the)h(exp)5 b(onen)-5 b(ts)59 b(of)h Fn(L)2116 8259 y Fg(2)2195 8232 y Fp(\()p Fn(T)25 b Fp(\))60 b(to)g(b)5 b(e)61 b(bigger)g(than)f(those)g(of)g Fn(L)4775 8259 y Fg(1)4854 8232 y Fp(\()p Fn(T)25 b Fp(\).)-201 8458 y(iv\))72 b(W)-15 b(e)72 b(b)5 b(eliev)-5 b(e)72 b(a)g(stronger)f(v)-5 b(ersion)72 b(of)g(Theorem)e(B.3)h(to)h(b)5 b(e)72 b(true,)i(namely:) 101 b Fn(L)5667 8488 y Fl( )5772 8458 y Fp(\()p Fn(T)25 b Fp(\))70 b Fm(\025)e Fn(c)6404 8485 y Fg(1)6483 8458 y Fn(L)6607 8485 y Fg(1)6686 8458 y Fp(\()p Fn(T)25 b Fp(\))69 b Fm(\025)-201 8684 y Fn(c)-122 8711 y Fg(2)-43 8684 y Fn(L)81 8711 y Fg(2)159 8684 y Fp(\()p Fn(T)25 b Fp(\).)-201 9246 y Fo(C)269 b(A)90 b(su\016cien)-7 b(t)89 b(condition)i(for)f(Hyp)7 b(othesis)91 b(\(H\))-201 9729 y Fp(The)67 b(follo)-5 b(wing)68 b(statemen)-5 b(t)63 b(giv)-5 b(es)67 b(a)f(su\016cien)-5 b(t)66 b(condition)h(for)f(\(H\))h (to)f(hold,)i(whic)-5 b(h)67 b(can)g(b)5 b(e)66 b(useful)h(for)-201 9955 y(applications.)-201 10275 y Fe(Prop)6 b(osition)69 b(C.1.)90 b Fq(L)-9 b(et)65 b Fp(0)51 b Fn(<)e(q)58 b(<)50 b Fp(1)p Fq(.)83 b(Assume)65 b(that,)1180 10690 y Fp(\()p Fe(H1)p Fp(\))184 b(for)60 b(some)f Fn(\025)51 b(>)2877 10567 y Fp(1)41 b Fm(\000)f Fn(q)p 2877 10648 401 8 v 3034 10814 a(q)3298 10690 y(;)81 b Fp(one)60 b(has)4168 10442 y Fi(Z)4269 10855 y Fa(R)4429 10690 y Fm(j)p Fn(x)p Fm(j)4635 10615 y Fl(\025)4725 10690 y Fp(d)p Fn(\026)p Fp(\(x\))49 b Fn(<)h Fp(+)p Fm(1)p Fn(:)-201 11133 y Fq(Then)65 b Fp(0)51 b Fm(\024)e Fn(D)762 11067 y Fk(\006)757 11178 y Fl(\026)880 11133 y Fp(\()p Fn(q)7 b Fp(\))50 b Fm(\024)g Fp(1)p Fq(.)3393 11631 y Fp(22)p eop %%Page: 23 23 23 22 bop -201 1158 a Fe(Pro)6 b(of)69 b(of)g(Prop)6 b(osition)68 b(C.1.)-201 1384 y Fp(Let)60 b Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))49 b(=)h Fn(\026)p Fp(\([)p Fn(x)39 b Fm(\000)h Fn(";)30 b(x)40 b Fp(+)g Fn(")p Fp(]\).)79 b(De\014ne)2169 1736 y(\012\()p Fn(")p Fp(\))50 b(=)g Fm(f)p Fn(x)g Fm(2)h Fp(supp)p Fn(\026)60 b Fm(j)g Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))49 b Fm(\024)h Fn(")p Fm(g)p Fn(;)-201 2088 y Fp(and)61 b Fn(I)233 2115 y Fl(j)356 2088 y Fp(=)50 b([\()p Fn(j)g Fm(\000)40 b Fp(1)p Fn(=)p Fp(2\))p Fn(";)30 b Fp(\()p Fn(j)49 b Fp(+)40 b(1)p Fn(=)p Fp(2\))p Fn(")p Fp(\))p Fn(;)89 b(j)61 b Fm(2)51 b Ff(Z)8 b Fp(.)89 b(F)-15 b(or)61 b(an)-5 b(y)60 b Fn(x)51 b Fm(2)f Fn(I)4140 2115 y Fl(j)4213 2088 y Fn(;)1684 2441 y(\026)p Fp(\([)p Fn(x)39 b Fm(\000)g Fn(";)30 b(x)40 b Fp(+)g Fn(")p Fp(]\))50 b Fm(\025)g Fn(\026)p Fp(\()p Fn(I)3442 2468 y Fl(j)3514 2441 y Fp(\))g Fm(\025)g Fn(\026)p Fp(\()p Fn(I)4088 2468 y Fl(j)4201 2441 y Fm(\\)40 b Fp(\012\()p Fn(")p Fp(\)\))50 b(:=)f Fn(b)5161 2468 y Fl(j)5234 2441 y Fn(:)1470 b Fp(\(C.1\))-201 2793 y(W)-15 b(e)67 b(\014rst)g(remark)e(that)i(for)g(an)-5 b(y)67 b Fn(j;)97 b(b)2466 2820 y Fl(j)2600 2793 y Fm(\024)61 b Fn(")p Fp(.)100 b(Indeed,)68 b(if)f Fn(b)3940 2820 y Fl(j)4074 2793 y Fp(=)61 b(0,)68 b(it)g(is)f(trivially)i(true.)100 b(And)67 b(if)h Fn(b)6691 2820 y Fl(j)6825 2793 y Fn(>)61 b Fp(0,)-201 3019 y(there)f(exists)g Fn(x)870 3046 y Fg(0)1000 3019 y Fm(2)50 b Fn(I)1251 3046 y Fl(j)1365 3019 y Fm(\\)40 b Fp(\012\()p Fn(")p Fp(\).)80 b(The)61 b(inequalit)-5 b(y)61 b(\(C.1\))f(and)h(the)f(de\014nition)h(of)f (\012\()p Fn(")p Fp(\))g(imply)2392 3371 y Fn(b)2470 3398 y Fl(j)2594 3371 y Fm(\024)50 b Fn(\026)p Fp(\([)p Fn(x)3122 3398 y Fg(0)3240 3371 y Fm(\000)40 b Fn(";)30 b(x)3692 3398 y Fg(0)3811 3371 y Fp(+)39 b Fn(")p Fp(]\))50 b Fm(\024)g Fn(":)-201 3723 y Fp(Next,)60 b(the)g(inequalit)-5 b(y)62 b(\(C.1\))d(yields)757 3911 y Fi(Z)858 4323 y Fg(\012\()p Fl(")p Fg(\))1173 4159 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))1663 4084 y Fl(q)5 b Fk(\000)p Fg(1)1919 4159 y Fp(d)p Fn(\026)p Fp(\()p Fn(x)p Fp(\))165 b(=)2922 3986 y Fi(X)2848 4381 y Fl(j)8 b Fg(:)p Fl(b)3012 4401 y Fh(j)3078 4381 y Fl(>)p Fg(0)3288 3911 y Fi(Z)3389 4323 y Fl(I)3450 4343 y Fh(j)3515 4323 y Fk(\\)p Fg(\012\()p Fl(")p Fg(\))3925 4159 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))4415 4084 y Fl(q)5 b Fk(\000)p Fg(1)4670 4159 y Fp(d)p Fn(\026)p Fp(\()p Fn(x)p Fp(\))2541 4696 y Fm(\024)2922 4524 y Fi(X)2848 4919 y Fl(j)j Fg(:)p Fl(b)3012 4939 y Fh(j)3078 