• Non ci sono risultati.

Extremal synthesis and Morse property for minimum time

N/A
N/A
Protected

Academic year: 2021

Condividi "Extremal synthesis and Morse property for minimum time"

Copied!
145
0
0

Testo completo

(1) 

(2)      !" #$ %& ' (  ) * + ,-* . .0/1324526/798. :<;>=!8!?'@4A:CB ?. ;6DFE G0EFHJIKMLON. =PQESR5TUGUV*NCVXWCVXYJYZE[=!LOI*IXEF\]L. 7_^CVXHQLOH3HJ`CaCb LOYQYQV*WcRdEFPeYQ^CVfWCV*DFPJV*VfEMR g 2EhIiYZEFPe=!^<L]\]EMHQEFjC^<LkKMVXl /3IKMWCVXb[LOI>mnVKMPfoqpMpFpsrFtMuMuFu.

(3)

(4)  

(5)      n  #$ %& ' (  )  + ,- . .0/1324526/798. :<;>=!8!?'@4A:CB ?. ;6DFE G0EFHQI*KML]N. =PQEMR5T!GUV*NCVXWCVXYJYZE=LOI*I*EM\]L. 7_^CVXHQL]H9HJ`CaCb LOYQYQV*WRdEFPeYZ^<V W<V*DFPJV*VfEMR g 2EhIiYZEFP9=^CLO\]EFHJEFjC^CL]KMV*l />I*KMWCVXb[LOI>mnVKMPfoqpFpMpsrFtMuFuMu.

(6)

(7) 4 \"j<PQV*HJV*NsYZV \]K EFPJEI*EFHAYZL YZ`CHJI*V \kK YZVXHQL"j<PQV*HJV*NsY K Y KcW K;6DFE@L YQYZEMPQL]E[G0EFHJIKMLONHQESYQYZE \kK WCLOPQV*L]EMNCV_WCV*\ =PJEMR5TG0VXNCV*WCViYQYQE=L]IXI*EF\OL  KM\CNCV9WCL EMYQYQV*NCVXPQV6L]\CW<L]jC\OEFb K3WCL g 2E I YZEMP =^CL]\OEFHQE KMV*l[jCPQVXHQHQE\kK :hI*`<EF\kK4 NsYZVXPQN K *L]EMN KM\]V WCL: YZ`CWCL"/ KMN*KSYZL WCL"7 PQLOV*HJYQV  .0\kKSHQHQ V K YZV*b[KSYQL]IK  :hVXYJYZEFPJVfWCL'/>NCKM\]LOHQ L

(8) `CN XL]EFNCKM\]VVXW /3jCjC\OL]IK *L]EMNCL T />L HQVXNCHQLWCVX\2VXI*PQViYZEWCVX\ LONCL]HAYZV*PJEWCVX\]\kK =!`<aCaC\]LOIK 4 HAYZPJ` *LOEFNCV t CT CT oqp  N'T Coqp Y KS\]V

(9) W<L]jC\OEFb K WCLPJL]I*VXPQI*Kj EFHAY `CNCL VXPQHQL Y KMPJLkK V

(10)  V  `CL]j EF\O\]V*NsYQV KM\ YQLOYQEF\]E WCL g 2 ESYQYZEMPQV WCL ?9L]IXV*PQI*K L]N KSYQV*b[KSYZLOIKMlCT 7 PJL]VXHJYZV  KMNCNCE KMIXIKMWCVXb[LOI*EoqpFpMpsrFtMuFuMu.

(11)

(12) 

(13)      !#"%$!&%')(*",+.-/0+1&2$43536+798$!:;$=<#$7"5",+>-/?A@=@B+7(C?ED;&2+7F3='G#$!3H"A?C:#I"AJ;$LK;0+NM(E$4O:;< &2+7PJQ?R3L@B+7:Q3H"2:S"T3='HKQKU+7H"WVYXZJ[=KU",$4]\^D[_GD;`)D;aDcb

(14) dC36$=$fehgGgiDjg1\GDjgi_GD;gi`GDjga5kEl@=+1:;"2?C: 0$!3H')(2"m3L?C:n@B+7(C(hQMQ+14#"A?A+7:o/?p"mJqJQ?RV ro/+s')(E<t(R?Cus$ri(C30+",+v"AJ[:Quv-/6+7&2$43W30+7

(15) wf:;< 0$4?Yw 4 @xJ;$7yn&2+7zKj6+0KU+735?R:#"mJ;$ Kj6+NM(A$!{+7&FXZJ[BKU"%$!}|~dEeC!kEl€:S<~&2+79J;$4(Kj&%')(P<^?C36@7')3W35?A+1:Q3

(16) "mJ[#"‚J[ y7$.@=+7:S"A5?,MN'Q"%$B< "%+„ƒQ:S<+s'#""AJ;$F5?  JS"U?C:Sy05?h:S"5V.

(17)

(18) 

(19) .

(20)

(21)  .

(22)     !"#%$'&)(* + + , oFT o 8*. YZPJV*b[KM\]H9G0L Rd`CPQI*KSYZLONCDRdPQEMb0/132%/4 T T TfT T T T T T T T 6 798 &;:!<>=?@  A@&BC thT o =PQVX\]LOb[LON KMPFE KMIiYZH6KMNCW : YZKSYZVXb[VXN Y6EMR YZ^<V KML]N?9V*HQ`<\OYZH thT oFT o 13VHG PZKMb V .0`CP V*H T T T T T T T TfT T T T T T T T thT oFT t :hL]N<DF`C\kKSPQLOYQL]VXHeKM\OEFNCD/132%/4 T T T TfT T T T T T T T thT oFTJI 13`Cb

(23) a VXP6ESR"jCPJVLK LOb KSDFV*H T T T T T TfT T T T T T T T thT oFT 7_^CVNMPORQTSV6U HQL]N<DF`C\kKSPQLOYWE T T T T T TfT T T T T T T T thT t : YQPQLOjCH9KMNCWYZ^CVf/3\]DFEFPJLOYQ^Cb T T T T T T T T TfT T T T T T T T thT thT o : YZPJL]jG0EFPJWCV*PJH"Y YZ^<V .0H9EMR[fZ LONCW\/B]>KSNCW_^ T T T thTJI /3aCNCEFPJb KM\'8[. YQPQV*b[KM\OH T T T T T T T T T T TfT T T T T T T T thTJ<I T o : YZPJL]ja EFPQWCVXPQH9EMR,` L]NCWa^cb KSNCWd^fe T T T T T T T thTJ<I T t :hL]N<DF`C\kKSPQLOYQL]VXH TfT T T T T T T T T T TfT T T T T T T T thT : YQPQLOjCH98 EF\O`<YZLOEFNKMNCW PQKMb V = EFLONsYZH T T TfT T T T T T T T thT CT o PZKMb Vf.0`CP V*H>KMNCW PZKMb V = EML]NsYZH6KM\OEFNCDhQ KMNCW0iQ thT CT t PZKMb Vf.0`CP V*H>KMNCW = EFLONsYZH6KM\]EMNCD/B] T T T T T T T T thT CTJI PZKMb Vf.0`CP V*H>KMNCW = EFLONsYZH6KM\]EMNCD3^ T T T T T T T thTj5 8*. YZPJV*b[KM\ :BE NsYZ^CVXHQL]H TfT T T T T T T T T T TfT T T T T T T T thTJk .0\]KMHQHJL I*KSYZLOEFNcEMR YZ^CVfHQLONCDF`C\]KMPQL YZLOV*H T T T T TfT T UTT n T T T T T thTJk<T o .0\kKMHJHQL IKSYQL]EFNcESR YQ^CV :hL]NCDM`C\kKMPJLOYQL]V*HUL]Nml Opo T T thTJ<k T t =PQErJq VXIXYZLOEFNHQLONCDF`C\]KMPQL YZL]VXHT T T T T TfT T T T T T T T s t\u vr:w!< 798 &B:w!< <I T o =PQEMj VXPJYZLOV*H_EMR"/>aCN<EFPQb[KM\'8*. YZPJV*b[KM\]H9T T T TfT T T T T T T T <I T t .0\]KMHQHJL I*KSYZLOEFNcEMR />aCNCEMPQb[KM\ 8*. YZPQVXb KS\]H T TfT T T T T T T T <I TJI /3N 8*<. KMb jC\]V T T T T TfT T T T T T T T T T TfT T T T T T T T { | A&_

(24) + +!<~}T + + ,N=&€ CT o 7_^CVf\OEhIX`CH>‚T3] L]NK NCV*LODF^ a EFPJ^CE EhWcEMR YZ^<V EMPQL]DML]NT T T T T T

(25).

(26). .

(27). . 

(28). .

(29). .

(30). .

(31). 

(32). . . . . L. . T T fT T T T T T T T T o 5 BD T T fT T T T TfT T T TfT T T TfT T T TfT T T TfT T T TfT T T TfT T T TfT T T TfT T T TfT T T TfT T T TfT T T TfT T T TfT T T TfT T T TfT T T TfT. TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT. TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT TTT. T T fT T T T T T T T T T TfT T T T T T T T T TfT T T T T T T T T TfT T T T T T T. T o T tho T tFt T t I T t  T Xt 5 T t  T tMp TgIFu TgI<o TgI. TgI TgI TgIFp T su. T ) 5 T. T ) 5  . !x y Tz5Mu Tz5 TgkXI { Tgk. . .

(33) CT t 4 N YQV*PJHQV*IiYZLOEFN SE R"VL.hYQPQVXb KM\ jCKML]PJH_L]NcYZ^CVfIXEMY KMN<DFV*NsY6aC`CNCW<\]V&T T T T T T T T T T T g T kMp CTjI _7 ^CVf\]LOR YeEMR[‚ 3] LONcYZ^CVNM  S0HQjCKMI*VST T TfT T T T T T T T T T T T T T T T T T T T Su . x cv

(34) & T

(35) R&) &B v3 A& f# #: : | :w&    6 h5 TOo 4 N YQPQE WC`CIiYZL]EMNT T T TfT T T T T T T T T T TfT T T T T T T T T T T T T T T T T T T T Mt h5 T t GeKMHQLOI 7 E EF\OH T T T TfT T T T T T T T T T TfT T T T T T T T T T T T T T T T T T T T h5 TjI =!PJEFj V*PJYQL]VXH_EMR YQ^CV L]N<L]b`Cb 7_L]b V PQEFNsY T T T T T T T T T T T T T T T T T T T T h5 TjhI TOo 2V NCLOYQL]EFNcESR: YQPQLOjCH$T T T T T T TfT T T T T T T T T T T T T T T T T T T T h5 TjhI T t L]NK 13VXL]DF^ a EFPQ^<EhE WcEMR  ] T TfT T T T T T T T T T T T T T T T T T T T Sp h5 TjhI TjI L]NK 13VXL]DF^ a EFPQ^<EhE WcEMR/ 1 2%/  4 T T T T T T T T T T T T T T T T T T T Mu h5 TjhI T 7_^CV 7 EFNYZ^CV B>YZ^<V*P6GeKMHJV*H TfT T T T T T T T T T T T T T T T T T T T h5 TjhI T 5 7_^CV 7 EFN Bj VXN: YQPQLOjCH T T TfT T T T T T T T T T T T T T T T T T T T X5 h5 TjhI Tjk EFNcYZ^<V

(36) B V*PQ\]KMj .0`CP V*H T T TfT T T T T T T T T T T T T T T T T T T T h5 TjhI T EFNcYZ^<V GUEFPQWCVXPQH T T T T T T TfT T T T T T T T T T T T T T T T T T T T Mp h5 TjhI T =PQE EMR EMR 7_^CV*EFPJV*b tX5 T T T T T TfT T T T T T T T T T T T T T T T T T T Tpho h5 TjhI T p 7_^CV 8*. YZPJV*b[KM\ PQEFNsY T T T T T TfT T T T T T T T T T T T T T T T T T T Tpho h5 T =!PJEhESR"EMR 7_^CVXEFPQVXb t T T T T T T T T T TfT T T T T T T T T T T T T T T T T T T TpI h5 T 5 :hV*b L]IXEFNCIK LOYW[E RdEFP9K YW0G E WCL]b V*N<HQL]EMN KM\ YZKMPQDMVXY9EFNYZ^CVfjC\]KMNCV T T T T T T T T T TpX5  t

(37) 

(38) ,<#X + C =&;X  hr&)\$m  &)r&B  !< 7  @ + - <k TOo : Y KSYQb[VXNsY9EMR YQ^CV =PQEFaC\OV*b T T T T T T T TfT T T T T T T T T T T T T T T T T T T Tp <k T t 8[<. KMb jC\OV*H T T T T TfT T T T T T T T T T TfT T T T T T T T T T T T T T T T T T T T_oquFt <k T t TOo 2`  N 8 `CKSYZLOEFN T T T T T T T T TfT T T T T T T T T T T T T T T T T T T T_oquFt <k T t T t @nKMNWCV*P6= EM\ V ` KSYQL]EFN T T T T TfT T T T T T T T T T T T T T T T T T T T_oquFt <k T t TjI /3NCEMYZ^<V*P9VH<. KMb jC\]V T T T T T T T TfT T T T T T T T T T T T T T T T T T T T_oquI <k TjI B jhYZL]b[KM\ HFE NsYZ^CVXHQVXH>RdEFP9G0EF\ K =PQEFa<\]V*b H T T T T T T T T T T T T T T T T T T T T_oqu  =  u <# L?  ! T<+!  %= "  rA&B =?@

(39) C&;:w By hTOo : Y KSYQb[VXNsY9EMR YQ^CV KMLON ?9V*HJ`C\OYQH T T T T TfT T T T T T T T T T T T T T T T T T T T_oquk hT t =!PJEhESR"EMR YZ^<V

(40) : Y KMaCLO\]L YW[E 7_^<V*EFPJV*b T T T T TfT T T T T T T T T T T T T T T T T T T T_oFoCI hT t TOo 7_^CVfI*KMHQV L]N'9G ^CLOI ^# KMN<W$-^ K V a ESYZ^I*EFb jC\OVHc. VXL]DFVXN KS\]`CVXH T T T T T_oFoCI hT t T t 7_^CV[IKMHJV LON 9G ^CLOI ^%# KMNCW&$ ^ K V EMNCV IXEFb[j<\]VH. KMNCW&YQ^CV[ESYZ^CVXP

(41) PQV*KM\ VXL]DFVXN KM\O`CV*H T T T T T T T T T T TfT T T T T T T T T T T T T T T T T T T T_oFo hTjI : YZ`CW;cE EMR YZ^CV : YZKMaCL]\OLOYWE 2EFb[KML]N T T T T TfT T T T T T T T T T T T T T T T T T T T_o tMt hTjhI TOo : YZKMaCLO\]LOYWE WCEMb KMLONcL]NcYZ^<V

(42) .0EMb[jC\OVH.€<K .0EFb jC\OVHc. I*KMHQV T T T T T T T T T T T_o tMt hTjhI T t : YZKMaCLO\]LOYWE WCEMb KMLONcL]NcYZ^<V ?9VKS\ <K .0EFb jC\OVH. IKMHJV[T T T T T T T T T T T T T T_o t I hT "L]N KS\'?9V*b[KMP ` H9T T TfT T T T T T T T T T TfT T T T T T T T T T T T T T T T T T T T_o t   u <#+  'vr

(43) *A? sy .  .

