Caos em sistemas abertos e gravitação
167
0
0
Texto
(2)
(3) !"#
(4) $
(5) &% ' (
(6) ) &*
(7) ,+-/.0 (12 *
(8) ,+- 3%4 4+65847 % 9 2* : ,+- ;< =# 84
(9) &% ' (
(10) ) &*
(11) ,+- >? @,+- A ) ;B%
(12) &% C4%. D EFHG I
(13) J GLKMGONIJ EG EQP9IRSNFHG I T/RECUVKWNXEZ[0Y E\ F. ]^`_ba"ced hf gikjlnm@oqpo@irmqs?m@tutwvyx z cM{b|~}=_ba"cd xumw 01x) twxwir=imfho-r @jXvtuvjikvyxum@t@m&Lm@x.
(14)
(15) !"$%'# (& *) + ,.-0/1/324/65798;:=<>6?@<0<0/,07A?CB9D9/F:*E <./6DG:I>=H :@J ?*KGBG:=8LDG: -0/6,0/MD9/3N4OPDG:@5/6BQ-R/S>?C<0<.OUTCOPDG:/SD9/VW/B9D9OPDG:7A?C< XZY[]\_^6`Aa bac[W` de`Gffgih / :@7j<0?kN=:@DG: 7A/68U: >?C5lOP,0,:@J ?!m.n98UTQ:=D9?C<R:4o p :@579OPBG:@,6qsrMDj/M5l:@<t>6H ?uD9/(v@wCwQvio x hy`{zR|S}Zhi| x~ fkht[]Q[W`XZaLW ~ \ gfg4\_[WgihZs`{f`I ~ `{h uht[_giaIf ~ Y`{h L:@B9>6:l+2j:@5OUBG:@Dj?C<R:j <.?@Vo<6oc:=-R<.OU>OU?u!BP :@8/3-R/68POU/<4?@-0?C5:@?C<M_?C<.OU/B-R:@D9?C<R ¡¢¤£¥+ p¦p¦§@¨!© ¢ p £¥ <.?@Vo<6oª8 /6<¤-R?¬«:@6®n9/'4:C:¡¢¤£¥+ p¦p¦§@¨!© ¢ p £¥ <.?@Vo<6o p /8U,.?°¯<0/ ?CT@OI¡¢± §@¨ j <.?@Vo<6o¯/6?@<0TC/M+5:=Binj/68ªNi<0:C:@5²£¥:t-R,R:=,¦¡¢±c³ §@¨!© +´4 <.?@Vo<6o¯/6<.,0?CBµ±G<R:@Bj>6OU,.>6?'¡¢±³ §@¨ª© +j <.?@Vo<6o4:@5'n9/8·¶¸?i>º¹G:uD9/(»8POPN@/6OU<0:Z_,.n9798P/6BQ-R/ L¡¢¤£¥+ p¦p¦§@¨ª© ¢ p £¥ <.?@V_:jo<0:jo¼C?C½=?±Gn9<.njQ:µ_,.n9798U/BQ-R/k ¡¢±¯¾ §=¨!© ¢ p £¥ ³/6,./Z:@79<./6,0/BQ-º:@DG:¥:@?µ¢¿Bj,.-ROÀ-Rnj-0?¥D9/£¥:=-0/65Á:= -ROP>:jq +,.-R:=- ,.-0OU>:M/ p ?@5l79n4-º:I>=H :@J ? p OP/6BQ-k KG>:jq ¨ BjOU>:=5l7q >?C5l? <0/6®n9OP,0OÀ-R?Â7G:=<0>6OU:@87G:@<R: : ? -0/6B>=H :@J ?ÃD9? ³S -Rn98P?¬D9/M?Cnj-R?@<¦/65²£¥:t-R/65Á:= -0OU>:'ª798UOP>:@D9:jo [_[.
(16) gi^6g*Y·g }Z`·f`Ah ~ Y·` Y·gz giacY[]Y ~ g4 *Y·g ~ hC `$Y·g g ~ hy`
(17) ~ Y ~ gi\ ~ '~ a ~ b ~ F[_a ~ Y·`{h ~ C`A `A^f ~ gi\W`I^u^6g[]aIfg4^ hy`Az g4^6^6`{htgi^. <.?@Vo<o:=-0<0OP>6OU?M!BU :@8{/3-R/68POU/<i?@-R?C5l:C?C< <.?@Vo<6oª8 /6<¤-R?¬«:@6®n9/'4:C: <.?@Vo<6o p /8U,.?°¯<0/ ?CT@O <.?@Vo<6o¯/6?@<0TC/M+5:=Binj/68ªNi<0:C:@5²£¥:t-R,R:=, <.?@Vo<6o¯/6<.,0?CBµ±G<R:@Bj>6OU,.>6?. [_[][.
(18)
(19) !" #$%&')(#$ *,+.-/
(20) 10 2 2!,#3 4'0 !+ 5' #6%-/7 ! ! #8+9 :#$)(
(21) , ;5<,,
(22) = >? 8 @,1
(23) A
(24) * =>5 B !!+ #$,8 C& 7 !D E>FG@(@,G
(25) 7/,!+ * !,>,''',C
(26) 2 $GH
(27) GA+ G! !!/
(28) A #%
(29) A C B * !JIKG#$'', G L G*2 #6! !!/ JMGMGM 3N. £µ:@<0TCnj/6<0OÀ-R/ ?Cnj<0>6/BG:@<qA£µ/65Á?C <0OU:@,¦D9/S!Dj<0O;:=B9?. OP@QSRLT:UVP@WHX YZX[P:WP]Y_ \ ^a`STRYcb Yed. [.
(30)
(31) . !TC<0:@D9/4>H ?9q /57j<0OU5/6OP<0?"8Un9TC:@<6q:@?*<0?=Vo*<6oµ:t-R<0OP>6OP?*/-0/68UOP/6<(:¥?C<.OU/6BQ-R:I>@H :@J ?jqBG:*:=>6/67c>@H :@J ?*7j8U/6B9:¥DG: 7G:@8;:Ni<R:4q9/M:@?<.?@Vo<6o NOUB9Tt¡ p ¹9/B9T·:@O:u>?C8;: ?C<0:I>@H :=J ?¬/SK9BG:@B9>O;:@5/6BQ-R?uB9?@,ª+ ¨ :@?@,<0?=VW,6o <0,o !B9Dj<i/* ¶O /6OP<0?9q£ :@ <.>6OP? ¶?C,R:4q£¥:@<.>6? ªBQ-?C B9OP?9q£¥:=<0>6nj,D9/µ!TCn9OU:@<u/ ¶¸/BG:=-R? /6D9<.?C,R:4q /65 >6?C5? :@?C,'<.?@VW,6o$<0,o$®n9/Z>?C579n9,0/<R:@5 : :@B9>6: /32j:@5OUBG:@Dj?C<R:jq:@, ,0n9TC/,.-6?CJ /6,ª/<0/VW/< / B9>6OU:@, :@?¥¢¿B9,.-0OP-Rn4-R? D9/1£µ:=-R/5 := -0OU>6:*+,.-º:t-k ,¤-ROP>:¥/ p ?@5l79n4-º:I>=H :@J ? p OU/BQ-k K9>:jq®n9/1:=-0<R:N/6 ,¬D9? ,./6n D9OU<./-R?@<6q79<.?@Vo¬<6o @?C,i/u ?@8UD9<.OUB9O]qs/uD9?1,0/n$>?4?C<.D9/6B9:@D9?C<D9/u7?@ ,¤¡¿T@<R:@D9n9:I>@H :@J ?jq79<0?@Vo'<6o @?@,i/ £¥:@<.-0OUB9/@q9-0?C<0B9?@n"7A?C,., N@/68:¬<0/6:@8UOP:I>=H :@J ?¬D9/6,¤-R/M79<0?ym./-R? :@?@,¦7?C ,¤¡ D9?Cnj-0?C<R:=B9D9?C,¦ª8U/6,.,R:@BjD9<0?9q{+D9n9:@<0D9?u/S³c:@½t:@,0¹9O·:=,¦>6?C8U: ?@<R:I>=H ?CJ /6,L/S>?CBQNC/6<.,R:@,¸OUBj,079O ¡ <R:@D9?@<R:@, {:@?u!8U/,0,0:@B9D9<.?-R:@5 / 5Â:u¹9?C,07jOP-º:=8UOUD9:@D9/!/5óc/5l7A/! :@?@,>6?@8U/6TC:@,'!8P/32j:@B9Dj<0/Z±G?CBQ-R/,6qn9OUl!8 /<.-R?jqn9OU,u¯<0/T?C <.OU?9q£¥:@n9<.OU>6OP?9q£¥:y2jOP5lOP8UOU:@B9?1/ ¶ª:=V_:=/68:@,D9OP,0>n9,0,?CJ /6,ª/6,.-0OU5'nj8;:@BQ-R/, :@?@,VWn9B9>OU?CB:= <0OU?@,D9?C,Z¢¿Bj,.-ROÀ-Rnj-0?C,ZD9/ ± ,0OP>: /£µ:=-R/5 := -0OU>6:jq/65 /,07A/6>O;:@8l: E ±':= -ROP5:/ :@? £ :@ <0>OU?9qj?7j<0?CBQ-R?l:=-0/6B9D9OP5l/BQ-R?*:@E ,B9?C,.,R:@,B9/>6/6,.,0OPDG:@D9/, 7A?C<·KG5µq{:!E ±{:@7A/6,.7'/M:¸E 5lOPB9¹G:¦V_:@5µ 8UOU:L?:@7A?COU?KGBG:=B9>6/OU<0?!/B:@J ?¸KGBG:@Bj>6/6OP<0?9q=<0/,07A/6>-0OPN=:@5/6BQ-R/=o.
(32) . + ,.-0n9DG:@5?C,¸:¬VW?C<05l:I>@H :=J ?Dj/M/5:=<R:@B9¹9:@D9?C,¹9?C5?i>68 B9OU>?C,/5Ã5l?kNiOU5/6BQ-0?C,TC/6?iD´/6 ,.OU>?C,¸:@,0,.?=¡ >6O;:=D9?C,·:"?C < OP-º:=,B:@J ?8UOP5lOÀ-º:@D9:@,IDj/7A?@-0/6B9>O;:@OP,D9?¦-ROP7I?¦5?CB9?C7¦?C 8U?L5l:@OP,®nG:@D9<.n97?C 8P?9ocªBG:@8POU,R:=5l?C, :"D9OPB :@ 5OU>6:D9/u/6,.7G:@8U¹9:@5l/BQ-R?C,S>:?@ -ROP>6?C,q?@B9D9/u>6?CBj,0OUDj/6<R:=5l?C,5 / -0?4Dj?C,7G:@<0:1?">:= 8U>6nj8U?ZD9/uD9O ¡ 5l/B9,6?CJ /,VW<R:@>3-º:@OP,6qC8P/6OU,D9//6,0>6:@8;:/5 OÀVWn9<0>6:I>@H ?CJ /,-R?C7A?C8k?@ TCOU>6:@,c//3VW/6OP-0?C,D9/¦7A/6®n9/BG:@,D9OU,.,0OU79:I>@H ?CJ /, /65 79<0?i>6/,0,.?C,'B:@J ?µ¹9OU7A/6< ?C 8POU>6?@,6o°¢¿BQ-R<.?4Djn96OP5l?C,S-4/ >6B9OP>:@,(7G:@<0:µ?¥/,.-0n9D9?*D9?µ>:@?@,':µ79:@<.-0OU<SD9/ -R<R:=B9,0OP/6BQ-R/,´>6:?@ -ROP>6?C,o¢¿BQNC/,.-0OUTQ:@5?C,:BG:=-0n9<0/:SOUBQN=:@<0OU:@BQ-R/@qQ7A?C<<./67G:@<0:@5/-R<.OU6:I>@H ?CJ /,-R/5l7A?C<R:=OU,6q D9?°>:=?C,!/5>?C,05?C8P?CTCO;:=,¦5lO 2j5l:@,¤-R/6<(_O;:@Bj>º¹9O·¢ S ¸/(DG:lBs:@J ?OPB-0/6TC<0: OP8UOUD9:@D9//65²>?C,05?C8U?@TCO;:@, D9/M±{<.OU/D95:=B9B4¡¶? /6<¤-R,0?@B4¡ ¾ :@8U½=/6<o. ·[.
(33) . ¸?C5l?i>68POUB9OP>¬>6<.?C,0,.OUB9TC,u:=<0/°,¤-Rn9D9OP/6D. PO BFTC/6?iD9/,0OU>5l?@-0OU?CBj,:@,.,0?i>6OU:=-R/DOP-R¹ n9B ?CnjB9D9/6D ?C<¡ OP-0,?@V¦5?CB9?@7I?C8P/u798Un9,(®nG:@D9<.n97I?@8U/68POU½=/l7A?@-R/B9>6OU:@8U,o1³¦¹9/°DjiBG:@5OU>,(?=V>º¹G:@?@-0OU>,0>:t-0-R/<0OPB9TC,OP, :@BG:@8À4/6D´/>6?@B9,0OPD9/6<5/-R¹j?4D9,¦-0?l>?C5l7jnj-R/VW<R:=>-º:=8D9OU5/6B9,.OU?CBj,6qG,0>6:@8UOPB9Tu8;:,OUB1-R?C7A?C8P?CTCOU>6:@8 OPVWn9<.>:=-0OU?CBj,6q:=B9DF/I/6>3-R,'?=V,05l:@8U8D9OP,0,.OU7G:=-0OU?CBj,(OPB B9?CBj¹i7A/6< ?C8POU>79<0?i>6/,0,./6,6o ³/6>º¹jB9OU®n9/,'-R? ,.-RnjDj >º¹G:@?C,q :@,0/DÁ?CB -R¹j/1:@BG:@8À4,.OU,¬?@Vª>º¹G:@?=-ROU>°-0<R:@Bj,0OU/BQ-R,6q´:@<./ZOUBQ-R<.?4D9nj>6/6Dso ³¦¹9/1OUBQN=:@<0OU:@BQBG:=-Rnj<0/¸?@V>º¹G:=?C,´OPBu5lO 2j5l:@,¤-R/6<>?C,05?C8P?CTCOU/,]´O;:@B9>º¹jOA¢ :@B9DBj?CB9OUBQ-0/6TC<0: OU8POP-¿MOUBl±G<0OP/6D95l:@B9B4¡ ¶¸? /6<¤-R,.?CB4¡ ¾ :@8P½@/6<¦>?C,05?C8P?CTCOU/,LOU,¦OPBQNC/6,¤-ROPTQ:=-R/DµnjB9D9/6<¦-0OU5/<0/679:@<R:@5/-0<0OP:=-0OU?CB9,o. ·[_[.