4919 y Fl(>)p Fg(0)3288 4696 y Fn(\026)p Fp(\()p Fn(I)3549 4723 y Fl(j)3662 4696 y Fm(\\)40 b Fp(\012\()p Fn(")p Fp(\)\))4252 4621 y Fl(q)5 b Fk(\000)p Fg(1)4508 4696 y Fn(\026)p Fp(\()p Fn(I)4769 4723 y Fl(j)4882 4696 y Fm(\\)40 b Fp(\012\()p Fn(")p Fp(\)\))50 b(=)5714 4524 y Fi(X)5722 4918 y Fl(j)8 b Fk(2)p Fj(Z)6007 4696 y Fn(b)6085 4608 y Fl(q)6085 4751 y(j)6161 4696 y Fn(:)543 b Fp(\(C.2\))-201 5246 y(One)60 b(can)g(rewrite)i(this)e(summation)e (as)i(follo)-5 b(ws:)2245 5542 y Fi(X)2253 5936 y Fl(j)8 b Fk(2)p Fj(Z)2538 5714 y Fn(b)2616 5626 y Fl(q)2616 5769 y(j)2742 5714 y Fp(=)2940 5487 y Fg(+)p Fk(1)2934 5542 y Fi(X)2937 5937 y Fl(k)t Fg(=0)3227 5714 y Fn(S)3339 5744 y Fl(k)3424 5714 y Fn(;)212 b(S)3799 5744 y Fl(k)3934 5714 y Fp(:=)4201 5542 y Fi(X)4177 5936 y Fl(j)8 b Fk(2)p Fl(J)4413 5959 y Fh(k)4519 5714 y Fn(b)4597 5626 y Fl(q)4597 5769 y(j)4673 5714 y Fn(;)2031 b Fp(\(C.3\))-201 6281 y(where)61 b Fn(J)426 6311 y Fl(k)563 6281 y Fp(=)50 b Fm(f)p Fn(j)62 b Fm(2)51 b Ff(Z)79 b Fm(j)60 b Fn(I)1529 6308 y Fl(j)1653 6281 y Fm(\032)51 b Fp([)p Fn(e)1982 6215 y Fl(k)2066 6281 y Fn(;)30 b(e)2232 6215 y Fl(k)t Fg(+1)2498 6281 y Fp(\))40 b Fm([)h Fp([)p Fm(\000)p Fn(e)3049 6215 y Fl(k)t Fg(+1)3313 6281 y Fn(;)30 b Fm(\000)p Fn(e)3621 6215 y Fl(k)3705 6281 y Fp(\))p Fm(g)61 b Fp(for)g Fn(k)56 b(>)51 b Fp(0)61 b(and)g Fn(J)5158 6308 y Fg(0)5288 6281 y Fp(=)50 b Fm(f)p Fn(j)72 b Fm(j)60 b Fn(I)5909 6308 y Fl(j)6033 6281 y Fm(\032)51 b Fp([)p Fm(\000)p Fn(e;)30 b(e)p Fp(\))p Fm(g)p Fp(.)79 b(T)-15 b(o)-201 6507 y(b)5 b(e)58 b(rigourous,)h(Equalit)-5 b(y)58 b(\(C.3\))g(holds)g (if)h(one)e(replaces)i(in)f(the)g(de\014nition)h(of)e(the)h(sets)f Fn(J)6048 6537 y Fl(k)6192 6507 y Fp(the)h(quan)-5 b(tit)g(y)-201 6733 y Fn(e)-116 6667 y Fl(k)29 6733 y Fp(b)g(y)60 b([)p Fn(e)417 6667 y Fl(k)501 6733 y Fn(=")p Fp(])p Fn(")38 b Fp(+)h Fn("=)p Fp(2,)59 b(where)h([)p Fm(\001)p Fp(])e(stands)h(for)h (the)f(in)-5 b(teger)60 b(part,)g(but)f(for)h(a)f(sak)-5 b(e)60 b(of)f(simplicit)-5 b(y)60 b(w)-5 b(e)60 b(shall)-201 6959 y(use)g(the)g(de\014nition)i(of)e Fn(J)1543 6989 y Fl(k)1688 6959 y Fp(giv)-5 b(en)61 b(ab)5 b(o)-5 b(v)g(e.)81 7185 y(Let)61 b Fn(\015)g Fm(2)51 b Fp(\(0)p Fn(;)30 b Fp(1\).)81 b(F)-15 b(or)60 b Fn(k)d Fm(\025)51 b Fp(0,)60 b(H\177)-91 b(older)62 b(inequalit)-5 b(y)62 b(and)f(the)f(fact)g(that) g(Card)p Fn(J)5496 7215 y Fl(k)5633 7185 y Fm(\024)51 b Fp(2\()p Fn(e)6073 7119 y Fl(k)t Fg(+1)6378 7185 y Fm(\000)40 b Fn(e)6645 7119 y Fl(k)6730 7185 y Fp(\))p Fn(=")51 b Fm(\024)-201 7411 y Fp(4)p Fn(e)-25 7345 y Fl(k)60 7411 y Fn(=")60 b Fp(and)h Fn(b)728 7438 y Fl(j)852 7411 y Fm(\024)49 b Fn(")61 b Fp(imply)775 8012 y Fn(S)887 8042 y Fl(k)1138 8012 y Fp(=)1470 7840 y Fi(X)1446 8233 y Fl(j)8 b Fk(2)p Fl(J)1682 8256 y Fh(k)1788 8012 y Fn(b)1866 7924 y Fl(q)1866 8067 y(j)1993 8012 y Fp(=)2209 7840 y Fi(X)2185 8233 y Fl(j)g Fk(2)p Fl(J)2421 8256 y Fh(k)2527 8012 y Fn(b)2605 7924 y Fl(\015)g(q)2605 8067 y(j)2762 8012 y Fn(b)2840 7916 y Fg(\(1)p Fk(\000)p Fl(\015)g Fg(\))p Fl(q)2840 8067 y(j)3337 8012 y Fm(\024)3529 7647 y Fi(0)3529 7974 y(@)3713 7840 y(X)3688 8233 y Fl(j)g Fk(2)p Fl(J)3924 8256 y Fh(k)4031 8012 y Fn(b)4109 8039 y Fl(j)4182 7647 y Fi(1)4182 7974 y(A)4341 7692 y Fl(\015)g(q)4528 7647 y Fi(0)4528 7974 y(@)4711 7840 y(X)4687 8233 y Fl(j)g Fk(2)p Fl(J)4923 8256 y Fh(k)5029 8012 y Fn(b)5127 7811 y Fd(\(1)p Fb(\000)p Fh(\015)e Fd(\))p Fh(q)p 5127 7848 385 6 v 5175 7930 a Fd(1)p Fb(\000)p Fh(\015)g(q)5107 8067 y Fl(j)5540 7647 y Fi(1)5540 7974 y(A)5699 7692 y Fg(1)p Fk(\000)p Fl(\015)i(q)1138 8738 y Fm(\024)166 b Fn(")1531 8663 y Fg(\(1)p Fk(\000)p Fl(\015)8 b Fg(\))p Fl(q)2008 8481 y Fi(\022)2161 8615 y Fp(4)p Fn(e)2337 8549 y Fl(k)p 2161 8696 261 8 v 2249 8863 a Fn(")2442 8481 y Fi(\023)2576 8509 y Fg(1)p Fk(\000)p Fl(\015)g(q)2943 8372 y Fi(0)2943 8700 y(@)3127 8565 y(X)3102 8959 y Fl(j)g Fk(2)p Fl(J)3338 8982 y Fh(k)3445 8738 y Fn(b)3523 8765 y Fl(j)3596 8372 y Fi(1)3596 8700 y(A)3755 8418 y Fl(\015)g(q)3962 8738 y Fp(=)50 b(4)p Fn(")4330 8663 y Fl(q)5 b Fk(\000)p Fg(1)4586 8738 y Fn(e)4671 8663 y Fl(k)t Fg(\(1)p Fk(\000)p Fl(\015)j(q)d Fg(\))5225 8372 y Fi(0)5225 8700 y(@)5409 8565 y(X)5384 8959 y Fl(j)j Fk(2)p