Cartesian Grid Adaption in CFD
45
0
0
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Cartesian grid adaption in CFD Marie-H´el`ene Lallemand. No 3406 Avril 98 ` THEME 4. ISSN 0249-6399. apport de recherche.
(3)
(4)
(5)
(6) !#"%$'&(*),+*-."0/1 ),)#"*23 4-65.7 8 94:<;>=@?ACB*DE;GF4HJILKMDENPOQ=RKSNUT KMDE;>DEVWILKMDENUO X =VMY*VZKM:<;=<V [<NU;T4HE=<\*=<V ]_^MN
(7) `a=RKcb0dLe fSILT4TgNU^MK X =c^Z=<[a94=<^Z[W9 =hOijdL?jk%lAmon*^MDEH.pUqrA?tsuTtILvU=<V wyx_zR{|P}t~P{%1=.T4^Z=<VM=<O*K6IVMDEO4v%HE= HN*[a cI X IPT KMDENUOuVMKM^aIPKZ=<vUYu,N%^odM[
(8) IL^MKM=RVMDJIPOv%^MD X V8 94=1I X IPT4KZDENUO T4^ZN*[<=<VMVuT4^MN*[<=R= X VcILVILOGDEOjKZ=<^IP[<=@ DEKM9GKZ94=c].@@.eSM BTtIL[W UILvU=UK IPHEHENP V6[<NUO*KZDO*F4N%F4V6^ZF4O4V NU^ F4O VMKM=I X Y0[IPHE[<F4HJIPKZDENUO4V *Y>^Z=<[<N%O4VMKZ^MF4[<KZDEO4vKM94=DEO*KM=R^MTgNUHJIPKZ= X VMN%HEF4KMDENUON%OKZ94=O4=R;>=<VZ9ILK =
(9) IP[a9 I X IPT4KZDENUO>VZKM=<T68.NTg=<^,N%^M;KM94=I X IPT4KZDENUOo%1= X =atO =QIO =<;=<KM^ZDE[StILVM= X NUOIPO X T4^MN%TtN%^MKZDN%OtIPH KZNcKZ94= S=RVMVMDJILOGNPKM94=F4O4 *O4NP OnUIP^ZDIL4HE=<V
(10) 8 94= I X ILT4KM= X vU^MD X DEV X =agO4= X *Y=RjF D X DVZKM^ZD F4KMDEO4vuKM94= O4N X =RV
(11) u8 94=DEO*KM=<^ZTtN%HILKM= X VMNUHEF4KZDENUODEVS[<N%;>T4F4KZ= X *YF VMDEO4vGDEKMVutIP^ZYj[R=<O*KM=<^@[<N*NU^ X DEOtIPKZ=<V@KMN%vU=<KZ94=<^ DEKM9DEKMVg^MVMK N%^ X =R^STtIL^MKMDJILH X =<^MDEnUILKMDEnU=<V *gW ¡g|U¢.zP£m X IPT4KZDEnU=6;=<KM94N X Pd¤¥¦[
(12) IP^ZKM=<VZDILO;>=RVM94=<VU§DEO4DEKM=1uD©¨ª=R^M=<O4[R=ILO X §DEO4DEKM=1.HE=<;=<O*K b=RKM94N X Vª]_c@.eSM B« E¬ o®¥¯°
(13) ± ®³²´E¯µ#¶<· ÊgÆPÆP¾U»,ÈRÈ<¸gÇUÄÁMºg¹.¹Zź,ÄPßP»#ÄP¼a¼<¹½WÅM¼RÆPÃP¾ÀĹ.¿<¼6ÅMÄPÈ<È<ÁMĺ#ÆPÁº#Ât»,»#¾À¼aáPÁM½<¼<ÆPÈR¿ÀÁg¾À¾ÀÂ#»¹MÁÄ ÇUÃP¹MÇP¼<»#¼<Ö ÄP»#Â4¾Àº#Âg¿À¾À¹¹oÃPÅMÚ6¹¼<¿À¿EÃP¼× ¹¥»#Øj»,¹tÁZ¹ZÃP¼<ÅMÆ ¿Àº#¾ÀÆPÂ#ÇP¼<¹M»#º,»ZÈa¾ÀÙ¤ÈRÉ,͹ZÄ6º*¹MÃP滅 ¹o˹ZÅZÌg»,¹ÅZÍo¾ÀÇP¹MÎJ»#Ö ÏGÈaÉ,¹MÐ@¹ZÄRºMº,Î,ÜaÂ4¸gÂ#¼R¼<Ñ0ÆPÄPÂ,ÂtÒaÂ#ÓRÈR¾PÔ<ÆPÚ Õ<áPÕ.Ì4¿À¾ÀÙ¹M¹Mº4Ûj»t¹³ÄPâÈRÙÏjÆPÞo¼RÂ4¹Z¿À¿À»,»,¹M¹Z¾ÀÅ<º#Ö ¼<Ü<ã<Ý«¹M¹»#Ù¤ÅMÃPÞ¾ÀÈ<¹¹MÄPŸgÂ*ßÞo¿Àº¼6ѹM¸gºoÐ È<¸Ö ÙPÖ ÆPÐ@¾P¾À¼<Â#ÄPÂ,»#ÈR¾Àº,ÈRÆP¾ÀÄÄ Â à¼äEÈ<ÆP»,ÄP¾P¿À¹.Â#Èaäºæåt¼<»#¹oÌgßPȹMÄP¾ÀÅMÂg¼<¾ÀÄPÂ#¾ à ÆP¹.º#È<ÆP¿À¹MÂÖ ÈÃPÆP¿À¹M Ã*× ¾ÀÄ
(14) º#¹M»æä¼<ÅZ¹ÄPÁMÅZ¹MÂ#Â,¼<¾À»#¹MÂZÙ à ç Ðc¼R»,¾À¹¥èÞ¹M¿À¹ZÄP¹<Ù Û*¼<¿À¿ ¹MÖ ¼aÄPäé¾ÀÄP»#¾À¼Ù ä». Unit´e de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) T´el´ephone : 01 39 63 55 11 - International : +33 1 39 63 55 11 T´el´ecopie : (33) 01 39 63 53 30 - International : +33 1 39 63 53 30.
(15) h@.
(16)
(17) .
(18) d¤¥ zo .HEHE =G=<VZKQSF4O KZDET4HDE^V <<VM=G=<O*n*KZD=GIF4F4O4O ==>VMDEKMO*^aKMIP=<K^¥< vUIPDE[<= =>XI n%I =<X [>ILT4HE=KWIL[<KMN DENUX O=;>]_cN%O4@NU. HeSN*M[@ TgB¦NUF4=<^KX Tt=<=<V@^Z;>v%^M=<DEK HEH=RXVS =a[
(19) ¨ªIL=R^M[<KKMRF4VMDE=R=<^ O4O4X =R=<VV [
(20) ILHE[<F4HEVRnUNUHEF4KZD©,V@TtIP^HJI^M=R[<NUO4VZKM^ZF4[<KMDEN%O X F O4=GVMN%HF KMDENUODEO*KM=<^ZTtN%H<=GVMF4^HE=GO4NUF nU=
(21) ILF;IPDEHEHJIPv%= [a9tILjF = <KaIPTg= X I X IPT KWIPKZDENUOo I X ILTtIPKZDN%O =<VZK=a¨ª=R[<KM F R= =<O3[IPHE[<F4HJIPO*KF4O4= ; <KZ^MDE*F4= X atO4DE= [<N%;>;!= <KWILO*KQT4^ZNUTgNU^ZKMDENUO4O =<HEH=GIPFu=<VMVZDE=<O X =<VDO [<NUO4O*F4=RV X F VZY*VMKM:R;>=U" oIv%^MDEHEHE= I X IPT4K <=>=RVMK =<O VMF4DEKM= X <KM=R^M;>DE O R=c=RO=RjF D^ <TtIL^MKMDEVZVWIPO*K HE=<V O #@F X V X F;IPDEHEHJIvU=U$ DEO*KM=R^MTgNUHJIPKZDN%O X =<VunUIP^MDJIL4HE=<V VZF4^H=O4N%F4nU=IPF3;IPDEHEHILvP=>=<VZK>[
(22) ILHE[<F4H <= H ILD X = X =<V[<N*N%^ X N%O4 O <=<VtIL^MY*[<=<O*KZ^MDE*F4=<V X = H ILO4[<DE=<O ;IPDEHEHILvU==<KSF KMDEHEDVZ=SVZ=<V X R^MDE%n <=RVSTtIL^MKMDE=<HEHE=<V T4^Z=<;>DE:<^Z=<V
(23) &uD©,¨¡gR{¤^Mz'=<'O4(~ [R') ¦=<V §oDEO4"b DE=<<VKZ494].N Xc=G@I .X euILT4M KWILBKMDEnU=U4b IPDEHEHILvU=<V [IP^MK <VMDE=<O Vrd¤¥4"b RKM94N X =<V X +* H <;=<O*KMVS§DEO4DEV =<K.
