Multiresolution Representation in Unstructured Meshes : I. Preliminary Report

Texte intégral

(1)Multiresolution Representation in Unstructured Meshes : I. Preliminary Report Remi Abgrall, Ami Harten. To cite this version: Remi Abgrall, Ami Harten. Multiresolution Representation in Unstructured Meshes : I. Preliminary Report. [Research Report] RR-2342, INRIA. 1994. �inria-00074335�. HAL Id: inria-00074335 https://hal.inria.fr/inria-00074335 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Multiresolution Representation in Unstructured Meshes: I. Preliminary Report Re´mi Abgrall et Ami Harten. N˚ 2342 Septembre 1994. PROGRAMME 6 Calcul scientifique, mode´lisation et logiciel nume´rique. ISSN 0249-6399. apport de recherche. 1994.

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(26) 7 0 'çcp1c 0

(27) 8 1 .:9 <;>=8 1 . 'C65]

(28) ? 0 @~VfMOVA$ c]a{RaS|Rt\fVN@T1Rt|u|7c]euPQa{Rteun / cdaIR[ic]euV RtMaS|Rt\fVN@n`cdTUVfeuaOc]Nre 3 § e'gSu1 V1Nt[i[]N )c]euPVsaSuN uN ,gSNNQ7gRcde+TY^`[igOc]MOVfaSN@[]^7gOc]Nre'MOVf|uMOVfaSVfeQgRgOc]NQeªNt RteQ± n7c]aS\fMOVKgSV nRgRCB 8 mr{uVfMOVIgSuVa\R[]VĆnuVf\fNrTU|}NraOcpgOc]NreU\fNrMOMOVfaS|}NQeunuagSNgSuVI[dVKQV[]a)Nt>MOVfaSN@[]^7gOc]Nre·{7c]\ R@MOV1c]eQgSMON7nuû\fVfn+cde 'C7§]5 0S§w¨)`cdacda1RQV_Mv±+PrVfeuVfMSR[MSRtT·VKNQ=M #!{`cd\qÁR[p[dN ~aYNQMYn`cdaS\fMOVKgOc]RgOc]Nreua \_NQMOMOVfaS|}Nreun`cdeuPgSN1ûeua©gSMOû\KgSûMOVfn PQMvc]nuac]eEaVQVfMSR[baS|kR@\fVIn7c]T·Vfeua©cdNQeua_§ >c]MOaOg V~aSuN gSkRgReuVfaOgSVfn1aSVfjGûVfeu\fV)NtBn7cda\_MOVKgOc] RgOc]Nre1\fNQTUV_awVfjG^7cd|l|Vfn1 cigSRnlV_\Kc]T1RgOc]Nre Nr|}VfMSRgSNQM <;>= ~7cd\q³c]a{R[pcdelVRtM)T1Rt|u|7c]euPMONrT / 1 'D$&0 NreQgSN / <;>= 1 <;E= 'D$&0 <;>= C / ,I%F'G- )H% / <;E= 5 'C65Ü7 0 ¨)7c]aInuVf\c]T1RgOc]NQeE1 NQ|VfMSRgSNrMcdaInuVKhelV_n!Rta)Nt[p[dN ~/a C uNQMIR@eQ <±J;>= B cde / gSuVfMOV c]aRg~[]VRtaOg~NreuV 8K $ aSû\ gSRg 8 BLlgSuV nlV_\Kc]T1RgOc]NreNtMBUcda <;>=8NK / m`cÇ§áV@§pm B K / 0 B 1 8 0 <;E= B 1 <;E=8 5 'C65Ü?0 g Nt[i[]N ~aMONrT 'C7§]f 0gSRg <;E= cdaVK[p[iĆnuVKheuVfnQ± 'Cl§Ìt 0SmQcÇ§áV@§rcigSanuVKhe7cpgOcdNQe1c]a cdelnuVf|VfeunuVfeQgNt gSuV |RtMvgOcd\f^7[øRtM 8 §k¨NaSVfVIgSRg)[]Vg~ûa gR #tV 8= R@eln 8

(29) O c]eP$ aû\sgSRg 8Q= 1 B 1 8

(30) O 0 gSuVfeEQ± 'C7§]f 0 . 1 8= , Q8*O 1 ' 8Q= , 8*O 0R9 . 1 <;E= ' 8= , 8

(31) O 0 1 <;>=<8= , <;E=S8

(32) O ÔbÔ ÞIH/J,KLJ.

(33) Gc. O¥Q¡ø¡ ¦¥ . {7c]\|uMON QVfa{NQûM)\K[øRc]T³§ cprVfe B K / V \ R@esV@R[]^RgSV B #;E = r±MOVf|V RgSV_nsnuVf\KcdT1RgOcdNQe B <;E=1 <;>= B 0 1 0 5G5*5 0 5 'C65Ü 0 yQc]eu\f8V 'Cl§Ìt 0wc]T·|`[ic]Vfa)gSRg <;E= ' Q8 0 1 <;E=S8 NrM)RteQ± 8 K $ 'C65á 0 VYPQVKg{NQM RteQ± 8K $ NQM)~7cd\qNB 1 8 m}gSkRgB 1

(34) 8 NQMIR[p[ cde 'C7§Ü 0S§}²+VNQ^7[dn[pc #tV gSNUaOgSMOVfaSa)gSlV |Ntc]erggSR g 1 gS7c]a{nuVf\Kc]T RgOc]Nre cda~nuNQeuVI)cpgSuNQ^7g{Vl|7[pcd\Kcpg #GeuN [dVfnuPQVNt 8 § yQc]eu\fVr± 'C7§] RF0 / 'D$&0Sm}cpgIN@[p[dN_{a gSRg Rta¦R·MvcdPQQgO´Çc]erQVfMOaSV('CRg~[dV RtaOgINreuV50{`cd\q V nuVfeuNtgSVQ± C C / - $ 0 1 0 'C65 @ 0 {uVfMOV nuVfeuNtgSVfa gSuVc]1 nuVfeQ gOcigC±ENQ|VfMSRgSNrMc]e / §y@cdeu\f8V ' B 0 K $ c]a{RteERt|u|uMON_`c]T1RgOc]Nre gSN1R@eQ± 8NK $ NQM{`cd\q

(35) 8 B mlV MOVKVfMgSN Rta)RUMOVf\fNreua©gSMOû\KgOcdNQe³Nt § ~V`gEV«aSuN gSRg RteQ± aSVfjGûVfeu\fVNt.\fNrMOMOVfaS|}NQeun7c]euP'MOV_\fNQeuaOgSMOû\KgOc]Nre NQ|VfMSRgSNrMOa nuVKheuVfaR À z aS\quVfT· V¦NrM~n7c]aS\fMOVKgSV.nRgR B c]e / §¬yQgR@MvgOc]euP1MONQT B <;E= cde 'C7§Ü 0 V\ R@ePQVgRte R@|l|uMON_`cdT1RgOcdNQegSN B Q± B ' <;>= B <;E= 05 'C65ÜW7 0 ² VnuVfeuNtgSV < ;E= 1 C <;E= 0 < ;E= C / <;E= - / 'C#5ÌW ? 0 R@eln MOVKVfM~gSNcpg R@aI|uMOVfn7c]\KgOcdNQe! Nr|}VfMSRgSNQM§ gN@[p[]N {a cdTUTUVfn7cøRgSVK[p± MONQT gR <#Q;>cdel= P 8 1 <;E= B <;>= c]e 'Cl§ 0 R@elnEûa©cdeuP('C7§@ 0wgSRg <;E= cdaIRMvcdPQQgO´Çc]eQrVfMOaSV NtbgSuV nlV_\Kc]T1RgOc]Nre <;>= < ;>= 1

(36) <;>= 5 'C65ÌW 0 ² VNQuaSVfMvrV gSRggSuV |uMOVfn7c]\KgOcdNQeV_MOMONQM 1 B , < ;E= B <;E= 1 ' , < ;>= <;>= 0 B 'C65

(37) 6Q70 aRgOcdaOhkV_a gSuV MOVK[çRgOc]Nre <;E= 21 <;>= B , ' <;E= < ;E= 0 B <;>= 1 B <;>= , B <;E= 1 . R@elngSuVfMOVKNrMOV cig cda cde gSuV eG^7[p[aS|Rt\fVN@gSuV nuVf\KcdT1RgOcdNQe³NQ|}V_MSRgSNQM K ' <;>= 0 1 B B K / 0 <;>= B 1 . 5 'C#5 6? 0 ÑÓÔ¬ÑÕ.

(38) ¥Q¡ u¡

(39) ¤ ¡ø¡ U¥ ¡ø¡ ¥ ¢ u¤ ! . g{Nt[i[]N ~a MONrT C' l§ÌrR 0wgSRg. Gcpc. n7c]T ' <;E= 0 143 , 3 <;>= 'C65370 R@eun¦gSuVfMOVKNrMOV gSlV |uMO3 Vfn7cd\KgO3 c]NreVfMOMONrM m~7c]\cdanuVf aS\f1 Mvcd}Vfn c]eYgS; VfMOTUa$Nt 3 \fNQT·|}NQeuVfergSacde / ; m\ R@e VMOVf|uMOVfaSVfeQgSVfnUr±?' <, ;E= <;E= 0aS\ R[]VK´¸\fN7VKµ \Kc]VfergSa I = §GyG|Vf\Kcph\ R[p[i±rm[]VKg

(40) = V RteQ±³RtaOcda N@ ' 0Sm ' <;>= 0 1 aS|Rte I ; = 0 'C653?0 R@eun [dVKg nlV_elN@gSVgSlV \fN7NrMOn7c]eRgSVfaN@ cdesgS7c]a{RtaOc]a 1 ; 1 C 0 1 C 5 'C65Ü70 I= @{Vf MOV ; nuVfeuNtgSVfa gSuVNQ|VfMSRgSNrM~7c]\ERtaSaOc]PQeuagSN K ' <;>= 0wcpgSa) <;>\fN7= NQMOn7c]eRgSVfa cde gSuVRtaOc]a LlNQuaSVfMvrVgSkR I g c]agSuV cdnuVfeQgOcpg¸±Nr|}VfMSRgSNQM c]e ' 0SmlcÇ§áV@§ = 1 NQM)Rter± K ' <;E= 05 'C65Ü? 0 ~V7gwVaSlN gSkRgwgSuVfMOV c]a RINQeuVK´ÇgSNt´¸NQeuV\fNrMOMOVfaS|}NrelnuVfeu\fV VKgCV_Vfe B R@eln 0 B <;E= C cprVfe B VVK@R[d^kRgSV <;>= 1 <;>= B B. 1 ' < ;>= <;>= 0 B L , <. > ; =. P@cprVfe B Rteun V¦MOV_\fN QVfM B Q± < ;E= B <;E= 1 < ;>= <;>= B ' , < ;E= <;E= 0 B 1 < ;>= <;>= B ' < ;>= <;>= 0 B , 1 B 5 1 0 5G5G5 0 V PrVKggSkRg # |l|7[i±Gc]euPUgSuVYRt}N rVINQM B = - = 0 5*5G5 0 =<0 B 1 C B ! L 'C65i . 0 VMOVVfMgSN B ! R@agSuV T^7[igOc]MOVfaSNt[d^7gO1#c]NQeE" MOVf$ |uMOVfaSVfeQgRgOc]NQe ' À z 0NtMB § ¨)lV n7c]MOV_\Kg À z9gSMSRteuaONQMOT B ! B c]a{PtciQVfeEQ±gSuVR[]PrNQMvcpgSuT 1 0 5G5G5 0 % & B <;E= 1 <;>= B 'C65ir5 0 1 <;E= 1 C( ' B ' , <;E= 0 B ÔbÔ ÞIH/J,KLJ.

