tese - USP · !"#$ %$&&$ '()"+ )"* ,* -$./(+012 3+ 4567 &'$("#$)+$",$(+-.$+/(0$% 89.(#*:$ &"( (,;

!"#$%&$ '($#" )*+," )"!*+$*

!"!#$%&% '( )*+!%"(,-!* ./0-123*1+!* 4!$

5(,*!$1%"(,-! )06-$1+! 7 8(*(,9!091"(,-!

'( :0#!$1-"!* ;(,6-1+!* ! '!

!" #$% &'(") *'%+! $ ,!"$-+$() .!# '#!-)

'/#(-'01!) -$"&$(2! $ 3-'2(/1! &$+! '#!-

(4.!4/(.(!4'+ $ &$+' .!#&-$$4"1! /$ #(45'

'%"64.(' $# #%(2!" #!#$42!"7

!"#$%&'(%)*+,

!"#$%

!"#$ %$&&$ '()"*+* )"* ,* -$./(+*0*12

3+ 4567

&'$ ("#$ )*+$ " ,$ (+-.*$ +/(0$%

89.(#*:$ &"( (,;.(=(,*'/*5 0$'&*9";.(,

,* *,%.*&/(.2 89.(#*:$ ($ &*" 0$.(:B$ /$#$ (,$. )"* %"#*.(, ,*

#(.12

8"/$. C*&0$'?*0;#$

&' ("# -*('/*1'% 2+-34+#$%

3$. (++ /?$&* /;,*& D$" &/$$# >D ,*2 3$. (++ /?* /."/? /?(/ D$"

,(#* ,* &**2 3$. (++ /?* @$D D$" >.$"9?/ /$ ,D +;-*2 3$. (++ /?*

E.$'9 /?(/ D$" ,(#* .;9?/2 3$. *=*.D #.*(, D$" ,(#* 0$,* /."*2

3$. (++ /?* +$=* F -$"'# ;' D$"2 FG++ >* -$.*=*. /?('H-"+ >(>D22212

C;('* I(..*'

&'$ ("#$ *(+5'$%

2228,;9$ J 0$;&( %(.( &* 9"(.#(. '$ +(#$ *&)"*.#$ #$ %*;/$2 K*&,$

)"* $ /*,%$ * ( #;&/L'0;( #;9(, 'B$5 ,*&,$ *&)"*0*'#$ ( 0(':B$2

M )"* ;,%$./( J $"=;. ( =$< )"* =*, #$ 0$.(:B$22212

3*.'('#$ N.('/ * K;+/$' O(&0;,*'/$

&'$ )/'6"$$'/"$ 1' 7-$8+8#8' 1" 9+:-4+*$ ;*8"(79;9?

@ABC " 1* D$4'E* 1" D-5"-.*/+* 1" A0' 9*/E'$ >DDA9?@ABC%

M &P>;$ 'B$ J $ ?$,*, )"* -$.'*0* (& =*.#(#*;.(& .*&%$&/(&Q J $

)"* -$.,"+( (& =*.#(#*;.(& %*.9"'/(&12

R+("#* SJ=;AT/.("&&

&'$ 8F4-+4'$ " 6#-4+'-*12

C*,V0.;/$

&' ("# '/+"-8*1'/%

M %.$-*&&$. ,*#W$0.* 0$'/(2 M >$, %.$-*&&$. *X%+;0(2 M %.$-*&&$.

&"%*.;$. #*,$'&/.(2 M 9.('#* %.$-*&&$. ;'&%;.(12

I;++;(, 8./?". I(.#

G+-*E("-8"% *5/*1"=' , G&BDAB% )/'4"$$' -

oHIJKLMIN?N% )"E' *)'+' O-*-4"+/'

1*1' * "$8* )"$P#+$*Q

!"#$%$ &'($)*" " +,$ - )$%$../01"2 *$3"1. "

+,$ - 3"..45$62 $ *$ 0$3$)7$ 5"%8 $.7'0/ &'($)*"

" 1#3"..45$69:

;..1.

!"#$%

!"#$%#& '()( (*+,,-.( /#0#1"!2! 34 4$5#!0467#$ 0897%:;$%5#$ 7"%5# = 34$46?#9?%0467# 34 !91#"%70#$ 146>7%5#$

3#

5#09E# > 5#67"%B8%"

49>7"%5# 4 "426;=9# %74"!7%?!04674 !7> N84 ?!"%;?4%$ 34 5#67"#94 "4$897!674$ 3# 0#=

349# 680>"%5# $4 %18!940 K$ $8!$ E#0M9#1!$& 3474"0%6!3!$ 4R7"%5! "4!9. 4 !$ 043%3!$

5!9589!3!$ 6# 0#349# 680>"%5# *P8R# 34 5#""4674 49>7"%5! !"%5! 3#

5#67"!$74 49>7"%5# 5#0# 80

6!63# %9E! 4 54989!".( X 34$40

!"#"$ %& '()&* " +,"-&, %&.&/"%" !', 0, %&.&,#&12' !',#0)"!+'1"3 ,&32'*4

50"1%' !',#"*"%' "' %&.&,#&12' %". "*50+)&)0*". ,&.)*&6&.!*"7'4 +32" & !&303"*8

93 , %+..'4 &.)*") -+". #"*" ,&32'*"* " &:!+;1!+" %' "3-'*+),' ' %& +1' %& 7"$+' & !'&:!+&1)& %& .+,&)*+" %' &.!'",&1)'C4

" +1.&*=>' %& 0," )"(&3" % &% #"*" &7+)"* ' !A3!03' %& .'30=?&. /A &1!'1)*"%".4

' 0.' %& '#&*"%'*&. %& #*&%"=>' & %& (0.!" 3'!"38 D& "!'*%' !', '. *&.03)"%'.4

#'%&6.& !'1!30+* 50& " "*50+)&)0*" 2@(*+%" 0, , )'%' "#*'#*+"%' #"*" .'30=>'

%' #*'(3&," %& )','-*":" #'* +,#&%E1!+" &3 )*+!" %& &.!'",&1)'. ,03)+'8 F*'(3&," +17&*.'8 J&!'1.)*0=>' 10, *+!"8 K','-*":" #'* +,#&%E1!+"

&3 )*+!"8

!"#$%

!"#$%#& '()( (*+,,-.( /012%34!$5 6#7 2#8#9"!34: ;: 515

B4(C( D45$%$ > E$245 #32%8%J!2%#= #A 3"#

2# 245 ?5@51#385=2 #A $#102%#= 8524#?$ ;!$5? #= $35

T

$%?5$& $2"!259%5$ 2# %83"#@5 245 !19#"%248 5M

!"#!" "$%#!&'("#$ )*!"+*) %!#& (,* ,-."/'0 1$#20*)3* #% (,* (#!' ,"/ !#4

50*& 6+#") %!'/("#$ '$) .-&&*(!- /#*7/"*$( #% (,* 8#29: (,* "$.*!("#$ #% ' ,'.,

('50* (# '+#") (,* /'0/;0'("#$ #% .#0;("#$. '0!*')- %#;$): (,* ;.* #% !*)'("#$ '$)

0#/'0 .*'!/, # *!'(#!. 2*!* !# #.*)< =//#!)"$3 (# (,* !*.;0(.: "( ". #.."50* (#

/#$/0;)* (,'( (,* ,-5!") )*0 ". '$ ' !# !"'(* &*(,#) %#! .#0+"$3 (,* *0*/(!"/'0

"& *)'$/* (#!' ,- !#50*& #% &;0(" ,'.* 8#2.<

>*-2#!).? @'!'00*0 3*$*("/ '03#!"(,&< A;0(" ,'.* 8#2.< B ("&"C'("#$< D$+*!.*

!#50*&< E;&*!"/'0 !*/#$.(!;/("#$< F0*/(!"/'0 "& *)'$/* (#!' ,-

!"#$ %& '!()*$"

! "#$%$&' #$%$ '(&)*+,' -) ./$0)*1 -' )12'$/)*&' #'% /).' -$ 345! 67

6! 8%'2)-./)*&' #$%$ '(&)*+,' -) ./$0)*1 1)09*-' $ 345! ! ! ! ! ! :;

6!6 2.)1 -) '&./.?$+,' $11'2.$-$1 $' =9*2.'*$@ -) )%%' 2'/ #$A

&'@'0.$1 &.#' #@$&B ) #'*&' -) 1)@$! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! C6

6!: D'-)@' /)1&%)A)12%$E'! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! CF

6!G D'-)@' .@H$ -) #'#9@$+I)1 J9$1)A.1'@$-$1! ! ! ! ! ! ! ! ! ! ! ! ! ! KL

6!C D'-)@' 2)@9@$%! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! K6

6!K D'-)@' -) "M8 H>(%.-' N.@H$A2)@9@$%O! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! K:

:! N$O D$@H$ -) )@)/)*&'1 P*.&'1 &%.$*09@$%)1Q N(O )@)/)*&' P*.&' &%.A

$*09@$%! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ;6

:!6 N$O R'/>*.' -.12%)&' 2'*&)*-' ' 19(-'/>*.' Ω(i,j) NS%)$ 2.*?$OQ N(O)@)/)*&' -' 19(-'/>*.' Ω(i,j)T 29U$ -.1&%.(9.+,' -' 2'*&%$1&) σ )1&S%)#%)1)*&$-$ #)@$ *9/)%$+,' @'2$@ σL1! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ;K

G! !"##"$%! -) -'.1 #'*&'1! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 7:

G!6 4/$0)*1 -$ &%$*1.+,' -) 9/ )12'$/)*&' #&'( #$%$ 9/ )12'$/)*&'

$ ('@H$1! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 7C

C! R'/>*.' -.12%)&.?$-'T 2'/ .*2@91I)1 ) $#@.2$+,' -$1 2'*-.+I)1 -)

2'*&'%*' J9) 1./9@$/ ' #)%P@ -) )V2.&$+,' -.$/)&%$@! ! ! ! ! ! ! ! F:

C!6 W'/#'%&$/)*&' -'1 /'-)@'1 #$%$@)@'1! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! F;

C!: R.1&%.(9.+,' -) =%)JXY*2.$ NH.1&'0%$/$O -' *Z/)%' -) $E$@.$+I)1

-$ =9*+,' '(U)&.E' #$%$ 2$-$ /'-)@' #$%$@)@'! ! ! ! ! ! ! ! ! ! ! ! F7

C!G 4*&)%E$@' -) 2'*P$*+$ -'1 &)1&)1 )/ %)@$+,' [ -.=)%)*+$ )*&%) $1

/\-.$1 -' *Z/)%' -) $E$@.$+I)1 -$ =9*+,' '(U)&.E' -'1 "M81! ! ! FF

C!C W'/#'%&$/)*&' -' "M8] #$%$ 2$-$ 2$1'! ! ! ! ! ! ! ! ! ! ! ! ! ! LG

C!K R.1&%.(9.+,' -) =%)JXY*2.$ NH.1&'0%$/$O -' *Z/)%' -) $E$@.$+I)1

-$ =9*+,' '(U)&.E' #$%$ 2$-$ 2$1'! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! LC

C!; 4*&)%E$@' -) 2'*P$*+$ -'1 &)1&)1 )/ %)@$+,' [ -.=)%)*+$ )*&%) $1

/\-.$1 -' *Z/)%' -) $E$@.$+I)1 -$ =9*+,' '(U)&.E' #$%$ 2$-$ 2$1'! LK

C!7 3$/$*H' -$ &$()@$ )*#) × *Z/)%' -) $2)%&'1 $29/9@$-'1 -$ &$A()@$ )*#)T )/ 50 )V)29+I)1 -' "M8]! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! L7

C!F W'/#'%&$/)*&' -$ &$()@$ )*#) $' @'*0' -$1 0)%$+I)1T )/ 9/$

Z*.2$ )V)29+,' -' "M8]! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! LF

!"# $%&'%()*&+,)% -* )*.+/* !" ,*0 '(1&+1(*0 100 2+(*34+05 +&6&* 7,18* +9+863:% -% ;! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "#?

!"" $%&'%()*&+,)% -% ; '*(* 8*-* 8*0%! ! ! ! ! ! ! ! ! ! ! ! ! ! ""@

!"A B10)(1.613:% -+ C(+DEF,81* GH10)%2(*&*I -% ,7&+(% -+ *J*/1*34+0

-* C6,3:% %.K+)1J% '*(* 8*-* 8*0%! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ""L

!"@ M,)+(J*/% -+ 8%,N*,3* -%0 )+0)+0 +& (+/*3:% O -1C+(+,3* +,)(+ *0

&P-1*0 -% ,7&+(% -+ *J*/1*34+0 -* C6,3:% %.K+)1J% '*(* 8*-* 8*0%! ""

!"L $6(J* -+ 8%,J+(2F,81* -% ;! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ""Q

;!" R+((*&+,)* -+ &%,1)%(*3:% -% ,S &+0)(+! ! ! ! ! ! ! ! ! ! ! ! ! ! "LL

;!A R+((*&+,)* -+ &%,1)%(*3:% -% ,S +08(*J%! ! ! ! ! ! ! ! ! ! ! ! ! ! "L

T!" U+06/)*-%0 %.)1-%0 8%& % ;

!"#$ %& '$(&)$"

!" #$%&'() $*+,$ )- +$,.)- /& 0$*1+23& $ /)- 40-! ! ! ! ! ! ! ! ! ! ! 56

7!" 8)*9:;,&'() /)- .)/$%)- .$-+,$ 2%?&> 3$%;%&, $ ?@A,2/)! ! B5

7! 8).C&,&'() /) /$-$.C$*?) 3).C;+&32)*&% $*+,$ )- .)/$%)- .$-+,$<

$-3,&=)> 2%?&> 3$%;%&, $ ?@A,2/)! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! BD

7!E !"#$"% /&- &.)-+,&- 3). ,$%&'() &) *F.$,) /$ &=&%2&'G$- /& H;*<

'() )AI$+2=)! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "JJ

7!5 !"#$"% /&- &.)-+,&- 3). ,$%&'() K C,)C),'() /$ -;3$--)! ! ! ! ! "J"

7!7 8).C&,&'() /) /$-$.C$*?) /) 40LM> 3). & H;*'() )AI$+2=) 3).

&/2'() /$ 2*H),.&'() ! &'$('$ $ -$. 2*H),.&'() ! &'$('$! ! ! ! ! ! "J

7!D !"#$"% /&- &.)-+,&- 3). ,$%&'() &) *F.$,) /$ &=&%2&'G$- /& H;*<

'() )AI$+2=)! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "JN

7!N 8).C&,&'() /) /$-$.C$*?) 3).C;+&32)*&% /) 40LM 3). & 2*-$,<

'() /& C,$/&'() $ /& A;-3& %)3&%! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ""

7!6 !"#$"% /&- &.)-+,&- 3). ,$%&'() &) *F.$,) /$ &=&%2&'G$- /& H;*<

'() )AI$+2=)! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ""D

4!" 8)*9:;,&'() /&- &,O;2+$+;,&- .$-+,$ 2%?&> 3$%;%&, $ -$,2&%! "5

4! 8).C&,&'() /) /$-$.C$*?) 3).C;+&32)*&% $*+,$ &- &,O;2+$+;,&-

.$-+,$ 2%?&> 3$%;%&, $ -$,2&%! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "5E

P!E Q1/2& /& C),3$*+&:$. /$ 3)*=$,:R*32&> ,$-+,2+& & 5.000.000 /$&=&%2&'G$-> /) 40L ?@A,2/) C&,& 3&/& -)%;'() $*3)*+,&/& /;,&*+$

&- 210 $S$3;'G$-! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "5B

!"#$ %& '()&*!$#+)$"

!"#$%&'("& )#*+"%,-.

!" #$%&'()%" !*+,('-%"

!." #$%&'()%" !*+,('-%" ./&/#*#%"

!.0 #$%&'()% !*+,('-% ./&/#*#% 0*#1#/&

!.2 #$%&'()% !*+,('-% ./&/#*#% 234&'5%

!.6 #$%&'()% !*+,('-% ./&/#*#% 6#7/

!.89 #$%&'()% !*+,('-% ./&/#*#% 8*"(&*:*"-&/;%

8.602 ?

!"#$ %& '()*+,+"

!"#$%$ &'()*+,-$

A(e) !"# $% "&"'"()% )!*#(+,!. -#'.% "&/)!*0%

β -%"10*"()" $" 2*'")!*# $% "20%#'"()%βreal -%"10*"()" $" 2*'")!*# $% "20%#'"()% .!%3"(*"()" $%

'%$"&% "4."!*'"()#&

βaprox -%"10*"()" $" 2*'")!*# $% "20%#'"()% .!%3"(*"()" $%'%$"&% (,'/!*0%

a -%"10*"()" $% .%&*(5'*% &*("#!In -%'.%("()" $# 0%!!"()" "&/)!*0# 6%, 3%&)#+"'7 (#

$*!"89% $% 3")%! (%!'#& /

σ -%()!#2)" "&/)!*0%σaprox -%()!#2)" "&/)!*0% #.!%4*'#$% !"2,&)#()" $% '%$"&%

(,'/!*0%

σreal -%()!#2)" "&/)!*0% !"#& !"2,&)#()" $# '%()#+"'"4."!*'"()#&: %, ';(*'% +&%

!"#$%$ &'()*+,-$

qreal !"#$ %& '$((&)*& &!+*(,'- (&-! (&."!*-)*& %- /$)*-0&/&(,/&)*-!

α (-23$ %& 4-5,$ ,).*-)*6)&- %$ &.'$-/&)*$αreal (-23$ %& 4-5,$ %$ &.'$-/&)*$ $7*,%- 1&!$ /$%&!$

&(,/&)*-!

αaprox (-23$ %& 4-5,$ %$ &.'$-/&)*$ $7*,%- 1&!$ /$%&!$)"/+(,'$

∂Ω ($)*&,(- %$ %$/8),$Γq ($)*&,(- %$ %$/8),$ &/ 9"& - '$)%,23$ %& '$)*$()$ %&

:"#$ %& '$((&)*& + -1!,'-%-

e ")',$)-! %& &(($ $" ;")23$ $7&. %& ;$(/-

µ%sucesso =+%,- %- 1$('&)*-0&/ %& '$)4&(0@)',-A (&.*(,*- -BCDDDCDDD %& -4-!,-2>&.