(24)
(25)
(26) . d. ..G"!"³ 8 94=T4F4^ZTtN%VM=GNL_KZ94DEV@^M=<TgNU^ZKcDEV@KMNT4^M=RVM=<O*KQIyVMDEO4vUHE= HN*[a 0I X ILT4KMDEN%OVZKM^aIPKM=RvUY ,NU^@dM[
(27) IL^MKM=RVMDJIPO v%^MD X VKMNt=@F4VZ= X jYGKZ94=SVZNP,K IP^Z=c].@@.eSM Bg].c@.euM BDV I §. VMNL,K IP^M=u9tIn*DEO4vQI D X = TtILO4=<H4NLtT49*Y*VMDE[
(28) ILHj;N X =<HEVoIPO XX =<n%NUKZ= X KZN@KM94=F4VM=NPgOjF ;>=<^ZD[IPHUVZDE;GF4HJIPKMDEN%O4VtVZF4[a9>IPV«,F4^MOgIP[<= ;NP X =RHHEDEO4vg
(29) =ROjn*DE^MN%O4;>=ROjKT4^MN%4HE=<;>VDO*KZ=<^MOtILH4NU^.=<\*KZ=<^MOtIL$H #gNP V_IL^MN%F4O X ;IPO*YuVMKM^ZF4[<KZF4^M=<&V %J F4DEH X DO vUV
(30) ;IP^MDEO4=VMKZ^MF4[RKMF4^Z=<VG=<KM[%E( '<«;GF4HEKMD© T 9tIPVZ&= #tNP T4^MN%4HE=<;>VgKMF4^Z4F4HE=<O*)K #gNP Vc=RKM[ M8 9tILKSVZNP,K IP^Z= 9tILV6g=<=<OG[a94NUVZ=<OGDEOKM9 =,^WIL;>=<NU^Z SNPKM9 =S6B4]6f 8 [<N%OjKZ^WIL[<K6bM* m %,bN X =<H*,N%^oO X F VMKM^ZDJIPHt §. muT4T4HEDE[
(31) IPKZDN%O4V,e +&-Uk6p%lUl '6KZNQ[<^Z=
(32) IPKZ=QIG §. =<\*Tt=R^MKMDEVZ=O4=<KNU^Z >F4VZDO vGKM94=@O*KM=<^ZO4=<K ,NU^=<F4^ZNUTg=
(33) IPO VZ;IPHEHtILO X ;>= X DEF4; =<O*KZ=<^MT4^ZDEVM=<V1m n*DE^MKMFgIPHg^M=
(34) ILHDEKYDEOjKZ=<^IP[<=@IPHEHENP VO NUO*M §. =<O4vUDEO4=R=<^MV KZNTtN%VM= KZ94=<DE^ X =<VMDEv%O ILO X ILOtIPHEY*VMDEV T4^ZNU4HE=<; VMN%H=RHYDEO0T49*Y*VMDE[
(35) ILH6IPO X vU=<N%;>=<KZ^MDE[
(36) ILHoKM=R^M;>VuF4^@^MNUHE=DEVSKMN [<^Z=
(37) IPKZ=GO*F4;>=<^ZDE[
(38) IPHKMN*NUHEVSKZN>DE;>T ^MNPnU=@KZ94=Q
(39) = .>[<DE=<O4[<Y0NL6KM9tILKcVZNP,K IP^Z=Uum X IPT4KZDENUO0DEVSN%O4=NL1KM94N%VM= KZNjN%HEV KM9tILK 1= X =<VZ[<^MDEg=QDEOKM94=@T4^Z=<VM=<O*K@^M=RTtN%^MK
(40) 2547698;: 9< / 0 1 3 . =?>A@. B;C DEC F$G HJIKLFMG K$CONP. 8 94=G[RNUF4T4HEDEO4vGg=<K=<=<O ].@c_eSM BIPO X KZ94= I X IPT KWIPKZDENUO0KZNjN%H.DVu^M=<T ^M=<VZ=<O*KM= X NUO §oDEvgGsU@8 94= v%=<O4=<^aIPHoVZKM^aIPKM=RvUY[<NUO VMDEVMKZVSDERO Q sU^M=
(41) I X DEO4v KM9 =6DEOjKZ=<^IP[<= X IPKWI³gHS= %UTMv%^WI X T4K
(42) NUH XWV ' T4^MNPn*D X = X *Yc].@@.eSM B%JF4VZDEO4v KM94=6].@@ eSM B¦DO T4F4K X IPKaItHEJ= TW.m@fS m68 V 'RDEO 94DE[a9 ;=<VM9 X IPKaI0IPO X KM94=T4^Z=<VM=ROjKGnUILHEF4=>NLSKM94= [<NU;T4F4KZ= X § VZNUHEF4KZDN%O>DEV VMKZNU^Z= X -4[
(43) IPHE[<F HILKMDEO4vGIPO=<^Z^MNU^ =RVMKMDE;IPKM=% d4 I X ILT4KMDEO4vKM94=@;>=RVM9>*YG=<*F4D X DEVZKM^MDE4F KMDEO4vKM94=@O4=< O4N X =<V
(44) ^M=<v%DENUO>*YG^Z=<vUDENUO*DOy,F4O4[RKMDENUOGNL KM94DEV =<^Z^MN%^S=<VZKMDE;ILKM=U ?t ^MDEKMDEO4vGIO4=< DEO*KM=<^¥ IP[<= X IPKaI@tHEX= %YTZvU^aI X T K
(45) O4=< V '< 8 9 =1DEO*KM=<^aIP[<KZDENUO DEKM9KM94= ].c@.euM B[<N X =DV X NUO =1*Y@VMN%;>=6DEO*KM=<^¥ IP[R=1[<N X = TZeS8S6fu§UmS V ^ZDKZKM=<O DEO § NU^ZKM^WILOKM9tILK DEHEH[a9tILO4vU=IP[<[RNU^ X DO vUHEY0KM9 =GNUH X DEO4T4F4K X ILKWItHE)= Ta.mcfu m68 V DO*KZNI O4=RNUO4=@KM9gIPK DEHEHtg=^M=I X IPv*IPDEO>*Y>].@c_eSM B,N%^ KM94=@O4=R\jK ^ZF4Oo >.
(46) ..@ &\ 8 94= ;IPDEO@TtN%DEOjKNPtKZ94=SI X IPT4KZDN%OVMKZ^WILKM=<v%YDEVgIPVM= X NUOKM94= X =atO DKZDENUONPªIuO4=< ;>=<KZ^MDE[1ILVMVMN*[<DJILKM= X DEKM90Iv%Dn%=<O>;=<VM9VMN%HF KMDENUOo O X =<= X X F4^MDEO4v0ILF4KMN%;IPKZDE[S;>=RVM90v%=<O4=<^aIPKMDEN%O DEK@DEVSO4=<[R=<VMVaIP^MYKZN>9tIn%= ILVS;GF4[a90DEO*#NU^M;IPKZDN%O ILV1TgNUVZVMDE4HE=SN%OGKM94=@OtILKMF4^Z=cIPO X KM94=@HEN*[
(47) IPH4g=<9tIn*DENUF ^1NLoKM94=uVMNUHEF4KZDENUOo8 94NUVZ=SDEO X DE[
(48) ILKMDENUO V6vUNPn%=<^MO4V Z. [ 1. ÍÍ Ä]_^_`<ÓRÕ.
(49) ?.
(50) J$ ) +-,/. 021435 ?$@0 A&1B . 1 .DC %E ) N 6PO FQBIJ U6V7WP65X. !#". "PR. $&%&'( * 678:9;=<> GF:H>IJ876<LKM * +-,S. 02143T$&%&' Y-A&1 0 A&1W . 1 .DC %E. o§ DEv%F4^M=GsQ6b=<VM90I X IPT4KaIPKMDEN%OIPO X ]_c@.eSM B« KZ94=@vU^MD X vU=<O4=R^WIPKZDENUOo.muV1=IP^M=@DEO*KM=<^Z=<VMKZ= X DEO>KM9 =c[R=<HEHVMDZ<=U 1=uO4=<= X KMN[<N%Ojn%=<^MK VZNU;=<94NP 9tIPK = *O4NPIPgNUF4KuKM94=VZNUHEF4KZDN%O>KZN>VMN%;>=<KZ94DEO4v9tIn*DO vQKZ94= X DE;>=RO4VMDENUONP1IHE=<O4v%KM9 ILO X [<NUO*KWILDEO4DEO4v X DE^Z=<[<KMDEN%OtIPHDO ,NU^Z;IPKZDENUOo8 94DEV ;>DEvU9*K6g= X N%O4=@*Y>vUDEn*DEO4vGIPK =
(51) IL[W9 ;>=<VZ9TgNUDEO*K
(52) *VaIY\[o*VZD\TtIP^aI ;=<KM=<^ZV@DOD] ^_* X =<VM[R^MDE4DEO4v0IGHEN*[
(53) IPH.;=<KM^ZD[KM=<O4VZNU^8 9*F4V
(54) «KM94=GI X ILT4KWILKMDENUO ;>=<KZ^MDE[@;>=
(55) ILVMF4^Z=<V@KM94= D X =
(56) ILHHE=<O4vUKZ9R%æDOKM=<^Z;>V6NL[<=RHHO*F4;Gg=<^ '.NP.KM94=@;>=RVM9GDEO>=
(57) IL[a9 X DE^M=R[<KMDENUO0ILK1KZ94=S[<N%O4VMD X =R^M= X TgNUDEO*K
(58) `S>A@. a C b,Dc K2ced f D d g"K2hECji. COK$F2cek. O>I t^ZVMK6VZKWIPv%=U%KM94= ;=<KM^ZD[[
(59) ILOGt= =<\*T4^Z=<VMVZ= X IPV1I ,F O4[<KMDEN%OQNLªKZ94=SIP4VZNUHEF4KZ= nUIPHEF4=6NLªKZ94= 94=<VZVMDJIPO NL1KM94=VMN%HEF4KMDENUOnUIL^MDJIP4HE=<V@IPO X DKu[
(60) IPO t=n*D=R1= X IPVIG;=
(61) IPVZF4^M=NL1KM9 =HENj[IPH.=<^M^ZNU^X%JVZ=<=ml donMlÀ? n '< «=<:K pg=rInUIP^ZDJIP4HE= VMN%HEF4KMDENUOKM9tILK1=@VMF4T TtN%VM= *O4NP OIPK=
(62) IP[a9[<=<HEH[<=<O*KZ=<^MVIPO X HE=<Kqsrp@tt=@DEKMV 94=RVMVMDJILO[RNU;>T F4KM= X IPK=
(63) IP[a9[<=<HEHg IL[<=U.8 94=@;=<KM^ZD:[ uvrVpEtIPVZVMN*[<DJIPKZ= X KM(N p[
(64) IPOg=cVZDE;>T4HEY X ='tO4= X ILV uvrp@txwzy {|S}~ qrp@t~@. 94=R^M==y {|S}.DEV1I@F4VZ=<^ X =atO = X [<NUO4VZKWILOjK X =<Tg=<O X DO vNUOGKZ94=S;=<VM9GVZDZR= %JKY*T4DE[
(65) ILHEHY* y {|S}.DEV1IPT4T ^MNP\*D© ;IPKM=RHYT4^ZNUTgNU^MKZDENUOtILHKMNGKM9 =cDEO*nU=R^MVM=@NLKM9 =;>=<VZ9>VZDZR= ' IPO X ~ qsrVpEt~%DVKM9 =rIL4VMN%HEF4KM=@nUIPHEF4=uNP.KM94= 94=RVMVMDJILOGNPKM94=uVM[
(66) ILHIL^.nUIP^MDJIL4HEL= po 94=<O;>NU^Z=1KZ9tIPONUO = VM[
(67) ILHIL^6nUIP^ZDJIP4HE=6DEV6DEO*nUN%Hn%= X KZ94= X D©¨ª=R^M=<O*K DEO X DEn*D X FtILHt;=<KM^ZD[RVSIP^M=@DEO*KM=<^ZVM=<[RKM= X ,NUHEHENP DEO4v§4S=R[W9*Ku^MF4HEX= %JVZ=< = d ÀdQILO X lY-n '< 8 9 =c;IPDEO>TgNUDEO*K DEV KM94=R^M=a,N%^M=KMN X ='tO4=KZ94=VM=R[<NUO X NU^ X =<^uTtIP^ZKMDJIPH X =R^MDEnUIPKZDn%=@NP6KM94=VMNUHEF4KZDENUO nUIL^MDJIP4HE=<V6B*DEO4[<=@=rIL^M=^Z=<VMKZ^MDE[<KZ= X KZNG[
(68) IP^ZKM=<VZDJIPOvU^ZD X V
(69) 4=I X N%T4K I;>DE\*= X IPT4T ^MNP\*DE;IPKZDENUO[<NU;y 4DEO4DEO4vtN%KM9 s@§DO DKZ=c.HE=<;=<O*K1IPO X §oDEO4DEKZ=cuD©¨ª=<^Z=<O4[<=ILT4T4^MNP\*DE;ILKMDENUO V
(70) gmSHEVMNg*VM[
(71) ILHJIP^nUIP^MDJIL4HE=<V IL^M=vUDEnU=ROjYKZ94=0].c@.euM B TtIP[a UIPv%=ILKQ=
(72) IL[a9 [<=<HEH [<=ROjKZ=<^ILO X IKYjT D[IPH ;>=RVM9VMD Z<=[a94N%VM=<O *Y KM94=I X ILT4KMDENUO DEV X =atO4= X *Y KZ94=GDEO*KM=<^ZnUIPHEV1`aN%DO DO v>KN[R=<HEH6 IL[<=G[<=<O*KZ=<^MVGDEO=
(73) IL[W9 X D^Z=<[<KZDN%Oo 8 94N%VM= IL[<KMV.;NUKMDEnUILKM=.F4V.KMN@[a94N*NUVZ=S§oDEO4DEKZ=uD©¨ª=R^M=<O4[R=SIPT4T4^ZNP\*D;IPKZDN%OSKZN X =atO4= KZ94=1VZ=<[<N%O X NU^ X =<^ TtIL^MKZDILH X =<^ZDEnUIPKMDEn%=<VIPK@=
(74) IP[a9 IP[R=G[<=<O*KM=<^NPKM94=G;=<VM90[R=<HEHVG8 94DEV X =atO DKZDENUO DO*n%NUHEnU=<VutN%KM9 [<=<HEH Î
(75) ÍoÎJÑ.
