Content-Type: multipart/mixed; boundary="-------------9911210806273" This is a multi-part message in MIME format. ---------------9911210806273 Content-Type: text/plain; name="99-440.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="99-440.keywords" discrete kinetic models, dynamical phase transitions, hyperbolic conservation laws ---------------9911210806273 Content-Type: application/postscript; name="nata.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="nata.ps" %!PS-Adobe-2.0 %%Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %%Title: nata99.dvi %%Pages: 32 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentPaperSizes: a4 %%EndComments %DVIPSCommandLine: dvips nata99 -o nata.ps %DVIPSParameters: dpi=600, compressed, comments removed %DVIPSSource: TeX output 1999.11.09:1250 %%BeginProcSet: texc.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}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{dup dup 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 /IE 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 IE N end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /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 dup definefont setfont}B /ch-width{ch-data dup length 5 sub get}B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{ 128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup 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 /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 sub]/id ch-image N /rw ch-width 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 dup 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 dup gp add /gp X adv}B /nd{/cp 0 N rw exit}B /lsh{rw cp 2 copy get dup 0 eq{pop 1}{ dup 255 eq{pop 254}{dup dup add 255 and S 1 and or}ifelse}ifelse put 1 adv}B /rsh{rw cp 2 copy get dup 0 eq{pop 128}{dup 255 eq{pop 127}{dup 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}]dup{bind pop}forall N /D{/cc X dup type /stringtype ne{] }if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1 sub dup 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 dup 1 get dup mul exch 0 get dup 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 /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for 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 /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V {}B /RV statusdict begin /product where{pop product dup length 7 ge{0 7 getinterval dup(Display)eq exch 0 4 getinterval(NeXT)eq or}{pop false} ifelse}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale rulex ruley false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR rulex ruley scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave newpath transform round exch round exch itransform moveto rulex 0 rlineto 0 ruley neg rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta 0 N /tail {dup /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 (nata99.dvi) @start /Fa 26 121 df39 D45 DI49 DII<163FA25E5E5D5DA25D5D5D5DA25D92B5FCEC01F7EC03E7140715C7EC0F87EC 1F07143E147E147C14F8EB01F0EB03E0130714C0EB0F80EB1F00133E5BA25B485A485A48 5A120F5B48C7FC123E5A12FCB91280A5C8000F90C7FCAC027FB61280A531417DC038>I< EE1F80A24C7EA24C7EA34C7EA24B7FA34B7FA24B7FA34B7F169F031F80161F82033F80ED 3E07037E80157C8203FC804B7E02018115F0820203814B137F0207815D173F020F814B7F 021F8292C77EA24A82023E80027E82027FB7FCA291B87EA2498302F0C8FCA20103834A15 7F0107834A153FA249488284011F8491C97E4984133E017E82B6020FB612F0A54C457CC4 55>65 D<0107B7FCA590C7001F1300B3B3A9EA1FE0487E487EA2487EA44B5AA26C48495A 495C6C4813FF6C48485B260FFC0713C06CB65A6C4AC7FCC66C13F8010F138030457DC33A >74 D83 D<007FB6D8C003B61280 A5D8000F01E0C7D801F8C7FC6D4C5A6F14076D6D5D6D6D4A5A4E5A6D6D143F6E6C92C8FC 6E157E705B6EEBC0016E01E05B4D5A6E6D485A6EEBF80F6E01FC5B4D5A6E6D48C9FC6F6C 5A6F137E5F6F5B815F816F7F81836F7F707E93B5FC844B805D4B8004E77FDB0FC37FED1F 83DB3F817F04007F037E137F4B8002016E7F4B6D7F4A5A4A486D7F020F6E7F4B7F4A4881 4AC76C7F717F147E4A6F7E0101707F4A8149488349486F7F010F707FB600E00103B612FC A54E447DC355>88 D<903801FFE0011F13FE017F6D7E48B612E03A03FE007FF84848EB1F FC6D6D7E486C6D7EA26F7FA36F7F6C5A6C5AEA00F090C7FCA40203B5FC91B6FC1307013F 13F19038FFFC01000313E0000F1380381FFE00485A5B127F5B12FF5BA35DA26D5B6C6C5B 4B13F0D83FFE013EEBFFC03A1FFF80FC7F0007EBFFF86CECE01FC66CEB8007D90FFCC9FC 322F7DAD36>97 D99 DII<137C48B4FC4813804813C0A24813E0A56C13C0A26C 13806C1300EA007C90C7FCAAEB7FC0EA7FFFA512037EB3AFB6FCA518467CC520>105 D108 D<90277F8007FEEC0FFC B590263FFFC090387FFF8092B5D8F001B512E002816E4880913D87F01FFC0FE03FF8913D 8FC00FFE1F801FFC0003D99F009026FF3E007F6C019E6D013C130F02BC5D02F86D496D7E A24A5D4A5DA34A5DB3A7B60081B60003B512FEA5572D7CAC5E>I<90397F8007FEB59038 3FFF8092B512E0028114F8913987F03FFC91388F801F000390399F000FFE6C139E14BC02 F86D7E5CA25CA35CB3A7B60083B512FEA5372D7CAC3E>II<90397FC00FF8B590B57E02C314E002CF14F89139DFC03F FC9139FF001FFE000301FCEB07FF6C496D13804A15C04A6D13E05C7013F0A2EF7FF8A4EF 3FFCACEF7FF8A318F017FFA24C13E06E15C06E5B6E4913806E4913006E495A9139DFC07F FC02CFB512F002C314C002C091C7FCED1FF092C9FCADB67EA536407DAC3E>I<90387F80 7FB53881FFE0028313F0028F13F8ED8FFC91389F1FFE000313BE6C13BC14F8A214F0ED0F FC9138E007F8ED01E092C7FCA35CB3A5B612E0A5272D7DAC2E>114 D<90391FFC038090B51287000314FF120F381FF003383FC00049133F48C7121F127E00FE 140FA215077EA27F01E090C7FC13FE387FFFF014FF6C14C015F06C14FC6C800003806C15 806C7E010F14C0EB003F020313E0140000F0143FA26C141F150FA27EA26C15C06C141FA2 6DEB3F8001E0EB7F009038F803FE90B55A00FC5CD8F03F13E026E007FEC7FC232F7CAD2C >III120 D E /Fb 1 1 df0 D E /Fc 3 51 df<14E0B0B712C0A3C700E0C7FCB022237C9B2B>43 D<1360EA01E0120F12FF12F1 1201B3A3387FFF80A2111C7B9B1C>49 DI E /Fd 66 123 df<04FFEB03F003039038E00FFC923A0FC0F01F1E923A3F00783E0F923A7E01F8 7C3FDB7C03EBFC7F03FC14F8DA01F813F905F1137EDC01E1133C913B03F00003F000A314 074B130760A3140F4B130F60A3010FB812C0A3903C001F80001F8000A3023F143F92C790 C7FCA44A5C027E147EA402FE14FE4A5CA413014A13015FA313034A13035FA313074A495A A44948495AA44948495AA3001CD9038090C8FC007E90380FC03F013E143E00FE011F5B13 3C017C5C3AF8780F01E0D878F0EB07C0273FE003FFC9FC390F8000FC404C82BA33>11 DI<3901 E003C03907F00FE0000F131F01F813F0001F133FA3000F131F3907B00F6038003000A201 7013E0016013C0EBE00101C01380000113030180130000035B3807000E000E5B485B485B 485B48485A00C05B1C1971B92B>34 D39 D<150C151C153815F0EC01E0EC03C0EC0780EC0F00141E5C147C5C5C495A1303495A5C13 0F49C7FCA2133EA25BA25BA2485AA212035B12075BA2120F5BA2121FA290C8FCA25AA212 3EA2127EA2127CA412FC5AAD1278A57EA3121C121EA2120E7EA26C7E6C7EA212001E5274 BD22>I<140C140E80EC0380A2EC01C015E0A2140015F0A21578A4157C153CAB157CA715 FCA215F8A21401A215F0A21403A215E0A21407A215C0140F1580A2141F1500A2143EA25C A25CA2495AA2495A5C1307495A91C7FC5B133E133C5B5B485A12035B48C8FC120E5A1278 5A12C01E527FBD22>I44 D<387FFFF8A2B5FCA214 F0150579941E>I<120EEA3F80127F12FFA31300127E123C0909778819>I<151815381578 15F0140114031407EC0FE0141F147FEB03FF90383FEFC0148FEB1C1F13001580A2143FA2 1500A25CA2147EA214FEA25CA21301A25CA21303A25CA21307A25CA2130FA25CA2131FA2 5CA2133FA291C7FC497EB61280A31D3877B72A>49 DI I<16E0ED01F01503A3150716E0A3150F16C0A2151F1680A2ED3F00A3157EA2157C15FC5D 14015D14035D14075D140F5D141F92C7FC143EA25CECF81C153E903801F07EEB03E014C0 90380780FE130F49485A133EEB7C01137801F05BEA01E03803C003EA0FFE391FFFC3F048 13FB267C01FF13403AF0003FFFE000601307C71400EC0FE05DA3141F5DA3143F92C7FCA4 143E141C24487DB72A>I<010314186E13F8903907F007F091B512E016C01600495B15F8 010E13E0020CC7FC011EC8FC131CA3133C1338A313781370A2147F9038F3FFC09038EF83 E09038FC01F0496C7E485A497F49137CC8FC157EA315FEA41401000C5C123F5A1403485C 5A4A5A12F800E05C140F4A5A5D6C49C7FC0070137E00785B387C01F8383E07F0381FFFC0 6C90C8FCEA01F8253A77B72A>I<157F913803FFC0020F13E0EC3F8191387E00F002F813 70903903F003F0903807E007EB0FC0EB1F80020013E04914C0017E90C7FC13FE5B485AA2 1203485AA2380FE07E9038E3FF809038E783E0391FCE01F09038DC00F813F84848137C5B 49137EA2485AA290C7FC15FE5A5AA214015D5AA214035DA348495A5D140F5D4A5A6C49C7 FC127C147C6C485A6C485A6CB45A6C1380D801FCC8FC243A76B72A>I 56 DI<133C137E13FF5AA313 FE13FCEA00701300B2120EEA3F80127F12FFA31300127E123C102477A319>I65 D67 D<0103B612FEEFFFC018F0903B0007F8000FF84BEB 03FCEF00FE020F157FF03F804B141F19C0021F150F19E05D1807143F19F05DA2147FA292 C8FCA25C180F5CA2130119E04A151FA2130319C04A153FA201071780187F4A1600A2010F 16FEA24A4A5A60011F15034D5A4A5D4D5A013F4B5A173F4A4AC7FC17FC017FEC03F84C5A 91C7EA1FC04949B45A007F90B548C8FCB712F016803C397CB83F>I<0107B8FCA3903A00 0FF000034BEB007F183E141F181E5DA2143FA25D181C147FA29238000380A24A13071800 4A91C7FC5E13015E4A133E167E49B512FEA25EECF8000107147C163C4A1338A2010F1478 18E04A13701701011F16C016004A14031880013F150718004A5CA2017F151E173E91C812 3C177C4915FC4C5A4914070001ED7FF0B8FCA25F38397BB838>I<0107B712FEA3903A00 0FF000074B1300187C021F153CA25DA2143FA25D1838147FA292C8FCEE03804A13071800 4A91C7FCA201015CA24A131E163E010314FE91B5FC5EA2903807F800167C4A1378A2130F A24A1370A2011F14F0A24A90C8FCA2133FA25CA2137FA291CAFCA25BA25B487EB6FCA337 397BB836>I<0103B5D8F80FB512E0A390260007F8C7381FE0004B5DA2020F153F615DA2 021F157F96C7FC5DA2023F5D605DA2027F14016092C7FCA24A1403605CA249B7FC60A202 FCC712070103150F605CA20107151F605CA2010F153F605CA2011F157F95C8FC5CA2013F 5D5F5CA2017F14015F91C7FC491403007FD9FE01B512F8B55BA243397CB83E>72 D<0103B512F8A390390007F8005DA2140FA25DA2141FA25DA2143FA25DA2147FA292C7FC A25CA25CA21301A25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2133FA25CA213 7FA291C8FC497EB6FCA25C25397CB820>I<0207B512F0A391390007FC006F5AA215075E A3150F5EA3151F5EA3153F5EA3157F93C7FCA35D5DA314015DA314035DA31407A25DA214 0FA2003F5C5A141F485CA24A5A12FC00E049C8FC14FE00705B495A6C485A381E0FC06CB4 C9FCEA01F82C3B78B82C>I<0103B500F890387FFFE0A21AC090260007F8C7380FFC004B 15E061020F4BC7FC183E4B5C18F0021F4A5A4D5A4BEB0F804DC8FC023F143C5F4B5B4C5A 027FEB07C04CC9FCED001E5E4A5BED01FCECFE0315070101497E151FECFC7C4B7E903903 FDE07FDAFFC07F1580ED003F49488014F84A131F83130F160F4A801607011F81A24A1303 83133F16014A80A2017F6E7EA291C8FC494A7F007F01FE011F13FCB55CA243397CB840> I<0107B512FCA25E9026000FF8C7FC5D5D141FA25DA2143FA25DA2147FA292C8FCA25CA2 5CA21301A25CA21303A25CA21307A25CA2130F170C4A141CA2011F153C17384A1478A201 3F157017F04A14E01601017F140317C091C71207160F49EC1F80163F4914FF0001020713 00B8FCA25E2E397BB834>I<902607FFF8923807FFF0614F13E0D9000FEFF0004F5AA202 1F167FF1EFC0141DDA1CFCEC01CF023C16DF9538039F800238ED071FA20278ED0E3F97C7 FC0270151CA202F04B5AF0707E14E0037E14E0010117FE4D485A02C0EC0380A20103ED07 01610280140EA20107ED1C0305385B14006F137049160705E05B010EEC01C0A2011E9138 03800F61011CEC0700A2013C020E131F4C5C1338ED1FB80178163F04F091C8FC01705CA2 01F04A5B187E00015DD807F816FEB500C09039007FFFFC151E150E4C397AB84A>I<9026 03FFF891B512E0A281D90007923807F8006F6E5A61020F5E81DA0E7F5DA2021E6D130703 3F92C7FC141C82DA3C1F5C70130EEC380FA202786D131E0307141C147082DAF003143C70 133814E0150101016E1378030014705C8201036E13F0604A1480163F010715C1041F5B91 C7FC17E149EC0FE360010E15F31607011E15FF95C8FC011C80A2013C805F133816001378 5F01F8157CEA03FC267FFFE0143CB51538A243397CB83E>I<0107B612F817FF1880903B 000FF0003FE04BEB0FF0EF03F8141FEF01FC5DA2023F15FEA25DA2147FEF03FC92C7FCA2 4A15F817074A15F0EF0FE01301EF1FC04AEC3F80EFFE0001034A5AEE0FF091B612C04CC7 FCD907F8C9FCA25CA2130FA25CA2131FA25CA2133FA25CA2137FA291CAFCA25BA25B1201 B512FCA337397BB838>80 D<0103B612F017FEEFFF80903B0007F8003FC04BEB0FF01707 020FEC03F8EF01FC5DA2021F15FEA25DA2143FEF03FC5DA2027FEC07F818F092C7120F18 E04AEC1FC0EF3F004A14FEEE01F80101EC0FE091B6128004FCC7FC9138FC003F0103EC0F 80834A6D7E8301071403A25C83010F14075F5CA2011F140FA25CA2133F161F4AECE007A2 017F160F180E91C7FC49020F131C007F01FE153CB5913807F078040313F0CAEAFFE0EF3F 80383B7CB83D>82 D<92383FC00E913901FFF01C020713FC91391FC07E3C91393F001F7C 027CEB0FF84A130749481303495A4948EB01F0A2495AA2011F15E091C7FCA34915C0A36E 90C7FCA2806D7E14FCECFF806D13F015FE6D6D7E6D14E0010080023F7F14079138007FFC 150F15031501A21500A2167C120EA3001E15FC5EA3003E4A5AA24B5AA2007F4A5A4B5A6D 49C7FC6D133ED8F9F013FC39F8FC03F839F07FFFE0D8E01F138026C003FCC8FC2F3D7ABA 2F>I<0007B812E0A25AD9F800EB001F01C049EB07C0485AD900011403121E001C5C003C 17801403123800785C00701607140700F01700485CA2140FC792C7FC5DA2141FA25DA214 3FA25DA2147FA292C9FCA25CA25CA21301A25CA21303A25CA21307A25CA2130FA25CEB3F F0007FB512F8B6FCA2333971B83B>I<003FB539800FFFFEA326007F80C7EA7F8091C8EA 3F00173E49153CA2491538A20001167817705BA2000316F05F5BA2000715015F5BA2000F 15035F5BA2001F150794C7FC5BA2003F5D160E5BA2007F151E161C90C8FCA2163C481538 5A16781670A216F04B5A5E1503007E4A5A4BC8FC150E6C143E6C6C5B15F0390FC003E039 07F01FC00001B5C9FC38007FFCEB1FE0373B70B83E>I87 D<49B5D8F007B5FCA3D9000790C713E0DA03FCEC7F00 187C020115786F5C4D5A02005D6F495A4DC7FC6F5BEE801E5F033F5BEEC0705F92381FC1 C016E3EEE780DB0FEFC8FC16FE6F5A5EA2150382A2150782150F151CED3CFF5D4B7EDA01 E07FEDC03FDA03807FEC0700020E131F021E805C4A130F0270805C494813074948801307 49C71203011E81133E01FE81D807FF1407B500E090387FFFFC93B5FC6040397CB83E>I< EC0FFFA35C1500141EA2143EA2143CA2147CA21478A214F8A25CA21301A25CA21303A25C A21307A25CA2130FA291C7FCA25BA2131EA2133EA2133CA2137CA21378A213F8A25BA212 01A25BA21203A25BA21207A25BA2120FA290C8FCA25AA2121EA2123EA2123CA2127CA212 78A2EAFFF8A25BA220537CBD19>91 D<01181330013813709038F001E03901C003800180 130000035B3807000E000E5B000C1318001C1338485B00301360A2007013E000605BA238 EF01DE38FF81FFA66CC65A003C13781C196AB92B>II<14F8EB07FE90381F871C90383E03 FE137CEBF801120148486C5A485A120FEBC001001F5CA2EA3F801403007F5C1300A21407 485C5AA2140F5D48ECC1C0A2141F15831680143F1587007C017F1300ECFF076C485B9038 038F8E391F0F079E3907FE03FC3901F000F0222677A42A>97 D<133FEA1FFFA3C67E137E A313FE5BA312015BA312035BA31207EBE0F8EBE7FE9038EF0F80390FFC07C013F89038F0 03E013E0D81FC013F0A21380A2123F1300A214075A127EA2140F12FE4814E0A2141F15C0 5AEC3F80A215005C147E5C387801F8007C5B383C03E0383E07C0381E1F80D80FFEC7FCEA 01F01C3B77B926>I<147F903803FFC090380FC1E090381F0070017E13784913383901F8 01F83803F003120713E0120FD81FC013F091C7FC485AA2127F90C8FCA35A5AA45AA31530 15381578007C14F0007EEB01E0003EEB03C0EC0F806CEB3E00380F81F83803FFE0C690C7 FC1D2677A426>II<147F903803FFC090380FC1E090383F00F0017E13785B485A48 5A485A120F4913F8001F14F0383F8001EC07E0EC1F80397F81FF00EBFFF891C7FC90C8FC 5A5AA55AA21530007C14381578007E14F0003EEB01E0EC03C06CEB0F806CEB3E00380781 F83803FFE0C690C7FC1D2677A426>IIII< EB01C0EB07E014F0130F14E01307EB038090C7FCAB13F0EA03FCEA071EEA0E1F121CA212 385B1270A25BEAF07E12E013FEC65AA212015B1203A25B12075BA2000F13E013C013C100 1F13C01381A2EB83801303EB0700A2130E6C5AEA07F8EA01E0143879B619>I<150E153F 157FA3157E151C1500ABEC1F80EC7FC0ECF1F0EB01C090380380F813071401130F130E13 1EEB1C03133C013813F0A2EB0007A215E0A2140FA215C0A2141FA21580A2143FA21500A2 5CA2147EA214FEA25CA21301A25CA213035C121C387E07E0A238FE0FC05C49C7FCEAF83E EA787CEA3FF0EA0FC0204883B619>IIIII<147F903803FFC090380FC1F090381F00F8017E137C5B4848137E4848 133E0007143F5B120F485AA2485A157F127F90C7FCA215FF5A4814FEA2140115FC5AEC03 F8A2EC07F015E0140F007C14C0007EEB1F80003EEB3F00147E6C13F8380F83F03803FFC0 C648C7FC202677A42A>I<9039078007C090391FE03FF090393CF0787C903938F8E03E90 38787FC00170497EECFF00D9F0FE148013E05CEA01E113C15CA2D80003143FA25CA20107 147FA24A1400A2010F5C5E5C4B5A131F5EEC80035E013F495A6E485A5E6E48C7FC017F13 3EEC70FC90387E3FF0EC0F8001FEC9FCA25BA21201A25BA21203A25B1207B512C0A32935 80A42A>II<3903C003F0390FF01FFC391E 783C0F381C7C703A3C3EE03F8038383FC0EB7F800078150000701300151CD8F07E90C7FC EAE0FE5BA2120012015BA312035BA312075BA3120F5BA3121F5BA3123F90C9FC120E2126 79A423>I<14FE903807FF8090380F83C090383E00E04913F00178137001F813F0000113 0313F0A215E00003EB01C06DC7FC7FEBFFC06C13F814FE6C7F6D13807F010F13C0130014 3F141F140F123E127E00FE1480A348EB1F0012E06C133E00705B6C5B381E03E06CB45AD8 01FEC7FC1C267AA422>I I<13F8D803FEEB01C0D8078FEB03E0390E0F8007121E121C0038140F131F007815C01270 013F131F00F0130000E015805BD8007E133FA201FE14005B5D120149137EA215FE120349 EBFC0EA20201131E161C15F813E0163CD9F003133814070001ECF07091381EF8F03A00F8 3C78E090393FF03FC090390FC00F00272679A42D>I<01F0130ED803FC133FD8071EEB7F 80EA0E1F121C123C0038143F49131F0070140FA25BD8F07E140000E08013FEC6485B150E 12015B151E0003141C5BA2153C000714385B5DA35DA24A5A140300035C6D48C7FC000113 0E3800F83CEB7FF8EB0FC0212679A426>I<01F01507D803FC903903801F80D8071E9039 07C03FC0D80E1F130F121C123C0038021F131F49EC800F00701607A249133FD8F07E1680 00E0ED000313FEC64849130718000001147E5B03FE5B0003160E495BA2171E0007010114 1C01E05B173C1738A217781770020314F05F0003010713016D486C485A000190391E7C07 802800FC3C3E0FC7FC90393FF81FFE90390FE003F0322679A437>I<903907E007C09039 1FF81FF89039787C383C9038F03E703A01E01EE0FE3803C01F018013C0D8070014FC4814 80000E1570023F1300001E91C7FC121CA2C75AA2147EA214FEA25CA21301A24A1370A201 0314F016E0001C5B007E1401010714C000FEEC0380010F1307010EEB0F0039781CF81E90 38387C3C393FF03FF03907C00FC027267CA427>I<13F0D803FCEB01C0D8071EEB03E0D8 0E1F1307121C123C0038140F4914C01270A249131FD8F07E148012E013FEC648133F1600 12015B5D0003147E5BA215FE00075C5BA214015DA314035D14070003130FEBF01F3901F8 7FE038007FF7EB1FC7EB000F5DA2141F003F5C48133F92C7FC147E147C007E13FC387001 F8EB03E06C485A383C1F80D80FFEC8FCEA03F0233679A428>I<903903C0038090380FF0 07D91FF81300496C5A017F130E9038FFFE1E9038F83FFC3901F007F849C65A495B1401C7 485A4A5A4AC7FC141E5C5C5C495A495A495A49C8FC131E5B49131C5B4848133C48481338 491378000714F8390FF801F0391FFF07E0383E1FFFD83C0F5B00785CD8700790C7FC38F0 03FC38E000F021267BA422>I E /Fe 27 117 df44 D<167016F8A2150116F0A2150316E0150716C0A2150F16 80151F16005D153EA2157E157C15FC5DA214015D14035DA214075D140F5D141F92C7FCA2 5C143E147E147CA214FC5C13015CA213035C13075CA2130F5C131F91C8FC5B133EA2137E 137C13FC5BA212015B12035BA212075B120F5B121F90C9FCA25A123E127E127CA212FC5A A2127025537BBD30>47 D<49B4FC010F13E0017F13FC9038FF83FE4848C67E4848EB7F80 4848EB3FC04848EB1FE0A2001F15F0A24848EB0FF8A3007F15FCA500FF15FEB3007F15FC A4003F15F8A26D131F001F15F0A2000F15E06D133F000715C06C6CEB7F806C6CEBFF0039 00FF83FE6DB45A011F13F0010190C7FC27387CB630>I<141E143E14FE1307133FB5FCA3 13CFEA000FB3B3A6007FB61280A4213779B630>II II<001C15C0D81F80130701F8137F90B61280A216005D5D15 F05D15804AC7FC14F090C9FCA8EB07FE90383FFFE090B512F89038FC07FC9038E003FFD9 8001138090C713C0120EC813E0157F16F0A216F8A21206EA3F80EA7FE012FF7FA44914F0 A26C4813FF90C713E0007C15C06C5B6C491380D9C0071300390FF01FFE6CB512F8000114 E06C6C1380D90FF8C7FC25387BB630>II<123C123EEA3FE090B71280A41700485D5E5E5EA25E007CC7EA0FC000784A5A4BC7FC 00F8147E48147C15FC4A5A4A5AC7485A5D140F4A5A143F92C8FC5C147E14FE1301A2495A A31307A2130F5CA2131FA5133FA96D5A6D5A6D5A293A7BB830>I<49B47E010F13F0013F 13FC9038FE01FF3A01F8007F804848EB3FC04848EB1FE0150F485AED07F0121FA27FA27F 7F01FEEB0FE0EBFF809138E01FC06CEBF03F02FC13809138FF7F006C14FC6C5C7E6C14FE 6D7F6D14C04914E048B612F0EA07F848486C13F8261FE01F13FC383FC007EB8001007F6D 13FE90C7123F48140F48140715031501A21500A216FC7E6C14016D14F86C6CEB03F06D13 076C6CEB0FE0D80FFEEB7FC00003B61200C614FC013F13F00103138027387CB630>II65 D76 D80 D 82 D97 D<903803FF80011F13F0017F13FC3901FF83FE3A03FE007F804848 133F484814C0001FEC1FE05B003FEC0FF0A2485A16F8150712FFA290B6FCA301E0C8FCA4 127FA36C7E1678121F6C6C14F86D14F000071403D801FFEB0FE06C9038C07FC06DB51200 010F13FC010113E025257DA42C>101 D105 D<13FFB5FCA412077EAF 92380FFFE0A4923803FC0016F0ED0FE0ED1F804BC7FC157E5DEC03F8EC07E04A5A141FEC 7FE04A7E8181A2ECCFFEEC0FFF496C7F806E7F6E7F82157F6F7E6F7E82150F82B5D8F83F 13F8A42D3A7EB932>107 D<01FED97FE0EB0FFC00FF902601FFFC90383FFF80020701FF 90B512E0DA1F81903983F03FF0DA3C00903887801F000749DACF007F00034914DE6D48D9 7FFC6D7E4A5CA24A5CA291C75BB3A3B5D8FC1FB50083B512F0A44C257DA451>109 D<01FEEB7FC000FF903803FFF8020F13FE91381F03FFDA3C011380000713780003497E6D 4814C05CA25CA291C7FCB3A3B5D8FC3F13FFA430257DA435>I<903801FFC0010F13F801 7F13FFD9FF807F3A03FE003FE048486D7E48486D7E48486D7EA2003F81491303007F81A3 00FF1680A9007F1600A3003F5D6D1307001F5DA26C6C495A6C6C495A6C6C495A6C6C6CB4 5A6C6CB5C7FC011F13FC010113C029257DA430>I<9039FF01FF80B5000F13F0023F13FC 9138FE07FFDAF00113800003496C13C00280EB7FE091C713F0EE3FF8A2EE1FFCA3EE0FFE AA17FC161FA217F8163F17F06E137F6E14E06EEBFFC0DAF00313809139FC07FE0091383F FFF8020F13E0020390C7FC91C9FCACB512FCA42F357EA435>I<9038FE03F000FFEB0FFE EC3FFF91387C7F809138F8FFC000075B6C6C5A5CA29138807F80ED3F00150C92C7FC91C8 FCB3A2B512FEA422257EA427>114 D<90383FF0383903FFFEF8000F13FF381FC00F383F 0003007E1301007C130012FC15787E7E6D130013FCEBFFE06C13FCECFF806C14C06C14F0 6C14F81203C614FC131F9038007FFE140700F0130114007E157E7E157C6C14FC6C14F8EB 80019038F007F090B512C000F8140038E01FF81F257DA426>I<130FA55BA45BA25B5BA2 5A1207001FEBFFE0B6FCA3000390C7FCB21578A815F86CEB80F014816CEBC3E090383FFF C06D1380903803FE001D357EB425>I E /Ff 14 62 df0 D<0207131CA34A133C020E1338A3021E1378021C1370A4023C13F002385BA3EC7801B812 F8A33B0001E007800002C090C7FCA201035BEC800EA30107131EEC001CA249133CB812F8 A327003C00F0C7FC01385BA3EB780101705BA4EBF00301E05BA30001130701C090C8FCA3 2D337CA737>35 D<1306130C13181330136013E0EA01C0EA0380A2EA07005A120E121EA2 121C123CA35AA512F85AAB7E1278A57EA3121C121EA2120E120F7EEA0380A2EA01C0EA00 E0136013301318130C13060F3B7AAB1A>40 D<12C012607E7E7E120E7EEA0380A2EA01C0 13E0120013F0A213701378A3133CA5133E131EAB133E133CA51378A3137013F0A213E012 0113C0EA0380A2EA0700120E120C5A5A5A5A0F3B7DAB1A>I<140EB3A2B812E0A3C7000E C8FCB3A22B2B7DA333>43 D48 D<13381378EA01F8121F12FE12E01200B3AB 487EB512F8A215267BA521>I<13FF000313E0380E03F0381800F848137C48137E00787F 12FC6CEB1F80A4127CC7FC15005C143E147E147C5C495A495A5C495A010EC7FC5B5B9038 70018013E0EA0180390300030012065A001FB5FC5A485BB5FCA219267DA521>I<13FF00 0313E0380F01F8381C007C0030137E003C133E007E133FA4123CC7123E147E147C5C495A EB07E03801FF8091C7FC380001E06D7E147C80143F801580A21238127C12FEA21500485B 0078133E00705B6C5B381F01F03807FFC0C690C7FC19277DA521>I<1438A2147814F813 01A2130313071306130C131C131813301370136013C012011380EA03005A120E120C121C 5A12305A12E0B612E0A2C7EAF800A7497E90383FFFE0A21B277EA621>I<0018130C001F 137CEBFFF85C5C1480D819FCC7FC0018C8FCA7137F3819FFE0381F81F0381E0078001C7F 0018133EC7FC80A21580A21230127C12FCA3150012F00060133E127000305B001C5B380F 03E03803FFC0C648C7FC19277DA521>II<1238127C12FEA3127C12381200AB1238127C12FC12FEA212 7E123E1206A3120CA31218A212301270122007247B9813>59 D61 D E /Fg 50 123 df<003C13F0387E01F838FF03FCA2EB83FEA2EA7F 81383D80F600011306A30003130EEB000CA248131C00061318000E13384813704813E038 7001C00060138017157EAD23>34 D<123C127EB4FCA21380A2127F123D1201A312031300 A25A1206120E5A5A5A126009157A8714>44 D<123C127E12FFA4127E123C08087A8714> 46 D48 D<130C133C137CEA03FC12FFEAFC7C1200B3B113FE 387FFFFEA2172C7AAB23>III54 D<1230123C003FB512F8A215F05A15E039700001C000 601480140348EB0700140E140CC7121C5C143014705C495AA2495AA249C7FCA25B130E13 1EA2133EA3133C137CA413FCA913781D2E7CAC23>III<4A7E4A7EA34A7EA24A7EA3EC1BF81419A2EC30FCA2EC70FEEC607EA24A7EA349 486C7EA2010380EC000FA201066D7EA3496D7EA2011FB57EA29038180001496D7EA34914 7EA201E0147F4980A20001ED1F801203000716C0D80FF0EC3FE0D8FFFC0103B5FCA2302F 7EAE35>65 DIIIII73 D77 DI80 D82 D<90383F80303901FFF0703807C07C390F000EF0001E130748130348130114001270 00F01470A315307EA26C1400127E127FEA3FE013FE381FFFE06C13FC6C13FF00011480D8 003F13E013039038003FF0EC07F81401140015FC157C12C0153CA37EA215787E6C14706C 14F06CEB01E039F78003C039E3F00F0038E07FFE38C00FF01E2F7CAD27>I<007FB712F8 A29039000FC003007C150000701638A200601618A200E0161CA248160CA5C71500B3A94A 7E011FB512E0A22E2D7EAC33>III<0003130C48131C 000E13384813704813E0003013C0EA700100601380A2EAE00300C01300A300DE137800FF 13FCEB83FEA2EA7F81A2383F00FC001E1378171577AD23>92 D<13FF000713C0380F01F0 381C00F8003F137C80A2143F001E7FC7FCA4EB07FF137F3801FE1FEA07F0EA1FC0EA3F80 EA7F00127E00FE14065AA3143F7E007E137F007FEBEF8C391F83C7FC390FFF03F83901FC 01E01F207D9E23>97 DII<15F8141FA214011400ACEB0FE0EB7FF83801F81E3803E0073807C003380F8001 EA1F00481300123E127EA25AA9127C127EA2003E13017EEB8003000F13073903E00EFC3A 01F03CFFC038007FF090391FC0F800222F7EAD27>III<013F13F89038FFC3FE3903E1FF1E3807807C000F 140C391F003E00A2003E7FA76C133EA26C6C5A00071378380FE1F0380CFFC0D81C3FC7FC 90C8FCA3121E121F380FFFF814FF6C14C04814F0391E0007F848130048147C12F848143C A46C147C007C14F86CEB01F06CEB03E03907E01F803901FFFE0038003FF01F2D7E9D23> III<130FEB1F80EB 3FC0A4EB1F80EB0F0090C7FCA8EB07C013FFA2130F1307B3AD1230127838FC0F80A21400 485AEA783EEA3FF8EA07E0123C83AD16>III<2607C07FEB07F03BFFC3FFC03FFC903AC7 83F0783F3C0FCE01F8E01F803B07DC00F9C00F01F8D9FF8013C04990387F000749137EA2 49137CB2486C01FEEB0FE03CFFFE0FFFE0FFFEA2371E7E9D3C>I<3807C0FE39FFC3FF80 9038C703E0390FDE01F0EA07F8496C7EA25BA25BB2486C487E3AFFFE1FFFC0A2221E7E9D 27>II<3807C0FE39FFC7FF809038CF03E0390FDC01 F03907F800FC49137E49133E49133FED1F80A3ED0FC0A8151F1680A2ED3F00A26D137E6D 137C5D9038FC01F09038CE07E09038C7FF80D9C1FCC7FC01C0C8FCA9487EEAFFFEA2222B 7E9D27>I<380781F838FF87FEEB8E3FEA0F9CEA07B813B0EBF01EEBE000A45BB0487EB5 FCA2181E7E9D1C>114 D<3801FE183807FFB8381E01F8EA3C00481378481338A21418A2 7E7EB41300EA7FF06CB4FC6C13C06C13F0000113F838001FFC130138C0007E143EA26C13 1EA27EA26C133CA26C137838FF01F038E3FFC000C0130017207E9E1C>I<1360A413E0A3 12011203A21207121FB512F0A23803E000AF1418A714383801F03014703800F860EB3FE0 EB0F80152A7FA81B>II<3AFFFC01FFC0A23A 0FE0007E000007147C15380003143015706C6C1360A26C6C5BA390387C0180A26D48C7FC A2EB3F07EB1F06A2EB0F8CA214DCEB07D8A2EB03F0A36D5AA26D5A221E7F9C25>I<3AFF FC01FFC0A23A0FE0007E000007147C1538000314306D137000011460A26C6C5BA2EBFC01 017C5BEB7E03013E90C7FCA2EB1F06A2148EEB0F8CA2EB07D8A2EB03F0A36D5AA26D5AA2 495AA2130391C8FC1278EAFC06A25B131CEA7838EA7070EA3FE0EA0F80222B7F9C25> 121 D<003FB51280A2EB003F003C14000038137E00305BEA700100605B495A495A130F00 005B495A49C7FC5B137E9038FC0180EA01F8120313F03807E003EA0FC0001F1400138048 485A007E5B00FE133FB6FCA2191D7E9C1F>I E /Fh 2 122 df<136013701360A2004013 2000E0137038F861F0387E67E0381FFF803807FE00EA00F0EA07FE381FFF80387E67E038 F861F038E060700040132000001300A21370136014157B9620>3 D<136013F0A81360A4387C63E0B512F0A2387C63E038006000A313F0B3A21360A7142F7C A31E>121 D E /Fi 7 113 df0 D<1338A50060130C00F8133E 00FC137E00FE13FE383FBBF83807FFC000011300EA007C48B4FC000713C0383FBBF838FE 38FE00FC137E00F8133E0060130C00001300A517197B9A22>3 D<1406140EB3B812E0A3 C7000EC8FCB1B812E0A32B2B7CA834>6 D<176017F01770A217781738173C171C171E83 717E717E717EEF00F8BAFC19801900CB12F8EF01E04D5A4D5A4DC7FC171E171C173C1738 17781770A217F01760391F7C9D42>33 D<13E0EA01F0EA03F8A3EA07F0A313E0A2120F13 C0A3EA1F80A21300A25A123EA35AA3127812F8A25A12100D1E7D9F13>48 D<017F157F2601FFE0903803FFC0000701F890380FF1F0260F83FC90381F0038261E00FF 013C7F001890263F8078130C4890261FC0E07F007090260FE1C07F0060EB07E3913803F7 80486DB4C7EA01806E5A157E157F81824B7E0060DAF7E0EB0300913801E3F0DBC3F85B6C 90260381FC13066C90260F00FE5B001C011E90387F803C6C017C90381FE0F82607C7F86D B45A2601FFE0010313C06C6CC86CC7FC391B7C9942>I<186018E0170118C01703188017 07EF0F00170E171E171C173C17381778177017F05F16014C5A5F160794C7FC5E160E161E 161C163C1638486C147800075DD81FC05C003F1401D8F7E05C00C31403D803F05C000114 076D91C8FC00005C6D130E017C131E017E5B013E1338013F13786D1370EC80F0010F5B14 C101075B14E301035B14F76DB4C9FC5C13005C147C14781438333A7B8237>112 D E /Fj 17 113 df<007FB81280B912C0A26C17803204799641>0 D<121C127FEAFF80A5EA7F00121C0909799917>I<0060150600F8150F6C151F007E153F 6C157E6C6C14FC6C6CEB01F86C6CEB03F06C6CEB07E06C6CEB0FC06C6CEB1F80017EEB3F 006D137E6D6C5A90380FC1F8903807E3F0903803F7E06DB45A6D5B6EC7FCA24A7E497F90 3803F7E0903807E3F090380FC1F890381F80FC90383F007E017E7F49EB1F804848EB0FC0 4848EB07E04848EB03F04848EB01F84848EB00FC48C8127E007E153F48151F48150F0060 1506282874A841>I<15301578B3A6007FB812F8B912FCA26C17F8C80078C8FCB3A3007F B812F8B912FCA26C17F836367BB641>6 D15 D<007FB812F8B912FCA26C17F8CCFCAE007FB812 F8B912FCA26C17F8CCFCAE007FB812F8B912FCA26C17F836287BA841>17 D<020FB6128091B712C01303010F1680D91FF8C9FCEB7F8001FECAFCEA01F8485A485A48 5A5B48CBFCA2123EA25AA2127812F8A25AA87EA21278127CA27EA27EA26C7E7F6C7E6C7E 6C7EEA00FEEB7F80EB1FF86DB71280010316C01300020F158091CAFCAE001FB812804817 C0A26C1780324479B441>I20 D<126012F812FEEA7F80EA3FE0EA0FF8EA03FEC66C 7EEB3FE0EB0FF8EB03FE903800FF80EC3FE0EC0FF8EC03FE913800FF80ED3FE0ED0FF8ED 03FE923800FF80EE3FE0EE0FF8EE03FE933800FF80EF3FC0171FEF7F80933801FF00EE07 FCEE1FF0EE7FC04B48C7FCED07FCED1FF0ED7FC04A48C8FCEC07FCEC1FF0EC7FC04948C9 FCEB07FCEB1FF0EB7FC04848CAFCEA07FCEA1FF0EA7FC048CBFC12FC1270CCFCAE007FB8 1280B912C0A26C1780324479B441>I<181EA4181F84A285180785727EA2727E727E8519 7E85F11F80F10FC0F107F0007FBA12FCBCFCA26C19FCCCEA07F0F10FC0F11F80F13F0019 7E61614E5A4E5AA24E5A61180F96C7FCA260181EA4482C7BAA53>33 D49 D<91381FFFFE91B6FC1303010F14 FED91FF0C7FCEB7F8001FEC8FCEA01F8485A485A485A5B48C9FCA2123EA25AA2127812F8 A25AA2B712FE16FFA216FE00F0C9FCA27EA21278127CA27EA27EA26C7E7F6C7E6C7E6C7E EA00FEEB7F80EB1FF06DB512FE010314FF1300021F13FE283279AD37>I<4B7E4B7E4B7E A24B7EA24B7EA2ED3E7CED7E7EED7C3E4B7EA24A486C7EA24A486C7EA24A486C7EA24A48 6C7EA24AC77E4A80023E147C4A80A24A80A249486E7EA249486E7EA249486E7EA249486E 7EA249C97E4982013E167C4982A24982A24848EE0F80A24848EE07C0A24848EE03E0A248 48EE01F0001F18F890CBFC003E187CA248183EA2BBFCA36C18FE403C7BBB4B>52 D54 D<0060161800F0163CB3B26C167CA2007C16 F8A26CED01F0003F15036C6CEC07E06C6CEC0FC0D807F0EC3F80D803FE903801FF003A00 FFC00FFC6DB55A011F14E0010391C7FC9038007FF82E347CB137>91 D<126012F0B3B3B3B3A91260045377BD17>106 D112 D E /Fk 16 121 df15 D<497EA414FF01071380131F90387C7F0049C7FC485A485A 5B1207A2485AA46C7EA23803EFF06CB47E7E3803DFF0D80780C7FC000EC8FC121E5A1238 1278127012F0A37E7E7EEA7FC013F8EA3FFE380FFFC0000313F8C67F131FEB03FEEB007E 143E141CEB203CEB7838EB3FF0EB07C019347EA71E>24 D<1238127C12FE12FFA2127F12 3B1203A31206A3120C121812381270122008127A8614>59 D61 D78 D98 D I<130E131F5BA2133E131C90C7FCA7EA03E0487EEA0C78EA187C1230A212605B12C0A2EA 01F0A3485AA2485AA2EBC180EA0F81A2381F0300A213066C5A131CEA07F06C5A11287DA6 17>105 D<1407EC0F80141FA21500140E91C7FCA7EB03E0EB07F8EB0C3C1318EB303E13 6013C0A248485AA2C7FCA25CA4495AA4495AA4495AA4495AA21238D87C1FC7FC12FC133E 485AEA70F8EA7FE0EA1F80193380A61B>I<133EEA07FEA2EA007CA213FCA25BA21201A2 5BA21203EC07809038E01FC0EC38600007EB61E014C3EBC187EBC307D80FC613C09038CC 038001B8C7FC13E0487E13FEEB3F80EB0FC0486C7E1303003E1460A2127EECC0C0127CEC C18012FC903801E30038F800FE0070137C1B297CA723>I<137CEA0FFCA2EA00F8A21201 A213F0A21203A213E0A21207A213C0A2120FA21380A2121FA21300A25AA2123EA2127EA2 EA7C18A3EAF830A21320EA786013C0EA3F80EA0F000E297EA715>I<3807803E390FE0FF 803818F3C13930F703C0EBFE073860FC0F13F8158039C1F0070091C7FC1201A2485AA448 5AA4485AA448C8FCA2120E1A1B7D991F>114 DI<131C 133EA25BA45BA4485AB512E0A23801F000485AA4485AA4485AA448C7FC1460A214C0123E EB0180EB0300EA1E06EA1F1CEA0FF8EA03E013267EA419>II<90 387C03C03901FF0FF03907079C30390E03B078000CEBF0F8001813E1123015F0396007C0 E015001200A2495AA449C7FC15301238007C1460EAFC3E15C0EAF87E39F06F03803970C7 0700383F83FE381F01F81D1B7D9926>120 D E /Fl 47 123 df11 DI15 D<133F14C0EB07F06D7E801301A26D7EA3147F A36E7EA36E7EA36E7EA36E7EA36E7EA36E7EA26E7EA214014A7E5C4A7E91381E3F80143C 14784A6C7E1301EB03E049486C7EEB0F80EB1F00496D7E137E5B48486D7E485A485A000F 6E7E485A485A48C87E12FE167F4816800070151F293B7CB930>21 D<1406A6913807FFC04A13E091383F80609138FDFFE0903903F87F804948C7FC495A495A 495A137F91C8FC5B5B1201A25BA512007F137E90383F3FF090381FFFFC90380FC01C9038 1FFFF890383C7FE001F0C8FC485A485A485AA248C9FC121EA25AA2127C1278A312F87EA2 127E127F7FEA3FE013FC6CB4FC6C13E06C13F8000113FF6C6C13C0010F13F001037FEB00 7F140F14031400A4010C5BEB0E0190380783E0903801FF80D9007EC7FC234B7EB924>24 D<013FB612E090B712F05A120717E0270F807006C7FC391E00600E48140C003813E04813 C048141CEAC0011200148001035BA213071400A25B1578011E137CA3133E133C137C157E 13FC5B1201157F1203497FA3D801C0131C2C257EA32F>I<027FB512C00103B612E0130F 5B017F15C09026FF81FEC7FC3901FC007E48487F485A497F484880485AA248C7FCA2127E A2153F00FE92C7FC5AA25D157E5A5DA24A5AA24A5A007C495A5D003C495A003E013FC8FC 6C137C380F81F83803FFE0C66CC9FC2B257DA32F>27 D<1503A35DA21506A2150EA2150C A2151CA21518A21538A21530A21570A2EC07FE91383FFFC0903901FCE3F0903907E0E0F8 90391F80C03ED93E007FEB7C01D801F8EC0F80D803F0018013C0D807E014071403D80FC0 15E0D81F801300A248485AA2007E1306A2020E130F12FE48010C14C0A2021CEB1F80A202 18EB3F00A20238137E007C5D1430007E4A5A003E90387003F06CEC07C09138600F80D80F 80013FC7FC3903E0E0FC3901F8E7F039007FFF80D90FFCC8FCEB01C0A25CA21303A291C9 FCA25BA21306A2130EA2130CA22B4B7CB931>30 D<160C161C1618A316381630A3167016 60A316E05EA315015EA301F80103130FD803FE9138001F80D8070F153F000E018015C000 1C5C001814060038161F0030160FD8701F010E13070060140C1703D8E03F168000C0EB00 1C491318EA007E180001FE13384913305F000116064913700360130E5F000316184901E0 13384B133017705F0201495AD801F849485A4CC7FC160E2600FC035B017EEB0078013FEB 01E090390FE30F80902603FFFEC8FC9038003FF00206C9FCA2140E140CA3141C1418A314 381430A314701460324B7EB936>32 D<121C127FEAFF80A5EA7F00121C0909798817>58 D<121C127FEAFF80A213C0A3127F121C1200A412011380A2120313005A1206120E5A5A5A 12600A19798817>I I<150C151E153EA2153C157CA2157815F8A215F01401A215E01403A215C01407A2158014 0FA215005CA2141E143EA2143C147CA2147814F8A25C1301A25C1303A2495AA25C130FA2 91C7FC5BA2131E133EA2133C137CA2137813F8A25B1201A25B1203A25B1207A25B120FA2 90C8FC5AA2121E123EA2123C127CA2127812F8A25A12601F537BBD2A>I<126012FCB4FC EA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB01FF9038007FC0EC1FF0EC07FC EC01FF9138007FC0ED1FF0ED07FCED01FF9238007FC0EE1FF0EE07FCEE01FF9338007F80 EF1FC0A2EF7F80933801FF00EE07FCEE1FF0EE7FC04B48C7FCED07FCED1FF0ED7FC04A48 C8FCEC07FCEC1FF0EC7FC04948C9FCEB07FCEB1FF0EB7FC04848CAFCEA07FCEA3FF0EA7F C048CBFC12FC1270323279AD41>I<1760177017F01601A21603A21607160FA24C7EA216 331673166316C3A2ED0183A2ED0303150683150C160115181530A21560A215C014011580 DA03007FA202061300140E140C5C021FB5FC5CA20260C7FC5C83495A8349C8FC1306A25B A25B13385B01F01680487E000716FFB56C013F13FF5EA2383C7DBB3E>65 D<0103B77E4916F018FC903B0007F80003FE4BEB00FFF07F80020FED3FC0181F4B15E0A2 141FA25DA2143F19C04B143F1980027F157F190092C812FE4D5A4A4A5AEF0FF04AEC1FC0 05FFC7FC49B612FC5F02FCC7B4FCEF3FC00103ED0FE0717E5C717E1307844A1401A2130F 17035CA2131F4D5A5C4D5A133F4D5A4A4A5A4D5A017F4BC7FC4C5A91C7EA07FC49EC3FF0 B812C094C8FC16F83B397DB83F>I<9339FF8001C0030F13E0037F9038F80380913A01FF 807E07913A07F8000F0FDA1FE0EB079FDA3F80903803BF0002FFC76CB4FCD901FC80495A 4948157E495A495A4948153E017F163C49C9FC5B1201484816385B1207485A1830121F49 93C7FCA2485AA3127F5BA312FF90CCFCA41703A25F1706A26C160E170C171C5F6C7E5F00 1F5E6D4A5A6C6C4A5A16076C6C020EC8FC6C6C143C6C6C5C6CB4495A90393FE00FC0010F B5C9FC010313FC9038007FC03A3D7CBA3B>I<0103B7FC4916E018F8903B0007F80007FE 4BEB00FFF03F80020FED1FC0180F4B15E0F007F0021F1503A24B15F81801143F19FC5DA2 147FA292C8FCA25C18035CA2130119F84A1507A2130319F04A150FA2010717E0181F4A16 C0A2010FEE3F80A24AED7F00187E011F16FE4D5A4A5D4D5A013F4B5A4D5A4A4A5A057FC7 FC017F15FEEE03FC91C7EA0FF049EC7FC0B8C8FC16FC16C03E397DB845>I<0103B5D8F8 03B512F8495DA290260007F8C73807F8004B5DA2020F150F615DA2021F151F615DA2023F 153F615DA2027F157F96C7FC92C8FCA24A5D605CA249B7FC60A202FCC712010103150360 5CA201071507605CA2010F150F605CA2011F151F605CA2013F153F605CA2017F157F95C8 FC91C8FC496C4A7EB690B6FCA345397DB845>72 D<902603FFF893383FFF80496081D900 079438FF80000206DC01BFC7FCA2020E4C5A1A7E020C1606190CDA1C7E16FE4F5A021816 30A20238166162023016C1F00181DA703F158395380303F002601506A202E0ED0C076202 C01518183001016D6C140F06605B028015C0A20103923801801FDD03005B140092380FC0 0649173F4D91C8FC01065DA2010E4B5B4D137E130C6F6C5A011C17FEDCE1805B011802E3 C7FCA2013802E6130104EC5C1330ED03F8017016034C5C01F05CD807FC4C7EB500E0D9C0 07B512F01680150151397CB851>77 D<902603FFF891381FFFF8496D5CA2D90007030113 006FEC007C02061678DA0EFF157081020C6D1460A2DA1C3F15E0705CEC181F8202381501 6F6C5C1430150702706D1303030392C7FC02607FA2DAE0015C701306ECC0008201016E13 0EEF800C5C163F0103EDC01C041F131891C713E0160F49EDF03818300106140717F8010E 02031370EFFC60130CEE01FE011C16E004005B011815FF177F1338600130153FA2017015 1F95C8FC01F081EA07FCB512E01706A245397DB843>I<4BB4FC031F13F09238FE01FC91 3903F0007EDA07C0EB1F80DA1F80EB0FC0023EC7EA07E002FCEC03F0495A4948EC01F849 5A4948EC00FC495A49C912FE49167E13FE49167F1201485AA2485AA2120F5B001F17FFA2 485AA34848ED01FEA400FFEE03FC90C9FCA2EF07F8A2EF0FF0A218E0171F18C0EF3F806C 167F180017FE4C5A6C6C5D1603001F4B5A6D4A5A000FED1F806C6C4AC7FC6D147E0003EC 01F8D801FC495AD8007EEB0FC090263F807FC8FC903807FFF801001380383D7CBA3F>I< 0103B7FC4916E018F8903B0007F80007FC4BEB00FE187F020FED3F80F01FC05DA2021F16 E0A25DA2143FF03FC05DA2027FED7F80A292C8130018FE4A4A5A604AEC07F04D5A0101ED 3FC04CB4C7FC91B612FC17E0D903FCCAFCA25CA21307A25CA2130FA25CA2131FA25CA213 3FA25CA2137FA291CBFC497EB6FCA33B397DB835>I<0103B612F849EDFF8018E0903B00 07F8001FF84BEB03FCEF00FE020F157FA24BEC3F80A2021F16C0A25DA2143FF07F805DA2 027FEDFF006092C7485A4D5A4A4A5A4D5A4AEC1F80057FC7FC0101EC07F891B612E094C8 FC9139FC000FC00103EC03F0707E4A6D7E831307177E5C177F010F5D5F5CA2011F1401A2 5CA2133F16034A4A1360A2017F17E019C091C71401496C01011480B61503933900FE0700 EF7E0ECAEA1FFCEF07F03B3B7DB83F>82 D<92391FE00380DBFFFC130002036D5A91390F E01F8F91393F0007DF027EEB01FE02F81300495A4948147E177C4948143C495AA2011F15 3891C8FCA3491530A28094C7FC80806D7E14FEECFFE06D13FE6DEBFFC06D14F06D806D80 021F7F02037FEC003F03037F1500167F163F161FA3120C160FA2001C151F94C7FCA3003C 153EA25E003E5D127E007F4A5A6D495A6DEB0FC0D8F9F0495AD8F0FE01FEC8FC39E03FFF F8010F13E0D8C00190C9FC313D7CBA33>I<0003B812FEA25A903AF8003FC00101C09138 80007E4848163C90C7007F141C121E001C92C7FCA2485CA200305C007017180060130112 E0485CA21403C716005DA21407A25DA2140FA25DA2141FA25DA2143FA25DA2147FA292C9 FCA25CA25CA21301A25CA21303A25CEB0FFC003FB6FC5AA237397EB831>I<003FB56C48 B51280485DA226007F80C7381FF00091C8EA07C0604993C7FCA2491506A20001160E170C 5BA20003161C17185BA20007163817305BA2000F167017605BA2001F16E05F5BA2003F15 015F5BA2007F150394C8FC90C8FCA25E4815065A160E160C161C161816385E127E5E4B5A 6C4A5A4BC9FC6C6C131E6C6C5B6C6C13F83903F807E06CB55A6C6C48CAFCEB0FF0393B7B B839>I<277FFFFC01B500F890B51280B5FC60000390C7D807FCC7380FF80001FC4BEC03 E000016204035E98C7FC621A0604075DA2040F5DA2041B5D6216336D02735D1663000003 C34A5A83DB01834AC8FC04815CDB0301140603075D1506030C5DA203185D197003301560 6115606D01E04A5A15C090267F01804AC9FC17FEDA030014060400130E0206150C020E5D 140C4A5DA24A5D18E04A5D715A5C4A92CAFCA26DC85AA2013E157C1778133C1770133801 301560513B7CB84E>87 D<147E903803FF8090390FC1C38090391F00EFC0017E137F4913 3F485A4848EB1F8012075B000F143F48481400A2485A5D007F147E90C7FCA215FE485C5A A214015D48150CA21403EDF01C16181407007C1538007E010F1330003E131F027B13706C 01E113E03A0F83C0F9C03A03FF007F80D800FCEB1F0026267DA42C>97 D99 D<163FED1FFFA3ED007F167EA216FEA216FCA21501A216F8A21503A216F0A21507A2 027E13E0903803FF8790380FC1CF90381F00EF017EEB7FC049133F485A4848131F000715 805B000F143F485A1600485A5D127F90C7127EA215FE5A485CA21401A248ECF80CA21403 161CEDF0181407007C1538007E010F1330003E131F027B13706C01E113E03A0F83C0F9C0 3A03FF007F80D800FCEB1F00283B7DB92B>II<16F8ED03FEED0F8792381F0F80 ED3E3F167F157CA215FC1700161C4A48C7FCA414035DA414075DA20107B512F0A3902600 0FE0C7FC5DA4141F5DA4143F92C8FCA45C147EA514FE5CA413015CA4495AA45C1307A25C 121E123F387F8F80A200FF90C9FC131E12FEEA7C3CEA7878EA1FF0EA07C0294C7CBA29> II<14E0EB03F8A21307A314F0EB01C090C7FC AB13F8EA03FEEA070F000E1380121C121812381230EA701F1260133F00E0130012C05BEA 007EA213FE5B1201A25B12035BA20007131813E01438000F133013C01470EB806014E014 C01381EB838038078700EA03FEEA00F815397EB71D>105 D107 D109 D<90390F8003F090391FE00FFC903939F03C1F903A70 F8700F80903AE0FDE007C09038C0FF80030013E00001491303018015F05CEA038113015C A2D800031407A25CA20107140FA24A14E0A2010F141F17C05CEE3F80131FEE7F004A137E 16FE013F5C6E485A4B5A6E485A90397F700F80DA383FC7FC90387E1FFCEC07E001FEC9FC A25BA21201A25BA21203A25B1207B512C0A32C3583A42A>112 D<02FC13C0903803FF01 90380F838390383F01C790397E00EF8049137F485A4848133F000715005B485A001F5C15 7E485AA2007F14FE90C75AA3481301485CA31403485CA314075D140F127C141F007E495A 003E137F381F01EF380F839F3903FF1F80EA00FC1300143F92C7FCA35C147EA314FE5C13 0190387FFFF0A322357DA425>I<3903E001F83907F807FE390E3C1E07391C3E381F3A18 3F703F800038EBE07F0030EBC0FF00705B00601500EC007E153CD8E07F90C7FCEAC07EA2 120013FE5BA312015BA312035BA312075BA3120F5BA3121F5B0007C9FC21267EA425>I< 14FF010313C090380F80F090383E00380178131C153C4913FC0001130113E0A33903F000 F06D13007F3801FFE014FC14FF6C14806D13C0011F13E013039038003FF014071403001E 1301127FA24814E0A348EB03C012F800E0EB07800070EB0F006C133E001E13F83807FFE0 000190C7FC1E267CA427>II<13F8D803FE1438D8070F147C000E6D13FC121C1218003814011230D8701F5C126015 03EAE03F00C001005B5BD8007E1307A201FE5C5B150F1201495CA2151F120349EC80C0A2 153F1681EE0180A2ED7F0303FF130012014A5B3A00F8079F0E90397C0E0F1C90393FFC07 F8903907F001F02A267EA430>I<01F8EB03C0D803FEEB07E0D8070F130F000E018013F0 121C12180038140700301403D8701F130112601500D8E03F14E000C090C7FC5BEA007E16 C013FE5B1501000115805B150316001203495B1506150E150C151C151815385D00015C6D 485A6C6C485AD97E0FC7FCEB1FFEEB07F024267EA428>I<01F816F0D803FE9138E001F8 D8070F903801F003000ED9800314FC121C12180038020713010030EDE000D8701F167C12 60030F143CD8E03F163800C001005B5BD8007E131F183001FE5C5B033F14700001176049 91C7FCA218E000034A14C049137E17011880170318005F03FE1306170E000101015C01F8 01BF5B3B00FC039F8070903A7E0F0FC0E0903A1FFC03FFC0902703F0007FC7FC36267EA4 3B>I<903907E001F090391FF807FC9039783E0E0F9039E01F1C1FD801C09038383F803A 03800FF07F0100EBE0FF5A000E4A1300000C157E021F133C001C4AC7FC1218A2C7123FA2 92C8FCA25CA2147EA214FEA24A130CA20101141C001E1518003F5BD87F81143801835C00 FF1560010714E03AFE0E7C01C0D87C1C495A2778383E0FC7FC391FF00FFC3907C003F029 267EA42F>I122 D E /Fm 31 115 df<1430147014E0EB01C01303EB0780EB0F00A2131E5BA25B13F85B12 015B1203A2485AA3485AA3121F90C7FCA25AA3123EA2127EA6127C12FCB3A2127C127EA6 123EA2123FA37EA27F120FA36C7EA36C7EA212017F12007F13787FA27F7FA2EB0780EB03 C01301EB00E0147014301462738226>0 D<12C07E12707E123C7E7EA26C7E6C7EA26C7E 7F12007F1378137CA27FA37FA31480130FA214C0A31307A214E0A6130314F0B3A214E013 07A614C0A2130FA31480A2131F1400A3133EA35BA2137813F85B12015B485AA2485A48C7 FCA2121E5A12385A5A5A14627C8226>I<12F0B3B3B2043674811C>12 D<160F161F163E167C16F8ED01F0ED03E0ED07C0150FED1F801600153E157E5D4A5A5D14 034A5A5D140F4A5AA24AC7FC143E147E5CA2495AA2495AA2495AA2130F5CA2495AA2133F 91C8FCA25B137E13FEA25B1201A25B1203A35B1207A35B120FA35BA2121FA45B123FA690 C9FC5AAA12FEB3AC127FAA7E7FA6121F7FA4120FA27FA312077FA312037FA312017FA212 007FA2137E137F7FA280131FA26D7EA2801307A26D7EA26D7EA26D7EA2147E143E143F6E 7EA26E7E1407816E7E1401816E7E157E153E811680ED0FC01507ED03E0ED01F0ED00F816 7C163E161F160F28C66E823D>18 D<12F07E127C7E7E6C7E6C7E6C7E7F6C7E1200137C13 7E7F6D7E130F806D7E1303806D7EA26D7E147C147E80A26E7EA26E7EA26E7EA2811403A2 6E7EA2811400A281157E157FA2811680A2151F16C0A3150F16E0A3150716F0A31503A216 F8A4150116FCA6150016FEAA167FB3AC16FEAA16FC1501A616F81503A416F0A21507A316 E0150FA316C0151FA31680153FA216005DA2157E15FE5DA214015DA24A5AA214075DA24A 5AA24A5AA24AC7FCA2147E147C14FC495AA2495A5C1307495A5C131F49C8FC137E137C5B 1201485A5B485A485A48C9FC123E5A5A5A28C67E823D>III<161E167EED01FE1507ED0FF8ED3FE0ED7FC0EDFF80913801FE004A 5A4A5A5D140F4A5A5D143F5D147F92C7FCA25C5CB3B3B3A313015CA3495AA213075C495A A2495A495A137F49C8FC485A485AEA07F0EA1FE0485AB4C9FC12FCA2B4FCEA3FC06C7EEA 07F0EA03FC6C7E6C7E6D7E133F6D7E6D7EA26D7E801303A26D7EA3801300B3B3B3A38080 A281143F81141F816E7E1407816E7E6E7E913800FF80ED7FC0ED3FE0ED0FF8ED07FE1501 ED007E161E27C675823E>26 D32 D<12F07E127C7E123F7E6C7E6C7E6C7E 7F12016C7E7F137E133E133F6D7E130F806D7EA26D7E80130180130080147E147F808114 1F81140F81140781A2140381140181A2140081A2157FA36F7EA382151FA282150FA38215 07A382A21503A282A31501A282A31500A382A482A21780A7163F17C0AC161F17E0B3B3A2 17C0163FAC1780167FA71700A25EA45EA31501A35EA21503A35EA21507A25EA3150F5EA3 151F5EA2153F5EA34BC7FCA315FEA25D1401A25D14035D1407A25D140F5D141F5D143F92 C8FC5C147E14FE5C13015C13035C495AA2495A5C131F49C9FC133E137E5B5B485A12035B 485A485A48CAFC5A123E5A5A5A2BF87E8242>I<177C17FCEE01F8A2EE03F0EE07E0EE0F C0A2EE1F80EE3F005E167E5E15015E15034B5A5E150F5E151F4B5AA24BC7FCA215FEA24A 5AA24A5AA24A5AA2140F5D141F5D143F5DA2147F92C8FC5CA25C13015C1303A25C1307A3 495AA3495AA3133F5CA3137F5CA313FF91C9FCA35A5BA31203A25BA31207A35BA3120FA4 5BA2121FA65BA2123FA85BA2127FAE5B12FFB3A62E95688149>48 D<12F87E127EA27E6C7E6C7EA26C7E6C7E7F12016C7E7F137E137F6D7E131F80130F806D 7EA26D7EA26D7EA26D7EA2147FA26E7EA281141F81140F811407A281140381A214018114 0081A28182A36F7EA36F7EA382150FA3821507A3821503A3821501A382A281A31780A316 7FA317C0A4163FA217E0A6161FA217F0A8160FA217F8AE160717FCB3A62E957E8149>I< B612F0A600FCC8FCB3B3B3B3B3B3B3B01C94668137>II<12FCB3B3B3B3B3B3B3B0B612F0A61C94668237>II<12FCB3B3B00634668037>I<12FCB3B3B006346A8037> II58 D60 D62 D64 DIII80 D88 D90 D<1B301B781BF8A2F201F0A2F203E0A2F207C0A2F2 0F80A2F21F00A21A3EA262A262A24F5AA24F5AA24F5AA262190FA24FC7FCA2193EA261A2 61A24E5AA24E5AA24E5AA24E5AA24EC8FCA2183EA260131001305E13F800014C5A1203D8 0FFC4B5A121DD838FE4B5A12F0D8407F4B5A12004DC9FC6D7E173E6D7E5F6D7E5FA26D6C 495AA26D6C495AA26D6C5C1607A26D6C495AA2027F49CAFCA291383F803EA25EEC1FC05E EC0FE0EDE1F0EC07F1EDF3E0A26EB45AA26E5BA26E90CBFCA25D157E157C15384D647883 53>112 D<1B301B78A21BF8A21BF0A21A01A21BE0A21A03A21BC0A31A07A21B80A21A0F A21B00A262A21A1EA21A3EA21A3CA21A7CA21A78A21AF8A262A31901A262A21903A262A2 1907A262A2190FA297C7FCA261A2191EA2193EA2193CA3197CA21978A219F8A261A21801 A261A21803A261A21807A261A2180FA296C8FCA360A2181EA2183EA2183CA2187C131018 781330017016F8A201F85E120117011203486C5EA2120D001D16031219D830FE5E127000 60160712C000405FEA007F170FA295C9FC6D7E5FA2171EA26D6C143EA2173CA2177C6D7E 1778A36D6C14F8A25FA216016D7E5FA21603A26D6C5CA21607A26D6C5CA2160FA294CAFC 147F5EA2161EEC3F80A2163EA2163CEC1FC0167CA21678A291380FE0F8A25EA2EC07F1A2 5EA215F3EC03FB5EA215FFA26E5BA48093CBFCA4157EA4157C153C15384DC8788353> 114 D E /Fn 90 127 df0 D<15E0A34A7EA34A7EA34A7EA34A7EA2140DEC1DFF14191418A24A7F157FA202607F153F A202C07F151FA2D901807F150FA2D903007F1507A20106801503A2010E80130C1501011C 80131881A24981167FA24981163FA24981161FA20001821203486C81D81FF84A7EB50107 B512E0A3333C7DBB3A>3 D11 DIII<133C137EA213FE1201EA03FC13F0EA07E0EA0FC0EA1F80EA 1E005A5A5A12C00F0F6FB92A>19 D<001C131C007F137F39FF80FF80A26D13C0A3007F13 7F001C131C00001300A40001130101801380A20003130301001300485B00061306000E13 0E485B485B485B006013601A197DB92A>34 D<141FEC7FC0903801F0E0903803C0600107 137090380F803090381F00381518A25BA2133E133F15381530A215705D5D140190381F83 8092CAFC1487148E02DC49B51280EB0FF85C4A9039003FF8000107ED0FC06E5D71C7FC6E 140E010F150CD91DFC141C01391518D970FE143801E015302601C07F1470D803805D0007 6D6C5BD80F00EBC00148011F5C4890380FE003003E6E48C8FC007E903807F8060203130E 00FE6E5A6E6C5A1400ED7F706C4B13036F5A6F7E6C6C6D6C5B7013066C6C496C130E6DD9 