µAV =+%,- %$ )E/&($ %& -4-!,-2>&. %- ;")23$ $7

!"#$%$ &'()*+,-$

+./ !"#$ %! &'"!&$#( )*! +#'",- #( .'%&+!( %/ +#0*'/ %#(

+#!1+&!'"!( '2# '*0#( %/ -/"$&3 40#5/0

(/ !"#$ %! 6#'"#( 7*"*/'"!( )*! +#'",- #( +#!1+&!'"!(

'2# '*0#( %/ -/"$&3 40#5/0

ψ !"#$ %! 6#"!'+&/&( !0,"$&+#( '#%/&(0 !"#$ *'&"8$ '#$-/0 /# %#-.' ΩΩ #0*-! %! (!'(#$&/-!'"# #* (!:2# %/ "*5*0/:2#

(*5-!"&%/ ; "#-#4$/1/ #* %#-.'

V #0*-! %# !0!-!'"#

!"#$%&

!"#$%

&'"()*+(

, -.()%/#01% 23

! "#$%&'()# *'+' # ,+'-'./# ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 01

!2 3-45$% ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 0

!0 3+7'8%9'()# :# ,5;$# ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 02

2 !45"1% 65'75%8)9:+* ;<

2! ,#)%G

'7!$* ?%$%8)9:+% H,

G! D#8=7J+'()# :5 H.7#+%$

!"#$"# %&'()*+,# " -"#&.$/0,# 12

!" #$%&'( ') *+$( ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ,-

!- .)$%)$ /(0 ($ 0(')1($ 2+3+1)1($ ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ,4

!4 .)$%)$ /(0 2)5+167+89( '+ :&589( (;@

! .)$%)$ /(0 + 23)'+89( ) + ;&$/+ 1(/+1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "">

!A *(5$6')3+8B)$ C65+6$ ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ""@

3 4,5+."# 221

A!" *(5%36;&68B)$ ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "--

A!- D)3$2)/%6=+$ ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "-4

-"7")85+*/# 29

:;850*+" : < !"#$"# +,' :.=,)*$',# >"5($*+,# ?")*/. " @/)/."., 2A2

:;850*+" B < !"#$"# 0, :.=,)*$', CDE)*0, +,' F*7")"5$"# G/.H/#

4,';&$/+*,5/*# 2AI

:5"J, : < @)*5+D;*, 0,# @,$"5+*/*# K*)$&/*# 2 2

!"#$%&'

(

!"#$%&'($

!"#$%$&&$ $' (!&)*+!,*% * -.'/.&!01. !"#$%"* 2$ )' /%.-$&&. .) -.%/. -)3.

*-$&&. * 2!&/.&!#!(.& !"#%)&!(.& -.'. '!-%.4-5'$%*& 6 2!78-!+9 !"(!:($+9 .) '$&'.

!'/.&&8($+9 /%./.%-!.".) . 2$&$"(.+(!'$"#. 2$ '6#.2.& 2$ $!'*01. 2$ !'*;$"&9

-.'

C+6' 2!&&.9 $&&* #6-"!-* #*'

+0$$,"(1,9 QRRRT .(22 34 5679 UVVST +,$$,..% &!''!()*9 UVVW@B

L' 2$&$"(.+(!'$"#. 2$&2$ * 26-*2* 2$ 809 * IKL 6 )'* #6-"!-* 2$ '."!4

#.%*01. "1. !"#%)&!(*9 A)$ /$%'!#$ * .

!

!"#$%&'#() #!*#+%,&%) %&+- !% +.''%,&%/ %(0&'"+#/ % $%!"12. !. 3%'4( !% 5.(%,/

'%/7(,&%/ 3.' $%". !% %(%&'.!./ 3./"+".,#!./ #. '%!.' !# &787(#12. % #(",9#!./

%$ 7$ 3(#,. +.''%/3.,!%,&% # 7$# /%12. &'#,/5%'/#(: ;//%/ !#!./ /2. ?(./ % 3'.!7@"' 7$# "$#6%$ !# +.$3./"12.

",&%',# !. $%". /%,/.'"#!.: A 3'.+%!"$%,&. !%/+'"&. #,&%'".'$%,&% 3.!% /%' 5"/&.

,# B"67'# C:C:

B"67'# C:CD E3#'#&. 3#'# .8&%,12. !% "$#6%,/ !. %/+.#$%,&. 3.' $%". !# FG;:

G,"+"#($%,&%) . 3'.+%!"$%,&. !# FG;

!"#$%&'()% !

!"#$%& '$" & () $&*)"!$%+),- ."/0&$ %$*$&&1' " " &)2345) ($ 3! 6')72$!" %8$'&)

%" 9:;- )3 &$

? 6')72$!" $! @3$&+5) = %5)02 %$"'- 3!" 8$/ @3$ " .3%45) @3$ '$6'$&$%+"

" 8)2+"#$! )7+ (" %) *)%+)'%) (" +3732"45) ($6$%($ ($ .)'!" %5)02 %$"'- +"%+)

(" *)''$%+$ $2=+' *" "62 *"(" %)& $2$+')()&- @3"%+) (" ( &+' 73 45) ($ *)%+'"&+$

$&+ !"(" 6"'" " '$# 5) (" +3732"45) *3 :&&) 6)($ &$' .$ +) 6)' !$ ) ($

3! .3%* )%"2 ($ $'') @3$ @3"%+ T@3$ " ( .$'$%4" $%+'$ "& !$( ("& $P+$'%"& %5)

%+'3& 8"& EV3P) ($ *)''$%+$ $2=+' *" '$"2, $ "& !$( ("& *"2*32"("& %) !)($2)

%3!=' *) EV3P) ($ *)''$%+$ $2=+' *" "6')P !"(),>

9'"7"2R)& "%+$' )'$& E./(- %-) (-"1%0) !"!#$%& '(- JKKNI (-"1%0- JKKW,

6$'! + '"! *)%R$*$' $! ($+"2R$& "& 6' %* 6" & *"'"*+$'B&+ *"& +)6)2U# *"& () .3%0

* )%"2 ($ $'')- &)7'$+3() "@3$2"& "&&)* "("& ") !"3 *)%( * )%"!$%+) %+'B%&$*)

() 6')72$!"> ;&&"& *"'"*+$'B&+ *"&- ( +"& X6"+)2U# *"&Y- &5) ($+$'! %"%+$& %) ($0

&$%8)28 !$%+) ($ !=+)()& ($ )+ ! /"45) *"6"/$& ($ *)%8$'# ' 6"'" " &)2345) ()

! ! "#$%&'()# *'+' # ,+'-'./#

!"#$%&' %& (%& " ')%*+')" '!' ', ' $-.'/0%, %& 1-,('2

3-&+$'/0%, 4+&5!-.', %6(%4,-1', !%'$-7')', "! 8'!",-"9 :"$4-; % 3%$%! ?@AABC &",(!'!'& *+% ' !-4.- '$ '("$"

."!!%('9 4' !%,%4/' )% \ '("$"

,03),$ % &&,*24,9 XYY_M )#" 56 7899 @AAaC9 ' &'-"! '!(% )", %,(+)", '!'

!%."4,(!+/E" )% -&'

!"#$%&'()% !

!"#$%& '( )(*+ "&+% %,-+ !)( .!/"0%*& 12",!+"+!3"&45 *( !*+% !( '( '(/6*!(5 &%/ "

*%)%&&!'"'% '% %)(*&+ 2#7( +(/(0 89)"5 %*12"*+( 12% (& /-+('(& !*'! %+(&5 +"/:

;-/ )( *%)%/ 2/" !/"0%/

'% 3",( %& ";&(,2+(& '( )(*+ "&+% %,-+ !)( .!/"0%*& %"!&45 %&(,3%*'( ( ? (;,%/"

!*3% &(@

A ",0( !+/( '% (+!/!="#7( )(/ ;"&% %/ BCD&5 %/ %&+2'( *%&+% + ";",( '% !/?%'I*)!" %,-+ !)" - &!/?,%& '% 2&" % /2!+(

/"!& ;" "+( '( 12% (& +(/H0 ">(& '% "!(&:J % %&&(*I*)!" /"0*-+!)" . !""!#$%&

'()*5 KLLM45 +( *"*'(:( /"!& ")%&&63%, "(& )%*+ (& '% ?%&12!&" % !*'N&+ !"&@ B,-/

'!&&(5 *7( %O?$% 2&28 !(& " 12",12% +!?( '% "'!"#7(@

!" #$%&'()*+

P%&+% + ";",

Q%&&% /('(5 "& &%02!*+%& /%+"& !*+% /%'!8 !"& &7( "? %&%*+"'"&R

• S%3!&7( ;!;,!(0 89)" &(; % 2&( '% BC& *" &(,2#7( '% ? (;,%/"& !*3% &(&

/", )(*'!)!(*"'(& % &(; % ? ()%&&"/%*+( ?" ",%,(T

• D (0 "/"#7( % +%&+%& %O+%*&!3(& '% '!>% %*+%& !/?,%/%*+"#$%& '% BC& %

'%9*!#7( '% %&+ "+-0!"& % ?" "/%+ !="#7( H+!/"& ?" " ( ? (;,%/" %&+2'"'(T

• F/?,%/%*+"#7( '% BCD&5 +%&+%& %O+%*&!3(& )(/ '!>% %*+%& %&+ "+-0!"& '%

?" ",%,!="#7(T

• U",!'"#7( '" /%+('(,(0!" '%&%*3(,3!'" )(*> (*+"*'(:&% %&2,+"'(& *2/- !:

)(& )(/ 3",( %& %O?% !/%*+"!&@

A '%&%*3(,3!/%*+( '% 2/ ",0( !+/( (+!/!="'( ?" " "& )(*'!#$%& '( ? (;,%/"

+ "+"'( % !/?,%/%*+"'( '% /('( " (;+% " &(,2#7( .!/"0%/ ? ()2 "'"4 %/ +%/?(

3!83%, -5 ?( +"*+(5 ( (;V%+!3( >2*'"/%*+", '%&+% + ";",

! !" #$%&'()&*+, -, ./01,

!"#$%&'( )& #$*&+,-# )( .'(/&' 01(+)# ( 234 5#+1.1*& &' #$*&" ( ).16

*".$0.,-# )# 5#+*"(1*&7 80& &80.9(%& : ).1*".$0.,-# )& 5#+)0*.9.)()& !("( ;0.)#1

5#+)0*.9#1 #0 !&"'.11.9.)()& !("( ;0.)#1 .1#%(+*&17 80& '.+.'.# )& 5#""&+*& &%?*".5( '&).)# +#1 &%&*"#)#1 & # ;0># )& 5#""&+*& 5(%50%()#

+# '#)&%# 5#'!0*(5.#+(%7 )( 1&,-# )( *0$0%(,-# @50A( .'(/&' ? )&1&A()(BC

D 1#%0,-# )&11& !"#$%&'( )& #*.'.

!"#$%&'()%

• !" #$% &'! ()"*&*+,(-(& (& .!+./0&1*& -( )*&203&( -*&*+4!/43-( * &0(&

.!+,"350361*&% 5*$ .!$! )*"&)*.,34(& )("( &0( .!+,3+03-(-*7

• 8! 9):+-3.* 9 &'! ()"*&*+,(-!& !& "*&0/,(-!& -!& ,*&,*& +0$;"3.!& .!$)(<

"(+-! ! -*&*$)*+=! .!$)0,(.3!+(/ -!& 9>& &*"3(/ * )("(/*/!7 ?& "*&0/,(-!&

-!& ,*&,*& +0$;"3.!& .!$ ! 9> =@5"3-!% 0&(+-! $(/=(& .!$)0,(.3!+(3& -3<

A*"*+,*& )("( "*&!/4*" ! )"!5/*$( -* BCD% &'! ()"*&*+,(-!& +! 9):+-3.* E7

• 8! 9+*F! 9 ; ()"*&*+,(-( ( -*-06'! -! "3+.@)3! -!& !,*+.3(3& G3",0(3&7

! !" #$%&'()&*+, -, ./01,

!"#$%&'

(

!"#$%& '#()#&*+,-./

!"#$%& %' #&(&)*'+' ',-./'%' 0 1*!' (2%./'3 %!"%! ' %2/'%' %! 503 ! &

!"#$%& %' #&(&)*'+' ',-./'%' ' ,*&/!""&" .4%$"#*.'."3 %!"%! ' %2/'%' %! 803 %!"5

,!*#'( & .4#!*!""! %! ($.#&" ,!"6$."'%&*!" 4' !7&-$89& %'" #2/4./'" #&(&)*1+/'":

" ,*.(!.*&" #&(;)*'

K&"#!*.&*(!4#!3 #2/4./'" C'"!'%'" !( *'%.'89& )'('3 $-#*'5"&(3 /&**!4#! !-25

#*./'3 /'(,&" (')42#./&" ! (./*&&4%'"

(!%.%'" %! /','/.#D4/.' %'"

! !" #$%$&'()( *$' +%*,-./01( 2345'10(

! "#$%!& '& (& ) ) *+,'-. !/&0)$ '& '! "+!1-!23, ') %,$'-"!4!'&') ', /)!,

)$ ,+!&',5 6 %,/1!$&23, '& ",/,0+&7& *,+ %&*&%!"8$%!& ) +) ! "#$%!& ')-

,+!0)/ 9 :;

!"#$%&' ($)*$'+,-./0 !

2

4

~

......

3

1

!"#$% &'() *$+,-.!/-01+ 2%$% +31-045+ .- !/%"-06 6-"#0.+ % 789'

:66!/; + ,-$0- .% 789 < .-6,+3$!$ % .!61$!3#!45+ .+ ,+01$%61- -=-1+

?2+$ -@-/2=+; -6,+%/-01+A 2+$ /-!+ .- /-.!.%6 ,+=-1%.%6 0% B$+01-!$% 2+$ 6-0C

6+$-6 ?-=-1$+.+6A -; % 6-"#!$; #1!=!D%$ #/ ,+/2#1%.+$ 2%$% $-,+061$#!$ % !/%"-/

.+ +3>-1+' : .!61$!3#!45+ .% 2$+2$!-.%.- 2=+1%.% -/ 0EF-!6 .- ,!0D% < #6#%=/-01-

,G%/%.% .- !/%"-/ - 2+.- 6-$ #6%.% 2%$% .!%"0H61!,+ -/ ,-$1%6 %2=!,%4I-6 /-45+ /%!6 #6#%!6; 2%$% #/% J0!,% B+01- .- F+=1%"-/ ?+#

! !" #$%$&'()( *$' +%*,-./01( 2345'10(

!""#$%#&' ()! * *+,* #$%# # * +-*.#%"*/0 1 !$234"*5)! *+,* #$%# !$(-(%# #.

-$,#%*" 6!/%*3#$( 7!4 !""#$%#(& -34*-( # +# (-$*-( !8!(%!( #. #/#%"!+!( *+,* #$%#(0

9* !$234"*5)! +-*.#%"*/' !.! ! $!.# (43#"#' * -$,#5)! : ;#-%* #. #/#%"!+!(

/! */-' M4# : *8"#(#$%*+* * (#34-"0

!"!" #$%$&'(%)*$+,- .- /%-01(2$ .( 3-2-4%$5$ 6-% 726(8

.9:&)$ ;1

!"#$%&' ($)*$'+,-./0 !

!"#$"%!"&' ()%!*& !+& ,- .&!,$./0$!"& *% $1./"%2+&' 0%3 3/0 *& 0$.%!/30&

"#%!34%* $ *% #$35&3"%' */673$ ()$ & 5#&89$0% : /!;$#3&<

=/!%90$!"$' )0 5#&89$0% : */"& /!;$#3& "&0&>#-?.&' &) 3/059$30$!"$ "&0&7

>#-?.&' ()%!*& % /!.@>!/"% : & 0$.%!/30& "#%!34%* $ $1./"%2+& $ #$35&3"%

3+& .&!,$./*&3< A $1$059&' *$ %.*& .&0 % =/>)#% B$0 *& $3.&%7

0$!"&' ()$ 3$ 9/0/"% %& 59%!& .&05&3"& 5$9&3 $9$"#&*&3 1 $ 2H' *%*%3 %3 0$*/*%3

&8"/*%3 $0 1 $ 3<

I5$3%# *% %8*%>$0 $0 "$#0&3 *$ $1./"%2+& $ #$35&3"%3 3$# 3/059$3' 5#&7

89$0%3 /!;$#3&3' 0%"$0%"/.%0$!"$' 5$#"$!.$0 J .9%33$ *$ 5#&89$0%3 0%9 5&3"&3<

K$>)!*& L%*%0%#* GCMNOH' )0 5#&89$0% : */"& 8$0 5&3"& 3$ 3)% 3&9)2+& &8$*$.$#

.&!.&0/"%!"$0$!"$ J3 "#P3 .&!*/2Q$3 % 3$>)/#R

• 1/3"P!./% 7 & 5#&89$0% *$;$#- %5#$3$!"%# 3&9)2+&S

• T!/./*%*$ 7 % 3&9)2+& *$;$#- 3$# U!/.%S

• 3"%8/9/*%*$ 7 % 3&9)2+& *$;$#- $1/8/# *$5$!*P!./% .&!"V!)% $ 3)%;$ $0

#$9%2+& %&3 *%*&3 *$ $!"#%*%<

I ()$3"+& *% $1/3"P!./% *% 3&9)2+& F)3"/?.%73$ 5$9& 4%"& *$ ()$ ?3/.%0$!"$

$1/3"$ 3&9)2+& $' 0%"$0%"/.%0$!"$' &8":073$ )0% 3&9)2+& %5#&1/0%*%< E33& *$;$7

3$ %& 4%"& *$ ()$ & 0&*$9& 0%"$0-"/.& 5&*$ "$# %5#&1/0%2Q$3 $ $1/3"/# $##&3

!)0:#/.&3 $ $15$#/0$!"%/3<

0 #$9%2+& J )!/./*%*$' )0 #$3)9"%*& 3/>!/?.%"/;& %": & 0&0$!"&' 5%#% */7

0$!3Q$3 0%/$3 &) />)%/3 % "#P3' : 5%#% .&!*)"/;/*%*$3 3%"/34%6$!*& % .&!*/2+& *$

W/53.,/"6 G !"#!$"%&'( '%)*+%),-( .*/0'%%' BXXYH< I/!*% ()$ % )!/./*%*$

$!.&!"#$73$ >%#%!"/*%' Z.$% GBXXBH .&!.9)/) ()$' >$#%90$!"$' !+& : 5&33V;$9 %

$1/3"P!./% *$ )0% 4@#0)9% $159V./"% *$ #$.&!3"#)2+& *& /!"$#/ *& *&0V!/&< K$

)0 5#&89$0% $1/8$ 0U9"/59%3 3&9)2Q$3' %3 /!4%2Q$3 ()$ *$?!$0 & &5$#%* 3+&

/!3)?./$!"$3 5%#% *$3.#$;P79& .#$"%0$!"$< I33/0' .#/":#/&3 %*/./&!%/3 8%3$%*&3

$0 /!4%2Q$3 #$%9/3"%3 *% 0&*$9%>$0 *$;$0 3$# %*&"%*&3

! !" #$%$&'()( *$' +%*,-./01( 2345'10(

!"#$%&"' (! )*"!%$+$(!() , "$(' -'.' ' .!$* $./'#"!0")1 23 4&) , /#!"$-!5

.)0") $./'**67)+ -'07)#8$# /!#! ! *'+&9:' *). -'0*$()#!# '* );)$"'* ()8)0)#!"$7'*

(' #&6(' !($"$7' *'%#) '* (!('*1 ' '/)#!('#1 '& !", .)*.' !* +$.$"!9'# ?.1 '* /#'%+).!* $07)#*'* 7$'+!. ! ")#-)$#! -'0($9:' () @!(!.!#( /'#

*)#). $0"#$0*)-!.)0") .!+ -'0($-$'0!('*= A !7!+$!9:' , ($"! .!+ -'0($-$'0!(!