(76)
(77)
(78) . [<=ROjKZ=<^cILO X n%=<^MKZ=<\>nUILHEF4=<VNPKZ94=@VM[
(79) ILHJIP^nUIP^MDJIL4HE=<V64F4KSILHEVMN[<=RHH[R=<O*KM=<^@IPO X IP[<=@[<=ROjKZ=<^SnUILHEF4=<V6NL KZ94=@t^ZVMKSN%^ X =R^ TtIP^ZKMDJIPH X =R^MDEnUIPKZDn%=<V NP.KM94N%VM=VZ[
(80) IPHJIL^1nUIL^MDJIP4HE=<V | j} | ,}4x '#4z *|P{ j} ') .4z ¡
(81) S{ .0z
(82) ~L } ',} «=<K pg=QILOjYVM[
(83) ILHJIP^ nUIP^ZDJIP4HE=Sv%DEnU=<O0IPK =IP[a90[<=<HEH[<=<O*KM=<^uNP1IvUDEn%=<O;>=<VZ9> DEKM9 X DE;>=RO4VMDENUO V1eQ e IPO X e 6 =<K t=IvUDEnU=<O #tF D X [<=RHHNP6KM9 =;>=<VZ9ILO X0X =<O NUKMX= p NU^:p KZ94=[<=RHH[<=<O*KM=R^ nUILHF =cNL p.8 94=<OKM9 =cnUILHEF4=@NP p IPKKM94=n%=<^MKZ=< \ NP.[<=<HE H DEV X =agO4= X *&Y Q p r t"!. # p9;: <(p >=@yB?(?(CA 4DFEHG0I=r t %$&(' )+*-,+).0/21436587. . 94=R^M=JG0IrK tDV KZ94=@O*F4;Gt=R^1NL #tF4D X [<=<HEHEV 9tIn*DO vJ IPVSI[<N%;>;>N%OQn%=<^MKZ=<\Ey DEV KZ94=@[<=<HEH[<=<O*KM=R^ NLS[<=<HELH 8 94=G[<=<HEH[<=<O*KM=<^GnUILHEF4=QNLSKM94=vU^aI X DE=<O*K@NP p¦DV X ='tO4= X *Y0KM9 =G,N%HHENP DEO4v,N%^M;GF4HJI tILVM= X NUO0§DO DKZ=cuD©¨ª=R^M=<O4[R= ILT4T4^MNP\*DE;ILKMDENPO)Q p ryB\tN! O [ Gy;ryBs tQP O M p ry Y t ! G;y ry O BZGt P MXW M p ry ^ t ! Gy Vr y O `_ t P MX] M. M. p9R(S ? 9p R 5 [ RS ? [ R5 p R([ ? p R 5 WR[ ? WR5 p R(a ? p R 5 ] R(a ? ] R 5. :. :. :. p9RBT [ RT p R(\ WR\ p R(b. ? 9p R 5 ? [ R 5VU ? p R5 ? WR5 U ? p9R 5 ] R(b ? ] R 5 U. . 94=R^M= Gy ruzdctDEVGKM94=KMN%KWILHSO*F4;Gg=<^QNLcO4=RDv%9*tN%^MDEO4v #tF4D X [<=<HEHEVGDO X DE^Z=<[<KMDEN%Oec(cXw O `Z `_ euNUKWILKMDENUO V yBfS yhg %E#NU^GKM9 J= [ X DE^M=<[<KZDENUO 'R yBiG yhj5%E,N%^QKZ94= W X DE^M=<[RKMDENUO 'R:yBk ILO X yBl9%E#NU^KM94= ] X DE^Z=<[<KMDEN%O '6VZKWILO X ,N%^6KM9 =c6ILVMK
(84) *=RVMK
(85) *euNU^ZKM9o*B*NUF KM9o*uDv%9>IPO X «NP [<=<HEH[<=<O*KM=R^MV NPoKZ94=SO =<DEvU9* gNU^ZDO vc[R=<HEHV³NP0 DOKM9 =S].c@.euM BG[<N%Ojn%=<O*KMDENUO# r meonG`p toDEV6KZ94= VM=RK6NPDEO X =<\*=<V6^Z=<T4^Z=<VM=<O*KZDO v [<=RH0H %KM94=<OVZD;DEHIL^MHEY@[<=<HEHELV f g i j H k IPO X l ;IYg=S^Z=<VMTg=<[<KZDn%=<HEY>^Z=<T4^M=RVM=<O*KM= X *Y KZ94=,NUHEHENP DEO4vDO X =<\0VZ=<KMV Q(rKm0: O qnGBp2t<- rKm ? O on;Bp2tRx r meonr: O Bp2t<M rKm qn ? O Bp2tRx r meonG`ps: O t@IPO X r meonG`p ? O t³ 94=<O4=RnU=<^@KM9 NUVM=@VZ=<KMVu;IP %=SVZ=<O4VM=% tY ;=
(86) IPO VGNPW s0§oDEO4DEKZ=_H=R;>=<O*KGDEO*KM=<^ZTtN%HILKMDENUO6=;IY IPHEVMN X =atO4= p NUO3IPO*jY rV[ W ] t HEN*[
(87) IPKZDENUO>NL6KM94=@;>=RVM9>*&Y Q p r[ W ] tF!u# p r t xF& rV[ W ] t &vw 94=R^M=zyDEVoKZ94= VM=<K³NPªILHH*n%=<^MKZD[R=<V6NPgKM94= ;=<VM9ox & DV.KZ94=L stILVMDEV,F4O4[<KZDENUOGIPKMKaIP[a94= X KMN@n%=<^MKZ=<\{ % § ^MN%; KZ94DEV
(88) *=S[
(89) ILO X =R^MDEnU=@KM9 = ,N%HHENP DEO4vu[<=<HEH[<=<O*KM=R^SnUIPHEF4=RV6NPoKZ94=ut^MVZK NU^ X =<^1TgIP^MKZDJIPH X =<^MDEnUILKMDEnU=<V NLMp*KM9gIPK = X =<O4NUKZ=*Y}|~ rp@t ry ³t #NU^zc w O ` Z ` _SQ |s~erVpEtory F t 4w # p r t x &$ ~ery t &vw. B*DEO4[R=VM=<[RNUO X N%^ X =R^ TtIP^ZKMDJIPH X =R^MDEnUIPKZDn%=<VSIPK [R=<HEHg IP[<=@[<=ROjKZ=<^MV@ DEHEHt= X ='tO4= X F VMDEO4v>IPHEVZNQ[<=RHH« IP[R= [<=ROjKZ=<^6nUILHF =<VoNLjg^MVMK.N%^ X =<^.TtIL^MKZDILH X =R^MDEnUIPKZDn%=<VoNLEpo=6;GF4VMK X =atO4=KM94N%VM=*FtIPO*KMDEKZD=RVog=a,NU^Z=U= ÍÍ Ä]_^_`<ÓRÕ.
(90) l.
(91) J$. DEHEH X NKZ94DEVS*YF4VMDEO4vHDEO4=IP^SDEO*KM=R^MTgNUHJIPKZDN%Oo =<K@F4V X =<O NUKM=*Y |V$ ~ p r =tKZ94=t^ZVMK@NU^ X =<^@TtIP^ZKMDJIPH X =R^MDEnUIPKZDn%=<VNP p IPKGIvUDEn%=<O [<=RHH³ IL[<=[<=<O*KM=<^ DEO KM94= X DE^M=<[<KZDENUO c Jc w O `Z `_ c=R=<T4DEO4v KM94= ].@@.eSM B [<N%O*nU=<O*KMDEN%Oog1= DEHH X =<O4N%KM=G*Y G q IPO X KZ94=VMDE\[<=<HEH. IL[<=Q[R=<O*KM=<^ZV NLS[<=<HEzH =<HEH1[R=<O*KM=<^ZVG DHEH6g= X =<O4NUKZ= X *Y y ,NU^ QyBf ILO X y4g #NU^KZ94=6ILVMKGIPO X =<VMK O4=RDv%9*tN%^MDEO4v[<=<HEHEVNPz yBi ILO X y4j ,N%^cKZ94=GeSN%^MKZ9 IPO X B*N%F4KM9 O4=<DEv%9jgNU^ZDEO4v[<=<HEHEVQIPO X tOtILHEHY yBk IPO X yBl ,N%^@KM94=SDEvU9IPO X «NP O4=RDv%9*tN%^MDEO4v[<=<HEHEV
(92) f =<[IPHEH1IPHEVZN0KM9tILK@KM94=DO X =<s \ u[
(93) ILOt= ^Z=<T4^M=RVM=<O*KM= X jYKM94=@DEO X =R\>VM=RWK rKm on;Bp2tR sU 6IPVZK IL[<=Q #6[<=<HE8H rKm qnGBp2t6DEV VZF4[a90KM9tILK m e KM94=RO0VM=<K . . . . . .
(94) . . . 4w r[9R(S ? [ fQtdE2r[9R(S ? [ R t. . LI O XX =atO4= | $ ~ p r t 4w |s~erVpEtory t0:zr O #6[<=<HEH8rKm qnGBp2t6DEV VZF4[a90KM9tILK m w3eKM94=RO . . 4=<VMKIP[<=Q #6[<=<HEH8rKm qnGBp2t6DEV VZF4[a90KM9tILK. . | $ ~ p r=t 4w | ~. -. . ?. t(|s~erp@t rVyBfLt. . . rp@t rVy t. KZ94=<O. m O. | $ ~ p rjtF4w | $ ~ p r `$ h$ t. . 94=R^M= B$ 4$ DEV KZ94=6IPVZK IL[<=@[<=<O*KM=<^uNP.[<=<HEHo9tIn*DEO4vmrKm ? O qnGBp2t1ILV DEKMV DEO X =<\GVZ=<K #6[<=<HEH8rKm qnGBp2t6DEV VZF4[a90KM9tILK m w O KZ94=<O . . . "!. d4eSN%^MKM9 IL[<=Q #6[<=<HEH8rKm qnGBp2t6DEV VZF4[a90KM9tILK . | $ ~ p rjt hw | ~. e KM94=RO0VM=<K. n# . 4w r W R [ ? W i=t(E r W R [ ? W R. LI O XX =atO4= | $ ~
(95) p r \t 4w |s~erVpEtory t : r O #6[<=<HEH8rKm qnGBp2t6DEV VZF4[a90KM9tILK n=w3e KM94=RO . . rVpEtory t. . ? . t. t(|s~erVpEtoryBi=t. . | $ ~
(96) p r \tF4w |s~erp@t rVy t. Î
(97) ÍoÎJÑ.
(98)
(99)
(100) . ?t B*NUF KM9 IP[R=Q #6[<=<HEH8rKm qnGBp2t6DEV VZF4[a90KM9tILK . n#. KZ94=<O O. | $ ~
(101) p r -t hw | $ ~Vp r $
(102) B$ . t 94=R^M= $ B$ DV KZ94=@eSN%^MKM9y IP[R=c[R=<O*KM=<^uNPo[<=<HEH9tIn*DO vrKm qn #6[<=<HEH8rKm qnGBp2t6DEV VZF4[a90KM9tILK n=w O KZ94=<O | $ ~
(103) p r -t 4w |s~erp@t rVy t . .
(104) . 6IPV DEKZV1DEO X =R\GVM=<K. ? O B p2t. . SDEvU9y IP[R=Q #6[<=<HEH8rKm qnGBp2t6DEV VZF4[a90KM9tILK. er KM9 =<O0VM=RK. p . . 4w r ] R a ? ] k (t E r ] R a ? ] R. . LI O XX =atO4= | $ ~
(105) p rVq\tF4w |s~erVpEtory t : r O #6[<=<HEH8rKm qnGBp2t6DEV VZF4[a90KM9tILK p(w re KM9 =<O . . l4 NP IP[R=Q #6[<=<HEH8rKm qnGBp2t6DEV VZF4[a90KM9tILK . p. |V$ ~ p rVq\tF4w | ~. . O. | $ ~
(106) p r . . t(|s~erVpEtoryBk=t. . rp@t rVy t. KM94=<O t hw | $ ~
(107) p rVq. t 94=R^M=Wq $ h$ DEV KM94=@uDv%9G IL[<=@[<=<O*KM=R^cNL[<=RHH9tIn*DEO4vr meonG`p #6[<=<HEH8rKm qnGBp2t6DEV VZF4[a90KM9tILK p(w O KM94=<O | $ ~p r t 4w |s~erp@t rVy t . . ?. t. K$ h$.