79FE5B281FF001F07F133C3C07F80FE03FC0F86CB539800FFFF0C69026FE000313C0D91F F0D9007FC7FC393E7DBB41>38 D<121C127FEAFF80A213C0A3127F121C1200A412011380 A2120313005A1206120E5A5A5A12600A1979B917>I<146014E0EB01C0EB0380EB070013 0E131E5B5BA25B485AA2485AA212075B120F90C7FCA25A121EA2123EA35AA65AB2127CA6 7EA3121EA2121F7EA27F12077F1203A26C7EA26C7E1378A27F7F130E7FEB0380EB01C0EB 00E01460135278BD20>I<12C07E12707E7E7E120F6C7E6C7EA26C7E6C7EA21378A2137C 133C133E131EA2131F7FA21480A3EB07C0A6EB03E0B2EB07C0A6EB0F80A31400A25B131E A2133E133C137C1378A25BA2485A485AA2485A48C7FC120E5A5A5A5A5A13527CBD20>I< 15301578B3A6007FB812F8B912FCA26C17F8C80078C8FCB3A6153036367BAF41>43 D<121C127FEAFF80A213C0A3127F121C1200A412011380A2120313005A1206120E5A5A5A 12600A19798817>II<121C127FEAFF80A5EA7F00121C09097988 17>I<150C151E153EA2153C157CA2157815F8A215F01401A215E01403A215C01407A215 80140FA215005CA2141E143EA2143C147CA2147814F8A25C1301A25C1303A2495AA25C13 0FA291C7FC5BA2131E133EA2133C137CA2137813F8A25B1201A25B1203A25B1207A25B12 0FA290C8FC5AA2121E123EA2123C127CA2127812F8A25A12601F537BBD2A>IIIII<1538A2157815F8A2140114 031407A2140F141F141B14331473146314C313011483EB030313071306130C131C131813 301370136013C01201EA038013005A120E120C5A123812305A12E0B712F8A3C73803F800 AB4A7E0103B512F8A325397EB82A>I<0006140CD80780133C9038F003F890B5FC5D5D15 8092C7FC14FC38067FE090C9FCABEB07F8EB3FFE9038780F803907E007E090388003F049 6C7E12066E7EC87EA28181A21680A4123E127F487EA490C71300485C12E000605C127000 30495A00385C6C1303001E495A6C6C485A3907E03F800001B5C7FC38007FFCEB1FE0213A 7CB72A>II<12301238123E003FB612E0A316C05A16 8016000070C712060060140E5D151800E01438485C5D5DC712014A5A92C7FC5C140E140C 141C5CA25CA214F0495AA21303A25C1307A2130FA3495AA3133FA5137FA96DC8FC131E23 3B7BB82A>III<121C127FEAFF80 A5EA7F00121CC7FCB2121C127FEAFF80A5EA7F00121C092479A317>I<121C127FEAFF80 A5EA7F00121CC7FCB2121C127F5A1380A4127F121D1201A412031300A25A1206A2120E5A 121812385A1260093479A317>I<007FB812F8B912FCA26C17F8CCFCAE007FB812F8B912 FCA26C17F836167B9F41>61 D<1538A3157CA315FEA34A7EA34A6C7EA202077FEC063FA2 020E7FEC0C1FA2021C7FEC180FA202387FEC3007A202707FEC6003A202C07F1501A2D901 807F81A249C77F167FA20106810107B6FCA24981010CC7121FA2496E7EA3496E7EA3496E 7EA213E0707E1201486C81D80FFC02071380B56C90B512FEA3373C7DBB3E>65 DI<913A01FF800180020FEBE003027F13F8903A01FF807E07903A03 FC000F0FD90FF0EB039F4948EB01DFD93F80EB00FF49C8127F01FE153F12014848151F48 48150FA248481507A2485A1703123F5B007F1601A35B00FF93C7FCAD127F6DED0180A312 3F7F001F160318006C7E5F6C7E17066C6C150E6C6C5D00001618017F15386D6C5CD91FE0 5C6D6CEB03C0D903FCEB0F80902701FF803FC7FC9039007FFFFC020F13F002011380313D 7BBA3C>III< B812F8A30001903880001F6C90C71201EE00FC177C173C171CA2170CA4170E1706A2ED01 80A21700A41503A21507151F91B5FCA3EC001F15071503A21501A692C8FCAD4813C0B612 C0A32F397DB836>III I<013FB512E0A39039001FFC00EC07F8B3B3A3123FEA7F80EAFFC0A44A5A1380D87F005B 0070131F6C5C6C495A6C49C7FC380781FC3801FFF038007F80233B7DB82B>III< B5933807FFF86E5DA20001F0FC002600DFC0ED1BF8A2D9CFE01533A3D9C7F01563A3D9C3 F815C3A2D9C1FCEC0183A3D9C0FEEC0303A2027F1406A36E6C130CA36E6C1318A26E6C13 30A36E6C1360A26E6C13C0A3913901FC0180A3913900FE0300A2ED7F06A3ED3F8CA2ED1F D8A3ED0FF0A3486C6D5A487ED80FFC6D48497EB500C00203B512F8A2ED018045397DB84C >I IIIIII<003FB812E0A3D9C003EB001F273E0001FE130348EE 01F00078160000701770A300601730A400E01738481718A4C71600B3B0913807FF80011F B612E0A335397DB83C>IIII<007FB590383FFFFCA3C601F801071380D97F E0D903FCC7FC013FEC01F06D6C5C5F6D6C5C6D6C13034CC8FC6D6C1306160E6D6C5B6DEB 8018163891387FC0306E6C5A16E06E6C5A91380FF18015FB6EB4C9FC5D14036E7EA26E7F 6F7EA24B7E15DF9138019FF09138038FF8150F91380607FC91380E03FE140C4A6C7EEC38 000230804A6D7E14E04A6D7E49486D7E130391C76C7E01066E7E130E010C6E7E011C1401 013C8101FE822607FF80010713E0B500E0013FEBFF80A339397EB83E>II<003FB7FCA39039FC0001FE01C0130349495A003EC7 FC003C4A5A5E0038141F00784A5A12704B5A5E006014FF4A90C7FCA24A5A5DC712074A5A A24A5A5D143F4A5AA24A5A92C8FC5B495AA2495A5C130F4948EB0180A2495A5C137F495A 16034890C7FC5B1203485AEE0700485A495C001F5D48485C5E4848495A49130FB8FCA329 397BB833>II<3901800180000313 033907000700000E130E485B0018131800381338003013300070137000601360A200E013 E0485BA400CE13CE39FF80FF806D13C0A3007F137FA2393F803F80390E000E001A1974B9 2A>II<13101338137C13FE487E38 03C780380783C0380F01E0381E00F04813780070131C48130E00401304170D77B92A>I< 121E123FEA7F80A2EAFFC0EA7F80A2EA3F00121E0A097AB717>IIIIIII<147E903803FF8090380FC1E0EB 1F8790383F0FF0137EA213FCA23901F803C091C7FCADB512FCA3D801F8C7FCB3AB487E38 7FFFF8A31C3B7FBA19>IIIII< EA03F012FFA3120F1203B1913801FFFCA39138007FC01600157C15705D4A5A4A5A4AC7FC 141E1438147814FC13F1EBF3FEEBF73F01FE7FEBF81F496C7E8114076E7E6E7E81140015 7E157F811680ED1FC0486CEB3FF0B500C0B5FCA3283A7EB92C>II<2703F00FF0EB1FE000FFD93FFCEB7FF8913AF0 3F01E07E903BF1C01F83803F3D0FF3800FC7001F802603F70013CE01FE14DC49D907F8EB 0FC0A2495CA3495CB3A3486C496CEB1FE0B500C1B50083B5FCA340257EA445>I<3903F0 0FF000FFEB3FFCECF03F9039F1C01F803A0FF3800FC03803F70013FE496D7EA25BA35BB3 A3486C497EB500C1B51280A329257EA42E>II<3903F01FE000FFEB7F F89038F1E07E9039F3801F803A07F7000FC0D803FEEB07E049EB03F04914F849130116FC 150016FEA3167FAA16FEA3ED01FCA26DEB03F816F06D13076DEB0FE001F614C09039F780 3F009038F1E07E9038F0FFF8EC1FC091C8FCAB487EB512C0A328357EA42E>II<3807 E01F00FFEB7FC09038E1E3E09038E387F0380FE707EA03E613EE9038EC03E09038FC0080 491300A45BB3A2487EB512F0A31C257EA421>II<1318A51338A31378A313F8120112031207001FB5 FCB6FCA2D801F8C7FCB215C0A93800FC011580EB7C03017E13006D5AEB0FFEEB01F81A34 7FB220>I IIIII<003FB512FCA2EB8003D83E0013F8003CEB07F00038EB0FE012300070 EB1FC0EC3F800060137F150014FE495AA2C6485A495AA2495A495A495AA290387F000613 FEA2485A485A0007140E5B4848130C4848131CA24848133C48C7127C48EB03FC90B5FCA2 1F247EA325>I124 D126 D E /Fo 28 118 df12 D<157815FC14031407141F14FF130F0007B5FCB6FCA214 7F13F0EAF800C7FCB3B3B3A6007FB712FEA52F4E76CD43>49 DI<91380FFFC091B512FC0107ECFF80011F15E090263FF8077F9026FF800113FC 4848C76C7ED803F86E7E491680D807FC8048B416C080486D15E0A4805CA36C17C06C5B6C 90C75AD801FC1680C9FC4C13005FA24C5A4B5B4B5B4B13C04B5BDBFFFEC7FC91B512F816 E016FCEEFF80DA000713E0030113F89238007FFE707E7013807013C018E07013F0A218F8 A27013FCA218FEA2EA03E0EA0FF8487E487E487EB57EA318FCA25E18F891C7FC6C17F049 5C6C4816E001F04A13C06C484A1380D80FF84A13006CB44A5A6CD9F0075BC690B612F06D 5D011F1580010302FCC7FCD9001F1380374F7ACD43>I<177C17FEA2160116031607160F A2161F163F167FA216FF5D5DA25D5DED1FBFED3F3F153E157C15FCEC01F815F0EC03E014 07EC0FC01580EC1F005C147E147C5C1301495A495A5C495A131F49C7FC133E5B13FC485A 5B485A1207485A485A90C8FC123E127E5ABA12C0A5C96C48C7FCAF020FB712C0A53A4F7C CE43>II68 D<932601FFFCEC01C0047FD9FFC013030307B600 F81307033F03FE131F92B8EA803F0203DAE003EBC07F020F01FCC7383FF0FF023F01E0EC 0FF94A01800203B5FC494848C9FC4901F8824949824949824949824949824990CA7E4948 83A2484983485B1B7F485B481A3FA24849181FA3485B1B0FA25AA298C8FC5CA2B5FCAE6C 057FB712E0A280A36C94C7003FEBC000A36C7FA36C7FA27E6C7FA26C7F6C7FA26D7E6D7F 6D7F6D6D5E6D7F6D01FC93B5FC6D13FF6D6C6D5C6E01F0EC07FB020F01FEEC1FF1020390 3AFFF001FFE0020091B6EAC07F033FEE001F030703FC1307DB007F02E01301040149CAFC 5B5479D26A>71 D73 D78 D82 D<91260FFF80130791B5 00F85B010702FF5B011FEDC03F49EDF07F9026FFFC006D5A4801E0EB0FFD4801800101B5 FC4848C87E48488149150F001F824981123F4981007F82A28412FF84A27FA26D82A27F7F 6D93C7FC14C06C13F014FF15F86CECFF8016FC6CEDFFC017F06C16FC6C16FF6C17C06C83 6C836D826D82010F821303010082021F16801400030F15C0ED007F040714E01600173F05 0F13F08383A200788200F882A3187FA27EA219E07EA26CEFFFC0A27F6D4B13806D17006D 5D01FC4B5A01FF4B5A02C04A5A02F8EC7FF0903B1FFFC003FFE0486C90B65AD8FC0393C7 FC48C66C14FC48010F14F048D9007F90C8FC3C5479D24B>I97 D<913801FFF8021FEBFF8091B612F00103 15FC010F9038C00FFE903A1FFE0001FFD97FFC491380D9FFF05B4817C048495B5C5A485B A2486F138091C7FC486F1300705A4892C8FC5BA312FFAD127F7FA27EA2EF03E06C7F1707 6C6D15C07E6E140F6CEE1F806C6DEC3F006C6D147ED97FFE5C6D6CEB03F8010F9038E01F F0010390B55A01001580023F49C7FC020113E033387CB63C>99 D<4DB47E0407B5FCA5EE 001F1707B3A4913801FFE0021F13FC91B6FC010315C7010F9038E03FE74990380007F7D9 7FFC0101B5FC49487F4849143F484980485B83485B5A91C8FC5AA3485AA412FFAC127FA3 6C7EA37EA26C7F5F6C6D5C7E6C6D5C6C6D49B5FC6D6C4914E0D93FFED90FEFEBFF80903A 0FFFC07FCF6D90B5128F0101ECFE0FD9003F13F8020301C049C7FC41547CD24B>I<9138 03FFC0023F13FC49B6FC010715C04901817F903A3FFC007FF849486D7E49486D7E484913 0F48496D7E48178048497F18C0488191C7FC4817E0A248815B18F0A212FFA490B8FCA318 E049CAFCA6127FA27F7EA218E06CEE01F06E14037E6C6DEC07E0A26C6DEC0FC06C6D141F 6C6DEC3F806D6CECFF00D91FFEEB03FE903A0FFFC03FF8010390B55A010015C0021F49C7 FC020113F034387CB63D>II 104 D<137F497E000313E0487FA2487FA76C5BA26C5BC613806DC7FC90C8FCADEB3FF0B5 FCA512017EB3B3A6B612E0A51B547BD325>I108 DII<913801 FFE0021F13FE91B612C0010315F0010F9038807FFC903A1FFC000FFED97FF86D6C7E4948 6D7F48496D7F48496D7F4A147F48834890C86C7EA24883A248486F7EA3007F1880A400FF 18C0AC007F1880A3003F18006D5DA26C5FA26C5F6E147F6C5F6C6D4A5A6C6D495B6C6D49 5B6D6C495BD93FFE011F90C7FC903A0FFF807FFC6D90B55A010015C0023F91C8FC020113 E03A387CB643>I<903A3FF001FFE0B5010F13FE033FEBFFC092B612F002F301017F913A F7F8007FFE0003D9FFE0EB1FFFC602806D7F92C76C7F4A824A6E7F4A6E7FA2717FA28518 7F85A4721380AC1A0060A36118FFA2615F616E4A5BA26E4A5B6E4A5B6F495B6F4990C7FC 03F0EBFFFC9126FBFE075B02F8B612E06F1480031F01FCC8FC030313C092CBFCB1B612F8 A5414D7BB54B>I<90397FE003FEB590380FFF80033F13E04B13F09238FE1FF89139E1F8 3FFC0003D9E3E013FEC6ECC07FECE78014EF150014EE02FEEB3FFC5CEE1FF8EE0FF04A90 C7FCA55CB3AAB612FCA52F367CB537>114 D<903903FFF00F013FEBFE1F90B7FC120348 EB003FD80FF81307D81FE0130148487F4980127F90C87EA24881A27FA27F01F091C7FC13 FCEBFFC06C13FF15F86C14FF16C06C15F06C816C816C81C681013F1580010F15C0130002 0714E0EC003F030713F015010078EC007F00F8153F161F7E160FA27E17E07E6D141F17C0 7F6DEC3F8001F8EC7F0001FEEB01FE9039FFC00FFC6DB55AD8FC1F14E0D8F807148048C6 01F8C7FC2C387CB635>I<143EA6147EA414FEA21301A313031307A2130F131F133F13FF 5A000F90B6FCB8FCA426003FFEC8FCB3A9EE07C0AB011FEC0F8080A26DEC1F0015806DEB C03E6DEBF0FC6DEBFFF86D6C5B021F5B020313802A4D7ECB34>II E /Fp 30 123 df<123C127EB4FCA21380A2127F123D1201A412031300A25A 1206120E120C121C5A5A126009177A8715>44 DI<123C127E12 FFA4127E123C08087A8715>I73 D82 D<90381FE00390387FFC0748B5FC3907F01F CF390F8003FF48C7FC003E80814880A200788000F880A46C80A27E92C7FC127F13C0EA3F F013FF6C13F06C13FF6C14C06C14F0C680013F7F01037F9038003FFF140302001380157F 153FED1FC0150F12C0A21507A37EA26CEC0F80A26C15006C5C6C143E6C147E01C05B39F1 FC03F800E0B512E0011F138026C003FEC7FC22377CB42B>I97 DII<153FEC0FFFA3EC00 7F81AEEB07F0EB3FFCEBFC0F3901F003BF3907E001FF48487E48487F8148C7FCA25A127E 12FEAA127E127FA27E6C6C5BA26C6C5B6C6C4813803A03F007BFFC3900F81E3FEB3FFCD9 0FE0130026357DB32B>I II<151F90391FC07F809039FFF8 E3C03901F07FC73907E03F033A0FC01F83809039800F8000001F80EB00074880A66C5CEB 800F000F5CEBC01F6C6C48C7FCEBF07C380EFFF8380C1FC0001CC9FCA3121EA2121F380F FFFEECFFC06C14F06C14FC4880381F0001003EEB007F4880ED1F8048140FA56C141F007C 15006C143E6C5C390FC001F83903F007E0C6B51280D91FFCC7FC22337EA126>III107 DI< 2703F01FE013FF00FF90267FF80313C0903BF1E07C0F03E0903BF3803E1C01F02807F700 3F387FD803FE1470496D486C7EA2495CA2495CB3486C496C487EB53BC7FFFE3FFFF0A33C 217EA041>I<3903F01FC000FFEB7FF09038F1E0FC9038F3807C3907F7007EEA03FE497F A25BA25BB3486CEB7F80B538C7FFFCA326217EA02B>II<3903F03F8000FFEBFFE09038F3C0F89038F7007ED807FE7F 6C48EB1F804914C049130F16E0ED07F0A3ED03F8A9150716F0A216E0150F16C06D131F6D EB3F80160001FF13FC9038F381F89038F1FFE0D9F07FC7FC91C8FCAA487EB512C0A32530 7EA02B>I<3803E07C38FFE1FF9038E38F809038E71FC0EA07EEEA03ECA29038FC0F8049 C7FCA35BB2487EB512E0A31A217FA01E>114 DI<1330A51370A313F0A21201A212031207381FFFFEB5FCA23803F000AF 1403A814073801F806A23800FC0EEB7E1CEB1FF8EB07E0182F7FAD1E>III II<3A7FFF807FF8A33A07F8001FC00003EC0F800001EC070015066C6C5BA26D131C 017E1318A26D5BA2EC8070011F1360ECC0E0010F5BA2903807E180A214F3010390C7FC14 FBEB01FEA26D5AA31478A21430A25CA214E05CA2495A1278D8FC03C8FCA21306130EEA70 1CEA7838EA1FF0EA0FC025307F9F29>I<003FB512F0A2EB000F003C14E00038EB1FC000 30EB3F800070137F1500006013FE495A13035CC6485A495AA2495A495A49C7FC153013FE 485A12035B48481370485A001F14604913E0485A387F000348130F90B5FCA21C207E9F22 >I E /Fq 7 117 df65 D97 DI<903807FF80013F13F090B512FC3903FE01FE 4848487EEA0FF8EA1FF0EA3FE0A2007F6D5A496C5A153000FF91C7FCA9127F7FA2003FEC 07807F6C6C130F000FEC1F00D807FE133E3903FF80FCC6EBFFF8013F13E0010790C7FC21 217DA027>I<3901F81F8000FFEB7FF0ECFFF89038F9E3FC9038FBC7FE380FFF876C1307 A213FEEC03FCEC01F8EC0060491300B1B512F0A41F217EA024>114 D<9038FFE1C0000713FF5A383F803F387E000F14075A14037EA26C6CC7FC13FCEBFFE06C 13FC806CEBFF80000F14C06C14E0C6FC010F13F0EB007F140F00F0130714037EA26C14E0 6C13076CEB0FC09038C01F8090B5120000F913FC38E03FE01C217DA023>I<133CA5137C A313FCA21201A212031207001FB51280B6FCA3D807FCC7FCB0EC03C0A79038FE07801203 3901FF0F006C13FEEB3FFCEB0FF01A2F7EAE22>I E /Fr 2 122 df<130C131EA50060EB01800078130739FC0C0FC0007FEB3F80393F8C7F003807CCF838 01FFE038007F80011EC7FCEB7F803801FFE03807CCF8383F8C7F397F0C3F8000FCEB0FC0 39781E078000601301000090C7FCA5130C1A1D7C9E23>3 D<1338137CA81338A7007C13 7CB512FEA3387C387C00001300A5137CB3A41338AD173D7CAE20>121 D E /Fs 18 117 df<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A312 011380120313005A1206120E5A5A5A12600B1D78891B>44 D78 D82 D<49B41303010FEBE007013F13F89039FE00FE0FD801F8131F D807E0EB079F49EB03DF48486DB4FC48C8FC4881003E81127E82127C00FC81A282A37E82 A27EA26C6C91C7FC7F7FEA3FF813FE381FFFE06C13FE6CEBFFE06C14FC6C14FF6C15C001 3F14F0010F80010180D9001F7F14019138001FFF03031380816F13C0167F163F161F17E0 00C0150FA31607A37EA36C16C0160F7E17806C151F6C16006C5D6D147ED8FBC05CD8F9F0 495AD8F07C495A90393FC00FE0D8E00FB51280010149C7FC39C0003FF02B487BC536>I< 003FB912F8A3903BF0001FF8001F01806D481303003EC7150048187C0078183CA2007018 1CA30060180CA5481806A5C81600B3B3A54B7EED7FFE49B77EA33F447DC346>I97 DI<167FED3FFF A315018182B3EC7F80903803FFF090380FC07C90383F000E017E1307496D5AD803F87F48 487F5B000F81485AA2485AA2127FA290C8FC5AAB7E7FA2123FA26C7EA2000F5D7F6C6C5B 00035C6C6C9038077F806C6C010E13C0013F011C13FE90380FC0F8903803FFE09026007F 0013002F467DC436>100 DI103 DII108 D<3901FC01FE00FF903807FFC091381E07F091383801F8000701707F00 03EBE0002601FDC07F5C01FF147F91C7FCA25BA35BB3A8486CECFF80B5D8F83F13FEA32F 2C7DAB36>110 DI<91387F8003903903FF E00790380FE07890393F801C0F90387E000E496D5AD803F8EB039F0007EC01BF4914FF48 487F121F5B003F81A2485AA348C8FCAB6C7EA3123F7F121F6D5C120F6D5B12076C6C5B6C 6C497E6C6C130E013F131C90380FC0F8903803FFE09038007F0091C7FCAEEEFF80033F13 FEA32F3F7DAB33>113 D<3903F803F000FFEB1FFCEC3C3EEC707F0007EBE0FF3803F9C0 00015B13FBEC007E153C01FF13005BA45BB3A748B4FCB512FEA3202C7DAB26>I<1306A5 130EA4131EA3133E137EA213FE12011207001FB512F0B6FCA2C648C7FCB3A4150CAA017E 131C017F1318A26D133890381F8030ECC070903807E0E0903801FFC09038007F001E3E7E BC26>116 D E /Ft 20 122 df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end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: a4 %%BeginPaperSize: a4 a4 %%EndPaperSize %%EndSetup %%Page: 1 1 1 0 bop 637 872 a Ft(Discrete)45 b(Kinetic)h(Mo)t(dels)d(for)g (Dynamical)i(Phase)1627 1054 y(T)-11 b(ransitions)1086 1295 y Fs(Rob)s(erto)32 b(Natalini)1811 1259 y Fr(\003)1840 1295 y Fs(,)h(and)g(Shao)s(qiang)e(T)-8 b(ang)2808 1259 y Fr(y)1778 1677 y Fq(Abstract)837 1807 y Fp(In)22 b(this)h(pap)r(er,)h (w)n(e)f(shall)h(describ)r(e)f(discrete)g(kinetic)g(mo)r(dels,)g(whic)n (h)g(serv)n(e)g(as)722 1899 y(a)f(no)n(v)n(el)f(and)h(systematic)f(w)n (a)n(y)h(to)f(regularized)i(a)f(mixed-t)n(yp)r(e)d(system)i(describing) 722 1990 y(the)j(dynamical)f(phase)i(transitions.)35 b(In)23 b(the)h(limit)g(of)h(zero)f(mean)g(free)g(path,)h(it)f(is)722 2081 y(exp)r(ected)g(to)g(pro)n(vide)g(abundan)n(t)f(reasonable)i (kinetic)g(relations)g(and)f(n)n(ucleation)722 2172 y(criteria)33 b(for)e(constructing)h(Riemann)e(solv)n(ers.)51 b(Some)30 b(particular)i(mo)r(dels)f(ha)n(v)n(e)722 2264 y(b)r(een)26 b(in)n(v)n(estigated)g(theoretically)g(and)g(n)n(umerically)-6 b(.)515 2538 y Fo(1)134 b(In)l(tro)t(duction)515 2720 y Fn(Phase)22 b(transitions)g(o)r(ccur)h(in)h(man)n(y)f(ph)n(ysical)f (systems,)i(suc)n(h)f(as)g(w)n(ater-v)-5 b(ap)r(or)21 b(mixture,)515 2820 y(liquid)33 b(crystal,)h(shap)r(e-memory)e(allo)n (y)-7 b(,)33 b(etc.)54 b([5,)33 b(17)o(,)h(20)o(,)f(29)o(].)54 b(Despite)34 b(of)f(the)h(e\013orts)515 2919 y(b)n(y)25 b(man)n(y)h(ingenious)f(scien)n(tists,)g(it)i(remains)e(an)g(in)n (terdisciplinary)g(c)n(hallenge)g(to)g(math-)515 3019 y(ematicians,)h(ph)n(ysicists,)h(as)f(w)n(ell)h(as)f(engineers.)35 b(There)27 b(are)f(t)n(w)n(o)g(main)h(asp)r(ects)f(for)h(the)515 3119 y(study:)34 b(the)22 b(constitutiv)n(e)f(theory)-7 b(,)22 b(and)f(the)h(dynamics.)34 b(In)22 b(this)g(pap)r(er)f(w)n(e)g (shall)g(concern)515 3218 y(only)j(with)h(the)g(dynamics,)g(namely)f (the)h(ev)n(olution)f(of)g(a)g(system)h(for)f(phase)g(transitions.)639 3318 y(Some)36 b(of)f(the)h(crucial)f(features,)i(also)e(di\016culties) h(for)f(phase)g(transitions)g(are)g(the)515 3418 y(sharp)21 b(free)g(in)n(terface,)i(non-lo)r(cal)e(in)n(teraction,)h(and)g (instabilit)n(y)-7 b(.)35 b(Mathematical)21 b(mo)r(dels)515 3517 y(re\015ecting)d(these)h(features)g(are)f(t)n(ypically)h(partial)f (di\013eren)n(tial)h(equations)f(of)h(mixed-t)n(yp)r(e.)515 3617 y(F)-7 b(or)28 b(instance,)g(the)h(w)n(ell-kno)n(wn)e(v)-5 b(an)28 b(der)g(W)-7 b(aals)28 b(gas)g(is)g(describ)r(ed)g(in)h(the)g (Lagrangian)515 3716 y(co)r(ordinates)d(b)n(y)1567 3828 y Fm(\032)1671 3894 y Fl(v)1714 3906 y Fk(t)1762 3894 y Fj(\000)18 b Fl(u)1893 3906 y Fk(x)2123 3894 y Fn(=)23 b(0)p Fl(;)1671 3994 y(u)1719 4006 y Fk(t)1766 3994 y Fn(+)18 b Fl(p)p Fn(\()p Fl(v)s Fn(\))1998 4006 y Fk(x)2123 3994 y Fn(=)23 b(0)p Fl(;)3273 3945 y Fn(\(1\))515 4144 y(where)38 b Fl(v)43 b Fn(is)38 b(the)i(densit)n(y)-7 b(,)42 b Fl(u)c Fn(the)i(v)n(elo)r(cit)n(y)-7 b(,)41 b(and)e Fl(p)p Fn(\()p Fl(v)s Fn(\))g(the)h(pressure.)69 b(The)39 b(function)515 4244 y Fl(p)p Fn(\()p Fl(v)s Fn(\))32 b(here)e(is)h(non-monotone,)g(hence)g(the)h(c)n (haracteristics)c Fl(\025)i Fn(=)e Fj(\006)2701 4173 y Fm(p)p 2784 4173 238 4 v 71 x Fj(\000)p Fl(p)2891 4220 y Fi(0)2914 4244 y Fn(\()p Fl(v)s Fn(\))k(migh)n(t)f(b)r(e)515 4343 y(either)g(pure)g(imaginary)e(or)i(real.)46 b(Accordingly)-7 b(,)31 b(the)h(system)f(\(1\))g(b)r(ecomes)g(elliptic)h(or)515 4443 y(h)n(yp)r(erb)r(olic.)p 515 4512 1146 4 v 606 4566 a Fh(\003)642 4589 y Fg(Istituto)23 b(p)r(er)f(le)g(Applicazione)h(del) f(Calcolo,)g(\\Mauro)g(Picone",)h(CNR,)e(Viale)g(del)h(P)n(oliclinico)g (137,)515 4668 y(Roma)h(00161,)h(Italy)-6 b(.)609 4726 y Fh(y)642 4750 y Fg(Departmen)n(t)22 b(of)g(Mec)n(hanics)i(and)e (Engineering)h(Science,)h(P)n(eking)f(Univ)n(ersit)n(y)-6 b(,)22 b(Beijing)g(100871,)h(P)-6 b(.)515 4828 y(R.)26 b(China.)39 b(This)26 b(researc)n(h)h(is)e(partially)h(supp)r(orted)i (b)n(y)f(an)f(Italian)i(CNR)e(p)r(ostdo)r(ctoral)h(gran)n(t)h(under)515 4907 y(con)n(tract)34 b(n)n(um)n(b)r(er)d(2110131,)36 b(Chinese)d(State)h(P)n(andeng)g(Pro)t(ject)f(\\Nonlinear)f(Science")i (and)f(NSF)n(C)515 4986 y(under)24 b(con)n(tract)h(No.)31 b(19771080.)1926 5255 y Fn(1)p eop %%Page: 2 2 2 1 bop 639 523 a Fn(As)22 b(is)g(w)n(ell-kno)n(wn,)g(the)g(Cauc)n(h)n (y)f(problem)g(for)g(suc)n(h)h(a)f(system)h(is)g(ill-p)r(osed.)34 b(Numer-)515 623 y(ical)23 b(sim)n(ulation)g(is)g(th)n(us)g(imp)r (ossible)h(due)f(to)h(the)g(immediate)f(blo)n(w-up.)35 b(T)-7 b(o)23 b(resolv)n(e)f(this)515 722 y(di\016cult)n(y)-7 b(,)35 b(appropriate)c(regularization)f(is)j(needed.)54 b(One)32 b(w)n(a)n(y)g(is)h(to)g(add)g(high)f(order)515 822 y(dissipation)27 b(terms.)38 b(As)28 b(viscosit)n(y)f(alone)g(in)i (the)f(momen)n(tum)g(equation)g(is)g(not)g(enough)515 922 y(to)23 b(con)n(trol)f(the)i(instabilit)n(y)f([15)o(],)i(further)e (dissipation)g(mec)n(hanisms)f(are)h(included,)h(suc)n(h)515 1021 y(as)j(capillarit)n(y)g([25)o(,)h(6)o(],)g(arti\014cial)f (viscosit)n(y)g(in)h(the)g(mass)g(equation)f([16)o(],)h(and)g(heat)g (dif-)515 1121 y(fusion)i([13)o(,)g(27)o(].)45 b(Ho)n(w)n(ev)n(er,)29 b(this)i(approac)n(h)d(is)i(quite)h(restrictiv)n(e,)e(as)h(w)n(e)g(do)g (not)g(kno)n(w)515 1220 y(ho)n(w)d(to)i(include)f(high-order)f(terms)h (to)g(mak)n(e)f(the)i(system)f(stable)g(and)g(ph)n(ysically)f(rea-)515 1320 y(sonable.)36 b(Moreo)n(v)n(er,)24 b(the)k(resolution)f(of)g (high-order)e(deriv)-5 b(ativ)n(es)27 b(usually)g(cause)f(tough)515 1420 y(n)n(umerical)g(di\016culties.)639 1519 y(Mean)n(while,)f(there)g (is)f(another)g(w)n(a)n(y)g(to)g(resolv)n(e)f(the)i(instabilit)n(y)-7 b(,)26 b(namely)e(to)h(sp)r(ecify)515 1619 y(a)34 b(Riemann)h(solv)n (er.)57 b(The)35 b(crucial)f(issue)g(is)h(to)f(iden)n(tify)i(the)f (class)f(of)g(discon)n(tin)n(uities)515 1719 y(that)i(is)f(allo)n(w)n (ed)g(\(admissible\).)61 b(In)36 b(the)h(curren)n(t)d(system)i(for)f (phase)h(transitions,)g(w)n(e)515 1818 y(should)j(distinguish)g(t)n(w)n (o)f(kinds)h(of)g(sharp)f(discon)n(tin)n(uities,)k(namely)c(the)i(sup)r (ersonic)515 1918 y(phase)21 b(b)r(oundary)g(and)g(the)h(subsonic)f (one.)35 b(The)21 b(sup)r(ersonic)g(phase)g(b)r(oundary)g(is)h(indeed) 515 2017 y(a)35 b(normal)f(sho)r(c)n(k)g(as)h(in)h(h)n(yp)r(erb)r(olic) e(systems.)60 b(Usually)35 b(an)g(en)n(trop)n(y)f(condition)h(\(e.g.) 515 2117 y(the)25 b(Lax)f(geometrical)g(en)n(trop)n(y)f(condition\))i (singles)f(out)h(the)g(ph)n(ysically)f(correct)g(sho)r(c)n(k.)515 2217 y(The)f(discon)n(tin)n(uit)n(y)f(that)h(demands)f(sp)r(ecial)h (care)e(is)i(the)g(subsonic)f(phase)h(b)r(oundary)-7 b(,)23 b(for)515 2316 y(whic)n(h)33 b(the)h(propagating)d(sp)r(eed)j (determined)f(b)n(y)h(the)f(Rankine-Hugoniot)g(relation)f(is)515 2416 y(smaller)24 b(than)i(the)g(sound)f(sp)r(eeds)h(at)f(b)r(oth)i (end-states.)35 b(It)26 b(can)f(b)r(e)h(sho)n(wn)f(that)h(normal)515 2516 y(en)n(trop)n(y)32 b(conditions)g(are)h(not)g(v)-5 b(alid)33 b(an)n(y)f(more.)53 b(T)-7 b(o)33 b(sp)r(ecify)g(a)g(Riemann) h(solv)n(er,)e(one)515 2615 y(either)27 b(generalizes)e(en)n(trop)n(y)h (conditions)h(arising)e(in)j(the)f(study)h(of)f(h)n(yp)r(erb)r(olic)g (systems)515 2715 y([11)o(,)41 b(14)o(,)f(24)o(],)k(or)c(in)n(v)n (estigates)f(the)i(limiting)g(b)r(eha)n(vior)e(of)h(the)h(systems)f (with)i(high-)515 2814 y(order)33 b(dissipations)i([25)o(].)59 b(Since)35 b(the)h(sup)r(ersonic)e(phase)h(b)r(oundaries)f(are)g(sub)5 b(ject)35 b(to)515 2914 y(normal)k(en)n(trop)n(y)g(condition,)44 b(essen)n(tially)39 b(what)i(is)f(done)g(here)g(can)g(b)r(e)h(regarded) e(as)515 3014 y(sp)r(ecifying)25 b(a)h(kinetic)g(relation)f(for)g (subsonic)g(phase)g(b)r(oundaries)g([1,)g(4,)h(7)o(,)g(9,)g(10)o(,)f (8,)h(21)o(].)515 3113 y(More)i(precisely)-7 b(,)30 b(a)f(kinetic)h (relation)f(con\014nes)g(the)h(t)n(w)n(o)f(end-states)g(across)e(a)j (subsonic)515 3213 y(phase)22 b(b)r(oundary)f(with)j(certain)d (relation,)i(whic)n(h)g(is)f(usually)g(algebraic.)33 b(In)23 b(certain)f(case)515 3313 y(when)32 b(m)n(ultiple)g(solutions)f (app)r(ear)g(according)f(to)i(the)g(prescrib)r(ed)f(kinetic)h (relation,)g(a)515 3412 y(n)n(ucleation)38 b(criterion)f(is)i(also)f (sp)r(eci\014ed)h(for)f(the)h(uniqueness.)70 b(The)39 b(idea)f(of)h(kinetic)515 3512 y(relation)31 b(broadens)h(the)g(viewp)r (oin)n(t)h(of)f(Riemann)h(solv)n(er)e(approac)n(h.)50 b(Nev)n(ertheless,)33 b(it)515 3611 y(can)h(hardly)g(reac)n(h)g(far,)i (unless)f(w)n(e)f(disco)n(v)n(ered)f(a)i(big)f(v)-5 b(ariet)n(y)34 b(of)h(reasonable)e(kinetic)515 3711 y(relations)26 b(and)i(n)n (ucleation)f(criteria.)639 3811 y(In)g(this)f(pap)r(er,)h(w)n(e)f (shall)g(describ)r(e)g(a)f(new)i(and)f(systematic)g(w)n(a)n(y)f(of)h (regularization,)515 3910 y(namely)c(the)h(discrete)f(kinetic)h(mo)r (dels)g(\(DKM's\).)35 b(A)23 b(DKM)g(is)g(a)f(semilinear)g(h)n(yp)r (erb)r(olic)515 4010 y(system)30 b(with)i(source)e(terms.)46 b(The)31 b(DKM's)g(are)f(easy)g(to)h(construct)g(and)g(to)f(sim)n (ulate.)515 4110 y(In)f(the)h(limit)g(of)f(zero)f(mean)h(free)g(path,)h (it)f(is)g(consisten)n(t)g(with)h(the)f(original)f(system)h(of)515 4209 y(mixed-t)n(yp)r(e)j(partial)g(di\013eren)n(tial)g(equations,)h (and)g(pro)n(vides)e(a)h(v)-5 b(ariet)n(y)32 b(of)g(reasonable)515 4309 y(kinetic)c(relations)e(and)h(n)n(ucleation)g(criteria.)639 4408 y(W)-7 b(e)29 b(shall)f(construct)f(general)g(discrete)h(kinetic)h (mo)r(dels)f(in)g(Sections)g(2.)39 b(In)28 b(Section)515 4508 y(3,)k(the)g(sc)n(heme)f(is)h(presen)n(ted.)48 b(Then)32 b(w)n(e)f(shall)h(describ)r(e)f(three)g(particular)g(examples,)515 4608 y(namely)i(Suliciu's)h(mo)r(del,)h(Jin-Xin's)e(relaxation)f(mo)r (del,)j(and)e(a)g(six-sp)r(eed)g(mo)r(del)h(in)515 4707 y(Section)27 b(4.)37 b(W)-7 b(e)28 b(conclude)f(b)n(y)g(some)g(general) g(remarks)e(in)j(Section)g(5.)1926 5255 y(2)p eop %%Page: 3 3 3 2 bop 515 523 a Fo(2)134 b(General)46 b(form)l(ulation)515 705 y Fn(Consider)26 b(phase)h(transitions)g(for:)1564 816 y Fm(\032)1668 883 y Fl(u)1716 895 y Fk(t)1763 883 y Fn(+)18 b Fl(v)1886 895 y Fk(x)2126 883 y Fn(=)23 b(0)p Fl(;)1668 982 y(v)1708 994 y Fk(t)1756 982 y Fn(+)18 b Fl(\033)s Fn(\()p Fl(u)p Fn(\))2001 994 y Fk(x)2126 982 y Fn(=)23 b(0)p Fl(;)3273 933 y Fn(\(2\))515 1127 y(where)37 b Fl(u)g Fn(is)h(the)g(strain,)h Fl(v)i Fn(the)d(sp)r(eed,)j (and)c Fl(\033)s Fn(\()p Fl(u)p Fn(\))i(the)f(stress.)66 b(The)37 b(non-monotone)515 1226 y(constitutiv)n(e)27 b(relation)g Fl(\033)s Fn(\()p Fl(u)p Fn(\))h(mak)n(es)f(the)h(system)f (of)g(mixed-t)n(yp)r(e.)639 1376 y(W)-7 b(e)20 b(shall)g(appro)n (ximate)e(the)i(solution)f(b)n(y)1981 1259 y Fm(\022)2084 1325 y Fl(u)2132 1295 y Fk(\017)2084 1425 y Fl(v)2127 1394 y Fk(\017)2205 1259 y Fm(\023)2289 1376 y Fn(=)2395 1355 y(~)2376 1376 y Fl(P)2459 1354 y Fn(~)2441 1376 y Fl(f)29 b Fn(where)2761 1354 y(~)2743 1376 y Fl(f)f Fn(solv)n(es)18 b(a)i(discrete)515 1525 y(kinetic)28 b(mo)r(del)f(\(DKM\))i(system)1177 1721 y(~)1159 1743 y Fl(f)1200 1755 y Fk(t)1247 1743 y Fn(+)1338 1722 y(~)1330 1743 y(\003)1406 1721 y(~)1388 1743 y Fl(f)1429 1755 y Fk(x)1493 1743 y Fn(=)1591 1686 y(1)p 1591 1724 42 4 v 1595 1800 a Fl(\017)1643 1743 y Fn(\()1706 1722 y(~)1675 1743 y Fl(M)8 b Fn(\()1815 1722 y(~)1796 1743 y Fl(P)1879 1721 y Fn(~)1862 1743 y Fl(f)g Fn(\))19 b Fj(\000)2063 1721 y Fn(~)2045 1743 y Fl(f)8 b Fn(\))p Fl(;)2348 1721 y Fn(~)2330 1743 y Fl(f)g(;)2447 1722 y Fn(~)2416 1743 y Fl(M)32 b Fj(2)23 b Fl(R)2671 1708 y Fk(k)2712 1743 y Fl(:)538 b Fn(\(3\))515 1929 y(Here)718 1908 y(~)710 1929 y(\003)23 b(=)f Fl(diag)s Fn(\()1072 1907 y(~)1069 1929 y Fl(\025)1117 1941 y Ff(1)1154 1929 y Fl(;)14 b Fj(\001)g(\001)g(\001)g Fl(;)1342 1907 y Fn(~)1339 1929 y Fl(\025)1387 1941 y Fk(k)1428 1929 y Fn(\),)1529 1908 y(~)1510 1929 y Fl(P)35 b Fn(=)23 b(\()7 b(~)-49 b Fl(p)1760 1941 y Fk(ij)1818 1929 y Fn(\))27 b(is)g(a)f(2)15 b Fj(\002)h Fl(k)30 b Fn(matrix,)c(and)2722 1908 y(~)2691 1929 y Fl(M)9 b Fn(\()2832 1908 y(~)2813 1929 y Fl(P)2896 1907 y Fn(~)2878 1929 y Fl(f)g Fn(\))26 b(is)h(the)g(lo)r(cal)515 2039 y(Maxw)n(ellian.)33 b(As)21 b(the)h(so-called)d(mean)i(free)g (path)g Fl(\017)i Fj(!)g Fn(0,)f(formally)2711 2017 y(~)2694 2039 y Fl(f)29 b Fn(tends)21 b(to)g(the)h(lo)r(cal)515 2138 y(Maxw)n(ellian,)g(and)g(w)n(e)h(exp)r(ect)f(the)h(resulting)f (appro)n(ximating)f(solution)h(w)n(ould)g(solv)n(e)f(\(2\))515 2238 y(at)27 b(the)h(leading)f(order.)36 b(Therefore,)26 b(naturally)h(come)g(the)h(compatibilit)n(y)f(conditions)1495 2518 y(~)1476 2539 y Fl(P)1572 2518 y Fn(~)1541 2539 y Fl(M)1645 2422 y Fm(\022)1747 2489 y Fl(w)1806 2501 y Ff(1)1747 2588 y Fl(w)1806 2600 y Ff(2)1886 2422 y Fm(\023)1970 2539 y Fn(=)2057 2422 y Fm(\022)2160 2489 y Fl(w)2219 2501 y Ff(1)2160 2588 y Fl(w)2219 2600 y Ff(2)2298 2422 y Fm(\023)2373 2539 y Fl(;)877 b Fn(\(4\))1336 2751 y(~)1318 2772 y Fl(P)1391 2751 y Fn(~)1382 2772 y(\003)1471 2751 y(~)1440 2772 y Fl(M)1544 2655 y Fm(\022)1646 2721 y Fl(w)1705 2733 y Ff(1)1646 2821 y Fl(w)1705 2833 y Ff(2)1784 2655 y Fm(\023)1869 2772 y Fn(=)1956 2655 y Fm(\022)2059 2721 y Fl(w)2118 2733 y Ff(2)2059 2821 y Fl(\033)s Fn(\()p Fl(w)2200 2833 y Ff(1)2238 2821 y Fn(\))2312 2655 y Fm(\023)2387 2772 y Fl(;)863 b Fn(\(5\))515 3000 y(for)27 b(an)n(y)g(\()p Fl(w)890 3012 y Ff(1)928 3000 y Fl(;)14 b(w)1024 3012 y Ff(2)1061 3000 y Fn(\))24 b Fj(2)f Fl(R)1259 2970 y Ff(2)1296 3000 y Fn(.)639 3099 y(The)28 b(general)e(form)h(of)h(DKM)g(\(3\))f(can)h(b)r(e)g(put)g(in)n (to)f(a)g(canonical)g(form.)515 3272 y Fe(Prop)s(osition)j(1)41 b Fd(The)31 b(system)e(\(3\))i(is)f(e)l(quivalent)g(to)1102 3378 y Fm(0)1102 3524 y(B)1102 3574 y(B)1102 3627 y(@)1217 3444 y Fl(f)1258 3456 y Ff(1+)1217 3544 y Fl(f)1258 3556 y Ff(2+)1217 3643 y Fl(f)1258 3655 y Ff(1)p Fi(\000)1217 3743 y Fl(f)1258 3755 y Ff(2)p Fi(\000)1388 3378 y Fm(1)1388 3524 y(C)1388 3574 y(C)1388 3627 y(A)1460 3777 y Fk(t)1508 3594 y Fj(\000)1591 3378 y Fm(0)1591 3524 y(B)1591 3574 y(B)1591 3627 y(@)1705 3444 y Fn(\003)1846 3544 y(\003)1987 3643 y Fj(\000)p Fn(\003)2192 3743 y Fj(\000)p Fn(\003)2356 3378 y Fm(1)2356 3524 y(C)2356 3574 y(C)2356 3627 y(A)2442 3378 y(0)2442 3524 y(B)2442 3574 y(B)2442 3627 y(@)2556 3444 y Fl(f)2597 3456 y Ff(1+)2556 3544 y Fl(f)2597 3556 y Ff(2+)2556 3643 y Fl(f)2597 3655 y Ff(1)p Fi(\000)2556 3743 y Fl(f)2597 3755 y Ff(2)p Fi(\000)2728 3378 y Fm(1)2728 3524 y(C)2728 3574 y(C)2728 3627 y(A)2800 3777 y Fk(x)955 4030 y Fn(=)1321 3974 y(1)p 1321 4011 V 1325 4087 a Fl(\017)1386 3813 y Fm(2)1386 3960 y(6)1386 4009 y(6)1386 4063 y(4)1442 3813 y(0)1442 3960 y(B)1442 4009 y(B)1442 4063 y(@)1556 3880 y Fl(M)1637 3892 y Ff(1+)1725 3880 y Fn(\()p Fl(u)1805 3850 y Fk(\017)1836 3880 y Fl(;)14 b(v)1916 3850 y Fk(\017)1948 3880 y Fn(\))1556 3980 y Fl(M)1637 3992 y Ff(2+)1725 3980 y Fn(\()p Fl(u)1805 3949 y Fk(\017)1836 3980 y Fl(;)g(v)1916 3949 y Fk(\017)1948 3980 y Fn(\))1556 4079 y Fl(M)1637 4091 y Ff(1)p Fi(\000)1725 4079 y Fn(\()p Fl(u)1805 4049 y Fk(\017)1837 4079 y Fl(;)g(v)1917 4049 y Fk(\017)1949 4079 y Fn(\))1556 4179 y Fl(M)1637 4191 y Ff(2)p Fi(\000)1725 4179 y Fn(\()p Fl(u)1805 4149 y Fk(\017)1837 4179 y Fl(;)g(v)1917 4149 y Fk(\017)1949 4179 y Fn(\))2023 3813 y Fm(1)2023 3960 y(C)2023 4009 y(C)2023 4063 y(A)2114 4030 y Fj(\000)2197 3813 y Fm(0)2197 3960 y(B)2197 4009 y(B)2197 4063 y(@)2311 3880 y Fl(f)2352 3892 y Ff(1+)2311 3980 y Fl(f)2352 3992 y Ff(2+)2311 4079 y Fl(f)2352 4091 y Ff(1)p Fi(\000)2311 4179 y Fl(f)2352 4191 y Ff(2)p Fi(\000)2482 3813 y Fm(1)2482 3960 y(C)2482 4009 y(C)2482 4063 y(A)2555 3813 y(3)2555 3960 y(7)2555 4009 y(7)2555 4063 y(5)2624 4030 y Fl(:)626 b Fn(\(6\))515 4352 y Fd(Her)l(e)33 b Fl(f)758 4364 y Ff(1)p Fi(\006)846 4352 y Fl(;)14 b(f)924 4364 y Ff(2)p Fi(\006)1013 4352 y Fl(;)g(M)1131 4364 y Ff(1)p Fi(\006)1220 4352 y Fl(;)g(M)1338 4364 y Ff(2)p Fi(\006)1459 4352 y Fd(ar)l(e)34 b(c)l(olumns)e(of)i(length)g Fl(N)9 b Fd(,)34 b Fn(\003)28 b(=)h Fl(diag)s Fn(\()p Fl(\025)2830 4364 y Ff(1)2867 4352 y Fl(;)14 b Fj(\001)g(\001)g(\001)g Fl(;)g(\025)3100 4364 y Fk(N)3163 4352 y Fn(\))33 b Fd(with)515 4452 y Fl(\025)563 4464 y Ff(1)627 4452 y Fl(>)26 b(\025)766 4464 y Ff(2)830 4452 y Fl(>)g Fj(\001)14 b(\001)g(\001)26 b Fl(>)g(\025)1183 4464 y Fk(N)1273 4452 y Fj(\025)f Fn(0)p Fd(.)44 b(Denote)31 b Fn(1)1803 4464 y Fk(N)1897 4452 y Fd(the)h(r)l(ow)g(ve)l(ctor)g(with)g Fl(N)40 b Fd(entries)32 b(identic)l(al)t(ly)515 4552 y Fn(1)p Fd(,)1035 4869 y Fl(P)j Fn(=)1211 4752 y Fm(\022)1313 4819 y Fn(1)1355 4831 y Fk(N)1501 4819 y Fn(0)145 b(1)1730 4831 y Fk(N)1876 4819 y Fn(0)1313 4918 y(0)h(1)1543 4930 y Fk(N)1688 4918 y Fn(0)g(1)1918 4930 y Fk(N)2022 4752 y Fm(\023)2097 4869 y Fl(;)183 b(f)32 b Fn(=)2464 4653 y Fm(0)2464 4799 y(B)2464 4848 y(B)2464 4902 y(@)2578 4719 y Fl(f)2619 4731 y Ff(1+)2578 4819 y Fl(f)2619 4831 y Ff(2+)2578 4918 y Fl(f)2619 4930 y Ff(1)p Fi(\000)2578 5018 y Fl(f)2619 5030 y Ff(2)p Fi(\000)2749 4653 y Fm(1)2749 4799 y(C)2749 4848 y(C)2749 4902 y(A)2836 4869 y Fl(:)1926 5255 y Fn(3)p eop %%Page: 4 4 4 3 bop 515 560 a Fd(The)30 b(primitive)i(variables)g(ar)l(e)e(r)l(e)l (c)l(over)l(e)l(d)g(fr)l(om)2076 443 y Fm(\022)2179 510 y Fl(u)2227 480 y Fk(\017)2179 609 y Fl(v)2222 579 y Fk(\017)2300 443 y Fm(\023)2384 560 y Fn(=)23 b Fl(P)12 b(f)d Fd(,)29 b(i.e.)1546 738 y Fl(u)1594 708 y Fk(\017)1648 738 y Fn(=)83 b(1)1838 750 y Fk(N)1900 738 y Fn(\()p Fl(f)1973 750 y Ff(1+)2080 738 y Fn(+)18 b Fl(f)2204 750 y Ff(1)p Fi(\000)2293 738 y Fn(\))p Fl(;)1546 838 y(v)1589 808 y Fk(\017)1644 838 y Fn(=)87 b(1)1838 850 y Fk(N)1900 838 y Fn(\()p Fl(f)1973 850 y Ff(2+)2080 838 y Fn(+)18 b Fl(f)2204 850 y Ff(2)p Fi(\000)2293 838 y Fn(\))p Fl(:)3273 789 y Fn(\(7\))515 1017 y Fd(Pr)l(o)l(of)132 b Fn(Without)32 b(loss)e(of)g(generalit)n(y)-7 b(,)31 b(assume)f(that)h(there)f(are)g Fl(N)39 b Fn(distinct)32 b(absolute)515 1116 y(v)-5 b(alues)29 b(of)h(propagating)d(sp)r(eeds)j (in)g(\(3\))g(as)f Fl(\025)1975 1128 y Ff(1)2039 1116 y Fl(>)d(\025)2178 1128 y Ff(2)2242 1116 y Fl(>)g Fj(\001)14 b(\001)g(\001)g Fl(;)g(\025)2529 1128 y Fk(N)2619 1116 y Fj(\025)26 b Fn(0.)42 b(Assume)30 b(further)515 1216 y(that)20 b(there)f(are)1040 1194 y(~)1022 1216 y Fl(f)1063 1228 y Ff(1)1100 1216 y Fl(;)14 b Fj(\001)g(\001)g(\001)g Fl(;)1302 1194 y Fn(~)1285 1216 y Fl(f)1326 1228 y Fk(k)1386 1216 y Fn(corresp)r(onding)k(to)h(sp)r(eed)h Fl(\025)2274 1228 y Ff(1)2312 1216 y Fn(,)h(and)2528 1194 y(~)2510 1216 y Fl(f)2551 1228 y Fk(k)q Ff(+1)2676 1216 y Fl(;)14 b Fj(\001)g(\001)g(\001)f Fl(;)2878 1194 y Fn(~)2860 1216 y Fl(f)2901 1228 y Fk(s)2956 1216 y Fn(corresp)r(ond-)515 1315 y(ing)27 b(to)h(sp)r(eed)f Fj(\000)p Fl(\025)1096 1327 y Ff(1)1134 1315 y Fn(.)37 b(Let)600 1451 y Fm(0)600 1597 y(B)600 1647 y(B)600 1700 y(@)714 1518 y Fl(f)755 1530 y Ff(1)p Fk(;)p Ff(1+)714 1617 y Fl(f)755 1629 y Ff(1)p Fk(;)p Ff(1)p Fi(\000)714 1717 y Fl(f)755 1729 y Ff(1)p Fk(;)p Ff(2+)714 1816 y Fl(f)755 1828 y Ff(1)p Fk(;)p Ff(2)p Fi(\000)938 1451 y Fm(1)938 1597 y(C)938 1647 y(C)938 1700 y(A)1034 1668 y Fn(=)1122 1426 y Fm(0)1122 1572 y(B)1122 1622 y(B)1122 1672 y(B)1122 1725 y(@)1236 1446 y(P)1323 1466 y Fk(k)1323 1533 y(i)p Ff(=1)1456 1508 y Fn(~)-49 b Fl(p)1491 1520 y Ff(1)p Fk(i)1569 1486 y Fn(~)1552 1508 y Fl(f)1593 1520 y Fk(i)1236 1553 y Fm(P)1323 1573 y Fk(s)1323 1640 y(i)p Ff(=1+)p Fk(k)1544 1615 y Fn(~)g Fl(p)1579 1627 y Ff(1)p Fk(i)1657 1593 y Fn(~)1639 1615 y Fl(f)1680 1627 y Fk(i)1236 1667 y Fm(P)1323 1687 y Fk(k)1323 1754 y(i)p Ff(=1)1456 1729 y Fn(~)g Fl(p)1491 1741 y Ff(2)p Fk(i)1569 1707 y Fn(~)1552 1729 y Fl(f)1593 1741 y Fk(i)1236 1774 y Fm(P)1323 1795 y Fk(s)1323 1861 y(i)p Ff(=1+)p Fk(k)1544 1836 y Fn(~)g Fl(p)1579 1848 y Ff(2)p Fk(i)1657 1815 y Fn(~)1639 1836 y Fl(f)1680 1848 y Fk(i)1749 1426 y Fm(1)1749 1572 y(C)1749 1622 y(C)1749 1672 y(C)1749 1725 y(A)1835 1668 y Fl(;)1955 1451 y Fm(0)1955 1597 y(B)1955 1647 y(B)1955 1700 y(@)2070 1518 y Fl(M)2151 1530 y Ff(1)p Fk(;)p Ff(1+)2070 1617 y Fl(M)2151 1629 y Ff(1)p Fk(;)p Ff(1)p Fi(\000)2070 1717 y Fl(M)2151 1729 y Ff(1)p Fk(;)p Ff(2+)2070 1816 y Fl(M)2151 1828 y Ff(1)p Fk(;)p Ff(2)p Fi(\000)2334 1451 y Fm(1)2334 1597 y(C)2334 1647 y(C)2334 1700 y(A)2429 1668 y Fn(=)2517 1426 y Fm(0)2517 1572 y(B)2517 1622 y(B)2517 1672 y(B)2517 1725 y(@)2631 1447 y(P)2719 1467 y Fk(k)2719 1534 y(i)p Ff(=1)2851 1509 y Fn(~)g Fl(p)2886 1521 y Ff(1)p Fk(i)2978 1488 y Fn(~)2947 1509 y Fl(M)3028 1521 y Fk(i)2631 1553 y Fm(P)2719 1573 y Fk(s)2719 1640 y(i)p Ff(=1+)p Fk(k)2939 1615 y Fn(~)g Fl(p)2974 1627 y Ff(1)p Fk(i)3065 1594 y Fn(~)3034 1615 y Fl(M)3115 1627 y Fk(i)2631 1667 y Fm(P)2719 1687 y Fk(k)2719 1754 y(i)p Ff(=1)2851 1729 y Fn(~)g Fl(p)2886 1741 y Ff(2)p Fk(i)2978 1708 y Fn(~)2947 1729 y Fl(M)3028 1741 y Fk(i)2631 1773 y Fm(P)2719 1794 y Fk(s)2719 1860 y(i)p Ff(=1+)p Fk(k)2939 1835 y Fn(~)g Fl(p)2974 1847 y Ff(2)p Fk(i)3065 1815 y Fn(~)3034 1835 y Fl(M)3115 1847 y Fk(i)3184 1426 y Fm(1)3184 1572 y(C)3184 1622 y(C)3184 1672 y(C)3184 1725 y(A)3271 1668 y Fl(:)515 2020 y Fn(Then)28 b Fl(f)773 2032 y Ff(1)p Fk(;)p Ff(1)p Fi(\006)914 2020 y Fl(;)14 b(f)992 2032 y Ff(1)p Fk(;)p Ff(2)p Fi(\006)1161 2020 y Fn(satisfy)1207 2238 y Fl(f)1248 2250 y Ff(1)p Fk(;)p Ff(1+;)p Fk(t)1451 2238 y Fn(+)k Fl(\025)1582 2250 y Ff(1)1620 2238 y Fl(f)1661 2250 y Ff(1)p Fk(;)p Ff(1+;)p Fk(x)1943 2238 y Fn(=)2041 2182 y(1)p 2041 2219 42 4 v 2045 2295 a Fl(\017)2092 2238 y Fn(\()p Fl(M)2205 2250 y Ff(1)p Fk(;)p Ff(1+)2364 2238 y Fj(\000)g Fl(f)2488 2250 y Ff(1)p Fk(;)p Ff(1+)2629 2238 y Fn(\))p Fl(;)1207 2404 y(f)1248 2416 y Ff(1)p Fk(;)p Ff(1)p Fi(\000)p Ff(;)p Fk(t)1452 2404 y Fj(\000)g Fl(\025)1583 2416 y Ff(1)1621 2404 y Fl(f)1662 2416 y Ff(1)p Fk(;)p Ff(1)p Fi(\000)p Ff(;)p Fk(x)1943 2404 y Fn(=)2041 2348 y(1)p 2041 2385 V 2045 2461 a Fl(\017)2092 2404 y Fn(\()p Fl(M)2205 2416 y Ff(1)p Fk(;)p Ff(1)p Fi(\000)2365 2404 y Fj(\000)g Fl(f)2489 2416 y Ff(1)p Fk(;)p Ff(1)p Fi(\000)2631 2404 y Fn(\))p Fl(;)1207 2571 y(f)1248 2583 y Ff(1)p Fk(;)p Ff(2+;)p Fk(t)1451 2571 y Fn(+)g Fl(\025)1582 2583 y Ff(1)1620 2571 y Fl(f)1661 2583 y Ff(1)p Fk(;)p Ff(2+;)p Fk(x)1943 2571 y Fn(=)2041 2515 y(1)p 2041 2552 V 2045 2628 a Fl(\017)2092 2571 y Fn(\()p Fl(M)2205 2583 y Ff(1)p Fk(;)p Ff(2+)2364 2571 y Fj(\000)g Fl(f)2488 2583 y Ff(1)p Fk(;)p Ff(2+)2629 2571 y Fn(\))p Fl(;)1207 2738 y(f)1248 2750 y Ff(1)p Fk(;)p Ff(2)p Fi(\000)p Ff(;)p Fk(t)1452 2738 y Fj(\000)g Fl(\025)1583 2750 y Ff(1)1621 2738 y Fl(f)1662 2750 y Ff(1)p Fk(;)p Ff(2)p Fi(\000)p Ff(;)p Fk(x)1943 2738 y Fn(=)2041 2681 y(1)p 2041 2719 V 2045 2795 a Fl(\017)2092 2738 y Fn(\()p Fl(M)2205 2750 y Ff(1)p Fk(;)p Ff(2)p Fi(\000)2365 2738 y Fj(\000)g Fl(f)2489 2750 y Ff(1)p Fk(;)p Ff(2)p Fi(\000)2631 2738 y Fn(\))p Fl(:)3273 2482 y Fn(\(8\))639 2930 y(Note)41 b(that)g(if)g(there)f(is)h (no)1603 2908 y(~)1585 2930 y Fl(f)1626 2942 y Fk(i)1694 2930 y Fn(corresp)r(onding)d(to)j Fl(\025)2403 2942 y Ff(1)2441 2930 y Fn(,)j(w)n(e)c(tak)n(e)g Fl(f)2877 2942 y Ff(1)p Fk(;)p Ff(1)p Fi(\006)3059 2930 y Fn(as)g(dum)n(b)515 3030 y(v)-5 b(ariables,)23 b(and)h(corresp)r(onding)f(lo)r(cal)g(Maxw)n (ellian)g(functions)i(are)e(set)h(to)g(b)r(e)h(zero.)35 b(P)n(er-)515 3129 y(forming)28 b(the)h(same)f(treatmen)n(t)h(with)g (other)f Fl(\025)2019 3141 y Fk(i)2047 3129 y Fn('s,)h(the)g(canonical) f(form)g(is)h(obtained.)40 b(If)515 3229 y(w)n(e)29 b(tak)n(e)h(the)g (initial)h(data)e(\(and)h(b)r(oundary)g(data\))g(accordingly)-7 b(,)29 b(the)h(t)n(w)n(o)f(systems)h(\(3\))515 3329 y(and)d(\(6\))h (are)f(equiv)-5 b(alen)n(t)27 b(in)h(the)g(sense)f(of)g(giving)g(the)h (same)f(appro)n(ximating)f(solution.)639 3528 y(As)41 b(the)g(discon)n(tin)n(uities)f(of)g(\(2\))h(are)e(the)i(limit)g(of)g (tra)n(v)n(eling)e(w)n(a)n(v)n(es)f(of)j(\(6\),)i(one)515 3627 y(requires)32 b(the)h(end-states)g(of)g(the)h(hetero)r(clinic)f (orbit)g(of)g(\(6\))g(satisfying)g(the)h(Rankine-)515 3727 y(Hugoniot)c(relation.)44 b(This)30 b(is)g(actually)g(true)g(for)g (our)g(DKM)g(under)h(the)f(compatibilit)n(y)515 3827 y(conditions.)515 4009 y Fe(Prop)s(osition)g(2)41 b Fd(Under)36 b(the)g(the)f(c)l(omp)l(atibility)j(c)l(onditions)f(\(4\)-\(5\),)h(the) d(end-states)515 4109 y(of)30 b(a)g(tr)l(aveling)h(wave)g(with)f(sp)l (e)l(e)l(d)g Fl(c)g Fd(to)f(\(6\))h(verify)i(the)e(R)l(ankine-Hugoniot) f(r)l(elation)1470 4220 y Fm(\032)1574 4287 y Fj(\000)p Fl(c)p Fn([)p Fl(u)1746 4257 y Fk(\017)1777 4287 y Fn(])18 b(+)g([)p Fl(v)1967 4257 y Fk(\017)1999 4287 y Fn(])198 b(=)23 b(0)p Fl(;)1574 4386 y Fj(\000)p Fl(c)p Fn([)p Fl(v)1741 4356 y Fk(\017)1772 4386 y Fn(])c(+)f([)p Fl(\033)s Fn(\()p Fl(u)2050 4356 y Fk(\017)2082 4386 y Fn(\)])83 b(=)23 b(0)p Fl(;)3273 4337 y Fn(\(9\))515 4537 y Fd(wher)l(e)30 b Fn([)p Fj(\001)p Fn(])23 b(=)g(\()107 b(lim)961 4586 y Fk(x)p Fi(\000)p Fk(ct)p Fi(!)p Ff(+)p Fi(1)1303 4537 y Fj(\000)120 b Fn(lim)1382 4586 y Fk(x)p Fi(\000)p Fk(ct)p Fi(!\0001)1710 4537 y Fn(\)\()p Fj(\001)p Fn(\))30 b Fd(is)h(the)e(jump)h(b)l(etwe)l(en)g(the)g(two)g(end-states.)515 4761 y(Pr)l(o)l(of)130 b Fn(T)-7 b(ak)n(e)27 b Fl(W)1116 4773 y Fk(i)1167 4761 y Fn(=)d Fl(P)12 b(diag)s Fn(\()p Fl(\025)1560 4731 y Fk(i)1560 4782 y Ff(1)1597 4761 y Fl(;)i Fj(\001)g(\001)g(\001)f Fl(;)h(\025)1829 4731 y Fk(i)1829 4784 y(N)1893 4761 y Fn(\))p Fl(f)9 b Fn(,)28 b(and)f Fl(M)2268 4773 y Fk(i)2319 4761 y Fn(=)d Fl(P)12 b(diag)s Fn(\()p Fl(\025)2712 4731 y Fk(i)2712 4782 y Ff(1)2749 4761 y Fl(;)i Fj(\001)g(\001)g(\001)f Fl(;)h(\025)2981 4731 y Fk(i)2981 4784 y(N)3044 4761 y Fn(\))p Fl(M)9 b Fn(,)29 b(then)515 4861 y(the)c(equations)f(for)g Fl(W)1226 4873 y Ff(0)1288 4861 y Fn(and)h Fl(W)1525 4873 y Ff(1)1587 4861 y Fn(are,)g(with)g(the)g(help)g(of)g(the)g(compatibilit)n(y)f (conditions,)1926 5255 y(4)p eop %%Page: 5 5 5 4 bop 1001 531 a Fm(8)1001 606 y(<)1001 756 y(:)1116 601 y Fl(W)1194 613 y Ff(0)p Fk(t)1275 601 y Fn(+)18 b Fl(W)1436 613 y Ff(1)p Fk(x)1535 601 y Fn(=)82 b Fl(W)1760 613 y Ff(0)1816 601 y Fj(\000)18 b Fl(M)1980 613 y Ff(0)2100 601 y Fn(=)23 b(0)p Fl(;)1116 751 y(W)1194 763 y Ff(1)p Fk(t)1275 751 y Fn(+)18 b Fl(W)1436 763 y Ff(2)p Fk(x)1535 751 y Fn(=)82 b Fl(W)1760 763 y Ff(1)1816 751 y Fj(\000)18 b Fl(M)1980 763 y Ff(1)2100 751 y Fn(=)23 b Fl(W)2266 763 y Ff(1)2322 751 y Fj(\000)2405 634 y Fm(\022)2508 701 y Fl(v)2551 671 y Fk(\017)2508 800 y Fl(\033)s Fn(\()p Fl(u)2638 770 y Fk(\017)2670 800 y Fn(\))2743 634 y Fm(\023)2818 751 y Fl(:)639 939 y Fn(F)-7 b(or)27 b(a)g(tra)n(v)n(eling)f(w)n(a)n(v) n(e)g Fl(f)9 b Fn(\()p Fl(x)19 b Fj(\000)f Fl(ct)p Fn(\),)28 b(w)n(e)f(ha)n(v)n(e)1643 1138 y Fj(\000)p Fl(cW)1834 1104 y Fi(0)1822 1159 y Ff(0)1877 1138 y Fn(+)18 b Fl(W)2050 1104 y Fi(0)2038 1159 y Ff(1)2099 1138 y Fn(=)23 b(0)p Fl(;)515 1276 y Fn(or)1615 1475 y Fj(\000)p Fl(cW)1794 1487 y Ff(0)1850 1475 y Fn(+)18 b Fl(W)2011 1487 y Ff(1)2071 1475 y Fn(=)23 b Fl(C)2218 1487 y Ff(1)2256 1475 y Fl(;)515 1613 y Fn(with)28 b Fl(C)763 1625 y Ff(1)828 1613 y Fn(a)f(constan)n(t) g(v)n(ector.)36 b(In)28 b(particular,)e(at)h(the)h(end-states,)f(w)n(e) h(ha)n(v)n(e)1075 1812 y(lim)969 1862 y Fk(x)p Fi(\000)p Fk(ct)p Fi(!\0001)1297 1812 y Fn([)p Fj(\000)p Fl(cW)1499 1824 y Ff(0)1555 1812 y Fn(+)18 b Fl(W)1716 1824 y Ff(1)1754 1812 y Fn(])23 b(=)129 b(lim)1888 1862 y Fk(x)p Fi(\000)p Fk(ct)p Fi(!)p Ff(+)p Fi(1)2215 1812 y Fn([)p Fj(\000)p Fl(cW)2417 1824 y Ff(0)2473 1812 y Fn(+)18 b Fl(W)2634 1824 y Ff(1)2671 1812 y Fn(])24 b(=)e Fl(C)2864 1824 y Ff(1)2902 1812 y Fl(:)639 1981 y Fn(Mean)n(while,)29 b(as)f(the)h(end-states)f(are)f(stationary)g(p)r(oin)n(ts,)i(the)g (second)f(equation)g(re-)515 2080 y(quires)1442 2309 y(lim)1336 2359 y Fk(x)p Fi(\000)p Fk(ct)p Fi(!\0061)1678 2192 y Fm(\024)1722 2309 y Fl(W)1800 2321 y Ff(1)1856 2309 y Fj(\000)1939 2192 y Fm(\022)2042 2258 y Fl(v)2085 2228 y Fk(\017)2042 2358 y Fl(\033)s Fn(\()p Fl(u)2172 2328 y Fk(\017)2204 2358 y Fn(\))2278 2192 y Fm(\023\025)2406 2309 y Fn(=)22 b(0)p Fl(:)515 2554 y Fn(Noticing)27 b(that)h Fl(W)1107 2566 y Ff(0)1168 2554 y Fn(=)1255 2437 y Fm(\022)1358 2504 y Fl(u)1406 2474 y Fk(\017)1358 2603 y Fl(v)1401 2573 y Fk(\017)1479 2437 y Fm(\023)1540 2554 y Fn(,)g(w)n(e)f(get)g (the)h(Rankine-Hugoniot)f(relation)f(\(9\))i(from)650 2825 y(lim)544 2875 y Fk(x)p Fi(\000)p Fk(ct)p Fi(!)p Ff(+)p Fi(1)885 2708 y Fm(\024)929 2825 y Fj(\000)p Fl(c)1044 2708 y Fm(\022)1146 2775 y Fl(u)1194 2744 y Fk(\017)1146 2874 y Fl(v)1189 2844 y Fk(\017)1267 2708 y Fm(\023)1346 2825 y Fn(+)1429 2708 y Fm(\022)1532 2775 y Fl(v)1575 2744 y Fk(\017)1532 2874 y Fl(\033)s Fn(\()p Fl(u)1662 2844 y Fk(\017)1694 2874 y Fn(\))1768 2708 y Fm(\023\025)1896 2825 y Fn(=)129 b(lim)1983 2875 y Fk(x)p Fi(\000)p Fk(ct)p Fi(!\0001)2326 2708 y Fm(\024)2370 2825 y Fj(\000)p Fl(c)2485 2708 y Fm(\022)2586 2775 y Fl(u)2634 2744 y Fk(\017)2586 2874 y Fl(v)2629 2844 y Fk(\017)2707 2708 y Fm(\023)2787 2825 y Fn(+)2870 2708 y Fm(\022)2973 2775 y Fl(v)3016 2744 y Fk(\017)2973 2874 y Fl(\033)s Fn(\()p Fl(u)3103 2844 y Fk(\017)3135 2874 y Fn(\))3208 2708 y Fm(\023)q(\025)3327 2825 y Fl(:)639 3088 y Fn(T)-7 b(o)37 b(mak)n(e)g(the)h(mo)r(dels)g (more)f(sp)r(eci\014c,)j(w)n(e)d(con\014ne)g(DKM's)h(with)g(the)g (follo)n(wing)515 3187 y(reasonable)25 b(assumptions.)36 b(In)28 b(the)g(text)f(follo)n(w)n(ed,)g(w)n(e)g(shall)g(drop)f(the)i (sup)r(er-scription)515 3287 y Fl(\017)f Fn(for)g(clarit)n(y)-7 b(.)616 3450 y(1.)41 b(\\Linear")24 b(lo)r(cal)h(Maxw)n(ellian:)35 b(the)26 b(lo)r(cal)f(Maxw)n(ellians)g(are)f(linear)h(com)n(binations) 722 3550 y(of)j Fl(u;)14 b(v)s(;)g(\033)s Fn(\()p Fl(u)p Fn(\).)616 3708 y(2.)41 b(Symmetry:)49 b(if)34 b(there)g(is)f(a)h(righ) n(t-going)d(tra)n(v)n(eling)h(w)n(a)n(v)n(e)g Fl(f)9 b Fn(\()p Fl(x)23 b Fj(\000)f Fl(ct)p Fn(\))34 b(connecting)722 3816 y(\()p Fl(u)802 3786 y Fi(\000)858 3816 y Fl(;)14 b(v)938 3786 y Fi(\000)994 3816 y Fn(\))23 b(to)f(\()p Fl(u)1225 3786 y Ff(+)1280 3816 y Fl(;)14 b(v)1360 3786 y Ff(+)1415 3816 y Fn(\),)24 b(then)f(there)f(exists)g(a)g(left-going)g (tra)n(v)n(eling)e(w)n(a)n(v)n(e)3089 3795 y(^)3071 3816 y Fl(f)9 b Fn(\()p Fl(x)f Fn(+)g Fl(ct)p Fn(\))722 3916 y(connecting)27 b(\()p Fl(u)1217 3886 y Fi(\000)1273 3916 y Fl(;)14 b Fj(\000)p Fl(v)1418 3886 y Fi(\000)1474 3916 y Fn(\))28 b(to)f(\()p Fl(u)1715 3886 y Ff(+)1770 3916 y Fl(;)14 b Fj(\000)p Fl(v)1915 3886 y Ff(+)1970 3916 y Fn(\),)28 b(and)g Fd(vic)l(e)i(versa)p Fn(.)515 4079 y Fe(Prop)s(osition)g(3)41 b Fd(If)30 b(we)g(take)g(the)g(lo)l(c)l (al)h(Maxwel)t(lian)h(as)1167 4407 y Fl(M)f Fn(=)1367 4190 y Fm(0)1367 4336 y(B)1367 4386 y(B)1367 4439 y(@)1513 4257 y Fl(m)1586 4269 y Ff(1)1771 4257 y Fl(m)1844 4269 y Ff(2)2029 4257 y Fl(m)2102 4269 y Ff(3)1513 4356 y Fl(m)1586 4368 y Ff(4)1771 4356 y Fl(m)1844 4368 y Ff(5)2029 4356 y Fl(m)2102 4368 y Ff(6)1513 4456 y Fl(m)1586 4468 y Ff(1)1739 4456 y Fj(\000)p Fl(m)1877 4468 y Ff(2)2029 4456 y Fl(m)2102 4468 y Ff(3)1481 4556 y Fj(\000)p Fl(m)1619 4568 y Ff(4)1771 4556 y Fl(m)1844 4568 y Ff(5)1997 4556 y Fj(\000)p Fl(m)2135 4568 y Ff(6)2213 4190 y Fm(1)2213 4336 y(C)2213 4386 y(C)2213 4439 y(A)2299 4240 y(0)2299 4390 y(@)2471 4307 y Fl(u)2473 4406 y(v)2413 4506 y(\033)s Fn(\()p Fl(u)p Fn(\))2617 4240 y Fm(1)2617 4390 y(A)2704 4407 y Fl(;)504 b Fn(\(10\))515 4694 y Fd(then)31 b(the)g(system)g (\(6\))g(p)l(ossesses)h(the)g(symmetry)f(describ)l(e)l(d)i(ab)l(ove.)44 b(The)32 b(c)l(omp)l(atibility)515 4794 y(c)l(onditions)e(then)g(b)l(e) l(c)l(ome)566 4985 y Fn(1)608 4997 y Fk(N)671 4985 y Fl(m)744 4997 y Ff(1)804 4985 y Fn(=)22 b(1)933 4997 y Fk(N)996 4985 y Fl(m)1069 4997 y Ff(5)1129 4985 y Fn(=)h(1)1259 4997 y Fk(N)1321 4985 y Fn(\003)1379 4997 y Ff(1)1416 4985 y Fl(m)1489 4997 y Ff(2)1549 4985 y Fn(=)g(1)1679 4997 y Fk(N)1741 4985 y Fn(\003)1799 4997 y Ff(1)1836 4985 y Fl(m)1909 4997 y Ff(6)1970 4985 y Fn(=)f(0)p Fl(:)p Fn(5)p Fl(;)183 b Fn(1)2412 4997 y Fk(N)2474 4985 y Fl(m)2547 4997 y Ff(3)2608 4985 y Fn(=)22 b(1)2737 4997 y Fk(N)2800 4985 y Fn(\003)2858 4997 y Ff(1)2895 4985 y Fl(m)2968 4997 y Ff(4)3028 4985 y Fn(=)g(0)p Fl(:)51 b Fn(\(11\))1926 5255 y(5)p eop %%Page: 6 6 6 5 bop 515 554 a Fd(Pr)l(o)l(of)129 b Fn(The)28 b(tra)n(v)n(eling)e(w) n(a)n(v)n(e)g Fl(f)9 b Fn(\()p Fl(x)18 b Fj(\000)g Fl(ct)p Fn(\))28 b(is)g(the)g(solution)f(to)g(\()2584 524 y Fi(0)2631 554 y Fn(=)c Fl(\017)2902 498 y(d)p 2763 535 323 4 v 2763 611 a(d)p Fn(\()p Fl(x)c Fj(\000)f Fl(ct)p Fn(\))3095 554 y(\))987 732 y Fj(\000)p Fl(cf)1138 701 y Fi(0)1129 752 y Ff(1+)1235 732 y Fn(+)g(\003)p Fl(f)1426 701 y Fi(0)1417 752 y Ff(1+)1589 732 y Fn(=)83 b(\()p Fl(m)1842 744 y Ff(1)1879 732 y Fl(u)18 b Fn(+)g Fl(m)2101 744 y Ff(2)2138 732 y Fl(v)k Fn(+)c Fl(m)2356 744 y Ff(3)2393 732 y Fl(\033)s Fn(\()p Fl(u)p Fn(\)\))h Fj(\000)f Fl(f)2730 744 y Ff(1+)2818 732 y Fl(;)987 831 y Fj(\000)p Fl(cf)1138 801 y Fi(0)1129 852 y Ff(1)p Fi(\000)1236 831 y Fj(\000)g Fn(\003)p Fl(f)1427 801 y Fi(0)1418 852 y Ff(1)p Fi(\000)1589 831 y Fn(=)83 b(\()p Fl(m)1842 843 y Ff(1)1879 831 y Fl(u)18 b Fj(\000)g Fl(m)2101 843 y Ff(2)2138 831 y Fl(v)k Fn(+)c Fl(m)2356 843 y Ff(3)2393 831 y Fl(\033)s Fn(\()p Fl(u)p Fn(\)\))h Fj(\000)f Fl(f)2730 843 y Ff(1)p Fi(\000)2819 831 y Fl(;)987 931 y Fj(\000)p Fl(cf)1138 901 y Fi(0)1129 951 y Ff(2+)1235 931 y Fn(+)g(\003)p Fl(f)1426 901 y Fi(0)1417 951 y Ff(2+)1589 931 y Fn(=)83 b(\()p Fl(m)1842 943 y Ff(4)1879 931 y Fl(u)18 b Fn(+)g Fl(m)2101 943 y Ff(5)2138 931 y Fl(v)k Fn(+)c Fl(m)2356 943 y Ff(6)2393 931 y Fl(\033)s Fn(\()p Fl(u)p Fn(\)\))h Fj(\000)f Fl(f)2730 943 y Ff(2+)2818 931 y Fl(;)987 1030 y Fj(\000)p Fl(cf)1138 1000 y Fi(0)1129 1051 y Ff(2)p Fi(\000)1236 1030 y Fj(\000)g Fn(\003)p Fl(f)1427 1000 y Fi(0)1418 1051 y Ff(2)p Fi(\000)1589 1030 y Fn(=)83 b(\()p Fj(\000)p Fl(m)1907 1042 y Ff(4)1944 1030 y Fl(u)18 b Fn(+)g Fl(m)2166 1042 y Ff(5)2203 1030 y Fl(v)k Fj(\000)c Fl(m)2421 1042 y Ff(6)2458 1030 y Fl(\033)s Fn(\()p Fl(u)p Fn(\)\))h Fj(\000)f Fl(f)2795 1042 y Ff(2)p Fi(\000)2884 1030 y Fl(;)3231 882 y Fn(\(12\))515 1170 y(and)1469 1320 y(lim)1362 1370 y Fk(x)p Fi(\000)p Fk(ct)p Fi(!