(44). . .  . . .

(45).  .

(46). . . . . .

(47). . . . . . . . . .  . . .  .  .

(48). . LOL.

(49) !+_X[ 4 N YZ^<L]H 7_^CV*HJL]H GUV HAYZ`CW E K I*\]KMHQH EMR3aCLOWCL]b V*NCHJL]EFNCKM\0EFjhYZL]b[KM\UI*EFNsYZPJEF\_jCPJEFaC\]VXb[HYQ^ KSY LOH HJ`<R  CI*L]VXNsYZ\ E DFVXNCV*PQKM\nYQEa V[`CHQVXW RdEFP

(50) HJEFb[V KMjCjC\OL]I*KSYZLOEFNCHfaC`<Y HJL]b jC\]V V*N<EF`CDF^ YQEPQV*KMI ^CV*H KW<V*V*j `<NCWCV*PJHJYZKMNCWCLONCD EMRYQ^CV DMV*EFb VXYQPFE `CNCW<V*PQ\ E L]NCD YZ^CV = EFNsYZPVEsKMDML]N Kr.hL]b`Cb =PQLONCI*LOjC\]VMdL]N YZ^CV RdEM\]\]E G9LONCD = = SiT &V WCVKS\ G9LOYZ^YZ^CV b L]NCLOb`Cb-YZL]b V HJYZKMaCLO\]L *KSYZLOEFNjCPJEFaC\OV*b YZE YZ^<V EFPJL]DFLONRdEFP YQ^CVfjC\kKSN KMP_HQLONCDF\OV  LONCjC`<Y0I*EFNsYQPQEF\ VH EhHAYZVXbdY M5o S    M  S 

(51) NM  S   l U   o  o    M €u S  u   G9^<V*PQV  KMNCW

(52) KMPQV9WY GUE  VXIXYZEMP  VX\]WCHnEFN YZ^CV6jC\]KMNCVMT

(53) EMP`CH  K HJEF\]`hYZL]EMN YQE YQ^CV6jCPQEFa<\]V*b$L]H DML VXN€a EKSNEFj<YQL]b[KM\ FH E NsYZ^CVXHQLOH  YQ^ KSYeLOHeK GeCK E[EMR KMHQHJEhIXLkKSYQL]NCD K

(54) `CN<L  `CV>EMj<YZLOb KM\CYQPZK qJVXIXYQEFFP E YZE V VXFP EL]N<LOYZL]KM\ j EFLONsY9EMR YQ^CVfjC\kKSNCVMT!;6NCWCV*P9DFVXNCV*PJL]IfI*EMNCWCLOYQL]EFN<H  YQ^CVfEFj<YQL]b[KM\ VH EhNsYQ^CU V*HJL]H>^CKMjCj V*NCH YQE>a VUDMV*NCVXPZKSYQV*W

(55) €a E K3j<L]V*IX

(56) V G9LOHQVnHQb EhEMYQ^ RdVXV*WCaCKMI ` PJV*\]KSYZVXW YQEK3HAYZPQKSYZL  IKSYQL]EFNfEMR l  HJV*V  o t  op  I T7_^<L]H_jCPJEFaC\]VXb G0KMH9KM\OHQE HAYZ`CWCLOV*WL]N Su  H0)a EcGeKMLOYQb KSNCN G9^CE KMN KS\ E *VXWYZ^CV IXEFNsYZPQEM\]\kKSaCL]\OLOWY E KSNCWYQ^CVfj EMHQLOYQL]EFNcESR"VH G9LOYZI ^<L]NCD I*`<P VXH MdHQV*V  5  k SiT 7_^CV I*EFN<I*V*jhYEMR"PQV*DM`C\kKMP_VH E N YQ^CV*HJL]9H G0KMH6L]NsYZPJEhW<`CI*VXW L]NYZ^<V jCLOEFNCVXV*PQLONCD G0EMP `EMRGUEF\OYQLkKMNCFH ` L    HQV*V

(57) KM\]HJE  tMu  KSNCW  I€5 T

(58) EFP6K[WCLOHQIX`CHQHJL]EFN EMR"YQ^CV IXEFNCIXV*j<Y>EMRVH EhNsYQ^CV*HJL]H KMN<W LOYQH9PQV*\]KSYZLOEFNcYZE j<L]V*IX

(59) V G9LOHQVfHQb EhESYZ^cRdV*VXWCa KMI ` H GUVfPQViRdV*P_YZ^CVfPJVKMWCVXP_YZE  IXI T 7_^C3V G0VX\]R\ ` NCE G9N = EFNsYZFP EFKMDFLON K .<LOb`Cb =PJL]NCIXL]jC\O%V M HQVXV  Xt 5  I   IFp  SDFL V*H K  PJHJY EFPJWCV*P IXEFNCWCL YZLOEFN RdEMP YQ^CVEFj<YQL]b[KM\0YQPZK qJVXIXYZEMPQL]VX"H YV V*VP E YQL]b VEMj<YZLOb KM\eYQPZK qJVXIXYQEFFP E ^ KMH K \OLOR Y YZE YZ^CV IXEMY KSNCDFV*NsY3HQj KSI*V  RdEFPJb[VXW€a E VXIXYQEFP  I*E VXIXYZEMP>j KMLOPQH  HZKSYQL]HJR E LONCD K b[rK .hL]b L K YZL]EMN I*EMNCWCLOYQL]EFNEMR K6HQ`CL Y KMa<\]!V >KMb L]\ YZEFN<LkKMhN MdHQVXV_.0^ KMjhYZV*PUonRdEMP WCViY KMLO\]H SiT 7_^CV0j<PQEFj V*PAYZL]VXH ESRCHV . YQPQV*b[KM\sYZPQK qJV*IiYZEFPJL]VXH  YQ^ KSYnL]HYQPZK qJVXIXYZEMPQL]VXHUHQKSYZLOHJR E L]N<DfYQ^CV3= =  ^ K V6a VXV*NHAYZ`CWCLOV*W L]N WCVXYZKML]\OHL]N  Ik  I T EFPJV*E VXP  LON K>HJV*PQLOV*HEMR jCKMj VXPQH  o   oqp  I<o  Ist   YZ^<VeHV .hL]HAYZVXNCI*V9EMR K>HAYZPJ`CIXYQ`CPZKM\O\ E HJYZKMaC\OVeEFj<YQL]b[KM\ FH E NsYZ^CVXHQL]H RdEMP6DMV*NCVXPQL]IfHJb[E EMYZ^VH EhHAYZVXb[>H GeKSH3jCPJE V*WKMNCWI*EFb jC\]ViYZV IX\kKMHJHQL CIKSYQL]EFNCH9EMR YZ^<V IXEFPQPJV*HQj EFNCW<L]NCD MdNCEFNHJb[E EMYQv^ S#"CE G9H9KSNCWPQVX\kKSYQL V3HJL]NCDF`<\kKMPJLOYZLOV*RH GUV*PQV>DFL V*N  L]N YQ^CV>HQKMb[V3HQjCLOPQL Y0EMR YQ^CV GUEFFP `[EMR = V*L .<ESYZE RdEFPeWY G0E WCLOb[VXNCHQLOEFN KM\ W E N KMb L]IKS\'FH E HJYQV*b H MdHQVXV  IFu  SiT 4 N&KM\]\ j KMj V*PQH  YQ^CV KM`<YQ^CEFPQHf`CHJV YQ^CV = = YZEN KMPJPQE G$YQ^CV I*\kKSHQHfEMRUj EFHJHQLOaC\ EEMj<YZLOb KM\ YZPQK  qJVXIXYQEFPQLOV*H*T BNCVjCPJE V*H YZ^ KSY YZ^CV[HQViY EMR_LV .hYQPQVXb KM\!YZPQK qJV*IiYZEFPJL]VXH

(60) IKSN a V[WCV*HJI*PJL]a V*W €a E K  NCL YZV W<L]b V*NCHJL]EFN KS\ PQVXWC`CIiYZL]EMN  b[EFPJV jCPQVXI*LOHQV*\ EcV V*VP E LV . YZPQVXb KS\'YZPZK qJV*IXYQEFFP EL]H6K  NCLOYQVfI*EFNCI*KSYZVXN KSYQL]EFN ESR KMPQIXHUYZ^CKSY_KMPJV>VXLOYZ^<V*P0aCKMNCmD MdI*EFPJPQV*HJj EMNCWCL]N<D

(61) YZE K I*EFNCHAY KMNsY_IXEFNsYZPJEF\ V  ` KM\ YQ%E $ o SnEFPUHQLONCDF`C\]KMP MdI*EFPJPQVXHQj EFNCWCLONCD>YZEK>HQb EhESYZ^

(62) RdVXV*WCa KSI `

(63) WCV  NCV*W EMNHQEFb VeHJj VXI*LkKS\hIX`CP V*H S  G9LOYZ^K3a EF`CNCW EFN YZ^CV N `Cb

(64) a VXP6ESRKMPJI*H_RdEFP9K  .hV*W YQL]b 'V &)( u<T!7_^CV*N  YQ^CVfI*EFN<HJYZPJ`CIXYQL]EFNEMR YZ^CNV M VXHQHJV*NsYZL]KM\]\ E`CNCL  `CV S EMj<YZLOb KM\ FH E NsYZ^CVXHQLOH3IXEFNCHQLOHJYQH3LONIXEFNCHJL]WCVXPQL]N<D[KS\]\ LV . YZPQVXb KS\'YZPZK qJV*IXYQEFPQLOV*H G9LOYQ^K ;.<VXW N `Cba V*P9EMR KSPQI*H6KMN<W EFj V*PQKSYZLONCD HQEMb[V g IX`<YZHJl YQE LV .hI*\]`<WCV YZ^CVfNCEMY6EFjhYZL]b[KM\ EFNCVXH*T 4 N .0^ KMj<YQV*Pt  GUVjCPJEFj EFHQV K&NC

(65) V G KMj<jCPQEsKSI ^'T 7_^CLOHKMb EF`CNsYQH[YZE&I*EFNCHAYZPJ`CIXYKS\]\9HV . YZPJV*b[KM\]H  YQ^ KSYUL]HYZPQK qJV*IiYZEFVP E I*E V*IXYQEFPej KSL]PQH!HQKSYZLOHJR E L]NCDfYZ^<V= =  KMNCW[jCPQE qJV*IXYQL]NCDfYZ^<V>EFa<YZKML]N<V*W HQVXY0EFNsYZE YQ^CV jC\kKMN<VMT7_^CLOH HJV*IXEFNCW b VXYQ^CEhW L]H L]N YZ^<L]HfIKMHJV b EFPQV LON EF\ V*W  aC`<Y L]NCW<`CI*VXHKb[EFPJV I*\]V*KMP `<NCWCV*PJHJYZKMNCWCLONCD EMR0YZ^CV jCPQEMj VXPJYZLOV*HfEMR_LV . YZPQVXb KS\YZPZK qJV*IXYQEFPQLOV*H KMNCW YZ^CV PQVX\kKSYQL]EFN G9LOYQ^ YQ^CV b L]N  LOb`Cb YQL]b V Rd`<NCIXYQL]EFN'T4 N j KSPJYZLOI*`C\]KMP YZ^CV g I*`<YQHQl  IKM\O\]V*W E VXPQ\kKSjCHL]N  IFt   KMjCj VKMPJL]NCD L]N YZ^CV o.

(66) EFj<YQL]b[KM\_HFE NsYZ^CVXHQLOHKMPQV PQV*\]KSYZVXW YZE&jCPQErqJVXIXYQL]EFN HQL]N<DF`C\kKSPQLOYQL]VXH ESRYZ^CV HQVXYEMR VH. YQPQV*b[KM\OH  a V*L]N<D \]E IKM\O\ EEFjhYZL]b[KM\ YZ^CV LV . YZPQVXb KS\"YZPQKqJV*IiYZEFPJL]V*H IXEFb L]NCD RdPJEFb a EMYQ^ HQL]W<V*H EMR!YZ^<V E V*PQ\]KMj'T 4 N YQ^CL]H KMHQj V*IiY  EF`<~P G0EFFP `L]H_PJV*\]KSYZVXWYQE YZ^CVfPQVXI*VXN Y6LON YQV*PJV*HJYQL]NCD KMNCKM\ E HQLOHeEMR jCPQEqJV*IXYQL]EFNHJL]NCDF`<\kKMPJLOYZLOV*HUEMR HQb EhESYZ^cR KMb L]\]LOV*HnEMR HV . YZPJV*b[KM\ j KMLOPQH  jCPQEFj EFHJV*WL]N  t k T &V HJY KSPJY3I*EFNCHAYZPJ`CIXYQL]NCDcKS\]\'YZ^<V

(67) HV . YQPQV*b[KM\ j KMLOPQH LkK KSNKM\ODFEFPQL YZ^Cb YZ^ K Y3YQV*PQb L]NCKSYZVXH  `CNCWCVXP DFV*N<V*PQLOI I*EFN<WCLOYQL]EFNCHUEFNcYZ^CV jCKML]P M  

(68) S  LONK  NCLOYQVN `Cba V*P9EMR HJYQV*jCHXT#&V IXEFNCHQLOWCV*PeYQ^CV V `CL  KM\]VXNsY0jCPJEFaC\OV*b EMR'HJY KSPJYZLONCDfRdPQEFb YQ^CV3EMPQL]DML]N KMNCW[PQVKSI ^CL]NCD

(69) KM\]\ j EFLON YQHUESR YZ^<V>jC\]KMNCV6L]N b[LONCL]b`<b YZLOb[VST fVXNCV*PJL]IKS\]\ E KM\O\'HV . YZPJV*b[KM\'YZPQK qJV*IiYZEFPJL]VXH6\OVK V YQ^CVfEFPQLODFL]\N G9L YZ^I*EFNsYQPQEF\ o EFP  oMTU7_^ `CH  LO@R / KMPQVYQ^CV HV . YZPJV*b[KM\ KMPJI*H9I*EMPQPQVXHQj EFNCWCLONCD YZE IXEFNCHJYZKMNsY6I*EFNsYZPJEF\]H $ o KMNCWHV .hL YZL]N<DYZ^CVfEFPJL]DFLON  YZ^CVXN VKSI ^ HV . YZPJV*b[KM\!YZPZK qJV*IXYQEFFP E aCL Rd`CPQI*KSYZVXH RdPJEFb /"T7_^CV HJVXY