(108) . ? O. t IPV DEKZV1DEO X =R\>VM=RK. "!. euNUKZ=GKM9tILKc DEKZ9KM94N%VM= X =agO4DEKMDENUO4VvUDEnU=<OIPgNPnU=%D©N%O4=GNP KM94= X D;=<O4VZDN%O4V@e oe NU^@er DEV>=RjFgIPHSKZN N%O4=0KM9 =<O3KM9 =t^MVZKNU^ X =<^ X =R^MDEnUIPKZDn%= DKZ9 ^M=<VZTt=<[RK0KMN KM9tILK X DE^M=<[<KZDENUOILK>KM9 =0[<=<HEH IL[<=[<=ROjKZ=<^MVIP^M=tN%KM90=<*FtILHoKZNGKM94=[<=<HEHo[R=<O*KM=<^@nUIPHEF4=@NL_KZ94=t^MVZKSNU^ X =<^ X =<^MDEnUILKMDEnU=@DEO0KM9 =VWIL;>= X DE^Z=<[<KMDEN%Oo. ÍÍ Ä]_^_`<ÓRÕ. !.
(109) q.
(110) J$. 4 ~L¡ 6¢ ¡t|U¢*| } |P{ #} '1¢*|K *}4{ t4z euNPKZ9tIPKSILHHgKM9 =T4^M=RnjDEN%F4V X =atO DKZDENUO4V 9tIn%=Sg=<=<O0VZ=<K
(111) 1=@;IY X ='tO4=KZ94=VM=R[<NUO X N%^ X =<^uTtIP^ZKMDJIPH X =R^MDEnUIPKZDn%=<V NPpIPK =IP[a90[<=<HEH« IP[<=@[<=ROjKZ=<^MV@*Y>;=
(112) IPO V1NL[<=<O*KZ=<^M= X §DEO4DEKM=uD ¨=<^Z=<O4[<=GIPT4T ^MNP\*DE;I KZDN%OoF4VZDEO4vKM94=>InUILDHJIL4HE=cnUILHEF4=<V@NP KM94=g^MVMKNU^ X =<^ X =<^ZDEnUIPKMDEn%=<V
(113) =vUDEnU=t=RHNP£KM94=G[RNU;>T H=RKM= X ='tO4DEKMDENUO NPL | $ ~ rVpEtor =tRX | $ ~ rp@t r =t IPO X | $ ~ rVpEtor =t&%2cQw [ W ] ' X =RO4NUKZDO v>KM9 =VM=<[RNUO X NU^ X =<^ TtIL^MKZDILH X =R^MDEnUIPKZDn%=<VSNL p ILKSIGKM9 =@ IP[R=[<=<O*KM=R^MV w hIPO X w NP6[<=RHFH ILVcILO0=<\4IP;T4HE=U 8 94=NUKM9 =<^ X =atO DKZDENUO4V [
(114) ILOt==IPVMDEHEY X =<^ZDEnU= X ,^ZNU;hKZ94NUVZ=@,NU^Z;GF4HJIP=U sU 6IPVZK IL[<=Q %,I '>N%;>T4F4KaIPKZDN%OGNP | $ ~ p r =t Q #6[<=RHQH r meonG`p tDV VZF4[a9KM9tILK m e KM9 =<Ot^MVZKSVM=RK . . . . . . . . . . . . . . . . . ILO XX =atO = |. $ ~ p r=tFhw . w rV[ R S ? [ f t(E r[ R S ? [ R t. . |V$ ~ p r=t ? | ~ rp@t [9f ? [9R m w . . #6[<=RHHQr meonG`p tDV VZF4[a9KM9tILK . |. . e KM9 =<O. $ ~ p r=t hw . J N%;>T4F4KaIPKZDN%OGNP | $ ~ p r =t Q #6[<=RHHQr meonG`p tDV VZF4[a9KM9tILK % '. . . . . ryot : r O. O. ?. t | ~ Vr pEtor9[ y R(f S t ? 9[ | f $ ~ p r =t ? . . | $ ~ p r=t ? | $ ~ p rjt [9f ? [g.
(115). . e KZ94=<Og^MVMK VZ=<K. Qn z . w r W f0[. ? W f (t E2r W f [ ? W f0\ t \r em on : B p2t Br em on ? O `p t O. 9 =<^M= i DEVSKZ94=Q6ILVMKu IP[R=[<=<O*KM=R^NP1[R=<HEH9gInjDEO4v. IPVuDEKMVSDEO X =<\VM=<K ILV6DEKMV.DEO X =<\VM=RK1IPO XGX =atO4= j DEV6KM94=S³IPVMK_ IP[<= [R=<O*KM=<^ NLª[<=RHH 9tIn*DO v . . | . . $ ~ p r=tF4w . | $ ~
(116) p r=t ? | $ ~
(117) p r j@t | $ ~
(118) p rzi t ? | $ ~ p rt :zr ? t Wf ? Wf \ Wf [ ? Wf O n>w z O O | $ ~p rzi t ? | $ ~p r=t | $ ~ p rtF4w . W f0[ ? W f. #6[<=RHHQr meonG`p tDV VZF4[a9KM9tILK. ILO X e. . KZ94=<O. äEÈ<»¼<ÄSáP¹ Â,à ¹ZÆP»,½<¾ÀÃP¹ ¾Àº,Â#ßPº#»,¼<¾Àº*áPº#ÆPßPºJ¹Z¾ÀÂ%Ã1äÈ<Ö »#¹ZÖ1Â,ÆPß*¿ÀÙ ¼LÜ ¼RÂjº#ßP¹ äÈ<¿À¿ÀÈaå¾ÀÄPãÈ<ÄP¹ZÂMÜM»#¹MÃPÆPÅZ¹MÂ%º,ȼÂ#º#¼<ÄPÃP¼<»#ÃÒÇUÈ<¾ÀĺUÅZ¹Mĺ,¹Z»,¹ZÃoÃP¾ Ø*¹M»#¹MÄPÅM¹*Â#ÅßP¹MÖ ¹ . Î
(119) ÍoÎJÑ.
(120) p.
(121)
(122) . #6[<=RHHQr meonG`p tDV VZF4[a9KM9tILK >n w ez IPO X e . |. KZ94=<O. O. | $ ~ p r=t ? | $ ~ p r j Wf ? Wf \ z. $ ~ p r=tFhw . . . #6[<=RHHQr meonG`p tDV VZF4[a9KM9tILK >n w O w e KZ94=<O . |. $ ~ p r=t 4w . . J[ N%;>T4F4KaIPKZDN%OGNP | $ ~ p r =tOQ #6[<=RHHQr meonG`p tDV VZF4[a9KM9tILK % '. | $ ~ p r \t ? | $ ~ p r xt Wi ? Wj. . . . . O. . w r] f. p. t . w. . e KM94=<Ot^ZVMKuVM=<K . a ? ] ftdE2r ] f0a ? ] f0bt \rKm qnGBp: O XrKm qGn Bp ? O t. 9 =<^M= k DEVSKZ94= ³IPVMKu IL[<=[<=ROjKZ=<^NL1[<=<HEH.9tIn*DEO4v t@IPVuDEKMVSDEO X =<\VM=<K .IPV³DKZV6DEO X =<\VM=RK1IPO XGX =atO4= l DEV6KZ94=S6IPVZK. IL[<= [<=<O*KM=R^ NP[<=<HEHt9gInjDEO4v . . |. . . $ ~ p rt 4w . | $ ~Vp r=t ? | $ ~p rzlt | $ ~
(123) p rzk t ? | $ ~ p rt :zr ? t ] f ? ] f0b ]f a ? ]f O p(w O O | $ ~ p rzk t ? | $ ~p r=t | $ ~ p rt 4w ]f a ? ]f (p w r O | $ ~ p r=t ? | $ ~ p r l t | $ ~ p r=t 4w ] f ? ] f0b (p w O w | $ ~ p rqDt ? | $ V~ p r t | $ ~ p r=t 4w w ]k ? ]l. . #6[<=RHHQr meonG`p tDV VZF4[a9KM9tILK. IPO X e. . #6[<=RHHQr meonG`p tDV VZF4[a9KM9tILK. e ILO X e. #6[<=RHHQr meonG`p tDV VZF4[a9KM9tILK. KM94=<O. KM9 =<O. e KM94=<O. . 4=<VMKIP[<=Q %,I 'G#6[<=<HE8 H rKm qnGBp2t6DEV VZF4[a90KM9tILK -. . m. Q O. $ ~ p r jt 4w | $ ~ p r `$ h$ t 94=R^M= B$ 4$ DEV KZ94=6IPVZK IL[<=@[<=<O*KM=<^uNP.[<=<HEHo9tIn*DEO4vmrKm ? O qnGBp2t1ILV DEKMV DEO X =<\GVZ=<K %J '#6[<=<HEH8rKm qnGBp2t6DEV VZF4[a90KM9tILK m w O Q |. . ÍÍ Ä]_^_`<ÓRÕ. . . . . . . "!.
(124) sk.
(125) J$. N%;>T4F KWIPKZDENUOGNP . | $ ~ p r jt Q. |. N%;>T4F KWIPKZDENUOGNP | $ ~ p r jt Q D#[<=RHH8rKm qnGBp2t³DV VZF4[a90KM9gIPK . . . | $ ~ p r=t ? | $ ~ p r jt [9f ? [g. $ ~ p rjtF4w . . . e KM94=RO>g^MVMKuVM=<K. n# . O. t 94=<^Z= i DEVSKM9 ==<VMKIP[<=[R=<O*KM=<^@NP6[<=RHH9tIn*DEO4vr meon : O `p t IPVSDEKZV DO X =<\ VM=<K CjDEV1KZ94=@=<VMKIP[<=@[<=<O*KZ=<^SNL[<=<HEH9tIn*DEO4vmrKm q n ? O Bp2t1ILV DEKMVDO X =<\>VZ=<K . w rW g. [ ? W i (t E r W g[ ? W g \. . IPO XX =atO =. . |. | $ ~
(126) p r jt ? | $ ~p r CjEt : r Wg ? Wg \ O n>w z O | $ ~ p r Vi=t ? | $ ~ p r jt 4w W g[ ? >n w z . $ ~ p r jt 4w . . $ ~ p rjt 4w . . O. e ILO X e. DEDED ³#[<=RHH8rKm qnGBp2t³DV VZF4[a90KM9gIPK |. . IPO X e. DED#[<=RHH8rKm qnGBp2t³DV VZF4[a90KM9gIPK. t | $ ~p r VW g i [ t . ?. KM94=RO. | $ ~p rjt Wg. . . $ ~ p rjtF4w . . N%;>T4F KWIPKZDENUOGNP | $ ~ p r jtOQ D#[<=RHH8rKm qnGBp2t³DV VZF4[a90KM9gIPK . | $ ~p r jt ? | $ ~p r CjEt Wg ? Wg \ w . | $ ~p r \t ? | $ ~p r -t Wi ? Wj. . . w r] g. O. 8p . . . . KZ94=<O. O. DEn#[<=RHH8rKm qnGBp2t³DV VZF4[a90KM9gIPK >n w O 3e KM94=RO |. ? | $ ~ p r jt ? Wg. wV. er KM94=<Ot^MVZK VM=<K. a ? ] g\t(E r ] g a ? ] g b@t. . . 94=<^Z= k DEV KM9 ==<VMK IP[R=[<=<O*KM=R^cNL6[<=<HEH.9tIn*DO vr meonG`p: O ut IPV DEKMVuDO X =<\ VM=<KSILO X l DVKM9 =c=RVMK³ IP[<=@[<=ROjKZ=<^SNL[<=RHH9gInjDEO4v rKm qnGBp ? O 1t ILV DEKMVDO X =<\ VM=<KSILO XX =atO = . |. . . $ ~ p r jtF4w . | $ ~ p rjt ? | $ ~ p r l ] g ? ] gb. t: r O ?. . t. |V$ ~ p r k t ? | $ ~ p r jt ]g a ? ]g. Î
(127) ÍoÎJÑ. .