(41) Gcicpc. O¥Q¡ø¡ ¦¥ . ¨)uV cdeQrVfMOaSV À z9gSMSRteuaONQMOT B 1#" >; = $ B ! cda P@cprVfer± % 1 0 5G5G5 0 & 'C#5i 0 1 < ;>= B <;E= 5 B ²+V$MOVfT1R@=M #IgSkRg>c]eTY <^7;>[p= gOc]PrMvc]n gSVfMOTcdelN@[]NrPt± <;E= cda)®MOVfaOgSMvcd\KgOc]Nrel°{Rteun < ;>= c]a)®S|uMONt[]NreuPGRgOcdNQe¬§ ° e«aOc]PreR[|uMON7\fV_aaOcdelP |7[øRf±7a gSlV1MON@[]V1N@.®©[]N )Ć|R@aaIhu[igSVfMO°{`ci[]V& ' m>~7c]\c]aYnlVhkeuVfnc]e 'Cl§iQ 0Sml|7[øRf±7agSuV¦MON@[]V Nt ®S`cdPQ7´¸|kR@aSa hu[igSVfM§ ° e'NrMOnuVfMgSN!Rt|u|7[p±gS7c]a.T^7[pgOcdMOVfaSNt[d^`gOcdNQe MOVf|uMOVfaSVfeQgRgOcdNQegSNMOV R[p´Ç[pcpV1|uMONr`[dVfTUaYNQM |u^lMO|NQaSVfa N@R@ekR[p±7aOcdaIRteunnRgR·\_NQTU|uMOVfaSaOc]NreBmlVYRfQV gSNT1R #@VaSûMOV gSkRgIgSuVn7cdMOVf\Kg À z gSMSR@elaONrMOT R@eln cigSa~c]eQrVfMOaSVUR@MOVaOgR@`[dV¦)cpgS MOVfaS|}Vf\Kg{gSN|}VfMvgSûMORgOcdNQeua_§ e ) r$ +V|uMOVfaSVfergIaOgRt7cp[icpg¸±!RteR[p±7aOc]a)NQM À z aS\quVfTUV_a RteunnlV_MvcprV1R aS^7µ1\KcdVfeQg \fNreun`cigOc]Nre {7c]\aV_VfTUaIgSN³}V®S\K[]NraV_°UgSNeuVf\fVfaSaRtMv±.LgS7c]a \fNreun`cigOc]NresR[]aSNcdTU|7[pcdVfa VK`c]aOgSVfeu\fVN@RTY^`[igOc]MOVfaSN@[]^7gOc]NresRtaOcda NrMûel\gOc]NQeuac]e $ § eR@|l|Vfeun7c£ # VYMOVKGcdVK aSNQTUV VK[dVfTUVfeQgSa NtgS`cdaRteR[p±7aOc]a RteunMOV[øRgSV gSuVfT gSN·gSuVY|RtMvgOc]\_^`[çRtM{VkRtT·|`[dVfa~N@wgSuV |uMOVfaSVfeQg{|Rt|VfM§ egSlVUN@[p[dN_)c]euP³V1nlV_a\_Mvc]}V.gSVf\que7c]j`^lV_a¦gSNPrVfeuVfMSRgSV ReuVfaOgSVfnaV_jGûVfeu\fV1Ntn7c]aS\fMOVgOc] RgOc]NQO e {7c]\'\fNQMOMOV_a|NQeunuagSN!ûeuaOgSMO^l\gS^lMOV_nTUVfaSuVfacde+[zIm$R@eun+|uMOVfaSVfeQg1aS|Vf\Kcph\³R[dPQNrMvcpgSuTUaNrM¦[z § ¨)uV¦T Rc]e Rt|u|7[pc]\RgOc]NreN@gS7cdaITUVKgSuN7nuNt[dNQPt±1cda gSN1gSuVe`^lT·VfMvc]\ R[baSNt[]^7gOcdNQeN@L a cde\fNQT·|`[dV PrVfNQTUVgSMvc]Vfa_§ IûM RtaOc]\¦Rt|u|uMONGRt\1gSNgS7c]a{Rt|u|7[pcd\ RgOcdNQe1c]a gSRg·®OgSlV ^laSVfMO°.aSlNr^7[]n|uMON_`c]nuV RTUV_a R@elnR@e!Rt|u|uMONQ|uMvcçRgSVe`^lT·VfMvc]\ R[TUVgSlN7n¬m>RteunVUR@aSaûTUV gSRguVYc]aaRgOcda©hVfnE cigS gSuV.jG^R[pcigC± N@gSuVfaSVeGûTUV_Mvc]\ R[>MOVfaS^7[pgSa*LlûMvgSlV_MOTUNQMOV@mlV R@aSaûTUV{gSkRg gSuVaSNt[d^7gOc]NQec]a)N QV_MOMOVfaSNt[prVfnc]e³[øRtMOPrV |RtMvgSabN@7gSlV \fNQTU|u^7gRgOcdNQeR[`nuNQT1Rc]2e 'çgS7c]aT1Rf± }VnuûVwgSN{|lMONr|RtPGRgOc]NreIc]egOc]TUV N@uV`cda©gOcdeuP~MOVfP@c]NQeua N@>[øRtMOPrV~@RtMvcçRgOcdNQe¬m`NrMnuûVIgSNgSuVeRgSûMSR[}[øR@Kc]euVfaSaNtR ®ûaSVfMO°u§i§p

(42) § 0S§ IûMgRta #Uc]a gSN|uMON GcdnlV R À z aS\lV_TUV {7c]\·)cp[i[BVfeR@`[dV~ûagSNY\ R[d\f^7[øRgSV)gSuVfaSV~aRtTUV{MOVfaS^7[pgSa_m@)cpgS7cdesR ûaSVfMvĆaSû|u|7[pc]V_nUgSNt[]V_MSRteu\fV NrM>VfMOMONQMbu^7gcdeR)Tû\ÇR@a©gSV_MB)R±Gm_Q± |VfMvNQMOTcdeuP~gSuV \fNQTU|u^7gRgOcdNQec]e gSuV aS^`cigRt7[]V$[]N7\ R[t[dVKQV[uNt MOVfaSN@[]^7gOc]NreB§G¨NnuNaSN VRt|u|7[p±sR¦\fN`RtMOaSVfe7c]euPY|uMON7\fVfnuûMOV~gSN¦gSuVIP@cprVfeTUVfaS1gSNPrVfeuVfMSRgSV R $ aSVfjGûVfeu\fV Nt n7c]aS\fMOVKgOcd RgOcdNQe¬mR@eunªheun9Rte9Rt|u|uMONQ|uMvcçRgSVaSVfjGûVfeu\fV Nt MOVf\fNreua©gSMOû\KgOcdNQe¶NQ|VfMSRgSNrMOa_§ Ieu\fV1gS7c]acda1Rt\f\_NQTU|7[pcdaSlV_n«V³^laSVgSuVsT1R@\q7cdelV_Mv±+N@~gS7c]aUaSVf\gOc]NQegSNNQ7gRcde+TY^`[igOc]MOVfaSN@[]^7gOc]Nre MOVf|uMOVfaSVfergRgOc]NresN@nkRgR¦cde gSuVûaSVfMvĆaSû|u|7[pc]V_nsTUV_a¬§`² VMOVfT1R@=M #UgSRggSuV¦|uMOVK[ic]TcdeRtMv±³MOVfaS^7[pgSa)Nt R@|l|7[i±Gc]euP gS7cda|uMONrPQMSRtT gSN~Q±7|VfMO}N@[pcd\ \fNQeuaSVfMv@RgOcdNQeI[çR{aRtMOVV_el\_NQûMSRtP@c]euP 'ÒaSVfV ) `mr_ +CFm )A@7m5W +Çm ) +10S§ # TUNrMOVIR@T7cpgOcdNQûa |uMONQPrMSRtT c]agSN VfeunuN_¶gSuV À z¶aS\quVfT·V)cpgS1gSuV~\ R@|Rt7cp[icpgC±.gSN¦cdeu\fMOVfaSV gSuV [dVKQV[kN@}MOV_aN@[]^7gOc]NreUR@}N QVgSRg$NtgSlV)ûaSVfMvĆaSû|u|7[pc]V_nTUVfaScikgSuV{RteR[i±7aOc]a$NtgSlV)aS\ R[dV \fN7VKµ1\c]VfeQgSa cdeln7cd\ RgSV)gSlV{euVfVfnUgSNYnlNYaSN nlûV)gSNnuVKrVK[]Nr|uTUVfeQg N@B[øR@MOPQV@RtMvcçRgOc]Nre1NQeRaST1R[i[]VfM a\R[]>V 'ÒNt\fNQûMOaSV gSuV ûaSVfMbkR@agSN aû|u|7[p±YR [ic]TcigNQe gSlV aST1R[p[dVfaOgaS\ R[]VwgSRguVcda)cp[i[pc]euP~gSN |kRf±Nr,M 0S§ # g|uMOVfaSVfeQgV R@MOVelN@gnuNtc]euPgSRg_mkRteun1gSuVfMOVKNQMOVIgSuV T1Rc]e1c]eQgSV_MOVfaOg cde gS7c]a)|Rt|VfM c]a c]eEnlVQVK[dNQ|7c]euP.\fNGR@MOaV_e`cdeuP |uMON7\fVfnuûMOVfagSRg{MOVfaS^`[igc]eR.aV_jGûVfeu\fVNteuVfaOgSVfn³n`cdaS\fMOVKgOc]RgOc]Nre LluN_VQVfMVaSR[p[R[]aSN.\fNQeuaOc]nuVfM gSuVjGûVfaOgOcdNQe Nt7MOVhkeuVfT·VfeQg_§_² VNr^`[dn[pc #@VgSN)|}NtcdeQgbNQ^7gR@PGRcdeIgSRg>gSuVT1Rc]e ûaV$NtuûeuaOgSMO^l\gS^lMOV_n ÑÓÔ¬ÑÕ.