(34)
(35) . .
(36) !. aIfht`Y ~ ` b\Wgi giaIfk`A^'Y·g ^[_^fkgi ~ ^uY[]a~ F[_C`A^ rCoÀr iOU,.-0/65l:@, !:=5lOP8P-R?@B9O;:@Bj?C, oMoMo(oMo(oMoMo(oMo(oSoMo(oMoMo(oMo(oMoMo(oSoMo(oMo(oMo rCo v p :=?C,/65Â,.OU,.-0/65l:@,¦VW/6>º¹G:=D9?C, oMo(oMo(oMoMo(oMo(oSoMo(oMoMo(oMo(oMoMo(oSoMo(oMo(oMo rC o
(37) p :=?C,/65Â,.OU,.-0/65l:@,¸: /6<.-0?C, oMo(oMo(oMoMo(oMo(oSoMo(oMoMo(oMo(oMoMo(oSoMo(oMo(oMo b\Wgi giaIfk`A^'Y·g*hygi\ ~ fk[ ·[_Y ~ Yg {gh ~ \ v4oÀr +®nG:I>=H ?CJ /6,¸DG:u<0/8;:=-0OPNiOUDG:=D9/TC/<R:@8oMo(oMoMo(oMo(oSoMo(oMoMo(oMo(oMoMo(oSoMo(oMo(oMo v4o v p ?@,05?C8U?CT@O;:<./68;:t-ROPNI ,.-ROP>: oMoMo(oMo(oMoMo(oMo(oSoMo(oMoMo(oMo(oMoMo(oSoMo(oMo(oMo v4 o
(38) p :=?C,BG:@,/6®nG:I>=H ?CJ /6,¸D9/M+OUB9,¤-R/OUB1/SDG:T@/6?iD/6 ,.OU>: o(oMoMo(oMo(oMoMo(oSoMo(oMo(oMo ~ `A^ug4 ^[_^fkgi ~ ^ ~ ghyf`I^ug {h ~ ·[Wf ~ ~ `
(39) joÀr +5l:@<R:=B9¹G:@D9?@,¦¹9?C5?4>8 BjOU>6?@,/65 ,0OU,¤-R/5:@,: /<.-R?@,oMoMo(oMo(oMoMo(oSoMo(oMo(oMo
(40) jo v +,.7G:@8U¹9:@5l/BQ-R?u>:?= -ROU>?°oMoMoMoMo(oMo(oMoMo(oMo(oSoMo(oMoMo(oMo(oMoMo(oSoMo(oMo(oMo
(41) j o
(42) ±G<0:@>-R:@OU,L/5Â,0OP,.-0/65l:@,¸: /<.-0?C , >:@?C,¦/5Ã,0OP,.-R/5:=,LVW/6>º¹G:@Dj?C, oMo(oSoMo(oMo(oMo
(43) jo p :=?C,/65Â>?C,05?C8U?@TCO;:oMoMoMoMoMo(oMo(oMoMo(oMo(oSoMo(oMoMo(oMo(oMoMo(oSoMo(oMo(oMo `AaQ\ ^ ~ `. . r. v
(44)
(45)
(46) . v Qv. . 9r .
(47) . .
(48) .
(49) . X " `I$`Q\][_a[]lCht`A^^6[]a F[_aÁ` gia ^ ^fkgiF^ ~ `A^l[_a ght[_`Y[_ ~ \]\ ghkf ·h giY `Aa·` `I\Wg ~ Yh `I\Wgi\][{g G ` fkgiaIfy[ ~ \_^ ~ c^6Y`{h Y[]$g4a^[W`Aa `{zªhyg gi\]\Wght^ [_aÁ\W` ^6giac^[ fy[ Ag¥^ ^fkgiF^ ^ ^ ~ \_[_a g ~ ·[W`Ah°[]a z h ~ @f ~ \LY[_ giac^[W`Aa `{z¸ ~ `Gfy[_µ^6 ~ ffkght[]a } }1[_^^[ c~ fk[ Ag" ~ `Gfy[_µ^6 ~ ffkght[]a b X°h [Wfkh ~ ht[_agi^^[]a Y· g a[_a Fz h ~ @f ~ \ ~ ^[_ac^ gi\ ~ fy[W`Aac^ gQf 'ggiaÁ` gia ~ acY Q\W`A^6giY ^ ^fg4 ^ ! X z h ~ @f ~ \´ gQ"f ·`Y z `{h°# ~ `I^ [_aÁC`Aa^6gh ~ fy[ Ag*Q\W`I^g4YÁ^ ^fkgiF^¬`{zª^6g Igh ~ \LY[_ giac^[W`Aac^ $ de[ · ~ ^fgihl# ~ `A^ !% & C`A^$`I\W` A[_gi^ gQf 'ggia ~ `A^ ~ acY [_aIfkg {h ~ [_\_[Wf . . . . . .
(50) . » /6,¤-Rn9D9?1D9?Z7j<0? 8P/65l:D9/'-0< /6 ,>?C<07A?C,/5 5/6> :@ B9OU>6:>6/8U/,.-R/¬8P/N@?Cnc?COPB9>:@<i/µ :°E D9/,0>6? /<¤¡ -º:jqB9?*K9BG:@8Dj? ,i/6 >n98U? !¢'qDj? >:@?C,/65 VW/B ?C 5/6B9?@,'¹9?C5?4>8 B9OU>?C, r]o/6,.D9/Z/6BQ-:=J ?*VW?C<R:@5 /6,.-0n9DG:@Dj?C,¬OUB!n9 5/6<.?C,S,0OP,.-R/5:=,®n9/Z:@7j<0/6,./6BQ-º:=5 >6?@5l7A?C<.-R:@5/6BQ-R?">:?= -ROU>?9q/°:@>6<./6D9OÀ-º:t¡ ,0/¹9?tm./ ®inj/@q/65,0OP,.-0/65l:@,!D9OPB :@ 5OU>?C,6qA>:@?@,,0/¿m0:Z:<0/TC<R:/B:@J ?1:/ 2j>/4>=H :@J ?9o p ?C5?°>6?CBj,0/6® n / B9>6OU:jq>:=?C, -R/65 ,./¸-0?C<0BG:=D9?n95l:$:@ <0/6:M5'nj8P-ROPD9OU,.>6OP798UOPBG:@<D9/!><0/6,.>6/B-0/OUBQ-0/6<0/,0,./!/65 D9OP,0>OU798POUBG:@,-6:@J ?MD9OPN@/6<0,0:@, >6?C5?1/6B9TC/B9¹G:@<.O;:jq OP?C8U?@TCO;:jqA/6>?CB9?C5O;:4q®in 5OU>:l/>O / B9>6OU:@,S,0?i>6O;:=OU , v ]ol+5 V ,0OP>:jqnj5: :@ <./: 7G:@<.-0OU>n98;:@<.5l/BQ-R/OP B
(51) Gn9/B9>6OU:@DG:¬7I?@<¸/,.-0/6,ª:kN=:@Bc>6H ?C,°/M :'V¤ ,0OP>:'/,.-º:t-k ,¤-ROP>:
(52) o /7I?COP,LD9/Mc?@OUB9>6:@<i/= qG79<0? 8U/65l:@,LDj/MT@<R:NiOP-º:A>@H :@J ?u>6?@B-0OUBnG:@<0:@5Â:¬>?CBQ-R<0O n9OP<¦D9/VW?C<05l:',0OPTCB9OÀ¡ KG>:=-0OPN=:¬7G:@<0::u>6?@5l79<./6/B9,6:@J ?DG:¬>6?@5l798POU>6:@DG:'D9OPB :@ 5OU>:(D9?C,,0OP,.-R/5:=,¦>:?@ -0OU>?C,6o+24/65798U?@,¸,:@J ? ?C,OUB
(53) Gn9/6BQ-0/6,-R<0: :@8P¹9?C,ªD9/ 1/ B9?CB / ¸/6OU8P/6,ªB9?Z5l?iD9/8;:@5/6BQ-R?D9/'TC:@8k:t 24OU:@, /'D9/¬·:@,.½=:=<B9? /6,.-0n9D9?¬D9?,0OU,¤-R/5:,.?C8;:=< ]o D9OPB :@ 5OU>:SDG:<./68U:=-ROÀN4OPDG:@D9/¸TC/<R:@8/! OPB-0<0OPB9,0/>:@5/6BQ-R/!B:@J ?8POUB9/6:@<6q /">?C5? -R:@8/1 /32i-R<./65l:@5/6BQ-R/1<0OP>:jo + BG:=-Rnj<R:@8]q7A?C<¤-º:@BQ-R?jq´OPBN@/6,¤-ROUTC:@<: / 24OU,.- /6 B9>O;:jqBG:=-0n9<0/: /OU5798POU>:A>@H ?CJ /,D9?¥>6:@?C,Bj/6,.-0/°>6?@B-0/32i-R?jo¥+,.-R: / nj5:18UOPB9¹G:1<0/6>/6BQ-R/D9/7A/6,.®injOU,R:µ/°:@79<./6,./6BQ-º: 5'n9OP-0?¬OUBQ-R/<0/,0,0/S-º:=B-0?lDj?7A?CBQ-R?D9/NiOU,¤-º:'V¤ ,.OU>6?¬®nG:=B-0?l5l:=-0/65Á:= -ROP>6? ]o © /6,.-R:*-R/6,./1/6,.-0n9DG:@5?C,u>:=?C, >', !=!*_B:@J ? ®n :@ BQ-0OU>6?Q /65 ,.OU,¤-R/65l:@, ;A1W5l?kNiOU5/6BQ-R?@, B:@J ? >6?CB4KGBG:@D9?@,µ:Fnj5:F<./6TCO]:@J ?FKGB9OÀ-º:FD9? /6,.7G:I>H ? D9/*V_:=,0/k q!>?CBQ-R/32i-0nG:@8UOP:@Dj? 7j<0OUBj>6OU79:@8U5/6BQ-R/ /65²>6?C,.5l?@8U?CTCOU:'/(/5Ã79<0? 8U/5:@,¸:@,¤-R<.?@V¤ ,.OU>6?@,¸Dj/(TC<0:N4OÀ-º:I>=H :@J ?B9/ ¦-0?CB9O;:=BG:l/M<0/8;:=-0OPNiOUDG:=D9/TC/6<0:@8 o :@<0:¥-º:@BQ-R? nj,R:@5?C,6q/BQ-R<0/Z?@nj-R<0:@,6q-4/6 >6BjOU>:=,VW<R:@>3-º:@OP,'D9/°/,07G:=8U¹G:@5/6BQ-0?*>:?= -ROU>?9o p ?C5?*>6?@B4¡ ,0/6 ® n / B9>6OU:°:@8UT@n9B9,D9?C,ª<0/6,.n98P-R:@D9?C,ª>6/B-0<R:@OP,ªDj?B9?C,.,0?-0<R: :@8U¹9?D9OP6/65²<./6,07A/6OÀ-R?l/324>68Pn9,0OÀN@:=5l/B-0/.
(54) .
(55) . u: /,07G:=8U¹G:@5/6BQ-0?¬>:?@ -0OU>?9o+5 TC<0:N4OÀ-º:I>=H :@J ?¬B9/ ¦-R?CB9OU:@BG:'>?CB9,0OPD9/6<0:@5?C,L®n9/6,¤-?CJ /,ª®n9/=qG:@7A/6,0:@<¦D9? 8U?CB9T@?¥¹9OP,.-{?@ <0OU>?¥D9/l7I/,0®n9OP,R:*BG: := <0/:4q>6?CBQ-0OUBnG:N=:@5 Bs:@J ?*<0/,07A?CB9D9OPDG:@,(5l/,05?¥7G:@<0:¥,0OP,.-0/65l:@, -:@J ?Z,.OU5798U/,ª>?C5l??Z79<0? 8U/65l:D9/'¼S/798U/<7A/6<.-0n9< :@D9?9oS+5 <./68U:=-ROÀN4OPDG:@D9/MTC/<R:@8c/'>6?C,.5l?@8U?CTCOU:jq ?79<.? 8U/5:u>6/BQ-R<R:=8®n9/':=BG:@8UOP,R:@5?C,¦D9OP<./6,07A/6OÀ-R? :E :@7G:=<0/6BQ-0/OUBj>6?C57G:=-0O OP8UOUD9:@D9/!/BQ-R<0/>:@?C,ª/ -R/6?@<0O;:=,ªOPBN=:@<.O;:@BQ-0/6,7I?@<ª5'njDG:@B>6H :@,!D9/(>6?i?C<0Dj/6BG:@D9:@,ª/,07G:A>6H ?=B¡ #3
(56) , 3o © /,.-0/'>6?CBQ-0/32i-R?9qAD9/3N4O ¡ D9? :"E OUB9/ 2jOP,.- /6 B9>O;:1D9/lnj5 -R/657A?¥: ,0?C8Pnj-R?9q·- / 5 ,0OPD9?*:@5 TCn9:@,S:@,M<0/6,.7I?@,.-º:=,":"E VWnjB9DG:@5/6BQ-º:=8 ®inj/6,.-6:@J ? Dj/",./1D9/-0/6<05OUB9:@D9? ,0OP,.-R/5: /1 >:?@ -ROP>6? ?Cn B:@J ?9o /,05OU,.-0OPKG>6:@5?C,'/6,¤-R/179<.? 8U/5: /=q /65 7G:@<¤-ROU>n98;:=<6q5l?C,¤-R<0:@5l?@,M®n9/?¥7G:@<0:@D9OPTC5 :t -ROU>?Z5l?iD9/8U?">6?C,.5l?C8?C TCOP>6?15lO 245:@,¤-R/< /l 5l/,05? >:?@ -0OU>?9o :=79<0/,0/6BQ-R:I>@H :@J ?/6,¤-{:¬ D9OÀN4OPD9OUD9:(/65 D9nG:@,¦79:@<.-0/6,6o 79<.OU5/6OP<R:jqQVW?C<.5:@D9:7I/8U?C, p :@7 -0n98U?@,!rS/ v4qª/ nj5:OPBQ-R<0?iD9n>=H :@J ?°D9/>:@<9:= -R/<5l?@B9?CTC<9:= KG>6?°:,0OP,.-R/5:=,!D9OPB :@ 5OU>6?@,ª/'<./68U:=-ROÀN4OPDG:@D9/MTC/<R:@8]o ,0/6T@n9B9DG:jq>?C5l7A?C,¤-º:D9? p :@7 -Rn98P?