\0001)1705 1320 y Fn(1)1747 1332 y Fk(N)1809 1320 y Fn(\()p Fl(f)1882 1332 y Ff(1+)1989 1320 y Fn(+)g Fl(f)2113 1332 y Ff(1)p Fi(\000)2202 1320 y Fn(\))83 b(=)23 b Fl(u)2453 1290 y Fi(\000)2508 1320 y Fl(;)1469 1455 y Fn(lim)1362 1505 y Fk(x)p Fi(\000)p Fk(ct)p Fi(!\0001)1705 1455 y Fn(1)1747 1467 y Fk(N)1809 1455 y Fn(\()p Fl(f)1882 1467 y Ff(2+)1989 1455 y Fn(+)18 b Fl(f)2113 1467 y Ff(2)p Fi(\000)2202 1455 y Fn(\))83 b(=)23 b Fl(v)2448 1425 y Fi(\000)2504 1455 y Fl(;)1469 1590 y Fn(lim)1362 1639 y Fk(x)p Fi(\000)p Fk(ct)p Fi(!)p Ff(+)p Fi(1)1704 1590 y Fn(1)1746 1602 y Fk(N)1808 1590 y Fn(\()p Fl(f)1881 1602 y Ff(1+)1988 1590 y Fn(+)18 b Fl(f)2112 1602 y Ff(1)p Fi(\000)2201 1590 y Fn(\))84 b(=)23 b Fl(u)2453 1559 y Ff(+)2507 1590 y Fl(;)1469 1724 y Fn(lim)1362 1774 y Fk(x)p Fi(\000)p Fk(ct)p Fi(!)p Ff(+)p Fi(1)1704 1724 y Fn(1)1746 1736 y Fk(N)1808 1724 y Fn(\()p Fl(f)1881 1736 y Ff(2+)1988 1724 y Fn(+)18 b Fl(f)2112 1736 y Ff(2)p Fi(\000)2201 1724 y Fn(\))84 b(=)23 b Fl(v)2448 1694 y Ff(+)2503 1724 y Fl(:)639 1950 y Fn(Then)c(\()897 1928 y(^)879 1950 y Fl(f)920 1962 y Ff(1+)1008 1950 y Fn(\()p Fl(\030)t Fn(\))p Fl(;)1167 1928 y Fn(^)1149 1950 y Fl(f)1190 1962 y Ff(1)p Fi(\000)1279 1950 y Fn(\()p Fl(\030)t Fn(\))p Fl(;)1439 1928 y Fn(^)1420 1950 y Fl(f)1461 1962 y Ff(2+)1550 1950 y Fn(\()p Fl(\030)t Fn(\))p Fl(;)1709 1928 y Fn(^)1691 1950 y Fl(f)1732 1962 y Ff(2)p Fi(\000)1821 1950 y Fn(\()p Fl(\030)t Fn(\)\))24 b(=)f(\()p Fl(f)2142 1962 y Ff(1)p Fi(\000)2231 1950 y Fn(\()p Fj(\000)p Fl(\030)t Fn(\))p Fl(;)14 b(f)2478 1962 y Ff(1+)2566 1950 y Fn(\()p Fj(\000)p Fl(\030)t Fn(\))p Fl(;)g Fj(\000)p Fl(f)2878 1962 y Ff(2)p Fi(\000)2967 1950 y Fn(\()p Fj(\000)p Fl(\030)t Fn(\))p Fl(;)g Fj(\000)p Fl(f)3279 1962 y Ff(2+)3366 1950 y Fn(\()p Fj(\000)p Fl(\030)t Fn(\)\))515 2093 y(solv)n(es)26 b(\(`)d(=)g Fl(\017)1100 2036 y(d)p 961 2073 V 961 2150 a(d)p Fn(\()p Fl(x)c Fn(+)f Fl(ct)p Fn(\))1293 2093 y(\))996 2280 y Fl(c)1050 2258 y Fn(^)1032 2280 y Fl(f)1073 2292 y Ff(1+)1161 2280 y Fn(`)g(+)g(\003)1361 2258 y(^)1343 2280 y Fl(f)1384 2292 y Ff(1+)1472 2280 y Fn(`)85 b(=)e(\()p Fl(m)1833 2292 y Ff(1)1875 2280 y Fn(^)-47 b Fl(u)18 b Fn(+)g Fl(m)2092 2292 y Ff(2)2132 2280 y Fn(^)-45 b Fl(v)22 b Fn(+)c Fl(m)2347 2292 y Ff(3)2384 2280 y Fl(\033)s Fn(\()5 b(^)-47 b Fl(u)p Fn(\)\))19 b Fj(\000)2698 2258 y Fn(^)2680 2280 y Fl(f)2721 2292 y Ff(1+)2809 2280 y Fl(;)996 2390 y(c)1050 2368 y Fn(^)1032 2390 y Fl(f)1073 2402 y Ff(1)p Fi(\000)1162 2390 y Fn(`)f Fj(\000)g Fn(\003)1362 2368 y(^)1344 2390 y Fl(f)1385 2402 y Ff(1)p Fi(\000)1474 2390 y Fn(`)83 b(=)g(\()p Fl(m)1833 2402 y Ff(1)1875 2390 y Fn(^)-47 b Fl(u)18 b Fj(\000)g Fl(m)2092 2402 y Ff(2)2132 2390 y Fn(^)-45 b Fl(v)22 b Fn(+)c Fl(m)2347 2402 y Ff(3)2384 2390 y Fl(\033)s Fn(\()5 b(^)-47 b Fl(u)p Fn(\)\))19 b Fj(\000)2698 2368 y Fn(^)2680 2390 y Fl(f)2721 2402 y Ff(1)p Fi(\000)2810 2390 y Fl(;)996 2499 y(c)1050 2477 y Fn(^)1032 2499 y Fl(f)1073 2511 y Ff(2+)1161 2499 y Fn(`)f(+)g(\003)1361 2477 y(^)1343 2499 y Fl(f)1384 2511 y Ff(2+)1472 2499 y Fn(`)85 b(=)e(\()p Fl(m)1833 2511 y Ff(4)1875 2499 y Fn(^)-47 b Fl(u)18 b Fn(+)g Fl(m)2092 2511 y Ff(5)2132 2499 y Fn(^)-45 b Fl(v)22 b Fn(+)c Fl(m)2347 2511 y Ff(6)2384 2499 y Fl(\033)s Fn(\()5 b(^)-47 b Fl(u)p Fn(\)\))19 b Fj(\000)2698 2477 y Fn(^)2680 2499 y Fl(f)2721 2511 y Ff(2+)2809 2499 y Fl(;)996 2608 y(c)1050 2586 y Fn(^)1032 2608 y Fl(f)1073 2620 y Ff(2)p Fi(\000)1162 2608 y Fn(`)f Fj(\000)g Fn(\003)1362 2586 y(^)1344 2608 y Fl(f)1385 2620 y Ff(2)p Fi(\000)1474 2608 y Fn(`)83 b(=)g(\()p Fj(\000)p Fl(m)1898 2620 y Ff(4)1940 2608 y Fn(^)-48 b Fl(u)18 b Fn(+)g Fl(m)2156 2620 y Ff(5)2197 2608 y Fn(^)-45 b Fl(v)21 b Fj(\000)d Fl(m)2411 2620 y Ff(6)2448 2608 y Fl(\033)s Fn(\()5 b(^)-47 b Fl(u)q Fn(\)\))19 b Fj(\000)2763 2586 y Fn(^)2745 2608 y Fl(f)2786 2620 y Ff(2)p Fi(\000)2875 2608 y Fl(;)3231 2440 y Fn(\(13\))515 2748 y(and)1439 2908 y(lim)1333 2958 y Fk(x)p Ff(+)p Fk(ct)p Fi(!\0001)1674 2908 y Fn(1)1716 2920 y Fk(N)1779 2908 y Fn(\()1829 2886 y(^)1811 2908 y Fl(f)1852 2920 y Ff(1+)1958 2908 y Fn(+)2059 2886 y(^)2041 2908 y Fl(f)2082 2920 y Ff(1)p Fi(\000)2171 2908 y Fn(\))83 b(=)23 b Fl(u)2422 2878 y Ff(+)2477 2908 y Fl(;)1439 3053 y Fn(lim)1333 3102 y Fk(x)p Ff(+)p Fk(ct)p Fi(!\0001)1674 3053 y Fn(1)1716 3065 y Fk(N)1779 3053 y Fn(\()1829 3031 y(^)1811 3053 y Fl(f)1852 3065 y Ff(2+)1958 3053 y Fn(+)2059 3031 y(^)2041 3053 y Fl(f)2082 3065 y Ff(2)p Fi(\000)2171 3053 y Fn(\))83 b(=)23 b Fj(\000)p Fl(v)2482 3022 y Ff(+)2537 3053 y Fl(;)1438 3197 y Fn(lim)1333 3247 y Fk(x)p Ff(+)p Fk(ct)p Fi(!)p Ff(+)p Fi(1)1673 3197 y Fn(1)1715 3209 y Fk(N)1778 3197 y Fn(\()1828 3175 y(^)1810 3197 y Fl(f)1851 3209 y Ff(1+)1957 3197 y Fn(+)2058 3175 y(^)2040 3197 y Fl(f)2081 3209 y Ff(1)p Fi(\000)2170 3197 y Fn(\))84 b(=)23 b Fl(u)2422 3167 y Fi(\000)2478 3197 y Fl(;)1438 3342 y Fn(lim)1333 3392 y Fk(x)p Ff(+)p Fk(ct)p Fi(!)p Ff(+)p Fi(1)1673 3342 y Fn(1)1715 3354 y Fk(N)1778 3342 y Fn(\()1828 3320 y(^)1810 3342 y Fl(f)1851 3354 y Ff(2+)1957 3342 y Fn(+)2058 3320 y(^)2040 3342 y Fl(f)2081 3354 y Ff(2)p Fi(\000)2170 3342 y Fn(\))84 b(=)23 b Fj(\000)p Fl(v)2482 3312 y Fi(\000)2538 3342 y Fl(:)639 3550 y Fn(Substituting)30 b(the)f(particular)e(form)h (of)g(lo)r(cal)g(Maxw)n(ellians)f(\(10\))i(in)n(to)f(\(4\))h(and)f (\(5\),)515 3649 y(w)n(e)f(obtain)g(the)h(compatibilit)n(y)g (conditions)f(as)g(\(11\).)639 3849 y(As)h(a)f(summary)-7 b(,)27 b(a)g(DKM)h(under)f(our)g(consideration)f(tak)n(es)h(the)h(form) 1102 4032 y Fm(0)1102 4178 y(B)1102 4228 y(B)1102 4281 y(@)1217 4099 y Fl(f)1258 4111 y Ff(1+)1217 4198 y Fl(f)1258 4210 y Ff(2+)1217 4298 y Fl(f)1258 4310 y Ff(1)p Fi(\000)1217 4398 y Fl(f)1258 4410 y Ff(2)p Fi(\000)1388 4032 y Fm(1)1388 4178 y(C)1388 4228 y(C)1388 4281 y(A)1460 4432 y Fk(t)1508 4249 y Fj(\000)1591 4032 y Fm(0)1591 4178 y(B)1591 4228 y(B)1591 4281 y(@)1705 4099 y Fn(\003)1846 4198 y(\003)1987 4298 y Fj(\000)p Fn(\003)2192 4398 y Fj(\000)p Fn(\003)2356 4032 y Fm(1)2356 4178 y(C)2356 4228 y(C)2356 4281 y(A)2442 4032 y(0)2442 4178 y(B)2442 4228 y(B)2442 4281 y(@)2556 4099 y Fl(f)2597 4111 y Ff(1+)2556 4198 y Fl(f)2597 4210 y Ff(2+)2556 4298 y Fl(f)2597 4310 y Ff(1)p Fi(\000)2556 4398 y Fl(f)2597 4410 y Ff(2)p Fi(\000)2728 4032 y Fm(1)2728 4178 y(C)2728 4228 y(C)2728 4281 y(A)2800 4432 y Fk(x)951 4685 y Fn(=)1108 4629 y(1)p 1108 4666 42 4 v 1112 4742 a Fl(\017)1173 4468 y Fm(2)1173 4614 y(6)1173 4664 y(6)1173 4717 y(4)1229 4468 y(0)1229 4614 y(B)1229 4664 y(B)1229 4717 y(@)1343 4535 y Fl(m)1416 4547 y Ff(1)1453 4535 y Fl(u)18 b Fn(+)g Fl(m)1675 4547 y Ff(2)1712 4535 y Fl(v)k Fn(+)c Fl(m)1930 4547 y Ff(3)1967 4535 y Fl(\033)s Fn(\()p Fl(u)p Fn(\))1343 4634 y Fl(m)1416 4646 y Ff(4)1453 4634 y Fl(u)g Fn(+)g Fl(m)1675 4646 y Ff(5)1712 4634 y Fl(v)k Fn(+)c Fl(m)1930 4646 y Ff(6)1967 4634 y Fl(\033)s Fn(\()p Fl(u)p Fn(\))1343 4734 y Fl(m)1416 4746 y Ff(1)1453 4734 y Fl(u)g Fj(\000)g Fl(m)1675 4746 y Ff(2)1712 4734 y Fl(v)k Fn(+)c Fl(m)1930 4746 y Ff(3)1967 4734 y Fl(\033)s Fn(\()p Fl(u)p Fn(\))1343 4833 y Fj(\000)p Fl(m)1481 4845 y Ff(4)1518 4833 y Fl(u)g Fn(+)g Fl(m)1740 4845 y Ff(5)1777 4833 y Fl(v)j Fj(\000)e Fl(m)1995 4845 y Ff(6)2032 4833 y Fl(\033)s Fn(\()p Fl(u)p Fn(\))2236 4468 y Fm(1)2236 4614 y(C)2236 4664 y(C)2236 4717 y(A)2327 4685 y Fj(\000)2410 4468 y Fm(0)2410 4614 y(B)2410 4664 y(B)2410 4717 y(@)2524 4535 y Fl(f)2565 4547 y Ff(1+)2524 4634 y Fl(f)2565 4646 y Ff(2+)2524 4734 y Fl(f)2565 4746 y Ff(1)p Fi(\000)2524 4833 y Fl(f)2565 4845 y Ff(2)p Fi(\000)2695 4468 y Fm(1)2695 4614 y(C)2695 4664 y(C)2695 4717 y(A)2768 4468 y(3)2768 4614 y(7)2768 4664 y(7)2768 4717 y(5)2837 4685 y Fl(;)371 b Fn(\(14\))515 5006 y(with)28 b Fl(u)22 b Fn(=)h(1)904 5018 y Fk(N)967 5006 y Fn(\()p Fl(f)1040 5018 y Ff(1+)1146 5006 y Fn(+)18 b Fl(f)1270 5018 y Ff(1)p Fi(\000)1359 5006 y Fn(\))p Fl(;)c(v)26 b Fn(=)d(1)1624 5018 y Fk(N)1687 5006 y Fn(\()p Fl(f)1760 5018 y Ff(2+)1866 5006 y Fn(+)18 b Fl(f)1990 5018 y Ff(2)p Fi(\000)2079 5006 y Fn(\).)1926 5255 y(6)p eop %%Page: 7 7 7 6 bop 515 523 a Fe(Remark)31 b(4)41 b Fd(As)32 b(a)h(DKM)f(is)h (devise)l(d)h(to)e(mo)l(del)h(the)g(mixe)l(d-typ)l(e)f(system)g(\(2\),) i(namely)515 623 y(not)g(only)i(to)f(r)l(esolve)g(the)g(phase)i(b)l (oundaries)f(in)f(a)g(c)l(orr)l(e)l(ct)g(way,)i(but)d(also)i(the)f(hyp) l(er-)515 722 y(b)l(olic)29 b(waves.)39 b(It)27 b(is)h(wel)t(l-known)h (that)f(hyp)l(erb)l(olic)i(systems,)e(in)g(gener)l(al,)h(p)l(ossesses)g (such)515 822 y(symmetries.)58 b(F)-6 b(or)36 b(phase)h(b)l(oundaries,) i(on)d(the)h(other)f(hand,)j(these)e(symmetries)f(also)515 922 y(c)l(ome)g(natur)l(al)t(ly)h(fr)l(om)f(the)g(b)l(asic)h(physic)l (al)h(c)l(onsider)l(ations)g(of)f(the)f(invarianc)l(e)h(under)515 1021 y(the)30 b(change)g(of)h(r)l(efer)l(enc)l(e)f(fr)l(ame.)515 1204 y Fe(Remark)h(5)41 b Fd(F)-6 b(or)28 b(the)g(sake)g(of)h(such)f (symmetries,)h(a)f(\\line)l(ar")g(lo)l(c)l(al)h(Maxwel)t(lian)g(turns) 515 1303 y(out)43 b(to)h(b)l(e)g(the)g(simplest)h(mo)l(del)f(one)h(may) f(think)g(of.)82 b(Some)45 b(p)l(articular)f(nonline)l(ar)515 1403 y(Maxwel)t(lians)29 b(may)f(also)g(serve)g(the)f(purp)l(ose,)i (yet)e(neither)h(e)l(asy)g(to)f(c)l(onstruct,)g(nor)g(e)l(asy)515 1503 y(to)34 b(pr)l(ove)h(the)f(symmetry.)52 b(A)n(t)34 b(this)g(moment,)i(as)e(the)h(gener)l(al)f(nonline)l(ar)h(Maxwel)t (lian)515 1602 y(do)l(es)30 b(not)f(pr)l(ovide)i(us)d(any)i (advantages,)h(we)f(shal)t(l)g(c)l(on\014ne)f(ourselves)h(with)g(the)f (curr)l(ent)515 1702 y(mo)l(del.)515 1885 y Fe(Remark)i(6)41 b Fd(Ther)l(e)30 b(ar)l(e)g(many)f(di\013er)l(ent)g(ways)h(to)f(gener)l (alize)i(our)e(mo)l(del,)i(for)f(c)l(ertain)515 1984 y(sp)l(e)l(ci\014c)j(purp)l(oses.)48 b(F)-6 b(or)33 b(instanc)l(e,)h (taking)f(a)g(non-c)l(onstant)f(r)l(elaxation)h(p)l(ar)l(ameter)h(as) 515 2084 y(in)1313 2204 y Fm(8)1313 2279 y(>)1313 2304 y(>)1313 2329 y(>)1313 2354 y(>)1313 2379 y(>)1313 2404 y(<)1313 2553 y(>)1313 2578 y(>)1313 2603 y(>)1313 2628 y(>)1313 2653 y(>)1313 2677 y(:)1428 2262 y Fl(u)1476 2274 y Fk(t)1523 2262 y Fn(+)18 b Fl(w)1665 2274 y Fk(x)1876 2262 y Fn(=)23 b(0)p Fl(;)1428 2361 y(v)1468 2373 y Fk(t)1516 2361 y Fn(+)18 b Fl(z)1638 2373 y Fk(x)1876 2361 y Fn(=)23 b(0)p Fl(;)1428 2521 y(w)1487 2533 y Fk(t)1535 2521 y Fn(+)18 b Fl(\025)1666 2491 y Ff(2)1704 2521 y Fl(u)1752 2533 y Fk(x)1876 2521 y Fn(=)1974 2465 y Fl(u)2022 2435 y Ff(5)p Fk(=)p Ff(2)p 1974 2502 152 4 v 2033 2578 a Fl(\017)2136 2521 y Fn(\()p Fl(v)k Fj(\000)c Fl(w)r Fn(\))p Fl(;)1428 2708 y(z)1467 2720 y Fk(t)1514 2708 y Fn(+)g Fl(\025)1645 2678 y Ff(2)1683 2708 y Fl(v)1723 2720 y Fk(x)1876 2708 y Fn(=)1974 2652 y Fl(u)2022 2621 y Ff(5)p Fk(=)p Ff(2)p 1974 2689 V 2033 2765 a Fl(\017)2136 2708 y Fn(\()p Fl(\033)s Fn(\()p Fl(u)p Fn(\))h Fj(\000)f Fl(z)t Fn(\))p Fl(;)3231 2499 y Fn(\(15\))515 2880 y Fd(one)32 b(essential)t(ly)i(obtains)f(the)f(same)g(kinetic)h(r)l (elation,)h(at)e(le)l(ast)h(at)f(the)g(tr)l(aveling)h(wave)515 2980 y(analysis)e(level,)g(as)f(the)g(visc)l(osity-c)l(apil)t(larity)j (mo)l(del)967 3093 y Fm(\032)1071 3158 y Fl(u)1119 3170 y Fk(t)1166 3158 y Fn(+)18 b Fl(v)1289 3170 y Fk(x)1529 3158 y Fn(=)k(0)p Fl(;)1071 3261 y(v)1111 3273 y Fk(t)1158 3261 y Fn(+)c Fl(\033)s Fn(\()p Fl(u)p Fn(\))1403 3273 y Fk(x)1529 3261 y Fn(=)k(\(2)p Fl(u)1738 3231 y Fi(\000)p Ff(5)p Fk(=)p Ff(2)1894 3261 y Fl(u)1942 3273 y Fk(x)1983 3261 y Fn(\))2015 3273 y Fk(x)2076 3261 y Fj(\000)c Fl(u)2207 3231 y Fi(\000)p Ff(1)2296 3261 y Fn([)p Fl(u)2367 3231 y Fi(\000)p Ff(1)2455 3261 y Fn(\()p Fl(u)2535 3231 y Fi(\000)p Ff(3)2624 3261 y Fl(u)2672 3273 y Fk(x)2714 3261 y Fn(\))2746 3273 y Fk(x)2788 3261 y Fn(])2811 3273 y Fk(x)2852 3261 y Fl(:)3231 3210 y Fn(\(16\))639 3445 y(According)23 b(to)i(the)f(ideas)g(prop)r(osed)f(b)n(y)h(T.P)-7 b(.)24 b(Liu)g([22)o(],)h(to)f(understand)g(the)h(dissipa-)515 3544 y(tiv)n(e)j(role)g(of)g(the)h(kinetic)g(appro)n(ximations)e(w)n(e) h(ha)n(v)n(e)f(to)i(p)r(erform)f(a)g(Chapman-Ensk)n(og)515 3644 y(t)n(yp)r(e)33 b(expansion)g(as)f(in)i([2],)h(whic)n(h)e(\014xes) g(some)g(stabilit)n(y)g(dissipation)g(conditions.)54 b(In)515 3744 y(the)28 b(presen)n(t)f(case)f(these)i(conditions)f(are)g (con)n(tained)g(in)h(the)g(follo)n(wing)e(statemen)n(t.)515 3910 y Fe(Prop)s(osition)k(7)41 b Fd(A)30 b(DKM)f(\(14\))i(is)f(dissip) l(ative)i(if)1009 4092 y Fn(min\(1)1221 4104 y Fk(N)1284 4092 y Fn(\003)1342 4058 y Ff(2)1379 4092 y Fn(\()p Fl(m)1484 4104 y Ff(1)1539 4092 y Fj(\000)g Fn(_)-37 b Fl(\033)t(m)1746 4104 y Ff(3)1783 4092 y Fn(\))19 b Fj(\000)f Fn(0)p Fl(:)p Fn(5)c(_)-37 b Fl(\033)r(;)14 b Fn(1)2152 4104 y Fk(N)2215 4092 y Fn(\003)2273 4058 y Ff(2)2310 4092 y Fl(m)2383 4104 y Ff(5)2438 4092 y Fj(\000)k Fn(0)p Fl(:)p Fn(5)c(_)-37 b Fl(\033)s Fn(\))23 b Fj(\025)g Fn(0)p Fl(:)345 b Fn(\(17\))515 4275 y Fd(Pr)l(o)l(of)129 b Fn(As)28 b(in)g([2)o(],)g(m)n(ultiplying)g Fl(P)39 b Fn(to)28 b(\(14\),)f(w)n(e)g(ha)n(v)n(e)1639 4474 y Fl(P)12 b(f)1745 4486 y Fk(t)1792 4474 y Fn(+)18 b Fl(P)12 b Fn(\003)p Fl(f)2039 4486 y Fk(x)2103 4474 y Fn(=)22 b(0)p Fl(;)515 4624 y Fn(or,)1565 4735 y Fm(\022)1668 4801 y Fl(u)1670 4901 y(v)1757 4735 y Fm(\023)1818 4935 y Fk(t)1865 4852 y Fn(+)d Fl(P)12 b Fn(\003)p Fl(f)2113 4864 y Fk(x)2176 4852 y Fn(=)23 b(0)p Fl(:)1926 5255 y Fn(7)p eop %%Page: 8 8 8 7 bop 639 523 a Fn(Substituting)35 b Fl(f)43 b Fn(=)34 b Fl(M)d Fj(\000)22 b Fl(\017)p Fn(\()p Fl(f)1610 535 y Fk(t)1662 523 y Fn(+)g(\003)p Fl(f)1848 535 y Fk(x)1890 523 y Fn(\))34 b(in)n(to)g(it,)i(retaining)e(only)f(terms)h(up)h(to)f (the)515 623 y(order)26 b(of)i Fl(\017)p Fn(,)f(w)n(e)g(ha)n(v)n(e,)g (with)h(the)g(help)g(of)f(the)h(compatibilit)n(y)g(conditions,)704 850 y Fl(P)783 733 y Fm(\022)885 799 y Fl(u)887 899 y(v)974 733 y Fm(\023)1035 933 y Fk(t)1083 850 y Fn(+)1166 733 y Fm(\022)1328 799 y Fl(v)1269 899 y(\033)s Fn(\()p Fl(u)p Fn(\))1473 733 y Fm(\023)556 1003 y Fn(=)83 b Fl(\017P)12 b Fn(\003\()p Fl(f)934 1015 y Fk(t)981 1003 y Fn(+)18 b(\003)p Fl(f)1163 1015 y Fk(x)1204 1003 y Fn(\))1236 1015 y Fk(x)556 1102 y Fn(=)83 b Fl(\017)p Fn(\()p Fl(P)12 b Fn(\003)p Fl(M)974 1114 y Fk(t)1021 1102 y Fn(+)18 b Fl(P)12 b Fn(\003)1227 1072 y Ff(2)1263 1102 y Fl(M)1344 1114 y Fk(x)1386 1102 y Fn(\))1418 1114 y Fk(x)1478 1102 y Fn(+)18 b Fl(O)r Fn(\()p Fl(\017)1692 1072 y Ff(2)1730 1102 y Fn(\))556 1252 y(=)83 b Fl(\017)752 1135 y Fm(\024)o(\022)957 1202 y Fl(v)898 1301 y(\033)s Fn(\()p Fl(u)p Fn(\))1102 1135 y Fm(\023)1163 1335 y Fk(t)1211 1252 y Fn(+)18 b Fl(P)12 b Fn(\003)1417 1222 y Ff(2)1453 1252 y Fl(M)1534 1264 y Fk(x)1576 1135 y Fm(\025)1620 1340 y Fk(x)1680 1252 y Fn(+)18 b Fl(O)r Fn(\()p Fl(\017)1894 1222 y Ff(2)1932 1252 y Fn(\))556 1460 y(=)83 b Fl(\017)752 1343 y Fm(\024)795 1460 y Fj(\000)874 1343 y Fm(\022)990 1409 y Fn(_)-37 b Fl(\033)t Fn(\()p Fl(u)p Fn(\))p Fl(u)1187 1421 y Fk(x)994 1509 y Fn(_)g Fl(\033)s Fn(\()p Fl(u)p Fn(\))p Fl(v)1182 1521 y Fk(x)1270 1343 y Fm(\023)1349 1460 y Fn(+)18 b(2)1488 1343 y Fm(\022)1590 1409 y Fn(1)1632 1421 y Fk(N)1695 1409 y Fn(\003)1753 1379 y Ff(2)1790 1409 y Fn(\()p Fl(m)1895 1421 y Ff(1)1950 1409 y Fj(\000)32 b Fn(_)-37 b Fl(\033)t(m)2157 1421 y Ff(3)2194 1409 y Fn(\))p Fl(u)2274 1421 y Fk(x)1757 1509 y Fn(1)1799 1521 y Fk(N)1862 1509 y Fn(\003)1920 1479 y Ff(2)1956 1509 y Fl(m)2029 1521 y Ff(5)2067 1509 y Fl(v)2107 1521 y Fk(x)2357 1343 y Fm(\023\025)2462 1543 y Fk(x)2522 1460 y Fn(+)18 b Fl(O)r Fn(\()p Fl(\017)2736 1430 y Ff(2)2774 1460 y Fn(\))p Fl(:)556 1663 y Fn(=)83 b(2)p Fl(\017)794 1546 y Fm(\024)837 1663 y Fj(\000)916 1546 y Fm(\022)1018 1613 y Fn(1)1060 1625 y Fk(N)1122 1613 y Fn(\003)1180 1583 y Ff(2)1217 1613 y Fn(\()p Fl(m)1322 1625 y Ff(1)1378 1613 y Fj(\000)32 b Fn(_)-37 b Fl(\033)s(m)1584 1625 y Ff(3)1622 1613 y Fn(\))18 b Fj(\000)g Fn(0)p Fl(:)p Fn(5)c(_)-37 b Fl(\033)s Fn(\()p Fl(u)p Fn(\))402 b(0)1500 1712 y(0)565 b(1)2149 1724 y Fk(N)2211 1712 y Fn(\003)2269 1682 y Ff(2)2306 1712 y Fl(m)2379 1724 y Ff(5)2435 1712 y Fj(\000)18 b Fn(0)p Fl(:)p Fn(5)c(_)-37 b Fl(\033)r Fn(\()p Fl(u)p Fn(\))2828 1546 y Fm(\023)14 b(\022)3006 1613 y Fl(u)3054 1625 y Fk(x)3009 1712 y Fl(v)3049 1724 y Fk(x)3136 1546 y Fm(\023)q(\025)3241 1746 y Fk(x)3302 1663 y Fn(+)k Fl(O)r Fn(\()p Fl(\017)3516 1633 y Ff(2)3554 1663 y Fn(\))p Fl(:)639 1895 y Fn(The)28 b(dissipativit)n(y)f (condition)g(then)h(follo)n(ws.)515 2176 y Fe(Remark)j(8)41 b Fd(This)35 b(Chapmann-Ensko)l(g)h(exp)l(ansion)f(yields)h(normal)f (sub)l(char)l(acteristic)515 2276 y(c)l(ondition)d([22)r(],)h(and)f(it) f(is)h(worth)g(mentioning)g(that)g(no)f(further)h(r)l(estriction)g(is)g (c)l(ause)l(d)515 2375 y(due)e(to)f(the)h(non-monotonicity.)639 2557 y Fn(F)-7 b(or)38 b(some)g(systems)g(of)g(dynamical)f(phase)h (transitions,)i(e.g.)69 b(in)39 b(v)-5 b(an)38 b(der)g(W)-7 b(aals)515 2657 y(\015uids,)32 b(it)f(is)f(kno)n(wn)g(from)h(ph)n (ysics)f(that)h(stationary)e(phase)h(b)r(oundary)g(solution)g(m)n(ust) 515 2756 y(follo)n(w)f(the)h(Maxw)n(ell)g(construction)f(of)h (equal-area)d(la)n(w.)44 b(More)29 b(precisely)-7 b(,)30 b(b)r(esides)g(the)515 2856 y(Rankine-Hugoniot)c(relation)h(for)g(the)h (t)n(w)n(o)f(states)g(across)e(the)j(discon)n(tin)n(uit)n(y)-7 b(,)28 b(namely)1655 3054 y([)p Fl(v)s Fn(])23 b(=)g([)p Fl(\033)s Fn(\()p Fl(u)p Fn(\)])h(=)e(0)p Fl(;)515 3236 y Fn(it)30 b(also)f(requires)f(that)i(the)g(t)n(w)n(o)f(regions)f (separated)h(b)n(y)g(the)i(curv)n(e)d Fl(\033)s Fn(\()p Fl(u)p Fn(\))j(and)e(the)i(lev)n(el)515 3336 y(line)d(of)f Fl(\033)s Fn(\()p Fl(u)896 3305 y Fi(\000)952 3336 y Fn(\))h(tak)n(e)f(equal)g(area,)f(i.e.)1479 3476 y Fm(Z)1562 3496 y Fk(u)1601 3471 y Fc(+)1525 3664 y Fk(u)1564 3648 y Fb(\000)1666 3589 y Fl(\033)s Fn(\()p Fl(u)p Fn(\))19 b Fj(\000)f Fl(\033)s Fn(\()p Fl(u)2060 3554 y Fi(\000)2116 3589 y Fn(\))p Fl(du)23 b Fn(=)g(0)p Fl(:)816 b Fn(\(18\))639 3780 y(This)31 b(is)f(not)g(true)g(in)h(general)e(for)h(the)g(DKM's.)45 b(Ho)n(w)n(ev)n(er,)30 b(a)g(sub-category)e(of)i(our)515 3879 y(DKM's)24 b(admit)h(solutions)e(with)i(this)g(prop)r(ert)n(y)-7 b(.)35 b(In)24 b(particular,)g(if)h(w)n(e)f(tak)n(e)f Fl(m)3033 3891 y Ff(1)3094 3879 y Fn(=)f Fl(m)3254 3891 y Ff(5)3314 3879 y Fj(\021)515 4013 y Fl(\013;)14 b(m)678 4025 y Ff(2)745 4013 y Fn(=)30 b Fl(m)913 4025 y Ff(6)980 4013 y Fj(\021)f Fl(\014)34 b Fn(=)1417 3957 y(1)p 1260 3994 356 4 v 1260 4156 a(2)1345 4052 y Fk(N)1315 4077 y Fm(X)1321 4254 y Fk(i)p Ff(=1)1449 4156 y Fl(\025)1497 4122 y Ff(2)1497 4177 y Fk(i)1534 4156 y Fl(\013)1587 4168 y Fk(i)1625 4013 y Fn(\003)1683 4025 y Ff(1)1720 4013 y Fl(\013;)14 b(m)1883 4025 y Ff(3)1950 4013 y Fn(=)30 b Fl(m)2118 4025 y Ff(4)2185 4013 y Fn(=)f(0)2321 4025 y Fk(N)2384 4013 y Fn(,)j(then)h(a)e(stationary)f(w)n(a)n(v)n(e)g(of) 515 4384 y(\(14\))d(solv)n(es)f(\()958 4354 y Fi(0)1005 4384 y Fn(=)c Fl(\017)1160 4328 y(d)p 1136 4365 91 4 v 1136 4441 a(dx)1237 4384 y Fn(\))1289 4492 y Fm(8)1289 4567 y(>)1289 4592 y(>)1289 4617 y(<)1289 4766 y(>)1289 4791 y(>)1289 4816 y(:)1404 4562 y Fn(\003)p Fl(f)1512 4532 y Fi(0)1503 4583 y Ff(1+)1739 4562 y Fn(=)83 b Fl(\013u)18 b Fn(+)g Fl(\014)t(v)k Fj(\000)c Fl(f)2326 4574 y Ff(1+)2414 4562 y Fl(;)1404 4662 y Fn(\003)p Fl(f)1512 4632 y Fi(0)1503 4682 y Ff(2+)1739 4662 y Fn(=)83 b Fl(\013v)22 b Fn(+)c Fl(\014)t(\033)s Fn(\()p Fl(u)p Fn(\))h Fj(\000)f Fl(f)2441 4674 y Ff(2+)2529 4662 y Fl(;)1404 4761 y Fj(\000)p Fn(\003)p Fl(f)1577 4731 y Fi(0)1568 4782 y Ff(1)p Fi(\000)1739 4761 y Fn(=)83 b Fl(\013u)18 b Fj(\000)g Fl(\014)t(v)k Fj(\000)c Fl(f)2326 4773 y Ff(1)p Fi(\000)2415 4761 y Fl(;)1404 4861 y Fj(\000)p Fn(\003)p Fl(f)1577 4831 y Fi(0)1568 4882 y Ff(2)p Fi(\000)1739 4861 y Fn(=)83 b Fl(\013v)22 b Fj(\000)c Fl(\014)t(\033)s Fn(\()p Fl(u)p Fn(\))h Fj(\000)f Fl(f)2441 4873 y Ff(2)p Fi(\000)2530 4861 y Fl(:)3231 4712 y Fn(\(19\))639 5006 y(It)28 b(admits)g(a)f(sp)r (ecial)g(solution)1926 5255 y(8)p eop %%Page: 9 9 9 8 bop 1346 535 a Fm(0)1346 681 y(B)1346 731 y(B)1346 784 y(@)1460 601 y Fl(f)1501 613 y Ff(1+)1460 701 y Fl(f)1501 713 y Ff(2+)1460 800 y Fl(f)1501 812 y Ff(1)p Fi(\000)1460 900 y Fl(f)1501 912 y Ff(2)p Fi(\000)1631 535 y Fm(1)1631 681 y(C)1631 731 y(C)1631 784 y(A)1727 751 y Fn(=)1815 535 y Fm(0)1815 681 y(B)1815 731 y(B)1815 784 y(@)1929 601 y Fl(u\013)18 b Fn(+)g Fl(v)2174 571 y Fi(\000)2230 601 y Fl(\014)1929 701 y(v)s(\013)h Fn(+)f Fl(\033)s Fn(\()p Fl(u)2257 671 y Fi(\000)2313 701 y Fn(\))p Fl(\014)1929 800 y(u\013)g Fj(\000)g Fl(v)2174 770 y Fi(\000)2230 800 y Fl(\014)1929 900 y(v)s(\013)h Fj(\000)f Fl(\033)s Fn(\()p Fl(u)2257 870 y Fi(\000)2313 900 y Fn(\))p Fl(\014)2438 535 y Fm(1)2438 681 y(C)2438 731 y(C)2438 784 y(A)2525 751 y Fl(;)515 1050 y Fn(where)27 b(\()p Fl(u;)14 b(v)s Fn(\))28 b(satis\014es)1169 1310 y(\(2)1287 1206 y Fk(N)1257 1231 y Fm(X)1263 1408 y Fk(i)p Ff(=1)1391 1310 y Fl(\025)1439 1276 y Ff(2)1439 1330 y Fk(i)1476 1310 y Fl(\013)1529 1276 y Ff(2)1529 1330 y Fk(i)1567 1310 y Fn(\))1613 1193 y Fm(\022)1716 1259 y Fl(u)1716 1359 y(v)1805 1193 y Fm(\023)1866 1210 y Fi(0)1912 1310 y Fn(=)2000 1193 y Fm(\022)2102 1259 y Fl(v)22 b Fj(\000)c Fl(v)2290 1229 y Fi(\000)2102 1359 y Fl(\033)s Fn(\()p Fl(u)p Fn(\))h Fj(\000)f Fl(\033)s Fn(\()p Fl(u)2496 1329 y Fi(\000)2553 1359 y Fn(\))2627 1193 y Fm(\023)2701 1310 y Fl(:)507 b Fn(\(20\))515 1532 y(It)30 b(is)g(then)g(easily)f(v)n(eri\014ed)g (that)i(along)d(eac)n(h)h(tra)5 b(jectory)-7 b(,)29 b(w)n(e)h(ha)n(v)n (e)f(the)h(follo)n(wing)f(con-)515 1632 y(stan)n(t)e(energy)1276 1863 y Fl(H)j Fn(=)1473 1807 y(\()p Fl(v)22 b Fj(\000)c Fl(v)1693 1777 y Fi(\000)1749 1807 y Fn(\))1781 1777 y Ff(2)p 1473 1844 346 4 v 1625 1920 a Fn(2)1847 1863 y Fj(\000)1930 1750 y Fm(Z)2013 1771 y Fk(u)1976 1939 y(u)2015 1922 y Fb(\000)2069 1863 y Fn(\()p Fl(\033)k Fj(\000)c Fl(\033)s Fn(\()p Fl(u)2383 1829 y Fi(\000)2439 1863 y Fn(\)\))p Fl(du:)614 b Fn(\(21\))515 2063 y(As)33 b(\()p Fl(u)723 2033 y Ff(+)778 2063 y Fl(;)14 b(v)858 2033 y Ff(+)913 2063 y Fn(\))33 b(is)g(a)g(stationary)e(p)r(oin)n(t)j (of)e(\(20\),)j(w)n(e)d(kno)n(w)g(that)i Fl(v)2648 2033 y Ff(+)2735 2063 y Fn(=)e Fl(v)2875 2033 y Fi(\000)2931 2063 y Fn(.)53 b(Therefore,)515 2163 y(the)28 b(equal)f(area)f(la)n(w)h (is)g(implied)h(as)1510 2302 y Fm(Z)1593 2323 y Fk(u)1632 2298 y Fc(+)1556 2491 y Fk(u)1595 2474 y Fb(\000)1683 2415 y Fn(\()p Fl(\033)22 b Fj(\000)c Fl(\033)s Fn(\()p Fl(u)1997 2381 y Fi(\000)2053 2415 y Fn(\)\))p Fl(du)24 b Fn(=)e(0)p Fl(:)515 2734 y Fn(Moreo)n(v)n(er,)j(the)j(c)n (haracteristic)d(width)j(of)g(the)g(phase)f(b)r(oundary)g(is)g Fl(\017)p Fn(\(2)2869 2630 y Fk(N)2839 2655 y Fm(X)2845 2832 y Fk(i)p Ff(=1)2972 2734 y Fl(\025)3020 2700 y Ff(2)3020 2755 y Fk(i)3058 2734 y Fl(\013)3111 2700 y Ff(2)3111 2755 y Fk(i)3149 2734 y Fn(\).)515 3057 y Fo(3)134 b(Numerical)46 b(sc)l(hemes)515 3239 y Fn(As)24 b(the)h(DKM)g(here)f(is)g(of)g(the)h (same)f(form)g(as)g(that)h(for)f(appro)n(ximating)e(h)n(yp)r(erb)r (olic)i(sys-)515 3338 y(tems,)h(it)f(tak)n(es)g(all)f(the)i(same)e (nice)i(prop)r(erties,)e(suc)n(h)h(as)g(easy)f(to)h(implemen)n(t,)h (relativ)n(ely)515 3438 y(lo)n(w)c(computing)g(load,)i(easy)e(to)g (generalize)f(to)i(m)n(ulti-dimensional)f(problems)g(in)h(co)r(ding,) 515 3538 y(etc.)41 b(Please)28 b(refer)h(to)g([2)o(])h(for)e(details.) 42 b(Here)28 b(w)n(e)h(only)g(describ)r(e)g(the)g(framew)n(ork)f(of)h (the)515 3637 y(sc)n(heme.)639 3737 y(W)-7 b(e)26 b(emplo)n(y)f(the)h (\014rst-order)d(splitting)j(metho)r(d)g(in)g(solving)e(the)i(DKM)f (\(14\).)36 b(Giv)n(en)515 3836 y(data)27 b Fl(f)9 b Fn(\()p Fl(x;)14 b Fn(0\))28 b(at)f(time)h Fl(t)23 b Fn(=)g(0,)k(w)n(e)g(\014rst)h(solv)n(e)e(the)i(homogeneous)e(system) 1366 4014 y(^)1348 4036 y Fl(f)1389 4048 y Fk(t)1437 4036 y Fn(+)18 b(\003)1595 4014 y(^)1578 4036 y Fl(f)1619 4048 y Fk(x)1683 4036 y Fn(=)k(0)p Fl(;)1950 4014 y Fn(^)1932 4036 y Fl(f)8 b Fn(\()p Fl(x;)14 b Fn(0\))24 b(=)e Fl(f)9 b Fn(\()p Fl(x;)14 b Fn(0\))p Fl(;)686 b Fn(\(22\))515 4185 y(for)31 b(a)g(time)h(step)g Fj(4)p Fl(t)p Fn(.)48 b(As)32 b(this)g(is)g(a)f(linear)g(system,)h(w)n(e)g(ma)n(y)f(tak)n(e)g (either)g(an)h(up)n(wind)515 4285 y(sc)n(heme,)j(or)e(a)g(second)h (order)e(sc)n(heme.)55 b(In)34 b(fact,)i(since)e(it)g(is)g(diagonal,)g (w)n(e)f(ma)n(y)h(ev)n(en)515 4384 y(get)c(the)h(solution)g(explicitly) -7 b(.)46 b(The)31 b(n)n(umerical)f(sim)n(ulations)g(sho)n(wn)g(in)h (this)g(pap)r(er)f(are)515 4484 y(p)r(erformed)d(b)n(y)g(a)g(second)g (order)g(sc)n(heme)g(with)h(minmo)r(d)g(limiter.)639 4584 y(Then,)g(w)n(e)f(solv)n(e)g(the)h(ordinary)e(di\013eren)n(tial)h (equations)g(with)h(source)e(terms)1204 4779 y(~)1186 4801 y Fl(f)1227 4813 y Fk(t)1279 4801 y Fn(=)1376 4745 y(1)p 1376 4782 42 4 v 1380 4858 a Fl(\017)1428 4801 y Fn(\()p Fl(M)9 b Fn(\()p Fl(P)1665 4779 y Fn(~)1647 4801 y Fl(f)f Fn(\))19 b Fj(\000)1848 4779 y Fn(~)1830 4801 y Fl(f)9 b Fn(\))p Fl(;)2050 4779 y Fn(~)2032 4801 y Fl(f)f Fn(\()p Fl(x;)14 b Fn(0\))24 b(=)2400 4779 y(^)2383 4801 y Fl(f)8 b Fn(\()p Fl(x;)14 b Fj(4)p Fl(t)p Fn(\))p Fl(;)523 b Fn(\(23\))1926 5255 y(9)p eop %%Page: 10 10 10 9 bop 515 523 a Fn(for)32 b(one)g(time)h(step,)i(and)d(tak)n(e)g Fl(f)9 b Fn(\()p Fl(x;)14 b Fj(4)p Fl(t)p Fn(\))31 b(=)2003 501 y(~)1985 523 y Fl(f)9 b Fn(\()p Fl(x;)14 b Fj(4)p Fl(t)p Fn(\).)52 b(This)32 b(step)h(can)g(also)e(b)r(e)i(made)515 623 y(explicit.)k(Due)27 b(to)g(the)h(fact)f(that)g(the)h(primary)e(v) -5 b(ariables)26 b(\()p Fl(u;)14 b(v)s Fn(\))27 b(remain)g(unc)n (hanged)f(in)515 722 y(this)i(step,)f(and)h(M)g(dep)r(ends)g(only)f(on) g(\()p Fl(u;)14 b(v)s Fn(\),)28 b(w)n(e)f(get)h(the)g(exact)f(solution) g(as)1161 922 y(~)1143 944 y Fl(f)9 b Fn(\()p Fl(x;)14 b Fj(4)p Fl(t)p Fn(\))23 b(=)82 b(exp\()p Fj(\000)1850 888 y(4)p Fl(t)p 1850 925 104 4 v 1885 1001 a(\017)1964 944 y Fn(\))2014 922 y(~)1996 944 y Fl(f)9 b Fn(\()p Fl(x;)14 b Fn(0\))1616 1115 y(+\(1)k Fj(\000)g Fn(exp\()p Fj(\000)2090 1059 y(4)p Fl(t)p 2090 1096 V 2125 1172 a(\017)2204 1115 y Fn(\)\))p Fl(M)9 b Fn(\()p Fl(P)2473 1093 y Fn(~)2455 1115 y Fl(f)g Fn(\()p Fl(x;)14 b Fn(0\)\))p Fl(:)639 1291 y Fn(W)-7 b(e)36 b(ma)n(y)e(ev)n(en)h(directly)f(tak)n(e) h(the)g(limit)h Fl(\017)f Fn(=)g(0)g(in)g(this)h(step,)h(namely)3068 1269 y(~)3050 1291 y Fl(f)9 b Fn(\()p Fl(t;)14 b(x)p Fn(\))36 b(=)515 1391 y Fl(M)9 b Fn(\()p Fl(P)719 1369 y Fn(~)702 1391 y Fl(f)f Fn(\(0)p Fl(;)14 b(x)p Fn(\)\))p Fl(:)30 b Fn(The)f(resulting)g(relaxed)f(sc)n(heme)g(consists)h(of)g(a) g(w)n(a)n(v)n(e)e(propagation)g(up-)515 1491 y(dated)40 b(with)h(lo)r(cal)f(Maxw)n(ellian.)74 b(Numerical)40 b(sim)n(ulations)g(rep)r(orted)f(here)h(are)f(p)r(er-)515 1590 y(formed)29 b(with)h(this)g(relaxed)f(sc)n(heme.)43 b(In)30 b(our)f(n)n(umerical)g(exp)r(erimen)n(ts,)h(it)g(is)g(observ)n (ed)515 1690 y(that)21 b(non-zero)f Fl(\017)h Fn(giv)n(es)g(the)g(same) g(result)g(but)h(with)g(sligh)n(tly)f(stronger)f(smo)r(othing)h (e\013ect,)515 1789 y(the)28 b(same)f(as)g(what)g(happ)r(ens)h(with)g (DKM's)g(for)f(h)n(yp)r(erb)r(olic)g(systems)g([2)o(].)639 1889 y(In)i(our)g(sim)n(ulations,)f(w)n(e)h(use)g(the)g(lo)r(cal)g (Maxw)n(ellians)f(as)g(the)h(initial)h(or)e(b)r(oundary)515 1989 y(data)e(for)f Fl(f)878 1959 y Fi(0)869 2010 y Fk(i)901 1989 y Fl(s)p Fn(.)37 b(A)26 b(non-Maxw)n(ellian)f(data)h(will)g(cause) g(a)f(thin)i(initial)g(la)n(y)n(er)d(or)i(b)r(oundary)515 2088 y(la)n(y)n(er,)g(whic)n(h)h(will)h(b)r(e)g(a)f(topic)h(for)f (future)h(study)-7 b(.)639 2188 y(W)g(e)34 b(ha)n(v)n(e)f(also)f (applied)i(a)f(second-order)f(splitting)i(sc)n(heme)f(prop)r(osed)f(b)n (y)i(Jin.)55 b(A)515 2288 y(semi-discrete)27 b(v)n(ersion)g(for)h(the)h (relaxed)f(sc)n(heme)g(has)g(also)g(b)r(een)h(implemen)n(ted,)g(whic)n (h)515 2387 y(allo)n(ws)f(a)h(natural)f(high-order)g(time)i(splitting,) g(e.g.)41 b(with)30 b(fourth-order)e(Runge-Kutta)515 2487 y(metho)r(d.)36 b(The)26 b(accuracy)d(is)i(of)g(great)f(imp)r (ortance)h(for)g(general)e(initial)j(b)r(oundary)e(v)-5 b(alue)515 2586 y(problems,)26 b(particularly)-7 b(,)25 b(when)i(there)f(are)f(in)n(teractions)g(among)h(w)n(a)n(v)n(es.)34 b(Nev)n(ertheless,)515 2686 y(as)k(w)n(e)h(shall)f(describ)r(e)h(in)g (the)g(follo)n(wing)f(sections,)j(the)f(main)f(issue)f(in)i(the)f (curren)n(t)515 2786 y(pap)r(er)31 b(is)h(the)h(kinetic)f(relation)g (that)g(c)n(hanges)f(along)g(with)h(di\013eren)n(t)h(mo)r(dels.)50 b(Unless)515 2885 y(men)n(tioned,)27 b(the)i(n)n(umerical)d(results)h (exp)r(osed)h(here)f(are)f(p)r(erformed)i(with)g(a)f(\014rst-order)515 2985 y(time)h(splitting.)515 3255 y Fo(4)134 b(Sp)t(eci\014c)44 b(mo)t(dels)515 3437 y Fn(In)39 b(this)g(section,)j(w)n(e)c(shall)h (describ)r(e)g(some)f(sp)r(eci\014c)h(DKM's.)71 b(T)-7 b(o)39 b(illustrate)g(b)r(etter)515 3536 y(the)31 b(idea)f(instead)h (of)f(stepping)h(in)n(to)f(the)i(complexities)e(caused)g(b)n(y)g(the)h (in)n(teraction)f(of)515 3636 y(h)n(yp)r(erb)r(olic)d(w)n(a)n(v)n(es,)f (w)n(e)h(shall)g(tak)n(e)g(the)h(tri-linear)e(constitutiv)n(e)i (relation,)e(i.e.)1268 3914 y Fl(\033)s Fn(\()p Fl(u)p Fn(\))d(=)1541 3744 y Fm(8)1541 3819 y(<)1541 3968 y(:)1656 3814 y Fn(2)p Fl(u;)184 b Fn(for)82 b Fl(u)23 b(<)f Fn(1)p Fl(;)1656 3913 y Fn(3)c Fj(\000)g Fl(u;)83 b Fn(for)f(1)23 b Fl(<)f(u)h(<)g Fn(1)p Fl(:)p Fn(5)p Fl(;)1656 4013 y(u;)226 b Fn(for)82 b Fl(u)23 b(>)f Fn(1)p Fl(:)p Fn(5)p Fl(:)3231 3914 y Fn(\(24\))639 4143 y(As)35 b(men)n(tioned)h(b)r (efore,)g(a)f(DKM)g(has)g(t)n(w)n(o-fold)f(usages.)58 b(First,)37 b(it)f(ma)n(y)e(serv)n(e)g(as)515 4242 y(a)g(systematic)g (w)n(a)n(y)g(to)h(regularized)e(the)i(ill-p)r(osed)f(dynamical)h(phase) f(transition)g(sys-)515 4342 y(tem)41 b(\(2\).)76 b(Indeed,)44 b(it)d(ma)n(y)f(b)r(e)h(used)g(to)f(solv)n(e)g(general)f(initial)i(v)-5 b(alue)40 b(problems)g(or)515 4442 y(initial-b)r(oundary)24 b(v)-5 b(alue)25 b(problems.)35 b(Secondly)-7 b(,)25 b(a)g(DKM)g(dictates)g(a)f(particular)g(kinetic)515 4541 y(relation)i(and)i(n)n(ucleation)f(criterion.)639 4641 y(As)33 b(a)f(\014rst)g(step)h(of)f(the)h(study)-7 b(,)34 b(w)n(e)e(only)g(presen)n(t)g(here)g(the)h(solution)f(of)g(Riemann)515 4741 y(problems,)27 b(namely)-7 b(,)27 b(the)h(Cauc)n(h)n(y)f(problem)g (with)h(Riemann)f(initial)h(data)1120 4969 y(\()p Fl(u)p Fn(\()p Fl(x;)14 b Fn(0\))p Fl(;)g(v)s Fn(\()p Fl(x;)g Fn(0\)\))24 b(=)1803 4852 y Fm(\032)1907 4918 y Fn(\()p Fl(u)1987 4888 y Fi(\000)2043 4918 y Fl(;)14 b(v)2123 4888 y Fi(\000)2179 4918 y Fn(\))p Fl(;)84 b Fn(for)e Fl(x)23 b(<)g Fn(0)p Fl(;)1907 5018 y Fn(\()p Fl(u)1987 4988 y Ff(+)2042 5018 y Fl(;)14 b(v)2122 4988 y Ff(+)2177 5018 y Fn(\))p Fl(;)86 b Fn(for)c Fl(x)23 b(>)g Fn(0)p Fl(:)3231 4969 y Fn(\(25\))1905 5255 y(10)p eop %%Page: 11 11 11 10 bop 639 523 a Fn(In)29 b(particular,)f(w)n(e)h(shall)f(in)n(v)n (estigate)g(tra)n(v)n(eling)f(w)n(a)n(v)n(es)g(of)h(\(14\))h(to)g (obtain)f(elemen-)515 623 y(tary)f(w)n(a)n(v)n(es)g(and)h(kinetic)h (relations,)e(analyze)g(Riemann)i(problem)f(with)h(these)f(elemen-)515 722 y(tary)c(w)n(a)n(v)n(es,)f(and)i(p)r(erform)f(n)n(umerical)g(sim)n (ulations)g(to)g(v)n(erify)g(our)g(Riemann)h(solv)n(er,)f(as)515 822 y(w)n(ell)j(as)g(to)g(get)h(the)g(n)n(ucleation)f(criterion)f(when) i(necessary)-7 b(.)515 1054 y Fa(4.1)112 b(Suliciu's)36 b(mo)s(del)515 1208 y Fn(This)23 b(mo)r(del)h(w)n(as)e(prop)r(osed)g(b) n(y)i(Suliciu)g(in)f(studying)h(visco)r(elasticit)n(y)e([26)o(].)35 b(It)24 b(tak)n(es)f(the)515 1307 y(form)k(of)1362 1424 y Fm(8)1362 1498 y(>)1362 1523 y(<)1362 1673 y(>)1362 1698 y(:)1477 1485 y Fl(u)1525 1497 y Fk(t)1572 1485 y Fn(+)18 b Fl(v)1695 1497 y Fk(x)1918 1485 y Fn(=)23 b(0)p Fl(;)1477 1584 y(v)1517 1596 y Fk(t)1565 1584 y Fn(+)18 b Fl(w)1707 1596 y Fk(x)1918 1584 y Fn(=)23 b(0)p Fl(;)1477 1724 y(w)1536 1736 y Fk(t)1584 1724 y Fn(+)18 b Fl(\025)1715 1694 y Ff(2)1753 1724 y Fl(v)1793 1736 y Fk(x)1918 1724 y Fn(=)2016 1668 y(1)p 2016 1705 42 4 v 2020 1781 a Fl(\017)2067 1724 y Fn(\()p Fl(\033)s Fn(\()p Fl(u)p Fn(\))h Fj(\000)f Fl(w)r Fn(\))p Fl(:)3231 1619 y Fn(\(26\))639 1897 y(Using)k(the)g(tec)n(hnique)f(in)h(pro)n (ving)e(Prop)r(osition)g(1,)i(w)n(e)g(ma)n(y)e(recast)h(it)h(in)n(to)f (an)h(equiv-)515 1996 y(alen)n(t)27 b(system)g(\(14\))h(with)899 2725 y(\003)23 b(=)1068 2607 y Fm(\024)1153 2674 y Fl(\025)1284 2774 y Fn(0)1367 2607 y Fm(\025)1425 2725 y Fl(;)132 b(M)32 b Fn(=)1780 2109 y Fm(2)1780 2255 y(6)1780 2305 y(6)1780 2355 y(6)1780 2405 y(6)1780 2455 y(6)1780 2505 y(6)1780 2554 y(6)1780 2604 y(6)1780 2654 y(6)1780 2704 y(6)1780 2754 y(6)1780 2803 y(6)1780 2853 y(6)1780 2903 y(6)1780 2953 y(6)1780 3003 y(6)1780 3052 y(6)1780 3102 y(6)1780 3155 y(4)1887 2214 y Fn(0)2088 2158 y(1)p 2064 2195 90 4 v 2064 2271 a(2)p Fl(\025)2364 2158 y Fn(1)p 2321 2195 128 4 v 2321 2271 a(2)p Fl(\025)2411 2247 y Ff(2)1887 2324 y Fn(1)p 1887 2362 42 4 v 1887 2438 a(2)2088 2381 y(0)149 b Fj(\000)2396 2324 y Fn(1)p 2354 2362 128 4 v 2354 2438 a(2)p Fl(\025)2444 2414 y Ff(2)1887 2547 y Fn(0)2088 2491 y(1)p 2088 2528 42 4 v 2088 2604 a(2)2364 2491 y(1)p 2340 2528 90 4 v 2340 2604 a(2)p Fl(\025)1887 2674 y Fn(0)159 b(0)234 b(0)1887 2813 y(0)93 b Fj(\000)2120 2757 y Fn(1)p 2097 2794 V 2097 2870 a(2)p Fl(\025)2364 2757 y Fn(1)p 2321 2794 128 4 v 2321 2870 a(2)p Fl(\025)2411 2846 y Ff(2)1887 2924 y Fn(1)p 1887 2961 42 4 v 1887 3037 a(2)2088 2980 y(0)149 b Fj(\000)2396 2924 y Fn(1)p 2354 2961 128 4 v 2354 3037 a(2)p Fl(\025)2444 3013 y Ff(2)1887 3147 y Fn(0)2088 3091 y(1)p 2088 3128 42 4 v 2088 3204 a(2)2298 3147 y Fj(\000)2396 3091 y Fn(1)p 2373 3128 90 4 v 2373 3204 a(2)p Fl(\025)1887 3273 y Fn(0)159 b(0)234 b(0)2532 2109 y Fm(3)2532 2255 y(7)2532 2305 y(7)2532 2355 y(7)2532 2405 y(7)2532 2455 y(7)2532 2505 y(7)2532 2554 y(7)2532 2604 y(7)2532 2654 y(7)2532 2704 y(7)2532 2754 y(7)2532 2803 y(7)2532 2853 y(7)2532 2903 y(7)2532 2953 y(7)2532 3003 y(7)2532 3052 y(7)2532 3102 y(7)2532 3155 y(5)2601 2558 y(2)2601 2707 y(4)2756 2624 y Fl(u)2758 2724 y(v)2698 2823 y(\033)s Fn(\()p Fl(u)p Fn(\))2902 2558 y Fm(3)2902 2707 y(5)2972 2725 y Fl(:)639 3419 y Fn(The)28 b(stabilit)n(y)f(condition)h(can)f(b)r(e)h (found)g(as)1139 3647 y Fl(P)12 b Fn(\003)1262 3613 y Ff(2)1298 3647 y Fl(M)1388 3613 y Fi(0)1430 3647 y Fj(\000)1513 3530 y Fm(\022)1629 3597 y Fn(_)-37 b Fl(\033)91 b Fn(0)1620 3696 y(0)100 b(_)-36 b Fl(\033)1841 3530 y Fm(\023)1925 3647 y Fn(=)2013 3530 y Fm(\022)2115 3597 y Fn(0)181 b(0)2115 3696 y(0)83 b Fl(\025)2288 3666 y Ff(2)2344 3696 y Fj(\000)31 b Fn(_)-36 b Fl(\033)2519 3530 y Fm(\023)2603 3647 y Fj(\025)23 b Fn(0)p Fl(:)515 3852 y Fn(Or,)k Fl(\025)711 3822 y Ff(2)767 3852 y Fj(\000)k Fn(_)-36 b Fl(\033)26 b Fj(\025)d Fn(0.)639 3952 y(A)28 b(smo)r(oth)g(tra)n(v)n(eling)d(w)n (a)n(v)n(e)h(of)i(\(26\))f(at)h(sp)r(eed)f Fl(c)h Fn(satis\014es)1321 4068 y Fm(8)1321 4143 y(>)1321 4168 y(<)1321 4317 y(>)1321 4342 y(:)1437 4129 y Fj(\000)p Fl(cu)1586 4099 y Fi(0)1626 4129 y Fn(+)18 b Fl(v)1752 4099 y Fi(0)1959 4129 y Fn(=)k(0)p Fl(;)1437 4229 y Fj(\000)p Fl(cv)1581 4199 y Fi(0)1622 4229 y Fn(+)c Fl(w)1766 4199 y Fi(0)1959 4229 y Fn(=)k(0)p Fl(;)1437 4368 y Fj(\000)p Fl(cw)1599 4338 y Fi(0)1640 4368 y Fn(+)c Fl(\025)1771 4338 y Ff(2)1809 4368 y Fl(v)1852 4338 y Fi(0)1959 4368 y Fn(=)2056 4312 y(1)p 2056 4349 42 4 v 2060 4425 a Fl(\017)2108 4368 y Fn(\()p Fl(\033)s Fn(\()p Fl(u)p Fn(\))h Fj(\000)f Fl(w)r Fn(\))p Fl(:)3231 4263 y Fn(\(27\))639 4541 y(By)28 b(in)n(tegration,)e(this)i(amoun)n (ts)f(to)1325 4759 y Fl(c)p Fn(\()p Fl(\025)1441 4724 y Ff(2)1498 4759 y Fj(\000)18 b Fl(c)1617 4724 y Ff(2)1654 4759 y Fn(\))p Fl(u)1734 4724 y Fi(0)1780 4759 y Fn(=)1878 4703 y(1)p 1878 4740 V 1882 4816 a Fl(\017)1929 4759 y Fn(\()p Fl(\033)s Fn(\()p Fl(u)p Fn(\))h Fj(\000)f Fl(c)2261 4724 y Ff(2)2299 4759 y Fl(u)g Fn(+)g Fl(C)6 b Fn(\))p Fl(;)663 b Fn(\(28\))1905 5255 y(11)p eop %%Page: 12 12 12 11 bop 515 523 a Fn(where)22 b Fl(C)28 b Fn(is)23 b(a)f(constan)n(t.)34 b(By)22 b(standard)g(phase)g(plane)g(analysis,)g (it)h(is)f(easy)g(to)g(kno)n(w)g(that)515 623 y(a)h(tra)n(v)n(eling)g (w)n(a)n(v)n(e)f(solution)i(exists)g(if)h(and)f(only)f(if)i(the)g(c)n (hord)e(connecting)g(the)i(Riemann)515 722 y(data)i(k)n(eeps)g(on)g (one)g(side)h(of)f(the)h(constitutiv)n(e)g(curv)n(e)e Fl(\033)s Fn(\()p Fl(u)p Fn(\).)639 822 y(Mean)n(while,)c(w)n(e)e (observ)n(e)e(that)j(\(26\))f(admits)g(stationary)f(phase)h(b)r (oundary)g(solutions)515 922 y(as)36 b(w)n(ell,)i(with)f Fl(v)1066 934 y Fk(l)1130 922 y Fn(=)g Fl(v)1272 934 y Fk(r)1309 922 y Fl(;)14 b(\033)s Fn(\()p Fl(u)1476 934 y Fk(l)1502 922 y Fn(\))38 b(=)f Fl(\033)s Fn(\()p Fl(u)1804 934 y Fk(r)1841 922 y Fn(\).)64 b(W)-7 b(e)37 b(shall)f(call)g(it)h(0)2610 891 y Ff(#)2668 922 y Fn(-w)n(a)n(v)n(e)e (and)h(0)3120 891 y Fk(b)3153 922 y Fn(-w)n(a)n(v)n(e,)515 1021 y(dep)r(ending)28 b(on)f(the)h(relativ)n(e)e(p)r(osition)i(of)f Fl(u)1926 1033 y Fk(l)1979 1021 y Fn(and)g Fl(u)2188 1033 y Fk(r)2225 1021 y Fn(.)639 1121 y(As)h(a)f(summary)-7 b(,)27 b(there)g(are)g(\014v)n(e)g(classes)g(of)g(elemen)n(tary)g(w)n (a)n(v)n(es.)639 1303 y Fj(\017)41 b Fn(Bac)n(kw)n(ard)23 b(and)h(forw)n(ard)f(slip)i(line)f(\()p Fj(\006)1964 1235 y(p)p 2034 1235 42 4 v 2034 1303 a Fn(2)o(-)g(and)h Fj(\006)p Fn(1-)e(w)n(a)n(v)n(e\):)34 b(The)25 b(end-states)f(are)722 1403 y(in)k(the)f(same)g(stable)g(phase,)f Fl(v)31 b Fn(ma)n(y)26 b(either)h(increase)f(or)h(decrease.)35 b(By)27 b(Rankine-)722 1503 y(Hugoniot)33 b(condition,)i(the)e(sp)r (eed)h(is)f Fj(\006)2022 1434 y(p)p 2091 1434 V 69 x Fn(2)g(or)f Fj(\006)p Fn(1)g(dep)r(ending)i(on)f(the)h(phase)f(it)722 1602 y(falls)28 b(in.)639 1768 y Fj(\017)41 b Fn(Subsonic)34 b(phase)f(b)r(oundary)f(with)j(one)e(end-state)g(as)g Fl(u)f Fn(=)h(1)g(\()p Fl(T)12 b Fj(\006)p Fn(-w)n(a)n(v)n(e\):)46 b(The)722 1868 y(other)41 b(end-state)f(is)h(in)h(the)f(phase)g Fl(u)k(>)g Fn(2,)f Fl(v)g Fn(decreases)39 b(when)i(crossing)f(the)722 1968 y(discon)n(tin)n(uit)n(y)32 b(from)f(left)i(to)e(the)h(righ)n(t.) 49 b(The)32 b(sp)r(eed)g(is)g(giv)n(en)f(b)n(y)g(the)i(Rankine-)722 2067 y(Hugoniot)23 b(condition)g(with)h(absolute)f(v)-5 b(alue)23 b(less)g(than)h(1,)f(p)r(ositiv)n(e)g(if)h Fl(u)f Fn(=)f(1)h(is)h(the)722 2167 y(righ)n(t)j(end-state,)g(and)h (negativ)n(e)e(if)i(left.)639 2333 y Fj(\017)41 b Fn(Subsonic)28 b(phase)g(b)r(oundary)f(with)i(one)f(end-state)g(as)f Fl(u)d Fn(=)f(1)p Fl(:)p Fn(5)28 b(\()p Fl(B)t Fj(\006)p Fn(-w)n(a)n(v)n(e\):)36 b(The)722 2433 y(other)e(end-state)h(is)f(in)h (the)g(phase)g Fl(u)f(<)g Fn(0)p Fl(:)p Fn(75,)i Fl(v)i Fn(increases)33 b(when)i(crossing)e(the)722 2532 y(discon)n(tin)n(uit)n (y)f(from)f(left)i(to)e(the)h(righ)n(t.)49 b(The)32 b(sp)r(eed)g(is)g (giv)n(en)f(b)n(y)g(the)i(Rankine-)722 2632 y(Hugoniot)c(condition)h (with)g(absolute)f(v)-5 b(alue)29 b(less)g(than)h(1,)g(p)r(ositiv)n(e)f (if)h Fl(u)c Fn(=)f(1)p Fl(:)p Fn(5)k(is)722 2731 y(the)f(left)h (end-state,)e(and)g(negativ)n(e)g(if)h(righ)n(t.)639 2897 y Fj(\017)41 b Fn(Sup)r(ersonic)30 b(phase)f(b)r(oundary)h(or)f (sho)r(c)n(k)g(\()p Fl(S)5 b Fj(\006)p Fn(-w)n(a)n(v)n(e\):)39 b(The)30 b(t)n(w)n(o)g(end-states)f(are)722 2997 y(in)h(the)g (di\013eren)n(t)f(phases)g Fl(u)c Fj(\024)h Fn(0)j(and)g Fl(u)d Fj(\025)f Fn(1)p Fl(:)p Fn(5,)30 b(resp)r(ectiv)n(ely)-7 b(,)29 b(and)g Fl(v)k Fn(ma)n(y)28 b(either)722 3097 y(decrease)k(or)h(increase)f(across)f(the)j(discon)n(tin)n(uit)n(y)-7 b(.)53 b(The)33 b(sp)r(eed)h(is)f(giv)n(en)g(b)n(y)g(the)722 3196 y(Rankine-Hugoniot)27 b(condition)g(with)h(absolute)f(v)-5 b(alue)28 b(no)f(less)g(than)h(1.)639 3362 y Fj(\017)41 b Fn(Stationary)d(phase)h(b)r(oundaries)f(\(0)1893 3332 y Ff(#)1951 3362 y Fn(-,)k(0)2086 3332 y Fk(b)2119 3362 y Fn(-w)n(a)n(v)n(e:)58 b(The)39 b(t)n(w)n(o)f(end-states)h(are)f(in) 722 3462 y(di\013eren)n(t)20 b(stable)f(phases.)33 b(The)20 b(propagating)d(sp)r(eed)i(is)h(0,)g(and)g Fl(v)i Fn(k)n(eeps)d(unc)n (hanged)722 3562 y(across)26 b(the)i(b)r(oundary)-7 b(.)639 3744 y(F)g(or)31 b(b)r(etter)h(comprehension,)g(please)f(refer)g(to)g (T)-7 b(able)32 b(1)f(and)g(Figure)g(1,)i(where)e(the)515 3844 y(arro)n(w)25 b(is)j(from)f(the)h(left)g(end-state)f(to)h(the)g (righ)n(t)f(end-state.)515 4027 y Fe(Remark)k(9)41 b Fd(The)33 b(tr)l(aveling)h(wave)f(e)l(quation)g(\(28\))g(is)g(the)g (same)g(as)g(that)g(yielde)l(d)h(fr)l(om)515 4126 y(the)e(visc)l(osity) h(formulation)f(of)h(\(2\).)45 b(The)33 b(kinetic)f(r)l(elation)h(is)f (the)f(same)i(as)f(chor)l(d)h(cri-)515 4226 y(terion)d(studie)l(d)g(by) g(She)l(ar)l(er)g([24)r(].)1905 5255 y Fn(12)p eop %%Page: 13 13 13 12 bop 1120 523 a Fn(T)-7 b(able)27 b(1.)37 b(Elemen)n(tary)26 b(w)n(a)n(v)n(es)g(in)i(Suliciu's)g(mo)r(del)p 515 634 2732 4 v 515 650 V 513 750 4 100 v 565 720 a(W)-7 b(a)n(v)n(e)p 816 750 V 105 w(Sp)r(eed)28 b(c)p 1405 750 V 310 w(u)p 2308 750 V 857 w([v])p 3245 750 V 515 753 2732 4 v 513 859 4 106 v 565 829 a(+)630 760 y Fj(p)p 698 760 42 4 v 698 829 a Fn(2-)p 816 859 4 106 v 867 760 a Fj(p)p 936 760 42 4 v 69 x Fn(2)p 1405 859 4 106 v 478 w Fl(u)1504 841 y Fk(l;r)1605 829 y Fj(\024)22 b Fn(1)p 2308 859 V 2359 760 a Fj(p)p 2428 760 42 4 v 69 x Fn(2[)p Fl(u)p Fn(])p 3245 859 4 106 v 515 862 2732 4 v 513 967 4 106 v 565 937 a Fj(\000)630 869 y(p)p 698 869 42 4 v 698 937 a Fn(2-)p 816 967 4 106 v 99 w Fj(\000)932 869 y(p)p 1001 869 42 4 v 68 x Fn(2)p 1405 967 4 106 v 413 w Fl(u)1504 949 y Fk(l;r)1605 937 y Fj(\024)g Fn(1)p 2308 967 V 625 w Fj(\000)2424 869 y(p)p 2493 869 42 4 v 68 x Fn(2)o([)p Fl(u)p Fn(])p 3245 967 4 106 v 515 970 2732 4 v 513 1070 4 100 v 565 1040 a(+1-)p 816 1070 V 167 w(1)p 1405 1070 V 547 w Fl(u)1504 1052 y Fk(l;r)1605 1040 y Fj(\025)g Fn(1)p Fl(:)p Fn(5)p 2308 1070 V 560 w([)p Fl(u)p Fn(])p 3245 1070 V 515 1073 2732 4 v 513 1173 4 100 v 565 1143 a Fj(\000)p Fn(1-)p 816 1173 V 167 w Fj(\000)p Fn(1)p 1405 1173 V 482 w Fl(u)1504 1155 y Fk(l;r)1605 1143 y Fj(\025)g Fn(1)p Fl(:)p Fn(5)p 2308 1173 V 560 w Fj(\000)p Fn([)p Fl(u)p Fn(])p 3245 1173 V 515 1176 2732 4 v 513 1277 4 101 v 565 1247 a(0)607 1217 y Ff(#)665 1247 y Fn(-)p 816 1277 V 174 w(0)p 1405 1277 V 547 w Fl(u)1504 1259 y Fk(r)1564 1247 y Fn(=)g(2)p Fl(u)1741 1259 y Fk(l)1789 1247 y Fj(2)h Fn([1)p Fl(:)p Fn(5)p Fl(;)14 b Fn(2])p 2308 1277 V 260 w(0)p 3245 1277 V 515 1280 2732 4 v 513 1380 4 101 v 565 1351 a(0)607 1320 y Fk(b)639 1351 y Fn(-)p 816 1380 V 200 w(0)p 1405 1380 V 547 w Fl(u)1504 1363 y Fk(l)1552 1351 y Fn(=)23 b(2)p Fl(u)1730 1363 y Fk(r)1789 1351 y Fj(2)g Fn([1)p Fl(:)p Fn(5)p Fl(;)14 b Fn(2])p 2308 1380 V 260 w(0)p 3245 1380 V 515 1384 2732 4 v 513 1586 4 203 v 565 1511 a Fl(T)614 1523 y Ff(+)668 1511 y Fn(-)p 816 1586 V 867 1390 a Fm(r)p 950 1390 236 4 v 960 1454 a Fl(u)1008 1466 y Fk(l)1052 1454 y Fj(\000)k Fn(2)p 960 1491 216 4 v 960 1567 a Fl(u)1008 1579 y Fk(l)1052 1567 y Fj(\000)g Fn(1)p 1405 1586 4 203 v 1456 1511 a Fl(u)1504 1523 y Fk(r)1564 1511 y Fn(=)k(1)p Fl(;)14 b(u)1778 1523 y Fk(l)1826 1511 y Fl(>)22 b Fn(2)p 2308 1586 V 404 w Fj(\000)2424 1440 y Fm(p)p 2507 1440 562 4 v 71 x Fn(\()p Fl(u)2587 1523 y Fk(l)2630 1511 y Fj(\000)c Fn(2\)\()p Fl(u)2867 1523 y Fk(l)2911 1511 y Fj(\000)g Fn(1\))p 3245 1586 4 203 v 515 1590 2732 4 v 513 1792 4 203 v 565 1716 a Fl(T)614 1728 y Fi(\000)669 1716 y Fn(-)p 816 1792 V 170 w Fj(\000)932 1596 y Fm(r)p 1015 1596 248 4 v 1025 1660 a Fl(u)1073 1672 y Fk(r)1127 1660 y Fj(\000)g Fn(2)p 1025 1697 228 4 v 1025 1773 a Fl(u)1073 1785 y Fk(r)1127 1773 y Fj(\000)g Fn(1)p 1405 1792 4 203 v 1456 1716 a Fl(u)1504 1728 y Fk(r)1564 1716 y Fl(>)k Fn(2)p Fl(;)14 b(u)1778 1728 y Fk(l)1826 1716 y Fn(=)22 b(1)p 2308 1792 V 404 w Fj(\000)2424 1645 y Fm(p)p 2507 1645 584 4 v 71 x Fn(\()p Fl(u)2587 1728 y Fk(r)2642 1716 y Fj(\000)c Fn(2\)\()p Fl(u)2879 1728 y Fk(r)2933 1716 y Fj(\000)g Fn(1\))p 3245 1792 4 203 v 515 1796 2732 4 v 513 1998 4 203 v 565 1922 a Fl(B)628 1934 y Ff(+)683 1922 y Fn(-)p 816 1998 V 867 1802 a Fm(r)p 950 1802 343 4 v 960 1866 a Fn(1)p