(43) ¥Q¡ u¡

(44) ¤ ¡ø¡ U¥ ¡ø¡ ¥ ¢ u¤ ! . c£. PrMvc]nuac]a NQMIgSuV1PQV_NQTUVKgSMv±N@ gSuV |uMONr`[dVfT³mR@eun gS`^laYc]e}N@gS \_NGRtMOaSVfe7cdelP RteunMOVKheuVfTUVfeQg.NQeuV R@aIgSNs|Rf±aS|}V_\KcøR[RgOgSVfeQgOc]Nre!gSN gSuVUNQûeunkR@Mvc]Vfa_mBRteunT1R#tV.aûMOVgSRgIgSuVK±RtMOV Rt|u|uMONQ|uMvcøRgSVK[p± MOV_aN@[prVfn¬§ egS7c]a |uMOVK[pcdTc]eR@Mv±MOVf|}NrMvgVU|uMOVfaSVfeQgYaSNQTUV.eGûTUVfMvc]\R[VKl|}VfMvcdTUVfeQgSaYNtnkRgRs\fNrTU|uMOVfaSaOc]NQe cdeûelaOgSMOû\KgSûMOVfn¶TUVfaSuVfa_mRteun\fNrTU|RtMOVgSlV_T gSNa©cdTcp[çRtMUVKl|}VfMvcdTUVfeQgSaU)cpgS À z aS\quVfT·VfaNQM ûe7cpNrMOT gSVfeuaNrMvĆ|uMON7nuû\KgYPQMvcdnla 'ç~7cd\qªRtMOV #GeuN ~egSN}VaOgRt7[]V 0S§¨ uVfaSV1Vl|VfMvc]T·VfeQgSacdeln7cd\ RgSV gSRg_m`c]euaS|7cpgSV Nt>gSuV aOgSMONQeuPeuNQe`^le7ciNQMOTcigC±³c]e³NQûM^leuaOgSMOû\KgSûMOVfnTUV_auVfa_mGgSlV \fNrTU|uMOVfaSaOc]NQeMSRgOc]N R@eungSuV \_NQTU|uMOVfaSaOc]NreVfMOMONrMwR@MOVNtgSlV)aRtTUV NrMOnuVfMR@agSuNQaSVNtgSuV ûe7cpNrMOT4gSVfeuaNrMvĆ|uMON7nuû\Kg$PQMvc]nua_§. ÔbÔ ÞIH/J,KLJ.

(45) . O¥Q¡ø¡ ¦¥ .

(46) $#! -

(47) G 1 ª.U! "

(48) $~ I IY Z NQeuaOc]nuVfM}NrûelnuVfn³ûel\gOc]NQeua 8 K $ 8 C[z , - [z 0 $ 1 ' 0 0 'C65]50 {uVfMOV

(49) Ác]a R}NrûelnuVfnEnuNQT1Rc]e¬m`gR #@VYRteQ±³aSVfjGûVfeu\fV. 1 0 K 0 'C65Ü70 R@eln³nuVKheuV B 1 8 Q± B 1 ' 8 0 1 8 ' 0 0 B 1 B # *5 'C#5Ì ?0 ² VMOVKVfM gS(N 'Cl§Ì 0 R@a 3 n7c]aS\fMOVgOc] RgOc]NQe³Q±³|}N@c] eQgO@R[]ûV@§ {NtgSVIgSRg{uVfMOVIgSuV cdeunlVK³aOgR@MvgSaMONrT 1 . R@elngSGûa gSuVfMOV.RtMOV ¦VK[]VfT·VfeQgSa cde § ¨ uV aSVfjGûVfeu\fV Ntn7c]aS\fMOVgOc] RgOc]NQe * cd*e 'Cl§Ì 0wcda~euVfaOgSVfncp©m}Rteun³NQe7[p±ci©mlNQM)R[i[ <;>= L 'C65Ü 0 nuVf\KcdT1RgOcdNQeUcdeUgS`cda \ RtaSV RtTUNr^lergSawgSNMOV_TU <;EN = Gc]euPMONrT B \fNrTU|}NrelV_eQgSaB 1 8 ' 0NQM K <;>= § ~N@gSVIgSRg)gSlV nuVf\KcdT1RgOcdNQe³NQ|VfMSRgSNrM cda~nuVKheuVfnn7c]MOV_\KgO[p±MONQT gSuV aSVfjGûVfeu\fV * § >VKg ' L B 0 nuVfeuN@gSV ¥ {c]eQgSV_MO|}Nt[çRgOcdNQe³Nt B RggSuV¦\_NQMOMOVfaS|}Nreun`cdeuPUeuN7nlV_a mlcÇ§áV@§ ' LB 0 1 B NrM)R[p[ K 0 'C65á 70 R@eln³NQuaSVfMvrVgSkRg. . . . ' $ L B 0 1 B 5 'C#5 ?0 ¨ uVR@}N QV.MOVK[øRgOc]Nre aSuN ~agSRg MOV_\fNQeuaOgSMOû <;>\KgO= c]Nre cde!gS`cda\RtaSVUR@TUNQ ûeQgSagSNRaSVK[]V_\KgOc]Nre N@Rte cdeQgSVfMO|}N@[øRgOc]NQe9gSVf\l e7cdjGûV cde 'Cl§ GRF0S§ cprVfe B V«R@|u|lMON_`cdT1RgSV B r± 'Cl§ÌWrR 0Sm R@eln9PQVgsgSuV |uMOVfn7c]\gOc]NQeEVfMOMONQM 'C7

(50) § 6tFR 0 1 B , <;>= ' L B <;E= 0 NrM)R[p[ K L 'C65 @ 0 ûaOc]euPYT^7[pgOcdPQMvcdn·gSV_MOTc]euNt[dNQP@±UgS7c]a |uMOVfn7c]\KgOcdNQe\ R@e1}V~ <;>VKl= |uMOVfaSaV_n r±1aR±`c]euP¦gSRgVIûaSV c]exOVf\gOc]NQe N@wgSuV¦@R[] <û;EVf= aI\_NQMOMOVfaS|}Nreun`cdeuPUgSN ~7c]\RtMOV c]e 1 mBRteuncdeQgSVfMO|}N@[øRgOc]NQeENQM gSu NraV {` <;Ecd\q= RtMOV euNtg cde § IuaSVfMvrVUgSkRggSu V1 |uMOVfn7 c]\KgOcdNQe VfMOMONQM .³NQM.R[p[IaS ^l\gSk <R;Eg = K §² V nuVKheuVgSlV aS\ R[]VK´¸\fN7VKµ1\c]VfeQgSa R@agSuV |uMOVfn7c]\KgOcdNQeV_MOMONQMc]e , mlcC§ V@§ 1 NrM)R[p[ K <;>= 0 'C65ÜW7 0 ÑÓÔ¬ÑÕ.

(51) ¥Q¡ u¡

(52) ¤ ¡ø¡ U¥ ¡ø¡ ¥ ¢ u¤ ! . `c. {uVfMOV NrM 1 0 5*5G5 0 ' 3 , 3 < ;>= 0c]a)aNrTUVNQMOnuVfMvcdeuP1NtbgSuV¦|NtcdeQgSacde , <;>= ; I = 1 , <;>= 5 'C65ÜW?0 > !ø º

(53) ¾I C¾ u_]

(54) ø¾9¾

(55) >VKg{^la)\fNrelaOcdnlV_M \fNreQgOc]e`^lNrûaûeu\KgOc]Nreua 8 c]e³gSuV cdeQgSVfMv@R[ )A.7m] + 1 2 )A. 0 + 0 8 K $ R@eun [dVKg V RteR@MO7cpgSMSRtMv±³|RtMvgOcigOc]NreNt )A. 0 + 1 0 1 . 0 1 0A3 1 3 'C65

(56) 6Q70 {u Vf1 MOVgSu V.aV_jG0 ûVf eu \1fVU R@}N QV 0 c]aaO0 gSMvcd\KgO[p±cdeu\fMOV RtaOcdelP³R@eln 3 cdaIaSNQTUV c]eQgSV_PQVfM§B²+VYnuVKhelVYgSuVPQMvcdnua. . , 5G5G5 Q±gSuV¦\_NGRtMOaSVfe7cdelP <;E= 1 O 0 1 . 0 5G5G5 0G3 <;>= 1 C 3 0 'C65

(57) 6Q?0 cdeU~7cd\q1VInuVK[dVKgSV MONrT R[p[gSuVI|}N@c]eQgSa)cpgSN7nunUc]eun7c]\fV_a 'Ò¨ uVINre`[i±1MOV R@aNregSRg V{MOVfTUN QV 5,UN@gSuVfM |}NtcdeQgYc]a gSNaOc]TU|7[pciø±gSlVeuNtgRgOc]Nrela 0S§ ¬VgûaY\fNQeuaOc]nuVfM euN gSuVn`cdaS\fMOVKgSVU@R[dûVfacde 'Cl§Ì@ 0Lu\K[]V R@Mv[p±PB <;E= cda~NQ7gRc]euVfnMONQT B Q±³gSuV nlV_\Kc]T1RgOc]Nre B <;>= 1 C ' <;>= B 0 1 B O 0 1 . 0 5G5*5 0G3 <;>= 5 'C6