(57) /¦D9?C,ª7 /6 BjD9OU>/6,¸¡ (qC>?CB9,0OP,.-0/¦D9?C,<0/,0n98À-º:@Dj?C,?C<0OPTCOUB9:@OU,DG: -R/6,./@o!»,!!7 /6 B9D9OP>6/,!,6:=J ?°<0/79<0?iD9n>=H ?CJ /6,ªD9/':@<¤-ROPTC?C,79n 8POU>6:@D9?C,¸?Cn¥,.n 5/-0OUD9?C,¸7G:@<0:l79n 8UOP>:I>=H :@J ? /65Â7A/6<.Ok?C D9OP>6?C,OUBQ-R/<0BG:@>OU?CB9:@OU,o» p :@7 -Rnj8U?
(58) '-R<0:@n95l:'D9OU,.>6n9,.,6:@J ?D9?C,79<.OUB9>OU7G:@OP,<./6,0nj8P-º:=D9?C,/ OU5798UOP>:I>=H ?CJ /6,LDj/6,.-0/6,-R<0: :@8P¹9?C,6o © ? p :@7 -Rn98P?rCq4:@79<./6,0/BQ-º:@5?C,L>?CB9>6/OP-0?C, :@ ,.OU>?C,D9/!,0OU,¤-R/5:@,´D9OUB :@ 5lOP>6?C,/ª-4/6 >B9OU>6:@,L7G:@<0:? /6,.-0n9D9?uD9?¬>6:@?C,6o p ?@B9,0OPD9/6<0:@5l?@,L®n9/6,¤-?CJ /,¸>?C5?'OUBQ-R/TC<R: OU8POUDG:@Dj/¸/!>:@?C,/65 ,.OU,¤-R/65l:@,¦: /<.-R?@,L/ VW/6>º¹G:@Dj?C,6qi/65 79:@<.-0OU>6nj8;:@</5 ,0OP,.-0/65l:@,¹G:@5OU8À-R?CB9OU:@B9?C,oOU,0>nj-ROP5l?@,?-R/?C<0/5:S¼£$qQ,./4>=H ?CJ /6,D9/ c?COPB9>:@<i/@ qs-0/6?C<./65l:°D9/45l:@8U/ ¡OP<0½¹9? cq{5 /3 -R?iD9?ZD9/u£"/68UBjOU½@?kNAq/3247A?4/BQ-R/6,SD9/'C:@79n9Bj?yNAq·>6?@B4¡ m.n9BQ-R?C,SVW<R:@>3-º:@OP,6q·/6,.7G:@8P¹G:@5/6BQ-R?µ>:?@ -0OU>?"/3-R>=o © ?",0/TCn9B9D9? p :@7 -0n98U?jqOUBQ-R<.?4D9nj6OU5?C,/8U/65/6BQ-0?C, :@ ,0OP>6?C,D9/"<0/8;:=-0OPNiOUDG:=D9/°TC/<R:@8¦/">6?C,.5l?@8U?CTCOU:*5:t-R/65Á:= -0OU>:4o !79<./6,0/BQ-º:@5?C,°:=,/®nG:I>@H ?@J /6,lVWnjB4¡ DG:@5/6BQ-º:@OP,uDG: <0/68U:=-ROÀNiOUDG:@Dj/ZTC/6<0:@8L/"D9OU,.>6nj-0OU5?C,¬: >68;:=,0,0OÀKG>:A>@H :@J ?D9/"O;:=B9>º¹9O¦DG:@,u>?C,05?C8U?@TCO;:@, /6,079:@>6OU:@8U5/6BQ-R/S¹9?@5l?CT/6 B9/6:@,6q /65Ã>?C5l?u?C,¸5?4D9/8U?C,>6?C,.5l?C8?C TCOP>6?C,¦D9/M±G<0OP/6D95l:@B9Bi¡¶? /<.-0,0?CB4¡ ¾F:@8P½@/<6oZ¢¿BQ-R<.?4D9nj6OU5?C,S?¥7j<0? 8P/65l:"Dj?¥>:=?C,(Bj/6,.-0/>?CBQ-R/32i-0?*/°:@7j<0/6,./6BQ-º:=5l?C,Mn95l: <./N@/<0/ ¡ N4OP,6:@J ?uD9/-0<R: :@8U¹9?@,:@BQ-R/6<.OU?C<./6,o!BG:@8POU,0:@5l?@,?C,¦>6:@,0?C,/5®n9/M:uDjOUB :@ 5OU>6:/ D9/3-R/6<.5lOPBG:@DG:'7A/68U: /6®nG:I>=H :@J ?µD9:1T@/6?iD/6 ,.OU>:4q>6?C5?Z/65 5?kNiOU5/6BQ-R?C,!D9/¬7G:@<¤-k >n98;:=,Bn95:ZDG:=DG:ZTC/6?C5/-0<0OU:jqs/¬7A/68U:@, /6®nG:I>=H ?CJ /6,ªD9/M+OPB9,.-0/6OPBq9>6?@5l?uBG:¬/N@?C8Unc>@H :@J ?D9/S5l?iD9/8U?C,L>?C,05?C8?C TCOU>?C,6o © ?Á!7 /6 B9D9OP>6/$q¸/6,.-0n9DG:@5?C,¥: VW?C<05l:I>=H :@J ? Dj/ /65l:@<0:@B9¹G:@Dj?C,µ¹j?C5l?i>68 B9OP>6?C,1:=,0,0?i>6OU:@D9?C,µ: ?C < OÀ-º:@,(B:@J ? 8POUTQ:@D9:@,D9/7I?@-0/6B9>O;:@OP,TC<0:N4OÀ-º:@>OU?CB9:@OU,o*!BG:=8UOU,0:@5?C,(7A/6<¤-Rn9< :I>=H ?CJ /6,¬7A/6<.Ok?C D9OP>:@,(D9/.
(59) . .
(60) . 7I?@-0/6B9>O;:@OP,ZD9? -ROP7I? 5?CB9?C7?@ 8U?F5l:@OU,Z®nG:=D9<0n97¦?C 8U?9o p 8U:@,0,.OU>6:@5l/BQ-R/ /6,¤-R/6,",0OP,.-0/65l:@,15l?iD9/68U:@5 ? 5?kNiOU5/6BQ-R? D9/ 7G:=<.- >6n98U:@,°/5 -R?@<0B9? D9/ >6/BQ-R<0?@,µ:t-R<R:t-R?C<./6,ZD9/3VW?C<05l:@D9?C,q!>?C5l? /,.-0<0/68U:@,1/ TQ:@8k:y 2jOU:@,6o'+5 <0/68U:=-ROÀNiOUDG:@Dj/'TC/6<0:@8 qs5l?iD9/68U:@57G:@<.- >n98;:@,¡ -0/6,.-0/¬/65 -0?C<0Bj?"Dj/nj5 n9<0:@>6?"B9/6T@<0? D9/'i>º¹ :@<.6,0>º¹jOU8UDso p ?@5l7G:=>-º:=5l?C,¸:u7G:@<¤-R/M<0/68P/N=:@BQ-R/MD9?l/6,079:I>6H ?°Dj/MV_:@,./(>?C5²:lOPBQ-R<0?iD9n>=H :@J ?uD9/ >6?i?C<0D9/BG:@DG:=,¬:@D9/®in9:@DG:@,o$+,¤-Rn9DG:=5l?C,u:=,/6®nG:A>@H ?CJ /,<./6,.n98P-R:@BQ-R/6,u:t-R<R:N/6 ,D9? 5 /3 -R?iD9?¥Dj/"£µ/68 ¡ B9OU½=?yNÁ/*D9?F-0/6?C<./65l:F¹9?C5?4>8 BjOU>6?D9/ i5:@8P/3¡¿OU<.½i¹j? ?C,°®nG:@OP,°? ,./6<.N=:@5?C,°>?CBQ-ROPBin9:@<0/5 NL:= 8UOUDj?C,¸:@7I/,R:@<ªDG:lBs:@J ?¹9OP7I/< ?C8UOP>6OPDG:@D9/Dj?7A?CBQ-R?lK42j?¹9?C5?4>8 BjOU>6? /(Dj?5 / -R?iD9?lD9/(,./4>=H ?CJ /6, D9/Mc?COPB9>:@<i/@ o © ?C,!7 /6 B9D9OP>6/,´ªq p /'q=>6?CBj,0OUDj/6<R:=5l?C,79<0? 8U/65l:@,Dj/¦/6,079:@8U¹G:=5l/B-0?>:?= -ROU>?9oOP,0>nj-ROP5l?C, 5 /3 -R?iD9?C,¬7G:@<0:>6:@8U>n98;:=<¬: D9OU5/6B9,:@J ? D9/"<0/67A/68P?C<0/,¬/65 ,.OU,.-0/65l:@,¬>6?@5 -R< /6 ,?Cn 5:@OP,¬TC<R:=n9,¬D9/ 8UO /6<.DG:@D9/¥>6ntm.? >[email protected]? OUBQN=:@<.O;:@BQ-R/µVWnj-Rn9<.? -R/65 >6?iD9OU5/6Bj,6:@J ? 5l:@OU?@<®n9/ n95"o © /6,.-0/$>6:@,0?jq ?F5 /3 -R?iD9?Fn9,.nG:@8ªD9/*OUBj>6/6<¤-R/:@,°Bs:@J ? ,0/ :=798UOP>:jo +,.-RnjDG:@5?C,-º:=5 /6 5 ?F>?C5l7A?C<¤-º:@5/6BQ-R?$DG: D9OU5/6B9,:@J ?¥Dj?*>6?CBym.n9BQ-R?*OPBN=:@<.O;:@BQ-0/l/5 OPVWn9<.>:I>=H ?CJ /6,M-R?C7A?C8k?@ TCOU>6:@,D9/,.OU,¤-R/65l:@,(>6?C5 D9?COP,(/-R< /6 , TC<R:@nj,¦D9/8UO /<0DG:@Dj/@o» -R/5l?@,Ln95l:'8U/6OID9/S/6,.>:@8U:'/5l?C,¤-R<0:@5l?@,L®n9/@qG>?C5l?'VWnjB>@H :@J ?uDG:'/B9/6<.TCO;:4q :$D9OP5l/B9,6:@J ?$:@79<./6,./6BQ-º: nj5 5¥ B9OU5? /65 VW?C<.5: D9V/ A FB9? 7A?CBQ-R?$D9/ OPVWn9<.>:I>=H :@J ?9oÁc?C<uKG5"q OUBQNC/,.-ROPTQ:@5?C,!/,07G:=8U¹G:@5/6BQ-0?Z>:?@ -0OU>?°/65<0/TCOU5/D9OP,0,.OU7G:=-0OPN@?9oM£µ?C,¤-R<R:=5l?C,ª®n9/u:°D9OUB :@ 5lOP>:uD9/ 79<0?i>6/,0,0?@,MBs:@J ?°¹9OP7I/< ?C 8POU>?C,ª,.?@VW<0/n95:l5l/3-º:@5?C<.VW?@,0/®nG:=B9D9?Z,0nym./6OP-R:Z:7A/6®n9/6B9:@,SD9OU,.,0OU79:I>@H ?CJ /, -k 7jOU>:=,¦D9/S,0OU,¤-R/5:@,¦<./:@OP,6o © ?C,·!7 / B9D9OU>/6,c+¥/±qk:@B9:@8UOP,R:@5?C,<./68;:A>@H ?CJ /,/BQ-R<0/´:¦/324OU,¤- / B9>6OU:¸D9/>6:@?C,·Bn95 ,0OP,.-R/5:LVW/>º¹G:@D9? /l:179<./6,0/B>H :"D9//6,.-0<0nj-0n9<R:=,MVW<0:@>-R:@OU,Bn95 ,.OU,.-0/65l:1: /<.-0?µ:=,0,0?i>6OU:@D9?9oc:@<R:Z-º:@BQ-0?9q·?µ,.OU,.-0/65l: : /<.-0? / D9/3KGB9OUDj?Á: 7G:@<¤-ROP<ZD9? ,.OU,¤-R/65l:FVW/6>º¹G:=D9?Á7A/68U: OPBQ-R<0?iD9n>=H :@J ? D9/ ,R:j DG:@,1?Cn <0/TCO ?CJ /,ZD9/ /6,0>6:@7A/@oÁ» ,0/6<¤N=:@5l?@,¬®inj/µ>?CBtm.n9BQ-R?@,OPBQN@:=<0O;:=B-0/6,'VW<0:@>-R:@OU,¬/5 TC/6<0:@8LOP5l798POU>6:@5 /65 D9OPB :@ 5OU>6: >:?@ -0OU>6:uBj?l,.OU,.-0/65l:¬?C<0OPTCOUBG:=8s/S7I?iD9/5µqG7A?C<.-R:@BQ-R?9qj,0/6<¸n9,0:@D9?C,¸>6?C5?uOUB9DjOU>:=D9?C<0/,¦D9/S>:@?@,6o´+,¤-º: ? ,0/<.N=:I>=H :@J ? /¬ ?Z7I?CBQ-0?ZD9/¬7G:@<¤-ROUD9:°7G:@<R:Z:°OP5l7j8U/65/6BQ-R:I>@H :@J ?lD9/¬n955 /3 -R?iD9?°>:=7G:@¬D9/¬8P?4>6:@8UOP:@< <0/6T@O ?CJ /,°>:?= -ROU>6:@,°/5 ,0OP,.-0/65l:@,Z>6?CBj,0/6<¤N=:=-ROÀNC?C,Z>?C5 -0< /6 ,Z?@n 5:@OP,TC<0:@n9,ZD9/ 8PO /6<.DG:@D9/=oe+,¤-º: -4/6 >B9OU>6: /¬ 5l:@B9OÀVW/6,¤-º:@5/6BQ-R/OUBQN=:@<0OU:@BQ-R/¬7A?C<!-R<.?4>6:ZD9/u>6?i?C<0D9/BG:@DG:=,M/,07G:A>6H ?=¡ -R/657A?C<R:@OP,6q?1®n9/: -R?C<.BG:'N4O:= NC/8/65Ã,.OU,.-0/65l:@,¦<0/8;:=-0OPNI ,¤-ROP>6?C,o © ?C,(ª7 /6 BjD9OU>/6,¬¯Â/ (q·/6,¤-Rn9D9:@5l?@,?¥7j<0? 8P/65l:ZD9?¥>6:@?C,/5 >6?C,.5l?@8U?CTCOU:jo p ?CB9,0OPD9/6<0:@5?C, ?",.OU,¤-R/65l:°5OÀ245:=,.-R/<6qI®inj/u-0/65,0/6<¤NiOUD9?1>6?@5l?Z5?4Dj/68U?7G:@<R:Zn95OUBQ-R/B9,0?1D9/ :=-0/¬,0? <./:°B:@J ? . .
