Content-Type: multipart/mixed; boundary="-------------0204260659782" This is a multi-part message in MIME format. ---------------0204260659782 Content-Type: text/plain; name="02-199.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="02-199.keywords" Asymptotic, Dirac equation, Cauchy problem, continuous spectrum ---------------0204260659782 Content-Type: application/postscript; name="fineng.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="fineng.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: fineng.dvi %%CreationDate: Fri Apr 26 00:00:40 2002 %%Pages: 9 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: C:\TEXNEW\TEXMF\MIKTEX\BIN\DVIPS.EXE fineng %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2002.04.25:2341 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: special.pro %! TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N /vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N /rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N /@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ /hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B /@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ /urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known {userdict/md get type/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale }if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState save N userdict maxlength dict begin/magscale true def normalscale currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts /psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{ psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict begin/SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{ CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR }{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end} repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N /@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X /yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet TeXDict begin 39158280 55380996 1000 600 600 (fineng.dvi) @start %DVIPSBitmapFont: Fa cmmi5 5 1 /Fa 1 79 df78 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb cmbx7 7 1 /Fb 1 89 df<3B7FFFF807FFFCA30003902680007FC7FC6C6D137E6C6D5B017F5C6D6C48 5A6E485A6D6C485A6D6C485A0107131FD903FF90C8FC6D13BE15FC6D5B6E5A143F6E7E81 6E7E141F4A7E4A7F027D7F02F87F49486C7E903803E03F49486C7E010F804A6C7E49486C 7E013E7F496D7F498100016E7F00036F7EB5D88007B51280A331287DA738>88 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmr5 5 1 /Fc 1 51 df50 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd cmsy5 5 1 /Fd 1 49 df48 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe cmsy7 7 5 /Fe 5 63 df0 D<13E0EA01F0EA03F8A3EA07F0A313E0A2120F 13C0A3EA1F80A21300A25A123EA35AA3127812F8A25A12100D1E7D9F13>48 D<017F157F2601FFE0903803FFC0000701F890380FF1F0260F83FC90381F0038261E00FF 013C7F001890263F8078130C4890261FC0E07F007090260FE1C07F0060EB07E3913803F7 80486DB4C7EA01806E5A157E157F81824B7E0060DAF7E0EB0300913801E3F0DBC3F85B6C 90260381FC13066C90260F00FE5B001C011E90387F803C6C017C90381FE0F82607C7F86D B45A2601FFE0010313C06C6CC86CC7FC391B7C9942>I<49B5FC130F133F01FFC7FCEA01 F8EA03E0EA078048C8FC121E121C123C123812781270A212F05AA2B7FCA300E0C8FCA27E 1270A212781238123C121C121E7E6C7EEA03E0EA01F86CB4FC013FB5FC130F130120277A A12D>I<007FB712E0B8FC7EC7000EC8FCB3B214062B287CA734>62 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff cmbx10 10 12 /Ff 12 127 df<0107B612FCA490C701E0C8FCA9020F13FC49B612E0010F15FCD97FFC90 38EFFF802601FFE001E113E04801809038E07FF048496E7E48486F7E48486F7E003F8300 7F1880498100FF18C0A7007F18806D5D003F1800001F5F6C6C4B5A6C6C4B5A6C6D4A5A6C 01E09038E1FFE026007FFC01EF1380010FB600FCC7FC010115E0D9000F01FCC8FC020013 E0A90107B612FCA43A397BB845>8 D<49B7FCA490C7D83FF8C8FCA8D87FF0EE1FFE486C 163F6D167FD81FFEEEFFF0000F18E0A26D5D6C18C0A96C188002805CA36C01C04A1300A2 6C01E04A5A017F5ED93FF04A5AD91FF84A5AD90FFC4A5AD907FF9038F9FFC06D90B65A01 004BC7FC021F14F0020191C8FC9138003FF8A949B7FCA43F397BB84A>I70 D<007FB5D8F803B512F8A4C66C48C7D80FF0C7FC6D6C5D6D5E6F495A6D6D49C8FC7F6D6D 137E6F5B6DEBF8016D5D6F485A6E6C485A023F130FDA1FFF5BEE9F806E01FFC9FC805E6E 5B6E5B80826F7E153F826F7F5D4B7F92B57EA2DA01F97FDA03F17F03F07F913807E07FDA 0FC07F021F6D7E4B7E4A486C7F027E8102FE6D7F4A7F49488149486D7F0107804A6E7E49 488149486E7E013F81017F83B60107B61280A441397DB848>88 D97 D<903801FFC0010F13FC017F13FFD9FF8013802603FE0013C048485AEA0FF8121F13F012 3F6E13804848EB7F00151C92C7FC12FFA9127FA27F123FED01E06C7E15036C6CEB07C06C 6C14806C6C131FC69038C07E006DB45A010F13F00101138023257DA42A>99 D102 D<161FD907FEEBFFC090387FFFE348B6EAEFE02607FE07138F260FF801131F48486C138F 003F15CF4990387FC7C0EEC000007F81A6003F5DA26D13FF001F5D6C6C4890C7FC3907FE 07FE48B512F86D13E0261E07FEC8FC90CAFCA2123E123F7F6C7E90B512F8EDFF8016E06C 15F86C816C815A001F81393FC0000F48C8138048157F5A163FA36C157F6C16006D5C6C6C 495AD81FF0EB07FCD807FEEB3FF00001B612C06C6C91C7FC010713F02B377DA530>I<13 FFB5FCA412077EAFED7FC0913803FFF8020F13FE91381F03FFDA3C01138014784A7E4A14 C05CA25CA291C7FCB3A3B5D8FC3F13FFA4303A7DB935>I<903801FFC0010F13F8017F13 FFD9FF807F3A03FE003FE048486D7E48486D7E48486D7EA2003F81491303007F81A300FF 1680A9007F1600A3003F5D6D1307001F5DA26C6C495A6C6C495A6C6C495A6C6C6CB45A6C 6CB5C7FC011F13FC010113C029257DA430>111 D118 D126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg lati1000 10 41 /Fg 41 123 df<04FFEB03F003039038E00FFC923A0FC0F01F1E923A3F00783E0F923A7E 01F87C3FDB7C03EBFC7F03FC14F8DA01F813F905F1137EDC01E1133C913B03F00003F000 A314074B130760A3140F4B130F60A3010FB812C0A3903C001F80001F8000A3023F143F92 C790C7FCA44A5C027E147EA402FE14FE4A5CA413014A13015FA313034A13035FA313074A 495AA44948495AA44948495AA3001CD9038090C8FC007E90380FC03F013E143E00FE011F 5B133C017C5C3AF8780F01E0D878F0EB07C0273FE003FFC9FC390F8000FC404C82BA33> 27 DI< DC7FC0EB1FFF922603FFF890B512E0923C0FC07C03F801F0923C1F001E0FC00078033E90 267E1F80137C4BD9FE3FC712FC03FC027E13015D02014A5A057815F84A48D901F8EB00E0 1B00A302074A5A5DA31707020F5D5DA3010FBA12C0A21B80903D001F80000FC0001FA21A 3F023F021F150092C75BA2621A7E4A143F027E92C7FC1AFE62A25F02FE027E13014A5FA3 05FE130301014B5C4A1870A219070401EDE0F001034B15E05CA2F2E1C0010714034D14C3 4A933803E380F101E7963800FF00010F4A48143C4A94C7FCA34A495A131F5F001CEB0380 007E90380FC01F013F92CAFC26FE3E1F133E013C5C5E3AF8780F01F0D878F0EB83E03A3F E003FF80270F8000FECBFC4E4C82BA49>30 D39 D<150C151C153815F0EC01E0EC03C0EC0780EC0F00141E5C147C5C5C495A1303495A5C13 0F49C7FCA2133EA25BA25BA2485AA212035B12075BA2120F5BA2121FA290C8FCA25AA212 3EA2127EA2127CA412FC5AAD1278A57EA3121C121EA2120E7EA26C7E6C7EA212001E5274 BD22>I<140C140E80EC0380A2EC01C015E0A2140015F0A21578A4157C153CAB157CA715 FCA215F8A21401A215F0A21403A215E0A21407A215C0140F1580A2141F1500A2143EA25C A25CA2495AA2495A5C1307495A91C7FC5B133E133C5B5B485A12035B48C8FC120E5A1278 5A12C01E527FBD22>I<120EEA3F80127F12FFA31300127E123C0909778819>46 D48 D<1538A2157015F014011403EC07E0140F143F14FF010713C0EB3FCF141F131001001380 A2143FA21500A25CA2147EA214FEA25CA21301A25CA21303A25CA21307A25CA2130FA25C A2131FA25CA2133FA291C7FC497EB61280A31D3777B62A>I<133C137E13FF5AA313FE13 FCEA00701300B2120EEA3F80127F12FFA31300127E123C102477A319>58 D67 D<0103B612FEEFFFC018F0903B0007F8000FF84BEB03FCEF00FE020F157FF03F804B141F 19C0021F150F19E05D1807143F19F05DA2147FA292C8FCA25C180F5CA2130119E04A151F A2130319C04A153FA201071780187F4A1600A2010F16FEA24A4A5A60011F15034D5A4A5D 4D5A013F4B5A173F4A4AC7FC17FC017FEC03F84C5A91C7EA1FC04949B45A007F90B548C8 FCB712F016803C397CB83F>I<0107B712FEA3903A000FF000074B1300187C021F153CA2 5DA2143FA25D1838147FA292C8FCEE03804A130718004A91C7FCA201015CA24A131E163E 010314FE91B5FC5EA2903807F800167C4A1378A2130FA24A1370A2011F14F0A24A90C8FC A2133FA25CA2137FA291CAFCA25BA25B487EB6FCA337397BB836>70 D<0103B5D8F80FB512E0A390260007F8C7381FE0004B5DA2020F153F615DA2021F157F96 C7FC5DA2023F5D605DA2027F14016092C7FCA24A1403605CA249B7FC60A202FCC7120701 03150F605CA20107151F605CA2010F153F605CA2011F157F95C8FC5CA2013F5D5F5CA201 7F14015F91C7FC491403007FD9FE01B512F8B55BA243397CB83E>72 D<0103B512F8A390390007F8005DA2140FA25DA2141FA25DA2143FA25DA2147FA292C7FC A25CA25CA21301A25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2133FA25CA213 7FA291C8FC497EB6FCA25C25397CB820>I<92383FC00E913901FFF01C020713FC91391F C07E3C91393F001F7C027CEB0FF84A130749481303495A4948EB01F0A2495AA2011F15E0 91C7FCA34915C0A36E90C7FCA2806D7E14FCECFF806D13F015FE6D6D7E6D14E001008002 3F7F14079138007FFC150F15031501A21500A2167C120EA3001E15FC5EA3003E4A5AA24B 5AA2007F4A5A4B5A6D49C7FC6D133ED8F9F013FC39F8FC03F839F07FFFE0D8E01F138026 C003FCC8FC2F3D7ABA2F>83 D<0007B812E0A25AD9F800EB001F01C049EB07C0485AD900 011403121E001C5C003C17801403123800785C00701607140700F01700485CA2140FC792 C7FC5DA2141FA25DA2143FA25DA2147FA292C9FCA25CA25CA21301A25CA21303A25CA213 07A25CA2130FA25CEB3FF0007FB512F8B6FCA2333971B83B>I<14F8EB07FE90381F871C 90383E03FE137CEBF801120148486C5A485A120FEBC001001F5CA2EA3F801403007F5C13 00A21407485C5AA2140F5D48ECC1C0A2141F15831680143F1587007C017F1300ECFF076C 485B9038038F8E391F0F079E3907FE03FC3901F000F0222677A42A>97 D<133FEA1FFFA3C67E137EA313FE5BA312015BA312035BA31207EBE0F8EBE7FE9038EF0F 80390FFC07C013F89038F003E013E0D81FC013F0A21380A2123F1300A214075A127EA214 0F12FE4814E0A2141F15C05AEC3F80A215005C147E5C387801F8007C5B383C03E0383E07 C0381E1F80D80FFEC7FCEA01F01C3B77B926>I<147F903803FFC090380FC1E090381F00 70017E13784913383901F801F83803F003120713E0120FD81FC013F091C7FC485AA2127F 90C8FCA35A5AA45AA3153015381578007C14F0007EEB01E0003EEB03C0EC0F806CEB3E00 380F81F83803FFE0C690C7FC1D2677A426>II<147F903803FFC090380FC1E09038 3F00F0017E13785B485A485A485A120F4913F8001F14F0383F8001EC07E0EC1F80397F81 FF00EBFFF8148090C8FC5A5AA55AA21530007C14381578007E14F0003EEB01E0EC03C06C EB0F806CEB3E00380781F83803FFE0C690C7FC1D2677A426>IIIII108 DII<147F903803FFC090380FC1F090381F00F8 017E137C5B4848137E4848133E0007143F5B120F485AA2485A157F127F90C7FCA215FF5A 4814FEA2140115FC5AEC03F8A2EC07F015E0140F007C14C0007EEB1F80003EEB3F00147E 6C13F8380F83F03803FFC0C648C7FC202677A42A>I<9039078007C090391FE03FF09039 3CF0787C903938F8E03E9038787FC00170497EECFF00D9F0FE148013E05CEA01E113C15C A2D80003143FA25CA20107147FA24A1400A2010F5C5E5C4B5A131F5EEC80035E013F495A 6E485A5E6E48C7FC017F133EEC70FC90387E3FF0EC0F8001FEC9FCA25BA21201A25BA212 03A25B1207B512C0A3293580A42A>II<39 03C003F0390FF01FFC391E783C0F381C7C703A3C3EE03F8038383FC0EB7F800078150000 701300151CD8F07E90C7FCEAE0FE5BA2120012015BA312035BA312075BA3120F5BA3121F 5BA3123F90C9FC120E212679A423>I<14FE903807FF8090380F83C090383E00E04913F0 0178137001F813F00001130313F0A215E00003EB01C06DC7FC7FEBFFC06C13F814FE6C7F 6D13807F010F13C01300143F141F140F123E127E00FE1480A348EB1F0012E06C133E0070 5B6C5B381E03E06CB45AD801FEC7FC1C267AA422>II<13F8D803FEEB01C0D8078FEB03E0390E0F8007121E121C00 38140F131F007815C01270013F131F00F0130000E015805BD8007E133FA201FE14005B5D 120149137EA215FE120349EBFC0EA20201131E161C15F813E0163CD9F003133814070001 ECF07091381EF8F03A00F83C78E090393FF03FC090390FC00F00272679A42D>I<01F013 0ED803FC133FD8071EEB7F80EA0E1F121C123C0038143F49131F0070140FA25BD8F07E14 0000E08013FEC6485B150E12015B151E0003141C5BA2153C000714385B5DA35DA24A5A14 0300035C6D48C7FC0001130E3800F83CEB7FF8EB0FC0212679A426>I<01F01507D803FC 903903801F80D8071E903907C03FC0D80E1F130F121C123C0038021F131F49EC800F0070 1607A249133FD8F07E168000E0ED000313FEC64849130718000001147E5B03FE5B000316 0E495BA2171E00070101141C01E05B173C1738A217781770020314F05F0003010713016D 486C485A000190391E7C07802800FC3C3E0FC7FC90393FF81FFE90390FE003F0322679A4 37>I<903907E007C090391FF81FF89039787C383C9038F03E703A01E01EE0FE3803C01F 018013C0D8070014FC481480000E1570023F1300001E91C7FC121CA2C75AA2147EA214FE A25CA21301A24A1370A2010314F016E0001C5B007E1401010714C000FEEC0380010F1307 010EEB0F0039781CF81E9038387C3C393FF03FF03907C00FC027267CA427>I<13F0D803 FCEB01C0D8071EEB03E0D80E1F1307121C123C0038140F4914C01270A249131FD8F07E14 