(70) EMR_aCL Rd`CPQI*KSYZLONCD LV . YZPQVXb KS\!YQPZK  qJV*IiYZEFPJL]V*H6KMPJVfWCL L]W<V*WL]NsYZE g HAYZPQLOjCHQl  YZ^ KSY3KMPJVfEFNCV WCL]b V*NCHJL]EFNCKM\ R KMb L]\OL]VXH0jCPJV*HQVXNsYZL]N<D[YZ^<V HQKMb[V HQV  `<V*NCIXV EMR>KMPQIXdH M a KMN<D KSNCW HJL]NCDM`C\kKMP SiT 7_^CV*N YZ^CVcV EF\O`<YZLOEFN EMR g HJYZPJL]jCHJl L]H HJYQ`CWCLOV*W `CNCWCVXP DFV*N<V*PQLOI IXEFNCWCL YZLOEFNCH*T 7_^CV EFahY KMLONCV*W HQViYEMR>HV . YZPJV*b[KM\9j KML]PJH[^CKMH[HJEFb V PJV*DF`C\]KMPQL WY E jCPJEFj VXPJYQL]V*H HQ`Cb b[KMPQL *V*WLONYZ^CV WCV  NCL YZL]EMNEMRnHV . YZPJV*b[KM\FH E NsYZ^CVXHQLOH  HQV*V[:hVXIXYQL]EFN thT oFT

(71) 7_^<V HJVXY  ESR0j KSL]PQH YZ^ K YfKMPQV PJVKMI ^<V*W )a EKMN U HV . YZPJV*b[KM\ YQPZK qJVXIXYQEFFP E R KML]\OH3YZEca V Kb[KMNCLORdEM\]W a<`<YfL]HHAYZLO\]\ K  LOYZ^<NC

(72) V E HJYQPZKSYQL  VXW HQ`Ca<HQVXY EMR   l  l EMR9WCLOb[VXNCHQLOEF N I<T EFPQVXE V*P  YQ^CVLV .hYQPQVXb KM\nYZPQK qJV*IiYZEFPJL]V*\H M LON  NCL YZVfYZL]b  V S_KMPJV

(73) KSDsKML]N  N<LOYZV I*EMNCIKSYQV*N K YZL]EMNCH3ESRa KMNCD KMNCW HQL]N<DF`C\kKSP3KSPQI*H>KMNCWYZ^CV HQViY>RdEFPJb[VXW €a Ej EFLONsYZH6KS>Y G9^CL]I

(74) ^  R KML]\OHeYZE a V K b KMN<LORdEF\OWL]H_YZ^<V `CN<L]EFNEMRK I*EM`CNsY KMaC\OVfI*EF\O\]V*IiYZLOEFNEMR"WY GUE WCL]b V*N<HQL]EMN KM\ HJYZPQKSY KhT"7_^CV_IXE V*IiYZEFP!KMHJHQE I*L]KSYZVXWYZEfKMNLV . UYZPQn VXb KS\Cj KMLOP"L]H WCV CNCV*W `Cj YZEKj EFHJLOYQL V b`C\ YZL]j<\]L]I*KSYZLOEFN I*EFNCHAY KMNsY  ^CV*NCIXV GUV jCPQrE qJVXIX Y  EFNsYQ3E l Opo0EFa<Y KSL]NCLONCD K HJYQPZKSYQL  VXW HJVXY ‚ EMR WCL]b V*N<HQL]EMNWY G0E Y ‚  M U  n S  l U n O o Y'YZ^CVXPQV HV .hL]HAYZH KYZLOb[V  ( uKMNCW KMN HV . YZPJV*b[KM\j KMLOhP M+/  S Y  u   l O o HJ`CI ^ YQ^ KSY /*M €u S  u  /*M  S   M  S   T 7_^CV*N GUV HAYZ`C;W EYZ^CV HAY KMa<\]V HQLONCDF`C\]KMPQL YZLOV*H6EMR!YZ^CV jCPJrE qJV*IiYZLOEFN EMpR ‚ EMN YQ'E l U T

(75) /eYfj EFL]NsYQ9H G9^CV*PJV ‚ LOH3K b KSNCLORdEF\OW  GUVKMPJV LON YQ^CV HJLOYQ` KSYZLOEFNEMRYZ^<V jCPJrE qJV*IiYZLOEFN EMRK WY GUEWCL]b V*N<HQL]EMN KM\'b[KMNCL RdEF\]W EFN YQ^CV

(76) jC\]KMNCV  ^<V*NCIXV G0V

(77) b CK EHV .hj V*IXY>YZE CNCW YZ^<V

(78) I*\]KMHQHJL]I*KM \  ^CLOYQNC

(79) V EHQLONCDF`C\]KMPQL YZLOV*H_EMRHJb[E EMYQ^ b KSjCH a VXWY GUV*VXNWY GUE WCL]b V*N<HQL]EMN KM\9b KSNCLORdEF\OWCH  N KMb V*\ E RdEM\]WCH KMNCW I*`<HQjCHXT /3j KMPAY RdPQEMb HJEFb[V HQj V*IXLkKM\ HQLONCDF`C\]KMPQL YZL]VXH M V*PJYQL]I*KM\  HQVXV7_^CV*EMPQV*b I  .0^ KMj<YQV*Pft S9WC`<V

(80) YZE YZ^CV R KMIXY3YZ^ KSY3YZ^CV Y KMPJDFVXY L]H9Kj EFL]NsY  YZ^CV HAY KMa<\]V jCPJrE qJV*IiYZL]EMNHJL]NCDM`C\kKMPJLOYQL]V*HUV*NCIXEFb j KMHQH  a VXHQLOWCVRdEF\]W<H9KMNCWI*`CHJjCH  WY GUE[N<

(81) V G HQLONCDF`C\]KMPQL YZL]VXH[I*KM\]\OV*W a<LORdEF\OW KMNCW PJL]aCa EFN'T 7_^CV  PJHJYKMj<j V*KMPQHLON PQVX\kKSYQL]EFN G9LOYZ^ N<EMYcEFj<YQL]b[KM\ YZPQK qJV*IiYZEFPJL]V*HUKM\OEFNCDfRdEF\]W[j EFLONsYZH  G9^CLO\]V9YZ^CV3HQVXI*EFNCWKMjCj VKMPJH0EFNC\ E EFNKSaCNCEFPJb KM\ LV . YZPQVXb KS\]H*T7_^<V \kKSYJYZVXPQHeKSPQVLV .hYQPQVXb KM\ YZPQK qJV*IiYZEFPJL]V*pH G9LOYZ^ KSNCL]HJ^CL]NCD >KMb L]\ YZEFNCL]KMN  KW<VXY KSL]\]VXWcKMN KS\ E HQLOH0EMR G9^CLOI ^ L]HLON .0^ KMjhYZV*mP IhT EFPQVHAYZPJ`CIXYQ`CPQVEMR ‚ N<VKMP YQ^CVEFPJL]DFLON LOHHJYQ`CWCL]VXW L]N.0^ KSj<YZVXP CT 4 YcL]H NCV*IXV*HJHZKMVP EcYZE j EML]NsY_EF`<Y_YQ^ KSY_a V*LONC3D ‚ EFNC\ EK HJYQPZKSYQL  VXWHQVXY6KSNCWNCEMY6K HQb EhESYZ^cb[KMNCLORdEM\]W  YZ^<V I*\]KMHQHJL  I*KSYZLOEFNcEMR HJY KSaC\]VfjCPJrE qJV*IiYZL]EMNHJL]NCDM`C\kKMPJLOYQL]V*HUL]HeYQE a VfL]NsYZVXNCWCVXW LONYQEFj EF\]EFDML]IKS\ HJV*NCHJVMT 7_^CVfHJYZPQKSY K EMR WCLOb[VXNCHQLOEFNEFN<VfKMNCW *VXPQE EM,R ‚ KMPQV I*KM\]\OV*W

(82) PZKSb[V.0`CP V*H3KMNCW= EFLONsYZH*T!/3H9K €a Ehj<PQE WC`CIXY GUV DMVXY3K I*EFb jC\]ViYZV IX\kKMHJHQL CIKSYQL]EFNcEMR

(83) PZKMb V .0`CP V*H>KMNCW= EML]NsYZH  HQV*V

(84) :hVXIXYZLOEFN thJT k<T  ViY `CHfDFL V HJEFb V b EFPJVWCVXYZKML]\OHRdEFPfKa ViYQYZVXPf`CNCWCVXPQHJYZKMNCWCLONCDEMRUYQ^CV HQL YZ` KSYQL]EFN T .0EFNCHJL]WCVXP YZ^CV HJj KMIXV[EMR!YQ^CV YZ^CPJV*V KMPQL]KMaC\OmV M    S G9^CV*PJdV M   S    l U  l KMNCW  L]H>YQ^CV YZL]b VMT  V t.

(85) PJVXRdVXP9YQE YZ^CV RdEF\O\]EG9L]NCD

(86) jCL]IiYZ`CPJVY * 2. T R Π1. 2. T* R R (x,p). 5. R R (x,p,t). (manifold). Π. 3. 2. 4. normalization. 2. S. R. R R (x,t). 1. (Witney Stratified Set). Π’2 Π. 4. Π. 2. R. 2. 7_^<V = =WCViYZVXPQb L]NCVXHK JH VXY LON YZ^<VmM    S6HJj KMI*V YZ^ KSY>L]H3K[YZ^<PQV*V  WCLOb[VXNCHQLOEFN KM\ jCLOV*IXV

(87) G9L]HJV *o b[KMNCL RdEF\]W T"=PQEqJV*IXYQL]NCD

(88) L]N YQC^ V M   SUHJj KMI*V3YZ^CPJEF`CDF^ o  L Yeb[KCE[^CKMjCj V*N YQ^ KSY0YWGUE PQVXDFL]EMNCH0DF\O`CV YQEFDFViYZ^CVXP"Y. 7_^CLOH>LOH3YZ^<VPQV*KMHQEFN_G9^€E_‚ L]H>K  ^CLOYQNCV

(89) EHAYZPZK YZL CV*WHQViY  a<`<YNCESY Kb[KMNCLORdEM\]W'T97_^CVHJLOYQ` KSYZLOEFN LOH W<V*HQIXPQLOa VXW €a E 7_^<V*EFPJV*b p .0^ KSj<YZVXP thTc7_^CV[HQL]N<DF`C\kKSPQLOYQL]VXH EMR0YQ^CV jCPJErqJV*IiYZLOEFNU KMPQV YZ^<EFHQV IX\kKMHJHQL  V*WL]N.0^ KSj<YZVXPmt M IX`CHQj  RdEM\]W  V*PAYZLOIKM\  aCLORdEM\]W  PQL]a<a EFN!SiT BNYZ^<V>EMYQ^CV*PUHQL]W<V KM\]HJE YQ^CV>U jCn PJErqJV*IiYZLOEFN_EMN YZ^CV M  S!HQj KMIXV KMNCW EFN YQ^CV  HJj KMI*VfKSPQV LONsYZV*PJV*HAYZL]N<DCT8 V*VP E&IX`CHQj LON l O o IXEFPQPJV*HJj EFN<WCH YQEK HVGeKS\]\]EG_YZKML]\LON YQ^CV M  SfHJj KMIXVKMNCW YQ^CL]H_LOH_WC`CVfYZE YZ^<V j<PQV*HJV*NCIXV

(90) EMR"KMNE VXPQ\kKSj IX`CP V LONYQ^CVfEFj<YQL]b[KM\ HVEhNsYQ^CV*HJL]H"Y. I.

(91) Cusp (x,p). R. 2. Swallowtail S. (x,t) R 2 R. 1. Π2’. # preimage 1. Π4 overlap. 3. 4 N.0^ KMj<YQV*P I G0V>KMN KM\ E XV3YQ^CVDFVXNCV*PJL]I6jCPQEFj V*PAYZLOV*H0ESR KMaCNCEMPQb[KM\ VH. YZPJV*b[KM\]HXT &V>jCPQE V3YZ^ KSY YZ^CVXHQV_KSPQV CNCLOYQV0I*EMNCIKSYQV*N K YZL]EMNCH"EMRCa KMNCD KSPQI*H~MdYQ^ KSYLOH IXEFPQPJV*HJj EFN<WCL]NCD3YZE>IXEFNCHAY KMNsY!$ oeI*EMN YQPQEF\ SiT. EFPJV*E VXP YQ^CV HVG9LOYQI ^CL]NCDMH M W<L]HQIXEFNsYZLON `<LOYWEj EFL]NsYZH3EMRYQ^CV IXEFNsYZPJEF\ S_^ KMjCj V*N<HVH.<KMIiYZ\ E'G9^<V*NYZ^<V KMaCNCEMPQb[KM\  LV . YZPQVXb KS\ I*PJEFHQHJV*H_YZ^<VHQViY9EMR *V*PJEhVXH_EMR YZ^<VRd`CNCIXYQL]EFN  

(92) YZ^ K YeL]HpG9^CV*NcYZ^<V YWG0E V*IiYZEFP  V*\OWCH  KSNCW

(93) -KMPQV I*EM\]\]LONCVKSP*T04 N b KM€N EI*KMHQVXH  KSNKMaCN<EFPQb[KM\ VH. YQPQV*b[KM\ L]H9RdEFPJb[VXW €a E RdEF\OW j EFL]NsYQH  YZ^ KSY3L]H6YZ^CVXPQV

(94) KMPQV WY G0EcHJ^CV*ViYZHEMRYQ^CV

(95) IXEMY KSNCDFV*NsY a<`CNCWC\OV

(96) I*E V*PQVXW )a ELV .hYQPQVXb KM\ YZPQK qJV*IiYZEFPJL]V*H YZ^CKSY jCPQrE qJVXIXYQH EFNsYZE YZ^<V HQKMb[VPQVXDFL]EMN EMR3YZ^CVjC\]KMNCVKMNCW YZ^CVa EM`CNCW KMVP E EMR>YQ^CL]H PQVXDFL]EFN L]H!YZ^<V3jCPJrE qJV*IiYZLOEFN EMR YZ^CV>KMaCNCEMPQb[KM\ HV . YZPJV*b[KM\ T />\O\ j EFHJHQL]a<\]V9DFV*N<V*PQLOI3HJL]NCDM`C\kKMPJLOYQL]V*HESR YZ^<V FH E NsYZ^CVXHQLOH"EFNfYZ^CVnjC\]KMNCV!EhIXI*`CPJPQLONCD>KS\]EFNCD MdjCPQE qJV*IXYQL]EFN<H EMR S KMaCNCEMPQb[KM\FHV . YQPQV*b[KM\OH KSPQV!I*\]KMHQHJL  VXW LON .0^ KMj<YQV*P"thT 3EG0V VXP  EFN<VU^ KSH YQE3j<PQE V!YZ^ K Y"KS\]\FHJL]NCDF`<\kKMPJLOYZLOV*H L]NCWCVXV*W

(97) KMjCj VKMPJH RdEMP HJEFb VDFV*NCVXPQLOI FH E HJYQV*b  LON j KMPJYQL]IX`C\kKMP3YZ^CEFHJV[IXEFPQPJV*HJj EFN<WCL]NCDcYQEYQ^CV NC