Fl(:)p Fn(5)g Fj(\000)g Fn(2)p Fl(u)1258 1878 y Fk(l)p 960 1903 323 4 v 981 1979 a Fn(1)p Fl(:)p Fn(5)f Fj(\000)h Fl(u)1236 1991 y Fk(l)p 1405 1998 4 203 v 1456 1922 a Fl(u)1504 1934 y Fk(r)1564 1922 y Fn(=)k(1)p Fl(:)p Fn(5)p Fl(;)14 b(u)1843 1934 y Fk(l)1890 1922 y Fj(2)24 b Fn(\(0)p Fl(;)14 b Fn(0)p Fl(:)p Fn(75\))p 2308 1998 V 2359 1851 a Fm(p)p 2442 1851 732 4 v 71 x Fn(\(1)p Fl(:)p Fn(5)k Fj(\000)g Fn(2)p Fl(u)2772 1934 y Fk(l)2796 1922 y Fn(\)\(1)p Fl(:)p Fn(5)g Fj(\000)h Fl(u)3117 1934 y Fk(l)3142 1922 y Fn(\))p 3245 1998 4 203 v 515 2001 2732 4 v 513 2204 4 203 v 565 2128 a Fl(B)628 2140 y Fi(\000)684 2128 y Fn(-)p 816 2204 V 155 w Fj(\000)932 2008 y Fm(r)p 1015 2008 343 4 v 1025 2072 a Fn(1)p Fl(:)p Fn(5)e Fj(\000)h Fn(2)p Fl(u)1322 2084 y Fk(l)p 1025 2109 323 4 v 1045 2185 a Fn(1)p Fl(:)p Fn(5)g Fj(\000)g Fl(u)1301 2197 y Fk(l)p 1405 2204 4 203 v 1456 2128 a Fl(u)1504 2140 y Fk(r)1564 2128 y Fj(2)23 b Fn(\(0)p Fl(;)14 b Fn(0)p Fl(:)p Fn(75\))p Fl(;)g(u)2019 2140 y Fk(l)2066 2128 y Fn(=)22 b(1)p Fl(:)p Fn(5)p 2308 2204 V 2359 2057 a Fm(p)p 2442 2057 755 4 v 71 x Fn(\(1)p Fl(:)p Fn(5)c Fj(\000)g Fn(2)p Fl(u)2772 2140 y Fk(r)2808 2128 y Fn(\)\(1)p Fl(:)p Fn(5)g Fj(\000)g Fl(u)3128 2140 y Fk(r)3164 2128 y Fn(\))p 3245 2204 4 203 v 515 2207 2732 4 v 513 2410 4 203 v 565 2334 a Fl(S)616 2346 y Ff(+)671 2334 y Fn(-)p 816 2410 V 867 2214 a Fm(r)p 950 2214 321 4 v 960 2278 a Fl(u)1008 2290 y Fk(r)1063 2278 y Fj(\000)g Fn(2)p Fl(u)1236 2290 y Fk(l)p 960 2315 301 4 v 981 2391 a Fl(u)1029 2403 y Fk(r)1084 2391 y Fj(\000)g Fl(u)1215 2403 y Fk(l)p 1405 2410 4 203 v 1456 2334 a Fl(u)1504 2346 y Fk(r)1564 2334 y Fl(>)k Fn(1)p Fl(:)p Fn(5)p Fl(;)14 b(u)1843 2346 y Fk(l)1890 2334 y Fj(\024)23 b Fn(0)p 2308 2410 V 2359 2263 a Fm(p)p 2442 2263 689 4 v 71 x Fn(\()p Fl(u)2522 2346 y Fk(r)2577 2334 y Fj(\000)18 b Fn(2)p Fl(u)2750 2346 y Fk(l)2775 2334 y Fn(\)\()p Fl(u)2887 2346 y Fk(r)2942 2334 y Fj(\000)g Fl(u)3073 2346 y Fk(l)3098 2334 y Fn(\))p 3245 2410 4 203 v 515 2413 2732 4 v 513 2616 4 203 v 565 2540 a Fl(S)616 2552 y Fi(\000)671 2540 y Fn(-)p 816 2616 V 168 w Fj(\000)932 2420 y Fm(r)p 1015 2420 321 4 v 1025 2484 a Fl(u)1073 2496 y Fk(l)1116 2484 y Fj(\000)g Fn(2)p Fl(u)1289 2496 y Fk(r)p 1025 2521 301 4 v 1045 2597 a Fl(u)1093 2609 y Fk(l)1137 2597 y Fj(\000)g Fl(u)1268 2609 y Fk(r)p 1405 2616 4 203 v 1456 2540 a Fl(u)1504 2552 y Fk(r)1564 2540 y Fj(\024)k Fn(0)p Fl(;)14 b(u)1778 2552 y Fk(l)1826 2540 y Fl(>)22 b Fn(1)p Fl(:)p Fn(5)p 2308 2616 V 2359 2469 a Fm(p)p 2442 2469 689 4 v 71 x Fn(\()p Fl(u)2522 2552 y Fk(l)2566 2540 y Fj(\000)c Fn(2)p Fl(u)2739 2552 y Fk(r)2775 2540 y Fn(\)\()p Fl(u)2887 2552 y Fk(l)2931 2540 y Fj(\000)g Fl(u)3062 2552 y Fk(r)3098 2540 y Fn(\))p 3245 2616 4 203 v 515 2619 2732 4 v 639 2827 a(No)n(w)27 b(w)n(e)g(shall)g(construct)g(a)g(Riemann)g(solv)n(er)f(with)h(these)h (elemen)n(tary)e(w)n(a)n(v)n(es.)35 b(Let)515 2926 y(\()p Fl(u)595 2896 y Fi(\003)633 2926 y Fl(;)14 b(v)713 2896 y Fi(\003)751 2926 y Fn(\))30 b(=)f(\()p Fl(u)p Fn(\(0)p Fj(\000)p Fl(;)14 b(t)p Fn(\))p Fl(;)g(v)s Fn(\(0)p Fj(\000)p Fl(;)g(t)p Fn(\)\),)32 b(b)n(y)f(studying)g(the)h(elemen)n(tary)e(w)n (a)n(v)n(es,)h(w)n(e)g(ma)n(y)g(\014nd)515 3026 y(that)d(starting)e (from)i(\()p Fl(u)1281 2996 y Fi(\000)1336 3026 y Fl(;)14 b(v)1416 2996 y Fi(\000)1473 3026 y Fn(\),)28 b(the)g(jump)g(in)g Fl(v)j Fn(led)d(b)n(y)f(left-going)g(w)n(a)n(v)n(es)e(is)515 3126 y Fl(v)558 3095 y Fi(\003)615 3126 y Fj(\000)18 b Fl(v)741 3095 y Fi(\000)820 3126 y Fn(=)639 3225 y(if)28 b Fl(u)763 3195 y Fi(\000)842 3225 y Fj(\024)23 b Fn(1,)595 3426 y Fm(\032)699 3491 y Fj(\000)764 3423 y(p)p 833 3423 42 4 v 68 x Fn(2)o(\()p Fl(u)954 3461 y Fi(\003)1011 3491 y Fj(\000)18 b Fl(u)1142 3461 y Fi(\000)1197 3491 y Fn(\))p Fl(;)811 b Fn(for)82 b Fl(u)2293 3461 y Fi(\003)2354 3491 y Fj(\024)22 b Fn(1)p Fl(;)83 b Fn(b)n(y)27 b Fj(\000)2769 3423 y(p)p 2838 3423 V 68 x Fn(2-w)n(a)n(v)n(e)m Fl(;)699 3599 y Fj(\000)764 3530 y(p)p 833 3530 V 69 x Fn(2)o(\(1)19 b Fj(\000)f Fl(u)1098 3569 y Fi(\000)1153 3599 y Fn(\))h Fj(\000)1287 3528 y Fm(p)p 1370 3528 587 4 v 71 x Fn(\()p Fl(u)1450 3575 y Fi(\003)1506 3599 y Fj(\000)f Fn(1\)\()p Fl(u)1743 3575 y Fi(\003)1800 3599 y Fj(\000)g Fn(2\))o Fl(;)84 b Fn(for)e Fl(u)2293 3569 y Fi(\003)2354 3599 y Fl(>)22 b Fn(2)p Fl(;)83 b Fn(b)n(y)27 b Fj(\000)2769 3530 y(p)p 2838 3530 42 4 v 69 x Fn(2)p Fl(;)14 b(T)2966 3611 y Fi(\000)3021 3599 y Fn(-w)n(a)n(v)n(e)n(;)3231 3699 y(\(29\))639 3799 y(and)28 b(if)g Fl(u)925 3769 y Fi(\000)1003 3799 y Fj(\025)23 b Fn(1)p Fl(:)p Fn(5,)515 3998 y Fm(8)515 4073 y(<)515 4222 y(:)630 4060 y Fj(\000)p Fn(\()p Fl(u)775 4030 y Fi(\003)831 4060 y Fj(\000)18 b Fl(u)962 4030 y Fi(\000)1018 4060 y Fn(\))p Fl(;)1045 b Fn(for)82 b Fl(u)2348 4030 y Fi(\003)2409 4060 y Fj(\025)23 b Fn(1)p Fl(:)p Fn(5)p Fl(;)257 b Fn(b)n(y)28 b Fj(\000)p Fn(1-w)n(a)n(v)n(e)m Fl(;)630 4167 y Fj(\000)p Fn(\(1)p Fl(:)p Fn(5)17 b Fj(\000)h Fl(u)982 4137 y Fi(\000)1038 4167 y Fn(\))h(+)1172 4096 y Fm(p)p 1255 4096 758 4 v 71 x Fn(\(1)p Fl(:)p Fn(5)f Fj(\000)g Fl(u)1543 4143 y Fi(\003)1580 4167 y Fn(\)\(1)p Fl(:)p Fn(5)g Fj(\000)g Fn(2)p Fl(u)1942 4143 y Fi(\003)1980 4167 y Fn(\))p Fl(;)83 b Fn(for)f Fl(u)2348 4137 y Fi(\003)2409 4167 y Fj(2)24 b Fn(\(0)p Fl(;)14 b Fn(0)p Fl(:)p Fn(75\))p Fl(;)81 b Fn(b)n(y)28 b Fj(\000)p Fn(1)p Fl(;)14 b(B)3207 4179 y Fi(\000)3262 4167 y Fn(-w)n(a)n(v)n(e)n Fl(;)630 4204 y Fm(p)p 713 4204 753 4 v 71 x Fn(\()p Fl(u)793 4251 y Fi(\000)867 4275 y Fj(\000)k Fn(2)p Fl(u)1040 4251 y Fi(\003)1078 4275 y Fn(\)\()p Fl(u)1190 4251 y Fi(\000)1264 4275 y Fj(\000)g Fl(u)1395 4251 y Fi(\003)1433 4275 y Fn(\))p Fl(;)630 b Fn(for)82 b Fl(u)2348 4245 y Fi(\003)2409 4275 y Fj(\024)23 b Fn(0)p Fl(;)322 b Fn(b)n(y)28 b Fl(S)3051 4287 y Fi(\000)3107 4275 y Fn(-w)n(a)n(v)n(e)m Fl(:)3231 4375 y Fn(\(30\))639 4475 y(It)h(is)g(observ)n(ed)e(that)i(for)f(an)n (y)g(giv)n(en)g Fl(u)1891 4445 y Fi(\000)1947 4475 y Fn(,)h Fl(v)2042 4445 y Fi(\003)2099 4475 y Fj(\000)19 b Fl(v)2226 4445 y Fi(\000)2311 4475 y Fn(is)29 b(a)f(monotonically)g (decreasing)515 4574 y(function)g(of)f Fl(u)982 4544 y Fi(\003)1020 4574 y Fn(,)h(with)g(a)f(gap)g(in)h(\(1)p Fl(;)14 b Fn(2\))27 b(or)g(\(0)p Fl(:)p Fn(75)p Fl(;)14 b Fn(1\).)35 b(See)28 b(Figure)f(2)g(\(a\)\(b\).)639 4674 y(Mean)n(while,)40 b(starting)c(from)h(\()p Fl(u)1695 4644 y Ff(+)1750 4674 y Fl(;)14 b(v)1830 4644 y Ff(+)1885 4674 y Fn(\),)40 b(the)e(jump)g(in)g Fl(v)j Fn(led)c(b)n(y)g(righ)n (t-going)e(and)515 4774 y(stationary)26 b(w)n(a)n(v)n(es)f(is)515 4873 y Fl(v)558 4843 y Fi(\003)615 4873 y Fj(\000)18 b Fl(v)741 4843 y Ff(+)819 4873 y Fn(=)639 4973 y(if)28 b Fl(u)763 4943 y Ff(+)841 4973 y Fj(\024)23 b Fn(1,)1905 5255 y(13)p eop %%Page: 14 14 14 13 bop 533 624 a Fm(8)533 699 y(<)533 848 y(:)648 621 y Fj(p)p 717 621 42 4 v 69 x Fn(2\()p Fl(u)839 660 y Fi(\003)895 690 y Fj(\000)18 b Fl(u)1026 660 y Ff(+)1081 690 y Fn(\))p Fl(;)810 b Fn(for)82 b Fl(u)2176 660 y Fi(\003)2237 690 y Fj(\024)23 b Fn(1)p Fl(;)262 b Fn(b)n(y)28 b(+)2833 621 y Fj(p)p 2901 621 V 2901 690 a Fn(2-w)n(a)n(v)n(e)n Fl(;)648 726 y Fj(p)p 717 726 V 69 x Fn(2\(0)p Fl(:)p Fn(5)p Fl(u)946 765 y Fi(\003)1001 795 y Fj(\000)18 b Fl(u)1132 765 y Ff(+)1187 795 y Fn(\))p Fl(;)704 b Fn(for)82 b Fl(u)2176 765 y Fi(\003)2237 795 y Fj(2)24 b Fn([1)p Fl(:)p Fn(5)p Fl(;)14 b Fn(2])p Fl(;)81 b Fn(b)n(y)28 b(0)2810 765 y Fk(b)2843 795 y Fl(;)14 b Fn(+)2945 726 y Fj(p)p 3013 726 V 3013 795 a Fn(2-w)n(a)n(v)n(e)n Fl(;)648 834 y Fj(p)p 717 834 V 68 x Fn(2\(1)k Fj(\000)g Fl(u)982 872 y Ff(+)1037 902 y Fn(\))g(+)1170 831 y Fm(p)p 1253 831 587 4 v 71 x Fn(\()p Fl(u)1333 878 y Fi(\003)1390 902 y Fj(\000)g Fn(1\)\()p Fl(u)1627 878 y Fi(\003)1683 902 y Fj(\000)g Fn(2\))p Fl(;)83 b Fn(for)f Fl(u)2176 872 y Fi(\003)2237 902 y Fl(>)23 b Fn(2)p Fl(;)262 b Fn(b)n(y)28 b Fl(T)2817 914 y Ff(+)2871 902 y Fl(;)14 b Fn(+)2973 834 y Fj(p)p 3042 834 42 4 v 68 x Fn(2)o(-w)n(a)n(v)n(e)n (;)3231 1003 y(\(31\))639 1102 y(and)28 b(if)g Fl(u)925 1072 y Ff(+)1003 1102 y Fj(\025)22 b Fn(1)p Fl(:)p Fn(5,)515 1302 y Fm(8)515 1376 y(>)515 1401 y(>)515 1426 y(<)515 1576 y(>)515 1601 y(>)515 1625 y(:)630 1363 y Fl(u)678 1333 y Fi(\003)734 1363 y Fj(\000)c Fl(u)865 1333 y Ff(+)920 1363 y Fl(;)1045 b Fn(for)82 b Fl(u)2218 1333 y Fi(\003)2279 1363 y Fj(\025)23 b Fn(1)p Fl(:)p Fn(5)p Fl(;)257 b Fn(b)n(y)28 b(+1-w)n(a)n(v)n(e)m Fl(;)630 1464 y Fn(2)p Fl(u)720 1433 y Fi(\003)776 1464 y Fj(\000)18 b Fl(u)907 1433 y Ff(+)961 1464 y Fl(;)1004 b Fn(for)82 b Fl(u)2218 1433 y Fi(\003)2279 1464 y Fj(2)24 b Fn([0)p Fl(:)p Fn(75)p Fl(;)14 b Fn(1])p Fl(;)99 b Fn(b)n(y)28 b(0)2912 1433 y Ff(#)2970 1464 y Fl(;)14 b Fn(+1-w)n(a)n(v)n(e)m Fl(;)630 1571 y Fn(1)p Fl(:)p Fn(5)k Fj(\000)g Fl(u)886 1541 y Ff(+)959 1571 y Fj(\000)1042 1500 y Fm(p)p 1125 1500 758 4 v 71 x Fn(\(1)p Fl(:)p Fn(5)g Fj(\000)g Fl(u)1413 1547 y Fi(\003)1450 1571 y Fn(\)\(1)p Fl(:)p Fn(5)g Fj(\000)g Fn(2)p Fl(u)1812 1547 y Fi(\003)1850 1571 y Fn(\))p Fl(;)83 b Fn(for)f Fl(u)2218 1541 y Fi(\003)2279 1571 y Fj(2)24 b Fn(\(0)p Fl(;)14 b Fn(0)p Fl(:)p Fn(75\))p Fl(;)81 b Fn(b)n(y)28 b Fl(B)2933 1583 y Ff(+)2988 1571 y Fl(;)14 b Fn(+1-w)n(a)n(v)n(e)m Fl(;)630 1679 y Fj(\000)695 1608 y Fm(p)p 778 1608 751 4 v 71 x Fn(\()p Fl(u)858 1655 y Ff(+)931 1679 y Fj(\000)k Fn(2)p Fl(u)1104 1655 y Fi(\003)1141 1679 y Fn(\)\()p Fl(u)1253 1655 y Ff(+)1327 1679 y Fj(\000)g Fl(u)1458 1655 y Fi(\003)1496 1679 y Fn(\))p Fl(;)437 b Fn(for)82 b Fl(u)2218 1648 y Fi(\003)2279 1679 y Fj(\024)23 b Fn(0)p Fl(;)322 b Fn(b)n(y)28 b Fl(S)2921 1691 y Ff(+)2976 1679 y Fn(-w)n(a)n(v)n(e)m Fl(:)3231 1779 y Fn(\(32\))639 1879 y(It)33 b(is)e(observ)n(ed)g(that)h(for)f(an)n(y)h(giv)n(en)f Fl(u)1914 1849 y Ff(+)1968 1879 y Fn(,)i Fl(v)2067 1849 y Fi(\003)2127 1879 y Fj(\000)21 b Fl(v)2256 1849 y Ff(+)2343 1879 y Fn(is)32 b(a)g(piecewise)f(monotonically)515 1978 y(increasing)26 b(function)i(of)g Fl(u)1371 1948 y Fi(\003)1408 1978 y Fn(,)g(with)g(a)f(gap)g(in)h(\(1)p Fl(;)14 b Fn(2\))27 b(or)g(\(0)p Fl(:)p Fn(75)p Fl(;)14 b Fn(1\).)35 b(See)28 b(Figure)f(2\(c\)\(d\).)639 2078 y(W)-7 b(e)26 b(note)e(here)h(that)g (the)g(w)n(a)n(v)n(e)e(pro\014les)h(listed)h(here)g(exhaust)f(all)h (the)g(p)r(ossible)g(com-)515 2178 y(binations)39 b(of)g(the)h(elemen)n (tary)e(w)n(a)n(v)n(es,)i(except)g(the)f(com)n(bination)g(of)g(0)2917 2147 y Ff(#)2975 2178 y Fn(-w)n(a)n(v)n(e)f(with)515 2277 y(0)557 2247 y Fk(b)590 2277 y Fn(-w)n(a)n(v)n(e.)64 b(The)37 b(latter)g(indeed)h(means)f(a)g(single)g(line)g Fl(x)j Fn(=)f(0)e(in)h(\()p Fl(x;)14 b(t)p Fn(\)-plane,)40 b(across)515 2377 y(whic)n(h)33 b(the)h(solution)f(is)h(con)n(tin)n (uous.)53 b(It)34 b(is)f(equiv)-5 b(alen)n(t)34 b(to)f(no)g(discon)n (tin)n(uit)n(y)g(in)h(w)n(eak)515 2476 y(sense,)k(and)e(the)h(n)n (umerical)e(sim)n(ulations)g(sho)n(w)h(that)g(it)h(is)f(unstable,)j(th) n(us)d(excluded)515 2576 y(here.)639 2676 y(No)n(w)22 b(to)g(solv)n(e)g(a)g(Riemann)g(problem)g(\(2\)-\(25\),)h(one)f(solv)n (es)f(the)h(algebraic)f(equations)515 2775 y(\(29\))39 b(\(or)f(\(30\)\))h(and)g(\(31\))g(\(or)f(\(32\)\))i(to)f(\014nd)g Fl(u)2129 2745 y Fi(\003)2167 2775 y Fn(.)71 b(Or)39 b(equiv)-5 b(alen)n(tly)e(,)42 b(one)c(\014nds)i(the)515 2875 y(in)n(tersection)26 b(p)r(oin)n(t)i(of)f(the)h(t)n(w)n(o)f(curv)n (es)f(in)h(Figure)g(2)g(\(a\))h(\(or)e(\(b\)\))j(and)e(\(c\))h(\(or)f (\(d\)\).)38 b(It)515 2975 y(can)27 b(b)r(e)i(easily)e(sho)n(wn)g(that) h(there)g(exists)f(one)h(and)f(only)h(one)f(suc)n(h)h(in)n(tersection)f (p)r(oin)n(t.)515 3074 y(It)22 b(is)h(in)n(teresting)e(that)i(the)f (gap)g(in)g(the)h(\014rst)f(t)n(w)n(o)g(curv)n(es)f(just)i(\014ts)f(in) h(the)f(non-monotone)515 3174 y(part)j(of)h(the)g(latter)g(t)n(w)n(o)f (curv)n(es,)g(and)h(in)g(turn)g(unique)g(in)n(tersection)f(p)r(oin)n(t) h(follo)n(ws)f(if)h Fl(u)3341 3144 y Fi(\003)515 3273 y Fn(lies)h(in)h(the)g(in)n(terv)-5 b(al.)639 3373 y(The)35 b(Riemann)g(solv)n(er)f(is)h(describ)r(ed)f(in)i(T)-7 b(able)34 b(2)h(and)g(Figure)f(3.)59 b(Numerical)35 b(ex-)515 3473 y(p)r(erimen)n(ts)e(with)i(\(14\)-\(25\))e(rev)n(eal)f(that)i(the) g(Riemann)g(solv)n(er)e(listed)i(here)g(describ)r(es)515 3572 y(correctly)f(the)h(limiting)h(b)r(eha)n(vior)e(of)h(the)h (Suliciu's)g(mo)r(del.)57 b(F)-7 b(or)34 b(example,)i(w)n(e)e(com-)515 3672 y(pute)40 b(the)f(solution)g(with)h(\()p Fl(u)1477 3642 y Fi(\000)1533 3672 y Fl(;)14 b(v)1613 3642 y Fi(\000)1669 3672 y Fn(\))43 b(=)f(\()p Fj(\000)p Fn(0)p Fl(:)p Fn(2)p Fl(;)14 b Fn(0\))p Fl(;)g Fn(\()p Fl(u)2283 3642 y Ff(+)2337 3672 y Fl(;)g(v)2417 3642 y Ff(+)2472 3672 y Fn(\))43 b(=)f(\(3)p Fl(;)14 b Fn(0\).)72 b(By)39 b(the)g(Rie-)515 3772 y(mann)29 b(solv)n(er,)f(the)h(solution)f(for)h(\(2\))g(comprises) f(a)g Fj(\000)2247 3703 y(p)p 2316 3703 42 4 v 69 x Fn(2-w)n(a)n(v)n (e,)f(a)i(0)2726 3741 y Ff(#)2784 3772 y Fn(-w)n(a)n(v)n(e,)e(and)i(a)g (+1)515 3871 y(w)n(a)n(v)n(e,)39 b(i.e.)69 b(falls)38 b(in)n(to)g(the)h(category)d(C)j(in)f(T)-7 b(able)38 b(2.)69 b(The)38 b(n)n(umerical)g(results)g(with)515 3971 y Fl(\025)27 b Fn(=)g(2)p Fl(;)14 b Fj(4)p Fl(x)26 b Fn(=)h(0)p Fl(:)p Fn(01)p Fl(;)14 b Fj(4)p Fl(t)25 b Fn(=)i(0)p Fl(:)p Fn(005)h(is)i(plotted)g(in)h(Figure)e(4.)44 b(The)31 b(data)e(sho)n(ws)g(that)i(the)515 4070 y(in)n(termediate)19 b(state)h(\()p Fl(u)1265 4040 y Fi(\003)1303 4070 y Fl(;)14 b(v)1383 4040 y Fi(\003)1421 4070 y Fn(\))21 b(agrees)d(v)n(ery)g(w)n (ell)i(with)g(that)h(obtained)e(with)i(the)f(Riemann)515 4170 y(solv)n(er.)639 4270 y(Let)39 b(us)g(no)n(w)f(tak)n(e)g(an)g (example)g(to)h(illustrate)f(the)h(elemen)n(tary)f(w)n(a)n(v)n(es,)h (and)g(the)515 4369 y(generic)21 b(pro\014les.)34 b(W)-7 b(e)23 b(consider)f(the)g(pro\014le)g(A,)h(whic)n(h)f(constitutes)h (consequen)n(tly)-7 b(,)22 b(from)515 4469 y(left)30 b(to)f(righ)n(t)f(in)h(the)h(\()p Fl(t;)14 b(x)p Fn(\))30 b(plane,)f Fj(\000)1729 4400 y(p)p 1798 4400 V 69 x Fn(2-w)n(a)n(v)n (e,)e Fl(T)2144 4481 y Ff(+)2199 4469 y Fn(-w)n(a)n(v)n(e,)h Fl(T)2504 4481 y Fi(\000)2559 4469 y Fn(-w)n(a)n(v)n(e,)g(and)h(+)3043 4400 y Fj(p)p 3111 4400 V 3111 4469 a Fn(2-w)n(a)n(v)n(e,)515 4569 y(as)f(sho)n(wn)g(in)i(Figure)e(5.)41 b(Because)28 b(b)r(oth)h(+)1920 4500 y Fj(p)p 1989 4500 V 69 x Fn(2)o(-w)n(a)n(v)n (e)e(and)i Fj(\000)2490 4500 y(p)p 2559 4500 V 69 x Fn(2)o(-w)n(a)n(v)n (e)e(tak)n(e)i(end-states)515 4668 y(in)f Fl(u)23 b(<)g Fn(1,)k(this)h(pro\014le)f(only)h(solv)n(es)e(Riemann)i(problem)f(with) h Fl(u)2610 4680 y Fi(\000)2666 4668 y Fl(;)14 b(u)2751 4680 y Ff(+)2829 4668 y Fj(\024)23 b Fn(1.)37 b(Moreo)n(v)n(er,)515 4768 y(b)n(y)27 b(Rankine-Hugoniot)f(relation,)h(w)n(e)g(kno)n(w)g (that)1476 4967 y Fl(v)1516 4979 y Ff(1)1572 4967 y Fj(\000)18 b Fl(v)1698 4932 y Fi(\000)1777 4967 y Fn(=)23 b Fj(\000)1930 4894 y(p)p 1999 4894 V 73 x Fn(2)o(\()p Fl(u)2120 4979 y Ff(1)2176 4967 y Fj(\000)18 b Fl(u)2307 4932 y Fi(\000)2362 4967 y Fn(\))p Fl(:)1905 5255 y Fn(14)p eop %%Page: 15 15 15 14 bop 515 523 a Fn(F)-7 b(or)27 b Fl(T)713 535 y Fi(\000)768 523 y Fn(-w)n(a)n(v)n(e,)f(the)i(left)g(end-states,)f(i.e.) 37 b Fl(u)1917 535 y Ff(1)1977 523 y Fn(=)23 b(0,)k(and)1383 725 y Fl(v)1426 691 y Fi(\003)1483 725 y Fj(\000)18 b Fl(v)1606 737 y Ff(1)1666 725 y Fn(=)23 b Fj(\000)1819 650 y Fm(p)p 1901 650 587 4 v 1901 725 a Fn(\()p Fl(u)1981 701 y Fi(\003)2038 725 y Fj(\000)18 b Fn(1\)\()p Fl(u)2275 701 y Fi(\003)2331 725 y Fj(\000)g Fn(2\))p Fl(:)515 908 y Fn(Therefore,)26 b(for)h(these)h(t)n(w)n(o)f(left-going)f(w)n(a)n (v)n(es,)g(w)n(e)h(ha)n(v)n(e,)1110 1106 y Fl(v)1153 1072 y Fi(\003)1210 1106 y Fj(\000)18 b Fl(v)1336 1072 y Fi(\000)1415 1106 y Fn(=)23 b Fj(\000)1568 1034 y(p)p 1637 1034 42 4 v 72 x Fn(2)o(\(1)c Fj(\000)f Fl(u)1902 1072 y Fi(\000)1957 1106 y Fn(\))h Fj(\000)2091 1031 y Fm(p)p 2174 1031 587 4 v 75 x Fn(\()p Fl(u)2254 1083 y Fi(\003)2310 1106 y Fj(\000)f Fn(1\)\()p Fl(u)2547 1083 y Fi(\003)2604 1106 y Fj(\000)g Fn(2\))o Fl(;)515 1289 y Fn(whic)n(h)27 b(is)h(exactly)f(the)h(second)f(line)g(of)h (\(29\).)639 1389 y(Similarly)-7 b(,)27 b(for)h Fl(T)1185 1401 y Ff(+)1239 1389 y Fn(-w)n(a)n(v)n(e,)e(the)i(righ)n(t)f (endstates,)g(i.e.)37 b Fl(u)2416 1401 y Ff(2)2476 1389 y Fn(=)23 b(0,)k(and)1383 1591 y Fl(v)1423 1603 y Ff(2)1479 1591 y Fj(\000)18 b Fl(v)1605 1557 y Fi(\003)1666 1591 y Fn(=)23 b Fj(\000)1819 1516 y Fm(p)p 1901 1516 V 1901 1591 a Fn(\()p Fl(u)1981 1567 y Fi(\003)2038 1591 y Fj(\000)18 b Fn(1\)\()p Fl(u)2275 1567 y Fi(\003)2331 1591 y Fj(\000)g Fn(2\))p Fl(:)515 1773 y Fn(Mean)n(while,)27 b(b)n(y)g(+)1133 1705 y Fj(p)p 1202 1705 42 4 v 68 x Fn(2)o(-w)n(a)n(v)n(e,)f(one)h(has) 1531 1972 y Fl(v)1574 1938 y Ff(+)1648 1972 y Fj(\000)18 b Fl(v)1771 1984 y Ff(2)1831 1972 y Fn(=)1919 1900 y Fj(p)p 1988 1900 V 72 x Fn(2\()p Fl(u)2110 1938 y Ff(+)2183 1972 y Fj(\000)g Fn(1\))p Fl(:)515 2155 y Fn(Therefore,)26 b(for)h(these)h(t)n(w)n(o)f(righ)n(t-going)e(w)n(a)n(v)n(es,)h(w)n(e)h (ha)n(v)n(e,)1143 2354 y Fl(v)1186 2319 y Ff(+)1260 2354 y Fj(\000)18 b Fl(v)1386 2319 y Fi(\003)1448 2354 y Fn(=)1535 2281 y Fj(p)p 1605 2281 V 1605 2354 a Fn(2)o(\()p Fl(u)1726 2319 y Ff(+)1799 2354 y Fj(\000)g Fn(1\))h Fj(\000)2058 2279 y Fm(p)p 2141 2279 587 4 v 75 x Fn(\()p Fl(u)2221 2330 y Fi(\003)2277 2354 y Fj(\000)f Fn(1\)\()p Fl(u)2514 2330 y Fi(\003)2570 2354 y Fj(\000)g Fn(2\))p Fl(;)515 2536 y Fn(whic)n(h)27 b(is)h(the)g(third)g(line)f(of)h(\(31\).)639 2636 y(As)g(a)f(result,)h(w)n(e)f(ha)n(v)n(e)f(an)h(equation)g(for)h Fl(u)2029 2606 y Fi(\003)2066 2636 y Fn(,)979 2835 y Fl(v)1022 2801 y Ff(+)1096 2835 y Fj(\000)18 b Fl(v)1222 2801 y Fi(\000)1301 2835 y Fn(=)23 b Fj(\000)1454 2762 y(p)p 1522 2762 42 4 v 1522 2835 a Fn(2\(2)18 b Fj(\000)g Fl(u)1787 2801 y Ff(+)1860 2835 y Fj(\000)g Fl(u)1991 2801 y Fi(\000)2047 2835 y Fn(\))h Fj(\000)f Fn(2)2223 2760 y Fm(p)p 2305 2760 587 4 v 2305 2835 a Fn(\()p Fl(u)2385 2811 y Fi(\003)2442 2835 y Fj(\000)g Fn(1\)\()p Fl(u)2679 2811 y Fi(\003)2735 2835 y Fj(\000)g Fn(2\))p Fl(:)316 b Fn(\(33\))639 2985 y(By)29 b(some)g(basic)g(calculations,)g(one)g (kno)n(ws)f(that)i(this)g(quadratic)e(equation)h(admits)515 3084 y(t)n(w)n(o)e(real)f(solutions)h(if)h(and)g(only)f(if)1385 3283 y Fl(v)1428 3249 y Ff(+)1502 3283 y Fj(\000)18 b Fl(v)1628 3249 y Fi(\000)1707 3283 y Fj(\024)23 b(\000)1860 3210 y(p)p 1929 3210 42 4 v 73 x Fn(2)o(\(2)18 b Fj(\000)h Fl(u)2194 3249 y Ff(+)2267 3283 y Fj(\000)f Fl(u)2398 3249 y Fi(\000)2453 3283 y Fn(\))p Fl(:)515 3466 y Fn(Moreo)n(v)n(er,) 30 b(as)i(the)g(sum)h(of)f(these)g(t)n(w)n(o)f(ro)r(ots)g(equals)h(to)f (3,)i(w)n(e)f(select)g(the)h(bigger)d(one)515 3565 y(as)39 b Fl(u)677 3535 y Fi(\003)755 3565 y Fn(to)h(satisfy)g(the)g(condition) g(of)g Fl(u)1828 3535 y Fi(\003)1909 3565 y Fj(\025)k Fn(1)p Fl(:)p Fn(5)39 b(for)g Fl(T)2352 3577 y Ff(+)2407 3565 y Fl(;)14 b(T)2493 3577 y Fi(\000)2548 3565 y Fn(-w)n(a)n(v)n(es.) 72 b(So,)43 b(in)e(Figure)515 3665 y(3,)32 b(pro\014le)f(A)i(solv)n(es) d(uniquely)-7 b(,)33 b(and)f(in)g(fact)g(con)n(tin)n(uously)-7 b(,)32 b(Riemann)g(problems)f(with)515 3765 y Fl(u)563 3734 y Ff(+)617 3765 y Fl(;)14 b(u)702 3734 y Fi(\000)781 3765 y Fl(<)23 b Fn(1)p Fl(;)14 b(v)991 3734 y Ff(+)1064 3765 y Fj(\000)k Fl(v)1190 3734 y Fi(\000)1269 3765 y Fj(\024)23 b(\000)1422 3696 y(p)p 1490 3696 V 1490 3765 a Fn(2\(2)18 b Fj(\000)g Fl(u)1755 3734 y Ff(+)1828 3765 y Fj(\000)g Fl(u)1959 3734 y Fi(\000)2015 3765 y Fn(\).)639 3864 y(Other)27 b(generic)g(w)n(a)n(v)n(e)f(pro\014les)h(can)g(b)r(e)h (deriv)n(ed)f(in)g(the)h(same)f(fashion.)639 3964 y(W)-7 b(e)28 b(ma)n(y)f(conclude)g(this)h(section)g(b)n(y)f(summarize)g(the)h (results.)515 4146 y Fe(Prop)s(osition)i(10)41 b Fd(Kinetic)36 b(r)l(elation)g(yielde)l(d)h(by)f(Suliciu's)g(mo)l(del)g(\(26\))g(is)g (the)g(chor)l(d)515 4246 y(criterion.)j(With)30 b(this)g(kinetic)g(r)l (elation,)g(the)g(R)n(iemann)f(pr)l(oblem)i(is)e(uniquely)h(solvable.) 1905 5255 y Fn(15)p eop %%Page: 16 16 16 15 bop 711 523 a Fn(T)-7 b(able)27 b(2.)36 b(Generic)28 b(w)n(a)n(v)n(e)e(pro\014les)g(for)h(Riemann)h(problem)f(\()p Fl(u)2717 535 y Fi(\003)2778 523 y Fn(=)c Fl(u)p Fn(\(0)p Fj(\000)p Fl(;)14 b(t)p Fn(\)\))p 515 638 3196 4 v 515 655 V 513 755 4 100 v 689 755 V 740 725 a(Pro\014le)p 1447 755 V 521 w([)p Fl(v)s Fn(])p 3131 755 V 1594 w(P)n(arameter)p 3708 755 V 515 758 3196 4 v 513 866 4 108 v 565 836 a(A)p 689 866 V 113 w Fj(\000)805 767 y(p)p 874 767 42 4 v 69 x Fn(2)23 b Fj(!)g Fl(T)1094 848 y Fi(\000)1172 836 y Fj(!)g Fl(T)1327 848 y Ff(+)p 1447 866 4 108 v 1499 767 a Fj(p)p 1568 767 42 4 v 69 x Fn(2)o(\()p Fl(u)1689 805 y Ff(+)1763 836 y Fn(+)18 b Fl(u)1894 805 y Fi(\000)1968 836 y Fj(\000)g Fn(2)p Fl(u)2141 848 y Fi(\003)2178 836 y Fn(\))h Fj(\000)f Fn(2)2354 765 y Fm(p)p 2436 765 587 4 v 2436 836 a Fn(\()p Fl(u)2516 848 y Fi(\003)2573 836 y Fj(\000)g Fn(2\)\()p Fl(u)2810 848 y Fi(\003)2866 836 y Fj(\000)g Fn(1\))p 3131 866 4 108 v 159 w Fl(u)3230 848 y Fi(\003)3291 836 y Fl(>)23 b Fn(2)p 3708 866 V 513 971 4 106 v 689 971 V 906 941 a Fj(!)g Fn(+)1077 872 y Fj(p)p 1146 872 42 4 v 69 x Fn(2)p 1447 971 4 106 v 3131 971 V 3708 971 V 515 974 3196 4 v 513 1082 4 108 v 565 1052 a(B)p 689 1082 V 116 w Fj(\000)805 983 y(p)p 874 983 42 4 v 69 x Fn(2)g Fj(!)g Fl(T)1094 1064 y Fi(\000)1172 1052 y Fj(!)g Fn(+1)p 1447 1082 4 108 v 114 w Fj(\000)1564 983 y(p)p 1632 983 42 4 v 1632 1052 a Fn(2\(1)18 b Fj(\000)g Fl(u)1897 1022 y Fi(\000)1953 1052 y Fn(\))g Fj(\000)2086 981 y Fm(p)p 2169 981 587 4 v 71 x Fn(\()p Fl(u)2249 1064 y Fi(\003)2306 1052 y Fj(\000)g Fn(2\)\()p Fl(u)2543 1064 y Fi(\003)2599 1052 y Fj(\000)g Fn(1\))p 3131 1082 4 108 v 426 w Fl(u)3230 1064 y Fi(\003)3291 1052 y Fl(>)23 b Fn(2)p 3708 1082 V 513 1181 4 100 v 689 1181 V 1447 1181 V 1665 1151 a(+)p Fl(u)1778 1121 y Ff(+)1850 1151 y Fj(\000)18 b Fl(u)1981 1163 y Fi(\003)p 3131 1181 V 3708 1181 V 515 1184 3196 4 v 513 1290 4 106 v 565 1260 a Fn(C)p 689 1290 V 115 w Fj(\000)805 1191 y(p)p 874 1191 42 4 v 69 x Fn(2)23 b Fj(!)g Fn(0)1087 1230 y Ff(#)1168 1260 y Fj(!)g Fn(+1)p 1447 1290 4 106 v 118 w Fj(\000)1564 1191 y(p)p 1632 1191 42 4 v 1632 1260 a Fn(2\()p Fl(u)1754 1272 y Fi(\003)1810 1260 y Fj(\000)18 b Fl(u)1941 1230 y Fi(\000)1997 1260 y Fn(\))h(+)f(\()p Fl(u)2211 1230 y Ff(+)2284 1260 y Fj(\000)g Fn(2)p Fl(u)2457 1272 y Fi(\003)2494 1260 y Fn(\))p 3131 1290 4 106 v 656 w Fl(u)3230 1272 y Fi(\003)3291 1260 y Fj(2)23 b Fn([0)p Fl(:)p Fn(75)p Fl(;)14 b Fn(1])p 3708 1290 V 515 1293 3196 4 v 513 1401 4 108 v 565 1371 a(D)p 689 1401 V 112 w Fj(\000)805 1302 y(p)p 874 1302 42 4 v 69 x Fn(2)23 b Fj(!)g Fl(B)1108 1383 y Ff(+)1186 1371 y Fj(!)g Fn(+1)p 1447 1401 4 108 v 100 w Fj(\000)1564 1302 y(p)p 1632 1302 42 4 v 1632 1371 a Fn(2\()p Fl(u)1754 1383 y Fi(\003)1810 1371 y Fj(\000)18 b Fl(u)1941 1341 y Fi(\000)1997 1371 y Fn(\))h(+)2131 1300 y Fm(p)p 2214 1300 758 4 v 71 x Fn(\(1)p Fl(:)p Fn(5)e Fj(\000)h Fn(2)p Fl(u)2543 1383 y Fi(\003)2581 1371 y Fn(\)\(1)p Fl(:)p Fn(5)g Fj(\000)g Fl(u)2901 1383 y Fi(\003)2938 1371 y Fn(\))p 3131 1401 4 108 v 212 w Fl(u)3230 1383 y Fi(\003)3291 1371 y Fj(2)23 b Fn(\(0)p Fl(;)14 b Fn(0)p Fl(:)p Fn(75\))p 3708 1401 V 513 1500 4 100 v 689 1500 V 1447 1500 V 1665 1470 a(+)p Fl(u)1778 1440 y Ff(+)1850 1470 y Fj(\000)k Fn(1)p Fl(:)p Fn(5)p 3131 1500 V 3708 1500 V 515 1503 3196 4 v 513 1611 4 108 v 565 1581 a(E)p 689 1611 V 118 w Fj(\000)805 1512 y(p)p 874 1512 42 4 v 69 x Fn(2)23 b Fj(!)g Fl(S)1096 1593 y Ff(+)p 1447 1611 4 108 v 1499 1581 a Fj(\000)1564 1512 y(p)p 1632 1512 42 4 v 1632 1581 a Fn(2\()p Fl(u)1754 1593 y Fi(\003)1810 1581 y Fj(\000)18 b Fl(u)1941 1551 y Fi(\000)1997 1581 y Fn(\))h(+)2131 1510 y Fm(p)p 2214 1510 751 4 v 71 x Fn(\()p Fl(u)2294 1557 y Ff(+)2367 1581 y Fj(\000)f Fn(2)p Fl(u)2540 1593 y Fi(\003)2577 1581 y Fn(\)\()p Fl(u)2689 1557 y Ff(+)2763 1581 y Fj(\000)g Fl(u)2894 1593 y Fi(\003)2932 1581 y Fn(\))p 3131 1611 4 108 v 218 w Fl(u)3230 1593 y Fi(\003)3291 1581 y Fj(\024)23 b Fn(0)p 3708 1611 V 515 1614 3196 4 v 513 1720 4 106 v 565 1690 a(F)p 689 1720 V 121 w Fj(\000)805 1621 y(p)p 874 1621 42 4 v 69 x Fn(2)g Fj(!)g Fn(+)1110 1621 y Fj(p)p 1178 1621 V 1178 1690 a Fn(2)p 1447 1720 4 106 v 1499 1621 a Fj(p)p 1568 1621 42 4 v 69 x Fn(2)o(\()p Fl(u)1689 1660 y Fi(\000)1764 1690 y Fn(+)18 b Fl(u)1895 1660 y Ff(+)1968 1690 y Fj(\000)g Fn(2)p Fl(u)2141 1702 y Fi(\003)2178 1690 y Fn(\))p 3131 1720 4 106 v 972 w Fl(u)3230 1702 y Fi(\003)3291 1690 y Fj(\024)23 b Fn(1)p 3708 1720 V 515 1723 3196 4 v 513 1830 4 108 v 565 1800 a(G)p 689 1830 V 110 w Fl(S)791 1812 y Fi(\000)870 1800 y Fj(!)g Fl(S)1027 1812 y Ff(+)p 1447 1830 V 1499 1729 a Fm(p)p 1582 1729 753 4 v 71 x Fn(\()p Fl(u)1662 1776 y Fi(\000)1736 1800 y Fj(\000)18 b Fn(2)p Fl(u)1909 1812 y Fi(\003)1946 1800 y Fn(\)\()p Fl(u)2058 1776 y Fi(\000)2133 1800 y Fj(\000)g Fl(u)2264 1812 y Fi(\003)2301 1800 y Fn(\))p 3131 1830 4 108 v 849 w Fl(u)3230 1812 y Fi(\003)3291 1800 y Fj(\024)23 b Fn(0)p 3708 1830 V 513 1938 V 689 1938 V 1447 1938 V 1665 1908 a(+)1730 1837 y Fm(p)p 1812 1837 751 4 v 1812 1908 a Fn(\()p Fl(u)1892 1884 y Ff(+)1966 1908 y Fj(\000)18 b Fn(2)p Fl(u)2139 1920 y Fi(\003)2176 1908 y Fn(\)\()p Fl(u)2288 1884 y Ff(+)2361 1908 y Fj(\000)g Fl(u)2492 1920 y Fi(\003)2530 1908 y Fn(\))p 3131 1938 4 108 v 3708 1938 V 515 1941 3196 4 v 513 2049 4 108 v 565 2019 a(H)p 689 2049 V 113 w Fl(S)791 2031 y Fi(\000)870 2019 y Fj(!)23 b Fn(+)1041 1950 y Fj(p)p 1110 1950 42 4 v 69 x Fn(2)p 1447 2049 4 108 v 1499 1948 a Fm(p)p 1582 1948 753 4 v 71 x Fn(\()p Fl(u)1662 1995 y Fi(\000)1736 2019 y Fj(\000)18 b Fn(2)p Fl(u)1909 2031 y Fi(\003)1946 2019 y Fn(\)\()p Fl(u)2058 1995 y Fi(\000)2133 2019 y Fj(\000)g Fl(u)2264 2031 y Fi(\003)2301 2019 y Fn(\))h(+)2435 1950 y Fj(p)p 2504 1950 42 4 v 69 x Fn(2\()p Fl(u)2626 1989 y Ff(+)2699 2019 y Fj(\000)f Fl(u)2830 2031 y Fi(\003)2868 2019 y Fn(\))p 3131 2049 4 108 v 282 w Fl(u)3230 2031 y Fi(\003)3291 2019 y Fj(\024)23 b Fn(0)p 3708 2049 V 515 2052 3196 4 v 513 2160 4 108 v 565 2130 a(I)p 689 2160 V 145 w Fj(\000)p Fn(1)f Fj(!)i Fl(B)1039 2142 y Fi(\000)1118 2130 y Fj(!)f Fl(B)t Fn(+)p 1447 2160 V 143 w(\()p Fl(u)1579 2100 y Fi(\000)1653 2130 y Fn(+)18 b Fl(u)1784 2100 y Ff(+)1857 2130 y Fj(\000)g Fn(2)p Fl(u)2030 2142 y Fi(\003)2067 2130 y Fn(\))h(+)f(2)2243 2059 y Fm(p)p 2325 2059 758 4 v 2325 2130 a Fn(\(1)p Fl(:)p Fn(5)g Fj(\000)g Fn(2)p Fl(u)2655 2142 y Fi(\003)2693 2130 y Fn(\)\(1)p Fl(:)p Fn(5)g Fj(\000)g Fl(u)3013 2142 y Fi(\003)3050 2130 y Fn(\))p 3131 2160 4 108 v 100 w Fl(u)3230 2142 y Fi(\003)3291 2130 y Fj(2)23 b Fn(\(0)p Fl(;)14 b Fn(0)p Fl(:)p Fn(75\))p 3708 2160 V 513 2259 4 100 v 689 2259 V 906 2229 a Fj(!)23 b Fn(+1)p 1447 2259 V 3131 2259 V 3708 2259 V 515 2262 3196 4 v 513 2370 4 108 v 565 2340 a(J)p 689 2370 V 132 w Fj(\000)p Fn(1)f Fj(!)i Fl(B)1039 2352 y Fi(\000)1118 2340 y Fj(!)f Fn(+)1289 2271 y Fj(p)p 1357 2271 42 4 v 1357 2340 a Fn(2)p 1447 2370 4 108 v 100 w Fl(u)1547 2310 y Fi(\000)1621 2340 y Fj(\000)18 b Fl(u)1752 2352 y Fi(\003)1808 2340 y Fn(+)1891 2269 y Fm(p)p 1974 2269 758 4 v 71 x Fn(\(1)p Fl(:)p Fn(5)g Fj(\000)g Fn(2)p Fl(u)2304 2352 y Fi(\003)2341 2340 y Fn(\)\(1)p Fl(:)p Fn(5)g Fj(\000)g Fl(u)2661 2352 y Fi(\003)2699 2340 y Fn(\))p 3131 2370 4 108 v 451 w Fl(u)3230 2352 y Fi(\003)3291 2340 y Fj(2)23 b Fn(\(0)p Fl(;)14 b Fn(0)p Fl(:)p Fn(75\))p 3708 2370 V 513 2475 4 106 v 689 2475 V 1447 2475 V 1665 2445 a(+)1730 2377 y Fj(p)p 1798 2377 42 4 v 1798 2445 a Fn(2\()p Fl(u)1920 2415 y Ff(+)1993 2445 y Fj(\000)k Fl(u)2124 2457 y Fi(\003)2162 2445 y Fn(\))p 3131 2475 4 106 v 3708 2475 V 515 2479 3196 4 v 513 2584 4 106 v 565 2554 a(K)p 689 2584 V 110 w Fj(\000)p Fn(1)k Fj(!)i Fn(0)1018 2524 y Fk(b)1073 2554 y Fj(!)g Fn(+)1245 2485 y Fj(p)p 1313 2485 42 4 v 1313 2554 a Fn(2)p 1447 2584 4 106 v 144 w Fl(u)1547 2524 y Fi(\000)1621 2554 y Fj(\000)18 b Fl(u)1752 2566 y Fi(\003)1808 2554 y Fn(+)1891 2485 y Fj(p)p 1960 2485 42 4 v 69 x Fn(2)o(\()p Fl(u)2081 2524 y Ff(+)2155 2554 y Fj(\000)g Fl(u)2286 2566 y Fi(\003)2324 2554 y Fl(=)p Fn(2\))p 3131 2584 4 106 v 742 w Fl(u)3230 2566 y Fi(\003)3291 2554 y Fj(2)23 b Fn([1)p Fl(:)p Fn(5)p Fl(;)14 b Fn(2])p 3708 2584 V 515 2587 3196 4 v 513 2695 4 108 v 565 2665 a(L)p 689 2695 V 123 w Fj(\000)p Fn(1)22 b Fj(!)i Fl(T)1025 2677 y Ff(+)1102 2665 y Fj(!)f Fn(+)1273 2596 y Fj(p)p 1342 2596 42 4 v 69 x Fn(2)p 1447 2695 4 108 v 115 w Fl(u)1547 2635 y Fi(\000)1621 2665 y Fj(\000)18 b Fl(u)1752 2677 y Fi(\003)1808 2665 y Fj(\000)1891 2594 y Fm(p)p 1974 2594 587 4 v 71 x Fn(\()p Fl(u)2054 2677 y Fi(\003)2110 2665 y Fj(\000)g Fn(2\)\()p Fl(u)2347 2677 y Fi(\003)2403 2665 y Fj(\000)g Fn(1\))p 3131 2695 4 108 v 622 w Fl(u)3230 2677 y Fi(\003)3291 2665 y Fl(>)23 b Fn(2)p 3708 2695 V 513 2800 4 106 v 689 2800 V 1447 2800 V 1665 2770 a(+)1730 2701 y Fj(p)p 1798 2701 42 4 v 1798 2770 a Fn(2\()p Fl(u)1920 2740 y Ff(+)1993 2770 y Fj(\000)18 b Fl(u)2124 2782 y Fi(\003)2162 2770 y Fn(\))p 3131 2800 4 106 v 3708 2800 V 515 2803 3196 4 v 513 2903 4 100 v 565 2873 a(M)p 689 2903 V 99 w Fj(\000)p Fn(1)k Fj(!)i Fn(+1)p 1447 2903 V 416 w Fl(u)1547 2843 y Fi(\000)1621 2873 y Fn(+)18 b Fl(u)1752 2843 y Ff(+)1825 2873 y Fj(\000)g Fn(2)p Fl(u)1998 2885 y Fi(\003)p 3131 2903 V 3182 2873 a Fl(u)3230 2885 y Fi(\003)3291 2873 y Fj(\025)23 b Fn(1)p Fl(:)p Fn(5)p 3708 2903 V 515 2906 3196 4 v 515 3246 a Fa(4.2)112 b(Jin-Xin's)36 b(relaxation)h(mo)s(del)515 3400 y Fn(Jin)31 b(and)g(Xin)h(prop)r(osed)e(a)h(relaxation)f(mo)r(del)h(to)g(appro)n (ximate)f(a)h(h)n(yp)r(erb)r(olic)f(system)515 3499 y([18)o(].)36 b(By)26 b(an)f(example,)h(Jin)g(sho)n(ws)f(that)h(it)g(also)f(applies)h (to)f(mixed-t)n(yp)r(e)h(partial)f(di\013er-)515 3599 y(en)n(tial)i(equations)g([19)o(].)37 b(The)28 b(mo)r(del)f(is)1379 3724 y Fm(8)1379 3799 y(>)1379 3824 y(>)1379 3849 y(>)1379 3873 y(>)1379 3898 y(<)1379 4048 y(>)1379 4073 y(>)1379 4098 y(>)1379 4122 y(>)1379 4147 y(:)1495 3777 y Fl(u)1543 3789 y Fk(t)1590 3777 y Fn(+)18 b Fl(w)1732 3789 y Fk(x)1943 3777 y Fn(=)23 b(0)1495 3876 y Fl(v)1535 3888 y Fk(t)1583 3876 y Fn(+)18 b Fl(z)1705 3888 y Fk(x)1943 3876 y Fn(=)23 b(0)1495 4016 y Fl(w)1554 4028 y Fk(t)1602 4016 y Fn(+)18 b Fl(\025)1733 3986 y Ff(2)1771 4016 y Fl(u)1819 4028 y Fk(x)1943 4016 y Fn(=)2041 3960 y(1)p 2041 3997 42 4 v 2045 4073 a Fl(\017)2092 4016 y Fn(\()p Fl(v)k Fj(\000)c Fl(w)r Fn(\))1495 4182 y Fl(z)1534 4194 y Fk(t)1581 4182 y Fn(+)g Fl(\025)1712 4152 y Ff(2)1750 4182 y Fl(v)1790 4194 y Fk(x)1943 4182 y Fn(=)2041 4126 y(1)p 2041 4163 V 2045 4239 a Fl(\017)2092 4182 y Fn(\()p Fl(\033)s Fn(\()p Fl(u)p Fn(\))h Fj(\000)f Fl(z)t Fn(\))3231 3994 y(\(34\))639 4355 y(In)28 b(this)g(case,)f(w)n(e)g(ha)n(v)n(e)991 4683 y(\003)22 b(=)h(\()p Fl(\025)p Fn(\))p Fl(;)251 b(M)32 b Fn(=)1779 4627 y(1)p 1755 4664 90 4 v 1755 4740 a(2)p Fl(\025)1869 4466 y Fm(2)1869 4612 y(6)1869 4662 y(6)1869 4715 y(4)1966 4533 y Fl(\025)119 b Fn(1)151 b(0)1969 4632 y(0)86 b Fj(\000)p Fl(\025)116 b Fn(1)1966 4732 y Fl(\025)87 b Fj(\000)p Fn(1)118 b(0)1969 4832 y(0)h Fl(\025)c Fj(\000)p Fn(1)2441 4466 y Fm(3)2441 4612 y(7)2441 4662 y(7)2441 4715 y(5)2510 4516 y(2)2510 4666 y(4)2664 4583 y Fl(u)2667 4682 y(v)2607 4782 y(\033)s Fn(\()p Fl(u)p Fn(\))2811 4516 y Fm(3)2811 4666 y(5)2880 4683 y Fl(:)515 4987 y Fn(The)27 b(stabilit)n(y)h(condition)f(is)h Fl(\025)1505 4957 y Ff(2)1561 4987 y Fj(\000)j Fn(_)-36 b Fl(\033)26 b Fj(\025)d Fn(0.)1905 5255 y(16)p eop %%Page: 17 17 17 16 bop 639 523 a Fn(W)-7 b(e)34 b(start)e(with)i(the)g(study)f(of)g (tra)n(v)n(eling)e(w)n(a)n(v)n(es)h(to)h(\014nd)g(the)h(kinetic)f (relation.)53 b(A)515 623 y(tra)n(v)n(eling)39 b(w)n(a)n(v)n(e)f(with)k (sp)r(eed)e Fl(c)h Fn(satis\014es)f(a)g(set)g(of)h(ordinary)e (di\013eren)n(tial)h(equations)515 761 y(\(`)23 b(=)g Fl(\017)864 705 y(d)p 725 742 323 4 v 725 818 a(d)p Fn(\()p Fl(x)c Fj(\000)f Fl(ct)p Fn(\))1057 761 y(\))1392 869 y Fm(8)1392 944 y(>)1392 968 y(>)1392 993 y(<)1392 1143 y(>)1392 1168 y(>)1392 1193 y(:)1507 939 y Fj(\000)p Fl(cu)p Fn(`)g(+)g Fl(w)r Fn(`)169 b(=)23 b(0)p Fl(;)1507 1038 y Fj(\000)p Fl(cv)s Fn(`)c(+)f Fl(z)t Fn(`)191 b(=)23 b(0)p Fl(;)1507 1138 y Fj(\000)p Fl(cw)r Fn(`)c(+)f Fl(\025)1842 1108 y Ff(2)1880 1138 y Fl(u)p Fn(`)82 b(=)23 b Fl(v)f Fj(\000)c Fl(w)r(;)1507 1237 y Fj(\000)p Fl(cz)t Fn(`)g(+)g Fl(\025)1823 1207 y Ff(2)1860 1237 y Fl(v)s Fn(`)107 b(=)23 b Fl(\033)s Fn(\()p Fl(u)p Fn(\))c Fj(\000)f Fl(z)t(:)3231 1089 y Fn(\(35\))639 1383 y(The)33 b(\014rst)f(t)n(w)n(o)g(equations)g (can)g(b)r(e)h(in)n(tegrated,)g(and)f(the)h(in)n(tegration)e(constan)n (t)h(in)515 1483 y(the)c(\014rst)h(one)f(can)g(b)r(e)g(set)h(to)f(0,)g (b)n(y)g(virtue)g(of)h(the)g(translation)e(in)n(v)-5 b(ariance)27 b(of)h Fl(v)s Fn(.)40 b(After)515 1621 y(a)27 b(rescaling,)f(i.e.)37 b(taking)1348 1591 y Fi(0)1394 1621 y Fn(=)1512 1565 y Fl(d)p 1492 1602 84 4 v 1492 1678 a(d\030)1613 1621 y Fn(with)28 b Fl(\030)f Fn(=)2035 1565 y Fl(x)19 b Fj(\000)f Fl(ct)p 1963 1602 359 4 v 1963 1678 a(\017)p Fn(\()p Fl(\025)2077 1654 y Ff(2)2133 1678 y Fj(\000)g Fl(c)2252 1654 y Ff(2)2289 1678 y Fn(\))2331 1621 y(,)28 b(w)n(e)f(ha)n(v)n(e)1522 1732 y Fm(\032)1626 1799 y Fl(u)1674 1769 y Fi(0)1780 1799 y Fn(=)c Fl(v)e Fj(\000)d Fl(cu;)1626 1898 y(v)1669 1868 y Fi(0)1780 1898 y Fn(=)23 b Fl(\033)f Fj(\000)c Fl(cv)j Fj(\000)d Fl(C)2259 1910 y Ff(1)2297 1898 y Fl(:)3231 1849 y Fn(\(36\))639 2049 y(W)-7 b(e)20 b(observ)n(e)e(that)i(\(36\))g(is)f(the)h(same)g(as) f(the)h(tra)n(v)n(eling)e(w)n(a)n(v)n(e)g(equations)g(in)i(Slemro)r (d's)515 2148 y(viscosit)n(y-capillarit)n(y)28 b(mo)r(del)j([25)o(].)48 b(Consequen)n(tly)30 b(the)i(kinetic)f(relation)f(is)h(the)h(same.)515 2248 y(In)26 b(particular,)f(a)h(stationary)f(tra)n(v)n(eling)f(w)n(a)n (v)n(e)g(m)n(ust)j(v)n(erify)e(the)i(Maxw)n(ell)e(construction)515 2347 y(of)i(equal)g(area)f(la)n(w.)639 2447 y(There)f(are)e(t)n(w)n(o)h (kinds)h(of)g(subsonic)f(phase)g(b)r(oundaries)g(according)f(to)i(the)g (tra)n(v)n(eling)515 2547 y(w)n(a)n(v)n(e)f(equations.)36 b(One)25 b(is)h(exactly)g(the)g Fl(T)12 b Fj(\006)p Fn(-)25 b(or)g Fl(B)t Fj(\006)p Fn(-w)n(a)n(v)n(es)e(as)j(in)g(the)g(Suliciu's) h(mo)r(del.)515 2646 y(In)33 b(fact,)h(b)n(y)f(phase)f(plane)g (analysis)g(it)h(can)g(b)r(e)g(sho)n(wn)f(that)h(corresp)r(onding)e (tra)n(v)n(eling)515 2746 y(w)n(a)n(v)n(e)j(alw)n(a)n(ys)f(exists)j(if) g(the)g(c)n(hord)e(connects)i(\()p Fl(u)2134 2716 y Fi(\000)2189 2746 y Fl(;)14 b(\033)s Fn(\()p Fl(u)2356 2716 y Fi(\000)2413 2746 y Fn(\)\))36 b(and)f(\()p Fl(u)2762 2716 y Ff(+)2817 2746 y Fl(;)14 b(\033)s Fn(\()p Fl(u)2984 2716 y Ff(+)3040 2746 y Fn(\)\))36 b(lies)f(on)515 2846 y(one)27 b(side)g(of)h(the)g (constitutiv)n(e)f(curv)n(e)g(on)g(the)h(\()p Fl(u;)14 b(\033)s Fn(\()p Fl(u)p Fn(\)\)-plane,)28 b(that)g(is,)f(there)h(are)e (only)515 2945 y(t)n(w)n(o)31 b(critical)g(p)r(oin)n(ts)g(in)h(\()p Fl(u;)14 b(v)s Fn(\)-plane)32 b(for)f(the)h(dynamical)f(system)h (\(36\),)g(i.e.)50 b(\()p Fl(u)3157 2915 y Ff(+)3211 2945 y Fl(;)14 b(v)3291 2915 y Ff(+)3347 2945 y Fn(\))515 3045 y(and)30 b(\()p Fl(u)759 3015 y Fi(\000)815 3045 y Fl(;)14 b(v)895 3015 y Fi(\000)951 3045 y Fn(\).)46 b(Ho)n(w)n(ev)n(er,)29 b(through)g(n)n(umerical)h(exp)r(erimen)n(ts,)h (it)f(is)h(found)f(that)h(these)515 3144 y(w)n(a)n(v)n(es)24 b(are)h(not)h(stable.)36 b(F)-7 b(or)25 b(instance,)i(taking)e(Riemann) h(data)g(exactly)f(corresp)r(onding)515 3244 y(to)c(a)g Fl(T)722 3256 y Ff(+)777 3244 y Fn(-w)n(a)n(v)n(e,)f(\()p Fl(u)1105 3214 y Fi(\000)1161 3244 y Fl(;)14 b(v)1241 3214 y Fi(\000)1297 3244 y Fn(\))24 b(=)e(\(1)p Fl(;)14 b Fn(0\))p Fl(;)g Fn(\()p Fl(u)1742 3214 y Ff(+)1797 3244 y Fl(;)g(v)1877 3214 y Ff(+)1932 3244 y Fn(\))23 b(=)g(\(3)p Fl(;)14 b Fj(\000)p Fn(1\),)22 b(the)g(n)n(umerical)e (solution)h(turns)515 3344 y(out)30 b(to)g(comprise)f(a)g Fj(\000)1254 3275 y(p)p 1323 3275 42 4 v 69 x Fn(2-w)n(a)n(v)n(e,)f(a)i (left-going)f(subsonic)g(phase)h(b)r(oundary)f(\(kno)n(wn)h(as)515 3443 y Fl(D)584 3455 y Fi(\000)640 3443 y Fn(-w)n(a)n(v)n(e)35 b(in)j(the)g(coming)f(discussion\),)i(and)f(a)f(+1-w)n(a)n(v)n(e.)64 b(See)37 b(\()p Fl(u)p Fn(\()p Fl(x;)14 b Fn(1\))p Fl(;)g(v)s Fn(\()p Fl(x;)g Fn(1\)\))39 b(in)515 3543 y(Figure)31 b(6.)50 b(These)32 b Fl(T)1190 3555 y Fi(\006)1245 3543 y Fn(-,)h Fl(B)1392 3555 y Fi(\006)1448 3543 y Fn(-w)n(a)n(v)n(es)d (are)h(th)n(us)h(excluded)g(from)g(the)g(elemen)n(tary)f(w)n(a)n(v)n (es)515 3643 y(for)c(constructing)g(the)h(Riemann)f(solv)n(er.)639 3742 y(F)-7 b(or)39 b(the)g(other)f(kind)h(of)g(subsonic)f(phase)h(b)r (oundaries,)h(there)f(are)f(three)h(critical)515 3842 y(p)r(oin)n(ts)22 b(in)h(\(36\),)h(namely)e(\()p Fl(u)1409 3812 y Ff(+)1464 3842 y Fl(;)14 b(v)1544 3812 y Ff(+)1599 3842 y Fn(\),)25 b(\()p Fl(u)1759 3812 y Fi(\000)1814 3842 y Fl(;)14 b(v)1894 3812 y Fi(\000)1951 3842 y Fn(\),)24 b(and)e(\()p Fl(u)2266 3854 y Ff(0)2303 3842 y Fl(;)14 b(v)2380 3854 y Ff(0)2418 3842 y Fn(\))23 b(whic)n(h)f(lies)h(in)g(the) g(unstable)515 3941 y(phase.)38 b(F)-7 b(or)27 b(the)i(tri-linear)e (constitutiv)n(e)h(relation)f(\(24\),)h(w)n(e)g(shall)g(w)n(ork)f(out)h (explicitly)515 4041 y(the)d(relation)e(b)r(et)n(w)n(een)h(\()p Fl(u)1353 4011 y Fi(\000)1409 4041 y Fl(;)14 b(v)1489 4011 y Fi(\000)1545 4041 y Fn(\))25 b(and)f(\()p Fl(u)1840 4011 y Ff(+)1895 4041 y Fl(;)14 b(v)1975 4011 y Ff(+)2031 4041 y Fn(\))24 b(for)g(supp)r(orting)g(an)g(hetero)r(clinic)g(orbit,) 515 4141 y(i.e.)48 b(the)32 b(kinetic)g(relation.)47 b(Without)32 b(loss)f(of)g(generalit)n(y)-7 b(,)31 b(w)n(e)g(consider)g (here)g(only)g(the)515 4240 y(case)26 b Fl(c)d(<)g Fn(0.)515 4423 y Fe(Lemma)29 b(11)41 b Fd(F)-6 b(or)26 b(any)g(heter)l(o)l (clinic)g(orbit)g(for)g(system)g(\(36\),)h Fl(u)p Fn(\()p Fl(\030)t Fn(\))f Fd(must)e(b)l(e)h(monotone.)639 4606 y Fn(This)j(is)f(pro)n(v)n(ed)f(in)i([28)o(],)g(and)g(is)f(only)g(sk)n (etc)n(hed)g(here.)36 b(First,)28 b(w)n(e)f(rewrite)g(\(36\))g(as)1374 4717 y Fm(\032)1478 4783 y Fl(u)1526 4753 y Fi(0)1646 4783 y Fn(=)c Fl(w)r(;)1478 4883 y(w)1539 4853 y Fi(0)1646 4883 y Fn(=)g Fl(\033)f Fj(\000)c Fl(c)1922 4853 y Ff(2)1959 4883 y Fl(u)g Fj(\000)g Fl(C)2167 4895 y Ff(1)2223 4883 y Fj(\000)g Fn(2)p Fl(cw)r(:)3231 4834 y Fn(\(37\))1905 5255 y(17)p eop %%Page: 18 18 18 17 bop 639 523 a Fn(Then)28 b(w)n(e)g(compare)f(the)h(v)n(ector)f (\014eld)h(generated)f(b)n(y)h(\(37\))f(along)g(an)n(y)g(curv)n(e)g (\000)3208 493 y Ff(+)3291 523 y Fn(on)515 623 y(the)38 b(upp)r(er)f(half)h(phase)f(plane)g(and)g(the)h(v)n(ector)e(\014eld)i (on)f(the)h(re\015ected)f(curv)n(e)f(\(with)515 722 y(resp)r(ect)27 b(to)h(the)g Fl(u)p Fn(-axis\))e Fj(\000)p Fn(\000)1437 692 y Ff(+)1491 722 y Fn(,)1288 888 y Fl(dw)p 1288 925 105 4 v 1295 1001 a(du)1403 849 y Fm(\014)1403 898 y(\014)1403 948 y(\014)1430 1002 y Fi(\000)p Ff(\000)1523 986 y Fc(+)1597 944 y Fn(=)d Fj(\000)p Fn(4)p Fl(c)17 b Fj(\000)1938 888 y Fl(dw)p 1938 925 V 1945 1001 a(du)2053 849 y Fm(\014)2053 898 y(\014)2053 948 y(\014)2081 1002 y Ff(\000)2122 986 y Fc(+)2196 944 y Fl(<)23 b Fj(\000)2359 888 y Fl(dw)p 2359 925 V 2366 1001 a(du)2473 849 y Fm(\014)2473 898 y(\014)2473 948 y(\014)2501 1002 y Ff(\000)2542 986 y Fc(+)2593 944 y Fl(:)639 1133 y Fn(The)29 b(eigen)n(v)-5 b(alues)28 b(at)h(a)g(\014x)g(p)r(oin)n(t)g(is)g Fj(\000)p Fl(c)19 b Fj(\006)2042 1063 y(p)p 2111 1063 51 4 v 2125 1133 a Fn(_)-37 b Fl(\033)t Fn(,)29 b(so)g(\()p Fl(u)2398 1145 y Ff(0)2435 1133 y Fl(;)14 b(v)2512 1145 y Ff(0)2549 1133 y Fn(\))29 b(is)g(a)g(stable)g(fo)r(cus,)g(and)515 1232 y(\()p Fl(u)595 1244 y Fi(\006)651 1232 y Fl(;)14 b(v)728 1244 y Fi(\006)784 1232 y Fn(\))25 b(are)f(saddles.)35 b(The)25 b(monotonicit)n(y)f(of)h(the)h(pro\014le)e(in)h Fl(u)g Fn(then)g(follo)n(ws)f(from)h(the)515 1332 y(geometrical)19 b(analysis)h(with)i(the)g(w)n(ell-kno)n(wn)e(fact)h(that)h(an)f(in)n (tersection)g(of)g(tra)5 b(jectories)515 1431 y(o)r(ccurs)26 b(only)i(at)f(critical)g(p)r(oin)n(ts.)639 1631 y(Using)h(this)g (monotonicit)n(y)-7 b(,)26 b(w)n(e)i(can)f(express)f(explicitly)i(the)g (solution)f(of)g(the)h(piece-)515 1730 y(wise)f(linear)g(system)g (\(37\))h(as,)f(if)h Fl(u)1626 1700 y Fi(\000)1704 1730 y Fl(<)23 b Fn(1,)k(and)h Fl(u)2094 1700 y Ff(+)2171 1730 y Fl(>)23 b Fn(1)p Fl(:)p Fn(5)k(\(noted)h(as)f Fl(U)2815 1742 y Fi(\000)2870 1730 y Fn(-w)n(a)n(v)n(e\),)985 2018 y Fl(u)p Fn(\()p Fl(\030)t Fn(\))c(=)1248 1848 y Fm(8)1248 1923 y(<)1248 2072 y(:)1363 1922 y Fl(u)1411 1892 y Fi(\000)1485 1922 y Fn(+)18 b Fl(Ae)1669 1892 y Ff(\()1695 1844 y Fi(p)p 1750 1844 34 3 v 48 x Ff(2)p Fi(\000)p Fk(c)p Ff(\))p Fk(\030)1927 1922 y Fl(;)330 b Fn(for)82 b Fl(\030)27 b Fj(\024)c Fl(\030)2649 1934 y Ff(1)2687 1922 y Fl(;)1363 2023 y(u)1411 2035 y Ff(0)1467 2023 y Fn(+)18 b Fl(B)t(e)1656 1993 y Fi(\000)p Fk(c\030)1787 2023 y Fn(sin)c(\()p Fl(\030)t Fn(\))q Fl(;)249 b Fn(for)82 b Fl(\030)27 b Fj(2)d Fn([)p Fl(\030)2663 2035 y Ff(1)2700 2023 y Fl(;)14 b(\030)2773 2035 y Ff(2)2811 2023 y Fn(])p Fl(;)1363 2126 y(u)1411 2096 y Ff(+)1485 2126 y Fn(+)k Fl(C)6 b(e)1672 2096 y Fi(\000)p Ff(\(1+)p Fk(c)p Ff(\))p Fk(\030)1925 2126 y Fl(;)332 b Fn(for)82 b Fl(\030)27 b Fj(\025)c Fl(\030)2649 2138 y Ff(2)2687 2126 y Fl(;)3231 2018 y Fn(\(38\))515 2271 y(with)28 b Fl(C)769 2241 y Ff(1)834 2271 y Fn(con)n(tin)n(uit)n(y)f(conditions)922 2398 y Fm(8)922 2473 y(>)922 2498 y(>)922 2523 y(>)922 2548 y(>)922 2573 y(>)922 2598 y(>)922 2622 y(<)922 2772 y(>)922 2797 y(>)922 2822 y(>)922 2847 y(>)922 2871 y(>)922 2896 y(>)922 2921 y(:)1038 2463 y Fl(u)1086 2433 y Fi(\000)1160 2463 y Fn(+)18 b Fl(Ae)1344 2433 y Ff(\()1370 2385 y Fi(p)p 1424 2385 V 1424 2433 a Ff(2)p Fi(\000)p Fk(c)p Ff(\))p Fk(\030)1595 2441 y Fc(1)1887 2463 y Fn(=)k(1)p Fl(;)1038 2564 y(u)1086 2576 y Ff(0)1141 2564 y Fn(+)c Fl(B)t(e)1330 2534 y Fi(\000)p Fk(c\030)1442 2542 y Fc(1)1492 2564 y Fn(sin)c Fl(\030)1644 2576 y Ff(1)1887 2564 y Fn(=)22 b(1)p Fl(;)1038 2664 y(u)1086 2676 y Ff(0)1141 2664 y Fn(+)c Fl(B)t(e)1330 2634 y Fi(\000)p Fk(c\030)1442 2642 y Fc(2)1492 2664 y Fn(sin)c Fl(\030)1644 2676 y Ff(2)1887 2664 y Fn(=)22 b(1)p Fl(:)p Fn(5)p Fl(;)1038 2768 y(u)1086 2737 y Ff(+)1159 2768 y Fn(+)c Fl(C)6 b(e)1346 2737 y Fi(\000)p Ff(\(1+)p Fk(c)p Ff(\))p Fk(\030)1594 2745 y Fc(2)1887 2768 y Fn(=)22 b(1)p Fl(:)p Fn(5)p Fl(;)1038 2882 y Fn(\()p Fj(\000)p Fl(c)c Fn(+)1272 2813 y Fj(p)p 1341 2813 42 4 v 69 x Fn(2\))p Fl(Ae)1516 2852 y Ff(\()1542 2803 y Fi(p)p 1596 2803 34 3 v 1596 2852 a Ff(2)p Fi(\000)p Fk(c)p Ff(\))p Fk(\030)1767 2860 y Fc(1)1887 2882 y Fn(=)k Fl(B)t(e)2080 2852 y Fi(\000)p Fk(c\030)2192 2860 y Fc(1)2229 2882 y Fn(\()p Fj(\000)p Fl(c)14 b Fn(sin)f Fl(\030)2527 2894 y Ff(1)2583 2882 y Fn(+)18 b(cos)13 b Fl(\030)2827 2894 y Ff(1)2864 2882 y Fn(\))p Fl(;)1038 2985 y Fj(\000)p Fn(\(1)18 b(+)g Fl(c)p Fn(\))p Fl(C)6 b(e)1450 2955 y Fi(\000)p Ff(\(1+)p Fk(c)p Ff(\))p Fk(\030)1698 2963 y Fc(2)1887 2985 y Fn(=)22 b Fl(B)t(e)2080 2955 y Fi(\000)p Fk(c\030)2192 2963 y Fc(2)2229 2985 y Fn(\()p Fj(\000)p Fl(c)14 b Fn(sin)f Fl(\030)2527 2997 y Ff(1)2583 2985 y Fn(+)18 b(cos)13 b Fl(\030)2827 2997 y Ff(2)2864 2985 y Fn(\))p Fl(:)3231 2718 y Fn(\(39\))515 3120 y(T)-7 b(ogether)26 b(with)i(the)g(stationary)e(p)r(oin)n(t)i(equations)1136 3319 y Fl(\033)s Fn(\()p Fl(u)1266 3285 y Ff(+)1321 3319 y Fn(\))19 b Fj(\000)f Fl(c)1491 3285 y Ff(2)1528 3319 y Fl(u)1576 3285 y Ff(+)1654 3319 y Fn(=)k Fl(\033)s Fn(\()p Fl(u)1871 3331 y Ff(0)1909 3319 y Fn(\))d Fj(\000)f Fl(u)2091 3331 y Ff(0)2150 3319 y Fn(=)23 b Fl(\033)s Fn(\()p Fl(u)2368 3285 y Fi(\000)2424 3319 y Fn(\))c Fj(\000)f Fl(c)2594 3285 y Ff(2)2631 3319 y Fl(u)2679 3285 y Fi(\000)2735 3319 y Fl(;)515 3458 y Fn(w)n(e)27 b(can)g(\014nd)1392 3711 y Fl(\030)1428 3723 y Ff(1)1549 3711 y Fn(=)c Fl(ctg)1746 3681 y Fi(\000)p Ff(1)1848 3569 y Fm( )1924 3586 y Fj(p)p 1993 3586 42 4 v 69 x Fn(2)o Fl(c)c Fj(\000)f Fn(1)p 1924 3692 290 4 v 1944 3709 a Fj(p)p 2014 3709 42 4 v 2014 3777 a Fn(2)g(+)g Fl(c)2223 3569 y Fm(!)2307 3711 y Fj(\000)g Fl(\031)s(;)1392 3935 y(\030)1428 3947 y Ff(2)1549 3935 y Fn(=)23 b Fl(ctg)1746 3905 y Fi(\000)p Ff(1)1848 3818 y Fm(\022)1919 3879 y Fn(1)18 b(+)g Fl(c)p 1919 3916 179 4 v 1919 3992 a Fn(1)g Fj(\000)g Fl(c)2108 3818 y Fm(\023)2188 3935 y Fn(+)g Fl(k)s(\031)s(;)1392 4098 y(A)95 b Fn(=)23 b(\(1)18 b Fj(\000)g Fl(u)1860 4068 y Fi(\000)1915 4098 y Fn(\))p Fl(e)1986 4068 y Fi(\000)p Ff(\()2064 4020 y Fi(p)p 2119 4020 34 3 v 48 x Ff(2)p Fi(\000)p Fk(c)p Ff(\))p Fk(\030)2290 4076 y Fc(1)2349 4098 y Fl(>)23 b Fn(0)p Fl(;)1392 4199 y(B)94 b Fn(=)23 b(\(1)18 b Fj(\000)g Fl(u)1860 4211 y Ff(0)1897 4199 y Fn(\))p Fl(e)1968 4169 y Fk(c\030)2028 4177 y Fc(1)2064 4199 y Fl(=)c Fn(sin)f Fl(\030)2271 4211 y Ff(1)2309 4199 y Fl(:)1392 4302 y(C)98 b Fn(=)23 b(\(1)p Fl(:)p Fn(5)17 b Fj(\000)h Fl(u)1924 4272 y Ff(+)1979 4302 y Fn(\))p Fl(e)2050 4272 y Ff(\(1+)p Fk(c)p Ff(\))p Fk(\030)2246 4280 y Fc(2)3231 3970 y Fn(\(40\))639 4442 y(The)k(monotonicit)n(y)f(of)h Fl(u)f Fn(is)h(v)n(eri\014ed)f(in)h Fl(\030)27 b Fj(2)d Fn(\()p Fj(\0001)p Fl(;)14 b(\030)2308 4454 y Ff(1)2345 4442 y Fn(\))7 b Fj([)g Fn(\()p Fl(\030)2514 4454 y Ff(2)2552 4442 y Fl(;)14 b Fn(+)p Fj(1)p Fn(\))22 b(as)f Fl(A)i(>)g Fn(0)p Fl(;)14 b(C)29 b(<)22 b Fn(0.)515 4541 y(In)30 b(the)g(in)n(terv)-5 b(al)30 b([)p Fl(\030)1128 4553 y Ff(1)1165 4541 y Fl(;)14 b(\030)1238 4553 y Ff(2)1276 4541 y Fn(],)31 b(the)f(monotonicit)n(y)f(requires)g Fl(B)t Fn(\()p Fj(\000)p Fl(c)14 b Fn(sin)f Fl(\030)25 b Fn(+)19 b(cos)13 b Fl(\030)t Fn(\))28 b Fj(\025)e Fn(0.)44 b(This)515 4641 y(is)30 b(equiv)-5 b(alen)n(t)29 b(to)h(\()p Fl(\030)1169 4653 y Ff(1)1207 4641 y Fl(;)14 b(\030)1280 4653 y Ff(2)1317 4641 y Fn(\))27 b Fj(\022)g Fn(\()p Fl(ctg)1609 4611 y Fi(\000)p Ff(1)1698 4641 y Fl(c)20 b Fj(\000)f Fl(\031)s(;)14 b(ctg)2034 4611 y Fi(\000)p Ff(1)2123 4641 y Fl(c)p Fn(\).)44 b(Th)n(us,)30 b(w)n(e)g(should)g(c)n (ho)r(ose)e Fl(k)i Fn(=)c(0,)515 4741 y(and)1570 4969 y Fl(\030)1606 4981 y Ff(2)1667 4969 y Fn(=)c Fl(ctg)1863 4935 y Fi(\000)p Ff(1)1966 4852 y Fm(\022)2037 4913 y Fn(1)c(+)g Fl(c)p 2037 4950 179 4 v 2037 5026 a Fn(1)g Fj(\000)g Fl(c)2226 4852 y Fm(\023)2301 4969 y Fl(:)1905 5255 y Fn(18)p eop %%Page: 19 19 19 18 bop 639 523 a Fn(By)28 b(a)f(straigh)n(tforw)n(ard)d (calculation,)j(w)n(e)g(\014nd)h(that)961 762 y Fl(u)1009 