(58) 5 6 0 egS7c]a)\ RtaSV~gSuVIn7cdMOVf\Kg{T^7[pgOcdMOVfaSNt[d^`gOcdNQe³MOVf|uMOVfaSVfeQgRgOc]NQe ' À z 0gSMSR@eua©NrMOT B ! - B ! c]e 'C7§ir5 0 \Rte³}V Vl|uMOVfaSaSVfn³Q± 1 0 5G5G5 0 &% B <;E= 1 B O 0 1 . 0 5G5G5 0*3 <;E= 'C#573 0 1 B O ;E= , <;E= ' O ;E= L B <;E= 0 0 1 0 5*5G5 0G3 <;E= 5 yQcdTcp[çRtMv[p±gSuVc]eQrVfMOaSV À z gSMSRteuaONQMOT B ! - B \ Rte³}VVu|lMOV_aaSVfnEQ± % 1 0 5G5G5 0 B O 1 B <;>= 0 1 . 0 5G5G5 0G3 <;E= 'C#5Ì 0 B O ;E= 1 <;E= ' O ;>= L B <;>= 0 0 1 0 5G5G5 0G3 <;E= 0 . ² VMOVKV_M gSN Rta gSuVYaS\ R[dVKĆ\_N7VKµ1\KcdVfeQgSa~N@gSuV ´ÇgS[dVKQV[wN@wMOVfaSN@[]^7gOc]NreB§ uNQM)gSlV.|7c]Vf\fV cdaV´ [ic]euV R@M cdeQgSVfMO|Nt[øRgOc]Nre 0. 1 , ;E= ' L B 0 B ;E= '(B , B ;E= 0 NQM ;># 'C65i . 0 = " " , ;E= ÔbÔ ÞIH/J,KLJ.

(59) `cic. O¥Q¡ø¡ ¦¥ . V PQVgNrM)RteQ± 8 NQM {`cd\q B 1 8 gSkRg 1 ' O ;E= 0 ' O 0 $ 8 ) O ; O 0 O ;E= 0 O + 0 '8 0 'C#5iQ70 , {uVfMOV 8 ) = 0 EO 0 +Bc]a gSuV <aS;EVf= \f0 Nrel <n1;E= n7ciGc]nuVfnEn`ci¯BVfMOV_el\_VINt 8 R@eln 1 C , ;>= §@~Vfeu\fV~ci 8 ' 0wc]a g¸ cd\fV n`ci¯BVfMOV_eQgOcøR@`[dVc]e ) ;E= +>gSuVfe 1 ' O ;E= 0 ' O 0 8 ' 0 NQM)aSNQTUV K ' <;E;E== 0 <;E= 05 '8 0 'C65]Q?0 , ©mkNQesgSuVYNtgSuVfM)Rteun¬m 8 cda n7c]aS\fNreQgOc]e`^lNrûaIRg RU|}N@c]eQg_mlgSuVfeEgSlV aS\ R[]VK´¸\fN7VKµ1\c]VfeQgSa ' 8 0 Rg gS7c]a [dN7\ RgOcdNQe.RtMOV|uMONQ|}NrMvgOc]NrekR[7gSNIgSuV aOc]_VN@kgSuVxOûTU|[email protected]c]e[çRtMOPQV cdelnuVf|VfeunuVfeQgN@}MOVhkeuVfT·VfeQg_§ ²+V \ R@esNr7gRc]e³nRgR\_NQTU|uMOVfaSaOc]NresQ±³aSVKgOgOcdelPUgSN·fVfMONR[i[>aS\ R[dV\fN7VKµ1\c]VfeQgSa{`cd\q³ÇR[i[>}VK[dN R|uMOVfaS\fMvcd}Vfn³gSNt[dVfMSRteu\fV@§ ¬Vg~ûa)nlV_elN@gSV . " . p c 1 'C#5i 70 cp 0 R@eln B 1 " ;E= $ 0 5G5*5 0 = 0 B 5 'C65] ? 0 yQc]eu\fVYgSuV|7c]Vf\_VK cdaSVK´Ò[ic]euV R@M~c]eQgSV_MO|}Nt[çRgOcdNQec]a `cdVfMSRtMO\7c](\ 'ÒaSVfV·Rt|u|}V_eln7cp # 0V.PQVKg gSlVYNt[i[]N cdeuP NQûeunsNresgSuV \fNQTU|uMOVfaSaOc]NreVfMOMONQMC 'C#5i 70 T1 R B , B " I= 5 cprVfe RteQ± .YV¦\RtegR #@V 1 <; ;E= 'C65] ? 0 R@elngSGûa~V_elaSûMOV Q± 'C7§] QFR 0wgSkRg 'C65] 0 T1 R B , B 5 ²+V{MOVfT1R@=M #gSRgaS|7[pcdelV)c]eQgSV_MO|}Nt[çRgOcdNQeRteunUaS|Vf\KgSMSR[\fN@[p[]N7\RgOc]NreUR@MOV~PQV_elV_MSR[p[i±U7c]V_MSRtMO\`cd\IR@eln gSuVfMOVKNrMOV gSuV~\_NQMOMOVfaS|}Nreun`cdeuP À zaS\lV_TUVfa R@MOVIRt^7gSNrT1RgOcd\ R[i[p±.a©gR@7[]>V 'ÒaV_V ) / +10S§ @{N_VQVfM$NQMwgSuV R@|l|7[ic]\ RgOc]NQeYgSRgwV)RfQV)c]eUTcdeunBmGR@eln.NQMwT RteQ±.NtgSuVfMOa_mtV euVfV_n1R~[]N7\ R[7c]eQgSV_MO|}Nt[çRgOcdNQ eUTUVgSlN7n § uNQM gS7c]a{|lûMO|NQaSVV^laSVgSuVNt[p[dN cdelP·|`cdVf\fVK)c]aSVK´¸|}N@[p±7 euNrTcøR[} c]ergSVfMO|}N@[øRgOcdNQe C >VKg nlV_elN@gSV R aOgSVfeu\Kci[BNt Y\fNrelaSVf\_^`gOciQV |}NtcdeQgSaNt ~7c]\c]eu\K[]ûnuVfa Rteu n = Rteun1[]VKg ' LB 0wnuVfeuNtgSVIgSuV ûe7c]jGûVY|}N@[p±7euNQT.cøR[bN@wnuVfPrMOVf8V ' , 5 0{`cd\qEc]eQgSVfMO |Nt[çRgS VfaB Rg~gSuVY|}N@c]eQgSa{NtgS`cda~aOgSVfeu\Kci[ §k² V nuVKheuVgSlV |7c]V_\fVK)c]aSVK´¸|}Nt[i±7euNQTcçR[c]eQgSVfMO|Nt[çRgOc]Nre ' L B 0 Q± ' L B 0 1 ' L B 0NQM " " = 5 'C#5i_ 0 . . . . . . . .

(60) . . . . . . . . . . . . . . . . ÑÓÔ¬ÑÕ.

(61) ¥Q¡ u¡

(62) ¤ ¡ø¡ U¥ ¡ø¡ ¥ ¢ u¤ ! . `cicpc. gSNU 0 euN 9VkRfrV elN@g)a|Vf\KcihkV_n·gSuV aOgSVfeu\Kcp[ Nt Y\fNQeuaSVf\f^7gOcprV|}N@ c]eQgSa)Nt gSkRgV RtaSaOc]PQe gSN ) = +C§wZ$[dV RtMv[i±cp V1\uN7NQaSV c]eunuVf|}VfeunuVfeQgO[i±Nt gSuV1nRgR B gSuVfe1 gSuVUTUNQaOgYR@\f\fûMSRgSV \uNtcd\fVIc]agSRg{Nt$RU\fVfeQgSV_MOVfnaOgSVfeu\KciI[ 'CR)Rf±1MONrT gSuV }NrûelnR@Mvc]Vfa 0Sm`cC§ V@§lNrM V gR#tV 1 ; = 0 5*5G5 0 NQM " " 3 0 'C65i @7 0 , , R@eunseuV R@MgSuV }Nr^leunRtMvcdVfa 1 = 0 5*5G5 0 NQM . " " , 'C#5i @ ?0 1 ; = 0 5*5G5 0 NQM 3 " " 3 5 , e ) 5 +VE|uMOVfaSVfeQgSVfn¶R!nRgRĆnuVf|VfeunlV_eQg1|7c]Vf\_VK cdaSVKĆ|Nt[i±7euNQTcçR[ c]ergSVfMO|}N@[øRgOcdNQe'gSVf\ue7c]jGûVs{7c]\ RfrNtcdnlagSuV c]uuaOĆ|uuVfeuNQT·VfeuNQeQ±RteR@nkR@|7gOcprV1aV[]Vf\KgOcdNQe!N@a©gSV_el\cp[ c]e 'Cl_ 0AL>VUMOVKVfMgSN gS7cdaIgSVf\que7c]j`^lVR@a aSaSVfeQgOcøR[p[i± ~ Nr0 e`´ IaS\Kcp[i[øRgSNrMv*± ' 0 c]eQgSVfMO|Nt[çRgOc]Nre¬§¬¨)lV.RtaOc]\Yc]nuV RNt cdeQgSVfMO|Nt[øRgOc]Nre1 c]a~gSNE0 RtaSaOc]0 PresgSN*) = +b{`1 cd\qcdaIc]egSuV.aT·N7NtgS|RtMvg¦NtwgSuV.aqR@TU|7[]VfnE^leu\KgOcdNQe¬m R.a©gSV_el\cp[ 5G5G5