8012E013FEC648133F160012015B5D0003147E5BA215FE00075C5BA214015DA314035D14 070003130FEBF01F3901F87FE038007FF7EB1FC7EB000F5DA2141F003F5C48133F92C7FC 147E147C007E13FC387001F8EB03E06C485A383C1F80D80FFEC8FCEA03F0233679A428> I<903903C0038090380FF007D91FF81300496C5A017F130E9038FFFE1E9038F83FFC3901 F007F849C65A495B1401C7485A4A5A4AC7FC141E5C5C5C495A495A495A49C8FC131E5B49 131C5B4848133C48481338491378000714F8390FF801F0391FFF07E0383E1FFFD83C0F5B 00785CD8700790C7FC38F003FC38E000F021267BA422>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh labx1000 10 17 /Fh 17 116 df46 D<141E143E14FE1307137FB5FCA3138FEA000FB3B3A5007FB61280A4213679B530> 49 DII76 D82 D<003FB91280A4D9F800EBF003D87FC09238007FC049161F007EC7150FA2007C1707A200 781703A400F818E0481701A4C892C7FCB3AE010FB7FCA43B387DB742>84 D97 D<903801FFC0010F13FC017F13FFD9FF8013802603FE0013C048485AEA 0FF8121F13F0123F6E13804848EB7F00151C92C7FC12FFA9127FA27F123FED01E06C7E15 036C6CEB07C06C6C14806C6C131FC69038C07E006DB45A010F13F00101138023257DA42A >99 D<903803FF80011F13F0017F13FC3901FF83FE3A03FE007F804848133F484814C000 1FEC1FE05B003FEC0FF0A2485A16F8150712FFA290B6FCA301E0C8FCA4127FA36C7E1678 121F6C6C14F86D14F000071403D801FFEB0FE06C9038C07FC06DB51200010F13FC010113 E025257DA42C>101 DI<13FFB5FCA412077EAFED7FC0913803FFF8020F13FE91381F03FFDA3C0113 8014784A7E4A14C05CA25CA291C7FCB3A3B5D8FC3F13FFA4303A7DB935>104 D<01FED97FE0EB0FFC00FF902601FFFC90383FFF80020701FF90B512E0DA1F81903983F0 3FF0DA3C00903887801F000749DACF007F00034914DE6D48D97FFC6D7E4A5CA24A5CA291 C75BB3A3B5D8FC1FB50083B512F0A44C257DA451>109 D<01FEEB7FC000FF903803FFF8 020F13FE91381F03FFDA3C011380000713780003497E6D4814C05CA25CA291C7FCB3A3B5 D8FC3F13FFA430257DA435>I<903801FFC0010F13F8017F13FFD9FF807F3A03FE003FE0 48486D7E48486D7E48486D7EA2003F81491303007F81A300FF1680A9007F1600A3003F5D 6D1307001F5DA26C6C495A6C6C495A6C6C495A6C6C6CB45A6C6CB5C7FC011F13FC010113 C029257DA430>I<9038FE03F000FFEB0FFEEC3FFF91387C7F809138F8FFC000075B6C6C 5A5CA29138807F80ED3F00150C92C7FC91C8FCB3A2B512FEA422257EA427>114 D<90383FF0383903FFFEF8000F13FF381FC00F383F0003007E1301007C130012FC15787E 7E6D130013FCEBFFE06C13FCECFF806C14C06C14F06C14F81203C614FC131F9038007FFE 140700F0130114007E157E7E157C6C14FC6C14F8EB80019038F007F090B512C000F81400 38E01FF81F257DA426>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fi larm0800 8 27 /Fi 27 122 df45 D48 D<130C133C137CEA03FC12FFEAFC7C1200B3B113FE387FFFFEA2172C7AAB23>II<1230123C003FB512F8A215F05A15E039700001C000601480140348EB0700140E140C C7121C5C143014705C495AA2495AA249C7FCA25B130E131EA2133EA3133C137CA413FCA9 13781D2E7CAC23>55 DII70 D73 D82 D<007FB712F8A29039000FC003007C150000701638A200601618A200E0161CA248160CA5 C71500B3A94A7E011FB512E0A22E2D7EAC33>84 D<13FF000713C0380F01F0381C00F800 3F137C80A2143F001E7FC7FCA4EB07FF137F3801FE1FEA07F0EA1FC0EA3F80EA7F00127E 00FE14065AA3143F7E007E137F007FEBEF8C391F83C7FC390FFF03F83901FC01E01F207D 9E23>97 DI<15F8141FA214011400ACEB 0FE0EB7FF83801F81E3803E0073807C003380F8001EA1F00481300123E127EA25AA9127C 127EA2003E13017EEB8003000F13073903E00EFC3A01F03CFFC038007FF090391FC0F800 222F7EAD27>100 DI<013F13F89038FFC3FE39 03E1FF1E3807807C000F140C391F003E00A2003E7FA76C133EA26C6C5A00071378380FE1 F0380CFFC0D81C3FC7FC90C8FCA3121E121F380FFFF814FF6C14C04814F0391E0007F848 130048147C12F848143CA46C147C007C14F86CEB01F06CEB03E03907E01F803901FFFE00 38003FF01F2D7E9D23>103 DII<3807C0FE39FFC3FF809038C703E0390FDE01F0EA07F8496C7EA25BA25BB2 486C487E3AFFFE1FFFC0A2221E7E9D27>110 DI<38 07C0FE39FFC7FF809038CF03E0390FDC01F03907F800FC49137E49133E49133FED1F80A3 ED0FC0A8151F1680A2ED3F00A26D137E6D137C5D9038FC01F09038CE07E09038C7FF80D9 C1FCC7FC01C0C8FCA9487EEAFFFEA2222B7E9D27>I<380781F038FF87FCEB9E7EEA0F98 EA07B813B0EBF03CEBE000A35BB1487EB5FCA2171E7E9D1B>114 D<3801FE183807FFB8381E01F8EA3C00481378481338A21418A27E7EB41300EA7FF06CB4 FC6C13C06C13F0000113F838001FFC130138C0007E143EA26C131EA27EA26C133CA26C13 7838FF01F038E3FFC000C0130017207E9E1C>I<1360A413E0A312011203A21207121FB5 12F0A23803E000AF1418A714383801F03014703800F860EB3FE0EB0F80152A7FA81B>I< D807C013F800FF131FA2000F130100071300B21401A314033803E007EC0EFC3A01F81CFF C038007FF890391FE0F800221F7E9D27>I<3BFFFC3FFE07FFA23B0FE003F001F801C090 38E000F00007010114E0812603E00314C0A2913807F8012701F006781380A29039F80E7C 030000D90C3C1300A290397C181E06A2151F6D486C5AA2168C90391F600798A216D89039 0FC003F0A36D486C5AA36DC75A301E7F9C33>119 D<3AFFFC01FFC0A23A0FE0007E0000 07147C1538000314306D137000011460A26C6C5BA2EBFC01017C5BEB7E03013E90C7FCA2 EB1F06A2148EEB0F8CA2EB07D8A2EB03F0A36D5AA26D5AA2495AA2130391C8FC1278EAFC 06A25B131CEA7838EA7070EA3FE0EA0F80222B7F9C25>121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj cmsy6 6 1 /Fj 1 4 df<136013701360A20040132000E0137038F861F0387E67E0381FFF803807FE 00EA00F0EA07FE381FFF80387E67E038F861F038E060700040132000001300A213701360 14157B9620>3 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmex10 10 10 /Fk 10 91 df<12F0B3B3B2043674811C>12 D<160F161F163E167C16F8ED01F0ED03E0 ED07C0150FED1F801600153E157E5D4A5A5D14034A5A5D140F4A5AA24AC7FC143E147E5C A2495AA2495AA2495AA2130F5CA2495AA2133F91C8FCA25B137E13FEA25B1201A25B1203 A35B1207A35B120FA35BA2121FA45B123FA690C9FC5AAA12FEB3AC127FAA7E7FA6121F7F A4120FA27FA312077FA312037FA312017FA212007FA2137E137F7FA280131FA26D7EA280 1307A26D7EA26D7EA26D7EA2147E143E143F6E7EA26E7E1407816E7E1401816E7E157E15 3E811680ED0FC01507ED03E0ED01F0ED00F8167C163E161F160F28C66E823D>18 D<12F07E127C7E7E6C7E6C7E6C7E7F6C7E1200137C137E7F6D7E130F806D7E1303806D7E A26D7E147C147E80A26E7EA26E7EA26E7EA2811403A26E7EA2811400A281157E157FA281 1680A2151F16C0A3150F16E0A3150716F0A31503A216F8A4150116FCA6150016FEAA167F B3AC16FEAA16FC1501A616F81503A416F0A21507A316E0150FA316C0151FA31680153FA2 16005DA2157E15FE5DA214015DA24A5AA214075DA24A5AA24A5AA24AC7FCA2147E147C14 FC495AA2495A5C1307495A5C131F49C8FC137E137C5B1201485A5B485A485A48C9FC123E 5A5A5A28C67E823D>III<161E167EED01 FE1507ED0FF8ED3FE0ED7FC0EDFF80913801FE004A5A4A5A5D140F4A5A5D143F5D147F92 C7FCA25C5CB3B3B3A313015CA3495AA213075C495AA2495A495A137F49C8FC485A485AEA 07F0EA1FE0485AB4C9FC12FCA2B4FCEA3FC06C7EEA07F0EA03FC6C7E6C7E6D7E133F6D7E 6D7EA26D7E801303A26D7EA3801300B3B3B3A38080A281143F81141F816E7E1407816E7E 6E7E913800FF80ED7FC0ED3FE0ED0FF8ED07FE1501ED007E161E27C675823E>26 D32 D<12F07E127C7E123F7E6C7E6C7E6C7E7F12016C7E7F137E133E133F 6D7E130F806D7EA26D7E80130180130080147E147F8081141F81140F81140781A2140381 140181A2140081A2157FA36F7EA382151FA282150FA3821507A382A21503A282A31501A2 82A31500A382A482A21780A7163F17C0AC161F17E0B3B3A217C0163FAC1780167FA71700 A25EA45EA31501A35EA21503A35EA21507A25EA3150F5EA3151F5EA2153F5EA34BC7FCA3 15FEA25D1401A25D14035D1407A25D140F5D141F5D143F92C8FC5C147E14FE5C13015C13 035C495AA2495A5C131F49C9FC133E137E5B5B485A12035B485A485A48CAFC5A123E5A5A 5A2BF87E8242>I88 D90 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmr7 7 13 /Fl 13 121 df<1306130C13181330136013E0EA01C0EA0380A2EA07005A120E121EA212 1C123CA35AA512F85AAB7E1278A57EA3121C121EA2120E120F7EEA0380A2EA01C0EA00E0 136013301318130C13060F3B7AAB1A>40 D<12C012607E7E7E120E7EEA0380A2EA01C013 E0120013F0A213701378A3133CA5133E131EAB133E133CA51378A3137013F0A213E01201 13C0EA0380A2EA0700120E120C5A5A5A5A0F3B7DAB1A>I<140EB3A2B812E0A3C7000EC8 FCB3A22B2B7DA333>43 D48 D<13381378EA01F8121F12FE12E01200B3AB48 7EB512F8A215267BA521>I<13FF000313E0380E03F0381800F848137C48137E00787F12 FC6CEB1F80A4127CC7FC15005C143E147E147C5C495A495A5C495A010EC7FC5B5B903870 018013E0EA0180390300030012065A001FB5FC5A485BB5FCA219267DA521>I<13FF0003 13E0380F01F8381C007C0030137E003C133E007E133FA4123CC7123E147E147C5C495AEB 07E03801FF8091C7FC380001E06D7E147C80143F801580A21238127C12FEA21500485B00 78133E00705B6C5B381F01F03807FFC0C690C7FC19277DA521>I61 D91 D93 D<120EEA3F80A5EA0E00C7FCA7EA0780 12FFA2121F120FB3121FEAFFF8A20D287EA713>105 D<13C0A41201A312031207120F12 1FB512E0A23807C000AC1430A73803E060A23801F0C03800FF80EB3F0014257FA31A> 116 D<39FFF81FFCA2390FF00FE0D807E01380D803F013003801F80E00005BEB7C386D5A EB3FE06D5A130F130780497EEB1DF8EB38FCEB707EEBE03E48487E0003EB0F80000714C0 001F14E039FFE01FFEA21F197F9823>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmmi7 7 14 /Fm 14 121 df21 D<48B512F8000714FC4814F84814F0D83C07C7FC1270EAC006130E1200A3131E 131CA2133CA35BA313F8A3485AA26C5A1E1A7D981F>28 D<1238127C12FE12FFA2127F12 3B1203A31206A3120C121812381270122008127A8614>59 D64 D<90383FFFF8A2D901FCC7FC5CA21303A25CA21307A25CA2130FA2 5CA2131FA25CA2133FA291C8FCA249141C1618137E163801FE1430167049146016E00001 1401ED03C0491307ED0F800003147FB7FC160026287DA72E>76 D78 D<130E131F5BA2133E131C90C7FCA7EA 03E0487EEA0C78EA187C1230A212605B12C0A2EA01F0A3485AA2485AA2EBC180EA0F81A2 381F0300A213066C5A131CEA07F06C5A11287DA617>105 D<1407EC0F80141FA2150014 0E91C7FCA7EB03E0EB07F8EB0C3C1318EB303E136013C0A248485AA2C7FCA25CA4495AA4 495AA4495AA4495AA21238D87C1FC7FC12FC133E485AEA70F8EA7FE0EA1F80193380A61B >I<133EEA07FEA2EA007CA213FCA25BA21201A25BA21203EC07809038E01FC0EC386000 07EB61E014C3EBC187EBC307D80FC613C09038CC038001B8C7FC13E0487E13FEEB3F80EB 0FC0486C7E1303003E1460A2127EECC0C0127CECC18012FC903801E30038F800FE007013 7C1B297CA723>I<137CEA0FFCA2EA00F8A21201A213F0A21203A213E0A21207A213C0A2 120FA21380A2121FA21300A25AA2123EA2127EA2EA7C18A3EAF830A21320EA786013C0EA 3F80EA0F000E297EA715>I<3B07801FC007E03B0FE07FF01FF83B18F0E0F8783C3B30F1 807CE03E903AFB007D801ED860FEEB3F005B49133E00C14A133E5B1201A24848495BA35F 4848485A1830EE01F0A23C0F8003E003E060A218C0933801E180271F0007C013E3933800 FF00000E6D48137C341B7D993B>I111 D<131C133EA25BA45BA4485AB512E0 A23801F000485AA4485AA4485AA448C7FC1460A214C0123EEB0180EB0300EA1E06EA1F1C EA0FF8EA03E013267EA419>116 D<90387C03C03901FF0FF03907079C30390E03B07800 0CEBF0F8001813E1123015F0396007C0E015001200A2495AA449C7FC15301238007C1460 EAFC3E15C0EAF87E39F06F03803970C70700383F83FE381F01F81D1B7D9926>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn cmr10 10 27 /Fn 27 127 df<1506150FA24B7EA24B7EA24B7EA2EDDFF0A29138018FF8A291380307FC A291380603FEA291380E01FF140CDA1C007F141802386D7E143002706D7E146002E06D7E 5C01016E7E5C01036E7E91C7FC496E7E1306010E6E7E130C011C6E7F131801386F7E1330 01706F7E136001E06F7E5B170F484882170748C97F17030006831701488383481880001F B9FC4818C0A24818E0A2BA12F0A23C3C7CBB45>1 D<011FB512FEA39026001FFEC8FCEC 07F8A8EC3FFE0103B512E0D91FF713FC90397F07F87F01FCEC1F80D803F8EC0FE0D807F0 6E7ED80FE06E7E001F82D83FC06E7EA2007F8201808000FF1780A7007F170001C05C003F 5EA2D81FE04A5A000F5ED807F04A5AD803F84A5AD800FCEC1F80017F027FC7FC90391FF7 FFFC0103B512E09026003FFEC8FCEC07F8A8EC1FFE011FB512FEA331397BB83C>8 D<010FB612C0A3D900070180C7FCDA01FEC8FCA7D8FF80ED07FC01E0151F001F17E001F0 153F000F17C001F8157F00071780ACD803FCEDFF00A4D801FE4A5AA200005E017F4A5A02 811307013F5DD91FC1495AD90FE1495AD903F9017FC7FC0100B512FC023F13F0020390C8 FC6E5AA8913807FF80010FB612C0A336397BB841>I<146014E0EB01C0EB0380EB070013 0E131E5B5BA25B485AA2485AA212075B120F90C7FCA25A121EA2123EA35AA65AB2127CA6 7EA3121EA2121F7EA27F12077F1203A26C7EA26C7E1378A27F7F130E7FEB0380EB01C0EB 00E01460135278BD20>40 D<12C07E12707E7E7E120F6C7E6C7EA26C7E6C7EA21378A213 7C133C133E131EA2131F7FA21480A3EB07C0A6EB03E0B2EB07C0A6EB0F80A31400A25B13 1EA2133E133C137C1378A25BA2485A485AA2485A48C7FC120E5A5A5A5A5A13527CBD20> I<15301578B3A6007FB812F8B912FCA26C17F8C80078C8FCB3A6153036367BAF41>43 D48 DII<121C127FEAFF80A5EA7F00121C C7FCB2121C127F5A1380A4127F121D1201A412031300A25A1206A2120E5A121812385A12 60093479A317>59 D<007FB812F8B912FCA26C17F8CCFCAE007FB812F8B912FCA26C17F8 36167B9F41>61 D72 D77 D83 D86 D91 D93 D<13101338137C13FE487E3803C780380783C0380F01E038 1E00F04813780070131C48130E00401304170D77B92A>I97 D100 DI105 D<2703F00FF0EB1FE000FFD93FFCEB7FF891 3AF03F01E07E903BF1C01F83803F3D0FF3800FC7001F802603F70013CE01FE14DC49D907 F8EB0FC0A2495CA3495CB3A3486C496CEB1FE0B500C1B50083B5FCA340257EA445>109 D<3903F01FE000FFEB7FF89038F1E07E9039F3801F803A07F7000FC0D803FEEB07E049EB 