Fl(J)5620 8982 y Fh(k)5726 8738 y Fn(b)5804 8765 y Fl(j)5877 8372 y Fi(1)5877 8700 y(A)6036 8418 y Fl(\015)g(q)6755 8738 y Fp(\(C.4\))-201 9299 y(F)-15 b(rom)59 b(Assumption)g(\(H1\))h(it)h(is)g(straigh)-5 b(tforw)g(ard)60 b(that)g(there)g(exists)g Fn(C)13 b Fp(\()p Fn(\025)p Fp(\))50 b Fn(<)g Fm(1)61 b Fp(suc)-5 b(h)60 b(that)g(for)g(all)i Fn(k)2245 9505 y Fi(X)2220 9899 y Fl(j)8 b Fk(2)p Fl(J)2456 9922 y Fh(k)2563 9678 y Fn(b)2641 9705 y Fl(j)2764 9678 y Fm(\024)2981 9505 y Fi(X)2956 9899 y Fl(j)g Fk(2)p Fl(J)3192 9922 y Fh(k)3299 9678 y Fn(\026)p Fp(\()p Fn(I)3560 9705 y Fl(j)3632 9678 y Fp(\))50 b Fm(\024)g Fn(C)13 b Fp(\()p Fn(\025)p Fp(\))p Fn(e)4421 9603 y Fk(\000)p Fl(k)t(\025)4698 9678 y Fn(:)2006 b Fp(\(C.5\))-201 10223 y(with)64 b Fn(\025)f Fp(from)e(the)i(statemen) -5 b(t)60 b(of)i(the)h(Prop)5 b(osition.)88 b(Then)63 b(one)g(can)g(\014nd)g Fn(\015)i Fm(2)55 b Fp(\(0)p Fn(;)30 b Fp(1\))62 b(suc)-5 b(h)62 b(that)h Fn(\025\015)10 b(q)49 b Fm(\000)-201 10448 y Fp(\(1)40 b Fm(\000)g Fn(\015)10 b(q)d Fp(\))50 b Fn(>)g Fp(0.)80 b(Then)61 b(\(C.3\)-\(C.5\))e(imply) 1301 10790 y Fi(X)1400 11181 y Fl(j)1594 10962 y Fn(b)1672 10874 y Fl(q)1672 11017 y(j)1799 10962 y Fm(\024)50 b Fp(4)p Fn(C)2225 10887 y Fl(\015)8 b(q)2381 10962 y Fp(\()p Fn(\025)p Fp(\))p Fn(")2714 10887 y Fl(q)d Fk(\000)p Fg(1)3006 10735 y(+)p Fk(1)3000 10790 y Fi(X)3003 11185 y Fl(k)t Fg(=0)3293 10962 y Fn(e)3378 10887 y Fk(\000)p Fl(k)t Fg(\()p Fl(\025\015)j(q)d Fk(\000)p Fg(\(1)p Fk(\000)p Fl(\015)j(q)d Fg(\)\))4512 10962 y Fm(\024)50 b Fn(D)5 b Fp(\()p Fn(q)i(;)30 b(\025)p Fp(\))p Fn(")5362 10887 y Fl(q)5 b Fk(\000)p Fg(1)5617 10962 y Fn(:)1087 b Fp(\(C.6\))3393 11631 y(23)p eop %%Page: 24 24 24 23 bop 81 1158 a Fp(The)61 b(pro)5 b(of)60 b(is)h(completed)e(as)h (follo)-5 b(ws.)81 b(One)60 b(can)g(write)h Fn(I)4135 1185 y Fl(\026)4228 1158 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))60 b(as)1307 1729 y Fn(I)1387 1756 y Fl(\026)1480 1729 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))50 b(=)2118 1418 y Fi( )2262 1481 y(Z)2363 1894 y Fg(\012\()p Fl(")p Fg(\))2678 1729 y Fp(+)2850 1481 y Fi(Z)2951 1894 y Fj(R)8 b Fk(n)p Fg(\012\()p Fl(")p Fg(\))3402 1418 y Fi(!)3577 1729 y Fn(b)p Fp(\()p Fn(x;)30 b(")p Fp(\))4067 1654 y Fl(q)5 b Fk(\000)p Fg(1)4322 1729 y Fp(d)p Fn(\026)p Fp(\()p Fn(x)p Fp(\))49 b(=:)h Fn(I)5151 1756 y Fg(1)5270 1729 y Fp(+)40 b Fn(I)5532 1756 y Fg(2)5611 1729 y Fn(:)-201 2307 y Fp(The)57 b(b)5 b(ounds)56 b(\(C.2\))g(and)h(\(C.6\))e(giv)-5 b(e)57 b Fn(I)2538 2334 y Fg(1)2668 2307 y Fm(\024)49 b Fn(D)5 b(")3100 2241 y Fl(q)g Fk(\000)p Fg(1)3356 2307 y Fp(.)79 b(F)-15 b(urthermore,)55 b(due)i(to)f(the)g(de\014nition)h (of)f(\012\()p Fn(")p Fp(\))g(and)-201 2533 y Fn(q)h Fm(2)51 b Fp(\(0)p Fn(;)30 b Fp(1\),)59 b(w)-5 b(e)61 b(ha)-5 b(v)g(e)2340 2759 y Fn(I)2420 2786 y Fg(2)2550 2759 y Fm(\024)49 b Fn(")2826 2684 y Fl(q)5 b Fk(\000)p Fg(1)3083 2759 y Fn(\026)p Fp(\()p Ff(R)75 b Fm(n)40 b Fp(\012\()p Fn(")p Fp(\)\))50 b Fm(\024)g Fn(")4322 2684 y Fl(q)5 b Fk(\000)p Fg(1)4578 2759 y Fn(:)-201 3092 y Fp(W)-15 b(e)60 b(obtain)h(so)f Fn(I)981 3119 y Fl(\026)1074 3092 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))50 b Fm(\024)f Fp(\()p Fn(D)c Fp(+)40 b(1\))p Fn(")2407 3026 y Fl(q)5 b Fk(\000)p Fg(1)2723 3092 y Fp(and)61 b(th)-5 b(us)60 b Fn(D)3633 3026 y Fk(\006)3628 3137 y Fl(\026)3751 3092 y Fp(\()p Fn(q)7 b Fp(\))49 b Fm(\024)h Fp(1.)7028 3318 y Fc(\003)-201 3694 y Fe(Corollary)69 b(C.1.)91 b Fq(L)-9 b(et)65 b Fn(\026)f Fq(b)-9 b(e)64 b(such)h(that)2081 3928 y Fi(Z)2182 4340 y Fj(R)2317 4176 y Fm(j)p Fn(x)p Fm(j)2523 4101 y Fl(\025)2612 4176 y Fp(d)p Fn(\026)p Fp(\()p Fn(x)p Fp(\))50 b Fn(<)g Fp(+)p Fm(1)129 b Fp(for)65 b(an)-5 b(y)67 b Fn(\025)51 b(>)f Fp(0)p Fn(:)-201 4686 y Fq(Then)67 b Fn(D)431 4620 y Fk(\006)426 4731 y Fl(\026)548 4686 y Fp(\()p Fn(s)p Fp(\))53 b Fm(2)h Fp([0)p Fn(;)30 b Fp(1])65 b Fq(for)h(any)i Fn(s)53 b Fm(2)h Fp(\(0)p Fn(;)30 b Fp(1\))66 b Fq(and)g(thus)h Fp(\(H\))g Fq(holds.)87 b(In)67 b(p)-9 b(articular,)65 b(this)i(is)g(true)f(if)g Fn(\026)g Fq(has)-201 4912 y(a)f(c)-9 b(omp)g(act)64 b(supp)-9 b(ort.)-201 5485 y Fo(D)269 b(An)110 b(example)e(of)i(\014nite)f(pure)g(p)7 b(oin)-7 b(t)110 b(measure)f(with)g(non)h(trivial)274 5784 y(generalized)89 b(fractal)f(dimensions.)