4&!0(' &. /)4&)0' )##' 0' /'0"' () !7!+$!9:' !;)"! ;'#").)0") ' 7!+'# (! ;&09:'=

B31 4&!0(' )*"! , %). -'0($-$'0!(!1 ' 7!+'# (! ;&09:' 0:' , !;)"!(' *$80$?-!"$5

7!.)0")= C) !-'#(' -'. D$+7! E)"' ) F'! E)"' GHIIJK1 &. )##' 0' -3+-&+'1

/'# .)$' () &. (!(' )L/)#$.)0"!+ '& () &. !##)('0(!.)0"'1 /'() /#'(&M$#

($7)#*'* );)$"'* 0' #)*&+"!(' ?0!+1 -'.' #)(&9:'1 /)#.!0)-)# /)4&)0' '&1 !$0(!1

!./+$!9:'=

N'8'1 ' /#'%+).! () OPQ , $0"#$0*)-!.)0") .!+ -'0($-$'0!(' )1 ()**) .'('1

)L"#).!.)0") *)0*67)+ 0! /#)*)09! () )##'* "!0"' () 0!")M! )L/)#$.)0"!+ 0!*

.)($(!*1 4&!0"' () !##)('0(!.)0"' 0'* (!('* (' /#'-)**' -'./&"!-$'0!+= Q**!

*)0*$%$+$(!() , -'./#'7!(! /'# D)+)8R$. B# ) F$+$'+$ GHIISK 0! #)*'+&9:' () R$*"'5

8#!.!* () ($T.)"#'*1 ! /!#"$# (' R$*"'8#!.! () -'#(!*1 '%"$(' () &.! *'0(! ()

()")-9:' () ;!*)1 $.)#*! ). )*-'!.)0"' ! %'+R!*= * !&"'#)* /#'7!#!. 4&) )##'*

(! '#(). () 0, 01% ). !./+$"&()1 0'* (!('* () )0"#!(! G-'#(!*K1 /#'(&M$#!.

()*7$'* () .!$* () 100, 00% 0! *'+&9:' #)-'0*"#&6(! 0&.)#$-!.)0")=

C)7$(' !' .!& -'0($-$'0!.)0"'1 !* ",-0$-!* () #)-'0*"#&9:' -+3**$-!* *:' "$(!*

-'.' $./#U/#$!*1 7$*"' 4&) /'**&). #)*'+&9:' /'%#)1 %!$L! ($*"$08&$%$+$(!() )

/#'(&M). !#");!"'* 4&)1 ). 8)#!+1 7$'+!. +)$* ;6*$-!* -'.' ;#!9

!"#$%&' ($)*$'+,-./0 !

!"#$%&' ( )*&"!"+,)-) $.) /&"0" -"!1&%234 !4/&" 4! ,&5! *)!!4! )1%.)' 6$"

14.*7". ) ,(1+%1) -" 89:;

!"! #$%&'%( )* #+,+-.(/( 0+. 1,0*)2&%'( 34$5.'%(

4&.)27"! "!*)1%)%! " ,".*4&)%! -4 ?$%-4 *4& ."%4

-" -%0"&!4! !"+!4&"! *4!%1%4+)-4! )4 &"-4& -) &"#%34 -" %.*4&,@+1%);

4&.A0"B H !"# $%L' 6$"

"!,)/"B"1". $. 1).*4 14+O+)-4 " $+%>4&." +) &"#%34 -" !"+!4&%)."+,4; B(.

-%!!4' 4 1).*4 "!,)/"B"1%-4 %+-"*"+-" -) -%!,&%/$%234 -) *&4*&%"-)-" -"+,&4 -4

04B$." -" !"+!4&%)."+,4' 14.4 4! &)%4!=P; N4 "+,)+,4' ) ,4.4#&)O) -" *&41"!!4!

>)D $!4' +) .)%4&%) -)! 0"D"!' -" !"+!4&"! -" 1).*4 -">4&.A0"B H'()* $%L' 6$"

#"&). $. 1).*4 +34 C4.4#5+"4 " 14. $.) -"*"+-5+1%) +34 B%+")& ". &"B)234

Q -%!,&%/$%234 -) *&4*&%"-)-"' *4& "R".*B4' 4! !"+!4&"! "B(,&%14!;

%+?$5+1%) "+,&" 4 1).*4 "B(,&%14 " 4 ."%4 !"+!4&%)-4' +4 $!4 -" !"+!4&"!'

>)D 14. 6$" )! B%+C)! "6$%*4,"+1%)%! H1).%+C4 *"&14&&%-4 *"B) 14&&"+," "B(,&%1) 4$

,"+!34L !" -">4&.". ". ,4-)! )! -%&"27"!; S"!!" .4-4' 4 ">"%,4 '()* $% T$!,%O1)

) -%!1&"*@+1%) "+,&" ) %.)#". &")B " ) #"&)-) *4& ."%4 -" !"+!4&"! "B(,&%14!

$!)+-4 $. .(,4-4 ,&)-%1%4+)B -" &"14+!,&$234; :!!) -%O1$B-)-" +) &"14+!,&$234

-" %.)#"+! ,4.4#&AO1)! ( "!1B)&"1%-) *4& U"%+"1G" " V"W"! HIJJKL;

X%!,4 6$" 4! !"+!4&"! "B(,&%14! !34 !"+!Y0"%! Q! .$-)+2)! +) -%!,&%/$%234 -4

14+,&)!,"' !$) %+!,)B)234 -"0" *"&.%,%& 6$" 4! !%+)%! &"!$B,)+,"! -" 1)-) !"+!4&

-"*"+-). -) 14+!,%,$%234 -4 ?$%-4 +4 %+,"&%4& -) &"#%34 !"+!4&%)-); 8&)-%1%4=

+)B."+," !34 %+!,)B)-4! N "B",&4-4! &"#$B)&."+," "!*)2)-4! )4 &"-4& -4 4/T",4

" $. *B)+4 H14&,"L ( -"O+%-4; :. !"#$%-)' N − 1 "B",&4-4! !34 -"O+%-4! *)&)

."-%& 14+14.%,)+,"."+," ,"+!34 4$ 14&&"+," &"1"/%-) ) O. -" #"&)& N(N − 1)/2

! !" #$%$&'()( *$' +%*,-./01( 2345'10(

!"#"$% #&"!'!&"!&(!% ! ) !*!(+)") +!%($&(! , -(#*#.$") /) ) 0)&(! "! /)++!&(! )-

(!&%1)2

3)4)5 $ +!/)&%(+-61) %! *# #($ $) '*$&) /) ')%() '!*)% !*!(+)")%2 7)&(-")5

8!(9!+$** !( $*2 :;2 E*, "#%%)5 )% $-()+!% #&0!+#+$ @-! '$+$ FGH (+#"# !&%#)&$* :3D> 0$.I

%! &!/!%%A+#$ - $ +!/)&%(+-61) () )4+AJ/$ $ '$+(#+ "! "$")% )B(#")% "! ()"$ $

0+)&(!#+$ ") ?)*- ! ") )BC!()2

E $"#61) "! !*!(+)")% "! 4-$+"$ )B+#4$&") - $ "#%(+#B-#61) '$+$*!*$ ! /)&JI

&$"$ ! - '*$&) ") /$ ') %!&%)+#$") , - $ $*(!+&$(#?$ '+)')%($ ')+

8$ !( $*2 :;

!"#$%&' ($)*$'+,-./0 !

!"# $%!&$'()"!!*#"+,(-.

/ 01*234*4" 4* 3#*5"# "!,6 '"2*)3(+*4* *( 5'*1 4" 3+,'1!373234*4" *)"3,68"2

)(# '"!$"3,( *( !3!,"#* 4" !"+!('3*#"+,(. 9"51+4( 9"2"5:3# ;' " >?-@

4(3! '"013!3,(! A1+4*#"+,*3! 4"8"# !"' )(+!34"'*4(!B

• / !(+4* +C( 4"8" !"' 3+,'1!38*@ (1 !"D*@ (7D",(! 4" #"43EC( +C( 4"8"# !"'

3+,'(41F34(! +* ,1712*EC(@ "G)213+4(@ *!!3#@ ( 1!( 4" H(! $'($(!,( $(' I*!

" J*,,*+*K*L =>>M-N

• O 8(21#" 4" !"+!('3*#"+,( 4"8" !"' 23#3,*4(@ (1 !"D*@ ( 3+,13,( P '"41F3'

(! "A"3,(! 4" #P43* 2(+53,143+*2 " *1#"+,*' * '"!(21EC( +"!!* 43'"EC(@ '"!&

,'3+53+4( * *4(EC( 4" "2",'(4(! 2(+5(! $'($(!,* $(' ?- )(+!3!,"

"# 4(3! "2",'(4(! "# A('#* 4" *+"2 43!$(!,(! *( '"4(' 4* ,1712*EC(. /2P# 43!!(@

"2* P 7*!"*4* +( *!$"),( ('353+*2#"+," "!)(2:34( $(' /!*23 =>?U-@ " $(!,"'3('&

#"+," $(' /+4'"1!!3 =>??-.

V 3#$(',*+," '"!!*2,*' 01" * !(+4* 4" 83!1*23F*EC( 43'",* *$'"!"+,*4* $('

9"2"5:3# ;' " >?- $'(41F 3#*5"+! 4" *2,* $'")3!C( " "# ,"#$( '"*2.

W3+*2#"+,"@ )(# '"2*EC( X '"!(21EC( 4( $'(72"#* 3+8"'!(@ * 23,"'*,1'* !"#

$%&@ =>?MN '!()**@ =>?MN +,&+!&@ =>?>- *$(+,* 4(3! 5'1$(! 4" #P,(4(! $*'* *

!(21EC( 4( $'(72"#* 3+8"'!(B (! *25('3,#(! +C(&3,"'*,38(! " (! *25('3,#(! 3,"'*,3&

8(!@ 01" !C( *$'"!"+,*4(! * !"513'.

!"!# $%&'()*+', -.(. /01'2,*(345' 6. 7+.&0+ 2. 8'+'9

&(.:. -'( 7+-06;21). >\N $.)*-/ 9&!!$*%"/

+&%("@ =>>UN ').,@ Q\\^-@ '")(+!,'1EC( 4" 3#*5"+! 3D -:&), / ;)< % 2@

Q\\\N &%'")2@ Q\\M-@ #(4"2(! 4" "2",'(4(! $*'* #"2:(' '"$'"!"+,*EC( 4*! )(+43&

E_"! 4" )(+,('+( 8)$$!&/ )$,, $%"/ "!(!''@ =>>\- " #P,(4(! +1#P'3)(! )(#

!" #$%$&'()( *$' +%*,-./01( 2345'10(

!"#$ %&'( $&)*+',()+- ( & &()"-.()+- ( / !"#$ % &$'()$"0 12345 *+*#!,-0

677389

:* #&;

!"#$%&' ($)*$'+,-./0 !

!" #$%& '( )(*#% +#" "!,#%&)( " - % ./ 0 !(% '" 0(!# 1"/ 2(. )(%%"*#" "!,#%&) 3

&/-(+#(4 '"#"%/&* 5+" '&+#%&6.&78( '( ) /-( &*#"%*( '" #"*+9"+ 2-(#"*)& &+

"!,#%&)(+3 '( '(/:*&( +.6/"#&'( ; #(/(1% < 4 =."4 "/ +"1.&' 4 , )(/- % ' )(/

'&+#%&6.&78( '" #"*+9"+ /"'&' -%"0& /"*#">

? '&@"%"*7 "*#%" + '&+#%&6.&79"+ ' + #"*+9"+ 2-(#"*)& &+ "!,#%&)(+3 /"'&' "

) !).! ' -('" +"% .#&!&A ' - % 1.& % ( !1(%/(4 C" / *"&% *G!(1 4 +"

( 0 !(% '"++ '&@"%"*7 2@.*)&(* ! '" "%%(3 @(% *.!( (. "+#&0"% 6"/ -%$B&/( '"

A"%(4 "*#8( '&+#%&6.&78( '( )(*#% +#" "!,#%&)( , )(*+&'"% 0"!/"*#" -%$B&/ '

'&+#%&6.&78( %" ! 2&/ 1"/ -%().% ' 3>

H(1(4 -('"5+" @(%/.! % ( -%(6!"/ &*0"%+( '" IJK )(/( ./ -%(6!"/ '" (#&5

/&A 78( "/ =." '&+#%&6.&78( '( )(*#% +#" "!,#%&)( , %"

P&/4 Q"6+#"% " I(/-R&*+ 2MNOS3 '"+"*0(!0"% / ./ /,#('( "% #&0( =."

)(*+&+#" "/ -"%#.%6 % / #%&A '" +"*+&6&!&' '"+ '" /('( =."4 "/ ) ' "% 78(4

'&+#%&6.&78( '( )(*#% +#" "!,#%&)( "+#&/ ' +"D )(%%&1&' > L.#%(+ !1(%/(+

"% #&0(+ 6"/ )(*T")&'(+ +8( (+ 6 +" '(+ *( /,#('( '" U"V#(*5W -T+(* 2$"#%%

&' ()*4 MNNX34 # &+ )(/( ( !"#$%" U"V#(*5W -T+(* 2+,"-#+. /# %0#"4 MNOY34

( &%'(!)*+ ,)% -(%. /00!0 1%2!)+(032(#!) 212#3#+ &' ()*4 MNNZ3 " (.#%(+ 2/,,

&' ()*4 MNNS[ #451 &' ()*4 MNNO3>

C&0"%+(+ !1(%/(+ '" %")(*+#%.78( '" &/ 1"*+ -!&)G0"&+ ; IJK @(% / -%(5

-(+#(+ 2 !" #"4 MNON[ 12#3#+. 5%!!1%,3. 3#/#664 MNNN[ ,"1#!4 XZZX34 (65

D"#&0 *'( *8( +$ /"!T(%& * =. !&' '" ' &/ 1"/4 / + # /6,/ ( ./"*#(

' 0"!()&' '" * (6#"*78( ' &/ 1"/> \(% "B"/-!(4 (+ !1(%/(+ "% #&0(+

+8( / &+ +"*+:0"&+ %.:'(+ *(+ ' '(+ @(%*")&'(+ ( !1(%/( " &/ 1"/ , (65

! ! "#$%&'()%* +,-.('/%*

!"# $% &% $%'( %#!() *+"( ,(%'#)#"# # !%#-$% (. !"# '() #/-()! %(0

+1(2! $)# !3(04 5+ )$ #+ (6 (0 #/-()! %(0 ! $)# !3(0 '$)%! $% $0 !%#) (0 3#/()$0

#.0(/& (0 "( ,(+ )#0 $ $/7 )!,( ,(% &%# ')$,!01( %#!()6 '(!0 +1( &0#% 8!'9 $0$0

0!%'/!:,#"()#0 ,(%( "!0 )!.&!;1( 8(%(-/-()! %(0 T$+7 !,(0 A%9;6/ 16&6/ T $ 0 #'/!,#;1( $% ')(./$%#0 "$ ?@54 >T0 '#)#/$/(0

#%.7% 01( #')$0$+ #"(04

! "#$%&'()%* +,-.('/%*

Z% #/-()! %( 7 ,(+0!"$)#"( &% %7 ("( 8$&)Y0 !,( *+"( B()+$,$ 0(/&;[$0

0$% &% /!%! $ B()%#/ "$ */!"#"$6 &0/%$+ $ #3#/!#"( "$ %("( $%'Y)!,( $%

$)%(0 "$ ,(%'/$=!"#"$ A%7"!#C $ */!"#"$ "#0 0(/&;[$0 A.'' '26 FGGUC4

\ $0 &"( 0(.)$ ( "$0$%'$+8( "$ %7 ("(0 8$&)Y0 !,(06 )$#/!W#"( "&)#+ $ "72

,#"#06 ')('(),!(+(& # $/#.()#;1( "$ $0 )# 7-!#0 -$+7)!,#0 '#)# # ,(+0 )&;1( "$

8$&)Y0 !,#04 500#0 $0 )# 7-!#0 01( ,(+8$,!"#0 ,(%( %$ #28$&)Y0 !,#0 A.'2'&5'/

2%"2!/ 6!&!6 ROOSC4

]$ #28$&)Y0 !,#0 01( 8$&)Y0 !,#0 "$ .&0,# +( $0'#;( "$ 0(/&;[$0 '("$+"( 0$)

,/#00!:,#"#0 $% "(!0 -)&'(04 J( ')!%$!)( -)&'( $+,(+ )#%20$ (0 %7 ("(0 ,&X(

!'( "$ 3#))$"&)# "( $0'#;( "$ 0(/&;[$0 -$)# &% ,#%!+8( (& )#X$ 9)!# "$ 0(/&;[$06

!"#$%&' ($)*$'+,-./0 !