774 y Ff(0)1069 762 y Fn(=)22 b Fl(\036)1205 774 y Ff(0)1243 762 y Fn(\()p Fj(\000)p Fl(c)p Fn(\))h Fj(\021)1608 638 y(p)p 1677 638 107 4 v 68 x Fn(1)p Fl(:)p Fn(5)o(\(1)18 b Fj(\000)g Fl(c)p Fn(\))h(+)f(1)p Fl(:)p Fn(5\()2267 638 y Fj(p)p 2335 638 42 4 v 2335 706 a Fn(2)g(+)g Fl(c)p Fn(\))p Fl(e)2585 676 y Fi(\000)p Fk(c)p Ff(\()p Fk(\030)2723 684 y Fc(1)2755 676 y Fi(\000)p Fk(\030)2837 684 y Fc(2)2870 676 y Ff(\))p 1608 743 1293 4 v 1661 760 a Fj(p)p 1730 760 107 4 v 69 x Fn(1)p Fl(:)p Fn(5)o(\(1)g Fj(\000)g Fl(c)p Fn(\))h(+)f(\()2213 760 y Fj(p)p 2282 760 42 4 v 69 x Fn(2)g(+)g Fl(c)p Fn(\))p Fl(e)2532 805 y Fi(\000)p Fk(c)p Ff(\()p Fk(\030)2670 813 y Fc(1)2702 805 y Fi(\000)p Fk(\030)2784 813 y Fc(2)2817 805 y Ff(\))2910 762 y Fl(;)961 973 y(u)1009 943 y Ff(+)1087 973 y Fn(=)k Fl(\036)1223 985 y Ff(2)1261 973 y Fn(\()p Fj(\000)p Fl(c)p Fn(\))h Fj(\021)1608 917 y Fn(3)17 b Fj(\000)h Fn(\(1)h(+)f Fl(c)1962 887 y Ff(2)1999 917 y Fn(\))p Fl(\036)2080 929 y Ff(0)2118 917 y Fn(\()p Fj(\000)p Fl(c)p Fn(\))p 1608 954 676 4 v 1837 1030 a(1)g Fj(\000)g Fl(c)2016 1006 y Ff(2)2293 973 y Fl(;)961 1161 y(u)1009 1131 y Fi(\000)1087 1161 y Fn(=)23 b Fl(\036)1224 1173 y Ff(1)1262 1161 y Fn(\()p Fj(\000)p Fl(c)p Fn(\))g Fj(\021)1608 1105 y Fn(3)17 b Fj(\000)h Fn(\(1)h(+)f Fl(c)1962 1074 y Ff(2)1999 1105 y Fn(\))p Fl(\036)2080 1117 y Ff(0)2118 1105 y Fn(\()p Fj(\000)p Fl(c)p Fn(\))p 1608 1142 V 1837 1218 a(2)g Fj(\000)g Fl(c)2016 1194 y Ff(2)2293 1161 y Fl(:)3231 949 y Fn(\(41\))639 1349 y(So)35 b(for)f(eac)n(h)f Fl(c)i Fj(2)g Fn(\()p Fj(\000)p Fn(1)p Fl(;)14 b Fn(0\),)35 b(there)g(is)f(a)g(unique)h Fl(u)2269 1361 y Ff(0)2306 1349 y Fn(,)h Fl(u)2413 1319 y Ff(+)2502 1349 y Fn(and)f Fl(u)2719 1319 y Fi(\000)2774 1349 y Fn(.)58 b(It)35 b(is)f(quite)h(un-)515 1448 y(exp)r(ected)j(that)f(the)h(range)e(of)i Fl(u)1602 1460 y Ff(0)1676 1448 y Fn(do)r(es)f(not)h(co)n(v)n(er)e(the) i(whole)f(in)n(terv)-5 b(al)37 b([1)p Fl(;)14 b Fn(1)p Fl(:)p Fn(5].)65 b(As)515 1548 y Fl(c)23 b Fj(!)g(\000)p Fn(1,)k(w)n(e)g(\014nd)h Fl(u)1173 1560 y Ff(0)1233 1548 y Fj(!)23 b Fn(1)p Fl(:)p Fn(0144,)i Fl(u)1668 1518 y Fi(\000)1747 1548 y Fj(!)e Fn(0)p Fl(:)p Fn(9712,)i(whereas)i Fl(u)2497 1518 y Ff(+)2574 1548 y Fj(!)c Fn(+)p Fj(1)p Fn(.)639 1648 y(Similarly)-7 b(,)35 b(for)d(the)i(case)e Fl(u)1526 1618 y Fi(\000)1614 1648 y Fj(\025)g Fn(1)p Fl(:)p Fn(5)p Fl(;)14 b(u)1903 1618 y Ff(+)1989 1648 y Fj(\024)32 b Fn(1)h(\(noted)h(as)e Fl(D)2606 1660 y Fi(\000)2662 1648 y Fn(-w)n(a)n(v)n(e\),)h(w)n(e)g(can)g(\014nd)515 1747 y(the)28 b(hetero)r(clinic)f(orbit)g(as)604 2120 y Fl(u)p Fn(\()p Fl(\030)t Fn(\))c(=)867 1950 y Fm(8)867 2024 y(<)867 2174 y(:)982 2012 y Fl(u)1030 1982 y Fi(\000)1104 2012 y Fn(+)18 b(\()p Fl(u)1267 2024 y Ff(2)1323 2012 y Fj(\000)g Fl(u)1454 1982 y Fi(\000)1509 2012 y Fn(\))p Fl(e)1580 1982 y Ff(\(1)p Fi(\000)p Fk(c)p Ff(\)\()p Fk(\030)r Fi(\000)p Fk(\030)1887 1990 y Fc(1)1919 1982 y Ff(\))1950 2012 y Fl(;)540 b Fn(for)83 b Fl(\030)27 b Fj(\024)c Fl(\030)2883 2024 y Ff(1)2920 2012 y Fl(;)982 2116 y(u)1030 2128 y Ff(0)1085 2116 y Fn(+)18 b(\()p Fl(u)1248 2128 y Ff(2)1304 2116 y Fj(\000)g Fl(u)1435 2128 y Ff(0)1472 2116 y Fn(\))p Fl(e)1543 2085 y Fi(\000)p Fk(c)p Ff(\()p Fk(\030)r Fi(\000)p Fk(\030)1765 2093 y Fc(1)1797 2085 y Ff(\))1841 2116 y Fn(sin)c Fl(\030)t(=)g Fn(sin)f Fl(\030)2204 2128 y Ff(1)2241 2116 y Fl(;)249 b Fn(for)83 b Fl(\030)27 b Fj(2)d Fn([)p Fl(\030)2897 2128 y Ff(1)2934 2116 y Fl(;)14 b(\030)3007 2128 y Ff(2)3045 2116 y Fn(])p Fl(;)982 2230 y(u)1030 2200 y Ff(+)1103 2230 y Fn(+)k(\()p Fl(u)1266 2242 y Ff(1)1322 2230 y Fj(\000)g Fl(u)1453 2200 y Ff(+)1507 2230 y Fn(\))p Fl(e)1578 2200 y Fi(\000)p Ff(\()1656 2151 y Fi(p)p 1711 2151 34 3 v 49 x Ff(2+)p Fk(c)p Ff(\)\()p Fk(\030)r Fi(\000)p Fk(\030)1991 2208 y Fc(2)2023 2200 y Ff(\))2053 2230 y Fl(;)437 b Fn(for)83 b Fl(\030)27 b Fj(\025)c Fl(\030)2883 2242 y Ff(2)2920 2230 y Fl(;)3231 2120 y Fn(\(42\))515 2409 y(with)1483 2637 y Fl(\030)1519 2649 y Ff(1)1639 2637 y Fn(=)g Fl(ctg)1836 2607 y Fi(\000)p Ff(1)1938 2520 y Fm(\022)2009 2581 y Fl(c)c Fj(\000)f Fn(1)p 2009 2618 179 4 v 2009 2694 a Fl(c)h Fn(+)f(1)2198 2520 y Fm(\023)2278 2637 y Fj(\000)g Fl(\031)1483 2861 y(\030)1519 2873 y Ff(2)1639 2861 y Fn(=)23 b Fl(ctg)1836 2831 y Fi(\000)p Ff(1)1938 2719 y Fm( )2014 2805 y Fn(1)18 b(+)2157 2736 y Fj(p)p 2226 2736 42 4 v 69 x Fn(2)p Fl(c)p 2014 2842 290 4 v 2035 2859 a Fj(p)p 2104 2859 42 4 v 68 x Fn(2)g Fj(\000)g Fl(c)2314 2719 y Fm(!)3231 2761 y Fn(\(43\))515 3081 y(and)959 3320 y Fl(u)1007 3332 y Ff(0)1066 3320 y Fn(=)23 b Fl( )1208 3332 y Ff(0)1245 3320 y Fn(\()p Fj(\000)p Fl(c)p Fn(\))g Fj(\021)1610 3264 y Fn(1)p Fl(:)p Fn(5\()1749 3195 y Fj(p)p 1817 3195 V 1817 3264 a Fn(2)18 b Fj(\000)g Fl(c)p Fn(\))h(+)2130 3195 y Fj(p)p 2199 3195 107 4 v 69 x Fn(1)p Fl(:)p Fn(5)o(\(1)g(+)f Fl(c)p Fn(\))p Fl(e)2588 3234 y Fi(\000)p Fk(c)p Ff(\()p Fk(\030)2726 3242 y Fc(1)2758 3234 y Fi(\000)p Fk(\030)2840 3242 y Fc(2)2872 3234 y Ff(\))p 1610 3301 1293 4 v 1663 3386 a Fn(\()1695 3318 y Fj(p)p 1764 3318 42 4 v 68 x Fn(2)g Fj(\000)g Fl(c)p Fn(\))h(+)2077 3318 y Fj(p)p 2146 3318 107 4 v 68 x Fn(1)p Fl(:)p Fn(5)o(\(1)g(+)f Fl(c)p Fn(\))p Fl(e)2535 3362 y Fi(\000)p Fk(c)p Ff(\()p Fk(\030)2673 3370 y Fc(1)2705 3362 y Fi(\000)p Fk(\030)2787 3370 y Fc(2)2819 3362 y Ff(\))2912 3320 y Fl(;)959 3531 y(u)1007 3501 y Fi(\000)1085 3531 y Fn(=)23 b Fl( )1227 3543 y Ff(1)1264 3531 y Fn(\()p Fj(\000)p Fl(c)p Fn(\))g Fj(\021)1610 3475 y Fn(3)18 b Fj(\000)g Fn(\(1)g(+)g Fl(c)1964 3444 y Ff(2)2001 3475 y Fn(\))p Fl( )2087 3487 y Ff(0)2125 3475 y Fn(\()p Fj(j)p Fl(c)p Fj(j)p Fn(\))p 1610 3512 662 4 v 1833 3588 a(2)g Fj(\000)g Fl(c)2012 3564 y Ff(2)2281 3531 y Fl(;)959 3718 y(u)1007 3688 y Ff(+)1084 3718 y Fn(=)23 b Fl( )1226 3730 y Ff(2)1263 3718 y Fn(\()p Fj(\000)p Fl(c)p Fn(\))g Fj(\021)1610 3662 y Fn(3)18 b Fj(\000)g Fn(\(1)g(+)g Fl(c)1964 3632 y Ff(2)2001 3662 y Fn(\))p Fl( )2087 3674 y Ff(0)2125 3662 y Fn(\()p Fj(j)p Fl(c)p Fj(j)p Fn(\))p 1610 3699 V 1833 3775 a(1)g Fj(\000)g Fl(c)2012 3751 y Ff(2)2281 3718 y Fl(:)3231 3506 y Fn(\(44\))639 3906 y(F)-7 b(or)33 b(this)g(one,)i(though)e(the)g(range)f(of)h Fl(u)1959 3918 y Ff(0)2029 3906 y Fn(co)n(v)n(ers)e([1)p Fl(;)14 b Fn(1)p Fl(:)p Fn(5],)34 b(and)f(that)g(of)g Fl(u)3071 3876 y Ff(+)3159 3906 y Fn(co)n(v)n(ers)515 4006 y([0)p Fl(;)14 b Fn(1],)27 b Fl(u)780 3976 y Fi(\000)863 4006 y Fn(tends)h(to)f(ab)r(out)h(1)p Fl(:)p Fn(5445)d(as)i Fl(c)c Fj(!)g(\000)p Fn(1.)639 4106 y(F)-7 b(or)40 b(the)i(case)e Fl(c)k(>)h Fn(0,)f(i.e.)76 b(the)41 b Fl(U)1841 4118 y Ff(+)1896 4106 y Fn(-)g(and)f Fl(D)2208 4118 y Ff(+)2263 4106 y Fn(-w)n(a)n(v)n(es,)i(the)f(kinetic)g(relation)f(is)515 4205 y(obtained)27 b(b)n(y)g(a)h(c)n(hange)e(of)i(v)-5 b(ariables)26 b(as)h(\()p Fl(u;)14 b(v)s(;)g(\030)t Fn(;)g Fl(c)p Fn(\))23 b Fj(\000)-14 b(!)23 b Fn(\()p Fl(u;)14 b Fj(\000)p Fl(v)s(;)g Fj(\000)p Fl(\030)t Fn(;)g Fj(\000)p Fl(c)p Fn(\).)639 4305 y(W)-7 b(e)31 b(demonstrate)e(the)i(kinetic)g (relation)e(in)i(Figure)e(7.)45 b(Instead)30 b(of)g Fl(u)2904 4275 y Fi(\006)2960 4305 y Fn(,)h(w)n(e)f(denote)515 4405 y(the)23 b(end-states)f(of)g(the)h(subsonic)f(w)n(a)n(v)n(e)f(as)h Fl(u)1939 4417 y Fk(r)n(;l)2013 4405 y Fn(,)i(to)e(a)n(v)n(oid)g (confusion)g(with)h(the)g(Riemann)515 4504 y(data)g(in)i(the)f(Riemann) g(solv)n(er)f(describ)r(ed)g(so)r(on.)35 b(It)25 b(is)f(noticed)g(that) g Fl(u)2778 4516 y Fk(l)2803 4504 y Fn(\()p Fl(c)p Fn(\))h(for)e Fl(D)3120 4516 y Fi(\000)3176 4504 y Fn(-w)n(a)n(v)n(e)515 4604 y(and)k Fl(T)725 4616 y Ff(+)780 4604 y Fn(-w)n(a)n(v)n(e)e(is)j (smo)r(oth)f(at)h Fl(c)23 b Fn(=)f(0,)28 b(and)f(this)h(can)f(b)r(e)h (rigorously)d(pro)n(v)n(ed.)639 4703 y(W)-7 b(e)23 b(ma)n(y)g(then)g (summarize)f(the)h(elemen)n(tary)f(w)n(a)n(v)n(es)f(in)i(the)g(follo)n (wing)f(table.)35 b(Please)515 4803 y(see)27 b(Figure)g(8)g(as)g(w)n (ell.)1905 5255 y(19)p eop %%Page: 20 20 20 19 bop 1107 523 a Fn(T)-7 b(able)27 b(3.)37 b(Elemen)n(tary)26 b(w)n(a)n(v)n(es)f(in)j(Jin-Xin's)g(mo)r(del)p 515 634 2769 4 v 515 650 V 513 750 4 100 v 565 720 a(W)-7 b(a)n(v)n(e)p 816 750 V 105 w(Sp)r(eed)28 b(c)p 1383 750 V 289 w(u)p 2411 750 V 982 w([v])p 3282 750 V 515 753 2769 4 v 513 859 4 106 v 565 829 a(+)630 760 y Fj(p)p 698 760 42 4 v 698 829 a Fn(2-)p 816 859 4 106 v 867 760 a Fj(p)p 936 760 42 4 v 69 x Fn(2)p 1383 859 4 106 v 457 w Fl(u)1483 841 y Fk(l;r)1583 829 y Fj(\024)23 b Fn(1)p 2411 859 V 2463 760 a Fj(p)p 2532 760 42 4 v 69 x Fn(2)o([)p Fl(u)p Fn(])p 3282 859 4 106 v 515 862 2769 4 v 513 967 4 106 v 565 937 a Fj(\000)630 869 y(p)p 698 869 42 4 v 698 937 a Fn(2-)p 816 967 4 106 v 99 w Fj(\000)932 869 y(p)p 1001 869 42 4 v 68 x Fn(2)p 1383 967 4 106 v 392 w Fl(u)1483 949 y Fk(l;r)1583 937 y Fj(\024)g Fn(1)p 2411 967 V 750 w Fj(\000)2528 869 y(p)p 2596 869 42 4 v 2596 937 a Fn(2[)p Fl(u)p Fn(])p 3282 967 4 106 v 515 970 2769 4 v 513 1070 4 100 v 565 1040 a(+1-)p 816 1070 V 167 w(1)p 1383 1070 V 526 w Fl(u)1483 1052 y Fk(l;r)1583 1040 y Fj(\025)g Fn(1)p Fl(:)p Fn(5)p 2411 1070 V 685 w([)p Fl(u)p Fn(])p 3282 1070 V 515 1073 2769 4 v 513 1173 4 100 v 565 1143 a Fj(\000)p Fn(1-)p 816 1173 V 167 w Fj(\000)p Fn(1)p 1383 1173 V 461 w Fl(u)1483 1155 y Fk(l;r)1583 1143 y Fj(\025)g Fn(1)p Fl(:)p Fn(5)p 2411 1173 V 685 w Fj(\000)p Fn([)p Fl(u)p Fn(])p 3282 1173 V 515 1176 2769 4 v 513 1276 4 100 v 565 1246 a Fl(U)622 1258 y Ff(+)676 1246 y Fn(-)p 816 1276 V 163 w Fl(c)g Fj(\025)g Fn(0)p 1383 1276 V 379 w Fl(u)1483 1258 y Fk(r)1542 1246 y Fn(=)g Fl(\036)1679 1258 y Ff(1)1716 1246 y Fn(\()p Fl(c)p Fn(\))p Fl(;)14 b(u)1901 1258 y Fk(l)1950 1246 y Fn(=)22 b Fl(\036)2086 1258 y Ff(2)2124 1246 y Fn(\()p Fl(c)p Fn(\))p 2411 1276 V 239 w Fl(c)p Fn([)p Fl(u)p Fn(])g Fj(\024)h Fn(0)p 3282 1276 V 515 1279 2769 4 v 513 1379 4 100 v 565 1349 a Fl(U)622 1361 y Fi(\000)677 1349 y Fn(-)p 816 1379 V 162 w Fl(c)g Fj(\024)g Fn(0)p 1383 1379 V 379 w Fl(u)1483 1361 y Fk(r)1542 1349 y Fn(=)g Fl(\036)1679 1361 y Ff(2)1716 1349 y Fn(\()p Fj(\000)p Fl(c)p Fn(\))p Fl(;)14 b(u)1966 1361 y Fk(l)2014 1349 y Fn(=)23 b Fl(\036)2151 1361 y Ff(1)2189 1349 y Fn(\()p Fj(\000)p Fl(c)p Fn(\))p 2411 1379 V 109 w Fl(c)p Fn([)p Fl(u)p Fn(])f Fj(\024)h Fn(0)p 3282 1379 V 515 1382 2769 4 v 513 1482 4 100 v 565 1452 a Fl(D)634 1464 y Ff(+)688 1452 y Fn(-)p 816 1482 V 151 w Fl(c)g Fj(\025)g Fn(0)p 1383 1482 V 379 w Fl(u)1483 1464 y Fk(r)1542 1452 y Fn(=)g Fl( )1684 1464 y Ff(2)1721 1452 y Fn(\()p Fl(c)p Fn(\))p Fl(;)14 b(u)1906 1464 y Fk(l)1954 1452 y Fn(=)23 b Fl( )2096 1464 y Ff(1)2133 1452 y Fn(\()p Fl(c)p Fn(\))p 2411 1482 V 230 w Fl(c)p Fn([)p Fl(u)p Fn(])f Fj(\025)h Fn(0)p 3282 1482 V 515 1485 2769 4 v 513 1585 4 100 v 565 1555 a Fl(D)634 1567 y Fi(\000)689 1555 y Fn(-)p 816 1585 V 150 w Fl(c)g Fj(\024)g Fn(0)p 1383 1585 V 379 w Fl(u)1483 1567 y Fk(r)1542 1555 y Fn(=)g Fl( )1684 1567 y Ff(1)1721 1555 y Fn(\()p Fj(\000)p Fl(c)p Fn(\))p Fl(;)14 b(u)1971 1567 y Fk(l)2019 1555 y Fn(=)23 b Fl( )2161 1567 y Ff(2)2198 1555 y Fn(\()p Fj(\000)p Fl(c)p Fn(\))p 2411 1585 V 100 w Fl(c)p Fn([)p Fl(u)p Fn(])f Fj(\025)h Fn(0)p 3282 1585 V 515 1588 2769 4 v 513 1791 4 203 v 565 1715 a Fl(S)616 1727 y Ff(+)671 1715 y Fn(-)p 816 1791 V 867 1595 a Fm(r)p 950 1595 321 4 v 960 1659 a Fl(u)1008 1671 y Fk(r)1063 1659 y Fj(\000)18 b Fn(2)p Fl(u)1236 1671 y Fk(l)p 960 1696 301 4 v 981 1772 a Fl(u)1029 1784 y Fk(r)1084 1772 y Fj(\000)g Fl(u)1215 1784 y Fk(l)p 1383 1791 4 203 v 1435 1715 a Fl(u)1483 1727 y Fk(r)1542 1715 y Fl(>)23 b Fn(1)p Fl(:)p Fn(5)p Fl(;)14 b(u)1822 1727 y Fk(l)1869 1715 y Fj(\024)22 b Fn(0)p 2411 1791 V 2463 1644 a Fm(p)p 2546 1644 689 4 v 71 x Fn(\()p Fl(u)2626 1727 y Fk(r)2681 1715 y Fj(\000)c Fn(2)p Fl(u)2854 1727 y Fk(l)2878 1715 y Fn(\)\()p Fl(u)2990 1727 y Fk(r)3045 1715 y Fj(\000)g Fl(u)3176 1727 y Fk(l)3201 1715 y Fn(\))p 3282 1791 4 203 v 515 1794 2769 4 v 513 1997 4 203 v 565 1921 a Fl(S)616 1933 y Fi(\000)671 1921 y Fn(-)p 816 1997 V 168 w Fj(\000)932 1801 y Fm(r)p 1015 1801 321 4 v 1025 1865 a Fl(u)1073 1877 y Fk(l)1116 1865 y Fj(\000)g Fn(2)p Fl(u)1289 1877 y Fk(r)p 1025 1902 301 4 v 1045 1978 a Fl(u)1093 1990 y Fk(l)1137 1978 y Fj(\000)g Fl(u)1268 1990 y Fk(r)p 1383 1997 4 203 v 1435 1921 a Fl(u)1483 1933 y Fk(r)1542 1921 y Fj(\024)23 b Fn(0)p Fl(;)14 b(u)1757 1933 y Fk(l)1804 1921 y Fl(>)23 b Fn(1)p Fl(:)p Fn(5)p 2411 1997 V 2463 1850 a Fm(p)p 2546 1850 689 4 v 71 x Fn(\()p Fl(u)2626 1933 y Fk(l)2669 1921 y Fj(\000)18 b Fn(2)p Fl(u)2842 1933 y Fk(r)2878 1921 y Fn(\)\()p Fl(u)2990 1933 y Fk(l)3034 1921 y Fj(\000)g Fl(u)3165 1933 y Fk(r)3201 1921 y Fn(\))p 3282 1997 4 203 v 515 2000 2769 4 v 997 2290 a(T)-7 b(able)28 b(4.)36 b(Generic)27 b(w)n(a)n(v)n(e)f(pro\014les)h(for)g(Riemann)h(problem)p 515 2401 3039 4 v 515 2418 V 513 2518 4 100 v 678 2518 V 729 2488 a(Pro\014le)p 1442 2518 V 526 w([)p Fl(v)s Fn(])p 3074 2518 V 1544 w(P)n(arameter)p 3551 2518 V 515 2521 3039 4 v 513 2626 4 106 v 565 2596 a(A)p 678 2626 V 102 w Fj(\000)794 2527 y(p)p 863 2527 42 4 v 69 x Fn(2)23 b Fj(!)g Fl(U)1091 2608 y Fi(\000)1170 2596 y Fj(!)g Fl(U)1333 2608 y Ff(+)p 1442 2626 4 106 v 1493 2527 a Fj(p)p 1563 2527 42 4 v 1563 2596 a Fn(2)o(\()p Fl(u)1684 2608 y Ff(+)1757 2596 y Fn(+)18 b Fl(u)1888 2608 y Fi(\000)1962 2596 y Fj(\000)h Fn(2)p Fl(\036)2137 2608 y Ff(1)2174 2596 y Fn(\()p Fl(c)p Fn(\)\))g(+)f(2)p Fl(c)p Fn(\()p Fl(\036)2567 2608 y Ff(1)2604 2596 y Fn(\()p Fl(c)p Fn(\))h Fj(\000)f Fl(\036)2855 2608 y Ff(2)2893 2596 y Fn(\()p Fl(c)p Fn(\)\))p 3074 2626 4 106 v 101 w Fl(c)23 b Fj(2)g Fn([0)p Fl(;)14 b Fn(1])p 3551 2626 V 513 2731 V 678 2731 V 895 2701 a Fj(!)23 b Fn(+)1066 2633 y Fj(p)p 1135 2633 42 4 v 68 x Fn(2)p 1442 2731 4 106 v 3074 2731 V 3551 2731 V 515 2735 3039 4 v 513 2840 4 106 v 565 2810 a(B)p 678 2840 V 105 w Fj(\000)794 2741 y(p)p 863 2741 42 4 v 69 x Fn(2)g Fj(!)g Fl(U)1091 2822 y Fi(\000)1170 2810 y Fj(!)g Fn(+1)p 1442 2840 4 106 v 110 w Fj(\000)1558 2741 y(p)p 1627 2741 42 4 v 69 x Fn(2\()p Fl(\036)1750 2822 y Ff(1)1788 2810 y Fn(\()p Fl(c)p Fn(\))c Fj(\000)f Fl(u)2038 2822 y Fi(\000)2093 2810 y Fn(\))h(+)f Fl(c)p Fn(\()p Fl(\036)2344 2822 y Ff(1)2382 2810 y Fn(\()p Fl(c)p Fn(\))h Fj(\000)f Fl(\036)2633 2822 y Ff(2)2671 2810 y Fn(\()p Fl(c)p Fn(\)\))p 3074 2840 4 106 v 323 w Fl(c)23 b Fj(2)g Fn([0)p Fl(;)14 b Fn(1])p 3551 2840 V 513 2939 4 100 v 678 2939 V 1442 2939 V 1659 2910 a(+)p Fl(u)1772 2922 y Ff(+)1845 2910 y Fj(\000)k Fl(\036)1977 2922 y Ff(2)2015 2910 y Fn(\()p Fl(c)p Fn(\))p 3074 2939 V 3551 2939 V 515 2943 3039 4 v 513 3048 4 106 v 565 3018 a(C)p 678 3048 V 104 w Fj(\000)794 2949 y(p)p 863 2949 42 4 v 69 x Fn(2)23 b Fj(!)g Fl(D)1103 3030 y Ff(+)1181 3018 y Fj(!)g Fn(+1)p 1442 3048 4 106 v 99 w Fj(\000)1558 2949 y(p)p 1627 2949 42 4 v 69 x Fn(2\()p Fl( )1755 3030 y Ff(1)1792 3018 y Fn(\()p Fl(c)p Fn(\))c Fj(\000)f Fl(u)2042 3030 y Fi(\000)2098 3018 y Fn(\))h(+)f Fl(c)p Fn(\()p Fl( )2354 3030 y Ff(2)2391 3018 y Fn(\()p Fl(c)p Fn(\))h Fj(\000)f Fl( )2647 3030 y Ff(1)2684 3018 y Fn(\()p Fl(c)p Fn(\)\))p 3074 3048 4 106 v 310 w Fl(c)23 b Fj(2)g Fn([0)p Fl(;)14 b Fn(1])p 3551 3048 V 513 3148 4 100 v 678 3148 V 1442 3148 V 1659 3118 a(+)p Fl(u)1772 3130 y Ff(+)1845 3118 y Fj(\000)k Fl( )1982 3130 y Ff(2)2019 3118 y Fn(\()p Fl(c)p Fn(\))p 3074 3148 V 3551 3148 V 515 3151 3039 4 v 513 3258 4 108 v 565 3228 a(D)p 678 3258 V 101 w Fj(\000)794 3160 y(p)p 863 3160 42 4 v 68 x Fn(2)23 b Fj(!)g Fl(S)5 b Fn(+)p 1442 3258 4 108 v 338 w Fj(\000)1558 3160 y(p)p 1627 3160 42 4 v 68 x Fn(2\()p Fl(u)1749 3240 y Fi(\003)1805 3228 y Fj(\000)18 b Fl(u)1936 3240 y Fi(\000)1992 3228 y Fn(\))g(+)2125 3158 y Fm(p)p 2208 3158 751 4 v 70 x Fn(\()p Fl(u)2288 3240 y Ff(+)2362 3228 y Fj(\000)g Fn(2)p Fl(u)2535 3240 y Fi(\003)2572 3228 y Fn(\)\()p Fl(u)2684 3240 y Ff(+)2758 3228 y Fj(\000)g Fl(u)2889 3240 y Fi(\003)2926 3228 y Fn(\))p 3074 3258 4 108 v 168 w Fl(u)3174 3240 y Fi(\003)3234 3228 y Fj(\024)23 b Fn(0)p 3551 3258 V 515 3262 3039 4 v 513 3367 4 106 v 565 3337 a(E)p 678 3367 V 107 w Fj(\000)794 3268 y(p)p 863 3268 42 4 v 69 x Fn(2)g Fj(!)g Fn(+)1099 3268 y Fj(p)p 1167 3268 V 1167 3337 a Fn(2)p 1442 3367 4 106 v 1493 3268 a Fj(p)p 1563 3268 42 4 v 1563 3337 a Fn(2)o(\()p Fl(u)1684 3349 y Fi(\000)1758 3337 y Fn(+)18 b Fl(u)1889 3349 y Ff(+)1962 3337 y Fj(\000)h Fn(2)p Fl(u)2136 3349 y Fi(\003)2173 3337 y Fn(\))p 3074 3367 4 106 v 921 w Fl(u)3174 3349 y Fi(\003)3234 3337 y Fj(\024)k Fn(1)p 3551 3367 V 515 3370 3039 4 v 513 3475 4 106 v 565 3446 a(F)p 678 3475 V 110 w Fj(\000)p Fn(1)f Fj(!)i Fl(U)1022 3458 y Ff(+)1099 3446 y Fj(!)g Fn(+)1271 3377 y Fj(p)p 1339 3377 42 4 v 1339 3446 a Fn(2)p 1442 3475 4 106 v 112 w Fl(u)1541 3458 y Fi(\000)1615 3446 y Fj(\000)18 b Fl(\036)1747 3458 y Ff(2)1785 3446 y Fn(\()p Fl(c)p Fn(\))h(+)f Fl(c)p Fn(\()p Fl(\036)2104 3458 y Ff(1)2142 3446 y Fn(\()p Fl(c)p Fn(\))h Fj(\000)f Fl(\036)2393 3458 y Ff(2)2431 3446 y Fn(\()p Fl(c)p Fn(\)\))p 3074 3475 V 563 w Fl(c)23 b Fj(2)g Fn([0)p Fl(;)14 b Fn(1])p 3551 3475 V 513 3581 V 678 3581 V 1442 3581 V 1659 3551 a(+)1724 3482 y Fj(p)p 1793 3482 42 4 v 69 x Fn(2\()p Fl(u)1915 3563 y Ff(+)1988 3551 y Fj(\000)k Fl(\036)2120 3563 y Ff(1)2158 3551 y Fn(\()p Fl(c)p Fn(\)\))p 3074 3581 4 106 v 3551 3581 V 515 3584 3039 4 v 513 3684 4 100 v 565 3654 a(G)p 678 3684 V 99 w Fj(\000)p Fn(1)k Fj(!)i Fl(D)1034 3666 y Fi(\000)1112 3654 y Fj(!)f Fl(D)1287 3666 y Ff(+)p 1442 3684 V 1493 3654 a Fn(\()p Fl(u)1573 3666 y Fi(\000)1648 3654 y Fn(+)18 b Fl(u)1779 3666 y Ff(+)1852 3654 y Fj(\000)g Fn(2)p Fl( )2031 3666 y Ff(2)2068 3654 y Fn(\()p Fl(c)p Fn(\)\))h(+)f(2)p Fl(c)p Fn(\()p Fl( )2466 3666 y Ff(2)2503 3654 y Fn(\()p Fl(c)p Fn(\))h Fj(\000)f Fl( )2759 3666 y Ff(1)2796 3654 y Fn(\()p Fl(c)p Fn(\)\))p 3074 3684 V 198 w Fl(c)23 b Fj(2)g Fn([0)p Fl(;)14 b Fn(1])p 3551 3684 V 513 3783 V 678 3783 V 895 3753 a Fj(!)23 b Fn(+1)p 1442 3783 V 3074 3783 V 3551 3783 V 515 3787 3039 4 v 513 3892 4 106 v 565 3862 a(H)p 678 3892 V 102 w Fj(\000)p Fn(1)f Fj(!)i Fl(D)1034 3874 y Fi(\000)1112 3862 y Fj(!)f Fn(+)1283 3793 y Fj(p)p 1352 3793 42 4 v 69 x Fn(2)p 1442 3892 4 106 v 99 w Fl(u)1541 3874 y Fi(\000)1615 3862 y Fj(\000)18 b Fl( )1752 3874 y Ff(2)1790 3862 y Fn(\()p Fl(c)p Fn(\))h(+)f Fl(c)p Fn(\()p Fl( )2114 3874 y Ff(2)2151 3862 y Fn(\()p Fl(c)p Fn(\))h Fj(\000)f Fl( )2407 3874 y Ff(1)2445 3862 y Fn(\()p Fl(c)p Fn(\)\))p 3074 3892 V 549 w Fl(c)23 b Fj(2)g Fn([0)p Fl(;)14 b Fn(1])p 3551 3892 V 513 3997 V 678 3997 V 1442 3997 V 1659 3967 a(+)1724 3898 y Fj(p)p 1793 3898 42 4 v 69 x Fn(2\()p Fl(u)1915 3979 y Ff(+)1988 3967 y Fj(\000)k Fl( )2125 3979 y Ff(1)2162 3967 y Fn(\()p Fl(c)p Fn(\)\))p 3074 3997 4 106 v 3551 3997 V 515 4000 3039 4 v 513 4100 4 100 v 565 4070 a(I)p 678 4100 V 134 w Fj(\000)p Fn(1)k Fj(!)i Fn(+1)p 1442 4100 V 421 w Fl(u)1541 4082 y Fi(\000)1615 4070 y Fn(+)18 b Fl(u)1746 4082 y Ff(+)1819 4070 y Fj(\000)h Fn(2)p Fl(u)1993 4082 y Fi(\003)p 3074 4100 V 3126 4070 a Fl(u)3174 4082 y Fi(\003)3234 4070 y Fj(\025)k Fn(1)p Fl(:)p Fn(5)p 3551 4100 V 515 4103 3039 4 v 513 4211 4 108 v 565 4181 a(J)p 678 4211 V 121 w Fl(S)5 b Fj(\000)23 b(!)g Fl(S)5 b Fn(+)p 1442 4211 V 1493 4110 a Fm(p)p 1576 4110 753 4 v 71 x Fn(\()p Fl(u)1656 4193 y Fi(\000)1731 4181 y Fj(\000)18 b Fn(2)p Fl(u)1904 4193 y Fi(\003)1941 4181 y Fn(\)\()p Fl(u)2053 4193 y Fi(\000)2128 4181 y Fj(\000)g Fl(u)2259 4193 y Fi(\003)2296 4181 y Fn(\))p 3074 4211 4 108 v 798 w Fl(u)3174 4193 y Fi(\003)3234 4181 y Fj(\024)23 b Fn(0)p 3551 4211 V 513 4318 V 678 4318 V 1442 4318 V 1659 4288 a(+)1724 4217 y Fm(p)p 1807 4217 751 4 v 71 x Fn(\()p Fl(u)1887 4300 y Ff(+)1960 4288 y Fj(\000)18 b Fn(2)p Fl(u)2133 4300 y Fi(\003)2171 4288 y Fn(\)\()p Fl(u)2283 4300 y Ff(+)2356 4288 y Fj(\000)g Fl(u)2487 4300 y Fi(\003)2525 4288 y Fn(\))p 3074 4318 4 108 v 3551 4318 V 515 4322 3039 4 v 513 4429 4 108 v 565 4399 a(K)p 678 4429 V 99 w Fl(S)5 b Fj(\000)23 b(!)g Fn(+)1044 4331 y Fj(p)p 1112 4331 42 4 v 1112 4399 a Fn(2)p 1442 4429 4 108 v 1493 4328 a Fm(p)p 1576 4328 753 4 v 71 x Fn(\()p Fl(u)1656 4411 y Fi(\000)1731 4399 y Fj(\000)18 b Fn(2)p Fl(u)1904 4411 y Fi(\003)1941 4399 y Fn(\)\()p Fl(u)2053 4411 y Fi(\000)2128 4399 y Fj(\000)g Fl(u)2259 4411 y Fi(\003)2296 4399 y Fn(\))h(+)2430 4331 y Fj(p)p 2499 4331 42 4 v 68 x Fn(2\()p Fl(u)2621 4411 y Ff(+)2694 4399 y Fj(\000)f Fl(u)2825 4411 y Fi(\003)2863 4399 y Fn(\))p 3074 4429 4 108 v 231 w Fl(u)3174 4411 y Fi(\003)3234 4399 y Fj(\024)23 b Fn(0)p 3551 4429 V 515 4432 3039 4 v 639 4640 a(The)30 b(same)f(as)g(what)g(has)g(b)r(een) h(done)g(for)f(Suliciu's)h(mo)r(dels,)g(w)n(e)f(ma)n(y)g(solv)n(e)f(a)h (Rie-)515 4740 y(mann)c(problem)g(b)n(y)h(\014nding)g(the)f (appropriate)f Fl(u)2087 4709 y Fi(\003)2148 4740 y Fn(=)f Fl(u)p Fn(\(0)p Fj(\000)p Fl(;)14 b(t)p Fn(\).)35 b(Note)26 b(that)g(when)f(a)h Fl(U)3296 4752 y Fi(\000)3351 4740 y Fn(-)515 4839 y(or)32 b Fl(D)691 4851 y Fi(\000)746 4839 y Fn(-w)n(a)n(v)n(e)f(app)r(ears)g(in)i(the)g(w)n(a)n(v)n(e)e (pro\014le,)j(there)e(is)h(a)f(one-to-one)f(corresp)r(ondence)515 4939 y(b)r(et)n(w)n(een)g Fl(u)887 4909 y Fi(\003)955 4939 y Fn(and)g(the)g(sp)r(eed)g Fl(c)p Fn(.)47 b(Therefore,)30 b(it)h(causes)f(no)h(confusion)f(to)h(use)g Fl(c)g Fn(as)f(the)1905 5255 y(20)p eop %%Page: 21 21 21 20 bop 515 523 a Fn(parameter)19 b(instead)h(of)h Fl(u)1320 493 y Fi(\003)1378 523 y Fn(in)g(this)g(case.)34 b(W)-7 b(e)21 b(exhaust)f(all)h(p)r(ossibilities)f(of)h(w)n(a)n(v)n(e)e (pro\014les,)515 623 y(and)27 b(list)h(them)g(in)g(T)-7 b(able)27 b(4.)639 722 y(Lik)n(e)g(in)g(Suliciu's)g(mo)r(del,)h(again)d (w)n(e)i(ha)n(v)n(e)f(the)h(monotonicit)n(y)g(with)g(resp)r(ect)g(to)g (the)515 822 y(parameters.)52 b(Ho)n(w)n(ev)n(er,)33 b(there)g(are)f(o)n(v)n(erlapp)r(ed)g(regions)g(for)h(the)h(pro\014les) e(A)i(with)f(E,)515 922 y(and)k(G)g(with)g(I.)g(See)g(Figure)g(9,)i (where)d(the)i(o)n(v)n(erlapp)r(ed)d(regions)g(are)h(shaded.)65 b(This)515 1021 y(means)33 b(that)i(m)n(ultiple)f(solutions)f(app)r (ear)h(if)g(\()p Fl(u)2090 991 y Ff(+)2145 1021 y Fl(;)14 b(v)2225 991 y Ff(+)2280 1021 y Fn(\))35 b(falls)e(in)n(to)h(the)h (shaded)e(region.)515 1121 y(F)-7 b(or)26 b(instance,)h(for)f(the)h(o)n (v)n(erlapp)r(ed)e(region)h(of)g(A)h(and)g(E,)f(a)h(w)n(a)n(v)n(e)e (pro\014le)h(comprising)f(a)515 1220 y Fj(\000)580 1152 y(p)p 648 1152 42 4 v 648 1220 a Fn(2-w)n(a)n(v)n(e)j(and)h(a)h(+)1223 1152 y Fj(p)p 1292 1152 V 68 x Fn(2)o(-w)n(a)n(v)n(e)e(solv)n(es)g(the) i(Riemann)g(problem,)g(and)g(so)f(do)r(es)g(the)h(one)515 1320 y(comprising)24 b(consequen)n(tly)g(a)g Fj(\000)1553 1251 y(p)p 1622 1251 V 69 x Fn(2)o(-w)n(a)n(v)n(e,)g(a)h Fl(U)2039 1332 y Fi(\000)2094 1320 y Fn(-w)n(a)n(v)n(e,)f(a)h Fl(U)2470 1332 y Ff(+)2524 1320 y Fn(-w)n(a)n(v)n(e)e(and)i(a)g(+)3043 1251 y Fj(p)p 3111 1251 V 3111 1320 a Fn(2-w)n(a)n(v)n(e.)515 1420 y(F)-7 b(or)21 b(the)h(\014rst)f(one,)i(the)f(solution)f(k)n(eeps) g(in)h(the)g(same)f(phase)g Fl(u)i Fj(\024)g Fn(1,)f(whereas)f(the)h (second)515 1519 y(one)30 b(jumps)g(in)n(to)g(the)h(other)e(phase)h Fl(u)d Fj(\025)g Fn(1)p Fl(:)p Fn(5.)44 b(A)30 b(n)n(ucleation)g (criterion)f(is)h(th)n(us)g(needed)515 1619 y(here.)35 b(Though)23 b(an)h(rigorous)e(stabilit)n(y)h(analysis)g(w)n(ould)h(b)r (e)g(quite)g(complicated,)h(n)n(umer-)515 1719 y(ical)i(exp)r(erimen)n (ts)g(suggests)f(that)i(the)g(system)f(select)h(the)g(w)n(a)n(v)n(e)e (pro\014le)g(E)h(rather)g(than)515 1818 y(A.)35 b(F)-7 b(or)35 b(instance,)i(with)f(Riemann)f(data)g(\()p Fl(u)1981 1788 y Fi(\000)2036 1818 y Fl(;)14 b(v)2116 1788 y Fi(\000)2173 1818 y Fn(\))36 b(=)f(\(0)p Fl(:)p Fn(3)p Fl(;)14 b Fn(0\))p Fl(;)g Fn(\()p Fl(u)2708 1788 y Ff(+)2762 1818 y Fl(;)g(v)2842 1788 y Ff(+)2897 1818 y Fn(\))36 b(=)f(\(0)p Fl(:)p Fn(8)p Fl(;)14 b Fj(\000)p Fn(1\))515 1918 y(whic)n(h)34 b(falls)h(in)n(to)f (the)i(o)n(v)n(erlapp)r(ed)d(region)g(of)i(A)g(and)f(E,)h(The)g (solution)f(b)n(y)g(Jin-Xin's)515 2017 y(mo)r(del)27 b(is)h(depicted)g(in)g(Figure)f(10,)g(con)n(taining)f(only)h(the)h Fj(\006)2463 1949 y(p)p 2532 1949 V 68 x Fn(2-w)n(a)n(v)n(es.)639 2117 y(T)-7 b(o)27 b(summarize)g(this)h(subsection,)f(w)n(e)h(ha)n(v)n (e)e(the)i(follo)n(wing)f(Prop)r(osition.)515 2300 y Fe(Prop)s(osition)j(12)41 b Fd(Kinetic)31 b(r)l(elation)g(yielde)l(d)h (by)f(Jin-Xin)-8 b('s)29 b(r)l(elaxation)i(mo)l(del)h(\(34\))f(is)515 2399 y(the)40 b(Slemr)l(o)l(d's)h(visc)l(osity-c)l(apil)t(larity)j (criterion.)70 b(In)40 b(c)l(ase)h(of)g(tri-line)l(ar)f(c)l (onstitutive)515 2499 y(r)l(elation)d(\(24\),)i(it)e(c)l(an)f(b)l(e)h (expr)l(esse)l(d)f(p)l(ar)l(ametric)l(al)t(ly)j(by)e Fl(\036)2480 2511 y Ff(1)2518 2499 y Fn(\()p Fl(c)p Fn(\))g Fd(and)g Fl(\036)2872 2511 y Ff(2)2909 2499 y Fn(\()p Fl(c)p Fn(\))p Fd(,)i(or)e Fl( )3241 2511 y Ff(1)3278 2499 y Fn(\()p Fl(c)p Fn(\))515 2599 y Fd(and)31 b Fl( )731 2611 y Ff(2)769 2599 y Fn(\()p Fl(c)p Fn(\))p Fd(.)42 b(the)31 b(nucle)l(ation)h(criterion)f(is:)42 b(new)31 b(phase)h(is)g(gener)l(ate)l(d)f(only)g(when)h(ther)l(e)515 2698 y(exists)f(no)h(solution)g(that)g(ke)l(eps)g(in)g(the)g(same)g (phase.)46 b(With)32 b(this)h(kinetic)f(r)l(elation)g(and)515 2798 y(nucle)l(ation)e(criterion,)h(the)f(R)n(iemann)f(pr)l(oblem)i(is) f(uniquely)g(solvable.)515 3030 y Fa(4.3)112 b(A)37 b(six-sp)s(eed)h (mo)s(del)515 3183 y Fn(With)23 b(our)e(general)g(form)n(ulation)h(of)g (DKM's,)h(w)n(e)f(ma)n(y)g(construct)g(system)g(of)g(larger)e(size.)515 3283 y(F)-7 b(or)27 b(instance,)g(a)g(six-sp)r(eed)g(system)h(tak)n(es) e(the)i(form)g(of)1170 3405 y Fm(8)1170 3480 y(>)1170 3504 y(>)1170 3529 y(>)1170 3554 y(>)1170 3579 y(>)1170 3604 y(>)1170 3629 y(>)1170 3654 y(>)1170 3679 y(>)1170 3704 y(>)1170 3729 y(>)1170 3754 y(<)1170 3903 y(>)1170 3928 y(>)1170 3953 y(>)1170 3978 y(>)1170 4003 y(>)1170 4028 y(>)1170 4052 y(>)1170 4077 y(>)1170 4102 y(>)1170 4127 y(>)1170 4152 y(>)1170 4177 y(:)1286 3461 y Fl(u)1334 3473 y Fk(t)1381 3461 y Fn(+)18 b Fl(\025p)1554 3473 y Fk(x)1679 3461 y Fn(=)23 b(0)p Fl(;)1286 3560 y(v)1326 3572 y Fk(t)1374 3560 y Fn(+)18 b Fl(\025q)1542 3572 y Fk(x)1679 3560 y Fn(=)23 b(0)p Fl(;)1286 3700 y(p)1328 3712 y Fk(t)1375 3700 y Fn(+)18 b Fl(\025r)1543 3712 y Fk(x)1679 3700 y Fn(=)1777 3644 y(1)p 1777 3681 V 1781 3757 a Fl(\017)1828 3700 y Fn(\()1873 3644 y Fl(v)p 1870 3681 49 4 v 1870 3757 a(\025)1947 3700 y Fj(\000)g Fl(p)p Fn(\))p Fl(;)1286 3875 y(q)1323 3887 y Fk(t)1371 3875 y Fn(+)g Fl(\025s)1541 3887 y Fk(x)1679 3875 y Fn(=)1777 3819 y(1)p 1777 3856 42 4 v 1781 3932 a Fl(\017)1828 3875 y Fn(\()1870 3819 y Fl(\033)s Fn(\()p Fl(u)p Fn(\))p 1870 3856 163 4 v 1927 3932 a Fl(\025)2061 3875 y Fj(\000)g Fl(q)s Fn(\))p Fl(;)1286 4042 y(r)1323 4054 y Fk(t)1371 4042 y Fn(+)g Fl(\025p)1544 4054 y Fk(x)1679 4042 y Fn(=)1777 3986 y(1)p 1777 4023 42 4 v 1781 4099 a Fl(\017)1828 4042 y Fn(\(2)p Fl(m)1975 4054 y Ff(1)2012 4042 y Fl(u)g Fn(+)g(2)p Fl(m)2276 4054 y Ff(3)2313 4042 y Fl(\033)s Fn(\()p Fl(u)p Fn(\))h Fj(\000)f Fl(r)r Fn(\))p Fl(;)1286 4209 y(s)1325 4221 y Fk(t)1372 4209 y Fn(+)g Fl(\025q)1540 4221 y Fk(x)1679 4209 y Fn(=)1777 4152 y(1)p 1777 4189 V 1781 4266 a Fl(\017)1828 4209 y Fn(\(2)p Fl(m)1975 4221 y Ff(2)2012 4209 y Fl(v)k Fj(\000)c Fl(s)p Fn(\))p Fl(:)3231 3849 y Fn(\(45\))515 4386 y(Here)27 b Fl(m)784 4398 y Ff(1)844 4386 y Fj(2)d Fn([0)p Fl(;)14 b Fn(0)p Fl(:)p Fn(5])p Fl(;)g(m)1265 4398 y Ff(2)1323 4386 y Fj(2)24 b Fn([0)p Fl(;)14 b Fn(0)p Fl(:)p Fn(5])p Fl(;)g(m)p Fn(3)21 b Fj(\025)h Fn(0)28 b(are)e(constan)n(ts.)36 b(In)28 b(this)g(case,)1905 5255 y(21)p eop %%Page: 22 22 22 21 bop 696 1057 a Fn(\003)23 b(=)865 940 y Fm(\024)950 1006 y Fl(\025)83 b Fn(0)953 1106 y(0)j(0)1164 940 y Fm(\025)1222 1057 y Fl(;)180 b(M)32 b Fn(=)1625 616 y Fm(2)1625 762 y(6)1625 812 y(6)1625 862 y(6)1625 911 y(6)1625 961 y(6)1625 1011 y(6)1625 1061 y(6)1625 1111 y(6)1625 1160 y(6)1625 1210 y(6)1625 1260 y(6)1625 1313 y(4)1814 713 y Fl(m)1887 725 y Ff(1)2226 657 y Fn(1)p 2202 694 90 4 v 2202 770 a(2)p Fl(\025)2530 713 y(m)2603 725 y Ff(3)1849 879 y Fn(0)301 b Fl(m)2265 891 y Ff(2)2565 823 y Fn(1)p 2541 860 V 2541 936 a(2)p Fl(\025)1722 1006 y Fn(1)18 b Fj(\000)g Fn(2)p Fl(m)1980 1018 y Ff(1)2226 1006 y Fn(0)209 b Fj(\000)p Fn(2)p Fl(m)2657 1018 y Ff(3)1849 1106 y Fn(0)g(1)18 b Fj(\000)g Fn(2)p Fl(m)2358 1118 y Ff(2)2565 1106 y Fn(0)1814 1245 y Fl(m)1887 1257 y Ff(1)2160 1245 y Fj(\000)2259 1189 y Fn(1)p 2235 1226 V 2235 1302 a(2)p Fl(\025)2565 1245 y Fn(0)1849 1412 y(0)301 b Fl(m)2265 1424 y Ff(2)2498 1412 y Fj(\000)2597 1356 y Fn(1)p 2573 1393 V 2573 1469 a(2)p Fl(\025)2735 616 y Fm(3)2735 762 y(7)2735 812 y(7)2735 862 y(7)2735 911 y(7)2735 961 y(7)2735 1011 y(7)2735 1061 y(7)2735 1111 y(7)2735 1160 y(7)2735 1210 y(7)2735 1260 y(7)2735 1313 y(5)2804 890 y(2)2804 1039 y(4)2959 956 y Fl(u)2961 1056 y(v)2901 1155 y(\033)s Fn(\()p Fl(u)p Fn(\))3105 890 y Fm(3)3105 1039 y(5)3174 1057 y Fl(:)515 1619 y Fn(The)27 b(stabilit)n(y)h(condition)f(is)h(min\()1627 1552 y Fm(\000)1707 1618 y Fn(2)p Fl(\025)1797 1588 y Ff(2)1834 1618 y Fn(\()p Fl(m)1939 1630 y Ff(1)1995 1618 y Fn(+)18 b Fl(m)2151 1630 y Ff(3)2202 1618 y Fn(_)-37 b Fl(\033)s Fn(\))19 b Fj(\000)32 b Fn(_)-37 b Fl(\033)t(;)14 b Fn(2)p Fl(\025)2550 1588 y Ff(2)2587 1618 y Fl(m)2660 1630 y Ff(2)2715 1618 y Fj(\000)32 b Fn(_)-37 b Fl(\033)2890 1552 y Fm(\001)2951 1619 y Fj(\025)23 b Fn(0)p Fl(:)639 1719 y Fn(Again,)i(w)n(e)g(tak)n(e)f(tra)n(v)n(eling)f(w)n(a)n(v)n(e)g (analysis)h(for)g(seeking)g(the)h(kinetic)g(relations.)35 b(The)515 1857 y(equations)26 b(read)h(\()1103 1827 y Fi(0)1150 1857 y Fn(=)22 b Fl(\017)1421 1801 y(d)p 1281 1838 323 4 v 1281 1914 a(d)p Fn(\()p Fl(x)e Fj(\000)e Fl(ct)p Fn(\))1614 1857 y(\))1163 1978 y Fm(8)1163 2052 y(>)1163 2077 y(>)1163 2102 y(>)1163 2127 y(>)1163 2152 y(>)1163 2177 y(>)1163 2202 y(>)1163 2227 y(>)1163 2252 y(<)1163 2401 y(>)1163 2426 y(>)1163 2451 y(>)1163 2476 y(>)1163 2501 y(>)1163 2526 y(>)1163 2551 y(>)1163 2576 y(>)1163 2600 y(:)1278 2035 y Fj(\000)p Fl(cu)1427 2005 y Fi(0)1468 2035 y Fn(+)g Fl(\025p)1641 2005 y Fi(0)1748 2035 y Fn(=)k(0)p Fl(;)1278 2134 y Fj(\000)p Fl(cv)1422 2104 y Fi(0)1464 2134 y Fn(+)c Fl(\025q)1635 2104 y Fi(0)1748 2134 y Fn(=)k(0)p Fl(;)1278 2256 y Fj(\000)p Fl(cp)1421 2226 y Fi(0)1462 2256 y Fn(+)d Fl(\025r)1633 2226 y Fi(0)1748 2256 y Fn(=)j(\()1880 2200 y Fl(v)p 1877 2237 49 4 v 1877 2313 a(\025)1955 2256 y Fj(\000)c Fl(p)p Fn(\))p Fl(;)1278 2432 y Fj(\000)p Fl(cq)1419 2402 y Fi(0)1461 2432 y Fn(+)g Fl(\025s)1631 2402 y Fi(0)1748 2432 y Fn(=)k(\()1877 2375 y Fl(\033)s Fn(\()p Fl(u)p Fn(\))p 1877 2413 163 4 v 1935 2489 a Fl(\025)2069 2432 y Fj(\000)c Fl(q)s Fn(\))p Fl(;)1278 2558 y Fj(\000)p Fl(cr)1418 2528 y Fi(0)1460 2558 y Fn(+)g Fl(\025p)1633 2528 y Fi(0)1748 2558 y Fn(=)k(\(2)p Fl(m)1982 2570 y Ff(1)2019 2558 y Fl(u)c Fn(+)g(2)p Fl(m)2283 2570 y Ff(3)2320 2558 y Fl(\033)s Fn(\()p Fl(u)p Fn(\))h Fj(\000)f Fl(r)r Fn(\))p Fl(;)1278 2658 y Fj(\000)p Fl(cs)1418 2628 y Fi(0)1460 2658 y Fn(+)g Fl(\025q)1631 2628 y Fi(0)1748 2658 y Fn(=)k(\(2)p Fl(m)1982 2670 y Ff(2)2019 2658 y Fl(v)g Fj(\000)c Fl(s)p Fn(\))p Fl(:)3231 2347 y Fn(\(46\))639 2797 y(W)-7 b(e)28 b(ma)n(y)f(in)n (tegrate)g(the)h(\014rst)f(t)n(w)n(o)g(equations,)g(and)g(obtain)1194 2905 y Fm(8)1194 2979 y(>)1194 3004 y(>)1194 3029 y(<)1194 3179 y(>)1194 3204 y(>)1194 3229 y(:)1309 2974 y Fl(\025)1357 2944 y Ff(2)1395 2974 y Fl(r)1434 2944 y Fi(0)1476 2974 y Fj(\000)18 b Fl(c)1595 2944 y Ff(2)1632 2974 y Fl(u)1680 2944 y Fi(0)1786 2974 y Fn(=)23 b Fl(v)f Fj(\000)c Fl(cu)g Fj(\000)g Fl(C)2263 2986 y Ff(1)2300 2974 y Fl(;)1309 3074 y(\025)1357 3044 y Ff(2)1395 3074 y Fl(s)1434 3044 y Fi(0)1475 3074 y Fj(\000)g Fl(c)1594 3044 y Ff(2)1632 3074 y Fl(v)1675 3044 y Fi(0)1786 3074 y Fn(=)23 b Fl(\033)s Fn(\()p Fl(u)p Fn(\))c Fj(\000)f Fl(cv)k Fj(\000)c Fl(C)2378 3086 y Ff(2)2415 3074 y Fl(;)1309 3174 y(cu)1393 3144 y Fi(0)1434 3174 y Fj(\000)g Fl(cr)1592 3144 y Fi(0)1786 3174 y Fn(=)23 b(2)p Fl(m)1989 3186 y Ff(1)2026 3174 y Fl(u)18 b Fn(+)g(2)p Fl(m)2290 3186 y Ff(3)2326 3174 y Fl(\033)s Fn(\()p Fl(u)p Fn(\))h Fj(\000)f Fl(r)n(;)1309 3273 y(cv)1388 3243 y Fi(0)1430 3273 y Fj(\000)g Fl(cs)1588 3243 y Fi(0)1786 3273 y Fn(=)23 b(2)p Fl(m)1989 3285 y Ff(2)2026 3273 y Fl(v)e Fj(\000)d Fl(s:)3231 3125 y Fn(\(47\))639 3412 y(It)35 b(seems)e(imp)r(ossible)h(to)g(describ)r(e)g (the)g(hetero)r(clinic)g(orbit)g(for)f(this)i(fourth-order)515 3512 y(dynamical)27 b(system)g(in)h(general.)35 b(Nev)n(ertheless,)27 b(there)g(are)g(a)g(few)h(facts)g(clear.)639 3611 y(First,)40 b(for)d Fl(m)1087 3623 y Ff(3)1164 3611 y Fn(=)j(0,)g(a)d(stationary)f (phase)h(b)r(oundary)g(solution)g(m)n(ust)h(v)n(erify)f(the)515 3711 y(equal-area)25 b(la)n(w.)639 3811 y(Secondly)-7 b(,)36 b(the)e(existence)g(of)g(a)f(hetero)r(clinic)h(orbit)g(dep)r (ends)g(also)f(on)h Fl(\025)p Fn(.)56 b(F)-7 b(or)33 b(tri-)515 3910 y(linear)27 b(structure)h(relation,)g(w)n(e)g(ma)n(y)g (try)g(the)h(approac)n(h)e(as)h(for)g(Jin-Xin's)g(mo)r(del)h(for)e(a) 515 4010 y(kinetic)32 b(relation.)50 b(Ho)n(w)n(ev)n(er,)32 b(the)h(hea)n(vy)e(calculation)g(mak)n(es)h(it)h(virtually)e(imp)r (ossible)515 4110 y(b)n(y)e(hand.)41 b(W)-7 b(e)30 b(only)f(mak)n(e)f (a)h(n)n(umerical)f(comparison)g(here.)41 b(T)-7 b(aking)29 b(the)g(same)g(initial)515 4209 y(data)f(\()p Fl(u)785 4179 y Fi(\000)841 4209 y Fl(;)14 b(v)921 4179 y Fi(\000)977 4209 y Fn(\))25 b(=)g(\(0)p Fl(:)p Fn(8)p Fl(;)14 b Fn(0\))p Fl(;)g Fn(\()p Fl(u)1491 4179 y Ff(+)1545 4209 y Fl(;)g(v)1625 4179 y Ff(+)1680 4209 y Fn(\)\(1)p Fl(:)p Fn(7)p Fl(;)g Fn(0)p Fl(:)p Fn(8\),)28 b(the)i(di\013eren)n(t)f(solutions)f(at)g (time)i Fl(t)25 b Fn(=)f(1)515 4309 y(for)j Fl(\025)c Fn(=)g(1)p Fl(:)p Fn(6)k(and)g Fl(\025)d Fn(=)e(10)27 b(are)g(displa)n(y)n(ed)f(in)i(Figure)f(11.)639 4408 y(Thirdly)-7 b(,)42 b(in)d(general,)i(the)e(existence)g(of)g(a)g (hetero)r(clinic)f(orbit)h(dep)r(ends)g(also)f(on)515 4508 y Fl(m)588 4520 y Ff(1)625 4508 y Fl(;)14 b(m)735 4520 y Ff(2)772 4508 y Fl(;)g(m)882 4520 y Ff(3)919 4508 y Fn(.)55 b(F)-7 b(or)34 b(example,)h(consider)d Fl(m)1911 4520 y Ff(2)1982 4508 y Fn(=)h(1)p Fl(=)p Fn(3)p Fl(;)14 b(m)2316 4520 y Ff(3)2385 4508 y Fn(=)33 b(0,)i(and)e(v)-5 b(ary)33 b Fl(m)3014 4520 y Ff(1)3051 4508 y Fn(.)56 b(T)-7 b(aking)515 4608 y(initial)27 b(data)f(\()p Fl(u)1022 4578 y Fi(\000)1078 4608 y Fl(;)14 b(v)1158 4578 y Fi(\000)1214 4608 y Fn(\))23 b(=)g(\(0)p Fl(:)p Fn(8)p Fl(;)14 b Fn(0\))p Fl(;)g Fn(\()p Fl(u)1724 4578 y Ff(+)1778 4608 y Fl(;)g(v)1858 4578 y Ff(+)1913 4608 y Fn(\))23 b(=)g(\(1)p Fl(:)p Fn(6)p Fl(;)14 b Fn(0)p Fl(:)p Fn(4\),)26 b(the)h(solutions)f(at)h(time)g Fl(t)c Fn(=)f(1)515 4707 y(for)27 b Fl(m)715 4719 y Ff(1)775 4707 y Fn(=)c(0)p Fl(:)p Fn(1)p Fl(;)14 b Fn(0)p Fl(:)p Fn(3)p Fl(;)g Fn(0)p Fl(:)p Fn(5)24 b(are)j(displa)n(y)n(ed)f(in)i (Figure)f(12.)639 4807 y(F)-7 b(ourthly)g(,)29 b(for)f Fl(m)1198 4819 y Ff(1)1260 4807 y Fn(=)d Fl(m)1423 4819 y Ff(2)1485 4807 y Fj(6)p Fn(=)f(0,)29 b(when)f Fl(\025)i Fn(b)r(ecomes)e(large,)f(w)n(e)i(ma)n(y)f(\014nd)h(the)g(kinetic)515 4907 y(relation)h(approac)n(hes)f(to)i(that)h(of)f(Jin-Xin's)h(mo)r (del.)48 b(In)31 b(fact,)i(from)e(\(47\),)h(the)g(spatial)515 5006 y(scale)27 b(is)g(of)h(order)e Fl(\025)1157 4976 y Ff(2)1194 5006 y Fn(.)37 b(Let)1905 5255 y(22)p eop %%Page: 23 23 23 22 bop 1448 541 a Fm(8)1448 616 y(>)1448 640 y(>)1448 665 y(>)1448 690 y(>)1448 715 y(>)1448 740 y(>)1448 765 y(>)1448 790 y(<)1448 939 y(>)1448 964 y(>)1448 989 y(>)1448 1014 y(>)1448 1039 y(>)1448 1064 y(>)1448 1089 y(>)1448 1114 y(:)1564 641 y Fl(u)82 b Fn(=)23 b Fl(u)1830 653 y Ff(0)1885 641 y Fn(+)2000 585 y(1)p 1978 622 86 4 v 1978 698 a Fl(\025)2026 674 y Ff(2)2074 641 y Fl(u)2122 653 y Ff(1)2177 641 y Fn(+)18 b Fj(\001)c(\001)g(\001)g Fl(;)1564 808 y(v)90 b Fn(=)23 b Fl(v)1822 820 y Ff(0)1878 808 y Fn(+)1993 751 y(1)p 1971 789 V 1971 865 a Fl(\025)2019 841 y Ff(2)2067 808 y Fl(v)2107 820 y Ff(1)2162 808 y Fn(+)18 b Fj(\001)c(\001)g(\001)g Fl(;)1564 974 y(r)93 b Fn(=)23 b Fl(r)1819 986 y Ff(0)1875 974 y Fn(+)1990 918 y(1)p 1968 955 V 1968 1031 a Fl(\025)2016 1007 y Ff(2)2064 974 y Fl(r)2101 986 y Ff(1)2157 974 y Fn(+)18 b Fj(\001)c(\001)g(\001)g Fl(;)1564 1141 y(s)91 b Fn(=)23 b Fl(s)1821 1153 y Ff(0)1877 1141 y Fn(+)1992 1085 y(1)p 1970 1122 V 1970 1198 a Fl(\025)2018 1174 y Ff(2)2065 1141 y Fl(s)2104 1153 y Ff(1)2160 1141 y Fn(+)18 b Fj(\001)c(\001)g (\001)g Fl(:)3231 885 y Fn(\(48\))515 1312 y(Then,)28 b(up)f(to)h(the)g(leading)f(order,)f(w)n(e)h(ha)n(v)n(e)1422 1416 y Fm(8)1422 1491 y(>)1422 1515 y(>)1422 1540 y(<)1422 1690 y(>)1422 1715 y(>)1422 1740 y(:)1537 1486 y Fl(r)1576 1455 y Fi(0)1574 1506 y Ff(0)1697 1486 y Fn(=)22 b Fl(v)1824 1498 y Ff(0)1880 1486 y Fj(\000)c Fl(cu)2047 1498 y Ff(0)2102 1486 y Fj(\000)g Fl(C)2244 1498 y Ff(1)2282 1486 y Fl(;)1537 1585 y(s)1576 1555 y Fi(0)1576 1606 y Ff(0)1697 1585 y Fn(=)k Fl(\033)s Fn(\()p Fl(u)1914 1597 y Ff(0)1952 1585 y Fn(\))d Fj(\000)f Fl(cv)2162 1597 y Ff(0)2217 1585 y Fj(\000)g Fl(C)2359 1597 y Ff(2)2397 1585 y Fl(;)1537 1685 y Fn(0)118 b(=)22 b(2)p Fl(m)1899 1697 y Ff(1)1936 1685 y Fl(u)1984 1697 y Ff(0)2039 1685 y Fj(\000)c Fl(r)2159 1697 y Ff(0)2197 1685 y Fl(:)1537 1784 y Fn(0)118 b(=)22 b(2)p Fl(M)27 b Fj(\000)18 b Fn(2)p Fl(v)2099 1796 y Ff(0)2154 1784 y Fj(\000)g Fl(s)2276 1796 y Ff(0)2314 1784 y Fl(:)3231 1636 y Fn(\(49\))515 1960 y(As)34 b Fl(m)717 1972 y Ff(1)788 1960 y Fn(=)f Fl(m)959 1972 y Ff(2)996 1960 y Fn(,)j(this)e(is)g(equiv)-5 b(alen)n(t)34 b(to)g(Jin-Xin's)g(mo)r(del.)56 b(The)35 b(c)n(haracteristic)d(phase) 515 2060 y(b)r(oundary)27 b(width)h(is)f Fl(\017\025)1289 2030 y Ff(2)1327 2060 y Fn(.)639 2159 y(Finally)-7 b(,)29 b(if)f(w)n(e)g(tak)n(e)g Fl(m)1392 2171 y Ff(1)1453 2159 y Fn(=)c(0)p Fl(;)14 b(m)1694 2171 y Ff(2)1755 2159 y Fl(>)23 b Fn(0)p Fl(;)14 b(m)1995 2171 y Ff(3)2056 2159 y Fl(>)24 b Fn(0,)k(then)h(there)f(are)f(stationary)g(phase)515 2259 y(b)r(oundary)h(solutions)h(as)g(in)h(Suliciu's)f(mo)r(del.)43 b(P)n(ositiv)n(e)28 b Fl(m)2444 2271 y Ff(2)2481 2259 y Fl(;)14 b(m)2591 2271 y Ff(3)2657 2259 y Fn(ma)n(y)29 b(ensure)g(the)h(sta-)515 2359 y(bilit)n(y)e(conditions.)39 b(Ho)n(w)n(ev)n(er,)27 b(b)r(oth)i(stationary)d(phase)i(b)r(oundary)g (and)g(mo)n(ving)g(phase)515 2458 y(b)r(oundary)33 b(ha)n(v)n(e)f(b)r (een)j(observ)n(ed.)54 b(F)-7 b(or)33 b(instance,)i(the)f(solutions)g Fl(u)p Fn(\()p Fl(x;)14 b Fn(1\))33 b(with)i(initial)515 2558 y(data)27 b(\()p Fl(u)784 2528 y Fi(\000)840 2558 y Fl(;)14 b(v)920 2528 y Fi(\000)976 2558 y Fn(\))25 b(=)e(\(0)p Fl(:)p Fn(8)p Fl(;)14 b Fn(0\))p Fl(;)g Fn(\()p Fl(u)1488 2528 y Ff(+)1542 2558 y Fl(;)g(v)1622 2528 y Ff(+)1678 2558 y Fn(\))24 b(=)f(\(1)p Fl(:)p Fn(7)p Fl(;)14 b Fn(0\),)28 b(and)g(\()p Fl(u)2365 2528 y Fi(\000)2421 2558 y Fl(;)14 b(v)2501 2528 y Fi(\000)2557 2558 y Fn(\))24 b(=)g(\(0)p Fl(:)p Fn(8)p Fl(;)14 b Fn(0\))p Fl(;)g Fn(\()p Fl(u)3069 2528 y Ff(+)3123 2558 y Fl(;)g(v)3203 2528 y Ff(+)3258 2558 y Fn(\))24 b(=)515 2657 y(\(1)p Fl(:)p Fn(7)p Fl(;)14 b Fn(0)p Fl(:)p Fn(4\),)26 b(are)h(depicted)h(in)g (Figure)f(13\(a\))f(and)i(Figure)f(13\(b\),)g(resp)r(ectiv)n(ely)-7 b(.)515 2931 y Fo(5)134 b(Discussions)515 3113 y Fn(In)25 b(this)f(pap)r(er,)h(w)n(e)f(ha)n(v)n(e)g(constructed)g(a)g(general)f (DKM)i(mo)r(del)g(for)f(mo)r(deling)g(dynami-)515 3213 y(cal)d(phase)g(transitions.)34 b(As)22 b(stable)f(regularization-s,)f (DKM's)i(are)f(exp)r(ected)h(to)f(pro)n(vide)515 3313 y(a)j(v)-5 b(ariet)n(y)23 b(of)h(reasonable)e(kinetic)j(relations)e (and)h(n)n(ucleation)f(criteria,)h(whic)n(h)g(ma)n(y)g(then)515 3412 y(b)r(e)19 b(applied)f(to)h(appro)n(ximate)e(those)h(app)r(earing) g(in)h(real)e(systems)i(or)e(exp)r(erimen)n(ts.)34 b(DKM)515 3512 y(therefore)d(ma)n(y)h(serv)n(e)f(as)h(a)g(uniform)h(and)f (\015exible)h(approac)n(h)d(of)j(pro)n(viding)e(Riemann)515 3611 y(solv)n(ers)24 b(to)i(dynamical)f(phase)h(transition)f(problems.) 36 b(Moreo)n(v)n(er,)24 b(the)i(P)n(articular)e(mo)r(d-)515 3711 y(els)29 b(ha)n(v)n(e)g(also)g(b)r(een)h(studied)h(b)r(oth)f (theoretically)f(and)h(n)n(umerically)-7 b(.)43 b(It)30 b(is)g(found)g(that)515 3811 y(the)25 b(kinetic)g(relation)f(yielded)g (b)n(y)h(Suliciu's)g(mo)r(del)g(is)f(indeed)h(the)g(c)n(hord)f (criterion,)g(and)515 3910 y(that)33 b(b)n(y)g(Jin-Xin's)h(relaxation)d (mo)r(del)j(is)f(the)h(viscosit)n(y-capillarit)n(y)c(criterion.)53 b(F)-7 b(or)32 b(a)515 4010 y(tri-linear)20 b(constitutiv)n(e)g (relation,)i(it)f(is)g(sho)n(wn)g(that)g(the)g(Riemann)h(problem)e(is)h (uniquely)515 4110 y(solv)-5 b(able,)27 b(with)h(certain)f(n)n (ucleation)g(criterion)f(prescrib)r(ed)h(for)g(Jin-Xin's)h(mo)r(del.) 639 4209 y(The)43 b(ob)5 b(jectiv)n(e)42 b(of)g(studying)h(DKM's)f(is)h (t)n(w)n(o-fold.)81 b(First,)46 b(this)d(is)f(a)h(new)f(and)515 4309 y(systematic-Al)37 b(w)n(a)n(y)g(to)h(regularized)f(the)h(ill-p)r (osed)g(system)g(\(2\).)69 b(As)38 b(demonstrated)515 4408 y(b)n(y)26 b(our)g(preliminary)g(theoretical)g(and)g(n)n(umerical) g(in)n(v)n(estigations,)f(this)i(approac)n(h)e(pro-)515 4508 y(vides)31 b(stable)g(pictures)h(of)f(the)h(phase)g(transition)f (phenomena,)h(and)f(di\013eren)n(t)h(DKM's)515 4608 y(giv)n(e)17 b(di\013eren)n(t)i(pro\014les)f(in)h(general.)32 b(The)19 b(n)n(umerics)f(are)f(simple)i(and)f(easy)g(to)g(implemen)n(t,)515 4707 y(and)26 b(without)i(Riemann)f(solv)n(er.)35 b(Mean)n(while,)26 b(the)h(study)g(of)g(DKM's,)g(particularly)f(the)515 4807 y(tra)n(v)n(eling)31 b(w)n(a)n(v)n(e)g(pro\014les,)i(naturally)f (yields)g(admissibilit)n(y)h(conditions)f(of)h(discon)n(tin)n(u-)515 4907 y(ities,)40 b(in)e(particular,)g(kinetic)g(relations)f(for)g (subsonic)g(phase)g(b)r(oundaries,)i(when)e(w)n(e)515 5006 y(tak)n(e)e Fl(\017)i Fj(\000)-15 b(!)37 b Fn(0+.)61 b(Nucleation)36 b(criteria)f(also)g(follo)n(ws)g(from)g(a)h(theoretic)f (study)-7 b(,)39 b(and/)1905 5255 y(23)p eop %%Page: 24 24 24 23 bop 515 523 a Fn(or)30 b(n)n(umerical)h(study)h(of)f(the)h (stabilit)n(y)g(of)f(w)n(a)n(v)n(e)f(pro\014les.)48 b(A)32 b(Riemann)g(solv)n(er)e(th)n(us)h(is)515 623 y(obtained)c(for)g(suc)n (h)g(a)h(DKM.)639 722 y(It)f(w)n(ould)g(b)r(e)g(v)n(ery)f(in)n (teresting)g(to)h(see)f(ho)n(w)g(the)i(w)n(a)n(v)n(e)d(patterns)h (di\013ers)h(along)f(with)515 822 y(the)d(DKM's,)i(for)d(general)g (initial)i(b)r(oundary)e(data.)35 b(Moreo)n(v)n(er,)22 b(in)h(high)g(dimensions)g([3],)515 922 y(the)28 b(b)r(eha)n(vior)e(of) i(the)f(mo)r(del)h(is)g(still)g(to)f(b)r(e)h(explored,)f(mainly)g(n)n (umerically)-7 b(.)515 1196 y Fo(References)556 1378 y Fn([1])41 b(Ab)r(ey)n(aratne,)27 b(and)g(J.)h(K.)f(Kno)n(wles,)f (Kinetic)i(Relations)f(and)g(the)h(Propagation)d(of)685 1478 y(Phase)34 b(b)r(oundaries)g(in)h(Solids,)h Fd(A)n(r)l(ch.)h(R)l (ational)g(Me)l(ch.)g(A)n(nal.)72 b Fe(114,)77 b Fn(119-154,)685 1577 y(1991.)556 1743 y([2])41 b(D.)26 b(Aregba-Driollet,)e(and)h(R.)h (Natalini,)g(Discrete)f(Kinetic)g(Sc)n(hemes)g(for)f(Multidi-)685 1843 y(mensional)j(Conserv)-5 b(ation)26 b(La)n(ws,)h(to)g(app)r(ear)g (in)h Fd(SIAM)h(J.)h(Num.)g(A)n(nal.)p Fn(.)556 2009 y([3])41 b(S.)35 b(Benzoni,)h(Stabilit)n(y)e(of)h(m)n(ulti-dimensional) f(phase)g(transitions)f(in)i(a)f(v)-5 b(an)34 b(der)685 2109 y(W)-7 b(aals)27 b(\015uid,)h Fd(Nonline)l(ar)j(A)n(nalysis)f (T.M.A.)g Fe(31,)c Fn(243-263,)f(1998.)556 2275 y([4])41 b(B.)30 b(Ha)n(y)n(es,)e(and)h(P)-7 b(.)29 b(LeFlo)r(c)n(h,)g (Nonclassical)f(Sho)r(c)n(ks)g(and)h(Kinetic)h(Relations:)39 b(Fi-)685 2374 y(nite)28 b(Di\013erence)g(Sc)n(hemes,)g Fd(SIAM)h(J.)h(Numer.)f(A)n(nal.)f Fe(35,)f Fn(2169-2194,)d(1998.)556 2540 y([5])41 b(Z.)20 b(Chen,)i(and)e(K.H.)g(Ho\013mann,)i(On)e(a)f (One-Dimensional)h(Nonlinear)f(Thermo)n(vis-)685 2640 y(co)r(elastic)26 b(Mo)r(del)g(for)g(Structural)g(Phase)f(T)-7 b(ransitions)25 b(in)i(Shap)r(e)f(Memory)g(Allo)n(ys,)685 2739 y Fd(J.)k(Di\013.)g(Eqn.)f Fe(112)p Fn(,)e(325-350,)d(1994.)556 2906 y([6])41 b(B.)23 b(Co)r(c)n(kburn,)g(and)f(H.)h(Gau,)h(A)f(Mo)r (del)g(Numerical)f(Sc)n(heme)h(for)f(the)h(Propagation)685 3005 y(of)28 b(Phase)e(T)-7 b(ransitions)27 b(in)h(Solids,)f Fd(SIAM)j(J.)f(Sci.)i(Comp.)e Fe(17,)e Fn(1092-1121,)c(1996.)556 3171 y([7])41 b(A.)24 b(Corli,)g(Nonc)n(haracteristic)e(phase)h(b)r (oundaries)g(for)g(general)f(systems)h(of)h(conser-)685 3271 y(v)-5 b(ation)28 b(la)n(ws,)e(to)i(app)r(ear)f(in)g Fd(R)n(iv.)k(Mat.)f(Pur)l(a)g(Appl.)p Fn(.)556 3437 y([8])41 b(A.)30 b(Corli,)e(On)h(the)g(visco-capillarit)n(y)e(kinetic)i (condition)g(for)f(sonic)h(phase)f(b)r(ound-)685 3537 y(aries,)f(preprin)n(t)g(1999.)556 3703 y([9])41 b(R.M.)f(Colom)n(b)r (o)f(e)g(A.)h(Corli,)i(Con)n(tin)n(uous)c(dep)r(endence)i(in)g(conserv) -5 b(ation)38 b(la)n(ws)685 3802 y(with)28 b(phase)g(transitions,)e(to) i(app)r(ear)e(in)i Fd(SIAM)i(J.)g(Math.)h(A)n(nal.)p Fn(.)515 3968 y([10])40 b(A.)24 b(Corli)e(e)h(M.)g(Sabl)n(\023)-39 b(e-T)-7 b(ougeron,)21 b(Kinetic)i(stabilization)f(of)h(a)f(sonic)h (phase)f(b)r(ound-)685 4068 y(ary)-7 b(,)27 b(to)h(app)r(ear)e(in)i Fd(A)n(r)l(ch.)i(R)l(at.)g(Me)l(ch.)h(A)n(nal.)p Fn(.)515 4234 y([11])40 b(H.)26 b(Hattori,)e(The)h(Riemann)g(Problem)f(for)g(a)g (v)-5 b(an)25 b(der)f(W)-7 b(aals)24 b(Fluid)h(with)h(En)n(trop)n(y)685 4334 y(Rate)42 b(Admissibilit)n(y)f(Criterion)g(|)g(Isothermal)g(Case,) j Fd(A)n(r)l(ch.)f(R)l(ational)g(Me)l(ch.)685 4433 y(A)n(nal.)58 b Fe(92,)h Fn(247-263,)24 b(1986.)515 4599 y([12])40 b(C.H.)28 b(He,)g(MPhil)g(thesis,)f(Math)h(Dept,)h(Hong)e(Kong)f(Univ)i (of)g(Sci)f(&)h(T)-7 b(ec)n(h,)27 b(1998.)515 4765 y([13])40 b(L.)23 b(Hsiao,)g(and)f(T.)h(Luo,)g(Large-time)e(Beha)n(vior)g(of)i (Solutions)f(of)g(One-dimensional)685 4865 y(Nonlinear)27 b(Thermo)n(visco)r(elasticit)n(y)-7 b(,)26 b(to)h(app)r(ear)g(in)h Fd(Pr)l(o)l(c.)i(R)l(oy.)g(So)l(c.)h(Edin.)g(A)p Fn(.)1905 5255 y(24)p eop %%Page: 25 25 25 24 bop 515 523 a Fn([14])40 b(L.)28 b(Hsiao,)g(and)f(P)-7 b(.)28 b(de)g(Mottoni,)g(Existence)f(and)h(Uniqueness)g(of)g(Riemann)g (Prob-)685 623 y(lem)39 b(for)g(Nonlinear)f(System)h(of)f(Conserv)-5 b(ation)38 b(La)n(ws)f(of)i(Mixed)g(T)n(yp)r(e,)j Fd(T)-6 b(r)l(ans.)685 722 y(A)n(mer.)30 b(Math.)h(So)l(c.)d Fe(322)p Fn(,)f(121-158,)e(1990.)515 877 y([15])40 b(D.)32 b(Y.)g(Hsieh,)g(S.)g(Q.)f(T)-7 b(ang,)32 b(and)f(X.)g(P)-7 b(.)31 b(W)-7 b(ang,)32 b(On)f(Hydro)r(dynamic)g(Instabilit)n(y)-7 b(,)685 976 y(Chaos,)27 b(and)g(Phase)g(T)-7 b(ransition,)27 b Fd(A)l(cta)i(Me)l(chanic)l(a)j(Sinic)l(a)i Fe(12)p Fn(,)28 b(1-14,)d(1996.)515 1131 y([16])40 b(D.Y.)e(Hsieh,)i(and)d(X.P) -7 b(.)37 b(W)-7 b(ang,)39 b(Phase)d(T)-7 b(ransitions)35 b(in)j(v)-5 b(an)36 b(der)h(W)-7 b(aals)36 b(Fluid,)685 1230 y Fd(SIAM)30 b(J.)g(Appl.)h(Math.)e Fe(57)p Fn(,)e(871-892,)d (1997.)515 1385 y([17])40 b(R.)33 b(D.)h(James,)f(Co-existence)e (Phases)g(in)i(the)h(One-Dimensional)d(Static)i(Theory)685 1484 y(of)28 b(Elastic)f(Bars,)f Fd(A)n(r)l(ch.)k(R)l(ational)g(Me)l (ch.)i(A)n(nal.)c Fe(72)f Fn(,)h(99-140,)c(1979.)515 1639 y([18])40 b(S.)c(Jin,)i(and)e(Z.)g(P)-7 b(.)35 b(Xin,)k(The)d (relaxation)e(sc)n(hemes)h(for)g(systems)h(of)g(h)n(yp)r(erb)r(olic)685 1738 y(conserv)-5 b(ation)26 b(la)n(ws,)h Fd(Comm.)k(Pur)l(e.)f(Appl.)h (Math.)e Fe(48)p Fn(,)e(235-278,)e(1995.)515 1893 y([19])40 b(S.)34 b(Jin,)h(Numerical)f(In)n(tegrations)d(of)j(Systems)g(of)f (onserv)-5 b(ation)32 b(La)n(ws)h(of)g(Mixed-)685 1993 y(t)n(yp)r(e,)28 b Fd(SIAM)i(J.)g(Appl.)h(Math.)e Fe(55)p Fn(,)e(1536-1551,)c(1995.)515 2147 y([20])40 b(L.)25 b(D.)f(Landau,)h(On)f(the)g(Theory)f(of)h(Phase)f(T)-7 b(ransitions,)51 b Fd(Col)t(le)l(cte)l(d)28 b(Pap)l(ers)g(of)f(L.)685 2247 y(D.)j(L)l(andau,)h(D.)f(T)-6 b(er)30 b(Haar)g(e)l(d.