-201 6189 y Fp(F)-15 b(or)55 b Fn(\025)c(>)e Fp(1)56 b(and)f Fn(\013)c(>)f Fp(0,)56 b(let)f Fn(a)1873 6216 y Fl(n)2017 6189 y Fp(=)50 b Fn(a=n)2505 6123 y Fl(\025)2596 6189 y Fp(,)56 b Fn(x)2807 6216 y Fl(n)2951 6189 y Fp(=)50 b(1)p Fn(=n)3434 6123 y Fl(\013)3533 6189 y Fp(,)56 b(where)f Fn(a)c(>)f Fp(0)55 b(is)g(a)g(normalization)g(constan)-5 b(t.)77 b(W)-15 b(e)-201 6415 y(de\014ne)57 b(the)f(\014nite)g(pure)h(p)5 b(oin)-5 b(t)57 b(probabilit)-5 b(y)58 b(measure)c Fn(\026)c Fp(=)3954 6279 y Fi(P)4146 6331 y Fk(1)4146 6469 y Fl(n)p Fg(=1)4451 6415 y Fn(a)4547 6442 y Fl(n)4641 6415 y Fn(\016)4722 6442 y Fl(x)4801 6459 y Fh(n)4951 6415 y Fp(on)57 b Ff(R)26 b Fp(.)88 b(As)57 b(the)f(measure)e Fn(\026)j Fp(has)-201 6641 y(a)66 b(b)5 b(ounded)66 b(supp)5 b(ort,)67 b(0)59 b Fm(\024)g Fn(D)1942 6575 y Fk(\006)1937 6686 y Fl(\026)2060 6641 y Fp(\()p Fn(q)7 b Fp(\))59 b Fm(\024)g Fp(1)66 b(for)f(an)-5 b(y)66 b Fn(q)h Fm(2)60 b Fp(\(0)p Fn(;)30 b Fp(1\))65 b(-)g(see)h(P)-5 b(oin)g(t)66 b(iv\))g(of)f(Prop)5 b(osition)67 b(2.1.)96 b(W)-15 b(e)-201 6867 y(denote)59 b(b)-5 b(y)59 b Fn(B)9 b Fp(\()p Fn(x;)30 b(")p Fp(\))58 b(the)h(closed)h(ball)g(of)f(cen)-5 b(ter)58 b Fn(x)i Fp(and)f(radius)h Fn(")p Fp(.)79 b(F)-15 b(or)59 b(an)-5 b(y)60 b(giv)-5 b(en)59 b Fn(")50 b(>)g Fp(0,)59 b(tak)-5 b(e)59 b Fn(N)79 b Fp(to)59 b(b)5 b(e)-201 7093 y(the)63 b(in)-5 b(teger)63 b(part)f(of)h Fn(")1410 7027 y Fk(\000)p Fg(1)p Fl(=)p Fg(\(1+)p Fl(\013)p Fg(\))2050 7093 y Fp(.)87 b(Th)-5 b(us,)63 b(there)g(exists)f(a)h(constan)-5 b(t)62 b Fn(c)54 b(>)g Fp(0)63 b(uniform)e(in)j Fn(N)83 b Fp(\(and)62 b Fn(")p Fp(\))h(suc)-5 b(h)-201 7319 y(that)60 b(for)g(all)i Fn(n)51 b Fm(\024)f Fn(cN)20 b Fp(,)59 b Fn(\026)p Fp(\()p Fn(B)9 b Fp(\()p Fn(x)1934 7346 y Fl(n)2027 7319 y Fn(;)30 b(")p Fp(\)\))50 b(=)g Fn(\026)p Fp(\()p Fm(f)p Fn(x)2953 7346 y Fl(n)3046 7319 y Fm(g)p Fp(\))g(=)g Fn(a)3546 7346 y Fl(n)3640 7319 y Fp(.)80 b(Let)60 b Fn(q)d(<)50 b Fp(1)p Fn(=\025)p Fp(.)80 b(Then)61 b(w)-5 b(e)60 b(ha)-5 b(v)g(e)209 7899 y Fn(I)289 7926 y Fl(\026)382 7899 y Fp(\()p Fn(q)7 b(;)30 b(")p Fp(\))49 b(=)1019 7727 y Fi(X)1107 8109 y Fl(n)1312 7899 y Fn(a)1408 7926 y Fl(n)1502 7899 y Fn(\026)p Fp(\()p Fn(B)9 b Fp(\()p Fn(x)2005 7926 y Fl(n)2098 7899 y Fn(;)30 b(")p Fp(\)\))2406 7824 y Fl(q)5 b Fk(\000)p Fg(1)2712 7899 y Fm(\025)2943 7672 y Fl(cN)2905 7727 y Fi(X)2904 8115 y Fl(n)p Fg(=1)3200 7899 y Fn(\026)p Fp(\()p Fn(B)k Fp(\()p Fn(x)3703 7926 y Fl(n)3796 7899 y Fn(;)30 b(")p Fp(\)\))4104 7824 y Fl(q)5 b Fk(\000)p Fg(1)4359 7899 y Fn(a)4455 7926 y Fl(n)4600 7899 y Fp(=)4831 7672 y Fl(cN)4793 7727 y Fi(X)4792 8115 y Fl(n)p Fg(=1)5088 7899 y Fn(a)5184 7824 y Fl(q)5184 7944 y(n)5329 7899 y Fm(\030)49 b Fn(C)44 b(")5779 7814 y Fk(\000)5909 7752 y Fd(1)p Fb(\000)p Fh(q)t(\025)p 5908 7784 291 6 v 5936 7866 a Fd(1+)p Fh(\013)6288 7899 y Fn(:)409 b Fp(\(D.1\))-201 8459 y(Therefore)2510 8725 y Fn(D)2666 8650 y Fk(\006)2661 8770 y Fl(\026)2783 8725 y Fp(\()p Fn(q)7 b Fp(\))50 b Fm(\025)3578 8602 y Fp(1)40 b Fm(\000)g Fn(q)7 b(\025)p 3275 8683 1114 8 v 3275 8850 a Fp(\(1)40 b Fm(\000)g Fn(q)7 b Fp(\)\(1)39 b(+)h Fn(\013)q Fp(\))4408 8725 y Fn(:)-201 9156 y Fp(This)57 b(implies)f(that)g(for)g (0)51 b Fn(<)e(q)58 b(<)50 b Fp(1)p Fn(=\025)p Fp(,)56 b(one)g(obtains)h(strictly)f(p)5 b(ositiv)-5 b(e)57 b(generalized)g (fractal)f(dimensions)-201 9382 y Fn(D)-45 9316 y Fk(\006)-50 9427 y Fl(\026)73 9382 y Fp(\()p Fn(q)7 b Fp(\))51 b(for)i(the)e(pure)i (p)5 b(oin)-5 b(t)53 b(measure)d Fn(\026)p Fp(.)77 b(Moreo)-5 b(v)g(er,)53 b(b)-5 b(y)52 b(taking)h Fn(q)59 b Fp(and)52 b Fn(\013)i Fp(small,)e(one)h(can)f(render)g(these)-201 9608 y(dimensions)60 b(as)g(close)g(to)g(1)h(as)f(one)g(w)-5 b(an)g(ts.)81 9833 y(The)58 b(estimate)c(\(D.1\))i(is)h(actually)g (also)g(v)-10 b(alid)58 b(for)f Fn(q)g(<)50 b Fp(0)57 b(\(and)f(one)h(can)g(sho)-5 b(w)57 b(that)f(the)h(dimensions)-201 10059 y Fn(D)-45 9993 y Fk(\006)-50 10104 y Fl(\026)73 10059 y Fp(\()p Fn(q)7 b Fp(\))68 b(are)h(\014nite)g(for)f(an)-5 b(y)69 b Fn(q)i(<)64 b Fp(0\).)104 b(Ho)-5 b(w)g(ev)g(er,)71 b(the)d(b)5 b(eha)-5 b(viour)70 b(of)e(the)g(fractal)h(dimensions)e(is) i(rather)-201 10285 y(strange:)80 b(they)60 b(can)g(b)5 b(e)61 b(greater)f(than)g(1)h(and)f(the)g(bigger)h(is)g Fn(\025)p Fp(,)f(the)g(bigger)h(are)g Fn(D)5622 10219 y Fk(\006)5617 10330 y Fl(\026)5740 10285 y Fp(\()p Fn(q)7 b Fp(\))59 b(as)h Fn(q)e Fm(!)50 b(\0001)p Fp(:)2418 10804 y(lim)30 b(inf)2440 10915 y Fl(q)5 b Fk(!