03F04914F849130116FC150016FEA3167FAA16FEA3ED01FCA26DEB03F816F06D13076DEB 0FE001F614C09039F7803F009038F1E07E9038F0FFF8EC1FC091C8FCAB487EB512C0A328 357EA42E>112 D<1318A51338A31378A313F8120112031207001FB5FCB6FCA2D801F8C7 FCB215C0A93800FC011580EB7C03017E13006D5AEB0FFEEB01F81A347FB220>116 D120 D126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo cmmi10 10 41 /Fo 41 122 df<1403EC3FF891387FFF80D901E313C014800103133F9138001F80ED0700 92C7FC80A280A2808013018080130080147F81143F8149B47E130790380F8FF0EB3E0F49 6C7E13F83801F003D803E07F1207380FC0011380121FEA3F0014005A127EA212FE5D4813 01A35DA24813035D6C13075D127C4A5A6C91C7FC5C6C133E6C6C5A3807C0F03801FFE0D8 003FC8FC223D7DBB25>14 D<133F14C0EB07F06D7E801301A26D7EA3147FA36E7EA36E7E A36E7EA36E7EA36E7EA36E7EA26E7EA214014A7E5C4A7E91381E3F80143C14784A6C7E13 01EB03E049486C7EEB0F80EB1F00496D7E137E5B48486D7E485A485A000F6E7E485A485A 48C87E12FE167F4816800070151F293B7CB930>21 D<013FB612E090B712F05A120717E0 270F807006C7FC391E00600E48140C003813E04813C048141CEAC0011200148001035BA2 13071400A25B1578011E137CA3133E133C137C157E13FC5B1201157F1203497FA3D801C0 131C2C257EA32F>25 D<027FB512C00103B612E0130F5B017F15C09026FF81FEC7FC3901 FC007E48487F485A497F484880485AA248C7FCA2127EA2153F00FE92C7FC5AA25D157E5A 5DA24A5AA24A5A007C495A5D003C495A003E013FC8FC6C137C380F81F83803FFE0C66CC9 FC2B257DA32F>27 D<013FB512FE90B7FC5A5A4815FE260F801CC7FCEA1E005A00385B5A 5A481378C7FC147014F0A4495AA31303A3495AA3130FA25C131FA3133FA291C8FC131E28 257EA324>I<1503A35DA21506A2150EA2150CA2151CA21518A21538A21530A21570A2EC 07FE91383FFFC0903901FCE3F0903907E0E0F890391F80C03ED93E007FEB7C01D801F8EC 0F80D803F0018013C0D807E014071403D80FC015E0D81F801300A248485AA2007E1306A2 020E130F12FE48010C14C0A2021CEB1F80A20218EB3F00A20238137E007C5D1430007E4A 5A003E90387003F06CEC07C09138600F80D80F80013FC7FC3903E0E0FC3901F8E7F03900 7FFF80D90FFCC8FCEB01C0A25CA21303A291C9FCA25BA21306A2130EA2130CA22B4B7CB9 31>30 D<160C161C1618A316381630A316701660A316E05EA315015EA301F80103130FD8 03FE9138001F80D8070F153F000E018015C0001C5C001814060038161F0030160FD8701F 010E13070060140C1703D8E03F168000C0EB001C491318EA007E180001FE13384913305F 000116064913700360130E5F000316184901E013384B133017705F0201495AD801F84948 5A4CC7FC160E2600FC035B017EEB0078013FEB01E090390FE30F80902603FFFEC8FC9038 003FF00206C9FCA2140E140CA3141C1418A314381430A314701460324B7EB936>32 D34 D<121C127FEAFF80A5EA7F00121C0909798817> 58 D<121C127FEAFF80A213C0A3127F121C1200A412011380A2120313005A1206120E5A 5A5A12600A19798817>II<150C151E153EA2153C157CA2157815F8A215F01401A215E01403A215C01407A215 80140FA215005CA2141E143EA2143C147CA2147814F8A25C1301A25C1303A2495AA25C13 0FA291C7FC5BA2131E133EA2133C137CA2137813F8A25B1201A25B1203A25B1207A25B12 0FA290C8FC5AA2121E123EA2123C127CA2127812F8A25A12601F537BBD2A>I<126012FC B4FCEA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB01FF9038007FC0EC1FF0EC 07FCEC01FF9138007FC0ED1FF0ED07FCED01FF9238007FC0EE1FF0EE07FCEE01FF933800 7F80EF1FC0A2EF7F80933801FF00EE07FCEE1FF0EE7FC04B48C7FCED07FCED1FF0ED7FC0 4A48C8FCEC07FCEC1FF0EC7FC04948C9FCEB07FCEB1FF0EB7FC04848CAFCEA07FCEA3FF0 EA7FC048CBFC12FC1270323279AD41>I64 D<9339FF8001C0030F13E0 037F9038F80380913A01FF807E07913A07F8000F0FDA1FE0EB079FDA3F80903803BF0002 FFC76CB4FCD901FC80495A4948157E495A495A4948153E017F163C49C9FC5B1201484816 385B1207485A1830121F4993C7FCA2485AA3127F5BA312FF90CCFCA41703A25F1706A26C 160E170C171C5F6C7E5F001F5E6D4A5A6C6C4A5A16076C6C020EC8FC6C6C143C6C6C5C6C B4495A90393FE00FC0010FB5C9FC010313FC9038007FC03A3D7CBA3B>67 D<0103B812E05BA290260007F8C7123F4B140FF003C0140F18015DA2141FA25D1980143F A25D1760027F14E095C7FC92C75AA24A1301A24A495A16070101141F91B6FC94C8FCA290 3903FC001F824A130EA21307A24A130CA2010F141CA24A90C9FCA2131FA25CA2133FA25C A2137FA291CBFC497EB612C0A33B397DB835>70 D<0103B5D8F803B512F8495DA2902600 07F8C73807F8004B5DA2020F150F615DA2021F151F615DA2023F153F615DA2027F157F96 C7FC92C8FCA24A5D605CA249B7FC60A202FCC7120101031503605CA201071507605CA201 0F150F605CA2011F151F605CA2013F153F605CA2017F157F95C8FC91C8FC496C4A7EB690 B6FCA345397DB845>72 D<0107B512FCA216F890390007F8005DA2140FA25DA2141FA25D A2143FA25DA2147FA292C7FCA25CA25CA21301A25CA21303A25CA21307A25CA2130FA25C A2131FA25CA2133FA25CA2137FA291C8FC497EB6FCA326397DB824>I<0103B500F89038 07FFFC5BA290260007F8C813804BEDFC0019F0020F4B5AF003804B4AC7FC180E021F1538 604B5CEF0380023F4AC8FC170E4B133C1770027F5C4C5ADB0007C9FC160E4A5B167E4A13 FE4B7E01015B92380E7F80ECFC1CED383F010301E07FECFDC04A486C7EECFF00D907FC6D 7E5C4A130783130F707E5C1601011F81A24A6D7EA2013F6F7EA24A143F84137F717E91C8 123F496C81B60107B512C0A26146397DB847>75 D<0103B6FC5B5E90260007FCC8FC5D5D 140FA25DA2141FA25DA2143FA25DA2147FA292C9FCA25CA25CA21301A25CA21303A25CA2 130718404A15C0A2010F150118804A1403A2011F16005F4A1406170E013F151E171C4A14 3C177C017F5D160391C7120F49EC7FF0B8FCA25F32397DB839>I<902603FFF893383FFF 80496081D900079438FF80000206DC01BFC7FCA2020E4C5A1A7E020C1606190CDA1C7E16 FE4F5A02181630A20238166162023016C1F00181DA703F158395380303F002601506A202 E0ED0C076202C01518183001016D6C140F06605B028015C0A20103923801801FDD03005B 140092380FC00649173F4D91C8FC01065DA2010E4B5B4D137E130C6F6C5A011C17FEDCE1 805B011802E3C7FCA2013802E6130104EC5C1330ED03F8017016034C5C01F05CD807FC4C 7EB500E0D9C007B512F01680150151397CB851>I<902603FFF891381FFFF8496D5CA2D9 0007030113006FEC007C02061678DA0EFF157081020C6D1460A2DA1C3F15E0705CEC181F 82023815016F6C5C1430150702706D1303030392C7FC02607FA2DAE0015C701306ECC000 8201016E130EEF800C5C163F0103EDC01C041F131891C713E0160F49EDF0381830010614 0717F8010E02031370EFFC60130CEE01FE011C16E004005B011815FF177F133860013015 3FA20170151F95C8FC01F081EA07FCB512E01706A245397DB843>I<4BB4FC031F13F092 38FE01FC913903F0007EDA07C0EB1F80DA1F80EB0FC0023EC7EA07E002FCEC03F0495A49 48EC01F8495A4948EC00FC495A49C912FE49167E13FE49167F1201485AA2485AA2120F5B 001F17FFA2485AA34848ED01FEA400FFEE03FC90C9FCA2EF07F8A2EF0FF0A218E0171F18 C0EF3F806C167F180017FE4C5A6C6C5D1603001F4B5A6D4A5A000FED1F806C6C4AC7FC6D 147E0003EC01F8D801FC495AD8007EEB0FC090263F807FC8FC903807FFF801001380383D 7CBA3F>I<0103B7FC4916E018F8903B0007F80007FC4BEB00FE187F020FED3F80F01FC0 5DA2021F16E0A25DA2143FF03FC05DA2027FED7F80A292C8130018FE4A4A5A604AEC07F0 4D5A0101ED3FC04CB4C7FC91B612FC17E0D903FCCAFCA25CA21307A25CA2130FA25CA213 1FA25CA2133FA25CA2137FA291CBFC497EB6FCA33B397DB835>I<4BB4FC031F13F09238 FE01FC913903F0007EDA07C0EB1F80DA1F80EB0FC0023EC7EA07E002FCEC03F0495A4948 EC01F8495A4948EC00FC495A013F16FE49C9FC13FE187F485A12035B12075B120F4916FF 121FA2485AA34848ED01FEA448C9EA03FCA3EF07F8A218F0170F18E0171F18C0EF3F807E EF7F0017FEDA07C05B6C90391FF001F8903980383803001F496C485A9139E00C0FE0260F C0C0EB1F80D807E1D90E3FC7FC0280137ED803F1EB07F8D801F95C3A007FC00FC0903A3F E07F0003903807FFFE0100018F5BDA000F1306170E171E705A177CEEC1F816FF5FA25F5F 6F5B6F48C7FCED00F8384B7CBA42>I<92391FE00380DBFFFC130002036D5A91390FE01F 8F91393F0007DF027EEB01FE02F81300495A4948147E177C4948143C495AA2011F153891 C8FCA3491530A28094C7FC80806D7E14FEECFFE06D13FE6DEBFFC06D14F06D806D80021F 7F02037FEC003F03037F1500167F163F161FA3120C160FA2001C151F94C7FCA3003C153E A25E003E5D127E007F4A5A6D495A6DEB0FC0D8F9F0495AD8F0FE01FEC8FC39E03FFFF801 0F13E0D8C00190C9FC313D7CBA33>83 D<49B500F890387FFFF095B5FC1AE0D900030180 90380FFC004BC713E00201ED07804EC7FC6E6C140E606F5C705B606F6C485A4D5A031F91 C8FCEEE0065F6F6C5A5F03075B705A16F96FB45A94C9FC6F5AA36F7EA34B7FED037F9238 063FC0150E4B6C7E1538ED700F03E07F15C04A486C7EEC0300020613034A805C4A6D7E14 704A1300494880495A49C86C7E130E011E153F017E4B7ED803FF4B7E007F01E0011FEBFF C0B5FC6144397EB845>88 D<147E903803FF8090390FC1C38090391F00EFC0017E137F49 133F485A4848EB1F8012075B000F143F48481400A2485A5D007F147E90C7FCA215FE485C 5AA214015D48150CA21403EDF01C16181407007C1538007E010F1330003E131F027B1370 6C01E113E03A0F83C0F9C03A03FF007F80D800FCEB1F0026267DA42C>97 D<133FEA1FFFA3C67E137EA313FE5BA312015BA312035BA31207EBE0FCEBE3FF9038E707 C0390FFE03E09038F801F001F013F8EBE000485A15FC5BA2123F90C7FCA214015A127EA2 140312FE4814F8A2140715F05AEC0FE0A215C0EC1F80143F00781400007C137E5C383C01 F86C485A380F07C06CB4C7FCEA01FC1E3B7CB924>II<163FED1FFFA3ED007F167EA216 FEA216FCA21501A216F8A21503A216F0A21507A2027E13E0903803FF8790380FC1CF9038 1F00EF017EEB7FC049133F485A4848131F000715805B000F143F485A1600485A5D127F90 C7127EA215FE5A485CA21401A248ECF80CA21403161CEDF0181407007C1538007E010F13 30003E131F027B13706C01E113E03A0F83C0F9C03A03FF007F80D800FCEB1F00283B7DB9 2B>I<14E0EB03F8A21307A314F0EB01C090C7FCAB13F8EA03FEEA070F000E1380121C12 1812381230EA701F1260133F00E0130012C05BEA007EA213FE5B1201A25B12035BA20007 131813E01438000F133013C01470EB806014E014C01381EB838038078700EA03FEEA00F8 15397EB71D>105 D107 DII 111 D<90390F8003F090391FE00FFC903939F03C1F903A70F8700F80903AE0FDE007C090 38C0FF80030013E00001491303018015F05CEA038113015CA2D800031407A25CA2010714 0FA24A14E0A2010F141F17C05CEE3F80131FEE7F004A137E16FE013F5C6E485A4B5A6E48 5A90397F700F80DA383FC7FC90387E1FFCEC07E001FEC9FCA25BA21201A25BA21203A25B 1207B512C0A32C3583A42A>I<02FC13C0903803FF0190380F838390383F01C790397E00 EF8049137F485A4848133F000715005B485A001F5C157E485AA2007F14FE90C75AA34813 01485CA31403485CA314075D140F127C141F007E495A003E137F381F01EF380F839F3903 FF1F80EA00FC1300143F92C7FCA35C147EA314FE5C130190387FFFF0A322357DA425>I< EB01C0497E1307A4130F5CA3131F5CA3133F91C7FC007FB51280A2B6FCD8007EC7FCA313 FE5BA312015BA312035BA312075BA3120FEBC006A2140E001F130CEB801C141814385C14 6014E0380F81C038078780D803FEC7FCEA00F819357EB31E>116 D<903907E001F090391FF807FC9039783E0E0F9039E01F1C1FD801C09038383F803A0380 0FF07F0100EBE0FF5A000E4A1300000C157E021F133C001C4AC7FC1218A2C7123FA292C8 FCA25CA2147EA214FEA24A130CA20101141C001E1518003F5BD87F81143801835C00FF15 60010714E03AFE0E7C01C0D87C1C495A2778383E0FC7FC391FF00FFC3907C003F029267E A42F>120 D<13F8D803FE1470D8070F14F8000EEB8001121C121800381403003015F0EA 701F1260013F130700E0010013E012C05BD8007E130F16C013FE5B151F000115805BA215 3F000315005BA25D157EA315FE5D1401000113033800F80790387C1FF8EB3FF9EB0FE1EB 00035DA2000E1307D83F805B007F495AA24A5A92C7FCEB003E007C5B00705B6C485A381E 07C06CB4C8FCEA01FC25367EA429>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmsy10 10 15 /Fp 15 108 df<007FB81280B912C0A26C17803204799641>0 D<0060150600F8150F6C 151F007E153F6C157E6C6C14FC6C6CEB01F86C6CEB03F06C6CEB07E06C6CEB0FC06C6CEB 1F80017EEB3F006D137E6D6C5A90380FC1F8903807E3F0903803F7E06DB45A6D5B6EC7FC A24A7E497F903803F7E0903807E3F090380FC1F890381F80FC90383F007E017E7F49EB1F 804848EB0FC04848EB07E04848EB03F04848EB01F84848EB00FC48C8127E007E153F4815 1F48150F00601506282874A841>2 D<15301578B3A6007FB812F8B912FCA26C17F8C800 78C8FCB3A3007FB812F8B912FCA26C17F836367BB641>6 D15 D20 D<126012F812FEEA7F80EA3FE0EA0FF8EA03FEC66C7EEB3FE0EB0FF8EB03FE903800FF80 EC3FE0EC0FF8EC03FE913800FF80ED3FE0ED0FF8ED03FE923800FF80EE3FE0EE0FF8EE03 FE933800FF80EF3FC0171FEF7F80933801FF00EE07FCEE1FF0EE7FC04B48C7FCED07FCED 1FF0ED7FC04A48C8FCEC07FCEC1FF0EC7FC04948C9FCEB07FCEB1FF0EB7FC04848CAFCEA 07FCEA1FF0EA7FC048CBFC12FC1270CCFCAE007FB81280B912C0A26C1780324479B441> I<05041402051E140F057E143FDC01FE14FF4C48EB01FEDC0FF0EB07F8DC3FC0EB1FE04C C7EA3F80DB01FEECFF00DB07F8EB03FCDB0FE0EB07F0DB3FC0EB1FE003FFC7EA7F80DA01 FC02FEC7FCDA07F8EB03FCDA1FE0EB0FF0DA3F80EB1FC002FFC7EA7F80D903FCD901FEC8 FCD90FF0EB07F84948495AD97F80EB3FC0D801FEC7B4C9FCD803F8EB01FCD80FF0EB07F8 D83FC0EB1FE048C7EA3F8000FE4ACAFCA2007F6E7ED83FC0EB1FE0D80FF0EB07F8D803F8 EB01FCD801FE6DB4FC26007F80EB3FC0D91FE0EB0FF06D6C6D7ED903FCEB01FED900FF90 38007F80DA3F80EB1FC0DA1FE0EB0FF0DA07F8EB03FCDA01FCEB00FE6EB4EC7F80DB3FC0 EB1FE0DB0FE0EB07F0DB07F8EB03FCDB01FEEB00FFDB007FEC3F80DC3FC0EB1FE0DC0FF0 EB07F8DC03FCEB01FE706CEB00FFDC007E143F051E140F48377BB053>28 D<0040142000F0147800FC147EB4EC7F806C6C6D7ED81FE0EB0FF0D807F8EB03FCD801FC EB00FE6CB4EC7F80D93FC0EB1FE0D90FE0EB07F0D907F8EB03FCD901FEEB00FFD9007FEC 3F80DA3FC0EB1FE0DA0FF0EB07F8DA03F8EB01FCDA01FE6DB4FC9126007F80EB3FC0DB1F E0EB0FF06F6C6D7EDB03FCEB01FEDB00FF9038007F80DC3F80EB1FC0DC1FE0EB0FF0DC07 