!"#$% &'(% ")%*+#,- $' ./% + (.,- &%)% .")% $' %0 )$ 0 / + / 1#/'*" +

&')/#"#$ + &'(% /'"%23'.)4+"#0%5 6'++' 7).& & $'2+' 0#"%) 0 / '8'/&( + %

9.+0% :%!. ; !"#$%& !' ()'< =>>?@< !"#$%&'( )**'%$!*+ ;$ !$*$< =>>A@ '

B(7 )#"/ C.( + ;+"%,$) -. /01< DAA=@5

E +'7.*$ 7).& 0 /&)''*$' + /F" $ + G.' & ++.'/ '+")%"F7#%+ $' !.+0%

0%&%H'+ $' '8&( )%)< % /'+/ "'/& < 1I)#%+ )'7#J'+ $ '+&%, $' + (.,J'+5 B++#/<

% ( *7 $%+ #"')%,J'+ *- +' !"F/ ./% ")%K'"L)#% M*#0% $' !.+0%< 1#+" G.' * 1%+

+ (.,J'+ +- '*0 *")%$%+ & ) /'# $' 0 /!#*%,- $' + (.,J'+ %*"')# )'+5 E+ BC+

; "!23$% < =>N>O ,4+5'!$64+7< =>>P@ ' % ,%&&'- '%-,. ; !"#$%< =>>Q@ +-

'8'/&( + $' /F" $ + $'++' 7).& 5

E+ BC+ R )%/ 0)#%$ + & ) S ((%*$ ;=>>D@ *% T*#1')+#$%$' $' U#03#7%*< *%

$F0%$% $' 60< ' %&)#/ )%$ + & +"')# )/'*"' ;$F0%$%+ $' 60 ' 70@5 V*#0#%(/'*"'<

S ((%*$ *- "#*3% 0 / !K'"#1 7')%) ./ &) K'" $' ./ %(7 )#"/ G.' + (.0# 2

*%++' &) !('/%+ '+&'04W0 +< /%+ +#/ %*%(#+%) R'*X/'* $% %$%&"%,- 0 ))#$

*% *%".)'H% ' $'+'*1 (1') R'))%/'*"%+ G.' #/& )"%++'/ /'0%*#+/ + $% %$%&"%,-

*%".)%( &%)% ./ +#+"'/% 0 /&."%0# *%(5

Y'7.*$ S ((%*$ ;=>>D@< + BC+ ")%*+R )/%/ ./% & &.(%,- #*#0#%( '/ ./%

* 1% & &.(%,- & ) /'# $% +'(',- *%".)%( K.*"%/'*"' 0 / + &')%$ )'+ #*+2

)%$ + *% 7'*F"#0%< . +'K%< &%)"'/ $ &)#*04 G.' #*$#14$. + *% & &.(%,-

/'* + %$%&"%$ + "Z/ 7)%*$' 03%*0' $' +')'/ '(#/#*%$ + %*"'+ /'+/ $' 7')%)'/

$'+0'*$'*"'+5

[%)% % %&(#0%,- $ BC< &) !('/% $'1' & ++.#) ./ '+&%, $' !.+0% * G.%(

)'+#$%/ " $%+ %+ & ++41'#+ + (.,J'+< ' ./% R.*,- !K'"#1 &%)% %1%(#%) %+ + (.,J'+

&) $.H#$%+< %")#!.#*$ % 0%$% + (.,- ./% * "% ;!'+$%2'& +'%#'!5"< =>>>@5

E"#/#H%) ./ &) !('/%< '/ "')/ + /%"'/I"#0 +< F '*0 *")%) % + (.,- 0 ))'+2

& *$'*"' % & *" $' /I8#/ . $' /4*#/ $% R.*,- !K'"#1 < . +'K%< /%8#2

/#H%*$ 7%*3 . /#*#/#H%*$ 0.+" 5 B(F/ $#++ < C ($!')7 ;=>N>@ +#*"'"#H . %+

&)#*0#&%#+ $#R')'*,%+ '*")' + BC+ ' + %(7 )#"/ + $' "#/#H%,- 0 *1'*0# *%#+<

+'*$ '(%+\

• ]#$%) 0 / ./ 0 *K.*" $' + (.,J'+ 0 $#W0%$%+ ' *- 0 / %+ + (.,J'+ )'%#+O

• ^'%(#H%) % !.+0% 0 / )'(%,- % ./% & &.(%,- $' + (.,J'+ ' *- 0 / %&'*%+

./% + (.,- O

! ! "#$%&'()%* +,-.('/%*

• !"#"$%& "'()&*%+,-. /% (0'+1) )23-!"4) - '1) /- .0%. /-&"4%/%. )0 50%#50-&

)0!&) 6)'7-6"*-'!)8

• !"#"$%& 9&"'6:9"). 9&)2%2"#:.!"6). - '1) /-!-&*"':.!"6).;

!"#$%&' ($)*$'+,-./0 !

!"#$%$&$'('" )*"+",-" ,.+ /+ )*.0.1( . (23+-" '" +3( 1.,453*(67.8 1.9.

( "+1.&:( ()*.)*$('( '( 1.'$41(67.8 ( $,$1$(&$;(67. '( ).)3&(67.8 .+ .)"*('.*"+

'" *")*.'367.8 "-1< 1.,453*(67. '" /+ = ()*"+",-('( ( +"53$*<

! !" #$%&'()*+,$ -. /0'$)123$4 5.%6217$4

)*"+",-(>+"8 ,"+-( +"67.8 ( 1.,453*(67. '" /+8 $,1&3$,'. ( 1.'$41(67. '.

)*.%&"9(8 ( $,$1$(&$;(67. '( ).)3&(67.8 ( +"&"67.8 .+ .)"*('.*"+ '" *")*.'367. "

. 1*$-=*$. '" )(*('(<

?*$9"$*(9",-"8 '"0">+" 1.,+$'"*(* ( *")*"+",-(67. '. )*.%&"9( ,( $9)&"9",>

-(67. '. /8 $+-. =8 ( *")*"+",-(67. '"0" 9()"(* . "+)(6. '" +.&36@"+ ,. "+)(6.

'( 1.'$41(67. '" 9(,"$*( A3" +" )*"+"*0"9 (+ 1(*(1-"*B+-$1(+ C3,'(9",-($+ '.

)*.%&"9( .*$5$,(&<

1.'$41(67. = 39 '.+ ).,-.+>1:(0" +"53,'. /", " D:",5 EFGGHI< J9( 0";

A3" 39( 1.'$41(67. $,('"A3('( ).'" C(0.*"1"* 39( 1.,0"*5K,1$( )*"9(-3*( '.

(&5.*$-9.8 .3 +"2(8 ( .%-",67. '" 39 L-$9. &.1(&< J9 (&5.*$-9.8 ).* "#"9>

)&.8 A3" ).++3( *")*"+",-(67. %$,M*$(8 ()&$1('. ( )*.%&"9(+ 93&-$'$9",+$.,($+8

'" (&-( )*"1$+7.8 '.9B,$.+ 1.,-B,3.+ " A3" ).++3(9 *"+-*$6@"+ ,7. -*$0$($+8 )*.>

'3; $,1.,0",$",-"+ 1.9. "&"0('. -"9). 1.9)3-(1$.,(& )(*( ",1.,-*(* ( +.&367.

L-$9(8 A3(,'. ",1.,-*(8 " C(&-( '" :(%$&$'('" "9 .)"*(* ,( )*"+",6( '" *"+-*$>

6@"+ ,7. -*$0$($+< N,-*"-(,-.8 ,( 1.'$41(67. *"(&8 39 $,'$0B'3. = 1.'$41('. 1.9.

39 0"-.* '" ).,-.+ !3-3(,-"+8 . A3" )"*9$-" ( *"'367. '. -"9). 1.9)3-(1$.>

,(&8 0$+-. A3" . (&5.*$-9. ,7. ,"1"++$-( '" *.-$,(+ '" 1.'$41(67. " '"1.'$41(67.

E !"#$%&'!"(8 FGGOI<

/+ A3" ).++3"9 1.'$41(67. ,7.>%$,M*$( +7. ()&$1('.+ "9 93$-.+ )*.%&"9(+

'" ",5",:(*$(8 -($+ 1.9.P )*.2"-. '" +$+-"9(+ '" '$+-*$%3$67. '" ","*5$( "&=>

-*$1( E)*+ %!!8 QRRQI8 )*.2"-. ("*.'$,S9$1. '" (+(+ '" (0$@"+ E,-$ $+ ,.$-$)#!+

/$0$ *1$8 QRRFI8 .3 ($,'( -"&"1.,-*.&" '" 9B++"$+ E%!/+ %$!8 QRRFI< N +7. ()&$>

1('.+ -(9%=9 "9 )*.%&"9(+ -"L*$1.+ 0$+(,'. "+-$9(* )(*S9"-*.+ '( C3,67. '"

'$+-*$%3$67. '" T"$%3&& E2#, $) 34 5678 FGGUI .3 -*"$,(* *"'"+ ,"3*($+ *"1.**",-"+

E.%$/",+ 8&%9$8,+ :&9$%$;$18 QRRFI8 " "9 )*.%&"9(+ '" VWN E"#,+ 0! + %&&8

QRRFX #)!$,+ "#$#!/&+ 9* &1,

! ! "#$%&'()%* +,-.('/%*

!"#"$%&' ( #)"*%!+,"% -., )/0#% 10 234 10 5# 06( %#0*! #5/!"786"( 9 0 1 #:;

*" 6 1"6(,0! 6< !%#)=# . 6650# "*( >0*"0*!06 ( # 0/0>%1 !0#. ( #.5!%(" *%/

.%,% 0*( *!,%, % 6 /5&' +!"#% 0 56 0?(066"> 10 #0#+,"%@

A *6"10,%*1 !%#%*B 1% . .5/%&' < !0#;60 C50 ( # 5#% . .5/%&' .0;

C50*% 1060#.0*B 1 DE = )%"? < . "6 !%#%*B 1% %# 6!,% 1 06.%& 10

)56(% 1%6 6 /5&F06 *' = 6"G*"H(%!"> < 0*C5%*! C50 ( # 5#% . .5/%&' G,%*10

.,0>"*0;60 ( *>0,GI*("%6 .,0#%!5,%6< #%6< !0#. 10 0?0(5&' = %/! - !"#$

%#$ '(# (#< JKKKL ( !)< JKKM9@ N' 0?"6!0 5#% ,0G,% .%,% 60 10!0,#"*%,

!%#%*B "10%/ 1% . .5/%&' < #%6 = ( #5# 60, %/G5#%6 >0$06 !%#%*B 1

(, # 66 # .%,% C50 B%O% 5#% ) % %# 6!,%G0# 1 06.%& 10 )56(%@ P%,% (%1%

., )/0#%< = *0(0668," %>%/"%, 1">0,6 6 !%#%*B 6@ P, )/0#%6 ( # ( ,,0/%&F06

0*!,0 %6 >%,"8>0"6 ( 6!5#%# ,0C50,0, . .5/%&F06 #%" ,06@

D "*"("%/"$%&' %/0%!+,"% 1 6 "*1">:15 6 * 06.%& 10 6 /5&' = #=! 1 #%"6

56%1 *% (,"%&' 1% . .5/%&' "*"("%/ -*+%,&< JKKQ9@ D.06%, 1"66 < 60 B 5>0,

( *B0("#0*! .,=>" % ,06.0"! 1 ., )/0#%< 0660 . 10 60, %., >0"!%1 *% "*"("%;

/"$%&' 1% . .5/%&' ( # 5#% B05,:6!"(%@

R"70,0*!06 06!,%!=G"%6 10 60/0&' 6' 106(,"!%6 *% /"!0,%!5,% -- !!.&/< STTJL

0 !/%,(0< STUTL "#1-.!,2#1*< STTVL "#31-,!!< STTV9< (%1% 5#% ( # . 66:;

>0"6 >%,"%&F06 10.0*10*1 10 ,0C5"6"! 6 #%!0#8!"( 6 06.0(:H( 6 5 (,"!=," 6 10

1060#.0*B ( #.5!%(" *%/@

D6 06!,%!=G"%6 10 60/0&' #%"6 565%"6 6' % 60/0&' . , , /0!% 0 % 60/0&' . ,

! ,*0" @ N% 60/0&' . , , /0!% 6' 10H*"1%6 ., )%)"/"1%106 10 60/0&' ., . ,(" ;

*%"6 W %.!"1' 1 6 "*1">:15 6< 10 # 1 C50 6 #%"6 %.! 6 !0*B%# #%"6 (B%*(06

10 60,0# 60/0(" *%1 6@ N% 60/0&' . , ! ,*0" < "*1">:15 6 1% . .5/%&' 6'

%/0%! ,"%#0*!0 60/0(" *%1 6@ X "*1">:15 C50 )!">0, #%" , >%/ , 10 %.!"1' < . ,

0?0#./ < ,070,"*1 ;60 % 5# ., )/0#% 10 #%?"#"$%&' < = 60/0(" *%1 @

A # )O0!"> 10 )!0, 5# ,065/!%1 6%!"67%!+," < 0#.,0G%;60 6 .0,%1 ,06 10

,0., 15&' C50 !,%*67 ,#%# % . .5/%&' % / *G 1%6 G0,%&F06< . 10*1 #%*!0,

(%,%(!0,:6!"(%6 1 6 #0/B ,06 "*1">:15 6 0 "*!, 15$", 1">0,6"1%10 . .5/%(" *%/@ X6

.0,%1 ,06 10 !"#$$#%&" 0 #5!%&' 6' 6 .,"*(".%"6 .0,%1 ,06 56%1 6 0# DE6@

Y0G5*1 % /"!0,%!5,% -"#1-.!,2#1*< STTVL "#31-,!!< STTVL 0,&$ 1-,&0<

STTZ9< . 10;60 %./"(%, !"#$$#%&" .%,% ,0.,060*!%&' )"*8,"% 10 >8,"%6 #%*0",%6[

!"#$%&' ($)*$'+,-./0 !

• ! "#$%#& ' "'(%)( *+ ,! "#$%# +-.#/0)*# '/+'%#()'!+$%+ #, 0+,()-%).'1

!+$%+ '- )$2#(!'34+- 5+$6%).'- *#- "')- -+(7# %(#.'*'-8

• 9,/%)"#$%#-& *#)- #, !')- "#$%#- *+ .(,:'!+$%# "#*+! -+( ,%)/):'*#-;

,'/ ' "(#?'?)/)*'*+ *+

.'*' 5+$+ -+( %(#.'*# +$%(+ #- "')-;

@' (+"(+-+$%'37# +! "#$%#- A,%,'$%+-B # "(#.+--# *+ (+"(#*,37# "'(' 2#(1

!'( ' 5+('37# -,.+--#(' "#*+ -+( )!"/+!+$%'*# .#!?)$'$*#1-+ #- .(#!#--#!#-

*+ *#)- #, !')- "')- .#$2#(!+ (+5('- +-"+.CD.'-; E+--+ !#*#B '/5,$- %)"#- *+

!"##"$%! -7#& !"##"$%! 5+#!6%().# F !"#$%&&'B GHHI8 ()'! (* "' +,-.B GHHGJB

!"##"$%! '()%!6%).# F"!/%(B GHHG8 .'-* #0'-.B GHHK8 ,$-%1* ('$'.0%2 + B

LIIMJB !"##"$%! "#( (+.#!?)$'37# 5/#?'/ *)-.(+%' F'%3'-* (#0%))' (B GHHNJ +

!"##"$%! "#( (+.#!?)$'37# >,'*(=%).' F$%!-.* 4!,* -'56,-B GHHHJ;

O !"##"$%!B ,-,'/!+$%+B .#$2+(+ '# '/5#()%!# ,!' .'('.%+(C-%).' *+ ?,-.'