(63) ; " )cpgS ' 0Smk{7c]\sc]a[pc #tV cdaVcdesgSuV aT·N7NtgS³|kR@Mvg~N@bgSlV ûeu\KgOcdNQe 'Ò|uMON Gc]nuVfngSRggS7c]aIcda¦|NQaSaOc]7[]VQmucC§ V@§BgSRg n7c]aS\fNreQgOc]eG^7cigOc]VfaYRtMOVYVK[p[ aSVf|RtMSRgSV_nRteunRtMOV ÇR@MVfeuNQûPrUMONQT gSuVINQûeun RtMvc]V_a 0S §G¨)`cdac]a nuNQeuV{Q±1\lN7NraOc]euP gSNY}V)gSuVIaOgSVfeu\Kcp[NQMw{7c]\UgSlV cdeQgSVfMO|Nt[øRgOc]Nre1|}Nt[i±7euNQTcçR[ ' L B 0c]e 'C7§]f 0¬c]a gSuVI°raT· N7NtgSuVfaOgS° RtTUNreuPR[p[\ Rteun7 c]nRgSVĆaO gSVfeu\Kci[]a_m cC§ V@§ gSlNraSVNt )\fNQeuaSVf\f^7gOciQV|NtcdeQgSaN@ 'ÒaOgRtMvgOcdeuP~ cigS 0{7c]\\_NQeQgRc]e }N@gS Rteun = mV@§áPu§ r± gR #Qc]euP ' 0 gSNU}VgSuVc]eunuVsNQM ~7cd\q ;E= Tcde ;>= ' L B 0 B{|. . . . . . . . . . . . . . . . . . . . . . . cda~RgOgRcdelV_nRtT·NQeuPUR[p[b\ R@eln7cdnkRgSVK´¸a©gSV_el\cp[]a_§ > !ø º º#f¾ ¼ ¾B¿ bt k ø¿ )A. 0 + O ² V\fNQeuaOc]nuVfM)\fNQergOc]eGûNQûaûel\gOc]NQeua 8 8 C )A. 0 + )4. 0 + , - [z 'C65iW70 {7c]\R@MOVn`cdaS\fMOVKgOc]_VfnNre gSuVgSVfeuaSNQMv´¸|lMON7nuû\Kg{PQMvcdn 1 ' 0 0 'C#5i W ?0 r± 8 1 C Q8 0 8 1 8 ' 0 0 0 'C#5i W 0 {uVfMOV 1RtMOV1gSuVNrel3 VĆn7c]T·Vfeua©cdNQeR[PQMvc]nu|Ntc]ergSac]e 'Cl§ 60LeuN@gSV gSRg· uVfMOV VEMOVf|7[øR@\fVf3 n 3 1 r ± m aOO c]eu\fVVMOVfaSVfMvrV NQM1gSuV!n7c]TUV_elaOcdNQe¶NtgSuVrVf\KgSNQMaS|Rt\fV / cde 'Cl§i0Sm$cÇ§áV@§ ' 0 § # [igSuNQûPQUgS7c]a \RtaSVcda \fN QV_MOVfn1Q±UgSuVIPrVfeuVfMSR[uMSRtT·VKNQM=#Yc]e&'C7§] .F0Ò´ 'Cl§i F0Smtcpgcda TUNQMOV ÔbÔ ÞIH/J,KLJ.

(64) `ci. O¥Q¡ø¡ ¦¥ . \fNreQrVfe7c]VfeQggSN³nuVfaS\fMvc]V¦gSuVYgSVfeuaNrMvĆ|uMON7nuû\KgV7gSVfeua©cdNQe!N@wgSuVUNQeuVK´¸n7c]TUV_elaOcdNQeR[ À z4aS\quVfT·VQ± ûaOc]euPT RgSMvc£ «euN@gRgOc]Nre¬§ uNQMIgS7c]aY|uûMO|}NQ aSVV·MOVf|uMOVfaSVfeQg gSuVUgCNt´¸n7c]TUV_elaOcdNQeR[ RtMOMSRf±cde 'Cl§i W@\50 R@a~gSuV?' 0 ' 50 T1RgSMvc£ m>RteunûaSV¦gSuV.PQVfeuVfMSR[wR[]PrNQMvcpgSuT Nt Rt|u|}V_eln7cp {`cd\q nuVfaS\fMvcd}VfagSVfeuaSNQMv´¸|lMON7nuû\Kg)V`gSV_elaOcdNQeua~N@NreuVKĆn7cdTUVfeuaOc]NQeR[ À z aS\lV_TUVfaNQMgSlVcdel|u^7g § ²+V$MOVfT1R@=M #~gSRg>gSuVwgSVfeuaSNQMv´¸|uMON7nlû\KgR[]PrNQMvcigSlT9c]euuVfMvcpgSa>cigSa>a©gR@7cp[pcigC±IMONrT gSuVwNrelVĆn7c]T·Vfeua©cdNQeR[ À z aS\uVfTUV@mwR@elngSRg.V`c]aOgSVfeu\fVN@~R À z RtaOc]a NQMYNQeuVK´¸n7c]TUVfeuaOc]NreR[wûeu\KgOcdNQeuaPrN7Vfa N_rVfM gSN gSuVY\fNQMOMOVfaS|NQeun7c]euPUgCN@Ćn7c]T·Vfeua©cdNQeR[NrelV_af§ egS7c]aI|Rt|VfM VYaSR[p[ûaSVgSlVYgSVfeuaSNQMv´¸|lMON7nuû\Kg À z aS\lV_TUVfa NrM~R.^le7ciNQMOT PQMvc]n³ cigSgSuV |`cdVf\fVK)c]aSVK´¸|}N@[p±7euNrTcøR[Bc]eQgSV_MO|}Nt[çRgOcdNQ*e 'Cl§i_ 0Ò$´ 'C7§i @ 0 Rta)NQûM ®O±GR@MOnaOgOc],\ #G°IcdeNrMOnlV_MgSNIT·V RtaSûMOVgSuV|VfMvNQMOT·Vfeu\fV NtugSuV À z+aS\quVfTUV_aNrMûeuaOgSMOû\KgSûMOVfnUTUVfaSuVfa cdeaOc]Tci[øR@M\c]MO\fûTUaOgRteu\fV_af§ ²+V MOVfT Rt=M #gSkRgINrelV \ R@eV R@aOcp[p±³V7gSVfeungSlV gSVfeuaSNQMv´¸|uMON7nlû\Kg À z aS\quVfT·V cde!Rt|u|Vfeun`cp¶gSN gSuV PQMvcdn. 1 ' 0 0 # {uVfMOV c]aIR.n`ci¯BVfMOV_eQgI|RtMvgOcigOc]NreNt )A. 0 + 'ÒaSVf?V ) /W +10S§ !ø º øE !ø`ø¾ z[ O # aYRsMOVfaS^7[pg N@ gSuVUaS^l\_\fVfaSaNt >c]e7cpgSV []VfTUV_eQg À VKgSuN7n ' À 0~NQMIgSuVUe`^lT·VfMvc]\ R[ aSNt[d^`gOcdNQe N@ L a_m}VRfQV.T1Rter±gSMvcøR@euPQ^7[øRgOc]NQegSV_\que7c]jGûVf2a 'ÒaSNrTUVN@wgSuVfTR@MOV|Rt,\ #RtPrVfnRta \fNQTU|u^7gSVfM \fN7nuVfa 0~gSN\fNreua©gSMOû\Kg.RT·VfaS+Nt)nuVfaOc]MOV_n«MOVfaSN@[]^7gOc]Nre )cpgSªRPQN7N7nnuVfaS\fMvc]|7gOcdNQeNtgSuV NQûeunRtMv± NrM\_NQTU|7[]VKsPQVfNrTUVKgSMvc]V_afmuRteunER[]aSN.\fNQMOMOVfaS|NQ eun7c]euP0 cdeQgSVfMO|}N@[øRgOc]NQeTUVgSlN7nuaNQM gSuVeuN7 nlV_af§ >VKg)^la nuVfeuNtgSVgSuV gSMvcøRteuP@[]Vfa)c]eaSû\q RUTUVfaSQ± 1 " " ) m}RteunnuVfeuNtgSV Q± gSuVaSVKg Nt rVf MvgO1 c]\_Vfa c]e1gSu VfaSV~gSMvcøR@elP@[]Vfa*LQVIMOVKVfMgSN

(65) C ' = R@awgSuVIgSMvcøRteuPr^`[çRgOcdNQe1Nt I§ {uaSVfMvrV~gSRg C ' I = c]a{R|}N@[p±7PrNQeERteunsgSRg cda~R|7cdVf\fVK)c]aSVK´Ç[pcdelVRtM)Rt|u|uMON_`c]T1RgOc]Nre gSN I§ eENQûM|kR@MvgOc]\f^7[çRtM{Rt|u|7[pc]\RgOc]Nre1VR@MOVIc]eQgSV_MOVfaOgSVfnscde [dN7\ R[Rt|u|uMONf7c]T1RgOc]NQeua_§ uNQM gS7c]a)|u^l MO|NQaSV VE^laSV@m RtaU1 cdeVkR@ TU|7[]Vl§iQmgSuVsN@[p[dN_ )c]euP|7c]Vf\_VK cdaSVKĆ|Nt[i±7euNQTcçR[c]eQgSV_MO|}Nt[ç RgOcdNQe C >VKg }V R aOgSVfeu\Kci[}N@ F' 0 |}N@c]eQgSa N@ {7c]\1c]aRtaSaOc]PreuVfngSNgSuV~gSMvcçRteuPt[dV K

(66) RteunUc]eu\K[d^lnuVfa cigSa rVfMvgOc]\fV_a § >VKg ' L 8 0 nuVfeuNtgSVgSuV ûe`cdjGûV |}Nt[i±7euNQTcçR[>N@nlV_PQMOVfV2' , 50wNQM 9{`cd\q cdeQgSVfMO|}N@[øRgSVfa 8 ' 0)RggSuV¦|NtcdeQgSa~N@gSuV aOgSVfeu\Kcp[ m}Rteun³nlVhkeuV ' L 8 0 1 ' L 8 0ªNQM NK 'C#5i 60 Z[]V R@Mv[p±UgS7cda gSV_\que7c]jGûVIcdaVKkRt\Kg NrM nRgRN@>|}N@[p±7euNrTcøR[kûeu\KgOc]NreuaN@bnuVfPQMOVfV)[]VfaSaNQM V_jG^R[ , Q§ IuaSVfMvQVuN VKrVfMgSkRg)^le7[ic #@V· m c]a)euNtg)euVf\fVfaSaRtMvci[p±1\_NQeQgOcdeGûNQûa Nre gSuVNQûeunkR@Mv±³Nt L`c]e gS7c]a{\ RtaSV~1 VgR#tVA$ gSN1}VIgSuV aS|kR@ \fV ' 0)cpgSsgSuV aSû|seuNQMOTmkMSRgSuVf MgSkR@e ' 0S§ lNrM gSlVE|}N@c]eQgSa.Nt RtMOVeuVf\fVfaSaRtMvci[p±gSuV rVfMvgOc]\_VfaUNt mwRteun ' L 8 0c]agSuV |7c]V_\fVK)c]aSVK´Ç[pc]euV R@Mûeu\KgOc]Nre+{`cd\q'cdeQgSVfMO|Nt[øRgSVfa 8 RggSuVfaSVsgSuMOVfVE|}N@c]eQgSa_§ IlaSVfMvrVsgSRgUc]e'gS7c]a . . . . . . . . . . . ÑÓÔ¬ÑÕ.