F8EB03FCDC01FCEB00FE706C147FA24C4814FEDC07F8EB03FCDC1FE0EB0FF0DC3F80EB1F C004FFC7EA7F80DB03FC903801FE00DB0FF0EB07F84B48495ADB7F80EB3FC0DA01FEC7B4 C7FCDA03F8EB01FCDA0FF0EB07F8DA3FC0EB1FE04AC7EA3F80D901FE02FFC8FCD907F8EB 03FCD90FE0EB07F0D93FC0EB1FE001FFC7EA7F80D801FC02FEC9FCD807F8EB03FCD81FE0 EB0FF0D87F80EB3FC048C7485A00FC027ECAFC00F0147848377BB053>I<1478A414F85C A213015C1303495AA2495A49CCFC5B137E5B485A485AEA0FE0003FBA12FEBCFCA2003F19 FED80FE0CCFCEA03F06C7E6C7E137E7F7F6D7E6D7EA26D7E1301801300A2801478A4482C 7BAA53>32 D<181EA4181F84A285180785727EA2727E727E85197E85F11F80F10FC0F107 F0007FBA12FCBCFCA26C19FCCCEA07F0F10FC0F11F80F13F00197E61614E5A4E5AA24E5A 61180F96C7FCA260181EA4482C7BAA53>I49 D<91381FFFFE91B6FC1303010F14FED91FF0C7FCEB7F8001FEC8FCEA01F8485A48 5A485A5B48C9FCA2123EA25AA2127812F8A25AA2B712FE16FFA216FE00F0C9FCA27EA212 78127CA27EA27EA26C7E7F6C7E6C7E6C7EEA00FEEB7F80EB1FF06DB512FE010314FF1300 021F13FE283279AD37>I<0060161800F0163C6C167CA200781678007C16F8A2003C16F0 003E1501A26CED03E0A26C16C06D1407A2000716806D140FA26C6CEC1F00A26CB612FEA3 6C5D01F8C7127CA2017C5CA2013C5C013E1301A2011E5C011F1303A26D6C485AA201075C ECC00FA2010391C7FC6E5AA2903801F03EA20100133CECF87CA2EC7878EC7CF8A2EC3FF0 A26E5AA36E5AA36E5A6EC8FC2E3C80B92F>56 D<126012F0B3B3B3B3A91260045377BD17 >106 D<0070131C00F0131EB3B3B3B3A80070131C175277BD2A>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq labx1440 14.4 34 /Fq 34 122 df45 DI<151E153E15FE1403140F147FEB07FF0003 B5FCB6FCA3EBF87FEAFC00C7FCB3B3B3A6007FB712FCA52E4E76CD42>49 DI<913807FFC0027F13FC0103B67E010F15E090 261FF80313F890267FC0007F01FEC7EA3FFE48488148486E138013FE486C6C6D13C08048 17E080A66C5B18C06C5B6C90C75AD80038168090C8FC4C1300A24C5A5F4C5A4B5B4B13C0 030F5BDB7FFEC7FC91387FFFF816C016FCEEFF80DA000313E09238007FF8EE3FFE707E70 138018C07013E018F07013F8A218FC82A218FEA3EA03C0EA0FF0EA3FFC487EA2B5FCA218 FCA25E18F8A26C4816F0495C4916E0D83FE04A13C06C485CD80FF04A1380D807FE91387F FE003B03FFE003FFFC6C90B65A6C6C15E0010F92C7FC010114FCD9001F1380374F7BCD42 >I<17FC1601A216031607160FA2161F163F167FA216FF5D5DA25D5D5D167F153E157E15 FC15F8EC01F01403EC07E015C0EC0F80141FEC3F00143E5C14FC495A5C495A1307495A5C 49C7FC5B137E137C5B1201485A5B485A120F485A90C8FC123E127E5ABA1280A5C901FCC7 FCAF021FB71280A5394F7CCE42>I<486C150601F0153E01FEEC01FED9FFF0133F91B65A 5F5F5F5F5F94C7FC16FC5E16E093C8FC15FC01F0138091CAFCAC913807FF80023F13F891 B512FE01F36E7E9026FFFC0113E09139E0007FF891C76C7E496E7E01F86E7E5B70138049 16C0C9FC18E08218F0A418F8A31203EA0FE0EA3FF8487EA212FF7FA218F0A25B5E6C4816 E05B01C016C06CC85A18806C6C4A13007FD80FF04A5A6C6CECFFFCD803FE4913F02701FF E00F5B6C6CB612806D92C7FC010F14F8010114C09026003FFCC8FC354F7ACD42>I68 DII73 D76 D83 D97 DI<913803 FFE0023F13FE91B67E010315E0010F9038003FF8D93FFCEB07FC4948497E4948131F4849 497E485B485BA24890C7FC5A5B003F6F5A705A705A007F92C8FC5BA312FFAD127F7FA312 3F7F6CEE0F80A26C6D141F18006C6D5C6C6D143E6C6D147E6C6D5C6D6C495A6DB4EB07F0 010F9038C01FE06D90B5128001014AC7FCD9003F13F80203138031387CB63A>I<943803 FF80040FB5FCA5EE003F170FB3A4913803FF80023F13F849B512FE0107ECFF8F011F9038 C03FEF90273FFE0007B5FCD97FF8130149487F484980484980484980488291C8FC5A5B12 3FA2127F5BA312FFAD127FA37F123FA3121F7F6C5E6C6D5C5F6C6D91B5FC6C6D5B6C6D49 14E0D97FFCD90FEFEBFF80D91FFFEB7F8F010790B5120F010114FC6D6C13E00207010049 C7FC41547CD249>I<913807FF80027F13F849B512FE01076E7E011F010313E0903A3FFC 007FF0D97FF06D7E49486D7E4849130F48496D7E48824890C77E1880485A82003F17C0A3 485A18E082A212FFA290B8FCA401FCCAFCA6127FA37F123FA2EF03E06C7E17076C17C06C 6D140F18806C6D141F6C6DEC3F006C6D147ED97FFC495AD91FFFEB07F86D9038E03FF001 0390B512C001005D023F01FCC7FC020113E033387CB63C>IIII<133FEBFFC0487F487FA2487FA66C5BA26C5B 6C5B013FC7FC90C8FCAEEB1FF8B5FCA512017EB3B3A6B612F0A51C547CD324>I108 D II<913801FFC0023F13FE91B67E010315E0010F018013F8903A3FFC001FFED9 7FF0EB07FF49486D7F48496D7F48496D7F91C8127F4883488349153F001F83A2003F8349 151FA2007F83A400FF1880AC007F1800A3003F5F6D153FA2001F5FA26C6C4B5AA26C6D4A 5A6C5F6C6D495B6C6D495B6D6C4990C7FCD93FFCEB1FFE6DB46CB45A010790B512F00101 15C0D9003F49C8FC020313E039387CB642>II<912603FF80EB0F80023F01F0131F91B500FC133F01 0714FF499039C03F807F013F9038000FC0D97FFC903803E0FF4948EB01F14849EB00F948 49147F485B48824A805A91C87E5AA2485AA4485AAD6C7EA4123F7FA27E6E5C6C5E6C7F6E 5C6C93B5FC6C6D5B6C6DEB07EFD93FFEEB0FCF903A1FFF807F8F01079038FFFE0F010114 F86D6C13E00207130091C8FCB1040FB61280A5414D7CB545>I<90393FF001FCB590380F FF804B13E0037F13F09238FE1FF89138F1F83F00019138F07FFC6CEBF3E015C0ECF780A2 ECFF00EE3FF84AEB1FF0EE0FE093C7FC5CA45CB3ABB612FEA52E367DB535>I<903903FF C00E011FEBFC1E90B6127E000315FE3907FE003FD80FF0130F4848130348481301491300 127F90C8127EA248153EA27FA27F01F091C7FC13FCEBFF806C13FEECFFF06C14FE6F7E6C 15E06C816C15FC6C81C681133F010F15801301D9000F14C0EC003F030713E0150100F880 167F6C153FA2161F7EA217C07E6D143F17807F6DEC7F0001F85C6DEB03FE9039FF801FFC 486CB512F0D8F81F14C0D8F00791C7FC39E0007FF02B387CB634>I<147CA614FCA41301 A31303A21307A2130F131F133F137F13FF1203000F90B512FEB7FCA426007FFCC8FCB3A9 EE0F80ABEE1F006D7EA2011F143E806D6D5A6DEBC1F86DEBFFF001005C023F1380DA03FE C7FC294D7ECB33>III121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr larm1000 10 69 /Fr 69 160 df27 DI30 D36 D<121C127FEAFF80A213 C0A3127F121C1200A412011380A2120313005A1206120E5A5A5A12600A1979B917>39 D<146014E0EB01C0EB0380EB0700130E131E5B5BA25B485AA2485AA212075B120F90C7FC A25A121EA2123EA35AA65AB2127CA67EA3121EA2121F7EA27F12077F1203A26C7EA26C7E 1378A27F7F130E7FEB0380EB01C0EB00E01460135278BD20>I<12C07E12707E7E7E120F 6C7E6C7EA26C7E6C7EA21378A2137C133C133E131EA2131F7FA21480A3EB07C0A6EB03E0 B2EB07C0A6EB0F80A31400A25B131EA2133E133C137C1378A25BA2485A485AA2485A48C7 FC120E5A5A5A5A5A13527CBD20>I<121C127FEAFF80A213C0A3127F121C1200A4120113 80A2120313005A1206120E5A5A5A12600A19798817>44 DI<12 1C127FEAFF80A5EA7F00121C0909798817>I48 DIII<1538A2157815F8A2140114031407A2140F141F141B14331473146314C3 13011483EB030313071306130C131C131813301370136013C01201EA038013005A120E12 0C5A123812305A12E0B712F8A3C73803F800AA4A7E0103B512F8A325387EB72A>I<0006 140CD80780133C9038F003F890B5FC5D5D158092C7FC14FC38067FE090C9FCAAEB07F8EB 1FFE9038780F809038E007E03907C003F0496C7E130000066D7E81C8FC8181A21680A412 1C127F5A7FA390C713005D12FC00605C12704A5A6C5C6C1303001E495A6C6C485A3907E0 3F800001B5C7FC38007FFCEB1FE021397CB62A>I I<12301238123E003FB612E0A316C05A168016000070C712060060140E5D5D00E0143048 14705D5DC712014A5A4AC7FC1406140E5CA25C1478147014F05C1301A213035C1307A213 0FA3131F5CA2133FA5137FA96DC8FC131E233A7BB72A>III<121C127FEAFF80A5EA7F00121CC7FCB2121C127FEAFF80A5EA 7F00121C092479A317>I<1538A3157CA315FEA34A7EA34A6C7EA202077FEC063FA2020E 7FEC0C1FA2021C7FEC180FA202387FEC3007A202707FEC6003A202C07F1501A2D901807F 81A249C77F167FA20106810107B6FCA24981010CC7121FA2496E7EA3496E7EA3496E7EA2 13E0707E1201486C81D80FFC02071380B56C90B512FEA3373C7DBB3E>65 DI<913A01FF800180020FEBE003027F13F8903A01FF807E07903A03 FC000F0FD90FF0EB039F4948EB01DFD93F80EB00FF49C8127F01FE153F12014848151F48 48150FA248481507A2485A1703123F5B007F1601A35B00FF93C7FCAD127F6DED0180A312 3F7F001F160318006C7E5F6C7E17066C6C150E6C6C5D00001618017F15386D6C5CD91FE0 5C6D6CEB03C0D903FCEB0F80902701FF803FC7FC9039007FFFFC020F13F002011380313D 7BBA3C>II70 DIII<013FB512E0A39039001FFC00EC07F8B3B3A3123FEA7F80EAFFC0A44A5A 1380D87F005B0070131F6C5C6C495A6C49C7FC380781FC3801FFF038007F80233B7DB82B >I76 DIIII82 DI<003FB812E0A3D9C003EB001F273E0001FE130348EE01F000781600 00701770A300601730A400E01738481718A4C71600B3B0913807FF80011FB612E0A33539 7DB83C>I86 DI91 D 93 D97 DIIII<147E903803FF8090380FC1E0EB1F 8790383F0FF0137EA213FCA23901F803C091C7FCADB512FCA3D801F8C7FCB3AB487E387F FFF8A31C3B7FBA19>IIIIIII<2703F00FF0EB1FE000FFD93FFCEB7FF8913AF03F 01E07E903BF1C01F83803F3D0FF3800FC7001F802603F70013CE01FE14DC49D907F8EB0F C0A2495CA3495CB3A3486C496CEB1FE0B500C1B50083B5FCA340257EA445>I<3903F00F F000FFEB3FFCECF03F9039F1C01F803A0FF3800FC03803F70013FE496D7EA25BA35BB3A3 486C497EB500C1B51280A329257EA42E>II<3903F01FE000FFEB7FF8 9038F1E07E9039F3801F803A0FF7000FC0D803FEEB07E049EB03F04914F849130116FC15 0016FEA3167FAA16FEA3ED01FCA26DEB03F816F06D13076DEB0FE001F614C09039F7803F 009038F1E07E9038F0FFF8EC1FC091C8FCAB487EB512C0A328357EA42E>II<3807E0 1F00FFEB7FC09038E1E3E09038E387F0380FE707EA03E613EE9038EC03E09038FC008049 1300A45BB3A2487EB512F0A31C257EA421>II<1318A51338A31378A313F8120112031207001FB5FC B6FCA2D801F8C7FCB215C0A93800FC011580EB7C03017E13006D5AEB0FFEEB01F81A347F B220>II< B538803FFEA33A0FF8000FF06C48EB07E00003EC03C06D148000011500A26C6C1306A26D 130E017E130CA26D5BA2EC8038011F1330A26D6C5AA214E001075BA2903803F180A3D901 FBC7FCA214FF6D5AA2147CA31438A227257EA32C>IIII<003FB512FCA2EB8003D83E0013F8003CEB07F00038EB0FE0123000 70EB1FC0EC3F800060137F150014FE495AA2C6485A495AA2495A495A495AA290387F0006 13FEA2485A485A0007140E5B4848130C4848131CA24848133C48C7127C48EB03FC90B5FC A21F247EA325>I<137E3801FFC0380781E0380F0070001E133848131C007C130C007813 1E147E5AA3143C1400A27EA2127C127EEA7F806C7E13F0EA1FFC13FF6C13806C13E06C13 F0120F381F7FF8383E1FFCEA3C07387801FE130000F8137E48133F141F140FA47E7E007E 131F007F131E1380383FE03CEBF87C381FFEF8380FFFF014C06C13E0000113F06C13F813 3FEB0FFC1303EB01FEEB007E143E141FA2140FA2123C127EA3141E12780030133E003813 3C6C13786C13F0380781E03803FF8038007E00184C7ABA25>159 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs larm1200 12 20 /Fs 20 256 df<121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A0A78891B>46 D<14FF010713E090381F81F890383E007C01FC133F4848EB1F8049130F4848EB07C04848 EB03E0A2000F15F0491301001F15F8A2003F15FCA390C8FC4815FEA54815FFB3A46C15FE A56D1301003F15FCA3001F15F8A26C6CEB03F0A36C6CEB07E0000315C06D130F6C6CEB1F 806C6CEB3F00013E137C90381F81F8903807FFE0010090C7FC28447CC131>48 D50 D<000615C0D807C0130701FCEB7F 8090B612005D5D5D15E0158026063FFCC7FC90C9FCAE14FF010713C090381F01F0903838 00FC01F0137ED807C07F49EB1F8016C090C7120F000615E0C8EA07F0A316F81503A216FC A5123E127F487EA416F890C712075A006015F0A20070140F003015E00038EC1FC07E001E EC3F806CEC7F006C6C13FE6C6C485A3901F807F039007FFFE0011F90C7FCEB07F826447B C131>53 D<49B41303010FEBE007013F13F89039FE00FE0FD801F8131FD807E0EB079F49 EB03DF48486DB4FC48C8FC4881003E81127E82127C00FC81A282A37E82A27EA26C6C91C7 FC7F7FEA3FF813FE381FFFE06C13FE6CEBFFE06C14FC6C14FF6C15C0013F14F0010F8001 0180D9001F7F14019138001FFF03031380816F13C0167F163F161F17E000C0150FA31607 A37EA36C16C0160F7E17806C151F6C16006C5D6D147ED8FBC05CD8F9F0495AD8F07C495A 90393FC00FE0D8E00FB51280010149C7FC39C0003FF02B487BC536>83 D86 D97 D104 D107 D<3901FC01FE00FF903807FFC091381E07F091383801F8000701707F0003EBE0002601FD C07F5C01FF147F91C7FCA25BA35BB3A8486CECFF80B5D8F83F13FEA32F2C7DAB36>110 DI117 DI224 D227 D229 D<011FB71280A2903B00F8003FF0 0002386D5A02305CB114701460A714E05CA3EA3C0100FF5BA21303A291C7FC48484A7ED8 780E4A7ED8701C010FB51280EA3FF8D80FF090C9FC312C7FAA36>235 D239 D<3901FC03FC00FF90380FFF8091383C07E091387001F83A07 FDE000FE00030180137FD801FFEC3F8091C7EA1FC04915E049140F17F0160717F8160317 FCA3EE01FEABEE03FCA3EE07F8A217F0160F6D15E0EE1FC06D143F17806EEB7E00D9FDC0 5B9039FCF003F891383C0FE091381FFF80DA03FCC7FC91C9FCAE487EB512F8A32F3F7DAB 36>I<023FB512FE0107B6FC90261FE00013C0017FC7EA7F8001FE1500485A12035B1207 A51203A26C7EA26C7EEB3F80EB0FF00103B6FCEB001FEDC07F143FEC7F80ECFF005C1301 495A495A5C495A131F495A495AA249C7FC485A12074848ECFF80D83FFE4913C0B5D8E03F 13FEA22F2B7EAA35>255 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft cmsy10 12 1 /Ft 1 4 df<147014F8A81470007815F0007C1401B4EC07F8D87F80EB0FF0D83FE0EB3F E0D80FF0EB7F80D803F8EBFE003900FE73F890383F77E090380FFF80D903FEC7FCEB00F8 EB03FE90380FFF8090383F77E09038FE73F83903F870FED80FF0EB7F80D83FE0EB3FE0D8 7F80EB0FF0D8FF00EB07F8007CEC01F000781400C7140014F8A81470252B7AAD32>3 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu larm1728 17.28 22 /Fu 22 122 df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ndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%BeginPaperSize: a4 a4 %%EndPaperSize %%EndSetup %%Page: 1 1 1 0 bop 560 872 a Fu(Solutions)47 b(of)e(nonstationary)j(Dirac)e (equation)h(with)773 1054 y(the)e(p)t(oten)l(tial)i(slo)l(wly)g(dep)t (ending)e(on)g(time)3121 1002 y Ft(\003)1639 1295 y Fs(V.V.Sukhano)m(v) 1567 1478 y(25)32 b(\340\357\360\345\353\377)h(2002)f(\343)-8 b(.)639 1785 y Fr(Asymptotic)24 b(b)r(eha)n(viour)f(of)h(the)g (solution)f(of)h(the)g(Cauc)n(h)n(y)f(problem)g(for)h(the)g(nonsta-)515 1884 y(tionary)j(Dirac)g(equation)h(with)h(the)f(p)r(oten)n(tial)g(slo) n(wly)f(dep)r(ending)i(on)f(time)h(is)f(studied.)515 1984 y(Construction)i(of)g(asymptotic)g(solution)h(is)f(based)g(on)h (sp)r(ectral)f(decomp)r(osition)g(of)h(the)515 2084 y(solution)37 b(in)h(curren)n(t)e(momen)n(t)i(of)g(time.)g(It)g(do)r(esn't)g(use)f (the)h(adiabatic)f(theorem)g(in)515 2183 y(scattering)26 b(theory)-7 b(.)515 2458 y Fq(1)131 b(In)l(tro)t(duction)515 2640 y Fr(The)24 b(ob)5 b(jectiv)n(e)23 b(of)h(this)h(pap)r(er)e(is)h (the)h(in)n(v)n(estigation)d(of)i(the)h(solutions)e(of)h(nonstationary) 515 2739 y(Dirac)j(equation)1522 2839 y Fp(\000)p Fo(i)p Fn(\010)1676 2851 y Fm(t)1727 2839 y Fn(=)c(H\()p Fo("t)p Fn(\)\010)p Fo(;)70 b(")22 b Fp(\034)h Fn(1)901 b Fr(\(1\))515 2988 y(with)25 b(op)r(erator)f Fn(H)h Fr(whic)n(h)g(slo)n(wly)f(dep)r (end)i(on)f(time.)h(The)f(asymptotic)f(form)n(ulas)g(for)h(the)515 3088 y(op)r(erator)g Fn(H)j Fr(with)g(discrete)f(sp)r(ectrum)g(are)f(w) n(ell)h(kno)n(wn.)g(Construction)f(of)i(asymptotic)515 3188 y(form)n(ulas)33 b(for)h(the)h(solution)f(of)g(the)h(equation)f (\(1\))h(then)g(op)r(erator)d Fn(H)j Fr(has)f(con)n(tin)n(uous)515 3287 y(sp)r(ectrum)27 b(are)g(usually)g(based)g(on)g(adiabatic)g (theorem)g(in)h(scattering)e(theory)h(\(see)g([1]\).)515 3387 y(Application)36 b(of)h(this)g(metho)r(d)g(require)f(decomp)r (osition)g(of)g(op)r(erator)f Fn(H)i Fr(in)g(follo)n(wing)515 3487 y(sum)1584 3586 y Fn(H\()p Fo("t)p Fn(\))24 b(=)e(H)1952 3598 y Fl(0)2008 3586 y Fn(+)c(V\()p Fo("t)p Fn(\))p Fo(;)964 b Fr(\(2\))515 3736 y(where)33 b(op)r(erator)f Fn(H)1164 3748 y Fl(0)1235 3736 y Fr(do)r(esn't)i(dep)r(end)h(on)e Fo(t)h Fr(.In)g(particular)e(main)i(term)g(of)f(this)h(suc)n(h)515 3835 y(solution)20 b(is)h(completely)g(determined)g(b)n(y)g(v)-5 b(alue)21 b(of)g(op)r(erator)e Fn(H)j Fr(at)f Fo(t)i Fn(=)f(0)p Fr(.)f(Constructions)515 3935 y(of)38 b(this)h(metho)r(d)g (is)f(closely)f(connected)h(with)h(scattering)f(theory)f(for)h (nonstationary)515 4034 y(equation)21 b(\(1\)\(see)h([2])f(and)h ([3]\).)g(W)-7 b(e)22 b(use)g(another)e(metho)r(d)j(that)f(do)r(esn't)g (dep)r(end)g(on)g(the)515 4134 y(adiabatic)31 b(theorem)g(in)h (scattering)e(theory)-7 b(.W)g(e)32 b(consider)e(\(as)i(a)f(suitable)h (mo)r(del\))g(one-)515 4234 y(dimensional)27 b(Dirac)g(op)r(erator)f (on)h(the)h(whole)f(line)h(with)g(rapidly)f(deca)n(ying)f(p)r(oten)n (tial)1448 4462 y Fn(H\(t\))e(=)f(i)p Fo(\033)1788 4474 y Fl(3)1857 4406 y Fn(d)p 1836 4443 90 4 v 1836 4519 a(dx)1954 4462 y(+)2037 4345 y Fk(\022)2140 4411 y Fn(0)82 b Fo(p)p 2140 4465 42 4 v 2140 4511 a(p)h Fn(0)2348 4345 y Fk(\023)2423 4462 y Fo(:)827 b Fr(\(3\))515 4657 y(A)n(t)31 b(this)f(case)g(op)r(erator)f Fn(H)i Fr(has)e(con)n(tin)n(uous)h(sp)r (ectrum)g(on)h(the)g(whole)f(line)g(and)h(it)g(has)515 4756 y(not)25 b(discrete)g(sp)r(ectrum.)g(Construction)g(of)g (asymptotic)g(solution)g(is)g(based)g(on)g(sp)r(ectral)515 4856 y(decomp)r(osition)i(of)g(the)h(solution)f(in)h(curren)n(t)f (momen)n(t)g(of)h(time.)p 515 4925 1146 4 v 606 4979 a Fj(\003)642 5002 y Fi(This)23 b(pap)r(er)i(w)n(as)e(supp)r(orted)j(b) n(y)e(RFFI)g(gran)n(t)h(02-01-00798)1926 5255 y Fr(1)p eop %%Page: 2 2 2 1 bop 639 523 a Fr(In)26 b(\2372)f(w)n(e)h(consider)e(main)i (information)f(ab)r(out)g(sp)r(ectral)h(theory)e(for)i(the)g (stationary)515 623 y(Dirac)k(op)r(erator.)f(In)i($3)f(formal)h (solution)f(for)g(nonstationary)f(Dirac)i(equation)f(is)h(con-)515 722 y(structed)22 b(.In)g($4)f(w)n(e)h(pro)n(v)n(e)e(that)j(formal)e (solution)h(is)g(asymptotic)f(expansion)g(for)h(precise)515 822 y(solution)h(of)i(the)f(Cauc)n(h)n(y)f(problem)h(for)g(the)g (nonstationary)f(Dirac)g(equation.Finally)-7 b(,)24 b(in)515 922 y($5)k(w)n(e)h(compare)f(our)g(asymptotic)h(form)n(ulas)f(with)h (result)g(that)g(are)g(based)f(on)h(the)h(adi-)515 1021 y(abatic)d(theorem)g(in)h(scattering)e(theory)-7 b(.)515 1296 y Fq(2)131 b(Sp)t(ectral)44 b(theory)h(for)f(Dirac)g(op)t(erator) 515 1478 y Fr(Let)27 b(us)g(describ)r(e)g(some)f(information)g(ab)r (out)h(sp)r(ectral)g(theory)f(for)g(Dirac)h(op)r(erator)e(\(see)515 1577 y([4]\).)i(Consider)g(Dirac)g(op)r(erator)f(on)h(the)h(whole)f (line)h(with)g(rapidly)f(deca)n(ying)f(p)r(oten)n(tial)1068 1810 y Fn(H)e(=)e(i)p Fo(\033)1311 1822 y Fl(3)1381 1754 y Fn(d)p 1359 1791 90 4 v 1359 1867 a(dx)1477 1810 y(+)1560 1693 y Fk(\022)1719 1755 y Fn(0)139 b Fo(p)p Fn(\()p Fo(x)p Fn(\))p 1663 1791 154 4 v 1663 1864 a Fo(p)p Fn(\()p Fo(x)p Fn(\))h(0)2095 1693 y Fk(\023)2170 1810 y Fo(;)14 b(p)23 b Fp(2)g Fo(S)5 b Fn(\()p Fp(\0001)p Fo(;)14 b Fn(+)p Fp(1)p Fn(\))p Fo(:)639 2028 y Fr(Here)35 b Fn(S\()p Fp(\0001)p Fo(;)14 b Fn(+)p Fp(1)p Fn(\))35 b Fr(-)g(Sc)n(h)n(w)n(artz) e(class.)i(Let)g(us)g(\034x)g(solutions)g Fn(\011\()p Fo(x)p Fn(\))g Fr(and)3112 2007 y Fn(~)3100 2028 y(\011\()p Fo(x)p Fn(\))h Fr(of)515 2128 y(sp)r(ectral)27 b(equation)1438 2327 y Fn(H\010)d(=)e Fo(\025)p Fn(\010)p Fo(;)70 b Fn(\010)23 b Fp(2)g Fn(Mat\(2)18 b Fp(\002)h Fn(2\))p Fo(;)817 b Fr(\(4\))515 2476 y(whic)n(h)27 b(satisfy)g(conditions)1212 2659 y Fn(\011\()p Fo(x;)14 b(\025)p Fn(\))24 b(=)f(exp)o(\()p Fp(\000)p Fo(i\033)1884 2671 y Fl(3)1922 2659 y Fo(\025x)p Fn(\))c(+)f Fo(o)p Fn(\(1\))p Fo(;)c(x)24 b Fp(!)f Fn(+)p Fp(1)p Fo(;)1224 2920 y Fn(~)1212 2941 y(\011\()p Fo(x;)14 b(\025)p Fn(\))24 b(=)f(exp)o(\()p Fp(\000)p Fo(i\033)1884 2953 y Fl(3)1922 2941 y Fo(\025x)p Fn(\))c(+)f Fo(o)p Fn(\(1\))p Fo(;)c(x)24 b Fp(!)f(\0001)p Fo(:)639 3091 y Fh(Lemma)36 b(1.)69 b Fg(The)35 b(solutions)g Fn(\011\()p Fo(x)p Fn(\))h Fg(and)2044 3070 y Fn(~)2033 3091 y(\011)o(\()p Fo(x)p Fn(\))g Fg(exist)f(and)g(ar)l(e)g(unique.)g(They)h(ar)l(e)515 3190 y(in\034nitely)30 b(di\033er)l(entiable)h(functions)e(of)i Fo(x)f Fg(and)g Fo(\025)h Fg(and)f(have)h(fol)t(lowing)h(asymptotics) 874 3428 y Fn(\011\()p Fo(x;)14 b(\025)p Fn(\))24 b(=)f(exp\()p Fp(\000)p Fo(i\033)1547 3440 y Fl(3)1584 3428 y Fo(\025x)p Fn(\))1725 3311 y Fk(\022)1829 3377 y Fo(a)p Fn(\()p Fo(\025)p Fn(\))p 2073 3305 149 4 v 88 w Fo(b)p Fn(\()p Fo(\025)p Fn(\))1833 3486 y Fo(b)p Fn(\()p Fo(\025)p Fn(\))p 2069 3414 157 4 v 88 w Fo(a)p Fn(\()p Fo(\025)p Fn(\))2267 3311 y Fk(\023)2346 3428 y Fn(+)18 b Fo(o)p Fn(\(1\))p Fo(;)74 b(x)24 b Fp(!)f(\0001)p Fo(;)830 3689 y Fn(~)818 3710 y(\011\()p Fo(x;)14 b(\025)p Fn(\))24 b(=)f(exp\()p Fp(\000)p Fo(i\033)1491 3722 y Fl(3)1528 3710 y Fo(\025x)p Fn(\))1669 3593 y Fk(\022)p 1800 3592 V 1800 3664 a Fo(a)p Fn(\()p Fo(\025)p Fn(\))113 b Fp(\000)p 2134 3592 149 4 v Fo(b)p Fn(\()p Fo(\025)p Fn(\))1772 3764 y Fp(\000)p Fo(b)p Fn(\()p Fo(\025)p Fn(\))f Fo(a)p Fn(\()p Fo(\025)p Fn(\))2323 3593 y Fk(\023)2403 3710 y Fn(+)18 b Fo(o)p Fn(\(1\))p Fo(;)73 b(x)24 b Fp(!)f Fn(+)p Fp(1)p Fo(:)515 3910 y Fg(The)30 b(c)l(o)l(e\036cients)h Fo(a)e Fg(and)h Fo(b)g Fg(satisfy)g(fol)t(lowing)j(c)l(onditions)1170 4109 y Fo(a)p Fn(\()p Fo(\025)p Fn(\))24 b(=)f(1)18 b(+)h(~)-43 b Fo(a)p Fn(\()p Fo(\025)p Fn(\);)45 b(~)-43 b Fo(a)p Fn(\()p Fo(\025)p Fn(\))p Fo(;)14 b(b)p Fn(\()p Fo(\025)p Fn(\))25 b Fp(2)e Fo(S)5 b Fn(\()p Fp(\0001)p Fo(;)14 b Fn(+)p Fp(1)p Fn(\))p Fo(;)1685 4358 y Fp(j)p Fo(a)p Fp(j)1775 4324 y Fl(2)1836 4358 y Fn(=)22 b Fp(j)p Fo(b)p Fp(j)2005 4324 y Fl(2)2061 4358 y Fn(+)c(1)p Fo(:)639 4507 y Fr(The)43 b(pro)r(of)e(of)h(this)h(lemma)f(follo)n(ws)f(from)h (the)h(analysis)d(of)j(the)f(corresp)r(onding)515 4607 y(V)-7 b(olterra)26 b(in)n(tegral)g(equations.)639 4707 y(Consider)g Ff(\011)1059 4719 y Fl(1)1096 4707 y Fo(;)14 b Ff(\011)1207 4719 y Fl(2)1271 4707 y Fr(and)1445 4687 y Ff(~)1431 4707 y(\011)1505 4719 y Fl(1)1543 4707 y Fo(;)1593 4687 y Ff(~)1580 4707 y(\011)1654 4719 y Fl(2)1718 4707 y Fr(are)25 b(v)n(ector-functions)g(whic)n(h)i(are)e(column)i(v)n (ectors)515 4806 y(of)g(matrix)g Fn(\011)g Fr(and)1144 4785 y Fn(~)1133 4806 y(\011)1417 5006 y(\011)c(=)f(\()p Ff(\011)1698 5018 y Fl(1)1736 5006 y Fo(;)14 b Ff(\011)1847 5018 y Fl(2)1885 5006 y Fn(\))p Fo(;)1965 4985 y Fn(~)1954 5006 y(\011)22 b(=)h(\()2174 4985 y Ff(~)2161 5006 y(\011)2235 5018 y Fl(1)2273 5006 y Fo(;)2323 4985 y Ff(~)2310 5006 y(\011)2384 5018 y Fl(2)2421 5006 y Fn(\))p Fo(:)1926 5255 y Fr(2)p eop %%Page: 3 3 3 2 bop 515 523 a Fr(Op)r(erator)21 b Fn(H)j Fr(has)f(con)n(tin)n(uous) f(sp)r(ectrum)i(on)f(the)g(whole)g(line.)h(W)-7 b(e)24 b(can)f(consider)f(v)n(ector-)515 623 y(functions)28 b Ff(f)36 b Fr(and)28 b Ff(g)q Fr(,)1615 864 y Ff(f)k Fn(=)1787 788 y Ff(~)1774 808 y(\011)1848 820 y Fl(1)p 1774 845 112 4 v 1808 876 44 4 v 1808 921 a Fo(a)1895 864 y(;)70 b Ff(g)24 b Fn(=)2157 808 y Ff(\011)2231 820 y Fl(2)p 2157 845 112 4 v 2191 876 44 4 v 2191 921 a Fo(a)515 1040 y Fr(\(see[4]\))32 b(as)f(eigen-functions)h(of)g(the)g (con)n(tin)n(uous)f(sp)r(ectrum)i(for)e(op)r(erator)g Fo(H)7 b Fr(.)32 b(In)g(par-)515 1139 y(ticular)910 1252 y Fk(Z)993 1272 y Fe(1)956 1440 y(\0001)1092 1365 y Fo(d\025)p Fn(\()p Ff(f)9 b Fn(\()p Fo(x;)14 b(\025)p Fn(\))p 1449 1290 288 4 v Ff(f)1487 1341 y Fe(>)1546 1365 y Fn(\()p Fo(y)s(;)g(\025)p Fn(\))19 b(+)f Ff(g)q Fn(\()p Fo(x;)c(\025)p Fn(\))p 2086 1290 299 4 v Ff(g)2135 1341 y Fe(>)2192 1365 y Fn(\()p Fo(y)s(;)g(\025)p Fn(\))q(\))23 b(=)g(2)p Fo(I)7 b(\031)s(\016)s Fn(\()p Fo(x)19 b Fp(\000)f Fo(y)s Fn(\))p Fo(;)1666 1624 y(I)30 b Fn(=)1820 1507 y Fk(\022)1922 1573 y Fn(1)83 b(0)1922 1673 y(0)g(1)2130 1507 y Fk(\023)2205 1624 y Fo(:)515 1821 y Fr(Here)27 b Fo(\016)s Fn(\()p Fo(x)p Fn(\))i Fr(is)f(delta-function.)g(F)-7 b(unctions)28 b Ff(f)37 b Fr(and)28 b Ff(g)h Fr(ha)n(v)n(e)d(follo)n(wing)h (asymptotic)g(prop-)515 1921 y(erties:)966 2149 y Ff(f)9 b Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))25 b(=)e(exp)o(\()p Fp(\000)p Fo(i\033)1694 2161 y Fl(3)1731 2149 y Fo(\025x)p Fn(\))1872 2032 y Fk(\022)2004 2098 y Fn(1)p Fo(=)p 2088 2052 44 4 v(a)2033 2198 y Fn(0)2172 2032 y Fk(\023)2252 2149 y Fn(+)18 b Ff(o)p Fn(\(1\))p Fo(;)69 b(x)23 b Fp(!)g(\0001)p Fo(;)345 b Fr(\(5\))982 2404 y Ff(f)9 b Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))26 b(=)c(exp\()p Fp(\000)p Fo(i\033)1711 2416 y Fl(3)1748 2404 y Fo(\025x)p Fn(\))1889 2287 y Fk(\022)2033 2353 y Fn(1)1993 2453 y Fo(b=)p 2071 2407 V(a)2155 2287 y Fk(\023)2235 2404 y Fn(+)c Ff(o)p Fn(\(1\))p Fo(;)69 b(x)24 b Fp(!)f Fn(+)p Fp(1)p Fo(;)361 b Fr(\(6\))977 2662 y Ff(g)q Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))25 b(=)e(exp\()p Fp(\000)p Fo(i\033)1717 2674 y Fl(3)1754 2662 y Fo(\025x)p Fn(\))1895 2545 y Fk(\022)p 1998 2546 36 4 v 1998 2613 a Fo(b=)p 2076 2568 44 4 v(a)2038 2713 y Fn(1)2161 2545 y Fk(\023)2240 2662 y Fn(+)18 b Ff(o)p Fn(\(1\))p Fo(;)69 b(x)24 b Fp(!)f(\0001)p Fo(;)356 b Fr(\(7\))974 2919 y Ff(g)q Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))25 b(=)e(exp\()p Fp(\000)p Fo(i\033)1714 2931 y Fl(3)1751 2919 y Fo(\025x)p Fn(\))1892 2802 y Fk(\022)2038 2869 y Fn(0)1995 2968 y(1)p Fo(=)p 2079 2922 V(a)2164 2802 y Fk(\023)2243 2919 y Fn(+)18 b Ff(o)p Fn(\(1\))p Fo(;)69 b(x)24 b Fp(!)f Fn(+)p Fp(1)p Fo(;)353 b Fr(\(8\))515 3112 y(Let)27 b(us)h(consider)e(space)h(of)h(v)n(ector-functions)e Fo(S)2068 3124 y Fl(0)1110 3336 y Ff(c)e Fp(2)f Fo(S)1305 3348 y Fl(0)1366 3336 y Fp( )-14 b(!)23 b Ff(c)g Fn(=)1694 3219 y Fk(\022)1797 3285 y Fo(c)1833 3297 y Fl(1)1797 3385 y Fo(c)1833 3397 y Fl(2)1911 3219 y Fk(\023)1986 3336 y Fn(;)14 b Fo(c)2059 3348 