\0001)2952 10804 y Fn(D)3108 10729 y Fk(\006)3103 10849 y Fl(\026)3226 10804 y Fp(\()p Fn(q)i Fp(\))49 b Fm(\025)3879 10681 y Fn(\025)p 3717 10763 431 8 v 3717 10929 a Fp(1)40 b(+)g Fn(\013)4218 10804 y(>)50 b Fp(1)p Fn(;)3393 11631 y Fp(24)p eop %%Page: 25 25 25 24 bop -201 1158 a Fp(if)86 b Fn(\013)h Fp(is)e(small)g(enough.)155 b(F)-15 b(urthermore)84 b(note)h(that)g(if)g Fn(\026)h Fp(is)f(no)-5 b(w)86 b(de\014ned)g(with)g Fn(a)5787 1185 y Fl(n)5973 1158 y Fp(=)92 b Fn(ae)6388 1092 y Fk(\000)p Fl(\025n)6673 1158 y Fp(,)g(then)-201 1384 y Fn(D)-45 1318 y Fk(\006)-50 1429 y Fl(\026)73 1384 y Fp(\()p Fn(q)7 b Fp(\))49 b(=)h(+)p Fm(1)j Fp(whenev)-5 b(er)53 b Fn(q)58 b(<)49 b Fp(0.)78 b(This)54 b(sho)-5 b(ws)53 b(that)g(one)g(should)h(b) 5 b(e)53 b(v)-5 b(ery)53 b(cautious)g(when)h(considering)-201 1610 y(p)5 b(ossible)61 b(ph)-5 b(ysical)61 b(applications)g(of)f Fn(D)2555 1544 y Fk(\006)2550 1655 y Fl(\026)2673 1610 y Fp(\()p Fn(q)7 b Fp(\))60 b(with)h Fn(q)c(<)50 b Fp(0.)81 1836 y(T)-15 b(o)53 b(conclude,)g(w)-5 b(e)52 b(giv)-5 b(e)53 b(the)e(example)g(of)h(a)g(self-adjoin)-5 b(t)51 b(op)5 b(erator)52 b Fn(H)15 b Fp(,)53 b(and)f(a)g(state)f Fn( )58 b Fp(as)52 b(men)-5 b(tioned)-201 2062 y(in)61 b(Remark)e(2.3)h(ii\).)81 b(W)-15 b(e)60 b(shall)i(pro)-5 b(v)g(e:)-201 2437 y Fe(Theorem)68 b(D.1.)91 b Fq(L)-9 b(et)84 b Fn(\014)95 b(>)85 b Fp(0)f Fq(and)h Fn(\016)92 b(>)85 b Fp(0)p Fq(.)141 b(Ther)-9 b(e)83 b(exist)i(a)f(b)-9 b(ounde)g(d)83 b(self-adjoint)g(op)-9 b(er)g(ator)83 b Fn(H)99 b Fq(on)-201 2663 y Fm(H)52 b Fp(=)e Fn(`)273 2597 y Fg(2)352 2663 y Fp(\()p Ff(N)30 b Fp(\))73 b Fq(and)65 b(a)g(state)h Fn( )57 b Fm(2)50 b(H)67 b Fq(such)d(that,)i(with)f Fn(p)50 b Fp(=)g Fn(\014)10 b Fq(,)1446 3171 y Fp(lim)1380 3292 y Fl(T)20 b Fk(!1)1814 3045 y Fp(log)s Fm(hhj)p Fn(X)14 b Fm(j)2458 2979 y Fl(p)2536 3045 y Fm(ii)2678 3075 y Fl( )5 b(;T)p 1814 3129 1110 8 v 2170 3296 a Fp(log)34 b Fn(T)2994 3171 y Fp(=)50 b(0)p Fn(;)95 b Fq(but)129 b Fn(D)3950 3096 y Fk(\006)3945 3216 y Fl(\026)4030 3239 y Fh( )4162 2915 y Fi(\022)4483 3048 y Fp(1)p 4316 3129 426 8 v 4316 3296 a(1)40 b(+)g Fn(\014)4801 3171 y Fm(\000)g Fn(\016)5071 2915 y Fi(\023)5255 3171 y Fn(>)50 b Fp(0)p Fn(:)-201 3669 y Fe(Pro)6 b(of)69 b(of)g(Theorem)f(D.1)p Fp(.)-201 3895 y(Let)c Fn(\014)k(>)57 b Fp(0)65 b(and)g Fn(\016)f(>)57 b Fp(0)65 b(b)5 b(e)65 b(as)g(in)g(the)g(theorem,)e(and) i Fn(\027)70 b(>)57 b Fp(0)65 b(to)f(b)5 b(e)65 b(c)-5 b(hosen)64 b(later)i(on.)93 b(Let)64 b(\()p Fn(e)6479 3922 y Fl(n)6572 3895 y Fp(\))6643 3922 y Fl(n)p Fk(\025)p Fg(1)6982 3895 y Fp(b)5 b(e)-201 4121 y(the)59 b(canonical)h(basis)g (of)f Fn(`)1636 4055 y Fg(2)1714 4121 y Fp(\()p Ff(N)1907 4055 y Fk(\003)1995 4121 y Fp(\):)80 b Fn(e)2282 4148 y Fl(n)2375 4121 y Fp(\()p Fn(k)6 b Fp(\))50 b(=)f Fn(\016)2940 4151 y Fl(nk)3111 4121 y Fp(,)60 b Fn(k)6 b(;)30 b(n)49 b Fm(\025)h Fp(1.)80 b(De\014ne)59 b(a)h(self-adjoin)-5 b(t)58 b(op)5 b(erator)59 b Fn(H)75 b Fp(in)60 b Fm(H)h Fp(as)-201 4347 y(follo)-5 b(ws:)2175 4573 y Fn(H)15 b(e)2426 4600 y Fl(n)2570 4573 y Fp(=)50 b Fn(x)2866 4600 y Fl(n)2960 4573 y Fn(e)3045 4600 y Fl(n)3138 4573 y Fn(;)151 b(x)3444 4600 y Fl(n)3589 4573 y Fp(=)50 b Fn(n)3890 4498 y Fk(\000)p Fl(\013)4099 4573 y Fn(;)151 b(n)50 b Fm(\025)g Fp(1)p Fn(:)-201 4906 y Fp(It)83 b(is)i(easy)e(to)g (see)h(that)f(the)g(sp)5 b(ectral)84 b(measure)e Fn(\026)3514 4936 y Fl( )3702 4906 y Fp(asso)5 b(ciated)83 b(to)h(the)f(v)-5 b(ector)83 b Fn( )7 b Fp(\()p Fn(k)f Fp(\))88 b(=)6429 4775 y Fm(p)p 6581 4775 97 8 v 131 x Fn(ak)6778 4840 y Fk(\000)p Fl(\025=)p Fg(2)7119 4906 y Fp(,)-201 5132 y Fn(\025)60 b Fp(=)e(1)44 b(+)g Fn(\014)53 b Fp(+)43 b Fn(\027)12 b Fp(,)66 b(is)h(exactly)e(the)h(measure)e Fn(\026)h Fp(de\014ned)h(ab)5 b(o)-5 b(v)g(e)65 b(\(so)g(supp)p Fn(\026)5010 5162 y Fl( )5174 5132 y Fm(\032)59 b Fp([0)p Fn(;)30 b Fp(1])65 b(and)g(Theorem)g(2.1)-201 5358 