(61)
(62) . OUBQN=:@<0OU:@B>H :D9?(>:@?@,´BG:=,/®nG:I>@H ?@J /6,LD9/ª+OUB9,¤-R/OUBo ¨ ,R:@BjD9?n95l:N=:@<0OU:I>@H :@J ?SDG:S-4/ >6B9OP>:SD9OU,.>6nj-0OUDG:SB9? !7 / B9D9OU>/¬±qA5l?@,.-R<0:@5?C,®inj/'?°,0OP,.-0/65l: / Dj/(V_:=-0?>:?@ -ROP>6?/5<./68U:I>@H :@J ?:l®nG:@8P®n9/6</,0>?C8U¹G:D9/ >6?i?C<0D9/BG:@DG:=,6ou+,.-0n9DG:@5?C,-º:=5 /6 5 :Z>6?C,.5l?C8P?CTCOU:VW/6>º¹9:@DG:1D9/u±G<0OU/D95l:@B9B4¡¿¶¸? /6<¤-R,.?CB4¡ ¾ :@8P½@/6< >6?CBjVW?@<05/65/6BQ-R/M:@>?C798;:=DG:u:n95 >:@57I?u/,0>:=8;:@<5l:@,0,.OPNC?jqG7G:@<R::u®in9:@8<0/,0n98À-º:@D9?@,¸>?C B
(63) GOÀ-º:@BQ-0/6, ¹G:N4OU:@5 ,.OUD9?1/B9>6?CBQ-0<R:@D9?@,(/5 <0/8;:I>=H :@J ?1:ZD9OPVW/<0/6BQ-0/6,S7G:@< :@ 5l/3-R<.?C,-R/5l7A?C<R:=OU,6o'£µ?C,¤-R<R:=5l?C,®n9/=q ®in9:@8U®n9/<®n9/,./m0:*:"7G:@<0:@5l/3-R<.OU:A>@H :@J ?1-R/5l7A?C<R:=8 q·?¥,.OU,.-0/65l: /l B:@J ?¥>6:?@ -0OU>6?jqc7A?C<i/ 5µqcB:@J ?µOUBQ-R/ ¡ TC<G:= N@/68]o +,.-R/,°<0/,0n98À-º:@Dj?C,l7A?iD9/65 ,./6<>6?CB9>OU8PO;:@D9?@,¬>6?C5 :B:@J ?OUBQN=:@<0OU:@B>H : D9?C,/3247A?4/BQ-R/6,lD9/ C:@79n9Bj?yNAq4®inj/1/¸ :S?C<0OPTC/65 DG:M7A?C8 /6 5OU>:/5 <0/8;:I>=H :@J ?M:SBs:@J ?(OPBQN@:=<0O;:=B>H :D9?M>:@?@,/5 >6?C,.5l?@8U?CTCOU:jo p ?CBj>68Un 5?C,!®n9/=q®nG:=B9D9?",R:=-0OU,.VW/OP-R:@,:@,¹9OP7?@ -0/6,0/,B9/6>/6,.,G:@ <.O;:@,S7G:@<0:Z®inj/?@,/3247I?i/6BQ-0/6,SD9/ C:@79n9Bj?yN¥,0/¿m0:@5OPBQ-R/6<.79<0/3-{:= N@/6OP,>6?C5?°OPB9D9OU>6:@D9?C<./6,¸D9/'>6:@?C,6qI/3247A?4/B-0/6,S7A?C,0OÀ-ROPN@?C,¸D9/N@/65 7A/6<¡ 5:@Bj/6>6/<'7A?C,0OÀ-ROPN@?C,M,0? <./67G:=<R:@5/-0<0OU6:I>@H ?@J /6,/,07G:A>6H ?=¡ -R/657A?C<R:@OP,6oµc?C<¤-º:@BQ-0?9qD9OÀVW/6<0/BQ-R/65/6BQ-0/°D9? ®inj/¬,0/u:@><0/6DjOP-º:N=:jq>6:@?C,µ/ n95:°7j<0?C79<.OU/DG:@D9/'Dj?°,0OP,.-R/5:V ,0OP>6?9qA/¬B:@J ?ZD9?,0OU,¤-R/5:°D9/>6?i?C<0D9/ ¡ BG:@DG:@,q9-º:@5 /6 5Â/5Â<0/8;:=-0OPNiOUD9:@D9/TC/<R:@8]o.
(64)
(65) !
(66)
(67) . µ£ njOP-º:=,N@/6/6,!/5ÂV¤ ,.OU>:'-0<R:=-R:@5l?@,¦D9/(7j<0? 8P/65l:@,¦5?4D9/8;:@Dj?C,¦7I?@<¸,.OU,¤-R/65l:@,D9/M/6®nG:I>=H ?CJ /6,ªDG: VW?C<05l: rCoÀry
(68) ?CB9D9/ L/ ! "L 3q9?Cn"7A?C<¦5:=7G:@,¦DG:'VW?C<.5: rCo vC # $&%(' )
(69) * #+$&% ) ?CB9D9/ # -, ,. ,/ !/ * 102 03 04¦ q?C,®nG:@OP,>6?CB9,¤-ROÀ-Rn9/5 ? m./3-R?C,Dj/¬/6,.-0n9D9? D9/3 #$, G4 D # =!3o © /6,¤-R/ p :@7 -Rn98P?:@79<./6,./6BQ-º:@5?C,>?CB9>6/OP-0?C, :@ ,.OU>?C,D9/¦>6:@?C,/5 ,0OP,.-0/65l:@, D9OUB := 5lOP>6?C,o!,79<.OUB9>OU7G:@OP,L<0/3VW/6< /6 B9>O;:@,,6:=J ? 4q jq iqrkwjqr@r o 5 ) 5 6 c '87 ' 3 :9 6;9* »,,0OP,.-R/5:=,¦¹G:@5OU8P-0?CB9OU:@B9?C,´>6?C<.<0/6,.7I?@B9D9/65²:=?>6:@,0?l7G:@<¤-ROU>n98;:=<LD9/l¤rCoÀry /5îinj/=< v/> / /324OU,¤-R/65Ã>?4?@<0D9/BG:@DG:@, 1? A@ ´-º:=OU,¦®n9/ rC o
(70) Q B DCFEG H CJIKG 7G:@<R:n95l:>6/<.-R:VWnjB>@H :@J ?=G GF1? 1@ L 3qQ?@B9D9/M? NK NO NOPC / @ RQS Q QTPQ o!7A/6,0:@< DG: ,0/3NC/<R: <0/,.-R<.O.>=H :@J ?FOU57A?C,.-R: : q:F+®{o¤r@o
(71) Q u<0/79<0/,0/6BQ-R: nj5: N@:=,.-º:$>68;:=,0,0/¥D9/*,0OP,.-0/65l:@,.
(72) .
(73) . . . KG,0OP>:@5/6BQ-R/OUBQ-R/<0/6,.,R:@BQ-0/6,6qsOUB9>8Un9OPB9D9?l:5l/> :@ BjOU>:>68:@ ,0,.OU>:lB:@J ?DjOU,0,.OU7G:t-ROPN=:jq{DG:l®in9:@8c-0?C5:=5l?C, /6579<0/,.-º:=DG: ?Q:¬7G:@<¤-R/SDG:¬B9?C5/6Bj>68;:t-Rn9<0::=®injO/6579<0/TQ:@DG:jo » /,07G:A>6H ?*DG:=,>6?i?C<.D9/6BG:=DG:@, /l ?µ/6,079:I>6H ?*Dj/V_:@,./@q ? ,:@J ?*:@,M>6?i?C<.D9/6BG:=DG:@,T@/6B9/<R:@8POU:=DG:@,6q @ ,6:@J ?F?@,°5l?@5l/B-R:$TC/B9/6<0:@8UOP:@Dj?C,6q>/¥ ?FB!n9 5/6<.? D9/µTC<R:=n9,°D9/µ8UO /6<.DG:@D9/"/ G /¥ :$VWn9B>=H :@J ? ¹G:@5OU8P-0?CB9OU:@BG:jo nG:@B9Dj? /! D9/3KGB9OPDG:(7A/68U:<0/8;:I>=H :@J ?°rC o
(74) Q 3qj:+®{o!rCoÀry ,./<0/D9n9l:=E ,/6®nG:A>@H ?CJ /,LD9/ !:@5OU8À-R?CBo«:@<0O:= NC/OU,LDjOUB :@ 5OU>6:@, ?¥/ @ ®n9/S,0/S<0/8;:@>OU?CB9:@5 :t-R<R:N/6 ,DG:=,¦/6®nG:I>=H ?CJ /6,¸D9/ !:@5OU8À-R?CB ,6:@J ?D9OP-R:@,¦>:=B ?C B9OP>:@,o ³<R:@Bj,.VW?C<.5:I>=H ?CJ /6,l/6BQ-R<./ 7G:@<./6,°D9/¥>6?i?C<0D9/BG:@DG:=,°>:@B ?C B9OU>6:@,°,:@J ?F>º¹G:@5l:@DG:=,-R<0:@B9,.VW?@<05l:I>@H ?CJ /, >:@B ?@ B9OU>6:@,6o+,.-R:@,¦7A?4D9/5 ,./6<VW/OP-R:@,D9/ªVW?C<05l:,0OP,.-0/65Á:= -ROP>::(7G:@<.-0OU<´D9/!VWn9B>=H ?CJ /6,¦T@/6<R:t-R<0OP6/,6o ¨ 5 /324/65798U?D9/VWn9B>=H :@J ?TC/6<0:=-R<.OU¥/ 1? @ L q{:®nG:=8D9/KGBj/:¬-R<0:@B9,.VW?@<05l:I>@H :@J ?µ ? A@ ? @ DG:@DG:uOU5798UOP>6OÀ-º:@5/6BQ-R/¸7A?C< ? C E ¸ ? @ L @ C3I ¸ ? @ L rCo !,+®,6oMrCo L7I?iD9/65Ã,./6<ª<0/6,.?C8PNiOPDG:@,7G:@<0: ? / @ qG-R:@8®n9/':¹G:@5OU8P-0?CB9OU:@BG:7G:=,0,R:l:l,./6<¸/6,0><0OÀ-º: >6?C5? GF ? @ G 1? ? @ L A@ ? @ L L 1?c ? @ L @ L rCo C © :¬VW?@<05'n98U:I>@H :=J ?¬>:@B ?@ B9OU>6:jqjNC?@8Un95/6,¦D9?/6,.7G:I>H ?lD9/V_:@,./S ,6:@J ?u79<./6,0/<.N=:@D9?@,ª,.? /3NC?C8Pn>@H :=J ?-0/65¬¡ 7I?C<0:@8 qI?Z®n9/¬,0/TCn9/¬D9/ "C !$# 8 wjoM+,.-0/¬<0/6,.n98P-R:@D9?9qs>6?CB9¹j/6>6OPD9?Z>6?@5l?°-0/6?C<./65l:D9/uOU?Cn4N4OP8U8P/@q -R/65NL:= <0O;:=,OU5798UOP>:I>=H ?CJ /6,o ¨ 5:ZD9/8;:@,¥/u :1:@nj, /6 Bj>6O;:ZD9/:=-0<R:=-0?C<0/,B9?1/6,.7G:I>6H ?"D9/'V_:@,./@o»nj-0<R: / ?u-0/6?C<./65l:'D9/<0/>6?C<.< / B9>6OU:uDj/Sc?COPB9>:@<i/@ %o nG:@BjD9?:G B:@J ?¬D9/7I/B9D9/M/324798UOP>6OÀ-º:@5/6BQ-R/ªD9?¬-R/5l7A?¬/ -R?iDG:@,¦:@,°?C < OP-º:=,/6,¤-:@J ?¬8POU5OP-R:@DG:@,:nj5:<./6TCO]:@J ?(K9B9OP-R:(D9?¬/,07G:I>H ?¬D9/!V_:@,./@q9/,.-0/!-R/?C<0/5:':tKG<05l: ®inj/@,0? /N@?C8Un>=H :@J ?-0/657I?C<0:@8 q:=8UTCn9Bj,´D9?@,7A?CBQ-R?C,´D9/!n95l:(7A/6®n9/BG:'<0/TCO :=J ?(D9/¸NC?C8Pn95'/ &eD9?'/6,¡ 7G:I>6H ?uD9/V_:=,0/B9/>6/6,.,R:@<.O;:@5/6BQ-0/M<./-0?C<0BG:=5 :@?¬N@?C8Un95/OPB9OU>O;:@8A:-R/5l7A?C,L,.njKG>OU/6BQ-0/65/6BQ-R/M8U?CBjTC?C,6q ®in9:@8U®n9/<¸®n9/M,0/¿m0(: &uo ¨ 5:ZVWn9B>=H :@J ?µD9:@,(N=:@<.Ok:= N@/6OU,SD9OPB :@ 5OU>6:@,®n9/lBs:@J ?¥D9/7I/B9D9/l/324798UOP>6OÀ-º:@5/6BQ-R/uD9?1-R/5l7A?9*q ) )1? A@ 3q/ n95l:MOPB-0/6TC<0:@8GD9/¸5l?kNiOU5/6BQ-0?M,./!7A/6<.5:@Bj/6>6/<´>?CB9,¤-º:@BQ-R/ª:@?M8U?CBjTC?SDG:@,-R<R:km./-{?@ <0O;:=,6q?Cn ,0/m0:4q )1? A@ . w rCo Q . .