(128) sUs.
(129)
(130) . DED#[<=RHH8rKm qnGBp2t³DV VZF4[a90KM9gIPK Xp w O IPO X e. . O. KM9 =<O. | $ ~ p r k t ? | $ ~ p rjt . ] ga ? ] g pXw r O | $
(131) ~ p rjt ? | $
(132) ~ p r l t | $ ~ p rjt hw . ]g ? ]g b pXw w r O | $ ~ p rq\t ? | $ ~ p r t | $ ~ p rjtF4w w V ]k ? ]l |. . $ ~ p r jtF4w . DEDED ³#[<=RHH8rKm qnGBp2t³DV VZF4[a90KM9gIPK 3e ILO X e DEn#[<=RHH8rKm qnGBp2t³DV VZF4[a90KM9gIPK. KM9 =<O. e KM94=<O. . a C b,Dc K2ced f D d g"K2hECRC c Nh K$C i. `S> =. COK$F2cek. uO4[<=ILHHgVM=R[<NUO X N%^ X =<^ X =<^MDEnUIPKZDEnU=<V69gInU=Sg=<=<O[<N%;>T4F KM= X %= X =agO4=I@1=RDv%9*KM= X %,I X D;=<O4VZDN%OtIPH' 94=RVMVMDJILO IPKu=
(133) IP[a90[<=RHH« IP[R=[<=<O*KM=R^cTgNUDEO*K
(134) «=<K qsrVpEt g=KM9 =94=<VZVMDJIPO ILVMVZNj[RDILKM= X DKZ9 p X ='tO4= X N%OQKZ94= IP[R=1[<=ROjKZ=<^ NPt[R=<HEH IPO XX =<O NUKM= *YWp | IS^Z=a,=<^Z=<O4[<=unUIPHEF4=6NL p%JKZ9tIPK³ DHEH%t= X ='tO4= X HJIPKZ=<^ 'R4KZ94=<O0KZ94=@1=<DEv%9jKZ= X 94=<VZVMDJIPO X =<O NUKM= X *Y qsrVpEt DV X =atO4= X IPV Q qsrp@t w p qs: rVpE xtp | 94=R^M= p9hDEV.KM94=u[<=<HEH4[<=ROjKZ=< ^
(135) nUIPHEF4=NP pGIPO X SDEV1IuTgNUVMDEKZDn%=1^Z=
(136) IPH OjF ;Gt=<^. 94DE[a9GDEV.F4VM=<^ X =atO4= X %,I KY*T4DE[
(137) ILHUnUIPHEF4=.NUF4H X t= O '<8 94=6^Z=a,=<^Z=<O4[<=nUIPHEF4Q= p | uDEV X =atO4= X IPV.I³,F4O4[<KZDENUO@NP4KM9 =^Z=a,=<^Z=<O4[<= =<O*KZ9tIPHET*Y | S 9 D[a9@[
(138) ILO=<DEKM94=R^g= X ='tO4= X *YSDEKMV.InU=<^aIPvU=.nUILHF =NPn%=<^oKZ94=6[<N%;>T4F KWIPKZDENUOtILH X N%;ILDO N%^ jY | w | : | E | D©KZ94=S^Z=a,=<^Z=<O4[<=KMNUKaIPH=<O =<^Mv%Y |UKZ94=@^M=a,=R^M=<O4[R=T4^M=RVMVMF ^M= | >ILO X KZ94=S^Z=a,=<^Z=<O4[<= X =<O VMDEKY | IL^M=QInUILDHJIL4HE=Ug= X =atO4=KZ94=@^M=a#=<^M=<O [<=GnUIPHEF4=<VNP.KM94= X D©¨ª=<^Z=<O*KSnUIL^MDJIP4HE=<V*,Y Q ].^M=RVMVMF ^M=nUIP^MDJIL4HE=Q | w | | . =<HEN*[<DEKYG[<NU;TtN%O4=<O* K Q |W w r | 2 t @DO =<KMDE[@=<O4=<^ZvUYNP.KMF4^Z4F4HE=<O4[R"= %æD X =
(139) ILHDEO4v DEKM9KMF4^Z4F4HE=<O*SK #tNP T4^MN%4HE=<;>V ' Q p | w! | . . . . . . . . . ÍÍ Ä]_^_`<ÓRÕ.
(140) s-.
(141) J$. fSILKM=GNP X DVZVMDETtILKMDENUO NP KMF4^Z4F4HE=<O4[R= *DEO4=<KZDE[G=<O4=<^ZvUY;%JD© X =IPHEDEO4v DKZ9KMF4^Z4F4HE=<O*K&#tNP T4^ZNP 4HE=<;>V' Q | w r | t E | 94=<^Z= |>DEVSI^M=a,=R^M=<O4[R=QHE=<O4v%KM9KY*T4DE[
(142) IPHKZNGKM94=@KZF4^M4F H=RO4[<=T494=<O4N%;>=<O NU; #g1=SIL^M= X =
(143) IPHEDEO4vu DKZ9Q;GF HKZD© T49gIPVM= #tNP T4^MN%4HE=<;KM9 =<O>Iu^M=a,=R^M=<O4[R=S=<O*KM9gIPHET*YQIPO X I ^Z=a,=<^Z=<O4[<= X =RO4VMDEKYVM94N%F4H X g=T4^ZNPnjD X = X ,N%^ =
(144) IP[a9T49tILVM=U uO4[R=SKM9 =c=<DEvU9*KZ= X 94=<VZVMDJIPODEV X =agO4= X 1= t^MVZK1VZYj;;>=<KZ^MD Z<= IPO XX DJIPv%NUOtILHD Z<=DEK
(145) 8 94= X DILvUNL OtILHED ZR= X ,NU^Z; IPK =<n%=<^MYTtN%DEOj:K [ ] ^8_DEV1v%Dn%=<O*Y Q . .
(146) rV[Et. . Ms 94=R^M= YrV[Et `mw O B_IP^Z=cKZ94= rV[Et³=<DEvU=<O nUILHF =<VSIPO X r[@tDEV1KZ94=^MN%KWILKMDENUO;IPKZ^MDE\NL ILO4vUHE= r[@t6KZ9tIPK ;IPT4VKM94= ] ^P_@[
(147) IPO4N%O4DE[
(148) IPHtIPVZDEV1NPn%=<^ KM94= r[@t6F4O DK =RDv%=<O*nU=<[RKMNU^ZV
(149) 8 9 =<O>=S[<N%;>T4F KM= KM9 =cIP VMNUHEF4KZ=SnUILHF = NPoKM9 =c9 =<VMVZDILO>*YG^M=RT4HJIP[<DEO4vKZ94=S=RDv%=<O*nUIPHEF4=<V*YGKM94=RD^ IL4VMN%HF KM=@nUIPHEF4=<V DEO%Ms 'R. y } | M J $ !M#" $ #$ M\ J&%
(150) '$& Ms M
(151) '$& r[@t-w rV[Et. . rV[Et. _ rV[Et. . . rV[Et . % '.
(152) . . (W ) S ( $ *X & + " &($) _ -,.$W$ ; _ : J ($
(153)
(154) . ( J Y/$ 10 M )$ T 2 _ ! 3$ 4$W;
(155) 2!$+" X *,3 5$SM_ _ 6 $W$ _ &* $+$ 87 . `S>V`. 9DK$C F$IWC k 2K cedD d gJi. COK$F2cek I. 8 94=tOtILHoHEN*[
(156) IPH;>=<KZ^MDE[@DEV X =agO4= X jYDEO*KM=<^ZVM=<[RKMDEO4v0IPHEHonUIL^MDJIP H=' DEVM=@HEN*[
(157) IPH;>=<KZ^MDE[X%JVZ=<= ILHEVMNmlJs n '< =[
(158) IPO3IPVZVMN*[<DJIPKZ=0IPO =RHHEDET4VZNUD X;: < KMN KM94=;>=RKM^MDE[KM=<O4VZ NU^ 9tIn*DEO4v IPV>IL\*=<V>= .= ILO X = _ %æ=<DEvU=<O*nU=R[<KMN%^MV@NP 'SILO X DEKM9^M=<VZTt=R[<KMDEnU=GHE=<O vUKM9 V O E#? m-w O B_4³8 94DEV =<HEHDET4VZNUD X8: < DV KZ94=F4O4DEKVMT49 =<^M=DEO>KM9 DV v%=<NU;=<KM^ZYj B F4T4TgNUVM=O4NP*KM9tILKSVZ=<nU=<^aIPHnUIP^MDJIL4HE=<AV @ B@ C@ IL^M=v%Dn%=<Oo*KZ94=T4^ZNU4HE=<;t=R[<NU;=<V Q $ ($( J
(159) M MW J&%
(160) 3$& $ $ = M
(161) ED B,_& T ($3" #7o K DV [<HE=
(162) IL^
(163) ,^ZNU; KM9 =vU=<N%;>=<KZ^MDE[
(164) ILHoD X =<O*KMD©t[IPKMDEN%O=RHHEDET4VZNUD X F ;=<KM^ZDE[SKM9gIPKSKZ94=VZNUHEF4KMDEN%OKZN>KZ94=QT ^M=<n*DENUF4V ;DO D;D Z
(165) ILKMDENUO T4^ZNU4HE=<; DEVGKMN tO X KZ94=04DEvUv%=<VMKG=RHHEDET4VZNUD X [<N%O*KWIPDEO4= X DEO KM9 =0DEOjKZ=<^MVZ=<[<KZDN%ONLrILHH KZ94= =RHHEDET4VZNUD X V : : : [<NU^Z^M=<VZTtN%O X DEO4v KMN ;>=<KZ^MDE[<V e 0[<N%;>T4F4KZ= X ,^ZNU; KZ94=nUIP^MDJIL4HE=<V @ @ G@ P0KDEVO4N%K=
(166) IPVZYDEOvU=<O4=R^WIPH KZN0gO X KM94=NUT4KZDE;IPH.VZNUHEF4KMDEN%ONPSKM9 DV T4^ZNU4HE=<; ouNP1=RnU=<^4KM9 =S#NUHEHENP DO vrILHEvUNU^ZDEKM94; VM=R=<;>V KZNGt=@VMF DKaIP4HE=@=<O4N%F4vU9 %æVM=<=@gvt$ - X =<T D[RKM= X DEOKM9 = -M [
(167) IPVZ= '<B*F4T TtN%VM=>KZ9tIPK@DEO4DEKMDJILHHEYNUO HYKN0nUIP^ZDJIP4HE=<XV % @ IPO X @ 'IP^Z=GT4^MNPn*D X = X y= tO X ILO0IPT4T4^ZNP\*D;IPKZDN%OQNLKZ94=NUT KMDE;ILH4DEOjKZ=<^MVZ=<[<KZDN%O0=<HEHEDET4VMN%D X *YKM94=u,N%HHENP DEO4vT ^MN*[<= X F ^M= Q D© KZ94=6KN =<HEHEDT VMNUD X [<F4^ZnU=<V : : 9gInU=6O4N%KoIPO*YSDEO*KM=R^MVM=R[<KMDENUOTgNUDEO*K %JKM9 DV9tIPT Tt=<O V 9 =<ONUO = =<HEHEDT VMNUD X DEV[<NUO*KWILDEO4= X DEO*KMNIPO4N%KM94=<^ '<*KZ94=@NUO4=u DKZ9GVM;IPHEHE=<VMK1IL^M=
(168) IDEV1KaIP %=<OILV1DEO*KM=<^ZVM=<[RKMDENUO IPO X KZ94=@VMF4DEKWIL4HE=@;>=<KZ^MDE[SDEV KM9 =rILVMVZNj[RDILKM= X NUO4= . . . . . . . . . . . . . . . . !. Î
(169) ÍoÎJÑ.
(170) s
(171) d.