y Fl(1)2096 3336 y Fo(;)g(c)2169 3348 y Fl(2)2229 3336 y Fp(2)24 b Fo(S)5 b Fn(\()p Fp(\0001)p Fo(;)14 b Fn(+)p Fp(1)p Fn(\))p Fo(:)515 3560 y Fr(T)-7 b(ransformation)25 b Fo(F)1154 3572 y Fl(0)1220 3560 y Fr(whic)n(h)i(are)g(\034xed)g(b)n(y)g(functions)h Ff(f)37 b Fr(and)28 b Ff(g)g Fr(on)g(the)g(space)e Fo(S)3104 3572 y Fl(0)767 3693 y Fk(\022)870 3759 y Fo(d)913 3771 y Fl(1)950 3759 y Fn(\()p Fo(\025)p Fn(\))870 3859 y Fo(d)913 3871 y Fl(2)950 3859 y Fn(\()p Fo(\025)p Fn(\))1105 3693 y Fk(\023)1189 3810 y Fn(=)c Fo(F)1329 3822 y Fl(0)1381 3693 y Fk(\022)1483 3759 y Fo(c)1519 3771 y Fl(1)1557 3759 y Fn(\()p Fo(x)p Fn(\))1483 3859 y Fo(c)1519 3871 y Fl(2)1557 3859 y Fn(\()p Fo(x)p Fn(\))1710 3693 y Fk(\023)1794 3810 y Fn(=)1882 3697 y Fk(Z)1965 3717 y Fe(1)1928 3885 y(\0001)2064 3810 y Fo(dx)2168 3668 y Fk( )p 2281 3685 292 4 v 2281 3759 a Ff(f)2319 3735 y Fe(>)2376 3759 y Fn(\()p Fo(x;)14 b(\025)p Fn(\))p 2276 3796 303 4 v 2276 3870 a Ff(g)2325 3846 y Fe(>)2381 3870 y Fn(\()p Fo(x;)g(\025)p Fn(\))2620 3668 y Fk(!)2699 3693 y(\022)2802 3759 y Fo(c)2838 3771 y Fl(1)2875 3759 y Fn(\()p Fo(x)p Fn(\))2802 3859 y Fo(c)2838 3871 y Fl(2)2875 3859 y Fn(\()p Fo(x)p Fn(\))3029 3693 y Fk(\023)3104 3810 y Fo(;)515 4072 y Fr(\(here)40 b Ff(a)786 4042 y Fe(>)843 4072 y Fr(-denote)g(transp)r(osition)f(of)i (v)n(ector)e Ff(a)p Fr(\)has)i(prop)r(erties)f(that)h(are)e(analogous) 515 4171 y(to)f(prop)r(erties)g(of)h(the)g(F)-7 b(ourier)38 b(transformation.)f(In)i(particular,)e(w)n(e)i(ha)n(v)n(e)e(follo)n (wing)515 4271 y(form)n(ulae)26 b(for)h(the)h(in)n(v)n(erse)e (transformation)588 4462 y Fk(\022)691 4528 y Fo(c)727 4540 y Fl(1)764 4528 y Fn(\()p Fo(x)p Fn(\))691 4628 y Fo(c)727 4640 y Fl(2)764 4628 y Fn(\()p Fo(x)p Fn(\))918 4462 y Fk(\023)1002 4579 y Fn(=)d Fo(F)1155 4543 y Fe(\000)p Fl(1)1143 4601 y(0)1257 4462 y Fk(\022)1360 4528 y Fo(d)1403 4540 y Fl(1)1441 4528 y Fn(\()p Fo(\025)p Fn(\))1360 4628 y Fo(d)1403 4640 y Fl(2)1441 4628 y Fn(\()p Fo(\025)p Fn(\))1595 4462 y Fk(\023)1679 4579 y Fn(=)1802 4523 y(1)p 1777 4560 92 4 v 1777 4636 a(2)p Fo(\031)1892 4466 y Fk(Z)1975 4486 y Fe(1)1939 4655 y(\0001)2075 4579 y Fo(d\025)p Fn(\()p Ff(f)9 b Fn(\()p Fo(x;)14 b(\025)p Fn(\))p Fo(;)g Ff(g)q Fn(\()p Fo(x;)g(\025)p Fn(\)\))2760 4462 y Fk(\022)2866 4528 y Fo(d)2909 4540 y Fl(1)2947 4528 y Fn(\()p Fo(\025)p Fn(\))2866 4628 y Fo(d)2909 4640 y Fl(2)2947 4628 y Fn(\()p Fo(\025)p Fn(\))3101 4462 y Fk(\023)3176 4579 y Fo(:)74 b Fr(\(9\))515 4807 y(W)-7 b(e)28 b(can)f(\034nd)h(general)e(solution)h(of)h (nonhomogeneous)d(equation)1334 5006 y Fn(H)p Ff(v)20 b Fp(\000)e Fo(\025)p Ff(v)26 b Fn(=)c Ff(h)p Fn(\()p Fo(x)p Fn(\))p Fo(;)71 b Ff(h)23 b Fp(2)g Fo(S)5 b Fn(\()p Fp(\0001)p Fo(;)14 b Fp(1)p Fn(\))1926 5255 y Fr(3)p eop %%Page: 4 4 4 3 bop 515 523 a Fr(in)28 b(the)g(terms)f(of)g(functions)h Ff(f)37 b Fr(and)27 b Ff(g)1237 748 y(v)q Fn(\()p Fo(x)p Fn(\))e(=)1512 635 y Fk(Z)1595 656 y Fm(x)1558 824 y Fl(0)1650 748 y Fo(dy)s(K)1808 760 y Fm(\025)1851 748 y Fn(\()p Fo(x;)14 b(y)s Fn(\))p Ff(h)p Fn(\()p Fo(y)s Fn(\))20 b(+)e Fo(d)2350 760 y Fl(1)2387 748 y Ff(f)28 b Fn(+)18 b Fo(d)2570 760 y Fl(2)2607 748 y Ff(g)515 942 y Fr(Here)27 b Fo(d)754 954 y Fl(1)819 942 y Fr(and)g Fo(d)1023 954 y Fl(2)1089 942 y Fr(are)f(arbitrary)g(constan)n(t)g(co)r (e\036cien)n(ts,)i Fo(K)2430 954 y Fm(\025)2473 942 y Fn(\()p Fo(x;)14 b(y)s Fn(\))28 b Fr(is)f(matrix)g(2x2)1132 1175 y Fo(K)1203 1187 y Fm(\025)1246 1175 y Fn(\()p Fo(x;)14 b(y)s Fn(\))24 b(=)1550 1058 y Fk(\032)1653 1128 y Ff(g)q Fn(\()p Fo(x)p Fn(\)\()1864 1106 y(~)1845 1128 y Fo( )1899 1140 y Fl(21)1971 1128 y Fn(\()p Fo(y)s Fn(\))p Fo(;)2133 1106 y Fn(~)2116 1128 y Fo( )2170 1140 y Fl(11)2241 1128 y Fn(\()p Fo(y)s Fn(\)\))p Fo(;)69 b(x)24 b(>)f Fn(0)1659 1227 y Ff(f)9 b Fn(\()p Fo(x)p Fn(\)\()p Fo( )1894 1239 y Fl(22)1966 1227 y Fn(\()p Fo(y)s Fn(\))p Fo(;)14 b( )2165 1239 y Fl(12)2235 1227 y Fn(\()p Fo(y)s Fn(\)\))p Fo(;)70 b(x)24 b(<)e Fn(0)2738 1175 y Fo(;)515 1422 y Fr(where)27 b Fo( )809 1434 y Fm(ij)895 1422 y Fr(and)1073 1400 y Fn(~)1056 1422 y Fo( )1110 1434 y Fm(ij)1197 1422 y Fr(are)f(elemen)n (ts)i(of)f(matrix)g Fn(\011)g Fr(and)2304 1401 y Fn(~)2293 1422 y(\011)g Fr(.)515 1696 y Fq(3)131 b(F)-11 b(ormal)56 b(solution)h(of)g(nonstationary)g(Dirac)g(equa-)712 1845 y(tion.)515 2027 y Fr(Consider)26 b(solution)h(of)h(the)g(Cauc)n(h)n(y) e(problem)h(for)g(nonstationary)f(Dirac)h(equation)1386 2227 y Fp(\000)p Fo(i)p Ff(\010)1549 2239 y Fm(t)1601 2227 y Fn(=)22 b(H\()p Fo(\034)9 b Fn(\))r Ff(\010)p Fo(;)55 b(\034)33 b Fn(=)23 b Fo("t;)41 b(")23 b Fp(\034)g Fn(1)723 b Fr(\(10\))1678 2473 y Ff(\010)p Fp(j)1770 2485 y Fm(t)p Fl(=)p Fm(o)1906 2473 y Fn(=)23 b Fo(\036)2043 2485 y Fl(0)2081 2473 y Fn(\()p Fo(x)p Fn(\))p Fo(:)515 2620 y Fr(Here)k Ff(\010)p Fn(\()p Fo(x;)14 b(t)p Fn(\))28 b Fr(is)g(v)n(ector-function)e(with)i(t)n(w)n(o)f(comp)r(onen)n(ts,)g Fn(H\()p Fo(\034)9 b Fn(\))29 b Fr(is)f(Dirac)f(op)r(erator)1102 2854 y Fn(H\()p Fo(\034)9 b Fn(\))25 b(=)d(i)p Fo(\033)1455 2866 y Fl(3)1525 2798 y Fn(d)p 1503 2835 90 4 v 1503 2911 a(dx)1621 2854 y(+)1704 2737 y Fk(\022)1904 2798 y Fn(0)180 b Fo(p)p Fn(\()p Fo(x;)14 b(\034)9 b Fn(\))p 1807 2835 237 4 v 1807 2907 a Fo(p)p Fn(\()p Fo(x;)14 b(\034)9 b Fn(\))182 b(0)2404 2737 y Fk(\023)2479 2854 y Fo(;)42 b(\034)32 b Fn(=)23 b Fo("t;)1318 3087 y(p)p Fn(\()p Fo(x;)14 b(\034)9 b Fn(\))25 b Fp(2)e Fo(C)1721 3053 y Fe(1)1792 3087 y Fn(\(\()p Fp(\0001)p Fo(;)14 b Fn(+)p Fp(1)p Fn(\))k Fp(\002)g Fn([0)p Fo(;)c(\034)2460 3099 y Fl(0)2497 3087 y Fn(]\))p Fo(;)1092 3234 y(\036)1141 3246 y Fl(0)1179 3234 y Fn(\()p Fo(x)p Fn(\))24 b Fp(2)g Fo(S)1444 3246 y Fl(0)1481 3234 y Fo(;)69 b Fp(8)54 b Fo(l)25 b Fp(\025)e Fn(0)54 b Fo(@)1957 3200 y Fm(l)1952 3255 y(\034)1994 3234 y Fo(p)p Fn(\()p Fp(\017)p Fo(;)14 b(\034)9 b Fn(\))23 b Fp(2)h Fo(S)5 b Fn(\()p Fp(\0001)p Fo(;)14 b Fn(+)p Fp(1)p Fn(\))p Fo(;)639 3381 y(\033)686 3393 y Fl(3)747 3381 y Fr(is)23 b(P)n(auli)g(matrix.)g(W)-7 b(e)24 b(construct)e(formal)h(solution)f(of)h(the)h(Cauc)n(h)n(y)e (problem)g(\(10\))515 3481 y(for)27 b Fo(\034)33 b Fp(2)23 b Fn([0)p Fo(;)14 b(\034)927 3493 y Fl(0)964 3481 y Fn(])28 b Fr(with)g(the)g(help)g(of)f(follo)n(wing)g(decomp)r(osition)1188 3705 y Fn(^)1174 3726 y Ff(\010)p Fn(\()p Fo(x;)14 b(t)p Fn(\))24 b(=)1533 3613 y Fk(Z)1616 3633 y Fe(1)1579 3801 y(\0001)1715 3726 y Fo(d\025)14 b Fn(exp\()p Fo(i\025t)p Fn(\))2160 3622 y Fe(1)2133 3647 y Fk(X)2140 3826 y Fm(l)p Fl(=0)2267 3726 y Fo(")2306 3692 y Fm(l)2331 3726 y Ff(F)2391 3738 y Fm(l)2416 3726 y Fn(\()p Fo(x;)g(\025;)g(\034)9 b Fn(\))p Fo(:)514 b Fr(\(11\))639 3952 y Fh(Theorem)23 b(1.)h Fg(The)h(Cauchy)h(pr)l(oblem)f(\(10\))g(has)f(single)h(formal)g (solution)g(of)g(the)f(typ)l(e)515 4052 y(\(11\))30 b(with)g(fol)t (lowing)j(pr)l(op)l(erties:)520 4231 y Ff(F)580 4243 y Fm(l)606 4231 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))25 b Fp(2)e Fo(C)1052 4196 y Fe(1)1123 4231 y Fn(\(\()p Fp(\0001)p Fo(;)14 b Fn(+)p Fp(1)p Fn(\))k Fp(\002)g Fn(\()p Fp(\0001)p Fo(;)c Fn(+)p Fp(1)p Fn(\))k Fp(\002)g Fn([0)p Fo(;)c(\034)2289 4243 y Fl(0)2326 4231 y Fn(]\))p Fo(;)74 b(@)2522 4243 y Fm(\034)2564 4231 y Ff(F)2624 4243 y Fm(l)2649 4231 y Fn(\()p Fo(x;)14 b Fp(\017)p Fo(;)g(\034)9 b Fn(\))24 b Fp(2)g Fo(S)3075 4243 y Fl(0)3112 4231 y Fo(;)14 b Fp(8)p Fo(l)23 b Fp(\025)g Fn(0)978 4538 y Ff(F)1038 4550 y Fm(l)1086 4538 y Fn(=)g(exp\()p Fp(\000)p Fo(i\033)1474 4550 y Fl(3)1511 4538 y Fo(\025x)p Fn(\))1652 4421 y Fk(\022)1756 4487 y Fo(P)1809 4499 y Fm(l)1834 4487 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))1839 4587 y Fo(p)1881 4557 y Fl(0)1881 4611 y Fm(l)1918 4587 y Fn(\()p Fo(\025)p Fn(\))2156 4421 y Fk(\023)2236 4538 y Fn(+)18 b Ff(o)p Fn(\(1\))p Fo(;)73 b(x)23 b Fp(!)g(\0001)p Fo(;)315 b Fr(\(12\))972 4814 y Ff(F)1032 4826 y Fm(l)1080 4814 y Fn(=)23 b(exp\()p Fp(\000)p Fo(i\033)1468 4826 y Fl(3)1505 4814 y Fo(\025x)p Fn(\))1646 4697 y Fk(\022)1840 4763 y Fo(q)1880 4733 y Fl(0)1877 4787 y Fm(l)1917 4763 y Fn(\()p Fo(\025)p Fn(\))1750 4863 y Fo(Q)1816 4875 y Fm(l)1841 4863 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))2162 4697 y Fk(\023)2242 4814 y Fn(+)18 b Ff(o)p Fn(\(1\))p Fo(;)73 b(x)23 b Fp(!)g Fn(+)p Fp(1)p Fo(:)309 b Fr(\(13\))515 5006 y Fg(Her)l(e)29 b Fo(P)766 5018 y Fm(l)822 5006 y Fg(and)h Fo(Q)1049 5018 y Fm(l)1104 5006 y Fg(ar)l(e)g(p)l(olynomials)i(in)d Fo(x)1926 5255 y Fr(4)p eop %%Page: 5 5 5 4 bop 1109 684 a Fo(P)1162 696 y Fm(l)1211 684 y Fn(=)1360 580 y Fm(l)1310 605 y Fk(X)1299 781 y Fm(m)p Fl(=0)1456 684 y Fo(p)1498 696 y Fm(lm)1582 684 y Fn(\()p Fo(\034)5 b(;)14 b(\025)p Fn(\))p Fo(x)1819 649 y Fm(m)1883 684 y Fo(;)74 b(Q)2046 696 y Fm(l)2094 684 y Fn(=)2242 580 y Fm(l)2193 605 y Fk(X)2181 781 y Fm(m)p Fl(=0)2338 684 y Fo(q)2375 696 y Fm(lm)2460 684 y Fn(\()p Fo(\034)5 b(;)14 b(\025)p Fn(\))p Fo(x)2697 649 y Fm(m)2761 684 y Fo(;)515 905 y Fg(with)30 b(smo)l(oth)g(c)l(o)l(e\036cients)965 1087 y Fo(@)1014 1053 y Fm(l)1009 1108 y(\034)1051 1087 y Fo(p)1093 1099 y Fm(lm)1177 1087 y Fn(\()p Fp(\017)p Fo(;)14 b(\034)9 b Fn(\))23 b Fp(2)h Fo(S)5 b Fn(\()p Fp(\0001)p Fo(;)14 b Fn(+)p Fp(1)p Fn(\))p Fo(;)g(@)2006 1053 y Fm(l)2001 1108 y(\034)2042 1087 y Fo(q)2079 1099 y Fm(lm)2163 1087 y Fn(\()p Fp(\017)p Fo(;)g(\034)9 b Fn(\))24 b Fp(2)f Fo(S)5 b Fn(\()p Fp(\0001)p Fo(;)14 b Fn(+)p Fp(1)p Fn(\))p Fo(;)515 1270 y(p)557 1240 y Fl(0)557 1294 y Fm(l)594 1270 y Fn(\()p Fo(\025)p Fn(\))32 b Fg(and)g Fo(q)941 1240 y Fl(0)938 1294 y Fm(l)978 1270 y Fn(\()p Fo(\025)p Fn(\))h Fg(ar)l(e)e(functions)g(fr)l(om)h(Schwarz)g (class)g(\(they)g(don)-8 b('t)32 b(dep)l(end)g(on)f Fo(\034)41 b Fg(and)515 1370 y Fo(x)30 b Fg(\).)639 1469 y Fr(Let)20 b(us)f(substitute)h(series)f(\(11\))g(in)g(equation)g(\(10\).)g(W)-7 b(e)20 b(obtain)f(a)g(system)g(of)h(recurren)n(t)515 1569 y(relations)26 b(for)h(the)h(co)r(e\036cien)n(ts)f(of)h(the)g (series)1250 1768 y Fp(\000)p Fo(i)p Fn(\()p Ff(F)1436 1780 y Fm(l)1461 1768 y Fn(\))1493 1780 y Fm(\034)1558 1768 y Fn(=)23 b(\(H\()p Fo(\034)9 b Fn(\))20 b Fp(\000)e Fo(\025)p Fn(\))p Ff(F)2092 1780 y Fm(l)p Fl(+1)2202 1768 y Fo(;)c(l)25 b Fn(=)d(0)p Fo(;)14 b Fn(1)p Fo(;)g Fn(2)p Fo(:::)515 1918 y Fr(This)27 b(implies)h(that)1477 2117 y Fn(\(H\()p Fo(\034)9 b Fn(\))20 b Fp(\000)e Fo(\025)p Fn(\))p Ff(F)1923 2129 y Fl(0)1961 2117 y Fn(\()p Fo(x;)c(\025;)g(\034) 9 b Fn(\))25 b(=)e(0)p Fo(:)515 2266 y Fr(Th)n(us)32 b(function)h Ff(F)1120 2278 y Fl(0)1158 2266 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))35 b Fr(is)d(the)h(solution)g(of)f (stationary)f(equation)h(\(4\).)h(Arbitrary)515 2366 y(solution)27 b(of)g(the)h(stationary)e(equation)h(has)g(a)g(form)1041 2565 y Ff(F)1101 2577 y Fl(0)1138 2565 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))25 b(=)e Fo(d)1572 2531 y Fl(0)1572 2586 y(1)1609 2565 y Fn(\()p Fo(\025;)14 b(\034)9 b Fn(\))p Ff(f)g Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))23 b(+)18 b Fo(d)2268 2531 y Fl(0)2268 2586 y(2)2305 2565 y Fn(\()p Fo(\025;)c(\034)9 b Fn(\))p Ff(g)q Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))p Fo(:)515 2715 y Fr(Let)22 b(us)g(use)f(asymptotic)g(prop)r (erties)g(of)h(the)g(solutions)f Ff(f)9 b Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))25 b Fr(and)c Ff(g)q Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))24 b Fr(\(5\)-\(8\).)515 2814 y(W)-7 b(e)28 b(obtain)577 3128 y Ff(F)637 3140 y Fl(0)675 3128 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))25 b(=)d(exp\()p Fp(\000)p Fo(i\033)1365 3140 y Fl(3)1402 3128 y Fo(\025x)p Fn(\))1543 3011 y Fk(\024)1588 3128 y Fo(d)1631 3094 y Fl(0)1631 3148 y(1)1682 3011 y Fk(\022)1813 3077 y Fn(1)p Fo(=)p 1897 3032 44 4 v(a)1841 3177 y Fn(0)1981 3011 y Fk(\023)2061 3128 y Fn(+)c Fo(d)2187 3094 y Fl(0)2187 3148 