+-%#.=-%).' /#.'/ .'"': *+ .#$P+(5)( "'(' ,!' -#/,37#B "#(6! *+ !#*# /+$%# +

5('*,'/; Q#$%,*#B # '/5#()%!# 6 '"()-)#$'*# + %#($'1-+ )$.'"': *+ .#$P+(5)( "'('

' -#/,37# .#((+%' $' #.#((R$.)' *+ "'%#/#5)'- .#!# !C$)!#- /#.')-B "#$%#- *+ -+/'

#, (+5)4+- "/'$'- .)(.,$*'$*# ' (+5)7# *+ '%('37# *# !C$)!# 5/#?'/ F ,$-%1B

LIISJ; T/5,!'- *+--'- "'%#/#5)'- "#*+! -+( #?-+(P'*'- $' U)5,(' L;L;

! ! "#$%&'()%* +,-.('/%*

!"#$% &'&( )#*+$,-.!+/ 0+ 12!3!4%561 %//1.!%0%/ %1 ,#7.!17%8 0+ +$$1 .13 *%21819

"!%/ 2!*1 *8%2: + *1721 0+ /+8%'

172+( ;187!< + )+8+"=!3 >$ ?&@@AB'

C 3#2%561D 1#2$1 1*+$%01$ 0+ $+*$10#561 E%/2%72+ #2!8!4%01D %82+$% %8+%21$!%9

3+72+ #3 1# 3%!/ "+7+/ 0+ #3 .$131//131' C 2%F% 0+ 3#2%561 G 0+H7!0% .131

% *$1E%E!8!0%0+ 0+ 1.1$$I7.!% 0% 3#2%561 +3 #3 "+7+' J+$%83+72+D % 2%F% 0+

3#2%561 G E%!F%D *1!/ 1 1EK+2!L1 G "+$%$ 0!L+$/!0%0+ +F2$% 7% *1*#8%561 +L!2%701

#3% .17L+$"I7.!% *$+3%2#$%' M3% 2%F% 0+ 3#2%561 %82% *10+ .13*$13+2+$ %

+L18#561 KN %8.%75%0% *+8% E#/.%'

O% $+*$+/+72%561 E!7N$!%D % 3#2%561 *%0$61 /!3*8+/3+72+ !7L+$2+ 1 L%81$ 0+

#3 "+7+D *1$ +F+3*81D /+ 1 "+7+ /+8+.!17%01 2+3 L%81$ 1D +7261 .13 % 3#2%561D

+/2+ L%81$ *%//%$N % /+$ 0' >N 7% $+*$+/+72%561 +3 *1721 P#2#%72+D #3 1# 3%!/

"+7+/D /+8+.!17%01/ *%$% % 3#2%561D /61 %82+$%01/ /+"#701 #3 !72+$L%81 +/*+.-H.1'

Q//+ 2!*1 0+ 3#2%561 G 0+713!7%0% 3#2%561 #7!,1$3+ ? !"#$%&'!"(D RSSAB'

T Q8!2!/31D U#+ .17/+$L% #3 .+$21 7V3+$1 0+ 3+8=1$+/ !70!L-0#1/ *%$% %

*$WF!3% "+$%561 % H3 0+ *$+/+$L%$ % +L18#561 01 *$1.+//1D G 1 3+.%7!/31 0+

/+8+561 3%!/ #2!8!4%01 *%$% 3+8=1$%$ % .17L+$"I7.!% 01 CJ ? !)"#&%%D RSSAB'

!7%83+72+D .13 $+8%561 %1 .$!2G$!1 0+ *%$%0%D #/#%83+72+D !70!.% % +F!/2I79

.!% 7% *1*#8%561 0+ #3 !70!L-0#1 U#+ $+*$+/+72+ #3% /18#561 %03!//-L+8 *%$% 1

*$1E8+3%D 1#D U#+ 1 7V3+$1 3NF!31 0+ "+$%5X+/ ,1! %2!7"!01D 1#D U#+ 761 =1#L+

3%!/ 3+8=1$% 01 %8"1$!231 71 *$1.+//1 0+ .17L+$"I7.!%'

!"#$%&' ($)*$'+,-./0 !

!"##$%$&$'(') ') $*+,"'-.$, ,)#+,$/0)# ('$1$"*($#2 ,)!,)#)*+(+$3(# ') $*4",5(6

/7" 1"*8)1$'( !"#$"#2 9 -5( 3(*+(:)5 $5!",+(*+) '"# ;#2 *" +"1(*+) < #"&-/7"

') !,"%&)5(# $*3),#"# 5(& 1"*'$1$"*('"#= >) (1",'" 1"5 ;)* ) ?8)*: @ABBCD2 '$6

3),#(# )#+,(+9:$(# 4",(5 !,"!"#+(# !(,( 5(*$!-&(, ,)#+,$/0)# 1"5 ;#2 +($# 1"5"E

• "#$%&$'()& *+ %+,+)-./E ')#1(,+( +"'"# "# 1,"5"##"5"# $*3$F3)$# !,"3)6

*$)*+)# '" !,"1)##" )3"&-+$3"= G) " )#!(/" ') %-#1( 9 1"*3)H"2 )*+7" )#+(

)#+,(+9:$( 4-*1$"*( %)5= I*+,)+(*+"2 !(,( !,"%&)5(# ') "+$5$.(/7" 1"5 ,)#6

+,$/7"2 )5 J-) ( !"!-&(/7" 1"*#$#+) %(#$1(5)*+) ') 1,"5"##"5"# $*3$F3)$#2

+(& (%",'(:)5 (!,)#)*+( 1"*#$'),F3)$# &$5$+(/0)#K

• "#$%&$'()& *+ %+0&%&-./E +,(*#4",5( -5 1,"5"##"5" $*3$F3)& )5 -5

3$F3)& (!&$1(*'" (&:-5 !,"1)'$5)*+" ') ,)!(,(/7"= I##) !,"1)'$5)*+" 9 4(6

1$&5)*+) :),('" !(,( 5-$+"# !,"%&)5(# ') "+$5$.(/7" 1"5%$*(+L,$(= M",952

-5 (&:",$+5" ') ,)!(,(/7" )#!)1NO1" ')3) #), !,"P)+('" !(,( 1('( !,"%&)5(

!(,+$1-&(, ')3$'" < #-( ')!)*'Q*1$( )5 ,)&(/7" (" !,"%&)5(= &95 '$##"2 "

!,"1)'$5)*+" ') ,)!(,(, 1,"5"##"5"# $*3$F3)$#2 )5 (&:-*# 1(#"#2 !"') #),

+7" 1"5!&)H" J-(*+" #"&-1$"*(, " !,"%&)5( ",$:$*(&K

• "#$%&$'()& *+ 1/*)23&-./ */# /0+%&*/%+# (+4'$)3/#E !,"P)+( "!)6

,('",)# :)*9+$1"# )#!)1NO1"# !(,( " !,"%&)5(2 3$#(*'" 5(*+), ( 3$(%$&$'(')

'" 1,"5"##"5"= ##$52 )##( )#+,(+9:$( *-*1( !,"'-. #"&-/0)# $*3$F3)$#=

?"*+-'"2 !(,( !,"%&)5(# 1"5 ,)#+,$/0)# 5-$+" #)3),(# )5 J-) ( !,)#)*/(

') #"&-/0)# $*3$F3)$# *( !"!-&(/7" 9 #$:*$O1(+$3(2 5"'$O1(, "# "!),('",)#

:)*9+$1"# !"') #), +7" "- 5($# 1"5!&)H" J-(*+" #"&-1$"*(, " !,"%&)5( ",$6

:$*(&K

• "#$%&$'()& *+ 0+4&5)*&*+E (!&$1( !)*(&$'(')#

! ! "#$%&'()%* +,-.('/%*

!"#$%& ' ()*!+'*#+' , !"#$%&&- .//01 '())* +)%% (,- .///2- 345 56& #*)7

()8'%&5 !9 %):!+5&5 ;+&

!"#$%&' ($)*$'+,-./0

!"#$ %"& !!&'&()* $ +,%"-.$/ "0 !"#$ 1$!!&'#$(.&(.$ *' 2$+3*' & "0 !"#$

%"& #$.& !!&'&()*! )*()$ +,%"-.$ %"*()$ 2$+3*'4

5&*+-6*7'& $ #!$1&''$ .& * !"#*0&()$ &0 ."*' &)*#*'4 8* #!-0&-!* &)*#*/ $

9: ; *#+-1*.$ #*!* 1+*''-$ .$ -854 8* '& "(.* &)*#*/ * 1+*''-$ !""# A !""#$"%&&/

BCCBD ; *#+-1*.*/ 1$0 2*'& (* *+)&!*=>$ .$ ?*+$! .$ 1$()!*')& &+;)!-1$ .& "0 @(-1$

!"#$ .& 0*+3* *$ +$( $ .*' -)&!*=E&' .$ -85/ #*!* ?*+-.*! * 1+*''-$ $2)-.*

#&+$ 9:4

F' !&'"+)*.$' $2)-.$' #$! G3$/ H-0 & I&& AJKKBD (>$ 1$0#!$0&)&!*0 * !&7

'$+"=>$ &'#*1-*+ .* -0* &0 & 0$')!*!*0 !*#-.&6 (* $2)&(=>$ .* '$+"=>$ A-0* &0

$2)-.* &0 )&0#$ -(L&!-$! * 2 0-(")$'D4 M''$ .&?&7'& *$ L*)$ .& %"& 0;)$.$'

-)&!*)-?$'/ 1$0$ -85/ $2)N0 !*#-.*0&()& * -0* &0 & $ "'$ .* 0*+3* *.*#)*)-?*

2*'&*.* &0 "0 9:7 !""# (>$ 1$0#!$0&)& * !&'$+"=>$ &'#*1-*+ .* -0* &04

O()!&)*()$/ .* 0*(&-!* 1$0$ L$- L$!0"+*.$ $ #!$2+&0* A-0#$'-=>$ .& 1$!!&()&

&+;)!-1* ($' &+&)!$.$'D/ $ *+ $!-)0$ #$.& L*+3*! 1*'$ 3*P* *+ "0* 2$+3* (* #*!&.&

.* )"2"+*=>$ &0 1$()*)$ 1$0 $' &+&)!$.$'4 M''$ #$!%"& '& 3$"?&! 2$+3*' AQ"-.$

(>$ 1$(.")-?$D &0 1$()*)$ 1$0 * #*!&.& &0 %"& &+&)!$.$' &')>$ -(')*+*.$'/ *

!&'#$')* A)&('>$D * "0* &R1-)*=>$ &0 1$!!&()& &+;)!-1* )&(.&!S *$ -($ !&*+/ $ *+ $!-)0$ (>$ ; ?-S?&+4 U*!* $")!$' )-#$' .&

&'1$*0&()$'/ &0 %"& (>$ 3S Q"-.$ -'$+*()& &0 1$()*)$ 1$0 * #*!&.& .* )"2"+*=>$

A#$! &R&0#+$/ &'1$*0&()$ *("+*!D/ $ *+ $!-)0$ &0 %"&')>$ ; *.&%"*.$4

V'-*$/ G3*3-(& & :"0&!$? AJKKBD .&'&(?$+?&!*0 "0 0;)$.$ .& $)-0-6*=>$

A*+ $!-)0$ 3,2!-.$D 2*'&*.$ &0 9:' A'()*+#$'/ BCWCD & ($ 0;)$.$ .& U$X&++

A%,-(&/ BCCKY .$#// 01 234/ BCCJD #*!* !&'$+?&! $ #!$2+&0* -(?&!'$ .& ZMO4 9+;0

.-''$/ $ 1$(1&-)$ .& $)-0-6*=>$ .& U*!&)$ A,5#&'6 )!/ BCCWD/ *#+-1*.$ * #!$2+&0*'

0"+)-$2P&)-?$' .& ZMO/ L$- #!$#$')$ #*!* 0&+3$!*! $ .&'&0#&(3$ .$ 9:4

F *+ $!-)0$ 3,2!-.$ 1$('-')& &0 &R&1")*! $ 9: #!-0&-!*0&()&4 9#[' "0

.&)&!0-(*.$ (@0&!$ .& &!*=E&' ANgD/ $ 0;)$.$ .& U$X&++ ; *1-$(*.$4 9 0&+3$!

'$+"=>$ .* #$#"+*=>$ *)"*+ .$ 9: ; $ 13")& -(-1-*+ .$ 0;)$.$ .& U$X&++4 \& $

0;)$.$ .& U$X&++ (>$ *)-( & $ 1!-);!-$ #*!* $ 0,(-0$ +$2*+/ &()>$ * !$)-(* .&

$)-0-6*=>$ !&)$!(* *$ 9:/ %"& ; &R&1")*.$ ($?*0&()& #$! Ng &!*=E&'4 O''&

#!$1&''$ !&)&7'& *); %"& $ 1!-);!-$ .$ 0,(-0$ +$2*+ '&P* *)-( -.$4

! ! "#$%&'()%* +,-.('/%*

! "#!$%&'()! )*&+()! ,)" -!+'). /0'0+1# # 2$3#")4 567789 3)!&"'"'3 :$#

) ;2 ,)!!$+ #%#4'() #!)1!&"$E(' ,#%) '%D)"+&3) 0E*"+() @ 3#%0)" 5,"'&+>'3#1 >)+1>+(# >)3

' +3'D#3 "#'%9 () :$# '! +3'D#3 )*&+(' ,#%) ;2C

/)1&$(). -!+'). /0'0+1# # 2$3#")4 567789 &'3*@3 '()&'"'3 ' '*)"('D#3

(# +3,)!+=?) (# >)""#1 #%@&"+>' 1)! #%#&")()!. :$# >)3) (+&) '1"+)"3#1 1?)

@ $3' '*)"('D#3 4+I4#%C

; "#!)%$=?) () ,")*%#3' +14#"!) (# JKL $!'1() ',#1'! ;2! )3,'"'()! >)3 )! "#!$%&'()! )*&+()! ,)" O#!1+> 567789 $!'1() ) 3@&)() (#

,")D"'3'=?) :$'("I&+>' !#:P#1>+'%C ;2 )*# )! 3#%0)"#! "#!$%&'()! 5+3'D#3

"#>)1!&"$E(' *#3 ,"FG+3' (' +3'D#3 "#'%9. 3)!&"'1()Q!# $3 3@&)() #H>+#1

# ")*$!&). ,'"' (#>&'" ) &'3'10) # ' %)>'%+R'=?) (# +1>%$!S#! 5,)" #G#3,%).

*)%0'!9C L1&"#&'1&). 1#10$3' +1$!&) >)3,$&'>+)1'% () ;2 1'

"#>)1!&"$=?) (' +3'D#3 +)1'('C

M#"'. L%%+)&& # K1D0'3 5677T9 &'3*@3 (#!#14)%4#"'3 $3 3)(#%) (# "#($=?)

*'!#'() 1' 3'%0' () M@&)() ()! L%#3#1&)! (# /)1&)"1) 5 !"#$%& '%('#')(.

67769 ,'"' '$3#1&'" ' &'G' (# >)14#"DU1>+' () ;2 5*$!'& $%%("++& (,-.'*.

677V9. $!'() ,'"' "#!)%4#" ) ,")*%#3' +14#"!) (# JKLC L!!# 3@&)() @ $3' 4'"+'=?)

() ;2 +%0' ,"),)!&) ,)" L*W #& '%C 58XXY9C ; +(@+' @ :$# ) 3)(#%) (# "#($=?)

,"@Q'4'%+# )! >")3)!!)3)! D#"'()! ,#%) ;2 #. #1&?). (#>+(' :$'+! >")3)!!)3)!

(#4#3 !#" '4'%+'()! ,#%) ;2C

Z#!!# 3)(). #!,#"'Q!# (#>&'" #H>+#1#1. () ,)1&) (# 4+!&' (# ,)

>)3,$&'>+)1'%. $3' +1>%$!?) 5,)" #G#3,%). $3' *)%0' (# '"9 #3 $3 >E">$%) 5,)"

#G#3,%). !#=?) &"'1!4#"!'% (# $3' &$*$%'=?)9C ! "#!$%&'()! )*&+()! ,)" M#"'.

L%%+)&& # K1D0'3 5677T9 3)!&"'"'3 :$# ) ;2 ,"),)!&) @ $3 3@&)() ")*$!&) #

#H>+#1 ,'"' (#>&'" ) &'3'10) # ' %)>'%+R'=?) (# +1>%$!S#!C L1&"#&'1&). ) ,)

3@(+) (# #G#>$=?) () ;2 ,'"' "#!)%4#" ) ,")*%#3' &)3)D"IH>)

!"#$%&' ($)*$'+,-./0 !

!"#$% & '&"&()$* +, -.//01 2&3!"4&,5* 6* 78 &39&:$5"$;52! 5! 9,!

! ! "#$%&'()%* +,-.('/%*

!"# $% &%'($)*+,-$) % ()%&"..$'"/*% "/*)" /0.# % $,1%)+*'% "2"&!*" $()%2+3

'$4$'"/*" 5"6". '$+. )7(+4% !" % $,1%)+*'% ." 8"/&+$,9 :.." $!'"/*% 4"

5",%&+4$4" %;.")5$4% $% ." "2"&!*$) !' 4"*")'+/$4% ()%&"..% "' E". B (%..D5", 4"5+4% $% 1$/-% 4" *"'(% 4"

()%&"..$'"/*% (",$ 4+.*)+;!+>?% 4% ".C%)>% &%'(!*$&+%/$, "/*)" %. /0. " @. 5$/*$3

1"/. 4% ()0()+% $';+"/*" ($)$,",% (%..+;+,+*$/4% $/$,%1+$. &%' $ "5%,!>?% /$*!)$,

"2+.*"/*" "' (%(!,$>E". 4+.*)+;!D4$. ".($&+$,'"/*"9

F+5").%. "2"'(,%. 4" +'(,"'"/*$>E". ($)$,",$. (%4"' .") "/&%/*)$4%. /$ ,+*"3

)$*!)$# ."/4% !" $ '$+%) ($)*" 4",". !*+,+6$' $ $;%)4$1"' 4" G4+5+4+)3($)$3

&%/ !+.*$)H /% IJ 4" '$/"+)$. 4+5").$.9 I,1!/. 'B*%4%. !*+,+6$' !'$ A/+&$

(%(!,$>?%# "/ !$/*% %!*)%. ($)*+&+%/$' $ (%(!,$>?% "' 57)+$. .!;(%(!,$>E".

)",$*+5$'"/*" +.%,$4$.9 K!*)%.# $+/4$# !*+,+6$' ($)*". ".("&DL&$. 4$ ".*)!*!)$ 4%

IJ# &%'% $ $5$,+$>?% %! $ )"()%4!>?%# /$ ($)$,",+6$>?%9

K. *)M. '%4",%. ()+/&+($+. 4" IJN.# ."1!/4% $ ,+*")$*!)$ < !"#!$% &'()*+,#

OPPQR -#-.(#(/# OP PSR 0-$)123-4% !*#5+" # TUUUR 0-$)123-4# TUUU=# .?% %.