\))p Fn(,)e(Gordon)f(and)g(Breac)n(h)g(and)g(P)n(ergamon,)e(1965.)515 2401 y([21])40 b(P)-7 b(.)34 b(LeFlo)r(c)n(h,)i(Propagating)31 b(Phase)i(Boundaries:)49 b(F)-7 b(orm)n(ulation)33 b(of)h(the)g (Problem)685 2501 y(and)i(Existence)e(via)h(the)h(Glimm)g(Metho)r(d,)h Fd(A)n(r)l(ch.)g(R)l(ational)h(Me)l(ch.)g(A)n(nal.)e Fe(123)p Fn(,)685 2600 y(153-197,)25 b(1993.)515 2755 y([22])40 b(T.)c(P)-7 b(.)36 b(Liu,)i(Hyp)r(erb)r(olic)e(conserv)-5 b(ation)35 b(la)n(ws)g(with)h(relaxation,)76 b Fd(Comm.)39 b(Math.)685 2854 y(Phys.)30 b Fe(108)p Fn(,)c(153-175,)f(1987.)515 3009 y([23])40 b(R.)26 b(Natalini,)h(Recen)n(t)e(mathematical)h (Results)g(on)f(Hyp)r(erb)r(olic)h(Relaxation)f(Prob-)685 3108 y(lems,)j Fd(Pr)l(eprint)i(of)h(IA)n(C,)f(CNR)35 b Fe(7/1998)p Fn(,)26 b(Rome,)h(Italy)-7 b(.)515 3263 y([24])40 b(M.)33 b(Shearer,)g(Admissibilit)n(y)f(Criteria)g(for)g(Sho) r(c)n(k)g(W)-7 b(a)n(v)n(e)31 b(Solutions)h(of)h(a)f(System)685 3362 y(of)k(Conserv)-5 b(ation)34 b(La)n(ws)g(of)h(Mixed)h(T)n(yp)r(e,) h Fd(Pr)l(o)l(c.)h(R)l(oy.)f(So)l(c.)g(Edinbur)l(gh)45 b Fe(93)40 b(A)p Fn(,)685 3462 y(233-244,)25 b(1983.)515 3616 y([25])40 b(M.)26 b(Slemro)r(d,)g(Dynamical)g(Phase)e(T)-7 b(ransitions)25 b(in)h(a)f(v)-5 b(an)25 b(der)h(W)-7 b(aals)25 b(Fluid,)i Fd(A)n(r)l(ch.)685 3716 y(R)l(ational)k(Me)l(ch.)g (A)n(nal.)f Fe(81,)h Fn(301-315,)24 b(1983.)515 3870 y([26])40 b(I.)27 b(Suliciu,)g(A)f(Maxw)n(ell)g(Mo)r(del)g(for)g (Pseudo)r(elastic)f(materials,)g Fd(Scripta)k(Metal)t(lug-)685 3970 y(ic)l(a)i(Materialia)41 b Fe(31)p Fn(,)27 b(1399-1404,)c(1994.) 515 4125 y([27])40 b(S.Q.)d(T)-7 b(ang,)38 b(Phase)e(T)-7 b(ransition)36 b(in)h(a)f(Thermo)n(visco)r(elasticit)n(y)f(Mo)r(del,)k Fd(Pr)l(o)l(c)l(e)l(e)l(d-)685 4224 y(ings)32 b(of)g(the)g(3r)l(d)g (International)g(Confer)l(enc)l(e)g(on)g(Nonline)l(ar)g(Me)l(chanics)h (\(Shang-)685 4324 y(hai,)28 b(1998\))p Fn(,)e(\(W-Z)c(Chien)h (ed.\):373-376,)e(Shanghai)h(Univ)n(ersit)n(y)g(Press,)g(Shanghai,)685 4423 y(1998.)515 4578 y([28])40 b(S.Q.)22 b(T)-7 b(ang,)22 b(Steady)g(States)f(of)h(Some)g(mo)r(dels)f(for)h(V)-7 b(an)21 b(der)h(W)-7 b(aals)21 b(Fluids,)i(Comm.)685 4677 y(Nonlin.)28 b(Sci.)g(and)g(Numer.)f(Sim)n(ul.)h Fe(3)p Fn(,)g(163-167,)c(1998.)515 4832 y([29])40 b(L.)26 b(Y)-7 b(u,)27 b(and)f(B.L.)g(Hao,)55 b Fd(Phase)29 b(T)-6 b(r)l(ansitions)29 b(and)g(Critic)l(al)h(Phenomena)k Fn(\(in)26 b(Chi-)685 4932 y(nese\),)i(Scien)n(ti\014c)g(Press,)e (Beijing,)i(1984.)1905 5255 y(25)p eop %%Page: 26 26 26 25 bop 515 2359 a @beginspecial 0 @llx 0 @lly 452 @urx 465 @ury 2267 @rwi 2267 @rhi @setspecial %%BeginDocument: s1.eps %Magnification: 1.00 /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -89.0 473.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawSplineSection { /y3 exch def /x3 exch def /y2 exch def /x2 exch def /y1 exch def /x1 exch def /xa x1 x2 x1 sub 0.666667 mul add def /ya y1 y2 y1 sub 0.666667 mul add def /xb x3 x2 x3 sub 0.666667 mul add def /yb y3 y2 y3 sub 0.666667 mul add def x1 y1 lineto xa ya xb yb x3 y3 curveto } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin 10 setmiterlimit n 0 792 m 0 0 l 612 0 l 612 792 l cp clip 0.06000 0.06000 sc 7.500 slw % Polyline n 2400 7200 m 4800 2400 l 5400 3000 l 7800 600 l gs col-1 s gr % Polyline n 2550 5700 m 2550 5625 l 2625 5700 l 2625 5550 l 2775 5550 l gs col-1 s gr % Polyline n 2400 5550 m 2400 5700 l gs col-1 s gr % Polyline n 2325 5625 m 2475 5625 l gs col-1 s gr % Polyline n 2325 5700 m 2475 5700 l gs col-1 s gr % Polyline n 6150 2475 m 6300 2475 l gs col-1 s gr % Polyline n 6225 2400 m 6225 2550 l gs col-1 s gr % Polyline n 6150 2550 m 6300 2550 l gs col-1 s gr % Polyline gs clippath 4953 2745 m 5073 2775 l 4953 2805 l 5115 2805 l 5115 2745 l cp clip n 4875 2775 m 5100 2775 l gs col-1 s gr gr % arrowhead n 4953 2745 m 5073 2775 l 4953 2805 l col-1 s % Polyline gs clippath 5022 2955 m 4902 2925 l 5022 2895 l 4860 2895 l 4860 2955 l cp clip n 4875 2925 m 5100 2925 l gs col-1 s gr gr % arrowhead n 5022 2955 m 4902 2925 l 5022 2895 l col-1 s % Open spline gs clippath 3570 297 m 3600 177 l 3630 297 l 3630 135 l 3570 135 l cp clip n 3600.0 150.0 m 3600.0 4012.5 l 3600.0 7875.0 l gs col-1 s gr gr % arrowhead n 3570 297 m 3600 177 l 3630 297 l 3600 297 l 3570 297 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs clippath 8853 4770 m 8973 4800 l 8853 4830 l 9015 4830 l 9015 4770 l cp clip n 1500.0 4800.0 m 5250.0 4800.0 l 9000.0 4800.0 l gs col-1 s gr gr % arrowhead n 8853 4770 m 8973 4800 l 8853 4830 l 8853 4800 l 8853 4770 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs [15 50.0] 50.0 sd n 4800.0 2400.0 m 5400.0 2400.0 l 6000.0 2400.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [15 50.0] 50.0 sd n 4500.0 3000.0 m 4950.0 3000.0 l 5400.0 3000.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [15 50.0] 50.0 sd n 5400.0 3000.0 m 4500.0 3900.0 l 3600.0 4800.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 4800.0 2400.0 m 5850.0 1950.0 l 6900.0 1500.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 5400.0 3000.0 m 4762.5 3375.0 l 4125.0 3750.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 7350.0 1050.0 m 5025.0 3825.0 l 2700.0 6600.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 3300.0 5400.0 m 3112.5 5775.0 l 2925.0 6150.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 5850.0 2550.0 m 6112.5 2287.5 l 6375.0 2025.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 4800.0 4725.0 m 4800.0 4762.5 l 4800.0 4800.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 6000.0 4725.0 m 6000.0 4762.5 l 6000.0 4800.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 7200.0 4725.0 m 7200.0 4762.5 l 7200.0 4800.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 3600.0 2400.0 m 3637.5 2400.0 l 3675.0 2400.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 3600.0 3600.0 m 3637.5 3600.0 l 3675.0 3600.0 l gs col-1 s gr gr [] 0 sd % Open spline gs clippath 5548 1998 m 5425 2014 l 5525 1943 l 5375 2003 l 5397 2058 l cp clip n 5775.0 1875.0 m 5587.5 1950.0 l 5400.0 2025.0 l gs col-1 s gr gr % arrowhead n 5548 1998 m 5425 2014 l 5525 1943 l 5536 1970 l 5548 1998 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs clippath 5780 2064 m 5900 2037 l 5807 2118 l 5952 2045 l 5925 1991 l cp clip n 5475.0 2250.0 m 5700.0 2137.5 l 5925.0 2025.0 l gs col-1 s gr gr % arrowhead n 5780 2064 m 5900 2037 l 5807 2118 l 5794 2091 l 5780 2064 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs clippath 4734 3275 m 4851 3238 l 4764 3326 l 4903 3243 l 4872 3192 l cp clip n 4500.0 3450.0 m 4687.5 3337.5 l 4875.0 3225.0 l gs col-1 s gr gr % arrowhead n 4734 3275 m 4851 3238 l 4764 3326 l 4749 3301 l 4734 3275 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs clippath 4711 3536 m 4596 3583 l 4675 3488 l 4545 3585 l 4581 3633 l cp clip n 4875.0 3375.0 m 4725.0 3487.5 l 4575.0 3600.0 l gs col-1 s gr gr % arrowhead n 4711 3536 m 4596 3583 l 4675 3488 l 4693 3512 l 4711 3536 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs [66.7] 0 sd n 4575.0 2850.0 m 5062.5 2850.0 l 5550.0 2850.0 l gs col-1 s gr gr [] 0 sd % Open spline gs clippath 4760 3921 m 4858 3846 l 4807 3959 l 4908 3832 l 4861 3795 l cp clip n 4575.0 4200.0 m 4725.0 4012.5 l 4875.0 3825.0 l gs col-1 s gr gr % arrowhead n 4760 3921 m 4858 3846 l 4807 3959 l 4783 3940 l 4760 3921 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs clippath 4837 4250 m 4741 4328 l 4789 4214 l 4692 4344 l 4740 4380 l cp clip n 4950.0 4050.0 m 4837.5 4200.0 l 4725.0 4350.0 l gs col-1 s gr gr % arrowhead n 4837 4250 m 4741 4328 l 4789 4214 l 4813 4232 l 4837 4250 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs clippath 3018 5807 m 2937 5900 l 2964 5780 l 2891 5925 l 2945 5952 l cp clip 3058 5593 m 3137 5499 l 3111 5620 l 3184 5475 l 3130 5448 l cp clip n 3150.0 5475.0 m 3037.5 5700.0 l 2925.0 5925.0 l gs col-1 s gr gr % arrowhead n 3058 5593 m 3137 5499 l 3111 5620 l 3084 5607 l 3058 5593 l cp gs 0.00 setgray ef gr col-1 s % arrowhead n 3018 5807 m 2937 5900 l 2964 5780 l 2991 5794 l 3018 5807 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs clippath 6200 2392 m 6094 2455 l 6158 2350 l 6043 2464 l 6086 2507 l cp clip 6250 2258 m 6355 2194 l 6292 2300 l 6407 2186 l 6364 2143 l cp clip n 6375.0 2175.0 m 6225.0 2325.0 l 6075.0 2475.0 l gs col-1 s gr gr % arrowhead n 6250 2258 m 6355 2194 l 6292 2300 l 6271 2279 l 6250 2258 l cp gs 0.00 setgray ef gr col-1 s % arrowhead n 6200 2392 m 6094 2455 l 6158 2350 l 6179 2371 l 6200 2392 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs n 3600.0 1200.0 m 3637.5 1200.0 l 3675.0 1200.0 l gs col-1 s gr gr /Symbol ff 300.00 scf sf 3750 525 m gs 1 -1 sc (s) col-1 sh gr /Times-Roman ff 300.00 scf sf 3975 525 m gs 1 -1 sc (\(u\)) col-1 sh gr /Times-Roman ff 300.00 scf sf 8500 5175 m gs 1 -1 sc (u) col-1 sh gr /Times-Roman ff 180.00 scf sf 4800 5025 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 180.00 scf sf 3375 2400 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 180.00 scf sf 3375 3600 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 180.00 scf sf 6000 5100 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 180.00 scf sf 7200 5100 m gs 1 -1 sc (3) col-1 sh gr /Times-Roman ff 180.00 scf sf 5475 1875 m gs 1 -1 sc (T+) col-1 sh gr /Times-Roman ff 180.00 scf sf 5625 2325 m gs 1 -1 sc (T-) col-1 sh gr /Times-Roman ff 180.00 scf sf 4500 4050 m gs 1 -1 sc (S+) col-1 sh gr /Times-Roman ff 180.00 scf sf 4875 4350 m gs 1 -1 sc (S-) col-1 sh gr /Times-Roman ff 180.00 scf sf 4725 3600 m gs 1 -1 sc (B-) col-1 sh gr /Times-Roman ff 180.00 scf sf 4425 3375 m gs 1 -1 sc (B+) col-1 sh gr /Times-Roman ff 180.00 scf sf 6375 2550 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 180.00 scf sf 2700 5775 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 180.00 scf sf 3375 1200 m gs 1 -1 sc (3) col-1 sh gr /Times-Roman ff 180.00 scf sf 4950 3150 m gs 1 -1 sc (0) col-1 sh gr /Times-Roman ff 90.00 scf sf 5100 3075 m gs 1 -1 sc (b) col-1 sh gr /Times-Roman ff 180.00 scf sf 4950 2775 m gs 1 -1 sc (0) col-1 sh gr /Times-Roman ff 90.00 scf sf 5100 2700 m gs 1 -1 sc (#) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1092 2542 a Fn(Figure)27 b(1:)36 b(Elemen)n(tary)26 b(w)n(a)n(v)n(es)g(in)i(Suliciu's)g(mo)r(del.)515 4574 y @beginspecial 61 @llx 198 @lly 546 @urx 600 @ury 2267 @rwi 2267 @rhi @setspecial %%BeginDocument: sn1.ps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 519 135 5817 4833 rc 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6913 5186 rf 6 w 0 1782 2259 0 0 -1782 899 2171 4 MP PP -2259 0 0 1782 2259 0 0 -1782 899 2171 5 MP stroke 4 w DO SO 6 w 0 sg 899 2171 mt 3158 2171 L 899 389 mt 3158 389 L 3158 2171 mt 3158 389 L 899 2171 mt 899 389 L 899 2171 mt 3158 2171 L 899 2171 mt 899 389 L 899 2171 mt 899 2148 L 899 389 mt 899 412 L /Helvetica /ISOLatin1Encoding 120 FMSR 796 2317 mt (-1) s 1464 2171 mt 1464 2148 L 1464 389 mt 1464 412 L 1431 2317 mt (0) s 2029 2171 mt 2029 2148 L 2029 389 mt 2029 412 L 1996 2317 mt (1) s 2593 2171 mt 2593 2148 L 2593 389 mt 2593 412 L 2560 2317 mt (2) s 3158 2171 mt 3158 2148 L 3158 389 mt 3158 412 L 3125 2317 mt (3) s 899 2171 mt 922 2171 L 3158 2171 mt 3135 2171 L 728 2215 mt (-3) s 899 1874 mt 922 1874 L 3158 1874 mt 3135 1874 L 728 1918 mt (-2) s 899 1577 mt 922 1577 L 3158 1577 mt 3135 1577 L 728 1621 mt (-1) s 899 1280 mt 922 1280 L 3158 1280 mt 3135 1280 L 798 1324 mt (0) s 899 983 mt 922 983 L 3158 983 mt 3135 983 L 798 1027 mt (1) s 899 686 mt 922 686 L 3158 686 mt 3135 686 L 798 730 mt (2) s 899 389 mt 922 389 L 3158 389 mt 3135 389 L 798 433 mt (3) s 899 389 mt 3158 389 L 899 2171 mt 3158 2171 L 899 2171 mt 899 389 L 3158 2171 mt 3158 389 L gs 899 389 2260 1783 rc 29 21 28 21 28 21 28 21 29 21 28 21 28 21 28 21 29 21 28 21 28 21 28 21 29 21 28 21 28 21 28 21 29 21 28 21 28 21 28 21 28 21 29 21 28 21 28 21 28 21 29 21 28 21 28 21 28 21 29 21 28 21 28 21 28 21 29 21 28 21 28 21 28 21 29 21 28 21 28 21 899 650 41 MP stroke 28 16 28 16 29 16 28 16 28 16 28 16 29 16 28 17 28 17 28 17 29 17 28 18 28 18 28 19 29 19 28 20 28 23 28 24 29 31 28 68 2593 1490 21 MP stroke gr 1976 2496 mt (u) s /Helvetica /ISOLatin1Encoding 96 FMSR 2042 2436 mt (*) s /Helvetica /ISOLatin1Encoding 120 FMSR 673 1423 mt -90 rotate (v) s 90 rotate /Helvetica /ISOLatin1Encoding 96 FMSR 613 1363 mt -90 rotate (*) s 90 rotate /Helvetica /ISOLatin1Encoding 120 FMSR 673 1326 mt -90 rotate (-v) s 90 rotate /Helvetica /ISOLatin1Encoding 96 FMSR 613 1196 mt -90 rotate (-) s 90 rotate /Helvetica /ISOLatin1Encoding 120 FMSR 1956 294 mt (\(a\)) s 1 sg 0 1782 2259 0 0 -1782 3995 2171 4 MP PP -2259 0 0 1782 2259 0 0 -1782 3995 2171 5 MP stroke 4 w DO SO 6 w 0 sg 3995 2171 mt 6254 2171 L 3995 389 mt 6254 389 L 6254 2171 mt 6254 389 L 3995 2171 mt 3995 389 L 3995 2171 mt 6254 2171 L 3995 2171 mt 3995 389 L 3995 2171 mt 3995 2148 L 3995 389 mt 3995 412 L 3892 2317 mt (-1) s 4560 2171 mt 4560 2148 L 4560 389 mt 4560 412 L 4527 2317 mt (0) s 5125 2171 mt 5125 2148 L 5125 389 mt 5125 412 L 5092 2317 mt (1) s 5689 2171 mt 5689 2148 L 5689 389 mt 5689 412 L 5656 2317 mt (2) s 6254 2171 mt 6254 2148 L 6254 389 mt 6254 412 L 6221 2317 mt (3) s 3995 2171 mt 4018 2171 L 6254 2171 mt 6231 2171 L 3824 2215 mt (-1) s 3995 1815 mt 4018 1815 L 6254 1815 mt 6231 1815 L 3894 1859 mt (0) s 3995 1458 mt 4018 1458 L 6254 1458 mt 6231 1458 L 3894 1502 mt (1) s 3995 1102 mt 4018 1102 L 6254 1102 mt 6231 1102 L 3894 1146 mt (2) s 3995 745 mt 4018 745 L 6254 745 mt 6231 745 L 3894 789 mt (3) s 3995 389 mt 4018 389 L 6254 389 mt 6231 389 L 3894 433 mt (4) s 3995 389 mt 6254 389 L 3995 2171 mt 6254 2171 L 3995 2171 mt 3995 389 L 6254 2171 mt 6254 389 L gs 3995 389 2260 1783 rc 28 101 28 46 28 38 29 34 28 33 28 31 28 30 29 29 28 28 28 28 28 28 29 27 28 28 28 27 28 26 28 27 29 27 28 26 28 27 28 26 29 26 28 27 28 26 28 26 29 26 28 26 28 26 28 26 29 26 28 26 28 26 28 26 29 26 28 26 28 26 3995 400 36 MP stroke 28 18 28 18 29 18 28 17 28 18 28 18 29 18 28 18 28 18 28 17 29 18 28 18 28 18 28 18 29 17 28 18 28 18 28 18 29 18 28 18 28 17 28 18 28 18 29 18 28 18 28 18 28 17 29 18 28 18 28 18 5407 1458 31 MP stroke gr 5072 2496 mt (u) s /Helvetica /ISOLatin1Encoding 96 FMSR 5138 2436 mt (*) s /Helvetica /ISOLatin1Encoding 120 FMSR 3769 1423 mt -90 rotate (v) s 90 rotate /Helvetica /ISOLatin1Encoding 96 FMSR 3709 1363 mt -90 rotate (*) s 90 rotate /Helvetica /ISOLatin1Encoding 120 FMSR 3769 1326 mt -90 rotate (-v) s 90 rotate /Helvetica /ISOLatin1Encoding 96 FMSR 3709 1196 mt -90 rotate (-) s 90 rotate /Helvetica /ISOLatin1Encoding 120 FMSR 5052 294 mt (\(b\)) s 1 sg 0 1782 2259 0 0 -1782 899 4614 4 MP PP -2259 0 0 1782 2259 0 0 -1782 899 4614 5 MP stroke 4 w DO SO 6 w 0 sg 899 4614 mt 3158 4614 L 899 2832 mt 3158 2832 L 3158 4614 mt 3158 2832 L 899 4614 mt 899 2832 L 899 4614 mt 3158 4614 L 899 4614 mt 899 2832 L 899 4614 mt 899 4591 L 899 2832 mt 899 2855 L 796 4760 mt (-1) s 1464 4614 mt 1464 4591 L 1464 2832 mt 1464 2855 L 1431 4760 mt (0) s 2029 4614 mt 2029 4591 L 2029 2832 mt 2029 2855 L 1996 4760 mt (1) s 2593 4614 mt 2593 4591 L 2593 2832 mt 2593 2855 L 2560 4760 mt (2) s 3158 4614 mt 3158 4591 L 3158 2832 mt 3158 2855 L 3125 4760 mt (3) s 899 4614 mt 922 4614 L 3158 4614 mt 3135 4614 L 728 4658 mt (-3) s 899 4317 mt 922 4317 L 3158 4317 mt 3135 4317 L 728 4361 mt (-2) s 899 4020 mt 922 4020 L 3158 4020 mt 3135 4020 L 728 4064 mt (-1) s 899 3723 mt 922 3723 L 3158 3723 mt 3135 3723 L 798 3767 mt (0) s 899 3426 mt 922 3426 L 3158 3426 mt 3135 3426 L 798 3470 mt (1) s 899 3129 mt 922 3129 L 3158 3129 mt 3135 3129 L 798 3173 mt (2) s 899 2832 mt 922 2832 L 3158 2832 mt 3135 2832 L 798 2876 mt (3) s 899 2832 mt 3158 2832 L 899 4614 mt 3158 4614 L 899 4614 mt 899 2832 L 3158 4614 mt 3158 2832 L gs 899 2832 2260 1783 rc 29 -21 28 -21 28 -21 28 -21 29 -21 28 -21 28 -21 28 -21 29 -21 28 -21 28 -21 28 -21 29 -21 28 -21 28 -21 28 -21 29 -21 28 -21 28 -21 28 -21 28 -21 29 -21 28 -21 28 -21 28 -21 29 -21 28 -21 28 -21 28 -21 29 -21 28 -21 28 -21 28 -21 29 -21 28 -21 28 -21 28 -21 29 -21 28 -21 28 -21 899 4353 41 MP stroke 28 -16 28 -16 29 -16 28 -16 28 -16 28 -16 29 -16 28 -17 28 -17 28 -17 29 -17 28 -18 28 -18 28 -19 29 -19 28 -20 28 -23 28 -24 29 -31 28 -68 28 -10 28 -11 28 -10 29 -11 28 -10 28 -11 28 -10 29 -11 28 -10 28 -11 2311 3618 31 MP stroke gr 1976 4939 mt (u) s /Helvetica /ISOLatin1Encoding 96 FMSR 2042 4879 mt (*) s /Helvetica /ISOLatin1Encoding 120 FMSR 673 3866 mt -90 rotate (v) s 90 rotate /Helvetica /ISOLatin1Encoding 96 FMSR 613 3806 mt -90 rotate (*) s 90 rotate /Helvetica /ISOLatin1Encoding 120 FMSR 673 3769 mt -90 rotate (-v) s 90 rotate /Helvetica /ISOLatin1Encoding 96 FMSR 613 3639 mt -90 rotate (+) s 90 rotate /Helvetica /ISOLatin1Encoding 120 FMSR 1959 2737 mt (\(c\)) s 1 sg 0 1782 2259 0 0 -1782 3995 4614 4 MP PP -2259 0 0 1782 2259 0 0 -1782 3995 4614 5 MP stroke 4 w DO SO 6 w 0 sg 3995 4614 mt 6254 4614 L 3995 2832 mt 6254 2832 L 6254 4614 mt 6254 2832 L 3995 4614 mt 3995 2832 L 3995 4614 mt 6254 4614 L 3995 4614 mt 3995 2832 L 3995 4614 mt 3995 4591 L 3995 2832 mt 3995 2855 L 3892 4760 mt (-1) s 4560 4614 mt 4560 4591 L 4560 2832 mt 4560 2855 L 4527 4760 mt (0) s 5125 4614 mt 5125 4591 L 5125 2832 mt 5125 2855 L 5092 4760 mt (1) s 5689 4614 mt 5689 4591 L 5689 2832 mt 5689 2855 L 5656 4760 mt (2) s 6254 4614 mt 6254 4591 L 6254 2832 mt 6254 2855 L 6221 4760 mt (3) s 3995 4614 mt 4018 4614 L 6254 4614 mt 6231 4614 L 3824 4658 mt (-4) s 3995 4258 mt 4018 4258 L 6254 4258 mt 6231 4258 L 3824 4302 mt (-3) s 3995 3901 mt 4018 3901 L 6254 3901 mt 6231 3901 L 3824 3945 mt (-2) s 3995 3545 mt 4018 3545 L 6254 3545 mt 6231 3545 L 3824 3589 mt (-1) s 3995 3188 mt 4018 3188 L 6254 3188 mt 6231 3188 L 3894 3232 mt (0) s 3995 2832 mt 4018 2832 L 6254 2832 mt 6231 2832 L 3894 2876 mt (1) s 3995 2832 mt 6254 2832 L 3995 4614 mt 6254 4614 L 3995 4614 mt 3995 2832 L 6254 4614 mt 6254 2832 L gs 3995 2832 2260 1783 rc 29 -35 28 -36 28 -36 28 -35 29 -36 28 -101 28 -46 28 -38 29 -34 28 -33 28 -31 28 -30 29 -29 28 -28 28 -28 28 -28 29 -27 28 -28 28 -27 28 -26 28 -27 29 -27 28 -26 28 -27 28 -26 29 -26 28 -27 28 -26 28 -26 29 -26 28 -26 28 -26 28 -26 29 -26 28 -26 28 -26 28 -26 29 -26 28 -26 28 -26 3995 4603 41 MP stroke 28 -18 28 -18 29 -18 28 -17 28 -18 28 -18 29 -18 28 -18 28 -18 28 -17 29 -18 28 -18 28 -18 28 -18 29 -18 28 -17 28 -18 28 -18 29 -18 28 -18 28 -17 28 -18 28 -18 29 -18 28 -18 28 -18 28 -17 29 -18 28 -18 28 -18 5407 3545 31 MP stroke gr 5072 4939 mt (u) s /Helvetica /ISOLatin1Encoding 96 FMSR 5138 4879 mt (*) s /Helvetica /ISOLatin1Encoding 120 FMSR 3769 3866 mt -90 rotate (v) s 90 rotate /Helvetica /ISOLatin1Encoding 96 FMSR 3709 3806 mt -90 rotate (*) s 90 rotate /Helvetica /ISOLatin1Encoding 120 FMSR 3769 3769 mt -90 rotate (-v) s 90 rotate /Helvetica /ISOLatin1Encoding 96 FMSR 3709 3639 mt -90 rotate (+) s 90 rotate /Helvetica /ISOLatin1Encoding 120 FMSR 5052 2737 mt (\(d\)) s end eplot epage end showpage %%EndDocument @endspecial 183 x(Figure)40 b(2:)64 b(The)41 b(jump)h(in)f Fl(v)j Fn(through)d(\(a\))g(left-going)f(w)n(a)n(v)n(e\(s\))g(with)i Fl(u)2945 4726 y Fi(\000)3046 4757 y Fj(\024)j Fn(1;)i(\(b\))515 4856 y(left-going)32 b(w)n(a)n(v)n(e\(s\))f(with)j Fl(u)1435 4826 y Fi(\000)1522 4856 y Fj(\025)d Fn(1)p Fl(:)p Fn(5;)k(\(c\))f (righ)n(t-going)c(and)j(stationary)e(w)n(a)n(v)n(e\(s\))h(with)515 4956 y Fl(u)563 4926 y Ff(+)640 4956 y Fj(\024)23 b Fn(1;)k(\(d\))i (righ)n(t-going)c(and)i(stationary)f(w)n(a)n(v)n(e\(s\))h(with)h Fl(u)2475 4926 y Ff(+)2553 4956 y Fj(\025)22 b Fn(1)p Fl(:)p Fn(5.)1905 5255 y(26)p eop %%Page: 27 27 27 26 bop 279 2410 a @beginspecial 0 @llx 0 @lly 277 @urx 479 @ury 2267 @rwi 2267 @rhi @setspecial %%BeginDocument: s2.eps %Magnification: 1.00 /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -107.0 568.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin 10 setmiterlimit n 0 792 m 0 0 l 612 0 l 612 792 l cp clip 0.06000 0.06000 sc 7.500 slw % Polyline gs clippath 2670 1647 m 2700 1527 l 2730 1647 l 2730 1485 l 2670 1485 l cp clip n 2700 1500 m 2700 9375 l gs col-1 s gr gr % arrowhead n 2670 1647 m 2700 1527 l 2730 1647 l col-1 s 0.000 slw % Polyline [33.3] 0 sd n 5100 1800 m 5100 9300 l [] 0 sd % Polyline [33.3] 0 sd n 3900 1800 m 3900 9300 l [] 0 sd % Polyline [33.3] 0 sd n 3900 1800 m 3900 9000 l [] 0 sd % Polyline [33.3] 0 sd n 3900 1800 m 3900 9075 l 3900 9300 l [] 0 sd 7.500 slw % Polyline [15 50.0] 50.0 sd n 3600 1650 m 3600 9300 l gs col-1 s gr [] 0 sd % Polyline n 3900 1575 m 3900 9300 l gs col-1 s gr % Polyline n 4500 1575 m 4500 9300 l gs col-1 s gr % Polyline [66.7] 0 sd n 3900 6900 m 5100 6900 l gs col-1 s gr [] 0 sd % Polyline n 4500 7500 m 5700 6300 l gs col-1 s gr % Polyline [15 50.0] 50.0 sd n 5100 1650 m 5100 9300 l gs col-1 s gr [] 0 sd % Polyline n 3900 6900 m 2100 9450 l gs col-1 s gr % Polyline [66.7] 0 sd n 3900 6900 m 2700 5175 l gs col-1 s gr [] 0 sd % Polyline [66.7] 0 sd n 2700 5175 m 4500 3375 l gs col-1 s gr [] 0 sd % Polyline n 4500 3375 m 5700 2175 l gs col-1 s gr % Polyline [66.7] 0 sd n 3600 6450 m 4500 6450 l gs col-1 s gr [] 0 sd % Polyline n 4500 6450 m 5700 5250 l gs col-1 s gr % Polyline gs clippath 6228 5670 m 6348 5700 l 6228 5730 l 6390 5730 l 6390 5670 l cp clip n 1800 5700 m 6375 5700 l gs col-1 s gr gr % arrowhead n 6228 5670 m 6348 5700 l 6228 5730 l col-1 s /Times-Roman ff 180.00 scf sf 3300 6000 m gs 1 -1 sc (0.75) col-1 sh gr /Times-Roman ff 180.00 scf sf 3800 6000 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 180.00 scf sf 4300 6000 m gs 1 -1 sc (1.5) col-1 sh gr /Times-Roman ff 180.00 scf sf 5000 6000 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 300.00 scf sf 2925 1800 m gs 1 -1 sc (v) col-1 sh gr /Times-Roman ff 900.00 scf sf 3000 8700 m gs 1 -1 sc (A) col-1 sh gr /Times-Roman ff 900.00 scf sf 4725 6750 m gs 1 -1 sc (C) col-1 sh gr /Times-Roman ff 900.00 scf sf 4725 8400 m gs 1 -1 sc (B) col-1 sh gr /Times-Roman ff 900.00 scf sf 4725 4575 m gs 1 -1 sc (D) col-1 sh gr /Times-Roman ff 900.00 scf sf 4725 2475 m gs 1 -1 sc (E) col-1 sh gr /Times-Roman ff 900.00 scf sf 2025 4275 m gs 1 -1 sc (F) col-1 sh gr /Times-Roman ff 300.00 scf sf 6075 6000 m gs 1 -1 sc (u) col-1 sh gr /Times-Roman ff 180.00 scf sf 3075 5700 m gs 1 -1 sc (\(-\)) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1918 w @beginspecial 0 @llx 0 @lly 315 @urx 495 @ury 1700 @rwi 2267 @rhi @setspecial %%BeginDocument: s3.eps %Magnification: 1.00 /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -66.0 566.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin 10 setmiterlimit n 0 792 m 0 0 l 612 0 l 612 792 l cp clip 0.06000 0.06000 sc % Polyline [33.3] 0 sd n 5100 1800 m 5100 9300 l [] 0 sd % Polyline [33.3] 0 sd n 3900 1800 m 3900 9300 l [] 0 sd % Polyline [33.3] 0 sd n 3900 1800 m 3900 9000 l [] 0 sd % Polyline [33.3] 0 sd n 3900 1800 m 3900 9075 l 3900 9300 l [] 0 sd 7.500 slw % Polyline n 3900 1575 m 3900 9300 l gs col-1 s gr % Polyline n 4500 1575 m 4500 9300 l gs col-1 s gr % Polyline [15 50.0] 50.0 sd n 5100 1650 m 5100 9300 l gs col-1 s gr [] 0 sd % Polyline gs clippath 2670 1647 m 2700 1527 l 2730 1647 l 2730 1485 l 2670 1485 l cp clip n 2700 1500 m 2700 9375 l gs col-1 s gr gr % arrowhead n 2670 1647 m 2700 1527 l 2730 1647 l col-1 s % Polyline [15 50.0] 50.0 sd n 3600 1650 m 3600 9300 l gs col-1 s gr [] 0 sd % Polyline [66.7] 0 sd n 5100 6600 m 3900 6600 l gs col-1 s gr [] 0 sd % Polyline [66.7] 0 sd n 4500 6000 m 3600 6000 l gs col-1 s gr [] 0 sd % Polyline [66.7] 0 sd n 5400 6900 m 2700 4200 l 4500 2400 l gs col-1 s gr [] 0 sd % Polyline n 4500 2400 m 5700 1200 l gs col-1 s gr % Polyline n 4500 6000 m 5700 4800 l gs col-1 s gr % Polyline n 3900 6600 m 1875 9300 l gs col-1 s gr % Polyline n 3888 5616 m 1863 8316 l gs col-1 s gr % Polyline n 3900 2625 m 1875 5325 l gs col-1 s gr % Polyline gs clippath 6178 6870 m 6298 6900 l 6178 6930 l 6340 6930 l 6340 6870 l cp clip n 1125 6900 m 6325 6900 l gs col-1 s gr gr % arrowhead n 6178 6870 m 6298 6900 l 6178 6930 l col-1 s /Times-Roman ff 300.00 scf sf 2925 1800 m gs 1 -1 sc (v) col-1 sh gr /Times-Roman ff 180.00 scf sf 3300 7200 m gs 1 -1 sc (0.75) col-1 sh gr /Times-Roman ff 180.00 scf sf 3800 7200 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 180.00 scf sf 4225 7200 m gs 1 -1 sc (1.5) col-1 sh gr /Times-Roman ff 180.00 scf sf 5000 7200 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 900.00 scf sf 4575 1800 m gs 1 -1 sc (G) col-1 sh gr /Times-Roman ff 900.00 scf sf 4725 3975 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 900.00 scf sf 4800 8175 m gs 1 -1 sc (M) col-1 sh gr /Times-Roman ff 900.00 scf sf 3075 9300 m gs 1 -1 sc (L) col-1 sh gr /Times-Roman ff 900.00 scf sf 2100 8400 m gs 1 -1 sc (K) col-1 sh gr /Times-Roman ff 900.00 scf sf 1950 3525 m gs 1 -1 sc (H) col-1 sh gr /Times-Roman ff 180.00 scf sf 5400 6825 m gs 1 -1 sc (\(-\)) col-1 sh gr /Times-Roman ff 300.00 scf sf 6075 7200 m gs 1 -1 sc (u) col-1 sh gr /Times-Roman ff 900.00 scf sf 2025 6450 m gs 1 -1 sc (J) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 655 2593 a Fn(Figure)27 b(3:)36 b(Riemann)28 b(problem)f(for)g(Suliciu's)h(mo)r(del:)37 b Fl(u)2475 2563 y Fi(\000)2554 2593 y Fj(\024)23 b Fn(1,)k(and)g Fl(u)2943 2563 y Fi(\000)3022 2593 y Fj(\025)c Fn(1)p Fl(:)p Fn(5.)515 4727 y @beginspecial 65 @llx 210 @lly 550 @urx 589 @ury 2267 @rwi 2267 @rhi @setspecial %%BeginDocument: sn3.ps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 571 273 5815 4542 rc 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6913 5186 rf 6 w 0 4225 5355 0 0 -4225 899 4614 4 MP PP -5355 0 0 4225 5355 0 0 -4225 899 4614 5 MP stroke 4 w DO SO 6 w 0 sg 899 4614 mt 6254 4614 L 899 389 mt 6254 389 L 6254 4614 mt 6254 389 L 899 4614 mt 899 389 L 899 4614 mt 6254 4614 L 899 4614 mt 899 389 L 899 4614 mt 899 4560 L 899 389 mt 899 443 L /Helvetica /ISOLatin1Encoding 120 FMSR 746 4760 mt (-2.5) s 1435 4614 mt 1435 4560 L 1435 389 mt 1435 443 L 1332 4760 mt (-2) s 1970 4614 mt 1970 4560 L 1970 389 mt 1970 443 L 1817 4760 mt (-1.5) s 2506 4614 mt 2506 4560 L 2506 389 mt 2506 443 L 2403 4760 mt (-1) s 3041 4614 mt 3041 4560 L 3041 389 mt 3041 443 L 2888 4760 mt (-0.5) s 3577 4614 mt 3577 4560 L 3577 389 mt 3577 443 L 3544 4760 mt (0) s 4112 4614 mt 4112 4560 L 4112 389 mt 4112 443 L 4029 4760 mt (0.5) s 4648 4614 mt 4648 4560 L 4648 389 mt 4648 443 L 4615 4760 mt (1) s 5183 4614 mt 5183 4560 L 5183 389 mt 5183 443 L 5100 4760 mt (1.5) s 5719 4614 mt 5719 4560 L 5719 389 mt 5719 443 L 5686 4760 mt (2) s 6254 4614 mt 6254 4560 L 6254 389 mt 6254 443 L 6171 4760 mt (2.5) s 899 4614 mt 953 4614 L 6254 4614 mt 6200 4614 L 628 4658 mt (-1.5) s 899 4145 mt 953 4145 L 6254 4145 mt 6200 4145 L 728 4189 mt (-1) s 899 3675 mt 953 3675 L 6254 3675 mt 6200 3675 L 628 3719 mt (-0.5) s 899 3206 mt 953 3206 L 6254 3206 mt 6200 3206 L 798 3250 mt (0) s 899 2736 mt 953 2736 L 6254 2736 mt 6200 2736 L 698 2780 mt (0.5) s 899 2267 mt 953 2267 L 6254 2267 mt 6200 2267 L 798 2311 mt (1) s 899 1797 mt 953 1797 L 6254 1797 mt 6200 1797 L 698 1841 mt (1.5) s 899 1328 mt 953 1328 L 6254 1328 mt 6200 1328 L 798 1372 mt (2) s 899 858 mt 953 858 L 6254 858 mt 6200 858 L 698 902 mt (2.5) s 899 389 mt 953 389 L 6254 389 mt 6200 389 L 798 433 mt (3) s 899 389 mt 6254 389 L 899 4614 mt 6254 4614 L 899 4614 mt 899 389 L 6254 4614 mt 6254 389 L gs 899 389 5356 4226 rc 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 -1 11 0 11 0 10 -1 11 -1 11 -1 11 -2 10 -2 11 -3 11 -4 10 -5 11 -7 11 -8 10 -11 11 -13 11 -16 11 -19 10 -22 11 -26 11 -31 10 -34 11 -39 11 -43 11 -47 10 -50 11 -54 11 -57 10 -59 11 -60 11 -61 11 -61 10 -59 11 -58 11 -56 10 -52 11 -49 11 -45 11 -41 10 -36 11 -33 11 -28 10 -24 11 -21 11 -17 11 -14 10 -12 11 -9 11 -8 10 -6 11 -4 11 -3 10 -3 11 -2 11 -1 11 -1 10 -1 11 0 11 -1 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 -747 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 3046 2458 300 MP stroke 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 -1 11 0 11 0 11 0 10 0 11 0 11 0 10 -1 11 -1 11 -1 10 -1 11 -2 11 -3 11 -5 10 -5 11 -8 11 -9 10 -12 11 -16 11 -19 11 -22 10 -27 11 -31 11 -36 10 -40 11 -44 11 -47 11 -50 10 -52 11 -52 11 -53 10 -51 11 -49 11 -46 11 -42 10 -38 11 -33 11 -29 10 -25 11 -20 11 -16 10 -13 11 -10 11 -8 11 -5 10 -4 11 -3 11 -2 10 -1 11 -1 11 -1 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 904 3393 201 MP stroke DA 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 -1 11 0 10 -1 11 -1 11 -1 11 -2 10 -3 11 -3 11 -4 10 -6 11 -7 11 -10 10 -11 11 -14 11 -17 11 -20 10 -24 11 -28 11 -32 10 -36 11 -40 11 -45 11 -48 10 -52 11 -55 11 -58 10 -59 11 -61 11 -61 11 -60 10 -59 11 -57 11 -54 10 -52 11 -47 11 -44 11 -39 10 -35 11 -31 11 -26 10 -23 11 -19 11 -17 11 -13 10 -10 11 -9 11 -7 10 -5 11 -4 11 -3 10 -2 11 -2 11 -1 11 -1 10 -1 11 0 11 0 10 -1 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 1 10 -1 11 1 11 -1 10 1 11 -1 11 1 10 -1 11 1 11 -1 11 1 10 -1 11 1 11 -1 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 1 10 -1 11 1 11 -1 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 3046 4528 300 MP stroke 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 1 11 0 11 0 10 1 11 1 11 1 10 2 11 3 11 4 11 6 10 7 11 10 11 13 10 17 11 21 11 25 11 32 10 37 11 43 11 49 10 55 11 61 11 66 11 70 10 73 11 74 11 75 10 72 11 70 11 66 11 61 10 55 11 48 11 42 10 36 11 29 11 24 10 19 11 15 11 11 11 9 10 6 11 4 11 3 10 2 11 1 11 1 11 1 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 904 3206 201 MP stroke gr DA SO 1 sg 0 298 704 0 0 -298 5490 747 4 MP PP -704 0 0 298 704 0 0 -298 5490 747 5 MP stroke 4 w DO SO 6 w 0 sg 5490 747 mt 6194 747 L 5490 449 mt 6194 449 L 6194 747 mt 6194 449 L 5490 747 mt 5490 449 L 5490 747 mt 6194 747 L 5490 747 mt 5490 449 L 5490 449 mt 6194 449 L 5490 747 mt 6194 747 L 5490 747 mt 5490 449 L 6194 747 mt 6194 449 L 5823 571 mt (u\(x,1\)) s 5823 709 mt (v\(x,1\)) s gs 5490 449 705 299 rc 199 0 5557 531 2 MP stroke DA 199 0 5557 669 2 MP stroke gr DA SO end eplot epage end showpage %%EndDocument @endspecial 827 4909 a(Figure)k(4:)36 b(Solution)28 b(to)f(Riemann)h(initial)g(data)f(in)h(Suliciu's)g(mo)r(del.)1905 5255 y(27)p eop %%Page: 28 28 28 27 bop 515 2410 a @beginspecial 0 @llx 0 @lly 570 @urx 376 @ury 2267 @rwi 2267 @rhi @setspecial %%BeginDocument: sn4.eps /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -112.0 417.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /reencdict 12 dict def /ReEncode { reencdict begin /newcodesandnames exch def /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName newfontname put newcodesandnames aload pop 128 1 255 { newfont /Encoding get exch /.notdef put } for newcodesandnames length 2 idiv { newfont /Encoding get 3 1 roll put } repeat newfontname newfont definefont pop end } def /isovec [ 8#200 /grave 8#201 /acute 8#202 /circumflex 8#203 /tilde 8#204 /macron 8#205 /breve 8#206 /dotaccent 8#207 /dieresis 8#210 /ring 8#211 /cedilla 8#212 /hungarumlaut 8#213 /ogonek 8#214 /caron 8#220 /dotlessi 8#230 /oe 8#231 /OE 8#240 /space 8#241 /exclamdown 8#242 /cent 8#243 /sterling 8#244 /currency 8#245 /yen 8#246 /brokenbar 8#247 /section 8#250 /dieresis 8#251 /copyright 8#252 /ordfeminine 8#253 /guillemotleft 8#254 /logicalnot 8#255 /endash 8#256 /registered 8#257 /macron 8#260 /degree 8#261 /plusminus 8#262 /twosuperior 8#263 /threesuperior 8#264 /acute 8#265 /mu 8#266 /paragraph 8#267 /periodcentered 8#270 /cedilla 8#271 /onesuperior 8#272 /ordmasculine 8#273 /guillemotright 8#274 /onequarter 8#275 /onehalf 8#276 /threequarters 8#277 /questiondown 8#300 /Agrave 8#301 /Aacute 8#302 /Acircumflex 8#303 /Atilde 8#304 /Adieresis 8#305 /Aring 8#306 /AE 8#307 /Ccedilla 8#310 /Egrave 8#311 /Eacute 8#312 /Ecircumflex 8#313 /Edieresis 8#314 /Igrave 8#315 /Iacute 8#316 /Icircumflex 8#317 /Idieresis 8#320 /Eth 8#321 /Ntilde 8#322 /Ograve 8#323 /Oacute 8#324 /Ocircumflex 8#325 /Otilde 8#326 /Odieresis 8#327 /multiply 8#330 /Oslash 8#331 /Ugrave 8#332 /Uacute 8#333 /Ucircumflex 8#334 /Udieresis 8#335 /Yacute 8#336 /Thorn 8#337 /germandbls 8#340 /agrave 8#341 /aacute 8#342 /acircumflex 8#343 /atilde 8#344 /adieresis 8#345 /aring 8#346 /ae 8#347 /ccedilla 8#350 /egrave 8#351 /eacute 8#352 /ecircumflex 8#353 /edieresis 8#354 /igrave 8#355 /iacute 8#356 /icircumflex 8#357 /idieresis 8#360 /eth 8#361 /ntilde 8#362 /ograve 8#363 /oacute 8#364 /ocircumflex 8#365 /otilde 8#366 /odieresis 8#367 /divide 8#370 /oslash 8#371 /ugrave 8#372 /uacute 8#373 /ucircumflex 8#374 /udieresis 8#375 /yacute 8#376 /thorn 8#377 /ydieresis] def /Times-Roman /Times-Roman-iso isovec ReEncode /Times-Roman /Times-Roman-iso isovec ReEncode /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin 10 setmiterlimit n -1000 7615 m -1000 -1000 l 11822 -1000 l 11822 7615 l cp clip 0.06299 0.06299 sc % Polyline 7.500 slw gs clippath 10680 6270 m 10800 6300 l 10680 6330 l 10815 6330 l 10815 6270 l cp clip n 1800 6300 m 10800 6300 l gs col0 s gr gr % arrowhead n 10680 6270 m 10800 6300 l 10680 6330 l 10680 6300 l 10680 6270 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 6270 795 m 6300 675 l 6330 795 l 6330 660 l 6270 660 l cp clip n 6300 6300 m 6300 675 l gs col0 s gr gr % arrowhead n 6270 795 m 6300 675 l 6330 795 l 6300 795 l 6270 795 l cp gs 0.00 setgray ef gr col0 s % Polyline 15.000 slw n 6300 6300 m 1800 3150 l gs col0 s gr % Polyline n 6300 6300 m 4725 1575 l gs col0 s gr % Polyline n 6300 6300 m 7875 1575 l gs col0 s gr % Polyline n 6300 6300 m 4725 1575 l gs col0 s gr % Polyline n 6300 6300 m 7875 1575 l gs col0 s gr % Polyline n 6300 6300 m 7875 1575 l gs col0 s gr % Polyline n 6300 6300 m 10800 3150 l gs col0 s gr % Polyline n 2205 3150 m 2250 3195 l 2295 2880 l 2565 2880 l gs col0 s gr % Polyline n 10350 3195 m 10440 3240 l 10440 2925 l 10620 2925 l gs col0 s gr /Times-Roman-iso ff 330.00 scf sf 2025 3150 m gs 1 -1 sc (-) col0 sh gr /Times-Roman-iso ff 330.00 scf sf 4725 1575 m gs 1 -1 sc (T-) col0 sh gr /Times-Roman-iso ff 330.00 scf sf 7875 1575 m gs 1 -1 sc (T+) col0 sh gr /Times-Roman-iso ff 330.00 scf sf 2340 3195 m gs 1 -1 sc (2) col0 sh gr /Times-Roman-iso ff 330.00 scf sf 10215 3240 m gs 1 -1 sc (+ 2) col0 sh gr /Times-Roman-iso ff 330.00 scf sf 10485 6615 m gs 1 -1 sc (x) col0 sh gr /Times-Roman-iso ff 330.00 scf sf 6435 945 m gs 1 -1 sc (t) col0 sh gr /Times-Roman-iso ff 300.00 scf sf 4140 3825 m gs 1 -1 sc (\(u ,v \)) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 5865 2310 m gs 1 -1 sc (*) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 6150 2310 m gs 1 -1 sc (*) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 4380 3900 m gs 1 -1 sc (1) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 4635 3915 m gs 1 -1 sc (1) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 8475 3285 m gs 1 -1 sc (2) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 8745 3270 m gs 1 -1 sc (2) col0 sh gr /Times-Roman-iso ff 300.00 scf sf 5595 2415 m gs 1 -1 sc (\(u ,v \)) col0 sh gr /Times-Roman-iso ff 300.00 scf sf 8265 3210 m gs 1 -1 sc (\(u ,v \)) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 2430 5310 m gs 1 -1 sc (-) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 2700 5310 m gs 1 -1 sc (-) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 9900 4995 m gs 1 -1 sc (+) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 10170 4995 m gs 1 -1 sc (+) col0 sh gr /Times-Roman-iso ff 300.00 scf sf 2205 5445 m gs 1 -1 sc (\(u ,v \)) col0 sh gr /Times-Roman-iso ff 300.00 scf sf 9675 5130 m gs 1 -1 sc (\(u ,v \)) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 1148 2592 a Fn(Figure)27 b(5:)36 b(W)-7 b(a)n(v)n(e)27 b(pro\014le)g(A)h(in)g(Suliciu's)g(mo)r(del.)515 4724 y @beginspecial 62 @llx 201 @lly 546 @urx 601 @ury 2267 @rwi 2267 @rhi @setspecial %%BeginDocument: j0.eps % MathWorks dictionary /MathWorks 150 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 531 132 5805 4798 MR c np 88 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6912 5185 PR 6 w 0 4225 2260 0 0 -4225 3994 4613 4 MP PP -2260 0 0 4225 2260 0 0 -4225 3994 4613 5 MP stroke DO 4 w SO 6 w 0 sg 3994 4613 mt 6254 4613 L 3994 388 mt 6254 388 L 3994 4613 mt 3994 388 L 6254 4613 mt 6254 388 L 3994 4613 mt 6254 4613 L 3994 4613 mt 3994 388 L 3994 4613 mt 3994 4571 L 3994 388 mt 3994 430 L /Helvetica /ISOLatin1Encoding 120 FMSR 3891 4759 mt (-2) s 4559 4613 mt 4559 4571 L 4559 388 mt 4559 430 L 4456 4759 mt (-1) s 5124 4613 mt 5124 4571 L 5124 388 mt 5124 430 L 5091 4759 mt (0) s 5689 4613 mt 5689 4571 L 5689 388 mt 5689 430 L 5656 4759 mt (1) s 6254 4613 mt 6254 4571 L 6254 388 mt 6254 430 L 6221 4759 mt (2) s 3994 4613 mt 4036 4613 L 6254 4613 mt 6212 4613 L 3723 4657 mt (-1.4) s 3994 4085 mt 4036 4085 L 6254 4085 mt 6212 4085 L 3723 4129 mt (-1.2) s 3994 3557 mt 4036 3557 L 6254 3557 mt 6212 3557 L 3823 3601 mt (-1) s 3994 3029 mt 4036 3029 L 6254 3029 mt 6212 3029 L 3723 3073 mt (-0.8) s 3994 2501 mt 4036 2501 L 6254 2501 mt 6212 2501 L 3723 2545 mt (-0.6) s 3994 1972 mt 4036 1972 L 6254 1972 mt 6212 1972 L 3723 2016 mt (-0.4) s 3994 1444 mt 4036 1444 L 6254 1444 mt 6212 1444 L 3723 1488 mt (-0.2) s 3994 916 mt 4036 916 L 6254 916 mt 6212 916 L 3893 960 mt (0) s 3994 388 mt 4036 388 L 6254 388 mt 6212 388 L 3793 432 mt (0.2) s 3994 4613 mt 6254 4613 L 3994 388 mt 6254 388 L 3994 4613 mt 3994 388 L 6254 4613 mt 6254 388 L gs 3994 388 2261 4226 MR c np DA 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 5125 3557 100 MP stroke 11 2641 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 4007 916 100 MP stroke 12 0 3995 916 2 MP stroke SO 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 -1 12 -1 11 -3 11 -5 11 -10 12 -16 11 -25 11 -35 12 -45 11 -55 11 -61 12 -62 11 -60 11 -52 11 -43 12 -31 11 -22 11 -14 12 -7 11 -4 11 -1 12 0 11 0 11 1 11 0 12 0 11 1 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 1 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 5125 4107 100 MP stroke 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 -1 11 0 11 1 12 0 11 0 11 -1 12 0 11 1 11 0 12 0 11 1 11 7 11 50 12 329 11 2131 11 842 12 -2 11 -1 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 -1 11 0 12 0 11 0 11 0 11 0 12 -1 11 -2 11 -4 12 -6 11 -11 11 -15 12 -20 11 -23 11 -23 11 -21 12 -16 11 -11 11 -7 12 -3 11 -1 11 -1 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 4007 916 100 MP stroke 12 0 3995 916 2 MP stroke gr 5094 4901 mt (x) s 5052 292 mt (\(b\)) s 1 sg 0 425 781 0 0 -425 5335 917 4 MP PP -781 0 0 425 781 0 0 -425 5335 917 5 MP stroke DO 4 w SO 6 w 0 sg 5335 917 mt 6116 917 L 5335 492 mt 6116 492 L 5335 917 mt 5335 492 L 6116 917 mt 6116 492 L 5335 917 mt 6116 917 L 5335 917 mt 5335 492 L 5335 917 mt 6116 917 L 5335 492 mt 6116 492 L 5335 917 mt 5335 492 L 6116 917 mt 6116 492 L 5674 678 mt (v\(0,x\)) s gs 5335 492 782 426 MR c np DA 181 0 5380 634 2 MP stroke gr DA 5674 819 mt (v\(1,x\)) s gs 5335 492 782 426 MR c np SO 181 0 5380 775 2 MP stroke gr SO 1 sg 0 4225 2259 0 0 -4225 898 4613 4 MP PP -2259 0 0 4225 2259 0 0 -4225 898 4613 5 MP stroke DO 4 w SO 6 w 0 sg 898 4613 mt 3157 4613 L 898 388 mt 3157 388 L 898 4613 mt 898 388 L 3157 4613 mt 3157 388 L 898 4613 mt 3157 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4571 L 898 388 mt 898 430 L 795 4759 mt (-2) s 1463 4613 mt 1463 4571 L 1463 388 mt 1463 430 L 1360 4759 mt (-1) s 2028 4613 mt 2028 4571 L 2028 388 mt 2028 430 L 1995 4759 mt (0) s 2592 4613 mt 2592 4571 L 2592 388 mt 2592 430 L 2559 4759 mt (1) s 3157 4613 mt 3157 4571 L 3157 388 mt 3157 430 L 3124 4759 mt (2) s 898 4613 mt 940 4613 L 3157 4613 mt 3115 4613 L 697 4657 mt (0.5) s 898 3768 mt 940 3768 L 3157 3768 mt 3115 3768 L 797 3812 mt (1) s 898 2923 mt 940 2923 L 3157 2923 mt 3115 2923 L 697 2967 mt (1.5) s 898 2078 mt 940 2078 L 3157 2078 mt 3115 2078 L 797 2122 mt (2) s 898 1233 mt 940 1233 L 3157 1233 mt 3115 1233 L 697 1277 mt (2.5) s 898 388 mt 940 388 L 3157 388 mt 3115 388 L 797 432 mt (3) s 898 4613 mt 3157 4613 L 898 388 mt 3157 388 L 898 4613 mt 898 388 L 3157 4613 mt 3157 388 L gs 898 388 2260 4226 MR c np DA 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 2029 388 100 MP stroke 11 -3380 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 911 3768 100 MP stroke 12 0 899 3768 2 MP stroke SO 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 -1 11 0 12 -2 11 -4 11 -6 12 -10 11 -16 11 -23 11 -29 12 -35 11 -39 11 -40 12 -38 11 -33 11 -27 12 -20 11 -14 11 -9 11 -5 12 -2 11 -1 11 0 12 0 11 0 11 1 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 1 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 2029 740 100 MP stroke 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 -1 12 1 11 0 11 0 11 0 12 -1 11 0 11 1 12 0 11 0 11 -1 12 -6 11 -32 11 -202 11 -1333 12 -1530 11 1 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 1 11 1 12 1 11 3 11 5 11 7 12 9 11 10 11 11 12 9 11 8 11 5 12 3 11 1 11 1 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 911 3768 100 MP stroke 12 0 899 3768 2 MP stroke gr 1998 4900 mt (x) s 1956 291 mt (\(a\)) s 1 sg 0 425 780 0 0 -425 2239 4509 4 MP PP -780 0 0 425 780 0 0 -425 2239 4509 5 MP stroke DO 4 w SO 6 w 0 sg 2239 4509 mt 3019 4509 L 2239 4084 mt 3019 4084 L 2239 4509 mt 2239 4084 L 3019 4509 mt 3019 4084 L 2239 4509 mt 3019 4509 L 2239 4509 mt 2239 4084 L 2239 4509 mt 3019 4509 L 2239 4084 mt 3019 4084 L 2239 4509 mt 2239 4084 L 3019 4509 mt 3019 4084 L 2577 4270 mt (u\(0,x\)) s gs 2239 4084 781 426 MR c np DA 181 0 2284 4226 2 MP stroke gr DA 2577 4411 mt (u\(1,x\)) s gs 2239 4084 781 426 MR c np SO 181 0 2284 4367 2 MP stroke gr SO end eplot epage end showpage %%EndDocument @endspecial 1353 4907 a(Figure)f(6:)37 b(Instabilit)n(y)27 b(of)h Fl(T)2260 4919 y Ff(+)2314 4907 y Fn(-w)n(a)n(v)n(e.)1905 5255 y(28)p eop %%Page: 29 29 29 28 bop 148 1938 a @beginspecial 62 @llx 201 @lly 546 @urx 600 @ury 1417 @rwi 1700 @rhi @setspecial %%BeginDocument: j1a.eps % MathWorks dictionary /MathWorks 150 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 531 133 5805 4797 MR c np 88 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6912 5185 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke DO 4 w SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 120 FMSR 795 4759 mt (-1) s 1434 4613 mt 1434 4559 L 1434 388 mt 1434 442 L 1281 4759 mt (-0.8) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1816 4759 mt (-0.6) s 2505 4613 mt 2505 4559 L 2505 388 mt 2505 442 L 2352 4759 mt (-0.4) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2887 4759 mt (-0.2) s 3576 4613 mt 3576 4559 L 3576 388 mt 3576 442 L 3543 4759 mt (0) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 4029 4759 mt (0.2) s 4647 4613 mt 4647 4559 L 4647 388 mt 4647 442 L 4564 4759 mt (0.4) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5100 4759 mt (0.6) s 5718 4613 mt 5718 4559 L 5718 388 mt 5718 442 L 5635 4759 mt (0.8) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6221 4759 mt (1) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 797 4657 mt (0) s 898 4191 mt 952 4191 L 6254 4191 mt 6200 4191 L 697 4235 mt (0.1) s 898 3768 mt 952 3768 L 6254 3768 mt 6200 3768 L 697 3812 mt (0.2) s 898 3346 mt 952 3346 L 6254 3346 mt 6200 3346 L 697 3390 mt (0.3) s 898 2923 mt 952 2923 L 6254 2923 mt 6200 2923 L 697 2967 mt (0.4) s 898 2501 mt 952 2501 L 6254 2501 mt 6200 2501 L 697 2545 mt (0.5) s 898 2078 mt 952 2078 L 6254 2078 mt 6200 2078 L 697 2122 mt (0.6) s 898 1655 mt 952 1655 L 6254 1655 mt 6200 1655 L 697 1699 mt (0.7) s 898 1233 mt 952 1233 L 6254 1233 mt 6200 1233 L 697 1277 mt (0.8) s 898 811 mt 952 811 L 6254 811 mt 6200 811 L 697 855 mt (0.9) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 797 432 mt (1) s 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np 3 1 2 1 3 1 3 1 2 0 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 0 3 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 0 2 1 3 1 3 1 2 1 3 1 3 1 2 0 3 1 3 1 2 1 3 1 3 1 2 1 3 0 3 1 2 1 3 1 3 1 2 1 3 0 3 1 3 1 2 1 3 1 3 1 2 0 3 1 3 1 2 1 3 1 3 1 2 0 3 1 3 1 2 1 3 1 3 1 2 0 3 1 3 1 2 1 3 1 3 0 2 1 3 1 3 1 2 1 3 0 3 1 2 1 3 1 3 1 3 0 2 1 3 1 3 1 2 1 3 0 3 1 2 1 3 1 3 0 2 1 3 1 3 1 2 1 3 0 3 1 2 1 3 1 3 0 2 1 3 1 3 1 2 1 3 0 3311 872 100 MP stroke 3 1 2 1 3 1 3 0 3 1 2 1 3 1 3 0 2 1 3 1 3 1 2 0 3 1 3 1 2 1 3 0 3 1 2 1 3 1 3 0 2 1 3 1 3 0 2 1 3 1 3 1 2 0 3 1 3 1 2 1 3 0 3 1 2 1 3 0 3 1 3 1 2 1 3 0 3 1 2 1 3 0 3 1 2 1 3 1 3 0 2 1 3 1 3 0 2 1 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 3 0 2 1 3 0 3 1 2 1 3046 802 100 MP stroke 3 0 3 1 2 1 3 0 3 1 2 1 3 0 3 1 2 1 3 0 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 0 2 1 3 1 3 0 3 1 2 1 3 0 3 1 2 0 3 1 3 1 