(67) ¥Q¡ u¡

(68) ¤ ¡ø¡ U¥ ¡ø¡ ¥ ¢ u¤ ! . `. \RtaSV ' L 8 0 cdaI R aSVfjGûVfeu\fV N@w\fNreQgOc]e`^lNrûaûeu\KgOc]Nreua {`cd\q³NQMOTUa RteE`cdVfMSRtMO\7c]\ aSVfjGûVfeu\fV N@$Rt|u|uMONf7c]T1RgOc]NQec]e ' 0S§ uNQM 1VRfrVUaSVKQV_MSR[$MOV RtaSNQeR@`[dV\uNtc]\_VfaINta©gSV_el\cp[]a*L>RtaIcde VKkRtTU|7[dVU7§]NreuV\ R@e!^laSV gS7cda MOVfVfnuNrT gSNR@nRt|7g gSuVc]ergSVfMO|}N@[øRgOcdNQegSNUgSuV eRgSûMOVYNtbgSuVnRgR.Q±\uN7NQaOc]euPgSuV aOgSVfeu\Kcp[bcde {7c]\sgSuV nRgRcda aSTUN7N@gSlV_a©g_mRteun gS`^la¦RrNtcdn gSuV c]uua k|luVfeuNrTUVfeuNQe 'ÒaSVfV ) , +Rteun )£ @ +0S§ e.aS^luaSVf\KgOcdNQe @7§]@§ÜV nuVfaS\fMvc]VR~aOc]TU|71 [dV a©gSMSRgSVfPt±gSN aV[]Vf\Kg$R·®\fVfergSVfMOVfnu°IaOgSVfeu\Kcp[lNtWrVfMvgOc]\_Vfa NrM|`cdVf\fVK)c]aSVK´¸jG^RtnuMSRgOc]\Ic]ergSVfMO|}N@[øRgOcdNQe ' 0S§ IûMT1Rcde |uMONr`[dVfT cda gSNEnuVfaOc]PQe!|uMON7\fV_nlûMOVfaNrMI\fNGR@MOaSVfe7c]euPR@eun!MOVKhelV_TUVfeQg NQMI{7c]\!gSlV rVfMvgOcd\fVfa)Nt

(69) <;E= RtMOV\fNreQgRcdelV_n·cde gSuNraVN@

(70) § IlaSVfMvrVIgSRgc]e³TY^`[igOc]PrMvc]n³TUVKgSuN7nuagS7c]a cda euNtg R1MOVfj`^`cdMOVfTUVferg l^7g R1nuVfaOc]MSR@7[]VNr|7gOc]NQe¬§}¨)lV.nuVfaOc]PQe NtaSû\|uMON7\fVfnuûMOVfaIc]a~gSuVYgSNQ|7c]\YNt aV_\KgOc]Nre @l§Ìl§ . . ÔbÔ ÞIH/J,KLJ.

(71) ``c. O¥Q¡ø¡ ¦¥ .

(72) $#! -

(73) G1 { ¬ 1 "

(74) $~ I IY Z NQeuaOc]nuVfM)RtuaSNt[d^7gSVK[p±c]ergSVfPQMSR@`[dVIûel\gOc]NQeua 8JK $ 8 C [z ,I- [z 0 $ 1 = ' 0 'Ò 5]

(75) 70 {uVfMOV

(76) Ác]a R\fNrTU|Rt\Kg)aSVKg_m}Rteun[]VKg 1 =}V RaSVKg{Nt\fVK[i[]a)aS^l\sgSRg 1 Nr 0 1 C I = M 1 0 'Ò >5i?0 ² VnuVKhelVgSuV \fVK[i[p´©RrVfMSR@PQVIn7c]aS\fMOVgOc] RgOc]NQeENt 8 Q± 1 A 5 'Ò 5i 0 ' 8 0 1 A 8 ' 0 0 . ~VK`g[dVKg1ûaU\fNrelaOcdnlV_MUR!MOVKheuVfTUVfeQg aV_jGûVfeu\fV # mwc]e+{7c]\. c]aNrMOTUVfn+MONrT <;E= Q± n7cp`c]n7c]euP1V R@\q³\fVK[i[ <;E= cdeQgSNumlaRf ±

(77) rmkn`cdaxONtc]erg \_VK[p[da I= m I= 1 <;>= 5 'Ò 5Ü70 # [igSVfMOeRgOciQVK[i±sVY\ R@es\fNreua©cdnuVf M 'Ò k§ÌrR 0gSN1} <VY;E=R\fN`RtMOaSVfe7c]euPU|uMON7\fVfnuûMOVc]e{7c]\sV.RtPrPt[]NrTUVfMSRgSV. VKrVfMv±

(78) 1\fV[p[]aN@ c]eQgSN R·[çRtMOPQV_MI\fVK[i[wN@ L}gSuVUNQe7[p± MOV RtaSNQeEgSkRgVgR #@VUuVfMOV·R·hllVf n

(79) Uc]a gSN³aOc]TU|7[pciø±gSuVeuN@gRgOc]Nreuaf§ e«R@eQ±\RtaSVgSlV·aV_jGûVfeu\fVN@ n7c]aS\fMOVKgOcd RgOcdNQe

(80) c]aIeuVfaOgSVfnR@eln cig N@[p[]N {a MONQT gSuVR@nun`cigOcpGcigC±ENtbgSuVc]eQgSVfPrMSR[>gSRg ' <;>=<8 0 1 < ;E= ' 8 0 1 C ' <;>= 8 0 'Ò >5Ì ? 0 = . . {7c]\«n7c]MOV_\KgO[p±nuVKheuVfagSlV1nuVf\c]T1RgOc]NQeNr|}Vf MSRgSNQMIc]e 'C7§Ü 0S§

(81) >VKg nuVfeuNtgSV RteQ±MOVf\_NQeuaOgSMO^l\gOc]NQe MONrT \fVK[p[i´vRfrVfMSRtPrVfa_m`[pcdeuV RtM)NQMeuNtg_m}R@eln[]Vg nuVfeuNtgSVgSuV |uMOVfn7c]\KgOcdNQeV_MOMONQMc]e*'Cl§6@R 0Sm`gSuVfe <;>= 1 .:9 = 1 .65 'Ò 5Ü 0 ¨)7c]a MOVK[øRgOc]Nre aSuN ~aIgSRg¦V·\ RtenuVKheuVUgSlV·a\R[]V·\fN7VKµ1 \KcdVfeQgSa Q±!gR#Qcdeu P* <';>

(82) = , 50~|uMONQ|VfMv[p± \uNQaSVfe[ic]euV RtM \fNQTY7c]eRgOcdNQeua NtgSlV

(83) I|uMOVfn7c]\KgOcdNQeVfMOMONQMOa = cde1V Rt\1\fVK[i[ §r¨)uVfaSV [pcdeuV RtM \fNrT7cdekRgOc]NrelaaSuNQ^7[]n9}V!\uNQaSVfe9aSN«gSRg³gSNQPrVKgSuVfM1 cigS 'Ò k§Ì 0gSuVK±9\fNrelaOgO cigS <^`;>gS= VR@eªcdeQrVfMvgOc]7[]V aO±7aOgSVfT N@

(84) [ic]euV RtMVfj`^kRgOc]NrelaNQMgSuV |uMOVfn7c]\KgOcdNQe³VfMOMONQMOa I= cdesgSuV\fVK[i[ §G'ÒaSVfVIV@§áPu§E)£ W + NrMaSû\\fNrT7c]eRgOc]NQeuac]eEMOVf|uMOVfaSVfeQgRgOcdNQeENtT1RgSMvcd\fVfa 0S§ !ø º

(85) E¾ M C¾ l

(86) ]ø¾9¾

(87) >VKg~ûa)\fNQeuaOc]nuVfM{RtuaSNt[d^7gSVK[p±1cdeQgSVfPQMSR@7[]Vûel\gOc]NQeua 8 c]e )A.7m] + 1 = )4. 0 + 0 8NK $ ÑÓÔ¬ÑÕ.

(88) ¥Q¡ u¡

(89) ¤ ¡ø¡ U¥ ¡ø¡ ¥ ¢ u¤ ! . R@eun [dVKg. 7Gcpc. 1 I = 0 1 ' ;>= 0 0 0 'Ò 5á 70 {uVfMOV R@MOV gSuV PQMvcdnu|}NtcdeQgSa)Nt ]c e 'C7§

(90) 60LkNQuaSVfMvrVIgSRg <;>= 1 O ;E= O 5 'Ò 5á ?0 >VKg B 1 8 nuVfeuN@gSVIgSlV \fV[p[p´©RfQV_MSRtPQV_ac]* e 'Ò k§i_5\ 0L B <;>= cda Nr7gRc]euVfnMONQT B Q±gSuVnlV_\Kc]T1RgOc]Nre 'Ò k§Ì@ 0Sm7cÇ§ VQ§ B <;E= 1 < ;E= ' AO ;>= B O ;E= AO B O 0 0 1 0 5G5G5 0G3 <;>= 5 'Ò >57@ 0 g N@[p[dN_{aMONQT 'Ò u§Ü 0gSRg)gSlV |uMOVfn7c]\gOc]NQeEVfMOMONQM aRgOcda©hVfa gSuV MOVK[øRgOc]Nre O ;E= O ;>= O O 1 . NQM 1 0 5G5G5 0*3 <;E= 5 'Ò 5ÜW70 . . . . . ¨)uVfMOVKNrMOV@m`cpV nuVKhelV 1 < ;>= ' O ;E= O ;>= O O 0 NQM 1 0 5*5G5 0G3 <;E= , V\RteMOV_\fN QVfMgSuV |lMOV_n`cd\KgOc]NreVfMOMONrM r± 1 $ O ;>= O ;E= O > ; = 1 $ O ;E= O O , 1 # " $ ¨)lV n7c]MOV_\Kg À z9gSMSRteuaONQMOT B ! B c]a{PtciQVfeEQ±gSuVR[]PrNQMvcpgSuT 1 0 5G5G5 0 %

(91) & <;>= 1 0 1 0 0G3 < ;>= ' O ;E= B O ;>= O B O 0 5G5G5 <;>= B 1 B ' <;E= B <;E= 0 ' 0 + <;E= 0 1 0 5G5G5 0G3 <;>= ) O E ; = O E ; = , O ;E= ¨)uVIc]eQrVfMOaSV À z gSMSRteuaONQMOT B 1 " ;E= $ B ! c]a)PtcprVfeEQ± % 1 0 5G5G5 0 % 1 0 5*5G5 0G3 <;E= 1 ) 2 ' <;E= B <;>= 0 ' 0 <;>= + B O ;E= O ;E= O ;E= 1 B ' <;E= B <;E= , O ;E= B O ;E= 0 O O ÔbÔ ÞIH/J,KLJ. 'Ò 5ÜW?0. 'Ò 5ÜW 0. 'Ò >560. 'Ò >573 0.