y(applies\).)77 b(Notice)49 b(that)g Fn( )7 b Fp(\()p Fn(t;)30 b(k)6 b Fp(\))48 b(=)i(exp\()p Fm(\000)p Fn(itx)2966 5388 y Fl(k)3049 5358 y Fp(\))p Fn( )7 b Fp(\()p Fn(k)f Fp(\).)74 b(Then,)52 b(as)d Fn(d)h Fp(=)g(1)f(one)g(has)g Fn(\014)60 b Fp(=)50 b Fn(p)p Fp(,)h(and)e(one)g(c)-5 b(hec)g(ks)-201 5584 y(that)1892 5810 y Fm(h)p Fn( )2082 5837 y Fl(t)2140 5810 y Fn(;)30 b Fm(j)p Fn(X)14 b Fm(j)2488 5735 y Fl(p)2566 5810 y Fn( )2685 5837 y Fl(t)2744 5810 y Fm(i)50 b Fp(=)3057 5637 y Fi(X)3059 6032 y Fl(k)t Fk(\025)p Fg(1)3350 5810 y Fn(ak)3547 5735 y Fl(\014)7 b Fk(\000)p Fl(\025)3883 5810 y Fp(=)50 b Fn(C)13 b Fp(\()p Fn(\027)f Fp(\))49 b Fn(<)h Fp(+)p Fm(1)p Fn(:)-201 6334 y Fp(Therefore,)85 b(lim)952 6362 y Fl(T)20 b Fk(!1)1375 6334 y Fp(log)r Fm(hhj)p Fn(X)14 b Fm(j)2018 6268 y Fl(p)2096 6334 y Fm(ii)2238 6364 y Fl( )5 b(;T)2484 6334 y Fn(=)30 b Fp(log)j Fn(T)110 b Fp(=)84 b(0.)141 b(On)80 b(the)h(other)f(hand,)86 b(as)80 b(w)-5 b(e)81 b(ha)-5 b(v)g(e)81 b(seen)f(ab)5 b(o)-5 b(v)g(e,)-201 6560 y Fn(D)-45 6494 y Fk(\006)-50 6604 y Fl(\026)35 6627 y Fh( )136 6560 y Fp(\()p Fn(q)7 b Fp(\))83 b Fn(>)g Fp(0)d(for)g(an)-5 b(y)80 b Fn(q)91 b(<)82 b Fp(1)p Fn(=\025)i Fp(=)2710 6488 y Fg(1)p 2519 6518 455 8 v 2519 6622 a(1+)p Fl(\014)7 b Fg(+)p Fl(\027)2993 6560 y Fp(.)139 b(T)-15 b(aking)81 b Fn(\027)92 b Fp(small)79 b(enough,)85 b Fq(e.g.)139 b Fp(suc)-5 b(h)80 b(that)6662 6488 y Fg(1)p 6470 6518 V 6470 6622 a(1+)p Fl(\014)7 b Fg(+)p Fl(\027)7028 6560 y Fp(=)-83 6750 y Fg(1)p -181 6780 267 8 v -181 6885 a(1+)p Fl(\014)146 6822 y Fm(\000)40 b Fn(\016)7 b(=)p Fp(2,)59 b(one)i(gets)e(the)h(required)i(example.) 3881 b Fc(\003)-201 7334 y Fe(Remark)69 b(D.1.)91 b Fp(on)72 b(can)g(easily)g(construct)f(suc)-5 b(h)72 b(an)g(example)f(on)h Fm(H)f Fp(=)e Fn(`)5184 7268 y Fg(2)5263 7334 y Fp(\()p Ff(Z)5445 7268 y Fl(d)5535 7334 y Fp(\))j(to)5 b(o,)74 b(b)-5 b(y)72 b(n)-5 b(um)g(b)5 b(ering)-201 7560 y(the)55 b(canonical)i(basis)e(\()p Fn(e)1498 7587 y Fl(n)1592 7560 y Fp(\))1663 7604 y Fl(n)p Fk(2)p Fj(Z)1930 7567 y Fh(d)2067 7560 y Fp(in)h(a)g(\\spiral")g(w)-5 b(a)g(y)-15 b(,)56 b(and)g(taking)g Fn(\014)k Fp(=)50 b Fn(p=d)55 b Fp(as)g(usual.)79 b(Indeed,)55 b(one)h(then)-201 7786 y(gets)k Fn(e)259 7813 y Fl(n)353 7786 y Fp(\()p Fn(k)6 b Fp(\))49 b(=)h(1)60 b(for)h(some)d Fn(k)e Fm(\030)50 b Fn(n)2174 7720 y Fg(1)p Fl(=d)2396 7786 y Fp(.)-201 8359 y Fo(References)-110 8765 y Fp([1])90 b(Barbaroux)67 b(J-M.,)e(Com)-5 b(b)5 b(es)65 b(J-M.,)h(Mon)-5 b(tc)g(ho)66 b(R.,)h Fq(R)-9 b(emarks)69 b(on)h(the)h(r)-9 b(elation)69 b(b)-9 b(etwe)g(en)69 b(quantum)173 8990 y(dynamics)c(and)g(fr)-9 b(actal)63 b(sp)-9 b(e)g(ctr)g(a)p Fp(,)59 b(J.)h(Math.)f(Anal)j(and)e (Appl.)h Fe(213)p Fp(,)e(698-722)h(\(1997\).)-110 9366 y([2])90 b(Barbaroux)76 b(J-M.,)h(Germinet)d(F.,)k(Tc)-5 b(heremc)g(han)g(tsev)73 b(S.,)78 b Fq(Non)h(line)-9 b(ar)78 b(V)-14 b(ariation)78 b(of)h(Di\013usion)173 9592 y(Exp)-9 b(onents)66 b(in)f(Quantum)f(Dynamics)p Fp(,)c(C.R.)g(Acad.)g(Sci,)h(P)-5 b(aris,)60 b(S)-5 b(\023)-86 b(erie)61 b(I,)e Fe(330)p Fp(,)g(409-414)h(\(2000\).)-110 9967 y([3])90 b(Barbaroux)h(J-M.,)97 b(Germinet)90 b(F.,)98 b(Tc)-5 b(heremc)g(han)g(tsev)88 b(S.,)98 b Fq(Quantum)92 b(di\013usion)h(and)g(gener)-9 b(al-)173 10193 y(ize)g(d)64 b(R)-5 b(\023)-88 b(enyi)64 b(dimensions)h(of)f(sp)-9 b(e)g(ctr)g(al)63 b(me)-9 b(asur)g(es)p Fp(,)58 b(Journ)-5 b(\023)-86 b(ees)60 b(Equations)f(aux)h(D)-5 b(\023)-86 b(eriv)-5 b(\023)-86 b(ees)60 b(P)-5 b(artielles,)173 10418 y(Nan)g(tes)60 b(\(2000\).)-110 10794 y([4])90 b(Barbaroux)81 b(J-M.,)j(Sc)-5 b(h)g(ulz-Baldes)81 b(H.,)86 b Fq(A)-5 b(nomalous)83 b(quantum)g(tr)-9 b(ansp)g(ort)84 b(in)g(pr)-9 b(esenc)g(e)82 b(of)i(self-)173 11020 y(similar)64 b(sp)-9 b(e)g(ctr)g(a)p Fp(,)58 b(Ann.)j(Inst.)e(Henri)j(P)-5 b(oincar)g(\023)-86 b(e,)60 b Fe(V)-17 b(ol)69 b(71)p Fp(,)59 b(1-21)h(\(1999\).)3393 11631 y(25)p eop %%Page: 26 26 26 25 bop -110 1158 a Fp([5])90 b(Barbaroux)64 b(J-M.,)f(Tc)-5 b(heremc)g(han)g(tsev)61 b(S.,)j Fq(Universal)j(lower)g(b)-9 b(ounds)67 b(for)h(quantum)f(di\013usion)p Fp(,)c(J.)173 1384 y(F)-15 b(unct.)59 b(Anal.)i Fe(168)p Fp(,)e(327-354)g(\(1999\).) -110 1760 y([6])90 b(Bellissard)67 b(J.,)g(Sc)-5 b(h)g(ulz-Baldes)65 b(H.,)j Fq(A)-5 b(nomalous)70 b(tr)-9 b(ansp)g(ort:)94 b(A)71 b(mathematic)-9 b(al)68 b(fr)-9 b(amework)p Fp(,)65 b(Rev.)173 1985 y(Math.)59 b(Ph)-5 b(ys.)60 b Fe(10)p Fp(,)f(1-46)h(\(1998\).)