2 0 3 1 3 0 2 1 3 1 3 0 2 1 3 1 3 0 2 1 3 0 3 1 2 1 3 0 3 1 2 0 3 1 3 1 2 0 3 1 3 0 2 1 3 1 3 0 3 1 2 0 3 1 3 0 2 1 3 1 3 0 2 1 3 0 3 1 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 1 2 0 3 1 3 0 3 1 2 0 3 1 3 0 2 1 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 1 2 0 3 1 3 0 2 1 2781 743 100 MP stroke 3 0 3 1 2 0 3 1 3 0 2 1 3 1 3 0 2 1 3 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 3 0 2 1 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 0 3 1 3 0 2 1 2516 693 100 MP stroke 3 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 3 0 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 0 3 1 2 0 3 1 3 0 3 1 2 0 3 0 3 1 2 0 3 1 3 0 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 0 3 1 2 0 3 1 3 0 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 0 3 1 3 0 2 1 3 0 3 0 2 1 3 0 3 1 2 0 3 0 3 1 2250 650 100 MP stroke 2 0 3 1 3 0 2 0 3 1 3 0 2 1 3 0 3 0 2 1 3 0 3 1 2 0 3 0 3 1 2 0 3 0 3 1 2 0 3 1 3 0 3 0 2 1 3 0 3 1 2 0 3 0 3 1 2 0 3 0 3 1 2 0 3 1 3 0 2 0 3 1 3 0 2 1 3 0 3 0 2 1 3 0 3 0 2 1 3 0 3 1 2 0 3 0 3 1 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 1 3 0 3 0 2 1 3 0 3 0 2 1 3 0 3 1 2 0 3 0 3 1 2 0 3 0 3 1 2 0 3 0 3 1 2 0 3 0 3 1 2 0 3 1 3 0 3 0 2 1 3 0 3 0 2 1 3 0 3 0 2 1 3 0 3 0 2 1 3 0 3 0 2 1 3 0 3 0 2 1 3 0 3 0 1985 614 100 MP stroke 2 1 3 0 3 1 2 0 3 0 3 1 2 0 3 0 3 1 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 0 3 1 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 0 3 1 2 0 3 0 3 1 2 0 3 0 3 1 3 0 2 0 3 1 3 0 2 0 3 0 3 1 2 0 3 0 3 1 2 0 3 0 3 1 2 0 3 0 3 1 2 0 3 0 3 0 2 1 3 0 3 0 2 1 3 0 3 0 2 1 3 0 3 0 2 0 3 1 3 0 1720 582 100 MP stroke 3 0 2 1 3 0 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 0 3 1 2 0 3 0 3 1 2 0 3 0 3 1 2 0 3 0 3 0 2 1 3 0 3 0 2 1 3 0 3 0 3 0 2 1 3 0 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 0 3 1 2 0 3 0 3 1 2 0 3 0 3 0 2 1 3 0 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 0 3 0 3 1 3 0 2 0 3 0 3 1 2 0 3 0 3 0 2 1 3 0 3 0 2 1 3 0 3 0 2 0 3 1 3 0 2 0 3 0 3 1 2 0 3 0 3 0 2 1 3 0 3 0 2 0 3 1 3 0 3 0 2 1 3 0 3 0 2 0 3 1 3 0 2 0 3 0 3 1 2 0 3 0 1455 555 100 MP stroke 3 0 2 1 3 0 3 0 2 0 3 1 3 0 2 0 3 0 3 1 2 0 3 0 3 0 2 1 3 0 3 0 3 0 2 1 3 0 3 0 2 0 3 1 3 0 2 0 3 0 3 1 2 0 3 0 3 0 2 1 3 0 3 0 2 0 3 0 3 1 2 0 3 0 3 0 2 1 3 0 3 0 2 0 3 1 3 0 2 0 3 0 3 1 3 0 2 0 3 0 3 1 2 0 3 0 3 0 2 0 3 1 3 0 2 0 3 0 3 1 2 0 3 0 3 0 2 1 3 0 3 0 2 0 3 0 3 1 2 0 3 0 3 0 2 1 3 0 3 0 3 0 2 0 3 1 3 0 2 0 3 0 3 1 2 0 3 0 3 0 2 1 3 0 3 0 2 0 3 0 3 1 2 0 3 0 3 0 2 0 3 1 3 0 2 0 3 0 1190 532 100 MP stroke 3 1 2 0 3 0 3 0 2 0 3 1 3 0 3 0 2 0 3 1 3 0 2 0 3 0 3 0 2 1 3 0 3 0 2 0 3 0 3 1 2 0 3 0 3 0 2 1 3 0 3 0 2 0 3 0 3 1 2 0 3 0 3 0 2 0 3 1 3 0 3 0 2 0 3 0 3 1 2 0 3 0 3 0 2 0 3 1 3 0 2 0 3 0 3 0 2 1 3 0 3 0 2 0 3 0 3 1 2 0 3 0 3 0 2 0 3 1 3 0 2 0 3 0 3 0 2 1 3 0 3 0 3 0 2 0 3 1 3 0 2 0 3 0 3 0 2 1 3 0 3 0 2 0 3 0 3 1 2 0 3 0 3 0 2 0 3 1 3 0 2 0 3 0 3 0 2 1 3 0 3 0 2 0 3 0 3 0 3 1 2 0 3 0 3 0 2 0 925 512 100 MP stroke 3 1 3 0 2 0 3 0 3 0 2 1 3 0 3 0 2 0 3 0 898 510 11 MP stroke DA -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -2 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -2 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 3841 1052 100 MP stroke -3 -1 -2 -1 -3 -1 -3 -2 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -2 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -2 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -1 -2 -1 -3 -2 -3 -1 -2 -1 -3 -1 -3 -1 -2 -2 -3 -1 -3 -1 -2 -1 -3 -1 -3 -2 -3 -1 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -1 -2 -1 -3 -2 -3 -1 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -1 -2 -2 -3 -1 -3 -1 -2 -1 -3 -2 -3 -1 -2 -1 -3 -2 -3 -1 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -2 -3 -1 -2 -1 -3 -1 -3 -2 -2 -1 4106 1170 100 MP stroke -3 -1 -3 -2 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -2 -3 -1 -2 -2 -3 -1 -3 -1 -2 -2 -3 -1 -3 -1 -2 -2 -3 -1 -3 -2 -2 -1 -3 -1 -3 -2 -2 -1 -3 -2 -3 -1 -2 -1 -3 -2 -3 -1 -2 -2 -3 -1 -3 -2 -2 -1 -3 -1 -3 -2 -2 -1 -3 -2 -3 -1 -3 -2 -2 -1 -3 -1 -3 -2 -2 -1 -3 -2 -3 -1 -2 -2 -3 -1 -3 -2 -2 -1 -3 -2 -3 -1 -2 -2 -3 -1 -3 -2 -2 -1 -3 -2 -3 -1 -2 -2 -3 -1 -3 -2 -2 -1 -3 -2 -3 -1 -2 -2 -3 -1 -3 -2 -2 -1 -3 -2 -3 -1 -3 -2 -2 -1 -3 -2 -3 -2 -2 -1 -3 -2 -3 -1 -2 -2 -3 -1 -3 -2 -2 -1 -3 -2 -3 -2 -2 -1 -3 -2 -3 -1 -2 -2 4371 1313 100 MP stroke -3 -2 -3 -1 -2 -2 -3 -1 -3 -2 -2 -2 -3 -1 -3 -2 -2 -1 -3 -2 -3 -2 -3 -1 -2 -2 -3 -2 -3 -1 -2 -2 -3 -1 -3 -2 -2 -2 -3 -1 -3 -2 -2 -2 -3 -1 -3 -2 -2 -2 -3 -1 -3 -2 -2 -2 -3 -2 -3 -1 -2 -2 -3 -2 -3 -1 -2 -2 -3 -2 -3 -1 -2 -2 -3 -2 -3 -2 -2 -1 -3 -2 -3 -2 -3 -2 -2 -1 -3 -2 -3 -2 -2 -2 -3 -1 -3 -2 -2 -2 -3 -2 -3 -1 -2 -2 -3 -2 -3 -2 -2 -2 -3 -1 -3 -2 -2 -2 -3 -2 -3 -2 -2 -1 -3 -2 -3 -2 -2 -2 -3 -2 -3 -1 -2 -2 -3 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -1 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -1 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -1 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 4636 1488 100 MP stroke -3 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -3 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -3 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -3 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -3 -3 -2 -3 -2 -2 -2 -3 -2 -3 -3 -2 -2 -3 -2 -3 -2 -2 -2 -3 -3 -3 -2 -2 -2 -3 -2 -3 -3 -3 -2 -2 -2 -3 -2 -3 -3 -2 -2 -3 -2 -3 -3 -2 -2 -3 -2 -3 -2 -2 -3 -3 -2 -3 -2 -2 -3 -3 -2 -3 -2 -2 -3 -3 -2 -3 -2 -2 -3 -3 -2 -3 -3 -2 -2 -3 -2 -3 -3 -2 -2 -3 -2 -3 -3 -3 -2 -2 -3 -3 -2 -3 -3 -2 -2 -3 -2 -3 -3 -2 -2 -3 -3 -3 -2 4902 1706 100 MP stroke -2 -3 -3 -2 -3 -3 -2 -2 -3 -3 -3 -2 -2 -3 -3 -2 -3 -3 -2 -2 -3 -3 -3 -2 -2 -3 -3 -2 -3 -3 -2 -2 -3 -3 -3 -3 -2 -2 -3 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -2 -2 -3 -3 -3 -3 -2 -2 -3 -3 -3 -3 -2 -2 -3 -3 -3 -3 -2 -2 -3 -3 -3 -3 -2 -2 -3 -3 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -3 -3 -3 -3 -2 -2 -3 -3 -3 -3 -3 -2 -2 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -4 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -4 5167 1983 100 MP stroke -2 -3 -3 -3 -3 -3 -2 -3 -3 -4 -3 -3 -2 -3 -3 -3 -3 -3 -3 -4 -2 -3 -3 -3 -3 -3 -2 -4 -3 -3 -3 -3 -2 -4 -3 -3 -3 -3 -2 -3 -3 -4 -3 -3 -2 -3 -3 -4 -3 -3 -2 -4 -3 -3 -3 -3 -2 -4 -3 -3 -3 -4 -2 -3 -3 -4 -3 -3 -2 -3 -3 -4 -3 -3 -2 -4 -3 -3 -3 -4 -3 -3 -2 -4 -3 -3 -3 -4 -2 -4 -3 -3 -3 -4 -2 -3 -3 -4 -3 -3 -2 -4 -3 -4 -3 -3 -2 -4 -3 -4 -3 -3 -2 -4 -3 -4 -3 -3 -2 -4 -3 -4 -3 -4 -2 -3 -3 -4 -3 -4 -2 -4 -3 -3 -3 -4 -3 -4 -2 -4 -3 -4 -3 -3 -2 -4 -3 -4 -3 -4 -2 -4 -3 -4 -3 -4 -2 -4 -3 -4 -3 -3 -2 -4 -3 -4 -3 -4 -2 -4 -3 -4 -3 -4 -2 -4 -3 -4 -3 -4 -2 -4 -3 -5 -3 -4 -2 -4 -3 -4 -3 -4 -2 -4 -3 -4 -3 -4 5432 2341 100 MP stroke -3 -4 -2 -5 -3 -4 -3 -4 -2 -4 -3 -4 -3 -5 -2 -4 -3 -4 -3 -4 -2 -5 -3 -4 -3 -4 -2 -5 -3 -4 -3 -4 -2 -5 -3 -4 -3 -4 -2 -5 -3 -4 -3 -5 -2 -4 -3 -5 -3 -4 -2 -4 -3 -5 -3 -4 -3 -5 -2 -5 -3 -4 -3 -5 -2 -4 -3 -5 -3 -4 -2 -5 -3 -5 -3 -4 -2 -5 -3 -5 -3 -4 -2 -5 -3 -5 -3 -5 -2 -4 -3 -5 -3 -5 -2 -5 -3 -4 -3 -5 -2 -5 -3 -5 -3 -5 -2 -5 -3 -5 -3 -4 -3 -5 -2 -5 -3 -5 -3 -5 -2 -5 -3 -5 -3 -5 -2 -5 -3 -5 -3 -5 -2 -6 -3 -5 -3 -5 -2 -5 -3 -5 -3 -5 -2 -5 -3 -6 -3 -5 -2 -5 -3 -5 -3 -6 -2 -5 -3 -5 -3 -6 -2 -5 -3 -5 -3 -6 -2 -5 -3 -5 -3 -6 -3 -5 -2 -6 -3 -5 -3 -6 -2 -5 -3 -6 -3 -5 -2 -6 -3 -6 -3 -5 -2 -6 -3 -5 5697 2821 100 MP stroke -3 -6 -2 -6 -3 -5 -3 -6 -2 -6 -3 -6 -3 -5 -2 -6 -3 -6 -3 -6 -2 -6 -3 -6 -3 -6 -2 -6 -3 -5 -3 -6 -3 -6 -2 -6 -3 -6 -3 -6 -2 -7 -3 -6 -3 -6 -2 -6 -3 -6 -3 -6 -2 -6 -3 -7 -3 -6 -2 -6 -3 -6 -3 -7 -2 -6 -3 -6 -3 -7 -2 -6 -3 -7 -3 -6 -2 -6 -3 -7 -3 -6 -2 -7 -3 -7 -3 -6 -2 -7 -3 -6 -3 -7 -3 -7 -2 -6 -3 -7 -3 -7 -2 -7 -3 -6 -3 -7 -2 -7 -3 -7 -3 -7 -2 -7 -3 -7 -3 -7 -2 -7 -3 -7 -3 -7 -2 -7 -3 -7 -3 -7 -2 -7 -3 -7 -3 -7 -2 -8 -3 -7 -3 -7 -2 -8 -3 -7 -3 -7 -3 -8 -2 -7 -3 -8 -3 -7 -2 -8 -3 -7 -3 -8 -2 -7 -3 -8 -3 -8 -2 -7 -3 -8 -3 -8 -2 -7 -3 -8 -3 -8 -2 -8 -3 -8 -3 -8 -2 -8 -3 -8 -3 -8 -2 -8 -3 -8 5962 3492 100 MP stroke -3 -8 -2 -8 -3 -8 -3 -8 -2 -9 -3 -8 -3 -8 -3 -9 -2 -8 -3 -8 -3 -9 -2 -8 -3 -9 -3 -8 -2 -9 -3 -9 -3 -8 -2 -9 -3 -9 -3 -8 -2 -9 -3 -9 -3 -9 -2 -9 -3 -9 -3 -9 -2 -9 -3 -9 -3 -9 -2 -9 -3 -9 -3 -9 -2 -10 -3 -9 -3 -9 -3 -9 -2 -10 -3 -9 -3 -10 -2 -9 -3 -10 -3 -9 -2 -10 -3 -10 -3 -9 -2 -10 -3 -10 -3 -10 -2 -10 -3 -10 -3 -10 -2 -10 -3 -10 -3 -10 -2 -10 -3 -10 -3 -10 -2 -11 -3 -10 -3 -10 -2 -11 -3 -10 -3 -11 -2 -10 -3 -11 -3 -10 -3 -11 -2 -11 -3 -11 -3 -11 -2 -10 -3 -11 -3 -11 -2 -11 -3 -11 -3 -12 -2 -11 -3 -11 -3 -11 -2 -12 -3 -11 -3 -12 -2 -11 -3 -12 -3 -11 -2 -12 -3 -12 -3 -11 -2 -12 -3 -12 -3 -12 -2 -12 -3 -12 -3 -12 -3 -12 -2 -13 -3 -12 -3 -12 -2 -13 6227 4486 100 MP stroke -3 -12 -3 -13 -2 -12 -3 -13 -3 -13 -2 -12 -3 -13 -3 -13 -2 -13 -3 -13 6254 4613 11 MP stroke 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 0 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 3 -1 2 -1 3 -1 3 0 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 3 0 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -2 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -2 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3311 1052 100 MP stroke 3 -1 2 -1 3 -1 3 -2 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -2 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -2 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -2 3 -1 3 -1 2 -1 3 -1 3 -1 3 -2 2 -1 3 -1 3 -1 2 -1 3 -1 3 -2 2 -1 3 -1 3 -1 2 -1 3 -1 3 -2 2 -1 3 -1 3 -1 2 -1 3 -2 3 -1 2 -1 3 -1 3 -1 2 -2 3 -1 3 -1 2 -1 3 -1 3 -2 3 -1 2 -1 3 -1 3 -2 2 -1 3 -1 3 -1 2 -1 3 -2 3 -1 2 -1 3 -1 3 -2 2 -1 3 -1 3 -1 2 -2 3 -1 3 -1 2 -1 3 -2 3 -1 2 -1 3 -2 3 -1 2 -1 3 -1 3 -2 2 -1 3 -1 3 -2 3 -1 2 -1 3 -1 3 -2 2 -1 3046 1170 100 MP stroke 3 -1 3 -2 2 -1 3 -1 3 -2 2 -1 3 -1 3 -2 2 -1 3 -1 3 -2 2 -1 3 -1 3 -2 2 -1 3 -1 3 -2 2 -1 3 -1 3 -2 2 -1 3 -1 3 -2 3 -1 2 -2 3 -1 3 -1 2 -2 3 -1 3 -1 2 -2 3 -1 3 -2 2 -1 3 -1 3 -2 2 -1 3 -2 3 -1 2 -1 3 -2 3 -1 2 -2 3 -1 3 -2 2 -1 3 -1 3 -2 2 -1 3 -2 3 -1 2 -2 3 -1 3 -1 3 -2 2 -1 3 -2 3 -1 2 -2 3 -1 3 -2 2 -1 3 -2 3 -1 2 -2 3 -1 3 -2 2 -1 3 -2 3 -1 2 -2 3 -1 3 -2 2 -1 3 -2 3 -1 2 -2 3 -1 3 -2 2 -1 3 -2 3 -1 3 -2 2 -1 3 -2 3 -2 2 -1 3 -2 3 -1 2 -2 3 -1 3 -2 2 -1 3 -2 3 -2 2 -1 3 -2 3 -1 2 -2 2781 1313 100 MP stroke 3 -2 3 -1 2 -2 3 -1 3 -2 2 -2 3 -1 3 -2 2 -1 3 -2 3 -2 3 -1 2 -2 3 -2 3 -1 2 -2 3 -1 3 -2 2 -2 3 -1 3 -2 2 -2 3 -1 3 -2 2 -2 3 -1 3 -2 2 -2 3 -2 3 -1 2 -2 3 -2 3 -1 2 -2 3 -2 3 -1 2 -2 3 -2 3 -2 2 -1 3 -2 3 -2 3 -2 2 -1 3 -2 3 -2 2 -2 3 -1 3 -2 2 -2 3 -2 3 -1 2 -2 3 -2 3 -2 2 -2 3 -1 3 -2 2 -2 3 -2 3 -2 2 -1 3 -2 3 -2 2 -2 3 -2 3 -1 2 -2 3 -2 3 -2 3 -2 2 -2 3 -2 3 -1 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -1 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -1 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 2516 1488 100 MP stroke 3 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -3 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 3 -2 2 -2 3 -2 3 -3 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -3 3 -2 3 -2 2 -2 3 -2 3 -2 2 -3 3 -2 3 -2 2 -2 3 -2 3 -3 2 -2 3 -2 3 -2 2 -2 3 -3 3 -2 2 -2 3 -2 3 -3 3 -2 2 -2 3 -2 3 -3 2 -2 3 -2 3 -3 2 -2 3 -2 3 -2 2 -3 3 -2 3 -2 2 -3 3 -2 3 -2 2 -3 3 -2 3 -2 2 -3 3 -2 3 -3 2 -2 3 -2 3 -3 2 -2 3 -2 3 -3 3 -2 2 -3 3 -2 3 -3 2 -2 3 -2 3 -3 2 -2 3 -3 3 -2 2250 1706 100 MP stroke 2 -3 3 -2 3 -3 2 -2 3 -3 3 -2 2 -3 3 -2 3 -3 2 -2 3 -3 3 -2 2 -3 3 -2 3 -3 2 -2 3 -3 3 -3 2 -2 3 -3 3 -2 3 -3 2 -3 3 -2 3 -3 2 -2 3 -3 3 -3 2 -2 3 -3 3 -3 2 -2 3 -3 3 -3 2 -2 3 -3 3 -3 2 -2 3 -3 3 -3 2 -3 3 -2 3 -3 2 -3 3 -2 3 -3 2 -3 3 -3 3 -3 3 -2 2 -3 3 -3 3 -3 2 -2 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 3 -2 3 -3 2 -3 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 3 -2 3 -3 2 -3 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 3 -3 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 3 -3 3 -4 2 -3 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 3 -3 3 -4 1985 1983 100 MP stroke 2 -3 3 -3 3 -3 2 -3 3 -4 3 -3 2 -3 3 -3 3 -3 3 -4 2 -3 3 -3 3 -3 2 -4 3 -3 3 -3 2 -4 3 -3 3 -3 2 -3 3 -4 3 -3 2 -3 3 -4 3 -3 2 -4 3 -3 3 -3 2 -4 3 -3 3 -4 2 -3 3 -4 3 -3 2 -3 3 -4 3 -3 2 -4 3 -3 3 -4 3 -3 2 -4 3 -3 3 -4 2 -4 3 -3 3 -4 2 -3 3 -4 3 -3 2 -4 3 -4 3 -3 2 -4 3 -4 3 -3 2 -4 3 -4 3 -3 2 -4 3 -4 3 -4 2 -3 3 -4 3 -4 2 -4 3 -3 3 -4 3 -4 2 -4 3 -4 3 -3 2 -4 3 -4 3 -4 2 -4 3 -4 3 -4 2 -4 3 -4 3 -3 2 -4 3 -4 3 -4 2 -4 3 -4 3 -4 2 -4 3 -4 3 -4 2 -4 3 -5 3 -4 2 -4 3 -4 3 -4 2 -4 3 -4 3 -4 1720 2341 100 MP stroke 3 -4 2 -5 3 -4 3 -4 2 -4 3 -4 3 -5 2 -4 3 -4 3 -4 2 -5 3 -4 3 -4 2 -5 3 -4 3 -4 2 -5 3 -4 3 -4 2 -5 3 -4 3 -5 2 -4 3 -5 3 -4 2 -4 3 -5 3 -4 3 -5 2 -5 3 -4 3 -5 2 -4 3 -5 3 -4 2 -5 3 -5 3 -4 2 -5 3 -5 3 -4 2 -5 3 -5 3 -5 2 -4 3 -5 3 -5 2 -5 3 -4 3 -5 2 -5 3 -5 3 -5 2 -5 3 -5 3 -4 2 -5 3 -5 3 -5 3 -5 2 -5 3 -5 3 -5 2 -5 3 -5 3 -5 2 -6 3 -5 3 -5 2 -5 3 -5 3 -5 2 -5 3 -6 3 -5 2 -5 3 -5 3 -6 2 -5 3 -5 3 -6 2 -5 3 -5 3 -6 2 -5 3 -5 3 -6 3 -5 2 -6 3 -5 3 -6 2 -5 3 -6 3 -5 2 -6 3 -6 3 -5 2 -6 3 -5 1455 2821 100 MP stroke 3 -6 2 -6 3 -5 3 -6 2 -6 3 -6 3 -5 2 -6 3 -6 3 -6 2 -6 3 -6 3 -6 2 -6 3 -5 3 -6 3 -6 2 -6 3 -6 3 -6 2 -7 3 -6 3 -6 2 -6 3 -6 3 -6 2 -6 3 -7 3 -6 2 -6 3 -6 3 -7 2 -6 3 -6 3 -7 2 -6 3 -7 3 -6 2 -6 3 -7 3 -6 2 -7 3 -7 3 -6 2 -7 3 -6 3 -7 3 -7 2 -6 3 -7 3 -7 2 -7 3 -6 3 -7 2 -7 3 -7 3 -7 2 -7 3 -7 3 -7 2 -7 3 -7 3 -7 2 -7 3 -7 3 -7 2 -7 3 -7 3 -7 2 -8 3 -7 3 -7 2 -8 3 -7 3 -7 3 -8 2 -7 3 -8 3 -7 2 -8 3 -7 3 -8 2 -7 3 -8 3 -8 2 -7 3 -8 3 -8 2 -7 3 -8 3 -8 2 -8 3 -8 3 -8 2 -8 3 -8 3 -8 2 -8 3 -8 1190 3492 100 MP stroke 3 -8 2 -8 3 -8 3 -8 2 -9 3 -8 3 -8 3 -9 2 -8 3 -8 3 -9 2 -8 3 -9 3 -8 2 -9 3 -9 3 -8 2 -9 3 -9 3 -8 2 -9 3 -9 3 -9 2 -9 3 -9 3 -9 2 -9 3 -9 3 -9 2 -9 3 -9 3 -9 2 -10 3 -9 3 -9 3 -9 2 -10 3 -9 3 -10 2 -9 3 -10 3 -9 2 -10 3 -10 3 -9 2 -10 3 -10 3 -10 2 -10 3 -10 3 -10 2 -10 3 -10 3 -10 2 -10 3 -10 3 -10 2 -11 3 -10 3 -10 2 -11 3 -10 3 -11 2 -10 3 -11 3 -10 3 -11 2 -11 3 -11 3 -11 2 -10 3 -11 3 -11 2 -11 3 -11 3 -12 2 -11 3 -11 3 -11 2 -12 3 -11 3 -12 2 -11 3 -12 3 -11 2 -12 3 -12 3 -11 2 -12 3 -12 3 -12 2 -12 3 -12 3 -12 3 -12 2 -13 3 -12 3 -12 2 -13 925 4486 100 MP stroke 3 -12 3 -13 2 -12 3 -13 3 -13 2 -12 3 -13 3 -13 2 -13 3 -13 898 4613 11 MP stroke SO -3 1 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 1 -2 1 -3 0 -3 1 -3 1 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 1 -3 0 3841 872 100 MP stroke -3 1 -2 1 -3 1 -3 0 -3 1 -2 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 0 -2 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 0 -2 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -3 0 -2 1 -3 0 -3 1 -2 1 4106 802 100 MP stroke -3 0 -3 1 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 0 -2 1 -3 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 0 -2 1 -3 1 -3 0 -2 1 -3 1 -3 0 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 1 -3 0 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 0 -2 1 4371 743 100 MP stroke -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 1 -3 0 -2 1 -3 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -3 0 -2 1 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 1 4636 693 100 MP stroke -3 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 1 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 0 -3 1 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 1 -2 0 -3 0 -3 1 4902 650 100 MP stroke -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 1 -3 0 -3 0 -2 1 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 1 -2 0 -3 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 1 -3 0 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 0 5167 614 100 MP stroke -2 1 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 1 -3 0 5432 582 100 MP stroke -3 0 -2 1 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 1 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 5697 555 100 MP stroke -3 0 -2 1 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 1 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 5962 532 100 MP stroke -3 1 -2 0 -3 0 -3 0 -2 0 -3 1 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 0 -3 1 -3 0 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 0 -3 1 -3 0 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 0 -3 0 -3 1 -2 0 -3 0 -3 0 -2 0 6227 512 100 MP stroke -3 1 -3 0 -2 0 -3 0 -3 0 -2 1 -3 0 -3 0 -2 0 -3 0 6254 510 11 MP stroke gr 3546 4901 mt (c) s 642 2547 mt -90 rotate (ul) s 90 rotate 3504 292 mt (\(a\)) s 1969 2122 mt (D-) s 4915 2122 mt (D+) s 1969 855 mt (U-) s 4915 855 mt (U+) s end eplot epage end showpage %%EndDocument @endspecial 1208 w @beginspecial 56 @llx 201 @lly 546 @urx 601 @ury 1417 @rwi 1700 @rhi @setspecial %%BeginDocument: j1b.eps % MathWorks dictionary /MathWorks 150 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 464 132 5872 4798 MR c np 88 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6912 5185 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke DO 4 w SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 120 FMSR 795 4759 mt (-1) s 1434 4613 mt 1434 4559 L 1434 388 mt 1434 442 L 1281 4759 mt (-0.8) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1816 4759 mt (-0.6) s 2505 4613 mt 2505 4559 L 2505 388 mt 2505 442 L 2352 4759 mt (-0.4) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2887 4759 mt (-0.2) s 3576 4613 mt 3576 4559 L 3576 388 mt 3576 442 L 3543 4759 mt (0) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 4029 4759 mt (0.2) s 4647 4613 mt 4647 4559 L 4647 388 mt 4647 442 L 4564 4759 mt (0.4) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5100 4759 mt (0.6) s 5718 4613 mt 5718 4559 L 5718 388 mt 5718 442 L 5635 4759 mt (0.8) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6221 4759 mt (1) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 797 4657 mt (1) s 898 4191 mt 952 4191 L 6254 4191 mt 6200 4191 L 630 4235 mt (1.05) s 898 3768 mt 952 3768 L 6254 3768 mt 6200 3768 L 697 3812 mt (1.1) s 898 3346 mt 952 3346 L 6254 3346 mt 6200 3346 L 630 3390 mt (1.15) s 898 2923 mt 952 2923 L 6254 2923 mt 6200 2923 L 697 2967 mt (1.2) s 898 2501 mt 952 2501 L 6254 2501 mt 6200 2501 L 630 2545 mt (1.25) s 898 2078 mt 952 2078 L 6254 2078 mt 6200 2078 L 697 2122 mt (1.3) s 898 1655 mt 952 1655 L 6254 1655 mt 6200 1655 L 630 1699 mt (1.35) s 898 1233 mt 952 1233 L 6254 1233 mt 6200 1233 L 697 1277 mt (1.4) s 898 811 mt 952 811 L 6254 811 mt 6200 811 L 630 855 mt (1.45) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 697 432 mt (1.5) s 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np 3 -3 2 -4 3 -4 3 -3 2 -4 3 -4 3 -3 2 -4 3 -3 3 -4 2 -4 3 -3 3 -4 2 -4 3 -3 3 -4 3 -3 2 -4 3 -4 3 -3 2 -4 3 -4 3 -3 2 -4 3 -3 3 -4 2 -4 3 -3 3 -4 2 -4 3 -3 3 -4 2 -3 3 -4 3 -4 2 -3 3 -4 3 -4 2 -3 3 -4 3 -3 2 -4 3 -4 3 -3 3 -4 2 -4 3 -3 3 -4 2 -3 3 -4 3 -4 2 -3 3 -4 3 -4 2 -3 3 -4 3 -3 2 -4 3 -4 3 -3 2 -4 3 -3 3 -4 2 -4 3 -3 3 -4 2 -3 3 -4 3 -4 2 -3 3 -4 3 -3 2 -4 3 -4 3 -3 3 -4 2 -3 3 -4 3 -4 2 -3 3 -4 3 -3 2 -4 3 -4 3 -3 2 -4 3 -3 3 -4 2 -4 3 -3 3 -4 2 -3 3 -4 3 -3 2 -4 3 -4 3 -3 2 -4 3 -3 3311 2706 100 MP stroke 3 -4 2 -3 3 -4 3 -4 3 -3 2 -4 3 -3 3 -4 2 -3 3 -4 3 -3 2 -4 3 -4 3 -3 2 -4 3 -3 3 -4 2 -3 3 -4 3 -3 2 -4 3 -3 3 -4 2 -3 3 -4 3 -4 2 -3 3 -4 3 -3 2 -4 3 -3 3 -4 2 -3 3 -4 3 -3 3 -4 2 -3 3 -4 3 -3 2 -4 3 -3 3 -4 2 -3 3 -4 3 -3 2 -4 3 -3 3 -4 2 -3 3 -4 3 -3 2 -4 3 -3 3 -3 2 -4 3 -3 3 -4 2 -3 3 -4 3 -3 2 -4 3 -3 3 -4 3 -3 2 -3 3 -4 3 -3 2 -4 3 -3 3 -4 2 -3 3 -3 3 -4 2 -3 3 -4 3 -3 2 -4 3 -3 3 -3 2 -4 3 -3 3 -4 2 -3 3 -3 3 -4 2 -3 3 -3 3 -4 2 -3 3 -4 3 -3 2 -3 3 -4 3 -3 3 -3 2 -4 3 -3 3 -3 2 -4 3046 3050 100 MP stroke 3 -3 3 -4 2 -3 3 -3 3 -4 2 -3 3 -3 3 -4 2 -3 3 -3 3 -3 2 -4 3 -3 3 -3 2 -4 3 -3 3 -3 2 -4 3 -3 3 -3 2 -3 3 -4 3 -3 3 -3 2 -4 3 -3 3 -3 2 -3 3 -4 3 -3 2 -3 3 -3 3 -4 2 -3 3 -3 3 -3 2 -3 3 -4 3 -3 2 -3 3 -3 3 -4 2 -3 3 -3 3 -3 2 -3 3 -4 3 -3 2 -3 3 -3 3 -3 2 -4 3 -3 3 -3 3 -3 2 -3 3 -3 3 -4 2 -3 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 3 -4 3 -3 2 -3 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 3 -4 3 -3 2 -3 3 -3 3 -3 2 -3 3 -3 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 3 -4 3 -3 2 -3 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 2781 3365 100 MP stroke 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 3 -2 3 -3 2 -3 3 -3 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 3 -2 3 -3 2 -3 3 -3 3 -3 2 -3 3 -3 3 -3 2 -3 3 -2 3 -3 2 -3 3 -3 3 -3 2 -3 3 -3 3 -2 2 -3 3 -3 3 -3 3 -3 2 -2 3 -3 3 -3 2 -3 3 -3 3 -3 2 -2 3 -3 3 -3 2 -3 3 -2 3 -3 2 -3 3 -3 3 -2 2 -3 3 -3 3 -3 2 -2 3 -3 3 -3 2 -3 3 -2 3 -3 2 -3 3 -3 3 -2 3 -3 2 -3 3 -2 3 -3 2 -3 3 -2 3 -3 2 -3 3 -2 3 -3 2 -3 3 -2 3 -3 2 -3 3 -2 3 -3 2 -3 3 -2 3 -3 2 -2 3 -3 3 -3 2 -2 3 -3 3 -2 2 -3 3 -3 3 -2 2 -3 2516 3641 100 MP stroke 3 -2 3 -3 3 -2 2 -3 3 -3 3 -2 2 -3 3 -2 3 -3 2 -2 3 -3 3 -2 2 -3 3 -2 3 -3 2 -2 3 -3 3 -2 2 -3 3 -2 3 -3 2 -2 3 -3 3 -2 2 -3 3 -2 3 -3 2 -2 3 -3 3 -2 3 -2 2 -3 3 -2 3 -3 2 -2 3 -3 3 -2 2 -2 3 -3 3 -2 2 -3 3 -2 3 -2 2 -3 3 -2 3 -2 2 -3 3 -2 3 -3 2 -2 3 -2 3 -3 2 -2 3 -2 3 -3 2 -2 3 -2 3 -3 2 -2 3 -2 3 -2 3 -3 2 -2 3 -2 3 -3 2 -2 3 -2 3 -2 2 -3 3 -2 3 -2 2 -3 3 -2 3 -2 2 -2 3 -2 3 -3 2 -2 3 -2 3 -2 2 -3 3 -2 3 -2 2 -2 3 -2 3 -3 2 -2 3 -2 3 -2 3 -2 2 -3 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -3 3 -2 2250 3874 100 MP stroke 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -3 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -3 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -1 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -1 3 -2 2 -2 3 -2 3 -2 2 -2 3 -2 3 -2 2 -1 3 -2 3 -2 2 -2 3 -2 3 -2 2 -2 3 -1 3 -2 2 -2 3 -2 3 -2 2 -2 3 -1 3 -2 2 -2 3 -2 3 -2 3 -1 2 -2 3 -2 3 -2 2 -1 3 -2 3 -2 2 -2 3 -2 3 -1 2 -2 3 -2 3 -1 2 -2 3 -2 3 -2 2 -1 3 -2 3 -2 1985 4064 100 MP stroke 2 -2 3 -1 3 -2 2 -2 3 -1 3 -2 2 -2 3 -1 3 -2 3 -2 2 -1 3 -2 3 -2 2 -1 3 -2 3 -2 2 -1 3 -2 3 -2 2 -1 3 -2 3 -2 2 -1 3 -2 3 -1 2 -2 3 -2 3 -1 2 -2 3 -1 3 -2 2 -2 3 -1 3 -2 2 -1 3 -2 3 -2 2 -1 3 -2 3 -1 3 -2 2 -1 3 -2 3 -1 2 -2 3 -2 3 -1 2 -2 3 -1 3 -2 2 -1 3 -2 3 -1 2 -2 3 -1 3 -2 2 -1 3 -2 3 -1 2 -2 3 -1 3 -2 2 -1 3 -2 3 -1 2 -1 3 -2 3 -1 3 -2 2 -1 3 -2 3 -1 2 -2 3 -1 3 -1 2 -2 3 -1 3 -2 2 -1 3 -2 3 -1 2 -1 3 -2 3 -1 2 -2 3 -1 3 -1 2 -2 3 -1 3 -1 2 -2 3 -1 3 -2 2 -1 3 -1 3 -2 2 -1 3 -1 3 -2 1720 4215 100 MP stroke 3 -1 2 -1 3 -2 3 -1 2 -1 3 -2 3 -1 2 -1 3 -2 3 -1 2 -1 3 -1 3 -2 2 -1 3 -1 3 -2 2 -1 3 -1 3 -2 2 -1 3 -1 3 -1 2 -2 3 -1 3 -1 2 -1 3 -2 3 -1 3 -1 2 -1 3 -2 3 -1 2 -1 3 -1 3 -1 2 -2 3 -1 3 -1 2 -1 3 -2 3 -1 2 -1 3 -1 3 -1 2 -2 3 -1 3 -1 2 -1 3 -1 3 -1 2 -2 3 -1 3 -1 2 -1 3 -1 3 -1 2 -2 3 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -2 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -2 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -2 3 -1 2 -1 3 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 1455 4331 100 MP stroke 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 0 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 3 0 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 -1 3 0 2 -1 3 -1 3 -1 2 -1 3 -1 3 -1 2 0 3 -1 3 -1 2 -1 3 -1 3 -1 2 -1 3 0 3 -1 2 -1 3 -1 3 -1 3 -1 2 0 3 -1 3 -1 2 -1 3 -1 3 0 2 -1 3 -1 3 -1 2 -1 3 0 3 -1 2 -1 3 -1 3 -1 2 0 3 -1 3 -1 2 -1 3 -1 3 0 2 -1 3 -1 1190 4420 100 MP stroke 3 -1 2 0 3 -1 3 -1 2 -1 3 0 3 -1 3 -1 2 -1 3 0 3 -1 2 -1 3 -1 3 0 2 -1 3 -1 3 -1 2 0 3 -1 3 -1 2 -1 3 0 3 -1 2 -1 3 0 3 -1 2 -1 3 -1 3 0 2 -1 3 -1 3 0 2 -1 3 -1 3 0 3 -1 2 -1 3 -1 3 0 2 -1 3 -1 3 0 2 -1 3 -1 3 0 2 -1 3 -1 3 0 2 -1 3 -1 3 0 2 -1 3 -1 3 0 2 -1 3 -1 3 0 2 -1 3 0 3 -1 2 -1 3 0 3 -1 2 -1 3 0 3 -1 3 -1 2 0 3 -1 3 0 2 -1 3 -1 3 0 2 -1 3 -1 3 0 2 -1 3 0 3 -1 2 -1 3 0 3 -1 2 0 3 -1 3 -1 2 0 3 -1 3 0 2 -1 3 -1 3 0 2 -1 3 0 3 -1 3 0 2 -1 3 -1 3 0 2 -1 925 4486 100 MP stroke 3 0 3 -1 2 0 3 -1 3 -1 2 0 3 -1 3 0 2 -1 3 0 898 4491 11 MP stroke DA -3 4 -2 3 -3 4 -3 4 -2 3 -3 4 -3 4 -2 3 -3 4 -3 3 -2 4 -3 4 -3 3 -2 4 -3 3 -3 4 -3 4 -2 3 -3 4 -3 4 -2 3 -3 4 -3 3 -2 4 -3 4 -3 3 -2 4 -3 3 -3 4 -2 4 -3 3 -3 4 -2 3 -3 4 -3 4 -2 3 -3 4 -3 3 -2 4 -3 4 -3 3 -2 4 -3 3 -3 4 -3 4 -2 3 -3 4 -3 3 -2 4 -3 3 -3 4 -2 4 -3 3 -3 4 -2 3 -3 4 -3 4 -2 3 -3 4 -3 3 -2 4 -3 3 -3 4 -2 3 -3 4 -3 4 -2 3 -3 4 -3 3 -2 4 -3 3 -3 4 -2 3 -3 4 -3 4 -3 3 -2 4 -3 3 -3 4 -2 3 -3 4 -3 3 -2 4 -3 3 -3 4 -2 3 -3 4 -3 3 -2 4 -3 3 -3 4 -2 4 -3 3 -3 4 -2 3 -3 4 -3 3 -2 4 -3 3 3841 1995 100 MP stroke -3 4 -2 3 -3 4 -3 3 -3 3 -2 4 -3 3 -3 4 -2 3 -3 4 -3 3 -2 4 -3 3 -3 4 -2 3 -3 4 -3 3 -2 4 -3 3 -3 4 -2 3 -3 3 -3 4 -2 3 -3 4 -3 3 -2 4 -3 3 -3 3 -2 4 -3 3 -3 4 -2 3 -3 4 -3 3 -3 3 -2 4 -3 3 -3 4 -2 3 -3 3 -3 4 -2 3 -3 4 -3 3 -2 3 -3 4 -3 3 -2 3 -3 4 -3 3 -2 4 -3 3 -3 3 -2 4 -3 3 -3 3 -2 4 -3 3 -3 3 -2 4 -3 3 -3 3 -3 4 -2 3 -3 3 -3 4 -2 3 -3 3 -3 4 -2 3 -3 3 -3 4 -2 3 -3 3 -3 3 -2 4 -3 3 -3 3 -2 4 -3 3 -3 3 -2 3 -3 4 -3 3 -2 3 -3 3 -3 4 -2 3 -3 3 -3 3 -2 4 -3 3 -3 3 -3 3 -2 4 -3 3 -3 3 -2 3 4106 1662 100 MP stroke -3 3 -3 4 -2 3 -3 3 -3 3 -2 3 -3 4 -3 3 -2 3 -3 3 -3 3 -2 3 -3 4 -3 3 -2 3 -3 3 -3 3 -2 3 -3 4 -3 3 -2 3 -3 3 -3 3 -3 3 -2 3 -3 3 -3 4 -2 3 -3 3 -3 3 -2 3 -3 3 -3 3 -2 3 -3 3 -3 3 -2 3 -3 3 -3 4 -2 3 -3 3 -3 3 -2 3 -3 3 -3 3 -2 3 -3 3 -3 3 -2 3 -3 3 -3 3 -3 3 -2 3 -3 3 -3 3 -2 3 -3 3 -3 3 -2 3 -3 3 -3 3 -2 3 -3 3 -3 3 -2 3 -3 3 -3 3 -2 3 -3 3 -3 3 -2 3 -3 2 -3 3 -2 3 -3 3 -3 3 -2 3 -3 3 -3 3 -2 3 -3 3 -3 2 -3 3 -2 3 -3 3 -3 3 -2 3 -3 3 -3 3 -2 2 -3 3 -3 3 -2 3 -3 3 -3 3 -2 2 -3 3 -3 3 -2 3 4371 1363 100 MP stroke -3 3 -3 3 -2 2 -3 3 -3 3 -2 3 -3 2 -3 3 -2 3 -3 3 -3 3 -3 2 -2 3 -3 3 -3 3 -2 2 -3 3 -3 3 -2 3 -3 2 -3 3 -2 3 -3 2 -3 3 -2 3 -3 2 -3 3 -2 3 -3 3 -3 2 -2 3 -3 3 -3 2 -2 3 -3 3 -3 2 -2 3 -3 2 -3 3 -2 3 -3 2 -3 3 -3 3 -2 2 -3 3 -3 2 -2 3 -3 3 -3 2 -2 3 -3 2 -3 3 -2 3 -3 2 -3 3 -2 2 -3 3 -3 2 -2 3 -3 2 -3 3 -2 3 -3 2 -3 3 -2 2 -3 3 -3 2 -2 3 -3 2 -3 3 -3 2 -2 3 -3 2 -3 3 -2 2 -3 2 -3 3 -2 2 -3 3 -3 2 -2 3 -3 2 -3 3 -2 2 -3 2 -3 3 -2 2 -3 3 -3 2 -2 3 -3 2 -3 2 -2 3 -3 2 -3 2 -2 3 -3 2 -3 3 -2 2 4636 1107 100 MP stroke -3 2 -3 3 -3 2 -2 2 -3 3 -3 2 -2 2 -3 3 -3 2 -2 2 -3 3 -3 2 -2 2 -3 2 -3 3 -2 2 -3 2 -3 3 -2 2 -3 2 -3 2 -2 3 -3 2 -3 2 -2 2 -3 3 -3 2 -2 2 -3 2 -3 2 -3 3 -2 2 -3 2 -3 2 -2 3 -3 2 -3 2 -2 2 -3 2 -3 2 -2 3 -3 2 -3 2 -2 2 -3 2 -3 2 -2 2 -3 3 -3 2 -2 2 -3 2 -3 2 -2 2 -3 2 -3 2 -2 3 -3 2 -3 2 -2 2 -3 2 -3 2 -3 2 -2 2 -3 2 -3 2 -2 2 -3 2 -3 2 -2 2 -3 2 -3 2 -2 2 -3 2 -3 2 -2 3 -3 2 -3 2 -2 2 -3 1 -3 2 -2 2 -3 2 -3 2 -2 2 -3 2 -3 2 -2 2 -3 2 -3 2 -3 2 -2 2 -3 2 -3 2 -2 2 -3 2 -3 2 -2 2 -3 1 -3 2 4902 897 100 MP stroke -2 2 -3 2 -3 2 -2 2 -3 2 -3 2 -2 2 -3 1 -3 2 -2 2 -3 2 -3 2 -2 2 -3 2 -3 1 -2 2 -3 2 -3 2 -2 2 -3 1 -3 2 -3 2 -2 2 -3 2 -3 1 -2 2 -3 2 -3 2 -2 2 -3 1 -3 2 -2 2 -3 2 -3 1 -2 2 -3 2 -3 2 -2 1 -3 2 -3 2 -2 2 -3 1 -3 2 -2 2 -3 1 -3 2 -2 2 -3 1 -3 2 -3 2 -2 1 -3 2 -3 2 -2 1 -3 2 -3 2 -2 1 -3 2 -3 2 -2 1 -3 2 -3 2 -2 1 -3 2 -3 2 -2 1 -3 2 -3 1 -2 2 -3 2 -3 1 -2 2 -3 1 -3 2 -2 1 -3 2 -3 2 -2 1 -3 2 -3 1 -3 2 -2 1 -3 2 -3 1 -2 2 -3 2 -3 1 -2 2 -3 1 -3 2 -2 1 -3 2 -3 1 -2 2 -3 1 -3 2 -2 1 -3 2 -3 1 5167 730 100 MP stroke -2 2 -3 1 -3 2 -2 1 -3 1 -3 2 -2 1 -3 2 -3 1 -3 2 -2 1 -3 2 -3 1 -2 1 -3 2 -3 1 -2 2 -3 1 -3 1 -2 2 -3 1 -3 2 -2 1 -3 1 -3 2 -2 1 -3 2 -3 1 -2 1 -3 2 -3 1 -2 1 -3 2 -3 1 -2 1 -3 2 -3 1 -2 1 -3 2 -3 1 -3 1 -2 2 -3 1 -3 1 -2 2 -3 1 -3 1 -2 2 -3 1 -3 1 -2 1 -3 2 -3 1 -2 1 -3 1 -3 2 -2 1 -3 1 -3 2 -2 1 -3 1 -3 1 -2 2 -3 1 -3 1 -2 1 -3 1 -3 2 -3 1 -2 1 -3 1 -3 2 -2 1 -3 1 -3 1 -2 1 -3 1 -3 2 -2 1 -3 1 -3 1 -2 1 -3 2 -3 1 -2 1 -3 1 -3 1 -2 1 -3 2 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 2 -3 1 -3 1 5432 602 100 MP stroke -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 2 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 2 -3 1 -3 1 -2 1 -3 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 1 -3 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 1 -3 1 5697 507 100 MP stroke -3 0 -2 1 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 1 -3 0 -3 1 -3 1 -2 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 0 -2 1 -3 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 0 -2 1 -3 1 -3 0 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 5962 439 100 MP stroke -3 0 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -3 1 -2 0 -3 0 -3 1 -2 0 6227 392 100 MP stroke -3 1 -3 0 -2 0 -3 1 -3 0 -2 0 -3 1 -3 0 -2 1 -3 0 6254 388 11 MP stroke 3 4 2 3 3 4 3 4 2 3 3 4 3 4 2 3 3 4 3 3 2 4 3 4 3 3 2 4 3 3 3 4 3 4 2 3 3 4 3 4 2 3 3 4 3 3 2 4 3 4 3 3 2 4 3 3 3 4 2 4 3 3 3 4 2 3 3 4 3 4 2 3 3 4 3 3 2 4 3 4 3 3 2 4 3 3 3 4 3 4 2 3 3 4 3 3 2 4 3 3 3 4 2 4 3 3 3 4 2 3 3 4 3 4 2 3 3 4 3 3 2 4 3 3 3 4 2 3 3 4 3 4 2 3 3 4 3 3 2 4 3 3 3 4 2 3 3 4 3 4 3 3 2 4 3 3 3 4 2 3 3 4 3 3 2 4 3 3 3 4 2 3 3 4 3 3 2 4 3 3 3 4 2 4 3 3 3 4 2 3 3 4 3 3 2 4 3 3 3311 1995 100 MP stroke 3 4 2 3 3 4 3 3 3 3 2 4 3 3 3 4 2 3 3 4 3 3 2 4 3 3 3 4 2 3 3 4 3 3 2 4 3 3 3 4 2 3 3 3 3 4 2 3 3 4 3 3 2 4 3 3 3 3 2 4 3 3 3 4 2 3 3 4 3 3 3 3 2 4 3 3 3 4 2 3 3 3 3 4 2 3 3 4 3 3 2 3 3 4 3 3 2 3 3 4 3 3 2 4 3 3 3 3 2 4 3 3 3 3 2 4 3 3 3 3 2 4 3 3 3 3 3 4 2 3 3 3 3 4 2 3 3 3 3 4 2 3 3 3 3 4 2 3 3 3 3 3 2 4 3 3 3 3 2 4 3 3 3 3 2 3 3 4 3 3 2 3 3 3 3 4 2 3 3 3 3 3 2 4 3 3 3 3 3 3 2 4 3 3 3 3 2 3 3046 1662 100 MP stroke 3 3 3 4 2 3 3 3 3 3 2 3 3 4 3 3 2 3 3 3 3 3 2 3 3 4 3 3 2 3 3 3 3 3 2 3 3 4 3 3 2 3 3 3 3 3 3 3 2 3 3 3 3 4 2 3 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 4 2 3 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 3 2 3 3 2 3 3 2 3 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 2 3 3 2 3 3 3 3 3 2 3 3 3 3 3 2 2 3 3 3 3 2 3 3 3 3 3 2 2 3 3 3 3 2 3 2781 1363 100 MP stroke 3 3 3 3 2 2 3 3 3 3 2 3 3 2 3 3 2 3 3 3 3 3 3 2 2 3 3 3 3 3 2 2 3 3 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 3 3 2 2 3 3 3 3 2 2 3 3 3 3 2 2 3 3 2 3 3 2 3 3 2 3 3 3 3 2 2 3 3 3 2 2 3 3 3 3 2 2 3 3 2 3 3 2 3 3 2 3 3 2 2 3 3 3 2 2 3 3 2 3 3 2 3 3 2 3 3 2 2 3 3 3 2 2 3 3 2 3 3 3 2 2 3 3 2 3 3 2 2 3 2 3 3 2 2 3 3 3 2 2 3 3 2 3 3 2 2 3 2 3 3 2 2 3 3 3 2 2 3 3 2 3 2 2 3 3 2 3 2 2 3 3 2 3 3 2 2 2516 1107 100 MP stroke 3 2 3 3 3 2 2 2 3 3 3 2 2 2 3 3 3 2 2 2 3 3 3 2 2 2 3 2 3 3 2 2 3 2 3 3 2 2 3 2 3 2 2 3 3 2 3 2 2 2 3 3 3 2 2 2 3 2 3 2 3 3 2 2 3 2 3 2 2 3 3 2 3 2 2 2 3 2 3 2 2 3 3 2 3 2 2 2 3 2 3 2 2 2 3 3 3 2 2 2 3 2 3 2 2 2 3 2 3 2 2 3 3 2 3 2 2 2 3 2 3 2 3 2 2 2 3 2 3 2 2 2 3 2 3 2 2 2 3 2 3 2 2 2 3 2 3 2 2 3 3 2 3 2 2 2 3 1 3 2 2 2 3 2 3 2 2 2 3 2 3 2 2 2 3 2 3 2 3 2 2 2 3 2 3 2 2 2 3 2 3 2 2 2 3 1 3 2 2250 897 100 MP stroke 2 2 3 2 3 2 2 2 3 2 3 2 2 2 3 1 3 2 2 2 3 2 3 2 2 2 3 2 3 1 2 2 3 2 3 2 2 2 3 1 3 2 3 2 2 2 3 2 3 1 2 2 3 2 3 2 2 2 3 1 3 2 2 2 3 2 3 1 2 2 3 2 3 2 2 1 3 2 3 2 2 2 3 1 3 2 2 2 3 1 3 2 2 2 3 1 3 2 3 2 2 1 3 2 3 2 2 1 3 2 3 2 2 1 3 2 3 2 2 1 3 2 3 2 2 1 3 2 3 2 2 1 3 2 3 1 2 2 3 2 3 1 2 2 3 1 3 2 2 1 3 2 3 2 2 1 3 2 3 1 3 2 2 1 3 2 3 1 2 2 3 2 3 1 2 2 3 1 3 2 2 1 3 2 3 1 2 2 3 1 3 2 2 1 3 2 3 1 1985 730 100 MP stroke 2 2 3 1 3 2 2 1 3 1 3 2 2 1 3 2 3 1 3 2 2 1 3 2 3 1 2 1 3 2 3 1 2 2 3 1 3 1 2 2 3 1 3 2 2 1 3 1 3 2 2 1 3 2 3 1 2 1 3 2 3 1 2 1 3 2 3 1 2 1 3 2 3 1 2 1 3 2 3 1 3 1 2 2 3 1 3 1 2 2 3 1 3 1 2 2 3 1 3 1 2 1 3 2 3 1 2 1 3 1 3 2 2 1 3 1 3 2 2 1 3 1 3 1 2 2 3 1 3 1 2 1 3 1 3 2 3 1 2 1 3 1 3 2 2 1 3 1 3 1 2 1 3 1 3 2 2 1 3 1 3 1 2 1 3 2 3 1 2 1 3 1 3 1 2 1 3 2 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 2 3 1 3 1 1720 602 100 MP stroke 3 1 2 1 3 1 3 1 2 1 3 1 3 2 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 2 3 1 3 1 2 1 3 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 0 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 3 1 2 1 3 1 3 1 2 0 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 0 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 0 3 1 3 1 2 1 3 1 3 1 3 0 2 1 3 1 3 1 2 1 3 1 3 0 2 1 3 1 3 1 2 1 3 1 1455 507 100 MP stroke 3 0 2 1 3 1 3 1 2 1 3 0 3 1 2 1 3 1 3 1 2 0 3 1 3 1 2 1 3 0 3 1 3 1 2 1 3 1 3 0 2 1 3 1 3 1 2 0 3 1 3 1 2 1 3 0 3 1 2 1 3 0 3 1 2 1 3 1 3 0 2 1 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 0 2 1 3 1 3 0 3 1 2 1 3 0 3 1 2 0 3 1 3 1 2 0 3 1 3 0 2 1 3 1 3 0 2 1 3 0 3 1 2 1 3 0 3 1 2 0 3 1 3 1 2 0 3 1 1190 439 100 MP stroke 3 0 2 1 3 0 3 1 2 1 3 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 0 3 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 0 3 1 2 0 3 1 3 0 2 0 3 1 3 0 3 1 2 0 3 0 3 1 2 0 925 392 100 MP stroke 3 1 3 0 2 0 3 1 3 0 2 0 3 1 3 0 2 1 3 0 898 388 11 MP stroke SO -3 -3 -2 -4 -3 -4 -3 -3 -2 -4 -3 -4 -3 -3 -2 -4 -3 -3 -3 -4 -2 -4 -3 -3 -3 -4 -2 -4 -3 -3 -3 -4 -3 -3 -2 -4 -3 -4 -3 -3 -2 -4 -3 -4 -3 -3 -2 -4 -3 -3 -3 -4 -2 -4 -3 -3 -3 -4 -2 -4 -3 -3 -3 -4 -2 -3 -3 -4 -3 -4 -2 -3 -3 -4 -3 -4 -2 -3 -3 -4 -3 -3 -2 -4 -3 -4 -3 -3 -3 -4 -2 -4 -3 -3 -3 -4 -2 -3 -3 -4 -3 -4 -2 -3 -3 -4 -3 -4 -2 -3 -3 -4 -3 -3 -2 -4 -3 -4 -3 -3 -2 -4 -3 -3 -3 -4 -2 -4 -3 -3 -3 -4 -2 -3 -3 -4 -3 -4 -2 -3 -3 -4 -3 -3 -2 -4 -3 -4 -3 -3 -3 -4 -2 -3 -3 -4 -3 -4 -2 -3 -3 -4 -3 -3 -2 -4 -3 -4 -3 -3 -2 -4 -3 -3 -3 -4 -2 -4 -3 -3 -3 -4 -2 -3 -3 -4 -3 -3 -2 -4 -3 -4 -3 -3 -2 -4 -3 -3 3841 2706 100 MP stroke -3 -4 -2 -3 -3 -4 -3 -4 -3 -3 -2 -4 -3 -3 -3 -4 -2 -3 -3 -4 -3 -3 -2 -4 -3 -4 -3 -3 -2 -4 -3 -3 -3 -4 -2 -3 -3 -4 -3 -3 -2 -4 -3 -3 -3 -4 -2 -3 -3 -4 -3 -4 -2 -3 -3 -4 -3 -3 -2 -4 -3 -3 -3 -4 -2 -3 -3 -4 -3 -3 -3 -4 -2 -3 -3 -4 -3 -3 -2 -4 -3 -3 -3 -4 -2 -3 -3 -4 -3 -3 -2 -4 -3 -3 -3 -4 -2 -3 -3 -4 -3 -3 -2 -4 -3 -3 -3 -3 -2 -4 -3 -3 -3 -4 -2 -3 -3 -4 -3 -3 -2 -4 -3 -3 -3 -4 -3 -3 -2 -3 -3 -4 -3 -3 -2 -4 -3 -3 -3 -4 -2 -3 -3 -3 -3 -4 -2 -3 -3 -4 -3 -3 -2 -4 -3 -3 -3 -3 -2 -4 -3 -3 -3 -4 -2 -3 -3 -3 -3 -4 -2 -3 -3 -3 -3 -4 -2 -3 -3 -4 -3 -3 -2 -3 -3 -4 -3 -3 -3 -3 -2 -4 -3 -3 -3 -3 -2 -4 4106 3050 100 MP stroke -3 -3 -3 -4 -2 -3 -3 -3 -3 -4 -2 -3 -3 -3 -3 -4 -2 -3 -3 -3 -3 -3 -2 -4 -3 -3 -3 -3 -2 -4 -3 -3 -3 -3 -2 -4 -3 -3 -3 -3 -2 -3 -3 -4 -3 -3 -3 -3 -2 -4 -3 -3 -3 -3 -2 -3 -3 -4 -3 -3 -2 -3 -3 -3 -3 -4 -2 -3 -3 -3 -3 -3 -2 -3 -3 -4 -3 -3 -2 -3 -3 -3 -3 -4 -2 -3 -3 -3 -3 -3 -2 -3 -3 -4 -3 -3 -2 -3 -3 -3 -3 -3 -3 -4 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -4 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -4 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -4 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -4 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 4371 3365 100 MP stroke -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -3 -3 -3 -2 -3 -3 -3 -3 -2 -2 -3 -3 -3 -3 -3 -3 -3 -2 -2 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3 -2 -2 -3 -3 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -3 -3 -2 -2 -3 -3 -3 -3 -3 -2 -2 -3 -3 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -2 -3 -3 -2 -2 -3 -3 -3 -3 -2 -2 -3 -3 -3 -2 -2 -3 -3 -3 -3 -2 -2 -3 4636 3641 100 MP stroke -3 -2 -3 -3 -3 -2 -2 -3 -3 -3 -3 -2 -2 -3 -3 -2 -3 -3 -2 -2 -3 -3 -3 -2 -2 -3 -3 -2 -3 -3 -2 -2 -3 -3 -3 -2 -2 -3 -3 -2 -3 -3 -2 -2 -3 -3 -3 -2 -2 -3 -3 -2 -3 -3 -2 -2 -3 -3 -3 -2 -3 -2 -2 -3 -3 -2 -3 -3 -2 -2 -3 -3 -3 -2 -2 -2 -3 -3 -3 -2 -2 -3 -3 -2 -3 -2 -2 -3 -3 -2 -3 -2 -2 -3 -3 -2 -3 -3 -2 -2 -3 -2 -3 -3 -2 -2 -3 -2 -3 -3 -2 -2 -3 -2 -3 -3 -2 -2 -3 -2 -3 -2 -3 -3 -2 -2 -3 -2 -3 -3 -2 -2 -3 -2 -3 -2 -2 -3 -3 -2 -3 -2 -2 -3 -3 -2 -3 -2 -2 -2 -3 -2 -3 -3 -2 -2 -3 -2 -3 -2 -2 -3 -3 -2 -3 -2 -2 -2 -3 -2 -3 -3 -2 -2 -3 -2 -3 -2 -3 -2 -2 -3 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -3 -3 -2 4902 3874 100 MP stroke -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -3 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -3 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -1 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -1 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -1 -3 -2 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -1 -3 -2 -2 -2 -3 -2 -3 -2 -2 -2 -3 -1 -3 -2 -2 -2 -3 -2 -3 -2 -3 -1 -2 -2 -3 -2 -3 -2 -2 -1 -3 -2 -3 -2 -2 -2 -3 -2 -3 -1 -2 -2 -3 -2 -3 -1 -2 -2 -3 -2 -3 -2 -2 -1 -3 -2 -3 -2 5167 4064 100 MP stroke -2 -2 -3 -1 -3 -2 -2 -2 -3 -1 -3 -2 -2 -2 -3 -1 -3 -2 -3 -2 -2 -1 -3 -2 -3 -2 -2 -1 -3 -2 -3 -2 -2 -1 -3 -2 -3 -2 -2 -1 -3 -2 -3 -2 -2 -1 -3 -2 -3 -1 -2 -2 -3 -2 -3 -1 -2 -2 -3 -1 -3 -2 -2 -2 -3 -1 -3 -2 -2 -1 -3 -2 -3 -2 -2 -1 -3 -2 -3 -1 -3 -2 -2 -1 -3 -2 -3 -1 -2 -2 -3 -2 -3 -1 -2 -2 -3 -1 -3 -2 -2 -1 -3 -2 -3 -1 -2 -2 -3 -1 -3 -2 -2 -1 -3 -2 -3 -1 -2 -2 -3 -1 -3 -2 -2 -1 -3 -2 -3 -1 -2 -1 -3 -2 -3 -1 -3 -2 -2 -1 -3 -2 -3 -1 -2 -2 -3 -1 -3 -1 -2 -2 -3 -1 -3 -2 -2 -1 -3 -2 -3 -1 -2 -1 -3 -2 -3 -1 -2 -2 -3 -1 -3 -1 -2 -2 -3 -1 -3 -1 -2 -2 -3 -1 -3 -2 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -2 5432 4215 100 MP stroke -3 -1 -2 -1 -3 -2 -3 -1 -2 -1 -3 -2 -3 -1 -2 -1 -3 -2 -3 -1 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -1 -2 -2 -3 -1 -3 -1 -2 -1 -3 -2 -3 -1 -3 -1 -2 -1 -3 -2 -3 -1 -2 -1 -3 -1 -3 -1 -2 -2 -3 -1 -3 -1 -2 -1 -3 -2 -3 -1 -2 -1 -3 -1 -3 -1 -2 -2 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -2 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -2 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -2 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -2 -3 -1 -2 -1 -3 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 5697 4331 100 MP stroke -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 0 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 0 -3 -1 -3 -1 -2 -1 -3 -1 -3 -1 -2 -1 -3 0 -3 -1 -2 -1 -3 -1 -3 -1 -3 -1 -2 0 -3 -1 -3 -1 -2 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 -1 -2 -1 -3 0 -3 -1 -2 -1 -3 -1 -3 -1 -2 0 -3 -1 -3 -1 -2 -1 -3 -1 -3 0 -2 -1 -3 -1 5962 4420 100 MP stroke -3 -1 -2 0 -3 -1 -3 -1 -2 -1 -3 0 -3 -1 -3 -1 -2 -1 -3 0 -3 -1 -2 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 -1 -2 0 -3 -1 -3 -1 -2 -1 -3 0 -3 -1 -2 -1 -3 0 -3 -1 -2 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 0 -3 -1 -2 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 0 -2 -1 -3 0 -3 -1 -2 -1 -3 0 -3 -1 -2 -1 -3 0 -3 -1 -3 -1 -2 0 -3 -1 -3 0 -2 -1 -3 -1 -3 0 -2 -1 -3 -1 -3 0 -2 -1 -3 0 -3 -1 -2 -1 -3 0 -3 -1 -2 0 -3 -1 -3 -1 -2 0 -3 -1 -3 0 -2 -1 -3 -1 -3 0 -2 -1 -3 0 -3 -1 -3 0 -2 -1 -3 -1 -3 0 -2 -1 6227 4486 100 MP stroke -3 0 -3 -1 -2 0 -3 -1 -3 -1 -2 0 -3 -1 -3 0 -2 -1 -3 0 6254 4491 11 MP stroke gr 3546 4901 mt (c) s 575 2567 mt -90 rotate (u0) s 90 rotate 3504 291 mt (\(b\)) s 1969 1277 mt (D-) s 4915 1277 mt (D+) s 1969 3812 mt (U-) s 4915 3812 mt (U+) s end eplot epage end showpage %%EndDocument @endspecial 1209 w @beginspecial 62 @llx 201 @lly 546 @urx 600 @ury 1417 @rwi 1700 @rhi @setspecial %%BeginDocument: j1c.eps % MathWorks dictionary /MathWorks 150 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 531 133 5805 4797 MR c np 88 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6912 5185 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke DO 4 w SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 120 FMSR 795 4759 mt (-1) s 1434 4613 mt 1434 4559 L 1434 388 mt 1434 442 L 1281 4759 mt (-0.8) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1816 4759 mt (-0.6) s 2505 4613 mt 2505 4559 L 2505 388 mt 2505 442 L 2352 4759 mt (-0.4) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2887 4759 mt (-0.2) s 3576 4613 mt 3576 4559 L 3576 388 mt 3576 442 L 3543 4759 mt (0) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 4029 4759 mt (0.2) s 4647 4613 mt 4647 4559 L 4647 388 mt 4647 442 L 4564 4759 mt (0.4) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5100 4759 mt (0.6) s 5718 4613 mt 5718 4559 L 5718 388 mt 5718 442 L 5635 4759 mt (0.8) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6221 4759 mt (1) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 697 4657 mt (1.5) s 898 4009 mt 952 4009 L 6254 4009 mt 6200 4009 L 797 4053 mt (2) s 898 3406 mt 952 3406 L 6254 3406 mt 6200 3406 L 697 3450 mt (2.5) s 898 2802 mt 952 2802 L 6254 2802 mt 6200 2802 L 797 2846 mt (3) s 898 2199 mt 952 2199 L 6254 2199 mt 6200 2199 L 697 2243 mt (3.5) s 898 1595 mt 952 1595 L 6254 1595 mt 6200 1595 L 797 1639 mt (4) s 898 992 mt 952 992 L 6254 992 mt 6200 992 L 697 1036 mt (4.5) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 797 432 mt (5) s 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 2 1 3 0 3 1 2 0 3 1 3 0 2 1 3 1 3 0 3 1 2 0 3 1 3 0 2 1 3 1 3 0 2 1 3 0 3 1 2 0 3 1 3 1 2 0 3 1 3 0 2 1 3 1 3 0 2 1 3 0 3 1 2 1 3 0 3 1 2 0 3 1 3 1 2 0 3 1 3 1 3 0 2 1 3 0 3 1 2 1 3 0 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 0 2 1 3 1 3 0 2 1 3 1 3311 4275 100 MP stroke 3 0 2 1 3 1 3 0 3 1 2 1 3 0 3 1 2 1 3 0 3 1 2 1 3 0 3 1 2 1 3 0 3 1 2 1 3 0 3 1 2 1 3 1 3 0 2 1 3 1 3 0 2 1 3 1 3 0 2 1 3 1 3 1 2 0 3 1 3 1 3 0 2 1 3 1 3 1 2 0 3 1 3 1 2 0 3 1 3 1 2 1 3 0 3 1 2 1 3 1 3 0 2 1 3 1 3 1 2 0 3 1 3 1 2 1 3 0 3 1 2 1 3 1 3 0 3 1 2 1 3 1 3 0 2 1 3 1 3 1 2 1 3 0 3 1 2 1 3 1 3 0 2 1 3 1 3 1 2 1 3 0 3 1 2 1 3 1 3 1 2 1 3 0 3 1 2 1 3 1 3 1 2 0 3 1 3 1 3 1 2 1 3 1 3 0 2 1 3046 4202 100 MP stroke 3 1 3 1 2 1 3 1 3 1 2 0 3 1 3 1 2 1 3 1 3 1 2 1 3 0 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 0 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 0 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 0 3 1 2 1 3 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 2 2 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 2 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 1 2 2 2781 4105 100 MP stroke 3 1 3 1 2 1 3 1 3 1 2 1 3 1 3 2 2 1 3 1 3 1 3 1 2 1 3 2 3 1 2 1 3 1 3 1 2 1 3 2 3 1 2 1 3 1 3 1 2 2 3 1 3 1 2 1 3 1 3 2 2 1 3 1 3 1 2 2 3 1 3 1 2 1 3 2 3 1 2 1 3 1 3 2 3 1 2 1 3 1 3 2 2 1 3 1 3 2 2 1 3 1 3 2 2 1 3 1 3 2 2 1 3 1 3 2 2 1 3 1 3 2 2 1 3 1 3 2 2 1 3 1 3 2 2 1 3 2 3 1 3 1 2 2 3 1 3 2 2 1 3 1 3 2 2 1 3 2 3 1 2 2 3 1 3 2 2 1 3 1 3 2 2 1 3 2 3 1 2 2 3 1 3 2 2 1 3 2 3 1 2 2 3 1 3 2 2 2 2516 3975 100 MP stroke 3 1 3 2 3 1 2 2 3 1 3 2 2 1 3 2 3 2 2 1 3 2 3 1 2 2 3 2 3 1 2 2 3 1 3 2 2 2 3 1 3 2 2 2 3 1 3 2 2 2 3 1 3 2 2 2 3 2 3 1 3 2 2 2 3 1 3 2 2 2 3 2 3 1 2 2 3 2 3 2 2 1 3 2 3 2 2 2 3 2 3 1 2 2 3 2 3 2 2 2 3 2 3 1 2 2 3 2 3 2 2 2 3 2 3 2 2 2 3 2 3 1 3 2 2 2 3 2 3 2 2 2 3 2 3 2 2 2 3 2 3 2 2 2 3 2 3 2 2 2 3 2 3 2 2 2 3 2 3 2 2 2 3 3 3 2 2 2 3 2 3 2 2 2 3 2 3 2 3 2 2 3 3 2 3 2 2 2 3 2 3 3 2 2 3 2 3 2 2250 3792 100 MP stroke 2 2 3 3 3 2 2 2 3 2 3 3 2 2 3 2 3 3 2 2 3 2 3 3 2 2 3 2 3 3 2 2 3 2 3 3 2 2 3 3 3 2 3 3 2 2 3 3 3 2 2 2 3 3 3 2 2 3 3 3 3 2 2 3 3 2 3 3 2 2 3 3 3 3 2 2 3 3 3 2 2 3 3 3 3 2 2 3 3 3 3 2 2 3 3 3 3 3 3 2 2 3 3 3 3 3 2 3 3 2 3 3 2 3 3 3 3 3 2 3 3 3 3 3 2 2 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 3 2 3 3 4 3 3 2 3 3 3 3 3 2 3 3 3 3 3 3 4 2 3 3 3 3 3 2 4 3 3 3 3 2 3 3 4 3 3 2 3 3 4 3 3 2 3 3 4 3 3 2 4 3 3 3 4 1985 3515 100 MP stroke 2 3 3 4 3 3 2 4 3 3 3 4 2 4 3 3 3 4 3 4 2 3 3 4 3 4 2 3 3 4 3 4 2 4 3 4 3 3 2 4 3 4 3 4 2 4 3 4 3 4 2 4 3 4 3 4 2 4 3 4 3 4 2 4 3 4 3 4 2 5 3 4 3 4 2 4 3 5 3 4 3 4 2 5 3 4 3 4 2 5 3 4 3 5 2 4 3 5 3 4 2 5 3 4 3 5 2 5 3 4 3 5 2 5 3 5 3 4 2 5 3 5 3 5 2 5 3 5 3 5 2 5 3 5 3 5 3 5 2 5 3 5 3 5 2 5 3 6 3 5 2 5 3 6 3 5 2 5 3 6 3 5 2 6 3 5 3 6 2 6 3 5 3 6 2 6 3 5 3 6 2 6 3 6 3 6 2 6 3 6 3 6 2 6 3 6 3 6 1720 3056 100 MP stroke 3 6 2 6 3 7 3 6 2 6 3 7 3 6 2 6 3 7 3 7 2 6 3 7 3 6 2 7 3 7 3 7 2 7 3 7 3 7 2 7 3 7 3 7 2 7 3 7 3 8 2 7 3 7 3 8 3 7 2 8 3 7 3 8 2 8 3 8 3 7 2 8 3 8 3 8 2 8 3 8 3 9 2 8 3 8 3 9 2 8 3 8 3 9 2 9 3 8 3 9 2 9 3 9 3 9 2 9 3 9 3 9 2 10 3 9 3 9 3 10 2 9 3 10 3 10 2 10 3 10 3 10 2 10 3 10 3 10 2 10 3 11 3 10 2 11 3 11 3 10 2 11 3 11 3 11 2 11 3 12 3 11 2 12 3 11 3 12 2 12 3 11 3 12 3 13 2 12 3 12 3 13 2 12 3 13 3 13 2 12 3 14 3 13 2 13 3 13 1455 2154 100 MP stroke 3 14 2 14 3 13 3 14 2 14 3 15 3 14 2 15 3 14 3 15 2 15 3 15 3 15 2 16 3 15 3 16 3 16 2 16 3 16 3 17 2 17 3 16 3 17 2 17 3 18 3 17 2 18 3 18 3 18 2 18 3 19 3 19 2 19 3 19 3 19 2 20 3 20 3 20 2 20 3 21 3 21 2 21 3 21 3 22 2 22 3 22 3 22 3 23 2 23 3 23 3 24 2 24 3 24 3 24 2 25 3 25 3 26 2 25 3 27 3 26 2 27 3 27 3 28 2 28 3 28 3 29 2 29 3 30 3 30 2 31 3 30 3 32 2 32 3 32 3 33 3 33 2 34 3 34 3 35 2 36 3 36 3 36 2 37 3 38 3 39 2 39 3 39 3 41 2 41 3 41 3 42 2 43 2 25 1207 -100 94 MP stroke DA -3 0 -2 -1 -3 0 -3 -1 -2 0 -3 -1 -3 0 -2 -1 -3 0 -3 -1 -2 -1 -3 0 -3 -1 -2 0 -3 -1 -3 0 -3 -1 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 -1 -3 0 -3 -1 -2 0 -3 -1 -3 0 -2 -1 -3 0 -3 -1 -2 0 -3 -1 -3 0 -2 -1 -3 0 -3 -1 -2 0 -3 -1 -3 0 -2 -1 -3 0 -3 -1 -3 0 -2 -1 -3 0 -3 0 -2 -1 -3 0 -3 -1 -2 0 -3 -1 -3 0 -2 -1 -3 0 -3 -1 -2 0 -3 0 -3 -1 -2 0 -3 -1 -3 0 -2 -1 -3 0 -3 -1 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 -1 -3 0 -3 -1 -3 0 -2 -1 -3 0 -3 0 -2 -1 -3 0 -3 -1 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 -1 -3 0 -3 -1 -2 0 -3 0 -3 -1 -2 0 -3 -1 -3 0 -2 0 -3 -1 3841 4379 100 MP stroke -3 0 -2 -1 -3 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 -1 -3 0 -3 0 -2 -1 -3 0 -3 -1 -2 0 -3 0 -3 -1 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 -1 -3 0 -3 0 -2 -1 -3 0 -3 -1 -2 0 -3 0 -3 -1 -2 0 -3 -1 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 -1 -3 0 -3 -1 -2 0 -3 0 -3 -1 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 -1 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 -1 -3 0 -3 0 -3 -1 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 -1 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 -1 -3 0 -3 0 -3 -1 -2 0 -3 0 -3 -1 -2 0 4106 4416 100 MP stroke -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 -1 4371 4447 100 MP stroke -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 -1 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 4636 4472 100 MP stroke -3 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 4902 4493 100 MP stroke -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 5167 4511 100 MP stroke -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 5432 4526 100 MP stroke -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 5697 4539 100 MP stroke -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 5962 4549 100 MP stroke -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 -1 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 -1 -3 0 -3 0 -2 0 -3 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 6227 4558 100 MP stroke -3 -1 -3 0 -2 0 -3 0 -3 0 -2 0 -3 0 -3 0 -2 0 6251 4559 10 MP stroke 3 0 2 -1 3 0 3 -1 2 0 3 -1 3 0 2 -1 3 0 3 -1 2 -1 3 0 3 -1 2 0 3 -1 3 0 3 -1 2 0 3 -1 3 0 2 0 3 -1 3 0 2 -1 3 0 3 -1 2 0 3 -1 3 0 2 -1 3 0 3 -1 2 0 3 -1 3 0 2 -1 3 0 3 -1 2 0 3 -1 3 0 2 -1 3 0 3 -1 3 0 2 -1 3 0 3 0 2 -1 3 0 3 -1 2 0 3 -1 3 0 2 -1 3 0 3 -1 2 0 3 0 3 -1 2 0 3 -1 3 0 2 -1 3 0 3 -1 2 0 3 -1 3 0 2 0 3 -1 3 0 2 -1 3 0 3 -1 3 0 2 -1 3 