(92) ``cpcpc. O¥Q¡ø¡ ¦¥ . IuaSVfMvQVgSRggSuV [øRtaOg)aOgRgSVfT·VfeQg{Nt 'Ò u§3 0wc]a{NQ7gRcdelV_n MONrT 'Ò u§7@F0S§ e ) 6/w+ V·auN Vfn!gSRg.Rter±c]eQgSV_MO|}Nt[çRgOcdNQeTUVKgSuN7n!c]eVkRtT·|`[dV17§]P@cprVfa Mvc]aSVUgSNR³\fNQMOMOV_a©´. |NQeun7c]euPTUVgSlN7n!NrMMOVf\fNQeuaOgSMOû\KgOc]Nre MONrT\fVK[i[p´©RfQVfMSR@PQ Vf1ar±!gSlVUN@[p[dN_)c]euPª®MOVf\_NQeuaOgSMO^l\gOc]NQe!GcçR |uMvc]T.cpgOcprVIûeu\KgOc]Nrel° gSVf\ue`cdjGûV C cprVfe\fVK[i[p´©RfQVfMSR@PQVfaB 8 VI\ R[]\f^7[çRgSV gSuV{|}NtcdeQg @R[dûVfaNt gSuVE®|uMvc]T.cpgOcprV ^leu\KgOcdNQeu° 1 ' 0 0 ' 0 1 8 ' 0 Q± 'Ò 5Ü7 0 1 . 0 1 = B 0 " " 3 0 R@eln³nuVKheuV ' B 0 ' 0 1 ' L 0 0 'Ò >5Ì ?0 {uVfMOV ' L 0 cda~R@eQ±³c]eQgSVfMO|Nt[çRgOc]NresN@gSuV@R[dûVfa 1 IRg gSuV PQMvcdn|}N@c]eQgSa{Nt c]e 'Cl§ 60S§ uNQM)VkR@TU|7[]V@mkcp$V¦gR #tV gSuV|7cdVf\fVK)c]aSVK´Ç[pcdelVRtMc]eQgSVfMO|Nt[çRgOc]Nre 'C7§] .F0SmlVPrVKg gSRg B c]a gSuV |7c]Vf\fV cdaVĆ\fNreua©gR@eQgMOVf\fNreua©gSMOû\KgOcdNQe ' B 0 ' 0 1 B NQM K 5 'Ò >5i . 0 !øº º6bf¾ ¼ ¾B¿ @ ºGbºG )4. 0 + O ²+V\_NQeuaOc]nuVfM{RtuaSNt[]^7gSVK[i±1c]eQgSV_PQMSRt7[dV ûeu\KgOcdNQeua 8 8 CG)4. 0 + )4. 0 + , - [z 'Ò >5iQ7 0 {7c]\RtMOVn7cda\_MOVKgOc]fV_nNQe³gSuV gSV_elaSNrMvĆ|uMON7nuû\Kg)TUVfaS 1 I= 'Ò 5]Q? 0 Q± 8 1 C 8 I= 0 8 1 $ 2 A 8 ' .= 0 EO 0 .= EO 'Ò 5]Q 0 . {uVfMOV =UR@MOVgSu3 VNQeuVK´¸n7c]TUVfeuaOc]NreR[)\fVK[i[]aUc]e 'Ò k§ GFR 0L$euN@gSVsgSR guVfMOVV MOVf|7[ø3 Rt\_Vf1 n 3 QO ± m>a©cdeu\fVVUMOVfaSVfMvrV NrMIgSlV·n`cdTUVfeuaOc]Nre N@gSuVrVf\KgSNQM aS|Rt\fV / c]e 'C7§]5 0Sm}cÇ§ VQ§ ' 0 § # [igSuNQûPQYgS`cda\ R@aVcdaw\fN rVfMOVfnUr±gSuV)PQVfeuVfMSR[7MSRtTUVKNr=M #c]( e 'Cl§i .F0Ò´ 'Cl§i 0Sm_cigcdaTUNQMOV\fNreQrVfe7c]VfeQg gSN!nuVfaS\fMvcd}V1gSuV·gSV_elaSNrMvĆ|uMON7nuû\KgVK`gSVfeuaOc]NQe NtgSuVNQeuVK´¸n`cdTUVfeuaOc]NrekR[ À z aS\lV_TUVQ±+ûaOc]euPgSuV T1RgSMvc£seuNtgRgOc]Nre N@bRt|u|Vfeun`cp {§`¨)lV_MOVKNQMOV~V MOVf|uMOVfaSVfeQggSuVIgCNt´¸n7c]TUV_elaOcdNQeR[¬RtMOMSRf±Ucd;e 'Ò k§iQ_5\ 0 Q±gSuV T1RgSMvc£ mwR@eun+ûaSV·gSuVPQV_elV_MSR[)R[dPQNrMvcpgSuTNt{Rt|u|}V_eln7cp gSN!nlV_a\_Mvc]}V1gSuV gSVfeuaSNQMv´¸|uMON7nu^l\g À z a\uVfTUVNQM gSuVc]eu|u^7g § ²+V MOVfT1Rt=M #UgSRg_mkRta c]egSuV\fNQMOMOV_a|NQeun7c]euPYVkRtT·|`[dV 7§Ü7mQgSlV\_VK[p[da cd;e 'Ò k§irf 0w\ RteVnlVhkeuVfn R@a~RgSV_elaSNrMvĆ|uMON7nuû\Kg)Ntn7cp¯BV_MOVfeQgI|R@MvgOcpgOc]Nreua c]egSuVgCN1aS|Rt\fVI@R@MvcøRt7[dVfa_§ ÑÓÔ¬ÑÕ.

(93) ¥Q¡ u¡

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(95) 8 0 ' 0 1 ' L 8 0ÁNrM K 5 'Ò >5i 0 Z[]VRtMv[p± 'Ò u§] F0¦nuVKheuVfa1R!MOVf\fNrelaOgSMOû\KgOcdNQe'N@

(96) 8 ~7c]\+cda1VkRt\gNQM.|}N@[p±7euNQT.cøR[ ûeu\KgOcdNQeuaUNt nuVfPrMOVfVI[]V_aa)NQM)VfjG^R[ ' , 0SmkRteunsgS`^la)c]a ´ÒgSENQMOnuVfM{Rt\f\fûMSRgSV@§}yGû\q R|}N@[p±7euNQT.cøR[V`c]aOgSa)cp @§ ' 0 1 F' 0 lm 7§~R R@elnuVfMOT·NQeunuV~gC±7|V\_NQeun7cpgOc]NresNre cda aRgOcdaOhkV_nB§ uNQM)RPrVfeuVfMSR[¬n7c]aS\fûaSa©cdNQe³NQegS7c]a #Qc]eunN@|}Nt[i±7euNQTcçR[bR@|u|lMON_`cdT1RgOcdNQeERteuncpgSa)\fNQTU|u^7gRgOcdNQe¬mlaSVfV )£$+R@eln ) @ +Ç§ eUgSlVNt[i[]N )c]euPumV R[p)Rf±7a RtaSaSûTUV gSkRgwgSuV~aOgSVfeu\Kci[]aV \fNreua©gSMOû\Kg RtMOV)RtnuTcdaaOcd`[dV@§ e|uMSRt\gOc]\fV@mlgSuVfMOVcda eu1 N1|RtMvgOcd\f^7[øRtM)MOVfaOgSMvc]\gOc]NQe¬mkaSVf?V )£$ 1 +C§ ~N@gSV gSRgsNrM !c]e 'Ò k§i 0VkRfrV ' 0 Rteun VPrVKgsgSuV|7c]Vf\_VK cdaSVKĆ\_NQeuaOgRteQg MOV_\fNQeuaOgSMOû\KgOc]Nre ' G

(97) 8 0 ' 0 1 ' 8 0

(98) ' 0 0 'Ò 5i 0 {uVfMOV

(99) ' 0 nuVfeuN@gSVfagSuV \kR@MSRt\KgSV_Mvc]aOgOc]\ûeu\KgOc]NresN@gSuV aSVKg m 1 K 'Ò 5i_ 0

(100) ' 0 . N@gSuVfMv cdaSV 5 e )£ @+@V|uMOVfaSVfeQgR@e7c]VfMSR@MO\q7cøR[GR[]PrNQMvcpgSuT9NQMBgSuVaSVK[]V_\KgOc]NreINtuR.®\_VfeQgSVfMOVfnu°{a©gSV_el\cp[ÇmK{`cd\qcda R@|u|`[ic]\ R@7[]V~VQVfegSN\_NQTU|7[]VgSVK[p±ûeuaOgSMO^l\gS^lMOV_nsTUV_auVfa c]e1[z § egS7c]a)\fNQergSV`g gSuV³®\fV_eQgSVfMOVfnu° aOgSVfeu\Kci[ cda1nuVKhelV_n R@aUgSuVNQeuVs{7c]\¶Tc]e7c]T.c]fVfaUgSuVMOV_\fNQeuaOgSMOû\KgOc]NreÁV_MOMONQMNrMUgSlVENQeuVK´¸7c]PQuVfM nuVfPrMOVfV|}N@[p ±7euNrTcøR[]a 'çcÇ§áV@§knuVfPQMOVfV 0S§k¨)7c]a{R[dPQNQMvcigSuT,c]a)Nt ®\fMv±la©gR[>PQMON )gSu°gC±l|}V CkaOgRtMvgOcdeuP cigS gSuVU\_VK[p[ VU}VfP@c]egSN Rtnun!aS^l\_\fVfaSaOcprVK[p±rm>NQeuV\_VK[p[RgYR1gOc]TUV@m>gSN gSuV1\K[d^laOgSVfMN@ \fVK[i[]agSRgV '. . . . . . . . . . . ÔbÔ ÞIH/J,KLJ.