(172)
(173) . First ellipse Second ellipse Approximated intersection ellipse. 0.15. 0.1. 0.05. 0. -0.05. -0.1. -0.15. o§ DEv%F4^M=)-$QmST T4^MNP\*DE;ILKM= X NUT4KZD;IPH4=RHHEDET4VZ=cNLKNP=<HEHEDT VM=SDEO*KM=R^MVM=R[<KMDENUO NUKZ94=<^M DEVZ=U HE=<K IPO X zmWw O B_n w O `Z KM94==<DEv%=<O*nUIPHEF4=<V>ILO X =<DEvU=<O*nU=R[<KMN%^MV %J^Z=<VMTo( 'yNP * n>w O `Z o8 94=DO*KZ=<^MVZ=<[<KMDEN%O;=<KM^ZDE[U *DEV X =atO4= X *Y -0.15. . . -0.1. . . -0.05. 0. 0.05. 0.1. 0.15. . . w . . :. . Z. . % -' . 94=<^Z= %J^Z=<VMT '@9gIPVKZ94=>VaIP;>==<DEvU=RO* n%=<[<KZNU^MVGIPV ?% _ 'IPO X 9tILV@,NU^ =<DEvU=<O nUILHF =<V w r t Nm w O `_ %,d' O0NUKZ94=<^@NU^ X V
(174) g1=[<NU;TtIP^Z=KM94= mEKM9 =<DEvU=<O*nUILHF =cNL DEKM9 KM94=QfuIY*H=RDv%9jF NUKMDE=<O*K NL DEKMV [<N%^M^M=RVMTgNUO X DEO4v=<DEvU=<O*n%=<[<KMN%^ DEO euNPUD© GnUIP^ZDJIP4HE=<V6IP^Z= vUDEnU=ROoPKM9 =tOtIPH DO*KZ=<^MVZ=<[<KMDEN%OG;>=<KZ^MDE[1DEV6[RNU;>T F4KM= X ^M=R[<F4^MVZDEnU=<HEYGIPV.,N%HEHNP V Q w DEOjKZ=<^MVZ=<[<KZDN%xO r U th ,NU^ m w _2 BG w DEOjKZ=<^MVZ=<[<KZDN%xO r Vt4 `S>
(175) a Cb,Dc K2ced Dfd g"K2hECji C I&h I&c C c D K2h C D C i COK$F2cek euNPKZ9tIPK KZ94=;>=RKM^MDE[ DEV X =agO4= X ILK =
(176) IP[a9[<=<HEHIP[<=[R=<O*KM=<^t=@;GF4VMK[<N%;>T4F4KZ=@KM94=@HE=<O4v%KM94V NL KZ94=;>=RVM9>VZD Z<=@KMNVMKWIL^MK KZ94=QI X IPT4KZDN%OGT4^MN*[<=RVMV
(177) «=<K F4Vt^ZVMK ^M=R[
(178) IPHEHoKZ94= X =atO DKZDENUO>NLKZ94=@;>=
(179) ILVMF4^Z= NL³ITtIL^WIP;=<KM^ZDE[S[<F4^ZnU=DEOKM94=;=<KM^ZDE[ . . . . . . . . . . . . . . . . . . ÍÍ Ä]_^_`<ÓRÕ. . . . . .
(180) sR?.
(181) J$. «=<K ILO X g=K1NGv%DEnU=<OTgNUDEO*KMV NP6ItN%F4O X = X0X NU;IPDEO DEOm] ^8_QIPO X KZ94=NU^ZDEvUDEOo.8 94= ;=
(182) IPVZF4^M=@NP.KM94=@TtIL^WIL;>=<KZ^MDE[ [<F4^ZnU= r YtQw r O ? Yt ?A : ? ?-A DEKM9
(183) 2 O DEO>KZ94=@HN*[
(184) ILH;>=<KZ^MDE[ DEV ^MDEKMKZ=<Oj&Y Q rEt hw rYt r r Ytet rYt == 94=R^M= r r YtetDEVKM94=6T ^M=<n*DENUF4VZHEYc[RNU;>T F4KM = X HEN*[
(185) IPHUI X IPT KM= X ;=<KM^ZDE[U UF VMKoHEN*NU *DEO4v IPKKM94DEVVM=RvU;>=ROjK
(186) W HN*[
(187) ILHEHYDEON%O4= X DE;=<O4VMDEN%OIPO X VZDEO4[<=KM94=D X =IPHoHE=<O vUKM9 1= IPO*K KZN>^M=IP[a90DEOKM94=GI X ILT4KM= X VZ=<vU;=< O*KSVM9 NUF4H X g=Q=RjFgIPH.KMNNUO =UgKM94=O4=
(188) IL^M=<VZKDEOjKZ=<vU=R^cnUILHEF4=@NP1KZ9tIPK@;>=IPVMF ^M= DEHEHov%Dn%=F4VuKM94= O*F4;Gg=<^.NPO4N X =<VKM9tILK6VM9 NUF4H X t=SI X4X = X %æD oKZ9tIPK.;=
(189) IPVZF4^M= DEV.vU^Z=
(190) IPKZ=<^1KZ9tIPOGN%O4= '.N%^.^M=<;NPnU= X %JD©DK DEV6HE=<VZV1KZ9tIPONUO4=SILO X DEOQKZ94=SVZ=<O4VZ=SKM9gIPK6KZ94DEV6vUDEnU=RV6F4V6KZ94= IP[RKMNU^_,^MN%; 94DE[a9GKM94DEV6VZ=<vU;=<O*K.VM94N%F4H X g==<O4HJIL^MvU= X 'DEO>KM9 =DEOjKZ=<^MnUILH X =atO = X * Y IPO X 6B DO [<==rIL^M= X =
(191) ILHEDO vQ DEKM9[
(192) IP^ZKM=<VZDJIPO0;=<VM9o KZ94=@TtN%DO*KZV ILO X DEHEH X =atO4=@KZ94=DEO4DEKMDJIPH [<=<HEHHE=<O4vUKZ9DO=
(193) IP[a9 X DE^M=R[<KMDENUO %V[o W ILO X ] 'DO 94DE[a9 ^Z=atO4=<;=<O*K1N%^6[<N*IP^MVZ=<O4DEO4vVZ94NUF H X g=STg=<^¥,NU^Z;>= X 8 94= tOtIPH T4^MN*[<=<VZV DEHH [<NUO4VZDEVMK6DEO X =agO4DEO4v@t^ZVMK I*FtILVMD©HN*[
(194) ILH X DE^M=R[<KMDENUOgIPH;>=<VZ9H=RO4vUKZ;9 %E,N%^=
(195) IP[a9 X DE^M=<[<KZDENUO ' Q#NU^=U v0KZ94= [ X DE^M=<[<KZDENUOo.=G DEHH X ='tO4=cI [*HE=<O4vUKZ9GKM9tILK6 DEHEHjN%O4HEY X =<Tt=RO X N%OGKM94= mEHENj[IPKMDEN%OoPVMNKWIP *DEO4v@KM9 =S;IL\*D;F4; NPnU=<^ nrIPO X p¦NP KM94=HN*[
(196) IL H [ HE=<O4v%KM94VIPO4VZ1=<^ZVGKM94DEV^Z=<*F4DE^M=<;=<O*K
(197) 8.N *O4NP KM94=KMNUKaIPHO*F4;Gt=R^cNLcI X ILT4KM= X [<=RHHEVDEOGKM94= [* X DE^M=<[RKMDENUOo%=`aF4VZK1KaIP %= KM94=uVMF4;hNPn%=<L^ mKMNvU=<KKM94=uKMN%KWIPHgHE=<O4v%KM9GDEO>KZ94=SO4=R3;>=<KZ^MDE[ NLSKM94=VM=<v%;>=<O* K
(198) 2Ze 8 94=GO4=
(199) IL^M=<VZKGDEOjKZ=<vU=R^QIPT4T ^MNjIL[a94DEO4v0KM9 DVH=RO4vUKZ9 DHEH6v%DEnU=F4VQKZ94=GO4=< O*F4;Gg=<^SNLL [ [<=RHHEVuDO KM94=O4=< I X ILT4KM= X ;>=<VZ9oS=IPT4T4HEYKM9 =QVaIP;>=@T4^ZN*[<=<VMVr,NU^uKM94=K1NNUKZ94=<^ X DE^Z=<[<KMDEN%O4V
(200) Gf =RKMF4^ZO4DEO4vtIP[a 0KZNN%F4^@HENj[IPH.VM=<v%;>=<O* K
(201) X gKZ94=GTtN%DEOjKZV ILO !X ^Z=<T4^M=RVM=<O*KKM94= IL[<=[<=ROjKZ=<^MVuNP6=
(202) IL[W9[<=RHH K$ h$ QILO X [W9 NUVM=RO,NU^=
(203) IL[W9 X DE^Z=<[< KMDEN%O*&Y Q [* X DE^M=R[<KMDENU)O Q . . . X DE^M=<[RKMDENUO)Q W. . . hw . ]. . 4w . X DE^M=<[RKMDENUO)Q. 4w . 4w . z. hw . . hw . . . q. . =uO4=<= X ,NU^KM94=r,NUHEHENP DEO4v@KMNGVM=RKSVMN%;>=u[<NUO*nU=ROjKZDENUO>O NUKWILKMDENUO Vt^MVZK)%JVM=R=Q§Dvg4d' Q
(204). O#". % ".
(205). m ? n ? O p ? O m ? O n ? O p O. . . ILO X =
(206) IP[a9 IP[R=DEV X =RO4NUKZ= X IPV.
(207). Z. ".
(208). & ". m n ? p ? O m O n ? p O. . .
(209). _. ". n. p ? m O.
(210). ' ". m. p. n. .
(211). $. ".
(212). ( ". m ? n O p ? m ? O n O p. . . J?. % '. Î
(213) ÍoÎJÑ.
(214) s.
(215)
(216) . [* X DE^M=R[<KMDENUO. X DE^M=<[RKMDENUO ] X DE^M=<[RKMDENUO W. 4. ' & $ IP[<=(r Z2B_2 ( t " %J=
(217) ILVMK' IP[<=(r $ O ( ' %Gt " %æ1=<VZK' IP[<=(r & B_Gt " e %æO4NU^ZKM9 ' IP[<=(r O 2% & BZGt " B%æVMNUF KM9 ' IP[<=(r O 2% B$ZGt " æ% 94DEvU9 ' IP[<=(r O BZ2B_2 t " %æHENP '. . (i-1,j,k-1). 3. (i,j,k-1). 2. (i,j-1,k-1). N (i-1,j,k). 8. 7. (i,j,k). L W. E H. 1. 5. (i-1,j-1,k-1). S. (i-1,j-1,k). 6. (i,j-1,k). § DEvUF ^M=d$Q6=<HEH0 $ 4$ B*DEO4[R= DEV6O NUK. *O4NP OG=<nU=R^MY* 94=<^Z=S4F4K³NUO4HEYN%OGKM94= [<=RHH IL[<= [<=<O*KM=R^1HEN*[
(218) IPKZDENUO4VP1=SILT4T4^ZNP\jDE;IPKM= rEt *YIPVMVZF4;>DEO4vKM94=@HEN*[
(219) IPH;=<KM^ZD[uKMNt=@HEDEO4=
(220) IL^1N%O=IP[a9NPKZ94=@VM=<v%;>=<O*KZV
(221) X %JVM=R(= l n 'R «=<K F4V X =<O4N%KM=@*Y u 4w r r Gt t :u 4w r r O t t= ILO X VM=<K c w ? ?-A r r tet ?+?-A w ? ? A B u ?+?-A c w ? ?-A r r tet ?+?-A w ? ? A u ? ? A O . . ÍÍ Ä]_^_`<ÓRÕ.
(222) sl.