y(2)2238 3011 y Fk(\022)p 2340 3012 36 4 v 2340 3080 a Fo(b=)p 2418 3034 44 4 v(a)2380 3179 y Fn(1)2503 3011 y Fk(\023)2583 3128 y Fn(+)g Ff(o)p Fn(\(1\))2820 3011 y Fk(\025)2877 3128 y Fo(;)69 b(x)24 b Fp(!)f(\0001)p Fo(;)591 3421 y Ff(F)651 3433 y Fl(0)688 3421 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))25 b(=)e(exp\()p Fp(\000)p Fo(i\033)1379 3433 y Fl(3)1416 3421 y Fo(\025x)p Fn(\))1557 3304 y Fk(\024)1602 3421 y Fo(d)1645 3386 y Fl(0)1645 3441 y(1)1696 3304 y Fk(\022)1838 3370 y Fn(1)1799 3470 y Fo(b=)p 1877 3424 V(a)1961 3304 y Fk(\023)2041 3421 y Fn(+)18 b Fo(d)2167 3386 y Fl(0)2167 3441 y(2)2218 3304 y Fk(\022)2363 3370 y Fn(0)2321 3470 y(1)p Fo(=)p 2405 3424 V(a)2489 3304 y Fk(\023)2569 3421 y Fn(+)g Ff(o)p Fn(\(1\))2806 3304 y Fk(\025)2863 3421 y Fo(;)69 b(x)24 b Fp(!)f Fn(+)p Fp(1)p Fo(:)515 3615 y Fr(This)k(implies)h(that) g(,)1562 3715 y Fn(\()p Fo(d)1637 3681 y Fl(0)1637 3736 y(1)1675 3715 y Fn(\))1707 3727 y Fm(\034)1772 3715 y Fn(=)22 b(0)p Fo(;)69 b Fn(\()p Fo(d)2068 3681 y Fl(0)2068 3736 y(2)2106 3715 y Fn(\))2138 3727 y Fm(\034)2203 3715 y Fn(=)22 b(0)515 3864 y Fr(\(see)27 b(\(12\))g(and)h(\(13\)\).)f(F)-7 b(rom)27 b(initial)h(data)f(of)h(Cauc)n(h)n(y)e(problem)h(\(10\))h(w)n (e)f(ha)n(v)n(e)1109 4001 y Fk(\022)1212 4067 y Fo(d)1255 4037 y Fl(0)1255 4088 y(1)1212 4167 y Fo(d)1255 4136 y Fl(0)1255 4187 y(2)1334 4001 y Fk(\023)1418 4118 y Fn(=)1541 4061 y(1)p 1515 4099 92 4 v 1515 4175 a(2)p Fo(\031)1631 4005 y Fk(Z)1714 4025 y Fl(+)p Fe(1)1677 4193 y(\0001)1849 4118 y Fo(dx)1953 3976 y Fk( )p 2066 3993 371 4 v 2066 4067 a Ff(f)2104 4043 y Fe(>)2161 4067 y Fn(\()p Fo(x;)14 b(\025;)g Fn(0\))p 2061 4104 381 4 v 2061 4178 a Ff(g)2110 4154 y Fe(>)2166 4178 y Fn(\()p Fo(x;)g(\025;)g Fn(0\))2483 3976 y Fk(!)2563 4118 y Fo(\036)2612 4130 y Fl(0)2650 4118 y Fn(\()p Fo(x)p Fn(\))p Fo(:)447 b Fr(\(14\))515 4337 y(Let)36 b(us)g(use)g(the)g(induction)h(on)f Fo(l)h Fr(for)f(further)g(pro)r(of)f(of)h(theorem.)g(Let)g(statemen)n (t)g(of)515 4437 y(theorem)27 b(is)g(true)h(for)f(all)g Fo(l)d Fp(\024)f Fo(N)9 b Fr(.)28 b(In)f(particular)g(w)n(e)g(ha)n(v)n (e)706 4612 y Fo(@)5 b Ff(F)815 4624 y Fm(N)878 4612 y Fn(\()p Fo(y)s(;)14 b(\025;)g(\034)9 b Fn(\))p 706 4649 448 4 v 883 4725 a Fo(@)c(\034)1187 4668 y Fn(=)23 b(exp\()p Fp(\000)p Fo(i\033)1575 4680 y Fl(3)1612 4668 y Fo(\025x)p Fn(\))1753 4551 y Fk(\022)1875 4600 y Fn(~)1856 4621 y Fo(P)1909 4633 y Fm(N)1973 4621 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))2034 4720 y(0)2294 4551 y Fk(\023)2374 4668 y Fn(+)18 b Ff(o)p Fn(\(1\))p Fo(;)69 b(x)23 b Fp(!)g(\0001)p Fo(;)181 b Fr(\(15\))700 4909 y Fo(@)5 b Ff(F)809 4921 y Fm(N)872 4909 y Fn(\()p Fo(y)s(;)14 b(\025;)g(\034)9 b Fn(\))p 700 4946 V 877 5022 a Fo(@)c(\034)1181 4965 y Fn(=)23 b(exp)o(\()p Fp(\000)p Fo(i\033)1568 4977 y Fl(3)1606 4965 y Fo(\025x)p Fn(\))1747 4848 y Fk(\022)2034 4911 y Fn(0)1869 4997 y(~)1850 5018 y Fo(Q)1916 5030 y Fm(N)1979 5018 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))2300 4848 y Fk(\023)2380 4965 y Fn(+)18 b Ff(o)p Fn(\(1\))p Fo(;)69 b(x)23 b Fp(!)g Fn(+)p Fp(1)p Fo(:)175 b Fr(\(16\))1926 5255 y(5)p eop %%Page: 6 6 6 5 bop 515 523 a Fr(Here)1279 624 y Fn(~)1260 645 y Fo(P)1313 657 y Fm(l)1339 645 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))25 b(=)1739 589 y Fo(@)5 b(P)1841 601 y Fm(l)p 1739 626 128 4 v 1756 702 a Fo(@)g(\034)1877 645 y(;)1988 624 y Fn(~)1969 645 y Fo(Q)2035 657 y Fm(l)2060 645 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))25 b(=)2461 589 y Fo(@)5 b(Q)2576 601 y Fm(l)p 2461 626 140 4 v 2484 702 a Fo(@)g(\034)2611 645 y(:)515 815 y Fr(F)-7 b(or)27 b Fo(l)d Fn(=)f Fo(N)k Fn(+)18 b(1)27 b Fr(w)n(e)g(ha)n(v)n(e)1021 1042 y Ff(F)1081 1054 y Fm(N)6 b Fl(+1)1228 1042 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))25 b(=)e Fp(\000)p Fo(i)1727 929 y Fk(Z)1809 949 y Fm(x)1772 1117 y Fl(0)1864 1042 y Fo(dy)s(K)2022 1054 y Fm(\025)2065 1042 y Fn(\()p Fo(x;)14 b(y)s(;)g(\034)9 b Fn(\))2349 986 y Fo(@)c Ff(F)2458 998 y Fm(N)2522 986 y Fn(\()p Fo(y)s(;)14 b(\025;)g(\034)9 b Fn(\))p 2349 1023 448 4 v 2527 1099 a Fo(@)c(\034)2808 1042 y Fn(+)358 b Fr(\(17\))1143 1288 y Fn(+)p Fo(d)1251 1253 y Fm(N)6 b Fl(+1)1251 1310 y(1)1398 1288 y Fn(\()p Fo(\025;)14 b(\034)9 b Fn(\))p Ff(f)g Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))22 b(+)c Fo(d)2056 1253 y Fm(N)6 b Fl(+1)2056 1310 y(2)2203 1288 y Fn(\()p Fo(\025;)14 b(\034)9 b Fn(\))p Ff(g)q Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))p Fo(:)515 1435 y Fr(Here)26 b Fo(K)781 1447 y Fm(\025)824 1435 y Fn(\()p Fo(x;)14 b(y)s(;)g(\034)9 b Fn(\))28 b Fr(is)f(matrix)g(function.)g(It)g(is)g(constructed)f(with) i(the)f(help)g(of)g(functions)515 1535 y Ff(f)37 b Fr(and)27 b Ff(g)858 1767 y Fo(K)929 1779 y Fm(\025)972 1767 y Fn(\()p Fo(x;)14 b(y)s(;)g(\034)9 b Fn(\))24 b(=)1357 1650 y Fk(\032)1461 1720 y Ff(g)q Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\)\()1839 1698 y(~)1820 1720 y Fo( )1874 1732 y Fl(21)1947 1720 y Fn(\()p Fo(y)s(;)14 b(\025;)g(\034)9 b Fn(\))p Fo(;)2277 1698 y Fn(~)2259 1720 y Fo( )2313 1732 y Fl(11)2384 1720 y Fn(\()p Fo(y)s(;)14 b(\025;)g(\034)9 b Fn(\)\))p Fo(;)71 b(x)24 b(>)e Fn(0)1467 1820 y Ff(f)9 b Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\)\()p Fo( )1869 1832 y Fl(22)1941 1820 y Fn(\()p Fo(y)s(;)14 b(\025;)g(\034)9 b Fn(\))p Fo(;)14 b( )2307 1832 y Fl(12)2379 1820 y Fn(\()p Fo(y)s(;)g(\025;)g(\034)9 b Fn(\)\))p Fo(;)71 b(x)23 b(<)g Fn(0)515 1968 y Fr(Consider)f(asymptotic)h(b)r(eha)n(viour)f(of)i (the)f(function)142 b Ff(F)2389 1980 y Fm(N)6 b Fl(+1)2536 1968 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))120 b Fr(as)23 b Fo(x)g Fp(!)g(\0001)p Fr(.)515 2067 y(Let)e(us)g (substitute)g(asymptotic)g(form)n(ulas)e(\(5\))i(and)g(\(7\))g(for)g (the)g(functions)g Ff(f)9 b Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))23 b Fr(and)515 2167 y Ff(g)q Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))23 b Fr(and)d(asymptotics)g(for)g(deriv)-5 b(ativ)n(e)20 b(of)h(the)g(function)g Ff(F)2568 2179 y Fm(N)2652 2167 y Fr(\(15\))g(in)g(relation)e(\(17\).)515 2266 y(In)n(tegral)26 b(in)i(the)g(righ)n(t)f(part)g(of)g(relation)g (\(17\))g(has)g(follo)n(wing)f(asymptotic)h(b)r(eha)n(viour)575 2578 y Fp(\000)p Fo(i)683 2465 y Fk(Z)765 2486 y Fm(x)728 2654 y Fl(0)821 2578 y Fo(dy)s(K)979 2590 y Fm(\025)1022 2578 y Fn(\()p Fo(x;)14 b(y)s(;)g(\034)9 b Fn(\))1306 2522 y Fo(@)c Ff(F)1415 2534 y Fm(N)1479 2522 y Fn(\()p Fo(y)s(;)14 b(\025;)g(\034)9 b Fn(\))p 1306 2559 V 1484 2635 a Fo(@)c(\034)1788 2578 y Fn(=)23 b(exp)o(\()p Fp(\000)p Fo(i\033)2175 2590 y Fl(3)2213 2578 y Fo(\025x)p Fn(\))2354 2461 y Fk(\022)2476 2511 y Fn(^)2457 2532 y Fo(P)2510 2544 y Fm(N)6 b Fl(+1)2658 2532 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))2512 2632 y(^)-49 b Fo(p)2547 2644 y Fm(N)6 b Fl(+1)2694 2632 y Fn(\()p Fo(\025;)14 b(\034)9 b Fn(\))2979 2461 y Fk(\023)3059 2578 y Fn(+)18 b Ff(o)p Fn(\(1\))p Fo(;)515 2827 y Fr(as)72 b Fo(x)24 b Fp(!)f(\0001)p Fr(,)h(where)1289 2806 y Fn(^)1271 2827 y Fo(P)1324 2839 y Fm(N)6 b Fl(+1)1471 2827 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))26 b Fr(is)f(appropriate)d(p)r(olynomial)i(in)g Fo(x)h Fr(\(it)g(has)f (degree)515 2927 y Fo(N)j Fn(+)18 b(1)p Fr(\))27 b(and)35 b Fn(^)-49 b Fo(p)997 2939 y Fm(N)6 b Fl(+1)1144 2927 y Fn(\()p Fo(\025;)14 b(\034)9 b Fn(\))29 b Fr(is)e(co)r(e\036cien)n(t) h(whic)n(h)f(do)r(es)g(not)h(dep)r(end)g(on)f Fo(x)p Fr(.)1000 3160 y Ff(F)1060 3172 y Fm(N)6 b Fl(+1)1207 3160 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))25 b(=)d(exp\()p Fp(\000)p Fo(i\033)1897 3172 y Fl(3)1934 3160 y Fo(\025x)p Fn(\))2075 3043 y Fk(\024)q(\022)2241 3093 y Fn(^)2223 3114 y Fo(P)2276 3126 y Fm(N)6 b Fl(+1)2423 3114 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))2278 3213 y(^)-49 b Fo(p)2313 3225 y Fm(N)6 b Fl(+1)2460 3213 y Fn(\()p Fo(\025;)14 b(\034)9 b Fn(\))2745 3043 y Fk(\023)2820 3160 y Fn(+)936 3453 y(+)23 b Fo(d)1067 3417 y Fm(N)6 b Fl(+1)1067 3475 y(1)1228 3336 y Fk(\022)1358 3402 y Fn(1)p Fo(=)p 1442 3356 44 4 v(a)1387 3502 y Fn(0)1527 3336 y Fk(\023)1606 3453 y Fn(+)18 b Fo(d)1732 3417 y Fm(N)6 b Fl(+1)1732 3475 y(2)1893 3336 y Fk(\022)p 1996 3337 36 4 v 1996 3404 a Fo(b=)p 2074 3359 44 4 v(a)2036 3504 y Fn(1)2159 3336 y Fk(\023\025)2282 3453 y Fn(+)18 b Ff(o)p Fn(\(1\))p Fo(;)69 b(x)23 b Fp(!)h(\0001)p Fo(:)515 3652 y Fr(T)-7 b(aking)30 b(in)n(to)g(consideration)f(the)i(relation)f(\(12\))g(w)n(e) h(receiv)n(e)e(follo)n(wing)h(represen)n(tation)515 3751 y(for)d(the)h(co)r(e\036cien)n(t)f Fo(d)1215 3716 y Fm(N)6 b Fl(+1)1215 3774 y(1)1261 3930 y Fo(d)1304 3894 y Fm(N)g Fl(+1)1304 3952 y(1)1451 3930 y Fn(\()p Fo(\025;)14 b(\034)9 b Fn(\))25 b(=)d Fp(\000)7 b Fn(^)-49 b Fo(p)1864 3942 y Fm(N)6 b Fl(+1)2011 3930 y Fn(\()p Fo(\025;)14 b(\034)9 b Fn(\))20 b(+)e Fo(p)2350 3896 y Fl(0)2350 3951 y Fm(N)6 b Fl(+1)2497 3930 y Fn(\()p Fo(\025)p Fn(\))p Fo(;)515 4109 y Fr(where)19 b Fo(p)789 4078 y Fl(0)789 4131 y Fm(N)6 b Fl(+1)936 4109 y Fn(\()p Fo(\025)p Fn(\))21 b Fr(is)g(unkno)n(wn)e(constan)n(t)h(\(in)41 b Fo(t)p Fr(\).)20 b(With)h(the)g(help)f(of)g(analogous)e(construc-)515 4208 y(tion)32 b(for)h(the)g(function)g Ff(F)1361 4220 y Fm(N)6 b Fl(+1)1508 4208 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))35 b Fr(as)d Fo(x)g Fp(!)f Fn(+)p Fp(1)i Fr(w)n(e)f(can)h (receiv)n(e)e(represen)n(tation)515 4308 y(for)25 b(the)h(co)r (e\036cien)n(t)f Fo(d)1209 4272 y Fm(N)6 b Fl(+1)1209 4330 y(2)1357 4308 y Fr(.)25 b(The)h(unkno)n(wn)f(constan)n(ts)g(can)g (b)r(e)h(found)g(from)g(initial)g(data)515 4407 y(of)h(Cauc)n(h)n(y)g (problem)1481 4436 y Fk(Z)1564 4457 y Fe(1)1527 4625 y(\0001)1663 4549 y Fo(d\025)p Ff(F)1814 4561 y Fm(N)6 b Fl(+1)1962 4549 y Fn(\()p Fo(x;)14 b(\025;)g Fn(0\))24 b(=)e(0)p Fo(:)515 4745 y Fr(Th)n(us,)27 b(w)n(e)g(ha)n(v)n(e)807 4852 y Fk(\022)912 4918 y Fo(q)952 4888 y Fl(0)949 4941 y Fm(N)6 b Fl(+1)1096 4918 y Fn(\()p Fo(\025)p Fn(\))910 5018 y Fo(p)952 4988 y Fl(0)952 5041 y Fm(N)g Fl(+1)1099 5018 y Fn(\()p Fo(\025)p Fn(\))1253 4852 y Fk(\023)1337 4969 y Fn(=)23 b Fo(F)1490 4933 y Fe(\000)p Fl(1)1478 4991 y(0)1579 4969 y Fn(\(0\))1699 4852 y Fk(\024)1743 4969 y Fo(i)1786 4856 y Fk(Z)1868 4876 y Fm(x)1831 5045 y Fl(0)1924 4969 y Fo(dy)s(K)2082 4981 y Fm(\025)2125 4969 y Fn(\()p Fo(x;)14 b(y)s(;)g Fn(0\))2406 4913 y Fo(@)5 b Ff(F)2515 4925 y Fm(N)2577 4913 y Fn(\()p Fo(y)s(;)14 b(\025;)g(\034)9 b Fn(\))p 2406 4950 448 4 v 2582 5026 a Fo(@)c(\034)2864 4969 y Fp(j)2887 4981 y Fm(\034)i Fl(=0)3012 4969 y Fn(+)1926 5255 y Fr(6)p eop %%Page: 7 7 7 6 bop 1144 523 a Fn(+)7 b(^)-49 b Fo(p)1251 535 y Fm(N)6 b Fl(+1)1397 523 y Fn(\()p Fo(\025;)14 b Fn(0\))p Ff(f)9 b Fn(\()p Fo(x;)14 b(\025;)g Fn(0\))20 b(+)k(^)-48 b Fo(q)2041 535 y Fm(N)6 b Fl(+1)2188 523 y Fn(\()p Fo(\025;)14 b Fn(0\))p Ff(g)q Fn(\()p Fo(x;)g(\025;)g Fn(0\)])p Fo(:)515 672 y Fr(Here)32 b Fo(F)781 637 y Fe(\000)p Fl(1)769 695 y(0)870 672 y Fn(\(0\))h Fr(is)g(transformation)e(whic)n(h)i(is)f (determined)h(b)n(y)g(form)n(ula)e(\(9\))i(for)g Fo(\034)41 b Fn(=)31 b(0)p Fr(.)515 772 y(Th)n(us,)26 b(w)n(e)g(ha)n(v)n(e)g (single)g(function)h Ff(F)1673 784 y Fm(N)6 b Fl(+1)1820 772 y Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))28 b Fr(with)g(prop)r(erties)d(\(12\))h(and)h(\(13\).)f(The)515 872 y(theorem)h(is)g(pro)n(v)n(ed.)515 1146 y Fq(4)131 b(Estimates)44 b(of)f(the)h(formal)g(solution)515 1328 y Fr(Consider)26 b(part)h(of)h(the)g(series)e(\(11\))1136 1588 y Ff(\010)1205 1600 y Fm(N)1268 1588 y Fn(\()p Fo(x;)14 b(t)p Fn(\))24 b(=)1558 1475 y Fk(Z)1641 1495 y Fl(+)p Fe(1)1604 1663 y(\0001)1776 1588 y Fo(d\025)14 b Fn(exp\()p Fo(i\025t)p Fn(\))2224 1484 y Fm(N)2194 1509 y Fk(X)2201 1688 y Fm(l)p Fl(=0)2328 1588 y Fo(")2367 1554 y Fm(l)2392 1588 y Ff(F)2452 