'%4",%. 4" ($)$,",+6$>?% 1,%;$,# 1)$/!,$)+4$4" 1)%..$ " 1)$/!,$)+4$4" L/$9

K '%4",% 4"/%'+/$4% 4" IJN 1,%;$, B &$)$&*")+6$4% (%) IJ. !" "2"&!*$'

$ )%*+/$ 4" $5$,+$>?% 4%. +/4+5D4!%. E". ()%.("&*+5$. 4% ()%;,"'$ 4" VW:=

4"/*)% 4% $';+"/*" ($)$,",%9 I ()+/&+($, 5$/*$1"' 4".." '%4",% B % '",-%)

$()%5"+*$'"/*% 4% (%4") &%'(!*$&+%/$, ($)$,",%# 5+.*% !"# % '$+%) &%/.!'% 4"

*"'(% 4% IJ# /$ '$+%)+$ 4%. ()%;,"'$. )"$+.# B "'()"1$4% /$ $5$,+$>?% 4%.

+/4+5D4!%.9

K '%4",% '".*)"3".&)$5%# )"()"."/*$4% (",$ X+1!)$ T9Q# &%/.+.*" /$ $5$,+$>?%

.+'!,*Y/"$ 4%. +/4+5D4!%. (%) '"+% 4$ !*+,+6$>?% 4%. 4+5").%. /0.9 Z"1!/4% [$/*A3

N$6 ?% 4" +/4+5D4!%.9 :/*)"*$/*%# % /A'")% 4" /0. ".&)$5%. B

!"#$%&' ($)*$'+,-./0 !

!"#$"%&"'"%&" '"%(! )( #*" ( %+'"!( )" ,%),-.)*(/ )0 1(1*2034( "5,6,%)( *'0

),/&!,7*,34( ,6*02,&8!,0 )(/ ,%),-.)*(/ "%&!" (/ %9/:

m e s t r e

e s c r a v o e s c r a v o e s c r a v o. . .

;,6*!0 ?()"2( '"/&!"@"/A!0-(:

B ,'12"'"%&034( )( BCD 62(702 E 01!"/"%&0)0 %( B26(!,&'( 1:

"#$%&'()% *> D/"*)(@A9),6( )( B26(!,&'( ?"/&!"@F/A!0-(

G%,A,02,H" 0 1(1*2034( )" ,%),-.)*(/

+,&, (%-%. (/ ,%),-.)*(/ /,0, "' 10!02"2(

B-02," (/ ,%),-.)*(/

1') -% /,0, "' 10!02"2(

2345,3(% ( A!,&E!,( )" 10!0)0 %4( E /0&,/ ",&( /,0,

I"2"A,(%" (/ ,%),-.)*(/ '0,/ 01&(/ 10!0 A!*H0'"%&(

C"!" )"/A"%)"%&"/

?*&" (/ ,%),-.)*(/ A(' 1!(707,2,)0)" Pmut+,&, (%-%. (/ ,%),-.)*(/ /,0, "' 10!02"2(

B-02," (/ ,%),-.)*(/

1') -% /,0, "' 10!02"2(

1') -% 6345,3(%

J 026(!,&'( 10!02"2( &!,-,02K *' 1!,'",!( &,1( )" BCD )" 6!0%*20!,)0)" 6!(//0K

*&,2,H0 (/ %9/ 10!0 "5"A*&0! 1!(72"'0/ ,%)"1"%)"%&"/ ,% "!,%)( #*" 0 A('*%,A034(

"%&!" (/ %9/ E */*02'"%&" )"/%"A"//8!,0: L *' 'E&()( '*,&( +&,2K )0)0 0 %0&*!"H0

"/&(A8/&,A0 )( BCK 1(,/ 1"!',&" 6"!0! "/&0&./&,A0/ )" )"/"'1"%M( 1(! '",( )0

"5"A*34( )" ),-"!/0/ -"!/N"/ )( '"/'( 1!(72"'0 A(' 1(1*203N"/ ,%,A,0,/ ),/&,%&0/:

! ! "#$%&'()%* +,-.('/%*

!"!#$%&' (! )*+,-. )!+./!. (' 0!.0' 1+'23!0- #'0 (,4!+!56!. 1-+70!6+'.

86-0-59' (- 1'1$3-%&': 5;0!+' (!

#,-5(' ' .$+E. ! '26!+ .'3$C

%/!. 0!39'+!.: '+,$5(-. (! )*+,-. 1'1$3-%/!. #'5#'++!56!.: (' A$! -. '26,(-. 1'+

$0- ;5,#- 1'1$3-%&'B F.6! 0'(!3': 6-02?0 (! ? 0-56,(-: -(,#,'5-5(' .'0!56! ' '1!+-('+

(! 0,

!"#$%&' ($)*$'+,-./0 !

"#$%&'()% * !"#$%&'()%*+& %& ,-+&.*/0& 1-23

14*(*# P "$56&6$-378#"9 (3%3 $03 %# /30342& N:;0#.& %# +#.378#" ← 1+,-./,(% & (.*/#*/& 0/1/

2/&/ 3/4/ "$56&6$-37=& 0/1/ #0 63.3-#-&

,?3-*# # "#-#(*&4# *4%*?@%$&" %# 3(&.%& (&0 3 36/*%=&

56 & 4;0#.& %# +#.378#" >&. 0;-/*6-& %3 >.#ABC4(*3 6,(7%

D4?*# k < N *4%*?@%$&" 03*" 36/&" 63.3 $03 "$56&6$-37=& ?*E*423F#(#53 k *4%*?@%$&" 43 "$56&6$-37=&

8') 4% 96

G#.# %#"(#4%#4/#"

H$/# &" *4%*?@%$&" (&0 6.&535*-*%3%# Pmut8') 4% 0/1/ #0 63.3-#-&

:;0#.& %# +#.378#" ← 4;0#.& %# +#.378#" + 18') 4% 6,-./,(%

, ?3.*I?#- >.#ABC4(*3 4& 6"#$%&'3-+&.*/0& 3(*03 .#6.#"#4/3 & 4;0#.& %# +#.3'

78#" 4#(#""I.*3" 34/#" %3 /.&(3 %# *4%*?@%$&"J , "$5"/*/$*7=& %&" k 6*&.#" *4%*?@'

%$&" %3 "$56&6$-37=& 6&. &$/.&" k *4%*?@%$&" ?*4%&" %3 0*+.37=& < & 0&.03 /&.&*%3-9 (&0& $03 03-23 $4*%*0#4"*&43- O1DR &$ 2D9 (&0 $0 *4%*?@%$&

#0 (3%3 6&"*7=& %3 03-23J

, 3?3-*37=& < .#3-*E3%3 "*0$-/34#30#4/# 63.3 /&%&" &" *4%*?@%$&"9 #4A$34/&

A$# 3 "#-#7=& # .#6.&%$7=& "=& .#3-*E3%3" -&(3-0#4/# %#4/.& %# $03 6#A$#43 ?*'

E*423473J D0 &$/.3" 63-3?.3"9 &" *4%*?@%$&" "=& %*?*%*%&" # #4?*3%&" (&0 "$3

.#"6#(/*?3 ?*E*423473 63.3 &" 4)" %*"6&4@?#*"9 &4%# 6&"/#.*&.0#4/# "#.=& 3?3-*3'

%&" # .#6.&%$E*.30J D""3" 6&.78#" "#0*'*"&-3%3" %# *4%*?@%$&" +#4#/*(30#4/#

2&0&+C4#&" #0#.+#0 6&. 0#*& %3 +.3%# (&0& .#"$-/3%& %# $03 -#4/3 %*>$"=&

*4%*?*%$3- O#()!**+"+9 UVVVRJ

X 0&%#-& %# ,G! (#-$-3. < #Y#06-*N(3%& 6#-3 M*+$.3 PJZJ

! ! "#$%&'()%* +,-.('/%*

!"#$% &'() *+,-.+ /-.#.%$'

0 !12.-1-34%56+ ,+ 078 /-.#.%$ 9 %2$-:-34%,% 3+ 0."+$!41+ 3'

"#$%&'()% *) 8:-#,+;/% /,0,7-$- #1 !3,!?@,#+ %.-%4+: - %: 1+?!1-34%5C-:

%12.%: ,- %."#3: !3,!?@,#+: :-"#!3,+ 1-/%3!:1+: ,- 2%::-!+ %.-%4

!"#$%&' ($)*$'+,-./0 !

!"# $%!&'#(")* +* ,-% - ./ 0*##-"+*$ +% - ! 12")! 3$!2+% 0*0-&!45*6 .&7

+"##*8 ! )*29%$3:2)"! +*# ./# ($!+")"*2!"# +";)-&(! ! 9!$"!%# +% !"#$$8 ?@ ,-%8 % - ! 12")! 0*0-&!45* * "2+"9'+-* )* ! %&A*$

0*2(-!45* 7 !2("+* 0%&! #%&%45*6

B-##!"+C2% %( !&6 DEFFGH !0*2(! ! "3$!45* )* * - ! #*&-45* 0!$! * 0$*=

%# +! 0*0-&!45*8 9"#(* ,-% ! "3$!45* %2($% 0*0-&!4>%#

+"#("2(!# "2#%$% 9!$"%+!+% 3%27(")! 2!# #-%#6

J% !)*$+* )* ! &"(%$!(-$! D !"#$%&!'8 EFFKL !()!* #+,-!8 EFFFL !"#$%

&!'* .,(/)0+.8 MNNNH8 ! A"

! !" #$%&'()*+,-)& .'%+'&

! "#$"%&'%() *# #+,$($+-*./"# 0( *-1(234!( 5&,236( 42(%*! 307(2!*./"#)

$*2* 8+" (# 30639&6+(# !*3# *$4(# !312"! 6" +!* $($+-*.:( $*2* (+42*) #"1+06(

+! $*62:( "#4*,"-"%36(; 3!$-"!"04*.:( 6( >@A 5&,236( B *$2"#"04*6* 0( >-1(234!( 4;

"#$%&'()% !C A#"+6(D%E631( 6( >-1(234!( F&,236(

G03%3" P #+,$($+-*./"#) %*6* +!* 6" 4*!*05( N*+&+ ,+-+ %B-+-* i 0* !*-5* .+/+@"2" +! 30639&6+( *-"*4E23( i

0') -% .+/+

HI!"2( 6" 1"2*./"# ← 11234+2(% ( %234B23( 6" $*2*6* 0:( B #*43#7"34( .+/+

*+&+ ,+-+ #+,$($+-*.:( .+/+ "! $*2*-"-(

>9*-3" " #"-"%3(0" 30639&6+(# 6" *%(26( %(! * *$436:(

56 ( 0I!"2( 6" 1"2*./"# 7(2 !I-43$-( 6* 72"8JK0%3* 62(7%

093" k < N 30639&6+(# !*3# *$4(# $*2* +!* #+,$($+-*.:( 93?305*L"%",* k 30639&6+(# 0* #+,$($+-*.:(

0') -% 86

*+&+ ,+-+ %B-+-* i .+/+M"-"%3(0" +! 30639&6+( 93?305( j@"2" 6"#%"06"04"# $(2 !"3( 6" i " j>423,+* +! 6(# 6"#%"06"04"# * iN+4" i %(! $2(,*,3-3*6" Pmut

0') -% .+/+

0') -% .+/+ "! $*2*-"-(

HI!"2( 6" 1"2*./"# ← 0I!"2( 6" 1"2*./"# + 10') -% 6234+2(%

!" #$%&'()*+,-)& .'%+'&

H"#4" %*$&4+-( 7(3 *$2"#"04*6* +!* ,2"9" 2"93#:( 6(# $230%3$*3# 4"!*# *,(2D

6*6(# 0"#4" 42*,*-5(C 4(!(12*'* $(2 3!$"6O0%3* "-B423%* " *-1(234!(# 1"0B43%(#;

> =G %(0#3#4" "! 93#+*-3?*2 * %(!$(#3.:( 304"20* 6" +! %(2$( (+ $2(D

%"##( $(2 !"3( 6" !"636*# "P4"20*# 0:( 3042+#39*#; #$"%3'%*!"04") *$-3%*D#"

+! %*!$( "-B423%( 6" "P%34*.:( #(,2" * 72(04"32* "P4"20* " !"6"D#" * 2"#$(#4*

#(,2" "#4* !"#!* #+$"27&%3"; ##"# 6*6(# #:( 7(20"%36(# * +! %(!$+4*6(2 8+"

!"#$%&' ($)*$'+,-./0 !

!"!#$ %#&'!(($)*&( ! %#& +,-# +./ -./0!. / '&.%&(-12& -34!#3/ & .!-& (!3(&)

#-/ &5 6((/ -./0!. 4!. #!(&*+12& 7/-8/9 :+/3 & '&.%/#/ / ; -./0!. &74- / %

&+4#/( 4/ % #/-&)?@5 A &+4#& */ &9 / 4

!" #$%&'()*+,-)& .'%+'&

!"#$%&'

(

!"#$%&'(! )! *"!+%,#& ),

-!#!."&/& 0!" 1#0,)2345& 6%78"54&

!"#$%&'()" *" +#",&-$' *- ./0 1 *'*' +"# %$' -2%'()" *3!-#-453'& +'#6

53'& - +"# 5"4*3(7-8 *- 5"49"#4" '*-2%'*'8: 83$%&'4*" " +#"5-88" *- -89;$%&" -

#-8+"89' ? 089- 5'+;9%&" '+#-8-49' '8 !"#$%&'(7-8

*"8 +#",&-$'8 *3#-9" - 34@-#8"? $"*-&'F-$ $'9-$C935' *' 8-()" 8%,$-93*' E

./0: %8'4*" " H0I +'#' *385#-93J'# " *"$;43" :

9'$,1$ 1 '+#-8-49'*'?

!" #$%&'()*+$ &),-&.,/0)

M -$+#-F" *- %$ 5'$+" *- -=539'()" 8",#- ' !#"49-3#' -=9-#4' *- %$' 8%6

+-#!;53- - " 5C&5%&" *' #-8+"89' 8",#- -89' $-8$' 8%+-#!;53- +-#$39-$ " $'+-'6

$-49" *' 5"$+"83()" *- %$ A%3*" $%&93!C835" +"# $-3" *- 8-48"#3'$-49" -&19#35"?

N"483*-#'4*"68- %$ *"$;43" !-5O'*": 4" 5'8" %$ 5"#9- 9#'48@-#8'& *' 9%,%&'()":

- '88%$34*"68- 2%- " $-3" +"88%3 5'#'59-#;8935'

+%#'$-49- 5"4*%93@': " 5'$+" -&-9#"89C935" #-8%&9'49- ",-*-5- '8 -2%'(7-8 *-

H'=P-&&? L'#' #-*%J3# ' 5"$+&-=3*'*- *" +#",&-$': 4" 5'8" *' ./0: '&F%$'8

QR

! !" #$%&'()*+$ &),-&.,/0)

!"#$%&%& &!'"(!)*+,-.+& &/- +,-$+,+&0 1 2.%3456*!+ ,+ *-..%6$% %(7$.!*+ +"(!*+,+

7 *-6&!,%.+,+ 8+!9+ % +,'!$%:&% - ,-';6!- *-'- -

,%&+*-"(+'%6$- %6$.% -& ".-8(%'+& !,.-,!6?'!*- % %(7$.!*- &% ,@>

F-6&%34%6$%'%6$%> *-6&!,%.+:&% 6 E 7 - *+'"- %(7$.!*-> ρ̂ 7 + ,%6&!,+,% ,% *+.C+>

εr % εo &/-> .%&"%*$!A+'%6$%> +& "%.'!&&!A!,+,%& .%(+$!A+ % %&"%*;)*+0

R *+'"- %(7$.!*- E "-,% &%. %&*.!$- %' $%.'-& ,- "-$%6*!+( %(7$.!*- JφO

E = −∇φ. JP0PO

S

∇ · J = 0. JP0NO

S

-8$7':&% + A%.&/- &!'"(!)*+,+ ,+ %3 % Ω ,%6-$+ - ,-';6!- ,- ".-8(%'+

!"#$%&'()" *" +#",&-$' *- ."$"/#'0' 1"# 2$1-*3456' 7&89#65' !

!" #$%&'()*+)" , -!() .) $)*$ /%'()*+ 0 12%$+) !( *3()/ %*#*%+ .) .%$4

+/%5!%67)$ φ 8!) /)$ -,)( ' )8!'69 :;0$$%(" & *.%67)$ .) & *+ /* " 8!)

.)+)/(%*'( '-?!*$ @'/A()+/ $ .) & *+/ -) *' $!@)/BC&%) . . (C*% " $9 '@-%&'4

.'$ @'/' -%(%+'/ *3()/ .) $ -!67)$ : !"#" DEFG=0 H'% /)$ .)+'-I)$ $ 5/) '$

& *.%67)$ .) & *+ /* $9 '@/)$)*+'. $ ' $)?!%/0

> %*+)/'69 )*+/) . (C*% Ω ) '(5%)*+) )2+)/* & //) @ / ()% .) $)!

& *+ /* ∂Ω ) J .)#*%.' @)-'$ /)-'67)$ )*+/) )2&%+'69 ) /)$@ $+' )-J+/%&'$0 1(

+)/( $ @/K+%& $" %$$ @ .) $)/ B)%+ '@-%&'*. !(' .%$+/%5!%69 .) +)*$7)$ )-J+/%&'$

$ 5/) & *+ /* ) ().%*. ' .%$+/%5!%69 .) & //)*+)$ )-J+/%&'$ /)$!-+'*+)$ !" '

& *+/K/% " %*L)+'*. 4$) & //)*+)$ ) ().%*. '$ +)*$7)$ /)$!-+'*+)$0 >@)$'/ .) ()4

* $ !$!'-" IK !(' +)/&)%/' @ $$%5%-%.'.) 8!) & *$%$+) )( /)'-%M'/ '(5'$ '$ & %$'$

& *+!. )( @'/+)$ & (@-)()*+'/)$ . & *+ /* 0 N)$+) +/'5'-I " & *$%.)/ !4$)

'@)*'$ @/%()%/ &'$ " &!L' +/'*$&/%69 *' +)/(%* - ?%' ('+)(K+%&' '. +'.' J

.'.' @ /

φ(ξ, η) = φexc(ξ, η) @'/' (ξ, η) ∈ ∂Ω, :;0F=

q(ξ, η) = −σ∇φ · n|ξ,η @'/' (ξ, η) ∈ ∂Ω. :;0E=

N'$ )8!'67)$ :;0F= ) :;0E=" φexc .)* +' @)/#- .) +)*$7)$ .) )2&%+'69 :+'(4

5J( &I'('.' .) & *.%69 .) O%/%&I-)+ ! )$$)*&%'- * L'/?9 ('+)(K+%& =" q

/)@/)$)*+' P!2 /)$!-+'*+) :& *.%69 .) N)!('** ! *'+!/'-= ) n J ,)+ /

!*%+K/% " * /('- ' . (C*% Ω ) /%)*+'. @'/' B /'0 Q ,K-%. $'-%)*+'/ 8!)" #4

$%&'()*+)" & *$%.)/'*. 4$) !( @/ 5-)(' &'@'&%+%, " φexc /)@/)$)*+' +)*$7)$ )(

R -+$" q .)* +' &'/?'$ )-J+/%&'$ )( S !- (5 ) σ & //)$@ *.) ' @)/(%$$%,%.'.)" 8!)