-110 2361 y([7])90 b(Com)-5 b(b)5 b(es)45 b(J-M.,)i Fq(Conne)-9 b(ction)52 b(b)-9 b(etwe)g(en)50 b(quantum)h(dynamics)h(and)g(sp)-9 b(e)g(ctr)g(al)50 b(pr)-9 b(op)g(erties)51 b(of)g(time)h(evo-)173 2586 y(lution)72 b(op)-9 b(er)g(ators)67 b Fp(in)j(\\Di\013eren)-5 b(tial)69 b(Equations)f(and)h(Applications)h(in)f(Mathematical)d(Ph)-5 b(ysics",)173 2812 y(Eds.)60 b(W.F.)f(Ames,)f(E.M.)h(Harrel,)i(J.V.)f (Hero)5 b(d,)60 b(Academic)g(Press,)f(59-69)h(\(1993\).)-110 3187 y([8])90 b(Cutler)68 b(C.D.,)g Fq(Some)j(r)-9 b(esults)71 b(on)g(the)h(b)-9 b(ehaviour)69 b(and)i(estimation)h(of)f(the)g(fr)-9 b(actal)70 b(dimensions)i(of)173 3413 y(distributions)65 b(on)g(attr)-9 b(actors)p Fp(,)60 b(J.)g(Stat.)f(Ph)-5 b(ys.)60 b Fe(62)p Fp(,)f(Nos)h(3/4,)g(651-708)g(\(1991\).)-110 3789 y([9])90 b(De)66 b(Bi)-5 b(\022)-86 b(evre)67 b(S.,)h(F)-15 b(orni)67 b(G.,)g Fq(T)-14 b(r)-9 b(ansp)g(ort)70 b(pr)-9 b(op)g(erties)69 b(of)i(kicke)-9 b(d)68 b(and)j(quasi-p)-9 b(erio)g(dic)68 b(Hamiltonians)p Fp(,)173 4014 y(J.)59 b(Stat.)h(Ph)-5 b(ys.)59 b Fe(90)p Fp(,)h(1201-1223)f(\(1998\).)-201 4390 y([10])90 b(De)115 b(Bi)-5 b(\022)-86 b(evre)116 b(S.,)128 b(Germinet)114 b(F.,)128 b Fq(Dynamic)-9 b(al)115 b(L)-9 b(o)g(c)g(alization)114 b(for)h(the)g(r)-9 b(andom)115 b(dimer)f(mo)-9 b(del)p Fp(,)173 4615 y(J.)59 b(Stat.)h(Ph)-5 b(ys.)59 b Fe(98)p Fp(,)h(1135-1148)f(\(2000\).)-201 4991 y([11])90 b(Del)g(Rio)h(R.,)97 b(Jitomirsk)-10 b(a)-5 b(y)g(a)88 b(S.,)97 b(Last)89 b(Y.,)97 b(Simon)89 b(B.,)97 b Fq(Op)-9 b(er)g(ators)91 b(with)h(singular)f(c)-9 b(ontinuous)173 5217 y(sp)g(e)g(ctrum)59 b(IV:)j(Hausdor\013)e(dimensions,)h(r)-9 b(ank)61 b(one)g(p)-9 b(ertub)g(ations)60 b(and)h(lo)-9 b(c)g(alization)p Fp(,)55 b(J.)h(d'Analyse)173 5442 y(Math.)j Fe(69)p Fp(,)h(153-200)f(\(1996\).)-201 5818 y([12])90 b(Dunlap)69 b(D.H.,)h(W)-15 b(u)68 b(H.-L.,)h(Phillips)i(P)-15 b(.,)69 b Fq(A)-5 b(bsenc)c(e)72 b(of)g(lo)-9 b(c)g(alization)71 b(in)i(a)f(r)-9 b(andom)72 b(Dimer)f(mo)-9 b(del)p Fp(,)173 6043 y(Ph)k(ys.)59 b(Rev.)h(Lett.)f Fe(65)p Fp(,)g(p.)h(88)h(\(1990\).) -201 6419 y([13])90 b(F)-15 b(alconer)60 b(K.)g(J.,)f Fq(T)-14 b(e)-9 b(chniques)63 b(in)i(F)-14 b(r)-9 b(actal)64 b(Ge)-9 b(ometry)p Fp(,)58 b(John)i(Wiley)i(and)e(sons,)g(New)h(Y)-15 b(ork)61 b(1997.)-201 6794 y([14])90 b(Guarneri)100 b(I.,)108 b Fq(Sp)-9 b(e)g(ctr)g(al)99 b(pr)-9 b(op)g(erties)99 b(of)i(quantum)f(di\013usion)g(on)h(discr)-9 b(ete)100 b(lattic)-9 b(es)p Fp(,)108 b(Europh)-5 b(ys.)173 7020 y(Lett.)56 b(10)h(\(1989\),)g(95-100;)g Fq(On)62 b(an)g(estimate)g(c)-9 b(onc)g(erning)60 b(quantum)h(di\013usion)g(in)h(the)g(pr)-9 b(esenc)g(e)61 b(of)173 7246 y(a)k(fr)-9 b(actal)63 b(sp)-9 b(e)g(ctrum)p Fp(,)59 b(Europh)-5 b(ys.)59 b(Lett.)g Fe(21)p Fp(,)h(729-733)f(\(1993\).)-201 7621 y([15])90 b(Guarneri)66 b(I.,)g(Sc)-5 b(h)g(ulz-Baldes)66 b(H.,)h Fq(L)-9 b(ower)69 b(b)-9 b(ounds)69 b(on)h(wave)f(p)-9 b(acket)69 b(pr)-9 b(op)g(agation)69 b(by)h(p)-9 b(acking)69 b(di-)173 7847 y(mensions)c(of)g(sp)-9 b(e)g(ctr)g(al)63 b(me)-9 b(asur)g(es)p Fp(,)58 b(Math.)i(Ph)-5 b(ys.)59 b(Elec.)h(J.)g Fe(5)p Fp(,)f(pap)5 b(er)61 b(1)g(\(1999\).)-201 8222 y([16])90 b(Guarneri)69 b(I.,)g(Sc)-5 b(h)g(ulz-Baldes)68 b(H.,)h Fq(Upp)-9 b(er)71 b(b)-9 b(ounds)72 b(for)g(quantum)f(dynamics) h(governe)-9 b(d)70 b(by)i(Jac)-9 b(obi)173 8448 y(matric)g(es)64 b(with)h(self-similar)e(sp)-9 b(e)g(ctr)g(a)p Fp(,)58 b(Rev.)i(Math.)g(Ph)-5 b(ys.)59 b Fe(11)p Fp(,)g(1249-1268)h(\(1999\).) -201 8823 y([17])90 b(Guarneri)i(I.,)98 b(Sc)-5 b(h)g(ulz-Baldes)91 b(H.,)99 b Fq(Intermittent)94 b(lower)f(b)-9 b(ound)92 b(on)i(quantum)f(di\013usion)p Fp(,)98 b(Lett.)173 9049 y(Math.)59 b(Ph)-5 b(ys.)60 b Fe(49)p Fp(,)f(317-324)h(\(1999\).)-201 9424 y([18])90 b(Halsey)c(T.C.,)92 b(Jensen)84 b(M.,)91 b(Kaddano)-5 b(v)85 b(L.,)91 b(Pro)5 b(caccia)86 b(I.,)k(Sc)-5 b(hraiman)85 b(B.,)91 b Fq(F)-14 b(r)-9 b(actal)87 b(me)-9 b(asur)g(es)173 9650 y(and)65 b(their)g(singularities:)82 b(the)65 b(char)-9 b(acterization)64 b(of)h(str)-9 b(ange)64 b(sets)p Fp(,)d(Ph)-5 b(ys.)60 b(Rev.)g(A)h Fe(33)p Fp(,)e(1141-1151) 173 9876 y(\(1986\).)