(98) V G j<PQrE qJVXIXYZLOEFN HQLONCDF`C\]KMPQL YZL]VXHaCL RdEF\]WKSNCW PQLOaCa EMN'T97_^CVHQViYEMR!j EFHJHQL]a<\]V HQL]N<DF`C\kKSPQLOYQL]VXH_L]H9RdEFPQb V*W EMRUt _MdV  `CL KS\]V*N<I*V

(99) IX\kKMHJHQVXHEMR S9HJL]NCDF`<\kKMP j EML]NsYZH  aC`<Y6NCEMY3KM\O\ HJV  `CV*N<I*V*H>EMR"HJL]NCDM`C\kKMPJLOYQL]V*HUIKMNa V PJVKM\OL XV*W'T &V PQVXIKM\O\YZ^ KSY KHQViY

(100) EMR GUEFPQWCH  RdPJEFb KDFL V*N  NCLOYQV KM\]jC^CKMa ViY L]H PQVXI*EFDMNCL *KMaC\]V L RUYQ^CV*PJV HV .hL]HAYZH KMN KS`<YZEFb[KSYQEFN&YZ^CKSY DFV*N<V*PZK YZV*H LV .<KMIXYQ\ E&YQ^C\V GUEFPQWCH ESR T />N KM`hYZEFb[KSYZEMN L]HPJEF`CDF^<\ E HQj VK ` LONCDK

(101) DMPZKMjC^  G9L YZ^ \]KMa V*\]\OV*W V*W<DFV*H  KMNCW EFNCV6I*EFNCHAYZPJ`CIXYQH G0EMPQWCHeIXEFNCHJL]WCVXPQL]N<DKM\O\CYZ^CV3j KSYZ^<H HJYZKMPJYQL]NCD>RdPJEFb KDFL V*NHJVXY!EMR j EFLON YQHKMN<W V*NCWCLONCD>YQEfKMNCEMYQ^CV*P  .hV*W HQViY!EMR j EML]NsYZHXT"/>N

(102) L]b j EFPAY KMNsY PQEF\OV3LON YZ^<V*EFPJVXYZLOIKM\ I*EMb[jC`hYZV*PUHQIXL]V*N<I*V L]HnjC\]K EMV*Wc€a E[PQV*IXEFDFNCL KMa<\]V>HJVXYQHeEMR GUEFPQWCH M HQVXV  t  SiT  V KMPQV6KMa<\]VeYZE jCPJE V6YQ^ KSY!YZ^<V6DMV*NCVXPQL]I9HJV  `CV*N<I*V*H0EMR'HJL]NCDF`<\kKMPJLOYZLOV*H"KM\]EFN<D KSaCNCEFPJb KM\<HV . YZPJV*b[KM\]HI*KMN a V6I*\]KMHQHJL  VX3W G9L YZ^ K PJV*I*EMDFNCL *KMaC\OV6HJVXYUEMR GUEFPJWCH*T/3H0K )a E j<PQE WC`CIXY  GUV6EFa<Y KSL]N YZ^CV6HV .hL]HAYZVXNCI*V3EMR FH E HJYQV*b H9jCPQVXHQV*NsYQL]NCD HQLONCDF`C\]KMP0j EFL]NsYQHeI*EFPJPQVXHQj EFNCWCLONCD YZE jCPJrE qJV*IiYZL]EMNHJL]NCDM`C\kKMPJLOYQL]V*HnEMR aCLORdEM\]WKSNCW PQLOaCa EMNWY E j VMT .

(103) 4 N .0^ KMjhYZV*P h G0V KMPJVfI*EFNCIXV*PJNCV*W%G9LOYZ^cYQ^CV ?C:Q?2"m? i( @B+7:;<^?2"m?A+1:Q3Y30$1" ‚ ]Y ‚ ]  M U  n  S  l Uhn O o Y YQ^CV*PJV HV .hL]HAYZHfK YZLOb[V  ( ucKMNCW KSNVH. YZPJV*b[KM\j KMLOP M /   S Y  u     l O o HQ`CI ^YZ^ K Y /[M €u S  u  /*M  S   M u€S    T  V_WCViYZV*PJb[LONCV_HV .hjC\OL]IXLOYZ\ EfYZ^CLOH\]E I*`CHLON KNCV*LODF^ a EMPQ^CE EhW EMR YZ^<V6EMPQL]DML]NKSNCW G0V9DFL V9KHQ` [IXL]VXN Y IXEFNCWCL YZLOEFNCH_`CNCW<V*>P G9^CL]I ^LOY9LOH9K jCLOV*IX

(104) V G9L]HJLV K  o b[KMNCL RdEF\]3W G9LOYZ^a EF`CNCW KSFP EFT!7_^CV HQViY ‚ ]3LOH_b[EMPQV V*KMHQLO\ EIXEFb jC`<YZVXW YQ^ KM N ‚ HQLONCI*V  EF`hYZHQLOWCV O#   M+/1 S[2O   M+/4S  YQ^CV LV . YZPQVXb KS\YZPZKqJV*IXYQEFPQLOV*H KSPQV_\]V VX\ HQ`CPAR KMI*VXHUEMR ‚T]*T EFPJV*E VXP  ‚T]!R KML]\OH YZEfa V6Kfb[KMNCL RdEF\]W  aC`hYUL YZHHJL]NCDF`<\kKMPJLOYZLOU V*H n KMPQV  `CL YZV W<L V*PQVXNsY>RdPQEMb YZ^CEFHJV

(105) EMRR ‚ T64 R M €u S_WCV*N<EMYZVXH K[NCVXL]DF^ a EFPQ^<EhE W ESRYZ^CV EFPQLODFL]NLOaN l Opo_YQ^CV*N YQ^CV ` NCE G9\]V*W<DFV ES[R ‚ ] ] L]H_j V*PQb LOYQH0YZE WCViYZVXPQb L]NCV YZ^<V j<PQEFj V*PAYZL]VXH_EM*R ‚ ] T . .  .  . 61 EMYZLOI*V YZ^ KSY YZ^CV[KMN KS\ E HQLOH EMR9.0^ KMj<YQV*P t  I KSNCW  PJV*\OL]V*H EFN \]E IKM\!KMPJDF`Cb V*NsYZH  ^CVXNCI*V[YZ^CV PJV*HJ`C\OYQH6^<EF\]WL]NcYQ^CVfb[EFPJV DFV*N<V*PZKS\ IKMHJV ESRK HQb E EMYZ^cYWGUE[WCLOb[VXNCHQLOEFN KM\ b KSNCLORdEF\OW T /3HeKMN[KMjCjC\OL]I*KSYZLOEFN  LON.0^ KSj<YZVXP 5 G0V3I*EFNCHJL]WCVXPnYQ^CV9RdEF\]\OEG9LONCD DFVXEFb[ViYZPJL]IKS\ jCPQEFa<\]V*bT L V*N K[HQb EhEMYQ^ b[KMNCL RdEF\]W KMNCW WY G0EcHJb[E EMYZ^ VXIXYZEMP  V*\OWCH KSNCW EMN  GUV G0KMNsYYZEHAYZVXV*P K j EFLON Y   YQE Kj EFL]NsY  LON b L]N<L]b`Cb YZLOb[V `<HQL]N<D EFN<\ ELON YQV*DFPQKM\I*`<P VXHEMRUYZ^CV YWG0E V*IiYZEFP  VX\]WCH KMNCW [T 8 V*N LORnYZ^CVXPQV HV .hLOHJYZHfHJ`CI ^ KYZPQK qJV*IiYZEFVP EDFEFLONCDRdPQEMb  YZE  LOY b[CK E ^CKMjCj V*N YZ^CKSY

(106) YQ^CVb L]NCLOb`Cb YQL]b V[LOH

(107) EFa<YZKML]N<V*W&EMNC\ E €a E K YQPZK qJVXIXYQEFFP E / G9^CEFHQV V*\OEhIXLOWY E /* M  S a V*\OEFNCDFHnYZE YZ^CVHJV*DFb V*Ns@Y qJEFL]NCLONCD M+/*M  SFSUKMN<W \M /[M  S S M NCEMY0a VXL]NCD

(108) KMNLV .hYQPQVXb`Cb EMR LOY SiT7_^ `CH GUV  PQHAY>IXEFN HV .hL R EcYZ^CV HQViY3ESR VX\]E I*L YZL]VXH_\]ViYQYZLONCD \M  S   M  S  M5o  S NM  S Y u o a VYZ^<V HQVXY9ESR"KSWCb[LOHQHJL]aC\OV VX\]E I*L YZL]VXHeKSY6KDMV*NCVXPQL]I>j EFLONsY  ESR Tn4 R GUV  .YQ^CV j EML]NsY  KMNCWc\OVXY KMVP E[EMN GUV>WCV  NCV6YZ^CV6Rd`CNCIXYQL]EFN | M XS!KMHnYZ^CV6b[LONCL]b

(109) `Cb YQL]b V9YQE

(110) PJVKMI ^ YQ^CV6j EFLONsY RdPQEMb LOHeWY G0E[WCL]b V*NCHJL]EFNCKM\'KMN<W  L]H9K HAY KMaC\OVfj EFLONsY  YQ^ KSY6L]H9u  M  S  YQ^CL]H_LOH_jCPQVXI*LOHQV*\ E  T  ^<V*N YQ^CV b L]NCLOb`CbYZLOb[V jCPQEFa<\]V*b RdEFP KcFH E HAYZV*b ESRnWY E j dV MAo SMdHQViYQYZLONCD  4U   1 U SiT &V KSPQVfL]NsYZVXPQVXHJYZVXW LONL]N VXHJYZLODsKSYQL]NCDYQ^CVfDFV*NCVXPQLOI j<PQEFj V*PAYZL]VXH9EMR YQ^CV Rd`CNCIiYZL]EMN | T 8 VXN LOR!YQ^CV HQj KMIXV[ESR_KM\O\KMWCb L]HJHQLOaC\]V

(111) YQPZK qJVXIXYQEFPQLOV*HfL]H LON  NCL YZV WCLOb[VXNCHQLOEFN KM\  GUNV ` NCE G YQ^ KSY YQ^ KSY YZ^CV YZLOb[V EMj<YZLOb KM\ YZPZK qJV*IXYQEFPQLOV*H KMPJV[LONCWCV*VXW  N<LOYZV I*EMNCIKSYQV*N K YZL]EMNCHfEMR YZPZK qJV*IXYQEFPQLOV*H  YQPZK qJVXIXYQEFPQLOV*H KMNCW HQLONCDF`C\]KMP>YZPQK qJV*IiYZEFPJL]VXH*T EFPJV*E VXP  LOYfL]H ` NCE G9N YZ^ KSY KRd`CNCIiYZLOEFNYZ^ KSY LOHYZ^CV b L]N<L]b`Cb EMR!K  N<LOYZV N `Cba V*P>ESR!HQb EhEMYQ^ Rd`CN<IXYZLOEFNCH3L]N DMV*NCVXPQL]I

(112) j EFHJLOYQL]EFNL]H3K EFPJHQV

(113) Rd`<NCIXYQL]EFN LON YQEFj EM\]EFDFLOIKM\ HQV*N<HQV  t  tSp  T  VDFL V K j EMHQLOYQL V

(114) KMN<FH GUV*P>YQE YZ^C V  `CV*HAYZL]EMNEMR@T 4 T />PQN<EF\]W Y0L]H YQ^CV Rd`CNCIiYZL]EMN | DFVXNCV*PJL]I*KM\]\ EK EFPJHQV Rd`CNCIiYZL]EMN LONYZEFj EF\]EMDFL]I*KM\ HJV*NCHJV 7_^CL]H PJV*HJ`C\OY L]H LONYZ^CV HQKMb VHQjCLOPQL YEMR  t  tSp   a VXL]NCDcN<E G YQ^CV b[LONCL]b L *KSYZLOEFNY K `MV*N E VXPfK  NCL YZVW<L]b V*NCHJL]EFN KS\ HJVXYfEMR Rd`<NCIXYQL]EFNCHXT4 N EFPJWCV*P

(115) YQEjCPJE VcEF`CP PQV*HJ`C\OY  G0VKMN KM\ E XV YZ^<V L]N<L]b`Cb 7_LOb[V

(116) PQEFNsYZ\H M aCPJL]V " E. 7

(117) RSfYQ^ KSY

(118) KMPQV YZ^CV[\]V V*\nHQViYZH

(119) ESReYZ^CV[b[LONCL]b

(120) `Cb YQL]b V Rd`CN<IXYZLOEFN | T7_^CVjCPJEFj V*PJYQL]VXH EMR0YZ^CV. 7

(121) "H6KMPQV DFL VXN LONc7_^CV*EFPJV*b X t 5 TnB N<V IKMNWCV CNCV YZ^CVfHV . YQPQV*b[KM\ RdPJEFNsY9L]NKMNEFa L]EF`<~H GeCK EFTn4 Y LOH!L]NsYZVXPQV*HAYZLONCD YQE N<EMYZLOI*V_YZ^ K YnYQ^CV6HV . YZPJV*b[KM\ RdPQEFNsYUKSYnHQEFb V9HQLONCDF`C\]KMPj EML]NsYZH!EMR YZ^CV6EFj<YQL]b[KM\<EFN<V  DMV*NCVXPQL]I*KM\]\ E W<V VX\]EFj<H3EFN<\ EHAY KMN<W KMPQWHJL]NCDF`<\kKMPJLOYZLOV*H0KMH_WY G0E WCL]b V*N<HQL]EMN KM\ G0K VfRdPQEFNsY  HQV*V  I   T. EFPQVXE V*P YZ^CVXHQV HQLONCDF`C\]KMPQL YZLOV*H9I*EFPJPQVXHQj EFNCW HV .<KMIiYZ\ EYZEcj<PQr E qJVXIXYZLOEFNHJL]NCDF`<\kKMPJLOYZLOV*H  ESRYZ^CV HJVXY EMR  \OLOR YQV*WYZPQK qJV*IiYZEFPJL]VXH  EMR I*`CHJj WY E j V W<L]HQIX`CHQHJV*WLON.0^ KMj<YQV*P>thT

(122). 

(123).

(124). . . . . 

(125).

(126). . . . . .  .  . . . . !

(127). 

(128). " #. $. %

(129). . &. ('. *). . ('. +). ,". -. /.. ,". 5. 0". .