J '.%()*$% *'-" )*8!'*+ 8!) @'/' !( @/ 5-)(' /)$%$+%, " φexc +'(5J( .)* +'

+)*$7)$ )( R -+$" q /)@/)$)*+' & //)*+)$ )-J+/%&'$ )( (%-%>(@T/) ) σ /)@/)$)*+'

& *.!+%,%.'.) )( (Ωm)−10

S *$%.)/'*. 4$) ' /)& *$+/!69 + ( ?/K#&'" φexc ) q $9 )$$)*&%'%$" !(' ,)M

8!) ?)/'( !( @'/ & *L!?'. @)- & *+/'$+) %*+)/* " '$$ &%'. .%/)+'()*+) U

.%$+/%5!%69 .'$ .%$+%*+'$ B'$)$ . )$& '()*+ * %*+)/% / . , -!() .) ().%.' Ω0

1( +)/( $ ('%$ )2'+ $" ' /)-'69 )*+/) )2&%+'69 " & *+/'$+) ) /)$@ $+' @ .) $)/

.)#*%.' @ / ()% . @)/'. / B /('- :@/ 5-)(' .%/)+ =

q = ℑ[φexc, σ], :;0DV=

! !" #$%&'()*+$ &),-&.,/0)

!"# #$%& ' # () *+#,-.&+/#+ # &,(0$%& () 10+0 23)* )/ &,(0$%& () 4)!/#,,

+).)+),*)- #& /)-/& 5+&63)/# () 7#3&+ () &,*&+,&8 9,:!#,*& :!) # +) &,-*+!$%&

() σ *),(& &/& (#(&- φexc ) q ' (#(# 5)3# 0,7)+-%& () ℑ ;5+&63)/# 0,7)+-&<

σ = ℑ−1[φexc,q]. ;=8>><

9/ *)+/&- /#*)/?*0 &- 0--& :!)+ (0@)+ :!)A ,& 5+&63)/# (0+)*& & &,*+#-*) σ

' &,2) 0(& ) φA & 5&*), 0#3 )3'*+0 &A ' &6*0(& !,0 #/),*) 5)3# ):!#$%& (0.)+), 0#3

;=8B< ) 5&+ !/# (#- &,(0$C)- () &,*&+,&A ):!#$%& ;=8D< &! ;=8E< ;,& #-& (#

&,(0$%& () 4)!/#,,A ' &6*0(& # /),&- () !/# &,-*#,*)

!"#$%&'()" *" +#",&-$' *- ."$"/#'0' 1"# 2$1-*3456' 7&89#65' !

! "#$%&$' (!) σreal *+,*-# $.+*$ /0 %#0 ,) e1 2)33)3 ")4$ 3' # 4)- +3"4!5

67 , - +"4#3") σreal # 8#4"*4 ,) )3".$!0 3 ) 4)38 3"#3 3 %4) - +" 4+ ∂Ω' !

$#*3 )9#"#$)+")' # 3 0!67 , 84 %0)$# *+:)43 & ;)*"# %!3-#+, 53) $*+*$*1?JA

2# )(!#67 =>1?JA' ψk 37 ;!+6C)3 ,) %#3) - +:)+*)+")$)+") )3- 0K*,#3 ) σk

3 4)38)-"*: 3 - )H-*)+")3 ,) ,)- $8 3*67 1 E / ' # 3 0!67 ,# )(!#67 =>1?@A

8 ,) 3)4 %"*,# "*$*

! !" #$%&'( )* +,-).%'/')$)* 0*1.-), , #2%,), ),0 34*5*-%,0 6'-'%,0

• !"#$%& '( )%)#*!" "+,-.$%/( ,*$"'" 0*+( !-#('( - )%!-#$%/"1 0()%#%2"3

'*45%'"1 *)0"$)" * 0('* #*$ ."5'"6 )%!*#$%" '" !"#$%& 7aij = aji 1 ∀ i, j81

" 0()%#%2%'"'* 7xT Ax = 01 ∀x 6= 08 * " *)0"$)%'"'* 0('*! )*$ /(54$!"'")

"'%"5#*1 0($ !*%( '" *9:";?@ "0+%/"'" "( 0$(.+*!" '* AB? - '*)/$%#" :)"5'(3)* ")

*9:";C*) ,(2*$5"5#*) '" AB?1 '"'" 0*+") *9:";C*) 7D6E837D6F86 G 0(#*5/%"+ *+-3

#$%/( 0('* )*$ '*#*$!%5"'( *! /"'" 0(5#( '( '(!H5%( '%)/$*#( )*,:5'( ( !('*+(

'( >?@ 7 !"#$% '#(#1 IFJK86 L*)#* #$"."+M(1 :! '(!H5%( 0+"5( 72D8 -

/(5)%'*$"'( 0"$" " )*;

!"#$%&'()" *" +#",&-$' *- ."$"/#'0' 1"# 2$1-*3456' 7&89#65' !

! "!#$%&'() $)*#+'&!, -$./% ! ( #$!+'( ! 0123 !4 .+(/4 $ )'5$+ ( $ $ /6

$)$6$%#! 7%'#! $4#8! +$)(&'!%( !4 &!6 !4 "!#$%&'('4 $)*#+'&!4 %! ('4 4$./% ! (

$9"+$448!

φ = Nψ, :;,

$6 ?/$ φ * ! @$#!+ ?/$ &!%#*6 !4 "!#$%&'('4 $)*#+'&!4 $6 &( ( @*+#'&$ ! $)$6$%#!3

N * ( 6(#+'A $ B!+6( ! $)$6$%#! $ ψ * ! @$#!+ ?/$ &!%#*6 !4 "!#$%&'('4 $)*#+'&!4

%! ('4,

C! $D4$ $#$+6'%(+ ! "!#$%&'() $)*#+'&! %! $)$6$%#! #+'(%./)(+ "!+ /6 "!)'%ED

6'! $ "+'6$'+( !+ $6 : !"#$3

φ(e) = a1 + a2x + a3y, :;,

#() ?/$ φ(e) * ! "!#$%&'() $)*#+'&! ! $)$6$%#!3 a13 a2 $ a3 48! !4 &!$7&'$%#$4 !

"!)'%E6'! )'%$(+3 x $ y 48! (4 &!!+ $%( (4 .)!5('4 ! $)$6$%#!, H$44$ 6! !3

&!%4' $+(% ! ! @()!+ ! "!#$%&'() $)*#+'&! $6 &( ( %I ! $)$6$%#! #+'(%./)(+

: $%!6'%( !4 %I4 '%#+J%4$&!4 !/ )!&('43 %/6$+( !4 )!&()6$%#$ %! $)$6$%#! .$+()D

6$%#$ $ 6! ! (%#'DK!+L+'! &!6! %( 2'./+( ;,>3 #$6D4$

ϕ(e)1 = a1 + a2x1 + a3y1,

ϕ(e)2 = a1 + a2x2 + a3y2, :;,MN>

ϕ(e)3 = a1 + a2x3 + a3y3.

-!)/&'!%(% ! ! 4'4#$6( $ $?/(OP$4 :;,MN> "(+( a13 a2 $ a3 !5#*6D4$

a1 =1

2A(e)[ϕ

(e)1 (x2y3 − x3y2) + ϕ

(e)2 (x3y1 − x1y3)

+ ϕ(e)3 (x1y2 − x2y1)], :;,M

a2 =1

2A(e)[ϕ

(e)1 (y2 − y3) + ϕ

(e)2 (y3 − y1) + ϕ

(e)3 (y1 − y2)], :;,MM>

a3 =1

2A(e)[ϕ

(e)1 (x3 − x2) + ϕ

(e)2 (x1 − x3) + ϕ

(e)3 (x2 − x1)], :;,M;>

$6 ?/$ A(e) * ( L+$( ! $)$6$%#! #+'(%./)(+ ( ( "!+

A(e) =1

2[(x2y3 − x3y2) + (x3y1 − x1y3) + (x1y2 − x2y1)] . :;,MQ>

-/54#'#/'% !D4$ (4 $?/(OP$4 :;,MD:;,M;> %( $?/(O8! :;, $ (.+/"(% !D4$

&!%@$%'$%#$6$%#$ ()./%4 #$+6!43 ( +$)(O8! ( $?/(O8! :;, * 4(#'4B$'#( $ ( 6(#+'A

! !" #$%&'( )* +,-).%'/')$)* 0*1.-), , #2%,), ),0 34*5*-%,0 6'-'%,0

!" #$%&'(" ( #)*+! ,"- . ! ! /)*

N1 = α1 + β1x + γ1y, ,0123-

N2 = α2 + β2x + γ2y, ,0124-

N3 = α3 + β3x + γ3y, ,0125-

(+ 6$(

α1 = x2y3 − x3y2, α2 = x3y1 − x1y3, α3 = x1y2 − x2y1,

β1 = y2 − y3, β2 = y3 − y1, β3 = y1 − y2, ,0127-

γ1 = x3 − x2, γ2 = x1 − x3, γ3 = x2 − x1.

8( !9)* ) 9)+ ! :()*;! ) ? /) (@"( )A:(* ! +!:*;B ( 9)%:*!":( (C.:*;9)

) (C(+(%:) ! /!*:;* ! (D/*(""E) ) F*;%9G/;) )" F):(%9;!;" H;*:$!;"

∫

V(e)

∇φTσ∇φdV(e) =

∫

Γq(e)

φqIndΓ(e), ,012I-

(+ 6$( V . ) J)C$+( ) (C(+(%:)? Γq . ! #*)%:(;*! ) )+G%;)? (+ 6$( ! 9)% ;@

&E) ( 9)%:)*%) ( :(%"'(" (C.:*;9!" . !/C;9! !? φ . ! ;":*;A$;&E) ( /):(%9;!;"

(C.:*;9)" J;*:$!;"? φq . ! ;":*;A$;&E) ( /):(%9;!;" (C.:*;9)" J;*:$!;" (+ Γq? In . !

9)+/)%(%:( ! 9)**(%:( (C.:*;9! ,)$ J)C:!K(+- %! ;*(&E) ) J(:)* %)*+!C n !)

9)%:)*%) ) )+G%;) ( σ . ) 9)%:*!":( (C.:*;9)1

8;"9*(:;B!% )@"( ) )+G%;) ,"(&E) ! :$A$C!&E) "$A+(:; ! L :)+)K*!M!- /(C)

? ! (6$!&E) ,012I- :)*%!@"(

M∑

e=1

∫

V(e)

∇φT

(e)σ(e)∇φ(e)dV(e) =M∑

e=1

∫

Γq(e)

φq(e)In(e)dΓ(e), ,010N-

(+ 6$( M . ) %O+(*) :):!C ( (C(+(%:)" ( 9! ! :(*+) ! (6$!&E) . :)+! ) (+

$+ (:(*+;%! ) (C(+(%:) ,(-1 P)%"; (*!% )@"( ! (6$!&E) ,01Q7- ( ! ;K$!C ! (

∇φ(e) =

∂φ(e)

∂x

∂φ(e)

∂y

, ,010Q-

:(+@"(

∂φ(e)

∂x

∂φ(e)

∂y

=

(∂N1∂x

∂N2∂x

∂N3∂x

∂N1∂y

∂N2∂y

∂N3∂y

)

∂ϕ(e)

∂x

∂ϕ(e)

∂y

= B(e)ϕ(e), ,0102-

!"!#$%& !' "(#'$%& )*+,-. )!"#$%/ 0--1./ ' 2'3453 !' "(#'$%& )*+6./ 7 '23"8"94'!' 9&

9":& +

!"#$%&'()" *" +#",&-$' *- ."$"/#'0' 1"# 2$1-*3456' 7&89#65' !

!" #$% B(e) & ! '! ()* +% ,-%(!+,(%. +)/%(%01)!). +,. -,")02'),. ")0%!(%. +! '! ()*

+% /$034%. +% /,('! N 5%#$!34%. 56789: ; 5678%0+,;.% #$% !0 , -!(! ,. -, %01)!. φ #$!0 , -!(! ,. -, %01)!). φ? & @A")+!

! (%"!3B, +! %#$!3B, 567CD:? %0 B, -,+%;.% (%%.1(%@%( ! %#$!3B, 5676E:

M∑

e=1

ϕT(e)

∫

V(e)

BT(e)σ(e)B(e)dV(e)ϕ(e) =M∑

e=1

∫

Γq(e)

φq(e)In(e)dΓ(e), 56766:

,$

M∑

e=1

ϕT(e)k(e)ϕ(e) =M∑

e=1

∫

Γq(e)

φq(e)In(e)dΓ(e), 5676F:

%' #$% k(e) & ! '! ()* +% 1,0 (!. % %"& ()1, +, %"%'%0 ,? +%G0)+! -,( $'! )0 %H(!"

+% @,"$'%7

I,0.)+%(!0+, ! %.-%..$(! 5h: +, %"%'%0 , 1,0. !0 %? %';.%

dV(e) = h(e)dA(e). 56769:

J%%.1(%@%0+, ! %#$!3B, #$% +%G0% ! '! ()* k(e) ,> &';.%

k(e) =

∫

V(e)

BT(e)σ(e)B(e)h(e)dA(e). 5676K:

L..)'? +%G0%;.% ! '! ()* +% 1,0 (!. % %"& ()1, +, %"%'%0 , %' %(',. +!.

1,,(+%0!+!. H",>!). (x, y)7 =!>%0+,;.% #$% ,. -,")02'),. $.!+,. 0! +% %(')0!3B,

+, -, %01)!" %"& ()1,? 0, %"%'%0 , ()!0H$"!(? .B, +% -()'%)(! ,(+%'? %';.% #$% !

'! ()* +,. ,-%(!+,(%. +)/%(%01)!). B(e) +! '! ()* +% /,('! N & 1,0. !0 %7 M,H,?

-,+%;.% (%.,"@%( ! )0 %H(!" +! %#$!3B, 5676K: !0!") )1!'%0 %

k(e) =σ(e)

4A(e)

β21 β1β2 β1β3β1β2 β

22 β2β3

β1β3 β2β3 β23

+

γ21 γ1γ2 γ1γ3γ1γ2 γ

22 γ2γ3

γ1γ3 γ2γ3 γ23

. 5676 %03B, +,. -, %01)!).

%"& ()1,. 0,+!).? 0, +,'U0), +).1(% )*!+, %' %"%'%0 ,. G0) ,. ()!0H$"!(%.7 N%

! ! "#$#%&'()*+, -,. /,$#(0')'. 123$%'0,. 4,-)'.

!"#$" !"% &'"#( $" )*+, % (- $' !". /&' '01(!" $" '0'%'.&" 1 (./'#($

'% 2% % (- $' !". /&' 30"4 0 K 52' #'6#'/'.& &"$" " $"%7.("8 9 (./'#:;"

"!"##' 6"# %'(" $' 2% % (- $' !".'!&( Bi, jC,

6"# 'G'%60", $'/, 52' !"##'/6".$'% "/

!"#$%&'()" *" +#",&-$' *- ."$"/#'0' 1"# 2$1-*3456' 7&89#65'

!"#$%"&'"()* !* +*,$%-#$. / !-!- 0.1* 2.$*%

σ =

σ1σ23

3

3

σG3

3

3

σG+(2(Nx−1)−1)σG+2(Nx−1)

3

3

3

σM

453567

$-1 8'. Nx / * ,9:.%* !. 0*,$*# ,- !"%.()* x . M / * ,9:.%* !. .1.:.,$*# 8'.

+*:0;.: * !*: ,- ,':.%-()*

?1*&-1> / !-!* 0*% σG .,8'-,$* 8'.> ,- ,':.%-()* 1*+-1> 0*!. #.% %.0%.#.,$-!*

0*% σL1> +*,@*%:. A"?'%- 53B4&73 ,-1*?-:.,$.> σL2 +*%%.#0*,!. - σG+1> σL3

+*%%.#0*,!. - σG+2> σL4 - σG+(2(Nx−1)−1)> σL5 - σG+2(Nx−1) . σL6 - σG+(2(Nx−1)+1)3

C. -+*%!* +*: * 0%*+.!":.,$* !.#+%"$* -,$.%"*%:.,$.> * #"#$.:- 1",.-% %.0%.D

#.,$-!* 0.1- .8'-()* 4535E7 $*%,-D#.