-201 10251 y([19])90 b(Hen)-5 b(tsc)g(hel)54 b(H.G.E.,)f(Pro)5 b(caccia)54 b(I.,)g Fq(The)k(in\014nite)i(numb)-9 b(er)57 b(of)i(gener)-9 b(alize)g(d)56 b(dimensions)j(of)f(fr)-9 b(actals)173 10477 y(and)65 b(str)-9 b(ange)65 b(attr)-9 b(actors)p Fp(,)60 b(Ph)-5 b(ys.)59 b(D)i Fe(8)p Fp(,)e(435-444)h (\(1983\).)-201 10852 y([20])90 b(Jitomirsk)-10 b(a)-5 b(y)g(a)62 b(S.,)j(Last)e(Y.,)i Fq(Power-law)i(sub)-9 b(or)g(dinacy)67 b(and)i(singular)e(sp)-9 b(e)g(ctr)g(a.)67 b(I.)h(Half-line)f(op)-9 b(er-)173 11078 y(ators)p Fp(,)60 b(Acta)h(Math.)e Fe(183)p Fp(,)g(171{189)h(\(1999\).)3393 11631 y(26)p eop %%Page: 27 27 27 26 bop -201 1158 a Fp([21])90 b(Ketzmeric)-5 b(k)58 b(R.,)h(Kruze)h(K.,)e(Kraut)i(S.,)f(Geisel)i(T.,)f Fq(What)k (determines)g(the)h(spr)-9 b(e)g(ading)63 b(of)i(a)f(wave)173 1384 y(p)-9 b(acket)p Fp(,)59 b(Ph)-5 b(ys.)59 b(Rev.)h(A)h Fe(79)p Fp(,)e(1959-1963)h(\(1997\).)-201 1760 y([22])90 b(Ketzmeric)-5 b(k)73 b(R.,)79 b(P)-5 b(etsc)g(hel)75 b(G.,)j(Geisel)e(T,)g Fq(Slow)j(de)-9 b(c)g(ay)78 b(of)h(temp)-9 b(or)g(al)77 b(c)-9 b(orr)g(elations)77 b(in)i(quantum)173 1985 y(systems)66 b(with)f(Cantor)g(sp)-9 b(e)g(ctr)g(a)p Fp(,)59 b(Ph)-5 b(ys.)60 b(Rev.)f(Lett.)g Fe(69)p Fp(,)g(695-698)h (\(1992\).)-201 2361 y([23])90 b(Kiselev)83 b(A.,)k(Last)82 b(Y.,)88 b Fq(Solutions,)i(sp)-9 b(e)g(ctrum,)89 b(and)d(dynamics)f (for)g(Schr\177)-93 b(odinger)84 b(op)-9 b(er)g(ators)84 b(on)173 2586 y(in\014nite)65 b(domains)p Fp(,)60 b(Duk)-5 b(e)60 b(Math.)g(J.)f Fe(102)p Fp(,)g(125-150)h(\(2000\).)-201 2962 y([24])90 b(Kunz)85 b(H.,)92 b(Souillard)c(B.,)k Fq(Sur)c(le)g(sp)-9 b(e)g(ctr)g(e)87 b(des)h(op)-5 b(\023)-88 b(er)-9 b(ateurs)87 b(aux)i(di\013)-5 b(\023)-88 b(er)-9 b(enc)g(es)86 b(\014nies)i(al)-5 b(\023)-88 b(eatoir)-9 b(es)p Fp(,)173 3187 y(Comm)k(un.)57 b(Math.)j(Ph)-5 b(ys.)59 b Fe(78)p Fp(,)g(201-246)h(\(1980\).)-201 3563 y([25])90 b(Last)41 b(Y.,)46 b Fq(Quantum)h(dynamics)h(and)g(de)-9 b(c)g(omp)g(osition)47 b(of)h(singular)f(c)-9 b(ontinuous)47 b(sp)-9 b(e)g(ctrum)p Fp(,)44 b(J.)e(F)-15 b(unct.)173 3789 y(Anal)61 b Fe(142)p Fp(,)e(406-445)h(\(1996\).)-201 4164 y([26])90 b(Man)-5 b(tica)48 b(G.)g Fq(Quantum)53 b(intermittency)h(in)g(almost)g(p)-9 b(erio)g(dic)52 b(systems)j(derive)-9 b(d)53 b(fr)-9 b(om)53 b(their)g(sp)-9 b(e)g(ctr)g(al)173 4390 y(pr)g(op)g(erties)p Fp(,)71 b(Ph)-5 b(ysica)70 b(D)g Fe(103)p Fp(,)h(576-589)e(\(1997\);)74 b Fq(Wave)f(pr)-9 b(op)g(agation)73 b(in)h(almost-p)-9 b(erio)g(dic)72 b(struc-)173 4615 y(tur)-9 b(es)p Fp(,)59 b(Ph)-5 b(ysica)61 b(D)f Fe(109)p Fp(,)f(113-127)g(\(1997\).)-201 4991 y([27])90 b(Olsen)60 b(L.,)f Fq(A)65 b(multifr)-9 b(actal)63 b(F)-14 b(ormalism)p Fp(,)58 b(Adv.)j(Math.)e Fe(116)p Fp(,)g(82-195)h(\(1995\).)-201 5366 y([28])90 b(P)-5 b(esin)56 b(Y.B.,)g Fq(Dimension)61 b(The)-9 b(ory)61 b(in)g(Dynamic)-9 b(als)60 b(Systems:)83 b(Contemp)-9 b(or)g(ary)60 b(Views)h(and)g(Appli-)173 5592 y(c)-9 b(ations)p Fp(,)60 b(Univ.)h(Chicago)g(Press,)e(1996.)-201 5967 y([29])90 b(Piec)-5 b(hon)50 b(F.,)h Fq(A)-5 b(nomalous)55 b(di\013usion)f(pr)-9 b(op)g(erties)54 b(of)h(wave)f(p)-9 b(acket)54 b(on)i(quasip)-9 b(erio)g(dic)52 b(chains)p Fp(,)f(Ph)-5 b(ys.)173 6193 y(Rev.)60 b(Lett.)f Fe(76)p Fp(,)g Fn(n)1471 6127 y Fg(o)1550 6193 y Fp(23,)h(4372-4375)f (\(1996\).)-201 6568 y([30])90 b(Reed)68 b(M.,)i(Simon)e(B.)g Fq(Metho)-9 b(ds)73 b(of)g(Mo)-9 b(dern)72 b(Mathematic)-9 b(al)71 b(Physics)p Fp(,)g(V)-15 b(ol.)69 b(1,)i(New)e(Y)-15 b(ork:)98 b(Aca-)173 6794 y(demic)59 b(Press,)h(\(1972\).)-201 7169 y([31])90 b(T)-15 b(a)-5 b(ylor)59 b(S.)f(J.,)g(T)-15 b(ricot)58 b(C.,)h Fq(Packing)j(me)-9 b(asur)g(e,)61 b(and)i(its)h(evaluation)e(for)g(a)h(Br)-9 b(ownian)62 b(p)-9 b(ath)p Fp(,)59 b(T)-15 b(rans.)173 7395 y(Amer.)59 b(Math.)g(So)5 b(c.)60 b Fe(288)p Fp(,)f(679-699)h(\(1985\).)-201 7770 y([32])90 b(Wilkinson)45 b(M.,)h(Austin)f(E.J.,)g Fq(Sp)-9 b(e)g(ctr)g(al)48 b(dimension)i(and)g(dynamics)f(for)h(Harp)-9 b(er's)49 b(e)-9 b(quation)p Fp(,)45 b(Ph)-5 b(ys.)173 7996 y(Rev.)60 b(B)g Fe(50)p Fp(,)f(1420-1429)h(\(1994\).)3393 11631 y(27)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0012210616900--