(130) _7 ^CVDFVXNCV*PJL]I j<PQEFj V*PAYZL]VXH EMR>YZ^CV b[LONCL]b`<b YZLOb[VcRdPQEMN Y EFN j EFL]NsYQH[PJVKMI ^CVXW a)E KMaCN<EFPQb[KM\ VH. YZPJV*b[KM\]H M YZ^ K Y L]H'YZPQKqJV*IiYZEFPJL]VXH G9LOYZ^ KMNCLOHQ^CLONCD >KSb[LO\OYZEMNCLkKMN!S KMPJVHJYQ`CWCL]VXW'T GpEfK_\]E IKM\MKMN KM\ E HQL]H G0V HQ^<EG YZ^ KSY6K Y6YQ^CV*HJVfj EFLONsYZH_YZ^CVfb L]NCLOb`Cb YZLOb[VRdPJEFNsY9L]H6KM\ GeKCE H_Y KMNCDMV*NsY9YZE YZ^CV KMaCN<EFPQb[KM\ HV . YZPJV*b[KM\]HXT7_^CL]H_R KMIiY GeKSH3PJV*b[KMP `SV*W KM\]HJE LON   KMNCU WL]N  Co RdEFP9K  ` KMWCPQKSYZLOI I*EFHAYT

(131) "L]N KS\]\ E G0V[HJYQ`CW E YZ^CV IKSHQV L]N G9^CL]I ^  l KSNCW  L]HfPQVXjC\kKSI*V*W a€E&KHQb E EMYZ^ YWG0E WCL   b[VXNCHQLOEFN KM\ b[KMNCL RdEF\]TW G9LOYZ^[a EM`CNCW KMVP EFT4 N YZ^CLOH!IKMHJV  `CNCWCVXPeKf\]E IKM\CIXEFNsYZPJEF\]\]KMaCL]\OLOWY E KMHJHQ`Cb j<YZLOEFN  G0VIKSN KM\OHQE jCPQE VYZ^<V HJV*b L]I*EMNCIK LOWY E EMR3YZ^CVb L]NCLOb`Cb YZL]b VRd`CNCIiYZLOEFN'T 7_^CL]H jCPQEMj VXPJYWE L]H YWE jCL]I*KM\]\ EV*N<I*EF`CNsYQV*PQVXWL]NI*KM\]IX`C\]`CH_ESR KMPJLkKSYQL]EFNcjCPJEFaC\OV*b H_EFP9EFj<YZLOb KS\ I*EMN YQPQEF\ j<PQEFaC\OV*b ~H G9LOYQ^ HQViY EMR VX\]E I*L YZL]VXH NM  S ESReYZ^CV HZKMb V WCLOb[VXNCHQLOEFN&ESR_YZ^CV[HJY K YZVHJj KMI*V  HQVXV  t o eKSNCW PQViRdV*PJV*NCIXV*H YZ^CVXPQVXL]N'T M 16EMYZLOI*VYQ^ KSY  `CNCWCVXP6DMV*NCVXPQL]IfIXEFNCWCL YZL]EMNCH  HJV*b L]IXEFNCIK LOWY E R KML]\ G9LOYZ^  K j EFLONsYjT S 4 N.0^CKMj<YZVXP k YQ^CV*PJV3LOH!K HQL]b jC\OV_KMjCjC\OL]I*KSYZLOEFN' T &V9HAYZ`CW EHQEFb V9I*EFNsYZPJEF\]\OV*W W E N KSb[LOI*HnKMjCj VKMPJL]NCD L]N  KMDFPQKMNCDFL]KMNcFH E HJYQV*b H3ESR"b[KSYZ^<V*b[KSYZLOIKM\ jC€^ E HQL]IXH*Tn4 N jCKMPJYQL]I*`<\kKMP GUVfHJYQ`CW EcYZ^<VfRdEM\]\]E G9LONCD Y. T u <&B:  X +7:Q35?E<Q$4z"AJ;$ #'Q"%+1:;+7}+s') 3  ?R: l  M Xt S 

(132) M   S  U

(133)    M+l S 

(134) M u  €u S  u "mJ #"<Q$!30@4W?,M#$43

(135) "mJS$zq+s"A?A+7:I+7&‚ K/+1?C:S" '):;<#$4."mJS$€^@7"A?A+7: +1&*r&2+10@=$ <#$%KU$4:;<^?R:# +7: "mJS$ KU+735?2"m?A+1:z:;<€y7$!(A+s@4?p" +7&j"AJ;$jK/+1?C:S"UdC&2+7 ?R:Q3H"2:;@B$ <['s$*"%+YYri :S$7"m?E@ ƒ;$!(A<z+7P"mJ;$*y1?C36@=+73W?p" +7&Z  ')?A<)l7V Z$7"L')3F=KQK;( >$ j",$45: ( &2+70@B$=D "AJ[#"YoP$F3='HKQKU+730$ MQ+^'):;<Q$B<vdA$1V  V g0l 

(136). .  . % 

(137) M    S  . X +7:S"m6+7(C(R?C:#>"AJ;$f$c",$4W:[(S&2+70@B$=DjoP$ oZ:S"*",+96$0^@xJqK/+1?C:S" M ]  ]HS +7&/"AJ;$@=+7:QƒN[')4N"m?A+1: 3pKc^@=$BDj& 6+7 "AJ;$F0$!3H"/3H"2#"%$ M u  u€S D ?C:q>?R:Q?C ') "m?C}$7V 4 Y9YZ`CPJNCH3EM`<Y9YZ^ KSY9YQ^CVfFH E NsYZ^CVXHQL]H3WCV*HJI*PJL]aCLONCD YQ^CV HQEF\O`<YZLOEFNCHeYZE YZ^<L]H_jCPJEFaC\]VXb b[KEa V I*\]KMHQHJL  VXW KMHQHJL]DFN<L]NCDKMNEMPQWCVXPQV*W I*EM`CjC\]V ESRUVX\]VXb[VXN YQH EMRnYZ^CV HJVXY %2   T /3jCjC\]LOIKSYQL]EFN<H>YZEYQ^CV 2`  N KMNCW@nKMNWCV*P6= EF\ V  ` KSYQL]EFN<H3KSPQVfDFL V*N'T 4 N .0^ KMjhYZV*P mGUV WCV*KMR\ G9LOYQ^ K W<L V*PQVXNsYjCPJEFaC\]VXb L]N G9^CL]I ^ G0V[`CHQV[HQEFb V[ESReYZ^CV YZVXI ^CNCL  `CVXH WCV V*\OEFj VXWL]N YQ^CVjCPJV L]EM`CHf.0^ KMjhYZV*PJH*T  VHJYQ`CW EYZ^CV

(138) HJY KSaCL]\OLOWY EEMRnK a<L]WCLOb[VXNCHQLOEFN KM\ VH G9LOYZI ^<V*W HFE HJYQV*b H6RdEMP9KMPQaCL YZPQKMFP E FH G9LOYQI ^CL]N<D Rd`<NCIXYQL]EFNCHXT pG E KVH G9LOYQI ^CV*W FH E HJYQV*b G0V b[V*KMN KR KMb L]\ EEMReIXEFNsYZL]N `CEM`CH K YQL]b V W E N KMb L]I*KM\FH E HJYQV*b H

(139) KSNCW KPQ`C\OV YZ^ K Y WCVXYQV*PQb L]N<V*H KSY KM€N E YZL]b V G9^CLOI ^ ;W EhNCKMb[LOIKM\UFH E HJYQV*b LOHPQVXHQj EFNCHQLOaC\]VcESR6YQ^CVcYZLOb[V V EF\]`<YQL]EFN T EFPQVjCPJV*I*LOHQVX\ E \OVXY 

(140)  Y !  a V K M CNCLOYQVcEFP L]N  N<LOYZCV S

(141) HQViY[ESRHQ` [IXL]VXN YQ\ E PQVXDF`C\kKSP V*IiYZEFP  VX\]WCH9EFN K b KSNCLORdEF\OW  KMN<W IXEFNCHQLOWCV*P_YQ^CV R KMb[LO\ E EMR W E N KMb L]I*KM\'FH E HAYZV*b "H Y . .

(142). . "

(143) # M . S  k. $

(144). M#I€S.

(145) 7_^<VPQ`C\OV[LOH DML VXN KMHJHQLODFNCL]N<DYQ^CV HJEIKM\O\]VXW HVG9LOYZI ^<L]NCD Rd`<NCIXYQL]EFN *M  S Y  u     T 6V*PQVNG0V IXEFNCHJL]WCVXP>YZ^CV HJLOYQ` KSYZLOEFN LOH G9^CLOI ^YZ^CVHVG9LOYQI ^CL]NCDRd`<NCIXYQL]EFNI*KMNCNCESY a V

(146) jCPQVXWCL]IiYZV*W KjCPJL]EFPJL  LOY>L]H DML VXN RdPQEFb)EF`<YQHQLOWCVcKMNCW PJV*jCPJV*HQVXNsYZH HQEFb VjC^<V*NCEFb V*NCK MdVMT DCT KWCL]HAYZ`CPJa KMNCIXVS YQ^ KSY L YL]H

(147) NCEMY j EFHJHQL]a<\]VYZE IXEFNsYZPQEM\ EFP_L]NCIX\]`CW<V L]NcYZ^CVfW E N KSb[LOIKM\'HVE HJYZVXbb[E WCVX\ T :h`<jCj EMHQV>N<E G YQ^ KSYUKM\O\CYZ^CV

(148)  ^CK VKfDFL V*N[jCPQEFj V*PAYWE RdEFP!V V*PFE  T/ YWE jCL]I*KM\ jCPQEMaC\]VXb LOH YQEHJYQ`CW E `CNCW<V*P G9^CLOI ^ I*EMNCWCLOYQL]EFN<H YQ^CL]H jCPQEMj VXPJWY E ^CEF\OWCH RdEFPfYZ^<V FH E HAYZV*b M#IXS RdEFP

(149) KMPQa<LOYZPQKMFP E HVG9LOYQI ^CL]NCD Rd`CNCIiYZL]EMNCH*T

(150) EFPnK WCL]HJI*`CHJHQL]EMNEMR KMPJL]EF`<HnLOHQHJ`CV*HePJV*\]KSYZVXW YQE

(151) FH G9L YZI ^CVXWFH E HAYZV*b GUV>PQViRdV*P YQ^CVfPQV*KMWCV*P_YQE  t  T 4 N  o  t  YQ^CVfIKMHJV ESRFH G9L YZI ^CVXW \OL]NCV*KMPeVH EhHAYZVXb[>H GeKSH3IXEFNCHQLOWCV*PJV*W Y    #   . . l .  . #. l . . M )S. . . SK NCW YQ^CV6jCPQEFa<\]V*b$EMR YQ^CV6KMHFE b j<YZEMYQL]I9HJYZKMaCLO\]LOYWE EMR YZ^CV6EFPQLODFL]NRdEMP!KMPQaCL YZPQKMPFE HVG9LOYQI ^CL]NCDfRd`CNCIiYZLOEFNCH G0KMHLON V*HAYZLODsKSYZVXW'T .0\OVKMPJ\ E G0V NCV*VXW YQ^CVKSHFE b[jhYZEMYQL]I HAY KMa<L]\]L YWE EMR V*KMI ^ HQL]N<DF\]VHQ`Ca)K HFE HJYQV*b    #    LON EMPQWCVXP YQE ^CK V YQ^CV KSHFE b[jhYZEMYQL]IcHJYZKMaCLO\]LOYWE&EMRhM )S

(152) RdEFP VKMI ^ HFG9L YZI ^CLONCD Rd`<NCIXYQL]EFN MdL T VMT YZ^<V V*L]DMV*N KM\]`CVXHEMRnVKSI ^ b[KSYQPQL .#  b

(153) `CHJY ^CK V HJYZPJL]IiYZ\ ENCVXDsKSYQL V PJVKM\ j KMPAYLSiTf7_^CLOH G9L]\O\ a V KMHQHJ`Cb V*W YQE a V YZ^CV I*KMHQVST 4 N  o  t   L YfL]H HQ^<EG9N YZ^ K Y YQ^CV HJYQPQ`CIiYZ`CPJV EMRnYZ^CV  L]V KM\ODFV*a<PZK DMV*NCVXPZKSYQV*W €a EYQ^CVfb K YZPQLOI*VXH #  Y. Y     LOH>IXPQ`CIXLkKM\ RdEFP9YZ^CVHAY KMa<L]\]L YWEEMRYQ^CVHFE HAYZV*b M )STM L T VST3YZ^<V

(154) L]NsYQV*PQPJV*\]KSYZLOEFN a VXYWGUV*VXNYZ^CVHVE HJYZVXb[H SiT 7_^<V

(155) b[KML]NPQVXHQ`C\ Y>EMR  t  L]H9YZ^CVfRdEF\]\OEG9L]NCDCTU4 R ' L]H6K[HJEF\ KMaC\OV  LOV KM\]DFVXaCPZK YQ^CV*N YZ^CV HFG9L YZI ^CVXW HVE HJYZVXb M )S0LOH9KMHFE b j<YZEMYQL]I*KM\]\ E[HAY KMa<\]V RdEFP_VKSI ^ HV9G LOYZI ^<L]NCD Rd`CNCIiYZLOEFN) ,M  S Y  u     T 4 N  o0K DFVXNCV*PQKM\]L KSYQL]EFN G0KMH

(156) DFL VXN'T  ViY '   a V[YQ^CV  V LnWCV*IXEFb j EFHJLOYQL]EFN EMR ' L]N L YZHfPZKSWCL]I*KM\>M L T VST YQ^CV b K.<LOb KS\"HQEM\ KMaC\OV L]WCV*KM\EMR ' S KMNCW&KHJV*b L K HJL]b jC\]V HQ`CaBK KM\]DFVXaCPZK G9^<V*PQV YQ^CV HVE ba EM\ L]NCWCLOIKSYQV*HfYZ^CV[HQVXb[LOWCL]PJV*IXY HQ`<b T 7_^CVDFVXNCV*PQKM\]L KSYQL]EFN L]H YZ^CV RdEF\]\OE9G L]NCDCTc4 R L]H KI*EFb j KMIiY  LOV KM\ODFV*a<PZKYQ^CV*N YZ^CV[HFE HJYQV*b M ) S L]H KMHFE b j<YZESYZL]I*KM\]\ E HAY KMaC\OV[RdEFPfV V*PVE HV9G LOYZI ^<L]NCD Rd`<NCIXYQL]EFN ,M jS Y  u     T/>N€E)eG KCE YZ^<V6IXEFN VXPQHQV>EMR YQ^CL]H!PJV*HQ`<\OYnL]HNCESYnYQPQ`CV9LON[DFVXNCV*PQKM\PY LOR L]H N<EFN I*EFb j KMIiY YQ^CVeHFE HAYZV*b$IKMN a VeHJYZKMaC\]V0EFP`CNCHAY KMa<\]VMT"4 R LOHNCEFN IXEFb j KMIXY"YZ^CVXN L YIXEFNsY KMLONCHKMH K HJ`CaBhK KM\ODFV*a<PZK

(157)  FM t  lveS KSNCW YQ^ KMN ` HYZE YQ^CL]HR KMIiYYZ^CV9KS`<YZ^CEMPQHR0G VXPQV6KMaC\OVeYZEfPQVXWC`CIXV9YQ^CV9jCPQEMaC\]VXb ESRYZ^CV KSHFE b[jhYZEMYQL]I HJY KSaCL]\OLOYWE EMRYQ^CVHFE HAYZV*b M )STM+9G ^CVXN L]H3NCEMYIXEFb j KMIXY 9S YQE YZ^CV