1600 y Fm(l)2477 1588 y Fn(\()p Fo(x;)g(\025;)g(\034)9 b Fn(\))515 1816 y Fr(and)27 b(corresp)r(onding)f(discrepancy)g(at)h (the)h(equation)f(\(10\))1308 2042 y Fn(\001)p Ff(\010)1446 2054 y Fm(N)1509 2042 y Fn(\()p Fo(x;)14 b(t)p Fn(\))24 b(=)f Fp(\000)p Fo(i)1903 1986 y(@)5 b Ff(\010)2021 1998 y Fm(N)p 1902 2023 181 4 v 1953 2099 a Fo(@)g(t)2111 2042 y Fp(\000)18 b Fn(H\()p Fo(\034)9 b Fn(\))p Ff(\010)2434 2054 y Fm(N)2521 2042 y Fn(=)1218 2352 y(=)23 b Fp(\000)p Fo(i")1439 2317 y Fm(N)6 b Fl(+1)1599 2239 y Fk(Z)1682 2259 y Fe(1)1645 2427 y(\0001)1781 2352 y Fo(d\025)14 b Fn(exp\()p Fo(i\025t)p Fn(\))2194 2295 y Fo(@)5 b Ff(F)2303 2307 y Fm(N)2366 2295 y Fn(\()p Fo(y)s(;)14 b(\025;)g(\034)9 b Fn(\))p 2194 2332 448 4 v 2371 2409 a Fo(@)c(\034)2652 2352 y(:)556 b Fr(\(18\))639 2555 y Fh(Theorem)31 b(2.)g Fg(Discr)l(ep)l(ancy)f Fn(\001)p Ff(\010)1753 2567 y Fm(N)1816 2555 y Fn(\()p Fo(x;)14 b(t)p Fn(\))31 b Fg(satis\034es)f (fol)t(lowing)i(estimates)1246 2737 y Fn(\001)p Ff(\010)1384 2749 y Fm(N)1448 2737 y Fn(\()p Fo(x;)14 b(t)p Fn(\))23 b Fp(2)h Fo(C)1793 2703 y Fe(1)1863 2737 y Fn(\(\()p Fp(\0001)p Fo(;)14 b Fn(+)p Fp(1)p Fn(\))19 b Fp(\002)f Fn([0)p Fo(;)c(\034)2532 2749 y Fl(0)2569 2737 y Fn(]\))p Fo(;)1389 2920 y Fp(8)p Fo(k)s(;)g(l)r(;)g(m)57 b Fp(k)p Fn(\001)p Ff(\010)p Fp(k)1935 2932 y Fm(lk)q(m)2078 2920 y Fn(=)23 b Fo(O)r Fn(\()p Fo(")2302 2886 y Fm(N)6 b Fl(+1)2450 2920 y Fn(\))p Fo(:)515 3069 y Fg(Her)l(e)878 3230 y Fp(k)p Ff(F)p Fn(\()p Fo(x;)14 b(t)p Fn(\))p Fp(k)1200 3242 y Fm(lk)q(m)1344 3230 y Fn(=)1452 3151 y Fk(X)1431 3328 y Fm(i)p Fl(=1)p Fm(;)p Fl(2)1659 3126 y Fm(l)1610 3151 y Fk(X)1606 3330 y Fm(l)1627 3313 y Fd(0)1649 3330 y Fl(=0)1801 3126 y Fm(k)1759 3151 y Fk(X)1747 3330 y Fm(k)1783 3313 y Fd(0)1806 3330 y Fl(=0)1958 3126 y Fm(m)1927 3151 y Fk(X)1904 3329 y Fm(m)1963 3313 y Fd(0)1986 3329 y Fl(=0)2084 3230 y Fn(max)2114 3280 y Fm(x;\034)2252 3085 y Fk(\014)2252 3135 y(\014)2252 3184 y(\014)2252 3234 y(\014)2252 3284 y(\014)2290 3174 y Fo(@)2339 3144 y Fm(l)2360 3119 y Fd(0)2382 3144 y Fl(+)p Fm(k)2469 3119 y Fd(0)2496 3174 y Fo(F)2549 3186 y Fm(i)p 2290 3211 288 4 v 2291 3287 a Fo(@)2340 3263 y Fm(l)2361 3246 y Fd(0)2387 3287 y Fo(x@)2483 3263 y Fm(k)2519 3246 y Fd(0)2547 3287 y Fo(t)2587 3230 y Fn(\()p Fp(j)p Fo(x)p Fp(j)2712 3196 y Fm(m)2795 3230 y Fn(+)k(1\))2952 3085 y Fk(\014)2952 3135 y(\014)2952 3184 y(\014)2952 3234 y(\014)2952 3284 y(\014)2993 3230 y Fo(:)639 3463 y Fr(The)40 b(pro)r(of)f(of)h(this)g(theorem)f(is)h(corollary)d(of)i(construction)g (of)h(formal)f(solution)528 3542 y Fn(^)515 3563 y Ff(\010)p Fn(\()p Fo(x;)14 b(t)p Fn(\))p Fr(.)639 3671 y Fh(Theorem)27 b(3.)g Fg(F)-6 b(ormal)28 b(series)1672 3650 y Fn(^)1658 3671 y Ff(\010)f Fg(is)g(asymptotic)h(exp)l(ansion)g(of)f(pr)l(e)l (cise)h(solution)f Ff(\010)515 3771 y Fg(of)j(the)g(Cauchy)h(pr)l (oblem)g(for)f Fo(\034)j Fp(2)24 b Fn([0)p Fo(;)14 b(\034)1776 3783 y Fl(0)1813 3771 y Fn(])p Fg(.)30 b(It)f(satis\034es)h(fol)t (lowing)i(estimates)1318 3953 y Fp(8)p Fo(k)s(;)14 b(l)r(;)g(m)58 b Fp(k)p Ff(\010)17 b Fp(\000)h Ff(\010)1923 3965 y Fm(N)1986 3953 y Fp(k)2028 3965 y Fm(lk)q(m)2172 3953 y Fn(=)23 b Fo(O)r Fn(\()p Fo(")2396 3919 y Fm(N)6 b Fl(+1)2543 3953 y Fn(\))639 4136 y Fr(Let)28 b(in)n(tro)r(duce)f(precise)g (solution)g(of)g(Cauc)n(h)n(y)g(problem)g(\(10\))1386 4318 y Fp(\000)p Fo(i)p Ff(\010)1549 4330 y Fm(t)1601 4318 y Fn(=)22 b(H\()p Fo(\034)9 b Fn(\))r Ff(\010)p Fo(;)55 b(\034)33 b Fn(=)23 b Fo("t;)41 b(")23 b Fp(\034)g Fn(1)1678 4501 y Ff(\010)p Fp(j)1770 4513 y Fm(t)p Fl(=)p Fm(o)1906 4501 y Fn(=)g Fo(\036)2043 4513 y Fl(0)2081 4501 y Fn(\()p Fo(x)p Fn(\))p Fo(:)515 4651 y Fr(This)29 b(solution)g(w)n(e)g(can)g(consider)f(as)h(result)g(of)g(action)g(op)r (erator)e Fo(M)9 b Fn(\()p Fo(t)p Fn(\))30 b Fr(on)f(initial)h(data)515 4750 y(of)d(Cauc)n(h)n(y)g(problem)1663 4850 y Ff(\010)p Fn(\()p Fo(t)p Fn(\))c(=)g Fo(M)9 b Fn(\()p Fo(t)p Fn(\))p Fo(\036)2170 4862 y Fl(0)2208 4850 y Fo(:)1926 5255 y Fr(7)p eop %%Page: 8 8 8 7 bop 515 523 a Fr(Op)r(erator)30 b Fn(H\()p Fo(\034)9 b Fn(\))33 b Fr(is)f(selfadjoin)n(t)g(in)g Fo(L)1731 535 y Fl(2)1768 523 y Fn(\()p Fp(\0001)p Fo(;)14 b Fp(1)p Fn(\))p Fr(.)32 b(Th)n(us)f Fo(M)9 b Fn(\()p Fo(t)p Fn(\))33 b Fr(is)e(unitary)h(op)r(erator)e(in)515 623 y Fo(L)572 635 y Fl(2)608 623 y Fn(\()p Fp(\0001)p Fo(;)14 b Fp(1)p Fn(\))p Fr(.)28 b(Let)g(us)g(consider)e(function)1661 790 y Ff(X)1733 802 y Fm(N)1819 790 y Fn(=)d Ff(\010)18 b Fp(\000)h Ff(\010)2147 802 y Fm(N)2209 790 y Fo(:)515 957 y Fr(It)28 b(satis\034es)e(nonhomogeneous)g(equation)1420 1162 y Fp(\000)p Fo(i)1524 1106 y(@)5 b Ff(X)1645 1118 y Fm(N)p 1523 1143 184 4 v 1575 1219 a Fo(@)g(t)1735 1162 y Fp(\000)18 b Fo(H)7 b Fn(\()p Fo(\034)i Fn(\))p Ff(X)2075 1174 y Fm(N)2162 1162 y Fn(=)23 b(\001)p Ff(\010)2388 1174 y Fm(N)2451 1162 y Fo(:)757 b Fr(\(19\))515 1357 y(W)-7 b(e)28 b(can)f(calculate)g(solution)g(of)g(this)h(equation)f (with)h(the)g(help)g(of)f(op)r(erator)f Fo(M)9 b Fn(\()p Fo(t)p Fn(\))1280 1582 y Ff(X)1352 1594 y Fm(N)1438 1582 y Fn(=)23 b Fo(iM)9 b Fn(\()p Fo(t)p Fn(\))1753 1469 y Fk(Z)1836 1490 y Fm(t)1799 1658 y Fl(0)1879 1582 y Fo(M)1969 1548 y Fe(\000)p Fl(1)2057 1582 y Fn(\()p Fo(t)2119 1548 y Fe(0)2143 1582 y Fn(\)\001)p Ff(\010)2313 1594 y Fm(N)2376 1582 y Fn(\()p Fo(t)2438 1548 y Fe(0)2462 1582 y Fn(\))p Fo(dt)2567 1548 y Fe(0)2591 1582 y Fo(:)515 1791 y Fr(F)-7 b(rom)27 b(this)h(relation)e(w)n(e)h(obtain)h(estimate)f (for)g(the)h(norm)f(of)h(function)g Fo(X)2888 1803 y Fm(N)1052 1958 y Fp(k)p Ff(X)1166 1970 y Fm(N)1229 1958 y Fn(\()p Fo(t)p Fn(\))p Fp(k)1365 1973 y Fm(L)1411 1981 y Fc(2)1443 1973 y Fl(\()p Fe(\0001)p Fm(;)p Fe(1)p Fl(\))1726 1958 y Fp(\024)22 b Fo(t)41 b Fn(max)1857 2016 y Fm(t)1882 1999 y Fd(0)1905 2016 y Fe(2)p Fl([0)p Fm(;t)p Fl(])2079 1958 y Fp(k)p Fn(\001)p Ff(\010)2259 1970 y Fm(N)2321 1958 y Fn(\()p Fo(t)2383 1924 y Fe(0)2407 1958 y Fn(\))p Fp(k)2481 1973 y Fm(L)2527 1981 y Fc(2)2559 1973 y Fl(\()p Fe(\0001)p Fm(;)p Fe(1)p Fl(\))2819 1958 y Fo(:)515 2189 y Fr(In)32 b(order)f(to)h(obtain)g(estimates)g(for)f(deriv)-5 b(ativ)n(e)2143 2155 y Fm(@)t Fb(X)2238 2163 y Fa(N)p 2143 2170 149 4 v 2179 2217 a Fm(@)t(x)2366 2189 y Fr(let)33 b(us)f(di\033eren)n(tiate)g(equation)515 2288 y(\(19\))835 2521 y Fp(\000)p Fo(i)939 2465 y(@)988 2435 y Fl(2)1024 2465 y Ff(X)1096 2477 y Fm(N)p 938 2502 222 4 v 961 2578 a Fo(@)5 b(t@)g(x)1188 2521 y Fp(\000)18 b Fo(H)7 b Fn(\()p Fo(\034)i Fn(\))1466 2465 y Fo(@)c Ff(X)1587 2477 y Fm(N)p 1467 2502 184 4 v 1511 2578 a Fo(@)g(x)1684 2521 y Fn(=)1781 2465 y Fo(@)g Fn(\(\001)p Ff(\010)2000 2477 y Fm(N)2063 2465 y Fn(\))p 1781 2502 315 4 v 1890 2578 a Fo(@)g(x)2124 2521 y Fn(+)2207 2404 y Fk(\022)2387 2466 y Fn(0)159 b Fo(p)2630 2478 y Fm(x)2672 2466 y Fn(\()p Fo(x)p Fn(\))p 2310 2502 196 4 v 2310 2575 a Fo(p)2352 2587 y Fm(x)2393 2575 y Fn(\()p Fo(x)p Fn(\))i(0)2825 2404 y Fk(\023)2900 2521 y Ff(X)2972 2533 y Fm(N)3036 2521 y Fo(:)515 2728 y Fr(W)-7 b(e)28 b(again)f(receiv)n(e)g(nonhomogeneous)e(equation)j (for)f(the)2443 2694 y Fm(@)t Fb(X)2538 2702 y Fa(N)p 2443 2709 149 4 v 2479 2756 a Fm(@)t(x)2657 2728 y Fr(that)i(is)f (analogous)d(to)515 2839 y(\(19\).)g(By)h(analogous)e(metho)r(ds)i(w)n (e)g(can)f(obtain)h(estimates)g(for)2608 2805 y Fm(@)t Fb(X)2703 2813 y Fa(N)p 2608 2820 V 2650 2868 a Fm(@)t(t)2819 2839 y Fr(and)g Fo(x)3026 2809 y Fm(l)3052 2839 y Ff(X)3124 2851 y Fm(N)3187 2839 y Fr(.)g(The)515 2939 y(theorem)h(is)g(pro)n(v)n (ed.)515 3211 y Fq(5)131 b(Large)53 b(time)h(asymptotic)h(b)t(eha)l (viour)f(of)g(the)g(solu-)712 3360 y(tion)515 3542 y Fr(Main)27 b(term)h(of)f(our)g(solution)g(as)g Fo(")c Fp(!)g Fn(0)k Fr(has)g(a)g(form)987 3767 y Ff(\010)1056 3779 y Fl(0)1093 3767 y Fn(\()p Fo(x;)14 b(t)p Fn(\))24 b(=)1417 3711 y(1)p 1392 3748 92 4 v 1392 3824 a(2)p Fo(\031)1508 3654 y Fk(Z)1591 3675 y Fe(1)1554 3843 y(\0001)1690 3767 y Fo(d\025)14 b Fn(exp\()p Fo(i\025t)p Fn(\)\()p Ff(f)9 b Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))p Fo(;)14 b Ff(g)q Fn(\()p Fo(x;)g(\025;)g(\034)9 b Fn(\)\))p Fp(\002)1376 3931 y Fk(Z)1459 3951 y Fl(+)p Fe(1)1422 4120 y(\0001)1594 4044 y Fo(dy)1695 3902 y Fk( )p 1807 3919 367 4 v 1807 3993 a Ff(f)1845 3969 y Fe(>)1902 3993 y Fn(\()p Fo(y)s(;)14 b(\025;)g Fn(0\))p 1802 4030 378 4 v 1802 4104 a Ff(g)1851 4080 y Fe(>)1907 4104 y Fn(\()p Fo(y)s(;)g(\025;)g Fn(0\))2220 3902 y Fk(!)2300 4044 y Fo(\036)2349 4056 y Fl(0)2387 4044 y Fn(\()p Fo(y)s Fn(\))p Fo(:)515 4254 y Fr(It)21 b(is)h(easy)e(to)h(see,)g(that)h (\034rst)f(in)n(tegral)f(has)g(large)g(parameter)g Fo(t)p Fr(.)h(W)-7 b(e)22 b(can)f(use)g(corresp)r(ond-)515 4354 y(ing)f(asymptotic)f(metho)r(ds)h(for)g(calculation)f(of)h(this)g(in)n (tegral.)f(As)h Fo(t)j Fp(\035)g Fn(1)d Fr(in)n(tegral)f(is)g(small)515 4453 y(if)32 b Fo(x)h Fr(is)e(limited.)i(As)f Fo(x)f Fp(!)f(\0061)i Fr(w)n(e)f(can)h(use)g(asymptotics)f(of)g(the)i (solutions)e Ff(f)9 b Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))515 4553 y Fr(and)26 b Ff(g)q Fn(\()p Fo(x;)14 b(\025;)g(\034)9 b Fn(\))30 b Fr(\(5\)-\(8\).)c(Only)h(solutions)f (that)h(ha)n(v)n(e)f(exp)r(onen)n(tial)g Fn(exp\()p Fo(i\025t)p Fn(\))14 b(exp\()p Fp(\000)p Fo(i\025x)p Fn(\))515 4653 y Fr(as)28 b Fo(x)f Fp(!)f(1)j Fr(or)g(exp)r(onen)n(tial)f Fn(exp\()p Fo(i\025t)p Fn(\))14 b(exp\()p Fo(i\025x)p Fn(\))31 b Fr(as)e Fo(x)d Fp(!)g(\0001)j Fr(giv)n(e)f(the)i(con)n (tributions)515 4752 y(to)d(asymptotics)g(of)g(the)h(in)n(tegral.)f (Finally)-7 b(,)27 b(w)n(e)g(receiv)n(e)1123 4965 y Ff(\010)1192 4977 y Fl(0)1229 4965 y Fn(\()p Fo(x;)14 b(t)p Fn(\))24 b(=)1554 4909 y(1)p 1529 4946 92 4 v 1529 5022 a(2)p Fo(\031)1644 4852 y Fk(Z)1727 4873 y Fe(1)1690 5041 y(\0001)1826 4965 y Fo(d\025)1931 4848 y Fk(\022)2035 4915 y Fn(e)2072 4884 y Fm(i\025t)p Fe(\000)p Fm(i\025x)2513 4915 y Fn(0)2155 5015 y(0)202 b(e)2436 4985 y Fl(i)p Fm(\025)p Fl(t+i)p Fm(\025)p Fl(x)2710 4848 y Fk(\023)1926 5255 y Fr(8)p eop %%Page: 9 9 9 8 bop 1248 564 a Fk(Z)1331 584 y Fl(+)p Fe(1)1294 752 y(\0001)1466 677 y Fo(dy)1567 535 y Fk( )p 1680 552 367 4 v 1680 626 a Ff(f)1718 602 y Fe(>)1774 626 y Fn(\()p Fo(y)s(;)14 b(\025;)g Fn(0\))p 1674 663 378 4 v 1674 737 a Ff(g)1723 713 y Fe(>)1779 737 y Fn(\()p Fo(y)s(;)g(\025;)g Fn(0\))2093 535 y Fk(!)2172 677 y Fo(\036)2221 689 y Fl(0)2259 677 y Fn(\()p Fo(y)s Fn(\))19 b(+)f Ff(o)p Fn(\(1\))p Fo(:)515 901 y Fr(In)32 b(particular)f(w)n(e)h(see)g(that)g (solution)g(is)g(completely)g(determined)g(b)n(y)g(op)r(erator)f Fn(H\(0\))p Fr(.)515 1000 y(This)f(result)h(is)f(in)h(accordance)e (with)i(results)f(that)h(can)f(b)r(e)h(receiv)n(ed)f(with)h(the)g(help) g(of)515 1100 y(the)d(adiabatic)e(theorem)h(in)h(scattering)f(theory)-7 b(.)639 1200 y(The)34 b(author)f(w)n(ould)h(lik)n(e)g(to)g(thanks)f (V.S.Buslaev)h(for)f(his)h(in)n(terest)g(in)g(the)g(w)n(ork,)515 1299 y(and)27 b(A.A.F)-7 b(edoto)n(v)27 b(for)g(his)h(v)-5 b(aluable)27 b(remarks.)1723 1482 y Fh(References)639 1665 y Fr([1])g(J.D.Dollard.)g(A)n(diabatic)f(switc)n(hing)h(in)g(the)g (Shro)r(edinger)f(theory)g(of)h(scattering)515 1764 y(-)g(J.Math.Ph)n (ys.,)g(V.7,)h(1966)e(pp)i(802-810.)639 1864 y([2])33 b(G.Nenciu.)g(On)g(the)g(adiabatic)f(limit)h(for)f(Dirac)h(particles)e (in)i(external)f(\034elds.-)515 1963 y(Com.Math.Ph)n(ys.,)27 b(V.76,1980,)e(pp.)j(117-128)639 2063 y([3])20 b(A.Martinez,)h(Sh.Nak) -5 b(am)n(ura.A)n(diabatic)18 b(limit)j(and)g(scattering.-)e(C.R.A)n (cad.)h(Sci.)515 2163 y(P)n(aris)26 b(ser)h(I)h(Math.,)g(V.318,)e(N)i (12,)f(pp.)h(1153-1158)639 2262 y([4])22 b(L.A.T)-7 b(akh)n(ta)5 b(jan,)21 b(L.D.F)-7 b(addeev.)21 b(Hamilton)h(Approac)n(h)f(to)h(the)g (Soliton)f(Theory)-7 b(.-)515 2362 y(M.,)28 b(Nauk)-5 b(a,)27 b(1986)1926 5255 y(9)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0204260659782--