(75) . . . . © ?u/6,.7G:I>6H ?uD9/V_:=,0/@qj?C,¦>6?CBym.n9BQ-R?C,¦D9/B NC/8D9/n95l:OPB-0/6TC<0:@8sDj/5l?kNiOU5/6BQ-R?jq) ? A@ >-0/@q9D9/ ¡ KGB9/65 ,0n97A/6<¤V¤ >6OP/6,¦D9/SD9OP5l/B9,6:=J ?v/> H r:@E ,®nG:@OP,:@,"?C < OP-R:@,KG>6:@5Â>6?@BjKGBG:@D9:@,6o!,OPB-0/6TC<0:@OU,´D9/ 5l?kNiOU5/6BQ-R?) ) ) % ,6:=J ?°D9OP-R:@,!OPB9D9/7I/B9D9/6BQ-0/6,,0/¬?@,ªNC/3-R?C<./6,B9?@<05l:@OU, C"! ) C"! ) C ! ) % ,:@J ?8POUB9/6:@<05/6BQ-0/¸OPB9D9/7I/B9D9/6BQ-0/6,6o nG:@B9Dj??,.OU,¤-R/65l:S7I?C,.,0n9 O OPBQ-R/6T@<R:@OP,´D9/¸5?yNiOP5l/B-0? " OUB9D9/7I/B9D9/B-0/6,q:@,(-R<R:km./-{?@ <0O;:=,MKG>6:@5 >?CBjKGB9:@DG:@,µ:µE OUBQ-R/<0,0/i>@H :@J ? Dj/ $,0n97A/6<¤V¤ >OU/6,(-R<R:=B9,.N@/6<0,0:@OU,q <0/6,¤-R<.OUB9TCOPB9D9?Z?Z5?kN4OP5l/BQ-R?1:°n95l:°,0n97A/6<¤V¤ >OU/1]v/> H 9 ¿¡ D9OU5/6Bj,0OU?@BG:@8 oMi/ G B:@J ?1D9/67A/6BjD9/u/32¡ 798UOP>6OP-R:@5/6BQ-R/'Dj?"-0/657I?9q:179<G?@ 79<0OU:°¹G:@5OU8P-0?CB9OU:@BG:5l:@BQ-4/ 5u¡ ,0/¬>6?@B9,.-R:@BQ-R/ OPTCnG:@8ª:1E >6?@B9,.-R:@BQ-R/ D9/S/6B9/<0TCOU :
(76) /S?u,0OU,¤-R/5: / >6?CBj,0/6<¤N=:=-ROÀNC?9oc?@<¸?@<R:¬B9?C,>6?@B9>6/B-0<R:@5?C,B9/,.-R/M>:=,0?9o » 7j<0? 8P/65l:Dj/(/B9>6?CBQ-0<R:@<ª,0?C8Pn>@H ?CJ /,ªT@/6<R:=OU,D9/nj5Ã,0OU,¤-R/5:u¹G:@5OU8À-R?CB9OU:@B9?'7A?iD9/(,./6<ª<0/6/,.-R:t¡ /8U/6>OUD9?l>6?C5?°?lD9/'/6Bj>6?CBQ-R<0:@<n95l:-0 <R:@Bj,.VW?C <.5:I>=H :@J ?>6:@B ?C BjOU>:*1? A@ ?c ? @ A@ ? @ . ¸®n9/ 8U/N@/ G ? A@ l: n95l:$¹9:@5lOP8P-0?CB9O;:=BG: G G @ q¦®inj/*B:@J ?FDj/67A/6B9D9/¥DG:@,>?4?@<0D9/BG:@DG:@,TC/6B9/ ¡ <R:@8POU:=DG:@,6o nG:=B9D9?$-R:@8¦-R<0:@B9,.VW?@<05l:I>@H :@J ?$/324OU,¤-R/=q¦?C, > 5l?@5l/B-R: Q Q QT P ,:@J ? OPBQ-R/6T@<R:@OP, D9/l5?kNiOU5/6BQ-R?1/l:@,(>?4?@<0D9/BG:@DG:@, ?F /N@?C8Unj/65 8UOPB9/:@<.5l/BQ-R/¬>6?@5 ?"-0/657I?9o!83/6 5 DjOU,0,.?9q/6,.-R:@, OUBQ-R/TC<R:@OP,¬D9/15l?kNiOU5/6BQ-0? /6,.-6:@J ?/65 OPBN@?C8Unc>@H :@J ? 7A?COU,¬,0:=-ROP,.V_:@/65 Q Q % w 7G:@<0: -0?4D9? Aq ?CB9D9/ ) C3I )(#.C E H CFE ) #.CJI rCo C D9/6B9?=-º:'?'7G:=< /6 BQ-0/6,0/,D9/c?@OU,0,.?CB1/6BQ-R<./:@,VWnjB>@H ?CJ /, )1? A@ / 1? A@ 3o © /6,¤-R/79<.?4>/6,0,.? / 79<0/>6OP,0? <0/6,.?C8PN@/6<n95l:°/6®nG:A>@H :@J ?1:°D9/<0OÀN@:=DG:@,7G:@<.>6OU:@OU,¸D9/¬79<.OU5/6OU<0:l?C<.D9/65>6?C5 >FN=:@<0O:= NC/OU,q:°/6®nG:A>@H :@J ? D9/ !:@5OU8À-R?CB4¡ C:@>6? O G ? CJI G @
(77) rC o Q ?CB9D9/ :OUB9>?C TCB9OÀ-º: 1? @ /¥ :VWn9Bc>@H :@J ?FT@/6<R:t-R<0OP¥:$,0/6<lD9/-0/6<.5lOPBG:@DG:jo 4/µ/6,.-R: /6®nG:A>@H :@J ? 7I?C,.,0n9Oi,0?@8Un>=H :@J ?9qt?C,cBj?yN@?C,5?C5/6BQ-º:¦7A?4Dj/65 ,0/<c/,0>?C8U¹9OPD9?C,>6?C5?¸>6?C5 OUBG:I>=H ?CJ /6,·DG:=, >>6?CBj,.-º:=B-0/6, :@< OÀ-R<9:@ <0OU:@,LD9/SOUBQ-0/6TC<0:I>@H :@J ?jq9/S?,.OU,¤-R/65l:F/S D9OP-0?¬OUBQ-R/TC<G:= N@/68]o ?4D9/,0/6<5?C,¤-R<R:=D9?°®n9/u:@,,.n97I/<.V¤ >6OU/,D9?Z/,07G:I>H ?1D9/'V_:@,0/BG:@,®nG:@OP,:@, ?C < OP-R:@,!8POU5OP-R:@DG:@, D9/ n95 ,.OU,¤-R/65l: OPB-0/6TC<9:= NC/8/6,¤-:@J ? >?CBjKGB9:@DG:@,Z,:@J ? -R?C7A?C8U?@TCOU>6:@5l/BQ-R/1/6®n9OÀN@:=8U/6BQ-0/6,1: -R?@<0?C, >{¡ D9OU5/6B9,.OU?CB9:@OU,o © /,.-0/l>6:@,0?"?C,S5l?@5l/B-R: @ 7A?iD9/65 ,./6<S/6,.>6?C8P¹9OUDj?C,>6?C5?":@,N=:@<0O:= NC/OU,D9/:I>=H :@J ? . .
(78) .
(79) . K ! P@ 3q . . . . . r @ #? rCo Q v ?CB9D9/ P!,6:@J ?S>6nj<.N=:@,VW/6>º¹G:=DG:@,OU<.<0/6Djnj-k NC/6OP,/OUB9Dj/67A/6B9D9/BQ-R/6,B9?-R?@<0?9oc!,>6?i?C<.D9/6BG:=DG:@, >:@B9?@B9OU>6:@5l/BQ-R/>[email protected]:@D9:@,: *,6:@J ?:@,LN=:@<.Ok:= N@/6OP,LD9/ :@ B9T@n98U? / !PC 3q9>ntm0:¬/N@?C8Un>=H :@J ? -R/657A?C<R:@8ª/M D9:@DG:¬7I?@< . . . .
(80). . . . . @ 5l?iD v ¤r@oPrkwC VW?C<.5:DG:@,-0<R:ym./3-{?C <.O;:@,/65 >:@D9:$-R?C<.?FD9/7I/B9D9/*DG:$7G:@<.-0OU>n98;:@<<0/8;:I>=H :@J ? / 24OU,.-0/6BQ-R/ /BQ-R<0/*:@, VW<0/6® n / B9>6OU:@, ko . . . . . . !#$& " !( : <7>.0, % '*)+-,/.0,213!(,4.657/89;!=. ®inj/6,.-6:@J ?S®n9/L,0/TCn9//L ?!®inj/:@>6?CBQ-0/6>6/¦>?C5 :/6,¤-R<0n4-Rn9<0:D9/-R?@<0?C,cD9?/6,.7G:I>6H ?Dj/V_:@,0/®in9:@B9D9? n95:¬¹G:=5lOP8P-R?@B9O;:@B9:(OUBQ-0/6TC<9:= NC/8 G k /S 7A/6<.-0n9< :@DG:u7I?C<¦nj5 -R/<05?7A/6®n9/B9? .G G s G k /G 3 ¤r@oPrCrk /NiOUD9?µ:@? * B/> #$ E
(81) -/7 " ,# G*', B !3q·:1-R/6?@<0O;:Z>8k:@ ,.,0OU>6:"Dj/l7A/6<¤-Rn9< :I>@H ?@J /6,$/u OUBi¡ >:@7G:=°D9/VW?C<.B9/6>/6<'nj5:¥<./6,.7I?C,¤-º:*,0:=-ROP,.V_:=-G?C <0OU:µ:¥<./6,.7I/OP-R?¥DG:*OUBQ-R/TC<R: OU8POUDG:@Dj/¬D9/ G q?@n ,0/m0:4q ,0/°/ 2jOP,.-0/65 B9?kN=:@,(N=:@<.Ok:= N@/6OU,MD9/ :@ B9TCn98P?µ/:I>@H :=J ? -º:@OP,(®n9/ G G s 3o1 ,.?C8Unc>@H :@J ?µD9/6,¤-R/ 79<0? 8U/65l:¬VW?CO·/6B9>?CBQ-R<R:=DG:jqAB9?/B-R:@BQ-R?9qA7A?C<!¼?C8P5l?@TC?C<0?kNAq9ª<0B9?C8PDµ/£µ?C,./6<qs/SKG>6?Cn¥>6?CB9¹j/6>6OPDG: >6?C5? !, B #$ *o c:@<R::G !,0n4KG>6OP/6BQ-R/5l/B-0/D9OÀVW/6<./6B9>Ok:= N@/68·/(Bs:@J ?lDj/6TC/B9/6<0:@DG: WD9/-k % w4qA?@B9D9/ G 3qG?u-R/?C<0/5:u¼£ :=KG<.5:¬/,0,0/B9>6OU:@8U5/6BQ-0/(®n9/= Ri/(:=,¸VW<./6® n /6 B9>O;:@, !,:@J ? ; = #%
(82) A G!,#% @ ¬? -0?C<0?$>6?C<.<0/,07A?CB9D9/B-0/ /* :@7A/6BG:=,°D9/VW?@<05l:@D9?9o p :@,0? >?CBQ-R<9:@ <0OP? ? -R?C<.? /M D9/6,¤-R<0n D9?9qA/':=,¸-0<R:ym./3-{?C <.O;:@,7G:@,.,R:@5:u-R/6<!:@>6/,0,.?Z:ln95l:u<0/6T@O :@J ?D9/5l:@OP?C<¦D9OU5/6Bj,6:@J ?B9? /6,079:I>6H ?"D9/'V_:@,./@oªOUB9D9:jq:°5/6D9OPDG:D9/u/ /6,.TCn9/uDG:@,<./6TCO]?CJ /6,!D9/6,¤-R<0n DG:@,N=:@O:°6/6<.?1®in9:@B9D9?": 7I/<.-Rnj< :I>=H :@J ? /M <./6D9nj6OUD9::u6/<0?9o » >6?CB9>/6OÀ-R?SD9/ .,0n4KG>6OP/6BQ-R/5l/B-0/ªOPB9>6?@5l/B9,0n9<9:= NC/8 /¦ n95 -R:@BQ-R?S-4/6 >B9OU>?lWNC/¿m0:jq7I?@</324/65798U?jq rCr o +,.-R/ZDj/67A/6B9D9/ZDj/ "//6,¤-{: :@,.,0?i>6OU:@D9? :@?¥TC<R:@n D9/°OU579<./6>6OP,6:@J ?µ>6?C5®n9/°D9/3-R/<05OUBG:@D9:@, ?. ?. @. ?. @. B A. ?. . A. A. CEDEF.