(158) jCPQEFa<\]V*b EMR YQ^CV KMHFE b j<YZEMYQL]IfHJYZKMaCLO\]LOYWE EMRKSNKM`;h. LO\]LkKSPF[E aCL]WCLOb[VXNCHQLOEFN KM\ HFE HJYQV*bT &V PQViRdV*P9YZ^CV PQV*KMWCVXP6YQE  o RdEMP>WCViY KMLO\]H*T EFP6YQ^CL]H>PQVKSHQEFN YQ^CVaCLOWCL]b V*N<HQL]EMN KM\ jCPJEFaC\]VXb KSHQHQ`<b[VXH K j KMPAYZLOI*`C\]KMP3LONsYZV*PJV*HAYCY>0G V DML V YQ^CVfI*EFb jC\]ViYZV WCVXHQIXPQL]jhYZL]EMNESR YQ^ KSY9IKSHQVfRdEFP9K HQL]N<DF\]VLONCjC`<Y6HVhE HAYZVXb T EMPQVfjCPQVXI*LOHQV*\ E\UG V HAYZ`CW cE YQ^CVfHJYZKMaCL]\OLOYW[E EMR YZ^CVfEFPJL]DFLON RdEFPeYZ^<V HV9G LOYQI ^CV*W HFE HJYQV*b%Y M#5XS   M  S  ,M  S #  M  S  AM o  ,M  SFS $  M  S  9G ^<V*PQV # KMNCW $ U KSPQV YWUG E t n t PJVKM\6b[KSYZPJL]I*VXHN9G L YZ^ VXL]DFVXN KM\O`CV*H ^ K LONCD HAYZPQLOIXYQ\ E NCVXDsKSYZL V PJVKM\ j KMPAY   l KMNCW ,M  S Y  u      u  o L]H3KMNKSPQaCL YZPZKSPFEb VKMHJ`CPZKMa<\]V HFG9LOYQI ^CL]N<D Rd`CNCIiYZL]EMN'T EFPQVXE V*P UG VHJ`CjCj EFHQVcYQ^ KSY KSY\]VKSHJY #EFP$ ^CKMH I*EFb jC\OVH&. V*L]DMV*N KM\]`CVXH KMNCW YQ^ KSYYQ^CV

(159) E KSPQV '. . # . . . . . . +. +. . . . .

(160). . . .

(161) WCLkKSDFEFN KM\OL *KMaC\]VST &V  NCWcK NCV*IXV*HJHZKMPVEKMN<WHQ`  IXL]V*NsY0I*EFNCW<LOYZLOEFN `CNCWCVXPpG9^CLOI ^ YZ^<V>EFPJL]DFLON EMR'YZ^<V HFE HJYQV*b MP5XS9L]H3KMFH E b j<YZEMYQL]I*KM\]\ EcHJYZKMaC\]V RdEFP>V*KMI ^Rd`CNCIiYZLOEFN ,M jSiTB`CP>PJV*HQ`<\OYLOH3EMa<Y KMLONCV*WdG9LOYZ^K WCL]PJV*IiY0b VXYQ^CEh3W G9LOYQ^CEF`<Y0\]E EX` L]NCD RdEFPUK IXEFb[b EFN  EFKMjC`CN<E Rd`CNCIiYZLOEFN  aC`<Y_KSN KM\ E XL]NCDfYZ^CV3\]E I*`CH L]N G9^CLOI ^ YQ^CV WY G0E VXIXYQEFP CV*\]W<HfKMPQV IXEF\]\OL]NCV*KMP  HJL]b L]\]KMPQ\ EYZE'G9^ KSY WCEMNCV L]N .0^ KMjhYZV*P tcKMNCWI<T &Vb[K `MVKM\OHQE `CHQVEMR>YQ^CVI*EFNCIXV*j<Y[EMR3RdV*V*W<a KMI ` T

(162) EFP YZ^CVWCL  IX`C\OYWE ESR  NCW<L]NCD K IXEFb b[EFN b GUVfPQViRdV*P_YZ^CVfPJVKMWCVXP_YZE  t I T  EsKMjC`<NCE Rd`CNCIXYQL]EFNcRdEFPeYQ^CL]H9jCPJEFaC\OV*0 13EMYQL]I*VeYQ^ KSYL vR G0V_HJVXY  M  S  M #   $  S Ft KMN<W

(163) NM  S  M #   $  S Ft YQ^CV*N YZ^<V_HFG9LOYQI ^CL]N<D FH E HJYQV*b MP5S0^ KMH9HV .<KMIiYZ\ E YZ^CV RdEFPJb MAo SpG9LOYZ^  t  o KMNC)W

(164) M €u S  u<T ~7 G0EI*KMHQVXHeKMPJV6KMN KM\ E XV*W[HQV*jCKMPZKSYQV*\ EFT7_^CV  PQHAY0LO3N G9^<L]I ^ a EMYQ^ YQ^CV3b[KSYQPQL]IXV*H!^ K V3I*EFb jC\OHV . V*LODFV*N KM\]`<V*9H M L]N YZ^CV6RdEF\]\OE G9L]NCD }h} I*KMHQCV SUKMN<W[YZ^<V>HQVXI*EFN<WcL]hN G9^CL]I ^EMNCV>EMR YZ^CV9WY G0E

(165) b KSYQPQLOI*V*H ^ KMHfPQV*KM\KMN<W YQ^CV EMYZ^<V*P ^ KMHfIXEFb[j<\]HV . V*LODFV*N KM\O`CV*3H MdL]NYZ^CVRdEM\]\]E G9LONCD } IKSHQV S T 7_^CV IKMHJV L]N G9^CL]I ^ a EMYQ^ b K YZPQLOI*VXH ^ K VPQV*KM\!V*L]DMV*N KM\]`CVXH

(166) LOH HJL]b L]\kKSPfKMNCW L Y LOH YQPQVK YZV*W&L]N  oqu  T7_^CV*PJV KMPQV EFNC\ E YZ^CPJV*V PJV*\OV KMNsYj KSPZKMb VXYQV*PQ

(167) H YEFNCV WCV*j V*NCW<HEFN YQ^CV VXL]DFVXN KM\O`CV*H EMR #  EFNCV EFN YZ^<V V*LODFV*N KM\]`<V*H>ESR $  KMNCW YQ^CV

(168) \]KMHJY3I*EFNsYZKML]NCH6YZ^CV L]NsYZVXPQPJV*\kK YZL]EMN a VXWY GUV*VXN YQ^CV WY GUEVH EhHAYZVXb[HfKMN<WLOY L]HeYQ^CVfI*PQEMHQH6PZKSYQL]E EMR YZ^CV RdEF`<P_V*L]DMV*N VXIXYZEMPQH6EMR # KMN<W $ L]NcYQ^CVfjCPQrE qJVXIXYQL V \]LONCV } o T

(169) "L .hV*W YZ^<V KM\O`CV EMRnYZ^CV I*PJEFHQH PZK YZL]\E GUV HJYZ`<W E YZ^CV KMVH Ehb j<YQEMYZLOI HJY KSaCL]\OLOWY E WCEFb[KML]N'T 4 N YZ^<V }h} IKSHQV_LOYL]H RdEMPQb V*W €a EEFN<VeEFP"WY GUEfEFj VXN `CN a EF`<NCWCV*W IXEFN HV . PJV*DFLOEFNCHXT  ^CLO\]V0LON

(170) YZ^<V } IKMHJV L Y_L]H9KSN EFj V*N`CN a EF`CNCW<V*W PJV*DFLOEFNNCEMY6KM\ GeCK E H6I*EFN LV . T . . . . . . . . . . .

(171)       

(172)   ,  4 N YZ^<L]H!.0^ KSj<YZVXP GUV6PQV*I*KM\]\ YZ^CV9NCESY KSYQL]EFNCH"EMR  o   I<o  IFt KMNCW GUV3DML VeYQ^CV_a KMHJL]I_WCV NCL YZL]EMN `CHQVXW LONKM\]\ .0^CKMj<YZVXPQH>t  I  5  k<T &V PQViRdV*P_YZE YQ^CVfjCPQEFa<\]V*b EMR"HAY KMa<L]\]L *LONCDL]Nb L]NCLOb`Cb YZLOb[VYQE YZ^CV EMPQL]DML]NYZ^<V IXEFNsYZPJEF\'HFE HAYZV*b%Y U o MAoFT oS     M  S

(173) M  S   l . G9^<V*PQV GUV

(174) KMHJHQ`Cb V  M €u S  uhT L V*N KHJVXY # GUVcL]N<WCL]I*KSYZV[)a E"M # S L YZH

(175) I*KMPQW<L]N KM\OLOWY EMT

(176) EFP KM€N E Rd`CNCIiYZL]EMN

(177) Y #  $  #  $ HJVXYQH  YQ^CV WCEFb[KML]NL]H9L]N<WCL]I*KSYZVXW €a E M

(178) S T_4 R LOH3K YZEFj EF\OEFDFL]I*KM\ HJj KMIXV KMNCW K HJ`CaCHJVXY EMR YQ^CV*N GUV[LONCWCL]I*KSYZV €a E Q  )M S>YZ^<V I*\]EMHQ`CPJV ESR L]N T/ HQ`Ca<HQVXY # EMR L]HHQKML]WYQEca V DMV*NCVXPQL]I LOR"LOY6I*EFNsYZKML]NCH>KMN EMj VXNKMNCW WCV*NCHJVHQViYT6/>N KS\]EFDFEM`CHQ\ EK[jCPJEFj V*PJWY E L]H6HZKSL]W DMV*NCVXPQL]I LOR YQ^CV HQVXY

(179) EMRej EFLON YQHfHZKSYQL]HJR E LONCD LOH DMV*NCVXPQL]IST4 R L]H K b[KMNCL RdEF\]WYQ^CV* N  M SfL]NCW<L]IK YZV*HfL YZH W<L]b V*NCHJL]EFN'T  . !. .

(180).

(181). -

(182). . . ,

(183).

(184). $'&€(* , + !#"%$'&)(*"%&+"-,%/.0&214365708:9';<   ; =!;)&>./14?A@B14CD0CB&A"E9%?F;)&G@*"%3H&;I"%8D9J03H;),4"%&;),%/ 1K=L"%CB$143M9J03N&(*"%&O"%3P'Q014RSCT9JU9V14C&(B>WX(B148<O@T8:"%CD#Y EFP>V VXPFE IXEF`CjC\OV EMR!  V*IiYZEFP VX\]WCHNM  

(185) TS UG V I*EFNCHJL]WCVXP YZ^CV b L]NCLOb`CbYZLOb[V

(186) HJY KSaCL]\OL K YZL]EMN j<PQEFaC\OV*b YQEYQ^CV EFPQLODFL]NRdEFP YQ^CV I*EFNsYZPJEF\!HFE HJYQV*b AM oMTOoS T ?9V V*PJHQL]N<D YZLOb[VUG V IKMN I*EFNCHJL]WCVXP YZ^CV V `CL KM\OV*NsY0j<PQEFaC\OV*b ESR'PQV*KMI ^CLONCD

(187) V V*PVE j EFLONsYUESR YZ^<V3jC\]KMNCV6L]N b[LONCL]b

(188) `Cb YQL]b VeRdPQEFb YQ^CV6EFPQLODFL]N'T L V*NcK b[V*KMHQ`CPQKMaC\OV9Rd`<NCIXYQL]EFN aY [ Z P\   o U o K YQPZKJq VXIXYQEFPFE EMR 5M oFT o!S IXEFPQPJV*HJj EFN<WCL]NCD YZE. L]H9KMNKMa<HQEF\O`<YZVX\ E IXEFNsYZLON `<EF`CH9b KSj\/ Y ]Z /\  l HJ`CI ^ YQ^ KSY /* M  S   M /[M  S S  ,M  S

(189) NM+/*M  S S RdEMPfKM\]b EFHJYfV VXPFE   [ Z P\  T :hL]NCIXV YZ^CV HFE HJYQV*b LOH KS`<YZEFN<EFb[EM`CH G0V IKSU N&KM\ GeKCE H KMHQHJ`Cb V YQ^ KSY ^4 M / S   u PZ  RdEMPHQEFb V Z  'l T U / YQPZKJq VXIXYZEMPFE /gY  u /Z 

(190)  l LOH dM YQL]b V[S EMj<YZLOb KM\3LOR RdEMPV V*PFE&YZPZKqJV*IXYQEFPFE/  Y  u /\   l G9LOYZ^ /*M Z S  /  M \ STGUVc^ K V Z \ T / YQPZKqJVXIXYQEFPFE/ IXEFPQPJV*HJj EFN<WCL]NCDcYQE KcIXEFNCHJYZKMNsY I*EFNsYZPJEF\!$ o LOH IKM\O\]VXW K M):#0@ T/ MG:#E!_ MG:N YZPZKJq V*IXYQEFPFE L]H K NCL YZV I*EFNCI*KSYZVXN KSYQL]EFN EMR_a KMN<DKMPJI*HKSNCW KYZL]b V 9G ^CV*PJV[YQ^CV IXEFNsYZPQEM\UI ^ KSNCDFV*H HQLODFN&LOH I*KM\]\OV*W

(191). . . . . . 3Bo/?p",@xJQ?C:#"A?C}$ T. p.