0 3 0 2 -1 3 0 3 -1 2 0 3 -1 3 0 2 0 3 -1 3 0 2 -1 3 0 3 -1 2 0 3 0 3 -1 2 0 3 -1 3 0 2 0 3 -1 3311 4379 100 MP stroke 3 0 2 -1 3 0 3 -1 3 0 2 0 3 -1 3 0 2 -1 3 0 3 0 2 -1 3 0 3 -1 2 0 3 0 3 -1 2 0 3 -1 3 0 2 0 3 -1 3 0 2 -1 3 0 3 0 2 -1 3 0 3 -1 2 0 3 0 3 -1 2 0 3 -1 3 0 3 0 2 -1 3 0 3 0 2 -1 3 0 3 -1 2 0 3 0 3 -1 2 0 3 -1 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 2 -1 3 0 3 0 2 -1 3 0 3 0 2 -1 3 0 3 0 3 -1 2 0 3 -1 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 2 -1 3 0 3 0 2 -1 3 0 3 0 2 -1 3 0 3 0 2 -1 3 0 3 0 2 -1 3 0 3 0 2 -1 3 0 3 0 3 -1 2 0 3 0 3 -1 2 0 3046 4416 100 MP stroke 3 -1 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 2 0 3 0 3 -1 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 2 0 3 0 3 -1 2 0 3 0 3 -1 2 0 3 0 3 -1 2 0 3 0 3 -1 3 0 2 0 3 0 3 -1 2 0 3 0 3 -1 2 0 3 0 3 -1 2 0 3 0 3 -1 2 0 3 0 3 0 2 -1 3 0 3 0 2 -1 3 0 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 2 0 3 0 3 -1 2 0 3 0 3 -1 2 0 3 0 3 0 2 -1 2781 4447 100 MP stroke 3 0 3 0 2 -1 3 0 3 0 2 0 3 -1 3 0 2 0 3 -1 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 -1 2 0 3 0 3 -1 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 -1 2 0 3 0 3 -1 2 0 3 0 3 0 2 -1 3 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 -1 3 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 -1 3 0 2 0 2516 4472 100 MP stroke 3 0 3 -1 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 -1 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 -1 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2250 4493 100 MP stroke 2 0 3 -1 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 1985 4511 100 MP stroke 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 1720 4526 100 MP stroke 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 -1 1455 4539 100 MP stroke 3 0 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 2 0 3 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 2 0 3 0 1190 4549 100 MP stroke 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 -1 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 -1 3 0 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 -1 3 0 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 0 2 0 3 0 3 0 2 -1 3 0 3 0 2 0 3 0 3 0 3 0 2 0 3 0 3 0 2 0 925 4558 100 MP stroke 3 -1 3 0 2 0 3 0 3 0 2 0 3 0 3 0 2 0 901 4559 10 MP stroke SO -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 1 -3 0 -3 1 -2 0 -3 1 -3 0 -2 1 -3 1 -3 0 -2 1 -3 0 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 0 -2 1 -3 1 -3 0 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -3 0 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 0 -2 1 -3 1 -3 0 -2 1 -3 1 3841 4275 100 MP stroke -3 0 -2 1 -3 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 0 -2 1 -3 1 -3 0 -2 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 0 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 0 -3 1 -2 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 0 -2 1 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -3 1 -2 1 -3 1 -3 0 -2 1 4106 4202 100 MP stroke -3 1 -3 1 -2 1 -3 1 -3 1 -2 0 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 0 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 0 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 0 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 2 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 2 -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 1 -2 2 4371 4105 100 MP stroke -3 1 -3 1 -2 1 -3 1 -3 1 -2 1 -3 1 -3 2 -2 1 -3 1 -3 1 -3 1 -2 1 -3 2 -3 1 -2 1 -3 1 -3 1 -2 1 -3 2 -3 1 -2 1 -3 1 -3 1 -2 2 -3 1 -3 1 -2 1 -3 1 -3 2 -2 1 -3 1 -3 1 -2 2 -3 1 -3 1 -2 1 -3 2 -3 1 -2 1 -3 1 -3 2 -3 1 -2 1 -3 1 -3 2 -2 1 -3 1 -3 2 -2 1 -3 1 -3 2 -2 1 -3 1 -3 2 -2 1 -3 1 -3 2 -2 1 -3 1 -3 2 -2 1 -3 1 -3 2 -2 1 -3 1 -3 2 -2 1 -3 2 -3 1 -3 1 -2 2 -3 1 -3 2 -2 1 -3 1 -3 2 -2 1 -3 2 -3 1 -2 2 -3 1 -3 2 -2 1 -3 1 -3 2 -2 1 -3 2 -3 1 -2 2 -3 1 -3 2 -2 1 -3 2 -3 1 -2 2 -3 1 -3 2 -2 2 4636 3975 100 MP stroke -3 1 -3 2 -3 1 -2 2 -3 1 -3 2 -2 1 -3 2 -3 2 -2 1 -3 2 -3 1 -2 2 -3 2 -3 1 -2 2 -3 1 -3 2 -2 2 -3 1 -3 2 -2 2 -3 1 -3 2 -2 2 -3 1 -3 2 -2 2 -3 2 -3 1 -3 2 -2 2 -3 1 -3 2 -2 2 -3 2 -3 1 -2 2 -3 2 -3 2 -2 1 -3 2 -3 2 -2 2 -3 2 -3 1 -2 2 -3 2 -3 2 -2 2 -3 2 -3 1 -2 2 -3 2 -3 2 -2 2 -3 2 -3 2 -2 2 -3 2 -3 1 -3 2 -2 2 -3 2 -3 2 -2 2 -3 2 -3 2 -2 2 -3 2 -3 2 -2 2 -3 2 -3 2 -2 2 -3 2 -3 2 -2 2 -3 2 -3 2 -2 2 -3 3 -3 2 -2 2 -3 2 -3 2 -2 2 -3 2 -3 2 -3 2 -2 3 -3 2 -3 2 -2 2 -3 2 -3 3 -2 2 -3 2 -3 2 4902 3792 100 MP stroke -2 2 -3 3 -3 2 -2 2 -3 2 -3 3 -2 2 -3 2 -3 3 -2 2 -3 2 -3 3 -2 2 -3 2 -3 3 -2 2 -3 2 -3 3 -2 2 -3 3 -3 2 -3 3 -2 2 -3 3 -3 2 -2 2 -3 3 -3 2 -2 3 -3 3 -3 2 -2 3 -3 2 -3 3 -2 2 -3 3 -3 3 -2 2 -3 3 -3 2 -2 3 -3 3 -3 2 -2 3 -3 3 -3 2 -2 3 -3 3 -3 3 -3 2 -2 3 -3 3 -3 3 -2 3 -3 2 -3 3 -2 3 -3 3 -3 3 -2 3 -3 3 -3 3 -2 2 -3 3 -3 3 -2 3 -3 3 -3 3 -2 3 -3 3 -3 3 -2 3 -3 4 -3 3 -2 3 -3 3 -3 3 -2 3 -3 3 -3 3 -3 4 -2 3 -3 3 -3 3 -2 4 -3 3 -3 3 -2 3 -3 4 -3 3 -2 3 -3 4 -3 3 -2 3 -3 4 -3 3 -2 4 -3 3 -3 4 5167 3515 100 MP stroke -2 3 -3 4 -3 3 -2 4 -3 3 -3 4 -2 4 -3 3 -3 4 -3 4 -2 3 -3 4 -3 4 -2 3 -3 4 -3 4 -2 4 -3 4 -3 3 -2 4 -3 4 -3 4 -2 4 -3 4 -3 4 -2 4 -3 4 -3 4 -2 4 -3 4 -3 4 -2 4 -3 4 -3 4 -2 5 -3 4 -3 4 -2 4 -3 5 -3 4 -3 4 -2 5 -3 4 -3 4 -2 5 -3 4 -3 5 -2 4 -3 5 -3 4 -2 5 -3 4 -3 5 -2 5 -3 4 -3 5 -2 5 -3 5 -3 4 -2 5 -3 5 -3 5 -2 5 -3 5 -3 5 -2 5 -3 5 -3 5 -3 5 -2 5 -3 5 -3 5 -2 5 -3 6 -3 5 -2 5 -3 6 -3 5 -2 5 -3 6 -3 5 -2 6 -3 5 -3 6 -2 6 -3 5 -3 6 -2 6 -3 5 -3 6 -2 6 -3 6 -3 6 -2 6 -3 6 -3 6 -2 6 -3 6 -3 6 5432 3056 100 MP stroke -3 6 -2 6 -3 7 -3 6 -2 6 -3 7 -3 6 -2 6 -3 7 -3 7 -2 6 -3 7 -3 6 -2 7 -3 7 -3 7 -2 7 -3 7 -3 7 -2 7 -3 7 -3 7 -2 7 -3 7 -3 8 -2 7 -3 7 -3 8 -3 7 -2 8 -3 7 -3 8 -2 8 -3 8 -3 7 -2 8 -3 8 -3 8 -2 8 -3 8 -3 9 -2 8 -3 8 -3 9 -2 8 -3 8 -3 9 -2 9 -3 8 -3 9 -2 9 -3 9 -3 9 -2 9 -3 9 -3 9 -3 10 -2 9 -3 9 -3 10 -2 9 -3 10 -3 10 -2 10 -3 10 -3 10 -2 10 -3 10 -3 10 -2 10 -3 11 -3 10 -2 11 -3 11 -3 10 -2 11 -3 11 -3 11 -2 11 -3 12 -3 11 -2 12 -3 11 -3 12 -2 12 -3 11 -3 12 -3 13 -2 12 -3 12 -3 13 -2 12 -3 13 -3 13 -2 12 -3 14 -3 13 -2 13 -3 13 5697 2154 100 MP stroke -3 14 -2 14 -3 13 -3 14 -2 14 -3 15 -3 14 -2 15 -3 14 -3 15 -2 15 -3 15 -3 15 -2 16 -3 15 -3 16 -3 16 -2 16 -3 16 -3 17 -2 17 -3 16 -3 17 -2 17 -3 18 -3 17 -2 18 -3 18 -3 18 -2 18 -3 19 -3 19 -2 19 -3 19 -3 19 -2 20 -3 20 -3 20 -2 20 -3 21 -3 21 -2 21 -3 21 -3 22 -2 22 -3 22 -3 22 -3 23 -2 23 -3 23 -3 24 -2 24 -3 24 -3 24 -2 25 -3 25 -3 26 -2 25 -3 27 -3 26 -2 27 -3 27 -3 28 -2 28 -3 28 -3 29 -2 29 -3 30 -3 30 -2 31 -3 30 -3 32 -2 32 -3 32 -3 33 -3 33 -2 34 -3 34 -3 35 -2 36 -3 36 -3 36 -2 37 -3 38 -3 39 -2 39 -3 39 -3 41 -2 41 -3 41 -3 42 -2 43 -2 25 5945 -100 94 MP stroke gr 3546 4901 mt (c) s 642 2554 mt -90 rotate (ur) s 90 rotate 3507 292 mt (\(c\)) s 1969 4416 mt (D-) s 4915 4416 mt (D+) s 1969 3450 mt (U-) s 4915 3450 mt (U+) s end eplot epage end showpage %%EndDocument @endspecial 1106 2121 a Fn(Figure)27 b(7:)36 b(Kinetic)28 b(relation)e(for)h(Jin-Xin's)h(mo)r(del.)515 4727 y @beginspecial 0 @llx 0 @lly 452 @urx 465 @ury 2267 @rwi 2834 @rhi @setspecial %%BeginDocument: j2.eps %Magnification: 1.00 /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -89.0 473.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawSplineSection { /y3 exch def /x3 exch def /y2 exch def /x2 exch def /y1 exch def /x1 exch def /xa x1 x2 x1 sub 0.666667 mul add def /ya y1 y2 y1 sub 0.666667 mul add def /xb x3 x2 x3 sub 0.666667 mul add def /yb y3 y2 y3 sub 0.666667 mul add def x1 y1 lineto xa ya xb yb x3 y3 curveto } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin 10 setmiterlimit n 0 792 m 0 0 l 612 0 l 612 792 l cp clip 0.06000 0.06000 sc 7.500 slw % Polyline n 2550 5700 m 2550 5625 l 2625 5700 l 2625 5550 l 2775 5550 l gs col-1 s gr % Polyline n 2400 5550 m 2400 5700 l gs col-1 s gr % Polyline n 2325 5625 m 2475 5625 l gs col-1 s gr % Polyline n 2325 5700 m 2475 5700 l gs col-1 s gr % Polyline n 6150 2475 m 6300 2475 l gs col-1 s gr % Polyline n 6225 2400 m 6225 2550 l gs col-1 s gr % Polyline n 6150 2550 m 6300 2550 l gs col-1 s gr % Polyline [66.7] 0 sd n 4725 2625 m 6450 1950 l gs col-1 s gr [] 0 sd % Polyline [66.7] 0 sd n 5625 2775 m 4350 3225 l gs col-1 s gr [] 0 sd % Polyline n 2400 7200 m 4800 2400 l 5400 3000 l 7800 600 l gs col-1 s gr % Open spline gs clippath 3570 297 m 3600 177 l 3630 297 l 3630 135 l 3570 135 l cp clip n 3600.0 150.0 m 3600.0 4012.5 l 3600.0 7875.0 l gs col-1 s gr gr % arrowhead n 3570 297 m 3600 177 l 3630 297 l 3600 297 l 3570 297 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs clippath 8853 4770 m 8973 4800 l 8853 4830 l 9015 4830 l 9015 4770 l cp clip n 1500.0 4800.0 m 5250.0 4800.0 l 9000.0 4800.0 l gs col-1 s gr gr % arrowhead n 8853 4770 m 8973 4800 l 8853 4830 l 8853 4800 l 8853 4770 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs [66.7] 0 sd n 7350.0 1050.0 m 5025.0 3825.0 l 2700.0 6600.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 3300.0 5400.0 m 3112.5 5775.0 l 2925.0 6150.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 5850.0 2550.0 m 6112.5 2287.5 l 6375.0 2025.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 4800.0 4725.0 m 4800.0 4762.5 l 4800.0 4800.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 6000.0 4725.0 m 6000.0 4762.5 l 6000.0 4800.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 7200.0 4725.0 m 7200.0 4762.5 l 7200.0 4800.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 3600.0 2400.0 m 3637.5 2400.0 l 3675.0 2400.0 l gs col-1 s gr gr [] 0 sd % Open spline gs [66.7] 0 sd n 3600.0 3600.0 m 3637.5 3600.0 l 3675.0 3600.0 l gs col-1 s gr gr [] 0 sd % Open spline gs clippath 4760 3921 m 4858 3846 l 4807 3959 l 4908 3832 l 4861 3795 l cp clip n 4575.0 4200.0 m 4725.0 4012.5 l 4875.0 3825.0 l gs col-1 s gr gr % arrowhead n 4760 3921 m 4858 3846 l 4807 3959 l 4783 3940 l 4760 3921 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs clippath 4837 4250 m 4741 4328 l 4789 4214 l 4692 4344 l 4740 4380 l cp clip n 4950.0 4050.0 m 4837.5 4200.0 l 4725.0 4350.0 l gs col-1 s gr gr % arrowhead n 4837 4250 m 4741 4328 l 4789 4214 l 4813 4232 l 4837 4250 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs clippath 3018 5807 m 2937 5900 l 2964 5780 l 2891 5925 l 2945 5952 l cp clip 3058 5593 m 3137 5499 l 3111 5620 l 3184 5475 l 3130 5448 l cp clip n 3150.0 5475.0 m 3037.5 5700.0 l 2925.0 5925.0 l gs col-1 s gr gr % arrowhead n 3058 5593 m 3137 5499 l 3111 5620 l 3084 5607 l 3058 5593 l cp gs 0.00 setgray ef gr col-1 s % arrowhead n 3018 5807 m 2937 5900 l 2964 5780 l 2991 5794 l 3018 5807 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs clippath 6200 2392 m 6094 2455 l 6158 2350 l 6043 2464 l 6086 2507 l cp clip 6250 2258 m 6355 2194 l 6292 2300 l 6407 2186 l 6364 2143 l cp clip n 6375.0 2175.0 m 6225.0 2325.0 l 6075.0 2475.0 l gs col-1 s gr gr % arrowhead n 6250 2258 m 6355 2194 l 6292 2300 l 6271 2279 l 6250 2258 l cp gs 0.00 setgray ef gr col-1 s % arrowhead n 6200 2392 m 6094 2455 l 6158 2350 l 6179 2371 l 6200 2392 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs n 3600.0 1200.0 m 3637.5 1200.0 l 3675.0 1200.0 l gs col-1 s gr gr % Open spline gs [66.7] 0 sd n 4650.0 2700.0 m 5137.5 2700.0 l 5625.0 2700.0 l gs col-1 s gr gr [] 0 sd % Open spline gs clippath 5393 2285 m 5270 2301 l 5370 2230 l 5220 2290 l 5242 2345 l cp clip n 5620.0 2162.0 m 5432.5 2237.0 l 5245.0 2312.0 l gs col-1 s gr gr % arrowhead n 5393 2285 m 5270 2301 l 5370 2230 l 5381 2257 l 5393 2285 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs clippath 5557 2365 m 5679 2348 l 5580 2420 l 5730 2360 l 5708 2305 l cp clip n 5330.0 2488.0 m 5517.5 2413.0 l 5705.0 2338.0 l gs col-1 s gr gr % arrowhead n 5557 2365 m 5679 2348 l 5580 2420 l 5569 2393 l 5557 2365 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs clippath 4943 2960 m 4820 2976 l 4920 2905 l 4770 2965 l 4792 3020 l cp clip n 5170.0 2837.0 m 4982.5 2912.0 l 4795.0 2987.0 l gs col-1 s gr gr % arrowhead n 4943 2960 m 4820 2976 l 4920 2905 l 4931 2932 l 4943 2960 l cp gs 0.00 setgray ef gr col-1 s % Open spline gs clippath 5037 3053 m 5159 3036 l 5060 3108 l 5210 3048 l 5188 2993 l cp clip n 4810.0 3176.0 m 4997.5 3101.0 l 5185.0 3026.0 l gs col-1 s gr gr % arrowhead n 5037 3053 m 5159 3036 l 5060 3108 l 5049 3081 l 5037 3053 l cp gs 0.00 setgray ef gr col-1 s /Symbol ff 300.00 scf sf 3750 525 m gs 1 -1 sc (s) col-1 sh gr /Times-Roman ff 300.00 scf sf 3975 525 m gs 1 -1 sc (\(u\)) col-1 sh gr /Times-Roman ff 300.00 scf sf 8500 5175 m gs 1 -1 sc (u) col-1 sh gr /Times-Roman ff 180.00 scf sf 4800 5025 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 180.00 scf sf 3375 2400 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 180.00 scf sf 3375 3600 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 180.00 scf sf 6000 5100 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 180.00 scf sf 7200 5100 m gs 1 -1 sc (3) col-1 sh gr /Times-Roman ff 180.00 scf sf 4500 4050 m gs 1 -1 sc (S+) col-1 sh gr /Times-Roman ff 180.00 scf sf 4875 4350 m gs 1 -1 sc (S-) col-1 sh gr /Times-Roman ff 180.00 scf sf 6375 2550 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 180.00 scf sf 2700 5775 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 180.00 scf sf 3375 1200 m gs 1 -1 sc (3) col-1 sh gr /Symbol ff 180.00 scf sf 5250 3075 m gs 1 -1 sc (y) col-1 sh gr /Symbol ff 180.00 scf sf 5625 2850 m gs 1 -1 sc (y) col-1 sh gr /Times-Roman ff 120.00 scf sf 4950 2475 m gs 1 -1 sc ( 0) col-1 sh gr /Times-Roman ff 120.00 scf sf 4575 2700 m gs 1 -1 sc ( 1) col-1 sh gr /Symbol ff 180.00 scf sf 4500 2625 m gs 1 -1 sc (j) col-1 sh gr /Symbol ff 180.00 scf sf 4875 2400 m gs 1 -1 sc (j) col-1 sh gr /Symbol ff 180.00 scf sf 6300 1875 m gs 1 -1 sc (j) col-1 sh gr /Times-Roman ff 120.00 scf sf 6375 1950 m gs 1 -1 sc ( 2) col-1 sh gr /Times-Roman ff 120.00 scf sf 5775 2925 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 120.00 scf sf 5400 3150 m gs 1 -1 sc (0) col-1 sh gr /Symbol ff 180.00 scf sf 4200 3150 m gs 1 -1 sc (y) col-1 sh gr /Times-Roman ff 120.00 scf sf 4350 3225 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 180.00 scf sf 4875 2850 m gs 1 -1 sc (D+) col-1 sh gr /Times-Roman ff 180.00 scf sf 4875 3300 m gs 1 -1 sc (D-) col-1 sh gr /Times-Roman ff 180.00 scf sf 5325 2175 m gs 1 -1 sc (U+) col-1 sh gr /Times-Roman ff 180.00 scf sf 5400 2625 m gs 1 -1 sc (U-) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1078 4909 a(Figure)f(8:)37 b(Elemen)n(tary)26 b(w)n(a)n(v)n(es)g(in)i(Jin-Xin's)f(mo)r(del.)1905 5255 y(29)p eop %%Page: 30 30 30 29 bop 516 2410 a @beginspecial 0 @llx 0 @lly 277 @urx 479 @ury 1700 @rwi 2267 @rhi @setspecial %%BeginDocument: j3.eps %Magnification: 1.00 /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -107.0 568.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin 10 setmiterlimit n 0 792 m 0 0 l 612 0 l 612 792 l cp clip 0.06000 0.06000 sc 7.500 slw % Polyline gs clippath 2670 1647 m 2700 1527 l 2730 1647 l 2730 1485 l 2670 1485 l cp clip n 2700 1500 m 2700 9375 l gs col-1 s gr gr % arrowhead n 2670 1647 m 2700 1527 l 2730 1647 l col-1 s 0.000 slw % Polyline [33.3] 0 sd n 3900 1800 m 3900 9300 l [] 0 sd % Polyline [33.3] 0 sd n 3900 1800 m 3900 9000 l [] 0 sd % Polyline [33.3] 0 sd n 3900 1800 m 3900 9075 l 3900 9300 l [] 0 sd 7.500 slw % Polyline n 4500 1575 m 4500 9300 l gs col-1 s gr % Polyline n 3900 6900 m 2100 9450 l gs col-1 s gr % Polyline [66.7] 0 sd n 3900 6900 m 2700 5175 l gs col-1 s gr [] 0 sd % Polyline [66.7] 0 sd n 2700 5175 m 4500 3375 l gs col-1 s gr [] 0 sd % Polyline n 4500 3375 m 5700 2175 l gs col-1 s gr % Polyline gs clippath 6228 5670 m 6348 5700 l 6228 5730 l 6390 5730 l 6390 5670 l cp clip n 1800 5700 m 6375 5700 l gs col-1 s gr gr % arrowhead n 6228 5670 m 6348 5700 l 6228 5730 l col-1 s % Polyline [15 50.0] 50.0 sd n 3675 1650 m 3675 9300 l gs col-1 s gr [] 0 sd % Polyline n 3900 1575 m 3900 9300 l gs col-1 s gr % Polyline [66.7] 0 sd n 3675 6525 m 4800 6525 l gs col-1 s gr [] 0 sd % Polyline [15 50.0] 50.0 sd n 4800 1725 m 4800 9375 l gs col-1 s gr [] 0 sd % Polyline n 4500 6825 m 5700 5625 l gs col-1 s gr 0.000 slw % Polyline [33.3] 0 sd n 5100 1800 m 5100 9300 l [] 0 sd 7.500 slw % Polyline n 2100 9450 m 3900 6900 l 3900 6150 l 2100 8775 l gs 0.95 setgray ef gr gs col-1 s gr /Times-Roman ff 300.00 scf sf 2925 1800 m gs 1 -1 sc (v) col-1 sh gr /Times-Roman ff 300.00 scf sf 6075 6000 m gs 1 -1 sc (u) col-1 sh gr /Times-Roman ff 180.00 scf sf 3075 5700 m gs 1 -1 sc (\(-\)) col-1 sh gr /Times-Roman ff 180.00 scf sf 4650 5925 m gs 1 -1 sc (1.732) col-1 sh gr /Times-Roman ff 180.00 scf sf 3950 5925 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 180.00 scf sf 4225 5925 m gs 1 -1 sc (1.5) col-1 sh gr /Times-Roman ff 180.00 scf sf 3450 5925 m gs 1 -1 sc (0.866) col-1 sh gr /Times-Roman ff 900.00 scf sf 2850 9225 m gs 1 -1 sc (A) col-1 sh gr /Times-Roman ff 900.00 scf sf 2025 4500 m gs 1 -1 sc (E) col-1 sh gr /Times-Roman ff 900.00 scf sf 4725 2325 m gs 1 -1 sc (D) col-1 sh gr /Times-Roman ff 900.00 scf sf 4725 4800 m gs 1 -1 sc (C) col-1 sh gr /Times-Roman ff 900.00 scf sf 4725 8325 m gs 1 -1 sc (B) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1445 w @beginspecial 0 @llx 0 @lly 315 @urx 493 @ury 1700 @rwi 2267 @rhi @setspecial %%BeginDocument: j4.eps %Magnification: 1.00 /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -66.0 564.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin 10 setmiterlimit n 0 792 m 0 0 l 612 0 l 612 792 l cp clip 0.06000 0.06000 sc % Polyline [33.3] 0 sd n 5100 1800 m 5100 9300 l [] 0 sd % Polyline [33.3] 0 sd n 3900 1800 m 3900 9300 l [] 0 sd % Polyline [33.3] 0 sd n 3900 1800 m 3900 9000 l [] 0 sd % Polyline [33.3] 0 sd n 3900 1800 m 3900 9075 l 3900 9300 l [] 0 sd 7.500 slw % Polyline n 3900 1575 m 3900 9300 l gs col-1 s gr % Polyline n 4500 1575 m 4500 9300 l gs col-1 s gr % Polyline [66.7] 0 sd n 5400 6900 m 2700 4200 l 4500 2400 l gs col-1 s gr [] 0 sd % Polyline n 4500 2400 m 5700 1200 l gs col-1 s gr % Polyline n 3900 2625 m 1875 5325 l gs col-1 s gr % Polyline gs clippath 6178 6870 m 6298 6900 l 6178 6930 l 6340 6930 l 6340 6870 l cp clip n 1125 6900 m 6325 6900 l gs col-1 s gr gr % arrowhead n 6178 6870 m 6298 6900 l 6178 6930 l col-1 s % Polyline [15 50.0] 50.0 sd n 3675 1650 m 3675 9300 l gs col-1 s gr [] 0 sd % Polyline [15 50.0] 50.0 sd n 4800 1650 m 4800 9300 l gs col-1 s gr [] 0 sd % Polyline n 4500 6600 m 5700 5400 l gs col-1 s gr % Polyline n 4500 6000 m 5700 4800 l gs col-1 s gr % Polyline [66.7] 0 sd n 4800 6300 m 3675 6300 l gs col-1 s gr [] 0 sd % Polyline n 3936 6027 m 1911 8727 l gs col-1 s gr % Polyline gs clippath 2670 1647 m 2700 1527 l 2730 1647 l 2730 1485 l 2670 1485 l cp clip n 2700 1500 m 2700 9375 l gs col-1 s gr gr % arrowhead n 2670 1647 m 2700 1527 l 2730 1647 l col-1 s % Polyline n 5700 4800 m 4500 6000 l 4500 6600 l 5700 5400 l gs 0.95 setgray ef gr gs col-1 s gr /Times-Roman ff 300.00 scf sf 2925 1800 m gs 1 -1 sc (v) col-1 sh gr /Times-Roman ff 180.00 scf sf 3300 7200 m gs 1 -1 sc (0.75) col-1 sh gr /Times-Roman ff 180.00 scf sf 3800 7200 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 180.00 scf sf 4225 7200 m gs 1 -1 sc (1.5) col-1 sh gr /Times-Roman ff 180.00 scf sf 5000 7200 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 180.00 scf sf 5400 6825 m gs 1 -1 sc (\(-\)) col-1 sh gr /Times-Roman ff 300.00 scf sf 6075 7200 m gs 1 -1 sc (u) col-1 sh gr /Times-Roman ff 900.00 scf sf 1950 6600 m gs 1 -1 sc (H) col-1 sh gr /Times-Roman ff 900.00 scf sf 1950 3600 m gs 1 -1 sc (K) col-1 sh gr /Times-Roman ff 900.00 scf sf 3150 8925 m gs 1 -1 sc (F) col-1 sh gr /Times-Roman ff 900.00 scf sf 5175 7950 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 900.00 scf sf 4800 4350 m gs 1 -1 sc (G) col-1 sh gr /Times-Roman ff 900.00 scf sf 4800 1800 m gs 1 -1 sc (J) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 642 2592 a Fn(Figure)27 b(9:)36 b(Riemann)28 b(problem)f(for)g(Jin-Xin's)h(mo)r(del:)37 b Fl(u)2489 2604 y Fi(\000)2567 2592 y Fl(<)23 b Fn(1,)k(and)h Fl(u)2957 2604 y Fi(\000)3035 2592 y Fl(>)23 b Fn(1)p Fl(:)p Fn(5.)515 4728 y @beginspecial 62 @llx 201 @lly 546 @urx 601 @ury 3401 @rwi 2267 @rhi @setspecial %%BeginDocument: j5.eps % MathWorks dictionary /MathWorks 150 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 531 132 5805 4798 MR c np 88 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6912 5185 PR 6 w 0 4225 2260 0 0 -4225 3994 4613 4 MP PP -2260 0 0 4225 2260 0 0 -4225 3994 4613 5 MP stroke DO 4 w SO 6 w 0 sg 3994 4613 mt 6254 4613 L 3994 388 mt 6254 388 L 3994 4613 mt 3994 388 L 6254 4613 mt 6254 388 L 3994 4613 mt 6254 4613 L 3994 4613 mt 3994 388 L 3994 4613 mt 3994 4571 L 3994 388 mt 3994 430 L /Helvetica /ISOLatin1Encoding 120 FMSR 3891 4759 mt (-2) s 4559 4613 mt 4559 4571 L 4559 388 mt 4559 430 L 4456 4759 mt (-1) s 5124 4613 mt 5124 4571 L 5124 388 mt 5124 430 L 5091 4759 mt (0) s 5689 4613 mt 5689 4571 L 5689 388 mt 5689 430 L 5656 4759 mt (1) s 6254 4613 mt 6254 4571 L 6254 388 mt 6254 430 L 6221 4759 mt (2) s 3994 4613 mt 4036 4613 L 6254 4613 mt 6212 4613 L 3823 4657 mt (-1) s 3994 4191 mt 4036 4191 L 6254 4191 mt 6212 4191 L 3723 4235 mt (-0.9) s 3994 3768 mt 4036 3768 L 6254 3768 mt 6212 3768 L 3723 3812 mt (-0.8) s 3994 3346 mt 4036 3346 L 6254 3346 mt 6212 3346 L 3723 3390 mt (-0.7) s 3994 2923 mt 4036 2923 L 6254 2923 mt 6212 2923 L 3723 2967 mt (-0.6) s 3994 2501 mt 4036 2501 L 6254 2501 mt 6212 2501 L 3723 2545 mt (-0.5) s 3994 2078 mt 4036 2078 L 6254 2078 mt 6212 2078 L 3723 2122 mt (-0.4) s 3994 1655 mt 4036 1655 L 6254 1655 mt 6212 1655 L 3723 1699 mt (-0.3) s 3994 1233 mt 4036 1233 L 6254 1233 mt 6212 1233 L 3723 1277 mt (-0.2) s 3994 811 mt 4036 811 L 6254 811 mt 6212 811 L 3723 855 mt (-0.1) s 3994 388 mt 4036 388 L 6254 388 mt 6212 388 L 3893 432 mt (0) s 3994 4613 mt 6254 4613 L 3994 388 mt 6254 388 L 3994 4613 mt 3994 388 L 6254 4613 mt 6254 388 L gs 3994 388 2261 4226 MR c np DA 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 5125 4613 100 MP stroke 11 4225 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 4007 388 100 MP stroke 12 0 3995 388 2 MP stroke SO 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 1 11 1 11 4 12 9 11 19 11 34 12 53 11 72 11 85 12 87 11 80 11 64 11 46 12 30 11 17 11 9 12 5 11 2 11 0 12 1 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 5125 3994 100 MP stroke 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 2 11 3 11 9 12 21 11 44 11 87 12 153 11 244 11 347 12 445 11 504 11 505 11 441 12 338 11 225 11 130 12 66 11 28 11 10 12 3 11 1 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 4007 388 100 MP stroke 12 0 3995 388 2 MP stroke gr 5052 292 mt (\(b\)) s 5094 4901 mt (x) s 1 sg 0 425 781 0 0 -425 5335 917 4 MP PP -781 0 0 425 781 0 0 -425 5335 917 5 MP stroke DO 4 w SO 6 w 0 sg 5335 917 mt 6116 917 L 5335 492 mt 6116 492 L 5335 917 mt 5335 492 L 6116 917 mt 6116 492 L 5335 917 mt 6116 917 L 5335 917 mt 5335 492 L 5335 917 mt 6116 917 L 5335 492 mt 6116 492 L 5335 917 mt 5335 492 L 6116 917 mt 6116 492 L 5674 678 mt (v\(0,x\)) s gs 5335 492 782 426 MR c np DA 181 0 5380 634 2 MP stroke gr DA 5674 819 mt (v\(1,x\)) s gs 5335 492 782 426 MR c np SO 181 0 5380 775 2 MP stroke gr SO 1 sg 0 4225 2259 0 0 -4225 898 4613 4 MP PP -2259 0 0 4225 2259 0 0 -4225 898 4613 5 MP stroke DO 4 w SO 6 w 0 sg 898 4613 mt 3157 4613 L 898 388 mt 3157 388 L 898 4613 mt 898 388 L 3157 4613 mt 3157 388 L 898 4613 mt 3157 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4571 L 898 388 mt 898 430 L 795 4759 mt (-2) s 1463 4613 mt 1463 4571 L 1463 388 mt 1463 430 L 1360 4759 mt (-1) s 2028 4613 mt 2028 4571 L 2028 388 mt 2028 430 L 1995 4759 mt (0) s 2592 4613 mt 2592 4571 L 2592 388 mt 2592 430 L 2559 4759 mt (1) s 3157 4613 mt 3157 4571 L 3157 388 mt 3157 430 L 3124 4759 mt (2) s 898 4613 mt 940 4613 L 3157 4613 mt 3115 4613 L 697 4657 mt (0.2) s 898 4085 mt 940 4085 L 3157 4085 mt 3115 4085 L 697 4129 mt (0.3) s 898 3557 mt 940 3557 L 3157 3557 mt 3115 3557 L 697 3601 mt (0.4) s 898 3029 mt 940 3029 L 3157 3029 mt 3115 3029 L 697 3073 mt (0.5) s 898 2500 mt 940 2500 L 3157 2500 mt 3115 2500 L 697 2544 mt (0.6) s 898 1972 mt 940 1972 L 3157 1972 mt 3115 1972 L 697 2016 mt (0.7) s 898 1444 mt 940 1444 L 3157 1444 mt 3115 1444 L 697 1488 mt (0.8) s 898 916 mt 940 916 L 3157 916 mt 3115 916 L 697 960 mt (0.9) s 898 388 mt 940 388 L 3157 388 mt 3115 388 L 797 432 mt (1) s 898 4613 mt 3157 4613 L 898 388 mt 3157 388 L 898 4613 mt 898 388 L 3157 4613 mt 3157 388 L gs 898 388 2260 4226 MR c np DA 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 2029 1444 100 MP stroke 11 -2641 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 911 4085 100 MP stroke 12 0 899 4085 2 MP stroke SO 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 1 11 4 12 8 11 17 11 30 12 47 11 63 11 75 11 78 12 70 11 57 11 40 12 27 11 15 11 8 12 4 11 2 11 0 11 1 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 2029 897 100 MP stroke 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 -1 12 0 11 -1 11 -3 12 -8 11 -18 11 -40 12 -76 11 -136 11 -215 11 -307 12 -393 11 -446 11 -446 12 -390 11 -298 11 -200 12 -115 11 -57 11 -25 11 -9 12 -3 11 -1 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 12 0 11 0 11 0 11 0 12 0 11 0 11 0 911 4085 100 MP stroke 12 0 899 4085 2 MP stroke gr 1998 4901 mt (x) s 1956 291 mt (\(a\)) s 1 sg 0 425 780 0 0 -425 2239 4509 4 MP PP -780 0 0 425 780 0 0 -425 2239 4509 5 MP stroke DO 4 w SO 6 w 0 sg 2239 4509 mt 3019 4509 L 2239 4084 mt 3019 4084 L 2239 4509 mt 2239 4084 L 3019 4509 mt 3019 4084 L 2239 4509 mt 3019 4509 L 2239 4509 mt 2239 4084 L 2239 4509 mt 3019 4509 L 2239 4084 mt 3019 4084 L 2239 4509 mt 2239 4084 L 3019 4509 mt 3019 4084 L 2577 4270 mt (u\(0,x\)) s gs 2239 4084 781 426 MR c np DA 181 0 2284 4226 2 MP stroke gr DA 2577 4411 mt (u\(1,x\)) s gs 2239 4084 781 426 MR c np SO 181 0 2284 4367 2 MP stroke gr SO end eplot epage end showpage %%EndDocument @endspecial 1008 4910 a(Figure)k(10:)36 b(Nucleation)27 b(criterion)f(for)i(Jin-Xin's)f(mo)r(del.)1905 5255 y(30)p eop %%Page: 31 31 31 30 bop 515 2410 a @beginspecial 62 @llx 201 @lly 550 @urx 609 @ury 3401 @rwi 2267 @rhi @setspecial %%BeginDocument: six5.eps % MathWorks dictionary /MathWorks 150 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 532 33 5854 4897 MR c np 88 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6912 5185 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke DO 4 w SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 120 FMSR 745 4759 mt (-2.5) s 1434 4613 mt 1434 4559 L 1434 388 mt 1434 442 L 1331 4759 mt (-2) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1816 4759 mt (-1.5) s 2505 4613 mt 2505 4559 L 2505 388 mt 2505 442 L 2402 4759 mt (-1) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2887 4759 mt (-0.5) s 3576 4613 mt 3576 4559 L 3576 388 mt 3576 442 L 3543 4759 mt (0) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 4029 4759 mt (0.5) s 4647 4613 mt 4647 4559 L 4647 388 mt 4647 442 L 4614 4759 mt (1) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5100 4759 mt (1.5) s 5718 4613 mt 5718 4559 L 5718 388 mt 5718 442 L 5685 4759 mt (2) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6171 4759 mt (2.5) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 697 4657 mt (0.6) s 898 4009 mt 952 4009 L 6254 4009 mt 6200 4009 L 697 4053 mt (0.8) s 898 3406 mt 952 3406 L 6254 3406 mt 6200 3406 L 797 3450 mt (1) s 898 2802 mt 952 2802 L 6254 2802 mt 6200 2802 L 697 2846 mt (1.2) s 898 2199 mt 952 2199 L 6254 2199 mt 6200 2199 L 697 2243 mt (1.4) s 898 1595 mt 952 1595 L 6254 1595 mt 6200 1595 L 697 1639 mt (1.6) s 898 992 mt 952 992 L 6254 992 mt 6200 992 L 697 1036 mt (1.8) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 797 432 mt (2) s 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 5188 1293 100 MP stroke 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 -1 11 0 11 0 10 -1 11 -1 11 -3 10 -3 11 -7 11 -10 11 -15 10 -24 11 -33 11 -47 10 -63 11 -74 11 -64 11 -47 10 -36 11 -23 11 -15 10 -10 11 -6 11 -2 11 -2 10 0 11 0 11 0 10 0 11 0 11 1 11 -1 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 -1 11 0 10 13 4128 1768 100 MP stroke 11 -135 11 -2557 10 136 11 -78 11 -73 11 38 10 17 11 -16 11 -2 10 5 11 0 11 -1 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 1 10 0 11 0 11 -1 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 -1 10 0 11 0 11 0 10 1 11 0 11 1 11 0 10 0 11 0 11 -1 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 3067 4434 100 MP stroke 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 1 11 0 11 1 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 1 10 3 11 7 11 13 11 23 10 40 11 64 11 83 10 67 11 45 11 29 11 19 10 11 2007 4027 100 MP stroke 11 8 11 4 10 2 11 2 11 1 11 0 10 0 11 0 11 1 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 946 4009 100 MP stroke 11 0 10 0 11 0 11 0 903 4009 5 MP stroke DA 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5721 1293 100 MP stroke 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5191 1293 100 MP stroke 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 -1 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 -1 6 0 5 0 5 0 6 -1 5 0 6 0 5 -1 5 0 6 -1 5 0 5 -1 6 -1 5 -1 5 0 6 -2 5 -1 5 -1 6 -1 5 -2 6 -2 5 -1 5 -2 6 -3 5 -2 5 -3 6 -3 5 -3 5 -3 6 -4 5 -4 5 -4 6 -4 5 -5 6 -5 5 -5 5 -6 6 -6 5 -6 5 -7 6 -7 5 -8 5 -7 6 -9 5 -8 5 -9 6 -9 5 -9 5 -10 6 -10 5 -10 6 -11 5 -10 5 -11 6 -11 5 -12 5 -11 6 -12 5 -11 5 -12 4661 1583 100 MP stroke 6 -11 5 -12 5 -12 6 -11 5 -12 6 -11 5 -11 5 -11 6 -11 5 -11 5 -10 6 -10 5 -10 5 -10 6 -9 5 -9 5 -8 6 -9 5 -7 6 -8 5 -7 5 -7 6 -6 5 -6 5 -6 6 -5 5 -5 5 -5 6 -4 5 -4 5 -4 6 -4 5 -3 6 -3 5 -2 5 -3 6 -2 5 -2 5 -2 6 -1 5 -2 5 -1 6 -1 5 -2 5 0 6 -1 5 -1 5 -1 6 0 5 -1 6 0 5 -1 5 0 6 0 5 0 5 -1 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 -1 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 4130 1880 100 MP stroke 5 0 5 0 6 0 5 0 5 1 6 -1 5 -27 6 -249 5 -836 5 -1052 6 -351 5 -42 5 -2 6 -1 5 -1 5 -1 6 1 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 3600 4441 100 MP stroke 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 3070 4441 100 MP stroke 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 2540 4441 100 MP stroke 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 1 5 0 5 0 6 0 5 0 6 0 5 1 5 0 6 0 5 1 5 0 6 1 5 0 5 1 6 0 5 1 5 1 6 1 5 1 6 1 5 2 5 1 6 2 5 2 5 2 6 2 5 2 5 2 6 3 5 3 5 3 6 4 5 3 6 4 5 4 5 5 6 4 5 5 5 5 6 6 5 5 5 6 6 6 5 7 5 7 6 6 5 8 6 7 5 7 5 8 6 8 5 8 5 8 6 9 5 8 5 8 6 9 5 8 5 9 6 9 5 8 5 9 6 8 5 8 6 9 5 8 5 8 6 7 2009 4151 100 MP stroke 5 8 5 7 6 8 5 7 5 6 6 7 5 6 5 6 6 6 5 6 6 5 5 5 5 5 6 4 5 5 5 4 6 3 5 4 5 3 6 3 5 3 5 3 6 3 5 2 6 2 5 2 5 2 6 2 5 1 5 2 6 1 5 1 5 1 6 1 5 1 5 1 6 0 5 1 6 0 5 1 5 0 6 1 5 0 5 0 6 1 5 0 5 0 6 0 5 1 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 1 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 1479 4009 100 MP stroke 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 6 0 5 0 949 4009 100 MP stroke 5 0 6 0 5 0 6 0 5 0 5 0 6 0 5 0 5 0 901 4009 10 MP stroke gr DA SO 1 sg 0 425 1683 0 0 -425 4433 917 4 MP PP -1683 0 0 425 1683 0 0 -425 4433 917 5 MP stroke DO 4 w SO 6 w 0 sg 4433 917 mt 6116 917 L 4433 492 mt 6116 492 L 4433 917 mt 4433 492 L 6116 917 mt 6116 492 L 4433 917 mt 6116 917 L 4433 917 mt 4433 492 L 4433 917 mt 6116 917 L 4433 492 mt 6116 492 L 4433 917 mt 4433 492 L 6116 917 mt 6116 492 L 5236 678 mt (lambda=1.6) s gs 4433 492 1684 426 MR c np 428 0 4540 634 2 MP stroke gr 5236 819 mt (lambda=10 ) s gs 4433 492 1684 426 MR c np DA 428 0 4540 775 2 MP stroke gr DA SO end eplot epage end showpage %%EndDocument @endspecial 670 2593 a Fn(Figure)27 b(11:)36 b(Comparison)26 b(b)r(et)n(w)n(een)h(the)h(six-sp)r(eed)f(mo)r(dels)h(with)g (di\013eren)n(t)g Fl(\025)p Fn(.)515 4727 y @beginspecial 62 @llx 201 @lly 550 @urx 600 @ury 3401 @rwi 2267 @rhi @setspecial %%BeginDocument: six2.eps % MathWorks dictionary /MathWorks 150 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 532 133 5854 4797 MR c np 88 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6912 5185 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke DO 4 w SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 120 FMSR 745 4759 mt (-2.5) s 1434 4613 mt 1434 4559 L 1434 388 mt 1434 442 L 1331 4759 mt (-2) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1816 4759 mt (-1.5) s 2505 4613 mt 2505 4559 L 2505 388 mt 2505 442 L 2402 4759 mt (-1) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2887 4759 mt (-0.5) s 3576 4613 mt 3576 4559 L 3576 388 mt 3576 442 L 3543 4759 mt (0) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 4029 4759 mt (0.5) s 4647 4613 mt 4647 4559 L 4647 388 mt 4647 442 L 4614 4759 mt (1) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5100 4759 mt (1.5) s 5718 4613 mt 5718 4559 L 5718 388 mt 5718 442 L 5685 4759 mt (2) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6171 4759 mt (2.5) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 697 4657 mt (0.7) s 898 4191 mt 952 4191 L 6254 4191 mt 6200 4191 L 697 4235 mt (0.8) s 898 3768 mt 952 3768 L 6254 3768 mt 6200 3768 L 697 3812 mt (0.9) s 898 3346 mt 952 3346 L 6254 3346 mt 6200 3346 L 797 3390 mt (1) s 898 2923 mt 952 2923 L 6254 2923 mt 6200 2923 L 697 2967 mt (1.1) s 898 2500 mt 952 2500 L 6254 2500 mt 6200 2500 L 697 2544 mt (1.2) s 898 2078 mt 952 2078 L 6254 2078 mt 6200 2078 L 697 2122 mt (1.3) s 898 1655 mt 952 1655 L 6254 1655 mt 6200 1655 L 697 1699 mt (1.4) s 898 1233 mt 952 1233 L 6254 1233 mt 6200 1233 L 697 1277 mt (1.5) s 898 811 mt 952 811 L 6254 811 mt 6200 811 L 697 855 mt (1.6) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 697 432 mt (1.7) s 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 5188 811 100 MP stroke 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 -1 11 0 10 0 11 0 11 0 11 0 10 -1 11 0 11 0 10 -1 11 0 11 0 11 -1 10 0 11 0 11 -1 10 0 11 0 11 -1 10 0 11 0 11 -1 11 0 10 0 11 0 11 0 10 0 11 0 11 1 11 0 10 0 11 1 11 1 10 0 11 1 11 1 11 1 10 2 11 1 11 2 10 1 11 2 11 2 11 2 10 2 11 2 11 2 10 2 11 2 11 2 11 2 10 2 11 2 11 2 10 2 11 2 11 2 11 1 10 2 11 1 11 2 10 1 11 1 11 1 11 1 10 1 11 1 11 1 10 0 11 1 11 0 11 1 10 0 11 1 11 0 10 0 11 1 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 1 10 0 11 0 11 0 11 0 10 0 4128 756 100 MP stroke 11 -1 11 0 10 0 11 -1 11 -2 11 -5 10 -12 11 -28 11 -66 10 -151 11 -339 11 -636 11 -879 10 -727 11 -408 11 -205 10 -103 11 -54 11 -29 11 -15 10 -7 11 -4 11 -1 10 -1 11 -1 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 -1 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 1 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 3067 4431 100 MP stroke 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 1 11 0 11 0 10 0 11 0 11 1 11 0 10 0 11 1 11 0 10 1 11 1 11 0 11 1 10 1 11 1 11 2 10 1 11 2 11 1 11 2 10 2 11 2 11 3 10 3 11 3 11 3 11 3 10 4 11 4 11 4 10 4 11 5 11 5 11 5 10 6 11 5 11 6 10 6 11 6 11 7 10 6 11 7 11 7 11 6 10 7 11 7 11 6 10 7 11 6 11 6 11 6 10 6 11 6 11 5 10 5 11 4 11 5 11 4 10 4 2007 4219 100 MP stroke 11 3 11 4 10 3 11 2 11 3 11 2 10 2 11 2 11 1 10 2 11 1 11 1 11 0 10 1 11 1 11 0 10 1 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 946 4190 100 MP stroke 11 0 10 0 11 0 11 0 903 4190 5 MP stroke DD 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 5188 811 100 MP stroke 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 -1 10 0 11 0 11 0 10 0 11 -1 11 0 11 0 10 -1 11 0 11 -1 10 0 11 -1 11 0 10 -1 11 0 11 -1 11 0 10 -1 11 0 11 -1 10 0 11 -1 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 1 10 0 11 1 11 0 10 1 11 1 11 1 11 1 10 2 11 1 11 1 10 2 11 1 11 1 11 2 10 1 11 2 11 1 10 1 11 2 11 1 11 1 10 1 11 1 11 1 10 1 11 1 11 0 11 1 10 0 11 1 11 0 10 1 11 0 11 0 11 1 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 1 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 4128 786 100 MP stroke 11 0 11 0 10 0 11 0 11 -1 11 0 10 -1 11 -5 11 -13 10 -38 11 -108 11 -304 11 -687 10 -1047 11 -794 11 -378 10 -157 11 -65 11 -28 11 -13 10 -6 11 -2 11 -1 10 -1 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 3067 4435 100 MP stroke 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 1 11 0 11 0 10 0 11 0 11 0 10 0 11 1 11 0 11 0 10 1 11 0 11 1 10 1 11 0 11 1 11 1 10 2 11 1 11 1 10 2 11 2 11 2 11 2 10 3 11 3 11 3 10 4 11 3 11 4 11 5 10 4 11 5 11 5 10 6 11 6 11 6 10 6 11 6 11 7 11 7 10 7 11 7 11 7 10 7 11 8 11 7 11 7 10 6 11 7 11 6 10 6 11 6 11 6 11 5 10 5 2007 4236 100 MP stroke 11 4 11 5 10 4 11 3 11 4 11 3 10 2 11 3 11 2 10 2 11 2 11 2 11 1 10 1 11 1 11 1 10 1 11 1 11 1 11 0 10 0 11 1 11 0 10 0 11 1 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 1 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 946 4190 100 MP stroke 11 0 10 0 11 0 11 0 903 4190 5 MP stroke DO 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 5188 811 100 MP stroke 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 -1 11 0 10 0 11 -1 11 0 11 -1 10 0 11 -1 11 -1 10 -1 11 -1 11 -1 10 -2 11 -1 11 -2 11 -2 10 -2 11 -3 11 -2 10 -3 11 -4 11 -3 11 -3 10 -4 11 -4 11 -4 10 -5 11 -4 11 -4 11 -5 10 -4 11 -5 11 -4 10 -4 11 -4 11 -4 11 -4 10 -3 11 -4 11 -3 10 -3 11 -2 11 -3 11 -2 10 -2 11 -1 11 -2 10 -1 11 -1 11 -1 11 -1 10 -1 11 0 11 -1 10 0 11 -1 11 0 11 0 10 0 11 -1 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 4128 938 100 MP stroke 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 -1 11 -1 10 -4 11 -23 11 -145 10 -602 11 -1363 11 -987 11 -307 10 -68 11 -12 11 -2 10 -1 11 0 11 -1 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 3067 4455 100 MP stroke 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 1 10 0 11 0 11 0 11 1 10 0 11 0 11 1 10 0 11 1 11 1 11 1 10 1 11 2 11 1 10 2 11 2 11 3 11 2 10 3 11 4 11 4 10 4 11 4 11 5 10 6 11 5 11 7 11 6 10 7 11 8 11 7 10 8 11 9 11 8 11 9 10 8 11 9 11 9 10 8 11 9 11 8 11 8 10 7 2007 4266 100 MP stroke 11 7 11 7 10 6 11 6 11 6 11 5 10 4 11 5 11 4 10 3 11 3 11 3 11 2 10 2 11 2 11 2 10 1 11 1 11 2 11 0 10 1 11 1 11 0 10 1 11 0 11 0 11 1 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 1 11 0 11 0 10 0 11 0 11 0 946 4190 100 MP stroke 11 0 10 0 11 0 11 0 903 4190 5 MP stroke gr DO 3546 4901 mt (x) s 643 2534 mt -90 rotate (u) s 90 rotate SO 1 sg 0 624 1350 0 0 -624 4766 4509 4 MP PP -1350 0 0 624 1350 0 0 -624 4766 4509 5 MP stroke DO 4 w SO 6 w 0 sg 4766 4509 mt 6116 4509 L 4766 3885 mt 6116 3885 L 4766 4509 mt 4766 3885 L 6116 4509 mt 6116 3885 L 4766 4509 mt 6116 4509 L 4766 4509 mt 4766 3885 L 4766 4509 mt 6116 4509 L 4766 3885 mt 6116 3885 L 4766 4509 mt 4766 3885 L 6116 4509 mt 6116 3885 L 5569 4085 mt (m1=0.5) s gs 4766 3885 1351 625 MR c np 428 0 4873 4041 2 MP stroke gr 5569 4241 mt (m1=0.3) s gs 4766 3885 1351 625 MR c np DD 428 0 4873 4197 2 MP stroke gr DD 5569 4397 mt (m1=0.1) s gs 4766 3885 1351 625 MR c np DO 428 0 4873 4353 2 MP stroke gr DO SO end eplot epage end showpage %%EndDocument @endspecial 639 4909 a(Figure)f(12:)36 b(Comparison)26 b(b)r(et)n(w)n(een)h(the)h(six-sp)r(eed)f(mo)r(dels)h(with)g (di\013eren)n(t)g Fl(m)3195 4921 y Ff(1)3232 4909 y Fn(.)1905 5255 y(31)p eop %%Page: 32 32 32 31 bop 530 3569 a @beginspecial 62 @llx 201 @lly 550 @urx 600 @ury 1700 @rwi 2267 @rhi @setspecial %%BeginDocument: six3.eps % MathWorks dictionary /MathWorks 150 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 532 133 5854 4797 MR c np 88 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6912 5185 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke DO 4 w SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 120 FMSR 745 4759 mt (-2.5) s 1434 4613 mt 1434 4559 L 1434 388 mt 1434 442 L 1331 4759 mt (-2) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1816 4759 mt (-1.5) s 2505 4613 mt 2505 4559 L 2505 388 mt 2505 442 L 2402 4759 mt (-1) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2887 4759 mt (-0.5) s 3576 4613 mt 3576 4559 L 3576 388 mt 3576 442 L 3543 4759 mt (0) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 4029 4759 mt (0.5) s 4647 4613 mt 4647 4559 L 4647 388 mt 4647 442 L 4614 4759 mt (1) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5100 4759 mt (1.5) s 5718 4613 mt 5718 4559 L 5718 388 mt 5718 442 L 5685 4759 mt (2) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6171 4759 mt (2.5) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 697 4657 mt (0.8) s 898 4191 mt 952 4191 L 6254 4191 mt 6200 4191 L 697 4235 mt (0.9) s 898 3768 mt 952 3768 L 6254 3768 mt 6200 3768 L 797 3812 mt (1) s 898 3346 mt 952 3346 L 6254 3346 mt 6200 3346 L 697 3390 mt (1.1) s 898 2923 mt 952 2923 L 6254 2923 mt 6200 2923 L 697 2967 mt (1.2) s 898 2501 mt 952 2501 L 6254 2501 mt 6200 2501 L 697 2545 mt (1.3) s 898 2078 mt 952 2078 L 6254 2078 mt 6200 2078 L 697 2122 mt (1.4) s 898 1656 mt 952 1656 L 6254 1656 mt 6200 1656 L 697 1700 mt (1.5) s 898 1233 mt 952 1233 L 6254 1233 mt 6200 1233 L 697 1277 mt (1.6) s 898 810 mt 952 810 L 6254 810 mt 6200 810 L 697 854 mt (1.7) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 697 432 mt (1.8) s 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 5188 811 100 MP stroke 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 -1 11 -1 11 -1 10 -1 11 -2 11 -3 10 -4 11 -4 11 -6 11 -8 10 -10 11 -11 11 -13 10 -15 11 -15 11 -14 11 -12 10 -11 11 -9 11 -8 10 -6 11 -5 11 -4 11 -3 10 -2 11 -2 11 -1 10 -1 11 0 11 -1 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 -1 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 4128 986 100 MP stroke 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 1 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 -3504 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 3067 4489 100 MP stroke 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 -1 11 0 11 0 10 0 11 -1 11 -1 11 -1 10 -2 11 -2 11 -4 10 -3 11 -5 11 -6 11 -8 10 -8 11 -10 11 -11 10 -12 11 -10 11 -9 11 -7 10 -6 2007 4596 100 MP stroke 11 -4 11 -4 10 -2 11 -2 11 -2 11 -1 10 -1 11 0 11 0 10 -1 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 946 4613 100 MP stroke 11 0 10 0 11 0 11 0 903 4613 5 MP stroke gr 3546 4901 mt (x) s 643 2534 mt -90 rotate (u) s 90 rotate 3504 292 mt (\(a\)) s end eplot epage end showpage %%EndDocument @endspecial 1445 w @beginspecial 62 @llx 201 @lly 550 @urx 600 @ury 1700 @rwi 2267 @rhi @setspecial %%BeginDocument: six4.eps % MathWorks dictionary /MathWorks 150 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 532 133 5854 4797 MR c np 88 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6912 5185 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke DO 4 w SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 120 FMSR 745 4759 mt (-2.5) s 1434 4613 mt 1434 4559 L 1434 388 mt 1434 442 L 1331 4759 mt (-2) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1816 4759 mt (-1.5) s 2505 4613 mt 2505 4559 L 2505 388 mt 2505 442 L 2402 4759 mt (-1) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2887 4759 mt (-0.5) s 3576 4613 mt 3576 4559 L 3576 388 mt 3576 442 L 3543 4759 mt (0) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 4029 4759 mt (0.5) s 4647 4613 mt 4647 4559 L 4647 388 mt 4647 442 L 4614 4759 mt (1) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5100 4759 mt (1.5) s 5718 4613 mt 5718 4559 L 5718 388 mt 5718 442 L 5685 4759 mt (2) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6171 4759 mt (2.5) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 697 4657 mt (0.7) s 898 4191 mt 952 4191 L 6254 4191 mt 6200 4191 L 697 4235 mt (0.8) s 898 3768 mt 952 3768 L 6254 3768 mt 6200 3768 L 697 3812 mt (0.9) s 898 3346 mt 952 3346 L 6254 3346 mt 6200 3346 L 797 3390 mt (1) s 898 2923 mt 952 2923 L 6254 2923 mt 6200 2923 L 697 2967 mt (1.1) s 898 2500 mt 952 2500 L 6254 2500 mt 6200 2500 L 697 2544 mt (1.2) s 898 2078 mt 952 2078 L 6254 2078 mt 6200 2078 L 697 2122 mt (1.3) s 898 1655 mt 952 1655 L 6254 1655 mt 6200 1655 L 697 1699 mt (1.4) s 898 1233 mt 952 1233 L 6254 1233 mt 6200 1233 L 697 1277 mt (1.5) s 898 811 mt 952 811 L 6254 811 mt 6200 811 L 697 855 mt (1.6) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 697 432 mt (1.7) s 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 5188 388 100 MP stroke 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 -1 11 0 10 0 11 -1 11 -1 10 -2 11 -3 11 -4 11 -5 10 -8 11 -10 11 -14 10 -18 11 -24 11 -31 11 -38 10 -45 11 -54 11 -62 10 -67 11 -63 11 -57 11 -51 10 -43 11 -37 11 -30 10 -24 11 -19 11 -14 11 -11 10 -8 11 -6 11 -4 10 -3 11 -2 11 -1 11 -1 10 -1 11 0 11 0 10 -1 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 4128 1152 100 MP stroke 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 -1 11 0 11 0 10 0 11 0 11 0 11 0 10 1 11 0 11 0 10 0 11 -2 11 -2 11 1 10 11 11 8 11 -4 10 -47 11 -68 11 -706 11 -2480 10 -81 11 -14 11 16 10 75 11 99 11 24 11 -12 10 -48 11 -68 11 -25 10 2 11 17 11 41 11 32 10 4 11 -6 11 -22 10 -27 11 -9 11 2 10 10 11 19 11 10 11 1 10 -4 11 -11 11 -10 10 -2 11 1 11 5 11 8 10 3 11 0 11 -2 10 -5 11 -4 11 0 11 1 10 2 11 4 11 1 10 0 11 -2 11 -2 11 -1 10 0 11 0 11 1 10 2 11 0 11 0 11 -1 10 -1 11 0 11 0 10 0 11 1 11 0 11 0 10 0 11 0 11 -1 10 0 11 0 11 0 3067 4418 100 MP stroke 11 1 10 0 11 0 11 0 10 0 11 -1 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 1 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 1 11 0 11 0 10 0 11 0 11 1 10 1 11 1 11 1 11 2 10 2 11 3 11 4 10 6 11 6 11 9 11 10 10 12 11 14 11 16 10 18 11 20 11 20 11 17 10 14 2007 4239 100 MP stroke 11 12 11 9 10 7 11 6 11 4 11 3 10 3 11 1 11 1 10 1 11 1 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 11 0 10 0 11 0 11 0 10 0 11 0 11 0 946 4191 100 MP stroke 11 0 10 0 11 0 11 0 903 4191 5 MP stroke gr 3504 292 mt (\(b\)) s end eplot epage end showpage %%EndDocument @endspecial 990 3751 a Fn(Figure)27 b(13:)36 b(Stationary)26 b(and)h(mo)n(ving)g(phase)g(b)r(oundaries.)1905 5255 y(32)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------9911210806273--