(223) J$. § NU^u=<\4IP;>T H=%Xc g NUF H X t==<*FtIPH.KZN utR*1=@9tIn%=. ?4?4A. #. . rEt w. . Z. w w. . #. ! =. c : 2r c ? c t D. 7. . O. _ c Z c _ _ c Z c _. w. r r jt ? ?4A B*DEO4[R= r rYt tr! u : ru c : rc ? c t D. ? c 7 ? c_ ? c : c c : c c : c. ?. D©Jc w%c . =utOtILHEHYGv%=<K KM9 =S#NUHEHENP DO vrILT4T4^ZNP\jDE;IPKMDEN%O)Q rEt. !. Z c :Qc Jc :Qc _ c V: c . . ,^ZNU;h 9 D[a9=c[IPO X = X F [<=U ,NU^SIvUDEn%=<O[<=<HEH $ 4$ KM94=@[<=<HEHH=RO4vUKZ94V DEO=IP[a9 X DE^M=<[<KZDENUO*Y,Q OKM94W= [ X DE^M=<[<KZDENUORQS% A )' r Kg $ h$ f tQw Z_ c g : cg c g : c f c+f :Qc f OKM94= W X D^Z=<[<KZDN%O QS% A ' r j $ h $ i tQw _Z c j : cjJc j : c i c+i : c i OKM94= ] X D^Z=<[<KZDN%O Q?% A q '
(224) r l$ 4 $ k t-w _Z c l :Qc l}c+l: c+kec+k : c k B DO [<=>=GILO*KKMN0 %=<=<T NUO X =
(225) ILHEDO v0 DEKM9[
(226) IL^MKM=RVMDJIPO vU^MD X V.KM94N%VM= X =atO4DEKZDN%O4VQILtNPn%=GVM94N%F4H X O4N%K X =<Tg=<O X NUOKZ94=>HEN*[
(227) IPKZDENUO NP KM94=[<=<HEHEV4F4KN%O4HEY0NUOKZ94=>[RNjN%^ X DEOtILKM=G[<N%;>TgNUO4=ROjKILVMVMN*[<DJILKM= X DEKM9 KM94=[<NU^Z^M=<VZTtN%O X DEO4v X DE^Z=<[<KMDEN%O D =U0KZ94=>O4=R HE=<O4v%KM94VKM9gIPK DHEH6g=>F VM= X ,N%^KM94=0I X IPT4KZDENUO T4^ZN*[<=<VMV DEHH³t=ytOtIPHEHEY X ='tO4= X IPVKM94=;>NUVZK X =<;ILO X DEO4vHE=<O4v%KM9 IP;NUO4vIPHEH6TgNUVZVMDE4HE=>= X vU=<VDEO KZ9tIPK X DE^Z=<[<KMDEN%)O Q [* X DE^M=R[<KMDENUO Q m w O eZe rKmVtF4w h$ r g $ h$ f t . . . . . . . . . . . . . . . . . . . Î
(228) ÍoÎJÑ.
(229) s.
(230)
(231) . X DE^M=<[RKMDENUO Q >n w O eZez W. . r+nGt 4w K$ r j $ h$ i t . . X DE^M=<[RKMDENUO Q (p w O Me. ]. . .
(232) rKp t hw $
(233) r l$ h $ k t 8 9 =GHN*[
(234) ILH1HE=<O vUKM9 V IL^M=GVMKZNU^Z= X DOKZ94=GgH=GOgIP;>= X TZ;>=<KZHENj[% v%=<Oo NUF K V KZN0vUDEnU=>ILOD X =
(235) I NP KM94= v%HN%tIPH *FtILHEDKY NP@KM94= ;>=<VZ9 KMNKZ94=F4VM=R^
(236) ,N%^Q=IP[a9 X DE^M=R[<KMDENUO [ W IPO X ] DEKM9 KM94=#NUHEHENP DO v ,N%^M;IPK %æKM9tILK [
(237) IPO0g=@F4VM= X *Y>IvU^WILT494DE[@VMNL,KIL^M=@VMF [W90ILVTMv%OjF T4HENUK V Q m w eZe h n=w YZz e hX pXw O eZre O O (rKm qnGBp2t(r meonG`p t (r meonG`p2t r Kj $ h $ i t 94=R^M= =
(238) IL^M=>KZ94=>[R=<HEH6 IL[<=G[<=<O*KZ=<^G[<N*NU^ X DEOtIPKZ=<V
(239) 8 94=>O4=R HE=<O vUKM9 VQDEO KM94m= [;%J^Z=<VMT W IPO X ] ' X D^Z=<[<KZDN%OIP^Z=VMKMN%^M= X DO KZ94=tHE=<V>OtIL;>= X TZ;>=RKM\*HENj[% N%F4K V %æ^M=<VZTo TM;=<KY*HENj[% N%F4K V IPO X TZ;>=<K Z<HEN*[U NUF4K V '_,NU^SIv%DEnU=<OT4HJIPO4X = %J=% vgQ [ W T4HJILO4= X =atO4= X *YIvUDEnU=<CO p(w p 8p re ' DEKM9KZ94=u,NUHEHENP DEO4v@,N%^M;ILK %J9 =<^M=QILHEVMNvUDEnU?=<Oy,NU^ KZ94=@F4VM=NPKZ94=v%^WIPT 94DE[SVMNL,K IP ^MS= TZvUO*F4T4 HEN%K V ' Q m w eZe ILO X n>w YZez O O (r meonG`p t(rKm on;Bp t rKmVt rJ^Z=<VMT r n;t t [ 1 >.
(240) . 1 S>A@ dMi KLG K2ced D d g K2hEC5D C kddF:cAD G K$C I uO4[<=SILHEHj;=<VM9H=RO4vUKZ94V1IP^Z=1[RNU;>T F4KM= X
(241) KZ94=SI X IPT4KZDN%O[<N%O4VMDEVMKZV6DEO=<*F4D X DEVMKZ^MDE4F4KZDEO4vSKZ94= O4=< O4N X =<V DEKM9G^Z=<VMTg=<[<K KZNKM9 =<VM=@O4=< HEN*[
(242) IPHgHE=<O4v%KM94V§ NU^6=IP|[a 9 X DE^Z=<[<KMDEN%OoU=% Xv [* X DE^M=<[RKMDENUOoL1= t^MVZK6[<NU;T4F4KZ= KZ94=;IL\*D;>ILH*OjF ;Gt=<^NP6O4N X =RV X =<O4N%KM= X *Y IPV DEK6#NUHEHENP V Q | w eSs 8 r r tet 94=R^M=eSs8 r t DVuKM94=O4=
(243) IP^Z=<VMK@DEO*KM=<v%=<^ #NU^ KM9 =vUDEnU=ROTgNUVZDEKMDEnU=@^M=IPHoO*F4;Gg=<^ ILO X r mt rm-w DV X =atO4= X IPVKM94=uKMN%KWIPHI X IPT4KZ= X H=RO4vUKZ9>NPoKZ94=@TtIPKZ9c`aN%DEO4DEO4v@KM94=uNU^MDEv%DOGNLKZ94= X N%;ILDO KZNGKM94=T ^M=<VZ=<O*KSO4N X =@DEOKM94== [ X DE^Z=<[<KMDEN%Oo*D =%.DKDEV X =atO = X IPV KZ94=u,NUHEHENP DEO4v[<F ;GF4HJIPKM= X H=RO4vUKZ)9 Q "! r mtQw # rKp t % ' #!. . . . . . . . ÍÍ Ä]_^_`<ÓRÕ. . . .
(244) sq.
(245) J$. DEKM9 KZ94=0[<N%Ojn%=<O*KMDENUO | r Gtmw | 4 8 94=VWIL|;> =DEV X NUO4=,N%^GKM94=N%KM94=<^ X DE^M=<[RKMDENUO4VHE=
(246) I X DEO4v KMN KZ94= O =< X DE;>=<O VMDENUO4V ILO X ,N%^>KZ94= I X IPT4KZ= X ;>=RVM9o8 9 =0[<N*NU^ X DEOtIPKZ=<V>NL KZ94NUVZ=GO4=< O N X =<VQIP^Z= X =atO4= X ^Z=<vUDEN%O *Y0^Z=<vUDENUO@8 94=GO4N X =<V X =<HEDE;>DEKaIPKMDEO4v=
(247) IL[W9^Z=<vUDEN%O0^M=<;IPDEO t\*= X X F4^ZDO vKZ94=>I X IPT4KZDN%O T ^MN*[<=<VZV
(248) =S`aF4VZK@^M=<[
(249) ILHEH1KZ9tIPKDEO VMNL,KIL^M=<VVMF4[a9 ILV].94N*=<O4DE[<V.KM94= ^Z=<vUDENUO VSIP^M= t^MVZK X =atO = X HN*[
(250) ILHEHY X DE^M=R[<KMDENUO*Y X DE^M=<[<KZDENUOo6§ NU^KM94==[ X D^Z=<[<KZDN%Oo4I@^Z=<vUDENUONP.DO X =<\ m [=m [sw YZe @fS DEV X =atO4= X *Y0DEKMV[<=RHHHEDE;>DEK DEO X =<\*=<VJm Bm Z> 9 =<^M=Vm DEV@KM9 =[* DEO X =R\ NL1KM94=GO [R=<HEH6VMKaIP^MKZDEO4vKM94=G^Z=<vUDENUO NP DEO X =<\ m [ILO X m ZDEV@KM94= [ O DO X =<\NP KM94=G [RO =<HEH6=<O X DEO4v KZ9tIPK^Z=<vUDEN% O Q@KM94N%VM=GDEO*,N%^M;IPKMDEN%OIP^Z=GT4^MNPn*D X = X *Y IKaIP4HE=NP H=RO4vUKZ9 Z e @fS X =<O4N%KM= X *Y Mfu @eQ*VZF4[a90KM9gIPK Mfu @=e r ZLm [@tQw me| MfS @=e r ZLm [ : O t-w mV|
(251) zm [ w O Me cfu f 94=R^M= m e| %æ^M=<VZTo m |
(252) 'DEVKM94=t^ZVMK %J^M=RVMTo HILVMK '[<=RHHuDEO X =<\ VMKWIL^MKZDO v %æ^M=<VZTo3=<O X DEO4v 'KZ94\= [* ^Z=<vUDENUO m [ B IP;>=DEO*,N%^M;ILKMDENUO IP^M=T4^MNPn*D X = X #NU^KM94= W ILO X ] X D^Z=<[<KZDN%O4V>IPO X [<NU^Z^M=<VZTtN%O X DEO4v KaIP4HE=<VQIL^M= X =<O4N%KM= X *Y *fS re %JNL X D;=<O4VZDN%CO Z ze fS &'ILO X fS re %æNP X DE;>=<O VMDENUCO Z e fS )' ^M=<VZTt=R[<KMDEnU=RHY*§ NU^S=IPVM=NPT4^MN%vU^WIL;>;D O4vgU=[<^Z=
(253) IPKZ=>IPO I X4X DEKMDENUOgIPHKWIL4HE= X =<O NUKM= X *Y Mf ! «Mb rKm Bm = m `m2cKm\Bm tm`m w O Zecfu XJm =m w O `_ mc m w O `Z m w O BZ KZ9tIPK@vUDEn%=<VSF4V@KZ94=Q[R=<HEHDEO X =<\0HEDE;>DEKM&V %Et^ZVMK@DEO X =<\ [<NU^Z^M=<VZTtN%O X DEO4vKMVN mcKm w O IPO X HJILVMK@DEO X =<\KMN m2cKm w Z'uNPSI>v%HENUtILH^Z=<vUDEN%O m DEO KZ94= X DE^M=R[<KMDENUO m = m ,NU^@KZ94=GNUH X ;>=<VZ9 % m w '@IPO X O4=< I X IPT4KZ= X ;=<VM9 %Km w Z' ILO X 94=<^M=ecfu zw3e cfS 6ze fS 6re fu G @DEnUO =<OIKM^MDET4HE=<K NL_DEO X D[R=<=V rKm [ Bm W Bm ] t<4=@[
(254) IPO X ='tO4=KZ94=IPVMVZN*[<DJIPKM= X vUHENUgIPHg^M=<v%DN%ONPDEO X =< \ m *Y>VM=RKMKMDEO4v m w r e fu \rPe rfu \r m [ ? O t0:zrKm W ? O t2t0: m ] 8 94=>ILtNPn%=#NU^M;GF HIDEV@VMDE;T4HEY X =<^MDEnU= X *Y ^M=<O*F4;Gg=<^MDEO4vKM^ZDT H=RKDEO X =<\0=ROjKZDEKMDE=<VKZNVZDEO4vUHE=DO X =<\ =<O*KZDKZDE=<V@DO[