(192) _7 ^CVdGUV*\O\ ` NCEG9N = EFNsYZPFEFKMDFLON rK .hLOb'U `Cn b =U PQLONCI*n LOjC\]VL]N YZ^<L]H HQj V*I*L]KM\9U IKMHJV AH Y KSYQV*H[YQ^CVRdEF\  \]EG9L]N<DCT&2V NCVRdEFP

(193) V VXPFE M   S  l +M l S   o  o  G9^CV*PJVwM+l S  L]H YZC^ VcHJVXY EMR6PQEG VXIXYZEMPQH"Y. M    S . KMNCW Y. M S  

(194) M  S.   . M   S  b[Kr.    M  S  

(195) M  S Y  o  o   MAoMT tXS 4 R~/ Y  u /Z   l U L]H KwMdYZLOb[VCSEFj<YZLOb KS\"YZPQKqJV*IiYZEFPVE IXEFPQPJV*HJj EFN<WCL]NCDYZE KIXEFNsYZPQEM\ Y  u /Z     o  o  YQ^CV*U N YQ^CV*PJVVHh. L]HAY  :S+7:S"m5?2y1? (Lƒ;$!(A< +7&€@B+)y7$=@1"%+7W3~(A+1:# / YZ^CKSY LOHK Rd`<NCIXYQL]EFN  Y  u /Z  M+l S  NCV V*P KMNCL]HJ^CL]N<D KMNCWK I*EFN<HJY KSN Y  ] u HQ`<I ^ YZ^CKSYCY L S   M  S    M  S  M    ,M  S 

(196) TS"M /[M  S S LOL S M+/*M  S  M  S  ,M  S S   ]  uRdEFP9KS\]b EFHJY_V VXPFE   4 M /S L]L]L S M+/*M  S  M  S  ,M  S S   M+/*M  S  M  SFUS RdEFP9KM\]b EFHAY_V V*PFE    M+/iS T 4 NYZ^CLOH>IKSHQVUG VHZKCE YQ^ KSY3YZ^CVjCKML]P M+/  6S LOH>VH. YQPQV*b[KM\ T EFPJV*E VXP L R  ]  u[YQ^CV*N_UG V HZKCE YZ^ K Y M /   S L]HnKMNcKSaCNCEFPJb KM\ VL. YZPQVXb KS\ T"4 R/ LOH!EFj<YZLOb KS\ 0G V3HZKCE YZ^ KSYnYZ^<V>j KMLOP M+/  !S LOHnEMj<YZLOb KM\ T 13EMYQL]I*V3YZ^ KSYp9G LOYQ^YZ^CVW<V NCL YZLOEFN oFT tTUG V IKMN\9G PJLOYZV6YZ^CV>V ` KSYQL]EFNCHURdEFP M /   US LON[YQ^CV >KMb L]\ YZEFN<LkKMNcRdEFPJbdY    M  S    

(197)   M  S  3EUG V VXP  L]H_N<EMY6K HJb[E EMYQ^Rd`CNCIXYQL]EFN T $'&)(* + + 6  0&3M"%&I; 57.U"%&; 14C 1K= l U ;<" 8<1 .U"%8)8 $F5+CB;)&2-@*"%3H&;)&I; 14C  1K= l U ;)CB&21./14CBCD/.0&2U9 0? Q0U9E9JU9>0R Q#? "%CB; = 148:94     .U"%8)8<U9L0&3M"%& "  #"%&I;<=H$ ;)C -&)(BX= 148)8<14W ;)C EY  0& o  U    &(B0C  =

(198) Q  )M o S  U    &)(B0C 

(199) U ! Q  BM o S "%CT9  M UHS "  M o S Y AM oMTjI€S $'&)(* + + s  3P %RSU8:"%3 1/@T&I;)? "%8 0$4CB&(B/0;< = 143 #%$E&Y $(' ;<" ./148)8</.0&I; 14C 1K= &I3U" ) /.0&2143H+$ *U./14CB&I3P148 @*"%;)3P  M+/  S Y  l  #"%&I;<=H$4;)C^&(B+= 148)8<14W ;)C @T3/1/@B03H&I; /-, $E/Y . 143'0,%030$  l U @/ Y  u 0  l U 0&2/03P>&(BF143H1; %;)C&21  ;)C ?F;)CB;)?FRJ?&I;)?^#Y 2 Y = % / M  S = 143 14?^   4 M / S &)(B0C 4/ 3 ;<>&(B>3P/0&I3H; .0&; 14C &21  u   1K= / Y Y 6 (B03P  8 ;<0&)!" 0&3M"%&I; 57.U"%&; 14C 1K= l U 0RG./(-&(*"%& ,M  S  M 0 S ;<O0?^1 14&)(^14C U"J./(L0&I3M"%&RJ? Y 57 . . . . . . . . . . . ".

(200).

(201).

(202).

(203).

(204).

(205). oqu.

(206).

(207).

(208).

(209) a VYQ^CV HQViY SE ReKM\O\"IXEF`CjC\OV*H EMR  VXIXYZEMP CV*\]W<H M  

(210) S6HQ`CI ^ YZ^ KSY NM uXS  u<T

(211) PQEMb <N EG EFN'G0V V*N<WCE G G9L YZ^cYZ^<VYZ^CV  YZEMj EF\OEFDE  YZ^CKSY9L]HeYQ^CV YZEFj EF\]EMDE L]NCWC`<I*V*Wa€EcYZ^CV N<EFPQb%Y  M  

(212) S   HJ`C j .   1  

(213)    U M 

(214) S    .  1  

(215)

(216) / WU M

(217)  S  Y  l U   o   o   o  t  o   U  2  u    o   U I   4 N  o   I<o   L Y GeKMH[jCPQE V*W YQ^ KSY YZ^CVXPQVHV .hL]HAYZH[K MdV*HJHQV*NsYQLkKM\O\ E `CN<L  `CV S PQVXDF`C\]KMP FH E NsYZ^CVXHQL]H RdEFP V VXFP E IXEF`CjC\OV EMR V*IiYZEFP CV*\]W<H

(218) L]N KMN EFj V*N W<V*NCHJVcHQ`CaCHJVXY ESR eT EFPJV*E VXP  YZ^<V I*EMN YQPQEF\ ,M  S LOHI*EMNCHJYZKMNsYZ\ E V  ` KS\>YZ E oEFP[YZE  oEFN V V*FP E WY G0E WCLOb[VXNCHQLOEFN KM\6HJYQPZKSYQ`CbT B N V*KMI ^ EFNCV W<L]b V*NCHJL]EFN KS\ HJYQPZKSYQ`Cb L Y9L]H_V  ` KS\'YZE  o  YZE  o EFPeYQE YZ^CV RdV*VXWCa KMI `IXEFNsYZPQEMP\ Y  pM S  M S MAoFT )S  M  S    pM  S 

(219) M  S  G9^<V*PQV Y pM  S 

(220) NM  S    

(221)  M  S 

(222) o M  S   

(223)  UM  S 

(224) UM  S   

(225)  o M  S  MAoFjT 5XS KSNCW   

(226) UL]HfYZ^CV  LOV[a<PZKMI `SVXY EMR  KMN<W

(227) T 7_^CV RdVXV*WCa KSI `  DML VXH

(228) YZ^<V HQ\OL]WCLONCDb[EMYQL]EFN EFN 4!o M €u SiT 4 R / I*EMPQPQVXHQj EFNCWCH YQEYZ^CVRdVXV*WCa KSI `  EMR MAoFT )S6YQ^CV*N / L]HI*KM\]\OV*W K 35?R:#[')(h9i0@ T

(229) EFP \]KSYZVXP_`CHQV GUV

(230) KS\]HQE WCV  NCV YZ^<VfRd`<NCIXYQL]EFN Y [M  S  NM  S )

(231) M  S   o M  S

(232) UrM  S  ,UM  S

(233) o M  S  MAoFJT k€S

(234) EFP9IXEFN V*N<L]V*N<I*T V GUV HQVXY   

(235) KMNCW   

(236) T  VXY / Y   o  U  l U a V K YZPQK qJV*IiYZEFVP E ESR M5oFTOo SiT  4 [R / I*EFPJPQVXHQj EFNCW YQE IXEFNCHAY KMNsYIXEFNsYZPJEF\  o M PJV*HJj'T  o SeL]N   o  U @G0V HZCK EYZ^ K Y /    

(237)  LOH>K K YQPZK qJVXIXYZEMFP EwM PJV*HQj T dK YZPQK qJV*IiYZEFVP E S6KMN<%W GUTV G9PJLOYZV /    

(238)   7 PQK qCM STMdPQV*HJj'~T /    

(239)   7 PQK qCM SFSiT N M5oFT )S S*GUV3HQK E YQ^ KSY /    

(240)   4 R /cIXEFPQPJV*HQj EFNCW[YZEfYZ^CV9I*EMN YQPQEF\  M /*M  S SLON   o  U ,MdWCV  N<V*WLOa L]H9"K ! K YQPZK qJVXIXYZEMFP EKMN<%W GUV G9PJLOYQV / #   

(241)   7 PZK qCM! S T. EFPQVXE V*PL * R / o Y   o  U   l U  /BU Y   U     l U M  o "  U "  HS6KMPJV WY GUEYZPQK qJV*IiYZEFPJL]VXH3EM>R MAoFT o S G9L YZ'^ / o M  UHS  /;UM  UHSpGUV HJVXCY Y M+/BU%$p/ o S"M  S~Y  //BUo MM  SUSURdRdEFEFPP     Uo  U    L V*N&KMN LV . YZPQVXb KS\!YQPZK qJVXIXYQEFFP E / GUV[W<V*NCEMYQV €a E'&RM /S YQ^CV[HJb KS\]\]VXHJYfLON YQV*DFVXPfHQ`CI ^&YQ^ KSY YZ^CVXPQV LV .hL]HJ>Y /4  7 PQK qCM SF27 PQK qCM S 27 PZK qCM! S    o     &RM / S0HQKSYZLOHJR E L]N<D Y /  /  )( $  *$p/ o  MAoFT XS oFo  VXY. ,. . . . . -. . . . #. . . #. . .

(242) _7 ^CVcRd`CNCIiYZL]EMN &[M+/S

(243) L]H I*KM\]\OV*W YQ^CVN `<ba VXP EMRKSPQI*H ESR / T 4 N  Iho_LOY G0KMH HQ^<EG9N YZ^ K Y `CNCWCVXP DFV*N<V*PQLOII*EFNCW<LOYZLOEFNCH V*KMI ^ VL.hYQPQVXb KM\_YQPZKqJVXIXYZEMPFE / I*KMN KS\ G0KE H a V'G9PJLOYQYQV*N L]N YZ^CVcRdEFPJb MAoMT XS G9LOYQ^ &RM+/S"  KSNCWcVKMI ^KMPJIL]HUa KMNCD EMPeHQLONCDF`C\]KMP*T 7_^CV*HJV DMV*NCVXPQL]I>I*EFNCW<LOYZLOEFNCH0KMPQV6YZ^CVRdEF\O\]EG  L]NCD Y. N 7_^<V V*IXYQEFPQH

(244) NM €u SeKMN<W   

(245)  M Xu SeKMPQV \OL]NCV*KMPQ\ E LONCWCV*j V*N<WCV*NsYT. 6

(246) EFP_V VXFP E  l U  u LOH9K PQV*DM`C\kKMP KM\O`CVRdEFP  KMNCW T. s 7_^<V HJVXY 4!o M €u S 4!o M €u S0L]H_\OEhI*KM\]\ E  NCLOYQVMT  VXY  Z &  a VfYZ^CV HQViY>EMRj EFLONsYZH   4!o M €u SeHQ`CI ^ YZ^ KSY M  S9EFP M  S_L]H9Y KMNCDMV*NsY3YQE 4!o M €u SiT 2V  N<V  Z &  L]NcYZ^<V HQKMb V G0CK E`CHQLONCD  PZK YZ^CVXP9YQ^ KMN "T. {  Z &  KSNCW  Z &  KMPQVf\OEhI*KM\]\ E CNCLOYQV HQVXYQH*T Y $ Z NY  M 4!o M €u S  4!o M Xu S S 2  Z &  2  Z & T  VX!. x $ Z [LOH_\]E IKM\O\ E  NCL YZVST 13EMYQL]IXVYZ^ KSY x L]H9K I*EMNCHQV  `<V*NCIXVEMR s KMN<W { T N  M  S  aM S"M  S   u KMNCW  M  S  aM "S

(247) M  S   u<T.  4 R  $ Z  

(248) NM  S  u YQ^CV* M  S   *M  S  u .  4 R   $ Z  

(249) M  S   u   M 4!o M €u S  4!o M €u SFS   Z &   HZCK E YZ^CVXN 3€M    S 3    u  M S   u  \M S   u  G9^<V*PQV YZK `MVXH KM\]`<V*H

(250) EMN 4!o M €u SfL]N&K NCV*LODF^ a EMPQ^CE EhWcESR  T. D 4 R  $ Z     Z &  YQ^CV*N [M  S/  u<T. - 4 R  $ Z  

(251) NM  S   u  M  S  u EMP 'M  S  u YZ^<V*N " M  S/  u<T 7_^CV DFV*NCVXPQLOI I*EFNCW<LOYZLOEFNCH     D KSPQV HQ^<E GUV*W L]NcYZ^CV RdEF\O\]E G9L]N< D  DF`<PQV Y . . . . . . ,. . . . . . . . . . . . . . ,. . . . . . . . /. . . . . ∆ =0 Β. 0. . . . . ∆ =0. ∆ =0. Α. F(x). . Β. X. ∆ =0 Α. X. ∆ =0. ∆Α(x)=0. Β. X X(x). Y G(x)=0 P6. P7. P8. "LODF`CPQV

(252) oFTOo  VXY &($u<T &V IKS\]\ 6$0^@xJ[#M(A$„30$1" G9LOYZ^<L]NYZLOb[V & YZ^<V HJVXY M &!S Y     l U Y'YQ^CV*PJV[VL.<LOHJYQH U '  u  &"KMNCWK YZPZKqJV*IXYQEFPFE%/ Y  u  &  l EMR M5oFT o S9HJ`CI ^YZ^ K Y9/*M u€S  u  /*M  S    T34 N YZ^<V RdEF\]\OEG9L]NCD GUV I*EFNCHJL]WCVXP9K DMV*NCVXPQL]I &LONYQ^CVfHQVXNCHQVfYZ^ K Y GUV KMHQHJ`Cb V YQ^CVfDFV*NCVXPQLOI I*EFNCW<LOYZLOEFN Y ot

(253).

(254) VXY%M /  hS Y  u  &  l U n l Ua VX\]EFNCDYZE T 7_^CV*N YZ^<V I*EMNCWCLOYQL]EFN *M &!S   M &vS 

(255) M /[M &vSFS  u LOb[j<\]L]VXHUYQ^CV RdEF\]\OEG9LONCD Y  &              M HQVXV

(256) 2V  NCL YZL]EMNm5XS   /[M &vS  4!o M €u SiT7_^CVfR KMIiY_YZ^ KSY9YQ^CL]H_LOH_DFV*NCVXPQLOIfRdEM\]\]EG9H0RdPJEFb 7_^<V*EFPJV*b oI KMNCWdI  ( u HJ`CI ^ YQ^ KSY /IXEFPQPJV*HQj EFNCWYZE YZ^<V HJL]NCDM`C\kKMP0I*EFNsYZPJEF\  L]N  /[M &vS  4!o M Xu S  &   &  KMNCW  M /*M &vSFS 4" o  E Q EFP $iQ IX`CP V*H MdHQVXV

(257) : V*IXYQL]EFN thT oFT oSiT  M+/*M &!S SeKMN<W M+/*M &!S S_KMPQV N<EMY9Y KMNCDMV*NsY9YZ3  VeI*KM\]\€/ Y  u    l U YQ^CVeLV .hYQPQVXb KM\ YZPQK qJV*IiYZEFPJL]V*H HV .hLOYQL]NCD6YZ^CV0EFPQLODFL]N G9LOYQ^ I*EFN<HJY KSN YI*EFNsYZPJEF\ $ o  G9^CVXPQV   KSPQVYZ^<V \kKMHAY YZL]b V*H>L]_N G9^CLOI ^ /  KMPQV LV . YZPQVXb KS\ M LOR!YQ^C

(258) V E KSPQV \]VXHQH YZ^CKM N &vS>EFP & MdEMYZ^<V*FP G9LOHQCV SiT $'&€(* , + {  0& M /   STY  u  & l U Q0 "%C 8 &3P0? "%8 @*"%;)3 Y 6 (B^./14303P/2@B14CT9%;)C0W ;)&K./(J;)C . t. &. . . . . . .  . . . . %. =HRJCD.0&I; 14C ;<L9J5+CDU9"4 *M  S Y   M  S 

(259) M /[M  S S Y  Vf^ K VfYZ^CV RdEF\O\]E9G L]N<D Y.  