(83) .
(84) KG. HG. . ML. PO. QL. RO. S@. . JI. . +. N.
(85) . . . . <0/68U:I>@H ?@J /6,/6BQ-R<./!:@,VW<0/® n /6 B9>O;:@, L,6:@J ?:@79<.?k24OP5:@D9:@,7I?@<B!nj 5l/<0?C,<R:=>6OU?@BG:@OU,o © ??Cn4-R<0?M/32i-0<0/65? /6,.-6:@J ? ?C,M-R?C<.?C,'<0/,0,.?CBG:@BQ-R/,6q:@®n9/8U/6,>6ntm0:@,(VW<0/6 ® n / B9>6OU:@,',R:t-ROU,¤V_:@6/5 # w¥7G:@<0:*:@8PTCn95l: < H n97j8;:1D9/lOPBQ-R/6OP<0?C, o³c?C<.?C,S<0/,0,0?@BG:@BQ-R/,(VW?C<.5:@5n95 >?CBtm.n9BQ-R?µD9/6Bj,0?¥Bj?"/,07G:A>6H ?¥Dj/V_:@,./ D9?l,.OU,¤-R/65l:¬B:@J ?u7A/6<.-0n9< :@D9?9o+,.-0/6,-R?C<.?C,¦,6:@J ?u-ROP79OU>6:@5/6BQ-R/Dj/6,.-0<0n D9?C,7A/68;:¬7A/6<¤-Rn9< :I>@H :=J ?9o c:@<R: OP8Un9,¤-R<R:=<*: D9OPB :@ 5OU>: BG:@, <./6TCO]?CJ /6,*/5 ®n9/ ?C,*-0?C<0?@,*,6:@J ? Dj/6,.-0<0n D9?C, >?CBQN/ 5 >6?@B4¡ ,0OUDj/6<R:=<Zn95: ¹G:=5lOP8P-R?@B9O;:@B9:$>6?@5 D9?COP,ZTC<R:@nj,ZD9/ 8UO /6<.DG:@D9/=q G / O G y ! .G / !º 3o © /6,.-0/>6:@,0?9qc?
(86) Gni2j?¥/6,.-G:µ <./6,.-0<0OÀ-R?µ) :"-R< )/6 ,MD9OU5/6Bj,6 ?CJ ) /,7G:@ <0):">6:@DG:1N@:=8U?C<Kj24? DG:/6Bj/6<0T@O;:jo ¨ 55l:@7G:D9/,./4>=H :@J ?°D9/c?COPB9>:@<i/ * $&% $&% $ %(' $&%(' 7A?4Dj/(/B-6:@J ?°,./6< D9/KGBjOUD9?(7I/8U?C,7A?CBQ-R?C,! / . D9/!,.n9>6/,0,.OPN=:@,OPBQ-R/6<.,0/i>@H ?CJ /,DG:@,-R<0:ym./-G?C <0OU:@,>6?C5 :S,0nj7I/<.V¤ >OU/ >-R/l !"/ Dj/-R/<05OUBG:=D9?u7I/8;:'>6?@B9D9O.>=H :@J ?D9/S>6?CB9,./6<¤N@:A>@H :@J ?D9/S/6B9/<0TCOU:Q 3 ¤r@oPryv@ $&%(' )) $&% )) Áv u ) $&% ) ) ) $ % ) $&% ) $5?4D v ¤r@oP r
(87) C $ % ' $ % $ % $&% ?CB9D9/ ) / ,:@J ?¥?@,M-0/6<05?C,MD9/7A/6<¤-Rn9< :I>=H :@J ?9q/ o nG:=B9D9? wjq?C,S-R?@<0?C,M>6?C<¡ <0/6,.7I?@B9D9/65 :>6OP<0>n9BjVW/6< /6 B9>O;:@,>6?CB9>!/6 BQ-R<.OU>6:@,LOUBQN=:@<.O;:@BQ-R/,B9?5:@79:(D9/,./4>=H :@J ?9q9>?C5l?(OU8Pn9,.-0<R:@D9?(BG: ±OUT9or@oPr_:Q 3o+5²7G:@<¤-ROP>6n98U:@<6q9-0?C<0?C,¸<0/,0,.?CBG:@BQ-R/,>6?C<.<0/,07A?CB9D9/5 :>6OU<.>6n9B4VW/6< / B9>6OU:@,!7j<0/6/B9>º¹9OPDG:@, 7I?C<¬?C < OÀ-º:@,7I/<0Ok?@ D9OU>6:@,6o © :79<./6,./6B>6H :MDG:7A/6<¤-Rn9< :I>=H :@J ?9qQ?-R/?C<0/5:Dj/c?COPB9>:@<i/3 ¡¿OU<.½i¹j? °:tKG<05l: ®inj/:¬D9/,.-R<.n9O.>=H :@J ?D9/Sn95 -R?@<0?u<0/,0,0?@BG:@BQ-R/M8U/3N@:¬TC/B9/6<.OU>6:@5l/BQ-R/°:¬E >6<0OU:I>@H :=J ?Dj/M7A?CBQ-R?@,¸7A/6<.Ok?C DjOU>6?@, OUB9,¤-{:= N@/6OU,_¹jOU7A/6< ?C 8UOP>6?C,R /5l:@<0TCOPBG:@8P5l/B-0//6,¤-{:= N@/6OP,_/8 74-ROU>?C,º qy>6?C5?ª5?C,¤-R<R:=D9?ªB9:!±OPT9orCoPrQ o »,7I?@B-0?C,/68 7j-0OU>6?@,¦,6:@J ?>6OP<0>6njB9DG:@D9?@,ª7A?C<¦OU8P¹G:@,¦D9/MB9?kNC?@,¸-0?C<0?C,><0O;:=D9?C,7I/8;:¬7A/6<.-0n9< :I>@H :@J ?jo !?C,7A?CBQ-R?@,!¹9OP7I/< ?C 8POU>?C,/6,.-6:@J ?1:@,.,0?i>6O;:=DG:@,N@:=<0OU/DG:@D9/,/6,¤-{:= N@/6OP,/OPB9,.-G:= NC/OU,6qI>6ntm.?@,7I?@B-0?C,!,:@J ? :=-R<0:9 D9?@,(/l<0/67A/68POUD9?@,M7A/68P?C,7A?CBQ-R?@,(7A/6<.Ok?C D9OP>6?C,q<./6,07A/6>3-ROÀN@:=5l/B-0/@oµ+,.-º:=,N=:@<0OP/6DG:@Dj/6,M,0/°OPB-0/6<¡ >6/674-º:@5 /65 OPBjKGB9OÀ-R?C,7I?CBQ-0?C,VW?C<.5:@BjD9?Fn95l:F>6?C5798POU>:=DG:$/,.-R<.nj-Rnj<R: >º¹G:@5l:@DG:F/5:@<0:@B9¹G:=D9? ¹9/-0/6<0?i>68 B9OP>6?9qi®n9/¥/ :?@<0OUT@/65 DG:'D9OPB :@ 5OU>:M>:?= -ROU>6:D9OP,0>6n4-ROUD9:BG:@,L7j<G?= 24OU5l:@,L4/4>=H ?CJ /6,o» -R/?C<0/ ¡ 5:uD9/(c?COPB9>:@<i/3 ¡¿OU<.½i¹j? 7A?4D9/M/6BQ-6:@J ?,./6<¸<0/67A/-0OUDG:=5l/B-0/M:@798UOP>:@Dj?l:=?C,¦-R?C<.?C,ª<./6,.,0?CBG:=B-0/6,D9:@, 7I/®inj/6BG:@,OU8P¹G:@,><0OU:@DG:@,7A/68U:S7A/6<¤-Rn9< :I>=H :@J ?9q7G:@<0:S5?C,¤-R<R:=<®n9/ª?S5/6,.5l?-ROP7I?Dj/VW?@<05l:I>@H :@J ?jqC>6?C5 /65l:@<R:@Bj¹G:@D9?C,/OP8U¹G:@,q9/6,¤-{:u 79<0/,0/B-0/(/5Â/6,.>:@8U:@,5l/B9?C<./6,/S5l/B9?C<0/,6o ²±OPT9oÁr@oPr1<0/3VW/6<./3¡¿,./¥:=? >:@,.?$D9/1D9?@OU,¬TC<0:@n9,¬D9/18UO /<0DG:=D9/@oFÃDj/6,.-0<0n9O¤>@H :@J ?D9/Z-R?@<0?C,¬8P/N=: BG:=-Rnj<R:@8P5l/B-0/u:°n95l:°D9OUB := 5lOP>:>?C5l7j8UOU>6:@DG:l-R:@5 / 5 B9?1>6:@,0?1D9/¬N:@ <0OP?C,TC<0:@n9,SD9/¬8PO /6<0D9:@D9/@o *:¥ n95l:µDjOPVW/6<./6B>6H :jqB9?¥/6BQ-º:@BQ-0?9o © ?*>:@,.?F>
(88) jqn95 -R?@<0? > H DjOU5/6B9,.OU?CBG:=8Bs:@J ? / >6:@7G:@lD9/ =. @. . . . . . . . ?. . ?. . . . . . . Q@. . . . @.
(89) . . . . @. . ?. @. ?. . . . . G . @.
(90)
(91) .
(92) . . . 9D OPNiOUDjOU<'n95l: ,0n97A/6<¤V¤ >OU/1D9/1/6B9/<0TCOU:Á]v/> H ry H DjOU5/6B9,.OU?CBG:=8/65 DjnG:@,u7G:@<¤-R/6,qLn95l: OUBQ-R/<0BG: / ?Cnj-R<0: /32i-R/<0BG: : /68P/@o p ?C5l? >?CB9,./6® n /6 B9>O;:jqª?C,°-R?@<0?C,ZD9/,.-0<0n D9?C,Z7A/68;:F7A/6<¤-Rn9< :I>=H :@J ? 7I?iD9/65 VW?C<05l:@<!nj5: n9 BjOU>:l<0/6T@O :@J ?°>?CB9/>-º:=DG:jo(+5>6/<.-0?C,>:@,.?C,6qM?@ < OÀ-º:@,ªD9/6,¤-º:Z<0/TCO :@J ?7I?iD9/65>º¹9/TQ:@< :@< OÀ-R<0:@<0OU:@5l/BQ-R/7j<G?= 24OU5l:@,:°-0?4D9?@,?C,7I?@B-0?C,/6Bj/6<0T@/-ROP>:@5/6BQ-0/l:=>6/6,., NC/6OP,6q·DG:@BjD9?1?C<0OPTC/65:@? VW/6B ?C 5/6Bj?F>6?CBj¹9/6>OUD9?$>6?C5? D9OÀVWn9,6:=J ? D9/µ!<0Bj?C8UD ryv o +,.-0/¥VW/6B ?@ 5l/B9? 7A?4Dj/µ,./6<NiOU,¤-R?$>6?C5? n95:NC/6<.,6:@J ?Z7A/6<¤-Rn9< :=-0OPN=:lDG:l¹9OU7?= -R/6,./'DG:/<0TC?iD9OP>6OUD9:@D9/@qA,0/TCn9B9Dj?1:®nG:@8,0OU,¤-R/5:@,ªD9/'5'njOP-º:=, 7G:@<.- >n98;:@,¦?i>6nj7G:@5 >?C5ÂOPTCnG:@87j<0? : OU8POUDG:@Dj/!®nG:@8P®inj/6</6,¤-º:@D9?l:@>/6,0,6 N@/68D9?u/6,079:I>6H ?D9/SV_:@,0/=o !()+' , '. 13!( !&5. 13'. : 5+. $ $. '9,. /6,¤-º: OP8UOPDG:@D9/SDG:@,*?C < OP-º:=,ª7A/6<.Ok?C D9OP>:@,D9/(n95²5:=7G:lD9/(,0/i>@H :@J ? * /M D9/3KGB9OUD9:°:l7G:=<.-ROP<ªDj?C, :@nj-R?kN=:@8P?C<0/,ªD9?,0OP,.-0/65l:l8UOPB9/:=<0OU6:@D9?9o»,ª7A?CBQ-R?@,!D9/Mn95l:Á?C < OP-R:Dj/(7A/6<6 ?iD9? °,:@J ?Bj/6>6/,0,0:@<0OU:t¡ 5l/B-0/´7A?CBQ-R?@,·K42j?@,cD9?5l:@7G: * o+,.-0/´5l:@7G:¦79<./6,./6<.N=:¥:@ <0/6:jq=/>?C5l?¦-R:@8 :@79<./6,0/BQ-º:!:=7I/BG :@,-R< /6 , 7I?C,.,0O OU8POUDG:@Dj/6,L7G:=<R:'?C,¸:@nj-0?kN@:=8U?C<./6, S´ / DG:¬5:t-R<0OPm0:@>? O;:=BG : * ¸_:Q
(93) r@q ?CB9D9/ u/ °,6:@J ?$<0/6:@OU, ' S / 247 3qL?@B9D9/ w /" <0/:=8 q/ D9/B9?@-º:>6?CBym.n4¡ TQ:I>@H :=J ?°>6?C5798P/32j: W>k S rCo]:C ¸/1 ª>6?@<0<0/,07A?CB9D9/5 <./6,07A/6>3-ROÀN@:=5l/B-0/¬:@?C,!7I?CBQ-0?C, ¹9OU7A/6< ?C 8UOP>6?C,¬/1/8 74-ROU>?C,6q5/6B9>OU?CB9:@D9?C,:@BQ-R/<0OP?C<05/6BQ-R/=q/$_> u<./679<./6,./6BQ-º: ?>:=,0?D9/6TC/B9/6<0:@D9? D9?C,7A?CBQ-R?@,(Kj24?C,(7G:@<R: ?C 8UOP>6?C,o°!,.,0OP5>?C5?µ?C,(7I?@B-0?C,/8 7j-ROP>6?C,q?@,7A?CBQ-R?C,M7G:@<0: ?C 8POU>6?@,M,:@J ? I. I. (b). (a). .. . .. .. Toros ressonantes. .. .. .. θ 2 = cte. ± OUTCnj<R:(r@oPrC´_:Q ci/4>@H :=J ?D9/L?COUB9>6:@<i/´ D9/Ln95e,.OU,.-0/65l:ªOPB-0/6TC<9:= NC/8 oL c/6<¤-Rn9< :I>=H :@J ?D9/nj5 ,.OU,.-0/65l: OUBQ-R/TC<G:= N@/68]o.