(255) IL^MKZ=<VMDJIPO %,ILO X ;NU^M=@v%=<O4=<^aIPHEHEYVZKM^ZF4[<KMF ^M= X 'r;>=<VZ94=<V Q =U v>KM9 =vUHENUgIPHo^Z=<vUDEN%O m w O [<N%^M^Z=<VMTgNUO X VGDO X =<= X KMN0KZ94=G^M=RvUDENUO 9tIn*DEO4v r m [w O Bm W w O Bm ] w O t@IPVIKM^ZDET4HE=<KNP DEO X DE[<=<V %æ^M=<T4HJIL[<DEO4v KZ94=nUIPHEF4=<VNP m [ m W IPO X m ] DEOKM9 =ILtNPn%=G,N%^M;GF4HJIHE=
(256) I X VQDEO X =R= X KZN m w '< § ^MN%; KM9gIPK@vUDEnU=RO v%HN%tIPH^M=< v%DENUO 1=[
(257) IPO X =atO4=GKZ94=GDEO X =<\0DEO*KM=R^MnUIPHEVuNP KM94=Gn%=<^MKZD[R=<V rKm@ qn@`p O 4t g=<HENUO4v%DEO4vQKZNGKM94=@O4=R I X ILT4KM= X ;=<VM9DOKZ9tIPK ^Z=<vUDENU)O Q. . . m. n p . m e| `m | w8n e| qn | w p e| ` p | . w. . . 94DE[a9 IP^Z=>T4^ZNPn*D X = X *Y KaIP *DEO4vKM94=GDEO*,N%^M;IPKMDEN%O>#^MNU; KZ94=GKWIL4HE=GMf! Mb . DEKM9 m w Z4mSV I ;ILKMKM=R^QNL IP[<K6=> *O4NPhKZ94=HE=<O4vUKZ94VDO KM94=O4=<;>=<KZ^MDE[>NLS=
(258) IP[a9 DEO*KM=<^ZnUIPH&%JDEO =
(259) IL[a9 X DE^M=R[a KZDN%O ' X =atO DO vI X DE^Z=<[<KMDEN%OtIPH6^Z=<vUDEN%Oo=Q;IY>KM9 =<^M=a#NU^M= X = X F [<=GKM94=GO*F4;Gg=<^@NP I X ILT4KM= X [R=<HEHV DEO4VZD X =S=
(260) IL[W9NLKM9 NUVM=@^Z=<vUDENUO VILO X KZ94=<^M=',NU^Z= X = X F4[<=KM94=@[<=<HEHDEO X DE[<=RV,%æDOKM94=@O4=R3O*F4;>=<^ZNUKaIPKMDEN%O ' X =RHDE;DKZDEO4v>KZ9tIPKVaIP;=G^M=<v%DN%Oo0 vt#NU^KM94m= [* X DE^M=<[RKMDENUOo=Gt^ZVMK^M= X ='tO4=KM94=KWIL4HE=GMfS@e %æVMDEO4[<=@DEO*,N%^M;ILKMDENUOr,NU^6KZ94=@NUH X DEO4DEKMDJIPH*;=<VM9>IL^M=@VWIn%= X DEO>KWIL4HE= M f ! Mb r m O O Z O t '.*YKM94= ,N%HEHNP DEO4vT4^MN*[<=<VZ V Q. Î
(261) ÍoÎJÑ.
(262) s
(263) p.
(264)
(265) .
(266) !"#%$&'. ( )* ,+-".#$. / )* ,+-" $ !"#%$&102/ 30%"4 )56%$7 98 / ! / :$;.<8 /: " !( =$?>A@CBD$ $ 1>< !%$. )* ,+-"E.'#$<' !
(267) >.
(268) <. )* ,+-" $<' !
(269) F. 94=R^M= 8 / VZKWIPO X V,NU^ X =atO4= X DO ,N%^M;GF4HJI% 'GIPO X eSmWr m [@tm [jw O Ze cfu VZKWIPO X V6#NU^.KM94= KZNUKaIPH4O*F4;Gg=<^.NPO4=< nU=R^MKMDE[<=RV1[<N%O*KWIPDEO4= X DOKM9 =:[*^M=<v%DENUONPDO X =<\m [B D;DEHIL^MHEYU =S DEHEH X =<O NUKM=@*Yez1mXrKm W t m W w O Merfu*%æ^M=<VZTo6egm(rKm ] t m ] w O MefS)' KZ94= KMN%KWIPH*O*F4;Gg=<^oNLªO =< n%=<^MKZD[R=<V1Tg=<^ W %æ^M=<VZTo ] ' ^Z=<vUDENUOo8 94N%VM= DEO*,N%^M;IPKMDEN%OcIP^Z=1F VM= X KZN X =atO4= KZ94,= TZvUHEN%tIPH V KWIL4HE=Mf ! «Mb r m `m = m O Z `Z t³,NU^ m w O ZecfSQm = m w O YB_,N%^ KM94= O4=R I X IPT4KZ= X ;=<VM9o=SILHVZN9tIn%=SKM9 =SDEO X =<\GDEO*KM=R^MnUIPHEV6NLoKM94=unU=<^ZKMDE[<=<XV rKm qnGBp2t.g=<HENUO4v%DEO4vKMNKM94= N%H X DEO4DEKMDJILH4;>=<VZ9DOKM94=VWIP;=S^Z=<vUDENUO %JT4^ZNPn*D X = X ,^MN%;hKWIL4HE=cMf Mb rKm Bm = m O Z2 O t 'OQ. n. w m e| `m |
(270) w n e| qn | w p e| YBp |
(271) . m p. § NU^gNUKZ9;>=<VZ94=<VoKZ94=>DEO X =R\ VZKWIP^ZKMDEO4vKM9 =>^M=RvUDENU O m [<N%DO [<D X =<V DEKM9KZ94=G[<=<HEHDEO X =<\ vUDEnU=RO *Y aK IP4HE=Mf! Mb =<\*[<=<T4Ku,N%^rm w O IPO X D©1NUO4=NP1KZ94 =QVZKWIL^MKMDEO4vDEO X =<\*=<V@DEVS=<*FtILH.KMN O gVMDEO4[<=DEO KZ9tIPKu[
(272) IPVZ=KM94=[<N%^M^M=RVMTgNUO X DEO4vnU=<^ZKM=<\DEO X =R\DEOKM9 =^M=<VZTt=R[<KMDEnU= X DE^M=R[<KMDENUO 9tIPVuKMNGg=VM=<K@KZN 4 B*Nt ,N%^6ISv%DEnU=<ODEO X =<\KZ^MDET4HE=<K:r m@on @Bp &tNL«IunU=R^MKM=R\Q^Z=<HJIPKM= X KMN@KM94= O =<3I X ILT4KM= X ;>=RVM9DOKM9 = vUHENUtILH ^Z=<vUDENUO m 4DEKMV O4N X =[<N*NU^ X DOgIPKM=RV [ Er m@on @Bp @`m =&tzm =Xw O BZ2B_IL^M= X ='tO4= X IPV KZ94=tIL^MY*[<=<O*KM=R^ [<N*N%^ X DEOtILKM=<V NL [ rKm m ? O tIPO X [ r mKmVt&%J^Z=<VMT W r n n ? O t1ILO X W r+nn;tR ] rKp9p ? O t ILO X ] rKp p t '_,NU^KM94==[ % m =Xw O '&%J^Z=<VMTo W %Km =Ww O 'R ] %Km =Ww%_'S' X DE^M=R[<KMDENU) OQ [ @r m@on @Bp @ O t w [ rKm m ? O t0:zr O ? t2[ rKm mt [ @r m@on @Bp @`Z t w W r n n ? O t0: r O ? t W r+nnGtW [ @r m@on @Bp @`_ t w ] rKp p ? O t0:zr O ? t ] rKp9p2t 94=R^M=:[ rKm mt %J^M=RVMTo W r+nn;Rt ] Kr p9p2t '«VMKWILO X V,N%^x[ rKm meon nGBp p O t %æ^M=<VZToQ[ r mKm on nGBp pBZGt< [ rKm meonn;Bp pB_GtA' ILO X w r r mKmVt ? c t E r Kr m mVt ? r mKm ? O tet w r +r nn;t ? c Y t E r +r nn;t r n n t t w r r p p2t ? c t E r r p p2t ? ? Kr p p ? ? O O tet DEKM9GKZ94= [ %J^Z=<VMTo W ] ' HE=<O4v%KM9 c %J^M=RVMTo"c c '³^M=RVMT4^Z=<VM=<O*KZVSKM9 =cIP[R[<F4;GF4HJIPKZ= X H=RO4vUKZ9GDOGKZ94= O4=< ;=<KM^ZD[@F4TKZNQKZ94=W[%J^Z=<VMTo W ] 'TgNUVZDEKMDENUONPKZ94=O4=RO4N X =@NL_DEO X =<\\Kr m@q n@` p &t Q . . . . . ÍÍ Ä]_^_`<ÓRÕ. . .
(273) %k.
(274) J$. -. c c. c. w Kr m e| w r+n e| w r p e | . ? Ot ? Ot ? Ot. r r m| t ? Kr m e| ? O et t E e Sm(r m [@t r r+n| t ? r n e| ? O t t E ze 1mXrKm W t= r rKp |
(275) t ? Kr p e| ? O t tNE re gm(rKm ] t . :frKm ? m e| : t :fr+n ? n e| : O t :frK p ? p e| : O t O. %æ^M=<[
(276) ILHEH6KM9tILK@1= *O4NPKM94=KMN%KWILHO*F4;Gg=<^uNP O4=< O N X =<V@ DKZ94DEO0=
(277) IL[W9 ^M=RvUDENUOIPO X KM9tILKcKZ94=<Y IL^M= =<*F4D X DEVZKM^MDE4F KM= X DEO4VZD X = =
(278) IP[a9GNPKM9 NUVM= ^Z=<vUDEN%O4V' UKZ94= DEO X =<\*=<V:r mKm on nGBp p2t6IL^M=,N%F4O X DO
(279) me| GBm|
(280) n e| &qn|
Documents relatifs
Dans chaque ville et pour toutes les lignes de tramway considérées, il faudrait disposer des trafics avant et après ouverture d’une ligne et de plusieurs projections d’évolution
Le fait d’écrire à partir d’une oeuvre d’art visuelle ressemble à une forme de contrainte; nous croyons par ailleurs que cette pratique a eu un effet durable sur l’écriture
variables d'ordre psychologique: soit f.amiliale ou personnelle, soit so- ciale, soit professionnelle, soit une combinaison de ces facteurs. Ce patient a récupéré
For the two coolest objects in Figure 3.6, HD 4539 and PG 1716+426, both at Ta < 27, 000 K, there is a good match between the predicted synthetic spectra and the FUSE data: the
lui inculquer le registre li'lquistioue, les l1abitudes alimen- taires et vestimentaires ainsi que le comportement des bour- geois de Québec. Pierrette Paul doit
La conciliation emploi-famille : des mesures à développer dans les milieux de travail Tableau 4 : Les dispositions favorisant la conciliation travailfamille dans les
Figure 2.4 Predicted (continuous lines) and observed values (filled circles: stands aged from trees with root collar; open circles: stands aged from trees without root collar)
Cette posture permet de dégager deux idées centrales : le poids des milieux professionnels locaux dans l’intermédiation et le transit des idées, modèles et pratiques