(260) R"+ +   0& M /   S9Y  u  &   l U Q0F"%C8 &3P0? "%8B@*"%;)3F"%CT9   o   U   u  & M  o "  UHS Y 6 (B0C WO (*"%,%N&(B+= 148)8<14W ;)CEY  C   o  U  / ./143H3P/2@B14CT94A&21 ./14C*0& "%CB& ./14CB&I3/148 $ # 3P/2@DY * $('L; = 143NU"J./(    o  U  WO (*"%,% *M  S u # 3P/2@DY *M  S u '^"%CT9 ?^U"4 M     o  U @Y ,M  S  u  S  u Y  C   o  U ~/ ./143H3//2@B14CT94 &21&)(B 0;)C %RS8:"%3 ./14CB&3P148  ; = 143 U"J./(     o  U  WO (*"%,% *M  S  u Y.  

(261) R"+ + 6  0& / Q0^"%C  8 &3P0? "%8 &I3U" ) /.0&2143H$"%CT9  i   M+/S " 0W ;)&K./(J;)C &;)?^#Y7 0& i;  /*M Ri S M "%SCT9F0R @EM @BS 1 (  u &)(*"%"%CT& 9 i i  ;<'" 4!o 0WM u€;)Sv&22./(J;)C 4! o &IM ;)u€?^S Y  6=H3P(B140? C i ;<>"&21 F0W ; ;)&2./(J;)C  R&IM ;)?^S  =H3P14M? S " &2u 1 Y   i i   i i  V HZKCE YZ^ KSY KMNEFj V*NI*EMNCNCV*IiYZVXW HJ`CaCHQViY O EMR 4!o M u€3S L]HK "5')W: Kj?Cu^$ M PJV*HJj'T :S"A?p"5'5: Kj?Rus$ 3S LOR RdEMP_VKMI ^  O 0G Vf^ K V YQ^CVRdEF\]\OE9G L]NCD Y  M  _S KMN<W M  _S KMPJV NCEMY_Y KSNCDFV*NsY_YQE O KMNCWj EFL]NsY YQEEFjCj EFHJLOYZV3HQLOWCV  # *M  S   u  # YZ^CVXPQV VL<. LOHJYQH_K

(262) HQb[KM\O\ N<V*L]DM^ a EFPJ^CEhE W EMR  HQ`CI ^cYQ^ KSY  4!o M uXS  4!o M u€6S ^ KSH>YW0G EcIXEFNCNCVXIXYQV*W I*EFb j EFNCV*NsYQH   M  S *M  S ( u dM PQV*HJj'T   M  S *M  S " uX0S EFNcYZ^CVfI*EMb[j EFNCVXN Y9LONsYZE 9G ^CL]I ^ M  0S j EML]NsYZH9KMN<W  pM  S *M  S " u dM PQVXHQj'T  " M  S RM  S ()u€S EFN YZ^CV I*EFb j EMNCV*NsYZH L]NsYZEw9G ^<L]I ^ \M  [S j EML]NsYZHXT 13EG LOR KMN VL. YZPQVXb KS\ej KMLOP'M+/  S V*PQL V*H/*M  S     4!o M u€S  M  S 

(263) M /*M  S S  uKMNCW 4!o M u€S L]H K YQ`CPQN<jCL S` V3LON[K NCVXL]DF^ a EFPQ^<EhE W EMR  YZ^CVXN YQ^CV*PJV3VL<. LOHJY ( u KMN<W KMN VH. YQPQV*b[KM\CYQPZKJq VXIXYZEMPFE WCV NCVXW EMN  u    IXEFL]N<I*L]W<L]NCD 9G L YZ^hc/ `Cj[YQE YQL]b V  KMN<W[IXEFPQPJV*HQj EFNCW<L]NCDfYZEfYZ^CV9RdV*VXWCa KMI ` IXEFNsYZPQEM\  EFN      T7_^ KSYeL]H UG VIKSNVXNsYZV*PUYZ`CPJNCjCL S` V*H~9G L YZ^KMNcVLh. YQPQVXb KM\ YZPQKJq V*IiYZEFPVE KSY_K

(264) HF9G L YZI ^CLONCDYZLOb[VST EFPQVXE V*P LOR YZ^CVXPQV

(265) VLh. L]HJYQHKMN VH. YZPJV*b[KM\ YZPZKJq V*IXYQEFPFEm/ K[YZLOb[V i ( u[KMNCW o  rU ( u HQ`CI ^YQ^ KSY / LOH0K

(266) aCKMNCD KMPJI>LON   i  o  i 'KMN<WcK

(267) HQLONCDF`C\]KMPUKMPQI3L]N  i  i  rU  YQ^CV*N%O   M /     1

(268)  S ! 4!o M u€S T 7_^<V RdEF\O\]EG9L]N<DjCPQEMj EFHJLOYQL]EFNHJ^CEG9H6YQ^ KSY6L]NcR KMIiY O   M+/     1

(269)  S0b

(270) `CHJY6a V K "W')5: K;?Cus$ T oI .

(271) . . . . . . . . $. .  . . . . .  . . . . . . . .  . . . . . . . . . . . . . .

(272) . . . . . . . . .  .  . . . . .  . .

(273) T

(274) RC  s  0& M /  S Q0N"%C 8 &I3P0? "%8J@*"%;)3 0RG./(&(*"%& /*M i S  4!o M u€S 4!o M uXS = 143 14?^  i   M+/S Y 0&  i Y  /*M  i S "%CT90R@E@B1 ^&)(*"%& M  i S "%CT9 \M  i S @B14;)CB& &K1 1/@E@B1 0;)&K 0;I9J 1K= 4!o M u€S Y  0& Q0 " 0? "%8)8XCD0;14(*Q0143P(B1 1#91K=  i 0RB./( &(*"%&  4!o M u€S  "%CT9 4!o M u€S (*"4N&IWO1./14CBCD/.0&KU9./14?A@B14CD0CB&#Y+"%8)8D&)(B/ -./14?A@B14CD0CB&)  "%CT9  8:"EQ008)8<U9 ;)C0RB./(" W "%$ M  i S @B14;)CB&)A;)C  Y GR@E@B1  &)(*"%&  "pM  i S [M  i S ( u 14C  "%CT9  " M  i S [M  i S " u 14C  Y 6 (B0C  M  i S 

(275) M /[M  i S S   u Y / PQV*KMI ^CVXH  RdPJEFb 9G LOYZ^ a KMN<D IXEFNsYZPJEF\  HQKE o HJE YQ^ KSYR/cVXNsYZV*PJH. T   "L]PJHJYHJ`CjCj EFHQV9YZ^CKSY   T>7_^<VRd`CNCIXYQL]EFN *M  STM HJV*V 2V NCLOYQL]EFN )6S HQKSYZLOH VXH>YZ^<V

(276) V ` K YZL]EMN ,M  S   M  S   

(277)  M+/*M  SFiS T :hL]N<I*V  4!o M u€S  0G V I*KMN_9G PQL YZV RdEMP     

(278)  M  S 

(279) M  S NM  S 

(280) M  S

(281) NM  S 9G ^CV*PJV S KMNCW M  S L]HK HJb[E EMYQ^Rd`CN<IXYZLOEFNM HQVXV  <I o  iS T 4 Y RdEF\O\]E9G H , M  S 

(282) M  S   pM  S *M  

(283) M+/*M  S S  M  S   M /*M  S S  M+/*M  SFS  M  S 

(284) M /[M  S _S RdEFP   i T13EG LORR/ LOHKMNKSaCNCEFPJb KM\ VLh. YQPQVXb KM\ YZ^CVXNYZ^CV

(285) I*EFNCW<LOYZLOEFN  M i S 

(286) M /[M i S S  u30G EF`<\]WL]b jC\ E\/*M i S  4!o M u€STM HJV*V .0^ KMjhYZV*P I€S HQE UG V b KCE KMHQHJ`Cb[V AM oMT €S  M  S  M  M /[M  S S 

(287) M /[M  S SFS     ( u RdEFP V V*PVE   M+/iS T /3HQHJ`Cb[Va€E IXEFNsYZPZKSWCL]IiYZL]EMN YZ^ KSY  M i S 

(288) M /*M i S S  u<T PJEFb 5M oFT €S Y K` LONCD    i HQ`  IXL]V*NsYQ\ E I*\]EMHQV YQE i UG V b KCE KMHQHJ`Cb V  M  S  NM+/*M  SF'S ( u[RdEFP6V V*PVE '     i  T 13EG RdEFP       i  UG V>^ K V

(289) M+/*M  S S ( u ^CVXNCI*V3LOR L]HnHQ`CI ^YQ^ KSY M  S " RdEMP   UG V>DFViY , M  S 

(290) M+/*M  SFS  M  S  NM+/*M  SF S  M+/*M  SFS  M  S 

(291) NM+/*M  S S (   *M  S       i   ,M   S  ] ( u  ^CV*N<I*V &L]H HJYQPQLOIXYZ\ E j EFHJLOYZL V EFN     i  PQV*KMI ^CL]N<D KcI*EMN YQPZKMW<L]IXYQL]EFN T

(292) 7_^CVXPQVXRdEMPQV YZ^CV EFN<\ E j EFHJHQL aCL]\OLOYWE LOH YZ^CKSY / V*NsYZVXPQH 9G LOYQ^ HQLONCDF`C\]KMP IXEFNsYZPJEF\  T 7_^CL]HI*KMN ^ KMj<j VXN EFNC\ E L ReYZ^CVXPQVcVL<. LOHJYQH   "  i KMNCW (-u HJ`CI ^&YZ^CKSYT/ IXEFPQPJV*HJj EFN<WCH

(293) YZEYZ^CV[HQLONCDF`C\]KMP I*EFNsYQPQEF\  LON         0KSNCW /*M  S   4!o M u€S  4!o M u€S a<`<Y

(294)  YQ^CL]H L]H VHh. I*\O`CWCV*W a€E YZ^CV RdEM\]\]E9G LONCDKMPQDF`<b[VXN YQH*T4 R NM+/*M   S S   M+/*M  S S

(295) NM+/*M  S S  u YQ^CV*N /*M  fS IKMN N<EMYa V PJVKMI ^CVXW L]N CNCLOYQV[YZLOb[V[KM\OEFNCD 4!o M u€iS T />HQHJ`Cb V NCEG YZ^ K Y NM+/*M   SFS   M+/*M   S S

(296) NM+/*M   S S   u<T_4 R

(297) NM+/*M   SFS  u YZ^<V*Na€E  /  4    I*KMNNCEMY3a V EFNYZ^CVfHQViY 4!o M u€S T L]N KM\O\ E YQ^CVfIKMHJV

(298) NM+/*M   SFS   u L]H_VL<. IX\]`CW<V*W a€EM D S T 4 N  o <I o sI tUYQ^CVcEFNCVcKSNCW *VXPQEWCLOb[VXNCHQLOEFN KM\!HJYQPZKSYZK M HJ`CaCb[KMNCLORdEM\]W EMR l U S EMR_YQ^CVEFj<YQL]b[KM\ HFE NsYZ^CVXHQLOH3KSPQVI*KM\]\OV*WPJV*HQj V*IiYZL V*\ E  4iq$ X]')Hy1$43 KMNCW 4iq$Y-P+7?R:;"A3 M LONYZ^CV3RdEF\]\OE9G LONCD aCPQLOV " E .0H

(299) KMN<W =H S T EMPQV*E V*P YZ^CV KM`<YQ^CEFPJH `CHJV*W&YQ^CV \]ViYQYZVXPQH   Q  O   PQVXHQj V*IXYQL V*\ E YQE L]NCW<L]IK YZV9YZ^CV .0HUI*EFPJPQVXHQj EFNCWCLONCD YQEHQ`Ca<HQVXYeEMR /1RM  u  1  S HJ`CaCHQViYZH_EMR/@4M  u  4  S I*`CP Vb[KMWCV EMReHV9G LOYQI ^CL]NCD j EML]NsYZHNM HV9G LOYQI ^CL]NCD I*`CP VXH S YZ`CPJNCjCL S` V*H

(300) KMNCW&E V*PQ\]KMjCH YZ^CKSY KMPQV I*`CP VXHb KSWCV EMR j EML]NsYZH!PQV*KMI ^CVXWEFj<YQL]b[KM\]\ E a€E YWUG E

(301) WCLOHJYQL]NCIiYnYQPZKJq VXIXYQEFPQLOV*H*T"4 N  sI t L YReG KSH0jCPJE V*W YQ^ KSY!YZ^<V*HQV3KMPJV DFV*N<V*PQLOIKM\O\ E KM\O\"j EFHQHJL]aC\OV .0H*T  ^CLO\]V

(302) K "=  YZ^ KSYL]H L]NsYQV*PQHJV*IiYZL]EMNEMRUYWUG E .0H  o KMNCW ,fU L]H IKM\O\]VXWKaM  o  UHS PZKMb V = EML]NsYT. . . . . . . .

(303). . . . . . . . . . . . . . .

(304). . . /. . . . . . . . . . . . . .

(305).

(306). . . . . . . . .

(307). . .

(308). . . .

Riferimenti

Documenti correlati

50. Come variano portata e pressione quando il diametro della girante di una pompa centrifuga viene ridotto?. A) diminuisce la portata ma aumenta la

Il convegno intende offrire un quadro dei temi, dei generi letterari, degli autori e delle lingue di vari Paesi, in un percorso di ricerca delle assonanze e degli intrecci, ma

Le parti INAIL Regionale Lazio ed Assessorato alle politiche della scuola della provincia di Roma concordano di mettere a disposizione per il presente progetto

Studi clinici dimostrano che l’utilizzo di Hygrovent Gold può essere esteso fino a 48 ore senza alterarne le capacità filtranti e umidificanti. Destinazione

With this basic principle the only difference between fixtures with the same width of clamping is the base (whose length determines the maximum opening of the vise), while the rest

Pneumo-hydraulic servo units (complete of hydraulic cylinder + support) for multiple clamping simultaneous or indipendent, from 2 to 6 vises.. 42Z Slittone base serie Zero Point /

Se la trasformazione viene fatta a temperature piu’ basse del “naso” della curva TTT cioe’ tra i 540 e 200 C si sviluppa una nuova forma di microstruttura (e’

TTT Tremonti Tennis Team (Tremonti Romagnoli Piccardi e Associati). Marcello Valenti