Aφij−1 + Bφi−1j + Cφij + Dφi+1j + Eφij+1 = 0, 453FG7

+*:

A = −1

2. (σL1 + σL2) , 453FH7

B = −1

2. (σL1 + σL4) , 453FB7

C = 1. (σL1 + σL6) +1

2. (σL2 + σL3 + σL4 + σL5) , 453F57

D = −1

2. (σL3 + σL6) , 453FF7

E = −1

2. (σL5 + σL6) . 453FI7

C.##. :*!*> ':- 1",J- !- :-$%"K ?1*&-1 / *&$"!- - +-!- ,L ",+L?,"$- 0.%+*%D

%"!*3 =# +*.M+".,$.# ,)* ,'1*# !- :-$%"K ?1*&-1 #)* -%:-K.,-!*# .: ': 2.$*%

!. 0*,$*# N'$'-,$.#> sa> . *# *'$%- 2-,$-?.: 0%":*%!"-1> .: -%:-K.,-% -0.,-# *# +*.M+".,$.# ,)* ,'1*#

. *#

! !" #$%$&'()*+,- .- /012- .$ 3-&&$)%$

!" #$% &'( ($) " *$(( &'( &$ " %$+! ",+-' " +( !./+& 0 &+"+%,+%&' *'%(+&$1

! 2$3"$%-$ ' -$"/' 4 (-' % !$('3,56' &' (+(-$" 3+%$ !7

8" !$3 56' 9 ('3,56' &' (+(-$" 3+%$ ! !$/!$($%- &' /$3 $:, 56' ;?0 /'&$1

($ ,-+3+# ! "@-'&'( *'"' A! &+$%-$( B'%),4 &'( ;AB? ; !""#$$ %& '()0 CDD=?0

-!+ %4,3 !+# 56' &$ A ,((1E'!& % ; !$*#0 CDDF?0 &$%-!$ ',-'(7 G$(-$ -! H 3I'0

&'-',1($ ' "@-'&' &'( A! &+$%-$( J+*'%),4 &'( K!@1B'%&+*+'% &' ;AJBK? / !

('3,56' &$ ;?7

L AJBK0 ," 2 !+ 56' &' "@-'&' &'( AB0 -$" * ! *-$!M(-+* &$ ('3,*+'% !

:, 3:,$! (+(-$" 3+%$ ! &$(&$ :,$ " -!+# %6' ($) (+%4,3 !7 L "@-'&' *'%(+(-$

$" ," " -!+# /!@1*'%&+*+'% &'! Ã :,$ ( -+(N 5 *'%&+56' Ã−1A ≈ 10 ',

($) 0 Ã /!OP+" &$ A7 Q +%-$%56' @ 4$! ! (+(-$" ( 3+%$ !$( ,P+3+ !$( &$ N.*+3

!$('3,56' :,$ /$!"+- " ," *'%2$!4R%*+ *$3$! & &' 34'!+-"' ;+"#,, %& '()0

CDDS?7 L ,(' & " -!+# /!@1*'%&+*+'% &'! &' AJBK0 *'"' ($%&' +%2$!( &

&+ 4'% 3 &$ A0 !$(,3-', $" ('3,5T$( ( -+(N -O!+ ( $" -$!"'( &$ /!$*+(6' $ ! /+&$#0

($4,%&' U'3%+V ;S>>

!"#$%&'()" *" +#",&-$' *- ."$"/#'0' 1"# 2$1-*3456' 7&89#65' !

!"# $% ''%()% $# *#$%+# (!*,'-. )#'(/01%

e = ‖qreal − qaprox‖∞ = maxj=1,...,n

|(qreal − qaprox)j|. 234567

)/+ 8!% ‖ · ‖∞'%9'%1%()/ / (#'*/ -(:(-)#. j $%(#)/ &/$/ *9#(%()% $/ $-;%'%(*%'# )#)/+ $% %+%*%()#1 )'-/(?!+/'%1

$/ ;'#()%-'/ $# $#*@(-# Γq. %* 8!% /9+-&/01% / ($-

! !" #$%&'()*+,-)& .'%+'&

!"#$%& '% #()%*+,# '# &-&)%./ 0-*%/" !%"$#""%*'# #& *1& -*$12*-)/& '#

'#.3*-# '-&$"%)#4 /# -*56& '#& %0%.%*)#&4 !#&&-(-0-)#7 7. /"./8%*/.%*)# #)-.-8/9

'# '/ ./)"-84 #7 &%:/4 ;#"/. /"./8%*/'#& /!%*/& #& $#% C& %D7/+E%&

!/"/ # $F0$70# '# =7G# '% $#""%*)% *# $#*)#"*# % !/"/ # $F0$70# '# ;7*$-#*/0 '%

%""# ;#"/. #()-'/& '% /$#"'# $#. # HIJ>

K% /$#"'# $#. / )%#"-/ '% !"#(0%./& -*5%"&4 / "%$#*&)"7+,# *7.6"-$/ '/

LMI 6 )"/)/'/ $#.# 7. !"#(0%./ '% .-*-.-8/+,# 20#(/0> H6)#'#& '% #)-.-8/+,#

!#'%"#&4 $#.# #& C?B&4 ;#"/. !"#!#&)#& !/"/ / +,# '# !"#(0%./ )#.#2"F9

C $/"/$)%"-8/+,# '# !"#(0%./ '% #)-.-8/+,# &%"F /!"%&%*)/'/ *# $/!3)70#

&%27-*)%>

!"#$%&'

(

!"#$%&'(! )* +%,!"-.#!/

0*12.-3!/ 4&"&%*%!/ &5%-3&)! &!

4"!6%*#& 7!#!,"893!

!"#$%&'( )*+&",# -& ./0 1 2#"'3%(-# 4#'# 3' !"#$%&'( -& #5)')6(78#

&' 93& ( -),5")$3)78# -# 4#*5"(,5& &%15")4# :4#*-35)+)-(-& !("( ;3)-#, 4#*-35)+#,

#3 !&"'),,)+)-(-& !("( ;3)-#, ),#%(*5&,< 1 "&=*(-( (51 93& # 23*4)#*(% -& &""# (5)*>

?( # '@*)'# A%#$(% :)'(A&' !"#43"(-(E&3"@,5)4(

-& #5)')6(78# -&+&>,&F !")*4)!(%'&*5&F &' "(68# -& ,3(, E($)%)-(-&, )*5"@*,&4(,

-& !#-&" G&,4(!("H -& '@*)'#, %#4(),B C E)$")-)6(78# -& CDI 1 !"#!#,5( ( ='

-& (3'&*5(" ( !"#$($)%)-(-& -& #$5&*78# -( ,#%378# J5)'( :)'(A&' -&,&?(-(<

&' 5&'!# (-&93(-#B K&,5& 4(!@53%# ,8# (!"&,&*5(-(, ( 4#*=A3"(78# -# CDI

,&A3*-# # !"#$%&'( -& ./0F (, "&,5")7L&, 2@,)4(, -# !"#$%&'( 5#'#A"M=4# & (,

&,5"(51A)(, !("( '&%E#"(" ( &=4)N*4)( -# (%A#")5'# -& #5)')6(78#F 4#'# 5($&%(

!" F #!&"(-#"&, -& !"&-(78# & $3,4( %#4(%B

!" #$%&'()*+,$ -. /0'$)123$4 5.%6217$4 4.'(%-$

$ 8)$90.3* :$3$');&7$

K&,5( ,&78#F (!"&,&*5(>,& ( 4#*=A3"(78# -# CDI !("( ( ,#%378# -# !"#$%&'(

5#'#A"M=4#F )*4%3)*-# ( 4#-)=4(78# -(, ,#%37L&, 4(*-)-(5(,F #, #!&"(-#"&, -&

"&!"#-378# & ( 23*78# #$?&5)+# -# !"#$%&'( -& #5)')6(78#B

O(%& '&*4)#*(" 93& ( 4#*=A3"(78# -# CDIF 93& ,&"M (!"&,&*5(-( ( ,&A3)"F 2#)

!"#!#,5( '&-)(*5& (*M%),& -#, "&,3%5(-#, #$5)-#, -& 5&,5&, &P5&*,)+#,F 4#*,)-&"(*-#>

,& +M")(, 4#*=A3"(7L&,B

QR

! !" #$%&'()*+,$ -. /0'$)123$4 5.%6217$4 4.'(%-$ $ 8)$90.3* :$3$');&7$

! "#$%&'( ) #*+"%+,-.% /# 0(/.10%&'(2 3"(34*5*# % 0(/.10%&'( 6.78".%2 9.*+(

:;# ( 3"(6$#!% /# #*0(%!#7+( 6.

!"#$%&'()" *+ ,&-"#./$"0 1+23/.4"0 5'#'&+&"0 '6&.4'*" '" 5#"7&+$' 8"$"-#9:4" !

1

P a i 1 F i l h o 1

p o n t o 1

d o i s p o n t o s

p o n t o 2

c r o s s o v e r

F i l h o 2P a i 2

11

1

11

1

111

1

11

1

000

0

00

100

1

11

0

110

0

10

1

000

0

11

111

1

11

0

110

0

11

1

000

0

00

100

1

11

1

111

1

10

1

000

0

11

!"#$% &'() !"##"$%! *+ *,!- .,/0,-'

1 2#0%34, .,*+ +5!0%$ ,# $+*#6!$ , .$,78+2% *+ %.$!-!,/%2+/0, *, %8",$!02,9

#2% 5+6 :#+ .+$2!0+ :#+ ,- *+-;+/*+/0+- 0+/

! !" #$%&'()*$% +,%(-.% /0 1'023$4. 50406'78-0

!" #$% e & ! '$()*+ +,-% ./+ 0!0! 1%"! (+23! .(4(. + +$ (+23! 0% 56%,786%/9 #$%

0% %23.(! + 3!.+2 /!"+2 !,8+"$ + 0! 0.'%2%()! %( 2% +8 :$;+8 0% % +8

$8!(0+ %"%3%( +8 4(. +8 =qaprox>@ A88.39 1+0%B8% +, %2 ! 8+"$)*+ 0+ 12+,"%3!

.(/%28+ 0% CDE 3.(.3.F!(0+ ! %#$!)*+ =G@H>@

E( 2% !( +9 0.'%2%( %8 0.8 2.,$.)I%8 0%

8% 8+"$)I%8 8%3 8.J(.4

J.3% 0% %8@ D88+ 1+0% 8%2 '%. + 1+2 3%.+ 0! .(

12+,"%3! 0% CDE9 1+0%B8% $8!2 !8 .3!J%(8 #$!". ! ./!8 0+ %8@

A8 .3!J%(8 J%2!0!8 1%"! 8+(0! 0% /.8$!".F!)*+ 8*+ +, .0!8 1+2 3%.+ 0% 8.B

(!.8 '+2(%

!"#$%&'()" *+ ,&-"#./$"0 1+23/.4"0 5'#'&+&"0 '6&.4'*" '" 5#"7&+$' 8"$"-#9:4" !

!"#$%&! '()*+( ! ,*-." $ "/01 /$2$3"/"# 4.$ " +!%5" 6/!5.7 (#"-$%+ $# &$#6!

/$"3 $ 4."3(&"&(2"#$%&$ /( "+1 (5$%&(8 "%5! -/"%5$+ $+&/.&./"+ ,6(+&9$+ 5$ "/1 6!/

$:$#63!0 $ 5$&"3;$+ /$3"&(2"#$%&$ 8%!+ 5" -$!#$&/(" 5"+ )"+$+< =3-.#"+ (#"-$%+

6/!5.7(5"+ 6$3" +!%5" 5$ 2(+."3(7">?! 6!5$# +$/ 2(+&"+ %" @(-./" A?! 5$ .# $+ !"#$%&! !"# 6"/" .# $+ !"#$%&! "

'!3;"+<

@!%&$C E$3$-;(# F/ $ G$/2($. ,HIIJ0<

K!-!1 6!/ #$(! 5" "%*3(+$ 5"+ (#"-$%+ (%( ("(+ 6/!5.7(5"+ 6$3" +!%5" 5$ 2(L

+."3(7">?!1 M 6!++N2$3 $+&(#"/ " 5(+&/('.(>?! 5! !%&/"+&$ $3M&/( ! %" +$>?! 5"

&.'.3">?! +.'#$&(5" O &!#!-/"8"< P$++$ #!5!1 6!5$L+$ !%+&/.(/ .#" ;$./N+L

&( " 5$ (%( ("3(7">?! 5!+ (%5(2N5.!+ '"+$"5" %" 5(+&/('.(>?! 5! !%&/"+&$1 !. +$Q"1

!%+(5$/"%5!L+$ .# $+ !"#$%&! '()*+( ! ,*-." $ "/01 "5" -$%$ 6!5$ /$ $'$/ ! 2"L

3!/ 5! !%&/"+&$ 5" *-." ,σ = 800 !. 5! "/ ,σ = 10 5$ " !/5! !# 6/!'"'(3(5"5$+

6/ML5$&$/#(%"5"+<

=(%5" !# /$3">?! O (%&/!5.>?! 5$ (%)!/#">9$+ )N+( "+ 5! 6/!'3$#" 5$ RDS1

!+ +(%"(+ )!/%$ (5!+ 6$3" +!%5" 5$ 2(+."3(7">?! 6!5$# +$/ .+"5!+ $1 "3M# 5"+

(#"-$%+ (%( ("(+1 M 6!++N2$3 "3 .3"/ " )/">?! 5$ 2"7(! (%+&"%&T%$" 5! $+ !"#$%&!1

α1 $ ! !$8 ($%&$ 5$ +(#$&/(" 5! $+ !"#$%&!1 β1 6!/ #$(! 5$ #!5$3!+ 5$ "3('/">?!

6/$2("#$%&$ 5$&$/#(%"5!+

! !" #$%&'()*$% +,%(-.% /0 1'023$4. 50406'78-0

!"#$!"%&!$#'"#( α # β )*+#$ ,#- +#"#-$%'!+*, )*- *)#-!+*-#, %'"#.-!%,( */

,#0!(

α =

∫

Ω

C (x, y, z) σ (x, y, z) dxdydz, 12345

β =

∫

Ω

xyzC (x, y, z) σ (x, y, z) dxdydz, 12365

"!7 8/# C(x, y, z) +#'*"! * $*+#7* +# &!7%9-!:;* 8/#( )*- ,%$)7%&%+!+#( )*+# ,#-

!-9%"-!+* C ≡ 1( ,#$ )#-+! +# .#'#-!7%+!+#3

?!:!$ !, #8/!:@#, 12345 # 123653 A*.*( /$! )*,,B=#7 !7"#-'!"%=! +# %$)7#$#'"!:;*

C -#0#%"!- *, %'+%=B+/*, %'=%D=#%,( * 8/# ';* C &*$)/"!&%*'!7$#'"# #E&%#'"#( */

!+!)"!- *, )-*+%$#'"*, +# -#)-*+/:;* # $/"!:;*( .#-!'+* +#,'+#'"#, ,#$)-#

=%D=#%,( * 8/# '#$ ,#$)-# C )*,,B=#73 F7"#-'!"%=!, %'"#-#,,!'"#, )!-! #,,# )-*>

97#$! ,;* ! #,"-!"C.%! +# -#)!-!:;* +*, %'+%=B+/*, %'=%D=#%, ,#./'+* G#' # HI#'.

1JKKL5 # ! #,"-!"C.%! +# )#'!7%+!+# +! ?/':;* *90#"%=* &*'?*-$# M*7'%N # O#7#.I%$

P- 14QQR53

F #,"-!"C.%! $!%, &*$/$ /,!+! )!-! 7%+!- &*$ ,*7/:@#, %'=%D=#%, 1*/ ,*7/>

:@#, =%D=#%,( )*-C$ +%,"!'"#, +! ,*7/:;* &*--#"!5 #$ )-*97#$!, +# *"%$%S!:;*

&*$ -#,"-%:@#, C ! #,"-!"C.%! +# )#'!7%+!+# 1 !"# $%!" ( JKKL5( !)-#,#'"!+! '*

H!)B"/7* 23 H*',%+#-!'+*>,# ! %'"-*+/:;* +# %'?*-$!:@#, ?B,%&!, +* )-*97#$! +#

TUV( )*+#>,# )#'!7%S!- ! ?/':;* *90#"%=*( %'&7/%'+* %'?*-$!:@#, !"#$"# "!'"* +!

?-!:;* +# =!S%* %',"!'"W'#! +* #,&*!$#'"* 8/!'"* +* &*#E&%#'"# +# ,%$#"-%! +*

#,&*!$#'"*3

A*.*( ! ?/':;* *90#"%=* +!+! )#7! #8/!:;* 123J5 )*+# ,#- #,&-%"! )*-

$%' e (σ) = ‖qreal − qaprox‖∞ + (αreal − αaprox)2 + (βreal − βaprox)

2, 12325

"!7 8/# αreal # αaprox ,;*( -#,)#&"%=!$#'"#( !, ?-!:@#, +# =!S%* +* #,&*!$#'"*(

*9"%+!, )*- $#%* +# $#+%:@#, +# /$ $*+#7* #X)#-%$#'"!7 # +# /$ $*+#7* '/$C>

-%&*3 F'!7*.!$#'"#( βreal # βaprox ,;* *, &*#E&%#'"#, +# ,%$#"-%! +* #,&*!$#'"*(

)-*=#'%#'"#, +# $#+%:@#, +# /$ $*+#7* #X)#-%$#'"!7 # +# /$ $*+#7* '/$C-%&*(

-#,)#&"%=!$#'"#3

Y#E'%+!, !, -#,"-%:@#, +#-%=!+!, +# &*'I#&%$#'"*, ?B,%&*, +* )-*97#$! +# TUV(

)*+#>,# %'"-*+/S%- /$! "!9#7! % &% 1 &""!'( JKZ2[ $&()!" *+ ,-.( 4QQJ5( *)#-!>

!"#$%&'()" *+ ,&-"#./$"0 1+23/.4"0 5'#'&+&"0 '6&.4'*" '" 5#"7&+$' 8"$"-#9:4" !

!"#$ # %"# &'(! ) !"#$% &'(")*'"% +'#,+*)* +,,-. -.% )/*(,+-!"0* /00/.

1+'1' '% ). 2,)% 0,-#, * /0012 # 34$5& 6!5&6 )-.!"3% $!'% ",4*'"* +,,,.

+,),"0,% )'/)!% 5.!"!* /001. ('')% )*/*6-,* /0072 8!$ 9:;$* &

=#8?&" & %"!3&3@6@ & # # !3?#8'(! & $!64'(!

Documents

tese - USP · !"#$ %$&&$ '()"*+* )"* ,* -$./(+*0*12 3+ 4567 &'$("#$)*+$",$(+-.*$+/(0$% 89.(#*:$ &"( (,;

tese - USP · !"#$ %$&&$ '()"+ )"* ,* -$./(+012 3+ 4567 &'$("#$)+$",$(+-.$+/(0$% 89.(#*:$ &"( (,;