(101) G. O¥Q¡ø¡ ¦¥ . RfQVRggSuV1}VfP@c]eue7c]euPsN@V Rt\aOgSVf|¬§¨ uVU\_VK[p[{7c]\!c]aY}VKcdelPERtnunuVfnc]a aSVK[]V_\KgSVfn!MONQT gSuV1aSVKg N@ R[i[IaOc]nuVK´¸euVKc]PrG}NrMOaUNtgSuVV7c]aOgOc]euP+\[]ûaOgSVfM1Q±'gSuVMOVfj`^`cdMOVfTUVfergsgSRg1cig1 ci[p[ Tc]e7c]T.c]fVgSuV MOVf\_NQeuaOgSMO^l\gOc]NQeEVfMOMONQM)NtaS^7cpgR@`[i±³\quNQaSVfe³TUNrelNrTcøR[]a_§ e )£ @ +IVR[daN |uMOVfaSVfeQg Rte RtnRt|7gOcprV9®\_Mv±7aOgR[PrMON_)gSu°R[dPQNrMvcpgSuT ~7cd\q9c]a³nlV_a©cdPQeuVfn¶gSN R@aaOcdPQe¶R«aOgSVfeu\Kci[ MONrT gSuVaSTUN7NtgS¶|RtMvgN@ 8 ' 0Sm cp.Rf@Rcp[çRt7[]VQm$gSN'R[p[ \fVK[p[da ~7c]\ RtMOV gSuVfTUaSVK[iQV_aIc]egSuVaSTUN7N@gS|RtMvgN@ 8 ' 0S§¨)7c]aI)Rf± R c]uuaO´Ò[ic #@V|uuVfeuNQTUV_elNrec]a¦RrNtcdnuVfn¬m¬R@eln gSuVIMOVfaS^7[pgOcdeuPURt|u|uMON_`c]T RgOc]Nre1c]a ´ÒgS³NQMOnuVfMR@\f\fûMSRgSV{VKQV_Mv±G~uVfMOVQmkVl\fVf|7g)Rg\fVK[p[da ~7c]\\fNQergRc]e R~n7cda\_NQeQgOcdeG^7cpgC±G§t¨ 7c]abc]a$Rt\_\fNQTU|7[ic]aSuVfn Q±YaV[]Vf\KgOcdeuP~gSuV \fVK[p[`MONQT gSuVaVgN@a©cdnuVKĆeuVKcdPQGNQMOa>{`cd\q Tcde7c]TcdfVfa gSuV nuVfMvcp@RgOcprVfaIN@gSuV aSNt´¸nuVKhelV_n MOV_\fNQeuaOgSMOû\KgOc]NreB§ ²+VMOVVfMgSuV MOV R@nlV_MgS;N )£$ +>NrMnuVKgRcp[da~NtaS|}V_\KcøR[ MOVf\fNrelaOgSMOû\KgOcdNQegSVf\que7c]j`^lV_a~NQM gSMvcøR@e7´ Pr^`[çRgSVfn³TUVfaSuVfa_§ uNt[p[dN cdelP.gSlV aRtT·V¦|uMvcdel\c]|7[]Vfa_mlV |uMOVfaSVfeQg{c]eaSVf\gOc]NQ&e @7§ÜURUaOc]TU|7[dV gSV_\que7c]jGûV gSN!\fNrTU|u^7gSVsRÁ®\fVfergSMSR[]° a©gSV_el\cp[ÇmgSRg NQ=M #àNre«gSMvcøR@euPQ^7[øRgSVfn+TUV_auVfa_§¨)7c]a.\fVfeQgSMSR[a©gSV_el\cp[ c]a gSuVfeE^laSVfn³gSNUnuVKheuV gSuV |}N@[p±7euNrTcøR[ ' L 8 0 N@ 'Ò k§iQR 0wcdeaSVf \KgOcdNQeEW7§ ²+V MOVfT Rt=M # gSk Rg~ciVYPQVfeuVfMSRgSVgSlVYeuVfaOgSVfnaSVfj`^lV_el\_VN@ # r±MOVKheuVfTUV_eQgNt RgSMvcøR@e7´ Pr^`[çRgSVfnTUVfaS mgSuVfeªR[p[ gSuVTUVfaSuVfaYT1Rf±}V1gSMvcøR@elPr^7[øRgOcdNQeua.Rteun gSuVfeV\ RteûaVaS|}V_\KcøR[ aOgSMSRgSV_Ptc]V_a¬NrMwR@aSa©cdPQeuTUVfergbNtaOgSVfeu\Kcp[daf§ # acdeVRtTU|7[]Vl§Ì VheungSRggSuVfMOV)RtMOV aSNrTUV MOVKheuVfTUVfeQg TUVgSlN7nuawgSRg RrV{R u^7cp[igO´Òcde1\fNQerQVfe7cdVfeQg)RtaSaOc]PreuTUVfeQg$Nt¬a©gSV_el\cp[]a$NQMwgSuV)|lûMO|NQaSV N@BMOVf\_NQeuaOgSMO^l\´ gOcdNQe¬§ e gSuVU\ R@aSVNt\_VK[p[i´vRfrVfMSRtPrVn7c]aS\fMOVKgOcd RgOcdNQe!gSuVfaSV1RtMOVYgC±7|7cd\ R[i[p±Nt gSuV®Snu^kR[TUV_au°gC±7|V C V@§áPu§lNreuV\ Rte³aOgRtMvg cigSR\_N_rVfMvcdelP·Q±³lVKkRtPrNQeua_mlV Rt\³\fNQeQgRc]e7c]euP·WgSMvcøR@elP@[]Vfa_mkR@eun gSuVfeEn`ciGc]nuV V R@\q'gSMvcçRteuPt[dVscdeQgSN« Q±\_NQeueuVf\KgOc]euP!gSuVTcdnl|NtcdeQgSa1NtIcigSa1aOc]nuVfaRta·}VKNrMOV@§$ ¨)7c]a1MOVfaS^7[pgSaUcde¶R euVK aO±7aOgSVfT Nt$aT R[p[dVfM~uVRtPQNreua 'Ò gOc]TUVfa¦Rta~T RteQ± 0S§B¨N VRt\gSMvcøR@elP@[]VYNt

(102) VR@aaOcdPQesgSuV.W gSMvcçRteuPt[dVfa~N@wgSuVuVRtPQNresgSNU{7c]\cpgIVK[]NreuPQ:a % gS7cda~c]aRU\_NQeQrVfe7c]Vferg RtaSaOc]PrelT·VfeQg{Nt$a©gSV_el\cp[bNQM ĆMOn³NQMOnuVfM{Rt\f\_^lMSRgSVMOVf\fNrelaOgSMOû\KgOcdNQesMONrT \fVK[i[p´©RrVfMSR@PQVfa_§ . . . ÑÓÔ¬ÑÕ.

(103) ¥Q¡ u¡

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(105) nu Vfeu1 NtgS V gSuVgSMvcøR@euPQ^7[øRgOc]NQeERteun[]VKg Q= nuVfeuN@gSVIcp gSa~1 euN7nuVfa_§ # a)}VNQMOVIVnuVfeuNtgSV Q± gSuV~heuVfaOg []VQVK[¬Nt>MOV_aN@[]^7gOc]NreUc]e1gSuVIaSVfjGûVfeu\fVR@eun1Q± .c]a gSuVI\fN`RtMOaSVfaOg_§ e³PQVfeuVfMSR[kV{aR[p[ MOVVfMgSN.gSlV eGûTY}VfM{NteuN7nuVfa r± R@eunsgSNgSuV eGûTVfM~N@bgSMvcøRteuP@[]Vfa)Q± ) § . . .

(106) !" #%$'&()*. eNQMOnuVfM)gSN1nuVKhelV.R1euVfaOgSVfnaSVfjGûVfeu\fVY Nt$n7c]aS\fMOVKgOcd < ;>R= gOcdNQe * Q= R@a cdeaSVf\KgOc]NrelmNreuV¦R@a gSN nuVKheuVYRaSVfjGûVfeu\fVN@euVfaOgSVfn³aSVKgSa = 6 m § e\_NQeuaOgSMO^l\gOc]euPgSuVfaSV aVgSaVRfQV gSN1T R#@VaSûMOV¦gSRgIV R@\qENtgSlVYaSVKgSa Rt a{VfeuNQûPQE|}N@c]eQgSa{NQesgSuVY}Nr^leunRtMv±ENt aSNUgSRg)gSlV R@|u|lMON_`cdT1RgOcdNQeUgSN c]aRtnuVfj`^kRgSV~NQM$gSlV ´ÇgS1[]VKrVK[¬NtbMOVf aSNt[d^7gOc]NQe¬§G¨ uVI|uûMO|}NraSV~Nt¬gS`cdaaV_\KgOc]Nre cda~gSN³nlV_a\_Mvc]}V CwK´ gCN)Rf±7aNt \fNQeuaOgSMOû\KgOc]euPgSuVaSVKgSa m¬´ gSlV.aOgSVfeu\Kcp[ RtaSaOc]PrelV_TUVfeQg{gSN VRt\ N@bgSlVgSMvcçRteuPt[dVfa {`cd\q³c]a{^laSVfngSN1nuVKheuV gSuVc]ergSVfMO|}N@[øRgOcdNQe³|}N@[p±7euNQT.cøR[¬c]e*'Cl§i60S§ . . . . . +

(107)