(94) . . . . 5:@<.TCOUB9:@8U5/6BQ-R/ª/6,¤-{:= N@/6OU,o+24/65798P?C,¦D9/-º:@OP,¦7I?@B-0?C,,6:@J ?l:@®n9/8U/6,/5 -R?C<.?C,<0/,0,0?@BG:@BQ-R/,6o » !, B #$',1, ;= '' !1G
(95) , ;&
(96) A !c:=KG<05l:!®n9/=q4:=,0,0?i>6OU:@D9?:nj5 7A?CBQ-R?Kj24?¹9OP7I/< ?C 8POU>? D9/Mn95Ã5:=7G:¬,0nG:NC/(/(OPBQNC/6<., NC/68]q{/324OU,¤-R/Mn95: n9 B9OP>:'N=:@<0OP/6DG:=D9/S,0nG:NC/ 6 D9/S7A?CBQ-R?C,¸®n9/ -R/6BjD9/65 / 247I?CBj/6B9>O;:@8P5l/B-0/u:@?Z7A?CBQ-R?ZKj24?1,0? OP-0/6<0:I>@H ?CJ /,D9?15l:@7G: WN=:@<.OU/DG:@D9/'/,.-G:= NC/8 3q·/¬?Cni¡ -R<R:¥N=:@<.OU/DG:@D9/ 4 M>6?C5 :*5l/,05l:¥79<0?@79<0OP/6DG:@Dj/°/65 <0/68U:I>@H :=J ? :@? 5:=7G:¥OUBQN@/6<0,.? WN=:@<0OP/6DG:=D9/ OUB9,¤-{:= N@/68 o'?CBQ-R?C,Kj24?C,S¹9OP7I/< ?C 8POU>?C,!,:@J ?1/6,.-0<0nj-0n9<R:=8U5/6BQ-R/¬/,.-{:t NC/6OP,6qB9?1,0/B-0OUD9?1®n9/=q,.? 7I/ ¡ ®inj/6BG:@,7A/6<¤-Rn9< :I>@H ?@J /6,6qj,6:@J ?'-0<R:@B9,¤VW?C<05l:@D9?@,/657A?CBQ-R?C,LKj24?C,D9/5l/,05l:BG:=-0n9<0/:'79<9?= 24OU5?C,L:=?C, ?C<0OPTCOUBG:=OU,6o» 5/6,05?Bs:@J ?¬:@>?CBQ-R/6>/>6?@57A?CBQ-R?@,7G:@<0: ?C 8POU>?C,6q®n9/!®nG:=B9D9?'7A/6<¤-Rn9< :@D9?C,7I?iD9/65 ,0/!-0<R:@B9,¤VW?C<05l:@</657A?CBQ-R?C,´/68 7j-ROP>6?C,qQ¹9OU7A/6< ?C 8POU>6?@,?@nZ:@7A/6<0O?C D9OP>6?C,qi>?C5??i>6?C<.<0/¸BG:D9/,.-R<.n9O.>=H :@J ? D9/´-0?C<0?C,<0/,0,.?CBG:@BQ-R/,6oª83/6 5eD9OP,0,.?9qC:@,·N=:@<0OP/6DG:=D9/6,cOUBQN=:@<0OU:@BQ-R/6,c:@,.,0?i>6O;:=DG:@,c:ª7A?CBQ-R?C,c¹9OU7A/6< ?C 8UOP>6?C, ,0/MD9/VW?C<.5:=5 ,0n9:kN@/65/6BQ-R/M,0? ::I>@H :=J ?Dj/M7A/6<¤-Rn9< :I>=H ?CJ /6,¸,0nG:N@/6,6o :LD9/3KGB9O¤>@H :@J ?¦DG:=,N@:=<0OU/DG:@D9/,OUBQN=:@<0OU:@BQ-R/,,0/6T@n9/®inj/B:@J ?7I?iD9/5 /324OP,.-ROP<7A?CBQ-R?C,D9/OPBQ-R/6<.,0/i>@H :@J ? /6BQ-R<./¬D9nG:@,!N=:@<.OU/DG:@D9/,D9/'5/6,.5l?-0OU7A? /,.-{:t NC/68>6?C5/6,¤-{:= N@/68?Cn*OPB9,.-G:= NC/8>6?@5OPB9,.-G:= NC/8 o?=¡ D9/65²/324OP,.-ROP<6q{B9?l/6BQ-º:@BQ-0?9qIOPBQ-R/6<.,0/i>@H ?CJ /,/6BQ-R<./n95l:¬N@:=<0OU/DG:@D9/M/6,¤-{:= N@/68 0 ¦/Mn95:¬N=:@<0OP/6DG:=D9/ OUB9,¤-{:= N@/68 i 3 o4/¦/,.-R/¦VW?C<?>6:@,0?jq-0?4D9:@,:@,OU5l:@TC/B9, * c/79<i/ ¡¿OP5:@T@/6B9, * D9/n95 7I?CBQ-0?Dj/OUBQ-R/<0,./4>@H :=J ?
(97) J . ´,:@J ?¬-º:@5 /6 57I?@B-0?C,¦D9/OPB-0/6<.,0/4>=H :@J ?9o p ?C5?'<0/,0n98 ¡ -º:@D9?jq4:SOUBQ-0/6<0,./4>=H :@J ?/B-0<0/ª:@,N@:=<0OU/DG:@D9/,/6,.-G:= NC/8I/¸OUBj,.-{:t NC/68G,./ªD¦:( B9/>6/6,.,R:@<.O;:@5/6BQ-0/ªBn95 B!n9 5/6<.? OUBjKGBjOP-R?¥D9/Z7I?@B-0?C,6o$³:=OU,'7A?CBQ-R?C,,6:@J ? >º¹G:@5l:@D9?@,'D9/Z¹9?C5?i>68 B9OU>?C,M®in9:@B9D9? /Z¹j/-R/ ¡ <0?i>68 B9OU>?C,¸®in9:@B9D9? ko p ?C5l?5l/B9>6OP?CBG:@D9?jq7I?@B-0?C,¹9/3-R/<0?i>68 B9OU>?C,!,:@J ?1?C,<./6,07A?CB9,9:= NC/OU, 7I/8;:¬D9OUB :@ 5lOP>:>?C5798UOP>:@DG:'®n9/S/5l/<0TC/SDG:¬D9/,.-R<.n9O.>=H :@J ?D9/-R?C<.?C,¦<0/,0,0?@BG:@BQ-R/,6o ¨ 5 /65l:@<0:@B9¹G:@Dj?¦D9/OUBQ-R/<0,./4>@H ?@J /6,¹9?C5?4>8 BjOU>:=,A-0<R:@B9,¤NC/<0,R:=OU,/ OU8Pn9,.-0<R:@D9?BG:±OUT9orCo v4qk?CBjD9/?C, 8k? nj8U?C, / * 7I?C,.,0n9/5 5l/,05l: :@ <./:M®in9:@B9D9?'?M5l:@7G: /ª >?CB9,0/<.N=:=-0OPNC?jo» OUBjKGBjOP-R?SB!n9 5/6<.? D9/8k? nj8U?C,c/6BQ-R<./68;:A>H :@D9?@,OP5l7j8UOU>6:ª/5 TC<0:@B9D9/,0/B9,0O OU8POUDG:=D9/L:>6?@B9D9O.>=H ?CJ /6,OPB9OU>O;:@OP,6q=B9?S,0/6BQ-0OUD9?S®n9/ :'D9OU,¤-:@ B9>O;:/BQ-R<0/ ?C < OÀ-º:@,´OUB9OP>6OU:@8U5/6BQ-R/79<9?= 24OU5l:@,><0/,0>6/S<0:@79OUD9:@5l/BQ-R/!,.? OP-0/6<0:I>@H ?CJ /,LD9?¬5l:@7G:jo © ?¥>6:@,0?¥/65 ®n9/ * / n95 D9OÀVW/6?C5?C<.K9,05?"Bj?¥798U:@B9? _B:@J ?µB9/6>/6,.,R:@<.O;:@5/6BQ-R/l>6?CBj,0/6<¤N=:=-ROÀNC? q? -R/6?@<0/65l:*¹9?C5?i>68 B9OU>?µDj/145l:@8U/ ¡OP<0½¹9? :=KG<.5:µ®inj/"OPBQ-R/6<.,0/i>@H ?CJ /,¬¹9?C5?4>8 BjOU>:=,M-0<R:@B9,¤NC/<0,R:=OU, <0/6,.n98P-R:@5BG:*/324OU,¤- / B9>6OU:*D9/Zn95>6?CBtm.njB-0? OUBQN=:@<0OU:@BQ-R/Dj/ * % q7G:=<R: :@8PTCn95 Iq>6?@5 D9OPB :@ 5OU>6: ,0OU5 ?C 8UOP>:/®n9OPN=:@8P/6BQ-R/°:uE D9?u>6?CBtm.njB-0?OPBN=:@<.O;:@BQ-0/D9?5:@79:uDj/SVW/<0<0:@D9n9<0:D9/(45l:@8P/@qj>ntm0:@,¸79<0?t¡ 79<0OP/6DG:@Dj/6,,:@J ? /65 >?CB9¹9/>6OPDG:@,6o"¶/6,.n98P-R:@D9?C,M,0/5l/8U¹G:@BQ-0/6,7A?iD9/65 ,./6</,.-R: /8U/>6OUDj?C,(Bj?¥>:=,0? I. .
(98) .
(99) . . . ¹9/-0/6<0?i>68 B9OP>6?9o M(A). A. Ws. .. Wu. ±OUTCnj<R:°rCo v4+5:=<R:@B9¹9:@D9?u¹9?C5?4>8 B9OU>?9o ² D9OPB :@ 5OU>:*Dj?>?CBtm.n9BQ-0? OUBQN=:@<.O;:@BQ-R/ D9?5l:@7G: D9/ZVW/6<.<R:@D9nj<R: D9/*i5:@8P/ /1 D9/KGBjOUDG: DG: ,0/6T@n9OUBQ-R/uVW?C<.5:jo p :@DG:17I?CBQ-0? / <./679<./6,./6BQ-º:@Dj?¥7A?C<n95l:1,./6® n /6 Bj>6O;: O ¡¿OUB4KGB9OP-R:D9/uD9?COP, , 5 ?C8P?C,6q # ¤r@oPr Q ?CB9D9/ tw r qj/M:u:I>@H :@J ?D9?u5l:@7G:F/S D9/KGBjOUDG:¬7A/68;:'-0<R:@B9,.8;:I>=H :@J ?¬D9?C,,6 5 ?C8U?@,(:¬E /6,0®n9/<0DG:4 ¤r@oPr @ %# +,¤-R/'5l:@7G:u7A?C,0,.n9Ocnj5B!nj 5l/<0?>6?CBQ-{:t NC/68]qs7A?C<i/ 5²OUBjKGBjOP-R?jqGD9/ ?C < OP-R:@,¸7I/<0Ok?@ D9OU>6:@,6qGn95²B!n9 5/6<.? OUB9>?CBQ-{:= N@/68D9/$?C < OP-R:@,¦B:@J ?u7A/6<0O?C D9OP>:@,L/Sn95l: ?C < OP-R:'D9/6B9,0:l/ 5 !o¸ © ?u/6,.7G:I>6H ?D9?C,,6 5 ?C8U?@,L: 5 /3 -R<0OP>:µ/¦ n9,.nG:@8P5l/B-0/¦D9/K9B9OUDG:7A?C<
(100) H @v o ¬»,7A?CBQ-R?C,7A/6<.Ok?C DjOU>6?@,VW?C<05l:@5 n95Â>[email protected]?D9/6Bj,0?/ 5 !qj/M?u,./6n¥B!nj 5l/<0?¬>6<./6,.>6// 247I?CBj/6B9>O;:@8P5l/B-0/>6?C5 ?7A/6<6 ?iD9?9o » -0/6?C<./65l:µD9/1i5:@8P/3¡¿OU<.½i¹j? F-R/5N:@ <.O;:@,MOU5798POU>:A>@H ?CJ /,MBs:@J ?µ-0<0OPNiOU:@OU,oµ+5 7G:@<¤-ROP>6n98U:@<6qB9? >:@,.?/5 ®n9/ * / n95 5l:@7G:(D9/,0/i>@H :@J ?D9/Sc?@OUB9>6:@<i/ Dj/n95:'¹9:@5lOP8P-0?CB9O;:=BG: G qG:'/324OP,.- / B9>6OU:'D9/ n95: ?C < OP-R:'D9/6Bj,R:lBj?>?CBtm.n9BQ-0?lOPBN=:@<.O;:@BQ-0/D9/ * % OU5798UOP>:BG:¬B:=J ?OPBQ-R/6T@<R: OP8UOPDG:@D9/ªD9/=G o . . G. . : /'. )+'. . )+. . 5+.9'2<. ¨ 5:u,0OÀ-RnG:I>=H :@J ?uVW<0/6® n9 /B-0/(/5²,0OU,¤-R/5:@,OPB-0/6TC<9:= NC/OU,"/( :=®inj/68;:/65în9/(/324OU,¤-R/nj5Ã7I?CBQ-0?lKj24? ¹9OU7A/6< ?C 8UOP>6?L>ntm0:@,N=:@<0OP/6DG:=D9/6,·/6,¤-{:= N@/68/OUB9,¤-{:= N@/68Q,./OPBQ-R/6<.>6/7j-º:@5 VW?C<05l:@B9D9?¦nj5 >51(
(101) ,#%>!
(102) =!.
(103) . . . . r qt>6?C5?5l?@,.-R<0:@D9?BG:¸±OUTjorCo
(104) 9]:Q o+,.-R:¸>?CBjKGT@n9<R:I>=H :@J ?1/ Bs:@J ?ªT@/6B´/ <0OU>6:jqtn95:LN@/6®inj/´?C,·<0:@5l?@,. >6?COPB9>6OPD9/6BQ-R/,µD9:@,"N=:@<.OU/DG:@D9/,µOPBN=:@<.O;:@BQ-0/6,Z-R?C<.BG:@5¬¡¿,./@q/5 TC/6<0:@8 qªD9OPVW/<0/6BQ-0/6,¥B9: 79<./6,./6B>6H :ÁD9/ 7I/<.-Rnj< :I>=H ?CJ /6,qI8P/N=:@B9Dj?:un95l:u5n9DG:@B>6H :5/-R:@5Á?C <.KG>6:¬BG:DjOUB :@ 5OU>6:'D9?,.OU,¤-R/65l:jo © /,.-º:4/4>=H :@J ? /" D9OP,0>6n4-ROUDj?$n95 5 / -0?4D9?jq>6?@B9¹9/6>OUD9?$>6?C5?5 /3 -R?iD9? D9/¥£µ/8UB9OP½@?kN r
(105) q¦®n9/µ7I?iD9/",0/<n9,0:@D9? 7G:@<R: N@/6<.OPKG>6:@<Z? :@7G:@<./6>6OP5l/BQ-R?FD9/ OPBQ-R/6<.,0/i>@H ?CJ /,µ¹9?@5l?i>68 B9OP>:@,¬-R<0:@B9,¤NC/6<.,R:@OP,1®in9:@B9D9? ,0OP,.-0/65l:@, OUBQ-R/TC<G:= N@/6OP,¸,:@J ?u,0n 5l/3-ROUDj?C,¸:u7A/6<¤-Rn9< :I>=H ?CJ /6,o p ?CBj,0OUDj/6<R:=5l?C,Sn95 ,.OU,¤-R/65l:µ¹9:@5lOP8P-0?CB9O;:=B9?°>6?@B9,0/<.N=:=-ROÀNC?µ>6?C5 n95 T@<R:@n$D9/l8PO /6<.DG:@D9/u,0n ¡ 5l/3-ROUDj?u:n95l:'7A/6<.-0n9< :I>@H :@J ?7A/6<0O?C D9OP>:'B9?u-R/5l7A?9q G N Q L G yN QA /G 3N Q L ¤r@oP r C ?CB9D9/ G 3-N Q L uv G -N Q 3o!,0,.n95OU5?C,·®inj/G (/ OUBQ-R/TC<G:= N@/68i/7A?C,0,.n9Oin95e7I?CBQ-0?ªKj24? ¹9OU7A/6< ?C 8UOP>6?Z>ntm0:@,SN@:=<0OU/DG:@D9/,(OPBQN@:=<0O;:=B-0/6,S,0/OUBQ-0/6<0>/67j-R:@5 :@?18U?@B9TC?1D9/n95 8;:I>H ?1¹9?C5?4>8 BjOU>6? qi>6?@5l?(BG:±OPT9or@o
(106) G_:Q 3o!,/®nG:I>@H ?@J /6,LD9/,.-0/,0OP,. -R/5:M 7I?iD9/5 ,0/6<´/6,.>6<0OÀ-º:@,´/65 VW?C<.5:M:@nj- ?C B9?C5l: _,0/5ÃD9/67A/6BjD /6 B9>O;:u/324798 >6OÀ-º:'B9?u-R/5l7A? ´/5 y @ ¤r@oPr @ . ¤r@oP r C r ?CB9D9/ v 6 C o © ?/6,.7G:I>H ? @ 3q?7A?CBQ-R?$K42j?-R?C<.BG:t¡ ,0/1n95l: ?C < OP-R : 7I/<0Ok?@ D9OU>6: >6?C5 N=:@<0OP/6DG:=D9/6,/6,¤-{:= N@/68 /OUB9,¤-{:= N@/68 4 ®inj/,0/OUBQ-0/6<0>/67j-R:@5e/65 o n9:@B9D9? wjq -R<0:@B9,.VW?@<05l:t¡¿,./¬Binj5:ZB9?kN=: ?C < OÀ-º:°7A/6<.Ok?C D9OP>: q79<G?= 24OP5:$:1E ?C<0OPTCOUB9:@8 qA/:@,. N@:=<0OU/DG:@D9/,OPBN=:@<.O;:@BQ-0/6, D9/VW?@<05l:@5u¡ ,0/,0nG:N@/65/6BQ-R/ZBG:=,B9?kN=:@,N=:@<.OU/6D9:@D9/6, 0 o » 5 / -0?4Dj? D9/*£µ/68PB9OU½=?yN :@,./6OU:t¡¿,./¥/65 5/6D9OP<lDjOU,.- :@ B9>O;:@,/6BQ-R<./ º ¬/ i R u:$KG5 D9/ 8U?i>:@8POU:=<7A?C,0,6 NC/OU,OUBQ-0/6<0,./4>=H ?CJ /6,-R<0:@B9,.N@/6<.,R:@OP,6o 4/¿m0 :
(107) ´:M,./4>@H :=J ?(D9/3KGB9OPDG:M7A?C< _5?4Dlv 3qC/ *
(108)
(109)
(110) ´?S>?C<0<./6,07A?CB9Dj/6BQ-R/ 5:@79:'D9/Sc?COPB9>:=<i/@ o p ?@B9,0OPD9/6<./MBj/6,.-R:¬,0/4>=H :@J ?:@,¦OUBQ-0/6<0,./4>=H ?CJ /6,/6BQ-0<0/M:'<0/3-º:¬B9?C<.5:@8s: B9? 7I?CBQ-0?
(111) M/:@,SN@:=<0OU/DG:@D9/, i 0 3ol/6Bj?@-R/u7A?C< ?C,S7A?CBQ-R?C,SD9/OUBQ-0/6<0,./4>=H :@J ?µ5l:@OP, 79<G?= 24OP5l?C,¦Dj/ o/3KGB9OP5l?C, 3
(112) k y H 3 0 @ H @ ¤r@oP r C
(113) . @. >G .
(114) . . . @. . . . >G . . . . @. . I. . . S. . &. . G . . . . . . . . . @. . @.
(115) .
(116) . . . ?CB9D9/ @ ª,:@J ?¥:=,,0?C8Pn>@H ?CJ /,SDG:@,M+®i,o*rCoÀr C ¿¡ ¤rCoÀr Q ®n9/u7G:@,0,0:@5 7A?C< /65 kq / t /Z :*,.?C8Unc>@H :@J ? D9? ,.OU,¤-R/65l:¥B:=J ? 7I/<.-Rnj< :@Dj? ®inj/Z7G:@,0,0: 7I?C< /5 wjo»Ã79<.?4D9n4-R? >6n9B9¹9:/65rCoPr Q °/M D9/3KGB9OUDj?7A?C< H = o ¨ 5:¬NC/'®n9/ µ/M -R:@B9TC/B-0/: q 3 y / :'DjOU,.- :@ B9>O;:(/BQ-R<0/ 0 ´/ i º B9?C<05l:@8I:Z
(117) ¦B9?'7A?CBQ-R? 6qG>6?C5?u5l?C,¤-R<0:@D9?¬BG:±OUTjoLrC o
(118) G o . @. . . . . ?. . G. . . . (a). Γ. (b). W u(γε ) Σθ0 U. Σθ0. .. γε. ... U. U. γ0. Γx {θ0 }. Σθ0. Au. As. W s(γε ) Σθ0 U. x0 Σθ0. ±cOUTCn9<0:°rCo
(119) j¸]:Q ¦·:I>H ?¹j?C5l?i>68 B9OP>6? oª ´«:@<0OP/6DG:=D9/6,OUBQN=:@<.O;:@BQ-R/,¦D9?u5:=7G: *
(120) o +5 79<0OP5l/OU<0:M?C<.D9/65 /5 -0/65¬¡¿,0/ i @ y SH @ 3q/:(+®{oª¤r@oPr C -R<R:=B9,.VW?C<.5:y¡¿,0//5 k 3 y y H 3 0 @ H2 C ¤r@o v@wC ?CB9D9/ ,R:=-0OU,¤V_:@ 3 k y H 3 0* # C k H 3 L ¤r@o v4rk . Â+®{o ¤rCo v@wQ 7A?4D9/,0/<'D9OÀN4OPD9OUD9:"/5 D9n9:@,7G:=<.-R/,6qDj/KGB9OPDG:@,'>?C5? 3 y y H 3 0 @ 3o © ?>:=,0?/5în9/':u5:t-R<0OP´m0:@>6? O;:@B9:uDj/ ¸-R/5Â-R<R:A>6H ?Binj8U?/65 q{>6?C5? ?4>?C<0<./M®nG:=B9D9? N Q{ ´,6:@J ?>6?i?C<.D9/6BG:=DG:@,>:@B ?C B9OU>6:@,6q ,0:=-ROP,.V_:@ 4 t t H 0 3 y H 3 ¤r@o vCv@
(121) . @. . . @. . . . . @. . . . . . . . . @. . @. . @. @. . . . . @. . . . . . . . . .
(122) . . . . ¨ 5l:µ<0/8;:I>=H :@J ?"OUBQ-R/TC<R:@87G:=<R: 3 H u/ /6BQ-:@J ?¥? -ROPDG:":µ7G:@<¤-ROP< DG:'OUBQ-R/TC<R:A>@H :@J ?(D9/ 4 3 / 3 Bj?C,LOUBQ-0/6<.N=:@8P?C, H ´/¬ 3q4<0/,07A/6>-0OPN=:@5/6BQ-R/= 3 ' y y . 6 t L 3 ¤r@o v
(123) C VWn9Bc>@H :@J ?D9/(£µ/68PB9OU½=?kN /S D9/KGBjOUDG:¬ >6?@5l? 0 ' y y 0 6 t L 3 ¤r@o v Q ?M-0/6?C<./65l:MDG:SVWn9B>=H :@J ?OPBN@/6<.,R:(,./6TCnj/!®n9/!,./ 0 7A?C,.,0n9O{6/<0?C,´,0OP5l798P/6,qQ/6BQ-:@J ? 0
(124) / 4 0
Documentos relacionados
Peça aos alunos para completarem as frases, usando os pronomes ou determinantes possessivos do quadro. Nós temos um carro vermelho. Eles têm um jardim muito grande. Nós temos
Equações de regressão polinomial e coeficiente de determinação em função da altura do tronco (x) para a densidade básica da madeira (Y) dos clones das 2 espécies e híbrido
As demonstrações contábeis foram elaboradas de acordo com as novas práticas contábeis adotadas no Brasil, com atendimento integral da Lei nº. As demonstrações
No primeiro ciclo, o nível médio dos sólidos foi de 24,8 mg/L e a maior amplitude ocorreu em setembro/94, cujos valores oscilaram entre 13,6 e 47,8 mg/L (Figura 4), sendo este último
No presente estudo assinalamos a primeira ocorrência de Bosmina huaroensis Delachaux, 1918 na bacia do alto Rio Paraná, constituindo, possivelmente, o primeiro registro no Brasil..
[=] – Caso seja deliberada a saída da Companhia do Novo Mercado para que os valores mobiliários por ela emitidos passem a ter registro para negociação fora do Novo Mercado, ou em
Como você estudou no módulo anterior, a legislação de trânsito brasileira regula- menta aspectos importantes para a circulação de veículos de emergência, sendo ressaltada a
Atualmente, a região MAPITOPA (Maranhão, Piauí, Tocantins e Para) uma das novas fronteiras agrícola do Brasil, possui 55.000 ha plantados e disponibilidade de 1.200.00
